LMFDB - Embedded newform 1441.2.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, 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("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.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:	$11.5064429313$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.84752 q^{2} +2.72852 q^{3} +1.41334 q^{4} +1.47029 q^{5} -5.04100 q^{6} -2.80791 q^{7} +1.08387 q^{8} +4.44483 q^{9} +O(q^{10})$	\(q-1.84752 q^{2} +2.72852 q^{3} +1.41334 q^{4} +1.47029 q^{5} -5.04100 q^{6} -2.80791 q^{7} +1.08387 q^{8} +4.44483 q^{9} -2.71640 q^{10} +1.00000 q^{11} +3.85632 q^{12} -6.14488 q^{13} +5.18767 q^{14} +4.01172 q^{15} -4.82915 q^{16} -4.41326 q^{17} -8.21192 q^{18} -7.60311 q^{19} +2.07802 q^{20} -7.66143 q^{21} -1.84752 q^{22} -0.405111 q^{23} +2.95737 q^{24} -2.83824 q^{25} +11.3528 q^{26} +3.94224 q^{27} -3.96852 q^{28} -3.69481 q^{29} -7.41174 q^{30} +1.28621 q^{31} +6.75422 q^{32} +2.72852 q^{33} +8.15360 q^{34} -4.12844 q^{35} +6.28204 q^{36} -11.3339 q^{37} +14.0469 q^{38} -16.7664 q^{39} +1.59361 q^{40} +5.02394 q^{41} +14.1547 q^{42} +4.21317 q^{43} +1.41334 q^{44} +6.53519 q^{45} +0.748451 q^{46} +8.45465 q^{47} -13.1764 q^{48} +0.884343 q^{49} +5.24372 q^{50} -12.0417 q^{51} -8.68480 q^{52} -5.29479 q^{53} -7.28338 q^{54} +1.47029 q^{55} -3.04341 q^{56} -20.7452 q^{57} +6.82624 q^{58} -11.5452 q^{59} +5.66992 q^{60} +1.76342 q^{61} -2.37629 q^{62} -12.4807 q^{63} -2.82027 q^{64} -9.03477 q^{65} -5.04100 q^{66} +9.56036 q^{67} -6.23743 q^{68} -1.10535 q^{69} +7.62739 q^{70} -0.0487157 q^{71} +4.81762 q^{72} +16.1284 q^{73} +20.9396 q^{74} -7.74421 q^{75} -10.7458 q^{76} -2.80791 q^{77} +30.9764 q^{78} +3.58157 q^{79} -7.10026 q^{80} -2.57800 q^{81} -9.28185 q^{82} +10.5543 q^{83} -10.8282 q^{84} -6.48878 q^{85} -7.78393 q^{86} -10.0814 q^{87} +1.08387 q^{88} +0.445350 q^{89} -12.0739 q^{90} +17.2543 q^{91} -0.572559 q^{92} +3.50944 q^{93} -15.6201 q^{94} -11.1788 q^{95} +18.4290 q^{96} -3.24911 q^{97} -1.63384 q^{98} +4.44483 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9}+O(q^{10}) $ 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} - 2 q^{10} + 23 q^{11} + 8 q^{12} - 24 q^{13} - 13 q^{14} - 27 q^{15} + 7 q^{16} - 7 q^{17} - 14 q^{18} - 18 q^{19} - 4 q^{20} - 29 q^{21} - 7 q^{22} - 26 q^{23} - 4 q^{24} + 18 q^{25} + 8 q^{26} - 3 q^{27} - 11 q^{28} - 45 q^{29} + 19 q^{30} - 23 q^{31} - 34 q^{32} - 3 q^{33} - 2 q^{34} - 18 q^{35} - 6 q^{36} - 2 q^{37} - 8 q^{38} - 40 q^{39} - 24 q^{40} - 23 q^{41} + 59 q^{42} - 14 q^{43} + 15 q^{44} - 18 q^{45} - 12 q^{46} - 55 q^{47} + 10 q^{48} + 11 q^{49} - 41 q^{50} - 21 q^{51} - 37 q^{52} - 10 q^{53} - 68 q^{54} - 9 q^{55} + 2 q^{56} - 18 q^{57} + 27 q^{58} - 75 q^{59} - 63 q^{60} - 55 q^{61} + 14 q^{62} - 16 q^{63} + 19 q^{64} - 25 q^{65} - 11 q^{66} + 17 q^{67} + 41 q^{68} - 22 q^{69} + 27 q^{70} - 105 q^{71} - 11 q^{72} - 3 q^{73} - 39 q^{74} + 25 q^{75} - 30 q^{76} - 12 q^{77} + 25 q^{78} - 48 q^{79} - 37 q^{80} + 3 q^{81} + 36 q^{82} + 4 q^{83} - 111 q^{84} - 30 q^{85} + 22 q^{86} + 5 q^{87} - 21 q^{88} - 39 q^{89} + 100 q^{90} - 22 q^{91} - 30 q^{92} - 5 q^{93} + 11 q^{94} - 88 q^{95} + 13 q^{96} + 24 q^{97} - 91 q^{98} + 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9 - 2 * q^10 + 23 * q^11 + 8 * q^12 - 24 * q^13 - 13 * q^14 - 27 * q^15 + 7 * q^16 - 7 * q^17 - 14 * q^18 - 18 * q^19 - 4 * q^20 - 29 * q^21 - 7 * q^22 - 26 * q^23 - 4 * q^24 + 18 * q^25 + 8 * q^26 - 3 * q^27 - 11 * q^28 - 45 * q^29 + 19 * q^30 - 23 * q^31 - 34 * q^32 - 3 * q^33 - 2 * q^34 - 18 * q^35 - 6 * q^36 - 2 * q^37 - 8 * q^38 - 40 * q^39 - 24 * q^40 - 23 * q^41 + 59 * q^42 - 14 * q^43 + 15 * q^44 - 18 * q^45 - 12 * q^46 - 55 * q^47 + 10 * q^48 + 11 * q^49 - 41 * q^50 - 21 * q^51 - 37 * q^52 - 10 * q^53 - 68 * q^54 - 9 * q^55 + 2 * q^56 - 18 * q^57 + 27 * q^58 - 75 * q^59 - 63 * q^60 - 55 * q^61 + 14 * q^62 - 16 * q^63 + 19 * q^64 - 25 * q^65 - 11 * q^66 + 17 * q^67 + 41 * q^68 - 22 * q^69 + 27 * q^70 - 105 * q^71 - 11 * q^72 - 3 * q^73 - 39 * q^74 + 25 * q^75 - 30 * q^76 - 12 * q^77 + 25 * q^78 - 48 * q^79 - 37 * q^80 + 3 * q^81 + 36 * q^82 + 4 * q^83 - 111 * q^84 - 30 * q^85 + 22 * q^86 + 5 * q^87 - 21 * q^88 - 39 * q^89 + 100 * q^90 - 22 * q^91 - 30 * q^92 - 5 * q^93 + 11 * q^94 - 88 * q^95 + 13 * q^96 + 24 * q^97 - 91 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.84752	−1.30640	−0.653198	−	0.757187i	$-0.726573\pi$
$2$	−1.84752	−1.30640	−0.653198	+	0.757187i	$0.726573\pi$
$3$	2.72852	1.57531	0.787656	−	0.616115i	$-0.211294\pi$
$3$	2.72852	1.57531	0.787656	+	0.616115i	$0.211294\pi$
$4$	1.41334	0.706669
$5$	1.47029	0.657534	0.328767	−	0.944411i	$-0.393367\pi$
$5$	1.47029	0.657534	0.328767	+	0.944411i	$0.393367\pi$
$6$	−5.04100	−2.05798
$7$	−2.80791	−1.06129	−0.530645	−	0.847594i	$-0.678050\pi$
$7$	−2.80791	−1.06129	−0.530645	+	0.847594i	$0.678050\pi$
$8$	1.08387	0.383206
$9$	4.44483	1.48161
$10$	−2.71640	−0.859000
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.85632	1.11322
$13$	−6.14488	−1.70428	−0.852142	−	0.523311i	$-0.824697\pi$
$13$	−6.14488	−1.70428	−0.852142	+	0.523311i	$0.824697\pi$
$14$	5.18767	1.38646
$15$	4.01172	1.03582
$16$	−4.82915	−1.20729
$17$	−4.41326	−1.07037	−0.535187	−	0.844734i	$-0.679759\pi$
$17$	−4.41326	−1.07037	−0.535187	+	0.844734i	$0.679759\pi$
$18$	−8.21192	−1.93557
$19$	−7.60311	−1.74427	−0.872136	−	0.489263i	$-0.837266\pi$
$19$	−7.60311	−1.74427	−0.872136	+	0.489263i	$0.837266\pi$
$20$	2.07802	0.464659
$21$	−7.66143	−1.67186
$22$	−1.84752	−0.393893
$23$	−0.405111	−0.0844715	−0.0422357	−	0.999108i	$-0.513448\pi$
$23$	−0.405111	−0.0844715	−0.0422357	+	0.999108i	$0.513448\pi$
$24$	2.95737	0.603670
$25$	−2.83824	−0.567649
$26$	11.3528	2.22647
$27$	3.94224	0.758684
$28$	−3.96852	−0.749980
$29$	−3.69481	−0.686109	−0.343054	−	0.939316i	$-0.611462\pi$
$29$	−3.69481	−0.686109	−0.343054	+	0.939316i	$0.611462\pi$
$30$	−7.41174	−1.35319
$31$	1.28621	0.231009	0.115505	−	0.993307i	$-0.463151\pi$
$31$	1.28621	0.231009	0.115505	+	0.993307i	$0.463151\pi$
$32$	6.75422	1.19399
$33$	2.72852	0.474975
$34$	8.15360	1.39833
$35$	−4.12844	−0.697834
$36$	6.28204	1.04701
$37$	−11.3339	−1.86328	−0.931640	−	0.363382i	$-0.881622\pi$
$37$	−11.3339	−1.86328	−0.931640	+	0.363382i	$0.881622\pi$
$38$	14.0469	2.27871
$39$	−16.7664	−2.68478
$40$	1.59361	0.251971
$41$	5.02394	0.784608	0.392304	−	0.919836i	$-0.371678\pi$
$41$	5.02394	0.784608	0.392304	+	0.919836i	$0.371678\pi$
$42$	14.1547	2.18411
$43$	4.21317	0.642503	0.321251	−	0.946994i	$-0.395897\pi$
$43$	4.21317	0.642503	0.321251	+	0.946994i	$0.395897\pi$
$44$	1.41334	0.213069
$45$	6.53519	0.974208
$46$	0.748451	0.110353
$47$	8.45465	1.23324	0.616618	−	0.787262i	$-0.288502\pi$
$47$	8.45465	1.23324	0.616618	+	0.787262i	$0.288502\pi$
$48$	−13.1764	−1.90186
$49$	0.884343	0.126335
$50$	5.24372	0.741574
$51$	−12.0417	−1.68617
$52$	−8.68480	−1.20436
$53$	−5.29479	−0.727296	−0.363648	−	0.931536i	$-0.618469\pi$
$53$	−5.29479	−0.727296	−0.363648	+	0.931536i	$0.618469\pi$
$54$	−7.28338	−0.991142
$55$	1.47029	0.198254
$56$	−3.04341	−0.406693
$57$	−20.7452	−2.74777
$58$	6.82624	0.896330
$59$	−11.5452	−1.50305	−0.751527	−	0.659703i	$-0.770682\pi$
$59$	−11.5452	−1.50305	−0.751527	+	0.659703i	$0.770682\pi$
$60$	5.66992	0.731983
$61$	1.76342	0.225783	0.112891	−	0.993607i	$-0.463989\pi$
$61$	1.76342	0.225783	0.112891	+	0.993607i	$0.463989\pi$
$62$	−2.37629	−0.301789
$63$	−12.4807	−1.57242
$64$	−2.82027	−0.352534
$65$	−9.03477	−1.12062
$66$	−5.04100	−0.620505
$67$	9.56036	1.16798	0.583992	−	0.811759i	$-0.301490\pi$
$67$	9.56036	1.16798	0.583992	+	0.811759i	$0.301490\pi$
$68$	−6.23743	−0.756400
$69$	−1.10535	−0.133069
$70$	7.62739	0.911647
$71$	−0.0487157	−0.00578149	−0.00289074	−	0.999996i	$-0.500920\pi$
$71$	−0.0487157	−0.00578149	−0.00289074	+	0.999996i	$0.500920\pi$
$72$	4.81762	0.567762
$73$	16.1284	1.88769	0.943845	−	0.330388i	$-0.107180\pi$
$73$	16.1284	1.88769	0.943845	+	0.330388i	$0.107180\pi$
$74$	20.9396	2.43418
$75$	−7.74421	−0.894224
$76$	−10.7458	−1.23262
$77$	−2.80791	−0.319991
$78$	30.9764	3.50738
$79$	3.58157	0.402958	0.201479	−	0.979493i	$-0.435425\pi$
$79$	3.58157	0.402958	0.201479	+	0.979493i	$0.435425\pi$
$80$	−7.10026	−0.793833
$81$	−2.57800	−0.286444
$82$	−9.28185	−1.02501
$83$	10.5543	1.15848	0.579241	−	0.815156i	$-0.303349\pi$
$83$	10.5543	1.15848	0.579241	+	0.815156i	$0.303349\pi$
$84$	−10.8282	−1.18145
$85$	−6.48878	−0.703807
$86$	−7.78393	−0.839362
$87$	−10.0814	−1.08084
$88$	1.08387	0.115541
$89$	0.445350	0.0472070	0.0236035	−	0.999721i	$-0.492486\pi$
$89$	0.445350	0.0472070	0.0236035	+	0.999721i	$0.492486\pi$
$90$	−12.0739	−1.27270
$91$	17.2543	1.80874
$92$	−0.572559	−0.0596934
$93$	3.50944	0.363912
$94$	−15.6201	−1.61110
$95$	−11.1788	−1.14692
$96$	18.4290	1.88091
$97$	−3.24911	−0.329897	−0.164949	−	0.986302i	$-0.552746\pi$
$97$	−3.24911	−0.329897	−0.164949	+	0.986302i	$0.552746\pi$
$98$	−1.63384	−0.165043
$99$	4.44483	0.446722
$100$	−4.01140	−0.401140
$101$	5.60615	0.557833	0.278917	−	0.960315i	$-0.410025\pi$
$101$	5.60615	0.557833	0.278917	+	0.960315i	$0.410025\pi$
$102$	22.2473	2.20281
$103$	2.36122	0.232658	0.116329	−	0.993211i	$-0.462887\pi$
$103$	2.36122	0.232658	0.116329	+	0.993211i	$0.462887\pi$
$104$	−6.66026	−0.653092
$105$	−11.2645	−1.09931
$106$	9.78225	0.950136
$107$	11.9068	1.15108	0.575539	−	0.817774i	$-0.304792\pi$
$107$	11.9068	1.15108	0.575539	+	0.817774i	$0.304792\pi$
$108$	5.57172	0.536139
$109$	4.18011	0.400382	0.200191	−	0.979757i	$-0.435844\pi$
$109$	4.18011	0.400382	0.200191	+	0.979757i	$0.435844\pi$
$110$	−2.71640	−0.258998
$111$	−30.9248	−2.93525
$112$	13.5598	1.28128
$113$	7.46577	0.702321	0.351160	−	0.936315i	$-0.385787\pi$
$113$	7.46577	0.702321	0.351160	+	0.936315i	$0.385787\pi$
$114$	38.3273	3.58968
$115$	−0.595631	−0.0555429
$116$	−5.22201	−0.484852
$117$	−27.3129	−2.52508
$118$	21.3300	1.96358
$119$	12.3920	1.13598
$120$	4.34819	0.396933
$121$	1.00000	0.0909091
$122$	−3.25795	−0.294961
$123$	13.7079	1.23600
$124$	1.81784	0.163247
$125$	−11.5245	−1.03078
$126$	23.0583	2.05420
$127$	15.1534	1.34465	0.672323	−	0.740258i	$-0.265297\pi$
$127$	15.1534	1.34465	0.672323	+	0.740258i	$0.265297\pi$
$128$	−8.29793	−0.733440
$129$	11.4957	1.01214
$130$	16.6919	1.46398
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	3.85632	0.335650
$133$	21.3488	1.85118
$134$	−17.6630	−1.52585
$135$	5.79624	0.498861
$136$	−4.78341	−0.410174
$137$	−5.69801	−0.486814	−0.243407	−	0.969924i	$-0.578265\pi$
$137$	−5.69801	−0.486814	−0.243407	+	0.969924i	$0.578265\pi$
$138$	2.04217	0.173841
$139$	−6.32950	−0.536861	−0.268431	−	0.963299i	$-0.586505\pi$
$139$	−6.32950	−0.536861	−0.268431	+	0.963299i	$0.586505\pi$
$140$	−5.83488	−0.493138
$141$	23.0687	1.94273
$142$	0.0900033	0.00755291
$143$	−6.14488	−0.513861
$144$	−21.4647	−1.78873
$145$	−5.43245	−0.451140
$146$	−29.7976	−2.46607
$147$	2.41295	0.199017
$148$	−16.0186	−1.31672
$149$	−12.5926	−1.03163	−0.515814	−	0.856701i	$-0.672510\pi$
$149$	−12.5926	−1.03163	−0.515814	+	0.856701i	$0.672510\pi$
$150$	14.3076	1.16821
$151$	−22.8926	−1.86297	−0.931487	−	0.363775i	$-0.881488\pi$
$151$	−22.8926	−1.86297	−0.931487	+	0.363775i	$0.881488\pi$
$152$	−8.24079	−0.668416
$153$	−19.6162	−1.58588
$154$	5.18767	0.418034
$155$	1.89110	0.151896
$156$	−23.6967	−1.89725
$157$	−6.39952	−0.510737	−0.255369	−	0.966844i	$-0.582197\pi$
$157$	−6.39952	−0.510737	−0.255369	+	0.966844i	$0.582197\pi$
$158$	−6.61703	−0.526423
$159$	−14.4470	−1.14572
$160$	9.93067	0.785089
$161$	1.13751	0.0896487
$162$	4.76290	0.374209
$163$	1.65975	0.130001	0.0650007	−	0.997885i	$-0.479295\pi$
$163$	1.65975	0.130001	0.0650007	+	0.997885i	$0.479295\pi$
$164$	7.10053	0.554458
$165$	4.01172	0.312312
$166$	−19.4993	−1.51344
$167$	−22.4685	−1.73866	−0.869331	−	0.494230i	$-0.835450\pi$
$167$	−22.4685	−1.73866	−0.869331	+	0.494230i	$0.835450\pi$
$168$	−8.30401	−0.640668
$169$	24.7596	1.90458
$170$	11.9882	0.919451
$171$	−33.7945	−2.58433
$172$	5.95463	0.454037
$173$	19.7122	1.49869	0.749347	−	0.662178i	$-0.230368\pi$
$173$	19.7122	1.49869	0.749347	+	0.662178i	$0.230368\pi$
$174$	18.6255	1.41200
$175$	7.96953	0.602440
$176$	−4.82915	−0.364011
$177$	−31.5012	−2.36778
$178$	−0.822793	−0.0616710
$179$	12.1698	0.909610	0.454805	−	0.890591i	$-0.349709\pi$
$179$	12.1698	0.909610	0.454805	+	0.890591i	$0.349709\pi$
$180$	9.23643	0.688443
$181$	−4.65447	−0.345964	−0.172982	−	0.984925i	$-0.555340\pi$
$181$	−4.65447	−0.345964	−0.172982	+	0.984925i	$0.555340\pi$
$182$	−31.8776	−2.36293
$183$	4.81152	0.355678
$184$	−0.439088	−0.0323700
$185$	−16.6641	−1.22517
$186$	−6.48376	−0.475413
$187$	−4.41326	−0.322730
$188$	11.9493	0.871490
$189$	−11.0694	−0.805184
$190$	20.6530	1.49833
$191$	−12.0520	−0.872051	−0.436025	−	0.899934i	$-0.643614\pi$
$191$	−12.0520	−0.872051	−0.436025	+	0.899934i	$0.643614\pi$
$192$	−7.69517	−0.555351
$193$	−12.0123	−0.864664	−0.432332	−	0.901715i	$-0.642309\pi$
$193$	−12.0123	−0.864664	−0.432332	+	0.901715i	$0.642309\pi$
$194$	6.00280	0.430976
$195$	−24.6516	−1.76533
$196$	1.24987	0.0892768
$197$	4.87210	0.347123	0.173561	−	0.984823i	$-0.444472\pi$
$197$	4.87210	0.347123	0.173561	+	0.984823i	$0.444472\pi$
$198$	−8.21192	−0.583595
$199$	−23.7281	−1.68204	−0.841019	−	0.541006i	$-0.818044\pi$
$199$	−23.7281	−1.68204	−0.841019	+	0.541006i	$0.818044\pi$
$200$	−3.07629	−0.217527
$201$	26.0856	1.83994
$202$	−10.3575	−0.728751
$203$	10.3747	0.728160
$204$	−17.0190	−1.19157
$205$	7.38666	0.515907
$206$	−4.36240	−0.303943
$207$	−1.80065	−0.125154
$208$	29.6746	2.05756
$209$	−7.60311	−0.525918
$210$	20.8115	1.43613
$211$	−27.6121	−1.90089	−0.950447	−	0.310885i	$-0.899375\pi$
$211$	−27.6121	−1.90089	−0.950447	+	0.310885i	$0.899375\pi$
$212$	−7.48333	−0.513957
$213$	−0.132922	−0.00910765
$214$	−21.9982	−1.50376
$215$	6.19459	0.422467
$216$	4.27288	0.290733
$217$	−3.61154	−0.245168
$218$	−7.72284	−0.523057
$219$	44.0068	2.97370
$220$	2.07802	0.140100
$221$	27.1190	1.82422
$222$	57.1342	3.83460
$223$	−6.35094	−0.425290	−0.212645	−	0.977129i	$-0.568208\pi$
$223$	−6.35094	−0.425290	−0.212645	+	0.977129i	$0.568208\pi$
$224$	−18.9652	−1.26717
$225$	−12.6155	−0.841034
$226$	−13.7932	−0.917509
$227$	−27.3078	−1.81248	−0.906241	−	0.422762i	$-0.861060\pi$
$227$	−27.3078	−1.81248	−0.906241	+	0.422762i	$0.861060\pi$
$228$	−29.3200	−1.94177
$229$	9.83097	0.649649	0.324824	−	0.945774i	$-0.394695\pi$
$229$	9.83097	0.649649	0.324824	+	0.945774i	$0.394695\pi$
$230$	1.10044	0.0725610
$231$	−7.66143	−0.504085
$232$	−4.00470	−0.262921
$233$	17.2649	1.13106	0.565532	−	0.824726i	$-0.308671\pi$
$233$	17.2649	1.13106	0.565532	+	0.824726i	$0.308671\pi$
$234$	50.4613	3.29876
$235$	12.4308	0.810895
$236$	−16.3172	−1.06216
$237$	9.77240	0.634785
$238$	−22.8946	−1.48403
$239$	−5.29455	−0.342476	−0.171238	−	0.985230i	$-0.554777\pi$
$239$	−5.29455	−0.342476	−0.171238	+	0.985230i	$0.554777\pi$
$240$	−19.3732	−1.25053
$241$	−5.07432	−0.326866	−0.163433	−	0.986554i	$-0.552257\pi$
$241$	−5.07432	−0.326866	−0.163433	+	0.986554i	$0.552257\pi$
$242$	−1.84752	−0.118763
$243$	−18.8608	−1.20992
$244$	2.49231	0.159554
$245$	1.30024	0.0830693
$246$	−25.3257	−1.61471
$247$	46.7202	2.97274
$248$	1.39408	0.0885242
$249$	28.7976	1.82497
$250$	21.2918	1.34661
$251$	9.52067	0.600939	0.300470	−	0.953791i	$-0.402857\pi$
$251$	9.52067	0.600939	0.300470	+	0.953791i	$0.402857\pi$
$252$	−17.6394	−1.11118
$253$	−0.405111	−0.0254691
$254$	−27.9962	−1.75664
$255$	−17.7048	−1.10872
$256$	20.9712	1.31070
$257$	−9.43597	−0.588600	−0.294300	−	0.955713i	$-0.595086\pi$
$257$	−9.43597	−0.588600	−0.294300	+	0.955713i	$0.595086\pi$
$258$	−21.2386	−1.32226
$259$	31.8245	1.97748
$260$	−12.7692	−0.791911
$261$	−16.4228	−1.01655
$262$	−1.84752	−0.114140
$263$	−18.4629	−1.13847	−0.569237	−	0.822173i	$-0.692761\pi$
$263$	−18.4629	−1.13847	−0.569237	+	0.822173i	$0.692761\pi$
$264$	2.95737	0.182013
$265$	−7.78489	−0.478222
$266$	−39.4424	−2.41837
$267$	1.21515	0.0743657
$268$	13.5120	0.825378
$269$	10.6765	0.650956	0.325478	−	0.945550i	$-0.394475\pi$
$269$	10.6765	0.650956	0.325478	+	0.945550i	$0.394475\pi$
$270$	−10.7087	−0.651710
$271$	−4.21201	−0.255861	−0.127931	−	0.991783i	$-0.540833\pi$
$271$	−4.21201	−0.255861	−0.127931	+	0.991783i	$0.540833\pi$
$272$	21.3123	1.29225
$273$	47.0786	2.84933
$274$	10.5272	0.635972
$275$	−2.83824	−0.171153
$276$	−1.56224	−0.0940357
$277$	14.3084	0.859707	0.429853	−	0.902899i	$-0.358565\pi$
$277$	14.3084	0.859707	0.429853	+	0.902899i	$0.358565\pi$
$278$	11.6939	0.701353
$279$	5.71696	0.342265
$280$	−4.47470	−0.267414
$281$	−3.14409	−0.187561	−0.0937803	−	0.995593i	$-0.529895\pi$
$281$	−3.14409	−0.187561	−0.0937803	+	0.995593i	$0.529895\pi$
$282$	−42.6199	−2.53798
$283$	21.0182	1.24940	0.624701	−	0.780864i	$-0.285221\pi$
$283$	21.0182	1.24940	0.624701	+	0.780864i	$0.285221\pi$
$284$	−0.0688517	−0.00408560
$285$	−30.5015	−1.80676
$286$	11.3528	0.671306
$287$	−14.1068	−0.832696
$288$	30.0213	1.76902
$289$	2.47691	0.145700
$290$	10.0366	0.589367
$291$	−8.86527	−0.519691
$292$	22.7949	1.33397
$293$	0.278663	0.0162797	0.00813983	−	0.999967i	$-0.497409\pi$
$293$	0.278663	0.0162797	0.00813983	+	0.999967i	$0.497409\pi$
$294$	−4.45797	−0.259994
$295$	−16.9748	−0.988309
$296$	−12.2845	−0.714021
$297$	3.94224	0.228752
$298$	23.2651	1.34771
$299$	2.48936	0.143963
$300$	−10.9452	−0.631921
$301$	−11.8302	−0.681881
$302$	42.2946	2.43378
$303$	15.2965	0.878761
$304$	36.7166	2.10584
$305$	2.59274	0.148460
$306$	36.2414	2.07178
$307$	−29.0530	−1.65814	−0.829072	−	0.559143i	$-0.811130\pi$
$307$	−29.0530	−1.65814	−0.829072	+	0.559143i	$0.811130\pi$
$308$	−3.96852	−0.226128
$309$	6.44264	0.366509
$310$	−3.49384	−0.198437
$311$	−20.1000	−1.13976	−0.569882	−	0.821726i	$-0.693011\pi$
$311$	−20.1000	−1.13976	−0.569882	+	0.821726i	$0.693011\pi$
$312$	−18.1727	−1.02882
$313$	6.84000	0.386620	0.193310	−	0.981138i	$-0.438078\pi$
$313$	6.84000	0.386620	0.193310	+	0.981138i	$0.438078\pi$
$314$	11.8233	0.667225
$315$	−18.3502	−1.03392
$316$	5.06197	0.284758
$317$	−32.5586	−1.82867	−0.914337	−	0.404955i	$-0.867287\pi$
$317$	−32.5586	−1.82867	−0.914337	+	0.404955i	$0.867287\pi$
$318$	26.6911	1.49676
$319$	−3.69481	−0.206870
$320$	−4.14662	−0.231803
$321$	32.4881	1.81331
$322$	−2.10158	−0.117117
$323$	33.5545	1.86702
$324$	−3.64358	−0.202421
$325$	17.4407	0.967435
$326$	−3.06642	−0.169833
$327$	11.4055	0.630726
$328$	5.44531	0.300667
$329$	−23.7399	−1.30882
$330$	−7.41174	−0.408003
$331$	−11.4056	−0.626908	−0.313454	−	0.949603i	$-0.601486\pi$
$331$	−11.4056	−0.626908	−0.313454	+	0.949603i	$0.601486\pi$
$332$	14.9168	0.818663
$333$	−50.3772	−2.76065
$334$	41.5110	2.27138
$335$	14.0565	0.767989
$336$	36.9982	2.01842
$337$	−2.68962	−0.146513	−0.0732565	−	0.997313i	$-0.523339\pi$
$337$	−2.68962	−0.146513	−0.0732565	+	0.997313i	$0.523339\pi$
$338$	−45.7439	−2.48814
$339$	20.3705	1.10637
$340$	−9.17084	−0.497359
$341$	1.28621	0.0696519
$342$	62.4361	3.37616
$343$	17.1722	0.927212
$344$	4.56653	0.246211
$345$	−1.62519	−0.0874974
$346$	−36.4188	−1.95789
$347$	−6.75808	−0.362793	−0.181396	−	0.983410i	$-0.558062\pi$
$347$	−6.75808	−0.362793	−0.181396	+	0.983410i	$0.558062\pi$
$348$	−14.2484	−0.763793
$349$	24.8508	1.33023	0.665116	−	0.746740i	$-0.268382\pi$
$349$	24.8508	1.33023	0.665116	+	0.746740i	$0.268382\pi$
$350$	−14.7239	−0.787024
$351$	−24.2246	−1.29301
$352$	6.75422	0.360001
$353$	−16.6423	−0.885782	−0.442891	−	0.896575i	$-0.646047\pi$
$353$	−16.6423	−0.885782	−0.442891	+	0.896575i	$0.646047\pi$
$354$	58.1992	3.09326
$355$	−0.0716262	−0.00380153
$356$	0.629430	0.0333597
$357$	33.8119	1.78952
$358$	−22.4839	−1.18831
$359$	−3.70355	−0.195466	−0.0977329	−	0.995213i	$-0.531159\pi$
$359$	−3.70355	−0.195466	−0.0977329	+	0.995213i	$0.531159\pi$
$360$	7.08330	0.373323
$361$	38.8072	2.04249
$362$	8.59924	0.451966
$363$	2.72852	0.143210
$364$	24.3861	1.27818
$365$	23.7135	1.24122
$366$	−8.88940	−0.464656
$367$	21.7361	1.13462	0.567308	−	0.823506i	$-0.307985\pi$
$367$	21.7361	1.13462	0.567308	+	0.823506i	$0.307985\pi$
$368$	1.95634	0.101981
$369$	22.3306	1.16248
$370$	30.7873	1.60056
$371$	14.8673	0.771871
$372$	4.96002	0.257165
$373$	−3.58914	−0.185839	−0.0929193	−	0.995674i	$-0.529620\pi$
$373$	−3.58914	−0.185839	−0.0929193	+	0.995674i	$0.529620\pi$
$374$	8.15360	0.421613
$375$	−31.4448	−1.62380
$376$	9.16375	0.472584
$377$	22.7042	1.16932
$378$	20.4510	1.05189
$379$	17.1475	0.880809	0.440405	−	0.897799i	$-0.354835\pi$
$379$	17.1475	0.880809	0.440405	+	0.897799i	$0.354835\pi$
$380$	−15.7994	−0.810492
$381$	41.3463	2.11824
$382$	22.2663	1.13924
$383$	22.7705	1.16352	0.581759	−	0.813361i	$-0.302365\pi$
$383$	22.7705	1.16352	0.581759	+	0.813361i	$0.302365\pi$
$384$	−22.6411	−1.15540
$385$	−4.12844	−0.210405
$386$	22.1930	1.12959
$387$	18.7268	0.951938
$388$	−4.59209	−0.233128
$389$	−21.4419	−1.08715	−0.543573	−	0.839362i	$-0.682929\pi$
$389$	−21.4419	−1.08715	−0.543573	+	0.839362i	$0.682929\pi$
$390$	45.5443	2.30622
$391$	1.78786	0.0904161
$392$	0.958513	0.0484122
$393$	2.72852	0.137636
$394$	−9.00132	−0.453480
$395$	5.26595	0.264959
$396$	6.28204	0.315685
$397$	7.28800	0.365774	0.182887	−	0.983134i	$-0.441456\pi$
$397$	7.28800	0.365774	0.182887	+	0.983134i	$0.441456\pi$
$398$	43.8381	2.19741
$399$	58.2507	2.91618
$400$	13.7063	0.685316
$401$	−3.60815	−0.180182	−0.0900911	−	0.995934i	$-0.528716\pi$
$401$	−3.60815	−0.180182	−0.0900911	+	0.995934i	$0.528716\pi$
$402$	−48.1938	−2.40369
$403$	−7.90358	−0.393705
$404$	7.92339	0.394203
$405$	−3.79040	−0.188347
$406$	−19.1675	−0.951265
$407$	−11.3339	−0.561800
$408$	−13.0516	−0.646152
$409$	−25.2246	−1.24727	−0.623637	−	0.781714i	$-0.714346\pi$
$409$	−25.2246	−1.24727	−0.623637	+	0.781714i	$0.714346\pi$
$410$	−13.6470	−0.673978
$411$	−15.5471	−0.766884
$412$	3.33720	0.164412
$413$	32.4178	1.59517
$414$	3.32674	0.163500
$415$	15.5179	0.761742
$416$	−41.5039	−2.03490
$417$	−17.2702	−0.845724
$418$	14.0469	0.687057
$419$	16.1006	0.786566	0.393283	−	0.919417i	$-0.371339\pi$
$419$	16.1006	0.786566	0.393283	+	0.919417i	$0.371339\pi$
$420$	−15.9206	−0.776846
$421$	11.4695	0.558991	0.279496	−	0.960147i	$-0.409833\pi$
$421$	11.4695	0.558991	0.279496	+	0.960147i	$0.409833\pi$
$422$	51.0140	2.48332
$423$	37.5794	1.82717
$424$	−5.73887	−0.278704
$425$	12.5259	0.607597
$426$	0.245576	0.0118982
$427$	−4.95151	−0.239621
$428$	16.8284	0.813432
$429$	−16.7664	−0.809492
$430$	−11.4446	−0.551909
$431$	−38.8054	−1.86919	−0.934595	−	0.355714i	$-0.884238\pi$
$431$	−38.8054	−1.86919	−0.934595	+	0.355714i	$0.884238\pi$
$432$	−19.0377	−0.915951
$433$	−21.6733	−1.04155	−0.520775	−	0.853694i	$-0.674357\pi$
$433$	−21.6733	−1.04155	−0.520775	+	0.853694i	$0.674357\pi$
$434$	6.67241	0.320286
$435$	−14.8225	−0.710686
$436$	5.90791	0.282937
$437$	3.08010	0.147341
$438$	−81.3035	−3.88483
$439$	−11.5386	−0.550709	−0.275354	−	0.961343i	$-0.588795\pi$
$439$	−11.5386	−0.550709	−0.275354	+	0.961343i	$0.588795\pi$
$440$	1.59361	0.0759722
$441$	3.93075	0.187179
$442$	−50.1029	−2.38315
$443$	−1.46584	−0.0696440	−0.0348220	−	0.999394i	$-0.511086\pi$
$443$	−1.46584	−0.0696440	−0.0348220	+	0.999394i	$0.511086\pi$
$444$	−43.7071	−2.07425
$445$	0.654794	0.0310402
$446$	11.7335	0.555597
$447$	−34.3592	−1.62514
$448$	7.91906	0.374140
$449$	21.1727	0.999204	0.499602	−	0.866255i	$-0.333480\pi$
$449$	21.1727	0.999204	0.499602	+	0.866255i	$0.333480\pi$
$450$	23.3074	1.09872
$451$	5.02394	0.236568
$452$	10.5517	0.496308
$453$	−62.4629	−2.93477
$454$	50.4517	2.36782
$455$	25.3688	1.18931
$456$	−22.4852	−1.05296
$457$	13.7316	0.642339	0.321170	−	0.947022i	$-0.395924\pi$
$457$	13.7316	0.642339	0.321170	+	0.947022i	$0.395924\pi$
$458$	−18.1629	−0.848698
$459$	−17.3982	−0.812076
$460$	−0.841828	−0.0392504
$461$	−0.739394	−0.0344370	−0.0172185	−	0.999852i	$-0.505481\pi$
$461$	−0.739394	−0.0344370	−0.0172185	+	0.999852i	$0.505481\pi$
$462$	14.1547	0.658535
$463$	−16.3121	−0.758089	−0.379044	−	0.925378i	$-0.623747\pi$
$463$	−16.3121	−0.758089	−0.379044	+	0.925378i	$0.623747\pi$
$464$	17.8428	0.828331
$465$	5.15989	0.239284
$466$	−31.8974	−1.47762
$467$	37.9506	1.75614	0.878071	−	0.478530i	$-0.158830\pi$
$467$	37.9506	1.75614	0.878071	+	0.478530i	$0.158830\pi$
$468$	−38.6024	−1.78440
$469$	−26.8446	−1.23957
$470$	−22.9662	−1.05935
$471$	−17.4612	−0.804570
$472$	−12.5135	−0.575980
$473$	4.21317	0.193722
$474$	−18.0547	−0.829281
$475$	21.5795	0.990134
$476$	17.5141	0.802759
$477$	−23.5344	−1.07757
$478$	9.78180	0.447409
$479$	−37.9234	−1.73277	−0.866383	−	0.499380i	$-0.833561\pi$
$479$	−37.9234	−1.73277	−0.866383	+	0.499380i	$0.833561\pi$
$480$	27.0960	1.23676
$481$	69.6454	3.17556
$482$	9.37492	0.427016
$483$	3.10373	0.141225
$484$	1.41334	0.0642426
$485$	−4.77714	−0.216919
$486$	34.8458	1.58064
$487$	−29.4936	−1.33648	−0.668240	−	0.743946i	$-0.732952\pi$
$487$	−29.4936	−1.33648	−0.668240	+	0.743946i	$0.732952\pi$
$488$	1.91132	0.0865213
$489$	4.52865	0.204793
$490$	−2.40222	−0.108521
$491$	29.0546	1.31121	0.655607	−	0.755102i	$-0.272413\pi$
$491$	29.0546	1.31121	0.655607	+	0.755102i	$0.272413\pi$
$492$	19.3739	0.873445
$493$	16.3062	0.734393
$494$	−86.3166	−3.88357
$495$	6.53519	0.293735
$496$	−6.21128	−0.278895
$497$	0.136789	0.00613583
$498$	−53.2041	−2.38413
$499$	28.0690	1.25654	0.628270	−	0.777995i	$-0.283763\pi$
$499$	28.0690	1.25654	0.628270	+	0.777995i	$0.283763\pi$
$500$	−16.2880	−0.728422
$501$	−61.3057	−2.73894
$502$	−17.5896	−0.785064
$503$	13.1864	0.587954	0.293977	−	0.955813i	$-0.405021\pi$
$503$	13.1864	0.587954	0.293977	+	0.955813i	$0.405021\pi$
$504$	−13.5274	−0.602560
$505$	8.24268	0.366794
$506$	0.748451	0.0332727
$507$	67.5571	3.00031
$508$	21.4169	0.950220
$509$	−18.4363	−0.817176	−0.408588	−	0.912719i	$-0.633979\pi$
$509$	−18.4363	−0.817176	−0.408588	+	0.912719i	$0.633979\pi$
$510$	32.7100	1.44842
$511$	−45.2871	−2.00338
$512$	−22.1488	−0.978848
$513$	−29.9733	−1.32335
$514$	17.4332	0.768944
$515$	3.47168	0.152980
$516$	16.2473	0.715249
$517$	8.45465	0.371835
$518$	−58.7965	−2.58337
$519$	53.7852	2.36091
$520$	−9.79252	−0.429431
$521$	25.4525	1.11510	0.557548	−	0.830145i	$-0.311742\pi$
$521$	25.4525	1.11510	0.557548	+	0.830145i	$0.311742\pi$
$522$	30.3415	1.32801
$523$	9.00030	0.393556	0.196778	−	0.980448i	$-0.436952\pi$
$523$	9.00030	0.393556	0.196778	+	0.980448i	$0.436952\pi$
$524$	1.41334	0.0617420
$525$	21.7450	0.949031
$526$	34.1107	1.48730
$527$	−5.67636	−0.247266
$528$	−13.1764	−0.573431
$529$	−22.8359	−0.992865
$530$	14.3828	0.624747
$531$	−51.3163	−2.22694
$532$	30.1731	1.30817
$533$	−30.8716	−1.33720
$534$	−2.24501	−0.0971511
$535$	17.5065	0.756873
$536$	10.3622	0.447579
$537$	33.2054	1.43292
$538$	−19.7250	−0.850406
$539$	0.884343	0.0380913
$540$	8.19205	0.352530
$541$	−23.4102	−1.00649	−0.503243	−	0.864145i	$-0.667860\pi$
$541$	−23.4102	−1.00649	−0.503243	+	0.864145i	$0.667860\pi$
$542$	7.78178	0.334256
$543$	−12.6998	−0.545002
$544$	−29.8082	−1.27801
$545$	6.14598	0.263265
$546$	−86.9788	−3.72235
$547$	0.852571	0.0364533	0.0182267	−	0.999834i	$-0.494198\pi$
$547$	0.852571	0.0364533	0.0182267	+	0.999834i	$0.494198\pi$
$548$	−8.05322	−0.344016
$549$	7.83809	0.334521
$550$	5.24372	0.223593
$551$	28.0920	1.19676
$552$	−1.19806	−0.0509929
$553$	−10.0567	−0.427655
$554$	−26.4350	−1.12312
$555$	−45.4684	−1.93003
$556$	−8.94573	−0.379383
$557$	−28.3986	−1.20329	−0.601644	−	0.798764i	$-0.705487\pi$
$557$	−28.3986	−1.20329	−0.601644	+	0.798764i	$0.705487\pi$
$558$	−10.5622	−0.447134
$559$	−25.8894	−1.09501
$560$	19.9369	0.842486
$561$	−12.0417	−0.508400
$562$	5.80877	0.245028
$563$	−6.85492	−0.288900	−0.144450	−	0.989512i	$-0.546141\pi$
$563$	−6.85492	−0.288900	−0.144450	+	0.989512i	$0.546141\pi$
$564$	32.6038	1.37287
$565$	10.9769	0.461800
$566$	−38.8316	−1.63221
$567$	7.23877	0.304000
$568$	−0.0528015	−0.00221550
$569$	31.8370	1.33468	0.667338	−	0.744755i	$-0.267434\pi$
$569$	31.8370	1.33468	0.667338	+	0.744755i	$0.267434\pi$
$570$	56.3523	2.36034
$571$	32.1961	1.34736	0.673682	−	0.739021i	$-0.264712\pi$
$571$	32.1961	1.34736	0.673682	+	0.739021i	$0.264712\pi$
$572$	−8.68480	−0.363130
$573$	−32.8841	−1.37375
$574$	26.0626	1.08783
$575$	1.14980	0.0479501
$576$	−12.5356	−0.522317
$577$	3.47621	0.144717	0.0723584	−	0.997379i	$-0.476947\pi$
$577$	3.47621	0.144717	0.0723584	+	0.997379i	$0.476947\pi$
$578$	−4.57614	−0.190342
$579$	−32.7758	−1.36212
$580$	−7.67788	−0.318807
$581$	−29.6354	−1.22948
$582$	16.3788	0.678922
$583$	−5.29479	−0.219288
$584$	17.4811	0.723375
$585$	−40.1580	−1.66033
$586$	−0.514836	−0.0212677
$587$	32.5326	1.34276	0.671381	−	0.741112i	$-0.265701\pi$
$587$	32.5326	1.34276	0.671381	+	0.741112i	$0.265701\pi$
$588$	3.41031	0.140639
$589$	−9.77915	−0.402943
$590$	31.3613	1.29112
$591$	13.2936	0.546827
$592$	54.7331	2.24952
$593$	−37.4873	−1.53942	−0.769710	−	0.638394i	$-0.779599\pi$
$593$	−37.4873	−1.53942	−0.769710	+	0.638394i	$0.779599\pi$
$594$	−7.28338	−0.298841
$595$	18.2199	0.746943
$596$	−17.7976	−0.729019
$597$	−64.7425	−2.64974
$598$	−4.59915	−0.188073
$599$	−25.3085	−1.03408	−0.517038	−	0.855962i	$-0.672965\pi$
$599$	−25.3085	−1.03408	−0.517038	+	0.855962i	$0.672965\pi$
$600$	−8.39372	−0.342672
$601$	−40.5535	−1.65421	−0.827105	−	0.562047i	$-0.810014\pi$
$601$	−40.5535	−1.65421	−0.827105	+	0.562047i	$0.810014\pi$
$602$	21.8565	0.890806
$603$	42.4942	1.73050
$604$	−32.3550	−1.31651
$605$	1.47029	0.0597758
$606$	−28.2606	−1.14801
$607$	−38.0039	−1.54253	−0.771265	−	0.636514i	$-0.780376\pi$
$607$	−38.0039	−1.54253	−0.771265	+	0.636514i	$0.780376\pi$
$608$	−51.3531	−2.08264
$609$	28.3075	1.14708
$610$	−4.79014	−0.193947
$611$	−51.9528	−2.10179
$612$	−27.7243	−1.12069
$613$	−12.0979	−0.488628	−0.244314	−	0.969696i	$-0.578563\pi$
$613$	−12.0979	−0.488628	−0.244314	+	0.969696i	$0.578563\pi$
$614$	53.6761	2.16619
$615$	20.1547	0.812714
$616$	−3.04341	−0.122622
$617$	32.5718	1.31129	0.655646	−	0.755068i	$-0.272396\pi$
$617$	32.5718	1.31129	0.655646	+	0.755068i	$0.272396\pi$
$618$	−11.9029	−0.478805
$619$	6.61845	0.266018	0.133009	−	0.991115i	$-0.457536\pi$
$619$	6.61845	0.266018	0.133009	+	0.991115i	$0.457536\pi$
$620$	2.67276	0.107341
$621$	−1.59704	−0.0640872
$622$	37.1351	1.48898
$623$	−1.25050	−0.0501003
$624$	80.9677	3.24130
$625$	−2.75315	−0.110126
$626$	−12.6371	−0.505078
$627$	−20.7452	−0.828485
$628$	−9.04468	−0.360922
$629$	50.0195	1.99441
$630$	33.9024	1.35070
$631$	40.5848	1.61566	0.807828	−	0.589419i	$-0.200643\pi$
$631$	40.5848	1.61566	0.807828	+	0.589419i	$0.200643\pi$
$632$	3.88196	0.154416
$633$	−75.3402	−2.99450
$634$	60.1527	2.38897
$635$	22.2799	0.884151
$636$	−20.4184	−0.809643
$637$	−5.43418	−0.215310
$638$	6.82624	0.270254
$639$	−0.216533	−0.00856591
$640$	−12.2004	−0.482262
$641$	−5.22959	−0.206556	−0.103278	−	0.994653i	$-0.532933\pi$
$641$	−5.22959	−0.206556	−0.103278	+	0.994653i	$0.532933\pi$
$642$	−60.0225	−2.36890
$643$	−40.8718	−1.61183	−0.805914	−	0.592033i	$-0.798326\pi$
$643$	−40.8718	−1.61183	−0.805914	+	0.592033i	$0.798326\pi$
$644$	1.60769	0.0633519
$645$	16.9021	0.665518
$646$	−61.9927	−2.43907
$647$	−24.7616	−0.973479	−0.486740	−	0.873547i	$-0.661814\pi$
$647$	−24.7616	−0.973479	−0.486740	+	0.873547i	$0.661814\pi$
$648$	−2.79421	−0.109767
$649$	−11.5452	−0.453188
$650$	−32.2220	−1.26385
$651$	−9.85417	−0.386216
$652$	2.34578	0.0918679
$653$	22.6610	0.886794	0.443397	−	0.896325i	$-0.353773\pi$
$653$	22.6610	0.886794	0.443397	+	0.896325i	$0.353773\pi$
$654$	−21.0719	−0.823978
$655$	1.47029	0.0574490
$656$	−24.2614	−0.947248
$657$	71.6881	2.79682
$658$	43.8599	1.70984
$659$	3.09738	0.120657	0.0603283	−	0.998179i	$-0.480785\pi$
$659$	3.09738	0.120657	0.0603283	+	0.998179i	$0.480785\pi$
$660$	5.66992	0.220701
$661$	14.7370	0.573201	0.286601	−	0.958050i	$-0.407475\pi$
$661$	14.7370	0.573201	0.286601	+	0.958050i	$0.407475\pi$
$662$	21.0721	0.818990
$663$	73.9948	2.87372
$664$	11.4395	0.443938
$665$	31.3890	1.21721
$666$	93.0730	3.60650
$667$	1.49681	0.0579566
$668$	−31.7555	−1.22866
$669$	−17.3287	−0.669965
$670$	−25.9697	−1.00330
$671$	1.76342	0.0680760
$672$	−51.7470	−1.99618
$673$	11.4587	0.441700	0.220850	−	0.975308i	$-0.429117\pi$
$673$	11.4587	0.441700	0.220850	+	0.975308i	$0.429117\pi$
$674$	4.96913	0.191404
$675$	−11.1890	−0.430666
$676$	34.9937	1.34591
$677$	36.5536	1.40487	0.702435	−	0.711748i	$-0.252096\pi$
$677$	36.5536	1.40487	0.702435	+	0.711748i	$0.252096\pi$
$678$	−37.6350	−1.44536
$679$	9.12320	0.350116
$680$	−7.03300	−0.269703
$681$	−74.5099	−2.85522
$682$	−2.37629	−0.0909929
$683$	−18.3913	−0.703723	−0.351861	−	0.936052i	$-0.614451\pi$
$683$	−18.3913	−0.703723	−0.351861	+	0.936052i	$0.614451\pi$
$684$	−47.7630	−1.82627
$685$	−8.37774	−0.320097
$686$	−31.7260	−1.21130
$687$	26.8240	1.02340
$688$	−20.3460	−0.775686
$689$	32.5359	1.23952
$690$	3.00258	0.114306
$691$	6.36330	0.242072	0.121036	−	0.992648i	$-0.461378\pi$
$691$	6.36330	0.242072	0.121036	+	0.992648i	$0.461378\pi$
$692$	27.8600	1.05908
$693$	−12.4807	−0.474101
$694$	12.4857	0.473951
$695$	−9.30621	−0.353005
$696$	−10.9269	−0.414183
$697$	−22.1720	−0.839824
$698$	−45.9123	−1.73781
$699$	47.1078	1.78178
$700$	11.2636	0.425725
$701$	−7.52453	−0.284198	−0.142099	−	0.989852i	$-0.545385\pi$
$701$	−7.52453	−0.284198	−0.142099	+	0.989852i	$0.545385\pi$
$702$	44.7555	1.68919
$703$	86.1728	3.25007
$704$	−2.82027	−0.106293
$705$	33.9177	1.27741
$706$	30.7471	1.15718
$707$	−15.7416	−0.592022
$708$	−44.5219	−1.67324
$709$	20.2172	0.759273	0.379636	−	0.925136i	$-0.376049\pi$
$709$	20.2172	0.759273	0.379636	+	0.925136i	$0.376049\pi$
$710$	0.132331	0.00496630
$711$	15.9195	0.597027
$712$	0.482702	0.0180900
$713$	−0.521056	−0.0195137
$714$	−62.4683	−2.33782
$715$	−9.03477	−0.337881
$716$	17.2000	0.642793
$717$	−14.4463	−0.539507
$718$	6.84239	0.255356
$719$	−12.0182	−0.448203	−0.224101	−	0.974566i	$-0.571945\pi$
$719$	−12.0182	−0.448203	−0.224101	+	0.974566i	$0.571945\pi$
$720$	−31.5594	−1.17615
$721$	−6.63008	−0.246917
$722$	−71.6972	−2.66829
$723$	−13.8454	−0.514916
$724$	−6.57834	−0.244482
$725$	10.4868	0.389469
$726$	−5.04100	−0.187089
$727$	−5.11993	−0.189888	−0.0949439	−	0.995483i	$-0.530267\pi$
$727$	−5.11993	−0.189888	−0.0949439	+	0.995483i	$0.530267\pi$
$728$	18.7014	0.693120
$729$	−43.7282	−1.61956
$730$	−43.8112	−1.62152
$731$	−18.5938	−0.687718
$732$	6.80031	0.251347
$733$	−14.1602	−0.523019	−0.261509	−	0.965201i	$-0.584220\pi$
$733$	−14.1602	−0.523019	−0.261509	+	0.965201i	$0.584220\pi$
$734$	−40.1579	−1.48226
$735$	3.54773	0.130860
$736$	−2.73621	−0.100858
$737$	9.56036	0.352160
$738$	−41.2562	−1.51866
$739$	−44.3692	−1.63215	−0.816073	−	0.577949i	$-0.803853\pi$
$739$	−44.3692	−1.63215	−0.816073	+	0.577949i	$0.803853\pi$
$740$	−23.5520	−0.865790
$741$	127.477	4.68299
$742$	−27.4676	−1.00837
$743$	21.8744	0.802495	0.401248	−	0.915970i	$-0.368577\pi$
$743$	21.8744	0.802495	0.401248	+	0.915970i	$0.368577\pi$
$744$	3.80378	0.139453
$745$	−18.5148	−0.678330
$746$	6.63101	0.242779
$747$	46.9119	1.71642
$748$	−6.23743	−0.228063
$749$	−33.4333	−1.22163
$750$	58.0950	2.12133
$751$	6.12470	0.223493	0.111747	−	0.993737i	$-0.464355\pi$
$751$	6.12470	0.223493	0.111747	+	0.993737i	$0.464355\pi$
$752$	−40.8288	−1.48887
$753$	25.9773	0.946667
$754$	−41.9465	−1.52760
$755$	−33.6588	−1.22497
$756$	−15.6449	−0.568998
$757$	−37.1035	−1.34855	−0.674275	−	0.738480i	$-0.735544\pi$
$757$	−37.1035	−1.34855	−0.674275	+	0.738480i	$0.735544\pi$
$758$	−31.6804	−1.15069
$759$	−1.10535	−0.0401218
$760$	−12.1164	−0.439506
$761$	−7.08893	−0.256974	−0.128487	−	0.991711i	$-0.541012\pi$
$761$	−7.08893	−0.256974	−0.128487	+	0.991711i	$0.541012\pi$
$762$	−76.3883	−2.76726
$763$	−11.7374	−0.424921
$764$	−17.0335	−0.616251
$765$	−28.8415	−1.04277
$766$	−42.0690	−1.52002
$767$	70.9437	2.56163
$768$	57.2202	2.06476
$769$	−10.6917	−0.385552	−0.192776	−	0.981243i	$-0.561749\pi$
$769$	−10.6917	−0.385552	−0.192776	+	0.981243i	$0.561749\pi$
$770$	7.62739	0.274872
$771$	−25.7463	−0.927229
$772$	−16.9774	−0.611031
$773$	37.3932	1.34494	0.672471	−	0.740124i	$-0.265233\pi$
$773$	37.3932	1.34494	0.672471	+	0.740124i	$0.265233\pi$
$774$	−34.5982	−1.24361
$775$	−3.65056	−0.131132
$776$	−3.52162	−0.126419
$777$	86.8339	3.11515
$778$	39.6143	1.42024
$779$	−38.1976	−1.36857
$780$	−34.8410	−1.24751
$781$	−0.0487157	−0.00174318
$782$	−3.30311	−0.118119
$783$	−14.5658	−0.520540
$784$	−4.27062	−0.152522
$785$	−9.40915	−0.335827
$786$	−5.04100	−0.179807
$787$	−49.4411	−1.76239	−0.881193	−	0.472756i	$-0.843259\pi$
$787$	−49.4411	−1.76239	−0.881193	+	0.472756i	$0.843259\pi$
$788$	6.88593	0.245301
$789$	−50.3765	−1.79345
$790$	−9.72897	−0.346141
$791$	−20.9632	−0.745366
$792$	4.81762	0.171187
$793$	−10.8360	−0.384798
$794$	−13.4647	−0.477846
$795$	−21.2412	−0.753349
$796$	−33.5358	−1.18864
$797$	18.3767	0.650936	0.325468	−	0.945553i	$-0.394478\pi$
$797$	18.3767	0.650936	0.325468	+	0.945553i	$0.394478\pi$
$798$	−107.619	−3.80969
$799$	−37.3126	−1.32002
$800$	−19.1701	−0.677767
$801$	1.97950	0.0699423
$802$	6.66613	0.235389
$803$	16.1284	0.569160
$804$	36.8678	1.30023
$805$	1.67248	0.0589470
$806$	14.6020	0.514335
$807$	29.1310	1.02546
$808$	6.07635	0.213765
$809$	43.9311	1.54453	0.772267	−	0.635298i	$-0.219123\pi$
$809$	43.9311	1.54453	0.772267	+	0.635298i	$0.219123\pi$
$810$	7.00285	0.246055
$811$	42.4899	1.49202	0.746012	−	0.665933i	$-0.231966\pi$
$811$	42.4899	1.49202	0.746012	+	0.665933i	$0.231966\pi$
$812$	14.6629	0.514568
$813$	−11.4926	−0.403062
$814$	20.9396	0.733933
$815$	2.44031	0.0854803
$816$	58.1511	2.03570
$817$	−32.0332	−1.12070
$818$	46.6029	1.62943
$819$	76.6922	2.67984
$820$	10.4398	0.364575
$821$	−53.5056	−1.86736	−0.933680	−	0.358109i	$-0.883422\pi$
$821$	−53.5056	−1.86736	−0.933680	+	0.358109i	$0.883422\pi$
$822$	28.7237	1.00185
$823$	24.6213	0.858246	0.429123	−	0.903246i	$-0.358823\pi$
$823$	24.6213	0.858246	0.429123	+	0.903246i	$0.358823\pi$
$824$	2.55926	0.0891560
$825$	−7.74421	−0.269619
$826$	−59.8926	−2.08393
$827$	10.0806	0.350538	0.175269	−	0.984521i	$-0.443921\pi$
$827$	10.0806	0.350538	0.175269	+	0.984521i	$0.443921\pi$
$828$	−2.54492	−0.0884422
$829$	−27.0505	−0.939504	−0.469752	−	0.882799i	$-0.655657\pi$
$829$	−27.0505	−0.939504	−0.469752	+	0.882799i	$0.655657\pi$
$830$	−28.6696	−0.995136
$831$	39.0407	1.35431
$832$	17.3302	0.600818
$833$	−3.90284	−0.135225
$834$	31.9070	1.10485
$835$	−33.0352	−1.14323
$836$	−10.7458	−0.371650
$837$	5.07053	0.175263
$838$	−29.7462	−1.02757
$839$	−48.2194	−1.66472	−0.832359	−	0.554236i	$-0.813010\pi$
$839$	−48.2194	−1.66472	−0.832359	+	0.554236i	$0.813010\pi$
$840$	−12.2093	−0.421261
$841$	−15.3484	−0.529255
$842$	−21.1902	−0.730264
$843$	−8.57871	−0.295467
$844$	−39.0252	−1.34330
$845$	36.4038	1.25233
$846$	−69.4288	−2.38701
$847$	−2.80791	−0.0964808
$848$	25.5694	0.878055
$849$	57.3486	1.96820
$850$	−23.1419	−0.793761
$851$	4.59148	0.157394
$852$	−0.187863	−0.00643609
$853$	44.9615	1.53945	0.769726	−	0.638375i	$-0.220393\pi$
$853$	44.9615	1.53945	0.769726	+	0.638375i	$0.220393\pi$
$854$	9.14803	0.313039
$855$	−49.6877	−1.69928
$856$	12.9055	0.441101
$857$	8.38613	0.286465	0.143232	−	0.989689i	$-0.454250\pi$
$857$	8.38613	0.286465	0.143232	+	0.989689i	$0.454250\pi$
$858$	30.9764	1.05752
$859$	26.5535	0.905992	0.452996	−	0.891513i	$-0.350355\pi$
$859$	26.5535	0.905992	0.452996	+	0.891513i	$0.350355\pi$
$860$	8.75505	0.298545
$861$	−38.4906	−1.31176
$862$	71.6938	2.44190
$863$	−41.9322	−1.42739	−0.713694	−	0.700457i	$-0.752979\pi$
$863$	−41.9322	−1.42739	−0.713694	+	0.700457i	$0.752979\pi$
$864$	26.6268	0.905861
$865$	28.9827	0.985442
$866$	40.0418	1.36068
$867$	6.75829	0.229524
$868$	−5.10433	−0.173252
$869$	3.58157	0.121497
$870$	27.3850	0.928438
$871$	−58.7473	−1.99058
$872$	4.53070	0.153429
$873$	−14.4417	−0.488779
$874$	−5.69056	−0.192486
$875$	32.3597	1.09396
$876$	62.1964	2.10142
$877$	48.6651	1.64330	0.821652	−	0.569989i	$-0.193052\pi$
$877$	48.6651	1.64330	0.821652	+	0.569989i	$0.193052\pi$
$878$	21.3179	0.719444
$879$	0.760337	0.0256455
$880$	−7.10026	−0.239350
$881$	21.4960	0.724220	0.362110	−	0.932135i	$-0.382056\pi$
$881$	21.4960	0.724220	0.362110	+	0.932135i	$0.382056\pi$
$882$	−7.26215	−0.244529
$883$	−33.3367	−1.12187	−0.560935	−	0.827860i	$-0.689558\pi$
$883$	−33.3367	−1.12187	−0.560935	+	0.827860i	$0.689558\pi$
$884$	38.3283	1.28912
$885$	−46.3160	−1.55690
$886$	2.70816	0.0909825
$887$	12.4634	0.418480	0.209240	−	0.977864i	$-0.432901\pi$
$887$	12.4634	0.418480	0.209240	+	0.977864i	$0.432901\pi$
$888$	−33.5185	−1.12481
$889$	−42.5493	−1.42706
$890$	−1.20975	−0.0405508
$891$	−2.57800	−0.0863661
$892$	−8.97603	−0.300540
$893$	−64.2816	−2.15110
$894$	63.4794	2.12307
$895$	17.8931	0.598100
$896$	23.2998	0.778392
$897$	6.79227	0.226787
$898$	−39.1171	−1.30536
$899$	−4.75228	−0.158497
$900$	−17.8300	−0.594332
$901$	23.3673	0.778478
$902$	−9.28185	−0.309052
$903$	−32.2789	−1.07418
$904$	8.09194	0.269134
$905$	−6.84343	−0.227483
$906$	115.402	3.83396
$907$	8.42823	0.279855	0.139927	−	0.990162i	$-0.455313\pi$
$907$	8.42823	0.279855	0.139927	+	0.990162i	$0.455313\pi$
$908$	−38.5951	−1.28082
$909$	24.9184	0.826490
$910$	−46.8694	−1.55371
$911$	−48.7751	−1.61599	−0.807996	−	0.589188i	$-0.799448\pi$
$911$	−48.7751	−1.61599	−0.807996	+	0.589188i	$0.799448\pi$
$912$	100.182	3.31735
$913$	10.5543	0.349296
$914$	−25.3695	−0.839149
$915$	7.07434	0.233870
$916$	13.8945	0.459087
$917$	−2.80791	−0.0927253
$918$	32.1435	1.06089
$919$	−30.3345	−1.00064	−0.500321	−	0.865840i	$-0.666785\pi$
$919$	−30.3345	−1.00064	−0.500321	+	0.865840i	$0.666785\pi$
$920$	−0.645587	−0.0212844
$921$	−79.2718	−2.61209
$922$	1.36605	0.0449883
$923$	0.299352	0.00985330
$924$	−10.8282	−0.356221
$925$	32.1684	1.05769
$926$	30.1370	0.990364
$927$	10.4952	0.344708
$928$	−24.9556	−0.819207
$929$	−37.5108	−1.23069	−0.615345	−	0.788258i	$-0.710983\pi$
$929$	−37.5108	−1.23069	−0.615345	+	0.788258i	$0.710983\pi$
$930$	−9.53302	−0.312600
$931$	−6.72375	−0.220362
$932$	24.4012	0.799288
$933$	−54.8432	−1.79549
$934$	−70.1145	−2.29422
$935$	−6.48878	−0.212206
$936$	−29.6037	−0.967627
$937$	−2.50629	−0.0818769	−0.0409385	−	0.999162i	$-0.513035\pi$
$937$	−2.50629	−0.0818769	−0.0409385	+	0.999162i	$0.513035\pi$
$938$	49.5960	1.61937
$939$	18.6631	0.609047
$940$	17.5689	0.573035
$941$	−10.3616	−0.337777	−0.168889	−	0.985635i	$-0.554018\pi$
$941$	−10.3616	−0.337777	−0.168889	+	0.985635i	$0.554018\pi$
$942$	32.2600	1.05109
$943$	−2.03525	−0.0662770
$944$	55.7534	1.81462
$945$	−16.2753	−0.529436
$946$	−7.78393	−0.253077
$947$	−16.9914	−0.552146	−0.276073	−	0.961137i	$-0.589033\pi$
$947$	−16.9914	−0.552146	−0.276073	+	0.961137i	$0.589033\pi$
$948$	13.8117	0.448583
$949$	−99.1073	−3.21716
$950$	−39.8686	−1.29351
$951$	−88.8368	−2.88073
$952$	13.4314	0.435313
$953$	21.0749	0.682685	0.341342	−	0.939939i	$-0.389118\pi$
$953$	21.0749	0.682685	0.341342	+	0.939939i	$0.389118\pi$
$954$	43.4804	1.40773
$955$	−17.7199	−0.573403
$956$	−7.48299	−0.242017
$957$	−10.0814	−0.325884
$958$	70.0644	2.26368
$959$	15.9995	0.516651
$960$	−11.3141	−0.365162
$961$	−29.3457	−0.946635
$962$	−128.672	−4.14854
$963$	52.9239	1.70545
$964$	−7.17173	−0.230986
$965$	−17.6616	−0.568546
$966$	−5.73421	−0.184495
$967$	16.0356	0.515669	0.257835	−	0.966189i	$-0.416991\pi$
$967$	16.0356	0.515669	0.257835	+	0.966189i	$0.416991\pi$
$968$	1.08387	0.0348369
$969$	91.5542	2.94115
$970$	8.82587	0.283382
$971$	−47.7964	−1.53386	−0.766930	−	0.641731i	$-0.778217\pi$
$971$	−47.7964	−1.53386	−0.766930	+	0.641731i	$0.778217\pi$
$972$	−26.6567	−0.855015
$973$	17.7727	0.569765
$974$	54.4900	1.74597
$975$	47.5873	1.52401
$976$	−8.51581	−0.272585
$977$	−22.6148	−0.723512	−0.361756	−	0.932273i	$-0.617823\pi$
$977$	−22.6148	−0.723512	−0.361756	+	0.932273i	$0.617823\pi$
$978$	−8.36678	−0.267540
$979$	0.445350	0.0142334
$980$	1.83768	0.0587025
$981$	18.5799	0.593209
$982$	−53.6790	−1.71296
$983$	−35.3123	−1.12629	−0.563143	−	0.826359i	$-0.690408\pi$
$983$	−35.3123	−1.12629	−0.563143	+	0.826359i	$0.690408\pi$
$984$	14.8576	0.473644
$985$	7.16341	0.228245
$986$	−30.1260	−0.959408
$987$	−64.7747	−2.06180
$988$	66.0314	2.10074
$989$	−1.70680	−0.0542731
$990$	−12.0739	−0.383734
$991$	60.4695	1.92088	0.960438	−	0.278494i	$-0.0898352\pi$
$991$	60.4695	1.92088	0.960438	+	0.278494i	$0.0898352\pi$
$992$	8.68731	0.275823
$993$	−31.1204	−0.987576
$994$	−0.252721	−0.00801582
$995$	−34.8872	−1.10600
$996$	40.7007	1.28965
$997$	−38.9095	−1.23228	−0.616138	−	0.787638i	$-0.711304\pi$
$997$	−38.9095	−1.23228	−0.616138	+	0.787638i	$0.711304\pi$
$998$	−51.8581	−1.64154
$999$	−44.6809	−1.41364

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.c.1.5	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.c.1.5	✓	23	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-1.84752 q^{2} +2.72852 q^{3} +1.41334 q^{4} +1.47029 q^{5} -5.04100 q^{6} -2.80791 q^{7} +1.08387 q^{8} +4.44483 q^{9} +O(q^{10})\)	\(q-1.84752 q^{2} +2.72852 q^{3} +1.41334 q^{4} +1.47029 q^{5} -5.04100 q^{6} -2.80791 q^{7} +1.08387 q^{8} +4.44483 q^{9} -2.71640 q^{10} +1.00000 q^{11} +3.85632 q^{12} -6.14488 q^{13} +5.18767 q^{14} +4.01172 q^{15} -4.82915 q^{16} -4.41326 q^{17} -8.21192 q^{18} -7.60311 q^{19} +2.07802 q^{20} -7.66143 q^{21} -1.84752 q^{22} -0.405111 q^{23} +2.95737 q^{24} -2.83824 q^{25} +11.3528 q^{26} +3.94224 q^{27} -3.96852 q^{28} -3.69481 q^{29} -7.41174 q^{30} +1.28621 q^{31} +6.75422 q^{32} +2.72852 q^{33} +8.15360 q^{34} -4.12844 q^{35} +6.28204 q^{36} -11.3339 q^{37} +14.0469 q^{38} -16.7664 q^{39} +1.59361 q^{40} +5.02394 q^{41} +14.1547 q^{42} +4.21317 q^{43} +1.41334 q^{44} +6.53519 q^{45} +0.748451 q^{46} +8.45465 q^{47} -13.1764 q^{48} +0.884343 q^{49} +5.24372 q^{50} -12.0417 q^{51} -8.68480 q^{52} -5.29479 q^{53} -7.28338 q^{54} +1.47029 q^{55} -3.04341 q^{56} -20.7452 q^{57} +6.82624 q^{58} -11.5452 q^{59} +5.66992 q^{60} +1.76342 q^{61} -2.37629 q^{62} -12.4807 q^{63} -2.82027 q^{64} -9.03477 q^{65} -5.04100 q^{66} +9.56036 q^{67} -6.23743 q^{68} -1.10535 q^{69} +7.62739 q^{70} -0.0487157 q^{71} +4.81762 q^{72} +16.1284 q^{73} +20.9396 q^{74} -7.74421 q^{75} -10.7458 q^{76} -2.80791 q^{77} +30.9764 q^{78} +3.58157 q^{79} -7.10026 q^{80} -2.57800 q^{81} -9.28185 q^{82} +10.5543 q^{83} -10.8282 q^{84} -6.48878 q^{85} -7.78393 q^{86} -10.0814 q^{87} +1.08387 q^{88} +0.445350 q^{89} -12.0739 q^{90} +17.2543 q^{91} -0.572559 q^{92} +3.50944 q^{93} -15.6201 q^{94} -11.1788 q^{95} +18.4290 q^{96} -3.24911 q^{97} -1.63384 q^{98} +4.44483 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9}+O(q^{10}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} - 2 q^{10} + 23 q^{11} + 8 q^{12} - 24 q^{13} - 13 q^{14} - 27 q^{15} + 7 q^{16} - 7 q^{17} - 14 q^{18} - 18 q^{19} - 4 q^{20} - 29 q^{21} - 7 q^{22} - 26 q^{23} - 4 q^{24} + 18 q^{25} + 8 q^{26} - 3 q^{27} - 11 q^{28} - 45 q^{29} + 19 q^{30} - 23 q^{31} - 34 q^{32} - 3 q^{33} - 2 q^{34} - 18 q^{35} - 6 q^{36} - 2 q^{37} - 8 q^{38} - 40 q^{39} - 24 q^{40} - 23 q^{41} + 59 q^{42} - 14 q^{43} + 15 q^{44} - 18 q^{45} - 12 q^{46} - 55 q^{47} + 10 q^{48} + 11 q^{49} - 41 q^{50} - 21 q^{51} - 37 q^{52} - 10 q^{53} - 68 q^{54} - 9 q^{55} + 2 q^{56} - 18 q^{57} + 27 q^{58} - 75 q^{59} - 63 q^{60} - 55 q^{61} + 14 q^{62} - 16 q^{63} + 19 q^{64} - 25 q^{65} - 11 q^{66} + 17 q^{67} + 41 q^{68} - 22 q^{69} + 27 q^{70} - 105 q^{71} - 11 q^{72} - 3 q^{73} - 39 q^{74} + 25 q^{75} - 30 q^{76} - 12 q^{77} + 25 q^{78} - 48 q^{79} - 37 q^{80} + 3 q^{81} + 36 q^{82} + 4 q^{83} - 111 q^{84} - 30 q^{85} + 22 q^{86} + 5 q^{87} - 21 q^{88} - 39 q^{89} + 100 q^{90} - 22 q^{91} - 30 q^{92} - 5 q^{93} + 11 q^{94} - 88 q^{95} + 13 q^{96} + 24 q^{97} - 91 q^{98} + 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9 - 2 * q^10 + 23 * q^11 + 8 * q^12 - 24 * q^13 - 13 * q^14 - 27 * q^15 + 7 * q^16 - 7 * q^17 - 14 * q^18 - 18 * q^19 - 4 * q^20 - 29 * q^21 - 7 * q^22 - 26 * q^23 - 4 * q^24 + 18 * q^25 + 8 * q^26 - 3 * q^27 - 11 * q^28 - 45 * q^29 + 19 * q^30 - 23 * q^31 - 34 * q^32 - 3 * q^33 - 2 * q^34 - 18 * q^35 - 6 * q^36 - 2 * q^37 - 8 * q^38 - 40 * q^39 - 24 * q^40 - 23 * q^41 + 59 * q^42 - 14 * q^43 + 15 * q^44 - 18 * q^45 - 12 * q^46 - 55 * q^47 + 10 * q^48 + 11 * q^49 - 41 * q^50 - 21 * q^51 - 37 * q^52 - 10 * q^53 - 68 * q^54 - 9 * q^55 + 2 * q^56 - 18 * q^57 + 27 * q^58 - 75 * q^59 - 63 * q^60 - 55 * q^61 + 14 * q^62 - 16 * q^63 + 19 * q^64 - 25 * q^65 - 11 * q^66 + 17 * q^67 + 41 * q^68 - 22 * q^69 + 27 * q^70 - 105 * q^71 - 11 * q^72 - 3 * q^73 - 39 * q^74 + 25 * q^75 - 30 * q^76 - 12 * q^77 + 25 * q^78 - 48 * q^79 - 37 * q^80 + 3 * q^81 + 36 * q^82 + 4 * q^83 - 111 * q^84 - 30 * q^85 + 22 * q^86 + 5 * q^87 - 21 * q^88 - 39 * q^89 + 100 * q^90 - 22 * q^91 - 30 * q^92 - 5 * q^93 + 11 * q^94 - 88 * q^95 + 13 * q^96 + 24 * q^97 - 91 * q^98 + 12 * q^99

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