LMFDB - Embedded newform 8015.2.a.m.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$67$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.50021 q^{2} +0.266806 q^{3} +0.250644 q^{4} +1.00000 q^{5} -0.400267 q^{6} -1.00000 q^{7} +2.62441 q^{8} -2.92881 q^{9} +O(q^{10})$	\(q-1.50021 q^{2} +0.266806 q^{3} +0.250644 q^{4} +1.00000 q^{5} -0.400267 q^{6} -1.00000 q^{7} +2.62441 q^{8} -2.92881 q^{9} -1.50021 q^{10} -2.55030 q^{11} +0.0668733 q^{12} +6.27542 q^{13} +1.50021 q^{14} +0.266806 q^{15} -4.43846 q^{16} +0.504865 q^{17} +4.39385 q^{18} +3.47987 q^{19} +0.250644 q^{20} -0.266806 q^{21} +3.82599 q^{22} -7.56441 q^{23} +0.700209 q^{24} +1.00000 q^{25} -9.41448 q^{26} -1.58185 q^{27} -0.250644 q^{28} -5.18542 q^{29} -0.400267 q^{30} +2.19885 q^{31} +1.40983 q^{32} -0.680435 q^{33} -0.757406 q^{34} -1.00000 q^{35} -0.734088 q^{36} +5.38561 q^{37} -5.22055 q^{38} +1.67432 q^{39} +2.62441 q^{40} -6.93512 q^{41} +0.400267 q^{42} +5.47623 q^{43} -0.639215 q^{44} -2.92881 q^{45} +11.3482 q^{46} +8.38893 q^{47} -1.18421 q^{48} +1.00000 q^{49} -1.50021 q^{50} +0.134701 q^{51} +1.57289 q^{52} -4.09118 q^{53} +2.37311 q^{54} -2.55030 q^{55} -2.62441 q^{56} +0.928452 q^{57} +7.77924 q^{58} -6.46570 q^{59} +0.0668733 q^{60} +1.98590 q^{61} -3.29874 q^{62} +2.92881 q^{63} +6.76188 q^{64} +6.27542 q^{65} +1.02080 q^{66} +8.62225 q^{67} +0.126541 q^{68} -2.01823 q^{69} +1.50021 q^{70} -9.38322 q^{71} -7.68641 q^{72} +3.60124 q^{73} -8.07957 q^{74} +0.266806 q^{75} +0.872207 q^{76} +2.55030 q^{77} -2.51184 q^{78} -5.42500 q^{79} -4.43846 q^{80} +8.36440 q^{81} +10.4042 q^{82} +1.16863 q^{83} -0.0668733 q^{84} +0.504865 q^{85} -8.21552 q^{86} -1.38350 q^{87} -6.69302 q^{88} +1.25561 q^{89} +4.39385 q^{90} -6.27542 q^{91} -1.89597 q^{92} +0.586666 q^{93} -12.5852 q^{94} +3.47987 q^{95} +0.376151 q^{96} +18.1951 q^{97} -1.50021 q^{98} +7.46934 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) $ 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * 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 $

$2$	−1.50021	−1.06081	−0.530406	−	0.847744i	$-0.677960\pi$
$2$	−1.50021	−1.06081	−0.530406	+	0.847744i	$0.677960\pi$
$3$	0.266806	0.154041	0.0770204	−	0.997030i	$-0.475459\pi$
$3$	0.266806	0.154041	0.0770204	+	0.997030i	$0.475459\pi$
$4$	0.250644	0.125322
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.400267	−0.163408
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.62441	0.927869
$9$	−2.92881	−0.976271
$10$	−1.50021	−0.474409
$11$	−2.55030	−0.768943	−0.384472	−	0.923137i	$-0.625616\pi$
$11$	−2.55030	−0.768943	−0.384472	+	0.923137i	$0.625616\pi$
$12$	0.0668733	0.0193047
$13$	6.27542	1.74049	0.870244	−	0.492620i	$-0.163961\pi$
$13$	6.27542	1.74049	0.870244	+	0.492620i	$0.163961\pi$
$14$	1.50021	0.400949
$15$	0.266806	0.0688891
$16$	−4.43846	−1.10962
$17$	0.504865	0.122448	0.0612239	−	0.998124i	$-0.480500\pi$
$17$	0.504865	0.122448	0.0612239	+	0.998124i	$0.480500\pi$
$18$	4.39385	1.03564
$19$	3.47987	0.798337	0.399169	−	0.916877i	$-0.369299\pi$
$19$	3.47987	0.798337	0.399169	+	0.916877i	$0.369299\pi$
$20$	0.250644	0.0560456
$21$	−0.266806	−0.0582219
$22$	3.82599	0.815704
$23$	−7.56441	−1.57729	−0.788645	−	0.614849i	$-0.789217\pi$
$23$	−7.56441	−1.57729	−0.788645	+	0.614849i	$0.789217\pi$
$24$	0.700209	0.142930
$25$	1.00000	0.200000
$26$	−9.41448	−1.84633
$27$	−1.58185	−0.304426
$28$	−0.250644	−0.0473672
$29$	−5.18542	−0.962908	−0.481454	−	0.876471i	$-0.659891\pi$
$29$	−5.18542	−0.962908	−0.481454	+	0.876471i	$0.659891\pi$
$30$	−0.400267	−0.0730784
$31$	2.19885	0.394924	0.197462	−	0.980310i	$-0.436730\pi$
$31$	2.19885	0.394924	0.197462	+	0.980310i	$0.436730\pi$
$32$	1.40983	0.249225
$33$	−0.680435	−0.118449
$34$	−0.757406	−0.129894
$35$	−1.00000	−0.169031
$36$	−0.734088	−0.122348
$37$	5.38561	0.885389	0.442694	−	0.896673i	$-0.354023\pi$
$37$	5.38561	0.885389	0.442694	+	0.896673i	$0.354023\pi$
$38$	−5.22055	−0.846886
$39$	1.67432	0.268106
$40$	2.62441	0.414956
$41$	−6.93512	−1.08308	−0.541542	−	0.840674i	$-0.682159\pi$
$41$	−6.93512	−1.08308	−0.541542	+	0.840674i	$0.682159\pi$
$42$	0.400267	0.0617625
$43$	5.47623	0.835117	0.417559	−	0.908650i	$-0.362886\pi$
$43$	5.47623	0.835117	0.417559	+	0.908650i	$0.362886\pi$
$44$	−0.639215	−0.0963653
$45$	−2.92881	−0.436602
$46$	11.3482	1.67321
$47$	8.38893	1.22365	0.611825	−	0.790993i	$-0.290435\pi$
$47$	8.38893	1.22365	0.611825	+	0.790993i	$0.290435\pi$
$48$	−1.18421	−0.170926
$49$	1.00000	0.142857
$50$	−1.50021	−0.212162
$51$	0.134701	0.0188619
$52$	1.57289	0.218121
$53$	−4.09118	−0.561967	−0.280983	−	0.959713i	$-0.590661\pi$
$53$	−4.09118	−0.561967	−0.280983	+	0.959713i	$0.590661\pi$
$54$	2.37311	0.322939
$55$	−2.55030	−0.343882
$56$	−2.62441	−0.350702
$57$	0.928452	0.122976
$58$	7.77924	1.02146
$59$	−6.46570	−0.841762	−0.420881	−	0.907116i	$-0.638279\pi$
$59$	−6.46570	−0.841762	−0.420881	+	0.907116i	$0.638279\pi$
$60$	0.0668733	0.00863330
$61$	1.98590	0.254268	0.127134	−	0.991886i	$-0.459422\pi$
$61$	1.98590	0.254268	0.127134	+	0.991886i	$0.459422\pi$
$62$	−3.29874	−0.418941
$63$	2.92881	0.368996
$64$	6.76188	0.845235
$65$	6.27542	0.778370
$66$	1.02080	0.125652
$67$	8.62225	1.05338	0.526688	−	0.850059i	$-0.323434\pi$
$67$	8.62225	1.05338	0.526688	+	0.850059i	$0.323434\pi$
$68$	0.126541	0.0153454
$69$	−2.01823	−0.242967
$70$	1.50021	0.179310
$71$	−9.38322	−1.11358	−0.556792	−	0.830652i	$-0.687968\pi$
$71$	−9.38322	−1.11358	−0.556792	+	0.830652i	$0.687968\pi$
$72$	−7.68641	−0.905852
$73$	3.60124	0.421493	0.210747	−	0.977541i	$-0.432410\pi$
$73$	3.60124	0.421493	0.210747	+	0.977541i	$0.432410\pi$
$74$	−8.07957	−0.939231
$75$	0.266806	0.0308081
$76$	0.872207	0.100049
$77$	2.55030	0.290633
$78$	−2.51184	−0.284410
$79$	−5.42500	−0.610361	−0.305180	−	0.952295i	$-0.598717\pi$
$79$	−5.42500	−0.610361	−0.305180	+	0.952295i	$0.598717\pi$
$80$	−4.43846	−0.496235
$81$	8.36440	0.929377
$82$	10.4042	1.14895
$83$	1.16863	0.128274	0.0641372	−	0.997941i	$-0.479570\pi$
$83$	1.16863	0.128274	0.0641372	+	0.997941i	$0.479570\pi$
$84$	−0.0668733	−0.00729647
$85$	0.504865	0.0547603
$86$	−8.21552	−0.885902
$87$	−1.38350	−0.148327
$88$	−6.69302	−0.713478
$89$	1.25561	0.133094	0.0665471	−	0.997783i	$-0.478802\pi$
$89$	1.25561	0.133094	0.0665471	+	0.997783i	$0.478802\pi$
$90$	4.39385	0.463152
$91$	−6.27542	−0.657843
$92$	−1.89597	−0.197669
$93$	0.586666	0.0608344
$94$	−12.5852	−1.29806
$95$	3.47987	0.357027
$96$	0.376151	0.0383908
$97$	18.1951	1.84744	0.923718	−	0.383072i	$-0.125134\pi$
$97$	18.1951	1.84744	0.923718	+	0.383072i	$0.125134\pi$
$98$	−1.50021	−0.151545
$99$	7.46934	0.750697
$100$	0.250644	0.0250644
$101$	3.60580	0.358791	0.179395	−	0.983777i	$-0.442586\pi$
$101$	3.60580	0.358791	0.179395	+	0.983777i	$0.442586\pi$
$102$	−0.202081	−0.0200090
$103$	−0.693412	−0.0683240	−0.0341620	−	0.999416i	$-0.510876\pi$
$103$	−0.693412	−0.0683240	−0.0341620	+	0.999416i	$0.510876\pi$
$104$	16.4693	1.61495
$105$	−0.266806	−0.0260376
$106$	6.13765	0.596141
$107$	8.05582	0.778786	0.389393	−	0.921072i	$-0.372685\pi$
$107$	8.05582	0.778786	0.389393	+	0.921072i	$0.372685\pi$
$108$	−0.396479	−0.0381512
$109$	−15.0474	−1.44128	−0.720638	−	0.693312i	$-0.756151\pi$
$109$	−15.0474	−1.44128	−0.720638	+	0.693312i	$0.756151\pi$
$110$	3.82599	0.364794
$111$	1.43691	0.136386
$112$	4.43846	0.419396
$113$	−14.4370	−1.35812	−0.679062	−	0.734081i	$-0.737613\pi$
$113$	−14.4370	−1.35812	−0.679062	+	0.734081i	$0.737613\pi$
$114$	−1.39288	−0.130455
$115$	−7.56441	−0.705385
$116$	−1.29969	−0.120673
$117$	−18.3795	−1.69919
$118$	9.69993	0.892951
$119$	−0.504865	−0.0462809
$120$	0.700209	0.0639201
$121$	−4.49599	−0.408727
$122$	−2.97927	−0.269730
$123$	−1.85033	−0.166839
$124$	0.551127	0.0494926
$125$	1.00000	0.0894427
$126$	−4.39385	−0.391435
$127$	12.9788	1.15168	0.575840	−	0.817562i	$-0.304675\pi$
$127$	12.9788	1.15168	0.575840	+	0.817562i	$0.304675\pi$
$128$	−12.9639	−1.14586
$129$	1.46109	0.128642
$130$	−9.41448	−0.825704
$131$	−13.9304	−1.21711	−0.608553	−	0.793513i	$-0.708250\pi$
$131$	−13.9304	−1.21711	−0.608553	+	0.793513i	$0.708250\pi$
$132$	−0.170547	−0.0148442
$133$	−3.47987	−0.301743
$134$	−12.9352	−1.11743
$135$	−1.58185	−0.136144
$136$	1.32497	0.113615
$137$	1.96693	0.168046	0.0840231	−	0.996464i	$-0.473223\pi$
$137$	1.96693	0.168046	0.0840231	+	0.996464i	$0.473223\pi$
$138$	3.02778	0.257742
$139$	19.5592	1.65899	0.829496	−	0.558513i	$-0.188628\pi$
$139$	19.5592	1.65899	0.829496	+	0.558513i	$0.188628\pi$
$140$	−0.250644	−0.0211832
$141$	2.23822	0.188492
$142$	14.0768	1.18130
$143$	−16.0042	−1.33834
$144$	12.9994	1.08329
$145$	−5.18542	−0.430626
$146$	−5.40263	−0.447125
$147$	0.266806	0.0220058
$148$	1.34987	0.110958
$149$	−8.31376	−0.681090	−0.340545	−	0.940228i	$-0.610612\pi$
$149$	−8.31376	−0.681090	−0.340545	+	0.940228i	$0.610612\pi$
$150$	−0.400267	−0.0326816
$151$	1.71856	0.139854	0.0699272	−	0.997552i	$-0.477723\pi$
$151$	1.71856	0.139854	0.0699272	+	0.997552i	$0.477723\pi$
$152$	9.13261	0.740753
$153$	−1.47866	−0.119542
$154$	−3.82599	−0.308307
$155$	2.19885	0.176616
$156$	0.419658	0.0335995
$157$	−1.72011	−0.137279	−0.0686397	−	0.997642i	$-0.521866\pi$
$157$	−1.72011	−0.137279	−0.0686397	+	0.997642i	$0.521866\pi$
$158$	8.13867	0.647478
$159$	−1.09155	−0.0865658
$160$	1.40983	0.111457
$161$	7.56441	0.596159
$162$	−12.5484	−0.985895
$163$	−24.6303	−1.92920	−0.964598	−	0.263726i	$-0.915049\pi$
$163$	−24.6303	−1.92920	−0.964598	+	0.263726i	$0.915049\pi$
$164$	−1.73824	−0.135734
$165$	−0.680435	−0.0529718
$166$	−1.75320	−0.136075
$167$	−13.3179	−1.03057	−0.515285	−	0.857019i	$-0.672314\pi$
$167$	−13.3179	−1.03057	−0.515285	+	0.857019i	$0.672314\pi$
$168$	−0.700209	−0.0540223
$169$	26.3809	2.02930
$170$	−0.757406	−0.0580904
$171$	−10.1919	−0.779394
$172$	1.37258	0.104658
$173$	−2.50942	−0.190788	−0.0953940	−	0.995440i	$-0.530411\pi$
$173$	−2.50942	−0.190788	−0.0953940	+	0.995440i	$0.530411\pi$
$174$	2.07555	0.157347
$175$	−1.00000	−0.0755929
$176$	11.3194	0.853232
$177$	−1.72509	−0.129666
$178$	−1.88368	−0.141188
$179$	20.2006	1.50986	0.754932	−	0.655803i	$-0.227670\pi$
$179$	20.2006	1.50986	0.754932	+	0.655803i	$0.227670\pi$
$180$	−0.734088	−0.0547157
$181$	13.9823	1.03930	0.519649	−	0.854380i	$-0.326063\pi$
$181$	13.9823	1.03930	0.519649	+	0.854380i	$0.326063\pi$
$182$	9.41448	0.697848
$183$	0.529849	0.0391676
$184$	−19.8521	−1.46352
$185$	5.38561	0.395958
$186$	−0.880125	−0.0645339
$187$	−1.28755	−0.0941553
$188$	2.10263	0.153350
$189$	1.58185	0.115062
$190$	−5.22055	−0.378739
$191$	−16.3439	−1.18261	−0.591303	−	0.806450i	$-0.701386\pi$
$191$	−16.3439	−1.18261	−0.591303	+	0.806450i	$0.701386\pi$
$192$	1.80411	0.130201
$193$	12.0381	0.866519	0.433260	−	0.901269i	$-0.357363\pi$
$193$	12.0381	0.866519	0.433260	+	0.901269i	$0.357363\pi$
$194$	−27.2966	−1.95978
$195$	1.67432	0.119901
$196$	0.250644	0.0179031
$197$	20.7841	1.48081	0.740403	−	0.672164i	$-0.234635\pi$
$197$	20.7841	1.48081	0.740403	+	0.672164i	$0.234635\pi$
$198$	−11.2056	−0.796348
$199$	−19.1145	−1.35499	−0.677496	−	0.735527i	$-0.736935\pi$
$199$	−19.1145	−1.35499	−0.677496	+	0.735527i	$0.736935\pi$
$200$	2.62441	0.185574
$201$	2.30047	0.162263
$202$	−5.40948	−0.380609
$203$	5.18542	0.363945
$204$	0.0337620	0.00236381
$205$	−6.93512	−0.484370
$206$	1.04027	0.0724789
$207$	22.1548	1.53986
$208$	−27.8532	−1.93127
$209$	−8.87470	−0.613876
$210$	0.400267	0.0276210
$211$	17.0273	1.17221	0.586104	−	0.810236i	$-0.300661\pi$
$211$	17.0273	1.17221	0.586104	+	0.810236i	$0.300661\pi$
$212$	−1.02543	−0.0704267
$213$	−2.50350	−0.171537
$214$	−12.0855	−0.826145
$215$	5.47623	0.373476
$216$	−4.15141	−0.282468
$217$	−2.19885	−0.149267
$218$	22.5743	1.52892
$219$	0.960834	0.0649271
$220$	−0.639215	−0.0430959
$221$	3.16824	0.213119
$222$	−2.15568	−0.144680
$223$	15.6832	1.05022	0.525112	−	0.851033i	$-0.324023\pi$
$223$	15.6832	1.05022	0.525112	+	0.851033i	$0.324023\pi$
$224$	−1.40983	−0.0941982
$225$	−2.92881	−0.195254
$226$	21.6587	1.44071
$227$	11.0446	0.733059	0.366529	−	0.930406i	$-0.380546\pi$
$227$	11.0446	0.733059	0.366529	+	0.930406i	$0.380546\pi$
$228$	0.232710	0.0154116
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	11.3482	0.748281
$231$	0.680435	0.0447693
$232$	−13.6087	−0.893453
$233$	6.05794	0.396869	0.198434	−	0.980114i	$-0.436414\pi$
$233$	6.05794	0.396869	0.198434	+	0.980114i	$0.436414\pi$
$234$	27.5733	1.80252
$235$	8.38893	0.547233
$236$	−1.62058	−0.105491
$237$	−1.44743	−0.0940204
$238$	0.757406	0.0490953
$239$	20.8162	1.34649	0.673244	−	0.739421i	$-0.264900\pi$
$239$	20.8162	1.34649	0.673244	+	0.739421i	$0.264900\pi$
$240$	−1.18421	−0.0764405
$241$	−4.38625	−0.282543	−0.141272	−	0.989971i	$-0.545119\pi$
$241$	−4.38625	−0.282543	−0.141272	+	0.989971i	$0.545119\pi$
$242$	6.74495	0.433582
$243$	6.97721	0.447588
$244$	0.497752	0.0318653
$245$	1.00000	0.0638877
$246$	2.77590	0.176985
$247$	21.8377	1.38950
$248$	5.77067	0.366438
$249$	0.311799	0.0197595
$250$	−1.50021	−0.0948819
$251$	−4.60395	−0.290599	−0.145299	−	0.989388i	$-0.546415\pi$
$251$	−4.60395	−0.290599	−0.145299	+	0.989388i	$0.546415\pi$
$252$	0.734088	0.0462432
$253$	19.2915	1.21285
$254$	−19.4709	−1.22172
$255$	0.134701	0.00843531
$256$	5.92492	0.370307
$257$	23.5742	1.47052	0.735259	−	0.677786i	$-0.237061\pi$
$257$	23.5742	1.47052	0.735259	+	0.677786i	$0.237061\pi$
$258$	−2.19195	−0.136465
$259$	−5.38561	−0.334646
$260$	1.57289	0.0975467
$261$	15.1871	0.940060
$262$	20.8986	1.29112
$263$	3.54528	0.218611	0.109306	−	0.994008i	$-0.465137\pi$
$263$	3.54528	0.218611	0.109306	+	0.994008i	$0.465137\pi$
$264$	−1.78574	−0.109905
$265$	−4.09118	−0.251319
$266$	5.22055	0.320093
$267$	0.335004	0.0205019
$268$	2.16111	0.132011
$269$	−5.26431	−0.320971	−0.160485	−	0.987038i	$-0.551306\pi$
$269$	−5.26431	−0.320971	−0.160485	+	0.987038i	$0.551306\pi$
$270$	2.37311	0.144423
$271$	−2.88615	−0.175321	−0.0876605	−	0.996150i	$-0.527939\pi$
$271$	−2.88615	−0.175321	−0.0876605	+	0.996150i	$0.527939\pi$
$272$	−2.24083	−0.135870
$273$	−1.67432	−0.101335
$274$	−2.95082	−0.178265
$275$	−2.55030	−0.153789
$276$	−0.505857	−0.0304490
$277$	1.36957	0.0822892	0.0411446	−	0.999153i	$-0.486900\pi$
$277$	1.36957	0.0822892	0.0411446	+	0.999153i	$0.486900\pi$
$278$	−29.3430	−1.75988
$279$	−6.44001	−0.385553
$280$	−2.62441	−0.156838
$281$	13.5515	0.808416	0.404208	−	0.914667i	$-0.367547\pi$
$281$	13.5515	0.808416	0.404208	+	0.914667i	$0.367547\pi$
$282$	−3.35781	−0.199955
$283$	−6.77186	−0.402545	−0.201273	−	0.979535i	$-0.564508\pi$
$283$	−6.77186	−0.402545	−0.201273	+	0.979535i	$0.564508\pi$
$284$	−2.35184	−0.139556
$285$	0.928452	0.0549967
$286$	24.0097	1.41972
$287$	6.93512	0.409367
$288$	−4.12913	−0.243311
$289$	−16.7451	−0.985007
$290$	7.77924	0.456813
$291$	4.85458	0.284580
$292$	0.902628	0.0528223
$293$	−7.32664	−0.428027	−0.214013	−	0.976831i	$-0.568654\pi$
$293$	−7.32664	−0.428027	−0.214013	+	0.976831i	$0.568654\pi$
$294$	−0.400267	−0.0233440
$295$	−6.46570	−0.376447
$296$	14.1340	0.821525
$297$	4.03417	0.234086
$298$	12.4724	0.722508
$299$	−47.4699	−2.74525
$300$	0.0668733	0.00386093
$301$	−5.47623	−0.315645
$302$	−2.57821	−0.148359
$303$	0.962051	0.0552684
$304$	−15.4453	−0.885848
$305$	1.98590	0.113712
$306$	2.21830	0.126812
$307$	−10.8411	−0.618736	−0.309368	−	0.950942i	$-0.600117\pi$
$307$	−10.8411	−0.618736	−0.309368	+	0.950942i	$0.600117\pi$
$308$	0.639215	0.0364227
$309$	−0.185007	−0.0105247
$310$	−3.29874	−0.187356
$311$	−11.4789	−0.650907	−0.325454	−	0.945558i	$-0.605517\pi$
$311$	−11.4789	−0.650907	−0.325454	+	0.945558i	$0.605517\pi$
$312$	4.39411	0.248767
$313$	−23.4091	−1.32316	−0.661581	−	0.749874i	$-0.730114\pi$
$313$	−23.4091	−1.32316	−0.661581	+	0.749874i	$0.730114\pi$
$314$	2.58053	0.145628
$315$	2.92881	0.165020
$316$	−1.35974	−0.0764915
$317$	15.7970	0.887248	0.443624	−	0.896213i	$-0.353693\pi$
$317$	15.7970	0.887248	0.443624	+	0.896213i	$0.353693\pi$
$318$	1.63756	0.0918300
$319$	13.2244	0.740422
$320$	6.76188	0.378001
$321$	2.14934	0.119965
$322$	−11.3482	−0.632413
$323$	1.75687	0.0977546
$324$	2.09648	0.116471
$325$	6.27542	0.348098
$326$	36.9508	2.04651
$327$	−4.01473	−0.222015
$328$	−18.2006	−1.00496
$329$	−8.38893	−0.462497
$330$	1.02080	0.0561931
$331$	16.1759	0.889110	0.444555	−	0.895751i	$-0.353362\pi$
$331$	16.1759	0.889110	0.444555	+	0.895751i	$0.353362\pi$
$332$	0.292911	0.0160756
$333$	−15.7735	−0.864380
$334$	19.9797	1.09324
$335$	8.62225	0.471084
$336$	1.18421	0.0646040
$337$	24.6685	1.34378	0.671890	−	0.740651i	$-0.265483\pi$
$337$	24.6685	1.34378	0.671890	+	0.740651i	$0.265483\pi$
$338$	−39.5770	−2.15271
$339$	−3.85190	−0.209206
$340$	0.126541	0.00686266
$341$	−5.60771	−0.303674
$342$	15.2900	0.826790
$343$	−1.00000	−0.0539949
$344$	14.3719	0.774879
$345$	−2.01823	−0.108658
$346$	3.76468	0.202390
$347$	−5.07605	−0.272497	−0.136248	−	0.990675i	$-0.543504\pi$
$347$	−5.07605	−0.272497	−0.136248	+	0.990675i	$0.543504\pi$
$348$	−0.346766	−0.0185886
$349$	0.670535	0.0358929	0.0179465	−	0.999839i	$-0.494287\pi$
$349$	0.670535	0.0358929	0.0179465	+	0.999839i	$0.494287\pi$
$350$	1.50021	0.0801898
$351$	−9.92674	−0.529850
$352$	−3.59548	−0.191640
$353$	24.4851	1.30321	0.651605	−	0.758558i	$-0.274096\pi$
$353$	24.4851	1.30321	0.651605	+	0.758558i	$0.274096\pi$
$354$	2.58800	0.137551
$355$	−9.38322	−0.498010
$356$	0.314710	0.0166796
$357$	−0.134701	−0.00712914
$358$	−30.3052	−1.60168
$359$	32.6609	1.72378	0.861889	−	0.507097i	$-0.169281\pi$
$359$	32.6609	1.72378	0.861889	+	0.507097i	$0.169281\pi$
$360$	−7.68641	−0.405109
$361$	−6.89049	−0.362657
$362$	−20.9765	−1.10250
$363$	−1.19956	−0.0629605
$364$	−1.57289	−0.0824420
$365$	3.60124	0.188498
$366$	−0.794888	−0.0415494
$367$	−18.0468	−0.942033	−0.471017	−	0.882124i	$-0.656113\pi$
$367$	−18.0468	−0.942033	−0.471017	+	0.882124i	$0.656113\pi$
$368$	33.5744	1.75019
$369$	20.3117	1.05738
$370$	−8.07957	−0.420037
$371$	4.09118	0.212404
$372$	0.147044	0.00762388
$373$	−1.39975	−0.0724763	−0.0362381	−	0.999343i	$-0.511537\pi$
$373$	−1.39975	−0.0724763	−0.0362381	+	0.999343i	$0.511537\pi$
$374$	1.93161	0.0998811
$375$	0.266806	0.0137778
$376$	22.0160	1.13539
$377$	−32.5407	−1.67593
$378$	−2.37311	−0.122059
$379$	−6.54587	−0.336239	−0.168120	−	0.985767i	$-0.553769\pi$
$379$	−6.54587	−0.336239	−0.168120	+	0.985767i	$0.553769\pi$
$380$	0.872207	0.0447433
$381$	3.46282	0.177406
$382$	24.5194	1.25452
$383$	−20.0299	−1.02348	−0.511741	−	0.859140i	$-0.670999\pi$
$383$	−20.0299	−1.02348	−0.511741	+	0.859140i	$0.670999\pi$
$384$	−3.45886	−0.176509
$385$	2.55030	0.129975
$386$	−18.0597	−0.919214
$387$	−16.0389	−0.815301
$388$	4.56049	0.231524
$389$	−0.889458	−0.0450973	−0.0225486	−	0.999746i	$-0.507178\pi$
$389$	−0.889458	−0.0450973	−0.0225486	+	0.999746i	$0.507178\pi$
$390$	−2.51184	−0.127192
$391$	−3.81901	−0.193136
$392$	2.62441	0.132553
$393$	−3.71672	−0.187484
$394$	−31.1806	−1.57086
$395$	−5.42500	−0.272962
$396$	1.87214	0.0940787
$397$	−4.67200	−0.234481	−0.117240	−	0.993104i	$-0.537405\pi$
$397$	−4.67200	−0.234481	−0.117240	+	0.993104i	$0.537405\pi$
$398$	28.6759	1.43739
$399$	−0.928452	−0.0464807
$400$	−4.43846	−0.221923
$401$	8.54573	0.426753	0.213377	−	0.976970i	$-0.431554\pi$
$401$	8.54573	0.426753	0.213377	+	0.976970i	$0.431554\pi$
$402$	−3.45120	−0.172130
$403$	13.7987	0.687362
$404$	0.903771	0.0449643
$405$	8.36440	0.415630
$406$	−7.77924	−0.386077
$407$	−13.7349	−0.680814
$408$	0.353511	0.0175014
$409$	−15.5282	−0.767821	−0.383911	−	0.923370i	$-0.625423\pi$
$409$	−15.5282	−0.767821	−0.383911	+	0.923370i	$0.625423\pi$
$410$	10.4042	0.513825
$411$	0.524789	0.0258859
$412$	−0.173799	−0.00856248
$413$	6.46570	0.318156
$414$	−33.2369	−1.63350
$415$	1.16863	0.0573660
$416$	8.84727	0.433773
$417$	5.21852	0.255552
$418$	13.3140	0.651207
$419$	36.5913	1.78760	0.893802	−	0.448461i	$-0.148028\pi$
$419$	36.5913	1.78760	0.893802	+	0.448461i	$0.148028\pi$
$420$	−0.0668733	−0.00326308
$421$	27.5923	1.34477	0.672384	−	0.740203i	$-0.265271\pi$
$421$	27.5923	1.34477	0.672384	+	0.740203i	$0.265271\pi$
$422$	−25.5446	−1.24349
$423$	−24.5696	−1.19462
$424$	−10.7369	−0.521432
$425$	0.504865	0.0244895
$426$	3.75579	0.181969
$427$	−1.98590	−0.0961042
$428$	2.01914	0.0975988
$429$	−4.27002	−0.206158
$430$	−8.21552	−0.396188
$431$	20.0442	0.965495	0.482748	−	0.875759i	$-0.339639\pi$
$431$	20.0442	0.965495	0.482748	+	0.875759i	$0.339639\pi$
$432$	7.02096	0.337796
$433$	−1.00206	−0.0481560	−0.0240780	−	0.999710i	$-0.507665\pi$
$433$	−1.00206	−0.0481560	−0.0240780	+	0.999710i	$0.507665\pi$
$434$	3.29874	0.158345
$435$	−1.38350	−0.0663339
$436$	−3.77152	−0.180623
$437$	−26.3232	−1.25921
$438$	−1.44146	−0.0688755
$439$	7.65740	0.365468	0.182734	−	0.983162i	$-0.441505\pi$
$439$	7.65740	0.365468	0.182734	+	0.983162i	$0.441505\pi$
$440$	−6.69302	−0.319077
$441$	−2.92881	−0.139467
$442$	−4.75304	−0.226079
$443$	−4.54703	−0.216036	−0.108018	−	0.994149i	$-0.534450\pi$
$443$	−4.54703	−0.216036	−0.108018	+	0.994149i	$0.534450\pi$
$444$	0.360153	0.0170921
$445$	1.25561	0.0595215
$446$	−23.5282	−1.11409
$447$	−2.21816	−0.104916
$448$	−6.76188	−0.319469
$449$	11.7624	0.555100	0.277550	−	0.960711i	$-0.410478\pi$
$449$	11.7624	0.555100	0.277550	+	0.960711i	$0.410478\pi$
$450$	4.39385	0.207128
$451$	17.6866	0.832830
$452$	−3.61855	−0.170202
$453$	0.458523	0.0215433
$454$	−16.5693	−0.777638
$455$	−6.27542	−0.294196
$456$	2.43664	0.114106
$457$	−0.717119	−0.0335454	−0.0167727	−	0.999859i	$-0.505339\pi$
$457$	−0.717119	−0.0335454	−0.0167727	+	0.999859i	$0.505339\pi$
$458$	1.50021	0.0701004
$459$	−0.798618	−0.0372763
$460$	−1.89597	−0.0884001
$461$	39.9072	1.85866	0.929331	−	0.369247i	$-0.120385\pi$
$461$	39.9072	1.85866	0.929331	+	0.369247i	$0.120385\pi$
$462$	−1.02080	−0.0474918
$463$	−34.9321	−1.62343	−0.811716	−	0.584053i	$-0.801466\pi$
$463$	−34.9321	−1.62343	−0.811716	+	0.584053i	$0.801466\pi$
$464$	23.0153	1.06846
$465$	0.586666	0.0272060
$466$	−9.08821	−0.421003
$467$	13.5806	0.628434	0.314217	−	0.949351i	$-0.398258\pi$
$467$	13.5806	0.628434	0.314217	+	0.949351i	$0.398258\pi$
$468$	−4.60671	−0.212945
$469$	−8.62225	−0.398139
$470$	−12.5852	−0.580512
$471$	−0.458935	−0.0211466
$472$	−16.9686	−0.781045
$473$	−13.9660	−0.642158
$474$	2.17145	0.0997379
$475$	3.47987	0.159667
$476$	−0.126541	−0.00580000
$477$	11.9823	0.548632
$478$	−31.2288	−1.42837
$479$	−34.2006	−1.56266	−0.781332	−	0.624116i	$-0.785459\pi$
$479$	−34.2006	−1.56266	−0.781332	+	0.624116i	$0.785459\pi$
$480$	0.376151	0.0171689
$481$	33.7970	1.54101
$482$	6.58032	0.299725
$483$	2.01823	0.0918328
$484$	−1.12689	−0.0512223
$485$	18.1951	0.826199
$486$	−10.4673	−0.474807
$487$	−38.5276	−1.74585	−0.872925	−	0.487854i	$-0.837780\pi$
$487$	−38.5276	−1.74585	−0.872925	+	0.487854i	$0.837780\pi$
$488$	5.21180	0.235927
$489$	−6.57152	−0.297175
$490$	−1.50021	−0.0677728
$491$	−3.60129	−0.162524	−0.0812619	−	0.996693i	$-0.525895\pi$
$491$	−3.60129	−0.162524	−0.0812619	+	0.996693i	$0.525895\pi$
$492$	−0.463774	−0.0209086
$493$	−2.61794	−0.117906
$494$	−32.7612	−1.47400
$495$	7.46934	0.335722
$496$	−9.75950	−0.438215
$497$	9.38322	0.420895
$498$	−0.467766	−0.0209611
$499$	7.90035	0.353668	0.176834	−	0.984241i	$-0.443414\pi$
$499$	7.90035	0.353668	0.176834	+	0.984241i	$0.443414\pi$
$500$	0.250644	0.0112091
$501$	−3.55330	−0.158750
$502$	6.90691	0.308270
$503$	4.07786	0.181823	0.0909113	−	0.995859i	$-0.471022\pi$
$503$	4.07786	0.181823	0.0909113	+	0.995859i	$0.471022\pi$
$504$	7.68641	0.342380
$505$	3.60580	0.160456
$506$	−28.9414	−1.28660
$507$	7.03859	0.312595
$508$	3.25305	0.144331
$509$	28.1655	1.24842	0.624208	−	0.781259i	$-0.285422\pi$
$509$	28.1655	1.24842	0.624208	+	0.781259i	$0.285422\pi$
$510$	−0.202081	−0.00894828
$511$	−3.60124	−0.159309
$512$	17.0392	0.753034
$513$	−5.50462	−0.243035
$514$	−35.3663	−1.55994
$515$	−0.693412	−0.0305554
$516$	0.366213	0.0161216
$517$	−21.3942	−0.940918
$518$	8.07957	0.354996
$519$	−0.669530	−0.0293891
$520$	16.4693	0.722226
$521$	4.45422	0.195143	0.0975715	−	0.995229i	$-0.468893\pi$
$521$	4.45422	0.195143	0.0975715	+	0.995229i	$0.468893\pi$
$522$	−22.7840	−0.997227
$523$	14.1787	0.619992	0.309996	−	0.950738i	$-0.399672\pi$
$523$	14.1787	0.619992	0.309996	+	0.950738i	$0.399672\pi$
$524$	−3.49157	−0.152530
$525$	−0.266806	−0.0116444
$526$	−5.31868	−0.231905
$527$	1.11012	0.0483576
$528$	3.02009	0.131432
$529$	34.2204	1.48784
$530$	6.13765	0.266602
$531$	18.9368	0.821788
$532$	−0.872207	−0.0378150
$533$	−43.5208	−1.88510
$534$	−0.502578	−0.0217487
$535$	8.05582	0.348284
$536$	22.6283	0.977395
$537$	5.38965	0.232581
$538$	7.89760	0.340490
$539$	−2.55030	−0.109849
$540$	−0.396479	−0.0170617
$541$	−7.84973	−0.337486	−0.168743	−	0.985660i	$-0.553971\pi$
$541$	−7.84973	−0.337486	−0.168743	+	0.985660i	$0.553971\pi$
$542$	4.32984	0.185983
$543$	3.73057	0.160094
$544$	0.711773	0.0305170
$545$	−15.0474	−0.644558
$546$	2.51184	0.107497
$547$	−8.17810	−0.349670	−0.174835	−	0.984598i	$-0.555939\pi$
$547$	−8.17810	−0.349670	−0.174835	+	0.984598i	$0.555939\pi$
$548$	0.492998	0.0210598
$549$	−5.81632	−0.248234
$550$	3.82599	0.163141
$551$	−18.0446	−0.768726
$552$	−5.29667	−0.225441
$553$	5.42500	0.230695
$554$	−2.05464	−0.0872934
$555$	1.43691	0.0609936
$556$	4.90239	0.207908
$557$	46.3539	1.96408	0.982039	−	0.188677i	$-0.0604200\pi$
$557$	46.3539	1.96408	0.982039	+	0.188677i	$0.0604200\pi$
$558$	9.66140	0.409000
$559$	34.3656	1.45351
$560$	4.43846	0.187559
$561$	−0.343528	−0.0145038
$562$	−20.3302	−0.857577
$563$	16.7672	0.706654	0.353327	−	0.935500i	$-0.385050\pi$
$563$	16.7672	0.706654	0.353327	+	0.935500i	$0.385050\pi$
$564$	0.560995	0.0236222
$565$	−14.4370	−0.607371
$566$	10.1592	0.427025
$567$	−8.36440	−0.351272
$568$	−24.6254	−1.03326
$569$	27.8896	1.16919	0.584597	−	0.811324i	$-0.301253\pi$
$569$	27.8896	1.16919	0.584597	+	0.811324i	$0.301253\pi$
$570$	−1.39288	−0.0583412
$571$	20.3398	0.851195	0.425597	−	0.904913i	$-0.360064\pi$
$571$	20.3398	0.851195	0.425597	+	0.904913i	$0.360064\pi$
$572$	−4.01134	−0.167723
$573$	−4.36066	−0.182169
$574$	−10.4042	−0.434262
$575$	−7.56441	−0.315458
$576$	−19.8043	−0.825179
$577$	8.06791	0.335872	0.167936	−	0.985798i	$-0.446290\pi$
$577$	8.06791	0.335872	0.167936	+	0.985798i	$0.446290\pi$
$578$	25.1213	1.04491
$579$	3.21183	0.133479
$580$	−1.29969	−0.0539668
$581$	−1.16863	−0.0484831
$582$	−7.28291	−0.301886
$583$	10.4337	0.432121
$584$	9.45113	0.391091
$585$	−18.3795	−0.759901
$586$	10.9915	0.454056
$587$	13.9056	0.573945	0.286972	−	0.957939i	$-0.407351\pi$
$587$	13.9056	0.573945	0.286972	+	0.957939i	$0.407351\pi$
$588$	0.0668733	0.00275781
$589$	7.65170	0.315283
$590$	9.69993	0.399340
$591$	5.54533	0.228104
$592$	−23.9038	−0.982442
$593$	25.1526	1.03289	0.516447	−	0.856319i	$-0.327254\pi$
$593$	25.1526	1.03289	0.516447	+	0.856319i	$0.327254\pi$
$594$	−6.05212	−0.248322
$595$	−0.504865	−0.0206974
$596$	−2.08379	−0.0853554
$597$	−5.09987	−0.208724
$598$	71.2150	2.91220
$599$	36.0591	1.47333	0.736667	−	0.676256i	$-0.236399\pi$
$599$	36.0591	1.47333	0.736667	+	0.676256i	$0.236399\pi$
$600$	0.700209	0.0285859
$601$	41.8375	1.70659	0.853294	−	0.521430i	$-0.174601\pi$
$601$	41.8375	1.70659	0.853294	+	0.521430i	$0.174601\pi$
$602$	8.21552	0.334840
$603$	−25.2530	−1.02838
$604$	0.430746	0.0175268
$605$	−4.49599	−0.182788
$606$	−1.44328	−0.0586293
$607$	−37.5804	−1.52534	−0.762670	−	0.646788i	$-0.776112\pi$
$607$	−37.5804	−1.52534	−0.762670	+	0.646788i	$0.776112\pi$
$608$	4.90603	0.198966
$609$	1.38350	0.0560624
$610$	−2.97927	−0.120627
$611$	52.6441	2.12975
$612$	−0.370615	−0.0149812
$613$	42.0722	1.69928	0.849641	−	0.527362i	$-0.176819\pi$
$613$	42.0722	1.69928	0.849641	+	0.527362i	$0.176819\pi$
$614$	16.2640	0.656362
$615$	−1.85033	−0.0746127
$616$	6.69302	0.269670
$617$	−31.2591	−1.25844	−0.629222	−	0.777226i	$-0.716626\pi$
$617$	−31.2591	−1.25844	−0.629222	+	0.777226i	$0.716626\pi$
$618$	0.277550	0.0111647
$619$	16.0603	0.645517	0.322758	−	0.946481i	$-0.395390\pi$
$619$	16.0603	0.645517	0.322758	+	0.946481i	$0.395390\pi$
$620$	0.551127	0.0221338
$621$	11.9657	0.480168
$622$	17.2208	0.690490
$623$	−1.25561	−0.0503049
$624$	−7.43142	−0.297495
$625$	1.00000	0.0400000
$626$	35.1187	1.40362
$627$	−2.36783	−0.0945619
$628$	−0.431133	−0.0172041
$629$	2.71901	0.108414
$630$	−4.39385	−0.175055
$631$	4.89969	0.195054	0.0975269	−	0.995233i	$-0.468907\pi$
$631$	4.89969	0.195054	0.0975269	+	0.995233i	$0.468907\pi$
$632$	−14.2374	−0.566335
$633$	4.54299	0.180568
$634$	−23.6989	−0.941203
$635$	12.9788	0.515047
$636$	−0.273591	−0.0108486
$637$	6.27542	0.248641
$638$	−19.8394	−0.785448
$639$	27.4817	1.08716
$640$	−12.9639	−0.512444
$641$	−18.9168	−0.747168	−0.373584	−	0.927596i	$-0.621871\pi$
$641$	−18.9168	−0.747168	−0.373584	+	0.927596i	$0.621871\pi$
$642$	−3.22448	−0.127260
$643$	−29.6676	−1.16997	−0.584987	−	0.811043i	$-0.698900\pi$
$643$	−29.6676	−1.16997	−0.584987	+	0.811043i	$0.698900\pi$
$644$	1.89597	0.0747117
$645$	1.46109	0.0575305
$646$	−2.63567	−0.103699
$647$	−45.9479	−1.80640	−0.903199	−	0.429223i	$-0.858788\pi$
$647$	−45.9479	−1.80640	−0.903199	+	0.429223i	$0.858788\pi$
$648$	21.9516	0.862341
$649$	16.4894	0.647267
$650$	−9.41448	−0.369266
$651$	−0.586666	−0.0229933
$652$	−6.17343	−0.241770
$653$	32.7092	1.28001	0.640006	−	0.768370i	$-0.278932\pi$
$653$	32.7092	1.28001	0.640006	+	0.768370i	$0.278932\pi$
$654$	6.02296	0.235516
$655$	−13.9304	−0.544306
$656$	30.7813	1.20181
$657$	−10.5474	−0.411492
$658$	12.5852	0.490622
$659$	−9.45410	−0.368279	−0.184140	−	0.982900i	$-0.558950\pi$
$659$	−9.45410	−0.368279	−0.184140	+	0.982900i	$0.558950\pi$
$660$	−0.170547	−0.00663852
$661$	32.4826	1.26343	0.631714	−	0.775202i	$-0.282352\pi$
$661$	32.4826	1.26343	0.631714	+	0.775202i	$0.282352\pi$
$662$	−24.2674	−0.943179
$663$	0.845306	0.0328290
$664$	3.06698	0.119022
$665$	−3.47987	−0.134944
$666$	23.6636	0.916944
$667$	39.2247	1.51879
$668$	−3.33804	−0.129153
$669$	4.18438	0.161777
$670$	−12.9352	−0.499732
$671$	−5.06462	−0.195517
$672$	−0.376151	−0.0145104
$673$	49.8803	1.92274	0.961371	−	0.275255i	$-0.0887621\pi$
$673$	49.8803	1.92274	0.961371	+	0.275255i	$0.0887621\pi$
$674$	−37.0080	−1.42550
$675$	−1.58185	−0.0608852
$676$	6.61220	0.254316
$677$	−20.3386	−0.781678	−0.390839	−	0.920459i	$-0.627815\pi$
$677$	−20.3386	−0.781678	−0.390839	+	0.920459i	$0.627815\pi$
$678$	5.77867	0.221928
$679$	−18.1951	−0.698266
$680$	1.32497	0.0508104
$681$	2.94678	0.112921
$682$	8.41277	0.322141
$683$	−20.7758	−0.794965	−0.397482	−	0.917610i	$-0.630116\pi$
$683$	−20.7758	−0.794965	−0.397482	+	0.917610i	$0.630116\pi$
$684$	−2.55453	−0.0976750
$685$	1.96693	0.0751525
$686$	1.50021	0.0572785
$687$	−0.266806	−0.0101793
$688$	−24.3061	−0.926660
$689$	−25.6739	−0.978097
$690$	3.02778	0.115266
$691$	−21.4273	−0.815133	−0.407566	−	0.913176i	$-0.633623\pi$
$691$	−21.4273	−0.815133	−0.407566	+	0.913176i	$0.633623\pi$
$692$	−0.628971	−0.0239099
$693$	−7.46934	−0.283737
$694$	7.61516	0.289068
$695$	19.5592	0.741924
$696$	−3.63088	−0.137628
$697$	−3.50130	−0.132621
$698$	−1.00595	−0.0380756
$699$	1.61630	0.0611339
$700$	−0.250644	−0.00947343
$701$	24.5272	0.926380	0.463190	−	0.886259i	$-0.346705\pi$
$701$	24.5272	0.926380	0.463190	+	0.886259i	$0.346705\pi$
$702$	14.8922	0.562072
$703$	18.7412	0.706839
$704$	−17.2448	−0.649938
$705$	2.23822	0.0842962
$706$	−36.7329	−1.38246
$707$	−3.60580	−0.135610
$708$	−0.432382	−0.0162499
$709$	22.8344	0.857563	0.428782	−	0.903408i	$-0.358943\pi$
$709$	22.8344	0.857563	0.428782	+	0.903408i	$0.358943\pi$
$710$	14.0768	0.528295
$711$	15.8888	0.595878
$712$	3.29523	0.123494
$713$	−16.6330	−0.622910
$714$	0.202081	0.00756268
$715$	−16.0042	−0.598522
$716$	5.06315	0.189219
$717$	5.55389	0.207414
$718$	−48.9984	−1.82860
$719$	21.4181	0.798762	0.399381	−	0.916785i	$-0.369225\pi$
$719$	21.4181	0.798762	0.399381	+	0.916785i	$0.369225\pi$
$720$	12.9994	0.484461
$721$	0.693412	0.0258240
$722$	10.3372	0.384711
$723$	−1.17028	−0.0435232
$724$	3.50458	0.130247
$725$	−5.18542	−0.192582
$726$	1.79960	0.0667893
$727$	34.3606	1.27436	0.637182	−	0.770714i	$-0.280100\pi$
$727$	34.3606	1.27436	0.637182	+	0.770714i	$0.280100\pi$
$728$	−16.4693	−0.610392
$729$	−23.2316	−0.860431
$730$	−5.40263	−0.199960
$731$	2.76476	0.102258
$732$	0.132803	0.00490855
$733$	2.78415	0.102835	0.0514175	−	0.998677i	$-0.483626\pi$
$733$	2.78415	0.102835	0.0514175	+	0.998677i	$0.483626\pi$
$734$	27.0740	0.999320
$735$	0.266806	0.00984130
$736$	−10.6645	−0.393100
$737$	−21.9893	−0.809986
$738$	−30.4719	−1.12169
$739$	26.2525	0.965712	0.482856	−	0.875700i	$-0.339599\pi$
$739$	26.2525	0.965712	0.482856	+	0.875700i	$0.339599\pi$
$740$	1.34987	0.0496221
$741$	5.82643	0.214039
$742$	−6.13765	−0.225320
$743$	−15.4977	−0.568555	−0.284278	−	0.958742i	$-0.591754\pi$
$743$	−15.4977	−0.568555	−0.284278	+	0.958742i	$0.591754\pi$
$744$	1.53965	0.0564464
$745$	−8.31376	−0.304593
$746$	2.09992	0.0768837
$747$	−3.42271	−0.125231
$748$	−0.322717	−0.0117997
$749$	−8.05582	−0.294353
$750$	−0.400267	−0.0146157
$751$	20.0604	0.732014	0.366007	−	0.930612i	$-0.380725\pi$
$751$	20.0604	0.732014	0.366007	+	0.930612i	$0.380725\pi$
$752$	−37.2340	−1.35778
$753$	−1.22836	−0.0447640
$754$	48.8180	1.77785
$755$	1.71856	0.0625448
$756$	0.396479	0.0144198
$757$	42.7063	1.55219	0.776094	−	0.630617i	$-0.217198\pi$
$757$	42.7063	1.55219	0.776094	+	0.630617i	$0.217198\pi$
$758$	9.82022	0.356686
$759$	5.14709	0.186828
$760$	9.13261	0.331275
$761$	−36.5625	−1.32539	−0.662696	−	0.748889i	$-0.730588\pi$
$761$	−36.5625	−1.32539	−0.662696	+	0.748889i	$0.730588\pi$
$762$	−5.19497	−0.188194
$763$	15.0474	0.544751
$764$	−4.09650	−0.148206
$765$	−1.47866	−0.0534609
$766$	30.0492	1.08572
$767$	−40.5750	−1.46508
$768$	1.58080	0.0570424
$769$	3.34947	0.120785	0.0603924	−	0.998175i	$-0.480765\pi$
$769$	3.34947	0.120785	0.0603924	+	0.998175i	$0.480765\pi$
$770$	−3.82599	−0.137879
$771$	6.28974	0.226520
$772$	3.01726	0.108594
$773$	35.7937	1.28741	0.643705	−	0.765274i	$-0.277397\pi$
$773$	35.7937	1.28741	0.643705	+	0.765274i	$0.277397\pi$
$774$	24.0617	0.864881
$775$	2.19885	0.0789849
$776$	47.7515	1.71418
$777$	−1.43691	−0.0515490
$778$	1.33438	0.0478397
$779$	−24.1333	−0.864667
$780$	0.419658	0.0150262
$781$	23.9300	0.856283
$782$	5.72933	0.204880
$783$	8.20253	0.293135
$784$	−4.43846	−0.158517
$785$	−1.72011	−0.0613932
$786$	5.57588	0.198885
$787$	31.4755	1.12198	0.560990	−	0.827822i	$-0.310420\pi$
$787$	31.4755	1.12198	0.560990	+	0.827822i	$0.310420\pi$
$788$	5.20940	0.185577
$789$	0.945902	0.0336750
$790$	8.13867	0.289561
$791$	14.4370	0.513322
$792$	19.6026	0.696549
$793$	12.4623	0.442550
$794$	7.00900	0.248740
$795$	−1.09155	−0.0387134
$796$	−4.79093	−0.169810
$797$	24.9451	0.883602	0.441801	−	0.897113i	$-0.354340\pi$
$797$	24.9451	0.883602	0.441801	+	0.897113i	$0.354340\pi$
$798$	1.39288	0.0493073
$799$	4.23528	0.149833
$800$	1.40983	0.0498450
$801$	−3.67744	−0.129936
$802$	−12.8204	−0.452705
$803$	−9.18423	−0.324104
$804$	0.576598	0.0203351
$805$	7.56441	0.266611
$806$	−20.7010	−0.729161
$807$	−1.40455	−0.0494426
$808$	9.46310	0.332911
$809$	54.2917	1.90880	0.954398	−	0.298537i	$-0.0964987\pi$
$809$	54.2917	1.90880	0.954398	+	0.298537i	$0.0964987\pi$
$810$	−12.5484	−0.440905
$811$	−50.8645	−1.78609	−0.893047	−	0.449964i	$-0.851437\pi$
$811$	−50.8645	−1.78609	−0.893047	+	0.449964i	$0.851437\pi$
$812$	1.29969	0.0456102
$813$	−0.770042	−0.0270066
$814$	20.6053	0.722215
$815$	−24.6303	−0.862762
$816$	−0.597866	−0.0209295
$817$	19.0566	0.666705
$818$	23.2957	0.814514
$819$	18.3795	0.642233
$820$	−1.73824	−0.0607021
$821$	−31.6110	−1.10323	−0.551615	−	0.834099i	$-0.685988\pi$
$821$	−31.6110	−1.10323	−0.551615	+	0.834099i	$0.685988\pi$
$822$	−0.787296	−0.0274601
$823$	48.6036	1.69422	0.847108	−	0.531420i	$-0.178341\pi$
$823$	48.6036	1.69422	0.847108	+	0.531420i	$0.178341\pi$
$824$	−1.81980	−0.0633957
$825$	−0.680435	−0.0236897
$826$	−9.69993	−0.337504
$827$	1.39817	0.0486192	0.0243096	−	0.999704i	$-0.492261\pi$
$827$	1.39817	0.0486192	0.0243096	+	0.999704i	$0.492261\pi$
$828$	5.55295	0.192978
$829$	8.80210	0.305710	0.152855	−	0.988249i	$-0.451153\pi$
$829$	8.80210	0.305710	0.152855	+	0.988249i	$0.451153\pi$
$830$	−1.75320	−0.0608546
$831$	0.365409	0.0126759
$832$	42.4337	1.47112
$833$	0.504865	0.0174925
$834$	−7.82890	−0.271093
$835$	−13.3179	−0.460885
$836$	−2.22439	−0.0769320
$837$	−3.47823	−0.120225
$838$	−54.8949	−1.89631
$839$	15.6338	0.539739	0.269870	−	0.962897i	$-0.413019\pi$
$839$	15.6338	0.539739	0.269870	+	0.962897i	$0.413019\pi$
$840$	−0.700209	−0.0241595
$841$	−2.11142	−0.0728077
$842$	−41.3944	−1.42655
$843$	3.61563	0.124529
$844$	4.26778	0.146903
$845$	26.3809	0.907531
$846$	36.8597	1.26726
$847$	4.49599	0.154484
$848$	18.1586	0.623568
$849$	−1.80677	−0.0620083
$850$	−0.757406	−0.0259788
$851$	−40.7390	−1.39651
$852$	−0.627487	−0.0214973
$853$	−37.9243	−1.29850	−0.649252	−	0.760573i	$-0.724918\pi$
$853$	−37.9243	−1.29850	−0.649252	+	0.760573i	$0.724918\pi$
$854$	2.97927	0.101948
$855$	−10.1919	−0.348556
$856$	21.1418	0.722611
$857$	2.05854	0.0703185	0.0351592	−	0.999382i	$-0.488806\pi$
$857$	2.05854	0.0703185	0.0351592	+	0.999382i	$0.488806\pi$
$858$	6.40594	0.218695
$859$	21.0555	0.718403	0.359201	−	0.933260i	$-0.383049\pi$
$859$	21.0555	0.718403	0.359201	+	0.933260i	$0.383049\pi$
$860$	1.37258	0.0468046
$861$	1.85033	0.0630592
$862$	−30.0706	−1.02421
$863$	−44.5512	−1.51654	−0.758270	−	0.651940i	$-0.773955\pi$
$863$	−44.5512	−1.51654	−0.758270	+	0.651940i	$0.773955\pi$
$864$	−2.23013	−0.0758706
$865$	−2.50942	−0.0853230
$866$	1.50331	0.0510844
$867$	−4.46770	−0.151731
$868$	−0.551127	−0.0187065
$869$	13.8354	0.469333
$870$	2.07555	0.0703678
$871$	54.1083	1.83339
$872$	−39.4904	−1.33731
$873$	−53.2902	−1.80360
$874$	39.4904	1.33578
$875$	−1.00000	−0.0338062
$876$	0.240827	0.00813678
$877$	33.1561	1.11960	0.559802	−	0.828627i	$-0.310877\pi$
$877$	33.1561	1.11960	0.559802	+	0.828627i	$0.310877\pi$
$878$	−11.4877	−0.387693
$879$	−1.95479	−0.0659335
$880$	11.3194	0.381577
$881$	3.18444	0.107287	0.0536433	−	0.998560i	$-0.482917\pi$
$881$	3.18444	0.107287	0.0536433	+	0.998560i	$0.482917\pi$
$882$	4.39385	0.147949
$883$	−35.7053	−1.20158	−0.600790	−	0.799407i	$-0.705147\pi$
$883$	−35.7053	−1.20158	−0.600790	+	0.799407i	$0.705147\pi$
$884$	0.794099	0.0267084
$885$	−1.72509	−0.0579882
$886$	6.82152	0.229174
$887$	29.7558	0.999101	0.499551	−	0.866285i	$-0.333498\pi$
$887$	29.7558	0.999101	0.499551	+	0.866285i	$0.333498\pi$
$888$	3.77105	0.126548
$889$	−12.9788	−0.435294
$890$	−1.88368	−0.0631411
$891$	−21.3317	−0.714638
$892$	3.93089	0.131616
$893$	29.1924	0.976886
$894$	3.32772	0.111296
$895$	20.2006	0.675232
$896$	12.9639	0.433095
$897$	−12.6653	−0.422881
$898$	−17.6461	−0.588857
$899$	−11.4019	−0.380276
$900$	−0.734088	−0.0244696
$901$	−2.06549	−0.0688116
$902$	−26.5337	−0.883476
$903$	−1.46109	−0.0486221
$904$	−37.8887	−1.26016
$905$	13.9823	0.464788
$906$	−0.687883	−0.0228534
$907$	2.91199	0.0966910	0.0483455	−	0.998831i	$-0.484605\pi$
$907$	2.91199	0.0966910	0.0483455	+	0.998831i	$0.484605\pi$
$908$	2.76827	0.0918682
$909$	−10.5607	−0.350277
$910$	9.41448	0.312087
$911$	40.4821	1.34123	0.670616	−	0.741805i	$-0.266030\pi$
$911$	40.4821	1.34123	0.670616	+	0.741805i	$0.266030\pi$
$912$	−4.12090	−0.136457
$913$	−2.98036	−0.0986356
$914$	1.07583	0.0355854
$915$	0.529849	0.0175163
$916$	−0.250644	−0.00828149
$917$	13.9304	0.460023
$918$	1.19810	0.0395431
$919$	−33.0028	−1.08866	−0.544331	−	0.838870i	$-0.683217\pi$
$919$	−33.0028	−1.08866	−0.544331	+	0.838870i	$0.683217\pi$
$920$	−19.8521	−0.654505
$921$	−2.89248	−0.0953105
$922$	−59.8693	−1.97169
$923$	−58.8837	−1.93818
$924$	0.170547	0.00561057
$925$	5.38561	0.177078
$926$	52.4056	1.72216
$927$	2.03088	0.0667027
$928$	−7.31056	−0.239981
$929$	31.9297	1.04758	0.523789	−	0.851848i	$-0.324518\pi$
$929$	31.9297	1.04758	0.523789	+	0.851848i	$0.324518\pi$
$930$	−0.880125	−0.0288604
$931$	3.47987	0.114048
$932$	1.51838	0.0497363
$933$	−3.06264	−0.100266
$934$	−20.3738	−0.666651
$935$	−1.28755	−0.0421075
$936$	−48.2355	−1.57663
$937$	15.6006	0.509650	0.254825	−	0.966987i	$-0.417982\pi$
$937$	15.6006	0.509650	0.254825	+	0.966987i	$0.417982\pi$
$938$	12.9352	0.422350
$939$	−6.24570	−0.203821
$940$	2.10263	0.0685802
$941$	−37.8710	−1.23456	−0.617280	−	0.786744i	$-0.711765\pi$
$941$	−37.8710	−1.23456	−0.617280	+	0.786744i	$0.711765\pi$
$942$	0.688501	0.0224326
$943$	52.4602	1.70834
$944$	28.6978	0.934033
$945$	1.58185	0.0514574
$946$	20.9520	0.681208
$947$	5.69975	0.185217	0.0926085	−	0.995703i	$-0.470479\pi$
$947$	5.69975	0.185217	0.0926085	+	0.995703i	$0.470479\pi$
$948$	−0.362788	−0.0117828
$949$	22.5993	0.733604
$950$	−5.22055	−0.169377
$951$	4.21474	0.136672
$952$	−1.32497	−0.0429426
$953$	38.5064	1.24735	0.623673	−	0.781685i	$-0.285640\pi$
$953$	38.5064	1.24735	0.623673	+	0.781685i	$0.285640\pi$
$954$	−17.9760	−0.581996
$955$	−16.3439	−0.528877
$956$	5.21744	0.168744
$957$	3.52834	0.114055
$958$	51.3082	1.65769
$959$	−1.96693	−0.0635155
$960$	1.80411	0.0582275
$961$	−26.1651	−0.844035
$962$	−50.7027	−1.63472
$963$	−23.5940	−0.760306
$964$	−1.09939	−0.0354088
$965$	12.0381	0.387519
$966$	−3.02778	−0.0974173
$967$	27.1018	0.871536	0.435768	−	0.900059i	$-0.356477\pi$
$967$	27.1018	0.871536	0.435768	+	0.900059i	$0.356477\pi$
$968$	−11.7993	−0.379245
$969$	0.468743	0.0150582
$970$	−27.2966	−0.876442
$971$	−0.643820	−0.0206612	−0.0103306	−	0.999947i	$-0.503288\pi$
$971$	−0.643820	−0.0206612	−0.0103306	+	0.999947i	$0.503288\pi$
$972$	1.74879	0.0560925
$973$	−19.5592	−0.627040
$974$	57.7996	1.85202
$975$	1.67432	0.0536212
$976$	−8.81433	−0.282140
$977$	−38.9530	−1.24622	−0.623108	−	0.782136i	$-0.714130\pi$
$977$	−38.9530	−1.24622	−0.623108	+	0.782136i	$0.714130\pi$
$978$	9.85870	0.315246
$979$	−3.20217	−0.102342
$980$	0.250644	0.00800651
$981$	44.0709	1.40708
$982$	5.40270	0.172407
$983$	2.10401	0.0671076	0.0335538	−	0.999437i	$-0.489317\pi$
$983$	2.10401	0.0671076	0.0335538	+	0.999437i	$0.489317\pi$
$984$	−4.85604	−0.154805
$985$	20.7841	0.662236
$986$	3.92747	0.125076
$987$	−2.23822	−0.0712433
$988$	5.47347	0.174134
$989$	−41.4245	−1.31722
$990$	−11.2056	−0.356138
$991$	−8.43483	−0.267941	−0.133971	−	0.990985i	$-0.542773\pi$
$991$	−8.43483	−0.267941	−0.133971	+	0.990985i	$0.542773\pi$
$992$	3.10000	0.0984250
$993$	4.31584	0.136959
$994$	−14.0768	−0.446491
$995$	−19.1145	−0.605971
$996$	0.0781504	0.00247629
$997$	45.8934	1.45346	0.726729	−	0.686924i	$-0.241039\pi$
$997$	45.8934	1.45346	0.726729	+	0.686924i	$0.241039\pi$
$998$	−11.8522	−0.375176
$999$	−8.51920	−0.269536

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.m.1.18	✓	67

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.m.1.18	✓	67	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.50021 q^{2} +0.266806 q^{3} +0.250644 q^{4} +1.00000 q^{5} -0.400267 q^{6} -1.00000 q^{7} +2.62441 q^{8} -2.92881 q^{9} +O(q^{10})\)	\(q-1.50021 q^{2} +0.266806 q^{3} +0.250644 q^{4} +1.00000 q^{5} -0.400267 q^{6} -1.00000 q^{7} +2.62441 q^{8} -2.92881 q^{9} -1.50021 q^{10} -2.55030 q^{11} +0.0668733 q^{12} +6.27542 q^{13} +1.50021 q^{14} +0.266806 q^{15} -4.43846 q^{16} +0.504865 q^{17} +4.39385 q^{18} +3.47987 q^{19} +0.250644 q^{20} -0.266806 q^{21} +3.82599 q^{22} -7.56441 q^{23} +0.700209 q^{24} +1.00000 q^{25} -9.41448 q^{26} -1.58185 q^{27} -0.250644 q^{28} -5.18542 q^{29} -0.400267 q^{30} +2.19885 q^{31} +1.40983 q^{32} -0.680435 q^{33} -0.757406 q^{34} -1.00000 q^{35} -0.734088 q^{36} +5.38561 q^{37} -5.22055 q^{38} +1.67432 q^{39} +2.62441 q^{40} -6.93512 q^{41} +0.400267 q^{42} +5.47623 q^{43} -0.639215 q^{44} -2.92881 q^{45} +11.3482 q^{46} +8.38893 q^{47} -1.18421 q^{48} +1.00000 q^{49} -1.50021 q^{50} +0.134701 q^{51} +1.57289 q^{52} -4.09118 q^{53} +2.37311 q^{54} -2.55030 q^{55} -2.62441 q^{56} +0.928452 q^{57} +7.77924 q^{58} -6.46570 q^{59} +0.0668733 q^{60} +1.98590 q^{61} -3.29874 q^{62} +2.92881 q^{63} +6.76188 q^{64} +6.27542 q^{65} +1.02080 q^{66} +8.62225 q^{67} +0.126541 q^{68} -2.01823 q^{69} +1.50021 q^{70} -9.38322 q^{71} -7.68641 q^{72} +3.60124 q^{73} -8.07957 q^{74} +0.266806 q^{75} +0.872207 q^{76} +2.55030 q^{77} -2.51184 q^{78} -5.42500 q^{79} -4.43846 q^{80} +8.36440 q^{81} +10.4042 q^{82} +1.16863 q^{83} -0.0668733 q^{84} +0.504865 q^{85} -8.21552 q^{86} -1.38350 q^{87} -6.69302 q^{88} +1.25561 q^{89} +4.39385 q^{90} -6.27542 q^{91} -1.89597 q^{92} +0.586666 q^{93} -12.5852 q^{94} +3.47987 q^{95} +0.376151 q^{96} +18.1951 q^{97} -1.50021 q^{98} +7.46934 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * q^99

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