LMFDB - Embedded newform 4007.2.a.a.1.15

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			1.15
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)

$f(q)$	$=$	$q-2.38393 q^{2} -0.401819 q^{3} +3.68311 q^{4} -0.901205 q^{5} +0.957907 q^{6} -4.24761 q^{7} -4.01240 q^{8} -2.83854 q^{9} +O(q^{10})$	\(q-2.38393 q^{2} -0.401819 q^{3} +3.68311 q^{4} -0.901205 q^{5} +0.957907 q^{6} -4.24761 q^{7} -4.01240 q^{8} -2.83854 q^{9} +2.14841 q^{10} -4.16429 q^{11} -1.47994 q^{12} +2.41900 q^{13} +10.1260 q^{14} +0.362121 q^{15} +2.19907 q^{16} +1.73192 q^{17} +6.76688 q^{18} -1.31439 q^{19} -3.31923 q^{20} +1.70677 q^{21} +9.92736 q^{22} +3.24463 q^{23} +1.61226 q^{24} -4.18783 q^{25} -5.76672 q^{26} +2.34604 q^{27} -15.6444 q^{28} -3.04665 q^{29} -0.863270 q^{30} +8.65003 q^{31} +2.78240 q^{32} +1.67329 q^{33} -4.12878 q^{34} +3.82796 q^{35} -10.4547 q^{36} -5.37898 q^{37} +3.13341 q^{38} -0.972000 q^{39} +3.61600 q^{40} +7.59869 q^{41} -4.06881 q^{42} +5.83438 q^{43} -15.3375 q^{44} +2.55811 q^{45} -7.73496 q^{46} +11.1492 q^{47} -0.883626 q^{48} +11.0422 q^{49} +9.98348 q^{50} -0.695919 q^{51} +8.90944 q^{52} +1.94852 q^{53} -5.59278 q^{54} +3.75288 q^{55} +17.0431 q^{56} +0.528146 q^{57} +7.26300 q^{58} +0.809463 q^{59} +1.33373 q^{60} +7.11433 q^{61} -20.6210 q^{62} +12.0570 q^{63} -11.0312 q^{64} -2.18001 q^{65} -3.98900 q^{66} +2.89421 q^{67} +6.37886 q^{68} -1.30375 q^{69} -9.12559 q^{70} +2.61966 q^{71} +11.3894 q^{72} -2.79512 q^{73} +12.8231 q^{74} +1.68275 q^{75} -4.84103 q^{76} +17.6883 q^{77} +2.31718 q^{78} -10.3469 q^{79} -1.98181 q^{80} +7.57294 q^{81} -18.1147 q^{82} -8.13330 q^{83} +6.28621 q^{84} -1.56082 q^{85} -13.9087 q^{86} +1.22420 q^{87} +16.7088 q^{88} +3.51461 q^{89} -6.09834 q^{90} -10.2750 q^{91} +11.9503 q^{92} -3.47575 q^{93} -26.5788 q^{94} +1.18453 q^{95} -1.11802 q^{96} -14.9937 q^{97} -26.3237 q^{98} +11.8205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.38393	−1.68569	−0.842845	−	0.538156i	$-0.819121\pi$
$2$	−2.38393	−1.68569	−0.842845	+	0.538156i	$0.819121\pi$
$3$	−0.401819	−0.231990	−0.115995	−	0.993250i	$-0.537006\pi$
$3$	−0.401819	−0.231990	−0.115995	+	0.993250i	$0.537006\pi$
$4$	3.68311	1.84155
$5$	−0.901205	−0.403031	−0.201516	−	0.979485i	$-0.564587\pi$
$5$	−0.901205	−0.403031	−0.201516	+	0.979485i	$0.564587\pi$
$6$	0.957907	0.391064
$7$	−4.24761	−1.60544	−0.802722	−	0.596353i	$-0.796616\pi$
$7$	−4.24761	−1.60544	−0.802722	+	0.596353i	$0.796616\pi$
$8$	−4.01240	−1.41860
$9$	−2.83854	−0.946181
$10$	2.14841	0.679386
$11$	−4.16429	−1.25558	−0.627790	−	0.778383i	$-0.716040\pi$
$11$	−4.16429	−1.25558	−0.627790	+	0.778383i	$0.716040\pi$
$12$	−1.47994	−0.427222
$13$	2.41900	0.670910	0.335455	−	0.942056i	$-0.391110\pi$
$13$	2.41900	0.670910	0.335455	+	0.942056i	$0.391110\pi$
$14$	10.1260	2.70628
$15$	0.362121	0.0934993
$16$	2.19907	0.549766
$17$	1.73192	0.420053	0.210027	−	0.977696i	$-0.432645\pi$
$17$	1.73192	0.420053	0.210027	+	0.977696i	$0.432645\pi$
$18$	6.76688	1.59497
$19$	−1.31439	−0.301541	−0.150771	−	0.988569i	$-0.548176\pi$
$19$	−1.31439	−0.301541	−0.150771	+	0.988569i	$0.548176\pi$
$20$	−3.31923	−0.742203
$21$	1.70677	0.372447
$22$	9.92736	2.11652
$23$	3.24463	0.676552	0.338276	−	0.941047i	$-0.390156\pi$
$23$	3.24463	0.676552	0.338276	+	0.941047i	$0.390156\pi$
$24$	1.61226	0.329101
$25$	−4.18783	−0.837566
$26$	−5.76672	−1.13095
$27$	2.34604	0.451495
$28$	−15.6444	−2.95651
$29$	−3.04665	−0.565749	−0.282875	−	0.959157i	$-0.591288\pi$
$29$	−3.04665	−0.565749	−0.282875	+	0.959157i	$0.591288\pi$
$30$	−0.863270	−0.157611
$31$	8.65003	1.55359	0.776796	−	0.629752i	$-0.216844\pi$
$31$	8.65003	1.55359	0.776796	+	0.629752i	$0.216844\pi$
$32$	2.78240	0.491863
$33$	1.67329	0.291282
$34$	−4.12878	−0.708080
$35$	3.82796	0.647044
$36$	−10.4547	−1.74244
$37$	−5.37898	−0.884299	−0.442150	−	0.896941i	$-0.645784\pi$
$37$	−5.37898	−0.884299	−0.442150	+	0.896941i	$0.645784\pi$
$38$	3.13341	0.508306
$39$	−0.972000	−0.155645
$40$	3.61600	0.571740
$41$	7.59869	1.18672	0.593358	−	0.804939i	$-0.297802\pi$
$41$	7.59869	1.18672	0.593358	+	0.804939i	$0.297802\pi$
$42$	−4.06881	−0.627831
$43$	5.83438	0.889734	0.444867	−	0.895597i	$-0.353251\pi$
$43$	5.83438	0.889734	0.444867	+	0.895597i	$0.353251\pi$
$44$	−15.3375	−2.31222
$45$	2.55811	0.381340
$46$	−7.73496	−1.14046
$47$	11.1492	1.62627	0.813137	−	0.582072i	$-0.197758\pi$
$47$	11.1492	1.62627	0.813137	+	0.582072i	$0.197758\pi$
$48$	−0.883626	−0.127540
$49$	11.0422	1.57745
$50$	9.98348	1.41188
$51$	−0.695919	−0.0974482
$52$	8.90944	1.23552
$53$	1.94852	0.267650	0.133825	−	0.991005i	$-0.457274\pi$
$53$	1.94852	0.267650	0.133825	+	0.991005i	$0.457274\pi$
$54$	−5.59278	−0.761081
$55$	3.75288	0.506038
$56$	17.0431	2.27748
$57$	0.528146	0.0699547
$58$	7.26300	0.953679
$59$	0.809463	0.105383	0.0526915	−	0.998611i	$-0.483220\pi$
$59$	0.809463	0.105383	0.0526915	+	0.998611i	$0.483220\pi$
$60$	1.33373	0.172184
$61$	7.11433	0.910897	0.455448	−	0.890262i	$-0.349479\pi$
$61$	7.11433	0.910897	0.455448	+	0.890262i	$0.349479\pi$
$62$	−20.6210	−2.61888
$63$	12.0570	1.51904
$64$	−11.0312	−1.37890
$65$	−2.18001	−0.270398
$66$	−3.98900	−0.491012
$67$	2.89421	0.353584	0.176792	−	0.984248i	$-0.443428\pi$
$67$	2.89421	0.353584	0.176792	+	0.984248i	$0.443428\pi$
$68$	6.37886	0.773550
$69$	−1.30375	−0.156953
$70$	−9.12559	−1.09072
$71$	2.61966	0.310896	0.155448	−	0.987844i	$-0.450318\pi$
$71$	2.61966	0.310896	0.155448	+	0.987844i	$0.450318\pi$
$72$	11.3894	1.34225
$73$	−2.79512	−0.327144	−0.163572	−	0.986531i	$-0.552302\pi$
$73$	−2.79512	−0.327144	−0.163572	+	0.986531i	$0.552302\pi$
$74$	12.8231	1.49066
$75$	1.68275	0.194307
$76$	−4.84103	−0.555305
$77$	17.6883	2.01576
$78$	2.31718	0.262369
$79$	−10.3469	−1.16411	−0.582056	−	0.813149i	$-0.697752\pi$
$79$	−10.3469	−1.16411	−0.582056	+	0.813149i	$0.697752\pi$
$80$	−1.98181	−0.221573
$81$	7.57294	0.841438
$82$	−18.1147	−2.00044
$83$	−8.13330	−0.892746	−0.446373	−	0.894847i	$-0.647285\pi$
$83$	−8.13330	−0.892746	−0.446373	+	0.894847i	$0.647285\pi$
$84$	6.28621	0.685882
$85$	−1.56082	−0.169294
$86$	−13.9087	−1.49982
$87$	1.22420	0.131248
$88$	16.7088	1.78116
$89$	3.51461	0.372548	0.186274	−	0.982498i	$-0.440359\pi$
$89$	3.51461	0.372548	0.186274	+	0.982498i	$0.440359\pi$
$90$	−6.09834	−0.642822
$91$	−10.2750	−1.07711
$92$	11.9503	1.24591
$93$	−3.47575	−0.360418
$94$	−26.5788	−2.74140
$95$	1.18453	0.121531
$96$	−1.11802	−0.114107
$97$	−14.9937	−1.52238	−0.761188	−	0.648532i	$-0.775383\pi$
$97$	−14.9937	−1.52238	−0.761188	+	0.648532i	$0.775383\pi$
$98$	−26.3237	−2.65909
$99$	11.8205	1.18801
$100$	−15.4242	−1.54242
$101$	−9.77904	−0.973051	−0.486525	−	0.873666i	$-0.661736\pi$
$101$	−9.77904	−0.973051	−0.486525	+	0.873666i	$0.661736\pi$
$102$	1.65902	0.164268
$103$	−12.9875	−1.27969	−0.639846	−	0.768503i	$-0.721002\pi$
$103$	−12.9875	−1.27969	−0.639846	+	0.768503i	$0.721002\pi$
$104$	−9.70601	−0.951752
$105$	−1.53815	−0.150108
$106$	−4.64514	−0.451176
$107$	3.21760	0.311057	0.155529	−	0.987831i	$-0.450292\pi$
$107$	3.21760	0.311057	0.155529	+	0.987831i	$0.450292\pi$
$108$	8.64070	0.831452
$109$	13.4035	1.28382	0.641910	−	0.766780i	$-0.278142\pi$
$109$	13.4035	1.28382	0.641910	+	0.766780i	$0.278142\pi$
$110$	−8.94658	−0.853023
$111$	2.16138	0.205149
$112$	−9.34076	−0.882619
$113$	−0.632353	−0.0594867	−0.0297434	−	0.999558i	$-0.509469\pi$
$113$	−0.632353	−0.0594867	−0.0297434	+	0.999558i	$0.509469\pi$
$114$	−1.25906	−0.117922
$115$	−2.92408	−0.272671
$116$	−11.2212	−1.04186
$117$	−6.86643	−0.634802
$118$	−1.92970	−0.177643
$119$	−7.35653	−0.674372
$120$	−1.45298	−0.132638
$121$	6.34129	0.576481
$122$	−16.9600	−1.53549
$123$	−3.05330	−0.275307
$124$	31.8590	2.86102
$125$	8.28012	0.740596
$126$	−28.7430	−2.56063
$127$	−14.2071	−1.26068	−0.630340	−	0.776319i	$-0.717084\pi$
$127$	−14.2071	−1.26068	−0.630340	+	0.776319i	$0.717084\pi$
$128$	20.7327	1.83253
$129$	−2.34436	−0.206410
$130$	5.19700	0.455807
$131$	−1.79067	−0.156451	−0.0782256	−	0.996936i	$-0.524925\pi$
$131$	−1.79067	−0.156451	−0.0782256	+	0.996936i	$0.524925\pi$
$132$	6.16290	0.536412
$133$	5.58300	0.484108
$134$	−6.89959	−0.596033
$135$	−2.11426	−0.181966
$136$	−6.94918	−0.595887
$137$	7.56199	0.646064	0.323032	−	0.946388i	$-0.395298\pi$
$137$	7.56199	0.646064	0.323032	+	0.946388i	$0.395298\pi$
$138$	3.10805	0.264575
$139$	5.27812	0.447684	0.223842	−	0.974625i	$-0.428140\pi$
$139$	5.27812	0.447684	0.223842	+	0.974625i	$0.428140\pi$
$140$	14.0988	1.19157
$141$	−4.47995	−0.377280
$142$	−6.24507	−0.524075
$143$	−10.0734	−0.842381
$144$	−6.24214	−0.520178
$145$	2.74566	0.228015
$146$	6.66336	0.551463
$147$	−4.43695	−0.365953
$148$	−19.8114	−1.62848
$149$	3.09056	0.253188	0.126594	−	0.991955i	$-0.459595\pi$
$149$	3.09056	0.253188	0.126594	+	0.991955i	$0.459595\pi$
$150$	−4.01155	−0.327542
$151$	−3.33472	−0.271375	−0.135688	−	0.990752i	$-0.543324\pi$
$151$	−3.33472	−0.271375	−0.135688	+	0.990752i	$0.543324\pi$
$152$	5.27386	0.427766
$153$	−4.91614	−0.397446
$154$	−42.1675	−3.39795
$155$	−7.79545	−0.626146
$156$	−3.57998	−0.286628
$157$	−3.54371	−0.282819	−0.141409	−	0.989951i	$-0.545163\pi$
$157$	−3.54371	−0.282819	−0.141409	+	0.989951i	$0.545163\pi$
$158$	24.6661	1.96233
$159$	−0.782954	−0.0620923
$160$	−2.50751	−0.198236
$161$	−13.7819	−1.08617
$162$	−18.0533	−1.41840
$163$	0.633255	0.0496004	0.0248002	−	0.999692i	$-0.492105\pi$
$163$	0.633255	0.0496004	0.0248002	+	0.999692i	$0.492105\pi$
$164$	27.9868	2.18540
$165$	−1.50798	−0.117396
$166$	19.3892	1.50489
$167$	1.75484	0.135794	0.0678968	−	0.997692i	$-0.478371\pi$
$167$	1.75484	0.135794	0.0678968	+	0.997692i	$0.478371\pi$
$168$	−6.84825	−0.528354
$169$	−7.14844	−0.549880
$170$	3.72088	0.285378
$171$	3.73095	0.285313
$172$	21.4886	1.63849
$173$	−8.39796	−0.638485	−0.319243	−	0.947673i	$-0.603429\pi$
$173$	−8.39796	−0.638485	−0.319243	+	0.947673i	$0.603429\pi$
$174$	−2.91841	−0.221244
$175$	17.7883	1.34467
$176$	−9.15754	−0.690275
$177$	−0.325257	−0.0244478
$178$	−8.37857	−0.628001
$179$	10.1031	0.755145	0.377572	−	0.925980i	$-0.376759\pi$
$179$	10.1031	0.755145	0.377572	+	0.925980i	$0.376759\pi$
$180$	9.42179	0.702258
$181$	7.86195	0.584374	0.292187	−	0.956361i	$-0.405617\pi$
$181$	7.86195	0.584374	0.292187	+	0.956361i	$0.405617\pi$
$182$	24.4948	1.81567
$183$	−2.85867	−0.211319
$184$	−13.0188	−0.959756
$185$	4.84757	0.356400
$186$	8.28593	0.607554
$187$	−7.21223	−0.527410
$188$	41.0636	2.99487
$189$	−9.96504	−0.724850
$190$	−2.82384	−0.204863
$191$	15.3412	1.11005	0.555026	−	0.831833i	$-0.312708\pi$
$191$	15.3412	1.11005	0.555026	+	0.831833i	$0.312708\pi$
$192$	4.43253	0.319890
$193$	2.33390	0.167998	0.0839990	−	0.996466i	$-0.473231\pi$
$193$	2.33390	0.167998	0.0839990	+	0.996466i	$0.473231\pi$
$194$	35.7438	2.56625
$195$	0.875971	0.0627296
$196$	40.6694	2.90496
$197$	−12.5529	−0.894354	−0.447177	−	0.894446i	$-0.647571\pi$
$197$	−12.5529	−0.894354	−0.447177	+	0.894446i	$0.647571\pi$
$198$	−28.1792	−2.00261
$199$	−3.45973	−0.245254	−0.122627	−	0.992453i	$-0.539132\pi$
$199$	−3.45973	−0.245254	−0.122627	+	0.992453i	$0.539132\pi$
$200$	16.8033	1.18817
$201$	−1.16295	−0.0820281
$202$	23.3125	1.64026
$203$	12.9410	0.908279
$204$	−2.56315	−0.179456
$205$	−6.84798	−0.478283
$206$	30.9612	2.15717
$207$	−9.21001	−0.640140
$208$	5.31954	0.368844
$209$	5.47349	0.378609
$210$	3.66683	0.253035
$211$	8.16018	0.561770	0.280885	−	0.959741i	$-0.409372\pi$
$211$	8.16018	0.561770	0.280885	+	0.959741i	$0.409372\pi$
$212$	7.17662	0.492893
$213$	−1.05263	−0.0721248
$214$	−7.67053	−0.524347
$215$	−5.25797	−0.358591
$216$	−9.41325	−0.640490
$217$	−36.7419	−2.49421
$218$	−31.9529	−2.16413
$219$	1.12313	0.0758942
$220$	13.8222	0.931896
$221$	4.18952	0.281818
$222$	−5.15256	−0.345817
$223$	−14.1805	−0.949599	−0.474800	−	0.880094i	$-0.657479\pi$
$223$	−14.1805	−0.949599	−0.474800	+	0.880094i	$0.657479\pi$
$224$	−11.8185	−0.789659
$225$	11.8873	0.792489
$226$	1.50748	0.100276
$227$	17.8220	1.18289	0.591444	−	0.806346i	$-0.298558\pi$
$227$	17.8220	1.18289	0.591444	+	0.806346i	$0.298558\pi$
$228$	1.94522	0.128825
$229$	−12.1581	−0.803433	−0.401717	−	0.915764i	$-0.631586\pi$
$229$	−12.1581	−0.803433	−0.401717	+	0.915764i	$0.631586\pi$
$230$	6.97078	0.459640
$231$	−7.10747	−0.467637
$232$	12.2244	0.802572
$233$	−18.0399	−1.18183	−0.590917	−	0.806732i	$-0.701234\pi$
$233$	−18.0399	−1.18183	−0.590917	+	0.806732i	$0.701234\pi$
$234$	16.3691	1.07008
$235$	−10.0477	−0.655439
$236$	2.98134	0.194069
$237$	4.15756	0.270063
$238$	17.5374	1.13678
$239$	1.68381	0.108917	0.0544584	−	0.998516i	$-0.482657\pi$
$239$	1.68381	0.108917	0.0544584	+	0.998516i	$0.482657\pi$
$240$	0.796328	0.0514027
$241$	16.4123	1.05721	0.528605	−	0.848868i	$-0.322715\pi$
$241$	16.4123	1.05721	0.528605	+	0.848868i	$0.322715\pi$
$242$	−15.1172	−0.971769
$243$	−10.0811	−0.646700
$244$	26.2028	1.67747
$245$	−9.95125	−0.635762
$246$	7.27884	0.464082
$247$	−3.17951	−0.202307
$248$	−34.7074	−2.20392
$249$	3.26812	0.207108
$250$	−19.7392	−1.24842
$251$	5.47760	0.345743	0.172872	−	0.984944i	$-0.444695\pi$
$251$	5.47760	0.345743	0.172872	+	0.984944i	$0.444695\pi$
$252$	44.4072	2.79739
$253$	−13.5116	−0.849465
$254$	33.8688	2.12512
$255$	0.627166	0.0392747
$256$	−27.3629	−1.71018
$257$	14.8233	0.924651	0.462326	−	0.886710i	$-0.347015\pi$
$257$	14.8233	0.924651	0.462326	+	0.886710i	$0.347015\pi$
$258$	5.58879	0.347943
$259$	22.8478	1.41969
$260$	−8.02923	−0.497952
$261$	8.64805	0.535301
$262$	4.26882	0.263728
$263$	−9.50776	−0.586274	−0.293137	−	0.956070i	$-0.594699\pi$
$263$	−9.50776	−0.586274	−0.293137	+	0.956070i	$0.594699\pi$
$264$	−6.71391	−0.413213
$265$	−1.75602	−0.107871
$266$	−13.3095	−0.816056
$267$	−1.41224	−0.0864275
$268$	10.6597	0.651144
$269$	22.3400	1.36210	0.681048	−	0.732239i	$-0.261524\pi$
$269$	22.3400	1.36210	0.681048	+	0.732239i	$0.261524\pi$
$270$	5.04024	0.306739
$271$	26.8874	1.63329	0.816647	−	0.577137i	$-0.195830\pi$
$271$	26.8874	1.63329	0.816647	+	0.577137i	$0.195830\pi$
$272$	3.80861	0.230931
$273$	4.12867	0.249879
$274$	−18.0272	−1.08906
$275$	17.4393	1.05163
$276$	−4.80186	−0.289038
$277$	−24.7954	−1.48981	−0.744905	−	0.667170i	$-0.767505\pi$
$277$	−24.7954	−1.48981	−0.744905	+	0.667170i	$0.767505\pi$
$278$	−12.5827	−0.754657
$279$	−24.5535	−1.46998
$280$	−15.3593	−0.917896
$281$	18.5506	1.10664	0.553319	−	0.832970i	$-0.313361\pi$
$281$	18.5506	1.10664	0.553319	+	0.832970i	$0.313361\pi$
$282$	10.6799	0.635977
$283$	18.6674	1.10966	0.554831	−	0.831963i	$-0.312783\pi$
$283$	18.6674	1.10966	0.554831	+	0.831963i	$0.312783\pi$
$284$	9.64848	0.572532
$285$	−0.475968	−0.0281939
$286$	24.0143	1.41999
$287$	−32.2762	−1.90521
$288$	−7.89796	−0.465392
$289$	−14.0004	−0.823555
$290$	−6.54545	−0.384362
$291$	6.02474	0.353176
$292$	−10.2947	−0.602453
$293$	−16.4667	−0.961994	−0.480997	−	0.876722i	$-0.659725\pi$
$293$	−16.4667	−0.961994	−0.480997	+	0.876722i	$0.659725\pi$
$294$	10.5774	0.616884
$295$	−0.729492	−0.0424727
$296$	21.5827	1.25447
$297$	−9.76957	−0.566888
$298$	−7.36767	−0.426797
$299$	7.84876	0.453905
$300$	6.19775	0.357827
$301$	−24.7821	−1.42842
$302$	7.94972	0.457455
$303$	3.92940	0.225738
$304$	−2.89043	−0.165777
$305$	−6.41147	−0.367120
$306$	11.7197	0.669971
$307$	−12.5788	−0.717909	−0.358955	−	0.933355i	$-0.616867\pi$
$307$	−12.5788	−0.717909	−0.358955	+	0.933355i	$0.616867\pi$
$308$	65.1477	3.71214
$309$	5.21861	0.296876
$310$	18.5838	1.05549
$311$	−2.36214	−0.133944	−0.0669722	−	0.997755i	$-0.521334\pi$
$311$	−2.36214	−0.133944	−0.0669722	+	0.997755i	$0.521334\pi$
$312$	3.90006	0.220797
$313$	−24.4620	−1.38267	−0.691336	−	0.722533i	$-0.742978\pi$
$313$	−24.4620	−1.38267	−0.691336	+	0.722533i	$0.742978\pi$
$314$	8.44794	0.476745
$315$	−10.8658	−0.612220
$316$	−38.1086	−2.14377
$317$	−34.6292	−1.94497	−0.972485	−	0.232966i	$-0.925157\pi$
$317$	−34.6292	−1.94497	−0.972485	+	0.232966i	$0.925157\pi$
$318$	1.86650	0.104668
$319$	12.6871	0.710344
$320$	9.94134	0.555738
$321$	−1.29289	−0.0721623
$322$	32.8551	1.83094
$323$	−2.27642	−0.126663
$324$	27.8920	1.54955
$325$	−10.1304	−0.561931
$326$	−1.50963	−0.0836109
$327$	−5.38577	−0.297834
$328$	−30.4890	−1.68347
$329$	−47.3573	−2.61089
$330$	3.59491	0.197893
$331$	34.0619	1.87221	0.936107	−	0.351716i	$-0.114402\pi$
$331$	34.0619	1.87221	0.936107	+	0.351716i	$0.114402\pi$
$332$	−29.9558	−1.64404
$333$	15.2685	0.836707
$334$	−4.18341	−0.228906
$335$	−2.60828	−0.142505
$336$	3.75329	0.204759
$337$	6.81364	0.371163	0.185581	−	0.982629i	$-0.440583\pi$
$337$	6.81364	0.371163	0.185581	+	0.982629i	$0.440583\pi$
$338$	17.0414	0.926927
$339$	0.254091	0.0138003
$340$	−5.74866	−0.311765
$341$	−36.0212	−1.95066
$342$	−8.89430	−0.480949
$343$	−17.1695	−0.927065
$344$	−23.4099	−1.26218
$345$	1.17495	0.0632571
$346$	20.0201	1.07629
$347$	13.8386	0.742893	0.371446	−	0.928454i	$-0.378862\pi$
$347$	13.8386	0.742893	0.371446	+	0.928454i	$0.378862\pi$
$348$	4.50887	0.241701
$349$	−18.6488	−0.998249	−0.499124	−	0.866530i	$-0.666345\pi$
$349$	−18.6488	−0.998249	−0.499124	+	0.866530i	$0.666345\pi$
$350$	−42.4059	−2.26669
$351$	5.67506	0.302912
$352$	−11.5867	−0.617574
$353$	19.2166	1.02279	0.511397	−	0.859344i	$-0.329128\pi$
$353$	19.2166	1.02279	0.511397	+	0.859344i	$0.329128\pi$
$354$	0.775390	0.0412115
$355$	−2.36085	−0.125301
$356$	12.9447	0.686067
$357$	2.95599	0.156448
$358$	−24.0852	−1.27294
$359$	−6.97669	−0.368216	−0.184108	−	0.982906i	$-0.558940\pi$
$359$	−6.97669	−0.368216	−0.184108	+	0.982906i	$0.558940\pi$
$360$	−10.2642	−0.540969
$361$	−17.2724	−0.909073
$362$	−18.7423	−0.985075
$363$	−2.54805	−0.133738
$364$	−37.8438	−1.98355
$365$	2.51897	0.131849
$366$	6.81487	0.356219
$367$	−5.48960	−0.286555	−0.143277	−	0.989683i	$-0.545764\pi$
$367$	−5.48960	−0.286555	−0.143277	+	0.989683i	$0.545764\pi$
$368$	7.13515	0.371945
$369$	−21.5692	−1.12285
$370$	−11.5562	−0.600780
$371$	−8.27656	−0.429698
$372$	−12.8015	−0.663729
$373$	20.0760	1.03950	0.519748	−	0.854320i	$-0.326026\pi$
$373$	20.0760	1.03950	0.519748	+	0.854320i	$0.326026\pi$
$374$	17.1934	0.889050
$375$	−3.32711	−0.171811
$376$	−44.7350	−2.30703
$377$	−7.36986	−0.379567
$378$	23.7559	1.22187
$379$	−5.72166	−0.293902	−0.146951	−	0.989144i	$-0.546946\pi$
$379$	−5.72166	−0.293902	−0.146951	+	0.989144i	$0.546946\pi$
$380$	4.36276	0.223805
$381$	5.70870	0.292465
$382$	−36.5723	−1.87120
$383$	32.5594	1.66371	0.831854	−	0.554995i	$-0.187280\pi$
$383$	32.5594	1.66371	0.831854	+	0.554995i	$0.187280\pi$
$384$	−8.33079	−0.425129
$385$	−15.9407	−0.812415
$386$	−5.56385	−0.283193
$387$	−16.5611	−0.841849
$388$	−55.2233	−2.80354
$389$	7.75295	0.393090	0.196545	−	0.980495i	$-0.437028\pi$
$389$	7.75295	0.393090	0.196545	+	0.980495i	$0.437028\pi$
$390$	−2.08825	−0.105743
$391$	5.61945	0.284188
$392$	−44.3056	−2.23777
$393$	0.719524	0.0362952
$394$	29.9251	1.50760
$395$	9.32463	0.469173
$396$	43.5362	2.18778
$397$	−29.5210	−1.48162	−0.740809	−	0.671716i	$-0.765558\pi$
$397$	−29.5210	−1.48162	−0.740809	+	0.671716i	$0.765558\pi$
$398$	8.24774	0.413422
$399$	−2.24336	−0.112308
$400$	−9.20931	−0.460465
$401$	6.65031	0.332101	0.166050	−	0.986117i	$-0.446899\pi$
$401$	6.65031	0.332101	0.166050	+	0.986117i	$0.446899\pi$
$402$	2.77238	0.138274
$403$	20.9244	1.04232
$404$	−36.0173	−1.79193
$405$	−6.82477	−0.339126
$406$	−30.8504	−1.53108
$407$	22.3996	1.11031
$408$	2.79231	0.138240
$409$	−6.61638	−0.327159	−0.163579	−	0.986530i	$-0.552304\pi$
$409$	−6.61638	−0.327159	−0.163579	+	0.986530i	$0.552304\pi$
$410$	16.3251	0.806238
$411$	−3.03855	−0.149881
$412$	−47.8342	−2.35662
$413$	−3.43828	−0.169187
$414$	21.9560	1.07908
$415$	7.32977	0.359804
$416$	6.73062	0.329996
$417$	−2.12085	−0.103858
$418$	−13.0484	−0.638218
$419$	−31.7696	−1.55205	−0.776024	−	0.630703i	$-0.782766\pi$
$419$	−31.7696	−1.55205	−0.776024	+	0.630703i	$0.782766\pi$
$420$	−5.66516	−0.276432
$421$	13.5280	0.659314	0.329657	−	0.944101i	$-0.393067\pi$
$421$	13.5280	0.659314	0.329657	+	0.944101i	$0.393067\pi$
$422$	−19.4533	−0.946970
$423$	−31.6474	−1.53875
$424$	−7.81827	−0.379689
$425$	−7.25300	−0.351822
$426$	2.50939	0.121580
$427$	−30.2189	−1.46239
$428$	11.8508	0.572829
$429$	4.04769	0.195424
$430$	12.5346	0.604473
$431$	−13.9514	−0.672014	−0.336007	−	0.941859i	$-0.609077\pi$
$431$	−13.9514	−0.672014	−0.336007	+	0.941859i	$0.609077\pi$
$432$	5.15909	0.248217
$433$	−19.4166	−0.933102	−0.466551	−	0.884494i	$-0.654504\pi$
$433$	−19.4166	−0.933102	−0.466551	+	0.884494i	$0.654504\pi$
$434$	87.5901	4.20446
$435$	−1.10326	−0.0528972
$436$	49.3665	2.36423
$437$	−4.26470	−0.204008
$438$	−2.67746	−0.127934
$439$	−40.9954	−1.95660	−0.978302	−	0.207185i	$-0.933570\pi$
$439$	−40.9954	−1.95660	−0.978302	+	0.207185i	$0.933570\pi$
$440$	−15.0581	−0.717865
$441$	−31.3436	−1.49255
$442$	−9.98751	−0.475058
$443$	30.2827	1.43878	0.719388	−	0.694609i	$-0.244422\pi$
$443$	30.2827	1.43878	0.719388	+	0.694609i	$0.244422\pi$
$444$	7.96058	0.377793
$445$	−3.16738	−0.150148
$446$	33.8054	1.60073
$447$	−1.24184	−0.0587372
$448$	46.8561	2.21374
$449$	−12.3886	−0.584655	−0.292327	−	0.956318i	$-0.594430\pi$
$449$	−12.3886	−0.584655	−0.292327	+	0.956318i	$0.594430\pi$
$450$	−28.3385	−1.33589
$451$	−31.6431	−1.49002
$452$	−2.32902	−0.109548
$453$	1.33995	0.0629564
$454$	−42.4863	−1.99398
$455$	9.25984	0.434108
$456$	−2.11914	−0.0992376
$457$	−5.13577	−0.240241	−0.120121	−	0.992759i	$-0.538328\pi$
$457$	−5.13577	−0.240241	−0.120121	+	0.992759i	$0.538328\pi$
$458$	28.9841	1.35434
$459$	4.06315	0.189652
$460$	−10.7697	−0.502139
$461$	6.60229	0.307499	0.153750	−	0.988110i	$-0.450865\pi$
$461$	6.60229	0.307499	0.153750	+	0.988110i	$0.450865\pi$
$462$	16.9437	0.788292
$463$	7.11330	0.330583	0.165292	−	0.986245i	$-0.447143\pi$
$463$	7.11330	0.330583	0.165292	+	0.986245i	$0.447143\pi$
$464$	−6.69979	−0.311030
$465$	3.13236	0.145260
$466$	43.0059	1.99221
$467$	10.9549	0.506935	0.253467	−	0.967344i	$-0.418429\pi$
$467$	10.9549	0.506935	0.253467	+	0.967344i	$0.418429\pi$
$468$	−25.2898	−1.16902
$469$	−12.2935	−0.567659
$470$	23.9530	1.10487
$471$	1.42393	0.0656111
$472$	−3.24789	−0.149496
$473$	−24.2960	−1.11713
$474$	−9.91132	−0.455242
$475$	5.50444	0.252561
$476$	−27.0949	−1.24189
$477$	−5.53097	−0.253246
$478$	−4.01409	−0.183600
$479$	6.78215	0.309884	0.154942	−	0.987924i	$-0.450481\pi$
$479$	6.78215	0.309884	0.154942	+	0.987924i	$0.450481\pi$
$480$	1.00757	0.0459889
$481$	−13.0118	−0.593285
$482$	−39.1258	−1.78213
$483$	5.53783	0.251980
$484$	23.3557	1.06162
$485$	13.5124	0.613565
$486$	24.0325	1.09014
$487$	26.1531	1.18511	0.592555	−	0.805530i	$-0.298119\pi$
$487$	26.1531	1.18511	0.592555	+	0.805530i	$0.298119\pi$
$488$	−28.5456	−1.29220
$489$	−0.254454	−0.0115068
$490$	23.7230	1.07170
$491$	−7.68256	−0.346709	−0.173354	−	0.984859i	$-0.555461\pi$
$491$	−7.68256	−0.346709	−0.173354	+	0.984859i	$0.555461\pi$
$492$	−11.2456	−0.506992
$493$	−5.27657	−0.237645
$494$	7.57971	0.341027
$495$	−10.6527	−0.478803
$496$	19.0220	0.854112
$497$	−11.1273	−0.499126
$498$	−7.79095	−0.349121
$499$	−37.2528	−1.66767	−0.833833	−	0.552017i	$-0.813858\pi$
$499$	−37.2528	−1.66767	−0.833833	+	0.552017i	$0.813858\pi$
$500$	30.4966	1.36385
$501$	−0.705128	−0.0315028
$502$	−13.0582	−0.582816
$503$	22.2407	0.991662	0.495831	−	0.868419i	$-0.334864\pi$
$503$	22.2407	0.991662	0.495831	+	0.868419i	$0.334864\pi$
$504$	−48.3776	−2.15491
$505$	8.81292	0.392170
$506$	32.2106	1.43194
$507$	2.87238	0.127567
$508$	−52.3264	−2.32161
$509$	30.2521	1.34090	0.670451	−	0.741954i	$-0.266101\pi$
$509$	30.2521	1.34090	0.670451	+	0.741954i	$0.266101\pi$
$510$	−1.49512	−0.0662049
$511$	11.8726	0.525211
$512$	23.7658	1.05031
$513$	−3.08360	−0.136144
$514$	−35.3376	−1.55868
$515$	11.7044	0.515756
$516$	−8.63454	−0.380115
$517$	−46.4284	−2.04192
$518$	−54.4675	−2.39316
$519$	3.37446	0.148122
$520$	8.74710	0.383586
$521$	−8.88156	−0.389108	−0.194554	−	0.980892i	$-0.562326\pi$
$521$	−8.88156	−0.389108	−0.194554	+	0.980892i	$0.562326\pi$
$522$	−20.6163	−0.902352
$523$	9.14524	0.399894	0.199947	−	0.979807i	$-0.435923\pi$
$523$	9.14524	0.399894	0.199947	+	0.979807i	$0.435923\pi$
$524$	−6.59522	−0.288113
$525$	−7.14765	−0.311949
$526$	22.6658	0.988276
$527$	14.9812	0.652591
$528$	3.67967	0.160137
$529$	−12.4724	−0.542278
$530$	4.18622	0.181838
$531$	−2.29769	−0.0997114
$532$	20.5628	0.891511
$533$	18.3812	0.796180
$534$	3.36667	0.145690
$535$	−2.89972	−0.125366
$536$	−11.6127	−0.501594
$537$	−4.05964	−0.175186
$538$	−53.2570	−2.29607
$539$	−45.9827	−1.98062
$540$	−7.78704	−0.335101
$541$	−20.8578	−0.896745	−0.448372	−	0.893847i	$-0.647996\pi$
$541$	−20.8578	−0.896745	−0.448372	+	0.893847i	$0.647996\pi$
$542$	−64.0976	−2.75323
$543$	−3.15908	−0.135569
$544$	4.81890	0.206609
$545$	−12.0793	−0.517420
$546$	−9.84245	−0.421218
$547$	−30.1494	−1.28909	−0.644547	−	0.764565i	$-0.722954\pi$
$547$	−30.1494	−1.28909	−0.644547	+	0.764565i	$0.722954\pi$
$548$	27.8516	1.18976
$549$	−20.1943	−0.861873
$550$	−41.5741	−1.77272
$551$	4.00449	0.170597
$552$	5.23118	0.222654
$553$	43.9493	1.86892
$554$	59.1104	2.51136
$555$	−1.94784	−0.0826813
$556$	19.4399	0.824435
$557$	19.7687	0.837628	0.418814	−	0.908072i	$-0.362446\pi$
$557$	19.7687	0.837628	0.418814	+	0.908072i	$0.362446\pi$
$558$	58.5337	2.47793
$559$	14.1134	0.596932
$560$	8.41794	0.355723
$561$	2.89801	0.122354
$562$	−44.2233	−1.86545
$563$	−42.4035	−1.78709	−0.893547	−	0.448969i	$-0.851791\pi$
$563$	−42.4035	−1.78709	−0.893547	+	0.448969i	$0.851791\pi$
$564$	−16.5001	−0.694781
$565$	0.569879	0.0239750
$566$	−44.5017	−1.87055
$567$	−32.1669	−1.35088
$568$	−10.5111	−0.441037
$569$	−17.6477	−0.739829	−0.369915	−	0.929066i	$-0.620613\pi$
$569$	−17.6477	−0.739829	−0.369915	+	0.929066i	$0.620613\pi$
$570$	1.13467	0.0475262
$571$	26.8186	1.12232	0.561162	−	0.827706i	$-0.310354\pi$
$571$	26.8186	1.12232	0.561162	+	0.827706i	$0.310354\pi$
$572$	−37.1015	−1.55129
$573$	−6.16439	−0.257521
$574$	76.9442	3.21159
$575$	−13.5880	−0.566657
$576$	31.3124	1.30468
$577$	−43.3616	−1.80517	−0.902583	−	0.430515i	$-0.858332\pi$
$577$	−43.3616	−1.80517	−0.902583	+	0.430515i	$0.858332\pi$
$578$	33.3760	1.38826
$579$	−0.937806	−0.0389739
$580$	10.1126	0.419901
$581$	34.5471	1.43325
$582$	−14.3625	−0.595346
$583$	−8.11422	−0.336056
$584$	11.2151	0.464086
$585$	6.18806	0.255845
$586$	39.2554	1.62162
$587$	2.83770	0.117124	0.0585622	−	0.998284i	$-0.481348\pi$
$587$	2.83770	0.117124	0.0585622	+	0.998284i	$0.481348\pi$
$588$	−16.3418	−0.673922
$589$	−11.3695	−0.468472
$590$	1.73906	0.0715958
$591$	5.04397	0.207481
$592$	−11.8287	−0.486158
$593$	−40.6765	−1.67038	−0.835192	−	0.549959i	$-0.814643\pi$
$593$	−40.6765	−1.67038	−0.835192	+	0.549959i	$0.814643\pi$
$594$	23.2899	0.955598
$595$	6.62974	0.271793
$596$	11.3829	0.466260
$597$	1.39018	0.0568965
$598$	−18.7109	−0.765144
$599$	−14.0760	−0.575131	−0.287565	−	0.957761i	$-0.592846\pi$
$599$	−14.0760	−0.575131	−0.287565	+	0.957761i	$0.592846\pi$
$600$	−6.75187	−0.275644
$601$	7.82146	0.319044	0.159522	−	0.987194i	$-0.449005\pi$
$601$	7.82146	0.319044	0.159522	+	0.987194i	$0.449005\pi$
$602$	59.0788	2.40787
$603$	−8.21534	−0.334554
$604$	−12.2821	−0.499752
$605$	−5.71480	−0.232340
$606$	−9.36741	−0.380525
$607$	13.1864	0.535221	0.267611	−	0.963527i	$-0.413766\pi$
$607$	13.1864	0.535221	0.267611	+	0.963527i	$0.413766\pi$
$608$	−3.65715	−0.148317
$609$	−5.19993	−0.210712
$610$	15.2845	0.618850
$611$	26.9699	1.09108
$612$	−18.1067	−0.731918
$613$	27.3117	1.10311	0.551554	−	0.834139i	$-0.314035\pi$
$613$	27.3117	1.10311	0.551554	+	0.834139i	$0.314035\pi$
$614$	29.9869	1.21017
$615$	2.75165	0.110957
$616$	−70.9724	−2.85956
$617$	5.35291	0.215500	0.107750	−	0.994178i	$-0.465635\pi$
$617$	5.35291	0.215500	0.107750	+	0.994178i	$0.465635\pi$
$618$	−12.4408	−0.500442
$619$	24.6472	0.990654	0.495327	−	0.868707i	$-0.335048\pi$
$619$	24.6472	0.990654	0.495327	+	0.868707i	$0.335048\pi$
$620$	−28.7115	−1.15308
$621$	7.61202	0.305460
$622$	5.63116	0.225789
$623$	−14.9287	−0.598105
$624$	−2.13749	−0.0855681
$625$	13.4771	0.539083
$626$	58.3156	2.33076
$627$	−2.19935	−0.0878337
$628$	−13.0519	−0.520826
$629$	−9.31598	−0.371453
$630$	25.9034	1.03201
$631$	−15.1609	−0.603547	−0.301774	−	0.953380i	$-0.597579\pi$
$631$	−15.1609	−0.603547	−0.301774	+	0.953380i	$0.597579\pi$
$632$	41.5158	1.65141
$633$	−3.27891	−0.130325
$634$	82.5535	3.27862
$635$	12.8035	0.508093
$636$	−2.88370	−0.114346
$637$	26.7110	1.05833
$638$	−30.2452	−1.19742
$639$	−7.43600	−0.294164
$640$	−18.6844	−0.738566
$641$	42.7277	1.68764	0.843821	−	0.536624i	$-0.180301\pi$
$641$	42.7277	1.68764	0.843821	+	0.536624i	$0.180301\pi$
$642$	3.08216	0.121643
$643$	−22.7226	−0.896090	−0.448045	−	0.894011i	$-0.647880\pi$
$643$	−22.7226	−0.896090	−0.448045	+	0.894011i	$0.647880\pi$
$644$	−50.7602	−2.00023
$645$	2.11275	0.0831895
$646$	5.42682	0.213515
$647$	−17.0812	−0.671530	−0.335765	−	0.941946i	$-0.608995\pi$
$647$	−17.0812	−0.671530	−0.335765	+	0.941946i	$0.608995\pi$
$648$	−30.3857	−1.19366
$649$	−3.37084	−0.132317
$650$	24.1500	0.947242
$651$	14.7636	0.578631
$652$	2.33235	0.0913418
$653$	−35.4487	−1.38722	−0.693608	−	0.720353i	$-0.743980\pi$
$653$	−35.4487	−1.38722	−0.693608	+	0.720353i	$0.743980\pi$
$654$	12.8393	0.502056
$655$	1.61376	0.0630547
$656$	16.7100	0.652416
$657$	7.93406	0.309537
$658$	112.896	4.40116
$659$	−19.1307	−0.745228	−0.372614	−	0.927986i	$-0.621538\pi$
$659$	−19.1307	−0.745228	−0.372614	+	0.927986i	$0.621538\pi$
$660$	−5.55404	−0.216191
$661$	33.8928	1.31828	0.659139	−	0.752021i	$-0.270921\pi$
$661$	33.8928	1.31828	0.659139	+	0.752021i	$0.270921\pi$
$662$	−81.2012	−3.15597
$663$	−1.68343	−0.0653790
$664$	32.6341	1.26645
$665$	−5.03143	−0.195111
$666$	−36.3989	−1.41043
$667$	−9.88526	−0.382759
$668$	6.46327	0.250071
$669$	5.69801	0.220298
$670$	6.21794	0.240220
$671$	−29.6261	−1.14370
$672$	4.74891	0.183193
$673$	−5.10892	−0.196934	−0.0984671	−	0.995140i	$-0.531394\pi$
$673$	−5.10892	−0.196934	−0.0984671	+	0.995140i	$0.531394\pi$
$674$	−16.2432	−0.625666
$675$	−9.82480	−0.378157
$676$	−26.3285	−1.01263
$677$	−21.7238	−0.834913	−0.417457	−	0.908697i	$-0.637078\pi$
$677$	−21.7238	−0.834913	−0.417457	+	0.908697i	$0.637078\pi$
$678$	−0.605735	−0.0232631
$679$	63.6872	2.44409
$680$	6.26263	0.240161
$681$	−7.16121	−0.274418
$682$	85.8720	3.28821
$683$	26.2021	1.00260	0.501298	−	0.865275i	$-0.332856\pi$
$683$	26.2021	1.00260	0.501298	+	0.865275i	$0.332856\pi$
$684$	13.7415	0.525418
$685$	−6.81490	−0.260384
$686$	40.9308	1.56275
$687$	4.88537	0.186389
$688$	12.8302	0.489146
$689$	4.71348	0.179569
$690$	−2.80099	−0.106632
$691$	15.8371	0.602473	0.301236	−	0.953550i	$-0.402601\pi$
$691$	15.8371	0.602473	0.301236	+	0.953550i	$0.402601\pi$
$692$	−30.9306	−1.17581
$693$	−50.2088	−1.90728
$694$	−32.9901	−1.25229
$695$	−4.75667	−0.180431
$696$	−4.91200	−0.186189
$697$	13.1603	0.498484
$698$	44.4574	1.68274
$699$	7.24878	0.274174
$700$	65.5160	2.47627
$701$	26.7297	1.00957	0.504784	−	0.863246i	$-0.331572\pi$
$701$	26.7297	1.00957	0.504784	+	0.863246i	$0.331572\pi$
$702$	−13.5289	−0.510617
$703$	7.07007	0.266653
$704$	45.9369	1.73131
$705$	4.03735	0.152056
$706$	−45.8109	−1.72412
$707$	41.5375	1.56218
$708$	−1.19796	−0.0450220
$709$	−34.4098	−1.29229	−0.646143	−	0.763216i	$-0.723619\pi$
$709$	−34.4098	−1.29229	−0.646143	+	0.763216i	$0.723619\pi$
$710$	5.62809	0.211218
$711$	29.3700	1.10146
$712$	−14.1020	−0.528496
$713$	28.0661	1.05109
$714$	−7.04687	−0.263722
$715$	9.07821	0.339506
$716$	37.2110	1.39064
$717$	−0.676588	−0.0252676
$718$	16.6319	0.620698
$719$	4.23831	0.158062	0.0790311	−	0.996872i	$-0.474817\pi$
$719$	4.23831	0.158062	0.0790311	+	0.996872i	$0.474817\pi$
$720$	5.62545	0.209648
$721$	55.1656	2.05448
$722$	41.1761	1.53242
$723$	−6.59478	−0.245263
$724$	28.9564	1.07616
$725$	12.7589	0.473852
$726$	6.07436	0.225441
$727$	−32.9534	−1.22218	−0.611088	−	0.791563i	$-0.709268\pi$
$727$	−32.9534	−1.22218	−0.611088	+	0.791563i	$0.709268\pi$
$728$	41.2273	1.52799
$729$	−18.6681	−0.691410
$730$	−6.00505	−0.222257
$731$	10.1047	0.373736
$732$	−10.5288	−0.389156
$733$	−44.4893	−1.64325	−0.821624	−	0.570029i	$-0.806932\pi$
$733$	−44.4893	−1.64325	−0.821624	+	0.570029i	$0.806932\pi$
$734$	13.0868	0.483043
$735$	3.99860	0.147491
$736$	9.02785	0.332771
$737$	−12.0523	−0.443953
$738$	51.4194	1.89277
$739$	27.1042	0.997045	0.498522	−	0.866877i	$-0.333876\pi$
$739$	27.1042	0.997045	0.498522	+	0.866877i	$0.333876\pi$
$740$	17.8541	0.656330
$741$	1.27759	0.0469333
$742$	19.7307	0.724338
$743$	43.4341	1.59344	0.796722	−	0.604346i	$-0.206566\pi$
$743$	43.4341	1.59344	0.796722	+	0.604346i	$0.206566\pi$
$744$	13.9461	0.511289
$745$	−2.78523	−0.102043
$746$	−47.8597	−1.75227
$747$	23.0867	0.844699
$748$	−26.5634	−0.971254
$749$	−13.6671	−0.499385
$750$	7.93158	0.289620
$751$	−7.95258	−0.290194	−0.145097	−	0.989417i	$-0.546349\pi$
$751$	−7.95258	−0.290194	−0.145097	+	0.989417i	$0.546349\pi$
$752$	24.5178	0.894071
$753$	−2.20100	−0.0802091
$754$	17.5692	0.639833
$755$	3.00526	0.109373
$756$	−36.7023	−1.33485
$757$	18.0956	0.657697	0.328848	−	0.944383i	$-0.393339\pi$
$757$	18.0956	0.657697	0.328848	+	0.944383i	$0.393339\pi$
$758$	13.6400	0.495428
$759$	5.42920	0.197068
$760$	−4.75283	−0.172403
$761$	−43.2612	−1.56822	−0.784108	−	0.620624i	$-0.786879\pi$
$761$	−43.2612	−1.56822	−0.784108	+	0.620624i	$0.786879\pi$
$762$	−13.6091	−0.493006
$763$	−56.9327	−2.06110
$764$	56.5034	2.04422
$765$	4.43045	0.160183
$766$	−77.6192	−2.80450
$767$	1.95809	0.0707025
$768$	10.9949	0.396745
$769$	−14.3979	−0.519200	−0.259600	−	0.965716i	$-0.583591\pi$
$769$	−14.3979	−0.519200	−0.259600	+	0.965716i	$0.583591\pi$
$770$	38.0016	1.36948
$771$	−5.95628	−0.214510
$772$	8.59601	0.309377
$773$	−20.5650	−0.739672	−0.369836	−	0.929097i	$-0.620586\pi$
$773$	−20.5650	−0.739672	−0.369836	+	0.929097i	$0.620586\pi$
$774$	39.4805	1.41910
$775$	−36.2249	−1.30124
$776$	60.1606	2.15964
$777$	−9.18068	−0.329355
$778$	−18.4825	−0.662629
$779$	−9.98763	−0.357844
$780$	3.22630	0.115520
$781$	−10.9090	−0.390355
$782$	−13.3964	−0.479053
$783$	−7.14756	−0.255433
$784$	24.2824	0.867229
$785$	3.19361	0.113985
$786$	−1.71529	−0.0611824
$787$	−3.52025	−0.125483	−0.0627417	−	0.998030i	$-0.519984\pi$
$787$	−3.52025	−0.125483	−0.0627417	+	0.998030i	$0.519984\pi$
$788$	−46.2335	−1.64700
$789$	3.82040	0.136010
$790$	−22.2292	−0.790881
$791$	2.68599	0.0955027
$792$	−47.4286	−1.68530
$793$	17.2096	0.611130
$794$	70.3760	2.49755
$795$	0.705602	0.0250251
$796$	−12.7426	−0.451648
$797$	−37.7216	−1.33617	−0.668084	−	0.744086i	$-0.732885\pi$
$797$	−37.7216	−1.33617	−0.668084	+	0.744086i	$0.732885\pi$
$798$	5.34800	0.189317
$799$	19.3095	0.683122
$800$	−11.6522	−0.411968
$801$	−9.97637	−0.352498
$802$	−15.8539	−0.559819
$803$	11.6397	0.410755
$804$	−4.28326	−0.151059
$805$	12.4203	0.437759
$806$	−49.8823	−1.75703
$807$	−8.97665	−0.315993
$808$	39.2375	1.38037
$809$	−38.9238	−1.36849	−0.684245	−	0.729252i	$-0.739868\pi$
$809$	−38.9238	−1.36849	−0.684245	+	0.729252i	$0.739868\pi$
$810$	16.2698	0.571661
$811$	35.7219	1.25436	0.627182	−	0.778872i	$-0.284208\pi$
$811$	35.7219	1.25436	0.627182	+	0.778872i	$0.284208\pi$
$812$	47.6630	1.67264
$813$	−10.8039	−0.378908
$814$	−53.3991	−1.87164
$815$	−0.570693	−0.0199905
$816$	−1.53037	−0.0535737
$817$	−7.66864	−0.268292
$818$	15.7730	0.551488
$819$	29.1659	1.01914
$820$	−25.2218	−0.880785
$821$	1.59870	0.0557950	0.0278975	−	0.999611i	$-0.491119\pi$
$821$	1.59870	0.0557950	0.0278975	+	0.999611i	$0.491119\pi$
$822$	7.24368	0.252652
$823$	3.22870	0.112545	0.0562727	−	0.998415i	$-0.482078\pi$
$823$	3.22870	0.112545	0.0562727	+	0.998415i	$0.482078\pi$
$824$	52.1110	1.81537
$825$	−7.00745	−0.243968
$826$	8.19660	0.285196
$827$	10.2920	0.357889	0.178945	−	0.983859i	$-0.442732\pi$
$827$	10.2920	0.357889	0.178945	+	0.983859i	$0.442732\pi$
$828$	−33.9215	−1.17885
$829$	42.4336	1.47378	0.736889	−	0.676013i	$-0.236294\pi$
$829$	42.4336	1.47378	0.736889	+	0.676013i	$0.236294\pi$
$830$	−17.4736	−0.606519
$831$	9.96326	0.345622
$832$	−26.6844	−0.925115
$833$	19.1242	0.662613
$834$	5.05595	0.175073
$835$	−1.58147	−0.0547291
$836$	20.1595	0.697229
$837$	20.2933	0.701439
$838$	75.7365	2.61627
$839$	8.01805	0.276814	0.138407	−	0.990375i	$-0.455802\pi$
$839$	8.01805	0.276814	0.138407	+	0.990375i	$0.455802\pi$
$840$	6.17167	0.212943
$841$	−19.7179	−0.679928
$842$	−32.2498	−1.11140
$843$	−7.45399	−0.256729
$844$	30.0548	1.03453
$845$	6.44221	0.221619
$846$	75.4451	2.59386
$847$	−26.9353	−0.925508
$848$	4.28493	0.147145
$849$	−7.50091	−0.257431
$850$	17.2906	0.593063
$851$	−17.4528	−0.598274
$852$	−3.87694	−0.132822
$853$	−33.1230	−1.13411	−0.567054	−	0.823680i	$-0.691917\pi$
$853$	−33.1230	−1.13411	−0.567054	+	0.823680i	$0.691917\pi$
$854$	72.0396	2.46514
$855$	−3.36235	−0.114990
$856$	−12.9103	−0.441266
$857$	−29.4666	−1.00656	−0.503280	−	0.864123i	$-0.667874\pi$
$857$	−29.4666	−1.00656	−0.503280	+	0.864123i	$0.667874\pi$
$858$	−9.64939	−0.329425
$859$	−6.62937	−0.226191	−0.113096	−	0.993584i	$-0.536077\pi$
$859$	−6.62937	−0.226191	−0.113096	+	0.993584i	$0.536077\pi$
$860$	−19.3657	−0.660364
$861$	12.9692	0.441989
$862$	33.2591	1.13281
$863$	−7.61813	−0.259324	−0.129662	−	0.991558i	$-0.541389\pi$
$863$	−7.61813	−0.259324	−0.129662	+	0.991558i	$0.541389\pi$
$864$	6.52761	0.222074
$865$	7.56829	0.257329
$866$	46.2877	1.57292
$867$	5.62564	0.191057
$868$	−135.324	−4.59321
$869$	43.0873	1.46164
$870$	2.63009	0.0891683
$871$	7.00110	0.237223
$872$	−53.7802	−1.82123
$873$	42.5601	1.44044
$874$	10.1667	0.343895
$875$	−35.1707	−1.18899
$876$	4.13661	0.139763
$877$	2.25023	0.0759849	0.0379924	−	0.999278i	$-0.487904\pi$
$877$	2.25023	0.0759849	0.0379924	+	0.999278i	$0.487904\pi$
$878$	97.7300	3.29823
$879$	6.61662	0.223173
$880$	8.25282	0.278202
$881$	36.6872	1.23602	0.618012	−	0.786169i	$-0.287938\pi$
$881$	36.6872	1.23602	0.618012	+	0.786169i	$0.287938\pi$
$882$	74.7209	2.51598
$883$	46.0155	1.54854	0.774272	−	0.632853i	$-0.218116\pi$
$883$	46.0155	1.54854	0.774272	+	0.632853i	$0.218116\pi$
$884$	15.4305	0.518983
$885$	0.293124	0.00985324
$886$	−72.1918	−2.42533
$887$	−45.3301	−1.52204	−0.761019	−	0.648730i	$-0.775300\pi$
$887$	−45.3301	−1.52204	−0.761019	+	0.648730i	$0.775300\pi$
$888$	−8.67232	−0.291024
$889$	60.3463	2.02395
$890$	7.55081	0.253104
$891$	−31.5359	−1.05649
$892$	−52.2284	−1.74874
$893$	−14.6544	−0.490389
$894$	2.96047	0.0990128
$895$	−9.10501	−0.304347
$896$	−88.0643	−2.94202
$897$	−3.15378	−0.105302
$898$	29.5335	0.985547
$899$	−26.3537	−0.878944
$900$	43.7823	1.45941
$901$	3.37469	0.112427
$902$	75.4349	2.51171
$903$	9.95793	0.331379
$904$	2.53726	0.0843879
$905$	−7.08523	−0.235521
$906$	−3.19435	−0.106125
$907$	−6.92614	−0.229979	−0.114989	−	0.993367i	$-0.536683\pi$
$907$	−6.92614	−0.229979	−0.114989	+	0.993367i	$0.536683\pi$
$908$	65.6403	2.17835
$909$	27.7582	0.920682
$910$	−22.0748	−0.731772
$911$	11.4507	0.379379	0.189690	−	0.981844i	$-0.439252\pi$
$911$	11.4507	0.379379	0.189690	+	0.981844i	$0.439252\pi$
$912$	1.16143	0.0384587
$913$	33.8694	1.12091
$914$	12.2433	0.404972
$915$	2.57625	0.0851682
$916$	−44.7798	−1.47957
$917$	7.60604	0.251174
$918$	−9.68626	−0.319694
$919$	−13.7191	−0.452552	−0.226276	−	0.974063i	$-0.572655\pi$
$919$	−13.7191	−0.452552	−0.226276	+	0.974063i	$0.572655\pi$
$920$	11.7326	0.386811
$921$	5.05439	0.166548
$922$	−15.7394	−0.518349
$923$	6.33695	0.208583
$924$	−26.1776	−0.861179
$925$	22.5263	0.740659
$926$	−16.9576	−0.557261
$927$	36.8655	1.21082
$928$	−8.47701	−0.278271
$929$	19.6939	0.646136	0.323068	−	0.946376i	$-0.395286\pi$
$929$	19.6939	0.646136	0.323068	+	0.946376i	$0.395286\pi$
$930$	−7.46732	−0.244863
$931$	−14.5137	−0.475667
$932$	−66.4430	−2.17641
$933$	0.949150	0.0310738
$934$	−26.1158	−0.854535
$935$	6.49969	0.212563
$936$	27.5509	0.900530
$937$	−12.2715	−0.400892	−0.200446	−	0.979705i	$-0.564239\pi$
$937$	−12.2715	−0.400892	−0.200446	+	0.979705i	$0.564239\pi$
$938$	29.3067	0.956898
$939$	9.82928	0.320767
$940$	−37.0067	−1.20703
$941$	1.26235	0.0411513	0.0205757	−	0.999788i	$-0.493450\pi$
$941$	1.26235	0.0411513	0.0205757	+	0.999788i	$0.493450\pi$
$942$	−3.39454	−0.110600
$943$	24.6549	0.802875
$944$	1.78006	0.0579361
$945$	8.98054	0.292137
$946$	57.9200	1.88314
$947$	14.6646	0.476536	0.238268	−	0.971199i	$-0.423420\pi$
$947$	14.6646	0.476536	0.238268	+	0.971199i	$0.423420\pi$
$948$	15.3127	0.497335
$949$	−6.76139	−0.219484
$950$	−13.1222	−0.425739
$951$	13.9147	0.451214
$952$	29.5174	0.956663
$953$	13.9788	0.452818	0.226409	−	0.974032i	$-0.427301\pi$
$953$	13.9788	0.452818	0.226409	+	0.974032i	$0.427301\pi$
$954$	13.1854	0.426894
$955$	−13.8256	−0.447385
$956$	6.20167	0.200576
$957$	−5.09793	−0.164793
$958$	−16.1682	−0.522369
$959$	−32.1203	−1.03722
$960$	−3.99462	−0.128926
$961$	43.8231	1.41365
$962$	31.0191	1.00010
$963$	−9.13330	−0.294317
$964$	60.4483	1.94691
$965$	−2.10332	−0.0677084
$966$	−13.2018	−0.424760
$967$	−28.3305	−0.911046	−0.455523	−	0.890224i	$-0.650548\pi$
$967$	−28.3305	−0.911046	−0.455523	+	0.890224i	$0.650548\pi$
$968$	−25.4438	−0.817795
$969$	0.914708	0.0293847
$970$	−32.2125	−1.03428
$971$	−6.40480	−0.205540	−0.102770	−	0.994705i	$-0.532771\pi$
$971$	−6.40480	−0.205540	−0.102770	+	0.994705i	$0.532771\pi$
$972$	−37.1296	−1.19093
$973$	−22.4194	−0.718732
$974$	−62.3471	−1.99773
$975$	4.07057	0.130363
$976$	15.6449	0.500780
$977$	41.4440	1.32591	0.662955	−	0.748659i	$-0.269302\pi$
$977$	41.4440	1.32591	0.662955	+	0.748659i	$0.269302\pi$
$978$	0.606600	0.0193969
$979$	−14.6358	−0.467764
$980$	−36.6515	−1.17079
$981$	−38.0463	−1.21473
$982$	18.3147	0.584444
$983$	−17.1002	−0.545411	−0.272706	−	0.962098i	$-0.587918\pi$
$983$	−17.1002	−0.545411	−0.272706	+	0.962098i	$0.587918\pi$
$984$	12.2511	0.390550
$985$	11.3127	0.360452
$986$	12.5790	0.400596
$987$	19.0291	0.605702
$988$	−11.7105	−0.372559
$989$	18.9304	0.601951
$990$	25.3952	0.807114
$991$	1.86934	0.0593815	0.0296907	−	0.999559i	$-0.490548\pi$
$991$	1.86934	0.0593815	0.0296907	+	0.999559i	$0.490548\pi$
$992$	24.0678	0.764155
$993$	−13.6867	−0.434335
$994$	26.5266	0.841373
$995$	3.11793	0.0988449
$996$	12.0368	0.381401
$997$	−15.1704	−0.480451	−0.240225	−	0.970717i	$-0.577221\pi$
$997$	−15.1704	−0.480451	−0.240225	+	0.970717i	$0.577221\pi$
$998$	88.8080	2.81117
$999$	−12.6193	−0.399257

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.a.1.15	✓	139

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.a.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-2.38393 q^{2} -0.401819 q^{3} +3.68311 q^{4} -0.901205 q^{5} +0.957907 q^{6} -4.24761 q^{7} -4.01240 q^{8} -2.83854 q^{9} +O(q^{10})\)	\(q-2.38393 q^{2} -0.401819 q^{3} +3.68311 q^{4} -0.901205 q^{5} +0.957907 q^{6} -4.24761 q^{7} -4.01240 q^{8} -2.83854 q^{9} +2.14841 q^{10} -4.16429 q^{11} -1.47994 q^{12} +2.41900 q^{13} +10.1260 q^{14} +0.362121 q^{15} +2.19907 q^{16} +1.73192 q^{17} +6.76688 q^{18} -1.31439 q^{19} -3.31923 q^{20} +1.70677 q^{21} +9.92736 q^{22} +3.24463 q^{23} +1.61226 q^{24} -4.18783 q^{25} -5.76672 q^{26} +2.34604 q^{27} -15.6444 q^{28} -3.04665 q^{29} -0.863270 q^{30} +8.65003 q^{31} +2.78240 q^{32} +1.67329 q^{33} -4.12878 q^{34} +3.82796 q^{35} -10.4547 q^{36} -5.37898 q^{37} +3.13341 q^{38} -0.972000 q^{39} +3.61600 q^{40} +7.59869 q^{41} -4.06881 q^{42} +5.83438 q^{43} -15.3375 q^{44} +2.55811 q^{45} -7.73496 q^{46} +11.1492 q^{47} -0.883626 q^{48} +11.0422 q^{49} +9.98348 q^{50} -0.695919 q^{51} +8.90944 q^{52} +1.94852 q^{53} -5.59278 q^{54} +3.75288 q^{55} +17.0431 q^{56} +0.528146 q^{57} +7.26300 q^{58} +0.809463 q^{59} +1.33373 q^{60} +7.11433 q^{61} -20.6210 q^{62} +12.0570 q^{63} -11.0312 q^{64} -2.18001 q^{65} -3.98900 q^{66} +2.89421 q^{67} +6.37886 q^{68} -1.30375 q^{69} -9.12559 q^{70} +2.61966 q^{71} +11.3894 q^{72} -2.79512 q^{73} +12.8231 q^{74} +1.68275 q^{75} -4.84103 q^{76} +17.6883 q^{77} +2.31718 q^{78} -10.3469 q^{79} -1.98181 q^{80} +7.57294 q^{81} -18.1147 q^{82} -8.13330 q^{83} +6.28621 q^{84} -1.56082 q^{85} -13.9087 q^{86} +1.22420 q^{87} +16.7088 q^{88} +3.51461 q^{89} -6.09834 q^{90} -10.2750 q^{91} +11.9503 q^{92} -3.47575 q^{93} -26.5788 q^{94} +1.18453 q^{95} -1.11802 q^{96} -14.9937 q^{97} -26.3237 q^{98} +11.8205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) \) 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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