LMFDB - Embedded newform 8015.2.a.o.1.11

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:	$73$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-2.19612 q^{2} +2.45439 q^{3} +2.82293 q^{4} +1.00000 q^{5} -5.39013 q^{6} +1.00000 q^{7} -1.80725 q^{8} +3.02403 q^{9} +O(q^{10})$	\(q-2.19612 q^{2} +2.45439 q^{3} +2.82293 q^{4} +1.00000 q^{5} -5.39013 q^{6} +1.00000 q^{7} -1.80725 q^{8} +3.02403 q^{9} -2.19612 q^{10} -4.94555 q^{11} +6.92857 q^{12} -5.58880 q^{13} -2.19612 q^{14} +2.45439 q^{15} -1.67693 q^{16} -1.65223 q^{17} -6.64113 q^{18} -6.19834 q^{19} +2.82293 q^{20} +2.45439 q^{21} +10.8610 q^{22} +7.68759 q^{23} -4.43569 q^{24} +1.00000 q^{25} +12.2737 q^{26} +0.0589907 q^{27} +2.82293 q^{28} -4.21500 q^{29} -5.39013 q^{30} +5.11417 q^{31} +7.29723 q^{32} -12.1383 q^{33} +3.62848 q^{34} +1.00000 q^{35} +8.53664 q^{36} +4.28782 q^{37} +13.6123 q^{38} -13.7171 q^{39} -1.80725 q^{40} +0.661754 q^{41} -5.39013 q^{42} +11.9278 q^{43} -13.9609 q^{44} +3.02403 q^{45} -16.8828 q^{46} +9.56527 q^{47} -4.11584 q^{48} +1.00000 q^{49} -2.19612 q^{50} -4.05521 q^{51} -15.7768 q^{52} +4.84349 q^{53} -0.129550 q^{54} -4.94555 q^{55} -1.80725 q^{56} -15.2132 q^{57} +9.25663 q^{58} -2.63539 q^{59} +6.92857 q^{60} -5.46300 q^{61} -11.2313 q^{62} +3.02403 q^{63} -12.6717 q^{64} -5.58880 q^{65} +26.6572 q^{66} -2.39421 q^{67} -4.66412 q^{68} +18.8683 q^{69} -2.19612 q^{70} +7.36214 q^{71} -5.46518 q^{72} -1.58835 q^{73} -9.41656 q^{74} +2.45439 q^{75} -17.4975 q^{76} -4.94555 q^{77} +30.1244 q^{78} -3.65057 q^{79} -1.67693 q^{80} -8.92732 q^{81} -1.45329 q^{82} -7.40723 q^{83} +6.92857 q^{84} -1.65223 q^{85} -26.1948 q^{86} -10.3453 q^{87} +8.93784 q^{88} +13.4338 q^{89} -6.64113 q^{90} -5.58880 q^{91} +21.7015 q^{92} +12.5522 q^{93} -21.0065 q^{94} -6.19834 q^{95} +17.9103 q^{96} +4.86127 q^{97} -2.19612 q^{98} -14.9555 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) $ 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * q^98 + 49 * 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 $

$2$	−2.19612	−1.55289	−0.776445	−	0.630186i	$-0.782979\pi$
$2$	−2.19612	−1.55289	−0.776445	+	0.630186i	$0.782979\pi$
$3$	2.45439	1.41704	0.708522	−	0.705689i	$-0.249362\pi$
$3$	2.45439	1.41704	0.708522	+	0.705689i	$0.249362\pi$
$4$	2.82293	1.41146
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−5.39013	−2.20051
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.80725	−0.638959
$9$	3.02403	1.00801
$10$	−2.19612	−0.694473
$11$	−4.94555	−1.49114	−0.745570	−	0.666427i	$-0.767823\pi$
$11$	−4.94555	−1.49114	−0.745570	+	0.666427i	$0.767823\pi$
$12$	6.92857	2.00011
$13$	−5.58880	−1.55005	−0.775027	−	0.631928i	$-0.782264\pi$
$13$	−5.58880	−1.55005	−0.775027	+	0.631928i	$0.782264\pi$
$14$	−2.19612	−0.586937
$15$	2.45439	0.633721
$16$	−1.67693	−0.419232
$17$	−1.65223	−0.400724	−0.200362	−	0.979722i	$-0.564212\pi$
$17$	−1.65223	−0.400724	−0.200362	+	0.979722i	$0.564212\pi$
$18$	−6.64113	−1.56533
$19$	−6.19834	−1.42200	−0.710999	−	0.703193i	$-0.751757\pi$
$19$	−6.19834	−1.42200	−0.710999	+	0.703193i	$0.751757\pi$
$20$	2.82293	0.631226
$21$	2.45439	0.535592
$22$	10.8610	2.31558
$23$	7.68759	1.60297	0.801486	−	0.598013i	$-0.204043\pi$
$23$	7.68759	1.60297	0.801486	+	0.598013i	$0.204043\pi$
$24$	−4.43569	−0.905432
$25$	1.00000	0.200000
$26$	12.2737	2.40706
$27$	0.0589907	0.0113528
$28$	2.82293	0.533483
$29$	−4.21500	−0.782705	−0.391353	−	0.920241i	$-0.627993\pi$
$29$	−4.21500	−0.782705	−0.391353	+	0.920241i	$0.627993\pi$
$30$	−5.39013	−0.984098
$31$	5.11417	0.918531	0.459266	−	0.888299i	$-0.348113\pi$
$31$	5.11417	0.918531	0.459266	+	0.888299i	$0.348113\pi$
$32$	7.29723	1.28998
$33$	−12.1383	−2.11301
$34$	3.62848	0.622280
$35$	1.00000	0.169031
$36$	8.53664	1.42277
$37$	4.28782	0.704914	0.352457	−	0.935828i	$-0.385346\pi$
$37$	4.28782	0.704914	0.352457	+	0.935828i	$0.385346\pi$
$38$	13.6123	2.20820
$39$	−13.7171	−2.19649
$40$	−1.80725	−0.285751
$41$	0.661754	0.103349	0.0516743	−	0.998664i	$-0.483544\pi$
$41$	0.661754	0.103349	0.0516743	+	0.998664i	$0.483544\pi$
$42$	−5.39013	−0.831715
$43$	11.9278	1.81897	0.909485	−	0.415736i	$-0.136476\pi$
$43$	11.9278	1.81897	0.909485	+	0.415736i	$0.136476\pi$
$44$	−13.9609	−2.10469
$45$	3.02403	0.450796
$46$	−16.8828	−2.48924
$47$	9.56527	1.39524	0.697619	−	0.716469i	$-0.254243\pi$
$47$	9.56527	1.39524	0.697619	+	0.716469i	$0.254243\pi$
$48$	−4.11584	−0.594071
$49$	1.00000	0.142857
$50$	−2.19612	−0.310578
$51$	−4.05521	−0.567843
$52$	−15.7768	−2.18785
$53$	4.84349	0.665304	0.332652	−	0.943050i	$-0.392057\pi$
$53$	4.84349	0.665304	0.332652	+	0.943050i	$0.392057\pi$
$54$	−0.129550	−0.0176296
$55$	−4.94555	−0.666858
$56$	−1.80725	−0.241504
$57$	−15.2132	−2.01503
$58$	9.25663	1.21545
$59$	−2.63539	−0.343098	−0.171549	−	0.985176i	$-0.554877\pi$
$59$	−2.63539	−0.343098	−0.171549	+	0.985176i	$0.554877\pi$
$60$	6.92857	0.894475
$61$	−5.46300	−0.699465	−0.349733	−	0.936850i	$-0.613728\pi$
$61$	−5.46300	−0.699465	−0.349733	+	0.936850i	$0.613728\pi$
$62$	−11.2313	−1.42638
$63$	3.02403	0.380993
$64$	−12.6717	−1.58396
$65$	−5.58880	−0.693206
$66$	26.6572	3.28127
$67$	−2.39421	−0.292499	−0.146249	−	0.989248i	$-0.546720\pi$
$67$	−2.39421	−0.292499	−0.146249	+	0.989248i	$0.546720\pi$
$68$	−4.66412	−0.565608
$69$	18.8683	2.27148
$70$	−2.19612	−0.262486
$71$	7.36214	0.873725	0.436863	−	0.899528i	$-0.356090\pi$
$71$	7.36214	0.873725	0.436863	+	0.899528i	$0.356090\pi$
$72$	−5.46518	−0.644078
$73$	−1.58835	−0.185902	−0.0929511	−	0.995671i	$-0.529630\pi$
$73$	−1.58835	−0.185902	−0.0929511	+	0.995671i	$0.529630\pi$
$74$	−9.41656	−1.09465
$75$	2.45439	0.283409
$76$	−17.4975	−2.00710
$77$	−4.94555	−0.563598
$78$	30.1244	3.41091
$79$	−3.65057	−0.410721	−0.205360	−	0.978686i	$-0.565837\pi$
$79$	−3.65057	−0.410721	−0.205360	+	0.978686i	$0.565837\pi$
$80$	−1.67693	−0.187486
$81$	−8.92732	−0.991924
$82$	−1.45329	−0.160489
$83$	−7.40723	−0.813049	−0.406525	−	0.913640i	$-0.633259\pi$
$83$	−7.40723	−0.813049	−0.406525	+	0.913640i	$0.633259\pi$
$84$	6.92857	0.755969
$85$	−1.65223	−0.179209
$86$	−26.1948	−2.82466
$87$	−10.3453	−1.10913
$88$	8.93784	0.952777
$89$	13.4338	1.42398	0.711988	−	0.702192i	$-0.247795\pi$
$89$	13.4338	1.42398	0.711988	+	0.702192i	$0.247795\pi$
$90$	−6.64113	−0.700037
$91$	−5.58880	−0.585866
$92$	21.7015	2.26254
$93$	12.5522	1.30160
$94$	−21.0065	−2.16665
$95$	−6.19834	−0.635937
$96$	17.9103	1.82796
$97$	4.86127	0.493587	0.246794	−	0.969068i	$-0.420623\pi$
$97$	4.86127	0.493587	0.246794	+	0.969068i	$0.420623\pi$
$98$	−2.19612	−0.221841
$99$	−14.9555	−1.50309
$100$	2.82293	0.282293
$101$	6.02446	0.599456	0.299728	−	0.954025i	$-0.403104\pi$
$101$	6.02446	0.599456	0.299728	+	0.954025i	$0.403104\pi$
$102$	8.90572	0.881798
$103$	13.6572	1.34568	0.672840	−	0.739788i	$-0.265074\pi$
$103$	13.6572	1.34568	0.672840	+	0.739788i	$0.265074\pi$
$104$	10.1004	0.990421
$105$	2.45439	0.239524
$106$	−10.6369	−1.03314
$107$	−10.8007	−1.04414	−0.522069	−	0.852903i	$-0.674840\pi$
$107$	−10.8007	−1.04414	−0.522069	+	0.852903i	$0.674840\pi$
$108$	0.166526	0.0160240
$109$	16.4942	1.57986	0.789928	−	0.613200i	$-0.210118\pi$
$109$	16.4942	1.57986	0.789928	+	0.613200i	$0.210118\pi$
$110$	10.8610	1.03556
$111$	10.5240	0.998893
$112$	−1.67693	−0.158455
$113$	−2.95170	−0.277673	−0.138836	−	0.990315i	$-0.544336\pi$
$113$	−2.95170	−0.277673	−0.138836	+	0.990315i	$0.544336\pi$
$114$	33.4099	3.12912
$115$	7.68759	0.716871
$116$	−11.8986	−1.10476
$117$	−16.9007	−1.56247
$118$	5.78762	0.532793
$119$	−1.65223	−0.151459
$120$	−4.43569	−0.404922
$121$	13.4585	1.22350
$122$	11.9974	1.08619
$123$	1.62420	0.146449
$124$	14.4369	1.29647
$125$	1.00000	0.0894427
$126$	−6.64113	−0.591639
$127$	20.8814	1.85293	0.926464	−	0.376383i	$-0.122832\pi$
$127$	20.8814	1.85293	0.926464	+	0.376383i	$0.122832\pi$
$128$	13.2341	1.16974
$129$	29.2755	2.57756
$130$	12.2737	1.07647
$131$	−21.0653	−1.84049	−0.920244	−	0.391345i	$-0.872010\pi$
$131$	−21.0653	−1.84049	−0.920244	+	0.391345i	$0.872010\pi$
$132$	−34.2656	−2.98244
$133$	−6.19834	−0.537465
$134$	5.25796	0.454218
$135$	0.0589907	0.00507711
$136$	2.98599	0.256046
$137$	1.87977	0.160599	0.0802997	−	0.996771i	$-0.474412\pi$
$137$	1.87977	0.160599	0.0802997	+	0.996771i	$0.474412\pi$
$138$	−41.4371	−3.52736
$139$	7.48345	0.634738	0.317369	−	0.948302i	$-0.397201\pi$
$139$	7.48345	0.634738	0.317369	+	0.948302i	$0.397201\pi$
$140$	2.82293	0.238581
$141$	23.4769	1.97711
$142$	−16.1681	−1.35680
$143$	27.6397	2.31135
$144$	−5.07109	−0.422591
$145$	−4.21500	−0.350036
$146$	3.48820	0.288686
$147$	2.45439	0.202435
$148$	12.1042	0.994961
$149$	6.61991	0.542324	0.271162	−	0.962534i	$-0.412592\pi$
$149$	6.61991	0.542324	0.271162	+	0.962534i	$0.412592\pi$
$150$	−5.39013	−0.440102
$151$	−3.76214	−0.306158	−0.153079	−	0.988214i	$-0.548919\pi$
$151$	−3.76214	−0.306158	−0.153079	+	0.988214i	$0.548919\pi$
$152$	11.2019	0.908598
$153$	−4.99639	−0.403934
$154$	10.8610	0.875205
$155$	5.11417	0.410780
$156$	−38.7224	−3.10027
$157$	−9.63194	−0.768712	−0.384356	−	0.923185i	$-0.625576\pi$
$157$	−9.63194	−0.768712	−0.384356	+	0.923185i	$0.625576\pi$
$158$	8.01707	0.637804
$159$	11.8878	0.942764
$160$	7.29723	0.576897
$161$	7.68759	0.605867
$162$	19.6054	1.54035
$163$	17.9989	1.40978	0.704891	−	0.709316i	$-0.250996\pi$
$163$	17.9989	1.40978	0.704891	+	0.709316i	$0.250996\pi$
$164$	1.86808	0.145873
$165$	−12.1383	−0.944967
$166$	16.2671	1.26258
$167$	15.6341	1.20980	0.604902	−	0.796300i	$-0.293212\pi$
$167$	15.6341	1.20980	0.604902	+	0.796300i	$0.293212\pi$
$168$	−4.43569	−0.342221
$169$	18.2347	1.40267
$170$	3.62848	0.278292
$171$	−18.7440	−1.43339
$172$	33.6713	2.56741
$173$	3.07918	0.234106	0.117053	−	0.993126i	$-0.462655\pi$
$173$	3.07918	0.234106	0.117053	+	0.993126i	$0.462655\pi$
$174$	22.7194	1.72235
$175$	1.00000	0.0755929
$176$	8.29334	0.625134
$177$	−6.46827	−0.486185
$178$	−29.5021	−2.21128
$179$	−7.11863	−0.532072	−0.266036	−	0.963963i	$-0.585714\pi$
$179$	−7.11863	−0.532072	−0.266036	+	0.963963i	$0.585714\pi$
$180$	8.53664	0.636283
$181$	−17.8518	−1.32692	−0.663459	−	0.748213i	$-0.730912\pi$
$181$	−17.8518	−1.32692	−0.663459	+	0.748213i	$0.730912\pi$
$182$	12.2737	0.909784
$183$	−13.4083	−0.991173
$184$	−13.8934	−1.02423
$185$	4.28782	0.315247
$186$	−27.5660	−2.02124
$187$	8.17118	0.597536
$188$	27.0021	1.96933
$189$	0.0589907	0.00429094
$190$	13.6123	0.987539
$191$	6.12249	0.443008	0.221504	−	0.975159i	$-0.428903\pi$
$191$	6.12249	0.443008	0.221504	+	0.975159i	$0.428903\pi$
$192$	−31.1013	−2.24455
$193$	−22.6276	−1.62877	−0.814384	−	0.580326i	$-0.802925\pi$
$193$	−22.6276	−1.62877	−0.814384	+	0.580326i	$0.802925\pi$
$194$	−10.6759	−0.766487
$195$	−13.7171	−0.982302
$196$	2.82293	0.201638
$197$	−6.01958	−0.428877	−0.214439	−	0.976737i	$-0.568792\pi$
$197$	−6.01958	−0.428877	−0.214439	+	0.976737i	$0.568792\pi$
$198$	32.8441	2.33413
$199$	9.65352	0.684320	0.342160	−	0.939642i	$-0.388842\pi$
$199$	9.65352	0.684320	0.342160	+	0.939642i	$0.388842\pi$
$200$	−1.80725	−0.127792
$201$	−5.87632	−0.414483
$202$	−13.2304	−0.930889
$203$	−4.21500	−0.295835
$204$	−11.4476	−0.801491
$205$	0.661754	0.0462189
$206$	−29.9927	−2.08969
$207$	23.2475	1.61581
$208$	9.37203	0.649833
$209$	30.6542	2.12040
$210$	−5.39013	−0.371954
$211$	26.4355	1.81989	0.909947	−	0.414725i	$-0.136122\pi$
$211$	26.4355	1.81989	0.909947	+	0.414725i	$0.136122\pi$
$212$	13.6728	0.939053
$213$	18.0696	1.23811
$214$	23.7195	1.62143
$215$	11.9278	0.813468
$216$	−0.106611	−0.00725394
$217$	5.11417	0.347172
$218$	−36.2231	−2.45334
$219$	−3.89843	−0.263432
$220$	−13.9609	−0.941247
$221$	9.23397	0.621144
$222$	−23.1119	−1.55117
$223$	21.2564	1.42344	0.711718	−	0.702465i	$-0.247917\pi$
$223$	21.2564	1.42344	0.711718	+	0.702465i	$0.247917\pi$
$224$	7.29723	0.487567
$225$	3.02403	0.201602
$226$	6.48228	0.431195
$227$	−7.51651	−0.498888	−0.249444	−	0.968389i	$-0.580248\pi$
$227$	−7.51651	−0.498888	−0.249444	+	0.968389i	$0.580248\pi$
$228$	−42.9457	−2.84415
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−16.8828	−1.11322
$231$	−12.1383	−0.798643
$232$	7.61755	0.500116
$233$	14.6716	0.961169	0.480584	−	0.876949i	$-0.340425\pi$
$233$	14.6716	0.961169	0.480584	+	0.876949i	$0.340425\pi$
$234$	37.1160	2.42635
$235$	9.56527	0.623970
$236$	−7.43951	−0.484271
$237$	−8.95992	−0.582009
$238$	3.62848	0.235200
$239$	26.4836	1.71308	0.856539	−	0.516082i	$-0.172610\pi$
$239$	26.4836	1.71308	0.856539	+	0.516082i	$0.172610\pi$
$240$	−4.11584	−0.265676
$241$	−7.09957	−0.457323	−0.228662	−	0.973506i	$-0.573435\pi$
$241$	−7.09957	−0.457323	−0.228662	+	0.973506i	$0.573435\pi$
$242$	−29.5564	−1.89996
$243$	−22.0881	−1.41695
$244$	−15.4217	−0.987271
$245$	1.00000	0.0638877
$246$	−3.56694	−0.227420
$247$	34.6413	2.20417
$248$	−9.24257	−0.586904
$249$	−18.1802	−1.15213
$250$	−2.19612	−0.138895
$251$	−4.15242	−0.262098	−0.131049	−	0.991376i	$-0.541835\pi$
$251$	−4.15242	−0.262098	−0.131049	+	0.991376i	$0.541835\pi$
$252$	8.53664	0.537757
$253$	−38.0194	−2.39026
$254$	−45.8581	−2.87739
$255$	−4.05521	−0.253947
$256$	−3.72020	−0.232512
$257$	−17.0809	−1.06547	−0.532737	−	0.846281i	$-0.678837\pi$
$257$	−17.0809	−1.06547	−0.532737	+	0.846281i	$0.678837\pi$
$258$	−64.2923	−4.00267
$259$	4.28782	0.266432
$260$	−15.7768	−0.978435
$261$	−12.7463	−0.788976
$262$	46.2620	2.85807
$263$	10.9980	0.678168	0.339084	−	0.940756i	$-0.389883\pi$
$263$	10.9980	0.678168	0.339084	+	0.940756i	$0.389883\pi$
$264$	21.9370	1.35013
$265$	4.84349	0.297533
$266$	13.6123	0.834623
$267$	32.9717	2.01783
$268$	−6.75867	−0.412852
$269$	9.37029	0.571317	0.285658	−	0.958332i	$-0.407788\pi$
$269$	9.37029	0.571317	0.285658	+	0.958332i	$0.407788\pi$
$270$	−0.129550	−0.00788418
$271$	−22.6637	−1.37672	−0.688360	−	0.725369i	$-0.741669\pi$
$271$	−22.6637	−1.37672	−0.688360	+	0.725369i	$0.741669\pi$
$272$	2.77067	0.167997
$273$	−13.7171	−0.830197
$274$	−4.12819	−0.249393
$275$	−4.94555	−0.298228
$276$	53.2640	3.20612
$277$	32.4158	1.94767	0.973837	−	0.227248i	$-0.0729728\pi$
$277$	32.4158	1.94767	0.973837	+	0.227248i	$0.0729728\pi$
$278$	−16.4345	−0.985677
$279$	15.4654	0.925890
$280$	−1.80725	−0.108004
$281$	−28.6772	−1.71074	−0.855368	−	0.518021i	$-0.826669\pi$
$281$	−28.6772	−1.71074	−0.855368	+	0.518021i	$0.826669\pi$
$282$	−51.5581	−3.07024
$283$	21.4890	1.27739	0.638694	−	0.769461i	$-0.279475\pi$
$283$	21.4890	1.27739	0.638694	+	0.769461i	$0.279475\pi$
$284$	20.7828	1.23323
$285$	−15.2132	−0.901150
$286$	−60.7000	−3.58927
$287$	0.661754	0.0390621
$288$	22.0671	1.30032
$289$	−14.2701	−0.839420
$290$	9.25663	0.543568
$291$	11.9315	0.699435
$292$	−4.48380	−0.262394
$293$	−24.4590	−1.42891	−0.714455	−	0.699681i	$-0.753325\pi$
$293$	−24.4590	−1.42891	−0.714455	+	0.699681i	$0.753325\pi$
$294$	−5.39013	−0.314359
$295$	−2.63539	−0.153438
$296$	−7.74916	−0.450411
$297$	−0.291741	−0.0169286
$298$	−14.5381	−0.842169
$299$	−42.9644	−2.48469
$300$	6.92857	0.400021
$301$	11.9278	0.687506
$302$	8.26209	0.475430
$303$	14.7864	0.849455
$304$	10.3942	0.596148
$305$	−5.46300	−0.312810
$306$	10.9727	0.627265
$307$	−3.49370	−0.199396	−0.0996980	−	0.995018i	$-0.531788\pi$
$307$	−3.49370	−0.199396	−0.0996980	+	0.995018i	$0.531788\pi$
$308$	−13.9609	−0.795499
$309$	33.5200	1.90689
$310$	−11.2313	−0.637895
$311$	21.8624	1.23970	0.619850	−	0.784720i	$-0.287193\pi$
$311$	21.8624	1.23970	0.619850	+	0.784720i	$0.287193\pi$
$312$	24.7902	1.40347
$313$	−21.4076	−1.21003	−0.605015	−	0.796214i	$-0.706833\pi$
$313$	−21.4076	−1.21003	−0.605015	+	0.796214i	$0.706833\pi$
$314$	21.1529	1.19372
$315$	3.02403	0.170385
$316$	−10.3053	−0.579718
$317$	28.1015	1.57834	0.789169	−	0.614176i	$-0.210512\pi$
$317$	28.1015	1.57834	0.789169	+	0.614176i	$0.210512\pi$
$318$	−26.1070	−1.46401
$319$	20.8455	1.16712
$320$	−12.6717	−0.708370
$321$	−26.5090	−1.47959
$322$	−16.8828	−0.940844
$323$	10.2411	0.569829
$324$	−25.2012	−1.40007
$325$	−5.58880	−0.310011
$326$	−39.5276	−2.18923
$327$	40.4831	2.23872
$328$	−1.19595	−0.0660355
$329$	9.56527	0.527351
$330$	26.6572	1.46743
$331$	18.2913	1.00538	0.502690	−	0.864467i	$-0.332344\pi$
$331$	18.2913	1.00538	0.502690	+	0.864467i	$0.332344\pi$
$332$	−20.9101	−1.14759
$333$	12.9665	0.710561
$334$	−34.3344	−1.87869
$335$	−2.39421	−0.130809
$336$	−4.11584	−0.224538
$337$	13.8736	0.755745	0.377872	−	0.925858i	$-0.376656\pi$
$337$	13.8736	0.755745	0.377872	+	0.925858i	$0.376656\pi$
$338$	−40.0455	−2.17819
$339$	−7.24463	−0.393474
$340$	−4.66412	−0.252947
$341$	−25.2924	−1.36966
$342$	41.1640	2.22590
$343$	1.00000	0.0539949
$344$	−21.5565	−1.16225
$345$	18.8683	1.01584
$346$	−6.76224	−0.363540
$347$	−4.43945	−0.238322	−0.119161	−	0.992875i	$-0.538021\pi$
$347$	−4.43945	−0.238322	−0.119161	+	0.992875i	$0.538021\pi$
$348$	−29.2039	−1.56549
$349$	12.5880	0.673818	0.336909	−	0.941537i	$-0.390618\pi$
$349$	12.5880	0.673818	0.336909	+	0.941537i	$0.390618\pi$
$350$	−2.19612	−0.117387
$351$	−0.329687	−0.0175974
$352$	−36.0888	−1.92354
$353$	31.2812	1.66493	0.832465	−	0.554077i	$-0.186929\pi$
$353$	31.2812	1.66493	0.832465	+	0.554077i	$0.186929\pi$
$354$	14.2051	0.754991
$355$	7.36214	0.390742
$356$	37.9225	2.00989
$357$	−4.05521	−0.214625
$358$	15.6333	0.826248
$359$	−23.8120	−1.25675	−0.628375	−	0.777911i	$-0.716279\pi$
$359$	−23.8120	−1.25675	−0.628375	+	0.777911i	$0.716279\pi$
$360$	−5.46518	−0.288040
$361$	19.4195	1.02208
$362$	39.2047	2.06056
$363$	33.0324	1.73375
$364$	−15.7768	−0.826928
$365$	−1.58835	−0.0831380
$366$	29.4463	1.53918
$367$	12.2720	0.640594	0.320297	−	0.947317i	$-0.396217\pi$
$367$	12.2720	0.640594	0.320297	+	0.947317i	$0.396217\pi$
$368$	−12.8915	−0.672018
$369$	2.00117	0.104177
$370$	−9.41656	−0.489544
$371$	4.84349	0.251461
$372$	35.4339	1.83716
$373$	13.6385	0.706172	0.353086	−	0.935591i	$-0.385132\pi$
$373$	13.6385	0.706172	0.353086	+	0.935591i	$0.385132\pi$
$374$	−17.9449	−0.927907
$375$	2.45439	0.126744
$376$	−17.2868	−0.891500
$377$	23.5568	1.21324
$378$	−0.129550	−0.00666335
$379$	34.3728	1.76561	0.882807	−	0.469736i	$-0.155651\pi$
$379$	34.3728	1.76561	0.882807	+	0.469736i	$0.155651\pi$
$380$	−17.4975	−0.897602
$381$	51.2512	2.62568
$382$	−13.4457	−0.687942
$383$	−28.7891	−1.47105	−0.735526	−	0.677496i	$-0.763065\pi$
$383$	−28.7891	−1.47105	−0.735526	+	0.677496i	$0.763065\pi$
$384$	32.4816	1.65757
$385$	−4.94555	−0.252049
$386$	49.6928	2.52930
$387$	36.0700	1.83354
$388$	13.7230	0.696681
$389$	−13.0171	−0.659995	−0.329997	−	0.943982i	$-0.607048\pi$
$389$	−13.0171	−0.659995	−0.329997	+	0.943982i	$0.607048\pi$
$390$	30.1244	1.52541
$391$	−12.7016	−0.642350
$392$	−1.80725	−0.0912798
$393$	−51.7026	−2.60805
$394$	13.2197	0.665999
$395$	−3.65057	−0.183680
$396$	−42.2184	−2.12155
$397$	26.6535	1.33770	0.668850	−	0.743397i	$-0.266787\pi$
$397$	26.6535	1.33770	0.668850	+	0.743397i	$0.266787\pi$
$398$	−21.2002	−1.06267
$399$	−15.2132	−0.761611
$400$	−1.67693	−0.0838465
$401$	4.22919	0.211196	0.105598	−	0.994409i	$-0.466324\pi$
$401$	4.22919	0.211196	0.105598	+	0.994409i	$0.466324\pi$
$402$	12.9051	0.643647
$403$	−28.5821	−1.42377
$404$	17.0066	0.846111
$405$	−8.92732	−0.443602
$406$	9.25663	0.459399
$407$	−21.2057	−1.05113
$408$	7.32878	0.362828
$409$	20.3143	1.00448	0.502240	−	0.864728i	$-0.332510\pi$
$409$	20.3143	1.00448	0.502240	+	0.864728i	$0.332510\pi$
$410$	−1.45329	−0.0717728
$411$	4.61368	0.227576
$412$	38.5532	1.89938
$413$	−2.63539	−0.129679
$414$	−51.0543	−2.50918
$415$	−7.40723	−0.363607
$416$	−40.7828	−1.99954
$417$	18.3673	0.899451
$418$	−67.3203	−3.29274
$419$	−21.2343	−1.03736	−0.518682	−	0.854967i	$-0.673577\pi$
$419$	−21.2343	−1.03736	−0.518682	+	0.854967i	$0.673577\pi$
$420$	6.92857	0.338080
$421$	−6.97438	−0.339910	−0.169955	−	0.985452i	$-0.554362\pi$
$421$	−6.97438	−0.339910	−0.169955	+	0.985452i	$0.554362\pi$
$422$	−58.0554	−2.82609
$423$	28.9257	1.40642
$424$	−8.75338	−0.425102
$425$	−1.65223	−0.0801448
$426$	−39.6829	−1.92264
$427$	−5.46300	−0.264373
$428$	−30.4895	−1.47376
$429$	67.8387	3.27528
$430$	−26.1948	−1.26323
$431$	7.07766	0.340919	0.170459	−	0.985365i	$-0.445475\pi$
$431$	7.07766	0.340919	0.170459	+	0.985365i	$0.445475\pi$
$432$	−0.0989232	−0.00475944
$433$	4.58340	0.220264	0.110132	−	0.993917i	$-0.464873\pi$
$433$	4.58340	0.220264	0.110132	+	0.993917i	$0.464873\pi$
$434$	−11.2313	−0.539120
$435$	−10.3453	−0.496017
$436$	46.5619	2.22991
$437$	−47.6503	−2.27942
$438$	8.56141	0.409080
$439$	13.1942	0.629727	0.314863	−	0.949137i	$-0.398041\pi$
$439$	13.1942	0.629727	0.314863	+	0.949137i	$0.398041\pi$
$440$	8.93784	0.426095
$441$	3.02403	0.144002
$442$	−20.2789	−0.964568
$443$	−15.0463	−0.714870	−0.357435	−	0.933938i	$-0.616349\pi$
$443$	−15.0463	−0.714870	−0.357435	+	0.933938i	$0.616349\pi$
$444$	29.7085	1.40990
$445$	13.4338	0.636821
$446$	−46.6816	−2.21044
$447$	16.2478	0.768497
$448$	−12.6717	−0.598682
$449$	9.93890	0.469046	0.234523	−	0.972111i	$-0.424647\pi$
$449$	9.93890	0.469046	0.234523	+	0.972111i	$0.424647\pi$
$450$	−6.64113	−0.313066
$451$	−3.27274	−0.154107
$452$	−8.33244	−0.391925
$453$	−9.23375	−0.433840
$454$	16.5071	0.774718
$455$	−5.58880	−0.262007
$456$	27.4940	1.28752
$457$	−2.94162	−0.137603	−0.0688016	−	0.997630i	$-0.521918\pi$
$457$	−2.94162	−0.137603	−0.0688016	+	0.997630i	$0.521918\pi$
$458$	−2.19612	−0.102618
$459$	−0.0974660	−0.00454932
$460$	21.7015	1.01184
$461$	12.7864	0.595521	0.297760	−	0.954641i	$-0.403760\pi$
$461$	12.7864	0.595521	0.297760	+	0.954641i	$0.403760\pi$
$462$	26.6572	1.24020
$463$	2.34334	0.108904	0.0544521	−	0.998516i	$-0.482659\pi$
$463$	2.34334	0.108904	0.0544521	+	0.998516i	$0.482659\pi$
$464$	7.06825	0.328135
$465$	12.5522	0.582093
$466$	−32.2206	−1.49259
$467$	−25.8535	−1.19636	−0.598179	−	0.801362i	$-0.704109\pi$
$467$	−25.8535	−1.19636	−0.598179	+	0.801362i	$0.704109\pi$
$468$	−47.7096	−2.20538
$469$	−2.39421	−0.110554
$470$	−21.0065	−0.968956
$471$	−23.6405	−1.08930
$472$	4.76280	0.219226
$473$	−58.9895	−2.71234
$474$	19.6770	0.903796
$475$	−6.19834	−0.284400
$476$	−4.66412	−0.213780
$477$	14.6469	0.670634
$478$	−58.1610	−2.66022
$479$	−10.5695	−0.482935	−0.241467	−	0.970409i	$-0.577629\pi$
$479$	−10.5695	−0.482935	−0.241467	+	0.970409i	$0.577629\pi$
$480$	17.9103	0.817488
$481$	−23.9638	−1.09266
$482$	15.5915	0.710173
$483$	18.8683	0.858539
$484$	37.9924	1.72693
$485$	4.86127	0.220739
$486$	48.5080	2.20037
$487$	−26.2342	−1.18879	−0.594393	−	0.804175i	$-0.702608\pi$
$487$	−26.2342	−1.18879	−0.594393	+	0.804175i	$0.702608\pi$
$488$	9.87300	0.446930
$489$	44.1763	1.99772
$490$	−2.19612	−0.0992104
$491$	−16.8697	−0.761321	−0.380660	−	0.924715i	$-0.624303\pi$
$491$	−16.8697	−0.761321	−0.380660	+	0.924715i	$0.624303\pi$
$492$	4.58501	0.206708
$493$	6.96413	0.313649
$494$	−76.0764	−3.42284
$495$	−14.9555	−0.672201
$496$	−8.57610	−0.385078
$497$	7.36214	0.330237
$498$	39.9259	1.78912
$499$	12.7637	0.571383	0.285692	−	0.958322i	$-0.407777\pi$
$499$	12.7637	0.571383	0.285692	+	0.958322i	$0.407777\pi$
$500$	2.82293	0.126245
$501$	38.3722	1.71435
$502$	9.11919	0.407009
$503$	11.4691	0.511380	0.255690	−	0.966759i	$-0.417697\pi$
$503$	11.4691	0.511380	0.255690	+	0.966759i	$0.417697\pi$
$504$	−5.46518	−0.243439
$505$	6.02446	0.268085
$506$	83.4949	3.71180
$507$	44.7551	1.98764
$508$	58.9468	2.61534
$509$	−5.63743	−0.249875	−0.124937	−	0.992165i	$-0.539873\pi$
$509$	−5.63743	−0.249875	−0.124937	+	0.992165i	$0.539873\pi$
$510$	8.90572	0.394352
$511$	−1.58835	−0.0702645
$512$	−18.2982	−0.808674
$513$	−0.365644	−0.0161436
$514$	37.5116	1.65456
$515$	13.6572	0.601806
$516$	82.6425	3.63813
$517$	−47.3056	−2.08050
$518$	−9.41656	−0.413740
$519$	7.55751	0.331738
$520$	10.1004	0.442930
$521$	−26.3700	−1.15529	−0.577646	−	0.816287i	$-0.696029\pi$
$521$	−26.3700	−1.15529	−0.577646	+	0.816287i	$0.696029\pi$
$522$	27.9924	1.22519
$523$	−27.4718	−1.20126	−0.600628	−	0.799528i	$-0.705083\pi$
$523$	−27.4718	−1.20126	−0.600628	+	0.799528i	$0.705083\pi$
$524$	−59.4660	−2.59778
$525$	2.45439	0.107118
$526$	−24.1530	−1.05312
$527$	−8.44977	−0.368078
$528$	20.3551	0.885842
$529$	36.0990	1.56952
$530$	−10.6369	−0.462036
$531$	−7.96950	−0.345847
$532$	−17.4975	−0.758612
$533$	−3.69841	−0.160196
$534$	−72.4097	−3.13347
$535$	−10.8007	−0.466953
$536$	4.32692	0.186895
$537$	−17.4719	−0.753968
$538$	−20.5782	−0.887191
$539$	−4.94555	−0.213020
$540$	0.166526	0.00716616
$541$	13.8575	0.595778	0.297889	−	0.954600i	$-0.403717\pi$
$541$	13.8575	0.595778	0.297889	+	0.954600i	$0.403717\pi$
$542$	49.7721	2.13789
$543$	−43.8154	−1.88030
$544$	−12.0567	−0.516926
$545$	16.4942	0.706533
$546$	30.1244	1.28920
$547$	45.6047	1.94992	0.974958	−	0.222390i	$-0.0713859\pi$
$547$	45.6047	1.94992	0.974958	+	0.222390i	$0.0713859\pi$
$548$	5.30645	0.226680
$549$	−16.5203	−0.705069
$550$	10.8610	0.463115
$551$	26.1260	1.11301
$552$	−34.0998	−1.45138
$553$	−3.65057	−0.155238
$554$	−71.1888	−3.02452
$555$	10.5240	0.446719
$556$	21.1252	0.895910
$557$	17.9103	0.758885	0.379443	−	0.925215i	$-0.376116\pi$
$557$	17.9103	0.758885	0.379443	+	0.925215i	$0.376116\pi$
$558$	−33.9639	−1.43780
$559$	−66.6620	−2.81950
$560$	−1.67693	−0.0708632
$561$	20.0553	0.846734
$562$	62.9784	2.65658
$563$	0.0718832	0.00302951	0.00151476	−	0.999999i	$-0.499518\pi$
$563$	0.0718832	0.00302951	0.00151476	+	0.999999i	$0.499518\pi$
$564$	66.2737	2.79063
$565$	−2.95170	−0.124179
$566$	−47.1923	−1.98364
$567$	−8.92732	−0.374912
$568$	−13.3052	−0.558274
$569$	13.2603	0.555901	0.277951	−	0.960595i	$-0.410345\pi$
$569$	13.2603	0.555901	0.277951	+	0.960595i	$0.410345\pi$
$570$	33.4099	1.39939
$571$	19.0584	0.797568	0.398784	−	0.917045i	$-0.369432\pi$
$571$	19.0584	0.797568	0.398784	+	0.917045i	$0.369432\pi$
$572$	78.0249	3.26239
$573$	15.0270	0.627761
$574$	−1.45329	−0.0606591
$575$	7.68759	0.320594
$576$	−38.3197	−1.59665
$577$	−35.3975	−1.47362	−0.736810	−	0.676100i	$-0.763669\pi$
$577$	−35.3975	−1.47362	−0.736810	+	0.676100i	$0.763669\pi$
$578$	31.3389	1.30353
$579$	−55.5369	−2.30803
$580$	−11.8986	−0.494064
$581$	−7.40723	−0.307304
$582$	−26.2029	−1.08614
$583$	−23.9537	−0.992061
$584$	2.87054	0.118784
$585$	−16.9007	−0.698759
$586$	53.7148	2.21894
$587$	−8.53373	−0.352225	−0.176112	−	0.984370i	$-0.556352\pi$
$587$	−8.53373	−0.352225	−0.176112	+	0.984370i	$0.556352\pi$
$588$	6.92857	0.285729
$589$	−31.6994	−1.30615
$590$	5.78762	0.238272
$591$	−14.7744	−0.607737
$592$	−7.19038	−0.295523
$593$	30.4940	1.25224	0.626119	−	0.779728i	$-0.284643\pi$
$593$	30.4940	1.25224	0.626119	+	0.779728i	$0.284643\pi$
$594$	0.640698	0.0262882
$595$	−1.65223	−0.0677347
$596$	18.6875	0.765471
$597$	23.6935	0.969710
$598$	94.3548	3.85846
$599$	39.6689	1.62083	0.810413	−	0.585858i	$-0.199243\pi$
$599$	39.6689	1.62083	0.810413	+	0.585858i	$0.199243\pi$
$600$	−4.43569	−0.181086
$601$	−45.0305	−1.83683	−0.918417	−	0.395614i	$-0.870532\pi$
$601$	−45.0305	−1.83683	−0.918417	+	0.395614i	$0.870532\pi$
$602$	−26.1948	−1.06762
$603$	−7.24016	−0.294842
$604$	−10.6202	−0.432132
$605$	13.4585	0.547165
$606$	−32.4726	−1.31911
$607$	−30.8199	−1.25094	−0.625471	−	0.780247i	$-0.715093\pi$
$607$	−30.8199	−1.25094	−0.625471	+	0.780247i	$0.715093\pi$
$608$	−45.2307	−1.83435
$609$	−10.3453	−0.419211
$610$	11.9974	0.485760
$611$	−53.4584	−2.16270
$612$	−14.1045	−0.570139
$613$	6.52482	0.263535	0.131767	−	0.991281i	$-0.457935\pi$
$613$	6.52482	0.263535	0.131767	+	0.991281i	$0.457935\pi$
$614$	7.67258	0.309640
$615$	1.62420	0.0654942
$616$	8.93784	0.360116
$617$	−36.0035	−1.44945	−0.724723	−	0.689040i	$-0.758032\pi$
$617$	−36.0035	−1.44945	−0.724723	+	0.689040i	$0.758032\pi$
$618$	−73.6138	−2.96118
$619$	19.2311	0.772964	0.386482	−	0.922297i	$-0.373690\pi$
$619$	19.2311	0.772964	0.386482	+	0.922297i	$0.373690\pi$
$620$	14.4369	0.579801
$621$	0.453496	0.0181982
$622$	−48.0123	−1.92512
$623$	13.4338	0.538212
$624$	23.0026	0.920842
$625$	1.00000	0.0400000
$626$	47.0136	1.87904
$627$	75.2375	3.00470
$628$	−27.1903	−1.08501
$629$	−7.08446	−0.282476
$630$	−6.64113	−0.264589
$631$	−44.6267	−1.77656	−0.888280	−	0.459303i	$-0.848099\pi$
$631$	−44.6267	−1.77656	−0.888280	+	0.459303i	$0.848099\pi$
$632$	6.59748	0.262434
$633$	64.8830	2.57887
$634$	−61.7142	−2.45098
$635$	20.8814	0.828655
$636$	33.5584	1.33068
$637$	−5.58880	−0.221436
$638$	−45.7791	−1.81241
$639$	22.2634	0.880725
$640$	13.2341	0.523124
$641$	40.5712	1.60247	0.801233	−	0.598352i	$-0.204178\pi$
$641$	40.5712	1.60247	0.801233	+	0.598352i	$0.204178\pi$
$642$	58.2169	2.29764
$643$	−5.29777	−0.208924	−0.104462	−	0.994529i	$-0.533312\pi$
$643$	−5.29777	−0.208924	−0.104462	+	0.994529i	$0.533312\pi$
$644$	21.7015	0.855159
$645$	29.2755	1.15272
$646$	−22.4906	−0.884881
$647$	−6.63540	−0.260864	−0.130432	−	0.991457i	$-0.541636\pi$
$647$	−6.63540	−0.260864	−0.130432	+	0.991457i	$0.541636\pi$
$648$	16.1339	0.633799
$649$	13.0334	0.511607
$650$	12.2737	0.481413
$651$	12.5522	0.491958
$652$	50.8096	1.98986
$653$	−48.2227	−1.88710	−0.943550	−	0.331231i	$-0.892536\pi$
$653$	−48.2227	−1.88710	−0.943550	+	0.331231i	$0.892536\pi$
$654$	−88.9057	−3.47649
$655$	−21.0653	−0.823091
$656$	−1.10971	−0.0433271
$657$	−4.80322	−0.187392
$658$	−21.0065	−0.818917
$659$	−44.4986	−1.73342	−0.866710	−	0.498813i	$-0.833769\pi$
$659$	−44.4986	−1.73342	−0.866710	+	0.498813i	$0.833769\pi$
$660$	−34.2656	−1.33379
$661$	9.27332	0.360691	0.180345	−	0.983603i	$-0.442278\pi$
$661$	9.27332	0.360691	0.180345	+	0.983603i	$0.442278\pi$
$662$	−40.1698	−1.56124
$663$	22.6638	0.880188
$664$	13.3867	0.519505
$665$	−6.19834	−0.240361
$666$	−28.4760	−1.10342
$667$	−32.4032	−1.25466
$668$	44.1340	1.70760
$669$	52.1716	2.01707
$670$	5.25796	0.203133
$671$	27.0175	1.04300
$672$	17.9103	0.690903
$673$	−17.9728	−0.692802	−0.346401	−	0.938087i	$-0.612596\pi$
$673$	−17.9728	−0.692802	−0.346401	+	0.938087i	$0.612596\pi$
$674$	−30.4681	−1.17359
$675$	0.0589907	0.00227055
$676$	51.4753	1.97982
$677$	1.40251	0.0539027	0.0269514	−	0.999637i	$-0.491420\pi$
$677$	1.40251	0.0539027	0.0269514	+	0.999637i	$0.491420\pi$
$678$	15.9100	0.611022
$679$	4.86127	0.186559
$680$	2.98599	0.114507
$681$	−18.4484	−0.706946
$682$	55.5450	2.12693
$683$	8.22770	0.314824	0.157412	−	0.987533i	$-0.449685\pi$
$683$	8.22770	0.314824	0.157412	+	0.987533i	$0.449685\pi$
$684$	−52.9130	−2.02318
$685$	1.87977	0.0718222
$686$	−2.19612	−0.0838481
$687$	2.45439	0.0936409
$688$	−20.0021	−0.762572
$689$	−27.0693	−1.03126
$690$	−41.4371	−1.57748
$691$	47.0264	1.78897	0.894485	−	0.447098i	$-0.147543\pi$
$691$	47.0264	1.78897	0.894485	+	0.447098i	$0.147543\pi$
$692$	8.69231	0.330432
$693$	−14.9555	−0.568113
$694$	9.74956	0.370088
$695$	7.48345	0.283863
$696$	18.6964	0.708687
$697$	−1.09337	−0.0414143
$698$	−27.6446	−1.04637
$699$	36.0098	1.36202
$700$	2.82293	0.106697
$701$	−25.0204	−0.945007	−0.472504	−	0.881329i	$-0.656650\pi$
$701$	−25.0204	−0.945007	−0.472504	+	0.881329i	$0.656650\pi$
$702$	0.724031	0.0273268
$703$	−26.5774	−1.00239
$704$	62.6686	2.36191
$705$	23.4769	0.884192
$706$	−68.6972	−2.58545
$707$	6.02446	0.226573
$708$	−18.2595	−0.686233
$709$	16.2255	0.609362	0.304681	−	0.952454i	$-0.401450\pi$
$709$	16.2255	0.609362	0.304681	+	0.952454i	$0.401450\pi$
$710$	−16.1681	−0.606779
$711$	−11.0394	−0.414012
$712$	−24.2781	−0.909862
$713$	39.3156	1.47238
$714$	8.90572	0.333288
$715$	27.6397	1.03367
$716$	−20.0954	−0.751000
$717$	65.0010	2.42751
$718$	52.2939	1.95159
$719$	−15.4971	−0.577946	−0.288973	−	0.957337i	$-0.593314\pi$
$719$	−15.4971	−0.577946	−0.288973	+	0.957337i	$0.593314\pi$
$720$	−5.07109	−0.188989
$721$	13.6572	0.508619
$722$	−42.6474	−1.58717
$723$	−17.4251	−0.648047
$724$	−50.3945	−1.87290
$725$	−4.21500	−0.156541
$726$	−72.5430	−2.69232
$727$	−27.6644	−1.02602	−0.513008	−	0.858384i	$-0.671469\pi$
$727$	−27.6644	−1.02602	−0.513008	+	0.858384i	$0.671469\pi$
$728$	10.1004	0.374344
$729$	−27.4309	−1.01596
$730$	3.48820	0.129104
$731$	−19.7074	−0.728905
$732$	−37.8508	−1.39901
$733$	−1.98455	−0.0733010	−0.0366505	−	0.999328i	$-0.511669\pi$
$733$	−1.98455	−0.0733010	−0.0366505	+	0.999328i	$0.511669\pi$
$734$	−26.9508	−0.994772
$735$	2.45439	0.0905316
$736$	56.0981	2.06780
$737$	11.8407	0.436157
$738$	−4.39480	−0.161775
$739$	35.2231	1.29570	0.647852	−	0.761766i	$-0.275667\pi$
$739$	35.2231	1.29570	0.647852	+	0.761766i	$0.275667\pi$
$740$	12.1042	0.444960
$741$	85.0233	3.12341
$742$	−10.6369	−0.390491
$743$	36.9688	1.35625	0.678127	−	0.734945i	$-0.262792\pi$
$743$	36.9688	1.35625	0.678127	+	0.734945i	$0.262792\pi$
$744$	−22.6849	−0.831668
$745$	6.61991	0.242535
$746$	−29.9516	−1.09661
$747$	−22.3997	−0.819563
$748$	23.0667	0.843400
$749$	−10.8007	−0.394647
$750$	−5.39013	−0.196820
$751$	−0.0711650	−0.00259685	−0.00129842	−	0.999999i	$-0.500413\pi$
$751$	−0.0711650	−0.00259685	−0.00129842	+	0.999999i	$0.500413\pi$
$752$	−16.0403	−0.584929
$753$	−10.1917	−0.371405
$754$	−51.7335	−1.88402
$755$	−3.76214	−0.136918
$756$	0.166526	0.00605651
$757$	−45.4618	−1.65234	−0.826169	−	0.563422i	$-0.809485\pi$
$757$	−45.4618	−1.65234	−0.826169	+	0.563422i	$0.809485\pi$
$758$	−75.4867	−2.74180
$759$	−93.3144	−3.38710
$760$	11.2019	0.406337
$761$	−37.6826	−1.36599	−0.682997	−	0.730421i	$-0.739324\pi$
$761$	−37.6826	−1.36599	−0.682997	+	0.730421i	$0.739324\pi$
$762$	−112.554	−4.07739
$763$	16.4942	0.597129
$764$	17.2833	0.625290
$765$	−4.99639	−0.180645
$766$	63.2242	2.28438
$767$	14.7287	0.531821
$768$	−9.13082	−0.329480
$769$	3.73886	0.134827	0.0674133	−	0.997725i	$-0.478525\pi$
$769$	3.73886	0.134827	0.0674133	+	0.997725i	$0.478525\pi$
$770$	10.8610	0.391404
$771$	−41.9231	−1.50982
$772$	−63.8760	−2.29895
$773$	−32.0112	−1.15136	−0.575682	−	0.817674i	$-0.695263\pi$
$773$	−32.0112	−1.15136	−0.575682	+	0.817674i	$0.695263\pi$
$774$	−79.2140	−2.84729
$775$	5.11417	0.183706
$776$	−8.78553	−0.315382
$777$	10.5240	0.377546
$778$	28.5871	1.02490
$779$	−4.10178	−0.146961
$780$	−38.7224	−1.38648
$781$	−36.4098	−1.30285
$782$	27.8943	0.997498
$783$	−0.248645	−0.00888586
$784$	−1.67693	−0.0598903
$785$	−9.63194	−0.343779
$786$	113.545	4.05001
$787$	15.7829	0.562599	0.281300	−	0.959620i	$-0.409235\pi$
$787$	15.7829	0.562599	0.281300	+	0.959620i	$0.409235\pi$
$788$	−16.9928	−0.605345
$789$	26.9935	0.960994
$790$	8.01707	0.285235
$791$	−2.95170	−0.104950
$792$	27.0283	0.960410
$793$	30.5316	1.08421
$794$	−58.5342	−2.07730
$795$	11.8878	0.421617
$796$	27.2512	0.965893
$797$	10.5919	0.375183	0.187592	−	0.982247i	$-0.439932\pi$
$797$	10.5919	0.375183	0.187592	+	0.982247i	$0.439932\pi$
$798$	33.4099	1.18270
$799$	−15.8040	−0.559106
$800$	7.29723	0.257996
$801$	40.6242	1.43538
$802$	−9.28780	−0.327964
$803$	7.85527	0.277206
$804$	−16.5884	−0.585029
$805$	7.68759	0.270952
$806$	62.7695	2.21096
$807$	22.9984	0.809580
$808$	−10.8877	−0.383028
$809$	−22.3987	−0.787498	−0.393749	−	0.919218i	$-0.628822\pi$
$809$	−22.3987	−0.787498	−0.393749	+	0.919218i	$0.628822\pi$
$810$	19.6054	0.688865
$811$	−28.2714	−0.992742	−0.496371	−	0.868110i	$-0.665334\pi$
$811$	−28.2714	−0.992742	−0.496371	+	0.868110i	$0.665334\pi$
$812$	−11.8986	−0.417560
$813$	−55.6255	−1.95087
$814$	46.5701	1.63228
$815$	17.9989	0.630473
$816$	6.80031	0.238058
$817$	−73.9325	−2.58657
$818$	−44.6127	−1.55985
$819$	−16.9007	−0.590559
$820$	1.86808	0.0652363
$821$	53.4893	1.86679	0.933394	−	0.358852i	$-0.116832\pi$
$821$	53.4893	1.86679	0.933394	+	0.358852i	$0.116832\pi$
$822$	−10.1322	−0.353401
$823$	44.2763	1.54338	0.771688	−	0.636001i	$-0.219413\pi$
$823$	44.2763	1.54338	0.771688	+	0.636001i	$0.219413\pi$
$824$	−24.6819	−0.859833
$825$	−12.1383	−0.422602
$826$	5.78762	0.201377
$827$	−35.2492	−1.22574	−0.612868	−	0.790185i	$-0.709984\pi$
$827$	−35.2492	−1.22574	−0.612868	+	0.790185i	$0.709984\pi$
$828$	65.6261	2.28067
$829$	37.7323	1.31050	0.655248	−	0.755414i	$-0.272564\pi$
$829$	37.7323	1.31050	0.655248	+	0.755414i	$0.272564\pi$
$830$	16.2671	0.564641
$831$	79.5609	2.75994
$832$	70.8197	2.45523
$833$	−1.65223	−0.0572463
$834$	−40.3368	−1.39675
$835$	15.6341	0.541041
$836$	86.5347	2.99287
$837$	0.301688	0.0104279
$838$	46.6331	1.61091
$839$	42.0150	1.45052	0.725260	−	0.688476i	$-0.241720\pi$
$839$	42.0150	1.45052	0.725260	+	0.688476i	$0.241720\pi$
$840$	−4.43569	−0.153046
$841$	−11.2338	−0.387372
$842$	15.3165	0.527843
$843$	−70.3850	−2.42419
$844$	74.6255	2.56872
$845$	18.2347	0.627293
$846$	−63.5243	−2.18401
$847$	13.4585	0.462439
$848$	−8.12218	−0.278917
$849$	52.7424	1.81011
$850$	3.62848	0.124456
$851$	32.9630	1.12996
$852$	51.0091	1.74754
$853$	33.9468	1.16232	0.581158	−	0.813791i	$-0.302600\pi$
$853$	33.9468	1.16232	0.581158	+	0.813791i	$0.302600\pi$
$854$	11.9974	0.410542
$855$	−18.7440	−0.641032
$856$	19.5195	0.667161
$857$	−15.4007	−0.526079	−0.263040	−	0.964785i	$-0.584725\pi$
$857$	−15.4007	−0.526079	−0.263040	+	0.964785i	$0.584725\pi$
$858$	−148.982	−5.08615
$859$	9.31017	0.317659	0.158829	−	0.987306i	$-0.449228\pi$
$859$	9.31017	0.317659	0.158829	+	0.987306i	$0.449228\pi$
$860$	33.6713	1.14818
$861$	1.62420	0.0553527
$862$	−15.5434	−0.529409
$863$	−56.1301	−1.91069	−0.955345	−	0.295493i	$-0.904516\pi$
$863$	−56.1301	−1.91069	−0.955345	+	0.295493i	$0.904516\pi$
$864$	0.430468	0.0146448
$865$	3.07918	0.104695
$866$	−10.0657	−0.342046
$867$	−35.0245	−1.18949
$868$	14.4369	0.490021
$869$	18.0541	0.612443
$870$	22.7194	0.770259
$871$	13.3807	0.453389
$872$	−29.8091	−1.00946
$873$	14.7007	0.497542
$874$	104.646	3.53969
$875$	1.00000	0.0338062
$876$	−11.0050	−0.371824
$877$	25.6779	0.867082	0.433541	−	0.901134i	$-0.357264\pi$
$877$	25.6779	0.867082	0.433541	+	0.901134i	$0.357264\pi$
$878$	−28.9761	−0.977895
$879$	−60.0320	−2.02483
$880$	8.29334	0.279569
$881$	5.02781	0.169391	0.0846955	−	0.996407i	$-0.473008\pi$
$881$	5.02781	0.169391	0.0846955	+	0.996407i	$0.473008\pi$
$882$	−6.64113	−0.223619
$883$	−39.5017	−1.32934	−0.664670	−	0.747137i	$-0.731428\pi$
$883$	−39.5017	−1.32934	−0.664670	+	0.747137i	$0.731428\pi$
$884$	26.0668	0.876723
$885$	−6.46827	−0.217428
$886$	33.0434	1.11011
$887$	15.0545	0.505480	0.252740	−	0.967534i	$-0.418668\pi$
$887$	15.0545	0.505480	0.252740	+	0.967534i	$0.418668\pi$
$888$	−19.0195	−0.638252
$889$	20.8814	0.700341
$890$	−29.5021	−0.988913
$891$	44.1505	1.47910
$892$	60.0054	2.00913
$893$	−59.2889	−1.98403
$894$	−35.6822	−1.19339
$895$	−7.11863	−0.237950
$896$	13.2341	0.442120
$897$	−105.451	−3.52092
$898$	−21.8270	−0.728376
$899$	−21.5562	−0.718939
$900$	8.53664	0.284555
$901$	−8.00254	−0.266603
$902$	7.18732	0.239311
$903$	29.2755	0.974226
$904$	5.33446	0.177421
$905$	−17.8518	−0.593415
$906$	20.2784	0.673705
$907$	−46.1079	−1.53099	−0.765493	−	0.643444i	$-0.777505\pi$
$907$	−46.1079	−1.53099	−0.765493	+	0.643444i	$0.777505\pi$
$908$	−21.2186	−0.704163
$909$	18.2182	0.604259
$910$	12.2737	0.406868
$911$	47.2701	1.56613	0.783064	−	0.621941i	$-0.213656\pi$
$911$	47.2701	1.56613	0.783064	+	0.621941i	$0.213656\pi$
$912$	25.5114	0.844767
$913$	36.6328	1.21237
$914$	6.46014	0.213682
$915$	−13.4083	−0.443266
$916$	2.82293	0.0932722
$917$	−21.0653	−0.695639
$918$	0.214047	0.00706459
$919$	4.03568	0.133125	0.0665625	−	0.997782i	$-0.478797\pi$
$919$	4.03568	0.133125	0.0665625	+	0.997782i	$0.478797\pi$
$920$	−13.8934	−0.458051
$921$	−8.57491	−0.282553
$922$	−28.0804	−0.924778
$923$	−41.1455	−1.35432
$924$	−34.2656	−1.12726
$925$	4.28782	0.140983
$926$	−5.14625	−0.169116
$927$	41.2997	1.35646
$928$	−30.7578	−1.00967
$929$	−23.2005	−0.761184	−0.380592	−	0.924743i	$-0.624280\pi$
$929$	−23.2005	−0.761184	−0.380592	+	0.924743i	$0.624280\pi$
$930$	−27.5660	−0.903925
$931$	−6.19834	−0.203143
$932$	41.4169	1.35666
$933$	53.6588	1.75671
$934$	56.7774	1.85781
$935$	8.17118	0.267226
$936$	30.5438	0.998356
$937$	28.5313	0.932079	0.466039	−	0.884764i	$-0.345681\pi$
$937$	28.5313	0.932079	0.466039	+	0.884764i	$0.345681\pi$
$938$	5.25796	0.171678
$939$	−52.5426	−1.71466
$940$	27.0021	0.880711
$941$	40.6349	1.32466	0.662329	−	0.749213i	$-0.269568\pi$
$941$	40.6349	1.32466	0.662329	+	0.749213i	$0.269568\pi$
$942$	51.9174	1.69156
$943$	5.08729	0.165665
$944$	4.41936	0.143838
$945$	0.0589907	0.00191897
$946$	129.548	4.21196
$947$	52.2132	1.69670	0.848350	−	0.529435i	$-0.177596\pi$
$947$	52.2132	1.69670	0.848350	+	0.529435i	$0.177596\pi$
$948$	−25.2932	−0.821486
$949$	8.87697	0.288159
$950$	13.6123	0.441641
$951$	68.9721	2.23657
$952$	2.98599	0.0967763
$953$	−25.8371	−0.836945	−0.418472	−	0.908230i	$-0.637434\pi$
$953$	−25.8371	−0.836945	−0.418472	+	0.908230i	$0.637434\pi$
$954$	−32.1662	−1.04142
$955$	6.12249	0.198119
$956$	74.7612	2.41795
$957$	51.1630	1.65386
$958$	23.2119	0.749944
$959$	1.87977	0.0607008
$960$	−31.1013	−1.00379
$961$	−4.84531	−0.156300
$962$	52.6273	1.69677
$963$	−32.6615	−1.05250
$964$	−20.0416	−0.645496
$965$	−22.6276	−0.728407
$966$	−41.4371	−1.33322
$967$	16.2900	0.523850	0.261925	−	0.965088i	$-0.415643\pi$
$967$	16.2900	0.523850	0.261925	+	0.965088i	$0.415643\pi$
$968$	−24.3228	−0.781765
$969$	25.1356	0.807472
$970$	−10.6759	−0.342783
$971$	−1.49540	−0.0479898	−0.0239949	−	0.999712i	$-0.507639\pi$
$971$	−1.49540	−0.0479898	−0.0239949	+	0.999712i	$0.507639\pi$
$972$	−62.3531	−1.99998
$973$	7.48345	0.239908
$974$	57.6134	1.84605
$975$	−13.7171	−0.439299
$976$	9.16107	0.293239
$977$	14.0931	0.450877	0.225439	−	0.974257i	$-0.427618\pi$
$977$	14.0931	0.450877	0.225439	+	0.974257i	$0.427618\pi$
$978$	−97.0163	−3.10224
$979$	−66.4374	−2.12335
$980$	2.82293	0.0901752
$981$	49.8789	1.59251
$982$	37.0479	1.18225
$983$	9.43406	0.300900	0.150450	−	0.988618i	$-0.451928\pi$
$983$	9.43406	0.300900	0.150450	+	0.988618i	$0.451928\pi$
$984$	−2.93534	−0.0935751
$985$	−6.01958	−0.191800
$986$	−15.2941	−0.487062
$987$	23.4769	0.747279
$988$	97.7900	3.11111
$989$	91.6959	2.91576
$990$	32.8441	1.04385
$991$	53.5621	1.70146	0.850728	−	0.525606i	$-0.176162\pi$
$991$	53.5621	1.70146	0.850728	+	0.525606i	$0.176162\pi$
$992$	37.3192	1.18489
$993$	44.8940	1.42467
$994$	−16.1681	−0.512822
$995$	9.65352	0.306037
$996$	−51.3215	−1.62618
$997$	30.0774	0.952561	0.476280	−	0.879294i	$-0.341985\pi$
$997$	30.0774	0.952561	0.476280	+	0.879294i	$0.341985\pi$
$998$	−28.0307	−0.887295
$999$	0.252942	0.00800272

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.o.1.11	✓	73

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.o.1.11	✓	73	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)

\(f(q)\)	\(=\)	\(q-2.19612 q^{2} +2.45439 q^{3} +2.82293 q^{4} +1.00000 q^{5} -5.39013 q^{6} +1.00000 q^{7} -1.80725 q^{8} +3.02403 q^{9} +O(q^{10})\)	\(q-2.19612 q^{2} +2.45439 q^{3} +2.82293 q^{4} +1.00000 q^{5} -5.39013 q^{6} +1.00000 q^{7} -1.80725 q^{8} +3.02403 q^{9} -2.19612 q^{10} -4.94555 q^{11} +6.92857 q^{12} -5.58880 q^{13} -2.19612 q^{14} +2.45439 q^{15} -1.67693 q^{16} -1.65223 q^{17} -6.64113 q^{18} -6.19834 q^{19} +2.82293 q^{20} +2.45439 q^{21} +10.8610 q^{22} +7.68759 q^{23} -4.43569 q^{24} +1.00000 q^{25} +12.2737 q^{26} +0.0589907 q^{27} +2.82293 q^{28} -4.21500 q^{29} -5.39013 q^{30} +5.11417 q^{31} +7.29723 q^{32} -12.1383 q^{33} +3.62848 q^{34} +1.00000 q^{35} +8.53664 q^{36} +4.28782 q^{37} +13.6123 q^{38} -13.7171 q^{39} -1.80725 q^{40} +0.661754 q^{41} -5.39013 q^{42} +11.9278 q^{43} -13.9609 q^{44} +3.02403 q^{45} -16.8828 q^{46} +9.56527 q^{47} -4.11584 q^{48} +1.00000 q^{49} -2.19612 q^{50} -4.05521 q^{51} -15.7768 q^{52} +4.84349 q^{53} -0.129550 q^{54} -4.94555 q^{55} -1.80725 q^{56} -15.2132 q^{57} +9.25663 q^{58} -2.63539 q^{59} +6.92857 q^{60} -5.46300 q^{61} -11.2313 q^{62} +3.02403 q^{63} -12.6717 q^{64} -5.58880 q^{65} +26.6572 q^{66} -2.39421 q^{67} -4.66412 q^{68} +18.8683 q^{69} -2.19612 q^{70} +7.36214 q^{71} -5.46518 q^{72} -1.58835 q^{73} -9.41656 q^{74} +2.45439 q^{75} -17.4975 q^{76} -4.94555 q^{77} +30.1244 q^{78} -3.65057 q^{79} -1.67693 q^{80} -8.92732 q^{81} -1.45329 q^{82} -7.40723 q^{83} +6.92857 q^{84} -1.65223 q^{85} -26.1948 q^{86} -10.3453 q^{87} +8.93784 q^{88} +13.4338 q^{89} -6.64113 q^{90} -5.58880 q^{91} +21.7015 q^{92} +12.5522 q^{93} -21.0065 q^{94} -6.19834 q^{95} +17.9103 q^{96} +4.86127 q^{97} -2.19612 q^{98} -14.9555 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * q^98 + 49 * q^99

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