LMFDB - Embedded newform 9251.2.a.ba.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9251,2,Mod(1,9251)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9251, 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("9251.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9251 = 11 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9251.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:	$73.8696069099$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	9251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.245772 q^{2} -1.67672 q^{3} -1.93960 q^{4} +1.54159 q^{5} +0.412090 q^{6} +0.822896 q^{7} +0.968242 q^{8} -0.188622 q^{9} +O(q^{10})$	\(q-0.245772 q^{2} -1.67672 q^{3} -1.93960 q^{4} +1.54159 q^{5} +0.412090 q^{6} +0.822896 q^{7} +0.968242 q^{8} -0.188622 q^{9} -0.378881 q^{10} +1.00000 q^{11} +3.25215 q^{12} +1.61145 q^{13} -0.202245 q^{14} -2.58482 q^{15} +3.64123 q^{16} -1.94638 q^{17} +0.0463580 q^{18} +1.11516 q^{19} -2.99007 q^{20} -1.37976 q^{21} -0.245772 q^{22} -3.51175 q^{23} -1.62347 q^{24} -2.62349 q^{25} -0.396050 q^{26} +5.34641 q^{27} -1.59609 q^{28} +0.635275 q^{30} -0.380152 q^{31} -2.83140 q^{32} -1.67672 q^{33} +0.478365 q^{34} +1.26857 q^{35} +0.365850 q^{36} +5.07290 q^{37} -0.274075 q^{38} -2.70195 q^{39} +1.49264 q^{40} +1.14256 q^{41} +0.339107 q^{42} +4.38603 q^{43} -1.93960 q^{44} -0.290778 q^{45} +0.863089 q^{46} -1.53427 q^{47} -6.10530 q^{48} -6.32284 q^{49} +0.644780 q^{50} +3.26352 q^{51} -3.12557 q^{52} -4.41795 q^{53} -1.31400 q^{54} +1.54159 q^{55} +0.796763 q^{56} -1.86980 q^{57} +2.64709 q^{59} +5.01350 q^{60} -6.10065 q^{61} +0.0934306 q^{62} -0.155216 q^{63} -6.58657 q^{64} +2.48421 q^{65} +0.412090 q^{66} -6.05336 q^{67} +3.77518 q^{68} +5.88821 q^{69} -0.311779 q^{70} +3.07524 q^{71} -0.182632 q^{72} +5.19404 q^{73} -1.24678 q^{74} +4.39884 q^{75} -2.16296 q^{76} +0.822896 q^{77} +0.664063 q^{78} -12.4771 q^{79} +5.61329 q^{80} -8.39856 q^{81} -0.280809 q^{82} -11.0454 q^{83} +2.67618 q^{84} -3.00052 q^{85} -1.07796 q^{86} +0.968242 q^{88} +6.19250 q^{89} +0.0714652 q^{90} +1.32606 q^{91} +6.81137 q^{92} +0.637406 q^{93} +0.377080 q^{94} +1.71912 q^{95} +4.74745 q^{96} +2.00667 q^{97} +1.55398 q^{98} -0.188622 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9}+O(q^{10}) $ 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9	\( 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9} - 25 q^{10} + 40 q^{11} - 17 q^{12} - 35 q^{13} + 3 q^{14} + 15 q^{15} - 6 q^{17} + 24 q^{18} + 2 q^{19} - 6 q^{20} - 5 q^{21} + 8 q^{23} - 18 q^{24} + 20 q^{25} - 20 q^{26} + q^{27} - 50 q^{28} - 5 q^{30} - 12 q^{31} - 6 q^{32} - 5 q^{33} - 26 q^{34} - 28 q^{35} - 22 q^{36} - 17 q^{37} - 12 q^{38} - 30 q^{39} + 30 q^{40} + 9 q^{41} - 34 q^{42} + 6 q^{43} + 28 q^{44} - 89 q^{45} - 7 q^{46} - 8 q^{47} + 33 q^{48} + q^{49} + 17 q^{50} - 52 q^{51} - 65 q^{52} - 51 q^{53} + 5 q^{54} - 12 q^{55} - 4 q^{56} - 49 q^{57} - 56 q^{59} + 15 q^{60} - 39 q^{61} + 53 q^{63} - 13 q^{64} - 13 q^{65} - 8 q^{66} - 68 q^{67} - 107 q^{68} - 31 q^{69} + 51 q^{70} - 47 q^{71} + 71 q^{72} + 19 q^{73} - 54 q^{74} - 22 q^{75} + 54 q^{76} - 15 q^{77} + 28 q^{78} + 10 q^{79} + 10 q^{80} - 4 q^{81} + 34 q^{82} - 40 q^{83} + 11 q^{84} + 26 q^{85} - 46 q^{86} - 3 q^{88} + 29 q^{89} - 100 q^{90} - 50 q^{91} + 76 q^{92} - 73 q^{93} - 116 q^{94} + 5 q^{95} + 13 q^{96} - 22 q^{97} + 102 q^{98} + 25 q^{99}+O(q^{100}) \) 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9 - 25 * q^10 + 40 * q^11 - 17 * q^12 - 35 * q^13 + 3 * q^14 + 15 * q^15 - 6 * q^17 + 24 * q^18 + 2 * q^19 - 6 * q^20 - 5 * q^21 + 8 * q^23 - 18 * q^24 + 20 * q^25 - 20 * q^26 + q^27 - 50 * q^28 - 5 * q^30 - 12 * q^31 - 6 * q^32 - 5 * q^33 - 26 * q^34 - 28 * q^35 - 22 * q^36 - 17 * q^37 - 12 * q^38 - 30 * q^39 + 30 * q^40 + 9 * q^41 - 34 * q^42 + 6 * q^43 + 28 * q^44 - 89 * q^45 - 7 * q^46 - 8 * q^47 + 33 * q^48 + q^49 + 17 * q^50 - 52 * q^51 - 65 * q^52 - 51 * q^53 + 5 * q^54 - 12 * q^55 - 4 * q^56 - 49 * q^57 - 56 * q^59 + 15 * q^60 - 39 * q^61 + 53 * q^63 - 13 * q^64 - 13 * q^65 - 8 * q^66 - 68 * q^67 - 107 * q^68 - 31 * q^69 + 51 * q^70 - 47 * q^71 + 71 * q^72 + 19 * q^73 - 54 * q^74 - 22 * q^75 + 54 * q^76 - 15 * q^77 + 28 * q^78 + 10 * q^79 + 10 * q^80 - 4 * q^81 + 34 * q^82 - 40 * q^83 + 11 * q^84 + 26 * q^85 - 46 * q^86 - 3 * q^88 + 29 * q^89 - 100 * q^90 - 50 * q^91 + 76 * q^92 - 73 * q^93 - 116 * q^94 + 5 * q^95 + 13 * q^96 - 22 * q^97 + 102 * q^98 + 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.245772	−0.173787	−0.0868935	−	0.996218i	$-0.527694\pi$
$2$	−0.245772	−0.173787	−0.0868935	+	0.996218i	$0.527694\pi$
$3$	−1.67672	−0.968053	−0.484026	−	0.875053i	$-0.660826\pi$
$3$	−1.67672	−0.968053	−0.484026	+	0.875053i	$0.660826\pi$
$4$	−1.93960	−0.969798
$5$	1.54159	0.689422	0.344711	−	0.938709i	$-0.387977\pi$
$5$	1.54159	0.689422	0.344711	+	0.938709i	$0.387977\pi$
$6$	0.412090	0.168235
$7$	0.822896	0.311025	0.155513	−	0.987834i	$-0.450297\pi$
$7$	0.822896	0.311025	0.155513	+	0.987834i	$0.450297\pi$
$8$	0.968242	0.342325
$9$	−0.188622	−0.0628740
$10$	−0.378881	−0.119813
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.25215	0.938816
$13$	1.61145	0.446936	0.223468	−	0.974711i	$-0.428262\pi$
$13$	1.61145	0.446936	0.223468	+	0.974711i	$0.428262\pi$
$14$	−0.202245	−0.0540522
$15$	−2.58482	−0.667397
$16$	3.64123	0.910306
$17$	−1.94638	−0.472065	−0.236033	−	0.971745i	$-0.575847\pi$
$17$	−1.94638	−0.472065	−0.236033	+	0.971745i	$0.575847\pi$
$18$	0.0463580	0.0109267
$19$	1.11516	0.255835	0.127917	−	0.991785i	$-0.459171\pi$
$19$	1.11516	0.255835	0.127917	+	0.991785i	$0.459171\pi$
$20$	−2.99007	−0.668600
$21$	−1.37976	−0.301089
$22$	−0.245772	−0.0523988
$23$	−3.51175	−0.732250	−0.366125	−	0.930566i	$-0.619316\pi$
$23$	−3.51175	−0.732250	−0.366125	+	0.930566i	$0.619316\pi$
$24$	−1.62347	−0.331389
$25$	−2.62349	−0.524698
$26$	−0.396050	−0.0776717
$27$	5.34641	1.02892
$28$	−1.59609	−0.301632
$29$	0	0
$29$	0	0
$30$	0.635275	0.115985
$31$	−0.380152	−0.0682772	−0.0341386	−	0.999417i	$-0.510869\pi$
$31$	−0.380152	−0.0682772	−0.0341386	+	0.999417i	$0.510869\pi$
$32$	−2.83140	−0.500525
$33$	−1.67672	−0.291879
$34$	0.478365	0.0820388
$35$	1.26857	0.214428
$36$	0.365850	0.0609750
$37$	5.07290	0.833980	0.416990	−	0.908911i	$-0.363085\pi$
$37$	5.07290	0.833980	0.416990	+	0.908911i	$0.363085\pi$
$38$	−0.274075	−0.0444608
$39$	−2.70195	−0.432658
$40$	1.49264	0.236007
$41$	1.14256	0.178438	0.0892190	−	0.996012i	$-0.471563\pi$
$41$	1.14256	0.178438	0.0892190	+	0.996012i	$0.471563\pi$
$42$	0.339107	0.0523254
$43$	4.38603	0.668864	0.334432	−	0.942420i	$-0.391456\pi$
$43$	4.38603	0.668864	0.334432	+	0.942420i	$0.391456\pi$
$44$	−1.93960	−0.292405
$45$	−0.290778	−0.0433467
$46$	0.863089	0.127256
$47$	−1.53427	−0.223796	−0.111898	−	0.993720i	$-0.535693\pi$
$47$	−1.53427	−0.223796	−0.111898	+	0.993720i	$0.535693\pi$
$48$	−6.10530	−0.881225
$49$	−6.32284	−0.903263
$50$	0.644780	0.0911856
$51$	3.26352	0.456984
$52$	−3.12557	−0.433438
$53$	−4.41795	−0.606852	−0.303426	−	0.952855i	$-0.598131\pi$
$53$	−4.41795	−0.606852	−0.303426	+	0.952855i	$0.598131\pi$
$54$	−1.31400	−0.178813
$55$	1.54159	0.207869
$56$	0.796763	0.106472
$57$	−1.86980	−0.247662
$58$	0	0
$59$	2.64709	0.344622	0.172311	−	0.985043i	$-0.444877\pi$
$59$	2.64709	0.344622	0.172311	+	0.985043i	$0.444877\pi$
$60$	5.01350	0.647240
$61$	−6.10065	−0.781108	−0.390554	−	0.920580i	$-0.627717\pi$
$61$	−6.10065	−0.781108	−0.390554	+	0.920580i	$0.627717\pi$
$62$	0.0934306	0.0118657
$63$	−0.155216	−0.0195554
$64$	−6.58657	−0.823322
$65$	2.48421	0.308128
$66$	0.412090	0.0507248
$67$	−6.05336	−0.739535	−0.369768	−	0.929124i	$-0.620563\pi$
$67$	−6.05336	−0.739535	−0.369768	+	0.929124i	$0.620563\pi$
$68$	3.77518	0.457808
$69$	5.88821	0.708857
$70$	−0.311779	−0.0372648
$71$	3.07524	0.364964	0.182482	−	0.983209i	$-0.441587\pi$
$71$	3.07524	0.364964	0.182482	+	0.983209i	$0.441587\pi$
$72$	−0.182632	−0.0215234
$73$	5.19404	0.607916	0.303958	−	0.952685i	$-0.401692\pi$
$73$	5.19404	0.607916	0.303958	+	0.952685i	$0.401692\pi$
$74$	−1.24678	−0.144935
$75$	4.39884	0.507935
$76$	−2.16296	−0.248108
$77$	0.822896	0.0937777
$78$	0.664063	0.0751903
$79$	−12.4771	−1.40379	−0.701893	−	0.712282i	$-0.747662\pi$
$79$	−12.4771	−1.40379	−0.701893	+	0.712282i	$0.747662\pi$
$80$	5.61329	0.627585
$81$	−8.39856	−0.933173
$82$	−0.280809	−0.0310102
$83$	−11.0454	−1.21239	−0.606193	−	0.795317i	$-0.707304\pi$
$83$	−11.0454	−1.21239	−0.606193	+	0.795317i	$0.707304\pi$
$84$	2.67618	0.291996
$85$	−3.00052	−0.325452
$86$	−1.07796	−0.116240
$87$	0	0
$88$	0.968242	0.103215
$89$	6.19250	0.656404	0.328202	−	0.944608i	$-0.393557\pi$
$89$	6.19250	0.656404	0.328202	+	0.944608i	$0.393557\pi$
$90$	0.0714652	0.00753309
$91$	1.32606	0.139009
$92$	6.81137	0.710135
$93$	0.637406	0.0660960
$94$	0.377080	0.0388928
$95$	1.71912	0.176378
$96$	4.74745	0.484534
$97$	2.00667	0.203747	0.101873	−	0.994797i	$-0.467516\pi$
$97$	2.00667	0.203747	0.101873	+	0.994797i	$0.467516\pi$
$98$	1.55398	0.156975
$99$	−0.188622	−0.0189572
$100$	5.08851	0.508851
$101$	8.86829	0.882428	0.441214	−	0.897402i	$-0.354548\pi$
$101$	8.86829	0.882428	0.441214	+	0.897402i	$0.354548\pi$
$102$	−0.802082	−0.0794179
$103$	4.78648	0.471626	0.235813	−	0.971798i	$-0.424225\pi$
$103$	4.78648	0.471626	0.235813	+	0.971798i	$0.424225\pi$
$104$	1.56028	0.152998
$105$	−2.12704	−0.207577
$106$	1.08581	0.105463
$107$	−9.71985	−0.939654	−0.469827	−	0.882759i	$-0.655684\pi$
$107$	−9.71985	−0.939654	−0.469827	+	0.882759i	$0.655684\pi$
$108$	−10.3699	−0.997843
$109$	16.9260	1.62121	0.810607	−	0.585590i	$-0.199137\pi$
$109$	16.9260	1.62121	0.810607	+	0.585590i	$0.199137\pi$
$110$	−0.378881	−0.0361248
$111$	−8.50582	−0.807337
$112$	2.99635	0.283128
$113$	7.25213	0.682223	0.341111	−	0.940023i	$-0.389197\pi$
$113$	7.25213	0.682223	0.341111	+	0.940023i	$0.389197\pi$
$114$	0.459546	0.0430404
$115$	−5.41369	−0.504829
$116$	0	0
$117$	−0.303955	−0.0281007
$118$	−0.650582	−0.0598909
$119$	−1.60166	−0.146824
$120$	−2.50273	−0.228467
$121$	1.00000	0.0909091
$122$	1.49937	0.135746
$123$	−1.91575	−0.172737
$124$	0.737341	0.0662151
$125$	−11.7523	−1.05116
$126$	0.0381478	0.00339848
$127$	1.68164	0.149221	0.0746106	−	0.997213i	$-0.476229\pi$
$127$	1.68164	0.149221	0.0746106	+	0.997213i	$0.476229\pi$
$128$	7.28159	0.643607
$129$	−7.35413	−0.647495
$130$	−0.610548	−0.0535486
$131$	6.46627	0.564961	0.282480	−	0.959273i	$-0.408843\pi$
$131$	6.46627	0.564961	0.282480	+	0.959273i	$0.408843\pi$
$132$	3.25215	0.283064
$133$	0.917659	0.0795712
$134$	1.48775	0.128522
$135$	8.24200	0.709359
$136$	−1.88456	−0.161600
$137$	−18.2462	−1.55888	−0.779440	−	0.626477i	$-0.784496\pi$
$137$	−18.2462	−1.55888	−0.779440	+	0.626477i	$0.784496\pi$
$138$	−1.44716	−0.123190
$139$	0.935774	0.0793713	0.0396856	−	0.999212i	$-0.487364\pi$
$139$	0.935774	0.0793713	0.0396856	+	0.999212i	$0.487364\pi$
$140$	−2.46052	−0.207952
$141$	2.57253	0.216646
$142$	−0.755808	−0.0634260
$143$	1.61145	0.134756
$144$	−0.686815	−0.0572346
$145$	0	0
$146$	−1.27655	−0.105648
$147$	10.6016	0.874406
$148$	−9.83938	−0.808792
$149$	−1.83834	−0.150603	−0.0753014	−	0.997161i	$-0.523992\pi$
$149$	−1.83834	−0.150603	−0.0753014	+	0.997161i	$0.523992\pi$
$150$	−1.08111	−0.0882725
$151$	−16.2781	−1.32469	−0.662345	−	0.749199i	$-0.730439\pi$
$151$	−16.2781	−1.32469	−0.662345	+	0.749199i	$0.730439\pi$
$152$	1.07974	0.0875788
$153$	0.367129	0.0296806
$154$	−0.202245	−0.0162973
$155$	−0.586039	−0.0470718
$156$	5.24069	0.419591
$157$	3.01942	0.240976	0.120488	−	0.992715i	$-0.461554\pi$
$157$	3.01942	0.240976	0.120488	+	0.992715i	$0.461554\pi$
$158$	3.06653	0.243960
$159$	7.40765	0.587465
$160$	−4.36486	−0.345073
$161$	−2.88980	−0.227748
$162$	2.06413	0.162173
$163$	14.1925	1.11164	0.555821	−	0.831302i	$-0.312404\pi$
$163$	14.1925	1.11164	0.555821	+	0.831302i	$0.312404\pi$
$164$	−2.21611	−0.173049
$165$	−2.58482	−0.201228
$166$	2.71464	0.210697
$167$	25.1294	1.94457	0.972285	−	0.233799i	$-0.0751157\pi$
$167$	25.1294	1.94457	0.972285	+	0.233799i	$0.0751157\pi$
$168$	−1.33595	−0.103070
$169$	−10.4032	−0.800248
$170$	0.737444	0.0565594
$171$	−0.210343	−0.0160854
$172$	−8.50713	−0.648663
$173$	1.68359	0.128001	0.0640004	−	0.997950i	$-0.479614\pi$
$173$	1.68359	0.128001	0.0640004	+	0.997950i	$0.479614\pi$
$174$	0	0
$175$	−2.15886	−0.163194
$176$	3.64123	0.274468
$177$	−4.43843	−0.333613
$178$	−1.52194	−0.114074
$179$	6.69634	0.500508	0.250254	−	0.968180i	$-0.419486\pi$
$179$	6.69634	0.500508	0.250254	+	0.968180i	$0.419486\pi$
$180$	0.563993	0.0420375
$181$	8.90247	0.661715	0.330858	−	0.943681i	$-0.392662\pi$
$181$	8.90247	0.661715	0.330858	+	0.943681i	$0.392662\pi$
$182$	−0.325908	−0.0241579
$183$	10.2291	0.756154
$184$	−3.40022	−0.250668
$185$	7.82036	0.574964
$186$	−0.156657	−0.0114866
$187$	−1.94638	−0.142333
$188$	2.97586	0.217037
$189$	4.39954	0.320020
$190$	−0.422512	−0.0306522
$191$	−0.700884	−0.0507142	−0.0253571	−	0.999678i	$-0.508072\pi$
$191$	−0.700884	−0.0507142	−0.0253571	+	0.999678i	$0.508072\pi$
$192$	11.0438	0.797019
$193$	−16.0370	−1.15437	−0.577183	−	0.816615i	$-0.695848\pi$
$193$	−16.0370	−1.15437	−0.577183	+	0.816615i	$0.695848\pi$
$194$	−0.493184	−0.0354085
$195$	−4.16531	−0.298284
$196$	12.2638	0.875983
$197$	19.6547	1.40034	0.700169	−	0.713978i	$-0.253108\pi$
$197$	19.6547	1.40034	0.700169	+	0.713978i	$0.253108\pi$
$198$	0.0463580	0.00329452
$199$	−16.6423	−1.17974	−0.589869	−	0.807499i	$-0.700821\pi$
$199$	−16.6423	−1.17974	−0.589869	+	0.807499i	$0.700821\pi$
$200$	−2.54017	−0.179617
$201$	10.1498	0.715909
$202$	−2.17958	−0.153355
$203$	0	0
$204$	−6.32991	−0.443182
$205$	1.76136	0.123019
$206$	−1.17638	−0.0819625
$207$	0.662393	0.0460395
$208$	5.86766	0.406849
$209$	1.11516	0.0771371
$210$	0.522766	0.0360743
$211$	17.0392	1.17302	0.586512	−	0.809940i	$-0.300501\pi$
$211$	17.0392	1.17302	0.586512	+	0.809940i	$0.300501\pi$
$212$	8.56904	0.588524
$213$	−5.15631	−0.353304
$214$	2.38887	0.163300
$215$	6.76148	0.461129
$216$	5.17662	0.352225
$217$	−0.312825	−0.0212360
$218$	−4.15993	−0.281746
$219$	−8.70893	−0.588495
$220$	−2.99007	−0.201590
$221$	−3.13649	−0.210983
$222$	2.09049	0.140305
$223$	12.7738	0.855398	0.427699	−	0.903921i	$-0.359324\pi$
$223$	12.7738	0.855398	0.427699	+	0.903921i	$0.359324\pi$
$224$	−2.32994	−0.155676
$225$	0.494847	0.0329898
$226$	−1.78237	−0.118561
$227$	−17.3801	−1.15356	−0.576780	−	0.816899i	$-0.695691\pi$
$227$	−17.3801	−1.15356	−0.576780	+	0.816899i	$0.695691\pi$
$228$	3.62667	0.240182
$229$	8.62648	0.570054	0.285027	−	0.958519i	$-0.407997\pi$
$229$	8.62648	0.570054	0.285027	+	0.958519i	$0.407997\pi$
$230$	1.33053	0.0877328
$231$	−1.37976	−0.0907818
$232$	0	0
$233$	−10.5345	−0.690141	−0.345070	−	0.938577i	$-0.612145\pi$
$233$	−10.5345	−0.690141	−0.345070	+	0.938577i	$0.612145\pi$
$234$	0.0747036	0.00488353
$235$	−2.36522	−0.154290
$236$	−5.13430	−0.334214
$237$	20.9206	1.35894
$238$	0.393644	0.0255162
$239$	−0.270372	−0.0174889	−0.00874446	−	0.999962i	$-0.502783\pi$
$239$	−0.270372	−0.0174889	−0.00874446	+	0.999962i	$0.502783\pi$
$240$	−9.41190	−0.607535
$241$	−5.90693	−0.380499	−0.190249	−	0.981736i	$-0.560930\pi$
$241$	−5.90693	−0.380499	−0.190249	+	0.981736i	$0.560930\pi$
$242$	−0.245772	−0.0157988
$243$	−1.95725	−0.125557
$244$	11.8328	0.757517
$245$	−9.74726	−0.622729
$246$	0.470838	0.0300195
$247$	1.79702	0.114342
$248$	−0.368079	−0.0233730
$249$	18.5200	1.17365
$250$	2.88839	0.182678
$251$	28.0947	1.77332	0.886660	−	0.462422i	$-0.153020\pi$
$251$	28.0947	1.77332	0.886660	+	0.462422i	$0.153020\pi$
$252$	0.301057	0.0189648
$253$	−3.51175	−0.220782
$254$	−0.413300	−0.0259327
$255$	5.03102	0.315055
$256$	11.3835	0.711471
$257$	−20.1817	−1.25890	−0.629449	−	0.777042i	$-0.716719\pi$
$257$	−20.1817	−1.25890	−0.629449	+	0.777042i	$0.716719\pi$
$258$	1.80744	0.112526
$259$	4.17447	0.259389
$260$	−4.81835	−0.298822
$261$	0	0
$262$	−1.58923	−0.0981828
$263$	10.3521	0.638337	0.319168	−	0.947698i	$-0.396596\pi$
$263$	10.3521	0.638337	0.319168	+	0.947698i	$0.396596\pi$
$264$	−1.62347	−0.0999175
$265$	−6.81069	−0.418377
$266$	−0.225535	−0.0138284
$267$	−10.3831	−0.635433
$268$	11.7411	0.717200
$269$	19.1218	1.16588	0.582939	−	0.812516i	$-0.301903\pi$
$269$	19.1218	1.16588	0.582939	+	0.812516i	$0.301903\pi$
$270$	−2.02565	−0.123277
$271$	−29.2958	−1.77960	−0.889798	−	0.456355i	$-0.849155\pi$
$271$	−29.2958	−1.77960	−0.889798	+	0.456355i	$0.849155\pi$
$272$	−7.08719	−0.429724
$273$	−2.22342	−0.134568
$274$	4.48441	0.270913
$275$	−2.62349	−0.158202
$276$	−11.4207	−0.687448
$277$	−16.9991	−1.02137	−0.510687	−	0.859766i	$-0.670609\pi$
$277$	−16.9991	−1.02137	−0.510687	+	0.859766i	$0.670609\pi$
$278$	−0.229987	−0.0137937
$279$	0.0717049	0.00429286
$280$	1.22828	0.0734041
$281$	14.6278	0.872623	0.436312	−	0.899796i	$-0.356285\pi$
$281$	14.6278	0.872623	0.436312	+	0.899796i	$0.356285\pi$
$282$	−0.632256	−0.0376503
$283$	−18.0651	−1.07386	−0.536929	−	0.843628i	$-0.680416\pi$
$283$	−18.0651	−1.07386	−0.536929	+	0.843628i	$0.680416\pi$
$284$	−5.96472	−0.353941
$285$	−2.88248	−0.170743
$286$	−0.396050	−0.0234189
$287$	0.940209	0.0554988
$288$	0.534063	0.0314700
$289$	−13.2116	−0.777154
$290$	0	0
$291$	−3.36462	−0.197237
$292$	−10.0743	−0.589556
$293$	5.64708	0.329906	0.164953	−	0.986301i	$-0.447253\pi$
$293$	5.64708	0.329906	0.164953	+	0.986301i	$0.447253\pi$
$294$	−2.60558	−0.151960
$295$	4.08075	0.237590
$296$	4.91180	0.285493
$297$	5.34641	0.310230
$298$	0.451813	0.0261728
$299$	−5.65902	−0.327269
$300$	−8.53198	−0.492594
$301$	3.60925	0.208034
$302$	4.00069	0.230214
$303$	−14.8696	−0.854237
$304$	4.06054	0.232888
$305$	−9.40472	−0.538513
$306$	−0.0902300	−0.00515811
$307$	6.97316	0.397980	0.198990	−	0.980002i	$-0.436234\pi$
$307$	6.97316	0.397980	0.198990	+	0.980002i	$0.436234\pi$
$308$	−1.59609	−0.0909454
$309$	−8.02557	−0.456559
$310$	0.144032	0.00818047
$311$	12.6941	0.719818	0.359909	−	0.932987i	$-0.382808\pi$
$311$	12.6941	0.719818	0.359909	+	0.932987i	$0.382808\pi$
$312$	−2.61614	−0.148110
$313$	−12.7025	−0.717990	−0.358995	−	0.933339i	$-0.616881\pi$
$313$	−12.7025	−0.717990	−0.358995	+	0.933339i	$0.616881\pi$
$314$	−0.742089	−0.0418785
$315$	−0.239280	−0.0134819
$316$	24.2006	1.36139
$317$	3.85222	0.216362	0.108181	−	0.994131i	$-0.465497\pi$
$317$	3.85222	0.216362	0.108181	+	0.994131i	$0.465497\pi$
$318$	−1.82059	−0.102094
$319$	0	0
$320$	−10.1538	−0.567616
$321$	16.2974	0.909634
$322$	0.710233	0.0395797
$323$	−2.17052	−0.120771
$324$	16.2898	0.904989
$325$	−4.22762	−0.234506
$326$	−3.48812	−0.193189
$327$	−28.3801	−1.56942
$328$	1.10628	0.0610838
$329$	−1.26254	−0.0696063
$330$	0.635275	0.0349708
$331$	8.15017	0.447974	0.223987	−	0.974592i	$-0.428093\pi$
$331$	8.15017	0.447974	0.223987	+	0.974592i	$0.428093\pi$
$332$	21.4236	1.17577
$333$	−0.956861	−0.0524356
$334$	−6.17610	−0.337941
$335$	−9.33182	−0.509852
$336$	−5.02403	−0.274083
$337$	18.9500	1.03227	0.516137	−	0.856506i	$-0.327369\pi$
$337$	18.9500	1.03227	0.516137	+	0.856506i	$0.327369\pi$
$338$	2.55682	0.139073
$339$	−12.1598	−0.660427
$340$	5.81980	0.315623
$341$	−0.380152	−0.0205864
$342$	0.0516965	0.00279543
$343$	−10.9633	−0.591963
$344$	4.24674	0.228969
$345$	9.07723	0.488701
$346$	−0.413778	−0.0222449
$347$	14.7640	0.792571	0.396286	−	0.918127i	$-0.370299\pi$
$347$	14.7640	0.792571	0.396286	+	0.918127i	$0.370299\pi$
$348$	0	0
$349$	−24.9687	−1.33654	−0.668271	−	0.743918i	$-0.732965\pi$
$349$	−24.9687	−1.33654	−0.668271	+	0.743918i	$0.732965\pi$
$350$	0.530587	0.0283610
$351$	8.61549	0.459861
$352$	−2.83140	−0.150914
$353$	5.41738	0.288338	0.144169	−	0.989553i	$-0.453949\pi$
$353$	5.41738	0.288338	0.144169	+	0.989553i	$0.453949\pi$
$354$	1.09084	0.0579775
$355$	4.74077	0.251614
$356$	−12.0109	−0.636579
$357$	2.68554	0.142134
$358$	−1.64577	−0.0869817
$359$	−30.3505	−1.60184	−0.800918	−	0.598774i	$-0.795655\pi$
$359$	−30.3505	−1.60184	−0.800918	+	0.598774i	$0.795655\pi$
$360$	−0.281544	−0.0148387
$361$	−17.7564	−0.934549
$362$	−2.18798	−0.114998
$363$	−1.67672	−0.0880048
$364$	−2.57202	−0.134810
$365$	8.00710	0.419111
$366$	−2.51402	−0.131410
$367$	−25.6406	−1.33843	−0.669215	−	0.743069i	$-0.733370\pi$
$367$	−25.6406	−1.33843	−0.669215	+	0.743069i	$0.733370\pi$
$368$	−12.7871	−0.666572
$369$	−0.215512	−0.0112191
$370$	−1.92202	−0.0999213
$371$	−3.63551	−0.188747
$372$	−1.23631	−0.0640997
$373$	−25.1977	−1.30469	−0.652345	−	0.757923i	$-0.726214\pi$
$373$	−25.1977	−1.30469	−0.652345	+	0.757923i	$0.726214\pi$
$374$	0.478365	0.0247356
$375$	19.7053	1.01758
$376$	−1.48554	−0.0766110
$377$	0	0
$378$	−1.08128	−0.0556153
$379$	3.39050	0.174158	0.0870792	−	0.996201i	$-0.472247\pi$
$379$	3.39050	0.174158	0.0870792	+	0.996201i	$0.472247\pi$
$380$	−3.33440	−0.171051
$381$	−2.81963	−0.144454
$382$	0.172258	0.00881347
$383$	−7.75583	−0.396304	−0.198152	−	0.980171i	$-0.563494\pi$
$383$	−7.75583	−0.396304	−0.198152	+	0.980171i	$0.563494\pi$
$384$	−12.2092	−0.623046
$385$	1.26857	0.0646524
$386$	3.94144	0.200614
$387$	−0.827302	−0.0420541
$388$	−3.89213	−0.197593
$389$	−14.8764	−0.754266	−0.377133	−	0.926159i	$-0.623090\pi$
$389$	−14.8764	−0.754266	−0.377133	+	0.926159i	$0.623090\pi$
$390$	1.02372	0.0518379
$391$	6.83518	0.345670
$392$	−6.12204	−0.309210
$393$	−10.8421	−0.546912
$394$	−4.83057	−0.243360
$395$	−19.2347	−0.967801
$396$	0.365850	0.0183847
$397$	28.7336	1.44210	0.721050	−	0.692883i	$-0.243660\pi$
$397$	28.7336	1.44210	0.721050	+	0.692883i	$0.243660\pi$
$398$	4.09020	0.205023
$399$	−1.53865	−0.0770291
$400$	−9.55271	−0.477635
$401$	−18.4548	−0.921589	−0.460794	−	0.887507i	$-0.652435\pi$
$401$	−18.4548	−0.921589	−0.460794	+	0.887507i	$0.652435\pi$
$402$	−2.49453	−0.124416
$403$	−0.612596	−0.0305156
$404$	−17.2009	−0.855777
$405$	−12.9472	−0.643350
$406$	0	0
$407$	5.07290	0.251455
$408$	3.15988	0.156437
$409$	2.41671	0.119499	0.0597494	−	0.998213i	$-0.480970\pi$
$409$	2.41671	0.119499	0.0597494	+	0.998213i	$0.480970\pi$
$410$	−0.432894	−0.0213791
$411$	30.5937	1.50908
$412$	−9.28384	−0.457382
$413$	2.17828	0.107186
$414$	−0.162798	−0.00800106
$415$	−17.0275	−0.835846
$416$	−4.56266	−0.223703
$417$	−1.56903	−0.0768356
$418$	−0.274075	−0.0134054
$419$	−13.8828	−0.678220	−0.339110	−	0.940747i	$-0.610126\pi$
$419$	−13.8828	−0.678220	−0.339110	+	0.940747i	$0.610126\pi$
$420$	4.12559	0.201308
$421$	−24.8368	−1.21047	−0.605235	−	0.796047i	$-0.706921\pi$
$421$	−24.8368	−1.21047	−0.605235	+	0.796047i	$0.706921\pi$
$422$	−4.18775	−0.203856
$423$	0.289397	0.0140709
$424$	−4.27765	−0.207741
$425$	5.10629	0.247692
$426$	1.26728	0.0613997
$427$	−5.02020	−0.242944
$428$	18.8526	0.911274
$429$	−2.70195	−0.130451
$430$	−1.66178	−0.0801383
$431$	−31.1579	−1.50082	−0.750412	−	0.660970i	$-0.770145\pi$
$431$	−31.1579	−1.50082	−0.750412	+	0.660970i	$0.770145\pi$
$432$	19.4675	0.936631
$433$	−10.6358	−0.511122	−0.255561	−	0.966793i	$-0.582260\pi$
$433$	−10.6358	−0.511122	−0.255561	+	0.966793i	$0.582260\pi$
$434$	0.0768837	0.00369053
$435$	0	0
$436$	−32.8296	−1.57225
$437$	−3.91616	−0.187335
$438$	2.14041	0.102273
$439$	2.41997	0.115499	0.0577495	−	0.998331i	$-0.481608\pi$
$439$	2.41997	0.115499	0.0577495	+	0.998331i	$0.481608\pi$
$440$	1.49264	0.0711587
$441$	1.19263	0.0567917
$442$	0.770862	0.0366661
$443$	−26.2209	−1.24579	−0.622896	−	0.782305i	$-0.714044\pi$
$443$	−26.2209	−1.24579	−0.622896	+	0.782305i	$0.714044\pi$
$444$	16.4979	0.782954
$445$	9.54632	0.452539
$446$	−3.13944	−0.148657
$447$	3.08238	0.145792
$448$	−5.42007	−0.256074
$449$	−36.8791	−1.74043	−0.870217	−	0.492669i	$-0.836021\pi$
$449$	−36.8791	−1.74043	−0.870217	+	0.492669i	$0.836021\pi$
$450$	−0.121620	−0.00573320
$451$	1.14256	0.0538011
$452$	−14.0662	−0.661618
$453$	27.2937	1.28237
$454$	4.27155	0.200474
$455$	2.04424	0.0958356
$456$	−1.81042	−0.0847809
$457$	−15.8074	−0.739441	−0.369720	−	0.929143i	$-0.620547\pi$
$457$	−15.8074	−0.739441	−0.369720	+	0.929143i	$0.620547\pi$
$458$	−2.12015	−0.0990680
$459$	−10.4061	−0.485717
$460$	10.5004	0.489583
$461$	14.2041	0.661549	0.330775	−	0.943710i	$-0.392690\pi$
$461$	14.2041	0.661549	0.330775	+	0.943710i	$0.392690\pi$
$462$	0.339107	0.0157767
$463$	3.56995	0.165910	0.0829549	−	0.996553i	$-0.473564\pi$
$463$	3.56995	0.165910	0.0829549	+	0.996553i	$0.473564\pi$
$464$	0	0
$465$	0.982622	0.0455680
$466$	2.58909	0.119937
$467$	−12.4480	−0.576026	−0.288013	−	0.957627i	$-0.592995\pi$
$467$	−12.4480	−0.576026	−0.288013	+	0.957627i	$0.592995\pi$
$468$	0.589550	0.0272520
$469$	−4.98128	−0.230014
$470$	0.581304	0.0268136
$471$	−5.06271	−0.233277
$472$	2.56303	0.117973
$473$	4.38603	0.201670
$474$	−5.14170	−0.236166
$475$	−2.92560	−0.134236
$476$	3.10658	0.142390
$477$	0.833322	0.0381552
$478$	0.0664499	0.00303935
$479$	−2.64060	−0.120652	−0.0603261	−	0.998179i	$-0.519214\pi$
$479$	−2.64060	−0.120652	−0.0603261	+	0.998179i	$0.519214\pi$
$480$	7.31864	0.334049
$481$	8.17474	0.372736
$482$	1.45176	0.0661257
$483$	4.84538	0.220473
$484$	−1.93960	−0.0881635
$485$	3.09347	0.140467
$486$	0.481036	0.0218203
$487$	26.2220	1.18823	0.594115	−	0.804380i	$-0.297502\pi$
$487$	26.2220	1.18823	0.594115	+	0.804380i	$0.297502\pi$
$488$	−5.90690	−0.267393
$489$	−23.7968	−1.07613
$490$	2.39560	0.108222
$491$	−18.4217	−0.831359	−0.415679	−	0.909511i	$-0.636456\pi$
$491$	−18.4217	−0.831359	−0.415679	+	0.909511i	$0.636456\pi$
$492$	3.71578	0.167520
$493$	0	0
$494$	−0.441658	−0.0198711
$495$	−0.290778	−0.0130695
$496$	−1.38422	−0.0621532
$497$	2.53060	0.113513
$498$	−4.55169	−0.203966
$499$	−24.8501	−1.11244	−0.556221	−	0.831035i	$-0.687749\pi$
$499$	−24.8501	−1.11244	−0.556221	+	0.831035i	$0.687749\pi$
$500$	22.7948	1.01941
$501$	−42.1349	−1.88245
$502$	−6.90488	−0.308180
$503$	−27.3615	−1.21999	−0.609995	−	0.792405i	$-0.708829\pi$
$503$	−27.3615	−1.21999	−0.609995	+	0.792405i	$0.708829\pi$
$504$	−0.150287	−0.00669431
$505$	13.6713	0.608365
$506$	0.863089	0.0383690
$507$	17.4433	0.774682
$508$	−3.26170	−0.144714
$509$	−25.6940	−1.13887	−0.569434	−	0.822037i	$-0.692838\pi$
$509$	−25.6940	−1.13887	−0.569434	+	0.822037i	$0.692838\pi$
$510$	−1.23648	−0.0547525
$511$	4.27415	0.189077
$512$	−17.3609	−0.767252
$513$	5.96210	0.263233
$514$	4.96009	0.218780
$515$	7.37881	0.325149
$516$	14.2640	0.627940
$517$	−1.53427	−0.0674770
$518$	−1.02597	−0.0450785
$519$	−2.82290	−0.123911
$520$	2.40531	0.105480
$521$	26.4637	1.15940	0.579698	−	0.814832i	$-0.303171\pi$
$521$	26.4637	1.15940	0.579698	+	0.814832i	$0.303171\pi$
$522$	0	0
$523$	−16.7646	−0.733065	−0.366533	−	0.930405i	$-0.619455\pi$
$523$	−16.7646	−0.733065	−0.366533	+	0.930405i	$0.619455\pi$
$524$	−12.5420	−0.547898
$525$	3.61979	0.157981
$526$	−2.54425	−0.110935
$527$	0.739918	0.0322313
$528$	−6.10530	−0.265699
$529$	−10.6676	−0.463810
$530$	1.67388	0.0727085
$531$	−0.499300	−0.0216678
$532$	−1.77989	−0.0771680
$533$	1.84118	0.0797504
$534$	2.55187	0.110430
$535$	−14.9841	−0.647818
$536$	−5.86112	−0.253162
$537$	−11.2279	−0.484518
$538$	−4.69961	−0.202614
$539$	−6.32284	−0.272344
$540$	−15.9862	−0.687935
$541$	−0.447413	−0.0192358	−0.00961790	−	0.999954i	$-0.503062\pi$
$541$	−0.447413	−0.0192358	−0.00961790	+	0.999954i	$0.503062\pi$
$542$	7.20010	0.309271
$543$	−14.9269	−0.640575
$544$	5.51096	0.236280
$545$	26.0930	1.11770
$546$	0.546455	0.0233861
$547$	38.8705	1.66198	0.830992	−	0.556284i	$-0.187773\pi$
$547$	38.8705	1.66198	0.830992	+	0.556284i	$0.187773\pi$
$548$	35.3903	1.51180
$549$	1.15072	0.0491113
$550$	0.644780	0.0274935
$551$	0	0
$552$	5.70121	0.242660
$553$	−10.2674	−0.436613
$554$	4.17789	0.177502
$555$	−13.1125	−0.556596
$556$	−1.81502	−0.0769741
$557$	−18.6150	−0.788744	−0.394372	−	0.918951i	$-0.629038\pi$
$557$	−18.6150	−0.788744	−0.394372	+	0.918951i	$0.629038\pi$
$558$	−0.0176231	−0.000746043 0
$559$	7.06788	0.298940
$560$	4.61916	0.195195
$561$	3.26352	0.137786
$562$	−3.59511	−0.151651
$563$	21.7049	0.914752	0.457376	−	0.889273i	$-0.348789\pi$
$563$	21.7049	0.914752	0.457376	+	0.889273i	$0.348789\pi$
$564$	−4.98967	−0.210103
$565$	11.1798	0.470339
$566$	4.43989	0.186622
$567$	−6.91114	−0.290241
$568$	2.97758	0.124936
$569$	−14.4382	−0.605279	−0.302640	−	0.953105i	$-0.597868\pi$
$569$	−14.4382	−0.605279	−0.302640	+	0.953105i	$0.597868\pi$
$570$	0.708433	0.0296730
$571$	40.7199	1.70407	0.852036	−	0.523483i	$-0.175367\pi$
$571$	40.7199	1.70407	0.852036	+	0.523483i	$0.175367\pi$
$572$	−3.12557	−0.130686
$573$	1.17518	0.0490940
$574$	−0.231077	−0.00964496
$575$	9.21303	0.384210
$576$	1.24237	0.0517655
$577$	0.112661	0.00469013	0.00234506	−	0.999997i	$-0.499254\pi$
$577$	0.112661	0.00469013	0.00234506	+	0.999997i	$0.499254\pi$
$578$	3.24705	0.135059
$579$	26.8894	1.11749
$580$	0	0
$581$	−9.08919	−0.377083
$582$	0.826929	0.0342773
$583$	−4.41795	−0.182973
$584$	5.02909	0.208105
$585$	−0.468575	−0.0193732
$586$	−1.38789	−0.0573334
$587$	2.31514	0.0955562	0.0477781	−	0.998858i	$-0.484786\pi$
$587$	2.31514	0.0955562	0.0477781	+	0.998858i	$0.484786\pi$
$588$	−20.5628	−0.847998
$589$	−0.423929	−0.0174677
$590$	−1.00293	−0.0412901
$591$	−32.9553	−1.35560
$592$	18.4716	0.759178
$593$	−39.8610	−1.63690	−0.818448	−	0.574581i	$-0.805165\pi$
$593$	−39.8610	−1.63690	−0.818448	+	0.574581i	$0.805165\pi$
$594$	−1.31400	−0.0539140
$595$	−2.46912	−0.101224
$596$	3.56564	0.146054
$597$	27.9043	1.14205
$598$	1.39083	0.0568752
$599$	18.1975	0.743530	0.371765	−	0.928327i	$-0.378753\pi$
$599$	18.1975	0.743530	0.371765	+	0.928327i	$0.378753\pi$
$600$	4.25915	0.173879
$601$	29.0791	1.18616	0.593081	−	0.805143i	$-0.297912\pi$
$601$	29.0791	1.18616	0.593081	+	0.805143i	$0.297912\pi$
$602$	−0.887052	−0.0361536
$603$	1.14180	0.0464975
$604$	31.5729	1.28468
$605$	1.54159	0.0626747
$606$	3.65453	0.148455
$607$	−28.2059	−1.14484	−0.572420	−	0.819960i	$-0.693995\pi$
$607$	−28.2059	−1.14484	−0.572420	+	0.819960i	$0.693995\pi$
$608$	−3.15745	−0.128052
$609$	0	0
$610$	2.31142	0.0935865
$611$	−2.47240	−0.100023
$612$	−0.712082	−0.0287842
$613$	−12.7412	−0.514613	−0.257307	−	0.966330i	$-0.582835\pi$
$613$	−12.7412	−0.514613	−0.257307	+	0.966330i	$0.582835\pi$
$614$	−1.71381	−0.0691637
$615$	−2.95331	−0.119089
$616$	0.796763	0.0321025
$617$	−23.0896	−0.929553	−0.464777	−	0.885428i	$-0.653865\pi$
$617$	−23.0896	−0.929553	−0.464777	+	0.885428i	$0.653865\pi$
$618$	1.97246	0.0793440
$619$	−11.2103	−0.450582	−0.225291	−	0.974292i	$-0.572333\pi$
$619$	−11.2103	−0.450582	−0.225291	+	0.974292i	$0.572333\pi$
$620$	1.13668	0.0456502
$621$	−18.7753	−0.753425
$622$	−3.11986	−0.125095
$623$	5.09578	0.204158
$624$	−9.83840	−0.393851
$625$	−4.99988	−0.199995
$626$	3.12193	0.124777
$627$	−1.86980	−0.0746728
$628$	−5.85646	−0.233698
$629$	−9.87378	−0.393693
$630$	0.0588084	0.00234298
$631$	−8.21628	−0.327085	−0.163542	−	0.986536i	$-0.552292\pi$
$631$	−8.21628	−0.327085	−0.163542	+	0.986536i	$0.552292\pi$
$632$	−12.0809	−0.480552
$633$	−28.5698	−1.13555
$634$	−0.946768	−0.0376010
$635$	2.59240	0.102876
$636$	−14.3679	−0.569722
$637$	−10.1890	−0.403701
$638$	0	0
$639$	−0.580058	−0.0229467
$640$	11.2253	0.443717
$641$	−30.7255	−1.21358	−0.606792	−	0.794861i	$-0.707544\pi$
$641$	−30.7255	−1.21358	−0.606792	+	0.794861i	$0.707544\pi$
$642$	−4.00545	−0.158083
$643$	13.0927	0.516325	0.258162	−	0.966102i	$-0.416883\pi$
$643$	13.0927	0.516325	0.258162	+	0.966102i	$0.416883\pi$
$644$	5.60505	0.220870
$645$	−11.3371	−0.446397
$646$	0.533452	0.0209884
$647$	7.59200	0.298472	0.149236	−	0.988802i	$-0.452319\pi$
$647$	7.59200	0.298472	0.149236	+	0.988802i	$0.452319\pi$
$648$	−8.13184	−0.319449
$649$	2.64709	0.103908
$650$	1.03903	0.0407542
$651$	0.524519	0.0205575
$652$	−27.5277	−1.07807
$653$	34.3895	1.34577	0.672883	−	0.739748i	$-0.265056\pi$
$653$	34.3895	1.34577	0.672883	+	0.739748i	$0.265056\pi$
$654$	6.97502	0.272745
$655$	9.96836	0.389496
$656$	4.16032	0.162433
$657$	−0.979709	−0.0382221
$658$	0.310298	0.0120967
$659$	−9.59473	−0.373757	−0.186879	−	0.982383i	$-0.559837\pi$
$659$	−9.59473	−0.373757	−0.186879	+	0.982383i	$0.559837\pi$
$660$	5.01350	0.195150
$661$	20.8582	0.811291	0.405646	−	0.914030i	$-0.367047\pi$
$661$	20.8582	0.811291	0.405646	+	0.914030i	$0.367047\pi$
$662$	−2.00308	−0.0778521
$663$	5.25901	0.204243
$664$	−10.6946	−0.415031
$665$	1.41466	0.0548581
$666$	0.235170	0.00911263
$667$	0	0
$668$	−48.7409	−1.88584
$669$	−21.4181	−0.828070
$670$	2.29350	0.0886056
$671$	−6.10065	−0.235513
$672$	3.90666	0.150703
$673$	3.52810	0.135998	0.0679991	−	0.997685i	$-0.478338\pi$
$673$	3.52810	0.135998	0.0679991	+	0.997685i	$0.478338\pi$
$674$	−4.65739	−0.179396
$675$	−14.0263	−0.539871
$676$	20.1780	0.776079
$677$	−32.4890	−1.24866	−0.624328	−	0.781163i	$-0.714627\pi$
$677$	−32.4890	−1.24866	−0.624328	+	0.781163i	$0.714627\pi$
$678$	2.98853	0.114774
$679$	1.65128	0.0633704
$680$	−2.90523	−0.111411
$681$	29.1416	1.11671
$682$	0.0934306	0.00357764
$683$	−31.4983	−1.20525	−0.602624	−	0.798025i	$-0.705878\pi$
$683$	−31.4983	−1.20525	−0.602624	+	0.798025i	$0.705878\pi$
$684$	0.407981	0.0155995
$685$	−28.1283	−1.07473
$686$	2.69448	0.102876
$687$	−14.4642	−0.551842
$688$	15.9705	0.608871
$689$	−7.11932	−0.271224
$690$	−2.23093	−0.0849300
$691$	14.7456	0.560949	0.280474	−	0.959862i	$-0.409508\pi$
$691$	14.7456	0.560949	0.280474	+	0.959862i	$0.409508\pi$
$692$	−3.26548	−0.124135
$693$	−0.155216	−0.00589618
$694$	−3.62857	−0.137739
$695$	1.44258	0.0547203
$696$	0	0
$697$	−2.22385	−0.0842344
$698$	6.13660	0.232274
$699$	17.6634	0.668092
$700$	4.18731	0.158266
$701$	−46.2447	−1.74664	−0.873319	−	0.487149i	$-0.838037\pi$
$701$	−46.2447	−1.74664	−0.873319	+	0.487149i	$0.838037\pi$
$702$	−2.11745	−0.0799179
$703$	5.65709	0.213361
$704$	−6.58657	−0.248241
$705$	3.96580	0.149361
$706$	−1.33144	−0.0501094
$707$	7.29768	0.274458
$708$	8.60876	0.323537
$709$	15.0656	0.565799	0.282899	−	0.959150i	$-0.408704\pi$
$709$	15.0656	0.565799	0.282899	+	0.959150i	$0.408704\pi$
$710$	−1.16515	−0.0437273
$711$	2.35346	0.0882616
$712$	5.99584	0.224704
$713$	1.33500	0.0499960
$714$	−0.660030	−0.0247010
$715$	2.48421	0.0929040
$716$	−12.9882	−0.485391
$717$	0.453338	0.0169302
$718$	7.45929	0.278378
$719$	−32.0478	−1.19518	−0.597591	−	0.801801i	$-0.703875\pi$
$719$	−32.0478	−1.19518	−0.597591	+	0.801801i	$0.703875\pi$
$720$	−1.05879	−0.0394588
$721$	3.93878	0.146688
$722$	4.36403	0.162412
$723$	9.90424	0.368343
$724$	−17.2672	−0.641730
$725$	0	0
$726$	0.412090	0.0152941
$727$	−4.29177	−0.159173	−0.0795865	−	0.996828i	$-0.525360\pi$
$727$	−4.29177	−0.159173	−0.0795865	+	0.996828i	$0.525360\pi$
$728$	1.28394	0.0475862
$729$	28.4774	1.05472
$730$	−1.96792	−0.0728360
$731$	−8.53687	−0.315747
$732$	−19.8402	−0.733316
$733$	−5.76042	−0.212766	−0.106383	−	0.994325i	$-0.533927\pi$
$733$	−5.76042	−0.212766	−0.106383	+	0.994325i	$0.533927\pi$
$734$	6.30175	0.232602
$735$	16.3434	0.602835
$736$	9.94315	0.366509
$737$	−6.05336	−0.222978
$738$	0.0529668	0.00194973
$739$	37.7198	1.38754	0.693772	−	0.720194i	$-0.255947\pi$
$739$	37.7198	1.38754	0.693772	+	0.720194i	$0.255947\pi$
$740$	−15.1683	−0.557599
$741$	−3.01310	−0.110689
$742$	0.893508	0.0328017
$743$	−34.5261	−1.26664	−0.633321	−	0.773890i	$-0.718309\pi$
$743$	−34.5261	−1.26664	−0.633321	+	0.773890i	$0.718309\pi$
$744$	0.617164	0.0226263
$745$	−2.83398	−0.103829
$746$	6.19290	0.226738
$747$	2.08340	0.0762276
$748$	3.77518	0.138034
$749$	−7.99843	−0.292256
$750$	−4.84301	−0.176842
$751$	19.6916	0.718557	0.359278	−	0.933230i	$-0.383023\pi$
$751$	19.6916	0.718557	0.359278	+	0.933230i	$0.383023\pi$
$752$	−5.58662	−0.203723
$753$	−47.1068	−1.71667
$754$	0	0
$755$	−25.0942	−0.913270
$756$	−8.53334	−0.310355
$757$	−44.7232	−1.62549	−0.812747	−	0.582617i	$-0.802029\pi$
$757$	−44.7232	−1.62549	−0.812747	+	0.582617i	$0.802029\pi$
$758$	−0.833290	−0.0302665
$759$	5.88821	0.213728
$760$	1.66453	0.0603787
$761$	−1.73906	−0.0630408	−0.0315204	−	0.999503i	$-0.510035\pi$
$761$	−1.73906	−0.0630408	−0.0315204	+	0.999503i	$0.510035\pi$
$762$	0.692986	0.0251042
$763$	13.9283	0.504239
$764$	1.35943	0.0491825
$765$	0.565964	0.0204625
$766$	1.90616	0.0688725
$767$	4.26567	0.154024
$768$	−19.0870	−0.688741
$769$	−52.4723	−1.89220	−0.946099	−	0.323877i	$-0.895014\pi$
$769$	−52.4723	−1.89220	−0.946099	+	0.323877i	$0.895014\pi$
$770$	−0.311779	−0.0112357
$771$	33.8389	1.21868
$772$	31.1052	1.11950
$773$	1.45778	0.0524327	0.0262164	−	0.999656i	$-0.491654\pi$
$773$	1.45778	0.0524327	0.0262164	+	0.999656i	$0.491654\pi$
$774$	0.203328	0.00730846
$775$	0.997323	0.0358249
$776$	1.94294	0.0697476
$777$	−6.99941	−0.251102
$778$	3.65621	0.131082
$779$	1.27414	0.0456507
$780$	8.07901	0.289275
$781$	3.07524	0.110041
$782$	−1.67990	−0.0600730
$783$	0	0
$784$	−23.0229	−0.822246
$785$	4.65472	0.166134
$786$	2.66468	0.0950462
$787$	0.189076	0.00673984	0.00336992	−	0.999994i	$-0.498927\pi$
$787$	0.189076	0.00673984	0.00336992	+	0.999994i	$0.498927\pi$
$788$	−38.1221	−1.35804
$789$	−17.3575	−0.617944
$790$	4.72734	0.168191
$791$	5.96775	0.212189
$792$	−0.182632	−0.00648953
$793$	−9.83090	−0.349106
$794$	−7.06192	−0.250618
$795$	11.4196	0.405011
$796$	32.2793	1.14411
$797$	−3.71986	−0.131764	−0.0658821	−	0.997827i	$-0.520986\pi$
$797$	−3.71986	−0.131764	−0.0658821	+	0.997827i	$0.520986\pi$
$798$	0.378158	0.0133867
$799$	2.98626	0.105646
$800$	7.42813	0.262624
$801$	−1.16804	−0.0412707
$802$	4.53567	0.160160
$803$	5.19404	0.183294
$804$	−19.6864	−0.694287
$805$	−4.45491	−0.157015
$806$	0.150559	0.00530321
$807$	−32.0619	−1.12863
$808$	8.58666	0.302078
$809$	−42.3794	−1.48998	−0.744990	−	0.667075i	$-0.767546\pi$
$809$	−42.3794	−1.48998	−0.744990	+	0.667075i	$0.767546\pi$
$810$	3.18205	0.111806
$811$	42.6291	1.49691	0.748455	−	0.663186i	$-0.230796\pi$
$811$	42.6291	1.49691	0.748455	+	0.663186i	$0.230796\pi$
$812$	0	0
$813$	49.1208	1.72274
$814$	−1.24678	−0.0436995
$815$	21.8791	0.766390
$816$	11.8832	0.415996
$817$	4.89112	0.171119
$818$	−0.593960	−0.0207673
$819$	−0.250123	−0.00874002
$820$	−3.41634	−0.119304
$821$	−33.0244	−1.15256	−0.576280	−	0.817252i	$-0.695496\pi$
$821$	−33.0244	−1.15256	−0.576280	+	0.817252i	$0.695496\pi$
$822$	−7.51909	−0.262258
$823$	−23.1108	−0.805590	−0.402795	−	0.915290i	$-0.631961\pi$
$823$	−23.1108	−0.805590	−0.402795	+	0.915290i	$0.631961\pi$
$824$	4.63447	0.161449
$825$	4.39884	0.153148
$826$	−0.535361	−0.0186276
$827$	40.3979	1.40477	0.702387	−	0.711795i	$-0.252118\pi$
$827$	40.3979	1.40477	0.702387	+	0.711795i	$0.252118\pi$
$828$	−1.28477	−0.0446490
$829$	10.8887	0.378182	0.189091	−	0.981960i	$-0.439446\pi$
$829$	10.8887	0.378182	0.189091	+	0.981960i	$0.439446\pi$
$830$	4.18488	0.145259
$831$	28.5026	0.988745
$832$	−10.6139	−0.367972
$833$	12.3066	0.426399
$834$	0.385623	0.0133530
$835$	38.7393	1.34063
$836$	−2.16296	−0.0748074
$837$	−2.03245	−0.0702517
$838$	3.41201	0.117866
$839$	29.7675	1.02769	0.513844	−	0.857883i	$-0.328221\pi$
$839$	29.7675	1.02769	0.513844	+	0.857883i	$0.328221\pi$
$840$	−2.05949	−0.0710590
$841$	0	0
$842$	6.10418	0.210364
$843$	−24.5267	−0.844745
$844$	−33.0491	−1.13760
$845$	−16.0375	−0.551708
$846$	−0.0711255	−0.00244535
$847$	0.822896	0.0282750
$848$	−16.0868	−0.552422
$849$	30.2900	1.03955
$850$	−1.25498	−0.0430456
$851$	−17.8148	−0.610682
$852$	10.0012	0.342634
$853$	11.4841	0.393209	0.196605	−	0.980483i	$-0.437008\pi$
$853$	11.4841	0.393209	0.196605	+	0.980483i	$0.437008\pi$
$854$	1.23382	0.0422206
$855$	−0.324264	−0.0110896
$856$	−9.41117	−0.321667
$857$	−25.1601	−0.859451	−0.429725	−	0.902960i	$-0.641390\pi$
$857$	−25.1601	−0.859451	−0.429725	+	0.902960i	$0.641390\pi$
$858$	0.664063	0.0226707
$859$	−15.1369	−0.516466	−0.258233	−	0.966083i	$-0.583140\pi$
$859$	−15.1369	−0.516466	−0.258233	+	0.966083i	$0.583140\pi$
$860$	−13.1145	−0.447202
$861$	−1.57646	−0.0537257
$862$	7.65774	0.260824
$863$	22.5929	0.769072	0.384536	−	0.923110i	$-0.374362\pi$
$863$	22.5929	0.769072	0.384536	+	0.923110i	$0.374362\pi$
$864$	−15.1378	−0.514999
$865$	2.59541	0.0882465
$866$	2.61397	0.0888264
$867$	22.1521	0.752326
$868$	0.606755	0.0205946
$869$	−12.4771	−0.423258
$870$	0	0
$871$	−9.75469	−0.330525
$872$	16.3884	0.554983
$873$	−0.378502	−0.0128104
$874$	0.962481	0.0325564
$875$	−9.67094	−0.326937
$876$	16.8918	0.570721
$877$	−18.1009	−0.611224	−0.305612	−	0.952156i	$-0.598861\pi$
$877$	−18.1009	−0.611224	−0.305612	+	0.952156i	$0.598861\pi$
$878$	−0.594761	−0.0200722
$879$	−9.46855	−0.319366
$880$	5.61329	0.189224
$881$	46.9968	1.58336	0.791682	−	0.610934i	$-0.209206\pi$
$881$	46.9968	1.58336	0.791682	+	0.610934i	$0.209206\pi$
$882$	−0.293114	−0.00986967
$883$	−45.1767	−1.52032	−0.760158	−	0.649738i	$-0.774879\pi$
$883$	−45.1767	−1.52032	−0.760158	+	0.649738i	$0.774879\pi$
$884$	6.08353	0.204611
$885$	−6.84225	−0.230000
$886$	6.44436	0.216502
$887$	20.7678	0.697314	0.348657	−	0.937250i	$-0.386638\pi$
$887$	20.7678	0.697314	0.348657	+	0.937250i	$0.386638\pi$
$888$	−8.23570	−0.276372
$889$	1.38381	0.0464116
$890$	−2.34622	−0.0786454
$891$	−8.39856	−0.281362
$892$	−24.7760	−0.829563
$893$	−1.71095	−0.0572548
$894$	−0.757562	−0.0253367
$895$	10.3230	0.345061
$896$	5.99199	0.200178
$897$	9.48856	0.316814
$898$	9.06385	0.302465
$899$	0	0
$900$	−0.959804	−0.0319935
$901$	8.59899	0.286474
$902$	−0.280809	−0.00934993
$903$	−6.05169	−0.201388
$904$	7.02181	0.233542
$905$	13.7240	0.456201
$906$	−6.70803	−0.222859
$907$	47.1551	1.56576	0.782880	−	0.622172i	$-0.213750\pi$
$907$	47.1551	1.56576	0.782880	+	0.622172i	$0.213750\pi$
$908$	33.7104	1.11872
$909$	−1.67275	−0.0554818
$910$	−0.502418	−0.0166550
$911$	−4.77097	−0.158069	−0.0790346	−	0.996872i	$-0.525184\pi$
$911$	−4.77097	−0.158069	−0.0790346	+	0.996872i	$0.525184\pi$
$912$	−6.80838	−0.225448
$913$	−11.0454	−0.365548
$914$	3.88503	0.128505
$915$	15.7691	0.521309
$916$	−16.7319	−0.552837
$917$	5.32107	0.175717
$918$	2.55754	0.0844112
$919$	24.9828	0.824106	0.412053	−	0.911160i	$-0.364812\pi$
$919$	24.9828	0.824106	0.412053	+	0.911160i	$0.364812\pi$
$920$	−5.24177	−0.172816
$921$	−11.6920	−0.385265
$922$	−3.49096	−0.114969
$923$	4.95560	0.163116
$924$	2.67618	0.0880400
$925$	−13.3087	−0.437587
$926$	−0.877395	−0.0288330
$927$	−0.902835	−0.0296530
$928$	0	0
$929$	4.33373	0.142185	0.0710926	−	0.997470i	$-0.477351\pi$
$929$	4.33373	0.142185	0.0710926	+	0.997470i	$0.477351\pi$
$930$	−0.241501	−0.00791913
$931$	−7.05097	−0.231086
$932$	20.4328	0.669297
$933$	−21.2845	−0.696822
$934$	3.05938	0.100106
$935$	−3.00052	−0.0981275
$936$	−0.294302	−0.00961957
$937$	−58.0852	−1.89756	−0.948781	−	0.315935i	$-0.897682\pi$
$937$	−58.0852	−1.89756	−0.948781	+	0.315935i	$0.897682\pi$
$938$	1.22426	0.0399735
$939$	21.2986	0.695052
$940$	4.58757	0.149630
$941$	−13.5398	−0.441385	−0.220693	−	0.975343i	$-0.570832\pi$
$941$	−13.5398	−0.441385	−0.220693	+	0.975343i	$0.570832\pi$
$942$	1.24427	0.0405406
$943$	−4.01239	−0.130661
$944$	9.63867	0.313712
$945$	6.78231	0.220629
$946$	−1.07796	−0.0350476
$947$	−1.34476	−0.0436988	−0.0218494	−	0.999761i	$-0.506955\pi$
$947$	−1.34476	−0.0436988	−0.0218494	+	0.999761i	$0.506955\pi$
$948$	−40.5775	−1.31790
$949$	8.36994	0.271700
$950$	0.719031	0.0233285
$951$	−6.45908	−0.209450
$952$	−1.55080	−0.0502617
$953$	−15.4447	−0.500304	−0.250152	−	0.968207i	$-0.580481\pi$
$953$	−15.4447	−0.500304	−0.250152	+	0.968207i	$0.580481\pi$
$954$	−0.204807	−0.00663088
$955$	−1.08048	−0.0349635
$956$	0.524413	0.0169607
$957$	0	0
$958$	0.648987	0.0209678
$959$	−15.0147	−0.484851
$960$	17.0251	0.549482
$961$	−30.8555	−0.995338
$962$	−2.00912	−0.0647767
$963$	1.83338	0.0590798
$964$	11.4571	0.369007
$965$	−24.7225	−0.795845
$966$	−1.19086	−0.0383153
$967$	−5.54578	−0.178340	−0.0891702	−	0.996016i	$-0.528422\pi$
$967$	−5.54578	−0.178340	−0.0891702	+	0.996016i	$0.528422\pi$
$968$	0.968242	0.0311205
$969$	3.63934	0.116913
$970$	−0.760289	−0.0244114
$971$	−12.5249	−0.401942	−0.200971	−	0.979597i	$-0.564410\pi$
$971$	−12.5249	−0.401942	−0.200971	+	0.979597i	$0.564410\pi$
$972$	3.79627	0.121765
$973$	0.770044	0.0246865
$974$	−6.44462	−0.206499
$975$	7.08853	0.227015
$976$	−22.2138	−0.711047
$977$	8.50497	0.272098	0.136049	−	0.990702i	$-0.456560\pi$
$977$	8.50497	0.272098	0.136049	+	0.990702i	$0.456560\pi$
$978$	5.84858	0.187017
$979$	6.19250	0.197913
$980$	18.9057	0.603922
$981$	−3.19261	−0.101932
$982$	4.52753	0.144479
$983$	−36.7994	−1.17372	−0.586860	−	0.809688i	$-0.699636\pi$
$983$	−36.7994	−1.17372	−0.586860	+	0.809688i	$0.699636\pi$
$984$	−1.85491	−0.0591324
$985$	30.2995	0.965423
$986$	0	0
$987$	2.11693	0.0673825
$988$	−3.48550	−0.110889
$989$	−15.4026	−0.489776
$990$	0.0714652	0.00227131
$991$	17.4601	0.554638	0.277319	−	0.960778i	$-0.410554\pi$
$991$	17.4601	0.554638	0.277319	+	0.960778i	$0.410554\pi$
$992$	1.07636	0.0341745
$993$	−13.6655	−0.433663
$994$	−0.621951	−0.0197271
$995$	−25.6556	−0.813337
$996$	−35.9212	−1.13821
$997$	−15.7473	−0.498721	−0.249361	−	0.968411i	$-0.580220\pi$
$997$	−15.7473	−0.498721	−0.249361	+	0.968411i	$0.580220\pi$
$998$	6.10745	0.193328
$999$	27.1218	0.858097

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9251.2.a.ba.1.20	✓	40
29.28	even	2		9251.2.a.bb.1.21	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9251.2.a.ba.1.20	✓	40	1.1	even	1	trivial
9251.2.a.bb.1.21	yes	40	29.28	even	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:	\( N \)	\(=\)	\( 9251 = 11 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9251.a (trivial)

\(f(q)\)	\(=\)	\(q-0.245772 q^{2} -1.67672 q^{3} -1.93960 q^{4} +1.54159 q^{5} +0.412090 q^{6} +0.822896 q^{7} +0.968242 q^{8} -0.188622 q^{9} +O(q^{10})\)	\(q-0.245772 q^{2} -1.67672 q^{3} -1.93960 q^{4} +1.54159 q^{5} +0.412090 q^{6} +0.822896 q^{7} +0.968242 q^{8} -0.188622 q^{9} -0.378881 q^{10} +1.00000 q^{11} +3.25215 q^{12} +1.61145 q^{13} -0.202245 q^{14} -2.58482 q^{15} +3.64123 q^{16} -1.94638 q^{17} +0.0463580 q^{18} +1.11516 q^{19} -2.99007 q^{20} -1.37976 q^{21} -0.245772 q^{22} -3.51175 q^{23} -1.62347 q^{24} -2.62349 q^{25} -0.396050 q^{26} +5.34641 q^{27} -1.59609 q^{28} +0.635275 q^{30} -0.380152 q^{31} -2.83140 q^{32} -1.67672 q^{33} +0.478365 q^{34} +1.26857 q^{35} +0.365850 q^{36} +5.07290 q^{37} -0.274075 q^{38} -2.70195 q^{39} +1.49264 q^{40} +1.14256 q^{41} +0.339107 q^{42} +4.38603 q^{43} -1.93960 q^{44} -0.290778 q^{45} +0.863089 q^{46} -1.53427 q^{47} -6.10530 q^{48} -6.32284 q^{49} +0.644780 q^{50} +3.26352 q^{51} -3.12557 q^{52} -4.41795 q^{53} -1.31400 q^{54} +1.54159 q^{55} +0.796763 q^{56} -1.86980 q^{57} +2.64709 q^{59} +5.01350 q^{60} -6.10065 q^{61} +0.0934306 q^{62} -0.155216 q^{63} -6.58657 q^{64} +2.48421 q^{65} +0.412090 q^{66} -6.05336 q^{67} +3.77518 q^{68} +5.88821 q^{69} -0.311779 q^{70} +3.07524 q^{71} -0.182632 q^{72} +5.19404 q^{73} -1.24678 q^{74} +4.39884 q^{75} -2.16296 q^{76} +0.822896 q^{77} +0.664063 q^{78} -12.4771 q^{79} +5.61329 q^{80} -8.39856 q^{81} -0.280809 q^{82} -11.0454 q^{83} +2.67618 q^{84} -3.00052 q^{85} -1.07796 q^{86} +0.968242 q^{88} +6.19250 q^{89} +0.0714652 q^{90} +1.32606 q^{91} +6.81137 q^{92} +0.637406 q^{93} +0.377080 q^{94} +1.71912 q^{95} +4.74745 q^{96} +2.00667 q^{97} +1.55398 q^{98} -0.188622 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9}+O(q^{10}) \) 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9	\( 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9} - 25 q^{10} + 40 q^{11} - 17 q^{12} - 35 q^{13} + 3 q^{14} + 15 q^{15} - 6 q^{17} + 24 q^{18} + 2 q^{19} - 6 q^{20} - 5 q^{21} + 8 q^{23} - 18 q^{24} + 20 q^{25} - 20 q^{26} + q^{27} - 50 q^{28} - 5 q^{30} - 12 q^{31} - 6 q^{32} - 5 q^{33} - 26 q^{34} - 28 q^{35} - 22 q^{36} - 17 q^{37} - 12 q^{38} - 30 q^{39} + 30 q^{40} + 9 q^{41} - 34 q^{42} + 6 q^{43} + 28 q^{44} - 89 q^{45} - 7 q^{46} - 8 q^{47} + 33 q^{48} + q^{49} + 17 q^{50} - 52 q^{51} - 65 q^{52} - 51 q^{53} + 5 q^{54} - 12 q^{55} - 4 q^{56} - 49 q^{57} - 56 q^{59} + 15 q^{60} - 39 q^{61} + 53 q^{63} - 13 q^{64} - 13 q^{65} - 8 q^{66} - 68 q^{67} - 107 q^{68} - 31 q^{69} + 51 q^{70} - 47 q^{71} + 71 q^{72} + 19 q^{73} - 54 q^{74} - 22 q^{75} + 54 q^{76} - 15 q^{77} + 28 q^{78} + 10 q^{79} + 10 q^{80} - 4 q^{81} + 34 q^{82} - 40 q^{83} + 11 q^{84} + 26 q^{85} - 46 q^{86} - 3 q^{88} + 29 q^{89} - 100 q^{90} - 50 q^{91} + 76 q^{92} - 73 q^{93} - 116 q^{94} + 5 q^{95} + 13 q^{96} - 22 q^{97} + 102 q^{98} + 25 q^{99}+O(q^{100}) \) 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9 - 25 * q^10 + 40 * q^11 - 17 * q^12 - 35 * q^13 + 3 * q^14 + 15 * q^15 - 6 * q^17 + 24 * q^18 + 2 * q^19 - 6 * q^20 - 5 * q^21 + 8 * q^23 - 18 * q^24 + 20 * q^25 - 20 * q^26 + q^27 - 50 * q^28 - 5 * q^30 - 12 * q^31 - 6 * q^32 - 5 * q^33 - 26 * q^34 - 28 * q^35 - 22 * q^36 - 17 * q^37 - 12 * q^38 - 30 * q^39 + 30 * q^40 + 9 * q^41 - 34 * q^42 + 6 * q^43 + 28 * q^44 - 89 * q^45 - 7 * q^46 - 8 * q^47 + 33 * q^48 + q^49 + 17 * q^50 - 52 * q^51 - 65 * q^52 - 51 * q^53 + 5 * q^54 - 12 * q^55 - 4 * q^56 - 49 * q^57 - 56 * q^59 + 15 * q^60 - 39 * q^61 + 53 * q^63 - 13 * q^64 - 13 * q^65 - 8 * q^66 - 68 * q^67 - 107 * q^68 - 31 * q^69 + 51 * q^70 - 47 * q^71 + 71 * q^72 + 19 * q^73 - 54 * q^74 - 22 * q^75 + 54 * q^76 - 15 * q^77 + 28 * q^78 + 10 * q^79 + 10 * q^80 - 4 * q^81 + 34 * q^82 - 40 * q^83 + 11 * q^84 + 26 * q^85 - 46 * q^86 - 3 * q^88 + 29 * q^89 - 100 * q^90 - 50 * q^91 + 76 * q^92 - 73 * q^93 - 116 * q^94 + 5 * q^95 + 13 * q^96 - 22 * q^97 + 102 * q^98 + 25 * q^99

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