LMFDB - Embedded newform 983.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,2,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("983.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	983.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:	$7.84929451869$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.53339 q^{2} +2.66681 q^{3} +0.351281 q^{4} +4.12109 q^{5} -4.08926 q^{6} +2.92035 q^{7} +2.52813 q^{8} +4.11188 q^{9} +O(q^{10})$	\(q-1.53339 q^{2} +2.66681 q^{3} +0.351281 q^{4} +4.12109 q^{5} -4.08926 q^{6} +2.92035 q^{7} +2.52813 q^{8} +4.11188 q^{9} -6.31924 q^{10} -5.32974 q^{11} +0.936800 q^{12} -4.48029 q^{13} -4.47803 q^{14} +10.9902 q^{15} -4.57916 q^{16} +7.84636 q^{17} -6.30510 q^{18} +4.17966 q^{19} +1.44766 q^{20} +7.78802 q^{21} +8.17256 q^{22} +2.49567 q^{23} +6.74203 q^{24} +11.9834 q^{25} +6.87002 q^{26} +2.96516 q^{27} +1.02586 q^{28} -6.82010 q^{29} -16.8522 q^{30} -8.14425 q^{31} +1.96538 q^{32} -14.2134 q^{33} -12.0315 q^{34} +12.0350 q^{35} +1.44442 q^{36} -0.299515 q^{37} -6.40904 q^{38} -11.9481 q^{39} +10.4186 q^{40} +4.42833 q^{41} -11.9421 q^{42} -8.42986 q^{43} -1.87224 q^{44} +16.9454 q^{45} -3.82683 q^{46} -10.6545 q^{47} -12.2118 q^{48} +1.52844 q^{49} -18.3752 q^{50} +20.9248 q^{51} -1.57384 q^{52} -7.07126 q^{53} -4.54674 q^{54} -21.9644 q^{55} +7.38301 q^{56} +11.1464 q^{57} +10.4579 q^{58} +7.30283 q^{59} +3.86064 q^{60} +0.241073 q^{61} +12.4883 q^{62} +12.0081 q^{63} +6.14463 q^{64} -18.4637 q^{65} +21.7947 q^{66} +5.32491 q^{67} +2.75628 q^{68} +6.65547 q^{69} -18.4544 q^{70} +1.55715 q^{71} +10.3953 q^{72} +4.58790 q^{73} +0.459273 q^{74} +31.9575 q^{75} +1.46823 q^{76} -15.5647 q^{77} +18.3210 q^{78} +2.93788 q^{79} -18.8712 q^{80} -4.42811 q^{81} -6.79034 q^{82} -3.37600 q^{83} +2.73578 q^{84} +32.3356 q^{85} +12.9263 q^{86} -18.1879 q^{87} -13.4743 q^{88} -4.76602 q^{89} -25.9839 q^{90} -13.0840 q^{91} +0.876681 q^{92} -21.7192 q^{93} +16.3374 q^{94} +17.2248 q^{95} +5.24131 q^{96} +3.41682 q^{97} -2.34369 q^{98} -21.9152 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) $ 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9 + 15 * q^10 + 8 * q^11 + 10 * q^12 + 34 * q^13 + q^14 + 3 * q^15 + 80 * q^16 + 32 * q^17 + 28 * q^18 + 15 * q^19 + 4 * q^20 + 11 * q^21 + 25 * q^22 + 15 * q^23 - 7 * q^24 + 125 * q^25 - 14 * q^26 + 12 * q^27 + 78 * q^28 + 8 * q^29 - 32 * q^30 + 16 * q^31 + 36 * q^32 + 38 * q^33 - 8 * q^34 - 2 * q^35 + 65 * q^36 + 80 * q^37 - 14 * q^38 + 16 * q^39 + 36 * q^40 + 30 * q^41 - 10 * q^42 + 53 * q^43 + 6 * q^44 + 3 * q^45 + 24 * q^46 + 22 * q^47 + 7 * q^48 + 111 * q^49 + 14 * q^50 - 10 * q^51 + 45 * q^52 + 10 * q^53 - 8 * q^54 + 12 * q^55 - 30 * q^56 + 106 * q^57 + 61 * q^58 - 4 * q^59 - 61 * q^60 + 24 * q^61 - 12 * q^62 + 73 * q^63 + 86 * q^64 + 32 * q^65 - 43 * q^66 + 54 * q^67 + 33 * q^68 - 30 * q^69 - 21 * q^70 - 6 * q^71 + 60 * q^72 + 172 * q^73 - 32 * q^74 - 36 * q^75 + 7 * q^76 - 12 * q^77 - 3 * q^78 + 28 * q^79 - 66 * q^80 + 86 * q^81 + 4 * q^82 + 14 * q^83 - 58 * q^84 + 99 * q^85 - 31 * q^86 - 27 * q^87 + 5 * q^88 - 5 * q^89 - 45 * q^90 - 11 * q^91 + 20 * q^92 + 27 * q^93 - 39 * q^94 + 5 * q^95 - 87 * q^96 + 127 * q^97 - 29 * q^98 - 21 * 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 $

$2$	−1.53339	−1.08427	−0.542135	−	0.840292i	$-0.682384\pi$
$2$	−1.53339	−1.08427	−0.542135	+	0.840292i	$0.682384\pi$
$3$	2.66681	1.53968	0.769842	−	0.638235i	$-0.220335\pi$
$3$	2.66681	1.53968	0.769842	+	0.638235i	$0.220335\pi$
$4$	0.351281	0.175641
$5$	4.12109	1.84301	0.921504	−	0.388368i	$-0.126961\pi$
$5$	4.12109	1.84301	0.921504	+	0.388368i	$0.126961\pi$
$6$	−4.08926	−1.66943
$7$	2.92035	1.10379	0.551894	−	0.833914i	$-0.313905\pi$
$7$	2.92035	1.10379	0.551894	+	0.833914i	$0.313905\pi$
$8$	2.52813	0.893828
$9$	4.11188	1.37063
$10$	−6.31924	−1.99832
$11$	−5.32974	−1.60698	−0.803489	−	0.595320i	$-0.797025\pi$
$11$	−5.32974	−1.60698	−0.803489	+	0.595320i	$0.797025\pi$
$12$	0.936800	0.270431
$13$	−4.48029	−1.24261	−0.621304	−	0.783570i	$-0.713397\pi$
$13$	−4.48029	−1.24261	−0.621304	+	0.783570i	$0.713397\pi$
$14$	−4.47803	−1.19680
$15$	10.9902	2.83765
$16$	−4.57916	−1.14479
$17$	7.84636	1.90302	0.951511	−	0.307614i	$-0.0995307\pi$
$17$	7.84636	1.90302	0.951511	+	0.307614i	$0.0995307\pi$
$18$	−6.30510	−1.48613
$19$	4.17966	0.958879	0.479440	−	0.877575i	$-0.340840\pi$
$19$	4.17966	0.958879	0.479440	+	0.877575i	$0.340840\pi$
$20$	1.44766	0.323707
$21$	7.78802	1.69948
$22$	8.17256	1.74240
$23$	2.49567	0.520383	0.260191	−	0.965557i	$-0.416214\pi$
$23$	2.49567	0.520383	0.260191	+	0.965557i	$0.416214\pi$
$24$	6.74203	1.37621
$25$	11.9834	2.39668
$26$	6.87002	1.34732
$27$	2.96516	0.570645
$28$	1.02586	0.193870
$29$	−6.82010	−1.26646	−0.633231	−	0.773963i	$-0.718272\pi$
$29$	−6.82010	−1.26646	−0.633231	+	0.773963i	$0.718272\pi$
$30$	−16.8522	−3.07678
$31$	−8.14425	−1.46275	−0.731376	−	0.681975i	$-0.761121\pi$
$31$	−8.14425	−1.46275	−0.731376	+	0.681975i	$0.761121\pi$
$32$	1.96538	0.347434
$33$	−14.2134	−2.47424
$34$	−12.0315	−2.06339
$35$	12.0350	2.03429
$36$	1.44442	0.240737
$37$	−0.299515	−0.0492400	−0.0246200	−	0.999697i	$-0.507838\pi$
$37$	−0.299515	−0.0492400	−0.0246200	+	0.999697i	$0.507838\pi$
$38$	−6.40904	−1.03968
$39$	−11.9481	−1.91322
$40$	10.4186	1.64733
$41$	4.42833	0.691588	0.345794	−	0.938310i	$-0.387610\pi$
$41$	4.42833	0.691588	0.345794	+	0.938310i	$0.387610\pi$
$42$	−11.9421	−1.84270
$43$	−8.42986	−1.28554	−0.642771	−	0.766059i	$-0.722215\pi$
$43$	−8.42986	−1.28554	−0.642771	+	0.766059i	$0.722215\pi$
$44$	−1.87224	−0.282250
$45$	16.9454	2.52607
$46$	−3.82683	−0.564235
$47$	−10.6545	−1.55411	−0.777057	−	0.629431i	$-0.783288\pi$
$47$	−10.6545	−1.55411	−0.777057	+	0.629431i	$0.783288\pi$
$48$	−12.2118	−1.76262
$49$	1.52844	0.218348
$50$	−18.3752	−2.59865
$51$	20.9248	2.93005
$52$	−1.57384	−0.218252
$53$	−7.07126	−0.971313	−0.485656	−	0.874150i	$-0.661419\pi$
$53$	−7.07126	−0.971313	−0.485656	+	0.874150i	$0.661419\pi$
$54$	−4.54674	−0.618734
$55$	−21.9644	−2.96167
$56$	7.38301	0.986597
$57$	11.1464	1.47637
$58$	10.4579	1.37319
$59$	7.30283	0.950747	0.475374	−	0.879784i	$-0.342313\pi$
$59$	7.30283	0.950747	0.475374	+	0.879784i	$0.342313\pi$
$60$	3.86064	0.498406
$61$	0.241073	0.0308663	0.0154331	−	0.999881i	$-0.495087\pi$
$61$	0.241073	0.0308663	0.0154331	+	0.999881i	$0.495087\pi$
$62$	12.4883	1.58602
$63$	12.0081	1.51288
$64$	6.14463	0.768079
$65$	−18.4637	−2.29014
$66$	21.7947	2.68274
$67$	5.32491	0.650542	0.325271	−	0.945621i	$-0.394545\pi$
$67$	5.32491	0.650542	0.325271	+	0.945621i	$0.394545\pi$
$68$	2.75628	0.334248
$69$	6.65547	0.801225
$70$	−18.4544	−2.20572
$71$	1.55715	0.184800	0.0923998	−	0.995722i	$-0.470546\pi$
$71$	1.55715	0.184800	0.0923998	+	0.995722i	$0.470546\pi$
$72$	10.3953	1.22510
$73$	4.58790	0.536973	0.268487	−	0.963283i	$-0.413476\pi$
$73$	4.58790	0.536973	0.268487	+	0.963283i	$0.413476\pi$
$74$	0.459273	0.0533894
$75$	31.9575	3.69013
$76$	1.46823	0.168418
$77$	−15.5647	−1.77376
$78$	18.3210	2.07445
$79$	2.93788	0.330537	0.165269	−	0.986249i	$-0.447151\pi$
$79$	2.93788	0.330537	0.165269	+	0.986249i	$0.447151\pi$
$80$	−18.8712	−2.10986
$81$	−4.42811	−0.492012
$82$	−6.79034	−0.749868
$83$	−3.37600	−0.370565	−0.185282	−	0.982685i	$-0.559320\pi$
$83$	−3.37600	−0.370565	−0.185282	+	0.982685i	$0.559320\pi$
$84$	2.73578	0.298498
$85$	32.3356	3.50729
$86$	12.9263	1.39387
$87$	−18.1879	−1.94995
$88$	−13.4743	−1.43636
$89$	−4.76602	−0.505197	−0.252599	−	0.967571i	$-0.581285\pi$
$89$	−4.76602	−0.505197	−0.252599	+	0.967571i	$0.581285\pi$
$90$	−25.9839	−2.73895
$91$	−13.0840	−1.37158
$92$	0.876681	0.0914003
$93$	−21.7192	−2.25217
$94$	16.3374	1.68508
$95$	17.2248	1.76722
$96$	5.24131	0.534939
$97$	3.41682	0.346926	0.173463	−	0.984840i	$-0.444504\pi$
$97$	3.41682	0.346926	0.173463	+	0.984840i	$0.444504\pi$
$98$	−2.34369	−0.236748
$99$	−21.9152	−2.20256
$100$	4.20955	0.420955
$101$	6.90385	0.686958	0.343479	−	0.939160i	$-0.388395\pi$
$101$	6.90385	0.686958	0.343479	+	0.939160i	$0.388395\pi$
$102$	−32.0858	−3.17697
$103$	−7.73542	−0.762194	−0.381097	−	0.924535i	$-0.624454\pi$
$103$	−7.73542	−0.762194	−0.381097	+	0.924535i	$0.624454\pi$
$104$	−11.3267	−1.11068
$105$	32.0951	3.13217
$106$	10.8430	1.05316
$107$	−8.26270	−0.798785	−0.399393	−	0.916780i	$-0.630779\pi$
$107$	−8.26270	−0.798785	−0.399393	+	0.916780i	$0.630779\pi$
$108$	1.04160	0.100228
$109$	3.57946	0.342850	0.171425	−	0.985197i	$-0.445163\pi$
$109$	3.57946	0.342850	0.171425	+	0.985197i	$0.445163\pi$
$110$	33.6799	3.21125
$111$	−0.798749	−0.0758139
$112$	−13.3728	−1.26361
$113$	8.21919	0.773196	0.386598	−	0.922248i	$-0.373650\pi$
$113$	8.21919	0.773196	0.386598	+	0.922248i	$0.373650\pi$
$114$	−17.0917	−1.60078
$115$	10.2849	0.959070
$116$	−2.39577	−0.222442
$117$	−18.4224	−1.70315
$118$	−11.1981	−1.03087
$119$	22.9141	2.10053
$120$	27.7846	2.53637
$121$	17.4061	1.58238
$122$	−0.369659	−0.0334674
$123$	11.8095	1.06483
$124$	−2.86092	−0.256918
$125$	28.7793	2.57410
$126$	−18.4131	−1.64037
$127$	0.188546	0.0167308	0.00836538	−	0.999965i	$-0.497337\pi$
$127$	0.188546	0.0167308	0.00836538	+	0.999965i	$0.497337\pi$
$128$	−13.3529	−1.18024
$129$	−22.4808	−1.97933
$130$	28.3120	2.48313
$131$	1.66574	0.145536	0.0727681	−	0.997349i	$-0.476817\pi$
$131$	1.66574	0.145536	0.0727681	+	0.997349i	$0.476817\pi$
$132$	−4.99290	−0.434576
$133$	12.2061	1.05840
$134$	−8.16516	−0.705363
$135$	12.2197	1.05170
$136$	19.8366	1.70097
$137$	−13.9399	−1.19097	−0.595483	−	0.803368i	$-0.703039\pi$
$137$	−13.9399	−1.19097	−0.595483	+	0.803368i	$0.703039\pi$
$138$	−10.2054	−0.868744
$139$	−4.35162	−0.369099	−0.184550	−	0.982823i	$-0.559083\pi$
$139$	−4.35162	−0.369099	−0.184550	+	0.982823i	$0.559083\pi$
$140$	4.22768	0.357304
$141$	−28.4134	−2.39284
$142$	−2.38772	−0.200373
$143$	23.8788	1.99684
$144$	−18.8290	−1.56908
$145$	−28.1063	−2.33410
$146$	−7.03504	−0.582224
$147$	4.07605	0.336187
$148$	−0.105214	−0.00864853
$149$	−5.62234	−0.460600	−0.230300	−	0.973120i	$-0.573971\pi$
$149$	−5.62234	−0.460600	−0.230300	+	0.973120i	$0.573971\pi$
$150$	−49.0032	−4.00110
$151$	3.75708	0.305747	0.152873	−	0.988246i	$-0.451147\pi$
$151$	3.75708	0.305747	0.152873	+	0.988246i	$0.451147\pi$
$152$	10.5667	0.857073
$153$	32.2633	2.60833
$154$	23.8667	1.92324
$155$	−33.5632	−2.69586
$156$	−4.19713	−0.336040
$157$	15.4337	1.23174	0.615870	−	0.787848i	$-0.288805\pi$
$157$	15.4337	1.23174	0.615870	+	0.787848i	$0.288805\pi$
$158$	−4.50491	−0.358392
$159$	−18.8577	−1.49551
$160$	8.09953	0.640324
$161$	7.28822	0.574392
$162$	6.79001	0.533473
$163$	10.5143	0.823541	0.411770	−	0.911288i	$-0.364911\pi$
$163$	10.5143	0.823541	0.411770	+	0.911288i	$0.364911\pi$
$164$	1.55559	0.121471
$165$	−58.5748	−4.56004
$166$	5.17673	0.401792
$167$	−20.4099	−1.57936	−0.789682	−	0.613516i	$-0.789755\pi$
$167$	−20.4099	−1.57936	−0.789682	+	0.613516i	$0.789755\pi$
$168$	19.6891	1.51905
$169$	7.07297	0.544075
$170$	−49.5830	−3.80284
$171$	17.1862	1.31426
$172$	−2.96125	−0.225793
$173$	20.2693	1.54105	0.770523	−	0.637412i	$-0.219995\pi$
$173$	20.2693	1.54105	0.770523	+	0.637412i	$0.219995\pi$
$174$	27.8892	2.11427
$175$	34.9957	2.64543
$176$	24.4058	1.83965
$177$	19.4753	1.46385
$178$	7.30816	0.547770
$179$	−4.88894	−0.365417	−0.182708	−	0.983167i	$-0.558486\pi$
$179$	−4.88894	−0.365417	−0.182708	+	0.983167i	$0.558486\pi$
$180$	5.95261	0.443681
$181$	−21.7892	−1.61958	−0.809790	−	0.586720i	$-0.800419\pi$
$181$	−21.7892	−1.61958	−0.809790	+	0.586720i	$0.800419\pi$
$182$	20.0629	1.48716
$183$	0.642897	0.0475243
$184$	6.30937	0.465133
$185$	−1.23433	−0.0907497
$186$	33.3039	2.44196
$187$	−41.8191	−3.05811
$188$	−3.74271	−0.272965
$189$	8.65930	0.629872
$190$	−26.4123	−1.91615
$191$	−5.73275	−0.414808	−0.207404	−	0.978255i	$-0.566501\pi$
$191$	−5.73275	−0.414808	−0.207404	+	0.978255i	$0.566501\pi$
$192$	16.3866	1.18260
$193$	21.4769	1.54594	0.772972	−	0.634441i	$-0.218769\pi$
$193$	21.4769	1.54594	0.772972	+	0.634441i	$0.218769\pi$
$194$	−5.23932	−0.376161
$195$	−49.2391	−3.52609
$196$	0.536911	0.0383508
$197$	−18.6964	−1.33206	−0.666031	−	0.745924i	$-0.732008\pi$
$197$	−18.6964	−1.33206	−0.666031	+	0.745924i	$0.732008\pi$
$198$	33.6046	2.38817
$199$	15.3165	1.08576	0.542879	−	0.839811i	$-0.317334\pi$
$199$	15.3165	1.08576	0.542879	+	0.839811i	$0.317334\pi$
$200$	30.2956	2.14222
$201$	14.2005	1.00163
$202$	−10.5863	−0.744848
$203$	−19.9171	−1.39791
$204$	7.35047	0.514636
$205$	18.2495	1.27460
$206$	11.8614	0.826423
$207$	10.2619	0.713250
$208$	20.5160	1.42253
$209$	−22.2765	−1.54090
$210$	−49.2143	−3.39611
$211$	25.3920	1.74806	0.874029	−	0.485873i	$-0.161498\pi$
$211$	25.3920	1.74806	0.874029	+	0.485873i	$0.161498\pi$
$212$	−2.48400	−0.170602
$213$	4.15262	0.284533
$214$	12.6699	0.866098
$215$	−34.7402	−2.36926
$216$	7.49630	0.510059
$217$	−23.7841	−1.61457
$218$	−5.48871	−0.371742
$219$	12.2351	0.826769
$220$	−7.71566	−0.520190
$221$	−35.1540	−2.36471
$222$	1.22479	0.0822027
$223$	1.35423	0.0906860	0.0453430	−	0.998971i	$-0.485562\pi$
$223$	1.35423	0.0906860	0.0453430	+	0.998971i	$0.485562\pi$
$224$	5.73961	0.383494
$225$	49.2743	3.28495
$226$	−12.6032	−0.838353
$227$	−13.8841	−0.921520	−0.460760	−	0.887525i	$-0.652423\pi$
$227$	−13.8841	−0.921520	−0.460760	+	0.887525i	$0.652423\pi$
$228$	3.91550	0.259310
$229$	8.51086	0.562413	0.281207	−	0.959647i	$-0.409265\pi$
$229$	8.51086	0.562413	0.281207	+	0.959647i	$0.409265\pi$
$230$	−15.7707	−1.03989
$231$	−41.5081	−2.73103
$232$	−17.2421	−1.13200
$233$	−6.84097	−0.448167	−0.224083	−	0.974570i	$-0.571939\pi$
$233$	−6.84097	−0.448167	−0.224083	+	0.974570i	$0.571939\pi$
$234$	28.2487	1.84667
$235$	−43.9080	−2.86424
$236$	2.56534	0.166990
$237$	7.83477	0.508923
$238$	−35.1362	−2.27754
$239$	22.3797	1.44762	0.723810	−	0.689999i	$-0.242389\pi$
$239$	22.3797	1.44762	0.723810	+	0.689999i	$0.242389\pi$
$240$	−50.3258	−3.24852
$241$	9.23991	0.595195	0.297597	−	0.954691i	$-0.403815\pi$
$241$	9.23991	0.595195	0.297597	+	0.954691i	$0.403815\pi$
$242$	−26.6904	−1.71572
$243$	−20.7044	−1.32819
$244$	0.0846845	0.00542137
$245$	6.29884	0.402418
$246$	−18.1086	−1.15456
$247$	−18.7261	−1.19151
$248$	−20.5897	−1.30745
$249$	−9.00316	−0.570552
$250$	−44.1298	−2.79102
$251$	−21.6401	−1.36591	−0.682955	−	0.730461i	$-0.739305\pi$
$251$	−21.6401	−1.36591	−0.682955	+	0.730461i	$0.739305\pi$
$252$	4.21822	0.265723
$253$	−13.3013	−0.836243
$254$	−0.289114	−0.0181406
$255$	86.2329	5.40011
$256$	8.18589	0.511618
$257$	−2.22708	−0.138921	−0.0694607	−	0.997585i	$-0.522128\pi$
$257$	−2.22708	−0.138921	−0.0694607	+	0.997585i	$0.522128\pi$
$258$	34.4719	2.14612
$259$	−0.874688	−0.0543505
$260$	−6.48594	−0.402241
$261$	−28.0434	−1.73584
$262$	−2.55422	−0.157800
$263$	1.94277	0.119796	0.0598982	−	0.998204i	$-0.480922\pi$
$263$	1.94277	0.119796	0.0598982	+	0.998204i	$0.480922\pi$
$264$	−35.9333	−2.21154
$265$	−29.1413	−1.79014
$266$	−18.7166	−1.14759
$267$	−12.7101	−0.777844
$268$	1.87054	0.114262
$269$	−5.81896	−0.354788	−0.177394	−	0.984140i	$-0.556767\pi$
$269$	−5.81896	−0.354788	−0.177394	+	0.984140i	$0.556767\pi$
$270$	−18.7376	−1.14033
$271$	22.5352	1.36892	0.684458	−	0.729052i	$-0.260039\pi$
$271$	22.5352	1.36892	0.684458	+	0.729052i	$0.260039\pi$
$272$	−35.9298	−2.17856
$273$	−34.8925	−2.11179
$274$	21.3753	1.29133
$275$	−63.8685	−3.85141
$276$	2.33794	0.140728
$277$	18.3423	1.10208	0.551041	−	0.834478i	$-0.314231\pi$
$277$	18.3423	1.10208	0.551041	+	0.834478i	$0.314231\pi$
$278$	6.67272	0.400203
$279$	−33.4882	−2.00488
$280$	30.4261	1.81831
$281$	31.4994	1.87910	0.939549	−	0.342414i	$-0.111245\pi$
$281$	31.4994	1.87910	0.939549	+	0.342414i	$0.111245\pi$
$282$	43.5688	2.59449
$283$	6.37617	0.379024	0.189512	−	0.981878i	$-0.439309\pi$
$283$	6.37617	0.379024	0.189512	+	0.981878i	$0.439309\pi$
$284$	0.546997	0.0324583
$285$	45.9352	2.72096
$286$	−36.6154	−2.16512
$287$	12.9323	0.763367
$288$	8.08141	0.476202
$289$	44.5654	2.62149
$290$	43.0979	2.53079
$291$	9.11202	0.534156
$292$	1.61164	0.0943143
$293$	−7.21609	−0.421569	−0.210784	−	0.977533i	$-0.567602\pi$
$293$	−7.21609	−0.421569	−0.210784	+	0.977533i	$0.567602\pi$
$294$	−6.25018	−0.364518
$295$	30.0956	1.75224
$296$	−0.757212	−0.0440120
$297$	−15.8035	−0.917014
$298$	8.62123	0.499414
$299$	−11.1813	−0.646632
$300$	11.2261	0.648137
$301$	−24.6181	−1.41897
$302$	−5.76106	−0.331512
$303$	18.4112	1.05770
$304$	−19.1393	−1.09772
$305$	0.993486	0.0568868
$306$	−49.4721	−2.82813
$307$	−0.100117	−0.00571398	−0.00285699	−	0.999996i	$-0.500909\pi$
$307$	−0.100117	−0.00571398	−0.00285699	+	0.999996i	$0.500909\pi$
$308$	−5.46758	−0.311545
$309$	−20.6289	−1.17354
$310$	51.4655	2.92304
$311$	−22.9765	−1.30288	−0.651439	−	0.758701i	$-0.725834\pi$
$311$	−22.9765	−1.30288	−0.651439	+	0.758701i	$0.725834\pi$
$312$	−30.2062	−1.71009
$313$	−16.6580	−0.941567	−0.470783	−	0.882249i	$-0.656029\pi$
$313$	−16.6580	−0.941567	−0.470783	+	0.882249i	$0.656029\pi$
$314$	−23.6658	−1.33554
$315$	49.4865	2.78825
$316$	1.03202	0.0580558
$317$	−20.3509	−1.14302	−0.571511	−	0.820595i	$-0.693642\pi$
$317$	−20.3509	−1.14302	−0.571511	+	0.820595i	$0.693642\pi$
$318$	28.9162	1.62154
$319$	36.3494	2.03517
$320$	25.3226	1.41558
$321$	−22.0350	−1.22988
$322$	−11.1757	−0.622796
$323$	32.7951	1.82477
$324$	−1.55551	−0.0864172
$325$	−53.6891	−2.97814
$326$	−16.1225	−0.892940
$327$	9.54575	0.527881
$328$	11.1954	0.618161
$329$	−31.1148	−1.71541
$330$	89.8179	4.94431
$331$	−7.35295	−0.404154	−0.202077	−	0.979370i	$-0.564769\pi$
$331$	−7.35295	−0.404154	−0.202077	+	0.979370i	$0.564769\pi$
$332$	−1.18593	−0.0650862
$333$	−1.23157	−0.0674895
$334$	31.2963	1.71246
$335$	21.9445	1.19895
$336$	−35.6626	−1.94555
$337$	−2.66326	−0.145077	−0.0725385	−	0.997366i	$-0.523110\pi$
$337$	−2.66326	−0.145077	−0.0725385	+	0.997366i	$0.523110\pi$
$338$	−10.8456	−0.589924
$339$	21.9190	1.19048
$340$	11.3589	0.616022
$341$	43.4068	2.35061
$342$	−26.3532	−1.42502
$343$	−15.9789	−0.862778
$344$	−21.3118	−1.14905
$345$	27.4278	1.47666
$346$	−31.0807	−1.67091
$347$	−5.09490	−0.273509	−0.136754	−	0.990605i	$-0.543667\pi$
$347$	−5.09490	−0.273509	−0.136754	+	0.990605i	$0.543667\pi$
$348$	−6.38907	−0.342490
$349$	−10.5013	−0.562122	−0.281061	−	0.959690i	$-0.590686\pi$
$349$	−10.5013	−0.562122	−0.281061	+	0.959690i	$0.590686\pi$
$350$	−53.6621	−2.86836
$351$	−13.2848	−0.709089
$352$	−10.4750	−0.558319
$353$	−13.5473	−0.721052	−0.360526	−	0.932749i	$-0.617403\pi$
$353$	−13.5473	−0.721052	−0.360526	+	0.932749i	$0.617403\pi$
$354$	−29.8631	−1.58721
$355$	6.41716	0.340587
$356$	−1.67421	−0.0887331
$357$	61.1076	3.23416
$358$	7.49665	0.396210
$359$	9.12962	0.481843	0.240922	−	0.970545i	$-0.422550\pi$
$359$	9.12962	0.481843	0.240922	+	0.970545i	$0.422550\pi$
$360$	42.8402	2.25788
$361$	−1.53047	−0.0805508
$362$	33.4113	1.75606
$363$	46.4188	2.43636
$364$	−4.59616	−0.240904
$365$	18.9072	0.989647
$366$	−0.985811	−0.0515291
$367$	9.46781	0.494216	0.247108	−	0.968988i	$-0.420520\pi$
$367$	9.46781	0.494216	0.247108	+	0.968988i	$0.420520\pi$
$368$	−11.4281	−0.595729
$369$	18.2087	0.947908
$370$	1.89271	0.0983971
$371$	−20.6506	−1.07212
$372$	−7.62954	−0.395573
$373$	−1.34037	−0.0694019	−0.0347010	−	0.999398i	$-0.511048\pi$
$373$	−1.34037	−0.0694019	−0.0347010	+	0.999398i	$0.511048\pi$
$374$	64.1249	3.31582
$375$	76.7489	3.96330
$376$	−26.9358	−1.38911
$377$	30.5560	1.57372
$378$	−13.2781	−0.682951
$379$	−11.9841	−0.615583	−0.307791	−	0.951454i	$-0.599590\pi$
$379$	−11.9841	−0.615583	−0.307791	+	0.951454i	$0.599590\pi$
$380$	6.05073	0.310396
$381$	0.502816	0.0257601
$382$	8.79054	0.449763
$383$	1.33874	0.0684063	0.0342032	−	0.999415i	$-0.489111\pi$
$383$	1.33874	0.0684063	0.0342032	+	0.999415i	$0.489111\pi$
$384$	−35.6096	−1.81719
$385$	−64.1436	−3.26906
$386$	−32.9325	−1.67622
$387$	−34.6625	−1.76200
$388$	1.20027	0.0609343
$389$	1.15655	0.0586392	0.0293196	−	0.999570i	$-0.490666\pi$
$389$	1.15655	0.0586392	0.0293196	+	0.999570i	$0.490666\pi$
$390$	75.5027	3.82323
$391$	19.5819	0.990300
$392$	3.86409	0.195166
$393$	4.44220	0.224080
$394$	28.6688	1.44431
$395$	12.1073	0.609184
$396$	−7.69840	−0.386859
$397$	−12.9981	−0.652356	−0.326178	−	0.945308i	$-0.605761\pi$
$397$	−12.9981	−0.652356	−0.326178	+	0.945308i	$0.605761\pi$
$398$	−23.4861	−1.17725
$399$	32.5512	1.62960
$400$	−54.8740	−2.74370
$401$	16.4506	0.821505	0.410752	−	0.911747i	$-0.365266\pi$
$401$	16.4506	0.821505	0.410752	+	0.911747i	$0.365266\pi$
$402$	−21.7749	−1.08604
$403$	36.4886	1.81763
$404$	2.42519	0.120658
$405$	−18.2486	−0.906782
$406$	30.5406	1.51571
$407$	1.59634	0.0791275
$408$	52.9004	2.61896
$409$	−0.263454	−0.0130270	−0.00651349	−	0.999979i	$-0.502073\pi$
$409$	−0.263454	−0.0130270	−0.00651349	+	0.999979i	$0.502073\pi$
$410$	−27.9836	−1.38201
$411$	−37.1751	−1.83371
$412$	−2.71731	−0.133872
$413$	21.3268	1.04942
$414$	−15.7354	−0.773355
$415$	−13.9128	−0.682954
$416$	−8.80548	−0.431724
$417$	−11.6049	−0.568296
$418$	34.1585	1.67075
$419$	−10.4957	−0.512749	−0.256375	−	0.966578i	$-0.582528\pi$
$419$	−10.4957	−0.512749	−0.256375	+	0.966578i	$0.582528\pi$
$420$	11.2744	0.550135
$421$	−29.7291	−1.44891	−0.724454	−	0.689323i	$-0.757908\pi$
$421$	−29.7291	−1.44891	−0.724454	+	0.689323i	$0.757908\pi$
$422$	−38.9358	−1.89537
$423$	−43.8098	−2.13011
$424$	−17.8770	−0.868186
$425$	94.0262	4.56094
$426$	−6.36758	−0.308510
$427$	0.704018	0.0340698
$428$	−2.90253	−0.140299
$429$	63.6801	3.07451
$430$	53.2703	2.56892
$431$	18.2989	0.881429	0.440715	−	0.897647i	$-0.354725\pi$
$431$	18.2989	0.881429	0.440715	+	0.897647i	$0.354725\pi$
$432$	−13.5780	−0.653270
$433$	14.7088	0.706862	0.353431	−	0.935461i	$-0.385015\pi$
$433$	14.7088	0.706862	0.353431	+	0.935461i	$0.385015\pi$
$434$	36.4702	1.75063
$435$	−74.9541	−3.59378
$436$	1.25740	0.0602184
$437$	10.4310	0.498984
$438$	−18.7611	−0.896441
$439$	−10.3396	−0.493481	−0.246740	−	0.969082i	$-0.579359\pi$
$439$	−10.3396	−0.493481	−0.246740	+	0.969082i	$0.579359\pi$
$440$	−55.5287	−2.64723
$441$	6.28475	0.299274
$442$	53.9047	2.56398
$443$	−15.0468	−0.714897	−0.357449	−	0.933933i	$-0.616353\pi$
$443$	−15.0468	−0.714897	−0.357449	+	0.933933i	$0.616353\pi$
$444$	−0.280586	−0.0133160
$445$	−19.6412	−0.931083
$446$	−2.07656	−0.0983280
$447$	−14.9937	−0.709178
$448$	17.9445	0.847796
$449$	−25.2953	−1.19376	−0.596880	−	0.802331i	$-0.703593\pi$
$449$	−25.2953	−1.19376	−0.596880	+	0.802331i	$0.703593\pi$
$450$	−75.5566	−3.56177
$451$	−23.6018	−1.11137
$452$	2.88724	0.135805
$453$	10.0194	0.470753
$454$	21.2897	0.999176
$455$	−53.9204	−2.52783
$456$	28.1794	1.31962
$457$	10.6699	0.499118	0.249559	−	0.968360i	$-0.419714\pi$
$457$	10.6699	0.499118	0.249559	+	0.968360i	$0.419714\pi$
$458$	−13.0505	−0.609808
$459$	23.2657	1.08595
$460$	3.61288	0.168452
$461$	−3.89256	−0.181295	−0.0906473	−	0.995883i	$-0.528894\pi$
$461$	−3.89256	−0.181295	−0.0906473	+	0.995883i	$0.528894\pi$
$462$	63.6481	2.96118
$463$	−22.4594	−1.04378	−0.521889	−	0.853013i	$-0.674773\pi$
$463$	−22.4594	−1.04378	−0.521889	+	0.853013i	$0.674773\pi$
$464$	31.2304	1.44983
$465$	−89.5068	−4.15078
$466$	10.4899	0.485933
$467$	−29.7660	−1.37741	−0.688704	−	0.725043i	$-0.741820\pi$
$467$	−29.7660	−1.37741	−0.688704	+	0.725043i	$0.741820\pi$
$468$	−6.47143	−0.299142
$469$	15.5506	0.718060
$470$	67.3281	3.10561
$471$	41.1586	1.89649
$472$	18.4625	0.849804
$473$	44.9290	2.06584
$474$	−12.0137	−0.551810
$475$	50.0865	2.29813
$476$	8.04929	0.368939
$477$	−29.0762	−1.33131
$478$	−34.3167	−1.56961
$479$	−42.9374	−1.96186	−0.980930	−	0.194362i	$-0.937736\pi$
$479$	−42.9374	−1.96186	−0.980930	+	0.194362i	$0.937736\pi$
$480$	21.5999	0.985897
$481$	1.34191	0.0611860
$482$	−14.1684	−0.645352
$483$	19.4363	0.884382
$484$	6.11444	0.277929
$485$	14.0811	0.639388
$486$	31.7479	1.44011
$487$	−20.3162	−0.920615	−0.460308	−	0.887759i	$-0.652261\pi$
$487$	−20.3162	−0.920615	−0.460308	+	0.887759i	$0.652261\pi$
$488$	0.609464	0.0275891
$489$	28.0396	1.26799
$490$	−9.65856	−0.436329
$491$	7.22018	0.325842	0.162921	−	0.986639i	$-0.447908\pi$
$491$	7.22018	0.325842	0.162921	+	0.986639i	$0.447908\pi$
$492$	4.14845	0.187027
$493$	−53.5130	−2.41010
$494$	28.7143	1.29192
$495$	−90.3147	−4.05934
$496$	37.2939	1.67454
$497$	4.54742	0.203980
$498$	13.8053	0.618633
$499$	−18.5819	−0.831841	−0.415921	−	0.909401i	$-0.636541\pi$
$499$	−18.5819	−0.831841	−0.415921	+	0.909401i	$0.636541\pi$
$500$	10.1096	0.452116
$501$	−54.4293	−2.43172
$502$	33.1827	1.48101
$503$	44.7394	1.99483	0.997415	−	0.0718588i	$-0.0228931\pi$
$503$	44.7394	1.99483	0.997415	+	0.0718588i	$0.0228931\pi$
$504$	30.3580	1.35225
$505$	28.4514	1.26607
$506$	20.3960	0.906713
$507$	18.8623	0.837703
$508$	0.0662327	0.00293860
$509$	−21.3660	−0.947029	−0.473515	−	0.880786i	$-0.657015\pi$
$509$	−21.3660	−0.947029	−0.473515	+	0.880786i	$0.657015\pi$
$510$	−132.229	−5.85518
$511$	13.3983	0.592705
$512$	14.1536	0.625507
$513$	12.3934	0.547180
$514$	3.41498	0.150628
$515$	−31.8784	−1.40473
$516$	−7.89709	−0.347650
$517$	56.7855	2.49742
$518$	1.34124	0.0589306
$519$	54.0544	2.37272
$520$	−46.6785	−2.04699
$521$	−7.05915	−0.309267	−0.154634	−	0.987972i	$-0.549420\pi$
$521$	−7.05915	−0.309267	−0.154634	+	0.987972i	$0.549420\pi$
$522$	43.0015	1.88212
$523$	44.4342	1.94297	0.971486	−	0.237096i	$-0.0761957\pi$
$523$	44.4342	1.94297	0.971486	+	0.237096i	$0.0761957\pi$
$524$	0.585142	0.0255620
$525$	93.3270	4.07312
$526$	−2.97903	−0.129892
$527$	−63.9028	−2.78365
$528$	65.0855	2.83248
$529$	−16.7716	−0.729202
$530$	44.6850	1.94099
$531$	30.0283	1.30312
$532$	4.28776	0.185898
$533$	−19.8402	−0.859373
$534$	19.4895	0.843393
$535$	−34.0513	−1.47217
$536$	13.4621	0.581472
$537$	−13.0379	−0.562626
$538$	8.92272	0.384686
$539$	−8.14618	−0.350881
$540$	4.29255	0.184722
$541$	29.6631	1.27532	0.637658	−	0.770320i	$-0.279903\pi$
$541$	29.6631	1.27532	0.637658	+	0.770320i	$0.279903\pi$
$542$	−34.5552	−1.48428
$543$	−58.1077	−2.49364
$544$	15.4211	0.661175
$545$	14.7513	0.631876
$546$	53.5038	2.28975
$547$	−14.1316	−0.604223	−0.302112	−	0.953273i	$-0.597691\pi$
$547$	−14.1316	−0.604223	−0.302112	+	0.953273i	$0.597691\pi$
$548$	−4.89682	−0.209182
$549$	0.991263	0.0423061
$550$	97.9352	4.17597
$551$	−28.5057	−1.21438
$552$	16.8259	0.716157
$553$	8.57964	0.364843
$554$	−28.1259	−1.19495
$555$	−3.29172	−0.139726
$556$	−1.52864	−0.0648288
$557$	12.7318	0.539465	0.269733	−	0.962935i	$-0.413065\pi$
$557$	12.7318	0.539465	0.269733	+	0.962935i	$0.413065\pi$
$558$	51.3504	2.17383
$559$	37.7682	1.59742
$560$	−55.1104	−2.32884
$561$	−111.524	−4.70853
$562$	−48.3009	−2.03745
$563$	−31.4614	−1.32594	−0.662969	−	0.748647i	$-0.730704\pi$
$563$	−31.4614	−1.32594	−0.662969	+	0.748647i	$0.730704\pi$
$564$	−9.98110	−0.420280
$565$	33.8720	1.42501
$566$	−9.77715	−0.410964
$567$	−12.9316	−0.543077
$568$	3.93667	0.165179
$569$	1.10925	0.0465021	0.0232511	−	0.999730i	$-0.492598\pi$
$569$	1.10925	0.0465021	0.0232511	+	0.999730i	$0.492598\pi$
$570$	−70.4365	−2.95026
$571$	33.0680	1.38385	0.691927	−	0.721968i	$-0.256762\pi$
$571$	33.0680	1.38385	0.691927	+	0.721968i	$0.256762\pi$
$572$	8.38816	0.350726
$573$	−15.2882	−0.638672
$574$	−19.8302	−0.827696
$575$	29.9066	1.24719
$576$	25.2660	1.05275
$577$	18.9616	0.789381	0.394691	−	0.918814i	$-0.370852\pi$
$577$	18.9616	0.789381	0.394691	+	0.918814i	$0.370852\pi$
$578$	−68.3361	−2.84241
$579$	57.2749	2.38026
$580$	−9.87321	−0.409963
$581$	−9.85911	−0.409025
$582$	−13.9723	−0.579169
$583$	37.6880	1.56088
$584$	11.5988	0.479962
$585$	−75.9204	−3.13892
$586$	11.0651	0.457094
$587$	17.6616	0.728974	0.364487	−	0.931209i	$-0.381244\pi$
$587$	17.6616	0.728974	0.364487	+	0.931209i	$0.381244\pi$
$588$	1.43184	0.0590481
$589$	−34.0402	−1.40260
$590$	−46.1483	−1.89990
$591$	−49.8597	−2.05095
$592$	1.37153	0.0563695
$593$	25.1356	1.03219	0.516097	−	0.856530i	$-0.327384\pi$
$593$	25.1356	1.03219	0.516097	+	0.856530i	$0.327384\pi$
$594$	24.2330	0.994291
$595$	94.4312	3.87130
$596$	−1.97502	−0.0809000
$597$	40.8462	1.67172
$598$	17.1453	0.701123
$599$	−0.347041	−0.0141797	−0.00708985	−	0.999975i	$-0.502257\pi$
$599$	−0.347041	−0.0141797	−0.00708985	+	0.999975i	$0.502257\pi$
$600$	80.7926	3.29834
$601$	−34.0024	−1.38699	−0.693493	−	0.720464i	$-0.743929\pi$
$601$	−34.0024	−1.38699	−0.693493	+	0.720464i	$0.743929\pi$
$602$	37.7492	1.53854
$603$	21.8954	0.891649
$604$	1.31979	0.0537015
$605$	71.7323	2.91633
$606$	−28.2316	−1.14683
$607$	−7.24347	−0.294004	−0.147002	−	0.989136i	$-0.546962\pi$
$607$	−7.24347	−0.294004	−0.147002	+	0.989136i	$0.546962\pi$
$608$	8.21463	0.333147
$609$	−53.1151	−2.15233
$610$	−1.52340	−0.0616807
$611$	47.7351	1.93115
$612$	11.3335	0.458128
$613$	−19.5957	−0.791464	−0.395732	−	0.918366i	$-0.629509\pi$
$613$	−19.5957	−0.791464	−0.395732	+	0.918366i	$0.629509\pi$
$614$	0.153518	0.00619549
$615$	48.6681	1.96249
$616$	−39.3495	−1.58544
$617$	14.3675	0.578415	0.289208	−	0.957266i	$-0.406608\pi$
$617$	14.3675	0.578415	0.289208	+	0.957266i	$0.406608\pi$
$618$	31.6321	1.27243
$619$	26.1535	1.05120	0.525599	−	0.850732i	$-0.323841\pi$
$619$	26.1535	1.05120	0.525599	+	0.850732i	$0.323841\pi$
$620$	−11.7901	−0.473503
$621$	7.40006	0.296954
$622$	35.2319	1.41267
$623$	−13.9184	−0.557631
$624$	54.7122	2.19024
$625$	58.6851	2.34740
$626$	25.5432	1.02091
$627$	−59.4072	−2.37249
$628$	5.42155	0.216343
$629$	−2.35010	−0.0937047
$630$	−75.8821	−3.02322
$631$	11.6819	0.465048	0.232524	−	0.972591i	$-0.425302\pi$
$631$	11.6819	0.465048	0.232524	+	0.972591i	$0.425302\pi$
$632$	7.42734	0.295444
$633$	67.7157	2.69146
$634$	31.2059	1.23934
$635$	0.777016	0.0308349
$636$	−6.62436	−0.262673
$637$	−6.84784	−0.271321
$638$	−55.7377	−2.20668
$639$	6.40280	0.253291
$640$	−55.0284	−2.17519
$641$	−30.6955	−1.21240	−0.606199	−	0.795313i	$-0.707307\pi$
$641$	−30.6955	−1.21240	−0.606199	+	0.795313i	$0.707307\pi$
$642$	33.7883	1.33352
$643$	24.4918	0.965863	0.482931	−	0.875658i	$-0.339572\pi$
$643$	24.4918	0.965863	0.482931	+	0.875658i	$0.339572\pi$
$644$	2.56021	0.100887
$645$	−92.6456	−3.64792
$646$	−50.2876	−1.97854
$647$	−9.15371	−0.359869	−0.179935	−	0.983679i	$-0.557589\pi$
$647$	−9.15371	−0.359869	−0.179935	+	0.983679i	$0.557589\pi$
$648$	−11.1948	−0.439774
$649$	−38.9222	−1.52783
$650$	82.3263	3.22910
$651$	−63.4276	−2.48592
$652$	3.69346	0.144647
$653$	29.4894	1.15401	0.577005	−	0.816740i	$-0.304221\pi$
$653$	29.4894	1.15401	0.577005	+	0.816740i	$0.304221\pi$
$654$	−14.6373	−0.572365
$655$	6.86466	0.268224
$656$	−20.2780	−0.791724
$657$	18.8649	0.735989
$658$	47.7110	1.85997
$659$	28.0270	1.09178	0.545889	−	0.837858i	$-0.316192\pi$
$659$	28.0270	1.09178	0.545889	+	0.837858i	$0.316192\pi$
$660$	−20.5762	−0.800928
$661$	−23.1960	−0.902222	−0.451111	−	0.892468i	$-0.648972\pi$
$661$	−23.1960	−0.902222	−0.451111	+	0.892468i	$0.648972\pi$
$662$	11.2749	0.438212
$663$	−93.7489	−3.64091
$664$	−8.53497	−0.331221
$665$	50.3023	1.95064
$666$	1.88847	0.0731768
$667$	−17.0207	−0.659045
$668$	−7.16961	−0.277400
$669$	3.61147	0.139628
$670$	−33.6494	−1.29999
$671$	−1.28486	−0.0496014
$672$	15.3064	0.590459
$673$	9.25719	0.356838	0.178419	−	0.983955i	$-0.442902\pi$
$673$	9.25719	0.356838	0.178419	+	0.983955i	$0.442902\pi$
$674$	4.08381	0.157303
$675$	35.5327	1.36766
$676$	2.48460	0.0955616
$677$	43.9188	1.68794	0.843969	−	0.536392i	$-0.180213\pi$
$677$	43.9188	1.68794	0.843969	+	0.536392i	$0.180213\pi$
$678$	−33.6104	−1.29080
$679$	9.97832	0.382933
$680$	81.7485	3.13491
$681$	−37.0262	−1.41885
$682$	−66.5594	−2.54869
$683$	38.3291	1.46662	0.733310	−	0.679894i	$-0.237974\pi$
$683$	38.3291	1.46662	0.733310	+	0.679894i	$0.237974\pi$
$684$	6.03720	0.230838
$685$	−57.4477	−2.19496
$686$	24.5018	0.935484
$687$	22.6968	0.865939
$688$	38.6017	1.47168
$689$	31.6813	1.20696
$690$	−42.0575	−1.60110
$691$	3.86100	0.146879	0.0734396	−	0.997300i	$-0.476602\pi$
$691$	3.86100	0.146879	0.0734396	+	0.997300i	$0.476602\pi$
$692$	7.12022	0.270670
$693$	−64.0001	−2.43116
$694$	7.81247	0.296557
$695$	−17.9334	−0.680254
$696$	−45.9814	−1.74292
$697$	34.7462	1.31611
$698$	16.1026	0.609492
$699$	−18.2436	−0.690035
$700$	12.2933	0.464645
$701$	26.0579	0.984192	0.492096	−	0.870541i	$-0.336231\pi$
$701$	26.0579	0.984192	0.492096	+	0.870541i	$0.336231\pi$
$702$	20.3707	0.768843
$703$	−1.25187	−0.0472152
$704$	−32.7493	−1.23428
$705$	−117.094	−4.41003
$706$	20.7733	0.781815
$707$	20.1616	0.758256
$708$	6.84129	0.257111
$709$	3.46791	0.130240	0.0651201	−	0.997877i	$-0.479257\pi$
$709$	3.46791	0.130240	0.0651201	+	0.997877i	$0.479257\pi$
$710$	−9.84000	−0.369289
$711$	12.0802	0.453043
$712$	−12.0491	−0.451559
$713$	−20.3254	−0.761191
$714$	−93.7017	−3.50670
$715$	98.4066	3.68020
$716$	−1.71739	−0.0641820
$717$	59.6823	2.22888
$718$	−13.9993	−0.522448
$719$	12.6005	0.469918	0.234959	−	0.972005i	$-0.424504\pi$
$719$	12.6005	0.469918	0.234959	+	0.972005i	$0.424504\pi$
$720$	−77.5959	−2.89183
$721$	−22.5901	−0.841300
$722$	2.34680	0.0873388
$723$	24.6411	0.916411
$724$	−7.65414	−0.284464
$725$	−81.7281	−3.03531
$726$	−71.1781	−2.64167
$727$	11.4007	0.422828	0.211414	−	0.977397i	$-0.432193\pi$
$727$	11.4007	0.422828	0.211414	+	0.977397i	$0.432193\pi$
$728$	−33.0780	−1.22595
$729$	−41.9304	−1.55298
$730$	−28.9921	−1.07304
$731$	−66.1437	−2.44641
$732$	0.225837	0.00834719
$733$	−18.4154	−0.680188	−0.340094	−	0.940391i	$-0.610459\pi$
$733$	−18.4154	−0.680188	−0.340094	+	0.940391i	$0.610459\pi$
$734$	−14.5178	−0.535863
$735$	16.7978	0.619596
$736$	4.90495	0.180799
$737$	−28.3804	−1.04541
$738$	−27.9211	−1.02779
$739$	−25.6620	−0.943992	−0.471996	−	0.881601i	$-0.656466\pi$
$739$	−25.6620	−0.943992	−0.471996	+	0.881601i	$0.656466\pi$
$740$	−0.433596	−0.0159393
$741$	−49.9389	−1.83455
$742$	31.6653	1.16247
$743$	−16.5309	−0.606461	−0.303230	−	0.952917i	$-0.598065\pi$
$743$	−16.5309	−0.606461	−0.303230	+	0.952917i	$0.598065\pi$
$744$	−54.9088	−2.01306
$745$	−23.1702	−0.848890
$746$	2.05531	0.0752504
$747$	−13.8817	−0.507905
$748$	−14.6902	−0.537129
$749$	−24.1300	−0.881690
$750$	−117.686	−4.29728
$751$	−34.9635	−1.27584	−0.637918	−	0.770105i	$-0.720204\pi$
$751$	−34.9635	−1.27584	−0.637918	+	0.770105i	$0.720204\pi$
$752$	48.7885	1.77913
$753$	−57.7100	−2.10307
$754$	−46.8543	−1.70633
$755$	15.4833	0.563494
$756$	3.04185	0.110631
$757$	38.0678	1.38360	0.691799	−	0.722090i	$-0.256819\pi$
$757$	38.0678	1.38360	0.691799	+	0.722090i	$0.256819\pi$
$758$	18.3763	0.667458
$759$	−35.4719	−1.28755
$760$	43.5464	1.57959
$761$	38.6416	1.40076	0.700378	−	0.713772i	$-0.253015\pi$
$761$	38.6416	1.40076	0.700378	+	0.713772i	$0.253015\pi$
$762$	−0.771013	−0.0279309
$763$	10.4533	0.378434
$764$	−2.01381	−0.0728570
$765$	132.960	4.80718
$766$	−2.05281	−0.0741709
$767$	−32.7188	−1.18141
$768$	21.8302	0.787730
$769$	42.0162	1.51514	0.757571	−	0.652753i	$-0.226386\pi$
$769$	42.0162	1.51514	0.757571	+	0.652753i	$0.226386\pi$
$770$	98.3570	3.54454
$771$	−5.93919	−0.213895
$772$	7.54444	0.271530
$773$	44.1689	1.58865	0.794323	−	0.607495i	$-0.207826\pi$
$773$	44.1689	1.58865	0.794323	+	0.607495i	$0.207826\pi$
$774$	53.1511	1.91048
$775$	−97.5959	−3.50575
$776$	8.63816	0.310092
$777$	−2.33263	−0.0836825
$778$	−1.77344	−0.0635807
$779$	18.5089	0.663150
$780$	−17.2968	−0.619324
$781$	−8.29920	−0.296969
$782$	−30.0267	−1.07375
$783$	−20.2227	−0.722701
$784$	−6.99897	−0.249963
$785$	63.6035	2.27011
$786$	−6.81163	−0.242963
$787$	−40.2925	−1.43627	−0.718136	−	0.695903i	$-0.755004\pi$
$787$	−40.2925	−1.43627	−0.718136	+	0.695903i	$0.755004\pi$
$788$	−6.56768	−0.233964
$789$	5.18100	0.184449
$790$	−18.5652	−0.660519
$791$	24.0029	0.853445
$792$	−55.4045	−1.96871
$793$	−1.08008	−0.0383547
$794$	19.9311	0.707329
$795$	−77.7144	−2.75625
$796$	5.38040	0.190703
$797$	19.2871	0.683183	0.341592	−	0.939848i	$-0.389034\pi$
$797$	19.2871	0.683183	0.341592	+	0.939848i	$0.389034\pi$
$798$	−49.9137	−1.76693
$799$	−83.5988	−2.95751
$800$	23.5520	0.832689
$801$	−19.5973	−0.692436
$802$	−25.2252	−0.890732
$803$	−24.4523	−0.862904
$804$	4.98838	0.175927
$805$	30.0354	1.05861
$806$	−55.9512	−1.97080
$807$	−15.5181	−0.546261
$808$	17.4538	0.614023
$809$	11.2893	0.396911	0.198455	−	0.980110i	$-0.436408\pi$
$809$	11.2893	0.396911	0.198455	+	0.980110i	$0.436408\pi$
$810$	27.9823	0.983196
$811$	3.16183	0.111027	0.0555135	−	0.998458i	$-0.482320\pi$
$811$	3.16183	0.111027	0.0555135	+	0.998458i	$0.482320\pi$
$812$	−6.99649	−0.245529
$813$	60.0971	2.10770
$814$	−2.44780	−0.0857955
$815$	43.3303	1.51779
$816$	−95.8179	−3.35430
$817$	−35.2339	−1.23268
$818$	0.403978	0.0141248
$819$	−53.7998	−1.87992
$820$	6.41072	0.223872
$821$	−31.5619	−1.10152	−0.550759	−	0.834664i	$-0.685662\pi$
$821$	−31.5619	−1.10152	−0.550759	+	0.834664i	$0.685662\pi$
$822$	57.0038	1.98824
$823$	28.5436	0.994967	0.497483	−	0.867473i	$-0.334258\pi$
$823$	28.5436	0.994967	0.497483	+	0.867473i	$0.334258\pi$
$824$	−19.5561	−0.681270
$825$	−170.325	−5.92996
$826$	−32.7023	−1.13786
$827$	−24.7030	−0.859006	−0.429503	−	0.903065i	$-0.641311\pi$
$827$	−24.7030	−0.859006	−0.429503	+	0.903065i	$0.641311\pi$
$828$	3.60480	0.125276
$829$	−17.6666	−0.613585	−0.306793	−	0.951776i	$-0.599256\pi$
$829$	−17.6666	−0.613585	−0.306793	+	0.951776i	$0.599256\pi$
$830$	21.3338	0.740506
$831$	48.9154	1.69686
$832$	−27.5297	−0.954421
$833$	11.9927	0.415522
$834$	17.7949	0.616186
$835$	−84.1111	−2.91078
$836$	−7.82531	−0.270644
$837$	−24.1490	−0.834712
$838$	16.0940	0.555958
$839$	38.1595	1.31741	0.658707	−	0.752400i	$-0.271104\pi$
$839$	38.1595	1.31741	0.658707	+	0.752400i	$0.271104\pi$
$840$	81.1406	2.79962
$841$	17.5138	0.603925
$842$	45.5863	1.57101
$843$	84.0030	2.89322
$844$	8.91973	0.307030
$845$	29.1484	1.00273
$846$	67.1775	2.30961
$847$	50.8320	1.74661
$848$	32.3805	1.11195
$849$	17.0040	0.583577
$850$	−144.179	−4.94529
$851$	−0.747490	−0.0256236
$852$	1.45874	0.0499755
$853$	36.1394	1.23739	0.618694	−	0.785632i	$-0.287662\pi$
$853$	36.1394	1.23739	0.618694	+	0.785632i	$0.287662\pi$
$854$	−1.07953	−0.0369409
$855$	70.8261	2.42220
$856$	−20.8891	−0.713976
$857$	−7.91561	−0.270392	−0.135196	−	0.990819i	$-0.543166\pi$
$857$	−7.91561	−0.270392	−0.135196	+	0.990819i	$0.543166\pi$
$858$	−97.6464	−3.33359
$859$	−2.39868	−0.0818420	−0.0409210	−	0.999162i	$-0.513029\pi$
$859$	−2.39868	−0.0818420	−0.0409210	+	0.999162i	$0.513029\pi$
$860$	−12.2036	−0.416139
$861$	34.4879	1.17534
$862$	−28.0594	−0.955707
$863$	−38.9876	−1.32715	−0.663576	−	0.748109i	$-0.730962\pi$
$863$	−38.9876	−1.32715	−0.663576	+	0.748109i	$0.730962\pi$
$864$	5.82768	0.198262
$865$	83.5317	2.84016
$866$	−22.5544	−0.766429
$867$	118.847	4.03627
$868$	−8.35489	−0.283583
$869$	−15.6581	−0.531166
$870$	114.934	3.89662
$871$	−23.8571	−0.808368
$872$	9.04934	0.306449
$873$	14.0496	0.475505
$874$	−15.9948	−0.541033
$875$	84.0456	2.84126
$876$	4.29795	0.145214
$877$	−42.5754	−1.43767	−0.718835	−	0.695181i	$-0.755324\pi$
$877$	−42.5754	−1.43767	−0.718835	+	0.695181i	$0.755324\pi$
$878$	15.8546	0.535066
$879$	−19.2439	−0.649082
$880$	100.578	3.39050
$881$	26.9102	0.906629	0.453315	−	0.891351i	$-0.350241\pi$
$881$	26.9102	0.906629	0.453315	+	0.891351i	$0.350241\pi$
$882$	−9.63696	−0.324493
$883$	−17.6909	−0.595345	−0.297672	−	0.954668i	$-0.596210\pi$
$883$	−17.6909	−0.595345	−0.297672	+	0.954668i	$0.596210\pi$
$884$	−12.3489	−0.415339
$885$	80.2593	2.69789
$886$	23.0727	0.775141
$887$	−36.1578	−1.21406	−0.607030	−	0.794679i	$-0.707639\pi$
$887$	−36.1578	−1.21406	−0.607030	+	0.794679i	$0.707639\pi$
$888$	−2.01934	−0.0677646
$889$	0.550620	0.0184672
$890$	30.1176	1.00955
$891$	23.6007	0.790652
$892$	0.475715	0.0159281
$893$	−44.5320	−1.49021
$894$	22.9912	0.768940
$895$	−20.1478	−0.673466
$896$	−38.9951	−1.30273
$897$	−29.8184	−0.995608
$898$	38.7875	1.29436
$899$	55.5447	1.85252
$900$	17.3091	0.576971
$901$	−55.4837	−1.84843
$902$	36.1908	1.20502
$903$	−65.6519	−2.18476
$904$	20.7792	0.691104
$905$	−89.7954	−2.98490
$906$	−15.3637	−0.510423
$907$	−4.78405	−0.158852	−0.0794259	−	0.996841i	$-0.525309\pi$
$907$	−4.78405	−0.158852	−0.0794259	+	0.996841i	$0.525309\pi$
$908$	−4.87722	−0.161856
$909$	28.3878	0.941562
$910$	82.6809	2.74085
$911$	−34.7536	−1.15144	−0.575719	−	0.817648i	$-0.695278\pi$
$911$	−34.7536	−1.15144	−0.575719	+	0.817648i	$0.695278\pi$
$912$	−51.0410	−1.69014
$913$	17.9932	0.595489
$914$	−16.3611	−0.541178
$915$	2.64944	0.0875877
$916$	2.98970	0.0987826
$917$	4.86453	0.160641
$918$	−35.6754	−1.17746
$919$	−37.6158	−1.24083	−0.620416	−	0.784273i	$-0.713036\pi$
$919$	−37.6158	−1.24083	−0.620416	+	0.784273i	$0.713036\pi$
$920$	26.0015	0.857244
$921$	−0.266993	−0.00879771
$922$	5.96881	0.196572
$923$	−6.97648	−0.229634
$924$	−14.5810	−0.479680
$925$	−3.58921	−0.118013
$926$	34.4390	1.13174
$927$	−31.8071	−1.04468
$928$	−13.4041	−0.440012
$929$	35.7829	1.17400	0.586999	−	0.809587i	$-0.300309\pi$
$929$	35.7829	1.17400	0.586999	+	0.809587i	$0.300309\pi$
$930$	137.249	4.50056
$931$	6.38835	0.209370
$932$	−2.40310	−0.0787162
$933$	−61.2739	−2.00602
$934$	45.6429	1.49348
$935$	−172.340	−5.63613
$936$	−46.5741	−1.52232
$937$	56.1336	1.83381	0.916903	−	0.399110i	$-0.130681\pi$
$937$	56.1336	1.83381	0.916903	+	0.399110i	$0.130681\pi$
$938$	−23.8451	−0.778571
$939$	−44.4238	−1.44971
$940$	−15.4241	−0.503077
$941$	−4.67130	−0.152280	−0.0761400	−	0.997097i	$-0.524260\pi$
$941$	−4.67130	−0.152280	−0.0761400	+	0.997097i	$0.524260\pi$
$942$	−63.1122	−2.05631
$943$	11.0516	0.359891
$944$	−33.4408	−1.08841
$945$	35.6858	1.16086
$946$	−68.8936	−2.23992
$947$	38.8181	1.26142	0.630710	−	0.776019i	$-0.282764\pi$
$947$	38.8181	1.26142	0.630710	+	0.776019i	$0.282764\pi$
$948$	2.75221	0.0893875
$949$	−20.5551	−0.667248
$950$	−76.8022	−2.49179
$951$	−54.2720	−1.75989
$952$	57.9298	1.87752
$953$	−26.3899	−0.854852	−0.427426	−	0.904050i	$-0.640579\pi$
$953$	−26.3899	−0.854852	−0.427426	+	0.904050i	$0.640579\pi$
$954$	44.5850	1.44349
$955$	−23.6252	−0.764494
$956$	7.86156	0.254261
$957$	96.9369	3.13352
$958$	65.8397	2.12718
$959$	−40.7094	−1.31457
$960$	67.5305	2.17954
$961$	35.3289	1.13964
$962$	−2.05767	−0.0663421
$963$	−33.9752	−1.09484
$964$	3.24580	0.104540
$965$	88.5084	2.84919
$966$	−29.8034	−0.958909
$967$	54.8154	1.76274	0.881372	−	0.472423i	$-0.156621\pi$
$967$	54.8154	1.76274	0.881372	+	0.472423i	$0.156621\pi$
$968$	44.0049	1.41437
$969$	87.4583	2.80957
$970$	−21.5917	−0.693268
$971$	−18.4377	−0.591694	−0.295847	−	0.955235i	$-0.595602\pi$
$971$	−18.4377	−0.591694	−0.295847	+	0.955235i	$0.595602\pi$
$972$	−7.27306	−0.233284
$973$	−12.7082	−0.407408
$974$	31.1526	0.998195
$975$	−143.179	−4.58539
$976$	−1.10391	−0.0353354
$977$	33.5679	1.07393	0.536966	−	0.843604i	$-0.319570\pi$
$977$	33.5679	1.07393	0.536966	+	0.843604i	$0.319570\pi$
$978$	−42.9955	−1.37485
$979$	25.4017	0.811840
$980$	2.21266	0.0706809
$981$	14.7183	0.469919
$982$	−11.0713	−0.353301
$983$	1.00000	0.0318950
$983$	1.00000	0.0318950
$984$	29.8559	0.951772
$985$	−77.0495	−2.45500
$986$	82.0562	2.61320
$987$	−82.9771	−2.64119
$988$	−6.57811	−0.209278
$989$	−21.0381	−0.668974
$990$	138.488	4.40142
$991$	35.9945	1.14340	0.571701	−	0.820462i	$-0.306284\pi$
$991$	35.9945	1.14340	0.571701	+	0.820462i	$0.306284\pi$
$992$	−16.0066	−0.508210
$993$	−19.6089	−0.622270
$994$	−6.97296	−0.221169
$995$	63.1207	2.00106
$996$	−3.16264	−0.100212
$997$	−46.4854	−1.47221	−0.736104	−	0.676868i	$-0.763337\pi$
$997$	−46.4854	−1.47221	−0.736104	+	0.676868i	$0.763337\pi$
$998$	28.4933	0.901940
$999$	−0.888110	−0.0280986

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.a.b.1.14	✓	54
3.2	odd	2		8847.2.a.g.1.41		54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.b.1.14	✓	54	1.1	even	1	trivial
8847.2.a.g.1.41		54	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-1.53339 q^{2} +2.66681 q^{3} +0.351281 q^{4} +4.12109 q^{5} -4.08926 q^{6} +2.92035 q^{7} +2.52813 q^{8} +4.11188 q^{9} +O(q^{10})\)	\(q-1.53339 q^{2} +2.66681 q^{3} +0.351281 q^{4} +4.12109 q^{5} -4.08926 q^{6} +2.92035 q^{7} +2.52813 q^{8} +4.11188 q^{9} -6.31924 q^{10} -5.32974 q^{11} +0.936800 q^{12} -4.48029 q^{13} -4.47803 q^{14} +10.9902 q^{15} -4.57916 q^{16} +7.84636 q^{17} -6.30510 q^{18} +4.17966 q^{19} +1.44766 q^{20} +7.78802 q^{21} +8.17256 q^{22} +2.49567 q^{23} +6.74203 q^{24} +11.9834 q^{25} +6.87002 q^{26} +2.96516 q^{27} +1.02586 q^{28} -6.82010 q^{29} -16.8522 q^{30} -8.14425 q^{31} +1.96538 q^{32} -14.2134 q^{33} -12.0315 q^{34} +12.0350 q^{35} +1.44442 q^{36} -0.299515 q^{37} -6.40904 q^{38} -11.9481 q^{39} +10.4186 q^{40} +4.42833 q^{41} -11.9421 q^{42} -8.42986 q^{43} -1.87224 q^{44} +16.9454 q^{45} -3.82683 q^{46} -10.6545 q^{47} -12.2118 q^{48} +1.52844 q^{49} -18.3752 q^{50} +20.9248 q^{51} -1.57384 q^{52} -7.07126 q^{53} -4.54674 q^{54} -21.9644 q^{55} +7.38301 q^{56} +11.1464 q^{57} +10.4579 q^{58} +7.30283 q^{59} +3.86064 q^{60} +0.241073 q^{61} +12.4883 q^{62} +12.0081 q^{63} +6.14463 q^{64} -18.4637 q^{65} +21.7947 q^{66} +5.32491 q^{67} +2.75628 q^{68} +6.65547 q^{69} -18.4544 q^{70} +1.55715 q^{71} +10.3953 q^{72} +4.58790 q^{73} +0.459273 q^{74} +31.9575 q^{75} +1.46823 q^{76} -15.5647 q^{77} +18.3210 q^{78} +2.93788 q^{79} -18.8712 q^{80} -4.42811 q^{81} -6.79034 q^{82} -3.37600 q^{83} +2.73578 q^{84} +32.3356 q^{85} +12.9263 q^{86} -18.1879 q^{87} -13.4743 q^{88} -4.76602 q^{89} -25.9839 q^{90} -13.0840 q^{91} +0.876681 q^{92} -21.7192 q^{93} +16.3374 q^{94} +17.2248 q^{95} +5.24131 q^{96} +3.41682 q^{97} -2.34369 q^{98} -21.9152 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9 + 15 * q^10 + 8 * q^11 + 10 * q^12 + 34 * q^13 + q^14 + 3 * q^15 + 80 * q^16 + 32 * q^17 + 28 * q^18 + 15 * q^19 + 4 * q^20 + 11 * q^21 + 25 * q^22 + 15 * q^23 - 7 * q^24 + 125 * q^25 - 14 * q^26 + 12 * q^27 + 78 * q^28 + 8 * q^29 - 32 * q^30 + 16 * q^31 + 36 * q^32 + 38 * q^33 - 8 * q^34 - 2 * q^35 + 65 * q^36 + 80 * q^37 - 14 * q^38 + 16 * q^39 + 36 * q^40 + 30 * q^41 - 10 * q^42 + 53 * q^43 + 6 * q^44 + 3 * q^45 + 24 * q^46 + 22 * q^47 + 7 * q^48 + 111 * q^49 + 14 * q^50 - 10 * q^51 + 45 * q^52 + 10 * q^53 - 8 * q^54 + 12 * q^55 - 30 * q^56 + 106 * q^57 + 61 * q^58 - 4 * q^59 - 61 * q^60 + 24 * q^61 - 12 * q^62 + 73 * q^63 + 86 * q^64 + 32 * q^65 - 43 * q^66 + 54 * q^67 + 33 * q^68 - 30 * q^69 - 21 * q^70 - 6 * q^71 + 60 * q^72 + 172 * q^73 - 32 * q^74 - 36 * q^75 + 7 * q^76 - 12 * q^77 - 3 * q^78 + 28 * q^79 - 66 * q^80 + 86 * q^81 + 4 * q^82 + 14 * q^83 - 58 * q^84 + 99 * q^85 - 31 * q^86 - 27 * q^87 + 5 * q^88 - 5 * q^89 - 45 * q^90 - 11 * q^91 + 20 * q^92 + 27 * q^93 - 39 * q^94 + 5 * q^95 - 87 * q^96 + 127 * q^97 - 29 * q^98 - 21 * q^99

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