LMFDB - Embedded newform 8015.2.a.k.1.18

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:	$1$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q-0.978041 q^{2} -3.27758 q^{3} -1.04343 q^{4} -1.00000 q^{5} +3.20561 q^{6} -1.00000 q^{7} +2.97661 q^{8} +7.74254 q^{9} +O(q^{10})$	\(q-0.978041 q^{2} -3.27758 q^{3} -1.04343 q^{4} -1.00000 q^{5} +3.20561 q^{6} -1.00000 q^{7} +2.97661 q^{8} +7.74254 q^{9} +0.978041 q^{10} +6.25469 q^{11} +3.41994 q^{12} +0.406151 q^{13} +0.978041 q^{14} +3.27758 q^{15} -0.824374 q^{16} +6.95990 q^{17} -7.57253 q^{18} +0.159258 q^{19} +1.04343 q^{20} +3.27758 q^{21} -6.11735 q^{22} +3.08939 q^{23} -9.75607 q^{24} +1.00000 q^{25} -0.397232 q^{26} -15.5441 q^{27} +1.04343 q^{28} +2.86877 q^{29} -3.20561 q^{30} -2.48040 q^{31} -5.14694 q^{32} -20.5003 q^{33} -6.80708 q^{34} +1.00000 q^{35} -8.07884 q^{36} -0.474329 q^{37} -0.155761 q^{38} -1.33119 q^{39} -2.97661 q^{40} -10.6188 q^{41} -3.20561 q^{42} +10.9079 q^{43} -6.52637 q^{44} -7.74254 q^{45} -3.02155 q^{46} -9.49376 q^{47} +2.70195 q^{48} +1.00000 q^{49} -0.978041 q^{50} -22.8117 q^{51} -0.423792 q^{52} -2.93386 q^{53} +15.2027 q^{54} -6.25469 q^{55} -2.97661 q^{56} -0.521982 q^{57} -2.80577 q^{58} -0.928638 q^{59} -3.41994 q^{60} -0.713388 q^{61} +2.42593 q^{62} -7.74254 q^{63} +6.68267 q^{64} -0.406151 q^{65} +20.0501 q^{66} -4.27091 q^{67} -7.26221 q^{68} -10.1257 q^{69} -0.978041 q^{70} +4.68217 q^{71} +23.0465 q^{72} -7.43786 q^{73} +0.463913 q^{74} -3.27758 q^{75} -0.166176 q^{76} -6.25469 q^{77} +1.30196 q^{78} +11.8977 q^{79} +0.824374 q^{80} +27.7193 q^{81} +10.3856 q^{82} -7.78070 q^{83} -3.41994 q^{84} -6.95990 q^{85} -10.6684 q^{86} -9.40262 q^{87} +18.6178 q^{88} +9.37649 q^{89} +7.57253 q^{90} -0.406151 q^{91} -3.22357 q^{92} +8.12971 q^{93} +9.28529 q^{94} -0.159258 q^{95} +16.8695 q^{96} -8.66452 q^{97} -0.978041 q^{98} +48.4272 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) $ 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9} + 3 q^{10} + 16 q^{11} - 26 q^{12} - 31 q^{13} + 3 q^{14} + 10 q^{15} + 49 q^{16} - 18 q^{17} + 4 q^{18} - 16 q^{19} - 49 q^{20} + 10 q^{21} + 10 q^{22} + 10 q^{23} + 2 q^{24} + 49 q^{25} - 22 q^{26} - 58 q^{27} - 49 q^{28} + 31 q^{29} - 10 q^{30} - 35 q^{31} - 5 q^{32} - 82 q^{33} - 41 q^{34} + 49 q^{35} + 49 q^{36} - 24 q^{37} - 20 q^{38} + 41 q^{39} + 6 q^{40} + 30 q^{41} - 10 q^{42} - 19 q^{43} + 27 q^{44} - 39 q^{45} + 15 q^{46} - 39 q^{47} - 51 q^{48} + 49 q^{49} - 3 q^{50} + 46 q^{51} - 94 q^{52} - 17 q^{53} + 9 q^{54} - 16 q^{55} + 6 q^{56} - 23 q^{57} - 46 q^{58} + 11 q^{59} + 26 q^{60} - 9 q^{61} - 49 q^{62} - 39 q^{63} + 10 q^{64} + 31 q^{65} - 10 q^{66} - 2 q^{67} - 73 q^{68} - 47 q^{69} - 3 q^{70} + 26 q^{71} - 39 q^{72} - 100 q^{73} + 8 q^{74} - 10 q^{75} - 71 q^{76} - 16 q^{77} - 51 q^{78} + 50 q^{79} - 49 q^{80} + 61 q^{81} - 36 q^{82} - 67 q^{83} + 26 q^{84} + 18 q^{85} + 33 q^{86} - 45 q^{87} - q^{88} - 19 q^{89} - 4 q^{90} + 31 q^{91} + 7 q^{92} + 9 q^{93} - 33 q^{94} + 16 q^{95} - 8 q^{96} - 85 q^{97} - 3 q^{98} + 27 q^{99}+O(q^{100}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9 + 3 * q^10 + 16 * q^11 - 26 * q^12 - 31 * q^13 + 3 * q^14 + 10 * q^15 + 49 * q^16 - 18 * q^17 + 4 * q^18 - 16 * q^19 - 49 * q^20 + 10 * q^21 + 10 * q^22 + 10 * q^23 + 2 * q^24 + 49 * q^25 - 22 * q^26 - 58 * q^27 - 49 * q^28 + 31 * q^29 - 10 * q^30 - 35 * q^31 - 5 * q^32 - 82 * q^33 - 41 * q^34 + 49 * q^35 + 49 * q^36 - 24 * q^37 - 20 * q^38 + 41 * q^39 + 6 * q^40 + 30 * q^41 - 10 * q^42 - 19 * q^43 + 27 * q^44 - 39 * q^45 + 15 * q^46 - 39 * q^47 - 51 * q^48 + 49 * q^49 - 3 * q^50 + 46 * q^51 - 94 * q^52 - 17 * q^53 + 9 * q^54 - 16 * q^55 + 6 * q^56 - 23 * q^57 - 46 * q^58 + 11 * q^59 + 26 * q^60 - 9 * q^61 - 49 * q^62 - 39 * q^63 + 10 * q^64 + 31 * q^65 - 10 * q^66 - 2 * q^67 - 73 * q^68 - 47 * q^69 - 3 * q^70 + 26 * q^71 - 39 * q^72 - 100 * q^73 + 8 * q^74 - 10 * q^75 - 71 * q^76 - 16 * q^77 - 51 * q^78 + 50 * q^79 - 49 * q^80 + 61 * q^81 - 36 * q^82 - 67 * q^83 + 26 * q^84 + 18 * q^85 + 33 * q^86 - 45 * q^87 - q^88 - 19 * q^89 - 4 * q^90 + 31 * q^91 + 7 * q^92 + 9 * q^93 - 33 * q^94 + 16 * q^95 - 8 * q^96 - 85 * q^97 - 3 * q^98 + 27 * 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 $

$2$	−0.978041	−0.691580	−0.345790	−	0.938312i	$-0.612389\pi$
$2$	−0.978041	−0.691580	−0.345790	+	0.938312i	$0.612389\pi$
$3$	−3.27758	−1.89231	−0.946156	−	0.323710i	$-0.895070\pi$
$3$	−3.27758	−1.89231	−0.946156	+	0.323710i	$0.895070\pi$
$4$	−1.04343	−0.521717
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.20561	1.30869
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.97661	1.05239
$9$	7.74254	2.58085
$10$	0.978041	0.309284
$11$	6.25469	1.88586	0.942931	−	0.332989i	$-0.108057\pi$
$11$	6.25469	1.88586	0.942931	+	0.332989i	$0.108057\pi$
$12$	3.41994	0.987252
$13$	0.406151	0.112646	0.0563230	−	0.998413i	$-0.482062\pi$
$13$	0.406151	0.112646	0.0563230	+	0.998413i	$0.482062\pi$
$14$	0.978041	0.261393
$15$	3.27758	0.846268
$16$	−0.824374	−0.206093
$17$	6.95990	1.68802	0.844012	−	0.536324i	$-0.180187\pi$
$17$	6.95990	1.68802	0.844012	+	0.536324i	$0.180187\pi$
$18$	−7.57253	−1.78486
$19$	0.159258	0.0365363	0.0182682	−	0.999833i	$-0.494185\pi$
$19$	0.159258	0.0365363	0.0182682	+	0.999833i	$0.494185\pi$
$20$	1.04343	0.233319
$21$	3.27758	0.715227
$22$	−6.11735	−1.30422
$23$	3.08939	0.644181	0.322091	−	0.946709i	$-0.395614\pi$
$23$	3.08939	0.644181	0.322091	+	0.946709i	$0.395614\pi$
$24$	−9.75607	−1.99145
$25$	1.00000	0.200000
$26$	−0.397232	−0.0779036
$27$	−15.5441	−2.99146
$28$	1.04343	0.197191
$29$	2.86877	0.532717	0.266358	−	0.963874i	$-0.414180\pi$
$29$	2.86877	0.532717	0.266358	+	0.963874i	$0.414180\pi$
$30$	−3.20561	−0.585262
$31$	−2.48040	−0.445493	−0.222746	−	0.974876i	$-0.571502\pi$
$31$	−2.48040	−0.445493	−0.222746	+	0.974876i	$0.571502\pi$
$32$	−5.14694	−0.909859
$33$	−20.5003	−3.56864
$34$	−6.80708	−1.16740
$35$	1.00000	0.169031
$36$	−8.07884	−1.34647
$37$	−0.474329	−0.0779792	−0.0389896	−	0.999240i	$-0.512414\pi$
$37$	−0.474329	−0.0779792	−0.0389896	+	0.999240i	$0.512414\pi$
$38$	−0.155761	−0.0252678
$39$	−1.33119	−0.213161
$40$	−2.97661	−0.470643
$41$	−10.6188	−1.65837	−0.829187	−	0.558972i	$-0.811196\pi$
$41$	−10.6188	−1.65837	−0.829187	+	0.558972i	$0.811196\pi$
$42$	−3.20561	−0.494636
$43$	10.9079	1.66344	0.831719	−	0.555197i	$-0.187357\pi$
$43$	10.9079	1.66344	0.831719	+	0.555197i	$0.187357\pi$
$44$	−6.52637	−0.983887
$45$	−7.74254	−1.15419
$46$	−3.02155	−0.445503
$47$	−9.49376	−1.38481	−0.692404	−	0.721510i	$-0.743448\pi$
$47$	−9.49376	−1.38481	−0.692404	+	0.721510i	$0.743448\pi$
$48$	2.70195	0.389993
$49$	1.00000	0.142857
$50$	−0.978041	−0.138316
$51$	−22.8117	−3.19427
$52$	−0.423792	−0.0587694
$53$	−2.93386	−0.402997	−0.201499	−	0.979489i	$-0.564581\pi$
$53$	−2.93386	−0.402997	−0.201499	+	0.979489i	$0.564581\pi$
$54$	15.2027	2.06883
$55$	−6.25469	−0.843383
$56$	−2.97661	−0.397766
$57$	−0.521982	−0.0691382
$58$	−2.80577	−0.368416
$59$	−0.928638	−0.120898	−0.0604492	−	0.998171i	$-0.519253\pi$
$59$	−0.928638	−0.120898	−0.0604492	+	0.998171i	$0.519253\pi$
$60$	−3.41994	−0.441513
$61$	−0.713388	−0.0913399	−0.0456700	−	0.998957i	$-0.514542\pi$
$61$	−0.713388	−0.0913399	−0.0456700	+	0.998957i	$0.514542\pi$
$62$	2.42593	0.308094
$63$	−7.74254	−0.975468
$64$	6.68267	0.835333
$65$	−0.406151	−0.0503768
$66$	20.0501	2.46800
$67$	−4.27091	−0.521774	−0.260887	−	0.965369i	$-0.584015\pi$
$67$	−4.27091	−0.521774	−0.260887	+	0.965369i	$0.584015\pi$
$68$	−7.26221	−0.880672
$69$	−10.1257	−1.21899
$70$	−0.978041	−0.116898
$71$	4.68217	0.555671	0.277835	−	0.960629i	$-0.410383\pi$
$71$	4.68217	0.555671	0.277835	+	0.960629i	$0.410383\pi$
$72$	23.0465	2.71605
$73$	−7.43786	−0.870536	−0.435268	−	0.900301i	$-0.643346\pi$
$73$	−7.43786	−0.870536	−0.435268	+	0.900301i	$0.643346\pi$
$74$	0.463913	0.0539288
$75$	−3.27758	−0.378463
$76$	−0.166176	−0.0190616
$77$	−6.25469	−0.712789
$78$	1.30196	0.147418
$79$	11.8977	1.33860	0.669298	−	0.742994i	$-0.266595\pi$
$79$	11.8977	1.33860	0.669298	+	0.742994i	$0.266595\pi$
$80$	0.824374	0.0921678
$81$	27.7193	3.07992
$82$	10.3856	1.14690
$83$	−7.78070	−0.854043	−0.427021	−	0.904241i	$-0.640437\pi$
$83$	−7.78070	−0.854043	−0.427021	+	0.904241i	$0.640437\pi$
$84$	−3.41994	−0.373146
$85$	−6.95990	−0.754908
$86$	−10.6684	−1.15040
$87$	−9.40262	−1.00807
$88$	18.6178	1.98466
$89$	9.37649	0.993905	0.496953	−	0.867778i	$-0.334452\pi$
$89$	9.37649	0.993905	0.496953	+	0.867778i	$0.334452\pi$
$90$	7.57253	0.798214
$91$	−0.406151	−0.0425762
$92$	−3.22357	−0.336081
$93$	8.12971	0.843011
$94$	9.28529	0.957705
$95$	−0.159258	−0.0163395
$96$	16.8695	1.72174
$97$	−8.66452	−0.879748	−0.439874	−	0.898059i	$-0.644977\pi$
$97$	−8.66452	−0.879748	−0.439874	+	0.898059i	$0.644977\pi$
$98$	−0.978041	−0.0987971
$99$	48.4272	4.86712
$100$	−1.04343	−0.104343
$101$	−2.22740	−0.221634	−0.110817	−	0.993841i	$-0.535347\pi$
$101$	−2.22740	−0.221634	−0.110817	+	0.993841i	$0.535347\pi$
$102$	22.3107	2.20909
$103$	−10.4149	−1.02621	−0.513107	−	0.858324i	$-0.671506\pi$
$103$	−10.4149	−1.02621	−0.513107	+	0.858324i	$0.671506\pi$
$104$	1.20895	0.118547
$105$	−3.27758	−0.319859
$106$	2.86944	0.278705
$107$	−0.975372	−0.0942928	−0.0471464	−	0.998888i	$-0.515013\pi$
$107$	−0.975372	−0.0942928	−0.0471464	+	0.998888i	$0.515013\pi$
$108$	16.2192	1.56070
$109$	−12.9016	−1.23575	−0.617874	−	0.786277i	$-0.712006\pi$
$109$	−12.9016	−1.23575	−0.617874	+	0.786277i	$0.712006\pi$
$110$	6.11735	0.583266
$111$	1.55465	0.147561
$112$	0.824374	0.0778960
$113$	−11.7624	−1.10652	−0.553259	−	0.833009i	$-0.686616\pi$
$113$	−11.7624	−1.10652	−0.553259	+	0.833009i	$0.686616\pi$
$114$	0.510520	0.0478146
$115$	−3.08939	−0.288087
$116$	−2.99337	−0.277928
$117$	3.14464	0.290722
$118$	0.908247	0.0836109
$119$	−6.95990	−0.638013
$120$	9.75607	0.890603
$121$	28.1212	2.55647
$122$	0.697723	0.0631688
$123$	34.8039	3.13816
$124$	2.58813	0.232421
$125$	−1.00000	−0.0894427
$126$	7.57253	0.674614
$127$	−8.93611	−0.792952	−0.396476	−	0.918045i	$-0.629767\pi$
$127$	−8.93611	−0.792952	−0.396476	+	0.918045i	$0.629767\pi$
$128$	3.75795	0.332159
$129$	−35.7515	−3.14775
$130$	0.397232	0.0348396
$131$	13.2420	1.15696	0.578481	−	0.815696i	$-0.303646\pi$
$131$	13.2420	1.15696	0.578481	+	0.815696i	$0.303646\pi$
$132$	21.3907	1.86182
$133$	−0.159258	−0.0138094
$134$	4.17712	0.360849
$135$	15.5441	1.33782
$136$	20.7169	1.77646
$137$	−17.9143	−1.53052	−0.765260	−	0.643721i	$-0.777390\pi$
$137$	−17.9143	−1.53052	−0.765260	+	0.643721i	$0.777390\pi$
$138$	9.90337	0.843031
$139$	−3.89523	−0.330389	−0.165194	−	0.986261i	$-0.552825\pi$
$139$	−3.89523	−0.330389	−0.165194	+	0.986261i	$0.552825\pi$
$140$	−1.04343	−0.0881863
$141$	31.1166	2.62049
$142$	−4.57935	−0.384291
$143$	2.54035	0.212435
$144$	−6.38275	−0.531896
$145$	−2.86877	−0.238238
$146$	7.27454	0.602045
$147$	−3.27758	−0.270330
$148$	0.494931	0.0406831
$149$	−9.75173	−0.798893	−0.399446	−	0.916757i	$-0.630798\pi$
$149$	−9.75173	−0.798893	−0.399446	+	0.916757i	$0.630798\pi$
$150$	3.20561	0.261737
$151$	1.20791	0.0982986	0.0491493	−	0.998791i	$-0.484349\pi$
$151$	1.20791	0.0982986	0.0491493	+	0.998791i	$0.484349\pi$
$152$	0.474049	0.0384504
$153$	53.8873	4.35653
$154$	6.11735	0.492950
$155$	2.48040	0.199230
$156$	1.38901	0.111210
$157$	−14.8486	−1.18505	−0.592523	−	0.805553i	$-0.701868\pi$
$157$	−14.8486	−1.18505	−0.592523	+	0.805553i	$0.701868\pi$
$158$	−11.6364	−0.925745
$159$	9.61598	0.762597
$160$	5.14694	0.406901
$161$	−3.08939	−0.243478
$162$	−27.1106	−2.13001
$163$	−1.56751	−0.122777	−0.0613885	−	0.998114i	$-0.519553\pi$
$163$	−1.56751	−0.122777	−0.0613885	+	0.998114i	$0.519553\pi$
$164$	11.0800	0.865202
$165$	20.5003	1.59594
$166$	7.60985	0.590639
$167$	13.3301	1.03151	0.515755	−	0.856736i	$-0.327511\pi$
$167$	13.3301	1.03151	0.515755	+	0.856736i	$0.327511\pi$
$168$	9.75607	0.752697
$169$	−12.8350	−0.987311
$170$	6.80708	0.522079
$171$	1.23306	0.0942947
$172$	−11.3817	−0.867845
$173$	−17.0873	−1.29912	−0.649562	−	0.760309i	$-0.725048\pi$
$173$	−17.0873	−1.29912	−0.649562	+	0.760309i	$0.725048\pi$
$174$	9.19615	0.697158
$175$	−1.00000	−0.0755929
$176$	−5.15621	−0.388664
$177$	3.04369	0.228778
$178$	−9.17059	−0.687365
$179$	−22.1282	−1.65394	−0.826971	−	0.562244i	$-0.809938\pi$
$179$	−22.1282	−1.65394	−0.826971	+	0.562244i	$0.809938\pi$
$180$	8.07884	0.602161
$181$	21.2474	1.57930	0.789652	−	0.613554i	$-0.210261\pi$
$181$	21.2474	1.57930	0.789652	+	0.613554i	$0.210261\pi$
$182$	0.397232	0.0294448
$183$	2.33819	0.172844
$184$	9.19588	0.677929
$185$	0.474329	0.0348734
$186$	−7.95119	−0.583010
$187$	43.5321	3.18338
$188$	9.90612	0.722478
$189$	15.5441	1.13066
$190$	0.155761	0.0113001
$191$	8.95078	0.647656	0.323828	−	0.946116i	$-0.395030\pi$
$191$	8.95078	0.647656	0.323828	+	0.946116i	$0.395030\pi$
$192$	−21.9030	−1.58071
$193$	−24.9737	−1.79764	−0.898822	−	0.438313i	$-0.855576\pi$
$193$	−24.9737	−1.79764	−0.898822	+	0.438313i	$0.855576\pi$
$194$	8.47426	0.608416
$195$	1.33119	0.0953286
$196$	−1.04343	−0.0745311
$197$	−13.5722	−0.966976	−0.483488	−	0.875351i	$-0.660630\pi$
$197$	−13.5722	−0.966976	−0.483488	+	0.875351i	$0.660630\pi$
$198$	−47.3638	−3.36600
$199$	−15.1051	−1.07077	−0.535387	−	0.844607i	$-0.679834\pi$
$199$	−15.1051	−1.07077	−0.535387	+	0.844607i	$0.679834\pi$
$200$	2.97661	0.210478
$201$	13.9982	0.987360
$202$	2.17849	0.153278
$203$	−2.86877	−0.201348
$204$	23.8025	1.66651
$205$	10.6188	0.741647
$206$	10.1862	0.709709
$207$	23.9197	1.66253
$208$	−0.334820	−0.0232156
$209$	0.996111	0.0689024
$210$	3.20561	0.221208
$211$	15.1280	1.04145	0.520726	−	0.853724i	$-0.325661\pi$
$211$	15.1280	1.04145	0.520726	+	0.853724i	$0.325661\pi$
$212$	3.06130	0.210251
$213$	−15.3462	−1.05150
$214$	0.953954	0.0652110
$215$	−10.9079	−0.743912
$216$	−46.2685	−3.14818
$217$	2.48040	0.168380
$218$	12.6183	0.854618
$219$	24.3782	1.64733
$220$	6.52637	0.440007
$221$	2.82677	0.190149
$222$	−1.52051	−0.102050
$223$	23.0631	1.54442	0.772209	−	0.635368i	$-0.219152\pi$
$223$	23.0631	1.54442	0.772209	+	0.635368i	$0.219152\pi$
$224$	5.14694	0.343894
$225$	7.74254	0.516169
$226$	11.5042	0.765245
$227$	−19.8662	−1.31857	−0.659284	−	0.751894i	$-0.729141\pi$
$227$	−19.8662	−1.31857	−0.659284	+	0.751894i	$0.729141\pi$
$228$	0.544654	0.0360706
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	3.02155	0.199235
$231$	20.5003	1.34882
$232$	8.53919	0.560625
$233$	−7.13612	−0.467503	−0.233751	−	0.972296i	$-0.575100\pi$
$233$	−7.13612	−0.467503	−0.233751	+	0.972296i	$0.575100\pi$
$234$	−3.07559	−0.201057
$235$	9.49376	0.619305
$236$	0.968974	0.0630748
$237$	−38.9957	−2.53304
$238$	6.80708	0.441237
$239$	−6.97273	−0.451029	−0.225514	−	0.974240i	$-0.572406\pi$
$239$	−6.97273	−0.451029	−0.225514	+	0.974240i	$0.572406\pi$
$240$	−2.70195	−0.174410
$241$	2.09451	0.134919	0.0674597	−	0.997722i	$-0.478511\pi$
$241$	2.09451	0.134919	0.0674597	+	0.997722i	$0.478511\pi$
$242$	−27.5037	−1.76800
$243$	−44.2201	−2.83672
$244$	0.744373	0.0476536
$245$	−1.00000	−0.0638877
$246$	−34.0396	−2.17029
$247$	0.0646828	0.00411567
$248$	−7.38317	−0.468832
$249$	25.5019	1.61612
$250$	0.978041	0.0618568
$251$	−14.9776	−0.945380	−0.472690	−	0.881229i	$-0.656717\pi$
$251$	−14.9776	−0.945380	−0.472690	+	0.881229i	$0.656717\pi$
$252$	8.07884	0.508919
$253$	19.3232	1.21484
$254$	8.73989	0.548389
$255$	22.8117	1.42852
$256$	−17.0408	−1.06505
$257$	−25.8775	−1.61420	−0.807098	−	0.590418i	$-0.798963\pi$
$257$	−25.8775	−1.61420	−0.807098	+	0.590418i	$0.798963\pi$
$258$	34.9665	2.17692
$259$	0.474329	0.0294734
$260$	0.423792	0.0262825
$261$	22.2115	1.37486
$262$	−12.9513	−0.800131
$263$	2.32532	0.143385	0.0716926	−	0.997427i	$-0.477160\pi$
$263$	2.32532	0.143385	0.0716926	+	0.997427i	$0.477160\pi$
$264$	−61.0212	−3.75560
$265$	2.93386	0.180226
$266$	0.155761	0.00955033
$267$	−30.7322	−1.88078
$268$	4.45641	0.272219
$269$	1.61241	0.0983105	0.0491552	−	0.998791i	$-0.484347\pi$
$269$	1.61241	0.0983105	0.0491552	+	0.998791i	$0.484347\pi$
$270$	−15.2027	−0.925209
$271$	27.5644	1.67442	0.837210	−	0.546882i	$-0.184185\pi$
$271$	27.5644	1.67442	0.837210	+	0.546882i	$0.184185\pi$
$272$	−5.73756	−0.347891
$273$	1.33119	0.0805674
$274$	17.5209	1.05848
$275$	6.25469	0.377172
$276$	10.5655	0.635970
$277$	2.96458	0.178125	0.0890623	−	0.996026i	$-0.471613\pi$
$277$	2.96458	0.178125	0.0890623	+	0.996026i	$0.471613\pi$
$278$	3.80969	0.228490
$279$	−19.2046	−1.14975
$280$	2.97661	0.177886
$281$	−19.3263	−1.15291	−0.576455	−	0.817129i	$-0.695564\pi$
$281$	−19.3263	−1.15291	−0.576455	+	0.817129i	$0.695564\pi$
$282$	−30.4333	−1.81228
$283$	−14.7273	−0.875444	−0.437722	−	0.899110i	$-0.644215\pi$
$283$	−14.7273	−0.875444	−0.437722	+	0.899110i	$0.644215\pi$
$284$	−4.88554	−0.289903
$285$	0.521982	0.0309195
$286$	−2.48457	−0.146915
$287$	10.6188	0.626806
$288$	−39.8504	−2.34821
$289$	31.4403	1.84943
$290$	2.80577	0.164761
$291$	28.3987	1.66476
$292$	7.76093	0.454174
$293$	13.0473	0.762232	0.381116	−	0.924527i	$-0.375540\pi$
$293$	13.0473	0.762232	0.381116	+	0.924527i	$0.375540\pi$
$294$	3.20561	0.186955
$295$	0.928638	0.0540674
$296$	−1.41189	−0.0820644
$297$	−97.2234	−5.64147
$298$	9.53759	0.552498
$299$	1.25476	0.0725644
$300$	3.41994	0.197450
$301$	−10.9079	−0.628721
$302$	−1.18139	−0.0679813
$303$	7.30048	0.419402
$304$	−0.131288	−0.00752990
$305$	0.713388	0.0408485
$306$	−52.7041	−3.01289
$307$	2.44577	0.139587	0.0697937	−	0.997561i	$-0.477766\pi$
$307$	2.44577	0.139587	0.0697937	+	0.997561i	$0.477766\pi$
$308$	6.52637	0.371874
$309$	34.1358	1.94192
$310$	−2.42593	−0.137784
$311$	−18.7571	−1.06362	−0.531810	−	0.846864i	$-0.678488\pi$
$311$	−18.7571	−1.06362	−0.531810	+	0.846864i	$0.678488\pi$
$312$	−3.96243	−0.224329
$313$	10.2655	0.580240	0.290120	−	0.956990i	$-0.406305\pi$
$313$	10.2655	0.580240	0.290120	+	0.956990i	$0.406305\pi$
$314$	14.5225	0.819554
$315$	7.74254	0.436243
$316$	−12.4145	−0.698369
$317$	−30.0861	−1.68981	−0.844903	−	0.534920i	$-0.820342\pi$
$317$	−30.0861	−1.68981	−0.844903	+	0.534920i	$0.820342\pi$
$318$	−9.40483	−0.527397
$319$	17.9433	1.00463
$320$	−6.68267	−0.373572
$321$	3.19686	0.178431
$322$	3.02155	0.168384
$323$	1.10842	0.0616742
$324$	−28.9233	−1.60685
$325$	0.406151	0.0225292
$326$	1.53309	0.0849101
$327$	42.2860	2.33842
$328$	−31.6079	−1.74525
$329$	9.49376	0.523408
$330$	−20.0501	−1.10372
$331$	−22.7395	−1.24987	−0.624937	−	0.780675i	$-0.714875\pi$
$331$	−22.7395	−1.24987	−0.624937	+	0.780675i	$0.714875\pi$
$332$	8.11866	0.445569
$333$	−3.67251	−0.201252
$334$	−13.0373	−0.713372
$335$	4.27091	0.233345
$336$	−2.70195	−0.147404
$337$	5.83713	0.317969	0.158984	−	0.987281i	$-0.449178\pi$
$337$	5.83713	0.317969	0.158984	+	0.987281i	$0.449178\pi$
$338$	12.5532	0.682804
$339$	38.5524	2.09388
$340$	7.26221	0.393848
$341$	−15.5141	−0.840137
$342$	−1.20599	−0.0652123
$343$	−1.00000	−0.0539949
$344$	32.4685	1.75058
$345$	10.1257	0.545150
$346$	16.7121	0.898448
$347$	−34.1402	−1.83274	−0.916372	−	0.400329i	$-0.868896\pi$
$347$	−34.1402	−1.83274	−0.916372	+	0.400329i	$0.868896\pi$
$348$	9.81102	0.525926
$349$	11.1373	0.596165	0.298082	−	0.954540i	$-0.403653\pi$
$349$	11.1373	0.596165	0.298082	+	0.954540i	$0.403653\pi$
$350$	0.978041	0.0522785
$351$	−6.31323	−0.336975
$352$	−32.1925	−1.71587
$353$	34.2623	1.82360	0.911800	−	0.410634i	$-0.134693\pi$
$353$	34.2623	1.82360	0.911800	+	0.410634i	$0.134693\pi$
$354$	−2.97685	−0.158218
$355$	−4.68217	−0.248504
$356$	−9.78375	−0.518538
$357$	22.8117	1.20732
$358$	21.6423	1.14383
$359$	4.54314	0.239778	0.119889	−	0.992787i	$-0.461746\pi$
$359$	4.54314	0.239778	0.119889	+	0.992787i	$0.461746\pi$
$360$	−23.0465	−1.21466
$361$	−18.9746	−0.998665
$362$	−20.7808	−1.09222
$363$	−92.1695	−4.83764
$364$	0.423792	0.0222127
$365$	7.43786	0.389316
$366$	−2.28684	−0.119535
$367$	12.5787	0.656602	0.328301	−	0.944573i	$-0.393524\pi$
$367$	12.5787	0.656602	0.328301	+	0.944573i	$0.393524\pi$
$368$	−2.54681	−0.132762
$369$	−82.2163	−4.28001
$370$	−0.463913	−0.0241177
$371$	2.93386	0.152319
$372$	−8.48282	−0.439814
$373$	25.4812	1.31937	0.659683	−	0.751544i	$-0.270691\pi$
$373$	25.4812	1.31937	0.659683	+	0.751544i	$0.270691\pi$
$374$	−42.5762	−2.20156
$375$	3.27758	0.169254
$376$	−28.2592	−1.45736
$377$	1.16515	0.0600084
$378$	−15.2027	−0.781945
$379$	2.79534	0.143587	0.0717934	−	0.997420i	$-0.477128\pi$
$379$	2.79534	0.143587	0.0717934	+	0.997420i	$0.477128\pi$
$380$	0.166176	0.00852463
$381$	29.2888	1.50051
$382$	−8.75423	−0.447906
$383$	15.6801	0.801215	0.400607	−	0.916250i	$-0.368799\pi$
$383$	15.6801	0.801215	0.400607	+	0.916250i	$0.368799\pi$
$384$	−12.3170	−0.628549
$385$	6.25469	0.318769
$386$	24.4253	1.24321
$387$	84.4548	4.29308
$388$	9.04086	0.458980
$389$	−8.60163	−0.436120	−0.218060	−	0.975935i	$-0.569973\pi$
$389$	−8.60163	−0.436120	−0.218060	+	0.975935i	$0.569973\pi$
$390$	−1.30196	−0.0659274
$391$	21.5018	1.08739
$392$	2.97661	0.150341
$393$	−43.4018	−2.18933
$394$	13.2741	0.668741
$395$	−11.8977	−0.598638
$396$	−50.5307	−2.53926
$397$	−12.4968	−0.627197	−0.313599	−	0.949556i	$-0.601535\pi$
$397$	−12.4968	−0.627197	−0.313599	+	0.949556i	$0.601535\pi$
$398$	14.7734	0.740525
$399$	0.521982	0.0261318
$400$	−0.824374	−0.0412187
$401$	6.92451	0.345794	0.172897	−	0.984940i	$-0.444687\pi$
$401$	6.92451	0.345794	0.172897	+	0.984940i	$0.444687\pi$
$402$	−13.6909	−0.682838
$403$	−1.00742	−0.0501829
$404$	2.32415	0.115631
$405$	−27.7193	−1.37738
$406$	2.80577	0.139248
$407$	−2.96678	−0.147058
$408$	−67.9013	−3.36162
$409$	−25.8226	−1.27684	−0.638422	−	0.769686i	$-0.720413\pi$
$409$	−25.8226	−1.27684	−0.638422	+	0.769686i	$0.720413\pi$
$410$	−10.3856	−0.512908
$411$	58.7155	2.89622
$412$	10.8673	0.535394
$413$	0.928638	0.0456953
$414$	−23.3945	−1.14977
$415$	7.78070	0.381940
$416$	−2.09043	−0.102492
$417$	12.7669	0.625199
$418$	−0.974238	−0.0476515
$419$	−2.31366	−0.113030	−0.0565148	−	0.998402i	$-0.517999\pi$
$419$	−2.31366	−0.113030	−0.0565148	+	0.998402i	$0.517999\pi$
$420$	3.41994	0.166876
$421$	−22.3362	−1.08860	−0.544300	−	0.838890i	$-0.683205\pi$
$421$	−22.3362	−1.08860	−0.544300	+	0.838890i	$0.683205\pi$
$422$	−14.7958	−0.720248
$423$	−73.5058	−3.57398
$424$	−8.73296	−0.424110
$425$	6.95990	0.337605
$426$	15.0092	0.727198
$427$	0.713388	0.0345232
$428$	1.01774	0.0491942
$429$	−8.32620	−0.401993
$430$	10.6684	0.514475
$431$	9.85710	0.474800	0.237400	−	0.971412i	$-0.423705\pi$
$431$	9.85710	0.474800	0.237400	+	0.971412i	$0.423705\pi$
$432$	12.8141	0.616520
$433$	−6.13505	−0.294832	−0.147416	−	0.989075i	$-0.547096\pi$
$433$	−6.13505	−0.294832	−0.147416	+	0.989075i	$0.547096\pi$
$434$	−2.42593	−0.116448
$435$	9.40262	0.450821
$436$	13.4620	0.644711
$437$	0.492010	0.0235360
$438$	−23.8429	−1.13926
$439$	−10.0889	−0.481517	−0.240758	−	0.970585i	$-0.577396\pi$
$439$	−10.0889	−0.481517	−0.240758	+	0.970585i	$0.577396\pi$
$440$	−18.6178	−0.887567
$441$	7.74254	0.368692
$442$	−2.76470	−0.131503
$443$	3.56541	0.169398	0.0846989	−	0.996407i	$-0.473007\pi$
$443$	3.56541	0.169398	0.0846989	+	0.996407i	$0.473007\pi$
$444$	−1.62218	−0.0769852
$445$	−9.37649	−0.444488
$446$	−22.5567	−1.06809
$447$	31.9621	1.51175
$448$	−6.68267	−0.315726
$449$	−0.118465	−0.00559073	−0.00279536	−	0.999996i	$-0.500890\pi$
$449$	−0.118465	−0.00559073	−0.00279536	+	0.999996i	$0.500890\pi$
$450$	−7.57253	−0.356972
$451$	−66.4172	−3.12746
$452$	12.2733	0.577290
$453$	−3.95903	−0.186012
$454$	19.4300	0.911895
$455$	0.406151	0.0190406
$456$	−1.55373	−0.0727602
$457$	−11.6386	−0.544431	−0.272215	−	0.962236i	$-0.587756\pi$
$457$	−11.6386	−0.544431	−0.272215	+	0.962236i	$0.587756\pi$
$458$	0.978041	0.0457009
$459$	−108.185	−5.04965
$460$	3.22357	0.150300
$461$	34.3478	1.59974	0.799868	−	0.600176i	$-0.204903\pi$
$461$	34.3478	1.59974	0.799868	+	0.600176i	$0.204903\pi$
$462$	−20.0501	−0.932816
$463$	7.75542	0.360425	0.180213	−	0.983628i	$-0.442321\pi$
$463$	7.75542	0.360425	0.180213	+	0.983628i	$0.442321\pi$
$464$	−2.36494	−0.109789
$465$	−8.12971	−0.377006
$466$	6.97942	0.323316
$467$	34.1340	1.57953	0.789766	−	0.613408i	$-0.210202\pi$
$467$	34.1340	1.57953	0.789766	+	0.613408i	$0.210202\pi$
$468$	−3.28123	−0.151675
$469$	4.27091	0.197212
$470$	−9.28529	−0.428299
$471$	48.6675	2.24248
$472$	−2.76419	−0.127232
$473$	68.2255	3.13701
$474$	38.1394	1.75180
$475$	0.159258	0.00730727
$476$	7.26221	0.332863
$477$	−22.7156	−1.04007
$478$	6.81962	0.311922
$479$	−18.1112	−0.827523	−0.413762	−	0.910385i	$-0.635785\pi$
$479$	−18.1112	−0.827523	−0.413762	+	0.910385i	$0.635785\pi$
$480$	−16.8695	−0.769984
$481$	−0.192649	−0.00878404
$482$	−2.04852	−0.0933075
$483$	10.1257	0.460736
$484$	−29.3426	−1.33376
$485$	8.66452	0.393435
$486$	43.2491	1.96182
$487$	−13.6731	−0.619586	−0.309793	−	0.950804i	$-0.600260\pi$
$487$	−13.6731	−0.619586	−0.309793	+	0.950804i	$0.600260\pi$
$488$	−2.12347	−0.0961251
$489$	5.13765	0.232332
$490$	0.978041	0.0441834
$491$	−39.6099	−1.78757	−0.893785	−	0.448496i	$-0.851960\pi$
$491$	−39.6099	−1.78757	−0.893785	+	0.448496i	$0.851960\pi$
$492$	−36.3156	−1.63723
$493$	19.9663	0.899239
$494$	−0.0632625	−0.00284631
$495$	−48.4272	−2.17664
$496$	2.04478	0.0918131
$497$	−4.68217	−0.210024
$498$	−24.9419	−1.11767
$499$	−10.7799	−0.482574	−0.241287	−	0.970454i	$-0.577570\pi$
$499$	−10.7799	−0.482574	−0.241287	+	0.970454i	$0.577570\pi$
$500$	1.04343	0.0466638
$501$	−43.6903	−1.95194
$502$	14.6488	0.653806
$503$	−13.4315	−0.598881	−0.299441	−	0.954115i	$-0.596800\pi$
$503$	−13.4315	−0.598881	−0.299441	+	0.954115i	$0.596800\pi$
$504$	−23.0465	−1.02657
$505$	2.22740	0.0991180
$506$	−18.8989	−0.840156
$507$	42.0679	1.86830
$508$	9.32425	0.413697
$509$	−10.0625	−0.446012	−0.223006	−	0.974817i	$-0.571587\pi$
$509$	−10.0625	−0.446012	−0.223006	+	0.974817i	$0.571587\pi$
$510$	−22.3107	−0.987936
$511$	7.43786	0.329032
$512$	9.15067	0.404406
$513$	−2.47552	−0.109297
$514$	25.3093	1.11634
$515$	10.4149	0.458937
$516$	37.3044	1.64223
$517$	−59.3806	−2.61155
$518$	−0.463913	−0.0203832
$519$	56.0050	2.45835
$520$	−1.20895	−0.0530160
$521$	−13.2246	−0.579382	−0.289691	−	0.957120i	$-0.593553\pi$
$521$	−13.2246	−0.579382	−0.289691	+	0.957120i	$0.593553\pi$
$522$	−21.7238	−0.950825
$523$	−19.2636	−0.842337	−0.421169	−	0.906982i	$-0.638380\pi$
$523$	−19.2636	−0.842337	−0.421169	+	0.906982i	$0.638380\pi$
$524$	−13.8172	−0.603607
$525$	3.27758	0.143045
$526$	−2.27426	−0.0991623
$527$	−17.2633	−0.752003
$528$	16.8999	0.735473
$529$	−13.4557	−0.585030
$530$	−2.86944	−0.124641
$531$	−7.19002	−0.312020
$532$	0.166176	0.00720462
$533$	−4.31282	−0.186809
$534$	30.0574	1.30071
$535$	0.975372	0.0421690
$536$	−12.7128	−0.549110
$537$	72.5271	3.12978
$538$	−1.57701	−0.0679895
$539$	6.25469	0.269409
$540$	−16.2192	−0.697964
$541$	−12.0499	−0.518064	−0.259032	−	0.965869i	$-0.583404\pi$
$541$	−12.0499	−0.518064	−0.259032	+	0.965869i	$0.583404\pi$
$542$	−26.9591	−1.15799
$543$	−69.6400	−2.98854
$544$	−35.8222	−1.53586
$545$	12.9016	0.552643
$546$	−1.30196	−0.0557188
$547$	19.1753	0.819878	0.409939	−	0.912113i	$-0.365550\pi$
$547$	19.1753	0.819878	0.409939	+	0.912113i	$0.365550\pi$
$548$	18.6924	0.798499
$549$	−5.52343	−0.235734
$550$	−6.11735	−0.260845
$551$	0.456875	0.0194635
$552$	−30.1403	−1.28285
$553$	−11.8977	−0.505941
$554$	−2.89949	−0.123187
$555$	−1.55465	−0.0659913
$556$	4.06442	0.172370
$557$	33.6238	1.42469	0.712343	−	0.701831i	$-0.247634\pi$
$557$	33.6238	1.42469	0.712343	+	0.701831i	$0.247634\pi$
$558$	18.7829	0.795143
$559$	4.43025	0.187380
$560$	−0.824374	−0.0348362
$561$	−142.680	−6.02395
$562$	18.9019	0.797329
$563$	11.6723	0.491927	0.245963	−	0.969279i	$-0.420896\pi$
$563$	11.6723	0.491927	0.245963	+	0.969279i	$0.420896\pi$
$564$	−32.4681	−1.36715
$565$	11.7624	0.494850
$566$	14.4039	0.605440
$567$	−27.7193	−1.16410
$568$	13.9370	0.584782
$569$	−2.08284	−0.0873173	−0.0436587	−	0.999047i	$-0.513901\pi$
$569$	−2.08284	−0.0873173	−0.0436587	+	0.999047i	$0.513901\pi$
$570$	−0.510520	−0.0213833
$571$	−6.92491	−0.289798	−0.144899	−	0.989446i	$-0.546286\pi$
$571$	−6.92491	−0.289798	−0.144899	+	0.989446i	$0.546286\pi$
$572$	−2.65069	−0.110831
$573$	−29.3369	−1.22557
$574$	−10.3856	−0.433487
$575$	3.08939	0.128836
$576$	51.7408	2.15587
$577$	−33.2343	−1.38356	−0.691781	−	0.722107i	$-0.743174\pi$
$577$	−33.2343	−1.38356	−0.691781	+	0.722107i	$0.743174\pi$
$578$	−30.7499	−1.27903
$579$	81.8533	3.40171
$580$	2.99337	0.124293
$581$	7.78070	0.322798
$582$	−27.7751	−1.15131
$583$	−18.3504	−0.759997
$584$	−22.1396	−0.916142
$585$	−3.14464	−0.130015
$586$	−12.7608	−0.527144
$587$	32.1297	1.32614	0.663068	−	0.748559i	$-0.269254\pi$
$587$	32.1297	1.32614	0.663068	+	0.748559i	$0.269254\pi$
$588$	3.41994	0.141036
$589$	−0.395024	−0.0162767
$590$	−0.908247	−0.0373919
$591$	44.4838	1.82982
$592$	0.391024	0.0160710
$593$	−3.02199	−0.124098	−0.0620491	−	0.998073i	$-0.519764\pi$
$593$	−3.02199	−0.124098	−0.0620491	+	0.998073i	$0.519764\pi$
$594$	95.0885	3.90153
$595$	6.95990	0.285328
$596$	10.1753	0.416796
$597$	49.5083	2.02624
$598$	−1.22720	−0.0501841
$599$	−28.7694	−1.17549	−0.587744	−	0.809047i	$-0.699984\pi$
$599$	−28.7694	−1.17549	−0.587744	+	0.809047i	$0.699984\pi$
$600$	−9.75607	−0.398290
$601$	30.2365	1.23337	0.616685	−	0.787210i	$-0.288475\pi$
$601$	30.2365	1.23337	0.616685	+	0.787210i	$0.288475\pi$
$602$	10.6684	0.434810
$603$	−33.0677	−1.34662
$604$	−1.26038	−0.0512841
$605$	−28.1212	−1.14329
$606$	−7.14017	−0.290050
$607$	−38.4891	−1.56222	−0.781112	−	0.624391i	$-0.785347\pi$
$607$	−38.4891	−1.56222	−0.781112	+	0.624391i	$0.785347\pi$
$608$	−0.819692	−0.0332429
$609$	9.40262	0.381013
$610$	−0.697723	−0.0282500
$611$	−3.85590	−0.155993
$612$	−56.2279	−2.27288
$613$	12.5024	0.504965	0.252483	−	0.967601i	$-0.418753\pi$
$613$	12.5024	0.504965	0.252483	+	0.967601i	$0.418753\pi$
$614$	−2.39206	−0.0965359
$615$	−34.8039	−1.40343
$616$	−18.6178	−0.750131
$617$	−16.5813	−0.667538	−0.333769	−	0.942655i	$-0.608321\pi$
$617$	−16.5813	−0.667538	−0.333769	+	0.942655i	$0.608321\pi$
$618$	−33.3863	−1.34299
$619$	3.36647	0.135310	0.0676548	−	0.997709i	$-0.478448\pi$
$619$	3.36647	0.135310	0.0676548	+	0.997709i	$0.478448\pi$
$620$	−2.58813	−0.103942
$621$	−48.0216	−1.92704
$622$	18.3453	0.735578
$623$	−9.37649	−0.375661
$624$	1.09740	0.0439312
$625$	1.00000	0.0400000
$626$	−10.0401	−0.401282
$627$	−3.26484	−0.130385
$628$	15.4935	0.618259
$629$	−3.30128	−0.131631
$630$	−7.57253	−0.301697
$631$	−34.9738	−1.39228	−0.696142	−	0.717904i	$-0.745102\pi$
$631$	−34.9738	−1.39228	−0.696142	+	0.717904i	$0.745102\pi$
$632$	35.4147	1.40872
$633$	−49.5832	−1.97075
$634$	29.4255	1.16864
$635$	8.93611	0.354619
$636$	−10.0336	−0.397860
$637$	0.406151	0.0160923
$638$	−17.5492	−0.694781
$639$	36.2519	1.43410
$640$	−3.75795	−0.148546
$641$	27.4469	1.08409	0.542043	−	0.840351i	$-0.317651\pi$
$641$	27.4469	1.08409	0.542043	+	0.840351i	$0.317651\pi$
$642$	−3.12666	−0.123400
$643$	−21.8284	−0.860826	−0.430413	−	0.902632i	$-0.641632\pi$
$643$	−21.8284	−0.860826	−0.430413	+	0.902632i	$0.641632\pi$
$644$	3.22357	0.127027
$645$	35.7515	1.40771
$646$	−1.08408	−0.0426527
$647$	−33.5464	−1.31885	−0.659423	−	0.751772i	$-0.729199\pi$
$647$	−33.5464	−1.31885	−0.659423	+	0.751772i	$0.729199\pi$
$648$	82.5095	3.24128
$649$	−5.80835	−0.227998
$650$	−0.397232	−0.0155807
$651$	−8.12971	−0.318628
$652$	1.63560	0.0640549
$653$	47.8325	1.87183	0.935916	−	0.352223i	$-0.114574\pi$
$653$	47.8325	1.87183	0.935916	+	0.352223i	$0.114574\pi$
$654$	−41.3575	−1.61721
$655$	−13.2420	−0.517409
$656$	8.75384	0.341780
$657$	−57.5880	−2.24672
$658$	−9.28529	−0.361978
$659$	11.2100	0.436680	0.218340	−	0.975873i	$-0.429936\pi$
$659$	11.2100	0.436680	0.218340	+	0.975873i	$0.429936\pi$
$660$	−21.3907	−0.832632
$661$	1.89785	0.0738179	0.0369089	−	0.999319i	$-0.488249\pi$
$661$	1.89785	0.0738179	0.0369089	+	0.999319i	$0.488249\pi$
$662$	22.2401	0.864387
$663$	−9.26497	−0.359822
$664$	−23.1601	−0.898785
$665$	0.159258	0.00617577
$666$	3.59187	0.139182
$667$	8.86273	0.343166
$668$	−13.9090	−0.538157
$669$	−75.5912	−2.92252
$670$	−4.17712	−0.161376
$671$	−4.46202	−0.172254
$672$	−16.8695	−0.650756
$673$	46.6773	1.79928	0.899639	−	0.436635i	$-0.143830\pi$
$673$	46.6773	1.79928	0.899639	+	0.436635i	$0.143830\pi$
$674$	−5.70895	−0.219901
$675$	−15.5441	−0.598291
$676$	13.3925	0.515097
$677$	−18.9603	−0.728705	−0.364352	−	0.931261i	$-0.618710\pi$
$677$	−18.9603	−0.728705	−0.364352	+	0.931261i	$0.618710\pi$
$678$	−37.7058	−1.44808
$679$	8.66452	0.332514
$680$	−20.7169	−0.794456
$681$	65.1132	2.49514
$682$	15.1735	0.581022
$683$	9.97057	0.381513	0.190757	−	0.981637i	$-0.438906\pi$
$683$	9.97057	0.381513	0.190757	+	0.981637i	$0.438906\pi$
$684$	−1.28662	−0.0491952
$685$	17.9143	0.684469
$686$	0.978041	0.0373418
$687$	3.27758	0.125048
$688$	−8.99218	−0.342824
$689$	−1.19159	−0.0453960
$690$	−9.90337	−0.377015
$691$	23.3836	0.889552	0.444776	−	0.895642i	$-0.353283\pi$
$691$	23.3836	0.889552	0.444776	+	0.895642i	$0.353283\pi$
$692$	17.8295	0.677776
$693$	−48.4272	−1.83960
$694$	33.3906	1.26749
$695$	3.89523	0.147754
$696$	−27.9879	−1.06088
$697$	−73.9056	−2.79938
$698$	−10.8927	−0.412296
$699$	23.3892	0.884662
$700$	1.04343	0.0394381
$701$	23.7835	0.898290	0.449145	−	0.893459i	$-0.351729\pi$
$701$	23.7835	0.898290	0.449145	+	0.893459i	$0.351729\pi$
$702$	6.17460	0.233045
$703$	−0.0755408	−0.00284907
$704$	41.7980	1.57532
$705$	−31.1166	−1.17192
$706$	−33.5100	−1.26116
$707$	2.22740	0.0837700
$708$	−3.17589	−0.119357
$709$	38.8764	1.46003	0.730017	−	0.683429i	$-0.239512\pi$
$709$	38.8764	1.46003	0.730017	+	0.683429i	$0.239512\pi$
$710$	4.57935	0.171860
$711$	92.1184	3.45471
$712$	27.9101	1.04598
$713$	−7.66291	−0.286978
$714$	−22.3107	−0.834959
$715$	−2.54035	−0.0950036
$716$	23.0894	0.862891
$717$	22.8537	0.853487
$718$	−4.44338	−0.165825
$719$	47.5781	1.77437	0.887183	−	0.461419i	$-0.152659\pi$
$719$	47.5781	1.77437	0.887183	+	0.461419i	$0.152659\pi$
$720$	6.38275	0.237871
$721$	10.4149	0.387873
$722$	18.5580	0.690657
$723$	−6.86493	−0.255310
$724$	−22.1703	−0.823951
$725$	2.86877	0.106543
$726$	90.1456	3.34562
$727$	−3.26849	−0.121222	−0.0606108	−	0.998161i	$-0.519305\pi$
$727$	−3.26849	−0.121222	−0.0606108	+	0.998161i	$0.519305\pi$
$728$	−1.20895	−0.0448067
$729$	61.7771	2.28804
$730$	−7.27454	−0.269243
$731$	75.9179	2.80792
$732$	−2.43974	−0.0901756
$733$	2.93901	0.108555	0.0542774	−	0.998526i	$-0.482714\pi$
$733$	2.93901	0.108555	0.0542774	+	0.998526i	$0.482714\pi$
$734$	−12.3025	−0.454093
$735$	3.27758	0.120895
$736$	−15.9009	−0.586114
$737$	−26.7132	−0.983994
$738$	80.4109	2.95997
$739$	−9.71564	−0.357396	−0.178698	−	0.983904i	$-0.557188\pi$
$739$	−9.71564	−0.357396	−0.178698	+	0.983904i	$0.557188\pi$
$740$	−0.494931	−0.0181940
$741$	−0.212003	−0.00778813
$742$	−2.86944	−0.105340
$743$	31.6351	1.16058	0.580290	−	0.814410i	$-0.302939\pi$
$743$	31.6351	1.16058	0.580290	+	0.814410i	$0.302939\pi$
$744$	24.1989	0.887176
$745$	9.75173	0.357276
$746$	−24.9217	−0.912447
$747$	−60.2424	−2.20415
$748$	−45.4229	−1.66083
$749$	0.975372	0.0356393
$750$	−3.20561	−0.117052
$751$	18.9999	0.693318	0.346659	−	0.937991i	$-0.387316\pi$
$751$	18.9999	0.693318	0.346659	+	0.937991i	$0.387316\pi$
$752$	7.82641	0.285400
$753$	49.0904	1.78895
$754$	−1.13957	−0.0415006
$755$	−1.20791	−0.0439605
$756$	−16.2192	−0.589887
$757$	−47.9625	−1.74323	−0.871613	−	0.490195i	$-0.836926\pi$
$757$	−47.9625	−1.74323	−0.871613	+	0.490195i	$0.836926\pi$
$758$	−2.73395	−0.0993017
$759$	−63.3332	−2.29885
$760$	−0.474049	−0.0171956
$761$	−37.8219	−1.37104	−0.685521	−	0.728053i	$-0.740425\pi$
$761$	−37.8219	−1.37104	−0.685521	+	0.728053i	$0.740425\pi$
$762$	−28.6457	−1.03772
$763$	12.9016	0.467069
$764$	−9.33956	−0.337893
$765$	−53.8873	−1.94830
$766$	−15.3358	−0.554104
$767$	−0.377167	−0.0136187
$768$	55.8525	2.01540
$769$	−5.91288	−0.213224	−0.106612	−	0.994301i	$-0.534000\pi$
$769$	−5.91288	−0.213224	−0.106612	+	0.994301i	$0.534000\pi$
$770$	−6.11735	−0.220454
$771$	84.8157	3.05456
$772$	26.0584	0.937863
$773$	32.0903	1.15421	0.577104	−	0.816671i	$-0.304183\pi$
$773$	32.0903	1.15421	0.577104	+	0.816671i	$0.304183\pi$
$774$	−82.6003	−2.96901
$775$	−2.48040	−0.0890985
$776$	−25.7908	−0.925837
$777$	−1.55465	−0.0557728
$778$	8.41275	0.301612
$779$	−1.69113	−0.0605909
$780$	−1.38901	−0.0497346
$781$	29.2855	1.04792
$782$	−21.0297	−0.752020
$783$	−44.5923	−1.59360
$784$	−0.824374	−0.0294419
$785$	14.8486	0.529969
$786$	42.4488	1.51410
$787$	8.20302	0.292406	0.146203	−	0.989255i	$-0.453295\pi$
$787$	8.20302	0.292406	0.146203	+	0.989255i	$0.453295\pi$
$788$	14.1617	0.504488
$789$	−7.62142	−0.271330
$790$	11.6364	0.414006
$791$	11.7624	0.418224
$792$	144.149	5.12210
$793$	−0.289743	−0.0102891
$794$	12.2224	0.433757
$795$	−9.61598	−0.341044
$796$	15.7612	0.558641
$797$	−48.1668	−1.70616	−0.853078	−	0.521784i	$-0.825267\pi$
$797$	−48.1668	−1.70616	−0.853078	+	0.521784i	$0.825267\pi$
$798$	−0.510520	−0.0180722
$799$	−66.0757	−2.33759
$800$	−5.14694	−0.181972
$801$	72.5978	2.56512
$802$	−6.77246	−0.239144
$803$	−46.5216	−1.64171
$804$	−14.6063	−0.515123
$805$	3.08939	0.108887
$806$	0.985294	0.0347055
$807$	−5.28481	−0.186034
$808$	−6.63009	−0.233246
$809$	−23.7584	−0.835302	−0.417651	−	0.908608i	$-0.637146\pi$
$809$	−23.7584	−0.835302	−0.417651	+	0.908608i	$0.637146\pi$
$810$	27.1106	0.952571
$811$	−0.570202	−0.0200225	−0.0100112	−	0.999950i	$-0.503187\pi$
$811$	−0.570202	−0.0200225	−0.0100112	+	0.999950i	$0.503187\pi$
$812$	2.99337	0.105047
$813$	−90.3446	−3.16852
$814$	2.90164	0.101702
$815$	1.56751	0.0549075
$816$	18.8053	0.658318
$817$	1.73717	0.0607759
$818$	25.2556	0.883040
$819$	−3.14464	−0.109883
$820$	−11.0800	−0.386930
$821$	32.1608	1.12242	0.561209	−	0.827674i	$-0.310336\pi$
$821$	32.1608	1.12242	0.561209	+	0.827674i	$0.310336\pi$
$822$	−57.4262	−2.00297
$823$	14.3586	0.500510	0.250255	−	0.968180i	$-0.419486\pi$
$823$	14.3586	0.500510	0.250255	+	0.968180i	$0.419486\pi$
$824$	−31.0012	−1.07998
$825$	−20.5003	−0.713728
$826$	−0.908247	−0.0316019
$827$	45.0432	1.56631	0.783153	−	0.621829i	$-0.213610\pi$
$827$	45.0432	1.56631	0.783153	+	0.621829i	$0.213610\pi$
$828$	−24.9586	−0.867373
$829$	−48.7429	−1.69291	−0.846455	−	0.532460i	$-0.821268\pi$
$829$	−48.7429	−1.69291	−0.846455	+	0.532460i	$0.821268\pi$
$830$	−7.60985	−0.264142
$831$	−9.71666	−0.337067
$832$	2.71417	0.0940969
$833$	6.95990	0.241146
$834$	−12.4866	−0.432375
$835$	−13.3301	−0.461306
$836$	−1.03938	−0.0359476
$837$	38.5555	1.33267
$838$	2.26285	0.0781690
$839$	−12.3932	−0.427861	−0.213931	−	0.976849i	$-0.568627\pi$
$839$	−12.3932	−0.427861	−0.213931	+	0.976849i	$0.568627\pi$
$840$	−9.75607	−0.336616
$841$	−20.7702	−0.716213
$842$	21.8457	0.752854
$843$	63.3435	2.18166
$844$	−15.7851	−0.543344
$845$	12.8350	0.441539
$846$	71.8918	2.47169
$847$	−28.1212	−0.966256
$848$	2.41860	0.0830551
$849$	48.2698	1.65661
$850$	−6.80708	−0.233481
$851$	−1.46538	−0.0502327
$852$	16.0127	0.548587
$853$	−26.6225	−0.911538	−0.455769	−	0.890098i	$-0.650636\pi$
$853$	−26.6225	−0.911538	−0.455769	+	0.890098i	$0.650636\pi$
$854$	−0.697723	−0.0238756
$855$	−1.23306	−0.0421699
$856$	−2.90330	−0.0992327
$857$	17.8318	0.609123	0.304561	−	0.952493i	$-0.401490\pi$
$857$	17.8318	0.609123	0.304561	+	0.952493i	$0.401490\pi$
$858$	8.14337	0.278010
$859$	4.75090	0.162099	0.0810494	−	0.996710i	$-0.474173\pi$
$859$	4.75090	0.162099	0.0810494	+	0.996710i	$0.474173\pi$
$860$	11.3817	0.388112
$861$	−34.8039	−1.18611
$862$	−9.64065	−0.328362
$863$	42.2984	1.43985	0.719927	−	0.694049i	$-0.244175\pi$
$863$	42.2984	1.43985	0.719927	+	0.694049i	$0.244175\pi$
$864$	80.0044	2.72180
$865$	17.0873	0.580986
$866$	6.00033	0.203900
$867$	−103.048	−3.49970
$868$	−2.58813	−0.0878470
$869$	74.4164	2.52440
$870$	−9.19615	−0.311779
$871$	−1.73463	−0.0587758
$872$	−38.4029	−1.30049
$873$	−67.0854	−2.27050
$874$	−0.481206	−0.0162770
$875$	1.00000	0.0338062
$876$	−25.4371	−0.859439
$877$	−44.0544	−1.48761	−0.743806	−	0.668396i	$-0.766981\pi$
$877$	−44.0544	−1.48761	−0.743806	+	0.668396i	$0.766981\pi$
$878$	9.86736	0.333007
$879$	−42.7636	−1.44238
$880$	5.15621	0.173816
$881$	−29.2700	−0.986130	−0.493065	−	0.869992i	$-0.664124\pi$
$881$	−29.2700	−0.986130	−0.493065	+	0.869992i	$0.664124\pi$
$882$	−7.57253	−0.254980
$883$	41.9012	1.41009	0.705043	−	0.709164i	$-0.250928\pi$
$883$	41.9012	1.41009	0.705043	+	0.709164i	$0.250928\pi$
$884$	−2.94955	−0.0992041
$885$	−3.04369	−0.102312
$886$	−3.48712	−0.117152
$887$	16.7120	0.561135	0.280567	−	0.959834i	$-0.409477\pi$
$887$	16.7120	0.561135	0.280567	+	0.959834i	$0.409477\pi$
$888$	4.62758	0.155292
$889$	8.93611	0.299708
$890$	9.17059	0.307399
$891$	173.376	5.80831
$892$	−24.0648	−0.805750
$893$	−1.51196	−0.0505958
$894$	−31.2602	−1.04550
$895$	22.1282	0.739666
$896$	−3.75795	−0.125544
$897$	−4.11257	−0.137315
$898$	0.115864	0.00386643
$899$	−7.11568	−0.237321
$900$	−8.07884	−0.269295
$901$	−20.4194	−0.680269
$902$	64.9587	2.16289
$903$	35.7515	1.18974
$904$	−35.0122	−1.16449
$905$	−21.2474	−0.706287
$906$	3.87210	0.128642
$907$	43.5775	1.44697	0.723484	−	0.690342i	$-0.242540\pi$
$907$	43.5775	1.44697	0.723484	+	0.690342i	$0.242540\pi$
$908$	20.7291	0.687920
$909$	−17.2457	−0.572005
$910$	−0.397232	−0.0131681
$911$	−31.6562	−1.04882	−0.524409	−	0.851467i	$-0.675714\pi$
$911$	−31.6562	−1.04882	−0.524409	+	0.851467i	$0.675714\pi$
$912$	0.430308	0.0142489
$913$	−48.6659	−1.61061
$914$	11.3830	0.376517
$915$	−2.33819	−0.0772980
$916$	1.04343	0.0344761
$917$	−13.2420	−0.437290
$918$	105.810	3.49224
$919$	12.7294	0.419905	0.209952	−	0.977712i	$-0.432669\pi$
$919$	12.7294	0.419905	0.209952	+	0.977712i	$0.432669\pi$
$920$	−9.19588	−0.303179
$921$	−8.01621	−0.264143
$922$	−33.5936	−1.10634
$923$	1.90166	0.0625941
$924$	−21.3907	−0.703702
$925$	−0.474329	−0.0155958
$926$	−7.58513	−0.249263
$927$	−80.6381	−2.64850
$928$	−14.7654	−0.484697
$929$	−53.6338	−1.75967	−0.879833	−	0.475283i	$-0.842346\pi$
$929$	−53.6338	−1.75967	−0.879833	+	0.475283i	$0.842346\pi$
$930$	7.95119	0.260730
$931$	0.159258	0.00521948
$932$	7.44608	0.243904
$933$	61.4781	2.01270
$934$	−33.3845	−1.09237
$935$	−43.5321	−1.42365
$936$	9.36035	0.305953
$937$	12.0167	0.392569	0.196284	−	0.980547i	$-0.437112\pi$
$937$	12.0167	0.392569	0.196284	+	0.980547i	$0.437112\pi$
$938$	−4.17712	−0.136388
$939$	−33.6460	−1.09800
$940$	−9.90612	−0.323102
$941$	40.7325	1.32784	0.663921	−	0.747803i	$-0.268891\pi$
$941$	40.7325	1.32784	0.663921	+	0.747803i	$0.268891\pi$
$942$	−47.5988	−1.55085
$943$	−32.8055	−1.06829
$944$	0.765545	0.0249164
$945$	−15.5441	−0.505648
$946$	−66.7274	−2.16949
$947$	51.1967	1.66367	0.831835	−	0.555022i	$-0.187290\pi$
$947$	51.1967	1.66367	0.831835	+	0.555022i	$0.187290\pi$
$948$	40.6894	1.32153
$949$	−3.02089	−0.0980623
$950$	−0.155761	−0.00505356
$951$	98.6097	3.19764
$952$	−20.7169	−0.671438
$953$	−47.1544	−1.52748	−0.763740	−	0.645524i	$-0.776639\pi$
$953$	−47.1544	−1.52748	−0.763740	+	0.645524i	$0.776639\pi$
$954$	22.2168	0.719294
$955$	−8.95078	−0.289640
$956$	7.27559	0.235309
$957$	−58.8105	−1.90107
$958$	17.7135	0.572298
$959$	17.9143	0.578482
$960$	21.9030	0.706916
$961$	−24.8476	−0.801536
$962$	0.188419	0.00607486
$963$	−7.55186	−0.243355
$964$	−2.18549	−0.0703898
$965$	24.9737	0.803931
$966$	−9.90337	−0.318636
$967$	−54.6252	−1.75663	−0.878314	−	0.478084i	$-0.841331\pi$
$967$	−54.6252	−1.75663	−0.878314	+	0.478084i	$0.841331\pi$
$968$	83.7057	2.69040
$969$	−3.63294	−0.116707
$970$	−8.47426	−0.272092
$971$	38.0400	1.22076	0.610381	−	0.792108i	$-0.291017\pi$
$971$	38.0400	1.22076	0.610381	+	0.792108i	$0.291017\pi$
$972$	46.1408	1.47997
$973$	3.89523	0.124875
$974$	13.3728	0.428493
$975$	−1.33119	−0.0426323
$976$	0.588098	0.0188246
$977$	−8.08574	−0.258686	−0.129343	−	0.991600i	$-0.541287\pi$
$977$	−8.08574	−0.258686	−0.129343	+	0.991600i	$0.541287\pi$
$978$	−5.02483	−0.160676
$979$	58.6470	1.87437
$980$	1.04343	0.0333313
$981$	−99.8911	−3.18928
$982$	38.7401	1.23625
$983$	−46.2785	−1.47605	−0.738027	−	0.674771i	$-0.764242\pi$
$983$	−46.2785	−1.47605	−0.738027	+	0.674771i	$0.764242\pi$
$984$	103.597	3.30257
$985$	13.5722	0.432445
$986$	−19.5279	−0.621895
$987$	−31.1166	−0.990452
$988$	−0.0674923	−0.00214722
$989$	33.6987	1.07156
$990$	47.3638	1.50532
$991$	39.3783	1.25089	0.625447	−	0.780267i	$-0.284917\pi$
$991$	39.3783	1.25089	0.625447	+	0.780267i	$0.284917\pi$
$992$	12.7665	0.405335
$993$	74.5304	2.36515
$994$	4.57935	0.145248
$995$	15.1051	0.478865
$996$	−26.6096	−0.843156
$997$	18.0434	0.571441	0.285720	−	0.958313i	$-0.407767\pi$
$997$	18.0434	0.571441	0.285720	+	0.958313i	$0.407767\pi$
$998$	10.5432	0.333738
$999$	7.37300	0.233271

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.k.1.18	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.k.1.18	✓	49	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)

\(f(q)\)	\(=\)	\(q-0.978041 q^{2} -3.27758 q^{3} -1.04343 q^{4} -1.00000 q^{5} +3.20561 q^{6} -1.00000 q^{7} +2.97661 q^{8} +7.74254 q^{9} +O(q^{10})\)	\(q-0.978041 q^{2} -3.27758 q^{3} -1.04343 q^{4} -1.00000 q^{5} +3.20561 q^{6} -1.00000 q^{7} +2.97661 q^{8} +7.74254 q^{9} +0.978041 q^{10} +6.25469 q^{11} +3.41994 q^{12} +0.406151 q^{13} +0.978041 q^{14} +3.27758 q^{15} -0.824374 q^{16} +6.95990 q^{17} -7.57253 q^{18} +0.159258 q^{19} +1.04343 q^{20} +3.27758 q^{21} -6.11735 q^{22} +3.08939 q^{23} -9.75607 q^{24} +1.00000 q^{25} -0.397232 q^{26} -15.5441 q^{27} +1.04343 q^{28} +2.86877 q^{29} -3.20561 q^{30} -2.48040 q^{31} -5.14694 q^{32} -20.5003 q^{33} -6.80708 q^{34} +1.00000 q^{35} -8.07884 q^{36} -0.474329 q^{37} -0.155761 q^{38} -1.33119 q^{39} -2.97661 q^{40} -10.6188 q^{41} -3.20561 q^{42} +10.9079 q^{43} -6.52637 q^{44} -7.74254 q^{45} -3.02155 q^{46} -9.49376 q^{47} +2.70195 q^{48} +1.00000 q^{49} -0.978041 q^{50} -22.8117 q^{51} -0.423792 q^{52} -2.93386 q^{53} +15.2027 q^{54} -6.25469 q^{55} -2.97661 q^{56} -0.521982 q^{57} -2.80577 q^{58} -0.928638 q^{59} -3.41994 q^{60} -0.713388 q^{61} +2.42593 q^{62} -7.74254 q^{63} +6.68267 q^{64} -0.406151 q^{65} +20.0501 q^{66} -4.27091 q^{67} -7.26221 q^{68} -10.1257 q^{69} -0.978041 q^{70} +4.68217 q^{71} +23.0465 q^{72} -7.43786 q^{73} +0.463913 q^{74} -3.27758 q^{75} -0.166176 q^{76} -6.25469 q^{77} +1.30196 q^{78} +11.8977 q^{79} +0.824374 q^{80} +27.7193 q^{81} +10.3856 q^{82} -7.78070 q^{83} -3.41994 q^{84} -6.95990 q^{85} -10.6684 q^{86} -9.40262 q^{87} +18.6178 q^{88} +9.37649 q^{89} +7.57253 q^{90} -0.406151 q^{91} -3.22357 q^{92} +8.12971 q^{93} +9.28529 q^{94} -0.159258 q^{95} +16.8695 q^{96} -8.66452 q^{97} -0.978041 q^{98} +48.4272 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9} + 3 q^{10} + 16 q^{11} - 26 q^{12} - 31 q^{13} + 3 q^{14} + 10 q^{15} + 49 q^{16} - 18 q^{17} + 4 q^{18} - 16 q^{19} - 49 q^{20} + 10 q^{21} + 10 q^{22} + 10 q^{23} + 2 q^{24} + 49 q^{25} - 22 q^{26} - 58 q^{27} - 49 q^{28} + 31 q^{29} - 10 q^{30} - 35 q^{31} - 5 q^{32} - 82 q^{33} - 41 q^{34} + 49 q^{35} + 49 q^{36} - 24 q^{37} - 20 q^{38} + 41 q^{39} + 6 q^{40} + 30 q^{41} - 10 q^{42} - 19 q^{43} + 27 q^{44} - 39 q^{45} + 15 q^{46} - 39 q^{47} - 51 q^{48} + 49 q^{49} - 3 q^{50} + 46 q^{51} - 94 q^{52} - 17 q^{53} + 9 q^{54} - 16 q^{55} + 6 q^{56} - 23 q^{57} - 46 q^{58} + 11 q^{59} + 26 q^{60} - 9 q^{61} - 49 q^{62} - 39 q^{63} + 10 q^{64} + 31 q^{65} - 10 q^{66} - 2 q^{67} - 73 q^{68} - 47 q^{69} - 3 q^{70} + 26 q^{71} - 39 q^{72} - 100 q^{73} + 8 q^{74} - 10 q^{75} - 71 q^{76} - 16 q^{77} - 51 q^{78} + 50 q^{79} - 49 q^{80} + 61 q^{81} - 36 q^{82} - 67 q^{83} + 26 q^{84} + 18 q^{85} + 33 q^{86} - 45 q^{87} - q^{88} - 19 q^{89} - 4 q^{90} + 31 q^{91} + 7 q^{92} + 9 q^{93} - 33 q^{94} + 16 q^{95} - 8 q^{96} - 85 q^{97} - 3 q^{98} + 27 q^{99}+O(q^{100}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9 + 3 * q^10 + 16 * q^11 - 26 * q^12 - 31 * q^13 + 3 * q^14 + 10 * q^15 + 49 * q^16 - 18 * q^17 + 4 * q^18 - 16 * q^19 - 49 * q^20 + 10 * q^21 + 10 * q^22 + 10 * q^23 + 2 * q^24 + 49 * q^25 - 22 * q^26 - 58 * q^27 - 49 * q^28 + 31 * q^29 - 10 * q^30 - 35 * q^31 - 5 * q^32 - 82 * q^33 - 41 * q^34 + 49 * q^35 + 49 * q^36 - 24 * q^37 - 20 * q^38 + 41 * q^39 + 6 * q^40 + 30 * q^41 - 10 * q^42 - 19 * q^43 + 27 * q^44 - 39 * q^45 + 15 * q^46 - 39 * q^47 - 51 * q^48 + 49 * q^49 - 3 * q^50 + 46 * q^51 - 94 * q^52 - 17 * q^53 + 9 * q^54 - 16 * q^55 + 6 * q^56 - 23 * q^57 - 46 * q^58 + 11 * q^59 + 26 * q^60 - 9 * q^61 - 49 * q^62 - 39 * q^63 + 10 * q^64 + 31 * q^65 - 10 * q^66 - 2 * q^67 - 73 * q^68 - 47 * q^69 - 3 * q^70 + 26 * q^71 - 39 * q^72 - 100 * q^73 + 8 * q^74 - 10 * q^75 - 71 * q^76 - 16 * q^77 - 51 * q^78 + 50 * q^79 - 49 * q^80 + 61 * q^81 - 36 * q^82 - 67 * q^83 + 26 * q^84 + 18 * q^85 + 33 * q^86 - 45 * q^87 - q^88 - 19 * q^89 - 4 * q^90 + 31 * q^91 + 7 * q^92 + 9 * q^93 - 33 * q^94 + 16 * q^95 - 8 * q^96 - 85 * q^97 - 3 * q^98 + 27 * q^99

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