LMFDB - Embedded newform 1339.2.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1339,2,Mod(1,1339)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1339, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1339.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1339 = 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1339.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:	$10.6919688306$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	1339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70794 q^{2} +2.09535 q^{3} +5.33295 q^{4} -1.11757 q^{5} -5.67408 q^{6} -3.78835 q^{7} -9.02545 q^{8} +1.39048 q^{9} +O(q^{10})$	\(q-2.70794 q^{2} +2.09535 q^{3} +5.33295 q^{4} -1.11757 q^{5} -5.67408 q^{6} -3.78835 q^{7} -9.02545 q^{8} +1.39048 q^{9} +3.02631 q^{10} +3.88337 q^{11} +11.1744 q^{12} -1.00000 q^{13} +10.2586 q^{14} -2.34169 q^{15} +13.7745 q^{16} +1.61038 q^{17} -3.76534 q^{18} -3.02549 q^{19} -5.95994 q^{20} -7.93790 q^{21} -10.5159 q^{22} +2.76971 q^{23} -18.9114 q^{24} -3.75104 q^{25} +2.70794 q^{26} -3.37251 q^{27} -20.2031 q^{28} +6.44575 q^{29} +6.34117 q^{30} +2.57083 q^{31} -19.2496 q^{32} +8.13700 q^{33} -4.36080 q^{34} +4.23373 q^{35} +7.41536 q^{36} +11.6432 q^{37} +8.19284 q^{38} -2.09535 q^{39} +10.0866 q^{40} +3.53269 q^{41} +21.4954 q^{42} -1.24439 q^{43} +20.7098 q^{44} -1.55395 q^{45} -7.50022 q^{46} +3.32888 q^{47} +28.8623 q^{48} +7.35157 q^{49} +10.1576 q^{50} +3.37429 q^{51} -5.33295 q^{52} +3.88978 q^{53} +9.13255 q^{54} -4.33993 q^{55} +34.1915 q^{56} -6.33944 q^{57} -17.4547 q^{58} -7.00399 q^{59} -12.4881 q^{60} +6.94321 q^{61} -6.96165 q^{62} -5.26762 q^{63} +24.5779 q^{64} +1.11757 q^{65} -22.0345 q^{66} +5.45894 q^{67} +8.58806 q^{68} +5.80351 q^{69} -11.4647 q^{70} +12.4932 q^{71} -12.5497 q^{72} -8.48227 q^{73} -31.5290 q^{74} -7.85974 q^{75} -16.1348 q^{76} -14.7115 q^{77} +5.67408 q^{78} +9.37867 q^{79} -15.3939 q^{80} -11.2380 q^{81} -9.56633 q^{82} +9.14392 q^{83} -42.3325 q^{84} -1.79970 q^{85} +3.36974 q^{86} +13.5061 q^{87} -35.0492 q^{88} +12.3812 q^{89} +4.20802 q^{90} +3.78835 q^{91} +14.7707 q^{92} +5.38677 q^{93} -9.01443 q^{94} +3.38119 q^{95} -40.3347 q^{96} -13.9351 q^{97} -19.9076 q^{98} +5.39974 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9}+O(q^{10}) $ 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9} + 5 q^{10} + q^{11} + 15 q^{12} - 30 q^{13} + 24 q^{14} + 6 q^{15} + 38 q^{16} + 17 q^{17} + 8 q^{18} + 9 q^{19} + 31 q^{20} + 27 q^{21} + 2 q^{22} + 14 q^{23} + 26 q^{24} + 47 q^{25} + 14 q^{27} - 6 q^{28} + 53 q^{29} + 25 q^{30} + 19 q^{31} - 4 q^{32} + q^{33} - 22 q^{34} + 9 q^{35} + 61 q^{36} + 46 q^{38} - 5 q^{39} - 35 q^{40} + 28 q^{41} - 7 q^{42} + 6 q^{43} - 12 q^{44} + 68 q^{45} + 7 q^{46} + 12 q^{47} + 13 q^{48} + 54 q^{49} - 18 q^{50} + 10 q^{51} - 34 q^{52} + 37 q^{53} + 22 q^{54} + 11 q^{55} + 67 q^{56} - 57 q^{57} - 5 q^{58} + 61 q^{59} - 102 q^{60} + 16 q^{61} - 2 q^{62} - 7 q^{63} + 29 q^{64} - 17 q^{65} - 83 q^{66} - 2 q^{67} + 57 q^{68} + 98 q^{69} - 10 q^{70} + 50 q^{71} - 8 q^{72} - 10 q^{73} - 13 q^{74} + 5 q^{75} - 19 q^{76} + 54 q^{77} - 3 q^{78} + 3 q^{79} + 76 q^{80} + 118 q^{81} + 7 q^{82} + 6 q^{83} + 44 q^{84} + 33 q^{85} - 29 q^{86} - 10 q^{87} - 13 q^{88} + 77 q^{89} + 38 q^{90} - 2 q^{91} - 3 q^{92} + 34 q^{93} - 25 q^{94} + 24 q^{95} - 28 q^{96} + 12 q^{97} - 14 q^{98} - 58 q^{99}+O(q^{100}) \) 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9 + 5 * q^10 + q^11 + 15 * q^12 - 30 * q^13 + 24 * q^14 + 6 * q^15 + 38 * q^16 + 17 * q^17 + 8 * q^18 + 9 * q^19 + 31 * q^20 + 27 * q^21 + 2 * q^22 + 14 * q^23 + 26 * q^24 + 47 * q^25 + 14 * q^27 - 6 * q^28 + 53 * q^29 + 25 * q^30 + 19 * q^31 - 4 * q^32 + q^33 - 22 * q^34 + 9 * q^35 + 61 * q^36 + 46 * q^38 - 5 * q^39 - 35 * q^40 + 28 * q^41 - 7 * q^42 + 6 * q^43 - 12 * q^44 + 68 * q^45 + 7 * q^46 + 12 * q^47 + 13 * q^48 + 54 * q^49 - 18 * q^50 + 10 * q^51 - 34 * q^52 + 37 * q^53 + 22 * q^54 + 11 * q^55 + 67 * q^56 - 57 * q^57 - 5 * q^58 + 61 * q^59 - 102 * q^60 + 16 * q^61 - 2 * q^62 - 7 * q^63 + 29 * q^64 - 17 * q^65 - 83 * q^66 - 2 * q^67 + 57 * q^68 + 98 * q^69 - 10 * q^70 + 50 * q^71 - 8 * q^72 - 10 * q^73 - 13 * q^74 + 5 * q^75 - 19 * q^76 + 54 * q^77 - 3 * q^78 + 3 * q^79 + 76 * q^80 + 118 * q^81 + 7 * q^82 + 6 * q^83 + 44 * q^84 + 33 * q^85 - 29 * q^86 - 10 * q^87 - 13 * q^88 + 77 * q^89 + 38 * q^90 - 2 * q^91 - 3 * q^92 + 34 * q^93 - 25 * q^94 + 24 * q^95 - 28 * q^96 + 12 * q^97 - 14 * q^98 - 58 * 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 $

$2$	−2.70794	−1.91480	−0.957402	−	0.288757i	$-0.906758\pi$
$2$	−2.70794	−1.91480	−0.957402	+	0.288757i	$0.906758\pi$
$3$	2.09535	1.20975	0.604875	−	0.796321i	$-0.293223\pi$
$3$	2.09535	1.20975	0.604875	+	0.796321i	$0.293223\pi$
$4$	5.33295	2.66648
$5$	−1.11757	−0.499791	−0.249896	−	0.968273i	$-0.580396\pi$
$5$	−1.11757	−0.499791	−0.249896	+	0.968273i	$0.580396\pi$
$6$	−5.67408	−2.31643
$7$	−3.78835	−1.43186	−0.715930	−	0.698172i	$-0.753997\pi$
$7$	−3.78835	−1.43186	−0.715930	+	0.698172i	$0.753997\pi$
$8$	−9.02545	−3.19098
$9$	1.39048	0.463493
$10$	3.02631	0.957003
$11$	3.88337	1.17088	0.585440	−	0.810716i	$-0.300922\pi$
$11$	3.88337	1.17088	0.585440	+	0.810716i	$0.300922\pi$
$12$	11.1744	3.22577
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	10.2586	2.74173
$15$	−2.34169	−0.604622
$16$	13.7745	3.44362
$17$	1.61038	0.390573	0.195287	−	0.980746i	$-0.437436\pi$
$17$	1.61038	0.390573	0.195287	+	0.980746i	$0.437436\pi$
$18$	−3.76534	−0.887498
$19$	−3.02549	−0.694094	−0.347047	−	0.937848i	$-0.612816\pi$
$19$	−3.02549	−0.694094	−0.347047	+	0.937848i	$0.612816\pi$
$20$	−5.95994	−1.33268
$21$	−7.93790	−1.73219
$22$	−10.5159	−2.24201
$23$	2.76971	0.577525	0.288762	−	0.957401i	$-0.406756\pi$
$23$	2.76971	0.577525	0.288762	+	0.957401i	$0.406756\pi$
$24$	−18.9114	−3.86028
$25$	−3.75104	−0.750209
$26$	2.70794	0.531071
$27$	−3.37251	−0.649039
$28$	−20.2031	−3.81802
$29$	6.44575	1.19695	0.598473	−	0.801143i	$-0.295774\pi$
$29$	6.44575	1.19695	0.598473	+	0.801143i	$0.295774\pi$
$30$	6.34117	1.15773
$31$	2.57083	0.461734	0.230867	−	0.972985i	$-0.425844\pi$
$31$	2.57083	0.461734	0.230867	+	0.972985i	$0.425844\pi$
$32$	−19.2496	−3.40289
$33$	8.13700	1.41647
$34$	−4.36080	−0.747872
$35$	4.23373	0.715632
$36$	7.41536	1.23589
$37$	11.6432	1.91413	0.957063	−	0.289881i	$-0.0936156\pi$
$37$	11.6432	1.91413	0.957063	+	0.289881i	$0.0936156\pi$
$38$	8.19284	1.32905
$39$	−2.09535	−0.335524
$40$	10.0866	1.59482
$41$	3.53269	0.551714	0.275857	−	0.961199i	$-0.411038\pi$
$41$	3.53269	0.551714	0.275857	+	0.961199i	$0.411038\pi$
$42$	21.4954	3.31681
$43$	−1.24439	−0.189768	−0.0948838	−	0.995488i	$-0.530248\pi$
$43$	−1.24439	−0.189768	−0.0948838	+	0.995488i	$0.530248\pi$
$44$	20.7098	3.12212
$45$	−1.55395	−0.231650
$46$	−7.50022	−1.10585
$47$	3.32888	0.485568	0.242784	−	0.970080i	$-0.421939\pi$
$47$	3.32888	0.485568	0.242784	+	0.970080i	$0.421939\pi$
$48$	28.8623	4.16592
$49$	7.35157	1.05022
$50$	10.1576	1.43650
$51$	3.37429	0.472496
$52$	−5.33295	−0.739548
$53$	3.88978	0.534303	0.267151	−	0.963655i	$-0.413918\pi$
$53$	3.88978	0.534303	0.267151	+	0.963655i	$0.413918\pi$
$54$	9.13255	1.24278
$55$	−4.33993	−0.585196
$56$	34.1915	4.56904
$57$	−6.33944	−0.839680
$58$	−17.4547	−2.29192
$59$	−7.00399	−0.911842	−0.455921	−	0.890020i	$-0.650690\pi$
$59$	−7.00399	−0.911842	−0.455921	+	0.890020i	$0.650690\pi$
$60$	−12.4881	−1.61221
$61$	6.94321	0.888987	0.444493	−	0.895782i	$-0.353384\pi$
$61$	6.94321	0.888987	0.444493	+	0.895782i	$0.353384\pi$
$62$	−6.96165	−0.884130
$63$	−5.26762	−0.663657
$64$	24.5779	3.07224
$65$	1.11757	0.138617
$66$	−22.0345	−2.71226
$67$	5.45894	0.666915	0.333458	−	0.942765i	$-0.391785\pi$
$67$	5.45894	0.666915	0.333458	+	0.942765i	$0.391785\pi$
$68$	8.58806	1.04145
$69$	5.80351	0.698660
$70$	−11.4647	−1.37029
$71$	12.4932	1.48267	0.741336	−	0.671134i	$-0.234192\pi$
$71$	12.4932	1.48267	0.741336	+	0.671134i	$0.234192\pi$
$72$	−12.5497	−1.47900
$73$	−8.48227	−0.992774	−0.496387	−	0.868101i	$-0.665340\pi$
$73$	−8.48227	−0.992774	−0.496387	+	0.868101i	$0.665340\pi$
$74$	−31.5290	−3.66518
$75$	−7.85974	−0.907564
$76$	−16.1348	−1.85079
$77$	−14.7115	−1.67654
$78$	5.67408	0.642463
$79$	9.37867	1.05518	0.527592	−	0.849498i	$-0.323095\pi$
$79$	9.37867	1.05518	0.527592	+	0.849498i	$0.323095\pi$
$80$	−15.3939	−1.72109
$81$	−11.2380	−1.24867
$82$	−9.56633	−1.05642
$83$	9.14392	1.00368	0.501838	−	0.864962i	$-0.332657\pi$
$83$	9.14392	1.00368	0.501838	+	0.864962i	$0.332657\pi$
$84$	−42.3325	−4.61885
$85$	−1.79970	−0.195205
$86$	3.36974	0.363368
$87$	13.5061	1.44800
$88$	−35.0492	−3.73625
$89$	12.3812	1.31240	0.656200	−	0.754587i	$-0.272163\pi$
$89$	12.3812	1.31240	0.656200	+	0.754587i	$0.272163\pi$
$90$	4.20802	0.443564
$91$	3.78835	0.397127
$92$	14.7707	1.53996
$93$	5.38677	0.558582
$94$	−9.01443	−0.929767
$95$	3.38119	0.346902
$96$	−40.3347	−4.11664
$97$	−13.9351	−1.41490	−0.707449	−	0.706764i	$-0.750154\pi$
$97$	−13.9351	−1.41490	−0.707449	+	0.706764i	$0.750154\pi$
$98$	−19.9076	−2.01097
$99$	5.39974	0.542694
$100$	−20.0041	−2.00041
$101$	17.7232	1.76352	0.881760	−	0.471699i	$-0.156359\pi$
$101$	17.7232	1.76352	0.881760	+	0.471699i	$0.156359\pi$
$102$	−9.13740	−0.904737
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	9.02545	0.885018
$105$	8.87114	0.865735
$106$	−10.5333	−1.02309
$107$	−6.22144	−0.601449	−0.300725	−	0.953711i	$-0.597228\pi$
$107$	−6.22144	−0.601449	−0.300725	+	0.953711i	$0.597228\pi$
$108$	−17.9854	−1.73065
$109$	−10.1564	−0.972806	−0.486403	−	0.873735i	$-0.661691\pi$
$109$	−10.1564	−0.972806	−0.486403	+	0.873735i	$0.661691\pi$
$110$	11.7523	1.12054
$111$	24.3965	2.31561
$112$	−52.1826	−4.93079
$113$	5.21232	0.490334	0.245167	−	0.969481i	$-0.421157\pi$
$113$	5.21232	0.490334	0.245167	+	0.969481i	$0.421157\pi$
$114$	17.1668	1.60782
$115$	−3.09534	−0.288642
$116$	34.3749	3.19163
$117$	−1.39048	−0.128550
$118$	18.9664	1.74600
$119$	−6.10066	−0.559246
$120$	21.1348	1.92934
$121$	4.08055	0.370959
$122$	−18.8018	−1.70224
$123$	7.40221	0.667435
$124$	13.7101	1.23120
$125$	9.77988	0.874739
$126$	14.2644	1.27077
$127$	−21.4833	−1.90634	−0.953169	−	0.302438i	$-0.902200\pi$
$127$	−21.4833	−1.90634	−0.953169	+	0.302438i	$0.902200\pi$
$128$	−28.0564	−2.47986
$129$	−2.60743	−0.229571
$130$	−3.02631	−0.265425
$131$	8.69776	0.759926	0.379963	−	0.925002i	$-0.375937\pi$
$131$	8.69776	0.759926	0.379963	+	0.925002i	$0.375937\pi$
$132$	43.3943	3.77699
$133$	11.4616	0.993846
$134$	−14.7825	−1.27701
$135$	3.76900	0.324384
$136$	−14.5344	−1.24631
$137$	21.8431	1.86619	0.933093	−	0.359635i	$-0.117099\pi$
$137$	21.8431	1.86619	0.933093	+	0.359635i	$0.117099\pi$
$138$	−15.7156	−1.33780
$139$	1.81094	0.153602	0.0768008	−	0.997046i	$-0.475529\pi$
$139$	1.81094	0.153602	0.0768008	+	0.997046i	$0.475529\pi$
$140$	22.5783	1.90822
$141$	6.97516	0.587415
$142$	−33.8309	−2.83903
$143$	−3.88337	−0.324744
$144$	19.1531	1.59610
$145$	−7.20356	−0.598223
$146$	22.9695	1.90097
$147$	15.4041	1.27051
$148$	62.0925	5.10397
$149$	−5.20606	−0.426497	−0.213248	−	0.976998i	$-0.568404\pi$
$149$	−5.20606	−0.426497	−0.213248	+	0.976998i	$0.568404\pi$
$150$	21.2837	1.73781
$151$	6.07792	0.494614	0.247307	−	0.968937i	$-0.420454\pi$
$151$	6.07792	0.494614	0.247307	+	0.968937i	$0.420454\pi$
$152$	27.3064	2.21484
$153$	2.23919	0.181028
$154$	39.8380	3.21024
$155$	−2.87307	−0.230771
$156$	−11.1744	−0.894667
$157$	−9.27904	−0.740548	−0.370274	−	0.928923i	$-0.620736\pi$
$157$	−9.27904	−0.740548	−0.370274	+	0.928923i	$0.620736\pi$
$158$	−25.3969	−2.02047
$159$	8.15045	0.646373
$160$	21.5128	1.70073
$161$	−10.4926	−0.826935
$162$	30.4319	2.39095
$163$	11.8781	0.930368	0.465184	−	0.885214i	$-0.345988\pi$
$163$	11.8781	0.930368	0.465184	+	0.885214i	$0.345988\pi$
$164$	18.8397	1.47113
$165$	−9.09365	−0.707940
$166$	−24.7612	−1.92184
$167$	−0.140196	−0.0108487	−0.00542435	−	0.999985i	$-0.501727\pi$
$167$	−0.140196	−0.0108487	−0.00542435	+	0.999985i	$0.501727\pi$
$168$	71.6431	5.52739
$169$	1.00000	0.0769231
$170$	4.87349	0.373780
$171$	−4.20687	−0.321708
$172$	−6.63627	−0.506011
$173$	−24.3957	−1.85477	−0.927385	−	0.374108i	$-0.877949\pi$
$173$	−24.3957	−1.85477	−0.927385	+	0.374108i	$0.877949\pi$
$174$	−36.5737	−2.77264
$175$	14.2103	1.07419
$176$	53.4914	4.03207
$177$	−14.6758	−1.10310
$178$	−33.5275	−2.51299
$179$	−13.0662	−0.976612	−0.488306	−	0.872673i	$-0.662385\pi$
$179$	−13.0662	−0.976612	−0.488306	+	0.872673i	$0.662385\pi$
$180$	−8.28717	−0.617689
$181$	18.2171	1.35406	0.677032	−	0.735953i	$-0.263266\pi$
$181$	18.2171	1.35406	0.677032	+	0.735953i	$0.263266\pi$
$182$	−10.2586	−0.760420
$183$	14.5484	1.07545
$184$	−24.9979	−1.84287
$185$	−13.0120	−0.956664
$186$	−14.5871	−1.06958
$187$	6.25368	0.457314
$188$	17.7528	1.29475
$189$	12.7762	0.929333
$190$	−9.15606	−0.664250
$191$	−7.27158	−0.526153	−0.263076	−	0.964775i	$-0.584737\pi$
$191$	−7.27158	−0.526153	−0.263076	+	0.964775i	$0.584737\pi$
$192$	51.4993	3.71664
$193$	8.74758	0.629665	0.314832	−	0.949147i	$-0.398052\pi$
$193$	8.74758	0.629665	0.314832	+	0.949147i	$0.398052\pi$
$194$	37.7355	2.70925
$195$	2.34169	0.167692
$196$	39.2056	2.80040
$197$	−18.9839	−1.35255	−0.676273	−	0.736651i	$-0.736406\pi$
$197$	−18.9839	−1.35255	−0.676273	+	0.736651i	$0.736406\pi$
$198$	−14.6222	−1.03915
$199$	18.6366	1.32112	0.660558	−	0.750775i	$-0.270320\pi$
$199$	18.6366	1.32112	0.660558	+	0.750775i	$0.270320\pi$
$200$	33.8549	2.39390
$201$	11.4384	0.806800
$202$	−47.9933	−3.37680
$203$	−24.4187	−1.71386
$204$	17.9950	1.25990
$205$	−3.94802	−0.275742
$206$	−2.70794	−0.188671
$207$	3.85122	0.267679
$208$	−13.7745	−0.955089
$209$	−11.7491	−0.812701
$210$	−24.0225	−1.65771
$211$	−2.06133	−0.141908	−0.0709540	−	0.997480i	$-0.522604\pi$
$211$	−2.06133	−0.141908	−0.0709540	+	0.997480i	$0.522604\pi$
$212$	20.7440	1.42471
$213$	26.1776	1.79366
$214$	16.8473	1.15166
$215$	1.39069	0.0948442
$216$	30.4384	2.07107
$217$	−9.73918	−0.661139
$218$	27.5029	1.86273
$219$	−17.7733	−1.20101
$220$	−23.1446	−1.56041
$221$	−1.61038	−0.108326
$222$	−66.0643	−4.43394
$223$	19.9779	1.33782	0.668908	−	0.743345i	$-0.266762\pi$
$223$	19.9779	1.33782	0.668908	+	0.743345i	$0.266762\pi$
$224$	72.9243	4.87246
$225$	−5.21575	−0.347716
$226$	−14.1147	−0.938894
$227$	−14.7534	−0.979215	−0.489607	−	0.871943i	$-0.662860\pi$
$227$	−14.7534	−0.979215	−0.489607	+	0.871943i	$0.662860\pi$
$228$	−33.8080	−2.23899
$229$	21.1551	1.39797	0.698985	−	0.715136i	$-0.253635\pi$
$229$	21.1551	1.39797	0.698985	+	0.715136i	$0.253635\pi$
$230$	8.38200	0.552693
$231$	−30.8258	−2.02819
$232$	−58.1758	−3.81943
$233$	30.2201	1.97979	0.989893	−	0.141816i	$-0.0452940\pi$
$233$	30.2201	1.97979	0.989893	+	0.141816i	$0.0452940\pi$
$234$	3.76534	0.246148
$235$	−3.72025	−0.242682
$236$	−37.3520	−2.43141
$237$	19.6516	1.27651
$238$	16.5202	1.07085
$239$	−11.8158	−0.764301	−0.382150	−	0.924100i	$-0.624816\pi$
$239$	−11.8158	−0.764301	−0.382150	+	0.924100i	$0.624816\pi$
$240$	−32.2556	−2.08209
$241$	−6.03832	−0.388962	−0.194481	−	0.980906i	$-0.562302\pi$
$241$	−6.03832	−0.388962	−0.194481	+	0.980906i	$0.562302\pi$
$242$	−11.0499	−0.710315
$243$	−13.4300	−0.861535
$244$	37.0278	2.37046
$245$	−8.21588	−0.524893
$246$	−20.0448	−1.27801
$247$	3.02549	0.192507
$248$	−23.2029	−1.47338
$249$	19.1597	1.21420
$250$	−26.4834	−1.67495
$251$	17.8596	1.12729	0.563644	−	0.826018i	$-0.309399\pi$
$251$	17.8596	1.12729	0.563644	+	0.826018i	$0.309399\pi$
$252$	−28.0920	−1.76963
$253$	10.7558	0.676212
$254$	58.1757	3.65027
$255$	−3.77100	−0.236149
$256$	26.8192	1.67620
$257$	12.3345	0.769406	0.384703	−	0.923040i	$-0.374304\pi$
$257$	12.3345	0.769406	0.384703	+	0.923040i	$0.374304\pi$
$258$	7.06077	0.439584
$259$	−44.1084	−2.74076
$260$	5.95994	0.369620
$261$	8.96268	0.554776
$262$	−23.5530	−1.45511
$263$	−17.2807	−1.06557	−0.532786	−	0.846250i	$-0.678855\pi$
$263$	−17.2807	−1.06557	−0.532786	+	0.846250i	$0.678855\pi$
$264$	−73.4401	−4.51993
$265$	−4.34710	−0.267040
$266$	−31.0373	−1.90302
$267$	25.9428	1.58767
$268$	29.1123	1.77831
$269$	18.3892	1.12121	0.560605	−	0.828083i	$-0.310569\pi$
$269$	18.3892	1.12121	0.560605	+	0.828083i	$0.310569\pi$
$270$	−10.2062	−0.621132
$271$	1.03948	0.0631440	0.0315720	−	0.999501i	$-0.489949\pi$
$271$	1.03948	0.0631440	0.0315720	+	0.999501i	$0.489949\pi$
$272$	22.1821	1.34499
$273$	7.93790	0.480424
$274$	−59.1500	−3.57338
$275$	−14.5667	−0.878404
$276$	30.9498	1.86296
$277$	18.0189	1.08265	0.541327	−	0.840812i	$-0.317922\pi$
$277$	18.0189	1.08265	0.541327	+	0.840812i	$0.317922\pi$
$278$	−4.90391	−0.294117
$279$	3.57468	0.214010
$280$	−38.2114	−2.28357
$281$	−20.5535	−1.22612	−0.613060	−	0.790036i	$-0.710062\pi$
$281$	−20.5535	−1.22612	−0.613060	+	0.790036i	$0.710062\pi$
$282$	−18.8883	−1.12478
$283$	−1.93187	−0.114838	−0.0574188	−	0.998350i	$-0.518287\pi$
$283$	−1.93187	−0.114838	−0.0574188	+	0.998350i	$0.518287\pi$
$284$	66.6258	3.95351
$285$	7.08476	0.419665
$286$	10.5159	0.621821
$287$	−13.3831	−0.789977
$288$	−26.7662	−1.57721
$289$	−14.4067	−0.847452
$290$	19.5068	1.14548
$291$	−29.1989	−1.71167
$292$	−45.2355	−2.64721
$293$	21.8531	1.27667	0.638335	−	0.769759i	$-0.279624\pi$
$293$	21.8531	1.27667	0.638335	+	0.769759i	$0.279624\pi$
$294$	−41.7134	−2.43278
$295$	7.82744	0.455731
$296$	−105.085	−6.10793
$297$	−13.0967	−0.759947
$298$	14.0977	0.816658
$299$	−2.76971	−0.160177
$300$	−41.9156	−2.42000
$301$	4.71418	0.271721
$302$	−16.4587	−0.947090
$303$	37.1362	2.13342
$304$	−41.6745	−2.39020
$305$	−7.75950	−0.444308
$306$	−6.06360	−0.346633
$307$	19.8935	1.13538	0.567690	−	0.823243i	$-0.307837\pi$
$307$	19.8935	1.13538	0.567690	+	0.823243i	$0.307837\pi$
$308$	−78.4560	−4.47045
$309$	2.09535	0.119200
$310$	7.78011	0.441881
$311$	−14.4296	−0.818230	−0.409115	−	0.912483i	$-0.634162\pi$
$311$	−14.4296	−0.818230	−0.409115	+	0.912483i	$0.634162\pi$
$312$	18.9114	1.07065
$313$	−17.9574	−1.01501	−0.507506	−	0.861648i	$-0.669432\pi$
$313$	−17.9574	−1.01501	−0.507506	+	0.861648i	$0.669432\pi$
$314$	25.1271	1.41800
$315$	5.88692	0.331690
$316$	50.0160	2.81362
$317$	−19.0930	−1.07237	−0.536185	−	0.844101i	$-0.680135\pi$
$317$	−19.0930	−1.07237	−0.536185	+	0.844101i	$0.680135\pi$
$318$	−22.0709	−1.23768
$319$	25.0312	1.40148
$320$	−27.4675	−1.53548
$321$	−13.0361	−0.727603
$322$	28.4134	1.58342
$323$	−4.87217	−0.271095
$324$	−59.9318	−3.32954
$325$	3.75104	0.208070
$326$	−32.1653	−1.78147
$327$	−21.2812	−1.17685
$328$	−31.8841	−1.76051
$329$	−12.6110	−0.695265
$330$	24.6251	1.35557
$331$	−13.1193	−0.721104	−0.360552	−	0.932739i	$-0.617412\pi$
$331$	−13.1193	−0.721104	−0.360552	+	0.932739i	$0.617412\pi$
$332$	48.7641	2.67628
$333$	16.1896	0.887184
$334$	0.379643	0.0207731
$335$	−6.10073	−0.333319
$336$	−109.341	−5.96502
$337$	−32.0888	−1.74799	−0.873994	−	0.485937i	$-0.838478\pi$
$337$	−32.0888	−1.74799	−0.873994	+	0.485937i	$0.838478\pi$
$338$	−2.70794	−0.147293
$339$	10.9216	0.593181
$340$	−9.59773	−0.520510
$341$	9.98347	0.540635
$342$	11.3920	0.616007
$343$	−1.33187	−0.0719145
$344$	11.2312	0.605544
$345$	−6.48581	−0.349184
$346$	66.0622	3.55152
$347$	−18.3110	−0.982984	−0.491492	−	0.870882i	$-0.663548\pi$
$347$	−18.3110	−0.982984	−0.491492	+	0.870882i	$0.663548\pi$
$348$	72.0273	3.86107
$349$	1.43133	0.0766174	0.0383087	−	0.999266i	$-0.487803\pi$
$349$	1.43133	0.0766174	0.0383087	+	0.999266i	$0.487803\pi$
$350$	−38.4805	−2.05687
$351$	3.37251	0.180011
$352$	−74.7535	−3.98437
$353$	−0.991763	−0.0527862	−0.0263931	−	0.999652i	$-0.508402\pi$
$353$	−0.991763	−0.0527862	−0.0263931	+	0.999652i	$0.508402\pi$
$354$	39.7412	2.11222
$355$	−13.9620	−0.741027
$356$	66.0281	3.49948
$357$	−12.7830	−0.676548
$358$	35.3825	1.87002
$359$	12.8407	0.677709	0.338854	−	0.940839i	$-0.389961\pi$
$359$	12.8407	0.677709	0.338854	+	0.940839i	$0.389961\pi$
$360$	14.0251	0.739189
$361$	−9.84643	−0.518233
$362$	−49.3308	−2.59277
$363$	8.55017	0.448768
$364$	20.2031	1.05893
$365$	9.47951	0.496180
$366$	−39.3963	−2.05928
$367$	27.6685	1.44428	0.722141	−	0.691746i	$-0.243158\pi$
$367$	27.6685	1.44428	0.722141	+	0.691746i	$0.243158\pi$
$368$	38.1514	1.98878
$369$	4.91213	0.255715
$370$	35.2358	1.83182
$371$	−14.7359	−0.765047
$372$	28.7274	1.48945
$373$	−0.234433	−0.0121385	−0.00606925	−	0.999982i	$-0.501932\pi$
$373$	−0.234433	−0.0121385	−0.00606925	+	0.999982i	$0.501932\pi$
$374$	−16.9346	−0.875668
$375$	20.4922	1.05821
$376$	−30.0447	−1.54944
$377$	−6.44575	−0.331973
$378$	−34.5973	−1.77949
$379$	26.2337	1.34753	0.673767	−	0.738944i	$-0.264675\pi$
$379$	26.2337	1.34753	0.673767	+	0.738944i	$0.264675\pi$
$380$	18.0317	0.925007
$381$	−45.0151	−2.30619
$382$	19.6910	1.00748
$383$	12.6689	0.647350	0.323675	−	0.946168i	$-0.395082\pi$
$383$	12.6689	0.647350	0.323675	+	0.946168i	$0.395082\pi$
$384$	−58.7879	−3.00001
$385$	16.4411	0.837919
$386$	−23.6879	−1.20568
$387$	−1.73030	−0.0879559
$388$	−74.3154	−3.77279
$389$	−8.32753	−0.422223	−0.211111	−	0.977462i	$-0.567708\pi$
$389$	−8.32753	−0.422223	−0.211111	+	0.977462i	$0.567708\pi$
$390$	−6.34117	−0.321097
$391$	4.46027	0.225566
$392$	−66.3512	−3.35124
$393$	18.2248	0.919320
$394$	51.4073	2.58986
$395$	−10.4813	−0.527371
$396$	28.7966	1.44708
$397$	−5.45404	−0.273731	−0.136865	−	0.990590i	$-0.543703\pi$
$397$	−5.45404	−0.273731	−0.136865	+	0.990590i	$0.543703\pi$
$398$	−50.4669	−2.52968
$399$	24.0160	1.20230
$400$	−51.6687	−2.58344
$401$	−13.3906	−0.668697	−0.334348	−	0.942450i	$-0.608516\pi$
$401$	−13.3906	−0.668697	−0.334348	+	0.942450i	$0.608516\pi$
$402$	−30.9744	−1.54487
$403$	−2.57083	−0.128062
$404$	94.5168	4.70239
$405$	12.5592	0.624073
$406$	66.1245	3.28171
$407$	45.2147	2.24121
$408$	−30.4545	−1.50772
$409$	−8.96975	−0.443526	−0.221763	−	0.975101i	$-0.571181\pi$
$409$	−8.96975	−0.443526	−0.221763	+	0.975101i	$0.571181\pi$
$410$	10.6910	0.527992
$411$	45.7690	2.25762
$412$	5.33295	0.262736
$413$	26.5336	1.30563
$414$	−10.4289	−0.512552
$415$	−10.2189	−0.501628
$416$	19.2496	0.943791
$417$	3.79454	0.185819
$418$	31.8158	1.55616
$419$	−1.70553	−0.0833208	−0.0416604	−	0.999132i	$-0.513265\pi$
$419$	−1.70553	−0.0833208	−0.0416604	+	0.999132i	$0.513265\pi$
$420$	47.3094	2.30846
$421$	−33.9959	−1.65686	−0.828430	−	0.560093i	$-0.810765\pi$
$421$	−33.9959	−1.65686	−0.828430	+	0.560093i	$0.810765\pi$
$422$	5.58197	0.271726
$423$	4.62874	0.225057
$424$	−35.1071	−1.70495
$425$	−6.04059	−0.293011
$426$	−70.8875	−3.43451
$427$	−26.3033	−1.27291
$428$	−33.1786	−1.60375
$429$	−8.13700	−0.392858
$430$	−3.76591	−0.181608
$431$	1.92458	0.0927038	0.0463519	−	0.998925i	$-0.485240\pi$
$431$	1.92458	0.0927038	0.0463519	+	0.998925i	$0.485240\pi$
$432$	−46.4546	−2.23505
$433$	25.2087	1.21145	0.605726	−	0.795674i	$-0.292883\pi$
$433$	25.2087	1.21145	0.605726	+	0.795674i	$0.292883\pi$
$434$	26.3731	1.26595
$435$	−15.0940	−0.723700
$436$	−54.1636	−2.59397
$437$	−8.37972	−0.400856
$438$	48.1291	2.29970
$439$	0.918591	0.0438419	0.0219210	−	0.999760i	$-0.493022\pi$
$439$	0.918591	0.0438419	0.0219210	+	0.999760i	$0.493022\pi$
$440$	39.1698	1.86735
$441$	10.2222	0.486772
$442$	4.36080	0.207422
$443$	−19.6901	−0.935506	−0.467753	−	0.883859i	$-0.654936\pi$
$443$	−19.6901	−0.935506	−0.467753	+	0.883859i	$0.654936\pi$
$444$	130.105	6.17453
$445$	−13.8368	−0.655926
$446$	−54.0989	−2.56166
$447$	−10.9085	−0.515954
$448$	−93.1098	−4.39902
$449$	38.4642	1.81524	0.907618	−	0.419796i	$-0.137898\pi$
$449$	38.4642	1.81524	0.907618	+	0.419796i	$0.137898\pi$
$450$	14.1239	0.665809
$451$	13.7187	0.645990
$452$	27.7971	1.30746
$453$	12.7354	0.598359
$454$	39.9513	1.87501
$455$	−4.23373	−0.198480
$456$	57.2163	2.67940
$457$	−1.63104	−0.0762967	−0.0381483	−	0.999272i	$-0.512146\pi$
$457$	−1.63104	−0.0762967	−0.0381483	+	0.999272i	$0.512146\pi$
$458$	−57.2869	−2.67684
$459$	−5.43100	−0.253497
$460$	−16.5073	−0.769657
$461$	−11.4684	−0.534139	−0.267069	−	0.963677i	$-0.586055\pi$
$461$	−11.4684	−0.534139	−0.267069	+	0.963677i	$0.586055\pi$
$462$	83.4745	3.88358
$463$	−5.83847	−0.271337	−0.135668	−	0.990754i	$-0.543318\pi$
$463$	−5.83847	−0.271337	−0.135668	+	0.990754i	$0.543318\pi$
$464$	88.7869	4.12183
$465$	−6.02008	−0.279175
$466$	−81.8344	−3.79090
$467$	−26.6302	−1.23230	−0.616150	−	0.787629i	$-0.711308\pi$
$467$	−26.6302	−1.23230	−0.616150	+	0.787629i	$0.711308\pi$
$468$	−7.41536	−0.342775
$469$	−20.6803	−0.954930
$470$	10.0742	0.464690
$471$	−19.4428	−0.895877
$472$	63.2142	2.90967
$473$	−4.83242	−0.222195
$474$	−53.2153	−2.44426
$475$	11.3487	0.520715
$476$	−32.5345	−1.49122
$477$	5.40866	0.247646
$478$	31.9965	1.46349
$479$	0.987576	0.0451235	0.0225617	−	0.999745i	$-0.492818\pi$
$479$	0.987576	0.0451235	0.0225617	+	0.999745i	$0.492818\pi$
$480$	45.0767	2.05746
$481$	−11.6432	−0.530883
$482$	16.3514	0.744787
$483$	−21.9857	−1.00038
$484$	21.7614	0.989155
$485$	15.5734	0.707154
$486$	36.3677	1.64967
$487$	−30.4270	−1.37878	−0.689389	−	0.724391i	$-0.742121\pi$
$487$	−30.4270	−1.37878	−0.689389	+	0.724391i	$0.742121\pi$
$488$	−62.6656	−2.83674
$489$	24.8888	1.12551
$490$	22.2481	1.00507
$491$	1.71347	0.0773279	0.0386639	−	0.999252i	$-0.487690\pi$
$491$	1.71347	0.0773279	0.0386639	+	0.999252i	$0.487690\pi$
$492$	39.4757	1.77970
$493$	10.3801	0.467495
$494$	−8.19284	−0.368613
$495$	−6.03458	−0.271234
$496$	35.4118	1.59004
$497$	−47.3287	−2.12298
$498$	−51.8833	−2.32495
$499$	−33.3551	−1.49318	−0.746590	−	0.665285i	$-0.768310\pi$
$499$	−33.3551	−1.49318	−0.746590	+	0.665285i	$0.768310\pi$
$500$	52.1557	2.33247
$501$	−0.293759	−0.0131242
$502$	−48.3628	−2.15854
$503$	41.7193	1.86017	0.930086	−	0.367342i	$-0.119732\pi$
$503$	41.7193	1.86017	0.930086	+	0.367342i	$0.119732\pi$
$504$	47.5426	2.11772
$505$	−19.8068	−0.881392
$506$	−29.1261	−1.29481
$507$	2.09535	0.0930576
$508$	−114.570	−5.08321
$509$	−28.1829	−1.24918	−0.624592	−	0.780951i	$-0.714735\pi$
$509$	−28.1829	−1.24918	−0.624592	+	0.780951i	$0.714735\pi$
$510$	10.2117	0.452180
$511$	32.1338	1.42151
$512$	−16.5121	−0.729738
$513$	10.2035	0.450494
$514$	−33.4012	−1.47326
$515$	−1.11757	−0.0492459
$516$	−13.9053	−0.612146
$517$	12.9273	0.568541
$518$	119.443	5.24802
$519$	−51.1175	−2.24381
$520$	−10.0866	−0.442325
$521$	22.2451	0.974573	0.487287	−	0.873242i	$-0.337987\pi$
$521$	22.2451	0.974573	0.487287	+	0.873242i	$0.337987\pi$
$522$	−24.2704	−1.06229
$523$	−3.86839	−0.169153	−0.0845765	−	0.996417i	$-0.526954\pi$
$523$	−3.86839	−0.169153	−0.0845765	+	0.996417i	$0.526954\pi$
$524$	46.3847	2.02633
$525$	29.7754	1.29951
$526$	46.7950	2.04036
$527$	4.13999	0.180341
$528$	112.083	4.87779
$529$	−15.3287	−0.666465
$530$	11.7717	0.511330
$531$	−9.73890	−0.422632
$532$	61.1241	2.65007
$533$	−3.53269	−0.153018
$534$	−70.2517	−3.04009
$535$	6.95288	0.300599
$536$	−49.2694	−2.12811
$537$	−27.3782	−1.18146
$538$	−49.7969	−2.14690
$539$	28.5489	1.22969
$540$	20.0999	0.864963
$541$	29.2913	1.25933	0.629666	−	0.776866i	$-0.283192\pi$
$541$	29.2913	1.25933	0.629666	+	0.776866i	$0.283192\pi$
$542$	−2.81485	−0.120908
$543$	38.1711	1.63808
$544$	−30.9991	−1.32908
$545$	11.3505	0.486200
$546$	−21.4954	−0.919917
$547$	34.6336	1.48083	0.740414	−	0.672151i	$-0.234630\pi$
$547$	34.6336	1.48083	0.740414	+	0.672151i	$0.234630\pi$
$548$	116.489	4.97614
$549$	9.65438	0.412039
$550$	39.4457	1.68197
$551$	−19.5015	−0.830793
$552$	−52.3793	−2.22941
$553$	−35.5297	−1.51087
$554$	−48.7943	−2.07307
$555$	−27.2647	−1.15732
$556$	9.65764	0.409575
$557$	−11.0710	−0.469093	−0.234547	−	0.972105i	$-0.575361\pi$
$557$	−11.0710	−0.469093	−0.234547	+	0.972105i	$0.575361\pi$
$558$	−9.68003	−0.409788
$559$	1.24439	0.0526321
$560$	58.3175	2.46437
$561$	13.1036	0.553236
$562$	55.6578	2.34778
$563$	−39.4034	−1.66066	−0.830328	−	0.557275i	$-0.811847\pi$
$563$	−39.4034	−1.66066	−0.830328	+	0.557275i	$0.811847\pi$
$564$	37.1982	1.56633
$565$	−5.82512	−0.245065
$566$	5.23139	0.219892
$567$	42.5735	1.78792
$568$	−112.757	−4.73118
$569$	−7.50706	−0.314712	−0.157356	−	0.987542i	$-0.550297\pi$
$569$	−7.50706	−0.314712	−0.157356	+	0.987542i	$0.550297\pi$
$570$	−19.1851	−0.803576
$571$	29.8681	1.24994	0.624971	−	0.780648i	$-0.285111\pi$
$571$	29.8681	1.24994	0.624971	+	0.780648i	$0.285111\pi$
$572$	−20.7098	−0.865921
$573$	−15.2365	−0.636513
$574$	36.2406	1.51265
$575$	−10.3893	−0.433264
$576$	34.1751	1.42396
$577$	13.4525	0.560035	0.280018	−	0.959995i	$-0.409660\pi$
$577$	13.4525	0.560035	0.280018	+	0.959995i	$0.409660\pi$
$578$	39.0125	1.62271
$579$	18.3292	0.761736
$580$	−38.4163	−1.59515
$581$	−34.6403	−1.43712
$582$	79.0690	3.27752
$583$	15.1055	0.625605
$584$	76.5563	3.16792
$585$	1.55395	0.0642481
$586$	−59.1768	−2.44457
$587$	−27.0068	−1.11469	−0.557345	−	0.830281i	$-0.688180\pi$
$587$	−27.0068	−1.11469	−0.557345	+	0.830281i	$0.688180\pi$
$588$	82.1493	3.38778
$589$	−7.77800	−0.320487
$590$	−21.1963	−0.872636
$591$	−39.7778	−1.63624
$592$	160.379	6.59153
$593$	1.14642	0.0470778	0.0235389	−	0.999723i	$-0.492507\pi$
$593$	1.14642	0.0470778	0.0235389	+	0.999723i	$0.492507\pi$
$594$	35.4651	1.45515
$595$	6.81790	0.279507
$596$	−27.7637	−1.13724
$597$	39.0502	1.59822
$598$	7.50022	0.306707
$599$	−40.6064	−1.65913	−0.829566	−	0.558408i	$-0.811412\pi$
$599$	−40.6064	−1.65913	−0.829566	+	0.558408i	$0.811412\pi$
$600$	70.9377	2.89602
$601$	−19.8717	−0.810585	−0.405292	−	0.914187i	$-0.632830\pi$
$601$	−19.8717	−0.810585	−0.405292	+	0.914187i	$0.632830\pi$
$602$	−12.7657	−0.520292
$603$	7.59054	0.309111
$604$	32.4133	1.31888
$605$	−4.56029	−0.185402
$606$	−100.563	−4.08508
$607$	−6.40393	−0.259928	−0.129964	−	0.991519i	$-0.541486\pi$
$607$	−6.40393	−0.259928	−0.129964	+	0.991519i	$0.541486\pi$
$608$	58.2395	2.36192
$609$	−51.1657	−2.07334
$610$	21.0123	0.850763
$611$	−3.32888	−0.134672
$612$	11.9415	0.482707
$613$	13.2992	0.537149	0.268574	−	0.963259i	$-0.413448\pi$
$613$	13.2992	0.537149	0.268574	+	0.963259i	$0.413448\pi$
$614$	−53.8703	−2.17403
$615$	−8.27247	−0.333578
$616$	132.778	5.34979
$617$	−10.4014	−0.418743	−0.209372	−	0.977836i	$-0.567142\pi$
$617$	−10.4014	−0.418743	−0.209372	+	0.977836i	$0.567142\pi$
$618$	−5.67408	−0.228245
$619$	18.7990	0.755594	0.377797	−	0.925888i	$-0.376682\pi$
$619$	18.7990	0.755594	0.377797	+	0.925888i	$0.376682\pi$
$620$	−15.3220	−0.615345
$621$	−9.34087	−0.374836
$622$	39.0746	1.56675
$623$	−46.9041	−1.87917
$624$	−28.8623	−1.15542
$625$	7.82554	0.313021
$626$	48.6276	1.94355
$627$	−24.6184	−0.983164
$628$	−49.4847	−1.97465
$629$	18.7499	0.747606
$630$	−15.9414	−0.635122
$631$	−48.8202	−1.94350	−0.971750	−	0.236012i	$-0.924160\pi$
$631$	−48.8202	−1.94350	−0.971750	+	0.236012i	$0.924160\pi$
$632$	−84.6467	−3.36707
$633$	−4.31920	−0.171673
$634$	51.7028	2.05338
$635$	24.0091	0.952772
$636$	43.4660	1.72354
$637$	−7.35157	−0.291280
$638$	−67.7831	−2.68356
$639$	17.3716	0.687208
$640$	31.3549	1.23941
$641$	6.42944	0.253948	0.126974	−	0.991906i	$-0.459474\pi$
$641$	6.42944	0.253948	0.126974	+	0.991906i	$0.459474\pi$
$642$	35.3009	1.39322
$643$	−21.3044	−0.840162	−0.420081	−	0.907487i	$-0.637998\pi$
$643$	−21.3044	−0.840162	−0.420081	+	0.907487i	$0.637998\pi$
$644$	−55.9567	−2.20500
$645$	2.91398	0.114738
$646$	13.1936	0.519093
$647$	33.5987	1.32090	0.660450	−	0.750870i	$-0.270366\pi$
$647$	33.5987	1.32090	0.660450	+	0.750870i	$0.270366\pi$
$648$	101.428	3.98447
$649$	−27.1991	−1.06766
$650$	−10.1576	−0.398414
$651$	−20.4070	−0.799812
$652$	63.3456	2.48080
$653$	29.9973	1.17389	0.586943	−	0.809628i	$-0.300331\pi$
$653$	29.9973	1.17389	0.586943	+	0.809628i	$0.300331\pi$
$654$	57.6282	2.25344
$655$	−9.72033	−0.379805
$656$	48.6610	1.89989
$657$	−11.7944	−0.460144
$658$	34.1498	1.33130
$659$	−37.1848	−1.44851	−0.724257	−	0.689530i	$-0.757817\pi$
$659$	−37.1848	−1.44851	−0.724257	+	0.689530i	$0.757817\pi$
$660$	−48.4960	−1.88771
$661$	−0.565056	−0.0219781	−0.0109891	−	0.999940i	$-0.503498\pi$
$661$	−0.565056	−0.0219781	−0.0109891	+	0.999940i	$0.503498\pi$
$662$	35.5264	1.38077
$663$	−3.37429	−0.131047
$664$	−82.5280	−3.20271
$665$	−12.8091	−0.496716
$666$	−43.8405	−1.69878
$667$	17.8529	0.691266
$668$	−0.747659	−0.0289278
$669$	41.8605	1.61842
$670$	16.5204	0.638240
$671$	26.9630	1.04090
$672$	152.802	5.89446
$673$	41.0336	1.58173	0.790865	−	0.611990i	$-0.209631\pi$
$673$	41.0336	1.58173	0.790865	+	0.611990i	$0.209631\pi$
$674$	86.8946	3.34705
$675$	12.6504	0.486915
$676$	5.33295	0.205114
$677$	9.58297	0.368303	0.184152	−	0.982898i	$-0.441046\pi$
$677$	9.58297	0.368303	0.184152	+	0.982898i	$0.441046\pi$
$678$	−29.5751	−1.13583
$679$	52.7911	2.02594
$680$	16.2431	0.622896
$681$	−30.9134	−1.18460
$682$	−27.0347	−1.03521
$683$	−40.0047	−1.53074	−0.765369	−	0.643592i	$-0.777444\pi$
$683$	−40.0047	−1.53074	−0.765369	+	0.643592i	$0.777444\pi$
$684$	−22.4351	−0.857826
$685$	−24.4112	−0.932704
$686$	3.60664	0.137702
$687$	44.3274	1.69119
$688$	−17.1408	−0.653488
$689$	−3.88978	−0.148189
$690$	17.5632	0.668620
$691$	−22.3764	−0.851240	−0.425620	−	0.904902i	$-0.639944\pi$
$691$	−22.3764	−0.851240	−0.425620	+	0.904902i	$0.639944\pi$
$692$	−130.101	−4.94570
$693$	−20.4561	−0.777063
$694$	49.5850	1.88222
$695$	−2.02384	−0.0767688
$696$	−121.898	−4.62055
$697$	5.68896	0.215485
$698$	−3.87596	−0.146707
$699$	63.3216	2.39504
$700$	75.7826	2.86431
$701$	−31.0393	−1.17234	−0.586169	−	0.810189i	$-0.699365\pi$
$701$	−31.0393	−1.17234	−0.586169	+	0.810189i	$0.699365\pi$
$702$	−9.13255	−0.344686
$703$	−35.2263	−1.32858
$704$	95.4452	3.59723
$705$	−7.79522	−0.293585
$706$	2.68564	0.101075
$707$	−67.1415	−2.52511
$708$	−78.2654	−2.94139
$709$	−37.6115	−1.41253	−0.706265	−	0.707948i	$-0.749621\pi$
$709$	−37.6115	−1.41253	−0.706265	+	0.707948i	$0.749621\pi$
$710$	37.8084	1.41892
$711$	13.0408	0.489070
$712$	−111.745	−4.18784
$713$	7.12045	0.266663
$714$	34.6156	1.29546
$715$	4.33993	0.162304
$716$	−69.6813	−2.60411
$717$	−24.7582	−0.924612
$718$	−34.7720	−1.29768
$719$	10.4217	0.388663	0.194332	−	0.980936i	$-0.437746\pi$
$719$	10.4217	0.388663	0.194332	+	0.980936i	$0.437746\pi$
$720$	−21.4049	−0.797715
$721$	−3.78835	−0.141085
$722$	26.6636	0.992316
$723$	−12.6524	−0.470547
$724$	97.1509	3.61058
$725$	−24.1783	−0.897959
$726$	−23.1534	−0.859303
$727$	−29.6583	−1.09997	−0.549983	−	0.835176i	$-0.685366\pi$
$727$	−29.6583	−1.09997	−0.549983	+	0.835176i	$0.685366\pi$
$728$	−34.1915	−1.26722
$729$	5.57350	0.206426
$730$	−25.6700	−0.950088
$731$	−2.00393	−0.0741182
$732$	77.5861	2.86767
$733$	−15.2116	−0.561854	−0.280927	−	0.959729i	$-0.590642\pi$
$733$	−15.2116	−0.561854	−0.280927	+	0.959729i	$0.590642\pi$
$734$	−74.9246	−2.76552
$735$	−17.2151	−0.634989
$736$	−53.3160	−1.96525
$737$	21.1991	0.780878
$738$	−13.3018	−0.489645
$739$	−8.85023	−0.325561	−0.162781	−	0.986662i	$-0.552046\pi$
$739$	−8.85023	−0.325561	−0.162781	+	0.986662i	$0.552046\pi$
$740$	−69.3926	−2.55092
$741$	6.33944	0.232885
$742$	39.9038	1.46492
$743$	−8.51665	−0.312446	−0.156223	−	0.987722i	$-0.549932\pi$
$743$	−8.51665	−0.312446	−0.156223	+	0.987722i	$0.549932\pi$
$744$	−48.6180	−1.78242
$745$	5.81812	0.213159
$746$	0.634832	0.0232429
$747$	12.7144	0.465196
$748$	33.3506	1.21942
$749$	23.5690	0.861191
$750$	−55.4918	−2.02628
$751$	32.9533	1.20248	0.601242	−	0.799067i	$-0.294673\pi$
$751$	32.9533	1.20248	0.601242	+	0.799067i	$0.294673\pi$
$752$	45.8537	1.67211
$753$	37.4221	1.36374
$754$	17.4547	0.635663
$755$	−6.79249	−0.247204
$756$	68.1350	2.47805
$757$	−35.5307	−1.29138	−0.645692	−	0.763598i	$-0.723431\pi$
$757$	−35.5307	−1.29138	−0.645692	+	0.763598i	$0.723431\pi$
$758$	−71.0393	−2.58026
$759$	22.5372	0.818047
$760$	−30.5167	−1.10696
$761$	22.5740	0.818306	0.409153	−	0.912466i	$-0.365824\pi$
$761$	22.5740	0.818306	0.409153	+	0.912466i	$0.365824\pi$
$762$	121.898	4.41591
$763$	38.4759	1.39292
$764$	−38.7790	−1.40297
$765$	−2.50245	−0.0904762
$766$	−34.3066	−1.23955
$767$	7.00399	0.252900
$768$	56.1955	2.02778
$769$	40.6142	1.46459	0.732293	−	0.680989i	$-0.238450\pi$
$769$	40.6142	1.46459	0.732293	+	0.680989i	$0.238450\pi$
$770$	−44.5217	−1.60445
$771$	25.8451	0.930788
$772$	46.6504	1.67899
$773$	10.3886	0.373653	0.186826	−	0.982393i	$-0.440180\pi$
$773$	10.3886	0.373653	0.186826	+	0.982393i	$0.440180\pi$
$774$	4.68555	0.168418
$775$	−9.64328	−0.346397
$776$	125.771	4.51491
$777$	−92.4223	−3.31563
$778$	22.5505	0.808474
$779$	−10.6881	−0.382941
$780$	12.4881	0.447147
$781$	48.5158	1.73603
$782$	−12.0782	−0.431914
$783$	−21.7383	−0.776864
$784$	101.264	3.61658
$785$	10.3699	0.370119
$786$	−49.3518	−1.76032
$787$	−45.2210	−1.61195	−0.805977	−	0.591946i	$-0.798360\pi$
$787$	−45.2210	−1.61195	−0.805977	+	0.591946i	$0.798360\pi$
$788$	−101.240	−3.60653
$789$	−36.2090	−1.28907
$790$	28.3828	1.00981
$791$	−19.7461	−0.702090
$792$	−48.7351	−1.73173
$793$	−6.94321	−0.246561
$794$	14.7692	0.524141
$795$	−9.10868	−0.323051
$796$	99.3883	3.52272
$797$	36.8271	1.30448	0.652241	−	0.758011i	$-0.273829\pi$
$797$	36.8271	1.30448	0.652241	+	0.758011i	$0.273829\pi$
$798$	−65.0340	−2.30218
$799$	5.36075	0.189650
$800$	72.2062	2.55288
$801$	17.2157	0.608288
$802$	36.2611	1.28042
$803$	−32.9398	−1.16242
$804$	61.0003	2.15131
$805$	11.7262	0.413295
$806$	6.96165	0.245214
$807$	38.5318	1.35638
$808$	−159.959	−5.62735
$809$	39.9508	1.40459	0.702297	−	0.711884i	$-0.252158\pi$
$809$	39.9508	1.40459	0.702297	+	0.711884i	$0.252158\pi$
$810$	−34.0097	−1.19498
$811$	2.59514	0.0911277	0.0455638	−	0.998961i	$-0.485492\pi$
$811$	2.59514	0.0911277	0.0455638	+	0.998961i	$0.485492\pi$
$812$	−130.224	−4.56997
$813$	2.17807	0.0763883
$814$	−122.439	−4.29148
$815$	−13.2746	−0.464990
$816$	46.4792	1.62710
$817$	3.76488	0.131717
$818$	24.2896	0.849265
$819$	5.26762	0.184065
$820$	−21.0546	−0.735259
$821$	−3.08257	−0.107582	−0.0537911	−	0.998552i	$-0.517131\pi$
$821$	−3.08257	−0.107582	−0.0537911	+	0.998552i	$0.517131\pi$
$822$	−123.940	−4.32290
$823$	−30.3623	−1.05836	−0.529181	−	0.848509i	$-0.677501\pi$
$823$	−30.3623	−1.05836	−0.529181	+	0.848509i	$0.677501\pi$
$824$	−9.02545	−0.314416
$825$	−30.5223	−1.06265
$826$	−71.8514	−2.50003
$827$	36.7151	1.27671	0.638355	−	0.769742i	$-0.279615\pi$
$827$	36.7151	1.27671	0.638355	+	0.769742i	$0.279615\pi$
$828$	20.5384	0.713759
$829$	19.4957	0.677112	0.338556	−	0.940946i	$-0.390062\pi$
$829$	19.4957	0.677112	0.338556	+	0.940946i	$0.390062\pi$
$830$	27.6723	0.960520
$831$	37.7559	1.30974
$832$	−24.5779	−0.852087
$833$	11.8388	0.410190
$834$	−10.2754	−0.355808
$835$	0.156679	0.00542208
$836$	−62.6573	−2.16705
$837$	−8.67012	−0.299683
$838$	4.61849	0.159543
$839$	30.7566	1.06184	0.530918	−	0.847423i	$-0.321847\pi$
$839$	30.7566	1.06184	0.530918	+	0.847423i	$0.321847\pi$
$840$	−80.0660	−2.76254
$841$	12.5477	0.432679
$842$	92.0590	3.17256
$843$	−43.0668	−1.48330
$844$	−10.9930	−0.378394
$845$	−1.11757	−0.0384455
$846$	−12.5344	−0.430940
$847$	−15.4585	−0.531162
$848$	53.5798	1.83994
$849$	−4.04794	−0.138925
$850$	16.3576	0.561060
$851$	32.2482	1.10545
$852$	139.604	4.78276
$853$	52.5586	1.79957	0.899785	−	0.436333i	$-0.143723\pi$
$853$	52.5586	1.79957	0.899785	+	0.436333i	$0.143723\pi$
$854$	71.2278	2.43736
$855$	4.70147	0.160787
$856$	56.1513	1.91921
$857$	−17.8081	−0.608312	−0.304156	−	0.952622i	$-0.598374\pi$
$857$	−17.8081	−0.608312	−0.304156	+	0.952622i	$0.598374\pi$
$858$	22.0345	0.752247
$859$	−56.8318	−1.93908	−0.969539	−	0.244938i	$-0.921232\pi$
$859$	−56.8318	−1.93908	−0.969539	+	0.244938i	$0.921232\pi$
$860$	7.41648	0.252900
$861$	−28.0422	−0.955674
$862$	−5.21165	−0.177510
$863$	42.7149	1.45403	0.727015	−	0.686621i	$-0.240907\pi$
$863$	42.7149	1.45403	0.727015	+	0.686621i	$0.240907\pi$
$864$	64.9195	2.20861
$865$	27.2638	0.926998
$866$	−68.2636	−2.31969
$867$	−30.1870	−1.02520
$868$	−51.9386	−1.76291
$869$	36.4208	1.23549
$870$	40.8736	1.38574
$871$	−5.45894	−0.184969
$872$	91.6660	3.10420
$873$	−19.3765	−0.655795
$874$	22.6918	0.767562
$875$	−37.0496	−1.25250
$876$	−94.7842	−3.20246
$877$	28.8885	0.975495	0.487747	−	0.872985i	$-0.337819\pi$
$877$	28.8885	0.975495	0.487747	+	0.872985i	$0.337819\pi$
$878$	−2.48749	−0.0839488
$879$	45.7897	1.54445
$880$	−59.7803	−2.01519
$881$	−22.9313	−0.772576	−0.386288	−	0.922378i	$-0.626243\pi$
$881$	−22.9313	−0.772576	−0.386288	+	0.922378i	$0.626243\pi$
$882$	−27.6811	−0.932073
$883$	−27.4305	−0.923110	−0.461555	−	0.887111i	$-0.652708\pi$
$883$	−27.4305	−0.923110	−0.461555	+	0.887111i	$0.652708\pi$
$884$	−8.58806	−0.288848
$885$	16.4012	0.551320
$886$	53.3197	1.79131
$887$	52.2549	1.75455	0.877274	−	0.479989i	$-0.159359\pi$
$887$	52.2549	1.75455	0.877274	+	0.479989i	$0.159359\pi$
$888$	−220.189	−7.38907
$889$	81.3864	2.72961
$890$	37.4692	1.25597
$891$	−43.6413	−1.46204
$892$	106.541	3.56726
$893$	−10.0715	−0.337030
$894$	29.5396	0.987951
$895$	14.6023	0.488102
$896$	106.287	3.55081
$897$	−5.80351	−0.193773
$898$	−104.159	−3.47582
$899$	16.5709	0.552670
$900$	−27.8153	−0.927178
$901$	6.26401	0.208684
$902$	−37.1496	−1.23695
$903$	9.87784	0.328714
$904$	−47.0436	−1.56465
$905$	−20.3588	−0.676750
$906$	−34.4866	−1.14574
$907$	−36.0056	−1.19555	−0.597774	−	0.801665i	$-0.703948\pi$
$907$	−36.0056	−1.19555	−0.597774	+	0.801665i	$0.703948\pi$
$908$	−78.6790	−2.61105
$909$	24.6437	0.817379
$910$	11.4647	0.380051
$911$	−3.41718	−0.113216	−0.0566082	−	0.998396i	$-0.518029\pi$
$911$	−3.41718	−0.113216	−0.0566082	+	0.998396i	$0.518029\pi$
$912$	−87.3226	−2.89154
$913$	35.5092	1.17518
$914$	4.41675	0.146093
$915$	−16.2589	−0.537501
$916$	112.819	3.72766
$917$	−32.9501	−1.08811
$918$	14.7068	0.485398
$919$	3.39656	0.112042	0.0560210	−	0.998430i	$-0.482159\pi$
$919$	3.39656	0.112042	0.0560210	+	0.998430i	$0.482159\pi$
$920$	27.9368	0.921050
$921$	41.6837	1.37352
$922$	31.0559	1.02277
$923$	−12.4932	−0.411219
$924$	−164.393	−5.40812
$925$	−43.6740	−1.43599
$926$	15.8103	0.519557
$927$	1.39048	0.0456693
$928$	−124.078	−4.07307
$929$	20.2008	0.662767	0.331384	−	0.943496i	$-0.392485\pi$
$929$	20.2008	0.662767	0.331384	+	0.943496i	$0.392485\pi$
$930$	16.3020	0.534565
$931$	−22.2421	−0.728955
$932$	161.163	5.27905
$933$	−30.2351	−0.989853
$934$	72.1131	2.35961
$935$	−6.98891	−0.228562
$936$	12.5497	0.410200
$937$	−38.9840	−1.27355	−0.636777	−	0.771048i	$-0.719733\pi$
$937$	−38.9840	−1.27355	−0.636777	+	0.771048i	$0.719733\pi$
$938$	56.0012	1.82850
$939$	−37.6270	−1.22791
$940$	−19.8399	−0.647107
$941$	5.53034	0.180284	0.0901420	−	0.995929i	$-0.471268\pi$
$941$	5.53034	0.180284	0.0901420	+	0.995929i	$0.471268\pi$
$942$	52.6500	1.71543
$943$	9.78453	0.318628
$944$	−96.4765	−3.14004
$945$	−14.2783	−0.464473
$946$	13.0859	0.425460
$947$	17.6829	0.574617	0.287309	−	0.957838i	$-0.407239\pi$
$947$	17.6829	0.574617	0.287309	+	0.957838i	$0.407239\pi$
$948$	104.801	3.40378
$949$	8.48227	0.275346
$950$	−30.7317	−0.997068
$951$	−40.0065	−1.29730
$952$	55.0612	1.78454
$953$	−14.0059	−0.453695	−0.226847	−	0.973930i	$-0.572842\pi$
$953$	−14.0059	−0.453695	−0.226847	+	0.973930i	$0.572842\pi$
$954$	−14.6463	−0.474193
$955$	8.12648	0.262967
$956$	−63.0132	−2.03799
$957$	52.4491	1.69544
$958$	−2.67430	−0.0864027
$959$	−82.7494	−2.67212
$960$	−57.5540	−1.85755
$961$	−24.3909	−0.786802
$962$	31.5290	1.01654
$963$	−8.65078	−0.278767
$964$	−32.2021	−1.03716
$965$	−9.77601	−0.314701
$966$	59.5360	1.91554
$967$	28.4851	0.916020	0.458010	−	0.888947i	$-0.348562\pi$
$967$	28.4851	0.916020	0.458010	+	0.888947i	$0.348562\pi$
$968$	−36.8288	−1.18372
$969$	−10.2089	−0.327956
$970$	−42.1720	−1.35406
$971$	42.9762	1.37917	0.689586	−	0.724204i	$-0.257793\pi$
$971$	42.9762	1.37917	0.689586	+	0.724204i	$0.257793\pi$
$972$	−71.6216	−2.29726
$973$	−6.86045	−0.219936
$974$	82.3946	2.64009
$975$	7.85974	0.251713
$976$	95.6392	3.06134
$977$	−47.3538	−1.51498	−0.757491	−	0.652846i	$-0.773575\pi$
$977$	−47.3538	−1.51498	−0.757491	+	0.652846i	$0.773575\pi$
$978$	−67.3975	−2.15513
$979$	48.0806	1.53666
$980$	−43.8149	−1.39962
$981$	−14.1223	−0.450889
$982$	−4.63998	−0.148068
$983$	27.5466	0.878601	0.439301	−	0.898340i	$-0.355226\pi$
$983$	27.5466	0.878601	0.439301	+	0.898340i	$0.355226\pi$
$984$	−66.8083	−2.12977
$985$	21.2158	0.675991
$986$	−28.1086	−0.895162
$987$	−26.4243	−0.841096
$988$	16.1348	0.513316
$989$	−3.44660	−0.109595
$990$	16.3413	0.519360
$991$	−30.8275	−0.979268	−0.489634	−	0.871928i	$-0.662870\pi$
$991$	−30.8275	−0.979268	−0.489634	+	0.871928i	$0.662870\pi$
$992$	−49.4875	−1.57123
$993$	−27.4896	−0.872355
$994$	128.163	4.06509
$995$	−20.8277	−0.660282
$996$	102.178	3.23762
$997$	21.5990	0.684049	0.342024	−	0.939691i	$-0.388887\pi$
$997$	21.5990	0.684049	0.342024	+	0.939691i	$0.388887\pi$
$998$	90.3237	2.85915
$999$	−39.2667	−1.24234

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.g.1.2	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.g.1.2	✓	30	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1339 = 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1339.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70794 q^{2} +2.09535 q^{3} +5.33295 q^{4} -1.11757 q^{5} -5.67408 q^{6} -3.78835 q^{7} -9.02545 q^{8} +1.39048 q^{9} +O(q^{10})\)	\(q-2.70794 q^{2} +2.09535 q^{3} +5.33295 q^{4} -1.11757 q^{5} -5.67408 q^{6} -3.78835 q^{7} -9.02545 q^{8} +1.39048 q^{9} +3.02631 q^{10} +3.88337 q^{11} +11.1744 q^{12} -1.00000 q^{13} +10.2586 q^{14} -2.34169 q^{15} +13.7745 q^{16} +1.61038 q^{17} -3.76534 q^{18} -3.02549 q^{19} -5.95994 q^{20} -7.93790 q^{21} -10.5159 q^{22} +2.76971 q^{23} -18.9114 q^{24} -3.75104 q^{25} +2.70794 q^{26} -3.37251 q^{27} -20.2031 q^{28} +6.44575 q^{29} +6.34117 q^{30} +2.57083 q^{31} -19.2496 q^{32} +8.13700 q^{33} -4.36080 q^{34} +4.23373 q^{35} +7.41536 q^{36} +11.6432 q^{37} +8.19284 q^{38} -2.09535 q^{39} +10.0866 q^{40} +3.53269 q^{41} +21.4954 q^{42} -1.24439 q^{43} +20.7098 q^{44} -1.55395 q^{45} -7.50022 q^{46} +3.32888 q^{47} +28.8623 q^{48} +7.35157 q^{49} +10.1576 q^{50} +3.37429 q^{51} -5.33295 q^{52} +3.88978 q^{53} +9.13255 q^{54} -4.33993 q^{55} +34.1915 q^{56} -6.33944 q^{57} -17.4547 q^{58} -7.00399 q^{59} -12.4881 q^{60} +6.94321 q^{61} -6.96165 q^{62} -5.26762 q^{63} +24.5779 q^{64} +1.11757 q^{65} -22.0345 q^{66} +5.45894 q^{67} +8.58806 q^{68} +5.80351 q^{69} -11.4647 q^{70} +12.4932 q^{71} -12.5497 q^{72} -8.48227 q^{73} -31.5290 q^{74} -7.85974 q^{75} -16.1348 q^{76} -14.7115 q^{77} +5.67408 q^{78} +9.37867 q^{79} -15.3939 q^{80} -11.2380 q^{81} -9.56633 q^{82} +9.14392 q^{83} -42.3325 q^{84} -1.79970 q^{85} +3.36974 q^{86} +13.5061 q^{87} -35.0492 q^{88} +12.3812 q^{89} +4.20802 q^{90} +3.78835 q^{91} +14.7707 q^{92} +5.38677 q^{93} -9.01443 q^{94} +3.38119 q^{95} -40.3347 q^{96} -13.9351 q^{97} -19.9076 q^{98} +5.39974 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9}+O(q^{10}) \) 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9} + 5 q^{10} + q^{11} + 15 q^{12} - 30 q^{13} + 24 q^{14} + 6 q^{15} + 38 q^{16} + 17 q^{17} + 8 q^{18} + 9 q^{19} + 31 q^{20} + 27 q^{21} + 2 q^{22} + 14 q^{23} + 26 q^{24} + 47 q^{25} + 14 q^{27} - 6 q^{28} + 53 q^{29} + 25 q^{30} + 19 q^{31} - 4 q^{32} + q^{33} - 22 q^{34} + 9 q^{35} + 61 q^{36} + 46 q^{38} - 5 q^{39} - 35 q^{40} + 28 q^{41} - 7 q^{42} + 6 q^{43} - 12 q^{44} + 68 q^{45} + 7 q^{46} + 12 q^{47} + 13 q^{48} + 54 q^{49} - 18 q^{50} + 10 q^{51} - 34 q^{52} + 37 q^{53} + 22 q^{54} + 11 q^{55} + 67 q^{56} - 57 q^{57} - 5 q^{58} + 61 q^{59} - 102 q^{60} + 16 q^{61} - 2 q^{62} - 7 q^{63} + 29 q^{64} - 17 q^{65} - 83 q^{66} - 2 q^{67} + 57 q^{68} + 98 q^{69} - 10 q^{70} + 50 q^{71} - 8 q^{72} - 10 q^{73} - 13 q^{74} + 5 q^{75} - 19 q^{76} + 54 q^{77} - 3 q^{78} + 3 q^{79} + 76 q^{80} + 118 q^{81} + 7 q^{82} + 6 q^{83} + 44 q^{84} + 33 q^{85} - 29 q^{86} - 10 q^{87} - 13 q^{88} + 77 q^{89} + 38 q^{90} - 2 q^{91} - 3 q^{92} + 34 q^{93} - 25 q^{94} + 24 q^{95} - 28 q^{96} + 12 q^{97} - 14 q^{98} - 58 q^{99}+O(q^{100}) \) 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9 + 5 * q^10 + q^11 + 15 * q^12 - 30 * q^13 + 24 * q^14 + 6 * q^15 + 38 * q^16 + 17 * q^17 + 8 * q^18 + 9 * q^19 + 31 * q^20 + 27 * q^21 + 2 * q^22 + 14 * q^23 + 26 * q^24 + 47 * q^25 + 14 * q^27 - 6 * q^28 + 53 * q^29 + 25 * q^30 + 19 * q^31 - 4 * q^32 + q^33 - 22 * q^34 + 9 * q^35 + 61 * q^36 + 46 * q^38 - 5 * q^39 - 35 * q^40 + 28 * q^41 - 7 * q^42 + 6 * q^43 - 12 * q^44 + 68 * q^45 + 7 * q^46 + 12 * q^47 + 13 * q^48 + 54 * q^49 - 18 * q^50 + 10 * q^51 - 34 * q^52 + 37 * q^53 + 22 * q^54 + 11 * q^55 + 67 * q^56 - 57 * q^57 - 5 * q^58 + 61 * q^59 - 102 * q^60 + 16 * q^61 - 2 * q^62 - 7 * q^63 + 29 * q^64 - 17 * q^65 - 83 * q^66 - 2 * q^67 + 57 * q^68 + 98 * q^69 - 10 * q^70 + 50 * q^71 - 8 * q^72 - 10 * q^73 - 13 * q^74 + 5 * q^75 - 19 * q^76 + 54 * q^77 - 3 * q^78 + 3 * q^79 + 76 * q^80 + 118 * q^81 + 7 * q^82 + 6 * q^83 + 44 * q^84 + 33 * q^85 - 29 * q^86 - 10 * q^87 - 13 * q^88 + 77 * q^89 + 38 * q^90 - 2 * q^91 - 3 * q^92 + 34 * q^93 - 25 * q^94 + 24 * q^95 - 28 * q^96 + 12 * q^97 - 14 * q^98 - 58 * q^99

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