LMFDB - Embedded newform 4015.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.63381 q^{2} -0.811587 q^{3} +4.93698 q^{4} +1.00000 q^{5} +2.13757 q^{6} +5.26915 q^{7} -7.73545 q^{8} -2.34133 q^{9} +O(q^{10})$	\(q-2.63381 q^{2} -0.811587 q^{3} +4.93698 q^{4} +1.00000 q^{5} +2.13757 q^{6} +5.26915 q^{7} -7.73545 q^{8} -2.34133 q^{9} -2.63381 q^{10} -1.00000 q^{11} -4.00678 q^{12} -3.11310 q^{13} -13.8780 q^{14} -0.811587 q^{15} +10.4998 q^{16} -1.87424 q^{17} +6.16662 q^{18} +0.651497 q^{19} +4.93698 q^{20} -4.27637 q^{21} +2.63381 q^{22} -2.26947 q^{23} +6.27799 q^{24} +1.00000 q^{25} +8.19931 q^{26} +4.33495 q^{27} +26.0137 q^{28} +1.91201 q^{29} +2.13757 q^{30} -3.24357 q^{31} -12.1836 q^{32} +0.811587 q^{33} +4.93640 q^{34} +5.26915 q^{35} -11.5591 q^{36} -2.93166 q^{37} -1.71592 q^{38} +2.52655 q^{39} -7.73545 q^{40} -8.89847 q^{41} +11.2632 q^{42} +5.24553 q^{43} -4.93698 q^{44} -2.34133 q^{45} +5.97736 q^{46} +6.50487 q^{47} -8.52148 q^{48} +20.7639 q^{49} -2.63381 q^{50} +1.52111 q^{51} -15.3693 q^{52} +9.03875 q^{53} -11.4175 q^{54} -1.00000 q^{55} -40.7592 q^{56} -0.528746 q^{57} -5.03588 q^{58} -6.80484 q^{59} -4.00678 q^{60} -2.23783 q^{61} +8.54296 q^{62} -12.3368 q^{63} +11.0897 q^{64} -3.11310 q^{65} -2.13757 q^{66} -6.16787 q^{67} -9.25308 q^{68} +1.84187 q^{69} -13.8780 q^{70} -13.9621 q^{71} +18.1112 q^{72} +1.00000 q^{73} +7.72144 q^{74} -0.811587 q^{75} +3.21642 q^{76} -5.26915 q^{77} -6.65446 q^{78} -3.39405 q^{79} +10.4998 q^{80} +3.50579 q^{81} +23.4369 q^{82} -10.9131 q^{83} -21.1123 q^{84} -1.87424 q^{85} -13.8157 q^{86} -1.55176 q^{87} +7.73545 q^{88} -12.1573 q^{89} +6.16662 q^{90} -16.4034 q^{91} -11.2043 q^{92} +2.63244 q^{93} -17.1326 q^{94} +0.651497 q^{95} +9.88803 q^{96} +3.31301 q^{97} -54.6883 q^{98} +2.34133 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9	\( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9} - 3 q^{10} - 23 q^{11} - 18 q^{12} - 5 q^{13} - 17 q^{14} - 5 q^{15} - q^{16} - 36 q^{17} + q^{18} + 6 q^{19} + 15 q^{20} - 18 q^{21} + 3 q^{22} - 14 q^{23} - 7 q^{24} + 23 q^{25} - 21 q^{26} - 29 q^{27} + 28 q^{28} - 36 q^{29} - 5 q^{30} - 16 q^{31} - 5 q^{32} + 5 q^{33} - 28 q^{34} - 14 q^{36} - 24 q^{37} + q^{38} - 10 q^{39} - 6 q^{40} - 36 q^{41} - 5 q^{42} + 17 q^{43} - 15 q^{44} + 8 q^{45} - 25 q^{46} - 21 q^{47} - 17 q^{48} - 27 q^{49} - 3 q^{50} + 19 q^{51} - 21 q^{52} - 28 q^{53} - 15 q^{54} - 23 q^{55} - 46 q^{56} - 23 q^{57} - 16 q^{58} - 61 q^{59} - 18 q^{60} - 17 q^{61} - 22 q^{62} - 9 q^{63} - 18 q^{64} - 5 q^{65} + 5 q^{66} + 2 q^{67} - 39 q^{68} - 36 q^{69} - 17 q^{70} - 50 q^{71} + 15 q^{72} + 23 q^{73} + 17 q^{74} - 5 q^{75} - 21 q^{76} + 49 q^{78} - 18 q^{79} - q^{80} - 57 q^{81} + 14 q^{82} - 20 q^{83} - 38 q^{84} - 36 q^{85} - 45 q^{86} + 37 q^{87} + 6 q^{88} - 93 q^{89} + q^{90} - 42 q^{91} - 39 q^{92} - 18 q^{93} - 6 q^{94} + 6 q^{95} - 9 q^{96} - 31 q^{97} - 31 q^{98} - 8 q^{99}+O(q^{100}) \) 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9 - 3 * q^10 - 23 * q^11 - 18 * q^12 - 5 * q^13 - 17 * q^14 - 5 * q^15 - q^16 - 36 * q^17 + q^18 + 6 * q^19 + 15 * q^20 - 18 * q^21 + 3 * q^22 - 14 * q^23 - 7 * q^24 + 23 * q^25 - 21 * q^26 - 29 * q^27 + 28 * q^28 - 36 * q^29 - 5 * q^30 - 16 * q^31 - 5 * q^32 + 5 * q^33 - 28 * q^34 - 14 * q^36 - 24 * q^37 + q^38 - 10 * q^39 - 6 * q^40 - 36 * q^41 - 5 * q^42 + 17 * q^43 - 15 * q^44 + 8 * q^45 - 25 * q^46 - 21 * q^47 - 17 * q^48 - 27 * q^49 - 3 * q^50 + 19 * q^51 - 21 * q^52 - 28 * q^53 - 15 * q^54 - 23 * q^55 - 46 * q^56 - 23 * q^57 - 16 * q^58 - 61 * q^59 - 18 * q^60 - 17 * q^61 - 22 * q^62 - 9 * q^63 - 18 * q^64 - 5 * q^65 + 5 * q^66 + 2 * q^67 - 39 * q^68 - 36 * q^69 - 17 * q^70 - 50 * q^71 + 15 * q^72 + 23 * q^73 + 17 * q^74 - 5 * q^75 - 21 * q^76 + 49 * q^78 - 18 * q^79 - q^80 - 57 * q^81 + 14 * q^82 - 20 * q^83 - 38 * q^84 - 36 * q^85 - 45 * q^86 + 37 * q^87 + 6 * q^88 - 93 * q^89 + q^90 - 42 * q^91 - 39 * q^92 - 18 * q^93 - 6 * q^94 + 6 * q^95 - 9 * q^96 - 31 * q^97 - 31 * q^98 - 8 * 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 $

$2$	−2.63381	−1.86239	−0.931194	−	0.364524i	$-0.881232\pi$
$2$	−2.63381	−1.86239	−0.931194	+	0.364524i	$0.881232\pi$
$3$	−0.811587	−0.468570	−0.234285	−	0.972168i	$-0.575275\pi$
$3$	−0.811587	−0.468570	−0.234285	+	0.972168i	$0.575275\pi$
$4$	4.93698	2.46849
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.13757	0.872659
$7$	5.26915	1.99155	0.995775	−	0.0918214i	$-0.0292689\pi$
$7$	5.26915	1.99155	0.995775	+	0.0918214i	$0.0292689\pi$
$8$	−7.73545	−2.73489
$9$	−2.34133	−0.780442
$10$	−2.63381	−0.832885
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−4.00678	−1.15666
$13$	−3.11310	−0.863417	−0.431709	−	0.902013i	$-0.642089\pi$
$13$	−3.11310	−0.863417	−0.431709	+	0.902013i	$0.642089\pi$
$14$	−13.8780	−3.70904
$15$	−0.811587	−0.209551
$16$	10.4998	2.62495
$17$	−1.87424	−0.454570	−0.227285	−	0.973828i	$-0.572985\pi$
$17$	−1.87424	−0.454570	−0.227285	+	0.973828i	$0.572985\pi$
$18$	6.16662	1.45349
$19$	0.651497	0.149464	0.0747318	−	0.997204i	$-0.476190\pi$
$19$	0.651497	0.149464	0.0747318	+	0.997204i	$0.476190\pi$
$20$	4.93698	1.10394
$21$	−4.27637	−0.933181
$22$	2.63381	0.561531
$23$	−2.26947	−0.473217	−0.236609	−	0.971605i	$-0.576036\pi$
$23$	−2.26947	−0.473217	−0.236609	+	0.971605i	$0.576036\pi$
$24$	6.27799	1.28149
$25$	1.00000	0.200000
$26$	8.19931	1.60802
$27$	4.33495	0.834262
$28$	26.0137	4.91612
$29$	1.91201	0.355051	0.177526	−	0.984116i	$-0.443191\pi$
$29$	1.91201	0.355051	0.177526	+	0.984116i	$0.443191\pi$
$30$	2.13757	0.390265
$31$	−3.24357	−0.582563	−0.291281	−	0.956637i	$-0.594082\pi$
$31$	−3.24357	−0.582563	−0.291281	+	0.956637i	$0.594082\pi$
$32$	−12.1836	−2.15377
$33$	0.811587	0.141279
$34$	4.93640	0.846585
$35$	5.26915	0.890649
$36$	−11.5591	−1.92651
$37$	−2.93166	−0.481961	−0.240981	−	0.970530i	$-0.577469\pi$
$37$	−2.93166	−0.481961	−0.240981	+	0.970530i	$0.577469\pi$
$38$	−1.71592	−0.278359
$39$	2.52655	0.404571
$40$	−7.73545	−1.22308
$41$	−8.89847	−1.38971	−0.694854	−	0.719151i	$-0.744531\pi$
$41$	−8.89847	−1.38971	−0.694854	+	0.719151i	$0.744531\pi$
$42$	11.2632	1.73794
$43$	5.24553	0.799936	0.399968	−	0.916529i	$-0.369021\pi$
$43$	5.24553	0.799936	0.399968	+	0.916529i	$0.369021\pi$
$44$	−4.93698	−0.744277
$45$	−2.34133	−0.349024
$46$	5.97736	0.881314
$47$	6.50487	0.948833	0.474417	−	0.880300i	$-0.342659\pi$
$47$	6.50487	0.948833	0.474417	+	0.880300i	$0.342659\pi$
$48$	−8.52148	−1.22997
$49$	20.7639	2.96628
$50$	−2.63381	−0.372478
$51$	1.52111	0.212998
$52$	−15.3693	−2.13134
$53$	9.03875	1.24157	0.620784	−	0.783982i	$-0.286814\pi$
$53$	9.03875	1.24157	0.620784	+	0.783982i	$0.286814\pi$
$54$	−11.4175	−1.55372
$55$	−1.00000	−0.134840
$56$	−40.7592	−5.44668
$57$	−0.528746	−0.0700341
$58$	−5.03588	−0.661243
$59$	−6.80484	−0.885915	−0.442957	−	0.896543i	$-0.646071\pi$
$59$	−6.80484	−0.885915	−0.442957	+	0.896543i	$0.646071\pi$
$60$	−4.00678	−0.517274
$61$	−2.23783	−0.286525	−0.143262	−	0.989685i	$-0.545759\pi$
$61$	−2.23783	−0.286525	−0.143262	+	0.989685i	$0.545759\pi$
$62$	8.54296	1.08496
$63$	−12.3368	−1.55429
$64$	11.0897	1.38621
$65$	−3.11310	−0.386132
$66$	−2.13757	−0.263116
$67$	−6.16787	−0.753526	−0.376763	−	0.926310i	$-0.622963\pi$
$67$	−6.16787	−0.753526	−0.376763	+	0.926310i	$0.622963\pi$
$68$	−9.25308	−1.12210
$69$	1.84187	0.221735
$70$	−13.8780	−1.65873
$71$	−13.9621	−1.65700	−0.828498	−	0.559993i	$-0.810804\pi$
$71$	−13.9621	−1.65700	−0.828498	+	0.559993i	$0.810804\pi$
$72$	18.1112	2.13443
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	7.72144	0.897599
$75$	−0.811587	−0.0937140
$76$	3.21642	0.368949
$77$	−5.26915	−0.600475
$78$	−6.65446	−0.753469
$79$	−3.39405	−0.381861	−0.190930	−	0.981604i	$-0.561150\pi$
$79$	−3.39405	−0.381861	−0.190930	+	0.981604i	$0.561150\pi$
$80$	10.4998	1.17391
$81$	3.50579	0.389533
$82$	23.4369	2.58817
$83$	−10.9131	−1.19787	−0.598933	−	0.800799i	$-0.704408\pi$
$83$	−10.9131	−1.19787	−0.598933	+	0.800799i	$0.704408\pi$
$84$	−21.1123	−2.30355
$85$	−1.87424	−0.203290
$86$	−13.8157	−1.48979
$87$	−1.55176	−0.166366
$88$	7.73545	0.824602
$89$	−12.1573	−1.28867	−0.644336	−	0.764742i	$-0.722866\pi$
$89$	−12.1573	−1.28867	−0.644336	+	0.764742i	$0.722866\pi$
$90$	6.16662	0.650019
$91$	−16.4034	−1.71954
$92$	−11.2043	−1.16813
$93$	2.63244	0.272971
$94$	−17.1326	−1.76710
$95$	0.651497	0.0668421
$96$	9.88803	1.00919
$97$	3.31301	0.336385	0.168192	−	0.985754i	$-0.446207\pi$
$97$	3.31301	0.336385	0.168192	+	0.985754i	$0.446207\pi$
$98$	−54.6883	−5.52435
$99$	2.34133	0.235312
$100$	4.93698	0.493698
$101$	−7.86534	−0.782630	−0.391315	−	0.920257i	$-0.627980\pi$
$101$	−7.86534	−0.782630	−0.391315	+	0.920257i	$0.627980\pi$
$102$	−4.00632	−0.396684
$103$	−12.0665	−1.18895	−0.594474	−	0.804115i	$-0.702640\pi$
$103$	−12.0665	−1.18895	−0.594474	+	0.804115i	$0.702640\pi$
$104$	24.0812	2.36136
$105$	−4.27637	−0.417331
$106$	−23.8064	−2.31228
$107$	1.71066	0.165376	0.0826878	−	0.996576i	$-0.473650\pi$
$107$	1.71066	0.165376	0.0826878	+	0.996576i	$0.473650\pi$
$108$	21.4015	2.05936
$109$	−6.43677	−0.616531	−0.308265	−	0.951300i	$-0.599748\pi$
$109$	−6.43677	−0.616531	−0.308265	+	0.951300i	$0.599748\pi$
$110$	2.63381	0.251124
$111$	2.37929	0.225833
$112$	55.3249	5.22771
$113$	4.13924	0.389387	0.194694	−	0.980864i	$-0.437629\pi$
$113$	4.13924	0.389387	0.194694	+	0.980864i	$0.437629\pi$
$114$	1.39262	0.130431
$115$	−2.26947	−0.211629
$116$	9.43954	0.876439
$117$	7.28877	0.673847
$118$	17.9227	1.64992
$119$	−9.87565	−0.905299
$120$	6.27799	0.573099
$121$	1.00000	0.0909091
$122$	5.89403	0.533620
$123$	7.22188	0.651175
$124$	−16.0134	−1.43805
$125$	1.00000	0.0894427
$126$	32.4928	2.89469
$127$	20.6168	1.82944	0.914722	−	0.404084i	$-0.132410\pi$
$127$	20.6168	1.82944	0.914722	+	0.404084i	$0.132410\pi$
$128$	−4.84107	−0.427894
$129$	−4.25720	−0.374826
$130$	8.19931	0.719127
$131$	−6.61863	−0.578273	−0.289136	−	0.957288i	$-0.593368\pi$
$131$	−6.61863	−0.578273	−0.289136	+	0.957288i	$0.593368\pi$
$132$	4.00678	0.348746
$133$	3.43283	0.297664
$134$	16.2450	1.40336
$135$	4.33495	0.373093
$136$	14.4981	1.24320
$137$	−6.26260	−0.535050	−0.267525	−	0.963551i	$-0.586206\pi$
$137$	−6.26260	−0.535050	−0.267525	+	0.963551i	$0.586206\pi$
$138$	−4.85115	−0.412957
$139$	13.5759	1.15149	0.575745	−	0.817629i	$-0.304712\pi$
$139$	13.5759	1.15149	0.575745	+	0.817629i	$0.304712\pi$
$140$	26.0137	2.19856
$141$	−5.27927	−0.444595
$142$	36.7735	3.08597
$143$	3.11310	0.260330
$144$	−24.5834	−2.04862
$145$	1.91201	0.158784
$146$	−2.63381	−0.217976
$147$	−16.8517	−1.38991
$148$	−14.4735	−1.18972
$149$	6.49350	0.531968	0.265984	−	0.963977i	$-0.414303\pi$
$149$	6.49350	0.531968	0.265984	+	0.963977i	$0.414303\pi$
$150$	2.13757	0.174532
$151$	−4.20036	−0.341820	−0.170910	−	0.985287i	$-0.554671\pi$
$151$	−4.20036	−0.341820	−0.170910	+	0.985287i	$0.554671\pi$
$152$	−5.03962	−0.408767
$153$	4.38821	0.354766
$154$	13.8780	1.11832
$155$	−3.24357	−0.260530
$156$	12.4735	0.998679
$157$	22.5181	1.79714	0.898571	−	0.438827i	$-0.144606\pi$
$157$	22.5181	1.79714	0.898571	+	0.438827i	$0.144606\pi$
$158$	8.93930	0.711173
$159$	−7.33573	−0.581761
$160$	−12.1836	−0.963196
$161$	−11.9582	−0.942436
$162$	−9.23361	−0.725461
$163$	−17.6534	−1.38272	−0.691361	−	0.722510i	$-0.742989\pi$
$163$	−17.6534	−1.38272	−0.691361	+	0.722510i	$0.742989\pi$
$164$	−43.9315	−3.43048
$165$	0.811587	0.0631819
$166$	28.7430	2.23089
$167$	−10.5553	−0.816793	−0.408396	−	0.912805i	$-0.633912\pi$
$167$	−10.5553	−0.816793	−0.408396	+	0.912805i	$0.633912\pi$
$168$	33.0797	2.55215
$169$	−3.30864	−0.254510
$170$	4.93640	0.378604
$171$	−1.52537	−0.116648
$172$	25.8970	1.97463
$173$	5.75014	0.437175	0.218587	−	0.975817i	$-0.429855\pi$
$173$	5.75014	0.437175	0.218587	+	0.975817i	$0.429855\pi$
$174$	4.08705	0.309838
$175$	5.26915	0.398310
$176$	−10.4998	−0.791451
$177$	5.52272	0.415113
$178$	32.0201	2.40001
$179$	−7.19275	−0.537611	−0.268806	−	0.963194i	$-0.586629\pi$
$179$	−7.19275	−0.537611	−0.268806	+	0.963194i	$0.586629\pi$
$180$	−11.5591	−0.861563
$181$	−8.09278	−0.601531	−0.300766	−	0.953698i	$-0.597242\pi$
$181$	−8.09278	−0.601531	−0.300766	+	0.953698i	$0.597242\pi$
$182$	43.2034	3.20245
$183$	1.81619	0.134257
$184$	17.5554	1.29420
$185$	−2.93166	−0.215540
$186$	−6.93336	−0.508378
$187$	1.87424	0.137058
$188$	32.1144	2.34218
$189$	22.8415	1.66147
$190$	−1.71592	−0.124486
$191$	−11.6535	−0.843214	−0.421607	−	0.906779i	$-0.638534\pi$
$191$	−11.6535	−0.843214	−0.421607	+	0.906779i	$0.638534\pi$
$192$	−9.00026	−0.649538
$193$	16.6613	1.19931	0.599653	−	0.800260i	$-0.295305\pi$
$193$	16.6613	1.19931	0.599653	+	0.800260i	$0.295305\pi$
$194$	−8.72584	−0.626479
$195$	2.52655	0.180930
$196$	102.511	7.32222
$197$	−19.0189	−1.35504	−0.677519	−	0.735505i	$-0.736945\pi$
$197$	−19.0189	−1.35504	−0.677519	+	0.735505i	$0.736945\pi$
$198$	−6.16662	−0.438243
$199$	−17.5591	−1.24473	−0.622366	−	0.782726i	$-0.713828\pi$
$199$	−17.5591	−1.24473	−0.622366	+	0.782726i	$0.713828\pi$
$200$	−7.73545	−0.546979
$201$	5.00576	0.353079
$202$	20.7158	1.45756
$203$	10.0747	0.707102
$204$	7.50967	0.525782
$205$	−8.89847	−0.621496
$206$	31.7809	2.21428
$207$	5.31357	0.369319
$208$	−32.6868	−2.26642
$209$	−0.651497	−0.0450650
$210$	11.2632	0.777232
$211$	−2.01582	−0.138774	−0.0693872	−	0.997590i	$-0.522104\pi$
$211$	−2.01582	−0.138774	−0.0693872	+	0.997590i	$0.522104\pi$
$212$	44.6241	3.06480
$213$	11.3314	0.776418
$214$	−4.50556	−0.307993
$215$	5.24553	0.357742
$216$	−33.5328	−2.28162
$217$	−17.0909	−1.16020
$218$	16.9533	1.14822
$219$	−0.811587	−0.0548419
$220$	−4.93698	−0.332851
$221$	5.83469	0.392484
$222$	−6.26662	−0.420588
$223$	−13.8494	−0.927425	−0.463712	−	0.885986i	$-0.653483\pi$
$223$	−13.8494	−0.927425	−0.463712	+	0.885986i	$0.653483\pi$
$224$	−64.1971	−4.28935
$225$	−2.34133	−0.156088
$226$	−10.9020	−0.725190
$227$	−15.8422	−1.05149	−0.525743	−	0.850644i	$-0.676213\pi$
$227$	−15.8422	−1.05149	−0.525743	+	0.850644i	$0.676213\pi$
$228$	−2.61041	−0.172878
$229$	−2.03181	−0.134266	−0.0671330	−	0.997744i	$-0.521385\pi$
$229$	−2.03181	−0.134266	−0.0671330	+	0.997744i	$0.521385\pi$
$230$	5.97736	0.394135
$231$	4.27637	0.281365
$232$	−14.7902	−0.971027
$233$	16.1844	1.06027	0.530137	−	0.847912i	$-0.322141\pi$
$233$	16.1844	1.06027	0.530137	+	0.847912i	$0.322141\pi$
$234$	−19.1973	−1.25497
$235$	6.50487	0.424331
$236$	−33.5953	−2.18687
$237$	2.75457	0.178928
$238$	26.0106	1.68602
$239$	21.5726	1.39541	0.697706	−	0.716384i	$-0.254204\pi$
$239$	21.5726	1.39541	0.697706	+	0.716384i	$0.254204\pi$
$240$	−8.52148	−0.550059
$241$	−3.77341	−0.243067	−0.121533	−	0.992587i	$-0.538781\pi$
$241$	−3.77341	−0.243067	−0.121533	+	0.992587i	$0.538781\pi$
$242$	−2.63381	−0.169308
$243$	−15.8501	−1.01678
$244$	−11.0481	−0.707283
$245$	20.7639	1.32656
$246$	−19.0211	−1.21274
$247$	−2.02817	−0.129049
$248$	25.0905	1.59325
$249$	8.85691	0.561284
$250$	−2.63381	−0.166577
$251$	−0.627958	−0.0396363	−0.0198182	−	0.999804i	$-0.506309\pi$
$251$	−0.627958	−0.0396363	−0.0198182	+	0.999804i	$0.506309\pi$
$252$	−60.9065	−3.83675
$253$	2.26947	0.142680
$254$	−54.3008	−3.40713
$255$	1.52111	0.0952555
$256$	−9.42893	−0.589308
$257$	−14.1332	−0.881606	−0.440803	−	0.897604i	$-0.645306\pi$
$257$	−14.1332	−0.881606	−0.440803	+	0.897604i	$0.645306\pi$
$258$	11.2127	0.698071
$259$	−15.4473	−0.959851
$260$	−15.3693	−0.953162
$261$	−4.47664	−0.277097
$262$	17.4323	1.07697
$263$	16.2078	0.999416	0.499708	−	0.866194i	$-0.333441\pi$
$263$	16.2078	0.999416	0.499708	+	0.866194i	$0.333441\pi$
$264$	−6.27799	−0.386383
$265$	9.03875	0.555246
$266$	−9.04144	−0.554366
$267$	9.86672	0.603833
$268$	−30.4506	−1.86007
$269$	2.85005	0.173771	0.0868855	−	0.996218i	$-0.472309\pi$
$269$	2.85005	0.173771	0.0868855	+	0.996218i	$0.472309\pi$
$270$	−11.4175	−0.694844
$271$	6.69254	0.406543	0.203271	−	0.979122i	$-0.434843\pi$
$271$	6.69254	0.406543	0.203271	+	0.979122i	$0.434843\pi$
$272$	−19.6791	−1.19322
$273$	13.3128	0.805724
$274$	16.4945	0.996471
$275$	−1.00000	−0.0603023
$276$	9.09327	0.547351
$277$	−2.17681	−0.130792	−0.0653958	−	0.997859i	$-0.520831\pi$
$277$	−2.17681	−0.130792	−0.0653958	+	0.997859i	$0.520831\pi$
$278$	−35.7563	−2.14452
$279$	7.59426	0.454657
$280$	−40.7592	−2.43583
$281$	−10.6795	−0.637084	−0.318542	−	0.947909i	$-0.603193\pi$
$281$	−10.6795	−0.637084	−0.318542	+	0.947909i	$0.603193\pi$
$282$	13.9046	0.828008
$283$	−23.6940	−1.40846	−0.704230	−	0.709972i	$-0.748708\pi$
$283$	−23.6940	−1.40846	−0.704230	+	0.709972i	$0.748708\pi$
$284$	−68.9305	−4.09027
$285$	−0.528746	−0.0313202
$286$	−8.19931	−0.484836
$287$	−46.8873	−2.76767
$288$	28.5257	1.68089
$289$	−13.4872	−0.793366
$290$	−5.03588	−0.295717
$291$	−2.68879	−0.157620
$292$	4.93698	0.288915
$293$	25.9107	1.51372	0.756860	−	0.653577i	$-0.226733\pi$
$293$	25.9107	1.51372	0.756860	+	0.653577i	$0.226733\pi$
$294$	44.3843	2.58855
$295$	−6.80484	−0.396193
$296$	22.6777	1.31811
$297$	−4.33495	−0.251539
$298$	−17.1027	−0.990731
$299$	7.06507	0.408584
$300$	−4.00678	−0.231332
$301$	27.6395	1.59311
$302$	11.0630	0.636602
$303$	6.38340	0.366717
$304$	6.84057	0.392334
$305$	−2.23783	−0.128138
$306$	−11.5577	−0.660711
$307$	20.8127	1.18784	0.593922	−	0.804522i	$-0.297579\pi$
$307$	20.8127	1.18784	0.593922	+	0.804522i	$0.297579\pi$
$308$	−26.0137	−1.48227
$309$	9.79301	0.557105
$310$	8.54296	0.485208
$311$	24.3736	1.38210	0.691049	−	0.722807i	$-0.257149\pi$
$311$	24.3736	1.38210	0.691049	+	0.722807i	$0.257149\pi$
$312$	−19.5440	−1.10646
$313$	16.5107	0.933239	0.466620	−	0.884458i	$-0.345472\pi$
$313$	16.5107	0.933239	0.466620	+	0.884458i	$0.345472\pi$
$314$	−59.3086	−3.34698
$315$	−12.3368	−0.695100
$316$	−16.7564	−0.942619
$317$	−29.8782	−1.67813	−0.839064	−	0.544032i	$-0.816897\pi$
$317$	−29.8782	−1.67813	−0.839064	+	0.544032i	$0.816897\pi$
$318$	19.3209	1.08347
$319$	−1.91201	−0.107052
$320$	11.0897	0.619933
$321$	−1.38835	−0.0774900
$322$	31.4956	1.75518
$323$	−1.22106	−0.0679416
$324$	17.3080	0.961556
$325$	−3.11310	−0.172683
$326$	46.4958	2.57516
$327$	5.22400	0.288888
$328$	68.8336	3.80070
$329$	34.2751	1.88965
$330$	−2.13757	−0.117669
$331$	−21.8178	−1.19921	−0.599607	−	0.800295i	$-0.704676\pi$
$331$	−21.8178	−1.19921	−0.599607	+	0.800295i	$0.704676\pi$
$332$	−53.8776	−2.95692
$333$	6.86397	0.376143
$334$	27.8007	1.52119
$335$	−6.16787	−0.336987
$336$	−44.9010	−2.44955
$337$	4.86616	0.265077	0.132538	−	0.991178i	$-0.457687\pi$
$337$	4.86616	0.265077	0.132538	+	0.991178i	$0.457687\pi$
$338$	8.71433	0.473997
$339$	−3.35936	−0.182455
$340$	−9.25308	−0.501818
$341$	3.24357	0.175649
$342$	4.01753	0.217243
$343$	72.5242	3.91594
$344$	−40.5765	−2.18774
$345$	1.84187	0.0991630
$346$	−15.1448	−0.814189
$347$	1.11016	0.0595964	0.0297982	−	0.999556i	$-0.490514\pi$
$347$	1.11016	0.0595964	0.0297982	+	0.999556i	$0.490514\pi$
$348$	−7.66101	−0.410673
$349$	−36.0326	−1.92878	−0.964390	−	0.264485i	$-0.914798\pi$
$349$	−36.0326	−1.92878	−0.964390	+	0.264485i	$0.914798\pi$
$350$	−13.8780	−0.741808
$351$	−13.4951	−0.720316
$352$	12.1836	0.649387
$353$	−33.2482	−1.76962	−0.884811	−	0.465951i	$-0.845712\pi$
$353$	−33.2482	−1.76962	−0.884811	+	0.465951i	$0.845712\pi$
$354$	−14.5458	−0.773101
$355$	−13.9621	−0.741031
$356$	−60.0204	−3.18107
$357$	8.01494	0.424196
$358$	18.9444	1.00124
$359$	27.0779	1.42912	0.714560	−	0.699574i	$-0.246627\pi$
$359$	27.0779	1.42912	0.714560	+	0.699574i	$0.246627\pi$
$360$	18.1112	0.954545
$361$	−18.5756	−0.977661
$362$	21.3149	1.12028
$363$	−0.811587	−0.0425973
$364$	−80.9830	−4.24466
$365$	1.00000	0.0523424
$366$	−4.78351	−0.250038
$367$	−35.7123	−1.86417	−0.932084	−	0.362243i	$-0.882011\pi$
$367$	−35.7123	−1.86417	−0.932084	+	0.362243i	$0.882011\pi$
$368$	−23.8289	−1.24217
$369$	20.8342	1.08459
$370$	7.72144	0.401418
$371$	47.6265	2.47265
$372$	12.9963	0.673826
$373$	17.9459	0.929201	0.464601	−	0.885520i	$-0.346198\pi$
$373$	17.9459	0.929201	0.464601	+	0.885520i	$0.346198\pi$
$374$	−4.93640	−0.255255
$375$	−0.811587	−0.0419102
$376$	−50.3181	−2.59496
$377$	−5.95227	−0.306557
$378$	−60.1603	−3.09431
$379$	17.5909	0.903585	0.451792	−	0.892123i	$-0.350785\pi$
$379$	17.5909	0.903585	0.451792	+	0.892123i	$0.350785\pi$
$380$	3.21642	0.164999
$381$	−16.7323	−0.857222
$382$	30.6930	1.57039
$383$	−5.84939	−0.298890	−0.149445	−	0.988770i	$-0.547749\pi$
$383$	−5.84939	−0.298890	−0.149445	+	0.988770i	$0.547749\pi$
$384$	3.92895	0.200498
$385$	−5.26915	−0.268541
$386$	−43.8827	−2.23357
$387$	−12.2815	−0.624304
$388$	16.3562	0.830362
$389$	2.63153	0.133424	0.0667119	−	0.997772i	$-0.478749\pi$
$389$	2.63153	0.133424	0.0667119	+	0.997772i	$0.478749\pi$
$390$	−6.65446	−0.336961
$391$	4.25353	0.215110
$392$	−160.618	−8.11245
$393$	5.37160	0.270961
$394$	50.0921	2.52361
$395$	−3.39405	−0.170773
$396$	11.5591	0.580865
$397$	−15.9403	−0.800020	−0.400010	−	0.916511i	$-0.630993\pi$
$397$	−15.9403	−0.800020	−0.400010	+	0.916511i	$0.630993\pi$
$398$	46.2474	2.31817
$399$	−2.78604	−0.139477
$400$	10.4998	0.524989
$401$	14.9140	0.744768	0.372384	−	0.928079i	$-0.378540\pi$
$401$	14.9140	0.744768	0.372384	+	0.928079i	$0.378540\pi$
$402$	−13.1843	−0.657571
$403$	10.0975	0.502995
$404$	−38.8310	−1.93191
$405$	3.50579	0.174204
$406$	−26.5348	−1.31690
$407$	2.93166	0.145317
$408$	−11.7665	−0.582526
$409$	−35.5269	−1.75669	−0.878346	−	0.478025i	$-0.841353\pi$
$409$	−35.5269	−1.75669	−0.878346	+	0.478025i	$0.841353\pi$
$410$	23.4369	1.15747
$411$	5.08264	0.250708
$412$	−59.5720	−2.93490
$413$	−35.8557	−1.76434
$414$	−13.9950	−0.687814
$415$	−10.9131	−0.535702
$416$	37.9286	1.85960
$417$	−11.0180	−0.539554
$418$	1.71592	0.0839284
$419$	4.94294	0.241479	0.120739	−	0.992684i	$-0.461474\pi$
$419$	4.94294	0.241479	0.120739	+	0.992684i	$0.461474\pi$
$420$	−21.1123	−1.03018
$421$	20.5559	1.00183	0.500917	−	0.865495i	$-0.332996\pi$
$421$	20.5559	1.00183	0.500917	+	0.865495i	$0.332996\pi$
$422$	5.30928	0.258452
$423$	−15.2300	−0.740510
$424$	−69.9188	−3.39556
$425$	−1.87424	−0.0909140
$426$	−29.8449	−1.44599
$427$	−11.7915	−0.570628
$428$	8.44548	0.408228
$429$	−2.52655	−0.121983
$430$	−13.8157	−0.666254
$431$	−5.67869	−0.273533	−0.136766	−	0.990603i	$-0.543671\pi$
$431$	−5.67869	−0.273533	−0.136766	+	0.990603i	$0.543671\pi$
$432$	45.5160	2.18989
$433$	21.3046	1.02383	0.511916	−	0.859036i	$-0.328936\pi$
$433$	21.3046	1.02383	0.511916	+	0.859036i	$0.328936\pi$
$434$	45.0141	2.16075
$435$	−1.55176	−0.0744012
$436$	−31.7782	−1.52190
$437$	−1.47855	−0.0707287
$438$	2.13757	0.102137
$439$	−25.2643	−1.20580	−0.602899	−	0.797817i	$-0.705988\pi$
$439$	−25.2643	−1.20580	−0.602899	+	0.797817i	$0.705988\pi$
$440$	7.73545	0.368773
$441$	−48.6151	−2.31501
$442$	−15.3675	−0.730956
$443$	−4.95562	−0.235449	−0.117724	−	0.993046i	$-0.537560\pi$
$443$	−4.95562	−0.235449	−0.117724	+	0.993046i	$0.537560\pi$
$444$	11.7465	0.557465
$445$	−12.1573	−0.576312
$446$	36.4767	1.72722
$447$	−5.27004	−0.249264
$448$	58.4333	2.76071
$449$	−32.0273	−1.51146	−0.755731	−	0.654882i	$-0.772718\pi$
$449$	−32.0273	−1.51146	−0.755731	+	0.654882i	$0.772718\pi$
$450$	6.16662	0.290697
$451$	8.89847	0.419012
$452$	20.4354	0.961198
$453$	3.40896	0.160167
$454$	41.7255	1.95827
$455$	−16.4034	−0.769002
$456$	4.09009	0.191536
$457$	−6.88262	−0.321956	−0.160978	−	0.986958i	$-0.551465\pi$
$457$	−6.88262	−0.321956	−0.160978	+	0.986958i	$0.551465\pi$
$458$	5.35142	0.250055
$459$	−8.12473	−0.379230
$460$	−11.2043	−0.522404
$461$	−7.37863	−0.343657	−0.171829	−	0.985127i	$-0.554968\pi$
$461$	−7.37863	−0.343657	−0.171829	+	0.985127i	$0.554968\pi$
$462$	−11.2632	−0.524010
$463$	−25.0596	−1.16462	−0.582308	−	0.812968i	$-0.697850\pi$
$463$	−25.0596	−1.16462	−0.582308	+	0.812968i	$0.697850\pi$
$464$	20.0757	0.931990
$465$	2.63244	0.122076
$466$	−42.6266	−1.97464
$467$	−27.1075	−1.25438	−0.627192	−	0.778864i	$-0.715796\pi$
$467$	−27.1075	−1.25438	−0.627192	+	0.778864i	$0.715796\pi$
$468$	35.9845	1.66338
$469$	−32.4994	−1.50068
$470$	−17.1326	−0.790269
$471$	−18.2754	−0.842087
$472$	52.6385	2.42288
$473$	−5.24553	−0.241190
$474$	−7.25502	−0.333234
$475$	0.651497	0.0298927
$476$	−48.7558	−2.23472
$477$	−21.1627	−0.968972
$478$	−56.8181	−2.59880
$479$	6.58303	0.300786	0.150393	−	0.988626i	$-0.451946\pi$
$479$	6.58303	0.300786	0.150393	+	0.988626i	$0.451946\pi$
$480$	9.88803	0.451325
$481$	9.12653	0.416134
$482$	9.93847	0.452685
$483$	9.70509	0.441597
$484$	4.93698	0.224408
$485$	3.31301	0.150436
$486$	41.7462	1.89365
$487$	37.7653	1.71131	0.855654	−	0.517548i	$-0.173155\pi$
$487$	37.7653	1.71131	0.855654	+	0.517548i	$0.173155\pi$
$488$	17.3106	0.783615
$489$	14.3273	0.647902
$490$	−54.6883	−2.47057
$491$	−14.4020	−0.649955	−0.324978	−	0.945722i	$-0.605357\pi$
$491$	−14.4020	−0.649955	−0.324978	+	0.945722i	$0.605357\pi$
$492$	35.6542	1.60742
$493$	−3.58356	−0.161396
$494$	5.34183	0.240340
$495$	2.34133	0.105235
$496$	−34.0568	−1.52920
$497$	−73.5683	−3.29999
$498$	−23.3275	−1.04533
$499$	35.6769	1.59712	0.798558	−	0.601918i	$-0.205597\pi$
$499$	35.6769	1.59712	0.798558	+	0.601918i	$0.205597\pi$
$500$	4.93698	0.220788
$501$	8.56653	0.382724
$502$	1.65392	0.0738182
$503$	−31.2119	−1.39167	−0.695835	−	0.718202i	$-0.744965\pi$
$503$	−31.2119	−1.39167	−0.695835	+	0.718202i	$0.744965\pi$
$504$	95.4307	4.25082
$505$	−7.86534	−0.350003
$506$	−5.97736	−0.265726
$507$	2.68525	0.119256
$508$	101.785	4.51596
$509$	−2.71242	−0.120226	−0.0601129	−	0.998192i	$-0.519146\pi$
$509$	−2.71242	−0.120226	−0.0601129	+	0.998192i	$0.519146\pi$
$510$	−4.00632	−0.177403
$511$	5.26915	0.233093
$512$	34.5162	1.52541
$513$	2.82420	0.124692
$514$	37.2243	1.64189
$515$	−12.0665	−0.531713
$516$	−21.0177	−0.925253
$517$	−6.50487	−0.286084
$518$	40.6854	1.78761
$519$	−4.66674	−0.204847
$520$	24.0812	1.05603
$521$	−10.8968	−0.477399	−0.238699	−	0.971094i	$-0.576721\pi$
$521$	−10.8968	−0.477399	−0.238699	+	0.971094i	$0.576721\pi$
$522$	11.7906	0.516062
$523$	15.6002	0.682151	0.341075	−	0.940036i	$-0.389209\pi$
$523$	15.6002	0.682151	0.341075	+	0.940036i	$0.389209\pi$
$524$	−32.6760	−1.42746
$525$	−4.27637	−0.186636
$526$	−42.6884	−1.86130
$527$	6.07923	0.264815
$528$	8.52148	0.370850
$529$	−17.8495	−0.776066
$530$	−23.8064	−1.03408
$531$	15.9324	0.691405
$532$	16.9478	0.734781
$533$	27.7018	1.19990
$534$	−25.9871	−1.12457
$535$	1.71066	0.0739582
$536$	47.7113	2.06081
$537$	5.83754	0.251908
$538$	−7.50651	−0.323629
$539$	−20.7639	−0.894366
$540$	21.4015	0.920976
$541$	−14.3193	−0.615635	−0.307818	−	0.951445i	$-0.599599\pi$
$541$	−14.3193	−0.615635	−0.307818	+	0.951445i	$0.599599\pi$
$542$	−17.6269	−0.757140
$543$	6.56799	0.281859
$544$	22.8349	0.979040
$545$	−6.43677	−0.275721
$546$	−35.0633	−1.50057
$547$	−45.0363	−1.92561	−0.962806	−	0.270194i	$-0.912912\pi$
$547$	−45.0363	−1.92561	−0.962806	+	0.270194i	$0.912912\pi$
$548$	−30.9183	−1.32076
$549$	5.23949	0.223616
$550$	2.63381	0.112306
$551$	1.24567	0.0530672
$552$	−14.2477	−0.606422
$553$	−17.8838	−0.760495
$554$	5.73330	0.243585
$555$	2.37929	0.100995
$556$	67.0238	2.84244
$557$	25.7450	1.09085	0.545426	−	0.838159i	$-0.316368\pi$
$557$	25.7450	1.09085	0.545426	+	0.838159i	$0.316368\pi$
$558$	−20.0019	−0.846747
$559$	−16.3298	−0.690678
$560$	55.3249	2.33790
$561$	−1.52111	−0.0642212
$562$	28.1277	1.18650
$563$	45.1289	1.90196	0.950979	−	0.309256i	$-0.100080\pi$
$563$	45.1289	1.90196	0.950979	+	0.309256i	$0.100080\pi$
$564$	−26.0636	−1.09748
$565$	4.13924	0.174139
$566$	62.4055	2.62310
$567$	18.4725	0.775774
$568$	108.003	4.53171
$569$	4.08624	0.171304	0.0856521	−	0.996325i	$-0.472703\pi$
$569$	4.08624	0.171304	0.0856521	+	0.996325i	$0.472703\pi$
$570$	1.39262	0.0583304
$571$	46.2248	1.93445	0.967225	−	0.253923i	$-0.0817209\pi$
$571$	46.2248	1.93445	0.967225	+	0.253923i	$0.0817209\pi$
$572$	15.3693	0.642622
$573$	9.45779	0.395105
$574$	123.493	5.15448
$575$	−2.26947	−0.0946434
$576$	−25.9646	−1.08186
$577$	−2.20000	−0.0915874	−0.0457937	−	0.998951i	$-0.514582\pi$
$577$	−2.20000	−0.0915874	−0.0457937	+	0.998951i	$0.514582\pi$
$578$	35.5228	1.47756
$579$	−13.5221	−0.561959
$580$	9.43954	0.391956
$581$	−57.5026	−2.38561
$582$	7.08178	0.293549
$583$	−9.03875	−0.374347
$584$	−7.73545	−0.320095
$585$	7.28877	0.301354
$586$	−68.2440	−2.81913
$587$	24.6990	1.01944	0.509719	−	0.860341i	$-0.329749\pi$
$587$	24.6990	1.01944	0.509719	+	0.860341i	$0.329749\pi$
$588$	−83.1966	−3.43097
$589$	−2.11318	−0.0870719
$590$	17.9227	0.737865
$591$	15.4355	0.634930
$592$	−30.7818	−1.26512
$593$	18.6841	0.767262	0.383631	−	0.923486i	$-0.374673\pi$
$593$	18.6841	0.767262	0.383631	+	0.923486i	$0.374673\pi$
$594$	11.4175	0.468464
$595$	−9.87565	−0.404862
$596$	32.0582	1.31316
$597$	14.2507	0.583244
$598$	−18.6081	−0.760942
$599$	34.1495	1.39531	0.697656	−	0.716433i	$-0.254226\pi$
$599$	34.1495	1.39531	0.697656	+	0.716433i	$0.254226\pi$
$600$	6.27799	0.256298
$601$	18.6556	0.760980	0.380490	−	0.924785i	$-0.375755\pi$
$601$	18.6556	0.760980	0.380490	+	0.924785i	$0.375755\pi$
$602$	−72.7972	−2.96699
$603$	14.4410	0.588083
$604$	−20.7371	−0.843780
$605$	1.00000	0.0406558
$606$	−16.8127	−0.682969
$607$	−26.0623	−1.05784	−0.528918	−	0.848673i	$-0.677402\pi$
$607$	−26.0623	−1.05784	−0.528918	+	0.848673i	$0.677402\pi$
$608$	−7.93756	−0.321910
$609$	−8.17646	−0.331327
$610$	5.89403	0.238642
$611$	−20.2503	−0.819239
$612$	21.6645	0.875735
$613$	−1.72911	−0.0698380	−0.0349190	−	0.999390i	$-0.511117\pi$
$613$	−1.72911	−0.0698380	−0.0349190	+	0.999390i	$0.511117\pi$
$614$	−54.8168	−2.21223
$615$	7.22188	0.291214
$616$	40.7592	1.64224
$617$	−8.82313	−0.355206	−0.177603	−	0.984102i	$-0.556834\pi$
$617$	−8.82313	−0.355206	−0.177603	+	0.984102i	$0.556834\pi$
$618$	−25.7930	−1.03755
$619$	25.9023	1.04110	0.520550	−	0.853831i	$-0.325727\pi$
$619$	25.9023	1.04110	0.520550	+	0.853831i	$0.325727\pi$
$620$	−16.0134	−0.643115
$621$	−9.83804	−0.394787
$622$	−64.1955	−2.57400
$623$	−64.0587	−2.56646
$624$	26.5282	1.06198
$625$	1.00000	0.0400000
$626$	−43.4861	−1.73805
$627$	0.528746	0.0211161
$628$	111.171	4.43623
$629$	5.49463	0.219085
$630$	32.4928	1.29455
$631$	−14.8617	−0.591634	−0.295817	−	0.955245i	$-0.595592\pi$
$631$	−14.8617	−0.591634	−0.295817	+	0.955245i	$0.595592\pi$
$632$	26.2545	1.04435
$633$	1.63601	0.0650255
$634$	78.6937	3.12533
$635$	20.6168	0.818152
$636$	−36.2163	−1.43607
$637$	−64.6401	−2.56113
$638$	5.03588	0.199372
$639$	32.6898	1.29319
$640$	−4.84107	−0.191360
$641$	24.5879	0.971164	0.485582	−	0.874191i	$-0.338608\pi$
$641$	24.5879	0.971164	0.485582	+	0.874191i	$0.338608\pi$
$642$	3.65665	0.144316
$643$	−30.9576	−1.22085	−0.610424	−	0.792075i	$-0.709001\pi$
$643$	−30.9576	−1.22085	−0.610424	+	0.792075i	$0.709001\pi$
$644$	−59.0372	−2.32639
$645$	−4.25720	−0.167627
$646$	3.21605	0.126534
$647$	6.48331	0.254885	0.127443	−	0.991846i	$-0.459323\pi$
$647$	6.48331	0.254885	0.127443	+	0.991846i	$0.459323\pi$
$648$	−27.1189	−1.06533
$649$	6.80484	0.267113
$650$	8.19931	0.321604
$651$	13.8707	0.543636
$652$	−87.1545	−3.41323
$653$	−4.29572	−0.168105	−0.0840523	−	0.996461i	$-0.526786\pi$
$653$	−4.29572	−0.168105	−0.0840523	+	0.996461i	$0.526786\pi$
$654$	−13.7590	−0.538021
$655$	−6.61863	−0.258611
$656$	−93.4320	−3.64791
$657$	−2.34133	−0.0913439
$658$	−90.2743	−3.51926
$659$	−3.60526	−0.140441	−0.0702205	−	0.997531i	$-0.522370\pi$
$659$	−3.60526	−0.140441	−0.0702205	+	0.997531i	$0.522370\pi$
$660$	4.00678	0.155964
$661$	−28.5151	−1.10911	−0.554555	−	0.832147i	$-0.687112\pi$
$661$	−28.5151	−1.10911	−0.554555	+	0.832147i	$0.687112\pi$
$662$	57.4640	2.23340
$663$	−4.73535	−0.183906
$664$	84.4176	3.27604
$665$	3.43283	0.133120
$666$	−18.0784	−0.700524
$667$	−4.33925	−0.168016
$668$	−52.1112	−2.01624
$669$	11.2400	0.434563
$670$	16.2450	0.627600
$671$	2.23783	0.0863904
$672$	52.1015	2.00986
$673$	−20.2151	−0.779233	−0.389617	−	0.920977i	$-0.627392\pi$
$673$	−20.2151	−0.779233	−0.389617	+	0.920977i	$0.627392\pi$
$674$	−12.8166	−0.493676
$675$	4.33495	0.166852
$676$	−16.3347	−0.628256
$677$	34.8253	1.33844	0.669222	−	0.743063i	$-0.266628\pi$
$677$	34.8253	1.33844	0.669222	+	0.743063i	$0.266628\pi$
$678$	8.84792	0.339802
$679$	17.4567	0.669927
$680$	14.4981	0.555976
$681$	12.8573	0.492695
$682$	−8.54296	−0.327127
$683$	24.0930	0.921894	0.460947	−	0.887428i	$-0.347510\pi$
$683$	24.0930	0.921894	0.460947	+	0.887428i	$0.347510\pi$
$684$	−7.53070	−0.287943
$685$	−6.26260	−0.239282
$686$	−191.015	−7.29299
$687$	1.64899	0.0629130
$688$	55.0769	2.09979
$689$	−28.1385	−1.07199
$690$	−4.85115	−0.184680
$691$	−48.4757	−1.84410	−0.922051	−	0.387067i	$-0.873488\pi$
$691$	−48.4757	−1.84410	−0.922051	+	0.387067i	$0.873488\pi$
$692$	28.3883	1.07916
$693$	12.3368	0.468636
$694$	−2.92395	−0.110992
$695$	13.5759	0.514962
$696$	12.0036	0.454994
$697$	16.6779	0.631719
$698$	94.9031	3.59214
$699$	−13.1350	−0.496812
$700$	26.0137	0.983224
$701$	−7.14282	−0.269780	−0.134890	−	0.990861i	$-0.543068\pi$
$701$	−7.14282	−0.269780	−0.134890	+	0.990861i	$0.543068\pi$
$702$	35.5436	1.34151
$703$	−1.90996	−0.0720357
$704$	−11.0897	−0.417959
$705$	−5.27927	−0.198829
$706$	87.5695	3.29572
$707$	−41.4436	−1.55865
$708$	27.2655	1.02470
$709$	−21.4294	−0.804799	−0.402400	−	0.915464i	$-0.631824\pi$
$709$	−21.4294	−0.804799	−0.402400	+	0.915464i	$0.631824\pi$
$710$	36.7735	1.38009
$711$	7.94659	0.298020
$712$	94.0423	3.52438
$713$	7.36119	0.275679
$714$	−21.1099	−0.790017
$715$	3.11310	0.116423
$716$	−35.5104	−1.32709
$717$	−17.5080	−0.653848
$718$	−71.3183	−2.66157
$719$	7.24775	0.270295	0.135148	−	0.990825i	$-0.456849\pi$
$719$	7.24775	0.270295	0.135148	+	0.990825i	$0.456849\pi$
$720$	−24.5834	−0.916170
$721$	−63.5802	−2.36785
$722$	48.9245	1.82078
$723$	3.06245	0.113894
$724$	−39.9538	−1.48487
$725$	1.91201	0.0710102
$726$	2.13757	0.0793326
$727$	41.9284	1.55504	0.777519	−	0.628859i	$-0.216478\pi$
$727$	41.9284	1.55504	0.777519	+	0.628859i	$0.216478\pi$
$728$	126.887	4.70276
$729$	2.34636	0.0869021
$730$	−2.63381	−0.0974818
$731$	−9.83138	−0.363627
$732$	8.96650	0.331411
$733$	−16.5663	−0.611889	−0.305945	−	0.952049i	$-0.598972\pi$
$733$	−16.5663	−0.611889	−0.305945	+	0.952049i	$0.598972\pi$
$734$	94.0596	3.47180
$735$	−16.8517	−0.621585
$736$	27.6502	1.01920
$737$	6.16787	0.227197
$738$	−54.8735	−2.01992
$739$	35.9265	1.32158	0.660789	−	0.750572i	$-0.270222\pi$
$739$	35.9265	1.32158	0.660789	+	0.750572i	$0.270222\pi$
$740$	−14.4735	−0.532057
$741$	1.64604	0.0604687
$742$	−125.439	−4.60503
$743$	−44.1103	−1.61825	−0.809124	−	0.587637i	$-0.800058\pi$
$743$	−44.1103	−1.61825	−0.809124	+	0.587637i	$0.800058\pi$
$744$	−20.3631	−0.746548
$745$	6.49350	0.237903
$746$	−47.2660	−1.73053
$747$	25.5511	0.934865
$748$	9.25308	0.338326
$749$	9.01371	0.329354
$750$	2.13757	0.0780530
$751$	−36.4781	−1.33110	−0.665552	−	0.746351i	$-0.731804\pi$
$751$	−36.4781	−1.33110	−0.665552	+	0.746351i	$0.731804\pi$
$752$	68.2997	2.49064
$753$	0.509642	0.0185724
$754$	15.6772	0.570929
$755$	−4.20036	−0.152867
$756$	112.768	4.10133
$757$	6.69043	0.243168	0.121584	−	0.992581i	$-0.461203\pi$
$757$	6.69043	0.243168	0.121584	+	0.992581i	$0.461203\pi$
$758$	−46.3312	−1.68283
$759$	−1.84187	−0.0668557
$760$	−5.03962	−0.182806
$761$	4.88274	0.176999	0.0884995	−	0.996076i	$-0.471793\pi$
$761$	4.88274	0.176999	0.0884995	+	0.996076i	$0.471793\pi$
$762$	44.0698	1.59648
$763$	−33.9163	−1.22785
$764$	−57.5328	−2.08146
$765$	4.38821	0.158656
$766$	15.4062	0.556649
$767$	21.1841	0.764914
$768$	7.65239	0.276132
$769$	43.1263	1.55517	0.777587	−	0.628775i	$-0.216443\pi$
$769$	43.1263	1.55517	0.777587	+	0.628775i	$0.216443\pi$
$770$	13.8780	0.500127
$771$	11.4703	0.413094
$772$	82.2564	2.96047
$773$	−1.13045	−0.0406593	−0.0203297	−	0.999793i	$-0.506472\pi$
$773$	−1.13045	−0.0406593	−0.0203297	+	0.999793i	$0.506472\pi$
$774$	32.3472	1.16270
$775$	−3.24357	−0.116513
$776$	−25.6276	−0.919977
$777$	12.5369	0.449757
$778$	−6.93096	−0.248487
$779$	−5.79732	−0.207711
$780$	12.4735	0.446623
$781$	13.9621	0.499603
$782$	−11.2030	−0.400619
$783$	8.28846	0.296205
$784$	218.017	7.78631
$785$	22.5181	0.803707
$786$	−14.1478	−0.504635
$787$	−52.3331	−1.86547	−0.932737	−	0.360559i	$-0.882586\pi$
$787$	−52.3331	−1.86547	−0.932737	+	0.360559i	$0.882586\pi$
$788$	−93.8957	−3.34489
$789$	−13.1540	−0.468296
$790$	8.93930	0.318046
$791$	21.8103	0.775485
$792$	−18.1112	−0.643554
$793$	6.96658	0.247390
$794$	41.9837	1.48995
$795$	−7.33573	−0.260172
$796$	−86.6889	−3.07261
$797$	−30.4349	−1.07806	−0.539030	−	0.842287i	$-0.681209\pi$
$797$	−30.4349	−1.07806	−0.539030	+	0.842287i	$0.681209\pi$
$798$	7.33791	0.259759
$799$	−12.1917	−0.431311
$800$	−12.1836	−0.430754
$801$	28.4642	1.00573
$802$	−39.2806	−1.38705
$803$	−1.00000	−0.0352892
$804$	24.7133	0.871572
$805$	−11.9582	−0.421470
$806$	−26.5951	−0.936771
$807$	−2.31307	−0.0814238
$808$	60.8419	2.14041
$809$	−25.5971	−0.899947	−0.449973	−	0.893042i	$-0.648567\pi$
$809$	−25.5971	−0.899947	−0.449973	+	0.893042i	$0.648567\pi$
$810$	−9.23361	−0.324436
$811$	−6.81387	−0.239267	−0.119634	−	0.992818i	$-0.538172\pi$
$811$	−6.81387	−0.239267	−0.119634	+	0.992818i	$0.538172\pi$
$812$	49.7383	1.74547
$813$	−5.43157	−0.190494
$814$	−7.72144	−0.270636
$815$	−17.6534	−0.618372
$816$	15.9713	0.559107
$817$	3.41744	0.119561
$818$	93.5713	3.27164
$819$	38.4056	1.34200
$820$	−43.9315	−1.53416
$821$	36.9057	1.28802	0.644009	−	0.765018i	$-0.277270\pi$
$821$	36.9057	1.28802	0.644009	+	0.765018i	$0.277270\pi$
$822$	−13.3867	−0.466916
$823$	−24.3140	−0.847534	−0.423767	−	0.905771i	$-0.639292\pi$
$823$	−24.3140	−0.847534	−0.423767	+	0.905771i	$0.639292\pi$
$824$	93.3398	3.25165
$825$	0.811587	0.0282558
$826$	94.4373	3.28589
$827$	−29.1662	−1.01421	−0.507104	−	0.861885i	$-0.669284\pi$
$827$	−29.1662	−1.01421	−0.507104	+	0.861885i	$0.669284\pi$
$828$	26.2330	0.911659
$829$	26.8342	0.931989	0.465994	−	0.884788i	$-0.345697\pi$
$829$	26.8342	0.931989	0.465994	+	0.884788i	$0.345697\pi$
$830$	28.7430	0.997685
$831$	1.76667	0.0612850
$832$	−34.5233	−1.19688
$833$	−38.9166	−1.34838
$834$	29.0194	1.00486
$835$	−10.5553	−0.365281
$836$	−3.21642	−0.111242
$837$	−14.0607	−0.486010
$838$	−13.0188	−0.449727
$839$	−54.0566	−1.86624	−0.933121	−	0.359563i	$-0.882926\pi$
$839$	−54.0566	−1.86624	−0.933121	+	0.359563i	$0.882926\pi$
$840$	33.0797	1.14136
$841$	−25.3442	−0.873939
$842$	−54.1405	−1.86580
$843$	8.66732	0.298518
$844$	−9.95203	−0.342563
$845$	−3.30864	−0.113821
$846$	40.1131	1.37912
$847$	5.26915	0.181050
$848$	94.9049	3.25905
$849$	19.2297	0.659962
$850$	4.93640	0.169317
$851$	6.65330	0.228072
$852$	55.9431	1.91658
$853$	22.7654	0.779471	0.389736	−	0.920927i	$-0.372566\pi$
$853$	22.7654	0.779471	0.389736	+	0.920927i	$0.372566\pi$
$854$	31.0565	1.06273
$855$	−1.52537	−0.0521664
$856$	−13.2327	−0.452285
$857$	−14.5543	−0.497165	−0.248583	−	0.968611i	$-0.579965\pi$
$857$	−14.5543	−0.497165	−0.248583	+	0.968611i	$0.579965\pi$
$858$	6.65446	0.227179
$859$	19.2700	0.657483	0.328742	−	0.944420i	$-0.393376\pi$
$859$	19.2700	0.657483	0.328742	+	0.944420i	$0.393376\pi$
$860$	25.8970	0.883082
$861$	38.0531	1.29685
$862$	14.9566	0.509424
$863$	40.4706	1.37764	0.688818	−	0.724934i	$-0.258130\pi$
$863$	40.4706	1.37764	0.688818	+	0.724934i	$0.258130\pi$
$864$	−52.8152	−1.79681
$865$	5.75014	0.195511
$866$	−56.1123	−1.90677
$867$	10.9461	0.371747
$868$	−84.3772	−2.86395
$869$	3.39405	0.115135
$870$	4.08705	0.138564
$871$	19.2012	0.650607
$872$	49.7913	1.68615
$873$	−7.75683	−0.262529
$874$	3.89423	0.131724
$875$	5.26915	0.178130
$876$	−4.00678	−0.135377
$877$	−53.0575	−1.79163	−0.895813	−	0.444432i	$-0.853406\pi$
$877$	−53.0575	−1.79163	−0.895813	+	0.444432i	$0.853406\pi$
$878$	66.5414	2.24566
$879$	−21.0288	−0.709283
$880$	−10.4998	−0.353948
$881$	19.8386	0.668380	0.334190	−	0.942506i	$-0.391537\pi$
$881$	19.8386	0.668380	0.334190	+	0.942506i	$0.391537\pi$
$882$	128.043	4.31144
$883$	−14.6769	−0.493916	−0.246958	−	0.969026i	$-0.579431\pi$
$883$	−14.6769	−0.493916	−0.246958	+	0.969026i	$0.579431\pi$
$884$	28.8057	0.968841
$885$	5.52272	0.185644
$886$	13.0522	0.438497
$887$	−43.6466	−1.46551	−0.732754	−	0.680493i	$-0.761766\pi$
$887$	−43.6466	−1.46551	−0.732754	+	0.680493i	$0.761766\pi$
$888$	−18.4049	−0.617628
$889$	108.633	3.64343
$890$	32.0201	1.07332
$891$	−3.50579	−0.117448
$892$	−68.3742	−2.28934
$893$	4.23790	0.141816
$894$	13.8803	0.464226
$895$	−7.19275	−0.240427
$896$	−25.5083	−0.852173
$897$	−5.73392	−0.191450
$898$	84.3540	2.81493
$899$	−6.20174	−0.206839
$900$	−11.5591	−0.385303
$901$	−16.9408	−0.564379
$902$	−23.4369	−0.780364
$903$	−22.4318	−0.746484
$904$	−32.0189	−1.06493
$905$	−8.09278	−0.269013
$906$	−8.97856	−0.298293
$907$	−16.4980	−0.547808	−0.273904	−	0.961757i	$-0.588315\pi$
$907$	−16.4980	−0.547808	−0.273904	+	0.961757i	$0.588315\pi$
$908$	−78.2127	−2.59558
$909$	18.4153	0.610798
$910$	43.2034	1.43218
$911$	11.7775	0.390205	0.195102	−	0.980783i	$-0.437496\pi$
$911$	11.7775	0.390205	0.195102	+	0.980783i	$0.437496\pi$
$912$	−5.55172	−0.183836
$913$	10.9131	0.361170
$914$	18.1276	0.599606
$915$	1.81619	0.0600415
$916$	−10.0310	−0.331434
$917$	−34.8746	−1.15166
$918$	21.3990	0.706274
$919$	−1.90513	−0.0628446	−0.0314223	−	0.999506i	$-0.510004\pi$
$919$	−1.90513	−0.0628446	−0.0314223	+	0.999506i	$0.510004\pi$
$920$	17.5554	0.578783
$921$	−16.8913	−0.556588
$922$	19.4340	0.640023
$923$	43.4653	1.43068
$924$	21.1123	0.694545
$925$	−2.93166	−0.0963923
$926$	66.0022	2.16897
$927$	28.2516	0.927905
$928$	−23.2951	−0.764699
$929$	−43.8049	−1.43719	−0.718597	−	0.695427i	$-0.755215\pi$
$929$	−43.8049	−1.43719	−0.718597	+	0.695427i	$0.755215\pi$
$930$	−6.93336	−0.227354
$931$	13.5276	0.443350
$932$	79.9018	2.61727
$933$	−19.7813	−0.647610
$934$	71.3961	2.33615
$935$	1.87424	0.0612942
$936$	−56.3819	−1.84290
$937$	−19.1371	−0.625183	−0.312592	−	0.949888i	$-0.601197\pi$
$937$	−19.1371	−0.625183	−0.312592	+	0.949888i	$0.601197\pi$
$938$	85.5975	2.79486
$939$	−13.3999	−0.437288
$940$	32.1144	1.04746
$941$	−10.0909	−0.328955	−0.164478	−	0.986381i	$-0.552594\pi$
$941$	−10.0909	−0.328955	−0.164478	+	0.986381i	$0.552594\pi$
$942$	48.1341	1.56829
$943$	20.1948	0.657633
$944$	−71.4493	−2.32548
$945$	22.8415	0.743034
$946$	13.8157	0.449189
$947$	5.52227	0.179450	0.0897248	−	0.995967i	$-0.471401\pi$
$947$	5.52227	0.179450	0.0897248	+	0.995967i	$0.471401\pi$
$948$	13.5992	0.441683
$949$	−3.11310	−0.101055
$950$	−1.71592	−0.0556718
$951$	24.2488	0.786320
$952$	76.3926	2.47590
$953$	15.2375	0.493590	0.246795	−	0.969068i	$-0.420622\pi$
$953$	15.2375	0.493590	0.246795	+	0.969068i	$0.420622\pi$
$954$	55.7385	1.80460
$955$	−11.6535	−0.377097
$956$	106.503	3.44456
$957$	1.55176	0.0501613
$958$	−17.3385	−0.560181
$959$	−32.9986	−1.06558
$960$	−9.00026	−0.290482
$961$	−20.4792	−0.660621
$962$	−24.0376	−0.775002
$963$	−4.00521	−0.129066
$964$	−18.6293	−0.600008
$965$	16.6613	0.536346
$966$	−25.5614	−0.822425
$967$	11.6332	0.374099	0.187050	−	0.982350i	$-0.440107\pi$
$967$	11.6332	0.374099	0.187050	+	0.982350i	$0.440107\pi$
$968$	−7.73545	−0.248627
$969$	0.990997	0.0318354
$970$	−8.72584	−0.280170
$971$	28.6228	0.918549	0.459274	−	0.888295i	$-0.348110\pi$
$971$	28.6228	0.918549	0.459274	+	0.888295i	$0.348110\pi$
$972$	−78.2516	−2.50992
$973$	71.5333	2.29325
$974$	−99.4667	−3.18712
$975$	2.52655	0.0809143
$976$	−23.4967	−0.752112
$977$	23.5839	0.754516	0.377258	−	0.926108i	$-0.376867\pi$
$977$	23.5839	0.754516	0.377258	+	0.926108i	$0.376867\pi$
$978$	−37.7354	−1.20664
$979$	12.1573	0.388549
$980$	102.511	3.27459
$981$	15.0706	0.481167
$982$	37.9323	1.21047
$983$	−17.3657	−0.553879	−0.276940	−	0.960887i	$-0.589320\pi$
$983$	−17.3657	−0.553879	−0.276940	+	0.960887i	$0.589320\pi$
$984$	−55.8645	−1.78089
$985$	−19.0189	−0.605991
$986$	9.43844	0.300581
$987$	−27.8172	−0.885433
$988$	−10.0130	−0.318557
$989$	−11.9046	−0.378543
$990$	−6.16662	−0.195988
$991$	4.27988	0.135955	0.0679774	−	0.997687i	$-0.478345\pi$
$991$	4.27988	0.135955	0.0679774	+	0.997687i	$0.478345\pi$
$992$	39.5183	1.25471
$993$	17.7070	0.561916
$994$	193.765	6.14586
$995$	−17.5591	−0.556661
$996$	43.7264	1.38552
$997$	18.6448	0.590488	0.295244	−	0.955422i	$-0.404599\pi$
$997$	18.6448	0.590488	0.295244	+	0.955422i	$0.404599\pi$
$998$	−93.9662	−2.97445
$999$	−12.7086	−0.402082

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.c.1.1	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.c.1.1	✓	23	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.63381 q^{2} -0.811587 q^{3} +4.93698 q^{4} +1.00000 q^{5} +2.13757 q^{6} +5.26915 q^{7} -7.73545 q^{8} -2.34133 q^{9} +O(q^{10})\)	\(q-2.63381 q^{2} -0.811587 q^{3} +4.93698 q^{4} +1.00000 q^{5} +2.13757 q^{6} +5.26915 q^{7} -7.73545 q^{8} -2.34133 q^{9} -2.63381 q^{10} -1.00000 q^{11} -4.00678 q^{12} -3.11310 q^{13} -13.8780 q^{14} -0.811587 q^{15} +10.4998 q^{16} -1.87424 q^{17} +6.16662 q^{18} +0.651497 q^{19} +4.93698 q^{20} -4.27637 q^{21} +2.63381 q^{22} -2.26947 q^{23} +6.27799 q^{24} +1.00000 q^{25} +8.19931 q^{26} +4.33495 q^{27} +26.0137 q^{28} +1.91201 q^{29} +2.13757 q^{30} -3.24357 q^{31} -12.1836 q^{32} +0.811587 q^{33} +4.93640 q^{34} +5.26915 q^{35} -11.5591 q^{36} -2.93166 q^{37} -1.71592 q^{38} +2.52655 q^{39} -7.73545 q^{40} -8.89847 q^{41} +11.2632 q^{42} +5.24553 q^{43} -4.93698 q^{44} -2.34133 q^{45} +5.97736 q^{46} +6.50487 q^{47} -8.52148 q^{48} +20.7639 q^{49} -2.63381 q^{50} +1.52111 q^{51} -15.3693 q^{52} +9.03875 q^{53} -11.4175 q^{54} -1.00000 q^{55} -40.7592 q^{56} -0.528746 q^{57} -5.03588 q^{58} -6.80484 q^{59} -4.00678 q^{60} -2.23783 q^{61} +8.54296 q^{62} -12.3368 q^{63} +11.0897 q^{64} -3.11310 q^{65} -2.13757 q^{66} -6.16787 q^{67} -9.25308 q^{68} +1.84187 q^{69} -13.8780 q^{70} -13.9621 q^{71} +18.1112 q^{72} +1.00000 q^{73} +7.72144 q^{74} -0.811587 q^{75} +3.21642 q^{76} -5.26915 q^{77} -6.65446 q^{78} -3.39405 q^{79} +10.4998 q^{80} +3.50579 q^{81} +23.4369 q^{82} -10.9131 q^{83} -21.1123 q^{84} -1.87424 q^{85} -13.8157 q^{86} -1.55176 q^{87} +7.73545 q^{88} -12.1573 q^{89} +6.16662 q^{90} -16.4034 q^{91} -11.2043 q^{92} +2.63244 q^{93} -17.1326 q^{94} +0.651497 q^{95} +9.88803 q^{96} +3.31301 q^{97} -54.6883 q^{98} +2.34133 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9	\( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9} - 3 q^{10} - 23 q^{11} - 18 q^{12} - 5 q^{13} - 17 q^{14} - 5 q^{15} - q^{16} - 36 q^{17} + q^{18} + 6 q^{19} + 15 q^{20} - 18 q^{21} + 3 q^{22} - 14 q^{23} - 7 q^{24} + 23 q^{25} - 21 q^{26} - 29 q^{27} + 28 q^{28} - 36 q^{29} - 5 q^{30} - 16 q^{31} - 5 q^{32} + 5 q^{33} - 28 q^{34} - 14 q^{36} - 24 q^{37} + q^{38} - 10 q^{39} - 6 q^{40} - 36 q^{41} - 5 q^{42} + 17 q^{43} - 15 q^{44} + 8 q^{45} - 25 q^{46} - 21 q^{47} - 17 q^{48} - 27 q^{49} - 3 q^{50} + 19 q^{51} - 21 q^{52} - 28 q^{53} - 15 q^{54} - 23 q^{55} - 46 q^{56} - 23 q^{57} - 16 q^{58} - 61 q^{59} - 18 q^{60} - 17 q^{61} - 22 q^{62} - 9 q^{63} - 18 q^{64} - 5 q^{65} + 5 q^{66} + 2 q^{67} - 39 q^{68} - 36 q^{69} - 17 q^{70} - 50 q^{71} + 15 q^{72} + 23 q^{73} + 17 q^{74} - 5 q^{75} - 21 q^{76} + 49 q^{78} - 18 q^{79} - q^{80} - 57 q^{81} + 14 q^{82} - 20 q^{83} - 38 q^{84} - 36 q^{85} - 45 q^{86} + 37 q^{87} + 6 q^{88} - 93 q^{89} + q^{90} - 42 q^{91} - 39 q^{92} - 18 q^{93} - 6 q^{94} + 6 q^{95} - 9 q^{96} - 31 q^{97} - 31 q^{98} - 8 q^{99}+O(q^{100}) \) 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9 - 3 * q^10 - 23 * q^11 - 18 * q^12 - 5 * q^13 - 17 * q^14 - 5 * q^15 - q^16 - 36 * q^17 + q^18 + 6 * q^19 + 15 * q^20 - 18 * q^21 + 3 * q^22 - 14 * q^23 - 7 * q^24 + 23 * q^25 - 21 * q^26 - 29 * q^27 + 28 * q^28 - 36 * q^29 - 5 * q^30 - 16 * q^31 - 5 * q^32 + 5 * q^33 - 28 * q^34 - 14 * q^36 - 24 * q^37 + q^38 - 10 * q^39 - 6 * q^40 - 36 * q^41 - 5 * q^42 + 17 * q^43 - 15 * q^44 + 8 * q^45 - 25 * q^46 - 21 * q^47 - 17 * q^48 - 27 * q^49 - 3 * q^50 + 19 * q^51 - 21 * q^52 - 28 * q^53 - 15 * q^54 - 23 * q^55 - 46 * q^56 - 23 * q^57 - 16 * q^58 - 61 * q^59 - 18 * q^60 - 17 * q^61 - 22 * q^62 - 9 * q^63 - 18 * q^64 - 5 * q^65 + 5 * q^66 + 2 * q^67 - 39 * q^68 - 36 * q^69 - 17 * q^70 - 50 * q^71 + 15 * q^72 + 23 * q^73 + 17 * q^74 - 5 * q^75 - 21 * q^76 + 49 * q^78 - 18 * q^79 - q^80 - 57 * q^81 + 14 * q^82 - 20 * q^83 - 38 * q^84 - 36 * q^85 - 45 * q^86 + 37 * q^87 + 6 * q^88 - 93 * q^89 + q^90 - 42 * q^91 - 39 * q^92 - 18 * q^93 - 6 * q^94 + 6 * q^95 - 9 * q^96 - 31 * q^97 - 31 * q^98 - 8 * q^99

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