LMFDB - Embedded newform 4007.2.a.a.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4007,2,Mod(1,4007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4007.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:	$31.9960560899$
Analytic rank:	$1$
Dimension:	$139$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	4007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41992 q^{2} +2.90998 q^{3} +3.85601 q^{4} -2.04833 q^{5} -7.04192 q^{6} +0.763772 q^{7} -4.49140 q^{8} +5.46800 q^{9} +O(q^{10})$	\(q-2.41992 q^{2} +2.90998 q^{3} +3.85601 q^{4} -2.04833 q^{5} -7.04192 q^{6} +0.763772 q^{7} -4.49140 q^{8} +5.46800 q^{9} +4.95680 q^{10} +0.863449 q^{11} +11.2209 q^{12} -5.11455 q^{13} -1.84827 q^{14} -5.96061 q^{15} +3.15680 q^{16} -3.20636 q^{17} -13.2321 q^{18} -5.40088 q^{19} -7.89839 q^{20} +2.22256 q^{21} -2.08948 q^{22} +7.89839 q^{23} -13.0699 q^{24} -0.804341 q^{25} +12.3768 q^{26} +7.18182 q^{27} +2.94511 q^{28} -2.47277 q^{29} +14.4242 q^{30} +8.16762 q^{31} +1.34359 q^{32} +2.51262 q^{33} +7.75914 q^{34} -1.56446 q^{35} +21.0847 q^{36} +3.95769 q^{37} +13.0697 q^{38} -14.8832 q^{39} +9.19987 q^{40} +4.36082 q^{41} -5.37842 q^{42} -3.96310 q^{43} +3.32947 q^{44} -11.2003 q^{45} -19.1135 q^{46} -6.69601 q^{47} +9.18623 q^{48} -6.41665 q^{49} +1.94644 q^{50} -9.33046 q^{51} -19.7217 q^{52} -1.16205 q^{53} -17.3794 q^{54} -1.76863 q^{55} -3.43040 q^{56} -15.7165 q^{57} +5.98390 q^{58} +14.3642 q^{59} -22.9842 q^{60} -5.56365 q^{61} -19.7650 q^{62} +4.17630 q^{63} -9.56499 q^{64} +10.4763 q^{65} -6.08034 q^{66} +5.90952 q^{67} -12.3638 q^{68} +22.9842 q^{69} +3.78586 q^{70} -12.0517 q^{71} -24.5589 q^{72} -13.5085 q^{73} -9.57730 q^{74} -2.34062 q^{75} -20.8259 q^{76} +0.659478 q^{77} +36.0162 q^{78} -2.05513 q^{79} -6.46617 q^{80} +4.49499 q^{81} -10.5528 q^{82} -5.37972 q^{83} +8.57023 q^{84} +6.56769 q^{85} +9.59039 q^{86} -7.19571 q^{87} -3.87809 q^{88} +0.285333 q^{89} +27.1037 q^{90} -3.90635 q^{91} +30.4563 q^{92} +23.7676 q^{93} +16.2038 q^{94} +11.0628 q^{95} +3.90983 q^{96} +8.86816 q^{97} +15.5278 q^{98} +4.72134 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) $ 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9} - 40 q^{10} - 17 q^{11} - 59 q^{12} - 89 q^{13} - 15 q^{14} - 29 q^{15} + 73 q^{16} - 58 q^{17} - 51 q^{18} - 37 q^{19} - 24 q^{20} - 37 q^{21} - 99 q^{22} - 42 q^{23} - 27 q^{24} - 11 q^{25} + 2 q^{26} - 73 q^{27} - 113 q^{28} - 57 q^{29} - 29 q^{30} - 51 q^{31} - 80 q^{32} - 78 q^{33} - 28 q^{34} - 34 q^{35} + 28 q^{36} - 117 q^{37} - 31 q^{38} - 36 q^{39} - 107 q^{40} - 60 q^{41} - 41 q^{42} - 109 q^{43} - 21 q^{44} - 62 q^{45} - 92 q^{46} - 26 q^{47} - 90 q^{48} - 7 q^{49} - 22 q^{50} - 47 q^{51} - 182 q^{52} - 83 q^{53} - 19 q^{54} - 53 q^{55} - 23 q^{56} - 201 q^{57} - 112 q^{58} + 14 q^{59} - 64 q^{60} - 73 q^{61} - 21 q^{62} - 94 q^{63} + 14 q^{64} - 123 q^{65} - 10 q^{66} - 135 q^{67} - 84 q^{68} - 50 q^{69} - 35 q^{70} - 29 q^{71} - 143 q^{72} - 266 q^{73} - 53 q^{74} - 32 q^{75} - 66 q^{76} - 69 q^{77} - 59 q^{78} - 124 q^{79} - 20 q^{80} - 33 q^{81} - 93 q^{82} - 28 q^{83} - 4 q^{84} - 179 q^{85} + 6 q^{86} - 40 q^{87} - 259 q^{88} - 41 q^{89} + 2 q^{90} - 50 q^{91} - 77 q^{92} - 60 q^{93} - 48 q^{94} - 37 q^{95} + 3 q^{96} - 220 q^{97} - 9 q^{98} - 35 q^{99}+O(q^{100}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9 - 40 * q^10 - 17 * q^11 - 59 * q^12 - 89 * q^13 - 15 * q^14 - 29 * q^15 + 73 * q^16 - 58 * q^17 - 51 * q^18 - 37 * q^19 - 24 * q^20 - 37 * q^21 - 99 * q^22 - 42 * q^23 - 27 * q^24 - 11 * q^25 + 2 * q^26 - 73 * q^27 - 113 * q^28 - 57 * q^29 - 29 * q^30 - 51 * q^31 - 80 * q^32 - 78 * q^33 - 28 * q^34 - 34 * q^35 + 28 * q^36 - 117 * q^37 - 31 * q^38 - 36 * q^39 - 107 * q^40 - 60 * q^41 - 41 * q^42 - 109 * q^43 - 21 * q^44 - 62 * q^45 - 92 * q^46 - 26 * q^47 - 90 * q^48 - 7 * q^49 - 22 * q^50 - 47 * q^51 - 182 * q^52 - 83 * q^53 - 19 * q^54 - 53 * q^55 - 23 * q^56 - 201 * q^57 - 112 * q^58 + 14 * q^59 - 64 * q^60 - 73 * q^61 - 21 * q^62 - 94 * q^63 + 14 * q^64 - 123 * q^65 - 10 * q^66 - 135 * q^67 - 84 * q^68 - 50 * q^69 - 35 * q^70 - 29 * q^71 - 143 * q^72 - 266 * q^73 - 53 * q^74 - 32 * q^75 - 66 * q^76 - 69 * q^77 - 59 * q^78 - 124 * q^79 - 20 * q^80 - 33 * q^81 - 93 * q^82 - 28 * q^83 - 4 * q^84 - 179 * q^85 + 6 * q^86 - 40 * q^87 - 259 * q^88 - 41 * q^89 + 2 * q^90 - 50 * q^91 - 77 * q^92 - 60 * q^93 - 48 * q^94 - 37 * q^95 + 3 * q^96 - 220 * q^97 - 9 * q^98 - 35 * 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 $

$2$	−2.41992	−1.71114	−0.855571	−	0.517686i	$-0.826794\pi$
$2$	−2.41992	−1.71114	−0.855571	+	0.517686i	$0.826794\pi$
$3$	2.90998	1.68008	0.840039	−	0.542525i	$-0.182532\pi$
$3$	2.90998	1.68008	0.840039	+	0.542525i	$0.182532\pi$
$4$	3.85601	1.92801
$5$	−2.04833	−0.916041	−0.458021	−	0.888942i	$-0.651441\pi$
$5$	−2.04833	−0.916041	−0.458021	+	0.888942i	$0.651441\pi$
$6$	−7.04192	−2.87485
$7$	0.763772	0.288679	0.144339	−	0.989528i	$-0.453894\pi$
$7$	0.763772	0.288679	0.144339	+	0.989528i	$0.453894\pi$
$8$	−4.49140	−1.58795
$9$	5.46800	1.82267
$10$	4.95680	1.56748
$11$	0.863449	0.260340	0.130170	−	0.991492i	$-0.458448\pi$
$11$	0.863449	0.260340	0.130170	+	0.991492i	$0.458448\pi$
$12$	11.2209	3.23920
$13$	−5.11455	−1.41852	−0.709260	−	0.704947i	$-0.750971\pi$
$13$	−5.11455	−1.41852	−0.709260	+	0.704947i	$0.750971\pi$
$14$	−1.84827	−0.493970
$15$	−5.96061	−1.53902
$16$	3.15680	0.789200
$17$	−3.20636	−0.777657	−0.388829	−	0.921310i	$-0.627120\pi$
$17$	−3.20636	−0.777657	−0.388829	+	0.921310i	$0.627120\pi$
$18$	−13.2321	−3.11884
$19$	−5.40088	−1.23905	−0.619523	−	0.784978i	$-0.712674\pi$
$19$	−5.40088	−1.23905	−0.619523	+	0.784978i	$0.712674\pi$
$20$	−7.89839	−1.76613
$21$	2.22256	0.485003
$22$	−2.08948	−0.445478
$23$	7.89839	1.64693	0.823464	−	0.567369i	$-0.192038\pi$
$23$	7.89839	1.64693	0.823464	+	0.567369i	$0.192038\pi$
$24$	−13.0699	−2.66788
$25$	−0.804341	−0.160868
$26$	12.3768	2.42729
$27$	7.18182	1.38214
$28$	2.94511	0.556574
$29$	−2.47277	−0.459182	−0.229591	−	0.973287i	$-0.573739\pi$
$29$	−2.47277	−0.459182	−0.229591	+	0.973287i	$0.573739\pi$
$30$	14.4242	2.63348
$31$	8.16762	1.46695	0.733474	−	0.679718i	$-0.237898\pi$
$31$	8.16762	1.46695	0.733474	+	0.679718i	$0.237898\pi$
$32$	1.34359	0.237516
$33$	2.51262	0.437391
$34$	7.75914	1.33068
$35$	−1.56446	−0.264442
$36$	21.0847	3.51411
$37$	3.95769	0.650641	0.325320	−	0.945604i	$-0.394528\pi$
$37$	3.95769	0.650641	0.325320	+	0.945604i	$0.394528\pi$
$38$	13.0697	2.12018
$39$	−14.8832	−2.38323
$40$	9.19987	1.45463
$41$	4.36082	0.681046	0.340523	−	0.940236i	$-0.389396\pi$
$41$	4.36082	0.681046	0.340523	+	0.940236i	$0.389396\pi$
$42$	−5.37842	−0.829909
$43$	−3.96310	−0.604368	−0.302184	−	0.953250i	$-0.597716\pi$
$43$	−3.96310	−0.604368	−0.302184	+	0.953250i	$0.597716\pi$
$44$	3.32947	0.501936
$45$	−11.2003	−1.66964
$46$	−19.1135	−2.81813
$47$	−6.69601	−0.976714	−0.488357	−	0.872644i	$-0.662404\pi$
$47$	−6.69601	−0.976714	−0.488357	+	0.872644i	$0.662404\pi$
$48$	9.18623	1.32592
$49$	−6.41665	−0.916665
$50$	1.94644	0.275268
$51$	−9.33046	−1.30653
$52$	−19.7217	−2.73491
$53$	−1.16205	−0.159620	−0.0798100	−	0.996810i	$-0.525431\pi$
$53$	−1.16205	−0.159620	−0.0798100	+	0.996810i	$0.525431\pi$
$54$	−17.3794	−2.36504
$55$	−1.76863	−0.238482
$56$	−3.43040	−0.458407
$57$	−15.7165	−2.08170
$58$	5.98390	0.785725
$59$	14.3642	1.87006	0.935030	−	0.354569i	$-0.115372\pi$
$59$	14.3642	1.87006	0.935030	+	0.354569i	$0.115372\pi$
$60$	−22.9842	−2.96724
$61$	−5.56365	−0.712352	−0.356176	−	0.934419i	$-0.615920\pi$
$61$	−5.56365	−0.712352	−0.356176	+	0.934419i	$0.615920\pi$
$62$	−19.7650	−2.51016
$63$	4.17630	0.526165
$64$	−9.56499	−1.19562
$65$	10.4763	1.29942
$66$	−6.08034	−0.748438
$67$	5.90952	0.721963	0.360981	−	0.932573i	$-0.382442\pi$
$67$	5.90952	0.721963	0.360981	+	0.932573i	$0.382442\pi$
$68$	−12.3638	−1.49933
$69$	22.9842	2.76697
$70$	3.78586	0.452497
$71$	−12.0517	−1.43027	−0.715135	−	0.698986i	$-0.753635\pi$
$71$	−12.0517	−1.43027	−0.715135	+	0.698986i	$0.753635\pi$
$72$	−24.5589	−2.89430
$73$	−13.5085	−1.58105	−0.790524	−	0.612431i	$-0.790192\pi$
$73$	−13.5085	−1.58105	−0.790524	+	0.612431i	$0.790192\pi$
$74$	−9.57730	−1.11334
$75$	−2.34062	−0.270271
$76$	−20.8259	−2.38889
$77$	0.659478	0.0751545
$78$	36.0162	4.07804
$79$	−2.05513	−0.231220	−0.115610	−	0.993295i	$-0.536882\pi$
$79$	−2.05513	−0.231220	−0.115610	+	0.993295i	$0.536882\pi$
$80$	−6.46617	−0.722940
$81$	4.49499	0.499444
$82$	−10.5528	−1.16537
$83$	−5.37972	−0.590501	−0.295250	−	0.955420i	$-0.595403\pi$
$83$	−5.37972	−0.590501	−0.295250	+	0.955420i	$0.595403\pi$
$84$	8.57023	0.935088
$85$	6.56769	0.712366
$86$	9.59039	1.03416
$87$	−7.19571	−0.771461
$88$	−3.87809	−0.413406
$89$	0.285333	0.0302453	0.0151226	−	0.999886i	$-0.495186\pi$
$89$	0.285333	0.0302453	0.0151226	+	0.999886i	$0.495186\pi$
$90$	27.1037	2.85699
$91$	−3.90635	−0.409496
$92$	30.4563	3.17529
$93$	23.7676	2.46459
$94$	16.2038	1.67130
$95$	11.0628	1.13502
$96$	3.90983	0.399045
$97$	8.86816	0.900425	0.450213	−	0.892921i	$-0.351348\pi$
$97$	8.86816	0.900425	0.450213	+	0.892921i	$0.351348\pi$
$98$	15.5278	1.56854
$99$	4.72134	0.474512
$100$	−3.10155	−0.310155
$101$	−14.7630	−1.46897	−0.734484	−	0.678626i	$-0.762576\pi$
$101$	−14.7630	−1.46897	−0.734484	+	0.678626i	$0.762576\pi$
$102$	22.5790	2.23565
$103$	−14.9168	−1.46980	−0.734899	−	0.678177i	$-0.762770\pi$
$103$	−14.9168	−1.46980	−0.734899	+	0.678177i	$0.762770\pi$
$104$	22.9715	2.25254
$105$	−4.55254	−0.444283
$106$	2.81207	0.273133
$107$	−4.10486	−0.396832	−0.198416	−	0.980118i	$-0.563580\pi$
$107$	−4.10486	−0.396832	−0.198416	+	0.980118i	$0.563580\pi$
$108$	27.6932	2.66478
$109$	−11.1677	−1.06967	−0.534837	−	0.844955i	$-0.679627\pi$
$109$	−11.1677	−1.06967	−0.534837	+	0.844955i	$0.679627\pi$
$110$	4.27994	0.408076
$111$	11.5168	1.09313
$112$	2.41108	0.227825
$113$	−1.70948	−0.160814	−0.0804070	−	0.996762i	$-0.525622\pi$
$113$	−1.70948	−0.160814	−0.0804070	+	0.996762i	$0.525622\pi$
$114$	38.0326	3.56208
$115$	−16.1785	−1.50865
$116$	−9.53502	−0.885305
$117$	−27.9663	−2.58549
$118$	−34.7602	−3.19994
$119$	−2.44893	−0.224493
$120$	26.7715	2.44389
$121$	−10.2545	−0.932223
$122$	13.4636	1.21894
$123$	12.6899	1.14421
$124$	31.4944	2.82828
$125$	11.8892	1.06340
$126$	−10.1063	−0.900342
$127$	4.01516	0.356288	0.178144	−	0.984004i	$-0.442991\pi$
$127$	4.01516	0.356288	0.178144	+	0.984004i	$0.442991\pi$
$128$	20.4593	1.80837
$129$	−11.5326	−1.01539
$130$	−25.3518	−2.22350
$131$	8.85990	0.774093	0.387046	−	0.922060i	$-0.373495\pi$
$131$	8.85990	0.774093	0.387046	+	0.922060i	$0.373495\pi$
$132$	9.68870	0.843293
$133$	−4.12504	−0.357686
$134$	−14.3006	−1.23538
$135$	−14.7108	−1.26610
$136$	14.4011	1.23488
$137$	−17.7021	−1.51239	−0.756197	−	0.654344i	$-0.772945\pi$
$137$	−17.7021	−1.51239	−0.756197	+	0.654344i	$0.772945\pi$
$138$	−55.6198	−4.73468
$139$	−1.97360	−0.167399	−0.0836993	−	0.996491i	$-0.526674\pi$
$139$	−1.97360	−0.167399	−0.0836993	+	0.996491i	$0.526674\pi$
$140$	−6.03257	−0.509845
$141$	−19.4853	−1.64096
$142$	29.1641	2.44740
$143$	−4.41615	−0.369297
$144$	17.2614	1.43845
$145$	5.06505	0.420629
$146$	32.6894	2.70540
$147$	−18.6723	−1.54007
$148$	15.2609	1.25444
$149$	19.0974	1.56452	0.782260	−	0.622952i	$-0.214067\pi$
$149$	19.0974	1.56452	0.782260	+	0.622952i	$0.214067\pi$
$150$	5.66411	0.462472
$151$	−21.2969	−1.73312	−0.866558	−	0.499076i	$-0.833673\pi$
$151$	−21.2969	−1.73312	−0.866558	+	0.499076i	$0.833673\pi$
$152$	24.2575	1.96754
$153$	−17.5324	−1.41741
$154$	−1.59588	−0.128600
$155$	−16.7300	−1.34378
$156$	−57.3899	−4.59487
$157$	−8.92639	−0.712403	−0.356202	−	0.934409i	$-0.615928\pi$
$157$	−8.92639	−0.712403	−0.356202	+	0.934409i	$0.615928\pi$
$158$	4.97325	0.395650
$159$	−3.38155	−0.268174
$160$	−2.75212	−0.217574
$161$	6.03257	0.475433
$162$	−10.8775	−0.854619
$163$	−8.42048	−0.659543	−0.329772	−	0.944061i	$-0.606972\pi$
$163$	−8.42048	−0.659543	−0.329772	+	0.944061i	$0.606972\pi$
$164$	16.8154	1.31306
$165$	−5.14668	−0.400669
$166$	13.0185	1.01043
$167$	1.86450	0.144280	0.0721399	−	0.997395i	$-0.477017\pi$
$167$	1.86450	0.144280	0.0721399	+	0.997395i	$0.477017\pi$
$168$	−9.98241	−0.770160
$169$	13.1586	1.01220
$170$	−15.8933	−1.21896
$171$	−29.5320	−2.25837
$172$	−15.2818	−1.16522
$173$	11.3929	0.866187	0.433094	−	0.901349i	$-0.357422\pi$
$173$	11.3929	0.866187	0.433094	+	0.901349i	$0.357422\pi$
$174$	17.4130	1.32008
$175$	−0.614333	−0.0464392
$176$	2.72574	0.205460
$177$	41.7996	3.14185
$178$	−0.690484	−0.0517539
$179$	−20.1590	−1.50676	−0.753378	−	0.657588i	$-0.771577\pi$
$179$	−20.1590	−1.50676	−0.753378	+	0.657588i	$0.771577\pi$
$180$	−43.1883	−3.21907
$181$	1.13009	0.0839991	0.0419995	−	0.999118i	$-0.486627\pi$
$181$	1.13009	0.0839991	0.0419995	+	0.999118i	$0.486627\pi$
$182$	9.45304	0.700706
$183$	−16.1901	−1.19681
$184$	−35.4748	−2.61524
$185$	−8.10667	−0.596014
$186$	−57.5157	−4.21726
$187$	−2.76853	−0.202455
$188$	−25.8199	−1.88311
$189$	5.48528	0.398995
$190$	−26.7711	−1.94218
$191$	−0.872705	−0.0631467	−0.0315733	−	0.999501i	$-0.510052\pi$
$191$	−0.872705	−0.0631467	−0.0315733	+	0.999501i	$0.510052\pi$
$192$	−27.8339	−2.00874
$193$	−15.8415	−1.14030	−0.570148	−	0.821542i	$-0.693114\pi$
$193$	−15.8415	−1.14030	−0.570148	+	0.821542i	$0.693114\pi$
$194$	−21.4602	−1.54076
$195$	30.4858	2.18313
$196$	−24.7427	−1.76733
$197$	−18.6228	−1.32682	−0.663409	−	0.748257i	$-0.730891\pi$
$197$	−18.6228	−1.32682	−0.663409	+	0.748257i	$0.730891\pi$
$198$	−11.4253	−0.811958
$199$	−6.25020	−0.443065	−0.221532	−	0.975153i	$-0.571106\pi$
$199$	−6.25020	−0.443065	−0.221532	+	0.975153i	$0.571106\pi$
$200$	3.61262	0.255451
$201$	17.1966	1.21295
$202$	35.7252	2.51361
$203$	−1.88863	−0.132556
$204$	−35.9784	−2.51899
$205$	−8.93240	−0.623866
$206$	36.0975	2.51503
$207$	43.1884	3.00180
$208$	−16.1456	−1.11950
$209$	−4.66338	−0.322573
$210$	11.0168	0.760231
$211$	−14.5052	−0.998582	−0.499291	−	0.866434i	$-0.666406\pi$
$211$	−14.5052	−0.998582	−0.499291	+	0.866434i	$0.666406\pi$
$212$	−4.48088	−0.307748
$213$	−35.0702	−2.40297
$214$	9.93344	0.679036
$215$	8.11775	0.553626
$216$	−32.2564	−2.19477
$217$	6.23820	0.423476
$218$	27.0250	1.83036
$219$	−39.3094	−2.65629
$220$	−6.81986	−0.459795
$221$	16.3991	1.10312
$222$	−27.8698	−1.87050
$223$	14.0164	0.938606	0.469303	−	0.883037i	$-0.344505\pi$
$223$	14.0164	0.938606	0.469303	+	0.883037i	$0.344505\pi$
$224$	1.02620	0.0685657
$225$	−4.39813	−0.293209
$226$	4.13680	0.275176
$227$	−5.89386	−0.391189	−0.195595	−	0.980685i	$-0.562664\pi$
$227$	−5.89386	−0.391189	−0.195595	+	0.980685i	$0.562664\pi$
$228$	−60.6029	−4.01352
$229$	20.9248	1.38275	0.691375	−	0.722496i	$-0.257005\pi$
$229$	20.9248	1.38275	0.691375	+	0.722496i	$0.257005\pi$
$230$	39.1507	2.58152
$231$	1.91907	0.126266
$232$	11.1062	0.729157
$233$	−18.3036	−1.19911	−0.599554	−	0.800335i	$-0.704655\pi$
$233$	−18.3036	−1.19911	−0.599554	+	0.800335i	$0.704655\pi$
$234$	67.6762	4.42413
$235$	13.7156	0.894710
$236$	55.3885	3.60549
$237$	−5.98039	−0.388468
$238$	5.92621	0.384139
$239$	27.6482	1.78842	0.894208	−	0.447652i	$-0.147740\pi$
$239$	27.6482	1.78842	0.894208	+	0.447652i	$0.147740\pi$
$240$	−18.8164	−1.21460
$241$	15.5313	1.00046	0.500229	−	0.865893i	$-0.333249\pi$
$241$	15.5313	1.00046	0.500229	+	0.865893i	$0.333249\pi$
$242$	24.8150	1.59517
$243$	−8.46512	−0.543038
$244$	−21.4535	−1.37342
$245$	13.1434	0.839703
$246$	−30.7086	−1.95791
$247$	27.6230	1.75761
$248$	−36.6840	−2.32944
$249$	−15.6549	−0.992088
$250$	−28.7709	−1.81963
$251$	−0.670446	−0.0423182	−0.0211591	−	0.999776i	$-0.506736\pi$
$251$	−0.670446	−0.0423182	−0.0211591	+	0.999776i	$0.506736\pi$
$252$	16.1039	1.01445
$253$	6.81986	0.428761
$254$	−9.71636	−0.609658
$255$	19.1119	1.19683
$256$	−30.3799	−1.89875
$257$	9.27043	0.578273	0.289137	−	0.957288i	$-0.406632\pi$
$257$	9.27043	0.578273	0.289137	+	0.957288i	$0.406632\pi$
$258$	27.9079	1.73747
$259$	3.02277	0.187826
$260$	40.3967	2.50529
$261$	−13.5211	−0.836934
$262$	−21.4402	−1.32458
$263$	17.8089	1.09814	0.549070	−	0.835776i	$-0.314982\pi$
$263$	17.8089	1.09814	0.549070	+	0.835776i	$0.314982\pi$
$264$	−11.2852	−0.694555
$265$	2.38027	0.146219
$266$	9.98226	0.612052
$267$	0.830315	0.0508144
$268$	22.7872	1.39195
$269$	14.1916	0.865279	0.432640	−	0.901567i	$-0.357582\pi$
$269$	14.1916	0.865279	0.432640	+	0.901567i	$0.357582\pi$
$270$	35.5988	2.16648
$271$	6.43870	0.391123	0.195562	−	0.980691i	$-0.437347\pi$
$271$	6.43870	0.391123	0.195562	+	0.980691i	$0.437347\pi$
$272$	−10.1218	−0.613727
$273$	−11.3674	−0.687986
$274$	42.8377	2.58792
$275$	−0.694508	−0.0418804
$276$	88.6272	5.33473
$277$	−12.1381	−0.729309	−0.364655	−	0.931143i	$-0.618813\pi$
$277$	−12.1381	−0.729309	−0.364655	+	0.931143i	$0.618813\pi$
$278$	4.77596	0.286443
$279$	44.6605	2.67375
$280$	7.02660	0.419920
$281$	15.3986	0.918601	0.459300	−	0.888281i	$-0.348100\pi$
$281$	15.3986	0.918601	0.459300	+	0.888281i	$0.348100\pi$
$282$	47.1528	2.80791
$283$	−27.5919	−1.64017	−0.820083	−	0.572245i	$-0.806073\pi$
$283$	−27.5919	−1.64017	−0.820083	+	0.572245i	$0.806073\pi$
$284$	−46.4714	−2.75757
$285$	32.1925	1.90692
$286$	10.6867	0.631920
$287$	3.33067	0.196603
$288$	7.34676	0.432912
$289$	−6.71924	−0.395249
$290$	−12.2570	−0.719756
$291$	25.8062	1.51279
$292$	−52.0889	−3.04827
$293$	−0.941353	−0.0549944	−0.0274972	−	0.999622i	$-0.508754\pi$
$293$	−0.941353	−0.0549944	−0.0274972	+	0.999622i	$0.508754\pi$
$294$	45.1856	2.63528
$295$	−29.4226	−1.71305
$296$	−17.7756	−1.03318
$297$	6.20114	0.359827
$298$	−46.2142	−2.67712
$299$	−40.3967	−2.33620
$300$	−9.02545	−0.521085
$301$	−3.02691	−0.174468
$302$	51.5368	2.96561
$303$	−42.9599	−2.46798
$304$	−17.0495	−0.977856
$305$	11.3962	0.652544
$306$	42.4269	2.42539
$307$	24.0911	1.37495	0.687476	−	0.726207i	$-0.258719\pi$
$307$	24.0911	1.37495	0.687476	+	0.726207i	$0.258719\pi$
$308$	2.54296	0.144898
$309$	−43.4077	−2.46938
$310$	40.4852	2.29941
$311$	16.2317	0.920415	0.460208	−	0.887811i	$-0.347775\pi$
$311$	16.2317	0.920415	0.460208	+	0.887811i	$0.347775\pi$
$312$	66.8466	3.78444
$313$	−5.92028	−0.334634	−0.167317	−	0.985903i	$-0.553510\pi$
$313$	−5.92028	−0.334634	−0.167317	+	0.985903i	$0.553510\pi$
$314$	21.6011	1.21902
$315$	−8.55445	−0.481988
$316$	−7.92460	−0.445793
$317$	5.44779	0.305978	0.152989	−	0.988228i	$-0.451110\pi$
$317$	5.44779	0.305978	0.152989	+	0.988228i	$0.451110\pi$
$318$	8.18308	0.458884
$319$	−2.13511	−0.119543
$320$	19.5923	1.09524
$321$	−11.9451	−0.666709
$322$	−14.5983	−0.813533
$323$	17.3172	0.963553
$324$	17.3327	0.962930
$325$	4.11384	0.228195
$326$	20.3769	1.12857
$327$	−32.4979	−1.79714
$328$	−19.5862	−1.08147
$329$	−5.11423	−0.281956
$330$	12.4546	0.685601
$331$	5.72343	0.314588	0.157294	−	0.987552i	$-0.449723\pi$
$331$	5.72343	0.314588	0.157294	+	0.987552i	$0.449723\pi$
$332$	−20.7443	−1.13849
$333$	21.6407	1.18590
$334$	−4.51195	−0.246883
$335$	−12.1047	−0.661348
$336$	7.01619	0.382764
$337$	−30.9069	−1.68361	−0.841804	−	0.539783i	$-0.818506\pi$
$337$	−30.9069	−1.68361	−0.841804	+	0.539783i	$0.818506\pi$
$338$	−31.8427	−1.73202
$339$	−4.97455	−0.270180
$340$	25.3251	1.37345
$341$	7.05232	0.381905
$342$	71.4650	3.86439
$343$	−10.2473	−0.553300
$344$	17.7999	0.959705
$345$	−47.0792	−2.53466
$346$	−27.5699	−1.48217
$347$	32.8275	1.76227	0.881136	−	0.472862i	$-0.156779\pi$
$347$	32.8275	1.76227	0.881136	+	0.472862i	$0.156779\pi$
$348$	−27.7467	−1.48738
$349$	1.22890	0.0657814	0.0328907	−	0.999459i	$-0.489529\pi$
$349$	1.22890	0.0657814	0.0328907	+	0.999459i	$0.489529\pi$
$350$	1.48664	0.0794641
$351$	−36.7318	−1.96060
$352$	1.16012	0.0618348
$353$	10.5093	0.559354	0.279677	−	0.960094i	$-0.409773\pi$
$353$	10.5093	0.559354	0.279677	+	0.960094i	$0.409773\pi$
$354$	−101.152	−5.37615
$355$	24.6858	1.31019
$356$	1.10025	0.0583131
$357$	−7.12634	−0.377166
$358$	48.7832	2.57827
$359$	−23.3776	−1.23382	−0.616912	−	0.787032i	$-0.711617\pi$
$359$	−23.3776	−1.23382	−0.616912	+	0.787032i	$0.711617\pi$
$360$	50.3049	2.65130
$361$	10.1695	0.535236
$362$	−2.73473	−0.143734
$363$	−29.8403	−1.56621
$364$	−15.0629	−0.789511
$365$	27.6698	1.44831
$366$	39.1788	2.04791
$367$	−30.8524	−1.61048	−0.805240	−	0.592949i	$-0.797964\pi$
$367$	−30.8524	−1.61048	−0.805240	+	0.592949i	$0.797964\pi$
$368$	24.9336	1.29976
$369$	23.8449	1.24132
$370$	19.6175	1.01986
$371$	−0.887542	−0.0460789
$372$	91.6482	4.75174
$373$	28.5757	1.47960	0.739798	−	0.672829i	$-0.234921\pi$
$373$	28.5757	1.47960	0.739798	+	0.672829i	$0.234921\pi$
$374$	6.69962	0.346429
$375$	34.5974	1.78660
$376$	30.0745	1.55097
$377$	12.6471	0.651358
$378$	−13.2739	−0.682737
$379$	−24.3674	−1.25167	−0.625834	−	0.779957i	$-0.715241\pi$
$379$	−24.3674	−1.25167	−0.625834	+	0.779957i	$0.715241\pi$
$380$	42.6582	2.18832
$381$	11.6840	0.598591
$382$	2.11188	0.108053
$383$	−30.6512	−1.56620	−0.783102	−	0.621894i	$-0.786364\pi$
$383$	−30.6512	−1.56620	−0.783102	+	0.621894i	$0.786364\pi$
$384$	59.5362	3.03820
$385$	−1.35083	−0.0688446
$386$	38.3351	1.95121
$387$	−21.6702	−1.10156
$388$	34.1957	1.73603
$389$	−7.00837	−0.355339	−0.177669	−	0.984090i	$-0.556856\pi$
$389$	−7.00837	−0.355339	−0.177669	+	0.984090i	$0.556856\pi$
$390$	−73.7732	−3.73565
$391$	−25.3251	−1.28075
$392$	28.8197	1.45562
$393$	25.7821	1.30054
$394$	45.0656	2.27037
$395$	4.20958	0.211807
$396$	18.2055	0.914862
$397$	−12.4328	−0.623983	−0.311992	−	0.950085i	$-0.600996\pi$
$397$	−12.4328	−0.623983	−0.311992	+	0.950085i	$0.600996\pi$
$398$	15.1250	0.758146
$399$	−12.0038	−0.600941
$400$	−2.53914	−0.126957
$401$	−7.02317	−0.350720	−0.175360	−	0.984504i	$-0.556109\pi$
$401$	−7.02317	−0.350720	−0.175360	+	0.984504i	$0.556109\pi$
$402$	−41.6144	−2.07554
$403$	−41.7737	−2.08089
$404$	−56.9261	−2.83218
$405$	−9.20723	−0.457511
$406$	4.57034	0.226822
$407$	3.41727	0.169388
$408$	41.9068	2.07470
$409$	−29.3262	−1.45009	−0.725044	−	0.688703i	$-0.758180\pi$
$409$	−29.3262	−1.45009	−0.725044	+	0.688703i	$0.758180\pi$
$410$	21.6157	1.06752
$411$	−51.5129	−2.54094
$412$	−57.5194	−2.83378
$413$	10.9710	0.539846
$414$	−104.512	−5.13650
$415$	11.0194	0.540923
$416$	−6.87186	−0.336921
$417$	−5.74314	−0.281243
$418$	11.2850	0.551968
$419$	−17.7342	−0.866373	−0.433187	−	0.901304i	$-0.642611\pi$
$419$	−17.7342	−0.866373	−0.433187	+	0.901304i	$0.642611\pi$
$420$	−17.5547	−0.856580
$421$	32.4963	1.58377	0.791886	−	0.610669i	$-0.209099\pi$
$421$	32.4963	1.58377	0.791886	+	0.610669i	$0.209099\pi$
$422$	35.1015	1.70871
$423$	−36.6138	−1.78022
$424$	5.21924	0.253469
$425$	2.57901	0.125100
$426$	84.8670	4.11182
$427$	−4.24936	−0.205641
$428$	−15.8284	−0.765095
$429$	−12.8509	−0.620448
$430$	−19.6443	−0.947332
$431$	10.7132	0.516036	0.258018	−	0.966140i	$-0.416931\pi$
$431$	10.7132	0.516036	0.258018	+	0.966140i	$0.416931\pi$
$432$	22.6716	1.09079
$433$	7.41105	0.356152	0.178076	−	0.984017i	$-0.443013\pi$
$433$	7.41105	0.356152	0.178076	+	0.984017i	$0.443013\pi$
$434$	−15.0959	−0.724628
$435$	14.7392	0.706691
$436$	−43.0629	−2.06234
$437$	−42.6582	−2.04062
$438$	95.1257	4.54528
$439$	18.3026	0.873536	0.436768	−	0.899574i	$-0.356123\pi$
$439$	18.3026	0.873536	0.436768	+	0.899574i	$0.356123\pi$
$440$	7.94362	0.378697
$441$	−35.0862	−1.67077
$442$	−39.6845	−1.88760
$443$	−12.2253	−0.580844	−0.290422	−	0.956899i	$-0.593796\pi$
$443$	−12.2253	−0.580844	−0.290422	+	0.956899i	$0.593796\pi$
$444$	44.4090	2.10756
$445$	−0.584457	−0.0277059
$446$	−33.9185	−1.60609
$447$	55.5731	2.62852
$448$	−7.30547	−0.345151
$449$	10.8983	0.514323	0.257162	−	0.966368i	$-0.417213\pi$
$449$	10.8983	0.514323	0.257162	+	0.966368i	$0.417213\pi$
$450$	10.6431	0.501722
$451$	3.76535	0.177303
$452$	−6.59176	−0.310050
$453$	−61.9736	−2.91177
$454$	14.2627	0.669380
$455$	8.00149	0.375116
$456$	70.5889	3.30563
$457$	−25.1139	−1.17478	−0.587390	−	0.809304i	$-0.699845\pi$
$457$	−25.1139	−1.17478	−0.587390	+	0.809304i	$0.699845\pi$
$458$	−50.6363	−2.36608
$459$	−23.0275	−1.07483
$460$	−62.3845	−2.90869
$461$	9.77241	0.455146	0.227573	−	0.973761i	$-0.426921\pi$
$461$	9.77241	0.455146	0.227573	+	0.973761i	$0.426921\pi$
$462$	−4.64399	−0.216058
$463$	31.0957	1.44514	0.722570	−	0.691298i	$-0.242961\pi$
$463$	31.0957	1.44514	0.722570	+	0.691298i	$0.242961\pi$
$464$	−7.80604	−0.362386
$465$	−48.6840	−2.25766
$466$	44.2932	2.05184
$467$	−7.31062	−0.338295	−0.169148	−	0.985591i	$-0.554101\pi$
$467$	−7.31062	−0.338295	−0.169148	+	0.985591i	$0.554101\pi$
$468$	−107.838	−4.98483
$469$	4.51353	0.208415
$470$	−33.1908	−1.53098
$471$	−25.9756	−1.19689
$472$	−64.5153	−2.96956
$473$	−3.42194	−0.157341
$474$	14.4721	0.664723
$475$	4.34415	0.199323
$476$	−9.44310	−0.432824
$477$	−6.35409	−0.290934
$478$	−66.9065	−3.06023
$479$	1.82718	0.0834860	0.0417430	−	0.999128i	$-0.486709\pi$
$479$	1.82718	0.0834860	0.0417430	+	0.999128i	$0.486709\pi$
$480$	−8.00862	−0.365542
$481$	−20.2418	−0.922947
$482$	−37.5844	−1.71192
$483$	17.5547	0.798765
$484$	−39.5413	−1.79733
$485$	−18.1649	−0.824827
$486$	20.4849	0.929215
$487$	21.2352	0.962257	0.481128	−	0.876650i	$-0.340227\pi$
$487$	21.2352	0.962257	0.481128	+	0.876650i	$0.340227\pi$
$488$	24.9886	1.13118
$489$	−24.5035	−1.10808
$490$	−31.8060	−1.43685
$491$	9.63980	0.435038	0.217519	−	0.976056i	$-0.430204\pi$
$491$	9.63980	0.435038	0.217519	+	0.976056i	$0.430204\pi$
$492$	48.9324	2.20604
$493$	7.92859	0.357086
$494$	−66.8456	−3.00752
$495$	−9.67086	−0.434673
$496$	25.7835	1.15772
$497$	−9.20473	−0.412889
$498$	37.8836	1.69760
$499$	−25.6177	−1.14681	−0.573404	−	0.819273i	$-0.694377\pi$
$499$	−25.6177	−1.14681	−0.573404	+	0.819273i	$0.694377\pi$
$500$	45.8449	2.05025
$501$	5.42568	0.242401
$502$	1.62243	0.0724124
$503$	−12.5346	−0.558888	−0.279444	−	0.960162i	$-0.590150\pi$
$503$	−12.5346	−0.558888	−0.279444	+	0.960162i	$0.590150\pi$
$504$	−18.7574	−0.835523
$505$	30.2394	1.34564
$506$	−16.5035	−0.733670
$507$	38.2912	1.70057
$508$	15.4825	0.686924
$509$	4.16738	0.184716	0.0923580	−	0.995726i	$-0.470560\pi$
$509$	4.16738	0.184716	0.0923580	+	0.995726i	$0.470560\pi$
$510$	−46.2492	−2.04795
$511$	−10.3174	−0.456415
$512$	32.5984	1.44066
$513$	−38.7882	−1.71254
$514$	−22.4337	−0.989507
$515$	30.5546	1.34640
$516$	−44.4697	−1.95767
$517$	−5.78167	−0.254277
$518$	−7.31487	−0.321397
$519$	33.1532	1.45526
$520$	−47.0532	−2.06342
$521$	12.9523	0.567451	0.283725	−	0.958906i	$-0.408430\pi$
$521$	12.9523	0.567451	0.283725	+	0.958906i	$0.408430\pi$
$522$	32.7199	1.43211
$523$	38.9169	1.70172	0.850859	−	0.525394i	$-0.176082\pi$
$523$	38.9169	1.70172	0.850859	+	0.525394i	$0.176082\pi$
$524$	34.1639	1.49246
$525$	−1.78770	−0.0780215
$526$	−43.0960	−1.87907
$527$	−26.1883	−1.14078
$528$	7.93185	0.345189
$529$	39.3845	1.71237
$530$	−5.76005	−0.250201
$531$	78.5434	3.40849
$532$	−15.9062	−0.689621
$533$	−22.3036	−0.966077
$534$	−2.00930	−0.0869507
$535$	8.40812	0.363515
$536$	−26.5420	−1.14644
$537$	−58.6624	−2.53147
$538$	−34.3426	−1.48062
$539$	−5.54045	−0.238644
$540$	−56.7248	−2.44105
$541$	12.8421	0.552126	0.276063	−	0.961140i	$-0.410970\pi$
$541$	12.8421	0.552126	0.276063	+	0.961140i	$0.410970\pi$
$542$	−15.5811	−0.669267
$543$	3.28855	0.141125
$544$	−4.30804	−0.184706
$545$	22.8752	0.979866
$546$	27.5082	1.17724
$547$	13.3048	0.568873	0.284436	−	0.958695i	$-0.408194\pi$
$547$	13.3048	0.568873	0.284436	+	0.958695i	$0.408194\pi$
$548$	−68.2596	−2.91591
$549$	−30.4220	−1.29838
$550$	1.68065	0.0716633
$551$	13.3551	0.568947
$552$	−103.231	−4.39381
$553$	−1.56965	−0.0667483
$554$	29.3733	1.24795
$555$	−23.5903	−1.00135
$556$	−7.61023	−0.322746
$557$	21.1288	0.895257	0.447629	−	0.894220i	$-0.352269\pi$
$557$	21.1288	0.895257	0.447629	+	0.894220i	$0.352269\pi$
$558$	−108.075	−4.57517
$559$	20.2695	0.857308
$560$	−4.93868	−0.208697
$561$	−8.05638	−0.340140
$562$	−37.2633	−1.57186
$563$	9.76897	0.411713	0.205856	−	0.978582i	$-0.434002\pi$
$563$	9.76897	0.411713	0.205856	+	0.978582i	$0.434002\pi$
$564$	−75.1355	−3.16377
$565$	3.50157	0.147312
$566$	66.7701	2.80656
$567$	3.43315	0.144179
$568$	54.1289	2.27120
$569$	−1.55393	−0.0651443	−0.0325721	−	0.999469i	$-0.510370\pi$
$569$	−1.55393	−0.0651443	−0.0325721	+	0.999469i	$0.510370\pi$
$570$	−77.9033	−3.26301
$571$	5.88542	0.246297	0.123149	−	0.992388i	$-0.460701\pi$
$571$	5.88542	0.246297	0.123149	+	0.992388i	$0.460701\pi$
$572$	−17.0287	−0.712007
$573$	−2.53956	−0.106091
$574$	−8.05996	−0.336416
$575$	−6.35300	−0.264938
$576$	−52.3013	−2.17922
$577$	45.1665	1.88031	0.940154	−	0.340751i	$-0.110681\pi$
$577$	45.1665	1.88031	0.940154	+	0.340751i	$0.110681\pi$
$578$	16.2600	0.676328
$579$	−46.0984	−1.91579
$580$	19.5309	0.810976
$581$	−4.10888	−0.170465
$582$	−62.4489	−2.58859
$583$	−1.00337	−0.0415554
$584$	60.6720	2.51062
$585$	57.2843	2.36841
$586$	2.27800	0.0941032
$587$	−27.7494	−1.14534	−0.572669	−	0.819786i	$-0.694092\pi$
$587$	−27.7494	−1.14534	−0.572669	+	0.819786i	$0.694092\pi$
$588$	−72.0008	−2.96926
$589$	−44.1123	−1.81762
$590$	71.2004	2.93127
$591$	−54.1919	−2.22916
$592$	12.4937	0.513486
$593$	12.6196	0.518223	0.259112	−	0.965847i	$-0.416570\pi$
$593$	12.6196	0.518223	0.259112	+	0.965847i	$0.416570\pi$
$594$	−15.0063	−0.615714
$595$	5.01622	0.205645
$596$	73.6398	3.01640
$597$	−18.1880	−0.744384
$598$	97.7567	3.99757
$599$	−18.4164	−0.752475	−0.376238	−	0.926523i	$-0.622782\pi$
$599$	−18.4164	−0.752475	−0.376238	+	0.926523i	$0.622782\pi$
$600$	10.5126	0.429177
$601$	43.2330	1.76351	0.881756	−	0.471705i	$-0.156361\pi$
$601$	43.2330	1.76351	0.881756	+	0.471705i	$0.156361\pi$
$602$	7.32487	0.298540
$603$	32.3132	1.31590
$604$	−82.1210	−3.34146
$605$	21.0045	0.853955
$606$	103.960	4.22307
$607$	−27.0686	−1.09868	−0.549340	−	0.835599i	$-0.685121\pi$
$607$	−27.0686	−1.09868	−0.549340	+	0.835599i	$0.685121\pi$
$608$	−7.25658	−0.294293
$609$	−5.49588	−0.222704
$610$	−27.5779	−1.11660
$611$	34.2471	1.38549
$612$	−67.6050	−2.73277
$613$	−7.14211	−0.288467	−0.144234	−	0.989544i	$-0.546072\pi$
$613$	−7.14211	−0.288467	−0.144234	+	0.989544i	$0.546072\pi$
$614$	−58.2985	−2.35274
$615$	−25.9931	−1.04814
$616$	−2.96198	−0.119342
$617$	−47.6275	−1.91741	−0.958706	−	0.284398i	$-0.908206\pi$
$617$	−47.6275	−1.91741	−0.958706	+	0.284398i	$0.908206\pi$
$618$	105.043	4.22545
$619$	6.51661	0.261925	0.130962	−	0.991387i	$-0.458193\pi$
$619$	6.51661	0.261925	0.130962	+	0.991387i	$0.458193\pi$
$620$	−64.5110	−2.59082
$621$	56.7248	2.27629
$622$	−39.2794	−1.57496
$623$	0.217930	0.00873116
$624$	−46.9834	−1.88084
$625$	−20.3313	−0.813253
$626$	14.3266	0.572606
$627$	−13.5704	−0.541948
$628$	−34.4203	−1.37352
$629$	−12.6898	−0.505975
$630$	20.7011	0.824751
$631$	6.46876	0.257517	0.128759	−	0.991676i	$-0.458901\pi$
$631$	6.46876	0.257517	0.128759	+	0.991676i	$0.458901\pi$
$632$	9.23040	0.367166
$633$	−42.2100	−1.67770
$634$	−13.1832	−0.523572
$635$	−8.22437	−0.326374
$636$	−13.0393	−0.517042
$637$	32.8183	1.30031
$638$	5.16679	0.204555
$639$	−65.8985	−2.60691
$640$	−41.9074	−1.65654
$641$	−39.2384	−1.54983	−0.774913	−	0.632068i	$-0.782206\pi$
$641$	−39.2384	−1.54983	−0.774913	+	0.632068i	$0.782206\pi$
$642$	28.9061	1.14083
$643$	15.9174	0.627719	0.313860	−	0.949469i	$-0.398378\pi$
$643$	15.9174	0.627719	0.313860	+	0.949469i	$0.398378\pi$
$644$	23.2616	0.916637
$645$	23.6225	0.930135
$646$	−41.9062	−1.64878
$647$	−13.4427	−0.528487	−0.264244	−	0.964456i	$-0.585122\pi$
$647$	−13.4427	−0.528487	−0.264244	+	0.964456i	$0.585122\pi$
$648$	−20.1888	−0.793091
$649$	12.4028	0.486851
$650$	−9.95516	−0.390474
$651$	18.1530	0.711474
$652$	−32.4695	−1.27160
$653$	−33.8320	−1.32395	−0.661974	−	0.749527i	$-0.730281\pi$
$653$	−33.8320	−1.32395	−0.661974	+	0.749527i	$0.730281\pi$
$654$	78.6423	3.07516
$655$	−18.1480	−0.709101
$656$	13.7662	0.537481
$657$	−73.8643	−2.88172
$658$	12.3760	0.482467
$659$	36.9392	1.43895	0.719474	−	0.694520i	$-0.244383\pi$
$659$	36.9392	1.43895	0.719474	+	0.694520i	$0.244383\pi$
$660$	−19.8457	−0.772491
$661$	−22.4505	−0.873222	−0.436611	−	0.899650i	$-0.643821\pi$
$661$	−22.4505	−0.873222	−0.436611	+	0.899650i	$0.643821\pi$
$662$	−13.8503	−0.538305
$663$	47.7211	1.85333
$664$	24.1625	0.937685
$665$	8.44944	0.327655
$666$	−52.3686	−2.02924
$667$	−19.5309	−0.756239
$668$	7.18955	0.278172
$669$	40.7874	1.57693
$670$	29.2923	1.13166
$671$	−4.80393	−0.185454
$672$	2.98622	0.115196
$673$	−21.5200	−0.829537	−0.414768	−	0.909927i	$-0.636137\pi$
$673$	−21.5200	−0.829537	−0.414768	+	0.909927i	$0.636137\pi$
$674$	74.7923	2.88089
$675$	−5.77664	−0.222343
$676$	50.7397	1.95153
$677$	42.1837	1.62125	0.810625	−	0.585565i	$-0.199127\pi$
$677$	42.1837	1.62125	0.810625	+	0.585565i	$0.199127\pi$
$678$	12.0380	0.462317
$679$	6.77325	0.259934
$680$	−29.4981	−1.13120
$681$	−17.1510	−0.657229
$682$	−17.0661	−0.653493
$683$	−11.9982	−0.459099	−0.229549	−	0.973297i	$-0.573725\pi$
$683$	−11.9982	−0.459099	−0.229549	+	0.973297i	$0.573725\pi$
$684$	−113.876	−4.35415
$685$	36.2598	1.38542
$686$	24.7975	0.946775
$687$	60.8908	2.32313
$688$	−12.5107	−0.476967
$689$	5.94337	0.226424
$690$	113.928	4.33716
$691$	−18.9656	−0.721487	−0.360744	−	0.932665i	$-0.617477\pi$
$691$	−18.9656	−0.721487	−0.360744	+	0.932665i	$0.617477\pi$
$692$	43.9312	1.67001
$693$	3.60602	0.136982
$694$	−79.4399	−3.01550
$695$	4.04259	0.153344
$696$	32.3188	1.22504
$697$	−13.9824	−0.529620
$698$	−2.97384	−0.112561
$699$	−53.2631	−2.01459
$700$	−2.36887	−0.0895351
$701$	46.9340	1.77267	0.886336	−	0.463043i	$-0.153242\pi$
$701$	46.9340	1.77267	0.886336	+	0.463043i	$0.153242\pi$
$702$	88.8879	3.35486
$703$	−21.3750	−0.806174
$704$	−8.25888	−0.311268
$705$	39.9123	1.50318
$706$	−25.4317	−0.957134
$707$	−11.2755	−0.424060
$708$	161.180	6.05750
$709$	13.1516	0.493919	0.246960	−	0.969026i	$-0.420569\pi$
$709$	13.1516	0.493919	0.246960	+	0.969026i	$0.420569\pi$
$710$	−59.7377	−2.24192
$711$	−11.2374	−0.421437
$712$	−1.28155	−0.0480280
$713$	64.5110	2.41596
$714$	17.2452	0.645384
$715$	9.04574	0.338291
$716$	−77.7334	−2.90503
$717$	80.4559	3.00468
$718$	56.5720	2.11125
$719$	−50.3362	−1.87722	−0.938612	−	0.344975i	$-0.887887\pi$
$719$	−50.3362	−1.87722	−0.938612	+	0.344975i	$0.887887\pi$
$720$	−35.3570	−1.31768
$721$	−11.3930	−0.424299
$722$	−24.6094	−0.915865
$723$	45.1957	1.68085
$724$	4.35765	0.161951
$725$	1.98895	0.0738677
$726$	72.2111	2.68000
$727$	−44.0910	−1.63524	−0.817622	−	0.575756i	$-0.804708\pi$
$727$	−44.0910	−1.63524	−0.817622	+	0.575756i	$0.804708\pi$
$728$	17.5450	0.650259
$729$	−38.1183	−1.41179
$730$	−66.9588	−2.47826
$731$	12.7071	0.469991
$732$	−62.4293	−2.30745
$733$	44.5311	1.64479	0.822397	−	0.568914i	$-0.192636\pi$
$733$	44.5311	1.64479	0.822397	+	0.568914i	$0.192636\pi$
$734$	74.6602	2.75576
$735$	38.2471	1.41077
$736$	10.6122	0.391171
$737$	5.10257	0.187956
$738$	−57.7028	−2.12407
$739$	−2.51888	−0.0926583	−0.0463292	−	0.998926i	$-0.514752\pi$
$739$	−2.51888	−0.0926583	−0.0463292	+	0.998926i	$0.514752\pi$
$740$	−31.2594	−1.14912
$741$	80.3826	2.95293
$742$	2.14778	0.0788475
$743$	36.7837	1.34946	0.674731	−	0.738064i	$-0.264260\pi$
$743$	36.7837	1.34946	0.674731	+	0.738064i	$0.264260\pi$
$744$	−106.750	−3.91364
$745$	−39.1178	−1.43317
$746$	−69.1510	−2.53180
$747$	−29.4163	−1.07629
$748$	−10.6755	−0.390334
$749$	−3.13518	−0.114557
$750$	−83.7229	−3.05713
$751$	22.2085	0.810399	0.405200	−	0.914228i	$-0.367202\pi$
$751$	22.2085	0.810399	0.405200	+	0.914228i	$0.367202\pi$
$752$	−21.1380	−0.770823
$753$	−1.95099	−0.0710979
$754$	−30.6049	−1.11457
$755$	43.6231	1.58761
$756$	21.1513	0.769265
$757$	35.2616	1.28160	0.640802	−	0.767706i	$-0.278602\pi$
$757$	35.2616	1.28160	0.640802	+	0.767706i	$0.278602\pi$
$758$	58.9671	2.14178
$759$	19.8457	0.720352
$760$	−49.6874	−1.80235
$761$	−27.5373	−0.998227	−0.499114	−	0.866536i	$-0.666341\pi$
$761$	−27.5373	−0.998227	−0.499114	+	0.866536i	$0.666341\pi$
$762$	−28.2744	−1.02427
$763$	−8.52960	−0.308792
$764$	−3.36516	−0.121747
$765$	35.9121	1.29841
$766$	74.1734	2.68000
$767$	−73.4664	−2.65272
$768$	−88.4051	−3.19004
$769$	−49.1265	−1.77155	−0.885774	−	0.464116i	$-0.846372\pi$
$769$	−49.1265	−1.77155	−0.885774	+	0.464116i	$0.846372\pi$
$770$	3.26890	0.117803
$771$	26.9768	0.971545
$772$	−61.0850	−2.19850
$773$	−17.3923	−0.625559	−0.312779	−	0.949826i	$-0.601260\pi$
$773$	−17.3923	−0.625559	−0.312779	+	0.949826i	$0.601260\pi$
$774$	52.4402	1.88493
$775$	−6.56955	−0.235985
$776$	−39.8304	−1.42983
$777$	8.79622	0.315563
$778$	16.9597	0.608035
$779$	−23.5523	−0.843847
$780$	117.554	4.20909
$781$	−10.4060	−0.372356
$782$	61.2847	2.19154
$783$	−17.7590	−0.634655
$784$	−20.2561	−0.723432
$785$	18.2842	0.652591
$786$	−62.3907	−2.22540
$787$	−19.5790	−0.697917	−0.348958	−	0.937138i	$-0.613465\pi$
$787$	−19.5790	−0.697917	−0.348958	+	0.937138i	$0.613465\pi$
$788$	−71.8096	−2.55811
$789$	51.8234	1.84496
$790$	−10.1869	−0.362432
$791$	−1.30565	−0.0464236
$792$	−21.2054	−0.753501
$793$	28.4555	1.01049
$794$	30.0863	1.06772
$795$	6.92653	0.245659
$796$	−24.1008	−0.854231
$797$	−10.7744	−0.381650	−0.190825	−	0.981624i	$-0.561116\pi$
$797$	−10.7744	−0.381650	−0.190825	+	0.981624i	$0.561116\pi$
$798$	29.0482	1.02830
$799$	21.4698	0.759548
$800$	−1.08071	−0.0382087
$801$	1.56020	0.0551270
$802$	16.9955	0.600132
$803$	−11.6639	−0.411610
$804$	66.3103	2.33858
$805$	−12.3567	−0.435516
$806$	101.089	3.56071
$807$	41.2974	1.45374
$808$	66.3063	2.33265
$809$	22.2579	0.782547	0.391274	−	0.920274i	$-0.372035\pi$
$809$	22.2579	0.782547	0.391274	+	0.920274i	$0.372035\pi$
$810$	22.2808	0.782866
$811$	8.50592	0.298683	0.149342	−	0.988786i	$-0.452285\pi$
$811$	8.50592	0.298683	0.149342	+	0.988786i	$0.452285\pi$
$812$	−7.28258	−0.255569
$813$	18.7365	0.657118
$814$	−8.26951	−0.289846
$815$	17.2479	0.604169
$816$	−29.4544	−1.03111
$817$	21.4042	0.748840
$818$	70.9671	2.48130
$819$	−21.3599	−0.746375
$820$	−34.4434	−1.20282
$821$	29.9824	1.04639	0.523196	−	0.852212i	$-0.324740\pi$
$821$	29.9824	1.04639	0.523196	+	0.852212i	$0.324740\pi$
$822$	124.657	4.34791
$823$	−2.89787	−0.101013	−0.0505067	−	0.998724i	$-0.516084\pi$
$823$	−2.89787	−0.101013	−0.0505067	+	0.998724i	$0.516084\pi$
$824$	66.9974	2.33396
$825$	−2.02100	−0.0703623
$826$	−26.5489	−0.923753
$827$	−53.5467	−1.86200	−0.931001	−	0.365016i	$-0.881064\pi$
$827$	−53.5467	−1.86200	−0.931001	+	0.365016i	$0.881064\pi$
$828$	166.535	5.78748
$829$	46.3145	1.60857	0.804284	−	0.594245i	$-0.202549\pi$
$829$	46.3145	1.60857	0.804284	+	0.594245i	$0.202549\pi$
$830$	−26.6662	−0.925596
$831$	−35.3217	−1.22530
$832$	48.9206	1.69602
$833$	20.5741	0.712851
$834$	13.8979	0.481247
$835$	−3.81912	−0.132166
$836$	−17.9821	−0.621923
$837$	58.6584	2.02753
$838$	42.9154	1.48249
$839$	3.36586	0.116203	0.0581013	−	0.998311i	$-0.481495\pi$
$839$	3.36586	0.116203	0.0581013	+	0.998311i	$0.481495\pi$
$840$	20.4473	0.705498
$841$	−22.8854	−0.789152
$842$	−78.6384	−2.71006
$843$	44.8095	1.54332
$844$	−55.9324	−1.92527
$845$	−26.9531	−0.927216
$846$	88.6024	3.04621
$847$	−7.83206	−0.269113
$848$	−3.66837	−0.125972
$849$	−80.2918	−2.75561
$850$	−6.24099	−0.214064
$851$	31.2594	1.07156
$852$	−135.231	−4.63294
$853$	−23.9909	−0.821433	−0.410716	−	0.911763i	$-0.634721\pi$
$853$	−23.9909	−0.821433	−0.410716	+	0.911763i	$0.634721\pi$
$854$	10.2831	0.351881
$855$	60.4913	2.06876
$856$	18.4366	0.630149
$857$	−53.6816	−1.83373	−0.916864	−	0.399200i	$-0.869288\pi$
$857$	−53.6816	−1.83373	−0.916864	+	0.399200i	$0.869288\pi$
$858$	31.0982	1.06167
$859$	−13.9614	−0.476358	−0.238179	−	0.971221i	$-0.576551\pi$
$859$	−13.9614	−0.476358	−0.238179	+	0.971221i	$0.576551\pi$
$860$	31.3021	1.06739
$861$	9.69219	0.330309
$862$	−25.9251	−0.883011
$863$	−25.0625	−0.853139	−0.426569	−	0.904455i	$-0.640278\pi$
$863$	−25.0625	−0.853139	−0.426569	+	0.904455i	$0.640278\pi$
$864$	9.64944	0.328281
$865$	−23.3365	−0.793463
$866$	−17.9342	−0.609427
$867$	−19.5529	−0.664050
$868$	24.0546	0.816465
$869$	−1.77450	−0.0601957
$870$	−35.6677	−1.20925
$871$	−30.2245	−1.02412
$872$	50.1587	1.69859
$873$	48.4911	1.64117
$874$	103.230	3.49179
$875$	9.08064	0.306982
$876$	−151.578	−5.12133
$877$	−25.5538	−0.862890	−0.431445	−	0.902139i	$-0.641996\pi$
$877$	−25.5538	−0.862890	−0.431445	+	0.902139i	$0.641996\pi$
$878$	−44.2909	−1.49474
$879$	−2.73932	−0.0923950
$880$	−5.58321	−0.188210
$881$	42.4556	1.43037	0.715183	−	0.698937i	$-0.246343\pi$
$881$	42.4556	1.43037	0.715183	+	0.698937i	$0.246343\pi$
$882$	84.9059	2.85893
$883$	7.08538	0.238442	0.119221	−	0.992868i	$-0.461960\pi$
$883$	7.08538	0.238442	0.119221	+	0.992868i	$0.461960\pi$
$884$	63.2351	2.12683
$885$	−85.6193	−2.87806
$886$	29.5844	0.993906
$887$	−8.94435	−0.300322	−0.150161	−	0.988662i	$-0.547979\pi$
$887$	−8.94435	−0.300322	−0.150161	+	0.988662i	$0.547979\pi$
$888$	−51.7266	−1.73583
$889$	3.06666	0.102853
$890$	1.41434	0.0474088
$891$	3.88120	0.130025
$892$	54.0473	1.80964
$893$	36.1644	1.21019
$894$	−134.482	−4.49777
$895$	41.2923	1.38025
$896$	15.6262	0.522036
$897$	−117.554	−3.92500
$898$	−26.3730	−0.880080
$899$	−20.1966	−0.673595
$900$	−16.9593	−0.565308
$901$	3.72596	0.124130
$902$	−9.11183	−0.303391
$903$	−8.80825	−0.293120
$904$	7.67794	0.255365
$905$	−2.31480	−0.0769466
$906$	149.971	4.98245
$907$	35.8511	1.19042	0.595209	−	0.803571i	$-0.297069\pi$
$907$	35.8511	1.19042	0.595209	+	0.803571i	$0.297069\pi$
$908$	−22.7268	−0.754215
$909$	−80.7238	−2.67744
$910$	−19.3630	−0.641876
$911$	−11.0950	−0.367594	−0.183797	−	0.982964i	$-0.558839\pi$
$911$	−11.0950	−0.367594	−0.183797	+	0.982964i	$0.558839\pi$
$912$	−49.6137	−1.64288
$913$	−4.64511	−0.153731
$914$	60.7737	2.01022
$915$	33.1627	1.09633
$916$	80.6863	2.66595
$917$	6.76694	0.223464
$918$	55.7248	1.83919
$919$	−46.1246	−1.52151	−0.760755	−	0.649039i	$-0.775171\pi$
$919$	−46.1246	−1.52151	−0.760755	+	0.649039i	$0.775171\pi$
$920$	72.6642	2.39567
$921$	70.1047	2.31003
$922$	−23.6484	−0.778820
$923$	61.6389	2.02887
$924$	7.39995	0.243441
$925$	−3.18334	−0.104667
$926$	−75.2491	−2.47284
$927$	−81.5651	−2.67895
$928$	−3.32239	−0.109063
$929$	−37.4421	−1.22843	−0.614217	−	0.789137i	$-0.710528\pi$
$929$	−37.4421	−1.22843	−0.614217	+	0.789137i	$0.710528\pi$
$930$	117.811	3.86318
$931$	34.6556	1.13579
$932$	−70.5788	−2.31189
$933$	47.2340	1.54637
$934$	17.6911	0.578871
$935$	5.67087	0.185457
$936$	125.608	4.10562
$937$	34.3802	1.12315	0.561576	−	0.827425i	$-0.310195\pi$
$937$	34.3802	1.12315	0.561576	+	0.827425i	$0.310195\pi$
$938$	−10.9224	−0.356628
$939$	−17.2279	−0.562211
$940$	52.8877	1.72501
$941$	56.1464	1.83032	0.915160	−	0.403092i	$-0.132065\pi$
$941$	56.1464	1.83032	0.915160	+	0.403092i	$0.132065\pi$
$942$	62.8589	2.04805
$943$	34.4434	1.12163
$944$	45.3449	1.47585
$945$	−11.2357	−0.365496
$946$	8.28082	0.269233
$947$	−5.84384	−0.189899	−0.0949496	−	0.995482i	$-0.530269\pi$
$947$	−5.84384	−0.189899	−0.0949496	+	0.995482i	$0.530269\pi$
$948$	−23.0604	−0.748968
$949$	69.0898	2.24275
$950$	−10.5125	−0.341070
$951$	15.8530	0.514068
$952$	10.9991	0.356483
$953$	13.9841	0.452991	0.226495	−	0.974012i	$-0.427273\pi$
$953$	13.9841	0.452991	0.226495	+	0.974012i	$0.427273\pi$
$954$	15.3764	0.497829
$955$	1.78759	0.0578450
$956$	106.612	3.44808
$957$	−6.21313	−0.200842
$958$	−4.42163	−0.142856
$959$	−13.5204	−0.436596
$960$	57.0131	1.84009
$961$	35.7100	1.15194
$962$	48.9836	1.57929
$963$	−22.4454	−0.723292
$964$	59.8888	1.92889
$965$	32.4486	1.04456
$966$	−42.4809	−1.36680
$967$	−8.46067	−0.272077	−0.136038	−	0.990704i	$-0.543437\pi$
$967$	−8.46067	−0.272077	−0.136038	+	0.990704i	$0.543437\pi$
$968$	46.0568	1.48032
$969$	50.3927	1.61885
$970$	43.9577	1.41140
$971$	−12.2417	−0.392855	−0.196428	−	0.980518i	$-0.562934\pi$
$971$	−12.2417	−0.392855	−0.196428	+	0.980518i	$0.562934\pi$
$972$	−32.6416	−1.04698
$973$	−1.50738	−0.0483244
$974$	−51.3874	−1.64656
$975$	11.9712	0.383385
$976$	−17.5633	−0.562189
$977$	24.6985	0.790176	0.395088	−	0.918643i	$-0.370714\pi$
$977$	24.6985	0.790176	0.395088	+	0.918643i	$0.370714\pi$
$978$	59.2964	1.89609
$979$	0.246371	0.00787405
$980$	50.6812	1.61895
$981$	−61.0651	−1.94966
$982$	−23.3275	−0.744412
$983$	6.83316	0.217944	0.108972	−	0.994045i	$-0.465244\pi$
$983$	6.83316	0.217944	0.108972	+	0.994045i	$0.465244\pi$
$984$	−56.9954	−1.81695
$985$	38.1456	1.21542
$986$	−19.1866	−0.611024
$987$	−14.8823	−0.473709
$988$	106.515	3.38869
$989$	−31.3021	−0.995350
$990$	23.4027	0.743787
$991$	0.829468	0.0263489	0.0131745	−	0.999913i	$-0.495806\pi$
$991$	0.829468	0.0263489	0.0131745	+	0.999913i	$0.495806\pi$
$992$	10.9739	0.348423
$993$	16.6551	0.528533
$994$	22.2747	0.706511
$995$	12.8025	0.405866
$996$	−60.3654	−1.91275
$997$	20.3623	0.644881	0.322441	−	0.946590i	$-0.395497\pi$
$997$	20.3623	0.644881	0.322441	+	0.946590i	$0.395497\pi$
$998$	61.9929	1.96235
$999$	28.4235	0.899279

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.a.1.13	✓	139

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.a.1.13	✓	139	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:	\( N \)	\(=\)	\( 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41992 q^{2} +2.90998 q^{3} +3.85601 q^{4} -2.04833 q^{5} -7.04192 q^{6} +0.763772 q^{7} -4.49140 q^{8} +5.46800 q^{9} +O(q^{10})\)	\(q-2.41992 q^{2} +2.90998 q^{3} +3.85601 q^{4} -2.04833 q^{5} -7.04192 q^{6} +0.763772 q^{7} -4.49140 q^{8} +5.46800 q^{9} +4.95680 q^{10} +0.863449 q^{11} +11.2209 q^{12} -5.11455 q^{13} -1.84827 q^{14} -5.96061 q^{15} +3.15680 q^{16} -3.20636 q^{17} -13.2321 q^{18} -5.40088 q^{19} -7.89839 q^{20} +2.22256 q^{21} -2.08948 q^{22} +7.89839 q^{23} -13.0699 q^{24} -0.804341 q^{25} +12.3768 q^{26} +7.18182 q^{27} +2.94511 q^{28} -2.47277 q^{29} +14.4242 q^{30} +8.16762 q^{31} +1.34359 q^{32} +2.51262 q^{33} +7.75914 q^{34} -1.56446 q^{35} +21.0847 q^{36} +3.95769 q^{37} +13.0697 q^{38} -14.8832 q^{39} +9.19987 q^{40} +4.36082 q^{41} -5.37842 q^{42} -3.96310 q^{43} +3.32947 q^{44} -11.2003 q^{45} -19.1135 q^{46} -6.69601 q^{47} +9.18623 q^{48} -6.41665 q^{49} +1.94644 q^{50} -9.33046 q^{51} -19.7217 q^{52} -1.16205 q^{53} -17.3794 q^{54} -1.76863 q^{55} -3.43040 q^{56} -15.7165 q^{57} +5.98390 q^{58} +14.3642 q^{59} -22.9842 q^{60} -5.56365 q^{61} -19.7650 q^{62} +4.17630 q^{63} -9.56499 q^{64} +10.4763 q^{65} -6.08034 q^{66} +5.90952 q^{67} -12.3638 q^{68} +22.9842 q^{69} +3.78586 q^{70} -12.0517 q^{71} -24.5589 q^{72} -13.5085 q^{73} -9.57730 q^{74} -2.34062 q^{75} -20.8259 q^{76} +0.659478 q^{77} +36.0162 q^{78} -2.05513 q^{79} -6.46617 q^{80} +4.49499 q^{81} -10.5528 q^{82} -5.37972 q^{83} +8.57023 q^{84} +6.56769 q^{85} +9.59039 q^{86} -7.19571 q^{87} -3.87809 q^{88} +0.285333 q^{89} +27.1037 q^{90} -3.90635 q^{91} +30.4563 q^{92} +23.7676 q^{93} +16.2038 q^{94} +11.0628 q^{95} +3.90983 q^{96} +8.86816 q^{97} +15.5278 q^{98} +4.72134 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9} - 40 q^{10} - 17 q^{11} - 59 q^{12} - 89 q^{13} - 15 q^{14} - 29 q^{15} + 73 q^{16} - 58 q^{17} - 51 q^{18} - 37 q^{19} - 24 q^{20} - 37 q^{21} - 99 q^{22} - 42 q^{23} - 27 q^{24} - 11 q^{25} + 2 q^{26} - 73 q^{27} - 113 q^{28} - 57 q^{29} - 29 q^{30} - 51 q^{31} - 80 q^{32} - 78 q^{33} - 28 q^{34} - 34 q^{35} + 28 q^{36} - 117 q^{37} - 31 q^{38} - 36 q^{39} - 107 q^{40} - 60 q^{41} - 41 q^{42} - 109 q^{43} - 21 q^{44} - 62 q^{45} - 92 q^{46} - 26 q^{47} - 90 q^{48} - 7 q^{49} - 22 q^{50} - 47 q^{51} - 182 q^{52} - 83 q^{53} - 19 q^{54} - 53 q^{55} - 23 q^{56} - 201 q^{57} - 112 q^{58} + 14 q^{59} - 64 q^{60} - 73 q^{61} - 21 q^{62} - 94 q^{63} + 14 q^{64} - 123 q^{65} - 10 q^{66} - 135 q^{67} - 84 q^{68} - 50 q^{69} - 35 q^{70} - 29 q^{71} - 143 q^{72} - 266 q^{73} - 53 q^{74} - 32 q^{75} - 66 q^{76} - 69 q^{77} - 59 q^{78} - 124 q^{79} - 20 q^{80} - 33 q^{81} - 93 q^{82} - 28 q^{83} - 4 q^{84} - 179 q^{85} + 6 q^{86} - 40 q^{87} - 259 q^{88} - 41 q^{89} + 2 q^{90} - 50 q^{91} - 77 q^{92} - 60 q^{93} - 48 q^{94} - 37 q^{95} + 3 q^{96} - 220 q^{97} - 9 q^{98} - 35 q^{99}+O(q^{100}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9 - 40 * q^10 - 17 * q^11 - 59 * q^12 - 89 * q^13 - 15 * q^14 - 29 * q^15 + 73 * q^16 - 58 * q^17 - 51 * q^18 - 37 * q^19 - 24 * q^20 - 37 * q^21 - 99 * q^22 - 42 * q^23 - 27 * q^24 - 11 * q^25 + 2 * q^26 - 73 * q^27 - 113 * q^28 - 57 * q^29 - 29 * q^30 - 51 * q^31 - 80 * q^32 - 78 * q^33 - 28 * q^34 - 34 * q^35 + 28 * q^36 - 117 * q^37 - 31 * q^38 - 36 * q^39 - 107 * q^40 - 60 * q^41 - 41 * q^42 - 109 * q^43 - 21 * q^44 - 62 * q^45 - 92 * q^46 - 26 * q^47 - 90 * q^48 - 7 * q^49 - 22 * q^50 - 47 * q^51 - 182 * q^52 - 83 * q^53 - 19 * q^54 - 53 * q^55 - 23 * q^56 - 201 * q^57 - 112 * q^58 + 14 * q^59 - 64 * q^60 - 73 * q^61 - 21 * q^62 - 94 * q^63 + 14 * q^64 - 123 * q^65 - 10 * q^66 - 135 * q^67 - 84 * q^68 - 50 * q^69 - 35 * q^70 - 29 * q^71 - 143 * q^72 - 266 * q^73 - 53 * q^74 - 32 * q^75 - 66 * q^76 - 69 * q^77 - 59 * q^78 - 124 * q^79 - 20 * q^80 - 33 * q^81 - 93 * q^82 - 28 * q^83 - 4 * q^84 - 179 * q^85 + 6 * q^86 - 40 * q^87 - 259 * q^88 - 41 * q^89 + 2 * q^90 - 50 * q^91 - 77 * q^92 - 60 * q^93 - 48 * q^94 - 37 * q^95 + 3 * q^96 - 220 * q^97 - 9 * q^98 - 35 * q^99

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