LMFDB - Embedded newform 60.4.e.a.11.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,4,Mod(11,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("60.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	60.e (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:	$3.54011460034$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.17
Character	$\chi$	$=$	60.11
Dual form			60.4.e.a.11.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.91554 - 2.08103i) q^{2} +(2.09257 - 4.75617i) q^{3} +(-0.661378 - 7.97261i) q^{4} -5.00000i q^{5} +(-5.88931 - 13.4654i) q^{6} +32.2690i q^{7} +(-17.8582 - 13.8955i) q^{8} +(-18.2423 - 19.9053i) q^{9} +O(q^{10})$	\(q+(1.91554 - 2.08103i) q^{2} +(2.09257 - 4.75617i) q^{3} +(-0.661378 - 7.97261i) q^{4} -5.00000i q^{5} +(-5.88931 - 13.4654i) q^{6} +32.2690i q^{7} +(-17.8582 - 13.8955i) q^{8} +(-18.2423 - 19.9053i) q^{9} +(-10.4052 - 9.57772i) q^{10} +32.4750 q^{11} +(-39.3031 - 13.5377i) q^{12} +44.9257 q^{13} +(67.1527 + 61.8126i) q^{14} +(-23.7808 - 10.4629i) q^{15} +(-63.1252 + 10.5458i) q^{16} -79.2204i q^{17} +(-76.3674 - 0.166722i) q^{18} +69.0323i q^{19} +(-39.8631 + 3.30689i) q^{20} +(153.477 + 67.5252i) q^{21} +(62.2073 - 67.5815i) q^{22} +72.8705 q^{23} +(-103.459 + 55.8589i) q^{24} -25.0000 q^{25} +(86.0572 - 93.4918i) q^{26} +(-132.846 + 45.1100i) q^{27} +(257.268 - 21.3420i) q^{28} +219.925i q^{29} +(-67.3268 + 29.4466i) q^{30} +28.4726i q^{31} +(-98.9729 + 151.566i) q^{32} +(67.9564 - 154.457i) q^{33} +(-164.860 - 151.750i) q^{34} +161.345 q^{35} +(-146.632 + 158.603i) q^{36} -152.826 q^{37} +(143.658 + 132.234i) q^{38} +(94.0104 - 213.674i) q^{39} +(-69.4777 + 89.2908i) q^{40} +104.817i q^{41} +(434.513 - 190.042i) q^{42} +96.6054i q^{43} +(-21.4783 - 258.911i) q^{44} +(-99.5264 + 91.2113i) q^{45} +(139.587 - 151.646i) q^{46} -103.880 q^{47} +(-81.9364 + 322.302i) q^{48} -698.285 q^{49} +(-47.8886 + 52.0258i) q^{50} +(-376.785 - 165.775i) q^{51} +(-29.7129 - 358.175i) q^{52} -544.398i q^{53} +(-160.597 + 362.867i) q^{54} -162.375i q^{55} +(448.395 - 576.264i) q^{56} +(328.329 + 144.455i) q^{57} +(457.671 + 421.276i) q^{58} -431.052 q^{59} +(-67.6883 + 196.515i) q^{60} +183.375 q^{61} +(59.2524 + 54.5406i) q^{62} +(642.322 - 588.659i) q^{63} +(125.827 + 496.298i) q^{64} -224.629i q^{65} +(-191.255 - 437.288i) q^{66} -290.222i q^{67} +(-631.593 + 52.3946i) q^{68} +(152.487 - 346.584i) q^{69} +(309.063 - 335.763i) q^{70} -489.128 q^{71} +(49.1785 + 608.958i) q^{72} -292.966 q^{73} +(-292.745 + 318.036i) q^{74} +(-52.3144 + 118.904i) q^{75} +(550.368 - 45.6564i) q^{76} +1047.93i q^{77} +(-264.582 - 604.941i) q^{78} +656.389i q^{79} +(52.7291 + 315.626i) q^{80} +(-63.4397 + 726.234i) q^{81} +(218.127 + 200.781i) q^{82} +392.339 q^{83} +(436.846 - 1268.27i) q^{84} -396.102 q^{85} +(201.039 + 185.052i) q^{86} +(1046.00 + 460.210i) q^{87} +(-579.944 - 451.258i) q^{88} +336.343i q^{89} +(-0.833612 + 381.837i) q^{90} +1449.71i q^{91} +(-48.1949 - 580.968i) q^{92} +(135.421 + 59.5811i) q^{93} +(-198.986 + 216.177i) q^{94} +345.161 q^{95} +(513.767 + 787.896i) q^{96} +1039.74 q^{97} +(-1337.60 + 1453.15i) q^{98} +(-592.417 - 646.424i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{4} + 30 q^{6} + 20 q^{9}+O(q^{10}) $ 24 * q + 6 * q^4 + 30 * q^6 + 20 * q^9	$ 24 q + 6 q^{4} + 30 q^{6} + 20 q^{9} - 30 q^{10} - 188 q^{12} + 72 q^{13} + 306 q^{16} + 256 q^{18} - 68 q^{21} - 300 q^{22} - 434 q^{24} - 600 q^{25} + 300 q^{28} - 40 q^{30} + 848 q^{33} - 468 q^{34} - 294 q^{36} + 504 q^{37} - 210 q^{40} - 228 q^{42} - 220 q^{45} + 684 q^{46} + 1212 q^{48} - 2256 q^{49} + 576 q^{52} - 1054 q^{54} + 1416 q^{57} + 3108 q^{58} + 490 q^{60} + 1992 q^{61} - 1842 q^{64} - 472 q^{66} - 1548 q^{69} + 540 q^{70} + 312 q^{72} - 2304 q^{73} - 420 q^{76} - 2792 q^{78} + 3840 q^{81} + 600 q^{82} - 176 q^{84} + 240 q^{85} - 372 q^{88} - 1170 q^{90} - 4384 q^{93} + 1044 q^{94} - 3846 q^{96} - 2448 q^{97}+O(q^{100}) $ 24 * q + 6 * q^4 + 30 * q^6 + 20 * q^9 - 30 * q^10 - 188 * q^12 + 72 * q^13 + 306 * q^16 + 256 * q^18 - 68 * q^21 - 300 * q^22 - 434 * q^24 - 600 * q^25 + 300 * q^28 - 40 * q^30 + 848 * q^33 - 468 * q^34 - 294 * q^36 + 504 * q^37 - 210 * q^40 - 228 * q^42 - 220 * q^45 + 684 * q^46 + 1212 * q^48 - 2256 * q^49 + 576 * q^52 - 1054 * q^54 + 1416 * q^57 + 3108 * q^58 + 490 * q^60 + 1992 * q^61 - 1842 * q^64 - 472 * q^66 - 1548 * q^69 + 540 * q^70 + 312 * q^72 - 2304 * q^73 - 420 * q^76 - 2792 * q^78 + 3840 * q^81 + 600 * q^82 - 176 * q^84 + 240 * q^85 - 372 * q^88 - 1170 * q^90 - 4384 * q^93 + 1044 * q^94 - 3846 * q^96 - 2448 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	1.91554	−	2.08103i	0.677247	−	0.735755i
$2$	1.91554	−	2.08103i	0.677247	−	0.735755i
$3$	2.09257	−	4.75617i	0.402716	−	0.915325i
$3$	2.09257	−	4.75617i	0.402716	−	0.915325i
$4$	−0.661378	−	7.97261i	−0.0826723	−	0.996577i
$5$		−	5.00000i		−	0.447214i
$5$		−	5.00000i		−	0.447214i
$6$	−5.88931	−	13.4654i	−0.400717	−	0.916202i
$7$			32.2690i			1.74236i	0.490964	+	0.871180i	$0.336645\pi$
$7$			32.2690i			1.74236i	−0.490964	+	0.871180i	$0.663355\pi$
$8$	−17.8582	−	13.8955i	−0.789226	−	0.614102i
$9$	−18.2423	−	19.9053i	−0.675639	−	0.737232i
$10$	−10.4052	−	9.57772i	−0.329040	−	0.302874i
$11$	32.4750			0.890144			0.445072	−	0.895495i	$-0.353178\pi$
$11$	32.4750			0.890144			0.445072	+	0.895495i	$0.353178\pi$
$12$	−39.3031	−	13.5377i	−0.945485	−	0.325666i
$13$	44.9257			0.958473			0.479237	−	0.877686i	$-0.340914\pi$
$13$	44.9257			0.958473			0.479237	+	0.877686i	$0.340914\pi$
$14$	67.1527	+	61.8126i	1.28195	+	1.18001i
$15$	−23.7808	−	10.4629i	−0.409346	−	0.180100i
$16$	−63.1252	+	10.5458i	−0.986331	+	0.164779i
$17$		−	79.2204i		−	1.13022i	−0.825015	−	0.565111i	$-0.808833\pi$
$17$		−	79.2204i		−	1.13022i	0.825015	−	0.565111i	$-0.191167\pi$
$18$	−76.3674	−	0.166722i	−0.999998	−	0.00218316i
$19$			69.0323i			0.833531i	0.909014	+	0.416765i	$0.136836\pi$
$19$			69.0323i			0.833531i	−0.909014	+	0.416765i	$0.863164\pi$
$20$	−39.8631	+	3.30689i	−0.445683	+	0.0369722i
$21$	153.477	+	67.5252i	1.59483	+	0.701676i
$22$	62.2073	−	67.5815i	0.602847	−	0.654928i
$23$	72.8705			0.660632			0.330316	−	0.943870i	$-0.392845\pi$
$23$	72.8705			0.660632			0.330316	+	0.943870i	$0.392845\pi$
$24$	−103.459	+	55.8589i	−0.879937	+	0.475090i
$25$	−25.0000			−0.200000
$26$	86.0572	−	93.4918i	0.649123	−	0.705202i
$27$	−132.846	+	45.1100i	−0.946898	+	0.321534i
$28$	257.268	−	21.3420i	1.73640	−	0.144045i
$29$			219.925i			1.40824i	0.710079	+	0.704122i	$0.248659\pi$
$29$			219.925i			1.40824i	−0.710079	+	0.704122i	$0.751341\pi$
$30$	−67.3268	+	29.4466i	−0.409738	+	0.179206i
$31$			28.4726i			0.164962i	0.996593	+	0.0824812i	$0.0262844\pi$
$31$			28.4726i			0.164962i	−0.996593	+	0.0824812i	$0.973716\pi$
$32$	−98.9729	+	151.566i	−0.546753	+	0.837294i
$33$	67.9564	−	154.457i	0.358475	−	0.814771i
$34$	−164.860	−	151.750i	−0.831566	−	0.765439i
$35$	161.345			0.779207
$36$	−146.632	+	158.603i	−0.678852	+	0.734275i
$37$	−152.826			−0.679039			−0.339520	−	0.940599i	$-0.610265\pi$
$37$	−152.826			−0.679039			−0.339520	+	0.940599i	$0.610265\pi$
$38$	143.658	+	132.234i	0.613275	+	0.564506i
$39$	94.0104	−	213.674i	0.385993	−	0.877314i
$40$	−69.4777	+	89.2908i	−0.274635	+	0.352953i
$41$			104.817i			0.399259i	0.979871	+	0.199629i	$0.0639738\pi$
$41$			104.817i			0.399259i	−0.979871	+	0.199629i	$0.936026\pi$
$42$	434.513	−	190.042i	1.59635	−	0.698193i
$43$			96.6054i			0.342609i	0.985218	+	0.171305i	$0.0547982\pi$
$43$			96.6054i			0.342609i	−0.985218	+	0.171305i	$0.945202\pi$
$44$	−21.4783	−	258.911i	−0.0735902	−	0.887097i
$45$	−99.5264	+	91.2113i	−0.329700	+	0.302155i
$46$	139.587	−	151.646i	0.447411	−	0.486064i
$47$	−103.880			−0.322391			−0.161196	−	0.986922i	$-0.551535\pi$
$47$	−103.880			−0.322391			−0.161196	+	0.986922i	$0.551535\pi$
$48$	−81.9364	+	322.302i	−0.246385	+	0.969172i
$49$	−698.285			−2.03582
$50$	−47.8886	+	52.0258i	−0.135449	+	0.147151i
$51$	−376.785	−	165.775i	−1.03452	−	0.455158i
$52$	−29.7129	−	358.175i	−0.0792391	−	0.955192i
$53$		−	544.398i		−	1.41092i	−0.708750	−	0.705460i	$-0.750740\pi$
$53$		−	544.398i		−	1.41092i	0.708750	−	0.705460i	$-0.249260\pi$
$54$	−160.597	+	362.867i	−0.404714	+	0.914444i
$55$		−	162.375i		−	0.398084i
$56$	448.395	−	576.264i	1.06999	−	1.37512i
$57$	328.329	+	144.455i	0.762952	+	0.335676i
$58$	457.671	+	421.276i	1.03612	+	0.953729i
$59$	−431.052			−0.951156			−0.475578	−	0.879674i	$-0.657761\pi$
$59$	−431.052			−0.951156			−0.475578	+	0.879674i	$0.657761\pi$
$60$	−67.6883	+	196.515i	−0.145642	+	0.422834i
$61$	183.375			0.384898			0.192449	−	0.981307i	$-0.438357\pi$
$61$	183.375			0.384898			0.192449	+	0.981307i	$0.438357\pi$
$62$	59.2524	+	54.5406i	0.121372	+	0.111720i
$63$	642.322	−	588.659i	1.28452	−	1.17721i
$64$	125.827	+	496.298i	0.245757	+	0.969332i
$65$		−	224.629i		−	0.428642i
$66$	−191.255	−	437.288i	−0.356696	−	0.815551i
$67$		−	290.222i		−	0.529198i	−0.964359	−	0.264599i	$-0.914760\pi$
$67$		−	290.222i		−	0.529198i	0.964359	−	0.264599i	$-0.0852395\pi$
$68$	−631.593	+	52.3946i	−1.12635	+	0.0934379i
$69$	152.487	−	346.584i	0.266047	−	0.604693i
$70$	309.063	−	335.763i	0.527716	−	0.573306i
$71$	−489.128			−0.817589			−0.408794	−	0.912627i	$-0.634051\pi$
$71$	−489.128			−0.817589			−0.408794	+	0.912627i	$0.634051\pi$
$72$	49.1785	+	608.958i	0.0804964	+	0.996755i
$73$	−292.966			−0.469713			−0.234856	−	0.972030i	$-0.575462\pi$
$73$	−292.966			−0.469713			−0.234856	+	0.972030i	$0.575462\pi$
$74$	−292.745	+	318.036i	−0.459878	+	0.499607i
$75$	−52.3144	+	118.904i	−0.0805432	+	0.183065i
$76$	550.368	−	45.6564i	0.830677	−	0.0689099i
$77$			1047.93i			1.55095i
$78$	−264.582	−	604.941i	−0.384076	−	0.878155i
$79$			656.389i			0.934805i	0.884045	+	0.467402i	$0.154810\pi$
$79$			656.389i			0.934805i	−0.884045	+	0.467402i	$0.845190\pi$
$80$	52.7291	+	315.626i	0.0736912	+	0.441100i
$81$	−63.4397	+	726.234i	−0.0870228	+	0.996206i
$82$	218.127	+	200.781i	0.293757	+	0.270397i
$83$	392.339			0.518853			0.259426	−	0.965763i	$-0.416467\pi$
$83$	392.339			0.518853			0.259426	+	0.965763i	$0.416467\pi$
$84$	436.846	−	1268.27i	0.567427	−	1.64738i
$85$	−396.102			−0.505450
$86$	201.039	+	185.052i	0.252076	+	0.232031i
$87$	1046.00	+	460.210i	1.28900	+	0.567122i
$88$	−579.944	−	451.258i	−0.702525	−	0.546639i
$89$			336.343i			0.400588i	0.979736	+	0.200294i	$0.0641897\pi$
$89$			336.343i			0.400588i	−0.979736	+	0.200294i	$0.935810\pi$
$90$	−0.833612	+	381.837i	−0.000976338	+	0.447213i
$91$			1449.71i			1.67000i
$92$	−48.1949	−	580.968i	−0.0546160	−	0.658371i
$93$	135.421	+	59.5811i	0.150994	+	0.0664330i
$94$	−198.986	+	216.177i	−0.218339	+	0.237201i
$95$	345.161			0.372766
$96$	513.767	+	787.896i	0.546210	+	0.837648i
$97$	1039.74			1.08834			0.544171	−	0.838974i	$-0.316844\pi$
$97$	1039.74			1.08834			0.544171	+	0.838974i	$0.316844\pi$
$98$	−1337.60	+	1453.15i	−1.37875	+	1.49786i
$99$	−592.417	−	646.424i	−0.601416	−	0.656243i
$100$	16.5345	+	199.315i	0.0165345	+	0.199315i
$101$		−	308.323i		−	0.303755i	−0.988399	−	0.151877i	$-0.951468\pi$
$101$		−	308.323i		−	0.303755i	0.988399	−	0.151877i	$-0.0485319\pi$
$102$	−1066.73	+	466.553i	−1.03551	+	0.452899i
$103$		−	264.352i		−	0.252887i	−0.991974	−	0.126443i	$-0.959644\pi$
$103$		−	264.352i		−	0.252887i	0.991974	−	0.126443i	$-0.0403562\pi$
$104$	−802.290	−	624.267i	−0.756452	−	0.588601i
$105$	337.626	−	767.383i	0.313799	−	0.713228i
$106$	−1132.91	−	1042.82i	−1.03809	−	0.955542i
$107$	−1561.77			−1.41104			−0.705522	−	0.708688i	$-0.749287\pi$
$107$	−1561.77			−1.41104			−0.705522	+	0.708688i	$0.749287\pi$
$108$	447.506	+	1029.30i	0.398716	+	0.917075i
$109$	2178.35			1.91420			0.957100	−	0.289757i	$-0.0935744\pi$
$109$	2178.35			1.91420			0.957100	+	0.289757i	$0.0935744\pi$
$110$	−337.907	−	311.037i	−0.292893	−	0.269602i
$111$	−319.800	+	726.867i	−0.273460	+	0.621542i
$112$	−340.303	−	2036.98i	−0.287103	−	1.71854i
$113$		−	1715.85i		−	1.42844i	−0.699920	−	0.714221i	$-0.746781\pi$
$113$		−	1715.85i		−	1.42844i	0.699920	−	0.714221i	$-0.253219\pi$
$114$	929.544	−	406.552i	0.763683	−	0.334010i
$115$		−	364.352i		−	0.295444i
$116$	1753.38	−	145.454i	1.40342	−	0.116423i
$117$	−819.547	−	894.258i	−0.647582	−	0.706617i
$118$	−825.699	+	897.033i	−0.644168	+	0.699818i
$119$	2556.36			1.96925
$120$	279.295	+	517.295i	0.212467	+	0.393520i
$121$	−276.374			−0.207644
$122$	351.263	−	381.610i	0.260671	−	0.283191i
$123$	498.525	+	219.337i	0.365451	+	0.160788i
$124$	227.001	−	18.8312i	0.164398	−	0.0136378i
$125$			125.000i			0.0894427i
$126$	5.37996	−	2464.29i	0.00380385	−	1.74236i
$127$		−	1396.37i		−	0.975652i	−0.872941	−	0.487826i	$-0.837790\pi$
$127$		−	1396.37i		−	0.975652i	0.872941	−	0.487826i	$-0.162210\pi$
$128$	1273.84	+	688.830i	0.879629	+	0.475660i
$129$	459.472	+	202.154i	0.313599	+	0.137974i
$130$	−467.459	−	430.286i	−0.315376	−	0.290297i
$131$	−1510.54			−1.00745			−0.503727	−	0.863863i	$-0.668038\pi$
$131$	−1510.54			−1.00745			−0.503727	+	0.863863i	$0.668038\pi$
$132$	−1276.37	−	439.636i	−0.841618	−	0.289889i
$133$	−2227.60			−1.45231
$134$	−603.961	−	555.933i	−0.389360	−	0.358398i
$135$	225.550	+	664.231i	0.143794	+	0.423466i
$136$	−1100.81	+	1414.73i	−0.694071	+	0.892000i
$137$		−	541.789i		−	0.337870i	−0.985627	−	0.168935i	$-0.945967\pi$
$137$		−	541.789i		−	0.337870i	0.985627	−	0.168935i	$-0.0540327\pi$
$138$	−429.157	−	981.227i	−0.264726	−	0.605272i
$139$			713.800i			0.435566i	0.975997	+	0.217783i	$0.0698825\pi$
$139$			713.800i			0.435566i	−0.975997	+	0.217783i	$0.930117\pi$
$140$	−106.710	−	1286.34i	−0.0644188	−	0.776540i
$141$	−217.376	+	494.069i	−0.129832	+	0.295093i
$142$	−936.946	+	1017.89i	−0.553710	+	0.601545i
$143$	1458.96			0.853179
$144$	1361.46	+	1064.14i	0.787884	+	0.615824i
$145$	1099.63			0.629786
$146$	−561.189	+	609.671i	−0.318112	+	0.345594i
$147$	−1461.21	+	3321.16i	−0.819857	+	1.86343i
$148$	101.076	+	1218.42i	0.0561377	+	0.676715i
$149$			109.018i			0.0599405i	0.999551	+	0.0299702i	$0.00954126\pi$
$149$			109.018i			0.0599405i	−0.999551	+	0.0299702i	$0.990459\pi$
$150$	147.233	+	336.634i	0.0801434	+	0.183240i
$151$		−	3186.38i		−	1.71725i	−0.512607	−	0.858623i	$-0.671320\pi$
$151$		−	3186.38i		−	1.71725i	0.512607	−	0.858623i	$-0.328680\pi$
$152$	959.241	−	1232.79i	0.511873	−	0.657845i
$153$	−1576.90	+	1445.16i	−0.833236	+	0.763622i
$154$	2180.78	+	2007.36i	1.14112	+	1.05038i
$155$	142.363			0.0737734
$156$	−1765.72	−	608.189i	−0.906222	−	0.312142i
$157$	−1029.37			−0.523266			−0.261633	−	0.965167i	$-0.584261\pi$
$157$	−1029.37			−0.523266			−0.261633	+	0.965167i	$0.584261\pi$
$158$	1365.97	+	1257.34i	0.687788	+	0.633094i
$159$	−2589.25	−	1139.19i	−1.29145	−	0.568200i
$160$	757.832	+	494.864i	0.374449	+	0.244515i
$161$			2351.45i			1.15106i
$162$	1389.79	+	1523.15i	0.674028	+	0.738706i
$163$		−	224.555i		−	0.107905i	−0.998544	−	0.0539524i	$-0.982818\pi$
$163$		−	224.555i		−	0.107905i	0.998544	−	0.0539524i	$-0.0171819\pi$
$164$	835.662	−	69.3234i	0.397892	−	0.0330076i
$165$	−772.283	−	339.782i	−0.364377	−	0.160315i
$166$	751.542	−	816.469i	0.351392	−	0.381749i
$167$	959.236			0.444479			0.222239	−	0.974992i	$-0.428663\pi$
$167$	959.236			0.444479			0.222239	+	0.974992i	$0.428663\pi$
$168$	−1802.51	−	3338.52i	−0.827777	−	1.53317i
$169$	−178.681			−0.0813294
$170$	−758.751	+	824.300i	−0.342315	+	0.371888i
$171$	1374.11	−	1259.30i	0.614506	−	0.563166i
$172$	770.198	−	63.8927i	0.341436	−	0.0283243i
$173$			1819.46i			0.799600i	0.916602	+	0.399800i	$0.130920\pi$
$173$			1819.46i			0.799600i	−0.916602	+	0.399800i	$0.869080\pi$
$174$	2961.37	−	1295.21i	1.29024	−	0.564307i
$175$		−	806.724i		−	0.348472i
$176$	−2049.99	+	342.476i	−0.877976	+	0.146677i
$177$	−902.008	+	2050.16i	−0.383046	+	0.870617i
$178$	699.941	+	644.280i	0.294735	+	0.271297i
$179$	−797.802			−0.333131			−0.166566	−	0.986030i	$-0.553268\pi$
$179$	−797.802			−0.333131			−0.166566	+	0.986030i	$0.553268\pi$
$180$	793.017	+	733.160i	0.328378	+	0.303592i
$181$	1893.23			0.777472			0.388736	−	0.921349i	$-0.372912\pi$
$181$	1893.23			0.777472			0.388736	+	0.921349i	$0.372912\pi$
$182$	3016.88	+	2776.98i	1.22872	+	1.13101i
$183$	383.726	−	872.164i	0.155005	−	0.352307i
$184$	−1301.33	−	1012.58i	−0.521388	−	0.405696i
$185$			764.131i			0.303676i
$186$	383.394	−	167.684i	0.151139	−	0.0661032i
$187$		−	2572.68i		−	1.00606i
$188$	68.7037	+	828.192i	0.0266528	+	0.321288i
$189$	−1455.65	−	4286.80i	−0.560228	−	1.64984i
$190$	661.172	−	718.291i	0.252455	−	0.274265i
$191$	2169.17			0.821759			0.410879	−	0.911690i	$-0.365222\pi$
$191$	2169.17			0.821759			0.410879	+	0.911690i	$0.365222\pi$
$192$	2623.78	+	440.084i	0.986223	+	0.165418i
$193$	4329.69			1.61481			0.807405	−	0.589998i	$-0.200872\pi$
$193$	4329.69			1.61481			0.807405	+	0.589998i	$0.200872\pi$
$194$	1991.66	−	2163.72i	0.737077	−	0.800754i
$195$	−1068.37	−	470.052i	−0.392347	−	0.172621i
$196$	461.831	+	5567.16i	0.168306	+	2.02885i
$197$		−	2110.47i		−	0.763274i	−0.924312	−	0.381637i	$-0.875360\pi$
$197$		−	2110.47i		−	0.763274i	0.924312	−	0.381637i	$-0.124640\pi$
$198$	−2480.03	−	5.41431i	−0.890142	−	0.00194333i
$199$			1465.10i			0.521899i	0.965352	+	0.260950i	$0.0840357\pi$
$199$			1465.10i			0.521899i	−0.965352	+	0.260950i	$0.915964\pi$
$200$	446.454	+	347.389i	0.157845	+	0.122820i
$201$	−1380.34	−	607.311i	−0.484388	−	0.213116i
$202$	−641.629	−	590.606i	−0.223489	−	0.205717i
$203$	−7096.75			−2.45367
$204$	−1072.46	+	3113.60i	−0.368074	+	1.06861i
$205$	524.083			0.178554
$206$	−550.124	−	506.377i	−0.186063	−	0.171267i
$207$	−1329.32	−	1450.51i	−0.446349	−	0.487039i
$208$	−2835.94	+	473.779i	−0.945371	+	0.157936i
$209$			2241.82i			0.741962i
$210$	−950.210	−	2172.57i	−0.312241	−	0.713911i
$211$			2400.96i			0.783361i	0.920101	+	0.391681i	$0.128106\pi$
$211$			2400.96i			0.783361i	−0.920101	+	0.391681i	$0.871894\pi$
$212$	−4340.27	+	360.053i	−1.40609	+	0.116644i
$213$	−1023.54	+	2326.37i	−0.329256	+	0.748359i
$214$	−2991.63	+	3250.08i	−0.955625	+	1.03818i
$215$	483.027			0.153219
$216$	2999.21	+	1040.39i	0.944772	+	0.327729i
$217$	−918.782			−0.287424
$218$	4172.72	−	4533.21i	1.29639	−	1.40838i
$219$	−613.052	+	1393.39i	−0.189161	+	0.429940i
$220$	−1294.55	+	107.391i	−0.396722	+	0.0329105i
$221$		−	3559.03i		−	1.08329i
$222$	900.041	+	2057.86i	0.272103	+	0.622137i
$223$			1227.21i			0.368521i	0.982877	+	0.184260i	$0.0589890\pi$
$223$			1227.21i			0.368521i	−0.982877	+	0.184260i	$0.941011\pi$
$224$	−4890.89	−	3193.75i	−1.45887	−	0.952640i
$225$	456.057	+	497.632i	0.135128	+	0.147446i
$226$	−3570.74	−	3286.79i	−1.05098	−	0.967408i
$227$	6004.46			1.75564			0.877820	−	0.478991i	$-0.158997\pi$
$227$	6004.46			1.75564			0.877820	+	0.478991i	$0.158997\pi$
$228$	934.536	−	2713.18i	0.271452	−	0.788091i
$229$	−3410.62			−0.984192			−0.492096	−	0.870541i	$-0.663769\pi$
$229$	−3410.62			−0.984192			−0.492096	+	0.870541i	$0.663769\pi$
$230$	−758.228	−	697.933i	−0.217374	−	0.200088i
$231$	4984.15	+	2192.88i	1.41962	+	0.624593i
$232$	3055.98	−	3927.46i	0.864806	−	1.11142i
$233$		−	6319.33i		−	1.77679i	−0.459076	−	0.888397i	$-0.651819\pi$
$233$		−	6319.33i		−	1.77679i	0.459076	−	0.888397i	$-0.348181\pi$
$234$	−3430.86	−	7.49012i	−0.958471	−	0.00209250i
$235$			519.398i			0.144178i
$236$	285.088	+	3436.61i	0.0786342	+	0.947900i
$237$	3121.90	+	1373.54i	0.855650	+	0.376461i
$238$	4896.82	−	5319.86i	1.33367	−	1.44889i
$239$	3563.80			0.964533			0.482266	−	0.876025i	$-0.339814\pi$
$239$	3563.80			0.964533			0.482266	+	0.876025i	$0.339814\pi$
$240$	1611.51	+	409.682i	0.433427	+	0.110187i
$241$	−2833.81			−0.757435			−0.378718	−	0.925512i	$-0.623635\pi$
$241$	−2833.81			−0.757435			−0.378718	+	0.925512i	$0.623635\pi$
$242$	−529.408	+	575.144i	−0.140626	+	0.152775i
$243$	3321.34	+	1821.43i	0.876807	+	0.480843i
$244$	−121.280	−	1461.98i	−0.0318204	−	0.383581i
$245$			3491.43i			0.910445i
$246$	1411.39	−	617.298i	0.365802	−	0.159990i
$247$			3101.32i			0.798917i
$248$	395.643	−	508.469i	0.101304	−	0.130193i
$249$	820.998	−	1866.03i	0.208950	−	0.474919i
$250$	260.129	+	239.443i	0.0658080	+	0.0605748i
$251$	−3865.84			−0.972149			−0.486075	−	0.873917i	$-0.661572\pi$
$251$	−3865.84			−0.972149			−0.486075	+	0.873917i	$0.661572\pi$
$252$	−5117.97	−	4731.66i	−1.27937	−	1.18280i
$253$	2366.47			0.588058
$254$	−2905.89	−	2674.81i	−0.717841	−	0.660757i
$255$	−828.873	+	1883.93i	−0.203553	+	0.462651i
$256$	3873.57	−	1331.41i	0.945696	−	0.325052i
$257$		−	2960.51i		−	0.718566i	−0.933229	−	0.359283i	$-0.883021\pi$
$257$		−	2960.51i		−	0.718566i	0.933229	−	0.359283i	$-0.116979\pi$
$258$	1300.83	−	568.939i	0.313899	−	0.137289i
$259$		−	4931.54i		−	1.18313i
$260$	−1790.88	+	148.564i	−0.427175	+	0.0354368i
$261$	4377.67	−	4011.93i	1.03820	−	0.951465i
$262$	−2893.50	+	3143.48i	−0.682295	+	0.741239i
$263$	−6555.46			−1.53699			−0.768493	−	0.639859i	$-0.778993\pi$
$263$	−6555.46			−1.53699			−0.768493	+	0.639859i	$0.778993\pi$
$264$	−3359.83	+	1814.02i	−0.783271	+	0.422898i
$265$	−2721.99			−0.630983
$266$	−4267.06	+	4635.70i	−0.983573	+	1.06855i
$267$	1599.70	+	703.823i	0.366668	+	0.161323i
$268$	−2313.83	+	191.946i	−0.527386	+	0.0437500i
$269$			8701.31i			1.97222i	0.166083	+	0.986112i	$0.446888\pi$
$269$			8701.31i			1.97222i	−0.166083	+	0.986112i	$0.553112\pi$
$270$	1814.34	+	802.987i	0.408952	+	0.180993i
$271$		−	2026.32i		−	0.454207i	−0.973871	−	0.227104i	$-0.927074\pi$
$271$		−	2026.32i		−	0.454207i	0.973871	−	0.227104i	$-0.0729256\pi$
$272$	835.444	+	5000.80i	0.186236	+	1.11477i
$273$	6895.04	+	3033.62i	1.52860	+	0.672538i
$274$	−1127.48	−	1037.82i	−0.248589	−	0.228821i
$275$	−811.875			−0.178029
$276$	−2864.03	−	986.496i	−0.624618	−	0.215145i
$277$	6200.10			1.34487			0.672433	−	0.740158i	$-0.265249\pi$
$277$	6200.10			1.34487			0.672433	+	0.740158i	$0.265249\pi$
$278$	1485.44	+	1367.31i	0.320470	+	0.294986i
$279$	566.755	−	519.405i	0.121616	−	0.111455i
$280$	−2881.32	−	2241.97i	−0.614971	−	0.478513i
$281$		−	8199.53i		−	1.74072i	−0.492413	−	0.870361i	$-0.663885\pi$
$281$		−	8199.53i		−	1.74072i	0.492413	−	0.870361i	$-0.336115\pi$
$282$	611.779	+	1398.78i	0.129188	+	0.295376i
$283$			7615.89i			1.59971i	0.600194	+	0.799854i	$0.295090\pi$
$283$			7615.89i			1.59971i	−0.600194	+	0.799854i	$0.704910\pi$
$284$	323.498	+	3899.63i	0.0675919	+	0.814790i
$285$	722.276	−	1641.64i	0.150119	−	0.341202i
$286$	2794.71	−	3036.15i	0.577813	−	0.627731i
$287$	−3382.32			−0.695652
$288$	4822.46	−	794.832i	0.986688	−	0.162625i
$289$	−1362.87			−0.277400
$290$	2106.38	−	2288.35i	0.426521	−	0.463368i
$291$	2175.72	−	4945.16i	0.438293	−	0.996186i
$292$	193.761	+	2335.70i	0.0388322	+	0.468105i
$293$			9294.47i			1.85320i	0.376044	+	0.926602i	$0.377284\pi$
$293$			9294.47i			1.85320i	−0.376044	+	0.926602i	$0.622716\pi$
$294$	4112.42	+	9402.67i	0.815787	+	1.86522i
$295$			2155.26i			0.425370i
$296$	2729.19	+	2123.60i	0.535916	+	0.417000i
$297$	−4314.18	+	1464.95i	−0.842875	+	0.286212i
$298$	226.871	+	208.830i	0.0441016	+	0.0405945i
$299$	3273.76			0.633198
$300$	982.577	+	338.442i	0.189097	+	0.0651331i
$301$	−3117.36			−0.596948
$302$	−6630.96	−	6103.66i	−1.26347	−	1.16300i
$303$	−1466.43	−	645.188i	−0.278034	−	0.122327i
$304$	−728.002	−	4357.67i	−0.137348	−	0.822137i
$305$		−	916.876i		−	0.172132i
$306$	−13.2078	+	6049.85i	−0.00246745	+	1.13022i
$307$		−	1982.97i		−	0.368646i	−0.982866	−	0.184323i	$-0.940991\pi$
$307$		−	1982.97i		−	0.368646i	0.982866	−	0.184323i	$-0.0590092\pi$
$308$	8354.78	−	693.081i	1.54564	−	0.128221i
$309$	−1257.30	−	553.176i	−0.231474	−	0.101842i
$310$	272.703	−	296.262i	0.0499629	−	0.0542792i
$311$	−326.148			−0.0594668			−0.0297334	−	0.999558i	$-0.509466\pi$
$311$	−326.148			−0.0594668			−0.0297334	+	0.999558i	$0.509466\pi$
$312$	−4647.97	+	2509.50i	−0.843396	+	0.455361i
$313$	1059.90			0.191403			0.0957014	−	0.995410i	$-0.469491\pi$
$313$	1059.90			0.191403			0.0957014	+	0.995410i	$0.469491\pi$
$314$	−1971.80	+	2142.15i	−0.354380	+	0.384996i
$315$	−2943.29	−	3211.61i	−0.526463	−	0.574457i
$316$	5233.14	−	434.122i	0.931605	−	0.0772824i
$317$		−	1007.99i		−	0.178595i	−0.996005	−	0.0892974i	$-0.971538\pi$
$317$		−	1007.99i		−	0.178595i	0.996005	−	0.0892974i	$-0.0284621\pi$
$318$	−7330.51	+	3206.13i	−1.29269	+	0.565380i
$319$			7142.07i			1.25354i
$320$	2481.49	−	629.137i	0.433498	−	0.109906i
$321$	−3268.11	+	7428.02i	−0.568250	+	1.29156i
$322$	4893.45	+	4504.31i	0.846898	+	0.779552i
$323$	5468.76			0.942074
$324$	5831.94	+	25.4643i	0.999990	+	0.00436631i
$325$	−1123.14			−0.191695
$326$	−467.305	−	430.145i	−0.0793916	−	0.0730783i
$327$	4558.35	−	10360.6i	0.770880	−	1.75212i
$328$	1456.48	−	1871.83i	0.245186	−	0.315105i
$329$		−	3352.09i		−	0.561722i
$330$	−2186.44	+	956.277i	−0.364726	+	0.159519i
$331$			3283.67i			0.545278i	0.962116	+	0.272639i	$0.0878965\pi$
$331$			3283.67i			0.545278i	−0.962116	+	0.272639i	$0.912104\pi$
$332$	−259.484	−	3127.97i	−0.0428947	−	0.517077i
$333$	2787.89	+	3042.05i	0.458786	+	0.500610i
$334$	1837.46	−	1996.20i	0.301022	−	0.327028i
$335$	−1451.11			−0.236664
$336$	−10400.3	−	2644.00i	−1.68865	−	0.429292i
$337$	−10806.5			−1.74678			−0.873391	−	0.487019i	$-0.838084\pi$
$337$	−10806.5			−1.74678			−0.873391	+	0.487019i	$0.838084\pi$
$338$	−342.271	+	371.840i	−0.0550801	+	0.0598385i
$339$	−8160.89	−	3590.55i	−1.30749	−	0.575257i
$340$	261.973	+	3157.97i	0.0417867	+	0.503720i
$341$			924.649i			0.146840i
$342$	11.5092	−	5271.81i	0.00181973	−	0.833529i
$343$		−	11464.7i		−	1.80477i
$344$	1342.39	−	1725.19i	0.210397	−	0.270396i
$345$	−1732.92	−	762.434i	−0.270427	−	0.118980i
$346$	3786.35	+	3485.25i	0.588310	+	0.541527i
$347$	−4257.61			−0.658676			−0.329338	−	0.944212i	$-0.606826\pi$
$347$	−4257.61			−0.658676			−0.329338	+	0.944212i	$0.606826\pi$
$348$	2977.27	−	8643.73i	0.458617	−	1.33147i
$349$	−1701.82			−0.261022			−0.130511	−	0.991447i	$-0.541662\pi$
$349$	−1701.82			−0.261022			−0.130511	+	0.991447i	$0.541662\pi$
$350$	−1678.82	−	1545.32i	−0.256390	−	0.236002i
$351$	−5968.21	+	2026.60i	−0.907576	+	0.308182i
$352$	−3214.14	+	4922.12i	−0.486689	+	0.745312i
$353$		−	3808.94i		−	0.574305i	−0.957885	−	0.287152i	$-0.907291\pi$
$353$		−	3808.94i		−	0.574305i	0.957885	−	0.287152i	$-0.0927086\pi$
$354$	2538.60	+	5804.27i	0.381144	+	0.871451i
$355$			2445.64i			0.365637i
$356$	2681.53	−	222.450i	0.399216	−	0.0331175i
$357$	5349.37	−	12158.5i	0.793050	−	1.80251i
$358$	−1528.22	+	1660.25i	−0.225612	+	0.245103i
$359$	3187.87			0.468660			0.234330	−	0.972157i	$-0.424710\pi$
$359$	3187.87			0.468660			0.234330	+	0.972157i	$0.424710\pi$
$360$	3044.79	−	245.892i	0.445762	−	0.0359991i
$361$	2093.55			0.305226
$362$	3626.56	−	3939.86i	0.526541	−	0.572029i
$363$	−578.334	+	1314.48i	−0.0836217	+	0.190062i
$364$	11557.9	−	958.804i	1.66429	−	0.138063i
$365$			1464.83i			0.210062i
$366$	−1079.95	−	2469.21i	−0.154235	−	0.352645i
$367$			10714.8i			1.52400i	0.647576	+	0.762001i	$0.275783\pi$
$367$			10714.8i			1.52400i	−0.647576	+	0.762001i	$0.724217\pi$
$368$	−4599.96	+	768.479i	−0.651602	+	0.108858i
$369$	2086.40	−	1912.09i	0.294346	−	0.269755i
$370$	1590.18	+	1463.73i	0.223431	+	0.205664i
$371$	17567.1			2.45833
$372$	385.453	−	1119.06i	0.0537226	−	0.155969i
$373$	−13485.1			−1.87194			−0.935969	−	0.352082i	$-0.885474\pi$
$373$	−13485.1			−1.87194			−0.935969	+	0.352082i	$0.885474\pi$
$374$	−5353.83	−	4928.09i	−0.740214	−	0.681351i
$375$	594.521	+	261.572i	0.0818691	+	0.0360200i
$376$	1855.10	+	1443.46i	0.254440	+	0.197981i
$377$			9880.29i			1.34976i
$378$	−11709.3	−	5182.31i	−1.59329	−	0.705157i
$379$		−	14560.5i		−	1.97341i	−0.162534	−	0.986703i	$-0.551967\pi$
$379$		−	14560.5i		−	1.97341i	0.162534	−	0.986703i	$-0.448033\pi$
$380$	−228.282	−	2751.84i	−0.0308174	−	0.371490i
$381$	−6641.37	−	2922.01i	−0.893038	−	0.392911i
$382$	4155.15	−	4514.12i	0.556534	−	0.604614i
$383$	−12768.6			−1.70352			−0.851759	−	0.523934i	$-0.824464\pi$
$383$	−12768.6			−1.70352			−0.851759	+	0.523934i	$0.824464\pi$
$384$	5941.79	−	4617.16i	0.789625	−	0.613590i
$385$	5239.67			0.693606
$386$	8293.72	−	9010.23i	1.09363	−	1.18810i
$387$	1922.96	−	1762.30i	0.252582	−	0.231480i
$388$	−687.658	−	8289.41i	−0.0899757	−	1.08462i
$389$			1614.55i			0.210439i	0.994449	+	0.105220i	$0.0335545\pi$
$389$			1614.55i			0.210439i	−0.994449	+	0.105220i	$0.966445\pi$
$390$	−3024.70	+	1322.91i	−0.392723	+	0.171764i
$391$		−	5772.82i		−	0.746660i
$392$	12470.1	+	9703.06i	1.60672	+	1.25020i
$393$	−3160.92	+	7184.38i	−0.405718	+	0.922147i
$394$	−4391.96	−	4042.70i	−0.561583	−	0.516925i
$395$	3281.95			0.418057
$396$	−4761.87	+	5150.65i	−0.604276	+	0.653610i
$397$	−3366.61			−0.425605			−0.212803	−	0.977095i	$-0.568259\pi$
$397$	−3366.61			−0.425605			−0.212803	+	0.977095i	$0.568259\pi$
$398$	3048.91	+	2806.46i	0.383990	+	0.353455i
$399$	−4661.42	+	10594.8i	−0.584869	+	1.32934i
$400$	1578.13	−	263.646i	0.197266	−	0.0329557i
$401$		−	2084.43i		−	0.259580i	−0.991542	−	0.129790i	$-0.958570\pi$
$401$		−	2084.43i		−	0.259580i	0.991542	−	0.129790i	$-0.0414303\pi$
$402$	−3907.94	+	1709.21i	−0.484852	+	0.212058i
$403$			1279.15i			0.158112i
$404$	−2458.14	+	203.918i	−0.302715	+	0.0251121i
$405$	3631.17	+	317.198i	0.445517	+	0.0389178i
$406$	−13594.1	+	14768.6i	−1.66174	+	1.80530i
$407$	−4963.03			−0.604443
$408$	4425.16	+	8196.07i	0.536956	+	0.994524i
$409$	9008.16			1.08906			0.544529	−	0.838742i	$-0.316708\pi$
$409$	9008.16			1.08906			0.544529	+	0.838742i	$0.316708\pi$
$410$	1003.90	−	1090.63i	0.120925	−	0.131372i
$411$	−2576.84	−	1133.73i	−0.309260	−	0.136066i
$412$	−2107.57	+	174.836i	−0.252021	+	0.0209067i
$413$		−	13909.6i		−	1.65726i
$414$	−5564.92	−	12.1491i	−0.660631	−	0.00144227i
$415$		−	1961.69i		−	0.232038i
$416$	−4446.43	+	6809.23i	−0.524048	+	0.802524i
$417$	3394.95	+	1493.68i	0.398685	+	0.175410i
$418$	4665.30	+	4294.31i	0.545903	+	0.502492i
$419$	8794.29			1.02537			0.512684	−	0.858577i	$-0.328651\pi$
$419$	8794.29			1.02537			0.512684	+	0.858577i	$0.328651\pi$
$420$	−6341.35	−	2184.23i	−0.736729	−	0.253761i
$421$	4897.05			0.566906			0.283453	−	0.958986i	$-0.408520\pi$
$421$	4897.05			0.566906			0.283453	+	0.958986i	$0.408520\pi$
$422$	4996.48	+	4599.15i	0.576362	+	0.530529i
$423$	1895.00	+	2067.75i	0.217820	+	0.237677i
$424$	−7564.71	+	9721.94i	−0.866449	+	1.11354i
$425$			1980.51i			0.226044i
$426$	2880.63	+	6586.28i	0.327622	+	0.749076i
$427$			5917.33i			0.670631i
$428$	1032.92	+	12451.4i	0.116654	+	1.40621i
$429$	3052.99	−	6939.07i	0.343589	−	0.780936i
$430$	925.260	−	1005.19i	0.103767	−	0.112732i
$431$	−11897.9			−1.32970			−0.664848	−	0.746978i	$-0.731504\pi$
$431$	−11897.9			−1.32970			−0.664848	+	0.746978i	$0.731504\pi$
$432$	7910.21	−	4248.55i	0.880972	−	0.473167i
$433$	1169.38			0.129785			0.0648925	−	0.997892i	$-0.479330\pi$
$433$	1169.38			0.129785			0.0648925	+	0.997892i	$0.479330\pi$
$434$	−1759.97	+	1912.01i	−0.194657	+	0.211474i
$435$	2301.05	−	5230.00i	0.253625	−	0.576459i
$436$	−1440.71	−	17367.1i	−0.158251	−	1.90765i
$437$			5030.41i			0.550657i
$438$	1725.37	+	3944.89i	0.188222	+	0.430352i
$439$			6786.60i			0.737829i	0.929463	+	0.368915i	$0.120270\pi$
$439$			6786.60i			0.737829i	−0.929463	+	0.368915i	$0.879730\pi$
$440$	−2256.29	+	2899.72i	−0.244465	+	0.314179i
$441$	12738.3	+	13899.6i	1.37548	+	1.50087i
$442$	−7406.45	−	6817.48i	−0.797034	−	0.733653i
$443$	9083.87			0.974238			0.487119	−	0.873336i	$-0.338048\pi$
$443$	9083.87			0.974238			0.487119	+	0.873336i	$0.338048\pi$
$444$	6006.54	+	2068.91i	0.642022	+	0.221140i
$445$	1681.72			0.179148
$446$	2553.86	+	2350.78i	0.271141	+	0.249580i
$447$	518.510	+	228.129i	0.0548650	+	0.0241390i
$448$	−16015.0	+	4060.32i	−1.68892	+	0.428196i
$449$		−	3214.97i		−	0.337914i	−0.985623	−	0.168957i	$-0.945960\pi$
$449$		−	3214.97i		−	0.337914i	0.985623	−	0.168957i	$-0.0540400\pi$
$450$	1909.18	+	4.16806i	0.200000	+	0.000436632i
$451$			3403.92i			0.355398i
$452$	−13679.8	+	1134.83i	−1.42355	+	0.118093i
$453$	−15155.0	−	6667.75i	−1.57184	−	0.691563i
$454$	11501.8	−	12495.5i	1.18900	−	1.29172i
$455$	7248.53			0.746849
$456$	−3856.07	−	7142.01i	−0.396002	−	0.733455i
$457$	12339.4			1.26304			0.631522	−	0.775358i	$-0.282431\pi$
$457$	12339.4			1.26304			0.631522	+	0.775358i	$0.282431\pi$
$458$	−6533.19	+	7097.60i	−0.666541	+	0.724125i
$459$	3573.63	+	10524.1i	0.363405	+	1.07020i
$460$	−2904.84	+	240.975i	−0.294432	+	0.0244250i
$461$			12038.7i			1.21626i	0.793837	+	0.608130i	$0.208080\pi$
$461$			12038.7i			1.21626i	−0.793837	+	0.608130i	$0.791920\pi$
$462$	14110.8	−	6171.61i	1.42098	−	0.621492i
$463$			2481.97i			0.249130i	0.992211	+	0.124565i	$0.0397535\pi$
$463$			2481.97i			0.249130i	−0.992211	+	0.124565i	$0.960247\pi$
$464$	−2319.29	−	13882.8i	−0.232048	−	1.38899i
$465$	297.905	−	677.103i	0.0297098	−	0.0675267i
$466$	−13150.7	−	12105.0i	−1.30729	−	1.20333i
$467$	1596.67			0.158212			0.0791060	−	0.996866i	$-0.474793\pi$
$467$	1596.67			0.158212			0.0791060	+	0.996866i	$0.474793\pi$
$468$	−6587.55	+	7125.37i	−0.650661	+	0.703783i
$469$	9365.16			0.922053
$470$	1080.88	+	994.930i	0.106080	+	0.0976440i
$471$	−2154.03	+	4895.86i	−0.210728	+	0.478958i
$472$	7697.79	+	5989.70i	0.750677	+	0.584107i
$473$			3137.26i			0.304971i
$474$	8838.52	−	3865.68i	0.856470	−	0.374592i
$475$		−	1725.81i		−	0.166706i
$476$	−1690.72	−	20380.9i	−0.162803	−	1.96251i
$477$	−10836.4	+	9931.05i	−1.04018	+	0.953273i
$478$	6826.63	−	7416.39i	0.653227	−	0.709660i
$479$	−13673.9			−1.30433			−0.652166	−	0.758076i	$-0.726139\pi$
$479$	−13673.9			−1.30433			−0.652166	+	0.758076i	$0.726139\pi$
$480$	3939.48	−	2568.84i	0.374608	−	0.244272i
$481$	−6865.82			−0.650841
$482$	−5428.29	+	5897.25i	−0.512971	+	0.557287i
$483$	11183.9	+	4920.59i	1.05359	+	0.463550i
$484$	182.788	+	2203.43i	0.0171664	+	0.206933i
$485$		−	5198.68i		−	0.486721i
$486$	10152.6	−	3422.78i	0.947598	−	0.319466i
$487$			2712.51i			0.252393i	0.992005	+	0.126197i	$0.0402770\pi$
$487$			2712.51i			0.252393i	−0.992005	+	0.126197i	$0.959723\pi$
$488$	−3274.74	−	2548.10i	−0.303772	−	0.236367i
$489$	−1068.02	−	469.898i	−0.0987680	−	0.0434550i
$490$	7265.77	+	6687.98i	0.669865	+	0.616597i
$491$	−7797.19			−0.716664			−0.358332	−	0.933594i	$-0.616654\pi$
$491$	−7797.19			−0.716664			−0.358332	+	0.933594i	$0.616654\pi$
$492$	1418.97	−	4119.61i	0.130025	−	0.377493i
$493$	17422.5			1.59163
$494$	6453.95	+	5940.72i	0.587807	+	0.541064i
$495$	−3232.12	+	2962.09i	−0.293481	+	0.268961i
$496$	−300.267	−	1797.34i	−0.0271823	−	0.162707i
$497$		−	15783.6i		−	1.42453i
$498$	−2310.61	−	5282.98i	−0.207913	−	0.475374i
$499$		−	10440.3i		−	0.936617i	−0.883565	−	0.468309i	$-0.844864\pi$
$499$		−	10440.3i		−	0.936617i	0.883565	−	0.468309i	$-0.155136\pi$
$500$	996.577	−	82.6723i	0.0891365	−	0.00739443i
$501$	2007.27	−	4562.29i	0.178999	−	0.406842i
$502$	−7405.18	+	8044.93i	−0.658386	+	0.715264i
$503$	14638.9			1.29764			0.648822	−	0.760940i	$-0.275262\pi$
$503$	14638.9			1.29764			0.648822	+	0.760940i	$0.275262\pi$
$504$	−19650.4	+	1586.94i	−1.73671	+	0.140254i
$505$	−1541.61			−0.135843
$506$	4533.07	−	4924.69i	0.398260	−	0.432667i
$507$	−373.903	+	849.835i	−0.0327527	+	0.0744428i
$508$	−11132.7	+	923.528i	−0.972312	+	0.0806593i
$509$		−	1254.81i		−	0.109270i	−0.998506	−	0.0546351i	$-0.982600\pi$
$509$		−	1254.81i		−	0.109270i	0.998506	−	0.0546351i	$-0.0173996\pi$
$510$	2332.77	+	5333.65i	0.202542	+	0.463095i
$511$		−	9453.70i		−	0.818409i
$512$	4649.28	−	10611.4i	0.401311	−	0.915942i
$513$	−3114.05	−	9170.67i	−0.268009	−	0.789269i
$514$	−6160.91	−	5670.99i	−0.528689	−	0.486647i
$515$	−1321.76			−0.113094
$516$	1307.81	−	3796.89i	0.111576	−	0.323932i
$517$	−3373.49			−0.286975
$518$	−10262.7	−	9446.58i	−0.870495	−	0.801272i
$519$	8653.65	+	3807.35i	0.731894	+	0.322012i
$520$	−3121.34	+	4011.45i	−0.263230	+	0.338296i
$521$		−	2219.01i		−	0.186596i	−0.995638	−	0.0932980i	$-0.970259\pi$
$521$		−	2219.01i		−	0.186596i	0.995638	−	0.0932980i	$-0.0297409\pi$
$522$	36.6665	−	16795.1i	0.00307442	−	1.40824i
$523$		−	11035.2i		−	0.922633i	−0.887236	−	0.461317i	$-0.847377\pi$
$523$		−	11035.2i		−	0.922633i	0.887236	−	0.461317i	$-0.152623\pi$
$524$	999.037	+	12042.9i	0.0832885	+	1.00400i
$525$	−3836.91	−	1688.13i	−0.318965	−	0.140335i
$526$	−12557.3	+	13642.1i	−1.04092	+	1.13085i
$527$	2255.61			0.186444
$528$	−2660.88	+	10466.7i	−0.219318	+	0.862702i
$529$	−6856.90			−0.563565
$530$	−5214.09	+	5664.54i	−0.427331	+	0.464249i
$531$	7863.36	+	8580.21i	0.642638	+	0.701223i
$532$	1473.29	+	17759.8i	0.120066	+	1.44734i
$533$			4708.96i			0.382679i
$534$	4528.98	−	1980.83i	0.367019	−	0.160522i
$535$			7808.83i			0.631038i
$536$	−4032.79	+	5182.83i	−0.324982	+	0.417657i
$537$	−1669.46	+	3794.48i	−0.134157	+	0.304923i
$538$	18107.7	+	16667.7i	1.45107	+	1.33568i
$539$	−22676.8			−1.81217
$540$	5146.48	−	2237.53i	0.410128	−	0.178311i
$541$	4389.37			0.348824			0.174412	−	0.984673i	$-0.444198\pi$
$541$	4389.37			0.348824			0.174412	+	0.984673i	$0.444198\pi$
$542$	−4216.83	−	3881.50i	−0.334185	−	0.307611i
$543$	3961.72	−	9004.50i	0.313101	−	0.711640i
$544$	12007.1	+	7840.67i	0.946327	+	0.617952i
$545$		−	10891.7i		−	0.856057i
$546$	19520.8	−	8537.77i	1.53006	−	0.669199i
$547$		−	11409.4i		−	0.891826i	−0.895076	−	0.445913i	$-0.852879\pi$
$547$		−	11409.4i		−	0.891826i	0.895076	−	0.445913i	$-0.147121\pi$
$548$	−4319.47	+	358.327i	−0.336713	+	0.0279324i
$549$	−3345.18	−	3650.13i	−0.260052	−	0.283759i
$550$	−1555.18	+	1689.54i	−0.120569	+	0.130986i
$551$	−15181.9			−1.17381
$552$	−7539.11	+	4070.46i	−0.581315	+	0.313860i
$553$	−21181.0			−1.62877
$554$	11876.6	−	12902.6i	0.910806	−	0.989492i
$555$	3634.33	+	1599.00i	0.277962	+	0.122295i
$556$	5690.85	−	472.091i	0.434075	−	0.0360092i
$557$			9758.39i			0.742327i	0.928567	+	0.371164i	$0.121041\pi$
$557$			9758.39i			0.742327i	−0.928567	+	0.371164i	$0.878959\pi$
$558$	4.74703	−	2174.38i	0.000360139	−	0.164962i
$559$			4340.07i			0.328382i
$560$	−10184.9	+	1701.51i	−0.768556	+	0.128397i
$561$	−12236.1	−	5383.53i	−0.920871	−	0.405156i
$562$	−17063.5	−	15706.6i	−1.28075	−	1.17890i
$563$	7722.59			0.578097			0.289048	−	0.957315i	$-0.406661\pi$
$563$	7722.59			0.578097			0.289048	+	0.957315i	$0.406661\pi$
$564$	4082.79	+	1406.29i	0.304816	+	0.104992i
$565$	−8579.27			−0.638818
$566$	15848.9	+	14588.6i	1.17699	+	1.08340i
$567$	−23434.8	−	2047.13i	−1.73575	−	0.151625i
$568$	8734.92	+	6796.70i	0.645262	+	0.502083i
$569$			10040.4i			0.739744i	0.929083	+	0.369872i	$0.120598\pi$
$569$			10040.4i			0.739744i	−0.929083	+	0.369872i	$0.879402\pi$
$570$	−2032.76	−	4647.72i	−0.149374	−	0.341529i
$571$			18510.6i			1.35664i	0.734764	+	0.678322i	$0.237293\pi$
$571$			18510.6i			1.35664i	−0.734764	+	0.678322i	$0.762707\pi$
$572$	−964.926	−	11631.7i	−0.0705342	−	0.850258i
$573$	4539.16	−	10317.0i	0.330936	−	0.752176i
$574$	−6478.99	+	7038.72i	−0.471129	+	0.511830i
$575$	−1821.76			−0.132126
$576$	7583.56	−	11558.2i	0.548580	−	0.836098i
$577$	21556.9			1.55533			0.777664	−	0.628680i	$-0.216404\pi$
$577$	21556.9			1.55533			0.777664	+	0.628680i	$0.216404\pi$
$578$	−2610.63	+	2836.16i	−0.187868	+	0.204098i
$579$	9060.21	−	20592.7i	0.650310	−	1.47807i
$580$	−727.268	−	8766.89i	−0.0520658	−	0.627630i
$581$			12660.4i			0.904028i
$582$	−6123.33	−	14000.4i	−0.436117	−	0.997141i
$583$		−	17679.3i		−	1.25592i
$584$	5231.83	+	4070.92i	0.370710	+	0.288452i
$585$	−4471.29	+	4097.73i	−0.316009	+	0.289608i
$586$	19342.1	+	17804.0i	1.36350	+	1.25508i
$587$	−7143.54			−0.502292			−0.251146	−	0.967949i	$-0.580807\pi$
$587$	−7143.54			−0.502292			−0.251146	+	0.967949i	$0.580807\pi$
$588$	27444.8	+	9453.15i	1.92484	+	0.662996i
$589$	−1965.53			−0.137501
$590$	4485.16	+	4128.50i	0.312968	+	0.288081i
$591$	−10037.8	−	4416.32i	−0.698643	−	0.307383i
$592$	9647.17	−	1611.68i	0.669757	−	0.111891i
$593$		−	8287.65i		−	0.573918i	−0.957943	−	0.286959i	$-0.907356\pi$
$593$		−	8287.65i		−	0.573918i	0.957943	−	0.286959i	$-0.0926443\pi$
$594$	−5215.40	+	11784.1i	−0.360253	+	0.813986i
$595$		−	12781.8i		−	0.880676i
$596$	869.162	−	72.1024i	0.0597353	−	0.00495542i
$597$	6968.25	+	3065.82i	0.477707	+	0.210177i
$598$	6271.03	−	6812.79i	0.428832	−	0.465879i
$599$	26207.7			1.78767			0.893837	−	0.448393i	$-0.148003\pi$
$599$	26207.7			1.78767			0.893837	+	0.448393i	$0.148003\pi$
$600$	2586.48	−	1396.47i	0.175987	−	0.0950179i
$601$	13315.0			0.903711			0.451855	−	0.892091i	$-0.350762\pi$
$601$	13315.0			0.903711			0.451855	+	0.892091i	$0.350762\pi$
$602$	−5971.43	+	6487.31i	−0.404282	+	0.439208i
$603$	−5776.95	+	5294.30i	−0.390142	+	0.357547i
$604$	−25403.8	+	2107.40i	−1.71137	+	0.141969i
$605$			1381.87i			0.0928613i
$606$	−4151.68	+	1815.81i	−0.278301	+	0.121720i
$607$		−	4763.81i		−	0.318546i	−0.987235	−	0.159273i	$-0.949085\pi$
$607$		−	4763.81i		−	0.318546i	0.987235	−	0.159273i	$-0.0509149\pi$
$608$	−10463.0	−	6832.32i	−0.697910	−	0.455735i
$609$	−14850.5	+	33753.3i	−0.988131	+	2.24590i
$610$	−1908.05	−	1756.32i	−0.126647	−	0.116576i
$611$	−4666.86			−0.309003
$612$	12564.6	+	11616.2i	0.829893	+	0.767253i
$613$	20511.4			1.35146			0.675731	−	0.737148i	$-0.263828\pi$
$613$	20511.4			1.35146			0.675731	+	0.737148i	$0.263828\pi$
$614$	−4126.63	−	3798.47i	−0.271233	−	0.249664i
$615$	1096.68	−	2492.63i	0.0719065	−	0.163435i
$616$	14561.6	−	18714.2i	0.952442	−	1.22405i
$617$		−	8679.39i		−	0.566320i	−0.959073	−	0.283160i	$-0.908617\pi$
$617$		−	8679.39i		−	0.566320i	0.959073	−	0.283160i	$-0.0913827\pi$
$618$	−3559.59	+	1556.85i	−0.231695	+	0.101336i
$619$		−	20896.1i		−	1.35684i	−0.734674	−	0.678420i	$-0.762665\pi$
$619$		−	20896.1i		−	1.35684i	0.734674	−	0.678420i	$-0.237335\pi$
$620$	−94.1559	−	1135.01i	−0.00609902	−	0.0735209i
$621$	−9680.56	+	3287.19i	−0.625551	+	0.212416i
$622$	−624.752	+	678.725i	−0.0402737	+	0.0437530i
$623$	−10853.4			−0.697968
$624$	−3681.05	+	14479.6i	−0.236154	+	0.928925i
$625$	625.000			0.0400000
$626$	2030.29	−	2205.68i	0.129627	−	0.140826i
$627$	10662.5	+	4691.18i	0.679136	+	0.298800i
$628$	680.803	+	8206.77i	0.0432596	+	0.521474i
$629$			12106.9i			0.767465i
$630$	−12321.5	−	26.8998i	−0.779205	−	0.00170113i
$631$			5444.29i			0.343477i	0.985143	+	0.171738i	$0.0549384\pi$
$631$			5444.29i			0.343477i	−0.985143	+	0.171738i	$0.945062\pi$
$632$	9120.89	−	11721.9i	0.574066	−	0.737773i
$633$	11419.4	+	5024.20i	0.717030	+	0.315472i
$634$	−2097.66	−	1930.86i	−0.131402	−	0.120953i
$635$	−6981.85			−0.436325
$636$	−7369.87	+	21396.5i	−0.459488	+	1.33400i
$637$	−31371.0			−1.95128
$638$	14862.9	+	13680.9i	0.922298	+	0.848956i
$639$	8922.80	+	9736.22i	0.552395	+	0.602753i
$640$	3444.15	−	6369.19i	0.212722	−	0.393382i
$641$			2664.42i			0.164178i	0.996625	+	0.0820890i	$0.0261592\pi$
$641$			2664.42i			0.164178i	−0.996625	+	0.0820890i	$0.973841\pi$
$642$	9197.73	+	21029.7i	0.565429	+	1.29280i
$643$			17860.6i			1.09542i	0.836668	+	0.547710i	$0.184500\pi$
$643$			17860.6i			1.09542i	−0.836668	+	0.547710i	$0.815500\pi$
$644$	18747.2	−	1555.20i	1.14712	−	0.0951607i
$645$	1010.77	−	2297.36i	0.0617039	−	0.140246i
$646$	10475.7	−	11380.7i	0.638017	−	0.693136i
$647$	21691.5			1.31805			0.659026	−	0.752120i	$-0.270969\pi$
$647$	21691.5			1.31805			0.659026	+	0.752120i	$0.270969\pi$
$648$	11224.3	−	12087.7i	0.680453	−	0.732791i
$649$	−13998.4			−0.846665
$650$	−2151.43	+	2337.29i	−0.129825	+	0.141040i
$651$	−1922.62	+	4369.88i	−0.115750	+	0.263086i
$652$	−1790.29	+	148.516i	−0.107535	+	0.00892074i
$653$		−	5849.05i		−	0.350522i	−0.984522	−	0.175261i	$-0.943923\pi$
$653$		−	5849.05i		−	0.350522i	0.984522	−	0.175261i	$-0.0560769\pi$
$654$	−12829.0	−	29332.2i	−0.767053	−	1.75379i
$655$			7552.69i			0.450547i
$656$	−1105.38	−	6616.56i	−0.0657892	−	0.393801i
$657$	5344.36	+	5831.56i	0.317356	+	0.346287i
$658$	−6975.79	−	6421.07i	−0.413290	−	0.380425i
$659$	−8922.46			−0.527420			−0.263710	−	0.964602i	$-0.584946\pi$
$659$	−8922.46			−0.527420			−0.263710	+	0.964602i	$0.584946\pi$
$660$	−2198.18	+	6381.84i	−0.129642	+	0.376383i
$661$	−2789.76			−0.164159			−0.0820796	−	0.996626i	$-0.526156\pi$
$661$	−2789.76			−0.164159			−0.0820796	+	0.996626i	$0.526156\pi$
$662$	6833.43	+	6290.02i	0.401191	+	0.369288i
$663$	−16927.3	−	7447.54i	−0.991559	−	0.436257i
$664$	−7006.45	−	5451.76i	−0.409492	−	0.318629i
$665$			11138.0i			0.649493i
$666$	11670.9	+	25.4795i	0.679038	+	0.00148245i
$667$			16026.0i			0.930331i
$668$	−634.418	−	7647.62i	−0.0367460	−	0.442957i
$669$	5836.82	+	2568.03i	0.337316	+	0.148409i
$670$	−2779.66	+	3019.80i	−0.160280	+	0.174127i
$671$	5955.11			0.342615
$672$	−25424.6	+	16578.7i	−1.45948	+	0.951694i
$673$	−18308.8			−1.04867			−0.524334	−	0.851513i	$-0.675686\pi$
$673$	−18308.8			−1.04867			−0.524334	+	0.851513i	$0.675686\pi$
$674$	−20700.3	+	22488.6i	−1.18300	+	1.28520i
$675$	3321.15	−	1127.75i	0.189380	−	0.0643068i
$676$	118.175	+	1424.55i	0.00672368	+	0.0810510i
$677$			10293.0i			0.584330i	0.956368	+	0.292165i	$0.0943756\pi$
$677$			10293.0i			0.584330i	−0.956368	+	0.292165i	$0.905624\pi$
$678$	−23104.6	+	10105.2i	−1.30874	+	0.572401i
$679$			33551.2i			1.89628i
$680$	7073.65	+	5504.05i	0.398915	+	0.310398i
$681$	12564.8	−	28558.2i	0.707025	−	1.60698i
$682$	1924.22	+	1771.21i	0.108039	+	0.0994472i
$683$	21101.1			1.18215			0.591077	−	0.806615i	$-0.298703\pi$
$683$	21101.1			1.18215			0.591077	+	0.806615i	$0.298703\pi$
$684$	−10948.8	−	10122.3i	−0.612041	−	0.565844i
$685$	−2708.94			−0.151100
$686$	−23858.4	−	21961.1i	−1.32787	−	1.22227i
$687$	−7136.97	+	16221.5i	−0.396350	+	0.900856i
$688$	−1018.78	−	6098.23i	−0.0564546	−	0.337926i
$689$		−	24457.5i		−	1.35233i
$690$	−4906.14	+	2145.78i	−0.270686	+	0.118389i
$691$		−	17707.2i		−	0.974841i	−0.873167	−	0.487420i	$-0.837938\pi$
$691$		−	17707.2i		−	0.974841i	0.873167	−	0.487420i	$-0.162062\pi$
$692$	14505.8	−	1203.35i	0.796863	−	0.0661048i
$693$	20859.4	−	19116.7i	1.14341	−	1.04788i
$694$	−8155.64	+	8860.22i	−0.446086	+	0.484624i
$695$	3569.00			0.194791
$696$	−12284.8	−	22753.3i	−0.669042	−	1.23917i
$697$	8303.61			0.451251
$698$	−3259.92	+	3541.55i	−0.176776	+	0.192048i
$699$	−30055.8	−	13223.7i	−1.62634	−	0.715544i
$700$	−6431.70	+	533.550i	−0.347279	+	0.0288090i
$701$		−	390.697i		−	0.0210505i	−0.999945	−	0.0105253i	$-0.996650\pi$
$701$		−	390.697i		−	0.0210505i	0.999945	−	0.0105253i	$-0.00335035\pi$
$702$	−7214.95	+	16302.1i	−0.387907	+	0.876470i
$703$		−	10549.9i		−	0.566000i
$704$	4086.24	+	16117.3i	0.218759	+	0.862844i
$705$	2470.34	+	1086.88i	0.131970	+	0.0580627i
$706$	−7926.53	−	7296.20i	−0.422548	−	0.388946i
$707$	9949.25			0.529250
$708$	16941.7	+	5835.44i	0.899304	+	0.309759i
$709$	3068.89			0.162559			0.0812797	−	0.996691i	$-0.474099\pi$
$709$	3068.89			0.162559			0.0812797	+	0.996691i	$0.474099\pi$
$710$	5089.45	+	4684.73i	0.269019	+	0.247626i
$711$	13065.6	−	11974.0i	0.689168	−	0.631591i
$712$	4673.67	−	6006.47i	0.246002	−	0.316154i
$713$			2074.81i			0.108979i
$714$	−15055.2	−	34422.3i	−0.789113	−	1.80423i
$715$		−	7294.81i		−	0.381553i
$716$	527.649	+	6360.57i	0.0275407	+	0.331991i
$717$	7457.53	−	16950.1i	0.388433	−	0.882861i
$718$	6106.50	−	6634.05i	0.317399	−	0.344819i
$719$	−4167.04			−0.216139			−0.108070	−	0.994143i	$-0.534467\pi$
$719$	−4167.04			−0.216139			−0.108070	+	0.994143i	$0.534467\pi$
$720$	5320.72	−	6807.32i	0.275405	−	0.352352i
$721$	8530.35			0.440620
$722$	4010.28	−	4356.74i	0.206714	−	0.224572i
$723$	−5929.96	+	13478.1i	−0.305031	+	0.693299i
$724$	−1252.14	−	15094.0i	−0.0642754	−	0.774811i
$725$		−	5498.13i		−	0.281649i
$726$	1627.66	+	3721.48i	0.0832065	+	0.190244i
$727$		−	36845.2i		−	1.87966i	−0.341640	−	0.939831i	$-0.610982\pi$
$727$		−	36845.2i		−	1.87966i	0.341640	−	0.939831i	$-0.389018\pi$
$728$	20144.5	−	25889.1i	1.02555	−	1.31801i
$729$	15613.2	−	11985.4i	0.793232	−	0.608920i
$730$	3048.35	+	2805.94i	0.154554	+	0.142264i
$731$	7653.12			0.387224
$732$	−7207.21	−	2482.47i	−0.363916	−	0.125348i
$733$	8332.32			0.419865			0.209933	−	0.977716i	$-0.432676\pi$
$733$	8332.32			0.419865			0.209933	+	0.977716i	$0.432676\pi$
$734$	22297.8	+	20524.7i	1.12129	+	1.03213i
$735$	16605.8	+	7306.07i	0.833353	+	0.366651i
$736$	−7212.20	+	11044.7i	−0.361203	+	0.553143i
$737$		−	9424.96i		−	0.471062i
$738$	17.4753	−	8004.57i	0.000871645	−	0.399258i
$739$			29386.0i			1.46276i	0.681970	+	0.731381i	$0.261124\pi$
$739$			29386.0i			1.46276i	−0.681970	+	0.731381i	$0.738876\pi$
$740$	6092.12	−	505.379i	0.302636	−	0.0251056i
$741$	14750.4	+	6489.75i	0.731269	+	0.321737i
$742$	33650.6	−	36557.8i	1.66490	−	1.80873i
$743$	15195.8			0.750311			0.375155	−	0.926962i	$-0.377589\pi$
$743$	15195.8			0.750311			0.375155	+	0.926962i	$0.377589\pi$
$744$	−1590.45	−	2945.75i	−0.0783719	−	0.145157i
$745$	545.092			0.0268062
$746$	−25831.3	+	28062.9i	−1.26777	+	1.37729i
$747$	−7157.15	−	7809.61i	−0.350557	−	0.382515i
$748$	−20511.0	+	1701.52i	−1.00262	+	0.0831732i
$749$		−	50396.6i		−	2.45854i
$750$	1683.17	−	736.164i	0.0819476	−	0.0358412i
$751$			4230.63i			0.205563i	0.994704	+	0.102782i	$0.0327742\pi$
$751$			4230.63i			0.205563i	−0.994704	+	0.102782i	$0.967226\pi$
$752$	6557.42	−	1095.50i	0.317984	−	0.0531232i
$753$	−8089.55	+	18386.6i	−0.391500	+	0.889833i
$754$	20561.2	+	18926.1i	0.993096	+	0.914124i
$755$	−15931.9			−0.767976
$756$	−33214.3	+	14440.6i	−1.59787	+	0.694706i
$757$	15946.8			0.765649			0.382825	−	0.923821i	$-0.374951\pi$
$757$	15946.8			0.765649			0.382825	+	0.923821i	$0.374951\pi$
$758$	−30300.8	−	27891.2i	−1.45194	−	1.33648i
$759$	4952.01	−	11255.3i	0.236820	−	0.538264i
$760$	−6163.94	−	4796.21i	−0.294197	−	0.228917i
$761$			6461.80i			0.307806i	0.988086	+	0.153903i	$0.0491843\pi$
$761$			6461.80i			0.307806i	−0.988086	+	0.153903i	$0.950816\pi$
$762$	−18802.6	+	8223.66i	−0.893894	+	0.390960i
$763$			70293.0i			3.33523i
$764$	−1434.64	−	17294.0i	−0.0679367	−	0.818946i
$765$	7225.79	+	7884.51i	0.341502	+	0.372634i
$766$	−24458.9	+	26571.9i	−1.15370	+	1.25337i
$767$	−19365.3			−0.911657
$768$	1773.31	−	21209.4i	0.0833187	−	0.996523i
$769$	−28578.2			−1.34013			−0.670064	−	0.742304i	$-0.733733\pi$
$769$	−28578.2			−1.34013			−0.670064	+	0.742304i	$0.733733\pi$
$770$	10036.8	−	10903.9i	0.469743	−	0.510325i
$771$	−14080.7	−	6195.09i	−0.657722	−	0.289378i
$772$	−2863.56	−	34519.0i	−0.133500	−	1.60928i
$773$			31061.7i			1.44530i	0.691216	+	0.722648i	$0.257075\pi$
$773$			31061.7i			1.44530i	−0.691216	+	0.722648i	$0.742925\pi$
$774$	16.1063	−	7377.50i	0.000747970	−	0.342608i
$775$		−	711.816i		−	0.0329925i
$776$	−18567.8	−	14447.7i	−0.858948	−	0.668353i
$777$	−23455.2	−	10319.6i	−1.08295	−	0.476466i
$778$	3359.92	+	3092.74i	0.154832	+	0.142519i
$779$	−7235.73			−0.332794
$780$	−3040.95	+	8828.59i	−0.139594	+	0.405275i
$781$	−15884.4			−0.727771
$782$	−12013.4	−	11058.1i	−0.549360	−	0.505674i
$783$	−9920.82	−	29216.2i	−0.452799	−	1.33346i
$784$	44079.4	−	7364.00i	2.00799	−	0.335459i
$785$			5146.85i			0.234011i
$786$	8896.03	+	20340.0i	0.403704	+	0.923031i
$787$			14851.0i			0.672657i	0.941745	+	0.336328i	$0.109185\pi$
$787$			14851.0i			0.672657i	−0.941745	+	0.336328i	$0.890815\pi$
$788$	−16826.0	+	1395.82i	−0.760661	+	0.0631016i
$789$	−13717.8	+	31178.9i	−0.618969	+	1.40684i
$790$	6286.71	−	6829.83i	0.283128	−	0.307588i
$791$	55368.8			2.48886
$792$	1597.07	+	19775.9i	0.0716534	+	0.887255i
$793$	8238.26			0.368915
$794$	−6448.89	+	7006.02i	−0.288240	+	0.313141i
$795$	−5695.96	+	12946.2i	−0.254107	+	0.577554i
$796$	11680.7	−	968.983i	0.520113	−	0.0431466i
$797$			19580.3i			0.870226i	0.900376	+	0.435113i	$0.143292\pi$
$797$			19580.3i			0.870226i	−0.900376	+	0.435113i	$0.856708\pi$
$798$	13119.0	+	29995.4i	0.581965	+	1.33061i
$799$			8229.38i			0.364374i
$800$	2474.32	−	3789.16i	0.109351	−	0.167459i
$801$	6695.00	−	6135.66i	0.295326	−	0.270653i
$802$	−4337.76	−	3992.82i	−0.190987	−	0.175800i
$803$	−9514.06			−0.418112
$804$	−3928.93	+	11406.6i	−0.172341	+	0.500349i
$805$	11757.3			0.514769
$806$	2661.96	+	2450.27i	0.116332	+	0.107081i
$807$	41384.9	+	18208.1i	1.80523	+	0.794246i
$808$	−4284.31	+	5506.07i	−0.186537	+	0.239731i
$809$		−	22199.3i		−	0.964754i	−0.875964	−	0.482377i	$-0.839774\pi$
$809$		−	22199.3i		−	0.964754i	0.875964	−	0.482377i	$-0.160226\pi$
$810$	7615.77	−	6948.97i	0.330359	−	0.301435i
$811$			16803.2i			0.727547i	0.931488	+	0.363773i	$0.118512\pi$
$811$			16803.2i			0.727547i	−0.931488	+	0.363773i	$0.881488\pi$
$812$	4693.64	+	56579.7i	0.202850	+	2.44527i
$813$	−9637.51	−	4240.22i	−0.415747	−	0.182917i
$814$	−9506.90	+	10328.2i	−0.409357	+	0.444722i
$815$	−1122.77			−0.0482565
$816$	25532.9	+	6491.03i	1.09538	+	0.278470i
$817$	−6668.89			−0.285575
$818$	17255.5	−	18746.3i	0.737562	−	0.801280i
$819$	28856.8	−	26445.9i	1.23118	−	1.12832i
$820$	−346.617	−	4178.31i	−0.0147615	−	0.177943i
$821$			3573.41i			0.151904i	0.997111	+	0.0759519i	$0.0241995\pi$
$821$			3573.41i			0.151904i	−0.997111	+	0.0759519i	$0.975800\pi$
$822$	−7295.38	+	3190.76i	−0.309557	+	0.135390i
$823$		−	9176.02i		−	0.388646i	−0.980938	−	0.194323i	$-0.937749\pi$
$823$		−	9176.02i		−	0.388646i	0.980938	−	0.194323i	$-0.0622510\pi$
$824$	−3673.31	+	4720.83i	−0.155298	+	0.199585i
$825$	−1698.91	+	3861.41i	−0.0716951	+	0.162954i
$826$	−28946.3	−	26644.5i	−1.21933	−	1.12237i
$827$	−14278.9			−0.600394			−0.300197	−	0.953877i	$-0.597052\pi$
$827$	−14278.9			−0.600394			−0.300197	+	0.953877i	$0.597052\pi$
$828$	−10685.1	+	11557.5i	−0.448471	+	0.485086i
$829$	20720.7			0.868105			0.434052	−	0.900888i	$-0.357083\pi$
$829$	20720.7			0.868105			0.434052	+	0.900888i	$0.357083\pi$
$830$	−4082.35	−	3757.71i	−0.170723	−	0.157147i
$831$	12974.2	−	29488.7i	0.541599	−	1.23099i
$832$	5652.89	+	22296.5i	0.235551	+	0.929078i
$833$			55318.4i			2.30092i
$834$	9611.57	−	4203.79i	0.399067	−	0.174539i
$835$		−	4796.18i		−	0.198777i
$836$	17873.2	−	1482.69i	0.739422	−	0.0613397i
$837$	−1284.40	−	3782.48i	−0.0530411	−	0.156203i
$838$	16845.9	−	18301.2i	0.694428	−	0.754420i
$839$	−26785.4			−1.10219			−0.551094	−	0.834443i	$-0.685789\pi$
$839$	−26785.4			−1.10219			−0.551094	+	0.834443i	$0.685789\pi$
$840$	−16692.6	+	9012.54i	−0.685653	+	0.370193i
$841$	−23978.1			−0.983150
$842$	9380.51	−	10190.9i	0.383935	−	0.417104i
$843$	−38998.4	−	17158.1i	−1.59333	−	0.701017i
$844$	19142.0	−	1587.95i	0.780680	−	0.0647622i
$845$			893.403i			0.0363716i
$846$	7933.01	+	17.3191i	0.322391	+	0.000703832i
$847$		−	8918.31i		−	0.361791i
$848$	5741.12	+	34365.2i	0.232489	+	1.39163i
$849$	36222.4	+	15936.8i	1.46425	+	0.644229i
$850$	4121.50	+	3793.75i	0.166313	+	0.153088i
$851$	−11136.5			−0.448595
$852$	19224.2	+	6621.65i	0.773018	+	0.266260i
$853$	−20065.4			−0.805425			−0.402713	−	0.915326i	$-0.631933\pi$
$853$	−20065.4			−0.805425			−0.402713	+	0.915326i	$0.631933\pi$
$854$	12314.1	+	11334.9i	0.493421	+	0.454183i
$855$	−6296.52	−	6870.53i	−0.251856	−	0.274815i
$856$	27890.3	+	21701.6i	1.11363	+	0.866525i
$857$			1780.43i			0.0709664i	0.999370	+	0.0354832i	$0.0112970\pi$
$857$			1780.43i			0.0709664i	−0.999370	+	0.0354832i	$0.988703\pi$
$858$	−8592.28	−	19645.5i	−0.341883	−	0.781684i
$859$		−	27394.4i		−	1.08811i	−0.839050	−	0.544054i	$-0.816889\pi$
$859$		−	27394.4i		−	1.08811i	0.839050	−	0.544054i	$-0.183111\pi$
$860$	−319.464	−	3850.99i	−0.0126670	−	0.152695i
$861$	−7077.76	+	16086.9i	−0.280150	+	0.636748i
$862$	−22790.9	+	24759.8i	−0.900534	+	0.978332i
$863$	−39367.0			−1.55280			−0.776400	−	0.630240i	$-0.782957\pi$
$863$	−39367.0			−1.55280			−0.776400	+	0.630240i	$0.782957\pi$
$864$	6311.00	−	24599.7i	0.248501	−	0.968632i
$865$	9097.29			0.357592
$866$	2240.00	−	2433.52i	0.0878965	−	0.0954900i
$867$	−2851.90	+	6482.02i	−0.111713	+	0.253911i
$868$	607.662	+	7325.09i	0.0237620	+	0.286440i
$869$			21316.2i			0.832110i
$870$	−6476.04	−	14806.9i	−0.252366	−	0.577011i
$871$		−	13038.4i		−	0.507222i
$872$	−38901.3	−	30269.3i	−1.51074	−	1.17552i
$873$	−18967.1	−	20696.2i	−0.735327	−	0.802361i
$874$	10468.4	+	9635.98i	0.405149	+	0.372931i
$875$	−4033.62			−0.155841
$876$	11514.5	+	3966.07i	0.444106	+	0.152969i
$877$	−32232.4			−1.24106			−0.620530	−	0.784183i	$-0.713082\pi$
$877$	−32232.4			−1.24106			−0.620530	+	0.784183i	$0.713082\pi$
$878$	14123.1	+	13000.0i	0.542862	+	0.499693i
$879$	44206.0	+	19449.4i	1.69628	+	0.746315i
$880$	1712.38	+	10249.9i	0.0655958	+	0.392643i
$881$		−	35922.0i		−	1.37372i	−0.726791	−	0.686858i	$-0.758989\pi$
$881$		−	35922.0i		−	1.37372i	0.726791	−	0.686858i	$-0.241011\pi$
$882$	53326.2	+	116.420i	2.03581	+	0.00444451i
$883$		−	33930.5i		−	1.29315i	−0.762851	−	0.646575i	$-0.776201\pi$
$883$		−	33930.5i		−	1.29315i	0.762851	−	0.646575i	$-0.223799\pi$
$884$	−28374.8	+	2353.87i	−1.07958	+	0.0895578i
$885$	10250.8	+	4510.04i	0.389352	+	0.171303i
$886$	17400.5	−	18903.8i	0.659800	−	0.716801i
$887$	6145.77			0.232643			0.116322	−	0.993212i	$-0.462890\pi$
$887$	6145.77			0.232643			0.116322	+	0.993212i	$0.462890\pi$
$888$	15811.3	−	8536.70i	0.597512	−	0.322605i
$889$	45059.4			1.69994
$890$	3221.40	−	3499.70i	0.121328	−	0.131809i
$891$	−2060.20	+	23584.5i	−0.0774628	+	0.886767i
$892$	9784.08	−	811.651i	0.367259	−	0.0304665i
$893$		−	7171.04i		−	0.268723i
$894$	1467.97	−	642.043i	0.0549176	−	0.0240192i
$895$			3989.01i			0.148981i
$896$	−22227.8	+	41105.4i	−0.828771	+	1.53263i
$897$	6850.58	−	15570.5i	0.254999	−	0.579582i
$898$	−6690.44	−	6158.41i	−0.248622	−	0.228852i
$899$	−6261.85			−0.232307
$900$	3665.80	−	3965.09i	0.135770	−	0.146855i
$901$	−43127.4			−1.59465
$902$	7083.66	+	6520.36i	0.261486	+	0.240692i
$903$	−6523.30	+	14826.7i	−0.240401	+	0.546402i
$904$	−23842.7	+	30642.0i	−0.877209	+	1.12736i
$905$		−	9466.13i		−	0.347696i
$906$	−42905.8	+	18765.6i	−1.57334	+	0.688130i
$907$		−	16054.2i		−	0.587731i	−0.955847	−	0.293866i	$-0.905058\pi$
$907$		−	16054.2i		−	0.587731i	0.955847	−	0.293866i	$-0.0949418\pi$
$908$	−3971.22	−	47871.3i	−0.145143	−	1.74963i
$909$	−6137.24	+	5624.50i	−0.223938	+	0.205229i
$910$	13884.9	−	15084.4i	0.505801	−	0.549498i
$911$	−5066.28			−0.184252			−0.0921259	−	0.995747i	$-0.529366\pi$
$911$	−5066.28			−0.184252			−0.0921259	+	0.995747i	$0.529366\pi$
$912$	−22249.2	−	5656.25i	−0.807835	−	0.205370i
$913$	12741.2			0.461853
$914$	23636.6	−	25678.6i	0.855393	−	0.929291i
$915$	−4360.82	−	1918.63i	−0.157556	−	0.0693202i
$916$	2255.71	+	27191.5i	0.0813654	+	0.980823i
$917$		−	48743.5i		−	1.75535i
$918$	28746.5	+	12722.6i	1.03352	+	0.457416i
$919$			3167.51i			0.113696i	0.998383	+	0.0568480i	$0.0181050\pi$
$919$			3167.51i			0.113696i	−0.998383	+	0.0568480i	$0.981895\pi$
$920$	−5062.88	+	6506.66i	−0.181433	+	0.233172i
$921$	−9431.36	−	4149.52i	−0.337431	−	0.148460i
$922$	25052.8	+	23060.6i	0.894871	+	0.823709i
$923$	−21974.4			−0.783637
$924$	14186.6	−	41187.0i	0.505091	−	1.46640i
$925$	3820.65			0.135808
$926$	5165.06	+	4754.33i	0.183299	+	0.168722i
$927$	−5261.99	+	4822.37i	−0.186436	+	0.170860i
$928$	−33333.3	−	21766.6i	−1.17911	−	0.769961i
$929$			11889.1i			0.419880i	0.977714	+	0.209940i	$0.0673269\pi$
$929$			11889.1i			0.419880i	−0.977714	+	0.209940i	$0.932673\pi$
$930$	−838.421	−	1916.97i	−0.0295623	−	0.0675914i
$931$		−	48204.2i		−	1.69692i
$932$	−50381.6	+	4179.47i	−1.77071	+	0.146892i
$933$	−682.490	+	1551.22i	−0.0239482	+	0.0544315i
$934$	3058.49	−	3322.72i	0.107149	−	0.116405i
$935$	−12863.4			−0.449923
$936$	2209.38	+	27357.9i	0.0771536	+	0.955363i
$937$	−34124.2			−1.18974			−0.594871	−	0.803822i	$-0.702797\pi$
$937$	−34124.2			−1.18974			−0.594871	+	0.803822i	$0.702797\pi$
$938$	17939.4	−	19489.2i	0.624458	−	0.678405i
$939$	2217.92	−	5041.06i	0.0770810	−	0.175196i
$940$	4140.96	−	343.518i	0.143684	−	0.0119195i
$941$		−	35775.5i		−	1.23937i	−0.784851	−	0.619685i	$-0.787260\pi$
$941$		−	35775.5i		−	1.23937i	0.784851	−	0.619685i	$-0.212740\pi$
$942$	6062.28	+	13860.8i	0.209681	+	0.479417i
$943$			7638.03i			0.263763i
$944$	27210.2	−	4545.80i	0.938154	−	0.156730i
$945$	−21434.0	+	7278.26i	−0.737830	+	0.250542i
$946$	6528.74	+	6009.56i	0.224384	+	0.206541i
$947$	1532.43			0.0525841			0.0262921	−	0.999654i	$-0.491630\pi$
$947$	1532.43			0.0525841			0.0262921	+	0.999654i	$0.491630\pi$
$948$	8885.98	−	25798.1i	0.304434	−	0.883844i
$949$	−13161.7			−0.450207
$950$	−3591.46	−	3305.86i	−0.122655	−	0.112901i
$951$	−4794.18	−	2109.30i	−0.163472	−	0.0719230i
$952$	−45651.8	−	35522.0i	−1.55419	−	1.20932i
$953$			50714.5i			1.72382i	0.507060	+	0.861911i	$0.330732\pi$
$953$			50714.5i			1.72382i	−0.507060	+	0.861911i	$0.669268\pi$
$954$	−90.7633	+	41574.2i	−0.00308026	+	1.41092i
$955$		−	10845.9i		−	0.367502i
$956$	−2357.02	−	28412.8i	−0.0797401	−	0.961231i
$957$	33968.9	+	14945.3i	1.14740	+	0.504821i
$958$	−26192.9	+	28455.7i	−0.883355	+	0.959669i
$959$	17483.0			0.588690
$960$	2200.42	−	13118.9i	0.0739773	−	0.441053i
$961$	28980.3			0.972787
$962$	−13151.8	+	14288.0i	−0.440780	+	0.478860i
$963$	28490.1	+	31087.4i	0.953356	+	1.04027i
$964$	1874.22	+	22592.9i	0.0626189	+	0.754842i
$965$		−	21648.5i		−	0.722165i
$966$	31663.2	−	13848.4i	1.05460	−	0.461249i
$967$		−	45357.2i		−	1.50837i	−0.656664	−	0.754183i	$-0.728033\pi$
$967$		−	45357.2i		−	1.50837i	0.656664	−	0.754183i	$-0.271967\pi$
$968$	4935.54	+	3840.37i	0.163878	+	0.127515i
$969$	11443.8	−	26010.3i	0.379388	−	0.862304i
$970$	−10818.6	−	9958.30i	−0.358108	−	0.329631i
$971$	33985.9			1.12323			0.561616	−	0.827398i	$-0.310180\pi$
$971$	33985.9			1.12323			0.561616	+	0.827398i	$0.310180\pi$
$972$	12324.9	−	27684.4i	0.406709	−	0.913558i
$973$	−23033.6			−0.758913
$974$	5644.82	+	5195.93i	0.185700	+	0.170933i
$975$	−2350.26	+	5341.86i	−0.0771985	+	0.175463i
$976$	−11575.6	+	1933.84i	−0.379637	+	0.0634230i
$977$			24747.5i			0.810382i	0.914232	+	0.405191i	$0.132795\pi$
$977$			24747.5i			0.810382i	−0.914232	+	0.405191i	$0.867205\pi$
$978$	−3023.71	+	1322.47i	−0.0988626	+	0.0432393i
$979$			10922.7i			0.356581i
$980$	27835.8	−	2309.15i	0.907329	−	0.0752686i
$981$	−39738.0	−	43360.6i	−1.29331	−	1.41121i
$982$	−14935.9	+	16226.2i	−0.485359	+	0.527290i
$983$	37535.3			1.21789			0.608947	−	0.793211i	$-0.291592\pi$
$983$	37535.3			1.21789			0.608947	+	0.793211i	$0.291592\pi$
$984$	−5854.94	−	10844.2i	−0.189684	−	0.351323i
$985$	−10552.4			−0.341346
$986$	33373.7	−	36256.9i	1.07792	−	1.17105i
$987$	−15943.1	−	7014.49i	−0.514158	−	0.226214i
$988$	24725.7	−	2051.15i	0.796182	−	0.0660483i
$989$			7039.68i			0.226339i
$990$	−27.0716	+	12400.1i	−0.000869081	+	0.398083i
$991$			41257.7i			1.32250i	0.750167	+	0.661248i	$0.229973\pi$
$991$			41257.7i			1.32250i	−0.750167	+	0.661248i	$0.770027\pi$
$992$	−4315.49	−	2818.02i	−0.138122	−	0.0901937i
$993$	15617.7	+	6871.33i	0.499107	+	0.219592i
$994$	−32846.2	−	30234.3i	−1.04811	−	0.964761i
$995$	7325.48			0.233400
$996$	−15420.1	−	5311.35i	−0.490567	−	0.168972i
$997$	27189.9			0.863704			0.431852	−	0.901945i	$-0.357860\pi$
$997$	27189.9			0.863704			0.431852	+	0.901945i	$0.357860\pi$
$998$	−21726.6	−	19998.9i	−0.689121	−	0.634321i
$999$	20302.4	−	6893.99i	0.642981	−	0.218334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.4.e.a.11.17	yes	24
3.2	odd	2	inner	60.4.e.a.11.8	yes	24
4.3	odd	2	inner	60.4.e.a.11.7	✓	24
8.3	odd	2		960.4.h.d.191.17		24
8.5	even	2		960.4.h.d.191.8		24
12.11	even	2	inner	60.4.e.a.11.18	yes	24
24.5	odd	2		960.4.h.d.191.18		24
24.11	even	2		960.4.h.d.191.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.4.e.a.11.7	✓	24	4.3	odd	2	inner
60.4.e.a.11.8	yes	24	3.2	odd	2	inner
60.4.e.a.11.17	yes	24	1.1	even	1	trivial
60.4.e.a.11.18	yes	24	12.11	even	2	inner
960.4.h.d.191.7		24	24.11	even	2
960.4.h.d.191.8		24	8.5	even	2
960.4.h.d.191.17		24	8.3	odd	2
960.4.h.d.191.18		24	24.5	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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	60.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.91554 - 2.08103i) q^{2} +(2.09257 - 4.75617i) q^{3} +(-0.661378 - 7.97261i) q^{4} -5.00000i q^{5} +(-5.88931 - 13.4654i) q^{6} +32.2690i q^{7} +(-17.8582 - 13.8955i) q^{8} +(-18.2423 - 19.9053i) q^{9} +O(q^{10})\)	\(q+(1.91554 - 2.08103i) q^{2} +(2.09257 - 4.75617i) q^{3} +(-0.661378 - 7.97261i) q^{4} -5.00000i q^{5} +(-5.88931 - 13.4654i) q^{6} +32.2690i q^{7} +(-17.8582 - 13.8955i) q^{8} +(-18.2423 - 19.9053i) q^{9} +(-10.4052 - 9.57772i) q^{10} +32.4750 q^{11} +(-39.3031 - 13.5377i) q^{12} +44.9257 q^{13} +(67.1527 + 61.8126i) q^{14} +(-23.7808 - 10.4629i) q^{15} +(-63.1252 + 10.5458i) q^{16} -79.2204i q^{17} +(-76.3674 - 0.166722i) q^{18} +69.0323i q^{19} +(-39.8631 + 3.30689i) q^{20} +(153.477 + 67.5252i) q^{21} +(62.2073 - 67.5815i) q^{22} +72.8705 q^{23} +(-103.459 + 55.8589i) q^{24} -25.0000 q^{25} +(86.0572 - 93.4918i) q^{26} +(-132.846 + 45.1100i) q^{27} +(257.268 - 21.3420i) q^{28} +219.925i q^{29} +(-67.3268 + 29.4466i) q^{30} +28.4726i q^{31} +(-98.9729 + 151.566i) q^{32} +(67.9564 - 154.457i) q^{33} +(-164.860 - 151.750i) q^{34} +161.345 q^{35} +(-146.632 + 158.603i) q^{36} -152.826 q^{37} +(143.658 + 132.234i) q^{38} +(94.0104 - 213.674i) q^{39} +(-69.4777 + 89.2908i) q^{40} +104.817i q^{41} +(434.513 - 190.042i) q^{42} +96.6054i q^{43} +(-21.4783 - 258.911i) q^{44} +(-99.5264 + 91.2113i) q^{45} +(139.587 - 151.646i) q^{46} -103.880 q^{47} +(-81.9364 + 322.302i) q^{48} -698.285 q^{49} +(-47.8886 + 52.0258i) q^{50} +(-376.785 - 165.775i) q^{51} +(-29.7129 - 358.175i) q^{52} -544.398i q^{53} +(-160.597 + 362.867i) q^{54} -162.375i q^{55} +(448.395 - 576.264i) q^{56} +(328.329 + 144.455i) q^{57} +(457.671 + 421.276i) q^{58} -431.052 q^{59} +(-67.6883 + 196.515i) q^{60} +183.375 q^{61} +(59.2524 + 54.5406i) q^{62} +(642.322 - 588.659i) q^{63} +(125.827 + 496.298i) q^{64} -224.629i q^{65} +(-191.255 - 437.288i) q^{66} -290.222i q^{67} +(-631.593 + 52.3946i) q^{68} +(152.487 - 346.584i) q^{69} +(309.063 - 335.763i) q^{70} -489.128 q^{71} +(49.1785 + 608.958i) q^{72} -292.966 q^{73} +(-292.745 + 318.036i) q^{74} +(-52.3144 + 118.904i) q^{75} +(550.368 - 45.6564i) q^{76} +1047.93i q^{77} +(-264.582 - 604.941i) q^{78} +656.389i q^{79} +(52.7291 + 315.626i) q^{80} +(-63.4397 + 726.234i) q^{81} +(218.127 + 200.781i) q^{82} +392.339 q^{83} +(436.846 - 1268.27i) q^{84} -396.102 q^{85} +(201.039 + 185.052i) q^{86} +(1046.00 + 460.210i) q^{87} +(-579.944 - 451.258i) q^{88} +336.343i q^{89} +(-0.833612 + 381.837i) q^{90} +1449.71i q^{91} +(-48.1949 - 580.968i) q^{92} +(135.421 + 59.5811i) q^{93} +(-198.986 + 216.177i) q^{94} +345.161 q^{95} +(513.767 + 787.896i) q^{96} +1039.74 q^{97} +(-1337.60 + 1453.15i) q^{98} +(-592.417 - 646.424i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{4} + 30 q^{6} + 20 q^{9}+O(q^{10}) \) 24 * q + 6 * q^4 + 30 * q^6 + 20 * q^9	\( 24 q + 6 q^{4} + 30 q^{6} + 20 q^{9} - 30 q^{10} - 188 q^{12} + 72 q^{13} + 306 q^{16} + 256 q^{18} - 68 q^{21} - 300 q^{22} - 434 q^{24} - 600 q^{25} + 300 q^{28} - 40 q^{30} + 848 q^{33} - 468 q^{34} - 294 q^{36} + 504 q^{37} - 210 q^{40} - 228 q^{42} - 220 q^{45} + 684 q^{46} + 1212 q^{48} - 2256 q^{49} + 576 q^{52} - 1054 q^{54} + 1416 q^{57} + 3108 q^{58} + 490 q^{60} + 1992 q^{61} - 1842 q^{64} - 472 q^{66} - 1548 q^{69} + 540 q^{70} + 312 q^{72} - 2304 q^{73} - 420 q^{76} - 2792 q^{78} + 3840 q^{81} + 600 q^{82} - 176 q^{84} + 240 q^{85} - 372 q^{88} - 1170 q^{90} - 4384 q^{93} + 1044 q^{94} - 3846 q^{96} - 2448 q^{97}+O(q^{100}) \) 24 * q + 6 * q^4 + 30 * q^6 + 20 * q^9 - 30 * q^10 - 188 * q^12 + 72 * q^13 + 306 * q^16 + 256 * q^18 - 68 * q^21 - 300 * q^22 - 434 * q^24 - 600 * q^25 + 300 * q^28 - 40 * q^30 + 848 * q^33 - 468 * q^34 - 294 * q^36 + 504 * q^37 - 210 * q^40 - 228 * q^42 - 220 * q^45 + 684 * q^46 + 1212 * q^48 - 2256 * q^49 + 576 * q^52 - 1054 * q^54 + 1416 * q^57 + 3108 * q^58 + 490 * q^60 + 1992 * q^61 - 1842 * q^64 - 472 * q^66 - 1548 * q^69 + 540 * q^70 + 312 * q^72 - 2304 * q^73 - 420 * q^76 - 2792 * q^78 + 3840 * q^81 + 600 * q^82 - 176 * q^84 + 240 * q^85 - 372 * q^88 - 1170 * q^90 - 4384 * q^93 + 1044 * q^94 - 3846 * q^96 - 2448 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more