LMFDB - Embedded newform 4009.2.a.c.1.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4009,2,Mod(1,4009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4009, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4009 = 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4009.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:	$32.0120261703$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.26
Character	$\chi$	$=$	4009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.17459 q^{2} -0.489237 q^{3} -0.620331 q^{4} +1.33755 q^{5} +0.574655 q^{6} +1.32499 q^{7} +3.07782 q^{8} -2.76065 q^{9} +O(q^{10})$	\(q-1.17459 q^{2} -0.489237 q^{3} -0.620331 q^{4} +1.33755 q^{5} +0.574655 q^{6} +1.32499 q^{7} +3.07782 q^{8} -2.76065 q^{9} -1.57107 q^{10} +2.55231 q^{11} +0.303489 q^{12} +6.09324 q^{13} -1.55632 q^{14} -0.654379 q^{15} -2.37453 q^{16} -3.00482 q^{17} +3.24264 q^{18} +1.00000 q^{19} -0.829723 q^{20} -0.648235 q^{21} -2.99793 q^{22} -7.30753 q^{23} -1.50579 q^{24} -3.21096 q^{25} -7.15707 q^{26} +2.81832 q^{27} -0.821933 q^{28} -7.45150 q^{29} +0.768629 q^{30} +0.252730 q^{31} -3.36654 q^{32} -1.24869 q^{33} +3.52944 q^{34} +1.77224 q^{35} +1.71252 q^{36} +5.35147 q^{37} -1.17459 q^{38} -2.98104 q^{39} +4.11674 q^{40} -2.36258 q^{41} +0.761412 q^{42} -3.17344 q^{43} -1.58328 q^{44} -3.69250 q^{45} +8.58338 q^{46} -10.5612 q^{47} +1.16171 q^{48} -5.24440 q^{49} +3.77158 q^{50} +1.47007 q^{51} -3.77983 q^{52} +2.29263 q^{53} -3.31038 q^{54} +3.41384 q^{55} +4.07809 q^{56} -0.489237 q^{57} +8.75248 q^{58} -7.14070 q^{59} +0.405932 q^{60} +10.1056 q^{61} -0.296855 q^{62} -3.65783 q^{63} +8.70337 q^{64} +8.15000 q^{65} +1.46670 q^{66} +4.59397 q^{67} +1.86398 q^{68} +3.57512 q^{69} -2.08166 q^{70} -2.95281 q^{71} -8.49678 q^{72} -12.7302 q^{73} -6.28579 q^{74} +1.57092 q^{75} -0.620331 q^{76} +3.38179 q^{77} +3.50151 q^{78} -5.71906 q^{79} -3.17604 q^{80} +6.90311 q^{81} +2.77507 q^{82} +5.98556 q^{83} +0.402121 q^{84} -4.01909 q^{85} +3.72750 q^{86} +3.64555 q^{87} +7.85556 q^{88} +8.59163 q^{89} +4.33718 q^{90} +8.07348 q^{91} +4.53309 q^{92} -0.123645 q^{93} +12.4051 q^{94} +1.33755 q^{95} +1.64704 q^{96} -9.86406 q^{97} +6.16004 q^{98} -7.04603 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) $ 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * 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 $

$2$	−1.17459	−0.830563	−0.415281	−	0.909693i	$-0.636317\pi$
$2$	−1.17459	−0.830563	−0.415281	+	0.909693i	$0.636317\pi$
$3$	−0.489237	−0.282461	−0.141231	−	0.989977i	$-0.545106\pi$
$3$	−0.489237	−0.282461	−0.141231	+	0.989977i	$0.545106\pi$
$4$	−0.620331	−0.310166
$5$	1.33755	0.598170	0.299085	−	0.954226i	$-0.403319\pi$
$5$	1.33755	0.598170	0.299085	+	0.954226i	$0.403319\pi$
$6$	0.574655	0.234602
$7$	1.32499	0.500799	0.250400	−	0.968143i	$-0.419438\pi$
$7$	1.32499	0.500799	0.250400	+	0.968143i	$0.419438\pi$
$8$	3.07782	1.08817
$9$	−2.76065	−0.920216
$10$	−1.57107	−0.496818
$11$	2.55231	0.769551	0.384775	−	0.923010i	$-0.374279\pi$
$11$	2.55231	0.769551	0.384775	+	0.923010i	$0.374279\pi$
$12$	0.303489	0.0876098
$13$	6.09324	1.68996	0.844980	−	0.534798i	$-0.179612\pi$
$13$	6.09324	1.68996	0.844980	+	0.534798i	$0.179612\pi$
$14$	−1.55632	−0.415945
$15$	−0.654379	−0.168960
$16$	−2.37453	−0.593632
$17$	−3.00482	−0.728776	−0.364388	−	0.931247i	$-0.618722\pi$
$17$	−3.00482	−0.728776	−0.364388	+	0.931247i	$0.618722\pi$
$18$	3.24264	0.764297
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−0.829723	−0.185532
$21$	−0.648235	−0.141456
$22$	−2.99793	−0.639160
$23$	−7.30753	−1.52373	−0.761863	−	0.647738i	$-0.775715\pi$
$23$	−7.30753	−1.52373	−0.761863	+	0.647738i	$0.775715\pi$
$24$	−1.50579	−0.307367
$25$	−3.21096	−0.642193
$26$	−7.15707	−1.40362
$27$	2.81832	0.542387
$28$	−0.821933	−0.155331
$29$	−7.45150	−1.38371	−0.691854	−	0.722037i	$-0.743206\pi$
$29$	−7.45150	−1.38371	−0.691854	+	0.722037i	$0.743206\pi$
$30$	0.768629	0.140332
$31$	0.252730	0.0453917	0.0226958	−	0.999742i	$-0.492775\pi$
$31$	0.252730	0.0453917	0.0226958	+	0.999742i	$0.492775\pi$
$32$	−3.36654	−0.595127
$33$	−1.24869	−0.217368
$34$	3.52944	0.605294
$35$	1.77224	0.299563
$36$	1.71252	0.285419
$37$	5.35147	0.879775	0.439888	−	0.898053i	$-0.355018\pi$
$37$	5.35147	0.879775	0.439888	+	0.898053i	$0.355018\pi$
$38$	−1.17459	−0.190544
$39$	−2.98104	−0.477349
$40$	4.11674	0.650913
$41$	−2.36258	−0.368973	−0.184487	−	0.982835i	$-0.559062\pi$
$41$	−2.36258	−0.368973	−0.184487	+	0.982835i	$0.559062\pi$
$42$	0.761412	0.117488
$43$	−3.17344	−0.483945	−0.241973	−	0.970283i	$-0.577794\pi$
$43$	−3.17344	−0.483945	−0.241973	+	0.970283i	$0.577794\pi$
$44$	−1.58328	−0.238688
$45$	−3.69250	−0.550445
$46$	8.58338	1.26555
$47$	−10.5612	−1.54050	−0.770252	−	0.637740i	$-0.779869\pi$
$47$	−10.5612	−1.54050	−0.770252	+	0.637740i	$0.779869\pi$
$48$	1.16171	0.167678
$49$	−5.24440	−0.749200
$50$	3.77158	0.533381
$51$	1.47007	0.205851
$52$	−3.77983	−0.524168
$53$	2.29263	0.314918	0.157459	−	0.987526i	$-0.449670\pi$
$53$	2.29263	0.314918	0.157459	+	0.987526i	$0.449670\pi$
$54$	−3.31038	−0.450486
$55$	3.41384	0.460322
$56$	4.07809	0.544957
$57$	−0.489237	−0.0648011
$58$	8.75248	1.14926
$59$	−7.14070	−0.929640	−0.464820	−	0.885405i	$-0.653881\pi$
$59$	−7.14070	−0.929640	−0.464820	+	0.885405i	$0.653881\pi$
$60$	0.405932	0.0524056
$61$	10.1056	1.29389	0.646944	−	0.762538i	$-0.276047\pi$
$61$	10.1056	1.29389	0.646944	+	0.762538i	$0.276047\pi$
$62$	−0.296855	−0.0377006
$63$	−3.65783	−0.460843
$64$	8.70337	1.08792
$65$	8.15000	1.01088
$66$	1.46670	0.180538
$67$	4.59397	0.561243	0.280621	−	0.959819i	$-0.409460\pi$
$67$	4.59397	0.561243	0.280621	+	0.959819i	$0.409460\pi$
$68$	1.86398	0.226041
$69$	3.57512	0.430394
$70$	−2.08166	−0.248806
$71$	−2.95281	−0.350434	−0.175217	−	0.984530i	$-0.556063\pi$
$71$	−2.95281	−0.350434	−0.175217	+	0.984530i	$0.556063\pi$
$72$	−8.49678	−1.00136
$73$	−12.7302	−1.48996	−0.744981	−	0.667085i	$-0.767542\pi$
$73$	−12.7302	−1.48996	−0.744981	+	0.667085i	$0.767542\pi$
$74$	−6.28579	−0.730709
$75$	1.57092	0.181395
$76$	−0.620331	−0.0711569
$77$	3.38179	0.385391
$78$	3.50151	0.396468
$79$	−5.71906	−0.643444	−0.321722	−	0.946834i	$-0.604262\pi$
$79$	−5.71906	−0.643444	−0.321722	+	0.946834i	$0.604262\pi$
$80$	−3.17604	−0.355092
$81$	6.90311	0.767012
$82$	2.77507	0.306456
$83$	5.98556	0.657001	0.328500	−	0.944504i	$-0.393457\pi$
$83$	5.98556	0.657001	0.328500	+	0.944504i	$0.393457\pi$
$84$	0.402121	0.0438749
$85$	−4.01909	−0.435932
$86$	3.72750	0.401947
$87$	3.64555	0.390844
$88$	7.85556	0.837406
$89$	8.59163	0.910711	0.455355	−	0.890310i	$-0.349512\pi$
$89$	8.59163	0.910711	0.455355	+	0.890310i	$0.349512\pi$
$90$	4.33718	0.457179
$91$	8.07348	0.846331
$92$	4.53309	0.472608
$93$	−0.123645	−0.0128214
$94$	12.4051	1.27948
$95$	1.33755	0.137230
$96$	1.64704	0.168100
$97$	−9.86406	−1.00154	−0.500772	−	0.865579i	$-0.666950\pi$
$97$	−9.86406	−1.00154	−0.500772	+	0.865579i	$0.666950\pi$
$98$	6.16004	0.622258
$99$	−7.04603	−0.708153
$100$	1.99186	0.199186
$101$	−4.27548	−0.425426	−0.212713	−	0.977115i	$-0.568230\pi$
$101$	−4.27548	−0.425426	−0.212713	+	0.977115i	$0.568230\pi$
$102$	−1.72673	−0.170972
$103$	15.0303	1.48098	0.740490	−	0.672068i	$-0.234594\pi$
$103$	15.0303	1.48098	0.740490	+	0.672068i	$0.234594\pi$
$104$	18.7539	1.83897
$105$	−0.867046	−0.0846150
$106$	−2.69291	−0.261559
$107$	−9.52925	−0.921227	−0.460614	−	0.887601i	$-0.652371\pi$
$107$	−9.52925	−0.921227	−0.460614	+	0.887601i	$0.652371\pi$
$108$	−1.74830	−0.168230
$109$	3.26348	0.312585	0.156293	−	0.987711i	$-0.450046\pi$
$109$	3.26348	0.312585	0.156293	+	0.987711i	$0.450046\pi$
$110$	−4.00987	−0.382326
$111$	−2.61814	−0.248503
$112$	−3.14622	−0.297290
$113$	16.5279	1.55481	0.777407	−	0.628998i	$-0.216535\pi$
$113$	16.5279	1.55481	0.777407	+	0.628998i	$0.216535\pi$
$114$	0.574655	0.0538214
$115$	−9.77418	−0.911447
$116$	4.62240	0.429179
$117$	−16.8213	−1.55513
$118$	8.38742	0.772124
$119$	−3.98136	−0.364970
$120$	−2.01406	−0.183858
$121$	−4.48571	−0.407791
$122$	−11.8699	−1.07465
$123$	1.15586	0.104221
$124$	−0.156776	−0.0140789
$125$	−10.9826	−0.982310
$126$	4.29646	0.382759
$127$	−11.3212	−1.00460	−0.502298	−	0.864695i	$-0.667512\pi$
$127$	−11.3212	−1.00460	−0.502298	+	0.864695i	$0.667512\pi$
$128$	−3.48983	−0.308460
$129$	1.55257	0.136696
$130$	−9.57293	−0.839602
$131$	−18.2045	−1.59054	−0.795268	−	0.606258i	$-0.792670\pi$
$131$	−18.2045	−1.59054	−0.795268	+	0.606258i	$0.792670\pi$
$132$	0.774599	0.0674202
$133$	1.32499	0.114891
$134$	−5.39604	−0.466147
$135$	3.76964	0.324439
$136$	−9.24830	−0.793035
$137$	−3.56259	−0.304372	−0.152186	−	0.988352i	$-0.548631\pi$
$137$	−3.56259	−0.304372	−0.152186	+	0.988352i	$0.548631\pi$
$138$	−4.19931	−0.357469
$139$	14.1386	1.19922	0.599611	−	0.800292i	$-0.295322\pi$
$139$	14.1386	1.19922	0.599611	+	0.800292i	$0.295322\pi$
$140$	−1.09938	−0.0929142
$141$	5.16691	0.435133
$142$	3.46835	0.291057
$143$	15.5518	1.30051
$144$	6.55523	0.546269
$145$	−9.96674	−0.827693
$146$	14.9529	1.23751
$147$	2.56576	0.211620
$148$	−3.31968	−0.272876
$149$	−13.9827	−1.14551	−0.572755	−	0.819726i	$-0.694125\pi$
$149$	−13.9827	−1.14551	−0.572755	+	0.819726i	$0.694125\pi$
$150$	−1.84520	−0.150660
$151$	1.75846	0.143101	0.0715506	−	0.997437i	$-0.477205\pi$
$151$	1.75846	0.143101	0.0715506	+	0.997437i	$0.477205\pi$
$152$	3.07782	0.249644
$153$	8.29524	0.670631
$154$	−3.97222	−0.320091
$155$	0.338039	0.0271519
$156$	1.84923	0.148057
$157$	2.47409	0.197454	0.0987271	−	0.995115i	$-0.468523\pi$
$157$	2.47409	0.197454	0.0987271	+	0.995115i	$0.468523\pi$
$158$	6.71756	0.534421
$159$	−1.12164	−0.0889520
$160$	−4.50292	−0.355987
$161$	−9.68241	−0.763081
$162$	−8.10834	−0.637052
$163$	−14.0912	−1.10371	−0.551855	−	0.833940i	$-0.686080\pi$
$163$	−14.0912	−1.10371	−0.551855	+	0.833940i	$0.686080\pi$
$164$	1.46558	0.114443
$165$	−1.67018	−0.130023
$166$	−7.03060	−0.545680
$167$	14.7612	1.14225	0.571127	−	0.820861i	$-0.306506\pi$
$167$	14.7612	1.14225	0.571127	+	0.820861i	$0.306506\pi$
$168$	−1.99515	−0.153929
$169$	24.1276	1.85597
$170$	4.72080	0.362068
$171$	−2.76065	−0.211112
$172$	1.96859	0.150103
$173$	−0.421407	−0.0320390	−0.0160195	−	0.999872i	$-0.505099\pi$
$173$	−0.421407	−0.0320390	−0.0160195	+	0.999872i	$0.505099\pi$
$174$	−4.28204	−0.324621
$175$	−4.25450	−0.321610
$176$	−6.06053	−0.456830
$177$	3.49350	0.262587
$178$	−10.0917	−0.756402
$179$	1.21765	0.0910117	0.0455059	−	0.998964i	$-0.485510\pi$
$179$	1.21765	0.0910117	0.0455059	+	0.998964i	$0.485510\pi$
$180$	2.29057	0.170729
$181$	−21.1645	−1.57314	−0.786571	−	0.617500i	$-0.788146\pi$
$181$	−21.1645	−1.57314	−0.786571	+	0.617500i	$0.788146\pi$
$182$	−9.48306	−0.702931
$183$	−4.94403	−0.365473
$184$	−22.4913	−1.65808
$185$	7.15784	0.526255
$186$	0.145233	0.0106490
$187$	−7.66923	−0.560830
$188$	6.55142	0.477811
$189$	3.73425	0.271627
$190$	−1.57107	−0.113978
$191$	8.01254	0.579767	0.289883	−	0.957062i	$-0.406383\pi$
$191$	8.01254	0.579767	0.289883	+	0.957062i	$0.406383\pi$
$192$	−4.25802	−0.307296
$193$	−13.5407	−0.974684	−0.487342	−	0.873211i	$-0.662034\pi$
$193$	−13.5407	−0.974684	−0.487342	+	0.873211i	$0.662034\pi$
$194$	11.5863	0.831844
$195$	−3.98729	−0.285535
$196$	3.25327	0.232376
$197$	−25.3322	−1.80484	−0.902421	−	0.430854i	$-0.858212\pi$
$197$	−25.3322	−1.80484	−0.902421	+	0.430854i	$0.858212\pi$
$198$	8.27622	0.588165
$199$	−12.0956	−0.857435	−0.428717	−	0.903439i	$-0.641034\pi$
$199$	−12.0956	−0.857435	−0.428717	+	0.903439i	$0.641034\pi$
$200$	−9.88278	−0.698818
$201$	−2.24754	−0.158529
$202$	5.02195	0.353343
$203$	−9.87316	−0.692960
$204$	−0.911931	−0.0638479
$205$	−3.16007	−0.220709
$206$	−17.6545	−1.23005
$207$	20.1735	1.40216
$208$	−14.4686	−1.00321
$209$	2.55231	0.176547
$210$	1.01843	0.0702780
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−1.42219	−0.0976766
$213$	1.44462	0.0989840
$214$	11.1930	0.765137
$215$	−4.24463	−0.289481
$216$	8.67430	0.590212
$217$	0.334865	0.0227321
$218$	−3.83326	−0.259621
$219$	6.22811	0.420857
$220$	−2.11771	−0.142776
$221$	−18.3091	−1.23160
$222$	3.07525	0.206397
$223$	8.22182	0.550574	0.275287	−	0.961362i	$-0.411227\pi$
$223$	8.22182	0.550574	0.275287	+	0.961362i	$0.411227\pi$
$224$	−4.46064	−0.298039
$225$	8.86434	0.590956
$226$	−19.4136	−1.29137
$227$	−4.39689	−0.291832	−0.145916	−	0.989297i	$-0.546613\pi$
$227$	−4.39689	−0.291832	−0.145916	+	0.989297i	$0.546613\pi$
$228$	0.303489	0.0200991
$229$	18.1983	1.20258	0.601288	−	0.799032i	$-0.294654\pi$
$229$	18.1983	1.20258	0.601288	+	0.799032i	$0.294654\pi$
$230$	11.4807	0.757014
$231$	−1.65450	−0.108858
$232$	−22.9344	−1.50572
$233$	7.44951	0.488033	0.244017	−	0.969771i	$-0.421535\pi$
$233$	7.44951	0.488033	0.244017	+	0.969771i	$0.421535\pi$
$234$	19.7582	1.29163
$235$	−14.1261	−0.921483
$236$	4.42960	0.288342
$237$	2.79798	0.181748
$238$	4.67647	0.303131
$239$	18.0117	1.16508	0.582540	−	0.812802i	$-0.302059\pi$
$239$	18.0117	1.16508	0.582540	+	0.812802i	$0.302059\pi$
$240$	1.55384	0.100300
$241$	22.5131	1.45020	0.725100	−	0.688644i	$-0.241794\pi$
$241$	22.5131	1.45020	0.725100	+	0.688644i	$0.241794\pi$
$242$	5.26888	0.338696
$243$	−11.8322	−0.759038
$244$	−6.26881	−0.401319
$245$	−7.01464	−0.448149
$246$	−1.35767	−0.0865619
$247$	6.09324	0.387703
$248$	0.777858	0.0493941
$249$	−2.92836	−0.185577
$250$	12.9000	0.815870
$251$	23.9899	1.51423	0.757113	−	0.653284i	$-0.226609\pi$
$251$	23.9899	1.51423	0.757113	+	0.653284i	$0.226609\pi$
$252$	2.26907	0.142938
$253$	−18.6511	−1.17258
$254$	13.2978	0.834379
$255$	1.96629	0.123134
$256$	−13.3076	−0.831726
$257$	7.20696	0.449558	0.224779	−	0.974410i	$-0.427834\pi$
$257$	7.20696	0.449558	0.224779	+	0.974410i	$0.427834\pi$
$258$	−1.82363	−0.113534
$259$	7.09064	0.440591
$260$	−5.05570	−0.313541
$261$	20.5710	1.27331
$262$	21.3829	1.32104
$263$	8.46636	0.522058	0.261029	−	0.965331i	$-0.415938\pi$
$263$	8.46636	0.522058	0.261029	+	0.965331i	$0.415938\pi$
$264$	−3.84324	−0.236535
$265$	3.06651	0.188374
$266$	−1.55632	−0.0954244
$267$	−4.20335	−0.257241
$268$	−2.84978	−0.174078
$269$	−13.9007	−0.847540	−0.423770	−	0.905770i	$-0.639293\pi$
$269$	−13.9007	−0.847540	−0.423770	+	0.905770i	$0.639293\pi$
$270$	−4.42780	−0.269467
$271$	23.0451	1.39989	0.699946	−	0.714196i	$-0.253208\pi$
$271$	23.0451	1.39989	0.699946	+	0.714196i	$0.253208\pi$
$272$	7.13502	0.432624
$273$	−3.94985	−0.239056
$274$	4.18459	0.252800
$275$	−8.19538	−0.494200
$276$	−2.21776	−0.133493
$277$	−25.4316	−1.52804	−0.764019	−	0.645194i	$-0.776776\pi$
$277$	−25.4316	−1.52804	−0.764019	+	0.645194i	$0.776776\pi$
$278$	−16.6071	−0.996028
$279$	−0.697698	−0.0417701
$280$	5.45464	0.325977
$281$	−3.65158	−0.217835	−0.108918	−	0.994051i	$-0.534738\pi$
$281$	−3.65158	−0.217835	−0.108918	+	0.994051i	$0.534738\pi$
$282$	−6.06902	−0.361405
$283$	−29.0423	−1.72639	−0.863193	−	0.504874i	$-0.831539\pi$
$283$	−29.0423	−1.72639	−0.863193	+	0.504874i	$0.831539\pi$
$284$	1.83172	0.108693
$285$	−0.654379	−0.0387621
$286$	−18.2671	−1.08016
$287$	−3.13040	−0.184782
$288$	9.29384	0.547645
$289$	−7.97106	−0.468886
$290$	11.7069	0.687451
$291$	4.82587	0.282897
$292$	7.89697	0.462135
$293$	−1.21527	−0.0709967	−0.0354984	−	0.999370i	$-0.511302\pi$
$293$	−1.21527	−0.0709967	−0.0354984	+	0.999370i	$0.511302\pi$
$294$	−3.01372	−0.175764
$295$	−9.55103	−0.556083
$296$	16.4709	0.957349
$297$	7.19324	0.417394
$298$	16.4240	0.951418
$299$	−44.5265	−2.57504
$300$	−0.974494	−0.0562624
$301$	−4.20478	−0.242359
$302$	−2.06547	−0.118855
$303$	2.09173	0.120166
$304$	−2.37453	−0.136188
$305$	13.5167	0.773964
$306$	−9.74353	−0.557001
$307$	−19.6030	−1.11880	−0.559402	−	0.828897i	$-0.688969\pi$
$307$	−19.6030	−1.11880	−0.559402	+	0.828897i	$0.688969\pi$
$308$	−2.09783	−0.119535
$309$	−7.35338	−0.418319
$310$	−0.397058	−0.0225514
$311$	4.66177	0.264345	0.132172	−	0.991227i	$-0.457805\pi$
$311$	4.66177	0.264345	0.132172	+	0.991227i	$0.457805\pi$
$312$	−9.17511	−0.519439
$313$	−9.44114	−0.533645	−0.266822	−	0.963746i	$-0.585974\pi$
$313$	−9.44114	−0.533645	−0.266822	+	0.963746i	$0.585974\pi$
$314$	−2.90605	−0.163998
$315$	−4.89253	−0.275663
$316$	3.54771	0.199574
$317$	−34.6966	−1.94875	−0.974377	−	0.224921i	$-0.927787\pi$
$317$	−34.6966	−1.94875	−0.974377	+	0.224921i	$0.927787\pi$
$318$	1.31747	0.0738802
$319$	−19.0185	−1.06483
$320$	11.6412	0.650762
$321$	4.66207	0.260211
$322$	11.3729	0.633787
$323$	−3.00482	−0.167193
$324$	−4.28222	−0.237901
$325$	−19.5652	−1.08528
$326$	16.5515	0.916701
$327$	−1.59662	−0.0882932
$328$	−7.27161	−0.401508
$329$	−13.9934	−0.771483
$330$	1.96178	0.107992
$331$	−5.91682	−0.325218	−0.162609	−	0.986691i	$-0.551991\pi$
$331$	−5.91682	−0.325218	−0.162609	+	0.986691i	$0.551991\pi$
$332$	−3.71303	−0.203779
$333$	−14.7735	−0.809583
$334$	−17.3384	−0.948714
$335$	6.14465	0.335718
$336$	1.53925	0.0839730
$337$	17.7645	0.967696	0.483848	−	0.875152i	$-0.339239\pi$
$337$	17.7645	0.967696	0.483848	+	0.875152i	$0.339239\pi$
$338$	−28.3401	−1.54150
$339$	−8.08607	−0.439175
$340$	2.49317	0.135211
$341$	0.645046	0.0349312
$342$	3.24264	0.175342
$343$	−16.2237	−0.875998
$344$	−9.76729	−0.526617
$345$	4.78189	0.257449
$346$	0.494981	0.0266104
$347$	−7.79420	−0.418415	−0.209207	−	0.977871i	$-0.567088\pi$
$347$	−7.79420	−0.418415	−0.209207	+	0.977871i	$0.567088\pi$
$348$	−2.26145	−0.121226
$349$	1.18004	0.0631659	0.0315830	−	0.999501i	$-0.489945\pi$
$349$	1.18004	0.0631659	0.0315830	+	0.999501i	$0.489945\pi$
$350$	4.99730	0.267117
$351$	17.1727	0.916612
$352$	−8.59247	−0.457980
$353$	−9.10660	−0.484695	−0.242348	−	0.970189i	$-0.577917\pi$
$353$	−9.10660	−0.484695	−0.242348	+	0.970189i	$0.577917\pi$
$354$	−4.10344	−0.218095
$355$	−3.94952	−0.209619
$356$	−5.32966	−0.282471
$357$	1.94783	0.103090
$358$	−1.43025	−0.0755909
$359$	−9.57650	−0.505428	−0.252714	−	0.967541i	$-0.581323\pi$
$359$	−9.57650	−0.505428	−0.252714	+	0.967541i	$0.581323\pi$
$360$	−11.3649	−0.598981
$361$	1.00000	0.0526316
$362$	24.8596	1.30659
$363$	2.19458	0.115185
$364$	−5.00824	−0.262503
$365$	−17.0273	−0.891251
$366$	5.80722	0.303548
$367$	−28.5711	−1.49140	−0.745700	−	0.666282i	$-0.767885\pi$
$367$	−28.5711	−1.49140	−0.745700	+	0.666282i	$0.767885\pi$
$368$	17.3519	0.904532
$369$	6.52226	0.339535
$370$	−8.40755	−0.437088
$371$	3.03772	0.157710
$372$	0.0767009	0.00397676
$373$	32.4226	1.67878	0.839388	−	0.543532i	$-0.182913\pi$
$373$	32.4226	1.67878	0.839388	+	0.543532i	$0.182913\pi$
$374$	9.00823	0.465804
$375$	5.37308	0.277465
$376$	−32.5054	−1.67634
$377$	−45.4038	−2.33841
$378$	−4.38623	−0.225603
$379$	−15.7838	−0.810757	−0.405379	−	0.914149i	$-0.632860\pi$
$379$	−15.7838	−0.810757	−0.405379	+	0.914149i	$0.632860\pi$
$380$	−0.829723	−0.0425639
$381$	5.53876	0.283759
$382$	−9.41147	−0.481533
$383$	−20.2453	−1.03449	−0.517244	−	0.855838i	$-0.673042\pi$
$383$	−20.2453	−1.03449	−0.517244	+	0.855838i	$0.673042\pi$
$384$	1.70736	0.0871281
$385$	4.52331	0.230529
$386$	15.9049	0.809536
$387$	8.76075	0.445334
$388$	6.11898	0.310644
$389$	27.9004	1.41461	0.707303	−	0.706911i	$-0.249912\pi$
$389$	27.9004	1.41461	0.707303	+	0.706911i	$0.249912\pi$
$390$	4.68344	0.237155
$391$	21.9578	1.11045
$392$	−16.1413	−0.815261
$393$	8.90633	0.449265
$394$	29.7550	1.49904
$395$	−7.64951	−0.384889
$396$	4.37087	0.219645
$397$	−11.2345	−0.563843	−0.281922	−	0.959437i	$-0.590972\pi$
$397$	−11.2345	−0.563843	−0.281922	+	0.959437i	$0.590972\pi$
$398$	14.2074	0.712153
$399$	−0.648235	−0.0324523
$400$	7.62452	0.381226
$401$	−9.09699	−0.454282	−0.227141	−	0.973862i	$-0.572938\pi$
$401$	−9.09699	−0.454282	−0.227141	+	0.973862i	$0.572938\pi$
$402$	2.63995	0.131669
$403$	1.53994	0.0767101
$404$	2.65221	0.131953
$405$	9.23324	0.458804
$406$	11.5969	0.575547
$407$	13.6586	0.677032
$408$	4.52461	0.224002
$409$	−1.49160	−0.0737550	−0.0368775	−	0.999320i	$-0.511741\pi$
$409$	−1.49160	−0.0737550	−0.0368775	+	0.999320i	$0.511741\pi$
$410$	3.71180	0.183312
$411$	1.74295	0.0859735
$412$	−9.32377	−0.459349
$413$	−9.46136	−0.465563
$414$	−23.6957	−1.16458
$415$	8.00598	0.392998
$416$	−20.5132	−1.00574
$417$	−6.91714	−0.338734
$418$	−2.99793	−0.146633
$419$	−29.6541	−1.44870	−0.724348	−	0.689434i	$-0.757859\pi$
$419$	−29.6541	−1.44870	−0.724348	+	0.689434i	$0.757859\pi$
$420$	0.537856	0.0262447
$421$	22.0585	1.07507	0.537534	−	0.843242i	$-0.319356\pi$
$421$	22.0585	1.07507	0.537534	+	0.843242i	$0.319356\pi$
$422$	−1.17459	−0.0571783
$423$	29.1556	1.41760
$424$	7.05632	0.342685
$425$	9.64837	0.468015
$426$	−1.69685	−0.0822124
$427$	13.3898	0.647978
$428$	5.91129	0.285733
$429$	−7.60854	−0.367344
$430$	4.98571	0.240432
$431$	1.10242	0.0531019	0.0265510	−	0.999647i	$-0.491548\pi$
$431$	1.10242	0.0531019	0.0265510	+	0.999647i	$0.491548\pi$
$432$	−6.69218	−0.321978
$433$	−6.81720	−0.327614	−0.163807	−	0.986492i	$-0.552377\pi$
$433$	−6.81720	−0.327614	−0.163807	+	0.986492i	$0.552377\pi$
$434$	−0.393330	−0.0188804
$435$	4.87610	0.233791
$436$	−2.02444	−0.0969532
$437$	−7.30753	−0.349567
$438$	−7.31550	−0.349548
$439$	21.5812	1.03002	0.515008	−	0.857186i	$-0.327789\pi$
$439$	21.5812	1.03002	0.515008	+	0.857186i	$0.327789\pi$
$440$	10.5072	0.500911
$441$	14.4779	0.689426
$442$	21.5057	1.02292
$443$	−26.1711	−1.24343	−0.621713	−	0.783245i	$-0.713563\pi$
$443$	−26.1711	−1.24343	−0.621713	+	0.783245i	$0.713563\pi$
$444$	1.62411	0.0770770
$445$	11.4917	0.544760
$446$	−9.65729	−0.457286
$447$	6.84088	0.323563
$448$	11.5319	0.544830
$449$	−19.5121	−0.920834	−0.460417	−	0.887703i	$-0.652300\pi$
$449$	−19.5121	−0.920834	−0.460417	+	0.887703i	$0.652300\pi$
$450$	−10.4120	−0.490826
$451$	−6.03005	−0.283944
$452$	−10.2528	−0.482250
$453$	−0.860303	−0.0404206
$454$	5.16455	0.242384
$455$	10.7987	0.506250
$456$	−1.50579	−0.0705149
$457$	15.9484	0.746035	0.373017	−	0.927824i	$-0.378323\pi$
$457$	15.9484	0.746035	0.373017	+	0.927824i	$0.378323\pi$
$458$	−21.3756	−0.998815
$459$	−8.46855	−0.395278
$460$	6.06323	0.282700
$461$	0.590979	0.0275246	0.0137623	−	0.999905i	$-0.495619\pi$
$461$	0.590979	0.0275246	0.0137623	+	0.999905i	$0.495619\pi$
$462$	1.94336	0.0904133
$463$	−6.00689	−0.279164	−0.139582	−	0.990211i	$-0.544576\pi$
$463$	−6.00689	−0.279164	−0.139582	+	0.990211i	$0.544576\pi$
$464$	17.6938	0.821413
$465$	−0.165381	−0.00766937
$466$	−8.75014	−0.405342
$467$	−2.90644	−0.134494	−0.0672469	−	0.997736i	$-0.521422\pi$
$467$	−2.90644	−0.134494	−0.0672469	+	0.997736i	$0.521422\pi$
$468$	10.4348	0.482347
$469$	6.08696	0.281070
$470$	16.5924	0.765349
$471$	−1.21042	−0.0557732
$472$	−21.9778	−1.01161
$473$	−8.09961	−0.372420
$474$	−3.28648	−0.150953
$475$	−3.21096	−0.147329
$476$	2.46976	0.113201
$477$	−6.32915	−0.289792
$478$	−21.1564	−0.967671
$479$	−36.5429	−1.66969	−0.834844	−	0.550487i	$-0.814442\pi$
$479$	−36.5429	−1.66969	−0.834844	+	0.550487i	$0.814442\pi$
$480$	2.20300	0.100553
$481$	32.6078	1.48679
$482$	−26.4438	−1.20448
$483$	4.73700	0.215541
$484$	2.78262	0.126483
$485$	−13.1937	−0.599093
$486$	13.8981	0.630429
$487$	−32.2172	−1.45990	−0.729949	−	0.683501i	$-0.760456\pi$
$487$	−32.2172	−1.45990	−0.729949	+	0.683501i	$0.760456\pi$
$488$	31.1032	1.40798
$489$	6.89396	0.311756
$490$	8.23935	0.372216
$491$	0.966820	0.0436320	0.0218160	−	0.999762i	$-0.493055\pi$
$491$	0.966820	0.0436320	0.0218160	+	0.999762i	$0.493055\pi$
$492$	−0.717019	−0.0323257
$493$	22.3904	1.00841
$494$	−7.15707	−0.322012
$495$	−9.42441	−0.423596
$496$	−0.600114	−0.0269459
$497$	−3.91244	−0.175497
$498$	3.43963	0.154134
$499$	−25.3032	−1.13273	−0.566364	−	0.824155i	$-0.691650\pi$
$499$	−25.3032	−1.13273	−0.566364	+	0.824155i	$0.691650\pi$
$500$	6.81283	0.304679
$501$	−7.22172	−0.322643
$502$	−28.1783	−1.25766
$503$	36.2722	1.61730	0.808649	−	0.588292i	$-0.200199\pi$
$503$	36.2722	1.61730	0.808649	+	0.588292i	$0.200199\pi$
$504$	−11.2582	−0.501478
$505$	−5.71866	−0.254477
$506$	21.9075	0.973905
$507$	−11.8041	−0.524239
$508$	7.02290	0.311591
$509$	−20.1783	−0.894387	−0.447193	−	0.894437i	$-0.647576\pi$
$509$	−20.1783	−0.894387	−0.447193	+	0.894437i	$0.647576\pi$
$510$	−2.30959	−0.102270
$511$	−16.8675	−0.746172
$512$	22.6107	0.999261
$513$	2.81832	0.124432
$514$	−8.46524	−0.373386
$515$	20.1037	0.885877
$516$	−0.963106	−0.0423984
$517$	−26.9554	−1.18550
$518$	−8.32862	−0.365938
$519$	0.206168	0.00904977
$520$	25.0843	1.10002
$521$	−35.5716	−1.55842	−0.779209	−	0.626764i	$-0.784379\pi$
$521$	−35.5716	−1.55842	−0.779209	+	0.626764i	$0.784379\pi$
$522$	−24.1625	−1.05756
$523$	−11.8127	−0.516533	−0.258266	−	0.966074i	$-0.583151\pi$
$523$	−11.8127	−0.516533	−0.258266	+	0.966074i	$0.583151\pi$
$524$	11.2928	0.493330
$525$	2.08146	0.0908423
$526$	−9.94452	−0.433602
$527$	−0.759408	−0.0330803
$528$	2.96504	0.129037
$529$	30.4000	1.32174
$530$	−3.60190	−0.156457
$531$	19.7130	0.855469
$532$	−0.821933	−0.0356353
$533$	−14.3958	−0.623551
$534$	4.93722	0.213654
$535$	−12.7458	−0.551050
$536$	14.1394	0.610730
$537$	−0.595722	−0.0257073
$538$	16.3276	0.703935
$539$	−13.3853	−0.576548
$540$	−2.33843	−0.100630
$541$	41.2122	1.77185	0.885925	−	0.463829i	$-0.153525\pi$
$541$	41.2122	1.77185	0.885925	+	0.463829i	$0.153525\pi$
$542$	−27.0686	−1.16270
$543$	10.3545	0.444352
$544$	10.1159	0.433714
$545$	4.36507	0.186979
$546$	4.63947	0.198551
$547$	36.0416	1.54103	0.770513	−	0.637424i	$-0.220000\pi$
$547$	36.0416	1.54103	0.770513	+	0.637424i	$0.220000\pi$
$548$	2.20999	0.0944059
$549$	−27.8979	−1.19066
$550$	9.62624	0.410464
$551$	−7.45150	−0.317445
$552$	11.0036	0.468344
$553$	−7.57769	−0.322236
$554$	29.8718	1.26913
$555$	−3.50189	−0.148647
$556$	−8.77062	−0.371957
$557$	41.3242	1.75096	0.875481	−	0.483253i	$-0.160545\pi$
$557$	41.3242	1.75096	0.875481	+	0.483253i	$0.160545\pi$
$558$	0.819512	0.0346927
$559$	−19.3365	−0.817848
$560$	−4.20823	−0.177830
$561$	3.75208	0.158413
$562$	4.28912	0.180926
$563$	−16.9200	−0.713095	−0.356548	−	0.934277i	$-0.616046\pi$
$563$	−16.9200	−0.713095	−0.356548	+	0.934277i	$0.616046\pi$
$564$	−3.20520	−0.134963
$565$	22.1069	0.930043
$566$	34.1129	1.43387
$567$	9.14656	0.384119
$568$	−9.08822	−0.381333
$569$	44.0306	1.84586	0.922928	−	0.384972i	$-0.125789\pi$
$569$	44.0306	1.84586	0.922928	+	0.384972i	$0.125789\pi$
$570$	0.768629	0.0321943
$571$	21.5150	0.900375	0.450188	−	0.892934i	$-0.351357\pi$
$571$	21.5150	0.900375	0.450188	+	0.892934i	$0.351357\pi$
$572$	−9.64730	−0.403374
$573$	−3.92003	−0.163762
$574$	3.67695	0.153473
$575$	23.4642	0.978526
$576$	−24.0269	−1.00112
$577$	39.3361	1.63758	0.818792	−	0.574090i	$-0.194644\pi$
$577$	39.3361	1.63758	0.818792	+	0.574090i	$0.194644\pi$
$578$	9.36275	0.389439
$579$	6.62464	0.275311
$580$	6.18268	0.256722
$581$	7.93081	0.329025
$582$	−5.66843	−0.234964
$583$	5.85152	0.242345
$584$	−39.1814	−1.62134
$585$	−22.4993	−0.930231
$586$	1.42745	0.0589672
$587$	0.853501	0.0352278	0.0176139	−	0.999845i	$-0.494393\pi$
$587$	0.853501	0.0352278	0.0176139	+	0.999845i	$0.494393\pi$
$588$	−1.59162	−0.0656373
$589$	0.252730	0.0104136
$590$	11.2186	0.461861
$591$	12.3935	0.509798
$592$	−12.7072	−0.522262
$593$	3.15059	0.129379	0.0646896	−	0.997905i	$-0.479394\pi$
$593$	3.15059	0.129379	0.0646896	+	0.997905i	$0.479394\pi$
$594$	−8.44913	−0.346672
$595$	−5.32526	−0.218314
$596$	8.67393	0.355298
$597$	5.91762	0.242192
$598$	52.3006	2.13873
$599$	−45.0686	−1.84145	−0.920726	−	0.390209i	$-0.872403\pi$
$599$	−45.0686	−1.84145	−0.920726	+	0.390209i	$0.872403\pi$
$600$	4.83503	0.197389
$601$	−1.54315	−0.0629466	−0.0314733	−	0.999505i	$-0.510020\pi$
$601$	−1.54315	−0.0629466	−0.0314733	+	0.999505i	$0.510020\pi$
$602$	4.93890	0.201295
$603$	−12.6823	−0.516464
$604$	−1.09083	−0.0443851
$605$	−5.99985	−0.243929
$606$	−2.45693	−0.0998058
$607$	−40.9109	−1.66052	−0.830260	−	0.557376i	$-0.811808\pi$
$607$	−40.9109	−1.66052	−0.830260	+	0.557376i	$0.811808\pi$
$608$	−3.36654	−0.136531
$609$	4.83032	0.195735
$610$	−15.8766	−0.642826
$611$	−64.3517	−2.60339
$612$	−5.14580	−0.208007
$613$	9.17661	0.370640	0.185320	−	0.982678i	$-0.440668\pi$
$613$	9.17661	0.370640	0.185320	+	0.982678i	$0.440668\pi$
$614$	23.0256	0.929237
$615$	1.54602	0.0623417
$616$	10.4085	0.419372
$617$	37.5819	1.51299	0.756494	−	0.654000i	$-0.226910\pi$
$617$	37.5819	1.51299	0.756494	+	0.654000i	$0.226910\pi$
$618$	8.63723	0.347440
$619$	21.0147	0.844651	0.422326	−	0.906444i	$-0.361214\pi$
$619$	21.0147	0.844651	0.422326	+	0.906444i	$0.361214\pi$
$620$	−0.209696	−0.00842160
$621$	−20.5950	−0.826449
$622$	−5.47569	−0.219555
$623$	11.3838	0.456083
$624$	7.07856	0.283369
$625$	1.36511	0.0546045
$626$	11.0895	0.443225
$627$	−1.24869	−0.0498677
$628$	−1.53476	−0.0612435
$629$	−16.0802	−0.641159
$630$	5.74673	0.228955
$631$	−38.1760	−1.51976	−0.759881	−	0.650062i	$-0.774743\pi$
$631$	−38.1760	−1.51976	−0.759881	+	0.650062i	$0.774743\pi$
$632$	−17.6022	−0.700180
$633$	−0.489237	−0.0194454
$634$	40.7544	1.61856
$635$	−15.1427	−0.600919
$636$	0.695790	0.0275899
$637$	−31.9554	−1.26612
$638$	22.3390	0.884411
$639$	8.15166	0.322475
$640$	−4.66782	−0.184512
$641$	−48.7915	−1.92715	−0.963574	−	0.267440i	$-0.913822\pi$
$641$	−48.7915	−1.92715	−0.963574	+	0.267440i	$0.913822\pi$
$642$	−5.47603	−0.216122
$643$	40.1343	1.58274	0.791371	−	0.611336i	$-0.209368\pi$
$643$	40.1343	1.58274	0.791371	+	0.611336i	$0.209368\pi$
$644$	6.00630	0.236682
$645$	2.07663	0.0817673
$646$	3.52944	0.138864
$647$	−9.57082	−0.376268	−0.188134	−	0.982143i	$-0.560244\pi$
$647$	−9.57082	−0.376268	−0.188134	+	0.982143i	$0.560244\pi$
$648$	21.2466	0.834643
$649$	−18.2253	−0.715405
$650$	22.9811	0.901393
$651$	−0.163828	−0.00642094
$652$	8.74124	0.342333
$653$	4.90316	0.191875	0.0959377	−	0.995387i	$-0.469415\pi$
$653$	4.90316	0.191875	0.0959377	+	0.995387i	$0.469415\pi$
$654$	1.87538	0.0733330
$655$	−24.3494	−0.951411
$656$	5.61002	0.219034
$657$	35.1437	1.37109
$658$	16.4366	0.640765
$659$	−32.0072	−1.24682	−0.623411	−	0.781894i	$-0.714254\pi$
$659$	−32.0072	−1.24682	−0.623411	+	0.781894i	$0.714254\pi$
$660$	1.03606	0.0403287
$661$	−0.329717	−0.0128245	−0.00641225	−	0.999979i	$-0.502041\pi$
$661$	−0.329717	−0.0128245	−0.00641225	+	0.999979i	$0.502041\pi$
$662$	6.94985	0.270114
$663$	8.95749	0.347880
$664$	18.4225	0.714931
$665$	1.77224	0.0687245
$666$	17.3529	0.672409
$667$	54.4521	2.10839
$668$	−9.15683	−0.354288
$669$	−4.02242	−0.155516
$670$	−7.21747	−0.278835
$671$	25.7926	0.995712
$672$	2.18231	0.0841845
$673$	−21.5702	−0.831471	−0.415735	−	0.909486i	$-0.636476\pi$
$673$	−21.5702	−0.831471	−0.415735	+	0.909486i	$0.636476\pi$
$674$	−20.8661	−0.803732
$675$	−9.04954	−0.348317
$676$	−14.9671	−0.575657
$677$	17.5821	0.675733	0.337867	−	0.941194i	$-0.390295\pi$
$677$	17.5821	0.675733	0.337867	+	0.941194i	$0.390295\pi$
$678$	9.49784	0.364762
$679$	−13.0698	−0.501572
$680$	−12.3700	−0.474370
$681$	2.15112	0.0824311
$682$	−0.757666	−0.0290125
$683$	−2.68622	−0.102785	−0.0513927	−	0.998679i	$-0.516366\pi$
$683$	−2.68622	−0.102785	−0.0513927	+	0.998679i	$0.516366\pi$
$684$	1.71252	0.0654797
$685$	−4.76513	−0.182066
$686$	19.0563	0.727571
$687$	−8.90328	−0.339681
$688$	7.53542	0.287285
$689$	13.9696	0.532198
$690$	−5.61678	−0.213827
$691$	−11.3403	−0.431405	−0.215703	−	0.976459i	$-0.569204\pi$
$691$	−11.3403	−0.431405	−0.215703	+	0.976459i	$0.569204\pi$
$692$	0.261412	0.00993739
$693$	−9.33592	−0.354642
$694$	9.15502	0.347520
$695$	18.9111	0.717338
$696$	11.2204	0.425307
$697$	7.09913	0.268899
$698$	−1.38606	−0.0524633
$699$	−3.64458	−0.137851
$700$	2.63920	0.0997523
$701$	40.8438	1.54265	0.771325	−	0.636441i	$-0.219594\pi$
$701$	40.8438	1.54265	0.771325	+	0.636441i	$0.219594\pi$
$702$	−20.1710	−0.761304
$703$	5.35147	0.201834
$704$	22.2137	0.837211
$705$	6.91100	0.260283
$706$	10.6965	0.402570
$707$	−5.66497	−0.213053
$708$	−2.16713	−0.0814456
$709$	−9.22757	−0.346549	−0.173274	−	0.984874i	$-0.555435\pi$
$709$	−9.22757	−0.346549	−0.173274	+	0.984874i	$0.555435\pi$
$710$	4.63908	0.174102
$711$	15.7883	0.592107
$712$	26.4435	0.991012
$713$	−1.84683	−0.0691645
$714$	−2.28791	−0.0856227
$715$	20.8013	0.777926
$716$	−0.755349	−0.0282287
$717$	−8.81199	−0.329090
$718$	11.2485	0.419790
$719$	−6.36575	−0.237403	−0.118701	−	0.992930i	$-0.537873\pi$
$719$	−6.36575	−0.237403	−0.118701	+	0.992930i	$0.537873\pi$
$720$	8.76793	0.326762
$721$	19.9150	0.741673
$722$	−1.17459	−0.0437138
$723$	−11.0143	−0.409625
$724$	13.1290	0.487935
$725$	23.9265	0.888608
$726$	−2.57773	−0.0956686
$727$	23.9695	0.888981	0.444491	−	0.895784i	$-0.353385\pi$
$727$	23.9695	0.888981	0.444491	+	0.895784i	$0.353385\pi$
$728$	24.8487	0.920956
$729$	−14.9206	−0.552613
$730$	20.0002	0.740240
$731$	9.53562	0.352688
$732$	3.06694	0.113357
$733$	−23.9814	−0.885775	−0.442887	−	0.896577i	$-0.646046\pi$
$733$	−23.9814	−0.885775	−0.442887	+	0.896577i	$0.646046\pi$
$734$	33.5594	1.23870
$735$	3.43182	0.126585
$736$	24.6011	0.906810
$737$	11.7252	0.431905
$738$	−7.66100	−0.282005
$739$	9.40829	0.346090	0.173045	−	0.984914i	$-0.444639\pi$
$739$	9.40829	0.346090	0.173045	+	0.984914i	$0.444639\pi$
$740$	−4.44024	−0.163226
$741$	−2.98104	−0.109511
$742$	−3.56808	−0.130988
$743$	25.8014	0.946563	0.473281	−	0.880911i	$-0.343069\pi$
$743$	25.8014	0.946563	0.473281	+	0.880911i	$0.343069\pi$
$744$	−0.380557	−0.0139519
$745$	−18.7026	−0.685210
$746$	−38.0833	−1.39433
$747$	−16.5240	−0.604582
$748$	4.75747	0.173950
$749$	−12.6262	−0.461350
$750$	−6.31118	−0.230452
$751$	13.5079	0.492909	0.246454	−	0.969154i	$-0.420734\pi$
$751$	13.5079	0.492909	0.246454	+	0.969154i	$0.420734\pi$
$752$	25.0777	0.914491
$753$	−11.7367	−0.427710
$754$	53.3309	1.94220
$755$	2.35202	0.0855988
$756$	−2.31647	−0.0842494
$757$	34.1451	1.24103	0.620513	−	0.784196i	$-0.286924\pi$
$757$	34.1451	1.24103	0.620513	+	0.784196i	$0.286924\pi$
$758$	18.5395	0.673385
$759$	9.12482	0.331210
$760$	4.11674	0.149330
$761$	−35.5302	−1.28797	−0.643984	−	0.765039i	$-0.722720\pi$
$761$	−35.5302	−1.28797	−0.643984	+	0.765039i	$0.722720\pi$
$762$	−6.50579	−0.235680
$763$	4.32408	0.156542
$764$	−4.97043	−0.179824
$765$	11.0953	0.401151
$766$	23.7800	0.859206
$767$	−43.5100	−1.57105
$768$	6.51058	0.234930
$769$	2.42789	0.0875520	0.0437760	−	0.999041i	$-0.486061\pi$
$769$	2.42789	0.0875520	0.0437760	+	0.999041i	$0.486061\pi$
$770$	−5.31304	−0.191469
$771$	−3.52591	−0.126983
$772$	8.39975	0.302314
$773$	12.0145	0.432131	0.216066	−	0.976379i	$-0.430678\pi$
$773$	12.0145	0.432131	0.216066	+	0.976379i	$0.430678\pi$
$774$	−10.2903	−0.369878
$775$	−0.811507	−0.0291502
$776$	−30.3598	−1.08985
$777$	−3.46901	−0.124450
$778$	−32.7716	−1.17492
$779$	−2.36258	−0.0846483
$780$	2.47344	0.0885633
$781$	−7.53649	−0.269677
$782$	−25.7915	−0.922302
$783$	−21.0007	−0.750505
$784$	12.4530	0.444749
$785$	3.30922	0.118111
$786$	−10.4613	−0.373143
$787$	−20.3697	−0.726103	−0.363051	−	0.931769i	$-0.618265\pi$
$787$	−20.3697	−0.726103	−0.363051	+	0.931769i	$0.618265\pi$
$788$	15.7143	0.559800
$789$	−4.14206	−0.147461
$790$	8.98507	0.319674
$791$	21.8993	0.778650
$792$	−21.6864	−0.770594
$793$	61.5757	2.18662
$794$	13.1960	0.468307
$795$	−1.50025	−0.0532084
$796$	7.50329	0.265947
$797$	35.5124	1.25791	0.628956	−	0.777441i	$-0.283483\pi$
$797$	35.5124	1.25791	0.628956	+	0.777441i	$0.283483\pi$
$798$	0.761412	0.0269537
$799$	31.7344	1.12268
$800$	10.8099	0.382186
$801$	−23.7184	−0.838050
$802$	10.6853	0.377310
$803$	−32.4916	−1.14660
$804$	1.39422	0.0491704
$805$	−12.9507	−0.456452
$806$	−1.80881	−0.0637125
$807$	6.80073	0.239397
$808$	−13.1592	−0.462938
$809$	11.6862	0.410865	0.205432	−	0.978671i	$-0.434140\pi$
$809$	11.6862	0.410865	0.205432	+	0.978671i	$0.434140\pi$
$810$	−10.8453	−0.381065
$811$	10.7844	0.378693	0.189346	−	0.981910i	$-0.439363\pi$
$811$	10.7844	0.378693	0.189346	+	0.981910i	$0.439363\pi$
$812$	6.12463	0.214933
$813$	−11.2745	−0.395415
$814$	−16.0433	−0.562317
$815$	−18.8477	−0.660206
$816$	−3.49072	−0.122200
$817$	−3.17344	−0.111025
$818$	1.75203	0.0612581
$819$	−22.2880	−0.778807
$820$	1.96029	0.0684563
$821$	13.8230	0.482425	0.241212	−	0.970472i	$-0.422455\pi$
$821$	13.8230	0.482425	0.241212	+	0.970472i	$0.422455\pi$
$822$	−2.04726	−0.0714064
$823$	−39.6693	−1.38278	−0.691392	−	0.722479i	$-0.743002\pi$
$823$	−39.6693	−1.38278	−0.691392	+	0.722479i	$0.743002\pi$
$824$	46.2606	1.61156
$825$	4.00949	0.139592
$826$	11.1132	0.386679
$827$	−22.5731	−0.784943	−0.392471	−	0.919764i	$-0.628380\pi$
$827$	−22.5731	−0.784943	−0.392471	+	0.919764i	$0.628380\pi$
$828$	−12.5143	−0.434901
$829$	−30.3642	−1.05459	−0.527295	−	0.849682i	$-0.676794\pi$
$829$	−30.3642	−1.05459	−0.527295	+	0.849682i	$0.676794\pi$
$830$	−9.40376	−0.326409
$831$	12.4421	0.431611
$832$	53.0317	1.83854
$833$	15.7585	0.545999
$834$	8.12482	0.281339
$835$	19.7438	0.683262
$836$	−1.58328	−0.0547589
$837$	0.712275	0.0246198
$838$	34.8315	1.20323
$839$	12.0201	0.414978	0.207489	−	0.978237i	$-0.433471\pi$
$839$	12.0201	0.414978	0.207489	+	0.978237i	$0.433471\pi$
$840$	−2.66861	−0.0920759
$841$	26.5248	0.914649
$842$	−25.9098	−0.892911
$843$	1.78649	0.0615300
$844$	−0.620331	−0.0213527
$845$	32.2718	1.11018
$846$	−34.2460	−1.17740
$847$	−5.94352	−0.204222
$848$	−5.44392	−0.186945
$849$	14.2086	0.487637
$850$	−11.3329	−0.388715
$851$	−39.1060	−1.34054
$852$	−0.896146	−0.0307015
$853$	38.1931	1.30771	0.653853	−	0.756621i	$-0.273151\pi$
$853$	38.1931	1.30771	0.653853	+	0.756621i	$0.273151\pi$
$854$	−15.7276	−0.538186
$855$	−3.69250	−0.126281
$856$	−29.3293	−1.00246
$857$	−46.8189	−1.59930	−0.799651	−	0.600465i	$-0.794982\pi$
$857$	−46.8189	−1.59930	−0.799651	+	0.600465i	$0.794982\pi$
$858$	8.93694	0.305102
$859$	12.3220	0.420423	0.210211	−	0.977656i	$-0.432585\pi$
$859$	12.3220	0.420423	0.210211	+	0.977656i	$0.432585\pi$
$860$	2.63308	0.0897872
$861$	1.53151	0.0521937
$862$	−1.29490	−0.0441045
$863$	26.8039	0.912414	0.456207	−	0.889874i	$-0.349208\pi$
$863$	26.8039	0.912414	0.456207	+	0.889874i	$0.349208\pi$
$864$	−9.48801	−0.322789
$865$	−0.563652	−0.0191647
$866$	8.00743	0.272104
$867$	3.89974	0.132442
$868$	−0.207727	−0.00705072
$869$	−14.5968	−0.495163
$870$	−5.72744	−0.194178
$871$	27.9921	0.948478
$872$	10.0444	0.340147
$873$	27.2312	0.921636
$874$	8.58338	0.290337
$875$	−14.5518	−0.491940
$876$	−3.86349	−0.130535
$877$	19.1003	0.644970	0.322485	−	0.946575i	$-0.395482\pi$
$877$	19.1003	0.644970	0.322485	+	0.946575i	$0.395482\pi$
$878$	−25.3491	−0.855492
$879$	0.594555	0.0200538
$880$	−8.10625	−0.273262
$881$	−49.1332	−1.65534	−0.827669	−	0.561216i	$-0.810334\pi$
$881$	−49.1332	−1.65534	−0.827669	+	0.561216i	$0.810334\pi$
$882$	−17.0057	−0.572611
$883$	41.2018	1.38655	0.693276	−	0.720672i	$-0.256167\pi$
$883$	41.2018	1.38655	0.693276	+	0.720672i	$0.256167\pi$
$884$	11.3577	0.382001
$885$	4.67272	0.157072
$886$	30.7404	1.03274
$887$	−37.9454	−1.27408	−0.637042	−	0.770829i	$-0.719842\pi$
$887$	−37.9454	−1.27408	−0.637042	+	0.770829i	$0.719842\pi$
$888$	−8.05816	−0.270414
$889$	−15.0005	−0.503101
$890$	−13.4981	−0.452457
$891$	17.6189	0.590255
$892$	−5.10025	−0.170769
$893$	−10.5612	−0.353416
$894$	−8.03525	−0.268739
$895$	1.62867	0.0544405
$896$	−4.62399	−0.154477
$897$	21.7841	0.727348
$898$	22.9188	0.764810
$899$	−1.88322	−0.0628088
$900$	−5.49883	−0.183294
$901$	−6.88895	−0.229504
$902$	7.08285	0.235833
$903$	2.05714	0.0684572
$904$	50.8699	1.69191
$905$	−28.3085	−0.941006
$906$	1.01051	0.0335718
$907$	−45.1706	−1.49987	−0.749933	−	0.661514i	$-0.769914\pi$
$907$	−45.1706	−1.49987	−0.749933	+	0.661514i	$0.769914\pi$
$908$	2.72753	0.0905161
$909$	11.8031	0.391484
$910$	−12.6840	−0.420472
$911$	20.2574	0.671157	0.335579	−	0.942012i	$-0.391068\pi$
$911$	20.2574	0.671157	0.335579	+	0.942012i	$0.391068\pi$
$912$	1.16171	0.0384680
$913$	15.2770	0.505595
$914$	−18.7329	−0.619629
$915$	−6.61288	−0.218615
$916$	−11.2890	−0.372998
$917$	−24.1208	−0.796539
$918$	9.94710	0.328303
$919$	48.8903	1.61274	0.806372	−	0.591409i	$-0.201428\pi$
$919$	48.8903	1.61274	0.806372	+	0.591409i	$0.201428\pi$
$920$	−30.0832	−0.991813
$921$	9.59053	0.316019
$922$	−0.694160	−0.0228609
$923$	−17.9922	−0.592219
$924$	1.02634	0.0337640
$925$	−17.1834	−0.564986
$926$	7.05565	0.231863
$927$	−41.4933	−1.36282
$928$	25.0858	0.823482
$929$	5.14538	0.168814	0.0844072	−	0.996431i	$-0.473100\pi$
$929$	5.14538	0.168814	0.0844072	+	0.996431i	$0.473100\pi$
$930$	0.194256	0.00636989
$931$	−5.24440	−0.171878
$932$	−4.62116	−0.151371
$933$	−2.28071	−0.0746672
$934$	3.41388	0.111706
$935$	−10.2580	−0.335472
$936$	−51.7729	−1.69225
$937$	−1.25214	−0.0409057	−0.0204529	−	0.999791i	$-0.506511\pi$
$937$	−1.25214	−0.0409057	−0.0204529	+	0.999791i	$0.506511\pi$
$938$	−7.14970	−0.233446
$939$	4.61896	0.150734
$940$	8.76284	0.285812
$941$	24.4965	0.798563	0.399282	−	0.916828i	$-0.369260\pi$
$941$	24.4965	0.798563	0.399282	+	0.916828i	$0.369260\pi$
$942$	1.42175	0.0463231
$943$	17.2647	0.562215
$944$	16.9558	0.551864
$945$	4.99474	0.162479
$946$	9.51375	0.309319
$947$	55.2160	1.79428	0.897139	−	0.441748i	$-0.145642\pi$
$947$	55.2160	1.79428	0.897139	+	0.441748i	$0.145642\pi$
$948$	−1.73567	−0.0563720
$949$	−77.5684	−2.51798
$950$	3.77158	0.122366
$951$	16.9749	0.550448
$952$	−12.2539	−0.397151
$953$	24.3405	0.788467	0.394234	−	0.919010i	$-0.371010\pi$
$953$	24.3405	0.788467	0.394234	+	0.919010i	$0.371010\pi$
$954$	7.43418	0.240690
$955$	10.7172	0.346799
$956$	−11.1732	−0.361368
$957$	9.30458	0.300775
$958$	42.9230	1.38678
$959$	−4.72040	−0.152430
$960$	−5.69530	−0.183815
$961$	−30.9361	−0.997940
$962$	−38.3008	−1.23487
$963$	26.3069	0.847728
$964$	−13.9656	−0.449802
$965$	−18.1114	−0.583027
$966$	−5.56405	−0.179020
$967$	−26.1066	−0.839533	−0.419766	−	0.907632i	$-0.637888\pi$
$967$	−26.1066	−0.839533	−0.419766	+	0.907632i	$0.637888\pi$
$968$	−13.8062	−0.443748
$969$	1.47007	0.0472255
$970$	15.4972	0.497584
$971$	−37.3721	−1.19933	−0.599663	−	0.800252i	$-0.704699\pi$
$971$	−37.3721	−1.19933	−0.599663	+	0.800252i	$0.704699\pi$
$972$	7.33991	0.235428
$973$	18.7335	0.600569
$974$	37.8420	1.21254
$975$	9.57201	0.306550
$976$	−23.9960	−0.768092
$977$	52.2766	1.67248	0.836239	−	0.548365i	$-0.184750\pi$
$977$	52.2766	1.67248	0.836239	+	0.548365i	$0.184750\pi$
$978$	−8.09760	−0.258933
$979$	21.9285	0.700838
$980$	4.35140	0.139000
$981$	−9.00932	−0.287646
$982$	−1.13562	−0.0362391
$983$	51.1772	1.63230	0.816149	−	0.577841i	$-0.196105\pi$
$983$	51.1772	1.63230	0.816149	+	0.577841i	$0.196105\pi$
$984$	3.55755	0.113410
$985$	−33.8830	−1.07960
$986$	−26.2996	−0.837550
$987$	6.84611	0.217914
$988$	−3.77983	−0.120252
$989$	23.1900	0.737400
$990$	11.0698	0.351823
$991$	−13.2670	−0.421441	−0.210721	−	0.977546i	$-0.567581\pi$
$991$	−13.2670	−0.421441	−0.210721	+	0.977546i	$0.567581\pi$
$992$	−0.850827	−0.0270138
$993$	2.89473	0.0918615
$994$	4.59553	0.145761
$995$	−16.1785	−0.512892
$996$	1.81655	0.0575597
$997$	3.22931	0.102273	0.0511367	−	0.998692i	$-0.483716\pi$
$997$	3.22931	0.102273	0.0511367	+	0.998692i	$0.483716\pi$
$998$	29.7210	0.940802
$999$	15.0822	0.477179

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4009.2.a.c.1.26	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4009.2.a.c.1.26	✓	71	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:	\( N \)	\(=\)	\( 4009 = 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4009.a (trivial)

\(f(q)\)	\(=\)	\(q-1.17459 q^{2} -0.489237 q^{3} -0.620331 q^{4} +1.33755 q^{5} +0.574655 q^{6} +1.32499 q^{7} +3.07782 q^{8} -2.76065 q^{9} +O(q^{10})\)	\(q-1.17459 q^{2} -0.489237 q^{3} -0.620331 q^{4} +1.33755 q^{5} +0.574655 q^{6} +1.32499 q^{7} +3.07782 q^{8} -2.76065 q^{9} -1.57107 q^{10} +2.55231 q^{11} +0.303489 q^{12} +6.09324 q^{13} -1.55632 q^{14} -0.654379 q^{15} -2.37453 q^{16} -3.00482 q^{17} +3.24264 q^{18} +1.00000 q^{19} -0.829723 q^{20} -0.648235 q^{21} -2.99793 q^{22} -7.30753 q^{23} -1.50579 q^{24} -3.21096 q^{25} -7.15707 q^{26} +2.81832 q^{27} -0.821933 q^{28} -7.45150 q^{29} +0.768629 q^{30} +0.252730 q^{31} -3.36654 q^{32} -1.24869 q^{33} +3.52944 q^{34} +1.77224 q^{35} +1.71252 q^{36} +5.35147 q^{37} -1.17459 q^{38} -2.98104 q^{39} +4.11674 q^{40} -2.36258 q^{41} +0.761412 q^{42} -3.17344 q^{43} -1.58328 q^{44} -3.69250 q^{45} +8.58338 q^{46} -10.5612 q^{47} +1.16171 q^{48} -5.24440 q^{49} +3.77158 q^{50} +1.47007 q^{51} -3.77983 q^{52} +2.29263 q^{53} -3.31038 q^{54} +3.41384 q^{55} +4.07809 q^{56} -0.489237 q^{57} +8.75248 q^{58} -7.14070 q^{59} +0.405932 q^{60} +10.1056 q^{61} -0.296855 q^{62} -3.65783 q^{63} +8.70337 q^{64} +8.15000 q^{65} +1.46670 q^{66} +4.59397 q^{67} +1.86398 q^{68} +3.57512 q^{69} -2.08166 q^{70} -2.95281 q^{71} -8.49678 q^{72} -12.7302 q^{73} -6.28579 q^{74} +1.57092 q^{75} -0.620331 q^{76} +3.38179 q^{77} +3.50151 q^{78} -5.71906 q^{79} -3.17604 q^{80} +6.90311 q^{81} +2.77507 q^{82} +5.98556 q^{83} +0.402121 q^{84} -4.01909 q^{85} +3.72750 q^{86} +3.64555 q^{87} +7.85556 q^{88} +8.59163 q^{89} +4.33718 q^{90} +8.07348 q^{91} +4.53309 q^{92} -0.123645 q^{93} +12.4051 q^{94} +1.33755 q^{95} +1.64704 q^{96} -9.86406 q^{97} +6.16004 q^{98} -7.04603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * q^99

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