LMFDB - Embedded newform 8035.2.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.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:	$64.1597980241$
Analytic rank:	$1$
Dimension:	$114$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49776 q^{2} +0.530865 q^{3} +4.23883 q^{4} +1.00000 q^{5} -1.32598 q^{6} +3.05763 q^{7} -5.59207 q^{8} -2.71818 q^{9} +O(q^{10})$	\(q-2.49776 q^{2} +0.530865 q^{3} +4.23883 q^{4} +1.00000 q^{5} -1.32598 q^{6} +3.05763 q^{7} -5.59207 q^{8} -2.71818 q^{9} -2.49776 q^{10} +3.61443 q^{11} +2.25024 q^{12} -0.556555 q^{13} -7.63725 q^{14} +0.530865 q^{15} +5.49001 q^{16} -3.15540 q^{17} +6.78938 q^{18} +7.04488 q^{19} +4.23883 q^{20} +1.62319 q^{21} -9.02800 q^{22} -2.38984 q^{23} -2.96863 q^{24} +1.00000 q^{25} +1.39014 q^{26} -3.03558 q^{27} +12.9608 q^{28} -10.5219 q^{29} -1.32598 q^{30} -0.183204 q^{31} -2.52862 q^{32} +1.91877 q^{33} +7.88144 q^{34} +3.05763 q^{35} -11.5219 q^{36} +7.94732 q^{37} -17.5964 q^{38} -0.295455 q^{39} -5.59207 q^{40} -11.4846 q^{41} -4.05435 q^{42} -5.15043 q^{43} +15.3210 q^{44} -2.71818 q^{45} +5.96926 q^{46} -0.982086 q^{47} +2.91445 q^{48} +2.34912 q^{49} -2.49776 q^{50} -1.67509 q^{51} -2.35914 q^{52} +3.73926 q^{53} +7.58217 q^{54} +3.61443 q^{55} -17.0985 q^{56} +3.73988 q^{57} +26.2812 q^{58} -11.0215 q^{59} +2.25024 q^{60} -11.4627 q^{61} +0.457600 q^{62} -8.31120 q^{63} -4.66413 q^{64} -0.556555 q^{65} -4.79265 q^{66} +5.31975 q^{67} -13.3752 q^{68} -1.26868 q^{69} -7.63725 q^{70} -4.29567 q^{71} +15.2003 q^{72} -12.0554 q^{73} -19.8505 q^{74} +0.530865 q^{75} +29.8620 q^{76} +11.0516 q^{77} +0.737978 q^{78} +5.23623 q^{79} +5.49001 q^{80} +6.54306 q^{81} +28.6858 q^{82} +9.86674 q^{83} +6.88042 q^{84} -3.15540 q^{85} +12.8646 q^{86} -5.58570 q^{87} -20.2121 q^{88} -4.55620 q^{89} +6.78938 q^{90} -1.70174 q^{91} -10.1301 q^{92} -0.0972564 q^{93} +2.45302 q^{94} +7.04488 q^{95} -1.34235 q^{96} -19.2721 q^{97} -5.86755 q^{98} -9.82469 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9}+O(q^{10}) $ 114 * q - 17 * q^2 - 10 * q^3 + 93 * q^4 + 114 * q^5 - 24 * q^6 - 11 * q^7 - 48 * q^8 + 66 * q^9	\( 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9} - 17 q^{10} - 44 q^{11} - 25 q^{12} - 26 q^{13} - 43 q^{14} - 10 q^{15} + 59 q^{16} - 57 q^{17} - 33 q^{18} - 69 q^{19} + 93 q^{20} - 107 q^{21} - 19 q^{22} - 45 q^{23} - 45 q^{24} + 114 q^{25} - 54 q^{26} - 34 q^{27} - 6 q^{28} - 166 q^{29} - 24 q^{30} - 67 q^{31} - 98 q^{32} - 38 q^{33} - 41 q^{34} - 11 q^{35} - 3 q^{36} - 44 q^{37} - 19 q^{38} - 66 q^{39} - 48 q^{40} - 141 q^{41} + q^{42} - 30 q^{43} - 125 q^{44} + 66 q^{45} - 59 q^{46} - 17 q^{47} - 35 q^{48} - 15 q^{49} - 17 q^{50} - 67 q^{51} - 26 q^{52} - 154 q^{53} - 45 q^{54} - 44 q^{55} - 118 q^{56} - 70 q^{57} + 11 q^{58} - 75 q^{59} - 25 q^{60} - 144 q^{61} - 35 q^{62} - 25 q^{63} + 16 q^{64} - 26 q^{65} - 68 q^{66} - 2 q^{67} - 99 q^{68} - 118 q^{69} - 43 q^{70} - 104 q^{71} - 73 q^{72} - 22 q^{73} - 107 q^{74} - 10 q^{75} - 172 q^{76} - 100 q^{77} - 2 q^{78} - 91 q^{79} + 59 q^{80} - 54 q^{81} + 20 q^{82} - 44 q^{83} - 156 q^{84} - 57 q^{85} - 50 q^{86} + 5 q^{87} - 13 q^{88} - 150 q^{89} - 33 q^{90} - 54 q^{91} - 77 q^{92} - 50 q^{93} - 105 q^{94} - 69 q^{95} - 78 q^{96} - 31 q^{97} - 64 q^{98} - 101 q^{99}+O(q^{100}) \) 114 * q - 17 * q^2 - 10 * q^3 + 93 * q^4 + 114 * q^5 - 24 * q^6 - 11 * q^7 - 48 * q^8 + 66 * q^9 - 17 * q^10 - 44 * q^11 - 25 * q^12 - 26 * q^13 - 43 * q^14 - 10 * q^15 + 59 * q^16 - 57 * q^17 - 33 * q^18 - 69 * q^19 + 93 * q^20 - 107 * q^21 - 19 * q^22 - 45 * q^23 - 45 * q^24 + 114 * q^25 - 54 * q^26 - 34 * q^27 - 6 * q^28 - 166 * q^29 - 24 * q^30 - 67 * q^31 - 98 * q^32 - 38 * q^33 - 41 * q^34 - 11 * q^35 - 3 * q^36 - 44 * q^37 - 19 * q^38 - 66 * q^39 - 48 * q^40 - 141 * q^41 + q^42 - 30 * q^43 - 125 * q^44 + 66 * q^45 - 59 * q^46 - 17 * q^47 - 35 * q^48 - 15 * q^49 - 17 * q^50 - 67 * q^51 - 26 * q^52 - 154 * q^53 - 45 * q^54 - 44 * q^55 - 118 * q^56 - 70 * q^57 + 11 * q^58 - 75 * q^59 - 25 * q^60 - 144 * q^61 - 35 * q^62 - 25 * q^63 + 16 * q^64 - 26 * q^65 - 68 * q^66 - 2 * q^67 - 99 * q^68 - 118 * q^69 - 43 * q^70 - 104 * q^71 - 73 * q^72 - 22 * q^73 - 107 * q^74 - 10 * q^75 - 172 * q^76 - 100 * q^77 - 2 * q^78 - 91 * q^79 + 59 * q^80 - 54 * q^81 + 20 * q^82 - 44 * q^83 - 156 * q^84 - 57 * q^85 - 50 * q^86 + 5 * q^87 - 13 * q^88 - 150 * q^89 - 33 * q^90 - 54 * q^91 - 77 * q^92 - 50 * q^93 - 105 * q^94 - 69 * q^95 - 78 * q^96 - 31 * q^97 - 64 * q^98 - 101 * 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 $

$2$	−2.49776	−1.76619	−0.883093	−	0.469198i	$-0.844543\pi$
$2$	−2.49776	−1.76619	−0.883093	+	0.469198i	$0.844543\pi$
$3$	0.530865	0.306495	0.153247	−	0.988188i	$-0.451027\pi$
$3$	0.530865	0.306495	0.153247	+	0.988188i	$0.451027\pi$
$4$	4.23883	2.11941
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.32598	−0.541327
$7$	3.05763	1.15568	0.577838	−	0.816151i	$-0.303896\pi$
$7$	3.05763	1.15568	0.577838	+	0.816151i	$0.303896\pi$
$8$	−5.59207	−1.97709
$9$	−2.71818	−0.906061
$10$	−2.49776	−0.789863
$11$	3.61443	1.08979	0.544896	−	0.838504i	$-0.316569\pi$
$11$	3.61443	1.08979	0.544896	+	0.838504i	$0.316569\pi$
$12$	2.25024	0.649590
$13$	−0.556555	−0.154361	−0.0771803	−	0.997017i	$-0.524592\pi$
$13$	−0.556555	−0.154361	−0.0771803	+	0.997017i	$0.524592\pi$
$14$	−7.63725	−2.04114
$15$	0.530865	0.137069
$16$	5.49001	1.37250
$17$	−3.15540	−0.765296	−0.382648	−	0.923894i	$-0.624988\pi$
$17$	−3.15540	−0.765296	−0.382648	+	0.923894i	$0.624988\pi$
$18$	6.78938	1.60027
$19$	7.04488	1.61621	0.808103	−	0.589041i	$-0.200494\pi$
$19$	7.04488	1.61621	0.808103	+	0.589041i	$0.200494\pi$
$20$	4.23883	0.947831
$21$	1.62319	0.354209
$22$	−9.02800	−1.92478
$23$	−2.38984	−0.498316	−0.249158	−	0.968463i	$-0.580154\pi$
$23$	−2.38984	−0.498316	−0.249158	+	0.968463i	$0.580154\pi$
$24$	−2.96863	−0.605969
$25$	1.00000	0.200000
$26$	1.39014	0.272630
$27$	−3.03558	−0.584198
$28$	12.9608	2.44936
$29$	−10.5219	−1.95386	−0.976932	−	0.213550i	$-0.931498\pi$
$29$	−10.5219	−1.95386	−0.976932	+	0.213550i	$0.931498\pi$
$30$	−1.32598	−0.242089
$31$	−0.183204	−0.0329044	−0.0164522	−	0.999865i	$-0.505237\pi$
$31$	−0.183204	−0.0329044	−0.0164522	+	0.999865i	$0.505237\pi$
$32$	−2.52862	−0.447001
$33$	1.91877	0.334016
$34$	7.88144	1.35166
$35$	3.05763	0.516834
$36$	−11.5219	−1.92032
$37$	7.94732	1.30653	0.653266	−	0.757129i	$-0.273398\pi$
$37$	7.94732	1.30653	0.653266	+	0.757129i	$0.273398\pi$
$38$	−17.5964	−2.85452
$39$	−0.295455	−0.0473107
$40$	−5.59207	−0.884183
$41$	−11.4846	−1.79359	−0.896797	−	0.442442i	$-0.854112\pi$
$41$	−11.4846	−1.79359	−0.896797	+	0.442442i	$0.854112\pi$
$42$	−4.05435	−0.625599
$43$	−5.15043	−0.785433	−0.392717	−	0.919660i	$-0.628465\pi$
$43$	−5.15043	−0.785433	−0.392717	+	0.919660i	$0.628465\pi$
$44$	15.3210	2.30972
$45$	−2.71818	−0.405203
$46$	5.96926	0.880119
$47$	−0.982086	−0.143252	−0.0716260	−	0.997432i	$-0.522819\pi$
$47$	−0.982086	−0.143252	−0.0716260	+	0.997432i	$0.522819\pi$
$48$	2.91445	0.420665
$49$	2.34912	0.335588
$50$	−2.49776	−0.353237
$51$	−1.67509	−0.234559
$52$	−2.35914	−0.327154
$53$	3.73926	0.513627	0.256814	−	0.966461i	$-0.417327\pi$
$53$	3.73926	0.513627	0.256814	+	0.966461i	$0.417327\pi$
$54$	7.58217	1.03180
$55$	3.61443	0.487370
$56$	−17.0985	−2.28488
$57$	3.73988	0.495359
$58$	26.2812	3.45089
$59$	−11.0215	−1.43488	−0.717439	−	0.696621i	$-0.754686\pi$
$59$	−11.0215	−1.43488	−0.717439	+	0.696621i	$0.754686\pi$
$60$	2.25024	0.290505
$61$	−11.4627	−1.46765	−0.733823	−	0.679341i	$-0.762266\pi$
$61$	−11.4627	−1.46765	−0.733823	+	0.679341i	$0.762266\pi$
$62$	0.457600	0.0581152
$63$	−8.31120	−1.04711
$64$	−4.66413	−0.583016
$65$	−0.556555	−0.0690322
$66$	−4.79265	−0.589934
$67$	5.31975	0.649910	0.324955	−	0.945729i	$-0.394651\pi$
$67$	5.31975	0.649910	0.324955	+	0.945729i	$0.394651\pi$
$68$	−13.3752	−1.62198
$69$	−1.26868	−0.152731
$70$	−7.63725	−0.912826
$71$	−4.29567	−0.509802	−0.254901	−	0.966967i	$-0.582043\pi$
$71$	−4.29567	−0.509802	−0.254901	+	0.966967i	$0.582043\pi$
$72$	15.2003	1.79137
$73$	−12.0554	−1.41098	−0.705491	−	0.708719i	$-0.749274\pi$
$73$	−12.0554	−1.41098	−0.705491	+	0.708719i	$0.749274\pi$
$74$	−19.8505	−2.30758
$75$	0.530865	0.0612990
$76$	29.8620	3.42541
$77$	11.0516	1.25945
$78$	0.737978	0.0835596
$79$	5.23623	0.589122	0.294561	−	0.955633i	$-0.404827\pi$
$79$	5.23623	0.589122	0.294561	+	0.955633i	$0.404827\pi$
$80$	5.49001	0.613802
$81$	6.54306	0.727007
$82$	28.6858	3.16782
$83$	9.86674	1.08302	0.541508	−	0.840696i	$-0.317854\pi$
$83$	9.86674	1.08302	0.541508	+	0.840696i	$0.317854\pi$
$84$	6.88042	0.750716
$85$	−3.15540	−0.342251
$86$	12.8646	1.38722
$87$	−5.58570	−0.598850
$88$	−20.2121	−2.15462
$89$	−4.55620	−0.482956	−0.241478	−	0.970406i	$-0.577632\pi$
$89$	−4.55620	−0.482956	−0.241478	+	0.970406i	$0.577632\pi$
$90$	6.78938	0.715664
$91$	−1.70174	−0.178391
$92$	−10.1301	−1.05614
$93$	−0.0972564	−0.0100850
$94$	2.45302	0.253010
$95$	7.04488	0.722789
$96$	−1.34235	−0.137003
$97$	−19.2721	−1.95678	−0.978390	−	0.206766i	$-0.933706\pi$
$97$	−19.2721	−1.95678	−0.978390	+	0.206766i	$0.933706\pi$
$98$	−5.86755	−0.592712
$99$	−9.82469	−0.987418
$100$	4.23883	0.423883
$101$	19.4397	1.93433	0.967163	−	0.254157i	$-0.0817980\pi$
$101$	19.4397	1.93433	0.967163	+	0.254157i	$0.0817980\pi$
$102$	4.18398	0.414276
$103$	−5.84912	−0.576331	−0.288165	−	0.957581i	$-0.593045\pi$
$103$	−5.84912	−0.576331	−0.288165	+	0.957581i	$0.593045\pi$
$104$	3.11229	0.305185
$105$	1.62319	0.158407
$106$	−9.33980	−0.907162
$107$	−15.9003	−1.53714	−0.768572	−	0.639763i	$-0.779032\pi$
$107$	−15.9003	−1.53714	−0.768572	+	0.639763i	$0.779032\pi$
$108$	−12.8673	−1.23816
$109$	9.03598	0.865490	0.432745	−	0.901516i	$-0.357545\pi$
$109$	9.03598	0.865490	0.432745	+	0.901516i	$0.357545\pi$
$110$	−9.02800	−0.860786
$111$	4.21895	0.400445
$112$	16.7864	1.58617
$113$	−17.1796	−1.61612	−0.808062	−	0.589097i	$-0.799483\pi$
$113$	−17.1796	−1.61612	−0.808062	+	0.589097i	$0.799483\pi$
$114$	−9.34134	−0.874896
$115$	−2.38984	−0.222854
$116$	−44.6005	−4.14105
$117$	1.51282	0.139860
$118$	27.5291	2.53426
$119$	−9.64805	−0.884435
$120$	−2.96863	−0.270998
$121$	2.06412	0.187647
$122$	28.6311	2.59214
$123$	−6.09677	−0.549727
$124$	−0.776569	−0.0697380
$125$	1.00000	0.0894427
$126$	20.7594	1.84940
$127$	8.28554	0.735223	0.367611	−	0.929980i	$-0.380176\pi$
$127$	8.28554	0.735223	0.367611	+	0.929980i	$0.380176\pi$
$128$	16.7071	1.47672
$129$	−2.73418	−0.240731
$130$	1.39014	0.121924
$131$	−16.1953	−1.41499	−0.707496	−	0.706718i	$-0.750175\pi$
$131$	−16.1953	−1.41499	−0.707496	+	0.706718i	$0.750175\pi$
$132$	8.13336	0.707918
$133$	21.5407	1.86781
$134$	−13.2875	−1.14786
$135$	−3.03558	−0.261261
$136$	17.6452	1.51306
$137$	14.2576	1.21811	0.609053	−	0.793129i	$-0.291550\pi$
$137$	14.2576	1.21811	0.609053	+	0.793129i	$0.291550\pi$
$138$	3.16887	0.269752
$139$	−20.6197	−1.74894	−0.874470	−	0.485080i	$-0.838790\pi$
$139$	−20.6197	−1.74894	−0.874470	+	0.485080i	$0.838790\pi$
$140$	12.9608	1.09539
$141$	−0.521355	−0.0439060
$142$	10.7296	0.900406
$143$	−2.01163	−0.168221
$144$	−14.9228	−1.24357
$145$	−10.5219	−0.873795
$146$	30.1117	2.49206
$147$	1.24706	0.102856
$148$	33.6873	2.76908
$149$	5.49574	0.450228	0.225114	−	0.974332i	$-0.427724\pi$
$149$	5.49574	0.450228	0.225114	+	0.974332i	$0.427724\pi$
$150$	−1.32598	−0.108265
$151$	12.5970	1.02513	0.512565	−	0.858649i	$-0.328695\pi$
$151$	12.5970	1.02513	0.512565	+	0.858649i	$0.328695\pi$
$152$	−39.3954	−3.19539
$153$	8.57695	0.693405
$154$	−27.6043	−2.22442
$155$	−0.183204	−0.0147153
$156$	−1.25239	−0.100271
$157$	1.50916	0.120444	0.0602220	−	0.998185i	$-0.480819\pi$
$157$	1.50916	0.120444	0.0602220	+	0.998185i	$0.480819\pi$
$158$	−13.0789	−1.04050
$159$	1.98504	0.157424
$160$	−2.52862	−0.199905
$161$	−7.30726	−0.575893
$162$	−16.3430	−1.28403
$163$	−0.485645	−0.0380387	−0.0190193	−	0.999819i	$-0.506054\pi$
$163$	−0.485645	−0.0380387	−0.0190193	+	0.999819i	$0.506054\pi$
$164$	−48.6813	−3.80137
$165$	1.91877	0.149376
$166$	−24.6448	−1.91281
$167$	−14.4524	−1.11836	−0.559182	−	0.829045i	$-0.688885\pi$
$167$	−14.4524	−1.11836	−0.559182	+	0.829045i	$0.688885\pi$
$168$	−9.07698	−0.700305
$169$	−12.6902	−0.976173
$170$	7.88144	0.604479
$171$	−19.1493	−1.46438
$172$	−21.8318	−1.66466
$173$	5.93688	0.451373	0.225686	−	0.974200i	$-0.427538\pi$
$173$	5.93688	0.451373	0.225686	+	0.974200i	$0.427538\pi$
$174$	13.9518	1.05768
$175$	3.05763	0.231135
$176$	19.8433	1.49574
$177$	−5.85093	−0.439783
$178$	11.3803	0.852990
$179$	−25.3669	−1.89601	−0.948006	−	0.318253i	$-0.896904\pi$
$179$	−25.3669	−1.89601	−0.948006	+	0.318253i	$0.896904\pi$
$180$	−11.5219	−0.858792
$181$	−1.30161	−0.0967479	−0.0483739	−	0.998829i	$-0.515404\pi$
$181$	−1.30161	−0.0967479	−0.0483739	+	0.998829i	$0.515404\pi$
$182$	4.25055	0.315072
$183$	−6.08513	−0.449826
$184$	13.3642	0.985218
$185$	7.94732	0.584299
$186$	0.242924	0.0178120
$187$	−11.4050	−0.834014
$188$	−4.16290	−0.303610
$189$	−9.28169	−0.675144
$190$	−17.5964	−1.27658
$191$	0.609639	0.0441119	0.0220560	−	0.999757i	$-0.492979\pi$
$191$	0.609639	0.0441119	0.0220560	+	0.999757i	$0.492979\pi$
$192$	−2.47602	−0.178691
$193$	−8.80860	−0.634057	−0.317028	−	0.948416i	$-0.602685\pi$
$193$	−8.80860	−0.634057	−0.317028	+	0.948416i	$0.602685\pi$
$194$	48.1371	3.45604
$195$	−0.295455	−0.0211580
$196$	9.95751	0.711251
$197$	−4.30452	−0.306684	−0.153342	−	0.988173i	$-0.549004\pi$
$197$	−4.30452	−0.306684	−0.153342	+	0.988173i	$0.549004\pi$
$198$	24.5398	1.74396
$199$	8.80472	0.624150	0.312075	−	0.950057i	$-0.398976\pi$
$199$	8.80472	0.624150	0.312075	+	0.950057i	$0.398976\pi$
$200$	−5.59207	−0.395419
$201$	2.82407	0.199194
$202$	−48.5559	−3.41638
$203$	−32.1721	−2.25804
$204$	−7.10042	−0.497129
$205$	−11.4846	−0.802120
$206$	14.6097	1.01791
$207$	6.49602	0.451505
$208$	−3.05549	−0.211860
$209$	25.4632	1.76133
$210$	−4.05435	−0.279776
$211$	−18.7813	−1.29296	−0.646478	−	0.762933i	$-0.723759\pi$
$211$	−18.7813	−1.29296	−0.646478	+	0.762933i	$0.723759\pi$
$212$	15.8501	1.08859
$213$	−2.28042	−0.156252
$214$	39.7153	2.71488
$215$	−5.15043	−0.351256
$216$	16.9752	1.15501
$217$	−0.560170	−0.0380268
$218$	−22.5698	−1.52862
$219$	−6.39981	−0.432459
$220$	15.3210	1.03294
$221$	1.75615	0.118132
$222$	−10.5380	−0.707261
$223$	6.19481	0.414835	0.207418	−	0.978252i	$-0.433494\pi$
$223$	6.19481	0.414835	0.207418	+	0.978252i	$0.433494\pi$
$224$	−7.73159	−0.516588
$225$	−2.71818	−0.181212
$226$	42.9107	2.85438
$227$	2.49941	0.165892	0.0829458	−	0.996554i	$-0.473567\pi$
$227$	2.49941	0.165892	0.0829458	+	0.996554i	$0.473567\pi$
$228$	15.8527	1.04987
$229$	8.61971	0.569606	0.284803	−	0.958586i	$-0.408072\pi$
$229$	8.61971	0.569606	0.284803	+	0.958586i	$0.408072\pi$
$230$	5.96926	0.393601
$231$	5.86691	0.386014
$232$	58.8391	3.86297
$233$	12.8465	0.841602	0.420801	−	0.907153i	$-0.361749\pi$
$233$	12.8465	0.841602	0.420801	+	0.907153i	$0.361749\pi$
$234$	−3.77866	−0.247019
$235$	−0.982086	−0.0640642
$236$	−46.7183	−3.04110
$237$	2.77973	0.180563
$238$	24.0986	1.56208
$239$	−19.1910	−1.24136	−0.620681	−	0.784063i	$-0.713144\pi$
$239$	−19.1910	−1.24136	−0.620681	+	0.784063i	$0.713144\pi$
$240$	2.91445	0.188127
$241$	−28.5500	−1.83907	−0.919534	−	0.393009i	$-0.871434\pi$
$241$	−28.5500	−1.83907	−0.919534	+	0.393009i	$0.871434\pi$
$242$	−5.15569	−0.331420
$243$	12.5802	0.807022
$244$	−48.5883	−3.11055
$245$	2.34912	0.150080
$246$	15.2283	0.970921
$247$	−3.92086	−0.249479
$248$	1.02449	0.0650550
$249$	5.23791	0.331939
$250$	−2.49776	−0.157973
$251$	−5.97018	−0.376834	−0.188417	−	0.982089i	$-0.560336\pi$
$251$	−5.97018	−0.376834	−0.188417	+	0.982089i	$0.560336\pi$
$252$	−35.2298	−2.21927
$253$	−8.63792	−0.543061
$254$	−20.6953	−1.29854
$255$	−1.67509	−0.104898
$256$	−32.4022	−2.02514
$257$	10.9485	0.682951	0.341475	−	0.939891i	$-0.389073\pi$
$257$	10.9485	0.682951	0.341475	+	0.939891i	$0.389073\pi$
$258$	6.82934	0.425176
$259$	24.3000	1.50993
$260$	−2.35914	−0.146308
$261$	28.6004	1.77032
$262$	40.4521	2.49914
$263$	20.4706	1.26227	0.631136	−	0.775672i	$-0.282589\pi$
$263$	20.4706	1.26227	0.631136	+	0.775672i	$0.282589\pi$
$264$	−10.7299	−0.660381
$265$	3.73926	0.229701
$266$	−53.8035	−3.29890
$267$	−2.41872	−0.148024
$268$	22.5495	1.37743
$269$	19.7455	1.20391	0.601954	−	0.798531i	$-0.294389\pi$
$269$	19.7455	1.20391	0.601954	+	0.798531i	$0.294389\pi$
$270$	7.58217	0.461436
$271$	−4.02448	−0.244470	−0.122235	−	0.992501i	$-0.539006\pi$
$271$	−4.02448	−0.244470	−0.122235	+	0.992501i	$0.539006\pi$
$272$	−17.3232	−1.05037
$273$	−0.903394	−0.0546759
$274$	−35.6121	−2.15140
$275$	3.61443	0.217958
$276$	−5.37773	−0.323701
$277$	−4.51163	−0.271077	−0.135539	−	0.990772i	$-0.543276\pi$
$277$	−4.51163	−0.271077	−0.135539	+	0.990772i	$0.543276\pi$
$278$	51.5031	3.08895
$279$	0.497981	0.0298134
$280$	−17.0985	−1.02183
$281$	−7.53166	−0.449301	−0.224651	−	0.974439i	$-0.572124\pi$
$281$	−7.53166	−0.449301	−0.224651	+	0.974439i	$0.572124\pi$
$282$	1.30222	0.0775462
$283$	−1.92606	−0.114492	−0.0572462	−	0.998360i	$-0.518232\pi$
$283$	−1.92606	−0.114492	−0.0572462	+	0.998360i	$0.518232\pi$
$284$	−18.2086	−1.08048
$285$	3.73988	0.221531
$286$	5.02458	0.297110
$287$	−35.1157	−2.07281
$288$	6.87325	0.405010
$289$	−7.04347	−0.414322
$290$	26.2812	1.54328
$291$	−10.2309	−0.599743
$292$	−51.1009	−2.99046
$293$	−23.3935	−1.36666	−0.683331	−	0.730109i	$-0.739469\pi$
$293$	−23.3935	−1.36666	−0.683331	+	0.730109i	$0.739469\pi$
$294$	−3.11487	−0.181663
$295$	−11.0215	−0.641697
$296$	−44.4419	−2.58314
$297$	−10.9719	−0.636655
$298$	−13.7271	−0.795187
$299$	1.33008	0.0769204
$300$	2.25024	0.129918
$301$	−15.7481	−0.907707
$302$	−31.4643	−1.81057
$303$	10.3199	0.592861
$304$	38.6765	2.21825
$305$	−11.4627	−0.656351
$306$	−21.4232	−1.22468
$307$	25.6071	1.46148	0.730738	−	0.682658i	$-0.239176\pi$
$307$	25.6071	1.46148	0.730738	+	0.682658i	$0.239176\pi$
$308$	46.8459	2.66929
$309$	−3.10509	−0.176642
$310$	0.457600	0.0259899
$311$	−0.281637	−0.0159702	−0.00798509	−	0.999968i	$-0.502542\pi$
$311$	−0.281637	−0.0159702	−0.00798509	+	0.999968i	$0.502542\pi$
$312$	1.65221	0.0935378
$313$	13.6399	0.770974	0.385487	−	0.922713i	$-0.374033\pi$
$313$	13.6399	0.770974	0.385487	+	0.922713i	$0.374033\pi$
$314$	−3.76953	−0.212727
$315$	−8.31120	−0.468283
$316$	22.1955	1.24859
$317$	30.5768	1.71737	0.858683	−	0.512507i	$-0.171283\pi$
$317$	30.5768	1.71737	0.858683	+	0.512507i	$0.171283\pi$
$318$	−4.95817	−0.278040
$319$	−38.0306	−2.12931
$320$	−4.66413	−0.260733
$321$	−8.44093	−0.471127
$322$	18.2518	1.01713
$323$	−22.2294	−1.23688
$324$	27.7349	1.54083
$325$	−0.556555	−0.0308721
$326$	1.21303	0.0671834
$327$	4.79688	0.265268
$328$	64.2227	3.54610
$329$	−3.00286	−0.165553
$330$	−4.79265	−0.263827
$331$	8.58987	0.472142	0.236071	−	0.971736i	$-0.424140\pi$
$331$	8.58987	0.472142	0.236071	+	0.971736i	$0.424140\pi$
$332$	41.8234	2.29536
$333$	−21.6023	−1.18380
$334$	36.0988	1.97524
$335$	5.31975	0.290649
$336$	8.91133	0.486153
$337$	−0.647813	−0.0352886	−0.0176443	−	0.999844i	$-0.505617\pi$
$337$	−0.647813	−0.0352886	−0.0176443	+	0.999844i	$0.505617\pi$
$338$	31.6972	1.72410
$339$	−9.12006	−0.495334
$340$	−13.3752	−0.725371
$341$	−0.662178	−0.0358589
$342$	47.8304	2.58637
$343$	−14.2207	−0.767845
$344$	28.8015	1.55288
$345$	−1.26868	−0.0683036
$346$	−14.8289	−0.797208
$347$	25.3120	1.35882	0.679409	−	0.733759i	$-0.262236\pi$
$347$	25.3120	1.35882	0.679409	+	0.733759i	$0.262236\pi$
$348$	−23.6768	−1.26921
$349$	8.43424	0.451474	0.225737	−	0.974188i	$-0.427521\pi$
$349$	8.43424	0.451474	0.225737	+	0.974188i	$0.427521\pi$
$350$	−7.63725	−0.408228
$351$	1.68947	0.0901772
$352$	−9.13952	−0.487138
$353$	−9.37336	−0.498893	−0.249447	−	0.968389i	$-0.580249\pi$
$353$	−9.37336	−0.498893	−0.249447	+	0.968389i	$0.580249\pi$
$354$	14.6142	0.776739
$355$	−4.29567	−0.227990
$356$	−19.3129	−1.02358
$357$	−5.12181	−0.271075
$358$	63.3606	3.34871
$359$	−26.9078	−1.42014	−0.710070	−	0.704131i	$-0.751337\pi$
$359$	−26.9078	−1.42014	−0.710070	+	0.704131i	$0.751337\pi$
$360$	15.2003	0.801124
$361$	30.6303	1.61212
$362$	3.25111	0.170875
$363$	1.09577	0.0575130
$364$	−7.21339	−0.378084
$365$	−12.0554	−0.631011
$366$	15.1992	0.794476
$367$	21.9473	1.14564	0.572819	−	0.819682i	$-0.305850\pi$
$367$	21.9473	1.14564	0.572819	+	0.819682i	$0.305850\pi$
$368$	−13.1202	−0.683940
$369$	31.2173	1.62511
$370$	−19.8505	−1.03198
$371$	11.4333	0.593587
$372$	−0.412253	−0.0213743
$373$	32.7795	1.69726	0.848628	−	0.528990i	$-0.177429\pi$
$373$	32.7795	1.69726	0.848628	+	0.528990i	$0.177429\pi$
$374$	28.4869	1.47302
$375$	0.530865	0.0274137
$376$	5.49189	0.283223
$377$	5.85601	0.301600
$378$	23.1835	1.19243
$379$	16.8383	0.864927	0.432463	−	0.901652i	$-0.357644\pi$
$379$	16.8383	0.864927	0.432463	+	0.901652i	$0.357644\pi$
$380$	29.8620	1.53189
$381$	4.39850	0.225342
$382$	−1.52273	−0.0779098
$383$	−23.9355	−1.22305	−0.611524	−	0.791226i	$-0.709443\pi$
$383$	−23.9355	−1.22305	−0.611524	+	0.791226i	$0.709443\pi$
$384$	8.86922	0.452606
$385$	11.0516	0.563242
$386$	22.0018	1.11986
$387$	13.9998	0.711650
$388$	−81.6909	−4.14723
$389$	17.5699	0.890830	0.445415	−	0.895324i	$-0.353056\pi$
$389$	17.5699	0.890830	0.445415	+	0.895324i	$0.353056\pi$
$390$	0.737978	0.0373690
$391$	7.54090	0.381360
$392$	−13.1364	−0.663490
$393$	−8.59752	−0.433688
$394$	10.7517	0.541661
$395$	5.23623	0.263463
$396$	−41.6452	−2.09275
$397$	28.6300	1.43690	0.718450	−	0.695579i	$-0.244852\pi$
$397$	28.6300	1.43690	0.718450	+	0.695579i	$0.244852\pi$
$398$	−21.9921	−1.10237
$399$	11.4352	0.572475
$400$	5.49001	0.274500
$401$	12.1082	0.604656	0.302328	−	0.953204i	$-0.402236\pi$
$401$	12.1082	0.604656	0.302328	+	0.953204i	$0.402236\pi$
$402$	−7.05385	−0.351814
$403$	0.101963	0.00507914
$404$	82.4017	4.09964
$405$	6.54306	0.325127
$406$	80.3582	3.98811
$407$	28.7251	1.42385
$408$	9.36721	0.463746
$409$	−4.11554	−0.203500	−0.101750	−	0.994810i	$-0.532444\pi$
$409$	−4.11554	−0.203500	−0.101750	+	0.994810i	$0.532444\pi$
$410$	28.6858	1.41669
$411$	7.56884	0.373344
$412$	−24.7934	−1.22148
$413$	−33.6997	−1.65826
$414$	−16.2255	−0.797442
$415$	9.86674	0.484339
$416$	1.40732	0.0689993
$417$	−10.9463	−0.536041
$418$	−63.6012	−3.11084
$419$	−5.54726	−0.271001	−0.135501	−	0.990777i	$-0.543264\pi$
$419$	−5.54726	−0.271001	−0.135501	+	0.990777i	$0.543264\pi$
$420$	6.88042	0.335730
$421$	−2.69331	−0.131264	−0.0656319	−	0.997844i	$-0.520906\pi$
$421$	−2.69331	−0.131264	−0.0656319	+	0.997844i	$0.520906\pi$
$422$	46.9112	2.28360
$423$	2.66949	0.129795
$424$	−20.9102	−1.01549
$425$	−3.15540	−0.153059
$426$	5.69595	0.275970
$427$	−35.0487	−1.69612
$428$	−67.3988	−3.25785
$429$	−1.06790	−0.0515589
$430$	12.8646	0.620384
$431$	−36.7628	−1.77080	−0.885400	−	0.464830i	$-0.846115\pi$
$431$	−36.7628	−1.77080	−0.885400	+	0.464830i	$0.846115\pi$
$432$	−16.6654	−0.801813
$433$	6.67356	0.320711	0.160355	−	0.987059i	$-0.448736\pi$
$433$	6.67356	0.320711	0.160355	+	0.987059i	$0.448736\pi$
$434$	1.39917	0.0671624
$435$	−5.58570	−0.267814
$436$	38.3020	1.83433
$437$	−16.8361	−0.805382
$438$	15.9852	0.763803
$439$	22.6356	1.08034	0.540169	−	0.841557i	$-0.318360\pi$
$439$	22.6356	1.08034	0.540169	+	0.841557i	$0.318360\pi$
$440$	−20.2121	−0.963576
$441$	−6.38533	−0.304063
$442$	−4.38646	−0.208642
$443$	−15.5672	−0.739620	−0.369810	−	0.929107i	$-0.620577\pi$
$443$	−15.5672	−0.739620	−0.369810	+	0.929107i	$0.620577\pi$
$444$	17.8834	0.848709
$445$	−4.55620	−0.215984
$446$	−15.4732	−0.732676
$447$	2.91749	0.137993
$448$	−14.2612	−0.673778
$449$	−26.0450	−1.22914	−0.614569	−	0.788863i	$-0.710670\pi$
$449$	−26.0450	−1.22914	−0.614569	+	0.788863i	$0.710670\pi$
$450$	6.78938	0.320054
$451$	−41.5103	−1.95464
$452$	−72.8215	−3.42524
$453$	6.68730	0.314197
$454$	−6.24294	−0.292995
$455$	−1.70174	−0.0797789
$456$	−20.9136	−0.979371
$457$	7.90759	0.369901	0.184951	−	0.982748i	$-0.440787\pi$
$457$	7.90759	0.369901	0.184951	+	0.982748i	$0.440787\pi$
$458$	−21.5300	−1.00603
$459$	9.57847	0.447085
$460$	−10.1301	−0.472320
$461$	8.46210	0.394119	0.197060	−	0.980391i	$-0.436861\pi$
$461$	8.46210	0.394119	0.197060	+	0.980391i	$0.436861\pi$
$462$	−14.6542	−0.681773
$463$	−12.9218	−0.600525	−0.300263	−	0.953857i	$-0.597074\pi$
$463$	−12.9218	−0.600525	−0.300263	+	0.953857i	$0.597074\pi$
$464$	−57.7652	−2.68168
$465$	−0.0972564	−0.00451016
$466$	−32.0875	−1.48643
$467$	8.41113	0.389221	0.194610	−	0.980881i	$-0.437656\pi$
$467$	8.41113	0.389221	0.194610	+	0.980881i	$0.437656\pi$
$468$	6.41258	0.296421
$469$	16.2658	0.751086
$470$	2.45302	0.113149
$471$	0.801160	0.0369155
$472$	61.6330	2.83689
$473$	−18.6159	−0.855959
$474$	−6.94311	−0.318908
$475$	7.04488	0.323241
$476$	−40.8964	−1.87448
$477$	−10.1640	−0.465378
$478$	47.9346	2.19248
$479$	40.5771	1.85402	0.927009	−	0.375040i	$-0.122371\pi$
$479$	40.5771	1.85402	0.927009	+	0.375040i	$0.122371\pi$
$480$	−1.34235	−0.0612698
$481$	−4.42312	−0.201677
$482$	71.3112	3.24814
$483$	−3.87917	−0.176508
$484$	8.74946	0.397703
$485$	−19.2721	−0.875099
$486$	−31.4224	−1.42535
$487$	−4.58493	−0.207763	−0.103882	−	0.994590i	$-0.533126\pi$
$487$	−4.58493	−0.207763	−0.103882	+	0.994590i	$0.533126\pi$
$488$	64.1001	2.90167
$489$	−0.257812	−0.0116587
$490$	−5.86755	−0.265069
$491$	28.4208	1.28261	0.641306	−	0.767285i	$-0.278393\pi$
$491$	28.4208	1.28261	0.641306	+	0.767285i	$0.278393\pi$
$492$	−25.8432	−1.16510
$493$	33.2007	1.49529
$494$	9.79339	0.440626
$495$	−9.82469	−0.441587
$496$	−1.00579	−0.0451613
$497$	−13.1346	−0.589166
$498$	−13.0831	−0.586266
$499$	30.3497	1.35864	0.679320	−	0.733842i	$-0.262275\pi$
$499$	30.3497	1.35864	0.679320	+	0.733842i	$0.262275\pi$
$500$	4.23883	0.189566
$501$	−7.67229	−0.342773
$502$	14.9121	0.665560
$503$	5.17733	0.230846	0.115423	−	0.993316i	$-0.463178\pi$
$503$	5.17733	0.230846	0.115423	+	0.993316i	$0.463178\pi$
$504$	46.4768	2.07024
$505$	19.4397	0.865057
$506$	21.5755	0.959148
$507$	−6.73680	−0.299192
$508$	35.1210	1.55824
$509$	13.3008	0.589546	0.294773	−	0.955567i	$-0.404756\pi$
$509$	13.3008	0.589546	0.294773	+	0.955567i	$0.404756\pi$
$510$	4.18398	0.185270
$511$	−36.8611	−1.63064
$512$	47.5189	2.10006
$513$	−21.3853	−0.944184
$514$	−27.3469	−1.20622
$515$	−5.84912	−0.257743
$516$	−11.5897	−0.510209
$517$	−3.54968	−0.156115
$518$	−60.6956	−2.66681
$519$	3.15168	0.138343
$520$	3.11229	0.136483
$521$	34.0701	1.49264	0.746319	−	0.665589i	$-0.231819\pi$
$521$	34.0701	1.49264	0.746319	+	0.665589i	$0.231819\pi$
$522$	−71.4371	−3.12672
$523$	32.0760	1.40259	0.701293	−	0.712873i	$-0.252607\pi$
$523$	32.0760	1.40259	0.701293	+	0.712873i	$0.252607\pi$
$524$	−68.6492	−2.99895
$525$	1.62319	0.0708418
$526$	−51.1308	−2.22941
$527$	0.578081	0.0251816
$528$	10.5341	0.458438
$529$	−17.2887	−0.751681
$530$	−9.33980	−0.405695
$531$	29.9585	1.30009
$532$	91.3071	3.95867
$533$	6.39181	0.276860
$534$	6.04141	0.261437
$535$	−15.9003	−0.687432
$536$	−29.7484	−1.28493
$537$	−13.4664	−0.581118
$538$	−49.3197	−2.12632
$539$	8.49073	0.365722
$540$	−12.8673	−0.553721
$541$	−31.1531	−1.33938	−0.669688	−	0.742643i	$-0.733572\pi$
$541$	−31.1531	−1.33938	−0.669688	+	0.742643i	$0.733572\pi$
$542$	10.0522	0.431779
$543$	−0.690979	−0.0296527
$544$	7.97880	0.342088
$545$	9.03598	0.387059
$546$	2.25647	0.0965679
$547$	42.2148	1.80497	0.902487	−	0.430717i	$-0.141739\pi$
$547$	42.2148	1.80497	0.902487	+	0.430717i	$0.141739\pi$
$548$	60.4354	2.58167
$549$	31.1577	1.32978
$550$	−9.02800	−0.384955
$551$	−74.1254	−3.15785
$552$	7.09456	0.301964
$553$	16.0105	0.680835
$554$	11.2690	0.478773
$555$	4.21895	0.179085
$556$	−87.4033	−3.70673
$557$	40.4394	1.71347	0.856735	−	0.515756i	$-0.172489\pi$
$557$	40.4394	1.71347	0.856735	+	0.515756i	$0.172489\pi$
$558$	−1.24384	−0.0526559
$559$	2.86650	0.121240
$560$	16.7864	0.709356
$561$	−6.05450	−0.255621
$562$	18.8123	0.793550
$563$	−12.1223	−0.510894	−0.255447	−	0.966823i	$-0.582223\pi$
$563$	−12.1223	−0.510894	−0.255447	+	0.966823i	$0.582223\pi$
$564$	−2.20993	−0.0930550
$565$	−17.1796	−0.722753
$566$	4.81085	0.202215
$567$	20.0063	0.840185
$568$	24.0217	1.00793
$569$	−4.81117	−0.201695	−0.100847	−	0.994902i	$-0.532155\pi$
$569$	−4.81117	−0.201695	−0.100847	+	0.994902i	$0.532155\pi$
$570$	−9.34134	−0.391265
$571$	−45.7437	−1.91431	−0.957156	−	0.289571i	$-0.906487\pi$
$571$	−45.7437	−1.91431	−0.957156	+	0.289571i	$0.906487\pi$
$572$	−8.52696	−0.356530
$573$	0.323636	0.0135201
$574$	87.7108	3.66098
$575$	−2.38984	−0.0996633
$576$	12.6779	0.528248
$577$	−10.1368	−0.422000	−0.211000	−	0.977486i	$-0.567672\pi$
$577$	−10.1368	−0.422000	−0.211000	+	0.977486i	$0.567672\pi$
$578$	17.5929	0.731769
$579$	−4.67617	−0.194335
$580$	−44.6005	−1.85193
$581$	30.1689	1.25162
$582$	25.5543	1.05926
$583$	13.5153	0.559747
$584$	67.4148	2.78965
$585$	1.51282	0.0625473
$586$	58.4314	2.41378
$587$	−31.2276	−1.28890	−0.644450	−	0.764647i	$-0.722914\pi$
$587$	−31.2276	−1.28890	−0.644450	+	0.764647i	$0.722914\pi$
$588$	5.28609	0.217995
$589$	−1.29065	−0.0531802
$590$	27.5291	1.13336
$591$	−2.28512	−0.0939971
$592$	43.6309	1.79322
$593$	13.8239	0.567681	0.283840	−	0.958872i	$-0.408391\pi$
$593$	13.8239	0.567681	0.283840	+	0.958872i	$0.408391\pi$
$594$	27.4052	1.12445
$595$	−9.64805	−0.395531
$596$	23.2955	0.954220
$597$	4.67412	0.191299
$598$	−3.32222	−0.135856
$599$	−14.4994	−0.592427	−0.296214	−	0.955122i	$-0.595724\pi$
$599$	−14.4994	−0.592427	−0.296214	+	0.955122i	$0.595724\pi$
$600$	−2.96863	−0.121194
$601$	−34.6380	−1.41291	−0.706457	−	0.707756i	$-0.749708\pi$
$601$	−34.6380	−1.41291	−0.706457	+	0.707756i	$0.749708\pi$
$602$	39.3351	1.60318
$603$	−14.4600	−0.588858
$604$	53.3965	2.17267
$605$	2.06412	0.0839185
$606$	−25.7766	−1.04710
$607$	−11.1950	−0.454391	−0.227196	−	0.973849i	$-0.572956\pi$
$607$	−11.1950	−0.454391	−0.227196	+	0.973849i	$0.572956\pi$
$608$	−17.8138	−0.722445
$609$	−17.0790	−0.692076
$610$	28.6311	1.15924
$611$	0.546585	0.0221125
$612$	36.3562	1.46961
$613$	−26.7139	−1.07896	−0.539481	−	0.841998i	$-0.681380\pi$
$613$	−26.7139	−1.07896	−0.539481	+	0.841998i	$0.681380\pi$
$614$	−63.9606	−2.58124
$615$	−6.09677	−0.245846
$616$	−61.8013	−2.49005
$617$	−6.20892	−0.249962	−0.124981	−	0.992159i	$-0.539887\pi$
$617$	−6.20892	−0.249962	−0.124981	+	0.992159i	$0.539887\pi$
$618$	7.75579	0.311983
$619$	−19.1850	−0.771112	−0.385556	−	0.922684i	$-0.625990\pi$
$619$	−19.1850	−0.771112	−0.385556	+	0.922684i	$0.625990\pi$
$620$	−0.776569	−0.0311878
$621$	7.25456	0.291115
$622$	0.703463	0.0282063
$623$	−13.9312	−0.558141
$624$	−1.62205	−0.0649341
$625$	1.00000	0.0400000
$626$	−34.0693	−1.36168
$627$	13.5175	0.539838
$628$	6.39707	0.255271
$629$	−25.0770	−0.999884
$630$	20.7594	0.827076
$631$	−33.2124	−1.32216	−0.661082	−	0.750314i	$-0.729903\pi$
$631$	−33.2124	−1.32216	−0.661082	+	0.750314i	$0.729903\pi$
$632$	−29.2814	−1.16475
$633$	−9.97031	−0.396284
$634$	−76.3737	−3.03319
$635$	8.28554	0.328802
$636$	8.41426	0.333647
$637$	−1.30741	−0.0518016
$638$	94.9916	3.76075
$639$	11.6764	0.461912
$640$	16.7071	0.660407
$641$	−15.8026	−0.624165	−0.312082	−	0.950055i	$-0.601027\pi$
$641$	−15.8026	−0.624165	−0.312082	+	0.950055i	$0.601027\pi$
$642$	21.0835	0.832098
$643$	23.3637	0.921375	0.460688	−	0.887562i	$-0.347603\pi$
$643$	23.3637	0.921375	0.460688	+	0.887562i	$0.347603\pi$
$644$	−30.9742	−1.22055
$645$	−2.73418	−0.107658
$646$	55.5238	2.18455
$647$	11.2997	0.444235	0.222118	−	0.975020i	$-0.428703\pi$
$647$	11.2997	0.444235	0.222118	+	0.975020i	$0.428703\pi$
$648$	−36.5892	−1.43736
$649$	−39.8365	−1.56372
$650$	1.39014	0.0545259
$651$	−0.297374	−0.0116550
$652$	−2.05857	−0.0806197
$653$	−30.6851	−1.20080	−0.600400	−	0.799700i	$-0.704992\pi$
$653$	−30.6851	−1.20080	−0.600400	+	0.799700i	$0.704992\pi$
$654$	−11.9815	−0.468513
$655$	−16.1953	−0.632803
$656$	−63.0506	−2.46171
$657$	32.7689	1.27844
$658$	7.50044	0.292397
$659$	5.86540	0.228484	0.114242	−	0.993453i	$-0.463556\pi$
$659$	5.86540	0.228484	0.114242	+	0.993453i	$0.463556\pi$
$660$	8.13336	0.316591
$661$	40.9285	1.59193	0.795966	−	0.605341i	$-0.206963\pi$
$661$	40.9285	1.59193	0.795966	+	0.605341i	$0.206963\pi$
$662$	−21.4555	−0.833890
$663$	0.932280	0.0362067
$664$	−55.1755	−2.14122
$665$	21.5407	0.835311
$666$	53.9574	2.09081
$667$	25.1456	0.973643
$668$	−61.2614	−2.37028
$669$	3.28861	0.127145
$670$	−13.2875	−0.513340
$671$	−41.4311	−1.59943
$672$	−4.10443	−0.158332
$673$	5.22751	0.201506	0.100753	−	0.994911i	$-0.467875\pi$
$673$	5.22751	0.201506	0.100753	+	0.994911i	$0.467875\pi$
$674$	1.61808	0.0623263
$675$	−3.03558	−0.116840
$676$	−53.7918	−2.06891
$677$	42.1744	1.62089	0.810447	−	0.585811i	$-0.199224\pi$
$677$	42.1744	1.62089	0.810447	+	0.585811i	$0.199224\pi$
$678$	22.7798	0.874852
$679$	−58.9269	−2.26141
$680$	17.6452	0.676662
$681$	1.32685	0.0508449
$682$	1.65396	0.0633336
$683$	−37.6563	−1.44088	−0.720440	−	0.693518i	$-0.756060\pi$
$683$	−37.6563	−1.44088	−0.720440	+	0.693518i	$0.756060\pi$
$684$	−81.1705	−3.10363
$685$	14.2576	0.544754
$686$	35.5199	1.35616
$687$	4.57590	0.174581
$688$	−28.2759	−1.07801
$689$	−2.08111	−0.0792838
$690$	3.16887	0.120637
$691$	34.3489	1.30670	0.653348	−	0.757058i	$-0.273364\pi$
$691$	34.3489	1.30670	0.653348	+	0.757058i	$0.273364\pi$
$692$	25.1654	0.956646
$693$	−30.0403	−1.14114
$694$	−63.2234	−2.39993
$695$	−20.6197	−0.782149
$696$	31.2356	1.18398
$697$	36.2385	1.37263
$698$	−21.0667	−0.797388
$699$	6.81975	0.257947
$700$	12.9608	0.489871
$701$	−4.51354	−0.170474	−0.0852371	−	0.996361i	$-0.527165\pi$
$701$	−4.51354	−0.170474	−0.0852371	+	0.996361i	$0.527165\pi$
$702$	−4.21989	−0.159270
$703$	55.9879	2.11162
$704$	−16.8582	−0.635366
$705$	−0.521355	−0.0196354
$706$	23.4124	0.881139
$707$	59.4396	2.23546
$708$	−24.8011	−0.932082
$709$	10.6942	0.401630	0.200815	−	0.979629i	$-0.435641\pi$
$709$	10.6942	0.401630	0.200815	+	0.979629i	$0.435641\pi$
$710$	10.7296	0.402674
$711$	−14.2330	−0.533780
$712$	25.4786	0.954849
$713$	0.437828	0.0163968
$714$	12.7931	0.478769
$715$	−2.01163	−0.0752307
$716$	−107.526	−4.01843
$717$	−10.1878	−0.380471
$718$	67.2094	2.50823
$719$	−5.52665	−0.206109	−0.103055	−	0.994676i	$-0.532862\pi$
$719$	−5.52665	−0.206109	−0.103055	+	0.994676i	$0.532862\pi$
$720$	−14.9228	−0.556142
$721$	−17.8845	−0.666052
$722$	−76.5073	−2.84731
$723$	−15.1562	−0.563665
$724$	−5.51730	−0.205049
$725$	−10.5219	−0.390773
$726$	−2.73698	−0.101579
$727$	37.7081	1.39852	0.699258	−	0.714870i	$-0.253514\pi$
$727$	37.7081	1.39852	0.699258	+	0.714870i	$0.253514\pi$
$728$	9.51625	0.352696
$729$	−12.9508	−0.479659
$730$	30.1117	1.11448
$731$	16.2517	0.601089
$732$	−25.7938	−0.953367
$733$	23.2529	0.858865	0.429432	−	0.903099i	$-0.358714\pi$
$733$	23.2529	0.858865	0.429432	+	0.903099i	$0.358714\pi$
$734$	−54.8191	−2.02341
$735$	1.24706	0.0459987
$736$	6.04300	0.222748
$737$	19.2279	0.708267
$738$	−77.9733	−2.87024
$739$	30.7371	1.13068	0.565341	−	0.824857i	$-0.308745\pi$
$739$	30.7371	1.13068	0.565341	+	0.824857i	$0.308745\pi$
$740$	33.6873	1.23837
$741$	−2.08145	−0.0764639
$742$	−28.5577	−1.04839
$743$	−24.8331	−0.911038	−0.455519	−	0.890226i	$-0.650546\pi$
$743$	−24.8331	−0.911038	−0.455519	+	0.890226i	$0.650546\pi$
$744$	0.543864	0.0199390
$745$	5.49574	0.201348
$746$	−81.8754	−2.99767
$747$	−26.8196	−0.981278
$748$	−48.3437	−1.76762
$749$	−48.6174	−1.77644
$750$	−1.32598	−0.0484178
$751$	−40.2911	−1.47024	−0.735121	−	0.677936i	$-0.762875\pi$
$751$	−40.2911	−1.47024	−0.735121	+	0.677936i	$0.762875\pi$
$752$	−5.39166	−0.196614
$753$	−3.16936	−0.115498
$754$	−14.6269	−0.532681
$755$	12.5970	0.458452
$756$	−39.3435	−1.43091
$757$	−25.5961	−0.930307	−0.465153	−	0.885230i	$-0.654001\pi$
$757$	−25.5961	−0.930307	−0.465153	+	0.885230i	$0.654001\pi$
$758$	−42.0582	−1.52762
$759$	−4.58557	−0.166446
$760$	−39.3954	−1.42902
$761$	−14.8557	−0.538520	−0.269260	−	0.963067i	$-0.586779\pi$
$761$	−14.8557	−0.538520	−0.269260	+	0.963067i	$0.586779\pi$
$762$	−10.9864	−0.397996
$763$	27.6287	1.00023
$764$	2.58415	0.0934914
$765$	8.57695	0.310100
$766$	59.7853	2.16013
$767$	6.13408	0.221489
$768$	−17.2012	−0.620695
$769$	53.6186	1.93354	0.966768	−	0.255657i	$-0.0822917\pi$
$769$	53.6186	1.93354	0.966768	+	0.255657i	$0.0822917\pi$
$770$	−27.6043	−0.994790
$771$	5.81219	0.209321
$772$	−37.3381	−1.34383
$773$	26.8958	0.967373	0.483687	−	0.875241i	$-0.339297\pi$
$773$	26.8958	0.967373	0.483687	+	0.875241i	$0.339297\pi$
$774$	−34.9682	−1.25691
$775$	−0.183204	−0.00658087
$776$	107.771	3.86874
$777$	12.9000	0.462785
$778$	−43.8855	−1.57337
$779$	−80.9076	−2.89882
$780$	−1.25239	−0.0448426
$781$	−15.5264	−0.555579
$782$	−18.8354	−0.673552
$783$	31.9400	1.14144
$784$	12.8967	0.460596
$785$	1.50916	0.0538642
$786$	21.4746	0.765973
$787$	−4.70696	−0.167785	−0.0838924	−	0.996475i	$-0.526735\pi$
$787$	−4.70696	−0.167785	−0.0838924	+	0.996475i	$0.526735\pi$
$788$	−18.2461	−0.649991
$789$	10.8671	0.386880
$790$	−13.0789	−0.465325
$791$	−52.5290	−1.86772
$792$	54.9403	1.95222
$793$	6.37961	0.226547
$794$	−71.5111	−2.53783
$795$	1.98504	0.0704022
$796$	37.3217	1.32283
$797$	−21.0965	−0.747276	−0.373638	−	0.927575i	$-0.621890\pi$
$797$	−21.0965	−0.747276	−0.373638	+	0.927575i	$0.621890\pi$
$798$	−28.5624	−1.01110
$799$	3.09887	0.109630
$800$	−2.52862	−0.0894002
$801$	12.3846	0.437588
$802$	−30.2435	−1.06794
$803$	−43.5736	−1.53768
$804$	11.9707	0.422175
$805$	−7.30726	−0.257547
$806$	−0.254680	−0.00897070
$807$	10.4822	0.368991
$808$	−108.708	−3.82434
$809$	−50.4204	−1.77269	−0.886344	−	0.463028i	$-0.846763\pi$
$809$	−50.4204	−1.77269	−0.886344	+	0.463028i	$0.846763\pi$
$810$	−16.3430	−0.574236
$811$	18.9988	0.667137	0.333568	−	0.942726i	$-0.391747\pi$
$811$	18.9988	0.667137	0.333568	+	0.942726i	$0.391747\pi$
$812$	−136.372	−4.78571
$813$	−2.13645	−0.0749287
$814$	−71.7484	−2.51478
$815$	−0.485645	−0.0170114
$816$	−9.19626	−0.321933
$817$	−36.2842	−1.26942
$818$	10.2796	0.359419
$819$	4.62564	0.161633
$820$	−48.6813	−1.70002
$821$	34.8526	1.21636	0.608182	−	0.793798i	$-0.291899\pi$
$821$	34.8526	1.21636	0.608182	+	0.793798i	$0.291899\pi$
$822$	−18.9052	−0.659394
$823$	5.19772	0.181181	0.0905906	−	0.995888i	$-0.471125\pi$
$823$	5.19772	0.181181	0.0905906	+	0.995888i	$0.471125\pi$
$824$	32.7087	1.13946
$825$	1.91877	0.0668032
$826$	84.1740	2.92879
$827$	−27.9454	−0.971758	−0.485879	−	0.874026i	$-0.661500\pi$
$827$	−27.9454	−0.971758	−0.485879	+	0.874026i	$0.661500\pi$
$828$	27.5355	0.956926
$829$	−10.7067	−0.371859	−0.185930	−	0.982563i	$-0.559530\pi$
$829$	−10.7067	−0.371859	−0.185930	+	0.982563i	$0.559530\pi$
$830$	−24.6448	−0.855433
$831$	−2.39506	−0.0830838
$832$	2.59584	0.0899946
$833$	−7.41240	−0.256825
$834$	27.3412	0.946748
$835$	−14.4524	−0.500147
$836$	107.934	3.73299
$837$	0.556130	0.0192227
$838$	13.8557	0.478639
$839$	−38.1705	−1.31779	−0.658897	−	0.752234i	$-0.728977\pi$
$839$	−38.1705	−1.31779	−0.658897	+	0.752234i	$0.728977\pi$
$840$	−9.07698	−0.313186
$841$	81.7100	2.81759
$842$	6.72725	0.231836
$843$	−3.99829	−0.137709
$844$	−79.6105	−2.74031
$845$	−12.6902	−0.436558
$846$	−6.66776	−0.229242
$847$	6.31133	0.216860
$848$	20.5286	0.704955
$849$	−1.02248	−0.0350914
$850$	7.88144	0.270331
$851$	−18.9928	−0.651066
$852$	−9.66631	−0.331162
$853$	−35.6391	−1.22026	−0.610130	−	0.792301i	$-0.708883\pi$
$853$	−35.6391	−1.22026	−0.610130	+	0.792301i	$0.708883\pi$
$854$	87.5433	2.99567
$855$	−19.1493	−0.654891
$856$	88.9158	3.03908
$857$	5.09965	0.174201	0.0871004	−	0.996200i	$-0.472240\pi$
$857$	5.09965	0.174201	0.0871004	+	0.996200i	$0.472240\pi$
$858$	2.66737	0.0910626
$859$	−21.7437	−0.741885	−0.370942	−	0.928656i	$-0.620965\pi$
$859$	−21.7437	−0.741885	−0.370942	+	0.928656i	$0.620965\pi$
$860$	−21.8318	−0.744458
$861$	−18.6417	−0.635307
$862$	91.8247	3.12756
$863$	−35.3515	−1.20338	−0.601689	−	0.798730i	$-0.705505\pi$
$863$	−35.3515	−1.20338	−0.601689	+	0.798730i	$0.705505\pi$
$864$	7.67583	0.261137
$865$	5.93688	0.201860
$866$	−16.6690	−0.566435
$867$	−3.73913	−0.126987
$868$	−2.37446	−0.0805946
$869$	18.9260	0.642021
$870$	13.9518	0.473009
$871$	−2.96073	−0.100321
$872$	−50.5298	−1.71115
$873$	52.3850	1.77296
$874$	42.0527	1.42245
$875$	3.05763	0.103367
$876$	−27.1277	−0.916560
$877$	−47.9265	−1.61836	−0.809181	−	0.587559i	$-0.800089\pi$
$877$	−47.9265	−1.61836	−0.809181	+	0.587559i	$0.800089\pi$
$878$	−56.5384	−1.90808
$879$	−12.4188	−0.418875
$880$	19.8433	0.668916
$881$	11.6877	0.393770	0.196885	−	0.980427i	$-0.436917\pi$
$881$	11.6877	0.393770	0.196885	+	0.980427i	$0.436917\pi$
$882$	15.9491	0.537033
$883$	25.2057	0.848240	0.424120	−	0.905606i	$-0.360583\pi$
$883$	25.2057	0.848240	0.424120	+	0.905606i	$0.360583\pi$
$884$	7.44403	0.250370
$885$	−5.85093	−0.196677
$886$	38.8832	1.30631
$887$	43.2904	1.45355	0.726774	−	0.686876i	$-0.241019\pi$
$887$	43.2904	1.45355	0.726774	+	0.686876i	$0.241019\pi$
$888$	−23.5927	−0.791718
$889$	25.3341	0.849680
$890$	11.3803	0.381469
$891$	23.6495	0.792287
$892$	26.2587	0.879208
$893$	−6.91868	−0.231525
$894$	−7.28721	−0.243721
$895$	−25.3669	−0.847922
$896$	51.0842	1.70660
$897$	0.706092	0.0235757
$898$	65.0542	2.17089
$899$	1.92765	0.0642907
$900$	−11.5219	−0.384064
$901$	−11.7989	−0.393077
$902$	103.683	3.45227
$903$	−8.36012	−0.278208
$904$	96.0697	3.19523
$905$	−1.30161	−0.0432670
$906$	−16.7033	−0.554930
$907$	24.8652	0.825636	0.412818	−	0.910813i	$-0.364544\pi$
$907$	24.8652	0.825636	0.412818	+	0.910813i	$0.364544\pi$
$908$	10.5946	0.351593
$909$	−52.8408	−1.75262
$910$	4.25055	0.140904
$911$	−45.6585	−1.51273	−0.756366	−	0.654148i	$-0.773027\pi$
$911$	−45.6585	−1.51273	−0.756366	+	0.654148i	$0.773027\pi$
$912$	20.5320	0.679881
$913$	35.6627	1.18026
$914$	−19.7513	−0.653315
$915$	−6.08513	−0.201168
$916$	36.5375	1.20723
$917$	−49.5193	−1.63527
$918$	−23.9248	−0.789635
$919$	−53.2597	−1.75688	−0.878438	−	0.477856i	$-0.841414\pi$
$919$	−53.2597	−1.75688	−0.878438	+	0.477856i	$0.841414\pi$
$920$	13.3642	0.440603
$921$	13.5939	0.447935
$922$	−21.1363	−0.696088
$923$	2.39078	0.0786934
$924$	24.8688	0.818124
$925$	7.94732	0.261306
$926$	32.2755	1.06064
$927$	15.8990	0.522191
$928$	26.6058	0.873379
$929$	40.6346	1.33318	0.666589	−	0.745426i	$-0.267754\pi$
$929$	40.6346	1.33318	0.666589	+	0.745426i	$0.267754\pi$
$930$	0.242924	0.00796578
$931$	16.5493	0.542380
$932$	54.4541	1.78370
$933$	−0.149511	−0.00489478
$934$	−21.0090	−0.687436
$935$	−11.4050	−0.372982
$936$	−8.45978	−0.276517
$937$	13.7374	0.448782	0.224391	−	0.974499i	$-0.427961\pi$
$937$	13.7374	0.448782	0.224391	+	0.974499i	$0.427961\pi$
$938$	−40.6282	−1.32656
$939$	7.24095	0.236300
$940$	−4.16290	−0.135779
$941$	−27.4427	−0.894608	−0.447304	−	0.894382i	$-0.647616\pi$
$941$	−27.4427	−0.894608	−0.447304	+	0.894382i	$0.647616\pi$
$942$	−2.00111	−0.0651996
$943$	27.4464	0.893777
$944$	−60.5082	−1.96937
$945$	−9.28169	−0.301934
$946$	46.4981	1.51178
$947$	−25.7176	−0.835708	−0.417854	−	0.908514i	$-0.637218\pi$
$947$	−25.7176	−0.835708	−0.417854	+	0.908514i	$0.637218\pi$
$948$	11.7828	0.382688
$949$	6.70952	0.217800
$950$	−17.5964	−0.570904
$951$	16.2322	0.526364
$952$	53.9525	1.74861
$953$	−41.4617	−1.34308	−0.671538	−	0.740971i	$-0.734366\pi$
$953$	−41.4617	−1.34308	−0.671538	+	0.740971i	$0.734366\pi$
$954$	25.3873	0.821944
$955$	0.609639	0.0197274
$956$	−81.3473	−2.63096
$957$	−20.1891	−0.652622
$958$	−101.352	−3.27454
$959$	43.5944	1.40774
$960$	−2.47602	−0.0799132
$961$	−30.9664	−0.998917
$962$	11.0479	0.356199
$963$	43.2200	1.39275
$964$	−121.019	−3.89775
$965$	−8.80860	−0.283559
$966$	9.68924	0.311746
$967$	−40.8261	−1.31288	−0.656440	−	0.754378i	$-0.727939\pi$
$967$	−40.8261	−1.31288	−0.656440	+	0.754378i	$0.727939\pi$
$968$	−11.5427	−0.370997
$969$	−11.8008	−0.379096
$970$	48.1371	1.54559
$971$	−25.0655	−0.804391	−0.402195	−	0.915554i	$-0.631753\pi$
$971$	−25.0655	−0.804391	−0.402195	+	0.915554i	$0.631753\pi$
$972$	53.3254	1.71041
$973$	−63.0474	−2.02121
$974$	11.4521	0.366948
$975$	−0.295455	−0.00946215
$976$	−62.9302	−2.01435
$977$	58.7774	1.88046	0.940229	−	0.340544i	$-0.110611\pi$
$977$	58.7774	1.88046	0.940229	+	0.340544i	$0.110611\pi$
$978$	0.643953	0.0205914
$979$	−16.4681	−0.526322
$980$	9.95751	0.318081
$981$	−24.5614	−0.784186
$982$	−70.9884	−2.26533
$983$	−33.1343	−1.05682	−0.528410	−	0.848989i	$-0.677212\pi$
$983$	−33.1343	−1.05682	−0.528410	+	0.848989i	$0.677212\pi$
$984$	34.0936	1.08686
$985$	−4.30452	−0.137153
$986$	−82.9276	−2.64095
$987$	−1.59411	−0.0507411
$988$	−16.6199	−0.528748
$989$	12.3087	0.391394
$990$	24.5398	0.779925
$991$	−18.3749	−0.583699	−0.291850	−	0.956464i	$-0.594271\pi$
$991$	−18.3749	−0.583699	−0.291850	+	0.956464i	$0.594271\pi$
$992$	0.463252	0.0147083
$993$	4.56006	0.144709
$994$	32.8071	1.04058
$995$	8.80472	0.279128
$996$	22.2026	0.703516
$997$	44.4781	1.40864	0.704318	−	0.709885i	$-0.251253\pi$
$997$	44.4781	1.40864	0.704318	+	0.709885i	$0.251253\pi$
$998$	−75.8065	−2.39961
$999$	−24.1247	−0.763273

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.b.1.10	✓	114

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.b.1.10	✓	114	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49776 q^{2} +0.530865 q^{3} +4.23883 q^{4} +1.00000 q^{5} -1.32598 q^{6} +3.05763 q^{7} -5.59207 q^{8} -2.71818 q^{9} +O(q^{10})\)	\(q-2.49776 q^{2} +0.530865 q^{3} +4.23883 q^{4} +1.00000 q^{5} -1.32598 q^{6} +3.05763 q^{7} -5.59207 q^{8} -2.71818 q^{9} -2.49776 q^{10} +3.61443 q^{11} +2.25024 q^{12} -0.556555 q^{13} -7.63725 q^{14} +0.530865 q^{15} +5.49001 q^{16} -3.15540 q^{17} +6.78938 q^{18} +7.04488 q^{19} +4.23883 q^{20} +1.62319 q^{21} -9.02800 q^{22} -2.38984 q^{23} -2.96863 q^{24} +1.00000 q^{25} +1.39014 q^{26} -3.03558 q^{27} +12.9608 q^{28} -10.5219 q^{29} -1.32598 q^{30} -0.183204 q^{31} -2.52862 q^{32} +1.91877 q^{33} +7.88144 q^{34} +3.05763 q^{35} -11.5219 q^{36} +7.94732 q^{37} -17.5964 q^{38} -0.295455 q^{39} -5.59207 q^{40} -11.4846 q^{41} -4.05435 q^{42} -5.15043 q^{43} +15.3210 q^{44} -2.71818 q^{45} +5.96926 q^{46} -0.982086 q^{47} +2.91445 q^{48} +2.34912 q^{49} -2.49776 q^{50} -1.67509 q^{51} -2.35914 q^{52} +3.73926 q^{53} +7.58217 q^{54} +3.61443 q^{55} -17.0985 q^{56} +3.73988 q^{57} +26.2812 q^{58} -11.0215 q^{59} +2.25024 q^{60} -11.4627 q^{61} +0.457600 q^{62} -8.31120 q^{63} -4.66413 q^{64} -0.556555 q^{65} -4.79265 q^{66} +5.31975 q^{67} -13.3752 q^{68} -1.26868 q^{69} -7.63725 q^{70} -4.29567 q^{71} +15.2003 q^{72} -12.0554 q^{73} -19.8505 q^{74} +0.530865 q^{75} +29.8620 q^{76} +11.0516 q^{77} +0.737978 q^{78} +5.23623 q^{79} +5.49001 q^{80} +6.54306 q^{81} +28.6858 q^{82} +9.86674 q^{83} +6.88042 q^{84} -3.15540 q^{85} +12.8646 q^{86} -5.58570 q^{87} -20.2121 q^{88} -4.55620 q^{89} +6.78938 q^{90} -1.70174 q^{91} -10.1301 q^{92} -0.0972564 q^{93} +2.45302 q^{94} +7.04488 q^{95} -1.34235 q^{96} -19.2721 q^{97} -5.86755 q^{98} -9.82469 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9}+O(q^{10}) \) 114 * q - 17 * q^2 - 10 * q^3 + 93 * q^4 + 114 * q^5 - 24 * q^6 - 11 * q^7 - 48 * q^8 + 66 * q^9	\( 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9} - 17 q^{10} - 44 q^{11} - 25 q^{12} - 26 q^{13} - 43 q^{14} - 10 q^{15} + 59 q^{16} - 57 q^{17} - 33 q^{18} - 69 q^{19} + 93 q^{20} - 107 q^{21} - 19 q^{22} - 45 q^{23} - 45 q^{24} + 114 q^{25} - 54 q^{26} - 34 q^{27} - 6 q^{28} - 166 q^{29} - 24 q^{30} - 67 q^{31} - 98 q^{32} - 38 q^{33} - 41 q^{34} - 11 q^{35} - 3 q^{36} - 44 q^{37} - 19 q^{38} - 66 q^{39} - 48 q^{40} - 141 q^{41} + q^{42} - 30 q^{43} - 125 q^{44} + 66 q^{45} - 59 q^{46} - 17 q^{47} - 35 q^{48} - 15 q^{49} - 17 q^{50} - 67 q^{51} - 26 q^{52} - 154 q^{53} - 45 q^{54} - 44 q^{55} - 118 q^{56} - 70 q^{57} + 11 q^{58} - 75 q^{59} - 25 q^{60} - 144 q^{61} - 35 q^{62} - 25 q^{63} + 16 q^{64} - 26 q^{65} - 68 q^{66} - 2 q^{67} - 99 q^{68} - 118 q^{69} - 43 q^{70} - 104 q^{71} - 73 q^{72} - 22 q^{73} - 107 q^{74} - 10 q^{75} - 172 q^{76} - 100 q^{77} - 2 q^{78} - 91 q^{79} + 59 q^{80} - 54 q^{81} + 20 q^{82} - 44 q^{83} - 156 q^{84} - 57 q^{85} - 50 q^{86} + 5 q^{87} - 13 q^{88} - 150 q^{89} - 33 q^{90} - 54 q^{91} - 77 q^{92} - 50 q^{93} - 105 q^{94} - 69 q^{95} - 78 q^{96} - 31 q^{97} - 64 q^{98} - 101 q^{99}+O(q^{100}) \) 114 * q - 17 * q^2 - 10 * q^3 + 93 * q^4 + 114 * q^5 - 24 * q^6 - 11 * q^7 - 48 * q^8 + 66 * q^9 - 17 * q^10 - 44 * q^11 - 25 * q^12 - 26 * q^13 - 43 * q^14 - 10 * q^15 + 59 * q^16 - 57 * q^17 - 33 * q^18 - 69 * q^19 + 93 * q^20 - 107 * q^21 - 19 * q^22 - 45 * q^23 - 45 * q^24 + 114 * q^25 - 54 * q^26 - 34 * q^27 - 6 * q^28 - 166 * q^29 - 24 * q^30 - 67 * q^31 - 98 * q^32 - 38 * q^33 - 41 * q^34 - 11 * q^35 - 3 * q^36 - 44 * q^37 - 19 * q^38 - 66 * q^39 - 48 * q^40 - 141 * q^41 + q^42 - 30 * q^43 - 125 * q^44 + 66 * q^45 - 59 * q^46 - 17 * q^47 - 35 * q^48 - 15 * q^49 - 17 * q^50 - 67 * q^51 - 26 * q^52 - 154 * q^53 - 45 * q^54 - 44 * q^55 - 118 * q^56 - 70 * q^57 + 11 * q^58 - 75 * q^59 - 25 * q^60 - 144 * q^61 - 35 * q^62 - 25 * q^63 + 16 * q^64 - 26 * q^65 - 68 * q^66 - 2 * q^67 - 99 * q^68 - 118 * q^69 - 43 * q^70 - 104 * q^71 - 73 * q^72 - 22 * q^73 - 107 * q^74 - 10 * q^75 - 172 * q^76 - 100 * q^77 - 2 * q^78 - 91 * q^79 + 59 * q^80 - 54 * q^81 + 20 * q^82 - 44 * q^83 - 156 * q^84 - 57 * q^85 - 50 * q^86 + 5 * q^87 - 13 * q^88 - 150 * q^89 - 33 * q^90 - 54 * q^91 - 77 * q^92 - 50 * q^93 - 105 * q^94 - 69 * q^95 - 78 * q^96 - 31 * q^97 - 64 * q^98 - 101 * q^99

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