LMFDB - Embedded newform 4007.2.a.a.1.2

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			1.2
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)

$f(q)$	$=$	$q-2.77109 q^{2} +1.88840 q^{3} +5.67894 q^{4} -0.563279 q^{5} -5.23292 q^{6} +0.553316 q^{7} -10.1947 q^{8} +0.566050 q^{9} +O(q^{10})$	\(q-2.77109 q^{2} +1.88840 q^{3} +5.67894 q^{4} -0.563279 q^{5} -5.23292 q^{6} +0.553316 q^{7} -10.1947 q^{8} +0.566050 q^{9} +1.56090 q^{10} +4.06073 q^{11} +10.7241 q^{12} -6.37400 q^{13} -1.53329 q^{14} -1.06370 q^{15} +16.8925 q^{16} +4.31320 q^{17} -1.56858 q^{18} +1.49204 q^{19} -3.19883 q^{20} +1.04488 q^{21} -11.2527 q^{22} -2.86473 q^{23} -19.2516 q^{24} -4.68272 q^{25} +17.6629 q^{26} -4.59627 q^{27} +3.14225 q^{28} -0.295435 q^{29} +2.94760 q^{30} +5.48212 q^{31} -26.4213 q^{32} +7.66829 q^{33} -11.9523 q^{34} -0.311672 q^{35} +3.21456 q^{36} -8.44258 q^{37} -4.13459 q^{38} -12.0367 q^{39} +5.74245 q^{40} -9.78682 q^{41} -2.89546 q^{42} -1.84442 q^{43} +23.0607 q^{44} -0.318844 q^{45} +7.93841 q^{46} +10.7761 q^{47} +31.8998 q^{48} -6.69384 q^{49} +12.9762 q^{50} +8.14504 q^{51} -36.1976 q^{52} +5.05791 q^{53} +12.7367 q^{54} -2.28733 q^{55} -5.64088 q^{56} +2.81757 q^{57} +0.818677 q^{58} -10.0881 q^{59} -6.04066 q^{60} +5.68368 q^{61} -15.1914 q^{62} +0.313205 q^{63} +39.4307 q^{64} +3.59034 q^{65} -21.2495 q^{66} -10.8289 q^{67} +24.4944 q^{68} -5.40974 q^{69} +0.863670 q^{70} +4.45122 q^{71} -5.77070 q^{72} -7.15132 q^{73} +23.3951 q^{74} -8.84284 q^{75} +8.47322 q^{76} +2.24687 q^{77} +33.3547 q^{78} +2.39024 q^{79} -9.51519 q^{80} -10.3777 q^{81} +27.1202 q^{82} +9.79707 q^{83} +5.93382 q^{84} -2.42953 q^{85} +5.11107 q^{86} -0.557899 q^{87} -41.3979 q^{88} +9.32229 q^{89} +0.883546 q^{90} -3.52684 q^{91} -16.2686 q^{92} +10.3524 q^{93} -29.8615 q^{94} -0.840436 q^{95} -49.8939 q^{96} +2.19310 q^{97} +18.5492 q^{98} +2.29858 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.77109	−1.95946	−0.979728	−	0.200330i	$-0.935798\pi$
$2$	−2.77109	−1.95946	−0.979728	+	0.200330i	$0.935798\pi$
$3$	1.88840	1.09027	0.545134	−	0.838349i	$-0.316479\pi$
$3$	1.88840	1.09027	0.545134	+	0.838349i	$0.316479\pi$
$4$	5.67894	2.83947
$5$	−0.563279	−0.251906	−0.125953	−	0.992036i	$-0.540199\pi$
$5$	−0.563279	−0.251906	−0.125953	+	0.992036i	$0.540199\pi$
$6$	−5.23292	−2.13633
$7$	0.553316	0.209134	0.104567	−	0.994518i	$-0.466654\pi$
$7$	0.553316	0.209134	0.104567	+	0.994518i	$0.466654\pi$
$8$	−10.1947	−3.60436
$9$	0.566050	0.188683
$10$	1.56090	0.493599
$11$	4.06073	1.22436	0.612179	−	0.790719i	$-0.290293\pi$
$11$	4.06073	1.22436	0.612179	+	0.790719i	$0.290293\pi$
$12$	10.7241	3.09578
$13$	−6.37400	−1.76783	−0.883915	−	0.467648i	$-0.845102\pi$
$13$	−6.37400	−1.76783	−0.883915	+	0.467648i	$0.845102\pi$
$14$	−1.53329	−0.409789
$15$	−1.06370	−0.274645
$16$	16.8925	4.22312
$17$	4.31320	1.04610	0.523052	−	0.852301i	$-0.324793\pi$
$17$	4.31320	1.04610	0.523052	+	0.852301i	$0.324793\pi$
$18$	−1.56858	−0.369717
$19$	1.49204	0.342298	0.171149	−	0.985245i	$-0.445252\pi$
$19$	1.49204	0.342298	0.171149	+	0.985245i	$0.445252\pi$
$20$	−3.19883	−0.715280
$21$	1.04488	0.228012
$22$	−11.2527	−2.39908
$23$	−2.86473	−0.597337	−0.298668	−	0.954357i	$-0.596542\pi$
$23$	−2.86473	−0.597337	−0.298668	+	0.954357i	$0.596542\pi$
$24$	−19.2516	−3.92972
$25$	−4.68272	−0.936543
$26$	17.6629	3.46399
$27$	−4.59627	−0.884552
$28$	3.14225	0.593830
$29$	−0.295435	−0.0548609	−0.0274305	−	0.999624i	$-0.508732\pi$
$29$	−0.295435	−0.0548609	−0.0274305	+	0.999624i	$0.508732\pi$
$30$	2.94760	0.538155
$31$	5.48212	0.984617	0.492308	−	0.870421i	$-0.336153\pi$
$31$	5.48212	0.984617	0.492308	+	0.870421i	$0.336153\pi$
$32$	−26.4213	−4.67066
$33$	7.66829	1.33488
$34$	−11.9523	−2.04980
$35$	−0.311672	−0.0526821
$36$	3.21456	0.535761
$37$	−8.44258	−1.38795	−0.693976	−	0.719999i	$-0.744142\pi$
$37$	−8.44258	−1.38795	−0.693976	+	0.719999i	$0.744142\pi$
$38$	−4.13459	−0.670718
$39$	−12.0367	−1.92741
$40$	5.74245	0.907961
$41$	−9.78682	−1.52844	−0.764222	−	0.644953i	$-0.776877\pi$
$41$	−9.78682	−1.52844	−0.764222	+	0.644953i	$0.776877\pi$
$42$	−2.89546	−0.446780
$43$	−1.84442	−0.281272	−0.140636	−	0.990061i	$-0.544915\pi$
$43$	−1.84442	−0.281272	−0.140636	+	0.990061i	$0.544915\pi$
$44$	23.0607	3.47653
$45$	−0.318844	−0.0475305
$46$	7.93841	1.17046
$47$	10.7761	1.57185	0.785927	−	0.618320i	$-0.212186\pi$
$47$	10.7761	1.57185	0.785927	+	0.618320i	$0.212186\pi$
$48$	31.8998	4.60433
$49$	−6.69384	−0.956263
$50$	12.9762	1.83512
$51$	8.14504	1.14053
$52$	−36.1976	−5.01970
$53$	5.05791	0.694758	0.347379	−	0.937725i	$-0.387072\pi$
$53$	5.05791	0.694758	0.347379	+	0.937725i	$0.387072\pi$
$54$	12.7367	1.73324
$55$	−2.28733	−0.308423
$56$	−5.64088	−0.753795
$57$	2.81757	0.373196
$58$	0.818677	0.107498
$59$	−10.0881	−1.31336	−0.656682	−	0.754168i	$-0.728041\pi$
$59$	−10.0881	−1.31336	−0.656682	+	0.754168i	$0.728041\pi$
$60$	−6.04066	−0.779846
$61$	5.68368	0.727720	0.363860	−	0.931454i	$-0.381459\pi$
$61$	5.68368	0.727720	0.363860	+	0.931454i	$0.381459\pi$
$62$	−15.1914	−1.92931
$63$	0.313205	0.0394601
$64$	39.4307	4.92884
$65$	3.59034	0.445327
$66$	−21.2495	−2.61563
$67$	−10.8289	−1.32296	−0.661482	−	0.749961i	$-0.730072\pi$
$67$	−10.8289	−1.32296	−0.661482	+	0.749961i	$0.730072\pi$
$68$	24.4944	2.97038
$69$	−5.40974	−0.651257
$70$	0.863670	0.103228
$71$	4.45122	0.528262	0.264131	−	0.964487i	$-0.414915\pi$
$71$	4.45122	0.528262	0.264131	+	0.964487i	$0.414915\pi$
$72$	−5.77070	−0.680083
$73$	−7.15132	−0.836999	−0.418500	−	0.908217i	$-0.637444\pi$
$73$	−7.15132	−0.836999	−0.418500	+	0.908217i	$0.637444\pi$
$74$	23.3951	2.71963
$75$	−8.84284	−1.02108
$76$	8.47322	0.971945
$77$	2.24687	0.256055
$78$	33.3547	3.77667
$79$	2.39024	0.268923	0.134462	−	0.990919i	$-0.457069\pi$
$79$	2.39024	0.268923	0.134462	+	0.990919i	$0.457069\pi$
$80$	−9.51519	−1.06383
$81$	−10.3777	−1.15308
$82$	27.1202	2.99492
$83$	9.79707	1.07537	0.537684	−	0.843146i	$-0.319299\pi$
$83$	9.79707	1.07537	0.537684	+	0.843146i	$0.319299\pi$
$84$	5.93382	0.647433
$85$	−2.42953	−0.263520
$86$	5.11107	0.551141
$87$	−0.557899	−0.0598131
$88$	−41.3979	−4.41303
$89$	9.32229	0.988160	0.494080	−	0.869416i	$-0.335505\pi$
$89$	9.32229	0.988160	0.494080	+	0.869416i	$0.335505\pi$
$90$	0.883546	0.0931339
$91$	−3.52684	−0.369713
$92$	−16.2686	−1.69612
$93$	10.3524	1.07350
$94$	−29.8615	−3.07998
$95$	−0.840436	−0.0862270
$96$	−49.8939	−5.09227
$97$	2.19310	0.222675	0.111338	−	0.993783i	$-0.464487\pi$
$97$	2.19310	0.222675	0.111338	+	0.993783i	$0.464487\pi$
$98$	18.5492	1.87376
$99$	2.29858	0.231016
$100$	−26.5929	−2.65929
$101$	0.941801	0.0937127	0.0468564	−	0.998902i	$-0.485080\pi$
$101$	0.941801	0.0937127	0.0468564	+	0.998902i	$0.485080\pi$
$102$	−22.5706	−2.23483
$103$	−15.1268	−1.49048	−0.745242	−	0.666794i	$-0.767666\pi$
$103$	−15.1268	−1.49048	−0.745242	+	0.666794i	$0.767666\pi$
$104$	64.9809	6.37190
$105$	−0.588560	−0.0574376
$106$	−14.0159	−1.36135
$107$	−10.2891	−0.994682	−0.497341	−	0.867555i	$-0.665690\pi$
$107$	−10.2891	−0.994682	−0.497341	+	0.867555i	$0.665690\pi$
$108$	−26.1019	−2.51166
$109$	3.62003	0.346736	0.173368	−	0.984857i	$-0.444535\pi$
$109$	3.62003	0.346736	0.173368	+	0.984857i	$0.444535\pi$
$110$	6.33839	0.604342
$111$	−15.9430	−1.51324
$112$	9.34689	0.883198
$113$	−0.730621	−0.0687311	−0.0343655	−	0.999409i	$-0.510941\pi$
$113$	−0.730621	−0.0687311	−0.0343655	+	0.999409i	$0.510941\pi$
$114$	−7.80775	−0.731262
$115$	1.61364	0.150473
$116$	−1.67776	−0.155776
$117$	−3.60800	−0.333560
$118$	27.9551	2.57348
$119$	2.38656	0.218776
$120$	10.8440	0.989920
$121$	5.48956	0.499051
$122$	−15.7500	−1.42594
$123$	−18.4814	−1.66641
$124$	31.1326	2.79579
$125$	5.45407	0.487827
$126$	−0.867918	−0.0773203
$127$	−17.9762	−1.59513	−0.797564	−	0.603234i	$-0.793878\pi$
$127$	−17.9762	−1.59513	−0.797564	+	0.603234i	$0.793878\pi$
$128$	−56.4236	−4.98719
$129$	−3.48301	−0.306662
$130$	−9.94916	−0.872599
$131$	−15.8833	−1.38773	−0.693864	−	0.720106i	$-0.744093\pi$
$131$	−15.8833	−1.38773	−0.693864	+	0.720106i	$0.744093\pi$
$132$	43.5477	3.79034
$133$	0.825572	0.0715861
$134$	30.0079	2.59229
$135$	2.58898	0.222824
$136$	−43.9717	−3.77054
$137$	−4.61139	−0.393978	−0.196989	−	0.980406i	$-0.563116\pi$
$137$	−4.61139	−0.393978	−0.196989	+	0.980406i	$0.563116\pi$
$138$	14.9909	1.27611
$139$	−2.10741	−0.178748	−0.0893739	−	0.995998i	$-0.528487\pi$
$139$	−2.10741	−0.178748	−0.0893739	+	0.995998i	$0.528487\pi$
$140$	−1.76996	−0.149589
$141$	20.3495	1.71374
$142$	−12.3347	−1.03511
$143$	−25.8831	−2.16446
$144$	9.56200	0.796833
$145$	0.166412	0.0138198
$146$	19.8170	1.64006
$147$	−12.6406	−1.04258
$148$	−47.9449	−3.94105
$149$	−12.8809	−1.05524	−0.527622	−	0.849479i	$-0.676916\pi$
$149$	−12.8809	−1.05524	−0.527622	+	0.849479i	$0.676916\pi$
$150$	24.5043	2.00077
$151$	−4.99527	−0.406509	−0.203255	−	0.979126i	$-0.565152\pi$
$151$	−4.99527	−0.406509	−0.203255	+	0.979126i	$0.565152\pi$
$152$	−15.2109	−1.23377
$153$	2.44149	0.197382
$154$	−6.22628	−0.501728
$155$	−3.08796	−0.248031
$156$	−68.3555	−5.47282
$157$	−18.8036	−1.50069	−0.750345	−	0.661047i	$-0.770113\pi$
$157$	−18.8036	−1.50069	−0.750345	+	0.661047i	$0.770113\pi$
$158$	−6.62358	−0.526944
$159$	9.55136	0.757472
$160$	14.8825	1.17657
$161$	−1.58510	−0.124923
$162$	28.7576	2.25941
$163$	10.4912	0.821738	0.410869	−	0.911694i	$-0.365225\pi$
$163$	10.4912	0.821738	0.410869	+	0.911694i	$0.365225\pi$
$164$	−55.5788	−4.33997
$165$	−4.31938	−0.336264
$166$	−27.1486	−2.10714
$167$	−18.7856	−1.45368	−0.726838	−	0.686809i	$-0.759011\pi$
$167$	−18.7856	−1.45368	−0.726838	+	0.686809i	$0.759011\pi$
$168$	−10.6522	−0.821838
$169$	27.6279	2.12522
$170$	6.73246	0.516356
$171$	0.844571	0.0645859
$172$	−10.4744	−0.798664
$173$	18.6589	1.41861	0.709307	−	0.704900i	$-0.249008\pi$
$173$	18.6589	1.41861	0.709307	+	0.704900i	$0.249008\pi$
$174$	1.54599	0.117201
$175$	−2.59102	−0.195863
$176$	68.5959	5.17061
$177$	−19.0504	−1.43192
$178$	−25.8329	−1.93626
$179$	22.9329	1.71408	0.857042	−	0.515246i	$-0.172299\pi$
$179$	22.9329	1.71408	0.857042	+	0.515246i	$0.172299\pi$
$180$	−1.81070	−0.134961
$181$	−17.4306	−1.29561	−0.647803	−	0.761808i	$-0.724312\pi$
$181$	−17.4306	−1.29561	−0.647803	+	0.761808i	$0.724312\pi$
$182$	9.77319	0.724437
$183$	10.7330	0.793410
$184$	29.2050	2.15302
$185$	4.75553	0.349633
$186$	−28.6875	−2.10347
$187$	17.5148	1.28081
$188$	61.1967	4.46323
$189$	−2.54319	−0.184990
$190$	2.32893	0.168958
$191$	21.3911	1.54781	0.773904	−	0.633303i	$-0.218301\pi$
$191$	21.3911	1.54781	0.773904	+	0.633303i	$0.218301\pi$
$192$	74.4610	5.37376
$193$	6.51163	0.468718	0.234359	−	0.972150i	$-0.424701\pi$
$193$	6.51163	0.468718	0.234359	+	0.972150i	$0.424701\pi$
$194$	−6.07727	−0.436322
$195$	6.78000	0.485526
$196$	−38.0139	−2.71528
$197$	8.97403	0.639373	0.319687	−	0.947523i	$-0.396422\pi$
$197$	8.97403	0.639373	0.319687	+	0.947523i	$0.396422\pi$
$198$	−6.36957	−0.452666
$199$	11.2098	0.794643	0.397322	−	0.917679i	$-0.369940\pi$
$199$	11.2098	0.794643	0.397322	+	0.917679i	$0.369940\pi$
$200$	47.7388	3.37564
$201$	−20.4493	−1.44239
$202$	−2.60982	−0.183626
$203$	−0.163469	−0.0114733
$204$	46.2552	3.23851
$205$	5.51271	0.385024
$206$	41.9176	2.92054
$207$	−1.62158	−0.112707
$208$	−107.673	−7.46576
$209$	6.05879	0.419095
$210$	1.63095	0.112546
$211$	−28.6360	−1.97138	−0.985690	−	0.168566i	$-0.946086\pi$
$211$	−28.6360	−1.97138	−0.985690	+	0.168566i	$0.946086\pi$
$212$	28.7236	1.97275
$213$	8.40568	0.575947
$214$	28.5119	1.94904
$215$	1.03893	0.0708542
$216$	46.8575	3.18825
$217$	3.03334	0.205917
$218$	−10.0314	−0.679414
$219$	−13.5046	−0.912553
$220$	−12.9896	−0.875758
$221$	−27.4923	−1.84933
$222$	44.1794	2.96512
$223$	−6.24278	−0.418048	−0.209024	−	0.977911i	$-0.567029\pi$
$223$	−6.24278	−0.418048	−0.209024	+	0.977911i	$0.567029\pi$
$224$	−14.6193	−0.976794
$225$	−2.65065	−0.176710
$226$	2.02462	0.134676
$227$	−10.8034	−0.717049	−0.358524	−	0.933520i	$-0.616720\pi$
$227$	−10.8034	−0.717049	−0.358524	+	0.933520i	$0.616720\pi$
$228$	16.0008	1.05968
$229$	0.461118	0.0304715	0.0152358	−	0.999884i	$-0.495150\pi$
$229$	0.461118	0.0304715	0.0152358	+	0.999884i	$0.495150\pi$
$230$	−4.47154	−0.294845
$231$	4.24299	0.279168
$232$	3.01187	0.197739
$233$	−27.3232	−1.79000	−0.895000	−	0.446065i	$-0.852825\pi$
$233$	−27.3232	−1.79000	−0.895000	+	0.446065i	$0.852825\pi$
$234$	9.99810	0.653596
$235$	−6.06994	−0.395959
$236$	−57.2899	−3.72926
$237$	4.51373	0.293199
$238$	−6.61338	−0.428682
$239$	2.53755	0.164140	0.0820701	−	0.996627i	$-0.473847\pi$
$239$	2.53755	0.164140	0.0820701	+	0.996627i	$0.473847\pi$
$240$	−17.9685	−1.15986
$241$	20.8942	1.34592	0.672958	−	0.739681i	$-0.265024\pi$
$241$	20.8942	1.34592	0.672958	+	0.739681i	$0.265024\pi$
$242$	−15.2121	−0.977869
$243$	−5.80850	−0.372616
$244$	32.2773	2.06634
$245$	3.77050	0.240888
$246$	51.2137	3.26527
$247$	−9.51028	−0.605125
$248$	−55.8884	−3.54892
$249$	18.5008	1.17244
$250$	−15.1137	−0.955876
$251$	21.0285	1.32731	0.663654	−	0.748040i	$-0.269005\pi$
$251$	21.0285	1.32731	0.663654	+	0.748040i	$0.269005\pi$
$252$	1.77867	0.112046
$253$	−11.6329	−0.731354
$254$	49.8136	3.12558
$255$	−4.58793	−0.287307
$256$	77.4934	4.84334
$257$	−6.78658	−0.423335	−0.211668	−	0.977342i	$-0.567889\pi$
$257$	−6.78658	−0.423335	−0.211668	+	0.977342i	$0.567889\pi$
$258$	9.65173	0.600891
$259$	−4.67142	−0.290268
$260$	20.3893	1.26449
$261$	−0.167231	−0.0103513
$262$	44.0140	2.71919
$263$	−5.85732	−0.361178	−0.180589	−	0.983559i	$-0.557800\pi$
$263$	−5.85732	−0.361178	−0.180589	+	0.983559i	$0.557800\pi$
$264$	−78.1757	−4.81138
$265$	−2.84902	−0.175014
$266$	−2.28773	−0.140270
$267$	17.6042	1.07736
$268$	−61.4969	−3.75652
$269$	−0.865022	−0.0527413	−0.0263707	−	0.999652i	$-0.508395\pi$
$269$	−0.865022	−0.0527413	−0.0263707	+	0.999652i	$0.508395\pi$
$270$	−7.17430	−0.436614
$271$	−0.974170	−0.0591766	−0.0295883	−	0.999562i	$-0.509420\pi$
$271$	−0.974170	−0.0591766	−0.0295883	+	0.999562i	$0.509420\pi$
$272$	72.8607	4.41783
$273$	−6.66008	−0.403086
$274$	12.7786	0.771982
$275$	−19.0153	−1.14666
$276$	−30.7216	−1.84922
$277$	6.14106	0.368981	0.184490	−	0.982834i	$-0.440937\pi$
$277$	6.14106	0.368981	0.184490	+	0.982834i	$0.440937\pi$
$278$	5.83981	0.350249
$279$	3.10315	0.185781
$280$	3.17739	0.189885
$281$	−20.8052	−1.24113	−0.620566	−	0.784154i	$-0.713097\pi$
$281$	−20.8052	−1.24113	−0.620566	+	0.784154i	$0.713097\pi$
$282$	−56.3904	−3.35800
$283$	13.1424	0.781237	0.390619	−	0.920553i	$-0.372261\pi$
$283$	13.1424	0.781237	0.390619	+	0.920553i	$0.372261\pi$
$284$	25.2782	1.49999
$285$	−1.58708	−0.0940105
$286$	71.7245	4.24116
$287$	−5.41521	−0.319650
$288$	−14.9558	−0.881277
$289$	1.60368	0.0943341
$290$	−0.461144	−0.0270793
$291$	4.14144	0.242776
$292$	−40.6119	−2.37663
$293$	−9.12092	−0.532850	−0.266425	−	0.963856i	$-0.585842\pi$
$293$	−9.12092	−0.532850	−0.266425	+	0.963856i	$0.585842\pi$
$294$	35.0284	2.04290
$295$	5.68244	0.330844
$296$	86.0694	5.00268
$297$	−18.6642	−1.08301
$298$	35.6941	2.06770
$299$	18.2598	1.05599
$300$	−50.2180	−2.89933
$301$	−1.02055	−0.0588235
$302$	13.8424	0.796538
$303$	1.77850	0.102172
$304$	25.2043	1.44557
$305$	−3.20150	−0.183317
$306$	−6.76558	−0.386762
$307$	−14.7143	−0.839787	−0.419894	−	0.907573i	$-0.637933\pi$
$307$	−14.7143	−0.839787	−0.419894	+	0.907573i	$0.637933\pi$
$308$	12.7598	0.727060
$309$	−28.5654	−1.62503
$310$	8.55702	0.486006
$311$	1.52907	0.0867054	0.0433527	−	0.999060i	$-0.486196\pi$
$311$	1.52907	0.0867054	0.0433527	+	0.999060i	$0.486196\pi$
$312$	122.710	6.94708
$313$	5.62343	0.317855	0.158928	−	0.987290i	$-0.449196\pi$
$313$	5.62343	0.317855	0.158928	+	0.987290i	$0.449196\pi$
$314$	52.1064	2.94054
$315$	−0.176422	−0.00994023
$316$	13.5741	0.763600
$317$	33.9067	1.90439	0.952196	−	0.305489i	$-0.0988198\pi$
$317$	33.9067	1.90439	0.952196	+	0.305489i	$0.0988198\pi$
$318$	−26.4677	−1.48423
$319$	−1.19968	−0.0671694
$320$	−22.2105	−1.24161
$321$	−19.4299	−1.08447
$322$	4.39245	0.244782
$323$	6.43548	0.358079
$324$	−58.9346	−3.27414
$325$	29.8476	1.65565
$326$	−29.0722	−1.61016
$327$	6.83606	0.378035
$328$	99.7735	5.50907
$329$	5.96258	0.328728
$330$	11.9694	0.658894
$331$	−10.3935	−0.571276	−0.285638	−	0.958338i	$-0.592205\pi$
$331$	−10.3935	−0.571276	−0.285638	+	0.958338i	$0.592205\pi$
$332$	55.6370	3.05348
$333$	−4.77892	−0.261883
$334$	52.0567	2.84841
$335$	6.09971	0.333263
$336$	17.6507	0.962923
$337$	−10.4905	−0.571455	−0.285727	−	0.958311i	$-0.592235\pi$
$337$	−10.4905	−0.571455	−0.285727	+	0.958311i	$0.592235\pi$
$338$	−76.5594	−4.16428
$339$	−1.37970	−0.0749353
$340$	−13.7972	−0.748257
$341$	22.2614	1.20552
$342$	−2.34038	−0.126553
$343$	−7.57703	−0.409121
$344$	18.8033	1.01381
$345$	3.04720	0.164056
$346$	−51.7056	−2.77971
$347$	−8.07380	−0.433424	−0.216712	−	0.976236i	$-0.569533\pi$
$347$	−8.07380	−0.433424	−0.216712	+	0.976236i	$0.569533\pi$
$348$	−3.16828	−0.169837
$349$	−6.53245	−0.349674	−0.174837	−	0.984597i	$-0.555940\pi$
$349$	−6.53245	−0.349674	−0.174837	+	0.984597i	$0.555940\pi$
$350$	7.17996	0.383785
$351$	29.2966	1.56374
$352$	−107.290	−5.71856
$353$	25.8338	1.37500	0.687498	−	0.726186i	$-0.258709\pi$
$353$	25.8338	1.37500	0.687498	+	0.726186i	$0.258709\pi$
$354$	52.7905	2.80578
$355$	−2.50728	−0.133073
$356$	52.9407	2.80585
$357$	4.50678	0.238524
$358$	−63.5491	−3.35867
$359$	−23.8298	−1.25769	−0.628844	−	0.777531i	$-0.716472\pi$
$359$	−23.8298	−1.25769	−0.628844	+	0.777531i	$0.716472\pi$
$360$	3.25051	0.171317
$361$	−16.7738	−0.882832
$362$	48.3018	2.53868
$363$	10.3665	0.544099
$364$	−20.0287	−1.04979
$365$	4.02819	0.210845
$366$	−29.7422	−1.55465
$367$	−5.52463	−0.288383	−0.144192	−	0.989550i	$-0.546058\pi$
$367$	−5.52463	−0.288383	−0.144192	+	0.989550i	$0.546058\pi$
$368$	−48.3924	−2.52263
$369$	−5.53983	−0.288392
$370$	−13.1780	−0.685091
$371$	2.79863	0.145297
$372$	58.7908	3.04816
$373$	16.6815	0.863736	0.431868	−	0.901937i	$-0.357855\pi$
$373$	16.6815	0.863736	0.431868	+	0.901937i	$0.357855\pi$
$374$	−48.5350	−2.50968
$375$	10.2995	0.531862
$376$	−109.859	−5.66553
$377$	1.88310	0.0969848
$378$	7.04741	0.362480
$379$	24.4215	1.25445	0.627223	−	0.778840i	$-0.284191\pi$
$379$	24.4215	1.25445	0.627223	+	0.778840i	$0.284191\pi$
$380$	−4.77279	−0.244839
$381$	−33.9462	−1.73912
$382$	−59.2768	−3.03286
$383$	12.6981	0.648841	0.324420	−	0.945913i	$-0.394831\pi$
$383$	12.6981	0.648841	0.324420	+	0.945913i	$0.394831\pi$
$384$	−106.550	−5.43737
$385$	−1.26562	−0.0645017
$386$	−18.0443	−0.918432
$387$	−1.04404	−0.0530714
$388$	12.4545	0.632280
$389$	−1.76441	−0.0894591	−0.0447295	−	0.998999i	$-0.514243\pi$
$389$	−1.76441	−0.0894591	−0.0447295	+	0.998999i	$0.514243\pi$
$390$	−18.7880	−0.951367
$391$	−12.3561	−0.624876
$392$	68.2416	3.44672
$393$	−29.9940	−1.51300
$394$	−24.8678	−1.25282
$395$	−1.34637	−0.0677435
$396$	13.0535	0.655963
$397$	21.0583	1.05688	0.528442	−	0.848969i	$-0.322776\pi$
$397$	21.0583	1.05688	0.528442	+	0.848969i	$0.322776\pi$
$398$	−31.0634	−1.55707
$399$	1.55901	0.0780480
$400$	−79.1028	−3.95514
$401$	25.1967	1.25826	0.629130	−	0.777300i	$-0.283411\pi$
$401$	25.1967	1.25826	0.629130	+	0.777300i	$0.283411\pi$
$402$	56.6670	2.82629
$403$	−34.9430	−1.74064
$404$	5.34843	0.266095
$405$	5.84556	0.290468
$406$	0.452988	0.0224814
$407$	−34.2831	−1.69935
$408$	−83.0361	−4.11090
$409$	−31.4503	−1.55512	−0.777558	−	0.628811i	$-0.783542\pi$
$409$	−31.4503	−1.55512	−0.777558	+	0.628811i	$0.783542\pi$
$410$	−15.2762	−0.754439
$411$	−8.70815	−0.429541
$412$	−85.9040	−4.23219
$413$	−5.58193	−0.274669
$414$	4.49354	0.220845
$415$	−5.51849	−0.270892
$416$	168.409	8.25694
$417$	−3.97962	−0.194883
$418$	−16.7895	−0.821199
$419$	−40.6885	−1.98776	−0.993882	−	0.110443i	$-0.964773\pi$
$419$	−40.6885	−1.98776	−0.993882	+	0.110443i	$0.964773\pi$
$420$	−3.34240	−0.163092
$421$	27.4189	1.33632	0.668158	−	0.744020i	$-0.267083\pi$
$421$	27.4189	1.33632	0.668158	+	0.744020i	$0.267083\pi$
$422$	79.3528	3.86284
$423$	6.09980	0.296582
$424$	−51.5638	−2.50416
$425$	−20.1975	−0.979722
$426$	−23.2929	−1.12854
$427$	3.14487	0.152191
$428$	−58.4310	−2.82437
$429$	−48.8777	−2.35984
$430$	−2.87896	−0.138836
$431$	−3.74635	−0.180455	−0.0902276	−	0.995921i	$-0.528759\pi$
$431$	−3.74635	−0.180455	−0.0902276	+	0.995921i	$0.528759\pi$
$432$	−77.6424	−3.73557
$433$	4.92452	0.236657	0.118329	−	0.992974i	$-0.462246\pi$
$433$	4.92452	0.236657	0.118329	+	0.992974i	$0.462246\pi$
$434$	−8.40567	−0.403485
$435$	0.314253	0.0150673
$436$	20.5579	0.984547
$437$	−4.27429	−0.204467
$438$	37.4223	1.78811
$439$	−37.6385	−1.79639	−0.898194	−	0.439600i	$-0.855120\pi$
$439$	−37.6385	−1.79639	−0.898194	+	0.439600i	$0.855120\pi$
$440$	23.3186	1.11167
$441$	−3.78905	−0.180431
$442$	76.1837	3.62369
$443$	−14.3264	−0.680669	−0.340334	−	0.940304i	$-0.610540\pi$
$443$	−14.3264	−0.680669	−0.340334	+	0.940304i	$0.610540\pi$
$444$	−90.5391	−4.29680
$445$	−5.25105	−0.248924
$446$	17.2993	0.819146
$447$	−24.3243	−1.15050
$448$	21.8177	1.03079
$449$	5.45727	0.257544	0.128772	−	0.991674i	$-0.458896\pi$
$449$	5.45727	0.257544	0.128772	+	0.991674i	$0.458896\pi$
$450$	7.34520	0.346256
$451$	−39.7417	−1.87136
$452$	−4.14916	−0.195160
$453$	−9.43307	−0.443204
$454$	29.9373	1.40503
$455$	1.98659	0.0931330
$456$	−28.7242	−1.34514
$457$	−30.9357	−1.44711	−0.723556	−	0.690266i	$-0.757494\pi$
$457$	−30.9357	−1.44711	−0.723556	+	0.690266i	$0.757494\pi$
$458$	−1.27780	−0.0597077
$459$	−19.8246	−0.925334
$460$	9.16377	0.427263
$461$	−31.6920	−1.47604	−0.738021	−	0.674778i	$-0.764239\pi$
$461$	−31.6920	−1.47604	−0.738021	+	0.674778i	$0.764239\pi$
$462$	−11.7577	−0.547018
$463$	28.7878	1.33788	0.668941	−	0.743315i	$-0.266748\pi$
$463$	28.7878	1.33788	0.668941	+	0.743315i	$0.266748\pi$
$464$	−4.99064	−0.231684
$465$	−5.83130	−0.270420
$466$	75.7150	3.50743
$467$	9.98010	0.461824	0.230912	−	0.972975i	$-0.425829\pi$
$467$	9.98010	0.461824	0.230912	+	0.972975i	$0.425829\pi$
$468$	−20.4896	−0.947134
$469$	−5.99182	−0.276677
$470$	16.8204	0.775865
$471$	−35.5087	−1.63615
$472$	102.845	4.73384
$473$	−7.48972	−0.344378
$474$	−12.5080	−0.574510
$475$	−6.98681	−0.320577
$476$	13.5532	0.621208
$477$	2.86303	0.131089
$478$	−7.03177	−0.321626
$479$	−10.1753	−0.464920	−0.232460	−	0.972606i	$-0.574677\pi$
$479$	−10.1753	−0.464920	−0.232460	+	0.972606i	$0.574677\pi$
$480$	28.1042	1.28277
$481$	53.8130	2.45366
$482$	−57.8998	−2.63726
$483$	−2.99330	−0.136200
$484$	31.1749	1.41704
$485$	−1.23533	−0.0560932
$486$	16.0959	0.730124
$487$	−31.4414	−1.42475	−0.712373	−	0.701801i	$-0.752380\pi$
$487$	−31.4414	−1.42475	−0.712373	+	0.701801i	$0.752380\pi$
$488$	−57.9433	−2.62297
$489$	19.8117	0.895914
$490$	−10.4484	−0.472010
$491$	−19.4237	−0.876580	−0.438290	−	0.898834i	$-0.644416\pi$
$491$	−19.4237	−0.876580	−0.438290	+	0.898834i	$0.644416\pi$
$492$	−104.955	−4.73173
$493$	−1.27427	−0.0573902
$494$	26.3539	1.18572
$495$	−1.29474	−0.0581943
$496$	92.6066	4.15816
$497$	2.46293	0.110478
$498$	−51.2673	−2.29734
$499$	−2.75372	−0.123273	−0.0616367	−	0.998099i	$-0.519632\pi$
$499$	−2.75372	−0.123273	−0.0616367	+	0.998099i	$0.519632\pi$
$500$	30.9734	1.38517
$501$	−35.4747	−1.58489
$502$	−58.2719	−2.60080
$503$	−5.56496	−0.248129	−0.124065	−	0.992274i	$-0.539593\pi$
$503$	−5.56496	−0.248129	−0.124065	+	0.992274i	$0.539593\pi$
$504$	−3.19302	−0.142228
$505$	−0.530497	−0.0236068
$506$	32.2358	1.43306
$507$	52.1725	2.31706
$508$	−102.086	−4.52932
$509$	−27.6087	−1.22373	−0.611867	−	0.790961i	$-0.709581\pi$
$509$	−27.6087	−1.22373	−0.611867	+	0.790961i	$0.709581\pi$
$510$	12.7136	0.562966
$511$	−3.95694	−0.175045
$512$	−101.894	−4.50312
$513$	−6.85783	−0.302781
$514$	18.8062	0.829507
$515$	8.52059	0.375462
$516$	−19.7798	−0.870758
$517$	43.7588	1.92451
$518$	12.9449	0.568767
$519$	35.2355	1.54667
$520$	−36.6024	−1.60512
$521$	24.5979	1.07765	0.538826	−	0.842417i	$-0.318868\pi$
$521$	24.5979	1.07765	0.538826	+	0.842417i	$0.318868\pi$
$522$	0.463412	0.0202830
$523$	−22.9783	−1.00477	−0.502385	−	0.864644i	$-0.667544\pi$
$523$	−22.9783	−1.00477	−0.502385	+	0.864644i	$0.667544\pi$
$524$	−90.2002	−3.94041
$525$	−4.89289	−0.213543
$526$	16.2311	0.707712
$527$	23.6455	1.03001
$528$	129.536	5.63735
$529$	−14.7933	−0.643189
$530$	7.89488	0.342932
$531$	−5.71039	−0.247810
$532$	4.68837	0.203267
$533$	62.3812	2.70203
$534$	−48.7828	−2.11104
$535$	5.79562	0.250566
$536$	110.397	4.76844
$537$	43.3064	1.86881
$538$	2.39705	0.103344
$539$	−27.1819	−1.17081
$540$	14.7027	0.632702
$541$	38.1961	1.64218	0.821089	−	0.570801i	$-0.193367\pi$
$541$	38.1961	1.64218	0.821089	+	0.570801i	$0.193367\pi$
$542$	2.69951	0.115954
$543$	−32.9159	−1.41256
$544$	−113.960	−4.88600
$545$	−2.03909	−0.0873449
$546$	18.4557	0.789830
$547$	−44.4624	−1.90108	−0.950538	−	0.310609i	$-0.899467\pi$
$547$	−44.4624	−1.90108	−0.950538	+	0.310609i	$0.899467\pi$
$548$	−26.1878	−1.11869
$549$	3.21725	0.137309
$550$	52.6930	2.24684
$551$	−0.440802	−0.0187788
$552$	55.1506	2.34737
$553$	1.32256	0.0562410
$554$	−17.0174	−0.723001
$555$	8.98033	0.381194
$556$	−11.9678	−0.507549
$557$	−12.8458	−0.544292	−0.272146	−	0.962256i	$-0.587733\pi$
$557$	−12.8458	−0.544292	−0.272146	+	0.962256i	$0.587733\pi$
$558$	−8.59911	−0.364029
$559$	11.7564	0.497241
$560$	−5.26491	−0.222483
$561$	33.0748	1.39642
$562$	57.6530	2.43195
$563$	10.7635	0.453629	0.226814	−	0.973938i	$-0.427169\pi$
$563$	10.7635	0.453629	0.226814	+	0.973938i	$0.427169\pi$
$564$	115.564	4.86612
$565$	0.411544	0.0173138
$566$	−36.4189	−1.53080
$567$	−5.74217	−0.241149
$568$	−45.3787	−1.90405
$569$	−3.41240	−0.143055	−0.0715277	−	0.997439i	$-0.522787\pi$
$569$	−3.41240	−0.143055	−0.0715277	+	0.997439i	$0.522787\pi$
$570$	4.39794	0.184209
$571$	20.4247	0.854748	0.427374	−	0.904075i	$-0.359439\pi$
$571$	20.4247	0.854748	0.427374	+	0.904075i	$0.359439\pi$
$572$	−146.989	−6.14591
$573$	40.3950	1.68752
$574$	15.0060	0.626340
$575$	13.4147	0.559432
$576$	22.3198	0.929990
$577$	−42.2053	−1.75703	−0.878514	−	0.477716i	$-0.841465\pi$
$577$	−42.2053	−1.75703	−0.878514	+	0.477716i	$0.841465\pi$
$578$	−4.44394	−0.184844
$579$	12.2966	0.511028
$580$	0.945046	0.0392409
$581$	5.42088	0.224896
$582$	−11.4763	−0.475708
$583$	20.5388	0.850632
$584$	72.9055	3.01685
$585$	2.03231	0.0840258
$586$	25.2749	1.04410
$587$	3.77989	0.156013	0.0780064	−	0.996953i	$-0.475145\pi$
$587$	3.77989	0.156013	0.0780064	+	0.996953i	$0.475145\pi$
$588$	−71.7855	−2.96038
$589$	8.17955	0.337032
$590$	−15.7465	−0.648275
$591$	16.9465	0.697088
$592$	−142.616	−5.86149
$593$	−23.8759	−0.980467	−0.490234	−	0.871591i	$-0.663089\pi$
$593$	−23.8759	−0.980467	−0.490234	+	0.871591i	$0.663089\pi$
$594$	51.7203	2.12211
$595$	−1.34430	−0.0551110
$596$	−73.1498	−2.99633
$597$	21.1686	0.866374
$598$	−50.5995	−2.06917
$599$	34.9643	1.42860	0.714301	−	0.699838i	$-0.246745\pi$
$599$	34.9643	1.42860	0.714301	+	0.699838i	$0.246745\pi$
$600$	90.1499	3.68035
$601$	−40.1744	−1.63875	−0.819375	−	0.573258i	$-0.805679\pi$
$601$	−40.1744	−1.63875	−0.819375	+	0.573258i	$0.805679\pi$
$602$	2.82804	0.115262
$603$	−6.12972	−0.249621
$604$	−28.3679	−1.15427
$605$	−3.09216	−0.125714
$606$	−4.92837	−0.200201
$607$	9.03554	0.366741	0.183371	−	0.983044i	$-0.441299\pi$
$607$	9.03554	0.366741	0.183371	+	0.983044i	$0.441299\pi$
$608$	−39.4217	−1.59876
$609$	−0.308695	−0.0125089
$610$	8.87164	0.359202
$611$	−68.6868	−2.77877
$612$	13.8651	0.560462
$613$	40.6502	1.64185	0.820924	−	0.571038i	$-0.193459\pi$
$613$	40.6502	1.64185	0.820924	+	0.571038i	$0.193459\pi$
$614$	40.7745	1.64553
$615$	10.4102	0.419780
$616$	−22.9061	−0.922914
$617$	28.4652	1.14596	0.572982	−	0.819568i	$-0.305786\pi$
$617$	28.4652	1.14596	0.572982	+	0.819568i	$0.305786\pi$
$618$	79.1572	3.18417
$619$	−20.7939	−0.835776	−0.417888	−	0.908498i	$-0.637230\pi$
$619$	−20.7939	−0.835776	−0.417888	+	0.908498i	$0.637230\pi$
$620$	−17.5363	−0.704277
$621$	13.1670	0.528375
$622$	−4.23718	−0.169895
$623$	5.15817	0.206658
$624$	−203.329	−8.13968
$625$	20.3414	0.813657
$626$	−15.5830	−0.622824
$627$	11.4414	0.456926
$628$	−106.784	−4.26116
$629$	−36.4145	−1.45194
$630$	0.488880	0.0194775
$631$	9.51649	0.378845	0.189423	−	0.981896i	$-0.439338\pi$
$631$	9.51649	0.378845	0.189423	+	0.981896i	$0.439338\pi$
$632$	−24.3678	−0.969298
$633$	−54.0761	−2.14933
$634$	−93.9586	−3.73157
$635$	10.1256	0.401822
$636$	54.2416	2.15082
$637$	42.6666	1.69051
$638$	3.32443	0.131615
$639$	2.51961	0.0996743
$640$	31.7822	1.25630
$641$	20.9090	0.825856	0.412928	−	0.910764i	$-0.364506\pi$
$641$	20.9090	0.825856	0.412928	+	0.910764i	$0.364506\pi$
$642$	53.8419	2.12497
$643$	7.78870	0.307156	0.153578	−	0.988137i	$-0.450920\pi$
$643$	7.78870	0.307156	0.153578	+	0.988137i	$0.450920\pi$
$644$	−9.00169	−0.354716
$645$	1.96191	0.0772500
$646$	−17.8333	−0.701641
$647$	−32.9627	−1.29590	−0.647948	−	0.761685i	$-0.724373\pi$
$647$	−32.9627	−1.29590	−0.647948	+	0.761685i	$0.724373\pi$
$648$	105.798	4.15613
$649$	−40.9652	−1.60803
$650$	−82.7105	−3.24417
$651$	5.72816	0.224504
$652$	59.5792	2.33330
$653$	−4.44457	−0.173930	−0.0869648	−	0.996211i	$-0.527717\pi$
$653$	−4.44457	−0.173930	−0.0869648	+	0.996211i	$0.527717\pi$
$654$	−18.9433	−0.740743
$655$	8.94672	0.349577
$656$	−165.324	−6.45481
$657$	−4.04801	−0.157928
$658$	−16.5229	−0.644128
$659$	39.2904	1.53054	0.765269	−	0.643711i	$-0.222606\pi$
$659$	39.2904	1.53054	0.765269	+	0.643711i	$0.222606\pi$
$660$	−24.5295	−0.954811
$661$	35.7676	1.39120	0.695600	−	0.718430i	$-0.255139\pi$
$661$	35.7676	1.39120	0.695600	+	0.718430i	$0.255139\pi$
$662$	28.8012	1.11939
$663$	−51.9165	−2.01627
$664$	−99.8780	−3.87602
$665$	−0.465027	−0.0180330
$666$	13.2428	0.513149
$667$	0.846340	0.0327704
$668$	−106.682	−4.12767
$669$	−11.7889	−0.455784
$670$	−16.9028	−0.653014
$671$	23.0799	0.890990
$672$	−27.6071	−1.06497
$673$	20.7088	0.798265	0.399132	−	0.916893i	$-0.369311\pi$
$673$	20.7088	0.798265	0.399132	+	0.916893i	$0.369311\pi$
$674$	29.0702	1.11974
$675$	21.5230	0.828422
$676$	156.897	6.03451
$677$	−32.0568	−1.23204	−0.616021	−	0.787730i	$-0.711256\pi$
$677$	−32.0568	−1.23204	−0.616021	+	0.787730i	$0.711256\pi$
$678$	3.82329	0.146832
$679$	1.21348	0.0465689
$680$	24.7683	0.949822
$681$	−20.4012	−0.781775
$682$	−61.6884	−2.36217
$683$	−9.06957	−0.347037	−0.173519	−	0.984831i	$-0.555514\pi$
$683$	−9.06957	−0.347037	−0.173519	+	0.984831i	$0.555514\pi$
$684$	4.79627	0.183390
$685$	2.59750	0.0992454
$686$	20.9966	0.801655
$687$	0.870775	0.0332221
$688$	−31.1569	−1.18785
$689$	−32.2392	−1.22821
$690$	−8.44405	−0.321460
$691$	7.43765	0.282941	0.141471	−	0.989942i	$-0.454817\pi$
$691$	7.43765	0.282941	0.141471	+	0.989942i	$0.454817\pi$
$692$	105.963	4.02811
$693$	1.27184	0.0483132
$694$	22.3732	0.849276
$695$	1.18706	0.0450277
$696$	5.68760	0.215588
$697$	−42.2125	−1.59891
$698$	18.1020	0.685171
$699$	−51.5971	−1.95158
$700$	−14.7143	−0.556147
$701$	7.50865	0.283598	0.141799	−	0.989895i	$-0.454711\pi$
$701$	7.50865	0.283598	0.141799	+	0.989895i	$0.454711\pi$
$702$	−81.1836	−3.06408
$703$	−12.5967	−0.475093
$704$	160.118	6.03466
$705$	−11.4625	−0.431702
$706$	−71.5879	−2.69425
$707$	0.521114	0.0195985
$708$	−108.186	−4.06589
$709$	−19.0943	−0.717101	−0.358550	−	0.933510i	$-0.616729\pi$
$709$	−19.0943	−0.717101	−0.358550	+	0.933510i	$0.616729\pi$
$710$	6.94789	0.260750
$711$	1.35300	0.0507414
$712$	−95.0377	−3.56169
$713$	−15.7048	−0.588148
$714$	−12.4887	−0.467378
$715$	14.5794	0.545240
$716$	130.235	4.86709
$717$	4.79190	0.178957
$718$	66.0345	2.46439
$719$	−18.0703	−0.673908	−0.336954	−	0.941521i	$-0.609397\pi$
$719$	−18.0703	−0.673908	−0.336954	+	0.941521i	$0.609397\pi$
$720$	−5.38607	−0.200727
$721$	−8.36988	−0.311711
$722$	46.4817	1.72987
$723$	39.4566	1.46741
$724$	−98.9874	−3.67884
$725$	1.38344	0.0513796
$726$	−28.7265	−1.06614
$727$	26.2656	0.974137	0.487068	−	0.873364i	$-0.338066\pi$
$727$	26.2656	0.974137	0.487068	+	0.873364i	$0.338066\pi$
$728$	35.9550	1.33258
$729$	20.1644	0.746831
$730$	−11.1625	−0.413142
$731$	−7.95537	−0.294240
$732$	60.9524	2.25286
$733$	19.5007	0.720276	0.360138	−	0.932899i	$-0.382730\pi$
$733$	19.5007	0.720276	0.360138	+	0.932899i	$0.382730\pi$
$734$	15.3092	0.565075
$735$	7.12021	0.262633
$736$	75.6897	2.78996
$737$	−43.9734	−1.61978
$738$	15.3514	0.565092
$739$	−30.9978	−1.14027	−0.570137	−	0.821550i	$-0.693110\pi$
$739$	−30.9978	−1.14027	−0.570137	+	0.821550i	$0.693110\pi$
$740$	27.0064	0.992773
$741$	−17.9592	−0.659748
$742$	−7.75525	−0.284704
$743$	−4.03191	−0.147917	−0.0739583	−	0.997261i	$-0.523563\pi$
$743$	−4.03191	−0.147917	−0.0739583	+	0.997261i	$0.523563\pi$
$744$	−105.540	−3.86927
$745$	7.25554	0.265822
$746$	−46.2260	−1.69245
$747$	5.54563	0.202904
$748$	99.4653	3.63681
$749$	−5.69311	−0.208022
$750$	−28.5407	−1.04216
$751$	−14.1230	−0.515355	−0.257678	−	0.966231i	$-0.582957\pi$
$751$	−14.1230	−0.515355	−0.257678	+	0.966231i	$0.582957\pi$
$752$	182.035	6.63813
$753$	39.7102	1.44712
$754$	−5.21825	−0.190037
$755$	2.81373	0.102402
$756$	−14.4426	−0.525273
$757$	13.9644	0.507546	0.253773	−	0.967264i	$-0.418328\pi$
$757$	13.9644	0.507546	0.253773	+	0.967264i	$0.418328\pi$
$758$	−67.6741	−2.45803
$759$	−21.9675	−0.797371
$760$	8.56798	0.310793
$761$	13.7905	0.499906	0.249953	−	0.968258i	$-0.419585\pi$
$761$	13.7905	0.499906	0.249953	+	0.968258i	$0.419585\pi$
$762$	94.0680	3.40772
$763$	2.00302	0.0725143
$764$	121.479	4.39496
$765$	−1.37524	−0.0497218
$766$	−35.1875	−1.27138
$767$	64.3018	2.32180
$768$	146.338	5.28053
$769$	46.4206	1.67397	0.836984	−	0.547227i	$-0.184317\pi$
$769$	46.4206	1.67397	0.836984	+	0.547227i	$0.184317\pi$
$770$	3.50713	0.126388
$771$	−12.8158	−0.461549
$772$	36.9792	1.33091
$773$	50.1478	1.80369	0.901846	−	0.432057i	$-0.142212\pi$
$773$	50.1478	1.80369	0.901846	+	0.432057i	$0.142212\pi$
$774$	2.89312	0.103991
$775$	−25.6712	−0.922136
$776$	−22.3579	−0.802602
$777$	−8.82150	−0.316469
$778$	4.88934	0.175291
$779$	−14.6024	−0.523184
$780$	38.5032	1.37864
$781$	18.0752	0.646782
$782$	34.2400	1.22442
$783$	1.35790	0.0485273
$784$	−113.076	−4.03842
$785$	10.5917	0.378033
$786$	83.1160	2.96465
$787$	−0.641628	−0.0228716	−0.0114358	−	0.999935i	$-0.503640\pi$
$787$	−0.641628	−0.0228716	−0.0114358	+	0.999935i	$0.503640\pi$
$788$	50.9630	1.81548
$789$	−11.0609	−0.393780
$790$	3.73093	0.132740
$791$	−0.404265	−0.0143740
$792$	−23.4333	−0.832665
$793$	−36.2278	−1.28649
$794$	−58.3544	−2.07092
$795$	−5.38008	−0.190812
$796$	63.6599	2.25637
$797$	−46.9402	−1.66271	−0.831353	−	0.555744i	$-0.812433\pi$
$797$	−46.9402	−1.66271	−0.831353	+	0.555744i	$0.812433\pi$
$798$	−4.32015	−0.152932
$799$	46.4794	1.64432
$800$	123.723	4.37428
$801$	5.27688	0.186449
$802$	−69.8222	−2.46551
$803$	−29.0396	−1.02479
$804$	−116.131	−4.09561
$805$	0.892853	0.0314689
$806$	96.8302	3.41070
$807$	−1.63351	−0.0575022
$808$	−9.60136	−0.337775
$809$	−49.4251	−1.73770	−0.868848	−	0.495080i	$-0.835139\pi$
$809$	−49.4251	−1.73770	−0.868848	+	0.495080i	$0.835139\pi$
$810$	−16.1986	−0.569160
$811$	22.5613	0.792234	0.396117	−	0.918200i	$-0.370357\pi$
$811$	22.5613	0.792234	0.396117	+	0.918200i	$0.370357\pi$
$812$	−0.928331	−0.0325780
$813$	−1.83962	−0.0645183
$814$	95.0015	3.32980
$815$	−5.90950	−0.207001
$816$	137.590	4.81661
$817$	−2.75196	−0.0962789
$818$	87.1515	3.04718
$819$	−1.99637	−0.0697587
$820$	31.3064	1.09327
$821$	24.1596	0.843178	0.421589	−	0.906787i	$-0.361473\pi$
$821$	24.1596	0.843178	0.421589	+	0.906787i	$0.361473\pi$
$822$	24.1311	0.841667
$823$	37.3890	1.30330	0.651650	−	0.758520i	$-0.274077\pi$
$823$	37.3890	1.30330	0.651650	+	0.758520i	$0.274077\pi$
$824$	154.212	5.37225
$825$	−35.9084	−1.25017
$826$	15.4680	0.538202
$827$	24.3812	0.847816	0.423908	−	0.905705i	$-0.360658\pi$
$827$	24.3812	0.847816	0.423908	+	0.905705i	$0.360658\pi$
$828$	−9.20885	−0.320030
$829$	−31.2493	−1.08533	−0.542666	−	0.839949i	$-0.682585\pi$
$829$	−31.2493	−1.08533	−0.542666	+	0.839949i	$0.682585\pi$
$830$	15.2922	0.530801
$831$	11.5968	0.402288
$832$	−251.332	−8.71335
$833$	−28.8719	−1.00035
$834$	11.0279	0.381865
$835$	10.5815	0.366190
$836$	34.4075	1.19001
$837$	−25.1973	−0.870945
$838$	112.752	3.89494
$839$	13.8609	0.478531	0.239265	−	0.970954i	$-0.423093\pi$
$839$	13.8609	0.478531	0.239265	+	0.970954i	$0.423093\pi$
$840$	6.00018	0.207026
$841$	−28.9127	−0.996990
$842$	−75.9803	−2.61845
$843$	−39.2885	−1.35317
$844$	−162.622	−5.59768
$845$	−15.5622	−0.535357
$846$	−16.9031	−0.581141
$847$	3.03747	0.104369
$848$	85.4408	2.93405
$849$	24.8182	0.851757
$850$	55.9691	1.91972
$851$	24.1857	0.829074
$852$	47.7353	1.63539
$853$	48.6846	1.66693	0.833464	−	0.552573i	$-0.186354\pi$
$853$	48.6846	1.66693	0.833464	+	0.552573i	$0.186354\pi$
$854$	−8.71472	−0.298212
$855$	−0.475729	−0.0162696
$856$	104.894	3.58519
$857$	−27.1212	−0.926441	−0.463221	−	0.886243i	$-0.653306\pi$
$857$	−27.1212	−0.926441	−0.463221	+	0.886243i	$0.653306\pi$
$858$	135.444	4.62400
$859$	−1.42312	−0.0485564	−0.0242782	−	0.999705i	$-0.507729\pi$
$859$	−1.42312	−0.0485564	−0.0242782	+	0.999705i	$0.507729\pi$
$860$	5.90000	0.201188
$861$	−10.2261	−0.348504
$862$	10.3815	0.353594
$863$	−13.3198	−0.453412	−0.226706	−	0.973963i	$-0.572796\pi$
$863$	−13.3198	−0.453412	−0.226706	+	0.973963i	$0.572796\pi$
$864$	121.439	4.13145
$865$	−10.5102	−0.357357
$866$	−13.6463	−0.463719
$867$	3.02839	0.102849
$868$	17.2262	0.584695
$869$	9.70615	0.329258
$870$	−0.870823	−0.0295237
$871$	69.0236	2.33878
$872$	−36.9050	−1.24976
$873$	1.24140	0.0420151
$874$	11.8445	0.400645
$875$	3.01783	0.102021
$876$	−76.6916	−2.59117
$877$	−8.61762	−0.290996	−0.145498	−	0.989359i	$-0.546478\pi$
$877$	−8.61762	−0.290996	−0.145498	+	0.989359i	$0.546478\pi$
$878$	104.300	3.51994
$879$	−17.2239	−0.580949
$880$	−38.6387	−1.30251
$881$	−52.9751	−1.78478	−0.892388	−	0.451268i	$-0.850972\pi$
$881$	−52.9751	−1.78478	−0.892388	+	0.451268i	$0.850972\pi$
$882$	10.4998	0.353547
$883$	33.4586	1.12597	0.562986	−	0.826466i	$-0.309652\pi$
$883$	33.4586	1.12597	0.562986	+	0.826466i	$0.309652\pi$
$884$	−156.127	−5.25113
$885$	10.7307	0.360709
$886$	39.6998	1.33374
$887$	10.5191	0.353196	0.176598	−	0.984283i	$-0.443491\pi$
$887$	10.5191	0.353196	0.176598	+	0.984283i	$0.443491\pi$
$888$	162.533	5.45426
$889$	−9.94651	−0.333595
$890$	14.5511	0.487755
$891$	−42.1412	−1.41178
$892$	−35.4524	−1.18703
$893$	16.0784	0.538042
$894$	67.4047	2.25435
$895$	−12.9176	−0.431788
$896$	−31.2201	−1.04299
$897$	34.4817	1.15131
$898$	−15.1226	−0.504647
$899$	−1.61961	−0.0540170
$900$	−15.0529	−0.501763
$901$	21.8158	0.726789
$902$	110.128	3.66685
$903$	−1.92721	−0.0641334
$904$	7.44845	0.247732
$905$	9.81829	0.326371
$906$	26.1399	0.868439
$907$	−10.9400	−0.363255	−0.181628	−	0.983367i	$-0.558137\pi$
$907$	−10.9400	−0.363255	−0.181628	+	0.983367i	$0.558137\pi$
$908$	−61.3520	−2.03604
$909$	0.533107	0.0176820
$910$	−5.50503	−0.182490
$911$	−36.9117	−1.22294	−0.611470	−	0.791267i	$-0.709422\pi$
$911$	−36.9117	−1.22294	−0.611470	+	0.791267i	$0.709422\pi$
$912$	47.5958	1.57605
$913$	39.7833	1.31664
$914$	85.7257	2.83555
$915$	−6.04570	−0.199865
$916$	2.61866	0.0865230
$917$	−8.78848	−0.290221
$918$	54.9358	1.81315
$919$	0.649363	0.0214205	0.0107103	−	0.999943i	$-0.496591\pi$
$919$	0.649363	0.0214205	0.0107103	+	0.999943i	$0.496591\pi$
$920$	−16.4505	−0.542358
$921$	−27.7864	−0.915593
$922$	87.8213	2.89224
$923$	−28.3721	−0.933878
$924$	24.0957	0.792690
$925$	39.5342	1.29988
$926$	−79.7736	−2.62152
$927$	−8.56250	−0.281229
$928$	7.80577	0.256237
$929$	11.3868	0.373587	0.186794	−	0.982399i	$-0.440190\pi$
$929$	11.3868	0.373587	0.186794	+	0.982399i	$0.440190\pi$
$930$	16.1591	0.529877
$931$	−9.98750	−0.327327
$932$	−155.167	−5.08266
$933$	2.88749	0.0945321
$934$	−27.6558	−0.904924
$935$	−9.86569	−0.322643
$936$	36.7824	1.20227
$937$	−18.1522	−0.593008	−0.296504	−	0.955032i	$-0.595821\pi$
$937$	−18.1522	−0.593008	−0.296504	+	0.955032i	$0.595821\pi$
$938$	16.6039	0.542136
$939$	10.6193	0.346547
$940$	−34.4708	−1.12431
$941$	9.82428	0.320262	0.160131	−	0.987096i	$-0.448808\pi$
$941$	9.82428	0.320262	0.160131	+	0.987096i	$0.448808\pi$
$942$	98.3977	3.20597
$943$	28.0366	0.912996
$944$	−170.414	−5.54650
$945$	1.43253	0.0466001
$946$	20.7547	0.674793
$947$	−11.0348	−0.358584	−0.179292	−	0.983796i	$-0.557381\pi$
$947$	−11.0348	−0.358584	−0.179292	+	0.983796i	$0.557381\pi$
$948$	25.6332	0.832529
$949$	45.5825	1.47967
$950$	19.3611	0.628157
$951$	64.0294	2.07630
$952$	−24.3302	−0.788548
$953$	29.4279	0.953262	0.476631	−	0.879103i	$-0.341858\pi$
$953$	29.4279	0.953262	0.476631	+	0.879103i	$0.341858\pi$
$954$	−7.93372	−0.256864
$955$	−12.0492	−0.389902
$956$	14.4106	0.466071
$957$	−2.26548	−0.0732326
$958$	28.1966	0.910991
$959$	−2.55156	−0.0823941
$960$	−41.9423	−1.35368
$961$	−0.946412	−0.0305294
$962$	−149.121	−4.80784
$963$	−5.82413	−0.187680
$964$	118.657	3.82169
$965$	−3.66787	−0.118073
$966$	8.29470	0.266878
$967$	16.7936	0.540046	0.270023	−	0.962854i	$-0.412969\pi$
$967$	16.7936	0.540046	0.270023	+	0.962854i	$0.412969\pi$
$968$	−55.9643	−1.79876
$969$	12.1527	0.390402
$970$	3.42320	0.109912
$971$	19.1853	0.615687	0.307843	−	0.951437i	$-0.400393\pi$
$971$	19.1853	0.615687	0.307843	+	0.951437i	$0.400393\pi$
$972$	−32.9861	−1.05803
$973$	−1.16606	−0.0373822
$974$	87.1270	2.79173
$975$	56.3643	1.80510
$976$	96.0115	3.07325
$977$	−9.17842	−0.293644	−0.146822	−	0.989163i	$-0.546904\pi$
$977$	−9.17842	−0.293644	−0.146822	+	0.989163i	$0.546904\pi$
$978$	−54.8999	−1.75550
$979$	37.8553	1.20986
$980$	21.4125	0.683996
$981$	2.04912	0.0654233
$982$	53.8249	1.71762
$983$	17.0110	0.542566	0.271283	−	0.962500i	$-0.412552\pi$
$983$	17.0110	0.542566	0.271283	+	0.962500i	$0.412552\pi$
$984$	188.412	6.00636
$985$	−5.05488	−0.161062
$986$	3.53112	0.112454
$987$	11.2597	0.358401
$988$	−54.0083	−1.71823
$989$	5.28377	0.168014
$990$	3.58784	0.114029
$991$	9.21688	0.292784	0.146392	−	0.989227i	$-0.453234\pi$
$991$	9.21688	0.292784	0.146392	+	0.989227i	$0.453234\pi$
$992$	−144.844	−4.59882
$993$	−19.6270	−0.622844
$994$	−6.82501	−0.216476
$995$	−6.31426	−0.200175
$996$	105.065	3.32911
$997$	57.3385	1.81593	0.907965	−	0.419047i	$-0.137636\pi$
$997$	57.3385	1.81593	0.907965	+	0.419047i	$0.137636\pi$
$998$	7.63080	0.241549
$999$	38.8043	1.22772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.a.1.2	✓	139

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.a.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-2.77109 q^{2} +1.88840 q^{3} +5.67894 q^{4} -0.563279 q^{5} -5.23292 q^{6} +0.553316 q^{7} -10.1947 q^{8} +0.566050 q^{9} +O(q^{10})\)	\(q-2.77109 q^{2} +1.88840 q^{3} +5.67894 q^{4} -0.563279 q^{5} -5.23292 q^{6} +0.553316 q^{7} -10.1947 q^{8} +0.566050 q^{9} +1.56090 q^{10} +4.06073 q^{11} +10.7241 q^{12} -6.37400 q^{13} -1.53329 q^{14} -1.06370 q^{15} +16.8925 q^{16} +4.31320 q^{17} -1.56858 q^{18} +1.49204 q^{19} -3.19883 q^{20} +1.04488 q^{21} -11.2527 q^{22} -2.86473 q^{23} -19.2516 q^{24} -4.68272 q^{25} +17.6629 q^{26} -4.59627 q^{27} +3.14225 q^{28} -0.295435 q^{29} +2.94760 q^{30} +5.48212 q^{31} -26.4213 q^{32} +7.66829 q^{33} -11.9523 q^{34} -0.311672 q^{35} +3.21456 q^{36} -8.44258 q^{37} -4.13459 q^{38} -12.0367 q^{39} +5.74245 q^{40} -9.78682 q^{41} -2.89546 q^{42} -1.84442 q^{43} +23.0607 q^{44} -0.318844 q^{45} +7.93841 q^{46} +10.7761 q^{47} +31.8998 q^{48} -6.69384 q^{49} +12.9762 q^{50} +8.14504 q^{51} -36.1976 q^{52} +5.05791 q^{53} +12.7367 q^{54} -2.28733 q^{55} -5.64088 q^{56} +2.81757 q^{57} +0.818677 q^{58} -10.0881 q^{59} -6.04066 q^{60} +5.68368 q^{61} -15.1914 q^{62} +0.313205 q^{63} +39.4307 q^{64} +3.59034 q^{65} -21.2495 q^{66} -10.8289 q^{67} +24.4944 q^{68} -5.40974 q^{69} +0.863670 q^{70} +4.45122 q^{71} -5.77070 q^{72} -7.15132 q^{73} +23.3951 q^{74} -8.84284 q^{75} +8.47322 q^{76} +2.24687 q^{77} +33.3547 q^{78} +2.39024 q^{79} -9.51519 q^{80} -10.3777 q^{81} +27.1202 q^{82} +9.79707 q^{83} +5.93382 q^{84} -2.42953 q^{85} +5.11107 q^{86} -0.557899 q^{87} -41.3979 q^{88} +9.32229 q^{89} +0.883546 q^{90} -3.52684 q^{91} -16.2686 q^{92} +10.3524 q^{93} -29.8615 q^{94} -0.840436 q^{95} -49.8939 q^{96} +2.19310 q^{97} +18.5492 q^{98} +2.29858 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) \) 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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