LMFDB - Embedded newform 8015.2.a.l.1.44

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.44
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.36004 q^{2} +3.37769 q^{3} -0.150287 q^{4} -1.00000 q^{5} +4.59380 q^{6} -1.00000 q^{7} -2.92448 q^{8} +8.40880 q^{9} +O(q^{10})$	\(q+1.36004 q^{2} +3.37769 q^{3} -0.150287 q^{4} -1.00000 q^{5} +4.59380 q^{6} -1.00000 q^{7} -2.92448 q^{8} +8.40880 q^{9} -1.36004 q^{10} +6.45750 q^{11} -0.507624 q^{12} +3.96000 q^{13} -1.36004 q^{14} -3.37769 q^{15} -3.67684 q^{16} -4.58527 q^{17} +11.4363 q^{18} +6.23815 q^{19} +0.150287 q^{20} -3.37769 q^{21} +8.78247 q^{22} +1.03015 q^{23} -9.87799 q^{24} +1.00000 q^{25} +5.38576 q^{26} +18.2692 q^{27} +0.150287 q^{28} -10.2138 q^{29} -4.59380 q^{30} -2.95134 q^{31} +0.848305 q^{32} +21.8114 q^{33} -6.23615 q^{34} +1.00000 q^{35} -1.26373 q^{36} -0.589617 q^{37} +8.48415 q^{38} +13.3757 q^{39} +2.92448 q^{40} +3.44305 q^{41} -4.59380 q^{42} +3.73038 q^{43} -0.970479 q^{44} -8.40880 q^{45} +1.40105 q^{46} -6.19041 q^{47} -12.4192 q^{48} +1.00000 q^{49} +1.36004 q^{50} -15.4876 q^{51} -0.595137 q^{52} +5.95352 q^{53} +24.8469 q^{54} -6.45750 q^{55} +2.92448 q^{56} +21.0706 q^{57} -13.8911 q^{58} +10.5027 q^{59} +0.507624 q^{60} -6.64857 q^{61} -4.01394 q^{62} -8.40880 q^{63} +8.50741 q^{64} -3.96000 q^{65} +29.6645 q^{66} +7.71541 q^{67} +0.689107 q^{68} +3.47953 q^{69} +1.36004 q^{70} -3.30265 q^{71} -24.5914 q^{72} -13.3597 q^{73} -0.801903 q^{74} +3.37769 q^{75} -0.937514 q^{76} -6.45750 q^{77} +18.1914 q^{78} -3.62340 q^{79} +3.67684 q^{80} +36.4815 q^{81} +4.68269 q^{82} -5.79752 q^{83} +0.507624 q^{84} +4.58527 q^{85} +5.07347 q^{86} -34.4989 q^{87} -18.8848 q^{88} +12.8246 q^{89} -11.4363 q^{90} -3.96000 q^{91} -0.154819 q^{92} -9.96870 q^{93} -8.41921 q^{94} -6.23815 q^{95} +2.86531 q^{96} +13.1504 q^{97} +1.36004 q^{98} +54.2998 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * 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 $

$2$	1.36004	0.961695	0.480847	−	0.876804i	$-0.340329\pi$
$2$	1.36004	0.961695	0.480847	+	0.876804i	$0.340329\pi$
$3$	3.37769	1.95011	0.975055	−	0.221961i	$-0.0712459\pi$
$3$	3.37769	1.95011	0.975055	+	0.221961i	$0.0712459\pi$
$4$	−0.150287	−0.0751436
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	4.59380	1.87541
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.92448	−1.03396
$9$	8.40880	2.80293
$10$	−1.36004	−0.430083
$11$	6.45750	1.94701	0.973505	−	0.228666i	$-0.0734363\pi$
$11$	6.45750	1.94701	0.973505	+	0.228666i	$0.0734363\pi$
$12$	−0.507624	−0.146538
$13$	3.96000	1.09831	0.549153	−	0.835722i	$-0.314950\pi$
$13$	3.96000	1.09831	0.549153	+	0.835722i	$0.314950\pi$
$14$	−1.36004	−0.363486
$15$	−3.37769	−0.872116
$16$	−3.67684	−0.919210
$17$	−4.58527	−1.11209	−0.556045	−	0.831152i	$-0.687682\pi$
$17$	−4.58527	−1.11209	−0.556045	+	0.831152i	$0.687682\pi$
$18$	11.4363	2.69557
$19$	6.23815	1.43113	0.715565	−	0.698546i	$-0.246169\pi$
$19$	6.23815	1.43113	0.715565	+	0.698546i	$0.246169\pi$
$20$	0.150287	0.0336052
$21$	−3.37769	−0.737073
$22$	8.78247	1.87243
$23$	1.03015	0.214801	0.107401	−	0.994216i	$-0.465747\pi$
$23$	1.03015	0.214801	0.107401	+	0.994216i	$0.465747\pi$
$24$	−9.87799	−2.01634
$25$	1.00000	0.200000
$26$	5.38576	1.05623
$27$	18.2692	3.51592
$28$	0.150287	0.0284016
$29$	−10.2138	−1.89665	−0.948323	−	0.317307i	$-0.897221\pi$
$29$	−10.2138	−1.89665	−0.948323	+	0.317307i	$0.897221\pi$
$30$	−4.59380	−0.838709
$31$	−2.95134	−0.530076	−0.265038	−	0.964238i	$-0.585384\pi$
$31$	−2.95134	−0.530076	−0.265038	+	0.964238i	$0.585384\pi$
$32$	0.848305	0.149961
$33$	21.8114	3.79689
$34$	−6.23615	−1.06949
$35$	1.00000	0.169031
$36$	−1.26373	−0.210622
$37$	−0.589617	−0.0969324	−0.0484662	−	0.998825i	$-0.515433\pi$
$37$	−0.589617	−0.0969324	−0.0484662	+	0.998825i	$0.515433\pi$
$38$	8.48415	1.37631
$39$	13.3757	2.14182
$40$	2.92448	0.462401
$41$	3.44305	0.537714	0.268857	−	0.963180i	$-0.413354\pi$
$41$	3.44305	0.537714	0.268857	+	0.963180i	$0.413354\pi$
$42$	−4.59380	−0.708839
$43$	3.73038	0.568877	0.284439	−	0.958694i	$-0.408193\pi$
$43$	3.73038	0.568877	0.284439	+	0.958694i	$0.408193\pi$
$44$	−0.970479	−0.146305
$45$	−8.40880	−1.25351
$46$	1.40105	0.206573
$47$	−6.19041	−0.902964	−0.451482	−	0.892280i	$-0.649104\pi$
$47$	−6.19041	−0.902964	−0.451482	+	0.892280i	$0.649104\pi$
$48$	−12.4192	−1.79256
$49$	1.00000	0.142857
$50$	1.36004	0.192339
$51$	−15.4876	−2.16870
$52$	−0.595137	−0.0825306
$53$	5.95352	0.817778	0.408889	−	0.912584i	$-0.365916\pi$
$53$	5.95352	0.817778	0.408889	+	0.912584i	$0.365916\pi$
$54$	24.8469	3.38124
$55$	−6.45750	−0.870729
$56$	2.92448	0.390800
$57$	21.0706	2.79086
$58$	−13.8911	−1.82399
$59$	10.5027	1.36733	0.683666	−	0.729795i	$-0.260385\pi$
$59$	10.5027	1.36733	0.683666	+	0.729795i	$0.260385\pi$
$60$	0.507624	0.0655339
$61$	−6.64857	−0.851262	−0.425631	−	0.904897i	$-0.639948\pi$
$61$	−6.64857	−0.851262	−0.425631	+	0.904897i	$0.639948\pi$
$62$	−4.01394	−0.509771
$63$	−8.40880	−1.05941
$64$	8.50741	1.06343
$65$	−3.96000	−0.491177
$66$	29.6645	3.65144
$67$	7.71541	0.942588	0.471294	−	0.881976i	$-0.343787\pi$
$67$	7.71541	0.942588	0.471294	+	0.881976i	$0.343787\pi$
$68$	0.689107	0.0835665
$69$	3.47953	0.418887
$70$	1.36004	0.162556
$71$	−3.30265	−0.391952	−0.195976	−	0.980609i	$-0.562788\pi$
$71$	−3.30265	−0.391952	−0.195976	+	0.980609i	$0.562788\pi$
$72$	−24.5914	−2.89812
$73$	−13.3597	−1.56363	−0.781815	−	0.623510i	$-0.785706\pi$
$73$	−13.3597	−1.56363	−0.781815	+	0.623510i	$0.785706\pi$
$74$	−0.801903	−0.0932193
$75$	3.37769	0.390022
$76$	−0.937514	−0.107540
$77$	−6.45750	−0.735901
$78$	18.1914	2.05978
$79$	−3.62340	−0.407665	−0.203832	−	0.979006i	$-0.565340\pi$
$79$	−3.62340	−0.407665	−0.203832	+	0.979006i	$0.565340\pi$
$80$	3.67684	0.411083
$81$	36.4815	4.05350
$82$	4.68269	0.517116
$83$	−5.79752	−0.636361	−0.318180	−	0.948030i	$-0.603072\pi$
$83$	−5.79752	−0.636361	−0.318180	+	0.948030i	$0.603072\pi$
$84$	0.507624	0.0553863
$85$	4.58527	0.497342
$86$	5.07347	0.547086
$87$	−34.4989	−3.69867
$88$	−18.8848	−2.01313
$89$	12.8246	1.35940	0.679702	−	0.733489i	$-0.262109\pi$
$89$	12.8246	1.35940	0.679702	+	0.733489i	$0.262109\pi$
$90$	−11.4363	−1.20549
$91$	−3.96000	−0.415121
$92$	−0.154819	−0.0161409
$93$	−9.96870	−1.03371
$94$	−8.41921	−0.868376
$95$	−6.23815	−0.640021
$96$	2.86531	0.292440
$97$	13.1504	1.33522	0.667609	−	0.744512i	$-0.267318\pi$
$97$	13.1504	1.33522	0.667609	+	0.744512i	$0.267318\pi$
$98$	1.36004	0.137385
$99$	54.2998	5.45734
$100$	−0.150287	−0.0150287
$101$	−3.40236	−0.338548	−0.169274	−	0.985569i	$-0.554142\pi$
$101$	−3.40236	−0.338548	−0.169274	+	0.985569i	$0.554142\pi$
$102$	−21.0638	−2.08563
$103$	12.5015	1.23181	0.615906	−	0.787820i	$-0.288790\pi$
$103$	12.5015	1.23181	0.615906	+	0.787820i	$0.288790\pi$
$104$	−11.5809	−1.13560
$105$	3.37769	0.329629
$106$	8.09703	0.786453
$107$	3.51408	0.339719	0.169860	−	0.985468i	$-0.445669\pi$
$107$	3.51408	0.339719	0.169860	+	0.985468i	$0.445669\pi$
$108$	−2.74563	−0.264199
$109$	4.62692	0.443179	0.221589	−	0.975140i	$-0.428876\pi$
$109$	4.62692	0.443179	0.221589	+	0.975140i	$0.428876\pi$
$110$	−8.78247	−0.837376
$111$	−1.99154	−0.189029
$112$	3.67684	0.347429
$113$	−0.924504	−0.0869700	−0.0434850	−	0.999054i	$-0.513846\pi$
$113$	−0.924504	−0.0869700	−0.0434850	+	0.999054i	$0.513846\pi$
$114$	28.6568	2.68396
$115$	−1.03015	−0.0960621
$116$	1.53500	0.142521
$117$	33.2988	3.07848
$118$	14.2841	1.31496
$119$	4.58527	0.420331
$120$	9.87799	0.901733
$121$	30.6993	2.79085
$122$	−9.04233	−0.818654
$123$	11.6296	1.04860
$124$	0.443548	0.0398318
$125$	−1.00000	−0.0894427
$126$	−11.4363	−1.01883
$127$	−16.0087	−1.42054	−0.710272	−	0.703927i	$-0.751428\pi$
$127$	−16.0087	−1.42054	−0.710272	+	0.703927i	$0.751428\pi$
$128$	9.87382	0.872731
$129$	12.6001	1.10937
$130$	−5.38576	−0.472363
$131$	−22.2455	−1.94360	−0.971800	−	0.235805i	$-0.924227\pi$
$131$	−22.2455	−1.94360	−0.971800	+	0.235805i	$0.924227\pi$
$132$	−3.27798	−0.285312
$133$	−6.23815	−0.540916
$134$	10.4933	0.906482
$135$	−18.2692	−1.57237
$136$	13.4095	1.14986
$137$	−2.69337	−0.230110	−0.115055	−	0.993359i	$-0.536704\pi$
$137$	−2.69337	−0.230110	−0.115055	+	0.993359i	$0.536704\pi$
$138$	4.73231	0.402841
$139$	−0.256702	−0.0217732	−0.0108866	−	0.999941i	$-0.503465\pi$
$139$	−0.256702	−0.0217732	−0.0108866	+	0.999941i	$0.503465\pi$
$140$	−0.150287	−0.0127016
$141$	−20.9093	−1.76088
$142$	−4.49174	−0.376938
$143$	25.5717	2.13841
$144$	−30.9178	−2.57648
$145$	10.2138	0.848206
$146$	−18.1697	−1.50374
$147$	3.37769	0.278587
$148$	0.0886118	0.00728384
$149$	2.32524	0.190491	0.0952457	−	0.995454i	$-0.469636\pi$
$149$	2.32524	0.190491	0.0952457	+	0.995454i	$0.469636\pi$
$150$	4.59380	0.375082
$151$	−10.5195	−0.856065	−0.428032	−	0.903763i	$-0.640793\pi$
$151$	−10.5195	−0.856065	−0.428032	+	0.903763i	$0.640793\pi$
$152$	−18.2433	−1.47973
$153$	−38.5566	−3.11712
$154$	−8.78247	−0.707712
$155$	2.95134	0.237057
$156$	−2.01019	−0.160944
$157$	7.41148	0.591501	0.295750	−	0.955265i	$-0.404430\pi$
$157$	7.41148	0.591501	0.295750	+	0.955265i	$0.404430\pi$
$158$	−4.92798	−0.392049
$159$	20.1091	1.59476
$160$	−0.848305	−0.0670644
$161$	−1.03015	−0.0811873
$162$	49.6163	3.89823
$163$	9.24420	0.724061	0.362031	−	0.932166i	$-0.382084\pi$
$163$	9.24420	0.724061	0.362031	+	0.932166i	$0.382084\pi$
$164$	−0.517446	−0.0404057
$165$	−21.8114	−1.69802
$166$	−7.88487	−0.611985
$167$	17.7621	1.37447	0.687236	−	0.726434i	$-0.258824\pi$
$167$	17.7621	1.37447	0.687236	+	0.726434i	$0.258824\pi$
$168$	9.87799	0.762103
$169$	2.68159	0.206276
$170$	6.23615	0.478291
$171$	52.4554	4.01136
$172$	−0.560628	−0.0427475
$173$	13.4338	1.02135	0.510675	−	0.859774i	$-0.329395\pi$
$173$	13.4338	1.02135	0.510675	+	0.859774i	$0.329395\pi$
$174$	−46.9199	−3.55699
$175$	−1.00000	−0.0755929
$176$	−23.7432	−1.78971
$177$	35.4748	2.66645
$178$	17.4420	1.30733
$179$	14.0462	1.04986	0.524931	−	0.851145i	$-0.324091\pi$
$179$	14.0462	1.04986	0.524931	+	0.851145i	$0.324091\pi$
$180$	1.26373	0.0941932
$181$	0.354696	0.0263643	0.0131822	−	0.999913i	$-0.495804\pi$
$181$	0.354696	0.0263643	0.0131822	+	0.999913i	$0.495804\pi$
$182$	−5.38576	−0.399219
$183$	−22.4568	−1.66006
$184$	−3.01266	−0.222096
$185$	0.589617	0.0433495
$186$	−13.5579	−0.994110
$187$	−29.6094	−2.16525
$188$	0.930339	0.0678519
$189$	−18.2692	−1.32889
$190$	−8.48415	−0.615505
$191$	19.2297	1.39141	0.695706	−	0.718326i	$-0.255092\pi$
$191$	19.2297	1.39141	0.695706	+	0.718326i	$0.255092\pi$
$192$	28.7354	2.07380
$193$	−19.2757	−1.38749	−0.693746	−	0.720220i	$-0.744041\pi$
$193$	−19.2757	−1.38749	−0.693746	+	0.720220i	$0.744041\pi$
$194$	17.8851	1.28407
$195$	−13.3757	−0.957850
$196$	−0.150287	−0.0107348
$197$	−24.4848	−1.74447	−0.872235	−	0.489087i	$-0.837330\pi$
$197$	−24.4848	−1.74447	−0.872235	+	0.489087i	$0.837330\pi$
$198$	73.8500	5.24829
$199$	17.9754	1.27424	0.637121	−	0.770764i	$-0.280125\pi$
$199$	17.9754	1.27424	0.637121	+	0.770764i	$0.280125\pi$
$200$	−2.92448	−0.206792
$201$	26.0603	1.83815
$202$	−4.62735	−0.325580
$203$	10.2138	0.716865
$204$	2.32759	0.162964
$205$	−3.44305	−0.240473
$206$	17.0026	1.18463
$207$	8.66234	0.602074
$208$	−14.5603	−1.00957
$209$	40.2829	2.78642
$210$	4.59380	0.317002
$211$	1.58864	0.109366	0.0546831	−	0.998504i	$-0.482585\pi$
$211$	1.58864	0.109366	0.0546831	+	0.998504i	$0.482585\pi$
$212$	−0.894737	−0.0614508
$213$	−11.1553	−0.764351
$214$	4.77930	0.326706
$215$	−3.73038	−0.254410
$216$	−53.4280	−3.63532
$217$	2.95134	0.200350
$218$	6.29281	0.426203
$219$	−45.1248	−3.04925
$220$	0.970479	0.0654297
$221$	−18.1577	−1.22142
$222$	−2.70858	−0.181788
$223$	14.2542	0.954532	0.477266	−	0.878759i	$-0.341628\pi$
$223$	14.2542	0.954532	0.477266	+	0.878759i	$0.341628\pi$
$224$	−0.848305	−0.0566798
$225$	8.40880	0.560587
$226$	−1.25736	−0.0836386
$227$	−12.9564	−0.859945	−0.429972	−	0.902842i	$-0.641477\pi$
$227$	−12.9564	−0.859945	−0.429972	+	0.902842i	$0.641477\pi$
$228$	−3.16663	−0.209715
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−1.40105	−0.0923824
$231$	−21.8114	−1.43509
$232$	29.8699	1.96106
$233$	0.404052	0.0264703	0.0132351	−	0.999912i	$-0.495787\pi$
$233$	0.404052	0.0264703	0.0132351	+	0.999912i	$0.495787\pi$
$234$	45.2878	2.96056
$235$	6.19041	0.403818
$236$	−1.57842	−0.102746
$237$	−12.2387	−0.794992
$238$	6.23615	0.404230
$239$	−25.4023	−1.64314	−0.821568	−	0.570111i	$-0.806900\pi$
$239$	−25.4023	−1.64314	−0.821568	+	0.570111i	$0.806900\pi$
$240$	12.4192	0.801658
$241$	−20.2053	−1.30154	−0.650768	−	0.759276i	$-0.725553\pi$
$241$	−20.2053	−1.30154	−0.650768	+	0.759276i	$0.725553\pi$
$242$	41.7524	2.68394
$243$	68.4155	4.38885
$244$	0.999195	0.0639669
$245$	−1.00000	−0.0638877
$246$	15.8167	1.00843
$247$	24.7031	1.57182
$248$	8.63112	0.548077
$249$	−19.5822	−1.24097
$250$	−1.36004	−0.0860166
$251$	−30.4644	−1.92290	−0.961448	−	0.274986i	$-0.911327\pi$
$251$	−30.4644	−1.92290	−0.961448	+	0.274986i	$0.911327\pi$
$252$	1.26373	0.0796078
$253$	6.65221	0.418221
$254$	−21.7725	−1.36613
$255$	15.4876	0.969872
$256$	−3.58601	−0.224126
$257$	−25.5667	−1.59481	−0.797404	−	0.603446i	$-0.793794\pi$
$257$	−25.5667	−1.59481	−0.797404	+	0.603446i	$0.793794\pi$
$258$	17.1366	1.06688
$259$	0.589617	0.0366370
$260$	0.595137	0.0369088
$261$	−85.8854	−5.31617
$262$	−30.2548	−1.86915
$263$	−4.76256	−0.293672	−0.146836	−	0.989161i	$-0.546909\pi$
$263$	−4.76256	−0.293672	−0.146836	+	0.989161i	$0.546909\pi$
$264$	−63.7871	−3.92583
$265$	−5.95352	−0.365722
$266$	−8.48415	−0.520196
$267$	43.3175	2.65099
$268$	−1.15953	−0.0708294
$269$	−19.8697	−1.21148	−0.605738	−	0.795664i	$-0.707122\pi$
$269$	−19.8697	−1.21148	−0.605738	+	0.795664i	$0.707122\pi$
$270$	−24.8469	−1.51214
$271$	−8.44148	−0.512784	−0.256392	−	0.966573i	$-0.582534\pi$
$271$	−8.44148	−0.512784	−0.256392	+	0.966573i	$0.582534\pi$
$272$	16.8593	1.02224
$273$	−13.3757	−0.809531
$274$	−3.66310	−0.221296
$275$	6.45750	0.389402
$276$	−0.522929	−0.0314766
$277$	−6.48803	−0.389828	−0.194914	−	0.980820i	$-0.562443\pi$
$277$	−6.48803	−0.389828	−0.194914	+	0.980820i	$0.562443\pi$
$278$	−0.349125	−0.0209391
$279$	−24.8172	−1.48577
$280$	−2.92448	−0.174771
$281$	−24.3084	−1.45012	−0.725059	−	0.688686i	$-0.758188\pi$
$281$	−24.3084	−1.45012	−0.725059	+	0.688686i	$0.758188\pi$
$282$	−28.4375	−1.69343
$283$	27.2146	1.61774	0.808869	−	0.587989i	$-0.200080\pi$
$283$	27.2146	1.61774	0.808869	+	0.587989i	$0.200080\pi$
$284$	0.496346	0.0294527
$285$	−21.0706	−1.24811
$286$	34.7786	2.05650
$287$	−3.44305	−0.203237
$288$	7.13323	0.420329
$289$	4.02468	0.236746
$290$	13.8911	0.815715
$291$	44.4179	2.60382
$292$	2.00779	0.117497
$293$	−20.1971	−1.17992	−0.589962	−	0.807431i	$-0.700857\pi$
$293$	−20.1971	−1.17992	−0.589962	+	0.807431i	$0.700857\pi$
$294$	4.59380	0.267916
$295$	−10.5027	−0.611489
$296$	1.72432	0.100224
$297$	117.974	6.84553
$298$	3.16243	0.183195
$299$	4.07940	0.235918
$300$	−0.507624	−0.0293077
$301$	−3.73038	−0.215015
$302$	−14.3070	−0.823273
$303$	−11.4921	−0.660206
$304$	−22.9367	−1.31551
$305$	6.64857	0.380696
$306$	−52.4386	−2.99771
$307$	28.6017	1.63238	0.816192	−	0.577781i	$-0.196081\pi$
$307$	28.6017	1.63238	0.816192	+	0.577781i	$0.196081\pi$
$308$	0.970479	0.0552982
$309$	42.2263	2.40217
$310$	4.01394	0.227976
$311$	6.15790	0.349183	0.174591	−	0.984641i	$-0.444140\pi$
$311$	6.15790	0.349183	0.174591	+	0.984641i	$0.444140\pi$
$312$	−39.1168	−2.21455
$313$	17.1771	0.970906	0.485453	−	0.874263i	$-0.338655\pi$
$313$	17.1771	0.970906	0.485453	+	0.874263i	$0.338655\pi$
$314$	10.0799	0.568843
$315$	8.40880	0.473782
$316$	0.544551	0.0306334
$317$	−6.33591	−0.355860	−0.177930	−	0.984043i	$-0.556940\pi$
$317$	−6.33591	−0.355860	−0.177930	+	0.984043i	$0.556940\pi$
$318$	27.3493	1.53367
$319$	−65.9553	−3.69279
$320$	−8.50741	−0.475579
$321$	11.8695	0.662490
$322$	−1.40105	−0.0780774
$323$	−28.6036	−1.59155
$324$	−5.48270	−0.304594
$325$	3.96000	0.219661
$326$	12.5725	0.696326
$327$	15.6283	0.864248
$328$	−10.0691	−0.555974
$329$	6.19041	0.341288
$330$	−29.6645	−1.63298
$331$	−3.24627	−0.178431	−0.0892157	−	0.996012i	$-0.528436\pi$
$331$	−3.24627	−0.178431	−0.0892157	+	0.996012i	$0.528436\pi$
$332$	0.871293	0.0478184
$333$	−4.95797	−0.271695
$334$	24.1572	1.32182
$335$	−7.71541	−0.421538
$336$	12.4192	0.677524
$337$	21.4690	1.16949	0.584745	−	0.811217i	$-0.301194\pi$
$337$	21.4690	1.16949	0.584745	+	0.811217i	$0.301194\pi$
$338$	3.64707	0.198375
$339$	−3.12269	−0.169601
$340$	−0.689107	−0.0373721
$341$	−19.0583	−1.03206
$342$	71.3415	3.85770
$343$	−1.00000	−0.0539949
$344$	−10.9094	−0.588196
$345$	−3.47953	−0.187332
$346$	18.2705	0.982227
$347$	−13.5146	−0.725500	−0.362750	−	0.931887i	$-0.618162\pi$
$347$	−13.5146	−0.725500	−0.362750	+	0.931887i	$0.618162\pi$
$348$	5.18474	0.277931
$349$	−7.79214	−0.417104	−0.208552	−	0.978011i	$-0.566875\pi$
$349$	−7.79214	−0.417104	−0.208552	+	0.978011i	$0.566875\pi$
$350$	−1.36004	−0.0726973
$351$	72.3462	3.86155
$352$	5.47793	0.291975
$353$	−26.8091	−1.42691	−0.713453	−	0.700704i	$-0.752870\pi$
$353$	−26.8091	−1.42691	−0.713453	+	0.700704i	$0.752870\pi$
$354$	48.2472	2.56431
$355$	3.30265	0.175286
$356$	−1.92737	−0.102150
$357$	15.4876	0.819692
$358$	19.1034	1.00965
$359$	19.0469	1.00526	0.502630	−	0.864502i	$-0.332366\pi$
$359$	19.0469	1.00526	0.502630	+	0.864502i	$0.332366\pi$
$360$	24.5914	1.29608
$361$	19.9145	1.04813
$362$	0.482401	0.0253544
$363$	103.693	5.44246
$364$	0.595137	0.0311936
$365$	13.3597	0.699277
$366$	−30.5422	−1.59647
$367$	0.744542	0.0388648	0.0194324	−	0.999811i	$-0.493814\pi$
$367$	0.744542	0.0388648	0.0194324	+	0.999811i	$0.493814\pi$
$368$	−3.78770	−0.197448
$369$	28.9519	1.50718
$370$	0.801903	0.0416890
$371$	−5.95352	−0.309091
$372$	1.49817	0.0776764
$373$	25.6146	1.32627	0.663137	−	0.748498i	$-0.269224\pi$
$373$	25.6146	1.32627	0.663137	+	0.748498i	$0.269224\pi$
$374$	−40.2700	−2.08231
$375$	−3.37769	−0.174423
$376$	18.1037	0.933628
$377$	−40.4464	−2.08310
$378$	−24.8469	−1.27799
$379$	−3.83861	−0.197176	−0.0985882	−	0.995128i	$-0.531433\pi$
$379$	−3.83861	−0.197176	−0.0985882	+	0.995128i	$0.531433\pi$
$380$	0.937514	0.0480935
$381$	−54.0725	−2.77022
$382$	26.1532	1.33811
$383$	8.49369	0.434007	0.217004	−	0.976171i	$-0.430372\pi$
$383$	8.49369	0.434007	0.217004	+	0.976171i	$0.430372\pi$
$384$	33.3507	1.70192
$385$	6.45750	0.329105
$386$	−26.2157	−1.33434
$387$	31.3680	1.59452
$388$	−1.97633	−0.100333
$389$	−16.6735	−0.845382	−0.422691	−	0.906274i	$-0.638914\pi$
$389$	−16.6735	−0.845382	−0.422691	+	0.906274i	$0.638914\pi$
$390$	−18.1914	−0.921160
$391$	−4.72352	−0.238879
$392$	−2.92448	−0.147709
$393$	−75.1385	−3.79024
$394$	−33.3003	−1.67765
$395$	3.62340	0.182313
$396$	−8.16056	−0.410084
$397$	13.3378	0.669403	0.334701	−	0.942324i	$-0.391365\pi$
$397$	13.3378	0.669403	0.334701	+	0.942324i	$0.391365\pi$
$398$	24.4473	1.22543
$399$	−21.0706	−1.05485
$400$	−3.67684	−0.183842
$401$	−17.2923	−0.863537	−0.431768	−	0.901985i	$-0.642110\pi$
$401$	−17.2923	−0.863537	−0.431768	+	0.901985i	$0.642110\pi$
$402$	35.4431	1.76774
$403$	−11.6873	−0.582185
$404$	0.511331	0.0254397
$405$	−36.4815	−1.81278
$406$	13.8911	0.689405
$407$	−3.80745	−0.188728
$408$	45.2932	2.24235
$409$	−25.9115	−1.28124	−0.640621	−	0.767857i	$-0.721323\pi$
$409$	−25.9115	−1.28124	−0.640621	+	0.767857i	$0.721323\pi$
$410$	−4.68269	−0.231261
$411$	−9.09738	−0.448741
$412$	−1.87882	−0.0925627
$413$	−10.5027	−0.516803
$414$	11.7811	0.579011
$415$	5.79752	0.284589
$416$	3.35929	0.164703
$417$	−0.867059	−0.0424601
$418$	54.7864	2.67969
$419$	−3.40443	−0.166317	−0.0831587	−	0.996536i	$-0.526501\pi$
$419$	−3.40443	−0.166317	−0.0831587	+	0.996536i	$0.526501\pi$
$420$	−0.507624	−0.0247695
$421$	−7.91794	−0.385897	−0.192948	−	0.981209i	$-0.561805\pi$
$421$	−7.91794	−0.385897	−0.192948	+	0.981209i	$0.561805\pi$
$422$	2.16061	0.105177
$423$	−52.0539	−2.53095
$424$	−17.4109	−0.845550
$425$	−4.58527	−0.222418
$426$	−15.1717	−0.735072
$427$	6.64857	0.321747
$428$	−0.528121	−0.0255277
$429$	86.3733	4.17014
$430$	−5.07347	−0.244664
$431$	32.0430	1.54346	0.771728	−	0.635953i	$-0.219393\pi$
$431$	32.0430	1.54346	0.771728	+	0.635953i	$0.219393\pi$
$432$	−67.1731	−3.23187
$433$	−17.7521	−0.853111	−0.426556	−	0.904461i	$-0.640273\pi$
$433$	−17.7521	−0.853111	−0.426556	+	0.904461i	$0.640273\pi$
$434$	4.01394	0.192675
$435$	34.4989	1.65410
$436$	−0.695367	−0.0333020
$437$	6.42624	0.307409
$438$	−61.3716	−2.93245
$439$	−18.6554	−0.890374	−0.445187	−	0.895438i	$-0.646863\pi$
$439$	−18.6554	−0.890374	−0.445187	+	0.895438i	$0.646863\pi$
$440$	18.8848	0.900299
$441$	8.40880	0.400419
$442$	−24.6952	−1.17463
$443$	−10.7790	−0.512128	−0.256064	−	0.966660i	$-0.582426\pi$
$443$	−10.7790	−0.512128	−0.256064	+	0.966660i	$0.582426\pi$
$444$	0.299303	0.0142043
$445$	−12.8246	−0.607944
$446$	19.3863	0.917968
$447$	7.85396	0.371479
$448$	−8.50741	−0.401937
$449$	38.5050	1.81716	0.908582	−	0.417706i	$-0.137166\pi$
$449$	38.5050	1.81716	0.908582	+	0.417706i	$0.137166\pi$
$450$	11.4363	0.539113
$451$	22.2335	1.04693
$452$	0.138941	0.00653524
$453$	−35.5316	−1.66942
$454$	−17.6212	−0.827004
$455$	3.96000	0.185648
$456$	−61.6204	−2.88564
$457$	−30.6274	−1.43269	−0.716346	−	0.697746i	$-0.754187\pi$
$457$	−30.6274	−1.43269	−0.716346	+	0.697746i	$0.754187\pi$
$458$	1.36004	0.0635506
$459$	−83.7694	−3.91002
$460$	0.154819	0.00721845
$461$	26.2669	1.22337	0.611685	−	0.791102i	$-0.290492\pi$
$461$	26.2669	1.22337	0.611685	+	0.791102i	$0.290492\pi$
$462$	−29.6645	−1.38012
$463$	4.00857	0.186294	0.0931471	−	0.995652i	$-0.470307\pi$
$463$	4.00857	0.186294	0.0931471	+	0.995652i	$0.470307\pi$
$464$	37.5543	1.74342
$465$	9.96870	0.462288
$466$	0.549527	0.0254563
$467$	25.2478	1.16833	0.584165	−	0.811635i	$-0.301422\pi$
$467$	25.2478	1.16833	0.584165	+	0.811635i	$0.301422\pi$
$468$	−5.00439	−0.231328
$469$	−7.71541	−0.356265
$470$	8.41921	0.388349
$471$	25.0337	1.15349
$472$	−30.7149	−1.41377
$473$	24.0889	1.10761
$474$	−16.6452	−0.764539
$475$	6.23815	0.286226
$476$	−0.689107	−0.0315852
$477$	50.0619	2.29218
$478$	−34.5481	−1.58019
$479$	−13.7155	−0.626678	−0.313339	−	0.949641i	$-0.601448\pi$
$479$	−13.7155	−0.626678	−0.313339	+	0.949641i	$0.601448\pi$
$480$	−2.86531	−0.130783
$481$	−2.33488	−0.106461
$482$	−27.4800	−1.25168
$483$	−3.47953	−0.158324
$484$	−4.61371	−0.209714
$485$	−13.1504	−0.597128
$486$	93.0479	4.22074
$487$	−17.5234	−0.794060	−0.397030	−	0.917806i	$-0.629959\pi$
$487$	−17.5234	−0.794060	−0.397030	+	0.917806i	$0.629959\pi$
$488$	19.4436	0.880171
$489$	31.2240	1.41200
$490$	−1.36004	−0.0614404
$491$	26.0639	1.17625	0.588124	−	0.808771i	$-0.299867\pi$
$491$	26.0639	1.17625	0.588124	+	0.808771i	$0.299867\pi$
$492$	−1.74777	−0.0787956
$493$	46.8328	2.10924
$494$	33.5972	1.51161
$495$	−54.2998	−2.44060
$496$	10.8516	0.487251
$497$	3.30265	0.148144
$498$	−26.6327	−1.19344
$499$	14.7288	0.659353	0.329676	−	0.944094i	$-0.393060\pi$
$499$	14.7288	0.659353	0.329676	+	0.944094i	$0.393060\pi$
$500$	0.150287	0.00672104
$501$	59.9949	2.68037
$502$	−41.4329	−1.84924
$503$	37.4425	1.66948	0.834739	−	0.550646i	$-0.185619\pi$
$503$	37.4425	1.66948	0.834739	+	0.550646i	$0.185619\pi$
$504$	24.5914	1.09539
$505$	3.40236	0.151403
$506$	9.04728	0.402200
$507$	9.05758	0.402261
$508$	2.40591	0.106745
$509$	−11.4069	−0.505600	−0.252800	−	0.967519i	$-0.581351\pi$
$509$	−11.4069	−0.505600	−0.252800	+	0.967519i	$0.581351\pi$
$510$	21.0638	0.932721
$511$	13.3597	0.590997
$512$	−24.6248	−1.08827
$513$	113.966	5.03174
$514$	−34.7718	−1.53372
$515$	−12.5015	−0.550883
$516$	−1.89363	−0.0833623
$517$	−39.9746	−1.75808
$518$	0.801903	0.0352336
$519$	45.3751	1.99175
$520$	11.5809	0.507858
$521$	−25.2331	−1.10548	−0.552741	−	0.833353i	$-0.686418\pi$
$521$	−25.2331	−1.10548	−0.552741	+	0.833353i	$0.686418\pi$
$522$	−116.808	−5.11253
$523$	−34.2126	−1.49601	−0.748006	−	0.663692i	$-0.768989\pi$
$523$	−34.2126	−1.49601	−0.748006	+	0.663692i	$0.768989\pi$
$524$	3.34322	0.146049
$525$	−3.37769	−0.147415
$526$	−6.47727	−0.282423
$527$	13.5327	0.589492
$528$	−80.1972	−3.49013
$529$	−21.9388	−0.953860
$530$	−8.09703	−0.351712
$531$	88.3149	3.83254
$532$	0.937514	0.0406464
$533$	13.6345	0.590574
$534$	58.9136	2.54944
$535$	−3.51408	−0.151927
$536$	−22.5636	−0.974598
$537$	47.4437	2.04735
$538$	−27.0236	−1.16507
$539$	6.45750	0.278144
$540$	2.74563	0.118153
$541$	−6.96248	−0.299340	−0.149670	−	0.988736i	$-0.547821\pi$
$541$	−6.96248	−0.299340	−0.149670	+	0.988736i	$0.547821\pi$
$542$	−11.4808	−0.493141
$543$	1.19805	0.0514134
$544$	−3.88971	−0.166770
$545$	−4.62692	−0.198196
$546$	−18.1914	−0.778522
$547$	30.8734	1.32005	0.660025	−	0.751244i	$-0.270546\pi$
$547$	30.8734	1.32005	0.660025	+	0.751244i	$0.270546\pi$
$548$	0.404779	0.0172913
$549$	−55.9065	−2.38603
$550$	8.78247	0.374486
$551$	−63.7149	−2.71435
$552$	−10.1758	−0.433112
$553$	3.62340	0.154083
$554$	−8.82399	−0.374896
$555$	1.99154	0.0845363
$556$	0.0385790	0.00163611
$557$	−12.8506	−0.544497	−0.272248	−	0.962227i	$-0.587767\pi$
$557$	−12.8506	−0.544497	−0.272248	+	0.962227i	$0.587767\pi$
$558$	−33.7524	−1.42885
$559$	14.7723	0.624801
$560$	−3.67684	−0.155375
$561$	−100.011	−4.22248
$562$	−33.0605	−1.39457
$563$	−6.95821	−0.293254	−0.146627	−	0.989192i	$-0.546842\pi$
$563$	−6.95821	−0.293254	−0.146627	+	0.989192i	$0.546842\pi$
$564$	3.14240	0.132319
$565$	0.924504	0.0388942
$566$	37.0129	1.55577
$567$	−36.4815	−1.53208
$568$	9.65853	0.405263
$569$	15.5638	0.652467	0.326233	−	0.945289i	$-0.394220\pi$
$569$	15.5638	0.652467	0.326233	+	0.945289i	$0.394220\pi$
$570$	−28.6568	−1.20030
$571$	−29.9752	−1.25442	−0.627212	−	0.778849i	$-0.715804\pi$
$571$	−29.9752	−1.25442	−0.627212	+	0.778849i	$0.715804\pi$
$572$	−3.84310	−0.160688
$573$	64.9520	2.71341
$574$	−4.68269	−0.195452
$575$	1.03015	0.0429603
$576$	71.5371	2.98071
$577$	23.9159	0.995631	0.497815	−	0.867283i	$-0.334136\pi$
$577$	23.9159	0.995631	0.497815	+	0.867283i	$0.334136\pi$
$578$	5.47373	0.227677
$579$	−65.1072	−2.70576
$580$	−1.53500	−0.0637372
$581$	5.79752	0.240522
$582$	60.4102	2.50408
$583$	38.4448	1.59222
$584$	39.0701	1.61673
$585$	−33.2988	−1.37674
$586$	−27.4688	−1.13473
$587$	−23.0481	−0.951297	−0.475648	−	0.879636i	$-0.657787\pi$
$587$	−23.0481	−0.951297	−0.475648	+	0.879636i	$0.657787\pi$
$588$	−0.507624	−0.0209340
$589$	−18.4109	−0.758607
$590$	−14.2841	−0.588066
$591$	−82.7021	−3.40191
$592$	2.16793	0.0891012
$593$	−45.3262	−1.86132	−0.930662	−	0.365879i	$-0.880768\pi$
$593$	−45.3262	−1.86132	−0.930662	+	0.365879i	$0.880768\pi$
$594$	160.449	6.58331
$595$	−4.58527	−0.187978
$596$	−0.349454	−0.0143142
$597$	60.7153	2.48491
$598$	5.54815	0.226881
$599$	−20.1009	−0.821299	−0.410649	−	0.911793i	$-0.634698\pi$
$599$	−20.1009	−0.821299	−0.410649	+	0.911793i	$0.634698\pi$
$600$	−9.87799	−0.403267
$601$	−42.2021	−1.72146	−0.860730	−	0.509062i	$-0.829992\pi$
$601$	−42.2021	−1.72146	−0.860730	+	0.509062i	$0.829992\pi$
$602$	−5.07347	−0.206779
$603$	64.8774	2.64201
$604$	1.58095	0.0643277
$605$	−30.6993	−1.24811
$606$	−15.6298	−0.634916
$607$	−20.9304	−0.849538	−0.424769	−	0.905302i	$-0.639645\pi$
$607$	−20.9304	−0.849538	−0.424769	+	0.905302i	$0.639645\pi$
$608$	5.29186	0.214613
$609$	34.4989	1.39797
$610$	9.04233	0.366113
$611$	−24.5140	−0.991731
$612$	5.79456	0.234231
$613$	−3.62915	−0.146580	−0.0732901	−	0.997311i	$-0.523350\pi$
$613$	−3.62915	−0.146580	−0.0732901	+	0.997311i	$0.523350\pi$
$614$	38.8995	1.56986
$615$	−11.6296	−0.468949
$616$	18.8848	0.760892
$617$	−11.9647	−0.481680	−0.240840	−	0.970565i	$-0.577423\pi$
$617$	−11.9647	−0.481680	−0.240840	+	0.970565i	$0.577423\pi$
$618$	57.4295	2.31015
$619$	−19.0617	−0.766154	−0.383077	−	0.923716i	$-0.625136\pi$
$619$	−19.0617	−0.766154	−0.383077	+	0.923716i	$0.625136\pi$
$620$	−0.443548	−0.0178133
$621$	18.8201	0.755224
$622$	8.37500	0.335807
$623$	−12.8246	−0.513806
$624$	−49.1801	−1.96878
$625$	1.00000	0.0400000
$626$	23.3615	0.933715
$627$	136.063	5.43384
$628$	−1.11385	−0.0444475
$629$	2.70355	0.107798
$630$	11.4363	0.455634
$631$	3.16427	0.125967	0.0629837	−	0.998015i	$-0.479938\pi$
$631$	3.16427	0.125967	0.0629837	+	0.998015i	$0.479938\pi$
$632$	10.5966	0.421509
$633$	5.36593	0.213276
$634$	−8.61710	−0.342229
$635$	16.0087	0.635287
$636$	−3.02214	−0.119836
$637$	3.96000	0.156901
$638$	−89.7020	−3.55133
$639$	−27.7713	−1.09862
$640$	−9.87382	−0.390297
$641$	2.87174	0.113427	0.0567134	−	0.998390i	$-0.481938\pi$
$641$	2.87174	0.113427	0.0567134	+	0.998390i	$0.481938\pi$
$642$	16.1430	0.637113
$643$	−11.4902	−0.453128	−0.226564	−	0.973996i	$-0.572749\pi$
$643$	−11.4902	−0.453128	−0.226564	+	0.973996i	$0.572749\pi$
$644$	0.154819	0.00610070
$645$	−12.6001	−0.496127
$646$	−38.9021	−1.53058
$647$	46.2754	1.81927	0.909636	−	0.415406i	$-0.136360\pi$
$647$	46.2754	1.81927	0.909636	+	0.415406i	$0.136360\pi$
$648$	−106.689	−4.19115
$649$	67.8210	2.66221
$650$	5.38576	0.211247
$651$	9.96870	0.390704
$652$	−1.38928	−0.0544085
$653$	−25.7640	−1.00822	−0.504112	−	0.863638i	$-0.668180\pi$
$653$	−25.7640	−1.00822	−0.504112	+	0.863638i	$0.668180\pi$
$654$	21.2552	0.831143
$655$	22.2455	0.869205
$656$	−12.6595	−0.494272
$657$	−112.339	−4.38275
$658$	8.41921	0.328215
$659$	9.40930	0.366534	0.183267	−	0.983063i	$-0.441333\pi$
$659$	9.40930	0.366534	0.183267	+	0.983063i	$0.441333\pi$
$660$	3.27798	0.127595
$661$	−38.6122	−1.50184	−0.750921	−	0.660392i	$-0.770390\pi$
$661$	−38.6122	−1.50184	−0.750921	+	0.660392i	$0.770390\pi$
$662$	−4.41507	−0.171596
$663$	−61.3309	−2.38190
$664$	16.9547	0.657971
$665$	6.23815	0.241905
$666$	−6.74304	−0.261288
$667$	−10.5217	−0.407402
$668$	−2.66941	−0.103283
$669$	48.1463	1.86144
$670$	−10.4933	−0.405391
$671$	−42.9332	−1.65742
$672$	−2.86531	−0.110532
$673$	−17.4897	−0.674177	−0.337088	−	0.941473i	$-0.609442\pi$
$673$	−17.4897	−0.674177	−0.337088	+	0.941473i	$0.609442\pi$
$674$	29.1987	1.12469
$675$	18.2692	0.703184
$676$	−0.403008	−0.0155003
$677$	4.16596	0.160111	0.0800555	−	0.996790i	$-0.474490\pi$
$677$	4.16596	0.160111	0.0800555	+	0.996790i	$0.474490\pi$
$678$	−4.24699	−0.163105
$679$	−13.1504	−0.504665
$680$	−13.4095	−0.514232
$681$	−43.7626	−1.67699
$682$	−25.9200	−0.992529
$683$	7.58991	0.290420	0.145210	−	0.989401i	$-0.453614\pi$
$683$	7.58991	0.290420	0.145210	+	0.989401i	$0.453614\pi$
$684$	−7.88337	−0.301428
$685$	2.69337	0.102908
$686$	−1.36004	−0.0519266
$687$	3.37769	0.128867
$688$	−13.7160	−0.522918
$689$	23.5759	0.898171
$690$	−4.73231	−0.180156
$691$	38.3885	1.46037	0.730183	−	0.683251i	$-0.239435\pi$
$691$	38.3885	1.46037	0.730183	+	0.683251i	$0.239435\pi$
$692$	−2.01892	−0.0767479
$693$	−54.2998	−2.06268
$694$	−18.3804	−0.697709
$695$	0.256702	0.00973725
$696$	100.891	3.82428
$697$	−15.7873	−0.597986
$698$	−10.5976	−0.401126
$699$	1.36476	0.0516200
$700$	0.150287	0.00568032
$701$	−3.40419	−0.128575	−0.0642873	−	0.997931i	$-0.520477\pi$
$701$	−3.40419	−0.128575	−0.0642873	+	0.997931i	$0.520477\pi$
$702$	98.3938	3.71364
$703$	−3.67812	−0.138723
$704$	54.9366	2.07050
$705$	20.9093	0.787489
$706$	−36.4615	−1.37225
$707$	3.40236	0.127959
$708$	−5.33140	−0.200366
$709$	−42.7334	−1.60488	−0.802442	−	0.596730i	$-0.796467\pi$
$709$	−42.7334	−1.60488	−0.802442	+	0.596730i	$0.796467\pi$
$710$	4.49174	0.168572
$711$	−30.4685	−1.14266
$712$	−37.5052	−1.40557
$713$	−3.04032	−0.113861
$714$	21.0638	0.788293
$715$	−25.5717	−0.956327
$716$	−2.11096	−0.0788904
$717$	−85.8010	−3.20430
$718$	25.9046	0.966752
$719$	41.7859	1.55835	0.779175	−	0.626806i	$-0.215638\pi$
$719$	41.7859	1.55835	0.779175	+	0.626806i	$0.215638\pi$
$720$	30.9178	1.15224
$721$	−12.5015	−0.465581
$722$	27.0846	1.00798
$723$	−68.2472	−2.53814
$724$	−0.0533062	−0.00198111
$725$	−10.2138	−0.379329
$726$	141.027	5.23399
$727$	−16.7980	−0.623003	−0.311501	−	0.950246i	$-0.600832\pi$
$727$	−16.7980	−0.623003	−0.311501	+	0.950246i	$0.600832\pi$
$728$	11.5809	0.429218
$729$	121.642	4.50525
$730$	18.1697	0.672491
$731$	−17.1048	−0.632643
$732$	3.37497	0.124743
$733$	−0.461723	−0.0170541	−0.00852707	−	0.999964i	$-0.502714\pi$
$733$	−0.461723	−0.0170541	−0.00852707	+	0.999964i	$0.502714\pi$
$734$	1.01261	0.0373760
$735$	−3.37769	−0.124588
$736$	0.873883	0.0322118
$737$	49.8223	1.83523
$738$	39.3758	1.44944
$739$	9.48506	0.348914	0.174457	−	0.984665i	$-0.444183\pi$
$739$	9.48506	0.348914	0.174457	+	0.984665i	$0.444183\pi$
$740$	−0.0886118	−0.00325743
$741$	83.4394	3.06522
$742$	−8.09703	−0.297251
$743$	10.9388	0.401305	0.200653	−	0.979662i	$-0.435694\pi$
$743$	10.9388	0.401305	0.200653	+	0.979662i	$0.435694\pi$
$744$	29.1533	1.06881
$745$	−2.32524	−0.0851903
$746$	34.8370	1.27547
$747$	−48.7502	−1.78368
$748$	4.44991	0.162705
$749$	−3.51408	−0.128402
$750$	−4.59380	−0.167742
$751$	−49.9282	−1.82190	−0.910952	−	0.412512i	$-0.864652\pi$
$751$	−49.9282	−1.82190	−0.910952	+	0.412512i	$0.864652\pi$
$752$	22.7611	0.830013
$753$	−102.899	−3.74986
$754$	−55.0088	−2.00330
$755$	10.5195	0.382844
$756$	2.74563	0.0998577
$757$	12.5798	0.457221	0.228610	−	0.973518i	$-0.426582\pi$
$757$	12.5798	0.457221	0.228610	+	0.973518i	$0.426582\pi$
$758$	−5.22067	−0.189623
$759$	22.4691	0.815577
$760$	18.2433	0.661756
$761$	−37.9549	−1.37587	−0.687933	−	0.725775i	$-0.741482\pi$
$761$	−37.9549	−1.37587	−0.687933	+	0.725775i	$0.741482\pi$
$762$	−73.5409	−2.66411
$763$	−4.62692	−0.167506
$764$	−2.88998	−0.104556
$765$	38.5566	1.39402
$766$	11.5518	0.417382
$767$	41.5906	1.50175
$768$	−12.1124	−0.437070
$769$	1.76521	0.0636551	0.0318276	−	0.999493i	$-0.489867\pi$
$769$	1.76521	0.0636551	0.0318276	+	0.999493i	$0.489867\pi$
$770$	8.78247	0.316498
$771$	−86.3564	−3.11005
$772$	2.89688	0.104261
$773$	33.5449	1.20653	0.603263	−	0.797542i	$-0.293867\pi$
$773$	33.5449	1.20653	0.603263	+	0.797542i	$0.293867\pi$
$774$	42.6618	1.53345
$775$	−2.95134	−0.106015
$776$	−38.4580	−1.38056
$777$	1.99154	0.0714462
$778$	−22.6767	−0.812999
$779$	21.4783	0.769538
$780$	2.01019	0.0719763
$781$	−21.3269	−0.763135
$782$	−6.42418	−0.229728
$783$	−186.598	−6.66845
$784$	−3.67684	−0.131316
$785$	−7.41148	−0.264527
$786$	−102.191	−3.64505
$787$	−8.04269	−0.286691	−0.143345	−	0.989673i	$-0.545786\pi$
$787$	−8.04269	−0.286691	−0.143345	+	0.989673i	$0.545786\pi$
$788$	3.67975	0.131086
$789$	−16.0864	−0.572693
$790$	4.92798	0.175330
$791$	0.924504	0.0328716
$792$	−158.799	−5.64267
$793$	−26.3283	−0.934946
$794$	18.1399	0.643761
$795$	−20.1091	−0.713198
$796$	−2.70147	−0.0957510
$797$	−23.0283	−0.815704	−0.407852	−	0.913048i	$-0.633722\pi$
$797$	−23.0283	−0.815704	−0.407852	+	0.913048i	$0.633722\pi$
$798$	−28.6568	−1.01444
$799$	28.3847	1.00418
$800$	0.848305	0.0299921
$801$	107.839	3.81032
$802$	−23.5183	−0.830458
$803$	−86.2701	−3.04440
$804$	−3.91653	−0.138125
$805$	1.03015	0.0363081
$806$	−15.8952	−0.559884
$807$	−67.1137	−2.36251
$808$	9.95014	0.350045
$809$	−10.3051	−0.362308	−0.181154	−	0.983455i	$-0.557983\pi$
$809$	−10.3051	−0.362308	−0.181154	+	0.983455i	$0.557983\pi$
$810$	−49.6163	−1.74334
$811$	−47.9310	−1.68308	−0.841542	−	0.540192i	$-0.818352\pi$
$811$	−47.9310	−1.68308	−0.841542	+	0.540192i	$0.818352\pi$
$812$	−1.53500	−0.0538678
$813$	−28.5127	−0.999985
$814$	−5.17829	−0.181499
$815$	−9.24420	−0.323810
$816$	56.9455	1.99349
$817$	23.2707	0.814138
$818$	−35.2407	−1.23216
$819$	−33.2988	−1.16356
$820$	0.517446	0.0180700
$821$	−41.1248	−1.43526	−0.717632	−	0.696422i	$-0.754774\pi$
$821$	−41.1248	−1.43526	−0.717632	+	0.696422i	$0.754774\pi$
$822$	−12.3728	−0.431551
$823$	13.0688	0.455551	0.227775	−	0.973714i	$-0.426855\pi$
$823$	13.0688	0.455551	0.227775	+	0.973714i	$0.426855\pi$
$824$	−36.5604	−1.27364
$825$	21.8114	0.759377
$826$	−14.2841	−0.497006
$827$	−40.2117	−1.39830	−0.699149	−	0.714976i	$-0.746438\pi$
$827$	−40.2117	−1.39830	−0.699149	+	0.714976i	$0.746438\pi$
$828$	−1.30184	−0.0452420
$829$	−16.8210	−0.584219	−0.292109	−	0.956385i	$-0.594357\pi$
$829$	−16.8210	−0.584219	−0.292109	+	0.956385i	$0.594357\pi$
$830$	7.88487	0.273688
$831$	−21.9146	−0.760208
$832$	33.6893	1.16797
$833$	−4.58527	−0.158870
$834$	−1.17924	−0.0408336
$835$	−17.7621	−0.614682
$836$	−6.05400	−0.209382
$837$	−53.9187	−1.86370
$838$	−4.63017	−0.159947
$839$	51.6954	1.78472	0.892362	−	0.451319i	$-0.149047\pi$
$839$	51.6954	1.78472	0.892362	+	0.451319i	$0.149047\pi$
$840$	−9.87799	−0.340823
$841$	75.3207	2.59727
$842$	−10.7687	−0.371115
$843$	−82.1063	−2.82789
$844$	−0.238752	−0.00821817
$845$	−2.68159	−0.0922495
$846$	−70.7955	−2.43400
$847$	−30.6993	−1.05484
$848$	−21.8901	−0.751710
$849$	91.9224	3.15477
$850$	−6.23615	−0.213898
$851$	−0.607395	−0.0208212
$852$	1.67650	0.0574360
$853$	34.8050	1.19170	0.595850	−	0.803096i	$-0.296815\pi$
$853$	34.8050	1.19170	0.595850	+	0.803096i	$0.296815\pi$
$854$	9.04233	0.309422
$855$	−52.4554	−1.79394
$856$	−10.2769	−0.351256
$857$	20.5379	0.701562	0.350781	−	0.936458i	$-0.385916\pi$
$857$	20.5379	0.701562	0.350781	+	0.936458i	$0.385916\pi$
$858$	117.471	4.01040
$859$	−0.0193579	−0.000660483 0	−0.000330242	−	1.00000i	$-0.500105\pi$
$859$	−0.0193579	−0.000660483 0	−0.000330242		1.00000i	$0.500105\pi$
$860$	0.560628	0.0191172
$861$	−11.6296	−0.396334
$862$	43.5798	1.48433
$863$	−17.6114	−0.599498	−0.299749	−	0.954018i	$-0.596903\pi$
$863$	−17.6114	−0.599498	−0.299749	+	0.954018i	$0.596903\pi$
$864$	15.4979	0.527249
$865$	−13.4338	−0.456762
$866$	−24.1436	−0.820433
$867$	13.5941	0.461681
$868$	−0.443548	−0.0150550
$869$	−23.3981	−0.793727
$870$	46.9199	1.59073
$871$	30.5530	1.03525
$872$	−13.5313	−0.458229
$873$	110.579	3.74253
$874$	8.73996	0.295633
$875$	1.00000	0.0338062
$876$	6.78168	0.229132
$877$	−0.199030	−0.00672076	−0.00336038	−	0.999994i	$-0.501070\pi$
$877$	−0.199030	−0.00672076	−0.00336038	+	0.999994i	$0.501070\pi$
$878$	−25.3721	−0.856268
$879$	−68.2194	−2.30098
$880$	23.7432	0.800383
$881$	−26.3858	−0.888962	−0.444481	−	0.895788i	$-0.646612\pi$
$881$	−26.3858	−0.888962	−0.444481	+	0.895788i	$0.646612\pi$
$882$	11.4363	0.385081
$883$	11.5555	0.388874	0.194437	−	0.980915i	$-0.437712\pi$
$883$	11.5555	0.388874	0.194437	+	0.980915i	$0.437712\pi$
$884$	2.72886	0.0917815
$885$	−35.4748	−1.19247
$886$	−14.6599	−0.492510
$887$	−4.46179	−0.149812	−0.0749061	−	0.997191i	$-0.523866\pi$
$887$	−4.46179	−0.149812	−0.0749061	+	0.997191i	$0.523866\pi$
$888$	5.82423	0.195448
$889$	16.0087	0.536915
$890$	−17.4420	−0.584656
$891$	235.579	7.89220
$892$	−2.14222	−0.0717269
$893$	−38.6167	−1.29226
$894$	10.6817	0.357250
$895$	−14.0462	−0.469513
$896$	−9.87382	−0.329861
$897$	13.7789	0.460066
$898$	52.3684	1.74756
$899$	30.1442	1.00537
$900$	−1.26373	−0.0421245
$901$	−27.2985	−0.909444
$902$	30.2385	1.00683
$903$	−12.6001	−0.419304
$904$	2.70369	0.0899235
$905$	−0.354696	−0.0117905
$906$	−48.3245	−1.60547
$907$	29.0786	0.965538	0.482769	−	0.875748i	$-0.339631\pi$
$907$	29.0786	0.965538	0.482769	+	0.875748i	$0.339631\pi$
$908$	1.94718	0.0646193
$909$	−28.6098	−0.948927
$910$	5.38576	0.178536
$911$	−11.5780	−0.383597	−0.191799	−	0.981434i	$-0.561432\pi$
$911$	−11.5780	−0.383597	−0.191799	+	0.981434i	$0.561432\pi$
$912$	−77.4730	−2.56539
$913$	−37.4375	−1.23900
$914$	−41.6546	−1.37781
$915$	22.4568	0.742400
$916$	−0.150287	−0.00496563
$917$	22.2455	0.734612
$918$	−113.930	−3.76025
$919$	−52.3713	−1.72757	−0.863785	−	0.503860i	$-0.831913\pi$
$919$	−52.3713	−1.72757	−0.863785	+	0.503860i	$0.831913\pi$
$920$	3.01266	0.0993244
$921$	96.6076	3.18333
$922$	35.7240	1.17651
$923$	−13.0785	−0.430484
$924$	3.27798	0.107838
$925$	−0.589617	−0.0193865
$926$	5.45183	0.179158
$927$	105.123	3.45268
$928$	−8.66438	−0.284422
$929$	−13.7941	−0.452570	−0.226285	−	0.974061i	$-0.572658\pi$
$929$	−13.7941	−0.452570	−0.226285	+	0.974061i	$0.572658\pi$
$930$	13.5579	0.444579
$931$	6.23815	0.204447
$932$	−0.0607237	−0.00198907
$933$	20.7995	0.680945
$934$	34.3381	1.12358
$935$	29.6094	0.968330
$936$	−97.3817	−3.18302
$937$	4.12464	0.134746	0.0673730	−	0.997728i	$-0.478538\pi$
$937$	4.12464	0.134746	0.0673730	+	0.997728i	$0.478538\pi$
$938$	−10.4933	−0.342618
$939$	58.0189	1.89337
$940$	−0.930339	−0.0303443
$941$	−33.8580	−1.10374	−0.551870	−	0.833930i	$-0.686086\pi$
$941$	−33.8580	−1.10374	−0.551870	+	0.833930i	$0.686086\pi$
$942$	34.0469	1.10931
$943$	3.54686	0.115502
$944$	−38.6166	−1.25686
$945$	18.2692	0.594299
$946$	32.7619	1.06518
$947$	17.3206	0.562843	0.281421	−	0.959584i	$-0.409194\pi$
$947$	17.3206	0.562843	0.281421	+	0.959584i	$0.409194\pi$
$948$	1.83933	0.0597385
$949$	−52.9043	−1.71734
$950$	8.48415	0.275262
$951$	−21.4008	−0.693967
$952$	−13.4095	−0.434605
$953$	0.954709	0.0309261	0.0154630	−	0.999880i	$-0.495078\pi$
$953$	0.954709	0.0309261	0.0154630	+	0.999880i	$0.495078\pi$
$954$	68.0863	2.20437
$955$	−19.2297	−0.622259
$956$	3.81763	0.123471
$957$	−222.777	−7.20135
$958$	−18.6537	−0.602672
$959$	2.69337	0.0869735
$960$	−28.7354	−0.927431
$961$	−22.2896	−0.719020
$962$	−3.17554	−0.102383
$963$	29.5492	0.952210
$964$	3.03659	0.0978021
$965$	19.2757	0.620505
$966$	−4.73231	−0.152260
$967$	4.66747	0.150096	0.0750478	−	0.997180i	$-0.476089\pi$
$967$	4.66747	0.150096	0.0750478	+	0.997180i	$0.476089\pi$
$968$	−89.7796	−2.88562
$969$	−96.6141	−3.10369
$970$	−17.8851	−0.574254
$971$	−55.8522	−1.79238	−0.896191	−	0.443669i	$-0.853677\pi$
$971$	−55.8522	−1.79238	−0.896191	+	0.443669i	$0.853677\pi$
$972$	−10.2820	−0.329794
$973$	0.256702	0.00822948
$974$	−23.8325	−0.763643
$975$	13.3757	0.428364
$976$	24.4457	0.782489
$977$	−39.7299	−1.27107	−0.635536	−	0.772071i	$-0.719221\pi$
$977$	−39.7299	−1.27107	−0.635536	+	0.772071i	$0.719221\pi$
$978$	42.4660	1.35791
$979$	82.8148	2.64677
$980$	0.150287	0.00480075
$981$	38.9069	1.24220
$982$	35.4480	1.13119
$983$	12.8512	0.409888	0.204944	−	0.978774i	$-0.434299\pi$
$983$	12.8512	0.409888	0.204944	+	0.978774i	$0.434299\pi$
$984$	−34.0104	−1.08421
$985$	24.4848	0.780151
$986$	63.6945	2.02845
$987$	20.9093	0.665550
$988$	−3.71255	−0.118112
$989$	3.84285	0.122196
$990$	−73.8500	−2.34711
$991$	−39.8412	−1.26560	−0.632799	−	0.774316i	$-0.718094\pi$
$991$	−39.8412	−1.26560	−0.632799	+	0.774316i	$0.718094\pi$
$992$	−2.50363	−0.0794905
$993$	−10.9649	−0.347961
$994$	4.49174	0.142469
$995$	−17.9754	−0.569858
$996$	2.94296	0.0932512
$997$	−20.6146	−0.652871	−0.326435	−	0.945220i	$-0.605848\pi$
$997$	−20.6146	−0.652871	−0.326435	+	0.945220i	$0.605848\pi$
$998$	20.0318	0.634096
$999$	−10.7719	−0.340806

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.44	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.44	✓	62	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q+1.36004 q^{2} +3.37769 q^{3} -0.150287 q^{4} -1.00000 q^{5} +4.59380 q^{6} -1.00000 q^{7} -2.92448 q^{8} +8.40880 q^{9} +O(q^{10})\)	\(q+1.36004 q^{2} +3.37769 q^{3} -0.150287 q^{4} -1.00000 q^{5} +4.59380 q^{6} -1.00000 q^{7} -2.92448 q^{8} +8.40880 q^{9} -1.36004 q^{10} +6.45750 q^{11} -0.507624 q^{12} +3.96000 q^{13} -1.36004 q^{14} -3.37769 q^{15} -3.67684 q^{16} -4.58527 q^{17} +11.4363 q^{18} +6.23815 q^{19} +0.150287 q^{20} -3.37769 q^{21} +8.78247 q^{22} +1.03015 q^{23} -9.87799 q^{24} +1.00000 q^{25} +5.38576 q^{26} +18.2692 q^{27} +0.150287 q^{28} -10.2138 q^{29} -4.59380 q^{30} -2.95134 q^{31} +0.848305 q^{32} +21.8114 q^{33} -6.23615 q^{34} +1.00000 q^{35} -1.26373 q^{36} -0.589617 q^{37} +8.48415 q^{38} +13.3757 q^{39} +2.92448 q^{40} +3.44305 q^{41} -4.59380 q^{42} +3.73038 q^{43} -0.970479 q^{44} -8.40880 q^{45} +1.40105 q^{46} -6.19041 q^{47} -12.4192 q^{48} +1.00000 q^{49} +1.36004 q^{50} -15.4876 q^{51} -0.595137 q^{52} +5.95352 q^{53} +24.8469 q^{54} -6.45750 q^{55} +2.92448 q^{56} +21.0706 q^{57} -13.8911 q^{58} +10.5027 q^{59} +0.507624 q^{60} -6.64857 q^{61} -4.01394 q^{62} -8.40880 q^{63} +8.50741 q^{64} -3.96000 q^{65} +29.6645 q^{66} +7.71541 q^{67} +0.689107 q^{68} +3.47953 q^{69} +1.36004 q^{70} -3.30265 q^{71} -24.5914 q^{72} -13.3597 q^{73} -0.801903 q^{74} +3.37769 q^{75} -0.937514 q^{76} -6.45750 q^{77} +18.1914 q^{78} -3.62340 q^{79} +3.67684 q^{80} +36.4815 q^{81} +4.68269 q^{82} -5.79752 q^{83} +0.507624 q^{84} +4.58527 q^{85} +5.07347 q^{86} -34.4989 q^{87} -18.8848 q^{88} +12.8246 q^{89} -11.4363 q^{90} -3.96000 q^{91} -0.154819 q^{92} -9.96870 q^{93} -8.41921 q^{94} -6.23815 q^{95} +2.86531 q^{96} +13.1504 q^{97} +1.36004 q^{98} +54.2998 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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