LMFDB - Embedded newform 6017.2.a.c.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0459868962$
Analytic rank:	$1$
Dimension:	$106$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.16812 q^{2} -0.750565 q^{3} +2.70073 q^{4} -2.22726 q^{5} +1.62731 q^{6} +3.66777 q^{7} -1.51925 q^{8} -2.43665 q^{9} +O(q^{10})$	\(q-2.16812 q^{2} -0.750565 q^{3} +2.70073 q^{4} -2.22726 q^{5} +1.62731 q^{6} +3.66777 q^{7} -1.51925 q^{8} -2.43665 q^{9} +4.82897 q^{10} +1.00000 q^{11} -2.02707 q^{12} -5.53446 q^{13} -7.95214 q^{14} +1.67171 q^{15} -2.10753 q^{16} +0.526283 q^{17} +5.28294 q^{18} -3.67540 q^{19} -6.01523 q^{20} -2.75290 q^{21} -2.16812 q^{22} -1.72453 q^{23} +1.14030 q^{24} -0.0392908 q^{25} +11.9993 q^{26} +4.08056 q^{27} +9.90563 q^{28} +5.60414 q^{29} -3.62445 q^{30} +3.40223 q^{31} +7.60788 q^{32} -0.750565 q^{33} -1.14104 q^{34} -8.16909 q^{35} -6.58073 q^{36} +6.79662 q^{37} +7.96869 q^{38} +4.15397 q^{39} +3.38378 q^{40} +2.64528 q^{41} +5.96860 q^{42} +5.66180 q^{43} +2.70073 q^{44} +5.42707 q^{45} +3.73897 q^{46} +0.658614 q^{47} +1.58184 q^{48} +6.45251 q^{49} +0.0851870 q^{50} -0.395010 q^{51} -14.9470 q^{52} -2.76317 q^{53} -8.84713 q^{54} -2.22726 q^{55} -5.57226 q^{56} +2.75862 q^{57} -12.1504 q^{58} +3.85275 q^{59} +4.51482 q^{60} -5.20538 q^{61} -7.37643 q^{62} -8.93707 q^{63} -12.2797 q^{64} +12.3267 q^{65} +1.62731 q^{66} -11.2392 q^{67} +1.42135 q^{68} +1.29437 q^{69} +17.7115 q^{70} -1.31749 q^{71} +3.70189 q^{72} -4.46428 q^{73} -14.7359 q^{74} +0.0294903 q^{75} -9.92624 q^{76} +3.66777 q^{77} -9.00628 q^{78} +0.912121 q^{79} +4.69404 q^{80} +4.24723 q^{81} -5.73528 q^{82} +11.7779 q^{83} -7.43482 q^{84} -1.17217 q^{85} -12.2754 q^{86} -4.20627 q^{87} -1.51925 q^{88} -10.4548 q^{89} -11.7665 q^{90} -20.2991 q^{91} -4.65747 q^{92} -2.55359 q^{93} -1.42795 q^{94} +8.18609 q^{95} -5.71021 q^{96} -7.47645 q^{97} -13.9898 q^{98} -2.43665 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) $ 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.16812	−1.53309	−0.766545	−	0.642191i	$-0.778026\pi$
$2$	−2.16812	−1.53309	−0.766545	+	0.642191i	$0.778026\pi$
$3$	−0.750565	−0.433339	−0.216669	−	0.976245i	$-0.569519\pi$
$3$	−0.750565	−0.433339	−0.216669	+	0.976245i	$0.569519\pi$
$4$	2.70073	1.35036
$5$	−2.22726	−0.996063	−0.498032	−	0.867159i	$-0.665944\pi$
$5$	−2.22726	−0.996063	−0.498032	+	0.867159i	$0.665944\pi$
$6$	1.62731	0.664347
$7$	3.66777	1.38629	0.693143	−	0.720800i	$-0.256226\pi$
$7$	3.66777	1.38629	0.693143	+	0.720800i	$0.256226\pi$
$8$	−1.51925	−0.537137
$9$	−2.43665	−0.812217
$10$	4.82897	1.52705
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.02707	−0.585165
$13$	−5.53446	−1.53498	−0.767491	−	0.641060i	$-0.778495\pi$
$13$	−5.53446	−1.53498	−0.767491	+	0.641060i	$0.778495\pi$
$14$	−7.95214	−2.12530
$15$	1.67171	0.431633
$16$	−2.10753	−0.526884
$17$	0.526283	0.127642	0.0638212	−	0.997961i	$-0.479671\pi$
$17$	0.526283	0.127642	0.0638212	+	0.997961i	$0.479671\pi$
$18$	5.28294	1.24520
$19$	−3.67540	−0.843194	−0.421597	−	0.906783i	$-0.638530\pi$
$19$	−3.67540	−0.843194	−0.421597	+	0.906783i	$0.638530\pi$
$20$	−6.01523	−1.34505
$21$	−2.75290	−0.600731
$22$	−2.16812	−0.462244
$23$	−1.72453	−0.359589	−0.179794	−	0.983704i	$-0.557543\pi$
$23$	−1.72453	−0.359589	−0.179794	+	0.983704i	$0.557543\pi$
$24$	1.14030	0.232762
$25$	−0.0392908	−0.00785816
$26$	11.9993	2.35326
$27$	4.08056	0.785304
$28$	9.90563	1.87199
$29$	5.60414	1.04066	0.520331	−	0.853965i	$-0.325809\pi$
$29$	5.60414	1.04066	0.520331	+	0.853965i	$0.325809\pi$
$30$	−3.62445	−0.661732
$31$	3.40223	0.611059	0.305529	−	0.952183i	$-0.401167\pi$
$31$	3.40223	0.611059	0.305529	+	0.952183i	$0.401167\pi$
$32$	7.60788	1.34490
$33$	−0.750565	−0.130657
$34$	−1.14104	−0.195687
$35$	−8.16909	−1.38083
$36$	−6.58073	−1.09679
$37$	6.79662	1.11736	0.558679	−	0.829384i	$-0.311308\pi$
$37$	6.79662	1.11736	0.558679	+	0.829384i	$0.311308\pi$
$38$	7.96869	1.29269
$39$	4.15397	0.665167
$40$	3.38378	0.535022
$41$	2.64528	0.413124	0.206562	−	0.978434i	$-0.433773\pi$
$41$	2.64528	0.413124	0.206562	+	0.978434i	$0.433773\pi$
$42$	5.96860	0.920975
$43$	5.66180	0.863416	0.431708	−	0.902013i	$-0.357911\pi$
$43$	5.66180	0.863416	0.431708	+	0.902013i	$0.357911\pi$
$44$	2.70073	0.407150
$45$	5.42707	0.809020
$46$	3.73897	0.551281
$47$	0.658614	0.0960687	0.0480344	−	0.998846i	$-0.484704\pi$
$47$	0.658614	0.0960687	0.0480344	+	0.998846i	$0.484704\pi$
$48$	1.58184	0.228319
$49$	6.45251	0.921787
$50$	0.0851870	0.0120473
$51$	−0.395010	−0.0553124
$52$	−14.9470	−2.07278
$53$	−2.76317	−0.379551	−0.189775	−	0.981828i	$-0.560776\pi$
$53$	−2.76317	−0.379551	−0.189775	+	0.981828i	$0.560776\pi$
$54$	−8.84713	−1.20394
$55$	−2.22726	−0.300324
$56$	−5.57226	−0.744625
$57$	2.75862	0.365389
$58$	−12.1504	−1.59543
$59$	3.85275	0.501585	0.250792	−	0.968041i	$-0.419309\pi$
$59$	3.85275	0.501585	0.250792	+	0.968041i	$0.419309\pi$
$60$	4.51482	0.582861
$61$	−5.20538	−0.666481	−0.333241	−	0.942842i	$-0.608142\pi$
$61$	−5.20538	−0.666481	−0.333241	+	0.942842i	$0.608142\pi$
$62$	−7.37643	−0.936807
$63$	−8.93707	−1.12597
$64$	−12.2797	−1.53496
$65$	12.3267	1.52894
$66$	1.62731	0.200308
$67$	−11.2392	−1.37308	−0.686542	−	0.727090i	$-0.740872\pi$
$67$	−11.2392	−1.37308	−0.686542	+	0.727090i	$0.740872\pi$
$68$	1.42135	0.172363
$69$	1.29437	0.155824
$70$	17.7115	2.11693
$71$	−1.31749	−0.156357	−0.0781785	−	0.996939i	$-0.524910\pi$
$71$	−1.31749	−0.156357	−0.0781785	+	0.996939i	$0.524910\pi$
$72$	3.70189	0.436272
$73$	−4.46428	−0.522504	−0.261252	−	0.965271i	$-0.584135\pi$
$73$	−4.46428	−0.522504	−0.261252	+	0.965271i	$0.584135\pi$
$74$	−14.7359	−1.71301
$75$	0.0294903	0.00340525
$76$	−9.92624	−1.13862
$77$	3.66777	0.417981
$78$	−9.00628	−1.01976
$79$	0.912121	0.102622	0.0513108	−	0.998683i	$-0.483660\pi$
$79$	0.912121	0.102622	0.0513108	+	0.998683i	$0.483660\pi$
$80$	4.69404	0.524809
$81$	4.24723	0.471915
$82$	−5.73528	−0.633355
$83$	11.7779	1.29280	0.646398	−	0.763000i	$-0.276274\pi$
$83$	11.7779	1.29280	0.646398	+	0.763000i	$0.276274\pi$
$84$	−7.43482	−0.811205
$85$	−1.17217	−0.127140
$86$	−12.2754	−1.32369
$87$	−4.20627	−0.450959
$88$	−1.51925	−0.161953
$89$	−10.4548	−1.10820	−0.554101	−	0.832449i	$-0.686938\pi$
$89$	−10.4548	−1.10820	−0.554101	+	0.832449i	$0.686938\pi$
$90$	−11.7665	−1.24030
$91$	−20.2991	−2.12792
$92$	−4.65747	−0.485575
$93$	−2.55359	−0.264795
$94$	−1.42795	−0.147282
$95$	8.18609	0.839875
$96$	−5.71021	−0.582796
$97$	−7.47645	−0.759119	−0.379559	−	0.925167i	$-0.623924\pi$
$97$	−7.47645	−0.759119	−0.379559	+	0.925167i	$0.623924\pi$
$98$	−13.9898	−1.41318
$99$	−2.43665	−0.244893
$100$	−0.106114	−0.0106114
$101$	−8.62240	−0.857961	−0.428980	−	0.903314i	$-0.641127\pi$
$101$	−8.62240	−0.857961	−0.428980	+	0.903314i	$0.641127\pi$
$102$	0.856426	0.0847988
$103$	−11.7955	−1.16225	−0.581125	−	0.813815i	$-0.697387\pi$
$103$	−11.7955	−1.16225	−0.581125	+	0.813815i	$0.697387\pi$
$104$	8.40824	0.824496
$105$	6.13143	0.598366
$106$	5.99087	0.581885
$107$	12.8117	1.23856	0.619279	−	0.785171i	$-0.287425\pi$
$107$	12.8117	1.23856	0.619279	+	0.785171i	$0.287425\pi$
$108$	11.0205	1.06045
$109$	11.7958	1.12983	0.564915	−	0.825149i	$-0.308909\pi$
$109$	11.7958	1.12983	0.564915	+	0.825149i	$0.308909\pi$
$110$	4.82897	0.460424
$111$	−5.10130	−0.484194
$112$	−7.72994	−0.730411
$113$	4.12435	0.387986	0.193993	−	0.981003i	$-0.437856\pi$
$113$	4.12435	0.387986	0.193993	+	0.981003i	$0.437856\pi$
$114$	−5.98102	−0.560174
$115$	3.84098	0.358173
$116$	15.1352	1.40527
$117$	13.4855	1.24674
$118$	−8.35320	−0.768974
$119$	1.93028	0.176949
$120$	−2.53975	−0.231846
$121$	1.00000	0.0909091
$122$	11.2859	1.02177
$123$	−1.98546	−0.179022
$124$	9.18849	0.825151
$125$	11.2238	1.00389
$126$	19.3766	1.72620
$127$	0.966178	0.0857345	0.0428672	−	0.999081i	$-0.486351\pi$
$127$	0.966178	0.0857345	0.0428672	+	0.999081i	$0.486351\pi$
$128$	11.4080	1.00834
$129$	−4.24955	−0.374152
$130$	−26.7257	−2.34400
$131$	1.08921	0.0951650	0.0475825	−	0.998867i	$-0.484848\pi$
$131$	1.08921	0.0951650	0.0475825	+	0.998867i	$0.484848\pi$
$132$	−2.02707	−0.176434
$133$	−13.4805	−1.16891
$134$	24.3678	2.10506
$135$	−9.08849	−0.782213
$136$	−0.799557	−0.0685615
$137$	9.00793	0.769600	0.384800	−	0.923000i	$-0.374270\pi$
$137$	9.00793	0.769600	0.384800	+	0.923000i	$0.374270\pi$
$138$	−2.80634	−0.238892
$139$	12.9830	1.10120	0.550602	−	0.834768i	$-0.314398\pi$
$139$	12.9830	1.10120	0.550602	+	0.834768i	$0.314398\pi$
$140$	−22.0625	−1.86462
$141$	−0.494332	−0.0416303
$142$	2.85646	0.239709
$143$	−5.53446	−0.462814
$144$	5.13533	0.427944
$145$	−12.4819	−1.03657
$146$	9.67907	0.801046
$147$	−4.84302	−0.399446
$148$	18.3558	1.50884
$149$	−8.44046	−0.691469	−0.345735	−	0.938332i	$-0.612370\pi$
$149$	−8.44046	−0.691469	−0.345735	+	0.938332i	$0.612370\pi$
$150$	−0.0639384	−0.00522054
$151$	1.90073	0.154679	0.0773396	−	0.997005i	$-0.475357\pi$
$151$	1.90073	0.154679	0.0773396	+	0.997005i	$0.475357\pi$
$152$	5.58386	0.452911
$153$	−1.28237	−0.103673
$154$	−7.95214	−0.640802
$155$	−7.57767	−0.608653
$156$	11.2187	0.898217
$157$	−12.6551	−1.00999	−0.504994	−	0.863123i	$-0.668505\pi$
$157$	−12.6551	−1.00999	−0.504994	+	0.863123i	$0.668505\pi$
$158$	−1.97758	−0.157328
$159$	2.07394	0.164474
$160$	−16.9448	−1.33960
$161$	−6.32516	−0.498492
$162$	−9.20849	−0.723487
$163$	22.4177	1.75589	0.877943	−	0.478765i	$-0.158915\pi$
$163$	22.4177	1.75589	0.877943	+	0.478765i	$0.158915\pi$
$164$	7.14418	0.557867
$165$	1.67171	0.130142
$166$	−25.5359	−1.98197
$167$	4.59803	0.355806	0.177903	−	0.984048i	$-0.443069\pi$
$167$	4.59803	0.355806	0.177903	+	0.984048i	$0.443069\pi$
$168$	4.18235	0.322675
$169$	17.6302	1.35617
$170$	2.54140	0.194917
$171$	8.95567	0.684857
$172$	15.2910	1.16593
$173$	12.2366	0.930333	0.465166	−	0.885223i	$-0.345995\pi$
$173$	12.2366	0.930333	0.465166	+	0.885223i	$0.345995\pi$
$174$	9.11968	0.691361
$175$	−0.144109	−0.0108936
$176$	−2.10753	−0.158861
$177$	−2.89174	−0.217356
$178$	22.6671	1.69897
$179$	20.3948	1.52438	0.762189	−	0.647355i	$-0.224125\pi$
$179$	20.3948	1.52438	0.762189	+	0.647355i	$0.224125\pi$
$180$	14.6570	1.09247
$181$	−26.2929	−1.95433	−0.977166	−	0.212476i	$-0.931847\pi$
$181$	−26.2929	−1.95433	−0.977166	+	0.212476i	$0.931847\pi$
$182$	44.0108	3.26229
$183$	3.90698	0.288812
$184$	2.61999	0.193148
$185$	−15.1379	−1.11296
$186$	5.53649	0.405955
$187$	0.526283	0.0384856
$188$	1.77874	0.129728
$189$	14.9665	1.08866
$190$	−17.7484	−1.28760
$191$	−3.19724	−0.231344	−0.115672	−	0.993287i	$-0.536902\pi$
$191$	−3.19724	−0.231344	−0.115672	+	0.993287i	$0.536902\pi$
$192$	9.21671	0.665159
$193$	8.22263	0.591878	0.295939	−	0.955207i	$-0.404367\pi$
$193$	8.22263	0.591878	0.295939	+	0.955207i	$0.404367\pi$
$194$	16.2098	1.16380
$195$	−9.25199	−0.662549
$196$	17.4264	1.24475
$197$	−7.12564	−0.507680	−0.253840	−	0.967246i	$-0.581694\pi$
$197$	−7.12564	−0.507680	−0.253840	+	0.967246i	$0.581694\pi$
$198$	5.28294	0.375442
$199$	−1.40097	−0.0993119	−0.0496560	−	0.998766i	$-0.515812\pi$
$199$	−1.40097	−0.0993119	−0.0496560	+	0.998766i	$0.515812\pi$
$200$	0.0596927	0.00422091
$201$	8.43573	0.595011
$202$	18.6944	1.31533
$203$	20.5547	1.44265
$204$	−1.06681	−0.0746918
$205$	−5.89174	−0.411497
$206$	25.5741	1.78183
$207$	4.20207	0.292064
$208$	11.6641	0.808757
$209$	−3.67540	−0.254233
$210$	−13.2936	−0.917349
$211$	18.4251	1.26844	0.634219	−	0.773153i	$-0.281322\pi$
$211$	18.4251	1.26844	0.634219	+	0.773153i	$0.281322\pi$
$212$	−7.46256	−0.512531
$213$	0.988859	0.0677555
$214$	−27.7773	−1.89882
$215$	−12.6103	−0.860017
$216$	−6.19940	−0.421816
$217$	12.4786	0.847101
$218$	−25.5746	−1.73213
$219$	3.35073	0.226421
$220$	−6.01523	−0.405547
$221$	−2.91269	−0.195929
$222$	11.0602	0.742313
$223$	−6.36478	−0.426217	−0.213109	−	0.977029i	$-0.568359\pi$
$223$	−6.36478	−0.426217	−0.213109	+	0.977029i	$0.568359\pi$
$224$	27.9039	1.86441
$225$	0.0957380	0.00638253
$226$	−8.94207	−0.594818
$227$	6.89072	0.457353	0.228677	−	0.973502i	$-0.426560\pi$
$227$	6.89072	0.457353	0.228677	+	0.973502i	$0.426560\pi$
$228$	7.45029	0.493407
$229$	−20.2722	−1.33962	−0.669811	−	0.742532i	$-0.733625\pi$
$229$	−20.2722	−1.33962	−0.669811	+	0.742532i	$0.733625\pi$
$230$	−8.32768	−0.549111
$231$	−2.75290	−0.181127
$232$	−8.51410	−0.558978
$233$	3.63481	0.238125	0.119062	−	0.992887i	$-0.462011\pi$
$233$	3.63481	0.238125	0.119062	+	0.992887i	$0.462011\pi$
$234$	−29.2382	−1.91136
$235$	−1.46691	−0.0956905
$236$	10.4052	0.677321
$237$	−0.684606	−0.0444699
$238$	−4.18508	−0.271278
$239$	11.5631	0.747958	0.373979	−	0.927437i	$-0.377993\pi$
$239$	11.5631	0.747958	0.373979	+	0.927437i	$0.377993\pi$
$240$	−3.52318	−0.227420
$241$	−11.2110	−0.722167	−0.361084	−	0.932533i	$-0.617593\pi$
$241$	−11.2110	−0.722167	−0.361084	+	0.932533i	$0.617593\pi$
$242$	−2.16812	−0.139372
$243$	−15.4295	−0.989803
$244$	−14.0583	−0.899991
$245$	−14.3714	−0.918158
$246$	4.30470	0.274457
$247$	20.3413	1.29429
$248$	−5.16885	−0.328222
$249$	−8.84011	−0.560219
$250$	−24.3346	−1.53905
$251$	−10.9324	−0.690044	−0.345022	−	0.938595i	$-0.612129\pi$
$251$	−10.9324	−0.690044	−0.345022	+	0.938595i	$0.612129\pi$
$252$	−24.1366	−1.52046
$253$	−1.72453	−0.108420
$254$	−2.09479	−0.131439
$255$	0.879791	0.0550946
$256$	−0.174559	−0.0109100
$257$	−23.7766	−1.48315	−0.741573	−	0.670872i	$-0.765920\pi$
$257$	−23.7766	−1.48315	−0.741573	+	0.670872i	$0.765920\pi$
$258$	9.21351	0.573608
$259$	24.9284	1.54898
$260$	33.2910	2.06462
$261$	−13.6553	−0.845244
$262$	−2.36154	−0.145896
$263$	13.3940	0.825907	0.412953	−	0.910752i	$-0.364497\pi$
$263$	13.3940	0.825907	0.412953	+	0.910752i	$0.364497\pi$
$264$	1.14030	0.0701805
$265$	6.15431	0.378056
$266$	29.2273	1.79204
$267$	7.84698	0.480227
$268$	−30.3539	−1.85416
$269$	−3.49436	−0.213055	−0.106527	−	0.994310i	$-0.533973\pi$
$269$	−3.49436	−0.213055	−0.106527	+	0.994310i	$0.533973\pi$
$270$	19.7049	1.19920
$271$	−9.84073	−0.597782	−0.298891	−	0.954287i	$-0.596617\pi$
$271$	−9.84073	−0.597782	−0.298891	+	0.954287i	$0.596617\pi$
$272$	−1.10916	−0.0672527
$273$	15.2358	0.922111
$274$	−19.5302	−1.17986
$275$	−0.0392908	−0.00236932
$276$	3.49573	0.210418
$277$	−0.328363	−0.0197294	−0.00986472	−	0.999951i	$-0.503140\pi$
$277$	−0.328363	−0.0197294	−0.00986472	+	0.999951i	$0.503140\pi$
$278$	−28.1487	−1.68825
$279$	−8.29005	−0.496312
$280$	12.4109	0.741694
$281$	−21.9982	−1.31230	−0.656152	−	0.754629i	$-0.727817\pi$
$281$	−21.9982	−1.31230	−0.656152	+	0.754629i	$0.727817\pi$
$282$	1.07177	0.0638230
$283$	−14.5127	−0.862692	−0.431346	−	0.902186i	$-0.641961\pi$
$283$	−14.5127	−0.862692	−0.431346	+	0.902186i	$0.641961\pi$
$284$	−3.55817	−0.211139
$285$	−6.14419	−0.363950
$286$	11.9993	0.709536
$287$	9.70227	0.572707
$288$	−18.5378	−1.09235
$289$	−16.7230	−0.983707
$290$	27.0622	1.58915
$291$	5.61156	0.328956
$292$	−12.0568	−0.705570
$293$	−17.1760	−1.00344	−0.501718	−	0.865031i	$-0.667298\pi$
$293$	−17.1760	−1.00344	−0.501718	+	0.865031i	$0.667298\pi$
$294$	10.5002	0.612386
$295$	−8.58109	−0.499610
$296$	−10.3258	−0.600174
$297$	4.08056	0.236778
$298$	18.2999	1.06008
$299$	9.54431	0.551962
$300$	0.0796452	0.00459832
$301$	20.7662	1.19694
$302$	−4.12100	−0.237137
$303$	6.47167	0.371788
$304$	7.74603	0.444265
$305$	11.5938	0.663857
$306$	2.78032	0.158941
$307$	−3.36688	−0.192158	−0.0960791	−	0.995374i	$-0.530630\pi$
$307$	−3.36688	−0.192158	−0.0960791	+	0.995374i	$0.530630\pi$
$308$	9.90563	0.564425
$309$	8.85332	0.503648
$310$	16.4293	0.933119
$311$	14.5059	0.822555	0.411277	−	0.911510i	$-0.365083\pi$
$311$	14.5059	0.822555	0.411277	+	0.911510i	$0.365083\pi$
$312$	−6.31093	−0.357286
$313$	−4.56542	−0.258053	−0.129026	−	0.991641i	$-0.541185\pi$
$313$	−4.56542	−0.258053	−0.129026	+	0.991641i	$0.541185\pi$
$314$	27.4378	1.54840
$315$	19.9052	1.12153
$316$	2.46339	0.138576
$317$	8.55964	0.480757	0.240379	−	0.970679i	$-0.422728\pi$
$317$	8.55964	0.480757	0.240379	+	0.970679i	$0.422728\pi$
$318$	−4.49654	−0.252153
$319$	5.60414	0.313771
$320$	27.3502	1.52892
$321$	−9.61604	−0.536715
$322$	13.7137	0.764233
$323$	−1.93430	−0.107627
$324$	11.4706	0.637256
$325$	0.217453	0.0120621
$326$	−48.6041	−2.69193
$327$	−8.85349	−0.489599
$328$	−4.01885	−0.221904
$329$	2.41564	0.133179
$330$	−3.62445	−0.199520
$331$	−25.9079	−1.42403	−0.712014	−	0.702165i	$-0.752217\pi$
$331$	−25.9079	−1.42403	−0.712014	+	0.702165i	$0.752217\pi$
$332$	31.8090	1.74574
$333$	−16.5610	−0.907537
$334$	−9.96906	−0.545483
$335$	25.0326	1.36768
$336$	5.80182	0.316515
$337$	−25.3650	−1.38172	−0.690861	−	0.722988i	$-0.742768\pi$
$337$	−25.3650	−1.38172	−0.690861	+	0.722988i	$0.742768\pi$
$338$	−38.2243	−2.07913
$339$	−3.09559	−0.168130
$340$	−3.16571	−0.171685
$341$	3.40223	0.184241
$342$	−19.4169	−1.04995
$343$	−2.00808	−0.108426
$344$	−8.60171	−0.463773
$345$	−2.88290	−0.155210
$346$	−26.5304	−1.42628
$347$	−22.5982	−1.21314	−0.606569	−	0.795031i	$-0.707454\pi$
$347$	−22.5982	−1.21314	−0.606569	+	0.795031i	$0.707454\pi$
$348$	−11.3600	−0.608959
$349$	−13.6111	−0.728585	−0.364292	−	0.931285i	$-0.618689\pi$
$349$	−13.6111	−0.728585	−0.364292	+	0.931285i	$0.618689\pi$
$350$	0.312446	0.0167009
$351$	−22.5837	−1.20543
$352$	7.60788	0.405502
$353$	21.8040	1.16051	0.580255	−	0.814435i	$-0.302953\pi$
$353$	21.8040	1.16051	0.580255	+	0.814435i	$0.302953\pi$
$354$	6.26962	0.333226
$355$	2.93439	0.155741
$356$	−28.2354	−1.49648
$357$	−1.44880	−0.0766788
$358$	−44.2182	−2.33701
$359$	24.6872	1.30294	0.651470	−	0.758674i	$-0.274152\pi$
$359$	24.6872	1.30294	0.651470	+	0.758674i	$0.274152\pi$
$360$	−8.24509	−0.434555
$361$	−5.49145	−0.289024
$362$	57.0060	2.99617
$363$	−0.750565	−0.0393944
$364$	−54.8223	−2.87347
$365$	9.94313	0.520447
$366$	−8.47078	−0.442775
$367$	22.7843	1.18933	0.594665	−	0.803973i	$-0.297285\pi$
$367$	22.7843	1.18933	0.594665	+	0.803973i	$0.297285\pi$
$368$	3.63450	0.189461
$369$	−6.44563	−0.335546
$370$	32.8207	1.70627
$371$	−10.1347	−0.526165
$372$	−6.89656	−0.357570
$373$	−24.3435	−1.26046	−0.630229	−	0.776409i	$-0.717039\pi$
$373$	−24.3435	−1.26046	−0.630229	+	0.776409i	$0.717039\pi$
$374$	−1.14104	−0.0590019
$375$	−8.42422	−0.435025
$376$	−1.00060	−0.0516021
$377$	−31.0159	−1.59740
$378$	−32.4492	−1.66901
$379$	22.5194	1.15674	0.578372	−	0.815773i	$-0.303688\pi$
$379$	22.5194	1.15674	0.578372	+	0.815773i	$0.303688\pi$
$380$	22.1084	1.13414
$381$	−0.725180	−0.0371521
$382$	6.93199	0.354671
$383$	4.26662	0.218014	0.109007	−	0.994041i	$-0.465233\pi$
$383$	4.26662	0.218014	0.109007	+	0.994041i	$0.465233\pi$
$384$	−8.56248	−0.436952
$385$	−8.16909	−0.416335
$386$	−17.8276	−0.907402
$387$	−13.7958	−0.701282
$388$	−20.1918	−1.02509
$389$	20.4773	1.03824	0.519119	−	0.854702i	$-0.326260\pi$
$389$	20.4773	1.03824	0.519119	+	0.854702i	$0.326260\pi$
$390$	20.0594	1.01575
$391$	−0.907589	−0.0458987
$392$	−9.80299	−0.495126
$393$	−0.817525	−0.0412387
$394$	15.4492	0.778319
$395$	−2.03153	−0.102218
$396$	−6.58073	−0.330694
$397$	−19.4244	−0.974881	−0.487440	−	0.873156i	$-0.662069\pi$
$397$	−19.4244	−0.974881	−0.487440	+	0.873156i	$0.662069\pi$
$398$	3.03746	0.152254
$399$	10.1180	0.506533
$400$	0.0828067	0.00414033
$401$	−35.6975	−1.78265	−0.891323	−	0.453368i	$-0.850222\pi$
$401$	−35.6975	−1.78265	−0.891323	+	0.453368i	$0.850222\pi$
$402$	−18.2896	−0.912204
$403$	−18.8295	−0.937964
$404$	−23.2867	−1.15856
$405$	−9.45971	−0.470057
$406$	−44.5649	−2.21172
$407$	6.79662	0.336896
$408$	0.600119	0.0297103
$409$	22.2105	1.09824	0.549120	−	0.835743i	$-0.314963\pi$
$409$	22.2105	1.09824	0.549120	+	0.835743i	$0.314963\pi$
$410$	12.7740	0.630862
$411$	−6.76104	−0.333497
$412$	−31.8565	−1.56946
$413$	14.1310	0.695340
$414$	−9.11057	−0.447760
$415$	−26.2326	−1.28771
$416$	−42.1055	−2.06439
$417$	−9.74459	−0.477195
$418$	7.96869	0.389761
$419$	−15.4531	−0.754933	−0.377466	−	0.926023i	$-0.623205\pi$
$419$	−15.4531	−0.754933	−0.377466	+	0.926023i	$0.623205\pi$
$420$	16.5593	0.808011
$421$	15.3680	0.748990	0.374495	−	0.927229i	$-0.377816\pi$
$421$	15.3680	0.748990	0.374495	+	0.927229i	$0.377816\pi$
$422$	−39.9478	−1.94463
$423$	−1.60481	−0.0780287
$424$	4.19795	0.203871
$425$	−0.0206781	−0.00100303
$426$	−2.14396	−0.103875
$427$	−19.0921	−0.923933
$428$	34.6010	1.67250
$429$	4.15397	0.200555
$430$	27.3406	1.31848
$431$	−7.27807	−0.350572	−0.175286	−	0.984518i	$-0.556085\pi$
$431$	−7.27807	−0.350572	−0.175286	+	0.984518i	$0.556085\pi$
$432$	−8.59992	−0.413764
$433$	−18.7803	−0.902524	−0.451262	−	0.892392i	$-0.649026\pi$
$433$	−18.7803	−0.902524	−0.451262	+	0.892392i	$0.649026\pi$
$434$	−27.0550	−1.29868
$435$	9.36848	0.449184
$436$	31.8571	1.52568
$437$	6.33832	0.303203
$438$	−7.26477	−0.347124
$439$	−15.7530	−0.751852	−0.375926	−	0.926650i	$-0.622675\pi$
$439$	−15.7530	−0.751852	−0.375926	+	0.926650i	$0.622675\pi$
$440$	3.38378	0.161315
$441$	−15.7225	−0.748691
$442$	6.31505	0.300376
$443$	15.6043	0.741384	0.370692	−	0.928756i	$-0.379121\pi$
$443$	15.6043	0.741384	0.370692	+	0.928756i	$0.379121\pi$
$444$	−13.7772	−0.653838
$445$	23.2855	1.10384
$446$	13.7996	0.653429
$447$	6.33511	0.299641
$448$	−45.0391	−2.12790
$449$	−11.8845	−0.560865	−0.280432	−	0.959874i	$-0.590478\pi$
$449$	−11.8845	−0.560865	−0.280432	+	0.959874i	$0.590478\pi$
$450$	−0.207571	−0.00978499
$451$	2.64528	0.124561
$452$	11.1387	0.523922
$453$	−1.42662	−0.0670285
$454$	−14.9399	−0.701163
$455$	45.2114	2.11955
$456$	−4.19105	−0.196264
$457$	−6.54730	−0.306270	−0.153135	−	0.988205i	$-0.548937\pi$
$457$	−6.54730	−0.306270	−0.153135	+	0.988205i	$0.548937\pi$
$458$	43.9524	2.05376
$459$	2.14753	0.100238
$460$	10.3734	0.483663
$461$	17.4877	0.814482	0.407241	−	0.913321i	$-0.366491\pi$
$461$	17.4877	0.814482	0.407241	+	0.913321i	$0.366491\pi$
$462$	5.96860	0.277684
$463$	−26.3093	−1.22270	−0.611348	−	0.791362i	$-0.709372\pi$
$463$	−26.3093	−1.22270	−0.611348	+	0.791362i	$0.709372\pi$
$464$	−11.8109	−0.548308
$465$	5.68753	0.263753
$466$	−7.88070	−0.365066
$467$	−20.3555	−0.941942	−0.470971	−	0.882149i	$-0.656096\pi$
$467$	−20.3555	−0.941942	−0.470971	+	0.882149i	$0.656096\pi$
$468$	36.4207	1.68355
$469$	−41.2227	−1.90349
$470$	3.18043	0.146702
$471$	9.49849	0.437667
$472$	−5.85330	−0.269420
$473$	5.66180	0.260330
$474$	1.48430	0.0681764
$475$	0.144409	0.00662595
$476$	5.21316	0.238945
$477$	6.73288	0.308278
$478$	−25.0702	−1.14669
$479$	17.4532	0.797455	0.398727	−	0.917069i	$-0.369452\pi$
$479$	17.4532	0.797455	0.398727	+	0.917069i	$0.369452\pi$
$480$	12.7182	0.580502
$481$	−37.6156	−1.71512
$482$	24.3068	1.10715
$483$	4.74744	0.216016
$484$	2.70073	0.122760
$485$	16.6520	0.756130
$486$	33.4529	1.51746
$487$	6.71867	0.304452	0.152226	−	0.988346i	$-0.451356\pi$
$487$	6.71867	0.304452	0.152226	+	0.988346i	$0.451356\pi$
$488$	7.90829	0.357992
$489$	−16.8259	−0.760894
$490$	31.1589	1.40762
$491$	−2.90298	−0.131010	−0.0655048	−	0.997852i	$-0.520866\pi$
$491$	−2.90298	−0.131010	−0.0655048	+	0.997852i	$0.520866\pi$
$492$	−5.36217	−0.241745
$493$	2.94936	0.132833
$494$	−44.1023	−1.98426
$495$	5.42707	0.243929
$496$	−7.17032	−0.321957
$497$	−4.83223	−0.216755
$498$	19.1664	0.858866
$499$	42.2982	1.89353	0.946763	−	0.321930i	$-0.104332\pi$
$499$	42.2982	1.89353	0.946763	+	0.321930i	$0.104332\pi$
$500$	30.3125	1.35562
$501$	−3.45112	−0.154185
$502$	23.7026	1.05790
$503$	34.6211	1.54368	0.771839	−	0.635818i	$-0.219337\pi$
$503$	34.6211	1.54368	0.771839	+	0.635818i	$0.219337\pi$
$504$	13.5777	0.604798
$505$	19.2044	0.854583
$506$	3.73897	0.166218
$507$	−13.2326	−0.587681
$508$	2.60938	0.115773
$509$	44.2777	1.96257	0.981287	−	0.192549i	$-0.0616754\pi$
$509$	44.2777	1.96257	0.981287	+	0.192549i	$0.0616754\pi$
$510$	−1.90749	−0.0844650
$511$	−16.3739	−0.724340
$512$	−22.4376	−0.991612
$513$	−14.9977	−0.662164
$514$	51.5505	2.27379
$515$	26.2718	1.15767
$516$	−11.4769	−0.505241
$517$	0.658614	0.0289658
$518$	−54.0477	−2.37472
$519$	−9.18437	−0.403149
$520$	−18.7274	−0.821250
$521$	12.9666	0.568077	0.284039	−	0.958813i	$-0.408326\pi$
$521$	12.9666	0.568077	0.284039	+	0.958813i	$0.408326\pi$
$522$	29.6063	1.29583
$523$	−29.1335	−1.27392	−0.636959	−	0.770898i	$-0.719808\pi$
$523$	−29.1335	−1.27392	−0.636959	+	0.770898i	$0.719808\pi$
$524$	2.94167	0.128507
$525$	0.108163	0.00472064
$526$	−29.0397	−1.26619
$527$	1.79054	0.0779970
$528$	1.58184	0.0688408
$529$	−20.0260	−0.870696
$530$	−13.3433	−0.579594
$531$	−9.38780	−0.407396
$532$	−36.4071	−1.57845
$533$	−14.6402	−0.634137
$534$	−17.0132	−0.736231
$535$	−28.5351	−1.23368
$536$	17.0752	0.737534
$537$	−15.3076	−0.660572
$538$	7.57617	0.326632
$539$	6.45251	0.277929
$540$	−24.5455	−1.05627
$541$	3.02481	0.130047	0.0650233	−	0.997884i	$-0.479288\pi$
$541$	3.02481	0.130047	0.0650233	+	0.997884i	$0.479288\pi$
$542$	21.3358	0.916452
$543$	19.7345	0.846888
$544$	4.00390	0.171666
$545$	−26.2723	−1.12538
$546$	−33.0329	−1.41368
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	24.3279	1.03924
$549$	12.6837	0.541328
$550$	0.0851870	0.00363239
$551$	−20.5974	−0.877480
$552$	−1.96647	−0.0836987
$553$	3.34545	0.142263
$554$	0.711930	0.0302470
$555$	11.3620	0.482288
$556$	35.0635	1.48703
$557$	−30.3839	−1.28741	−0.643703	−	0.765276i	$-0.722603\pi$
$557$	−30.3839	−1.28741	−0.643703	+	0.765276i	$0.722603\pi$
$558$	17.9738	0.760891
$559$	−31.3350	−1.32533
$560$	17.2166	0.727535
$561$	−0.395010	−0.0166773
$562$	47.6947	2.01188
$563$	−12.6324	−0.532394	−0.266197	−	0.963919i	$-0.585767\pi$
$563$	−12.6324	−0.532394	−0.266197	+	0.963919i	$0.585767\pi$
$564$	−1.33506	−0.0562160
$565$	−9.18603	−0.386459
$566$	31.4653	1.32258
$567$	15.5779	0.654208
$568$	2.00160	0.0839851
$569$	−3.49728	−0.146613	−0.0733067	−	0.997309i	$-0.523355\pi$
$569$	−3.49728	−0.146613	−0.0733067	+	0.997309i	$0.523355\pi$
$570$	13.3213	0.557968
$571$	20.3992	0.853680	0.426840	−	0.904327i	$-0.359627\pi$
$571$	20.3992	0.853680	0.426840	+	0.904327i	$0.359627\pi$
$572$	−14.9470	−0.624967
$573$	2.39974	0.100250
$574$	−21.0356	−0.878011
$575$	0.0677580	0.00282570
$576$	29.9214	1.24672
$577$	−0.992716	−0.0413273	−0.0206636	−	0.999786i	$-0.506578\pi$
$577$	−0.992716	−0.0413273	−0.0206636	+	0.999786i	$0.506578\pi$
$578$	36.2575	1.50811
$579$	−6.17162	−0.256484
$580$	−33.7102	−1.39974
$581$	43.1987	1.79218
$582$	−12.1665	−0.504318
$583$	−2.76317	−0.114439
$584$	6.78237	0.280656
$585$	−30.0359	−1.24183
$586$	37.2397	1.53836
$587$	24.2975	1.00286	0.501432	−	0.865197i	$-0.332807\pi$
$587$	24.2975	1.00286	0.501432	+	0.865197i	$0.332807\pi$
$588$	−13.0797	−0.539397
$589$	−12.5045	−0.515241
$590$	18.6048	0.765947
$591$	5.34825	0.219998
$592$	−14.3241	−0.588717
$593$	−16.3073	−0.669659	−0.334830	−	0.942279i	$-0.608679\pi$
$593$	−16.3073	−0.669659	−0.334830	+	0.942279i	$0.608679\pi$
$594$	−8.84713	−0.363002
$595$	−4.29925	−0.176252
$596$	−22.7954	−0.933734
$597$	1.05152	0.0430357
$598$	−20.6932	−0.846207
$599$	−13.1853	−0.538736	−0.269368	−	0.963037i	$-0.586815\pi$
$599$	−13.1853	−0.538736	−0.269368	+	0.963037i	$0.586815\pi$
$600$	−0.0448032	−0.00182908
$601$	−18.1390	−0.739906	−0.369953	−	0.929050i	$-0.620626\pi$
$601$	−18.1390	−0.739906	−0.369953	+	0.929050i	$0.620626\pi$
$602$	−45.0234	−1.83502
$603$	27.3860	1.11524
$604$	5.13335	0.208873
$605$	−2.22726	−0.0905512
$606$	−14.0313	−0.569984
$607$	17.5641	0.712904	0.356452	−	0.934314i	$-0.383986\pi$
$607$	17.5641	0.712904	0.356452	+	0.934314i	$0.383986\pi$
$608$	−27.9620	−1.13401
$609$	−15.4276	−0.625158
$610$	−25.1366	−1.01775
$611$	−3.64507	−0.147464
$612$	−3.46333	−0.139997
$613$	−4.24330	−0.171385	−0.0856926	−	0.996322i	$-0.527310\pi$
$613$	−4.24330	−0.171385	−0.0856926	+	0.996322i	$0.527310\pi$
$614$	7.29980	0.294596
$615$	4.42214	0.178318
$616$	−5.57226	−0.224513
$617$	−30.1821	−1.21509	−0.607543	−	0.794287i	$-0.707845\pi$
$617$	−30.1821	−1.21509	−0.607543	+	0.794287i	$0.707845\pi$
$618$	−19.1950	−0.772137
$619$	34.0647	1.36918	0.684589	−	0.728930i	$-0.259982\pi$
$619$	34.0647	1.36918	0.684589	+	0.728930i	$0.259982\pi$
$620$	−20.4652	−0.821902
$621$	−7.03703	−0.282386
$622$	−31.4505	−1.26105
$623$	−38.3456	−1.53628
$624$	−8.75463	−0.350466
$625$	−24.8020	−0.992080
$626$	9.89836	0.395618
$627$	2.75862	0.110169
$628$	−34.1780	−1.36385
$629$	3.57695	0.142622
$630$	−43.1568	−1.71941
$631$	1.17670	0.0468436	0.0234218	−	0.999726i	$-0.492544\pi$
$631$	1.17670	0.0468436	0.0234218	+	0.999726i	$0.492544\pi$
$632$	−1.38574	−0.0551219
$633$	−13.8293	−0.549664
$634$	−18.5583	−0.737044
$635$	−2.15194	−0.0853969
$636$	5.60114	0.222100
$637$	−35.7111	−1.41493
$638$	−12.1504	−0.481040
$639$	3.21026	0.126996
$640$	−25.4087	−1.00437
$641$	11.8699	0.468834	0.234417	−	0.972136i	$-0.424682\pi$
$641$	11.8699	0.468834	0.234417	+	0.972136i	$0.424682\pi$
$642$	20.8487	0.822832
$643$	−4.88951	−0.192823	−0.0964117	−	0.995342i	$-0.530737\pi$
$643$	−4.88951	−0.192823	−0.0964117	+	0.995342i	$0.530737\pi$
$644$	−17.0825	−0.673145
$645$	9.46487	0.372679
$646$	4.19379	0.165002
$647$	−42.5562	−1.67306	−0.836528	−	0.547924i	$-0.815418\pi$
$647$	−42.5562	−1.67306	−0.836528	+	0.547924i	$0.815418\pi$
$648$	−6.45262	−0.253483
$649$	3.85275	0.151233
$650$	−0.471464	−0.0184923
$651$	−9.36599	−0.367082
$652$	60.5439	2.37108
$653$	−1.14247	−0.0447083	−0.0223541	−	0.999750i	$-0.507116\pi$
$653$	−1.14247	−0.0447083	−0.0223541	+	0.999750i	$0.507116\pi$
$654$	19.1954	0.750599
$655$	−2.42597	−0.0947904
$656$	−5.57502	−0.217668
$657$	10.8779	0.424387
$658$	−5.23739	−0.204175
$659$	−32.5666	−1.26861	−0.634307	−	0.773081i	$-0.718715\pi$
$659$	−32.5666	−1.26861	−0.634307	+	0.773081i	$0.718715\pi$
$660$	4.51482	0.175739
$661$	40.2416	1.56522	0.782608	−	0.622515i	$-0.213889\pi$
$661$	40.2416	1.56522	0.782608	+	0.622515i	$0.213889\pi$
$662$	56.1714	2.18316
$663$	2.18616	0.0849035
$664$	−17.8937	−0.694409
$665$	30.0246	1.16431
$666$	35.9062	1.39134
$667$	−9.66448	−0.374210
$668$	12.4180	0.480468
$669$	4.77718	0.184697
$670$	−54.2736	−2.09677
$671$	−5.20538	−0.200952
$672$	−20.9437	−0.807921
$673$	−42.2389	−1.62819	−0.814094	−	0.580733i	$-0.802766\pi$
$673$	−42.2389	−1.62819	−0.814094	+	0.580733i	$0.802766\pi$
$674$	54.9943	2.11830
$675$	−0.160328	−0.00617105
$676$	47.6143	1.83132
$677$	−5.24802	−0.201698	−0.100849	−	0.994902i	$-0.532156\pi$
$677$	−5.24802	−0.201698	−0.100849	+	0.994902i	$0.532156\pi$
$678$	6.71161	0.257758
$679$	−27.4219	−1.05235
$680$	1.78083	0.0682915
$681$	−5.17193	−0.198189
$682$	−7.37643	−0.282458
$683$	4.26017	0.163011	0.0815054	−	0.996673i	$-0.474027\pi$
$683$	4.26017	0.163011	0.0815054	+	0.996673i	$0.474027\pi$
$684$	24.1868	0.924805
$685$	−20.0631	−0.766570
$686$	4.35375	0.166227
$687$	15.2156	0.580510
$688$	−11.9324	−0.454920
$689$	15.2926	0.582603
$690$	6.25046	0.237951
$691$	−37.9833	−1.44495	−0.722476	−	0.691396i	$-0.756996\pi$
$691$	−37.9833	−1.44495	−0.722476	+	0.691396i	$0.756996\pi$
$692$	33.0477	1.25629
$693$	−8.93707	−0.339491
$694$	48.9956	1.85985
$695$	−28.9166	−1.09687
$696$	6.39039	0.242227
$697$	1.39217	0.0527321
$698$	29.5104	1.11699
$699$	−2.72816	−0.103189
$700$	−0.389200	−0.0147104
$701$	−6.31743	−0.238606	−0.119303	−	0.992858i	$-0.538066\pi$
$701$	−6.31743	−0.238606	−0.119303	+	0.992858i	$0.538066\pi$
$702$	48.9640	1.84803
$703$	−24.9803	−0.942149
$704$	−12.2797	−0.462809
$705$	1.10101	0.0414664
$706$	−47.2736	−1.77917
$707$	−31.6249	−1.18938
$708$	−7.80978	−0.293510
$709$	13.9420	0.523605	0.261802	−	0.965122i	$-0.415683\pi$
$709$	13.9420	0.523605	0.261802	+	0.965122i	$0.415683\pi$
$710$	−6.36210	−0.238765
$711$	−2.22252	−0.0833511
$712$	15.8834	0.595257
$713$	−5.86723	−0.219730
$714$	3.14117	0.117555
$715$	12.3267	0.460992
$716$	55.0807	2.05846
$717$	−8.67889	−0.324119
$718$	−53.5247	−1.99752
$719$	−19.0983	−0.712247	−0.356124	−	0.934439i	$-0.615902\pi$
$719$	−19.0983	−0.712247	−0.356124	+	0.934439i	$0.615902\pi$
$720$	−11.4377	−0.426259
$721$	−43.2633	−1.61121
$722$	11.9061	0.443099
$723$	8.41462	0.312943
$724$	−71.0098	−2.63906
$725$	−0.220191	−0.00817769
$726$	1.62731	0.0603952
$727$	−17.1201	−0.634950	−0.317475	−	0.948267i	$-0.602835\pi$
$727$	−17.1201	−0.634950	−0.317475	+	0.948267i	$0.602835\pi$
$728$	30.8394	1.14299
$729$	−1.16085	−0.0429945
$730$	−21.5579	−0.797892
$731$	2.97971	0.110209
$732$	10.5517	0.390001
$733$	−38.8717	−1.43576	−0.717880	−	0.696167i	$-0.754887\pi$
$733$	−38.8717	−1.43576	−0.717880	+	0.696167i	$0.754887\pi$
$734$	−49.3990	−1.82335
$735$	10.7867	0.397873
$736$	−13.1200	−0.483609
$737$	−11.2392	−0.414000
$738$	13.9749	0.514422
$739$	5.89050	0.216686	0.108343	−	0.994114i	$-0.465446\pi$
$739$	5.89050	0.216686	0.108343	+	0.994114i	$0.465446\pi$
$740$	−40.8832	−1.50290
$741$	−15.2675	−0.560865
$742$	21.9731	0.806658
$743$	13.5219	0.496070	0.248035	−	0.968751i	$-0.420215\pi$
$743$	13.5219	0.496070	0.248035	+	0.968751i	$0.420215\pi$
$744$	3.87956	0.142231
$745$	18.7991	0.688747
$746$	52.7795	1.93240
$747$	−28.6987	−1.05003
$748$	1.42135	0.0519696
$749$	46.9905	1.71699
$750$	18.2647	0.666932
$751$	−22.8846	−0.835071	−0.417535	−	0.908661i	$-0.637106\pi$
$751$	−22.8846	−0.835071	−0.417535	+	0.908661i	$0.637106\pi$
$752$	−1.38805	−0.0506170
$753$	8.20544	0.299023
$754$	67.2460	2.44895
$755$	−4.23343	−0.154070
$756$	40.4205	1.47008
$757$	−5.01203	−0.182165	−0.0910826	−	0.995843i	$-0.529033\pi$
$757$	−5.01203	−0.182165	−0.0910826	+	0.995843i	$0.529033\pi$
$758$	−48.8247	−1.77339
$759$	1.29437	0.0469826
$760$	−12.4367	−0.451128
$761$	−42.0491	−1.52428	−0.762139	−	0.647413i	$-0.775851\pi$
$761$	−42.0491	−1.52428	−0.762139	+	0.647413i	$0.775851\pi$
$762$	1.57227	0.0569574
$763$	43.2641	1.56627
$764$	−8.63487	−0.312399
$765$	2.85618	0.103265
$766$	−9.25054	−0.334235
$767$	−21.3228	−0.769923
$768$	0.131018	0.00472771
$769$	−3.08597	−0.111283	−0.0556414	−	0.998451i	$-0.517720\pi$
$769$	−3.08597	−0.111283	−0.0556414	+	0.998451i	$0.517720\pi$
$770$	17.7115	0.638279
$771$	17.8459	0.642705
$772$	22.2071	0.799250
$773$	−28.7452	−1.03389	−0.516947	−	0.856017i	$-0.672932\pi$
$773$	−28.7452	−1.03389	−0.516947	+	0.856017i	$0.672932\pi$
$774$	29.9110	1.07513
$775$	−0.133676	−0.00480179
$776$	11.3586	0.407751
$777$	−18.7104	−0.671232
$778$	−44.3971	−1.59171
$779$	−9.72246	−0.348343
$780$	−24.9871	−0.894681
$781$	−1.31749	−0.0471434
$782$	1.96776	0.0703669
$783$	22.8680	0.817236
$784$	−13.5989	−0.485674
$785$	28.1863	1.00601
$786$	1.77249	0.0632226
$787$	15.4042	0.549099	0.274550	−	0.961573i	$-0.411471\pi$
$787$	15.4042	0.549099	0.274550	+	0.961573i	$0.411471\pi$
$788$	−19.2444	−0.685553
$789$	−10.0530	−0.357898
$790$	4.40460	0.156709
$791$	15.1272	0.537860
$792$	3.70189	0.131541
$793$	28.8090	1.02304
$794$	42.1143	1.49458
$795$	−4.61921	−0.163827
$796$	−3.78363	−0.134107
$797$	11.5401	0.408772	0.204386	−	0.978890i	$-0.434480\pi$
$797$	11.5401	0.408772	0.204386	+	0.978890i	$0.434480\pi$
$798$	−21.9370	−0.776560
$799$	0.346617	0.0122624
$800$	−0.298920	−0.0105684
$801$	25.4746	0.900102
$802$	77.3962	2.73296
$803$	−4.46428	−0.157541
$804$	22.7826	0.803480
$805$	14.0878	0.496530
$806$	40.8245	1.43798
$807$	2.62274	0.0923248
$808$	13.0996	0.460843
$809$	−31.7221	−1.11529	−0.557645	−	0.830080i	$-0.688295\pi$
$809$	−31.7221	−1.11529	−0.557645	+	0.830080i	$0.688295\pi$
$810$	20.5097	0.720639
$811$	19.1680	0.673080	0.336540	−	0.941669i	$-0.390743\pi$
$811$	19.1680	0.673080	0.336540	+	0.941669i	$0.390743\pi$
$812$	55.5125	1.94811
$813$	7.38610	0.259042
$814$	−14.7359	−0.516492
$815$	−49.9301	−1.74897
$816$	0.832496	0.0291432
$817$	−20.8094	−0.728028
$818$	−48.1550	−1.68370
$819$	49.4618	1.72834
$820$	−15.9120	−0.555670
$821$	−11.5761	−0.404008	−0.202004	−	0.979385i	$-0.564745\pi$
$821$	−11.5761	−0.404008	−0.202004	+	0.979385i	$0.564745\pi$
$822$	14.6587	0.511281
$823$	−25.3856	−0.884888	−0.442444	−	0.896796i	$-0.645888\pi$
$823$	−25.3856	−0.884888	−0.442444	+	0.896796i	$0.645888\pi$
$824$	17.9204	0.624287
$825$	0.0294903	0.00102672
$826$	−30.6376	−1.06602
$827$	−27.3636	−0.951524	−0.475762	−	0.879574i	$-0.657828\pi$
$827$	−27.3636	−0.951524	−0.475762	+	0.879574i	$0.657828\pi$
$828$	11.3486	0.394392
$829$	−3.75176	−0.130304	−0.0651521	−	0.997875i	$-0.520753\pi$
$829$	−3.75176	−0.130304	−0.0651521	+	0.997875i	$0.520753\pi$
$830$	56.8753	1.97417
$831$	0.246458	0.00854953
$832$	67.9615	2.35614
$833$	3.39584	0.117659
$834$	21.1274	0.731582
$835$	−10.2410	−0.354406
$836$	−9.92624	−0.343306
$837$	13.8830	0.479867
$838$	33.5041	1.15738
$839$	46.6639	1.61102	0.805508	−	0.592585i	$-0.201892\pi$
$839$	46.6639	1.61102	0.805508	+	0.592585i	$0.201892\pi$
$840$	−9.31519	−0.321405
$841$	2.40636	0.0829780
$842$	−33.3196	−1.14827
$843$	16.5111	0.568672
$844$	49.7612	1.71285
$845$	−39.2671	−1.35083
$846$	3.47942	0.119625
$847$	3.66777	0.126026
$848$	5.82348	0.199979
$849$	10.8927	0.373838
$850$	0.0448325	0.00153774
$851$	−11.7209	−0.401789
$852$	2.67064	0.0914945
$853$	−9.01516	−0.308673	−0.154337	−	0.988018i	$-0.549324\pi$
$853$	−9.01516	−0.308673	−0.154337	+	0.988018i	$0.549324\pi$
$854$	41.3939	1.41647
$855$	−19.9466	−0.682161
$856$	−19.4643	−0.665275
$857$	−16.2536	−0.555212	−0.277606	−	0.960695i	$-0.589541\pi$
$857$	−16.2536	−0.555212	−0.277606	+	0.960695i	$0.589541\pi$
$858$	−9.00628	−0.307469
$859$	40.2552	1.37349	0.686744	−	0.726899i	$-0.259039\pi$
$859$	40.2552	1.37349	0.686744	+	0.726899i	$0.259039\pi$
$860$	−34.0570	−1.16134
$861$	−7.28219	−0.248176
$862$	15.7797	0.537459
$863$	−6.55780	−0.223230	−0.111615	−	0.993752i	$-0.535602\pi$
$863$	−6.55780	−0.223230	−0.111615	+	0.993752i	$0.535602\pi$
$864$	31.0444	1.05615
$865$	−27.2542	−0.926670
$866$	40.7179	1.38365
$867$	12.5517	0.426279
$868$	33.7012	1.14389
$869$	0.912121	0.0309416
$870$	−20.3119	−0.688639
$871$	62.2027	2.10766
$872$	−17.9208	−0.606873
$873$	18.2175	0.616569
$874$	−13.7422	−0.464837
$875$	41.1664	1.39168
$876$	9.04940	0.305751
$877$	−37.2577	−1.25810	−0.629051	−	0.777364i	$-0.716556\pi$
$877$	−37.2577	−1.25810	−0.629051	+	0.777364i	$0.716556\pi$
$878$	34.1544	1.15266
$879$	12.8917	0.434827
$880$	4.69404	0.158236
$881$	21.1519	0.712626	0.356313	−	0.934367i	$-0.384034\pi$
$881$	21.1519	0.712626	0.356313	+	0.934367i	$0.384034\pi$
$882$	34.0882	1.14781
$883$	−40.8229	−1.37380	−0.686899	−	0.726753i	$-0.741029\pi$
$883$	−40.8229	−1.37380	−0.686899	+	0.726753i	$0.741029\pi$
$884$	−7.86638	−0.264575
$885$	6.44066	0.216500
$886$	−33.8320	−1.13661
$887$	−19.4412	−0.652772	−0.326386	−	0.945237i	$-0.605831\pi$
$887$	−19.4412	−0.652772	−0.326386	+	0.945237i	$0.605831\pi$
$888$	7.75017	0.260079
$889$	3.54372	0.118852
$890$	−50.4857	−1.69229
$891$	4.24723	0.142288
$892$	−17.1895	−0.575548
$893$	−2.42067	−0.0810046
$894$	−13.7353	−0.459376
$895$	−45.4246	−1.51838
$896$	41.8420	1.39784
$897$	−7.16363	−0.239186
$898$	25.7670	0.859856
$899$	19.0666	0.635906
$900$	0.258562	0.00861873
$901$	−1.45421	−0.0484467
$902$	−5.73528	−0.190964
$903$	−15.5863	−0.518681
$904$	−6.26594	−0.208402
$905$	58.5612	1.94664
$906$	3.09308	0.102761
$907$	−8.54748	−0.283815	−0.141907	−	0.989880i	$-0.545323\pi$
$907$	−8.54748	−0.283815	−0.141907	+	0.989880i	$0.545323\pi$
$908$	18.6099	0.617592
$909$	21.0098	0.696851
$910$	−98.0236	−3.24945
$911$	9.45569	0.313281	0.156640	−	0.987656i	$-0.449934\pi$
$911$	9.45569	0.313281	0.156640	+	0.987656i	$0.449934\pi$
$912$	−5.81390	−0.192517
$913$	11.7779	0.389793
$914$	14.1953	0.469539
$915$	−8.70187	−0.287675
$916$	−54.7495	−1.80898
$917$	3.99498	0.131926
$918$	−4.65609	−0.153674
$919$	−51.3133	−1.69267	−0.846335	−	0.532652i	$-0.821196\pi$
$919$	−51.3133	−1.69267	−0.846335	+	0.532652i	$0.821196\pi$
$920$	−5.83541	−0.192388
$921$	2.52707	0.0832696
$922$	−37.9153	−1.24867
$923$	7.29157	0.240005
$924$	−7.43482	−0.244587
$925$	−0.267045	−0.00878037
$926$	57.0415	1.87450
$927$	28.7416	0.943999
$928$	42.6356	1.39958
$929$	30.7015	1.00728	0.503642	−	0.863912i	$-0.331993\pi$
$929$	30.7015	1.00728	0.503642	+	0.863912i	$0.331993\pi$
$930$	−12.3312	−0.404357
$931$	−23.7155	−0.777245
$932$	9.81663	0.321555
$933$	−10.8876	−0.356445
$934$	44.1332	1.44408
$935$	−1.17217	−0.0383341
$936$	−20.4880	−0.669670
$937$	−25.5083	−0.833319	−0.416659	−	0.909063i	$-0.636799\pi$
$937$	−25.5083	−0.833319	−0.416659	+	0.909063i	$0.636799\pi$
$938$	89.3755	2.91821
$939$	3.42664	0.111824
$940$	−3.96171	−0.129217
$941$	4.61499	0.150444	0.0752221	−	0.997167i	$-0.476033\pi$
$941$	4.61499	0.150444	0.0752221	+	0.997167i	$0.476033\pi$
$942$	−20.5938	−0.670983
$943$	−4.56186	−0.148554
$944$	−8.11979	−0.264277
$945$	−33.3344	−1.08437
$946$	−12.2754	−0.399109
$947$	1.08975	0.0354121	0.0177060	−	0.999843i	$-0.494364\pi$
$947$	1.08975	0.0354121	0.0177060	+	0.999843i	$0.494364\pi$
$948$	−1.84893	−0.0600505
$949$	24.7073	0.802034
$950$	−0.313096	−0.0101582
$951$	−6.42457	−0.208331
$952$	−2.93259	−0.0950457
$953$	−22.0713	−0.714958	−0.357479	−	0.933921i	$-0.616364\pi$
$953$	−22.0713	−0.714958	−0.357479	+	0.933921i	$0.616364\pi$
$954$	−14.5977	−0.472617
$955$	7.12110	0.230433
$956$	31.2289	1.01001
$957$	−4.20627	−0.135969
$958$	−37.8405	−1.22257
$959$	33.0390	1.06688
$960$	−20.5281	−0.662540
$961$	−19.4248	−0.626607
$962$	81.5550	2.62944
$963$	−31.2178	−1.00598
$964$	−30.2780	−0.975187
$965$	−18.3140	−0.589548
$966$	−10.2930	−0.331172
$967$	−10.0099	−0.321895	−0.160948	−	0.986963i	$-0.551455\pi$
$967$	−10.0099	−0.321895	−0.160948	+	0.986963i	$0.551455\pi$
$968$	−1.51925	−0.0488306
$969$	1.45182	0.0466391
$970$	−36.1035	−1.15921
$971$	−20.8142	−0.667960	−0.333980	−	0.942580i	$-0.608392\pi$
$971$	−20.8142	−0.667960	−0.333980	+	0.942580i	$0.608392\pi$
$972$	−41.6708	−1.33659
$973$	47.6186	1.52658
$974$	−14.5669	−0.466752
$975$	−0.163213	−0.00522699
$976$	10.9705	0.351158
$977$	−5.00340	−0.160073	−0.0800364	−	0.996792i	$-0.525504\pi$
$977$	−5.00340	−0.160073	−0.0800364	+	0.996792i	$0.525504\pi$
$978$	36.4805	1.16652
$979$	−10.4548	−0.334136
$980$	−38.8133	−1.23985
$981$	−28.7422	−0.917667
$982$	6.29399	0.200849
$983$	−8.54761	−0.272626	−0.136313	−	0.990666i	$-0.543525\pi$
$983$	−8.54761	−0.272626	−0.136313	+	0.990666i	$0.543525\pi$
$984$	3.01641	0.0961596
$985$	15.8707	0.505682
$986$	−6.39456	−0.203644
$987$	−1.81310	−0.0577115
$988$	54.9363	1.74776
$989$	−9.76392	−0.310475
$990$	−11.7665	−0.373964
$991$	−5.42039	−0.172184	−0.0860922	−	0.996287i	$-0.527438\pi$
$991$	−5.42039	−0.172184	−0.0860922	+	0.996287i	$0.527438\pi$
$992$	25.8838	0.821810
$993$	19.4456	0.617087
$994$	10.4768	0.332305
$995$	3.12033	0.0989210
$996$	−23.8747	−0.756499
$997$	48.3550	1.53142	0.765709	−	0.643187i	$-0.222388\pi$
$997$	48.3550	1.53142	0.765709	+	0.643187i	$0.222388\pi$
$998$	−91.7074	−2.90295
$999$	27.7340	0.877466

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.c.1.17	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.c.1.17	✓	106	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.16812 q^{2} -0.750565 q^{3} +2.70073 q^{4} -2.22726 q^{5} +1.62731 q^{6} +3.66777 q^{7} -1.51925 q^{8} -2.43665 q^{9} +O(q^{10})\)	\(q-2.16812 q^{2} -0.750565 q^{3} +2.70073 q^{4} -2.22726 q^{5} +1.62731 q^{6} +3.66777 q^{7} -1.51925 q^{8} -2.43665 q^{9} +4.82897 q^{10} +1.00000 q^{11} -2.02707 q^{12} -5.53446 q^{13} -7.95214 q^{14} +1.67171 q^{15} -2.10753 q^{16} +0.526283 q^{17} +5.28294 q^{18} -3.67540 q^{19} -6.01523 q^{20} -2.75290 q^{21} -2.16812 q^{22} -1.72453 q^{23} +1.14030 q^{24} -0.0392908 q^{25} +11.9993 q^{26} +4.08056 q^{27} +9.90563 q^{28} +5.60414 q^{29} -3.62445 q^{30} +3.40223 q^{31} +7.60788 q^{32} -0.750565 q^{33} -1.14104 q^{34} -8.16909 q^{35} -6.58073 q^{36} +6.79662 q^{37} +7.96869 q^{38} +4.15397 q^{39} +3.38378 q^{40} +2.64528 q^{41} +5.96860 q^{42} +5.66180 q^{43} +2.70073 q^{44} +5.42707 q^{45} +3.73897 q^{46} +0.658614 q^{47} +1.58184 q^{48} +6.45251 q^{49} +0.0851870 q^{50} -0.395010 q^{51} -14.9470 q^{52} -2.76317 q^{53} -8.84713 q^{54} -2.22726 q^{55} -5.57226 q^{56} +2.75862 q^{57} -12.1504 q^{58} +3.85275 q^{59} +4.51482 q^{60} -5.20538 q^{61} -7.37643 q^{62} -8.93707 q^{63} -12.2797 q^{64} +12.3267 q^{65} +1.62731 q^{66} -11.2392 q^{67} +1.42135 q^{68} +1.29437 q^{69} +17.7115 q^{70} -1.31749 q^{71} +3.70189 q^{72} -4.46428 q^{73} -14.7359 q^{74} +0.0294903 q^{75} -9.92624 q^{76} +3.66777 q^{77} -9.00628 q^{78} +0.912121 q^{79} +4.69404 q^{80} +4.24723 q^{81} -5.73528 q^{82} +11.7779 q^{83} -7.43482 q^{84} -1.17217 q^{85} -12.2754 q^{86} -4.20627 q^{87} -1.51925 q^{88} -10.4548 q^{89} -11.7665 q^{90} -20.2991 q^{91} -4.65747 q^{92} -2.55359 q^{93} -1.42795 q^{94} +8.18609 q^{95} -5.71021 q^{96} -7.47645 q^{97} -13.9898 q^{98} -2.43665 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * q^99

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