LMFDB - Embedded newform 8026.2.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$0$
Dimension:	$86$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.09967 q^{3} +1.00000 q^{4} +3.00804 q^{5} +2.09967 q^{6} +1.34654 q^{7} -1.00000 q^{8} +1.40862 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.09967 q^{3} +1.00000 q^{4} +3.00804 q^{5} +2.09967 q^{6} +1.34654 q^{7} -1.00000 q^{8} +1.40862 q^{9} -3.00804 q^{10} -1.24941 q^{11} -2.09967 q^{12} +0.301458 q^{13} -1.34654 q^{14} -6.31589 q^{15} +1.00000 q^{16} +7.17405 q^{17} -1.40862 q^{18} +7.29625 q^{19} +3.00804 q^{20} -2.82729 q^{21} +1.24941 q^{22} -0.401333 q^{23} +2.09967 q^{24} +4.04828 q^{25} -0.301458 q^{26} +3.34137 q^{27} +1.34654 q^{28} -6.84104 q^{29} +6.31589 q^{30} +8.35113 q^{31} -1.00000 q^{32} +2.62335 q^{33} -7.17405 q^{34} +4.05044 q^{35} +1.40862 q^{36} +0.825735 q^{37} -7.29625 q^{38} -0.632962 q^{39} -3.00804 q^{40} +7.32252 q^{41} +2.82729 q^{42} +3.29145 q^{43} -1.24941 q^{44} +4.23719 q^{45} +0.401333 q^{46} +8.02381 q^{47} -2.09967 q^{48} -5.18683 q^{49} -4.04828 q^{50} -15.0631 q^{51} +0.301458 q^{52} +12.3821 q^{53} -3.34137 q^{54} -3.75827 q^{55} -1.34654 q^{56} -15.3197 q^{57} +6.84104 q^{58} -2.89041 q^{59} -6.31589 q^{60} -4.38492 q^{61} -8.35113 q^{62} +1.89676 q^{63} +1.00000 q^{64} +0.906795 q^{65} -2.62335 q^{66} -6.29483 q^{67} +7.17405 q^{68} +0.842668 q^{69} -4.05044 q^{70} -12.6810 q^{71} -1.40862 q^{72} -9.49410 q^{73} -0.825735 q^{74} -8.50006 q^{75} +7.29625 q^{76} -1.68238 q^{77} +0.632962 q^{78} +9.35312 q^{79} +3.00804 q^{80} -11.2417 q^{81} -7.32252 q^{82} -5.91425 q^{83} -2.82729 q^{84} +21.5798 q^{85} -3.29145 q^{86} +14.3639 q^{87} +1.24941 q^{88} +4.90163 q^{89} -4.23719 q^{90} +0.405924 q^{91} -0.401333 q^{92} -17.5346 q^{93} -8.02381 q^{94} +21.9474 q^{95} +2.09967 q^{96} -6.33495 q^{97} +5.18683 q^{98} -1.75995 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) $ 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.09967	−1.21225	−0.606123	−	0.795371i	$-0.707276\pi$
$3$	−2.09967	−1.21225	−0.606123	+	0.795371i	$0.707276\pi$
$4$	1.00000	0.500000
$5$	3.00804	1.34523	0.672617	−	0.739991i	$-0.265170\pi$
$5$	3.00804	1.34523	0.672617	+	0.739991i	$0.265170\pi$
$6$	2.09967	0.857187
$7$	1.34654	0.508944	0.254472	−	0.967080i	$-0.418098\pi$
$7$	1.34654	0.508944	0.254472	+	0.967080i	$0.418098\pi$
$8$	−1.00000	−0.353553
$9$	1.40862	0.469541
$10$	−3.00804	−0.951224
$11$	−1.24941	−0.376712	−0.188356	−	0.982101i	$-0.560316\pi$
$11$	−1.24941	−0.376712	−0.188356	+	0.982101i	$0.560316\pi$
$12$	−2.09967	−0.606123
$13$	0.301458	0.0836093	0.0418047	−	0.999126i	$-0.486689\pi$
$13$	0.301458	0.0836093	0.0418047	+	0.999126i	$0.486689\pi$
$14$	−1.34654	−0.359878
$15$	−6.31589	−1.63076
$16$	1.00000	0.250000
$17$	7.17405	1.73996	0.869981	−	0.493085i	$-0.164131\pi$
$17$	7.17405	1.73996	0.869981	+	0.493085i	$0.164131\pi$
$18$	−1.40862	−0.332015
$19$	7.29625	1.67388	0.836938	−	0.547298i	$-0.184344\pi$
$19$	7.29625	1.67388	0.836938	+	0.547298i	$0.184344\pi$
$20$	3.00804	0.672617
$21$	−2.82729	−0.616965
$22$	1.24941	0.266375
$23$	−0.401333	−0.0836838	−0.0418419	−	0.999124i	$-0.513323\pi$
$23$	−0.401333	−0.0836838	−0.0418419	+	0.999124i	$0.513323\pi$
$24$	2.09967	0.428594
$25$	4.04828	0.809656
$26$	−0.301458	−0.0591207
$27$	3.34137	0.643047
$28$	1.34654	0.254472
$29$	−6.84104	−1.27035	−0.635175	−	0.772368i	$-0.719072\pi$
$29$	−6.84104	−1.27035	−0.635175	+	0.772368i	$0.719072\pi$
$30$	6.31589	1.15312
$31$	8.35113	1.49991	0.749953	−	0.661491i	$-0.230076\pi$
$31$	8.35113	1.49991	0.749953	+	0.661491i	$0.230076\pi$
$32$	−1.00000	−0.176777
$33$	2.62335	0.456667
$34$	−7.17405	−1.23034
$35$	4.05044	0.684649
$36$	1.40862	0.234770
$37$	0.825735	0.135750	0.0678750	−	0.997694i	$-0.478378\pi$
$37$	0.825735	0.135750	0.0678750	+	0.997694i	$0.478378\pi$
$38$	−7.29625	−1.18361
$39$	−0.632962	−0.101355
$40$	−3.00804	−0.475612
$41$	7.32252	1.14359	0.571793	−	0.820398i	$-0.306248\pi$
$41$	7.32252	1.14359	0.571793	+	0.820398i	$0.306248\pi$
$42$	2.82729	0.436260
$43$	3.29145	0.501942	0.250971	−	0.967995i	$-0.419250\pi$
$43$	3.29145	0.501942	0.250971	+	0.967995i	$0.419250\pi$
$44$	−1.24941	−0.188356
$45$	4.23719	0.631642
$46$	0.401333	0.0591734
$47$	8.02381	1.17039	0.585196	−	0.810892i	$-0.301017\pi$
$47$	8.02381	1.17039	0.585196	+	0.810892i	$0.301017\pi$
$48$	−2.09967	−0.303062
$49$	−5.18683	−0.740976
$50$	−4.04828	−0.572513
$51$	−15.0631	−2.10926
$52$	0.301458	0.0418047
$53$	12.3821	1.70081	0.850407	−	0.526126i	$-0.176356\pi$
$53$	12.3821	1.70081	0.850407	+	0.526126i	$0.176356\pi$
$54$	−3.34137	−0.454703
$55$	−3.75827	−0.506766
$56$	−1.34654	−0.179939
$57$	−15.3197	−2.02915
$58$	6.84104	0.898273
$59$	−2.89041	−0.376299	−0.188150	−	0.982140i	$-0.560249\pi$
$59$	−2.89041	−0.376299	−0.188150	+	0.982140i	$0.560249\pi$
$60$	−6.31589	−0.815378
$61$	−4.38492	−0.561432	−0.280716	−	0.959791i	$-0.590572\pi$
$61$	−4.38492	−0.561432	−0.280716	+	0.959791i	$0.590572\pi$
$62$	−8.35113	−1.06059
$63$	1.89676	0.238970
$64$	1.00000	0.125000
$65$	0.906795	0.112474
$66$	−2.62335	−0.322913
$67$	−6.29483	−0.769036	−0.384518	−	0.923118i	$-0.625632\pi$
$67$	−6.29483	−0.769036	−0.384518	+	0.923118i	$0.625632\pi$
$68$	7.17405	0.869981
$69$	0.842668	0.101445
$70$	−4.05044	−0.484120
$71$	−12.6810	−1.50495	−0.752476	−	0.658619i	$-0.771141\pi$
$71$	−12.6810	−1.50495	−0.752476	+	0.658619i	$0.771141\pi$
$72$	−1.40862	−0.166008
$73$	−9.49410	−1.11120	−0.555600	−	0.831450i	$-0.687511\pi$
$73$	−9.49410	−1.11120	−0.555600	+	0.831450i	$0.687511\pi$
$74$	−0.825735	−0.0959897
$75$	−8.50006	−0.981502
$76$	7.29625	0.836938
$77$	−1.68238	−0.191725
$78$	0.632962	0.0716689
$79$	9.35312	1.05231	0.526154	−	0.850389i	$-0.323634\pi$
$79$	9.35312	1.05231	0.526154	+	0.850389i	$0.323634\pi$
$80$	3.00804	0.336309
$81$	−11.2417	−1.24907
$82$	−7.32252	−0.808637
$83$	−5.91425	−0.649174	−0.324587	−	0.945856i	$-0.605225\pi$
$83$	−5.91425	−0.649174	−0.324587	+	0.945856i	$0.605225\pi$
$84$	−2.82729	−0.308482
$85$	21.5798	2.34066
$86$	−3.29145	−0.354926
$87$	14.3639	1.53998
$88$	1.24941	0.133188
$89$	4.90163	0.519572	0.259786	−	0.965666i	$-0.416348\pi$
$89$	4.90163	0.519572	0.259786	+	0.965666i	$0.416348\pi$
$90$	−4.23719	−0.446639
$91$	0.405924	0.0425524
$92$	−0.401333	−0.0418419
$93$	−17.5346	−1.81826
$94$	−8.02381	−0.827593
$95$	21.9474	2.25175
$96$	2.09967	0.214297
$97$	−6.33495	−0.643217	−0.321608	−	0.946873i	$-0.604223\pi$
$97$	−6.33495	−0.643217	−0.321608	+	0.946873i	$0.604223\pi$
$98$	5.18683	0.523949
$99$	−1.75995	−0.176882
$100$	4.04828	0.404828
$101$	15.2076	1.51322	0.756608	−	0.653869i	$-0.226855\pi$
$101$	15.2076	1.51322	0.756608	+	0.653869i	$0.226855\pi$
$102$	15.0631	1.49147
$103$	17.1033	1.68523	0.842617	−	0.538514i	$-0.181014\pi$
$103$	17.1033	1.68523	0.842617	+	0.538514i	$0.181014\pi$
$104$	−0.301458	−0.0295604
$105$	−8.50459	−0.829963
$106$	−12.3821	−1.20266
$107$	11.1603	1.07891	0.539454	−	0.842015i	$-0.318631\pi$
$107$	11.1603	1.07891	0.539454	+	0.842015i	$0.318631\pi$
$108$	3.34137	0.321524
$109$	0.729959	0.0699173	0.0349587	−	0.999389i	$-0.488870\pi$
$109$	0.729959	0.0699173	0.0349587	+	0.999389i	$0.488870\pi$
$110$	3.75827	0.358337
$111$	−1.73377	−0.164562
$112$	1.34654	0.127236
$113$	0.833052	0.0783669	0.0391835	−	0.999232i	$-0.487524\pi$
$113$	0.833052	0.0783669	0.0391835	+	0.999232i	$0.487524\pi$
$114$	15.3197	1.43482
$115$	−1.20723	−0.112574
$116$	−6.84104	−0.635175
$117$	0.424640	0.0392580
$118$	2.89041	0.266084
$119$	9.66013	0.885543
$120$	6.31589	0.576559
$121$	−9.43897	−0.858088
$122$	4.38492	0.396992
$123$	−15.3749	−1.38631
$124$	8.35113	0.749953
$125$	−2.86281	−0.256058
$126$	−1.89676	−0.168977
$127$	17.5107	1.55383	0.776913	−	0.629608i	$-0.216784\pi$
$127$	17.5107	1.55383	0.776913	+	0.629608i	$0.216784\pi$
$128$	−1.00000	−0.0883883
$129$	−6.91097	−0.608477
$130$	−0.906795	−0.0795312
$131$	20.1475	1.76030	0.880148	−	0.474700i	$-0.157443\pi$
$131$	20.1475	1.76030	0.880148	+	0.474700i	$0.157443\pi$
$132$	2.62335	0.228334
$133$	9.82468	0.851908
$134$	6.29483	0.543790
$135$	10.0510	0.865049
$136$	−7.17405	−0.615170
$137$	−13.4504	−1.14915	−0.574573	−	0.818453i	$-0.694832\pi$
$137$	−13.4504	−1.14915	−0.574573	+	0.818453i	$0.694832\pi$
$138$	−0.842668	−0.0717327
$139$	−15.2602	−1.29435	−0.647177	−	0.762339i	$-0.724051\pi$
$139$	−15.2602	−1.29435	−0.647177	+	0.762339i	$0.724051\pi$
$140$	4.05044	0.342324
$141$	−16.8474	−1.41880
$142$	12.6810	1.06416
$143$	−0.376645	−0.0314966
$144$	1.40862	0.117385
$145$	−20.5781	−1.70892
$146$	9.49410	0.785737
$147$	10.8907	0.898246
$148$	0.825735	0.0678750
$149$	11.5873	0.949267	0.474633	−	0.880184i	$-0.342581\pi$
$149$	11.5873	0.949267	0.474633	+	0.880184i	$0.342581\pi$
$150$	8.50006	0.694027
$151$	−5.23203	−0.425777	−0.212888	−	0.977077i	$-0.568287\pi$
$151$	−5.23203	−0.425777	−0.212888	+	0.977077i	$0.568287\pi$
$152$	−7.29625	−0.591804
$153$	10.1055	0.816983
$154$	1.68238	0.135570
$155$	25.1205	2.01773
$156$	−0.632962	−0.0506775
$157$	−1.58456	−0.126461	−0.0632307	−	0.997999i	$-0.520140\pi$
$157$	−1.58456	−0.126461	−0.0632307	+	0.997999i	$0.520140\pi$
$158$	−9.35312	−0.744094
$159$	−25.9984	−2.06180
$160$	−3.00804	−0.237806
$161$	−0.540411	−0.0425903
$162$	11.2417	0.883227
$163$	15.8254	1.23954	0.619772	−	0.784782i	$-0.287225\pi$
$163$	15.8254	1.23954	0.619772	+	0.784782i	$0.287225\pi$
$164$	7.32252	0.571793
$165$	7.89114	0.614325
$166$	5.91425	0.459035
$167$	−6.61283	−0.511716	−0.255858	−	0.966714i	$-0.582358\pi$
$167$	−6.61283	−0.511716	−0.255858	+	0.966714i	$0.582358\pi$
$168$	2.82729	0.218130
$169$	−12.9091	−0.993009
$170$	−21.5798	−1.65509
$171$	10.2777	0.785953
$172$	3.29145	0.250971
$173$	−18.4520	−1.40288	−0.701439	−	0.712729i	$-0.747459\pi$
$173$	−18.4520	−1.40288	−0.701439	+	0.712729i	$0.747459\pi$
$174$	−14.3639	−1.08893
$175$	5.45116	0.412069
$176$	−1.24941	−0.0941779
$177$	6.06891	0.456167
$178$	−4.90163	−0.367393
$179$	−4.12681	−0.308453	−0.154226	−	0.988036i	$-0.549288\pi$
$179$	−4.12681	−0.308453	−0.154226	+	0.988036i	$0.549288\pi$
$180$	4.23719	0.315821
$181$	0.283105	0.0210430	0.0105215	−	0.999945i	$-0.496651\pi$
$181$	0.283105	0.0210430	0.0105215	+	0.999945i	$0.496651\pi$
$182$	−0.405924	−0.0300891
$183$	9.20690	0.680593
$184$	0.401333	0.0295867
$185$	2.48384	0.182616
$186$	17.5346	1.28570
$187$	−8.96334	−0.655464
$188$	8.02381	0.585196
$189$	4.49928	0.327275
$190$	−21.9474	−1.59223
$191$	4.37503	0.316566	0.158283	−	0.987394i	$-0.449404\pi$
$191$	4.37503	0.316566	0.158283	+	0.987394i	$0.449404\pi$
$192$	−2.09967	−0.151531
$193$	−27.3031	−1.96532	−0.982659	−	0.185421i	$-0.940635\pi$
$193$	−27.3031	−1.96532	−0.982659	+	0.185421i	$0.940635\pi$
$194$	6.33495	0.454823
$195$	−1.90397	−0.136346
$196$	−5.18683	−0.370488
$197$	1.97792	0.140921	0.0704605	−	0.997515i	$-0.477553\pi$
$197$	1.97792	0.140921	0.0704605	+	0.997515i	$0.477553\pi$
$198$	1.75995	0.125074
$199$	−5.51811	−0.391168	−0.195584	−	0.980687i	$-0.562660\pi$
$199$	−5.51811	−0.391168	−0.195584	+	0.980687i	$0.562660\pi$
$200$	−4.04828	−0.286257
$201$	13.2171	0.932261
$202$	−15.2076	−1.07000
$203$	−9.21173	−0.646536
$204$	−15.0631	−1.05463
$205$	22.0264	1.53839
$206$	−17.1033	−1.19164
$207$	−0.565327	−0.0392930
$208$	0.301458	0.0209023
$209$	−9.11602	−0.630568
$210$	8.50459	0.586872
$211$	−27.7025	−1.90712	−0.953560	−	0.301204i	$-0.902611\pi$
$211$	−27.7025	−1.90712	−0.953560	+	0.301204i	$0.902611\pi$
$212$	12.3821	0.850407
$213$	26.6258	1.82437
$214$	−11.1603	−0.762903
$215$	9.90080	0.675229
$216$	−3.34137	−0.227352
$217$	11.2451	0.763368
$218$	−0.729959	−0.0494390
$219$	19.9345	1.34705
$220$	−3.75827	−0.253383
$221$	2.16267	0.145477
$222$	1.73377	0.116363
$223$	−2.59638	−0.173867	−0.0869333	−	0.996214i	$-0.527707\pi$
$223$	−2.59638	−0.173867	−0.0869333	+	0.996214i	$0.527707\pi$
$224$	−1.34654	−0.0899694
$225$	5.70249	0.380166
$226$	−0.833052	−0.0554138
$227$	−16.5369	−1.09759	−0.548795	−	0.835957i	$-0.684913\pi$
$227$	−16.5369	−1.09759	−0.548795	+	0.835957i	$0.684913\pi$
$228$	−15.3197	−1.01457
$229$	21.8644	1.44484	0.722421	−	0.691454i	$-0.243029\pi$
$229$	21.8644	1.44484	0.722421	+	0.691454i	$0.243029\pi$
$230$	1.20723	0.0796021
$231$	3.53245	0.232418
$232$	6.84104	0.449136
$233$	2.99036	0.195905	0.0979526	−	0.995191i	$-0.468771\pi$
$233$	2.99036	0.195905	0.0979526	+	0.995191i	$0.468771\pi$
$234$	−0.424640	−0.0277596
$235$	24.1359	1.57445
$236$	−2.89041	−0.188150
$237$	−19.6385	−1.27566
$238$	−9.66013	−0.626173
$239$	14.3457	0.927945	0.463972	−	0.885850i	$-0.346424\pi$
$239$	14.3457	0.927945	0.463972	+	0.885850i	$0.346424\pi$
$240$	−6.31589	−0.407689
$241$	−8.56183	−0.551516	−0.275758	−	0.961227i	$-0.588929\pi$
$241$	−8.56183	−0.551516	−0.275758	+	0.961227i	$0.588929\pi$
$242$	9.43897	0.606760
$243$	13.5797	0.871136
$244$	−4.38492	−0.280716
$245$	−15.6022	−0.996787
$246$	15.3749	0.980267
$247$	2.19951	0.139952
$248$	−8.35113	−0.530297
$249$	12.4180	0.786958
$250$	2.86281	0.181060
$251$	3.98975	0.251831	0.125915	−	0.992041i	$-0.459813\pi$
$251$	3.98975	0.251831	0.125915	+	0.992041i	$0.459813\pi$
$252$	1.89676	0.119485
$253$	0.501431	0.0315247
$254$	−17.5107	−1.09872
$255$	−45.3105	−2.83745
$256$	1.00000	0.0625000
$257$	−14.9191	−0.930625	−0.465312	−	0.885146i	$-0.654058\pi$
$257$	−14.9191	−0.930625	−0.465312	+	0.885146i	$0.654058\pi$
$258$	6.91097	0.430258
$259$	1.11188	0.0690891
$260$	0.906795	0.0562371
$261$	−9.63645	−0.596481
$262$	−20.1475	−1.24472
$263$	−5.13508	−0.316643	−0.158321	−	0.987388i	$-0.550608\pi$
$263$	−5.13508	−0.316643	−0.158321	+	0.987388i	$0.550608\pi$
$264$	−2.62335	−0.161456
$265$	37.2458	2.28799
$266$	−9.82468	−0.602390
$267$	−10.2918	−0.629849
$268$	−6.29483	−0.384518
$269$	−6.75537	−0.411882	−0.205941	−	0.978564i	$-0.566026\pi$
$269$	−6.75537	−0.411882	−0.205941	+	0.978564i	$0.566026\pi$
$270$	−10.0510	−0.611682
$271$	23.1304	1.40507	0.702537	−	0.711648i	$-0.252051\pi$
$271$	23.1304	1.40507	0.702537	+	0.711648i	$0.252051\pi$
$272$	7.17405	0.434991
$273$	−0.852308	−0.0515840
$274$	13.4504	0.812569
$275$	−5.05797	−0.305007
$276$	0.842668	0.0507227
$277$	18.8568	1.13299	0.566497	−	0.824064i	$-0.308298\pi$
$277$	18.8568	1.13299	0.566497	+	0.824064i	$0.308298\pi$
$278$	15.2602	0.915247
$279$	11.7636	0.704267
$280$	−4.05044	−0.242060
$281$	9.36963	0.558945	0.279473	−	0.960154i	$-0.409840\pi$
$281$	9.36963	0.558945	0.279473	+	0.960154i	$0.409840\pi$
$282$	16.8474	1.00325
$283$	−4.48305	−0.266490	−0.133245	−	0.991083i	$-0.542540\pi$
$283$	−4.48305	−0.266490	−0.133245	+	0.991083i	$0.542540\pi$
$284$	−12.6810	−0.752476
$285$	−46.0823	−2.72968
$286$	0.376645	0.0222715
$287$	9.86006	0.582021
$288$	−1.40862	−0.0830039
$289$	34.4670	2.02747
$290$	20.5781	1.20839
$291$	13.3013	0.779737
$292$	−9.49410	−0.555600
$293$	12.0377	0.703251	0.351625	−	0.936141i	$-0.385629\pi$
$293$	12.0377	0.703251	0.351625	+	0.936141i	$0.385629\pi$
$294$	−10.8907	−0.635156
$295$	−8.69446	−0.506211
$296$	−0.825735	−0.0479949
$297$	−4.17475	−0.242243
$298$	−11.5873	−0.671233
$299$	−0.120985	−0.00699675
$300$	−8.50006	−0.490751
$301$	4.43207	0.255460
$302$	5.23203	0.301070
$303$	−31.9310	−1.83439
$304$	7.29625	0.418469
$305$	−13.1900	−0.755257
$306$	−10.1055	−0.577694
$307$	−20.9632	−1.19643	−0.598216	−	0.801335i	$-0.704124\pi$
$307$	−20.9632	−1.19643	−0.598216	+	0.801335i	$0.704124\pi$
$308$	−1.68238	−0.0958625
$309$	−35.9112	−2.04292
$310$	−25.1205	−1.42675
$311$	−16.0449	−0.909825	−0.454913	−	0.890536i	$-0.650330\pi$
$311$	−16.0449	−0.909825	−0.454913	+	0.890536i	$0.650330\pi$
$312$	0.632962	0.0358344
$313$	−25.0138	−1.41386	−0.706932	−	0.707282i	$-0.749921\pi$
$313$	−25.0138	−1.41386	−0.706932	+	0.707282i	$0.749921\pi$
$314$	1.58456	0.0894218
$315$	5.70553	0.321470
$316$	9.35312	0.526154
$317$	−17.0574	−0.958041	−0.479020	−	0.877804i	$-0.659008\pi$
$317$	−17.0574	−0.958041	−0.479020	+	0.877804i	$0.659008\pi$
$318$	25.9984	1.45792
$319$	8.54728	0.478556
$320$	3.00804	0.168154
$321$	−23.4330	−1.30790
$322$	0.540411	0.0301159
$323$	52.3437	2.91248
$324$	−11.2417	−0.624536
$325$	1.22038	0.0676948
$326$	−15.8254	−0.876489
$327$	−1.53267	−0.0847570
$328$	−7.32252	−0.404319
$329$	10.8044	0.595664
$330$	−7.89114	−0.434393
$331$	7.80455	0.428977	0.214488	−	0.976727i	$-0.431192\pi$
$331$	7.80455	0.428977	0.214488	+	0.976727i	$0.431192\pi$
$332$	−5.91425	−0.324587
$333$	1.16315	0.0637402
$334$	6.61283	0.361838
$335$	−18.9351	−1.03453
$336$	−2.82729	−0.154241
$337$	−23.0269	−1.25435	−0.627176	−	0.778877i	$-0.715789\pi$
$337$	−23.0269	−1.25435	−0.627176	+	0.778877i	$0.715789\pi$
$338$	12.9091	0.702164
$339$	−1.74914	−0.0950000
$340$	21.5798	1.17033
$341$	−10.4340	−0.565033
$342$	−10.2777	−0.555752
$343$	−16.4100	−0.886059
$344$	−3.29145	−0.177463
$345$	2.53478	0.136468
$346$	18.4520	0.991985
$347$	−27.6752	−1.48568	−0.742842	−	0.669467i	$-0.766522\pi$
$347$	−27.6752	−1.48568	−0.742842	+	0.669467i	$0.766522\pi$
$348$	14.3639	0.769988
$349$	17.5755	0.940797	0.470398	−	0.882454i	$-0.344110\pi$
$349$	17.5755	0.940797	0.470398	+	0.882454i	$0.344110\pi$
$350$	−5.45116	−0.291377
$351$	1.00728	0.0537647
$352$	1.24941	0.0665939
$353$	−18.9417	−1.00817	−0.504084	−	0.863655i	$-0.668170\pi$
$353$	−18.9417	−1.00817	−0.504084	+	0.863655i	$0.668170\pi$
$354$	−6.06891	−0.322559
$355$	−38.1448	−2.02451
$356$	4.90163	0.259786
$357$	−20.2831	−1.07350
$358$	4.12681	0.218109
$359$	35.0570	1.85024	0.925118	−	0.379679i	$-0.123965\pi$
$359$	35.0570	1.85024	0.925118	+	0.379679i	$0.123965\pi$
$360$	−4.23719	−0.223319
$361$	34.2353	1.80186
$362$	−0.283105	−0.0148797
$363$	19.8187	1.04021
$364$	0.405924	0.0212762
$365$	−28.5586	−1.49482
$366$	−9.20690	−0.481252
$367$	−15.2871	−0.797981	−0.398990	−	0.916955i	$-0.630639\pi$
$367$	−15.2871	−0.797981	−0.398990	+	0.916955i	$0.630639\pi$
$368$	−0.401333	−0.0209210
$369$	10.3147	0.536960
$370$	−2.48384	−0.129129
$371$	16.6730	0.865618
$372$	−17.5346	−0.909128
$373$	−2.34214	−0.121271	−0.0606357	−	0.998160i	$-0.519313\pi$
$373$	−2.34214	−0.121271	−0.0606357	+	0.998160i	$0.519313\pi$
$374$	8.96334	0.463483
$375$	6.01097	0.310405
$376$	−8.02381	−0.413796
$377$	−2.06228	−0.106213
$378$	−4.49928	−0.231418
$379$	−0.290363	−0.0149150	−0.00745748	−	0.999972i	$-0.502374\pi$
$379$	−0.290363	−0.0149150	−0.00745748	+	0.999972i	$0.502374\pi$
$380$	21.9474	1.12588
$381$	−36.7668	−1.88362
$382$	−4.37503	−0.223846
$383$	−1.94884	−0.0995811	−0.0497906	−	0.998760i	$-0.515855\pi$
$383$	−1.94884	−0.0995811	−0.0497906	+	0.998760i	$0.515855\pi$
$384$	2.09967	0.107148
$385$	−5.06066	−0.257915
$386$	27.3031	1.38969
$387$	4.63641	0.235682
$388$	−6.33495	−0.321608
$389$	3.13843	0.159125	0.0795623	−	0.996830i	$-0.474648\pi$
$389$	3.13843	0.159125	0.0795623	+	0.996830i	$0.474648\pi$
$390$	1.90397	0.0964114
$391$	−2.87919	−0.145607
$392$	5.18683	0.261975
$393$	−42.3031	−2.13391
$394$	−1.97792	−0.0996462
$395$	28.1345	1.41560
$396$	−1.75995	−0.0884408
$397$	7.50774	0.376803	0.188401	−	0.982092i	$-0.439669\pi$
$397$	7.50774	0.376803	0.188401	+	0.982092i	$0.439669\pi$
$398$	5.51811	0.276598
$399$	−20.6286	−1.03272
$400$	4.04828	0.202414
$401$	−0.714610	−0.0356859	−0.0178430	−	0.999841i	$-0.505680\pi$
$401$	−0.714610	−0.0356859	−0.0178430	+	0.999841i	$0.505680\pi$
$402$	−13.2171	−0.659208
$403$	2.51751	0.125406
$404$	15.2076	0.756608
$405$	−33.8153	−1.68029
$406$	9.21173	0.457170
$407$	−1.03168	−0.0511386
$408$	15.0631	0.745737
$409$	−1.10981	−0.0548764	−0.0274382	−	0.999624i	$-0.508735\pi$
$409$	−1.10981	−0.0548764	−0.0274382	+	0.999624i	$0.508735\pi$
$410$	−22.0264	−1.08781
$411$	28.2415	1.39305
$412$	17.1033	0.842617
$413$	−3.89205	−0.191515
$414$	0.565327	0.0277843
$415$	−17.7903	−0.873291
$416$	−0.301458	−0.0147802
$417$	32.0415	1.56908
$418$	9.11602	0.445879
$419$	−16.6803	−0.814885	−0.407443	−	0.913231i	$-0.633579\pi$
$419$	−16.6803	−0.814885	−0.407443	+	0.913231i	$0.633579\pi$
$420$	−8.50459	−0.414981
$421$	11.4149	0.556327	0.278163	−	0.960534i	$-0.410274\pi$
$421$	11.4149	0.556327	0.278163	+	0.960534i	$0.410274\pi$
$422$	27.7025	1.34854
$423$	11.3025	0.549547
$424$	−12.3821	−0.601328
$425$	29.0425	1.40877
$426$	−26.6258	−1.29003
$427$	−5.90447	−0.285737
$428$	11.1603	0.539454
$429$	0.790830	0.0381816
$430$	−9.90080	−0.477459
$431$	−33.0108	−1.59007	−0.795037	−	0.606561i	$-0.792548\pi$
$431$	−33.0108	−1.59007	−0.795037	+	0.606561i	$0.792548\pi$
$432$	3.34137	0.160762
$433$	−21.5112	−1.03376	−0.516881	−	0.856057i	$-0.672907\pi$
$433$	−21.5112	−1.03376	−0.516881	+	0.856057i	$0.672907\pi$
$434$	−11.2451	−0.539783
$435$	43.2073	2.07163
$436$	0.729959	0.0349587
$437$	−2.92823	−0.140076
$438$	−19.9345	−0.952507
$439$	−0.0972462	−0.00464131	−0.00232066	−	0.999997i	$-0.500739\pi$
$439$	−0.0972462	−0.00464131	−0.00232066	+	0.999997i	$0.500739\pi$
$440$	3.75827	0.179169
$441$	−7.30629	−0.347919
$442$	−2.16267	−0.102868
$443$	4.21016	0.200031	0.100015	−	0.994986i	$-0.468111\pi$
$443$	4.21016	0.200031	0.100015	+	0.994986i	$0.468111\pi$
$444$	−1.73377	−0.0822812
$445$	14.7443	0.698946
$446$	2.59638	0.122942
$447$	−24.3295	−1.15074
$448$	1.34654	0.0636180
$449$	−11.4382	−0.539803	−0.269902	−	0.962888i	$-0.586991\pi$
$449$	−11.4382	−0.539803	−0.269902	+	0.962888i	$0.586991\pi$
$450$	−5.70249	−0.268818
$451$	−9.14884	−0.430802
$452$	0.833052	0.0391835
$453$	10.9856	0.516146
$454$	16.5369	0.776114
$455$	1.22103	0.0572430
$456$	15.3197	0.717412
$457$	−17.6483	−0.825551	−0.412775	−	0.910833i	$-0.635441\pi$
$457$	−17.6483	−0.825551	−0.412775	+	0.910833i	$0.635441\pi$
$458$	−21.8644	−1.02166
$459$	23.9712	1.11888
$460$	−1.20723	−0.0562872
$461$	14.7626	0.687563	0.343781	−	0.939050i	$-0.388292\pi$
$461$	14.7626	0.687563	0.343781	+	0.939050i	$0.388292\pi$
$462$	−3.53245	−0.164344
$463$	29.9165	1.39034	0.695168	−	0.718847i	$-0.255330\pi$
$463$	29.9165	1.39034	0.695168	+	0.718847i	$0.255330\pi$
$464$	−6.84104	−0.317587
$465$	−52.7448	−2.44598
$466$	−2.99036	−0.138526
$467$	30.5913	1.41559	0.707797	−	0.706415i	$-0.249689\pi$
$467$	30.5913	1.41559	0.707797	+	0.706415i	$0.249689\pi$
$468$	0.424640	0.0196290
$469$	−8.47623	−0.391396
$470$	−24.1359	−1.11331
$471$	3.32705	0.153302
$472$	2.89041	0.133042
$473$	−4.11238	−0.189087
$474$	19.6385	0.902025
$475$	29.5373	1.35526
$476$	9.66013	0.442771
$477$	17.4417	0.798601
$478$	−14.3457	−0.656156
$479$	29.4178	1.34413	0.672067	−	0.740490i	$-0.265407\pi$
$479$	29.4178	1.34413	0.672067	+	0.740490i	$0.265407\pi$
$480$	6.31589	0.288280
$481$	0.248924	0.0113500
$482$	8.56183	0.389981
$483$	1.13469	0.0516300
$484$	−9.43897	−0.429044
$485$	−19.0558	−0.865277
$486$	−13.5797	−0.615986
$487$	10.6361	0.481968	0.240984	−	0.970529i	$-0.422530\pi$
$487$	10.6361	0.481968	0.240984	+	0.970529i	$0.422530\pi$
$488$	4.38492	0.198496
$489$	−33.2282	−1.50263
$490$	15.6022	0.704835
$491$	25.5947	1.15507	0.577537	−	0.816364i	$-0.304014\pi$
$491$	25.5947	1.15507	0.577537	+	0.816364i	$0.304014\pi$
$492$	−15.3749	−0.693154
$493$	−49.0780	−2.21036
$494$	−2.19951	−0.0989607
$495$	−5.29399	−0.237947
$496$	8.35113	0.374977
$497$	−17.0754	−0.765936
$498$	−12.4180	−0.556463
$499$	34.0337	1.52356	0.761778	−	0.647838i	$-0.224327\pi$
$499$	34.0337	1.52356	0.761778	+	0.647838i	$0.224327\pi$
$500$	−2.86281	−0.128029
$501$	13.8848	0.620326
$502$	−3.98975	−0.178071
$503$	−6.00660	−0.267821	−0.133911	−	0.990993i	$-0.542754\pi$
$503$	−6.00660	−0.267821	−0.133911	+	0.990993i	$0.542754\pi$
$504$	−1.89676	−0.0844886
$505$	45.7451	2.03563
$506$	−0.501431	−0.0222913
$507$	27.1049	1.20377
$508$	17.5107	0.776913
$509$	30.2694	1.34167	0.670834	−	0.741607i	$-0.265936\pi$
$509$	30.2694	1.34167	0.670834	+	0.741607i	$0.265936\pi$
$510$	45.3105	2.00638
$511$	−12.7842	−0.565538
$512$	−1.00000	−0.0441942
$513$	24.3795	1.07638
$514$	14.9191	0.658051
$515$	51.4472	2.26703
$516$	−6.91097	−0.304238
$517$	−10.0250	−0.440901
$518$	−1.11188	−0.0488534
$519$	38.7431	1.70063
$520$	−0.906795	−0.0397656
$521$	−1.99973	−0.0876096	−0.0438048	−	0.999040i	$-0.513948\pi$
$521$	−1.99973	−0.0876096	−0.0438048	+	0.999040i	$0.513948\pi$
$522$	9.63645	0.421776
$523$	17.1385	0.749415	0.374707	−	0.927143i	$-0.377743\pi$
$523$	17.1385	0.749415	0.374707	+	0.927143i	$0.377743\pi$
$524$	20.1475	0.880148
$525$	−11.4457	−0.499529
$526$	5.13508	0.223900
$527$	59.9114	2.60978
$528$	2.62335	0.114167
$529$	−22.8389	−0.992997
$530$	−37.2458	−1.61786
$531$	−4.07150	−0.176688
$532$	9.82468	0.425954
$533$	2.20743	0.0956144
$534$	10.2918	0.445371
$535$	33.5706	1.45138
$536$	6.29483	0.271895
$537$	8.66496	0.373920
$538$	6.75537	0.291245
$539$	6.48049	0.279135
$540$	10.0510	0.432525
$541$	−23.5377	−1.01197	−0.505983	−	0.862543i	$-0.668870\pi$
$541$	−23.5377	−1.01197	−0.505983	+	0.862543i	$0.668870\pi$
$542$	−23.1304	−0.993537
$543$	−0.594427	−0.0255093
$544$	−7.17405	−0.307585
$545$	2.19574	0.0940552
$546$	0.852308	0.0364754
$547$	10.9650	0.468829	0.234414	−	0.972137i	$-0.424683\pi$
$547$	10.9650	0.468829	0.234414	+	0.972137i	$0.424683\pi$
$548$	−13.4504	−0.574573
$549$	−6.17670	−0.263615
$550$	5.05797	0.215672
$551$	−49.9140	−2.12641
$552$	−0.842668	−0.0358664
$553$	12.5943	0.535565
$554$	−18.8568	−0.801147
$555$	−5.21525	−0.221375
$556$	−15.2602	−0.647177
$557$	−24.8035	−1.05096	−0.525479	−	0.850807i	$-0.676114\pi$
$557$	−24.8035	−1.05096	−0.525479	+	0.850807i	$0.676114\pi$
$558$	−11.7636	−0.497992
$559$	0.992233	0.0419670
$560$	4.05044	0.171162
$561$	18.8201	0.794584
$562$	−9.36963	−0.395234
$563$	33.7600	1.42281	0.711407	−	0.702781i	$-0.248058\pi$
$563$	33.7600	1.42281	0.711407	+	0.702781i	$0.248058\pi$
$564$	−16.8474	−0.709402
$565$	2.50585	0.105422
$566$	4.48305	0.188437
$567$	−15.1373	−0.635707
$568$	12.6810	0.532081
$569$	10.5218	0.441097	0.220548	−	0.975376i	$-0.429215\pi$
$569$	10.5218	0.441097	0.220548	+	0.975376i	$0.429215\pi$
$570$	46.0823	1.93018
$571$	−8.23418	−0.344590	−0.172295	−	0.985045i	$-0.555118\pi$
$571$	−8.23418	−0.344590	−0.172295	+	0.985045i	$0.555118\pi$
$572$	−0.376645	−0.0157483
$573$	−9.18614	−0.383756
$574$	−9.86006	−0.411551
$575$	−1.62471	−0.0677551
$576$	1.40862	0.0586926
$577$	46.8774	1.95153	0.975765	−	0.218820i	$-0.0702207\pi$
$577$	46.8774	1.95153	0.975765	+	0.218820i	$0.0702207\pi$
$578$	−34.4670	−1.43364
$579$	57.3275	2.38245
$580$	−20.5781	−0.854459
$581$	−7.96377	−0.330393
$582$	−13.3013	−0.551357
$583$	−15.4704	−0.640717
$584$	9.49410	0.392869
$585$	1.27733	0.0528112
$586$	−12.0377	−0.497273
$587$	−26.9838	−1.11374	−0.556870	−	0.830600i	$-0.687998\pi$
$587$	−26.9838	−1.11374	−0.556870	+	0.830600i	$0.687998\pi$
$588$	10.8907	0.449123
$589$	60.9319	2.51066
$590$	8.69446	0.357945
$591$	−4.15298	−0.170831
$592$	0.825735	0.0339375
$593$	21.2106	0.871014	0.435507	−	0.900185i	$-0.356569\pi$
$593$	21.2106	0.871014	0.435507	+	0.900185i	$0.356569\pi$
$594$	4.17475	0.171292
$595$	29.0580	1.19126
$596$	11.5873	0.474633
$597$	11.5862	0.474192
$598$	0.120985	0.00494745
$599$	24.2343	0.990186	0.495093	−	0.868840i	$-0.335134\pi$
$599$	24.2343	0.990186	0.495093	+	0.868840i	$0.335134\pi$
$600$	8.50006	0.347013
$601$	2.81505	0.114828	0.0574142	−	0.998350i	$-0.481714\pi$
$601$	2.81505	0.114828	0.0574142	+	0.998350i	$0.481714\pi$
$602$	−4.43207	−0.180638
$603$	−8.86704	−0.361094
$604$	−5.23203	−0.212888
$605$	−28.3928	−1.15433
$606$	31.9310	1.29711
$607$	−5.72669	−0.232439	−0.116220	−	0.993224i	$-0.537078\pi$
$607$	−5.72669	−0.232439	−0.116220	+	0.993224i	$0.537078\pi$
$608$	−7.29625	−0.295902
$609$	19.3416	0.783761
$610$	13.1900	0.534048
$611$	2.41884	0.0978557
$612$	10.1055	0.408492
$613$	27.7742	1.12179	0.560895	−	0.827887i	$-0.310457\pi$
$613$	27.7742	1.12179	0.560895	+	0.827887i	$0.310457\pi$
$614$	20.9632	0.846005
$615$	−46.2482	−1.86491
$616$	1.68238	0.0677850
$617$	10.8085	0.435132	0.217566	−	0.976046i	$-0.430188\pi$
$617$	10.8085	0.435132	0.217566	+	0.976046i	$0.430188\pi$
$618$	35.9112	1.44456
$619$	−27.4527	−1.10342	−0.551709	−	0.834036i	$-0.686024\pi$
$619$	−27.4527	−1.10342	−0.551709	+	0.834036i	$0.686024\pi$
$620$	25.1205	1.00886
$621$	−1.34100	−0.0538126
$622$	16.0449	0.643344
$623$	6.60024	0.264433
$624$	−0.632962	−0.0253388
$625$	−28.8528	−1.15411
$626$	25.0138	0.999752
$627$	19.1407	0.764404
$628$	−1.58456	−0.0632307
$629$	5.92386	0.236200
$630$	−5.70553	−0.227314
$631$	20.9502	0.834016	0.417008	−	0.908903i	$-0.363079\pi$
$631$	20.9502	0.834016	0.417008	+	0.908903i	$0.363079\pi$
$632$	−9.35312	−0.372047
$633$	58.1662	2.31190
$634$	17.0574	0.677437
$635$	52.6729	2.09026
$636$	−25.9984	−1.03090
$637$	−1.56361	−0.0619525
$638$	−8.54728	−0.338390
$639$	−17.8627	−0.706637
$640$	−3.00804	−0.118903
$641$	−19.5139	−0.770753	−0.385376	−	0.922760i	$-0.625928\pi$
$641$	−19.5139	−0.770753	−0.385376	+	0.922760i	$0.625928\pi$
$642$	23.4330	0.924826
$643$	2.38228	0.0939480	0.0469740	−	0.998896i	$-0.485042\pi$
$643$	2.38228	0.0939480	0.0469740	+	0.998896i	$0.485042\pi$
$644$	−0.540411	−0.0212952
$645$	−20.7884	−0.818544
$646$	−52.3437	−2.05943
$647$	11.0714	0.435263	0.217632	−	0.976031i	$-0.430167\pi$
$647$	11.0714	0.435263	0.217632	+	0.976031i	$0.430167\pi$
$648$	11.2417	0.441614
$649$	3.61131	0.141756
$650$	−1.22038	−0.0478674
$651$	−23.6110	−0.925390
$652$	15.8254	0.619772
$653$	−20.2191	−0.791234	−0.395617	−	0.918416i	$-0.629469\pi$
$653$	−20.2191	−0.791234	−0.395617	+	0.918416i	$0.629469\pi$
$654$	1.53267	0.0599323
$655$	60.6044	2.36801
$656$	7.32252	0.285896
$657$	−13.3736	−0.521754
$658$	−10.8044	−0.421198
$659$	39.4156	1.53542	0.767708	−	0.640800i	$-0.221397\pi$
$659$	39.4156	1.53542	0.767708	+	0.640800i	$0.221397\pi$
$660$	7.89114	0.307162
$661$	−16.7090	−0.649906	−0.324953	−	0.945730i	$-0.605348\pi$
$661$	−16.7090	−0.649906	−0.324953	+	0.945730i	$0.605348\pi$
$662$	−7.80455	−0.303332
$663$	−4.54090	−0.176354
$664$	5.91425	0.229517
$665$	29.5530	1.14602
$666$	−1.16315	−0.0450711
$667$	2.74554	0.106308
$668$	−6.61283	−0.255858
$669$	5.45155	0.210769
$670$	18.9351	0.731526
$671$	5.47857	0.211498
$672$	2.82729	0.109065
$673$	22.6415	0.872764	0.436382	−	0.899761i	$-0.356260\pi$
$673$	22.6415	0.872764	0.436382	+	0.899761i	$0.356260\pi$
$674$	23.0269	0.886961
$675$	13.5268	0.520647
$676$	−12.9091	−0.496505
$677$	21.9067	0.841942	0.420971	−	0.907074i	$-0.361689\pi$
$677$	21.9067	0.841942	0.420971	+	0.907074i	$0.361689\pi$
$678$	1.74914	0.0671752
$679$	−8.53025	−0.327361
$680$	−21.5798	−0.827547
$681$	34.7220	1.33055
$682$	10.4340	0.399538
$683$	21.4012	0.818893	0.409447	−	0.912334i	$-0.365722\pi$
$683$	21.4012	0.818893	0.409447	+	0.912334i	$0.365722\pi$
$684$	10.2777	0.392976
$685$	−40.4593	−1.54587
$686$	16.4100	0.626538
$687$	−45.9081	−1.75150
$688$	3.29145	0.125485
$689$	3.73268	0.142204
$690$	−2.53478	−0.0964973
$691$	−30.7957	−1.17152	−0.585762	−	0.810483i	$-0.699205\pi$
$691$	−30.7957	−1.17152	−0.585762	+	0.810483i	$0.699205\pi$
$692$	−18.4520	−0.701439
$693$	−2.36984	−0.0900227
$694$	27.6752	1.05054
$695$	−45.9033	−1.74121
$696$	−14.3639	−0.544464
$697$	52.5321	1.98980
$698$	−17.5755	−0.665244
$699$	−6.27878	−0.237485
$700$	5.45116	0.206035
$701$	−24.3345	−0.919101	−0.459550	−	0.888152i	$-0.651989\pi$
$701$	−24.3345	−0.919101	−0.459550	+	0.888152i	$0.651989\pi$
$702$	−1.00728	−0.0380174
$703$	6.02477	0.227229
$704$	−1.24941	−0.0470890
$705$	−50.6775	−1.90862
$706$	18.9417	0.712882
$707$	20.4776	0.770141
$708$	6.06891	0.228084
$709$	31.8759	1.19712	0.598562	−	0.801076i	$-0.295739\pi$
$709$	31.8759	1.19712	0.598562	+	0.801076i	$0.295739\pi$
$710$	38.1448	1.43155
$711$	13.1750	0.494101
$712$	−4.90163	−0.183697
$713$	−3.35159	−0.125518
$714$	20.2831	0.759076
$715$	−1.13296	−0.0423703
$716$	−4.12681	−0.154226
$717$	−30.1212	−1.12490
$718$	−35.0570	−1.30831
$719$	−5.41039	−0.201774	−0.100887	−	0.994898i	$-0.532168\pi$
$719$	−5.41039	−0.201774	−0.100887	+	0.994898i	$0.532168\pi$
$720$	4.23719	0.157911
$721$	23.0302	0.857689
$722$	−34.2353	−1.27411
$723$	17.9770	0.668573
$724$	0.283105	0.0105215
$725$	−27.6944	−1.02855
$726$	−19.8187	−0.735542
$727$	−2.69780	−0.100056	−0.0500278	−	0.998748i	$-0.515931\pi$
$727$	−2.69780	−0.100056	−0.0500278	+	0.998748i	$0.515931\pi$
$728$	−0.405924	−0.0150446
$729$	5.21211	0.193041
$730$	28.5586	1.05700
$731$	23.6130	0.873360
$732$	9.20690	0.340297
$733$	−16.0979	−0.594588	−0.297294	−	0.954786i	$-0.596084\pi$
$733$	−16.0979	−0.594588	−0.297294	+	0.954786i	$0.596084\pi$
$734$	15.2871	0.564258
$735$	32.7595	1.20835
$736$	0.401333	0.0147933
$737$	7.86483	0.289705
$738$	−10.3147	−0.379688
$739$	−16.3502	−0.601451	−0.300725	−	0.953711i	$-0.597229\pi$
$739$	−16.3502	−0.601451	−0.300725	+	0.953711i	$0.597229\pi$
$740$	2.48384	0.0913078
$741$	−4.61825	−0.169656
$742$	−16.6730	−0.612085
$743$	15.5867	0.571822	0.285911	−	0.958256i	$-0.407704\pi$
$743$	15.5867	0.571822	0.285911	+	0.958256i	$0.407704\pi$
$744$	17.5346	0.642851
$745$	34.8549	1.27699
$746$	2.34214	0.0857518
$747$	−8.33095	−0.304813
$748$	−8.96334	−0.327732
$749$	15.0278	0.549103
$750$	−6.01097	−0.219490
$751$	6.68681	0.244005	0.122003	−	0.992530i	$-0.461068\pi$
$751$	6.68681	0.244005	0.122003	+	0.992530i	$0.461068\pi$
$752$	8.02381	0.292598
$753$	−8.37717	−0.305281
$754$	2.06228	0.0751040
$755$	−15.7381	−0.572769
$756$	4.49928	0.163637
$757$	−14.2417	−0.517624	−0.258812	−	0.965928i	$-0.583331\pi$
$757$	−14.2417	−0.517624	−0.258812	+	0.965928i	$0.583331\pi$
$758$	0.290363	0.0105465
$759$	−1.05284	−0.0382157
$760$	−21.9474	−0.796115
$761$	−2.11706	−0.0767434	−0.0383717	−	0.999264i	$-0.512217\pi$
$761$	−2.11706	−0.0767434	−0.0383717	+	0.999264i	$0.512217\pi$
$762$	36.7668	1.33192
$763$	0.982917	0.0355840
$764$	4.37503	0.158283
$765$	30.3978	1.09903
$766$	1.94884	0.0704145
$767$	−0.871336	−0.0314621
$768$	−2.09967	−0.0757654
$769$	−15.9404	−0.574825	−0.287412	−	0.957807i	$-0.592795\pi$
$769$	−15.9404	−0.574825	−0.287412	+	0.957807i	$0.592795\pi$
$770$	5.06066	0.182374
$771$	31.3251	1.12815
$772$	−27.3031	−0.982659
$773$	−22.8712	−0.822621	−0.411310	−	0.911495i	$-0.634929\pi$
$773$	−22.8712	−0.822621	−0.411310	+	0.911495i	$0.634929\pi$
$774$	−4.63641	−0.166652
$775$	33.8077	1.21441
$776$	6.33495	0.227411
$777$	−2.33459	−0.0837530
$778$	−3.13843	−0.112518
$779$	53.4270	1.91422
$780$	−1.90397	−0.0681732
$781$	15.8437	0.566933
$782$	2.87919	0.102959
$783$	−22.8585	−0.816895
$784$	−5.18683	−0.185244
$785$	−4.76641	−0.170120
$786$	42.3031	1.50890
$787$	33.4603	1.19273	0.596365	−	0.802714i	$-0.296611\pi$
$787$	33.4603	1.19273	0.596365	+	0.802714i	$0.296611\pi$
$788$	1.97792	0.0704605
$789$	10.7820	0.383849
$790$	−28.1345	−1.00098
$791$	1.12174	0.0398844
$792$	1.75995	0.0625371
$793$	−1.32187	−0.0469409
$794$	−7.50774	−0.266440
$795$	−78.2040	−2.77361
$796$	−5.51811	−0.195584
$797$	24.4874	0.867388	0.433694	−	0.901060i	$-0.357210\pi$
$797$	24.4874	0.867388	0.433694	+	0.901060i	$0.357210\pi$
$798$	20.6286	0.730245
$799$	57.5632	2.03644
$800$	−4.04828	−0.143128
$801$	6.90455	0.243960
$802$	0.714610	0.0252338
$803$	11.8620	0.418602
$804$	13.2171	0.466130
$805$	−1.62557	−0.0572940
$806$	−2.51751	−0.0886756
$807$	14.1841	0.499303
$808$	−15.2076	−0.535002
$809$	4.05086	0.142421	0.0712103	−	0.997461i	$-0.477314\pi$
$809$	4.05086	0.142421	0.0712103	+	0.997461i	$0.477314\pi$
$810$	33.8153	1.18815
$811$	16.6280	0.583888	0.291944	−	0.956435i	$-0.405698\pi$
$811$	16.6280	0.583888	0.291944	+	0.956435i	$0.405698\pi$
$812$	−9.21173	−0.323268
$813$	−48.5663	−1.70329
$814$	1.03168	0.0361605
$815$	47.6034	1.66748
$816$	−15.0631	−0.527316
$817$	24.0153	0.840188
$818$	1.10981	0.0388035
$819$	0.571794	0.0199801
$820$	22.0264	0.769195
$821$	11.4519	0.399676	0.199838	−	0.979829i	$-0.435958\pi$
$821$	11.4519	0.399676	0.199838	+	0.979829i	$0.435958\pi$
$822$	−28.2415	−0.985034
$823$	34.2474	1.19379	0.596894	−	0.802320i	$-0.296401\pi$
$823$	34.2474	1.19379	0.596894	+	0.802320i	$0.296401\pi$
$824$	−17.1033	−0.595820
$825$	10.6201	0.369743
$826$	3.89205	0.135422
$827$	30.4626	1.05929	0.529644	−	0.848220i	$-0.322325\pi$
$827$	30.4626	1.05929	0.529644	+	0.848220i	$0.322325\pi$
$828$	−0.565327	−0.0196465
$829$	10.7126	0.372062	0.186031	−	0.982544i	$-0.440437\pi$
$829$	10.7126	0.372062	0.186031	+	0.982544i	$0.440437\pi$
$830$	17.7903	0.617510
$831$	−39.5930	−1.37347
$832$	0.301458	0.0104512
$833$	−37.2106	−1.28927
$834$	−32.0415	−1.10950
$835$	−19.8916	−0.688378
$836$	−9.11602	−0.315284
$837$	27.9042	0.964511
$838$	16.6803	0.576211
$839$	47.4398	1.63780	0.818901	−	0.573934i	$-0.194584\pi$
$839$	47.4398	1.63780	0.818901	+	0.573934i	$0.194584\pi$
$840$	8.50459	0.293436
$841$	17.7999	0.613789
$842$	−11.4149	−0.393382
$843$	−19.6732	−0.677579
$844$	−27.7025	−0.953560
$845$	−38.8311	−1.33583
$846$	−11.3025	−0.388589
$847$	−12.7099	−0.436719
$848$	12.3821	0.425203
$849$	9.41294	0.323051
$850$	−29.0425	−0.996151
$851$	−0.331395	−0.0113601
$852$	26.6258	0.912187
$853$	−52.6502	−1.80271	−0.901354	−	0.433083i	$-0.857426\pi$
$853$	−52.6502	−1.80271	−0.901354	+	0.433083i	$0.857426\pi$
$854$	5.90447	0.202047
$855$	30.9156	1.05729
$856$	−11.1603	−0.381451
$857$	45.9656	1.57015	0.785077	−	0.619398i	$-0.212623\pi$
$857$	45.9656	1.57015	0.785077	+	0.619398i	$0.212623\pi$
$858$	−0.790830	−0.0269985
$859$	−28.6664	−0.978086	−0.489043	−	0.872260i	$-0.662654\pi$
$859$	−28.6664	−0.978086	−0.489043	+	0.872260i	$0.662654\pi$
$860$	9.90080	0.337615
$861$	−20.7029	−0.705552
$862$	33.0108	1.12435
$863$	−38.0784	−1.29620	−0.648102	−	0.761554i	$-0.724437\pi$
$863$	−38.0784	−1.29620	−0.648102	+	0.761554i	$0.724437\pi$
$864$	−3.34137	−0.113676
$865$	−55.5042	−1.88720
$866$	21.5112	0.730980
$867$	−72.3693	−2.45779
$868$	11.2451	0.381684
$869$	−11.6859	−0.396417
$870$	−43.2073	−1.46486
$871$	−1.89762	−0.0642986
$872$	−0.729959	−0.0247195
$873$	−8.92355	−0.302016
$874$	2.92823	0.0990489
$875$	−3.85489	−0.130319
$876$	19.9345	0.673524
$877$	−20.3964	−0.688739	−0.344369	−	0.938834i	$-0.611907\pi$
$877$	−20.3964	−0.688739	−0.344369	+	0.938834i	$0.611907\pi$
$878$	0.0972462	0.00328190
$879$	−25.2752	−0.852513
$880$	−3.75827	−0.126691
$881$	−25.9506	−0.874298	−0.437149	−	0.899389i	$-0.644012\pi$
$881$	−25.9506	−0.874298	−0.437149	+	0.899389i	$0.644012\pi$
$882$	7.30629	0.246016
$883$	42.2968	1.42340	0.711700	−	0.702483i	$-0.247925\pi$
$883$	42.2968	1.42340	0.711700	+	0.702483i	$0.247925\pi$
$884$	2.16267	0.0727385
$885$	18.2555	0.613652
$886$	−4.21016	−0.141443
$887$	−14.0206	−0.470765	−0.235383	−	0.971903i	$-0.575634\pi$
$887$	−14.0206	−0.470765	−0.235383	+	0.971903i	$0.575634\pi$
$888$	1.73377	0.0581816
$889$	23.5789	0.790810
$890$	−14.7443	−0.494230
$891$	14.0454	0.470540
$892$	−2.59638	−0.0869333
$893$	58.5437	1.95909
$894$	24.3295	0.813699
$895$	−12.4136	−0.414941
$896$	−1.34654	−0.0449847
$897$	0.254029	0.00848178
$898$	11.4382	0.381698
$899$	−57.1304	−1.90541
$900$	5.70249	0.190083
$901$	88.8298	2.95935
$902$	9.14884	0.304623
$903$	−9.30588	−0.309680
$904$	−0.833052	−0.0277069
$905$	0.851589	0.0283078
$906$	−10.9856	−0.364970
$907$	−41.7460	−1.38615	−0.693076	−	0.720864i	$-0.743745\pi$
$907$	−41.7460	−1.38615	−0.693076	+	0.720864i	$0.743745\pi$
$908$	−16.5369	−0.548795
$909$	21.4218	0.710516
$910$	−1.22103	−0.0404769
$911$	−24.0281	−0.796088	−0.398044	−	0.917366i	$-0.630311\pi$
$911$	−24.0281	−0.796088	−0.398044	+	0.917366i	$0.630311\pi$
$912$	−15.3197	−0.507287
$913$	7.38934	0.244551
$914$	17.6483	0.583753
$915$	27.6947	0.915558
$916$	21.8644	0.722421
$917$	27.1294	0.895891
$918$	−23.9712	−0.791166
$919$	21.3849	0.705424	0.352712	−	0.935732i	$-0.385260\pi$
$919$	21.3849	0.705424	0.352712	+	0.935732i	$0.385260\pi$
$920$	1.20723	0.0398010
$921$	44.0158	1.45037
$922$	−14.7626	−0.486180
$923$	−3.82277	−0.125828
$924$	3.53245	0.116209
$925$	3.34280	0.109911
$926$	−29.9165	−0.983116
$927$	24.0920	0.791286
$928$	6.84104	0.224568
$929$	58.4843	1.91881	0.959403	−	0.282038i	$-0.0910105\pi$
$929$	58.4843	1.91881	0.959403	+	0.282038i	$0.0910105\pi$
$930$	52.7448	1.72957
$931$	−37.8445	−1.24030
$932$	2.99036	0.0979526
$933$	33.6891	1.10293
$934$	−30.5913	−1.00098
$935$	−26.9620	−0.881753
$936$	−0.424640	−0.0138798
$937$	2.22533	0.0726983	0.0363491	−	0.999339i	$-0.488427\pi$
$937$	2.22533	0.0726983	0.0363491	+	0.999339i	$0.488427\pi$
$938$	8.47623	0.276759
$939$	52.5208	1.71395
$940$	24.1359	0.787226
$941$	5.00192	0.163058	0.0815289	−	0.996671i	$-0.474020\pi$
$941$	5.00192	0.163058	0.0815289	+	0.996671i	$0.474020\pi$
$942$	−3.32705	−0.108401
$943$	−2.93877	−0.0956996
$944$	−2.89041	−0.0940748
$945$	13.5340	0.440261
$946$	4.11238	0.133705
$947$	49.3142	1.60250	0.801249	−	0.598332i	$-0.204169\pi$
$947$	49.3142	1.60250	0.801249	+	0.598332i	$0.204169\pi$
$948$	−19.6385	−0.637828
$949$	−2.86207	−0.0929067
$950$	−29.5373	−0.958315
$951$	35.8150	1.16138
$952$	−9.66013	−0.313087
$953$	−46.8135	−1.51644	−0.758219	−	0.652000i	$-0.773930\pi$
$953$	−46.8135	−1.51644	−0.758219	+	0.652000i	$0.773930\pi$
$954$	−17.4417	−0.564696
$955$	13.1603	0.425856
$956$	14.3457	0.463972
$957$	−17.9465	−0.580127
$958$	−29.4178	−0.950446
$959$	−18.1115	−0.584851
$960$	−6.31589	−0.203844
$961$	38.7413	1.24972
$962$	−0.248924	−0.00802564
$963$	15.7206	0.506591
$964$	−8.56183	−0.275758
$965$	−82.1286	−2.64381
$966$	−1.13469	−0.0365079
$967$	24.3602	0.783370	0.391685	−	0.920099i	$-0.371892\pi$
$967$	24.3602	0.783370	0.391685	+	0.920099i	$0.371892\pi$
$968$	9.43897	0.303380
$969$	−109.905	−3.53064
$970$	19.0558	0.611843
$971$	−37.1780	−1.19310	−0.596550	−	0.802576i	$-0.703462\pi$
$971$	−37.1780	−1.19310	−0.596550	+	0.802576i	$0.703462\pi$
$972$	13.5797	0.435568
$973$	−20.5485	−0.658754
$974$	−10.6361	−0.340803
$975$	−2.56241	−0.0820627
$976$	−4.38492	−0.140358
$977$	11.8076	0.377760	0.188880	−	0.982000i	$-0.439514\pi$
$977$	11.8076	0.377760	0.188880	+	0.982000i	$0.439514\pi$
$978$	33.2282	1.06252
$979$	−6.12416	−0.195729
$980$	−15.6022	−0.498393
$981$	1.02824	0.0328290
$982$	−25.5947	−0.816761
$983$	−50.4900	−1.61038	−0.805190	−	0.593017i	$-0.797937\pi$
$983$	−50.4900	−1.61038	−0.805190	+	0.593017i	$0.797937\pi$
$984$	15.3749	0.490134
$985$	5.94965	0.189572
$986$	49.0780	1.56296
$987$	−22.6856	−0.722091
$988$	2.19951	0.0699758
$989$	−1.32097	−0.0420044
$990$	5.29399	0.168254
$991$	−40.6550	−1.29145	−0.645725	−	0.763570i	$-0.723445\pi$
$991$	−40.6550	−1.29145	−0.645725	+	0.763570i	$0.723445\pi$
$992$	−8.35113	−0.265149
$993$	−16.3870	−0.520025
$994$	17.0754	0.541599
$995$	−16.5987	−0.526213
$996$	12.4180	0.393479
$997$	−4.69731	−0.148765	−0.0743827	−	0.997230i	$-0.523699\pi$
$997$	−4.69731	−0.148765	−0.0743827	+	0.997230i	$0.523699\pi$
$998$	−34.0337	−1.07732
$999$	2.75909	0.0872937

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.c.1.15	✓	86

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.c.1.15	✓	86	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.09967 q^{3} +1.00000 q^{4} +3.00804 q^{5} +2.09967 q^{6} +1.34654 q^{7} -1.00000 q^{8} +1.40862 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.09967 q^{3} +1.00000 q^{4} +3.00804 q^{5} +2.09967 q^{6} +1.34654 q^{7} -1.00000 q^{8} +1.40862 q^{9} -3.00804 q^{10} -1.24941 q^{11} -2.09967 q^{12} +0.301458 q^{13} -1.34654 q^{14} -6.31589 q^{15} +1.00000 q^{16} +7.17405 q^{17} -1.40862 q^{18} +7.29625 q^{19} +3.00804 q^{20} -2.82729 q^{21} +1.24941 q^{22} -0.401333 q^{23} +2.09967 q^{24} +4.04828 q^{25} -0.301458 q^{26} +3.34137 q^{27} +1.34654 q^{28} -6.84104 q^{29} +6.31589 q^{30} +8.35113 q^{31} -1.00000 q^{32} +2.62335 q^{33} -7.17405 q^{34} +4.05044 q^{35} +1.40862 q^{36} +0.825735 q^{37} -7.29625 q^{38} -0.632962 q^{39} -3.00804 q^{40} +7.32252 q^{41} +2.82729 q^{42} +3.29145 q^{43} -1.24941 q^{44} +4.23719 q^{45} +0.401333 q^{46} +8.02381 q^{47} -2.09967 q^{48} -5.18683 q^{49} -4.04828 q^{50} -15.0631 q^{51} +0.301458 q^{52} +12.3821 q^{53} -3.34137 q^{54} -3.75827 q^{55} -1.34654 q^{56} -15.3197 q^{57} +6.84104 q^{58} -2.89041 q^{59} -6.31589 q^{60} -4.38492 q^{61} -8.35113 q^{62} +1.89676 q^{63} +1.00000 q^{64} +0.906795 q^{65} -2.62335 q^{66} -6.29483 q^{67} +7.17405 q^{68} +0.842668 q^{69} -4.05044 q^{70} -12.6810 q^{71} -1.40862 q^{72} -9.49410 q^{73} -0.825735 q^{74} -8.50006 q^{75} +7.29625 q^{76} -1.68238 q^{77} +0.632962 q^{78} +9.35312 q^{79} +3.00804 q^{80} -11.2417 q^{81} -7.32252 q^{82} -5.91425 q^{83} -2.82729 q^{84} +21.5798 q^{85} -3.29145 q^{86} +14.3639 q^{87} +1.24941 q^{88} +4.90163 q^{89} -4.23719 q^{90} +0.405924 q^{91} -0.401333 q^{92} -17.5346 q^{93} -8.02381 q^{94} +21.9474 q^{95} +2.09967 q^{96} -6.33495 q^{97} +5.18683 q^{98} -1.75995 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * q^99

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