LMFDB - Embedded newform 8015.2.a.i.1.4

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:	$1$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-2.27226 q^{2} -1.26810 q^{3} +3.16315 q^{4} +1.00000 q^{5} +2.88144 q^{6} -1.00000 q^{7} -2.64298 q^{8} -1.39193 q^{9} +O(q^{10})$	\(q-2.27226 q^{2} -1.26810 q^{3} +3.16315 q^{4} +1.00000 q^{5} +2.88144 q^{6} -1.00000 q^{7} -2.64298 q^{8} -1.39193 q^{9} -2.27226 q^{10} -0.284402 q^{11} -4.01118 q^{12} +1.60249 q^{13} +2.27226 q^{14} -1.26810 q^{15} -0.320779 q^{16} -2.28481 q^{17} +3.16283 q^{18} +3.61700 q^{19} +3.16315 q^{20} +1.26810 q^{21} +0.646233 q^{22} -1.16917 q^{23} +3.35155 q^{24} +1.00000 q^{25} -3.64128 q^{26} +5.56939 q^{27} -3.16315 q^{28} -1.89956 q^{29} +2.88144 q^{30} -5.53287 q^{31} +6.01485 q^{32} +0.360648 q^{33} +5.19167 q^{34} -1.00000 q^{35} -4.40290 q^{36} +4.10886 q^{37} -8.21875 q^{38} -2.03212 q^{39} -2.64298 q^{40} -4.01065 q^{41} -2.88144 q^{42} -10.7029 q^{43} -0.899605 q^{44} -1.39193 q^{45} +2.65665 q^{46} +7.51508 q^{47} +0.406779 q^{48} +1.00000 q^{49} -2.27226 q^{50} +2.89735 q^{51} +5.06893 q^{52} +9.94282 q^{53} -12.6551 q^{54} -0.284402 q^{55} +2.64298 q^{56} -4.58670 q^{57} +4.31630 q^{58} -6.97804 q^{59} -4.01118 q^{60} +0.251325 q^{61} +12.5721 q^{62} +1.39193 q^{63} -13.0257 q^{64} +1.60249 q^{65} -0.819486 q^{66} +3.47498 q^{67} -7.22719 q^{68} +1.48262 q^{69} +2.27226 q^{70} +12.6321 q^{71} +3.67885 q^{72} +5.72987 q^{73} -9.33638 q^{74} -1.26810 q^{75} +11.4411 q^{76} +0.284402 q^{77} +4.61749 q^{78} -2.39631 q^{79} -0.320779 q^{80} -2.88672 q^{81} +9.11323 q^{82} -3.19708 q^{83} +4.01118 q^{84} -2.28481 q^{85} +24.3198 q^{86} +2.40883 q^{87} +0.751667 q^{88} -10.2043 q^{89} +3.16283 q^{90} -1.60249 q^{91} -3.69825 q^{92} +7.01621 q^{93} -17.0762 q^{94} +3.61700 q^{95} -7.62740 q^{96} -10.1282 q^{97} -2.27226 q^{98} +0.395868 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) $ 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * 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 $

$2$	−2.27226	−1.60673	−0.803364	−	0.595488i	$-0.796959\pi$
$2$	−2.27226	−1.60673	−0.803364	+	0.595488i	$0.796959\pi$
$3$	−1.26810	−0.732135	−0.366068	−	0.930588i	$-0.619296\pi$
$3$	−1.26810	−0.732135	−0.366068	+	0.930588i	$0.619296\pi$
$4$	3.16315	1.58158
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.88144	1.17634
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.64298	−0.934433
$9$	−1.39193	−0.463978
$10$	−2.27226	−0.718551
$11$	−0.284402	−0.0857503	−0.0428751	−	0.999080i	$-0.513652\pi$
$11$	−0.284402	−0.0857503	−0.0428751	+	0.999080i	$0.513652\pi$
$12$	−4.01118	−1.15793
$13$	1.60249	0.444452	0.222226	−	0.974995i	$-0.428668\pi$
$13$	1.60249	0.444452	0.222226	+	0.974995i	$0.428668\pi$
$14$	2.27226	0.607286
$15$	−1.26810	−0.327421
$16$	−0.320779	−0.0801948
$17$	−2.28481	−0.554147	−0.277073	−	0.960849i	$-0.589365\pi$
$17$	−2.28481	−0.554147	−0.277073	+	0.960849i	$0.589365\pi$
$18$	3.16283	0.745486
$19$	3.61700	0.829797	0.414898	−	0.909868i	$-0.363817\pi$
$19$	3.61700	0.829797	0.414898	+	0.909868i	$0.363817\pi$
$20$	3.16315	0.707302
$21$	1.26810	0.276721
$22$	0.646233	0.137777
$23$	−1.16917	−0.243788	−0.121894	−	0.992543i	$-0.538897\pi$
$23$	−1.16917	−0.243788	−0.121894	+	0.992543i	$0.538897\pi$
$24$	3.35155	0.684132
$25$	1.00000	0.200000
$26$	−3.64128	−0.714113
$27$	5.56939	1.07183
$28$	−3.16315	−0.597779
$29$	−1.89956	−0.352740	−0.176370	−	0.984324i	$-0.556436\pi$
$29$	−1.89956	−0.352740	−0.176370	+	0.984324i	$0.556436\pi$
$30$	2.88144	0.526076
$31$	−5.53287	−0.993733	−0.496866	−	0.867827i	$-0.665516\pi$
$31$	−5.53287	−0.993733	−0.496866	+	0.867827i	$0.665516\pi$
$32$	6.01485	1.06328
$33$	0.360648	0.0627808
$34$	5.19167	0.890364
$35$	−1.00000	−0.169031
$36$	−4.40290	−0.733816
$37$	4.10886	0.675492	0.337746	−	0.941237i	$-0.390335\pi$
$37$	4.10886	0.675492	0.337746	+	0.941237i	$0.390335\pi$
$38$	−8.21875	−1.33326
$39$	−2.03212	−0.325399
$40$	−2.64298	−0.417891
$41$	−4.01065	−0.626359	−0.313179	−	0.949694i	$-0.601394\pi$
$41$	−4.01065	−0.626359	−0.313179	+	0.949694i	$0.601394\pi$
$42$	−2.88144	−0.444616
$43$	−10.7029	−1.63218	−0.816092	−	0.577922i	$-0.803864\pi$
$43$	−10.7029	−1.63218	−0.816092	+	0.577922i	$0.803864\pi$
$44$	−0.899605	−0.135621
$45$	−1.39193	−0.207497
$46$	2.65665	0.391702
$47$	7.51508	1.09619	0.548094	−	0.836417i	$-0.315354\pi$
$47$	7.51508	1.09619	0.548094	+	0.836417i	$0.315354\pi$
$48$	0.406779	0.0587134
$49$	1.00000	0.142857
$50$	−2.27226	−0.321346
$51$	2.89735	0.405711
$52$	5.06893	0.702934
$53$	9.94282	1.36575	0.682876	−	0.730535i	$-0.260729\pi$
$53$	9.94282	1.36575	0.682876	+	0.730535i	$0.260729\pi$
$54$	−12.6551	−1.72214
$55$	−0.284402	−0.0383487
$56$	2.64298	0.353183
$57$	−4.58670	−0.607524
$58$	4.31630	0.566758
$59$	−6.97804	−0.908463	−0.454232	−	0.890884i	$-0.650086\pi$
$59$	−6.97804	−0.908463	−0.454232	+	0.890884i	$0.650086\pi$
$60$	−4.01118	−0.517841
$61$	0.251325	0.0321789	0.0160894	−	0.999871i	$-0.494878\pi$
$61$	0.251325	0.0321789	0.0160894	+	0.999871i	$0.494878\pi$
$62$	12.5721	1.59666
$63$	1.39193	0.175367
$64$	−13.0257	−1.62821
$65$	1.60249	0.198765
$66$	−0.819486	−0.100872
$67$	3.47498	0.424537	0.212268	−	0.977211i	$-0.431915\pi$
$67$	3.47498	0.424537	0.212268	+	0.977211i	$0.431915\pi$
$68$	−7.22719	−0.876425
$69$	1.48262	0.178486
$70$	2.27226	0.271587
$71$	12.6321	1.49915	0.749577	−	0.661917i	$-0.230257\pi$
$71$	12.6321	1.49915	0.749577	+	0.661917i	$0.230257\pi$
$72$	3.67885	0.433556
$73$	5.72987	0.670631	0.335315	−	0.942106i	$-0.391157\pi$
$73$	5.72987	0.670631	0.335315	+	0.942106i	$0.391157\pi$
$74$	−9.33638	−1.08533
$75$	−1.26810	−0.146427
$76$	11.4411	1.31239
$77$	0.284402	0.0324106
$78$	4.61749	0.522827
$79$	−2.39631	−0.269606	−0.134803	−	0.990872i	$-0.543040\pi$
$79$	−2.39631	−0.269606	−0.134803	+	0.990872i	$0.543040\pi$
$80$	−0.320779	−0.0358642
$81$	−2.88672	−0.320747
$82$	9.11323	1.00639
$83$	−3.19708	−0.350925	−0.175463	−	0.984486i	$-0.556142\pi$
$83$	−3.19708	−0.350925	−0.175463	+	0.984486i	$0.556142\pi$
$84$	4.01118	0.437655
$85$	−2.28481	−0.247822
$86$	24.3198	2.62248
$87$	2.40883	0.258254
$88$	0.751667	0.0801279
$89$	−10.2043	−1.08165	−0.540825	−	0.841135i	$-0.681888\pi$
$89$	−10.2043	−1.08165	−0.540825	+	0.841135i	$0.681888\pi$
$90$	3.16283	0.333392
$91$	−1.60249	−0.167987
$92$	−3.69825	−0.385570
$93$	7.01621	0.727547
$94$	−17.0762	−1.76127
$95$	3.61700	0.371096
$96$	−7.62740	−0.778468
$97$	−10.1282	−1.02836	−0.514180	−	0.857682i	$-0.671904\pi$
$97$	−10.1282	−1.02836	−0.514180	+	0.857682i	$0.671904\pi$
$98$	−2.27226	−0.229533
$99$	0.395868	0.0397862
$100$	3.16315	0.316315
$101$	1.63936	0.163122	0.0815611	−	0.996668i	$-0.474009\pi$
$101$	1.63936	0.163122	0.0815611	+	0.996668i	$0.474009\pi$
$102$	−6.58353	−0.651867
$103$	12.9668	1.27766	0.638830	−	0.769348i	$-0.279419\pi$
$103$	12.9668	1.27766	0.638830	+	0.769348i	$0.279419\pi$
$104$	−4.23535	−0.415311
$105$	1.26810	0.123753
$106$	−22.5926	−2.19439
$107$	13.7735	1.33154	0.665768	−	0.746159i	$-0.268104\pi$
$107$	13.7735	1.33154	0.665768	+	0.746159i	$0.268104\pi$
$108$	17.6168	1.69518
$109$	1.57449	0.150809	0.0754045	−	0.997153i	$-0.475975\pi$
$109$	1.57449	0.150809	0.0754045	+	0.997153i	$0.475975\pi$
$110$	0.646233	0.0616159
$111$	−5.21043	−0.494552
$112$	0.320779	0.0303108
$113$	−4.45901	−0.419469	−0.209734	−	0.977758i	$-0.567260\pi$
$113$	−4.45901	−0.419469	−0.209734	+	0.977758i	$0.567260\pi$
$114$	10.4222	0.976125
$115$	−1.16917	−0.109025
$116$	−6.00861	−0.557885
$117$	−2.23056	−0.206216
$118$	15.8559	1.45965
$119$	2.28481	0.209448
$120$	3.35155	0.305953
$121$	−10.9191	−0.992647
$122$	−0.571075	−0.0517027
$123$	5.08589	0.458579
$124$	−17.5013	−1.57166
$125$	1.00000	0.0894427
$126$	−3.16283	−0.281767
$127$	−13.6937	−1.21512	−0.607560	−	0.794273i	$-0.707852\pi$
$127$	−13.6937	−1.21512	−0.607560	+	0.794273i	$0.707852\pi$
$128$	17.5681	1.55281
$129$	13.5724	1.19498
$130$	−3.64128	−0.319361
$131$	11.1103	0.970713	0.485357	−	0.874316i	$-0.338690\pi$
$131$	11.1103	0.970713	0.485357	+	0.874316i	$0.338690\pi$
$132$	1.14078	0.0992926
$133$	−3.61700	−0.313634
$134$	−7.89606	−0.682115
$135$	5.56939	0.479337
$136$	6.03869	0.517813
$137$	6.78001	0.579255	0.289628	−	0.957139i	$-0.406469\pi$
$137$	6.78001	0.579255	0.289628	+	0.957139i	$0.406469\pi$
$138$	−3.36889	−0.286779
$139$	0.705506	0.0598403	0.0299201	−	0.999552i	$-0.490475\pi$
$139$	0.705506	0.0598403	0.0299201	+	0.999552i	$0.490475\pi$
$140$	−3.16315	−0.267335
$141$	−9.52984	−0.802557
$142$	−28.7034	−2.40873
$143$	−0.455752	−0.0381119
$144$	0.446503	0.0372086
$145$	−1.89956	−0.157750
$146$	−13.0197	−1.07752
$147$	−1.26810	−0.104591
$148$	12.9969	1.06834
$149$	1.63546	0.133982	0.0669910	−	0.997754i	$-0.478660\pi$
$149$	1.63546	0.133982	0.0669910	+	0.997754i	$0.478660\pi$
$150$	2.88144	0.235268
$151$	5.59363	0.455203	0.227602	−	0.973754i	$-0.426912\pi$
$151$	5.59363	0.455203	0.227602	+	0.973754i	$0.426912\pi$
$152$	−9.55965	−0.775390
$153$	3.18030	0.257112
$154$	−0.646233	−0.0520750
$155$	−5.53287	−0.444411
$156$	−6.42789	−0.514643
$157$	−7.13285	−0.569264	−0.284632	−	0.958637i	$-0.591871\pi$
$157$	−7.13285	−0.569264	−0.284632	+	0.958637i	$0.591871\pi$
$158$	5.44503	0.433183
$159$	−12.6084	−0.999915
$160$	6.01485	0.475515
$161$	1.16917	0.0921433
$162$	6.55937	0.515353
$163$	−0.306315	−0.0239925	−0.0119962	−	0.999928i	$-0.503819\pi$
$163$	−0.306315	−0.0239925	−0.0119962	+	0.999928i	$0.503819\pi$
$164$	−12.6863	−0.990633
$165$	0.360648	0.0280764
$166$	7.26459	0.563841
$167$	−16.3106	−1.26215	−0.631075	−	0.775721i	$-0.717386\pi$
$167$	−16.3106	−1.26215	−0.631075	+	0.775721i	$0.717386\pi$
$168$	−3.35155	−0.258577
$169$	−10.4320	−0.802463
$170$	5.19167	0.398183
$171$	−5.03463	−0.385007
$172$	−33.8550	−2.58142
$173$	13.0179	0.989736	0.494868	−	0.868968i	$-0.335216\pi$
$173$	13.0179	0.989736	0.494868	+	0.868968i	$0.335216\pi$
$174$	−5.47348	−0.414943
$175$	−1.00000	−0.0755929
$176$	0.0912301	0.00687673
$177$	8.84882	0.665118
$178$	23.1867	1.73792
$179$	−21.5363	−1.60970	−0.804850	−	0.593478i	$-0.797754\pi$
$179$	−21.5363	−1.60970	−0.804850	+	0.593478i	$0.797754\pi$
$180$	−4.40290	−0.328172
$181$	−19.2141	−1.42817	−0.714087	−	0.700057i	$-0.753158\pi$
$181$	−19.2141	−1.42817	−0.714087	+	0.700057i	$0.753158\pi$
$182$	3.64128	0.269909
$183$	−0.318704	−0.0235593
$184$	3.09008	0.227804
$185$	4.10886	0.302089
$186$	−15.9426	−1.16897
$187$	0.649802	0.0475183
$188$	23.7713	1.73370
$189$	−5.56939	−0.405114
$190$	−8.21875	−0.596251
$191$	−22.6531	−1.63912	−0.819561	−	0.572992i	$-0.805783\pi$
$191$	−22.6531	−1.63912	−0.819561	+	0.572992i	$0.805783\pi$
$192$	16.5179	1.19207
$193$	25.1483	1.81021	0.905106	−	0.425186i	$-0.139791\pi$
$193$	25.1483	1.81021	0.905106	+	0.425186i	$0.139791\pi$
$194$	23.0138	1.65229
$195$	−2.03212	−0.145523
$196$	3.16315	0.225939
$197$	−25.1237	−1.78999	−0.894994	−	0.446078i	$-0.852820\pi$
$197$	−25.1237	−1.78999	−0.894994	+	0.446078i	$0.852820\pi$
$198$	−0.899514	−0.0639257
$199$	13.4232	0.951543	0.475772	−	0.879569i	$-0.342169\pi$
$199$	13.4232	0.951543	0.475772	+	0.879569i	$0.342169\pi$
$200$	−2.64298	−0.186887
$201$	−4.40661	−0.310818
$202$	−3.72504	−0.262093
$203$	1.89956	0.133323
$204$	9.16476	0.641662
$205$	−4.01065	−0.280116
$206$	−29.4640	−2.05285
$207$	1.62740	0.113112
$208$	−0.514047	−0.0356427
$209$	−1.02868	−0.0711553
$210$	−2.88144	−0.198838
$211$	−3.46711	−0.238686	−0.119343	−	0.992853i	$-0.538079\pi$
$211$	−3.46711	−0.238686	−0.119343	+	0.992853i	$0.538079\pi$
$212$	31.4506	2.16004
$213$	−16.0187	−1.09758
$214$	−31.2970	−2.13942
$215$	−10.7029	−0.729935
$216$	−14.7198	−1.00155
$217$	5.53287	0.375596
$218$	−3.57765	−0.242309
$219$	−7.26603	−0.490993
$220$	−0.899605	−0.0606513
$221$	−3.66139	−0.246292
$222$	11.8394	0.794610
$223$	13.1126	0.878085	0.439042	−	0.898466i	$-0.355318\pi$
$223$	13.1126	0.878085	0.439042	+	0.898466i	$0.355318\pi$
$224$	−6.01485	−0.401884
$225$	−1.39193	−0.0927956
$226$	10.1320	0.673972
$227$	29.1250	1.93309	0.966546	−	0.256495i	$-0.0825676\pi$
$227$	29.1250	1.93309	0.966546	+	0.256495i	$0.0825676\pi$
$228$	−14.5084	−0.960844
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	2.65665	0.175174
$231$	−0.360648	−0.0237289
$232$	5.02051	0.329612
$233$	3.62640	0.237573	0.118787	−	0.992920i	$-0.462100\pi$
$233$	3.62640	0.237573	0.118787	+	0.992920i	$0.462100\pi$
$234$	5.06842	0.331333
$235$	7.51508	0.490230
$236$	−22.0726	−1.43680
$237$	3.03875	0.197388
$238$	−5.19167	−0.336526
$239$	15.6052	1.00942	0.504709	−	0.863290i	$-0.331600\pi$
$239$	15.6052	1.00942	0.504709	+	0.863290i	$0.331600\pi$
$240$	0.406779	0.0262575
$241$	4.23443	0.272764	0.136382	−	0.990656i	$-0.456453\pi$
$241$	4.23443	0.272764	0.136382	+	0.990656i	$0.456453\pi$
$242$	24.8110	1.59491
$243$	−13.0475	−0.837000
$244$	0.794979	0.0508933
$245$	1.00000	0.0638877
$246$	−11.5564	−0.736812
$247$	5.79622	0.368805
$248$	14.6233	0.928577
$249$	4.05420	0.256925
$250$	−2.27226	−0.143710
$251$	4.97698	0.314144	0.157072	−	0.987587i	$-0.449795\pi$
$251$	4.97698	0.314144	0.157072	+	0.987587i	$0.449795\pi$
$252$	4.40290	0.277356
$253$	0.332513	0.0209049
$254$	31.1156	1.95237
$255$	2.89735	0.181439
$256$	−13.8678	−0.866735
$257$	5.43747	0.339180	0.169590	−	0.985515i	$-0.445756\pi$
$257$	5.43747	0.339180	0.169590	+	0.985515i	$0.445756\pi$
$258$	−30.8399	−1.92001
$259$	−4.10886	−0.255312
$260$	5.06893	0.314362
$261$	2.64407	0.163664
$262$	−25.2455	−1.55967
$263$	18.0334	1.11199	0.555994	−	0.831186i	$-0.312338\pi$
$263$	18.0334	1.11199	0.555994	+	0.831186i	$0.312338\pi$
$264$	−0.953185	−0.0586645
$265$	9.94282	0.610783
$266$	8.21875	0.503924
$267$	12.9400	0.791914
$268$	10.9919	0.671437
$269$	11.5094	0.701739	0.350869	−	0.936424i	$-0.385886\pi$
$269$	11.5094	0.701739	0.350869	+	0.936424i	$0.385886\pi$
$270$	−12.6551	−0.770164
$271$	−13.3493	−0.810913	−0.405457	−	0.914114i	$-0.632887\pi$
$271$	−13.3493	−0.810913	−0.405457	+	0.914114i	$0.632887\pi$
$272$	0.732918	0.0444397
$273$	2.03212	0.122989
$274$	−15.4059	−0.930706
$275$	−0.284402	−0.0171501
$276$	4.68974	0.282289
$277$	0.0169464	0.00101821	0.000509104	−	1.00000i	$-0.499838\pi$
$277$	0.0169464	0.00101821	0.000509104		1.00000i	$0.499838\pi$
$278$	−1.60309	−0.0961470
$279$	7.70139	0.461070
$280$	2.64298	0.157948
$281$	10.0453	0.599253	0.299626	−	0.954057i	$-0.403138\pi$
$281$	10.0453	0.599253	0.299626	+	0.954057i	$0.403138\pi$
$282$	21.6542	1.28949
$283$	−11.8608	−0.705052	−0.352526	−	0.935802i	$-0.614677\pi$
$283$	−11.8608	−0.705052	−0.352526	+	0.935802i	$0.614677\pi$
$284$	39.9572	2.37103
$285$	−4.58670	−0.271693
$286$	1.03558	0.0612354
$287$	4.01065	0.236741
$288$	−8.37227	−0.493341
$289$	−11.7797	−0.692921
$290$	4.31630	0.253462
$291$	12.8435	0.752899
$292$	18.1245	1.06065
$293$	−10.9467	−0.639514	−0.319757	−	0.947500i	$-0.603601\pi$
$293$	−10.9467	−0.639514	−0.319757	+	0.947500i	$0.603601\pi$
$294$	2.88144	0.168049
$295$	−6.97804	−0.406277
$296$	−10.8596	−0.631202
$297$	−1.58394	−0.0919097
$298$	−3.71618	−0.215273
$299$	−1.87358	−0.108352
$300$	−4.01118	−0.231585
$301$	10.7029	0.616908
$302$	−12.7102	−0.731388
$303$	−2.07886	−0.119428
$304$	−1.16026	−0.0665454
$305$	0.251325	0.0143908
$306$	−7.22646	−0.413109
$307$	21.9591	1.25327	0.626637	−	0.779311i	$-0.284431\pi$
$307$	21.9591	1.25327	0.626637	+	0.779311i	$0.284431\pi$
$308$	0.899605	0.0512597
$309$	−16.4432	−0.935420
$310$	12.5721	0.714048
$311$	6.77657	0.384264	0.192132	−	0.981369i	$-0.438460\pi$
$311$	6.77657	0.384264	0.192132	+	0.981369i	$0.438460\pi$
$312$	5.37083	0.304064
$313$	11.3249	0.640120	0.320060	−	0.947397i	$-0.396297\pi$
$313$	11.3249	0.640120	0.320060	+	0.947397i	$0.396297\pi$
$314$	16.2077	0.914652
$315$	1.39193	0.0784266
$316$	−7.57989	−0.426402
$317$	−26.6955	−1.49937	−0.749684	−	0.661795i	$-0.769795\pi$
$317$	−26.6955	−1.49937	−0.749684	+	0.661795i	$0.769795\pi$
$318$	28.6496	1.60659
$319$	0.540239	0.0302476
$320$	−13.0257	−0.728160
$321$	−17.4661	−0.974864
$322$	−2.65665	−0.148049
$323$	−8.26415	−0.459829
$324$	−9.13113	−0.507285
$325$	1.60249	0.0888904
$326$	0.696027	0.0385494
$327$	−1.99661	−0.110413
$328$	10.6001	0.585290
$329$	−7.51508	−0.414320
$330$	−0.819486	−0.0451112
$331$	−9.48841	−0.521530	−0.260765	−	0.965402i	$-0.583975\pi$
$331$	−9.48841	−0.521530	−0.260765	+	0.965402i	$0.583975\pi$
$332$	−10.1128	−0.555014
$333$	−5.71926	−0.313413
$334$	37.0618	2.02793
$335$	3.47498	0.189859
$336$	−0.406779	−0.0221916
$337$	−24.0068	−1.30773	−0.653866	−	0.756610i	$-0.726854\pi$
$337$	−24.0068	−1.30773	−0.653866	+	0.756610i	$0.726854\pi$
$338$	23.7042	1.28934
$339$	5.65445	0.307108
$340$	−7.22719	−0.391949
$341$	1.57356	0.0852129
$342$	11.4400	0.618602
$343$	−1.00000	−0.0539949
$344$	28.2876	1.52517
$345$	1.48262	0.0798214
$346$	−29.5801	−1.59024
$347$	5.45859	0.293032	0.146516	−	0.989208i	$-0.453194\pi$
$347$	5.45859	0.293032	0.146516	+	0.989208i	$0.453194\pi$
$348$	7.61949	0.408448
$349$	10.0928	0.540253	0.270126	−	0.962825i	$-0.412935\pi$
$349$	10.0928	0.540253	0.270126	+	0.962825i	$0.412935\pi$
$350$	2.27226	0.121457
$351$	8.92491	0.476377
$352$	−1.71063	−0.0911770
$353$	13.7414	0.731381	0.365690	−	0.930737i	$-0.380833\pi$
$353$	13.7414	0.731381	0.365690	+	0.930737i	$0.380833\pi$
$354$	−20.1068	−1.06866
$355$	12.6321	0.670442
$356$	−32.2776	−1.71071
$357$	−2.89735	−0.153344
$358$	48.9360	2.58635
$359$	−0.00682211	−0.000360057 0	−0.000180029	−	1.00000i	$-0.500057\pi$
$359$	−0.00682211	−0.000360057 0	−0.000180029		1.00000i	$0.500057\pi$
$360$	3.67885	0.193892
$361$	−5.91730	−0.311437
$362$	43.6594	2.29469
$363$	13.8465	0.726752
$364$	−5.06893	−0.265684
$365$	5.72987	0.299915
$366$	0.724178	0.0378534
$367$	−7.69163	−0.401500	−0.200750	−	0.979642i	$-0.564338\pi$
$367$	−7.69163	−0.401500	−0.200750	+	0.979642i	$0.564338\pi$
$368$	0.375045	0.0195506
$369$	5.58256	0.290617
$370$	−9.33638	−0.485375
$371$	−9.94282	−0.516205
$372$	22.1933	1.15067
$373$	4.70712	0.243726	0.121863	−	0.992547i	$-0.461113\pi$
$373$	4.70712	0.243726	0.121863	+	0.992547i	$0.461113\pi$
$374$	−1.47652	−0.0763489
$375$	−1.26810	−0.0654842
$376$	−19.8622	−1.02431
$377$	−3.04404	−0.156776
$378$	12.6551	0.650907
$379$	37.3060	1.91628	0.958140	−	0.286299i	$-0.0924249\pi$
$379$	37.3060	1.91628	0.958140	+	0.286299i	$0.0924249\pi$
$380$	11.4411	0.586917
$381$	17.3649	0.889633
$382$	51.4737	2.63362
$383$	20.0660	1.02532	0.512662	−	0.858590i	$-0.328659\pi$
$383$	20.0660	1.02532	0.512662	+	0.858590i	$0.328659\pi$
$384$	−22.2780	−1.13687
$385$	0.284402	0.0144944
$386$	−57.1433	−2.90852
$387$	14.8978	0.757298
$388$	−32.0369	−1.62643
$389$	−10.4338	−0.529015	−0.264507	−	0.964384i	$-0.585209\pi$
$389$	−10.4338	−0.529015	−0.264507	+	0.964384i	$0.585209\pi$
$390$	4.61749	0.233816
$391$	2.67132	0.135095
$392$	−2.64298	−0.133490
$393$	−14.0889	−0.710693
$394$	57.0875	2.87602
$395$	−2.39631	−0.120571
$396$	1.25219	0.0629249
$397$	−24.1351	−1.21131	−0.605654	−	0.795728i	$-0.707088\pi$
$397$	−24.1351	−1.21131	−0.605654	+	0.795728i	$0.707088\pi$
$398$	−30.5009	−1.52887
$399$	4.58670	0.229622
$400$	−0.320779	−0.0160390
$401$	12.0048	0.599490	0.299745	−	0.954019i	$-0.403098\pi$
$401$	12.0048	0.599490	0.299745	+	0.954019i	$0.403098\pi$
$402$	10.0130	0.499401
$403$	−8.86639	−0.441666
$404$	5.18554	0.257990
$405$	−2.88672	−0.143442
$406$	−4.31630	−0.214214
$407$	−1.16857	−0.0579236
$408$	−7.65764	−0.379110
$409$	−15.1492	−0.749079	−0.374539	−	0.927211i	$-0.622199\pi$
$409$	−15.1492	−0.749079	−0.374539	+	0.927211i	$0.622199\pi$
$410$	9.11323	0.450070
$411$	−8.59770	−0.424093
$412$	41.0160	2.02071
$413$	6.97804	0.343367
$414$	−3.69788	−0.181741
$415$	−3.19708	−0.156938
$416$	9.63875	0.472579
$417$	−0.894650	−0.0438112
$418$	2.33743	0.114327
$419$	3.43074	0.167603	0.0838014	−	0.996482i	$-0.473294\pi$
$419$	3.43074	0.167603	0.0838014	+	0.996482i	$0.473294\pi$
$420$	4.01118	0.195725
$421$	−13.2161	−0.644114	−0.322057	−	0.946720i	$-0.604374\pi$
$421$	−13.2161	−0.644114	−0.322057	+	0.946720i	$0.604374\pi$
$422$	7.87817	0.383503
$423$	−10.4605	−0.508607
$424$	−26.2786	−1.27620
$425$	−2.28481	−0.110829
$426$	36.3986	1.76352
$427$	−0.251325	−0.0121625
$428$	43.5677	2.10592
$429$	0.577937	0.0279030
$430$	24.3198	1.17281
$431$	−27.7474	−1.33654	−0.668272	−	0.743917i	$-0.732966\pi$
$431$	−27.7474	−1.33654	−0.668272	+	0.743917i	$0.732966\pi$
$432$	−1.78654	−0.0859552
$433$	9.56206	0.459523	0.229762	−	0.973247i	$-0.426205\pi$
$433$	9.56206	0.459523	0.229762	+	0.973247i	$0.426205\pi$
$434$	−12.5721	−0.603480
$435$	2.40883	0.115495
$436$	4.98036	0.238516
$437$	−4.22888	−0.202295
$438$	16.5103	0.788892
$439$	−2.44470	−0.116679	−0.0583395	−	0.998297i	$-0.518581\pi$
$439$	−2.44470	−0.116679	−0.0583395	+	0.998297i	$0.518581\pi$
$440$	0.751667	0.0358343
$441$	−1.39193	−0.0662826
$442$	8.31961	0.395724
$443$	4.59612	0.218368	0.109184	−	0.994022i	$-0.465176\pi$
$443$	4.59612	0.218368	0.109184	+	0.994022i	$0.465176\pi$
$444$	−16.4814	−0.782171
$445$	−10.2043	−0.483728
$446$	−29.7952	−1.41084
$447$	−2.07392	−0.0980929
$448$	13.0257	0.615407
$449$	2.78512	0.131438	0.0657190	−	0.997838i	$-0.479066\pi$
$449$	2.78512	0.131438	0.0657190	+	0.997838i	$0.479066\pi$
$450$	3.16283	0.149097
$451$	1.14064	0.0537104
$452$	−14.1045	−0.663421
$453$	−7.09326	−0.333270
$454$	−66.1794	−3.10595
$455$	−1.60249	−0.0751261
$456$	12.1225	0.567690
$457$	13.3688	0.625366	0.312683	−	0.949858i	$-0.398772\pi$
$457$	13.3688	0.625366	0.312683	+	0.949858i	$0.398772\pi$
$458$	−2.27226	−0.106176
$459$	−12.7250	−0.593951
$460$	−3.69825	−0.172432
$461$	6.83148	0.318174	0.159087	−	0.987265i	$-0.449145\pi$
$461$	6.83148	0.318174	0.159087	+	0.987265i	$0.449145\pi$
$462$	0.819486	0.0381259
$463$	17.1201	0.795638	0.397819	−	0.917464i	$-0.369767\pi$
$463$	17.1201	0.795638	0.397819	+	0.917464i	$0.369767\pi$
$464$	0.609341	0.0282879
$465$	7.01621	0.325369
$466$	−8.24011	−0.381716
$467$	16.7944	0.777151	0.388575	−	0.921417i	$-0.372967\pi$
$467$	16.7944	0.777151	0.388575	+	0.921417i	$0.372967\pi$
$468$	−7.05561	−0.326146
$469$	−3.47498	−0.160460
$470$	−17.0762	−0.787666
$471$	9.04514	0.416778
$472$	18.4428	0.848898
$473$	3.04393	0.139960
$474$	−6.90482	−0.317149
$475$	3.61700	0.165959
$476$	7.22719	0.331258
$477$	−13.8397	−0.633678
$478$	−35.4591	−1.62186
$479$	8.13445	0.371673	0.185836	−	0.982581i	$-0.440501\pi$
$479$	8.13445	0.371673	0.185836	+	0.982581i	$0.440501\pi$
$480$	−7.62740	−0.348142
$481$	6.58442	0.300224
$482$	−9.62171	−0.438257
$483$	−1.48262	−0.0674614
$484$	−34.5388	−1.56995
$485$	−10.1282	−0.459897
$486$	29.6474	1.34483
$487$	−13.8703	−0.628523	−0.314262	−	0.949336i	$-0.601757\pi$
$487$	−13.8703	−0.628523	−0.314262	+	0.949336i	$0.601757\pi$
$488$	−0.664247	−0.0300690
$489$	0.388437	0.0175657
$490$	−2.27226	−0.102650
$491$	−23.3161	−1.05224	−0.526121	−	0.850410i	$-0.676354\pi$
$491$	−23.3161	−1.05224	−0.526121	+	0.850410i	$0.676354\pi$
$492$	16.0874	0.725278
$493$	4.34014	0.195470
$494$	−13.1705	−0.592569
$495$	0.395868	0.0177929
$496$	1.77483	0.0796922
$497$	−12.6321	−0.566627
$498$	−9.21219	−0.412808
$499$	0.993600	0.0444797	0.0222398	−	0.999753i	$-0.492920\pi$
$499$	0.993600	0.0444797	0.0222398	+	0.999753i	$0.492920\pi$
$500$	3.16315	0.141460
$501$	20.6834	0.924065
$502$	−11.3090	−0.504744
$503$	−15.2682	−0.680775	−0.340388	−	0.940285i	$-0.610558\pi$
$503$	−15.2682	−0.680775	−0.340388	+	0.940285i	$0.610558\pi$
$504$	−3.67885	−0.163869
$505$	1.63936	0.0729505
$506$	−0.755555	−0.0335885
$507$	13.2288	0.587511
$508$	−43.3153	−1.92181
$509$	9.78777	0.433835	0.216918	−	0.976190i	$-0.430400\pi$
$509$	9.78777	0.433835	0.216918	+	0.976190i	$0.430400\pi$
$510$	−6.58353	−0.291524
$511$	−5.72987	−0.253475
$512$	−3.62506	−0.160207
$513$	20.1445	0.889401
$514$	−12.3553	−0.544970
$515$	12.9668	0.571387
$516$	42.9314	1.88995
$517$	−2.13730	−0.0939984
$518$	9.33638	0.410217
$519$	−16.5080	−0.724621
$520$	−4.23535	−0.185733
$521$	25.7442	1.12787	0.563936	−	0.825818i	$-0.309286\pi$
$521$	25.7442	1.12787	0.563936	+	0.825818i	$0.309286\pi$
$522$	−6.00800	−0.262963
$523$	−23.8376	−1.04235	−0.521174	−	0.853451i	$-0.674506\pi$
$523$	−23.8376	−1.04235	−0.521174	+	0.853451i	$0.674506\pi$
$524$	35.1436	1.53526
$525$	1.26810	0.0553442
$526$	−40.9766	−1.78666
$527$	12.6415	0.550674
$528$	−0.115688	−0.00503469
$529$	−21.6330	−0.940567
$530$	−22.5926	−0.981361
$531$	9.71297	0.421507
$532$	−11.4411	−0.496035
$533$	−6.42704	−0.278386
$534$	−29.4029	−1.27239
$535$	13.7735	0.595481
$536$	−9.18430	−0.396701
$537$	27.3101	1.17852
$538$	−26.1523	−1.12750
$539$	−0.284402	−0.0122500
$540$	17.6168	0.758107
$541$	−13.1373	−0.564817	−0.282409	−	0.959294i	$-0.591133\pi$
$541$	−13.1373	−0.564817	−0.282409	+	0.959294i	$0.591133\pi$
$542$	30.3331	1.30292
$543$	24.3653	1.04562
$544$	−13.7428	−0.589216
$545$	1.57449	0.0674439
$546$	−4.61749	−0.197610
$547$	−2.09006	−0.0893644	−0.0446822	−	0.999001i	$-0.514228\pi$
$547$	−2.09006	−0.0893644	−0.0446822	+	0.999001i	$0.514228\pi$
$548$	21.4462	0.916136
$549$	−0.349828	−0.0149303
$550$	0.646233	0.0275555
$551$	−6.87073	−0.292703
$552$	−3.91852	−0.166783
$553$	2.39631	0.101901
$554$	−0.0385065	−0.00163598
$555$	−5.21043	−0.221170
$556$	2.23162	0.0946419
$557$	4.58585	0.194309	0.0971544	−	0.995269i	$-0.469026\pi$
$557$	4.58585	0.194309	0.0971544	+	0.995269i	$0.469026\pi$
$558$	−17.4995	−0.740814
$559$	−17.1514	−0.725427
$560$	0.320779	0.0135554
$561$	−0.824012	−0.0347898
$562$	−22.8255	−0.962836
$563$	0.758172	0.0319532	0.0159766	−	0.999872i	$-0.494914\pi$
$563$	0.758172	0.0319532	0.0159766	+	0.999872i	$0.494914\pi$
$564$	−30.1443	−1.26931
$565$	−4.45901	−0.187592
$566$	26.9508	1.13283
$567$	2.88672	0.121231
$568$	−33.3864	−1.40086
$569$	39.5510	1.65806	0.829031	−	0.559202i	$-0.188892\pi$
$569$	39.5510	1.65806	0.829031	+	0.559202i	$0.188892\pi$
$570$	10.4222	0.436537
$571$	21.2088	0.887560	0.443780	−	0.896136i	$-0.353637\pi$
$571$	21.2088	0.887560	0.443780	+	0.896136i	$0.353637\pi$
$572$	−1.44161	−0.0602768
$573$	28.7263	1.20006
$574$	−9.11323	−0.380379
$575$	−1.16917	−0.0487577
$576$	18.1309	0.755456
$577$	7.23035	0.301003	0.150502	−	0.988610i	$-0.451911\pi$
$577$	7.23035	0.301003	0.150502	+	0.988610i	$0.451911\pi$
$578$	26.7664	1.11334
$579$	−31.8904	−1.32532
$580$	−6.00861	−0.249494
$581$	3.19708	0.132637
$582$	−29.1837	−1.20970
$583$	−2.82775	−0.117114
$584$	−15.1439	−0.626660
$585$	−2.23056	−0.0922225
$586$	24.8737	1.02753
$587$	−32.6380	−1.34712	−0.673558	−	0.739134i	$-0.735235\pi$
$587$	−32.6380	−1.34712	−0.673558	+	0.739134i	$0.735235\pi$
$588$	−4.01118	−0.165418
$589$	−20.0124	−0.824597
$590$	15.8559	0.652777
$591$	31.8592	1.31051
$592$	−1.31804	−0.0541710
$593$	17.2519	0.708449	0.354224	−	0.935160i	$-0.384745\pi$
$593$	17.2519	0.708449	0.354224	+	0.935160i	$0.384745\pi$
$594$	3.59913	0.147674
$595$	2.28481	0.0936679
$596$	5.17320	0.211903
$597$	−17.0219	−0.696658
$598$	4.25726	0.174092
$599$	−16.0469	−0.655657	−0.327828	−	0.944737i	$-0.606317\pi$
$599$	−16.0469	−0.655657	−0.327828	+	0.944737i	$0.606317\pi$
$600$	3.35155	0.136826
$601$	−20.3984	−0.832069	−0.416035	−	0.909349i	$-0.636580\pi$
$601$	−20.3984	−0.832069	−0.416035	+	0.909349i	$0.636580\pi$
$602$	−24.3198	−0.991203
$603$	−4.83695	−0.196976
$604$	17.6935	0.719938
$605$	−10.9191	−0.443925
$606$	4.72371	0.191888
$607$	−46.7283	−1.89664	−0.948322	−	0.317310i	$-0.897220\pi$
$607$	−46.7283	−1.89664	−0.948322	+	0.317310i	$0.897220\pi$
$608$	21.7557	0.882310
$609$	−2.40883	−0.0976107
$610$	−0.571075	−0.0231222
$611$	12.0429	0.487202
$612$	10.0598	0.406642
$613$	−20.2247	−0.816869	−0.408435	−	0.912788i	$-0.633925\pi$
$613$	−20.2247	−0.816869	−0.408435	+	0.912788i	$0.633925\pi$
$614$	−49.8968	−2.01367
$615$	5.08589	0.205083
$616$	−0.751667	−0.0302855
$617$	−10.3113	−0.415117	−0.207559	−	0.978223i	$-0.566552\pi$
$617$	−10.3113	−0.415117	−0.207559	+	0.978223i	$0.566552\pi$
$618$	37.3631	1.50297
$619$	−13.4808	−0.541840	−0.270920	−	0.962602i	$-0.587328\pi$
$619$	−13.4808	−0.541840	−0.270920	+	0.962602i	$0.587328\pi$
$620$	−17.5013	−0.702869
$621$	−6.51155	−0.261300
$622$	−15.3981	−0.617408
$623$	10.2043	0.408825
$624$	0.651860	0.0260953
$625$	1.00000	0.0400000
$626$	−25.7330	−1.02850
$627$	1.30447	0.0520953
$628$	−22.5623	−0.900333
$629$	−9.38795	−0.374322
$630$	−3.16283	−0.126010
$631$	−3.17603	−0.126436	−0.0632179	−	0.998000i	$-0.520136\pi$
$631$	−3.17603	−0.126436	−0.0632179	+	0.998000i	$0.520136\pi$
$632$	6.33339	0.251929
$633$	4.39663	0.174750
$634$	60.6590	2.40908
$635$	−13.6937	−0.543419
$636$	−39.8824	−1.58144
$637$	1.60249	0.0634931
$638$	−1.22756	−0.0485996
$639$	−17.5830	−0.695575
$640$	17.5681	0.694439
$641$	29.9442	1.18273	0.591363	−	0.806406i	$-0.298590\pi$
$641$	29.9442	1.18273	0.591363	+	0.806406i	$0.298590\pi$
$642$	39.6875	1.56634
$643$	−43.1559	−1.70190	−0.850952	−	0.525244i	$-0.823974\pi$
$643$	−43.1559	−1.70190	−0.850952	+	0.525244i	$0.823974\pi$
$644$	3.69825	0.145732
$645$	13.5724	0.534411
$646$	18.7783	0.738821
$647$	27.6131	1.08558	0.542792	−	0.839867i	$-0.317367\pi$
$647$	27.6131	1.08558	0.542792	+	0.839867i	$0.317367\pi$
$648$	7.62953	0.299716
$649$	1.98456	0.0779010
$650$	−3.64128	−0.142823
$651$	−7.01621	−0.274987
$652$	−0.968921	−0.0379459
$653$	−2.55330	−0.0999184	−0.0499592	−	0.998751i	$-0.515909\pi$
$653$	−2.55330	−0.0999184	−0.0499592	+	0.998751i	$0.515909\pi$
$654$	4.53680	0.177403
$655$	11.1103	0.434116
$656$	1.28653	0.0502307
$657$	−7.97560	−0.311158
$658$	17.0762	0.665699
$659$	−26.5242	−1.03324	−0.516618	−	0.856216i	$-0.672809\pi$
$659$	−26.5242	−1.03324	−0.516618	+	0.856216i	$0.672809\pi$
$660$	1.14078	0.0444050
$661$	−35.4038	−1.37705	−0.688524	−	0.725214i	$-0.741741\pi$
$661$	−35.4038	−1.37705	−0.688524	+	0.725214i	$0.741741\pi$
$662$	21.5601	0.837957
$663$	4.64299	0.180319
$664$	8.44981	0.327916
$665$	−3.61700	−0.140261
$666$	12.9956	0.503570
$667$	2.22091	0.0859940
$668$	−51.5928	−1.99619
$669$	−16.6280	−0.642877
$670$	−7.89606	−0.305051
$671$	−0.0714773	−0.00275935
$672$	7.62740	0.294233
$673$	1.90918	0.0735936	0.0367968	−	0.999323i	$-0.488285\pi$
$673$	1.90918	0.0735936	0.0367968	+	0.999323i	$0.488285\pi$
$674$	54.5496	2.10117
$675$	5.56939	0.214366
$676$	−32.9980	−1.26916
$677$	−18.9022	−0.726470	−0.363235	−	0.931698i	$-0.618328\pi$
$677$	−18.9022	−0.726470	−0.363235	+	0.931698i	$0.618328\pi$
$678$	−12.8484	−0.493439
$679$	10.1282	0.388684
$680$	6.03869	0.231573
$681$	−36.9332	−1.41528
$682$	−3.57553	−0.136914
$683$	16.4179	0.628215	0.314108	−	0.949387i	$-0.398295\pi$
$683$	16.4179	0.628215	0.314108	+	0.949387i	$0.398295\pi$
$684$	−15.9253	−0.608918
$685$	6.78001	0.259051
$686$	2.27226	0.0867552
$687$	−1.26810	−0.0483809
$688$	3.43328	0.130893
$689$	15.9333	0.607011
$690$	−3.36889	−0.128251
$691$	−47.7668	−1.81713	−0.908566	−	0.417740i	$-0.862822\pi$
$691$	−47.7668	−1.81713	−0.908566	+	0.417740i	$0.862822\pi$
$692$	41.1777	1.56534
$693$	−0.395868	−0.0150378
$694$	−12.4033	−0.470824
$695$	0.705506	0.0267614
$696$	−6.36648	−0.241321
$697$	9.16356	0.347095
$698$	−22.9333	−0.868039
$699$	−4.59862	−0.173936
$700$	−3.16315	−0.119556
$701$	−43.7183	−1.65122	−0.825609	−	0.564243i	$-0.809168\pi$
$701$	−43.7183	−1.65122	−0.825609	+	0.564243i	$0.809168\pi$
$702$	−20.2797	−0.765408
$703$	14.8617	0.560521
$704$	3.70453	0.139620
$705$	−9.52984	−0.358915
$706$	−31.2240	−1.17513
$707$	−1.63936	−0.0616544
$708$	27.9901	1.05193
$709$	−2.03275	−0.0763417	−0.0381708	−	0.999271i	$-0.512153\pi$
$709$	−2.03275	−0.0763417	−0.0381708	+	0.999271i	$0.512153\pi$
$710$	−28.7034	−1.07722
$711$	3.33550	0.125091
$712$	26.9696	1.01073
$713$	6.46886	0.242261
$714$	6.58353	0.246382
$715$	−0.455752	−0.0170441
$716$	−68.1226	−2.54586
$717$	−19.7889	−0.739030
$718$	0.0155016	0.000578514 0
$719$	−48.9197	−1.82440	−0.912198	−	0.409749i	$-0.865616\pi$
$719$	−48.9197	−1.82440	−0.912198	+	0.409749i	$0.865616\pi$
$720$	0.446503	0.0166402
$721$	−12.9668	−0.482910
$722$	13.4456	0.500395
$723$	−5.36966	−0.199700
$724$	−60.7772	−2.25877
$725$	−1.89956	−0.0705481
$726$	−31.4628	−1.16769
$727$	−39.2681	−1.45637	−0.728186	−	0.685379i	$-0.759637\pi$
$727$	−39.2681	−1.45637	−0.728186	+	0.685379i	$0.759637\pi$
$728$	4.23535	0.156973
$729$	25.2057	0.933544
$730$	−13.0197	−0.481882
$731$	24.4542	0.904470
$732$	−1.00811	−0.0372608
$733$	−8.42886	−0.311327	−0.155663	−	0.987810i	$-0.549752\pi$
$733$	−8.42886	−0.311327	−0.155663	+	0.987810i	$0.549752\pi$
$734$	17.4774	0.645101
$735$	−1.26810	−0.0467744
$736$	−7.03237	−0.259216
$737$	−0.988291	−0.0364042
$738$	−12.6850	−0.466942
$739$	−26.4127	−0.971607	−0.485803	−	0.874068i	$-0.661473\pi$
$739$	−26.4127	−0.971607	−0.485803	+	0.874068i	$0.661473\pi$
$740$	12.9969	0.477777
$741$	−7.35016	−0.270015
$742$	22.5926	0.829402
$743$	5.67643	0.208248	0.104124	−	0.994564i	$-0.466796\pi$
$743$	5.67643	0.208248	0.104124	+	0.994564i	$0.466796\pi$
$744$	−18.5437	−0.679844
$745$	1.63546	0.0599186
$746$	−10.6958	−0.391601
$747$	4.45012	0.162821
$748$	2.05542	0.0751537
$749$	−13.7735	−0.503273
$750$	2.88144	0.105215
$751$	−18.3535	−0.669729	−0.334865	−	0.942266i	$-0.608691\pi$
$751$	−18.3535	−0.669729	−0.334865	+	0.942266i	$0.608691\pi$
$752$	−2.41068	−0.0879085
$753$	−6.31128	−0.229996
$754$	6.91684	0.251897
$755$	5.59363	0.203573
$756$	−17.6168	−0.640718
$757$	−46.2673	−1.68162	−0.840808	−	0.541334i	$-0.817919\pi$
$757$	−46.2673	−1.68162	−0.840808	+	0.541334i	$0.817919\pi$
$758$	−84.7688	−3.07894
$759$	−0.421658	−0.0153052
$760$	−9.55965	−0.346765
$761$	−26.3962	−0.956861	−0.478431	−	0.878125i	$-0.658794\pi$
$761$	−26.3962	−0.956861	−0.478431	+	0.878125i	$0.658794\pi$
$762$	−39.4576	−1.42940
$763$	−1.57449	−0.0570005
$764$	−71.6552	−2.59239
$765$	3.18030	0.114984
$766$	−45.5951	−1.64742
$767$	−11.1823	−0.403768
$768$	17.5856	0.634567
$769$	−8.24081	−0.297171	−0.148586	−	0.988900i	$-0.547472\pi$
$769$	−8.24081	−0.297171	−0.148586	+	0.988900i	$0.547472\pi$
$770$	−0.646233	−0.0232886
$771$	−6.89523	−0.248326
$772$	79.5477	2.86299
$773$	6.17891	0.222240	0.111120	−	0.993807i	$-0.464556\pi$
$773$	6.17891	0.222240	0.111120	+	0.993807i	$0.464556\pi$
$774$	−33.8516	−1.21677
$775$	−5.53287	−0.198747
$776$	26.7685	0.960934
$777$	5.21043	0.186923
$778$	23.7083	0.849983
$779$	−14.5065	−0.519750
$780$	−6.42789	−0.230155
$781$	−3.59259	−0.128553
$782$	−6.06993	−0.217060
$783$	−10.5794	−0.378078
$784$	−0.320779	−0.0114564
$785$	−7.13285	−0.254582
$786$	32.0137	1.14189
$787$	8.65196	0.308409	0.154204	−	0.988039i	$-0.450719\pi$
$787$	8.65196	0.308409	0.154204	+	0.988039i	$0.450719\pi$
$788$	−79.4700	−2.83100
$789$	−22.8681	−0.814126
$790$	5.44503	0.193726
$791$	4.45901	0.158544
$792$	−1.04627	−0.0371776
$793$	0.402747	0.0143020
$794$	54.8412	1.94624
$795$	−12.6084	−0.447175
$796$	42.4595	1.50494
$797$	35.6345	1.26224	0.631119	−	0.775686i	$-0.282596\pi$
$797$	35.6345	1.26224	0.631119	+	0.775686i	$0.282596\pi$
$798$	−10.4222	−0.368941
$799$	−17.1705	−0.607449
$800$	6.01485	0.212657
$801$	14.2037	0.501861
$802$	−27.2780	−0.963218
$803$	−1.62958	−0.0575068
$804$	−13.9388	−0.491583
$805$	1.16917	0.0412078
$806$	20.1467	0.709638
$807$	−14.5950	−0.513768
$808$	−4.33279	−0.152427
$809$	−26.8082	−0.942525	−0.471263	−	0.881993i	$-0.656202\pi$
$809$	−26.8082	−0.942525	−0.471263	+	0.881993i	$0.656202\pi$
$810$	6.55937	0.230473
$811$	19.8317	0.696386	0.348193	−	0.937423i	$-0.386795\pi$
$811$	19.8317	0.696386	0.348193	+	0.937423i	$0.386795\pi$
$812$	6.00861	0.210861
$813$	16.9282	0.593698
$814$	2.65528	0.0930676
$815$	−0.306315	−0.0107298
$816$	−0.929411	−0.0325359
$817$	−38.7126	−1.35438
$818$	34.4228	1.20357
$819$	2.23056	0.0779422
$820$	−12.6863	−0.443025
$821$	2.22397	0.0776172	0.0388086	−	0.999247i	$-0.487644\pi$
$821$	2.22397	0.0776172	0.0388086	+	0.999247i	$0.487644\pi$
$822$	19.5362	0.681403
$823$	1.45941	0.0508719	0.0254359	−	0.999676i	$-0.491903\pi$
$823$	1.45941	0.0508719	0.0254359	+	0.999676i	$0.491903\pi$
$824$	−34.2710	−1.19389
$825$	0.360648	0.0125562
$826$	−15.8559	−0.551697
$827$	38.3271	1.33276	0.666381	−	0.745611i	$-0.267842\pi$
$827$	38.3271	1.33276	0.666381	+	0.745611i	$0.267842\pi$
$828$	5.14772	0.178896
$829$	11.5441	0.400942	0.200471	−	0.979700i	$-0.435753\pi$
$829$	11.5441	0.400942	0.200471	+	0.979700i	$0.435753\pi$
$830$	7.26459	0.252157
$831$	−0.0214896	−0.000745466 0
$832$	−20.8736	−0.723663
$833$	−2.28481	−0.0791639
$834$	2.03287	0.0703926
$835$	−16.3106	−0.564451
$836$	−3.25387	−0.112537
$837$	−30.8147	−1.06511
$838$	−7.79553	−0.269292
$839$	−17.9856	−0.620932	−0.310466	−	0.950584i	$-0.600485\pi$
$839$	−17.9856	−0.620932	−0.310466	+	0.950584i	$0.600485\pi$
$840$	−3.35155	−0.115639
$841$	−25.3917	−0.875574
$842$	30.0304	1.03492
$843$	−12.7384	−0.438734
$844$	−10.9670	−0.377500
$845$	−10.4320	−0.358872
$846$	23.7689	0.817193
$847$	10.9191	0.375185
$848$	−3.18945	−0.109526
$849$	15.0406	0.516194
$850$	5.19167	0.178073
$851$	−4.80395	−0.164677
$852$	−50.6696	−1.73591
$853$	−52.8445	−1.80936	−0.904681	−	0.426090i	$-0.859891\pi$
$853$	−52.8445	−1.80936	−0.904681	+	0.426090i	$0.859891\pi$
$854$	0.571075	0.0195418
$855$	−5.03463	−0.172181
$856$	−36.4031	−1.24423
$857$	−17.4719	−0.596829	−0.298414	−	0.954436i	$-0.596458\pi$
$857$	−17.4719	−0.596829	−0.298414	+	0.954436i	$0.596458\pi$
$858$	−1.31322	−0.0448326
$859$	11.3965	0.388844	0.194422	−	0.980918i	$-0.437717\pi$
$859$	11.3965	0.388844	0.194422	+	0.980918i	$0.437717\pi$
$860$	−33.8550	−1.15445
$861$	−5.08589	−0.173327
$862$	63.0492	2.14746
$863$	9.04192	0.307791	0.153895	−	0.988087i	$-0.450818\pi$
$863$	9.04192	0.307791	0.153895	+	0.988087i	$0.450818\pi$
$864$	33.4990	1.13966
$865$	13.0179	0.442624
$866$	−21.7275	−0.738329
$867$	14.9377	0.507312
$868$	17.5013	0.594033
$869$	0.681514	0.0231188
$870$	−5.47348	−0.185568
$871$	5.56864	0.188686
$872$	−4.16135	−0.140921
$873$	14.0977	0.477136
$874$	9.60910	0.325033
$875$	−1.00000	−0.0338062
$876$	−22.9835	−0.776542
$877$	33.6124	1.13501	0.567505	−	0.823370i	$-0.307909\pi$
$877$	33.6124	1.13501	0.567505	+	0.823370i	$0.307909\pi$
$878$	5.55498	0.187471
$879$	13.8815	0.468211
$880$	0.0912301	0.00307537
$881$	1.56392	0.0526898	0.0263449	−	0.999653i	$-0.491613\pi$
$881$	1.56392	0.0526898	0.0263449	+	0.999653i	$0.491613\pi$
$882$	3.16283	0.106498
$883$	−38.2111	−1.28590	−0.642952	−	0.765906i	$-0.722291\pi$
$883$	−38.2111	−1.28590	−0.642952	+	0.765906i	$0.722291\pi$
$884$	−11.5815	−0.389529
$885$	8.84882	0.297450
$886$	−10.4436	−0.350859
$887$	−2.13903	−0.0718215	−0.0359107	−	0.999355i	$-0.511433\pi$
$887$	−2.13903	−0.0718215	−0.0359107	+	0.999355i	$0.511433\pi$
$888$	13.7710	0.462126
$889$	13.6937	0.459273
$890$	23.1867	0.777220
$891$	0.820987	0.0275041
$892$	41.4771	1.38876
$893$	27.1821	0.909613
$894$	4.71247	0.157609
$895$	−21.5363	−0.719880
$896$	−17.5681	−0.586908
$897$	2.37588	0.0793285
$898$	−6.32851	−0.211185
$899$	10.5100	0.350530
$900$	−4.40290	−0.146763
$901$	−22.7174	−0.756827
$902$	−2.59182	−0.0862980
$903$	−13.5724	−0.451660
$904$	11.7851	0.391966
$905$	−19.2141	−0.638699
$906$	16.1177	0.535475
$907$	−26.7791	−0.889186	−0.444593	−	0.895733i	$-0.646652\pi$
$907$	−26.7791	−0.889186	−0.444593	+	0.895733i	$0.646652\pi$
$908$	92.1266	3.05733
$909$	−2.28188	−0.0756851
$910$	3.64128	0.120707
$911$	−25.9349	−0.859260	−0.429630	−	0.903005i	$-0.641356\pi$
$911$	−25.9349	−0.859260	−0.429630	+	0.903005i	$0.641356\pi$
$912$	1.47132	0.0487202
$913$	0.909254	0.0300919
$914$	−30.3774	−1.00479
$915$	−0.318704	−0.0105360
$916$	3.16315	0.104513
$917$	−11.1103	−0.366895
$918$	28.9144	0.954318
$919$	10.1521	0.334888	0.167444	−	0.985882i	$-0.446449\pi$
$919$	10.1521	0.334888	0.167444	+	0.985882i	$0.446449\pi$
$920$	3.09008	0.101877
$921$	−27.8463	−0.917567
$922$	−15.5229	−0.511219
$923$	20.2429	0.666302
$924$	−1.14078	−0.0375291
$925$	4.10886	0.135098
$926$	−38.9012	−1.27837
$927$	−18.0490	−0.592806
$928$	−11.4256	−0.375063
$929$	29.2189	0.958642	0.479321	−	0.877640i	$-0.340883\pi$
$929$	29.2189	0.958642	0.479321	+	0.877640i	$0.340883\pi$
$930$	−15.9426	−0.522779
$931$	3.61700	0.118542
$932$	11.4708	0.375740
$933$	−8.59334	−0.281333
$934$	−38.1611	−1.24867
$935$	0.649802	0.0212508
$936$	5.89533	0.192695
$937$	−41.6925	−1.36204	−0.681018	−	0.732267i	$-0.738462\pi$
$937$	−41.6925	−1.36204	−0.681018	+	0.732267i	$0.738462\pi$
$938$	7.89606	0.257815
$939$	−14.3610	−0.468654
$940$	23.7713	0.775335
$941$	−28.2975	−0.922471	−0.461236	−	0.887278i	$-0.652594\pi$
$941$	−28.2975	−0.922471	−0.461236	+	0.887278i	$0.652594\pi$
$942$	−20.5529	−0.669649
$943$	4.68913	0.152699
$944$	2.23841	0.0728540
$945$	−5.56939	−0.181172
$946$	−6.91660	−0.224878
$947$	−42.6702	−1.38659	−0.693297	−	0.720652i	$-0.743843\pi$
$947$	−42.6702	−1.38659	−0.693297	+	0.720652i	$0.743843\pi$
$948$	9.61202	0.312184
$949$	9.18209	0.298063
$950$	−8.21875	−0.266652
$951$	33.8525	1.09774
$952$	−6.03869	−0.195715
$953$	−27.9085	−0.904044	−0.452022	−	0.892007i	$-0.649297\pi$
$953$	−27.9085	−0.904044	−0.452022	+	0.892007i	$0.649297\pi$
$954$	31.4475	1.01815
$955$	−22.6531	−0.733038
$956$	49.3616	1.59647
$957$	−0.685075	−0.0221453
$958$	−18.4836	−0.597177
$959$	−6.78001	−0.218938
$960$	16.5179	0.533111
$961$	−0.387337	−0.0124947
$962$	−14.9615	−0.482378
$963$	−19.1718	−0.617803
$964$	13.3941	0.431396
$965$	25.1483	0.809551
$966$	3.36889	0.108392
$967$	0.334954	0.0107714	0.00538570	−	0.999985i	$-0.498286\pi$
$967$	0.334954	0.0107714	0.00538570	+	0.999985i	$0.498286\pi$
$968$	28.8590	0.927562
$969$	10.4797	0.336657
$970$	23.0138	0.738929
$971$	−41.5800	−1.33437	−0.667184	−	0.744893i	$-0.732500\pi$
$971$	−41.5800	−1.33437	−0.667184	+	0.744893i	$0.732500\pi$
$972$	−41.2713	−1.32378
$973$	−0.705506	−0.0226175
$974$	31.5169	1.00987
$975$	−2.03212	−0.0650798
$976$	−0.0806199	−0.00258058
$977$	1.34487	0.0430263	0.0215131	−	0.999769i	$-0.493152\pi$
$977$	1.34487	0.0430263	0.0215131	+	0.999769i	$0.493152\pi$
$978$	−0.882628	−0.0282233
$979$	2.90211	0.0927517
$980$	3.16315	0.101043
$981$	−2.19159	−0.0699721
$982$	52.9802	1.69067
$983$	−23.8674	−0.761253	−0.380627	−	0.924729i	$-0.624292\pi$
$983$	−23.8674	−0.761253	−0.380627	+	0.924729i	$0.624292\pi$
$984$	−13.4419	−0.428512
$985$	−25.1237	−0.800507
$986$	−9.86191	−0.314067
$987$	9.52984	0.303338
$988$	18.3343	0.583292
$989$	12.5135	0.397908
$990$	−0.899514	−0.0285884
$991$	58.8812	1.87042	0.935211	−	0.354091i	$-0.115210\pi$
$991$	58.8812	1.87042	0.935211	+	0.354091i	$0.115210\pi$
$992$	−33.2794	−1.05662
$993$	12.0322	0.381831
$994$	28.7034	0.910416
$995$	13.4232	0.425543
$996$	12.8241	0.406346
$997$	−50.8587	−1.61071	−0.805356	−	0.592792i	$-0.798026\pi$
$997$	−50.8587	−1.61071	−0.805356	+	0.592792i	$0.798026\pi$
$998$	−2.25772	−0.0714667
$999$	22.8838	0.724013

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.i.1.4	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.i.1.4	✓	44	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)

\(f(q)\)	\(=\)	\(q-2.27226 q^{2} -1.26810 q^{3} +3.16315 q^{4} +1.00000 q^{5} +2.88144 q^{6} -1.00000 q^{7} -2.64298 q^{8} -1.39193 q^{9} +O(q^{10})\)	\(q-2.27226 q^{2} -1.26810 q^{3} +3.16315 q^{4} +1.00000 q^{5} +2.88144 q^{6} -1.00000 q^{7} -2.64298 q^{8} -1.39193 q^{9} -2.27226 q^{10} -0.284402 q^{11} -4.01118 q^{12} +1.60249 q^{13} +2.27226 q^{14} -1.26810 q^{15} -0.320779 q^{16} -2.28481 q^{17} +3.16283 q^{18} +3.61700 q^{19} +3.16315 q^{20} +1.26810 q^{21} +0.646233 q^{22} -1.16917 q^{23} +3.35155 q^{24} +1.00000 q^{25} -3.64128 q^{26} +5.56939 q^{27} -3.16315 q^{28} -1.89956 q^{29} +2.88144 q^{30} -5.53287 q^{31} +6.01485 q^{32} +0.360648 q^{33} +5.19167 q^{34} -1.00000 q^{35} -4.40290 q^{36} +4.10886 q^{37} -8.21875 q^{38} -2.03212 q^{39} -2.64298 q^{40} -4.01065 q^{41} -2.88144 q^{42} -10.7029 q^{43} -0.899605 q^{44} -1.39193 q^{45} +2.65665 q^{46} +7.51508 q^{47} +0.406779 q^{48} +1.00000 q^{49} -2.27226 q^{50} +2.89735 q^{51} +5.06893 q^{52} +9.94282 q^{53} -12.6551 q^{54} -0.284402 q^{55} +2.64298 q^{56} -4.58670 q^{57} +4.31630 q^{58} -6.97804 q^{59} -4.01118 q^{60} +0.251325 q^{61} +12.5721 q^{62} +1.39193 q^{63} -13.0257 q^{64} +1.60249 q^{65} -0.819486 q^{66} +3.47498 q^{67} -7.22719 q^{68} +1.48262 q^{69} +2.27226 q^{70} +12.6321 q^{71} +3.67885 q^{72} +5.72987 q^{73} -9.33638 q^{74} -1.26810 q^{75} +11.4411 q^{76} +0.284402 q^{77} +4.61749 q^{78} -2.39631 q^{79} -0.320779 q^{80} -2.88672 q^{81} +9.11323 q^{82} -3.19708 q^{83} +4.01118 q^{84} -2.28481 q^{85} +24.3198 q^{86} +2.40883 q^{87} +0.751667 q^{88} -10.2043 q^{89} +3.16283 q^{90} -1.60249 q^{91} -3.69825 q^{92} +7.01621 q^{93} -17.0762 q^{94} +3.61700 q^{95} -7.62740 q^{96} -10.1282 q^{97} -2.27226 q^{98} +0.395868 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * q^99

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