LMFDB - Embedded newform 60.5.f.a.19.14

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			19.14
Character	$\chi$	$=$	60.19
Dual form			60.5.f.a.19.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.828581 + 3.91324i) q^{2} +5.19615 q^{3} +(-14.6269 + 6.48488i) q^{4} +(-24.9254 - 1.93048i) q^{5} +(4.30543 + 20.3338i) q^{6} -67.1774 q^{7} +(-37.4965 - 51.8654i) q^{8} +27.0000 q^{9} +O(q^{10})$	\(q+(0.828581 + 3.91324i) q^{2} +5.19615 q^{3} +(-14.6269 + 6.48488i) q^{4} +(-24.9254 - 1.93048i) q^{5} +(4.30543 + 20.3338i) q^{6} -67.1774 q^{7} +(-37.4965 - 51.8654i) q^{8} +27.0000 q^{9} +(-13.0983 - 99.1385i) q^{10} +173.065i q^{11} +(-76.0036 + 33.6964i) q^{12} +157.105i q^{13} +(-55.6619 - 262.881i) q^{14} +(-129.516 - 10.0310i) q^{15} +(171.893 - 189.707i) q^{16} -469.297i q^{17} +(22.3717 + 105.657i) q^{18} +286.504i q^{19} +(377.100 - 133.401i) q^{20} -349.064 q^{21} +(-677.246 + 143.399i) q^{22} +41.9684 q^{23} +(-194.837 - 269.500i) q^{24} +(617.547 + 96.2356i) q^{25} +(-614.788 + 130.174i) q^{26} +140.296 q^{27} +(982.597 - 435.637i) q^{28} -817.252 q^{29} +(-68.0606 - 515.139i) q^{30} +1718.62i q^{31} +(884.798 + 515.470i) q^{32} +899.273i q^{33} +(1836.47 - 388.850i) q^{34} +(1674.42 + 129.684i) q^{35} +(-394.926 + 175.092i) q^{36} +76.9383i q^{37} +(-1121.16 + 237.392i) q^{38} +816.340i q^{39} +(834.488 + 1365.15i) q^{40} -192.833 q^{41} +(-289.228 - 1365.97i) q^{42} +1071.37 q^{43} +(-1122.31 - 2531.41i) q^{44} +(-672.985 - 52.1229i) q^{45} +(34.7742 + 164.232i) q^{46} -2699.92 q^{47} +(893.181 - 985.748i) q^{48} +2111.80 q^{49} +(135.094 + 2496.35i) q^{50} -2438.54i q^{51} +(-1018.80 - 2297.95i) q^{52} -442.419i q^{53} +(116.247 + 549.012i) q^{54} +(334.098 - 4313.71i) q^{55} +(2518.91 + 3484.18i) q^{56} +1488.72i q^{57} +(-677.159 - 3198.10i) q^{58} +573.252i q^{59} +(1959.47 - 693.172i) q^{60} +68.2349 q^{61} +(-6725.37 + 1424.02i) q^{62} -1813.79 q^{63} +(-1284.03 + 3889.53i) q^{64} +(303.287 - 3915.89i) q^{65} +(-3519.07 + 745.121i) q^{66} -5288.07 q^{67} +(3043.33 + 6864.36i) q^{68} +218.074 q^{69} +(879.907 + 6659.86i) q^{70} -5775.14i q^{71} +(-1012.40 - 1400.36i) q^{72} +1122.74i q^{73} +(-301.078 + 63.7496i) q^{74} +(3208.87 + 500.055i) q^{75} +(-1857.95 - 4190.67i) q^{76} -11626.1i q^{77} +(-3194.53 + 676.404i) q^{78} +5128.68i q^{79} +(-4650.71 + 4396.69i) q^{80} +729.000 q^{81} +(-159.778 - 754.604i) q^{82} +4327.01 q^{83} +(5105.72 - 2263.64i) q^{84} +(-905.966 + 11697.4i) q^{85} +(887.714 + 4192.51i) q^{86} -4246.56 q^{87} +(8976.09 - 6489.33i) q^{88} -6047.64 q^{89} +(-353.653 - 2676.74i) q^{90} -10553.9i q^{91} +(-613.868 + 272.160i) q^{92} +8930.21i q^{93} +(-2237.10 - 10565.4i) q^{94} +(553.090 - 7141.22i) q^{95} +(4597.54 + 2678.46i) q^{96} +2946.47i q^{97} +(1749.80 + 8263.98i) q^{98} +4672.76i 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 $

$2$	0.828581	+	3.91324i	0.207145	+	0.978310i
$2$	0.828581	+	3.91324i	0.207145	+	0.978310i
$3$	5.19615			0.577350
$3$	5.19615			0.577350
$4$	−14.6269	+	6.48488i	−0.914182	+	0.405305i
$5$	−24.9254	−	1.93048i	−0.997014	−	0.0772191i
$5$	−24.9254	−	1.93048i	−0.997014	−	0.0772191i
$6$	4.30543	+	20.3338i	0.119595	+	0.564828i
$7$	−67.1774			−1.37097			−0.685483	−	0.728088i	$-0.740409\pi$
$7$	−67.1774			−1.37097			−0.685483	+	0.728088i	$0.740409\pi$
$8$	−37.4965	−	51.8654i	−0.585882	−	0.810396i
$9$	27.0000			0.333333
$10$	−13.0983	−	99.1385i	−0.130983	−	0.991385i
$11$			173.065i			1.43029i	0.698976	+	0.715146i	$0.253640\pi$
$11$			173.065i			1.43029i	−0.698976	+	0.715146i	$0.746360\pi$
$12$	−76.0036	+	33.6964i	−0.527803	+	0.234003i
$13$			157.105i			0.929613i	0.885412	+	0.464807i	$0.153876\pi$
$13$			157.105i			0.929613i	−0.885412	+	0.464807i	$0.846124\pi$
$14$	−55.6619	−	262.881i	−0.283989	−	1.34123i
$15$	−129.516	−	10.0310i	−0.575626	−	0.0445824i
$16$	171.893	−	189.707i	0.671456	−	0.741044i
$17$		−	469.297i		−	1.62386i	−0.583752	−	0.811932i	$-0.698416\pi$
$17$		−	469.297i		−	1.62386i	0.583752	−	0.811932i	$-0.301584\pi$
$18$	22.3717	+	105.657i	0.0690484	+	0.326103i
$19$			286.504i			0.793641i	0.917896	+	0.396820i	$0.129886\pi$
$19$			286.504i			0.793641i	−0.917896	+	0.396820i	$0.870114\pi$
$20$	377.100	−	133.401i	0.942749	−	0.333502i
$21$	−349.064			−0.791528
$22$	−677.246	+	143.399i	−1.39927	+	0.296278i
$23$	41.9684			0.0793353			0.0396677	−	0.999213i	$-0.487370\pi$
$23$	41.9684			0.0793353			0.0396677	+	0.999213i	$0.487370\pi$
$24$	−194.837	−	269.500i	−0.338259	−	0.467882i
$25$	617.547	+	96.2356i	0.988074	+	0.153977i
$26$	−614.788	+	130.174i	−0.909450	+	0.192565i
$27$	140.296			0.192450
$28$	982.597	−	435.637i	1.25331	−	0.555659i
$29$	−817.252			−0.971762			−0.485881	−	0.874025i	$-0.661501\pi$
$29$	−817.252			−0.971762			−0.485881	+	0.874025i	$0.661501\pi$
$30$	−68.0606	−	515.139i	−0.0756229	−	0.572376i
$31$			1718.62i			1.78837i	0.447702	+	0.894183i	$0.352243\pi$
$31$			1718.62i			1.78837i	−0.447702	+	0.894183i	$0.647757\pi$
$32$	884.798	+	515.470i	0.864060	+	0.503388i
$33$			899.273i			0.825779i
$34$	1836.47	−	388.850i	1.58864	−	0.336376i
$35$	1674.42	+	129.684i	1.36687	+	0.105865i
$36$	−394.926	+	175.092i	−0.304727	+	0.135102i
$37$			76.9383i			0.0562004i	0.999605	+	0.0281002i	$0.00894574\pi$
$37$			76.9383i			0.0562004i	−0.999605	+	0.0281002i	$0.991054\pi$
$38$	−1121.16	+	237.392i	−0.776427	+	0.164399i
$39$			816.340i			0.536712i
$40$	834.488	+	1365.15i	0.521555	+	0.853218i
$41$	−192.833			−0.114714			−0.0573568	−	0.998354i	$-0.518267\pi$
$41$	−192.833			−0.114714			−0.0573568	+	0.998354i	$0.518267\pi$
$42$	−289.228	−	1365.97i	−0.163961	−	0.774360i
$43$	1071.37			0.579430			0.289715	−	0.957113i	$-0.406439\pi$
$43$	1071.37			0.579430			0.289715	+	0.957113i	$0.406439\pi$
$44$	−1122.31	−	2531.41i	−0.579704	−	1.30755i
$45$	−672.985	−	52.1229i	−0.332338	−	0.0257397i
$46$	34.7742	+	164.232i	0.0164339	+	0.0776146i
$47$	−2699.92			−1.22223			−0.611117	−	0.791540i	$-0.709280\pi$
$47$	−2699.92			−1.22223			−0.611117	+	0.791540i	$0.709280\pi$
$48$	893.181	−	985.748i	0.387665	−	0.427842i
$49$	2111.80			0.879550
$50$	135.094	+	2496.35i	0.0540378	+	0.998539i
$51$		−	2438.54i		−	0.937538i
$52$	−1018.80	−	2297.95i	−0.376777	−	0.849835i
$53$		−	442.419i		−	0.157501i	−0.996894	−	0.0787503i	$-0.974907\pi$
$53$		−	442.419i		−	0.157501i	0.996894	−	0.0787503i	$-0.0250930\pi$
$54$	116.247	+	549.012i	0.0398651	+	0.188276i
$55$	334.098	−	4313.71i	0.110446	−	1.42602i
$56$	2518.91	+	3484.18i	0.803225	+	1.11103i
$57$			1488.72i			0.458209i
$58$	−677.159	−	3198.10i	−0.201296	−	0.950684i
$59$			573.252i			0.164680i	0.996604	+	0.0823402i	$0.0262394\pi$
$59$			573.252i			0.164680i	−0.996604	+	0.0823402i	$0.973761\pi$
$60$	1959.47	−	693.172i	0.544297	−	0.192548i
$61$	68.2349			0.0183378			0.00916889	−	0.999958i	$-0.497081\pi$
$61$	68.2349			0.0183378			0.00916889	+	0.999958i	$0.497081\pi$
$62$	−6725.37	+	1424.02i	−1.74958	+	0.370452i
$63$	−1813.79			−0.456989
$64$	−1284.03	+	3889.53i	−0.313484	+	0.949593i
$65$	303.287	−	3915.89i	0.0717839	−	0.926838i
$66$	−3519.07	+	745.121i	−0.807868	+	0.171056i
$67$	−5288.07			−1.17801			−0.589003	−	0.808131i	$-0.700479\pi$
$67$	−5288.07			−1.17801			−0.589003	+	0.808131i	$0.700479\pi$
$68$	3043.33	+	6864.36i	0.658160	+	1.48451i
$69$	218.074			0.0458043
$70$	879.907	+	6659.86i	0.179573	+	1.35916i
$71$		−	5775.14i		−	1.14563i	−0.819684	−	0.572816i	$-0.805851\pi$
$71$		−	5775.14i		−	1.14563i	0.819684	−	0.572816i	$-0.194149\pi$
$72$	−1012.40	−	1400.36i	−0.195294	−	0.270132i
$73$			1122.74i			0.210686i	0.994436	+	0.105343i	$0.0335940\pi$
$73$			1122.74i			0.210686i	−0.994436	+	0.105343i	$0.966406\pi$
$74$	−301.078	+	63.7496i	−0.0549814	+	0.0116416i
$75$	3208.87	+	500.055i	0.570465	+	0.0888986i
$76$	−1857.95	−	4190.67i	−0.321666	−	0.725532i
$77$		−	11626.1i		−	1.96088i
$78$	−3194.53	+	676.404i	−0.525071	+	0.111177i
$79$			5128.68i			0.821772i	0.911687	+	0.410886i	$0.134781\pi$
$79$			5128.68i			0.821772i	−0.911687	+	0.410886i	$0.865219\pi$
$80$	−4650.71	+	4396.69i	−0.726674	+	0.686983i
$81$	729.000			0.111111
$82$	−159.778	−	754.604i	−0.0237624	−	0.112225i
$83$	4327.01			0.628104			0.314052	−	0.949406i	$-0.398313\pi$
$83$	4327.01			0.628104			0.314052	+	0.949406i	$0.398313\pi$
$84$	5105.72	−	2263.64i	0.723600	−	0.320810i
$85$	−905.966	+	11697.4i	−0.125393	+	1.61901i
$86$	887.714	+	4192.51i	0.120026	+	0.566862i
$87$	−4246.56			−0.561047
$88$	8976.09	−	6489.33i	1.15910	−	0.837982i
$89$	−6047.64			−0.763494			−0.381747	−	0.924267i	$-0.624677\pi$
$89$	−6047.64			−0.763494			−0.381747	+	0.924267i	$0.624677\pi$
$90$	−353.653	−	2676.74i	−0.0436609	−	0.330462i
$91$		−	10553.9i		−	1.27447i
$92$	−613.868	+	272.160i	−0.0725269	+	0.0321550i
$93$			8930.21i			1.03251i
$94$	−2237.10	−	10565.4i	−0.253180	−	1.19572i
$95$	553.090	−	7141.22i	0.0612842	−	0.791271i
$96$	4597.54	+	2678.46i	0.498865	+	0.290631i
$97$			2946.47i			0.313155i	0.987666	+	0.156577i	$0.0500460\pi$
$97$			2946.47i			0.313155i	−0.987666	+	0.156577i	$0.949954\pi$
$98$	1749.80	+	8263.98i	0.182195	+	0.860473i
$99$			4672.76i			0.476764i
$100$	−9656.87	+	2597.08i	−0.965687	+	0.259708i
$101$	18090.6			1.77341			0.886707	−	0.462332i	$-0.152987\pi$
$101$	18090.6			1.77341			0.886707	+	0.462332i	$0.152987\pi$
$102$	9542.58	−	2020.53i	0.917203	−	0.194207i
$103$	6936.39			0.653822			0.326911	−	0.945055i	$-0.393992\pi$
$103$	6936.39			0.653822			0.326911	+	0.945055i	$0.393992\pi$
$104$	8148.29	−	5890.87i	0.753355	−	0.544644i
$105$	8700.54	+	673.860i	0.789165	+	0.0611210i
$106$	1731.29	−	366.580i	0.154084	−	0.0326255i
$107$	10503.9			0.917453			0.458726	−	0.888578i	$-0.348306\pi$
$107$	10503.9			0.917453			0.458726	+	0.888578i	$0.348306\pi$
$108$	−2052.10	+	909.803i	−0.175934	+	0.0780009i
$109$	−12120.7			−1.02017			−0.510086	−	0.860123i	$-0.670386\pi$
$109$	−12120.7			−1.02017			−0.510086	+	0.860123i	$0.670386\pi$
$110$	17157.4	−	2266.85i	1.41797	−	0.187343i
$111$			399.783i			0.0324473i
$112$	−11547.3	+	12744.0i	−0.920544	+	1.01595i
$113$		−	13510.0i		−	1.05803i	−0.848612	−	0.529016i	$-0.822561\pi$
$113$		−	13510.0i		−	1.05803i	0.848612	−	0.529016i	$-0.177439\pi$
$114$	−5825.72	+	1233.53i	−0.448270	+	0.0949158i
$115$	−1046.08	−	81.0190i	−0.0790985	−	0.00612620i
$116$	11953.9	−	5299.78i	0.888367	−	0.393860i
$117$			4241.83i			0.309871i
$118$	−2243.27	+	474.986i	−0.161108	+	0.0341128i
$119$			31526.1i			2.22626i
$120$	4336.13	+	7093.52i	0.301120	+	0.492605i
$121$	−15310.6			−1.04573
$122$	56.5381	+	267.019i	0.00379858	+	0.0179400i
$123$	−1001.99			−0.0662299
$124$	−11145.0	−	25138.1i	−0.724833	−	1.63489i
$125$	−15206.8	−	3590.87i	−0.973234	−	0.229815i
$126$	−1502.87	−	7097.79i	−0.0946631	−	0.447077i
$127$	−5340.34			−0.331102			−0.165551	−	0.986201i	$-0.552940\pi$
$127$	−5340.34			−0.331102			−0.165551	+	0.986201i	$0.552940\pi$
$128$	−16284.6	−	1801.92i	−0.993934	−	0.109981i
$129$	5566.98			0.334534
$130$	15575.1	−	2057.80i	0.921604	−	0.121763i
$131$			18428.1i			1.07383i	0.843635	+	0.536917i	$0.180411\pi$
$131$			18428.1i			1.07383i	−0.843635	+	0.536917i	$0.819589\pi$
$132$	−5831.68	−	13153.6i	−0.334692	−	0.754912i
$133$		−	19246.6i		−	1.08806i
$134$	−4381.60	−	20693.5i	−0.244019	−	1.15246i
$135$	−3496.93	−	270.838i	−0.191875	−	0.0148608i
$136$	−24340.2	+	17597.0i	−1.31597	+	0.951393i
$137$			22720.6i			1.21054i	0.796021	+	0.605269i	$0.206934\pi$
$137$			22720.6i			1.21054i	−0.796021	+	0.605269i	$0.793066\pi$
$138$	180.692	+	853.377i	0.00948814	+	0.0448108i
$139$			33399.8i			1.72868i	0.502911	+	0.864338i	$0.332262\pi$
$139$			33399.8i			1.72868i	−0.502911	+	0.864338i	$0.667738\pi$
$140$	−25332.6	+	8961.52i	−1.29248	+	0.457221i
$141$	−14029.2			−0.705658
$142$	22599.5	−	4785.17i	1.12078	−	0.237313i
$143$	−27189.3			−1.32962
$144$	4641.10	−	5122.10i	0.223819	−	0.247015i
$145$	20370.3	+	1577.68i	0.968860	+	0.0750385i
$146$	−4393.57	+	930.285i	−0.206116	+	0.0436426i
$147$	10973.2			0.507808
$148$	−498.935	−	1125.37i	−0.0227783	−	0.0513773i
$149$	6236.40			0.280906			0.140453	−	0.990087i	$-0.455144\pi$
$149$	6236.40			0.280906			0.140453	+	0.990087i	$0.455144\pi$
$150$	701.971	+	12971.4i	0.0311987	+	0.576507i
$151$		−	10668.6i		−	0.467903i	−0.972248	−	0.233951i	$-0.924834\pi$
$151$		−	10668.6i		−	0.467903i	0.972248	−	0.233951i	$-0.0751656\pi$
$152$	14859.7	−	10742.9i	0.643164	−	0.464980i
$153$		−	12671.0i		−	0.541288i
$154$	45495.6	−	9633.14i	1.91835	−	0.406187i
$155$	3317.75	−	42837.2i	0.138096	−	1.78303i
$156$	−5293.86	−	11940.5i	−0.217532	−	0.490653i
$157$		−	5201.93i		−	0.211040i	−0.994417	−	0.105520i	$-0.966349\pi$
$157$		−	5201.93i		−	0.211040i	0.994417	−	0.105520i	$-0.0336508\pi$
$158$	−20069.8	+	4249.53i	−0.803948	+	0.170226i
$159$		−	2298.88i		−	0.0909330i
$160$	−21058.8	−	14556.3i	−0.822609	−	0.568607i
$161$	−2819.33			−0.108766
$162$	604.036	+	2852.75i	0.0230161	+	0.108701i
$163$	2913.74			0.109667			0.0548335	−	0.998496i	$-0.482537\pi$
$163$	2913.74			0.109667			0.0548335	+	0.998496i	$0.482537\pi$
$164$	2820.56	−	1250.50i	0.104869	−	0.0464940i
$165$	1736.03	−	22414.7i	0.0637659	−	0.823313i
$166$	3585.28	+	16932.6i	0.130109	+	0.614480i
$167$	−9729.46			−0.348864			−0.174432	−	0.984669i	$-0.555809\pi$
$167$	−9729.46			−0.348864			−0.174432	+	0.984669i	$0.555809\pi$
$168$	13088.7	+	18104.3i	0.463742	+	0.641451i
$169$	3879.13			0.135819
$170$	−46525.3	+	6146.97i	−1.60987	+	0.212698i
$171$			7735.62i			0.264547i
$172$	−15670.8	+	6947.68i	−0.529704	+	0.234846i
$173$			32421.7i			1.08329i	0.840608	+	0.541644i	$0.182198\pi$
$173$			32421.7i			1.08329i	−0.840608	+	0.541644i	$0.817802\pi$
$174$	−3518.62	−	16617.8i	−0.116218	−	0.548878i
$175$	−41485.2	−	6464.86i	−1.35462	−	0.211097i
$176$	32831.7	+	29748.7i	1.05991	+	0.960378i
$177$			2978.71i			0.0950782i
$178$	−5010.96	−	23665.9i	−0.158154	−	0.746934i
$179$		−	11239.0i		−	0.350769i	−0.984500	−	0.175384i	$-0.943883\pi$
$179$		−	11239.0i		−	0.350769i	0.984500	−	0.175384i	$-0.0561168\pi$
$180$	10181.7	−	3601.83i	0.314250	−	0.111167i
$181$	22847.7			0.697406			0.348703	−	0.937233i	$-0.386622\pi$
$181$	22847.7			0.697406			0.348703	+	0.937233i	$0.386622\pi$
$182$	41299.9	−	8744.75i	1.24683	−	0.264000i
$183$	354.559			0.0105873
$184$	−1573.67	−	2176.71i	−0.0464812	−	0.0642931i
$185$	148.528	−	1917.71i	0.00433974	−	0.0560325i
$186$	−34946.1	+	7399.41i	−1.01012	+	0.213880i
$187$	81218.9			2.32260
$188$	39491.4	−	17508.6i	1.11734	−	0.495378i
$189$	−9424.72			−0.263843
$190$	28403.6	−	3752.71i	0.786803	−	0.103953i
$191$		−	4768.54i		−	0.130713i	−0.997862	−	0.0653565i	$-0.979182\pi$
$191$		−	4768.54i		−	0.130713i	0.997862	−	0.0653565i	$-0.0208185\pi$
$192$	−6672.02	+	20210.6i	−0.180990	+	0.548248i
$193$			41315.5i			1.10917i	0.832127	+	0.554586i	$0.187123\pi$
$193$			41315.5i			1.10917i	−0.832127	+	0.554586i	$0.812877\pi$
$194$	−11530.3	+	2441.39i	−0.306362	+	0.0648685i
$195$	1575.92	−	20347.6i	0.0414444	−	0.535110i
$196$	−30889.1	+	13694.8i	−0.804068	+	0.356486i
$197$			36798.6i			0.948198i	0.880471	+	0.474099i	$0.157226\pi$
$197$			36798.6i			0.948198i	−0.880471	+	0.474099i	$0.842774\pi$
$198$	−18285.6	+	3871.76i	−0.466423	+	0.0987594i
$199$			5938.69i			0.149963i	0.997185	+	0.0749816i	$0.0238898\pi$
$199$			5938.69i			0.149963i	−0.997185	+	0.0749816i	$0.976110\pi$
$200$	−18164.5	−	35637.8i	−0.454113	−	0.890944i
$201$	−27477.6			−0.680122
$202$	14989.5	+	70792.9i	0.367354	+	1.73495i
$203$	54900.8			1.33225
$204$	15813.6	+	35668.2i	0.379989	+	0.857080i
$205$	4806.44	+	372.260i	0.114371	+	0.00885807i
$206$	5747.37	+	27143.8i	0.135436	+	0.639640i
$207$	1133.15			0.0264451
$208$	29803.9	+	27005.1i	0.688885	+	0.624194i
$209$	−49583.9			−1.13514
$210$	4572.13	+	34605.7i	0.103676	+	0.784709i
$211$		−	57008.1i		−	1.28048i	−0.768177	−	0.640238i	$-0.778836\pi$
$211$		−	57008.1i		−	1.28048i	0.768177	−	0.640238i	$-0.221164\pi$
$212$	2869.03	+	6471.22i	0.0638357	+	0.143984i
$213$		−	30008.5i		−	0.661431i
$214$	8703.35	+	41104.4i	0.190046	+	0.897554i
$215$	−26704.2	−	2068.25i	−0.577700	−	0.0447430i
$216$	−5260.61	−	7276.51i	−0.112753	−	0.155961i
$217$		−	115452.i		−	2.45179i
$218$	−10043.0	−	47431.1i	−0.211324	−	0.998045i
$219$			5833.95i			0.121639i
$220$	23087.1	+	65262.8i	0.477005	+	1.34841i
$221$	73728.7			1.50956
$222$	−1564.45	+	331.253i	−0.0317435	+	0.00672130i
$223$	−82458.9			−1.65817			−0.829083	−	0.559126i	$-0.811137\pi$
$223$	−82458.9			−1.65817			−0.829083	+	0.559126i	$0.811137\pi$
$224$	−59438.4	−	34627.9i	−1.18460	−	0.690129i
$225$	16673.8	+	2598.36i	0.329358	+	0.0513257i
$226$	52867.9	−	11194.1i	1.03508	−	0.219166i
$227$	−3967.64			−0.0769982			−0.0384991	−	0.999259i	$-0.512258\pi$
$227$	−3967.64			−0.0769982			−0.0384991	+	0.999259i	$0.512258\pi$
$228$	−9654.17	−	21775.4i	−0.185714	−	0.418886i
$229$	81701.1			1.55796			0.778981	−	0.627048i	$-0.215737\pi$
$229$	81701.1			1.55796			0.778981	+	0.627048i	$0.215737\pi$
$230$	−549.713	−	4160.68i	−0.0103916	−	0.0786518i
$231$		−	60410.8i		−	1.13212i
$232$	30644.0	+	42387.0i	0.569338	+	0.787512i
$233$			16309.3i			0.300416i	0.988654	+	0.150208i	$0.0479943\pi$
$233$			16309.3i			0.300416i	−0.988654	+	0.150208i	$0.952006\pi$
$234$	−16599.3	+	3514.70i	−0.303150	+	0.0641884i
$235$	67296.4	+	5212.13i	1.21859	+	0.0943798i
$236$	−3717.47	−	8384.91i	−0.0667457	−	0.150548i
$237$			26649.4i			0.474450i
$238$	−123369.	+	26121.9i	−2.17798	+	0.461160i
$239$		−	42742.9i		−	0.748287i	−0.927371	−	0.374143i	$-0.877937\pi$
$239$		−	42742.9i		−	0.748287i	0.927371	−	0.374143i	$-0.122063\pi$
$240$	−24165.8	+	22845.9i	−0.419545	+	0.396630i
$241$	−62415.6			−1.07463			−0.537315	−	0.843382i	$-0.680561\pi$
$241$	−62415.6			−1.07463			−0.537315	+	0.843382i	$0.680561\pi$
$242$	−12686.1	−	59913.9i	−0.216619	−	1.02305i
$243$	3788.00			0.0641500
$244$	−998.065	+	442.495i	−0.0167641	+	0.00743239i
$245$	−52637.3	−	4076.78i	−0.876924	−	0.0679180i
$246$	−830.232	−	3921.04i	−0.0137192	−	0.0647934i
$247$	−45011.2			−0.737779
$248$	89136.8	−	64442.2i	1.44929	−	1.04777i
$249$	22483.8			0.362636
$250$	1451.86	−	62483.1i	0.0232298	−	0.999730i
$251$			6192.56i			0.0982930i	0.998792	+	0.0491465i	$0.0156501\pi$
$251$			6192.56i			0.0982930i	−0.998792	+	0.0491465i	$0.984350\pi$
$252$	26530.1	−	11762.2i	0.417771	−	0.185220i
$253$			7263.27i			0.113473i
$254$	−4424.91	−	20898.0i	−0.0685862	−	0.323920i
$255$	−4707.54	+	60781.4i	−0.0723958	+	0.934739i
$256$	−6441.76	−	65218.6i	−0.0982935	−	0.995157i
$257$			93682.3i			1.41838i	0.705019	+	0.709188i	$0.250938\pi$
$257$			93682.3i			1.41838i	−0.705019	+	0.709188i	$0.749062\pi$
$258$	4612.70	+	21784.9i	0.0692972	+	0.327278i
$259$		−	5168.51i		−	0.0770488i
$260$	20957.9	+	59244.1i	0.310028	+	0.876392i
$261$	−22065.8			−0.323921
$262$	−72113.5	+	15269.2i	−1.05054	+	0.222440i
$263$	−83696.1			−1.21002			−0.605012	−	0.796217i	$-0.706832\pi$
$263$	−83696.1			−1.21002			−0.605012	+	0.796217i	$0.706832\pi$
$264$	46641.1	−	33719.6i	0.669208	−	0.483809i
$265$	−854.079	+	11027.4i	−0.0121620	+	0.157030i
$266$	75316.6	−	15947.4i	1.06446	−	0.225386i
$267$	−31424.4			−0.440803
$268$	77348.1	−	34292.5i	1.07691	−	0.477452i
$269$	−59007.1			−0.815454			−0.407727	−	0.913104i	$-0.633679\pi$
$269$	−59007.1			−0.815454			−0.407727	+	0.913104i	$0.633679\pi$
$270$	−1837.64	−	13908.7i	−0.0252076	−	0.190792i
$271$			136330.i			1.85632i	0.372183	+	0.928160i	$0.378610\pi$
$271$			136330.i			1.85632i	−0.372183	+	0.928160i	$0.621390\pi$
$272$	−89029.0	−	80668.7i	−1.20335	−	1.09035i
$273$		−	54839.6i		−	0.735815i
$274$	−88911.1	+	18825.9i	−1.18428	+	0.250757i
$275$	−16655.0	+	106876.i	−0.220232	+	1.41323i
$276$	−3189.75	+	1414.18i	−0.0418734	+	0.0185647i
$277$		−	47799.2i		−	0.622961i	−0.950253	−	0.311480i	$-0.899175\pi$
$277$		−	47799.2i		−	0.622961i	0.950253	−	0.311480i	$-0.100825\pi$
$278$	−130701.	+	27674.4i	−1.69118	+	0.358087i
$279$			46402.7i			0.596122i
$280$	−56058.7	−	91707.1i	−0.715034	−	1.16973i
$281$	145099.			1.83761			0.918804	−	0.394715i	$-0.129157\pi$
$281$	145099.			1.83761			0.918804	+	0.394715i	$0.129157\pi$
$282$	−11624.3	−	54899.6i	−0.146174	−	0.690352i
$283$	77522.1			0.967949			0.483975	−	0.875082i	$-0.339193\pi$
$283$	77522.1			0.967949			0.483975	+	0.875082i	$0.339193\pi$
$284$	37451.0	+	84472.4i	0.464330	+	1.04732i
$285$	2873.94	−	37106.9i	0.0353824	−	0.456841i
$286$	−22528.6	−	106398.i	−0.275424	−	1.30078i
$287$	12954.0			0.157268
$288$	23889.5	+	13917.7i	0.288020	+	0.167796i
$289$	−136718.			−1.63693
$290$	10704.6	+	81021.1i	0.127284	+	0.963390i
$291$			15310.3i			0.180800i
$292$	−7280.86	−	16422.3i	−0.0853919	−	0.192605i
$293$		−	58601.2i		−	0.682608i	−0.939953	−	0.341304i	$-0.889132\pi$
$293$		−	58601.2i		−	0.682608i	0.939953	−	0.341304i	$-0.110868\pi$
$294$	9092.21	+	42940.9i	0.105190	+	0.496794i
$295$	1106.65	−	14288.5i	0.0127165	−	0.164189i
$296$	3990.43	−	2884.91i	0.0455446	−	0.0329268i
$297$			24280.4i			0.275260i
$298$	5167.37	+	24404.6i	0.0581885	+	0.274814i
$299$			6593.43i			0.0737512i
$300$	−50178.6	+	13494.8i	−0.557540	+	0.149943i
$301$	−71971.6			−0.794379
$302$	41749.0	−	8839.84i	0.457754	−	0.0969239i
$303$	94001.5			1.02388
$304$	54352.0	+	49248.0i	0.588123	+	0.532895i
$305$	−1700.78	−	131.726i	−0.0182830	−	0.00141603i
$306$	49584.7	−	10499.0i	0.529547	−	0.112125i
$307$	−56954.8			−0.604301			−0.302151	−	0.953260i	$-0.597705\pi$
$307$	−56954.8			−0.604301			−0.302151	+	0.953260i	$0.597705\pi$
$308$	75393.6	+	170053.i	0.794755	+	1.79260i
$309$	36042.6			0.377484
$310$	170381.	−	22510.9i	1.77296	−	0.234245i
$311$			74530.8i			0.770575i	0.922797	+	0.385288i	$0.125898\pi$
$311$			74530.8i			0.770575i	−0.922797	+	0.385288i	$0.874102\pi$
$312$	42339.7	−	30609.9i	0.434950	−	0.314450i
$313$			162943.i			1.66321i	0.555366	+	0.831606i	$0.312578\pi$
$313$			162943.i			1.66321i	−0.555366	+	0.831606i	$0.687422\pi$
$314$	20356.4	−	4310.23i	0.206463	−	0.0437160i
$315$	45209.3	+	3501.48i	0.455624	+	0.0352883i
$316$	−33258.9	−	75016.7i	−0.333068	−	0.751249i
$317$			4541.66i			0.0451956i	0.999745	+	0.0225978i	$0.00719372\pi$
$317$			4541.66i			0.0451956i	−0.999745	+	0.0225978i	$0.992806\pi$
$318$	8996.06	−	1904.81i	0.0889607	−	0.0188363i
$319$		−	141438.i		−	1.38990i
$320$	39513.6	−	94469.2i	0.385875	−	0.922551i
$321$	54580.0			0.529692
$322$	−2336.04	−	11032.7i	−0.0225304	−	0.106407i
$323$	134456.			1.28876
$324$	−10663.0	+	4727.48i	−0.101576	+	0.0450339i
$325$	−15119.1	+	97019.4i	−0.143139	+	0.918527i
$326$	2414.27	+	11402.2i	0.0227170	+	0.107288i
$327$	−62980.8			−0.588997
$328$	7230.57	+	10001.4i	0.0672086	+	0.0929634i
$329$	181373.			1.67564
$330$	89152.6	−	11778.9i	0.818665	−	0.108163i
$331$			3981.35i			0.0363391i	0.999835	+	0.0181695i	$0.00578386\pi$
$331$			3981.35i			0.0363391i	−0.999835	+	0.0181695i	$0.994216\pi$
$332$	−63290.7	+	28060.1i	−0.574201	+	0.254574i
$333$			2077.33i			0.0187335i
$334$	−8061.65	−	38073.7i	−0.0722655	−	0.341297i
$335$	131807.	+	10208.5i	1.17449	+	0.0909645i
$336$	−60001.5	+	66220.0i	−0.531476	+	0.586557i
$337$		−	171148.i		−	1.50699i	−0.657451	−	0.753497i	$-0.728365\pi$
$337$		−	171148.i		−	1.50699i	0.657451	−	0.753497i	$-0.271635\pi$
$338$	3214.18	+	15180.0i	0.0281343	+	0.132873i
$339$		−	70200.1i		−	0.610855i
$340$	−62604.6	−	176972.i	−0.541562	−	1.53090i
$341$	−297433.			−2.55788
$342$	−30271.3	+	6409.59i	−0.258809	+	0.0547997i
$343$	19427.7			0.165133
$344$	−40172.4	−	55566.8i	−0.339478	−	0.469568i
$345$	−5435.58	−	420.987i	−0.0456675	−	0.00353696i
$346$	−126874.	+	26864.1i	−1.05979	+	0.224398i
$347$	−149128.			−1.23851			−0.619256	−	0.785189i	$-0.712566\pi$
$347$	−149128.			−1.23851			−0.619256	+	0.785189i	$0.712566\pi$
$348$	62114.1	−	27538.4i	0.512899	−	0.227395i
$349$	135689.			1.11403			0.557013	−	0.830504i	$-0.311947\pi$
$349$	135689.			1.11403			0.557013	+	0.830504i	$0.311947\pi$
$350$	−9075.29	−	167698.i	−0.0740840	−	1.36896i
$351$			22041.2i			0.178904i
$352$	−89209.9	+	153128.i	−0.719992	+	1.23586i
$353$		−	199881.i		−	1.60407i	−0.597280	−	0.802033i	$-0.703752\pi$
$353$		−	199881.i		−	1.60407i	0.597280	−	0.802033i	$-0.296248\pi$
$354$	−11656.4	+	2468.10i	−0.0930160	+	0.0196950i
$355$	−11148.8	+	143947.i	−0.0884647	+	1.14221i
$356$	88458.2	−	39218.2i	0.697972	−	0.309448i
$357$			163814.i			1.28533i
$358$	43980.9	−	9312.41i	0.343161	−	0.0726601i
$359$		−	108159.i		−	0.839213i	−0.907706	−	0.419607i	$-0.862168\pi$
$359$		−	108159.i		−	0.839213i	0.907706	−	0.419607i	$-0.137832\pi$
$360$	22531.2	+	36859.0i	0.173852	+	0.284406i
$361$	48236.3			0.370134
$362$	18931.2	+	89408.7i	0.144464	+	0.682280i
$363$	−79556.1			−0.603754
$364$	68440.6	+	154371.i	0.516548	+	1.16510i
$365$	2167.43	−	27984.8i	0.0162689	−	0.210057i
$366$	293.781	+	1387.47i	0.00219311	+	0.0103577i
$367$	90159.1			0.669387			0.334694	−	0.942327i	$-0.391367\pi$
$367$	90159.1			0.669387			0.334694	+	0.942327i	$0.391367\pi$
$368$	7214.06	−	7961.71i	0.0532702	−	0.0587910i
$369$	−5206.50			−0.0382379
$370$	7627.54	−	1007.76i	0.0557162	−	0.00736127i
$371$			29720.5i			0.215928i
$372$	−57911.3	−	130621.i	−0.418483	−	0.943905i
$373$			77478.4i			0.556882i	0.960453	+	0.278441i	$0.0898176\pi$
$373$			77478.4i			0.556882i	−0.960453	+	0.278441i	$0.910182\pi$
$374$	67296.5	+	317829.i	0.481115	+	2.27222i
$375$	−79016.8	−	18658.7i	−0.561897	−	0.132684i
$376$	101237.	+	140032.i	0.716086	+	0.990495i
$377$		−	128394.i		−	0.903363i
$378$	−7809.15	−	36881.2i	−0.0546538	−	0.258120i
$379$		−	193083.i		−	1.34420i	−0.740459	−	0.672101i	$-0.765392\pi$
$379$		−	193083.i		−	1.34420i	0.740459	−	0.672101i	$-0.234608\pi$
$380$	38220.0	+	108041.i	0.264681	+	0.748204i
$381$	−27749.2			−0.191162
$382$	18660.5	−	3951.13i	0.127878	−	0.0270766i
$383$	−27825.9			−0.189693			−0.0948465	−	0.995492i	$-0.530236\pi$
$383$	−27825.9			−0.189693			−0.0948465	+	0.995492i	$0.530236\pi$
$384$	−84617.3	−	9363.07i	−0.573848	−	0.0634974i
$385$	−22443.8	+	289784.i	−0.151417	+	1.95503i
$386$	−161678.	+	34233.3i	−1.08511	+	0.229760i
$387$	28926.9			0.193143
$388$	−19107.5	−	43097.8i	−0.126923	−	0.286280i
$389$	67636.2			0.446972			0.223486	−	0.974707i	$-0.428256\pi$
$389$	67636.2			0.446972			0.223486	+	0.974707i	$0.428256\pi$
$390$	80930.7	−	10692.6i	0.532089	−	0.0703000i
$391$		−	19695.6i		−	0.128830i
$392$	−79185.0	−	109529.i	−0.515313	−	0.712784i
$393$			95755.1i			0.619979i
$394$	−144002.	+	30490.7i	−0.927632	+	0.196415i
$395$	9900.80	−	127834.i	0.0634565	−	0.819319i
$396$	−30302.3	−	68348.0i	−0.193235	−	0.435849i
$397$		−	214354.i		−	1.36004i	−0.733195	−	0.680019i	$-0.761972\pi$
$397$		−	214354.i		−	1.36004i	0.733195	−	0.680019i	$-0.238028\pi$
$398$	−23239.5	+	4920.69i	−0.146711	+	0.0310642i
$399$		−	100008.i		−	0.628189i
$400$	124408.	−	100611.i	0.777552	−	0.628818i
$401$	77718.3			0.483320			0.241660	−	0.970361i	$-0.422308\pi$
$401$	77718.3			0.483320			0.241660	+	0.970361i	$0.422308\pi$
$402$	−22767.4	−	107527.i	−0.140884	−	0.665371i
$403$	−270003.			−1.66249
$404$	−264609.	+	117315.i	−1.62122	+	0.718773i
$405$	−18170.6	−	1407.32i	−0.110779	−	0.00857989i
$406$	45489.8	+	214840.i	0.275970	+	1.30336i
$407$	−13315.3			−0.0803829
$408$	−126476.	+	91436.5i	−0.759777	+	0.549287i
$409$	−134964.			−0.806809			−0.403405	−	0.915022i	$-0.632173\pi$
$409$	−134964.			−0.806809			−0.403405	+	0.915022i	$0.632173\pi$
$410$	2525.78	+	19117.2i	0.0150255	+	0.113725i
$411$			118060.i			0.698905i
$412$	−101458.	+	44981.7i	−0.597712	+	0.264997i
$413$		−	38509.6i		−	0.225771i
$414$	938.904	+	4434.28i	0.00547798	+	0.0258715i
$415$	−107852.	−	8353.19i	−0.626228	−	0.0485016i
$416$	−80982.7	+	139006.i	−0.467957	+	0.803242i
$417$			173550.i			0.998052i
$418$	−41084.3	−	194034.i	−0.235138	−	1.11052i
$419$		−	256385.i		−	1.46038i	−0.683246	−	0.730188i	$-0.739432\pi$
$419$		−	256385.i		−	1.46038i	0.683246	−	0.730188i	$-0.260568\pi$
$420$	−131632.	+	46565.4i	−0.746212	+	0.263976i
$421$	201100.			1.13462			0.567308	−	0.823506i	$-0.307985\pi$
$421$	201100.			1.13462			0.567308	+	0.823506i	$0.307985\pi$
$422$	223086.	−	47235.8i	1.25270	−	0.265245i
$423$	−72897.8			−0.407412
$424$	−22946.2	+	16589.1i	−0.127638	+	0.0922768i
$425$	45163.0	−	289812.i	0.250038	−	1.60450i
$426$	117430.	−	24864.5i	0.647085	−	0.137012i
$427$	−4583.84			−0.0251405
$428$	−153640.	+	68116.6i	−0.838719	+	0.371848i
$429$	−141280.			−0.767655
$430$	−14033.0	−	106214.i	−0.0758953	−	0.574438i
$431$		−	145064.i		−	0.780915i	−0.920621	−	0.390458i	$-0.872317\pi$
$431$		−	145064.i		−	0.780915i	0.920621	−	0.390458i	$-0.127683\pi$
$432$	24115.9	−	26615.2i	0.129222	−	0.142614i
$433$		−	210667.i		−	1.12362i	−0.827265	−	0.561812i	$-0.810104\pi$
$433$		−	210667.i		−	1.12362i	0.827265	−	0.561812i	$-0.189896\pi$
$434$	451793.	−	95661.7i	2.39861	−	0.507877i
$435$	105847.	+	8197.89i	0.559372	+	0.0433235i
$436$	177288.	−	78601.0i	0.932622	−	0.413481i
$437$			12024.1i			0.0629638i
$438$	−22829.6	+	4833.90i	−0.119001	+	0.0251970i
$439$			56805.2i			0.294754i	0.989080	+	0.147377i	$0.0470830\pi$
$439$			56805.2i			0.294754i	−0.989080	+	0.147377i	$0.952917\pi$
$440$	−236260.	+	144421.i	−1.22035	+	0.745975i
$441$	57018.6			0.293183
$442$	61090.2	+	288518.i	0.312699	+	1.47682i
$443$	207719.			1.05845			0.529223	−	0.848483i	$-0.322483\pi$
$443$	207719.			1.05845			0.529223	+	0.848483i	$0.322483\pi$
$444$	−2592.54	−	5847.59i	−0.0131510	−	0.0296627i
$445$	150739.	+	11674.8i	0.761214	+	0.0589563i
$446$	−68323.9	−	322682.i	−0.343481	−	1.62220i
$447$	32405.3			0.162181
$448$	86257.8	−	261289.i	0.429776	−	1.30186i
$449$	−224617.			−1.11416			−0.557082	−	0.830457i	$-0.688079\pi$
$449$	−224617.			−1.11416			−0.557082	+	0.830457i	$0.688079\pi$
$450$	3647.55	+	67401.4i	0.0180126	+	0.332846i
$451$		−	33372.8i		−	0.164074i
$452$	87610.8	+	197610.i	0.428826	+	0.967234i
$453$		−	55435.9i		−	0.270144i
$454$	−3287.51	−	15526.3i	−0.0159498	−	0.0753281i
$455$	−20374.0	+	263059.i	−0.0984133	+	1.27066i
$456$	77213.0	−	55821.7i	0.371331	−	0.268456i
$457$			298701.i			1.43023i	0.699009	+	0.715113i	$0.253625\pi$
$457$			298701.i			1.43023i	−0.699009	+	0.715113i	$0.746375\pi$
$458$	67696.0	+	319716.i	0.322725	+	1.52417i
$459$		−	65840.5i		−	0.312513i
$460$	15826.3	−	5598.62i	0.0747933	−	0.0264585i
$461$	−203098.			−0.955660			−0.477830	−	0.878452i	$-0.658577\pi$
$461$	−203098.			−0.955660			−0.477830	+	0.878452i	$0.658577\pi$
$462$	236402.	−	50055.3i	1.10756	−	0.234512i
$463$	340658.			1.58912			0.794560	−	0.607185i	$-0.207701\pi$
$463$	340658.			1.58912			0.794560	+	0.607185i	$0.207701\pi$
$464$	−140480.	+	155039.i	−0.652495	+	0.720119i
$465$	17239.6	−	222589.i	0.0797297	−	1.02943i
$466$	−63822.1	+	13513.5i	−0.293900	+	0.0622297i
$467$	−21171.0			−0.0970750			−0.0485375	−	0.998821i	$-0.515456\pi$
$467$	−21171.0			−0.0970750			−0.0485375	+	0.998821i	$0.515456\pi$
$468$	−27507.7	−	62044.8i	−0.125592	−	0.283278i
$469$	355239.			1.61501
$470$	35364.2	+	267666.i	0.160092	+	1.21170i
$471$		−	27030.0i		−	0.121844i
$472$	29731.9	−	21494.9i	0.133456	−	0.0964833i
$473$			185416.i			0.828754i
$474$	−104286.	+	22081.2i	−0.464160	+	0.0982802i
$475$	−27571.9	+	176930.i	−0.122202	+	0.784176i
$476$	−204443.	−	461129.i	−0.902315	−	2.03521i
$477$		−	11945.3i		−	0.0525002i
$478$	167263.	−	35416.0i	0.732056	−	0.155004i
$479$			235105.i			1.02469i	0.858781	+	0.512344i	$0.171223\pi$
$479$			235105.i			1.02469i	−0.858781	+	0.512344i	$0.828777\pi$
$480$	−109425.	−	75637.0i	−0.474934	−	0.328286i
$481$	−12087.4			−0.0522446
$482$	−51716.4	−	244247.i	−0.222605	−	1.05132i
$483$	−14649.6			−0.0627961
$484$	223946.	−	99287.1i	0.955989	−	0.423840i
$485$	5688.09	−	73441.9i	0.0241815	−	0.312220i
$486$	3138.66	+	14823.3i	0.0132884	+	0.0627586i
$487$	309654.			1.30563			0.652813	−	0.757519i	$-0.273589\pi$
$487$	309654.			1.30563			0.652813	+	0.757519i	$0.273589\pi$
$488$	−2558.57	−	3539.03i	−0.0107438	−	0.0148609i
$489$	15140.2			0.0633162
$490$	−27660.9	−	209361.i	−0.115206	−	0.871972i
$491$			159409.i			0.661225i	0.943767	+	0.330612i	$0.107255\pi$
$491$			159409.i			0.661225i	−0.943767	+	0.330612i	$0.892745\pi$
$492$	14656.0	−	6497.80i	0.0605462	−	0.0268433i
$493$			383533.i			1.57801i
$494$	−37295.4	−	176140.i	−0.152827	−	0.721777i
$495$	9020.65	−	116470.i	0.0368152	−	0.475340i
$496$	326035.	+	295418.i	1.32526	+	1.20081i
$497$			387958.i			1.57062i
$498$	18629.7	+	87984.5i	0.0751183	+	0.354770i
$499$			295471.i			1.18663i	0.804971	+	0.593314i	$0.202181\pi$
$499$			295471.i			1.18663i	−0.804971	+	0.593314i	$0.797819\pi$
$500$	245715.	−	46090.9i	0.982858	−	0.184363i
$501$	−50555.8			−0.201417
$502$	−24233.0	+	5131.04i	−0.0961610	+	0.0203609i
$503$	−454123.			−1.79489			−0.897444	−	0.441129i	$-0.854578\pi$
$503$	−454123.			−1.79489			−0.897444	+	0.441129i	$0.854578\pi$
$504$	68010.7	+	94072.8i	0.267742	+	0.370342i
$505$	−450914.	−	34923.5i	−1.76812	−	0.136941i
$506$	−28422.9	+	6018.21i	−0.111011	+	0.0235053i
$507$	20156.6			0.0784152
$508$	78112.7	−	34631.5i	0.302687	−	0.134197i
$509$	131760.			0.508568			0.254284	−	0.967130i	$-0.418160\pi$
$509$	131760.			0.508568			0.254284	+	0.967130i	$0.418160\pi$
$510$	−241753.	+	31940.6i	−0.929461	+	0.122801i
$511$		−	75423.0i		−	0.288843i
$512$	249879.	−	79247.1i	0.953212	−	0.302304i
$513$			40195.4i			0.152736i
$514$	−366601.	+	77623.4i	−1.38761	+	0.293810i
$515$	−172892.	−	13390.5i	−0.651869	−	0.0504875i
$516$	−81427.7	+	36101.2i	−0.305825	+	0.135588i
$517$		−	467262.i		−	1.74815i
$518$	20225.6	−	4282.53i	0.0753776	−	0.0159603i
$519$			168468.i			0.625437i
$520$	−214471.	+	131102.i	−0.793163	+	0.484844i
$521$	−68034.3			−0.250641			−0.125321	−	0.992116i	$-0.539996\pi$
$521$	−68034.3			−0.250641			−0.125321	+	0.992116i	$0.539996\pi$
$522$	−18283.3	−	86348.8i	−0.0670986	−	0.316895i
$523$	−23833.6			−0.0871336			−0.0435668	−	0.999051i	$-0.513872\pi$
$523$	−23833.6			−0.0871336			−0.0435668	+	0.999051i	$0.513872\pi$
$524$	−119504.	−	269546.i	−0.435230	−	0.981680i
$525$	−215563.	−	33592.4i	−0.782089	−	0.121877i
$526$	−69349.0	−	327523.i	−0.250651	−	1.18378i
$527$	806542.			2.90406
$528$	170599.	+	154579.i	0.611939	+	0.554474i
$529$	−278080.			−0.993706
$530$	−43860.7	+	5794.92i	−0.156144	+	0.0206298i
$531$			15477.8i			0.0548934i
$532$	124812.	+	281518.i	0.440994	+	0.994680i
$533$		−	30295.0i		−	0.106639i
$534$	−26037.7	−	122971.i	−0.0913104	−	0.431243i
$535$	−261814.	−	20277.6i	−0.914714	−	0.0708449i
$536$	198284.	+	274268.i	0.690173	+	0.954652i
$537$		−	58399.5i		−	0.202517i
$538$	−48892.2	−	230909.i	−0.168918	−	0.797767i
$539$			365479.i			1.25801i
$540$	52905.6	−	18715.6i	0.181432	−	0.0641826i
$541$	288228.			0.984785			0.492393	−	0.870373i	$-0.336122\pi$
$541$	288228.			0.984785			0.492393	+	0.870373i	$0.336122\pi$
$542$	−533492.	+	112960.i	−1.81606	+	0.384528i
$543$	118720.			0.402648
$544$	241908.	−	415232.i	0.817434	−	1.40312i
$545$	302112.	+	23398.7i	1.01713	+	0.0787767i
$546$	214600.	−	45439.0i	0.719855	−	0.152421i
$547$	−408815.			−1.36632			−0.683160	−	0.730269i	$-0.739395\pi$
$547$	−408815.			−1.36632			−0.683160	+	0.730269i	$0.739395\pi$
$548$	−147340.	−	332332.i	−0.490637	−	1.10665i
$549$	1842.34			0.00611259
$550$	−432031.	+	23380.1i	−1.42820	+	0.0772897i
$551$		−	234146.i		−	0.771230i
$552$	−8177.01	−	11310.5i	−0.0268359	−	0.0371196i
$553$		−	344531.i		−	1.12662i
$554$	187050.	−	39605.5i	0.609449	−	0.129043i
$555$	771.772	−	9964.73i	0.00250555	−	0.0323504i
$556$	−216593.	−	488535.i	−0.700641	−	1.58032i
$557$			203063.i			0.654518i	0.944935	+	0.327259i	$0.106125\pi$
$557$			203063.i			0.654518i	−0.944935	+	0.327259i	$0.893875\pi$
$558$	−181585.	+	38448.4i	−0.583192	+	0.123484i
$559$			168317.i			0.538646i
$560$	312423.	−	295358.i	0.996246	−	0.941830i
$561$	422026.			1.34095
$562$	120227.	+	567808.i	0.380652	+	1.79775i
$563$	−324004.			−1.02219			−0.511097	−	0.859523i	$-0.670761\pi$
$563$	−324004.			−1.02219			−0.511097	+	0.859523i	$0.670761\pi$
$564$	205203.	−	90977.5i	0.645099	−	0.286006i
$565$	−26080.8	+	336742.i	−0.0817003	+	1.05487i
$566$	64233.4	+	303363.i	0.200506	+	0.946955i
$567$	−48972.3			−0.152330
$568$	−299529.	+	216547.i	−0.928416	+	0.671206i
$569$	173926.			0.537204			0.268602	−	0.963251i	$-0.413438\pi$
$569$	173926.			0.537204			0.268602	+	0.963251i	$0.413438\pi$
$570$	147589.	−	19499.7i	0.454261	−	0.0600174i
$571$			94431.5i			0.289631i	0.989459	+	0.144815i	$0.0462588\pi$
$571$			94431.5i			0.289631i	−0.989459	+	0.144815i	$0.953741\pi$
$572$	397696.	−	176320.i	1.21551	−	0.538900i
$573$		−	24778.1i		−	0.0754672i
$574$	10733.5	+	50692.3i	0.0325774	+	0.153857i
$575$	25917.4	+	4038.85i	0.0783892	+	0.0122158i
$576$	−34668.8	+	105017.i	−0.104495	+	0.316531i
$577$		−	502118.i		−	1.50818i	−0.656769	−	0.754092i	$-0.728077\pi$
$577$		−	502118.i		−	1.50818i	0.656769	−	0.754092i	$-0.271923\pi$
$578$	−113282.	−	535011.i	−0.339083	−	1.60143i
$579$			214682.i			0.640380i
$580$	−308185.	+	109022.i	−0.916128	+	0.324085i
$581$	−290677.			−0.861110
$582$	−59913.0	+	12685.8i	−0.176878	+	0.0374519i
$583$	76567.3			0.225272
$584$	58231.5	−	42098.9i	0.170739	−	0.123437i
$585$	8188.74	−	105729.i	0.0239280	−	0.308946i
$586$	229321.	−	48555.8i	0.667802	−	0.141399i
$587$	−601788.			−1.74649			−0.873247	−	0.487278i	$-0.837990\pi$
$587$	−601788.			−1.74649			−0.873247	+	0.487278i	$0.837990\pi$
$588$	−160504.	+	71160.0i	−0.464229	+	0.205817i
$589$	−492392.			−1.41932
$590$	56831.3	−	7508.61i	0.163262	−	0.0215703i
$591$			191211.i			0.547443i
$592$	14595.8	+	13225.1i	0.0416470	+	0.0377361i
$593$			267892.i			0.761816i	0.924613	+	0.380908i	$0.124389\pi$
$593$			267892.i			0.761816i	−0.924613	+	0.380908i	$0.875611\pi$
$594$	−95015.0	+	20118.3i	−0.269289	+	0.0570188i
$595$	60860.4	−	785799.i	0.171910	−	2.21962i
$596$	−91219.3	+	40442.3i	−0.256800	+	0.113853i
$597$			30858.4i			0.0865813i
$598$	−25801.7	+	5463.19i	−0.0721515	+	0.0152772i
$599$		−	220852.i		−	0.615528i	−0.951463	−	0.307764i	$-0.900419\pi$
$599$		−	220852.i		−	0.615528i	0.951463	−	0.307764i	$-0.0995808\pi$
$600$	−94385.6	−	185179.i	−0.262182	−	0.514387i
$601$	−456805.			−1.26468			−0.632341	−	0.774690i	$-0.717906\pi$
$601$	−456805.			−1.26468			−0.632341	+	0.774690i	$0.717906\pi$
$602$	−59634.3	−	281642.i	−0.164552	−	0.777149i
$603$	−142778.			−0.392669
$604$	69184.9	+	156049.i	0.189643	+	0.427748i
$605$	381621.	+	29556.7i	1.04261	+	0.0807505i
$606$	77887.9	+	367850.i	0.212092	+	1.00167i
$607$	559003.			1.51718			0.758589	−	0.651569i	$-0.225889\pi$
$607$	559003.			1.51718			0.758589	+	0.651569i	$0.225889\pi$
$608$	−147684.	+	253498.i	−0.399510	+	0.685754i
$609$	285273.			0.769177
$610$	−893.758	−	6764.70i	−0.00240193	−	0.0181798i
$611$		−	424169.i		−	1.13621i
$612$	82169.9	+	185338.i	0.219387	+	0.494835i
$613$		−	373232.i		−	0.993250i	−0.867965	−	0.496625i	$-0.834573\pi$
$613$		−	373232.i		−	0.993250i	0.867965	−	0.496625i	$-0.165427\pi$
$614$	−47191.7	−	222878.i	−0.125178	−	0.591194i
$615$	24975.0	+	1934.32i	0.0660322	+	0.00511421i
$616$	−602990.	+	435936.i	−1.58909	+	1.14885i
$617$		−	54314.8i		−	0.142675i	−0.997452	−	0.0713375i	$-0.977273\pi$
$617$		−	54314.8i		−	0.142675i	0.997452	−	0.0713375i	$-0.0227267\pi$
$618$	29864.2	+	141043.i	0.0781941	+	0.369297i
$619$		−	185894.i		−	0.485159i	−0.970131	−	0.242580i	$-0.922006\pi$
$619$		−	185894.i		−	0.485159i	0.970131	−	0.242580i	$-0.0779936\pi$
$620$	229266.	+	648091.i	0.596424	+	1.68598i
$621$	5888.00			0.0152681
$622$	−291657.	+	61754.8i	−0.753862	+	0.159621i
$623$	406264.			1.04672
$624$	154866.	+	140323.i	0.397728	+	0.360379i
$625$	372102.	+	118860.i	0.952582	+	0.304281i
$626$	−637636.	+	135012.i	−1.62714	+	0.344527i
$627$	−257646.			−0.655372
$628$	33733.9	+	76088.2i	0.0855357	+	0.192929i
$629$	36106.9			0.0912617
$630$	23757.5	+	179816.i	0.0598576	+	0.453052i
$631$			204221.i			0.512911i	0.966556	+	0.256455i	$0.0825547\pi$
$631$			204221.i			0.512911i	−0.966556	+	0.256455i	$0.917445\pi$
$632$	266001.	−	192307.i	0.665961	−	0.481462i
$633$		−	296223.i		−	0.739283i
$634$	−17772.6	+	3763.14i	−0.0442153	+	0.00936206i
$635$	133110.	+	10309.4i	0.330113	+	0.0255674i
$636$	14907.9	+	33625.5i	0.0368556	+	0.0831293i
$637$			331773.i			0.817641i
$638$	553480.	−	117193.i	1.35976	−	0.287912i
$639$		−	155929.i		−	0.381878i
$640$	402421.	+	76350.6i	0.982473	+	0.186403i
$641$	−162514.			−0.395525			−0.197763	−	0.980250i	$-0.563367\pi$
$641$	−162514.			−0.395525			−0.197763	+	0.980250i	$0.563367\pi$
$642$	45223.9	+	213585.i	0.109723	+	0.518203i
$643$	−381649.			−0.923085			−0.461542	−	0.887118i	$-0.652704\pi$
$643$	−381649.			−0.923085			−0.461542	+	0.887118i	$0.652704\pi$
$644$	41238.0	−	18283.0i	0.0994320	−	0.0440834i
$645$	−138759.	−	10746.9i	−0.333535	−	0.0258324i
$646$	111407.	+	526157.i	0.266962	+	1.26081i
$647$	91144.8			0.217733			0.108866	−	0.994056i	$-0.465278\pi$
$647$	91144.8			0.217733			0.108866	+	0.994056i	$0.465278\pi$
$648$	−27334.9	−	37809.8i	−0.0650980	−	0.0900440i
$649$	−99210.0			−0.235541
$650$	−392188.	+	21224.0i	−0.928255	+	0.0502342i
$651$		−	599908.i		−	1.41554i
$652$	−42619.0	+	18895.2i	−0.100255	+	0.0444485i
$653$		−	134420.i		−	0.315238i	−0.987500	−	0.157619i	$-0.949618\pi$
$653$		−	134420.i		−	0.315238i	0.987500	−	0.157619i	$-0.0503818\pi$
$654$	−52184.7	−	246459.i	−0.122008	−	0.576221i
$655$	35575.0	−	459326.i	0.0829205	−	1.07063i
$656$	−33146.7	+	36581.9i	−0.0770251	+	0.0850078i
$657$			30314.1i			0.0702286i
$658$	150283.	+	709757.i	0.347102	+	1.63930i
$659$			636699.i			1.46610i	0.680176	+	0.733049i	$0.261904\pi$
$659$			636699.i			1.46610i	−0.680176	+	0.733049i	$0.738096\pi$
$660$	119964.	+	339116.i	0.275399	+	0.778502i
$661$	329381.			0.753870			0.376935	−	0.926240i	$-0.376978\pi$
$661$	329381.			0.753870			0.376935	+	0.926240i	$0.376978\pi$
$662$	−15580.0	+	3298.87i	−0.0355509	+	0.00752747i
$663$	383105.			0.871548
$664$	−162247.	−	224422.i	−0.367995	−	0.509013i
$665$	−37155.1	+	479729.i	−0.0840186	+	1.08481i
$666$	−8129.11	+	1721.24i	−0.0183271	+	0.00388055i
$667$	−34298.7			−0.0770951
$668$	142312.	−	63094.4i	0.318925	−	0.141396i
$669$	−428469.			−0.957342
$670$	69264.6	+	524251.i	0.154298	+	1.16786i
$671$			11809.1i			0.0262284i
$672$	−308851.	−	179932.i	−0.683928	−	0.398446i
$673$			631019.i			1.39320i	0.717461	+	0.696598i	$0.245304\pi$
$673$			631019.i			1.39320i	−0.717461	+	0.696598i	$0.754696\pi$
$674$	669743.	−	141810.i	1.47431	−	0.312167i
$675$	86639.4	+	13501.5i	0.190155	+	0.0296329i
$676$	−56739.7	+	25155.7i	−0.124163	+	0.0550482i
$677$			830008.i			1.81094i	0.424406	+	0.905472i	$0.360483\pi$
$677$			830008.i			1.81094i	−0.424406	+	0.905472i	$0.639517\pi$
$678$	274710.	−	58166.5i	0.597606	−	0.126536i
$679$		−	197936.i		−	0.429325i
$680$	640659.	−	391622.i	1.38551	−	0.846934i
$681$	−20616.5			−0.0444549
$682$	−246448.	−	1.16393e6i	−0.529854	−	2.50240i
$683$	552394.			1.18415			0.592077	−	0.805882i	$-0.298308\pi$
$683$	552394.			1.18415			0.592077	+	0.805882i	$0.298308\pi$
$684$	−50164.5	−	113148.i	−0.107222	−	0.241844i
$685$	43861.6	−	566319.i	0.0934766	−	1.20692i
$686$	16097.5	+	76025.4i	0.0342066	+	0.161551i
$687$	424531.			0.899490
$688$	184160.	−	203246.i	0.389062	−	0.429383i
$689$	69506.1			0.146415
$690$	−2856.39	−	21619.5i	−0.00599957	−	0.0454097i
$691$			254567.i			0.533147i	0.963815	+	0.266573i	$0.0858915\pi$
$691$			254567.i			0.533147i	−0.963815	+	0.266573i	$0.914109\pi$
$692$	−210251.	−	474230.i	−0.439062	−	0.990323i
$693$		−	313904.i		−	0.653627i
$694$	−123565.	−	583573.i	−0.256552	−	1.21165i
$695$	64477.4	−	832501.i	0.133487	−	1.72351i
$696$	159231.	+	220250.i	0.328707	+	0.454670i
$697$			90496.1i			0.186279i
$698$	112430.	+	530985.i	0.230765	+	1.08986i
$699$			84745.4i			0.173445i
$700$	648723.	−	174465.i	1.32392	−	0.356052i
$701$	626302.			1.27452			0.637262	−	0.770647i	$-0.280067\pi$
$701$	626302.			1.27452			0.637262	+	0.770647i	$0.280067\pi$
$702$	−86252.4	+	18262.9i	−0.175024	+	0.0370592i
$703$	−22043.2			−0.0446029
$704$	−673143.	−	222221.i	−1.35820	−	0.448373i
$705$	349682.	+	27083.0i	0.703551	+	0.0544902i
$706$	782183.	−	165618.i	1.56927	−	0.332275i
$707$	−1.21528e6			−2.43129
$708$	−19316.5	−	43569.3i	−0.0385357	−	0.0869188i
$709$	786562.			1.56473			0.782367	−	0.622817i	$-0.214012\pi$
$709$	786562.			1.56473			0.782367	+	0.622817i	$0.214012\pi$
$710$	−572538.	+	75644.2i	−1.13576	+	0.150058i
$711$			138474.i			0.273924i
$712$	226765.	+	313663.i	0.447318	+	0.618733i
$713$			72127.7i			0.141881i
$714$	−641045.	+	135734.i	−1.25745	+	0.266251i
$715$	677704.	+	52488.4i	1.32565	+	0.102672i
$716$	72883.4	+	164392.i	0.142168	+	0.320666i
$717$		−	222099.i		−	0.432023i
$718$	423251.	−	89618.2i	0.821011	−	0.173839i
$719$			331588.i			0.641417i	0.947178	+	0.320709i	$0.103921\pi$
$719$			331588.i			0.641417i	−0.947178	+	0.320709i	$0.896079\pi$
$720$	−125569.	+	118711.i	−0.242225	+	0.228994i
$721$	−465969.			−0.896368
$722$	39967.7	+	188760.i	0.0766716	+	0.362106i
$723$	−324321.			−0.620438
$724$	−334192.	+	148165.i	−0.637556	+	0.282662i
$725$	−504691.	−	78648.7i	−0.960173	−	0.149629i
$726$	−65918.7	−	311322.i	−0.125065	−	0.590659i
$727$	−575738.			−1.08932			−0.544660	−	0.838657i	$-0.683341\pi$
$727$	−575738.			−1.08932			−0.544660	+	0.838657i	$0.683341\pi$
$728$	−547381.	+	395733.i	−1.03282	+	0.746689i
$729$	19683.0			0.0370370
$730$	111307.	−	14706.0i	0.208871	−	0.0275962i
$731$		−	502788.i		−	0.940915i
$732$	−5186.10	+	2299.27i	−0.00967873	+	0.00429109i
$733$		−	142207.i		−	0.264675i	−0.991205	−	0.132338i	$-0.957752\pi$
$733$		−	142207.i		−	0.264675i	0.991205	−	0.132338i	$-0.0422483\pi$
$734$	74704.1	+	352814.i	0.138660	+	0.654868i
$735$	−273512.	−	21183.6i	−0.506292	−	0.0392125i
$736$	37133.5	+	21633.4i	0.0685505	+	0.0399365i
$737$		−	915181.i		−	1.68489i
$738$	−4314.01	−	20374.3i	−0.00792079	−	0.0374085i
$739$			657437.i			1.20383i	0.798560	+	0.601915i	$0.205595\pi$
$739$			657437.i			1.20383i	−0.798560	+	0.601915i	$0.794405\pi$
$740$	10263.6	+	29013.4i	0.0187430	+	0.0529828i
$741$	−233885.			−0.425957
$742$	−116304.	+	24625.9i	−0.211245	+	0.0447285i
$743$	19885.1			0.0360205			0.0180103	−	0.999838i	$-0.494267\pi$
$743$	19885.1			0.0360205			0.0180103	+	0.999838i	$0.494267\pi$
$744$	463169.	−	334851.i	0.836745	−	0.604931i
$745$	−155445.	−	12039.2i	−0.280068	−	0.0216913i
$746$	−303192.	+	64197.1i	−0.544803	+	0.115355i
$747$	116829.			0.209368
$748$	−1.18798e6	+	526695.i	−2.12328	+	0.941360i
$749$	−705626.			−1.25780
$750$	7544.10	−	324672.i	0.0134117	−	0.577194i
$751$		−	710161.i		−	1.25915i	−0.776941	−	0.629574i	$-0.783229\pi$
$751$		−	710161.i		−	1.25915i	0.776941	−	0.629574i	$-0.216771\pi$
$752$	−464096.	+	512194.i	−0.820677	+	0.905730i
$753$			32177.5i			0.0567495i
$754$	502437.	−	106385.i	0.883769	−	0.187127i
$755$	−20595.6	+	265920.i	−0.0361310	+	0.466506i
$756$	137855.	−	61118.2i	0.241200	−	0.106937i
$757$		−	509359.i		−	0.888857i	−0.895814	−	0.444428i	$-0.853407\pi$
$757$		−	509359.i		−	0.888857i	0.895814	−	0.444428i	$-0.146593\pi$
$758$	755579.	−	159985.i	1.31505	−	0.278445i
$759$			37741.1i			0.0655135i
$760$	−391121.	+	239084.i	−0.677148	+	0.413927i
$761$	−228429.			−0.394440			−0.197220	−	0.980359i	$-0.563191\pi$
$761$	−228429.			−0.394440			−0.197220	+	0.980359i	$0.563191\pi$
$762$	−22992.5	−	108589.i	−0.0395983	−	0.187015i
$763$	814234.			1.39862
$764$	30923.4	+	69749.0i	0.0529786	+	0.119495i
$765$	−24461.1	+	315829.i	−0.0417977	+	0.539672i
$766$	−23056.0	−	108889.i	−0.0392940	−	0.185579i
$767$	−90060.6			−0.153089
$768$	−33472.4	−	338886.i	−0.0567498	−	0.574554i
$769$	−266500.			−0.450655			−0.225328	−	0.974283i	$-0.572345\pi$
$769$	−266500.			−0.450655			−0.225328	+	0.974283i	$0.572345\pi$
$770$	−1.15259e6	+	152281.i	−1.94399	+	0.256841i
$771$			486788.i			0.818900i
$772$	−267926.	−	604318.i	−0.449552	−	1.01398i
$773$			295406.i			0.494379i	0.968967	+	0.247189i	$0.0795070\pi$
$773$			295406.i			0.494379i	−0.968967	+	0.247189i	$0.920493\pi$
$774$	23968.3	+	113198.i	0.0400087	+	0.188954i
$775$	−165392.	+	1.06133e6i	−0.275367	+	1.76704i
$776$	152820.	−	110482.i	0.253779	−	0.183472i
$777$		−	26856.4i		−	0.0444842i
$778$	56042.1	+	264677.i	0.0925881	+	0.437277i
$779$		−	55247.6i		−	0.0910414i
$780$	108900.	+	307841.i	0.178995	+	0.505985i
$781$	999475.			1.63859
$782$	77073.7	−	16319.4i	0.126035	−	0.0266865i
$783$	−114657.			−0.187016
$784$	363003.	−	400624.i	0.590579	−	0.651785i
$785$	−10042.2	+	129660.i	−0.0162963	+	0.210410i
$786$	−374713.	+	79340.9i	−0.606531	+	0.128426i
$787$	−629881.			−1.01697			−0.508486	−	0.861070i	$-0.669795\pi$
$787$	−629881.			−1.01697			−0.508486	+	0.861070i	$0.669795\pi$
$788$	−238635.	−	538250.i	−0.384309	−	0.866825i
$789$	−434898.			−0.698607
$790$	508450.	−	67176.8i	0.814692	−	0.107638i
$791$			907567.i			1.45053i
$792$	242354.	−	175212.i	0.386367	−	0.279327i
$793$			10720.0i			0.0170470i
$794$	838819.	−	177610.i	1.33054	−	0.281725i
$795$	−4437.93	+	57300.3i	−0.00702176	+	0.0906615i
$796$	−38511.7	−	86864.7i	−0.0607808	−	0.137094i
$797$		−	645614.i		−	1.01638i	−0.861245	−	0.508190i	$-0.830315\pi$
$797$		−	645614.i		−	1.01638i	0.861245	−	0.508190i	$-0.169685\pi$
$798$	391357.	−	82865.0i	0.614564	−	0.130126i
$799$			1.26706e6i			1.98474i
$800$	496797.	+	403476.i	0.776246	+	0.630431i
$801$	−163286.			−0.254498
$802$	64395.9	+	304130.i	0.100117	+	0.472837i
$803$	−194308.			−0.301342
$804$	401913.	−	178189.i	0.621755	−	0.275657i
$805$	70272.7	+	5442.64i	0.108441	+	0.00839882i
$806$	−223720.	−	1.05659e6i	−0.344377	−	1.62643i
$807$	−306610.			−0.470803
$808$	−678333.	−	938275.i	−1.03901	−	1.43717i
$809$	767971.			1.17340			0.586702	−	0.809803i	$-0.300426\pi$
$809$	767971.			1.17340			0.586702	+	0.809803i	$0.300426\pi$
$810$	−9548.64	−	72271.9i	−0.0145536	−	0.110154i
$811$			60142.3i			0.0914404i	0.998954	+	0.0457202i	$0.0145583\pi$
$811$			60142.3i			0.0914404i	−0.998954	+	0.0457202i	$0.985442\pi$
$812$	−803029.	+	356025.i	−1.21792	+	0.539969i
$813$			708391.i			1.07175i
$814$	−11032.8	−	52106.1i	−0.0166509	−	0.0786394i
$815$	−72626.0	−	5624.91i	−0.109339	−	0.00846838i
$816$	−462608.	−	419167.i	−0.694757	−	0.629516i
$817$			306951.i			0.459859i
$818$	−111829.	−	528146.i	−0.167127	−	0.789310i
$819$		−	284955.i		−	0.424823i
$820$	−72717.5	+	25724.2i	−0.108146	+	0.0382572i
$821$	−619797.			−0.919524			−0.459762	−	0.888042i	$-0.652065\pi$
$821$	−619797.			−0.919524			−0.459762	+	0.888042i	$0.652065\pi$
$822$	−461996.	+	97822.0i	−0.683745	+	0.144775i
$823$	−1.31597e6			−1.94288			−0.971442	−	0.237276i	$-0.923745\pi$
$823$	−1.31597e6			−1.94288			−0.971442	+	0.237276i	$0.923745\pi$
$824$	−260090.	−	359759.i	−0.383063	−	0.529855i
$825$	−86542.1	+	555343.i	−0.127151	+	0.815931i
$826$	150697.	−	31908.3i	0.220874	−	0.0467675i
$827$	1.09606e6			1.60259			0.801294	−	0.598270i	$-0.204145\pi$
$827$	1.09606e6			1.60259			0.801294	+	0.598270i	$0.204145\pi$
$828$	−16574.4	+	7348.32i	−0.0241756	+	0.0107183i
$829$	−128740.			−0.187328			−0.0936642	−	0.995604i	$-0.529858\pi$
$829$	−128740.			−0.187328			−0.0936642	+	0.995604i	$0.529858\pi$
$830$	−56676.3	−	428973.i	−0.0822707	−	0.622693i
$831$		−	248372.i		−	0.359667i
$832$	−611064.	−	201727.i	−0.882755	−	0.291419i
$833$		−	991060.i		−	1.42827i
$834$	−679144.	+	143800.i	−0.976404	+	0.206742i
$835$	242510.	+	18782.5i	0.347822	+	0.0269389i
$836$	725260.	−	321546.i	1.03772	−	0.460077i
$837$			241116.i			0.344171i
$838$	1.00330e6	−	212436.i	1.42870	−	0.302510i
$839$			483485.i			0.686846i	0.939181	+	0.343423i	$0.111586\pi$
$839$			483485.i			0.686846i	−0.939181	+	0.343423i	$0.888414\pi$
$840$	−291290.	−	476524.i	−0.412825	−	0.675346i
$841$	−39380.7			−0.0556791
$842$	166628.	+	786954.i	0.235030	+	1.11001i
$843$	753958.			1.06094
$844$	369690.	+	833852.i	0.518983	+	1.17059i
$845$	−96688.7	−	7488.57i	−0.135414	−	0.0104878i
$846$	−60401.7	−	285266.i	−0.0843934	−	0.398575i
$847$	1.02852e6			1.43366
$848$	−83930.1	−	76048.6i	−0.116715	−	0.105755i
$849$	402817.			0.558846
$850$	1.17153e6	−	63399.3i	1.62149	−	0.0877500i
$851$			3228.98i			0.00445867i
$852$	194601.	+	438931.i	0.268081	+	0.604668i
$853$			1.00959e6i			1.38754i	0.720197	+	0.693770i	$0.244051\pi$
$853$			1.00959e6i			1.38754i	−0.720197	+	0.693770i	$0.755949\pi$
$854$	−3798.08	−	17937.7i	−0.00520773	−	0.0245952i
$855$	14933.4	−	192813.i	0.0204281	−	0.263757i
$856$	−393860.	−	544790.i	−0.537519	−	0.743500i
$857$		−	308974.i		−	0.420688i	−0.977627	−	0.210344i	$-0.932542\pi$
$857$		−	308974.i		−	0.420688i	0.977627	−	0.210344i	$-0.0674585\pi$
$858$	−117062.	−	552863.i	−0.159016	−	0.751005i
$859$		−	728629.i		−	0.987461i	−0.869615	−	0.493731i	$-0.835633\pi$
$859$		−	728629.i		−	0.987461i	0.869615	−	0.493731i	$-0.164367\pi$
$860$	404012.	−	142921.i	0.546257	−	0.193241i
$861$	67311.2			0.0907990
$862$	567669.	−	120197.i	0.763978	−	0.161763i
$863$	−571918.			−0.767913			−0.383956	−	0.923351i	$-0.625439\pi$
$863$	−571918.			−0.767913			−0.383956	+	0.923351i	$0.625439\pi$
$864$	124134.	+	72318.4i	0.166288	+	0.0968771i
$865$	62589.4	−	808123.i	0.0836505	−	1.08005i
$866$	824391.	−	174555.i	1.09925	−	0.232754i
$867$	−710409.			−0.945083
$868$	748694.	+	1.68871e6i	0.993722	+	2.24138i
$869$	−887596.			−1.17537
$870$	55622.6	+	420998.i	0.0734874	+	0.556213i
$871$		−	830781.i		−	1.09509i
$872$	454482.	+	628643.i	0.597701	+	0.826743i
$873$			79554.7i			0.104385i
$874$	−47053.3	+	9962.97i	−0.0615981	+	0.0130427i
$875$	1.02155e6	+	241225.i	1.33427	+	0.315069i
$876$	−37832.4	−	85332.6i	−0.0493010	−	0.111201i
$877$			1.39530e6i			1.81413i	0.420994	+	0.907063i	$0.361681\pi$
$877$			1.39530e6i			1.81413i	−0.420994	+	0.907063i	$0.638319\pi$
$878$	−222292.	+	47067.7i	−0.288360	+	0.0610568i
$879$		−	304501.i		−	0.394104i
$880$	−760914.	−	804877.i	−0.982585	−	1.03936i
$881$	1.17759e6			1.51720			0.758599	−	0.651558i	$-0.225884\pi$
$881$	1.17759e6			1.51720			0.758599	+	0.651558i	$0.225884\pi$
$882$	47244.5	+	223127.i	0.0607316	+	0.286824i
$883$	420329.			0.539098			0.269549	−	0.962987i	$-0.413125\pi$
$883$	420329.			0.539098			0.269549	+	0.962987i	$0.413125\pi$
$884$	−1.07842e6	+	478121.i	−1.38002	+	0.611834i
$885$	5750.32	−	74245.3i	0.00734185	−	0.0947943i
$886$	172112.	+	812854.i	0.219252	+	1.03549i
$887$	1.07689e6			1.36875			0.684377	−	0.729128i	$-0.260074\pi$
$887$	1.07689e6			1.36875			0.684377	+	0.729128i	$0.260074\pi$
$888$	20734.9	−	14990.5i	0.0262952	−	0.0190103i
$889$	358750.			0.453930
$890$	79213.5	+	599553.i	0.100004	+	0.756916i
$891$			126165.i			0.158921i
$892$	1.20612e6	−	534736.i	1.51586	−	0.672062i
$893$		−	773538.i		−	0.970016i
$894$	26850.4	+	126810.i	0.0335951	+	0.158664i
$895$	−21696.6	+	280136.i	−0.0270860	+	0.349722i
$896$	1.09396e6	+	121048.i	1.36265	+	0.150780i
$897$			34260.5i			0.0425803i
$898$	−186113.	−	878979.i	−0.230794	−	1.09000i
$899$		−	1.40454e6i		−	1.73787i
$900$	−260736.	+	70121.3i	−0.321896	+	0.0865695i
$901$	−207626.			−0.255759
$902$	130596.	−	27652.1i	0.160515	−	0.0339871i
$903$	−373975.			−0.458635
$904$	−700702.	+	506578.i	−0.857425	+	0.619882i
$905$	−569488.	−	44107.0i	−0.695324	−	0.0538531i
$906$	216934.	−	45933.2i	0.264284	−	0.0559590i
$907$	−527683.			−0.641444			−0.320722	−	0.947173i	$-0.603925\pi$
$907$	−527683.			−0.641444			−0.320722	+	0.947173i	$0.603925\pi$
$908$	58034.3	−	25729.7i	0.0703904	−	0.0312077i
$909$	488446.			0.591138
$910$	−1.04630e6	+	138237.i	−1.26349	+	0.166933i
$911$			287925.i			0.346931i	0.984840	+	0.173465i	$0.0554965\pi$
$911$			287925.i			0.346931i	−0.984840	+	0.173465i	$0.944504\pi$
$912$	282421.	+	255900.i	0.339553	+	0.307667i
$913$			748855.i			0.898371i
$914$	−1.16889e6	+	247498.i	−1.39920	+	0.296265i
$915$	−8837.50	−	684.467i	−0.0105557	−	0.000817543i
$916$	−1.19503e6	+	529821.i	−1.42426	+	0.631449i
$917$		−	1.23795e6i		−	1.47219i
$918$	257650.	−	54554.2i	0.305734	−	0.0647355i
$919$		−	1.30507e6i		−	1.54527i	−0.634853	−	0.772633i	$-0.718939\pi$
$919$		−	1.30507e6i		−	1.54527i	0.634853	−	0.772633i	$-0.281061\pi$
$920$	35022.1	+	57293.1i	0.0413777	+	0.0676903i
$921$	−295946.			−0.348893
$922$	−168283.	−	794771.i	−0.197961	−	0.934932i
$923$	907301.			1.06500
$924$	391757.	+	883623.i	0.458852	+	1.03496i
$925$	−7404.20	+	47513.0i	−0.00865356	+	0.0555301i
$926$	282263.	+	1.33308e6i	0.329179	+	1.55465i
$927$	187283.			0.217941
$928$	−723102.	−	421268.i	−0.839661	−	0.489174i
$929$	368990.			0.427546			0.213773	−	0.976883i	$-0.431425\pi$
$929$	368990.			0.427546			0.213773	+	0.976883i	$0.431425\pi$
$930$	885327.	−	116970.i	1.02362	−	0.135241i
$931$			605040.i			0.698047i
$932$	−105764.	−	238554.i	−0.121760	−	0.274634i
$933$			387273.i			0.444892i
$934$	−17541.9	−	82847.2i	−0.0201086	−	0.0949695i
$935$	−2.02441e6	−	156791.i	−2.31566	−	0.179349i
$936$	220004.	−	159053.i	0.251118	−	0.181548i
$937$			916295.i			1.04365i	0.853052	+	0.521827i	$0.174749\pi$
$937$			916295.i			1.04365i	−0.853052	+	0.521827i	$0.825251\pi$
$938$	294344.	+	1.39013e6i	0.334541	+	1.57998i
$939$			846678.i			0.960256i
$940$	−1.01814e6	+	360171.i	−1.15226	+	0.407618i
$941$	369622.			0.417425			0.208713	−	0.977977i	$-0.433073\pi$
$941$	369622.			0.417425			0.208713	+	0.977977i	$0.433073\pi$
$942$	105775.	−	22396.6i	0.119201	−	0.0252395i
$943$	−8092.91			−0.00910084
$944$	108750.	+	98537.9i	0.122035	+	0.110576i
$945$	234915.	+	18194.2i	0.263055	+	0.0203737i
$946$	−725578.	+	153632.i	−0.810778	+	0.171672i
$947$	−191293.			−0.213304			−0.106652	−	0.994296i	$-0.534013\pi$
$947$	−191293.			−0.213304			−0.106652	+	0.994296i	$0.534013\pi$
$948$	−172818.	−	389798.i	−0.192297	−	0.433734i
$949$	−176388.			−0.195856
$950$	−715214.	+	38705.1i	−0.792481	+	0.0428866i
$951$			23599.2i			0.0260937i
$952$	1.63511e6	−	1.18212e6i	1.80415	−	1.30433i
$953$			389592.i			0.428967i	0.976728	+	0.214484i	$0.0688068\pi$
$953$			389592.i			0.428967i	−0.976728	+	0.214484i	$0.931193\pi$
$954$	46744.9	−	9897.66i	0.0513615	−	0.0108752i
$955$	−9205.56	+	118858.i	−0.0100935	+	0.130323i
$956$	277182.	+	625196.i	0.303284	+	0.684070i
$957$		−	734933.i		−	0.802460i
$958$	−920023.	+	194804.i	−1.00246	+	0.212259i
$959$		−	1.52631e6i		−	1.65961i
$960$	205319.	−	490877.i	0.222785	−	0.532635i
$961$	−2.03013e6			−2.19825
$962$	−10015.4	−	47300.8i	−0.0108222	−	0.0511114i
$963$	283606.			0.305818
$964$	912947.	−	404757.i	0.982407	−	0.435553i
$965$	79758.6	−	1.02980e6i	0.0856491	−	1.10586i
$966$	−12138.4	−	57327.6i	−0.0130079	−	0.0614341i
$967$	244501.			0.261474			0.130737	−	0.991417i	$-0.458266\pi$
$967$	244501.			0.261474			0.130737	+	0.991417i	$0.458266\pi$
$968$	574092.	+	794088.i	0.612676	+	0.847458i
$969$	698651.			0.744068
$970$	292109.	−	38593.7i	0.310457	−	0.0410178i
$971$			1.16665e6i			1.23738i	0.785635	+	0.618690i	$0.212336\pi$
$971$			1.16665e6i			1.23738i	−0.785635	+	0.618690i	$0.787664\pi$
$972$	−55406.6	+	24564.7i	−0.0586448	+	0.0260003i
$973$		−	2.24371e6i		−	2.36996i
$974$	256574.	+	1.21175e6i	0.270454	+	1.27731i
$975$	−78560.9	+	504128.i	−0.0826414	+	0.530312i
$976$	11729.1	−	12944.7i	0.0123130	−	0.0135891i
$977$			898266.i			0.941056i	0.882385	+	0.470528i	$0.155937\pi$
$977$			898266.i			0.941056i	−0.882385	+	0.470528i	$0.844063\pi$
$978$	12544.9	+	59247.4i	0.0131157	+	0.0619429i
$979$		−	1.04664e6i		−	1.09202i
$980$	796359.	−	281716.i	0.829195	−	0.293332i
$981$	−327258.			−0.340057
$982$	−623805.	+	132083.i	−0.646883	+	0.136970i
$983$	−820022.			−0.848630			−0.424315	−	0.905515i	$-0.639485\pi$
$983$	−820022.			−0.848630			−0.424315	+	0.905515i	$0.639485\pi$
$984$	37571.2	+	51968.7i	0.0388029	+	0.0536725i
$985$	71038.9	−	917219.i	0.0732190	−	0.945367i
$986$	−1.50086e6	+	317789.i	−1.54378	+	0.326877i
$987$	942443.			0.967433
$988$	658374.	−	291892.i	0.674464	−	0.299025i
$989$	44963.5			0.0459693
$990$	463250.	−	61205.1i	0.472656	−	0.0624478i
$991$		−	595036.i		−	0.605893i	−0.953007	−	0.302947i	$-0.902030\pi$
$991$		−	595036.i		−	0.605893i	0.953007	−	0.302947i	$-0.0979704\pi$
$992$	−885896.	+	1.52063e6i	−0.900243	+	1.54526i
$993$			20687.7i			0.0209804i
$994$	−1.51817e6	+	321455.i	−1.53656	+	0.325348i
$995$	11464.5	−	148024.i	0.0115800	−	0.149515i
$996$	−328868.	+	145805.i	−0.331515	+	0.146978i
$997$			1.51764e6i			1.52679i	0.645933	+	0.763394i	$0.276468\pi$
$997$			1.51764e6i			1.52679i	−0.645933	+	0.763394i	$0.723532\pi$
$998$	−1.15625e6	+	244822.i	−1.16089	+	0.245804i
$999$			10794.1i			0.0108158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.5.f.a.19.14	yes	24
3.2	odd	2		180.5.f.i.19.11		24
4.3	odd	2	inner	60.5.f.a.19.12	yes	24
5.2	odd	4		300.5.c.e.151.2		24
5.3	odd	4		300.5.c.e.151.23		24
5.4	even	2	inner	60.5.f.a.19.11	✓	24
8.3	odd	2		960.5.j.d.319.23		24
8.5	even	2		960.5.j.d.319.2		24
12.11	even	2		180.5.f.i.19.13		24
15.14	odd	2		180.5.f.i.19.14		24
20.3	even	4		300.5.c.e.151.24		24
20.7	even	4		300.5.c.e.151.1		24
20.19	odd	2	inner	60.5.f.a.19.13	yes	24
40.19	odd	2		960.5.j.d.319.11		24
40.29	even	2		960.5.j.d.319.14		24
60.59	even	2		180.5.f.i.19.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.f.a.19.11	✓	24	5.4	even	2	inner
60.5.f.a.19.12	yes	24	4.3	odd	2	inner
60.5.f.a.19.13	yes	24	20.19	odd	2	inner
60.5.f.a.19.14	yes	24	1.1	even	1	trivial
180.5.f.i.19.11		24	3.2	odd	2
180.5.f.i.19.12		24	60.59	even	2
180.5.f.i.19.13		24	12.11	even	2
180.5.f.i.19.14		24	15.14	odd	2
300.5.c.e.151.1		24	20.7	even	4
300.5.c.e.151.2		24	5.2	odd	4
300.5.c.e.151.23		24	5.3	odd	4
300.5.c.e.151.24		24	20.3	even	4
960.5.j.d.319.2		24	8.5	even	2
960.5.j.d.319.11		24	40.19	odd	2
960.5.j.d.319.14		24	40.29	even	2
960.5.j.d.319.23		24	8.3	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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	60.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.828581 + 3.91324i) q^{2} +5.19615 q^{3} +(-14.6269 + 6.48488i) q^{4} +(-24.9254 - 1.93048i) q^{5} +(4.30543 + 20.3338i) q^{6} -67.1774 q^{7} +(-37.4965 - 51.8654i) q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q+(0.828581 + 3.91324i) q^{2} +5.19615 q^{3} +(-14.6269 + 6.48488i) q^{4} +(-24.9254 - 1.93048i) q^{5} +(4.30543 + 20.3338i) q^{6} -67.1774 q^{7} +(-37.4965 - 51.8654i) q^{8} +27.0000 q^{9} +(-13.0983 - 99.1385i) q^{10} +173.065i q^{11} +(-76.0036 + 33.6964i) q^{12} +157.105i q^{13} +(-55.6619 - 262.881i) q^{14} +(-129.516 - 10.0310i) q^{15} +(171.893 - 189.707i) q^{16} -469.297i q^{17} +(22.3717 + 105.657i) q^{18} +286.504i q^{19} +(377.100 - 133.401i) q^{20} -349.064 q^{21} +(-677.246 + 143.399i) q^{22} +41.9684 q^{23} +(-194.837 - 269.500i) q^{24} +(617.547 + 96.2356i) q^{25} +(-614.788 + 130.174i) q^{26} +140.296 q^{27} +(982.597 - 435.637i) q^{28} -817.252 q^{29} +(-68.0606 - 515.139i) q^{30} +1718.62i q^{31} +(884.798 + 515.470i) q^{32} +899.273i q^{33} +(1836.47 - 388.850i) q^{34} +(1674.42 + 129.684i) q^{35} +(-394.926 + 175.092i) q^{36} +76.9383i q^{37} +(-1121.16 + 237.392i) q^{38} +816.340i q^{39} +(834.488 + 1365.15i) q^{40} -192.833 q^{41} +(-289.228 - 1365.97i) q^{42} +1071.37 q^{43} +(-1122.31 - 2531.41i) q^{44} +(-672.985 - 52.1229i) q^{45} +(34.7742 + 164.232i) q^{46} -2699.92 q^{47} +(893.181 - 985.748i) q^{48} +2111.80 q^{49} +(135.094 + 2496.35i) q^{50} -2438.54i q^{51} +(-1018.80 - 2297.95i) q^{52} -442.419i q^{53} +(116.247 + 549.012i) q^{54} +(334.098 - 4313.71i) q^{55} +(2518.91 + 3484.18i) q^{56} +1488.72i q^{57} +(-677.159 - 3198.10i) q^{58} +573.252i q^{59} +(1959.47 - 693.172i) q^{60} +68.2349 q^{61} +(-6725.37 + 1424.02i) q^{62} -1813.79 q^{63} +(-1284.03 + 3889.53i) q^{64} +(303.287 - 3915.89i) q^{65} +(-3519.07 + 745.121i) q^{66} -5288.07 q^{67} +(3043.33 + 6864.36i) q^{68} +218.074 q^{69} +(879.907 + 6659.86i) q^{70} -5775.14i q^{71} +(-1012.40 - 1400.36i) q^{72} +1122.74i q^{73} +(-301.078 + 63.7496i) q^{74} +(3208.87 + 500.055i) q^{75} +(-1857.95 - 4190.67i) q^{76} -11626.1i q^{77} +(-3194.53 + 676.404i) q^{78} +5128.68i q^{79} +(-4650.71 + 4396.69i) q^{80} +729.000 q^{81} +(-159.778 - 754.604i) q^{82} +4327.01 q^{83} +(5105.72 - 2263.64i) q^{84} +(-905.966 + 11697.4i) q^{85} +(887.714 + 4192.51i) q^{86} -4246.56 q^{87} +(8976.09 - 6489.33i) q^{88} -6047.64 q^{89} +(-353.653 - 2676.74i) q^{90} -10553.9i q^{91} +(-613.868 + 272.160i) q^{92} +8930.21i q^{93} +(-2237.10 - 10565.4i) q^{94} +(553.090 - 7141.22i) q^{95} +(4597.54 + 2678.46i) q^{96} +2946.47i q^{97} +(1749.80 + 8263.98i) q^{98} +4672.76i 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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