LMFDB - Embedded newform 983.2.a.a.1.12

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:	$1$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-0.875382 q^{2} +0.413140 q^{3} -1.23371 q^{4} +0.141089 q^{5} -0.361655 q^{6} -0.646767 q^{7} +2.83073 q^{8} -2.82932 q^{9} +O(q^{10})$	\(q-0.875382 q^{2} +0.413140 q^{3} -1.23371 q^{4} +0.141089 q^{5} -0.361655 q^{6} -0.646767 q^{7} +2.83073 q^{8} -2.82932 q^{9} -0.123507 q^{10} -0.501317 q^{11} -0.509693 q^{12} +1.72158 q^{13} +0.566168 q^{14} +0.0582894 q^{15} -0.0105529 q^{16} +4.80400 q^{17} +2.47673 q^{18} +3.13365 q^{19} -0.174062 q^{20} -0.267205 q^{21} +0.438844 q^{22} -4.27374 q^{23} +1.16949 q^{24} -4.98009 q^{25} -1.50704 q^{26} -2.40832 q^{27} +0.797921 q^{28} -10.1235 q^{29} -0.0510255 q^{30} -4.85649 q^{31} -5.65222 q^{32} -0.207114 q^{33} -4.20533 q^{34} -0.0912517 q^{35} +3.49055 q^{36} +1.57659 q^{37} -2.74314 q^{38} +0.711252 q^{39} +0.399384 q^{40} +2.34470 q^{41} +0.233906 q^{42} -3.02394 q^{43} +0.618479 q^{44} -0.399185 q^{45} +3.74115 q^{46} +9.52006 q^{47} -0.00435982 q^{48} -6.58169 q^{49} +4.35948 q^{50} +1.98472 q^{51} -2.12392 q^{52} -1.35146 q^{53} +2.10820 q^{54} -0.0707303 q^{55} -1.83082 q^{56} +1.29464 q^{57} +8.86196 q^{58} -12.9068 q^{59} -0.0719120 q^{60} -3.19467 q^{61} +4.25128 q^{62} +1.82991 q^{63} +4.96895 q^{64} +0.242896 q^{65} +0.181304 q^{66} -3.20726 q^{67} -5.92673 q^{68} -1.76565 q^{69} +0.0798800 q^{70} -8.67396 q^{71} -8.00902 q^{72} -9.90341 q^{73} -1.38012 q^{74} -2.05747 q^{75} -3.86601 q^{76} +0.324236 q^{77} -0.622617 q^{78} +3.51750 q^{79} -0.00148890 q^{80} +7.49297 q^{81} -2.05251 q^{82} -0.509907 q^{83} +0.329653 q^{84} +0.677791 q^{85} +2.64710 q^{86} -4.18243 q^{87} -1.41909 q^{88} -14.3756 q^{89} +0.349439 q^{90} -1.11346 q^{91} +5.27254 q^{92} -2.00641 q^{93} -8.33369 q^{94} +0.442123 q^{95} -2.33515 q^{96} +5.28099 q^{97} +5.76149 q^{98} +1.41839 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9} - 17 q^{10} - 10 q^{11} - 10 q^{12} - 28 q^{13} + 5 q^{14} - 9 q^{15} + 3 q^{16} - 24 q^{17} - 23 q^{18} - 13 q^{19} - 4 q^{20} - 21 q^{21} - 21 q^{22} - 9 q^{23} - 19 q^{24} - 33 q^{25} + 2 q^{26} - 12 q^{27} - 58 q^{28} - 14 q^{29} - 8 q^{30} - 16 q^{31} - 27 q^{32} - 34 q^{33} - 6 q^{34} - 2 q^{35} - 6 q^{36} - 58 q^{37} + 6 q^{38} - 12 q^{39} - 24 q^{40} - 24 q^{41} + 22 q^{42} - 43 q^{43} - 19 q^{45} - 28 q^{46} + 2 q^{47} + 19 q^{48} - 21 q^{49} + 17 q^{50} - 6 q^{51} - 47 q^{52} - 16 q^{53} + 16 q^{54} - 16 q^{55} + 30 q^{56} - 70 q^{57} - 31 q^{58} + 12 q^{59} - q^{60} - 22 q^{61} - 15 q^{63} - 3 q^{64} - 24 q^{65} + 41 q^{66} - 38 q^{67} + 11 q^{68} + 2 q^{69} + 19 q^{70} + 2 q^{71} - 15 q^{72} - 124 q^{73} + 14 q^{74} + 8 q^{75} + 3 q^{76} - 20 q^{77} + 21 q^{78} - 16 q^{79} + 10 q^{80} - 36 q^{81} + 2 q^{82} + 12 q^{83} + 6 q^{84} - 73 q^{85} + 41 q^{86} - 15 q^{87} - 61 q^{88} - 3 q^{89} + 39 q^{90} + 5 q^{91} + 44 q^{92} - 21 q^{93} + 9 q^{94} + 17 q^{95} - 3 q^{96} - 105 q^{97} + 16 q^{98} - 15 q^{99}+O(q^{100}) \) 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9 - 17 * q^10 - 10 * q^11 - 10 * q^12 - 28 * q^13 + 5 * q^14 - 9 * q^15 + 3 * q^16 - 24 * q^17 - 23 * q^18 - 13 * q^19 - 4 * q^20 - 21 * q^21 - 21 * q^22 - 9 * q^23 - 19 * q^24 - 33 * q^25 + 2 * q^26 - 12 * q^27 - 58 * q^28 - 14 * q^29 - 8 * q^30 - 16 * q^31 - 27 * q^32 - 34 * q^33 - 6 * q^34 - 2 * q^35 - 6 * q^36 - 58 * q^37 + 6 * q^38 - 12 * q^39 - 24 * q^40 - 24 * q^41 + 22 * q^42 - 43 * q^43 - 19 * q^45 - 28 * q^46 + 2 * q^47 + 19 * q^48 - 21 * q^49 + 17 * q^50 - 6 * q^51 - 47 * q^52 - 16 * q^53 + 16 * q^54 - 16 * q^55 + 30 * q^56 - 70 * q^57 - 31 * q^58 + 12 * q^59 - q^60 - 22 * q^61 - 15 * q^63 - 3 * q^64 - 24 * q^65 + 41 * q^66 - 38 * q^67 + 11 * q^68 + 2 * q^69 + 19 * q^70 + 2 * q^71 - 15 * q^72 - 124 * q^73 + 14 * q^74 + 8 * q^75 + 3 * q^76 - 20 * q^77 + 21 * q^78 - 16 * q^79 + 10 * q^80 - 36 * q^81 + 2 * q^82 + 12 * q^83 + 6 * q^84 - 73 * q^85 + 41 * q^86 - 15 * q^87 - 61 * q^88 - 3 * q^89 + 39 * q^90 + 5 * q^91 + 44 * q^92 - 21 * q^93 + 9 * q^94 + 17 * q^95 - 3 * q^96 - 105 * q^97 + 16 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.875382	−0.618988	−0.309494	−	0.950901i	$-0.600160\pi$
$2$	−0.875382	−0.618988	−0.309494	+	0.950901i	$0.600160\pi$
$3$	0.413140	0.238526	0.119263	−	0.992863i	$-0.461947\pi$
$3$	0.413140	0.238526	0.119263	+	0.992863i	$0.461947\pi$
$4$	−1.23371	−0.616854
$5$	0.141089	0.0630969	0.0315484	−	0.999502i	$-0.489956\pi$
$5$	0.141089	0.0630969	0.0315484	+	0.999502i	$0.489956\pi$
$6$	−0.361655	−0.147645
$7$	−0.646767	−0.244455	−0.122228	−	0.992502i	$-0.539004\pi$
$7$	−0.646767	−0.244455	−0.122228	+	0.992502i	$0.539004\pi$
$8$	2.83073	1.00081
$9$	−2.82932	−0.943105
$10$	−0.123507	−0.0390562
$11$	−0.501317	−0.151153	−0.0755764	−	0.997140i	$-0.524080\pi$
$11$	−0.501317	−0.151153	−0.0755764	+	0.997140i	$0.524080\pi$
$12$	−0.509693	−0.147136
$13$	1.72158	0.477480	0.238740	−	0.971084i	$-0.423266\pi$
$13$	1.72158	0.477480	0.238740	+	0.971084i	$0.423266\pi$
$14$	0.566168	0.151315
$15$	0.0582894	0.0150503
$16$	−0.0105529	−0.00263822
$17$	4.80400	1.16514	0.582571	−	0.812780i	$-0.302047\pi$
$17$	4.80400	1.16514	0.582571	+	0.812780i	$0.302047\pi$
$18$	2.47673	0.583771
$19$	3.13365	0.718909	0.359455	−	0.933163i	$-0.382963\pi$
$19$	3.13365	0.718909	0.359455	+	0.933163i	$0.382963\pi$
$20$	−0.174062	−0.0389215
$21$	−0.267205	−0.0583089
$22$	0.438844	0.0935619
$23$	−4.27374	−0.891136	−0.445568	−	0.895248i	$-0.646998\pi$
$23$	−4.27374	−0.891136	−0.445568	+	0.895248i	$0.646998\pi$
$24$	1.16949	0.238720
$25$	−4.98009	−0.996019
$26$	−1.50704	−0.295555
$27$	−2.40832	−0.463482
$28$	0.797921	0.150793
$29$	−10.1235	−1.87989	−0.939947	−	0.341321i	$-0.889126\pi$
$29$	−10.1235	−1.87989	−0.939947	+	0.341321i	$0.889126\pi$
$30$	−0.0510255	−0.00931593
$31$	−4.85649	−0.872252	−0.436126	−	0.899886i	$-0.643650\pi$
$31$	−4.85649	−0.872252	−0.436126	+	0.899886i	$0.643650\pi$
$32$	−5.65222	−0.999180
$33$	−0.207114	−0.0360539
$34$	−4.20533	−0.721209
$35$	−0.0912517	−0.0154243
$36$	3.49055	0.581758
$37$	1.57659	0.259190	0.129595	−	0.991567i	$-0.458632\pi$
$37$	1.57659	0.259190	0.129595	+	0.991567i	$0.458632\pi$
$38$	−2.74314	−0.444996
$39$	0.711252	0.113892
$40$	0.399384	0.0631482
$41$	2.34470	0.366180	0.183090	−	0.983096i	$-0.441390\pi$
$41$	2.34470	0.366180	0.183090	+	0.983096i	$0.441390\pi$
$42$	0.233906	0.0360925
$43$	−3.02394	−0.461146	−0.230573	−	0.973055i	$-0.574060\pi$
$43$	−3.02394	−0.461146	−0.230573	+	0.973055i	$0.574060\pi$
$44$	0.618479	0.0932392
$45$	−0.399185	−0.0595070
$46$	3.74115	0.551603
$47$	9.52006	1.38864	0.694322	−	0.719665i	$-0.255704\pi$
$47$	9.52006	1.38864	0.694322	+	0.719665i	$0.255704\pi$
$48$	−0.00435982	−0.000629285 0
$49$	−6.58169	−0.940242
$50$	4.35948	0.616524
$51$	1.98472	0.277917
$52$	−2.12392	−0.294535
$53$	−1.35146	−0.185637	−0.0928186	−	0.995683i	$-0.529588\pi$
$53$	−1.35146	−0.185637	−0.0928186	+	0.995683i	$0.529588\pi$
$54$	2.10820	0.286890
$55$	−0.0707303	−0.00953727
$56$	−1.83082	−0.244654
$57$	1.29464	0.171479
$58$	8.86196	1.16363
$59$	−12.9068	−1.68032	−0.840162	−	0.542336i	$-0.817540\pi$
$59$	−12.9068	−1.68032	−0.840162	+	0.542336i	$0.817540\pi$
$60$	−0.0719120	−0.00928380
$61$	−3.19467	−0.409035	−0.204518	−	0.978863i	$-0.565563\pi$
$61$	−3.19467	−0.409035	−0.204518	+	0.978863i	$0.565563\pi$
$62$	4.25128	0.539913
$63$	1.82991	0.230547
$64$	4.96895	0.621119
$65$	0.242896	0.0301275
$66$	0.181304	0.0223170
$67$	−3.20726	−0.391829	−0.195915	−	0.980621i	$-0.562768\pi$
$67$	−3.20726	−0.391829	−0.195915	+	0.980621i	$0.562768\pi$
$68$	−5.92673	−0.718721
$69$	−1.76565	−0.212559
$70$	0.0798800	0.00954749
$71$	−8.67396	−1.02941	−0.514705	−	0.857368i	$-0.672098\pi$
$71$	−8.67396	−1.02941	−0.514705	+	0.857368i	$0.672098\pi$
$72$	−8.00902	−0.943872
$73$	−9.90341	−1.15911	−0.579553	−	0.814935i	$-0.696773\pi$
$73$	−9.90341	−1.15911	−0.579553	+	0.814935i	$0.696773\pi$
$74$	−1.38012	−0.160436
$75$	−2.05747	−0.237577
$76$	−3.86601	−0.443462
$77$	0.324236	0.0369501
$78$	−0.622617	−0.0704975
$79$	3.51750	0.395750	0.197875	−	0.980227i	$-0.436596\pi$
$79$	3.51750	0.395750	0.197875	+	0.980227i	$0.436596\pi$
$80$	−0.00148890	−0.000166464 0
$81$	7.49297	0.832553
$82$	−2.05251	−0.226661
$83$	−0.509907	−0.0559696	−0.0279848	−	0.999608i	$-0.508909\pi$
$83$	−0.509907	−0.0559696	−0.0279848	+	0.999608i	$0.508909\pi$
$84$	0.329653	0.0359681
$85$	0.677791	0.0735167
$86$	2.64710	0.285444
$87$	−4.18243	−0.448404
$88$	−1.41909	−0.151276
$89$	−14.3756	−1.52381	−0.761903	−	0.647691i	$-0.775735\pi$
$89$	−14.3756	−1.52381	−0.761903	+	0.647691i	$0.775735\pi$
$90$	0.349439	0.0368341
$91$	−1.11346	−0.116722
$92$	5.27254	0.549701
$93$	−2.00641	−0.208055
$94$	−8.33369	−0.859554
$95$	0.442123	0.0453609
$96$	−2.33515	−0.238331
$97$	5.28099	0.536203	0.268101	−	0.963391i	$-0.413604\pi$
$97$	5.28099	0.536203	0.268101	+	0.963391i	$0.413604\pi$
$98$	5.76149	0.581999
$99$	1.41839	0.142553
$100$	6.14398	0.614398
$101$	−4.64728	−0.462422	−0.231211	−	0.972904i	$-0.574269\pi$
$101$	−4.64728	−0.462422	−0.231211	+	0.972904i	$0.574269\pi$
$102$	−1.73739	−0.172027
$103$	−3.51525	−0.346368	−0.173184	−	0.984889i	$-0.555406\pi$
$103$	−3.51525	−0.346368	−0.173184	+	0.984889i	$0.555406\pi$
$104$	4.87332	0.477868
$105$	−0.0376997	−0.00367911
$106$	1.18304	0.114907
$107$	19.8692	1.92083	0.960414	−	0.278577i	$-0.0898626\pi$
$107$	19.8692	1.92083	0.960414	+	0.278577i	$0.0898626\pi$
$108$	2.97116	0.285900
$109$	10.2142	0.978346	0.489173	−	0.872187i	$-0.337299\pi$
$109$	10.2142	0.978346	0.489173	+	0.872187i	$0.337299\pi$
$110$	0.0619160	0.00590346
$111$	0.651353	0.0618237
$112$	0.00682527	0.000644927 0
$113$	−19.0287	−1.79007	−0.895034	−	0.445997i	$-0.852849\pi$
$113$	−19.0287	−1.79007	−0.895034	+	0.445997i	$0.852849\pi$
$114$	−1.13330	−0.106143
$115$	−0.602977	−0.0562279
$116$	12.4895	1.15962
$117$	−4.87089	−0.450314
$118$	11.2984	1.04010
$119$	−3.10707	−0.284825
$120$	0.165001	0.0150625
$121$	−10.7487	−0.977153
$122$	2.79655	0.253188
$123$	0.968688	0.0873436
$124$	5.99149	0.538051
$125$	−1.40808	−0.125943
$126$	−1.60187	−0.142706
$127$	−12.7265	−1.12929	−0.564645	−	0.825334i	$-0.690987\pi$
$127$	−12.7265	−1.12929	−0.564645	+	0.825334i	$0.690987\pi$
$128$	6.95470	0.614715
$129$	−1.24931	−0.109995
$130$	−0.212626	−0.0186486
$131$	−11.4493	−1.00033	−0.500164	−	0.865931i	$-0.666727\pi$
$131$	−11.4493	−1.00033	−0.500164	+	0.865931i	$0.666727\pi$
$132$	0.255518	0.0222400
$133$	−2.02674	−0.175741
$134$	2.80758	0.242538
$135$	−0.339787	−0.0292442
$136$	13.5988	1.16609
$137$	21.4090	1.82909	0.914546	−	0.404482i	$-0.132548\pi$
$137$	21.4090	1.82909	0.914546	+	0.404482i	$0.132548\pi$
$138$	1.54562	0.131572
$139$	−9.43635	−0.800381	−0.400190	−	0.916432i	$-0.631056\pi$
$139$	−9.43635	−0.800381	−0.400190	+	0.916432i	$0.631056\pi$
$140$	0.112578	0.00951456
$141$	3.93311	0.331228
$142$	7.59302	0.637192
$143$	−0.863057	−0.0721725
$144$	0.0298575	0.00248812
$145$	−1.42832	−0.118615
$146$	8.66926	0.717473
$147$	−2.71916	−0.224272
$148$	−1.94505	−0.159882
$149$	3.24185	0.265583	0.132791	−	0.991144i	$-0.457606\pi$
$149$	3.24185	0.265583	0.132791	+	0.991144i	$0.457606\pi$
$150$	1.80107	0.147057
$151$	16.0342	1.30485	0.652424	−	0.757854i	$-0.273752\pi$
$151$	16.0342	1.30485	0.652424	+	0.757854i	$0.273752\pi$
$152$	8.87051	0.719494
$153$	−13.5920	−1.09885
$154$	−0.283830	−0.0228717
$155$	−0.685197	−0.0550363
$156$	−0.877477	−0.0702544
$157$	−14.8968	−1.18889	−0.594447	−	0.804135i	$-0.702629\pi$
$157$	−14.8968	−1.18889	−0.594447	+	0.804135i	$0.702629\pi$
$158$	−3.07916	−0.244964
$159$	−0.558341	−0.0442793
$160$	−0.797465	−0.0630451
$161$	2.76411	0.217843
$162$	−6.55921	−0.515340
$163$	−8.94289	−0.700461	−0.350231	−	0.936664i	$-0.613897\pi$
$163$	−8.94289	−0.700461	−0.350231	+	0.936664i	$0.613897\pi$
$164$	−2.89267	−0.225880
$165$	−0.0292215	−0.00227489
$166$	0.446363	0.0346445
$167$	9.34682	0.723279	0.361639	−	0.932318i	$-0.382217\pi$
$167$	9.34682	0.723279	0.361639	+	0.932318i	$0.382217\pi$
$168$	−0.756385	−0.0583564
$169$	−10.0362	−0.772013
$170$	−0.593326	−0.0455060
$171$	−8.86609	−0.678007
$172$	3.73065	0.284459
$173$	26.2014	1.99205	0.996026	−	0.0890604i	$-0.0283864\pi$
$173$	26.2014	1.99205	0.996026	+	0.0890604i	$0.0283864\pi$
$174$	3.66123	0.277557
$175$	3.22096	0.243482
$176$	0.00529035	0.000398775 0
$177$	−5.33231	−0.400801
$178$	12.5841	0.943218
$179$	15.4259	1.15298	0.576492	−	0.817103i	$-0.304421\pi$
$179$	15.4259	1.15298	0.576492	+	0.817103i	$0.304421\pi$
$180$	0.492477	0.0367071
$181$	−14.6966	−1.09239	−0.546194	−	0.837659i	$-0.683924\pi$
$181$	−14.6966	−1.09239	−0.546194	+	0.837659i	$0.683924\pi$
$182$	0.974703	0.0722498
$183$	−1.31984	−0.0975657
$184$	−12.0978	−0.891861
$185$	0.222440	0.0163541
$186$	1.75637	0.128784
$187$	−2.40833	−0.176114
$188$	−11.7450	−0.856590
$189$	1.55762	0.113300
$190$	−0.387027	−0.0280779
$191$	20.0579	1.45134	0.725670	−	0.688043i	$-0.241530\pi$
$191$	20.0579	1.45134	0.725670	+	0.688043i	$0.241530\pi$
$192$	2.05287	0.148153
$193$	13.4642	0.969176	0.484588	−	0.874742i	$-0.338970\pi$
$193$	13.4642	0.969176	0.484588	+	0.874742i	$0.338970\pi$
$194$	−4.62288	−0.331903
$195$	0.100350	0.00718620
$196$	8.11988	0.579991
$197$	14.5285	1.03511	0.517556	−	0.855649i	$-0.326842\pi$
$197$	14.5285	1.03511	0.517556	+	0.855649i	$0.326842\pi$
$198$	−1.24163	−0.0882387
$199$	−4.96359	−0.351859	−0.175930	−	0.984403i	$-0.556293\pi$
$199$	−4.96359	−0.351859	−0.175930	+	0.984403i	$0.556293\pi$
$200$	−14.0973	−0.996829
$201$	−1.32505	−0.0934615
$202$	4.06815	0.286234
$203$	6.54757	0.459550
$204$	−2.44857	−0.171434
$205$	0.330811	0.0231048
$206$	3.07719	0.214398
$207$	12.0918	0.840435
$208$	−0.0181676	−0.00125970
$209$	−1.57095	−0.108665
$210$	0.0330016	0.00227733
$211$	−0.701002	−0.0482590	−0.0241295	−	0.999709i	$-0.507681\pi$
$211$	−0.701002	−0.0482590	−0.0241295	+	0.999709i	$0.507681\pi$
$212$	1.66730	0.114511
$213$	−3.58355	−0.245541
$214$	−17.3931	−1.18897
$215$	−0.426644	−0.0290969
$216$	−6.81730	−0.463859
$217$	3.14102	0.213226
$218$	−8.94135	−0.605585
$219$	−4.09149	−0.276477
$220$	0.0872605	0.00588310
$221$	8.27047	0.556332
$222$	−0.570182	−0.0382681
$223$	−20.3130	−1.36026	−0.680129	−	0.733092i	$-0.738076\pi$
$223$	−20.3130	−1.36026	−0.680129	+	0.733092i	$0.738076\pi$
$224$	3.65567	0.244255
$225$	14.0903	0.939351
$226$	16.6574	1.10803
$227$	18.2305	1.21000	0.604999	−	0.796226i	$-0.293174\pi$
$227$	18.2305	1.21000	0.604999	+	0.796226i	$0.293174\pi$
$228$	−1.59720	−0.105777
$229$	−15.3769	−1.01613	−0.508067	−	0.861318i	$-0.669640\pi$
$229$	−15.3769	−1.01613	−0.508067	+	0.861318i	$0.669640\pi$
$230$	0.527835	0.0348044
$231$	0.133955	0.00881356
$232$	−28.6570	−1.88142
$233$	27.0014	1.76892	0.884461	−	0.466614i	$-0.154526\pi$
$233$	27.0014	1.76892	0.884461	+	0.466614i	$0.154526\pi$
$234$	4.26389	0.278739
$235$	1.34317	0.0876191
$236$	15.9232	1.03651
$237$	1.45322	0.0943967
$238$	2.71987	0.176303
$239$	18.5645	1.20084	0.600420	−	0.799685i	$-0.295000\pi$
$239$	18.5645	1.20084	0.600420	+	0.799685i	$0.295000\pi$
$240$	−0.000615122 0	−3.97059e−5 0
$241$	28.0300	1.80557	0.902785	−	0.430093i	$-0.141519\pi$
$241$	28.0300	1.80557	0.902785	+	0.430093i	$0.141519\pi$
$242$	9.40920	0.604846
$243$	10.3206	0.662067
$244$	3.94129	0.252315
$245$	−0.928603	−0.0593263
$246$	−0.847971	−0.0540647
$247$	5.39483	0.343265
$248$	−13.7474	−0.872961
$249$	−0.210663	−0.0133502
$250$	1.23261	0.0779569
$251$	−21.6326	−1.36544	−0.682718	−	0.730682i	$-0.739202\pi$
$251$	−21.6326	−1.36544	−0.682718	+	0.730682i	$0.739202\pi$
$252$	−2.25757	−0.142214
$253$	2.14250	0.134698
$254$	11.1405	0.699018
$255$	0.280022	0.0175357
$256$	−16.0259	−1.00162
$257$	−10.9276	−0.681643	−0.340821	−	0.940128i	$-0.610705\pi$
$257$	−10.9276	−0.681643	−0.340821	+	0.940128i	$0.610705\pi$
$258$	1.09362	0.0680859
$259$	−1.01969	−0.0633604
$260$	−0.299662	−0.0185843
$261$	28.6427	1.77294
$262$	10.0225	0.619192
$263$	−17.6858	−1.09055	−0.545275	−	0.838257i	$-0.683575\pi$
$263$	−17.6858	−1.09055	−0.545275	+	0.838257i	$0.683575\pi$
$264$	−0.586283	−0.0360832
$265$	−0.190676	−0.0117131
$266$	1.77417	0.108782
$267$	−5.93911	−0.363468
$268$	3.95682	0.241701
$269$	−19.9070	−1.21375	−0.606877	−	0.794796i	$-0.707578\pi$
$269$	−19.9070	−1.21375	−0.606877	+	0.794796i	$0.707578\pi$
$270$	0.297443	0.0181018
$271$	24.1524	1.46716	0.733578	−	0.679605i	$-0.237849\pi$
$271$	24.1524	1.46716	0.733578	+	0.679605i	$0.237849\pi$
$272$	−0.0506961	−0.00307390
$273$	−0.460015	−0.0278414
$274$	−18.7410	−1.13219
$275$	2.49661	0.150551
$276$	2.17830	0.131118
$277$	−16.4533	−0.988583	−0.494292	−	0.869296i	$-0.664572\pi$
$277$	−16.4533	−0.988583	−0.494292	+	0.869296i	$0.664572\pi$
$278$	8.26041	0.495426
$279$	13.7405	0.822625
$280$	−0.258309	−0.0154369
$281$	−23.3247	−1.39143	−0.695716	−	0.718317i	$-0.744913\pi$
$281$	−23.3247	−1.39143	−0.695716	+	0.718317i	$0.744913\pi$
$282$	−3.44298	−0.205026
$283$	−19.2688	−1.14541	−0.572704	−	0.819762i	$-0.694106\pi$
$283$	−19.2688	−1.14541	−0.572704	+	0.819762i	$0.694106\pi$
$284$	10.7011	0.634995
$285$	0.182659	0.0108198
$286$	0.755505	0.0446739
$287$	−1.51647	−0.0895147
$288$	15.9919	0.942332
$289$	6.07841	0.357554
$290$	1.25032	0.0734215
$291$	2.18178	0.127898
$292$	12.2179	0.714999
$293$	18.0314	1.05341	0.526704	−	0.850049i	$-0.323428\pi$
$293$	18.0314	1.05341	0.526704	+	0.850049i	$0.323428\pi$
$294$	2.38030	0.138822
$295$	−1.82101	−0.106023
$296$	4.46290	0.259401
$297$	1.20733	0.0700566
$298$	−2.83785	−0.164393
$299$	−7.35758	−0.425500
$300$	2.53832	0.146550
$301$	1.95578	0.112729
$302$	−14.0361	−0.807686
$303$	−1.91998	−0.110300
$304$	−0.0330691	−0.00189664
$305$	−0.450732	−0.0258089
$306$	11.8982	0.680176
$307$	21.1810	1.20886	0.604431	−	0.796657i	$-0.293400\pi$
$307$	21.1810	1.20886	0.604431	+	0.796657i	$0.293400\pi$
$308$	−0.400012	−0.0227928
$309$	−1.45229	−0.0826179
$310$	0.599809	0.0340668
$311$	34.6597	1.96537	0.982685	−	0.185283i	$-0.0593201\pi$
$311$	34.6597	1.96537	0.982685	+	0.185283i	$0.0593201\pi$
$312$	2.01336	0.113984
$313$	0.646000	0.0365141	0.0182570	−	0.999833i	$-0.494188\pi$
$313$	0.646000	0.0365141	0.0182570	+	0.999833i	$0.494188\pi$
$314$	13.0404	0.735911
$315$	0.258180	0.0145468
$316$	−4.33957	−0.244120
$317$	−24.6656	−1.38536	−0.692678	−	0.721247i	$-0.743569\pi$
$317$	−24.6656	−1.38536	−0.692678	+	0.721247i	$0.743569\pi$
$318$	0.488761	0.0274084
$319$	5.07511	0.284151
$320$	0.701064	0.0391907
$321$	8.20875	0.458168
$322$	−2.41966	−0.134842
$323$	15.0541	0.837630
$324$	−9.24414	−0.513563
$325$	−8.57363	−0.475579
$326$	7.82844	0.433577
$327$	4.21990	0.233361
$328$	6.63720	0.366478
$329$	−6.15726	−0.339461
$330$	0.0255799	0.00140813
$331$	5.84543	0.321294	0.160647	−	0.987012i	$-0.448642\pi$
$331$	5.84543	0.321294	0.160647	+	0.987012i	$0.448642\pi$
$332$	0.629076	0.0345250
$333$	−4.46068	−0.244444
$334$	−8.18203	−0.447701
$335$	−0.452509	−0.0247232
$336$	0.00281979	0.000153832 0
$337$	−3.98926	−0.217309	−0.108655	−	0.994080i	$-0.534654\pi$
$337$	−3.98926	−0.217309	−0.108655	+	0.994080i	$0.534654\pi$
$338$	8.78548	0.477867
$339$	−7.86151	−0.426978
$340$	−0.836195	−0.0453491
$341$	2.43464	0.131843
$342$	7.76121	0.419678
$343$	8.78419	0.474302
$344$	−8.55994	−0.461521
$345$	−0.249114	−0.0134118
$346$	−22.9362	−1.23306
$347$	−4.67478	−0.250955	−0.125478	−	0.992096i	$-0.540046\pi$
$347$	−4.67478	−0.250955	−0.125478	+	0.992096i	$0.540046\pi$
$348$	5.15990	0.276600
$349$	−7.10413	−0.380275	−0.190138	−	0.981757i	$-0.560893\pi$
$349$	−7.10413	−0.380275	−0.190138	+	0.981757i	$0.560893\pi$
$350$	−2.81957	−0.150712
$351$	−4.14611	−0.221303
$352$	2.83355	0.151029
$353$	−6.00265	−0.319489	−0.159744	−	0.987158i	$-0.551067\pi$
$353$	−6.00265	−0.319489	−0.159744	+	0.987158i	$0.551067\pi$
$354$	4.66781	0.248091
$355$	−1.22380	−0.0649525
$356$	17.7352	0.939965
$357$	−1.28365	−0.0679381
$358$	−13.5035	−0.713683
$359$	10.8191	0.571008	0.285504	−	0.958377i	$-0.407839\pi$
$359$	10.8191	0.571008	0.285504	+	0.958377i	$0.407839\pi$
$360$	−1.12998	−0.0595554
$361$	−9.18023	−0.483170
$362$	12.8651	0.676175
$363$	−4.44070	−0.233077
$364$	1.37368	0.0720006
$365$	−1.39726	−0.0731359
$366$	1.15537	0.0603920
$367$	−2.73606	−0.142821	−0.0714106	−	0.997447i	$-0.522750\pi$
$367$	−2.73606	−0.142821	−0.0714106	+	0.997447i	$0.522750\pi$
$368$	0.0451003	0.00235102
$369$	−6.63389	−0.345347
$370$	−0.194720	−0.0101230
$371$	0.874079	0.0453799
$372$	2.47532	0.128339
$373$	−13.6287	−0.705666	−0.352833	−	0.935686i	$-0.614782\pi$
$373$	−13.6287	−0.705666	−0.352833	+	0.935686i	$0.614782\pi$
$374$	2.10821	0.109013
$375$	−0.581734	−0.0300406
$376$	26.9487	1.38977
$377$	−17.4285	−0.897612
$378$	−1.36351	−0.0701316
$379$	−25.0944	−1.28901	−0.644507	−	0.764599i	$-0.722937\pi$
$379$	−25.0944	−1.28901	−0.644507	+	0.764599i	$0.722937\pi$
$380$	−0.545451	−0.0279810
$381$	−5.25780	−0.269365
$382$	−17.5583	−0.898362
$383$	−3.78198	−0.193250	−0.0966251	−	0.995321i	$-0.530805\pi$
$383$	−3.78198	−0.193250	−0.0966251	+	0.995321i	$0.530805\pi$
$384$	2.87326	0.146626
$385$	0.0457460	0.00233143
$386$	−11.7863	−0.599909
$387$	8.55567	0.434909
$388$	−6.51519	−0.330759
$389$	6.09259	0.308907	0.154453	−	0.988000i	$-0.450638\pi$
$389$	6.09259	0.308907	0.154453	+	0.988000i	$0.450638\pi$
$390$	−0.0878443	−0.00444817
$391$	−20.5310	−1.03830
$392$	−18.6310	−0.941006
$393$	−4.73015	−0.238605
$394$	−12.7180	−0.640722
$395$	0.496280	0.0249706
$396$	−1.74987	−0.0879344
$397$	−16.2827	−0.817203	−0.408601	−	0.912713i	$-0.633983\pi$
$397$	−16.2827	−0.817203	−0.408601	+	0.912713i	$0.633983\pi$
$398$	4.34503	0.217797
$399$	−0.837328	−0.0419188
$400$	0.0525544	0.00262772
$401$	14.1616	0.707194	0.353597	−	0.935398i	$-0.384958\pi$
$401$	14.1616	0.707194	0.353597	+	0.935398i	$0.384958\pi$
$402$	1.15992	0.0578516
$403$	−8.36083	−0.416483
$404$	5.73339	0.285247
$405$	1.05718	0.0525315
$406$	−5.73163	−0.284456
$407$	−0.790373	−0.0391774
$408$	5.61821	0.278143
$409$	−6.13881	−0.303544	−0.151772	−	0.988415i	$-0.548498\pi$
$409$	−6.13881	−0.303544	−0.151772	+	0.988415i	$0.548498\pi$
$410$	−0.289586	−0.0143016
$411$	8.84489	0.436286
$412$	4.33679	0.213658
$413$	8.34770	0.410764
$414$	−10.5849	−0.520220
$415$	−0.0719422	−0.00353150
$416$	−9.73074	−0.477089
$417$	−3.89853	−0.190912
$418$	1.37518	0.0672625
$419$	−5.14521	−0.251360	−0.125680	−	0.992071i	$-0.540111\pi$
$419$	−5.14521	−0.251360	−0.125680	+	0.992071i	$0.540111\pi$
$420$	0.0465103	0.00226947
$421$	4.84040	0.235906	0.117953	−	0.993019i	$-0.462367\pi$
$421$	4.84040	0.235906	0.117953	+	0.993019i	$0.462367\pi$
$422$	0.613645	0.0298718
$423$	−26.9353	−1.30964
$424$	−3.82561	−0.185788
$425$	−23.9244	−1.16050
$426$	3.13698	0.151987
$427$	2.06621	0.0999908
$428$	−24.5128	−1.18487
$429$	−0.356563	−0.0172150
$430$	0.373476	0.0180106
$431$	26.1109	1.25772	0.628858	−	0.777520i	$-0.283523\pi$
$431$	26.1109	1.25772	0.628858	+	0.777520i	$0.283523\pi$
$432$	0.0254148	0.00122277
$433$	−3.08683	−0.148344	−0.0741718	−	0.997245i	$-0.523631\pi$
$433$	−3.08683	−0.148344	−0.0741718	+	0.997245i	$0.523631\pi$
$434$	−2.74959	−0.131985
$435$	−0.590095	−0.0282929
$436$	−12.6014	−0.603496
$437$	−13.3924	−0.640646
$438$	3.58161	0.171136
$439$	30.5631	1.45870	0.729349	−	0.684142i	$-0.239823\pi$
$439$	30.5631	1.45870	0.729349	+	0.684142i	$0.239823\pi$
$440$	−0.200218	−0.00954503
$441$	18.6217	0.886747
$442$	−7.23981	−0.344363
$443$	5.22559	0.248275	0.124138	−	0.992265i	$-0.460384\pi$
$443$	5.22559	0.248275	0.124138	+	0.992265i	$0.460384\pi$
$444$	−0.803578	−0.0381361
$445$	−2.02823	−0.0961474
$446$	17.7816	0.841984
$447$	1.33934	0.0633484
$448$	−3.21376	−0.151836
$449$	18.3223	0.864684	0.432342	−	0.901710i	$-0.357687\pi$
$449$	18.3223	0.864684	0.432342	+	0.901710i	$0.357687\pi$
$450$	−12.3344	−0.581447
$451$	−1.17544	−0.0553492
$452$	23.4758	1.10421
$453$	6.62438	0.311241
$454$	−15.9586	−0.748974
$455$	−0.157097	−0.00736482
$456$	3.66476	0.171618
$457$	−9.56711	−0.447530	−0.223765	−	0.974643i	$-0.571835\pi$
$457$	−9.56711	−0.447530	−0.223765	+	0.974643i	$0.571835\pi$
$458$	13.4606	0.628975
$459$	−11.5696	−0.540021
$460$	0.743897	0.0346844
$461$	20.5843	0.958706	0.479353	−	0.877622i	$-0.340871\pi$
$461$	20.5843	0.958706	0.479353	+	0.877622i	$0.340871\pi$
$462$	−0.117261	−0.00545549
$463$	−28.9670	−1.34621	−0.673104	−	0.739548i	$-0.735039\pi$
$463$	−28.9670	−1.34621	−0.673104	+	0.739548i	$0.735039\pi$
$464$	0.106833	0.00495958
$465$	−0.283082	−0.0131276
$466$	−23.6366	−1.09494
$467$	13.1137	0.606828	0.303414	−	0.952859i	$-0.401873\pi$
$467$	13.1137	0.606828	0.303414	+	0.952859i	$0.401873\pi$
$468$	6.00925	0.277778
$469$	2.07435	0.0957846
$470$	−1.17579	−0.0542352
$471$	−6.15445	−0.283582
$472$	−36.5357	−1.68169
$473$	1.51595	0.0697035
$474$	−1.27212	−0.0584304
$475$	−15.6059	−0.716047
$476$	3.83321	0.175695
$477$	3.82370	0.175075
$478$	−16.2511	−0.743306
$479$	−12.8125	−0.585417	−0.292708	−	0.956202i	$-0.594557\pi$
$479$	−12.8125	−0.585417	−0.292708	+	0.956202i	$0.594557\pi$
$480$	−0.329464	−0.0150379
$481$	2.71423	0.123758
$482$	−24.5369	−1.11763
$483$	1.14197	0.0519612
$484$	13.2607	0.602760
$485$	0.745088	0.0338327
$486$	−9.03447	−0.409812
$487$	6.88630	0.312048	0.156024	−	0.987753i	$-0.450132\pi$
$487$	6.88630	0.312048	0.156024	+	0.987753i	$0.450132\pi$
$488$	−9.04324	−0.409368
$489$	−3.69466	−0.167078
$490$	0.812882	0.0367223
$491$	10.4297	0.470685	0.235343	−	0.971912i	$-0.424379\pi$
$491$	10.4297	0.470685	0.235343	+	0.971912i	$0.424379\pi$
$492$	−1.19508	−0.0538782
$493$	−48.6335	−2.19034
$494$	−4.72253	−0.212477
$495$	0.200118	0.00899465
$496$	0.0512500	0.00230119
$497$	5.61003	0.251644
$498$	0.184410	0.00826362
$499$	33.6492	1.50634	0.753172	−	0.657824i	$-0.228523\pi$
$499$	33.6492	1.50634	0.753172	+	0.657824i	$0.228523\pi$
$500$	1.73716	0.0776881
$501$	3.86154	0.172521
$502$	18.9368	0.845189
$503$	−19.7810	−0.881991	−0.440996	−	0.897509i	$-0.645375\pi$
$503$	−19.7810	−0.881991	−0.440996	+	0.897509i	$0.645375\pi$
$504$	5.17997	0.230734
$505$	−0.655680	−0.0291774
$506$	−1.87550	−0.0833764
$507$	−4.14634	−0.184145
$508$	15.7007	0.696607
$509$	−21.3721	−0.947300	−0.473650	−	0.880713i	$-0.657064\pi$
$509$	−21.3721	−0.947300	−0.473650	+	0.880713i	$0.657064\pi$
$510$	−0.245126	−0.0108544
$511$	6.40520	0.283349
$512$	0.119392	0.00527643
$513$	−7.54684	−0.333201
$514$	9.56579	0.421929
$515$	−0.495963	−0.0218547
$516$	1.54128	0.0678510
$517$	−4.77257	−0.209898
$518$	0.892617	0.0392193
$519$	10.8248	0.475157
$520$	0.687571	0.0301520
$521$	−34.2459	−1.50034	−0.750171	−	0.661244i	$-0.770029\pi$
$521$	−34.2459	−1.50034	−0.750171	+	0.661244i	$0.770029\pi$
$522$	−25.0733	−1.09743
$523$	16.1226	0.704990	0.352495	−	0.935814i	$-0.385333\pi$
$523$	16.1226	0.704990	0.352495	+	0.935814i	$0.385333\pi$
$524$	14.1251	0.617056
$525$	1.33071	0.0580768
$526$	15.4818	0.675038
$527$	−23.3306	−1.01630
$528$	0.00218565	9.51183e−5 0
$529$	−4.73515	−0.205876
$530$	0.166914	0.00725028
$531$	36.5174	1.58472
$532$	2.50041	0.108406
$533$	4.03658	0.174844
$534$	5.19899	0.224982
$535$	2.80332	0.121198
$536$	−9.07888	−0.392148
$537$	6.37304	0.275017
$538$	17.4263	0.751300
$539$	3.29952	0.142120
$540$	0.419198	0.0180394
$541$	−10.7239	−0.461058	−0.230529	−	0.973065i	$-0.574046\pi$
$541$	−10.7239	−0.461058	−0.230529	+	0.973065i	$0.574046\pi$
$542$	−21.1426	−0.908152
$543$	−6.07174	−0.260563
$544$	−27.1533	−1.16419
$545$	1.44111	0.0617306
$546$	0.402688	0.0172335
$547$	−44.3998	−1.89840	−0.949200	−	0.314673i	$-0.898105\pi$
$547$	−44.3998	−1.89840	−0.949200	+	0.314673i	$0.898105\pi$
$548$	−26.4124	−1.12828
$549$	9.03873	0.385763
$550$	−2.18548	−0.0931894
$551$	−31.7236	−1.35147
$552$	−4.99808	−0.212732
$553$	−2.27500	−0.0967430
$554$	14.4029	0.611921
$555$	0.0918986	0.00390088
$556$	11.6417	0.493718
$557$	−22.7154	−0.962482	−0.481241	−	0.876588i	$-0.659814\pi$
$557$	−22.7154	−0.962482	−0.481241	+	0.876588i	$0.659814\pi$
$558$	−12.0282	−0.509195
$559$	−5.20595	−0.220188
$560$	0.000962969 0	4.06929e−5 0
$561$	−0.994976	−0.0420079
$562$	20.4180	0.861280
$563$	32.7910	1.38197	0.690987	−	0.722867i	$-0.257176\pi$
$563$	32.7910	1.38197	0.690987	+	0.722867i	$0.257176\pi$
$564$	−4.85231	−0.204319
$565$	−2.68474	−0.112948
$566$	16.8675	0.708995
$567$	−4.84621	−0.203522
$568$	−24.5536	−1.03025
$569$	−29.8745	−1.25241	−0.626203	−	0.779660i	$-0.715392\pi$
$569$	−29.8745	−1.25241	−0.626203	+	0.779660i	$0.715392\pi$
$570$	−0.159896	−0.00669731
$571$	−10.7709	−0.450748	−0.225374	−	0.974272i	$-0.572360\pi$
$571$	−10.7709	−0.450748	−0.225374	+	0.974272i	$0.572360\pi$
$572$	1.06476	0.0445199
$573$	8.28672	0.346183
$574$	1.32749	0.0554085
$575$	21.2836	0.887588
$576$	−14.0587	−0.585781
$577$	30.4642	1.26824	0.634122	−	0.773233i	$-0.281362\pi$
$577$	30.4642	1.26824	0.634122	+	0.773233i	$0.281362\pi$
$578$	−5.32093	−0.221322
$579$	5.56260	0.231174
$580$	1.76213	0.0731683
$581$	0.329791	0.0136820
$582$	−1.90989	−0.0791676
$583$	0.677510	0.0280596
$584$	−28.0338	−1.16005
$585$	−0.687228	−0.0284134
$586$	−15.7844	−0.652047
$587$	22.4174	0.925264	0.462632	−	0.886550i	$-0.346905\pi$
$587$	22.4174	0.925264	0.462632	+	0.886550i	$0.346905\pi$
$588$	3.35464	0.138343
$589$	−15.2186	−0.627069
$590$	1.59408	0.0656271
$591$	6.00229	0.246901
$592$	−0.0166376	−0.000683802 0
$593$	−42.4936	−1.74500	−0.872501	−	0.488613i	$-0.837503\pi$
$593$	−42.4936	−1.74500	−0.872501	+	0.488613i	$0.837503\pi$
$594$	−1.05688	−0.0433642
$595$	−0.438373	−0.0179715
$596$	−3.99949	−0.163826
$597$	−2.05065	−0.0839277
$598$	6.44069	0.263379
$599$	10.4547	0.427168	0.213584	−	0.976925i	$-0.431486\pi$
$599$	10.4547	0.427168	0.213584	+	0.976925i	$0.431486\pi$
$600$	−5.82415	−0.237770
$601$	−16.0149	−0.653262	−0.326631	−	0.945152i	$-0.605913\pi$
$601$	−16.0149	−0.653262	−0.326631	+	0.945152i	$0.605913\pi$
$602$	−1.71206	−0.0697782
$603$	9.07435	0.369536
$604$	−19.7816	−0.804900
$605$	−1.51652	−0.0616553
$606$	1.68071	0.0682743
$607$	−9.23760	−0.374943	−0.187471	−	0.982270i	$-0.560029\pi$
$607$	−9.23760	−0.374943	−0.187471	+	0.982270i	$0.560029\pi$
$608$	−17.7121	−0.718320
$609$	2.70506	0.109615
$610$	0.394563	0.0159754
$611$	16.3895	0.663050
$612$	16.7686	0.677830
$613$	−25.6816	−1.03727	−0.518635	−	0.854996i	$-0.673560\pi$
$613$	−25.6816	−1.03727	−0.518635	+	0.854996i	$0.673560\pi$
$614$	−18.5414	−0.748272
$615$	0.136671	0.00551111
$616$	0.917823	0.0369801
$617$	−10.5160	−0.423360	−0.211680	−	0.977339i	$-0.567893\pi$
$617$	−10.5160	−0.423360	−0.211680	+	0.977339i	$0.567893\pi$
$618$	1.27131	0.0511395
$619$	37.5389	1.50882	0.754408	−	0.656406i	$-0.227924\pi$
$619$	37.5389	1.50882	0.754408	+	0.656406i	$0.227924\pi$
$620$	0.845332	0.0339494
$621$	10.2925	0.413025
$622$	−30.3405	−1.21654
$623$	9.29764	0.372502
$624$	−0.00750577	−0.000300471 0
$625$	24.7018	0.988072
$626$	−0.565496	−0.0226018
$627$	−0.649023	−0.0259195
$628$	18.3783	0.733373
$629$	7.57395	0.301993
$630$	−0.226006	−0.00900429
$631$	−33.8557	−1.34777	−0.673886	−	0.738835i	$-0.735376\pi$
$631$	−33.8557	−1.34777	−0.673886	+	0.738835i	$0.735376\pi$
$632$	9.95709	0.396072
$633$	−0.289612	−0.0115110
$634$	21.5918	0.857520
$635$	−1.79556	−0.0712547
$636$	0.688829	0.0273139
$637$	−11.3309	−0.448947
$638$	−4.44265	−0.175886
$639$	24.5414	0.970841
$640$	0.981231	0.0387866
$641$	−2.20306	−0.0870156	−0.0435078	−	0.999053i	$-0.513853\pi$
$641$	−2.20306	−0.0870156	−0.0435078	+	0.999053i	$0.513853\pi$
$642$	−7.18579	−0.283601
$643$	6.22438	0.245465	0.122733	−	0.992440i	$-0.460834\pi$
$643$	6.22438	0.245465	0.122733	+	0.992440i	$0.460834\pi$
$644$	−3.41011	−0.134377
$645$	−0.176263	−0.00694036
$646$	−13.1780	−0.518483
$647$	−27.6713	−1.08787	−0.543935	−	0.839127i	$-0.683066\pi$
$647$	−27.6713	−1.08787	−0.543935	+	0.839127i	$0.683066\pi$
$648$	21.2106	0.833230
$649$	6.47041	0.253986
$650$	7.50519	0.294378
$651$	1.29768	0.0508601
$652$	11.0329	0.432082
$653$	17.3609	0.679383	0.339692	−	0.940537i	$-0.389677\pi$
$653$	17.3609	0.679383	0.339692	+	0.940537i	$0.389677\pi$
$654$	−3.69403	−0.144448
$655$	−1.61537	−0.0631176
$656$	−0.0247434	−0.000966066 0
$657$	28.0199	1.09316
$658$	5.38996	0.210122
$659$	21.3828	0.832955	0.416477	−	0.909146i	$-0.363265\pi$
$659$	21.3828	0.832955	0.416477	+	0.909146i	$0.363265\pi$
$660$	0.0360507	0.00140327
$661$	−16.4961	−0.641624	−0.320812	−	0.947143i	$-0.603956\pi$
$661$	−16.4961	−0.641624	−0.320812	+	0.947143i	$0.603956\pi$
$662$	−5.11698	−0.198877
$663$	3.41686	0.132700
$664$	−1.44341	−0.0560151
$665$	−0.285951	−0.0110887
$666$	3.90480	0.151308
$667$	43.2654	1.67524
$668$	−11.5312	−0.446157
$669$	−8.39210	−0.324457
$670$	0.396118	0.0153034
$671$	1.60154	0.0618269
$672$	1.51030	0.0582611
$673$	−17.0009	−0.655335	−0.327667	−	0.944793i	$-0.606263\pi$
$673$	−17.0009	−0.655335	−0.327667	+	0.944793i	$0.606263\pi$
$674$	3.49213	0.134512
$675$	11.9937	0.461636
$676$	12.3817	0.476219
$677$	18.4424	0.708798	0.354399	−	0.935094i	$-0.384686\pi$
$677$	18.4424	0.708798	0.354399	+	0.935094i	$0.384686\pi$
$678$	6.88182	0.264295
$679$	−3.41557	−0.131077
$680$	1.91864	0.0735765
$681$	7.53172	0.288616
$682$	−2.13124	−0.0816095
$683$	−48.3050	−1.84834	−0.924170	−	0.381981i	$-0.875242\pi$
$683$	−48.3050	−1.84834	−0.924170	+	0.381981i	$0.875242\pi$
$684$	10.9382	0.418231
$685$	3.02057	0.115410
$686$	−7.68952	−0.293587
$687$	−6.35280	−0.242374
$688$	0.0319113	0.00121661
$689$	−2.32664	−0.0886380
$690$	0.218069	0.00830176
$691$	13.9818	0.531893	0.265946	−	0.963988i	$-0.414316\pi$
$691$	13.9818	0.531893	0.265946	+	0.963988i	$0.414316\pi$
$692$	−32.3248	−1.22880
$693$	−0.917365	−0.0348478
$694$	4.09222	0.155338
$695$	−1.33136	−0.0505015
$696$	−11.8393	−0.448769
$697$	11.2639	0.426652
$698$	6.21883	0.235386
$699$	11.1554	0.421934
$700$	−3.97372	−0.150193
$701$	29.5875	1.11750	0.558752	−	0.829335i	$-0.311280\pi$
$701$	29.5875	1.11750	0.558752	+	0.829335i	$0.311280\pi$
$702$	3.62943	0.136984
$703$	4.94049	0.186334
$704$	−2.49102	−0.0938839
$705$	0.554919	0.0208994
$706$	5.25461	0.197760
$707$	3.00571	0.113041
$708$	6.57851	0.247236
$709$	−0.0478953	−0.00179875	−0.000899374	−	1.00000i	$-0.500286\pi$
$709$	−0.0478953	−0.00179875	−0.000899374		1.00000i	$0.500286\pi$
$710$	1.07129	0.0402048
$711$	−9.95212	−0.373234
$712$	−40.6933	−1.52505
$713$	20.7554	0.777295
$714$	1.12369	0.0420529
$715$	−0.121768	−0.00455386
$716$	−19.0310	−0.711222
$717$	7.66975	0.286432
$718$	−9.47081	−0.353447
$719$	24.9067	0.928861	0.464431	−	0.885609i	$-0.346259\pi$
$719$	24.9067	0.928861	0.464431	+	0.885609i	$0.346259\pi$
$720$	0.00421256	0.000156993 0
$721$	2.27355	0.0846715
$722$	8.03620	0.299076
$723$	11.5803	0.430676
$724$	18.1313	0.673843
$725$	50.4162	1.87241
$726$	3.88731	0.144272
$727$	36.4328	1.35122	0.675608	−	0.737261i	$-0.263881\pi$
$727$	36.4328	1.35122	0.675608	+	0.737261i	$0.263881\pi$
$728$	−3.15190	−0.116817
$729$	−18.2151	−0.674632
$730$	1.22314	0.0452703
$731$	−14.5270	−0.537300
$732$	1.62830	0.0601837
$733$	37.2893	1.37731	0.688655	−	0.725089i	$-0.258201\pi$
$733$	37.2893	1.37731	0.688655	+	0.725089i	$0.258201\pi$
$734$	2.39510	0.0884046
$735$	−0.383643	−0.0141509
$736$	24.1561	0.890406
$737$	1.60785	0.0592261
$738$	5.80719	0.213766
$739$	50.7692	1.86758	0.933788	−	0.357827i	$-0.116482\pi$
$739$	50.7692	1.86758	0.933788	+	0.357827i	$0.116482\pi$
$740$	−0.274425	−0.0100881
$741$	2.22882	0.0818776
$742$	−0.765153	−0.0280897
$743$	9.19011	0.337152	0.168576	−	0.985689i	$-0.446083\pi$
$743$	9.19011	0.337152	0.168576	+	0.985689i	$0.446083\pi$
$744$	−5.67960	−0.208224
$745$	0.457389	0.0167574
$746$	11.9303	0.436799
$747$	1.44269	0.0527852
$748$	2.97117	0.108637
$749$	−12.8507	−0.469556
$750$	0.509239	0.0185948
$751$	6.14900	0.224380	0.112190	−	0.993687i	$-0.464213\pi$
$751$	6.14900	0.224380	0.112190	+	0.993687i	$0.464213\pi$
$752$	−0.100464	−0.00366355
$753$	−8.93727	−0.325692
$754$	15.2566	0.555611
$755$	2.26225	0.0823318
$756$	−1.92165	−0.0698898
$757$	−43.6841	−1.58773	−0.793863	−	0.608096i	$-0.791934\pi$
$757$	−43.6841	−1.58773	−0.793863	+	0.608096i	$0.791934\pi$
$758$	21.9672	0.797884
$759$	0.885151	0.0321290
$760$	1.25153	0.0453978
$761$	22.6246	0.820142	0.410071	−	0.912053i	$-0.365504\pi$
$761$	22.6246	0.820142	0.410071	+	0.912053i	$0.365504\pi$
$762$	4.60258	0.166734
$763$	−6.60623	−0.239162
$764$	−24.7456	−0.895264
$765$	−1.91768	−0.0693340
$766$	3.31068	0.119620
$767$	−22.2201	−0.802321
$768$	−6.62094	−0.238913
$769$	−48.3230	−1.74257	−0.871286	−	0.490776i	$-0.836713\pi$
$769$	−48.3230	−1.74257	−0.871286	+	0.490776i	$0.836713\pi$
$770$	−0.0400452	−0.00144313
$771$	−4.51461	−0.162590
$772$	−16.6109	−0.597840
$773$	40.2060	1.44611	0.723055	−	0.690791i	$-0.242738\pi$
$773$	40.2060	1.44611	0.723055	+	0.690791i	$0.242738\pi$
$774$	−7.48948	−0.269204
$775$	24.1858	0.868779
$776$	14.9490	0.536639
$777$	−0.421274	−0.0151131
$778$	−5.33334	−0.191210
$779$	7.34747	0.263250
$780$	−0.123802	−0.00443283
$781$	4.34840	0.155598
$782$	17.9725	0.642695
$783$	24.3807	0.871296
$784$	0.0694559	0.00248057
$785$	−2.10177	−0.0750155
$786$	4.14069	0.147693
$787$	−49.4751	−1.76360	−0.881798	−	0.471627i	$-0.843667\pi$
$787$	−49.4751	−1.76360	−0.881798	+	0.471627i	$0.843667\pi$
$788$	−17.9239	−0.638513
$789$	−7.30668	−0.260125
$790$	−0.434435	−0.0154565
$791$	12.3071	0.437591
$792$	4.01506	0.142669
$793$	−5.49987	−0.195306
$794$	14.2535	0.505839
$795$	−0.0787757	−0.00279389
$796$	6.12361	0.217046
$797$	3.66345	0.129766	0.0648830	−	0.997893i	$-0.479333\pi$
$797$	3.66345	0.129766	0.0648830	+	0.997893i	$0.479333\pi$
$798$	0.732981	0.0259473
$799$	45.7344	1.61797
$800$	28.1486	0.995202
$801$	40.6730	1.43711
$802$	−12.3968	−0.437745
$803$	4.96475	0.175202
$804$	1.63472	0.0576521
$805$	0.389986	0.0137452
$806$	7.31892	0.257798
$807$	−8.22439	−0.289512
$808$	−13.1552	−0.462798
$809$	36.7273	1.29126	0.645632	−	0.763649i	$-0.276594\pi$
$809$	36.7273	1.29126	0.645632	+	0.763649i	$0.276594\pi$
$810$	−0.925432	−0.0325164
$811$	−11.8763	−0.417034	−0.208517	−	0.978019i	$-0.566864\pi$
$811$	−11.8763	−0.417034	−0.208517	+	0.978019i	$0.566864\pi$
$812$	−8.07779	−0.283475
$813$	9.97833	0.349955
$814$	0.691878	0.0242503
$815$	−1.26174	−0.0441969
$816$	−0.0209446	−0.000733206 0
$817$	−9.47596	−0.331522
$818$	5.37380	0.187890
$819$	3.15033	0.110082
$820$	−0.408124	−0.0142523
$821$	−15.0419	−0.524968	−0.262484	−	0.964936i	$-0.584542\pi$
$821$	−15.0419	−0.524968	−0.262484	+	0.964936i	$0.584542\pi$
$822$	−7.74266	−0.270056
$823$	17.7407	0.618404	0.309202	−	0.950996i	$-0.399938\pi$
$823$	17.7407	0.618404	0.309202	+	0.950996i	$0.399938\pi$
$824$	−9.95073	−0.346650
$825$	1.03145	0.0359104
$826$	−7.30743	−0.254258
$827$	−3.54199	−0.123167	−0.0615836	−	0.998102i	$-0.519615\pi$
$827$	−3.54199	−0.123167	−0.0615836	+	0.998102i	$0.519615\pi$
$828$	−14.9177	−0.518425
$829$	−33.1244	−1.15046	−0.575228	−	0.817993i	$-0.695087\pi$
$829$	−33.1244	−1.15046	−0.575228	+	0.817993i	$0.695087\pi$
$830$	0.0629769	0.00218596
$831$	−6.79751	−0.235803
$832$	8.55445	0.296572
$833$	−31.6184	−1.09551
$834$	3.41270	0.118172
$835$	1.31873	0.0456366
$836$	1.93810	0.0670305
$837$	11.6960	0.404272
$838$	4.50402	0.155589
$839$	−49.2267	−1.69950	−0.849748	−	0.527189i	$-0.823246\pi$
$839$	−49.2267	−1.69950	−0.849748	+	0.527189i	$0.823246\pi$
$840$	−0.106717	−0.00368210
$841$	73.4860	2.53400
$842$	−4.23719	−0.146023
$843$	−9.63634	−0.331893
$844$	0.864832	0.0297687
$845$	−1.41599	−0.0487116
$846$	23.5786	0.810650
$847$	6.95190	0.238870
$848$	0.0142618	0.000489752 0
$849$	−7.96068	−0.273210
$850$	20.9430	0.718337
$851$	−6.73795	−0.230974
$852$	4.42106	0.151463
$853$	54.0741	1.85146	0.925731	−	0.378181i	$-0.123450\pi$
$853$	54.0741	1.85146	0.925731	+	0.378181i	$0.123450\pi$
$854$	−1.80872	−0.0618931
$855$	−1.25091	−0.0427801
$856$	56.2443	1.92239
$857$	−49.4903	−1.69056	−0.845278	−	0.534327i	$-0.820565\pi$
$857$	−49.4903	−1.69056	−0.845278	+	0.534327i	$0.820565\pi$
$858$	0.312129	0.0106559
$859$	40.6288	1.38624	0.693119	−	0.720823i	$-0.256236\pi$
$859$	40.6288	1.38624	0.693119	+	0.720823i	$0.256236\pi$
$860$	0.526353	0.0179485
$861$	−0.626515	−0.0213516
$862$	−22.8570	−0.778512
$863$	38.9250	1.32502	0.662511	−	0.749053i	$-0.269491\pi$
$863$	38.9250	1.32502	0.662511	+	0.749053i	$0.269491\pi$
$864$	13.6124	0.463102
$865$	3.69672	0.125692
$866$	2.70216	0.0918230
$867$	2.51123	0.0852859
$868$	−3.87510	−0.131529
$869$	−1.76338	−0.0598187
$870$	0.516558	0.0175130
$871$	−5.52155	−0.187091
$872$	28.9137	0.979142
$873$	−14.9416	−0.505696
$874$	11.7235	0.396552
$875$	0.910700	0.0307873
$876$	5.04770	0.170546
$877$	22.9245	0.774106	0.387053	−	0.922057i	$-0.373493\pi$
$877$	22.9245	0.774106	0.387053	+	0.922057i	$0.373493\pi$
$878$	−26.7544	−0.902917
$879$	7.44950	0.251265
$880$	0.000746409 0	2.51615e−5 0
$881$	−56.1755	−1.89260	−0.946301	−	0.323288i	$-0.895212\pi$
$881$	−56.1755	−1.89260	−0.946301	+	0.323288i	$0.895212\pi$
$882$	−16.3011	−0.548886
$883$	−36.9956	−1.24500	−0.622501	−	0.782619i	$-0.713883\pi$
$883$	−36.9956	−1.24500	−0.622501	+	0.782619i	$0.713883\pi$
$884$	−10.2033	−0.343175
$885$	−0.752330	−0.0252893
$886$	−4.57439	−0.153680
$887$	−22.3328	−0.749862	−0.374931	−	0.927053i	$-0.622334\pi$
$887$	−22.3328	−0.749862	−0.374931	+	0.927053i	$0.622334\pi$
$888$	1.84380	0.0618740
$889$	8.23106	0.276061
$890$	1.77548	0.0595141
$891$	−3.75636	−0.125843
$892$	25.0603	0.839080
$893$	29.8326	0.998309
$894$	−1.17243	−0.0392119
$895$	2.17642	0.0727496
$896$	−4.49808	−0.150270
$897$	−3.03971	−0.101493
$898$	−16.0390	−0.535229
$899$	49.1649	1.63974
$900$	−17.3833	−0.579442
$901$	−6.49241	−0.216293
$902$	1.02896	0.0342605
$903$	0.808011	0.0268889
$904$	−53.8651	−1.79152
$905$	−2.07352	−0.0689263
$906$	−5.79886	−0.192654
$907$	−30.3321	−1.00716	−0.503580	−	0.863949i	$-0.667984\pi$
$907$	−30.3321	−1.00716	−0.503580	+	0.863949i	$0.667984\pi$
$908$	−22.4910	−0.746391
$909$	13.1486	0.436113
$910$	0.137520	0.00455874
$911$	46.1986	1.53063	0.765313	−	0.643658i	$-0.222584\pi$
$911$	46.1986	1.53063	0.765313	+	0.643658i	$0.222584\pi$
$912$	−0.0136621	−0.000452399 0
$913$	0.255625	0.00845996
$914$	8.37487	0.277016
$915$	−0.186215	−0.00615609
$916$	18.9706	0.626805
$917$	7.40502	0.244535
$918$	10.1278	0.334267
$919$	41.7738	1.37799	0.688995	−	0.724766i	$-0.258052\pi$
$919$	41.7738	1.37799	0.688995	+	0.724766i	$0.258052\pi$
$920$	−1.70686	−0.0562736
$921$	8.75070	0.288345
$922$	−18.0191	−0.593428
$923$	−14.9329	−0.491522
$924$	−0.165261	−0.00543668
$925$	−7.85158	−0.258158
$926$	25.3571	0.833287
$927$	9.94576	0.326662
$928$	57.2204	1.87835
$929$	−40.3179	−1.32279	−0.661394	−	0.750039i	$-0.730035\pi$
$929$	−40.3179	−1.32279	−0.661394	+	0.750039i	$0.730035\pi$
$930$	0.247805	0.00812583
$931$	−20.6247	−0.675948
$932$	−33.3119	−1.09117
$933$	14.3193	0.468792
$934$	−11.4795	−0.375619
$935$	−0.339788	−0.0111123
$936$	−13.7882	−0.450680
$937$	6.91683	0.225963	0.112981	−	0.993597i	$-0.463960\pi$
$937$	6.91683	0.225963	0.112981	+	0.993597i	$0.463960\pi$
$938$	−1.81585	−0.0592895
$939$	0.266888	0.00870956
$940$	−1.65708	−0.0540481
$941$	−28.7366	−0.936787	−0.468394	−	0.883520i	$-0.655167\pi$
$941$	−28.7366	−0.936787	−0.468394	+	0.883520i	$0.655167\pi$
$942$	5.38750	0.175534
$943$	−10.0206	−0.326317
$944$	0.136204	0.00443307
$945$	0.219763	0.00714890
$946$	−1.32704	−0.0431457
$947$	−58.0650	−1.88686	−0.943429	−	0.331574i	$-0.892420\pi$
$947$	−58.0650	−1.88686	−0.943429	+	0.331574i	$0.892420\pi$
$948$	−1.79285	−0.0582289
$949$	−17.0495	−0.553450
$950$	13.6611	0.443225
$951$	−10.1903	−0.330444
$952$	−8.79527	−0.285056
$953$	12.3611	0.400415	0.200208	−	0.979753i	$-0.435838\pi$
$953$	12.3611	0.400415	0.200208	+	0.979753i	$0.435838\pi$
$954$	−3.34720	−0.108370
$955$	2.82995	0.0915750
$956$	−22.9032	−0.740743
$957$	2.09673	0.0677775
$958$	11.2158	0.362366
$959$	−13.8466	−0.447131
$960$	0.289637	0.00934800
$961$	−7.41450	−0.239177
$962$	−2.37599	−0.0766049
$963$	−56.2162	−1.81154
$964$	−34.5808	−1.11377
$965$	1.89965	0.0611520
$966$	−0.999655	−0.0321634
$967$	39.6606	1.27540	0.637700	−	0.770285i	$-0.279886\pi$
$967$	39.6606	1.27540	0.637700	+	0.770285i	$0.279886\pi$
$968$	−30.4266	−0.977948
$969$	6.21943	0.199797
$970$	−0.652237	−0.0209421
$971$	54.6196	1.75282	0.876412	−	0.481561i	$-0.159930\pi$
$971$	54.6196	1.75282	0.876412	+	0.481561i	$0.159930\pi$
$972$	−12.7326	−0.408398
$973$	6.10312	0.195657
$974$	−6.02814	−0.193154
$975$	−3.54210	−0.113438
$976$	0.0337130	0.00107913
$977$	29.5455	0.945243	0.472621	−	0.881266i	$-0.343308\pi$
$977$	29.5455	0.945243	0.472621	+	0.881266i	$0.343308\pi$
$978$	3.23424	0.103420
$979$	7.20672	0.230328
$980$	1.14562	0.0365956
$981$	−28.8993	−0.922684
$982$	−9.12996	−0.291349
$983$	−1.00000	−0.0318950
$983$	−1.00000	−0.0318950
$984$	2.74209	0.0874147
$985$	2.04981	0.0653123
$986$	42.5729	1.35580
$987$	−2.54381	−0.0809703
$988$	−6.65564	−0.211744
$989$	12.9235	0.410944
$990$	−0.175180	−0.00556758
$991$	−22.9959	−0.730488	−0.365244	−	0.930912i	$-0.619014\pi$
$991$	−22.9959	−0.730488	−0.365244	+	0.930912i	$0.619014\pi$
$992$	27.4499	0.871537
$993$	2.41498	0.0766370
$994$	−4.91092	−0.155765
$995$	−0.700307	−0.0222012
$996$	0.259896	0.00823512
$997$	3.04294	0.0963708	0.0481854	−	0.998838i	$-0.484656\pi$
$997$	3.04294	0.0963708	0.0481854	+	0.998838i	$0.484656\pi$
$998$	−29.4559	−0.932409
$999$	−3.79694	−0.120130

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.a.a.1.12	✓	28
3.2	odd	2		8847.2.a.b.1.17		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.a.1.12	✓	28	1.1	even	1	trivial
8847.2.a.b.1.17		28	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)

\(f(q)\)	\(=\)	\(q-0.875382 q^{2} +0.413140 q^{3} -1.23371 q^{4} +0.141089 q^{5} -0.361655 q^{6} -0.646767 q^{7} +2.83073 q^{8} -2.82932 q^{9} +O(q^{10})\)	\(q-0.875382 q^{2} +0.413140 q^{3} -1.23371 q^{4} +0.141089 q^{5} -0.361655 q^{6} -0.646767 q^{7} +2.83073 q^{8} -2.82932 q^{9} -0.123507 q^{10} -0.501317 q^{11} -0.509693 q^{12} +1.72158 q^{13} +0.566168 q^{14} +0.0582894 q^{15} -0.0105529 q^{16} +4.80400 q^{17} +2.47673 q^{18} +3.13365 q^{19} -0.174062 q^{20} -0.267205 q^{21} +0.438844 q^{22} -4.27374 q^{23} +1.16949 q^{24} -4.98009 q^{25} -1.50704 q^{26} -2.40832 q^{27} +0.797921 q^{28} -10.1235 q^{29} -0.0510255 q^{30} -4.85649 q^{31} -5.65222 q^{32} -0.207114 q^{33} -4.20533 q^{34} -0.0912517 q^{35} +3.49055 q^{36} +1.57659 q^{37} -2.74314 q^{38} +0.711252 q^{39} +0.399384 q^{40} +2.34470 q^{41} +0.233906 q^{42} -3.02394 q^{43} +0.618479 q^{44} -0.399185 q^{45} +3.74115 q^{46} +9.52006 q^{47} -0.00435982 q^{48} -6.58169 q^{49} +4.35948 q^{50} +1.98472 q^{51} -2.12392 q^{52} -1.35146 q^{53} +2.10820 q^{54} -0.0707303 q^{55} -1.83082 q^{56} +1.29464 q^{57} +8.86196 q^{58} -12.9068 q^{59} -0.0719120 q^{60} -3.19467 q^{61} +4.25128 q^{62} +1.82991 q^{63} +4.96895 q^{64} +0.242896 q^{65} +0.181304 q^{66} -3.20726 q^{67} -5.92673 q^{68} -1.76565 q^{69} +0.0798800 q^{70} -8.67396 q^{71} -8.00902 q^{72} -9.90341 q^{73} -1.38012 q^{74} -2.05747 q^{75} -3.86601 q^{76} +0.324236 q^{77} -0.622617 q^{78} +3.51750 q^{79} -0.00148890 q^{80} +7.49297 q^{81} -2.05251 q^{82} -0.509907 q^{83} +0.329653 q^{84} +0.677791 q^{85} +2.64710 q^{86} -4.18243 q^{87} -1.41909 q^{88} -14.3756 q^{89} +0.349439 q^{90} -1.11346 q^{91} +5.27254 q^{92} -2.00641 q^{93} -8.33369 q^{94} +0.442123 q^{95} -2.33515 q^{96} +5.28099 q^{97} +5.76149 q^{98} +1.41839 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9} - 17 q^{10} - 10 q^{11} - 10 q^{12} - 28 q^{13} + 5 q^{14} - 9 q^{15} + 3 q^{16} - 24 q^{17} - 23 q^{18} - 13 q^{19} - 4 q^{20} - 21 q^{21} - 21 q^{22} - 9 q^{23} - 19 q^{24} - 33 q^{25} + 2 q^{26} - 12 q^{27} - 58 q^{28} - 14 q^{29} - 8 q^{30} - 16 q^{31} - 27 q^{32} - 34 q^{33} - 6 q^{34} - 2 q^{35} - 6 q^{36} - 58 q^{37} + 6 q^{38} - 12 q^{39} - 24 q^{40} - 24 q^{41} + 22 q^{42} - 43 q^{43} - 19 q^{45} - 28 q^{46} + 2 q^{47} + 19 q^{48} - 21 q^{49} + 17 q^{50} - 6 q^{51} - 47 q^{52} - 16 q^{53} + 16 q^{54} - 16 q^{55} + 30 q^{56} - 70 q^{57} - 31 q^{58} + 12 q^{59} - q^{60} - 22 q^{61} - 15 q^{63} - 3 q^{64} - 24 q^{65} + 41 q^{66} - 38 q^{67} + 11 q^{68} + 2 q^{69} + 19 q^{70} + 2 q^{71} - 15 q^{72} - 124 q^{73} + 14 q^{74} + 8 q^{75} + 3 q^{76} - 20 q^{77} + 21 q^{78} - 16 q^{79} + 10 q^{80} - 36 q^{81} + 2 q^{82} + 12 q^{83} + 6 q^{84} - 73 q^{85} + 41 q^{86} - 15 q^{87} - 61 q^{88} - 3 q^{89} + 39 q^{90} + 5 q^{91} + 44 q^{92} - 21 q^{93} + 9 q^{94} + 17 q^{95} - 3 q^{96} - 105 q^{97} + 16 q^{98} - 15 q^{99}+O(q^{100}) \) 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9 - 17 * q^10 - 10 * q^11 - 10 * q^12 - 28 * q^13 + 5 * q^14 - 9 * q^15 + 3 * q^16 - 24 * q^17 - 23 * q^18 - 13 * q^19 - 4 * q^20 - 21 * q^21 - 21 * q^22 - 9 * q^23 - 19 * q^24 - 33 * q^25 + 2 * q^26 - 12 * q^27 - 58 * q^28 - 14 * q^29 - 8 * q^30 - 16 * q^31 - 27 * q^32 - 34 * q^33 - 6 * q^34 - 2 * q^35 - 6 * q^36 - 58 * q^37 + 6 * q^38 - 12 * q^39 - 24 * q^40 - 24 * q^41 + 22 * q^42 - 43 * q^43 - 19 * q^45 - 28 * q^46 + 2 * q^47 + 19 * q^48 - 21 * q^49 + 17 * q^50 - 6 * q^51 - 47 * q^52 - 16 * q^53 + 16 * q^54 - 16 * q^55 + 30 * q^56 - 70 * q^57 - 31 * q^58 + 12 * q^59 - q^60 - 22 * q^61 - 15 * q^63 - 3 * q^64 - 24 * q^65 + 41 * q^66 - 38 * q^67 + 11 * q^68 + 2 * q^69 + 19 * q^70 + 2 * q^71 - 15 * q^72 - 124 * q^73 + 14 * q^74 + 8 * q^75 + 3 * q^76 - 20 * q^77 + 21 * q^78 - 16 * q^79 + 10 * q^80 - 36 * q^81 + 2 * q^82 + 12 * q^83 + 6 * q^84 - 73 * q^85 + 41 * q^86 - 15 * q^87 - 61 * q^88 - 3 * q^89 + 39 * q^90 + 5 * q^91 + 44 * q^92 - 21 * q^93 + 9 * q^94 + 17 * q^95 - 3 * q^96 - 105 * q^97 + 16 * q^98 - 15 * q^99

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