LMFDB - Embedded newform 60.5.f.a.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,5,Mod(19,60)]

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, 0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("60.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	60.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:	$6.20219778503$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	60.19
Dual form			60.5.f.a.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.76887 - 1.34002i) q^{2} +5.19615 q^{3} +(12.4087 + 10.1007i) q^{4} +(11.9809 + 21.9421i) q^{5} +(-19.5836 - 6.96293i) q^{6} -63.7886 q^{7} +(-33.2317 - 54.6960i) q^{8} +27.0000 q^{9} +O(q^{10})$	\(q+(-3.76887 - 1.34002i) q^{2} +5.19615 q^{3} +(12.4087 + 10.1007i) q^{4} +(11.9809 + 21.9421i) q^{5} +(-19.5836 - 6.96293i) q^{6} -63.7886 q^{7} +(-33.2317 - 54.6960i) q^{8} +27.0000 q^{9} +(-15.7516 - 98.7516i) q^{10} +181.649i q^{11} +(64.4776 + 52.4847i) q^{12} +1.57359i q^{13} +(240.411 + 85.4778i) q^{14} +(62.2546 + 114.015i) q^{15} +(51.9524 + 250.673i) q^{16} +483.767i q^{17} +(-101.759 - 36.1804i) q^{18} -192.267i q^{19} +(-72.9630 + 393.289i) q^{20} -331.455 q^{21} +(243.413 - 684.611i) q^{22} +558.181 q^{23} +(-172.677 - 284.209i) q^{24} +(-337.916 + 525.774i) q^{25} +(2.10864 - 5.93066i) q^{26} +140.296 q^{27} +(-791.535 - 644.309i) q^{28} +51.9021 q^{29} +(-81.8478 - 513.129i) q^{30} +310.363i q^{31} +(140.104 - 1014.37i) q^{32} +943.876i q^{33} +(648.256 - 1823.25i) q^{34} +(-764.246 - 1399.66i) q^{35} +(335.035 + 272.718i) q^{36} -1463.27i q^{37} +(-257.641 + 724.628i) q^{38} +8.17663i q^{39} +(802.002 - 1384.48i) q^{40} -2629.66 q^{41} +(1249.21 + 444.156i) q^{42} -203.783 q^{43} +(-1834.78 + 2254.03i) q^{44} +(323.485 + 592.438i) q^{45} +(-2103.71 - 747.972i) q^{46} +3737.83 q^{47} +(269.953 + 1302.54i) q^{48} +1667.99 q^{49} +(1978.10 - 1528.76i) q^{50} +2513.73i q^{51} +(-15.8944 + 19.5263i) q^{52} +684.434i q^{53} +(-528.757 - 187.999i) q^{54} +(-3985.77 + 2176.32i) q^{55} +(2119.81 + 3488.98i) q^{56} -999.048i q^{57} +(-195.612 - 69.5497i) q^{58} -2367.17i q^{59} +(-379.127 + 2043.59i) q^{60} +5340.25 q^{61} +(415.892 - 1169.72i) q^{62} -1722.29 q^{63} +(-1887.31 + 3635.28i) q^{64} +(-34.5280 + 18.8531i) q^{65} +(1264.81 - 3557.34i) q^{66} -561.609 q^{67} +(-4886.38 + 6002.93i) q^{68} +2900.39 q^{69} +(1004.77 + 6299.23i) q^{70} -5996.88i q^{71} +(-897.256 - 1476.79i) q^{72} -6569.92i q^{73} +(-1960.81 + 5514.89i) q^{74} +(-1755.86 + 2732.00i) q^{75} +(1942.03 - 2385.79i) q^{76} -11587.1i q^{77} +(10.9568 - 30.8166i) q^{78} +1372.17i q^{79} +(-4877.87 + 4143.24i) q^{80} +729.000 q^{81} +(9910.82 + 3523.78i) q^{82} -3158.48 q^{83} +(-4112.94 - 3347.93i) q^{84} +(-10614.9 + 5795.97i) q^{85} +(768.030 + 273.072i) q^{86} +269.691 q^{87} +(9935.47 - 6036.51i) q^{88} +10777.4 q^{89} +(-425.294 - 2666.29i) q^{90} -100.377i q^{91} +(6926.31 + 5638.01i) q^{92} +1612.69i q^{93} +(-14087.4 - 5008.75i) q^{94} +(4218.75 - 2303.53i) q^{95} +(728.002 - 5270.82i) q^{96} +9156.50i q^{97} +(-6286.43 - 2235.13i) q^{98} +4904.52i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 14 q^{4} - 24 q^{5} - 18 q^{6} + 648 q^{9}+O(q^{10}) $ 24 * q + 14 * q^4 - 24 * q^5 - 18 * q^6 + 648 * q^9	$ 24 q + 14 q^{4} - 24 q^{5} - 18 q^{6} + 648 q^{9} + 274 q^{10} - 36 q^{14} + 594 q^{16} - 12 q^{20} - 594 q^{24} + 1208 q^{25} - 2868 q^{26} - 1680 q^{29} + 468 q^{30} + 3076 q^{34} + 378 q^{36} - 7222 q^{40} - 4848 q^{41} - 3828 q^{44} - 648 q^{45} - 15280 q^{46} + 5416 q^{49} + 14472 q^{50} - 486 q^{54} + 32172 q^{56} - 7506 q^{60} + 2896 q^{61} - 18298 q^{64} - 2688 q^{65} - 15588 q^{66} + 9792 q^{69} + 27608 q^{70} + 31836 q^{74} + 50136 q^{76} - 27348 q^{80} + 17496 q^{81} - 4284 q^{84} - 15680 q^{85} - 58152 q^{86} - 38544 q^{89} + 7398 q^{90} + 4808 q^{94} + 21978 q^{96}+O(q^{100}) $ 24 * q + 14 * q^4 - 24 * q^5 - 18 * q^6 + 648 * q^9 + 274 * q^10 - 36 * q^14 + 594 * q^16 - 12 * q^20 - 594 * q^24 + 1208 * q^25 - 2868 * q^26 - 1680 * q^29 + 468 * q^30 + 3076 * q^34 + 378 * q^36 - 7222 * q^40 - 4848 * q^41 - 3828 * q^44 - 648 * q^45 - 15280 * q^46 + 5416 * q^49 + 14472 * q^50 - 486 * q^54 + 32172 * q^56 - 7506 * q^60 + 2896 * q^61 - 18298 * q^64 - 2688 * q^65 - 15588 * q^66 + 9792 * q^69 + 27608 * q^70 + 31836 * q^74 + 50136 * q^76 - 27348 * q^80 + 17496 * q^81 - 4284 * q^84 - 15680 * q^85 - 58152 * q^86 - 38544 * q^89 + 7398 * q^90 + 4808 * q^94 + 21978 * q^96

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 $

$2$	−3.76887	−	1.34002i	−0.942217	−	0.335004i
$2$	−3.76887	−	1.34002i	−0.942217	−	0.335004i
$3$	5.19615			0.577350
$3$	5.19615			0.577350
$4$	12.4087	+	10.1007i	0.775545	+	0.631293i
$5$	11.9809	+	21.9421i	0.479236	+	0.877686i
$5$	11.9809	+	21.9421i	0.479236	+	0.877686i
$6$	−19.5836	−	6.96293i	−0.543989	−	0.193415i
$7$	−63.7886			−1.30181			−0.650904	−	0.759160i	$-0.725610\pi$
$7$	−63.7886			−1.30181			−0.650904	+	0.759160i	$0.725610\pi$
$8$	−33.2317	−	54.6960i	−0.519246	−	0.854625i
$9$	27.0000			0.333333
$10$	−15.7516	−	98.7516i	−0.157516	−	0.987516i
$11$			181.649i			1.50123i	0.660739	+	0.750616i	$0.270243\pi$
$11$			181.649i			1.50123i	−0.660739	+	0.750616i	$0.729757\pi$
$12$	64.4776	+	52.4847i	0.447761	+	0.364477i
$13$			1.57359i			0.00931120i	0.999989	+	0.00465560i	$0.00148193\pi$
$13$			1.57359i			0.00931120i	−0.999989	+	0.00465560i	$0.998518\pi$
$14$	240.411	+	85.4778i	1.22659	+	0.436111i
$15$	62.2546	+	114.015i	0.276687	+	0.506732i
$16$	51.9524	+	250.673i	0.202939	+	0.979191i
$17$			483.767i			1.67393i	0.547253	+	0.836967i	$0.315674\pi$
$17$			483.767i			1.67393i	−0.547253	+	0.836967i	$0.684326\pi$
$18$	−101.759	−	36.1804i	−0.314072	−	0.111668i
$19$		−	192.267i		−	0.532595i	−0.963891	−	0.266298i	$-0.914200\pi$
$19$		−	192.267i		−	0.532595i	0.963891	−	0.266298i	$-0.0858004\pi$
$20$	−72.9630	+	393.289i	−0.182407	+	0.983223i
$21$	−331.455			−0.751600
$22$	243.413	−	684.611i	0.502918	−	1.41449i
$23$	558.181			1.05516			0.527581	−	0.849504i	$-0.323099\pi$
$23$	558.181			1.05516			0.527581	+	0.849504i	$0.323099\pi$
$24$	−172.677	−	284.209i	−0.299787	−	0.493418i
$25$	−337.916	+	525.774i	−0.540665	+	0.841238i
$26$	2.10864	−	5.93066i	0.00311929	−	0.00877317i
$27$	140.296			0.192450
$28$	−791.535	−	644.309i	−1.00961	−	0.821822i
$29$	51.9021			0.0617148			0.0308574	−	0.999524i	$-0.490176\pi$
$29$	51.9021			0.0617148			0.0308574	+	0.999524i	$0.490176\pi$
$30$	−81.8478	−	513.129i	−0.0909420	−	0.570143i
$31$			310.363i			0.322959i	0.986876	+	0.161479i	$0.0516265\pi$
$31$			310.363i			0.322959i	−0.986876	+	0.161479i	$0.948374\pi$
$32$	140.104	−	1014.37i	0.136820	−	0.990596i
$33$			943.876i			0.866736i
$34$	648.256	−	1823.25i	0.560775	−	1.57721i
$35$	−764.246	−	1399.66i	−0.623874	−	1.14258i
$36$	335.035	+	272.718i	0.258515	+	0.210431i
$37$		−	1463.27i		−	1.06886i	−0.845212	−	0.534432i	$-0.820526\pi$
$37$		−	1463.27i		−	1.06886i	0.845212	−	0.534432i	$-0.179474\pi$
$38$	−257.641	+	724.628i	−0.178422	+	0.501820i
$39$			8.17663i			0.00537583i
$40$	802.002	−	1384.48i	0.501251	−	0.865302i
$41$	−2629.66			−1.56434			−0.782170	−	0.623065i	$-0.785887\pi$
$41$	−2629.66			−1.56434			−0.782170	+	0.623065i	$0.785887\pi$
$42$	1249.21	+	444.156i	0.708170	+	0.251789i
$43$	−203.783			−0.110212			−0.0551062	−	0.998480i	$-0.517550\pi$
$43$	−203.783			−0.110212			−0.0551062	+	0.998480i	$0.517550\pi$
$44$	−1834.78	+	2254.03i	−0.947716	+	1.16427i
$45$	323.485	+	592.438i	0.159745	+	0.292562i
$46$	−2103.71	−	747.972i	−0.994192	−	0.353484i
$47$	3737.83			1.69209			0.846046	−	0.533110i	$-0.178977\pi$
$47$	3737.83			1.69209			0.846046	+	0.533110i	$0.178977\pi$
$48$	269.953	+	1302.54i	0.117167	+	0.565336i
$49$	1667.99			0.694706
$50$	1978.10	−	1528.76i	0.791242	−	0.611504i
$51$			2513.73i			0.966447i
$52$	−15.8944	+	19.5263i	−0.00587810	+	0.00722126i
$53$			684.434i			0.243658i	0.992551	+	0.121829i	$0.0388759\pi$
$53$			684.434i			0.243658i	−0.992551	+	0.121829i	$0.961124\pi$
$54$	−528.757	−	187.999i	−0.181330	−	0.0644715i
$55$	−3985.77	+	2176.32i	−1.31761	+	0.719445i
$56$	2119.81	+	3488.98i	0.675959	+	1.11256i
$57$		−	999.048i		−	0.307494i
$58$	−195.612	−	69.5497i	−0.0581487	−	0.0206747i
$59$		−	2367.17i		−	0.680025i	−0.940421	−	0.340012i	$-0.889569\pi$
$59$		−	2367.17i		−	0.680025i	0.940421	−	0.340012i	$-0.110431\pi$
$60$	−379.127	+	2043.59i	−0.105313	+	0.567664i
$61$	5340.25			1.43516			0.717582	−	0.696474i	$-0.245249\pi$
$61$	5340.25			1.43516			0.717582	+	0.696474i	$0.245249\pi$
$62$	415.892	−	1169.72i	0.108192	−	0.304297i
$63$	−1722.29			−0.433936
$64$	−1887.31	+	3635.28i	−0.460768	+	0.887521i
$65$	−34.5280	+	18.8531i	−0.00817231	+	0.00446227i
$66$	1264.81	−	3557.34i	0.290360	−	0.816653i
$67$	−561.609			−0.125108			−0.0625539	−	0.998042i	$-0.519925\pi$
$67$	−561.609			−0.125108			−0.0625539	+	0.998042i	$0.519925\pi$
$68$	−4886.38	+	6002.93i	−1.05674	+	1.29821i
$69$	2900.39			0.609199
$70$	1004.77	+	6299.23i	0.205056	+	1.28556i
$71$		−	5996.88i		−	1.18962i	−0.803866	−	0.594811i	$-0.797227\pi$
$71$		−	5996.88i		−	1.18962i	0.803866	−	0.594811i	$-0.202773\pi$
$72$	−897.256	−	1476.79i	−0.173082	−	0.284875i
$73$		−	6569.92i		−	1.23286i	−0.787409	−	0.616431i	$-0.788578\pi$
$73$		−	6569.92i		−	1.23286i	0.787409	−	0.616431i	$-0.211422\pi$
$74$	−1960.81	+	5514.89i	−0.358074	+	1.00710i
$75$	−1755.86	+	2732.00i	−0.312153	+	0.485689i
$76$	1942.03	−	2385.79i	0.336224	−	0.413052i
$77$		−	11587.1i		−	1.95432i
$78$	10.9568	−	30.8166i	0.00180092	−	0.00506519i
$79$			1372.17i			0.219865i	0.993939	+	0.109932i	$0.0350634\pi$
$79$			1372.17i			0.219865i	−0.993939	+	0.109932i	$0.964937\pi$
$80$	−4877.87	+	4143.24i	−0.762167	+	0.647381i
$81$	729.000			0.111111
$82$	9910.82	+	3523.78i	1.47395	+	0.524060i
$83$	−3158.48			−0.458481			−0.229241	−	0.973370i	$-0.573624\pi$
$83$	−3158.48			−0.458481			−0.229241	+	0.973370i	$0.573624\pi$
$84$	−4112.94	−	3347.93i	−0.582899	−	0.474479i
$85$	−10614.9	+	5795.97i	−1.46919	+	0.802210i
$86$	768.030	+	273.072i	0.103844	+	0.0369216i
$87$	269.691			0.0356310
$88$	9935.47	−	6036.51i	1.28299	−	0.779508i
$89$	10777.4			1.36061			0.680304	−	0.732930i	$-0.261848\pi$
$89$	10777.4			1.36061			0.680304	+	0.732930i	$0.261848\pi$
$90$	−425.294	−	2666.29i	−0.0525054	−	0.329172i
$91$		−	100.377i		−	0.0121214i
$92$	6926.31	+	5638.01i	0.818326	+	0.666117i
$93$			1612.69i			0.186460i
$94$	−14087.4	−	5008.75i	−1.59432	−	0.566857i
$95$	4218.75	−	2303.53i	0.467451	−	0.255239i
$96$	728.002	−	5270.82i	0.0789933	−	0.571921i
$97$			9156.50i			0.973164i	0.873635	+	0.486582i	$0.161756\pi$
$97$			9156.50i			0.973164i	−0.873635	+	0.486582i	$0.838244\pi$
$98$	−6286.43	−	2235.13i	−0.654564	−	0.232729i
$99$			4904.52i			0.500410i
$100$	−9503.77	+	3111.00i	−0.950377	+	0.311100i
$101$	−10441.4			−1.02357			−0.511785	−	0.859114i	$-0.671016\pi$
$101$	−10441.4			−1.02357			−0.511785	+	0.859114i	$0.671016\pi$
$102$	3368.44	−	9473.91i	0.323763	−	0.910602i
$103$	5985.53			0.564194			0.282097	−	0.959386i	$-0.408970\pi$
$103$	5985.53			0.564194			0.282097	+	0.959386i	$0.408970\pi$
$104$	86.0693	−	52.2932i	0.00795759	−	0.00483480i
$105$	−3971.14	−	7272.84i	−0.360194	−	0.659668i
$106$	917.153	−	2579.54i	0.0816263	−	0.229578i
$107$	5338.95			0.466325			0.233162	−	0.972438i	$-0.425093\pi$
$107$	5338.95			0.466325			0.233162	+	0.972438i	$0.425093\pi$
$108$	1740.89	+	1417.09i	0.149254	+	0.121492i
$109$	12264.9			1.03231			0.516155	−	0.856495i	$-0.327363\pi$
$109$	12264.9			1.03231			0.516155	+	0.856495i	$0.327363\pi$
$110$	17938.1	−	2861.27i	1.48249	−	0.236468i
$111$		−	7603.40i		−	0.617109i
$112$	−3313.97	−	15990.1i	−0.264188	−	1.27472i
$113$			10701.5i			0.838085i	0.907967	+	0.419043i	$0.137634\pi$
$113$			10701.5i			0.838085i	−0.907967	+	0.419043i	$0.862366\pi$
$114$	−1338.74	+	3765.28i	−0.103012	+	0.289726i
$115$	6687.52	+	12247.7i	0.505672	+	0.926102i
$116$	644.039	+	524.247i	0.0478626	+	0.0389601i
$117$			42.4870i			0.00310373i
$118$	−3172.04	+	8921.54i	−0.227811	+	0.640731i
$119$		−	30858.8i		−	2.17914i
$120$	4167.32	−	7193.99i	0.289397	−	0.499582i
$121$	−18355.4			−1.25370
$122$	−20126.7	−	7156.01i	−1.35224	−	0.480786i
$123$	−13664.1			−0.903172
$124$	−3134.88	+	3851.21i	−0.203881	+	0.250469i
$125$	−15585.1	−	1115.35i	−0.997449	−	0.0713823i
$126$	6491.09	+	2307.90i	0.408862	+	0.145370i
$127$	−1449.56			−0.0898732			−0.0449366	−	0.998990i	$-0.514309\pi$
$127$	−1449.56			−0.0898732			−0.0449366	+	0.998990i	$0.514309\pi$
$128$	11984.3	−	11171.9i	0.731466	−	0.681878i
$129$	−1058.89			−0.0636312
$130$	155.395	−	24.7867i	0.00919497	−	0.00146667i
$131$			28167.7i			1.64138i	0.571374	+	0.820690i	$0.306411\pi$
$131$			28167.7i			1.64138i	−0.571374	+	0.820690i	$0.693589\pi$
$132$	−9533.79	+	11712.3i	−0.547164	+	0.672193i
$133$			12264.4i			0.693337i
$134$	2116.63	+	752.565i	0.117879	+	0.0419116i
$135$	1680.87	+	3078.40i	0.0922291	+	0.168911i
$136$	26460.1	−	16076.4i	1.43059	−	0.869183i
$137$			13639.8i			0.726720i	0.931649	+	0.363360i	$0.118371\pi$
$137$			13639.8i			0.726720i	−0.931649	+	0.363360i	$0.881629\pi$
$138$	−10931.2	−	3886.57i	−0.573997	−	0.204084i
$139$			6434.49i			0.333031i	0.986039	+	0.166515i	$0.0532516\pi$
$139$			6434.49i			0.333031i	−0.986039	+	0.166515i	$0.946748\pi$
$140$	4654.21	−	25087.4i	0.237460	−	1.27997i
$141$	19422.3			0.976930
$142$	−8035.92	+	22601.4i	−0.398528	+	1.12088i
$143$	−285.842			−0.0139783
$144$	1402.72	+	6768.17i	0.0676464	+	0.326397i
$145$	621.835	+	1138.84i	0.0295760	+	0.0541662i
$146$	−8803.80	+	24761.1i	−0.413013	+	1.16162i
$147$	8667.13			0.401089
$148$	14780.1	−	18157.4i	0.674766	−	0.828951i
$149$	28786.8			1.29664			0.648322	−	0.761367i	$-0.275471\pi$
$149$	28786.8			1.29664			0.648322	+	0.761367i	$0.275471\pi$
$150$	10278.5	−	7943.66i	0.456824	−	0.353052i
$151$			6225.15i			0.273021i	0.990639	+	0.136510i	$0.0435887\pi$
$151$			6225.15i			0.273021i	−0.990639	+	0.136510i	$0.956411\pi$
$152$	−10516.2	+	6389.36i	−0.455169	+	0.276548i
$153$			13061.7i			0.557978i
$154$	−15527.0	+	43670.4i	−0.654704	+	1.84139i
$155$	−6810.03	+	3718.43i	−0.283456	+	0.154773i
$156$	−82.5896	+	101.461i	−0.00339372	+	0.00416919i
$157$			11447.9i			0.464435i	0.972664	+	0.232218i	$0.0745982\pi$
$157$			11447.9i			0.464435i	−0.972664	+	0.232218i	$0.925402\pi$
$158$	1838.74	−	5171.54i	0.0736555	−	0.207160i
$159$			3556.42i			0.140676i
$160$	23936.0	−	9078.89i	0.935001	−	0.354644i
$161$	−35605.6			−1.37362
$162$	−2747.50	−	976.872i	−0.104691	−	0.0372227i
$163$	6026.05			0.226808			0.113404	−	0.993549i	$-0.463825\pi$
$163$	6026.05			0.226808			0.113404	+	0.993549i	$0.463825\pi$
$164$	−32630.6	−	26561.3i	−1.21322	−	0.987556i
$165$	−20710.7	+	11308.5i	−0.760722	+	0.415372i
$166$	11903.9	+	4232.41i	0.431989	+	0.153593i
$167$	−3209.79			−0.115092			−0.0575458	−	0.998343i	$-0.518328\pi$
$167$	−3209.79			−0.115092			−0.0575458	+	0.998343i	$0.518328\pi$
$168$	11014.8	+	18129.3i	0.390265	+	0.642336i
$169$	28558.5			0.999913
$170$	47772.8	−	7620.12i	1.65304	−	0.263672i
$171$		−	5191.21i		−	0.177532i
$172$	−2528.68	−	2058.35i	−0.0854747	−	0.0695763i
$173$		−	28165.6i		−	0.941080i	−0.882379	−	0.470540i	$-0.844059\pi$
$173$		−	28165.6i		−	0.941080i	0.882379	−	0.470540i	$-0.155941\pi$
$174$	−1016.43	−	361.391i	−0.0335722	−	0.0119365i
$175$	21555.2	−	33538.4i	0.703843	−	1.09513i
$176$	−45534.5	+	9437.10i	−1.46999	+	0.304659i
$177$		−	12300.2i		−	0.392613i
$178$	−40618.5	−	14441.9i	−1.28199	−	0.455809i
$179$			28427.5i			0.887224i	0.896219	+	0.443612i	$0.146303\pi$
$179$			28427.5i			0.887224i	−0.896219	+	0.443612i	$0.853697\pi$
$180$	−1970.00	+	10618.8i	−0.0608025	+	0.327741i
$181$	−1207.68			−0.0368635			−0.0184317	−	0.999830i	$-0.505867\pi$
$181$	−1207.68			−0.0368635			−0.0184317	+	0.999830i	$0.505867\pi$
$182$	−134.507	+	378.309i	−0.00406072	+	0.0114210i
$183$	27748.7			0.828592
$184$	−18549.3	−	30530.3i	−0.547889	−	0.901769i
$185$	32107.4	−	17531.4i	0.938126	−	0.512238i
$186$	2161.04	−	6078.03i	0.0624649	−	0.175686i
$187$	−87875.8			−2.51296
$188$	46381.7	+	37754.6i	1.31229	+	1.06821i
$189$	−8949.30			−0.250533
$190$	−18986.7	+	3028.52i	−0.525947	+	0.0838924i
$191$			28661.8i			0.785664i	0.919610	+	0.392832i	$0.128505\pi$
$191$			28661.8i			0.785664i	−0.919610	+	0.392832i	$0.871495\pi$
$192$	−9806.73	+	18889.5i	−0.266025	+	0.512410i
$193$		−	72324.9i		−	1.94166i	−0.239770	−	0.970830i	$-0.577072\pi$
$193$		−	72324.9i		−	1.94166i	0.239770	−	0.970830i	$-0.422928\pi$
$194$	12269.8	−	34509.6i	0.326014	−	0.916931i
$195$	−179.413	+	97.9635i	−0.00471829	+	0.00257629i
$196$	20697.6	+	16847.8i	0.538776	+	0.438563i
$197$			35723.7i			0.920500i	0.887789	+	0.460250i	$0.152240\pi$
$197$			35723.7i			0.920500i	−0.887789	+	0.460250i	$0.847760\pi$
$198$	6572.14	−	18484.5i	0.167639	−	0.471495i
$199$		−	70519.1i		−	1.78074i	−0.455237	−	0.890370i	$-0.650446\pi$
$199$		−	70519.1i		−	1.78074i	0.455237	−	0.890370i	$-0.349554\pi$
$200$	39987.2	+	1010.27i	0.999681	+	0.0252568i
$201$	−2918.21			−0.0722311
$202$	39352.4	+	13991.7i	0.964425	+	0.342900i
$203$	−3310.77			−0.0803408
$204$	−25390.4	+	31192.1i	−0.610111	+	0.749523i
$205$	−31505.7	−	57700.3i	−0.749688	−	1.37300i
$206$	−22558.7	−	8020.71i	−0.531593	−	0.189007i
$207$	15070.9			0.351721
$208$	−394.457	+	81.7520i	−0.00911745	+	0.00188961i
$209$	34925.1			0.799549
$210$	5220.96	+	32731.8i	0.118389	+	0.742217i
$211$		−	41676.9i		−	0.936118i	−0.883697	−	0.468059i	$-0.844953\pi$
$211$		−	41676.9i		−	0.936118i	0.883697	−	0.468059i	$-0.155047\pi$
$212$	−6913.25	+	8492.95i	−0.153819	+	0.188967i
$213$		−	31160.7i		−	0.686828i
$214$	−20121.8	−	7154.28i	−0.439379	−	0.156221i
$215$	−2441.50	−	4471.43i	−0.0528178	−	0.0967319i
$216$	−4662.28	−	7673.64i	−0.0999289	−	0.164473i
$217$		−	19797.6i		−	0.420430i
$218$	−46224.7	−	16435.1i	−0.972661	−	0.345828i
$219$		−	34138.3i		−	0.711793i
$220$	−71440.6	−	13253.7i	−1.47605	−	0.273836i
$221$	−761.253			−0.0155863
$222$	−10188.7	+	28656.2i	−0.206734	+	0.581450i
$223$	48504.3			0.975372			0.487686	−	0.873019i	$-0.337841\pi$
$223$	48504.3			0.975372			0.487686	+	0.873019i	$0.337841\pi$
$224$	−8937.05	+	64705.3i	−0.178114	+	1.28957i
$225$	−9123.72	+	14195.9i	−0.180222	+	0.280413i
$226$	14340.2	−	40332.6i	0.280762	−	0.789658i
$227$	−46494.5			−0.902299			−0.451149	−	0.892449i	$-0.648986\pi$
$227$	−46494.5			−0.902299			−0.451149	+	0.892449i	$0.648986\pi$
$228$	10091.1	−	12396.9i	0.194119	−	0.238475i
$229$	−13811.0			−0.263362			−0.131681	−	0.991292i	$-0.542038\pi$
$229$	−13811.0			−0.263362			−0.131681	+	0.991292i	$0.542038\pi$
$230$	−8792.26	−	55121.3i	−0.166205	−	1.04199i
$231$		−	60208.5i		−	1.12832i
$232$	−1724.80	−	2838.84i	−0.0320451	−	0.0527430i
$233$			40713.6i			0.749942i	0.927036	+	0.374971i	$0.122347\pi$
$233$			40713.6i			0.749942i	−0.927036	+	0.374971i	$0.877653\pi$
$234$	56.9333	−	160.128i	0.00103976	−	0.00292439i
$235$	44782.6	+	82016.0i	0.810912	+	1.48513i
$236$	23910.0	−	29373.5i	0.429295	−	0.527390i
$237$			7130.03i			0.126939i
$238$	−41351.3	+	116303.i	−0.730022	+	2.05323i
$239$			38798.0i			0.679225i	0.940565	+	0.339613i	$0.110296\pi$
$239$			38798.0i			0.679225i	−0.940565	+	0.339613i	$0.889704\pi$
$240$	−25346.1	+	21528.9i	−0.440037	+	0.373766i
$241$	80886.2			1.39264			0.696322	−	0.717730i	$-0.254819\pi$
$241$	80886.2			1.39264			0.696322	+	0.717730i	$0.254819\pi$
$242$	69178.9	+	24596.5i	1.18125	+	0.419993i
$243$	3788.00			0.0641500
$244$	66265.6	+	53940.1i	1.11303	+	0.906009i
$245$	19984.0	+	36599.3i	0.332928	+	0.609734i
$246$	51498.1	+	18310.1i	0.850984	+	0.302566i
$247$	302.550			0.00495910
$248$	16975.6	−	10313.9i	0.276008	−	0.167695i
$249$	−16411.9			−0.264704
$250$	57243.7	+	25087.9i	0.915900	+	0.401407i
$251$			99036.4i			1.57198i	0.618238	+	0.785991i	$0.287847\pi$
$251$			99036.4i			1.57198i	−0.618238	+	0.785991i	$0.712153\pi$
$252$	−21371.4	−	17396.3i	−0.336537	−	0.273941i
$253$			101393.i			1.58404i
$254$	5463.22	+	1942.44i	0.0846800	+	0.0301079i
$255$	−55156.6	+	30116.7i	−0.848237	+	0.463156i
$256$	−60137.9	+	26046.1i	−0.917631	+	0.397432i
$257$		−	69534.3i		−	1.05277i	−0.850247	−	0.526384i	$-0.823547\pi$
$257$		−	69534.3i		−	1.05277i	0.850247	−	0.526384i	$-0.176453\pi$
$258$	3990.80	+	1418.92i	0.0599544	+	0.0213167i
$259$			93340.3i			1.39146i
$260$	−618.877	−	114.814i	−0.00915499	−	0.00169843i
$261$	1401.36			0.0205716
$262$	37745.2	−	106160.i	0.549869	−	1.54654i
$263$	−47004.0			−0.679552			−0.339776	−	0.940506i	$-0.610351\pi$
$263$	−47004.0			−0.679552			−0.339776	+	0.940506i	$0.610351\pi$
$264$	51626.2	−	31366.6i	0.740735	−	0.450049i
$265$	−15018.0	+	8200.14i	−0.213855	+	0.116770i
$266$	16434.6	−	46223.1i	0.232271	−	0.653274i
$267$	56000.9			0.785548
$268$	−6968.85	−	5672.64i	−0.0970268	−	0.0789797i
$269$	−4070.41			−0.0562514			−0.0281257	−	0.999604i	$-0.508954\pi$
$269$	−4070.41			−0.0562514			−0.0281257	+	0.999604i	$0.508954\pi$
$270$	−2209.89	−	13854.5i	−0.0303140	−	0.190048i
$271$		−	83837.9i		−	1.14157i	−0.821100	−	0.570784i	$-0.806639\pi$
$271$		−	83837.9i		−	1.14157i	0.821100	−	0.570784i	$-0.193361\pi$
$272$	−121267.	+	25132.9i	−1.63910	+	0.339707i
$273$		−	521.576i		−	0.00699830i
$274$	18277.6	−	51406.6i	0.243454	−	0.684728i
$275$	−95506.3	−	61382.0i	−1.26289	−	0.811663i
$276$	35990.2	+	29296.0i	0.472461	+	0.384583i
$277$			66807.1i			0.870689i	0.900264	+	0.435344i	$0.143373\pi$
$277$			66807.1i			0.870689i	−0.900264	+	0.435344i	$0.856627\pi$
$278$	8622.32	−	24250.7i	0.111567	−	0.313787i
$279$			8379.81i			0.107653i
$280$	−51158.6	+	88314.3i	−0.652533	+	1.12646i
$281$	−38638.9			−0.489341			−0.244670	−	0.969606i	$-0.578680\pi$
$281$	−38638.9			−0.489341			−0.244670	+	0.969606i	$0.578680\pi$
$282$	−73200.2	−	26026.2i	−0.920479	−	0.327275i
$283$	−54011.8			−0.674397			−0.337199	−	0.941434i	$-0.609479\pi$
$283$	−54011.8			−0.674397			−0.337199	+	0.941434i	$0.609479\pi$
$284$	60572.6	−	74413.6i	0.750999	−	0.922604i
$285$	21921.3	−	11969.5i	0.269883	−	0.147362i
$286$	1077.30	+	383.032i	0.0131706	+	0.00468278i
$287$	167742.			2.03647
$288$	3782.81	−	27388.0i	0.0456068	−	0.330199i
$289$	−150510.			−1.80206
$290$	−817.543	−	5125.42i	−0.00972108	−	0.0609444i
$291$			47578.5i			0.561856i
$292$	66360.7	−	81524.2i	0.778296	−	0.956139i
$293$		−	35710.6i		−	0.415970i	−0.978132	−	0.207985i	$-0.933309\pi$
$293$		−	35710.6i		−	0.415970i	0.978132	−	0.207985i	$-0.0666906\pi$
$294$	−32665.3	−	11614.1i	−0.377913	−	0.134366i
$295$	51940.7	−	28360.8i	0.596848	−	0.325893i
$296$	−80035.2	+	48627.1i	−0.913478	+	0.555003i
$297$			25484.6i			0.288912i
$298$	−108494.	−	38574.7i	−1.22172	−	0.434381i
$299$			878.350i			0.00982484i
$300$	−49383.1	+	16165.2i	−0.548701	+	0.179614i
$301$	12999.0			0.143475
$302$	8341.80	−	23461.8i	0.0914631	−	0.257245i
$303$	−54255.3			−0.590958
$304$	48196.1	−	9988.73i	0.521513	−	0.108084i
$305$	63981.0	+	117176.i	0.687783	+	1.25962i
$306$	17502.9	−	49227.9i	0.186925	−	0.525736i
$307$	25563.9			0.271238			0.135619	−	0.990761i	$-0.456698\pi$
$307$	25563.9			0.271238			0.135619	+	0.990761i	$0.456698\pi$
$308$	117038.	−	143782.i	1.23375	−	1.51566i
$309$	31101.7			0.325737
$310$	30648.9	−	4888.72i	0.318927	−	0.0508712i
$311$		−	126950.i		−	1.31254i	−0.754525	−	0.656271i	$-0.772133\pi$
$311$		−	126950.i		−	1.31254i	0.754525	−	0.656271i	$-0.227867\pi$
$312$	447.229	−	271.724i	0.00459432	−	0.00279137i
$313$			119029.i			1.21497i	0.794331	+	0.607485i	$0.207821\pi$
$313$			119029.i			1.21497i	−0.794331	+	0.607485i	$0.792179\pi$
$314$	15340.3	−	43145.5i	0.155588	−	0.437599i
$315$	−20634.6	−	37790.8i	−0.207958	−	0.380860i
$316$	−13859.9	+	17026.9i	−0.138799	+	0.170515i
$317$		−	63752.8i		−	0.634426i	−0.948354	−	0.317213i	$-0.897253\pi$
$317$		−	63752.8i		−	0.634426i	0.948354	−	0.317213i	$-0.102747\pi$
$318$	4765.66	−	13403.7i	0.0471269	−	0.132547i
$319$			9427.97i			0.0926481i
$320$	−102378.	+	2142.47i	−0.999781	+	0.0209226i
$321$	27742.0			0.269233
$322$	134193.	+	47712.1i	1.29425	+	0.460168i
$323$	93012.4			0.891530
$324$	9045.95	+	7363.40i	0.0861716	+	0.0701436i
$325$	−827.354	−	531.742i	−0.00783294	−	0.00503424i
$326$	−22711.4	−	8075.01i	−0.213702	−	0.0759815i
$327$	63730.2			0.596005
$328$	87388.0	+	143832.i	0.812277	+	1.33692i
$329$	−238431.			−2.20278
$330$	93209.3	−	14867.6i	0.855916	−	0.136525i
$331$			80748.7i			0.737020i	0.929624	+	0.368510i	$0.120132\pi$
$331$			80748.7i			0.737020i	−0.929624	+	0.368510i	$0.879868\pi$
$332$	−39192.6	−	31902.8i	−0.355573	−	0.289436i
$333$		−	39508.4i		−	0.356288i
$334$	12097.3	+	4301.17i	0.108441	+	0.0385562i
$335$	−6728.59	−	12322.9i	−0.0599562	−	0.109805i
$336$	−17219.9	−	83086.9i	−0.152529	−	0.735960i
$337$		−	4819.25i		−	0.0424346i	−0.999775	−	0.0212173i	$-0.993246\pi$
$337$		−	4819.25i		−	0.0424346i	0.999775	−	0.0212173i	$-0.00675418\pi$
$338$	−107633.	−	38268.9i	−0.942135	−	0.334975i
$339$			55606.7i			0.483869i
$340$	−190260.	−	35297.1i	−1.64585	−	0.305338i
$341$	−56377.2			−0.484835
$342$	−6956.30	+	19565.0i	−0.0594739	+	0.167273i
$343$	46757.7			0.397434
$344$	6772.05	+	11146.1i	0.0572273	+	0.0941903i
$345$	34749.4	+	63640.9i	0.291950	+	0.534685i
$346$	−37742.3	+	106152.i	−0.315266	+	0.886701i
$347$	33254.1			0.276176			0.138088	−	0.990420i	$-0.455904\pi$
$347$	33254.1			0.276176			0.138088	+	0.990420i	$0.455904\pi$
$348$	3346.52	+	2724.07i	0.0276335	+	0.0224936i
$349$	−70719.7			−0.580617			−0.290309	−	0.956933i	$-0.593758\pi$
$349$	−70719.7			−0.580617			−0.290309	+	0.956933i	$0.593758\pi$
$350$	−126181.	+	97517.4i	−1.03005	+	0.796061i
$351$			220.769i			0.00179194i
$352$	184259.	+	25449.8i	1.48711	+	0.205399i
$353$		−	42812.9i		−	0.343578i	−0.985134	−	0.171789i	$-0.945045\pi$
$353$		−	42812.9i		−	0.343578i	0.985134	−	0.171789i	$-0.0549547\pi$
$354$	−16482.4	+	46357.7i	−0.131527	+	0.369926i
$355$	131584.	−	71848.1i	1.04411	−	0.570110i
$356$	133733.	+	108859.i	1.05521	+	0.858942i
$357$		−	160347.i		−	1.25813i
$358$	38093.4	−	107140.i	0.297224	−	0.835957i
$359$		−	93736.2i		−	0.727308i	−0.931534	−	0.363654i	$-0.881529\pi$
$359$		−	93736.2i		−	0.727308i	0.931534	−	0.363654i	$-0.118471\pi$
$360$	21654.0	−	37381.0i	0.167084	−	0.288434i
$361$	93354.4			0.716342
$362$	4551.60	+	1618.32i	0.0347334	+	0.0123494i
$363$	−95377.2			−0.723821
$364$	1013.88	−	1245.55i	0.00765216	−	0.00940069i
$365$	144158.	−	78713.6i	1.08207	−	0.590832i
$366$	−104581.	−	37183.7i	−0.780714	−	0.277582i
$367$	−240811.			−1.78790			−0.893951	−	0.448164i	$-0.852078\pi$
$367$	−240811.			−1.78790			−0.893951	+	0.448164i	$0.852078\pi$
$368$	28998.9	+	139921.i	0.214134	+	1.03321i
$369$	−71000.7			−0.521447
$370$	−144501.	+	23048.9i	−1.05552	+	0.168363i
$371$		−	43659.1i		−	0.317196i
$372$	−16289.3	+	20011.5i	−0.117711	+	0.144608i
$373$		−	132994.i		−	0.955905i	−0.878386	−	0.477953i	$-0.841379\pi$
$373$		−	132994.i		−	0.955905i	0.878386	−	0.477953i	$-0.158621\pi$
$374$	331192.	+	117755.i	2.36776	+	0.841853i
$375$	−80982.8	−	5795.52i	−0.575877	−	0.0412126i
$376$	−124215.	−	204444.i	−0.878611	−	1.44610i
$377$			81.6729i			0.000574639i
$378$	33728.7	+	11992.2i	0.236057	+	0.0839296i
$379$			64236.3i			0.447200i	0.974681	+	0.223600i	$0.0717810\pi$
$379$			64236.3i			0.447200i	−0.974681	+	0.223600i	$0.928219\pi$
$380$	75616.5	+	14028.4i	0.523660	+	0.0971494i
$381$	−7532.16			−0.0518883
$382$	38407.3	−	108022.i	0.263200	−	0.740265i
$383$	−263992.			−1.79967			−0.899834	−	0.436232i	$-0.856313\pi$
$383$	−263992.			−1.79967			−0.899834	+	0.436232i	$0.856313\pi$
$384$	62272.5	−	58050.8i	0.422312	−	0.393682i
$385$	254247.	−	138824.i	1.71528	−	0.936579i
$386$	−96916.5	+	272583.i	−0.650464	+	1.82946i
$387$	−5502.13			−0.0367375
$388$	−92486.9	+	113620.i	−0.614351	+	0.754732i
$389$	138202.			0.913305			0.456652	−	0.889645i	$-0.349048\pi$
$389$	138202.			0.913305			0.456652	+	0.889645i	$0.349048\pi$
$390$	807.456	−	128.795i	0.00530872	−	0.000846780i
$391$			270030.i			1.76627i
$392$	−55430.2	−	91232.4i	−0.360723	−	0.593713i
$393$			146364.i			0.947651i
$394$	47870.3	−	134638.i	0.308371	−	0.867310i
$395$	−30108.5	+	16439.9i	−0.192972	+	0.105367i
$396$	−49539.0	+	60858.8i	−0.315905	+	0.388091i
$397$			11996.9i			0.0761183i	0.999275	+	0.0380591i	$0.0121175\pi$
$397$			11996.9i			0.0761183i	−0.999275	+	0.0380591i	$0.987882\pi$
$398$	−94496.7	+	265777.i	−0.596555	+	1.67784i
$399$			63727.9i			0.400299i
$400$	−149353.	−	57391.1i	−0.933455	−	0.358694i
$401$	263132.			1.63639			0.818193	−	0.574944i	$-0.194976\pi$
$401$	263132.			1.63639			0.818193	+	0.574944i	$0.194976\pi$
$402$	10998.3	+	3910.44i	0.0680573	+	0.0241977i
$403$	−488.385			−0.00300713
$404$	−129565.	−	105466.i	−0.793824	−	0.646172i
$405$	8734.08	+	15995.8i	0.0532485	+	0.0975207i
$406$	12477.8	+	4436.48i	0.0756985	+	0.0269145i
$407$	265802.			1.60461
$408$	137491.	−	83535.5i	0.825950	−	0.501823i
$409$	97249.6			0.581355			0.290677	−	0.956821i	$-0.406119\pi$
$409$	97249.6			0.581355			0.290677	+	0.956821i	$0.406119\pi$
$410$	41421.3	+	259683.i	0.246409	+	1.54481i
$411$			70874.5i			0.419572i
$412$	74272.7	+	60458.0i	0.437557	+	0.356171i
$413$			150998.i			0.885262i
$414$	−56800.2	−	20195.2i	−0.331397	−	0.117828i
$415$	−37841.4	−	69303.8i	−0.219721	−	0.402403i
$416$	1596.21	+	220.467i	0.00922364	+	0.00127396i
$417$			33434.6i			0.192275i
$418$	−131628.	−	46800.2i	−0.753348	−	0.267852i
$419$		−	160268.i		−	0.912889i	−0.889752	−	0.456445i	$-0.849123\pi$
$419$		−	160268.i		−	0.912889i	0.889752	−	0.456445i	$-0.150877\pi$
$420$	24184.0	−	130358.i	0.137097	−	0.738990i
$421$	−221222.			−1.24814			−0.624070	−	0.781368i	$-0.714522\pi$
$421$	−221222.			−1.24814			−0.624070	+	0.781368i	$0.714522\pi$
$422$	−55847.7	+	157075.i	−0.313603	+	0.882026i
$423$	100921.			0.564031
$424$	37435.8	−	22744.9i	0.208236	−	0.126518i
$425$	−254352.	−	163472.i	−1.40818	−	0.905038i
$426$	−41755.8	+	117441.i	−0.230090	+	0.647141i
$427$	−340647.			−1.86831
$428$	66249.6	+	53927.1i	0.361656	+	0.294388i
$429$	−1485.28			−0.00807036
$430$	3209.91	+	20123.9i	0.0173602	+	0.108837i
$431$		−	67483.0i		−	0.363278i	−0.983365	−	0.181639i	$-0.941860\pi$
$431$		−	67483.0i		−	0.363278i	0.983365	−	0.181639i	$-0.0581403\pi$
$432$	7288.72	+	35168.4i	0.0390557	+	0.188445i
$433$		−	309587.i		−	1.65123i	−0.564234	−	0.825615i	$-0.690829\pi$
$433$		−	309587.i		−	1.65123i	0.564234	−	0.825615i	$-0.309171\pi$
$434$	−26529.2	+	74614.7i	−0.140846	+	0.396136i
$435$	3231.15	+	5917.61i	0.0170757	+	0.0312729i
$436$	152191.	+	123884.i	0.800603	+	0.651690i
$437$		−	107320.i		−	0.561975i
$438$	−45745.9	+	128663.i	−0.238453	+	0.670663i
$439$			159908.i			0.829738i	0.909881	+	0.414869i	$0.136173\pi$
$439$			159908.i			0.829738i	−0.909881	+	0.414869i	$0.863827\pi$
$440$	251490.	+	145683.i	1.29902	+	0.752494i
$441$	45035.7			0.231569
$442$	2869.06	+	1020.09i	0.0146857	+	0.00522149i
$443$	233445.			1.18953			0.594767	−	0.803898i	$-0.297244\pi$
$443$	233445.			1.18953			0.594767	+	0.803898i	$0.297244\pi$
$444$	76799.5	−	94348.4i	0.389576	−	0.478595i
$445$	129123.	+	236479.i	0.652053	+	1.19419i
$446$	−182806.	−	64996.5i	−0.919012	−	0.326754i
$447$	149580.			0.748617
$448$	120389.	−	231890.i	0.599832	−	1.15538i
$449$	−325853.			−1.61633			−0.808163	−	0.588959i	$-0.799538\pi$
$449$	−325853.			−1.61633			−0.808163	+	0.588959i	$0.799538\pi$
$450$	53408.8	−	41276.5i	0.263747	−	0.203835i
$451$		−	477674.i		−	2.34844i
$452$	−108093.	+	132792.i	−0.529077	+	0.649972i
$453$			32346.8i			0.157629i
$454$	175232.	+	62303.4i	0.850161	+	0.302274i
$455$	2202.50	−	1202.61i	0.0106388	−	0.00580902i
$456$	−54643.9	+	33200.1i	−0.262792	+	0.159665i
$457$		−	40325.4i		−	0.193084i	−0.995329	−	0.0965419i	$-0.969222\pi$
$457$		−	40325.4i		−	0.193084i	0.995329	−	0.0965419i	$-0.0307782\pi$
$458$	52051.8	+	18506.9i	0.248145	+	0.0882275i
$459$			67870.7i			0.322149i
$460$	−40726.6	+	219527.i	−0.192470	+	1.03746i
$461$	78771.6			0.370653			0.185327	−	0.982677i	$-0.440666\pi$
$461$	78771.6			0.370653			0.185327	+	0.982677i	$0.440666\pi$
$462$	−80680.4	+	226918.i	−0.377993	+	1.06313i
$463$	182974.			0.853545			0.426772	−	0.904359i	$-0.359651\pi$
$463$	182974.			0.853545			0.426772	+	0.904359i	$0.359651\pi$
$464$	2696.44	+	13010.5i	0.0125243	+	0.0604306i
$465$	−35386.0	+	19321.5i	−0.163653	+	0.0893585i
$466$	54556.9	−	153444.i	0.251234	−	0.706608i
$467$	52480.2			0.240637			0.120318	−	0.992735i	$-0.461608\pi$
$467$	52480.2			0.240637			0.120318	+	0.992735i	$0.461608\pi$
$468$	−429.148	+	527.209i	−0.00195937	+	0.00240709i
$469$	35824.3			0.162867
$470$	−58876.9	−	369117.i	−0.266532	−	1.67097i
$471$			59484.9i			0.268142i
$472$	−129475.	+	78665.0i	−0.581166	+	0.353100i
$473$		−	37016.9i		−	0.165454i
$474$	9554.35	−	26872.1i	0.0425250	−	0.119604i
$475$	101089.	+	64970.0i	0.448039	+	0.287956i
$476$	311695.	−	382919.i	1.37568	−	1.69002i
$477$			18479.7i			0.0812192i
$478$	51990.0	−	146225.i	0.227543	−	0.639977i
$479$			229621.i			1.00078i	0.865799	+	0.500392i	$0.166811\pi$
$479$			229621.i			1.00078i	−0.865799	+	0.500392i	$0.833189\pi$
$480$	124375.	−	47175.3i	0.539823	−	0.204754i
$481$	2302.60			0.00995241
$482$	−304849.	−	108389.i	−1.31217	−	0.466541i
$483$	−185012.			−0.793060
$484$	−227766.	−	185402.i	−0.972297	−	0.791449i
$485$	−200913.	+	109703.i	−0.854132	+	0.466375i
$486$	−14276.4	−	5075.97i	−0.0604432	−	0.0214905i
$487$	−262676.			−1.10755			−0.553773	−	0.832668i	$-0.686812\pi$
$487$	−262676.			−1.10755			−0.553773	+	0.832668i	$0.686812\pi$
$488$	−177466.	−	292090.i	−0.745203	−	1.22653i
$489$	31312.3			0.130947
$490$	−26273.5	−	164717.i	−0.109428	−	0.686034i
$491$		−	311182.i		−	1.29078i	−0.763854	−	0.645389i	$-0.776695\pi$
$491$		−	311182.i		−	1.29078i	0.763854	−	0.645389i	$-0.223305\pi$
$492$	−169554.	−	138017.i	−0.700450	−	0.570166i
$493$			25108.5i			0.103307i
$494$	−1140.27	−	405.422i	−0.00467255	−	0.00166132i
$495$	−107616.	+	58760.6i	−0.439203	+	0.239815i
$496$	−77799.7	+	16124.1i	−0.316238	+	0.0655409i
$497$			382533.i			1.54866i
$498$	61854.4	+	21992.2i	0.249409	+	0.0886770i
$499$		−	380967.i		−	1.52998i	−0.644042	−	0.764990i	$-0.722744\pi$
$499$		−	380967.i		−	1.52998i	0.644042	−	0.764990i	$-0.277256\pi$
$500$	−182126.	−	171261.i	−0.728503	−	0.685042i
$501$	−16678.6			−0.0664482
$502$	132710.	−	373255.i	0.526620	−	1.48115i
$503$	−45448.6			−0.179632			−0.0898162	−	0.995958i	$-0.528628\pi$
$503$	−45448.6			−0.179632			−0.0898162	+	0.995958i	$0.528628\pi$
$504$	57234.8	+	94202.5i	0.225320	+	0.370853i
$505$	−125098.	−	229108.i	−0.490532	−	0.898373i
$506$	135868.	−	382137.i	0.530661	−	1.49251i
$507$	148394.			0.577300
$508$	−17987.2	−	14641.6i	−0.0697007	−	0.0567363i
$509$	−243510.			−0.939898			−0.469949	−	0.882694i	$-0.655728\pi$
$509$	−243510.			−0.939898			−0.469949	+	0.882694i	$0.655728\pi$
$510$	248235.	−	39595.3i	0.954382	−	0.152231i
$511$			419086.i			1.60495i
$512$	261554.	−	17578.7i	0.997749	−	0.0670573i
$513$		−	26974.3i		−	0.102498i
$514$	−93177.1	+	262066.i	−0.352682	+	0.991936i
$515$	71712.1	+	131335.i	0.270382	+	0.495185i
$516$	−13139.4	−	10695.5i	−0.0493488	−	0.0401699i
$517$			678973.i			2.54022i
$518$	125077.	−	351787.i	0.466143	−	1.31105i
$519$		−	146353.i		−	0.543333i
$520$	2178.61	+	1262.02i	0.00805700	+	0.00466725i
$521$	134468.			0.495387			0.247694	−	0.968838i	$-0.420327\pi$
$521$	134468.			0.495387			0.247694	+	0.968838i	$0.420327\pi$
$522$	−5281.53	−	1877.84i	−0.0193829	−	0.00689156i
$523$	485105.			1.77350			0.886752	−	0.462245i	$-0.152956\pi$
$523$	485105.			1.77350			0.886752	+	0.462245i	$0.152956\pi$
$524$	−284513.	+	349525.i	−1.03619	+	1.27296i
$525$	112004.	−	174271.i	0.406364	−	0.632274i
$526$	177152.	+	62986.0i	0.640286	+	0.227653i
$527$	−150143.			−0.540612
$528$	−236604.	+	49036.6i	−0.848701	+	0.175895i
$529$	31725.2			0.113369
$530$	67589.0	−	10780.9i	0.240616	−	0.0383800i
$531$		−	63913.5i		−	0.226675i
$532$	−123879.	+	152186.i	−0.437699	+	0.537714i
$533$		−	4138.01i		−	0.0145659i
$534$	−211060.	−	75042.1i	−0.740156	−	0.263162i
$535$	63965.5	+	117148.i	0.223480	+	0.409287i
$536$	18663.2	+	30717.8i	0.0649617	+	0.106920i
$537$			147714.i			0.512239i
$538$	15340.8	+	5454.42i	0.0530011	+	0.0188445i
$539$			302989.i			1.04291i
$540$	−10236.4	+	55176.9i	−0.0351043	+	0.189221i
$541$	−236859.			−0.809275			−0.404638	−	0.914477i	$-0.632602\pi$
$541$	−236859.			−0.809275			−0.404638	+	0.914477i	$0.632602\pi$
$542$	−112344.	+	315974.i	−0.382430	+	1.07560i
$543$	−6275.31			−0.0212831
$544$	490719.	+	67777.7i	1.65819	+	0.229028i
$545$	146944.	+	269118.i	0.494721	+	0.906045i
$546$	−698.920	+	1965.75i	−0.00234446	+	0.00659391i
$547$	−269985.			−0.902330			−0.451165	−	0.892441i	$-0.648991\pi$
$547$	−269985.			−0.902330			−0.451165	+	0.892441i	$0.648991\pi$
$548$	−137771.	+	169253.i	−0.458773	+	0.563604i
$549$	144187.			0.478388
$550$	277697.	+	359321.i	0.918008	+	1.18784i
$551$		−	9979.06i		−	0.0328690i
$552$	−96385.1	−	158640.i	−0.316324	−	0.520636i
$553$		−	87529.1i		−	0.286222i
$554$	89522.5	−	251787.i	0.291684	−	0.820377i
$555$	166835.	−	91095.6i	0.541628	−	0.295741i
$556$	−64992.7	+	79843.8i	−0.210240	+	0.258280i
$557$		−	414410.i		−	1.33573i	−0.744280	−	0.667867i	$-0.767207\pi$
$557$		−	414410.i		−	1.33573i	0.744280	−	0.667867i	$-0.232793\pi$
$558$	11229.1	−	31582.4i	0.0360641	−	0.101432i
$559$		−	320.671i		−	0.00102621i
$560$	311152.	−	264291.i	0.992195	−	0.842766i
$561$	−456616.			−1.45086
$562$	145625.	+	51776.7i	0.461065	+	0.163931i
$563$	133946.			0.422585			0.211292	−	0.977423i	$-0.432233\pi$
$563$	133946.			0.422585			0.211292	+	0.977423i	$0.432233\pi$
$564$	241006.	+	196179.i	0.757653	+	0.616729i
$565$	−234814.	+	128214.i	−0.735575	+	0.401641i
$566$	203563.	+	72376.7i	0.635428	+	0.225926i
$567$	−46501.9			−0.144645
$568$	−328005.	+	199287.i	−1.01668	+	0.617706i
$569$	599677.			1.85222			0.926111	−	0.377250i	$-0.123130\pi$
$569$	599677.			1.85222			0.926111	+	0.377250i	$0.123130\pi$
$570$	−98657.7	+	15736.6i	−0.303655	+	0.0484353i
$571$			339910.i			1.04254i	0.853392	+	0.521269i	$0.174541\pi$
$571$			339910.i			1.04254i	−0.853392	+	0.521269i	$0.825459\pi$
$572$	−3546.93	−	2887.20i	−0.0108408	−	0.00882438i
$573$			148931.i			0.453603i
$574$	−632198.	−	224777.i	−1.91880	−	0.682226i
$575$	−188618.	+	293477.i	−0.570490	+	0.887643i
$576$	−50957.3	+	98152.7i	−0.153589	+	0.295840i
$577$			40584.1i			0.121900i	0.998141	+	0.0609501i	$0.0194131\pi$
$577$			40584.1i			0.121900i	−0.998141	+	0.0609501i	$0.980587\pi$
$578$	567251.	+	201685.i	1.69793	+	0.603696i
$579$		−	375811.i		−	1.12102i
$580$	−3786.93	+	20412.5i	−0.0112572	+	0.0606794i
$581$	201475.			0.596855
$582$	63756.0	−	179317.i	0.188224	−	0.529390i
$583$	−124327.			−0.365786
$584$	−359348.	+	218330.i	−1.05363	+	0.640158i
$585$	−932.257	+	509.033i	−0.00272410	+	0.00148742i
$586$	−47852.8	+	134589.i	−0.139352	+	0.391934i
$587$	−650353.			−1.88744			−0.943720	−	0.330746i	$-0.892700\pi$
$587$	−650353.			−1.88744			−0.943720	+	0.330746i	$0.892700\pi$
$588$	107548.	+	87543.9i	0.311062	+	0.253204i
$589$	59672.6			0.172006
$590$	−233762.	+	37286.7i	−0.671536	+	0.107115i
$591$			185626.i			0.531451i
$592$	366803.	−	76020.6i	1.04662	−	0.216914i
$593$			328124.i			0.933102i	0.884494	+	0.466551i	$0.154504\pi$
$593$			328124.i			0.933102i	−0.884494	+	0.466551i	$0.845496\pi$
$594$	34149.8	−	96048.2i	0.0967867	−	0.272218i
$595$	677109.	−	369717.i	1.91260	−	1.04432i
$596$	357207.	+	290766.i	1.00560	+	0.818561i
$597$		−	366428.i		−	1.02811i
$598$	1177.00	−	3310.39i	0.00329136	−	0.00925713i
$599$			448879.i			1.25105i	0.780203	+	0.625526i	$0.215116\pi$
$599$			448879.i			1.25105i	−0.780203	+	0.625526i	$0.784884\pi$
$600$	207780.	+	5249.53i	0.577166	+	0.0145820i
$601$	154903.			0.428855			0.214428	−	0.976740i	$-0.431211\pi$
$601$	154903.			0.428855			0.214428	+	0.976740i	$0.431211\pi$
$602$	−48991.6	−	17418.9i	−0.135185	−	0.0480649i
$603$	−15163.5			−0.0417026
$604$	−62878.3	+	77246.1i	−0.172356	+	0.211740i
$605$	−219914.	−	402756.i	−0.600816	−	1.10035i
$606$	204481.	+	72703.0i	0.556811	+	0.197973i
$607$	363935.			0.987750			0.493875	−	0.869533i	$-0.335580\pi$
$607$	363935.			0.987750			0.493875	+	0.869533i	$0.335580\pi$
$608$	−195030.	−	26937.4i	−0.527587	−	0.0728699i
$609$	−17203.2			−0.0463848
$610$	−84117.5	−	527358.i	−0.226062	−	1.41725i
$611$			5881.83i			0.0157554i
$612$	−131932.	+	162079.i	−0.352248	+	0.432737i
$613$			110251.i			0.293400i	0.989181	+	0.146700i	$0.0468652\pi$
$613$			110251.i			0.293400i	−0.989181	+	0.146700i	$0.953135\pi$
$614$	−96346.8	−	34256.0i	−0.255565	−	0.0908656i
$615$	−163708.	−	299819.i	−0.432833	−	0.792701i
$616$	−633770.	+	385061.i	−1.67021	+	1.01477i
$617$		−	85654.9i		−	0.225000i	−0.993652	−	0.112500i	$-0.964114\pi$
$617$		−	85654.9i		−	0.225000i	0.993652	−	0.112500i	$-0.0358858\pi$
$618$	−117218.	−	41676.8i	−0.306915	−	0.109123i
$619$		−	3038.45i		−	0.00792996i	−0.999992	−	0.00396498i	$-0.998738\pi$
$619$		−	3038.45i		−	0.00792996i	0.999992	−	0.00396498i	$-0.00126210\pi$
$620$	−122062.	−	22645.0i	−0.317540	−	0.0589101i
$621$	78310.6			0.203066
$622$	−170115.	+	478459.i	−0.439707	+	1.23670i
$623$	−687474.			−1.77125
$624$	−2049.66	+	424.796i	−0.00526396	+	0.00109097i
$625$	−162251.	−	355334.i	−0.415363	−	0.909656i
$626$	159501.	−	448606.i	0.407020	−	1.14476i
$627$	181476.			0.461620
$628$	−115631.	+	142053.i	−0.293195	+	0.360190i
$629$	707884.			1.78921
$630$	27128.9	+	170079.i	0.0683520	+	0.428519i
$631$		−	757296.i		−	1.90198i	−0.309215	−	0.950992i	$-0.600066\pi$
$631$		−	757296.i		−	1.90198i	0.309215	−	0.950992i	$-0.399934\pi$
$632$	75052.5	−	45599.7i	0.187902	−	0.114164i
$633$		−	216560.i		−	0.540468i
$634$	−85429.8	+	240276.i	−0.212535	+	0.597767i
$635$	−17367.1	−	31806.6i	−0.0430705	−	0.0788804i
$636$	−35922.3	+	44130.7i	−0.0888076	+	0.109100i
$637$			2624.74i			0.00646855i
$638$	12633.6	−	35532.8i	0.0310375	−	0.0872946i
$639$		−	161916.i		−	0.396540i
$640$	388718.	+	129113.i	0.949020	+	0.315217i
$641$	−255881.			−0.622761			−0.311380	−	0.950285i	$-0.600791\pi$
$641$	−255881.			−0.622761			−0.311380	+	0.950285i	$0.600791\pi$
$642$	−104556.	−	37174.7i	−0.253676	−	0.0901941i
$643$	−52773.8			−0.127643			−0.0638214	−	0.997961i	$-0.520329\pi$
$643$	−52773.8			−0.127643			−0.0638214	+	0.997961i	$0.520329\pi$
$644$	−441820.	−	359641.i	−1.06530	−	0.867156i
$645$	−12686.4	−	23234.2i	−0.0304944	−	0.0558482i
$646$	−350551.	−	124638.i	−0.840014	−	0.298666i
$647$	614453.			1.46784			0.733922	−	0.679233i	$-0.237688\pi$
$647$	614453.			1.46784			0.733922	+	0.679233i	$0.237688\pi$
$648$	−24225.9	−	39873.4i	−0.0576940	−	0.0949583i
$649$	429993.			1.02087
$650$	2405.65	+	3112.73i	0.00569383	+	0.00736741i
$651$		−	102872.i		−	0.242736i
$652$	74775.6	+	60867.2i	0.175899	+	0.143182i
$653$		−	477300.i		−	1.11935i	−0.828713	−	0.559674i	$-0.810926\pi$
$653$		−	477300.i		−	1.11935i	0.828713	−	0.559674i	$-0.189074\pi$
$654$	−240191.	−	85399.5i	−0.561566	−	0.199664i
$655$	−618060.	+	337475.i	−1.44062	+	0.786609i
$656$	−136617.	−	659183.i	−0.317466	−	1.53179i
$657$		−	177388.i		−	0.410954i
$658$	898615.	+	319501.i	2.07550	+	0.737940i
$659$		−	725334.i		−	1.67019i	−0.550102	−	0.835097i	$-0.685411\pi$
$659$		−	725334.i		−	1.67019i	0.550102	−	0.835097i	$-0.314589\pi$
$660$	−371216.	−	68868.0i	−0.852195	−	0.158099i
$661$	−248806.			−0.569453			−0.284726	−	0.958609i	$-0.591903\pi$
$661$	−248806.			−0.569453			−0.284726	+	0.958609i	$0.591903\pi$
$662$	108205.	−	304331.i	0.246905	−	0.694433i
$663$	−3955.59			−0.00899878
$664$	104962.	+	172756.i	0.238064	+	0.391830i
$665$	−269108.	+	146939.i	−0.608532	+	0.332272i
$666$	−52941.9	+	148902.i	−0.119358	+	0.335700i
$667$	28970.8			0.0651191
$668$	−39829.4	−	32421.1i	−0.0892587	−	0.0726565i
$669$	252036.			0.563131
$670$	8846.26	+	55459.8i	0.0197065	+	0.123546i
$671$			970050.i			2.15451i
$672$	−46438.3	+	336219.i	−0.102834	+	0.744532i
$673$		−	224759.i		−	0.496234i	−0.968730	−	0.248117i	$-0.920188\pi$
$673$		−	224759.i		−	0.496234i	0.968730	−	0.248117i	$-0.0798118\pi$
$674$	−6457.87	+	18163.1i	−0.0142157	+	0.0399825i
$675$	−47408.3	+	73764.0i	−0.104051	+	0.161896i
$676$	354375.	+	288461.i	0.775477	+	0.631238i
$677$			172658.i			0.376713i	0.982101	+	0.188356i	$0.0603160\pi$
$677$			172658.i			0.376713i	−0.982101	+	0.188356i	$0.939684\pi$
$678$	74513.8	−	209574.i	0.162098	−	0.455909i
$679$		−	584080.i		−	1.26687i
$680$	669767.	+	387982.i	1.44846	+	0.839061i
$681$	−241593.			−0.520942
$682$	212478.	+	75546.3i	0.456820	+	0.162422i
$683$	−164617.			−0.352885			−0.176443	−	0.984311i	$-0.556459\pi$
$683$	−164617.			−0.352885			−0.176443	+	0.984311i	$0.556459\pi$
$684$	52434.7	−	64416.2i	0.112075	−	0.137684i
$685$	−299287.	+	163417.i	−0.637832	+	0.348271i
$686$	−176224.	−	62656.1i	−0.374469	−	0.133142i
$687$	−71764.0			−0.152052
$688$	−10587.0	−	51082.8i	−0.0223664	−	0.107919i
$689$	−1077.02			−0.00226875
$690$	−45685.9	−	286419.i	−0.0959587	−	0.601594i
$691$			515480.i			1.07958i	0.841799	+	0.539792i	$0.181497\pi$
$691$			515480.i			1.07958i	−0.841799	+	0.539792i	$0.818503\pi$
$692$	284492.	−	349499.i	0.594097	−	0.729850i
$693$		−	312853.i		−	0.651439i
$694$	−125330.	−	44561.0i	−0.260218	−	0.0925200i
$695$	−141187.	+	77091.0i	−0.292297	+	0.159601i
$696$	−8962.31	−	14751.0i	−0.0185013	−	0.0304512i
$697$		−	1.27214e6i		−	2.61860i
$698$	266533.	+	94765.6i	0.547067	+	0.194509i
$699$			211554.i			0.432979i
$700$	606233.	−	198446.i	1.23721	−	0.404992i
$701$	64957.1			0.132188			0.0660938	−	0.997813i	$-0.478946\pi$
$701$	64957.1			0.132188			0.0660938	+	0.997813i	$0.478946\pi$
$702$	295.834	−	832.049i	0.000600308	−	0.00168840i
$703$	−281339.			−0.569272
$704$	−660346.	−	342827.i	−1.33237	−	0.691719i
$705$	232697.	+	426168.i	0.468180	+	0.857437i
$706$	−57370.0	+	161356.i	−0.115100	+	0.323725i
$707$	666045.			1.33249
$708$	124240.	−	152629.i	0.247853	−	0.304489i
$709$	194118.			0.386166			0.193083	−	0.981182i	$-0.438151\pi$
$709$	194118.			0.386166			0.193083	+	0.981182i	$0.438151\pi$
$710$	−592202.	+	94460.6i	−1.17477	+	0.187385i
$711$			37048.7i			0.0732882i
$712$	−358151.	−	589480.i	−0.706490	−	1.16281i
$713$			173239.i			0.340774i
$714$	−214868.	+	604327.i	−0.421478	+	1.18543i
$715$	−3424.64	−	6271.98i	−0.00669890	−	0.0122685i
$716$	−287138.	+	352749.i	−0.560098	+	0.688082i
$717$			201600.i			0.392151i
$718$	−125608.	+	353279.i	−0.243651	+	0.685282i
$719$		−	425180.i		−	0.822460i	−0.911532	−	0.411230i	$-0.865099\pi$
$719$		−	425180.i		−	0.822460i	0.911532	−	0.411230i	$-0.134901\pi$
$720$	−131702.	+	111867.i	−0.254056	+	0.215794i
$721$	−381809.			−0.734472
$722$	−351840.	−	125096.i	−0.674950	−	0.239977i
$723$	420297.			0.804043
$724$	−14985.8	−	12198.4i	−0.0285893	−	0.0232716i
$725$	−17538.5	+	27288.8i	−0.0333670	+	0.0519168i
$726$	359464.	+	127807.i	0.681997	+	0.242483i
$727$	614118.			1.16194			0.580969	−	0.813926i	$-0.302674\pi$
$727$	614118.			1.16194			0.580969	+	0.813926i	$0.302674\pi$
$728$	−5490.24	+	3335.71i	−0.0103593	+	0.00629399i
$729$	19683.0			0.0370370
$730$	−648790.	+	103487.i	−1.21747	+	0.194196i
$731$		−	98583.4i		−	0.184488i
$732$	344326.	+	280281.i	0.642610	+	0.523084i
$733$			966811.i			1.79942i	0.436484	+	0.899712i	$0.356223\pi$
$733$			966811.i			1.79942i	−0.436484	+	0.899712i	$0.643777\pi$
$734$	907584.	+	322690.i	1.68459	+	0.598954i
$735$	103840.	+	190175.i	0.192216	+	0.352030i
$736$	78203.4	−	566202.i	0.144368	−	1.04524i
$737$		−	102016.i		−	0.187816i
$738$	267592.	+	95142.0i	0.491316	+	0.174687i
$739$		−	241155.i		−	0.441578i	−0.975322	−	0.220789i	$-0.929137\pi$
$739$		−	241155.i		−	0.441578i	0.975322	−	0.220789i	$-0.0708632\pi$
$740$	575490.	+	106765.i	1.05093	+	0.194969i
$741$	1572.10			0.00286314
$742$	−58503.9	+	164545.i	−0.106262	+	0.298867i
$743$	−16577.0			−0.0300282			−0.0150141	−	0.999887i	$-0.504779\pi$
$743$	−16577.0			−0.0300282			−0.0150141	+	0.999887i	$0.504779\pi$
$744$	88207.9	−	53592.6i	0.159354	−	0.0968186i
$745$	344892.	+	631644.i	0.621398	+	1.13805i
$746$	−178214.	+	501237.i	−0.320232	+	0.900670i
$747$	−85278.9			−0.152827
$748$	−1.09043e6	−	887606.i	−1.94892	−	1.58642i
$749$	−340565.			−0.607066
$750$	297447.	+	130361.i	0.528795	+	0.231752i
$751$		−	401227.i		−	0.711395i	−0.934601	−	0.355697i	$-0.884243\pi$
$751$		−	401227.i		−	0.711395i	0.934601	−	0.355697i	$-0.115757\pi$
$752$	194189.	+	936973.i	0.343392	+	1.65688i
$753$			514608.i			0.907584i
$754$	109.443	−	307.814i	0.000192506	−	0.000541434i
$755$	−136593.	+	74583.0i	−0.239627	+	0.130842i
$756$	−111049.	−	90394.0i	−0.194300	−	0.158160i
$757$			41770.0i			0.0728907i	0.999336	+	0.0364454i	$0.0116035\pi$
$757$			41770.0i			0.0728907i	−0.999336	+	0.0364454i	$0.988397\pi$
$758$	86077.7	−	242098.i	0.149814	−	0.421360i
$759$			526854.i			0.914548i
$760$	−266190.	−	154198.i	−0.460856	−	0.266964i
$761$	−389716.			−0.672944			−0.336472	−	0.941694i	$-0.609234\pi$
$761$	−389716.			−0.672944			−0.336472	+	0.941694i	$0.609234\pi$
$762$	28387.7	+	10093.2i	0.0488900	+	0.0173828i
$763$	−782360.			−1.34387
$764$	−289504.	+	355656.i	−0.495984	+	0.609317i
$765$	−286602.	+	156491.i	−0.489730	+	0.267403i
$766$	994949.	+	353753.i	1.69568	+	0.602896i
$767$	3724.96			0.00633185
$768$	−312486.	+	135340.i	−0.529795	+	0.229458i
$769$	683543.			1.15588			0.577940	−	0.816079i	$-0.303857\pi$
$769$	683543.			1.15588			0.577940	+	0.816079i	$0.303857\pi$
$770$	−1.14425e6	+	182516.i	−1.92992	+	0.307837i
$771$		−	361311.i		−	0.607816i
$772$	730531.	−	897459.i	1.22576	−	1.50584i
$773$		−	316702.i		−	0.530020i	−0.964246	−	0.265010i	$-0.914625\pi$
$773$		−	316702.i		−	0.530020i	0.964246	−	0.265010i	$-0.0853752\pi$
$774$	20736.8	+	7372.95i	0.0346147	+	0.0123072i
$775$	−163181.	−	104877.i	−0.271685	−	0.174612i
$776$	500824.	−	304286.i	0.831690	−	0.505311i
$777$			485010.i			0.803357i
$778$	−520866.	−	185193.i	−0.860531	−	0.305961i
$779$			505596.i			0.833160i
$780$	−3215.78	−	596.592i	−0.00528564	−	0.000980591i
$781$	1.08933e6			1.78590
$782$	361844.	−	1.01771e6i	0.591709	−	1.66421i
$783$	7281.67			0.0118770
$784$	86656.1	+	418120.i	0.140983	+	0.680250i
$785$	−251191.	+	137156.i	−0.407628	+	0.222574i
$786$	196130.	−	551625.i	0.317467	−	0.892893i
$787$	−413663.			−0.667878			−0.333939	−	0.942595i	$-0.608378\pi$
$787$	−413663.			−0.667878			−0.333939	+	0.942595i	$0.608378\pi$
$788$	−360833.	+	443285.i	−0.581105	+	0.713888i
$789$	−244240.			−0.392340
$790$	135504.	−	21614.0i	0.217120	−	0.0346322i
$791$		−	682635.i		−	1.09103i
$792$	268258.	−	162986.i	0.427663	−	0.259836i
$793$			8403.38i			0.0133631i
$794$	16076.1	−	45214.8i	0.0254999	−	0.0717199i
$795$	−78035.6	+	42609.2i	−0.123469	+	0.0674169i
$796$	712291.	−	875051.i	1.12417	−	1.38104i
$797$			594420.i			0.935786i	0.883785	+	0.467893i	$0.154987\pi$
$797$			594420.i			0.935786i	−0.883785	+	0.467893i	$0.845013\pi$
$798$	85396.4	−	240182.i	0.134102	−	0.377168i
$799$			1.80824e6i			2.83245i
$800$	485986.	+	416435.i	0.759353	+	0.650679i
$801$	290989.			0.453536
$802$	−991711.	−	352602.i	−1.54183	−	0.548196i
$803$	1.19342e6			1.85081
$804$	−36211.2	−	29475.9i	−0.0560184	−	0.0455990i
$805$	−426588.	−	781264.i	−0.658289	−	1.20561i
$806$	1840.66	+	654.444i	0.00283337	+	0.00100740i
$807$	−21150.5			−0.0324768
$808$	346987.	+	571105.i	0.531484	+	0.874768i
$809$	83175.0			0.127085			0.0635427	−	0.997979i	$-0.479760\pi$
$809$	83175.0			0.127085			0.0635427	+	0.997979i	$0.479760\pi$
$810$	−11482.9	−	71989.9i	−0.0175018	−	0.109724i
$811$			350018.i			0.532168i	0.963950	+	0.266084i	$0.0857299\pi$
$811$			350018.i			0.532168i	−0.963950	+	0.266084i	$0.914270\pi$
$812$	−41082.3	−	33441.0i	−0.0623079	−	0.0507186i
$813$		−	435635.i		−	0.659085i
$814$	−1.00177e6	−	356179.i	−1.51189	−	0.537551i
$815$	72197.6	+	132225.i	0.108694	+	0.199066i
$816$	−630124.	+	130594.i	−0.946336	+	0.196130i
$817$			39180.7i			0.0586986i
$818$	−366521.	−	130316.i	−0.547762	−	0.194756i
$819$		−	2710.19i		−	0.00404047i
$820$	191868.	−	1.03421e6i	0.285347	−	1.53809i
$821$	−81508.7			−0.120925			−0.0604627	−	0.998170i	$-0.519258\pi$
$821$	−81508.7			−0.120925			−0.0604627	+	0.998170i	$0.519258\pi$
$822$	94973.0	−	267117.i	0.140558	−	0.395328i
$823$	71246.9			0.105188			0.0525940	−	0.998616i	$-0.483251\pi$
$823$	71246.9			0.105188			0.0525940	+	0.998616i	$0.483251\pi$
$824$	−198909.	−	327385.i	−0.292955	−	0.482174i
$825$	−496265.	−	318950.i	−0.729131	−	0.468614i
$826$	202340.	−	569093.i	0.296566	−	0.834109i
$827$	−1.14718e6			−1.67734			−0.838669	−	0.544641i	$-0.816666\pi$
$827$	−1.14718e6			−1.67734			−0.838669	+	0.544641i	$0.816666\pi$
$828$	187010.	+	152226.i	0.272775	+	0.222039i
$829$	−1.28951e6			−1.87635			−0.938177	−	0.346157i	$-0.887487\pi$
$829$	−1.28951e6			−1.87635			−0.938177	+	0.346157i	$0.887487\pi$
$830$	49751.1	+	311905.i	0.0722182	+	0.452758i
$831$			347140.i			0.502692i
$832$	−5720.46	−	2969.85i	−0.00826389	−	0.00429030i
$833$			806919.i			1.16289i
$834$	44802.9	−	126011.i	0.0644131	−	0.181165i
$835$	−38456.2	−	70429.7i	−0.0551561	−	0.101014i
$836$	433376.	+	352767.i	0.620086	+	0.504749i
$837$			43542.7i			0.0621534i
$838$	−214761.	+	604028.i	−0.305822	+	0.860140i
$839$		−	607521.i		−	0.863053i	−0.902100	−	0.431526i	$-0.857975\pi$
$839$		−	607521.i		−	0.863053i	0.902100	−	0.431526i	$-0.142025\pi$
$840$	−265828.	+	458894.i	−0.376740	+	0.650361i
$841$	−704587.			−0.996191
$842$	833755.	+	296441.i	1.17602	+	0.418132i
$843$	−200773.			−0.282521
$844$	420965.	−	517157.i	0.590964	−	0.726001i
$845$	342157.	+	626635.i	0.479195	+	0.877610i
$846$	−380359.	−	135236.i	−0.531439	−	0.188952i
$847$	1.17086e6			1.63207
$848$	−171569.	+	35558.0i	−0.238587	+	0.0494477i
$849$	−280654.			−0.389364
$850$	739563.	+	956942.i	1.02362	+	1.32449i
$851$		−	816772.i		−	1.12783i
$852$	314744.	−	386664.i	0.433590	−	0.532666i
$853$			435680.i			0.598783i	0.954130	+	0.299391i	$0.0967836\pi$
$853$			435680.i			0.598783i	−0.954130	+	0.299391i	$0.903216\pi$
$854$	1.28385e6	+	456472.i	1.76035	+	0.625891i
$855$	113906.	−	62195.4i	0.155817	−	0.0850797i
$856$	−177423.	−	292019.i	−0.242137	−	0.398533i
$857$			369941.i			0.503698i	0.967767	+	0.251849i	$0.0810387\pi$
$857$			369941.i			0.503698i	−0.967767	+	0.251849i	$0.918961\pi$
$858$	5597.81	+	1990.29i	0.00760403	+	0.00270360i
$859$		−	393542.i		−	0.533341i	−0.963788	−	0.266671i	$-0.914076\pi$
$859$		−	393542.i		−	0.533341i	0.963788	−	0.266671i	$-0.0859236\pi$
$860$	14868.6	−	80145.6i	0.0201036	−	0.108363i
$861$	871614.			1.17576
$862$	−90428.3	+	254334.i	−0.121700	+	0.342287i
$863$	664736.			0.892540			0.446270	−	0.894898i	$-0.352752\pi$
$863$	664736.			0.892540			0.446270	+	0.894898i	$0.352752\pi$
$864$	19656.1	−	142312.i	0.0263311	−	0.190640i
$865$	618013.	−	337449.i	0.825973	−	0.451000i
$866$	−414852.	+	1.16679e6i	−0.553168	+	1.55582i
$867$	−782071.			−1.04042
$868$	199970.	−	245663.i	0.265415	−	0.326062i
$869$	−249254.			−0.330068
$870$	−4248.08	−	26632.5i	−0.00561247	−	0.0351862i
$871$		−	883.745i		−	0.00116491i
$872$	−407583.	−	670840.i	−0.536023	−	0.882239i
$873$			247225.i			0.324388i
$874$	−143810.	+	404474.i	−0.188264	+	0.529502i
$875$	994155.	+	71146.6i	1.29849	+	0.0929261i
$876$	344820.	−	423612.i	0.449350	−	0.552027i
$877$			5196.63i			0.00675652i	0.999994	+	0.00337826i	$0.00107534\pi$
$877$			5196.63i			0.00675652i	−0.999994	+	0.00337826i	$0.998925\pi$
$878$	214279.	−	602672.i	0.277966	−	0.781793i
$879$		−	185558.i		−	0.240161i
$880$	−752615.	−	886060.i	−0.971868	−	1.14419i
$881$	−123673.			−0.159340			−0.0796700	−	0.996821i	$-0.525387\pi$
$881$	−123673.			−0.159340			−0.0796700	+	0.996821i	$0.525387\pi$
$882$	−169734.	−	60348.6i	−0.218188	−	0.0775764i
$883$	428180.			0.549168			0.274584	−	0.961563i	$-0.411460\pi$
$883$	428180.			0.549168			0.274584	+	0.961563i	$0.411460\pi$
$884$	−9446.17	−	7689.17i	−0.0120879	−	0.00983955i
$885$	269892.	−	147367.i	0.344590	−	0.188154i
$886$	−879823.	−	312820.i	−1.12080	−	0.398499i
$887$	570442.			0.725043			0.362522	−	0.931975i	$-0.381916\pi$
$887$	570442.			0.725043			0.362522	+	0.931975i	$0.381916\pi$
$888$	−415875.	+	252674.i	−0.527397	+	0.320431i
$889$	92465.8			0.116998
$890$	−169761.	−	1.06428e6i	−0.214318	−	1.34362i
$891$			132422.i			0.166803i
$892$	601876.	+	489926.i	0.756445	+	0.615745i
$893$		−	718661.i		−	0.901200i
$894$	−563749.	−	200440.i	−0.705360	−	0.250790i
$895$	−623761.	+	340588.i	−0.778704	+	0.425190i
$896$	−764465.	+	712639.i	−0.952229	+	0.887674i
$897$			4564.04i			0.00567237i
$898$	1.22810e6	+	436648.i	1.52293	+	0.541476i
$899$			16108.5i			0.0199313i
$900$	−256602.	+	83996.9i	−0.316792	+	0.103700i
$901$	−331107.			−0.407867
$902$	−640091.	+	1.80029e6i	−0.786735	+	2.21274i
$903$	67544.9			0.0828356
$904$	585330.	−	355630.i	0.716248	−	0.435172i
$905$	−14469.2	−	26499.2i	−0.0176663	−	0.0323546i
$906$	43345.3	−	121911.i	0.0528062	−	0.148520i
$907$	−376374.			−0.457514			−0.228757	−	0.973484i	$-0.573466\pi$
$907$	−376374.			−0.457514			−0.228757	+	0.973484i	$0.573466\pi$
$908$	−576938.	−	469627.i	−0.699773	−	0.569614i
$909$	−281919.			−0.341190
$910$	−9912.43	+	1581.11i	−0.0119701	+	0.00190932i
$911$			323647.i			0.389973i	0.980806	+	0.194987i	$0.0624664\pi$
$911$			323647.i			0.389973i	−0.980806	+	0.194987i	$0.937534\pi$
$912$	250434.	−	51903.0i	0.301096	−	0.0624026i
$913$		−	573734.i		−	0.688286i
$914$	−54036.6	+	151981.i	−0.0646838	+	0.181927i
$915$	332455.	+	608867.i	0.397092	+	0.727244i
$916$	−171377.	−	139500.i	−0.204249	−	0.166259i
$917$		−	1.79678e6i		−	2.13676i
$918$	90947.7	−	255795.i	0.107921	−	0.303534i
$919$		−	1.60199e6i		−	1.89683i	−0.317030	−	0.948416i	$-0.602685\pi$
$919$		−	1.60199e6i		−	1.89683i	0.317030	−	0.948416i	$-0.397315\pi$
$920$	447662.	−	772792.i	0.528901	−	0.913034i
$921$	132834.			0.156599
$922$	−296880.	−	105555.i	−0.349236	−	0.124170i
$923$	9436.65			0.0110768
$924$	608147.	−	747111.i	0.712303	−	0.875066i
$925$	769351.	+	494463.i	0.899169	+	0.577897i
$926$	−689603.	−	245187.i	−0.804224	−	0.285941i
$927$	161609.			0.188065
$928$	7271.70	−	52648.0i	0.00844384	−	0.0611344i
$929$	−530402.			−0.614573			−0.307286	−	0.951617i	$-0.599421\pi$
$929$	−530402.			−0.614573			−0.307286	+	0.951617i	$0.599421\pi$
$930$	159256.	−	25402.6i	0.184133	−	0.0293705i
$931$		−	320699.i		−	0.369997i
$932$	−411235.	+	505204.i	−0.473433	+	0.581614i
$933$		−	659653.i		−	0.757796i
$934$	−197791.	−	70324.3i	−0.226732	−	0.0806142i
$935$	−1.05283e6	−	1.92818e6i	−1.20430	−	2.20559i
$936$	2323.87	−	1411.92i	0.00265253	−	0.00161160i
$937$			683707.i			0.778737i	0.921082	+	0.389369i	$0.127307\pi$
$937$			683707.i			0.778737i	−0.921082	+	0.389369i	$0.872693\pi$
$938$	−135017.	−	48005.1i	−0.153456	−	0.0545609i
$939$			618494.i			0.701463i
$940$	−272723.	+	1.47005e6i	−0.308650	+	1.66370i
$941$	−233339.			−0.263517			−0.131759	−	0.991282i	$-0.542062\pi$
$941$	−233339.			−0.263517			−0.131759	+	0.991282i	$0.542062\pi$
$942$	79710.7	−	224191.i	0.0898286	−	0.252648i
$943$	−1.46782e6			−1.65063
$944$	593385.	−	122980.i	0.665874	−	0.138004i
$945$	−107221.	−	196367.i	−0.120065	−	0.219889i
$946$	−49603.3	+	139512.i	−0.0554279	+	0.155894i
$947$	−1.35456e6			−1.51043			−0.755213	−	0.655480i	$-0.772467\pi$
$947$	−1.35456e6			−1.51043			−0.755213	+	0.655480i	$0.772467\pi$
$948$	−72018.2	+	88474.5i	−0.0801356	+	0.0984467i
$949$	10338.4			0.0114794
$950$	−293930.	−	380324.i	−0.325684	−	0.421412i
$951$		−	331269.i		−	0.366286i
$952$	−1.68786e6	+	1.02549e6i	−1.86235	+	1.13151i
$953$		−	1.58804e6i		−	1.74854i	−0.485440	−	0.874270i	$-0.661340\pi$
$953$		−	1.58804e6i		−	1.74854i	0.485440	−	0.874270i	$-0.338660\pi$
$954$	24763.1	−	69647.6i	0.0272088	−	0.0765261i
$955$	−628901.	+	343394.i	−0.689566	+	0.376519i
$956$	−391887.	+	481434.i	−0.428790	+	0.526770i
$957$			48989.2i			0.0534904i
$958$	307696.	−	865411.i	0.335267	−	0.942955i
$959$		−	870065.i		−	0.946051i
$960$	−531970.	+	11132.6i	−0.577224	+	0.0120797i
$961$	827196.			0.895698
$962$	−8678.19	−	3085.52i	−0.00937732	−	0.00333410i
$963$	144152.			0.155442
$964$	1.00369e6	+	817005.i	1.08006	+	0.879166i
$965$	1.58696e6	−	866518.i	1.70417	−	0.930514i
$966$	697286.	+	247919.i	0.747234	+	0.265678i
$967$	1.26401e6			1.35175			0.675877	−	0.737014i	$-0.263765\pi$
$967$	1.26401e6			1.35175			0.675877	+	0.737014i	$0.263765\pi$
$968$	609980.	+	1.00396e6i	0.650976	+	1.07144i
$969$	483307.			0.514725
$970$	904219.	−	144230.i	0.961015	−	0.153289i
$971$			1.22249e6i			1.29660i	0.761384	+	0.648301i	$0.224520\pi$
$971$			1.22249e6i			1.29660i	−0.761384	+	0.648301i	$0.775480\pi$
$972$	47004.2	+	38261.3i	0.0497512	+	0.0404974i
$973$		−	410447.i		−	0.433543i
$974$	989989.	+	351989.i	1.04355	+	0.371032i
$975$	−4299.06	−	2763.01i	−0.00452235	−	0.00290652i
$976$	277439.	+	1.33866e6i	0.291251	+	1.40530i
$977$		−	302079.i		−	0.316469i	−0.987402	−	0.158234i	$-0.949420\pi$
$977$		−	302079.i		−	0.316469i	0.987402	−	0.158234i	$-0.0505802\pi$
$978$	−118012.	−	41959.0i	−0.123381	−	0.0438679i
$979$			1.95770e6i			2.04259i
$980$	−121702.	+	656002.i	−0.126720	+	0.683051i
$981$	331152.			0.344104
$982$	−416989.	+	1.17280e6i	−0.432416	+	1.21619i
$983$	129394.			0.133908			0.0669542	−	0.997756i	$-0.478672\pi$
$983$	129394.			0.133908			0.0669542	+	0.997756i	$0.478672\pi$
$984$	454081.	+	747371.i	0.468968	+	0.771873i
$985$	−783854.	+	428002.i	−0.807909	+	0.441137i
$986$	33645.8	−	94630.8i	0.0346081	−	0.0973371i
$987$	−1.23892e6			−1.27178
$988$	3754.26	+	3055.96i	0.00384601	+	0.00313065i
$989$	−113748.			−0.116292
$990$	484330.	−	77254.2i	0.494164	−	0.0788228i
$991$			350310.i			0.356702i	0.983967	+	0.178351i	$0.0570762\pi$
$991$			350310.i			0.356702i	−0.983967	+	0.178351i	$0.942924\pi$
$992$	314823.	+	43483.1i	0.319921	+	0.0441873i
$993$			419583.i			0.425519i
$994$	512600.	−	1.44172e6i	0.518807	−	1.45917i
$995$	1.54734e6	−	844883.i	1.56293	−	0.853395i
$996$	−203651.	−	165772.i	−0.205290	−	0.167106i
$997$			325626.i			0.327589i	0.986494	+	0.163794i	$0.0523734\pi$
$997$			325626.i			0.327589i	−0.986494	+	0.163794i	$0.947627\pi$
$998$	−510501.	+	1.43581e6i	−0.512549	+	1.44157i
$999$		−	205292.i		−	0.205703i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.5.f.a.19.3	✓	24
3.2	odd	2		180.5.f.i.19.22		24
4.3	odd	2	inner	60.5.f.a.19.21	yes	24
5.2	odd	4		300.5.c.e.151.15		24
5.3	odd	4		300.5.c.e.151.10		24
5.4	even	2	inner	60.5.f.a.19.22	yes	24
8.3	odd	2		960.5.j.d.319.13		24
8.5	even	2		960.5.j.d.319.12		24
12.11	even	2		180.5.f.i.19.4		24
15.14	odd	2		180.5.f.i.19.3		24
20.3	even	4		300.5.c.e.151.9		24
20.7	even	4		300.5.c.e.151.16		24
20.19	odd	2	inner	60.5.f.a.19.4	yes	24
40.19	odd	2		960.5.j.d.319.1		24
40.29	even	2		960.5.j.d.319.24		24
60.59	even	2		180.5.f.i.19.21		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.f.a.19.3	✓	24	1.1	even	1	trivial
60.5.f.a.19.4	yes	24	20.19	odd	2	inner
60.5.f.a.19.21	yes	24	4.3	odd	2	inner
60.5.f.a.19.22	yes	24	5.4	even	2	inner
180.5.f.i.19.3		24	15.14	odd	2
180.5.f.i.19.4		24	12.11	even	2
180.5.f.i.19.21		24	60.59	even	2
180.5.f.i.19.22		24	3.2	odd	2
300.5.c.e.151.9		24	20.3	even	4
300.5.c.e.151.10		24	5.3	odd	4
300.5.c.e.151.15		24	5.2	odd	4
300.5.c.e.151.16		24	20.7	even	4
960.5.j.d.319.1		24	40.19	odd	2
960.5.j.d.319.12		24	8.5	even	2
960.5.j.d.319.13		24	8.3	odd	2
960.5.j.d.319.24		24	40.29	even	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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	60.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.76887 - 1.34002i) q^{2} +5.19615 q^{3} +(12.4087 + 10.1007i) q^{4} +(11.9809 + 21.9421i) q^{5} +(-19.5836 - 6.96293i) q^{6} -63.7886 q^{7} +(-33.2317 - 54.6960i) q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q+(-3.76887 - 1.34002i) q^{2} +5.19615 q^{3} +(12.4087 + 10.1007i) q^{4} +(11.9809 + 21.9421i) q^{5} +(-19.5836 - 6.96293i) q^{6} -63.7886 q^{7} +(-33.2317 - 54.6960i) q^{8} +27.0000 q^{9} +(-15.7516 - 98.7516i) q^{10} +181.649i q^{11} +(64.4776 + 52.4847i) q^{12} +1.57359i q^{13} +(240.411 + 85.4778i) q^{14} +(62.2546 + 114.015i) q^{15} +(51.9524 + 250.673i) q^{16} +483.767i q^{17} +(-101.759 - 36.1804i) q^{18} -192.267i q^{19} +(-72.9630 + 393.289i) q^{20} -331.455 q^{21} +(243.413 - 684.611i) q^{22} +558.181 q^{23} +(-172.677 - 284.209i) q^{24} +(-337.916 + 525.774i) q^{25} +(2.10864 - 5.93066i) q^{26} +140.296 q^{27} +(-791.535 - 644.309i) q^{28} +51.9021 q^{29} +(-81.8478 - 513.129i) q^{30} +310.363i q^{31} +(140.104 - 1014.37i) q^{32} +943.876i q^{33} +(648.256 - 1823.25i) q^{34} +(-764.246 - 1399.66i) q^{35} +(335.035 + 272.718i) q^{36} -1463.27i q^{37} +(-257.641 + 724.628i) q^{38} +8.17663i q^{39} +(802.002 - 1384.48i) q^{40} -2629.66 q^{41} +(1249.21 + 444.156i) q^{42} -203.783 q^{43} +(-1834.78 + 2254.03i) q^{44} +(323.485 + 592.438i) q^{45} +(-2103.71 - 747.972i) q^{46} +3737.83 q^{47} +(269.953 + 1302.54i) q^{48} +1667.99 q^{49} +(1978.10 - 1528.76i) q^{50} +2513.73i q^{51} +(-15.8944 + 19.5263i) q^{52} +684.434i q^{53} +(-528.757 - 187.999i) q^{54} +(-3985.77 + 2176.32i) q^{55} +(2119.81 + 3488.98i) q^{56} -999.048i q^{57} +(-195.612 - 69.5497i) q^{58} -2367.17i q^{59} +(-379.127 + 2043.59i) q^{60} +5340.25 q^{61} +(415.892 - 1169.72i) q^{62} -1722.29 q^{63} +(-1887.31 + 3635.28i) q^{64} +(-34.5280 + 18.8531i) q^{65} +(1264.81 - 3557.34i) q^{66} -561.609 q^{67} +(-4886.38 + 6002.93i) q^{68} +2900.39 q^{69} +(1004.77 + 6299.23i) q^{70} -5996.88i q^{71} +(-897.256 - 1476.79i) q^{72} -6569.92i q^{73} +(-1960.81 + 5514.89i) q^{74} +(-1755.86 + 2732.00i) q^{75} +(1942.03 - 2385.79i) q^{76} -11587.1i q^{77} +(10.9568 - 30.8166i) q^{78} +1372.17i q^{79} +(-4877.87 + 4143.24i) q^{80} +729.000 q^{81} +(9910.82 + 3523.78i) q^{82} -3158.48 q^{83} +(-4112.94 - 3347.93i) q^{84} +(-10614.9 + 5795.97i) q^{85} +(768.030 + 273.072i) q^{86} +269.691 q^{87} +(9935.47 - 6036.51i) q^{88} +10777.4 q^{89} +(-425.294 - 2666.29i) q^{90} -100.377i q^{91} +(6926.31 + 5638.01i) q^{92} +1612.69i q^{93} +(-14087.4 - 5008.75i) q^{94} +(4218.75 - 2303.53i) q^{95} +(728.002 - 5270.82i) q^{96} +9156.50i q^{97} +(-6286.43 - 2235.13i) q^{98} +4904.52i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 14 q^{4} - 24 q^{5} - 18 q^{6} + 648 q^{9}+O(q^{10}) \) 24 * q + 14 * q^4 - 24 * q^5 - 18 * q^6 + 648 * q^9	\( 24 q + 14 q^{4} - 24 q^{5} - 18 q^{6} + 648 q^{9} + 274 q^{10} - 36 q^{14} + 594 q^{16} - 12 q^{20} - 594 q^{24} + 1208 q^{25} - 2868 q^{26} - 1680 q^{29} + 468 q^{30} + 3076 q^{34} + 378 q^{36} - 7222 q^{40} - 4848 q^{41} - 3828 q^{44} - 648 q^{45} - 15280 q^{46} + 5416 q^{49} + 14472 q^{50} - 486 q^{54} + 32172 q^{56} - 7506 q^{60} + 2896 q^{61} - 18298 q^{64} - 2688 q^{65} - 15588 q^{66} + 9792 q^{69} + 27608 q^{70} + 31836 q^{74} + 50136 q^{76} - 27348 q^{80} + 17496 q^{81} - 4284 q^{84} - 15680 q^{85} - 58152 q^{86} - 38544 q^{89} + 7398 q^{90} + 4808 q^{94} + 21978 q^{96}+O(q^{100}) \) 24 * q + 14 * q^4 - 24 * q^5 - 18 * q^6 + 648 * q^9 + 274 * q^10 - 36 * q^14 + 594 * q^16 - 12 * q^20 - 594 * q^24 + 1208 * q^25 - 2868 * q^26 - 1680 * q^29 + 468 * q^30 + 3076 * q^34 + 378 * q^36 - 7222 * q^40 - 4848 * q^41 - 3828 * q^44 - 648 * q^45 - 15280 * q^46 + 5416 * q^49 + 14472 * q^50 - 486 * q^54 + 32172 * q^56 - 7506 * q^60 + 2896 * q^61 - 18298 * q^64 - 2688 * q^65 - 15588 * q^66 + 9792 * q^69 + 27608 * q^70 + 31836 * q^74 + 50136 * q^76 - 27348 * q^80 + 17496 * q^81 - 4284 * q^84 - 15680 * q^85 - 58152 * q^86 - 38544 * q^89 + 7398 * q^90 + 4808 * q^94 + 21978 * q^96

Introduction

L-functions

Modular forms

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