LMFDB - Embedded newform 8027.2.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$143$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65785 q^{2} +2.82218 q^{3} +5.06415 q^{4} +0.881121 q^{5} -7.50092 q^{6} +1.80840 q^{7} -8.14403 q^{8} +4.96471 q^{9} +O(q^{10})$	\(q-2.65785 q^{2} +2.82218 q^{3} +5.06415 q^{4} +0.881121 q^{5} -7.50092 q^{6} +1.80840 q^{7} -8.14403 q^{8} +4.96471 q^{9} -2.34188 q^{10} -4.56984 q^{11} +14.2919 q^{12} -4.81374 q^{13} -4.80645 q^{14} +2.48668 q^{15} +11.5173 q^{16} +5.95790 q^{17} -13.1954 q^{18} -3.18839 q^{19} +4.46212 q^{20} +5.10363 q^{21} +12.1459 q^{22} +1.00000 q^{23} -22.9839 q^{24} -4.22363 q^{25} +12.7942 q^{26} +5.54477 q^{27} +9.15799 q^{28} +1.99933 q^{29} -6.60922 q^{30} +4.84701 q^{31} -14.3231 q^{32} -12.8969 q^{33} -15.8352 q^{34} +1.59342 q^{35} +25.1420 q^{36} -3.59926 q^{37} +8.47424 q^{38} -13.5853 q^{39} -7.17587 q^{40} -2.49119 q^{41} -13.5647 q^{42} -9.21016 q^{43} -23.1423 q^{44} +4.37451 q^{45} -2.65785 q^{46} -10.5497 q^{47} +32.5038 q^{48} -3.72969 q^{49} +11.2257 q^{50} +16.8143 q^{51} -24.3775 q^{52} +8.19390 q^{53} -14.7371 q^{54} -4.02658 q^{55} -14.7276 q^{56} -8.99821 q^{57} -5.31390 q^{58} -12.6026 q^{59} +12.5929 q^{60} +0.803386 q^{61} -12.8826 q^{62} +8.97817 q^{63} +15.0340 q^{64} -4.24149 q^{65} +34.2780 q^{66} -12.1659 q^{67} +30.1716 q^{68} +2.82218 q^{69} -4.23506 q^{70} -2.87320 q^{71} -40.4327 q^{72} +1.32995 q^{73} +9.56628 q^{74} -11.9198 q^{75} -16.1465 q^{76} -8.26409 q^{77} +36.1075 q^{78} +16.1149 q^{79} +10.1481 q^{80} +0.754210 q^{81} +6.62119 q^{82} +3.72993 q^{83} +25.8455 q^{84} +5.24962 q^{85} +24.4792 q^{86} +5.64246 q^{87} +37.2169 q^{88} -7.58720 q^{89} -11.6268 q^{90} -8.70516 q^{91} +5.06415 q^{92} +13.6791 q^{93} +28.0396 q^{94} -2.80935 q^{95} -40.4224 q^{96} -11.8725 q^{97} +9.91295 q^{98} -22.6879 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) $ 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * 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 $

$2$	−2.65785	−1.87938	−0.939690	−	0.342026i	$-0.888887\pi$
$2$	−2.65785	−1.87938	−0.939690	+	0.342026i	$0.888887\pi$
$3$	2.82218	1.62939	0.814694	−	0.579892i	$-0.196905\pi$
$3$	2.82218	1.62939	0.814694	+	0.579892i	$0.196905\pi$
$4$	5.06415	2.53207
$5$	0.881121	0.394049	0.197025	−	0.980399i	$-0.436872\pi$
$5$	0.881121	0.394049	0.197025	+	0.980399i	$0.436872\pi$
$6$	−7.50092	−3.06224
$7$	1.80840	0.683510	0.341755	−	0.939789i	$-0.388979\pi$
$7$	1.80840	0.683510	0.341755	+	0.939789i	$0.388979\pi$
$8$	−8.14403	−2.87935
$9$	4.96471	1.65490
$10$	−2.34188	−0.740568
$11$	−4.56984	−1.37786	−0.688929	−	0.724829i	$-0.741919\pi$
$11$	−4.56984	−1.37786	−0.688929	+	0.724829i	$0.741919\pi$
$12$	14.2919	4.12573
$13$	−4.81374	−1.33509	−0.667546	−	0.744569i	$-0.732655\pi$
$13$	−4.81374	−1.33509	−0.667546	+	0.744569i	$0.732655\pi$
$14$	−4.80645	−1.28458
$15$	2.48668	0.642059
$16$	11.5173	2.87932
$17$	5.95790	1.44500	0.722501	−	0.691370i	$-0.242993\pi$
$17$	5.95790	1.44500	0.722501	+	0.691370i	$0.242993\pi$
$18$	−13.1954	−3.11019
$19$	−3.18839	−0.731466	−0.365733	−	0.930720i	$-0.619182\pi$
$19$	−3.18839	−0.731466	−0.365733	+	0.930720i	$0.619182\pi$
$20$	4.46212	0.997761
$21$	5.10363	1.11370
$22$	12.1459	2.58952
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−22.9839	−4.69157
$25$	−4.22363	−0.844725
$26$	12.7942	2.50915
$27$	5.54477	1.06709
$28$	9.15799	1.73070
$29$	1.99933	0.371265	0.185633	−	0.982619i	$-0.440567\pi$
$29$	1.99933	0.371265	0.185633	+	0.982619i	$0.440567\pi$
$30$	−6.60922	−1.20667
$31$	4.84701	0.870548	0.435274	−	0.900298i	$-0.356651\pi$
$31$	4.84701	0.870548	0.435274	+	0.900298i	$0.356651\pi$
$32$	−14.3231	−2.53199
$33$	−12.8969	−2.24506
$34$	−15.8352	−2.71571
$35$	1.59342	0.269337
$36$	25.1420	4.19033
$37$	−3.59926	−0.591715	−0.295858	−	0.955232i	$-0.595605\pi$
$37$	−3.59926	−0.591715	−0.295858	+	0.955232i	$0.595605\pi$
$38$	8.47424	1.37470
$39$	−13.5853	−2.17538
$40$	−7.17587	−1.13460
$41$	−2.49119	−0.389058	−0.194529	−	0.980897i	$-0.562318\pi$
$41$	−2.49119	−0.389058	−0.194529	+	0.980897i	$0.562318\pi$
$42$	−13.5647	−2.09307
$43$	−9.21016	−1.40454	−0.702268	−	0.711912i	$-0.747829\pi$
$43$	−9.21016	−1.40454	−0.702268	+	0.711912i	$0.747829\pi$
$44$	−23.1423	−3.48883
$45$	4.37451	0.652113
$46$	−2.65785	−0.391878
$47$	−10.5497	−1.53884	−0.769420	−	0.638744i	$-0.779454\pi$
$47$	−10.5497	−1.53884	−0.769420	+	0.638744i	$0.779454\pi$
$48$	32.5038	4.69153
$49$	−3.72969	−0.532813
$50$	11.2257	1.58756
$51$	16.8143	2.35447
$52$	−24.3775	−3.38055
$53$	8.19390	1.12552	0.562760	−	0.826621i	$-0.309740\pi$
$53$	8.19390	1.12552	0.562760	+	0.826621i	$0.309740\pi$
$54$	−14.7371	−2.00547
$55$	−4.02658	−0.542943
$56$	−14.7276	−1.96806
$57$	−8.99821	−1.19184
$58$	−5.31390	−0.697749
$59$	−12.6026	−1.64071	−0.820357	−	0.571852i	$-0.806225\pi$
$59$	−12.6026	−1.64071	−0.820357	+	0.571852i	$0.806225\pi$
$60$	12.5929	1.62574
$61$	0.803386	0.102863	0.0514315	−	0.998677i	$-0.483622\pi$
$61$	0.803386	0.102863	0.0514315	+	0.998677i	$0.483622\pi$
$62$	−12.8826	−1.63609
$63$	8.97817	1.13114
$64$	15.0340	1.87925
$65$	−4.24149	−0.526092
$66$	34.2780	4.21933
$67$	−12.1659	−1.48630	−0.743149	−	0.669126i	$-0.766668\pi$
$67$	−12.1659	−1.48630	−0.743149	+	0.669126i	$0.766668\pi$
$68$	30.1716	3.65885
$69$	2.82218	0.339751
$70$	−4.23506	−0.506186
$71$	−2.87320	−0.340986	−0.170493	−	0.985359i	$-0.554536\pi$
$71$	−2.87320	−0.340986	−0.170493	+	0.985359i	$0.554536\pi$
$72$	−40.4327	−4.76504
$73$	1.32995	0.155659	0.0778295	−	0.996967i	$-0.475201\pi$
$73$	1.32995	0.155659	0.0778295	+	0.996967i	$0.475201\pi$
$74$	9.56628	1.11206
$75$	−11.9198	−1.37638
$76$	−16.1465	−1.85213
$77$	−8.26409	−0.941780
$78$	36.1075	4.08837
$79$	16.1149	1.81306	0.906532	−	0.422137i	$-0.138720\pi$
$79$	16.1149	1.81306	0.906532	+	0.422137i	$0.138720\pi$
$80$	10.1481	1.13459
$81$	0.754210	0.0838011
$82$	6.62119	0.731188
$83$	3.72993	0.409413	0.204706	−	0.978823i	$-0.434376\pi$
$83$	3.72993	0.409413	0.204706	+	0.978823i	$0.434376\pi$
$84$	25.8455	2.81998
$85$	5.24962	0.569402
$86$	24.4792	2.63966
$87$	5.64246	0.604935
$88$	37.2169	3.96733
$89$	−7.58720	−0.804241	−0.402121	−	0.915587i	$-0.631727\pi$
$89$	−7.58720	−0.804241	−0.402121	+	0.915587i	$0.631727\pi$
$90$	−11.6268	−1.22557
$91$	−8.70516	−0.912549
$92$	5.06415	0.527974
$93$	13.6791	1.41846
$94$	28.0396	2.89206
$95$	−2.80935	−0.288234
$96$	−40.4224	−4.12559
$97$	−11.8725	−1.20547	−0.602736	−	0.797941i	$-0.705923\pi$
$97$	−11.8725	−1.20547	−0.602736	+	0.797941i	$0.705923\pi$
$98$	9.91295	1.00136
$99$	−22.6879	−2.28022
$100$	−21.3891	−2.13891
$101$	−9.73151	−0.968322	−0.484161	−	0.874979i	$-0.660875\pi$
$101$	−9.73151	−0.968322	−0.484161	+	0.874979i	$0.660875\pi$
$102$	−44.6897	−4.42494
$103$	−14.6979	−1.44822	−0.724112	−	0.689682i	$-0.757750\pi$
$103$	−14.6979	−1.44822	−0.724112	+	0.689682i	$0.757750\pi$
$104$	39.2032	3.84419
$105$	4.49691	0.438854
$106$	−21.7781	−2.11528
$107$	−1.26726	−0.122510	−0.0612551	−	0.998122i	$-0.519510\pi$
$107$	−1.26726	−0.122510	−0.0612551	+	0.998122i	$0.519510\pi$
$108$	28.0795	2.70195
$109$	1.24197	0.118959	0.0594796	−	0.998230i	$-0.481056\pi$
$109$	1.24197	0.118959	0.0594796	+	0.998230i	$0.481056\pi$
$110$	10.7020	1.02040
$111$	−10.1578	−0.964133
$112$	20.8278	1.96804
$113$	4.71921	0.443946	0.221973	−	0.975053i	$-0.428750\pi$
$113$	4.71921	0.443946	0.221973	+	0.975053i	$0.428750\pi$
$114$	23.9158	2.23992
$115$	0.881121	0.0821649
$116$	10.1249	0.940071
$117$	−23.8988	−2.20945
$118$	33.4957	3.08352
$119$	10.7743	0.987674
$120$	−20.2516	−1.84871
$121$	9.88340	0.898491
$122$	−2.13528	−0.193319
$123$	−7.03058	−0.633926
$124$	24.5459	2.20429
$125$	−8.12713	−0.726912
$126$	−23.8626	−2.12585
$127$	15.1438	1.34379	0.671895	−	0.740646i	$-0.265480\pi$
$127$	15.1438	1.34379	0.671895	+	0.740646i	$0.265480\pi$
$128$	−11.3119	−0.999843
$129$	−25.9927	−2.28853
$130$	11.2732	0.988727
$131$	10.2269	0.893527	0.446763	−	0.894652i	$-0.352577\pi$
$131$	10.2269	0.893527	0.446763	+	0.894652i	$0.352577\pi$
$132$	−65.3118	−5.68466
$133$	−5.76587	−0.499965
$134$	32.3350	2.79332
$135$	4.88561	0.420486
$136$	−48.5212	−4.16066
$137$	19.4600	1.66258	0.831291	−	0.555838i	$-0.187602\pi$
$137$	19.4600	1.66258	0.831291	+	0.555838i	$0.187602\pi$
$138$	−7.50092	−0.638521
$139$	−7.20977	−0.611524	−0.305762	−	0.952108i	$-0.598911\pi$
$139$	−7.20977	−0.611524	−0.305762	+	0.952108i	$0.598911\pi$
$140$	8.06930	0.681980
$141$	−29.7733	−2.50737
$142$	7.63653	0.640843
$143$	21.9980	1.83957
$144$	57.1799	4.76499
$145$	1.76165	0.146297
$146$	−3.53481	−0.292543
$147$	−10.5259	−0.868159
$148$	−18.2272	−1.49827
$149$	−5.26779	−0.431554	−0.215777	−	0.976443i	$-0.569228\pi$
$149$	−5.26779	−0.431554	−0.215777	+	0.976443i	$0.569228\pi$
$150$	31.6811	2.58675
$151$	6.57380	0.534968	0.267484	−	0.963562i	$-0.413808\pi$
$151$	6.57380	0.534968	0.267484	+	0.963562i	$0.413808\pi$
$152$	25.9663	2.10615
$153$	29.5792	2.39134
$154$	21.9647	1.76996
$155$	4.27080	0.343039
$156$	−68.7977	−5.50822
$157$	−15.5874	−1.24401	−0.622007	−	0.783012i	$-0.713682\pi$
$157$	−15.5874	−1.24401	−0.622007	+	0.783012i	$0.713682\pi$
$158$	−42.8308	−3.40744
$159$	23.1247	1.83391
$160$	−12.6204	−0.997728
$161$	1.80840	0.142522
$162$	−2.00457	−0.157494
$163$	−2.89435	−0.226703	−0.113352	−	0.993555i	$-0.536159\pi$
$163$	−2.89435	−0.226703	−0.113352	+	0.993555i	$0.536159\pi$
$164$	−12.6157	−0.985123
$165$	−11.3637	−0.884665
$166$	−9.91357	−0.769442
$167$	17.1991	1.33091	0.665454	−	0.746439i	$-0.268238\pi$
$167$	17.1991	1.33091	0.665454	+	0.746439i	$0.268238\pi$
$168$	−41.5641	−3.20674
$169$	10.1721	0.782470
$170$	−13.9527	−1.07012
$171$	−15.8294	−1.21051
$172$	−46.6416	−3.55639
$173$	3.24623	0.246806	0.123403	−	0.992357i	$-0.460619\pi$
$173$	3.24623	0.246806	0.123403	+	0.992357i	$0.460619\pi$
$174$	−14.9968	−1.13690
$175$	−7.63800	−0.577379
$176$	−52.6321	−3.96729
$177$	−35.5667	−2.67336
$178$	20.1656	1.51148
$179$	−12.6957	−0.948921	−0.474460	−	0.880277i	$-0.657357\pi$
$179$	−12.6957	−0.948921	−0.474460	+	0.880277i	$0.657357\pi$
$180$	22.1531	1.65120
$181$	−3.01785	−0.224315	−0.112158	−	0.993690i	$-0.535776\pi$
$181$	−3.01785	−0.224315	−0.112158	+	0.993690i	$0.535776\pi$
$182$	23.1370	1.71503
$183$	2.26730	0.167604
$184$	−8.14403	−0.600386
$185$	−3.17138	−0.233165
$186$	−36.3570	−2.66583
$187$	−27.2266	−1.99101
$188$	−53.4255	−3.89645
$189$	10.0271	0.729368
$190$	7.46683	0.541701
$191$	16.2296	1.17433	0.587166	−	0.809466i	$-0.300243\pi$
$191$	16.2296	1.17433	0.587166	+	0.809466i	$0.300243\pi$
$192$	42.4287	3.06203
$193$	−19.6259	−1.41270	−0.706351	−	0.707862i	$-0.749660\pi$
$193$	−19.6259	−1.41270	−0.706351	+	0.707862i	$0.749660\pi$
$194$	31.5553	2.26554
$195$	−11.9702	−0.857207
$196$	−18.8877	−1.34912
$197$	5.98398	0.426341	0.213170	−	0.977015i	$-0.431621\pi$
$197$	5.98398	0.426341	0.213170	+	0.977015i	$0.431621\pi$
$198$	60.3010	4.28540
$199$	−6.59070	−0.467202	−0.233601	−	0.972332i	$-0.575051\pi$
$199$	−6.59070	−0.467202	−0.233601	+	0.972332i	$0.575051\pi$
$200$	34.3973	2.43226
$201$	−34.3343	−2.42175
$202$	25.8649	1.81985
$203$	3.61558	0.253764
$204$	85.1499	5.96168
$205$	−2.19503	−0.153308
$206$	39.0647	2.72176
$207$	4.96471	0.345071
$208$	−55.4412	−3.84415
$209$	14.5704	1.00786
$210$	−11.9521	−0.824774
$211$	9.00699	0.620067	0.310033	−	0.950726i	$-0.399660\pi$
$211$	9.00699	0.620067	0.310033	+	0.950726i	$0.399660\pi$
$212$	41.4951	2.84990
$213$	−8.10870	−0.555599
$214$	3.36817	0.230243
$215$	−8.11526	−0.553456
$216$	−45.1567	−3.07253
$217$	8.76532	0.595029
$218$	−3.30096	−0.223570
$219$	3.75336	0.253629
$220$	−20.3912	−1.37477
$221$	−28.6798	−1.92921
$222$	26.9978	1.81197
$223$	23.5128	1.57453	0.787267	−	0.616613i	$-0.211496\pi$
$223$	23.5128	1.57453	0.787267	+	0.616613i	$0.211496\pi$
$224$	−25.9019	−1.73064
$225$	−20.9691	−1.39794
$226$	−12.5429	−0.834343
$227$	−23.6386	−1.56895	−0.784475	−	0.620161i	$-0.787067\pi$
$227$	−23.6386	−1.56895	−0.784475	+	0.620161i	$0.787067\pi$
$228$	−45.5682	−3.01783
$229$	−18.3955	−1.21561	−0.607806	−	0.794086i	$-0.707950\pi$
$229$	−18.3955	−1.21561	−0.607806	+	0.794086i	$0.707950\pi$
$230$	−2.34188	−0.154419
$231$	−23.3228	−1.53452
$232$	−16.2826	−1.06900
$233$	19.7397	1.29319	0.646597	−	0.762832i	$-0.276192\pi$
$233$	19.7397	1.29319	0.646597	+	0.762832i	$0.276192\pi$
$234$	63.5194	4.15239
$235$	−9.29560	−0.606378
$236$	−63.8212	−4.15440
$237$	45.4791	2.95418
$238$	−28.6363	−1.85622
$239$	17.5393	1.13452	0.567262	−	0.823537i	$-0.308003\pi$
$239$	17.5393	1.13452	0.567262	+	0.823537i	$0.308003\pi$
$240$	28.6398	1.84869
$241$	5.09287	0.328060	0.164030	−	0.986455i	$-0.447551\pi$
$241$	5.09287	0.328060	0.164030	+	0.986455i	$0.447551\pi$
$242$	−26.2686	−1.68861
$243$	−14.5058	−0.930546
$244$	4.06847	0.260457
$245$	−3.28631	−0.209955
$246$	18.6862	1.19139
$247$	15.3481	0.976574
$248$	−39.4741	−2.50661
$249$	10.5265	0.667092
$250$	21.6007	1.36615
$251$	−18.2965	−1.15487	−0.577433	−	0.816438i	$-0.695946\pi$
$251$	−18.2965	−1.15487	−0.577433	+	0.816438i	$0.695946\pi$
$252$	45.4668	2.86414
$253$	−4.56984	−0.287303
$254$	−40.2498	−2.52549
$255$	14.8154	0.927776
$256$	−0.00267814	−0.000167384 0
$257$	6.33703	0.395293	0.197647	−	0.980273i	$-0.436670\pi$
$257$	6.33703	0.395293	0.197647	+	0.980273i	$0.436670\pi$
$258$	69.0847	4.30103
$259$	−6.50890	−0.404443
$260$	−21.4795	−1.33210
$261$	9.92607	0.614408
$262$	−27.1815	−1.67928
$263$	−3.94971	−0.243549	−0.121775	−	0.992558i	$-0.538859\pi$
$263$	−3.94971	−0.243549	−0.121775	+	0.992558i	$0.538859\pi$
$264$	105.033	6.46432
$265$	7.21982	0.443510
$266$	15.3248	0.939624
$267$	−21.4125	−1.31042
$268$	−61.6097	−3.76341
$269$	25.5739	1.55927	0.779633	−	0.626237i	$-0.215406\pi$
$269$	25.5739	1.55927	0.779633	+	0.626237i	$0.215406\pi$
$270$	−12.9852	−0.790254
$271$	−2.30188	−0.139829	−0.0699145	−	0.997553i	$-0.522273\pi$
$271$	−2.30188	−0.139829	−0.0699145	+	0.997553i	$0.522273\pi$
$272$	68.6187	4.16062
$273$	−24.5676	−1.48690
$274$	−51.7217	−3.12462
$275$	19.3013	1.16391
$276$	14.2919	0.860274
$277$	−12.8392	−0.771433	−0.385717	−	0.922617i	$-0.626046\pi$
$277$	−12.8392	−0.771433	−0.385717	+	0.922617i	$0.626046\pi$
$278$	19.1625	1.14929
$279$	24.0640	1.44067
$280$	−12.9768	−0.775514
$281$	7.62496	0.454867	0.227434	−	0.973794i	$-0.426967\pi$
$281$	7.62496	0.454867	0.227434	+	0.973794i	$0.426967\pi$
$282$	79.1329	4.71229
$283$	−0.708092	−0.0420917	−0.0210458	−	0.999779i	$-0.506700\pi$
$283$	−0.708092	−0.0420917	−0.0210458	+	0.999779i	$0.506700\pi$
$284$	−14.5503	−0.863402
$285$	−7.92850	−0.469644
$286$	−58.4673	−3.45724
$287$	−4.50506	−0.265925
$288$	−71.1100	−4.19020
$289$	18.4965	1.08803
$290$	−4.68219	−0.274947
$291$	−33.5064	−1.96418
$292$	6.73507	0.394140
$293$	−25.0737	−1.46482	−0.732411	−	0.680863i	$-0.761605\pi$
$293$	−25.0737	−1.46482	−0.732411	+	0.680863i	$0.761605\pi$
$294$	27.9762	1.63160
$295$	−11.1044	−0.646522
$296$	29.3125	1.70375
$297$	−25.3387	−1.47030
$298$	14.0010	0.811054
$299$	−4.81374	−0.278386
$300$	−60.3638	−3.48511
$301$	−16.6556	−0.960015
$302$	−17.4722	−1.00541
$303$	−27.4641	−1.57777
$304$	−36.7215	−2.10612
$305$	0.707880	0.0405331
$306$	−78.6170	−4.49423
$307$	6.50946	0.371514	0.185757	−	0.982596i	$-0.440526\pi$
$307$	6.50946	0.371514	0.185757	+	0.982596i	$0.440526\pi$
$308$	−41.8505	−2.38466
$309$	−41.4801	−2.35972
$310$	−11.3511	−0.644700
$311$	−33.8505	−1.91949	−0.959743	−	0.280878i	$-0.909374\pi$
$311$	−33.8505	−1.91949	−0.959743	+	0.280878i	$0.909374\pi$
$312$	110.639	6.26368
$313$	−27.5141	−1.55519	−0.777595	−	0.628766i	$-0.783560\pi$
$313$	−27.5141	−1.55519	−0.777595	+	0.628766i	$0.783560\pi$
$314$	41.4290	2.33798
$315$	7.91085	0.445726
$316$	81.6080	4.59081
$317$	−17.7608	−0.997545	−0.498773	−	0.866733i	$-0.666216\pi$
$317$	−17.7608	−0.997545	−0.498773	+	0.866733i	$0.666216\pi$
$318$	−61.4618	−3.44661
$319$	−9.13659	−0.511551
$320$	13.2468	0.740518
$321$	−3.57642	−0.199617
$322$	−4.80645	−0.267853
$323$	−18.9961	−1.05697
$324$	3.81943	0.212190
$325$	20.3314	1.12779
$326$	7.69274	0.426061
$327$	3.50506	0.193830
$328$	20.2883	1.12023
$329$	−19.0782	−1.05181
$330$	30.2030	1.66262
$331$	−12.1407	−0.667316	−0.333658	−	0.942694i	$-0.608283\pi$
$331$	−12.1407	−0.667316	−0.333658	+	0.942694i	$0.608283\pi$
$332$	18.8889	1.03666
$333$	−17.8693	−0.979231
$334$	−45.7126	−2.50128
$335$	−10.7196	−0.585674
$336$	58.7799	3.20671
$337$	−16.8070	−0.915535	−0.457768	−	0.889072i	$-0.651351\pi$
$337$	−16.8070	−0.915535	−0.457768	+	0.889072i	$0.651351\pi$
$338$	−27.0359	−1.47056
$339$	13.3185	0.723360
$340$	26.5849	1.44177
$341$	−22.1500	−1.19949
$342$	42.0721	2.27500
$343$	−19.4036	−1.04769
$344$	75.0078	4.04415
$345$	2.48668	0.133878
$346$	−8.62798	−0.463843
$347$	24.0087	1.28886	0.644428	−	0.764665i	$-0.277096\pi$
$347$	24.0087	1.28886	0.644428	+	0.764665i	$0.277096\pi$
$348$	28.5742	1.53174
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	20.3006	1.08511
$351$	−26.6911	−1.42466
$352$	65.4542	3.48872
$353$	28.1598	1.49879	0.749397	−	0.662120i	$-0.230343\pi$
$353$	28.1598	1.49879	0.749397	+	0.662120i	$0.230343\pi$
$354$	94.5308	5.02426
$355$	−2.53164	−0.134365
$356$	−38.4227	−2.03640
$357$	30.4069	1.60930
$358$	33.7432	1.78338
$359$	4.72116	0.249173	0.124587	−	0.992209i	$-0.460239\pi$
$359$	4.72116	0.249173	0.124587	+	0.992209i	$0.460239\pi$
$360$	−35.6261	−1.87766
$361$	−8.83419	−0.464957
$362$	8.02099	0.421574
$363$	27.8927	1.46399
$364$	−44.0842	−2.31064
$365$	1.17185	0.0613373
$366$	−6.02614	−0.314991
$367$	11.5392	0.602343	0.301171	−	0.953570i	$-0.402622\pi$
$367$	11.5392	0.602343	0.301171	+	0.953570i	$0.402622\pi$
$368$	11.5173	0.600379
$369$	−12.3680	−0.643853
$370$	8.42905	0.438205
$371$	14.8178	0.769304
$372$	69.2731	3.59164
$373$	−10.9890	−0.568990	−0.284495	−	0.958677i	$-0.591826\pi$
$373$	−10.9890	−0.568990	−0.284495	+	0.958677i	$0.591826\pi$
$374$	72.3641	3.74186
$375$	−22.9362	−1.18442
$376$	85.9174	4.43085
$377$	−9.62424	−0.495673
$378$	−26.6506	−1.37076
$379$	−29.0288	−1.49111	−0.745555	−	0.666444i	$-0.767815\pi$
$379$	−29.0288	−1.49111	−0.745555	+	0.666444i	$0.767815\pi$
$380$	−14.2270	−0.729828
$381$	42.7384	2.18956
$382$	−43.1358	−2.20702
$383$	−0.931188	−0.0475815	−0.0237907	−	0.999717i	$-0.507574\pi$
$383$	−0.931188	−0.0475815	−0.0237907	+	0.999717i	$0.507574\pi$
$384$	−31.9243	−1.62913
$385$	−7.28166	−0.371108
$386$	52.1626	2.65500
$387$	−45.7258	−2.32437
$388$	−60.1242	−3.05234
$389$	9.35924	0.474532	0.237266	−	0.971445i	$-0.423749\pi$
$389$	9.35924	0.474532	0.237266	+	0.971445i	$0.423749\pi$
$390$	31.8151	1.61102
$391$	5.95790	0.301304
$392$	30.3747	1.53416
$393$	28.8621	1.45590
$394$	−15.9045	−0.801256
$395$	14.1991	0.714436
$396$	−114.895	−5.77368
$397$	29.4330	1.47720	0.738601	−	0.674143i	$-0.235487\pi$
$397$	29.4330	1.47720	0.738601	+	0.674143i	$0.235487\pi$
$398$	17.5171	0.878051
$399$	−16.2723	−0.814636
$400$	−48.6447	−2.43223
$401$	35.4110	1.76834	0.884170	−	0.467165i	$-0.154725\pi$
$401$	35.4110	1.76834	0.884170	+	0.467165i	$0.154725\pi$
$402$	91.2553	4.55140
$403$	−23.3322	−1.16226
$404$	−49.2818	−2.45186
$405$	0.664550	0.0330218
$406$	−9.60965	−0.476919
$407$	16.4480	0.815299
$408$	−136.936	−6.77933
$409$	−2.79900	−0.138402	−0.0692008	−	0.997603i	$-0.522045\pi$
$409$	−2.79900	−0.138402	−0.0692008	+	0.997603i	$0.522045\pi$
$410$	5.83406	0.288124
$411$	54.9197	2.70899
$412$	−74.4321	−3.66701
$413$	−22.7904	−1.12144
$414$	−13.1954	−0.648520
$415$	3.28652	0.161329
$416$	68.9477	3.38044
$417$	−20.3473	−0.996410
$418$	−38.7259	−1.89415
$419$	6.40989	0.313144	0.156572	−	0.987667i	$-0.449956\pi$
$419$	6.40989	0.313144	0.156572	+	0.987667i	$0.449956\pi$
$420$	22.7730	1.11121
$421$	−8.37552	−0.408198	−0.204099	−	0.978950i	$-0.565426\pi$
$421$	−8.37552	−0.408198	−0.204099	+	0.978950i	$0.565426\pi$
$422$	−23.9392	−1.16534
$423$	−52.3764	−2.54663
$424$	−66.7314	−3.24076
$425$	−25.1639	−1.22063
$426$	21.5517	1.04418
$427$	1.45284	0.0703080
$428$	−6.41756	−0.310205
$429$	62.0824	2.99737
$430$	21.5691	1.04016
$431$	−20.2696	−0.976354	−0.488177	−	0.872745i	$-0.662338\pi$
$431$	−20.2696	−0.976354	−0.488177	+	0.872745i	$0.662338\pi$
$432$	63.8606	3.07249
$433$	−13.0949	−0.629302	−0.314651	−	0.949207i	$-0.601888\pi$
$433$	−13.0949	−0.629302	−0.314651	+	0.949207i	$0.601888\pi$
$434$	−23.2969	−1.11829
$435$	4.97169	0.238374
$436$	6.28952	0.301213
$437$	−3.18839	−0.152521
$438$	−9.97586	−0.476665
$439$	−4.78435	−0.228345	−0.114172	−	0.993461i	$-0.536422\pi$
$439$	−4.78435	−0.228345	−0.114172	+	0.993461i	$0.536422\pi$
$440$	32.7925	1.56332
$441$	−18.5168	−0.881755
$442$	76.2264	3.62572
$443$	−2.77088	−0.131649	−0.0658243	−	0.997831i	$-0.520968\pi$
$443$	−2.77088	−0.131649	−0.0658243	+	0.997831i	$0.520968\pi$
$444$	−51.4404	−2.44125
$445$	−6.68524	−0.316911
$446$	−62.4934	−2.95915
$447$	−14.8667	−0.703168
$448$	27.1875	1.28449
$449$	−30.0400	−1.41768	−0.708838	−	0.705371i	$-0.750780\pi$
$449$	−30.0400	−1.41768	−0.708838	+	0.705371i	$0.750780\pi$
$450$	55.7326	2.62726
$451$	11.3843	0.536066
$452$	23.8988	1.12410
$453$	18.5525	0.871671
$454$	62.8278	2.94865
$455$	−7.67030	−0.359589
$456$	73.2816	3.43173
$457$	−26.7575	−1.25166	−0.625832	−	0.779958i	$-0.715240\pi$
$457$	−26.7575	−1.25166	−0.625832	+	0.779958i	$0.715240\pi$
$458$	48.8925	2.28460
$459$	33.0351	1.54195
$460$	4.46212	0.208048
$461$	22.1126	1.02988	0.514942	−	0.857225i	$-0.327813\pi$
$461$	22.1126	1.02988	0.514942	+	0.857225i	$0.327813\pi$
$462$	61.9883	2.88396
$463$	29.6780	1.37926	0.689628	−	0.724164i	$-0.257774\pi$
$463$	29.6780	1.37926	0.689628	+	0.724164i	$0.257774\pi$
$464$	23.0268	1.06899
$465$	12.0530	0.558943
$466$	−52.4652	−2.43040
$467$	31.0158	1.43524	0.717620	−	0.696435i	$-0.245232\pi$
$467$	31.0158	1.43524	0.717620	+	0.696435i	$0.245232\pi$
$468$	−121.027	−5.59448
$469$	−22.0007	−1.01590
$470$	24.7063	1.13962
$471$	−43.9906	−2.02698
$472$	102.636	4.72418
$473$	42.0889	1.93525
$474$	−120.876	−5.55204
$475$	13.4666	0.617888
$476$	54.5624	2.50086
$477$	40.6803	1.86263
$478$	−46.6168	−2.13220
$479$	29.8548	1.36410	0.682050	−	0.731305i	$-0.261089\pi$
$479$	29.8548	1.36410	0.682050	+	0.731305i	$0.261089\pi$
$480$	−35.6170	−1.62569
$481$	17.3259	0.789994
$482$	−13.5361	−0.616551
$483$	5.10363	0.232223
$484$	50.0510	2.27504
$485$	−10.4611	−0.475015
$486$	38.5541	1.74885
$487$	5.94216	0.269265	0.134633	−	0.990896i	$-0.457015\pi$
$487$	5.94216	0.269265	0.134633	+	0.990896i	$0.457015\pi$
$488$	−6.54280	−0.296179
$489$	−8.16838	−0.369387
$490$	8.73451	0.394585
$491$	31.7580	1.43322	0.716610	−	0.697474i	$-0.245693\pi$
$491$	31.7580	1.43322	0.716610	+	0.697474i	$0.245693\pi$
$492$	−35.6039	−1.60515
$493$	11.9118	0.536479
$494$	−40.7928	−1.83535
$495$	−19.9908	−0.898519
$496$	55.8243	2.50659
$497$	−5.19589	−0.233068
$498$	−27.9779	−1.25372
$499$	−37.9184	−1.69746	−0.848731	−	0.528824i	$-0.822633\pi$
$499$	−37.9184	−1.69746	−0.848731	+	0.528824i	$0.822633\pi$
$500$	−41.1570	−1.84059
$501$	48.5391	2.16857
$502$	48.6293	2.17043
$503$	12.4562	0.555395	0.277698	−	0.960669i	$-0.410429\pi$
$503$	12.4562	0.555395	0.277698	+	0.960669i	$0.410429\pi$
$504$	−73.1185	−3.25696
$505$	−8.57464	−0.381566
$506$	12.1459	0.539952
$507$	28.7075	1.27495
$508$	76.6902	3.40258
$509$	−7.33031	−0.324910	−0.162455	−	0.986716i	$-0.551941\pi$
$509$	−7.33031	−0.324910	−0.162455	+	0.986716i	$0.551941\pi$
$510$	−39.3770	−1.74364
$511$	2.40508	0.106395
$512$	22.6310	1.00016
$513$	−17.6789	−0.780541
$514$	−16.8429	−0.742906
$515$	−12.9506	−0.570671
$516$	−131.631	−5.79473
$517$	48.2106	2.12030
$518$	17.2997	0.760103
$519$	9.16145	0.402143
$520$	34.5428	1.51480
$521$	27.4840	1.20410	0.602048	−	0.798460i	$-0.294352\pi$
$521$	27.4840	1.20410	0.602048	+	0.798460i	$0.294352\pi$
$522$	−26.3820	−1.15471
$523$	18.0594	0.789682	0.394841	−	0.918749i	$-0.370800\pi$
$523$	18.0594	0.789682	0.394841	+	0.918749i	$0.370800\pi$
$524$	51.7904	2.26247
$525$	−21.5558	−0.940773
$526$	10.4977	0.457722
$527$	28.8780	1.25794
$528$	−148.537	−6.46425
$529$	1.00000	0.0434783
$530$	−19.1892	−0.833524
$531$	−62.5680	−2.71522
$532$	−29.1992	−1.26595
$533$	11.9919	0.519428
$534$	56.9110	2.46278
$535$	−1.11660	−0.0482750
$536$	99.0791	4.27957
$537$	−35.8296	−1.54616
$538$	−67.9714	−2.93045
$539$	17.0441	0.734141
$540$	24.7414	1.06470
$541$	−4.40562	−0.189412	−0.0947061	−	0.995505i	$-0.530191\pi$
$541$	−4.40562	−0.189412	−0.0947061	+	0.995505i	$0.530191\pi$
$542$	6.11803	0.262792
$543$	−8.51693	−0.365497
$544$	−85.3355	−3.65873
$545$	1.09433	0.0468757
$546$	65.2968	2.79444
$547$	8.03383	0.343502	0.171751	−	0.985140i	$-0.445058\pi$
$547$	8.03383	0.343502	0.171751	+	0.985140i	$0.445058\pi$
$548$	98.5484	4.20978
$549$	3.98858	0.170228
$550$	−51.2998	−2.18743
$551$	−6.37462	−0.271568
$552$	−22.9839	−0.978261
$553$	29.1421	1.23925
$554$	34.1246	1.44982
$555$	−8.95022	−0.379916
$556$	−36.5113	−1.54842
$557$	−11.2669	−0.477392	−0.238696	−	0.971094i	$-0.576720\pi$
$557$	−11.2669	−0.477392	−0.238696	+	0.971094i	$0.576720\pi$
$558$	−63.9583	−2.70757
$559$	44.3353	1.87518
$560$	18.3518	0.775506
$561$	−76.8384	−3.24412
$562$	−20.2660	−0.854869
$563$	18.8644	0.795041	0.397521	−	0.917593i	$-0.369871\pi$
$563$	18.8644	0.795041	0.397521	+	0.917593i	$0.369871\pi$
$564$	−150.776	−6.34883
$565$	4.15819	0.174936
$566$	1.88200	0.0791063
$567$	1.36391	0.0572789
$568$	23.3994	0.981818
$569$	−11.8301	−0.495945	−0.247972	−	0.968767i	$-0.579764\pi$
$569$	−11.8301	−0.495945	−0.247972	+	0.968767i	$0.579764\pi$
$570$	21.0727	0.882640
$571$	−22.4240	−0.938414	−0.469207	−	0.883088i	$-0.655460\pi$
$571$	−22.4240	−0.938414	−0.469207	+	0.883088i	$0.655460\pi$
$572$	111.401	4.65791
$573$	45.8029	1.91344
$574$	11.9737	0.499775
$575$	−4.22363	−0.176137
$576$	74.6395	3.10998
$577$	−2.37439	−0.0988470	−0.0494235	−	0.998778i	$-0.515738\pi$
$577$	−2.37439	−0.0988470	−0.0494235	+	0.998778i	$0.515738\pi$
$578$	−49.1609	−2.04482
$579$	−55.3878	−2.30184
$580$	8.92123	0.370434
$581$	6.74520	0.279838
$582$	89.0549	3.69144
$583$	−37.4448	−1.55080
$584$	−10.8312	−0.448196
$585$	−21.0577	−0.870631
$586$	66.6420	2.75296
$587$	−14.8173	−0.611575	−0.305787	−	0.952100i	$-0.598920\pi$
$587$	−14.8173	−0.611575	−0.305787	+	0.952100i	$0.598920\pi$
$588$	−53.3046	−2.19824
$589$	−15.4541	−0.636776
$590$	29.5137	1.21506
$591$	16.8879	0.694674
$592$	−41.4537	−1.70374
$593$	28.4322	1.16757	0.583786	−	0.811908i	$-0.301571\pi$
$593$	28.4322	1.16757	0.583786	+	0.811908i	$0.301571\pi$
$594$	67.3463	2.76325
$595$	9.49341	0.389192
$596$	−26.6768	−1.09273
$597$	−18.6002	−0.761254
$598$	12.7942	0.523193
$599$	−10.1292	−0.413868	−0.206934	−	0.978355i	$-0.566349\pi$
$599$	−10.1292	−0.413868	−0.206934	+	0.978355i	$0.566349\pi$
$600$	97.0755	3.96309
$601$	−39.2844	−1.60245	−0.801223	−	0.598366i	$-0.795817\pi$
$601$	−39.2844	−1.60245	−0.801223	+	0.598366i	$0.795817\pi$
$602$	44.2681	1.80423
$603$	−60.4000	−2.45968
$604$	33.2907	1.35458
$605$	8.70847	0.354050
$606$	72.9953	2.96523
$607$	−4.53186	−0.183943	−0.0919713	−	0.995762i	$-0.529317\pi$
$607$	−4.53186	−0.183943	−0.0919713	+	0.995762i	$0.529317\pi$
$608$	45.6676	1.85206
$609$	10.2038	0.413480
$610$	−1.88144	−0.0761771
$611$	50.7838	2.05449
$612$	149.793	6.05504
$613$	−18.9005	−0.763383	−0.381691	−	0.924290i	$-0.624658\pi$
$613$	−18.9005	−0.763383	−0.381691	+	0.924290i	$0.624658\pi$
$614$	−17.3011	−0.698217
$615$	−6.19479	−0.249798
$616$	67.3029	2.71171
$617$	2.50990	0.101045	0.0505224	−	0.998723i	$-0.483911\pi$
$617$	2.50990	0.101045	0.0505224	+	0.998723i	$0.483911\pi$
$618$	110.248	4.43481
$619$	45.3878	1.82429	0.912146	−	0.409866i	$-0.134425\pi$
$619$	45.3878	1.82429	0.912146	+	0.409866i	$0.134425\pi$
$620$	21.6279	0.868599
$621$	5.54477	0.222504
$622$	89.9695	3.60745
$623$	−13.7207	−0.549707
$624$	−156.465	−6.26362
$625$	13.9572	0.558286
$626$	73.1283	2.92279
$627$	41.1203	1.64219
$628$	−78.9371	−3.14993
$629$	−21.4440	−0.855029
$630$	−21.0258	−0.837689
$631$	−4.34602	−0.173012	−0.0865062	−	0.996251i	$-0.527570\pi$
$631$	−4.34602	−0.173012	−0.0865062	+	0.996251i	$0.527570\pi$
$632$	−131.240	−5.22044
$633$	25.4194	1.01033
$634$	47.2054	1.87477
$635$	13.3435	0.529520
$636$	117.107	4.64358
$637$	17.9538	0.711355
$638$	24.2836	0.961399
$639$	−14.2646	−0.564299
$640$	−9.96717	−0.393987
$641$	8.31387	0.328378	0.164189	−	0.986429i	$-0.447499\pi$
$641$	8.31387	0.328378	0.164189	+	0.986429i	$0.447499\pi$
$642$	9.50558	0.375155
$643$	38.9541	1.53620	0.768100	−	0.640330i	$-0.221202\pi$
$643$	38.9541	1.53620	0.768100	+	0.640330i	$0.221202\pi$
$644$	9.15799	0.360876
$645$	−22.9027	−0.901795
$646$	50.4886	1.98645
$647$	−4.50676	−0.177179	−0.0885895	−	0.996068i	$-0.528236\pi$
$647$	−4.50676	−0.177179	−0.0885895	+	0.996068i	$0.528236\pi$
$648$	−6.14231	−0.241293
$649$	57.5916	2.26067
$650$	−54.0379	−2.11954
$651$	24.7373	0.969532
$652$	−14.6574	−0.574028
$653$	−39.8632	−1.55997	−0.779984	−	0.625799i	$-0.784773\pi$
$653$	−39.8632	−1.55997	−0.779984	+	0.625799i	$0.784773\pi$
$654$	−9.31592	−0.364281
$655$	9.01112	0.352093
$656$	−28.6917	−1.12022
$657$	6.60282	0.257601
$658$	50.7068	1.97676
$659$	34.0948	1.32815	0.664073	−	0.747668i	$-0.268827\pi$
$659$	34.0948	1.32815	0.664073	+	0.747668i	$0.268827\pi$
$660$	−57.5476	−2.24004
$661$	−27.0548	−1.05231	−0.526156	−	0.850388i	$-0.676367\pi$
$661$	−27.0548	−1.05231	−0.526156	+	0.850388i	$0.676367\pi$
$662$	32.2682	1.25414
$663$	−80.9395	−3.14343
$664$	−30.3766	−1.17884
$665$	−5.08043	−0.197011
$666$	47.4938	1.84035
$667$	1.99933	0.0774142
$668$	87.0989	3.36996
$669$	66.3574	2.56552
$670$	28.4910	1.10070
$671$	−3.67134	−0.141731
$672$	−73.0998	−2.81988
$673$	6.32755	0.243909	0.121955	−	0.992536i	$-0.461084\pi$
$673$	6.32755	0.243909	0.121955	+	0.992536i	$0.461084\pi$
$674$	44.6704	1.72064
$675$	−23.4190	−0.901399
$676$	51.5130	1.98127
$677$	−28.3479	−1.08950	−0.544749	−	0.838599i	$-0.683375\pi$
$677$	−28.3479	−1.08950	−0.544749	+	0.838599i	$0.683375\pi$
$678$	−35.3984	−1.35947
$679$	−21.4703	−0.823953
$680$	−42.7531	−1.63951
$681$	−66.7124	−2.55643
$682$	58.8713	2.25430
$683$	35.2807	1.34998	0.674990	−	0.737827i	$-0.264148\pi$
$683$	35.2807	1.34998	0.674990	+	0.737827i	$0.264148\pi$
$684$	−80.1624	−3.06509
$685$	17.1466	0.655139
$686$	51.5717	1.96902
$687$	−51.9156	−1.98070
$688$	−106.076	−4.04411
$689$	−39.4433	−1.50267
$690$	−6.60922	−0.251609
$691$	−23.2853	−0.885816	−0.442908	−	0.896567i	$-0.646053\pi$
$691$	−23.2853	−0.885816	−0.442908	+	0.896567i	$0.646053\pi$
$692$	16.4394	0.624931
$693$	−41.0288	−1.55855
$694$	−63.8115	−2.42225
$695$	−6.35267	−0.240971
$696$	−45.9523	−1.74182
$697$	−14.8422	−0.562189
$698$	−2.65785	−0.100601
$699$	55.7091	2.10711
$700$	−38.6799	−1.46196
$701$	−15.3020	−0.577948	−0.288974	−	0.957337i	$-0.593314\pi$
$701$	−15.3020	−0.577948	−0.288974	+	0.957337i	$0.593314\pi$
$702$	70.9408	2.67749
$703$	11.4758	0.432819
$704$	−68.7030	−2.58934
$705$	−26.2339	−0.988025
$706$	−74.8444	−2.81681
$707$	−17.5985	−0.661858
$708$	−180.115	−6.76913
$709$	0.439905	0.0165210	0.00826050	−	0.999966i	$-0.497371\pi$
$709$	0.439905	0.0165210	0.00826050	+	0.999966i	$0.497371\pi$
$710$	6.72870	0.252524
$711$	80.0056	3.00045
$712$	61.7903	2.31569
$713$	4.84701	0.181522
$714$	−80.8168	−3.02449
$715$	19.3829	0.724879
$716$	−64.2929	−2.40274
$717$	49.4991	1.84858
$718$	−12.5481	−0.468292
$719$	−49.6483	−1.85157	−0.925784	−	0.378054i	$-0.876594\pi$
$719$	−49.6483	−1.85157	−0.925784	+	0.378054i	$0.876594\pi$
$720$	50.3824	1.87764
$721$	−26.5796	−0.989876
$722$	23.4799	0.873832
$723$	14.3730	0.534538
$724$	−15.2829	−0.567983
$725$	−8.44440	−0.313617
$726$	−74.1346	−2.75139
$727$	36.6476	1.35918	0.679591	−	0.733591i	$-0.262157\pi$
$727$	36.6476	1.35918	0.679591	+	0.733591i	$0.262157\pi$
$728$	70.8951	2.62755
$729$	−43.2006	−1.60002
$730$	−3.11459	−0.115276
$731$	−54.8732	−2.02956
$732$	11.4819	0.424385
$733$	7.44768	0.275086	0.137543	−	0.990496i	$-0.456079\pi$
$733$	7.44768	0.275086	0.137543	+	0.990496i	$0.456079\pi$
$734$	−30.6695	−1.13203
$735$	−9.27456	−0.342097
$736$	−14.3231	−0.527956
$737$	55.5960	2.04791
$738$	32.8723	1.21004
$739$	−21.0408	−0.773999	−0.387000	−	0.922080i	$-0.626489\pi$
$739$	−21.0408	−0.773999	−0.387000	+	0.922080i	$0.626489\pi$
$740$	−16.0603	−0.590390
$741$	43.3150	1.59122
$742$	−39.3836	−1.44582
$743$	−33.3899	−1.22496	−0.612478	−	0.790487i	$-0.709827\pi$
$743$	−33.3899	−1.22496	−0.612478	+	0.790487i	$0.709827\pi$
$744$	−111.403	−4.08424
$745$	−4.64156	−0.170053
$746$	29.2072	1.06935
$747$	18.5180	0.677538
$748$	−137.879	−5.04137
$749$	−2.29170	−0.0837370
$750$	60.9610	2.22598
$751$	33.1081	1.20813	0.604066	−	0.796934i	$-0.293546\pi$
$751$	33.1081	1.20813	0.604066	+	0.796934i	$0.293546\pi$
$752$	−121.504	−4.43081
$753$	−51.6361	−1.88172
$754$	25.5797	0.931559
$755$	5.79231	0.210804
$756$	50.7789	1.84681
$757$	−14.2088	−0.516428	−0.258214	−	0.966088i	$-0.583134\pi$
$757$	−14.2088	−0.516428	−0.258214	+	0.966088i	$0.583134\pi$
$758$	77.1541	2.80236
$759$	−12.8969	−0.468128
$760$	22.8794	0.829925
$761$	10.8202	0.392232	0.196116	−	0.980581i	$-0.437167\pi$
$761$	10.8202	0.392232	0.196116	+	0.980581i	$0.437167\pi$
$762$	−113.592	−4.11501
$763$	2.24598	0.0813098
$764$	82.1890	2.97350
$765$	26.0629	0.942305
$766$	2.47495	0.0894237
$767$	60.6654	2.19050
$768$	−0.00755820	−0.000272733 0
$769$	49.5048	1.78519	0.892594	−	0.450862i	$-0.148883\pi$
$769$	49.5048	1.78519	0.892594	+	0.450862i	$0.148883\pi$
$770$	19.3535	0.697452
$771$	17.8843	0.644086
$772$	−99.3883	−3.57706
$773$	7.03383	0.252989	0.126495	−	0.991967i	$-0.459627\pi$
$773$	7.03383	0.252989	0.126495	+	0.991967i	$0.459627\pi$
$774$	121.532	4.36838
$775$	−20.4719	−0.735374
$776$	96.6901	3.47097
$777$	−18.3693	−0.658995
$778$	−24.8754	−0.891827
$779$	7.94286	0.284583
$780$	−60.6191	−2.17051
$781$	13.1301	0.469830
$782$	−15.8352	−0.566264
$783$	11.0858	0.396174
$784$	−42.9559	−1.53414
$785$	−13.7344	−0.490202
$786$	−76.7111	−2.73619
$787$	15.2611	0.543999	0.272000	−	0.962297i	$-0.412315\pi$
$787$	15.2611	0.543999	0.272000	+	0.962297i	$0.412315\pi$
$788$	30.3037	1.07953
$789$	−11.1468	−0.396836
$790$	−37.7391	−1.34270
$791$	8.53421	0.303442
$792$	184.771	6.56555
$793$	−3.86729	−0.137332
$794$	−78.2285	−2.77623
$795$	20.3756	0.722649
$796$	−33.3763	−1.18299
$797$	−32.0323	−1.13464	−0.567320	−	0.823497i	$-0.692020\pi$
$797$	−32.0323	−1.13464	−0.567320	+	0.823497i	$0.692020\pi$
$798$	43.2494	1.53101
$799$	−62.8543	−2.22363
$800$	60.4954	2.13883
$801$	−37.6682	−1.33094
$802$	−94.1169	−3.32338
$803$	−6.07766	−0.214476
$804$	−173.874	−6.13206
$805$	1.59342	0.0561606
$806$	62.0135	2.18433
$807$	72.1741	2.54065
$808$	79.2537	2.78813
$809$	16.4248	0.577467	0.288733	−	0.957410i	$-0.406766\pi$
$809$	16.4248	0.577467	0.288733	+	0.957410i	$0.406766\pi$
$810$	−1.76627	−0.0620605
$811$	1.34515	0.0472346	0.0236173	−	0.999721i	$-0.492482\pi$
$811$	1.34515	0.0472346	0.0236173	+	0.999721i	$0.492482\pi$
$812$	18.3098	0.642548
$813$	−6.49632	−0.227836
$814$	−43.7163	−1.53226
$815$	−2.55027	−0.0893321
$816$	193.654	6.77926
$817$	29.3656	1.02737
$818$	7.43931	0.260109
$819$	−43.2186	−1.51018
$820$	−11.1160	−0.388187
$821$	−49.6277	−1.73202	−0.866009	−	0.500028i	$-0.833323\pi$
$821$	−49.6277	−1.73202	−0.866009	+	0.500028i	$0.833323\pi$
$822$	−145.968	−5.09122
$823$	0.943082	0.0328738	0.0164369	−	0.999865i	$-0.494768\pi$
$823$	0.943082	0.0328738	0.0164369	+	0.999865i	$0.494768\pi$
$824$	119.700	4.16994
$825$	54.4717	1.89646
$826$	60.5735	2.10762
$827$	−4.02759	−0.140053	−0.0700266	−	0.997545i	$-0.522308\pi$
$827$	−4.02759	−0.140053	−0.0700266	+	0.997545i	$0.522308\pi$
$828$	25.1420	0.873745
$829$	45.1785	1.56911	0.784557	−	0.620057i	$-0.212890\pi$
$829$	45.1785	1.56911	0.784557	+	0.620057i	$0.212890\pi$
$830$	−8.73505	−0.303198
$831$	−36.2346	−1.25696
$832$	−72.3699	−2.50897
$833$	−22.2211	−0.769916
$834$	54.0799	1.87263
$835$	15.1545	0.524443
$836$	73.7866	2.55196
$837$	26.8755	0.928954
$838$	−17.0365	−0.588516
$839$	1.28178	0.0442521	0.0221261	−	0.999755i	$-0.492956\pi$
$839$	1.28178	0.0442521	0.0221261	+	0.999755i	$0.492956\pi$
$840$	−36.6230	−1.26361
$841$	−25.0027	−0.862162
$842$	22.2609	0.767160
$843$	21.5190	0.741155
$844$	45.6127	1.57005
$845$	8.96285	0.308332
$846$	139.209	4.78609
$847$	17.8731	0.614128
$848$	94.3714	3.24073
$849$	−1.99836	−0.0685837
$850$	66.8818	2.29403
$851$	−3.59926	−0.123381
$852$	−41.0636	−1.40682
$853$	−45.3448	−1.55257	−0.776287	−	0.630379i	$-0.782899\pi$
$853$	−45.3448	−1.55257	−0.776287	+	0.630379i	$0.782899\pi$
$854$	−3.86143	−0.132136
$855$	−13.9476	−0.476999
$856$	10.3206	0.352749
$857$	−53.4020	−1.82418	−0.912088	−	0.409994i	$-0.865531\pi$
$857$	−53.4020	−1.82418	−0.912088	+	0.409994i	$0.865531\pi$
$858$	−165.005	−5.63319
$859$	11.9030	0.406124	0.203062	−	0.979166i	$-0.434911\pi$
$859$	11.9030	0.406124	0.203062	+	0.979166i	$0.434911\pi$
$860$	−41.0969	−1.40139
$861$	−12.7141	−0.433295
$862$	53.8736	1.83494
$863$	22.0870	0.751849	0.375924	−	0.926650i	$-0.377325\pi$
$863$	22.0870	0.751849	0.375924	+	0.926650i	$0.377325\pi$
$864$	−79.4182	−2.70186
$865$	2.86032	0.0972538
$866$	34.8043	1.18270
$867$	52.2005	1.77282
$868$	44.3889	1.50666
$869$	−73.6423	−2.49814
$870$	−13.2140	−0.447996
$871$	58.5633	1.98434
$872$	−10.1146	−0.342525
$873$	−58.9436	−1.99494
$874$	8.47424	0.286645
$875$	−14.6971	−0.496852
$876$	19.0076	0.642207
$877$	−40.3167	−1.36140	−0.680700	−	0.732563i	$-0.738324\pi$
$877$	−40.3167	−1.36140	−0.680700	+	0.732563i	$0.738324\pi$
$878$	12.7161	0.429146
$879$	−70.7625	−2.38676
$880$	−46.3752	−1.56331
$881$	9.41956	0.317353	0.158676	−	0.987331i	$-0.449277\pi$
$881$	9.41956	0.317353	0.158676	+	0.987331i	$0.449277\pi$
$882$	49.2149	1.65715
$883$	−28.9414	−0.973955	−0.486977	−	0.873415i	$-0.661901\pi$
$883$	−28.9414	−0.973955	−0.486977	+	0.873415i	$0.661901\pi$
$884$	−145.238	−4.88490
$885$	−31.3386	−1.05343
$886$	7.36457	0.247418
$887$	−43.6765	−1.46651	−0.733257	−	0.679951i	$-0.762001\pi$
$887$	−43.6765	−1.46651	−0.733257	+	0.679951i	$0.762001\pi$
$888$	82.7252	2.77607
$889$	27.3859	0.918495
$890$	17.7683	0.595596
$891$	−3.44662	−0.115466
$892$	119.072	3.98683
$893$	33.6367	1.12561
$894$	39.5133	1.32152
$895$	−11.1864	−0.373921
$896$	−20.4565	−0.683403
$897$	−13.5853	−0.453598
$898$	79.8418	2.66435
$899$	9.69074	0.323204
$900$	−106.190	−3.53968
$901$	48.8184	1.62638
$902$	−30.2577	−1.00747
$903$	−47.0053	−1.56424
$904$	−38.4334	−1.27827
$905$	−2.65909	−0.0883913
$906$	−49.3096	−1.63820
$907$	52.8354	1.75437	0.877185	−	0.480153i	$-0.159419\pi$
$907$	52.8354	1.75437	0.877185	+	0.480153i	$0.159419\pi$
$908$	−119.709	−3.97269
$909$	−48.3141	−1.60248
$910$	20.3865	0.675805
$911$	13.8361	0.458412	0.229206	−	0.973378i	$-0.426387\pi$
$911$	13.8361	0.458412	0.229206	+	0.973378i	$0.426387\pi$
$912$	−103.635	−3.43169
$913$	−17.0452	−0.564112
$914$	71.1174	2.35235
$915$	1.99777	0.0660441
$916$	−93.1577	−3.07802
$917$	18.4943	0.610735
$918$	−87.8023	−2.89791
$919$	17.4977	0.577196	0.288598	−	0.957450i	$-0.406811\pi$
$919$	17.4977	0.577196	0.288598	+	0.957450i	$0.406811\pi$
$920$	−7.17587	−0.236581
$921$	18.3709	0.605341
$922$	−58.7718	−1.93555
$923$	13.8308	0.455248
$924$	−118.110	−3.88553
$925$	15.2019	0.499837
$926$	−78.8796	−2.59215
$927$	−72.9707	−2.39667
$928$	−28.6365	−0.940040
$929$	−28.5820	−0.937746	−0.468873	−	0.883266i	$-0.655340\pi$
$929$	−28.5820	−0.937746	−0.468873	+	0.883266i	$0.655340\pi$
$930$	−32.0349	−1.05047
$931$	11.8917	0.389735
$932$	99.9649	3.27446
$933$	−95.5323	−3.12759
$934$	−82.4352	−2.69736
$935$	−23.9899	−0.784554
$936$	194.633	6.36177
$937$	−11.8650	−0.387613	−0.193806	−	0.981040i	$-0.562083\pi$
$937$	−11.8650	−0.387613	−0.193806	+	0.981040i	$0.562083\pi$
$938$	58.4746	1.90926
$939$	−77.6498	−2.53401
$940$	−47.0743	−1.53539
$941$	24.1981	0.788835	0.394418	−	0.918931i	$-0.370946\pi$
$941$	24.1981	0.788835	0.394418	+	0.918931i	$0.370946\pi$
$942$	116.920	3.80947
$943$	−2.49119	−0.0811242
$944$	−145.147	−4.72414
$945$	8.83513	0.287407
$946$	−111.866	−3.63707
$947$	−27.6118	−0.897262	−0.448631	−	0.893717i	$-0.648088\pi$
$947$	−27.6118	−0.897262	−0.448631	+	0.893717i	$0.648088\pi$
$948$	230.313	7.48021
$949$	−6.40204	−0.207819
$950$	−35.7920	−1.16125
$951$	−50.1242	−1.62539
$952$	−87.7458	−2.84386
$953$	−57.6229	−1.86659	−0.933295	−	0.359112i	$-0.883080\pi$
$953$	−57.6229	−1.86659	−0.933295	+	0.359112i	$0.883080\pi$
$954$	−108.122	−3.50058
$955$	14.3002	0.462745
$956$	88.8216	2.87270
$957$	−25.7851	−0.833514
$958$	−79.3494	−2.56366
$959$	35.1915	1.13639
$960$	37.3848	1.20659
$961$	−7.50653	−0.242146
$962$	−46.0496	−1.48470
$963$	−6.29155	−0.202742
$964$	25.7910	0.830673
$965$	−17.2928	−0.556674
$966$	−13.5647	−0.436436
$967$	−18.5612	−0.596887	−0.298443	−	0.954427i	$-0.596467\pi$
$967$	−18.5612	−0.596887	−0.298443	+	0.954427i	$0.596467\pi$
$968$	−80.4907	−2.58707
$969$	−53.6104	−1.72221
$970$	27.8041	0.892734
$971$	21.0487	0.675485	0.337742	−	0.941239i	$-0.390337\pi$
$971$	21.0487	0.675485	0.337742	+	0.941239i	$0.390337\pi$
$972$	−73.4594	−2.35621
$973$	−13.0381	−0.417983
$974$	−15.7934	−0.506052
$975$	57.3790	1.83760
$976$	9.25282	0.296176
$977$	−27.9524	−0.894275	−0.447138	−	0.894465i	$-0.647557\pi$
$977$	−27.9524	−0.894275	−0.447138	+	0.894465i	$0.647557\pi$
$978$	21.7103	0.694219
$979$	34.6723	1.10813
$980$	−16.6424	−0.531620
$981$	6.16602	0.196866
$982$	−84.4080	−2.69357
$983$	2.03670	0.0649608	0.0324804	−	0.999472i	$-0.489659\pi$
$983$	2.03670	0.0649608	0.0324804	+	0.999472i	$0.489659\pi$
$984$	57.2572	1.82529
$985$	5.27260	0.167999
$986$	−31.6597	−1.00825
$987$	−53.8420	−1.71381
$988$	77.7248	2.47276
$989$	−9.21016	−0.292866
$990$	53.1324	1.68866
$991$	24.5138	0.778707	0.389354	−	0.921088i	$-0.372698\pi$
$991$	24.5138	0.778707	0.389354	+	0.921088i	$0.372698\pi$
$992$	−69.4241	−2.20422
$993$	−34.2634	−1.08732
$994$	13.8099	0.438023
$995$	−5.80720	−0.184101
$996$	53.3079	1.68912
$997$	28.6408	0.907063	0.453532	−	0.891240i	$-0.350164\pi$
$997$	28.6408	0.907063	0.453532	+	0.891240i	$0.350164\pi$
$998$	100.781	3.19018
$999$	−19.9571	−0.631414

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.c.1.6	✓	143

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.c.1.6	✓	143	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65785 q^{2} +2.82218 q^{3} +5.06415 q^{4} +0.881121 q^{5} -7.50092 q^{6} +1.80840 q^{7} -8.14403 q^{8} +4.96471 q^{9} +O(q^{10})\)	\(q-2.65785 q^{2} +2.82218 q^{3} +5.06415 q^{4} +0.881121 q^{5} -7.50092 q^{6} +1.80840 q^{7} -8.14403 q^{8} +4.96471 q^{9} -2.34188 q^{10} -4.56984 q^{11} +14.2919 q^{12} -4.81374 q^{13} -4.80645 q^{14} +2.48668 q^{15} +11.5173 q^{16} +5.95790 q^{17} -13.1954 q^{18} -3.18839 q^{19} +4.46212 q^{20} +5.10363 q^{21} +12.1459 q^{22} +1.00000 q^{23} -22.9839 q^{24} -4.22363 q^{25} +12.7942 q^{26} +5.54477 q^{27} +9.15799 q^{28} +1.99933 q^{29} -6.60922 q^{30} +4.84701 q^{31} -14.3231 q^{32} -12.8969 q^{33} -15.8352 q^{34} +1.59342 q^{35} +25.1420 q^{36} -3.59926 q^{37} +8.47424 q^{38} -13.5853 q^{39} -7.17587 q^{40} -2.49119 q^{41} -13.5647 q^{42} -9.21016 q^{43} -23.1423 q^{44} +4.37451 q^{45} -2.65785 q^{46} -10.5497 q^{47} +32.5038 q^{48} -3.72969 q^{49} +11.2257 q^{50} +16.8143 q^{51} -24.3775 q^{52} +8.19390 q^{53} -14.7371 q^{54} -4.02658 q^{55} -14.7276 q^{56} -8.99821 q^{57} -5.31390 q^{58} -12.6026 q^{59} +12.5929 q^{60} +0.803386 q^{61} -12.8826 q^{62} +8.97817 q^{63} +15.0340 q^{64} -4.24149 q^{65} +34.2780 q^{66} -12.1659 q^{67} +30.1716 q^{68} +2.82218 q^{69} -4.23506 q^{70} -2.87320 q^{71} -40.4327 q^{72} +1.32995 q^{73} +9.56628 q^{74} -11.9198 q^{75} -16.1465 q^{76} -8.26409 q^{77} +36.1075 q^{78} +16.1149 q^{79} +10.1481 q^{80} +0.754210 q^{81} +6.62119 q^{82} +3.72993 q^{83} +25.8455 q^{84} +5.24962 q^{85} +24.4792 q^{86} +5.64246 q^{87} +37.2169 q^{88} -7.58720 q^{89} -11.6268 q^{90} -8.70516 q^{91} +5.06415 q^{92} +13.6791 q^{93} +28.0396 q^{94} -2.80935 q^{95} -40.4224 q^{96} -11.8725 q^{97} +9.91295 q^{98} -22.6879 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * q^99

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