LMFDB - Embedded newform 6022.2.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, 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("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.32468 q^{3} +1.00000 q^{4} +2.75364 q^{5} -2.32468 q^{6} +1.28652 q^{7} +1.00000 q^{8} +2.40413 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.32468 q^{3} +1.00000 q^{4} +2.75364 q^{5} -2.32468 q^{6} +1.28652 q^{7} +1.00000 q^{8} +2.40413 q^{9} +2.75364 q^{10} +5.14313 q^{11} -2.32468 q^{12} -3.46944 q^{13} +1.28652 q^{14} -6.40132 q^{15} +1.00000 q^{16} +5.28330 q^{17} +2.40413 q^{18} +4.57314 q^{19} +2.75364 q^{20} -2.99075 q^{21} +5.14313 q^{22} -4.85233 q^{23} -2.32468 q^{24} +2.58252 q^{25} -3.46944 q^{26} +1.38520 q^{27} +1.28652 q^{28} -3.32316 q^{29} -6.40132 q^{30} -6.56627 q^{31} +1.00000 q^{32} -11.9561 q^{33} +5.28330 q^{34} +3.54261 q^{35} +2.40413 q^{36} +7.42952 q^{37} +4.57314 q^{38} +8.06533 q^{39} +2.75364 q^{40} +12.6309 q^{41} -2.99075 q^{42} +11.0586 q^{43} +5.14313 q^{44} +6.62010 q^{45} -4.85233 q^{46} +3.70952 q^{47} -2.32468 q^{48} -5.34486 q^{49} +2.58252 q^{50} -12.2820 q^{51} -3.46944 q^{52} +2.37727 q^{53} +1.38520 q^{54} +14.1623 q^{55} +1.28652 q^{56} -10.6311 q^{57} -3.32316 q^{58} +1.76611 q^{59} -6.40132 q^{60} -8.21660 q^{61} -6.56627 q^{62} +3.09297 q^{63} +1.00000 q^{64} -9.55357 q^{65} -11.9561 q^{66} +12.3428 q^{67} +5.28330 q^{68} +11.2801 q^{69} +3.54261 q^{70} -15.3500 q^{71} +2.40413 q^{72} -11.5550 q^{73} +7.42952 q^{74} -6.00352 q^{75} +4.57314 q^{76} +6.61674 q^{77} +8.06533 q^{78} -9.41291 q^{79} +2.75364 q^{80} -10.4325 q^{81} +12.6309 q^{82} -9.95973 q^{83} -2.99075 q^{84} +14.5483 q^{85} +11.0586 q^{86} +7.72527 q^{87} +5.14313 q^{88} +10.0941 q^{89} +6.62010 q^{90} -4.46350 q^{91} -4.85233 q^{92} +15.2645 q^{93} +3.70952 q^{94} +12.5928 q^{95} -2.32468 q^{96} -7.86047 q^{97} -5.34486 q^{98} +12.3648 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9}+O(q^{10}) $ 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9	\( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9} + 20 q^{10} + 46 q^{11} + 25 q^{12} + 30 q^{13} + 29 q^{14} + 13 q^{15} + 68 q^{16} + 73 q^{17} + 87 q^{18} + 56 q^{19} + 20 q^{20} - 5 q^{21} + 46 q^{22} + 63 q^{23} + 25 q^{24} + 88 q^{25} + 30 q^{26} + 67 q^{27} + 29 q^{28} + 43 q^{29} + 13 q^{30} + 68 q^{31} + 68 q^{32} + 26 q^{33} + 73 q^{34} + 50 q^{35} + 87 q^{36} + 8 q^{37} + 56 q^{38} + 6 q^{39} + 20 q^{40} + 64 q^{41} - 5 q^{42} + 52 q^{43} + 46 q^{44} + 7 q^{45} + 63 q^{46} + 94 q^{47} + 25 q^{48} + 91 q^{49} + 88 q^{50} + 20 q^{51} + 30 q^{52} + 38 q^{53} + 67 q^{54} + 37 q^{55} + 29 q^{56} + 4 q^{57} + 43 q^{58} + 84 q^{59} + 13 q^{60} + 26 q^{61} + 68 q^{62} + 22 q^{63} + 68 q^{64} - 20 q^{65} + 26 q^{66} + 54 q^{67} + 73 q^{68} - 11 q^{69} + 50 q^{70} + 46 q^{71} + 87 q^{72} + 62 q^{73} + 8 q^{74} + 54 q^{75} + 56 q^{76} + 67 q^{77} + 6 q^{78} + 67 q^{79} + 20 q^{80} + 120 q^{81} + 64 q^{82} + 130 q^{83} - 5 q^{84} - 24 q^{85} + 52 q^{86} + 72 q^{87} + 46 q^{88} + 61 q^{89} + 7 q^{90} + 43 q^{91} + 63 q^{92} + 40 q^{93} + 94 q^{94} + 55 q^{95} + 25 q^{96} + 41 q^{97} + 91 q^{98} + 106 q^{99}+O(q^{100}) \) 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9 + 20 * q^10 + 46 * q^11 + 25 * q^12 + 30 * q^13 + 29 * q^14 + 13 * q^15 + 68 * q^16 + 73 * q^17 + 87 * q^18 + 56 * q^19 + 20 * q^20 - 5 * q^21 + 46 * q^22 + 63 * q^23 + 25 * q^24 + 88 * q^25 + 30 * q^26 + 67 * q^27 + 29 * q^28 + 43 * q^29 + 13 * q^30 + 68 * q^31 + 68 * q^32 + 26 * q^33 + 73 * q^34 + 50 * q^35 + 87 * q^36 + 8 * q^37 + 56 * q^38 + 6 * q^39 + 20 * q^40 + 64 * q^41 - 5 * q^42 + 52 * q^43 + 46 * q^44 + 7 * q^45 + 63 * q^46 + 94 * q^47 + 25 * q^48 + 91 * q^49 + 88 * q^50 + 20 * q^51 + 30 * q^52 + 38 * q^53 + 67 * q^54 + 37 * q^55 + 29 * q^56 + 4 * q^57 + 43 * q^58 + 84 * q^59 + 13 * q^60 + 26 * q^61 + 68 * q^62 + 22 * q^63 + 68 * q^64 - 20 * q^65 + 26 * q^66 + 54 * q^67 + 73 * q^68 - 11 * q^69 + 50 * q^70 + 46 * q^71 + 87 * q^72 + 62 * q^73 + 8 * q^74 + 54 * q^75 + 56 * q^76 + 67 * q^77 + 6 * q^78 + 67 * q^79 + 20 * q^80 + 120 * q^81 + 64 * q^82 + 130 * q^83 - 5 * q^84 - 24 * q^85 + 52 * q^86 + 72 * q^87 + 46 * q^88 + 61 * q^89 + 7 * q^90 + 43 * q^91 + 63 * q^92 + 40 * q^93 + 94 * q^94 + 55 * q^95 + 25 * q^96 + 41 * q^97 + 91 * q^98 + 106 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.32468	−1.34215	−0.671077	−	0.741388i	$-0.734168\pi$
$3$	−2.32468	−1.34215	−0.671077	+	0.741388i	$0.734168\pi$
$4$	1.00000	0.500000
$5$	2.75364	1.23146	0.615732	−	0.787956i	$-0.288860\pi$
$5$	2.75364	1.23146	0.615732	+	0.787956i	$0.288860\pi$
$6$	−2.32468	−0.949046
$7$	1.28652	0.486259	0.243130	−	0.969994i	$-0.421826\pi$
$7$	1.28652	0.486259	0.243130	+	0.969994i	$0.421826\pi$
$8$	1.00000	0.353553
$9$	2.40413	0.801377
$10$	2.75364	0.870776
$11$	5.14313	1.55071	0.775356	−	0.631525i	$-0.217571\pi$
$11$	5.14313	1.55071	0.775356	+	0.631525i	$0.217571\pi$
$12$	−2.32468	−0.671077
$13$	−3.46944	−0.962249	−0.481124	−	0.876652i	$-0.659771\pi$
$13$	−3.46944	−0.962249	−0.481124	+	0.876652i	$0.659771\pi$
$14$	1.28652	0.343837
$15$	−6.40132	−1.65281
$16$	1.00000	0.250000
$17$	5.28330	1.28139	0.640694	−	0.767796i	$-0.278647\pi$
$17$	5.28330	1.28139	0.640694	+	0.767796i	$0.278647\pi$
$18$	2.40413	0.566659
$19$	4.57314	1.04915	0.524575	−	0.851364i	$-0.324224\pi$
$19$	4.57314	1.04915	0.524575	+	0.851364i	$0.324224\pi$
$20$	2.75364	0.615732
$21$	−2.99075	−0.652635
$22$	5.14313	1.09652
$23$	−4.85233	−1.01178	−0.505890	−	0.862598i	$-0.668836\pi$
$23$	−4.85233	−1.01178	−0.505890	+	0.862598i	$0.668836\pi$
$24$	−2.32468	−0.474523
$25$	2.58252	0.516503
$26$	−3.46944	−0.680413
$27$	1.38520	0.266583
$28$	1.28652	0.243130
$29$	−3.32316	−0.617095	−0.308547	−	0.951209i	$-0.599843\pi$
$29$	−3.32316	−0.617095	−0.308547	+	0.951209i	$0.599843\pi$
$30$	−6.40132	−1.16872
$31$	−6.56627	−1.17934	−0.589668	−	0.807646i	$-0.700742\pi$
$31$	−6.56627	−1.17934	−0.589668	+	0.807646i	$0.700742\pi$
$32$	1.00000	0.176777
$33$	−11.9561	−2.08129
$34$	5.28330	0.906078
$35$	3.54261	0.598811
$36$	2.40413	0.400689
$37$	7.42952	1.22141	0.610703	−	0.791860i	$-0.290887\pi$
$37$	7.42952	1.22141	0.610703	+	0.791860i	$0.290887\pi$
$38$	4.57314	0.741862
$39$	8.06533	1.29149
$40$	2.75364	0.435388
$41$	12.6309	1.97262	0.986311	−	0.164896i	$-0.0527287\pi$
$41$	12.6309	1.97262	0.986311	+	0.164896i	$0.0527287\pi$
$42$	−2.99075	−0.461483
$43$	11.0586	1.68642	0.843212	−	0.537581i	$-0.180662\pi$
$43$	11.0586	1.68642	0.843212	+	0.537581i	$0.180662\pi$
$44$	5.14313	0.775356
$45$	6.62010	0.986867
$46$	−4.85233	−0.715437
$47$	3.70952	0.541089	0.270544	−	0.962707i	$-0.412796\pi$
$47$	3.70952	0.541089	0.270544	+	0.962707i	$0.412796\pi$
$48$	−2.32468	−0.335538
$49$	−5.34486	−0.763552
$50$	2.58252	0.365223
$51$	−12.2820	−1.71982
$52$	−3.46944	−0.481124
$53$	2.37727	0.326544	0.163272	−	0.986581i	$-0.447795\pi$
$53$	2.37727	0.326544	0.163272	+	0.986581i	$0.447795\pi$
$54$	1.38520	0.188502
$55$	14.1623	1.90964
$56$	1.28652	0.171919
$57$	−10.6311	−1.40812
$58$	−3.32316	−0.436352
$59$	1.76611	0.229928	0.114964	−	0.993370i	$-0.463325\pi$
$59$	1.76611	0.229928	0.114964	+	0.993370i	$0.463325\pi$
$60$	−6.40132	−0.826407
$61$	−8.21660	−1.05203	−0.526014	−	0.850476i	$-0.676314\pi$
$61$	−8.21660	−1.05203	−0.526014	+	0.850476i	$0.676314\pi$
$62$	−6.56627	−0.833917
$63$	3.09297	0.389677
$64$	1.00000	0.125000
$65$	−9.55357	−1.18497
$66$	−11.9561	−1.47170
$67$	12.3428	1.50791	0.753954	−	0.656927i	$-0.228144\pi$
$67$	12.3428	1.50791	0.753954	+	0.656927i	$0.228144\pi$
$68$	5.28330	0.640694
$69$	11.2801	1.35797
$70$	3.54261	0.423423
$71$	−15.3500	−1.82171	−0.910854	−	0.412728i	$-0.864576\pi$
$71$	−15.3500	−1.82171	−0.910854	+	0.412728i	$0.864576\pi$
$72$	2.40413	0.283330
$73$	−11.5550	−1.35241	−0.676207	−	0.736711i	$-0.736378\pi$
$73$	−11.5550	−1.35241	−0.676207	+	0.736711i	$0.736378\pi$
$74$	7.42952	0.863664
$75$	−6.00352	−0.693227
$76$	4.57314	0.524575
$77$	6.61674	0.754048
$78$	8.06533	0.913218
$79$	−9.41291	−1.05904	−0.529518	−	0.848299i	$-0.677627\pi$
$79$	−9.41291	−1.05904	−0.529518	+	0.848299i	$0.677627\pi$
$80$	2.75364	0.307866
$81$	−10.4325	−1.15917
$82$	12.6309	1.39485
$83$	−9.95973	−1.09322	−0.546611	−	0.837386i	$-0.684083\pi$
$83$	−9.95973	−1.09322	−0.546611	+	0.837386i	$0.684083\pi$
$84$	−2.99075	−0.326317
$85$	14.5483	1.57798
$86$	11.0586	1.19248
$87$	7.72527	0.828236
$88$	5.14313	0.548259
$89$	10.0941	1.06997	0.534986	−	0.844861i	$-0.320317\pi$
$89$	10.0941	1.06997	0.534986	+	0.844861i	$0.320317\pi$
$90$	6.62010	0.697820
$91$	−4.46350	−0.467902
$92$	−4.85233	−0.505890
$93$	15.2645	1.58285
$94$	3.70952	0.382608
$95$	12.5928	1.29199
$96$	−2.32468	−0.237262
$97$	−7.86047	−0.798110	−0.399055	−	0.916927i	$-0.630662\pi$
$97$	−7.86047	−0.798110	−0.399055	+	0.916927i	$0.630662\pi$
$98$	−5.34486	−0.539913
$99$	12.3648	1.24270
$100$	2.58252	0.258252
$101$	6.42067	0.638881	0.319440	−	0.947606i	$-0.396505\pi$
$101$	6.42067	0.638881	0.319440	+	0.947606i	$0.396505\pi$
$102$	−12.2820	−1.21610
$103$	15.2169	1.49936	0.749682	−	0.661799i	$-0.230207\pi$
$103$	15.2169	1.49936	0.749682	+	0.661799i	$0.230207\pi$
$104$	−3.46944	−0.340206
$105$	−8.23544	−0.803696
$106$	2.37727	0.230901
$107$	−0.477006	−0.0461139	−0.0230570	−	0.999734i	$-0.507340\pi$
$107$	−0.477006	−0.0461139	−0.0230570	+	0.999734i	$0.507340\pi$
$108$	1.38520	0.133291
$109$	15.5422	1.48868	0.744338	−	0.667804i	$-0.232765\pi$
$109$	15.5422	1.48868	0.744338	+	0.667804i	$0.232765\pi$
$110$	14.1623	1.35032
$111$	−17.2712	−1.63931
$112$	1.28652	0.121565
$113$	−11.8569	−1.11540	−0.557702	−	0.830041i	$-0.688317\pi$
$113$	−11.8569	−1.11540	−0.557702	+	0.830041i	$0.688317\pi$
$114$	−10.6311	−0.995693
$115$	−13.3616	−1.24597
$116$	−3.32316	−0.308547
$117$	−8.34098	−0.771124
$118$	1.76611	0.162584
$119$	6.79708	0.623087
$120$	−6.40132	−0.584358
$121$	15.4518	1.40471
$122$	−8.21660	−0.743896
$123$	−29.3629	−2.64756
$124$	−6.56627	−0.589668
$125$	−6.65687	−0.595409
$126$	3.09297	0.275543
$127$	−11.7769	−1.04503	−0.522516	−	0.852629i	$-0.675007\pi$
$127$	−11.7769	−1.04503	−0.522516	+	0.852629i	$0.675007\pi$
$128$	1.00000	0.0883883
$129$	−25.7077	−2.26344
$130$	−9.55357	−0.837903
$131$	7.31422	0.639047	0.319523	−	0.947578i	$-0.396477\pi$
$131$	7.31422	0.639047	0.319523	+	0.947578i	$0.396477\pi$
$132$	−11.9561	−1.04065
$133$	5.88344	0.510159
$134$	12.3428	1.06625
$135$	3.81435	0.328287
$136$	5.28330	0.453039
$137$	3.52396	0.301072	0.150536	−	0.988605i	$-0.451900\pi$
$137$	3.52396	0.301072	0.150536	+	0.988605i	$0.451900\pi$
$138$	11.2801	0.960227
$139$	−5.21107	−0.441997	−0.220998	−	0.975274i	$-0.570932\pi$
$139$	−5.21107	−0.441997	−0.220998	+	0.975274i	$0.570932\pi$
$140$	3.54261	0.299405
$141$	−8.62344	−0.726224
$142$	−15.3500	−1.28814
$143$	−17.8438	−1.49217
$144$	2.40413	0.200344
$145$	−9.15077	−0.759930
$146$	−11.5550	−0.956302
$147$	12.4251	1.02480
$148$	7.42952	0.610703
$149$	0.237570	0.0194625	0.00973125	−	0.999953i	$-0.496902\pi$
$149$	0.237570	0.0194625	0.00973125	+	0.999953i	$0.496902\pi$
$150$	−6.00352	−0.490185
$151$	0.529147	0.0430613	0.0215307	−	0.999768i	$-0.493146\pi$
$151$	0.529147	0.0430613	0.0215307	+	0.999768i	$0.493146\pi$
$152$	4.57314	0.370931
$153$	12.7017	1.02688
$154$	6.61674	0.533192
$155$	−18.0811	−1.45231
$156$	8.06533	0.645743
$157$	9.72488	0.776130	0.388065	−	0.921632i	$-0.373144\pi$
$157$	9.72488	0.776130	0.388065	+	0.921632i	$0.373144\pi$
$158$	−9.41291	−0.748851
$159$	−5.52640	−0.438272
$160$	2.75364	0.217694
$161$	−6.24263	−0.491988
$162$	−10.4325	−0.819658
$163$	−4.22621	−0.331023	−0.165511	−	0.986208i	$-0.552927\pi$
$163$	−4.22621	−0.331023	−0.165511	+	0.986208i	$0.552927\pi$
$164$	12.6309	0.986311
$165$	−32.9228	−2.56304
$166$	−9.95973	−0.773025
$167$	7.03814	0.544628	0.272314	−	0.962208i	$-0.412211\pi$
$167$	7.03814	0.544628	0.272314	+	0.962208i	$0.412211\pi$
$168$	−2.99075	−0.230741
$169$	−0.963009	−0.0740776
$170$	14.5483	1.11580
$171$	10.9944	0.840765
$172$	11.0586	0.843212
$173$	−12.3281	−0.937288	−0.468644	−	0.883387i	$-0.655257\pi$
$173$	−12.3281	−0.937288	−0.468644	+	0.883387i	$0.655257\pi$
$174$	7.72527	0.585652
$175$	3.32246	0.251155
$176$	5.14313	0.387678
$177$	−4.10564	−0.308599
$178$	10.0941	0.756584
$179$	14.1104	1.05466	0.527332	−	0.849659i	$-0.323192\pi$
$179$	14.1104	1.05466	0.527332	+	0.849659i	$0.323192\pi$
$180$	6.62010	0.493433
$181$	−25.7773	−1.91601	−0.958006	−	0.286748i	$-0.907426\pi$
$181$	−25.7773	−1.91601	−0.958006	+	0.286748i	$0.907426\pi$
$182$	−4.46350	−0.330857
$183$	19.1009	1.41198
$184$	−4.85233	−0.357719
$185$	20.4582	1.50412
$186$	15.2645	1.11924
$187$	27.1727	1.98706
$188$	3.70952	0.270544
$189$	1.78209	0.129628
$190$	12.5928	0.913576
$191$	6.76734	0.489667	0.244834	−	0.969565i	$-0.421267\pi$
$191$	6.76734	0.489667	0.244834	+	0.969565i	$0.421267\pi$
$192$	−2.32468	−0.167769
$193$	−7.85379	−0.565328	−0.282664	−	0.959219i	$-0.591218\pi$
$193$	−7.85379	−0.565328	−0.282664	+	0.959219i	$0.591218\pi$
$194$	−7.86047	−0.564349
$195$	22.2090	1.59042
$196$	−5.34486	−0.381776
$197$	−15.6025	−1.11163	−0.555816	−	0.831306i	$-0.687594\pi$
$197$	−15.6025	−1.11163	−0.555816	+	0.831306i	$0.687594\pi$
$198$	12.3648	0.878725
$199$	9.63155	0.682763	0.341381	−	0.939925i	$-0.389105\pi$
$199$	9.63155	0.682763	0.341381	+	0.939925i	$0.389105\pi$
$200$	2.58252	0.182611
$201$	−28.6930	−2.02385
$202$	6.42067	0.451757
$203$	−4.27531	−0.300068
$204$	−12.2820	−0.859910
$205$	34.7810	2.42921
$206$	15.2169	1.06021
$207$	−11.6656	−0.810818
$208$	−3.46944	−0.240562
$209$	23.5203	1.62693
$210$	−8.23544	−0.568299
$211$	19.8331	1.36537	0.682685	−	0.730713i	$-0.260812\pi$
$211$	19.8331	1.36537	0.682685	+	0.730713i	$0.260812\pi$
$212$	2.37727	0.163272
$213$	35.6838	2.44501
$214$	−0.477006	−0.0326075
$215$	30.4514	2.07677
$216$	1.38520	0.0942512
$217$	−8.44764	−0.573463
$218$	15.5422	1.05265
$219$	26.8618	1.81515
$220$	14.1623	0.954822
$221$	−18.3301	−1.23301
$222$	−17.2712	−1.15917
$223$	20.7040	1.38645	0.693223	−	0.720723i	$-0.256190\pi$
$223$	20.7040	1.38645	0.693223	+	0.720723i	$0.256190\pi$
$224$	1.28652	0.0859593
$225$	6.20871	0.413914
$226$	−11.8569	−0.788709
$227$	−19.4365	−1.29005	−0.645024	−	0.764163i	$-0.723153\pi$
$227$	−19.4365	−1.29005	−0.645024	+	0.764163i	$0.723153\pi$
$228$	−10.6311	−0.704061
$229$	13.2265	0.874034	0.437017	−	0.899453i	$-0.356035\pi$
$229$	13.2265	0.874034	0.437017	+	0.899453i	$0.356035\pi$
$230$	−13.3616	−0.881035
$231$	−15.3818	−1.01205
$232$	−3.32316	−0.218176
$233$	−10.6925	−0.700492	−0.350246	−	0.936658i	$-0.613902\pi$
$233$	−10.6925	−0.700492	−0.350246	+	0.936658i	$0.613902\pi$
$234$	−8.34098	−0.545267
$235$	10.2147	0.666331
$236$	1.76611	0.114964
$237$	21.8820	1.42139
$238$	6.79708	0.440589
$239$	23.2680	1.50508	0.752542	−	0.658545i	$-0.228828\pi$
$239$	23.2680	1.50508	0.752542	+	0.658545i	$0.228828\pi$
$240$	−6.40132	−0.413204
$241$	9.67058	0.622937	0.311468	−	0.950257i	$-0.399179\pi$
$241$	9.67058	0.622937	0.311468	+	0.950257i	$0.399179\pi$
$242$	15.4518	0.993277
$243$	20.0967	1.28920
$244$	−8.21660	−0.526014
$245$	−14.7178	−0.940287
$246$	−29.3629	−1.87211
$247$	−15.8662	−1.00954
$248$	−6.56627	−0.416958
$249$	23.1532	1.46727
$250$	−6.65687	−0.421018
$251$	20.6071	1.30071	0.650354	−	0.759631i	$-0.274620\pi$
$251$	20.6071	1.30071	0.650354	+	0.759631i	$0.274620\pi$
$252$	3.09297	0.194839
$253$	−24.9562	−1.56898
$254$	−11.7769	−0.738949
$255$	−33.8201	−2.11790
$256$	1.00000	0.0625000
$257$	−30.2587	−1.88749	−0.943744	−	0.330678i	$-0.892723\pi$
$257$	−30.2587	−1.88749	−0.943744	+	0.330678i	$0.892723\pi$
$258$	−25.7077	−1.60049
$259$	9.55824	0.593920
$260$	−9.55357	−0.592487
$261$	−7.98931	−0.494526
$262$	7.31422	0.451874
$263$	30.1633	1.85995	0.929974	−	0.367625i	$-0.119829\pi$
$263$	30.1633	1.85995	0.929974	+	0.367625i	$0.119829\pi$
$264$	−11.9561	−0.735848
$265$	6.54615	0.402127
$266$	5.88344	0.360737
$267$	−23.4655	−1.43607
$268$	12.3428	0.753954
$269$	−9.77949	−0.596266	−0.298133	−	0.954524i	$-0.596364\pi$
$269$	−9.77949	−0.596266	−0.298133	+	0.954524i	$0.596364\pi$
$270$	3.81435	0.232134
$271$	−12.1839	−0.740121	−0.370060	−	0.929008i	$-0.620663\pi$
$271$	−12.1839	−0.740121	−0.370060	+	0.929008i	$0.620663\pi$
$272$	5.28330	0.320347
$273$	10.3762	0.627997
$274$	3.52396	0.212890
$275$	13.2822	0.800947
$276$	11.2801	0.678983
$277$	31.9370	1.91891	0.959453	−	0.281868i	$-0.0909540\pi$
$277$	31.9370	1.91891	0.959453	+	0.281868i	$0.0909540\pi$
$278$	−5.21107	−0.312539
$279$	−15.7862	−0.945093
$280$	3.54261	0.211712
$281$	−12.8092	−0.764131	−0.382066	−	0.924135i	$-0.624787\pi$
$281$	−12.8092	−0.764131	−0.382066	+	0.924135i	$0.624787\pi$
$282$	−8.62344	−0.513518
$283$	−8.09698	−0.481316	−0.240658	−	0.970610i	$-0.577363\pi$
$283$	−8.09698	−0.481316	−0.240658	+	0.970610i	$0.577363\pi$
$284$	−15.3500	−0.910854
$285$	−29.2742	−1.73405
$286$	−17.8438	−1.05512
$287$	16.2500	0.959206
$288$	2.40413	0.141665
$289$	10.9132	0.641956
$290$	−9.15077	−0.537352
$291$	18.2731	1.07119
$292$	−11.5550	−0.676207
$293$	−1.59473	−0.0931649	−0.0465825	−	0.998914i	$-0.514833\pi$
$293$	−1.59473	−0.0931649	−0.0465825	+	0.998914i	$0.514833\pi$
$294$	12.4251	0.724646
$295$	4.86322	0.283148
$296$	7.42952	0.431832
$297$	7.12428	0.413393
$298$	0.237570	0.0137621
$299$	16.8349	0.973585
$300$	−6.00352	−0.346613
$301$	14.2272	0.820039
$302$	0.529147	0.0304490
$303$	−14.9260	−0.857476
$304$	4.57314	0.262288
$305$	−22.6255	−1.29553
$306$	12.7017	0.726110
$307$	14.1431	0.807190	0.403595	−	0.914938i	$-0.367761\pi$
$307$	14.1431	0.807190	0.403595	+	0.914938i	$0.367761\pi$
$308$	6.61674	0.377024
$309$	−35.3744	−2.01238
$310$	−18.0811	−1.02694
$311$	−5.67367	−0.321724	−0.160862	−	0.986977i	$-0.551427\pi$
$311$	−5.67367	−0.321724	−0.160862	+	0.986977i	$0.551427\pi$
$312$	8.06533	0.456609
$313$	14.6127	0.825958	0.412979	−	0.910740i	$-0.364488\pi$
$313$	14.6127	0.825958	0.412979	+	0.910740i	$0.364488\pi$
$314$	9.72488	0.548806
$315$	8.51690	0.479873
$316$	−9.41291	−0.529518
$317$	−4.18417	−0.235007	−0.117503	−	0.993072i	$-0.537489\pi$
$317$	−4.18417	−0.235007	−0.117503	+	0.993072i	$0.537489\pi$
$318$	−5.52640	−0.309905
$319$	−17.0914	−0.956936
$320$	2.75364	0.153933
$321$	1.10889	0.0618920
$322$	−6.24263	−0.347888
$323$	24.1613	1.34437
$324$	−10.4325	−0.579586
$325$	−8.95988	−0.497005
$326$	−4.22621	−0.234068
$327$	−36.1307	−1.99803
$328$	12.6309	0.697427
$329$	4.77237	0.263109
$330$	−32.9228	−1.81234
$331$	8.45346	0.464644	0.232322	−	0.972639i	$-0.425368\pi$
$331$	8.45346	0.464644	0.232322	+	0.972639i	$0.425368\pi$
$332$	−9.95973	−0.546611
$333$	17.8615	0.978806
$334$	7.03814	0.385110
$335$	33.9875	1.85693
$336$	−2.99075	−0.163159
$337$	−4.53866	−0.247237	−0.123618	−	0.992330i	$-0.539450\pi$
$337$	−4.53866	−0.247237	−0.123618	+	0.992330i	$0.539450\pi$
$338$	−0.963009	−0.0523808
$339$	27.5635	1.49704
$340$	14.5483	0.788992
$341$	−33.7712	−1.82881
$342$	10.9944	0.594511
$343$	−15.8819	−0.857544
$344$	11.0586	0.596241
$345$	31.0613	1.67229
$346$	−12.3281	−0.662763
$347$	25.4724	1.36743	0.683715	−	0.729749i	$-0.260363\pi$
$347$	25.4724	1.36743	0.683715	+	0.729749i	$0.260363\pi$
$348$	7.72527	0.414118
$349$	4.77559	0.255632	0.127816	−	0.991798i	$-0.459203\pi$
$349$	4.77559	0.255632	0.127816	+	0.991798i	$0.459203\pi$
$350$	3.32246	0.177593
$351$	−4.80588	−0.256519
$352$	5.14313	0.274130
$353$	−1.02763	−0.0546954	−0.0273477	−	0.999626i	$-0.508706\pi$
$353$	−1.02763	−0.0546954	−0.0273477	+	0.999626i	$0.508706\pi$
$354$	−4.10564	−0.218212
$355$	−42.2683	−2.24337
$356$	10.0941	0.534986
$357$	−15.8010	−0.836279
$358$	14.1104	0.745760
$359$	−32.0426	−1.69114	−0.845571	−	0.533863i	$-0.820740\pi$
$359$	−32.0426	−1.69114	−0.845571	+	0.533863i	$0.820740\pi$
$360$	6.62010	0.348910
$361$	1.91363	0.100718
$362$	−25.7773	−1.35482
$363$	−35.9204	−1.88533
$364$	−4.46350	−0.233951
$365$	−31.8184	−1.66545
$366$	19.1009	0.998423
$367$	10.1030	0.527374	0.263687	−	0.964608i	$-0.415061\pi$
$367$	10.1030	0.527374	0.263687	+	0.964608i	$0.415061\pi$
$368$	−4.85233	−0.252945
$369$	30.3664	1.58081
$370$	20.4582	1.06357
$371$	3.05841	0.158785
$372$	15.2645	0.791426
$373$	−9.40765	−0.487110	−0.243555	−	0.969887i	$-0.578314\pi$
$373$	−9.40765	−0.487110	−0.243555	+	0.969887i	$0.578314\pi$
$374$	27.1727	1.40507
$375$	15.4751	0.799130
$376$	3.70952	0.191304
$377$	11.5295	0.593799
$378$	1.78209	0.0916610
$379$	−2.39183	−0.122860	−0.0614302	−	0.998111i	$-0.519566\pi$
$379$	−2.39183	−0.122860	−0.0614302	+	0.998111i	$0.519566\pi$
$380$	12.5928	0.645996
$381$	27.3775	1.40259
$382$	6.76734	0.346247
$383$	30.8497	1.57635	0.788174	−	0.615453i	$-0.211027\pi$
$383$	30.8497	1.57635	0.788174	+	0.615453i	$0.211027\pi$
$384$	−2.32468	−0.118631
$385$	18.2201	0.928583
$386$	−7.85379	−0.399748
$387$	26.5864	1.35146
$388$	−7.86047	−0.399055
$389$	−13.2542	−0.672013	−0.336006	−	0.941860i	$-0.609076\pi$
$389$	−13.2542	−0.672013	−0.336006	+	0.941860i	$0.609076\pi$
$390$	22.2090	1.12460
$391$	−25.6363	−1.29648
$392$	−5.34486	−0.269956
$393$	−17.0032	−0.857699
$394$	−15.6025	−0.786042
$395$	−25.9197	−1.30416
$396$	12.3648	0.621352
$397$	14.0751	0.706409	0.353205	−	0.935546i	$-0.385092\pi$
$397$	14.0751	0.706409	0.353205	+	0.935546i	$0.385092\pi$
$398$	9.63155	0.482786
$399$	−13.6771	−0.684712
$400$	2.58252	0.129126
$401$	14.6636	0.732264	0.366132	−	0.930563i	$-0.380682\pi$
$401$	14.6636	0.732264	0.366132	+	0.930563i	$0.380682\pi$
$402$	−28.6930	−1.43107
$403$	22.7813	1.13481
$404$	6.42067	0.319440
$405$	−28.7274	−1.42748
$406$	−4.27531	−0.212180
$407$	38.2110	1.89405
$408$	−12.2820	−0.608048
$409$	7.25058	0.358518	0.179259	−	0.983802i	$-0.442630\pi$
$409$	7.25058	0.358518	0.179259	+	0.983802i	$0.442630\pi$
$410$	34.7810	1.71771
$411$	−8.19207	−0.404085
$412$	15.2169	0.749682
$413$	2.27214	0.111805
$414$	−11.6656	−0.573335
$415$	−27.4255	−1.34626
$416$	−3.46944	−0.170103
$417$	12.1141	0.593228
$418$	23.5203	1.15041
$419$	26.7022	1.30449	0.652244	−	0.758009i	$-0.273828\pi$
$419$	26.7022	1.30449	0.652244	+	0.758009i	$0.273828\pi$
$420$	−8.23544	−0.401848
$421$	−5.10713	−0.248906	−0.124453	−	0.992225i	$-0.539718\pi$
$421$	−5.10713	−0.248906	−0.124453	+	0.992225i	$0.539718\pi$
$422$	19.8331	0.965463
$423$	8.91817	0.433616
$424$	2.37727	0.115451
$425$	13.6442	0.661841
$426$	35.6838	1.72889
$427$	−10.5708	−0.511558
$428$	−0.477006	−0.0230570
$429$	41.4810	2.00272
$430$	30.4514	1.46850
$431$	−34.2150	−1.64808	−0.824039	−	0.566533i	$-0.808284\pi$
$431$	−34.2150	−1.64808	−0.824039	+	0.566533i	$0.808284\pi$
$432$	1.38520	0.0666456
$433$	28.2637	1.35827	0.679134	−	0.734014i	$-0.262356\pi$
$433$	28.2637	1.35827	0.679134	+	0.734014i	$0.262356\pi$
$434$	−8.44764	−0.405500
$435$	21.2726	1.01994
$436$	15.5422	0.744338
$437$	−22.1904	−1.06151
$438$	26.8618	1.28350
$439$	23.7208	1.13213	0.566066	−	0.824360i	$-0.308465\pi$
$439$	23.7208	1.13213	0.566066	+	0.824360i	$0.308465\pi$
$440$	14.1623	0.675161
$441$	−12.8498	−0.611893
$442$	−18.3301	−0.871873
$443$	−37.3981	−1.77684	−0.888418	−	0.459035i	$-0.848195\pi$
$443$	−37.3981	−1.77684	−0.888418	+	0.459035i	$0.848195\pi$
$444$	−17.2712	−0.819657
$445$	27.7955	1.31763
$446$	20.7040	0.980365
$447$	−0.552274	−0.0261217
$448$	1.28652	0.0607824
$449$	−33.2581	−1.56955	−0.784774	−	0.619781i	$-0.787221\pi$
$449$	−33.2581	−1.56955	−0.784774	+	0.619781i	$0.787221\pi$
$450$	6.20871	0.292681
$451$	64.9626	3.05897
$452$	−11.8569	−0.557702
$453$	−1.23010	−0.0577949
$454$	−19.4365	−0.912201
$455$	−12.2909	−0.576205
$456$	−10.6311	−0.497846
$457$	41.0686	1.92111	0.960555	−	0.278091i	$-0.0897018\pi$
$457$	41.0686	1.92111	0.960555	+	0.278091i	$0.0897018\pi$
$458$	13.2265	0.618035
$459$	7.31844	0.341596
$460$	−13.3616	−0.622986
$461$	12.6454	0.588953	0.294477	−	0.955659i	$-0.404855\pi$
$461$	12.6454	0.588953	0.294477	+	0.955659i	$0.404855\pi$
$462$	−15.3818	−0.715626
$463$	16.3472	0.759718	0.379859	−	0.925044i	$-0.375973\pi$
$463$	16.3472	0.759718	0.379859	+	0.925044i	$0.375973\pi$
$464$	−3.32316	−0.154274
$465$	42.0328	1.94922
$466$	−10.6925	−0.495322
$467$	16.0979	0.744923	0.372461	−	0.928048i	$-0.378514\pi$
$467$	16.0979	0.744923	0.372461	+	0.928048i	$0.378514\pi$
$468$	−8.34098	−0.385562
$469$	15.8792	0.733235
$470$	10.2147	0.471167
$471$	−22.6072	−1.04169
$472$	1.76611	0.0812918
$473$	56.8759	2.61516
$474$	21.8820	1.00507
$475$	11.8102	0.541890
$476$	6.79708	0.311543
$477$	5.71528	0.261685
$478$	23.2680	1.06425
$479$	−2.54939	−0.116485	−0.0582423	−	0.998302i	$-0.518550\pi$
$479$	−2.54939	−0.116485	−0.0582423	+	0.998302i	$0.518550\pi$
$480$	−6.40132	−0.292179
$481$	−25.7762	−1.17530
$482$	9.67058	0.440483
$483$	14.5121	0.660323
$484$	15.4518	0.702353
$485$	−21.6449	−0.982844
$486$	20.0967	0.911605
$487$	−11.0793	−0.502052	−0.251026	−	0.967980i	$-0.580768\pi$
$487$	−11.0793	−0.502052	−0.251026	+	0.967980i	$0.580768\pi$
$488$	−8.21660	−0.371948
$489$	9.82459	0.444283
$490$	−14.7178	−0.664883
$491$	13.9967	0.631662	0.315831	−	0.948815i	$-0.397717\pi$
$491$	13.9967	0.631662	0.315831	+	0.948815i	$0.397717\pi$
$492$	−29.3629	−1.32378
$493$	−17.5572	−0.790738
$494$	−15.8662	−0.713855
$495$	34.0480	1.53035
$496$	−6.56627	−0.294834
$497$	−19.7481	−0.885823
$498$	23.1532	1.03752
$499$	−10.2275	−0.457847	−0.228924	−	0.973444i	$-0.573521\pi$
$499$	−10.2275	−0.457847	−0.228924	+	0.973444i	$0.573521\pi$
$500$	−6.65687	−0.297704
$501$	−16.3614	−0.730975
$502$	20.6071	0.919740
$503$	−21.6508	−0.965361	−0.482681	−	0.875796i	$-0.660337\pi$
$503$	−21.6508	−0.965361	−0.482681	+	0.875796i	$0.660337\pi$
$504$	3.09297	0.137772
$505$	17.6802	0.786759
$506$	−24.9562	−1.10944
$507$	2.23869	0.0994236
$508$	−11.7769	−0.522516
$509$	−36.6530	−1.62462	−0.812309	−	0.583228i	$-0.801789\pi$
$509$	−36.6530	−1.62462	−0.812309	+	0.583228i	$0.801789\pi$
$510$	−33.8201	−1.49758
$511$	−14.8658	−0.657624
$512$	1.00000	0.0441942
$513$	6.33473	0.279685
$514$	−30.2587	−1.33466
$515$	41.9018	1.84641
$516$	−25.7077	−1.13172
$517$	19.0785	0.839073
$518$	9.55824	0.419965
$519$	28.6589	1.25798
$520$	−9.55357	−0.418952
$521$	−8.30626	−0.363904	−0.181952	−	0.983307i	$-0.558242\pi$
$521$	−8.30626	−0.363904	−0.181952	+	0.983307i	$0.558242\pi$
$522$	−7.98931	−0.349683
$523$	27.1331	1.18645	0.593225	−	0.805037i	$-0.297855\pi$
$523$	27.1331	1.18645	0.593225	+	0.805037i	$0.297855\pi$
$524$	7.31422	0.319523
$525$	−7.72366	−0.337088
$526$	30.1633	1.31518
$527$	−34.6916	−1.51119
$528$	−11.9561	−0.520323
$529$	0.545110	0.0237005
$530$	6.54615	0.284347
$531$	4.24596	0.184259
$532$	5.88344	0.255080
$533$	−43.8223	−1.89815
$534$	−23.4655	−1.01545
$535$	−1.31350	−0.0567876
$536$	12.3428	0.533126
$537$	−32.8022	−1.41552
$538$	−9.77949	−0.421624
$539$	−27.4893	−1.18405
$540$	3.81435	0.164143
$541$	−10.2107	−0.438992	−0.219496	−	0.975613i	$-0.570441\pi$
$541$	−10.2107	−0.438992	−0.219496	+	0.975613i	$0.570441\pi$
$542$	−12.1839	−0.523344
$543$	59.9239	2.57158
$544$	5.28330	0.226520
$545$	42.7976	1.83325
$546$	10.3762	0.444061
$547$	−34.6087	−1.47976	−0.739881	−	0.672737i	$-0.765118\pi$
$547$	−34.6087	−1.47976	−0.739881	+	0.672737i	$0.765118\pi$
$548$	3.52396	0.150536
$549$	−19.7538	−0.843071
$550$	13.2822	0.566355
$551$	−15.1973	−0.647426
$552$	11.2801	0.480113
$553$	−12.1099	−0.514966
$554$	31.9370	1.35687
$555$	−47.5587	−2.01876
$556$	−5.21107	−0.220998
$557$	11.9780	0.507525	0.253762	−	0.967267i	$-0.418332\pi$
$557$	11.9780	0.507525	0.253762	+	0.967267i	$0.418332\pi$
$558$	−15.7862	−0.668282
$559$	−38.3672	−1.62276
$560$	3.54261	0.149703
$561$	−63.1678	−2.66694
$562$	−12.8092	−0.540322
$563$	22.8053	0.961130	0.480565	−	0.876959i	$-0.340432\pi$
$563$	22.8053	0.961130	0.480565	+	0.876959i	$0.340432\pi$
$564$	−8.62344	−0.363112
$565$	−32.6496	−1.37358
$566$	−8.09698	−0.340342
$567$	−13.4217	−0.563658
$568$	−15.3500	−0.644071
$569$	−32.8227	−1.37600	−0.688000	−	0.725711i	$-0.741511\pi$
$569$	−32.8227	−1.37600	−0.688000	+	0.725711i	$0.741511\pi$
$570$	−29.2742	−1.22616
$571$	25.1993	1.05456	0.527278	−	0.849693i	$-0.323213\pi$
$571$	25.1993	1.05456	0.527278	+	0.849693i	$0.323213\pi$
$572$	−17.8438	−0.746085
$573$	−15.7319	−0.657209
$574$	16.2500	0.678261
$575$	−12.5312	−0.522588
$576$	2.40413	0.100172
$577$	25.6310	1.06703	0.533517	−	0.845789i	$-0.320870\pi$
$577$	25.6310	1.06703	0.533517	+	0.845789i	$0.320870\pi$
$578$	10.9132	0.453931
$579$	18.2575	0.758758
$580$	−9.15077	−0.379965
$581$	−12.8134	−0.531590
$582$	18.2731	0.757443
$583$	12.2266	0.506375
$584$	−11.5550	−0.478151
$585$	−22.9680	−0.949611
$586$	−1.59473	−0.0658775
$587$	−31.3961	−1.29585	−0.647927	−	0.761703i	$-0.724364\pi$
$587$	−31.3961	−1.29585	−0.647927	+	0.761703i	$0.724364\pi$
$588$	12.4251	0.512402
$589$	−30.0285	−1.23730
$590$	4.86322	0.200216
$591$	36.2708	1.49198
$592$	7.42952	0.305351
$593$	28.7891	1.18223	0.591114	−	0.806588i	$-0.298688\pi$
$593$	28.7891	1.18223	0.591114	+	0.806588i	$0.298688\pi$
$594$	7.12428	0.292313
$595$	18.7167	0.767309
$596$	0.237570	0.00973125
$597$	−22.3903	−0.916373
$598$	16.8349	0.688428
$599$	23.1141	0.944416	0.472208	−	0.881487i	$-0.343457\pi$
$599$	23.1141	0.944416	0.472208	+	0.881487i	$0.343457\pi$
$600$	−6.00352	−0.245093
$601$	−35.4657	−1.44668	−0.723338	−	0.690494i	$-0.757393\pi$
$601$	−35.4657	−1.44668	−0.723338	+	0.690494i	$0.757393\pi$
$602$	14.2272	0.579855
$603$	29.6736	1.20840
$604$	0.529147	0.0215307
$605$	42.5485	1.72984
$606$	−14.9260	−0.606327
$607$	10.9343	0.443810	0.221905	−	0.975068i	$-0.428773\pi$
$607$	10.9343	0.443810	0.221905	+	0.975068i	$0.428773\pi$
$608$	4.57314	0.185465
$609$	9.93873	0.402738
$610$	−22.6255	−0.916081
$611$	−12.8699	−0.520662
$612$	12.7017	0.513438
$613$	2.76699	0.111758	0.0558789	−	0.998438i	$-0.482204\pi$
$613$	2.76699	0.111758	0.0558789	+	0.998438i	$0.482204\pi$
$614$	14.1431	0.570769
$615$	−80.8547	−3.26038
$616$	6.61674	0.266596
$617$	−1.74914	−0.0704178	−0.0352089	−	0.999380i	$-0.511210\pi$
$617$	−1.74914	−0.0704178	−0.0352089	+	0.999380i	$0.511210\pi$
$618$	−35.3744	−1.42297
$619$	−23.9933	−0.964370	−0.482185	−	0.876069i	$-0.660157\pi$
$619$	−23.9933	−0.964370	−0.482185	+	0.876069i	$0.660157\pi$
$620$	−18.0811	−0.726155
$621$	−6.72147	−0.269723
$622$	−5.67367	−0.227494
$623$	12.9863	0.520284
$624$	8.06533	0.322871
$625$	−31.2432	−1.24973
$626$	14.6127	0.584041
$627$	−54.6770	−2.18359
$628$	9.72488	0.388065
$629$	39.2524	1.56509
$630$	8.51690	0.339322
$631$	9.11546	0.362881	0.181440	−	0.983402i	$-0.441924\pi$
$631$	9.11546	0.362881	0.181440	+	0.983402i	$0.441924\pi$
$632$	−9.41291	−0.374425
$633$	−46.1057	−1.83254
$634$	−4.18417	−0.166175
$635$	−32.4293	−1.28692
$636$	−5.52640	−0.219136
$637$	18.5437	0.734727
$638$	−17.0914	−0.676656
$639$	−36.9034	−1.45988
$640$	2.75364	0.108847
$641$	−15.8314	−0.625301	−0.312651	−	0.949868i	$-0.601217\pi$
$641$	−15.8314	−0.625301	−0.312651	+	0.949868i	$0.601217\pi$
$642$	1.10889	0.0437642
$643$	43.7963	1.72716	0.863578	−	0.504215i	$-0.168218\pi$
$643$	43.7963	1.72716	0.863578	+	0.504215i	$0.168218\pi$
$644$	−6.24263	−0.245994
$645$	−70.7898	−2.78735
$646$	24.1613	0.950613
$647$	31.5190	1.23914	0.619570	−	0.784942i	$-0.287307\pi$
$647$	31.5190	1.23914	0.619570	+	0.784942i	$0.287307\pi$
$648$	−10.4325	−0.409829
$649$	9.08332	0.356552
$650$	−8.95988	−0.351435
$651$	19.6381	0.769676
$652$	−4.22621	−0.165511
$653$	−21.8209	−0.853916	−0.426958	−	0.904271i	$-0.640415\pi$
$653$	−21.8209	−0.853916	−0.426958	+	0.904271i	$0.640415\pi$
$654$	−36.1307	−1.41282
$655$	20.1407	0.786963
$656$	12.6309	0.493156
$657$	−27.7798	−1.08379
$658$	4.77237	0.186046
$659$	−30.2810	−1.17958	−0.589790	−	0.807557i	$-0.700789\pi$
$659$	−30.2810	−1.17958	−0.589790	+	0.807557i	$0.700789\pi$
$660$	−32.9228	−1.28152
$661$	−46.3551	−1.80300	−0.901502	−	0.432774i	$-0.857535\pi$
$661$	−46.3551	−1.80300	−0.901502	+	0.432774i	$0.857535\pi$
$662$	8.45346	0.328553
$663$	42.6115	1.65489
$664$	−9.95973	−0.386513
$665$	16.2009	0.628243
$666$	17.8615	0.692121
$667$	16.1251	0.624365
$668$	7.03814	0.272314
$669$	−48.1303	−1.86082
$670$	33.9875	1.31305
$671$	−42.2590	−1.63139
$672$	−2.99075	−0.115371
$673$	30.6298	1.18069	0.590347	−	0.807150i	$-0.298991\pi$
$673$	30.6298	1.18069	0.590347	+	0.807150i	$0.298991\pi$
$674$	−4.53866	−0.174823
$675$	3.57731	0.137691
$676$	−0.963009	−0.0370388
$677$	−17.8955	−0.687780	−0.343890	−	0.939010i	$-0.611745\pi$
$677$	−17.8955	−0.687780	−0.343890	+	0.939010i	$0.611745\pi$
$678$	27.5635	1.05857
$679$	−10.1127	−0.388088
$680$	14.5483	0.557901
$681$	45.1837	1.73144
$682$	−33.7712	−1.29316
$683$	0.0440593	0.00168588	0.000842941	−	1.00000i	$-0.499732\pi$
$683$	0.0440593	0.00168588	0.000842941		1.00000i	$0.499732\pi$
$684$	10.9944	0.420383
$685$	9.70370	0.370759
$686$	−15.8819	−0.606375
$687$	−30.7474	−1.17309
$688$	11.0586	0.421606
$689$	−8.24780	−0.314216
$690$	31.0613	1.18248
$691$	−25.8782	−0.984455	−0.492227	−	0.870467i	$-0.663817\pi$
$691$	−25.8782	−0.984455	−0.492227	+	0.870467i	$0.663817\pi$
$692$	−12.3281	−0.468644
$693$	15.9075	0.604277
$694$	25.4724	0.966919
$695$	−14.3494	−0.544303
$696$	7.72527	0.292826
$697$	66.7331	2.52769
$698$	4.77559	0.180759
$699$	24.8567	0.940168
$700$	3.32246	0.125577
$701$	24.9671	0.942993	0.471496	−	0.881868i	$-0.343714\pi$
$701$	24.9671	0.942993	0.471496	+	0.881868i	$0.343714\pi$
$702$	−4.80588	−0.181386
$703$	33.9763	1.28144
$704$	5.14313	0.193839
$705$	−23.7458	−0.894319
$706$	−1.02763	−0.0386755
$707$	8.26033	0.310662
$708$	−4.10564	−0.154299
$709$	−49.5780	−1.86194	−0.930970	−	0.365096i	$-0.881036\pi$
$709$	−49.5780	−1.86194	−0.930970	+	0.365096i	$0.881036\pi$
$710$	−42.2683	−1.58630
$711$	−22.6299	−0.848686
$712$	10.0941	0.378292
$713$	31.8617	1.19323
$714$	−15.8010	−0.591338
$715$	−49.1352	−1.83755
$716$	14.1104	0.527332
$717$	−54.0907	−2.02005
$718$	−32.0426	−1.19582
$719$	−29.0469	−1.08327	−0.541633	−	0.840615i	$-0.682194\pi$
$719$	−29.0469	−1.08327	−0.541633	+	0.840615i	$0.682194\pi$
$720$	6.62010	0.246717
$721$	19.5768	0.729079
$722$	1.91363	0.0712181
$723$	−22.4810	−0.836077
$724$	−25.7773	−0.958006
$725$	−8.58211	−0.318732
$726$	−35.9204	−1.33313
$727$	35.1526	1.30374	0.651869	−	0.758332i	$-0.273985\pi$
$727$	35.1526	1.30374	0.651869	+	0.758332i	$0.273985\pi$
$728$	−4.46350	−0.165428
$729$	−15.4208	−0.571139
$730$	−31.8184	−1.17765
$731$	58.4260	2.16096
$732$	19.1009	0.705991
$733$	−12.5629	−0.464022	−0.232011	−	0.972713i	$-0.574531\pi$
$733$	−12.5629	−0.464022	−0.232011	+	0.972713i	$0.574531\pi$
$734$	10.1030	0.372910
$735$	34.2142	1.26201
$736$	−4.85233	−0.178859
$737$	63.4804	2.33833
$738$	30.3664	1.11780
$739$	46.1250	1.69674	0.848368	−	0.529407i	$-0.177586\pi$
$739$	46.1250	1.69674	0.848368	+	0.529407i	$0.177586\pi$
$740$	20.4582	0.752058
$741$	36.8839	1.35496
$742$	3.05841	0.112278
$743$	−31.8410	−1.16813	−0.584067	−	0.811706i	$-0.698539\pi$
$743$	−31.8410	−1.16813	−0.584067	+	0.811706i	$0.698539\pi$
$744$	15.2645	0.559622
$745$	0.654182	0.0239674
$746$	−9.40765	−0.344438
$747$	−23.9445	−0.876084
$748$	27.1727	0.993532
$749$	−0.613678	−0.0224233
$750$	15.4751	0.565070
$751$	−30.7823	−1.12326	−0.561631	−	0.827388i	$-0.689826\pi$
$751$	−30.7823	−1.12326	−0.561631	+	0.827388i	$0.689826\pi$
$752$	3.70952	0.135272
$753$	−47.9049	−1.74575
$754$	11.5295	0.419879
$755$	1.45708	0.0530285
$756$	1.78209	0.0648141
$757$	17.9517	0.652465	0.326232	−	0.945290i	$-0.394221\pi$
$757$	17.9517	0.652465	0.326232	+	0.945290i	$0.394221\pi$
$758$	−2.39183	−0.0868754
$759$	58.0150	2.10581
$760$	12.5928	0.456788
$761$	25.7440	0.933219	0.466610	−	0.884463i	$-0.345475\pi$
$761$	25.7440	0.933219	0.466610	+	0.884463i	$0.345475\pi$
$762$	27.3775	0.991784
$763$	19.9954	0.723882
$764$	6.76734	0.244834
$765$	34.9760	1.26456
$766$	30.8497	1.11465
$767$	−6.12740	−0.221248
$768$	−2.32468	−0.0838846
$769$	−49.4839	−1.78444	−0.892218	−	0.451605i	$-0.850852\pi$
$769$	−49.4839	−1.78444	−0.892218	+	0.451605i	$0.850852\pi$
$770$	18.2201	0.656607
$771$	70.3418	2.53330
$772$	−7.85379	−0.282664
$773$	−2.78136	−0.100039	−0.0500193	−	0.998748i	$-0.515928\pi$
$773$	−2.78136	−0.100039	−0.0500193	+	0.998748i	$0.515928\pi$
$774$	26.5864	0.955628
$775$	−16.9575	−0.609131
$776$	−7.86047	−0.282175
$777$	−22.2198	−0.797132
$778$	−13.2542	−0.475185
$779$	57.7631	2.06958
$780$	22.2090	0.795209
$781$	−78.9470	−2.82494
$782$	−25.6363	−0.916753
$783$	−4.60325	−0.164507
$784$	−5.34486	−0.190888
$785$	26.7788	0.955776
$786$	−17.0032	−0.606485
$787$	−46.3604	−1.65257	−0.826285	−	0.563253i	$-0.809550\pi$
$787$	−46.3604	−1.65257	−0.826285	+	0.563253i	$0.809550\pi$
$788$	−15.6025	−0.555816
$789$	−70.1200	−2.49634
$790$	−25.9197	−0.922183
$791$	−15.2542	−0.542375
$792$	12.3648	0.439362
$793$	28.5070	1.01231
$794$	14.0751	0.499507
$795$	−15.2177	−0.539716
$796$	9.63155	0.341381
$797$	−53.0135	−1.87783	−0.938917	−	0.344144i	$-0.888169\pi$
$797$	−53.0135	−1.87783	−0.938917	+	0.344144i	$0.888169\pi$
$798$	−13.6771	−0.484165
$799$	19.5985	0.693345
$800$	2.58252	0.0913057
$801$	24.2675	0.857451
$802$	14.6636	0.517789
$803$	−59.4290	−2.09721
$804$	−28.6930	−1.01192
$805$	−17.1899	−0.605865
$806$	22.7813	0.802435
$807$	22.7342	0.800280
$808$	6.42067	0.225878
$809$	16.7686	0.589552	0.294776	−	0.955566i	$-0.404755\pi$
$809$	16.7686	0.589552	0.294776	+	0.955566i	$0.404755\pi$
$810$	−28.7274	−1.00938
$811$	2.05667	0.0722195	0.0361098	−	0.999348i	$-0.488503\pi$
$811$	2.05667	0.0722195	0.0361098	+	0.999348i	$0.488503\pi$
$812$	−4.27531	−0.150034
$813$	28.3237	0.993356
$814$	38.2110	1.33929
$815$	−11.6375	−0.407642
$816$	−12.2820	−0.429955
$817$	50.5727	1.76931
$818$	7.25058	0.253511
$819$	−10.7308	−0.374966
$820$	34.7810	1.21461
$821$	8.45134	0.294954	0.147477	−	0.989066i	$-0.452885\pi$
$821$	8.45134	0.294954	0.147477	+	0.989066i	$0.452885\pi$
$822$	−8.19207	−0.285731
$823$	10.9157	0.380497	0.190249	−	0.981736i	$-0.439071\pi$
$823$	10.9157	0.380497	0.190249	+	0.981736i	$0.439071\pi$
$824$	15.2169	0.530105
$825$	−30.8769	−1.07499
$826$	2.27214	0.0790577
$827$	25.2684	0.878669	0.439335	−	0.898324i	$-0.355214\pi$
$827$	25.2684	0.878669	0.439335	+	0.898324i	$0.355214\pi$
$828$	−11.6656	−0.405409
$829$	16.2964	0.565999	0.282999	−	0.959120i	$-0.408671\pi$
$829$	16.2964	0.565999	0.282999	+	0.959120i	$0.408671\pi$
$830$	−27.4255	−0.951953
$831$	−74.2432	−2.57547
$832$	−3.46944	−0.120281
$833$	−28.2385	−0.978406
$834$	12.1141	0.419475
$835$	19.3805	0.670690
$836$	23.5203	0.813465
$837$	−9.09562	−0.314391
$838$	26.7022	0.922412
$839$	−10.8527	−0.374678	−0.187339	−	0.982295i	$-0.559986\pi$
$839$	−10.8527	−0.374678	−0.187339	+	0.982295i	$0.559986\pi$
$840$	−8.23544	−0.284150
$841$	−17.9566	−0.619194
$842$	−5.10713	−0.176003
$843$	29.7772	1.02558
$844$	19.8331	0.682685
$845$	−2.65178	−0.0912239
$846$	8.91817	0.306613
$847$	19.8790	0.683051
$848$	2.37727	0.0816359
$849$	18.8229	0.646000
$850$	13.6442	0.467992
$851$	−36.0505	−1.23579
$852$	35.6838	1.22251
$853$	−18.1378	−0.621028	−0.310514	−	0.950569i	$-0.600501\pi$
$853$	−18.1378	−0.621028	−0.310514	+	0.950569i	$0.600501\pi$
$854$	−10.5708	−0.361726
$855$	30.2747	1.03537
$856$	−0.477006	−0.0163037
$857$	13.6034	0.464683	0.232341	−	0.972634i	$-0.425361\pi$
$857$	13.6034	0.464683	0.232341	+	0.972634i	$0.425361\pi$
$858$	41.4810	1.41614
$859$	−50.9977	−1.74002	−0.870010	−	0.493035i	$-0.835888\pi$
$859$	−50.9977	−1.74002	−0.870010	+	0.493035i	$0.835888\pi$
$860$	30.4514	1.03839
$861$	−37.7760	−1.28740
$862$	−34.2150	−1.16537
$863$	17.3810	0.591658	0.295829	−	0.955241i	$-0.404404\pi$
$863$	17.3810	0.591658	0.295829	+	0.955241i	$0.404404\pi$
$864$	1.38520	0.0471256
$865$	−33.9471	−1.15424
$866$	28.2637	0.960440
$867$	−25.3698	−0.861604
$868$	−8.44764	−0.286732
$869$	−48.4118	−1.64226
$870$	21.2726	0.721209
$871$	−42.8224	−1.45098
$872$	15.5422	0.526326
$873$	−18.8976	−0.639587
$874$	−22.1904	−0.750601
$875$	−8.56421	−0.289523
$876$	26.8618	0.907575
$877$	−2.38074	−0.0803918	−0.0401959	−	0.999192i	$-0.512798\pi$
$877$	−2.38074	−0.0803918	−0.0401959	+	0.999192i	$0.512798\pi$
$878$	23.7208	0.800538
$879$	3.70723	0.125042
$880$	14.1623	0.477411
$881$	23.2459	0.783173	0.391587	−	0.920141i	$-0.371926\pi$
$881$	23.2459	0.783173	0.391587	+	0.920141i	$0.371926\pi$
$882$	−12.8498	−0.432674
$883$	−18.8169	−0.633239	−0.316619	−	0.948553i	$-0.602548\pi$
$883$	−18.8169	−0.633239	−0.316619	+	0.948553i	$0.602548\pi$
$884$	−18.3301	−0.616507
$885$	−11.3054	−0.380028
$886$	−37.3981	−1.25641
$887$	39.4353	1.32411	0.662054	−	0.749456i	$-0.269685\pi$
$887$	39.4353	1.32411	0.662054	+	0.749456i	$0.269685\pi$
$888$	−17.2712	−0.579585
$889$	−15.1512	−0.508157
$890$	27.7955	0.931706
$891$	−53.6559	−1.79754
$892$	20.7040	0.693223
$893$	16.9642	0.567684
$894$	−0.552274	−0.0184708
$895$	38.8550	1.29878
$896$	1.28652	0.0429797
$897$	−39.1356	−1.30670
$898$	−33.2581	−1.10984
$899$	21.8207	0.727763
$900$	6.20871	0.206957
$901$	12.5599	0.418429
$902$	64.9626	2.16302
$903$	−33.0736	−1.10062
$904$	−11.8569	−0.394355
$905$	−70.9813	−2.35950
$906$	−1.23010	−0.0408672
$907$	−39.5852	−1.31440	−0.657202	−	0.753714i	$-0.728260\pi$
$907$	−39.5852	−1.31440	−0.657202	+	0.753714i	$0.728260\pi$
$908$	−19.4365	−0.645024
$909$	15.4361	0.511984
$910$	−12.2909	−0.407438
$911$	−11.9363	−0.395468	−0.197734	−	0.980256i	$-0.563358\pi$
$911$	−11.9363	−0.395468	−0.197734	+	0.980256i	$0.563358\pi$
$912$	−10.6311	−0.352030
$913$	−51.2242	−1.69527
$914$	41.0686	1.35843
$915$	52.5971	1.73881
$916$	13.2265	0.437017
$917$	9.40990	0.310742
$918$	7.31844	0.241545
$919$	−3.45453	−0.113954	−0.0569771	−	0.998375i	$-0.518146\pi$
$919$	−3.45453	−0.113954	−0.0569771	+	0.998375i	$0.518146\pi$
$920$	−13.3616	−0.440517
$921$	−32.8782	−1.08337
$922$	12.6454	0.416453
$923$	53.2558	1.75294
$924$	−15.3818	−0.506024
$925$	19.1869	0.630860
$926$	16.3472	0.537202
$927$	36.5834	1.20156
$928$	−3.32316	−0.109088
$929$	15.2547	0.500490	0.250245	−	0.968183i	$-0.419489\pi$
$929$	15.2547	0.500490	0.250245	+	0.968183i	$0.419489\pi$
$930$	42.0328	1.37831
$931$	−24.4428	−0.801081
$932$	−10.6925	−0.350246
$933$	13.1895	0.431804
$934$	16.0979	0.526740
$935$	74.8237	2.44700
$936$	−8.34098	−0.272633
$937$	−2.71609	−0.0887307	−0.0443653	−	0.999015i	$-0.514127\pi$
$937$	−2.71609	−0.0887307	−0.0443653	+	0.999015i	$0.514127\pi$
$938$	15.8792	0.518475
$939$	−33.9698	−1.10856
$940$	10.2147	0.333166
$941$	−57.0216	−1.85885	−0.929426	−	0.369008i	$-0.879697\pi$
$941$	−57.0216	−1.85885	−0.929426	+	0.369008i	$0.879697\pi$
$942$	−22.6072	−0.736583
$943$	−61.2895	−1.99586
$944$	1.76611	0.0574820
$945$	4.90724	0.159633
$946$	56.8759	1.84920
$947$	−42.3481	−1.37613	−0.688065	−	0.725649i	$-0.741540\pi$
$947$	−42.3481	−1.37613	−0.688065	+	0.725649i	$0.741540\pi$
$948$	21.8820	0.710694
$949$	40.0895	1.30136
$950$	11.8102	0.383174
$951$	9.72686	0.315415
$952$	6.79708	0.220295
$953$	−17.1038	−0.554048	−0.277024	−	0.960863i	$-0.589348\pi$
$953$	−17.1038	−0.554048	−0.277024	+	0.960863i	$0.589348\pi$
$954$	5.71528	0.185039
$955$	18.6348	0.603008
$956$	23.2680	0.752542
$957$	39.7321	1.28436
$958$	−2.54939	−0.0823671
$959$	4.53365	0.146399
$960$	−6.40132	−0.206602
$961$	12.1159	0.390835
$962$	−25.7762	−0.831060
$963$	−1.14678	−0.0369546
$964$	9.67058	0.311468
$965$	−21.6265	−0.696182
$966$	14.5121	0.466919
$967$	−28.7291	−0.923866	−0.461933	−	0.886915i	$-0.652844\pi$
$967$	−28.7291	−0.923866	−0.461933	+	0.886915i	$0.652844\pi$
$968$	15.4518	0.496638
$969$	−56.1672	−1.80435
$970$	−21.6449	−0.694975
$971$	21.5956	0.693036	0.346518	−	0.938043i	$-0.387364\pi$
$971$	21.5956	0.693036	0.346518	+	0.938043i	$0.387364\pi$
$972$	20.0967	0.644602
$973$	−6.70415	−0.214925
$974$	−11.0793	−0.355004
$975$	20.8288	0.667057
$976$	−8.21660	−0.263007
$977$	−3.22950	−0.103321	−0.0516605	−	0.998665i	$-0.516451\pi$
$977$	−3.22950	−0.103321	−0.0516605	+	0.998665i	$0.516451\pi$
$978$	9.82459	0.314156
$979$	51.9152	1.65922
$980$	−14.7178	−0.470143
$981$	37.3655	1.19299
$982$	13.9967	0.446653
$983$	−0.721994	−0.0230280	−0.0115140	−	0.999934i	$-0.503665\pi$
$983$	−0.721994	−0.0230280	−0.0115140	+	0.999934i	$0.503665\pi$
$984$	−29.3629	−0.936055
$985$	−42.9636	−1.36893
$986$	−17.5572	−0.559136
$987$	−11.0942	−0.353133
$988$	−15.8662	−0.504772
$989$	−53.6601	−1.70629
$990$	34.0480	1.08212
$991$	−48.8498	−1.55176	−0.775882	−	0.630878i	$-0.782695\pi$
$991$	−48.8498	−1.55176	−0.775882	+	0.630878i	$0.782695\pi$
$992$	−6.56627	−0.208479
$993$	−19.6516	−0.623624
$994$	−19.7481	−0.626371
$995$	26.5218	0.840798
$996$	23.1532	0.733637
$997$	31.1103	0.985273	0.492636	−	0.870235i	$-0.336033\pi$
$997$	31.1103	0.985273	0.492636	+	0.870235i	$0.336033\pi$
$998$	−10.2275	−0.323747
$999$	10.2914	0.325605

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.e.1.10	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.e.1.10	✓	68	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.32468 q^{3} +1.00000 q^{4} +2.75364 q^{5} -2.32468 q^{6} +1.28652 q^{7} +1.00000 q^{8} +2.40413 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.32468 q^{3} +1.00000 q^{4} +2.75364 q^{5} -2.32468 q^{6} +1.28652 q^{7} +1.00000 q^{8} +2.40413 q^{9} +2.75364 q^{10} +5.14313 q^{11} -2.32468 q^{12} -3.46944 q^{13} +1.28652 q^{14} -6.40132 q^{15} +1.00000 q^{16} +5.28330 q^{17} +2.40413 q^{18} +4.57314 q^{19} +2.75364 q^{20} -2.99075 q^{21} +5.14313 q^{22} -4.85233 q^{23} -2.32468 q^{24} +2.58252 q^{25} -3.46944 q^{26} +1.38520 q^{27} +1.28652 q^{28} -3.32316 q^{29} -6.40132 q^{30} -6.56627 q^{31} +1.00000 q^{32} -11.9561 q^{33} +5.28330 q^{34} +3.54261 q^{35} +2.40413 q^{36} +7.42952 q^{37} +4.57314 q^{38} +8.06533 q^{39} +2.75364 q^{40} +12.6309 q^{41} -2.99075 q^{42} +11.0586 q^{43} +5.14313 q^{44} +6.62010 q^{45} -4.85233 q^{46} +3.70952 q^{47} -2.32468 q^{48} -5.34486 q^{49} +2.58252 q^{50} -12.2820 q^{51} -3.46944 q^{52} +2.37727 q^{53} +1.38520 q^{54} +14.1623 q^{55} +1.28652 q^{56} -10.6311 q^{57} -3.32316 q^{58} +1.76611 q^{59} -6.40132 q^{60} -8.21660 q^{61} -6.56627 q^{62} +3.09297 q^{63} +1.00000 q^{64} -9.55357 q^{65} -11.9561 q^{66} +12.3428 q^{67} +5.28330 q^{68} +11.2801 q^{69} +3.54261 q^{70} -15.3500 q^{71} +2.40413 q^{72} -11.5550 q^{73} +7.42952 q^{74} -6.00352 q^{75} +4.57314 q^{76} +6.61674 q^{77} +8.06533 q^{78} -9.41291 q^{79} +2.75364 q^{80} -10.4325 q^{81} +12.6309 q^{82} -9.95973 q^{83} -2.99075 q^{84} +14.5483 q^{85} +11.0586 q^{86} +7.72527 q^{87} +5.14313 q^{88} +10.0941 q^{89} +6.62010 q^{90} -4.46350 q^{91} -4.85233 q^{92} +15.2645 q^{93} +3.70952 q^{94} +12.5928 q^{95} -2.32468 q^{96} -7.86047 q^{97} -5.34486 q^{98} +12.3648 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9}+O(q^{10}) \) 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9	\( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9} + 20 q^{10} + 46 q^{11} + 25 q^{12} + 30 q^{13} + 29 q^{14} + 13 q^{15} + 68 q^{16} + 73 q^{17} + 87 q^{18} + 56 q^{19} + 20 q^{20} - 5 q^{21} + 46 q^{22} + 63 q^{23} + 25 q^{24} + 88 q^{25} + 30 q^{26} + 67 q^{27} + 29 q^{28} + 43 q^{29} + 13 q^{30} + 68 q^{31} + 68 q^{32} + 26 q^{33} + 73 q^{34} + 50 q^{35} + 87 q^{36} + 8 q^{37} + 56 q^{38} + 6 q^{39} + 20 q^{40} + 64 q^{41} - 5 q^{42} + 52 q^{43} + 46 q^{44} + 7 q^{45} + 63 q^{46} + 94 q^{47} + 25 q^{48} + 91 q^{49} + 88 q^{50} + 20 q^{51} + 30 q^{52} + 38 q^{53} + 67 q^{54} + 37 q^{55} + 29 q^{56} + 4 q^{57} + 43 q^{58} + 84 q^{59} + 13 q^{60} + 26 q^{61} + 68 q^{62} + 22 q^{63} + 68 q^{64} - 20 q^{65} + 26 q^{66} + 54 q^{67} + 73 q^{68} - 11 q^{69} + 50 q^{70} + 46 q^{71} + 87 q^{72} + 62 q^{73} + 8 q^{74} + 54 q^{75} + 56 q^{76} + 67 q^{77} + 6 q^{78} + 67 q^{79} + 20 q^{80} + 120 q^{81} + 64 q^{82} + 130 q^{83} - 5 q^{84} - 24 q^{85} + 52 q^{86} + 72 q^{87} + 46 q^{88} + 61 q^{89} + 7 q^{90} + 43 q^{91} + 63 q^{92} + 40 q^{93} + 94 q^{94} + 55 q^{95} + 25 q^{96} + 41 q^{97} + 91 q^{98} + 106 q^{99}+O(q^{100}) \) 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9 + 20 * q^10 + 46 * q^11 + 25 * q^12 + 30 * q^13 + 29 * q^14 + 13 * q^15 + 68 * q^16 + 73 * q^17 + 87 * q^18 + 56 * q^19 + 20 * q^20 - 5 * q^21 + 46 * q^22 + 63 * q^23 + 25 * q^24 + 88 * q^25 + 30 * q^26 + 67 * q^27 + 29 * q^28 + 43 * q^29 + 13 * q^30 + 68 * q^31 + 68 * q^32 + 26 * q^33 + 73 * q^34 + 50 * q^35 + 87 * q^36 + 8 * q^37 + 56 * q^38 + 6 * q^39 + 20 * q^40 + 64 * q^41 - 5 * q^42 + 52 * q^43 + 46 * q^44 + 7 * q^45 + 63 * q^46 + 94 * q^47 + 25 * q^48 + 91 * q^49 + 88 * q^50 + 20 * q^51 + 30 * q^52 + 38 * q^53 + 67 * q^54 + 37 * q^55 + 29 * q^56 + 4 * q^57 + 43 * q^58 + 84 * q^59 + 13 * q^60 + 26 * q^61 + 68 * q^62 + 22 * q^63 + 68 * q^64 - 20 * q^65 + 26 * q^66 + 54 * q^67 + 73 * q^68 - 11 * q^69 + 50 * q^70 + 46 * q^71 + 87 * q^72 + 62 * q^73 + 8 * q^74 + 54 * q^75 + 56 * q^76 + 67 * q^77 + 6 * q^78 + 67 * q^79 + 20 * q^80 + 120 * q^81 + 64 * q^82 + 130 * q^83 - 5 * q^84 - 24 * q^85 + 52 * q^86 + 72 * q^87 + 46 * q^88 + 61 * q^89 + 7 * q^90 + 43 * q^91 + 63 * q^92 + 40 * q^93 + 94 * q^94 + 55 * q^95 + 25 * q^96 + 41 * q^97 + 91 * q^98 + 106 * q^99

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