LMFDB - Embedded newform 8015.2.a.n.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.66015 q^{2} -2.46219 q^{3} +5.07642 q^{4} -1.00000 q^{5} +6.54979 q^{6} +1.00000 q^{7} -8.18374 q^{8} +3.06236 q^{9} +O(q^{10})$	\(q-2.66015 q^{2} -2.46219 q^{3} +5.07642 q^{4} -1.00000 q^{5} +6.54979 q^{6} +1.00000 q^{7} -8.18374 q^{8} +3.06236 q^{9} +2.66015 q^{10} -5.02376 q^{11} -12.4991 q^{12} -2.68154 q^{13} -2.66015 q^{14} +2.46219 q^{15} +11.6172 q^{16} +6.72534 q^{17} -8.14636 q^{18} -5.29144 q^{19} -5.07642 q^{20} -2.46219 q^{21} +13.3640 q^{22} +7.99900 q^{23} +20.1499 q^{24} +1.00000 q^{25} +7.13330 q^{26} -0.153550 q^{27} +5.07642 q^{28} -0.0674062 q^{29} -6.54979 q^{30} +2.94213 q^{31} -14.5360 q^{32} +12.3694 q^{33} -17.8904 q^{34} -1.00000 q^{35} +15.5458 q^{36} +9.95414 q^{37} +14.0760 q^{38} +6.60245 q^{39} +8.18374 q^{40} +3.05409 q^{41} +6.54979 q^{42} +8.09608 q^{43} -25.5027 q^{44} -3.06236 q^{45} -21.2786 q^{46} -5.87527 q^{47} -28.6036 q^{48} +1.00000 q^{49} -2.66015 q^{50} -16.5591 q^{51} -13.6126 q^{52} -12.6743 q^{53} +0.408466 q^{54} +5.02376 q^{55} -8.18374 q^{56} +13.0285 q^{57} +0.179311 q^{58} +2.05296 q^{59} +12.4991 q^{60} -9.69579 q^{61} -7.82651 q^{62} +3.06236 q^{63} +15.4336 q^{64} +2.68154 q^{65} -32.9046 q^{66} +12.2432 q^{67} +34.1406 q^{68} -19.6950 q^{69} +2.66015 q^{70} +0.853933 q^{71} -25.0616 q^{72} +3.64796 q^{73} -26.4795 q^{74} -2.46219 q^{75} -26.8615 q^{76} -5.02376 q^{77} -17.5635 q^{78} +9.43234 q^{79} -11.6172 q^{80} -8.80902 q^{81} -8.12435 q^{82} -6.68142 q^{83} -12.4991 q^{84} -6.72534 q^{85} -21.5368 q^{86} +0.165967 q^{87} +41.1131 q^{88} +6.83126 q^{89} +8.14636 q^{90} -2.68154 q^{91} +40.6063 q^{92} -7.24407 q^{93} +15.6291 q^{94} +5.29144 q^{95} +35.7903 q^{96} +9.78665 q^{97} -2.66015 q^{98} -15.3846 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.66015	−1.88101	−0.940506	−	0.339776i	$-0.889649\pi$
$2$	−2.66015	−1.88101	−0.940506	+	0.339776i	$0.889649\pi$
$3$	−2.46219	−1.42154	−0.710772	−	0.703422i	$-0.751654\pi$
$3$	−2.46219	−1.42154	−0.710772	+	0.703422i	$0.751654\pi$
$4$	5.07642	2.53821
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	6.54979	2.67394
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−8.18374	−2.89339
$9$	3.06236	1.02079
$10$	2.66015	0.841214
$11$	−5.02376	−1.51472	−0.757360	−	0.652998i	$-0.773511\pi$
$11$	−5.02376	−1.51472	−0.757360	+	0.652998i	$0.773511\pi$
$12$	−12.4991	−3.60817
$13$	−2.68154	−0.743725	−0.371862	−	0.928288i	$-0.621281\pi$
$13$	−2.68154	−0.743725	−0.371862	+	0.928288i	$0.621281\pi$
$14$	−2.66015	−0.710956
$15$	2.46219	0.635734
$16$	11.6172	2.90429
$17$	6.72534	1.63114	0.815568	−	0.578661i	$-0.196425\pi$
$17$	6.72534	1.63114	0.815568	+	0.578661i	$0.196425\pi$
$18$	−8.14636	−1.92011
$19$	−5.29144	−1.21394	−0.606970	−	0.794725i	$-0.707615\pi$
$19$	−5.29144	−1.21394	−0.606970	+	0.794725i	$0.707615\pi$
$20$	−5.07642	−1.13512
$21$	−2.46219	−0.537293
$22$	13.3640	2.84921
$23$	7.99900	1.66791	0.833954	−	0.551834i	$-0.186072\pi$
$23$	7.99900	1.66791	0.833954	+	0.551834i	$0.186072\pi$
$24$	20.1499	4.11308
$25$	1.00000	0.200000
$26$	7.13330	1.39896
$27$	−0.153550	−0.0295507
$28$	5.07642	0.959352
$29$	−0.0674062	−0.0125170	−0.00625850	−	0.999980i	$-0.501992\pi$
$29$	−0.0674062	−0.0125170	−0.00625850	+	0.999980i	$0.501992\pi$
$30$	−6.54979	−1.19582
$31$	2.94213	0.528422	0.264211	−	0.964465i	$-0.414889\pi$
$31$	2.94213	0.528422	0.264211	+	0.964465i	$0.414889\pi$
$32$	−14.5360	−2.56962
$33$	12.3694	2.15324
$34$	−17.8904	−3.06819
$35$	−1.00000	−0.169031
$36$	15.5458	2.59097
$37$	9.95414	1.63645	0.818225	−	0.574897i	$-0.194958\pi$
$37$	9.95414	1.63645	0.818225	+	0.574897i	$0.194958\pi$
$38$	14.0760	2.28344
$39$	6.60245	1.05724
$40$	8.18374	1.29396
$41$	3.05409	0.476969	0.238484	−	0.971146i	$-0.423349\pi$
$41$	3.05409	0.476969	0.238484	+	0.971146i	$0.423349\pi$
$42$	6.54979	1.01066
$43$	8.09608	1.23464	0.617321	−	0.786712i	$-0.288218\pi$
$43$	8.09608	1.23464	0.617321	+	0.786712i	$0.288218\pi$
$44$	−25.5027	−3.84467
$45$	−3.06236	−0.456510
$46$	−21.2786	−3.13736
$47$	−5.87527	−0.856996	−0.428498	−	0.903543i	$-0.640957\pi$
$47$	−5.87527	−0.856996	−0.428498	+	0.903543i	$0.640957\pi$
$48$	−28.6036	−4.12858
$49$	1.00000	0.142857
$50$	−2.66015	−0.376202
$51$	−16.5591	−2.31873
$52$	−13.6126	−1.88773
$53$	−12.6743	−1.74095	−0.870476	−	0.492212i	$-0.836189\pi$
$53$	−12.6743	−1.74095	−0.870476	+	0.492212i	$0.836189\pi$
$54$	0.408466	0.0555852
$55$	5.02376	0.677403
$56$	−8.18374	−1.09360
$57$	13.0285	1.72567
$58$	0.179311	0.0235447
$59$	2.05296	0.267273	0.133637	−	0.991030i	$-0.457335\pi$
$59$	2.05296	0.267273	0.133637	+	0.991030i	$0.457335\pi$
$60$	12.4991	1.61362
$61$	−9.69579	−1.24142	−0.620710	−	0.784041i	$-0.713155\pi$
$61$	−9.69579	−1.24142	−0.620710	+	0.784041i	$0.713155\pi$
$62$	−7.82651	−0.993968
$63$	3.06236	0.385821
$64$	15.4336	1.92920
$65$	2.68154	0.332604
$66$	−32.9046	−4.05027
$67$	12.2432	1.49575	0.747874	−	0.663841i	$-0.231075\pi$
$67$	12.2432	1.49575	0.747874	+	0.663841i	$0.231075\pi$
$68$	34.1406	4.14016
$69$	−19.6950	−2.37100
$70$	2.66015	0.317949
$71$	0.853933	0.101343	0.0506716	−	0.998715i	$-0.483864\pi$
$71$	0.853933	0.101343	0.0506716	+	0.998715i	$0.483864\pi$
$72$	−25.0616	−2.95354
$73$	3.64796	0.426961	0.213481	−	0.976947i	$-0.431520\pi$
$73$	3.64796	0.426961	0.213481	+	0.976947i	$0.431520\pi$
$74$	−26.4795	−3.07818
$75$	−2.46219	−0.284309
$76$	−26.8615	−3.08123
$77$	−5.02376	−0.572510
$78$	−17.5635	−1.98868
$79$	9.43234	1.06122	0.530611	−	0.847616i	$-0.321963\pi$
$79$	9.43234	1.06122	0.530611	+	0.847616i	$0.321963\pi$
$80$	−11.6172	−1.29884
$81$	−8.80902	−0.978780
$82$	−8.12435	−0.897184
$83$	−6.68142	−0.733381	−0.366690	−	0.930343i	$-0.619509\pi$
$83$	−6.68142	−0.733381	−0.366690	+	0.930343i	$0.619509\pi$
$84$	−12.4991	−1.36376
$85$	−6.72534	−0.729466
$86$	−21.5368	−2.32238
$87$	0.165967	0.0177935
$88$	41.1131	4.38267
$89$	6.83126	0.724112	0.362056	−	0.932156i	$-0.382075\pi$
$89$	6.83126	0.724112	0.362056	+	0.932156i	$0.382075\pi$
$90$	8.14636	0.858701
$91$	−2.68154	−0.281102
$92$	40.6063	4.23350
$93$	−7.24407	−0.751175
$94$	15.6291	1.61202
$95$	5.29144	0.542890
$96$	35.7903	3.65283
$97$	9.78665	0.993684	0.496842	−	0.867841i	$-0.334493\pi$
$97$	9.78665	0.993684	0.496842	+	0.867841i	$0.334493\pi$
$98$	−2.66015	−0.268716
$99$	−15.3846	−1.54621
$100$	5.07642	0.507642
$101$	−12.4052	−1.23436	−0.617182	−	0.786820i	$-0.711726\pi$
$101$	−12.4052	−1.23436	−0.617182	+	0.786820i	$0.711726\pi$
$102$	44.0496	4.36156
$103$	0.966301	0.0952124	0.0476062	−	0.998866i	$-0.484841\pi$
$103$	0.966301	0.0952124	0.0476062	+	0.998866i	$0.484841\pi$
$104$	21.9450	2.15189
$105$	2.46219	0.240285
$106$	33.7156	3.27475
$107$	−6.20969	−0.600313	−0.300157	−	0.953890i	$-0.597039\pi$
$107$	−6.20969	−0.600313	−0.300157	+	0.953890i	$0.597039\pi$
$108$	−0.779483	−0.0750058
$109$	17.1329	1.64103	0.820516	−	0.571623i	$-0.193686\pi$
$109$	17.1329	1.64103	0.820516	+	0.571623i	$0.193686\pi$
$110$	−13.3640	−1.27420
$111$	−24.5090	−2.32629
$112$	11.6172	1.09772
$113$	−12.2692	−1.15419	−0.577096	−	0.816676i	$-0.695814\pi$
$113$	−12.2692	−1.15419	−0.577096	+	0.816676i	$0.695814\pi$
$114$	−34.6578	−3.24600
$115$	−7.99900	−0.745911
$116$	−0.342182	−0.0317708
$117$	−8.21184	−0.759185
$118$	−5.46120	−0.502744
$119$	6.72534	0.616511
$120$	−20.1499	−1.83942
$121$	14.2381	1.29438
$122$	25.7923	2.33513
$123$	−7.51974	−0.678032
$124$	14.9355	1.34124
$125$	−1.00000	−0.0894427
$126$	−8.14636	−0.725735
$127$	−15.8199	−1.40379	−0.701893	−	0.712283i	$-0.747661\pi$
$127$	−15.8199	−1.40379	−0.701893	+	0.712283i	$0.747661\pi$
$128$	−11.9837	−1.05922
$129$	−19.9341	−1.75510
$130$	−7.13330	−0.625632
$131$	4.37209	0.381992	0.190996	−	0.981591i	$-0.438828\pi$
$131$	4.37209	0.381992	0.190996	+	0.981591i	$0.438828\pi$
$132$	62.7924	5.46537
$133$	−5.29144	−0.458826
$134$	−32.5689	−2.81352
$135$	0.153550	0.0132155
$136$	−55.0385	−4.71951
$137$	16.5390	1.41302	0.706512	−	0.707701i	$-0.250267\pi$
$137$	16.5390	1.41302	0.706512	+	0.707701i	$0.250267\pi$
$138$	52.3918	4.45989
$139$	−8.93436	−0.757802	−0.378901	−	0.925437i	$-0.623698\pi$
$139$	−8.93436	−0.757802	−0.378901	+	0.925437i	$0.623698\pi$
$140$	−5.07642	−0.429035
$141$	14.4660	1.21826
$142$	−2.27159	−0.190628
$143$	13.4714	1.12654
$144$	35.5760	2.96467
$145$	0.0674062	0.00559778
$146$	−9.70412	−0.803119
$147$	−2.46219	−0.203078
$148$	50.5314	4.15365
$149$	−4.97235	−0.407351	−0.203675	−	0.979038i	$-0.565289\pi$
$149$	−4.97235	−0.407351	−0.203675	+	0.979038i	$0.565289\pi$
$150$	6.54979	0.534788
$151$	19.0243	1.54818	0.774089	−	0.633077i	$-0.218208\pi$
$151$	19.0243	1.54818	0.774089	+	0.633077i	$0.218208\pi$
$152$	43.3037	3.51240
$153$	20.5954	1.66504
$154$	13.3640	1.07690
$155$	−2.94213	−0.236317
$156$	33.5168	2.68349
$157$	23.0699	1.84118	0.920590	−	0.390532i	$-0.127709\pi$
$157$	23.0699	1.84118	0.920590	+	0.390532i	$0.127709\pi$
$158$	−25.0915	−1.99617
$159$	31.2065	2.47484
$160$	14.5360	1.14917
$161$	7.99900	0.630410
$162$	23.4333	1.84110
$163$	−17.9386	−1.40506	−0.702529	−	0.711655i	$-0.747946\pi$
$163$	−17.9386	−1.40506	−0.702529	+	0.711655i	$0.747946\pi$
$164$	15.5038	1.21065
$165$	−12.3694	−0.962959
$166$	17.7736	1.37950
$167$	−3.81019	−0.294841	−0.147421	−	0.989074i	$-0.547097\pi$
$167$	−3.81019	−0.294841	−0.147421	+	0.989074i	$0.547097\pi$
$168$	20.1499	1.55460
$169$	−5.80935	−0.446873
$170$	17.8904	1.37213
$171$	−16.2043	−1.23917
$172$	41.0991	3.13378
$173$	−3.22364	−0.245089	−0.122545	−	0.992463i	$-0.539105\pi$
$173$	−3.22364	−0.245089	−0.122545	+	0.992463i	$0.539105\pi$
$174$	−0.441496	−0.0334698
$175$	1.00000	0.0755929
$176$	−58.3618	−4.39919
$177$	−5.05478	−0.379941
$178$	−18.1722	−1.36206
$179$	−16.6744	−1.24630	−0.623150	−	0.782102i	$-0.714147\pi$
$179$	−16.6744	−1.24630	−0.623150	+	0.782102i	$0.714147\pi$
$180$	−15.5458	−1.15872
$181$	−2.39583	−0.178081	−0.0890404	−	0.996028i	$-0.528380\pi$
$181$	−2.39583	−0.178081	−0.0890404	+	0.996028i	$0.528380\pi$
$182$	7.13330	0.528756
$183$	23.8729	1.76473
$184$	−65.4618	−4.82590
$185$	−9.95414	−0.731843
$186$	19.2703	1.41297
$187$	−33.7865	−2.47071
$188$	−29.8253	−2.17523
$189$	−0.153550	−0.0111691
$190$	−14.0760	−1.02118
$191$	−0.937751	−0.0678532	−0.0339266	−	0.999424i	$-0.510801\pi$
$191$	−0.937751	−0.0678532	−0.0339266	+	0.999424i	$0.510801\pi$
$192$	−38.0003	−2.74244
$193$	4.08445	0.294005	0.147003	−	0.989136i	$-0.453037\pi$
$193$	4.08445	0.294005	0.147003	+	0.989136i	$0.453037\pi$
$194$	−26.0340	−1.86913
$195$	−6.60245	−0.472811
$196$	5.07642	0.362601
$197$	14.9209	1.06307	0.531534	−	0.847037i	$-0.321616\pi$
$197$	14.9209	1.06307	0.531534	+	0.847037i	$0.321616\pi$
$198$	40.9253	2.90844
$199$	−13.9642	−0.989898	−0.494949	−	0.868922i	$-0.664813\pi$
$199$	−13.9642	−0.989898	−0.494949	+	0.868922i	$0.664813\pi$
$200$	−8.18374	−0.578678
$201$	−30.1451	−2.12627
$202$	32.9998	2.32186
$203$	−0.0674062	−0.00473098
$204$	−84.0606	−5.88542
$205$	−3.05409	−0.213307
$206$	−2.57051	−0.179096
$207$	24.4959	1.70258
$208$	−31.1519	−2.15999
$209$	26.5829	1.83878
$210$	−6.54979	−0.451979
$211$	−5.63616	−0.388009	−0.194005	−	0.981001i	$-0.562148\pi$
$211$	−5.63616	−0.388009	−0.194005	+	0.981001i	$0.562148\pi$
$212$	−64.3401	−4.41890
$213$	−2.10254	−0.144064
$214$	16.5187	1.12920
$215$	−8.09608	−0.552148
$216$	1.25661	0.0855016
$217$	2.94213	0.199725
$218$	−45.5761	−3.08680
$219$	−8.98195	−0.606944
$220$	25.5027	1.71939
$221$	−18.0343	−1.21312
$222$	65.1976	4.37578
$223$	2.91471	0.195183	0.0975916	−	0.995227i	$-0.468886\pi$
$223$	2.91471	0.195183	0.0975916	+	0.995227i	$0.468886\pi$
$224$	−14.5360	−0.971225
$225$	3.06236	0.204158
$226$	32.6380	2.17105
$227$	14.4644	0.960038	0.480019	−	0.877258i	$-0.340630\pi$
$227$	14.4644	0.960038	0.480019	+	0.877258i	$0.340630\pi$
$228$	66.1381	4.38011
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	21.2786	1.40307
$231$	12.3694	0.813849
$232$	0.551634	0.0362166
$233$	3.11016	0.203754	0.101877	−	0.994797i	$-0.467515\pi$
$233$	3.11016	0.203754	0.101877	+	0.994797i	$0.467515\pi$
$234$	21.8448	1.42804
$235$	5.87527	0.383260
$236$	10.4217	0.678395
$237$	−23.2242	−1.50857
$238$	−17.8904	−1.15967
$239$	−10.6359	−0.687978	−0.343989	−	0.938974i	$-0.611778\pi$
$239$	−10.6359	−0.687978	−0.343989	+	0.938974i	$0.611778\pi$
$240$	28.6036	1.84636
$241$	15.4785	0.997057	0.498528	−	0.866873i	$-0.333874\pi$
$241$	15.4785	0.997057	0.498528	+	0.866873i	$0.333874\pi$
$242$	−37.8756	−2.43474
$243$	22.1501	1.42093
$244$	−49.2199	−3.15098
$245$	−1.00000	−0.0638877
$246$	20.0037	1.27539
$247$	14.1892	0.902837
$248$	−24.0776	−1.52893
$249$	16.4509	1.04253
$250$	2.66015	0.168243
$251$	−20.0893	−1.26803	−0.634013	−	0.773322i	$-0.718594\pi$
$251$	−20.0893	−1.26803	−0.634013	+	0.773322i	$0.718594\pi$
$252$	15.5458	0.979295
$253$	−40.1851	−2.52641
$254$	42.0832	2.64054
$255$	16.5591	1.03697
$256$	1.01142	0.0632137
$257$	−14.6725	−0.915243	−0.457622	−	0.889147i	$-0.651299\pi$
$257$	−14.6725	−0.915243	−0.457622	+	0.889147i	$0.651299\pi$
$258$	53.0277	3.30136
$259$	9.95414	0.618520
$260$	13.6126	0.844218
$261$	−0.206422	−0.0127772
$262$	−11.6304	−0.718531
$263$	−20.5518	−1.26728	−0.633638	−	0.773630i	$-0.718439\pi$
$263$	−20.5518	−1.26728	−0.633638	+	0.773630i	$0.718439\pi$
$264$	−101.228	−6.23016
$265$	12.6743	0.778577
$266$	14.0760	0.863057
$267$	−16.8198	−1.02936
$268$	62.1517	3.79652
$269$	5.37803	0.327904	0.163952	−	0.986468i	$-0.447576\pi$
$269$	5.37803	0.327904	0.163952	+	0.986468i	$0.447576\pi$
$270$	−0.408466	−0.0248585
$271$	8.07855	0.490737	0.245369	−	0.969430i	$-0.421091\pi$
$271$	8.07855	0.490737	0.245369	+	0.969430i	$0.421091\pi$
$272$	78.1295	4.73729
$273$	6.60245	0.399598
$274$	−43.9964	−2.65792
$275$	−5.02376	−0.302944
$276$	−99.9802	−6.01810
$277$	6.59034	0.395975	0.197988	−	0.980205i	$-0.436559\pi$
$277$	6.59034	0.395975	0.197988	+	0.980205i	$0.436559\pi$
$278$	23.7668	1.42544
$279$	9.00986	0.539406
$280$	8.18374	0.489072
$281$	−14.9070	−0.889280	−0.444640	−	0.895709i	$-0.646668\pi$
$281$	−14.9070	−0.889280	−0.444640	+	0.895709i	$0.646668\pi$
$282$	−38.4818	−2.29156
$283$	11.1471	0.662625	0.331313	−	0.943521i	$-0.392508\pi$
$283$	11.1471	0.662625	0.331313	+	0.943521i	$0.392508\pi$
$284$	4.33492	0.257230
$285$	−13.0285	−0.771742
$286$	−35.8360	−2.11903
$287$	3.05409	0.180277
$288$	−44.5144	−2.62304
$289$	28.2303	1.66060
$290$	−0.179311	−0.0105295
$291$	−24.0966	−1.41257
$292$	18.5185	1.08372
$293$	0.152951	0.00893549	0.00446774	−	0.999990i	$-0.498578\pi$
$293$	0.152951	0.00893549	0.00446774	+	0.999990i	$0.498578\pi$
$294$	6.54979	0.381992
$295$	−2.05296	−0.119528
$296$	−81.4621	−4.73489
$297$	0.771397	0.0447610
$298$	13.2272	0.766232
$299$	−21.4496	−1.24046
$300$	−12.4991	−0.721635
$301$	8.09608	0.466650
$302$	−50.6076	−2.91214
$303$	30.5439	1.75470
$304$	−61.4715	−3.52563
$305$	9.69579	0.555180
$306$	−54.7871	−3.13197
$307$	−15.7728	−0.900201	−0.450100	−	0.892978i	$-0.648612\pi$
$307$	−15.7728	−0.900201	−0.450100	+	0.892978i	$0.648612\pi$
$308$	−25.5027	−1.45315
$309$	−2.37921	−0.135349
$310$	7.82651	0.444516
$311$	0.783019	0.0444009	0.0222005	−	0.999754i	$-0.492933\pi$
$311$	0.783019	0.0444009	0.0222005	+	0.999754i	$0.492933\pi$
$312$	−54.0327	−3.05900
$313$	6.59123	0.372559	0.186279	−	0.982497i	$-0.440357\pi$
$313$	6.59123	0.372559	0.186279	+	0.982497i	$0.440357\pi$
$314$	−61.3695	−3.46328
$315$	−3.06236	−0.172545
$316$	47.8825	2.69360
$317$	−1.51653	−0.0851767	−0.0425884	−	0.999093i	$-0.513560\pi$
$317$	−1.51653	−0.0851767	−0.0425884	+	0.999093i	$0.513560\pi$
$318$	−83.0142	−4.65520
$319$	0.338632	0.0189598
$320$	−15.4336	−0.862763
$321$	15.2894	0.853372
$322$	−21.2786	−1.18581
$323$	−35.5868	−1.98010
$324$	−44.7183	−2.48435
$325$	−2.68154	−0.148745
$326$	47.7194	2.64293
$327$	−42.1844	−2.33280
$328$	−24.9939	−1.38006
$329$	−5.87527	−0.323914
$330$	32.9046	1.81134
$331$	17.8944	0.983563	0.491782	−	0.870719i	$-0.336346\pi$
$331$	17.8944	0.983563	0.491782	+	0.870719i	$0.336346\pi$
$332$	−33.9177	−1.86147
$333$	30.4832	1.67047
$334$	10.1357	0.554600
$335$	−12.2432	−0.668919
$336$	−28.6036	−1.56046
$337$	−3.97660	−0.216619	−0.108310	−	0.994117i	$-0.534544\pi$
$337$	−3.97660	−0.216619	−0.108310	+	0.994117i	$0.534544\pi$
$338$	15.4538	0.840574
$339$	30.2091	1.64073
$340$	−34.1406	−1.85154
$341$	−14.7805	−0.800411
$342$	43.1059	2.33090
$343$	1.00000	0.0539949
$344$	−66.2562	−3.57230
$345$	19.6950	1.06035
$346$	8.57539	0.461016
$347$	23.1516	1.24284	0.621421	−	0.783477i	$-0.286556\pi$
$347$	23.1516	1.24284	0.621421	+	0.783477i	$0.286556\pi$
$348$	0.842515	0.0451636
$349$	−8.46041	−0.452876	−0.226438	−	0.974026i	$-0.572708\pi$
$349$	−8.46041	−0.452876	−0.226438	+	0.974026i	$0.572708\pi$
$350$	−2.66015	−0.142191
$351$	0.411750	0.0219776
$352$	73.0252	3.89226
$353$	−25.7426	−1.37014	−0.685071	−	0.728476i	$-0.740229\pi$
$353$	−25.7426	−1.37014	−0.685071	+	0.728476i	$0.740229\pi$
$354$	13.4465	0.714673
$355$	−0.853933	−0.0453220
$356$	34.6783	1.83795
$357$	−16.5591	−0.876398
$358$	44.3564	2.34431
$359$	−7.69636	−0.406198	−0.203099	−	0.979158i	$-0.565101\pi$
$359$	−7.69636	−0.406198	−0.203099	+	0.979158i	$0.565101\pi$
$360$	25.0616	1.32086
$361$	8.99932	0.473649
$362$	6.37328	0.334972
$363$	−35.0570	−1.84001
$364$	−13.6126	−0.713494
$365$	−3.64796	−0.190943
$366$	−63.5055	−3.31948
$367$	−37.1540	−1.93942	−0.969711	−	0.244257i	$-0.921456\pi$
$367$	−37.1540	−1.93942	−0.969711	+	0.244257i	$0.921456\pi$
$368$	92.9258	4.84409
$369$	9.35273	0.486884
$370$	26.4795	1.37661
$371$	−12.6743	−0.658018
$372$	−36.7739	−1.90664
$373$	−28.8847	−1.49559	−0.747796	−	0.663929i	$-0.768888\pi$
$373$	−28.8847	−1.49559	−0.747796	+	0.663929i	$0.768888\pi$
$374$	89.8773	4.64744
$375$	2.46219	0.127147
$376$	48.0817	2.47962
$377$	0.180752	0.00930921
$378$	0.408466	0.0210092
$379$	8.80631	0.452350	0.226175	−	0.974087i	$-0.427378\pi$
$379$	8.80631	0.452350	0.226175	+	0.974087i	$0.427378\pi$
$380$	26.8615	1.37797
$381$	38.9514	1.99554
$382$	2.49456	0.127633
$383$	−13.4737	−0.688472	−0.344236	−	0.938883i	$-0.611862\pi$
$383$	−13.4737	−0.688472	−0.344236	+	0.938883i	$0.611862\pi$
$384$	29.5062	1.50573
$385$	5.02376	0.256034
$386$	−10.8653	−0.553027
$387$	24.7931	1.26031
$388$	49.6811	2.52218
$389$	31.8679	1.61577	0.807883	−	0.589343i	$-0.200613\pi$
$389$	31.8679	1.61577	0.807883	+	0.589343i	$0.200613\pi$
$390$	17.5635	0.889364
$391$	53.7961	2.72058
$392$	−8.18374	−0.413341
$393$	−10.7649	−0.543018
$394$	−39.6918	−1.99964
$395$	−9.43234	−0.474593
$396$	−78.0985	−3.92460
$397$	21.3937	1.07372	0.536859	−	0.843672i	$-0.319611\pi$
$397$	21.3937	1.07372	0.536859	+	0.843672i	$0.319611\pi$
$398$	37.1470	1.86201
$399$	13.0285	0.652241
$400$	11.6172	0.580858
$401$	27.4659	1.37158	0.685791	−	0.727799i	$-0.259457\pi$
$401$	27.4659	1.37158	0.685791	+	0.727799i	$0.259457\pi$
$402$	80.1906	3.99954
$403$	−7.88943	−0.393000
$404$	−62.9740	−3.13307
$405$	8.80902	0.437724
$406$	0.179311	0.00889904
$407$	−50.0072	−2.47876
$408$	135.515	6.70899
$409$	−34.5359	−1.70769	−0.853845	−	0.520527i	$-0.825735\pi$
$409$	−34.5359	−1.70769	−0.853845	+	0.520527i	$0.825735\pi$
$410$	8.12435	0.401233
$411$	−40.7222	−2.00868
$412$	4.90534	0.241669
$413$	2.05296	0.101020
$414$	−65.1627	−3.20257
$415$	6.68142	0.327978
$416$	38.9788	1.91109
$417$	21.9981	1.07725
$418$	−70.7146	−3.45876
$419$	−24.7333	−1.20830	−0.604151	−	0.796870i	$-0.706488\pi$
$419$	−24.7333	−1.20830	−0.604151	+	0.796870i	$0.706488\pi$
$420$	12.4991	0.609893
$421$	26.6583	1.29924	0.649622	−	0.760257i	$-0.274927\pi$
$421$	26.6583	1.29924	0.649622	+	0.760257i	$0.274927\pi$
$422$	14.9931	0.729851
$423$	−17.9922	−0.874811
$424$	103.723	5.03725
$425$	6.72534	0.326227
$426$	5.59308	0.270986
$427$	−9.69579	−0.469212
$428$	−31.5230	−1.52372
$429$	−33.1691	−1.60142
$430$	21.5368	1.03860
$431$	−30.5244	−1.47031	−0.735155	−	0.677899i	$-0.762890\pi$
$431$	−30.5244	−1.47031	−0.735155	+	0.677899i	$0.762890\pi$
$432$	−1.78381	−0.0858238
$433$	19.9744	0.959909	0.479954	−	0.877294i	$-0.340653\pi$
$433$	19.9744	0.959909	0.479954	+	0.877294i	$0.340653\pi$
$434$	−7.82651	−0.375684
$435$	−0.165967	−0.00795749
$436$	86.9736	4.16528
$437$	−42.3262	−2.02474
$438$	23.8934	1.14167
$439$	4.16376	0.198725	0.0993626	−	0.995051i	$-0.468320\pi$
$439$	4.16376	0.198725	0.0993626	+	0.995051i	$0.468320\pi$
$440$	−41.1131	−1.95999
$441$	3.06236	0.145827
$442$	47.9739	2.28189
$443$	30.9821	1.47201	0.736003	−	0.676978i	$-0.236711\pi$
$443$	30.9821	1.47201	0.736003	+	0.676978i	$0.236711\pi$
$444$	−124.418	−5.90460
$445$	−6.83126	−0.323833
$446$	−7.75357	−0.367142
$447$	12.2429	0.579067
$448$	15.4336	0.729168
$449$	6.83088	0.322369	0.161185	−	0.986924i	$-0.448469\pi$
$449$	6.83088	0.322369	0.161185	+	0.986924i	$0.448469\pi$
$450$	−8.14636	−0.384023
$451$	−15.3430	−0.722474
$452$	−62.2837	−2.92958
$453$	−46.8415	−2.20080
$454$	−38.4776	−1.80584
$455$	2.68154	0.125712
$456$	−106.622	−4.99303
$457$	29.1347	1.36286	0.681431	−	0.731882i	$-0.261358\pi$
$457$	29.1347	1.36286	0.681431	+	0.731882i	$0.261358\pi$
$458$	2.66015	0.124301
$459$	−1.03268	−0.0482012
$460$	−40.6063	−1.89328
$461$	−27.7180	−1.29095	−0.645477	−	0.763779i	$-0.723342\pi$
$461$	−27.7180	−1.29095	−0.645477	+	0.763779i	$0.723342\pi$
$462$	−32.9046	−1.53086
$463$	−16.8057	−0.781027	−0.390514	−	0.920597i	$-0.627703\pi$
$463$	−16.8057	−0.781027	−0.390514	+	0.920597i	$0.627703\pi$
$464$	−0.783069	−0.0363530
$465$	7.24407	0.335935
$466$	−8.27351	−0.383263
$467$	15.6728	0.725249	0.362624	−	0.931935i	$-0.381881\pi$
$467$	15.6728	0.725249	0.362624	+	0.931935i	$0.381881\pi$
$468$	−41.6867	−1.92697
$469$	12.2432	0.565340
$470$	−15.6291	−0.720917
$471$	−56.8024	−2.61732
$472$	−16.8009	−0.773325
$473$	−40.6728	−1.87014
$474$	61.7799	2.83764
$475$	−5.29144	−0.242788
$476$	34.1406	1.56483
$477$	−38.8134	−1.77714
$478$	28.2931	1.29410
$479$	27.7583	1.26831	0.634155	−	0.773206i	$-0.281348\pi$
$479$	27.7583	1.26831	0.634155	+	0.773206i	$0.281348\pi$
$480$	−35.7903	−1.63359
$481$	−26.6924	−1.21707
$482$	−41.1751	−1.87548
$483$	−19.6950	−0.896155
$484$	72.2787	3.28540
$485$	−9.78665	−0.444389
$486$	−58.9227	−2.67279
$487$	−18.0523	−0.818030	−0.409015	−	0.912528i	$-0.634128\pi$
$487$	−18.0523	−0.818030	−0.409015	+	0.912528i	$0.634128\pi$
$488$	79.3478	3.59191
$489$	44.1681	1.99735
$490$	2.66015	0.120173
$491$	−21.0719	−0.950962	−0.475481	−	0.879726i	$-0.657726\pi$
$491$	−21.0719	−0.950962	−0.475481	+	0.879726i	$0.657726\pi$
$492$	−38.1733	−1.72099
$493$	−0.453330	−0.0204169
$494$	−37.7454	−1.69825
$495$	15.3846	0.691485
$496$	34.1792	1.53469
$497$	0.853933	0.0383041
$498$	−43.7619	−1.96102
$499$	−35.6917	−1.59778	−0.798890	−	0.601477i	$-0.794579\pi$
$499$	−35.6917	−1.59778	−0.798890	+	0.601477i	$0.794579\pi$
$500$	−5.07642	−0.227024
$501$	9.38140	0.419130
$502$	53.4407	2.38517
$503$	−20.7164	−0.923700	−0.461850	−	0.886958i	$-0.652814\pi$
$503$	−20.7164	−0.923700	−0.461850	+	0.886958i	$0.652814\pi$
$504$	−25.0616	−1.11633
$505$	12.4052	0.552025
$506$	106.898	4.75221
$507$	14.3037	0.635250
$508$	−80.3082	−3.56310
$509$	8.91977	0.395362	0.197681	−	0.980266i	$-0.436659\pi$
$509$	8.91977	0.395362	0.197681	+	0.980266i	$0.436659\pi$
$510$	−44.0496	−1.95055
$511$	3.64796	0.161376
$512$	21.2769	0.940316
$513$	0.812500	0.0358727
$514$	39.0310	1.72158
$515$	−0.966301	−0.0425803
$516$	−101.194	−4.45480
$517$	29.5159	1.29811
$518$	−26.4795	−1.16344
$519$	7.93721	0.348405
$520$	−21.9450	−0.962352
$521$	31.5311	1.38140	0.690700	−	0.723141i	$-0.257302\pi$
$521$	31.5311	1.38140	0.690700	+	0.723141i	$0.257302\pi$
$522$	0.549115	0.0240341
$523$	−8.74985	−0.382604	−0.191302	−	0.981531i	$-0.561271\pi$
$523$	−8.74985	−0.382604	−0.191302	+	0.981531i	$0.561271\pi$
$524$	22.1946	0.969574
$525$	−2.46219	−0.107459
$526$	54.6708	2.38376
$527$	19.7868	0.861927
$528$	143.698	6.25364
$529$	40.9841	1.78192
$530$	−33.7156	−1.46451
$531$	6.28692	0.272829
$532$	−26.8615	−1.16460
$533$	−8.18966	−0.354734
$534$	44.7433	1.93623
$535$	6.20969	0.268468
$536$	−100.195	−4.32778
$537$	41.0554	1.77167
$538$	−14.3064	−0.616792
$539$	−5.02376	−0.216389
$540$	0.779483	0.0335436
$541$	−22.8451	−0.982185	−0.491093	−	0.871107i	$-0.663402\pi$
$541$	−22.8451	−0.982185	−0.491093	+	0.871107i	$0.663402\pi$
$542$	−21.4902	−0.923083
$543$	5.89899	0.253150
$544$	−97.7594	−4.19140
$545$	−17.1329	−0.733892
$546$	−17.5635	−0.751649
$547$	1.49164	0.0637780	0.0318890	−	0.999491i	$-0.489848\pi$
$547$	1.49164	0.0637780	0.0318890	+	0.999491i	$0.489848\pi$
$548$	83.9590	3.58655
$549$	−29.6920	−1.26723
$550$	13.3640	0.569841
$551$	0.356676	0.0151949
$552$	161.179	6.86024
$553$	9.43234	0.401104
$554$	−17.5313	−0.744834
$555$	24.5090	1.04035
$556$	−45.3545	−1.92346
$557$	−12.1635	−0.515385	−0.257693	−	0.966227i	$-0.582962\pi$
$557$	−12.1635	−0.515385	−0.257693	+	0.966227i	$0.582962\pi$
$558$	−23.9676	−1.01463
$559$	−21.7100	−0.918233
$560$	−11.6172	−0.490915
$561$	83.1887	3.51223
$562$	39.6550	1.67275
$563$	−15.7293	−0.662911	−0.331456	−	0.943471i	$-0.607540\pi$
$563$	−15.7293	−0.662911	−0.331456	+	0.943471i	$0.607540\pi$
$564$	73.4355	3.09219
$565$	12.2692	0.516170
$566$	−29.6530	−1.24641
$567$	−8.80902	−0.369944
$568$	−6.98836	−0.293225
$569$	32.7060	1.37111	0.685553	−	0.728022i	$-0.259560\pi$
$569$	32.7060	1.37111	0.685553	+	0.728022i	$0.259560\pi$
$570$	34.6578	1.45166
$571$	17.2218	0.720712	0.360356	−	0.932815i	$-0.382655\pi$
$571$	17.2218	0.720712	0.360356	+	0.932815i	$0.382655\pi$
$572$	68.3864	2.85938
$573$	2.30892	0.0964564
$574$	−8.12435	−0.339104
$575$	7.99900	0.333582
$576$	47.2632	1.96930
$577$	41.2999	1.71934	0.859668	−	0.510853i	$-0.170670\pi$
$577$	41.2999	1.71934	0.859668	+	0.510853i	$0.170670\pi$
$578$	−75.0968	−3.12362
$579$	−10.0567	−0.417941
$580$	0.342182	0.0142083
$581$	−6.68142	−0.277192
$582$	64.1006	2.65705
$583$	63.6727	2.63705
$584$	−29.8539	−1.23536
$585$	8.21184	0.339518
$586$	−0.406873	−0.0168078
$587$	21.1916	0.874671	0.437336	−	0.899298i	$-0.355922\pi$
$587$	21.1916	0.874671	0.437336	+	0.899298i	$0.355922\pi$
$588$	−12.4991	−0.515454
$589$	−15.5681	−0.641472
$590$	5.46120	0.224834
$591$	−36.7380	−1.51120
$592$	115.639	4.75273
$593$	−36.6543	−1.50521	−0.752605	−	0.658472i	$-0.771203\pi$
$593$	−36.6543	−1.50521	−0.752605	+	0.658472i	$0.771203\pi$
$594$	−2.05204	−0.0841960
$595$	−6.72534	−0.275712
$596$	−25.2417	−1.03394
$597$	34.3825	1.40718
$598$	57.0593	2.33333
$599$	−27.3253	−1.11648	−0.558241	−	0.829679i	$-0.688523\pi$
$599$	−27.3253	−1.11648	−0.558241	+	0.829679i	$0.688523\pi$
$600$	20.1499	0.822616
$601$	−26.8597	−1.09563	−0.547815	−	0.836600i	$-0.684540\pi$
$601$	−26.8597	−1.09563	−0.547815	+	0.836600i	$0.684540\pi$
$602$	−21.5368	−0.877775
$603$	37.4932	1.52684
$604$	96.5754	3.92960
$605$	−14.2381	−0.578863
$606$	−81.2516	−3.30062
$607$	−11.2817	−0.457910	−0.228955	−	0.973437i	$-0.573531\pi$
$607$	−11.2817	−0.457910	−0.228955	+	0.973437i	$0.573531\pi$
$608$	76.9162	3.11936
$609$	0.165967	0.00672530
$610$	−25.7923	−1.04430
$611$	15.7548	0.637369
$612$	104.551	4.22623
$613$	12.4477	0.502758	0.251379	−	0.967889i	$-0.419116\pi$
$613$	12.4477	0.502758	0.251379	+	0.967889i	$0.419116\pi$
$614$	41.9580	1.69329
$615$	7.51974	0.303225
$616$	41.1131	1.65649
$617$	43.1511	1.73720	0.868598	−	0.495517i	$-0.165021\pi$
$617$	43.1511	1.73720	0.868598	+	0.495517i	$0.165021\pi$
$618$	6.32907	0.254593
$619$	40.4541	1.62599	0.812994	−	0.582271i	$-0.197836\pi$
$619$	40.4541	1.62599	0.812994	+	0.582271i	$0.197836\pi$
$620$	−14.9355	−0.599822
$621$	−1.22825	−0.0492878
$622$	−2.08295	−0.0835187
$623$	6.83126	0.273689
$624$	76.7017	3.07053
$625$	1.00000	0.0400000
$626$	−17.5337	−0.700787
$627$	−65.4521	−2.61390
$628$	117.112	4.67330
$629$	66.9450	2.66927
$630$	8.14636	0.324559
$631$	−39.0702	−1.55536	−0.777680	−	0.628660i	$-0.783604\pi$
$631$	−39.0702	−1.55536	−0.777680	+	0.628660i	$0.783604\pi$
$632$	−77.1918	−3.07052
$633$	13.8773	0.551573
$634$	4.03420	0.160218
$635$	15.8199	0.627792
$636$	158.417	6.28166
$637$	−2.68154	−0.106246
$638$	−0.900814	−0.0356636
$639$	2.61505	0.103450
$640$	11.9837	0.473699
$641$	6.27190	0.247725	0.123863	−	0.992299i	$-0.460472\pi$
$641$	6.27190	0.247725	0.123863	+	0.992299i	$0.460472\pi$
$642$	−40.6722	−1.60520
$643$	17.9945	0.709633	0.354817	−	0.934936i	$-0.384543\pi$
$643$	17.9945	0.709633	0.354817	+	0.934936i	$0.384543\pi$
$644$	40.6063	1.60011
$645$	19.9341	0.784903
$646$	94.6662	3.72459
$647$	−34.3690	−1.35118	−0.675592	−	0.737275i	$-0.736112\pi$
$647$	−34.3690	−1.35118	−0.675592	+	0.737275i	$0.736112\pi$
$648$	72.0907	2.83199
$649$	−10.3136	−0.404844
$650$	7.13330	0.279791
$651$	−7.24407	−0.283917
$652$	−91.0637	−3.56633
$653$	31.6461	1.23841	0.619205	−	0.785230i	$-0.287455\pi$
$653$	31.6461	1.23841	0.619205	+	0.785230i	$0.287455\pi$
$654$	112.217	4.38803
$655$	−4.37209	−0.170832
$656$	35.4799	1.38526
$657$	11.1714	0.435837
$658$	15.6291	0.609286
$659$	11.2195	0.437051	0.218526	−	0.975831i	$-0.429875\pi$
$659$	11.2195	0.437051	0.218526	+	0.975831i	$0.429875\pi$
$660$	−62.7924	−2.44419
$661$	3.19836	0.124402	0.0622010	−	0.998064i	$-0.480188\pi$
$661$	3.19836	0.124402	0.0622010	+	0.998064i	$0.480188\pi$
$662$	−47.6018	−1.85009
$663$	44.4037	1.72450
$664$	54.6790	2.12196
$665$	5.29144	0.205193
$666$	−81.0900	−3.14217
$667$	−0.539182	−0.0208772
$668$	−19.3421	−0.748369
$669$	−7.17655	−0.277461
$670$	32.5689	1.25824
$671$	48.7093	1.88040
$672$	35.7903	1.38064
$673$	13.5020	0.520465	0.260232	−	0.965546i	$-0.416201\pi$
$673$	13.5020	0.520465	0.260232	+	0.965546i	$0.416201\pi$
$674$	10.5784	0.407463
$675$	−0.153550	−0.00591014
$676$	−29.4907	−1.13426
$677$	34.7512	1.33560	0.667799	−	0.744342i	$-0.267237\pi$
$677$	34.7512	1.33560	0.667799	+	0.744342i	$0.267237\pi$
$678$	−80.3609	−3.08624
$679$	9.78665	0.375577
$680$	55.0385	2.11063
$681$	−35.6141	−1.36474
$682$	39.3185	1.50558
$683$	46.7382	1.78839	0.894194	−	0.447679i	$-0.147749\pi$
$683$	46.7382	1.78839	0.894194	+	0.447679i	$0.147749\pi$
$684$	−82.2598	−3.14528
$685$	−16.5390	−0.631924
$686$	−2.66015	−0.101565
$687$	2.46219	0.0939383
$688$	94.0535	3.58576
$689$	33.9867	1.29479
$690$	−52.3918	−1.99452
$691$	−0.186806	−0.00710644	−0.00355322	−	0.999994i	$-0.501131\pi$
$691$	−0.186806	−0.00710644	−0.00355322	+	0.999994i	$0.501131\pi$
$692$	−16.3646	−0.622087
$693$	−15.3846	−0.584412
$694$	−61.5867	−2.33780
$695$	8.93436	0.338900
$696$	−1.35823	−0.0514835
$697$	20.5398	0.778001
$698$	22.5060	0.851865
$699$	−7.65780	−0.289645
$700$	5.07642	0.191870
$701$	−30.9513	−1.16902	−0.584508	−	0.811388i	$-0.698712\pi$
$701$	−30.9513	−1.16902	−0.584508	+	0.811388i	$0.698712\pi$
$702$	−1.09532	−0.0413401
$703$	−52.6717	−1.98655
$704$	−77.5345	−2.92219
$705$	−14.4660	−0.544821
$706$	68.4794	2.57726
$707$	−12.4052	−0.466546
$708$	−25.6602	−0.964368
$709$	−25.3159	−0.950757	−0.475378	−	0.879781i	$-0.657689\pi$
$709$	−25.3159	−0.950757	−0.475378	+	0.879781i	$0.657689\pi$
$710$	2.27159	0.0852513
$711$	28.8853	1.08328
$712$	−55.9052	−2.09514
$713$	23.5341	0.881358
$714$	44.0496	1.64852
$715$	−13.4714	−0.503802
$716$	−84.6460	−3.16337
$717$	26.1875	0.977992
$718$	20.4735	0.764064
$719$	2.70479	0.100872	0.0504358	−	0.998727i	$-0.483939\pi$
$719$	2.70479	0.100872	0.0504358	+	0.998727i	$0.483939\pi$
$720$	−35.5760	−1.32584
$721$	0.966301	0.0359869
$722$	−23.9396	−0.890939
$723$	−38.1109	−1.41736
$724$	−12.1622	−0.452006
$725$	−0.0674062	−0.00250340
$726$	93.2569	3.46109
$727$	−29.8820	−1.10826	−0.554132	−	0.832429i	$-0.686950\pi$
$727$	−29.8820	−1.10826	−0.554132	+	0.832429i	$0.686950\pi$
$728$	21.9450	0.813336
$729$	−28.1106	−1.04113
$730$	9.70412	0.359166
$731$	54.4490	2.01387
$732$	121.189	4.47926
$733$	−34.3779	−1.26978	−0.634888	−	0.772604i	$-0.718954\pi$
$733$	−34.3779	−1.26978	−0.634888	+	0.772604i	$0.718954\pi$
$734$	98.8352	3.64808
$735$	2.46219	0.0908191
$736$	−116.273	−4.28589
$737$	−61.5070	−2.26564
$738$	−24.8797	−0.915835
$739$	−13.1656	−0.484303	−0.242152	−	0.970238i	$-0.577853\pi$
$739$	−13.1656	−0.484303	−0.242152	+	0.970238i	$0.577853\pi$
$740$	−50.5314	−1.85757
$741$	−34.9365	−1.28342
$742$	33.7156	1.23774
$743$	21.4055	0.785290	0.392645	−	0.919690i	$-0.371560\pi$
$743$	21.4055	0.785290	0.392645	+	0.919690i	$0.371560\pi$
$744$	59.2835	2.17344
$745$	4.97235	0.182173
$746$	76.8377	2.81323
$747$	−20.4609	−0.748626
$748$	−171.514	−6.27119
$749$	−6.20969	−0.226897
$750$	−6.54979	−0.239165
$751$	39.7262	1.44963	0.724815	−	0.688943i	$-0.241925\pi$
$751$	39.7262	1.44963	0.724815	+	0.688943i	$0.241925\pi$
$752$	−68.2540	−2.48897
$753$	49.4637	1.80256
$754$	−0.480829	−0.0175107
$755$	−19.0243	−0.692366
$756$	−0.779483	−0.0283495
$757$	15.0983	0.548757	0.274379	−	0.961622i	$-0.411528\pi$
$757$	15.0983	0.548757	0.274379	+	0.961622i	$0.411528\pi$
$758$	−23.4261	−0.850875
$759$	98.9431	3.59141
$760$	−43.3037	−1.57079
$761$	28.1811	1.02156	0.510782	−	0.859710i	$-0.329356\pi$
$761$	28.1811	1.02156	0.510782	+	0.859710i	$0.329356\pi$
$762$	−103.617	−3.75364
$763$	17.1329	0.620252
$764$	−4.76041	−0.172226
$765$	−20.5954	−0.744630
$766$	35.8420	1.29503
$767$	−5.50510	−0.198778
$768$	−2.49030	−0.0898611
$769$	9.39819	0.338907	0.169454	−	0.985538i	$-0.445800\pi$
$769$	9.39819	0.338907	0.169454	+	0.985538i	$0.445800\pi$
$770$	−13.3640	−0.481604
$771$	36.1263	1.30106
$772$	20.7344	0.746246
$773$	−5.90845	−0.212512	−0.106256	−	0.994339i	$-0.533886\pi$
$773$	−5.90845	−0.212512	−0.106256	+	0.994339i	$0.533886\pi$
$774$	−65.9536	−2.37065
$775$	2.94213	0.105684
$776$	−80.0914	−2.87511
$777$	−24.5090	−0.879254
$778$	−84.7734	−3.03927
$779$	−16.1605	−0.579011
$780$	−33.5168	−1.20009
$781$	−4.28995	−0.153507
$782$	−143.106	−5.11745
$783$	0.0103502	0.000369886 0
$784$	11.6172	0.414899
$785$	−23.0699	−0.823400
$786$	28.6363	1.02142
$787$	32.1501	1.14603	0.573013	−	0.819546i	$-0.305774\pi$
$787$	32.1501	1.14603	0.573013	+	0.819546i	$0.305774\pi$
$788$	75.7445	2.69829
$789$	50.6023	1.80149
$790$	25.0915	0.892714
$791$	−12.2692	−0.436243
$792$	125.903	4.47378
$793$	25.9996	0.923275
$794$	−56.9105	−2.01968
$795$	−31.2065	−1.10678
$796$	−70.8882	−2.51257
$797$	−51.8085	−1.83515	−0.917575	−	0.397562i	$-0.869856\pi$
$797$	−51.8085	−1.83515	−0.917575	+	0.397562i	$0.869856\pi$
$798$	−34.6578	−1.22687
$799$	−39.5132	−1.39788
$800$	−14.5360	−0.513924
$801$	20.9198	0.739165
$802$	−73.0635	−2.57996
$803$	−18.3265	−0.646726
$804$	−153.029	−5.39692
$805$	−7.99900	−0.281928
$806$	20.9871	0.739239
$807$	−13.2417	−0.466130
$808$	101.521	3.57150
$809$	23.7745	0.835868	0.417934	−	0.908477i	$-0.362754\pi$
$809$	23.7745	0.835868	0.417934	+	0.908477i	$0.362754\pi$
$810$	−23.4333	−0.823364
$811$	−14.3237	−0.502974	−0.251487	−	0.967861i	$-0.580919\pi$
$811$	−14.3237	−0.502974	−0.251487	+	0.967861i	$0.580919\pi$
$812$	−0.342182	−0.0120082
$813$	−19.8909	−0.697605
$814$	133.027	4.66259
$815$	17.9386	0.628361
$816$	−192.369	−6.73427
$817$	−42.8399	−1.49878
$818$	91.8708	3.21219
$819$	−8.21184	−0.286945
$820$	−15.5038	−0.541417
$821$	32.9544	1.15012	0.575059	−	0.818112i	$-0.304979\pi$
$821$	32.9544	1.15012	0.575059	+	0.818112i	$0.304979\pi$
$822$	108.327	3.77835
$823$	−16.6287	−0.579642	−0.289821	−	0.957081i	$-0.593596\pi$
$823$	−16.6287	−0.579642	−0.289821	+	0.957081i	$0.593596\pi$
$824$	−7.90795	−0.275487
$825$	12.3694	0.430648
$826$	−5.46120	−0.190019
$827$	21.2676	0.739546	0.369773	−	0.929122i	$-0.379436\pi$
$827$	21.2676	0.739546	0.369773	+	0.929122i	$0.379436\pi$
$828$	124.351	4.32150
$829$	21.3125	0.740213	0.370106	−	0.928989i	$-0.379321\pi$
$829$	21.3125	0.740213	0.370106	+	0.928989i	$0.379321\pi$
$830$	−17.7736	−0.616931
$831$	−16.2266	−0.562896
$832$	−41.3857	−1.43479
$833$	6.72534	0.233019
$834$	−58.5182	−2.02632
$835$	3.81019	0.131857
$836$	134.946	4.66720
$837$	−0.451763	−0.0156152
$838$	65.7944	2.27283
$839$	33.4580	1.15510	0.577549	−	0.816356i	$-0.304009\pi$
$839$	33.4580	1.15510	0.577549	+	0.816356i	$0.304009\pi$
$840$	−20.1499	−0.695237
$841$	−28.9955	−0.999843
$842$	−70.9151	−2.44390
$843$	36.7039	1.26415
$844$	−28.6115	−0.984849
$845$	5.80935	0.199848
$846$	47.8620	1.64553
$847$	14.2381	0.489228
$848$	−147.240	−5.05623
$849$	−27.4462	−0.941951
$850$	−17.8904	−0.613637
$851$	79.6232	2.72945
$852$	−10.6734	−0.365664
$853$	−11.8084	−0.404311	−0.202156	−	0.979353i	$-0.564795\pi$
$853$	−11.8084	−0.404311	−0.202156	+	0.979353i	$0.564795\pi$
$854$	25.7923	0.882594
$855$	16.2043	0.554176
$856$	50.8185	1.73694
$857$	−26.2958	−0.898248	−0.449124	−	0.893469i	$-0.648264\pi$
$857$	−26.2958	−0.898248	−0.449124	+	0.893469i	$0.648264\pi$
$858$	88.2349	3.01229
$859$	29.4629	1.00526	0.502630	−	0.864502i	$-0.332366\pi$
$859$	29.4629	1.00526	0.502630	+	0.864502i	$0.332366\pi$
$860$	−41.0991	−1.40147
$861$	−7.51974	−0.256272
$862$	81.1996	2.76567
$863$	43.1878	1.47013	0.735065	−	0.677996i	$-0.237151\pi$
$863$	43.1878	1.47013	0.735065	+	0.677996i	$0.237151\pi$
$864$	2.23200	0.0759340
$865$	3.22364	0.109607
$866$	−53.1350	−1.80560
$867$	−69.5082	−2.36062
$868$	14.9355	0.506943
$869$	−47.3858	−1.60745
$870$	0.441496	0.0149681
$871$	−32.8307	−1.11243
$872$	−140.211	−4.74814
$873$	29.9703	1.01434
$874$	112.594	3.80856
$875$	−1.00000	−0.0338062
$876$	−45.5961	−1.54055
$877$	−2.26618	−0.0765234	−0.0382617	−	0.999268i	$-0.512182\pi$
$877$	−2.26618	−0.0765234	−0.0382617	+	0.999268i	$0.512182\pi$
$878$	−11.0762	−0.373805
$879$	−0.376594	−0.0127022
$880$	58.3618	1.96738
$881$	−36.1664	−1.21848	−0.609239	−	0.792986i	$-0.708525\pi$
$881$	−36.1664	−1.21848	−0.609239	+	0.792986i	$0.708525\pi$
$882$	−8.14636	−0.274302
$883$	−37.6357	−1.26654	−0.633271	−	0.773930i	$-0.718288\pi$
$883$	−37.6357	−1.26654	−0.633271	+	0.773930i	$0.718288\pi$
$884$	−91.5495	−3.07914
$885$	5.05478	0.169915
$886$	−82.4173	−2.76886
$887$	15.8373	0.531763	0.265882	−	0.964006i	$-0.414337\pi$
$887$	15.8373	0.531763	0.265882	+	0.964006i	$0.414337\pi$
$888$	200.575	6.73085
$889$	−15.8199	−0.530581
$890$	18.1722	0.609134
$891$	44.2544	1.48258
$892$	14.7963	0.495415
$893$	31.0886	1.04034
$894$	−32.5679	−1.08923
$895$	16.6744	0.557362
$896$	−11.9837	−0.400348
$897$	52.8130	1.76338
$898$	−18.1712	−0.606381
$899$	−0.198317	−0.00661426
$900$	15.5458	0.518194
$901$	−85.2391	−2.83973
$902$	40.8148	1.35898
$903$	−19.9341	−0.663364
$904$	100.408	3.33953
$905$	2.39583	0.0796402
$906$	124.605	4.13974
$907$	15.5452	0.516171	0.258086	−	0.966122i	$-0.416908\pi$
$907$	15.5452	0.516171	0.258086	+	0.966122i	$0.416908\pi$
$908$	73.4275	2.43678
$909$	−37.9893	−1.26002
$910$	−7.13330	−0.236467
$911$	5.43749	0.180152	0.0900760	−	0.995935i	$-0.471289\pi$
$911$	5.43749	0.180152	0.0900760	+	0.995935i	$0.471289\pi$
$912$	151.354	5.01184
$913$	33.5658	1.11087
$914$	−77.5027	−2.56356
$915$	−23.8729	−0.789212
$916$	−5.07642	−0.167730
$917$	4.37209	0.144379
$918$	2.74708	0.0906670
$919$	27.3260	0.901403	0.450701	−	0.892675i	$-0.351174\pi$
$919$	27.3260	0.901403	0.450701	+	0.892675i	$0.351174\pi$
$920$	65.4618	2.15821
$921$	38.8355	1.27967
$922$	73.7341	2.42830
$923$	−2.28985	−0.0753714
$924$	62.7924	2.06572
$925$	9.95414	0.327290
$926$	44.7057	1.46912
$927$	2.95916	0.0971917
$928$	0.979814	0.0321640
$929$	−10.8379	−0.355581	−0.177791	−	0.984068i	$-0.556895\pi$
$929$	−10.8379	−0.355581	−0.177791	+	0.984068i	$0.556895\pi$
$930$	−19.2703	−0.631899
$931$	−5.29144	−0.173420
$932$	15.7885	0.517169
$933$	−1.92794	−0.0631179
$934$	−41.6919	−1.36420
$935$	33.7865	1.10494
$936$	67.2036	2.19662
$937$	−45.2234	−1.47738	−0.738692	−	0.674043i	$-0.764556\pi$
$937$	−45.2234	−1.47738	−0.738692	+	0.674043i	$0.764556\pi$
$938$	−32.5689	−1.06341
$939$	−16.2288	−0.529608
$940$	29.8253	0.972794
$941$	41.9194	1.36653	0.683267	−	0.730169i	$-0.260559\pi$
$941$	41.9194	1.36653	0.683267	+	0.730169i	$0.260559\pi$
$942$	151.103	4.92321
$943$	24.4297	0.795540
$944$	23.8496	0.776239
$945$	0.153550	0.00499498
$946$	108.196	3.51775
$947$	−23.0588	−0.749312	−0.374656	−	0.927164i	$-0.622239\pi$
$947$	−23.0588	−0.749312	−0.374656	+	0.927164i	$0.622239\pi$
$948$	−117.896	−3.82907
$949$	−9.78214	−0.317542
$950$	14.0760	0.456687
$951$	3.73398	0.121082
$952$	−55.0385	−1.78381
$953$	41.2110	1.33496	0.667478	−	0.744630i	$-0.267374\pi$
$953$	41.2110	1.33496	0.667478	+	0.744630i	$0.267374\pi$
$954$	103.249	3.34283
$955$	0.937751	0.0303449
$956$	−53.9922	−1.74623
$957$	−0.833776	−0.0269521
$958$	−73.8414	−2.38571
$959$	16.5390	0.534073
$960$	38.0003	1.22646
$961$	−22.3439	−0.720771
$962$	71.0059	2.28932
$963$	−19.0163	−0.612793
$964$	78.5752	2.53074
$965$	−4.08445	−0.131483
$966$	52.3918	1.68568
$967$	−57.5220	−1.84978	−0.924892	−	0.380231i	$-0.875845\pi$
$967$	−57.5220	−1.84978	−0.924892	+	0.380231i	$0.875845\pi$
$968$	−116.521	−3.74513
$969$	87.6212	2.81480
$970$	26.0340	0.835901
$971$	−53.6721	−1.72242	−0.861209	−	0.508250i	$-0.830292\pi$
$971$	−53.6721	−1.72242	−0.861209	+	0.508250i	$0.830292\pi$
$972$	112.443	3.60662
$973$	−8.93436	−0.286422
$974$	48.0220	1.53872
$975$	6.60245	0.211448
$976$	−112.638	−3.60544
$977$	−19.8556	−0.635236	−0.317618	−	0.948219i	$-0.602883\pi$
$977$	−19.8556	−0.635236	−0.317618	+	0.948219i	$0.602883\pi$
$978$	−117.494	−3.75705
$979$	−34.3186	−1.09683
$980$	−5.07642	−0.162160
$981$	52.4671	1.67515
$982$	56.0545	1.78877
$983$	−2.49292	−0.0795118	−0.0397559	−	0.999209i	$-0.512658\pi$
$983$	−2.49292	−0.0795118	−0.0397559	+	0.999209i	$0.512658\pi$
$984$	61.5396	1.96181
$985$	−14.9209	−0.475418
$986$	1.20593	0.0384045
$987$	14.4660	0.460458
$988$	72.0303	2.29159
$989$	64.7606	2.05927
$990$	−40.9253	−1.30069
$991$	32.0827	1.01914	0.509570	−	0.860429i	$-0.329804\pi$
$991$	32.0827	1.01914	0.509570	+	0.860429i	$0.329804\pi$
$992$	−42.7667	−1.35784
$993$	−44.0593	−1.39818
$994$	−2.27159	−0.0720505
$995$	13.9642	0.442696
$996$	83.5116	2.64617
$997$	10.1371	0.321045	0.160523	−	0.987032i	$-0.448682\pi$
$997$	10.1371	0.321045	0.160523	+	0.987032i	$0.448682\pi$
$998$	94.9455	3.00545
$999$	−1.52846	−0.0483582

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.n.1.3	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.n.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.66015 q^{2} -2.46219 q^{3} +5.07642 q^{4} -1.00000 q^{5} +6.54979 q^{6} +1.00000 q^{7} -8.18374 q^{8} +3.06236 q^{9} +O(q^{10})\)	\(q-2.66015 q^{2} -2.46219 q^{3} +5.07642 q^{4} -1.00000 q^{5} +6.54979 q^{6} +1.00000 q^{7} -8.18374 q^{8} +3.06236 q^{9} +2.66015 q^{10} -5.02376 q^{11} -12.4991 q^{12} -2.68154 q^{13} -2.66015 q^{14} +2.46219 q^{15} +11.6172 q^{16} +6.72534 q^{17} -8.14636 q^{18} -5.29144 q^{19} -5.07642 q^{20} -2.46219 q^{21} +13.3640 q^{22} +7.99900 q^{23} +20.1499 q^{24} +1.00000 q^{25} +7.13330 q^{26} -0.153550 q^{27} +5.07642 q^{28} -0.0674062 q^{29} -6.54979 q^{30} +2.94213 q^{31} -14.5360 q^{32} +12.3694 q^{33} -17.8904 q^{34} -1.00000 q^{35} +15.5458 q^{36} +9.95414 q^{37} +14.0760 q^{38} +6.60245 q^{39} +8.18374 q^{40} +3.05409 q^{41} +6.54979 q^{42} +8.09608 q^{43} -25.5027 q^{44} -3.06236 q^{45} -21.2786 q^{46} -5.87527 q^{47} -28.6036 q^{48} +1.00000 q^{49} -2.66015 q^{50} -16.5591 q^{51} -13.6126 q^{52} -12.6743 q^{53} +0.408466 q^{54} +5.02376 q^{55} -8.18374 q^{56} +13.0285 q^{57} +0.179311 q^{58} +2.05296 q^{59} +12.4991 q^{60} -9.69579 q^{61} -7.82651 q^{62} +3.06236 q^{63} +15.4336 q^{64} +2.68154 q^{65} -32.9046 q^{66} +12.2432 q^{67} +34.1406 q^{68} -19.6950 q^{69} +2.66015 q^{70} +0.853933 q^{71} -25.0616 q^{72} +3.64796 q^{73} -26.4795 q^{74} -2.46219 q^{75} -26.8615 q^{76} -5.02376 q^{77} -17.5635 q^{78} +9.43234 q^{79} -11.6172 q^{80} -8.80902 q^{81} -8.12435 q^{82} -6.68142 q^{83} -12.4991 q^{84} -6.72534 q^{85} -21.5368 q^{86} +0.165967 q^{87} +41.1131 q^{88} +6.83126 q^{89} +8.14636 q^{90} -2.68154 q^{91} +40.6063 q^{92} -7.24407 q^{93} +15.6291 q^{94} +5.29144 q^{95} +35.7903 q^{96} +9.78665 q^{97} -2.66015 q^{98} -15.3846 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9}+O(q^{10}) \) 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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