LMFDB - Embedded newform 619.2.a.b.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [619,2,Mod(1,619)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(619, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("619.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	619.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:	$4.94273988512$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	619.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.192901 q^{2} -3.10998 q^{3} -1.96279 q^{4} +2.33409 q^{5} +0.599918 q^{6} -3.05253 q^{7} +0.764427 q^{8} +6.67195 q^{9} +O(q^{10})$	\(q-0.192901 q^{2} -3.10998 q^{3} -1.96279 q^{4} +2.33409 q^{5} +0.599918 q^{6} -3.05253 q^{7} +0.764427 q^{8} +6.67195 q^{9} -0.450249 q^{10} -6.12235 q^{11} +6.10423 q^{12} -5.12075 q^{13} +0.588836 q^{14} -7.25897 q^{15} +3.77812 q^{16} -0.896358 q^{17} -1.28703 q^{18} +2.17256 q^{19} -4.58133 q^{20} +9.49328 q^{21} +1.18101 q^{22} +4.34757 q^{23} -2.37735 q^{24} +0.447982 q^{25} +0.987800 q^{26} -11.4197 q^{27} +5.99147 q^{28} +3.04370 q^{29} +1.40026 q^{30} +2.83568 q^{31} -2.25766 q^{32} +19.0404 q^{33} +0.172909 q^{34} -7.12488 q^{35} -13.0956 q^{36} +6.95323 q^{37} -0.419089 q^{38} +15.9254 q^{39} +1.78424 q^{40} +3.82879 q^{41} -1.83127 q^{42} +12.6249 q^{43} +12.0169 q^{44} +15.5729 q^{45} -0.838652 q^{46} -11.9938 q^{47} -11.7499 q^{48} +2.31792 q^{49} -0.0864163 q^{50} +2.78765 q^{51} +10.0510 q^{52} -2.38334 q^{53} +2.20287 q^{54} -14.2901 q^{55} -2.33343 q^{56} -6.75661 q^{57} -0.587133 q^{58} +7.29784 q^{59} +14.2478 q^{60} +13.8005 q^{61} -0.547006 q^{62} -20.3663 q^{63} -7.12073 q^{64} -11.9523 q^{65} -3.67291 q^{66} +2.68532 q^{67} +1.75936 q^{68} -13.5208 q^{69} +1.37440 q^{70} +6.53661 q^{71} +5.10022 q^{72} -11.2484 q^{73} -1.34129 q^{74} -1.39321 q^{75} -4.26428 q^{76} +18.6887 q^{77} -3.07203 q^{78} -9.47425 q^{79} +8.81848 q^{80} +15.4990 q^{81} -0.738579 q^{82} +2.39915 q^{83} -18.6333 q^{84} -2.09218 q^{85} -2.43535 q^{86} -9.46583 q^{87} -4.68009 q^{88} -5.93380 q^{89} -3.00404 q^{90} +15.6312 q^{91} -8.53336 q^{92} -8.81889 q^{93} +2.31363 q^{94} +5.07095 q^{95} +7.02126 q^{96} +9.10352 q^{97} -0.447130 q^{98} -40.8480 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) $ 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9} + 5 q^{10} + 23 q^{11} - 6 q^{12} + 9 q^{13} + 7 q^{14} - 2 q^{15} + 35 q^{16} + 4 q^{17} + 10 q^{18} - q^{19} + 29 q^{20} + 30 q^{21} + 4 q^{23} + 4 q^{24} + 35 q^{25} + q^{26} - 5 q^{27} - 13 q^{28} + 90 q^{29} - 31 q^{30} + 2 q^{31} + 43 q^{32} - 6 q^{33} - 9 q^{34} + 9 q^{35} + 33 q^{36} + 19 q^{37} + 5 q^{38} + 32 q^{39} - 12 q^{40} + 59 q^{41} - 25 q^{42} - 4 q^{43} + 52 q^{44} + 30 q^{45} - q^{46} + 4 q^{47} - 44 q^{48} + 30 q^{49} + 31 q^{50} - 12 q^{52} + 34 q^{53} - 28 q^{54} - 17 q^{55} + 2 q^{56} - 8 q^{57} + 6 q^{58} + 13 q^{59} - 64 q^{60} + 16 q^{61} + 28 q^{62} - 40 q^{63} + 37 q^{64} + 31 q^{65} - 59 q^{66} - 11 q^{67} - 52 q^{68} + 6 q^{69} - 40 q^{70} + 42 q^{71} + 6 q^{72} - 4 q^{73} + 16 q^{74} - 52 q^{75} - 42 q^{76} + 29 q^{77} - 56 q^{78} + 3 q^{79} + 21 q^{80} + 30 q^{81} - 43 q^{82} - 11 q^{83} - 36 q^{84} + 19 q^{85} - 11 q^{86} - 20 q^{87} - 47 q^{88} + 58 q^{89} - 33 q^{90} - 39 q^{91} - 7 q^{92} - 15 q^{93} - 46 q^{94} + 23 q^{95} - 70 q^{96} - 9 q^{97} - 8 q^{99}+O(q^{100}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9 + 5 * q^10 + 23 * q^11 - 6 * q^12 + 9 * q^13 + 7 * q^14 - 2 * q^15 + 35 * q^16 + 4 * q^17 + 10 * q^18 - q^19 + 29 * q^20 + 30 * q^21 + 4 * q^23 + 4 * q^24 + 35 * q^25 + q^26 - 5 * q^27 - 13 * q^28 + 90 * q^29 - 31 * q^30 + 2 * q^31 + 43 * q^32 - 6 * q^33 - 9 * q^34 + 9 * q^35 + 33 * q^36 + 19 * q^37 + 5 * q^38 + 32 * q^39 - 12 * q^40 + 59 * q^41 - 25 * q^42 - 4 * q^43 + 52 * q^44 + 30 * q^45 - q^46 + 4 * q^47 - 44 * q^48 + 30 * q^49 + 31 * q^50 - 12 * q^52 + 34 * q^53 - 28 * q^54 - 17 * q^55 + 2 * q^56 - 8 * q^57 + 6 * q^58 + 13 * q^59 - 64 * q^60 + 16 * q^61 + 28 * q^62 - 40 * q^63 + 37 * q^64 + 31 * q^65 - 59 * q^66 - 11 * q^67 - 52 * q^68 + 6 * q^69 - 40 * q^70 + 42 * q^71 + 6 * q^72 - 4 * q^73 + 16 * q^74 - 52 * q^75 - 42 * q^76 + 29 * q^77 - 56 * q^78 + 3 * q^79 + 21 * q^80 + 30 * q^81 - 43 * q^82 - 11 * q^83 - 36 * q^84 + 19 * q^85 - 11 * q^86 - 20 * q^87 - 47 * q^88 + 58 * q^89 - 33 * q^90 - 39 * q^91 - 7 * q^92 - 15 * q^93 - 46 * q^94 + 23 * q^95 - 70 * q^96 - 9 * q^97 - 8 * 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 $

$2$	−0.192901	−0.136402	−0.0682009	−	0.997672i	$-0.521726\pi$
$2$	−0.192901	−0.136402	−0.0682009	+	0.997672i	$0.521726\pi$
$3$	−3.10998	−1.79555	−0.897773	−	0.440459i	$-0.854816\pi$
$3$	−3.10998	−1.79555	−0.897773	+	0.440459i	$0.854816\pi$
$4$	−1.96279	−0.981395
$5$	2.33409	1.04384	0.521919	−	0.852995i	$-0.325216\pi$
$5$	2.33409	1.04384	0.521919	+	0.852995i	$0.325216\pi$
$6$	0.599918	0.244916
$7$	−3.05253	−1.15375	−0.576873	−	0.816834i	$-0.695727\pi$
$7$	−3.05253	−1.15375	−0.576873	+	0.816834i	$0.695727\pi$
$8$	0.764427	0.270266
$9$	6.67195	2.22398
$10$	−0.450249	−0.142381
$11$	−6.12235	−1.84596	−0.922980	−	0.384849i	$-0.874254\pi$
$11$	−6.12235	−1.84596	−0.922980	+	0.384849i	$0.874254\pi$
$12$	6.10423	1.76214
$13$	−5.12075	−1.42024	−0.710121	−	0.704080i	$-0.751360\pi$
$13$	−5.12075	−1.42024	−0.710121	+	0.704080i	$0.751360\pi$
$14$	0.588836	0.157373
$15$	−7.25897	−1.87426
$16$	3.77812	0.944530
$17$	−0.896358	−0.217399	−0.108699	−	0.994075i	$-0.534669\pi$
$17$	−0.896358	−0.217399	−0.108699	+	0.994075i	$0.534669\pi$
$18$	−1.28703	−0.303355
$19$	2.17256	0.498419	0.249210	−	0.968450i	$-0.419829\pi$
$19$	2.17256	0.498419	0.249210	+	0.968450i	$0.419829\pi$
$20$	−4.58133	−1.02442
$21$	9.49328	2.07160
$22$	1.18101	0.251792
$23$	4.34757	0.906531	0.453265	−	0.891376i	$-0.350259\pi$
$23$	4.34757	0.906531	0.453265	+	0.891376i	$0.350259\pi$
$24$	−2.37735	−0.485274
$25$	0.447982	0.0895964
$26$	0.987800	0.193723
$27$	−11.4197	−2.19771
$28$	5.99147	1.13228
$29$	3.04370	0.565201	0.282600	−	0.959238i	$-0.408803\pi$
$29$	3.04370	0.565201	0.282600	+	0.959238i	$0.408803\pi$
$30$	1.40026	0.255652
$31$	2.83568	0.509303	0.254651	−	0.967033i	$-0.418039\pi$
$31$	2.83568	0.509303	0.254651	+	0.967033i	$0.418039\pi$
$32$	−2.25766	−0.399101
$33$	19.0404	3.31450
$34$	0.172909	0.0296536
$35$	−7.12488	−1.20432
$36$	−13.0956	−2.18260
$37$	6.95323	1.14310	0.571552	−	0.820566i	$-0.306342\pi$
$37$	6.95323	1.14310	0.571552	+	0.820566i	$0.306342\pi$
$38$	−0.419089	−0.0679853
$39$	15.9254	2.55011
$40$	1.78424	0.282113
$41$	3.82879	0.597957	0.298978	−	0.954260i	$-0.403354\pi$
$41$	3.82879	0.597957	0.298978	+	0.954260i	$0.403354\pi$
$42$	−1.83127	−0.282571
$43$	12.6249	1.92528	0.962638	−	0.270793i	$-0.0872858\pi$
$43$	12.6249	1.92528	0.962638	+	0.270793i	$0.0872858\pi$
$44$	12.0169	1.81161
$45$	15.5729	2.32148
$46$	−0.838652	−0.123652
$47$	−11.9938	−1.74948	−0.874741	−	0.484591i	$-0.838968\pi$
$47$	−11.9938	−1.74948	−0.874741	+	0.484591i	$0.838968\pi$
$48$	−11.7499	−1.69595
$49$	2.31792	0.331132
$50$	−0.0864163	−0.0122211
$51$	2.78765	0.390349
$52$	10.0510	1.39382
$53$	−2.38334	−0.327376	−0.163688	−	0.986512i	$-0.552339\pi$
$53$	−2.38334	−0.327376	−0.163688	+	0.986512i	$0.552339\pi$
$54$	2.20287	0.299772
$55$	−14.2901	−1.92688
$56$	−2.33343	−0.311818
$57$	−6.75661	−0.894934
$58$	−0.587133	−0.0770944
$59$	7.29784	0.950098	0.475049	−	0.879959i	$-0.342430\pi$
$59$	7.29784	0.950098	0.475049	+	0.879959i	$0.342430\pi$
$60$	14.2478	1.83939
$61$	13.8005	1.76697	0.883484	−	0.468462i	$-0.155192\pi$
$61$	13.8005	1.76697	0.883484	+	0.468462i	$0.155192\pi$
$62$	−0.547006	−0.0694698
$63$	−20.3663	−2.56591
$64$	−7.12073	−0.890092
$65$	−11.9523	−1.48250
$66$	−3.67291	−0.452104
$67$	2.68532	0.328064	0.164032	−	0.986455i	$-0.447550\pi$
$67$	2.68532	0.328064	0.164032	+	0.986455i	$0.447550\pi$
$68$	1.75936	0.213354
$69$	−13.5208	−1.62772
$70$	1.37440	0.164272
$71$	6.53661	0.775753	0.387877	−	0.921711i	$-0.373209\pi$
$71$	6.53661	0.775753	0.387877	+	0.921711i	$0.373209\pi$
$72$	5.10022	0.601066
$73$	−11.2484	−1.31653	−0.658263	−	0.752788i	$-0.728709\pi$
$73$	−11.2484	−1.31653	−0.658263	+	0.752788i	$0.728709\pi$
$74$	−1.34129	−0.155921
$75$	−1.39321	−0.160874
$76$	−4.26428	−0.489146
$77$	18.6887	2.12977
$78$	−3.07203	−0.347839
$79$	−9.47425	−1.06594	−0.532968	−	0.846135i	$-0.678923\pi$
$79$	−9.47425	−1.06594	−0.532968	+	0.846135i	$0.678923\pi$
$80$	8.81848	0.985936
$81$	15.4990	1.72211
$82$	−0.738579	−0.0815624
$83$	2.39915	0.263341	0.131670	−	0.991294i	$-0.457966\pi$
$83$	2.39915	0.263341	0.131670	+	0.991294i	$0.457966\pi$
$84$	−18.6333	−2.03306
$85$	−2.09218	−0.226929
$86$	−2.43535	−0.262611
$87$	−9.46583	−1.01484
$88$	−4.68009	−0.498900
$89$	−5.93380	−0.628981	−0.314491	−	0.949261i	$-0.601834\pi$
$89$	−5.93380	−0.628981	−0.314491	+	0.949261i	$0.601834\pi$
$90$	−3.00404	−0.316653
$91$	15.6312	1.63860
$92$	−8.53336	−0.889665
$93$	−8.81889	−0.914476
$94$	2.31363	0.238632
$95$	5.07095	0.520269
$96$	7.02126	0.716604
$97$	9.10352	0.924323	0.462161	−	0.886796i	$-0.347074\pi$
$97$	9.10352	0.924323	0.462161	+	0.886796i	$0.347074\pi$
$98$	−0.447130	−0.0451670
$99$	−40.8480	−4.10538
$100$	−0.879295	−0.0879295
$101$	5.90918	0.587985	0.293993	−	0.955808i	$-0.405016\pi$
$101$	5.90918	0.587985	0.293993	+	0.955808i	$0.405016\pi$
$102$	−0.537741	−0.0532443
$103$	−0.766934	−0.0755682	−0.0377841	−	0.999286i	$-0.512030\pi$
$103$	−0.766934	−0.0755682	−0.0377841	+	0.999286i	$0.512030\pi$
$104$	−3.91444	−0.383843
$105$	22.1582	2.16242
$106$	0.459749	0.0446547
$107$	−4.51674	−0.436650	−0.218325	−	0.975876i	$-0.570059\pi$
$107$	−4.51674	−0.436650	−0.218325	+	0.975876i	$0.570059\pi$
$108$	22.4144	2.15683
$109$	0.114687	0.0109850	0.00549251	−	0.999985i	$-0.498252\pi$
$109$	0.114687	0.0109850	0.00549251	+	0.999985i	$0.498252\pi$
$110$	2.75658	0.262830
$111$	−21.6244	−2.05249
$112$	−11.5328	−1.08975
$113$	−10.3205	−0.970869	−0.485434	−	0.874273i	$-0.661339\pi$
$113$	−10.3205	−0.970869	−0.485434	+	0.874273i	$0.661339\pi$
$114$	1.30336	0.122071
$115$	10.1476	0.946271
$116$	−5.97414	−0.554685
$117$	−34.1654	−3.15859
$118$	−1.40776	−0.129595
$119$	2.73616	0.250823
$120$	−5.54895	−0.506547
$121$	26.4832	2.40757
$122$	−2.66212	−0.241017
$123$	−11.9074	−1.07366
$124$	−5.56584	−0.499827
$125$	−10.6248	−0.950313
$126$	3.92868	0.349995
$127$	−10.9177	−0.968791	−0.484396	−	0.874849i	$-0.660960\pi$
$127$	−10.9177	−0.968791	−0.484396	+	0.874849i	$0.660960\pi$
$128$	5.88891	0.520511
$129$	−39.2630	−3.45692
$130$	2.30561	0.202216
$131$	14.4727	1.26449	0.632243	−	0.774770i	$-0.282134\pi$
$131$	14.4727	1.26449	0.632243	+	0.774770i	$0.282134\pi$
$132$	−37.3722	−3.25284
$133$	−6.63180	−0.575050
$134$	−0.518002	−0.0447486
$135$	−26.6545	−2.29406
$136$	−0.685200	−0.0587554
$137$	4.72791	0.403932	0.201966	−	0.979393i	$-0.435267\pi$
$137$	4.72791	0.403932	0.201966	+	0.979393i	$0.435267\pi$
$138$	2.60819	0.222024
$139$	2.38264	0.202093	0.101047	−	0.994882i	$-0.467781\pi$
$139$	2.38264	0.202093	0.101047	+	0.994882i	$0.467781\pi$
$140$	13.9846	1.18192
$141$	37.3006	3.14127
$142$	−1.26092	−0.105814
$143$	31.3511	2.62171
$144$	25.2074	2.10062
$145$	7.10427	0.589978
$146$	2.16983	0.179577
$147$	−7.20869	−0.594562
$148$	−13.6477	−1.12184
$149$	17.1483	1.40485	0.702424	−	0.711759i	$-0.252101\pi$
$149$	17.1483	1.40485	0.702424	+	0.711759i	$0.252101\pi$
$150$	0.268753	0.0219436
$151$	−22.6841	−1.84601	−0.923003	−	0.384792i	$-0.874273\pi$
$151$	−22.6841	−1.84601	−0.923003	+	0.384792i	$0.874273\pi$
$152$	1.66076	0.134706
$153$	−5.98045	−0.483491
$154$	−3.60506	−0.290504
$155$	6.61873	0.531629
$156$	−31.2582	−2.50266
$157$	15.4343	1.23179	0.615894	−	0.787829i	$-0.288795\pi$
$157$	15.4343	1.23179	0.615894	+	0.787829i	$0.288795\pi$
$158$	1.82759	0.145396
$159$	7.41212	0.587819
$160$	−5.26958	−0.416597
$161$	−13.2711	−1.04591
$162$	−2.98978	−0.234899
$163$	−18.6812	−1.46322	−0.731612	−	0.681721i	$-0.761232\pi$
$163$	−18.6812	−1.46322	−0.731612	+	0.681721i	$0.761232\pi$
$164$	−7.51511	−0.586832
$165$	44.4420	3.45980
$166$	−0.462799	−0.0359202
$167$	10.0226	0.775573	0.387787	−	0.921749i	$-0.373240\pi$
$167$	10.0226	0.775573	0.387787	+	0.921749i	$0.373240\pi$
$168$	7.25692	0.559884
$169$	13.2221	1.01709
$170$	0.403584	0.0309535
$171$	14.4952	1.10848
$172$	−24.7800	−1.88945
$173$	5.44221	0.413764	0.206882	−	0.978366i	$-0.433668\pi$
$173$	5.44221	0.413764	0.206882	+	0.978366i	$0.433668\pi$
$174$	1.82597	0.138426
$175$	−1.36748	−0.103372
$176$	−23.1310	−1.74356
$177$	−22.6961	−1.70594
$178$	1.14464	0.0857942
$179$	15.8771	1.18671	0.593354	−	0.804942i	$-0.297804\pi$
$179$	15.8771	1.18671	0.593354	+	0.804942i	$0.297804\pi$
$180$	−30.5664	−2.27828
$181$	2.92930	0.217733	0.108866	−	0.994056i	$-0.465278\pi$
$181$	2.92930	0.217733	0.108866	+	0.994056i	$0.465278\pi$
$182$	−3.01529	−0.223508
$183$	−42.9191	−3.17267
$184$	3.32340	0.245004
$185$	16.2295	1.19321
$186$	1.70117	0.124736
$187$	5.48782	0.401309
$188$	23.5414	1.71693
$189$	34.8588	2.53561
$190$	−0.978193	−0.0709656
$191$	19.6763	1.42373	0.711863	−	0.702318i	$-0.247852\pi$
$191$	19.6763	1.42373	0.711863	+	0.702318i	$0.247852\pi$
$192$	22.1453	1.59820
$193$	12.8235	0.923059	0.461529	−	0.887125i	$-0.347301\pi$
$193$	12.8235	0.923059	0.461529	+	0.887125i	$0.347301\pi$
$194$	−1.75608	−0.126079
$195$	37.1714	2.66190
$196$	−4.54960	−0.324971
$197$	8.15721	0.581177	0.290589	−	0.956848i	$-0.406149\pi$
$197$	8.15721	0.581177	0.290589	+	0.956848i	$0.406149\pi$
$198$	7.87963	0.559981
$199$	1.48857	0.105522	0.0527611	−	0.998607i	$-0.483198\pi$
$199$	1.48857	0.105522	0.0527611	+	0.998607i	$0.483198\pi$
$200$	0.342450	0.0242149
$201$	−8.35129	−0.589054
$202$	−1.13989	−0.0802023
$203$	−9.29098	−0.652099
$204$	−5.47157	−0.383087
$205$	8.93675	0.624170
$206$	0.147942	0.0103076
$207$	29.0068	2.01611
$208$	−19.3468	−1.34146
$209$	−13.3012	−0.920062
$210$	−4.27434	−0.294958
$211$	9.10315	0.626687	0.313343	−	0.949640i	$-0.398551\pi$
$211$	9.10315	0.626687	0.313343	+	0.949640i	$0.398551\pi$
$212$	4.67799	0.321285
$213$	−20.3287	−1.39290
$214$	0.871285	0.0595598
$215$	29.4676	2.00967
$216$	−8.72950	−0.593967
$217$	−8.65598	−0.587606
$218$	−0.0221233	−0.00149838
$219$	34.9823	2.36388
$220$	28.0485	1.89103
$221$	4.59003	0.308759
$222$	4.17137	0.279964
$223$	8.18333	0.547996	0.273998	−	0.961730i	$-0.411654\pi$
$223$	8.18333	0.547996	0.273998	+	0.961730i	$0.411654\pi$
$224$	6.89156	0.460462
$225$	2.98891	0.199261
$226$	1.99083	0.132428
$227$	−5.86743	−0.389435	−0.194717	−	0.980859i	$-0.562379\pi$
$227$	−5.86743	−0.389435	−0.194717	+	0.980859i	$0.562379\pi$
$228$	13.2618	0.878284
$229$	−21.6773	−1.43248	−0.716240	−	0.697854i	$-0.754138\pi$
$229$	−21.6773	−1.43248	−0.716240	+	0.697854i	$0.754138\pi$
$230$	−1.95749	−0.129073
$231$	−58.1212	−3.82410
$232$	2.32669	0.152754
$233$	−4.03046	−0.264044	−0.132022	−	0.991247i	$-0.542147\pi$
$233$	−4.03046	−0.264044	−0.132022	+	0.991247i	$0.542147\pi$
$234$	6.59055	0.430838
$235$	−27.9947	−1.82617
$236$	−14.3241	−0.932421
$237$	29.4647	1.91394
$238$	−0.527808	−0.0342127
$239$	12.9688	0.838882	0.419441	−	0.907783i	$-0.362226\pi$
$239$	12.9688	0.838882	0.419441	+	0.907783i	$0.362226\pi$
$240$	−27.4252	−1.77029
$241$	−25.7754	−1.66034	−0.830170	−	0.557511i	$-0.811756\pi$
$241$	−25.7754	−1.66034	−0.830170	+	0.557511i	$0.811756\pi$
$242$	−5.10865	−0.328396
$243$	−13.9426	−0.894418
$244$	−27.0874	−1.73409
$245$	5.41025	0.345648
$246$	2.29696	0.146449
$247$	−11.1251	−0.707876
$248$	2.16767	0.137647
$249$	−7.46130	−0.472841
$250$	2.04954	0.129624
$251$	−17.4975	−1.10443	−0.552217	−	0.833701i	$-0.686218\pi$
$251$	−17.4975	−1.10443	−0.552217	+	0.833701i	$0.686218\pi$
$252$	39.9747	2.51817
$253$	−26.6174	−1.67342
$254$	2.10604	0.132145
$255$	6.50663	0.407461
$256$	13.1055	0.819093
$257$	−14.9171	−0.930503	−0.465251	−	0.885179i	$-0.654036\pi$
$257$	−14.9171	−0.930503	−0.465251	+	0.885179i	$0.654036\pi$
$258$	7.57389	0.471530
$259$	−21.2249	−1.31885
$260$	23.4599	1.45492
$261$	20.3074	1.25700
$262$	−2.79180	−0.172478
$263$	6.59081	0.406407	0.203203	−	0.979137i	$-0.434865\pi$
$263$	6.59081	0.406407	0.203203	+	0.979137i	$0.434865\pi$
$264$	14.5550	0.895797
$265$	−5.56292	−0.341728
$266$	1.27928	0.0784378
$267$	18.4540	1.12936
$268$	−5.27072	−0.321961
$269$	−29.7208	−1.81211	−0.906056	−	0.423158i	$-0.860922\pi$
$269$	−29.7208	−1.81211	−0.906056	+	0.423158i	$0.860922\pi$
$270$	5.14169	0.312913
$271$	17.7722	1.07959	0.539793	−	0.841798i	$-0.318502\pi$
$271$	17.7722	1.07959	0.539793	+	0.841798i	$0.318502\pi$
$272$	−3.38655	−0.205340
$273$	−48.6128	−2.94218
$274$	−0.912019	−0.0550971
$275$	−2.74271	−0.165391
$276$	26.5385	1.59743
$277$	−24.3785	−1.46476	−0.732382	−	0.680894i	$-0.761591\pi$
$277$	−24.3785	−1.46476	−0.732382	+	0.680894i	$0.761591\pi$
$278$	−0.459615	−0.0275659
$279$	18.9195	1.13268
$280$	−5.44645	−0.325488
$281$	29.5644	1.76366	0.881831	−	0.471566i	$-0.156311\pi$
$281$	29.5644	1.76366	0.881831	+	0.471566i	$0.156311\pi$
$282$	−7.19532	−0.428475
$283$	−1.10776	−0.0658495	−0.0329248	−	0.999458i	$-0.510482\pi$
$283$	−1.10776	−0.0658495	−0.0329248	+	0.999458i	$0.510482\pi$
$284$	−12.8300	−0.761320
$285$	−15.7705	−0.934166
$286$	−6.04766	−0.357606
$287$	−11.6875	−0.689891
$288$	−15.0630	−0.887594
$289$	−16.1965	−0.952738
$290$	−1.37042	−0.0804740
$291$	−28.3117	−1.65966
$292$	22.0783	1.29203
$293$	11.5075	0.672278	0.336139	−	0.941812i	$-0.390879\pi$
$293$	11.5075	0.672278	0.336139	+	0.941812i	$0.390879\pi$
$294$	1.39056	0.0810994
$295$	17.0338	0.991747
$296$	5.31524	0.308942
$297$	69.9152	4.05689
$298$	−3.30794	−0.191624
$299$	−22.2628	−1.28749
$300$	2.73458	0.157881
$301$	−38.5378	−2.22128
$302$	4.37579	0.251799
$303$	−18.3774	−1.05575
$304$	8.20819	0.470772
$305$	32.2115	1.84443
$306$	1.15364	0.0659490
$307$	6.14683	0.350818	0.175409	−	0.984496i	$-0.443875\pi$
$307$	6.14683	0.350818	0.175409	+	0.984496i	$0.443875\pi$
$308$	−36.6819	−2.09014
$309$	2.38514	0.135686
$310$	−1.27676	−0.0725152
$311$	13.4926	0.765094	0.382547	−	0.923936i	$-0.375047\pi$
$311$	13.4926	0.765094	0.382547	+	0.923936i	$0.375047\pi$
$312$	12.1738	0.689207
$313$	−12.0457	−0.680865	−0.340433	−	0.940269i	$-0.610574\pi$
$313$	−12.0457	−0.680865	−0.340433	+	0.940269i	$0.610574\pi$
$314$	−2.97729	−0.168018
$315$	−47.5368	−2.67840
$316$	18.5960	1.04610
$317$	7.50974	0.421789	0.210895	−	0.977509i	$-0.432362\pi$
$317$	7.50974	0.421789	0.210895	+	0.977509i	$0.432362\pi$
$318$	−1.42981	−0.0801796
$319$	−18.6346	−1.04334
$320$	−16.6204	−0.929111
$321$	14.0470	0.784025
$322$	2.56001	0.142664
$323$	−1.94739	−0.108356
$324$	−30.4213	−1.69007
$325$	−2.29401	−0.127249
$326$	3.60363	0.199586
$327$	−0.356674	−0.0197241
$328$	2.92683	0.161607
$329$	36.6115	2.01846
$330$	−8.57291	−0.471923
$331$	33.9328	1.86512	0.932558	−	0.361021i	$-0.117572\pi$
$331$	33.9328	1.86512	0.932558	+	0.361021i	$0.117572\pi$
$332$	−4.70903	−0.258441
$333$	46.3916	2.54224
$334$	−1.93338	−0.105790
$335$	6.26779	0.342446
$336$	35.8668	1.95669
$337$	26.2816	1.43165	0.715826	−	0.698279i	$-0.246050\pi$
$337$	26.2816	1.43165	0.715826	+	0.698279i	$0.246050\pi$
$338$	−2.55056	−0.138732
$339$	32.0964	1.74324
$340$	4.10651	0.222707
$341$	−17.3610	−0.940152
$342$	−2.79614	−0.151198
$343$	14.2922	0.771704
$344$	9.65080	0.520336
$345$	−31.5589	−1.69907
$346$	−1.04981	−0.0564381
$347$	24.6552	1.32356	0.661780	−	0.749698i	$-0.269801\pi$
$347$	24.6552	1.32356	0.661780	+	0.749698i	$0.269801\pi$
$348$	18.5794	0.995962
$349$	−5.96668	−0.319389	−0.159695	−	0.987166i	$-0.551051\pi$
$349$	−5.96668	−0.319389	−0.159695	+	0.987166i	$0.551051\pi$
$350$	0.263788	0.0141001
$351$	58.4773	3.12129
$352$	13.8222	0.736725
$353$	−17.6586	−0.939870	−0.469935	−	0.882701i	$-0.655723\pi$
$353$	−17.6586	−0.939870	−0.469935	+	0.882701i	$0.655723\pi$
$354$	4.37811	0.232694
$355$	15.2571	0.809760
$356$	11.6468	0.617279
$357$	−8.50938	−0.450364
$358$	−3.06270	−0.161869
$359$	25.7625	1.35969	0.679847	−	0.733354i	$-0.262046\pi$
$359$	25.7625	1.35969	0.679847	+	0.733354i	$0.262046\pi$
$360$	11.9044	0.627415
$361$	−14.2800	−0.751578
$362$	−0.565065	−0.0296991
$363$	−82.3622	−4.32289
$364$	−30.6808	−1.60811
$365$	−26.2548	−1.37424
$366$	8.27914	0.432758
$367$	−3.26236	−0.170294	−0.0851468	−	0.996368i	$-0.527136\pi$
$367$	−3.26236	−0.170294	−0.0851468	+	0.996368i	$0.527136\pi$
$368$	16.4256	0.856246
$369$	25.5455	1.32985
$370$	−3.13069	−0.162757
$371$	7.27520	0.377710
$372$	17.3096	0.897462
$373$	−10.0770	−0.521767	−0.260883	−	0.965370i	$-0.584014\pi$
$373$	−10.0770	−0.521767	−0.260883	+	0.965370i	$0.584014\pi$
$374$	−1.05861	−0.0547393
$375$	33.0429	1.70633
$376$	−9.16842	−0.472825
$377$	−15.5860	−0.802722
$378$	−6.72431	−0.345861
$379$	21.4912	1.10393	0.551965	−	0.833867i	$-0.313878\pi$
$379$	21.4912	1.10393	0.551965	+	0.833867i	$0.313878\pi$
$380$	−9.95321	−0.510589
$381$	33.9538	1.73951
$382$	−3.79558	−0.194199
$383$	19.5424	0.998568	0.499284	−	0.866438i	$-0.333596\pi$
$383$	19.5424	0.998568	0.499284	+	0.866438i	$0.333596\pi$
$384$	−18.3144	−0.934602
$385$	43.6210	2.22313
$386$	−2.47368	−0.125907
$387$	84.2325	4.28178
$388$	−17.8683	−0.907125
$389$	−32.9546	−1.67086	−0.835432	−	0.549593i	$-0.814783\pi$
$389$	−32.9546	−1.67086	−0.835432	+	0.549593i	$0.814783\pi$
$390$	−7.17041	−0.363088
$391$	−3.89698	−0.197079
$392$	1.77188	0.0894936
$393$	−45.0098	−2.27044
$394$	−1.57354	−0.0792736
$395$	−22.1138	−1.11266
$396$	80.1760	4.02900
$397$	12.0311	0.603822	0.301911	−	0.953336i	$-0.402375\pi$
$397$	12.0311	0.603822	0.301911	+	0.953336i	$0.402375\pi$
$398$	−0.287148	−0.0143934
$399$	20.6247	1.03253
$400$	1.69253	0.0846265
$401$	19.1683	0.957219	0.478610	−	0.878028i	$-0.341141\pi$
$401$	19.1683	0.957219	0.478610	+	0.878028i	$0.341141\pi$
$402$	1.61097	0.0803481
$403$	−14.5208	−0.723333
$404$	−11.5985	−0.577046
$405$	36.1761	1.79761
$406$	1.79224	0.0889474
$407$	−42.5701	−2.11012
$408$	2.13096	0.105498
$409$	−3.17142	−0.156817	−0.0784084	−	0.996921i	$-0.524984\pi$
$409$	−3.17142	−0.156817	−0.0784084	+	0.996921i	$0.524984\pi$
$410$	−1.72391	−0.0851379
$411$	−14.7037	−0.725278
$412$	1.50533	0.0741622
$413$	−22.2769	−1.09617
$414$	−5.59544	−0.275001
$415$	5.59984	0.274885
$416$	11.5609	0.566820
$417$	−7.40996	−0.362867
$418$	2.56581	0.125498
$419$	30.6433	1.49702	0.748511	−	0.663123i	$-0.230769\pi$
$419$	30.6433	1.49702	0.748511	+	0.663123i	$0.230769\pi$
$420$	−43.4919	−2.12219
$421$	30.8789	1.50495	0.752474	−	0.658622i	$-0.228861\pi$
$421$	30.8789	1.50495	0.752474	+	0.658622i	$0.228861\pi$
$422$	−1.75601	−0.0854812
$423$	−80.0223	−3.89082
$424$	−1.82189	−0.0884786
$425$	−0.401552	−0.0194782
$426$	3.92143	0.189994
$427$	−42.1263	−2.03863
$428$	8.86541	0.428526
$429$	−97.5010	−4.70739
$430$	−5.68434	−0.274123
$431$	14.4654	0.696774	0.348387	−	0.937351i	$-0.386730\pi$
$431$	14.4654	0.696774	0.348387	+	0.937351i	$0.386730\pi$
$432$	−43.1448	−2.07581
$433$	7.59106	0.364803	0.182402	−	0.983224i	$-0.441613\pi$
$433$	7.59106	0.364803	0.182402	+	0.983224i	$0.441613\pi$
$434$	1.66975	0.0801506
$435$	−22.0941	−1.05933
$436$	−0.225107	−0.0107806
$437$	9.44535	0.451832
$438$	−6.74812	−0.322438
$439$	−24.1038	−1.15041	−0.575206	−	0.818009i	$-0.695078\pi$
$439$	−24.1038	−1.15041	−0.575206	+	0.818009i	$0.695078\pi$
$440$	−10.9238	−0.520770
$441$	15.4651	0.736432
$442$	−0.885422	−0.0421152
$443$	−19.9951	−0.949996	−0.474998	−	0.879987i	$-0.657551\pi$
$443$	−19.9951	−0.949996	−0.474998	+	0.879987i	$0.657551\pi$
$444$	42.4441	2.01431
$445$	−13.8500	−0.656554
$446$	−1.57857	−0.0747477
$447$	−53.3309	−2.52247
$448$	21.7362	1.02694
$449$	14.0576	0.663417	0.331709	−	0.943382i	$-0.392375\pi$
$449$	14.0576	0.663417	0.331709	+	0.943382i	$0.392375\pi$
$450$	−0.576565	−0.0271795
$451$	−23.4412	−1.10380
$452$	20.2569	0.952805
$453$	70.5470	3.31459
$454$	1.13183	0.0531196
$455$	36.4847	1.71043
$456$	−5.16493	−0.241870
$457$	−2.92697	−0.136918	−0.0684590	−	0.997654i	$-0.521808\pi$
$457$	−2.92697	−0.136918	−0.0684590	+	0.997654i	$0.521808\pi$
$458$	4.18159	0.195393
$459$	10.2361	0.477780
$460$	−19.9176	−0.928665
$461$	18.7341	0.872533	0.436267	−	0.899817i	$-0.356300\pi$
$461$	18.7341	0.872533	0.436267	+	0.899817i	$0.356300\pi$
$462$	11.2117	0.521614
$463$	−5.40895	−0.251375	−0.125688	−	0.992070i	$-0.540114\pi$
$463$	−5.40895	−0.251375	−0.125688	+	0.992070i	$0.540114\pi$
$464$	11.4995	0.533849
$465$	−20.5841	−0.954564
$466$	0.777481	0.0360161
$467$	−20.4289	−0.945337	−0.472668	−	0.881240i	$-0.656709\pi$
$467$	−20.4289	−0.945337	−0.472668	+	0.881240i	$0.656709\pi$
$468$	67.0595	3.09982
$469$	−8.19702	−0.378503
$470$	5.40022	0.249093
$471$	−48.0001	−2.21173
$472$	5.57866	0.256779
$473$	−77.2940	−3.55398
$474$	−5.68377	−0.261064
$475$	0.973268	0.0446566
$476$	−5.37050	−0.246156
$477$	−15.9015	−0.728079
$478$	−2.50170	−0.114425
$479$	−3.83097	−0.175041	−0.0875207	−	0.996163i	$-0.527894\pi$
$479$	−3.83097	−0.175041	−0.0875207	+	0.996163i	$0.527894\pi$
$480$	16.3883	0.748018
$481$	−35.6058	−1.62348
$482$	4.97211	0.226473
$483$	41.2727	1.87797
$484$	−51.9810	−2.36277
$485$	21.2485	0.964843
$486$	2.68954	0.122000
$487$	23.6208	1.07036	0.535179	−	0.844738i	$-0.320244\pi$
$487$	23.6208	1.07036	0.535179	+	0.844738i	$0.320244\pi$
$488$	10.5494	0.477551
$489$	58.0981	2.62728
$490$	−1.04364	−0.0471470
$491$	−0.0396717	−0.00179036	−0.000895180	−	1.00000i	$-0.500285\pi$
$491$	−0.0396717	−0.00179036	−0.000895180		1.00000i	$0.500285\pi$
$492$	23.3718	1.05368
$493$	−2.72824	−0.122874
$494$	2.14605	0.0965555
$495$	−95.3430	−4.28535
$496$	10.7135	0.481052
$497$	−19.9532	−0.895023
$498$	1.43929	0.0644963
$499$	22.3479	1.00043	0.500215	−	0.865901i	$-0.333254\pi$
$499$	22.3479	1.00043	0.500215	+	0.865901i	$0.333254\pi$
$500$	20.8543	0.932632
$501$	−31.1701	−1.39258
$502$	3.37529	0.150647
$503$	3.65604	0.163015	0.0815074	−	0.996673i	$-0.474027\pi$
$503$	3.65604	0.163015	0.0815074	+	0.996673i	$0.474027\pi$
$504$	−15.5685	−0.693478
$505$	13.7926	0.613761
$506$	5.13452	0.228257
$507$	−41.1205	−1.82622
$508$	21.4292	0.950766
$509$	−33.3734	−1.47925	−0.739625	−	0.673019i	$-0.764997\pi$
$509$	−33.3734	−1.47925	−0.739625	+	0.673019i	$0.764997\pi$
$510$	−1.25514	−0.0555784
$511$	34.3361	1.51894
$512$	−14.3059	−0.632237
$513$	−24.8099	−1.09538
$514$	2.87753	0.126922
$515$	−1.79009	−0.0788809
$516$	77.0651	3.39260
$517$	73.4305	3.22947
$518$	4.09431	0.179894
$519$	−16.9251	−0.742932
$520$	−9.13667	−0.400669
$521$	26.9294	1.17980	0.589900	−	0.807476i	$-0.299167\pi$
$521$	26.9294	1.17980	0.589900	+	0.807476i	$0.299167\pi$
$522$	−3.91732	−0.171457
$523$	6.84563	0.299338	0.149669	−	0.988736i	$-0.452179\pi$
$523$	6.84563	0.299338	0.149669	+	0.988736i	$0.452179\pi$
$524$	−28.4069	−1.24096
$525$	4.25282	0.185608
$526$	−1.27138	−0.0554346
$527$	−2.54178	−0.110722
$528$	71.9368	3.13065
$529$	−4.09864	−0.178202
$530$	1.07310	0.0466123
$531$	48.6908	2.11300
$532$	13.0168	0.564351
$533$	−19.6063	−0.849243
$534$	−3.55979	−0.154047
$535$	−10.5425	−0.455792
$536$	2.05273	0.0886646
$537$	−49.3773	−2.13079
$538$	5.73319	0.247175
$539$	−14.1911	−0.611256
$540$	52.3172	2.25137
$541$	39.0545	1.67908	0.839542	−	0.543295i	$-0.182824\pi$
$541$	39.0545	1.67908	0.839542	+	0.543295i	$0.182824\pi$
$542$	−3.42829	−0.147258
$543$	−9.11004	−0.390949
$544$	2.02367	0.0867641
$545$	0.267690	0.0114666
$546$	9.37746	0.401318
$547$	38.4058	1.64211	0.821057	−	0.570846i	$-0.193385\pi$
$547$	38.4058	1.64211	0.821057	+	0.570846i	$0.193385\pi$
$548$	−9.27988	−0.396417
$549$	92.0759	3.92970
$550$	0.529071	0.0225597
$551$	6.61262	0.281707
$552$	−10.3357	−0.439916
$553$	28.9204	1.22982
$554$	4.70265	0.199796
$555$	−50.4733	−2.14247
$556$	−4.67662	−0.198333
$557$	17.6576	0.748177	0.374088	−	0.927393i	$-0.377956\pi$
$557$	17.6576	0.748177	0.374088	+	0.927393i	$0.377956\pi$
$558$	−3.64959	−0.154500
$559$	−64.6489	−2.73436
$560$	−26.9186	−1.13752
$561$	−17.0670	−0.720569
$562$	−5.70300	−0.240567
$563$	15.6668	0.660277	0.330138	−	0.943933i	$-0.392905\pi$
$563$	15.6668	0.660277	0.330138	+	0.943933i	$0.392905\pi$
$564$	−73.2131	−3.08283
$565$	−24.0889	−1.01343
$566$	0.213688	0.00898199
$567$	−47.3112	−1.98688
$568$	4.99676	0.209660
$569$	32.7556	1.37319	0.686593	−	0.727042i	$-0.259105\pi$
$569$	32.7556	1.37319	0.686593	+	0.727042i	$0.259105\pi$
$570$	3.04216	0.127422
$571$	−0.652610	−0.0273109	−0.0136554	−	0.999907i	$-0.504347\pi$
$571$	−0.652610	−0.0273109	−0.0136554	+	0.999907i	$0.504347\pi$
$572$	−61.5355	−2.57293
$573$	−61.1928	−2.55636
$574$	2.25453	0.0941023
$575$	1.94763	0.0812220
$576$	−47.5091	−1.97955
$577$	−2.79694	−0.116438	−0.0582191	−	0.998304i	$-0.518542\pi$
$577$	−2.79694	−0.116438	−0.0582191	+	0.998304i	$0.518542\pi$
$578$	3.12433	0.129955
$579$	−39.8809	−1.65739
$580$	−13.9442	−0.579001
$581$	−7.32347	−0.303829
$582$	5.46137	0.226381
$583$	14.5916	0.604324
$584$	−8.59859	−0.355812
$585$	−79.7451	−3.29706
$586$	−2.21982	−0.0916999
$587$	−3.42878	−0.141521	−0.0707604	−	0.997493i	$-0.522543\pi$
$587$	−3.42878	−0.141521	−0.0707604	+	0.997493i	$0.522543\pi$
$588$	14.1491	0.583500
$589$	6.16068	0.253846
$590$	−3.28585	−0.135276
$591$	−25.3687	−1.04353
$592$	26.2701	1.07970
$593$	−28.3718	−1.16509	−0.582545	−	0.812798i	$-0.697943\pi$
$593$	−28.3718	−1.16509	−0.582545	+	0.812798i	$0.697943\pi$
$594$	−13.4867	−0.553367
$595$	6.38644	0.261819
$596$	−33.6586	−1.37871
$597$	−4.62943	−0.189470
$598$	4.29453	0.175616
$599$	−46.1714	−1.88651	−0.943256	−	0.332067i	$-0.892254\pi$
$599$	−46.1714	−1.88651	−0.943256	+	0.332067i	$0.892254\pi$
$600$	−1.06501	−0.0434789
$601$	2.63498	0.107483	0.0537416	−	0.998555i	$-0.482885\pi$
$601$	2.63498	0.107483	0.0537416	+	0.998555i	$0.482885\pi$
$602$	7.43399	0.302987
$603$	17.9163	0.729609
$604$	44.5241	1.81166
$605$	61.8143	2.51311
$606$	3.54502	0.144007
$607$	−28.4421	−1.15443	−0.577215	−	0.816592i	$-0.695860\pi$
$607$	−28.4421	−1.15443	−0.577215	+	0.816592i	$0.695860\pi$
$608$	−4.90490	−0.198920
$609$	28.8947	1.17087
$610$	−6.21364	−0.251583
$611$	61.4175	2.48469
$612$	11.7384	0.474495
$613$	7.10940	0.287146	0.143573	−	0.989640i	$-0.454141\pi$
$613$	7.10940	0.287146	0.143573	+	0.989640i	$0.454141\pi$
$614$	−1.18573	−0.0478522
$615$	−27.7931	−1.12072
$616$	14.2861	0.575604
$617$	13.9339	0.560959	0.280479	−	0.959860i	$-0.409507\pi$
$617$	13.9339	0.560959	0.280479	+	0.959860i	$0.409507\pi$
$618$	−0.460097	−0.0185078
$619$	1.00000	0.0401934
$619$	1.00000	0.0401934
$620$	−12.9912	−0.521738
$621$	−49.6478	−1.99230
$622$	−2.60274	−0.104360
$623$	18.1131	0.725685
$624$	60.1681	2.40865
$625$	−27.0392	−1.08157
$626$	2.32364	0.0928712
$627$	41.3663	1.65201
$628$	−30.2942	−1.20887
$629$	−6.23258	−0.248509
$630$	9.16991	0.365338
$631$	−33.1836	−1.32102	−0.660509	−	0.750818i	$-0.729660\pi$
$631$	−33.1836	−1.32102	−0.660509	+	0.750818i	$0.729660\pi$
$632$	−7.24237	−0.288086
$633$	−28.3106	−1.12524
$634$	−1.44864	−0.0575328
$635$	−25.4830	−1.01126
$636$	−14.5484	−0.576882
$637$	−11.8695	−0.470287
$638$	3.59464	0.142313
$639$	43.6119	1.72526
$640$	13.7453	0.543329
$641$	8.15248	0.322003	0.161002	−	0.986954i	$-0.448528\pi$
$641$	8.15248	0.322003	0.161002	+	0.986954i	$0.448528\pi$
$642$	−2.70968	−0.106942
$643$	8.80607	0.347277	0.173639	−	0.984809i	$-0.444448\pi$
$643$	8.80607	0.347277	0.173639	+	0.984809i	$0.444448\pi$
$644$	26.0483	1.02645
$645$	−91.6435	−3.60846
$646$	0.375654	0.0147799
$647$	−10.8997	−0.428510	−0.214255	−	0.976778i	$-0.568732\pi$
$647$	−10.8997	−0.428510	−0.214255	+	0.976778i	$0.568732\pi$
$648$	11.8479	0.465428
$649$	−44.6799	−1.75384
$650$	0.442517	0.0173569
$651$	26.9199	1.05507
$652$	36.6672	1.43600
$653$	47.3004	1.85101	0.925505	−	0.378736i	$-0.123641\pi$
$653$	47.3004	1.85101	0.925505	+	0.378736i	$0.123641\pi$
$654$	0.0688028	0.00269040
$655$	33.7806	1.31992
$656$	14.4656	0.564788
$657$	−75.0488	−2.92793
$658$	−7.06241	−0.275321
$659$	13.1863	0.513666	0.256833	−	0.966456i	$-0.417321\pi$
$659$	13.1863	0.513666	0.256833	+	0.966456i	$0.417321\pi$
$660$	−87.2302	−3.39543
$661$	24.8215	0.965445	0.482723	−	0.875773i	$-0.339648\pi$
$661$	24.8215	0.965445	0.482723	+	0.875773i	$0.339648\pi$
$662$	−6.54568	−0.254405
$663$	−14.2749	−0.554390
$664$	1.83398	0.0711720
$665$	−15.4792	−0.600258
$666$	−8.94899	−0.346766
$667$	13.2327	0.512372
$668$	−19.6723	−0.761143
$669$	−25.4500	−0.983952
$670$	−1.20906	−0.0467102
$671$	−84.4913	−3.26175
$672$	−21.4326	−0.826780
$673$	34.6977	1.33750	0.668749	−	0.743488i	$-0.266830\pi$
$673$	34.6977	1.33750	0.668749	+	0.743488i	$0.266830\pi$
$674$	−5.06976	−0.195280
$675$	−5.11581	−0.196907
$676$	−25.9522	−0.998163
$677$	−30.7289	−1.18101	−0.590504	−	0.807035i	$-0.701071\pi$
$677$	−30.7289	−1.18101	−0.590504	+	0.807035i	$0.701071\pi$
$678$	−6.19144	−0.237781
$679$	−27.7888	−1.06643
$680$	−1.59932	−0.0613311
$681$	18.2476	0.699248
$682$	3.34896	0.128238
$683$	−5.04846	−0.193174	−0.0965870	−	0.995325i	$-0.530793\pi$
$683$	−5.04846	−0.193174	−0.0965870	+	0.995325i	$0.530793\pi$
$684$	−28.4510	−1.08785
$685$	11.0354	0.421640
$686$	−2.75698	−0.105262
$687$	67.4160	2.57208
$688$	47.6983	1.81848
$689$	12.2045	0.464954
$690$	6.08774	0.231756
$691$	−12.3140	−0.468448	−0.234224	−	0.972183i	$-0.575255\pi$
$691$	−12.3140	−0.468448	−0.234224	+	0.972183i	$0.575255\pi$
$692$	−10.6819	−0.406066
$693$	124.690	4.73657
$694$	−4.75602	−0.180536
$695$	5.56131	0.210952
$696$	−7.23594	−0.274277
$697$	−3.43197	−0.129995
$698$	1.15098	0.0435652
$699$	12.5346	0.474103
$700$	2.68407	0.101448
$701$	−2.74300	−0.103602	−0.0518008	−	0.998657i	$-0.516496\pi$
$701$	−2.74300	−0.103602	−0.0518008	+	0.998657i	$0.516496\pi$
$702$	−11.2803	−0.425749
$703$	15.1063	0.569745
$704$	43.5957	1.64307
$705$	87.0629	3.27898
$706$	3.40636	0.128200
$707$	−18.0379	−0.678386
$708$	44.5477	1.67420
$709$	−36.1836	−1.35890	−0.679452	−	0.733720i	$-0.737782\pi$
$709$	−36.1836	−1.35890	−0.679452	+	0.733720i	$0.737782\pi$
$710$	−2.94310	−0.110453
$711$	−63.2117	−2.37062
$712$	−4.53596	−0.169992
$713$	12.3283	0.461699
$714$	1.64147	0.0614305
$715$	73.1763	2.73664
$716$	−31.1633	−1.16463
$717$	−40.3327	−1.50625
$718$	−4.96963	−0.185465
$719$	−7.81506	−0.291453	−0.145726	−	0.989325i	$-0.546552\pi$
$719$	−7.81506	−0.291453	−0.145726	+	0.989325i	$0.546552\pi$
$720$	58.8364	2.19270
$721$	2.34109	0.0871866
$722$	2.75463	0.102517
$723$	80.1608	2.98121
$724$	−5.74959	−0.213682
$725$	1.36352	0.0506400
$726$	15.8878	0.589650
$727$	−4.62432	−0.171507	−0.0857534	−	0.996316i	$-0.527330\pi$
$727$	−4.62432	−0.171507	−0.0857534	+	0.996316i	$0.527330\pi$
$728$	11.9489	0.442857
$729$	−3.13594	−0.116146
$730$	5.06459	0.187449
$731$	−11.3164	−0.418552
$732$	84.2411	3.11364
$733$	6.95390	0.256848	0.128424	−	0.991719i	$-0.459008\pi$
$733$	6.95390	0.256848	0.128424	+	0.991719i	$0.459008\pi$
$734$	0.629312	0.0232283
$735$	−16.8257	−0.620626
$736$	−9.81533	−0.361798
$737$	−16.4405	−0.605594
$738$	−4.92776	−0.181393
$739$	−11.7768	−0.433218	−0.216609	−	0.976258i	$-0.569500\pi$
$739$	−11.7768	−0.433218	−0.216609	+	0.976258i	$0.569500\pi$
$740$	−31.8550	−1.17101
$741$	34.5989	1.27102
$742$	−1.40340	−0.0515203
$743$	4.75069	0.174286	0.0871430	−	0.996196i	$-0.472226\pi$
$743$	4.75069	0.174286	0.0871430	+	0.996196i	$0.472226\pi$
$744$	−6.74140	−0.247152
$745$	40.0258	1.46643
$746$	1.94386	0.0711699
$747$	16.0070	0.585666
$748$	−10.7714	−0.393843
$749$	13.7875	0.503784
$750$	−6.37403	−0.232746
$751$	−34.8760	−1.27264	−0.636321	−	0.771425i	$-0.719545\pi$
$751$	−34.8760	−1.27264	−0.636321	+	0.771425i	$0.719545\pi$
$752$	−45.3142	−1.65244
$753$	54.4168	1.98306
$754$	3.00657	0.109493
$755$	−52.9468	−1.92693
$756$	−68.4205	−2.48843
$757$	−42.2809	−1.53672	−0.768362	−	0.640016i	$-0.778928\pi$
$757$	−42.2809	−1.53672	−0.768362	+	0.640016i	$0.778928\pi$
$758$	−4.14569	−0.150578
$759$	82.7793	3.00470
$760$	3.87637	0.140611
$761$	28.6763	1.03952	0.519758	−	0.854313i	$-0.326022\pi$
$761$	28.6763	1.03952	0.519758	+	0.854313i	$0.326022\pi$
$762$	−6.54974	−0.237272
$763$	−0.350085	−0.0126739
$764$	−38.6204	−1.39724
$765$	−13.9589	−0.504686
$766$	−3.76975	−0.136206
$767$	−37.3704	−1.34937
$768$	−40.7577	−1.47072
$769$	13.3613	0.481821	0.240910	−	0.970547i	$-0.422554\pi$
$769$	13.3613	0.481821	0.240910	+	0.970547i	$0.422554\pi$
$770$	−8.41455	−0.303239
$771$	46.3918	1.67076
$772$	−25.1699	−0.905885
$773$	−35.3199	−1.27037	−0.635185	−	0.772360i	$-0.719076\pi$
$773$	−35.3199	−1.27037	−0.635185	+	0.772360i	$0.719076\pi$
$774$	−16.2486	−0.584042
$775$	1.27033	0.0456317
$776$	6.95898	0.249813
$777$	66.0090	2.36806
$778$	6.35698	0.227909
$779$	8.31828	0.298033
$780$	−72.9596	−2.61237
$781$	−40.0195	−1.43201
$782$	0.751732	0.0268819
$783$	−34.7580	−1.24215
$784$	8.75739	0.312764
$785$	36.0250	1.28579
$786$	8.68244	0.309692
$787$	38.6584	1.37802	0.689011	−	0.724751i	$-0.258045\pi$
$787$	38.6584	1.37802	0.689011	+	0.724751i	$0.258045\pi$
$788$	−16.0109	−0.570364
$789$	−20.4973	−0.729722
$790$	4.26577	0.151769
$791$	31.5035	1.12014
$792$	−31.2253	−1.10954
$793$	−70.6687	−2.50952
$794$	−2.32081	−0.0823624
$795$	17.3006	0.613588
$796$	−2.92176	−0.103559
$797$	7.09882	0.251453	0.125727	−	0.992065i	$-0.459874\pi$
$797$	7.09882	0.251453	0.125727	+	0.992065i	$0.459874\pi$
$798$	−3.97853	−0.140839
$799$	10.7508	0.380335
$800$	−1.01139	−0.0357581
$801$	−39.5900	−1.39884
$802$	−3.69759	−0.130566
$803$	68.8667	2.43025
$804$	16.3918	0.578095
$805$	−30.9759	−1.09176
$806$	2.80108	0.0986639
$807$	92.4311	3.25373
$808$	4.51714	0.158912
$809$	29.9032	1.05134	0.525671	−	0.850688i	$-0.323814\pi$
$809$	29.9032	1.05134	0.525671	+	0.850688i	$0.323814\pi$
$810$	−6.97842	−0.245197
$811$	−5.52383	−0.193968	−0.0969839	−	0.995286i	$-0.530920\pi$
$811$	−5.52383	−0.193968	−0.0969839	+	0.995286i	$0.530920\pi$
$812$	18.2362	0.639966
$813$	−55.2712	−1.93845
$814$	8.21183	0.287825
$815$	−43.6036	−1.52737
$816$	10.5321	0.368697
$817$	27.4283	0.959594
$818$	0.611772	0.0213901
$819$	104.291	3.64422
$820$	−17.5410	−0.612557
$821$	16.1777	0.564607	0.282304	−	0.959325i	$-0.408901\pi$
$821$	16.1777	0.564607	0.282304	+	0.959325i	$0.408901\pi$
$822$	2.83636	0.0989293
$823$	4.49097	0.156545	0.0782727	−	0.996932i	$-0.475060\pi$
$823$	4.49097	0.156545	0.0782727	+	0.996932i	$0.475060\pi$
$824$	−0.586265	−0.0204235
$825$	8.52975	0.296968
$826$	4.29723	0.149520
$827$	21.2785	0.739927	0.369964	−	0.929046i	$-0.379370\pi$
$827$	21.2785	0.739927	0.369964	+	0.929046i	$0.379370\pi$
$828$	−56.9341	−1.97860
$829$	10.1423	0.352258	0.176129	−	0.984367i	$-0.443642\pi$
$829$	10.1423	0.352258	0.176129	+	0.984367i	$0.443642\pi$
$830$	−1.08022	−0.0374948
$831$	75.8166	2.63005
$832$	36.4635	1.26415
$833$	−2.07769	−0.0719877
$834$	1.42939	0.0494957
$835$	23.3937	0.809572
$836$	26.1074	0.902943
$837$	−32.3825	−1.11930
$838$	−5.91112	−0.204196
$839$	8.67984	0.299661	0.149831	−	0.988712i	$-0.452127\pi$
$839$	8.67984	0.299661	0.149831	+	0.988712i	$0.452127\pi$
$840$	16.9383	0.584428
$841$	−19.7359	−0.680548
$842$	−5.95659	−0.205277
$843$	−91.9444	−3.16673
$844$	−17.8676	−0.615027
$845$	30.8616	1.06167
$846$	15.4364	0.530714
$847$	−80.8408	−2.77772
$848$	−9.00453	−0.309217
$849$	3.44511	0.118236
$850$	0.0774600	0.00265686
$851$	30.2296	1.03626
$852$	39.9010	1.36698
$853$	−26.9142	−0.921523	−0.460762	−	0.887524i	$-0.652424\pi$
$853$	−26.9142	−0.921523	−0.460762	+	0.887524i	$0.652424\pi$
$854$	8.12621	0.278073
$855$	33.8331	1.15707
$856$	−3.45272	−0.118012
$857$	15.1059	0.516006	0.258003	−	0.966144i	$-0.416935\pi$
$857$	15.1059	0.516006	0.258003	+	0.966144i	$0.416935\pi$
$858$	18.8081	0.642097
$859$	−18.2394	−0.622322	−0.311161	−	0.950357i	$-0.600718\pi$
$859$	−18.2394	−0.622322	−0.311161	+	0.950357i	$0.600718\pi$
$860$	−57.8387	−1.97228
$861$	36.3478	1.23873
$862$	−2.79039	−0.0950412
$863$	18.5997	0.633140	0.316570	−	0.948569i	$-0.397469\pi$
$863$	18.5997	0.633140	0.316570	+	0.948569i	$0.397469\pi$
$864$	25.7817	0.877111
$865$	12.7026	0.431902
$866$	−1.46433	−0.0497598
$867$	50.3708	1.71068
$868$	16.9899	0.576674
$869$	58.0047	1.96767
$870$	4.26198	0.144495
$871$	−13.7509	−0.465931
$872$	0.0876699	0.00296888
$873$	60.7382	2.05568
$874$	−1.82202	−0.0616308
$875$	32.4326	1.09642
$876$	−68.6628	−2.31990
$877$	45.0998	1.52291	0.761456	−	0.648216i	$-0.224485\pi$
$877$	45.0998	1.52291	0.761456	+	0.648216i	$0.224485\pi$
$878$	4.64965	0.156918
$879$	−35.7882	−1.20710
$880$	−53.9898	−1.82000
$881$	6.30846	0.212537	0.106269	−	0.994337i	$-0.466110\pi$
$881$	6.30846	0.212537	0.106269	+	0.994337i	$0.466110\pi$
$882$	−2.98323	−0.100451
$883$	−28.9146	−0.973052	−0.486526	−	0.873666i	$-0.661736\pi$
$883$	−28.9146	−0.973052	−0.486526	+	0.873666i	$0.661736\pi$
$884$	−9.00926	−0.303014
$885$	−52.9748	−1.78073
$886$	3.85708	0.129581
$887$	−16.0395	−0.538552	−0.269276	−	0.963063i	$-0.586784\pi$
$887$	−16.0395	−0.538552	−0.269276	+	0.963063i	$0.586784\pi$
$888$	−16.5303	−0.554719
$889$	33.3266	1.11774
$890$	2.67169	0.0895552
$891$	−94.8905	−3.17895
$892$	−16.0622	−0.537801
$893$	−26.0573	−0.871975
$894$	10.2876	0.344069
$895$	37.0585	1.23873
$896$	−17.9761	−0.600538
$897$	69.2369	2.31175
$898$	−2.71172	−0.0904913
$899$	8.63095	0.287858
$900$	−5.86661	−0.195554
$901$	2.13632	0.0711712
$902$	4.52184	0.150561
$903$	119.852	3.98841
$904$	−7.88925	−0.262393
$905$	6.83724	0.227278
$906$	−13.6086	−0.452116
$907$	−27.7263	−0.920637	−0.460318	−	0.887754i	$-0.652265\pi$
$907$	−27.7263	−0.920637	−0.460318	+	0.887754i	$0.652265\pi$
$908$	11.5165	0.382189
$909$	39.4257	1.30767
$910$	−7.03795	−0.233306
$911$	37.3050	1.23597	0.617985	−	0.786190i	$-0.287949\pi$
$911$	37.3050	1.23597	0.617985	+	0.786190i	$0.287949\pi$
$912$	−25.5273	−0.845292
$913$	−14.6884	−0.486117
$914$	0.564616	0.0186759
$915$	−100.177	−3.31175
$916$	42.5481	1.40583
$917$	−44.1783	−1.45890
$918$	−1.97456	−0.0651701
$919$	−43.8040	−1.44496	−0.722481	−	0.691391i	$-0.756998\pi$
$919$	−43.8040	−1.44496	−0.722481	+	0.691391i	$0.756998\pi$
$920$	7.75712	0.255745
$921$	−19.1165	−0.629910
$922$	−3.61383	−0.119015
$923$	−33.4724	−1.10176
$924$	114.080	3.75295
$925$	3.11492	0.102418
$926$	1.04339	0.0342880
$927$	−5.11694	−0.168062
$928$	−6.87163	−0.225572
$929$	−33.8061	−1.10914	−0.554572	−	0.832136i	$-0.687118\pi$
$929$	−33.8061	−1.10914	−0.554572	+	0.832136i	$0.687118\pi$
$930$	3.97070	0.130204
$931$	5.03583	0.165043
$932$	7.91094	0.259132
$933$	−41.9616	−1.37376
$934$	3.94076	0.128946
$935$	12.8091	0.418902
$936$	−26.1169	−0.853659
$937$	2.84293	0.0928745	0.0464373	−	0.998921i	$-0.485213\pi$
$937$	2.84293	0.0928745	0.0464373	+	0.998921i	$0.485213\pi$
$938$	1.58122	0.0516285
$939$	37.4619	1.22252
$940$	54.9477	1.79220
$941$	48.3307	1.57554	0.787769	−	0.615971i	$-0.211236\pi$
$941$	48.3307	1.57554	0.787769	+	0.615971i	$0.211236\pi$
$942$	9.25929	0.301684
$943$	16.6459	0.542066
$944$	27.5721	0.897396
$945$	81.3637	2.64676
$946$	14.9101	0.484769
$947$	0.860898	0.0279754	0.0139877	−	0.999902i	$-0.495547\pi$
$947$	0.860898	0.0279754	0.0139877	+	0.999902i	$0.495547\pi$
$948$	−57.8329	−1.87833
$949$	57.6003	1.86979
$950$	−0.187745	−0.00609124
$951$	−23.3551	−0.757342
$952$	2.09159	0.0677889
$953$	49.7730	1.61230	0.806152	−	0.591708i	$-0.201546\pi$
$953$	49.7730	1.61230	0.806152	+	0.591708i	$0.201546\pi$
$954$	3.06742	0.0993113
$955$	45.9262	1.48614
$956$	−25.4550	−0.823275
$957$	57.9532	1.87336
$958$	0.738999	0.0238760
$959$	−14.4321	−0.466036
$960$	51.6892	1.66826
$961$	−22.9589	−0.740611
$962$	6.86840	0.221446
$963$	−30.1355	−0.971102
$964$	50.5917	1.62945
$965$	29.9313	0.963523
$966$	−7.96156	−0.256159
$967$	−22.4175	−0.720900	−0.360450	−	0.932779i	$-0.617377\pi$
$967$	−22.4175	−0.720900	−0.360450	+	0.932779i	$0.617377\pi$
$968$	20.2445	0.650682
$969$	6.05634	0.194558
$970$	−4.09885	−0.131606
$971$	19.3501	0.620974	0.310487	−	0.950578i	$-0.399508\pi$
$971$	19.3501	0.620974	0.310487	+	0.950578i	$0.399508\pi$
$972$	27.3664	0.877777
$973$	−7.27308	−0.233164
$974$	−4.55647	−0.145999
$975$	7.13430	0.228481
$976$	52.1398	1.66895
$977$	−40.6152	−1.29940	−0.649698	−	0.760193i	$-0.725105\pi$
$977$	−40.6152	−1.29940	−0.649698	+	0.760193i	$0.725105\pi$
$978$	−11.2072	−0.358366
$979$	36.3288	1.16107
$980$	−10.6192	−0.339217
$981$	0.765186	0.0244305
$982$	0.00765273	0.000244208 0
$983$	29.6287	0.945009	0.472504	−	0.881328i	$-0.343350\pi$
$983$	29.6287	0.945009	0.472504	+	0.881328i	$0.343350\pi$
$984$	−9.10237	−0.290173
$985$	19.0397	0.606654
$986$	0.526282	0.0167602
$987$	−113.861	−3.62423
$988$	21.8363	0.694705
$989$	54.8875	1.74532
$990$	18.3918	0.584529
$991$	25.0134	0.794577	0.397288	−	0.917694i	$-0.369951\pi$
$991$	25.0134	0.794577	0.397288	+	0.917694i	$0.369951\pi$
$992$	−6.40199	−0.203263
$993$	−105.530	−3.34890
$994$	3.84900	0.122083
$995$	3.47447	0.110148
$996$	14.6450	0.464043
$997$	−4.99363	−0.158150	−0.0790749	−	0.996869i	$-0.525197\pi$
$997$	−4.99363	−0.158150	−0.0790749	+	0.996869i	$0.525197\pi$
$998$	−4.31094	−0.136460
$999$	−79.4035	−2.51222

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	619.2.a.b.1.13	✓	30
3.2	odd	2		5571.2.a.g.1.18		30
4.3	odd	2		9904.2.a.n.1.29		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
619.2.a.b.1.13	✓	30	1.1	even	1	trivial
5571.2.a.g.1.18		30	3.2	odd	2
9904.2.a.n.1.29		30	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	619.a (trivial)

\(f(q)\)	\(=\)	\(q-0.192901 q^{2} -3.10998 q^{3} -1.96279 q^{4} +2.33409 q^{5} +0.599918 q^{6} -3.05253 q^{7} +0.764427 q^{8} +6.67195 q^{9} +O(q^{10})\)	\(q-0.192901 q^{2} -3.10998 q^{3} -1.96279 q^{4} +2.33409 q^{5} +0.599918 q^{6} -3.05253 q^{7} +0.764427 q^{8} +6.67195 q^{9} -0.450249 q^{10} -6.12235 q^{11} +6.10423 q^{12} -5.12075 q^{13} +0.588836 q^{14} -7.25897 q^{15} +3.77812 q^{16} -0.896358 q^{17} -1.28703 q^{18} +2.17256 q^{19} -4.58133 q^{20} +9.49328 q^{21} +1.18101 q^{22} +4.34757 q^{23} -2.37735 q^{24} +0.447982 q^{25} +0.987800 q^{26} -11.4197 q^{27} +5.99147 q^{28} +3.04370 q^{29} +1.40026 q^{30} +2.83568 q^{31} -2.25766 q^{32} +19.0404 q^{33} +0.172909 q^{34} -7.12488 q^{35} -13.0956 q^{36} +6.95323 q^{37} -0.419089 q^{38} +15.9254 q^{39} +1.78424 q^{40} +3.82879 q^{41} -1.83127 q^{42} +12.6249 q^{43} +12.0169 q^{44} +15.5729 q^{45} -0.838652 q^{46} -11.9938 q^{47} -11.7499 q^{48} +2.31792 q^{49} -0.0864163 q^{50} +2.78765 q^{51} +10.0510 q^{52} -2.38334 q^{53} +2.20287 q^{54} -14.2901 q^{55} -2.33343 q^{56} -6.75661 q^{57} -0.587133 q^{58} +7.29784 q^{59} +14.2478 q^{60} +13.8005 q^{61} -0.547006 q^{62} -20.3663 q^{63} -7.12073 q^{64} -11.9523 q^{65} -3.67291 q^{66} +2.68532 q^{67} +1.75936 q^{68} -13.5208 q^{69} +1.37440 q^{70} +6.53661 q^{71} +5.10022 q^{72} -11.2484 q^{73} -1.34129 q^{74} -1.39321 q^{75} -4.26428 q^{76} +18.6887 q^{77} -3.07203 q^{78} -9.47425 q^{79} +8.81848 q^{80} +15.4990 q^{81} -0.738579 q^{82} +2.39915 q^{83} -18.6333 q^{84} -2.09218 q^{85} -2.43535 q^{86} -9.46583 q^{87} -4.68009 q^{88} -5.93380 q^{89} -3.00404 q^{90} +15.6312 q^{91} -8.53336 q^{92} -8.81889 q^{93} +2.31363 q^{94} +5.07095 q^{95} +7.02126 q^{96} +9.10352 q^{97} -0.447130 q^{98} -40.8480 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9} + 5 q^{10} + 23 q^{11} - 6 q^{12} + 9 q^{13} + 7 q^{14} - 2 q^{15} + 35 q^{16} + 4 q^{17} + 10 q^{18} - q^{19} + 29 q^{20} + 30 q^{21} + 4 q^{23} + 4 q^{24} + 35 q^{25} + q^{26} - 5 q^{27} - 13 q^{28} + 90 q^{29} - 31 q^{30} + 2 q^{31} + 43 q^{32} - 6 q^{33} - 9 q^{34} + 9 q^{35} + 33 q^{36} + 19 q^{37} + 5 q^{38} + 32 q^{39} - 12 q^{40} + 59 q^{41} - 25 q^{42} - 4 q^{43} + 52 q^{44} + 30 q^{45} - q^{46} + 4 q^{47} - 44 q^{48} + 30 q^{49} + 31 q^{50} - 12 q^{52} + 34 q^{53} - 28 q^{54} - 17 q^{55} + 2 q^{56} - 8 q^{57} + 6 q^{58} + 13 q^{59} - 64 q^{60} + 16 q^{61} + 28 q^{62} - 40 q^{63} + 37 q^{64} + 31 q^{65} - 59 q^{66} - 11 q^{67} - 52 q^{68} + 6 q^{69} - 40 q^{70} + 42 q^{71} + 6 q^{72} - 4 q^{73} + 16 q^{74} - 52 q^{75} - 42 q^{76} + 29 q^{77} - 56 q^{78} + 3 q^{79} + 21 q^{80} + 30 q^{81} - 43 q^{82} - 11 q^{83} - 36 q^{84} + 19 q^{85} - 11 q^{86} - 20 q^{87} - 47 q^{88} + 58 q^{89} - 33 q^{90} - 39 q^{91} - 7 q^{92} - 15 q^{93} - 46 q^{94} + 23 q^{95} - 70 q^{96} - 9 q^{97} - 8 q^{99}+O(q^{100}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9 + 5 * q^10 + 23 * q^11 - 6 * q^12 + 9 * q^13 + 7 * q^14 - 2 * q^15 + 35 * q^16 + 4 * q^17 + 10 * q^18 - q^19 + 29 * q^20 + 30 * q^21 + 4 * q^23 + 4 * q^24 + 35 * q^25 + q^26 - 5 * q^27 - 13 * q^28 + 90 * q^29 - 31 * q^30 + 2 * q^31 + 43 * q^32 - 6 * q^33 - 9 * q^34 + 9 * q^35 + 33 * q^36 + 19 * q^37 + 5 * q^38 + 32 * q^39 - 12 * q^40 + 59 * q^41 - 25 * q^42 - 4 * q^43 + 52 * q^44 + 30 * q^45 - q^46 + 4 * q^47 - 44 * q^48 + 30 * q^49 + 31 * q^50 - 12 * q^52 + 34 * q^53 - 28 * q^54 - 17 * q^55 + 2 * q^56 - 8 * q^57 + 6 * q^58 + 13 * q^59 - 64 * q^60 + 16 * q^61 + 28 * q^62 - 40 * q^63 + 37 * q^64 + 31 * q^65 - 59 * q^66 - 11 * q^67 - 52 * q^68 + 6 * q^69 - 40 * q^70 + 42 * q^71 + 6 * q^72 - 4 * q^73 + 16 * q^74 - 52 * q^75 - 42 * q^76 + 29 * q^77 - 56 * q^78 + 3 * q^79 + 21 * q^80 + 30 * q^81 - 43 * q^82 - 11 * q^83 - 36 * q^84 + 19 * q^85 - 11 * q^86 - 20 * q^87 - 47 * q^88 + 58 * q^89 - 33 * q^90 - 39 * q^91 - 7 * q^92 - 15 * q^93 - 46 * q^94 + 23 * q^95 - 70 * q^96 - 9 * q^97 - 8 * q^99

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