LMFDB - Embedded newform 60.5.f.a.19.11

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			19.11
Character	$\chi$	$=$	60.19
Dual form			60.5.f.a.19.12

$q$-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} +(28.2071 + 95.9394i) 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} +(352.062 - 189.875i) 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} +(-146.568 - 498.516i) 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} +(-1034.74 - 1220.38i) 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} +(-888.281 - 2336.87i) 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} +(-1829.37 + 986.618i) 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} +(1894.88 + 6444.95i) 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} +(-3918.26 + 5060.36i) 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} +(761.592 + 2590.36i) 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	$-0.259591\pi$
$7$	67.1774			1.37097			0.685483	+	0.728088i	$0.259591\pi$
$8$	37.4965	+	51.8654i	0.585882	+	0.810396i
$9$	27.0000			0.333333
$10$	28.2071	+	95.9394i	0.282071	+	0.959394i
$11$			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	$-0.846124\pi$
$13$		−	157.105i		−	0.929613i	0.885412	−	0.464807i	$-0.153876\pi$
$14$	−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	$0.301584\pi$
$17$			469.297i			1.62386i	−0.583752	+	0.811932i	$0.698416\pi$
$18$	−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	$0.870114\pi$
$20$	352.062	−	189.875i	0.880155	−	0.474687i
$21$	−349.064			−0.791528
$22$	677.246	−	143.399i	1.39927	−	0.296278i
$23$	−41.9684			−0.0793353			−0.0396677	−	0.999213i	$-0.512630\pi$
$23$	−41.9684			−0.0793353			−0.0396677	+	0.999213i	$0.512630\pi$
$24$	−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	$0.661501\pi$
$30$	−146.568	−	498.516i	−0.162854	−	0.553906i
$31$			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	$-0.991054\pi$
$37$		−	76.9383i		−	0.0562004i	0.999605	−	0.0281002i	$-0.00894574\pi$
$38$	1121.16	−	237.392i	0.776427	−	0.164399i
$39$			816.340i			0.536712i
$40$	−1034.74	−	1220.38i	−0.646711	−	0.762735i
$41$	−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	$-0.593561\pi$
$43$	−1071.37			−0.579430			−0.289715	+	0.957113i	$0.593561\pi$
$44$	−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	$-0.290720\pi$
$47$	2699.92			1.22223			0.611117	+	0.791540i	$0.290720\pi$
$48$	−893.181	+	985.748i	−0.387665	+	0.427842i
$49$	2111.80			0.879550
$50$	−888.281	−	2336.87i	−0.355312	−	0.934748i
$51$		−	2438.54i		−	0.937538i
$52$	1018.80	+	2297.95i	0.376777	+	0.849835i
$53$			442.419i			0.157501i	0.996894	+	0.0787503i	$0.0250930\pi$
$53$			442.419i			0.157501i	−0.996894	+	0.0787503i	$0.974907\pi$
$54$	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	$0.973761\pi$
$60$	−1829.37	+	986.618i	−0.508158	+	0.274061i
$61$	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	$-0.299521\pi$
$67$	5288.07			1.17801			0.589003	+	0.808131i	$0.299521\pi$
$68$	−3043.33	−	6864.36i	−0.658160	−	1.48451i
$69$	218.074			0.0458043
$70$	1894.88	+	6444.95i	0.386710	+	1.31530i
$71$		−	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	$-0.966406\pi$
$73$		−	1122.74i		−	0.210686i	0.994436	−	0.105343i	$-0.0335940\pi$
$74$	−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	$0.865219\pi$
$80$	−3918.26	+	5060.36i	−0.612228	+	0.790681i
$81$	729.000			0.111111
$82$	159.778	+	754.604i	0.0237624	+	0.112225i
$83$	−4327.01			−0.628104			−0.314052	−	0.949406i	$-0.601687\pi$
$83$	−4327.01			−0.628104			−0.314052	+	0.949406i	$0.601687\pi$
$84$	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	$0.624677\pi$
$90$	761.592	+	2590.36i	0.0940237	+	0.319798i
$91$		−	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	$-0.949954\pi$
$97$		−	2946.47i		−	0.313155i	0.987666	−	0.156577i	$-0.0500460\pi$
$98$	−1749.80	−	8263.98i	−0.182195	−	0.860473i
$99$			4672.76i			0.476764i
$100$	−8408.72	+	5412.34i	−0.840872	+	0.541234i
$101$	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	$-0.606008\pi$
$103$	−6936.39			−0.653822			−0.326911	+	0.945055i	$0.606008\pi$
$104$	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	$-0.651694\pi$
$107$	−10503.9			−0.917453			−0.458726	+	0.888578i	$0.651694\pi$
$108$	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	$0.670386\pi$
$110$	−16603.8	+	4881.67i	−1.37221	+	0.403444i
$111$			399.783i			0.0324473i
$112$	11547.3	−	12744.0i	0.920544	−	1.01595i
$113$			13510.0i			1.05803i	0.848612	+	0.529016i	$0.177439\pi$
$113$			13510.0i			1.05803i	−0.848612	+	0.529016i	$0.822561\pi$
$114$	−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
$120$	5376.65	+	6341.26i	0.373379	+	0.440365i
$121$	−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	$-0.447060\pi$
$127$	5340.34			0.331102			0.165551	+	0.986201i	$0.447060\pi$
$128$	16284.6	+	1801.92i	0.993934	+	0.109981i
$129$	5566.98			0.334534
$130$	15072.5	−	4431.47i	0.891865	−	0.262217i
$131$			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	$-0.793066\pi$
$137$		−	22720.6i		−	1.21054i	0.796021	−	0.605269i	$-0.206934\pi$
$138$	−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	$0.667738\pi$
$140$	23650.6	−	12755.3i	1.20666	−	0.650780i
$141$	−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	$0.455144\pi$
$150$	4615.64	+	12142.7i	0.205140	+	0.539677i
$151$		−	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	$0.0336508\pi$
$157$			5201.93i			0.211040i	−0.994417	+	0.105520i	$0.966349\pi$
$158$	20069.8	−	4249.53i	0.803948	−	0.170226i
$159$		−	2298.88i		−	0.0909330i
$160$	23049.0	+	11140.2i	0.900351	+	0.435163i
$161$	−2819.33			−0.108766
$162$	−604.036	−	2852.75i	−0.0230161	−	0.108701i
$163$	−2913.74			−0.109667			−0.0548335	−	0.998496i	$-0.517463\pi$
$163$	−2913.74			−0.109667			−0.0548335	+	0.998496i	$0.517463\pi$
$164$	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	$-0.444191\pi$
$167$	9729.46			0.348864			0.174432	+	0.984669i	$0.444191\pi$
$168$	−13088.7	−	18104.3i	−0.463742	−	0.641451i
$169$	3879.13			0.135819
$170$	−45024.0	+	13237.5i	−1.55792	+	0.458045i
$171$			7735.62i			0.264547i
$172$	15670.8	−	6947.68i	0.529704	−	0.234846i
$173$		−	32421.7i		−	1.08329i	−0.840608	−	0.541644i	$-0.817802\pi$
$173$		−	32421.7i		−	1.08329i	0.840608	−	0.541644i	$-0.182198\pi$
$174$	−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	$-0.0561168\pi$
$180$	9505.67	−	5126.62i	0.293385	−	0.158229i
$181$	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
$190$	−27487.0	+	8081.46i	−0.761414	+	0.223863i
$191$		−	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	$-0.812877\pi$
$193$		−	41315.5i		−	1.10917i	0.832127	−	0.554586i	$-0.187123\pi$
$194$	−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	$-0.842774\pi$
$197$		−	36798.6i		−	0.948198i	0.880471	−	0.474099i	$-0.157226\pi$
$198$	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	$0.976110\pi$
$200$	28147.1	+	28420.8i	0.703678	+	0.710519i
$201$	−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
$210$	−9846.08	−	33489.0i	−0.223267	−	0.759387i
$211$		−	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
$220$	32860.7	+	60929.7i	0.678940	+	1.25888i
$221$	73728.7			1.50956
$222$	1564.45	−	331.253i	0.0317435	−	0.00672130i
$223$	82458.9			1.65817			0.829083	−	0.559126i	$-0.188863\pi$
$223$	82458.9			1.65817			0.829083	+	0.559126i	$0.188863\pi$
$224$	−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	$-0.487742\pi$
$227$	3967.64			0.0769982			0.0384991	+	0.999259i	$0.487742\pi$
$228$	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	$0.215737\pi$
$230$	−1183.81	−	4026.42i	−0.0223782	−	0.0761138i
$231$		−	60410.8i		−	1.13212i
$232$	−30644.0	−	42387.0i	−0.569338	−	0.787512i
$233$		−	16309.3i		−	0.300416i	−0.988654	−	0.150208i	$-0.952006\pi$
$233$		−	16309.3i		−	0.300416i	0.988654	−	0.150208i	$-0.0479943\pi$
$234$	−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	$-0.122063\pi$
$240$	20359.9	−	26294.4i	0.353470	−	0.456500i
$241$	−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
$250$	26652.0	+	56532.5i	0.426432	+	0.904520i
$251$			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	$-0.749062\pi$
$257$		−	93682.3i		−	1.41838i	0.705019	−	0.709188i	$-0.250938\pi$
$258$	−4612.70	−	21784.9i	−0.0692972	−	0.327278i
$259$		−	5168.51i		−	0.0770488i
$260$	−29830.2	−	55310.6i	−0.441275	−	0.818204i
$261$	−22065.8			−0.323921
$262$	72113.5	−	15269.2i	1.05054	−	0.222440i
$263$	83696.1			1.21002			0.605012	−	0.796217i	$-0.293168\pi$
$263$	83696.1			1.21002			0.605012	+	0.796217i	$0.293168\pi$
$264$	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	$0.633679\pi$
$270$	−3957.35	−	13459.9i	−0.0542846	−	0.184635i
$271$			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	$0.100825\pi$
$277$			47799.2i			0.622961i	−0.950253	+	0.311480i	$0.899175\pi$
$278$	130701.	−	27674.4i	1.69118	−	0.358087i
$279$			46402.7i			0.596122i
$280$	−69510.9	−	81981.7i	−0.886619	−	1.04568i
$281$	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	$-0.660807\pi$
$283$	−77522.1			−0.967949			−0.483975	+	0.875082i	$0.660807\pi$
$284$	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
$290$	−23052.3	−	78406.6i	−0.274106	−	0.932302i
$291$			15310.3i			0.180800i
$292$	7280.86	+	16422.3i	0.0853919	+	0.192605i
$293$			58601.2i			0.682608i	0.939953	+	0.341304i	$0.110868\pi$
$293$			58601.2i			0.682608i	−0.939953	+	0.341304i	$0.889132\pi$
$294$	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
$300$	43693.0	−	28123.4i	0.485478	−	0.312482i
$301$	−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	$-0.402295\pi$
$307$	56954.8			0.604301			0.302151	+	0.953260i	$0.402295\pi$
$308$	−75393.6	−	170053.i	−0.794755	−	1.79260i
$309$	36042.6			0.377484
$310$	−164883.	+	48477.3i	−1.71575	+	0.504446i
$311$			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	$-0.687422\pi$
$313$		−	162943.i		−	1.66321i	0.555366	−	0.831606i	$-0.312578\pi$
$314$	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	$-0.992806\pi$
$317$		−	4541.66i		−	0.0451956i	0.999745	−	0.0225978i	$-0.00719372\pi$
$318$	−8996.06	+	1904.81i	−0.0889607	+	0.0188363i
$319$		−	141438.i		−	1.38990i
$320$	24496.3	−	99426.8i	0.239221	−	0.970965i
$321$	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
$330$	86275.7	−	25365.9i	0.792247	−	0.232928i
$331$			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	$0.271635\pi$
$337$			171148.i			1.50699i	−0.657451	+	0.753497i	$0.728365\pi$
$338$	−3214.18	−	15180.0i	−0.0281343	−	0.132873i
$339$		−	70200.1i		−	0.610855i
$340$	89107.6	+	165221.i	0.770827	+	1.42925i
$341$	−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	$-0.287434\pi$
$347$	149128.			1.23851			0.619256	+	0.785189i	$0.287434\pi$
$348$	−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	$0.311947\pi$
$350$	−59672.4	−	156985.i	−0.487121	−	1.28151i
$351$			22041.2i			0.178904i
$352$	89209.9	−	153128.i	0.719992	−	1.23586i
$353$			199881.i			1.60407i	0.597280	+	0.802033i	$0.296248\pi$
$353$			199881.i			1.60407i	−0.597280	+	0.802033i	$0.703752\pi$
$354$	−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	$-0.137832\pi$
$360$	−27937.9	−	32950.2i	−0.215570	−	0.254245i
$361$	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	$-0.608633\pi$
$367$	−90159.1			−0.669387			−0.334694	+	0.942327i	$0.608633\pi$
$368$	−7214.06	+	7961.71i	−0.0532702	+	0.0587910i
$369$	−5206.50			−0.0382379
$370$	7381.41	−	2170.21i	0.0539183	−	0.0158525i
$371$			29720.5i			0.215928i
$372$	57911.3	+	130621.i	0.418483	+	0.943905i
$373$		−	77478.4i		−	0.556882i	−0.960453	−	0.278441i	$-0.910182\pi$
$373$		−	77478.4i		−	0.556882i	0.960453	−	0.278441i	$-0.0898176\pi$
$374$	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	$-0.234608\pi$
$380$	54399.9	+	100867.i	0.376731	+	0.698527i
$381$	−27749.2			−0.191162
$382$	−18660.5	+	3951.13i	−0.127878	+	0.0270766i
$383$	27825.9			0.189693			0.0948465	−	0.995492i	$-0.469764\pi$
$383$	27825.9			0.189693			0.0948465	+	0.995492i	$0.469764\pi$
$384$	−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	$0.428256\pi$
$390$	−78319.1	+	23026.6i	−0.514918	+	0.151391i
$391$		−	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	$0.238028\pi$
$397$			214354.i			1.36004i	−0.733195	+	0.680019i	$0.761972\pi$
$398$	23239.5	−	4920.69i	0.146711	−	0.0310642i
$399$		−	100008.i		−	0.628189i
$400$	87895.2	−	133695.i	0.549345	−	0.835596i
$401$	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	$0.632173\pi$
$410$	−5439.27	−	18500.3i	−0.0323574	−	0.110055i
$411$			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	$-0.260568\pi$
$420$	−122892.	+	66278.4i	−0.696667	+	0.375728i
$421$	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
$430$	−30220.1	−	102786.i	−0.163440	−	0.555901i
$431$		−	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	$0.189896\pi$
$433$			210667.i			1.12362i	−0.827265	+	0.561812i	$0.810104\pi$
$434$	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	$0.952917\pi$
$440$	211205.	−	179077.i	1.09093	−	0.924985i
$441$	57018.6			0.293183
$442$	−61090.2	−	288518.i	−0.312699	−	1.47682i
$443$	−207719.			−1.05845			−0.529223	−	0.848483i	$-0.677517\pi$
$443$	−207719.			−1.05845			−0.529223	+	0.848483i	$0.677517\pi$
$444$	−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	$0.688079\pi$
$450$	−23983.6	−	63095.5i	−0.118437	−	0.311583i
$451$		−	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	$-0.746375\pi$
$457$		−	298701.i		−	1.43023i	0.699009	−	0.715113i	$-0.253625\pi$
$458$	−67696.0	−	319716.i	−0.322725	−	1.52417i
$459$		−	65840.5i		−	0.312513i
$460$	−14775.5	+	7968.74i	−0.0698274	+	0.0376594i
$461$	−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	$-0.792299\pi$
$463$	−340658.			−1.58912			−0.794560	+	0.607185i	$0.792299\pi$
$464$	−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	$-0.484544\pi$
$467$	21171.0			0.0970750			0.0485375	+	0.998821i	$0.484544\pi$
$468$	27507.7	+	62044.8i	0.125592	+	0.283278i
$469$	355239.			1.61501
$470$	76156.8	+	259028.i	0.344757	+	1.17260i
$471$		−	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	$0.828777\pi$
$480$	−119766.	−	57886.1i	−0.519818	−	0.251242i
$481$	−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	$-0.726411\pi$
$487$	−309654.			−1.30563			−0.652813	+	0.757519i	$0.726411\pi$
$488$	2558.57	+	3539.03i	0.0107438	+	0.0148609i
$489$	15140.2			0.0633162
$490$	59567.7	+	202605.i	0.248096	+	0.843834i
$491$			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	$0.797819\pi$
$500$	199142.	−	151137.i	0.796568	−	0.604550i
$501$	−50555.8			−0.201417
$502$	24233.0	−	5131.04i	0.0961610	−	0.0203609i
$503$	454123.			1.79489			0.897444	−	0.441129i	$-0.145422\pi$
$503$	454123.			1.79489			0.897444	+	0.441129i	$0.145422\pi$
$504$	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	$0.418160\pi$
$510$	233952.	−	68784.0i	0.899468	−	0.264452i
$511$		−	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
$520$	−191727.	+	162562.i	−0.709049	+	0.601191i
$521$	−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	$-0.486128\pi$
$523$	23833.6			0.0871336			0.0435668	+	0.999051i	$0.486128\pi$
$524$	−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
$530$	−42445.4	+	12479.4i	−0.151105	+	0.0444263i
$531$			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
$540$	−49392.9	+	26638.7i	−0.169386	+	0.0913535i
$541$	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	$-0.260605\pi$
$547$	408815.			1.36632			0.683160	+	0.730269i	$0.260605\pi$
$548$	147340.	+	332332.i	0.490637	+	1.10665i
$549$	1842.34			0.00611259
$550$	404431.	−	153730.i	1.33696	−	0.508200i
$551$		−	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	$-0.893875\pi$
$557$		−	203063.i		−	0.654518i	0.944935	−	0.327259i	$-0.106125\pi$
$558$	181585.	−	38448.4i	0.583192	−	0.123484i
$559$			168317.i			0.538646i
$560$	−263219.	+	339942.i	−0.839345	+	1.08400i
$561$	422026.			1.34095
$562$	−120227.	−	567808.i	−0.380652	−	1.79775i
$563$	324004.			1.02219			0.511097	−	0.859523i	$-0.329239\pi$
$563$	324004.			1.02219			0.511097	+	0.859523i	$0.329239\pi$
$564$	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	$0.413438\pi$
$570$	142827.	−	41992.5i	0.439603	−	0.129247i
$571$			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	$0.271923\pi$
$577$			502118.i			1.50818i	−0.656769	+	0.754092i	$0.728077\pi$
$578$	113282.	+	535011.i	0.339083	+	1.60143i
$579$			214682.i			0.640380i
$580$	−287723.	+	155175.i	−0.855301	+	0.461283i
$581$	−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	$-0.162010\pi$
$587$	601788.			1.74649			0.873247	+	0.487278i	$0.162010\pi$
$588$	160504.	−	71160.0i	0.464229	−	0.205817i
$589$	−492392.			−1.41932
$590$	−54997.5	+	16169.8i	−0.157993	+	0.0464516i
$591$			191211.i			0.547443i
$592$	−14595.8	−	13225.1i	−0.0416470	−	0.0377361i
$593$		−	267892.i		−	0.761816i	−0.924613	−	0.380908i	$-0.875611\pi$
$593$		−	267892.i		−	0.761816i	0.924613	−	0.380908i	$-0.124389\pi$
$594$	−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	$-0.0995808\pi$
$600$	−146257.	−	147679.i	−0.406268	−	0.410219i
$601$	−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	$-0.774111\pi$
$607$	−559003.			−1.51718			−0.758589	+	0.651569i	$0.774111\pi$
$608$	147684.	−	253498.i	0.399510	−	0.685754i
$609$	285273.			0.769177
$610$	1924.71	+	6546.41i	0.00517255	+	0.0175931i
$611$		−	424169.i		−	1.13621i
$612$	−82169.9	−	185338.i	−0.219387	−	0.494835i
$613$			373232.i			0.993250i	0.867965	+	0.496625i	$0.165427\pi$
$613$			373232.i			0.993250i	−0.867965	+	0.496625i	$0.834573\pi$
$614$	−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	$0.0227267\pi$
$617$			54314.8i			0.142675i	−0.997452	+	0.0713375i	$0.977273\pi$
$618$	−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	$-0.0779936\pi$
$620$	326322.	+	605061.i	0.848914	+	1.57404i
$621$	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
$630$	51161.7	+	174014.i	0.128903	+	0.438432i
$631$			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
$640$	−409378.	−	13476.5i	−0.999459	−	0.0329017i
$641$	−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	$-0.347296\pi$
$643$	381649.			0.923085			0.461542	+	0.887118i	$0.347296\pi$
$644$	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	$-0.534722\pi$
$647$	−91144.8			−0.217733			−0.108866	+	0.994056i	$0.534722\pi$
$648$	27334.9	+	37809.8i	0.0650980	+	0.0900440i
$649$	−99210.0			−0.235541
$650$	−367133.	+	139553.i	−0.868954	+	0.330303i
$651$		−	599908.i		−	1.41554i
$652$	42619.0	−	18895.2i	0.100255	−	0.0444485i
$653$			134420.i			0.315238i	0.987500	+	0.157619i	$0.0503818\pi$
$653$			134420.i			0.315238i	−0.987500	+	0.157619i	$0.949618\pi$
$654$	−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	$0.738096\pi$
$660$	−170749.	−	316600.i	−0.391986	−	0.726813i
$661$	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
$670$	149161.	+	507334.i	0.332281	+	1.13017i
$671$			11809.1i			0.0262284i
$672$	308851.	+	179932.i	0.683928	+	0.398446i
$673$		−	631019.i		−	1.39320i	−0.717461	−	0.696598i	$-0.754696\pi$
$673$		−	631019.i		−	1.39320i	0.717461	−	0.696598i	$-0.245304\pi$
$674$	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	$-0.639517\pi$
$677$		−	830008.i		−	1.81094i	0.424406	−	0.905472i	$-0.360483\pi$
$678$	−274710.	+	58166.5i	−0.597606	+	0.126536i
$679$		−	197936.i		−	0.429325i
$680$	572718.	−	485599.i	1.23858	−	1.05017i
$681$	−20616.5			−0.0444549
$682$	246448.	+	1.16393e6i	0.529854	+	2.50240i
$683$	−552394.			−1.18415			−0.592077	−	0.805882i	$-0.701692\pi$
$683$	−552394.			−1.18415			−0.592077	+	0.805882i	$0.701692\pi$
$684$	−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
$690$	6151.24	+	20921.9i	0.0129201	+	0.0439443i
$691$			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
$700$	−564876.	+	363587.i	−1.15281	+	0.742014i
$701$	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	$0.214012\pi$
$710$	554063.	−	162900.i	1.09911	−	0.323150i
$711$			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	$0.896079\pi$
$720$	−105793.	+	136630.i	−0.204076	+	0.263560i
$721$	−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	$-0.316659\pi$
$727$	575738.			1.08932			0.544660	+	0.838657i	$0.316659\pi$
$728$	547381.	−	395733.i	1.03282	−	0.746689i
$729$	19683.0			0.0370370
$730$	107715.	−	31669.4i	0.202130	−	0.0594283i
$731$		−	502788.i		−	0.940915i
$732$	5186.10	−	2299.27i	0.00967873	−	0.00429109i
$733$			142207.i			0.264675i	0.991205	+	0.132338i	$0.0422483\pi$
$733$			142207.i			0.264675i	−0.991205	+	0.132338i	$0.957752\pi$
$734$	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	$0.794405\pi$
$740$	−14608.6	−	27087.0i	−0.0266776	−	0.0494650i
$741$	−233885.			−0.425957
$742$	116304.	−	24625.9i	0.211245	−	0.0447285i
$743$	−19885.1			−0.0360205			−0.0180103	−	0.999838i	$-0.505733\pi$
$743$	−19885.1			−0.0360205			−0.0180103	+	0.999838i	$0.505733\pi$
$744$	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
$750$	−138488.	−	293751.i	−0.246200	−	0.522225i
$751$		−	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	$0.146593\pi$
$757$			509359.i			0.888857i	−0.895814	+	0.444428i	$0.853407\pi$
$758$	−755579.	+	159985.i	−1.31505	+	0.278445i
$759$			37741.1i			0.0655135i
$760$	349643.	−	296457.i	0.605338	−	0.513256i
$761$	−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	$0.572345\pi$
$770$	−1.11540e6	+	327938.i	−1.88126	+	0.553108i
$771$			486788.i			0.818900i
$772$	267926.	+	604318.i	0.449552	+	1.01398i
$773$		−	295406.i		−	0.494379i	−0.968967	−	0.247189i	$-0.920493\pi$
$773$		−	295406.i		−	0.494379i	0.968967	−	0.247189i	$-0.0795070\pi$
$774$	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
$780$	155002.	+	287402.i	0.254770	+	0.472390i
$781$	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	$-0.330205\pi$
$787$	629881.			1.01697			0.508486	+	0.861070i	$0.330205\pi$
$788$	238635.	+	538250.i	0.384309	+	0.866825i
$789$	−434898.			−0.698607
$790$	−492042.	+	144665.i	−0.788403	+	0.231798i
$791$			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	$0.169685\pi$
$797$			645614.i			1.01638i	−0.861245	+	0.508190i	$0.830315\pi$
$798$	−391357.	+	82865.0i	−0.614564	+	0.130126i
$799$			1.26706e6i			1.98474i
$800$	−596010.	−	233177.i	−0.931266	−	0.364340i
$801$	−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	$0.300426\pi$
$810$	20563.0	+	69939.8i	0.0313412	+	0.106599i
$811$			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
$820$	−67889.3	+	36614.2i	−0.100966	+	0.0544530i
$821$	−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	$-0.0762547\pi$
$823$	1.31597e6			1.94288			0.971442	+	0.237276i	$0.0762547\pi$
$824$	−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	$-0.795855\pi$
$827$	−1.09606e6			−1.60259			−0.801294	+	0.598270i	$0.795855\pi$
$828$	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	$0.529858\pi$
$830$	−122052.	−	415130.i	−0.177170	−	0.602599i
$831$		−	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	$0.888414\pi$
$840$	361189.	+	425989.i	0.511890	+	0.603726i
$841$	−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
$850$	1.09668e6	−	416867.i	1.51790	−	0.576979i
$851$			3228.98i			0.00445867i
$852$	−194601.	−	438931.i	−0.268081	−	0.604668i
$853$		−	1.00959e6i		−	1.38754i	−0.720197	−	0.693770i	$-0.755949\pi$
$853$		−	1.00959e6i		−	1.38754i	0.720197	−	0.693770i	$-0.244051\pi$
$854$	−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	$0.0674585\pi$
$857$			308974.i			0.420688i	−0.977627	+	0.210344i	$0.932542\pi$
$858$	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	$-0.164367\pi$
$860$	−377187.	+	203425.i	−0.509988	+	0.275048i
$861$	67311.2			0.0907990
$862$	−567669.	+	120197.i	−0.763978	+	0.161763i
$863$	571918.			0.767913			0.383956	−	0.923351i	$-0.374561\pi$
$863$	571918.			0.767913			0.383956	+	0.923351i	$0.374561\pi$
$864$	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
$870$	119783.	+	407413.i	0.158255	+	0.538265i
$871$		−	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	$-0.638319\pi$
$877$		−	1.39530e6i		−	1.81413i	0.420994	−	0.907063i	$-0.361681\pi$
$878$	222292.	−	47067.7i	0.288360	−	0.0610568i
$879$		−	304501.i		−	0.394104i
$880$	−875772.	−	678115.i	−1.13090	−	0.875665i
$881$	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	$-0.586875\pi$
$883$	−420329.			−0.539098			−0.269549	+	0.962987i	$0.586875\pi$
$884$	−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	$-0.739926\pi$
$887$	−1.07689e6			−1.36875			−0.684377	+	0.729128i	$0.739926\pi$
$888$	−20734.9	+	14990.5i	−0.0262952	+	0.0190103i
$889$	358750.			0.453930
$890$	−170586.	−	580206.i	−0.215360	−	0.732491i
$891$			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
$900$	−227035.	+	146133.i	−0.280291	+	0.180411i
$901$	−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	$-0.396075\pi$
$907$	527683.			0.641444			0.320722	+	0.947173i	$0.396075\pi$
$908$	−58034.3	+	25729.7i	−0.0703904	+	0.0312077i
$909$	488446.			0.591138
$910$	1.01253e6	−	297694.i	1.22272	−	0.359491i
$911$			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	$-0.281061\pi$
$920$	43426.3	+	51217.2i	0.0513070	+	0.0605119i
$921$	−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	$0.431425\pi$
$930$	856759.	−	251895.i	0.990587	−	0.291242i
$931$			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	$-0.825251\pi$
$937$		−	916295.i		−	1.04365i	0.853052	−	0.521827i	$-0.174749\pi$
$938$	−294344.	−	1.39013e6i	−0.334541	−	1.57998i
$939$			846678.i			0.960256i
$940$	950538.	−	512646.i	1.07576	−	0.580179i
$941$	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	$-0.465987\pi$
$947$	191293.			0.213304			0.106652	+	0.994296i	$0.465987\pi$
$948$	172818.	+	389798.i	0.192297	+	0.433734i
$949$	−176388.			−0.195856
$950$	669523.	−	254496.i	0.741854	−	0.281990i
$951$			23599.2i			0.0260937i
$952$	−1.63511e6	+	1.18212e6i	−1.80415	+	1.30433i
$953$		−	389592.i		−	0.428967i	−0.976728	−	0.214484i	$-0.931193\pi$
$953$		−	389592.i		−	0.428967i	0.976728	−	0.214484i	$-0.0688068\pi$
$954$	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
$960$	−127286.	+	516637.i	−0.138114	+	0.560587i
$961$	−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	$-0.541734\pi$
$967$	−244501.			−0.261474			−0.130737	+	0.991417i	$0.541734\pi$
$968$	−574092.	−	794088.i	−0.612676	−	0.847458i
$969$	698651.			0.744068
$970$	282683.	−	83111.4i	0.300439	−	0.0883319i
$971$			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	$-0.844063\pi$
$977$		−	898266.i		−	0.941056i	0.882385	−	0.470528i	$-0.155937\pi$
$978$	−12544.9	−	59247.4i	−0.0131157	−	0.0619429i
$979$		−	1.04664e6i		−	1.09202i
$980$	743484.	−	400977.i	0.774140	−	0.417511i
$981$	−327258.			−0.340057
$982$	623805.	−	132083.i	0.646883	−	0.136970i
$983$	820022.			0.848630			0.424315	−	0.905515i	$-0.360515\pi$
$983$	820022.			0.848630			0.424315	+	0.905515i	$0.360515\pi$
$984$	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
$990$	−448302.	+	131805.i	−0.457404	+	0.134481i
$991$		−	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	$-0.723532\pi$
$997$		−	1.51764e6i		−	1.52679i	0.645933	−	0.763394i	$-0.276468\pi$
$998$	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.19.11	✓	24
3.2	odd	2		180.5.f.i.19.14		24
4.3	odd	2	inner	60.5.f.a.19.13	yes	24
5.2	odd	4		300.5.c.e.151.23		24
5.3	odd	4		300.5.c.e.151.2		24
5.4	even	2	inner	60.5.f.a.19.14	yes	24
8.3	odd	2		960.5.j.d.319.11		24
8.5	even	2		960.5.j.d.319.14		24
12.11	even	2		180.5.f.i.19.12		24
15.14	odd	2		180.5.f.i.19.11		24
20.3	even	4		300.5.c.e.151.1		24
20.7	even	4		300.5.c.e.151.24		24
20.19	odd	2	inner	60.5.f.a.19.12	yes	24
40.19	odd	2		960.5.j.d.319.23		24
40.29	even	2		960.5.j.d.319.2		24
60.59	even	2		180.5.f.i.19.13		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.f.a.19.11	✓	24	1.1	even	1	trivial
60.5.f.a.19.12	yes	24	20.19	odd	2	inner
60.5.f.a.19.13	yes	24	4.3	odd	2	inner
60.5.f.a.19.14	yes	24	5.4	even	2	inner
180.5.f.i.19.11		24	15.14	odd	2
180.5.f.i.19.12		24	12.11	even	2
180.5.f.i.19.13		24	60.59	even	2
180.5.f.i.19.14		24	3.2	odd	2
300.5.c.e.151.1		24	20.3	even	4
300.5.c.e.151.2		24	5.3	odd	4
300.5.c.e.151.23		24	5.2	odd	4
300.5.c.e.151.24		24	20.7	even	4
960.5.j.d.319.2		24	40.29	even	2
960.5.j.d.319.11		24	8.3	odd	2
960.5.j.d.319.14		24	8.5	even	2
960.5.j.d.319.23		24	40.19	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} +(28.2071 + 95.9394i) 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} +(352.062 - 189.875i) 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} +(-146.568 - 498.516i) 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} +(-1034.74 - 1220.38i) 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} +(-888.281 - 2336.87i) 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} +(-1829.37 + 986.618i) 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} +(1894.88 + 6444.95i) 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} +(-3918.26 + 5060.36i) 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} +(761.592 + 2590.36i) 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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