LMFDB - Embedded newform 4017.2.a.i.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.47736 q^{2} -1.00000 q^{3} +0.182601 q^{4} -3.64531 q^{5} +1.47736 q^{6} -4.01724 q^{7} +2.68496 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.47736 q^{2} -1.00000 q^{3} +0.182601 q^{4} -3.64531 q^{5} +1.47736 q^{6} -4.01724 q^{7} +2.68496 q^{8} +1.00000 q^{9} +5.38545 q^{10} +1.40836 q^{11} -0.182601 q^{12} -1.00000 q^{13} +5.93491 q^{14} +3.64531 q^{15} -4.33186 q^{16} -3.90013 q^{17} -1.47736 q^{18} -5.03400 q^{19} -0.665638 q^{20} +4.01724 q^{21} -2.08066 q^{22} -2.20102 q^{23} -2.68496 q^{24} +8.28832 q^{25} +1.47736 q^{26} -1.00000 q^{27} -0.733551 q^{28} -0.586179 q^{29} -5.38545 q^{30} -0.278880 q^{31} +1.02981 q^{32} -1.40836 q^{33} +5.76191 q^{34} +14.6441 q^{35} +0.182601 q^{36} +3.21756 q^{37} +7.43704 q^{38} +1.00000 q^{39} -9.78752 q^{40} +12.2852 q^{41} -5.93491 q^{42} +1.60661 q^{43} +0.257168 q^{44} -3.64531 q^{45} +3.25170 q^{46} -5.58673 q^{47} +4.33186 q^{48} +9.13818 q^{49} -12.2449 q^{50} +3.90013 q^{51} -0.182601 q^{52} -7.05706 q^{53} +1.47736 q^{54} -5.13392 q^{55} -10.7861 q^{56} +5.03400 q^{57} +0.866000 q^{58} -4.89897 q^{59} +0.665638 q^{60} +8.01477 q^{61} +0.412007 q^{62} -4.01724 q^{63} +7.14231 q^{64} +3.64531 q^{65} +2.08066 q^{66} +8.85563 q^{67} -0.712168 q^{68} +2.20102 q^{69} -21.6346 q^{70} -1.06924 q^{71} +2.68496 q^{72} +13.8285 q^{73} -4.75350 q^{74} -8.28832 q^{75} -0.919213 q^{76} -5.65772 q^{77} -1.47736 q^{78} -3.44094 q^{79} +15.7910 q^{80} +1.00000 q^{81} -18.1498 q^{82} +13.3757 q^{83} +0.733551 q^{84} +14.2172 q^{85} -2.37355 q^{86} +0.586179 q^{87} +3.78139 q^{88} +18.3556 q^{89} +5.38545 q^{90} +4.01724 q^{91} -0.401908 q^{92} +0.278880 q^{93} +8.25362 q^{94} +18.3505 q^{95} -1.02981 q^{96} +15.6627 q^{97} -13.5004 q^{98} +1.40836 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - 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 $

$2$	−1.47736	−1.04465	−0.522327	−	0.852745i	$-0.674936\pi$
$2$	−1.47736	−1.04465	−0.522327	+	0.852745i	$0.674936\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.182601	0.0913005
$5$	−3.64531	−1.63023	−0.815117	−	0.579296i	$-0.803327\pi$
$5$	−3.64531	−1.63023	−0.815117	+	0.579296i	$0.803327\pi$
$6$	1.47736	0.603131
$7$	−4.01724	−1.51837	−0.759186	−	0.650874i	$-0.774403\pi$
$7$	−4.01724	−1.51837	−0.759186	+	0.650874i	$0.774403\pi$
$8$	2.68496	0.949276
$9$	1.00000	0.333333
$10$	5.38545	1.70303
$11$	1.40836	0.424637	0.212318	−	0.977201i	$-0.431899\pi$
$11$	1.40836	0.424637	0.212318	+	0.977201i	$0.431899\pi$
$12$	−0.182601	−0.0527124
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	5.93491	1.58617
$15$	3.64531	0.941216
$16$	−4.33186	−1.08296
$17$	−3.90013	−0.945921	−0.472960	−	0.881084i	$-0.656815\pi$
$17$	−3.90013	−0.945921	−0.472960	+	0.881084i	$0.656815\pi$
$18$	−1.47736	−0.348218
$19$	−5.03400	−1.15488	−0.577439	−	0.816434i	$-0.695948\pi$
$19$	−5.03400	−1.15488	−0.577439	+	0.816434i	$0.695948\pi$
$20$	−0.665638	−0.148841
$21$	4.01724	0.876633
$22$	−2.08066	−0.443598
$23$	−2.20102	−0.458944	−0.229472	−	0.973315i	$-0.573700\pi$
$23$	−2.20102	−0.458944	−0.229472	+	0.973315i	$0.573700\pi$
$24$	−2.68496	−0.548065
$25$	8.28832	1.65766
$26$	1.47736	0.289735
$27$	−1.00000	−0.192450
$28$	−0.733551	−0.138628
$29$	−0.586179	−0.108851	−0.0544254	−	0.998518i	$-0.517333\pi$
$29$	−0.586179	−0.108851	−0.0544254	+	0.998518i	$0.517333\pi$
$30$	−5.38545	−0.983245
$31$	−0.278880	−0.0500884	−0.0250442	−	0.999686i	$-0.507973\pi$
$31$	−0.278880	−0.0500884	−0.0250442	+	0.999686i	$0.507973\pi$
$32$	1.02981	0.182047
$33$	−1.40836	−0.245164
$34$	5.76191	0.988159
$35$	14.6441	2.47530
$36$	0.182601	0.0304335
$37$	3.21756	0.528963	0.264482	−	0.964391i	$-0.414799\pi$
$37$	3.21756	0.528963	0.264482	+	0.964391i	$0.414799\pi$
$38$	7.43704	1.20645
$39$	1.00000	0.160128
$40$	−9.78752	−1.54754
$41$	12.2852	1.91863	0.959316	−	0.282333i	$-0.0911084\pi$
$41$	12.2852	1.91863	0.959316	+	0.282333i	$0.0911084\pi$
$42$	−5.93491	−0.915777
$43$	1.60661	0.245006	0.122503	−	0.992468i	$-0.460908\pi$
$43$	1.60661	0.245006	0.122503	+	0.992468i	$0.460908\pi$
$44$	0.257168	0.0387695
$45$	−3.64531	−0.543411
$46$	3.25170	0.479437
$47$	−5.58673	−0.814908	−0.407454	−	0.913226i	$-0.633583\pi$
$47$	−5.58673	−0.814908	−0.407454	+	0.913226i	$0.633583\pi$
$48$	4.33186	0.625250
$49$	9.13818	1.30545
$50$	−12.2449	−1.73168
$51$	3.90013	0.546128
$52$	−0.182601	−0.0253222
$53$	−7.05706	−0.969362	−0.484681	−	0.874691i	$-0.661064\pi$
$53$	−7.05706	−0.969362	−0.484681	+	0.874691i	$0.661064\pi$
$54$	1.47736	0.201044
$55$	−5.13392	−0.692257
$56$	−10.7861	−1.44135
$57$	5.03400	0.666769
$58$	0.866000	0.113711
$59$	−4.89897	−0.637792	−0.318896	−	0.947790i	$-0.603312\pi$
$59$	−4.89897	−0.637792	−0.318896	+	0.947790i	$0.603312\pi$
$60$	0.665638	0.0859335
$61$	8.01477	1.02619	0.513093	−	0.858333i	$-0.328499\pi$
$61$	8.01477	1.02619	0.513093	+	0.858333i	$0.328499\pi$
$62$	0.412007	0.0523250
$63$	−4.01724	−0.506124
$64$	7.14231	0.892789
$65$	3.64531	0.452146
$66$	2.08066	0.256111
$67$	8.85563	1.08189	0.540944	−	0.841059i	$-0.318067\pi$
$67$	8.85563	1.08189	0.540944	+	0.841059i	$0.318067\pi$
$68$	−0.712168	−0.0863630
$69$	2.20102	0.264971
$70$	−21.6346	−2.58583
$71$	−1.06924	−0.126895	−0.0634476	−	0.997985i	$-0.520210\pi$
$71$	−1.06924	−0.126895	−0.0634476	+	0.997985i	$0.520210\pi$
$72$	2.68496	0.316425
$73$	13.8285	1.61850	0.809249	−	0.587466i	$-0.199874\pi$
$73$	13.8285	1.61850	0.809249	+	0.587466i	$0.199874\pi$
$74$	−4.75350	−0.552583
$75$	−8.28832	−0.957053
$76$	−0.919213	−0.105441
$77$	−5.65772	−0.644757
$78$	−1.47736	−0.167278
$79$	−3.44094	−0.387136	−0.193568	−	0.981087i	$-0.562006\pi$
$79$	−3.44094	−0.387136	−0.193568	+	0.981087i	$0.562006\pi$
$80$	15.7910	1.76549
$81$	1.00000	0.111111
$82$	−18.1498	−2.00431
$83$	13.3757	1.46818	0.734088	−	0.679055i	$-0.237610\pi$
$83$	13.3757	1.46818	0.734088	+	0.679055i	$0.237610\pi$
$84$	0.733551	0.0800370
$85$	14.2172	1.54207
$86$	−2.37355	−0.255947
$87$	0.586179	0.0628450
$88$	3.78139	0.403097
$89$	18.3556	1.94569	0.972843	−	0.231464i	$-0.0743516\pi$
$89$	18.3556	1.94569	0.972843	+	0.231464i	$0.0743516\pi$
$90$	5.38545	0.567677
$91$	4.01724	0.421121
$92$	−0.401908	−0.0419018
$93$	0.278880	0.0289185
$94$	8.25362	0.851296
$95$	18.3505	1.88272
$96$	−1.02981	−0.105105
$97$	15.6627	1.59030	0.795151	−	0.606411i	$-0.207392\pi$
$97$	15.6627	1.59030	0.795151	+	0.606411i	$0.207392\pi$
$98$	−13.5004	−1.36375
$99$	1.40836	0.141546
$100$	1.51346	0.151346
$101$	−1.13333	−0.112771	−0.0563853	−	0.998409i	$-0.517958\pi$
$101$	−1.13333	−0.112771	−0.0563853	+	0.998409i	$0.517958\pi$
$102$	−5.76191	−0.570514
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−2.68496	−0.263282
$105$	−14.6441	−1.42912
$106$	10.4258	1.01265
$107$	2.27367	0.219804	0.109902	−	0.993942i	$-0.464946\pi$
$107$	2.27367	0.219804	0.109902	+	0.993942i	$0.464946\pi$
$108$	−0.182601	−0.0175708
$109$	9.83162	0.941699	0.470849	−	0.882214i	$-0.343948\pi$
$109$	9.83162	0.941699	0.470849	+	0.882214i	$0.343948\pi$
$110$	7.58466	0.723169
$111$	−3.21756	−0.305397
$112$	17.4021	1.64434
$113$	−17.5909	−1.65481	−0.827407	−	0.561602i	$-0.810185\pi$
$113$	−17.5909	−1.65481	−0.827407	+	0.561602i	$0.810185\pi$
$114$	−7.43704	−0.696543
$115$	8.02340	0.748186
$116$	−0.107037	−0.00993813
$117$	−1.00000	−0.0924500
$118$	7.23756	0.666272
$119$	15.6677	1.43626
$120$	9.78752	0.893474
$121$	−9.01652	−0.819684
$122$	−11.8407	−1.07201
$123$	−12.2852	−1.10772
$124$	−0.0509238	−0.00457309
$125$	−11.9870	−1.07215
$126$	5.93491	0.528724
$127$	−10.1021	−0.896415	−0.448207	−	0.893930i	$-0.647937\pi$
$127$	−10.1021	−0.896415	−0.448207	+	0.893930i	$0.647937\pi$
$128$	−12.6114	−1.11470
$129$	−1.60661	−0.141455
$130$	−5.38545	−0.472335
$131$	−4.31857	−0.377316	−0.188658	−	0.982043i	$-0.560414\pi$
$131$	−4.31857	−0.377316	−0.188658	+	0.982043i	$0.560414\pi$
$132$	−0.257168	−0.0223836
$133$	20.2228	1.75354
$134$	−13.0830	−1.13020
$135$	3.64531	0.313739
$136$	−10.4717	−0.897940
$137$	−23.0396	−1.96840	−0.984201	−	0.177053i	$-0.943344\pi$
$137$	−23.0396	−1.96840	−0.984201	+	0.177053i	$0.943344\pi$
$138$	−3.25170	−0.276803
$139$	4.05257	0.343734	0.171867	−	0.985120i	$-0.445020\pi$
$139$	4.05257	0.343734	0.171867	+	0.985120i	$0.445020\pi$
$140$	2.67403	0.225996
$141$	5.58673	0.470487
$142$	1.57965	0.132561
$143$	−1.40836	−0.117773
$144$	−4.33186	−0.360988
$145$	2.13681	0.177452
$146$	−20.4296	−1.69077
$147$	−9.13818	−0.753705
$148$	0.587529	0.0482946
$149$	−6.54380	−0.536089	−0.268045	−	0.963407i	$-0.586377\pi$
$149$	−6.54380	−0.536089	−0.268045	+	0.963407i	$0.586377\pi$
$150$	12.2449	0.999788
$151$	−6.68177	−0.543755	−0.271877	−	0.962332i	$-0.587645\pi$
$151$	−6.68177	−0.543755	−0.271877	+	0.962332i	$0.587645\pi$
$152$	−13.5161	−1.09630
$153$	−3.90013	−0.315307
$154$	8.35850	0.673547
$155$	1.01661	0.0816557
$156$	0.182601	0.0146198
$157$	5.62535	0.448952	0.224476	−	0.974480i	$-0.427933\pi$
$157$	5.62535	0.448952	0.224476	+	0.974480i	$0.427933\pi$
$158$	5.08351	0.404423
$159$	7.05706	0.559662
$160$	−3.75399	−0.296779
$161$	8.84201	0.696848
$162$	−1.47736	−0.116073
$163$	6.27790	0.491723	0.245862	−	0.969305i	$-0.420929\pi$
$163$	6.27790	0.491723	0.245862	+	0.969305i	$0.420929\pi$
$164$	2.24330	0.175172
$165$	5.13392	0.399675
$166$	−19.7608	−1.53373
$167$	−18.7214	−1.44871	−0.724353	−	0.689430i	$-0.757861\pi$
$167$	−18.7214	−1.44871	−0.724353	+	0.689430i	$0.757861\pi$
$168$	10.7861	0.832166
$169$	1.00000	0.0769231
$170$	−21.0040	−1.61093
$171$	−5.03400	−0.384959
$172$	0.293369	0.0223692
$173$	−9.31194	−0.707974	−0.353987	−	0.935250i	$-0.615174\pi$
$173$	−9.31194	−0.707974	−0.353987	+	0.935250i	$0.615174\pi$
$174$	−0.866000	−0.0656513
$175$	−33.2961	−2.51695
$176$	−6.10082	−0.459867
$177$	4.89897	0.368229
$178$	−27.1178	−2.03257
$179$	19.7691	1.47761	0.738806	−	0.673918i	$-0.235390\pi$
$179$	19.7691	1.47761	0.738806	+	0.673918i	$0.235390\pi$
$180$	−0.665638	−0.0496137
$181$	5.01264	0.372587	0.186293	−	0.982494i	$-0.440352\pi$
$181$	5.01264	0.372587	0.186293	+	0.982494i	$0.440352\pi$
$182$	−5.93491	−0.439925
$183$	−8.01477	−0.592469
$184$	−5.90964	−0.435664
$185$	−11.7290	−0.862334
$186$	−0.412007	−0.0302098
$187$	−5.49279	−0.401673
$188$	−1.02014	−0.0744015
$189$	4.01724	0.292211
$190$	−27.1104	−1.96679
$191$	5.76003	0.416781	0.208391	−	0.978046i	$-0.433177\pi$
$191$	5.76003	0.416781	0.208391	+	0.978046i	$0.433177\pi$
$192$	−7.14231	−0.515452
$193$	2.70932	0.195021	0.0975107	−	0.995234i	$-0.468912\pi$
$193$	2.70932	0.195021	0.0975107	+	0.995234i	$0.468912\pi$
$194$	−23.1394	−1.66131
$195$	−3.64531	−0.261046
$196$	1.66864	0.119189
$197$	−12.9942	−0.925799	−0.462900	−	0.886411i	$-0.653191\pi$
$197$	−12.9942	−0.925799	−0.462900	+	0.886411i	$0.653191\pi$
$198$	−2.08066	−0.147866
$199$	15.3465	1.08789	0.543943	−	0.839122i	$-0.316931\pi$
$199$	15.3465	1.08789	0.543943	+	0.839122i	$0.316931\pi$
$200$	22.2538	1.57358
$201$	−8.85563	−0.624628
$202$	1.67434	0.117806
$203$	2.35482	0.165276
$204$	0.712168	0.0498617
$205$	−44.7836	−3.12782
$206$	1.47736	0.102933
$207$	−2.20102	−0.152981
$208$	4.33186	0.300360
$209$	−7.08969	−0.490404
$210$	21.6346	1.49293
$211$	−10.4011	−0.716044	−0.358022	−	0.933713i	$-0.616549\pi$
$211$	−10.4011	−0.716044	−0.358022	+	0.933713i	$0.616549\pi$
$212$	−1.28863	−0.0885033
$213$	1.06924	0.0732630
$214$	−3.35904	−0.229619
$215$	−5.85661	−0.399418
$216$	−2.68496	−0.182688
$217$	1.12033	0.0760528
$218$	−14.5249	−0.983749
$219$	−13.8285	−0.934440
$220$	−0.937458	−0.0632034
$221$	3.90013	0.262351
$222$	4.75350	0.319034
$223$	11.6360	0.779203	0.389601	−	0.920984i	$-0.372613\pi$
$223$	11.6360	0.779203	0.389601	+	0.920984i	$0.372613\pi$
$224$	−4.13700	−0.276415
$225$	8.28832	0.552555
$226$	25.9882	1.72871
$227$	−0.757937	−0.0503061	−0.0251530	−	0.999684i	$-0.508007\pi$
$227$	−0.757937	−0.0503061	−0.0251530	+	0.999684i	$0.508007\pi$
$228$	0.919213	0.0608764
$229$	−18.9478	−1.25211	−0.626054	−	0.779779i	$-0.715331\pi$
$229$	−18.9478	−1.25211	−0.626054	+	0.779779i	$0.715331\pi$
$230$	−11.8535	−0.781595
$231$	5.65772	0.372250
$232$	−1.57387	−0.103329
$233$	−9.97821	−0.653694	−0.326847	−	0.945077i	$-0.605986\pi$
$233$	−9.97821	−0.653694	−0.326847	+	0.945077i	$0.605986\pi$
$234$	1.47736	0.0965782
$235$	20.3654	1.32849
$236$	−0.894557	−0.0582307
$237$	3.44094	0.223513
$238$	−23.1469	−1.50039
$239$	19.3345	1.25064	0.625321	−	0.780368i	$-0.284968\pi$
$239$	19.3345	1.25064	0.625321	+	0.780368i	$0.284968\pi$
$240$	−15.7910	−1.01930
$241$	21.8569	1.40792	0.703962	−	0.710238i	$-0.251412\pi$
$241$	21.8569	1.40792	0.703962	+	0.710238i	$0.251412\pi$
$242$	13.3207	0.856285
$243$	−1.00000	−0.0641500
$244$	1.46351	0.0936913
$245$	−33.3116	−2.12820
$246$	18.1498	1.15719
$247$	5.03400	0.320306
$248$	−0.748781	−0.0475477
$249$	−13.3757	−0.847651
$250$	17.7091	1.12002
$251$	−14.5443	−0.918029	−0.459014	−	0.888429i	$-0.651797\pi$
$251$	−14.5443	−0.918029	−0.459014	+	0.888429i	$0.651797\pi$
$252$	−0.733551	−0.0462094
$253$	−3.09983	−0.194884
$254$	14.9244	0.936443
$255$	−14.2172	−0.890316
$256$	4.34700	0.271688
$257$	3.75164	0.234021	0.117011	−	0.993131i	$-0.462669\pi$
$257$	3.75164	0.234021	0.117011	+	0.993131i	$0.462669\pi$
$258$	2.37355	0.147771
$259$	−12.9257	−0.803163
$260$	0.665638	0.0412811
$261$	−0.586179	−0.0362836
$262$	6.38010	0.394164
$263$	−4.20926	−0.259554	−0.129777	−	0.991543i	$-0.541426\pi$
$263$	−4.20926	−0.259554	−0.129777	+	0.991543i	$0.541426\pi$
$264$	−3.78139	−0.232728
$265$	25.7252	1.58029
$266$	−29.8764	−1.83184
$267$	−18.3556	−1.12334
$268$	1.61705	0.0987768
$269$	5.27612	0.321690	0.160845	−	0.986980i	$-0.448578\pi$
$269$	5.27612	0.321690	0.160845	+	0.986980i	$0.448578\pi$
$270$	−5.38545	−0.327748
$271$	−10.2500	−0.622643	−0.311321	−	0.950305i	$-0.600772\pi$
$271$	−10.2500	−0.622643	−0.311321	+	0.950305i	$0.600772\pi$
$272$	16.8948	1.02440
$273$	−4.01724	−0.243134
$274$	34.0378	2.05630
$275$	11.6729	0.703905
$276$	0.401908	0.0241920
$277$	−4.54089	−0.272836	−0.136418	−	0.990651i	$-0.543559\pi$
$277$	−4.54089	−0.272836	−0.136418	+	0.990651i	$0.543559\pi$
$278$	−5.98711	−0.359083
$279$	−0.278880	−0.0166961
$280$	39.3188	2.34975
$281$	−3.30935	−0.197419	−0.0987097	−	0.995116i	$-0.531472\pi$
$281$	−3.30935	−0.197419	−0.0987097	+	0.995116i	$0.531472\pi$
$282$	−8.25362	−0.491496
$283$	−4.50617	−0.267864	−0.133932	−	0.990991i	$-0.542760\pi$
$283$	−4.50617	−0.267864	−0.133932	+	0.990991i	$0.542760\pi$
$284$	−0.195244	−0.0115856
$285$	−18.3505	−1.08699
$286$	2.08066	0.123032
$287$	−49.3527	−2.91320
$288$	1.02981	0.0606822
$289$	−1.78898	−0.105234
$290$	−3.15684	−0.185376
$291$	−15.6627	−0.918161
$292$	2.52509	0.147770
$293$	8.34537	0.487542	0.243771	−	0.969833i	$-0.421616\pi$
$293$	8.34537	0.487542	0.243771	+	0.969833i	$0.421616\pi$
$294$	13.5004	0.787360
$295$	17.8583	1.03975
$296$	8.63901	0.502132
$297$	−1.40836	−0.0817214
$298$	9.66757	0.560027
$299$	2.20102	0.127288
$300$	−1.51346	−0.0873794
$301$	−6.45415	−0.372011
$302$	9.87140	0.568035
$303$	1.13333	0.0651081
$304$	21.8066	1.25069
$305$	−29.2164	−1.67292
$306$	5.76191	0.329386
$307$	19.6167	1.11959	0.559793	−	0.828633i	$-0.310881\pi$
$307$	19.6167	1.11959	0.559793	+	0.828633i	$0.310881\pi$
$308$	−1.03310	−0.0588666
$309$	1.00000	0.0568880
$310$	−1.50190	−0.0853019
$311$	−17.5902	−0.997447	−0.498724	−	0.866761i	$-0.666198\pi$
$311$	−17.5902	−0.997447	−0.498724	+	0.866761i	$0.666198\pi$
$312$	2.68496	0.152006
$313$	−0.277281	−0.0156729	−0.00783643	−	0.999969i	$-0.502494\pi$
$313$	−0.277281	−0.0156729	−0.00783643	+	0.999969i	$0.502494\pi$
$314$	−8.31069	−0.468999
$315$	14.6441	0.825101
$316$	−0.628319	−0.0353457
$317$	−3.59790	−0.202078	−0.101039	−	0.994882i	$-0.532217\pi$
$317$	−3.59790	−0.202078	−0.101039	+	0.994882i	$0.532217\pi$
$318$	−10.4258	−0.584652
$319$	−0.825552	−0.0462220
$320$	−26.0360	−1.45546
$321$	−2.27367	−0.126904
$322$	−13.0628	−0.727964
$323$	19.6333	1.09242
$324$	0.182601	0.0101445
$325$	−8.28832	−0.459753
$326$	−9.27474	−0.513680
$327$	−9.83162	−0.543690
$328$	32.9854	1.82131
$329$	22.4432	1.23733
$330$	−7.58466	−0.417522
$331$	6.15083	0.338080	0.169040	−	0.985609i	$-0.445933\pi$
$331$	6.15083	0.338080	0.169040	+	0.985609i	$0.445933\pi$
$332$	2.44242	0.134045
$333$	3.21756	0.176321
$334$	27.6583	1.51340
$335$	−32.2815	−1.76373
$336$	−17.4021	−0.949362
$337$	−27.9915	−1.52479	−0.762397	−	0.647109i	$-0.775978\pi$
$337$	−27.9915	−1.52479	−0.762397	+	0.647109i	$0.775978\pi$
$338$	−1.47736	−0.0803579
$339$	17.5909	0.955408
$340$	2.59608	0.140792
$341$	−0.392764	−0.0212694
$342$	7.43704	0.402149
$343$	−8.58958	−0.463794
$344$	4.31369	0.232579
$345$	−8.02340	−0.431965
$346$	13.7571	0.739587
$347$	−17.6680	−0.948469	−0.474234	−	0.880399i	$-0.657275\pi$
$347$	−17.6680	−0.948469	−0.474234	+	0.880399i	$0.657275\pi$
$348$	0.107037	0.00573778
$349$	−9.14907	−0.489738	−0.244869	−	0.969556i	$-0.578745\pi$
$349$	−9.14907	−0.489738	−0.244869	+	0.969556i	$0.578745\pi$
$350$	49.1905	2.62934
$351$	1.00000	0.0533761
$352$	1.45035	0.0773037
$353$	16.7731	0.892742	0.446371	−	0.894848i	$-0.352716\pi$
$353$	16.7731	0.892742	0.446371	+	0.894848i	$0.352716\pi$
$354$	−7.23756	−0.384672
$355$	3.89771	0.206869
$356$	3.35175	0.177642
$357$	−15.6677	−0.829225
$358$	−29.2061	−1.54359
$359$	−34.7657	−1.83486	−0.917432	−	0.397892i	$-0.869742\pi$
$359$	−34.7657	−1.83486	−0.917432	+	0.397892i	$0.869742\pi$
$360$	−9.78752	−0.515847
$361$	6.34114	0.333744
$362$	−7.40549	−0.389224
$363$	9.01652	0.473245
$364$	0.733551	0.0384485
$365$	−50.4091	−2.63853
$366$	11.8407	0.618925
$367$	15.8910	0.829501	0.414751	−	0.909935i	$-0.363869\pi$
$367$	15.8910	0.829501	0.414751	+	0.909935i	$0.363869\pi$
$368$	9.53450	0.497020
$369$	12.2852	0.639544
$370$	17.3280	0.900840
$371$	28.3499	1.47185
$372$	0.0509238	0.00264028
$373$	10.5891	0.548282	0.274141	−	0.961690i	$-0.411607\pi$
$373$	10.5891	0.548282	0.274141	+	0.961690i	$0.411607\pi$
$374$	8.11484	0.419609
$375$	11.9870	0.619004
$376$	−15.0001	−0.773573
$377$	0.586179	0.0301898
$378$	−5.93491	−0.305259
$379$	27.8727	1.43172	0.715862	−	0.698242i	$-0.246034\pi$
$379$	27.8727	1.43172	0.715862	+	0.698242i	$0.246034\pi$
$380$	3.35082	0.171894
$381$	10.1021	0.517545
$382$	−8.50966	−0.435392
$383$	−13.5523	−0.692489	−0.346244	−	0.938144i	$-0.612543\pi$
$383$	−13.5523	−0.692489	−0.346244	+	0.938144i	$0.612543\pi$
$384$	12.6114	0.643573
$385$	20.6242	1.05110
$386$	−4.00265	−0.203730
$387$	1.60661	0.0816688
$388$	2.86002	0.145195
$389$	19.4174	0.984501	0.492251	−	0.870453i	$-0.336174\pi$
$389$	19.4174	0.984501	0.492251	+	0.870453i	$0.336174\pi$
$390$	5.38545	0.272703
$391$	8.58426	0.434124
$392$	24.5356	1.23924
$393$	4.31857	0.217843
$394$	19.1972	0.967139
$395$	12.5433	0.631122
$396$	0.257168	0.0129232
$397$	4.25227	0.213415	0.106708	−	0.994290i	$-0.465969\pi$
$397$	4.25227	0.213415	0.106708	+	0.994290i	$0.465969\pi$
$398$	−22.6724	−1.13646
$399$	−20.2228	−1.01240
$400$	−35.9038	−1.79519
$401$	2.03128	0.101437	0.0507186	−	0.998713i	$-0.483849\pi$
$401$	2.03128	0.101437	0.0507186	+	0.998713i	$0.483849\pi$
$402$	13.0830	0.652519
$403$	0.278880	0.0138920
$404$	−0.206947	−0.0102960
$405$	−3.64531	−0.181137
$406$	−3.47892	−0.172656
$407$	4.53148	0.224617
$408$	10.4717	0.518426
$409$	21.8397	1.07990	0.539951	−	0.841697i	$-0.318443\pi$
$409$	21.8397	1.07990	0.539951	+	0.841697i	$0.318443\pi$
$410$	66.1616	3.26749
$411$	23.0396	1.13646
$412$	−0.182601	−0.00899611
$413$	19.6803	0.968406
$414$	3.25170	0.159812
$415$	−48.7587	−2.39347
$416$	−1.02981	−0.0504907
$417$	−4.05257	−0.198455
$418$	10.4740	0.512302
$419$	−17.4391	−0.851955	−0.425978	−	0.904734i	$-0.640070\pi$
$419$	−17.4391	−0.851955	−0.425978	+	0.904734i	$0.640070\pi$
$420$	−2.67403	−0.130479
$421$	6.92733	0.337617	0.168809	−	0.985649i	$-0.446008\pi$
$421$	6.92733	0.337617	0.168809	+	0.985649i	$0.446008\pi$
$422$	15.3663	0.748018
$423$	−5.58673	−0.271636
$424$	−18.9479	−0.920192
$425$	−32.3255	−1.56802
$426$	−1.57965	−0.0765344
$427$	−32.1972	−1.55813
$428$	0.415175	0.0200683
$429$	1.40836	0.0679963
$430$	8.65234	0.417253
$431$	27.4987	1.32457	0.662284	−	0.749253i	$-0.269587\pi$
$431$	27.4987	1.32457	0.662284	+	0.749253i	$0.269587\pi$
$432$	4.33186	0.208417
$433$	40.5038	1.94649	0.973244	−	0.229775i	$-0.0737991\pi$
$433$	40.5038	1.94649	0.973244	+	0.229775i	$0.0737991\pi$
$434$	−1.65513	−0.0794488
$435$	−2.13681	−0.102452
$436$	1.79526	0.0859776
$437$	11.0799	0.530024
$438$	20.4296	0.976166
$439$	7.84809	0.374569	0.187284	−	0.982306i	$-0.440031\pi$
$439$	7.84809	0.374569	0.187284	+	0.982306i	$0.440031\pi$
$440$	−13.7844	−0.657143
$441$	9.13818	0.435152
$442$	−5.76191	−0.274066
$443$	−0.773850	−0.0367667	−0.0183834	−	0.999831i	$-0.505852\pi$
$443$	−0.773850	−0.0367667	−0.0183834	+	0.999831i	$0.505852\pi$
$444$	−0.587529	−0.0278829
$445$	−66.9118	−3.17193
$446$	−17.1906	−0.813997
$447$	6.54380	0.309511
$448$	−28.6924	−1.35559
$449$	−9.38089	−0.442712	−0.221356	−	0.975193i	$-0.571048\pi$
$449$	−9.38089	−0.442712	−0.221356	+	0.975193i	$0.571048\pi$
$450$	−12.2449	−0.577228
$451$	17.3021	0.814722
$452$	−3.21212	−0.151085
$453$	6.68177	0.313937
$454$	1.11975	0.0525524
$455$	−14.6441	−0.686525
$456$	13.5161	0.632948
$457$	−32.5181	−1.52113	−0.760567	−	0.649259i	$-0.775079\pi$
$457$	−32.5181	−1.52113	−0.760567	+	0.649259i	$0.775079\pi$
$458$	27.9928	1.30802
$459$	3.90013	0.182043
$460$	1.46508	0.0683098
$461$	33.2903	1.55048	0.775242	−	0.631664i	$-0.217628\pi$
$461$	33.2903	1.55048	0.775242	+	0.631664i	$0.217628\pi$
$462$	−8.35850	−0.388873
$463$	−29.1745	−1.35585	−0.677927	−	0.735129i	$-0.737122\pi$
$463$	−29.1745	−1.35585	−0.677927	+	0.735129i	$0.737122\pi$
$464$	2.53925	0.117882
$465$	−1.01661	−0.0471440
$466$	14.7414	0.682884
$467$	−6.81185	−0.315215	−0.157608	−	0.987502i	$-0.550378\pi$
$467$	−6.81185	−0.315215	−0.157608	+	0.987502i	$0.550378\pi$
$468$	−0.182601	−0.00844073
$469$	−35.5751	−1.64271
$470$	−30.0871	−1.38781
$471$	−5.62535	−0.259203
$472$	−13.1535	−0.605441
$473$	2.26269	0.104039
$474$	−5.08351	−0.233493
$475$	−41.7234	−1.91440
$476$	2.86095	0.131131
$477$	−7.05706	−0.323121
$478$	−28.5640	−1.30649
$479$	−13.9346	−0.636687	−0.318344	−	0.947975i	$-0.603127\pi$
$479$	−13.9346	−0.636687	−0.318344	+	0.947975i	$0.603127\pi$
$480$	3.75399	0.171345
$481$	−3.21756	−0.146708
$482$	−32.2905	−1.47079
$483$	−8.84201	−0.402325
$484$	−1.64643	−0.0748375
$485$	−57.0953	−2.59256
$486$	1.47736	0.0670145
$487$	−7.87107	−0.356672	−0.178336	−	0.983970i	$-0.557071\pi$
$487$	−7.87107	−0.356672	−0.178336	+	0.983970i	$0.557071\pi$
$488$	21.5193	0.974134
$489$	−6.27790	−0.283896
$490$	49.2132	2.22323
$491$	33.3735	1.50612	0.753062	−	0.657949i	$-0.228576\pi$
$491$	33.3735	1.50612	0.753062	+	0.657949i	$0.228576\pi$
$492$	−2.24330	−0.101136
$493$	2.28618	0.102964
$494$	−7.43704	−0.334608
$495$	−5.13392	−0.230752
$496$	1.20807	0.0542439
$497$	4.29538	0.192674
$498$	19.7608	0.885502
$499$	−39.8029	−1.78182	−0.890912	−	0.454176i	$-0.849934\pi$
$499$	−39.8029	−1.78182	−0.890912	+	0.454176i	$0.849934\pi$
$500$	−2.18883	−0.0978874
$501$	18.7214	0.836411
$502$	21.4872	0.959022
$503$	23.0862	1.02936	0.514681	−	0.857381i	$-0.327910\pi$
$503$	23.0862	1.02936	0.514681	+	0.857381i	$0.327910\pi$
$504$	−10.7861	−0.480451
$505$	4.13134	0.183842
$506$	4.57957	0.203587
$507$	−1.00000	−0.0444116
$508$	−1.84465	−0.0818431
$509$	31.8272	1.41071	0.705357	−	0.708852i	$-0.250787\pi$
$509$	31.8272	1.41071	0.705357	+	0.708852i	$0.250787\pi$
$510$	21.0040	0.930071
$511$	−55.5522	−2.45748
$512$	18.8007	0.830882
$513$	5.03400	0.222256
$514$	−5.54254	−0.244471
$515$	3.64531	0.160632
$516$	−0.293369	−0.0129149
$517$	−7.86813	−0.346040
$518$	19.0959	0.839027
$519$	9.31194	0.408749
$520$	9.78752	0.429211
$521$	−37.2506	−1.63198	−0.815988	−	0.578068i	$-0.803807\pi$
$521$	−37.2506	−1.63198	−0.815988	+	0.578068i	$0.803807\pi$
$522$	0.866000	0.0379038
$523$	−31.6289	−1.38304	−0.691518	−	0.722359i	$-0.743058\pi$
$523$	−31.6289	−1.38304	−0.691518	+	0.722359i	$0.743058\pi$
$524$	−0.788576	−0.0344491
$525$	33.2961	1.45316
$526$	6.21861	0.271144
$527$	1.08767	0.0473796
$528$	6.10082	0.265504
$529$	−18.1555	−0.789371
$530$	−38.0055	−1.65085
$531$	−4.89897	−0.212597
$532$	3.69270	0.160099
$533$	−12.2852	−0.532133
$534$	27.1178	1.17350
$535$	−8.28826	−0.358333
$536$	23.7770	1.02701
$537$	−19.7691	−0.853100
$538$	−7.79474	−0.336055
$539$	12.8699	0.554344
$540$	0.665638	0.0286445
$541$	11.7859	0.506716	0.253358	−	0.967373i	$-0.418465\pi$
$541$	11.7859	0.506716	0.253358	+	0.967373i	$0.418465\pi$
$542$	15.1430	0.650446
$543$	−5.01264	−0.215113
$544$	−4.01640	−0.172202
$545$	−35.8394	−1.53519
$546$	5.93491	0.253991
$547$	15.7930	0.675261	0.337631	−	0.941279i	$-0.390375\pi$
$547$	15.7930	0.675261	0.337631	+	0.941279i	$0.390375\pi$
$548$	−4.20705	−0.179716
$549$	8.01477	0.342062
$550$	−17.2452	−0.735336
$551$	2.95083	0.125709
$552$	5.90964	0.251531
$553$	13.8231	0.587816
$554$	6.70854	0.285019
$555$	11.7290	0.497869
$556$	0.740003	0.0313831
$557$	−36.5111	−1.54703	−0.773513	−	0.633781i	$-0.781502\pi$
$557$	−36.5111	−1.54703	−0.773513	+	0.633781i	$0.781502\pi$
$558$	0.412007	0.0174417
$559$	−1.60661	−0.0679525
$560$	−63.4361	−2.68067
$561$	5.49279	0.231906
$562$	4.88911	0.206235
$563$	−20.8915	−0.880472	−0.440236	−	0.897882i	$-0.645105\pi$
$563$	−20.8915	−0.880472	−0.440236	+	0.897882i	$0.645105\pi$
$564$	1.02014	0.0429557
$565$	64.1244	2.69774
$566$	6.65724	0.279825
$567$	−4.01724	−0.168708
$568$	−2.87086	−0.120459
$569$	3.31618	0.139022	0.0695108	−	0.997581i	$-0.477856\pi$
$569$	3.31618	0.139022	0.0695108	+	0.997581i	$0.477856\pi$
$570$	27.1104	1.13553
$571$	10.2207	0.427721	0.213861	−	0.976864i	$-0.431396\pi$
$571$	10.2207	0.427721	0.213861	+	0.976864i	$0.431396\pi$
$572$	−0.257168	−0.0107527
$573$	−5.76003	−0.240629
$574$	72.9119	3.04328
$575$	−18.2427	−0.760774
$576$	7.14231	0.297596
$577$	−1.81181	−0.0754266	−0.0377133	−	0.999289i	$-0.512007\pi$
$577$	−1.81181	−0.0754266	−0.0377133	+	0.999289i	$0.512007\pi$
$578$	2.64297	0.109933
$579$	−2.70932	−0.112596
$580$	0.390183	0.0162015
$581$	−53.7334	−2.22924
$582$	23.1394	0.959160
$583$	−9.93889	−0.411627
$584$	37.1288	1.53640
$585$	3.64531	0.150715
$586$	−12.3291	−0.509312
$587$	−13.4245	−0.554088	−0.277044	−	0.960857i	$-0.589355\pi$
$587$	−13.4245	−0.554088	−0.277044	+	0.960857i	$0.589355\pi$
$588$	−1.66864	−0.0688136
$589$	1.40388	0.0578460
$590$	−26.3832	−1.08618
$591$	12.9942	0.534510
$592$	−13.9380	−0.572849
$593$	38.0578	1.56285	0.781423	−	0.624002i	$-0.214494\pi$
$593$	38.0578	1.56285	0.781423	+	0.624002i	$0.214494\pi$
$594$	2.08066	0.0853705
$595$	−57.1139	−2.34144
$596$	−1.19490	−0.0489452
$597$	−15.3465	−0.628091
$598$	−3.25170	−0.132972
$599$	−39.5219	−1.61482	−0.807411	−	0.589989i	$-0.799132\pi$
$599$	−39.5219	−1.61482	−0.807411	+	0.589989i	$0.799132\pi$
$600$	−22.2538	−0.908507
$601$	11.7451	0.479094	0.239547	−	0.970885i	$-0.423001\pi$
$601$	11.7451	0.479094	0.239547	+	0.970885i	$0.423001\pi$
$602$	9.53512	0.388622
$603$	8.85563	0.360629
$604$	−1.22010	−0.0496451
$605$	32.8681	1.33628
$606$	−1.67434	−0.0680154
$607$	−37.6832	−1.52951	−0.764757	−	0.644319i	$-0.777141\pi$
$607$	−37.6832	−1.52951	−0.764757	+	0.644319i	$0.777141\pi$
$608$	−5.18407	−0.210242
$609$	−2.35482	−0.0954222
$610$	43.1632	1.74763
$611$	5.58673	0.226015
$612$	−0.712168	−0.0287877
$613$	17.9315	0.724247	0.362124	−	0.932130i	$-0.382052\pi$
$613$	17.9315	0.724247	0.362124	+	0.932130i	$0.382052\pi$
$614$	−28.9810	−1.16958
$615$	44.7836	1.80585
$616$	−15.1907	−0.612052
$617$	−0.871097	−0.0350690	−0.0175345	−	0.999846i	$-0.505582\pi$
$617$	−0.871097	−0.0350690	−0.0175345	+	0.999846i	$0.505582\pi$
$618$	−1.47736	−0.0594282
$619$	5.03274	0.202283	0.101141	−	0.994872i	$-0.467751\pi$
$619$	5.03274	0.202283	0.101141	+	0.994872i	$0.467751\pi$
$620$	0.185633	0.00745521
$621$	2.20102	0.0883238
$622$	25.9871	1.04199
$623$	−73.7387	−2.95428
$624$	−4.33186	−0.173413
$625$	2.25463	0.0901850
$626$	0.409645	0.0163727
$627$	7.08969	0.283135
$628$	1.02720	0.0409896
$629$	−12.5489	−0.500357
$630$	−21.6346	−0.861944
$631$	1.78650	0.0711196	0.0355598	−	0.999368i	$-0.488679\pi$
$631$	1.78650	0.0711196	0.0355598	+	0.999368i	$0.488679\pi$
$632$	−9.23877	−0.367499
$633$	10.4011	0.413408
$634$	5.31540	0.211102
$635$	36.8253	1.46137
$636$	1.28863	0.0510974
$637$	−9.13818	−0.362068
$638$	1.21964	0.0482860
$639$	−1.06924	−0.0422984
$640$	45.9726	1.81722
$641$	−6.75392	−0.266764	−0.133382	−	0.991065i	$-0.542584\pi$
$641$	−6.75392	−0.266764	−0.133382	+	0.991065i	$0.542584\pi$
$642$	3.35904	0.132571
$643$	18.3683	0.724376	0.362188	−	0.932105i	$-0.382030\pi$
$643$	18.3683	0.724376	0.362188	+	0.932105i	$0.382030\pi$
$644$	1.61456	0.0636225
$645$	5.85661	0.230604
$646$	−29.0054	−1.14120
$647$	38.1782	1.50094	0.750469	−	0.660905i	$-0.229828\pi$
$647$	38.1782	1.50094	0.750469	+	0.660905i	$0.229828\pi$
$648$	2.68496	0.105475
$649$	−6.89952	−0.270830
$650$	12.2449	0.480283
$651$	−1.12033	−0.0439091
$652$	1.14635	0.0448946
$653$	4.43171	0.173426	0.0867131	−	0.996233i	$-0.472364\pi$
$653$	4.43171	0.173426	0.0867131	+	0.996233i	$0.472364\pi$
$654$	14.5249	0.567968
$655$	15.7426	0.615113
$656$	−53.2179	−2.07781
$657$	13.8285	0.539499
$658$	−33.1568	−1.29258
$659$	31.4196	1.22393	0.611967	−	0.790883i	$-0.290379\pi$
$659$	31.4196	1.22393	0.611967	+	0.790883i	$0.290379\pi$
$660$	0.937458	0.0364905
$661$	−29.6635	−1.15378	−0.576888	−	0.816823i	$-0.695733\pi$
$661$	−29.6635	−1.15378	−0.576888	+	0.816823i	$0.695733\pi$
$662$	−9.08700	−0.353176
$663$	−3.90013	−0.151469
$664$	35.9132	1.39370
$665$	−73.7183	−2.85867
$666$	−4.75350	−0.184194
$667$	1.29019	0.0499564
$668$	−3.41855	−0.132268
$669$	−11.6360	−0.449873
$670$	47.6916	1.84249
$671$	11.2877	0.435756
$672$	4.13700	0.159588
$673$	33.0370	1.27348	0.636742	−	0.771077i	$-0.280282\pi$
$673$	33.0370	1.27348	0.636742	+	0.771077i	$0.280282\pi$
$674$	41.3536	1.59288
$675$	−8.28832	−0.319018
$676$	0.182601	0.00702312
$677$	19.1800	0.737146	0.368573	−	0.929599i	$-0.379846\pi$
$677$	19.1800	0.737146	0.368573	+	0.929599i	$0.379846\pi$
$678$	−25.9882	−0.998070
$679$	−62.9206	−2.41467
$680$	38.1726	1.46385
$681$	0.757937	0.0290442
$682$	0.580255	0.0222191
$683$	−45.1104	−1.72610	−0.863050	−	0.505118i	$-0.831449\pi$
$683$	−45.1104	−1.72610	−0.863050	+	0.505118i	$0.831449\pi$
$684$	−0.919213	−0.0351470
$685$	83.9865	3.20896
$686$	12.6899	0.484504
$687$	18.9478	0.722905
$688$	−6.95963	−0.265333
$689$	7.05706	0.268853
$690$	11.8535	0.451254
$691$	0.849568	0.0323191	0.0161595	−	0.999869i	$-0.494856\pi$
$691$	0.849568	0.0323191	0.0161595	+	0.999869i	$0.494856\pi$
$692$	−1.70037	−0.0646384
$693$	−5.65772	−0.214919
$694$	26.1021	0.990821
$695$	−14.7729	−0.560368
$696$	1.57387	0.0596573
$697$	−47.9141	−1.81487
$698$	13.5165	0.511607
$699$	9.97821	0.377410
$700$	−6.07991	−0.229799
$701$	27.5679	1.04123	0.520613	−	0.853793i	$-0.325704\pi$
$701$	27.5679	1.04123	0.520613	+	0.853793i	$0.325704\pi$
$702$	−1.47736	−0.0557595
$703$	−16.1972	−0.610888
$704$	10.0590	0.379111
$705$	−20.3654	−0.767005
$706$	−24.7800	−0.932606
$707$	4.55285	0.171228
$708$	0.894557	0.0336195
$709$	42.8537	1.60940	0.804702	−	0.593679i	$-0.202325\pi$
$709$	42.8537	1.60940	0.804702	+	0.593679i	$0.202325\pi$
$710$	−5.75833	−0.216106
$711$	−3.44094	−0.129045
$712$	49.2839	1.84699
$713$	0.613820	0.0229877
$714$	23.1469	0.866253
$715$	5.13392	0.191998
$716$	3.60986	0.134907
$717$	−19.3345	−0.722058
$718$	51.3616	1.91680
$719$	37.3848	1.39422	0.697110	−	0.716964i	$-0.254469\pi$
$719$	37.3848	1.39422	0.697110	+	0.716964i	$0.254469\pi$
$720$	15.7910	0.588495
$721$	4.01724	0.149610
$722$	−9.36817	−0.348647
$723$	−21.8569	−0.812865
$724$	0.915314	0.0340174
$725$	−4.85844	−0.180438
$726$	−13.3207	−0.494377
$727$	35.9800	1.33442	0.667212	−	0.744868i	$-0.267488\pi$
$727$	35.9800	1.33442	0.667212	+	0.744868i	$0.267488\pi$
$728$	10.7861	0.399760
$729$	1.00000	0.0370370
$730$	74.4725	2.75635
$731$	−6.26601	−0.231757
$732$	−1.46351	−0.0540927
$733$	−2.36659	−0.0874119	−0.0437060	−	0.999044i	$-0.513916\pi$
$733$	−2.36659	−0.0874119	−0.0437060	+	0.999044i	$0.513916\pi$
$734$	−23.4767	−0.866541
$735$	33.3116	1.22872
$736$	−2.26663	−0.0835492
$737$	12.4719	0.459409
$738$	−18.1498	−0.668102
$739$	8.69327	0.319787	0.159894	−	0.987134i	$-0.448885\pi$
$739$	8.69327	0.319787	0.159894	+	0.987134i	$0.448885\pi$
$740$	−2.14173	−0.0787315
$741$	−5.03400	−0.184929
$742$	−41.8831	−1.53758
$743$	20.7492	0.761214	0.380607	−	0.924737i	$-0.375715\pi$
$743$	20.7492	0.761214	0.380607	+	0.924737i	$0.375715\pi$
$744$	0.748781	0.0274517
$745$	23.8542	0.873951
$746$	−15.6439	−0.572765
$747$	13.3757	0.489392
$748$	−1.00299	−0.0366729
$749$	−9.13389	−0.333745
$750$	−17.7091	−0.646644
$751$	−26.1706	−0.954977	−0.477488	−	0.878638i	$-0.658453\pi$
$751$	−26.1706	−0.954977	−0.477488	+	0.878638i	$0.658453\pi$
$752$	24.2009	0.882517
$753$	14.5443	0.530024
$754$	−0.866000	−0.0315378
$755$	24.3572	0.886448
$756$	0.733551	0.0266790
$757$	−8.47370	−0.307982	−0.153991	−	0.988072i	$-0.549213\pi$
$757$	−8.47370	−0.307982	−0.153991	+	0.988072i	$0.549213\pi$
$758$	−41.1781	−1.49565
$759$	3.09983	0.112517
$760$	49.2703	1.78722
$761$	45.8783	1.66309	0.831544	−	0.555459i	$-0.187458\pi$
$761$	45.8783	1.66309	0.831544	+	0.555459i	$0.187458\pi$
$762$	−14.9244	−0.540656
$763$	−39.4959	−1.42985
$764$	1.05179	0.0380523
$765$	14.2172	0.514024
$766$	20.0216	0.723411
$767$	4.89897	0.176892
$768$	−4.34700	−0.156859
$769$	−16.9229	−0.610256	−0.305128	−	0.952311i	$-0.598699\pi$
$769$	−16.9229	−0.610256	−0.305128	+	0.952311i	$0.598699\pi$
$770$	−30.4694	−1.09804
$771$	−3.75164	−0.135112
$772$	0.494725	0.0178055
$773$	44.4352	1.59822	0.799112	−	0.601182i	$-0.205303\pi$
$773$	44.4352	1.59822	0.799112	+	0.601182i	$0.205303\pi$
$774$	−2.37355	−0.0853156
$775$	−2.31145	−0.0830296
$776$	42.0536	1.50964
$777$	12.9257	0.463707
$778$	−28.6865	−1.02846
$779$	−61.8439	−2.21579
$780$	−0.665638	−0.0238337
$781$	−1.50587	−0.0538843
$782$	−12.6821	−0.453510
$783$	0.586179	0.0209483
$784$	−39.5853	−1.41376
$785$	−20.5062	−0.731897
$786$	−6.38010	−0.227571
$787$	−28.4735	−1.01497	−0.507485	−	0.861661i	$-0.669425\pi$
$787$	−28.4735	−1.01497	−0.507485	+	0.861661i	$0.669425\pi$
$788$	−2.37276	−0.0845259
$789$	4.20926	0.149854
$790$	−18.5310	−0.659304
$791$	70.6669	2.51263
$792$	3.78139	0.134366
$793$	−8.01477	−0.284613
$794$	−6.28214	−0.222945
$795$	−25.7252	−0.912380
$796$	2.80229	0.0993246
$797$	−39.3439	−1.39363	−0.696815	−	0.717250i	$-0.745400\pi$
$797$	−39.3439	−1.39363	−0.696815	+	0.717250i	$0.745400\pi$
$798$	29.8764	1.05761
$799$	21.7890	0.770838
$800$	8.53541	0.301772
$801$	18.3556	0.648562
$802$	−3.00093	−0.105967
$803$	19.4754	0.687274
$804$	−1.61705	−0.0570288
$805$	−32.2319	−1.13602
$806$	−0.412007	−0.0145123
$807$	−5.27612	−0.185728
$808$	−3.04294	−0.107050
$809$	−1.55610	−0.0547096	−0.0273548	−	0.999626i	$-0.508708\pi$
$809$	−1.55610	−0.0547096	−0.0273548	+	0.999626i	$0.508708\pi$
$810$	5.38545	0.189226
$811$	−16.0906	−0.565017	−0.282508	−	0.959265i	$-0.591166\pi$
$811$	−16.0906	−0.565017	−0.282508	+	0.959265i	$0.591166\pi$
$812$	0.429993	0.0150898
$813$	10.2500	0.359483
$814$	−6.69464	−0.234647
$815$	−22.8849	−0.801624
$816$	−16.8948	−0.591437
$817$	−8.08769	−0.282953
$818$	−32.2651	−1.12812
$819$	4.01724	0.140374
$820$	−8.17753	−0.285572
$821$	−39.5212	−1.37930	−0.689650	−	0.724142i	$-0.742236\pi$
$821$	−39.5212	−1.37930	−0.689650	+	0.724142i	$0.742236\pi$
$822$	−34.0378	−1.18720
$823$	39.8014	1.38739	0.693695	−	0.720269i	$-0.255981\pi$
$823$	39.8014	1.38739	0.693695	+	0.720269i	$0.255981\pi$
$824$	−2.68496	−0.0935349
$825$	−11.6729	−0.406400
$826$	−29.0750	−1.01165
$827$	−33.4628	−1.16362	−0.581808	−	0.813326i	$-0.697655\pi$
$827$	−33.4628	−1.16362	−0.581808	+	0.813326i	$0.697655\pi$
$828$	−0.401908	−0.0139673
$829$	−36.6922	−1.27437	−0.637187	−	0.770709i	$-0.719902\pi$
$829$	−36.6922	−1.27437	−0.637187	+	0.770709i	$0.719902\pi$
$830$	72.0343	2.50035
$831$	4.54089	0.157522
$832$	−7.14231	−0.247615
$833$	−35.6401	−1.23486
$834$	5.98711	0.207317
$835$	68.2454	2.36173
$836$	−1.29458	−0.0447741
$837$	0.278880	0.00963951
$838$	25.7639	0.889998
$839$	−3.24881	−0.112161	−0.0560807	−	0.998426i	$-0.517860\pi$
$839$	−3.24881	−0.112161	−0.0560807	+	0.998426i	$0.517860\pi$
$840$	−39.3188	−1.35663
$841$	−28.6564	−0.988152
$842$	−10.2342	−0.352693
$843$	3.30935	0.113980
$844$	−1.89926	−0.0653752
$845$	−3.64531	−0.125403
$846$	8.25362	0.283765
$847$	36.2215	1.24459
$848$	30.5702	1.04979
$849$	4.50617	0.154651
$850$	47.7565	1.63804
$851$	−7.08190	−0.242764
$852$	0.195244	0.00668894
$853$	−49.0428	−1.67919	−0.839596	−	0.543211i	$-0.817209\pi$
$853$	−49.0428	−1.67919	−0.839596	+	0.543211i	$0.817209\pi$
$854$	47.5670	1.62771
$855$	18.3505	0.627574
$856$	6.10472	0.208655
$857$	−41.1048	−1.40411	−0.702056	−	0.712121i	$-0.747735\pi$
$857$	−41.1048	−1.40411	−0.702056	+	0.712121i	$0.747735\pi$
$858$	−2.08066	−0.0710325
$859$	14.1838	0.483945	0.241973	−	0.970283i	$-0.422206\pi$
$859$	14.1838	0.483945	0.241973	+	0.970283i	$0.422206\pi$
$860$	−1.06942	−0.0364670
$861$	49.3527	1.68194
$862$	−40.6256	−1.38371
$863$	26.9643	0.917876	0.458938	−	0.888468i	$-0.348230\pi$
$863$	26.9643	0.917876	0.458938	+	0.888468i	$0.348230\pi$
$864$	−1.02981	−0.0350349
$865$	33.9450	1.15416
$866$	−59.8388	−2.03340
$867$	1.78898	0.0607569
$868$	0.204573	0.00694366
$869$	−4.84608	−0.164392
$870$	3.15684	0.107027
$871$	−8.85563	−0.300061
$872$	26.3975	0.893932
$873$	15.6627	0.530101
$874$	−16.3691	−0.553692
$875$	48.1544	1.62792
$876$	−2.52509	−0.0853149
$877$	−43.7499	−1.47733	−0.738664	−	0.674073i	$-0.764543\pi$
$877$	−43.7499	−1.47733	−0.738664	+	0.674073i	$0.764543\pi$
$878$	−11.5945	−0.391295
$879$	−8.34537	−0.281482
$880$	22.2394	0.749690
$881$	−21.8429	−0.735906	−0.367953	−	0.929844i	$-0.619941\pi$
$881$	−21.8429	−0.735906	−0.367953	+	0.929844i	$0.619941\pi$
$882$	−13.5004	−0.454583
$883$	16.3483	0.550165	0.275083	−	0.961421i	$-0.411295\pi$
$883$	16.3483	0.550165	0.275083	+	0.961421i	$0.411295\pi$
$884$	0.712168	0.0239528
$885$	−17.8583	−0.600300
$886$	1.14326	0.0384085
$887$	−41.5718	−1.39584	−0.697922	−	0.716173i	$-0.745892\pi$
$887$	−41.5718	−1.39584	−0.697922	+	0.716173i	$0.745892\pi$
$888$	−8.63901	−0.289906
$889$	40.5825	1.36109
$890$	98.8531	3.31356
$891$	1.40836	0.0471819
$892$	2.12474	0.0711416
$893$	28.1236	0.941120
$894$	−9.66757	−0.323332
$895$	−72.0646	−2.40885
$896$	50.6630	1.69253
$897$	−2.20102	−0.0734898
$898$	13.8590	0.462480
$899$	0.163474	0.00545216
$900$	1.51346	0.0504485
$901$	27.5235	0.916940
$902$	−25.5614	−0.851102
$903$	6.45415	0.214781
$904$	−47.2309	−1.57088
$905$	−18.2727	−0.607404
$906$	−9.87140	−0.327955
$907$	4.03250	0.133897	0.0669484	−	0.997756i	$-0.478674\pi$
$907$	4.03250	0.133897	0.0669484	+	0.997756i	$0.478674\pi$
$908$	−0.138400	−0.00459297
$909$	−1.13333	−0.0375902
$910$	21.6346	0.717181
$911$	−15.6059	−0.517047	−0.258523	−	0.966005i	$-0.583236\pi$
$911$	−15.6059	−0.517047	−0.258523	+	0.966005i	$0.583236\pi$
$912$	−21.8066	−0.722088
$913$	18.8378	0.623441
$914$	48.0411	1.58906
$915$	29.2164	0.965863
$916$	−3.45989	−0.114318
$917$	17.3487	0.572905
$918$	−5.76191	−0.190171
$919$	42.8385	1.41311	0.706555	−	0.707658i	$-0.250248\pi$
$919$	42.8385	1.41311	0.706555	+	0.707658i	$0.250248\pi$
$920$	21.5425	0.710235
$921$	−19.6167	−0.646393
$922$	−49.1819	−1.61972
$923$	1.06924	0.0351944
$924$	1.03310	0.0339867
$925$	26.6681	0.876843
$926$	43.1013	1.41640
$927$	−1.00000	−0.0328443
$928$	−0.603654	−0.0198159
$929$	−56.3261	−1.84800	−0.924000	−	0.382394i	$-0.875100\pi$
$929$	−56.3261	−1.84800	−0.924000	+	0.382394i	$0.875100\pi$
$930$	1.50190	0.0492491
$931$	−46.0016	−1.50764
$932$	−1.82203	−0.0596826
$933$	17.5902	0.575876
$934$	10.0636	0.329290
$935$	20.0229	0.654820
$936$	−2.68496	−0.0877606
$937$	34.0931	1.11377	0.556886	−	0.830589i	$-0.311996\pi$
$937$	34.0931	1.11377	0.556886	+	0.830589i	$0.311996\pi$
$938$	52.5574	1.71606
$939$	0.277281	0.00904873
$940$	3.71874	0.121292
$941$	33.7614	1.10059	0.550296	−	0.834970i	$-0.314515\pi$
$941$	33.7614	1.10059	0.550296	+	0.834970i	$0.314515\pi$
$942$	8.31069	0.270777
$943$	−27.0400	−0.880545
$944$	21.2217	0.690706
$945$	−14.6441	−0.476372
$946$	−3.34282	−0.108684
$947$	−41.7515	−1.35674	−0.678371	−	0.734720i	$-0.737314\pi$
$947$	−41.7515	−1.35674	−0.678371	+	0.734720i	$0.737314\pi$
$948$	0.628319	0.0204068
$949$	−13.8285	−0.448891
$950$	61.6406	1.99988
$951$	3.59790	0.116670
$952$	42.0672	1.36341
$953$	−42.4938	−1.37651	−0.688255	−	0.725469i	$-0.741623\pi$
$953$	−42.4938	−1.37651	−0.688255	+	0.725469i	$0.741623\pi$
$954$	10.4258	0.337549
$955$	−20.9971	−0.679451
$956$	3.53049	0.114184
$957$	0.825552	0.0266863
$958$	20.5864	0.665117
$959$	92.5554	2.98877
$960$	26.0360	0.840307
$961$	−30.9222	−0.997491
$962$	4.75350	0.153259
$963$	2.27367	0.0732681
$964$	3.99108	0.128544
$965$	−9.87633	−0.317930
$966$	13.0628	0.420290
$967$	−26.6395	−0.856669	−0.428335	−	0.903620i	$-0.640900\pi$
$967$	−26.6395	−0.856669	−0.428335	+	0.903620i	$0.640900\pi$
$968$	−24.2090	−0.778106
$969$	−19.6333	−0.630711
$970$	84.3505	2.70833
$971$	19.5391	0.627041	0.313521	−	0.949581i	$-0.398492\pi$
$971$	19.5391	0.627041	0.313521	+	0.949581i	$0.398492\pi$
$972$	−0.182601	−0.00585693
$973$	−16.2801	−0.521917
$974$	11.6284	0.372599
$975$	8.28832	0.265439
$976$	−34.7189	−1.11132
$977$	1.28431	0.0410888	0.0205444	−	0.999789i	$-0.493460\pi$
$977$	1.28431	0.0410888	0.0205444	+	0.999789i	$0.493460\pi$
$978$	9.27474	0.296573
$979$	25.8513	0.826210
$980$	−6.08272	−0.194305
$981$	9.83162	0.313900
$982$	−49.3048	−1.57338
$983$	45.4311	1.44903	0.724513	−	0.689261i	$-0.242065\pi$
$983$	45.4311	1.44903	0.724513	+	0.689261i	$0.242065\pi$
$984$	−32.9854	−1.05153
$985$	47.3680	1.50927
$986$	−3.37751	−0.107562
$987$	−22.4432	−0.714375
$988$	0.919213	0.0292441
$989$	−3.53619	−0.112444
$990$	7.58466	0.241056
$991$	38.9585	1.23756	0.618779	−	0.785565i	$-0.287628\pi$
$991$	38.9585	1.23756	0.618779	+	0.785565i	$0.287628\pi$
$992$	−0.287194	−0.00911842
$993$	−6.15083	−0.195191
$994$	−6.34583	−0.201278
$995$	−55.9429	−1.77351
$996$	−2.44242	−0.0773910
$997$	58.1689	1.84223	0.921114	−	0.389293i	$-0.127280\pi$
$997$	58.1689	1.84223	0.921114	+	0.389293i	$0.127280\pi$
$998$	58.8034	1.86139
$999$	−3.21756	−0.101799

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.i.1.8	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.i.1.8	✓	25	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-1.47736 q^{2} -1.00000 q^{3} +0.182601 q^{4} -3.64531 q^{5} +1.47736 q^{6} -4.01724 q^{7} +2.68496 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.47736 q^{2} -1.00000 q^{3} +0.182601 q^{4} -3.64531 q^{5} +1.47736 q^{6} -4.01724 q^{7} +2.68496 q^{8} +1.00000 q^{9} +5.38545 q^{10} +1.40836 q^{11} -0.182601 q^{12} -1.00000 q^{13} +5.93491 q^{14} +3.64531 q^{15} -4.33186 q^{16} -3.90013 q^{17} -1.47736 q^{18} -5.03400 q^{19} -0.665638 q^{20} +4.01724 q^{21} -2.08066 q^{22} -2.20102 q^{23} -2.68496 q^{24} +8.28832 q^{25} +1.47736 q^{26} -1.00000 q^{27} -0.733551 q^{28} -0.586179 q^{29} -5.38545 q^{30} -0.278880 q^{31} +1.02981 q^{32} -1.40836 q^{33} +5.76191 q^{34} +14.6441 q^{35} +0.182601 q^{36} +3.21756 q^{37} +7.43704 q^{38} +1.00000 q^{39} -9.78752 q^{40} +12.2852 q^{41} -5.93491 q^{42} +1.60661 q^{43} +0.257168 q^{44} -3.64531 q^{45} +3.25170 q^{46} -5.58673 q^{47} +4.33186 q^{48} +9.13818 q^{49} -12.2449 q^{50} +3.90013 q^{51} -0.182601 q^{52} -7.05706 q^{53} +1.47736 q^{54} -5.13392 q^{55} -10.7861 q^{56} +5.03400 q^{57} +0.866000 q^{58} -4.89897 q^{59} +0.665638 q^{60} +8.01477 q^{61} +0.412007 q^{62} -4.01724 q^{63} +7.14231 q^{64} +3.64531 q^{65} +2.08066 q^{66} +8.85563 q^{67} -0.712168 q^{68} +2.20102 q^{69} -21.6346 q^{70} -1.06924 q^{71} +2.68496 q^{72} +13.8285 q^{73} -4.75350 q^{74} -8.28832 q^{75} -0.919213 q^{76} -5.65772 q^{77} -1.47736 q^{78} -3.44094 q^{79} +15.7910 q^{80} +1.00000 q^{81} -18.1498 q^{82} +13.3757 q^{83} +0.733551 q^{84} +14.2172 q^{85} -2.37355 q^{86} +0.586179 q^{87} +3.78139 q^{88} +18.3556 q^{89} +5.38545 q^{90} +4.01724 q^{91} -0.401908 q^{92} +0.278880 q^{93} +8.25362 q^{94} +18.3505 q^{95} -1.02981 q^{96} +15.6627 q^{97} -13.5004 q^{98} +1.40836 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - q^99

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