LMFDB - Embedded newform 2679.2.a.n.1.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2679,2,Mod(1,2679)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2679, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2679.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2679 = 3 \cdot 19 \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2679.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:	$21.3919227015$
Analytic rank:	$0$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
Character	$\chi$	$=$	2679.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.70026 q^{2} +1.00000 q^{3} +5.29141 q^{4} +2.20508 q^{5} +2.70026 q^{6} +0.381908 q^{7} +8.88768 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.70026 q^{2} +1.00000 q^{3} +5.29141 q^{4} +2.20508 q^{5} +2.70026 q^{6} +0.381908 q^{7} +8.88768 q^{8} +1.00000 q^{9} +5.95430 q^{10} -0.541461 q^{11} +5.29141 q^{12} -4.39015 q^{13} +1.03125 q^{14} +2.20508 q^{15} +13.4162 q^{16} -7.56447 q^{17} +2.70026 q^{18} +1.00000 q^{19} +11.6680 q^{20} +0.381908 q^{21} -1.46209 q^{22} +4.83305 q^{23} +8.88768 q^{24} -0.137605 q^{25} -11.8545 q^{26} +1.00000 q^{27} +2.02083 q^{28} -2.92584 q^{29} +5.95430 q^{30} +10.0216 q^{31} +18.4520 q^{32} -0.541461 q^{33} -20.4261 q^{34} +0.842139 q^{35} +5.29141 q^{36} -6.82713 q^{37} +2.70026 q^{38} -4.39015 q^{39} +19.5981 q^{40} -1.66489 q^{41} +1.03125 q^{42} -8.47623 q^{43} -2.86509 q^{44} +2.20508 q^{45} +13.0505 q^{46} +1.00000 q^{47} +13.4162 q^{48} -6.85415 q^{49} -0.371569 q^{50} -7.56447 q^{51} -23.2301 q^{52} +5.12841 q^{53} +2.70026 q^{54} -1.19397 q^{55} +3.39428 q^{56} +1.00000 q^{57} -7.90055 q^{58} -6.38720 q^{59} +11.6680 q^{60} +9.65918 q^{61} +27.0609 q^{62} +0.381908 q^{63} +22.9928 q^{64} -9.68064 q^{65} -1.46209 q^{66} +6.65611 q^{67} -40.0268 q^{68} +4.83305 q^{69} +2.27400 q^{70} +8.57056 q^{71} +8.88768 q^{72} -8.65829 q^{73} -18.4350 q^{74} -0.137605 q^{75} +5.29141 q^{76} -0.206788 q^{77} -11.8545 q^{78} -2.49612 q^{79} +29.5839 q^{80} +1.00000 q^{81} -4.49563 q^{82} +5.42636 q^{83} +2.02083 q^{84} -16.6803 q^{85} -22.8880 q^{86} -2.92584 q^{87} -4.81233 q^{88} -12.6622 q^{89} +5.95430 q^{90} -1.67663 q^{91} +25.5737 q^{92} +10.0216 q^{93} +2.70026 q^{94} +2.20508 q^{95} +18.4520 q^{96} -8.67832 q^{97} -18.5080 q^{98} -0.541461 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q + 5 q^{2} + 23 q^{3} + 25 q^{4} + 12 q^{5} + 5 q^{6} - 2 q^{7} + 12 q^{8} + 23 q^{9}+O(q^{10}) $ 23 * q + 5 * q^2 + 23 * q^3 + 25 * q^4 + 12 * q^5 + 5 * q^6 - 2 * q^7 + 12 * q^8 + 23 * q^9	\( 23 q + 5 q^{2} + 23 q^{3} + 25 q^{4} + 12 q^{5} + 5 q^{6} - 2 q^{7} + 12 q^{8} + 23 q^{9} + q^{10} + 13 q^{11} + 25 q^{12} + 5 q^{13} + 11 q^{14} + 12 q^{15} + 33 q^{16} + 22 q^{17} + 5 q^{18} + 23 q^{19} + 23 q^{20} - 2 q^{21} + q^{22} + 23 q^{23} + 12 q^{24} + 31 q^{25} + 21 q^{26} + 23 q^{27} - 22 q^{28} + 24 q^{29} + q^{30} + 20 q^{31} + 19 q^{32} + 13 q^{33} - 14 q^{34} + 15 q^{35} + 25 q^{36} + 8 q^{37} + 5 q^{38} + 5 q^{39} - 15 q^{40} + 28 q^{41} + 11 q^{42} - 6 q^{43} + q^{44} + 12 q^{45} + 29 q^{46} + 23 q^{47} + 33 q^{48} + 39 q^{49} + 27 q^{50} + 22 q^{51} + 12 q^{52} + 22 q^{53} + 5 q^{54} - 28 q^{55} + 30 q^{56} + 23 q^{57} - 5 q^{58} + 53 q^{59} + 23 q^{60} + 4 q^{61} + 38 q^{62} - 2 q^{63} + 30 q^{64} + 27 q^{65} + q^{66} - 6 q^{68} + 23 q^{69} + 30 q^{70} + 54 q^{71} + 12 q^{72} + 15 q^{73} - 12 q^{74} + 31 q^{75} + 25 q^{76} + 33 q^{77} + 21 q^{78} - 8 q^{79} + 45 q^{80} + 23 q^{81} - 69 q^{82} + 20 q^{83} - 22 q^{84} - 25 q^{85} + 50 q^{86} + 24 q^{87} + 48 q^{88} + 26 q^{89} + q^{90} + 11 q^{91} + 81 q^{92} + 20 q^{93} + 5 q^{94} + 12 q^{95} + 19 q^{96} - 4 q^{97} - 55 q^{98} + 13 q^{99}+O(q^{100}) \) 23 * q + 5 * q^2 + 23 * q^3 + 25 * q^4 + 12 * q^5 + 5 * q^6 - 2 * q^7 + 12 * q^8 + 23 * q^9 + q^10 + 13 * q^11 + 25 * q^12 + 5 * q^13 + 11 * q^14 + 12 * q^15 + 33 * q^16 + 22 * q^17 + 5 * q^18 + 23 * q^19 + 23 * q^20 - 2 * q^21 + q^22 + 23 * q^23 + 12 * q^24 + 31 * q^25 + 21 * q^26 + 23 * q^27 - 22 * q^28 + 24 * q^29 + q^30 + 20 * q^31 + 19 * q^32 + 13 * q^33 - 14 * q^34 + 15 * q^35 + 25 * q^36 + 8 * q^37 + 5 * q^38 + 5 * q^39 - 15 * q^40 + 28 * q^41 + 11 * q^42 - 6 * q^43 + q^44 + 12 * q^45 + 29 * q^46 + 23 * q^47 + 33 * q^48 + 39 * q^49 + 27 * q^50 + 22 * q^51 + 12 * q^52 + 22 * q^53 + 5 * q^54 - 28 * q^55 + 30 * q^56 + 23 * q^57 - 5 * q^58 + 53 * q^59 + 23 * q^60 + 4 * q^61 + 38 * q^62 - 2 * q^63 + 30 * q^64 + 27 * q^65 + q^66 - 6 * q^68 + 23 * q^69 + 30 * q^70 + 54 * q^71 + 12 * q^72 + 15 * q^73 - 12 * q^74 + 31 * q^75 + 25 * q^76 + 33 * q^77 + 21 * q^78 - 8 * q^79 + 45 * q^80 + 23 * q^81 - 69 * q^82 + 20 * q^83 - 22 * q^84 - 25 * q^85 + 50 * q^86 + 24 * q^87 + 48 * q^88 + 26 * q^89 + q^90 + 11 * q^91 + 81 * q^92 + 20 * q^93 + 5 * q^94 + 12 * q^95 + 19 * q^96 - 4 * q^97 - 55 * q^98 + 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.70026	1.90937	0.954687	−	0.297612i	$-0.0961903\pi$
$2$	2.70026	1.90937	0.954687	+	0.297612i	$0.0961903\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.29141	2.64571
$5$	2.20508	0.986144	0.493072	−	0.869989i	$-0.335874\pi$
$5$	2.20508	0.986144	0.493072	+	0.869989i	$0.335874\pi$
$6$	2.70026	1.10238
$7$	0.381908	0.144348	0.0721738	−	0.997392i	$-0.477006\pi$
$7$	0.381908	0.144348	0.0721738	+	0.997392i	$0.477006\pi$
$8$	8.88768	3.14227
$9$	1.00000	0.333333
$10$	5.95430	1.88292
$11$	−0.541461	−0.163256	−0.0816282	−	0.996663i	$-0.526012\pi$
$11$	−0.541461	−0.163256	−0.0816282	+	0.996663i	$0.526012\pi$
$12$	5.29141	1.52750
$13$	−4.39015	−1.21761	−0.608804	−	0.793321i	$-0.708350\pi$
$13$	−4.39015	−1.21761	−0.608804	+	0.793321i	$0.708350\pi$
$14$	1.03125	0.275614
$15$	2.20508	0.569350
$16$	13.4162	3.35406
$17$	−7.56447	−1.83465	−0.917327	−	0.398135i	$-0.869658\pi$
$17$	−7.56447	−1.83465	−0.917327	+	0.398135i	$0.869658\pi$
$18$	2.70026	0.636458
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	11.6680	2.60905
$21$	0.381908	0.0833392
$22$	−1.46209	−0.311718
$23$	4.83305	1.00776	0.503880	−	0.863774i	$-0.331905\pi$
$23$	4.83305	1.00776	0.503880	+	0.863774i	$0.331905\pi$
$24$	8.88768	1.81419
$25$	−0.137605	−0.0275210
$26$	−11.8545	−2.32487
$27$	1.00000	0.192450
$28$	2.02083	0.381902
$29$	−2.92584	−0.543316	−0.271658	−	0.962394i	$-0.587572\pi$
$29$	−2.92584	−0.543316	−0.271658	+	0.962394i	$0.587572\pi$
$30$	5.95430	1.08710
$31$	10.0216	1.79993	0.899963	−	0.435965i	$-0.143593\pi$
$31$	10.0216	1.79993	0.899963	+	0.435965i	$0.143593\pi$
$32$	18.4520	3.26188
$33$	−0.541461	−0.0942562
$34$	−20.4261	−3.50304
$35$	0.842139	0.142348
$36$	5.29141	0.881902
$37$	−6.82713	−1.12237	−0.561186	−	0.827690i	$-0.689655\pi$
$37$	−6.82713	−1.12237	−0.561186	+	0.827690i	$0.689655\pi$
$38$	2.70026	0.438040
$39$	−4.39015	−0.702986
$40$	19.5981	3.09873
$41$	−1.66489	−0.260012	−0.130006	−	0.991513i	$-0.541500\pi$
$41$	−1.66489	−0.260012	−0.130006	+	0.991513i	$0.541500\pi$
$42$	1.03125	0.159126
$43$	−8.47623	−1.29261	−0.646306	−	0.763078i	$-0.723687\pi$
$43$	−8.47623	−1.29261	−0.646306	+	0.763078i	$0.723687\pi$
$44$	−2.86509	−0.431929
$45$	2.20508	0.328715
$46$	13.0505	1.92419
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	13.4162	1.93647
$49$	−6.85415	−0.979164
$50$	−0.371569	−0.0525478
$51$	−7.56447	−1.05924
$52$	−23.2301	−3.22143
$53$	5.12841	0.704441	0.352221	−	0.935917i	$-0.385427\pi$
$53$	5.12841	0.704441	0.352221	+	0.935917i	$0.385427\pi$
$54$	2.70026	0.367459
$55$	−1.19397	−0.160994
$56$	3.39428	0.453579
$57$	1.00000	0.132453
$58$	−7.90055	−1.03739
$59$	−6.38720	−0.831543	−0.415771	−	0.909469i	$-0.636488\pi$
$59$	−6.38720	−0.831543	−0.415771	+	0.909469i	$0.636488\pi$
$60$	11.6680	1.50633
$61$	9.65918	1.23673	0.618366	−	0.785890i	$-0.287795\pi$
$61$	9.65918	1.23673	0.618366	+	0.785890i	$0.287795\pi$
$62$	27.0609	3.43673
$63$	0.381908	0.0481159
$64$	22.9928	2.87410
$65$	−9.68064	−1.20074
$66$	−1.46209	−0.179970
$67$	6.65611	0.813174	0.406587	−	0.913612i	$-0.366719\pi$
$67$	6.65611	0.813174	0.406587	+	0.913612i	$0.366719\pi$
$68$	−40.0268	−4.85396
$69$	4.83305	0.581831
$70$	2.27400	0.271795
$71$	8.57056	1.01714	0.508569	−	0.861021i	$-0.330175\pi$
$71$	8.57056	1.01714	0.508569	+	0.861021i	$0.330175\pi$
$72$	8.88768	1.04742
$73$	−8.65829	−1.01338	−0.506688	−	0.862130i	$-0.669130\pi$
$73$	−8.65829	−1.01338	−0.506688	+	0.862130i	$0.669130\pi$
$74$	−18.4350	−2.14303
$75$	−0.137605	−0.0158892
$76$	5.29141	0.606967
$77$	−0.206788	−0.0235657
$78$	−11.8545	−1.34226
$79$	−2.49612	−0.280836	−0.140418	−	0.990092i	$-0.544845\pi$
$79$	−2.49612	−0.280836	−0.140418	+	0.990092i	$0.544845\pi$
$80$	29.5839	3.30759
$81$	1.00000	0.111111
$82$	−4.49563	−0.496459
$83$	5.42636	0.595621	0.297810	−	0.954625i	$-0.403744\pi$
$83$	5.42636	0.595621	0.297810	+	0.954625i	$0.403744\pi$
$84$	2.02083	0.220491
$85$	−16.6803	−1.80923
$86$	−22.8880	−2.46808
$87$	−2.92584	−0.313683
$88$	−4.81233	−0.512996
$89$	−12.6622	−1.34219	−0.671094	−	0.741372i	$-0.734175\pi$
$89$	−12.6622	−1.34219	−0.671094	+	0.741372i	$0.734175\pi$
$90$	5.95430	0.627639
$91$	−1.67663	−0.175759
$92$	25.5737	2.66624
$93$	10.0216	1.03919
$94$	2.70026	0.278511
$95$	2.20508	0.226237
$96$	18.4520	1.88325
$97$	−8.67832	−0.881150	−0.440575	−	0.897716i	$-0.645225\pi$
$97$	−8.67832	−0.881150	−0.440575	+	0.897716i	$0.645225\pi$
$98$	−18.5080	−1.86959
$99$	−0.541461	−0.0544188
$100$	−0.728124	−0.0728124
$101$	9.77259	0.972409	0.486204	−	0.873845i	$-0.338381\pi$
$101$	9.77259	0.972409	0.486204	+	0.873845i	$0.338381\pi$
$102$	−20.4261	−2.02248
$103$	11.0004	1.08391	0.541953	−	0.840409i	$-0.317685\pi$
$103$	11.0004	1.08391	0.541953	+	0.840409i	$0.317685\pi$
$104$	−39.0182	−3.82605
$105$	0.842139	0.0821844
$106$	13.8480	1.34504
$107$	−7.79770	−0.753832	−0.376916	−	0.926247i	$-0.623015\pi$
$107$	−7.79770	−0.753832	−0.376916	+	0.926247i	$0.623015\pi$
$108$	5.29141	0.509167
$109$	16.7420	1.60359	0.801796	−	0.597597i	$-0.203878\pi$
$109$	16.7420	1.60359	0.801796	+	0.597597i	$0.203878\pi$
$110$	−3.22402	−0.307398
$111$	−6.82713	−0.648002
$112$	5.12377	0.484151
$113$	−14.0364	−1.32043	−0.660216	−	0.751076i	$-0.729535\pi$
$113$	−14.0364	−1.32043	−0.660216	+	0.751076i	$0.729535\pi$
$114$	2.70026	0.252903
$115$	10.6573	0.993796
$116$	−15.4819	−1.43745
$117$	−4.39015	−0.405869
$118$	−17.2471	−1.58773
$119$	−2.88893	−0.264828
$120$	19.5981	1.78905
$121$	−10.7068	−0.973347
$122$	26.0823	2.36138
$123$	−1.66489	−0.150118
$124$	53.0283	4.76208
$125$	−11.3288	−1.01328
$126$	1.03125	0.0918712
$127$	−11.7591	−1.04345	−0.521727	−	0.853112i	$-0.674712\pi$
$127$	−11.7591	−1.04345	−0.521727	+	0.853112i	$0.674712\pi$
$128$	25.1825	2.22584
$129$	−8.47623	−0.746290
$130$	−26.1403	−2.29265
$131$	−6.71779	−0.586936	−0.293468	−	0.955969i	$-0.594809\pi$
$131$	−6.71779	−0.586936	−0.293468	+	0.955969i	$0.594809\pi$
$132$	−2.86509	−0.249374
$133$	0.381908	0.0331156
$134$	17.9733	1.55265
$135$	2.20508	0.189783
$136$	−67.2306	−5.76498
$137$	12.5363	1.07104	0.535522	−	0.844521i	$-0.320115\pi$
$137$	12.5363	1.07104	0.535522	+	0.844521i	$0.320115\pi$
$138$	13.0505	1.11093
$139$	−8.93314	−0.757699	−0.378849	−	0.925458i	$-0.623680\pi$
$139$	−8.93314	−0.757699	−0.378849	+	0.925458i	$0.623680\pi$
$140$	4.45611	0.376610
$141$	1.00000	0.0842152
$142$	23.1428	1.94210
$143$	2.37709	0.198782
$144$	13.4162	1.11802
$145$	−6.45173	−0.535787
$146$	−23.3796	−1.93491
$147$	−6.85415	−0.565320
$148$	−36.1252	−2.96947
$149$	4.20717	0.344664	0.172332	−	0.985039i	$-0.444870\pi$
$149$	4.20717	0.344664	0.172332	+	0.985039i	$0.444870\pi$
$150$	−0.371569	−0.0303385
$151$	18.0236	1.46674	0.733369	−	0.679831i	$-0.237947\pi$
$151$	18.0236	1.46674	0.733369	+	0.679831i	$0.237947\pi$
$152$	8.88768	0.720886
$153$	−7.56447	−0.611551
$154$	−0.558382	−0.0449957
$155$	22.0984	1.77499
$156$	−23.2301	−1.85989
$157$	17.2290	1.37503	0.687514	−	0.726171i	$-0.258702\pi$
$157$	17.2290	1.37503	0.687514	+	0.726171i	$0.258702\pi$
$158$	−6.74019	−0.536221
$159$	5.12841	0.406709
$160$	40.6882	3.21669
$161$	1.84578	0.145468
$162$	2.70026	0.212153
$163$	6.95091	0.544437	0.272219	−	0.962235i	$-0.412243\pi$
$163$	6.95091	0.544437	0.272219	+	0.962235i	$0.412243\pi$
$164$	−8.80960	−0.687914
$165$	−1.19397	−0.0929501
$166$	14.6526	1.13726
$167$	−9.99053	−0.773090	−0.386545	−	0.922270i	$-0.626332\pi$
$167$	−9.99053	−0.773090	−0.386545	+	0.922270i	$0.626332\pi$
$168$	3.39428	0.261874
$169$	6.27337	0.482567
$170$	−45.0412	−3.45450
$171$	1.00000	0.0764719
$172$	−44.8512	−3.41987
$173$	−8.92035	−0.678202	−0.339101	−	0.940750i	$-0.610123\pi$
$173$	−8.92035	−0.678202	−0.339101	+	0.940750i	$0.610123\pi$
$174$	−7.90055	−0.598939
$175$	−0.0525524	−0.00397259
$176$	−7.26437	−0.547572
$177$	−6.38720	−0.480092
$178$	−34.1912	−2.56274
$179$	19.7358	1.47512	0.737561	−	0.675281i	$-0.235978\pi$
$179$	19.7358	1.47512	0.737561	+	0.675281i	$0.235978\pi$
$180$	11.6680	0.869682
$181$	−2.51847	−0.187196	−0.0935982	−	0.995610i	$-0.529837\pi$
$181$	−2.51847	−0.187196	−0.0935982	+	0.995610i	$0.529837\pi$
$182$	−4.52735	−0.335589
$183$	9.65918	0.714027
$184$	42.9546	3.16666
$185$	−15.0544	−1.10682
$186$	27.0609	1.98420
$187$	4.09586	0.299519
$188$	5.29141	0.385916
$189$	0.381908	0.0277797
$190$	5.95430	0.431971
$191$	18.3243	1.32590	0.662952	−	0.748662i	$-0.269303\pi$
$191$	18.3243	1.32590	0.662952	+	0.748662i	$0.269303\pi$
$192$	22.9928	1.65936
$193$	24.2325	1.74429	0.872146	−	0.489246i	$-0.162728\pi$
$193$	24.2325	1.74429	0.872146	+	0.489246i	$0.162728\pi$
$194$	−23.4337	−1.68245
$195$	−9.68064	−0.693245
$196$	−36.2681	−2.59058
$197$	15.3067	1.09055	0.545277	−	0.838256i	$-0.316424\pi$
$197$	15.3067	1.09055	0.545277	+	0.838256i	$0.316424\pi$
$198$	−1.46209	−0.103906
$199$	15.1884	1.07668	0.538339	−	0.842728i	$-0.319052\pi$
$199$	15.1884	1.07668	0.538339	+	0.842728i	$0.319052\pi$
$200$	−1.22299	−0.0864783
$201$	6.65611	0.469486
$202$	26.3885	1.85669
$203$	−1.11740	−0.0784264
$204$	−40.0268	−2.80243
$205$	−3.67121	−0.256409
$206$	29.7041	2.06958
$207$	4.83305	0.335920
$208$	−58.8993	−4.08393
$209$	−0.541461	−0.0374536
$210$	2.27400	0.156921
$211$	−10.0965	−0.695070	−0.347535	−	0.937667i	$-0.612981\pi$
$211$	−10.0965	−0.695070	−0.347535	+	0.937667i	$0.612981\pi$
$212$	27.1365	1.86375
$213$	8.57056	0.587245
$214$	−21.0558	−1.43935
$215$	−18.6908	−1.27470
$216$	8.88768	0.604730
$217$	3.82732	0.259815
$218$	45.2078	3.06186
$219$	−8.65829	−0.585073
$220$	−6.31777	−0.425944
$221$	33.2091	2.23389
$222$	−18.4350	−1.23728
$223$	19.4848	1.30480	0.652400	−	0.757875i	$-0.273762\pi$
$223$	19.4848	1.30480	0.652400	+	0.757875i	$0.273762\pi$
$224$	7.04697	0.470845
$225$	−0.137605	−0.00917366
$226$	−37.9019	−2.52120
$227$	14.1735	0.940727	0.470363	−	0.882473i	$-0.344123\pi$
$227$	14.1735	0.940727	0.470363	+	0.882473i	$0.344123\pi$
$228$	5.29141	0.350433
$229$	−15.0866	−0.996951	−0.498475	−	0.866904i	$-0.666107\pi$
$229$	−15.0866	−0.996951	−0.498475	+	0.866904i	$0.666107\pi$
$230$	28.7774	1.89753
$231$	−0.206788	−0.0136057
$232$	−26.0040	−1.70724
$233$	29.5646	1.93684	0.968421	−	0.249321i	$-0.0802075\pi$
$233$	29.5646	1.93684	0.968421	+	0.249321i	$0.0802075\pi$
$234$	−11.8545	−0.774956
$235$	2.20508	0.143844
$236$	−33.7973	−2.20002
$237$	−2.49612	−0.162141
$238$	−7.80087	−0.505656
$239$	2.73697	0.177040	0.0885199	−	0.996074i	$-0.471786\pi$
$239$	2.73697	0.177040	0.0885199	+	0.996074i	$0.471786\pi$
$240$	29.5839	1.90964
$241$	−13.2806	−0.855477	−0.427738	−	0.903903i	$-0.640690\pi$
$241$	−13.2806	−0.855477	−0.427738	+	0.903903i	$0.640690\pi$
$242$	−28.9112	−1.85848
$243$	1.00000	0.0641500
$244$	51.1107	3.27203
$245$	−15.1140	−0.965596
$246$	−4.49563	−0.286631
$247$	−4.39015	−0.279338
$248$	89.0685	5.65586
$249$	5.42636	0.343882
$250$	−30.5909	−1.93474
$251$	−13.6733	−0.863049	−0.431525	−	0.902101i	$-0.642024\pi$
$251$	−13.6733	−0.863049	−0.431525	+	0.902101i	$0.642024\pi$
$252$	2.02083	0.127301
$253$	−2.61690	−0.164523
$254$	−31.7527	−1.99234
$255$	−16.6803	−1.04456
$256$	22.0138	1.37586
$257$	−11.9308	−0.744222	−0.372111	−	0.928188i	$-0.621366\pi$
$257$	−11.9308	−0.744222	−0.372111	+	0.928188i	$0.621366\pi$
$258$	−22.8880	−1.42495
$259$	−2.60733	−0.162012
$260$	−51.2243	−3.17679
$261$	−2.92584	−0.181105
$262$	−18.1398	−1.12068
$263$	−20.6566	−1.27374	−0.636871	−	0.770970i	$-0.719772\pi$
$263$	−20.6566	−1.27374	−0.636871	+	0.770970i	$0.719772\pi$
$264$	−4.81233	−0.296178
$265$	11.3086	0.694680
$266$	1.03125	0.0632301
$267$	−12.6622	−0.774912
$268$	35.2203	2.15142
$269$	−28.6700	−1.74804	−0.874020	−	0.485889i	$-0.838496\pi$
$269$	−28.6700	−1.74804	−0.874020	+	0.485889i	$0.838496\pi$
$270$	5.95430	0.362367
$271$	9.20417	0.559114	0.279557	−	0.960129i	$-0.409812\pi$
$271$	9.20417	0.559114	0.279557	+	0.960129i	$0.409812\pi$
$272$	−101.487	−6.15354
$273$	−1.67663	−0.101474
$274$	33.8512	2.04502
$275$	0.0745076	0.00449298
$276$	25.5737	1.53935
$277$	−19.8425	−1.19222	−0.596111	−	0.802902i	$-0.703288\pi$
$277$	−19.8425	−1.19222	−0.596111	+	0.802902i	$0.703288\pi$
$278$	−24.1218	−1.44673
$279$	10.0216	0.599976
$280$	7.48467	0.447294
$281$	32.7137	1.95153	0.975767	−	0.218811i	$-0.0702178\pi$
$281$	32.7137	1.95153	0.975767	+	0.218811i	$0.0702178\pi$
$282$	2.70026	0.160798
$283$	−26.7479	−1.59000	−0.794999	−	0.606611i	$-0.792528\pi$
$283$	−26.7479	−1.59000	−0.794999	+	0.606611i	$0.792528\pi$
$284$	45.3504	2.69105
$285$	2.20508	0.130618
$286$	6.41877	0.379550
$287$	−0.635833	−0.0375321
$288$	18.4520	1.08729
$289$	40.2212	2.36595
$290$	−17.4214	−1.02302
$291$	−8.67832	−0.508732
$292$	−45.8146	−2.68110
$293$	−5.15932	−0.301411	−0.150705	−	0.988579i	$-0.548154\pi$
$293$	−5.15932	−0.301411	−0.150705	+	0.988579i	$0.548154\pi$
$294$	−18.5080	−1.07941
$295$	−14.0843	−0.820021
$296$	−60.6773	−3.52680
$297$	−0.541461	−0.0314187
$298$	11.3604	0.658093
$299$	−21.2178	−1.22706
$300$	−0.728124	−0.0420383
$301$	−3.23714	−0.186586
$302$	48.6684	2.80055
$303$	9.77259	0.561420
$304$	13.4162	0.769474
$305$	21.2993	1.21959
$306$	−20.4261	−1.16768
$307$	5.44081	0.310523	0.155262	−	0.987873i	$-0.450378\pi$
$307$	5.44081	0.310523	0.155262	+	0.987873i	$0.450378\pi$
$308$	−1.09420	−0.0623479
$309$	11.0004	0.625793
$310$	59.6715	3.38911
$311$	21.0326	1.19265	0.596323	−	0.802744i	$-0.296628\pi$
$311$	21.0326	1.19265	0.596323	+	0.802744i	$0.296628\pi$
$312$	−39.0182	−2.20897
$313$	−15.1762	−0.857808	−0.428904	−	0.903350i	$-0.641100\pi$
$313$	−15.1762	−0.857808	−0.428904	+	0.903350i	$0.641100\pi$
$314$	46.5229	2.62544
$315$	0.842139	0.0474492
$316$	−13.2080	−0.743010
$317$	−4.90155	−0.275298	−0.137649	−	0.990481i	$-0.543955\pi$
$317$	−4.90155	−0.275298	−0.137649	+	0.990481i	$0.543955\pi$
$318$	13.8480	0.776560
$319$	1.58423	0.0886998
$320$	50.7010	2.83427
$321$	−7.79770	−0.435225
$322$	4.98409	0.277752
$323$	−7.56447	−0.420898
$324$	5.29141	0.293967
$325$	0.604105	0.0335097
$326$	18.7693	1.03953
$327$	16.7420	0.925835
$328$	−14.7970	−0.817027
$329$	0.381908	0.0210553
$330$	−3.22402	−0.177477
$331$	−36.1520	−1.98709	−0.993545	−	0.113434i	$-0.963815\pi$
$331$	−36.1520	−1.98709	−0.993545	+	0.113434i	$0.963815\pi$
$332$	28.7131	1.57584
$333$	−6.82713	−0.374124
$334$	−26.9770	−1.47612
$335$	14.6773	0.801906
$336$	5.12377	0.279525
$337$	−19.5250	−1.06359	−0.531796	−	0.846873i	$-0.678483\pi$
$337$	−19.5250	−1.06359	−0.531796	+	0.846873i	$0.678483\pi$
$338$	16.9398	0.921401
$339$	−14.0364	−0.762352
$340$	−88.2623	−4.78670
$341$	−5.42628	−0.293850
$342$	2.70026	0.146013
$343$	−5.29101	−0.285688
$344$	−75.3340	−4.06174
$345$	10.6573	0.573768
$346$	−24.0873	−1.29494
$347$	1.91679	0.102899	0.0514493	−	0.998676i	$-0.483616\pi$
$347$	1.91679	0.102899	0.0514493	+	0.998676i	$0.483616\pi$
$348$	−15.4819	−0.829915
$349$	17.4874	0.936079	0.468040	−	0.883708i	$-0.344960\pi$
$349$	17.4874	0.936079	0.468040	+	0.883708i	$0.344960\pi$
$350$	−0.141905	−0.00758515
$351$	−4.39015	−0.234329
$352$	−9.99103	−0.532524
$353$	−13.1334	−0.699021	−0.349510	−	0.936933i	$-0.613652\pi$
$353$	−13.1334	−0.699021	−0.349510	+	0.936933i	$0.613652\pi$
$354$	−17.2471	−0.916674
$355$	18.8988	1.00304
$356$	−67.0008	−3.55104
$357$	−2.88893	−0.152899
$358$	53.2918	2.81656
$359$	−16.6782	−0.880241	−0.440121	−	0.897939i	$-0.645064\pi$
$359$	−16.6782	−0.880241	−0.440121	+	0.897939i	$0.645064\pi$
$360$	19.5981	1.03291
$361$	1.00000	0.0526316
$362$	−6.80053	−0.357428
$363$	−10.7068	−0.561962
$364$	−8.87175	−0.465006
$365$	−19.0923	−0.999334
$366$	26.0823	1.36334
$367$	−1.77145	−0.0924688	−0.0462344	−	0.998931i	$-0.514722\pi$
$367$	−1.77145	−0.0924688	−0.0462344	+	0.998931i	$0.514722\pi$
$368$	64.8413	3.38009
$369$	−1.66489	−0.0866705
$370$	−40.6508	−2.11333
$371$	1.95858	0.101684
$372$	53.0283	2.74939
$373$	−2.63760	−0.136570	−0.0682848	−	0.997666i	$-0.521753\pi$
$373$	−2.63760	−0.136570	−0.0682848	+	0.997666i	$0.521753\pi$
$374$	11.0599	0.571894
$375$	−11.3288	−0.585019
$376$	8.88768	0.458347
$377$	12.8449	0.661545
$378$	1.03125	0.0530419
$379$	7.01437	0.360304	0.180152	−	0.983639i	$-0.442341\pi$
$379$	7.01437	0.360304	0.180152	+	0.983639i	$0.442341\pi$
$380$	11.6680	0.598556
$381$	−11.7591	−0.602439
$382$	49.4805	2.53164
$383$	−19.4874	−0.995761	−0.497880	−	0.867246i	$-0.665888\pi$
$383$	−19.4874	−0.995761	−0.497880	+	0.867246i	$0.665888\pi$
$384$	25.1825	1.28509
$385$	−0.455985	−0.0232392
$386$	65.4340	3.33050
$387$	−8.47623	−0.430871
$388$	−45.9206	−2.33127
$389$	5.96803	0.302591	0.151296	−	0.988489i	$-0.451655\pi$
$389$	5.96803	0.302591	0.151296	+	0.988489i	$0.451655\pi$
$390$	−26.1403	−1.32366
$391$	−36.5594	−1.84889
$392$	−60.9175	−3.07680
$393$	−6.71779	−0.338868
$394$	41.3320	2.08228
$395$	−5.50416	−0.276944
$396$	−2.86509	−0.143976
$397$	6.34949	0.318672	0.159336	−	0.987224i	$-0.449065\pi$
$397$	6.34949	0.318672	0.159336	+	0.987224i	$0.449065\pi$
$398$	41.0127	2.05578
$399$	0.381908	0.0191193
$400$	−1.84614	−0.0923070
$401$	20.4053	1.01899	0.509496	−	0.860473i	$-0.329832\pi$
$401$	20.4053	1.01899	0.509496	+	0.860473i	$0.329832\pi$
$402$	17.9733	0.896424
$403$	−43.9961	−2.19160
$404$	51.7108	2.57271
$405$	2.20508	0.109572
$406$	−3.01728	−0.149745
$407$	3.69662	0.183235
$408$	−67.2306	−3.32841
$409$	12.3652	0.611421	0.305710	−	0.952125i	$-0.401106\pi$
$409$	12.3652	0.611421	0.305710	+	0.952125i	$0.401106\pi$
$410$	−9.91324	−0.489580
$411$	12.5363	0.618368
$412$	58.2079	2.86770
$413$	−2.43932	−0.120031
$414$	13.0505	0.641397
$415$	11.9656	0.587368
$416$	−81.0070	−3.97169
$417$	−8.93314	−0.437458
$418$	−1.46209	−0.0715129
$419$	−13.4073	−0.654992	−0.327496	−	0.944853i	$-0.606205\pi$
$419$	−13.4073	−0.654992	−0.327496	+	0.944853i	$0.606205\pi$
$420$	4.45611	0.217436
$421$	9.55704	0.465782	0.232891	−	0.972503i	$-0.425182\pi$
$421$	9.55704	0.465782	0.232891	+	0.972503i	$0.425182\pi$
$422$	−27.2631	−1.32715
$423$	1.00000	0.0486217
$424$	45.5797	2.21354
$425$	1.04091	0.0504914
$426$	23.1428	1.12127
$427$	3.68892	0.178519
$428$	−41.2609	−1.99442
$429$	2.37709	0.114767
$430$	−50.4700	−2.43388
$431$	−12.6183	−0.607804	−0.303902	−	0.952703i	$-0.598289\pi$
$431$	−12.6183	−0.607804	−0.303902	+	0.952703i	$0.598289\pi$
$432$	13.4162	0.645489
$433$	16.0281	0.770262	0.385131	−	0.922862i	$-0.374156\pi$
$433$	16.0281	0.770262	0.385131	+	0.922862i	$0.374156\pi$
$434$	10.3348	0.496084
$435$	−6.45173	−0.309337
$436$	88.5889	4.24264
$437$	4.83305	0.231196
$438$	−23.3796	−1.11712
$439$	3.06186	0.146135	0.0730674	−	0.997327i	$-0.476721\pi$
$439$	3.06186	0.146135	0.0730674	+	0.997327i	$0.476721\pi$
$440$	−10.6116	−0.505888
$441$	−6.85415	−0.326388
$442$	89.6733	4.26533
$443$	9.52124	0.452368	0.226184	−	0.974085i	$-0.427375\pi$
$443$	9.52124	0.452368	0.226184	+	0.974085i	$0.427375\pi$
$444$	−36.1252	−1.71442
$445$	−27.9212	−1.32359
$446$	52.6141	2.49135
$447$	4.20717	0.198992
$448$	8.78112	0.414869
$449$	31.2958	1.47694	0.738469	−	0.674287i	$-0.235549\pi$
$449$	31.2958	1.47694	0.738469	+	0.674287i	$0.235549\pi$
$450$	−0.371569	−0.0175159
$451$	0.901470	0.0424486
$452$	−74.2724	−3.49348
$453$	18.0236	0.846822
$454$	38.2721	1.79620
$455$	−3.69711	−0.173323
$456$	8.88768	0.416204
$457$	3.14927	0.147317	0.0736583	−	0.997284i	$-0.476533\pi$
$457$	3.14927	0.147317	0.0736583	+	0.997284i	$0.476533\pi$
$458$	−40.7378	−1.90355
$459$	−7.56447	−0.353079
$460$	56.3921	2.62929
$461$	36.5366	1.70168	0.850840	−	0.525424i	$-0.176093\pi$
$461$	36.5366	1.70168	0.850840	+	0.525424i	$0.176093\pi$
$462$	−0.558382	−0.0259783
$463$	2.42169	0.112546	0.0562728	−	0.998415i	$-0.482078\pi$
$463$	2.42169	0.112546	0.0562728	+	0.998415i	$0.482078\pi$
$464$	−39.2538	−1.82231
$465$	22.0984	1.02479
$466$	79.8322	3.69815
$467$	9.54643	0.441756	0.220878	−	0.975301i	$-0.429108\pi$
$467$	9.54643	0.441756	0.220878	+	0.975301i	$0.429108\pi$
$468$	−23.2301	−1.07381
$469$	2.54202	0.117380
$470$	5.95430	0.274652
$471$	17.2290	0.793873
$472$	−56.7674	−2.61293
$473$	4.58954	0.211027
$474$	−6.74019	−0.309587
$475$	−0.137605	−0.00631374
$476$	−15.2865	−0.700657
$477$	5.12841	0.234814
$478$	7.39053	0.338035
$479$	−13.5642	−0.619763	−0.309881	−	0.950775i	$-0.600289\pi$
$479$	−13.5642	−0.619763	−0.309881	+	0.950775i	$0.600289\pi$
$480$	40.6882	1.85715
$481$	29.9721	1.36661
$482$	−35.8610	−1.63342
$483$	1.84578	0.0839859
$484$	−56.6542	−2.57519
$485$	−19.1364	−0.868941
$486$	2.70026	0.122486
$487$	−27.7764	−1.25867	−0.629335	−	0.777134i	$-0.716672\pi$
$487$	−27.7764	−1.25867	−0.629335	+	0.777134i	$0.716672\pi$
$488$	85.8478	3.88615
$489$	6.95091	0.314331
$490$	−40.8117	−1.84368
$491$	−13.7552	−0.620762	−0.310381	−	0.950612i	$-0.600457\pi$
$491$	−13.7552	−0.620762	−0.310381	+	0.950612i	$0.600457\pi$
$492$	−8.80960	−0.397168
$493$	22.1325	0.996796
$494$	−11.8545	−0.533361
$495$	−1.19397	−0.0536648
$496$	134.452	6.03706
$497$	3.27317	0.146822
$498$	14.6526	0.656599
$499$	12.9853	0.581304	0.290652	−	0.956829i	$-0.406128\pi$
$499$	12.9853	0.581304	0.290652	+	0.956829i	$0.406128\pi$
$500$	−59.9456	−2.68085
$501$	−9.99053	−0.446344
$502$	−36.9214	−1.64788
$503$	0.878196	0.0391568	0.0195784	−	0.999808i	$-0.493768\pi$
$503$	0.878196	0.0391568	0.0195784	+	0.999808i	$0.493768\pi$
$504$	3.39428	0.151193
$505$	21.5494	0.958935
$506$	−7.06633	−0.314137
$507$	6.27337	0.278610
$508$	−62.2225	−2.76067
$509$	21.1285	0.936502	0.468251	−	0.883595i	$-0.344884\pi$
$509$	21.1285	0.936502	0.468251	+	0.883595i	$0.344884\pi$
$510$	−45.0412	−1.99446
$511$	−3.30667	−0.146278
$512$	9.07795	0.401193
$513$	1.00000	0.0441511
$514$	−32.2162	−1.42100
$515$	24.2569	1.06889
$516$	−44.8512	−1.97447
$517$	−0.541461	−0.0238134
$518$	−7.04049	−0.309341
$519$	−8.92035	−0.391560
$520$	−86.0384	−3.77304
$521$	−21.4364	−0.939146	−0.469573	−	0.882894i	$-0.655592\pi$
$521$	−21.4364	−0.939146	−0.469573	+	0.882894i	$0.655592\pi$
$522$	−7.90055	−0.345798
$523$	8.62069	0.376957	0.188478	−	0.982077i	$-0.439644\pi$
$523$	8.62069	0.376957	0.188478	+	0.982077i	$0.439644\pi$
$524$	−35.5466	−1.55286
$525$	−0.0525524	−0.00229357
$526$	−55.7783	−2.43205
$527$	−75.8079	−3.30224
$528$	−7.26437	−0.316141
$529$	0.358354	0.0155806
$530$	30.5361	1.32640
$531$	−6.38720	−0.277181
$532$	2.02083	0.0876143
$533$	7.30909	0.316592
$534$	−34.1912	−1.47960
$535$	−17.1946	−0.743387
$536$	59.1574	2.55521
$537$	19.7358	0.851662
$538$	−77.4165	−3.33766
$539$	3.71125	0.159855
$540$	11.6680	0.502111
$541$	36.7599	1.58043	0.790216	−	0.612828i	$-0.209968\pi$
$541$	36.7599	1.58043	0.790216	+	0.612828i	$0.209968\pi$
$542$	24.8537	1.06756
$543$	−2.51847	−0.108078
$544$	−139.580	−5.98443
$545$	36.9175	1.58137
$546$	−4.52735	−0.193752
$547$	−20.6459	−0.882756	−0.441378	−	0.897321i	$-0.645510\pi$
$547$	−20.6459	−0.882756	−0.441378	+	0.897321i	$0.645510\pi$
$548$	66.3345	2.83367
$549$	9.65918	0.412244
$550$	0.201190	0.00857877
$551$	−2.92584	−0.124645
$552$	42.9546	1.82827
$553$	−0.953290	−0.0405380
$554$	−53.5800	−2.27640
$555$	−15.0544	−0.639023
$556$	−47.2689	−2.00465
$557$	−23.6903	−1.00379	−0.501896	−	0.864928i	$-0.667364\pi$
$557$	−23.6903	−1.00379	−0.501896	+	0.864928i	$0.667364\pi$
$558$	27.0609	1.14558
$559$	37.2119	1.57389
$560$	11.2983	0.477442
$561$	4.09586	0.172927
$562$	88.3355	3.72621
$563$	9.84108	0.414752	0.207376	−	0.978261i	$-0.433508\pi$
$563$	9.84108	0.414752	0.207376	+	0.978261i	$0.433508\pi$
$564$	5.29141	0.222809
$565$	−30.9514	−1.30214
$566$	−72.2263	−3.03590
$567$	0.381908	0.0160386
$568$	76.1724	3.19612
$569$	1.63516	0.0685495	0.0342748	−	0.999412i	$-0.489088\pi$
$569$	1.63516	0.0685495	0.0342748	+	0.999412i	$0.489088\pi$
$570$	5.95430	0.249398
$571$	−3.22029	−0.134765	−0.0673824	−	0.997727i	$-0.521465\pi$
$571$	−3.22029	−0.134765	−0.0673824	+	0.997727i	$0.521465\pi$
$572$	12.5782	0.525920
$573$	18.3243	0.765511
$574$	−1.71692	−0.0716627
$575$	−0.665051	−0.0277345
$576$	22.9928	0.958032
$577$	16.4921	0.686577	0.343288	−	0.939230i	$-0.388459\pi$
$577$	16.4921	0.686577	0.343288	+	0.939230i	$0.388459\pi$
$578$	108.608	4.51749
$579$	24.2325	1.00707
$580$	−34.1388	−1.41754
$581$	2.07237	0.0859765
$582$	−23.4337	−0.971360
$583$	−2.77683	−0.115005
$584$	−76.9521	−3.18430
$585$	−9.68064	−0.400245
$586$	−13.9315	−0.575506
$587$	18.4883	0.763095	0.381548	−	0.924349i	$-0.375391\pi$
$587$	18.4883	0.763095	0.381548	+	0.924349i	$0.375391\pi$
$588$	−36.2681	−1.49567
$589$	10.0216	0.412932
$590$	−38.0313	−1.56573
$591$	15.3067	0.629632
$592$	−91.5944	−3.76451
$593$	−43.4614	−1.78475	−0.892373	−	0.451299i	$-0.850961\pi$
$593$	−43.4614	−1.78475	−0.892373	+	0.451299i	$0.850961\pi$
$594$	−1.46209	−0.0599901
$595$	−6.37034	−0.261158
$596$	22.2619	0.911881
$597$	15.1884	0.621621
$598$	−57.2936	−2.34291
$599$	23.3190	0.952788	0.476394	−	0.879232i	$-0.341944\pi$
$599$	23.3190	0.952788	0.476394	+	0.879232i	$0.341944\pi$
$600$	−1.22299	−0.0499283
$601$	−34.0943	−1.39074	−0.695368	−	0.718654i	$-0.744759\pi$
$601$	−34.0943	−1.39074	−0.695368	+	0.718654i	$0.744759\pi$
$602$	−8.74112	−0.356262
$603$	6.65611	0.271058
$604$	95.3703	3.88056
$605$	−23.6094	−0.959860
$606$	26.3885	1.07196
$607$	−11.0254	−0.447507	−0.223754	−	0.974646i	$-0.571831\pi$
$607$	−11.0254	−0.447507	−0.223754	+	0.974646i	$0.571831\pi$
$608$	18.4520	0.748328
$609$	−1.11740	−0.0452795
$610$	57.5137	2.32866
$611$	−4.39015	−0.177606
$612$	−40.0268	−1.61799
$613$	−4.46689	−0.180416	−0.0902081	−	0.995923i	$-0.528753\pi$
$613$	−4.46689	−0.180416	−0.0902081	+	0.995923i	$0.528753\pi$
$614$	14.6916	0.592905
$615$	−3.67121	−0.148038
$616$	−1.83787	−0.0740498
$617$	6.29671	0.253496	0.126748	−	0.991935i	$-0.459546\pi$
$617$	6.29671	0.253496	0.126748	+	0.991935i	$0.459546\pi$
$618$	29.7041	1.19487
$619$	−36.2640	−1.45757	−0.728787	−	0.684741i	$-0.759915\pi$
$619$	−36.2640	−1.45757	−0.728787	+	0.684741i	$0.759915\pi$
$620$	116.932	4.69609
$621$	4.83305	0.193944
$622$	56.7934	2.27721
$623$	−4.83579	−0.193742
$624$	−58.8993	−2.35786
$625$	−24.2930	−0.971722
$626$	−40.9796	−1.63788
$627$	−0.541461	−0.0216239
$628$	91.1660	3.63792
$629$	51.6436	2.05916
$630$	2.27400	0.0905982
$631$	−10.7987	−0.429891	−0.214945	−	0.976626i	$-0.568957\pi$
$631$	−10.7987	−0.429891	−0.214945	+	0.976626i	$0.568957\pi$
$632$	−22.1848	−0.882462
$633$	−10.0965	−0.401299
$634$	−13.2355	−0.525648
$635$	−25.9299	−1.02900
$636$	27.1365	1.07603
$637$	30.0907	1.19224
$638$	4.27783	0.169361
$639$	8.57056	0.339046
$640$	55.5295	2.19499
$641$	27.5198	1.08697	0.543483	−	0.839420i	$-0.317105\pi$
$641$	27.5198	1.08697	0.543483	+	0.839420i	$0.317105\pi$
$642$	−21.0558	−0.831008
$643$	9.75948	0.384876	0.192438	−	0.981309i	$-0.438361\pi$
$643$	9.75948	0.384876	0.192438	+	0.981309i	$0.438361\pi$
$644$	9.76679	0.384865
$645$	−18.6908	−0.735949
$646$	−20.4261	−0.803652
$647$	24.2245	0.952363	0.476181	−	0.879347i	$-0.342021\pi$
$647$	24.2245	0.952363	0.476181	+	0.879347i	$0.342021\pi$
$648$	8.88768	0.349141
$649$	3.45842	0.135755
$650$	1.63124	0.0639826
$651$	3.82732	0.150004
$652$	36.7801	1.44042
$653$	12.6373	0.494535	0.247268	−	0.968947i	$-0.420467\pi$
$653$	12.6373	0.494535	0.247268	+	0.968947i	$0.420467\pi$
$654$	45.2078	1.76776
$655$	−14.8133	−0.578803
$656$	−22.3365	−0.872094
$657$	−8.65829	−0.337792
$658$	1.03125	0.0402024
$659$	29.8421	1.16248	0.581241	−	0.813731i	$-0.302567\pi$
$659$	29.8421	1.16248	0.581241	+	0.813731i	$0.302567\pi$
$660$	−6.31777	−0.245919
$661$	−8.01684	−0.311819	−0.155909	−	0.987771i	$-0.549831\pi$
$661$	−8.01684	−0.311819	−0.155909	+	0.987771i	$0.549831\pi$
$662$	−97.6197	−3.79410
$663$	33.2091	1.28974
$664$	48.2278	1.87160
$665$	0.842139	0.0326568
$666$	−18.4350	−0.714343
$667$	−14.1407	−0.547532
$668$	−52.8640	−2.04537
$669$	19.4848	0.753327
$670$	39.6325	1.53114
$671$	−5.23007	−0.201904
$672$	7.04697	0.271843
$673$	−38.4718	−1.48298	−0.741489	−	0.670965i	$-0.765880\pi$
$673$	−38.4718	−1.48298	−0.741489	+	0.670965i	$0.765880\pi$
$674$	−52.7225	−2.03079
$675$	−0.137605	−0.00529641
$676$	33.1950	1.27673
$677$	−10.1601	−0.390486	−0.195243	−	0.980755i	$-0.562550\pi$
$677$	−10.1601	−0.390486	−0.195243	+	0.980755i	$0.562550\pi$
$678$	−37.9019	−1.45561
$679$	−3.31432	−0.127192
$680$	−148.249	−5.68510
$681$	14.1735	0.543129
$682$	−14.6524	−0.561069
$683$	−26.6293	−1.01894	−0.509471	−	0.860488i	$-0.670159\pi$
$683$	−26.6293	−1.01894	−0.509471	+	0.860488i	$0.670159\pi$
$684$	5.29141	0.202322
$685$	27.6435	1.05620
$686$	−14.2871	−0.545485
$687$	−15.0866	−0.575590
$688$	−113.719	−4.33550
$689$	−22.5145	−0.857733
$690$	28.7774	1.09554
$691$	−22.8073	−0.867631	−0.433816	−	0.901002i	$-0.642833\pi$
$691$	−22.8073	−0.867631	−0.433816	+	0.901002i	$0.642833\pi$
$692$	−47.2013	−1.79432
$693$	−0.206788	−0.00785523
$694$	5.17583	0.196472
$695$	−19.6983	−0.747200
$696$	−26.0040	−0.985678
$697$	12.5940	0.477031
$698$	47.2206	1.78732
$699$	29.5646	1.11824
$700$	−0.278077	−0.0105103
$701$	−37.4962	−1.41621	−0.708105	−	0.706107i	$-0.750450\pi$
$701$	−37.4962	−1.41621	−0.708105	+	0.706107i	$0.750450\pi$
$702$	−11.8545	−0.447421
$703$	−6.82713	−0.257490
$704$	−12.4497	−0.469215
$705$	2.20508	0.0830483
$706$	−35.4636	−1.33469
$707$	3.73223	0.140365
$708$	−33.7973	−1.27018
$709$	−19.6326	−0.737318	−0.368659	−	0.929565i	$-0.620183\pi$
$709$	−19.6326	−0.737318	−0.368659	+	0.929565i	$0.620183\pi$
$710$	51.0317	1.91519
$711$	−2.49612	−0.0936120
$712$	−112.537	−4.21752
$713$	48.4347	1.81389
$714$	−7.80087	−0.291940
$715$	5.24168	0.196028
$716$	104.430	3.90274
$717$	2.73697	0.102214
$718$	−45.0355	−1.68071
$719$	−3.20241	−0.119430	−0.0597150	−	0.998215i	$-0.519019\pi$
$719$	−3.20241	−0.119430	−0.0597150	+	0.998215i	$0.519019\pi$
$720$	29.5839	1.10253
$721$	4.20115	0.156459
$722$	2.70026	0.100493
$723$	−13.2806	−0.493910
$724$	−13.3263	−0.495267
$725$	0.402610	0.0149526
$726$	−28.9112	−1.07300
$727$	20.1186	0.746157	0.373078	−	0.927800i	$-0.378302\pi$
$727$	20.1186	0.746157	0.373078	+	0.927800i	$0.378302\pi$
$728$	−14.9014	−0.552282
$729$	1.00000	0.0370370
$730$	−51.5541	−1.90810
$731$	64.1182	2.37150
$732$	51.1107	1.88911
$733$	−42.8614	−1.58312	−0.791560	−	0.611091i	$-0.790731\pi$
$733$	−42.8614	−1.58312	−0.791560	+	0.611091i	$0.790731\pi$
$734$	−4.78337	−0.176557
$735$	−15.1140	−0.557487
$736$	89.1794	3.28720
$737$	−3.60402	−0.132756
$738$	−4.49563	−0.165486
$739$	43.3153	1.59338	0.796689	−	0.604389i	$-0.206583\pi$
$739$	43.3153	1.59338	0.796689	+	0.604389i	$0.206583\pi$
$740$	−79.6590	−2.92832
$741$	−4.39015	−0.161276
$742$	5.28868	0.194154
$743$	−15.7700	−0.578544	−0.289272	−	0.957247i	$-0.593413\pi$
$743$	−15.7700	−0.578544	−0.289272	+	0.957247i	$0.593413\pi$
$744$	89.0685	3.26541
$745$	9.27715	0.339889
$746$	−7.12220	−0.260762
$747$	5.42636	0.198540
$748$	21.6729	0.792440
$749$	−2.97800	−0.108814
$750$	−30.5909	−1.11702
$751$	25.1146	0.916445	0.458223	−	0.888837i	$-0.348486\pi$
$751$	25.1146	0.916445	0.458223	+	0.888837i	$0.348486\pi$
$752$	13.4162	0.489240
$753$	−13.6733	−0.498282
$754$	34.6845	1.26314
$755$	39.7435	1.44641
$756$	2.02083	0.0734970
$757$	−48.6599	−1.76857	−0.884287	−	0.466944i	$-0.845355\pi$
$757$	−48.6599	−1.76857	−0.884287	+	0.466944i	$0.845355\pi$
$758$	18.9407	0.687955
$759$	−2.61690	−0.0949876
$760$	19.5981	0.710897
$761$	15.5719	0.564481	0.282241	−	0.959344i	$-0.408922\pi$
$761$	15.5719	0.564481	0.282241	+	0.959344i	$0.408922\pi$
$762$	−31.7527	−1.15028
$763$	6.39390	0.231475
$764$	96.9617	3.50795
$765$	−16.6803	−0.603077
$766$	−52.6212	−1.90128
$767$	28.0407	1.01249
$768$	22.0138	0.794353
$769$	−24.5292	−0.884545	−0.442273	−	0.896881i	$-0.645828\pi$
$769$	−24.5292	−0.884545	−0.442273	+	0.896881i	$0.645828\pi$
$770$	−1.23128	−0.0443722
$771$	−11.9308	−0.429677
$772$	128.224	4.61488
$773$	24.2794	0.873271	0.436635	−	0.899639i	$-0.356170\pi$
$773$	24.2794	0.873271	0.436635	+	0.899639i	$0.356170\pi$
$774$	−22.8880	−0.822693
$775$	−1.37902	−0.0495357
$776$	−77.1302	−2.76881
$777$	−2.60733	−0.0935376
$778$	16.1152	0.577760
$779$	−1.66489	−0.0596507
$780$	−51.2243	−1.83412
$781$	−4.64062	−0.166054
$782$	−98.7201	−3.53022
$783$	−2.92584	−0.104561
$784$	−91.9569	−3.28417
$785$	37.9915	1.35597
$786$	−18.1398	−0.647025
$787$	−26.0922	−0.930086	−0.465043	−	0.885288i	$-0.653961\pi$
$787$	−26.0922	−0.930086	−0.465043	+	0.885288i	$0.653961\pi$
$788$	80.9939	2.88529
$789$	−20.6566	−0.735395
$790$	−14.8627	−0.528791
$791$	−5.36061	−0.190601
$792$	−4.81233	−0.170999
$793$	−42.4052	−1.50585
$794$	17.1453	0.608463
$795$	11.3086	0.401074
$796$	80.3682	2.84858
$797$	12.5351	0.444017	0.222009	−	0.975045i	$-0.428739\pi$
$797$	12.5351	0.444017	0.222009	+	0.975045i	$0.428739\pi$
$798$	1.03125	0.0365059
$799$	−7.56447	−0.267612
$800$	−2.53909	−0.0897702
$801$	−12.6622	−0.447396
$802$	55.0997	1.94564
$803$	4.68812	0.165440
$804$	35.2203	1.24212
$805$	4.07010	0.143452
$806$	−118.801	−4.18459
$807$	−28.6700	−1.00923
$808$	86.8556	3.05557
$809$	8.65520	0.304301	0.152150	−	0.988357i	$-0.451380\pi$
$809$	8.65520	0.304301	0.152150	+	0.988357i	$0.451380\pi$
$810$	5.95430	0.209213
$811$	32.2900	1.13385	0.566927	−	0.823768i	$-0.308132\pi$
$811$	32.2900	1.13385	0.566927	+	0.823768i	$0.308132\pi$
$812$	−5.91265	−0.207493
$813$	9.20417	0.322804
$814$	9.98184	0.349863
$815$	15.3273	0.536893
$816$	−101.487	−3.55275
$817$	−8.47623	−0.296546
$818$	33.3893	1.16743
$819$	−1.67663	−0.0585863
$820$	−19.4259	−0.678382
$821$	47.9178	1.67234	0.836172	−	0.548468i	$-0.184789\pi$
$821$	47.9178	1.67234	0.836172	+	0.548468i	$0.184789\pi$
$822$	33.8512	1.18070
$823$	47.1327	1.64294	0.821471	−	0.570250i	$-0.193154\pi$
$823$	47.1327	1.64294	0.821471	+	0.570250i	$0.193154\pi$
$824$	97.7684	3.40592
$825$	0.0745076	0.00259402
$826$	−6.58681	−0.229185
$827$	46.0328	1.60072	0.800358	−	0.599522i	$-0.204643\pi$
$827$	46.0328	1.60072	0.800358	+	0.599522i	$0.204643\pi$
$828$	25.5737	0.888746
$829$	−18.0705	−0.627616	−0.313808	−	0.949486i	$-0.601605\pi$
$829$	−18.0705	−0.627616	−0.313808	+	0.949486i	$0.601605\pi$
$830$	32.3102	1.12150
$831$	−19.8425	−0.688330
$832$	−100.942	−3.49952
$833$	51.8480	1.79643
$834$	−24.1218	−0.835270
$835$	−22.0300	−0.762378
$836$	−2.86509	−0.0990913
$837$	10.0216	0.346396
$838$	−36.2034	−1.25062
$839$	−8.19390	−0.282885	−0.141442	−	0.989946i	$-0.545174\pi$
$839$	−8.19390	−0.282885	−0.141442	+	0.989946i	$0.545174\pi$
$840$	7.48467	0.258246
$841$	−20.4394	−0.704808
$842$	25.8065	0.889351
$843$	32.7137	1.12672
$844$	−53.4246	−1.83895
$845$	13.8333	0.475881
$846$	2.70026	0.0928369
$847$	−4.08902	−0.140500
$848$	68.8040	2.36274
$849$	−26.7479	−0.917985
$850$	2.81072	0.0964070
$851$	−32.9958	−1.13108
$852$	45.3504	1.55368
$853$	23.0917	0.790646	0.395323	−	0.918542i	$-0.370633\pi$
$853$	23.0917	0.790646	0.395323	+	0.918542i	$0.370633\pi$
$854$	9.96105	0.340860
$855$	2.20508	0.0754123
$856$	−69.3035	−2.36874
$857$	29.1910	0.997146	0.498573	−	0.866848i	$-0.333858\pi$
$857$	29.1910	0.997146	0.498573	+	0.866848i	$0.333858\pi$
$858$	6.41877	0.219133
$859$	−45.4744	−1.55157	−0.775783	−	0.630999i	$-0.782645\pi$
$859$	−45.4744	−1.55157	−0.775783	+	0.630999i	$0.782645\pi$
$860$	−98.9007	−3.37249
$861$	−0.635833	−0.0216691
$862$	−34.0728	−1.16052
$863$	31.0730	1.05774	0.528869	−	0.848703i	$-0.322616\pi$
$863$	31.0730	1.05774	0.528869	+	0.848703i	$0.322616\pi$
$864$	18.4520	0.627750
$865$	−19.6701	−0.668804
$866$	43.2801	1.47072
$867$	40.2212	1.36598
$868$	20.2519	0.687395
$869$	1.35155	0.0458483
$870$	−17.4214	−0.590640
$871$	−29.2213	−0.990126
$872$	148.798	5.03892
$873$	−8.67832	−0.293717
$874$	13.0505	0.441440
$875$	−4.32658	−0.146265
$876$	−45.8146	−1.54793
$877$	−4.04121	−0.136462	−0.0682311	−	0.997670i	$-0.521736\pi$
$877$	−4.04121	−0.136462	−0.0682311	+	0.997670i	$0.521736\pi$
$878$	8.26783	0.279026
$879$	−5.15932	−0.174020
$880$	−16.0185	−0.539985
$881$	−24.3680	−0.820980	−0.410490	−	0.911865i	$-0.634642\pi$
$881$	−24.3680	−0.820980	−0.410490	+	0.911865i	$0.634642\pi$
$882$	−18.5080	−0.623196
$883$	−45.8443	−1.54278	−0.771391	−	0.636362i	$-0.780439\pi$
$883$	−45.8443	−1.54278	−0.771391	+	0.636362i	$0.780439\pi$
$884$	175.723	5.91021
$885$	−14.0843	−0.473439
$886$	25.7098	0.863739
$887$	25.2072	0.846375	0.423187	−	0.906042i	$-0.360911\pi$
$887$	25.2072	0.846375	0.423187	+	0.906042i	$0.360911\pi$
$888$	−60.6773	−2.03620
$889$	−4.49091	−0.150620
$890$	−75.3944	−2.52723
$891$	−0.541461	−0.0181396
$892$	103.102	3.45212
$893$	1.00000	0.0334637
$894$	11.3604	0.379950
$895$	43.5191	1.45468
$896$	9.61739	0.321294
$897$	−21.2178	−0.708441
$898$	84.5068	2.82003
$899$	−29.3216	−0.977928
$900$	−0.728124	−0.0242708
$901$	−38.7937	−1.29241
$902$	2.43421	0.0810502
$903$	−3.23714	−0.107725
$904$	−124.751	−4.14916
$905$	−5.55344	−0.184603
$906$	48.6684	1.61690
$907$	−28.6832	−0.952409	−0.476205	−	0.879335i	$-0.657988\pi$
$907$	−28.6832	−0.952409	−0.476205	+	0.879335i	$0.657988\pi$
$908$	74.9978	2.48889
$909$	9.77259	0.324136
$910$	−9.98318	−0.330939
$911$	44.0242	1.45859	0.729293	−	0.684201i	$-0.239849\pi$
$911$	44.0242	1.45859	0.729293	+	0.684201i	$0.239849\pi$
$912$	13.4162	0.444256
$913$	−2.93816	−0.0972390
$914$	8.50385	0.281282
$915$	21.2993	0.704133
$916$	−79.8295	−2.63764
$917$	−2.56558	−0.0847229
$918$	−20.4261	−0.674160
$919$	−23.2387	−0.766573	−0.383287	−	0.923629i	$-0.625208\pi$
$919$	−23.2387	−0.766573	−0.383287	+	0.923629i	$0.625208\pi$
$920$	94.7185	3.12278
$921$	5.44081	0.179281
$922$	98.6585	3.24914
$923$	−37.6260	−1.23848
$924$	−1.09420	−0.0359966
$925$	0.939446	0.0308888
$926$	6.53920	0.214892
$927$	11.0004	0.361302
$928$	−53.9877	−1.77223
$929$	−41.4909	−1.36127	−0.680636	−	0.732622i	$-0.738296\pi$
$929$	−41.4909	−1.36127	−0.680636	+	0.732622i	$0.738296\pi$
$930$	59.6715	1.95670
$931$	−6.85415	−0.224636
$932$	156.439	5.12432
$933$	21.0326	0.688575
$934$	25.7779	0.843477
$935$	9.03172	0.295369
$936$	−39.0182	−1.27535
$937$	−20.6869	−0.675812	−0.337906	−	0.941180i	$-0.609719\pi$
$937$	−20.6869	−0.675812	−0.337906	+	0.941180i	$0.609719\pi$
$938$	6.86413	0.224122
$939$	−15.1762	−0.495256
$940$	11.6680	0.380569
$941$	42.9252	1.39932	0.699661	−	0.714475i	$-0.253334\pi$
$941$	42.9252	1.39932	0.699661	+	0.714475i	$0.253334\pi$
$942$	46.5229	1.51580
$943$	−8.04648	−0.262029
$944$	−85.6923	−2.78905
$945$	0.842139	0.0273948
$946$	12.3930	0.402930
$947$	54.2239	1.76204	0.881020	−	0.473079i	$-0.156857\pi$
$947$	54.2239	1.76204	0.881020	+	0.473079i	$0.156857\pi$
$948$	−13.2080	−0.428977
$949$	38.0111	1.23389
$950$	−0.371569	−0.0120553
$951$	−4.90155	−0.158944
$952$	−25.6759	−0.832161
$953$	29.3572	0.950972	0.475486	−	0.879723i	$-0.342272\pi$
$953$	29.3572	0.950972	0.475486	+	0.879723i	$0.342272\pi$
$954$	13.8480	0.448347
$955$	40.4067	1.30753
$956$	14.4824	0.468395
$957$	1.58423	0.0512109
$958$	−36.6268	−1.18336
$959$	4.78770	0.154603
$960$	50.7010	1.63637
$961$	69.4318	2.23974
$962$	80.9325	2.60937
$963$	−7.79770	−0.251277
$964$	−70.2730	−2.26334
$965$	53.4346	1.72012
$966$	4.98409	0.160360
$967$	−15.2193	−0.489420	−0.244710	−	0.969596i	$-0.578693\pi$
$967$	−15.2193	−0.489420	−0.244710	+	0.969596i	$0.578693\pi$
$968$	−95.1588	−3.05852
$969$	−7.56447	−0.243006
$970$	−51.6734	−1.65913
$971$	0.850186	0.0272838	0.0136419	−	0.999907i	$-0.495658\pi$
$971$	0.850186	0.0272838	0.0136419	+	0.999907i	$0.495658\pi$
$972$	5.29141	0.169722
$973$	−3.41164	−0.109372
$974$	−75.0036	−2.40327
$975$	0.604105	0.0193469
$976$	129.590	4.14807
$977$	1.29206	0.0413366	0.0206683	−	0.999786i	$-0.493421\pi$
$977$	1.29206	0.0413366	0.0206683	+	0.999786i	$0.493421\pi$
$978$	18.7693	0.600175
$979$	6.85607	0.219121
$980$	−79.9743	−2.55468
$981$	16.7420	0.534531
$982$	−37.1426	−1.18527
$983$	24.2367	0.773032	0.386516	−	0.922283i	$-0.373678\pi$
$983$	24.2367	0.773032	0.386516	+	0.922283i	$0.373678\pi$
$984$	−14.7970	−0.471711
$985$	33.7525	1.07544
$986$	59.7635	1.90326
$987$	0.381908	0.0121563
$988$	−23.2301	−0.739047
$989$	−40.9660	−1.30264
$990$	−3.22402	−0.102466
$991$	41.8952	1.33084	0.665422	−	0.746467i	$-0.268251\pi$
$991$	41.8952	1.33084	0.665422	+	0.746467i	$0.268251\pi$
$992$	184.918	5.87115
$993$	−36.1520	−1.14725
$994$	8.83841	0.280337
$995$	33.4917	1.06176
$996$	28.7131	0.909811
$997$	−13.4242	−0.425149	−0.212574	−	0.977145i	$-0.568185\pi$
$997$	−13.4242	−0.425149	−0.212574	+	0.977145i	$0.568185\pi$
$998$	35.0638	1.10993
$999$	−6.82713	−0.216001

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2679.2.a.n.1.23	✓	23
3.2	odd	2		8037.2.a.p.1.1		23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2679.2.a.n.1.23	✓	23	1.1	even	1	trivial
8037.2.a.p.1.1		23	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:	\( N \)	\(=\)	\( 2679 = 3 \cdot 19 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2679.a (trivial)

\(f(q)\)	\(=\)	\(q+2.70026 q^{2} +1.00000 q^{3} +5.29141 q^{4} +2.20508 q^{5} +2.70026 q^{6} +0.381908 q^{7} +8.88768 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.70026 q^{2} +1.00000 q^{3} +5.29141 q^{4} +2.20508 q^{5} +2.70026 q^{6} +0.381908 q^{7} +8.88768 q^{8} +1.00000 q^{9} +5.95430 q^{10} -0.541461 q^{11} +5.29141 q^{12} -4.39015 q^{13} +1.03125 q^{14} +2.20508 q^{15} +13.4162 q^{16} -7.56447 q^{17} +2.70026 q^{18} +1.00000 q^{19} +11.6680 q^{20} +0.381908 q^{21} -1.46209 q^{22} +4.83305 q^{23} +8.88768 q^{24} -0.137605 q^{25} -11.8545 q^{26} +1.00000 q^{27} +2.02083 q^{28} -2.92584 q^{29} +5.95430 q^{30} +10.0216 q^{31} +18.4520 q^{32} -0.541461 q^{33} -20.4261 q^{34} +0.842139 q^{35} +5.29141 q^{36} -6.82713 q^{37} +2.70026 q^{38} -4.39015 q^{39} +19.5981 q^{40} -1.66489 q^{41} +1.03125 q^{42} -8.47623 q^{43} -2.86509 q^{44} +2.20508 q^{45} +13.0505 q^{46} +1.00000 q^{47} +13.4162 q^{48} -6.85415 q^{49} -0.371569 q^{50} -7.56447 q^{51} -23.2301 q^{52} +5.12841 q^{53} +2.70026 q^{54} -1.19397 q^{55} +3.39428 q^{56} +1.00000 q^{57} -7.90055 q^{58} -6.38720 q^{59} +11.6680 q^{60} +9.65918 q^{61} +27.0609 q^{62} +0.381908 q^{63} +22.9928 q^{64} -9.68064 q^{65} -1.46209 q^{66} +6.65611 q^{67} -40.0268 q^{68} +4.83305 q^{69} +2.27400 q^{70} +8.57056 q^{71} +8.88768 q^{72} -8.65829 q^{73} -18.4350 q^{74} -0.137605 q^{75} +5.29141 q^{76} -0.206788 q^{77} -11.8545 q^{78} -2.49612 q^{79} +29.5839 q^{80} +1.00000 q^{81} -4.49563 q^{82} +5.42636 q^{83} +2.02083 q^{84} -16.6803 q^{85} -22.8880 q^{86} -2.92584 q^{87} -4.81233 q^{88} -12.6622 q^{89} +5.95430 q^{90} -1.67663 q^{91} +25.5737 q^{92} +10.0216 q^{93} +2.70026 q^{94} +2.20508 q^{95} +18.4520 q^{96} -8.67832 q^{97} -18.5080 q^{98} -0.541461 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q + 5 q^{2} + 23 q^{3} + 25 q^{4} + 12 q^{5} + 5 q^{6} - 2 q^{7} + 12 q^{8} + 23 q^{9}+O(q^{10}) \) 23 * q + 5 * q^2 + 23 * q^3 + 25 * q^4 + 12 * q^5 + 5 * q^6 - 2 * q^7 + 12 * q^8 + 23 * q^9	\( 23 q + 5 q^{2} + 23 q^{3} + 25 q^{4} + 12 q^{5} + 5 q^{6} - 2 q^{7} + 12 q^{8} + 23 q^{9} + q^{10} + 13 q^{11} + 25 q^{12} + 5 q^{13} + 11 q^{14} + 12 q^{15} + 33 q^{16} + 22 q^{17} + 5 q^{18} + 23 q^{19} + 23 q^{20} - 2 q^{21} + q^{22} + 23 q^{23} + 12 q^{24} + 31 q^{25} + 21 q^{26} + 23 q^{27} - 22 q^{28} + 24 q^{29} + q^{30} + 20 q^{31} + 19 q^{32} + 13 q^{33} - 14 q^{34} + 15 q^{35} + 25 q^{36} + 8 q^{37} + 5 q^{38} + 5 q^{39} - 15 q^{40} + 28 q^{41} + 11 q^{42} - 6 q^{43} + q^{44} + 12 q^{45} + 29 q^{46} + 23 q^{47} + 33 q^{48} + 39 q^{49} + 27 q^{50} + 22 q^{51} + 12 q^{52} + 22 q^{53} + 5 q^{54} - 28 q^{55} + 30 q^{56} + 23 q^{57} - 5 q^{58} + 53 q^{59} + 23 q^{60} + 4 q^{61} + 38 q^{62} - 2 q^{63} + 30 q^{64} + 27 q^{65} + q^{66} - 6 q^{68} + 23 q^{69} + 30 q^{70} + 54 q^{71} + 12 q^{72} + 15 q^{73} - 12 q^{74} + 31 q^{75} + 25 q^{76} + 33 q^{77} + 21 q^{78} - 8 q^{79} + 45 q^{80} + 23 q^{81} - 69 q^{82} + 20 q^{83} - 22 q^{84} - 25 q^{85} + 50 q^{86} + 24 q^{87} + 48 q^{88} + 26 q^{89} + q^{90} + 11 q^{91} + 81 q^{92} + 20 q^{93} + 5 q^{94} + 12 q^{95} + 19 q^{96} - 4 q^{97} - 55 q^{98} + 13 q^{99}+O(q^{100}) \) 23 * q + 5 * q^2 + 23 * q^3 + 25 * q^4 + 12 * q^5 + 5 * q^6 - 2 * q^7 + 12 * q^8 + 23 * q^9 + q^10 + 13 * q^11 + 25 * q^12 + 5 * q^13 + 11 * q^14 + 12 * q^15 + 33 * q^16 + 22 * q^17 + 5 * q^18 + 23 * q^19 + 23 * q^20 - 2 * q^21 + q^22 + 23 * q^23 + 12 * q^24 + 31 * q^25 + 21 * q^26 + 23 * q^27 - 22 * q^28 + 24 * q^29 + q^30 + 20 * q^31 + 19 * q^32 + 13 * q^33 - 14 * q^34 + 15 * q^35 + 25 * q^36 + 8 * q^37 + 5 * q^38 + 5 * q^39 - 15 * q^40 + 28 * q^41 + 11 * q^42 - 6 * q^43 + q^44 + 12 * q^45 + 29 * q^46 + 23 * q^47 + 33 * q^48 + 39 * q^49 + 27 * q^50 + 22 * q^51 + 12 * q^52 + 22 * q^53 + 5 * q^54 - 28 * q^55 + 30 * q^56 + 23 * q^57 - 5 * q^58 + 53 * q^59 + 23 * q^60 + 4 * q^61 + 38 * q^62 - 2 * q^63 + 30 * q^64 + 27 * q^65 + q^66 - 6 * q^68 + 23 * q^69 + 30 * q^70 + 54 * q^71 + 12 * q^72 + 15 * q^73 - 12 * q^74 + 31 * q^75 + 25 * q^76 + 33 * q^77 + 21 * q^78 - 8 * q^79 + 45 * q^80 + 23 * q^81 - 69 * q^82 + 20 * q^83 - 22 * q^84 - 25 * q^85 + 50 * q^86 + 24 * q^87 + 48 * q^88 + 26 * q^89 + q^90 + 11 * q^91 + 81 * q^92 + 20 * q^93 + 5 * q^94 + 12 * q^95 + 19 * q^96 - 4 * q^97 - 55 * q^98 + 13 * q^99

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