LMFDB - Embedded newform 6034.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.a (trivial)

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:	yes
Analytic conductor:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.32592 q^{3} +1.00000 q^{4} +4.15520 q^{5} +3.32592 q^{6} -1.00000 q^{7} -1.00000 q^{8} +8.06177 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.32592 q^{3} +1.00000 q^{4} +4.15520 q^{5} +3.32592 q^{6} -1.00000 q^{7} -1.00000 q^{8} +8.06177 q^{9} -4.15520 q^{10} -4.14779 q^{11} -3.32592 q^{12} +3.57182 q^{13} +1.00000 q^{14} -13.8199 q^{15} +1.00000 q^{16} -4.73909 q^{17} -8.06177 q^{18} -1.24934 q^{19} +4.15520 q^{20} +3.32592 q^{21} +4.14779 q^{22} +5.30793 q^{23} +3.32592 q^{24} +12.2657 q^{25} -3.57182 q^{26} -16.8350 q^{27} -1.00000 q^{28} +4.77434 q^{29} +13.8199 q^{30} -6.09042 q^{31} -1.00000 q^{32} +13.7952 q^{33} +4.73909 q^{34} -4.15520 q^{35} +8.06177 q^{36} -2.20058 q^{37} +1.24934 q^{38} -11.8796 q^{39} -4.15520 q^{40} -10.0070 q^{41} -3.32592 q^{42} +10.1230 q^{43} -4.14779 q^{44} +33.4983 q^{45} -5.30793 q^{46} +4.90806 q^{47} -3.32592 q^{48} +1.00000 q^{49} -12.2657 q^{50} +15.7618 q^{51} +3.57182 q^{52} -11.4933 q^{53} +16.8350 q^{54} -17.2349 q^{55} +1.00000 q^{56} +4.15521 q^{57} -4.77434 q^{58} -7.59229 q^{59} -13.8199 q^{60} +3.14417 q^{61} +6.09042 q^{62} -8.06177 q^{63} +1.00000 q^{64} +14.8417 q^{65} -13.7952 q^{66} -8.81508 q^{67} -4.73909 q^{68} -17.6538 q^{69} +4.15520 q^{70} +1.65761 q^{71} -8.06177 q^{72} +9.33675 q^{73} +2.20058 q^{74} -40.7948 q^{75} -1.24934 q^{76} +4.14779 q^{77} +11.8796 q^{78} -10.3461 q^{79} +4.15520 q^{80} +31.8068 q^{81} +10.0070 q^{82} -4.70569 q^{83} +3.32592 q^{84} -19.6919 q^{85} -10.1230 q^{86} -15.8791 q^{87} +4.14779 q^{88} -10.9995 q^{89} -33.4983 q^{90} -3.57182 q^{91} +5.30793 q^{92} +20.2563 q^{93} -4.90806 q^{94} -5.19127 q^{95} +3.32592 q^{96} -6.90179 q^{97} -1.00000 q^{98} -33.4385 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9} - 13 q^{11} - 4 q^{12} + 17 q^{13} + 25 q^{14} - 18 q^{15} + 25 q^{16} - 4 q^{17} - 25 q^{18} - 9 q^{19} + 4 q^{21} + 13 q^{22} - 14 q^{23} + 4 q^{24} + 23 q^{25} - 17 q^{26} - 7 q^{27} - 25 q^{28} - 4 q^{29} + 18 q^{30} - 15 q^{31} - 25 q^{32} - 15 q^{33} + 4 q^{34} + 25 q^{36} + 13 q^{37} + 9 q^{38} - 31 q^{39} - 31 q^{41} - 4 q^{42} + 29 q^{43} - 13 q^{44} + 10 q^{45} + 14 q^{46} - 31 q^{47} - 4 q^{48} + 25 q^{49} - 23 q^{50} - 9 q^{51} + 17 q^{52} + 23 q^{53} + 7 q^{54} - 48 q^{55} + 25 q^{56} + 32 q^{57} + 4 q^{58} - 50 q^{59} - 18 q^{60} - 2 q^{61} + 15 q^{62} - 25 q^{63} + 25 q^{64} - 4 q^{65} + 15 q^{66} - 8 q^{67} - 4 q^{68} - 57 q^{69} - 61 q^{71} - 25 q^{72} + 31 q^{73} - 13 q^{74} - 21 q^{75} - 9 q^{76} + 13 q^{77} + 31 q^{78} - 10 q^{79} + 61 q^{81} + 31 q^{82} - 47 q^{83} + 4 q^{84} + 2 q^{85} - 29 q^{86} + 17 q^{87} + 13 q^{88} - 44 q^{89} - 10 q^{90} - 17 q^{91} - 14 q^{92} - 13 q^{93} + 31 q^{94} - 7 q^{95} + 4 q^{96} + 10 q^{97} - 25 q^{98} - 47 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9 - 13 * q^11 - 4 * q^12 + 17 * q^13 + 25 * q^14 - 18 * q^15 + 25 * q^16 - 4 * q^17 - 25 * q^18 - 9 * q^19 + 4 * q^21 + 13 * q^22 - 14 * q^23 + 4 * q^24 + 23 * q^25 - 17 * q^26 - 7 * q^27 - 25 * q^28 - 4 * q^29 + 18 * q^30 - 15 * q^31 - 25 * q^32 - 15 * q^33 + 4 * q^34 + 25 * q^36 + 13 * q^37 + 9 * q^38 - 31 * q^39 - 31 * q^41 - 4 * q^42 + 29 * q^43 - 13 * q^44 + 10 * q^45 + 14 * q^46 - 31 * q^47 - 4 * q^48 + 25 * q^49 - 23 * q^50 - 9 * q^51 + 17 * q^52 + 23 * q^53 + 7 * q^54 - 48 * q^55 + 25 * q^56 + 32 * q^57 + 4 * q^58 - 50 * q^59 - 18 * q^60 - 2 * q^61 + 15 * q^62 - 25 * q^63 + 25 * q^64 - 4 * q^65 + 15 * q^66 - 8 * q^67 - 4 * q^68 - 57 * q^69 - 61 * q^71 - 25 * q^72 + 31 * q^73 - 13 * q^74 - 21 * q^75 - 9 * q^76 + 13 * q^77 + 31 * q^78 - 10 * q^79 + 61 * q^81 + 31 * q^82 - 47 * q^83 + 4 * q^84 + 2 * q^85 - 29 * q^86 + 17 * q^87 + 13 * q^88 - 44 * q^89 - 10 * q^90 - 17 * q^91 - 14 * q^92 - 13 * q^93 + 31 * q^94 - 7 * q^95 + 4 * q^96 + 10 * q^97 - 25 * q^98 - 47 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.32592	−1.92022	−0.960111	−	0.279618i	$-0.909792\pi$
$3$	−3.32592	−1.92022	−0.960111	+	0.279618i	$0.909792\pi$
$4$	1.00000	0.500000
$5$	4.15520	1.85826	0.929132	−	0.369749i	$-0.120556\pi$
$5$	4.15520	1.85826	0.929132	+	0.369749i	$0.120556\pi$
$6$	3.32592	1.35780
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	8.06177	2.68726
$10$	−4.15520	−1.31399
$11$	−4.14779	−1.25060	−0.625302	−	0.780383i	$-0.715024\pi$
$11$	−4.14779	−1.25060	−0.625302	+	0.780383i	$0.715024\pi$
$12$	−3.32592	−0.960111
$13$	3.57182	0.990646	0.495323	−	0.868709i	$-0.335050\pi$
$13$	3.57182	0.990646	0.495323	+	0.868709i	$0.335050\pi$
$14$	1.00000	0.267261
$15$	−13.8199	−3.56828
$16$	1.00000	0.250000
$17$	−4.73909	−1.14940	−0.574699	−	0.818365i	$-0.694881\pi$
$17$	−4.73909	−1.14940	−0.574699	+	0.818365i	$0.694881\pi$
$18$	−8.06177	−1.90018
$19$	−1.24934	−0.286619	−0.143309	−	0.989678i	$-0.545774\pi$
$19$	−1.24934	−0.286619	−0.143309	+	0.989678i	$0.545774\pi$
$20$	4.15520	0.929132
$21$	3.32592	0.725776
$22$	4.14779	0.884311
$23$	5.30793	1.10678	0.553389	−	0.832923i	$-0.313334\pi$
$23$	5.30793	1.10678	0.553389	+	0.832923i	$0.313334\pi$
$24$	3.32592	0.678901
$25$	12.2657	2.45314
$26$	−3.57182	−0.700493
$27$	−16.8350	−3.23991
$28$	−1.00000	−0.188982
$29$	4.77434	0.886572	0.443286	−	0.896380i	$-0.353813\pi$
$29$	4.77434	0.886572	0.443286	+	0.896380i	$0.353813\pi$
$30$	13.8199	2.52316
$31$	−6.09042	−1.09387	−0.546936	−	0.837174i	$-0.684206\pi$
$31$	−6.09042	−1.09387	−0.546936	+	0.837174i	$0.684206\pi$
$32$	−1.00000	−0.176777
$33$	13.7952	2.40144
$34$	4.73909	0.812747
$35$	−4.15520	−0.702358
$36$	8.06177	1.34363
$37$	−2.20058	−0.361773	−0.180887	−	0.983504i	$-0.557897\pi$
$37$	−2.20058	−0.361773	−0.180887	+	0.983504i	$0.557897\pi$
$38$	1.24934	0.202670
$39$	−11.8796	−1.90226
$40$	−4.15520	−0.656995
$41$	−10.0070	−1.56283	−0.781415	−	0.624012i	$-0.785502\pi$
$41$	−10.0070	−1.56283	−0.781415	+	0.624012i	$0.785502\pi$
$42$	−3.32592	−0.513201
$43$	10.1230	1.54375	0.771873	−	0.635777i	$-0.219320\pi$
$43$	10.1230	1.54375	0.771873	+	0.635777i	$0.219320\pi$
$44$	−4.14779	−0.625302
$45$	33.4983	4.99363
$46$	−5.30793	−0.782611
$47$	4.90806	0.715914	0.357957	−	0.933738i	$-0.383473\pi$
$47$	4.90806	0.715914	0.357957	+	0.933738i	$0.383473\pi$
$48$	−3.32592	−0.480056
$49$	1.00000	0.142857
$50$	−12.2657	−1.73463
$51$	15.7618	2.20710
$52$	3.57182	0.495323
$53$	−11.4933	−1.57873	−0.789366	−	0.613923i	$-0.789590\pi$
$53$	−11.4933	−1.57873	−0.789366	+	0.613923i	$0.789590\pi$
$54$	16.8350	2.29096
$55$	−17.2349	−2.32395
$56$	1.00000	0.133631
$57$	4.15521	0.550372
$58$	−4.77434	−0.626901
$59$	−7.59229	−0.988432	−0.494216	−	0.869339i	$-0.664545\pi$
$59$	−7.59229	−0.988432	−0.494216	+	0.869339i	$0.664545\pi$
$60$	−13.8199	−1.78414
$61$	3.14417	0.402570	0.201285	−	0.979533i	$-0.435488\pi$
$61$	3.14417	0.402570	0.201285	+	0.979533i	$0.435488\pi$
$62$	6.09042	0.773484
$63$	−8.06177	−1.01569
$64$	1.00000	0.125000
$65$	14.8417	1.84088
$66$	−13.7952	−1.69807
$67$	−8.81508	−1.07693	−0.538467	−	0.842647i	$-0.680996\pi$
$67$	−8.81508	−1.07693	−0.538467	+	0.842647i	$0.680996\pi$
$68$	−4.73909	−0.574699
$69$	−17.6538	−2.12526
$70$	4.15520	0.496642
$71$	1.65761	0.196722	0.0983610	−	0.995151i	$-0.468640\pi$
$71$	1.65761	0.196722	0.0983610	+	0.995151i	$0.468640\pi$
$72$	−8.06177	−0.950088
$73$	9.33675	1.09278	0.546392	−	0.837529i	$-0.316001\pi$
$73$	9.33675	1.09278	0.546392	+	0.837529i	$0.316001\pi$
$74$	2.20058	0.255812
$75$	−40.7948	−4.71058
$76$	−1.24934	−0.143309
$77$	4.14779	0.472684
$78$	11.8796	1.34510
$79$	−10.3461	−1.16403	−0.582016	−	0.813177i	$-0.697736\pi$
$79$	−10.3461	−1.16403	−0.582016	+	0.813177i	$0.697736\pi$
$80$	4.15520	0.464566
$81$	31.8068	3.53409
$82$	10.0070	1.10509
$83$	−4.70569	−0.516516	−0.258258	−	0.966076i	$-0.583148\pi$
$83$	−4.70569	−0.516516	−0.258258	+	0.966076i	$0.583148\pi$
$84$	3.32592	0.362888
$85$	−19.6919	−2.13588
$86$	−10.1230	−1.09159
$87$	−15.8791	−1.70242
$88$	4.14779	0.442155
$89$	−10.9995	−1.16595	−0.582974	−	0.812491i	$-0.698111\pi$
$89$	−10.9995	−1.16595	−0.582974	+	0.812491i	$0.698111\pi$
$90$	−33.4983	−3.53103
$91$	−3.57182	−0.374429
$92$	5.30793	0.553389
$93$	20.2563	2.10048
$94$	−4.90806	−0.506228
$95$	−5.19127	−0.532613
$96$	3.32592	0.339451
$97$	−6.90179	−0.700771	−0.350386	−	0.936606i	$-0.613949\pi$
$97$	−6.90179	−0.700771	−0.350386	+	0.936606i	$0.613949\pi$
$98$	−1.00000	−0.101015
$99$	−33.4385	−3.36069
$100$	12.2657	1.22657
$101$	−8.01224	−0.797248	−0.398624	−	0.917114i	$-0.630512\pi$
$101$	−8.01224	−0.797248	−0.398624	+	0.917114i	$0.630512\pi$
$102$	−15.7618	−1.56065
$103$	4.56273	0.449579	0.224790	−	0.974407i	$-0.427830\pi$
$103$	4.56273	0.449579	0.224790	+	0.974407i	$0.427830\pi$
$104$	−3.57182	−0.350246
$105$	13.8199	1.34868
$106$	11.4933	1.11633
$107$	−0.590211	−0.0570578	−0.0285289	−	0.999593i	$-0.509082\pi$
$107$	−0.590211	−0.0570578	−0.0285289	+	0.999593i	$0.509082\pi$
$108$	−16.8350	−1.61995
$109$	−7.56684	−0.724772	−0.362386	−	0.932028i	$-0.618038\pi$
$109$	−7.56684	−0.724772	−0.362386	+	0.932028i	$0.618038\pi$
$110$	17.2349	1.64328
$111$	7.31896	0.694685
$112$	−1.00000	−0.0944911
$113$	1.23216	0.115912	0.0579560	−	0.998319i	$-0.481542\pi$
$113$	1.23216	0.115912	0.0579560	+	0.998319i	$0.481542\pi$
$114$	−4.15521	−0.389171
$115$	22.0555	2.05669
$116$	4.77434	0.443286
$117$	28.7952	2.66212
$118$	7.59229	0.698927
$119$	4.73909	0.434431
$120$	13.8199	1.26158
$121$	6.20412	0.564011
$122$	−3.14417	−0.284660
$123$	33.2825	3.00098
$124$	−6.09042	−0.546936
$125$	30.1905	2.70032
$126$	8.06177	0.718199
$127$	1.07177	0.0951042	0.0475521	−	0.998869i	$-0.484858\pi$
$127$	1.07177	0.0951042	0.0475521	+	0.998869i	$0.484858\pi$
$128$	−1.00000	−0.0883883
$129$	−33.6684	−2.96434
$130$	−14.8417	−1.30170
$131$	14.0851	1.23062	0.615310	−	0.788285i	$-0.289031\pi$
$131$	14.0851	1.23062	0.615310	+	0.788285i	$0.289031\pi$
$132$	13.7952	1.20072
$133$	1.24934	0.108332
$134$	8.81508	0.761507
$135$	−69.9531	−6.02060
$136$	4.73909	0.406373
$137$	−9.87931	−0.844046	−0.422023	−	0.906585i	$-0.638680\pi$
$137$	−9.87931	−0.844046	−0.422023	+	0.906585i	$0.638680\pi$
$138$	17.6538	1.50279
$139$	4.69638	0.398342	0.199171	−	0.979965i	$-0.436175\pi$
$139$	4.69638	0.398342	0.199171	+	0.979965i	$0.436175\pi$
$140$	−4.15520	−0.351179
$141$	−16.3238	−1.37471
$142$	−1.65761	−0.139103
$143$	−14.8152	−1.23891
$144$	8.06177	0.671814
$145$	19.8383	1.64748
$146$	−9.33675	−0.772715
$147$	−3.32592	−0.274318
$148$	−2.20058	−0.180887
$149$	−23.0519	−1.88849	−0.944243	−	0.329251i	$-0.893204\pi$
$149$	−23.0519	−1.88849	−0.944243	+	0.329251i	$0.893204\pi$
$150$	40.7948	3.33088
$151$	−10.1651	−0.827227	−0.413613	−	0.910453i	$-0.635733\pi$
$151$	−10.1651	−0.827227	−0.413613	+	0.910453i	$0.635733\pi$
$152$	1.24934	0.101335
$153$	−38.2054	−3.08872
$154$	−4.14779	−0.334238
$155$	−25.3069	−2.03270
$156$	−11.8796	−0.951131
$157$	−0.331034	−0.0264194	−0.0132097	−	0.999913i	$-0.504205\pi$
$157$	−0.331034	−0.0264194	−0.0132097	+	0.999913i	$0.504205\pi$
$158$	10.3461	0.823095
$159$	38.2260	3.03152
$160$	−4.15520	−0.328498
$161$	−5.30793	−0.418323
$162$	−31.8068	−2.49898
$163$	10.7819	0.844507	0.422254	−	0.906478i	$-0.361239\pi$
$163$	10.7819	0.844507	0.422254	+	0.906478i	$0.361239\pi$
$164$	−10.0070	−0.781415
$165$	57.3219	4.46251
$166$	4.70569	0.365232
$167$	−20.9818	−1.62362	−0.811808	−	0.583924i	$-0.801517\pi$
$167$	−20.9818	−1.62362	−0.811808	+	0.583924i	$0.801517\pi$
$168$	−3.32592	−0.256601
$169$	−0.242067	−0.0186205
$170$	19.6919	1.51030
$171$	−10.0719	−0.770217
$172$	10.1230	0.771873
$173$	14.9567	1.13713	0.568567	−	0.822637i	$-0.307498\pi$
$173$	14.9567	1.13713	0.568567	+	0.822637i	$0.307498\pi$
$174$	15.8791	1.20379
$175$	−12.2657	−0.927201
$176$	−4.14779	−0.312651
$177$	25.2514	1.89801
$178$	10.9995	0.824449
$179$	17.4648	1.30538	0.652689	−	0.757626i	$-0.273641\pi$
$179$	17.4648	1.30538	0.652689	+	0.757626i	$0.273641\pi$
$180$	33.4983	2.49681
$181$	5.60412	0.416551	0.208276	−	0.978070i	$-0.433215\pi$
$181$	5.60412	0.416551	0.208276	+	0.978070i	$0.433215\pi$
$182$	3.57182	0.264761
$183$	−10.4573	−0.773024
$184$	−5.30793	−0.391305
$185$	−9.14386	−0.672270
$186$	−20.2563	−1.48526
$187$	19.6567	1.43744
$188$	4.90806	0.357957
$189$	16.8350	1.22457
$190$	5.19127	0.376614
$191$	21.2624	1.53849	0.769246	−	0.638953i	$-0.220632\pi$
$191$	21.2624	1.53849	0.769246	+	0.638953i	$0.220632\pi$
$192$	−3.32592	−0.240028
$193$	21.1435	1.52194	0.760972	−	0.648785i	$-0.224722\pi$
$193$	21.1435	1.52194	0.760972	+	0.648785i	$0.224722\pi$
$194$	6.90179	0.495520
$195$	−49.3622	−3.53490
$196$	1.00000	0.0714286
$197$	−2.33280	−0.166205	−0.0831027	−	0.996541i	$-0.526483\pi$
$197$	−2.33280	−0.166205	−0.0831027	+	0.996541i	$0.526483\pi$
$198$	33.4385	2.37637
$199$	4.24009	0.300572	0.150286	−	0.988643i	$-0.451981\pi$
$199$	4.24009	0.300572	0.150286	+	0.988643i	$0.451981\pi$
$200$	−12.2657	−0.867317
$201$	29.3183	2.06795
$202$	8.01224	0.563739
$203$	−4.77434	−0.335093
$204$	15.7618	1.10355
$205$	−41.5811	−2.90415
$206$	−4.56273	−0.317901
$207$	42.7913	2.97420
$208$	3.57182	0.247661
$209$	5.18200	0.358446
$210$	−13.8199	−0.953663
$211$	23.1931	1.59668	0.798341	−	0.602206i	$-0.205711\pi$
$211$	23.1931	1.59668	0.798341	+	0.602206i	$0.205711\pi$
$212$	−11.4933	−0.789366
$213$	−5.51308	−0.377750
$214$	0.590211	0.0403460
$215$	42.0632	2.86869
$216$	16.8350	1.14548
$217$	6.09042	0.413445
$218$	7.56684	0.512491
$219$	−31.0533	−2.09839
$220$	−17.2349	−1.16198
$221$	−16.9272	−1.13865
$222$	−7.31896	−0.491217
$223$	0.258124	0.0172852	0.00864262	−	0.999963i	$-0.497249\pi$
$223$	0.258124	0.0172852	0.00864262	+	0.999963i	$0.497249\pi$
$224$	1.00000	0.0668153
$225$	98.8833	6.59222
$226$	−1.23216	−0.0819621
$227$	24.1299	1.60156	0.800778	−	0.598962i	$-0.204420\pi$
$227$	24.1299	1.60156	0.800778	+	0.598962i	$0.204420\pi$
$228$	4.15521	0.275186
$229$	−4.98929	−0.329701	−0.164851	−	0.986319i	$-0.552714\pi$
$229$	−4.98929	−0.329701	−0.164851	+	0.986319i	$0.552714\pi$
$230$	−22.0555	−1.45430
$231$	−13.7952	−0.907659
$232$	−4.77434	−0.313451
$233$	1.11900	0.0733082	0.0366541	−	0.999328i	$-0.488330\pi$
$233$	1.11900	0.0733082	0.0366541	+	0.999328i	$0.488330\pi$
$234$	−28.7952	−1.88240
$235$	20.3940	1.33036
$236$	−7.59229	−0.494216
$237$	34.4105	2.23520
$238$	−4.73909	−0.307189
$239$	5.30099	0.342893	0.171446	−	0.985193i	$-0.445156\pi$
$239$	5.30099	0.342893	0.171446	+	0.985193i	$0.445156\pi$
$240$	−13.8199	−0.892070
$241$	19.9890	1.28760	0.643801	−	0.765193i	$-0.277356\pi$
$241$	19.9890	1.28760	0.643801	+	0.765193i	$0.277356\pi$
$242$	−6.20412	−0.398816
$243$	−55.2818	−3.54633
$244$	3.14417	0.201285
$245$	4.15520	0.265466
$246$	−33.2825	−2.12201
$247$	−4.46243	−0.283938
$248$	6.09042	0.386742
$249$	15.6508	0.991826
$250$	−30.1905	−1.90942
$251$	−24.1883	−1.52675	−0.763377	−	0.645953i	$-0.776460\pi$
$251$	−24.1883	−1.52675	−0.763377	+	0.645953i	$0.776460\pi$
$252$	−8.06177	−0.507844
$253$	−22.0161	−1.38414
$254$	−1.07177	−0.0672488
$255$	65.4936	4.10137
$256$	1.00000	0.0625000
$257$	−3.85068	−0.240199	−0.120099	−	0.992762i	$-0.538321\pi$
$257$	−3.85068	−0.240199	−0.120099	+	0.992762i	$0.538321\pi$
$258$	33.6684	2.09610
$259$	2.20058	0.136737
$260$	14.8417	0.920441
$261$	38.4896	2.38245
$262$	−14.0851	−0.870180
$263$	−6.21917	−0.383491	−0.191745	−	0.981445i	$-0.561415\pi$
$263$	−6.21917	−0.383491	−0.191745	+	0.981445i	$0.561415\pi$
$264$	−13.7952	−0.849037
$265$	−47.7572	−2.93370
$266$	−1.24934	−0.0766020
$267$	36.5836	2.23888
$268$	−8.81508	−0.538467
$269$	−31.9651	−1.94895	−0.974473	−	0.224503i	$-0.927924\pi$
$269$	−31.9651	−1.94895	−0.974473	+	0.224503i	$0.927924\pi$
$270$	69.9531	4.25721
$271$	−32.3490	−1.96506	−0.982530	−	0.186102i	$-0.940414\pi$
$271$	−32.3490	−1.96506	−0.982530	+	0.186102i	$0.940414\pi$
$272$	−4.73909	−0.287349
$273$	11.8796	0.718987
$274$	9.87931	0.596831
$275$	−50.8756	−3.06791
$276$	−17.6538	−1.06263
$277$	−2.59917	−0.156169	−0.0780846	−	0.996947i	$-0.524880\pi$
$277$	−2.59917	−0.156169	−0.0780846	+	0.996947i	$0.524880\pi$
$278$	−4.69638	−0.281670
$279$	−49.0996	−2.93951
$280$	4.15520	0.248321
$281$	3.96402	0.236474	0.118237	−	0.992985i	$-0.462276\pi$
$281$	3.96402	0.236474	0.118237	+	0.992985i	$0.462276\pi$
$282$	16.3238	0.972070
$283$	−27.6125	−1.64139	−0.820697	−	0.571364i	$-0.806415\pi$
$283$	−27.6125	−1.64139	−0.820697	+	0.571364i	$0.806415\pi$
$284$	1.65761	0.0983610
$285$	17.2658	1.02274
$286$	14.8152	0.876039
$287$	10.0070	0.590694
$288$	−8.06177	−0.475044
$289$	5.45894	0.321114
$290$	−19.8383	−1.16495
$291$	22.9548	1.34564
$292$	9.33675	0.546392
$293$	17.0053	0.993463	0.496732	−	0.867904i	$-0.334533\pi$
$293$	17.0053	0.993463	0.496732	+	0.867904i	$0.334533\pi$
$294$	3.32592	0.193972
$295$	−31.5475	−1.83677
$296$	2.20058	0.127906
$297$	69.8282	4.05184
$298$	23.0519	1.33536
$299$	18.9590	1.09643
$300$	−40.7948	−2.35529
$301$	−10.1230	−0.583481
$302$	10.1651	0.584938
$303$	26.6481	1.53089
$304$	−1.24934	−0.0716546
$305$	13.0647	0.748081
$306$	38.2054	2.18406
$307$	−12.1576	−0.693868	−0.346934	−	0.937890i	$-0.612777\pi$
$307$	−12.1576	−0.693868	−0.346934	+	0.937890i	$0.612777\pi$
$308$	4.14779	0.236342
$309$	−15.1753	−0.863293
$310$	25.3069	1.43734
$311$	27.3615	1.55153	0.775765	−	0.631022i	$-0.217364\pi$
$311$	27.3615	1.55153	0.775765	+	0.631022i	$0.217364\pi$
$312$	11.8796	0.672551
$313$	−0.716490	−0.0404984	−0.0202492	−	0.999795i	$-0.506446\pi$
$313$	−0.716490	−0.0404984	−0.0202492	+	0.999795i	$0.506446\pi$
$314$	0.331034	0.0186813
$315$	−33.4983	−1.88741
$316$	−10.3461	−0.582016
$317$	−12.0029	−0.674151	−0.337075	−	0.941478i	$-0.609438\pi$
$317$	−12.0029	−0.674151	−0.337075	+	0.941478i	$0.609438\pi$
$318$	−38.2260	−2.14361
$319$	−19.8029	−1.10875
$320$	4.15520	0.232283
$321$	1.96300	0.109564
$322$	5.30793	0.295799
$323$	5.92074	0.329439
$324$	31.8068	1.76704
$325$	43.8110	2.43020
$326$	−10.7819	−0.597157
$327$	25.1667	1.39172
$328$	10.0070	0.552544
$329$	−4.90806	−0.270590
$330$	−57.3219	−3.15547
$331$	−15.8687	−0.872225	−0.436113	−	0.899892i	$-0.643645\pi$
$331$	−15.8687	−0.872225	−0.436113	+	0.899892i	$0.643645\pi$
$332$	−4.70569	−0.258258
$333$	−17.7406	−0.972177
$334$	20.9818	1.14807
$335$	−36.6284	−2.00123
$336$	3.32592	0.181444
$337$	−10.8880	−0.593106	−0.296553	−	0.955016i	$-0.595837\pi$
$337$	−10.8880	−0.593106	−0.296553	+	0.955016i	$0.595837\pi$
$338$	0.242067	0.0131667
$339$	−4.09807	−0.222577
$340$	−19.6919	−1.06794
$341$	25.2618	1.36800
$342$	10.0719	0.544626
$343$	−1.00000	−0.0539949
$344$	−10.1230	−0.545796
$345$	−73.3549	−3.94930
$346$	−14.9567	−0.804075
$347$	16.0460	0.861396	0.430698	−	0.902496i	$-0.358267\pi$
$347$	16.0460	0.861396	0.430698	+	0.902496i	$0.358267\pi$
$348$	−15.8791	−0.851208
$349$	−12.8343	−0.687005	−0.343503	−	0.939152i	$-0.611613\pi$
$349$	−12.8343	−0.687005	−0.343503	+	0.939152i	$0.611613\pi$
$350$	12.2657	0.655630
$351$	−60.1318	−3.20960
$352$	4.14779	0.221078
$353$	−10.6659	−0.567687	−0.283844	−	0.958871i	$-0.591610\pi$
$353$	−10.6659	−0.567687	−0.283844	+	0.958871i	$0.591610\pi$
$354$	−25.2514	−1.34210
$355$	6.88770	0.365561
$356$	−10.9995	−0.582974
$357$	−15.7618	−0.834205
$358$	−17.4648	−0.923041
$359$	3.83799	0.202561	0.101281	−	0.994858i	$-0.467706\pi$
$359$	3.83799	0.202561	0.101281	+	0.994858i	$0.467706\pi$
$360$	−33.4983	−1.76551
$361$	−17.4391	−0.917850
$362$	−5.60412	−0.294546
$363$	−20.6344	−1.08303
$364$	−3.57182	−0.187214
$365$	38.7961	2.03068
$366$	10.4573	0.546610
$367$	−18.9031	−0.986735	−0.493368	−	0.869821i	$-0.664234\pi$
$367$	−18.9031	−0.986735	−0.493368	+	0.869821i	$0.664234\pi$
$368$	5.30793	0.276695
$369$	−80.6740	−4.19972
$370$	9.14386	0.475367
$371$	11.4933	0.596704
$372$	20.2563	1.05024
$373$	−8.28101	−0.428774	−0.214387	−	0.976749i	$-0.568775\pi$
$373$	−8.28101	−0.428774	−0.214387	+	0.976749i	$0.568775\pi$
$374$	−19.6567	−1.01642
$375$	−100.411	−5.18522
$376$	−4.90806	−0.253114
$377$	17.0531	0.878279
$378$	−16.8350	−0.865901
$379$	−30.2268	−1.55265	−0.776324	−	0.630334i	$-0.782918\pi$
$379$	−30.2268	−1.55265	−0.776324	+	0.630334i	$0.782918\pi$
$380$	−5.19127	−0.266306
$381$	−3.56462	−0.182621
$382$	−21.2624	−1.08788
$383$	−13.3018	−0.679690	−0.339845	−	0.940481i	$-0.610375\pi$
$383$	−13.3018	−0.679690	−0.339845	+	0.940481i	$0.610375\pi$
$384$	3.32592	0.169725
$385$	17.2349	0.878371
$386$	−21.1435	−1.07618
$387$	81.6094	4.14844
$388$	−6.90179	−0.350386
$389$	−25.2267	−1.27904	−0.639522	−	0.768772i	$-0.720868\pi$
$389$	−25.2267	−1.27904	−0.639522	+	0.768772i	$0.720868\pi$
$390$	49.3622	2.49955
$391$	−25.1547	−1.27213
$392$	−1.00000	−0.0505076
$393$	−46.8459	−2.36306
$394$	2.33280	0.117525
$395$	−42.9903	−2.16308
$396$	−33.4385	−1.68035
$397$	2.31922	0.116398	0.0581991	−	0.998305i	$-0.481464\pi$
$397$	2.31922	0.116398	0.0581991	+	0.998305i	$0.481464\pi$
$398$	−4.24009	−0.212536
$399$	−4.15521	−0.208021
$400$	12.2657	0.613286
$401$	−29.3403	−1.46519	−0.732593	−	0.680667i	$-0.761690\pi$
$401$	−29.3403	−1.46519	−0.732593	+	0.680667i	$0.761690\pi$
$402$	−29.3183	−1.46226
$403$	−21.7539	−1.08364
$404$	−8.01224	−0.398624
$405$	132.164	6.56726
$406$	4.77434	0.236946
$407$	9.12754	0.452435
$408$	−15.7618	−0.780327
$409$	−28.8272	−1.42541	−0.712707	−	0.701461i	$-0.752531\pi$
$409$	−28.8272	−1.42541	−0.712707	+	0.701461i	$0.752531\pi$
$410$	41.5811	2.05354
$411$	32.8578	1.62076
$412$	4.56273	0.224790
$413$	7.59229	0.373592
$414$	−42.7913	−2.10308
$415$	−19.5531	−0.959823
$416$	−3.57182	−0.175123
$417$	−15.6198	−0.764905
$418$	−5.18200	−0.253460
$419$	−35.2105	−1.72015	−0.860073	−	0.510170i	$-0.829582\pi$
$419$	−35.2105	−1.72015	−0.860073	+	0.510170i	$0.829582\pi$
$420$	13.8199	0.674342
$421$	13.1344	0.640131	0.320066	−	0.947395i	$-0.396295\pi$
$421$	13.1344	0.640131	0.320066	+	0.947395i	$0.396295\pi$
$422$	−23.1931	−1.12902
$423$	39.5676	1.92384
$424$	11.4933	0.558166
$425$	−58.1283	−2.81964
$426$	5.51308	0.267110
$427$	−3.14417	−0.152157
$428$	−0.590211	−0.0285289
$429$	49.2741	2.37898
$430$	−42.0632	−2.02847
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	−16.8350	−0.809977
$433$	39.7196	1.90880	0.954402	−	0.298525i	$-0.0964945\pi$
$433$	39.7196	1.90880	0.954402	+	0.298525i	$0.0964945\pi$
$434$	−6.09042	−0.292350
$435$	−65.9808	−3.16354
$436$	−7.56684	−0.362386
$437$	−6.63141	−0.317223
$438$	31.0533	1.48379
$439$	−36.9926	−1.76556	−0.882779	−	0.469788i	$-0.844330\pi$
$439$	−36.9926	−1.76556	−0.882779	+	0.469788i	$0.844330\pi$
$440$	17.2349	0.821641
$441$	8.06177	0.383894
$442$	16.9272	0.805144
$443$	8.62344	0.409712	0.204856	−	0.978792i	$-0.434327\pi$
$443$	8.62344	0.409712	0.204856	+	0.978792i	$0.434327\pi$
$444$	7.31896	0.347343
$445$	−45.7053	−2.16664
$446$	−0.258124	−0.0122225
$447$	76.6689	3.62631
$448$	−1.00000	−0.0472456
$449$	6.28680	0.296693	0.148346	−	0.988935i	$-0.452605\pi$
$449$	6.28680	0.296693	0.148346	+	0.988935i	$0.452605\pi$
$450$	−98.8833	−4.66141
$451$	41.5068	1.95448
$452$	1.23216	0.0579560
$453$	33.8084	1.58846
$454$	−24.1299	−1.13247
$455$	−14.8417	−0.695788
$456$	−4.15521	−0.194586
$457$	17.4681	0.817121	0.408561	−	0.912731i	$-0.366031\pi$
$457$	17.4681	0.817121	0.408561	+	0.912731i	$0.366031\pi$
$458$	4.98929	0.233134
$459$	79.7828	3.72394
$460$	22.0555	1.02834
$461$	1.45036	0.0675500	0.0337750	−	0.999429i	$-0.489247\pi$
$461$	1.45036	0.0675500	0.0337750	+	0.999429i	$0.489247\pi$
$462$	13.7952	0.641812
$463$	16.8795	0.784459	0.392229	−	0.919867i	$-0.371704\pi$
$463$	16.8795	0.784459	0.392229	+	0.919867i	$0.371704\pi$
$464$	4.77434	0.221643
$465$	84.1690	3.90324
$466$	−1.11900	−0.0518367
$467$	40.5671	1.87722	0.938610	−	0.344980i	$-0.112114\pi$
$467$	40.5671	1.87722	0.938610	+	0.344980i	$0.112114\pi$
$468$	28.7952	1.33106
$469$	8.81508	0.407042
$470$	−20.3940	−0.940704
$471$	1.10099	0.0507311
$472$	7.59229	0.349463
$473$	−41.9881	−1.93061
$474$	−34.4105	−1.58053
$475$	−15.3241	−0.703116
$476$	4.73909	0.217216
$477$	−92.6566	−4.24246
$478$	−5.30099	−0.242462
$479$	−42.6281	−1.94773	−0.973864	−	0.227132i	$-0.927065\pi$
$479$	−42.6281	−1.94773	−0.973864	+	0.227132i	$0.927065\pi$
$480$	13.8199	0.630789
$481$	−7.86009	−0.358389
$482$	−19.9890	−0.910472
$483$	17.6538	0.803274
$484$	6.20412	0.282005
$485$	−28.6784	−1.30222
$486$	55.2818	2.50763
$487$	24.0657	1.09052	0.545261	−	0.838267i	$-0.316431\pi$
$487$	24.0657	1.09052	0.545261	+	0.838267i	$0.316431\pi$
$488$	−3.14417	−0.142330
$489$	−35.8599	−1.62164
$490$	−4.15520	−0.187713
$491$	23.7124	1.07012	0.535062	−	0.844813i	$-0.320288\pi$
$491$	23.7124	1.07012	0.535062	+	0.844813i	$0.320288\pi$
$492$	33.2825	1.50049
$493$	−22.6260	−1.01902
$494$	4.46243	0.200774
$495$	−138.944	−6.24505
$496$	−6.09042	−0.273468
$497$	−1.65761	−0.0743539
$498$	−15.6508	−0.701327
$499$	−28.9386	−1.29547	−0.647736	−	0.761865i	$-0.724284\pi$
$499$	−28.9386	−1.29547	−0.647736	+	0.761865i	$0.724284\pi$
$500$	30.1905	1.35016
$501$	69.7837	3.11771
$502$	24.1883	1.07958
$503$	15.5335	0.692604	0.346302	−	0.938123i	$-0.387437\pi$
$503$	15.5335	0.692604	0.346302	+	0.938123i	$0.387437\pi$
$504$	8.06177	0.359100
$505$	−33.2925	−1.48150
$506$	22.0161	0.978736
$507$	0.805095	0.0357555
$508$	1.07177	0.0475521
$509$	4.82371	0.213807	0.106904	−	0.994269i	$-0.465906\pi$
$509$	4.82371	0.213807	0.106904	+	0.994269i	$0.465906\pi$
$510$	−65.4936	−2.90011
$511$	−9.33675	−0.413034
$512$	−1.00000	−0.0441942
$513$	21.0327	0.928617
$514$	3.85068	0.169846
$515$	18.9591	0.835437
$516$	−33.6684	−1.48217
$517$	−20.3576	−0.895325
$518$	−2.20058	−0.0966880
$519$	−49.7447	−2.18355
$520$	−14.8417	−0.650850
$521$	−3.28035	−0.143715	−0.0718574	−	0.997415i	$-0.522893\pi$
$521$	−3.28035	−0.143715	−0.0718574	+	0.997415i	$0.522893\pi$
$522$	−38.4896	−1.68464
$523$	28.6005	1.25061	0.625305	−	0.780380i	$-0.284974\pi$
$523$	28.6005	1.25061	0.625305	+	0.780380i	$0.284974\pi$
$524$	14.0851	0.615310
$525$	40.7948	1.78043
$526$	6.21917	0.271169
$527$	28.8630	1.25729
$528$	13.7952	0.600360
$529$	5.17407	0.224960
$530$	47.7572	2.07444
$531$	−61.2073	−2.65617
$532$	1.24934	0.0541658
$533$	−35.7432	−1.54821
$534$	−36.5836	−1.58313
$535$	−2.45245	−0.106029
$536$	8.81508	0.380753
$537$	−58.0864	−2.50661
$538$	31.9651	1.37811
$539$	−4.14779	−0.178658
$540$	−69.9531	−3.01030
$541$	−33.2566	−1.42981	−0.714907	−	0.699219i	$-0.753531\pi$
$541$	−33.2566	−1.42981	−0.714907	+	0.699219i	$0.753531\pi$
$542$	32.3490	1.38951
$543$	−18.6389	−0.799871
$544$	4.73909	0.203187
$545$	−31.4418	−1.34682
$546$	−11.8796	−0.508401
$547$	−6.31642	−0.270071	−0.135035	−	0.990841i	$-0.543115\pi$
$547$	−6.31642	−0.270071	−0.135035	+	0.990841i	$0.543115\pi$
$548$	−9.87931	−0.422023
$549$	25.3476	1.08181
$550$	50.8756	2.16934
$551$	−5.96478	−0.254108
$552$	17.6538	0.751394
$553$	10.3461	0.439963
$554$	2.59917	0.110428
$555$	30.4118	1.29091
$556$	4.69638	0.199171
$557$	8.47508	0.359101	0.179550	−	0.983749i	$-0.442536\pi$
$557$	8.47508	0.359101	0.179550	+	0.983749i	$0.442536\pi$
$558$	49.0996	2.07855
$559$	36.1576	1.52931
$560$	−4.15520	−0.175589
$561$	−65.3767	−2.76021
$562$	−3.96402	−0.167212
$563$	−2.94150	−0.123969	−0.0619847	−	0.998077i	$-0.519743\pi$
$563$	−2.94150	−0.123969	−0.0619847	+	0.998077i	$0.519743\pi$
$564$	−16.3238	−0.687357
$565$	5.11988	0.215395
$566$	27.6125	1.16064
$567$	−31.8068	−1.33576
$568$	−1.65761	−0.0695517
$569$	7.71137	0.323278	0.161639	−	0.986850i	$-0.448322\pi$
$569$	7.71137	0.323278	0.161639	+	0.986850i	$0.448322\pi$
$570$	−17.2658	−0.723183
$571$	−37.2380	−1.55836	−0.779181	−	0.626800i	$-0.784364\pi$
$571$	−37.2380	−1.55836	−0.779181	+	0.626800i	$0.784364\pi$
$572$	−14.8152	−0.619453
$573$	−70.7171	−2.95425
$574$	−10.0070	−0.417684
$575$	65.1055	2.71509
$576$	8.06177	0.335907
$577$	28.2235	1.17496	0.587481	−	0.809238i	$-0.300120\pi$
$577$	28.2235	1.17496	0.587481	+	0.809238i	$0.300120\pi$
$578$	−5.45894	−0.227062
$579$	−70.3217	−2.92247
$580$	19.8383	0.823742
$581$	4.70569	0.195225
$582$	−22.9548	−0.951509
$583$	47.6719	1.97437
$584$	−9.33675	−0.386358
$585$	119.650	4.94692
$586$	−17.0053	−0.702484
$587$	6.15159	0.253903	0.126952	−	0.991909i	$-0.459481\pi$
$587$	6.15159	0.253903	0.126952	+	0.991909i	$0.459481\pi$
$588$	−3.32592	−0.137159
$589$	7.60902	0.313524
$590$	31.5475	1.29879
$591$	7.75872	0.319151
$592$	−2.20058	−0.0904433
$593$	−44.5482	−1.82938	−0.914688	−	0.404160i	$-0.867564\pi$
$593$	−44.5482	−1.82938	−0.914688	+	0.404160i	$0.867564\pi$
$594$	−69.8282	−2.86508
$595$	19.6919	0.807288
$596$	−23.0519	−0.944243
$597$	−14.1022	−0.577165
$598$	−18.9590	−0.775290
$599$	−31.3101	−1.27929	−0.639647	−	0.768669i	$-0.720920\pi$
$599$	−31.3101	−1.27929	−0.639647	+	0.768669i	$0.720920\pi$
$600$	40.7948	1.66544
$601$	30.3111	1.23641	0.618207	−	0.786015i	$-0.287859\pi$
$601$	30.3111	1.23641	0.618207	+	0.786015i	$0.287859\pi$
$602$	10.1230	0.412583
$603$	−71.0651	−2.89399
$604$	−10.1651	−0.413613
$605$	25.7794	1.04808
$606$	−26.6481	−1.08251
$607$	−28.4492	−1.15472	−0.577358	−	0.816491i	$-0.695916\pi$
$607$	−28.4492	−1.15472	−0.577358	+	0.816491i	$0.695916\pi$
$608$	1.24934	0.0506675
$609$	15.8791	0.643453
$610$	−13.0647	−0.528973
$611$	17.5307	0.709217
$612$	−38.2054	−1.54436
$613$	8.30333	0.335368	0.167684	−	0.985841i	$-0.446371\pi$
$613$	8.30333	0.335368	0.167684	+	0.985841i	$0.446371\pi$
$614$	12.1576	0.490639
$615$	138.295	5.57661
$616$	−4.14779	−0.167119
$617$	30.0779	1.21089	0.605446	−	0.795886i	$-0.292995\pi$
$617$	30.0779	1.21089	0.605446	+	0.795886i	$0.292995\pi$
$618$	15.1753	0.610440
$619$	−2.20313	−0.0885512	−0.0442756	−	0.999019i	$-0.514098\pi$
$619$	−2.20313	−0.0885512	−0.0442756	+	0.999019i	$0.514098\pi$
$620$	−25.3069	−1.01635
$621$	−89.3592	−3.58586
$622$	−27.3615	−1.09710
$623$	10.9995	0.440687
$624$	−11.8796	−0.475565
$625$	64.1192	2.56477
$626$	0.716490	0.0286367
$627$	−17.2349	−0.688297
$628$	−0.331034	−0.0132097
$629$	10.4287	0.415821
$630$	33.4983	1.33460
$631$	47.6949	1.89870	0.949352	−	0.314215i	$-0.101741\pi$
$631$	47.6949	1.89870	0.949352	+	0.314215i	$0.101741\pi$
$632$	10.3461	0.411547
$633$	−77.1386	−3.06598
$634$	12.0029	0.476696
$635$	4.45342	0.176729
$636$	38.2260	1.51576
$637$	3.57182	0.141521
$638$	19.8029	0.784005
$639$	13.3633	0.528642
$640$	−4.15520	−0.164249
$641$	−25.7988	−1.01899	−0.509495	−	0.860474i	$-0.670168\pi$
$641$	−25.7988	−1.01899	−0.509495	+	0.860474i	$0.670168\pi$
$642$	−1.96300	−0.0774733
$643$	−5.68429	−0.224167	−0.112083	−	0.993699i	$-0.535752\pi$
$643$	−5.68429	−0.224167	−0.112083	+	0.993699i	$0.535752\pi$
$644$	−5.30793	−0.209162
$645$	−139.899	−5.50852
$646$	−5.92074	−0.232948
$647$	−22.5666	−0.887183	−0.443592	−	0.896229i	$-0.646296\pi$
$647$	−22.5666	−0.887183	−0.443592	+	0.896229i	$0.646296\pi$
$648$	−31.8068	−1.24949
$649$	31.4912	1.23614
$650$	−43.8110	−1.71841
$651$	−20.2563	−0.793906
$652$	10.7819	0.422254
$653$	13.4235	0.525302	0.262651	−	0.964891i	$-0.415403\pi$
$653$	13.4235	0.525302	0.262651	+	0.964891i	$0.415403\pi$
$654$	−25.1667	−0.984097
$655$	58.5264	2.28682
$656$	−10.0070	−0.390707
$657$	75.2707	2.93659
$658$	4.90806	0.191336
$659$	42.9028	1.67126	0.835628	−	0.549296i	$-0.185104\pi$
$659$	42.9028	1.67126	0.835628	+	0.549296i	$0.185104\pi$
$660$	57.3219	2.23125
$661$	35.5380	1.38227	0.691135	−	0.722726i	$-0.257111\pi$
$661$	35.5380	1.38227	0.691135	+	0.722726i	$0.257111\pi$
$662$	15.8687	0.616756
$663$	56.2985	2.18645
$664$	4.70569	0.182616
$665$	5.19127	0.201309
$666$	17.7406	0.687433
$667$	25.3418	0.981239
$668$	−20.9818	−0.811808
$669$	−0.858500	−0.0331915
$670$	36.6284	1.41508
$671$	−13.0413	−0.503456
$672$	−3.32592	−0.128300
$673$	33.6237	1.29610	0.648048	−	0.761599i	$-0.275585\pi$
$673$	33.6237	1.29610	0.648048	+	0.761599i	$0.275585\pi$
$674$	10.8880	0.419389
$675$	−206.494	−7.94796
$676$	−0.242067	−0.00931025
$677$	−36.1151	−1.38802	−0.694008	−	0.719967i	$-0.744157\pi$
$677$	−36.1151	−1.38802	−0.694008	+	0.719967i	$0.744157\pi$
$678$	4.09807	0.157386
$679$	6.90179	0.264867
$680$	19.6919	0.755149
$681$	−80.2541	−3.07534
$682$	−25.2618	−0.967323
$683$	−1.44088	−0.0551337	−0.0275669	−	0.999620i	$-0.508776\pi$
$683$	−1.44088	−0.0551337	−0.0275669	+	0.999620i	$0.508776\pi$
$684$	−10.0719	−0.385109
$685$	−41.0505	−1.56846
$686$	1.00000	0.0381802
$687$	16.5940	0.633100
$688$	10.1230	0.385936
$689$	−41.0522	−1.56396
$690$	73.3549	2.79257
$691$	13.1530	0.500362	0.250181	−	0.968199i	$-0.419510\pi$
$691$	13.1530	0.500362	0.250181	+	0.968199i	$0.419510\pi$
$692$	14.9567	0.568567
$693$	33.4385	1.27022
$694$	−16.0460	−0.609099
$695$	19.5144	0.740224
$696$	15.8791	0.601895
$697$	47.4240	1.79631
$698$	12.8343	0.485786
$699$	−3.72171	−0.140768
$700$	−12.2657	−0.463601
$701$	23.0296	0.869816	0.434908	−	0.900475i	$-0.356781\pi$
$701$	23.0296	0.869816	0.434908	+	0.900475i	$0.356781\pi$
$702$	60.1318	2.26953
$703$	2.74928	0.103691
$704$	−4.14779	−0.156326
$705$	−67.8288	−2.55458
$706$	10.6659	0.401416
$707$	8.01224	0.301331
$708$	25.2514	0.949005
$709$	17.8536	0.670505	0.335252	−	0.942128i	$-0.391178\pi$
$709$	17.8536	0.670505	0.335252	+	0.942128i	$0.391178\pi$
$710$	−6.88770	−0.258491
$711$	−83.4082	−3.12805
$712$	10.9995	0.412225
$713$	−32.3275	−1.21067
$714$	15.7618	0.589872
$715$	−61.5600	−2.30221
$716$	17.4648	0.652689
$717$	−17.6307	−0.658430
$718$	−3.83799	−0.143232
$719$	−0.739469	−0.0275775	−0.0137888	−	0.999905i	$-0.504389\pi$
$719$	−0.739469	−0.0275775	−0.0137888	+	0.999905i	$0.504389\pi$
$720$	33.4983	1.24841
$721$	−4.56273	−0.169925
$722$	17.4391	0.649018
$723$	−66.4818	−2.47248
$724$	5.60412	0.208276
$725$	58.5607	2.17489
$726$	20.6344	0.765816
$727$	−50.5461	−1.87465	−0.937325	−	0.348457i	$-0.886706\pi$
$727$	−50.5461	−1.87465	−0.937325	+	0.348457i	$0.886706\pi$
$728$	3.57182	0.132381
$729$	88.4426	3.27565
$730$	−38.7961	−1.43591
$731$	−47.9739	−1.77438
$732$	−10.4573	−0.386512
$733$	−15.5770	−0.575349	−0.287674	−	0.957728i	$-0.592882\pi$
$733$	−15.5770	−0.575349	−0.287674	+	0.957728i	$0.592882\pi$
$734$	18.9031	0.697727
$735$	−13.8199	−0.509754
$736$	−5.30793	−0.195653
$737$	36.5630	1.34682
$738$	80.6740	2.96965
$739$	7.73706	0.284612	0.142306	−	0.989823i	$-0.454548\pi$
$739$	7.73706	0.284612	0.142306	+	0.989823i	$0.454548\pi$
$740$	−9.14386	−0.336135
$741$	14.8417	0.545223
$742$	−11.4933	−0.421934
$743$	11.0845	0.406650	0.203325	−	0.979111i	$-0.434825\pi$
$743$	11.0845	0.406650	0.203325	+	0.979111i	$0.434825\pi$
$744$	−20.2563	−0.742631
$745$	−95.7853	−3.50930
$746$	8.28101	0.303189
$747$	−37.9361	−1.38801
$748$	19.6567	0.718721
$749$	0.590211	0.0215658
$750$	100.411	3.66651
$751$	−31.0469	−1.13292	−0.566459	−	0.824090i	$-0.691687\pi$
$751$	−31.0469	−1.13292	−0.566459	+	0.824090i	$0.691687\pi$
$752$	4.90806	0.178978
$753$	80.4486	2.93171
$754$	−17.0531	−0.621037
$755$	−42.2382	−1.53720
$756$	16.8350	0.612285
$757$	−52.9386	−1.92409	−0.962043	−	0.272897i	$-0.912018\pi$
$757$	−52.9386	−1.92409	−0.962043	+	0.272897i	$0.912018\pi$
$758$	30.2268	1.09789
$759$	73.2240	2.65786
$760$	5.19127	0.188307
$761$	−23.1218	−0.838166	−0.419083	−	0.907948i	$-0.637648\pi$
$761$	−23.1218	−0.838166	−0.419083	+	0.907948i	$0.637648\pi$
$762$	3.56462	0.129133
$763$	7.56684	0.273938
$764$	21.2624	0.769246
$765$	−158.751	−5.73966
$766$	13.3018	0.480613
$767$	−27.1183	−0.979186
$768$	−3.32592	−0.120014
$769$	8.48135	0.305845	0.152923	−	0.988238i	$-0.451131\pi$
$769$	8.48135	0.305845	0.152923	+	0.988238i	$0.451131\pi$
$770$	−17.2349	−0.621102
$771$	12.8071	0.461235
$772$	21.1435	0.760972
$773$	−12.1545	−0.437166	−0.218583	−	0.975818i	$-0.570143\pi$
$773$	−12.1545	−0.437166	−0.218583	+	0.975818i	$0.570143\pi$
$774$	−81.6094	−2.93339
$775$	−74.7034	−2.68342
$776$	6.90179	0.247760
$777$	−7.31896	−0.262566
$778$	25.2267	0.904421
$779$	12.5021	0.447936
$780$	−49.3622	−1.76745
$781$	−6.87541	−0.246021
$782$	25.1547	0.899531
$783$	−80.3762	−2.87241
$784$	1.00000	0.0357143
$785$	−1.37551	−0.0490942
$786$	46.8459	1.67094
$787$	−53.6656	−1.91297	−0.956487	−	0.291776i	$-0.905754\pi$
$787$	−53.6656	−1.91297	−0.956487	+	0.291776i	$0.905754\pi$
$788$	−2.33280	−0.0831027
$789$	20.6845	0.736387
$790$	42.9903	1.52953
$791$	−1.23216	−0.0438106
$792$	33.4385	1.18818
$793$	11.2304	0.398804
$794$	−2.31922	−0.0823059
$795$	158.837	5.63336
$796$	4.24009	0.150286
$797$	−53.2753	−1.88711	−0.943554	−	0.331219i	$-0.892540\pi$
$797$	−53.2753	−1.88711	−0.943554	+	0.331219i	$0.892540\pi$
$798$	4.15521	0.147093
$799$	−23.2597	−0.822869
$800$	−12.2657	−0.433659
$801$	−88.6756	−3.13320
$802$	29.3403	1.03604
$803$	−38.7268	−1.36664
$804$	29.3183	1.03398
$805$	−22.0555	−0.777355
$806$	21.7539	0.766249
$807$	106.313	3.74241
$808$	8.01224	0.281870
$809$	−42.0158	−1.47720	−0.738598	−	0.674146i	$-0.764512\pi$
$809$	−42.0158	−1.47720	−0.738598	+	0.674146i	$0.764512\pi$
$810$	−132.164	−4.64376
$811$	38.6749	1.35806	0.679030	−	0.734111i	$-0.262401\pi$
$811$	38.6749	1.35806	0.679030	+	0.734111i	$0.262401\pi$
$812$	−4.77434	−0.167546
$813$	107.590	3.77335
$814$	−9.12754	−0.319920
$815$	44.8012	1.56932
$816$	15.7618	0.551775
$817$	−12.6471	−0.442466
$818$	28.8272	1.00792
$819$	−28.7952	−1.00619
$820$	−41.5811	−1.45207
$821$	−23.7959	−0.830481	−0.415241	−	0.909712i	$-0.636303\pi$
$821$	−23.7959	−0.830481	−0.415241	+	0.909712i	$0.636303\pi$
$822$	−32.8578	−1.14605
$823$	43.9963	1.53362	0.766808	−	0.641876i	$-0.221844\pi$
$823$	43.9963	1.53362	0.766808	+	0.641876i	$0.221844\pi$
$824$	−4.56273	−0.158950
$825$	169.208	5.89107
$826$	−7.59229	−0.264170
$827$	−43.1459	−1.50033	−0.750164	−	0.661252i	$-0.770026\pi$
$827$	−43.1459	−1.50033	−0.750164	+	0.661252i	$0.770026\pi$
$828$	42.7913	1.48710
$829$	20.2308	0.702646	0.351323	−	0.936254i	$-0.385732\pi$
$829$	20.2308	0.702646	0.351323	+	0.936254i	$0.385732\pi$
$830$	19.5531	0.678697
$831$	8.64465	0.299880
$832$	3.57182	0.123831
$833$	−4.73909	−0.164200
$834$	15.6198	0.540870
$835$	−87.1834	−3.01711
$836$	5.18200	0.179223
$837$	102.533	3.54404
$838$	35.2105	1.21633
$839$	−39.3289	−1.35778	−0.678892	−	0.734238i	$-0.737540\pi$
$839$	−39.3289	−1.35778	−0.678892	+	0.734238i	$0.737540\pi$
$840$	−13.8199	−0.476831
$841$	−6.20570	−0.213990
$842$	−13.1344	−0.452641
$843$	−13.1840	−0.454082
$844$	23.1931	0.798341
$845$	−1.00584	−0.0346018
$846$	−39.5676	−1.36036
$847$	−6.20412	−0.213176
$848$	−11.4933	−0.394683
$849$	91.8371	3.15184
$850$	58.1283	1.99378
$851$	−11.6805	−0.400403
$852$	−5.51308	−0.188875
$853$	23.3314	0.798852	0.399426	−	0.916765i	$-0.369209\pi$
$853$	23.3314	0.798852	0.399426	+	0.916765i	$0.369209\pi$
$854$	3.14417	0.107591
$855$	−41.8508	−1.43127
$856$	0.590211	0.0201730
$857$	−53.3081	−1.82097	−0.910485	−	0.413542i	$-0.864291\pi$
$857$	−53.3081	−1.82097	−0.910485	+	0.413542i	$0.864291\pi$
$858$	−49.2741	−1.68219
$859$	18.3473	0.626002	0.313001	−	0.949753i	$-0.398666\pi$
$859$	18.3473	0.626002	0.313001	+	0.949753i	$0.398666\pi$
$860$	42.0632	1.43434
$861$	−33.2825	−1.13426
$862$	1.00000	0.0340601
$863$	−35.5783	−1.21110	−0.605550	−	0.795808i	$-0.707047\pi$
$863$	−35.5783	−1.21110	−0.605550	+	0.795808i	$0.707047\pi$
$864$	16.8350	0.572740
$865$	62.1479	2.11309
$866$	−39.7196	−1.34973
$867$	−18.1560	−0.616611
$868$	6.09042	0.206722
$869$	42.9136	1.45574
$870$	65.9808	2.23696
$871$	−31.4859	−1.06686
$872$	7.56684	0.256246
$873$	−55.6407	−1.88315
$874$	6.63141	0.224311
$875$	−30.1905	−1.02063
$876$	−31.0533	−1.04919
$877$	−14.9442	−0.504630	−0.252315	−	0.967645i	$-0.581192\pi$
$877$	−14.9442	−0.504630	−0.252315	+	0.967645i	$0.581192\pi$
$878$	36.9926	1.24844
$879$	−56.5585	−1.90767
$880$	−17.2349	−0.580988
$881$	−28.0210	−0.944052	−0.472026	−	0.881585i	$-0.656477\pi$
$881$	−28.0210	−0.944052	−0.472026	+	0.881585i	$0.656477\pi$
$882$	−8.06177	−0.271454
$883$	3.19223	0.107427	0.0537136	−	0.998556i	$-0.482894\pi$
$883$	3.19223	0.107427	0.0537136	+	0.998556i	$0.482894\pi$
$884$	−16.9272	−0.569323
$885$	104.925	3.52700
$886$	−8.62344	−0.289710
$887$	−40.6412	−1.36460	−0.682299	−	0.731073i	$-0.739020\pi$
$887$	−40.6412	−1.36460	−0.682299	+	0.731073i	$0.739020\pi$
$888$	−7.31896	−0.245608
$889$	−1.07177	−0.0359460
$890$	45.7053	1.53204
$891$	−131.928	−4.41974
$892$	0.258124	0.00864262
$893$	−6.13184	−0.205194
$894$	−76.6689	−2.56419
$895$	72.5696	2.42573
$896$	1.00000	0.0334077
$897$	−63.0561	−2.10538
$898$	−6.28680	−0.209793
$899$	−29.0777	−0.969797
$900$	98.8833	3.29611
$901$	54.4679	1.81459
$902$	−41.5068	−1.38203
$903$	33.6684	1.12041
$904$	−1.23216	−0.0409811
$905$	23.2863	0.774062
$906$	−33.8084	−1.12321
$907$	44.8515	1.48927	0.744635	−	0.667472i	$-0.232624\pi$
$907$	44.8515	1.48927	0.744635	+	0.667472i	$0.232624\pi$
$908$	24.1299	0.800778
$909$	−64.5928	−2.14241
$910$	14.8417	0.491996
$911$	35.9647	1.19156	0.595782	−	0.803146i	$-0.296842\pi$
$911$	35.9647	1.19156	0.595782	+	0.803146i	$0.296842\pi$
$912$	4.15521	0.137593
$913$	19.5182	0.645957
$914$	−17.4681	−0.577792
$915$	−43.4521	−1.43648
$916$	−4.98929	−0.164851
$917$	−14.0851	−0.465131
$918$	−79.7828	−2.63322
$919$	−25.9418	−0.855740	−0.427870	−	0.903840i	$-0.640736\pi$
$919$	−25.9418	−0.855740	−0.427870	+	0.903840i	$0.640736\pi$
$920$	−22.0555	−0.727149
$921$	40.4351	1.33238
$922$	−1.45036	−0.0477650
$923$	5.92069	0.194882
$924$	−13.7952	−0.453829
$925$	−26.9917	−0.887482
$926$	−16.8795	−0.554696
$927$	36.7837	1.20813
$928$	−4.77434	−0.156725
$929$	−5.69727	−0.186921	−0.0934606	−	0.995623i	$-0.529793\pi$
$929$	−5.69727	−0.186921	−0.0934606	+	0.995623i	$0.529793\pi$
$930$	−84.1690	−2.76001
$931$	−1.24934	−0.0409455
$932$	1.11900	0.0366541
$933$	−91.0024	−2.97928
$934$	−40.5671	−1.32740
$935$	81.6776	2.67114
$936$	−28.7952	−0.941201
$937$	25.7816	0.842248	0.421124	−	0.907003i	$-0.361636\pi$
$937$	25.7816	0.842248	0.421124	+	0.907003i	$0.361636\pi$
$938$	−8.81508	−0.287822
$939$	2.38299	0.0777660
$940$	20.3940	0.665178
$941$	13.1524	0.428755	0.214378	−	0.976751i	$-0.431228\pi$
$941$	13.1524	0.428755	0.214378	+	0.976751i	$0.431228\pi$
$942$	−1.10099	−0.0358723
$943$	−53.1163	−1.72971
$944$	−7.59229	−0.247108
$945$	69.9531	2.27557
$946$	41.9881	1.36515
$947$	−16.0989	−0.523144	−0.261572	−	0.965184i	$-0.584241\pi$
$947$	−16.0989	−0.523144	−0.261572	+	0.965184i	$0.584241\pi$
$948$	34.4105	1.11760
$949$	33.3492	1.08256
$950$	15.3241	0.497178
$951$	39.9208	1.29452
$952$	−4.73909	−0.153595
$953$	47.8822	1.55106	0.775528	−	0.631314i	$-0.217484\pi$
$953$	47.8822	1.55106	0.775528	+	0.631314i	$0.217484\pi$
$954$	92.6566	2.99987
$955$	88.3495	2.85892
$956$	5.30099	0.171446
$957$	65.8630	2.12905
$958$	42.6281	1.37725
$959$	9.87931	0.319020
$960$	−13.8199	−0.446035
$961$	6.09323	0.196556
$962$	7.86009	0.253419
$963$	−4.75814	−0.153329
$964$	19.9890	0.643801
$965$	87.8556	2.82817
$966$	−17.6538	−0.568000
$967$	−37.9383	−1.22001	−0.610006	−	0.792397i	$-0.708833\pi$
$967$	−37.9383	−1.22001	−0.610006	+	0.792397i	$0.708833\pi$
$968$	−6.20412	−0.199408
$969$	−19.6919	−0.632596
$970$	28.6784	0.920807
$971$	−25.9980	−0.834316	−0.417158	−	0.908834i	$-0.636974\pi$
$971$	−25.9980	−0.834316	−0.417158	+	0.908834i	$0.636974\pi$
$972$	−55.2818	−1.77316
$973$	−4.69638	−0.150559
$974$	−24.0657	−0.771115
$975$	−145.712	−4.66652
$976$	3.14417	0.100642
$977$	−22.0668	−0.705978	−0.352989	−	0.935627i	$-0.614835\pi$
$977$	−22.0668	−0.705978	−0.352989	+	0.935627i	$0.614835\pi$
$978$	35.8599	1.14667
$979$	45.6237	1.45814
$980$	4.15520	0.132733
$981$	−61.0021	−1.94765
$982$	−23.7124	−0.756692
$983$	0.414999	0.0132364	0.00661821	−	0.999978i	$-0.497893\pi$
$983$	0.414999	0.0132364	0.00661821	+	0.999978i	$0.497893\pi$
$984$	−33.2825	−1.06101
$985$	−9.69327	−0.308853
$986$	22.6260	0.720559
$987$	16.3238	0.519593
$988$	−4.46243	−0.141969
$989$	53.7322	1.70859
$990$	138.944	4.41592
$991$	0.211377	0.00671461	0.00335730	−	0.999994i	$-0.498931\pi$
$991$	0.211377	0.00671461	0.00335730	+	0.999994i	$0.498931\pi$
$992$	6.09042	0.193371
$993$	52.7782	1.67487
$994$	1.65761	0.0525762
$995$	17.6184	0.558542
$996$	15.6508	0.495913
$997$	47.1186	1.49226	0.746131	−	0.665799i	$-0.231909\pi$
$997$	47.1186	1.49226	0.746131	+	0.665799i	$0.231909\pi$
$998$	28.9386	0.916037
$999$	37.0469	1.17211

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.o.1.1	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.o.1.1	✓	25	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.32592 q^{3} +1.00000 q^{4} +4.15520 q^{5} +3.32592 q^{6} -1.00000 q^{7} -1.00000 q^{8} +8.06177 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.32592 q^{3} +1.00000 q^{4} +4.15520 q^{5} +3.32592 q^{6} -1.00000 q^{7} -1.00000 q^{8} +8.06177 q^{9} -4.15520 q^{10} -4.14779 q^{11} -3.32592 q^{12} +3.57182 q^{13} +1.00000 q^{14} -13.8199 q^{15} +1.00000 q^{16} -4.73909 q^{17} -8.06177 q^{18} -1.24934 q^{19} +4.15520 q^{20} +3.32592 q^{21} +4.14779 q^{22} +5.30793 q^{23} +3.32592 q^{24} +12.2657 q^{25} -3.57182 q^{26} -16.8350 q^{27} -1.00000 q^{28} +4.77434 q^{29} +13.8199 q^{30} -6.09042 q^{31} -1.00000 q^{32} +13.7952 q^{33} +4.73909 q^{34} -4.15520 q^{35} +8.06177 q^{36} -2.20058 q^{37} +1.24934 q^{38} -11.8796 q^{39} -4.15520 q^{40} -10.0070 q^{41} -3.32592 q^{42} +10.1230 q^{43} -4.14779 q^{44} +33.4983 q^{45} -5.30793 q^{46} +4.90806 q^{47} -3.32592 q^{48} +1.00000 q^{49} -12.2657 q^{50} +15.7618 q^{51} +3.57182 q^{52} -11.4933 q^{53} +16.8350 q^{54} -17.2349 q^{55} +1.00000 q^{56} +4.15521 q^{57} -4.77434 q^{58} -7.59229 q^{59} -13.8199 q^{60} +3.14417 q^{61} +6.09042 q^{62} -8.06177 q^{63} +1.00000 q^{64} +14.8417 q^{65} -13.7952 q^{66} -8.81508 q^{67} -4.73909 q^{68} -17.6538 q^{69} +4.15520 q^{70} +1.65761 q^{71} -8.06177 q^{72} +9.33675 q^{73} +2.20058 q^{74} -40.7948 q^{75} -1.24934 q^{76} +4.14779 q^{77} +11.8796 q^{78} -10.3461 q^{79} +4.15520 q^{80} +31.8068 q^{81} +10.0070 q^{82} -4.70569 q^{83} +3.32592 q^{84} -19.6919 q^{85} -10.1230 q^{86} -15.8791 q^{87} +4.14779 q^{88} -10.9995 q^{89} -33.4983 q^{90} -3.57182 q^{91} +5.30793 q^{92} +20.2563 q^{93} -4.90806 q^{94} -5.19127 q^{95} +3.32592 q^{96} -6.90179 q^{97} -1.00000 q^{98} -33.4385 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9} - 13 q^{11} - 4 q^{12} + 17 q^{13} + 25 q^{14} - 18 q^{15} + 25 q^{16} - 4 q^{17} - 25 q^{18} - 9 q^{19} + 4 q^{21} + 13 q^{22} - 14 q^{23} + 4 q^{24} + 23 q^{25} - 17 q^{26} - 7 q^{27} - 25 q^{28} - 4 q^{29} + 18 q^{30} - 15 q^{31} - 25 q^{32} - 15 q^{33} + 4 q^{34} + 25 q^{36} + 13 q^{37} + 9 q^{38} - 31 q^{39} - 31 q^{41} - 4 q^{42} + 29 q^{43} - 13 q^{44} + 10 q^{45} + 14 q^{46} - 31 q^{47} - 4 q^{48} + 25 q^{49} - 23 q^{50} - 9 q^{51} + 17 q^{52} + 23 q^{53} + 7 q^{54} - 48 q^{55} + 25 q^{56} + 32 q^{57} + 4 q^{58} - 50 q^{59} - 18 q^{60} - 2 q^{61} + 15 q^{62} - 25 q^{63} + 25 q^{64} - 4 q^{65} + 15 q^{66} - 8 q^{67} - 4 q^{68} - 57 q^{69} - 61 q^{71} - 25 q^{72} + 31 q^{73} - 13 q^{74} - 21 q^{75} - 9 q^{76} + 13 q^{77} + 31 q^{78} - 10 q^{79} + 61 q^{81} + 31 q^{82} - 47 q^{83} + 4 q^{84} + 2 q^{85} - 29 q^{86} + 17 q^{87} + 13 q^{88} - 44 q^{89} - 10 q^{90} - 17 q^{91} - 14 q^{92} - 13 q^{93} + 31 q^{94} - 7 q^{95} + 4 q^{96} + 10 q^{97} - 25 q^{98} - 47 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9 - 13 * q^11 - 4 * q^12 + 17 * q^13 + 25 * q^14 - 18 * q^15 + 25 * q^16 - 4 * q^17 - 25 * q^18 - 9 * q^19 + 4 * q^21 + 13 * q^22 - 14 * q^23 + 4 * q^24 + 23 * q^25 - 17 * q^26 - 7 * q^27 - 25 * q^28 - 4 * q^29 + 18 * q^30 - 15 * q^31 - 25 * q^32 - 15 * q^33 + 4 * q^34 + 25 * q^36 + 13 * q^37 + 9 * q^38 - 31 * q^39 - 31 * q^41 - 4 * q^42 + 29 * q^43 - 13 * q^44 + 10 * q^45 + 14 * q^46 - 31 * q^47 - 4 * q^48 + 25 * q^49 - 23 * q^50 - 9 * q^51 + 17 * q^52 + 23 * q^53 + 7 * q^54 - 48 * q^55 + 25 * q^56 + 32 * q^57 + 4 * q^58 - 50 * q^59 - 18 * q^60 - 2 * q^61 + 15 * q^62 - 25 * q^63 + 25 * q^64 - 4 * q^65 + 15 * q^66 - 8 * q^67 - 4 * q^68 - 57 * q^69 - 61 * q^71 - 25 * q^72 + 31 * q^73 - 13 * q^74 - 21 * q^75 - 9 * q^76 + 13 * q^77 + 31 * q^78 - 10 * q^79 + 61 * q^81 + 31 * q^82 - 47 * q^83 + 4 * q^84 + 2 * q^85 - 29 * q^86 + 17 * q^87 + 13 * q^88 - 44 * q^89 - 10 * q^90 - 17 * q^91 - 14 * q^92 - 13 * q^93 + 31 * q^94 - 7 * q^95 + 4 * q^96 + 10 * q^97 - 25 * q^98 - 47 * q^99

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