LMFDB - Embedded newform 619.2.a.b.1.29

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			1.29
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)

$f(q)$	$=$	$q+2.70888 q^{2} -2.72500 q^{3} +5.33801 q^{4} +4.10380 q^{5} -7.38169 q^{6} -3.88170 q^{7} +9.04227 q^{8} +4.42562 q^{9} +O(q^{10})$	\(q+2.70888 q^{2} -2.72500 q^{3} +5.33801 q^{4} +4.10380 q^{5} -7.38169 q^{6} -3.88170 q^{7} +9.04227 q^{8} +4.42562 q^{9} +11.1167 q^{10} +4.15204 q^{11} -14.5461 q^{12} -2.28601 q^{13} -10.5150 q^{14} -11.1828 q^{15} +13.8184 q^{16} -2.82134 q^{17} +11.9885 q^{18} -1.09008 q^{19} +21.9061 q^{20} +10.5776 q^{21} +11.2474 q^{22} -2.23319 q^{23} -24.6402 q^{24} +11.8412 q^{25} -6.19252 q^{26} -3.88480 q^{27} -20.7206 q^{28} +5.30363 q^{29} -30.2929 q^{30} -2.19049 q^{31} +19.3477 q^{32} -11.3143 q^{33} -7.64266 q^{34} -15.9297 q^{35} +23.6240 q^{36} -2.22927 q^{37} -2.95290 q^{38} +6.22938 q^{39} +37.1076 q^{40} +4.99227 q^{41} +28.6535 q^{42} -6.91455 q^{43} +22.1636 q^{44} +18.1618 q^{45} -6.04944 q^{46} -7.22331 q^{47} -37.6550 q^{48} +8.06759 q^{49} +32.0762 q^{50} +7.68815 q^{51} -12.2028 q^{52} -10.2495 q^{53} -10.5235 q^{54} +17.0391 q^{55} -35.0994 q^{56} +2.97048 q^{57} +14.3669 q^{58} +2.59333 q^{59} -59.6942 q^{60} -14.7739 q^{61} -5.93378 q^{62} -17.1789 q^{63} +24.7739 q^{64} -9.38133 q^{65} -30.6491 q^{66} -4.92889 q^{67} -15.0604 q^{68} +6.08544 q^{69} -43.1516 q^{70} -2.08262 q^{71} +40.0176 q^{72} +12.7349 q^{73} -6.03881 q^{74} -32.2671 q^{75} -5.81888 q^{76} -16.1170 q^{77} +16.8746 q^{78} +7.96074 q^{79} +56.7078 q^{80} -2.69076 q^{81} +13.5234 q^{82} -6.16542 q^{83} +56.4635 q^{84} -11.5782 q^{85} -18.7307 q^{86} -14.4524 q^{87} +37.5439 q^{88} -16.6485 q^{89} +49.1982 q^{90} +8.87361 q^{91} -11.9208 q^{92} +5.96909 q^{93} -19.5671 q^{94} -4.47348 q^{95} -52.7225 q^{96} +4.60917 q^{97} +21.8541 q^{98} +18.3753 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.70888	1.91547	0.957733	−	0.287660i	$-0.0928773\pi$
$2$	2.70888	1.91547	0.957733	+	0.287660i	$0.0928773\pi$
$3$	−2.72500	−1.57328	−0.786639	−	0.617413i	$-0.788181\pi$
$3$	−2.72500	−1.57328	−0.786639	+	0.617413i	$0.788181\pi$
$4$	5.33801	2.66901
$5$	4.10380	1.83527	0.917637	−	0.397420i	$-0.130094\pi$
$5$	4.10380	1.83527	0.917637	+	0.397420i	$0.130094\pi$
$6$	−7.38169	−3.01356
$7$	−3.88170	−1.46714	−0.733572	−	0.679612i	$-0.762148\pi$
$7$	−3.88170	−1.46714	−0.733572	+	0.679612i	$0.762148\pi$
$8$	9.04227	3.19693
$9$	4.42562	1.47521
$10$	11.1167	3.51540
$11$	4.15204	1.25189	0.625943	−	0.779868i	$-0.284714\pi$
$11$	4.15204	1.25189	0.625943	+	0.779868i	$0.284714\pi$
$12$	−14.5461	−4.19909
$13$	−2.28601	−0.634025	−0.317013	−	0.948421i	$-0.602680\pi$
$13$	−2.28601	−0.634025	−0.317013	+	0.948421i	$0.602680\pi$
$14$	−10.5150	−2.81026
$15$	−11.1828	−2.88740
$16$	13.8184	3.45459
$17$	−2.82134	−0.684276	−0.342138	−	0.939650i	$-0.611151\pi$
$17$	−2.82134	−0.684276	−0.342138	+	0.939650i	$0.611151\pi$
$18$	11.9885	2.82571
$19$	−1.09008	−0.250082	−0.125041	−	0.992152i	$-0.539906\pi$
$19$	−1.09008	−0.250082	−0.125041	+	0.992152i	$0.539906\pi$
$20$	21.9061	4.89836
$21$	10.5776	2.30823
$22$	11.2474	2.39795
$23$	−2.23319	−0.465652	−0.232826	−	0.972518i	$-0.574797\pi$
$23$	−2.23319	−0.465652	−0.232826	+	0.972518i	$0.574797\pi$
$24$	−24.6402	−5.02965
$25$	11.8412	2.36823
$26$	−6.19252	−1.21445
$27$	−3.88480	−0.747631
$28$	−20.7206	−3.91582
$29$	5.30363	0.984859	0.492430	−	0.870352i	$-0.336109\pi$
$29$	5.30363	0.984859	0.492430	+	0.870352i	$0.336109\pi$
$30$	−30.2929	−5.53071
$31$	−2.19049	−0.393424	−0.196712	−	0.980461i	$-0.563026\pi$
$31$	−2.19049	−0.393424	−0.196712	+	0.980461i	$0.563026\pi$
$32$	19.3477	3.42023
$33$	−11.3143	−1.96957
$34$	−7.64266	−1.31071
$35$	−15.9297	−2.69261
$36$	23.6240	3.93733
$37$	−2.22927	−0.366489	−0.183244	−	0.983067i	$-0.558660\pi$
$37$	−2.22927	−0.366489	−0.183244	+	0.983067i	$0.558660\pi$
$38$	−2.95290	−0.479024
$39$	6.22938	0.997498
$40$	37.1076	5.86723
$41$	4.99227	0.779662	0.389831	−	0.920886i	$-0.372533\pi$
$41$	4.99227	0.779662	0.389831	+	0.920886i	$0.372533\pi$
$42$	28.6535	4.42133
$43$	−6.91455	−1.05446	−0.527229	−	0.849723i	$-0.676769\pi$
$43$	−6.91455	−1.05446	−0.527229	+	0.849723i	$0.676769\pi$
$44$	22.1636	3.34130
$45$	18.1618	2.70741
$46$	−6.04944	−0.891941
$47$	−7.22331	−1.05363	−0.526814	−	0.849980i	$-0.676614\pi$
$47$	−7.22331	−1.05363	−0.526814	+	0.849980i	$0.676614\pi$
$48$	−37.6550	−5.43504
$49$	8.06759	1.15251
$50$	32.0762	4.53626
$51$	7.68815	1.07656
$52$	−12.2028	−1.69222
$53$	−10.2495	−1.40787	−0.703937	−	0.710263i	$-0.748576\pi$
$53$	−10.2495	−1.40787	−0.703937	+	0.710263i	$0.748576\pi$
$54$	−10.5235	−1.43206
$55$	17.0391	2.29756
$56$	−35.0994	−4.69035
$57$	2.97048	0.393449
$58$	14.3669	1.88646
$59$	2.59333	0.337623	0.168811	−	0.985648i	$-0.446007\pi$
$59$	2.59333	0.337623	0.168811	+	0.985648i	$0.446007\pi$
$60$	−59.6942	−7.70648
$61$	−14.7739	−1.89160	−0.945802	−	0.324743i	$-0.894722\pi$
$61$	−14.7739	−1.89160	−0.945802	+	0.324743i	$0.894722\pi$
$62$	−5.93378	−0.753591
$63$	−17.1789	−2.16434
$64$	24.7739	3.09673
$65$	−9.38133	−1.16361
$66$	−30.6491	−3.77264
$67$	−4.92889	−0.602160	−0.301080	−	0.953599i	$-0.597347\pi$
$67$	−4.92889	−0.602160	−0.301080	+	0.953599i	$0.597347\pi$
$68$	−15.0604	−1.82634
$69$	6.08544	0.732601
$70$	−43.1516	−5.15760
$71$	−2.08262	−0.247161	−0.123581	−	0.992335i	$-0.539438\pi$
$71$	−2.08262	−0.247161	−0.123581	+	0.992335i	$0.539438\pi$
$72$	40.0176	4.71612
$73$	12.7349	1.49051	0.745256	−	0.666778i	$-0.232327\pi$
$73$	12.7349	1.49051	0.745256	+	0.666778i	$0.232327\pi$
$74$	−6.03881	−0.701997
$75$	−32.2671	−3.72589
$76$	−5.81888	−0.667472
$77$	−16.1170	−1.83670
$78$	16.8746	1.91067
$79$	7.96074	0.895653	0.447827	−	0.894120i	$-0.352198\pi$
$79$	7.96074	0.895653	0.447827	+	0.894120i	$0.352198\pi$
$80$	56.7078	6.34012
$81$	−2.69076	−0.298974
$82$	13.5234	1.49341
$83$	−6.16542	−0.676743	−0.338371	−	0.941013i	$-0.609876\pi$
$83$	−6.16542	−0.676743	−0.338371	+	0.941013i	$0.609876\pi$
$84$	56.4635	6.16067
$85$	−11.5782	−1.25583
$86$	−18.7307	−2.01978
$87$	−14.4524	−1.54946
$88$	37.5439	4.00219
$89$	−16.6485	−1.76474	−0.882371	−	0.470555i	$-0.844054\pi$
$89$	−16.6485	−1.76474	−0.882371	+	0.470555i	$0.844054\pi$
$90$	49.1982	5.18594
$91$	8.87361	0.930207
$92$	−11.9208	−1.24283
$93$	5.96909	0.618966
$94$	−19.5671	−2.01819
$95$	−4.47348	−0.458970
$96$	−52.7225	−5.38097
$97$	4.60917	0.467990	0.233995	−	0.972238i	$-0.424820\pi$
$97$	4.60917	0.467990	0.233995	+	0.972238i	$0.424820\pi$
$98$	21.8541	2.20760
$99$	18.3753	1.84679
$100$	63.2083	6.32083
$101$	−2.47990	−0.246760	−0.123380	−	0.992360i	$-0.539373\pi$
$101$	−2.47990	−0.246760	−0.123380	+	0.992360i	$0.539373\pi$
$102$	20.8262	2.06211
$103$	12.2387	1.20591	0.602956	−	0.797774i	$-0.293989\pi$
$103$	12.2387	1.20591	0.602956	+	0.797774i	$0.293989\pi$
$104$	−20.6707	−2.02693
$105$	43.4084	4.23623
$106$	−27.7646	−2.69673
$107$	−6.93657	−0.670584	−0.335292	−	0.942114i	$-0.608835\pi$
$107$	−6.93657	−0.670584	−0.335292	+	0.942114i	$0.608835\pi$
$108$	−20.7371	−1.99543
$109$	−1.21249	−0.116135	−0.0580677	−	0.998313i	$-0.518494\pi$
$109$	−1.21249	−0.116135	−0.0580677	+	0.998313i	$0.518494\pi$
$110$	46.1569	4.40089
$111$	6.07474	0.576589
$112$	−53.6387	−5.06838
$113$	−3.02662	−0.284720	−0.142360	−	0.989815i	$-0.545469\pi$
$113$	−3.02662	−0.284720	−0.142360	+	0.989815i	$0.545469\pi$
$114$	8.04666	0.753638
$115$	−9.16456	−0.854600
$116$	28.3108	2.62860
$117$	−10.1170	−0.935318
$118$	7.02502	0.646705
$119$	10.9516	1.00393
$120$	−101.118	−9.23079
$121$	6.23943	0.567221
$122$	−40.0207	−3.62330
$123$	−13.6039	−1.22663
$124$	−11.6929	−1.05005
$125$	28.0747	2.51108
$126$	−46.5356	−4.14572
$127$	17.5287	1.55542	0.777712	−	0.628621i	$-0.216380\pi$
$127$	17.5287	1.55542	0.777712	+	0.628621i	$0.216380\pi$
$128$	28.4139	2.51146
$129$	18.8421	1.65896
$130$	−25.4129	−2.22885
$131$	−3.81334	−0.333173	−0.166586	−	0.986027i	$-0.553274\pi$
$131$	−3.81334	−0.333173	−0.166586	+	0.986027i	$0.553274\pi$
$132$	−60.3959	−5.25679
$133$	4.23138	0.366907
$134$	−13.3518	−1.15342
$135$	−15.9425	−1.37211
$136$	−25.5113	−2.18758
$137$	−17.6738	−1.50998	−0.754988	−	0.655739i	$-0.772357\pi$
$137$	−17.6738	−1.50998	−0.754988	+	0.655739i	$0.772357\pi$
$138$	16.4847	1.40327
$139$	−8.57652	−0.727451	−0.363725	−	0.931506i	$-0.618495\pi$
$139$	−8.57652	−0.727451	−0.363725	+	0.931506i	$0.618495\pi$
$140$	−85.0330	−7.18660
$141$	19.6835	1.65765
$142$	−5.64156	−0.473429
$143$	−9.49161	−0.793728
$144$	61.1548	5.09623
$145$	21.7650	1.80749
$146$	34.4974	2.85503
$147$	−21.9842	−1.81322
$148$	−11.8998	−0.978162
$149$	11.2980	0.925567	0.462783	−	0.886471i	$-0.346851\pi$
$149$	11.2980	0.925567	0.462783	+	0.886471i	$0.346851\pi$
$150$	−87.4077	−7.13681
$151$	1.42349	0.115842	0.0579211	−	0.998321i	$-0.481553\pi$
$151$	1.42349	0.115842	0.0579211	+	0.998321i	$0.481553\pi$
$152$	−9.85683	−0.799495
$153$	−12.4862	−1.00945
$154$	−43.6589	−3.51813
$155$	−8.98935	−0.722042
$156$	33.2525	2.66233
$157$	15.1931	1.21254	0.606272	−	0.795257i	$-0.292664\pi$
$157$	15.1931	1.21254	0.606272	+	0.795257i	$0.292664\pi$
$158$	21.5647	1.71559
$159$	27.9298	2.21498
$160$	79.3991	6.27705
$161$	8.66857	0.683179
$162$	−7.28895	−0.572674
$163$	18.6494	1.46073	0.730367	−	0.683055i	$-0.239349\pi$
$163$	18.6494	1.46073	0.730367	+	0.683055i	$0.239349\pi$
$164$	26.6488	2.08092
$165$	−46.4316	−3.61470
$166$	−16.7014	−1.29628
$167$	10.9849	0.850038	0.425019	−	0.905184i	$-0.360267\pi$
$167$	10.9849	0.850038	0.425019	+	0.905184i	$0.360267\pi$
$168$	95.6457	7.37923
$169$	−7.77415	−0.598012
$170$	−31.3639	−2.40550
$171$	−4.82429	−0.368923
$172$	−36.9100	−2.81436
$173$	18.7698	1.42704	0.713520	−	0.700635i	$-0.247100\pi$
$173$	18.7698	1.42704	0.713520	+	0.700635i	$0.247100\pi$
$174$	−39.1497	−2.96793
$175$	−45.9638	−3.47454
$176$	57.3744	4.32476
$177$	−7.06682	−0.531175
$178$	−45.0988	−3.38030
$179$	11.0361	0.824875	0.412437	−	0.910986i	$-0.364678\pi$
$179$	11.0361	0.824875	0.412437	+	0.910986i	$0.364678\pi$
$180$	96.9481	7.22609
$181$	−9.01951	−0.670415	−0.335207	−	0.942144i	$-0.608806\pi$
$181$	−9.01951	−0.670415	−0.335207	+	0.942144i	$0.608806\pi$
$182$	24.0375	1.78178
$183$	40.2589	2.97602
$184$	−20.1931	−1.48866
$185$	−9.14845	−0.672608
$186$	16.1695	1.18561
$187$	−11.7143	−0.856636
$188$	−38.5582	−2.81214
$189$	15.0796	1.09688
$190$	−12.1181	−0.879140
$191$	−1.40878	−0.101936	−0.0509680	−	0.998700i	$-0.516231\pi$
$191$	−1.40878	−0.101936	−0.0509680	+	0.998700i	$0.516231\pi$
$192$	−67.5087	−4.87202
$193$	6.95723	0.500793	0.250396	−	0.968143i	$-0.419439\pi$
$193$	6.95723	0.500793	0.250396	+	0.968143i	$0.419439\pi$
$194$	12.4857	0.896418
$195$	25.5641	1.83068
$196$	43.0649	3.07606
$197$	21.6819	1.54477	0.772384	−	0.635156i	$-0.219064\pi$
$197$	21.6819	1.54477	0.772384	+	0.635156i	$0.219064\pi$
$198$	49.7765	3.53746
$199$	−5.38906	−0.382020	−0.191010	−	0.981588i	$-0.561176\pi$
$199$	−5.38906	−0.382020	−0.191010	+	0.981588i	$0.561176\pi$
$200$	107.071	7.57106
$201$	13.4312	0.947366
$202$	−6.71775	−0.472659
$203$	−20.5871	−1.44493
$204$	41.0394	2.87334
$205$	20.4873	1.43089
$206$	33.1531	2.30988
$207$	−9.88325	−0.686933
$208$	−31.5889	−2.19030
$209$	−4.52607	−0.313075
$210$	117.588	8.11435
$211$	14.3809	0.990025	0.495012	−	0.868886i	$-0.335164\pi$
$211$	14.3809	0.990025	0.495012	+	0.868886i	$0.335164\pi$
$212$	−54.7118	−3.75762
$213$	5.67514	0.388854
$214$	−18.7903	−1.28448
$215$	−28.3759	−1.93522
$216$	−35.1274	−2.39012
$217$	8.50284	0.577210
$218$	−3.28449	−0.222453
$219$	−34.7027	−2.34499
$220$	90.9551	6.13219
$221$	6.44961	0.433848
$222$	16.4557	1.10444
$223$	−18.9906	−1.27171	−0.635853	−	0.771810i	$-0.719352\pi$
$223$	−18.9906	−1.27171	−0.635853	+	0.771810i	$0.719352\pi$
$224$	−75.1020	−5.01796
$225$	52.4044	3.49363
$226$	−8.19874	−0.545372
$227$	−5.35661	−0.355531	−0.177765	−	0.984073i	$-0.556887\pi$
$227$	−5.35661	−0.355531	−0.177765	+	0.984073i	$0.556887\pi$
$228$	15.8564	1.05012
$229$	3.66909	0.242460	0.121230	−	0.992624i	$-0.461316\pi$
$229$	3.66909	0.242460	0.121230	+	0.992624i	$0.461316\pi$
$230$	−24.8257	−1.63696
$231$	43.9187	2.88964
$232$	47.9568	3.14852
$233$	9.94989	0.651839	0.325919	−	0.945398i	$-0.394326\pi$
$233$	9.94989	0.651839	0.325919	+	0.945398i	$0.394326\pi$
$234$	−27.4057	−1.79157
$235$	−29.6430	−1.93370
$236$	13.8432	0.901118
$237$	−21.6930	−1.40911
$238$	29.6665	1.92299
$239$	14.8170	0.958433	0.479217	−	0.877697i	$-0.340921\pi$
$239$	14.8170	0.958433	0.479217	+	0.877697i	$0.340921\pi$
$240$	−154.529	−9.97478
$241$	−2.99421	−0.192874	−0.0964369	−	0.995339i	$-0.530745\pi$
$241$	−2.99421	−0.192874	−0.0964369	+	0.995339i	$0.530745\pi$
$242$	16.9019	1.08649
$243$	18.9867	1.21800
$244$	−78.8633	−5.04871
$245$	33.1077	2.11518
$246$	−36.8514	−2.34956
$247$	2.49194	0.158559
$248$	−19.8070	−1.25775
$249$	16.8008	1.06470
$250$	76.0509	4.80988
$251$	−20.8468	−1.31584	−0.657919	−	0.753088i	$-0.728563\pi$
$251$	−20.8468	−1.31584	−0.657919	+	0.753088i	$0.728563\pi$
$252$	−91.7013	−5.77664
$253$	−9.27230	−0.582944
$254$	47.4832	2.97936
$255$	31.5506	1.97578
$256$	27.4220	1.71387
$257$	4.90299	0.305840	0.152920	−	0.988239i	$-0.451132\pi$
$257$	4.90299	0.305840	0.152920	+	0.988239i	$0.451132\pi$
$258$	51.0410	3.17768
$259$	8.65334	0.537692
$260$	−50.0776	−3.10568
$261$	23.4718	1.45287
$262$	−10.3299	−0.638181
$263$	23.5776	1.45386	0.726929	−	0.686712i	$-0.240947\pi$
$263$	23.5776	1.45386	0.726929	+	0.686712i	$0.240947\pi$
$264$	−102.307	−6.29656
$265$	−42.0618	−2.58383
$266$	11.4623	0.702797
$267$	45.3672	2.77643
$268$	−26.3105	−1.60717
$269$	25.7238	1.56841	0.784204	−	0.620503i	$-0.213072\pi$
$269$	25.7238	1.56841	0.784204	+	0.620503i	$0.213072\pi$
$270$	−43.1861	−2.62822
$271$	32.2119	1.95673	0.978366	−	0.206883i	$-0.0663319\pi$
$271$	32.2119	1.95673	0.978366	+	0.206883i	$0.0663319\pi$
$272$	−38.9863	−2.36389
$273$	−24.1806	−1.46347
$274$	−47.8762	−2.89231
$275$	49.1649	2.96476
$276$	32.4842	1.95532
$277$	−4.75610	−0.285766	−0.142883	−	0.989740i	$-0.545637\pi$
$277$	−4.75610	−0.285766	−0.142883	+	0.989740i	$0.545637\pi$
$278$	−23.2327	−1.39341
$279$	−9.69429	−0.580382
$280$	−144.041	−8.60808
$281$	−23.5949	−1.40755	−0.703776	−	0.710422i	$-0.748504\pi$
$281$	−23.5949	−1.40755	−0.703776	+	0.710422i	$0.748504\pi$
$282$	53.3202	3.17517
$283$	10.1880	0.605615	0.302808	−	0.953052i	$-0.402076\pi$
$283$	10.1880	0.605615	0.302808	+	0.953052i	$0.402076\pi$
$284$	−11.1171	−0.659676
$285$	12.1902	0.722087
$286$	−25.7116	−1.52036
$287$	−19.3785	−1.14388
$288$	85.6256	5.04554
$289$	−9.04004	−0.531767
$290$	58.9588	3.46218
$291$	−12.5600	−0.736279
$292$	67.9793	3.97819
$293$	11.8891	0.694568	0.347284	−	0.937760i	$-0.387104\pi$
$293$	11.8891	0.694568	0.347284	+	0.937760i	$0.387104\pi$
$294$	−59.5524	−3.47317
$295$	10.6425	0.619631
$296$	−20.1576	−1.17164
$297$	−16.1299	−0.935949
$298$	30.6049	1.77289
$299$	5.10510	0.295235
$300$	−172.242	−9.94442
$301$	26.8402	1.54704
$302$	3.85606	0.221892
$303$	6.75773	0.388222
$304$	−15.0632	−0.863933
$305$	−60.6291	−3.47161
$306$	−33.8235	−1.93356
$307$	−0.903449	−0.0515626	−0.0257813	−	0.999668i	$-0.508207\pi$
$307$	−0.903449	−0.0515626	−0.0257813	+	0.999668i	$0.508207\pi$
$308$	−86.0326	−4.90216
$309$	−33.3504	−1.89724
$310$	−24.3510	−1.38305
$311$	−27.4811	−1.55831	−0.779155	−	0.626831i	$-0.784351\pi$
$311$	−27.4811	−1.55831	−0.779155	+	0.626831i	$0.784351\pi$
$312$	56.3277	3.18893
$313$	33.6828	1.90386	0.951932	−	0.306310i	$-0.0990944\pi$
$313$	33.6828	1.90386	0.951932	+	0.306310i	$0.0990944\pi$
$314$	41.1563	2.32259
$315$	−70.4988	−3.97216
$316$	42.4945	2.39051
$317$	6.60007	0.370697	0.185348	−	0.982673i	$-0.440659\pi$
$317$	6.60007	0.370697	0.185348	+	0.982673i	$0.440659\pi$
$318$	75.6584	4.24271
$319$	22.0209	1.23293
$320$	101.667	5.68335
$321$	18.9022	1.05502
$322$	23.4821	1.30861
$323$	3.07550	0.171125
$324$	−14.3633	−0.797963
$325$	−27.0690	−1.50152
$326$	50.5189	2.79798
$327$	3.30403	0.182713
$328$	45.1415	2.49252
$329$	28.0387	1.54583
$330$	−125.777	−6.92382
$331$	−11.3015	−0.621188	−0.310594	−	0.950543i	$-0.600528\pi$
$331$	−11.3015	−0.621188	−0.310594	+	0.950543i	$0.600528\pi$
$332$	−32.9111	−1.80623
$333$	−9.86587	−0.540647
$334$	29.7568	1.62822
$335$	−20.2272	−1.10513
$336$	146.165	7.97398
$337$	−23.1688	−1.26208	−0.631042	−	0.775748i	$-0.717373\pi$
$337$	−23.1688	−1.26208	−0.631042	+	0.775748i	$0.717373\pi$
$338$	−21.0592	−1.14547
$339$	8.24754	0.447945
$340$	−61.8047	−3.35183
$341$	−9.09502	−0.492523
$342$	−13.0684	−0.706659
$343$	−4.14404	−0.223757
$344$	−62.5232	−3.37103
$345$	24.9734	1.34452
$346$	50.8450	2.73345
$347$	−14.0849	−0.756119	−0.378060	−	0.925781i	$-0.623409\pi$
$347$	−14.0849	−0.756119	−0.378060	+	0.925781i	$0.623409\pi$
$348$	−77.1470	−4.13551
$349$	−2.01430	−0.107823	−0.0539115	−	0.998546i	$-0.517169\pi$
$349$	−2.01430	−0.107823	−0.0539115	+	0.998546i	$0.517169\pi$
$350$	−124.510	−6.65535
$351$	8.88070	0.474017
$352$	80.3325	4.28174
$353$	7.01496	0.373369	0.186684	−	0.982420i	$-0.440226\pi$
$353$	7.01496	0.373369	0.186684	+	0.982420i	$0.440226\pi$
$354$	−19.1432	−1.01745
$355$	−8.54665	−0.453609
$356$	−88.8701	−4.71011
$357$	−29.8431	−1.57946
$358$	29.8954	1.58002
$359$	21.0057	1.10864	0.554318	−	0.832305i	$-0.312979\pi$
$359$	21.0057	1.10864	0.554318	+	0.832305i	$0.312979\pi$
$360$	164.224	8.65538
$361$	−17.8117	−0.937459
$362$	−24.4327	−1.28416
$363$	−17.0024	−0.892397
$364$	47.3674	2.48273
$365$	52.2616	2.73550
$366$	109.056	5.70047
$367$	−17.1543	−0.895446	−0.447723	−	0.894172i	$-0.647765\pi$
$367$	−17.1543	−0.895446	−0.447723	+	0.894172i	$0.647765\pi$
$368$	−30.8591	−1.60864
$369$	22.0939	1.15016
$370$	−24.7820	−1.28836
$371$	39.7854	2.06555
$372$	31.8631	1.65203
$373$	6.63795	0.343700	0.171850	−	0.985123i	$-0.445026\pi$
$373$	6.63795	0.343700	0.171850	+	0.985123i	$0.445026\pi$
$374$	−31.7326	−1.64086
$375$	−76.5036	−3.95063
$376$	−65.3152	−3.36837
$377$	−12.1242	−0.624426
$378$	40.8489	2.10104
$379$	−4.92174	−0.252813	−0.126406	−	0.991979i	$-0.540344\pi$
$379$	−4.92174	−0.252813	−0.126406	+	0.991979i	$0.540344\pi$
$380$	−23.8795	−1.22499
$381$	−47.7658	−2.44711
$382$	−3.81622	−0.195255
$383$	0.0611665	0.00312546	0.00156273	−	0.999999i	$-0.499503\pi$
$383$	0.0611665	0.00312546	0.00156273	+	0.999999i	$0.499503\pi$
$384$	−77.4278	−3.95122
$385$	−66.1408	−3.37085
$386$	18.8463	0.959251
$387$	−30.6011	−1.55554
$388$	24.6038	1.24907
$389$	−29.7303	−1.50738	−0.753692	−	0.657228i	$-0.771729\pi$
$389$	−29.7303	−1.50738	−0.753692	+	0.657228i	$0.771729\pi$
$390$	69.2500	3.50661
$391$	6.30059	0.318635
$392$	72.9493	3.68450
$393$	10.3913	0.524173
$394$	58.7335	2.95895
$395$	32.6693	1.64377
$396$	98.0878	4.92910
$397$	−13.3529	−0.670163	−0.335082	−	0.942189i	$-0.608764\pi$
$397$	−13.3529	−0.670163	−0.335082	+	0.942189i	$0.608764\pi$
$398$	−14.5983	−0.731746
$399$	−11.5305	−0.577247
$400$	163.625	8.18127
$401$	−1.91203	−0.0954821	−0.0477411	−	0.998860i	$-0.515202\pi$
$401$	−1.91203	−0.0954821	−0.0477411	+	0.998860i	$0.515202\pi$
$402$	36.3835	1.81465
$403$	5.00749	0.249441
$404$	−13.2378	−0.658603
$405$	−11.0424	−0.548699
$406$	−55.7679	−2.76771
$407$	−9.25600	−0.458803
$408$	69.5183	3.44167
$409$	−9.97546	−0.493255	−0.246627	−	0.969110i	$-0.579322\pi$
$409$	−9.97546	−0.493255	−0.246627	+	0.969110i	$0.579322\pi$
$410$	55.4975	2.74083
$411$	48.1611	2.37561
$412$	65.3302	3.21859
$413$	−10.0665	−0.495342
$414$	−26.7725	−1.31580
$415$	−25.3016	−1.24201
$416$	−44.2291	−2.16851
$417$	23.3710	1.14448
$418$	−12.2606	−0.599684
$419$	34.4915	1.68502	0.842510	−	0.538681i	$-0.181077\pi$
$419$	34.4915	1.68502	0.842510	+	0.538681i	$0.181077\pi$
$420$	231.715	11.3065
$421$	−0.807068	−0.0393341	−0.0196670	−	0.999807i	$-0.506261\pi$
$421$	−0.807068	−0.0393341	−0.0196670	+	0.999807i	$0.506261\pi$
$422$	38.9562	1.89636
$423$	−31.9676	−1.55432
$424$	−92.6785	−4.50086
$425$	−33.4079	−1.62052
$426$	15.3732	0.744836
$427$	57.3479	2.77526
$428$	−37.0275	−1.78979
$429$	25.8646	1.24876
$430$	−76.8668	−3.70685
$431$	3.37040	0.162346	0.0811732	−	0.996700i	$-0.474133\pi$
$431$	3.37040	0.162346	0.0811732	+	0.996700i	$0.474133\pi$
$432$	−53.6817	−2.58276
$433$	14.0417	0.674801	0.337400	−	0.941361i	$-0.390452\pi$
$433$	14.0417	0.674801	0.337400	+	0.941361i	$0.390452\pi$
$434$	23.0331	1.10563
$435$	−59.3096	−2.84368
$436$	−6.47229	−0.309966
$437$	2.43437	0.116451
$438$	−94.0054	−4.49175
$439$	−2.18375	−0.104225	−0.0521124	−	0.998641i	$-0.516595\pi$
$439$	−2.18375	−0.104225	−0.0521124	+	0.998641i	$0.516595\pi$
$440$	154.072	7.34511
$441$	35.7040	1.70019
$442$	17.4712	0.831021
$443$	12.8888	0.612367	0.306183	−	0.951973i	$-0.400948\pi$
$443$	12.8888	0.612367	0.306183	+	0.951973i	$0.400948\pi$
$444$	32.4271	1.53892
$445$	−68.3222	−3.23878
$446$	−51.4433	−2.43591
$447$	−30.7870	−1.45617
$448$	−96.1646	−4.54335
$449$	−8.85779	−0.418025	−0.209013	−	0.977913i	$-0.567025\pi$
$449$	−8.85779	−0.418025	−0.209013	+	0.977913i	$0.567025\pi$
$450$	141.957	6.69192
$451$	20.7281	0.976048
$452$	−16.1561	−0.759921
$453$	−3.87901	−0.182252
$454$	−14.5104	−0.681006
$455$	36.4155	1.70718
$456$	26.8599	1.25783
$457$	−30.3371	−1.41911	−0.709554	−	0.704651i	$-0.751104\pi$
$457$	−30.3371	−1.41911	−0.709554	+	0.704651i	$0.751104\pi$
$458$	9.93912	0.464425
$459$	10.9604	0.511586
$460$	−48.9206	−2.28093
$461$	−18.4983	−0.861553	−0.430777	−	0.902459i	$-0.641760\pi$
$461$	−18.4983	−0.861553	−0.430777	+	0.902459i	$0.641760\pi$
$462$	118.970	5.53500
$463$	13.9424	0.647957	0.323979	−	0.946064i	$-0.394979\pi$
$463$	13.9424	0.647957	0.323979	+	0.946064i	$0.394979\pi$
$464$	73.2875	3.40229
$465$	24.4960	1.13597
$466$	26.9530	1.24857
$467$	−6.21206	−0.287460	−0.143730	−	0.989617i	$-0.545910\pi$
$467$	−6.21206	−0.287460	−0.143730	+	0.989617i	$0.545910\pi$
$468$	−54.0047	−2.49637
$469$	19.1325	0.883456
$470$	−80.2993	−3.70393
$471$	−41.4013	−1.90767
$472$	23.4496	1.07936
$473$	−28.7095	−1.32006
$474$	−58.7637	−2.69911
$475$	−12.9079	−0.592253
$476$	58.4598	2.67950
$477$	−45.3602	−2.07690
$478$	40.1375	1.83585
$479$	−23.3106	−1.06509	−0.532543	−	0.846403i	$-0.678764\pi$
$479$	−23.3106	−1.06509	−0.532543	+	0.846403i	$0.678764\pi$
$480$	−216.362	−9.87555
$481$	5.09612	0.232363
$482$	−8.11094	−0.369443
$483$	−23.6219	−1.07483
$484$	33.3062	1.51392
$485$	18.9151	0.858890
$486$	51.4328	2.33304
$487$	20.0800	0.909912	0.454956	−	0.890514i	$-0.349655\pi$
$487$	20.0800	0.909912	0.454956	+	0.890514i	$0.349655\pi$
$488$	−133.590	−6.04732
$489$	−50.8196	−2.29814
$490$	89.6848	4.05155
$491$	−11.9957	−0.541360	−0.270680	−	0.962669i	$-0.587249\pi$
$491$	−11.9957	−0.541360	−0.270680	+	0.962669i	$0.587249\pi$
$492$	−72.6180	−3.27387
$493$	−14.9633	−0.673915
$494$	6.75037	0.303713
$495$	75.4087	3.38937
$496$	−30.2691	−1.35912
$497$	8.08410	0.362622
$498$	45.5112	2.03941
$499$	9.16097	0.410102	0.205051	−	0.978751i	$-0.434264\pi$
$499$	9.16097	0.410102	0.205051	+	0.978751i	$0.434264\pi$
$500$	149.863	6.70209
$501$	−29.9339	−1.33735
$502$	−56.4714	−2.52044
$503$	−8.60683	−0.383760	−0.191880	−	0.981418i	$-0.561458\pi$
$503$	−8.60683	−0.383760	−0.191880	+	0.981418i	$0.561458\pi$
$504$	−155.336	−6.91923
$505$	−10.1770	−0.452871
$506$	−25.1175	−1.11661
$507$	21.1846	0.940839
$508$	93.5686	4.15144
$509$	0.394994	0.0175078	0.00875390	−	0.999962i	$-0.497214\pi$
$509$	0.394994	0.0175078	0.00875390	+	0.999962i	$0.497214\pi$
$510$	85.4667	3.78453
$511$	−49.4332	−2.18680
$512$	17.4551	0.771412
$513$	4.23476	0.186969
$514$	13.2816	0.585827
$515$	50.2250	2.21318
$516$	100.580	4.42777
$517$	−29.9915	−1.31902
$518$	23.4408	1.02993
$519$	−51.1476	−2.24513
$520$	−84.8285	−3.71997
$521$	11.9008	0.521383	0.260691	−	0.965422i	$-0.416050\pi$
$521$	11.9008	0.521383	0.260691	+	0.965422i	$0.416050\pi$
$522$	63.5823	2.78292
$523$	−20.0073	−0.874858	−0.437429	−	0.899253i	$-0.644111\pi$
$523$	−20.0073	−0.874858	−0.437429	+	0.899253i	$0.644111\pi$
$524$	−20.3556	−0.889240
$525$	125.251	5.46641
$526$	63.8689	2.78482
$527$	6.18013	0.269211
$528$	−156.345	−6.80405
$529$	−18.0129	−0.783168
$530$	−113.940	−4.94924
$531$	11.4771	0.498063
$532$	22.5871	0.979277
$533$	−11.4124	−0.494325
$534$	122.894	5.31815
$535$	−28.4663	−1.23071
$536$	−44.5684	−1.92506
$537$	−30.0733	−1.29776
$538$	69.6826	3.00423
$539$	33.4969	1.44281
$540$	−85.1010	−3.66217
$541$	13.3520	0.574046	0.287023	−	0.957924i	$-0.407334\pi$
$541$	13.3520	0.574046	0.287023	+	0.957924i	$0.407334\pi$
$542$	87.2580	3.74805
$543$	24.5781	1.05475
$544$	−54.5865	−2.34038
$545$	−4.97581	−0.213140
$546$	−65.5022	−2.80323
$547$	42.7351	1.82722	0.913611	−	0.406589i	$-0.133282\pi$
$547$	42.7351	1.82722	0.913611	+	0.406589i	$0.133282\pi$
$548$	−94.3431	−4.03014
$549$	−65.3837	−2.79051
$550$	133.182	5.67889
$551$	−5.78140	−0.246296
$552$	55.0262	2.34207
$553$	−30.9012	−1.31405
$554$	−12.8837	−0.547375
$555$	24.9295	1.05820
$556$	−45.7816	−1.94157
$557$	−6.49934	−0.275386	−0.137693	−	0.990475i	$-0.543969\pi$
$557$	−6.49934	−0.275386	−0.137693	+	0.990475i	$0.543969\pi$
$558$	−26.2606	−1.11170
$559$	15.8067	0.668553
$560$	−220.123	−9.30187
$561$	31.9215	1.34773
$562$	−63.9156	−2.69612
$563$	5.24244	0.220942	0.110471	−	0.993879i	$-0.464764\pi$
$563$	5.24244	0.220942	0.110471	+	0.993879i	$0.464764\pi$
$564$	105.071	4.42428
$565$	−12.4206	−0.522540
$566$	27.5981	1.16004
$567$	10.4447	0.438638
$568$	−18.8316	−0.790157
$569$	33.9033	1.42130	0.710651	−	0.703545i	$-0.248401\pi$
$569$	33.9033	1.42130	0.710651	+	0.703545i	$0.248401\pi$
$570$	33.0218	1.38313
$571$	−34.1968	−1.43109	−0.715546	−	0.698565i	$-0.753822\pi$
$571$	−34.1968	−1.43109	−0.715546	+	0.698565i	$0.753822\pi$
$572$	−50.6663	−2.11847
$573$	3.83893	0.160374
$574$	−52.4939	−2.19106
$575$	−26.4436	−1.10277
$576$	109.640	4.56832
$577$	−46.1838	−1.92266	−0.961328	−	0.275406i	$-0.911188\pi$
$577$	−46.1838	−1.92266	−0.961328	+	0.275406i	$0.911188\pi$
$578$	−24.4884	−1.01858
$579$	−18.9585	−0.787886
$580$	116.182	4.82419
$581$	23.9323	0.992879
$582$	−34.0234	−1.41032
$583$	−42.5562	−1.76250
$584$	115.153	4.76506
$585$	−41.5182	−1.71656
$586$	32.2061	1.33042
$587$	8.62935	0.356171	0.178086	−	0.984015i	$-0.443010\pi$
$587$	8.62935	0.356171	0.178086	+	0.984015i	$0.443010\pi$
$588$	−117.352	−4.83950
$589$	2.38782	0.0983885
$590$	28.8292	1.18688
$591$	−59.0830	−2.43035
$592$	−30.8048	−1.26607
$593$	−7.58718	−0.311568	−0.155784	−	0.987791i	$-0.549790\pi$
$593$	−7.58718	−0.311568	−0.155784	+	0.987791i	$0.549790\pi$
$594$	−43.6938	−1.79278
$595$	44.9431	1.84249
$596$	60.3088	2.47034
$597$	14.6852	0.601024
$598$	13.8291	0.565513
$599$	−15.6256	−0.638446	−0.319223	−	0.947680i	$-0.603422\pi$
$599$	−15.6256	−0.638446	−0.319223	+	0.947680i	$0.603422\pi$
$600$	−291.768	−11.9114
$601$	46.4236	1.89366	0.946828	−	0.321739i	$-0.104268\pi$
$601$	46.4236	1.89366	0.946828	+	0.321739i	$0.104268\pi$
$602$	72.7068	2.96331
$603$	−21.8134	−0.888310
$604$	7.59862	0.309183
$605$	25.6054	1.04101
$606$	18.3059	0.743625
$607$	−18.2412	−0.740386	−0.370193	−	0.928955i	$-0.620708\pi$
$607$	−18.2412	−0.740386	−0.370193	+	0.928955i	$0.620708\pi$
$608$	−21.0906	−0.855338
$609$	56.0998	2.27328
$610$	−164.237	−6.64975
$611$	16.5126	0.668027
$612$	−66.6514	−2.69422
$613$	−26.6444	−1.07616	−0.538078	−	0.842895i	$-0.680849\pi$
$613$	−26.6444	−1.07616	−0.538078	+	0.842895i	$0.680849\pi$
$614$	−2.44733	−0.0987663
$615$	−55.8278	−2.25119
$616$	−145.734	−5.87179
$617$	−17.0584	−0.686745	−0.343372	−	0.939199i	$-0.611569\pi$
$617$	−17.0584	−0.686745	−0.343372	+	0.939199i	$0.611569\pi$
$618$	−90.3421	−3.63409
$619$	1.00000	0.0401934
$619$	1.00000	0.0401934
$620$	−47.9853	−1.92713
$621$	8.67551	0.348136
$622$	−74.4429	−2.98489
$623$	64.6246	2.58913
$624$	86.0798	3.44595
$625$	56.0072	2.24029
$626$	91.2425	3.64678
$627$	12.3335	0.492554
$628$	81.1011	3.23629
$629$	6.28952	0.250779
$630$	−190.973	−7.60853
$631$	48.8532	1.94481	0.972407	−	0.233290i	$-0.0749490\pi$
$631$	48.8532	1.94481	0.972407	+	0.233290i	$0.0749490\pi$
$632$	71.9832	2.86334
$633$	−39.1880	−1.55758
$634$	17.8788	0.710057
$635$	71.9344	2.85463
$636$	149.090	5.91179
$637$	−18.4426	−0.730722
$638$	59.6518	2.36164
$639$	−9.21688	−0.364614
$640$	116.605	4.60921
$641$	49.9880	1.97441	0.987205	−	0.159459i	$-0.0509751\pi$
$641$	49.9880	1.97441	0.987205	+	0.159459i	$0.0509751\pi$
$642$	51.2036	2.02085
$643$	13.9573	0.550423	0.275212	−	0.961384i	$-0.411252\pi$
$643$	13.9573	0.550423	0.275212	+	0.961384i	$0.411252\pi$
$644$	46.2730	1.82341
$645$	77.3243	3.04464
$646$	8.33114	0.327784
$647$	24.7295	0.972217	0.486109	−	0.873898i	$-0.338416\pi$
$647$	24.7295	0.972217	0.486109	+	0.873898i	$0.338416\pi$
$648$	−24.3306	−0.955797
$649$	10.7676	0.422666
$650$	−73.3266	−2.87611
$651$	−23.1702	−0.908113
$652$	99.5507	3.89871
$653$	11.8827	0.465004	0.232502	−	0.972596i	$-0.425309\pi$
$653$	11.8827	0.465004	0.232502	+	0.972596i	$0.425309\pi$
$654$	8.95022	0.349981
$655$	−15.6492	−0.611463
$656$	68.9850	2.69341
$657$	56.3600	2.19881
$658$	75.9535	2.96097
$659$	−11.0618	−0.430906	−0.215453	−	0.976514i	$-0.569123\pi$
$659$	−11.0618	−0.430906	−0.215453	+	0.976514i	$0.569123\pi$
$660$	−247.853	−9.64765
$661$	3.71075	0.144332	0.0721658	−	0.997393i	$-0.477009\pi$
$661$	3.71075	0.144332	0.0721658	+	0.997393i	$0.477009\pi$
$662$	−30.6145	−1.18986
$663$	−17.5752	−0.682564
$664$	−55.7494	−2.16350
$665$	17.3647	0.673375
$666$	−26.7254	−1.03559
$667$	−11.8440	−0.458602
$668$	58.6376	2.26876
$669$	51.7494	2.00075
$670$	−54.7929	−2.11684
$671$	−61.3418	−2.36808
$672$	204.653	7.89466
$673$	−34.5301	−1.33104	−0.665518	−	0.746382i	$-0.731789\pi$
$673$	−34.5301	−1.33104	−0.665518	+	0.746382i	$0.731789\pi$
$674$	−62.7614	−2.41748
$675$	−46.0006	−1.77056
$676$	−41.4985	−1.59610
$677$	3.69322	0.141942	0.0709710	−	0.997478i	$-0.477390\pi$
$677$	3.69322	0.141942	0.0709710	+	0.997478i	$0.477390\pi$
$678$	22.3416	0.858022
$679$	−17.8914	−0.686609
$680$	−104.693	−4.01480
$681$	14.5967	0.559349
$682$	−24.6373	−0.943411
$683$	−35.4458	−1.35629	−0.678147	−	0.734926i	$-0.737217\pi$
$683$	−35.4458	−1.35629	−0.678147	+	0.734926i	$0.737217\pi$
$684$	−25.7521	−0.984658
$685$	−72.5298	−2.77122
$686$	−11.2257	−0.428599
$687$	−9.99827	−0.381458
$688$	−95.5478	−3.64272
$689$	23.4304	0.892627
$690$	67.6499	2.57539
$691$	−27.0332	−1.02839	−0.514195	−	0.857673i	$-0.671909\pi$
$691$	−27.0332	−1.02839	−0.514195	+	0.857673i	$0.671909\pi$
$692$	100.193	3.80878
$693$	−71.3275	−2.70951
$694$	−38.1544	−1.44832
$695$	−35.1963	−1.33507
$696$	−130.682	−4.95350
$697$	−14.0849	−0.533503
$698$	−5.45649	−0.206531
$699$	−27.1134	−1.02552
$700$	−245.355	−9.27356
$701$	−7.89822	−0.298312	−0.149156	−	0.988814i	$-0.547656\pi$
$701$	−7.89822	−0.298312	−0.149156	+	0.988814i	$0.547656\pi$
$702$	24.0567	0.907963
$703$	2.43009	0.0916524
$704$	102.862	3.87676
$705$	80.7772	3.04225
$706$	19.0027	0.715175
$707$	9.62624	0.362032
$708$	−37.7228	−1.41771
$709$	−0.227760	−0.00855370	−0.00427685	−	0.999991i	$-0.501361\pi$
$709$	−0.227760	−0.00855370	−0.00427685	+	0.999991i	$0.501361\pi$
$710$	−23.1518	−0.868872
$711$	35.2312	1.32127
$712$	−150.541	−5.64175
$713$	4.89179	0.183199
$714$	−80.8412	−3.02541
$715$	−38.9516	−1.45671
$716$	58.9107	2.20160
$717$	−40.3764	−1.50788
$718$	56.9018	2.12355
$719$	−0.528402	−0.0197061	−0.00985303	−	0.999951i	$-0.503136\pi$
$719$	−0.528402	−0.0197061	−0.00985303	+	0.999951i	$0.503136\pi$
$720$	250.967	9.35299
$721$	−47.5068	−1.76925
$722$	−48.2498	−1.79567
$723$	8.15921	0.303444
$724$	−48.1463	−1.78934
$725$	62.8011	2.33237
$726$	−46.0575	−1.70935
$727$	−42.1900	−1.56474	−0.782370	−	0.622814i	$-0.785989\pi$
$727$	−42.1900	−1.56474	−0.782370	+	0.622814i	$0.785989\pi$
$728$	80.2375	2.97380
$729$	−43.6666	−1.61728
$730$	141.570	5.23975
$731$	19.5083	0.721540
$732$	214.902	7.94302
$733$	26.5430	0.980388	0.490194	−	0.871613i	$-0.336926\pi$
$733$	26.5430	0.980388	0.490194	+	0.871613i	$0.336926\pi$
$734$	−46.4688	−1.71520
$735$	−90.2185	−3.32776
$736$	−43.2071	−1.59264
$737$	−20.4650	−0.753836
$738$	59.8496	2.20309
$739$	−8.56041	−0.314900	−0.157450	−	0.987527i	$-0.550327\pi$
$739$	−8.56041	−0.314900	−0.157450	+	0.987527i	$0.550327\pi$
$740$	−48.8346	−1.79519
$741$	−6.79054	−0.249457
$742$	107.774	3.95649
$743$	22.8919	0.839823	0.419912	−	0.907565i	$-0.362061\pi$
$743$	22.8919	0.839823	0.419912	+	0.907565i	$0.362061\pi$
$744$	53.9742	1.97879
$745$	46.3646	1.69867
$746$	17.9814	0.658346
$747$	−27.2858	−0.998335
$748$	−62.5312	−2.28637
$749$	26.9257	0.983843
$750$	−207.239	−7.56729
$751$	0.923364	0.0336940	0.0168470	−	0.999858i	$-0.494637\pi$
$751$	0.923364	0.0336940	0.0168470	+	0.999858i	$0.494637\pi$
$752$	−99.8144	−3.63986
$753$	56.8075	2.07018
$754$	−32.8428	−1.19607
$755$	5.84172	0.212602
$756$	80.4953	2.92759
$757$	−8.75497	−0.318205	−0.159102	−	0.987262i	$-0.550860\pi$
$757$	−8.75497	−0.318205	−0.159102	+	0.987262i	$0.550860\pi$
$758$	−13.3324	−0.484254
$759$	25.2670	0.917134
$760$	−40.4504	−1.46729
$761$	7.78983	0.282381	0.141191	−	0.989982i	$-0.454907\pi$
$761$	7.78983	0.282381	0.141191	+	0.989982i	$0.454907\pi$
$762$	−129.392	−4.68736
$763$	4.70652	0.170388
$764$	−7.52011	−0.272068
$765$	−51.2407	−1.85261
$766$	0.165692	0.00598671
$767$	−5.92838	−0.214062
$768$	−74.7249	−2.69640
$769$	41.8111	1.50775	0.753873	−	0.657020i	$-0.228183\pi$
$769$	41.8111	1.50775	0.753873	+	0.657020i	$0.228183\pi$
$770$	−179.167	−6.45674
$771$	−13.3607	−0.481172
$772$	37.1378	1.33662
$773$	47.8514	1.72110	0.860548	−	0.509370i	$-0.170122\pi$
$773$	47.8514	1.72110	0.860548	+	0.509370i	$0.170122\pi$
$774$	−82.8947	−2.97959
$775$	−25.9380	−0.931720
$776$	41.6773	1.49613
$777$	−23.5803	−0.845940
$778$	−80.5356	−2.88734
$779$	−5.44199	−0.194980
$780$	136.462	4.88611
$781$	−8.64712	−0.309418
$782$	17.0675	0.610334
$783$	−20.6036	−0.736311
$784$	111.481	3.98146
$785$	62.3495	2.22535
$786$	28.1488	1.00404
$787$	39.6388	1.41297	0.706485	−	0.707728i	$-0.250280\pi$
$787$	39.6388	1.41297	0.706485	+	0.707728i	$0.250280\pi$
$788$	115.738	4.12300
$789$	−64.2490	−2.28732
$790$	88.4970	3.14858
$791$	11.7484	0.417726
$792$	166.155	5.90405
$793$	33.7733	1.19933
$794$	−36.1714	−1.28367
$795$	114.618	4.06509
$796$	−28.7669	−1.01961
$797$	9.08109	0.321669	0.160834	−	0.986981i	$-0.448581\pi$
$797$	9.08109	0.321669	0.160834	+	0.986981i	$0.448581\pi$
$798$	−31.2347	−1.10570
$799$	20.3794	0.720972
$800$	229.099	8.09988
$801$	−73.6800	−2.60336
$802$	−5.17945	−0.182893
$803$	52.8760	1.86595
$804$	71.6961	2.52853
$805$	35.5741	1.25382
$806$	13.5647	0.477796
$807$	−70.0973	−2.46754
$808$	−22.4240	−0.788872
$809$	−23.6863	−0.832765	−0.416383	−	0.909190i	$-0.636702\pi$
$809$	−23.6863	−0.832765	−0.416383	+	0.909190i	$0.636702\pi$
$810$	−29.9124	−1.05101
$811$	−14.5214	−0.509916	−0.254958	−	0.966952i	$-0.582062\pi$
$811$	−14.5214	−0.509916	−0.254958	+	0.966952i	$0.582062\pi$
$812$	−109.894	−3.85653
$813$	−87.7773	−3.07848
$814$	−25.0734	−0.878821
$815$	76.5333	2.68085
$816$	106.238	3.71906
$817$	7.53744	0.263702
$818$	−27.0223	−0.944813
$819$	39.2712	1.37225
$820$	109.361	3.81906
$821$	−8.72070	−0.304354	−0.152177	−	0.988353i	$-0.548628\pi$
$821$	−8.72070	−0.304354	−0.152177	+	0.988353i	$0.548628\pi$
$822$	130.463	4.55040
$823$	0.614581	0.0214229	0.0107115	−	0.999943i	$-0.496590\pi$
$823$	0.614581	0.0214229	0.0107115	+	0.999943i	$0.496590\pi$
$824$	110.665	3.85521
$825$	−133.974	−4.66439
$826$	−27.2690	−0.948810
$827$	2.40324	0.0835690	0.0417845	−	0.999127i	$-0.486696\pi$
$827$	2.40324	0.0835690	0.0417845	+	0.999127i	$0.486696\pi$
$828$	−52.7569	−1.83343
$829$	8.77339	0.304712	0.152356	−	0.988326i	$-0.451314\pi$
$829$	8.77339	0.304712	0.152356	+	0.988326i	$0.451314\pi$
$830$	−68.5390	−2.37902
$831$	12.9604	0.449590
$832$	−56.6333	−1.96341
$833$	−22.7614	−0.788636
$834$	63.3091	2.19222
$835$	45.0798	1.56005
$836$	−24.1602	−0.835599
$837$	8.50964	0.294136
$838$	93.4332	3.22760
$839$	16.9858	0.586415	0.293208	−	0.956049i	$-0.405277\pi$
$839$	16.9858	0.586415	0.293208	+	0.956049i	$0.405277\pi$
$840$	392.511	13.5429
$841$	−0.871519	−0.0300524
$842$	−2.18625	−0.0753431
$843$	64.2960	2.21447
$844$	76.7656	2.64238
$845$	−31.9036	−1.09752
$846$	−86.5964	−2.97724
$847$	−24.2196	−0.832195
$848$	−141.631	−4.86363
$849$	−27.7624	−0.952802
$850$	−90.4980	−3.10405
$851$	4.97837	0.170656
$852$	30.2940	1.03785
$853$	48.5331	1.66174	0.830871	−	0.556464i	$-0.187842\pi$
$853$	48.5331	1.66174	0.830871	+	0.556464i	$0.187842\pi$
$854$	155.348	5.31591
$855$	−19.7979	−0.677075
$856$	−62.7224	−2.14381
$857$	37.5985	1.28434	0.642170	−	0.766563i	$-0.278035\pi$
$857$	37.5985	1.28434	0.642170	+	0.766563i	$0.278035\pi$
$858$	70.0641	2.39195
$859$	42.5582	1.45207	0.726034	−	0.687659i	$-0.241362\pi$
$859$	42.5582	1.45207	0.726034	+	0.687659i	$0.241362\pi$
$860$	−151.471	−5.16512
$861$	52.8064	1.79964
$862$	9.13000	0.310969
$863$	−32.3159	−1.10005	−0.550023	−	0.835150i	$-0.685381\pi$
$863$	−32.3159	−1.10005	−0.550023	+	0.835150i	$0.685381\pi$
$864$	−75.1621	−2.55707
$865$	77.0274	2.61901
$866$	38.0372	1.29256
$867$	24.6341	0.836618
$868$	45.3883	1.54058
$869$	33.0533	1.12126
$870$	−160.663	−5.44697
$871$	11.2675	0.381785
$872$	−10.9637	−0.371276
$873$	20.3984	0.690381
$874$	6.59440	0.223059
$875$	−108.978	−3.68411
$876$	−185.244	−6.25880
$877$	20.7729	0.701452	0.350726	−	0.936478i	$-0.385935\pi$
$877$	20.7729	0.701452	0.350726	+	0.936478i	$0.385935\pi$
$878$	−5.91551	−0.199639
$879$	−32.3977	−1.09275
$880$	235.453	7.93712
$881$	−40.3980	−1.36104	−0.680521	−	0.732728i	$-0.738247\pi$
$881$	−40.3980	−1.36104	−0.680521	+	0.732728i	$0.738247\pi$
$882$	96.7179	3.25666
$883$	56.0290	1.88553	0.942763	−	0.333464i	$-0.108217\pi$
$883$	56.0290	1.88553	0.942763	+	0.333464i	$0.108217\pi$
$884$	34.4281	1.15794
$885$	−29.0008	−0.974852
$886$	34.9143	1.17297
$887$	−21.4953	−0.721742	−0.360871	−	0.932616i	$-0.617521\pi$
$887$	−21.4953	−0.721742	−0.360871	+	0.932616i	$0.617521\pi$
$888$	54.9295	1.84331
$889$	−68.0413	−2.28203
$890$	−185.076	−6.20378
$891$	−11.1722	−0.374281
$892$	−101.372	−3.39419
$893$	7.87402	0.263494
$894$	−83.3982	−2.78925
$895$	45.2898	1.51387
$896$	−110.294	−3.68467
$897$	−13.9114	−0.464488
$898$	−23.9947	−0.800712
$899$	−11.6176	−0.387468
$900$	279.736	9.32452
$901$	28.9172	0.963373
$902$	56.1499	1.86959
$903$	−73.1395	−2.43393
$904$	−27.3675	−0.910230
$905$	−37.0142	−1.23039
$906$	−10.5078	−0.349097
$907$	23.3997	0.776973	0.388487	−	0.921454i	$-0.372998\pi$
$907$	23.3997	0.776973	0.388487	+	0.921454i	$0.372998\pi$
$908$	−28.5936	−0.948913
$909$	−10.9751	−0.364021
$910$	98.6451	3.27005
$911$	1.77309	0.0587452	0.0293726	−	0.999569i	$-0.490649\pi$
$911$	1.77309	0.0587452	0.0293726	+	0.999569i	$0.490649\pi$
$912$	41.0471	1.35921
$913$	−25.5991	−0.847205
$914$	−82.1794	−2.71825
$915$	165.214	5.46182
$916$	19.5857	0.647129
$917$	14.8022	0.488812
$918$	29.6903	0.979924
$919$	29.8514	0.984707	0.492353	−	0.870395i	$-0.336137\pi$
$919$	29.8514	0.984707	0.492353	+	0.870395i	$0.336137\pi$
$920$	−82.8685	−2.73209
$921$	2.46190	0.0811223
$922$	−50.1097	−1.65028
$923$	4.76089	0.156707
$924$	234.439	7.71247
$925$	−26.3971	−0.867930
$926$	37.7682	1.24114
$927$	54.1637	1.77897
$928$	102.613	3.36844
$929$	−23.5565	−0.772865	−0.386432	−	0.922318i	$-0.626293\pi$
$929$	−23.5565	−0.772865	−0.386432	+	0.922318i	$0.626293\pi$
$930$	66.3565	2.17592
$931$	−8.79434	−0.288223
$932$	53.1127	1.73976
$933$	74.8859	2.45166
$934$	−16.8277	−0.550619
$935$	−48.0732	−1.57216
$936$	−91.4807	−2.99014
$937$	10.1566	0.331803	0.165901	−	0.986142i	$-0.446947\pi$
$937$	10.1566	0.331803	0.165901	+	0.986142i	$0.446947\pi$
$938$	51.8275	1.69223
$939$	−91.7855	−2.99531
$940$	−158.235	−5.16105
$941$	−35.5623	−1.15930	−0.579649	−	0.814866i	$-0.696810\pi$
$941$	−35.5623	−1.15930	−0.579649	+	0.814866i	$0.696810\pi$
$942$	−112.151	−3.65407
$943$	−11.1487	−0.363051
$944$	35.8356	1.16635
$945$	61.8838	2.01308
$946$	−77.7704	−2.52853
$947$	−11.1765	−0.363189	−0.181595	−	0.983373i	$-0.558126\pi$
$947$	−11.1765	−0.363189	−0.181595	+	0.983373i	$0.558126\pi$
$948$	−115.798	−3.76093
$949$	−29.1122	−0.945023
$950$	−34.9658	−1.13444
$951$	−17.9852	−0.583209
$952$	99.0273	3.20949
$953$	−16.3382	−0.529246	−0.264623	−	0.964352i	$-0.585248\pi$
$953$	−16.3382	−0.529246	−0.264623	+	0.964352i	$0.585248\pi$
$954$	−122.875	−3.97823
$955$	−5.78136	−0.187081
$956$	79.0935	2.55807
$957$	−60.0069	−1.93975
$958$	−63.1455	−2.04014
$959$	68.6044	2.21535
$960$	−277.042	−8.94149
$961$	−26.2017	−0.845217
$962$	13.8048	0.445084
$963$	−30.6986	−0.989249
$964$	−15.9831	−0.514782
$965$	28.5511	0.919092
$966$	−63.9887	−2.05880
$967$	−46.9299	−1.50916	−0.754582	−	0.656206i	$-0.772160\pi$
$967$	−46.9299	−1.50916	−0.754582	+	0.656206i	$0.772160\pi$
$968$	56.4186	1.81336
$969$	−8.38073	−0.269228
$970$	51.2386	1.64517
$971$	16.0435	0.514862	0.257431	−	0.966297i	$-0.417124\pi$
$971$	16.0435	0.514862	0.257431	+	0.966297i	$0.417124\pi$
$972$	101.352	3.25085
$973$	33.2914	1.06727
$974$	54.3943	1.74291
$975$	73.7630	2.36231
$976$	−204.151	−6.53472
$977$	−36.7878	−1.17695	−0.588473	−	0.808517i	$-0.700271\pi$
$977$	−36.7878	−1.17695	−0.588473	+	0.808517i	$0.700271\pi$
$978$	−137.664	−4.40201
$979$	−69.1254	−2.20926
$980$	176.730	5.64542
$981$	−5.36602	−0.171324
$982$	−32.4950	−1.03696
$983$	5.32340	0.169790	0.0848950	−	0.996390i	$-0.472945\pi$
$983$	5.32340	0.169790	0.0848950	+	0.996390i	$0.472945\pi$
$984$	−123.010	−3.92143
$985$	88.9780	2.83507
$986$	−40.5339	−1.29086
$987$	−76.4055	−2.43201
$988$	13.3020	0.423194
$989$	15.4415	0.491011
$990$	204.273	6.49222
$991$	−47.9373	−1.52278	−0.761389	−	0.648295i	$-0.775482\pi$
$991$	−47.9373	−1.52278	−0.761389	+	0.648295i	$0.775482\pi$
$992$	−42.3811	−1.34560
$993$	30.7967	0.977302
$994$	21.8988	0.694589
$995$	−22.1156	−0.701112
$996$	89.6827	2.84171
$997$	20.8174	0.659293	0.329646	−	0.944104i	$-0.393070\pi$
$997$	20.8174	0.659293	0.329646	+	0.944104i	$0.393070\pi$
$998$	24.8160	0.785535
$999$	8.66026	0.273998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	619.2.a.b.1.29	✓	30
3.2	odd	2		5571.2.a.g.1.2		30
4.3	odd	2		9904.2.a.n.1.27		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
619.2.a.b.1.29	✓	30	1.1	even	1	trivial
5571.2.a.g.1.2		30	3.2	odd	2
9904.2.a.n.1.27		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)

\(f(q)\)	\(=\)	\(q+2.70888 q^{2} -2.72500 q^{3} +5.33801 q^{4} +4.10380 q^{5} -7.38169 q^{6} -3.88170 q^{7} +9.04227 q^{8} +4.42562 q^{9} +O(q^{10})\)	\(q+2.70888 q^{2} -2.72500 q^{3} +5.33801 q^{4} +4.10380 q^{5} -7.38169 q^{6} -3.88170 q^{7} +9.04227 q^{8} +4.42562 q^{9} +11.1167 q^{10} +4.15204 q^{11} -14.5461 q^{12} -2.28601 q^{13} -10.5150 q^{14} -11.1828 q^{15} +13.8184 q^{16} -2.82134 q^{17} +11.9885 q^{18} -1.09008 q^{19} +21.9061 q^{20} +10.5776 q^{21} +11.2474 q^{22} -2.23319 q^{23} -24.6402 q^{24} +11.8412 q^{25} -6.19252 q^{26} -3.88480 q^{27} -20.7206 q^{28} +5.30363 q^{29} -30.2929 q^{30} -2.19049 q^{31} +19.3477 q^{32} -11.3143 q^{33} -7.64266 q^{34} -15.9297 q^{35} +23.6240 q^{36} -2.22927 q^{37} -2.95290 q^{38} +6.22938 q^{39} +37.1076 q^{40} +4.99227 q^{41} +28.6535 q^{42} -6.91455 q^{43} +22.1636 q^{44} +18.1618 q^{45} -6.04944 q^{46} -7.22331 q^{47} -37.6550 q^{48} +8.06759 q^{49} +32.0762 q^{50} +7.68815 q^{51} -12.2028 q^{52} -10.2495 q^{53} -10.5235 q^{54} +17.0391 q^{55} -35.0994 q^{56} +2.97048 q^{57} +14.3669 q^{58} +2.59333 q^{59} -59.6942 q^{60} -14.7739 q^{61} -5.93378 q^{62} -17.1789 q^{63} +24.7739 q^{64} -9.38133 q^{65} -30.6491 q^{66} -4.92889 q^{67} -15.0604 q^{68} +6.08544 q^{69} -43.1516 q^{70} -2.08262 q^{71} +40.0176 q^{72} +12.7349 q^{73} -6.03881 q^{74} -32.2671 q^{75} -5.81888 q^{76} -16.1170 q^{77} +16.8746 q^{78} +7.96074 q^{79} +56.7078 q^{80} -2.69076 q^{81} +13.5234 q^{82} -6.16542 q^{83} +56.4635 q^{84} -11.5782 q^{85} -18.7307 q^{86} -14.4524 q^{87} +37.5439 q^{88} -16.6485 q^{89} +49.1982 q^{90} +8.87361 q^{91} -11.9208 q^{92} +5.96909 q^{93} -19.5671 q^{94} -4.47348 q^{95} -52.7225 q^{96} +4.60917 q^{97} +21.8541 q^{98} +18.3753 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) \) 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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