LMFDB - Embedded newform 8015.2.a.h.1.10

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:	$38$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-1.74109 q^{2} -0.00460406 q^{3} +1.03141 q^{4} +1.00000 q^{5} +0.00801611 q^{6} +1.00000 q^{7} +1.68640 q^{8} -2.99998 q^{9} +O(q^{10})$	\(q-1.74109 q^{2} -0.00460406 q^{3} +1.03141 q^{4} +1.00000 q^{5} +0.00801611 q^{6} +1.00000 q^{7} +1.68640 q^{8} -2.99998 q^{9} -1.74109 q^{10} -1.64546 q^{11} -0.00474868 q^{12} +2.97322 q^{13} -1.74109 q^{14} -0.00460406 q^{15} -4.99901 q^{16} -6.18426 q^{17} +5.22325 q^{18} -2.19801 q^{19} +1.03141 q^{20} -0.00460406 q^{21} +2.86490 q^{22} -4.05795 q^{23} -0.00776431 q^{24} +1.00000 q^{25} -5.17666 q^{26} +0.0276243 q^{27} +1.03141 q^{28} +6.30926 q^{29} +0.00801611 q^{30} +3.05155 q^{31} +5.33095 q^{32} +0.00757579 q^{33} +10.7674 q^{34} +1.00000 q^{35} -3.09421 q^{36} -3.54780 q^{37} +3.82695 q^{38} -0.0136889 q^{39} +1.68640 q^{40} +2.54569 q^{41} +0.00801611 q^{42} +7.24393 q^{43} -1.69715 q^{44} -2.99998 q^{45} +7.06528 q^{46} +9.14625 q^{47} +0.0230158 q^{48} +1.00000 q^{49} -1.74109 q^{50} +0.0284727 q^{51} +3.06661 q^{52} +2.17658 q^{53} -0.0480965 q^{54} -1.64546 q^{55} +1.68640 q^{56} +0.0101198 q^{57} -10.9850 q^{58} -4.52254 q^{59} -0.00474868 q^{60} +8.28628 q^{61} -5.31305 q^{62} -2.99998 q^{63} +0.716338 q^{64} +2.97322 q^{65} -0.0131902 q^{66} -9.22787 q^{67} -6.37852 q^{68} +0.0186831 q^{69} -1.74109 q^{70} +9.40835 q^{71} -5.05918 q^{72} -3.58253 q^{73} +6.17705 q^{74} -0.00460406 q^{75} -2.26705 q^{76} -1.64546 q^{77} +0.0238336 q^{78} -5.55547 q^{79} -4.99901 q^{80} +8.99981 q^{81} -4.43229 q^{82} +4.54533 q^{83} -0.00474868 q^{84} -6.18426 q^{85} -12.6124 q^{86} -0.0290482 q^{87} -2.77491 q^{88} +4.00198 q^{89} +5.22325 q^{90} +2.97322 q^{91} -4.18542 q^{92} -0.0140495 q^{93} -15.9245 q^{94} -2.19801 q^{95} -0.0245440 q^{96} -13.5634 q^{97} -1.74109 q^{98} +4.93634 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9}+O(q^{10}) $ 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9} - 6 q^{10} - 18 q^{11} - 20 q^{12} - 25 q^{13} - 6 q^{14} - 9 q^{15} - 21 q^{17} - 7 q^{18} - 14 q^{19} + 24 q^{20} - 9 q^{21} - 11 q^{22} - 16 q^{23} - 10 q^{24} + 38 q^{25} - 21 q^{26} - 15 q^{27} + 24 q^{28} - 52 q^{29} - 10 q^{30} - 30 q^{31} - 8 q^{32} - 13 q^{33} - 9 q^{34} + 38 q^{35} - 16 q^{36} - 47 q^{37} - 10 q^{38} - 50 q^{39} - 21 q^{40} - 35 q^{41} - 10 q^{42} - 18 q^{43} - 22 q^{44} + 13 q^{45} - 17 q^{46} - 23 q^{47} - 13 q^{48} + 38 q^{49} - 6 q^{50} - 5 q^{51} - 41 q^{52} - 12 q^{53} + 35 q^{54} - 18 q^{55} - 21 q^{56} - 3 q^{57} - 16 q^{58} - 16 q^{59} - 20 q^{60} - 47 q^{61} + 14 q^{62} + 13 q^{63} - 55 q^{64} - 25 q^{65} - 6 q^{66} - 54 q^{67} + 31 q^{68} - 95 q^{69} - 6 q^{70} - 41 q^{71} - 59 q^{73} - q^{74} - 9 q^{75} - 23 q^{76} - 18 q^{77} + 19 q^{78} - 117 q^{79} - 38 q^{81} + 19 q^{82} - 21 q^{83} - 20 q^{84} - 21 q^{85} - 12 q^{86} - 14 q^{87} - 40 q^{88} - 96 q^{89} - 7 q^{90} - 25 q^{91} + 53 q^{92} - 53 q^{93} - 28 q^{94} - 14 q^{95} + 40 q^{96} - 70 q^{97} - 6 q^{98} - 52 q^{99}+O(q^{100}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9 - 6 * q^10 - 18 * q^11 - 20 * q^12 - 25 * q^13 - 6 * q^14 - 9 * q^15 - 21 * q^17 - 7 * q^18 - 14 * q^19 + 24 * q^20 - 9 * q^21 - 11 * q^22 - 16 * q^23 - 10 * q^24 + 38 * q^25 - 21 * q^26 - 15 * q^27 + 24 * q^28 - 52 * q^29 - 10 * q^30 - 30 * q^31 - 8 * q^32 - 13 * q^33 - 9 * q^34 + 38 * q^35 - 16 * q^36 - 47 * q^37 - 10 * q^38 - 50 * q^39 - 21 * q^40 - 35 * q^41 - 10 * q^42 - 18 * q^43 - 22 * q^44 + 13 * q^45 - 17 * q^46 - 23 * q^47 - 13 * q^48 + 38 * q^49 - 6 * q^50 - 5 * q^51 - 41 * q^52 - 12 * q^53 + 35 * q^54 - 18 * q^55 - 21 * q^56 - 3 * q^57 - 16 * q^58 - 16 * q^59 - 20 * q^60 - 47 * q^61 + 14 * q^62 + 13 * q^63 - 55 * q^64 - 25 * q^65 - 6 * q^66 - 54 * q^67 + 31 * q^68 - 95 * q^69 - 6 * q^70 - 41 * q^71 - 59 * q^73 - q^74 - 9 * q^75 - 23 * q^76 - 18 * q^77 + 19 * q^78 - 117 * q^79 - 38 * q^81 + 19 * q^82 - 21 * q^83 - 20 * q^84 - 21 * q^85 - 12 * q^86 - 14 * q^87 - 40 * q^88 - 96 * q^89 - 7 * q^90 - 25 * q^91 + 53 * q^92 - 53 * q^93 - 28 * q^94 - 14 * q^95 + 40 * q^96 - 70 * q^97 - 6 * q^98 - 52 * 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 $

$2$	−1.74109	−1.23114	−0.615570	−	0.788082i	$-0.711074\pi$
$2$	−1.74109	−1.23114	−0.615570	+	0.788082i	$0.711074\pi$
$3$	−0.00460406	−0.00265816	−0.00132908	−	0.999999i	$-0.500423\pi$
$3$	−0.00460406	−0.00265816	−0.00132908	+	0.999999i	$0.500423\pi$
$4$	1.03141	0.515706
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.00801611	0.00327256
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.68640	0.596234
$9$	−2.99998	−0.999993
$10$	−1.74109	−0.550583
$11$	−1.64546	−0.496125	−0.248062	−	0.968744i	$-0.579794\pi$
$11$	−1.64546	−0.496125	−0.248062	+	0.968744i	$0.579794\pi$
$12$	−0.00474868	−0.00137083
$13$	2.97322	0.824622	0.412311	−	0.911043i	$-0.364722\pi$
$13$	2.97322	0.824622	0.412311	+	0.911043i	$0.364722\pi$
$14$	−1.74109	−0.465327
$15$	−0.00460406	−0.00118876
$16$	−4.99901	−1.24975
$17$	−6.18426	−1.49990	−0.749952	−	0.661492i	$-0.769923\pi$
$17$	−6.18426	−1.49990	−0.749952	+	0.661492i	$0.769923\pi$
$18$	5.22325	1.23113
$19$	−2.19801	−0.504258	−0.252129	−	0.967694i	$-0.581131\pi$
$19$	−2.19801	−0.504258	−0.252129	+	0.967694i	$0.581131\pi$
$20$	1.03141	0.230631
$21$	−0.00460406	−0.00100469
$22$	2.86490	0.610799
$23$	−4.05795	−0.846141	−0.423071	−	0.906097i	$-0.639048\pi$
$23$	−4.05795	−0.846141	−0.423071	+	0.906097i	$0.639048\pi$
$24$	−0.00776431	−0.00158488
$25$	1.00000	0.200000
$26$	−5.17666	−1.01523
$27$	0.0276243	0.00531629
$28$	1.03141	0.194919
$29$	6.30926	1.17160	0.585800	−	0.810456i	$-0.300780\pi$
$29$	6.30926	1.17160	0.585800	+	0.810456i	$0.300780\pi$
$30$	0.00801611	0.00146353
$31$	3.05155	0.548075	0.274038	−	0.961719i	$-0.411641\pi$
$31$	3.05155	0.548075	0.274038	+	0.961719i	$0.411641\pi$
$32$	5.33095	0.942388
$33$	0.00757579	0.00131878
$34$	10.7674	1.84659
$35$	1.00000	0.169031
$36$	−3.09421	−0.515702
$37$	−3.54780	−0.583254	−0.291627	−	0.956532i	$-0.594197\pi$
$37$	−3.54780	−0.583254	−0.291627	+	0.956532i	$0.594197\pi$
$38$	3.82695	0.620813
$39$	−0.0136889	−0.00219198
$40$	1.68640	0.266644
$41$	2.54569	0.397570	0.198785	−	0.980043i	$-0.436300\pi$
$41$	2.54569	0.397570	0.198785	+	0.980043i	$0.436300\pi$
$42$	0.00801611	0.00123691
$43$	7.24393	1.10469	0.552345	−	0.833616i	$-0.313733\pi$
$43$	7.24393	1.10469	0.552345	+	0.833616i	$0.313733\pi$
$44$	−1.69715	−0.255854
$45$	−2.99998	−0.447210
$46$	7.06528	1.04172
$47$	9.14625	1.33412	0.667059	−	0.745005i	$-0.267553\pi$
$47$	9.14625	1.33412	0.667059	+	0.745005i	$0.267553\pi$
$48$	0.0230158	0.00332204
$49$	1.00000	0.142857
$50$	−1.74109	−0.246228
$51$	0.0284727	0.00398698
$52$	3.06661	0.425263
$53$	2.17658	0.298976	0.149488	−	0.988764i	$-0.452237\pi$
$53$	2.17658	0.298976	0.149488	+	0.988764i	$0.452237\pi$
$54$	−0.0480965	−0.00654510
$55$	−1.64546	−0.221874
$56$	1.68640	0.225355
$57$	0.0101198	0.00134040
$58$	−10.9850	−1.44240
$59$	−4.52254	−0.588784	−0.294392	−	0.955685i	$-0.595117\pi$
$59$	−4.52254	−0.588784	−0.294392	+	0.955685i	$0.595117\pi$
$60$	−0.00474868	−0.000613052 0
$61$	8.28628	1.06095	0.530475	−	0.847701i	$-0.322014\pi$
$61$	8.28628	1.06095	0.530475	+	0.847701i	$0.322014\pi$
$62$	−5.31305	−0.674758
$63$	−2.99998	−0.377962
$64$	0.716338	0.0895423
$65$	2.97322	0.368782
$66$	−0.0131902	−0.00162360
$67$	−9.22787	−1.12736	−0.563682	−	0.825992i	$-0.690616\pi$
$67$	−9.22787	−1.12736	−0.563682	+	0.825992i	$0.690616\pi$
$68$	−6.37852	−0.773509
$69$	0.0186831	0.00224918
$70$	−1.74109	−0.208101
$71$	9.40835	1.11657	0.558283	−	0.829651i	$-0.311460\pi$
$71$	9.40835	1.11657	0.558283	+	0.829651i	$0.311460\pi$
$72$	−5.05918	−0.596230
$73$	−3.58253	−0.419303	−0.209651	−	0.977776i	$-0.567233\pi$
$73$	−3.58253	−0.419303	−0.209651	+	0.977776i	$0.567233\pi$
$74$	6.17705	0.718068
$75$	−0.00460406	−0.000531631 0
$76$	−2.26705	−0.260049
$77$	−1.64546	−0.187517
$78$	0.0238336	0.00269863
$79$	−5.55547	−0.625039	−0.312520	−	0.949911i	$-0.601173\pi$
$79$	−5.55547	−0.625039	−0.312520	+	0.949911i	$0.601173\pi$
$80$	−4.99901	−0.558907
$81$	8.99981	0.999979
$82$	−4.43229	−0.489465
$83$	4.54533	0.498915	0.249457	−	0.968386i	$-0.419748\pi$
$83$	4.54533	0.498915	0.249457	+	0.968386i	$0.419748\pi$
$84$	−0.00474868	−0.000518124 0
$85$	−6.18426	−0.670777
$86$	−12.6124	−1.36003
$87$	−0.0290482	−0.00311430
$88$	−2.77491	−0.295806
$89$	4.00198	0.424209	0.212104	−	0.977247i	$-0.431968\pi$
$89$	4.00198	0.424209	0.212104	+	0.977247i	$0.431968\pi$
$90$	5.22325	0.550579
$91$	2.97322	0.311678
$92$	−4.18542	−0.436360
$93$	−0.0140495	−0.00145687
$94$	−15.9245	−1.64249
$95$	−2.19801	−0.225511
$96$	−0.0245440	−0.00250501
$97$	−13.5634	−1.37716	−0.688579	−	0.725161i	$-0.741765\pi$
$97$	−13.5634	−1.37716	−0.688579	+	0.725161i	$0.741765\pi$
$98$	−1.74109	−0.175877
$99$	4.93634	0.496121
$100$	1.03141	0.103141
$101$	9.85427	0.980536	0.490268	−	0.871572i	$-0.336899\pi$
$101$	9.85427	0.980536	0.490268	+	0.871572i	$0.336899\pi$
$102$	−0.0495737	−0.00490853
$103$	−9.89130	−0.974618	−0.487309	−	0.873229i	$-0.662022\pi$
$103$	−9.89130	−0.974618	−0.487309	+	0.873229i	$0.662022\pi$
$104$	5.01405	0.491668
$105$	−0.00460406	−0.000449310 0
$106$	−3.78963	−0.368081
$107$	−0.374924	−0.0362453	−0.0181227	−	0.999836i	$-0.505769\pi$
$107$	−0.374924	−0.0362453	−0.0181227	+	0.999836i	$0.505769\pi$
$108$	0.0284920	0.00274164
$109$	−15.5601	−1.49039	−0.745193	−	0.666849i	$-0.767643\pi$
$109$	−15.5601	−1.49039	−0.745193	+	0.666849i	$0.767643\pi$
$110$	2.86490	0.273158
$111$	0.0163343	0.00155038
$112$	−4.99901	−0.472362
$113$	12.1055	1.13879	0.569395	−	0.822064i	$-0.307178\pi$
$113$	12.1055	1.13879	0.569395	+	0.822064i	$0.307178\pi$
$114$	−0.0176195	−0.00165022
$115$	−4.05795	−0.378406
$116$	6.50745	0.604201
$117$	−8.91959	−0.824617
$118$	7.87416	0.724876
$119$	−6.18426	−0.566910
$120$	−0.00776431	−0.000708781 0
$121$	−8.29246	−0.753860
$122$	−14.4272	−1.30618
$123$	−0.0117205	−0.00105680
$124$	3.14741	0.282646
$125$	1.00000	0.0894427
$126$	5.22325	0.465324
$127$	11.0093	0.976918	0.488459	−	0.872587i	$-0.337559\pi$
$127$	11.0093	0.976918	0.488459	+	0.872587i	$0.337559\pi$
$128$	−11.9091	−1.05263
$129$	−0.0333515	−0.00293644
$130$	−5.17666	−0.454023
$131$	−22.0201	−1.92391	−0.961955	−	0.273209i	$-0.911915\pi$
$131$	−22.0201	−1.92391	−0.961955	+	0.273209i	$0.911915\pi$
$132$	0.00781376	0.000680101 0
$133$	−2.19801	−0.190592
$134$	16.0666	1.38794
$135$	0.0276243	0.00237752
$136$	−10.4292	−0.894294
$137$	−18.1287	−1.54884	−0.774419	−	0.632673i	$-0.781958\pi$
$137$	−18.1287	−1.54884	−0.774419	+	0.632673i	$0.781958\pi$
$138$	−0.0325290	−0.00276905
$139$	−3.84533	−0.326157	−0.163078	−	0.986613i	$-0.552142\pi$
$139$	−3.84533	−0.326157	−0.163078	+	0.986613i	$0.552142\pi$
$140$	1.03141	0.0871702
$141$	−0.0421099	−0.00354630
$142$	−16.3808	−1.37465
$143$	−4.89231	−0.409115
$144$	14.9969	1.24974
$145$	6.30926	0.523956
$146$	6.23752	0.516221
$147$	−0.00460406	−0.000379737 0
$148$	−3.65924	−0.300788
$149$	−2.78896	−0.228481	−0.114240	−	0.993453i	$-0.536443\pi$
$149$	−2.78896	−0.228481	−0.114240	+	0.993453i	$0.536443\pi$
$150$	0.00801611	0.000654513 0
$151$	6.16620	0.501798	0.250899	−	0.968013i	$-0.419274\pi$
$151$	6.16620	0.501798	0.250899	+	0.968013i	$0.419274\pi$
$152$	−3.70673	−0.300656
$153$	18.5527	1.49989
$154$	2.86490	0.230860
$155$	3.05155	0.245107
$156$	−0.0141189	−0.00113041
$157$	−0.356872	−0.0284815	−0.0142407	−	0.999899i	$-0.504533\pi$
$157$	−0.356872	−0.0284815	−0.0142407	+	0.999899i	$0.504533\pi$
$158$	9.67260	0.769511
$159$	−0.0100211	−0.000794725 0
$160$	5.33095	0.421449
$161$	−4.05795	−0.319811
$162$	−15.6695	−1.23111
$163$	6.27022	0.491122	0.245561	−	0.969381i	$-0.421028\pi$
$163$	6.27022	0.491122	0.245561	+	0.969381i	$0.421028\pi$
$164$	2.62566	0.205029
$165$	0.00757579	0.000589775 0
$166$	−7.91385	−0.614234
$167$	−0.489460	−0.0378756	−0.0189378	−	0.999821i	$-0.506028\pi$
$167$	−0.489460	−0.0378756	−0.0189378	+	0.999821i	$0.506028\pi$
$168$	−0.00776431	−0.000599029 0
$169$	−4.15997	−0.319998
$170$	10.7674	0.825821
$171$	6.59399	0.504255
$172$	7.47148	0.569695
$173$	19.6509	1.49403	0.747015	−	0.664807i	$-0.231486\pi$
$173$	19.6509	1.49403	0.747015	+	0.664807i	$0.231486\pi$
$174$	0.0505757	0.00383414
$175$	1.00000	0.0755929
$176$	8.22567	0.620033
$177$	0.0208220	0.00156508
$178$	−6.96782	−0.522260
$179$	−3.67137	−0.274411	−0.137206	−	0.990543i	$-0.543812\pi$
$179$	−3.67137	−0.274411	−0.137206	+	0.990543i	$0.543812\pi$
$180$	−3.09421	−0.230629
$181$	−16.8798	−1.25466	−0.627331	−	0.778752i	$-0.715853\pi$
$181$	−16.8798	−1.25466	−0.627331	+	0.778752i	$0.715853\pi$
$182$	−5.17666	−0.383719
$183$	−0.0381506	−0.00282017
$184$	−6.84335	−0.504498
$185$	−3.54780	−0.260839
$186$	0.0244616	0.00179361
$187$	10.1760	0.744139
$188$	9.43356	0.688013
$189$	0.0276243	0.00200937
$190$	3.82695	0.277636
$191$	15.0242	1.08711	0.543556	−	0.839373i	$-0.317077\pi$
$191$	15.0242	1.08711	0.543556	+	0.839373i	$0.317077\pi$
$192$	−0.00329807	−0.000238017 0
$193$	6.40779	0.461243	0.230621	−	0.973044i	$-0.425924\pi$
$193$	6.40779	0.461243	0.230621	+	0.973044i	$0.425924\pi$
$194$	23.6152	1.69547
$195$	−0.0136889	−0.000980281 0
$196$	1.03141	0.0736723
$197$	−14.8024	−1.05463	−0.527314	−	0.849671i	$-0.676801\pi$
$197$	−14.8024	−1.05463	−0.527314	+	0.849671i	$0.676801\pi$
$198$	−8.59464	−0.610794
$199$	18.5143	1.31245	0.656223	−	0.754567i	$-0.272153\pi$
$199$	18.5143	1.31245	0.656223	+	0.754567i	$0.272153\pi$
$200$	1.68640	0.119247
$201$	0.0424857	0.00299671
$202$	−17.1572	−1.20718
$203$	6.30926	0.442823
$204$	0.0293671	0.00205611
$205$	2.54569	0.177799
$206$	17.2217	1.19989
$207$	12.1738	0.846135
$208$	−14.8632	−1.03057
$209$	3.61674	0.250175
$210$	0.00801611	0.000553164 0
$211$	−6.85906	−0.472197	−0.236099	−	0.971729i	$-0.575869\pi$
$211$	−6.85906	−0.472197	−0.236099	+	0.971729i	$0.575869\pi$
$212$	2.24495	0.154184
$213$	−0.0433166	−0.00296801
$214$	0.652779	0.0446231
$215$	7.24393	0.494032
$216$	0.0465857	0.00316975
$217$	3.05155	0.207153
$218$	27.0916	1.83487
$219$	0.0164942	0.00111457
$220$	−1.69715	−0.114422
$221$	−18.3872	−1.23685
$222$	−0.0284395	−0.00190874
$223$	−23.5555	−1.57739	−0.788696	−	0.614783i	$-0.789244\pi$
$223$	−23.5555	−1.57739	−0.788696	+	0.614783i	$0.789244\pi$
$224$	5.33095	0.356189
$225$	−2.99998	−0.199999
$226$	−21.0768	−1.40201
$227$	6.41689	0.425904	0.212952	−	0.977063i	$-0.431692\pi$
$227$	6.41689	0.425904	0.212952	+	0.977063i	$0.431692\pi$
$228$	0.0104377	0.000691251 0
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	7.06528	0.465871
$231$	0.00757579	0.000498451 0
$232$	10.6400	0.698548
$233$	−24.8139	−1.62562	−0.812808	−	0.582532i	$-0.802062\pi$
$233$	−24.8139	−1.62562	−0.812808	+	0.582532i	$0.802062\pi$
$234$	15.5299	1.01522
$235$	9.14625	0.596636
$236$	−4.66460	−0.303639
$237$	0.0255777	0.00166145
$238$	10.7674	0.697946
$239$	−9.79638	−0.633675	−0.316838	−	0.948480i	$-0.602621\pi$
$239$	−9.79638	−0.633675	−0.316838	+	0.948480i	$0.602621\pi$
$240$	0.0230158	0.00148566
$241$	−13.9609	−0.899300	−0.449650	−	0.893205i	$-0.648451\pi$
$241$	−13.9609	−0.899300	−0.449650	+	0.893205i	$0.648451\pi$
$242$	14.4380	0.928108
$243$	−0.124308	−0.00797439
$244$	8.54657	0.547138
$245$	1.00000	0.0638877
$246$	0.0204065	0.00130107
$247$	−6.53517	−0.415823
$248$	5.14615	0.326781
$249$	−0.0209270	−0.00132619
$250$	−1.74109	−0.110117
$251$	21.8827	1.38123	0.690613	−	0.723224i	$-0.257341\pi$
$251$	21.8827	1.38123	0.690613	+	0.723224i	$0.257341\pi$
$252$	−3.09421	−0.194917
$253$	6.67719	0.419791
$254$	−19.1682	−1.20272
$255$	0.0284727	0.00178303
$256$	19.3022	1.20639
$257$	−12.9203	−0.805946	−0.402973	−	0.915212i	$-0.632023\pi$
$257$	−12.9203	−0.805946	−0.402973	+	0.915212i	$0.632023\pi$
$258$	0.0580682	0.00361517
$259$	−3.54780	−0.220449
$260$	3.06661	0.190183
$261$	−18.9276	−1.17159
$262$	38.3392	2.36860
$263$	−23.9570	−1.47725	−0.738625	−	0.674116i	$-0.764525\pi$
$263$	−23.9570	−1.47725	−0.738625	+	0.674116i	$0.764525\pi$
$264$	0.0127759	0.000786299 0
$265$	2.17658	0.133706
$266$	3.82695	0.234645
$267$	−0.0184253	−0.00112761
$268$	−9.51773	−0.581388
$269$	−26.6162	−1.62282	−0.811408	−	0.584480i	$-0.801298\pi$
$269$	−26.6162	−1.62282	−0.811408	+	0.584480i	$0.801298\pi$
$270$	−0.0480965	−0.00292706
$271$	−25.5159	−1.54998	−0.774990	−	0.631973i	$-0.782245\pi$
$271$	−25.5159	−1.54998	−0.774990	+	0.631973i	$0.782245\pi$
$272$	30.9152	1.87451
$273$	−0.0136889	−0.000828489 0
$274$	31.5638	1.90684
$275$	−1.64546	−0.0992249
$276$	0.0192699	0.00115991
$277$	19.4852	1.17075	0.585375	−	0.810762i	$-0.300947\pi$
$277$	19.4852	1.17075	0.585375	+	0.810762i	$0.300947\pi$
$278$	6.69509	0.401545
$279$	−9.15460	−0.548072
$280$	1.68640	0.100782
$281$	−8.24603	−0.491917	−0.245959	−	0.969280i	$-0.579103\pi$
$281$	−8.24603	−0.491917	−0.245959	+	0.969280i	$0.579103\pi$
$282$	0.0733174	0.00436599
$283$	−7.22275	−0.429348	−0.214674	−	0.976686i	$-0.568869\pi$
$283$	−7.22275	−0.429348	−0.214674	+	0.976686i	$0.568869\pi$
$284$	9.70388	0.575819
$285$	0.0101198	0.000599444 0
$286$	8.51798	0.503678
$287$	2.54569	0.150267
$288$	−15.9927	−0.942381
$289$	21.2451	1.24971
$290$	−10.9850	−0.645063
$291$	0.0624469	0.00366070
$292$	−3.69506	−0.216237
$293$	12.3552	0.721797	0.360899	−	0.932605i	$-0.382470\pi$
$293$	12.3552	0.721797	0.360899	+	0.932605i	$0.382470\pi$
$294$	0.00801611	0.000467509 0
$295$	−4.52254	−0.263312
$296$	−5.98302	−0.347756
$297$	−0.0454546	−0.00263754
$298$	4.85585	0.281292
$299$	−12.0652	−0.697747
$300$	−0.00474868	−0.000274165 0
$301$	7.24393	0.417533
$302$	−10.7359	−0.617784
$303$	−0.0453696	−0.00260642
$304$	10.9879	0.630198
$305$	8.28628	0.474471
$306$	−32.3019	−1.84658
$307$	−4.27705	−0.244104	−0.122052	−	0.992524i	$-0.538947\pi$
$307$	−4.27705	−0.244104	−0.122052	+	0.992524i	$0.538947\pi$
$308$	−1.69715	−0.0967039
$309$	0.0455401	0.00259069
$310$	−5.31305	−0.301761
$311$	−8.67677	−0.492015	−0.246007	−	0.969268i	$-0.579119\pi$
$311$	−8.67677	−0.492015	−0.246007	+	0.969268i	$0.579119\pi$
$312$	−0.0230850	−0.00130693
$313$	20.8986	1.18126	0.590628	−	0.806944i	$-0.298880\pi$
$313$	20.8986	1.18126	0.590628	+	0.806944i	$0.298880\pi$
$314$	0.621348	0.0350647
$315$	−2.99998	−0.169030
$316$	−5.72998	−0.322336
$317$	6.28286	0.352880	0.176440	−	0.984311i	$-0.443542\pi$
$317$	6.28286	0.352880	0.176440	+	0.984311i	$0.443542\pi$
$318$	0.0174477	0.000978418 0
$319$	−10.3816	−0.581260
$320$	0.716338	0.0400445
$321$	0.00172618	9.63457e−5 0
$322$	7.06528	0.393733
$323$	13.5931	0.756339
$324$	9.28251	0.515695
$325$	2.97322	0.164924
$326$	−10.9171	−0.604640
$327$	0.0716396	0.00396168
$328$	4.29307	0.237045
$329$	9.14625	0.504249
$330$	−0.0131902	−0.000726095 0
$331$	−7.91765	−0.435193	−0.217597	−	0.976039i	$-0.569822\pi$
$331$	−7.91765	−0.435193	−0.217597	+	0.976039i	$0.569822\pi$
$332$	4.68811	0.257293
$333$	10.6433	0.583250
$334$	0.852197	0.0466302
$335$	−9.22787	−0.504172
$336$	0.0230158	0.00125561
$337$	−9.70696	−0.528772	−0.264386	−	0.964417i	$-0.585169\pi$
$337$	−9.70696	−0.528772	−0.264386	+	0.964417i	$0.585169\pi$
$338$	7.24290	0.393962
$339$	−0.0557345	−0.00302708
$340$	−6.37852	−0.345924
$341$	−5.02121	−0.271914
$342$	−11.4808	−0.620808
$343$	1.00000	0.0539949
$344$	12.2162	0.658653
$345$	0.0186831	0.00100586
$346$	−34.2141	−1.83936
$347$	2.74076	0.147132	0.0735660	−	0.997290i	$-0.476562\pi$
$347$	2.74076	0.147132	0.0735660	+	0.997290i	$0.476562\pi$
$348$	−0.0299607	−0.00160606
$349$	−5.18928	−0.277776	−0.138888	−	0.990308i	$-0.544353\pi$
$349$	−5.18928	−0.277776	−0.138888	+	0.990308i	$0.544353\pi$
$350$	−1.74109	−0.0930654
$351$	0.0821330	0.00438394
$352$	−8.77186	−0.467542
$353$	23.7397	1.26354	0.631768	−	0.775157i	$-0.282329\pi$
$353$	23.7397	1.26354	0.631768	+	0.775157i	$0.282329\pi$
$354$	−0.0362531	−0.00192683
$355$	9.40835	0.499343
$356$	4.12768	0.218767
$357$	0.0284727	0.00150694
$358$	6.39221	0.337839
$359$	−1.83018	−0.0965933	−0.0482967	−	0.998833i	$-0.515379\pi$
$359$	−1.83018	−0.0965933	−0.0482967	+	0.998833i	$0.515379\pi$
$360$	−5.05918	−0.266642
$361$	−14.1687	−0.745724
$362$	29.3893	1.54467
$363$	0.0381790	0.00200388
$364$	3.06661	0.160734
$365$	−3.58253	−0.187518
$366$	0.0664237	0.00347203
$367$	−34.1286	−1.78150	−0.890750	−	0.454494i	$-0.849820\pi$
$367$	−34.1286	−1.78150	−0.890750	+	0.454494i	$0.849820\pi$
$368$	20.2858	1.05747
$369$	−7.63702	−0.397568
$370$	6.17705	0.321130
$371$	2.17658	0.113002
$372$	−0.0144909	−0.000751317 0
$373$	13.5241	0.700250	0.350125	−	0.936703i	$-0.386139\pi$
$373$	13.5241	0.700250	0.350125	+	0.936703i	$0.386139\pi$
$374$	−17.7173	−0.916140
$375$	−0.00460406	−0.000237753 0
$376$	15.4243	0.795447
$377$	18.7588	0.966128
$378$	−0.0480965	−0.00247382
$379$	−9.33464	−0.479488	−0.239744	−	0.970836i	$-0.577064\pi$
$379$	−9.33464	−0.479488	−0.239744	+	0.970836i	$0.577064\pi$
$380$	−2.26705	−0.116297
$381$	−0.0506875	−0.00259680
$382$	−26.1586	−1.33839
$383$	−15.1288	−0.773045	−0.386523	−	0.922280i	$-0.626324\pi$
$383$	−15.1288	−0.773045	−0.386523	+	0.922280i	$0.626324\pi$
$384$	0.0548303	0.00279805
$385$	−1.64546	−0.0838604
$386$	−11.1566	−0.567854
$387$	−21.7316	−1.10468
$388$	−13.9895	−0.710209
$389$	34.5933	1.75395	0.876976	−	0.480534i	$-0.159557\pi$
$389$	34.5933	1.75395	0.876976	+	0.480534i	$0.159557\pi$
$390$	0.0238336	0.00120686
$391$	25.0954	1.26913
$392$	1.68640	0.0851763
$393$	0.101382	0.00511405
$394$	25.7724	1.29839
$395$	−5.55547	−0.279526
$396$	5.09140	0.255853
$397$	21.4465	1.07637	0.538184	−	0.842828i	$-0.319111\pi$
$397$	21.4465	1.07637	0.538184	+	0.842828i	$0.319111\pi$
$398$	−32.2352	−1.61580
$399$	0.0101198	0.000506623 0
$400$	−4.99901	−0.249951
$401$	−1.01504	−0.0506889	−0.0253444	−	0.999679i	$-0.508068\pi$
$401$	−1.01504	−0.0506889	−0.0253444	+	0.999679i	$0.508068\pi$
$402$	−0.0739716	−0.00368937
$403$	9.07294	0.451955
$404$	10.1638	0.505668
$405$	8.99981	0.447204
$406$	−10.9850	−0.545177
$407$	5.83776	0.289367
$408$	0.0480165	0.00237717
$409$	−22.3705	−1.10615	−0.553076	−	0.833131i	$-0.686546\pi$
$409$	−22.3705	−1.10615	−0.553076	+	0.833131i	$0.686546\pi$
$410$	−4.43229	−0.218895
$411$	0.0834656	0.00411705
$412$	−10.2020	−0.502616
$413$	−4.52254	−0.222539
$414$	−21.1957	−1.04171
$415$	4.54533	0.223121
$416$	15.8501	0.777114
$417$	0.0177041	0.000866975 0
$418$	−6.29708	−0.308000
$419$	−18.1731	−0.887816	−0.443908	−	0.896072i	$-0.646408\pi$
$419$	−18.1731	−0.887816	−0.443908	+	0.896072i	$0.646408\pi$
$420$	−0.00474868	−0.000231712 0
$421$	−28.6543	−1.39653	−0.698263	−	0.715841i	$-0.746043\pi$
$421$	−28.6543	−1.39653	−0.698263	+	0.715841i	$0.746043\pi$
$422$	11.9423	0.581341
$423$	−27.4386	−1.33411
$424$	3.67059	0.178260
$425$	−6.18426	−0.299981
$426$	0.0754183	0.00365403
$427$	8.28628	0.401001
$428$	−0.386701	−0.0186919
$429$	0.0225245	0.00108749
$430$	−12.6124	−0.608223
$431$	24.0773	1.15976	0.579881	−	0.814701i	$-0.303099\pi$
$431$	24.0773	1.15976	0.579881	+	0.814701i	$0.303099\pi$
$432$	−0.138094	−0.00664406
$433$	27.4255	1.31799	0.658993	−	0.752149i	$-0.270983\pi$
$433$	27.4255	1.31799	0.658993	+	0.752149i	$0.270983\pi$
$434$	−5.31305	−0.255034
$435$	−0.0290482	−0.00139276
$436$	−16.0489	−0.768601
$437$	8.91942	0.426674
$438$	−0.0287179	−0.00137219
$439$	8.98761	0.428955	0.214478	−	0.976729i	$-0.431195\pi$
$439$	8.98761	0.428955	0.214478	+	0.976729i	$0.431195\pi$
$440$	−2.77491	−0.132289
$441$	−2.99998	−0.142856
$442$	32.0138	1.52274
$443$	12.9981	0.617558	0.308779	−	0.951134i	$-0.400080\pi$
$443$	12.9981	0.617558	0.308779	+	0.951134i	$0.400080\pi$
$444$	0.0168474	0.000799541 0
$445$	4.00198	0.189712
$446$	41.0124	1.94199
$447$	0.0128406	0.000607338 0
$448$	0.716338	0.0338438
$449$	−16.5073	−0.779029	−0.389514	−	0.921020i	$-0.627357\pi$
$449$	−16.5073	−0.779029	−0.389514	+	0.921020i	$0.627357\pi$
$450$	5.22325	0.246226
$451$	−4.18883	−0.197244
$452$	12.4858	0.587280
$453$	−0.0283896	−0.00133386
$454$	−11.1724	−0.524348
$455$	2.97322	0.139387
$456$	0.0170660	0.000799190 0
$457$	34.8166	1.62865	0.814327	−	0.580406i	$-0.197106\pi$
$457$	34.8166	1.62865	0.814327	+	0.580406i	$0.197106\pi$
$458$	1.74109	0.0813560
$459$	−0.170836	−0.00797393
$460$	−4.18542	−0.195146
$461$	−40.1476	−1.86986	−0.934929	−	0.354834i	$-0.884537\pi$
$461$	−40.1476	−1.86986	−0.934929	+	0.354834i	$0.884537\pi$
$462$	−0.0131902	−0.000613663 0
$463$	−15.9683	−0.742109	−0.371055	−	0.928611i	$-0.621004\pi$
$463$	−15.9683	−0.742109	−0.371055	+	0.928611i	$0.621004\pi$
$464$	−31.5401	−1.46421
$465$	−0.0140495	−0.000651532 0
$466$	43.2034	2.00136
$467$	29.1336	1.34814	0.674071	−	0.738667i	$-0.264544\pi$
$467$	29.1336	1.34814	0.674071	+	0.738667i	$0.264544\pi$
$468$	−9.19977	−0.425260
$469$	−9.22787	−0.426103
$470$	−15.9245	−0.734542
$471$	0.00164306	7.57082e−5 0
$472$	−7.62682	−0.351053
$473$	−11.9196	−0.548064
$474$	−0.0445332	−0.00204548
$475$	−2.19801	−0.100852
$476$	−6.37852	−0.292359
$477$	−6.52969	−0.298974
$478$	17.0564	0.780143
$479$	27.6435	1.26306	0.631531	−	0.775350i	$-0.282427\pi$
$479$	27.6435	1.26306	0.631531	+	0.775350i	$0.282427\pi$
$480$	−0.0245440	−0.00112028
$481$	−10.5484	−0.480965
$482$	24.3072	1.10716
$483$	0.0186831	0.000850109 0
$484$	−8.55295	−0.388770
$485$	−13.5634	−0.615884
$486$	0.216433	0.00981760
$487$	−26.8775	−1.21793	−0.608967	−	0.793195i	$-0.708416\pi$
$487$	−26.8775	−1.21793	−0.608967	+	0.793195i	$0.708416\pi$
$488$	13.9740	0.632574
$489$	−0.0288685	−0.00130548
$490$	−1.74109	−0.0786547
$491$	−38.0920	−1.71907	−0.859534	−	0.511079i	$-0.829246\pi$
$491$	−38.0920	−1.71907	−0.859534	+	0.511079i	$0.829246\pi$
$492$	−0.0120887	−0.000545000 0
$493$	−39.0181	−1.75729
$494$	11.3783	0.511936
$495$	4.93634	0.221872
$496$	−15.2548	−0.684959
$497$	9.40835	0.422022
$498$	0.0364359	0.00163273
$499$	41.2019	1.84445	0.922225	−	0.386653i	$-0.126369\pi$
$499$	41.2019	1.84445	0.922225	+	0.386653i	$0.126369\pi$
$500$	1.03141	0.0461261
$501$	0.00225351	0.000100679 0
$502$	−38.0999	−1.70048
$503$	−23.9030	−1.06578	−0.532891	−	0.846184i	$-0.678894\pi$
$503$	−23.9030	−1.06578	−0.532891	+	0.846184i	$0.678894\pi$
$504$	−5.05918	−0.225354
$505$	9.85427	0.438509
$506$	−11.6256	−0.516822
$507$	0.0191528	0.000850604 0
$508$	11.3551	0.503802
$509$	−18.4243	−0.816641	−0.408321	−	0.912839i	$-0.633885\pi$
$509$	−18.4243	−0.816641	−0.408321	+	0.912839i	$0.633885\pi$
$510$	−0.0495737	−0.00219516
$511$	−3.58253	−0.158482
$512$	−9.78877	−0.432607
$513$	−0.0607185	−0.00268079
$514$	22.4955	0.992233
$515$	−9.89130	−0.435863
$516$	−0.0343991	−0.00151434
$517$	−15.0498	−0.661889
$518$	6.17705	0.271404
$519$	−0.0904740	−0.00397137
$520$	5.01405	0.219881
$521$	−37.8817	−1.65963	−0.829813	−	0.558041i	$-0.811553\pi$
$521$	−37.8817	−1.65963	−0.829813	+	0.558041i	$0.811553\pi$
$522$	32.9548	1.44239
$523$	11.0724	0.484161	0.242081	−	0.970256i	$-0.422170\pi$
$523$	11.0724	0.484161	0.242081	+	0.970256i	$0.422170\pi$
$524$	−22.7118	−0.992171
$525$	−0.00460406	−0.000200938 0
$526$	41.7114	1.81870
$527$	−18.8716	−0.822061
$528$	−0.0378715	−0.00164815
$529$	−6.53303	−0.284045
$530$	−3.78963	−0.164611
$531$	13.5675	0.588780
$532$	−2.26705	−0.0982893
$533$	7.56890	0.327845
$534$	0.0320803	0.00138825
$535$	−0.374924	−0.0162094
$536$	−15.5619	−0.672172
$537$	0.0169032	0.000729428 0
$538$	46.3413	1.99791
$539$	−1.64546	−0.0708749
$540$	0.0284920	0.00122610
$541$	−16.3764	−0.704076	−0.352038	−	0.935986i	$-0.614511\pi$
$541$	−16.3764	−0.704076	−0.352038	+	0.935986i	$0.614511\pi$
$542$	44.4256	1.90824
$543$	0.0777155	0.00333509
$544$	−32.9680	−1.41349
$545$	−15.5601	−0.666521
$546$	0.0238336	0.00101999
$547$	−4.42861	−0.189354	−0.0946769	−	0.995508i	$-0.530182\pi$
$547$	−4.42861	−0.189354	−0.0946769	+	0.995508i	$0.530182\pi$
$548$	−18.6981	−0.798745
$549$	−24.8587	−1.06094
$550$	2.86490	0.122160
$551$	−13.8678	−0.590789
$552$	0.0315072	0.00134103
$553$	−5.55547	−0.236243
$554$	−33.9255	−1.44136
$555$	0.0163343	0.000693352 0
$556$	−3.96612	−0.168201
$557$	−45.1640	−1.91366	−0.956831	−	0.290646i	$-0.906130\pi$
$557$	−45.1640	−1.91366	−0.956831	+	0.290646i	$0.906130\pi$
$558$	15.9390	0.674753
$559$	21.5378	0.910952
$560$	−4.99901	−0.211247
$561$	−0.0468507	−0.00197804
$562$	14.3571	0.605619
$563$	10.6352	0.448222	0.224111	−	0.974564i	$-0.428052\pi$
$563$	10.6352	0.448222	0.224111	+	0.974564i	$0.428052\pi$
$564$	−0.0434327	−0.00182885
$565$	12.1055	0.509282
$566$	12.5755	0.528587
$567$	8.99981	0.377956
$568$	15.8663	0.665734
$569$	−23.6631	−0.992010	−0.496005	−	0.868320i	$-0.665200\pi$
$569$	−23.6631	−0.992010	−0.496005	+	0.868320i	$0.665200\pi$
$570$	−0.0176195	−0.000737999 0
$571$	0.237561	0.00994163	0.00497081	−	0.999988i	$-0.498418\pi$
$571$	0.237561	0.00994163	0.00497081	+	0.999988i	$0.498418\pi$
$572$	−5.04599	−0.210983
$573$	−0.0691723	−0.00288972
$574$	−4.43229	−0.185000
$575$	−4.05795	−0.169228
$576$	−2.14900	−0.0895416
$577$	−31.6743	−1.31862	−0.659308	−	0.751873i	$-0.729151\pi$
$577$	−31.6743	−1.31862	−0.659308	+	0.751873i	$0.729151\pi$
$578$	−36.9897	−1.53857
$579$	−0.0295018	−0.00122605
$580$	6.50745	0.270207
$581$	4.54533	0.188572
$582$	−0.108726	−0.00450684
$583$	−3.58147	−0.148329
$584$	−6.04159	−0.250003
$585$	−8.91959	−0.368780
$586$	−21.5115	−0.888633
$587$	−24.1420	−0.996447	−0.498223	−	0.867049i	$-0.666014\pi$
$587$	−24.1420	−0.996447	−0.498223	+	0.867049i	$0.666014\pi$
$588$	−0.00474868	−0.000195832 0
$589$	−6.70735	−0.276372
$590$	7.87416	0.324174
$591$	0.0681512	0.00280336
$592$	17.7355	0.728924
$593$	16.1346	0.662567	0.331283	−	0.943531i	$-0.392518\pi$
$593$	16.1346	0.662567	0.331283	+	0.943531i	$0.392518\pi$
$594$	0.0791408	0.00324719
$595$	−6.18426	−0.253530
$596$	−2.87657	−0.117829
$597$	−0.0852411	−0.00348869
$598$	21.0066	0.859024
$599$	38.9118	1.58989	0.794947	−	0.606678i	$-0.207498\pi$
$599$	38.9118	1.58989	0.794947	+	0.606678i	$0.207498\pi$
$600$	−0.00776431	−0.000316977 0
$601$	14.8465	0.605603	0.302801	−	0.953054i	$-0.402078\pi$
$601$	14.8465	0.605603	0.302801	+	0.953054i	$0.402078\pi$
$602$	−12.6124	−0.514042
$603$	27.6834	1.12736
$604$	6.35989	0.258780
$605$	−8.29246	−0.337137
$606$	0.0789929	0.00320887
$607$	−24.2956	−0.986128	−0.493064	−	0.869993i	$-0.664123\pi$
$607$	−24.2956	−0.986128	−0.493064	+	0.869993i	$0.664123\pi$
$608$	−11.7175	−0.475207
$609$	−0.0290482	−0.00117709
$610$	−14.4272	−0.584141
$611$	27.1938	1.10014
$612$	19.1354	0.773504
$613$	7.28404	0.294200	0.147100	−	0.989122i	$-0.453006\pi$
$613$	7.28404	0.294200	0.147100	+	0.989122i	$0.453006\pi$
$614$	7.44675	0.300526
$615$	−0.0117205	−0.000472617 0
$616$	−2.77491	−0.111804
$617$	15.6232	0.628965	0.314482	−	0.949263i	$-0.398169\pi$
$617$	15.6232	0.628965	0.314482	+	0.949263i	$0.398169\pi$
$618$	−0.0792897	−0.00318950
$619$	−40.8608	−1.64233	−0.821166	−	0.570689i	$-0.806676\pi$
$619$	−40.8608	−1.64233	−0.821166	+	0.570689i	$0.806676\pi$
$620$	3.14741	0.126403
$621$	−0.112098	−0.00449834
$622$	15.1071	0.605739
$623$	4.00198	0.160336
$624$	0.0684309	0.00273943
$625$	1.00000	0.0400000
$626$	−36.3864	−1.45429
$627$	−0.0166517	−0.000665004 0
$628$	−0.368082	−0.0146881
$629$	21.9405	0.874826
$630$	5.22325	0.208099
$631$	45.3910	1.80699	0.903494	−	0.428601i	$-0.140993\pi$
$631$	45.3910	1.80699	0.903494	+	0.428601i	$0.140993\pi$
$632$	−9.36876	−0.372669
$633$	0.0315795	0.00125517
$634$	−10.9391	−0.434445
$635$	11.0093	0.436891
$636$	−0.0103359	−0.000409844 0
$637$	2.97322	0.117803
$638$	18.0754	0.715612
$639$	−28.2248	−1.11656
$640$	−11.9091	−0.470749
$641$	44.6982	1.76547	0.882736	−	0.469870i	$-0.155699\pi$
$641$	44.6982	1.76547	0.882736	+	0.469870i	$0.155699\pi$
$642$	−0.00300544	−0.000118615 0
$643$	2.85143	0.112450	0.0562248	−	0.998418i	$-0.482094\pi$
$643$	2.85143	0.112450	0.0562248	+	0.998418i	$0.482094\pi$
$644$	−4.18542	−0.164929
$645$	−0.0333515	−0.00131321
$646$	−23.6668	−0.931159
$647$	29.0950	1.14384	0.571922	−	0.820308i	$-0.306198\pi$
$647$	29.0950	1.14384	0.571922	+	0.820308i	$0.306198\pi$
$648$	15.1773	0.596221
$649$	7.44165	0.292110
$650$	−5.17666	−0.203045
$651$	−0.0140495	−0.000550645 0
$652$	6.46718	0.253274
$653$	15.6457	0.612264	0.306132	−	0.951989i	$-0.400965\pi$
$653$	15.6457	0.612264	0.306132	+	0.951989i	$0.400965\pi$
$654$	−0.124731	−0.00487738
$655$	−22.0201	−0.860398
$656$	−12.7259	−0.496865
$657$	10.7475	0.419300
$658$	−15.9245	−0.620802
$659$	1.79982	0.0701112	0.0350556	−	0.999385i	$-0.488839\pi$
$659$	1.79982	0.0701112	0.0350556	+	0.999385i	$0.488839\pi$
$660$	0.00781376	0.000304150 0
$661$	−14.5209	−0.564799	−0.282400	−	0.959297i	$-0.591130\pi$
$661$	−14.5209	−0.564799	−0.282400	+	0.959297i	$0.591130\pi$
$662$	13.7854	0.535784
$663$	0.0846556	0.00328775
$664$	7.66526	0.297470
$665$	−2.19801	−0.0852352
$666$	−18.5310	−0.718063
$667$	−25.6027	−0.991339
$668$	−0.504835	−0.0195327
$669$	0.108451	0.00419296
$670$	16.0666	0.620707
$671$	−13.6347	−0.526363
$672$	−0.0245440	−0.000946806 0
$673$	−36.9607	−1.42473	−0.712365	−	0.701809i	$-0.752376\pi$
$673$	−36.9607	−1.42473	−0.712365	+	0.701809i	$0.752376\pi$
$674$	16.9007	0.650992
$675$	0.0276243	0.00106326
$676$	−4.29064	−0.165025
$677$	−35.7886	−1.37547	−0.687734	−	0.725963i	$-0.741394\pi$
$677$	−35.7886	−1.37547	−0.687734	+	0.725963i	$0.741394\pi$
$678$	0.0970390	0.00372676
$679$	−13.5634	−0.520517
$680$	−10.4292	−0.399940
$681$	−0.0295438	−0.00113212
$682$	8.74240	0.334764
$683$	36.9185	1.41265	0.706324	−	0.707889i	$-0.250352\pi$
$683$	36.9185	1.41265	0.706324	+	0.707889i	$0.250352\pi$
$684$	6.80112	0.260047
$685$	−18.1287	−0.692662
$686$	−1.74109	−0.0664753
$687$	0.00460406	0.000175656 0
$688$	−36.2125	−1.38059
$689$	6.47145	0.246542
$690$	−0.0325290	−0.00123836
$691$	−27.3554	−1.04065	−0.520324	−	0.853969i	$-0.674189\pi$
$691$	−27.3554	−1.04065	−0.520324	+	0.853969i	$0.674189\pi$
$692$	20.2682	0.770480
$693$	4.93634	0.187516
$694$	−4.77193	−0.181140
$695$	−3.84533	−0.145862
$696$	−0.0489870	−0.00185685
$697$	−15.7432	−0.596317
$698$	9.03503	0.341981
$699$	0.114245	0.00432114
$700$	1.03141	0.0389837
$701$	−7.52008	−0.284029	−0.142015	−	0.989865i	$-0.545358\pi$
$701$	−7.52008	−0.284029	−0.142015	+	0.989865i	$0.545358\pi$
$702$	−0.143001	−0.00539724
$703$	7.79810	0.294111
$704$	−1.17870	−0.0444241
$705$	−0.0421099	−0.00158595
$706$	−41.3331	−1.55559
$707$	9.85427	0.370608
$708$	0.0214761	0.000807121 0
$709$	−41.2296	−1.54841	−0.774205	−	0.632935i	$-0.781850\pi$
$709$	−41.2296	−1.54841	−0.774205	+	0.632935i	$0.781850\pi$
$710$	−16.3808	−0.614761
$711$	16.6663	0.625035
$712$	6.74895	0.252928
$713$	−12.3831	−0.463749
$714$	−0.0495737	−0.00185525
$715$	−4.89231	−0.182962
$716$	−3.78670	−0.141516
$717$	0.0451031	0.00168441
$718$	3.18652	0.118920
$719$	−32.2087	−1.20118	−0.600590	−	0.799557i	$-0.705068\pi$
$719$	−32.2087	−1.20118	−0.600590	+	0.799557i	$0.705068\pi$
$720$	14.9969	0.558903
$721$	−9.89130	−0.368371
$722$	24.6691	0.918090
$723$	0.0642768	0.00239048
$724$	−17.4100	−0.647037
$725$	6.30926	0.234320
$726$	−0.0664733	−0.00246706
$727$	36.6924	1.36085	0.680423	−	0.732820i	$-0.261796\pi$
$727$	36.6924	1.36085	0.680423	+	0.732820i	$0.261796\pi$
$728$	5.01405	0.185833
$729$	−26.9989	−0.999958
$730$	6.23752	0.230861
$731$	−44.7984	−1.65693
$732$	−0.0393489	−0.00145438
$733$	−48.2253	−1.78124	−0.890621	−	0.454746i	$-0.849730\pi$
$733$	−48.2253	−1.78124	−0.890621	+	0.454746i	$0.849730\pi$
$734$	59.4212	2.19328
$735$	−0.00460406	−0.000169823 0
$736$	−21.6327	−0.797393
$737$	15.1841	0.559313
$738$	13.2968	0.489461
$739$	−49.6611	−1.82681	−0.913407	−	0.407047i	$-0.866559\pi$
$739$	−49.6611	−1.82681	−0.913407	+	0.407047i	$0.866559\pi$
$740$	−3.65924	−0.134516
$741$	0.0300883	0.00110532
$742$	−3.78963	−0.139122
$743$	15.3340	0.562551	0.281275	−	0.959627i	$-0.409243\pi$
$743$	15.3340	0.562551	0.281275	+	0.959627i	$0.409243\pi$
$744$	−0.0236932	−0.000868635 0
$745$	−2.78896	−0.102180
$746$	−23.5467	−0.862106
$747$	−13.6359	−0.498911
$748$	10.4956	0.383757
$749$	−0.374924	−0.0136994
$750$	0.00801611	0.000292707 0
$751$	−7.68163	−0.280307	−0.140153	−	0.990130i	$-0.544760\pi$
$751$	−7.68163	−0.280307	−0.140153	+	0.990130i	$0.544760\pi$
$752$	−45.7223	−1.66732
$753$	−0.100750	−0.00367152
$754$	−32.6609	−1.18944
$755$	6.16620	0.224411
$756$	0.0284920	0.00103624
$757$	46.5568	1.69214	0.846069	−	0.533074i	$-0.178963\pi$
$757$	46.5568	1.69214	0.846069	+	0.533074i	$0.178963\pi$
$758$	16.2525	0.590317
$759$	−0.0307422	−0.00111587
$760$	−3.70673	−0.134457
$761$	11.2009	0.406032	0.203016	−	0.979175i	$-0.434926\pi$
$761$	11.2009	0.406032	0.203016	+	0.979175i	$0.434926\pi$
$762$	0.0882518	0.00319703
$763$	−15.5601	−0.563313
$764$	15.4961	0.560631
$765$	18.5527	0.670773
$766$	26.3407	0.951727
$767$	−13.4465	−0.485525
$768$	−0.0888686	−0.00320677
$769$	−20.9544	−0.755635	−0.377817	−	0.925880i	$-0.623325\pi$
$769$	−20.9544	−0.755635	−0.377817	+	0.925880i	$0.623325\pi$
$770$	2.86490	0.103244
$771$	0.0594859	0.00214233
$772$	6.60907	0.237866
$773$	30.4907	1.09667	0.548337	−	0.836258i	$-0.315261\pi$
$773$	30.4907	1.09667	0.548337	+	0.836258i	$0.315261\pi$
$774$	37.8369	1.36002
$775$	3.05155	0.109615
$776$	−22.8734	−0.821108
$777$	0.0163343	0.000585989 0
$778$	−60.2303	−2.15936
$779$	−5.59546	−0.200478
$780$	−0.0141189	−0.000505537 0
$781$	−15.4811	−0.553956
$782$	−43.6935	−1.56248
$783$	0.174289	0.00622857
$784$	−4.99901	−0.178536
$785$	−0.356872	−0.0127373
$786$	−0.176516	−0.00629611
$787$	−22.7355	−0.810435	−0.405217	−	0.914220i	$-0.632804\pi$
$787$	−22.7355	−0.810435	−0.405217	+	0.914220i	$0.632804\pi$
$788$	−15.2674	−0.543877
$789$	0.110299	0.00392676
$790$	9.67260	0.344136
$791$	12.1055	0.430422
$792$	8.32467	0.295804
$793$	24.6369	0.874883
$794$	−37.3403	−1.32516
$795$	−0.0100211	−0.000355412 0
$796$	19.0959	0.676836
$797$	−14.6268	−0.518107	−0.259053	−	0.965863i	$-0.583411\pi$
$797$	−14.6268	−0.518107	−0.259053	+	0.965863i	$0.583411\pi$
$798$	−0.0176195	−0.000623723 0
$799$	−56.5628	−2.00105
$800$	5.33095	0.188478
$801$	−12.0058	−0.424206
$802$	1.76729	0.0624051
$803$	5.89490	0.208026
$804$	0.0438202	0.00154542
$805$	−4.05795	−0.143024
$806$	−15.7968	−0.556420
$807$	0.122542	0.00431370
$808$	16.6183	0.584629
$809$	24.2416	0.852288	0.426144	−	0.904655i	$-0.359872\pi$
$809$	24.2416	0.852288	0.426144	+	0.904655i	$0.359872\pi$
$810$	−15.6695	−0.550571
$811$	−26.6199	−0.934749	−0.467375	−	0.884059i	$-0.654800\pi$
$811$	−26.6199	−0.934749	−0.467375	+	0.884059i	$0.654800\pi$
$812$	6.50745	0.228367
$813$	0.117477	0.00412009
$814$	−10.1641	−0.356251
$815$	6.27022	0.219636
$816$	−0.142336	−0.00498274
$817$	−15.9222	−0.557049
$818$	38.9492	1.36183
$819$	−8.91959	−0.311676
$820$	2.62566	0.0916919
$821$	−29.5366	−1.03083	−0.515417	−	0.856939i	$-0.672363\pi$
$821$	−29.5366	−1.03083	−0.515417	+	0.856939i	$0.672363\pi$
$822$	−0.145322	−0.00506867
$823$	−1.79667	−0.0626280	−0.0313140	−	0.999510i	$-0.509969\pi$
$823$	−1.79667	−0.0626280	−0.0313140	+	0.999510i	$0.509969\pi$
$824$	−16.6807	−0.581101
$825$	0.00757579	0.000263755 0
$826$	7.87416	0.273977
$827$	6.38265	0.221947	0.110973	−	0.993823i	$-0.464603\pi$
$827$	6.38265	0.221947	0.110973	+	0.993823i	$0.464603\pi$
$828$	12.5562	0.436357
$829$	−29.2953	−1.01747	−0.508733	−	0.860924i	$-0.669886\pi$
$829$	−29.2953	−1.01747	−0.508733	+	0.860924i	$0.669886\pi$
$830$	−7.91385	−0.274694
$831$	−0.0897110	−0.00311204
$832$	2.12983	0.0738386
$833$	−6.18426	−0.214272
$834$	−0.0308246	−0.00106737
$835$	−0.489460	−0.0169385
$836$	3.73034	0.129017
$837$	0.0842970	0.00291373
$838$	31.6411	1.09303
$839$	−33.2119	−1.14660	−0.573301	−	0.819345i	$-0.694337\pi$
$839$	−33.2119	−1.14660	−0.573301	+	0.819345i	$0.694337\pi$
$840$	−0.00776431	−0.000267894 0
$841$	10.8068	0.372647
$842$	49.8899	1.71932
$843$	0.0379652	0.00130759
$844$	−7.07452	−0.243515
$845$	−4.15997	−0.143107
$846$	47.7732	1.64248
$847$	−8.29246	−0.284932
$848$	−10.8807	−0.373646
$849$	0.0332540	0.00114127
$850$	10.7674	0.369318
$851$	14.3968	0.493516
$852$	−0.0446773	−0.00153062
$853$	−5.10800	−0.174895	−0.0874473	−	0.996169i	$-0.527871\pi$
$853$	−5.10800	−0.174895	−0.0874473	+	0.996169i	$0.527871\pi$
$854$	−14.4272	−0.493689
$855$	6.59399	0.225510
$856$	−0.632274	−0.0216107
$857$	35.9247	1.22717	0.613583	−	0.789631i	$-0.289728\pi$
$857$	35.9247	1.22717	0.613583	+	0.789631i	$0.289728\pi$
$858$	−0.0392173	−0.00133886
$859$	5.90832	0.201589	0.100795	−	0.994907i	$-0.467861\pi$
$859$	5.90832	0.201589	0.100795	+	0.994907i	$0.467861\pi$
$860$	7.47148	0.254775
$861$	−0.0117205	−0.000399434 0
$862$	−41.9208	−1.42783
$863$	29.6923	1.01074	0.505370	−	0.862903i	$-0.331356\pi$
$863$	29.6923	1.01074	0.505370	+	0.862903i	$0.331356\pi$
$864$	0.147264	0.00501001
$865$	19.6509	0.668151
$866$	−47.7504	−1.62262
$867$	−0.0978138	−0.00332193
$868$	3.14741	0.106830
$869$	9.14130	0.310097
$870$	0.0505757	0.00171468
$871$	−27.4365	−0.929649
$872$	−26.2406	−0.888619
$873$	40.6900	1.37715
$874$	−15.5296	−0.525295
$875$	1.00000	0.0338062
$876$	0.0170123	0.000574792 0
$877$	2.29331	0.0774396	0.0387198	−	0.999250i	$-0.487672\pi$
$877$	2.29331	0.0774396	0.0387198	+	0.999250i	$0.487672\pi$
$878$	−15.6483	−0.528104
$879$	−0.0568840	−0.00191865
$880$	8.22567	0.277287
$881$	14.4212	0.485864	0.242932	−	0.970043i	$-0.421891\pi$
$881$	14.4212	0.485864	0.242932	+	0.970043i	$0.421891\pi$
$882$	5.22325	0.175876
$883$	−36.7107	−1.23541	−0.617707	−	0.786408i	$-0.711938\pi$
$883$	−36.7107	−1.23541	−0.617707	+	0.786408i	$0.711938\pi$
$884$	−18.9647	−0.637853
$885$	0.0208220	0.000699925 0
$886$	−22.6309	−0.760300
$887$	45.2032	1.51778	0.758888	−	0.651221i	$-0.225743\pi$
$887$	45.2032	1.51778	0.758888	+	0.651221i	$0.225743\pi$
$888$	0.0275462	0.000924390 0
$889$	11.0093	0.369240
$890$	−6.96782	−0.233562
$891$	−14.8088	−0.496114
$892$	−24.2954	−0.813471
$893$	−20.1036	−0.672740
$894$	−0.0223566	−0.000747718 0
$895$	−3.67137	−0.122720
$896$	−11.9091	−0.397855
$897$	0.0555488	0.00185472
$898$	28.7408	0.959094
$899$	19.2531	0.642125
$900$	−3.09421	−0.103140
$901$	−13.4605	−0.448435
$902$	7.29315	0.242835
$903$	−0.0333515	−0.00110987
$904$	20.4148	0.678985
$905$	−16.8798	−0.561102
$906$	0.0494290	0.00164217
$907$	−32.2600	−1.07118	−0.535588	−	0.844480i	$-0.679910\pi$
$907$	−32.2600	−1.07118	−0.535588	+	0.844480i	$0.679910\pi$
$908$	6.61846	0.219641
$909$	−29.5626	−0.980529
$910$	−5.17666	−0.171604
$911$	−11.0930	−0.367527	−0.183764	−	0.982970i	$-0.558828\pi$
$911$	−11.0930	−0.367527	−0.183764	+	0.982970i	$0.558828\pi$
$912$	−0.0505889	−0.00167517
$913$	−7.47915	−0.247524
$914$	−60.6191	−2.00510
$915$	−0.0381506	−0.00126122
$916$	−1.03141	−0.0340788
$917$	−22.0201	−0.727169
$918$	0.297441	0.00981703
$919$	−8.08387	−0.266662	−0.133331	−	0.991072i	$-0.542567\pi$
$919$	−8.08387	−0.266662	−0.133331	+	0.991072i	$0.542567\pi$
$920$	−6.84335	−0.225618
$921$	0.0196918	0.000648867 0
$922$	69.9007	2.30206
$923$	27.9731	0.920745
$924$	0.00781376	0.000257054 0
$925$	−3.54780	−0.116651
$926$	27.8023	0.913641
$927$	29.6737	0.974612
$928$	33.6343	1.10410
$929$	43.3134	1.42107	0.710533	−	0.703664i	$-0.248454\pi$
$929$	43.3134	1.42107	0.710533	+	0.703664i	$0.248454\pi$
$930$	0.0244616	0.000802127 0
$931$	−2.19801	−0.0720369
$932$	−25.5934	−0.838340
$933$	0.0399484	0.00130785
$934$	−50.7243	−1.65975
$935$	10.1760	0.332789
$936$	−15.0420	−0.491664
$937$	−55.4011	−1.80987	−0.904937	−	0.425545i	$-0.860082\pi$
$937$	−55.4011	−1.80987	−0.904937	+	0.425545i	$0.860082\pi$
$938$	16.0666	0.524593
$939$	−0.0962183	−0.00313996
$940$	9.43356	0.307689
$941$	−27.0903	−0.883118	−0.441559	−	0.897232i	$-0.645574\pi$
$941$	−27.0903	−0.883118	−0.441559	+	0.897232i	$0.645574\pi$
$942$	−0.00286072	−9.32074e−5 0
$943$	−10.3303	−0.336401
$944$	22.6082	0.735835
$945$	0.0276243	0.000898618 0
$946$	20.7531	0.674743
$947$	−2.06434	−0.0670821	−0.0335411	−	0.999437i	$-0.510678\pi$
$947$	−2.06434	−0.0670821	−0.0335411	+	0.999437i	$0.510678\pi$
$948$	0.0263812	0.000856820 0
$949$	−10.6516	−0.345767
$950$	3.82695	0.124163
$951$	−0.0289267	−0.000938011 0
$952$	−10.4292	−0.338011
$953$	47.7268	1.54602	0.773012	−	0.634392i	$-0.218749\pi$
$953$	47.7268	1.54602	0.773012	+	0.634392i	$0.218749\pi$
$954$	11.3688	0.368079
$955$	15.0242	0.486172
$956$	−10.1041	−0.326790
$957$	0.0477977	0.00154508
$958$	−48.1299	−1.55501
$959$	−18.1287	−0.585406
$960$	−0.00329807	−0.000106445 0
$961$	−21.6880	−0.699613
$962$	18.3657	0.592135
$963$	1.12477	0.0362451
$964$	−14.3994	−0.463774
$965$	6.40779	0.206274
$966$	−0.0325290	−0.00104660
$967$	20.2939	0.652608	0.326304	−	0.945265i	$-0.394197\pi$
$967$	20.2939	0.652608	0.326304	+	0.945265i	$0.394197\pi$
$968$	−13.9844	−0.449477
$969$	−0.0625834	−0.00201047
$970$	23.6152	0.758239
$971$	−40.1171	−1.28742	−0.643710	−	0.765270i	$-0.722606\pi$
$971$	−40.1171	−1.28742	−0.643710	+	0.765270i	$0.722606\pi$
$972$	−0.128213	−0.00411244
$973$	−3.84533	−0.123276
$974$	46.7963	1.49945
$975$	−0.0136889	−0.000438395 0
$976$	−41.4232	−1.32593
$977$	−7.81326	−0.249968	−0.124984	−	0.992159i	$-0.539888\pi$
$977$	−7.81326	−0.249968	−0.124984	+	0.992159i	$0.539888\pi$
$978$	0.0502628	0.00160723
$979$	−6.58509	−0.210460
$980$	1.03141	0.0329472
$981$	46.6799	1.49038
$982$	66.3218	2.11641
$983$	8.06606	0.257267	0.128634	−	0.991692i	$-0.458941\pi$
$983$	8.06606	0.257267	0.128634	+	0.991692i	$0.458941\pi$
$984$	−0.0197655	−0.000630102 0
$985$	−14.8024	−0.471644
$986$	67.9343	2.16347
$987$	−0.0421099	−0.00134037
$988$	−6.74045	−0.214442
$989$	−29.3955	−0.934723
$990$	−8.59464	−0.273156
$991$	−46.8424	−1.48800	−0.743999	−	0.668181i	$-0.767073\pi$
$991$	−46.8424	−1.48800	−0.743999	+	0.668181i	$0.767073\pi$
$992$	16.2677	0.516499
$993$	0.0364533	0.00115681
$994$	−16.3808	−0.519568
$995$	18.5143	0.586944
$996$	−0.0215843	−0.000683926 0
$997$	59.8578	1.89571	0.947857	−	0.318695i	$-0.103244\pi$
$997$	59.8578	1.89571	0.947857	+	0.318695i	$0.103244\pi$
$998$	−71.7364	−2.27078
$999$	−0.0980053	−0.00310075

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.h.1.10	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.h.1.10	✓	38	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)

\(f(q)\)	\(=\)	\(q-1.74109 q^{2} -0.00460406 q^{3} +1.03141 q^{4} +1.00000 q^{5} +0.00801611 q^{6} +1.00000 q^{7} +1.68640 q^{8} -2.99998 q^{9} +O(q^{10})\)	\(q-1.74109 q^{2} -0.00460406 q^{3} +1.03141 q^{4} +1.00000 q^{5} +0.00801611 q^{6} +1.00000 q^{7} +1.68640 q^{8} -2.99998 q^{9} -1.74109 q^{10} -1.64546 q^{11} -0.00474868 q^{12} +2.97322 q^{13} -1.74109 q^{14} -0.00460406 q^{15} -4.99901 q^{16} -6.18426 q^{17} +5.22325 q^{18} -2.19801 q^{19} +1.03141 q^{20} -0.00460406 q^{21} +2.86490 q^{22} -4.05795 q^{23} -0.00776431 q^{24} +1.00000 q^{25} -5.17666 q^{26} +0.0276243 q^{27} +1.03141 q^{28} +6.30926 q^{29} +0.00801611 q^{30} +3.05155 q^{31} +5.33095 q^{32} +0.00757579 q^{33} +10.7674 q^{34} +1.00000 q^{35} -3.09421 q^{36} -3.54780 q^{37} +3.82695 q^{38} -0.0136889 q^{39} +1.68640 q^{40} +2.54569 q^{41} +0.00801611 q^{42} +7.24393 q^{43} -1.69715 q^{44} -2.99998 q^{45} +7.06528 q^{46} +9.14625 q^{47} +0.0230158 q^{48} +1.00000 q^{49} -1.74109 q^{50} +0.0284727 q^{51} +3.06661 q^{52} +2.17658 q^{53} -0.0480965 q^{54} -1.64546 q^{55} +1.68640 q^{56} +0.0101198 q^{57} -10.9850 q^{58} -4.52254 q^{59} -0.00474868 q^{60} +8.28628 q^{61} -5.31305 q^{62} -2.99998 q^{63} +0.716338 q^{64} +2.97322 q^{65} -0.0131902 q^{66} -9.22787 q^{67} -6.37852 q^{68} +0.0186831 q^{69} -1.74109 q^{70} +9.40835 q^{71} -5.05918 q^{72} -3.58253 q^{73} +6.17705 q^{74} -0.00460406 q^{75} -2.26705 q^{76} -1.64546 q^{77} +0.0238336 q^{78} -5.55547 q^{79} -4.99901 q^{80} +8.99981 q^{81} -4.43229 q^{82} +4.54533 q^{83} -0.00474868 q^{84} -6.18426 q^{85} -12.6124 q^{86} -0.0290482 q^{87} -2.77491 q^{88} +4.00198 q^{89} +5.22325 q^{90} +2.97322 q^{91} -4.18542 q^{92} -0.0140495 q^{93} -15.9245 q^{94} -2.19801 q^{95} -0.0245440 q^{96} -13.5634 q^{97} -1.74109 q^{98} +4.93634 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9}+O(q^{10}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9} - 6 q^{10} - 18 q^{11} - 20 q^{12} - 25 q^{13} - 6 q^{14} - 9 q^{15} - 21 q^{17} - 7 q^{18} - 14 q^{19} + 24 q^{20} - 9 q^{21} - 11 q^{22} - 16 q^{23} - 10 q^{24} + 38 q^{25} - 21 q^{26} - 15 q^{27} + 24 q^{28} - 52 q^{29} - 10 q^{30} - 30 q^{31} - 8 q^{32} - 13 q^{33} - 9 q^{34} + 38 q^{35} - 16 q^{36} - 47 q^{37} - 10 q^{38} - 50 q^{39} - 21 q^{40} - 35 q^{41} - 10 q^{42} - 18 q^{43} - 22 q^{44} + 13 q^{45} - 17 q^{46} - 23 q^{47} - 13 q^{48} + 38 q^{49} - 6 q^{50} - 5 q^{51} - 41 q^{52} - 12 q^{53} + 35 q^{54} - 18 q^{55} - 21 q^{56} - 3 q^{57} - 16 q^{58} - 16 q^{59} - 20 q^{60} - 47 q^{61} + 14 q^{62} + 13 q^{63} - 55 q^{64} - 25 q^{65} - 6 q^{66} - 54 q^{67} + 31 q^{68} - 95 q^{69} - 6 q^{70} - 41 q^{71} - 59 q^{73} - q^{74} - 9 q^{75} - 23 q^{76} - 18 q^{77} + 19 q^{78} - 117 q^{79} - 38 q^{81} + 19 q^{82} - 21 q^{83} - 20 q^{84} - 21 q^{85} - 12 q^{86} - 14 q^{87} - 40 q^{88} - 96 q^{89} - 7 q^{90} - 25 q^{91} + 53 q^{92} - 53 q^{93} - 28 q^{94} - 14 q^{95} + 40 q^{96} - 70 q^{97} - 6 q^{98} - 52 q^{99}+O(q^{100}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9 - 6 * q^10 - 18 * q^11 - 20 * q^12 - 25 * q^13 - 6 * q^14 - 9 * q^15 - 21 * q^17 - 7 * q^18 - 14 * q^19 + 24 * q^20 - 9 * q^21 - 11 * q^22 - 16 * q^23 - 10 * q^24 + 38 * q^25 - 21 * q^26 - 15 * q^27 + 24 * q^28 - 52 * q^29 - 10 * q^30 - 30 * q^31 - 8 * q^32 - 13 * q^33 - 9 * q^34 + 38 * q^35 - 16 * q^36 - 47 * q^37 - 10 * q^38 - 50 * q^39 - 21 * q^40 - 35 * q^41 - 10 * q^42 - 18 * q^43 - 22 * q^44 + 13 * q^45 - 17 * q^46 - 23 * q^47 - 13 * q^48 + 38 * q^49 - 6 * q^50 - 5 * q^51 - 41 * q^52 - 12 * q^53 + 35 * q^54 - 18 * q^55 - 21 * q^56 - 3 * q^57 - 16 * q^58 - 16 * q^59 - 20 * q^60 - 47 * q^61 + 14 * q^62 + 13 * q^63 - 55 * q^64 - 25 * q^65 - 6 * q^66 - 54 * q^67 + 31 * q^68 - 95 * q^69 - 6 * q^70 - 41 * q^71 - 59 * q^73 - q^74 - 9 * q^75 - 23 * q^76 - 18 * q^77 + 19 * q^78 - 117 * q^79 - 38 * q^81 + 19 * q^82 - 21 * q^83 - 20 * q^84 - 21 * q^85 - 12 * q^86 - 14 * q^87 - 40 * q^88 - 96 * q^89 - 7 * q^90 - 25 * q^91 + 53 * q^92 - 53 * q^93 - 28 * q^94 - 14 * q^95 + 40 * q^96 - 70 * q^97 - 6 * q^98 - 52 * q^99

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