LMFDB - Embedded newform 8015.2.a.n.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.40730 q^{2} +0.0150324 q^{3} +3.79510 q^{4} -1.00000 q^{5} -0.0361876 q^{6} +1.00000 q^{7} -4.32135 q^{8} -2.99977 q^{9} +O(q^{10})$	\(q-2.40730 q^{2} +0.0150324 q^{3} +3.79510 q^{4} -1.00000 q^{5} -0.0361876 q^{6} +1.00000 q^{7} -4.32135 q^{8} -2.99977 q^{9} +2.40730 q^{10} -1.24626 q^{11} +0.0570496 q^{12} -0.904643 q^{13} -2.40730 q^{14} -0.0150324 q^{15} +2.81258 q^{16} -4.55036 q^{17} +7.22136 q^{18} +2.40461 q^{19} -3.79510 q^{20} +0.0150324 q^{21} +3.00012 q^{22} -5.57664 q^{23} -0.0649604 q^{24} +1.00000 q^{25} +2.17775 q^{26} -0.0901912 q^{27} +3.79510 q^{28} -1.34156 q^{29} +0.0361876 q^{30} -4.09048 q^{31} +1.87196 q^{32} -0.0187343 q^{33} +10.9541 q^{34} -1.00000 q^{35} -11.3844 q^{36} +10.8629 q^{37} -5.78863 q^{38} -0.0135990 q^{39} +4.32135 q^{40} -4.44199 q^{41} -0.0361876 q^{42} +0.567953 q^{43} -4.72968 q^{44} +2.99977 q^{45} +13.4247 q^{46} -9.43516 q^{47} +0.0422800 q^{48} +1.00000 q^{49} -2.40730 q^{50} -0.0684030 q^{51} -3.43321 q^{52} +0.0112945 q^{53} +0.217117 q^{54} +1.24626 q^{55} -4.32135 q^{56} +0.0361472 q^{57} +3.22954 q^{58} -13.7977 q^{59} -0.0570496 q^{60} -8.96801 q^{61} +9.84702 q^{62} -2.99977 q^{63} -10.1315 q^{64} +0.904643 q^{65} +0.0450992 q^{66} -9.00966 q^{67} -17.2691 q^{68} -0.0838306 q^{69} +2.40730 q^{70} +3.44666 q^{71} +12.9631 q^{72} +8.30667 q^{73} -26.1502 q^{74} +0.0150324 q^{75} +9.12575 q^{76} -1.24626 q^{77} +0.0327369 q^{78} +11.0887 q^{79} -2.81258 q^{80} +8.99797 q^{81} +10.6932 q^{82} +7.73366 q^{83} +0.0570496 q^{84} +4.55036 q^{85} -1.36723 q^{86} -0.0201669 q^{87} +5.38552 q^{88} -15.0474 q^{89} -7.22136 q^{90} -0.904643 q^{91} -21.1639 q^{92} -0.0614899 q^{93} +22.7133 q^{94} -2.40461 q^{95} +0.0281401 q^{96} -16.3881 q^{97} -2.40730 q^{98} +3.73850 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9}+O(q^{10}) $ 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9} - 9 q^{10} + 5 q^{11} + 9 q^{12} + 15 q^{13} + 9 q^{14} + 109 q^{16} + 7 q^{17} + 39 q^{18} + 20 q^{19} - 83 q^{20} + 56 q^{22} + 36 q^{23} + q^{24} + 68 q^{25} + q^{26} + 12 q^{27} + 83 q^{28} - 16 q^{29} - 5 q^{30} + 31 q^{31} + 79 q^{32} + 45 q^{33} + 31 q^{34} - 68 q^{35} + 114 q^{36} + 72 q^{37} + 8 q^{38} + 47 q^{39} - 30 q^{40} + 6 q^{41} + 5 q^{42} + 75 q^{43} + 15 q^{44} - 86 q^{45} + 29 q^{46} - 10 q^{47} + 44 q^{48} + 68 q^{49} + 9 q^{50} + 23 q^{51} + 37 q^{52} + 41 q^{53} + 4 q^{54} - 5 q^{55} + 30 q^{56} + 55 q^{57} + 66 q^{58} - 5 q^{59} - 9 q^{60} - 2 q^{61} + 3 q^{62} + 86 q^{63} + 162 q^{64} - 15 q^{65} - 23 q^{66} + 92 q^{67} + 35 q^{68} - 25 q^{69} - 9 q^{70} - 2 q^{71} + 128 q^{72} + 80 q^{73} + 18 q^{74} + 71 q^{76} + 5 q^{77} + 20 q^{78} + 100 q^{79} - 109 q^{80} + 140 q^{81} + 36 q^{82} - 60 q^{83} + 9 q^{84} - 7 q^{85} - 27 q^{86} + 24 q^{87} + 175 q^{88} + 19 q^{89} - 39 q^{90} + 15 q^{91} + 75 q^{92} + 37 q^{93} + 11 q^{94} - 20 q^{95} + 15 q^{96} + 96 q^{97} + 9 q^{98} + 3 q^{99}+O(q^{100}) \) 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9 - 9 * q^10 + 5 * q^11 + 9 * q^12 + 15 * q^13 + 9 * q^14 + 109 * q^16 + 7 * q^17 + 39 * q^18 + 20 * q^19 - 83 * q^20 + 56 * q^22 + 36 * q^23 + q^24 + 68 * q^25 + q^26 + 12 * q^27 + 83 * q^28 - 16 * q^29 - 5 * q^30 + 31 * q^31 + 79 * q^32 + 45 * q^33 + 31 * q^34 - 68 * q^35 + 114 * q^36 + 72 * q^37 + 8 * q^38 + 47 * q^39 - 30 * q^40 + 6 * q^41 + 5 * q^42 + 75 * q^43 + 15 * q^44 - 86 * q^45 + 29 * q^46 - 10 * q^47 + 44 * q^48 + 68 * q^49 + 9 * q^50 + 23 * q^51 + 37 * q^52 + 41 * q^53 + 4 * q^54 - 5 * q^55 + 30 * q^56 + 55 * q^57 + 66 * q^58 - 5 * q^59 - 9 * q^60 - 2 * q^61 + 3 * q^62 + 86 * q^63 + 162 * q^64 - 15 * q^65 - 23 * q^66 + 92 * q^67 + 35 * q^68 - 25 * q^69 - 9 * q^70 - 2 * q^71 + 128 * q^72 + 80 * q^73 + 18 * q^74 + 71 * q^76 + 5 * q^77 + 20 * q^78 + 100 * q^79 - 109 * q^80 + 140 * q^81 + 36 * q^82 - 60 * q^83 + 9 * q^84 - 7 * q^85 - 27 * q^86 + 24 * q^87 + 175 * q^88 + 19 * q^89 - 39 * q^90 + 15 * q^91 + 75 * q^92 + 37 * q^93 + 11 * q^94 - 20 * q^95 + 15 * q^96 + 96 * q^97 + 9 * q^98 + 3 * 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 $

$2$	−2.40730	−1.70222	−0.851110	−	0.524988i	$-0.824070\pi$
$2$	−2.40730	−1.70222	−0.851110	+	0.524988i	$0.824070\pi$
$3$	0.0150324	0.00867898	0.00433949	−	0.999991i	$-0.498619\pi$
$3$	0.0150324	0.00867898	0.00433949	+	0.999991i	$0.498619\pi$
$4$	3.79510	1.89755
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.0361876	−0.0147735
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−4.32135	−1.52783
$9$	−2.99977	−0.999925
$10$	2.40730	0.761256
$11$	−1.24626	−0.375761	−0.187881	−	0.982192i	$-0.560162\pi$
$11$	−1.24626	−0.375761	−0.187881	+	0.982192i	$0.560162\pi$
$12$	0.0570496	0.0164688
$13$	−0.904643	−0.250903	−0.125451	−	0.992100i	$-0.540038\pi$
$13$	−0.904643	−0.250903	−0.125451	+	0.992100i	$0.540038\pi$
$14$	−2.40730	−0.643378
$15$	−0.0150324	−0.00388136
$16$	2.81258	0.703146
$17$	−4.55036	−1.10362	−0.551812	−	0.833968i	$-0.686064\pi$
$17$	−4.55036	−1.10362	−0.551812	+	0.833968i	$0.686064\pi$
$18$	7.22136	1.70209
$19$	2.40461	0.551656	0.275828	−	0.961207i	$-0.411048\pi$
$19$	2.40461	0.551656	0.275828	+	0.961207i	$0.411048\pi$
$20$	−3.79510	−0.848610
$21$	0.0150324	0.00328035
$22$	3.00012	0.639628
$23$	−5.57664	−1.16281	−0.581405	−	0.813614i	$-0.697497\pi$
$23$	−5.57664	−1.16281	−0.581405	+	0.813614i	$0.697497\pi$
$24$	−0.0649604	−0.0132600
$25$	1.00000	0.200000
$26$	2.17775	0.427092
$27$	−0.0901912	−0.0173573
$28$	3.79510	0.717206
$29$	−1.34156	−0.249121	−0.124561	−	0.992212i	$-0.539752\pi$
$29$	−1.34156	−0.249121	−0.124561	+	0.992212i	$0.539752\pi$
$30$	0.0361876	0.00660692
$31$	−4.09048	−0.734672	−0.367336	−	0.930088i	$-0.619730\pi$
$31$	−4.09048	−0.734672	−0.367336	+	0.930088i	$0.619730\pi$
$32$	1.87196	0.330919
$33$	−0.0187343	−0.00326123
$34$	10.9541	1.87861
$35$	−1.00000	−0.169031
$36$	−11.3844	−1.89741
$37$	10.8629	1.78584	0.892921	−	0.450213i	$-0.148652\pi$
$37$	10.8629	1.78584	0.892921	+	0.450213i	$0.148652\pi$
$38$	−5.78863	−0.939040
$39$	−0.0135990	−0.00217758
$40$	4.32135	0.683265
$41$	−4.44199	−0.693722	−0.346861	−	0.937917i	$-0.612752\pi$
$41$	−4.44199	−0.693722	−0.346861	+	0.937917i	$0.612752\pi$
$42$	−0.0361876	−0.00558387
$43$	0.567953	0.0866120	0.0433060	−	0.999062i	$-0.486211\pi$
$43$	0.567953	0.0866120	0.0433060	+	0.999062i	$0.486211\pi$
$44$	−4.72968	−0.713026
$45$	2.99977	0.447180
$46$	13.4247	1.97936
$47$	−9.43516	−1.37626	−0.688130	−	0.725587i	$-0.741568\pi$
$47$	−9.43516	−1.37626	−0.688130	+	0.725587i	$0.741568\pi$
$48$	0.0422800	0.00610259
$49$	1.00000	0.142857
$50$	−2.40730	−0.340444
$51$	−0.0684030	−0.00957834
$52$	−3.43321	−0.476101
$53$	0.0112945	0.00155142	0.000775710	−	1.00000i	$-0.499753\pi$
$53$	0.0112945	0.00155142	0.000775710		1.00000i	$0.499753\pi$
$54$	0.217117	0.0295459
$55$	1.24626	0.168046
$56$	−4.32135	−0.577464
$57$	0.0361472	0.00478782
$58$	3.22954	0.424059
$59$	−13.7977	−1.79631	−0.898156	−	0.439676i	$-0.855093\pi$
$59$	−13.7977	−1.79631	−0.898156	+	0.439676i	$0.855093\pi$
$60$	−0.0570496	−0.00736507
$61$	−8.96801	−1.14824	−0.574118	−	0.818773i	$-0.694655\pi$
$61$	−8.96801	−1.14824	−0.574118	+	0.818773i	$0.694655\pi$
$62$	9.84702	1.25057
$63$	−2.99977	−0.377936
$64$	−10.1315	−1.26644
$65$	0.904643	0.112207
$66$	0.0450992	0.00555132
$67$	−9.00966	−1.10071	−0.550353	−	0.834932i	$-0.685507\pi$
$67$	−9.00966	−1.10071	−0.550353	+	0.834932i	$0.685507\pi$
$68$	−17.2691	−2.09418
$69$	−0.0838306	−0.0100920
$70$	2.40730	0.287728
$71$	3.44666	0.409043	0.204521	−	0.978862i	$-0.434436\pi$
$71$	3.44666	0.409043	0.204521	+	0.978862i	$0.434436\pi$
$72$	12.9631	1.52771
$73$	8.30667	0.972222	0.486111	−	0.873897i	$-0.338415\pi$
$73$	8.30667	0.972222	0.486111	+	0.873897i	$0.338415\pi$
$74$	−26.1502	−3.03989
$75$	0.0150324	0.00173580
$76$	9.12575	1.04680
$77$	−1.24626	−0.142024
$78$	0.0327369	0.00370672
$79$	11.0887	1.24758	0.623791	−	0.781591i	$-0.285592\pi$
$79$	11.0887	1.24758	0.623791	+	0.781591i	$0.285592\pi$
$80$	−2.81258	−0.314456
$81$	8.99797	0.999774
$82$	10.6932	1.18087
$83$	7.73366	0.848879	0.424440	−	0.905456i	$-0.360471\pi$
$83$	7.73366	0.848879	0.424440	+	0.905456i	$0.360471\pi$
$84$	0.0570496	0.00622462
$85$	4.55036	0.493556
$86$	−1.36723	−0.147433
$87$	−0.0201669	−0.00216212
$88$	5.38552	0.574098
$89$	−15.0474	−1.59503	−0.797513	−	0.603302i	$-0.793851\pi$
$89$	−15.0474	−1.59503	−0.797513	+	0.603302i	$0.793851\pi$
$90$	−7.22136	−0.761198
$91$	−0.904643	−0.0948324
$92$	−21.1639	−2.20649
$93$	−0.0614899	−0.00637620
$94$	22.7133	2.34270
$95$	−2.40461	−0.246708
$96$	0.0281401	0.00287204
$97$	−16.3881	−1.66396	−0.831981	−	0.554804i	$-0.812793\pi$
$97$	−16.3881	−1.66396	−0.831981	+	0.554804i	$0.812793\pi$
$98$	−2.40730	−0.243174
$99$	3.73850	0.375733
$100$	3.79510	0.379510
$101$	9.83314	0.978434	0.489217	−	0.872162i	$-0.337283\pi$
$101$	9.83314	0.978434	0.489217	+	0.872162i	$0.337283\pi$
$102$	0.164667	0.0163044
$103$	−17.1584	−1.69067	−0.845335	−	0.534237i	$-0.820599\pi$
$103$	−17.1584	−1.69067	−0.845335	+	0.534237i	$0.820599\pi$
$104$	3.90928	0.383336
$105$	−0.0150324	−0.00146702
$106$	−0.0271893	−0.00264086
$107$	12.4897	1.20743	0.603713	−	0.797202i	$-0.293687\pi$
$107$	12.4897	1.20743	0.603713	+	0.797202i	$0.293687\pi$
$108$	−0.342285	−0.0329364
$109$	19.2685	1.84558	0.922792	−	0.385298i	$-0.125901\pi$
$109$	19.2685	1.84558	0.922792	+	0.385298i	$0.125901\pi$
$110$	−3.00012	−0.286050
$111$	0.163295	0.0154993
$112$	2.81258	0.265764
$113$	−9.63998	−0.906853	−0.453426	−	0.891294i	$-0.649798\pi$
$113$	−9.63998	−0.906853	−0.453426	+	0.891294i	$0.649798\pi$
$114$	−0.0870172	−0.00814991
$115$	5.57664	0.520025
$116$	−5.09135	−0.472720
$117$	2.71373	0.250884
$118$	33.2153	3.05772
$119$	−4.55036	−0.417131
$120$	0.0649604	0.00593004
$121$	−9.44684	−0.858803
$122$	21.5887	1.95455
$123$	−0.0667739	−0.00602080
$124$	−15.5238	−1.39408
$125$	−1.00000	−0.0894427
$126$	7.22136	0.643330
$127$	−2.32013	−0.205878	−0.102939	−	0.994688i	$-0.532825\pi$
$127$	−2.32013	−0.205878	−0.102939	+	0.994688i	$0.532825\pi$
$128$	20.6457	1.82484
$129$	0.00853771	0.000751704 0
$130$	−2.17775	−0.191001
$131$	−6.91324	−0.604012	−0.302006	−	0.953306i	$-0.597656\pi$
$131$	−6.91324	−0.604012	−0.302006	+	0.953306i	$0.597656\pi$
$132$	−0.0710986	−0.00618834
$133$	2.40461	0.208507
$134$	21.6890	1.87364
$135$	0.0901912	0.00776242
$136$	19.6637	1.68615
$137$	5.76866	0.492850	0.246425	−	0.969162i	$-0.420744\pi$
$137$	5.76866	0.492850	0.246425	+	0.969162i	$0.420744\pi$
$138$	0.201805	0.0171788
$139$	−22.7022	−1.92558	−0.962788	−	0.270258i	$-0.912891\pi$
$139$	−22.7022	−1.92558	−0.962788	+	0.270258i	$0.912891\pi$
$140$	−3.79510	−0.320744
$141$	−0.141833	−0.0119445
$142$	−8.29714	−0.696280
$143$	1.12742	0.0942796
$144$	−8.43711	−0.703093
$145$	1.34156	0.111410
$146$	−19.9967	−1.65494
$147$	0.0150324	0.00123985
$148$	41.2256	3.38872
$149$	−4.16235	−0.340993	−0.170497	−	0.985358i	$-0.554537\pi$
$149$	−4.16235	−0.340993	−0.170497	+	0.985358i	$0.554537\pi$
$150$	−0.0361876	−0.00295471
$151$	−3.88793	−0.316396	−0.158198	−	0.987407i	$-0.550568\pi$
$151$	−3.88793	−0.316396	−0.158198	+	0.987407i	$0.550568\pi$
$152$	−10.3912	−0.842835
$153$	13.6501	1.10354
$154$	3.00012	0.241757
$155$	4.09048	0.328555
$156$	−0.0516095	−0.00413207
$157$	8.13590	0.649315	0.324658	−	0.945832i	$-0.394751\pi$
$157$	8.13590	0.649315	0.324658	+	0.945832i	$0.394751\pi$
$158$	−26.6940	−2.12366
$159$	0.000169784 0	1.34647e−5 0
$160$	−1.87196	−0.147991
$161$	−5.57664	−0.439501
$162$	−21.6608	−1.70183
$163$	4.83591	0.378778	0.189389	−	0.981902i	$-0.439349\pi$
$163$	4.83591	0.378778	0.189389	+	0.981902i	$0.439349\pi$
$164$	−16.8578	−1.31637
$165$	0.0187343	0.00145846
$166$	−18.6172	−1.44498
$167$	18.5990	1.43923	0.719617	−	0.694371i	$-0.244317\pi$
$167$	18.5990	1.43923	0.719617	+	0.694371i	$0.244317\pi$
$168$	−0.0649604	−0.00501180
$169$	−12.1816	−0.937048
$170$	−10.9541	−0.840140
$171$	−7.21330	−0.551615
$172$	2.15544	0.164351
$173$	6.35512	0.483171	0.241585	−	0.970380i	$-0.422333\pi$
$173$	6.35512	0.483171	0.241585	+	0.970380i	$0.422333\pi$
$174$	0.0485478	0.00368040
$175$	1.00000	0.0755929
$176$	−3.50521	−0.264215
$177$	−0.207414	−0.0155902
$178$	36.2237	2.71508
$179$	7.17436	0.536237	0.268119	−	0.963386i	$-0.413598\pi$
$179$	7.17436	0.536237	0.268119	+	0.963386i	$0.413598\pi$
$180$	11.3844	0.848546
$181$	13.6821	1.01698	0.508491	−	0.861067i	$-0.330203\pi$
$181$	13.6821	1.01698	0.508491	+	0.861067i	$0.330203\pi$
$182$	2.17775	0.161425
$183$	−0.134811	−0.00996552
$184$	24.0986	1.77657
$185$	−10.8629	−0.798653
$186$	0.148025	0.0108537
$187$	5.67093	0.414700
$188$	−35.8074	−2.61152
$189$	−0.0901912	−0.00656045
$190$	5.78863	0.419951
$191$	−8.07239	−0.584098	−0.292049	−	0.956403i	$-0.594337\pi$
$191$	−8.07239	−0.584098	−0.292049	+	0.956403i	$0.594337\pi$
$192$	−0.152302	−0.0109914
$193$	4.26372	0.306910	0.153455	−	0.988156i	$-0.450960\pi$
$193$	4.26372	0.306910	0.153455	+	0.988156i	$0.450960\pi$
$194$	39.4512	2.83243
$195$	0.0135990	0.000973844 0
$196$	3.79510	0.271079
$197$	6.87052	0.489505	0.244752	−	0.969586i	$-0.421293\pi$
$197$	6.87052	0.489505	0.244752	+	0.969586i	$0.421293\pi$
$198$	−8.99969	−0.639580
$199$	1.59944	0.113381	0.0566907	−	0.998392i	$-0.481945\pi$
$199$	1.59944	0.113381	0.0566907	+	0.998392i	$0.481945\pi$
$200$	−4.32135	−0.305565
$201$	−0.135437	−0.00955300
$202$	−23.6713	−1.66551
$203$	−1.34156	−0.0941590
$204$	−0.259596	−0.0181754
$205$	4.44199	0.310242
$206$	41.3055	2.87789
$207$	16.7287	1.16272
$208$	−2.54438	−0.176421
$209$	−2.99677	−0.207291
$210$	0.0361876	0.00249718
$211$	10.7921	0.742958	0.371479	−	0.928441i	$-0.378851\pi$
$211$	10.7921	0.742958	0.371479	+	0.928441i	$0.378851\pi$
$212$	0.0428638	0.00294390
$213$	0.0518116	0.00355007
$214$	−30.0665	−2.05530
$215$	−0.567953	−0.0387341
$216$	0.389747	0.0265190
$217$	−4.09048	−0.277680
$218$	−46.3850	−3.14159
$219$	0.124870	0.00843790
$220$	4.72968	0.318875
$221$	4.11645	0.276903
$222$	−0.393101	−0.0263832
$223$	16.2529	1.08837	0.544186	−	0.838965i	$-0.316839\pi$
$223$	16.2529	1.08837	0.544186	+	0.838965i	$0.316839\pi$
$224$	1.87196	0.125076
$225$	−2.99977	−0.199985
$226$	23.2063	1.54366
$227$	−0.702563	−0.0466307	−0.0233154	−	0.999728i	$-0.507422\pi$
$227$	−0.702563	−0.0466307	−0.0233154	+	0.999728i	$0.507422\pi$
$228$	0.137182	0.00908512
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−13.4247	−0.885196
$231$	−0.0187343	−0.00123263
$232$	5.79734	0.380614
$233$	16.4092	1.07500	0.537502	−	0.843262i	$-0.319368\pi$
$233$	16.4092	1.07500	0.537502	+	0.843262i	$0.319368\pi$
$234$	−6.53275	−0.427060
$235$	9.43516	0.615482
$236$	−52.3638	−3.40859
$237$	0.166691	0.0108277
$238$	10.9541	0.710048
$239$	−18.1220	−1.17222	−0.586108	−	0.810233i	$-0.699340\pi$
$239$	−18.1220	−1.17222	−0.586108	+	0.810233i	$0.699340\pi$
$240$	−0.0422800	−0.00272916
$241$	−18.0933	−1.16549	−0.582747	−	0.812654i	$-0.698022\pi$
$241$	−18.0933	−1.16549	−0.582747	+	0.812654i	$0.698022\pi$
$242$	22.7414	1.46187
$243$	0.405835	0.0260343
$244$	−34.0345	−2.17883
$245$	−1.00000	−0.0638877
$246$	0.160745	0.0102487
$247$	−2.17532	−0.138412
$248$	17.6764	1.12245
$249$	0.116256	0.00736741
$250$	2.40730	0.152251
$251$	−11.9353	−0.753348	−0.376674	−	0.926346i	$-0.622932\pi$
$251$	−11.9353	−0.753348	−0.376674	+	0.926346i	$0.622932\pi$
$252$	−11.3844	−0.717152
$253$	6.94995	0.436939
$254$	5.58524	0.350449
$255$	0.0684030	0.00428356
$256$	−29.4374	−1.83984
$257$	2.57684	0.160739	0.0803695	−	0.996765i	$-0.474390\pi$
$257$	2.57684	0.160739	0.0803695	+	0.996765i	$0.474390\pi$
$258$	−0.0205528	−0.00127956
$259$	10.8629	0.674985
$260$	3.43321	0.212919
$261$	4.02437	0.249102
$262$	16.6422	1.02816
$263$	10.4367	0.643552	0.321776	−	0.946816i	$-0.395720\pi$
$263$	10.4367	0.643552	0.321776	+	0.946816i	$0.395720\pi$
$264$	0.0809575	0.00498259
$265$	−0.0112945	−0.000693816 0
$266$	−5.78863	−0.354924
$267$	−0.226200	−0.0138432
$268$	−34.1926	−2.08864
$269$	22.1844	1.35261	0.676303	−	0.736623i	$-0.263581\pi$
$269$	22.1844	1.35261	0.676303	+	0.736623i	$0.263581\pi$
$270$	−0.217117	−0.0132133
$271$	−6.27734	−0.381321	−0.190661	−	0.981656i	$-0.561063\pi$
$271$	−6.27734	−0.381321	−0.190661	+	0.981656i	$0.561063\pi$
$272$	−12.7983	−0.776009
$273$	−0.0135990	−0.000823048 0
$274$	−13.8869	−0.838938
$275$	−1.24626	−0.0751523
$276$	−0.318145	−0.0191501
$277$	31.0783	1.86732	0.933658	−	0.358165i	$-0.116597\pi$
$277$	31.0783	1.86732	0.933658	+	0.358165i	$0.116597\pi$
$278$	54.6510	3.27775
$279$	12.2705	0.734617
$280$	4.32135	0.258250
$281$	−25.0706	−1.49559	−0.747795	−	0.663930i	$-0.768887\pi$
$281$	−25.0706	−1.49559	−0.747795	+	0.663930i	$0.768887\pi$
$282$	0.341436	0.0203322
$283$	7.98646	0.474746	0.237373	−	0.971419i	$-0.423714\pi$
$283$	7.98646	0.474746	0.237373	+	0.971419i	$0.423714\pi$
$284$	13.0804	0.776179
$285$	−0.0361472	−0.00214118
$286$	−2.71404	−0.160485
$287$	−4.44199	−0.262202
$288$	−5.61545	−0.330894
$289$	3.70579	0.217988
$290$	−3.22954	−0.189645
$291$	−0.246354	−0.0144415
$292$	31.5246	1.84484
$293$	−19.2566	−1.12498	−0.562492	−	0.826803i	$-0.690157\pi$
$293$	−19.2566	−1.12498	−0.562492	+	0.826803i	$0.690157\pi$
$294$	−0.0361876	−0.00211050
$295$	13.7977	0.803336
$296$	−46.9421	−2.72846
$297$	0.112402	0.00652221
$298$	10.0200	0.580445
$299$	5.04487	0.291753
$300$	0.0570496	0.00329376
$301$	0.567953	0.0327363
$302$	9.35943	0.538575
$303$	0.147816	0.00849181
$304$	6.76318	0.387895
$305$	8.96801	0.513507
$306$	−32.8598	−1.87847
$307$	13.6570	0.779448	0.389724	−	0.920932i	$-0.372570\pi$
$307$	13.6570	0.779448	0.389724	+	0.920932i	$0.372570\pi$
$308$	−4.72968	−0.269499
$309$	−0.257933	−0.0146733
$310$	−9.84702	−0.559273
$311$	17.4691	0.990579	0.495290	−	0.868728i	$-0.335062\pi$
$311$	17.4691	0.990579	0.495290	+	0.868728i	$0.335062\pi$
$312$	0.0587659	0.00332697
$313$	11.8908	0.672106	0.336053	−	0.941843i	$-0.390908\pi$
$313$	11.8908	0.672106	0.336053	+	0.941843i	$0.390908\pi$
$314$	−19.5856	−1.10528
$315$	2.99977	0.169018
$316$	42.0829	2.36735
$317$	−1.75183	−0.0983926	−0.0491963	−	0.998789i	$-0.515666\pi$
$317$	−1.75183	−0.0983926	−0.0491963	+	0.998789i	$0.515666\pi$
$318$	−0.000408721 0	−2.29199e−5 0
$319$	1.67193	0.0936101
$320$	10.1315	0.566370
$321$	0.187751	0.0104792
$322$	13.4247	0.748127
$323$	−10.9419	−0.608822
$324$	34.1482	1.89712
$325$	−0.904643	−0.0501806
$326$	−11.6415	−0.644762
$327$	0.289652	0.0160178
$328$	19.1954	1.05989
$329$	−9.43516	−0.520177
$330$	−0.0450992	−0.00248263
$331$	−1.07923	−0.0593201	−0.0296600	−	0.999560i	$-0.509442\pi$
$331$	−1.07923	−0.0593201	−0.0296600	+	0.999560i	$0.509442\pi$
$332$	29.3500	1.61079
$333$	−32.5861	−1.78571
$334$	−44.7734	−2.44989
$335$	9.00966	0.492250
$336$	0.0422800	0.00230656
$337$	−35.6496	−1.94196	−0.970978	−	0.239171i	$-0.923124\pi$
$337$	−35.6496	−1.94196	−0.970978	+	0.239171i	$0.923124\pi$
$338$	29.3248	1.59506
$339$	−0.144912	−0.00787056
$340$	17.2691	0.936547
$341$	5.09780	0.276061
$342$	17.3646	0.938969
$343$	1.00000	0.0539949
$344$	−2.45432	−0.132328
$345$	0.0838306	0.00451329
$346$	−15.2987	−0.822463
$347$	27.3566	1.46858	0.734289	−	0.678837i	$-0.237516\pi$
$347$	27.3566	1.46858	0.734289	+	0.678837i	$0.237516\pi$
$348$	−0.0765354	−0.00410273
$349$	6.92345	0.370604	0.185302	−	0.982682i	$-0.440674\pi$
$349$	6.92345	0.370604	0.185302	+	0.982682i	$0.440674\pi$
$350$	−2.40730	−0.128676
$351$	0.0815909	0.00435500
$352$	−2.33295	−0.124346
$353$	20.7772	1.10586	0.552930	−	0.833228i	$-0.313510\pi$
$353$	20.7772	1.10586	0.552930	+	0.833228i	$0.313510\pi$
$354$	0.499307	0.0265379
$355$	−3.44666	−0.182929
$356$	−57.1065	−3.02664
$357$	−0.0684030	−0.00362027
$358$	−17.2709	−0.912793
$359$	−34.9362	−1.84386	−0.921931	−	0.387355i	$-0.873389\pi$
$359$	−34.9362	−1.84386	−0.921931	+	0.387355i	$0.873389\pi$
$360$	−12.9631	−0.683213
$361$	−13.2178	−0.695675
$362$	−32.9369	−1.73113
$363$	−0.142009	−0.00745354
$364$	−3.43321	−0.179949
$365$	−8.30667	−0.434791
$366$	0.324531	0.0169635
$367$	−17.3240	−0.904308	−0.452154	−	0.891940i	$-0.649344\pi$
$367$	−17.3240	−0.904308	−0.452154	+	0.891940i	$0.649344\pi$
$368$	−15.6848	−0.817625
$369$	13.3250	0.693669
$370$	26.1502	1.35948
$371$	0.0112945	0.000586381 0
$372$	−0.233360	−0.0120992
$373$	−28.0903	−1.45446	−0.727230	−	0.686394i	$-0.759193\pi$
$373$	−28.0903	−1.45446	−0.727230	+	0.686394i	$0.759193\pi$
$374$	−13.6516	−0.705910
$375$	−0.0150324	−0.000776272 0
$376$	40.7726	2.10269
$377$	1.21363	0.0625052
$378$	0.217117	0.0111673
$379$	−10.0429	−0.515870	−0.257935	−	0.966162i	$-0.583042\pi$
$379$	−10.0429	−0.515870	−0.257935	+	0.966162i	$0.583042\pi$
$380$	−9.12575	−0.468141
$381$	−0.0348771	−0.00178681
$382$	19.4327	0.994263
$383$	−20.1625	−1.03025	−0.515127	−	0.857114i	$-0.672255\pi$
$383$	−20.1625	−1.03025	−0.515127	+	0.857114i	$0.672255\pi$
$384$	0.310356	0.0158378
$385$	1.24626	0.0635153
$386$	−10.2641	−0.522427
$387$	−1.70373	−0.0866055
$388$	−62.1946	−3.15745
$389$	18.9753	0.962084	0.481042	−	0.876698i	$-0.340259\pi$
$389$	18.9753	0.962084	0.481042	+	0.876698i	$0.340259\pi$
$390$	−0.0327369	−0.00165770
$391$	25.3757	1.28331
$392$	−4.32135	−0.218261
$393$	−0.103923	−0.00524221
$394$	−16.5394	−0.833244
$395$	−11.0887	−0.557935
$396$	14.1880	0.712972
$397$	−31.9448	−1.60326	−0.801632	−	0.597818i	$-0.796035\pi$
$397$	−31.9448	−1.60326	−0.801632	+	0.597818i	$0.796035\pi$
$398$	−3.85034	−0.193000
$399$	0.0361472	0.00180962
$400$	2.81258	0.140629
$401$	1.34651	0.0672413	0.0336207	−	0.999435i	$-0.489296\pi$
$401$	1.34651	0.0672413	0.0336207	+	0.999435i	$0.489296\pi$
$402$	0.326038	0.0162613
$403$	3.70043	0.184331
$404$	37.3177	1.85663
$405$	−8.99797	−0.447113
$406$	3.22954	0.160279
$407$	−13.5379	−0.671051
$408$	0.295593	0.0146340
$409$	22.1385	1.09468	0.547340	−	0.836910i	$-0.315640\pi$
$409$	22.1385	1.09468	0.547340	+	0.836910i	$0.315640\pi$
$410$	−10.6932	−0.528099
$411$	0.0867170	0.00427743
$412$	−65.1179	−3.20813
$413$	−13.7977	−0.678942
$414$	−40.2710	−1.97921
$415$	−7.73366	−0.379630
$416$	−1.69345	−0.0830285
$417$	−0.341269	−0.0167120
$418$	7.21414	0.352855
$419$	−7.23989	−0.353692	−0.176846	−	0.984239i	$-0.556589\pi$
$419$	−7.23989	−0.353692	−0.176846	+	0.984239i	$0.556589\pi$
$420$	−0.0570496	−0.00278374
$421$	32.1722	1.56798	0.783989	−	0.620775i	$-0.213182\pi$
$421$	32.1722	1.56798	0.783989	+	0.620775i	$0.213182\pi$
$422$	−25.9798	−1.26468
$423$	28.3034	1.37616
$424$	−0.0488075	−0.00237030
$425$	−4.55036	−0.220725
$426$	−0.124726	−0.00604300
$427$	−8.96801	−0.433992
$428$	47.3997	2.29115
$429$	0.0169479	0.000818251 0
$430$	1.36723	0.0659339
$431$	12.6041	0.607119	0.303560	−	0.952812i	$-0.401825\pi$
$431$	12.6041	0.607119	0.303560	+	0.952812i	$0.401825\pi$
$432$	−0.253670	−0.0122047
$433$	14.0345	0.674455	0.337228	−	0.941423i	$-0.390511\pi$
$433$	14.0345	0.674455	0.337228	+	0.941423i	$0.390511\pi$
$434$	9.84702	0.472672
$435$	0.0201669	0.000966929 0
$436$	73.1257	3.50209
$437$	−13.4097	−0.641472
$438$	−0.300599	−0.0143632
$439$	14.5345	0.693694	0.346847	−	0.937922i	$-0.387252\pi$
$439$	14.5345	0.693694	0.346847	+	0.937922i	$0.387252\pi$
$440$	−5.38552	−0.256745
$441$	−2.99977	−0.142846
$442$	−9.90954	−0.471349
$443$	7.30167	0.346913	0.173456	−	0.984842i	$-0.444506\pi$
$443$	7.30167	0.346913	0.173456	+	0.984842i	$0.444506\pi$
$444$	0.619721	0.0294107
$445$	15.0474	0.713317
$446$	−39.1255	−1.85265
$447$	−0.0625703	−0.00295947
$448$	−10.1315	−0.478670
$449$	0.442165	0.0208670	0.0104335	−	0.999946i	$-0.496679\pi$
$449$	0.442165	0.0208670	0.0104335	+	0.999946i	$0.496679\pi$
$450$	7.22136	0.340418
$451$	5.53587	0.260674
$452$	−36.5847	−1.72080
$453$	−0.0584451	−0.00274599
$454$	1.69128	0.0793757
$455$	0.904643	0.0424103
$456$	−0.156205	−0.00731495
$457$	−0.0243350	−0.00113834	−0.000569172	−	1.00000i	$-0.500181\pi$
$457$	−0.0243350	−0.00113834	−0.000569172		1.00000i	$0.500181\pi$
$458$	2.40730	0.112486
$459$	0.410403	0.0191560
$460$	21.1639	0.986773
$461$	−14.1974	−0.661238	−0.330619	−	0.943764i	$-0.607258\pi$
$461$	−14.1974	−0.661238	−0.330619	+	0.943764i	$0.607258\pi$
$462$	0.0450992	0.00209820
$463$	7.28314	0.338476	0.169238	−	0.985575i	$-0.445869\pi$
$463$	7.28314	0.338476	0.169238	+	0.985575i	$0.445869\pi$
$464$	−3.77324	−0.175168
$465$	0.0614899	0.00285153
$466$	−39.5020	−1.82989
$467$	−16.9943	−0.786402	−0.393201	−	0.919453i	$-0.628632\pi$
$467$	−16.9943	−0.786402	−0.393201	+	0.919453i	$0.628632\pi$
$468$	10.2989	0.476065
$469$	−9.00966	−0.416028
$470$	−22.7133	−1.04769
$471$	0.122302	0.00563540
$472$	59.6248	2.74445
$473$	−0.707817	−0.0325454
$474$	−0.401275	−0.0184312
$475$	2.40461	0.110331
$476$	−17.2691	−0.791527
$477$	−0.0338810	−0.00155130
$478$	43.6251	1.99537
$479$	−19.3428	−0.883793	−0.441896	−	0.897066i	$-0.645694\pi$
$479$	−19.3428	−0.883793	−0.441896	+	0.897066i	$0.645694\pi$
$480$	−0.0281401	−0.00128441
$481$	−9.82701	−0.448073
$482$	43.5561	1.98393
$483$	−0.0838306	−0.00381442
$484$	−35.8517	−1.62962
$485$	16.3881	0.744147
$486$	−0.976967	−0.0443161
$487$	−42.6583	−1.93303	−0.966517	−	0.256603i	$-0.917397\pi$
$487$	−42.6583	−1.93303	−0.966517	+	0.256603i	$0.917397\pi$
$488$	38.7539	1.75430
$489$	0.0726955	0.00328740
$490$	2.40730	0.108751
$491$	3.28964	0.148459	0.0742296	−	0.997241i	$-0.476350\pi$
$491$	3.28964	0.148459	0.0742296	+	0.997241i	$0.476350\pi$
$492$	−0.253414	−0.0114248
$493$	6.10458	0.274936
$494$	5.23665	0.235608
$495$	−3.73850	−0.168033
$496$	−11.5048	−0.516581
$497$	3.44666	0.154604
$498$	−0.279863	−0.0125409
$499$	−14.6730	−0.656854	−0.328427	−	0.944529i	$-0.606519\pi$
$499$	−14.6730	−0.656854	−0.328427	+	0.944529i	$0.606519\pi$
$500$	−3.79510	−0.169722
$501$	0.279588	0.0124911
$502$	28.7318	1.28236
$503$	34.0519	1.51830	0.759149	−	0.650917i	$-0.225615\pi$
$503$	34.0519	1.51830	0.759149	+	0.650917i	$0.225615\pi$
$504$	12.9631	0.577421
$505$	−9.83314	−0.437569
$506$	−16.7306	−0.743767
$507$	−0.183119	−0.00813262
$508$	−8.80511	−0.390664
$509$	−26.2156	−1.16198	−0.580992	−	0.813909i	$-0.697335\pi$
$509$	−26.2156	−1.16198	−0.580992	+	0.813909i	$0.697335\pi$
$510$	−0.164667	−0.00729156
$511$	8.30667	0.367466
$512$	29.5733	1.30697
$513$	−0.216875	−0.00957527
$514$	−6.20324	−0.273613
$515$	17.1584	0.756091
$516$	0.0324015	0.00142640
$517$	11.7587	0.517145
$518$	−26.1502	−1.14897
$519$	0.0955329	0.00419343
$520$	−3.90928	−0.171433
$521$	−3.27536	−0.143496	−0.0717480	−	0.997423i	$-0.522858\pi$
$521$	−3.27536	−0.143496	−0.0717480	+	0.997423i	$0.522858\pi$
$522$	−9.68788	−0.424027
$523$	45.5358	1.99114	0.995571	−	0.0940116i	$-0.0299691\pi$
$523$	45.5358	1.99114	0.995571	+	0.0940116i	$0.0299691\pi$
$524$	−26.2364	−1.14614
$525$	0.0150324	0.000656069 0
$526$	−25.1242	−1.09547
$527$	18.6132	0.810802
$528$	−0.0526918	−0.00229312
$529$	8.09896	0.352129
$530$	0.0271893	0.00118103
$531$	41.3901	1.79618
$532$	9.12575	0.395651
$533$	4.01841	0.174057
$534$	0.544531	0.0235642
$535$	−12.4897	−0.539977
$536$	38.9339	1.68169
$537$	0.107848	0.00465399
$538$	−53.4045	−2.30243
$539$	−1.24626	−0.0536802
$540$	0.342285	0.0147296
$541$	30.7399	1.32161	0.660805	−	0.750558i	$-0.270215\pi$
$541$	30.7399	1.32161	0.660805	+	0.750558i	$0.270215\pi$
$542$	15.1114	0.649092
$543$	0.205675	0.00882637
$544$	−8.51809	−0.365210
$545$	−19.2685	−0.825370
$546$	0.0327369	0.00140101
$547$	40.5632	1.73436	0.867179	−	0.497997i	$-0.165931\pi$
$547$	40.5632	1.73436	0.867179	+	0.497997i	$0.165931\pi$
$548$	21.8926	0.935207
$549$	26.9020	1.14815
$550$	3.00012	0.127926
$551$	−3.22593	−0.137429
$552$	0.362261	0.0154188
$553$	11.0887	0.471542
$554$	−74.8149	−3.17858
$555$	−0.163295	−0.00693149
$556$	−86.1571	−3.65388
$557$	−33.6974	−1.42780	−0.713902	−	0.700246i	$-0.753074\pi$
$557$	−33.6974	−1.42780	−0.713902	+	0.700246i	$0.753074\pi$
$558$	−29.5388	−1.25048
$559$	−0.513795	−0.0217312
$560$	−2.81258	−0.118853
$561$	0.0852479	0.00359917
$562$	60.3526	2.54582
$563$	36.0728	1.52029	0.760143	−	0.649756i	$-0.225129\pi$
$563$	36.0728	1.52029	0.760143	+	0.649756i	$0.225129\pi$
$564$	−0.538272	−0.0226653
$565$	9.63998	0.405557
$566$	−19.2258	−0.808121
$567$	8.99797	0.377879
$568$	−14.8942	−0.624946
$569$	−20.2731	−0.849892	−0.424946	−	0.905219i	$-0.639707\pi$
$569$	−20.2731	−0.849892	−0.424946	+	0.905219i	$0.639707\pi$
$570$	0.0870172	0.00364475
$571$	−9.03135	−0.377950	−0.188975	−	0.981982i	$-0.560517\pi$
$571$	−9.03135	−0.377950	−0.188975	+	0.981982i	$0.560517\pi$
$572$	4.27867	0.178900
$573$	−0.121348	−0.00506937
$574$	10.6932	0.446326
$575$	−5.57664	−0.232562
$576$	30.3923	1.26635
$577$	26.0700	1.08531	0.542654	−	0.839956i	$-0.317419\pi$
$577$	26.0700	1.08531	0.542654	+	0.839956i	$0.317419\pi$
$578$	−8.92095	−0.371063
$579$	0.0640942	0.00266366
$580$	5.09135	0.211407
$581$	7.73366	0.320846
$582$	0.593047	0.0245826
$583$	−0.0140759	−0.000582964 0
$584$	−35.8960	−1.48539
$585$	−2.71373	−0.112199
$586$	46.3565	1.91497
$587$	−37.2104	−1.53584	−0.767918	−	0.640548i	$-0.778707\pi$
$587$	−37.2104	−1.53584	−0.767918	+	0.640548i	$0.778707\pi$
$588$	0.0570496	0.00235269
$589$	−9.83603	−0.405286
$590$	−33.2153	−1.36745
$591$	0.103281	0.00424840
$592$	30.5527	1.25571
$593$	17.5755	0.721738	0.360869	−	0.932616i	$-0.382480\pi$
$593$	17.5755	0.721738	0.360869	+	0.932616i	$0.382480\pi$
$594$	−0.270585	−0.0111022
$595$	4.55036	0.186547
$596$	−15.7965	−0.647052
$597$	0.0240435	0.000984034 0
$598$	−12.1445	−0.496627
$599$	−0.556782	−0.0227495	−0.0113747	−	0.999935i	$-0.503621\pi$
$599$	−0.556782	−0.0227495	−0.0113747	+	0.999935i	$0.503621\pi$
$600$	−0.0649604	−0.00265200
$601$	3.17100	0.129348	0.0646738	−	0.997906i	$-0.479399\pi$
$601$	3.17100	0.129348	0.0646738	+	0.997906i	$0.479399\pi$
$602$	−1.36723	−0.0557243
$603$	27.0269	1.10062
$604$	−14.7551	−0.600376
$605$	9.44684	0.384069
$606$	−0.355838	−0.0144549
$607$	−1.23366	−0.0500728	−0.0250364	−	0.999687i	$-0.507970\pi$
$607$	−1.23366	−0.0500728	−0.0250364	+	0.999687i	$0.507970\pi$
$608$	4.50134	0.182553
$609$	−0.0201669	−0.000817204 0
$610$	−21.5887	−0.874101
$611$	8.53546	0.345308
$612$	51.8033	2.09403
$613$	43.2576	1.74716	0.873580	−	0.486681i	$-0.161792\pi$
$613$	43.2576	1.74716	0.873580	+	0.486681i	$0.161792\pi$
$614$	−32.8766	−1.32679
$615$	0.0667739	0.00269258
$616$	5.38552	0.216989
$617$	−34.3532	−1.38301	−0.691504	−	0.722373i	$-0.743051\pi$
$617$	−34.3532	−1.38301	−0.691504	+	0.722373i	$0.743051\pi$
$618$	0.620922	0.0249772
$619$	27.7024	1.11345	0.556727	−	0.830696i	$-0.312057\pi$
$619$	27.7024	1.11345	0.556727	+	0.830696i	$0.312057\pi$
$620$	15.5238	0.623450
$621$	0.502964	0.0201833
$622$	−42.0533	−1.68618
$623$	−15.0474	−0.602863
$624$	−0.0382483	−0.00153116
$625$	1.00000	0.0400000
$626$	−28.6246	−1.14407
$627$	−0.0450488	−0.00179908
$628$	30.8765	1.23211
$629$	−49.4299	−1.97090
$630$	−7.22136	−0.287706
$631$	13.9707	0.556167	0.278083	−	0.960557i	$-0.410301\pi$
$631$	13.9707	0.556167	0.278083	+	0.960557i	$0.410301\pi$
$632$	−47.9183	−1.90609
$633$	0.162231	0.00644812
$634$	4.21718	0.167486
$635$	2.32013	0.0920714
$636$	0.000644347 0	2.55500e−5 0
$637$	−0.904643	−0.0358433
$638$	−4.02484	−0.159345
$639$	−10.3392	−0.409012
$640$	−20.6457	−0.816094
$641$	−17.2422	−0.681025	−0.340513	−	0.940240i	$-0.610601\pi$
$641$	−17.2422	−0.681025	−0.340513	+	0.940240i	$0.610601\pi$
$642$	−0.451973	−0.0178379
$643$	49.1063	1.93657	0.968283	−	0.249857i	$-0.0803838\pi$
$643$	49.1063	1.93657	0.968283	+	0.249857i	$0.0803838\pi$
$644$	−21.1639	−0.833975
$645$	−0.00853771	−0.000336172 0
$646$	26.3404	1.03635
$647$	24.8060	0.975224	0.487612	−	0.873060i	$-0.337868\pi$
$647$	24.8060	0.975224	0.487612	+	0.873060i	$0.337868\pi$
$648$	−38.8833	−1.52748
$649$	17.1956	0.674985
$650$	2.17775	0.0854183
$651$	−0.0614899	−0.00240998
$652$	18.3528	0.718749
$653$	15.1878	0.594344	0.297172	−	0.954824i	$-0.403956\pi$
$653$	15.1878	0.594344	0.297172	+	0.954824i	$0.403956\pi$
$654$	−0.697280	−0.0272658
$655$	6.91324	0.270123
$656$	−12.4935	−0.487787
$657$	−24.9181	−0.972149
$658$	22.7133	0.885456
$659$	−22.0972	−0.860783	−0.430391	−	0.902642i	$-0.641624\pi$
$659$	−22.0972	−0.860783	−0.430391	+	0.902642i	$0.641624\pi$
$660$	0.0710986	0.00276751
$661$	24.0755	0.936428	0.468214	−	0.883615i	$-0.344898\pi$
$661$	24.0755	0.936428	0.468214	+	0.883615i	$0.344898\pi$
$662$	2.59804	0.100976
$663$	0.0618803	0.00240323
$664$	−33.4198	−1.29694
$665$	−2.40461	−0.0932469
$666$	78.4446	3.03967
$667$	7.48140	0.289681
$668$	70.5851	2.73102
$669$	0.244320	0.00944596
$670$	−21.6890	−0.837918
$671$	11.1765	0.431463
$672$	0.0281401	0.00108553
$673$	30.2748	1.16701	0.583504	−	0.812111i	$-0.301681\pi$
$673$	30.2748	1.16701	0.583504	+	0.812111i	$0.301681\pi$
$674$	85.8192	3.30563
$675$	−0.0901912	−0.00347146
$676$	−46.2305	−1.77809
$677$	−39.9404	−1.53503	−0.767517	−	0.641028i	$-0.778508\pi$
$677$	−39.9404	−1.53503	−0.767517	+	0.641028i	$0.778508\pi$
$678$	0.348848	0.0133974
$679$	−16.3881	−0.628919
$680$	−19.6637	−0.754068
$681$	−0.0105612	−0.000404707 0
$682$	−12.2719	−0.469917
$683$	40.2439	1.53989	0.769944	−	0.638111i	$-0.220284\pi$
$683$	40.2439	1.53989	0.769944	+	0.638111i	$0.220284\pi$
$684$	−27.3752	−1.04672
$685$	−5.76866	−0.220409
$686$	−2.40730	−0.0919112
$687$	−0.0150324	−0.000573523 0
$688$	1.59741	0.0609008
$689$	−0.0102175	−0.000389256 0
$690$	−0.201805	−0.00768260
$691$	−25.0030	−0.951159	−0.475580	−	0.879673i	$-0.657762\pi$
$691$	−25.0030	−0.951159	−0.475580	+	0.879673i	$0.657762\pi$
$692$	24.1183	0.916841
$693$	3.73850	0.142014
$694$	−65.8555	−2.49984
$695$	22.7022	0.861144
$696$	0.0871481	0.00330334
$697$	20.2126	0.765608
$698$	−16.6668	−0.630849
$699$	0.246671	0.00932994
$700$	3.79510	0.143441
$701$	−35.6530	−1.34659	−0.673297	−	0.739372i	$-0.735123\pi$
$701$	−35.6530	−1.34659	−0.673297	+	0.739372i	$0.735123\pi$
$702$	−0.196414	−0.00741316
$703$	26.1210	0.985171
$704$	12.6265	0.475880
$705$	0.141833	0.00534176
$706$	−50.0170	−1.88241
$707$	9.83314	0.369813
$708$	−0.787156	−0.0295831
$709$	−31.6689	−1.18935	−0.594676	−	0.803966i	$-0.702719\pi$
$709$	−31.6689	−1.18935	−0.594676	+	0.803966i	$0.702719\pi$
$710$	8.29714	0.311386
$711$	−33.2637	−1.24749
$712$	65.0252	2.43692
$713$	22.8112	0.854284
$714$	0.164667	0.00616250
$715$	−1.12742	−0.0421631
$716$	27.2274	1.01754
$717$	−0.272418	−0.0101736
$718$	84.1019	3.13866
$719$	32.9160	1.22756	0.613779	−	0.789478i	$-0.289648\pi$
$719$	32.9160	1.22756	0.613779	+	0.789478i	$0.289648\pi$
$720$	8.43711	0.314433
$721$	−17.1584	−0.639013
$722$	31.8193	1.18419
$723$	−0.271987	−0.0101153
$724$	51.9249	1.92977
$725$	−1.34156	−0.0498242
$726$	0.341858	0.0126876
$727$	−19.5550	−0.725255	−0.362627	−	0.931934i	$-0.618120\pi$
$727$	−19.5550	−0.725255	−0.362627	+	0.931934i	$0.618120\pi$
$728$	3.90928	0.144887
$729$	−26.9878	−0.999548
$730$	19.9967	0.740110
$731$	−2.58439	−0.0955871
$732$	−0.511621	−0.0189101
$733$	−13.7050	−0.506204	−0.253102	−	0.967440i	$-0.581451\pi$
$733$	−13.7050	−0.506204	−0.253102	+	0.967440i	$0.581451\pi$
$734$	41.7042	1.53933
$735$	−0.0150324	−0.000554480 0
$736$	−10.4392	−0.384796
$737$	11.2284	0.413603
$738$	−32.0772	−1.18078
$739$	34.2366	1.25941	0.629707	−	0.776832i	$-0.283175\pi$
$739$	34.2366	1.25941	0.629707	+	0.776832i	$0.283175\pi$
$740$	−41.2256	−1.51548
$741$	−0.0327003	−0.00120128
$742$	−0.0271893	−0.000998150 0
$743$	4.58651	0.168263	0.0841313	−	0.996455i	$-0.473188\pi$
$743$	4.58651	0.168263	0.0841313	+	0.996455i	$0.473188\pi$
$744$	0.265719	0.00974173
$745$	4.16235	0.152497
$746$	67.6218	2.47581
$747$	−23.1992	−0.848815
$748$	21.5218	0.786913
$749$	12.4897	0.456364
$750$	0.0361876	0.00132138
$751$	22.6391	0.826111	0.413055	−	0.910706i	$-0.364462\pi$
$751$	22.6391	0.826111	0.413055	+	0.910706i	$0.364462\pi$
$752$	−26.5372	−0.967711
$753$	−0.179416	−0.00653829
$754$	−2.92158	−0.106398
$755$	3.88793	0.141496
$756$	−0.342285	−0.0124488
$757$	28.8501	1.04857	0.524287	−	0.851542i	$-0.324332\pi$
$757$	28.8501	1.04857	0.524287	+	0.851542i	$0.324332\pi$
$758$	24.1763	0.878123
$759$	0.104475	0.00379219
$760$	10.3912	0.376927
$761$	16.4577	0.596589	0.298295	−	0.954474i	$-0.403582\pi$
$761$	16.4577	0.596589	0.298295	+	0.954474i	$0.403582\pi$
$762$	0.0839598	0.00304154
$763$	19.2685	0.697565
$764$	−30.6355	−1.10835
$765$	−13.6501	−0.493519
$766$	48.5372	1.75372
$767$	12.4820	0.450700
$768$	−0.442516	−0.0159679
$769$	−3.41024	−0.122976	−0.0614882	−	0.998108i	$-0.519585\pi$
$769$	−3.41024	−0.122976	−0.0614882	+	0.998108i	$0.519585\pi$
$770$	−3.00012	−0.108117
$771$	0.0387362	0.00139505
$772$	16.1813	0.582376
$773$	−29.8298	−1.07290	−0.536452	−	0.843931i	$-0.680236\pi$
$773$	−29.8298	−1.07290	−0.536452	+	0.843931i	$0.680236\pi$
$774$	4.10139	0.147421
$775$	−4.09048	−0.146934
$776$	70.8188	2.54225
$777$	0.163295	0.00585818
$778$	−45.6792	−1.63768
$779$	−10.6813	−0.382696
$780$	0.0516095	0.00184792
$781$	−4.29543	−0.153702
$782$	−61.0871	−2.18447
$783$	0.120997	0.00432407
$784$	2.81258	0.100449
$785$	−8.13590	−0.290383
$786$	0.250173	0.00892339
$787$	4.93931	0.176067	0.0880337	−	0.996117i	$-0.471942\pi$
$787$	4.93931	0.176067	0.0880337	+	0.996117i	$0.471942\pi$
$788$	26.0743	0.928859
$789$	0.156888	0.00558538
$790$	26.6940	0.949728
$791$	−9.63998	−0.342758
$792$	−16.1553	−0.574055
$793$	8.11285	0.288096
$794$	76.9008	2.72911
$795$	−0.000169784 0	−6.02161e−6 0
$796$	6.07004	0.215147
$797$	33.7409	1.19516	0.597581	−	0.801808i	$-0.296128\pi$
$797$	33.7409	1.19516	0.597581	+	0.801808i	$0.296128\pi$
$798$	−0.0870172	−0.00308038
$799$	42.9334	1.51887
$800$	1.87196	0.0661837
$801$	45.1389	1.59491
$802$	−3.24145	−0.114459
$803$	−10.3523	−0.365324
$804$	−0.513998	−0.0181273
$805$	5.57664	0.196551
$806$	−8.90804	−0.313772
$807$	0.333486	0.0117392
$808$	−42.4924	−1.49488
$809$	5.07637	0.178476	0.0892378	−	0.996010i	$-0.471557\pi$
$809$	5.07637	0.178476	0.0892378	+	0.996010i	$0.471557\pi$
$810$	21.6608	0.761084
$811$	−26.6169	−0.934647	−0.467323	−	0.884086i	$-0.654782\pi$
$811$	−26.6169	−0.934647	−0.467323	+	0.884086i	$0.654782\pi$
$812$	−5.09135	−0.178671
$813$	−0.0943637	−0.00330948
$814$	32.5899	1.14228
$815$	−4.83591	−0.169394
$816$	−0.192389	−0.00673497
$817$	1.36571	0.0477801
$818$	−53.2942	−1.86339
$819$	2.71373	0.0948252
$820$	16.8578	0.588699
$821$	25.3728	0.885518	0.442759	−	0.896641i	$-0.354000\pi$
$821$	25.3728	0.885518	0.442759	+	0.896641i	$0.354000\pi$
$822$	−0.208754	−0.00728113
$823$	27.6411	0.963508	0.481754	−	0.876306i	$-0.340000\pi$
$823$	27.6411	0.963508	0.481754	+	0.876306i	$0.340000\pi$
$824$	74.1475	2.58305
$825$	−0.0187343	−0.000652245 0
$826$	33.2153	1.15571
$827$	31.8827	1.10867	0.554335	−	0.832294i	$-0.312973\pi$
$827$	31.8827	1.10867	0.554335	+	0.832294i	$0.312973\pi$
$828$	63.4870	2.20633
$829$	0.842608	0.0292650	0.0146325	−	0.999893i	$-0.495342\pi$
$829$	0.842608	0.0292650	0.0146325	+	0.999893i	$0.495342\pi$
$830$	18.6172	0.646214
$831$	0.467183	0.0162064
$832$	9.16542	0.317754
$833$	−4.55036	−0.157661
$834$	0.821538	0.0284475
$835$	−18.5990	−0.643645
$836$	−11.3731	−0.393345
$837$	0.368925	0.0127519
$838$	17.4286	0.602061
$839$	45.2929	1.56368	0.781842	−	0.623476i	$-0.214280\pi$
$839$	45.2929	1.56368	0.781842	+	0.623476i	$0.214280\pi$
$840$	0.0649604	0.00224135
$841$	−27.2002	−0.937939
$842$	−77.4482	−2.66904
$843$	−0.376873	−0.0129802
$844$	40.9570	1.40980
$845$	12.1816	0.419060
$846$	−68.1347	−2.34252
$847$	−9.44684	−0.324597
$848$	0.0317667	0.00109087
$849$	0.120056	0.00412031
$850$	10.9541	0.375722
$851$	−60.5783	−2.07660
$852$	0.196630	0.00673644
$853$	21.1457	0.724015	0.362008	−	0.932175i	$-0.382091\pi$
$853$	21.1457	0.724015	0.362008	+	0.932175i	$0.382091\pi$
$854$	21.5887	0.738750
$855$	7.21330	0.246690
$856$	−53.9724	−1.84474
$857$	11.2295	0.383594	0.191797	−	0.981435i	$-0.438568\pi$
$857$	11.2295	0.383594	0.191797	+	0.981435i	$0.438568\pi$
$858$	−0.0407986	−0.00139284
$859$	−41.9898	−1.43267	−0.716336	−	0.697755i	$-0.754182\pi$
$859$	−41.9898	−1.43267	−0.716336	+	0.697755i	$0.754182\pi$
$860$	−2.15544	−0.0734998
$861$	−0.0667739	−0.00227565
$862$	−30.3419	−1.03345
$863$	−20.4441	−0.695926	−0.347963	−	0.937508i	$-0.613126\pi$
$863$	−20.4441	−0.695926	−0.347963	+	0.937508i	$0.613126\pi$
$864$	−0.168834	−0.00574386
$865$	−6.35512	−0.216081
$866$	−33.7853	−1.14807
$867$	0.0557071	0.00189191
$868$	−15.5238	−0.526911
$869$	−13.8195	−0.468793
$870$	−0.0485478	−0.00164592
$871$	8.15053	0.276170
$872$	−83.2657	−2.81973
$873$	49.1607	1.66384
$874$	32.2811	1.09193
$875$	−1.00000	−0.0338062
$876$	0.473892	0.0160113
$877$	−37.6184	−1.27028	−0.635141	−	0.772396i	$-0.719058\pi$
$877$	−37.6184	−1.27028	−0.635141	+	0.772396i	$0.719058\pi$
$878$	−34.9889	−1.18082
$879$	−0.289474	−0.00976371
$880$	3.50521	0.118161
$881$	36.2129	1.22004	0.610021	−	0.792385i	$-0.291161\pi$
$881$	36.2129	1.22004	0.610021	+	0.792385i	$0.291161\pi$
$882$	7.22136	0.243156
$883$	−3.43611	−0.115634	−0.0578171	−	0.998327i	$-0.518414\pi$
$883$	−3.43611	−0.115634	−0.0578171	+	0.998327i	$0.518414\pi$
$884$	15.6224	0.525437
$885$	0.207414	0.00697213
$886$	−17.5773	−0.590522
$887$	−28.2373	−0.948115	−0.474057	−	0.880494i	$-0.657211\pi$
$887$	−28.2373	−0.948115	−0.474057	+	0.880494i	$0.657211\pi$
$888$	−0.705655	−0.0236802
$889$	−2.32013	−0.0778145
$890$	−36.2237	−1.21422
$891$	−11.2138	−0.375677
$892$	61.6812	2.06524
$893$	−22.6879	−0.759223
$894$	0.150626	0.00503767
$895$	−7.17436	−0.239813
$896$	20.6457	0.689726
$897$	0.0758367	0.00253212
$898$	−1.06442	−0.0355203
$899$	5.48762	0.183022
$900$	−11.3844	−0.379481
$901$	−0.0513941	−0.00171218
$902$	−13.3265	−0.443724
$903$	0.00853771	0.000284117 0
$904$	41.6577	1.38551
$905$	−13.6821	−0.454808
$906$	0.140695	0.00467428
$907$	16.3101	0.541569	0.270784	−	0.962640i	$-0.412717\pi$
$907$	16.3101	0.541569	0.270784	+	0.962640i	$0.412717\pi$
$908$	−2.66629	−0.0884841
$909$	−29.4972	−0.978360
$910$	−2.17775	−0.0721917
$911$	−11.4570	−0.379586	−0.189793	−	0.981824i	$-0.560782\pi$
$911$	−11.4570	−0.379586	−0.189793	+	0.981824i	$0.560782\pi$
$912$	0.101667	0.00336653
$913$	−9.63815	−0.318976
$914$	0.0585817	0.00193771
$915$	0.134811	0.00445671
$916$	−3.79510	−0.125394
$917$	−6.91324	−0.228295
$918$	−0.987963	−0.0326076
$919$	26.6084	0.877730	0.438865	−	0.898553i	$-0.355381\pi$
$919$	26.6084	0.877730	0.438865	+	0.898553i	$0.355381\pi$
$920$	−24.0986	−0.794508
$921$	0.205299	0.00676482
$922$	34.1774	1.12557
$923$	−3.11799	−0.102630
$924$	−0.0710986	−0.00233897
$925$	10.8629	0.357168
$926$	−17.5327	−0.576161
$927$	51.4714	1.69054
$928$	−2.51134	−0.0824389
$929$	49.8819	1.63657	0.818285	−	0.574812i	$-0.194925\pi$
$929$	49.8819	1.63657	0.818285	+	0.574812i	$0.194925\pi$
$930$	−0.148025	−0.00485392
$931$	2.40461	0.0788081
$932$	62.2747	2.03987
$933$	0.262602	0.00859722
$934$	40.9104	1.33863
$935$	−5.67093	−0.185459
$936$	−11.7269	−0.383307
$937$	−50.1176	−1.63727	−0.818636	−	0.574313i	$-0.805269\pi$
$937$	−50.1176	−1.63727	−0.818636	+	0.574313i	$0.805269\pi$
$938$	21.6890	0.708170
$939$	0.178747	0.00583319
$940$	35.8074	1.16791
$941$	44.4926	1.45042	0.725209	−	0.688529i	$-0.241743\pi$
$941$	44.4926	1.45042	0.725209	+	0.688529i	$0.241743\pi$
$942$	−0.294419	−0.00959268
$943$	24.7714	0.806667
$944$	−38.8073	−1.26307
$945$	0.0901912	0.00293392
$946$	1.70393	0.0553995
$947$	43.9909	1.42951	0.714756	−	0.699374i	$-0.246538\pi$
$947$	43.9909	1.42951	0.714756	+	0.699374i	$0.246538\pi$
$948$	0.632609	0.0205462
$949$	−7.51457	−0.243933
$950$	−5.78863	−0.187808
$951$	−0.0263343	−0.000853948 0
$952$	19.6637	0.637304
$953$	−41.0744	−1.33053	−0.665265	−	0.746607i	$-0.731682\pi$
$953$	−41.0744	−1.33053	−0.665265	+	0.746607i	$0.731682\pi$
$954$	0.0815617	0.00264066
$955$	8.07239	0.261216
$956$	−68.7748	−2.22434
$957$	0.0251332	0.000812441 0
$958$	46.5638	1.50441
$959$	5.76866	0.186280
$960$	0.152302	0.00491551
$961$	−14.2680	−0.460257
$962$	23.6566	0.762718
$963$	−37.4663	−1.20734
$964$	−68.6660	−2.21158
$965$	−4.26372	−0.137254
$966$	0.201805	0.00649298
$967$	4.00065	0.128652	0.0643261	−	0.997929i	$-0.479510\pi$
$967$	4.00065	0.128652	0.0643261	+	0.997929i	$0.479510\pi$
$968$	40.8230	1.31210
$969$	−0.164483	−0.00528395
$970$	−39.4512	−1.26670
$971$	47.1907	1.51442	0.757211	−	0.653171i	$-0.226562\pi$
$971$	47.1907	1.51442	0.757211	+	0.653171i	$0.226562\pi$
$972$	1.54018	0.0494014
$973$	−22.7022	−0.727799
$974$	102.691	3.29045
$975$	−0.0135990	−0.000435516 0
$976$	−25.2233	−0.807377
$977$	21.8802	0.700008	0.350004	−	0.936748i	$-0.386180\pi$
$977$	21.8802	0.700008	0.350004	+	0.936748i	$0.386180\pi$
$978$	−0.175000	−0.00559588
$979$	18.7530	0.599349
$980$	−3.79510	−0.121230
$981$	−57.8010	−1.84545
$982$	−7.91915	−0.252710
$983$	53.6576	1.71141	0.855705	−	0.517464i	$-0.173124\pi$
$983$	53.6576	1.71141	0.855705	+	0.517464i	$0.173124\pi$
$984$	0.288553	0.00919873
$985$	−6.87052	−0.218913
$986$	−14.6956	−0.468002
$987$	−0.141833	−0.00451461
$988$	−8.25555	−0.262644
$989$	−3.16727	−0.100713
$990$	8.99969	0.286029
$991$	−13.9714	−0.443817	−0.221909	−	0.975067i	$-0.571229\pi$
$991$	−13.9714	−0.443817	−0.221909	+	0.975067i	$0.571229\pi$
$992$	−7.65721	−0.243117
$993$	−0.0162235	−0.000514838 0
$994$	−8.29714	−0.263169
$995$	−1.59944	−0.0507057
$996$	0.441202	0.0139800
$997$	49.9457	1.58180	0.790899	−	0.611947i	$-0.209613\pi$
$997$	49.9457	1.58180	0.790899	+	0.611947i	$0.209613\pi$
$998$	35.3224	1.11811
$999$	−0.979734	−0.0309974

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.n.1.6	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.n.1.6	✓	68	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.40730 q^{2} +0.0150324 q^{3} +3.79510 q^{4} -1.00000 q^{5} -0.0361876 q^{6} +1.00000 q^{7} -4.32135 q^{8} -2.99977 q^{9} +O(q^{10})\)	\(q-2.40730 q^{2} +0.0150324 q^{3} +3.79510 q^{4} -1.00000 q^{5} -0.0361876 q^{6} +1.00000 q^{7} -4.32135 q^{8} -2.99977 q^{9} +2.40730 q^{10} -1.24626 q^{11} +0.0570496 q^{12} -0.904643 q^{13} -2.40730 q^{14} -0.0150324 q^{15} +2.81258 q^{16} -4.55036 q^{17} +7.22136 q^{18} +2.40461 q^{19} -3.79510 q^{20} +0.0150324 q^{21} +3.00012 q^{22} -5.57664 q^{23} -0.0649604 q^{24} +1.00000 q^{25} +2.17775 q^{26} -0.0901912 q^{27} +3.79510 q^{28} -1.34156 q^{29} +0.0361876 q^{30} -4.09048 q^{31} +1.87196 q^{32} -0.0187343 q^{33} +10.9541 q^{34} -1.00000 q^{35} -11.3844 q^{36} +10.8629 q^{37} -5.78863 q^{38} -0.0135990 q^{39} +4.32135 q^{40} -4.44199 q^{41} -0.0361876 q^{42} +0.567953 q^{43} -4.72968 q^{44} +2.99977 q^{45} +13.4247 q^{46} -9.43516 q^{47} +0.0422800 q^{48} +1.00000 q^{49} -2.40730 q^{50} -0.0684030 q^{51} -3.43321 q^{52} +0.0112945 q^{53} +0.217117 q^{54} +1.24626 q^{55} -4.32135 q^{56} +0.0361472 q^{57} +3.22954 q^{58} -13.7977 q^{59} -0.0570496 q^{60} -8.96801 q^{61} +9.84702 q^{62} -2.99977 q^{63} -10.1315 q^{64} +0.904643 q^{65} +0.0450992 q^{66} -9.00966 q^{67} -17.2691 q^{68} -0.0838306 q^{69} +2.40730 q^{70} +3.44666 q^{71} +12.9631 q^{72} +8.30667 q^{73} -26.1502 q^{74} +0.0150324 q^{75} +9.12575 q^{76} -1.24626 q^{77} +0.0327369 q^{78} +11.0887 q^{79} -2.81258 q^{80} +8.99797 q^{81} +10.6932 q^{82} +7.73366 q^{83} +0.0570496 q^{84} +4.55036 q^{85} -1.36723 q^{86} -0.0201669 q^{87} +5.38552 q^{88} -15.0474 q^{89} -7.22136 q^{90} -0.904643 q^{91} -21.1639 q^{92} -0.0614899 q^{93} +22.7133 q^{94} -2.40461 q^{95} +0.0281401 q^{96} -16.3881 q^{97} -2.40730 q^{98} +3.73850 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9}+O(q^{10}) \) 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9} - 9 q^{10} + 5 q^{11} + 9 q^{12} + 15 q^{13} + 9 q^{14} + 109 q^{16} + 7 q^{17} + 39 q^{18} + 20 q^{19} - 83 q^{20} + 56 q^{22} + 36 q^{23} + q^{24} + 68 q^{25} + q^{26} + 12 q^{27} + 83 q^{28} - 16 q^{29} - 5 q^{30} + 31 q^{31} + 79 q^{32} + 45 q^{33} + 31 q^{34} - 68 q^{35} + 114 q^{36} + 72 q^{37} + 8 q^{38} + 47 q^{39} - 30 q^{40} + 6 q^{41} + 5 q^{42} + 75 q^{43} + 15 q^{44} - 86 q^{45} + 29 q^{46} - 10 q^{47} + 44 q^{48} + 68 q^{49} + 9 q^{50} + 23 q^{51} + 37 q^{52} + 41 q^{53} + 4 q^{54} - 5 q^{55} + 30 q^{56} + 55 q^{57} + 66 q^{58} - 5 q^{59} - 9 q^{60} - 2 q^{61} + 3 q^{62} + 86 q^{63} + 162 q^{64} - 15 q^{65} - 23 q^{66} + 92 q^{67} + 35 q^{68} - 25 q^{69} - 9 q^{70} - 2 q^{71} + 128 q^{72} + 80 q^{73} + 18 q^{74} + 71 q^{76} + 5 q^{77} + 20 q^{78} + 100 q^{79} - 109 q^{80} + 140 q^{81} + 36 q^{82} - 60 q^{83} + 9 q^{84} - 7 q^{85} - 27 q^{86} + 24 q^{87} + 175 q^{88} + 19 q^{89} - 39 q^{90} + 15 q^{91} + 75 q^{92} + 37 q^{93} + 11 q^{94} - 20 q^{95} + 15 q^{96} + 96 q^{97} + 9 q^{98} + 3 q^{99}+O(q^{100}) \) 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9 - 9 * q^10 + 5 * q^11 + 9 * q^12 + 15 * q^13 + 9 * q^14 + 109 * q^16 + 7 * q^17 + 39 * q^18 + 20 * q^19 - 83 * q^20 + 56 * q^22 + 36 * q^23 + q^24 + 68 * q^25 + q^26 + 12 * q^27 + 83 * q^28 - 16 * q^29 - 5 * q^30 + 31 * q^31 + 79 * q^32 + 45 * q^33 + 31 * q^34 - 68 * q^35 + 114 * q^36 + 72 * q^37 + 8 * q^38 + 47 * q^39 - 30 * q^40 + 6 * q^41 + 5 * q^42 + 75 * q^43 + 15 * q^44 - 86 * q^45 + 29 * q^46 - 10 * q^47 + 44 * q^48 + 68 * q^49 + 9 * q^50 + 23 * q^51 + 37 * q^52 + 41 * q^53 + 4 * q^54 - 5 * q^55 + 30 * q^56 + 55 * q^57 + 66 * q^58 - 5 * q^59 - 9 * q^60 - 2 * q^61 + 3 * q^62 + 86 * q^63 + 162 * q^64 - 15 * q^65 - 23 * q^66 + 92 * q^67 + 35 * q^68 - 25 * q^69 - 9 * q^70 - 2 * q^71 + 128 * q^72 + 80 * q^73 + 18 * q^74 + 71 * q^76 + 5 * q^77 + 20 * q^78 + 100 * q^79 - 109 * q^80 + 140 * q^81 + 36 * q^82 - 60 * q^83 + 9 * q^84 - 7 * q^85 - 27 * q^86 + 24 * q^87 + 175 * q^88 + 19 * q^89 - 39 * q^90 + 15 * q^91 + 75 * q^92 + 37 * q^93 + 11 * q^94 - 20 * q^95 + 15 * q^96 + 96 * q^97 + 9 * q^98 + 3 * q^99

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