LMFDB - Embedded newform 8014.2.a.d.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8014,2,Mod(1,8014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8014, 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("8014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8014 = 2 \cdot 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8014.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:	$63.9921121799$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.06866 q^{3} +1.00000 q^{4} -2.92371 q^{5} -2.06866 q^{6} +1.17237 q^{7} +1.00000 q^{8} +1.27934 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.06866 q^{3} +1.00000 q^{4} -2.92371 q^{5} -2.06866 q^{6} +1.17237 q^{7} +1.00000 q^{8} +1.27934 q^{9} -2.92371 q^{10} -1.76588 q^{11} -2.06866 q^{12} -4.05481 q^{13} +1.17237 q^{14} +6.04815 q^{15} +1.00000 q^{16} -5.55521 q^{17} +1.27934 q^{18} -8.32570 q^{19} -2.92371 q^{20} -2.42524 q^{21} -1.76588 q^{22} -4.22989 q^{23} -2.06866 q^{24} +3.54808 q^{25} -4.05481 q^{26} +3.55945 q^{27} +1.17237 q^{28} +0.285006 q^{29} +6.04815 q^{30} -5.71251 q^{31} +1.00000 q^{32} +3.65299 q^{33} -5.55521 q^{34} -3.42768 q^{35} +1.27934 q^{36} -0.103749 q^{37} -8.32570 q^{38} +8.38802 q^{39} -2.92371 q^{40} -3.23590 q^{41} -2.42524 q^{42} +5.22806 q^{43} -1.76588 q^{44} -3.74042 q^{45} -4.22989 q^{46} +4.40051 q^{47} -2.06866 q^{48} -5.62554 q^{49} +3.54808 q^{50} +11.4918 q^{51} -4.05481 q^{52} +3.75658 q^{53} +3.55945 q^{54} +5.16291 q^{55} +1.17237 q^{56} +17.2230 q^{57} +0.285006 q^{58} -4.33015 q^{59} +6.04815 q^{60} -5.22255 q^{61} -5.71251 q^{62} +1.49987 q^{63} +1.00000 q^{64} +11.8551 q^{65} +3.65299 q^{66} -6.23034 q^{67} -5.55521 q^{68} +8.75019 q^{69} -3.42768 q^{70} -10.6468 q^{71} +1.27934 q^{72} -5.30578 q^{73} -0.103749 q^{74} -7.33975 q^{75} -8.32570 q^{76} -2.07027 q^{77} +8.38802 q^{78} -2.26999 q^{79} -2.92371 q^{80} -11.2013 q^{81} -3.23590 q^{82} +3.50496 q^{83} -2.42524 q^{84} +16.2418 q^{85} +5.22806 q^{86} -0.589580 q^{87} -1.76588 q^{88} -5.03172 q^{89} -3.74042 q^{90} -4.75375 q^{91} -4.22989 q^{92} +11.8172 q^{93} +4.40051 q^{94} +24.3419 q^{95} -2.06866 q^{96} +4.41621 q^{97} -5.62554 q^{98} -2.25916 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9}+O(q^{10}) $ 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9	\( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9} + 25 q^{10} + 70 q^{11} + 22 q^{12} + 31 q^{13} + 33 q^{14} + 47 q^{15} + 88 q^{16} + 19 q^{17} + 108 q^{18} + 33 q^{19} + 25 q^{20} + 48 q^{21} + 70 q^{22} + 77 q^{23} + 22 q^{24} + 109 q^{25} + 31 q^{26} + 88 q^{27} + 33 q^{28} + 83 q^{29} + 47 q^{30} + 51 q^{31} + 88 q^{32} + 30 q^{33} + 19 q^{34} + 40 q^{35} + 108 q^{36} + 45 q^{37} + 33 q^{38} + 82 q^{39} + 25 q^{40} + 35 q^{41} + 48 q^{42} + 78 q^{43} + 70 q^{44} + 37 q^{45} + 77 q^{46} + 59 q^{47} + 22 q^{48} + 103 q^{49} + 109 q^{50} + 21 q^{51} + 31 q^{52} + 58 q^{53} + 88 q^{54} + 35 q^{55} + 33 q^{56} - 16 q^{57} + 83 q^{58} + 54 q^{59} + 47 q^{60} + 18 q^{61} + 51 q^{62} + 47 q^{63} + 88 q^{64} + 34 q^{65} + 30 q^{66} + 88 q^{67} + 19 q^{68} + 62 q^{69} + 40 q^{70} + 139 q^{71} + 108 q^{72} - 6 q^{73} + 45 q^{74} + 45 q^{75} + 33 q^{76} + 37 q^{77} + 82 q^{78} + 94 q^{79} + 25 q^{80} + 112 q^{81} + 35 q^{82} + 58 q^{83} + 48 q^{84} + 83 q^{85} + 78 q^{86} + 21 q^{87} + 70 q^{88} + 99 q^{89} + 37 q^{90} + 53 q^{91} + 77 q^{92} + 57 q^{93} + 59 q^{94} + 92 q^{95} + 22 q^{96} + 16 q^{97} + 103 q^{98} + 150 q^{99}+O(q^{100}) \) 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9 + 25 * q^10 + 70 * q^11 + 22 * q^12 + 31 * q^13 + 33 * q^14 + 47 * q^15 + 88 * q^16 + 19 * q^17 + 108 * q^18 + 33 * q^19 + 25 * q^20 + 48 * q^21 + 70 * q^22 + 77 * q^23 + 22 * q^24 + 109 * q^25 + 31 * q^26 + 88 * q^27 + 33 * q^28 + 83 * q^29 + 47 * q^30 + 51 * q^31 + 88 * q^32 + 30 * q^33 + 19 * q^34 + 40 * q^35 + 108 * q^36 + 45 * q^37 + 33 * q^38 + 82 * q^39 + 25 * q^40 + 35 * q^41 + 48 * q^42 + 78 * q^43 + 70 * q^44 + 37 * q^45 + 77 * q^46 + 59 * q^47 + 22 * q^48 + 103 * q^49 + 109 * q^50 + 21 * q^51 + 31 * q^52 + 58 * q^53 + 88 * q^54 + 35 * q^55 + 33 * q^56 - 16 * q^57 + 83 * q^58 + 54 * q^59 + 47 * q^60 + 18 * q^61 + 51 * q^62 + 47 * q^63 + 88 * q^64 + 34 * q^65 + 30 * q^66 + 88 * q^67 + 19 * q^68 + 62 * q^69 + 40 * q^70 + 139 * q^71 + 108 * q^72 - 6 * q^73 + 45 * q^74 + 45 * q^75 + 33 * q^76 + 37 * q^77 + 82 * q^78 + 94 * q^79 + 25 * q^80 + 112 * q^81 + 35 * q^82 + 58 * q^83 + 48 * q^84 + 83 * q^85 + 78 * q^86 + 21 * q^87 + 70 * q^88 + 99 * q^89 + 37 * q^90 + 53 * q^91 + 77 * q^92 + 57 * q^93 + 59 * q^94 + 92 * q^95 + 22 * q^96 + 16 * q^97 + 103 * q^98 + 150 * 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
$3$	−2.06866	−1.19434	−0.597170	−	0.802115i	$-0.703708\pi$
$3$	−2.06866	−1.19434	−0.597170	+	0.802115i	$0.703708\pi$
$4$	1.00000	0.500000
$5$	−2.92371	−1.30752	−0.653761	−	0.756701i	$-0.726810\pi$
$5$	−2.92371	−1.30752	−0.653761	+	0.756701i	$0.726810\pi$
$6$	−2.06866	−0.844526
$7$	1.17237	0.443115	0.221558	−	0.975147i	$-0.428886\pi$
$7$	1.17237	0.443115	0.221558	+	0.975147i	$0.428886\pi$
$8$	1.00000	0.353553
$9$	1.27934	0.426447
$10$	−2.92371	−0.924558
$11$	−1.76588	−0.532432	−0.266216	−	0.963913i	$-0.585773\pi$
$11$	−1.76588	−0.532432	−0.266216	+	0.963913i	$0.585773\pi$
$12$	−2.06866	−0.597170
$13$	−4.05481	−1.12460	−0.562301	−	0.826932i	$-0.690084\pi$
$13$	−4.05481	−1.12460	−0.562301	+	0.826932i	$0.690084\pi$
$14$	1.17237	0.313330
$15$	6.04815	1.56163
$16$	1.00000	0.250000
$17$	−5.55521	−1.34734	−0.673669	−	0.739033i	$-0.735283\pi$
$17$	−5.55521	−1.34734	−0.673669	+	0.739033i	$0.735283\pi$
$18$	1.27934	0.301544
$19$	−8.32570	−1.91005	−0.955024	−	0.296529i	$-0.904171\pi$
$19$	−8.32570	−1.91005	−0.955024	+	0.296529i	$0.904171\pi$
$20$	−2.92371	−0.653761
$21$	−2.42524	−0.529230
$22$	−1.76588	−0.376486
$23$	−4.22989	−0.881993	−0.440996	−	0.897509i	$-0.645375\pi$
$23$	−4.22989	−0.881993	−0.440996	+	0.897509i	$0.645375\pi$
$24$	−2.06866	−0.422263
$25$	3.54808	0.709615
$26$	−4.05481	−0.795214
$27$	3.55945	0.685017
$28$	1.17237	0.221558
$29$	0.285006	0.0529243	0.0264622	−	0.999650i	$-0.491576\pi$
$29$	0.285006	0.0529243	0.0264622	+	0.999650i	$0.491576\pi$
$30$	6.04815	1.10424
$31$	−5.71251	−1.02600	−0.512999	−	0.858389i	$-0.671466\pi$
$31$	−5.71251	−1.02600	−0.512999	+	0.858389i	$0.671466\pi$
$32$	1.00000	0.176777
$33$	3.65299	0.635905
$34$	−5.55521	−0.952711
$35$	−3.42768	−0.579383
$36$	1.27934	0.213224
$37$	−0.103749	−0.0170563	−0.00852813	−	0.999964i	$-0.502715\pi$
$37$	−0.103749	−0.0170563	−0.00852813	+	0.999964i	$0.502715\pi$
$38$	−8.32570	−1.35061
$39$	8.38802	1.34316
$40$	−2.92371	−0.462279
$41$	−3.23590	−0.505362	−0.252681	−	0.967550i	$-0.581312\pi$
$41$	−3.23590	−0.505362	−0.252681	+	0.967550i	$0.581312\pi$
$42$	−2.42524	−0.374222
$43$	5.22806	0.797272	0.398636	−	0.917109i	$-0.369484\pi$
$43$	5.22806	0.797272	0.398636	+	0.917109i	$0.369484\pi$
$44$	−1.76588	−0.266216
$45$	−3.74042	−0.557589
$46$	−4.22989	−0.623663
$47$	4.40051	0.641880	0.320940	−	0.947099i	$-0.396001\pi$
$47$	4.40051	0.641880	0.320940	+	0.947099i	$0.396001\pi$
$48$	−2.06866	−0.298585
$49$	−5.62554	−0.803649
$50$	3.54808	0.501774
$51$	11.4918	1.60918
$52$	−4.05481	−0.562301
$53$	3.75658	0.516005	0.258003	−	0.966144i	$-0.416936\pi$
$53$	3.75658	0.516005	0.258003	+	0.966144i	$0.416936\pi$
$54$	3.55945	0.484380
$55$	5.16291	0.696167
$56$	1.17237	0.156665
$57$	17.2230	2.28125
$58$	0.285006	0.0374231
$59$	−4.33015	−0.563738	−0.281869	−	0.959453i	$-0.590954\pi$
$59$	−4.33015	−0.563738	−0.281869	+	0.959453i	$0.590954\pi$
$60$	6.04815	0.780813
$61$	−5.22255	−0.668680	−0.334340	−	0.942453i	$-0.608513\pi$
$61$	−5.22255	−0.668680	−0.334340	+	0.942453i	$0.608513\pi$
$62$	−5.71251	−0.725490
$63$	1.49987	0.188965
$64$	1.00000	0.125000
$65$	11.8551	1.47044
$66$	3.65299	0.449652
$67$	−6.23034	−0.761157	−0.380578	−	0.924749i	$-0.624275\pi$
$67$	−6.23034	−0.761157	−0.380578	+	0.924749i	$0.624275\pi$
$68$	−5.55521	−0.673669
$69$	8.75019	1.05340
$70$	−3.42768	−0.409686
$71$	−10.6468	−1.26354	−0.631772	−	0.775155i	$-0.717672\pi$
$71$	−10.6468	−1.26354	−0.631772	+	0.775155i	$0.717672\pi$
$72$	1.27934	0.150772
$73$	−5.30578	−0.620995	−0.310497	−	0.950574i	$-0.600496\pi$
$73$	−5.30578	−0.620995	−0.310497	+	0.950574i	$0.600496\pi$
$74$	−0.103749	−0.0120606
$75$	−7.33975	−0.847522
$76$	−8.32570	−0.955024
$77$	−2.07027	−0.235929
$78$	8.38802	0.949756
$79$	−2.26999	−0.255394	−0.127697	−	0.991813i	$-0.540758\pi$
$79$	−2.26999	−0.255394	−0.127697	+	0.991813i	$0.540758\pi$
$80$	−2.92371	−0.326881
$81$	−11.2013	−1.24459
$82$	−3.23590	−0.357345
$83$	3.50496	0.384719	0.192360	−	0.981325i	$-0.438386\pi$
$83$	3.50496	0.384719	0.192360	+	0.981325i	$0.438386\pi$
$84$	−2.42524	−0.264615
$85$	16.2418	1.76167
$86$	5.22806	0.563756
$87$	−0.589580	−0.0632096
$88$	−1.76588	−0.188243
$89$	−5.03172	−0.533361	−0.266680	−	0.963785i	$-0.585927\pi$
$89$	−5.03172	−0.533361	−0.266680	+	0.963785i	$0.585927\pi$
$90$	−3.74042	−0.394275
$91$	−4.75375	−0.498328
$92$	−4.22989	−0.440996
$93$	11.8172	1.22539
$94$	4.40051	0.453878
$95$	24.3419	2.49743
$96$	−2.06866	−0.211131
$97$	4.41621	0.448398	0.224199	−	0.974543i	$-0.428023\pi$
$97$	4.41621	0.448398	0.224199	+	0.974543i	$0.428023\pi$
$98$	−5.62554	−0.568266
$99$	−2.25916	−0.227054
$100$	3.54808	0.354808
$101$	−1.77947	−0.177064	−0.0885319	−	0.996073i	$-0.528218\pi$
$101$	−1.77947	−0.177064	−0.0885319	+	0.996073i	$0.528218\pi$
$102$	11.4918	1.13786
$103$	2.83261	0.279105	0.139553	−	0.990215i	$-0.455434\pi$
$103$	2.83261	0.279105	0.139553	+	0.990215i	$0.455434\pi$
$104$	−4.05481	−0.397607
$105$	7.09069	0.691980
$106$	3.75658	0.364871
$107$	−8.09716	−0.782782	−0.391391	−	0.920224i	$-0.628006\pi$
$107$	−8.09716	−0.782782	−0.391391	+	0.920224i	$0.628006\pi$
$108$	3.55945	0.342508
$109$	14.6559	1.40378	0.701891	−	0.712285i	$-0.252340\pi$
$109$	14.6559	1.40378	0.701891	+	0.712285i	$0.252340\pi$
$110$	5.16291	0.492264
$111$	0.214621	0.0203710
$112$	1.17237	0.110779
$113$	14.8664	1.39852	0.699258	−	0.714869i	$-0.253514\pi$
$113$	14.8664	1.39852	0.699258	+	0.714869i	$0.253514\pi$
$114$	17.2230	1.61308
$115$	12.3670	1.15323
$116$	0.285006	0.0264622
$117$	−5.18749	−0.479584
$118$	−4.33015	−0.398623
$119$	−6.51278	−0.597026
$120$	6.04815	0.552118
$121$	−7.88168	−0.716516
$122$	−5.22255	−0.472828
$123$	6.69396	0.603574
$124$	−5.71251	−0.512999
$125$	4.24500	0.379685
$126$	1.49987	0.133619
$127$	0.737228	0.0654184	0.0327092	−	0.999465i	$-0.489586\pi$
$127$	0.737228	0.0654184	0.0327092	+	0.999465i	$0.489586\pi$
$128$	1.00000	0.0883883
$129$	−10.8151	−0.952213
$130$	11.8551	1.03976
$131$	−0.614440	−0.0536839	−0.0268419	−	0.999640i	$-0.508545\pi$
$131$	−0.614440	−0.0536839	−0.0268419	+	0.999640i	$0.508545\pi$
$132$	3.65299	0.317952
$133$	−9.76083	−0.846371
$134$	−6.23034	−0.538219
$135$	−10.4068	−0.895675
$136$	−5.55521	−0.476356
$137$	−8.55938	−0.731278	−0.365639	−	0.930757i	$-0.619149\pi$
$137$	−8.55938	−0.731278	−0.365639	+	0.930757i	$0.619149\pi$
$138$	8.75019	0.744866
$139$	−3.79484	−0.321874	−0.160937	−	0.986965i	$-0.551452\pi$
$139$	−3.79484	−0.321874	−0.160937	+	0.986965i	$0.551452\pi$
$140$	−3.42768	−0.289692
$141$	−9.10314	−0.766623
$142$	−10.6468	−0.893460
$143$	7.16030	0.598774
$144$	1.27934	0.106612
$145$	−0.833275	−0.0691997
$146$	−5.30578	−0.439110
$147$	11.6373	0.959830
$148$	−0.103749	−0.00852813
$149$	5.45553	0.446935	0.223467	−	0.974711i	$-0.428262\pi$
$149$	5.45553	0.446935	0.223467	+	0.974711i	$0.428262\pi$
$150$	−7.33975	−0.599288
$151$	−15.3888	−1.25232	−0.626161	−	0.779693i	$-0.715375\pi$
$151$	−15.3888	−1.25232	−0.626161	+	0.779693i	$0.715375\pi$
$152$	−8.32570	−0.675304
$153$	−7.10702	−0.574568
$154$	−2.07027	−0.166827
$155$	16.7017	1.34152
$156$	8.38802	0.671579
$157$	−4.23045	−0.337627	−0.168813	−	0.985648i	$-0.553994\pi$
$157$	−4.23045	−0.337627	−0.168813	+	0.985648i	$0.553994\pi$
$158$	−2.26999	−0.180591
$159$	−7.77107	−0.616286
$160$	−2.92371	−0.231140
$161$	−4.95901	−0.390824
$162$	−11.2013	−0.880058
$163$	10.2827	0.805400	0.402700	−	0.915332i	$-0.368072\pi$
$163$	10.2827	0.805400	0.402700	+	0.915332i	$0.368072\pi$
$164$	−3.23590	−0.252681
$165$	−10.6803	−0.831460
$166$	3.50496	0.272037
$167$	−8.25185	−0.638547	−0.319274	−	0.947663i	$-0.603439\pi$
$167$	−8.25185	−0.638547	−0.319274	+	0.947663i	$0.603439\pi$
$168$	−2.42524	−0.187111
$169$	3.44150	0.264731
$170$	16.2418	1.24569
$171$	−10.6514	−0.814534
$172$	5.22806	0.398636
$173$	0.498660	0.0379124	0.0189562	−	0.999820i	$-0.493966\pi$
$173$	0.498660	0.0379124	0.0189562	+	0.999820i	$0.493966\pi$
$174$	−0.589580	−0.0446959
$175$	4.15967	0.314441
$176$	−1.76588	−0.133108
$177$	8.95760	0.673294
$178$	−5.03172	−0.377143
$179$	20.3602	1.52179	0.760895	−	0.648875i	$-0.224760\pi$
$179$	20.3602	1.52179	0.760895	+	0.648875i	$0.224760\pi$
$180$	−3.74042	−0.278795
$181$	15.1290	1.12453	0.562267	−	0.826956i	$-0.309929\pi$
$181$	15.1290	1.12453	0.562267	+	0.826956i	$0.309929\pi$
$182$	−4.75375	−0.352371
$183$	10.8037	0.798630
$184$	−4.22989	−0.311832
$185$	0.303332	0.0223014
$186$	11.8172	0.866482
$187$	9.80982	0.717365
$188$	4.40051	0.320940
$189$	4.17300	0.303541
$190$	24.3419	1.76595
$191$	−20.0952	−1.45404	−0.727019	−	0.686617i	$-0.759095\pi$
$191$	−20.0952	−1.45404	−0.727019	+	0.686617i	$0.759095\pi$
$192$	−2.06866	−0.149292
$193$	−16.4536	−1.18436	−0.592179	−	0.805807i	$-0.701732\pi$
$193$	−16.4536	−1.18436	−0.592179	+	0.805807i	$0.701732\pi$
$194$	4.41621	0.317065
$195$	−24.5241	−1.75621
$196$	−5.62554	−0.401824
$197$	−7.30364	−0.520363	−0.260181	−	0.965560i	$-0.583782\pi$
$197$	−7.30364	−0.520363	−0.260181	+	0.965560i	$0.583782\pi$
$198$	−2.25916	−0.160552
$199$	−28.0781	−1.99041	−0.995203	−	0.0978303i	$-0.968810\pi$
$199$	−28.0781	−1.99041	−0.995203	+	0.0978303i	$0.968810\pi$
$200$	3.54808	0.250887
$201$	12.8884	0.909080
$202$	−1.77947	−0.125203
$203$	0.334133	0.0234516
$204$	11.4918	0.804589
$205$	9.46082	0.660772
$206$	2.83261	0.197357
$207$	−5.41147	−0.376123
$208$	−4.05481	−0.281151
$209$	14.7022	1.01697
$210$	7.09069	0.489304
$211$	10.2119	0.703014	0.351507	−	0.936185i	$-0.385669\pi$
$211$	10.2119	0.703014	0.351507	+	0.936185i	$0.385669\pi$
$212$	3.75658	0.258003
$213$	22.0246	1.50910
$214$	−8.09716	−0.553511
$215$	−15.2853	−1.04245
$216$	3.55945	0.242190
$217$	−6.69720	−0.454635
$218$	14.6559	0.992623
$219$	10.9758	0.741679
$220$	5.16291	0.348083
$221$	22.5253	1.51522
$222$	0.214621	0.0144044
$223$	−1.50855	−0.101020	−0.0505101	−	0.998724i	$-0.516085\pi$
$223$	−1.50855	−0.101020	−0.0505101	+	0.998724i	$0.516085\pi$
$224$	1.17237	0.0783324
$225$	4.53920	0.302613
$226$	14.8664	0.988900
$227$	8.35571	0.554588	0.277294	−	0.960785i	$-0.410562\pi$
$227$	8.35571	0.554588	0.277294	+	0.960785i	$0.410562\pi$
$228$	17.2230	1.14062
$229$	−1.05903	−0.0699828	−0.0349914	−	0.999388i	$-0.511140\pi$
$229$	−1.05903	−0.0699828	−0.0349914	+	0.999388i	$0.511140\pi$
$230$	12.3670	0.815454
$231$	4.28267	0.281779
$232$	0.285006	0.0187116
$233$	−5.82776	−0.381789	−0.190895	−	0.981611i	$-0.561139\pi$
$233$	−5.82776	−0.381789	−0.190895	+	0.981611i	$0.561139\pi$
$234$	−5.18749	−0.339117
$235$	−12.8658	−0.839273
$236$	−4.33015	−0.281869
$237$	4.69583	0.305027
$238$	−6.51278	−0.422161
$239$	−8.53593	−0.552143	−0.276072	−	0.961137i	$-0.589033\pi$
$239$	−8.53593	−0.552143	−0.276072	+	0.961137i	$0.589033\pi$
$240$	6.04815	0.390407
$241$	14.6546	0.943988	0.471994	−	0.881602i	$-0.343534\pi$
$241$	14.6546	0.943988	0.471994	+	0.881602i	$0.343534\pi$
$242$	−7.88168	−0.506653
$243$	12.4933	0.801446
$244$	−5.22255	−0.334340
$245$	16.4475	1.05079
$246$	6.69396	0.426791
$247$	33.7592	2.14804
$248$	−5.71251	−0.362745
$249$	−7.25056	−0.459485
$250$	4.24500	0.268477
$251$	7.19593	0.454203	0.227102	−	0.973871i	$-0.427075\pi$
$251$	7.19593	0.454203	0.227102	+	0.973871i	$0.427075\pi$
$252$	1.49987	0.0944826
$253$	7.46946	0.469601
$254$	0.737228	0.0462578
$255$	−33.5988	−2.10404
$256$	1.00000	0.0625000
$257$	8.28211	0.516624	0.258312	−	0.966062i	$-0.416834\pi$
$257$	8.28211	0.516624	0.258312	+	0.966062i	$0.416834\pi$
$258$	−10.8151	−0.673316
$259$	−0.121633	−0.00755789
$260$	11.8551	0.735222
$261$	0.364620	0.0225694
$262$	−0.614440	−0.0379602
$263$	17.3494	1.06981	0.534904	−	0.844913i	$-0.320348\pi$
$263$	17.3494	1.06981	0.534904	+	0.844913i	$0.320348\pi$
$264$	3.65299	0.224826
$265$	−10.9831	−0.674689
$266$	−9.76083	−0.598475
$267$	10.4089	0.637014
$268$	−6.23034	−0.380578
$269$	−1.61453	−0.0984397	−0.0492198	−	0.998788i	$-0.515673\pi$
$269$	−1.61453	−0.0984397	−0.0492198	+	0.998788i	$0.515673\pi$
$270$	−10.4068	−0.633338
$271$	−17.5765	−1.06770	−0.533849	−	0.845580i	$-0.679255\pi$
$271$	−17.5765	−1.06770	−0.533849	+	0.845580i	$0.679255\pi$
$272$	−5.55521	−0.336834
$273$	9.83388	0.595173
$274$	−8.55938	−0.517091
$275$	−6.26547	−0.377822
$276$	8.75019	0.526700
$277$	0.751268	0.0451393	0.0225697	−	0.999745i	$-0.492815\pi$
$277$	0.751268	0.0451393	0.0225697	+	0.999745i	$0.492815\pi$
$278$	−3.79484	−0.227599
$279$	−7.30826	−0.437534
$280$	−3.42768	−0.204843
$281$	9.02777	0.538551	0.269276	−	0.963063i	$-0.413216\pi$
$281$	9.02777	0.538551	0.269276	+	0.963063i	$0.413216\pi$
$282$	−9.10314	−0.542084
$283$	−0.601750	−0.0357703	−0.0178852	−	0.999840i	$-0.505693\pi$
$283$	−0.601750	−0.0357703	−0.0178852	+	0.999840i	$0.505693\pi$
$284$	−10.6468	−0.631772
$285$	−50.3551	−2.98278
$286$	7.16030	0.423397
$287$	−3.79368	−0.223934
$288$	1.27934	0.0753859
$289$	13.8604	0.815318
$290$	−0.833275	−0.0489316
$291$	−9.13562	−0.535539
$292$	−5.30578	−0.310497
$293$	−31.5181	−1.84131	−0.920653	−	0.390382i	$-0.872343\pi$
$293$	−31.5181	−1.84131	−0.920653	+	0.390382i	$0.872343\pi$
$294$	11.6373	0.678702
$295$	12.6601	0.737100
$296$	−0.103749	−0.00603030
$297$	−6.28555	−0.364725
$298$	5.45553	0.316031
$299$	17.1514	0.991891
$300$	−7.33975	−0.423761
$301$	6.12923	0.353283
$302$	−15.3888	−0.885526
$303$	3.68111	0.211474
$304$	−8.32570	−0.477512
$305$	15.2692	0.874314
$306$	−7.10702	−0.406281
$307$	24.5697	1.40227	0.701133	−	0.713030i	$-0.252678\pi$
$307$	24.5697	1.40227	0.701133	+	0.713030i	$0.252678\pi$
$308$	−2.07027	−0.117964
$309$	−5.85969	−0.333346
$310$	16.7017	0.948595
$311$	−8.81987	−0.500129	−0.250065	−	0.968229i	$-0.580452\pi$
$311$	−8.81987	−0.500129	−0.250065	+	0.968229i	$0.580452\pi$
$312$	8.38802	0.474878
$313$	−25.3636	−1.43364	−0.716818	−	0.697260i	$-0.754402\pi$
$313$	−25.3636	−1.43364	−0.716818	+	0.697260i	$0.754402\pi$
$314$	−4.23045	−0.238738
$315$	−4.38517	−0.247076
$316$	−2.26999	−0.127697
$317$	21.7608	1.22221	0.611105	−	0.791549i	$-0.290725\pi$
$317$	21.7608	1.22221	0.611105	+	0.791549i	$0.290725\pi$
$318$	−7.77107	−0.435780
$319$	−0.503286	−0.0281786
$320$	−2.92371	−0.163440
$321$	16.7502	0.934908
$322$	−4.95901	−0.276355
$323$	46.2511	2.57348
$324$	−11.2013	−0.622295
$325$	−14.3868	−0.798035
$326$	10.2827	0.569504
$327$	−30.3180	−1.67659
$328$	−3.23590	−0.178673
$329$	5.15904	0.284427
$330$	−10.6803	−0.587931
$331$	4.67759	0.257104	0.128552	−	0.991703i	$-0.458967\pi$
$331$	4.67759	0.257104	0.128552	+	0.991703i	$0.458967\pi$
$332$	3.50496	0.192360
$333$	−0.132731	−0.00727359
$334$	−8.25185	−0.451521
$335$	18.2157	0.995230
$336$	−2.42524	−0.132308
$337$	11.5634	0.629900	0.314950	−	0.949108i	$-0.398012\pi$
$337$	11.5634	0.629900	0.314950	+	0.949108i	$0.398012\pi$
$338$	3.44150	0.187193
$339$	−30.7535	−1.67030
$340$	16.2418	0.880837
$341$	10.0876	0.546274
$342$	−10.6514	−0.575963
$343$	−14.8018	−0.799224
$344$	5.22806	0.281878
$345$	−25.5830	−1.37734
$346$	0.498660	0.0268081
$347$	15.3760	0.825427	0.412714	−	0.910861i	$-0.364581\pi$
$347$	15.3760	0.825427	0.412714	+	0.910861i	$0.364581\pi$
$348$	−0.589580	−0.0316048
$349$	22.9589	1.22896	0.614480	−	0.788932i	$-0.289366\pi$
$349$	22.9589	1.22896	0.614480	+	0.788932i	$0.289366\pi$
$350$	4.15967	0.222344
$351$	−14.4329	−0.770372
$352$	−1.76588	−0.0941216
$353$	14.1805	0.754753	0.377377	−	0.926060i	$-0.376826\pi$
$353$	14.1805	0.754753	0.377377	+	0.926060i	$0.376826\pi$
$354$	8.95760	0.476091
$355$	31.1282	1.65211
$356$	−5.03172	−0.266680
$357$	13.4727	0.713051
$358$	20.3602	1.07607
$359$	31.1827	1.64576	0.822879	−	0.568217i	$-0.192366\pi$
$359$	31.1827	1.64576	0.822879	+	0.568217i	$0.192366\pi$
$360$	−3.74042	−0.197138
$361$	50.3173	2.64828
$362$	15.1290	0.795165
$363$	16.3045	0.855764
$364$	−4.75375	−0.249164
$365$	15.5126	0.811965
$366$	10.8037	0.564717
$367$	−1.17890	−0.0615382	−0.0307691	−	0.999527i	$-0.509796\pi$
$367$	−1.17890	−0.0615382	−0.0307691	+	0.999527i	$0.509796\pi$
$368$	−4.22989	−0.220498
$369$	−4.13982	−0.215510
$370$	0.303332	0.0157695
$371$	4.40411	0.228650
$372$	11.8172	0.612695
$373$	−23.3901	−1.21109	−0.605547	−	0.795810i	$-0.707046\pi$
$373$	−23.3901	−1.21109	−0.605547	+	0.795810i	$0.707046\pi$
$374$	9.80982	0.507254
$375$	−8.78145	−0.453472
$376$	4.40051	0.226939
$377$	−1.15565	−0.0595188
$378$	4.17300	0.214636
$379$	1.17861	0.0605410	0.0302705	−	0.999542i	$-0.490363\pi$
$379$	1.17861	0.0605410	0.0302705	+	0.999542i	$0.490363\pi$
$380$	24.3419	1.24872
$381$	−1.52507	−0.0781318
$382$	−20.0952	−1.02816
$383$	18.8663	0.964021	0.482010	−	0.876165i	$-0.339907\pi$
$383$	18.8663	0.964021	0.482010	+	0.876165i	$0.339907\pi$
$384$	−2.06866	−0.105566
$385$	6.05285	0.308482
$386$	−16.4536	−0.837467
$387$	6.68848	0.339994
$388$	4.41621	0.224199
$389$	30.2852	1.53552	0.767760	−	0.640737i	$-0.221371\pi$
$389$	30.2852	1.53552	0.767760	+	0.640737i	$0.221371\pi$
$390$	−24.5241	−1.24183
$391$	23.4979	1.18834
$392$	−5.62554	−0.284133
$393$	1.27107	0.0641168
$394$	−7.30364	−0.367952
$395$	6.63679	0.333933
$396$	−2.25916	−0.113527
$397$	−10.1143	−0.507622	−0.253811	−	0.967254i	$-0.581684\pi$
$397$	−10.1143	−0.507622	−0.253811	+	0.967254i	$0.581684\pi$
$398$	−28.0781	−1.40743
$399$	20.1918	1.01085
$400$	3.54808	0.177404
$401$	−10.7151	−0.535089	−0.267544	−	0.963546i	$-0.586212\pi$
$401$	−10.7151	−0.535089	−0.267544	+	0.963546i	$0.586212\pi$
$402$	12.8884	0.642816
$403$	23.1632	1.15384
$404$	−1.77947	−0.0885319
$405$	32.7494	1.62733
$406$	0.334133	0.0165828
$407$	0.183208	0.00908130
$408$	11.4918	0.568931
$409$	−12.8127	−0.633545	−0.316773	−	0.948502i	$-0.602599\pi$
$409$	−12.8127	−0.633545	−0.316773	+	0.948502i	$0.602599\pi$
$410$	9.46082	0.467237
$411$	17.7064	0.873394
$412$	2.83261	0.139553
$413$	−5.07655	−0.249801
$414$	−5.41147	−0.265959
$415$	−10.2475	−0.503029
$416$	−4.05481	−0.198804
$417$	7.85022	0.384427
$418$	14.7022	0.719107
$419$	−16.7957	−0.820524	−0.410262	−	0.911968i	$-0.634563\pi$
$419$	−16.7957	−0.820524	−0.410262	+	0.911968i	$0.634563\pi$
$420$	7.09069	0.345990
$421$	−0.401501	−0.0195680	−0.00978399	−	0.999952i	$-0.503114\pi$
$421$	−0.401501	−0.0195680	−0.00978399	+	0.999952i	$0.503114\pi$
$422$	10.2119	0.497106
$423$	5.62975	0.273728
$424$	3.75658	0.182435
$425$	−19.7103	−0.956091
$426$	22.0246	1.06709
$427$	−6.12278	−0.296302
$428$	−8.09716	−0.391391
$429$	−14.8122	−0.715140
$430$	−15.2853	−0.737124
$431$	−1.44182	−0.0694498	−0.0347249	−	0.999397i	$-0.511056\pi$
$431$	−1.44182	−0.0694498	−0.0347249	+	0.999397i	$0.511056\pi$
$432$	3.55945	0.171254
$433$	−18.8981	−0.908187	−0.454094	−	0.890954i	$-0.650037\pi$
$433$	−18.8981	−0.908187	−0.454094	+	0.890954i	$0.650037\pi$
$434$	−6.69720	−0.321476
$435$	1.72376	0.0826480
$436$	14.6559	0.701891
$437$	35.2168	1.68465
$438$	10.9758	0.524446
$439$	16.4936	0.787197	0.393598	−	0.919283i	$-0.371230\pi$
$439$	16.4936	0.787197	0.393598	+	0.919283i	$0.371230\pi$
$440$	5.16291	0.246132
$441$	−7.19699	−0.342714
$442$	22.5253	1.07142
$443$	14.9269	0.709197	0.354599	−	0.935019i	$-0.384618\pi$
$443$	14.9269	0.709197	0.354599	+	0.935019i	$0.384618\pi$
$444$	0.214621	0.0101855
$445$	14.7113	0.697381
$446$	−1.50855	−0.0714321
$447$	−11.2856	−0.533792
$448$	1.17237	0.0553894
$449$	−30.1025	−1.42062	−0.710312	−	0.703887i	$-0.751446\pi$
$449$	−30.1025	−1.42062	−0.710312	+	0.703887i	$0.751446\pi$
$450$	4.53920	0.213980
$451$	5.71420	0.269071
$452$	14.8664	0.699258
$453$	31.8342	1.49570
$454$	8.35571	0.392153
$455$	13.8986	0.651576
$456$	17.2230	0.806542
$457$	−38.8814	−1.81880	−0.909398	−	0.415927i	$-0.863457\pi$
$457$	−38.8814	−1.81880	−0.909398	+	0.415927i	$0.863457\pi$
$458$	−1.05903	−0.0494853
$459$	−19.7735	−0.922949
$460$	12.3670	0.576613
$461$	24.7603	1.15320	0.576600	−	0.817026i	$-0.304379\pi$
$461$	24.7603	1.15320	0.576600	+	0.817026i	$0.304379\pi$
$462$	4.28267	0.199248
$463$	27.8145	1.29265	0.646324	−	0.763063i	$-0.276306\pi$
$463$	27.8145	1.29265	0.646324	+	0.763063i	$0.276306\pi$
$464$	0.285006	0.0132311
$465$	−34.5502	−1.60223
$466$	−5.82776	−0.269966
$467$	−2.05337	−0.0950189	−0.0475094	−	0.998871i	$-0.515128\pi$
$467$	−2.05337	−0.0950189	−0.0475094	+	0.998871i	$0.515128\pi$
$468$	−5.18749	−0.239792
$469$	−7.30428	−0.337280
$470$	−12.8658	−0.593456
$471$	8.75136	0.403241
$472$	−4.33015	−0.199311
$473$	−9.23211	−0.424493
$474$	4.69583	0.215687
$475$	−29.5402	−1.35540
$476$	−6.51278	−0.298513
$477$	4.80594	0.220049
$478$	−8.53593	−0.390424
$479$	6.36291	0.290729	0.145364	−	0.989378i	$-0.453565\pi$
$479$	6.36291	0.290729	0.145364	+	0.989378i	$0.453565\pi$
$480$	6.04815	0.276059
$481$	0.420683	0.0191815
$482$	14.6546	0.667500
$483$	10.2585	0.466777
$484$	−7.88168	−0.358258
$485$	−12.9117	−0.586290
$486$	12.4933	0.566708
$487$	−2.46065	−0.111502	−0.0557512	−	0.998445i	$-0.517755\pi$
$487$	−2.46065	−0.111502	−0.0557512	+	0.998445i	$0.517755\pi$
$488$	−5.22255	−0.236414
$489$	−21.2713	−0.961921
$490$	16.4475	0.743020
$491$	14.7102	0.663862	0.331931	−	0.943304i	$-0.392300\pi$
$491$	14.7102	0.663862	0.331931	+	0.943304i	$0.392300\pi$
$492$	6.69396	0.301787
$493$	−1.58327	−0.0713069
$494$	33.7592	1.51890
$495$	6.60513	0.296878
$496$	−5.71251	−0.256499
$497$	−12.4820	−0.559895
$498$	−7.25056	−0.324905
$499$	13.8066	0.618070	0.309035	−	0.951051i	$-0.399994\pi$
$499$	13.8066	0.618070	0.309035	+	0.951051i	$0.399994\pi$
$500$	4.24500	0.189842
$501$	17.0702	0.762642
$502$	7.19593	0.321170
$503$	−15.2041	−0.677916	−0.338958	−	0.940801i	$-0.610075\pi$
$503$	−15.2041	−0.677916	−0.338958	+	0.940801i	$0.610075\pi$
$504$	1.49987	0.0668093
$505$	5.20265	0.231515
$506$	7.46946	0.332058
$507$	−7.11928	−0.316178
$508$	0.737228	0.0327092
$509$	18.6607	0.827123	0.413562	−	0.910476i	$-0.364285\pi$
$509$	18.6607	0.827123	0.413562	+	0.910476i	$0.364285\pi$
$510$	−33.5988	−1.48778
$511$	−6.22035	−0.275172
$512$	1.00000	0.0441942
$513$	−29.6349	−1.30841
$514$	8.28211	0.365308
$515$	−8.28172	−0.364936
$516$	−10.8151	−0.476107
$517$	−7.77076	−0.341758
$518$	−0.121633	−0.00534423
$519$	−1.03156	−0.0452803
$520$	11.8551	0.519880
$521$	−7.32625	−0.320969	−0.160484	−	0.987038i	$-0.551306\pi$
$521$	−7.32625	−0.320969	−0.160484	+	0.987038i	$0.551306\pi$
$522$	0.364620	0.0159590
$523$	3.53586	0.154612	0.0773061	−	0.997007i	$-0.475368\pi$
$523$	3.53586	0.154612	0.0773061	+	0.997007i	$0.475368\pi$
$524$	−0.614440	−0.0268419
$525$	−8.60493	−0.375550
$526$	17.3494	0.756469
$527$	31.7342	1.38237
$528$	3.65299	0.158976
$529$	−5.10803	−0.222088
$530$	−10.9831	−0.477077
$531$	−5.53974	−0.240404
$532$	−9.76083	−0.423185
$533$	13.1210	0.568332
$534$	10.4089	0.450437
$535$	23.6737	1.02351
$536$	−6.23034	−0.269110
$537$	−42.1182	−1.81754
$538$	−1.61453	−0.0696074
$539$	9.93402	0.427888
$540$	−10.4068	−0.447837
$541$	16.1196	0.693037	0.346519	−	0.938043i	$-0.387364\pi$
$541$	16.1196	0.693037	0.346519	+	0.938043i	$0.387364\pi$
$542$	−17.5765	−0.754977
$543$	−31.2968	−1.34307
$544$	−5.55521	−0.238178
$545$	−42.8496	−1.83548
$546$	9.83388	0.420851
$547$	13.2192	0.565213	0.282606	−	0.959236i	$-0.408801\pi$
$547$	13.2192	0.565213	0.282606	+	0.959236i	$0.408801\pi$
$548$	−8.55938	−0.365639
$549$	−6.68143	−0.285157
$550$	−6.26547	−0.267160
$551$	−2.37288	−0.101088
$552$	8.75019	0.372433
$553$	−2.66127	−0.113169
$554$	0.751268	0.0319183
$555$	−0.627491	−0.0266355
$556$	−3.79484	−0.160937
$557$	−34.8358	−1.47604	−0.738021	−	0.674778i	$-0.764239\pi$
$557$	−34.8358	−1.47604	−0.738021	+	0.674778i	$0.764239\pi$
$558$	−7.30826	−0.309383
$559$	−21.1988	−0.896614
$560$	−3.42768	−0.144846
$561$	−20.2932	−0.856778
$562$	9.02777	0.380813
$563$	−39.6216	−1.66985	−0.834925	−	0.550364i	$-0.814489\pi$
$563$	−39.6216	−1.66985	−0.834925	+	0.550364i	$0.814489\pi$
$564$	−9.10314	−0.383311
$565$	−43.4651	−1.82859
$566$	−0.601750	−0.0252935
$567$	−13.1321	−0.551497
$568$	−10.6468	−0.446730
$569$	33.9031	1.42129	0.710645	−	0.703550i	$-0.248403\pi$
$569$	33.9031	1.42129	0.710645	+	0.703550i	$0.248403\pi$
$570$	−50.3551	−2.10914
$571$	−24.9890	−1.04576	−0.522878	−	0.852408i	$-0.675142\pi$
$571$	−24.9890	−1.04576	−0.522878	+	0.852408i	$0.675142\pi$
$572$	7.16030	0.299387
$573$	41.5701	1.73662
$574$	−3.79368	−0.158345
$575$	−15.0080	−0.625876
$576$	1.27934	0.0533059
$577$	−11.8066	−0.491513	−0.245757	−	0.969332i	$-0.579036\pi$
$577$	−11.8066	−0.491513	−0.245757	+	0.969332i	$0.579036\pi$
$578$	13.8604	0.576517
$579$	34.0369	1.41452
$580$	−0.833275	−0.0345999
$581$	4.10912	0.170475
$582$	−9.13562	−0.378684
$583$	−6.63365	−0.274738
$584$	−5.30578	−0.219555
$585$	15.1667	0.627066
$586$	−31.5181	−1.30200
$587$	3.15856	0.130368	0.0651839	−	0.997873i	$-0.479237\pi$
$587$	3.15856	0.130368	0.0651839	+	0.997873i	$0.479237\pi$
$588$	11.6373	0.479915
$589$	47.5607	1.95970
$590$	12.6601	0.521208
$591$	15.1087	0.621490
$592$	−0.103749	−0.00426406
$593$	27.7877	1.14110	0.570551	−	0.821262i	$-0.306730\pi$
$593$	27.7877	1.14110	0.570551	+	0.821262i	$0.306730\pi$
$594$	−6.28555	−0.257899
$595$	19.0415	0.780624
$596$	5.45553	0.223467
$597$	58.0840	2.37722
$598$	17.1514	0.701373
$599$	−2.70345	−0.110460	−0.0552300	−	0.998474i	$-0.517589\pi$
$599$	−2.70345	−0.110460	−0.0552300	+	0.998474i	$0.517589\pi$
$600$	−7.33975	−0.299644
$601$	25.1981	1.02785	0.513926	−	0.857834i	$-0.328191\pi$
$601$	25.1981	1.02785	0.513926	+	0.857834i	$0.328191\pi$
$602$	6.12923	0.249809
$603$	−7.97073	−0.324593
$604$	−15.3888	−0.626161
$605$	23.0437	0.936861
$606$	3.68111	0.149535
$607$	−32.7331	−1.32859	−0.664297	−	0.747468i	$-0.731269\pi$
$607$	−32.7331	−1.32859	−0.664297	+	0.747468i	$0.731269\pi$
$608$	−8.32570	−0.337652
$609$	−0.691207	−0.0280091
$610$	15.2692	0.618233
$611$	−17.8432	−0.721860
$612$	−7.10702	−0.287284
$613$	−7.49275	−0.302629	−0.151315	−	0.988486i	$-0.548351\pi$
$613$	−7.49275	−0.302629	−0.151315	+	0.988486i	$0.548351\pi$
$614$	24.5697	0.991552
$615$	−19.5712	−0.789187
$616$	−2.07027	−0.0834134
$617$	−18.3295	−0.737919	−0.368960	−	0.929445i	$-0.620286\pi$
$617$	−18.3295	−0.737919	−0.368960	+	0.929445i	$0.620286\pi$
$618$	−5.85969	−0.235711
$619$	14.6521	0.588918	0.294459	−	0.955664i	$-0.404861\pi$
$619$	14.6521	0.588918	0.294459	+	0.955664i	$0.404861\pi$
$620$	16.7017	0.670758
$621$	−15.0561	−0.604180
$622$	−8.81987	−0.353645
$623$	−5.89905	−0.236340
$624$	8.38802	0.335789
$625$	−30.1515	−1.20606
$626$	−25.3636	−1.01373
$627$	−30.4137	−1.21461
$628$	−4.23045	−0.168813
$629$	0.576349	0.0229805
$630$	−4.38517	−0.174709
$631$	18.0602	0.718965	0.359483	−	0.933152i	$-0.382953\pi$
$631$	18.0602	0.718965	0.359483	+	0.933152i	$0.382953\pi$
$632$	−2.26999	−0.0902954
$633$	−21.1249	−0.839638
$634$	21.7608	0.864233
$635$	−2.15544	−0.0855361
$636$	−7.77107	−0.308143
$637$	22.8105	0.903786
$638$	−0.503286	−0.0199253
$639$	−13.6209	−0.538835
$640$	−2.92371	−0.115570
$641$	35.3336	1.39559	0.697797	−	0.716296i	$-0.254164\pi$
$641$	35.3336	1.39559	0.697797	+	0.716296i	$0.254164\pi$
$642$	16.7502	0.661080
$643$	−13.2174	−0.521245	−0.260622	−	0.965441i	$-0.583928\pi$
$643$	−13.2174	−0.521245	−0.260622	+	0.965441i	$0.583928\pi$
$644$	−4.95901	−0.195412
$645$	31.6201	1.24504
$646$	46.2511	1.81972
$647$	−20.2630	−0.796622	−0.398311	−	0.917250i	$-0.630404\pi$
$647$	−20.2630	−0.796622	−0.398311	+	0.917250i	$0.630404\pi$
$648$	−11.2013	−0.440029
$649$	7.64652	0.300152
$650$	−14.3868	−0.564296
$651$	13.8542	0.542989
$652$	10.2827	0.402700
$653$	0.292013	0.0114273	0.00571367	−	0.999984i	$-0.498181\pi$
$653$	0.292013	0.0114273	0.00571367	+	0.999984i	$0.498181\pi$
$654$	−30.3180	−1.18553
$655$	1.79644	0.0701929
$656$	−3.23590	−0.126341
$657$	−6.78791	−0.264822
$658$	5.15904	0.201120
$659$	−40.9023	−1.59333	−0.796664	−	0.604422i	$-0.793404\pi$
$659$	−40.9023	−1.59333	−0.796664	+	0.604422i	$0.793404\pi$
$660$	−10.6803	−0.415730
$661$	−40.0751	−1.55874	−0.779371	−	0.626563i	$-0.784461\pi$
$661$	−40.0751	−1.55874	−0.779371	+	0.626563i	$0.784461\pi$
$662$	4.67759	0.181800
$663$	−46.5972	−1.80969
$664$	3.50496	0.136019
$665$	28.5378	1.10665
$666$	−0.132731	−0.00514321
$667$	−1.20554	−0.0466789
$668$	−8.25185	−0.319274
$669$	3.12068	0.120652
$670$	18.2157	0.703734
$671$	9.22239	0.356026
$672$	−2.42524	−0.0935555
$673$	48.3723	1.86461	0.932307	−	0.361669i	$-0.117793\pi$
$673$	48.3723	1.86461	0.932307	+	0.361669i	$0.117793\pi$
$674$	11.5634	0.445406
$675$	12.6292	0.486098
$676$	3.44150	0.132365
$677$	−22.5755	−0.867649	−0.433824	−	0.900997i	$-0.642836\pi$
$677$	−22.5755	−0.867649	−0.433824	+	0.900997i	$0.642836\pi$
$678$	−30.7535	−1.18108
$679$	5.17744	0.198692
$680$	16.2418	0.622846
$681$	−17.2851	−0.662366
$682$	10.0876	0.386274
$683$	20.1278	0.770168	0.385084	−	0.922882i	$-0.374173\pi$
$683$	20.1278	0.770168	0.385084	+	0.922882i	$0.374173\pi$
$684$	−10.6514	−0.407267
$685$	25.0252	0.956162
$686$	−14.8018	−0.565137
$687$	2.19078	0.0835833
$688$	5.22806	0.199318
$689$	−15.2322	−0.580301
$690$	−25.5830	−0.973929
$691$	10.9715	0.417376	0.208688	−	0.977982i	$-0.433081\pi$
$691$	10.9715	0.417376	0.208688	+	0.977982i	$0.433081\pi$
$692$	0.498660	0.0189562
$693$	−2.64858	−0.100611
$694$	15.3760	0.583665
$695$	11.0950	0.420857
$696$	−0.589580	−0.0223480
$697$	17.9761	0.680893
$698$	22.9589	0.869006
$699$	12.0556	0.455986
$700$	4.15967	0.157221
$701$	−15.9861	−0.603787	−0.301893	−	0.953342i	$-0.597619\pi$
$701$	−15.9861	−0.603787	−0.301893	+	0.953342i	$0.597619\pi$
$702$	−14.4329	−0.544735
$703$	0.863785	0.0325783
$704$	−1.76588	−0.0665540
$705$	26.6149	1.00238
$706$	14.1805	0.533691
$707$	−2.08620	−0.0784597
$708$	8.95760	0.336647
$709$	−32.7313	−1.22925	−0.614624	−	0.788820i	$-0.710692\pi$
$709$	−32.7313	−1.22925	−0.614624	+	0.788820i	$0.710692\pi$
$710$	31.1282	1.16822
$711$	−2.90409	−0.108912
$712$	−5.03172	−0.188572
$713$	24.1633	0.904923
$714$	13.4727	0.504203
$715$	−20.9346	−0.782911
$716$	20.3602	0.760895
$717$	17.6579	0.659447
$718$	31.1827	1.16373
$719$	−7.13432	−0.266065	−0.133033	−	0.991112i	$-0.542472\pi$
$719$	−7.13432	−0.266065	−0.133033	+	0.991112i	$0.542472\pi$
$720$	−3.74042	−0.139397
$721$	3.32087	0.123676
$722$	50.3173	1.87262
$723$	−30.3154	−1.12744
$724$	15.1290	0.562267
$725$	1.01122	0.0375559
$726$	16.3045	0.605116
$727$	15.2639	0.566106	0.283053	−	0.959104i	$-0.408653\pi$
$727$	15.2639	0.566106	0.283053	+	0.959104i	$0.408653\pi$
$728$	−4.75375	−0.176186
$729$	7.75955	0.287391
$730$	15.5126	0.574146
$731$	−29.0430	−1.07419
$732$	10.8037	0.399315
$733$	−12.2601	−0.452836	−0.226418	−	0.974030i	$-0.572702\pi$
$733$	−12.2601	−0.452836	−0.226418	+	0.974030i	$0.572702\pi$
$734$	−1.17890	−0.0435141
$735$	−34.0241	−1.25500
$736$	−4.22989	−0.155916
$737$	11.0020	0.405264
$738$	−4.13982	−0.152389
$739$	−43.1350	−1.58675	−0.793374	−	0.608735i	$-0.791677\pi$
$739$	−43.1350	−1.58675	−0.793374	+	0.608735i	$0.791677\pi$
$740$	0.303332	0.0111507
$741$	−69.8361	−2.56549
$742$	4.40411	0.161680
$743$	35.5798	1.30530	0.652648	−	0.757661i	$-0.273658\pi$
$743$	35.5798	1.30530	0.652648	+	0.757661i	$0.273658\pi$
$744$	11.8172	0.433241
$745$	−15.9504	−0.584377
$746$	−23.3901	−0.856372
$747$	4.48404	0.164062
$748$	9.80982	0.358683
$749$	−9.49289	−0.346863
$750$	−8.78145	−0.320653
$751$	−2.01782	−0.0736314	−0.0368157	−	0.999322i	$-0.511721\pi$
$751$	−2.01782	−0.0736314	−0.0368157	+	0.999322i	$0.511721\pi$
$752$	4.40051	0.160470
$753$	−14.8859	−0.542473
$754$	−1.15565	−0.0420861
$755$	44.9924	1.63744
$756$	4.17300	0.151771
$757$	−45.9849	−1.67135	−0.835675	−	0.549225i	$-0.814923\pi$
$757$	−45.9849	−1.67135	−0.835675	+	0.549225i	$0.814923\pi$
$758$	1.17861	0.0428089
$759$	−15.4518	−0.560863
$760$	24.3419	0.882975
$761$	−6.26183	−0.226991	−0.113496	−	0.993538i	$-0.536205\pi$
$761$	−6.26183	−0.226991	−0.113496	+	0.993538i	$0.536205\pi$
$762$	−1.52507	−0.0552475
$763$	17.1822	0.622037
$764$	−20.0952	−0.727019
$765$	20.7789	0.751261
$766$	18.8663	0.681666
$767$	17.5580	0.633981
$768$	−2.06866	−0.0746462
$769$	50.6633	1.82696	0.913482	−	0.406880i	$-0.133383\pi$
$769$	50.6633	1.82696	0.913482	+	0.406880i	$0.133383\pi$
$770$	6.05285	0.218130
$771$	−17.1328	−0.617024
$772$	−16.4536	−0.592179
$773$	−46.8394	−1.68469	−0.842347	−	0.538935i	$-0.818827\pi$
$773$	−46.8394	−1.68469	−0.842347	+	0.538935i	$0.818827\pi$
$774$	6.68848	0.240412
$775$	−20.2684	−0.728064
$776$	4.41621	0.158533
$777$	0.251616	0.00902668
$778$	30.2852	1.08578
$779$	26.9411	0.965266
$780$	−24.5241	−0.878104
$781$	18.8009	0.672751
$782$	23.4979	0.840285
$783$	1.01447	0.0362540
$784$	−5.62554	−0.200912
$785$	12.3686	0.441455
$786$	1.27107	0.0453374
$787$	−44.2106	−1.57594	−0.787969	−	0.615715i	$-0.788867\pi$
$787$	−44.2106	−1.57594	−0.787969	+	0.615715i	$0.788867\pi$
$788$	−7.30364	−0.260181
$789$	−35.8899	−1.27772
$790$	6.63679	0.236126
$791$	17.4290	0.619704
$792$	−2.25916	−0.0802758
$793$	21.1765	0.751999
$794$	−10.1143	−0.358943
$795$	22.7203	0.805807
$796$	−28.0781	−0.995203
$797$	−27.6879	−0.980757	−0.490379	−	0.871510i	$-0.663141\pi$
$797$	−27.6879	−0.980757	−0.490379	+	0.871510i	$0.663141\pi$
$798$	20.1918	0.714782
$799$	−24.4458	−0.864829
$800$	3.54808	0.125443
$801$	−6.43729	−0.227450
$802$	−10.7151	−0.378365
$803$	9.36936	0.330638
$804$	12.8884	0.454540
$805$	14.4987	0.511012
$806$	23.1632	0.815888
$807$	3.33991	0.117570
$808$	−1.77947	−0.0626015
$809$	11.0728	0.389299	0.194649	−	0.980873i	$-0.437643\pi$
$809$	11.0728	0.389299	0.194649	+	0.980873i	$0.437643\pi$
$810$	32.7494	1.15070
$811$	−9.07566	−0.318689	−0.159345	−	0.987223i	$-0.550938\pi$
$811$	−9.07566	−0.318689	−0.159345	+	0.987223i	$0.550938\pi$
$812$	0.334133	0.0117258
$813$	36.3598	1.27519
$814$	0.183208	0.00642145
$815$	−30.0635	−1.05308
$816$	11.4918	0.402295
$817$	−43.5273	−1.52283
$818$	−12.8127	−0.447984
$819$	−6.08167	−0.212511
$820$	9.46082	0.330386
$821$	23.1214	0.806941	0.403470	−	0.914993i	$-0.367804\pi$
$821$	23.1214	0.806941	0.403470	+	0.914993i	$0.367804\pi$
$822$	17.7064	0.617583
$823$	−1.05228	−0.0366800	−0.0183400	−	0.999832i	$-0.505838\pi$
$823$	−1.05228	−0.0366800	−0.0183400	+	0.999832i	$0.505838\pi$
$824$	2.83261	0.0986786
$825$	12.9611	0.451248
$826$	−5.07655	−0.176636
$827$	43.7520	1.52141	0.760703	−	0.649100i	$-0.224854\pi$
$827$	43.7520	1.52141	0.760703	+	0.649100i	$0.224854\pi$
$828$	−5.41147	−0.188062
$829$	−40.1942	−1.39600	−0.698001	−	0.716097i	$-0.745927\pi$
$829$	−40.1942	−1.39600	−0.698001	+	0.716097i	$0.745927\pi$
$830$	−10.2475	−0.355695
$831$	−1.55412	−0.0539117
$832$	−4.05481	−0.140575
$833$	31.2511	1.08279
$834$	7.85022	0.271831
$835$	24.1260	0.834915
$836$	14.7022	0.508485
$837$	−20.3334	−0.702826
$838$	−16.7957	−0.580198
$839$	28.1771	0.972783	0.486391	−	0.873741i	$-0.338313\pi$
$839$	28.1771	0.972783	0.486391	+	0.873741i	$0.338313\pi$
$840$	7.09069	0.244652
$841$	−28.9188	−0.997199
$842$	−0.401501	−0.0138366
$843$	−18.6754	−0.643213
$844$	10.2119	0.351507
$845$	−10.0619	−0.346141
$846$	5.62975	0.193555
$847$	−9.24026	−0.317499
$848$	3.75658	0.129001
$849$	1.24481	0.0427219
$850$	−19.7103	−0.676059
$851$	0.438848	0.0150435
$852$	22.0246	0.754550
$853$	−16.2409	−0.556077	−0.278039	−	0.960570i	$-0.589684\pi$
$853$	−16.2409	−0.556077	−0.278039	+	0.960570i	$0.589684\pi$
$854$	−6.12278	−0.209517
$855$	31.1417	1.06502
$856$	−8.09716	−0.276755
$857$	−17.8529	−0.609844	−0.304922	−	0.952377i	$-0.598630\pi$
$857$	−17.8529	−0.609844	−0.304922	+	0.952377i	$0.598630\pi$
$858$	−14.8122	−0.505680
$859$	−43.5422	−1.48564	−0.742820	−	0.669491i	$-0.766512\pi$
$859$	−43.5422	−1.48564	−0.742820	+	0.669491i	$0.766512\pi$
$860$	−15.2853	−0.521225
$861$	7.84781	0.267453
$862$	−1.44182	−0.0491085
$863$	−46.9662	−1.59875	−0.799373	−	0.600835i	$-0.794835\pi$
$863$	−46.9662	−1.59875	−0.799373	+	0.600835i	$0.794835\pi$
$864$	3.55945	0.121095
$865$	−1.45794	−0.0495714
$866$	−18.8981	−0.642185
$867$	−28.6724	−0.973767
$868$	−6.69720	−0.227318
$869$	4.00852	0.135980
$870$	1.72376	0.0584409
$871$	25.2628	0.855999
$872$	14.6559	0.496312
$873$	5.64984	0.191218
$874$	35.2168	1.19123
$875$	4.97672	0.168244
$876$	10.9758	0.370839
$877$	−24.6245	−0.831509	−0.415755	−	0.909477i	$-0.636482\pi$
$877$	−24.6245	−0.831509	−0.415755	+	0.909477i	$0.636482\pi$
$878$	16.4936	0.556632
$879$	65.2001	2.19914
$880$	5.16291	0.174042
$881$	−38.0456	−1.28179	−0.640894	−	0.767629i	$-0.721436\pi$
$881$	−38.0456	−1.28179	−0.640894	+	0.767629i	$0.721436\pi$
$882$	−7.19699	−0.242335
$883$	−1.93335	−0.0650624	−0.0325312	−	0.999471i	$-0.510357\pi$
$883$	−1.93335	−0.0650624	−0.0325312	+	0.999471i	$0.510357\pi$
$884$	22.5253	0.757609
$885$	−26.1894	−0.880348
$886$	14.9269	0.501478
$887$	18.6316	0.625586	0.312793	−	0.949821i	$-0.398735\pi$
$887$	18.6316	0.625586	0.312793	+	0.949821i	$0.398735\pi$
$888$	0.214621	0.00720222
$889$	0.864306	0.0289879
$890$	14.7113	0.493123
$891$	19.7801	0.662659
$892$	−1.50855	−0.0505101
$893$	−36.6373	−1.22602
$894$	−11.2856	−0.377448
$895$	−59.5272	−1.98978
$896$	1.17237	0.0391662
$897$	−35.4804	−1.18466
$898$	−30.1025	−1.00453
$899$	−1.62810	−0.0543002
$900$	4.53920	0.151307
$901$	−20.8686	−0.695233
$902$	5.71420	0.190262
$903$	−12.6793	−0.421940
$904$	14.8664	0.494450
$905$	−44.2329	−1.47035
$906$	31.8342	1.05762
$907$	−6.85471	−0.227607	−0.113803	−	0.993503i	$-0.536303\pi$
$907$	−6.85471	−0.227607	−0.113803	+	0.993503i	$0.536303\pi$
$908$	8.35571	0.277294
$909$	−2.27655	−0.0755084
$910$	13.8986	0.460734
$911$	−35.8430	−1.18753	−0.593766	−	0.804638i	$-0.702360\pi$
$911$	−35.8430	−1.18753	−0.593766	+	0.804638i	$0.702360\pi$
$912$	17.2230	0.570311
$913$	−6.18932	−0.204837
$914$	−38.8814	−1.28608
$915$	−31.5868	−1.04423
$916$	−1.05903	−0.0349914
$917$	−0.720353	−0.0237881
$918$	−19.7735	−0.652623
$919$	−24.4497	−0.806521	−0.403261	−	0.915085i	$-0.632123\pi$
$919$	−24.4497	−0.806521	−0.403261	+	0.915085i	$0.632123\pi$
$920$	12.3670	0.407727
$921$	−50.8263	−1.67478
$922$	24.7603	0.815436
$923$	43.1708	1.42098
$924$	4.28267	0.140889
$925$	−0.368110	−0.0121034
$926$	27.8145	0.914040
$927$	3.62387	0.119024
$928$	0.285006	0.00935578
$929$	6.95007	0.228025	0.114012	−	0.993479i	$-0.463630\pi$
$929$	6.95007	0.228025	0.114012	+	0.993479i	$0.463630\pi$
$930$	−34.5502	−1.13294
$931$	46.8366	1.53501
$932$	−5.82776	−0.190895
$933$	18.2453	0.597324
$934$	−2.05337	−0.0671885
$935$	−28.6811	−0.937972
$936$	−5.18749	−0.169558
$937$	−5.78201	−0.188890	−0.0944451	−	0.995530i	$-0.530108\pi$
$937$	−5.78201	−0.188890	−0.0944451	+	0.995530i	$0.530108\pi$
$938$	−7.30428	−0.238493
$939$	52.4686	1.71225
$940$	−12.8658	−0.419636
$941$	1.77082	0.0577270	0.0288635	−	0.999583i	$-0.490811\pi$
$941$	1.77082	0.0577270	0.0288635	+	0.999583i	$0.490811\pi$
$942$	8.75136	0.285135
$943$	13.6875	0.445726
$944$	−4.33015	−0.140934
$945$	−12.2006	−0.396887
$946$	−9.23211	−0.300162
$947$	−55.6457	−1.80824	−0.904120	−	0.427278i	$-0.859473\pi$
$947$	−55.6457	−1.80824	−0.904120	+	0.427278i	$0.859473\pi$
$948$	4.69583	0.152514
$949$	21.5140	0.698372
$950$	−29.5402	−0.958412
$951$	−45.0157	−1.45973
$952$	−6.51278	−0.211080
$953$	3.77707	0.122351	0.0611757	−	0.998127i	$-0.480515\pi$
$953$	3.77707	0.122351	0.0611757	+	0.998127i	$0.480515\pi$
$954$	4.80594	0.155598
$955$	58.7525	1.90119
$956$	−8.53593	−0.276072
$957$	1.04113	0.0336548
$958$	6.36291	0.205576
$959$	−10.0348	−0.324040
$960$	6.04815	0.195203
$961$	1.63283	0.0526718
$962$	0.420683	0.0135634
$963$	−10.3590	−0.333815
$964$	14.6546	0.471994
$965$	48.1056	1.54857
$966$	10.2585	0.330061
$967$	−13.9084	−0.447264	−0.223632	−	0.974674i	$-0.571791\pi$
$967$	−13.9084	−0.447264	−0.223632	+	0.974674i	$0.571791\pi$
$968$	−7.88168	−0.253327
$969$	−95.6776	−3.07361
$970$	−12.9117	−0.414570
$971$	−54.3967	−1.74567	−0.872837	−	0.488012i	$-0.837722\pi$
$971$	−54.3967	−1.74567	−0.872837	+	0.488012i	$0.837722\pi$
$972$	12.4933	0.400723
$973$	−4.44896	−0.142627
$974$	−2.46065	−0.0788442
$975$	29.7613	0.953125
$976$	−5.22255	−0.167170
$977$	−6.17649	−0.197604	−0.0988018	−	0.995107i	$-0.531501\pi$
$977$	−6.17649	−0.197604	−0.0988018	+	0.995107i	$0.531501\pi$
$978$	−21.2713	−0.680181
$979$	8.88539	0.283978
$980$	16.4475	0.525395
$981$	18.7499	0.598639
$982$	14.7102	0.469421
$983$	25.0951	0.800409	0.400205	−	0.916426i	$-0.368939\pi$
$983$	25.0951	0.800409	0.400205	+	0.916426i	$0.368939\pi$
$984$	6.69396	0.213396
$985$	21.3537	0.680386
$986$	−1.58327	−0.0504216
$987$	−10.6723	−0.339702
$988$	33.7592	1.07402
$989$	−22.1141	−0.703188
$990$	6.60513	0.209925
$991$	−16.5761	−0.526558	−0.263279	−	0.964720i	$-0.584804\pi$
$991$	−16.5761	−0.526558	−0.263279	+	0.964720i	$0.584804\pi$
$992$	−5.71251	−0.181373
$993$	−9.67633	−0.307069
$994$	−12.4820	−0.395906
$995$	82.0923	2.60250
$996$	−7.25056	−0.229743
$997$	−25.1234	−0.795666	−0.397833	−	0.917458i	$-0.630238\pi$
$997$	−25.1234	−0.795666	−0.397833	+	0.917458i	$0.630238\pi$
$998$	13.8066	0.437041
$999$	−0.369290	−0.0116838

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8014.2.a.d.1.15	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8014.2.a.d.1.15	✓	88	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:	\( N \)	\(=\)	\( 8014 = 2 \cdot 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.06866 q^{3} +1.00000 q^{4} -2.92371 q^{5} -2.06866 q^{6} +1.17237 q^{7} +1.00000 q^{8} +1.27934 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.06866 q^{3} +1.00000 q^{4} -2.92371 q^{5} -2.06866 q^{6} +1.17237 q^{7} +1.00000 q^{8} +1.27934 q^{9} -2.92371 q^{10} -1.76588 q^{11} -2.06866 q^{12} -4.05481 q^{13} +1.17237 q^{14} +6.04815 q^{15} +1.00000 q^{16} -5.55521 q^{17} +1.27934 q^{18} -8.32570 q^{19} -2.92371 q^{20} -2.42524 q^{21} -1.76588 q^{22} -4.22989 q^{23} -2.06866 q^{24} +3.54808 q^{25} -4.05481 q^{26} +3.55945 q^{27} +1.17237 q^{28} +0.285006 q^{29} +6.04815 q^{30} -5.71251 q^{31} +1.00000 q^{32} +3.65299 q^{33} -5.55521 q^{34} -3.42768 q^{35} +1.27934 q^{36} -0.103749 q^{37} -8.32570 q^{38} +8.38802 q^{39} -2.92371 q^{40} -3.23590 q^{41} -2.42524 q^{42} +5.22806 q^{43} -1.76588 q^{44} -3.74042 q^{45} -4.22989 q^{46} +4.40051 q^{47} -2.06866 q^{48} -5.62554 q^{49} +3.54808 q^{50} +11.4918 q^{51} -4.05481 q^{52} +3.75658 q^{53} +3.55945 q^{54} +5.16291 q^{55} +1.17237 q^{56} +17.2230 q^{57} +0.285006 q^{58} -4.33015 q^{59} +6.04815 q^{60} -5.22255 q^{61} -5.71251 q^{62} +1.49987 q^{63} +1.00000 q^{64} +11.8551 q^{65} +3.65299 q^{66} -6.23034 q^{67} -5.55521 q^{68} +8.75019 q^{69} -3.42768 q^{70} -10.6468 q^{71} +1.27934 q^{72} -5.30578 q^{73} -0.103749 q^{74} -7.33975 q^{75} -8.32570 q^{76} -2.07027 q^{77} +8.38802 q^{78} -2.26999 q^{79} -2.92371 q^{80} -11.2013 q^{81} -3.23590 q^{82} +3.50496 q^{83} -2.42524 q^{84} +16.2418 q^{85} +5.22806 q^{86} -0.589580 q^{87} -1.76588 q^{88} -5.03172 q^{89} -3.74042 q^{90} -4.75375 q^{91} -4.22989 q^{92} +11.8172 q^{93} +4.40051 q^{94} +24.3419 q^{95} -2.06866 q^{96} +4.41621 q^{97} -5.62554 q^{98} -2.25916 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9}+O(q^{10}) \) 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9	\( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9} + 25 q^{10} + 70 q^{11} + 22 q^{12} + 31 q^{13} + 33 q^{14} + 47 q^{15} + 88 q^{16} + 19 q^{17} + 108 q^{18} + 33 q^{19} + 25 q^{20} + 48 q^{21} + 70 q^{22} + 77 q^{23} + 22 q^{24} + 109 q^{25} + 31 q^{26} + 88 q^{27} + 33 q^{28} + 83 q^{29} + 47 q^{30} + 51 q^{31} + 88 q^{32} + 30 q^{33} + 19 q^{34} + 40 q^{35} + 108 q^{36} + 45 q^{37} + 33 q^{38} + 82 q^{39} + 25 q^{40} + 35 q^{41} + 48 q^{42} + 78 q^{43} + 70 q^{44} + 37 q^{45} + 77 q^{46} + 59 q^{47} + 22 q^{48} + 103 q^{49} + 109 q^{50} + 21 q^{51} + 31 q^{52} + 58 q^{53} + 88 q^{54} + 35 q^{55} + 33 q^{56} - 16 q^{57} + 83 q^{58} + 54 q^{59} + 47 q^{60} + 18 q^{61} + 51 q^{62} + 47 q^{63} + 88 q^{64} + 34 q^{65} + 30 q^{66} + 88 q^{67} + 19 q^{68} + 62 q^{69} + 40 q^{70} + 139 q^{71} + 108 q^{72} - 6 q^{73} + 45 q^{74} + 45 q^{75} + 33 q^{76} + 37 q^{77} + 82 q^{78} + 94 q^{79} + 25 q^{80} + 112 q^{81} + 35 q^{82} + 58 q^{83} + 48 q^{84} + 83 q^{85} + 78 q^{86} + 21 q^{87} + 70 q^{88} + 99 q^{89} + 37 q^{90} + 53 q^{91} + 77 q^{92} + 57 q^{93} + 59 q^{94} + 92 q^{95} + 22 q^{96} + 16 q^{97} + 103 q^{98} + 150 q^{99}+O(q^{100}) \) 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9 + 25 * q^10 + 70 * q^11 + 22 * q^12 + 31 * q^13 + 33 * q^14 + 47 * q^15 + 88 * q^16 + 19 * q^17 + 108 * q^18 + 33 * q^19 + 25 * q^20 + 48 * q^21 + 70 * q^22 + 77 * q^23 + 22 * q^24 + 109 * q^25 + 31 * q^26 + 88 * q^27 + 33 * q^28 + 83 * q^29 + 47 * q^30 + 51 * q^31 + 88 * q^32 + 30 * q^33 + 19 * q^34 + 40 * q^35 + 108 * q^36 + 45 * q^37 + 33 * q^38 + 82 * q^39 + 25 * q^40 + 35 * q^41 + 48 * q^42 + 78 * q^43 + 70 * q^44 + 37 * q^45 + 77 * q^46 + 59 * q^47 + 22 * q^48 + 103 * q^49 + 109 * q^50 + 21 * q^51 + 31 * q^52 + 58 * q^53 + 88 * q^54 + 35 * q^55 + 33 * q^56 - 16 * q^57 + 83 * q^58 + 54 * q^59 + 47 * q^60 + 18 * q^61 + 51 * q^62 + 47 * q^63 + 88 * q^64 + 34 * q^65 + 30 * q^66 + 88 * q^67 + 19 * q^68 + 62 * q^69 + 40 * q^70 + 139 * q^71 + 108 * q^72 - 6 * q^73 + 45 * q^74 + 45 * q^75 + 33 * q^76 + 37 * q^77 + 82 * q^78 + 94 * q^79 + 25 * q^80 + 112 * q^81 + 35 * q^82 + 58 * q^83 + 48 * q^84 + 83 * q^85 + 78 * q^86 + 21 * q^87 + 70 * q^88 + 99 * q^89 + 37 * q^90 + 53 * q^91 + 77 * q^92 + 57 * q^93 + 59 * q^94 + 92 * q^95 + 22 * q^96 + 16 * q^97 + 103 * q^98 + 150 * q^99

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