LMFDB - Embedded newform 8015.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-2.76919 q^{2} +2.35151 q^{3} +5.66840 q^{4} -1.00000 q^{5} -6.51177 q^{6} +1.00000 q^{7} -10.1585 q^{8} +2.52960 q^{9} +O(q^{10})$	\(q-2.76919 q^{2} +2.35151 q^{3} +5.66840 q^{4} -1.00000 q^{5} -6.51177 q^{6} +1.00000 q^{7} -10.1585 q^{8} +2.52960 q^{9} +2.76919 q^{10} -2.01218 q^{11} +13.3293 q^{12} +1.38072 q^{13} -2.76919 q^{14} -2.35151 q^{15} +16.7940 q^{16} -2.26399 q^{17} -7.00494 q^{18} +5.32055 q^{19} -5.66840 q^{20} +2.35151 q^{21} +5.57210 q^{22} +1.27982 q^{23} -23.8878 q^{24} +1.00000 q^{25} -3.82349 q^{26} -1.10615 q^{27} +5.66840 q^{28} -6.62969 q^{29} +6.51177 q^{30} -5.76408 q^{31} -26.1887 q^{32} -4.73166 q^{33} +6.26940 q^{34} -1.00000 q^{35} +14.3388 q^{36} +6.34746 q^{37} -14.7336 q^{38} +3.24679 q^{39} +10.1585 q^{40} -6.28995 q^{41} -6.51177 q^{42} -0.270250 q^{43} -11.4058 q^{44} -2.52960 q^{45} -3.54407 q^{46} +3.63872 q^{47} +39.4912 q^{48} +1.00000 q^{49} -2.76919 q^{50} -5.32379 q^{51} +7.82650 q^{52} -1.02330 q^{53} +3.06313 q^{54} +2.01218 q^{55} -10.1585 q^{56} +12.5113 q^{57} +18.3589 q^{58} +14.3051 q^{59} -13.3293 q^{60} +3.80840 q^{61} +15.9618 q^{62} +2.52960 q^{63} +38.9335 q^{64} -1.38072 q^{65} +13.1029 q^{66} +3.60369 q^{67} -12.8332 q^{68} +3.00951 q^{69} +2.76919 q^{70} -5.49633 q^{71} -25.6969 q^{72} -6.18791 q^{73} -17.5773 q^{74} +2.35151 q^{75} +30.1590 q^{76} -2.01218 q^{77} -8.99097 q^{78} -3.54552 q^{79} -16.7940 q^{80} -10.1899 q^{81} +17.4181 q^{82} +13.2517 q^{83} +13.3293 q^{84} +2.26399 q^{85} +0.748374 q^{86} -15.5898 q^{87} +20.4407 q^{88} +15.5323 q^{89} +7.00494 q^{90} +1.38072 q^{91} +7.25455 q^{92} -13.5543 q^{93} -10.0763 q^{94} -5.32055 q^{95} -61.5831 q^{96} +10.2806 q^{97} -2.76919 q^{98} -5.09001 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9}+O(q^{10}) $ 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9} - 9 q^{10} + 5 q^{11} + 9 q^{12} + 15 q^{13} + 9 q^{14} + 109 q^{16} + 7 q^{17} + 39 q^{18} + 20 q^{19} - 83 q^{20} + 56 q^{22} + 36 q^{23} + q^{24} + 68 q^{25} + q^{26} + 12 q^{27} + 83 q^{28} - 16 q^{29} - 5 q^{30} + 31 q^{31} + 79 q^{32} + 45 q^{33} + 31 q^{34} - 68 q^{35} + 114 q^{36} + 72 q^{37} + 8 q^{38} + 47 q^{39} - 30 q^{40} + 6 q^{41} + 5 q^{42} + 75 q^{43} + 15 q^{44} - 86 q^{45} + 29 q^{46} - 10 q^{47} + 44 q^{48} + 68 q^{49} + 9 q^{50} + 23 q^{51} + 37 q^{52} + 41 q^{53} + 4 q^{54} - 5 q^{55} + 30 q^{56} + 55 q^{57} + 66 q^{58} - 5 q^{59} - 9 q^{60} - 2 q^{61} + 3 q^{62} + 86 q^{63} + 162 q^{64} - 15 q^{65} - 23 q^{66} + 92 q^{67} + 35 q^{68} - 25 q^{69} - 9 q^{70} - 2 q^{71} + 128 q^{72} + 80 q^{73} + 18 q^{74} + 71 q^{76} + 5 q^{77} + 20 q^{78} + 100 q^{79} - 109 q^{80} + 140 q^{81} + 36 q^{82} - 60 q^{83} + 9 q^{84} - 7 q^{85} - 27 q^{86} + 24 q^{87} + 175 q^{88} + 19 q^{89} - 39 q^{90} + 15 q^{91} + 75 q^{92} + 37 q^{93} + 11 q^{94} - 20 q^{95} + 15 q^{96} + 96 q^{97} + 9 q^{98} + 3 q^{99}+O(q^{100}) \) 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9 - 9 * q^10 + 5 * q^11 + 9 * q^12 + 15 * q^13 + 9 * q^14 + 109 * q^16 + 7 * q^17 + 39 * q^18 + 20 * q^19 - 83 * q^20 + 56 * q^22 + 36 * q^23 + q^24 + 68 * q^25 + q^26 + 12 * q^27 + 83 * q^28 - 16 * q^29 - 5 * q^30 + 31 * q^31 + 79 * q^32 + 45 * q^33 + 31 * q^34 - 68 * q^35 + 114 * q^36 + 72 * q^37 + 8 * q^38 + 47 * q^39 - 30 * q^40 + 6 * q^41 + 5 * q^42 + 75 * q^43 + 15 * q^44 - 86 * q^45 + 29 * q^46 - 10 * q^47 + 44 * q^48 + 68 * q^49 + 9 * q^50 + 23 * q^51 + 37 * q^52 + 41 * q^53 + 4 * q^54 - 5 * q^55 + 30 * q^56 + 55 * q^57 + 66 * q^58 - 5 * q^59 - 9 * q^60 - 2 * q^61 + 3 * q^62 + 86 * q^63 + 162 * q^64 - 15 * q^65 - 23 * q^66 + 92 * q^67 + 35 * q^68 - 25 * q^69 - 9 * q^70 - 2 * q^71 + 128 * q^72 + 80 * q^73 + 18 * q^74 + 71 * q^76 + 5 * q^77 + 20 * q^78 + 100 * q^79 - 109 * q^80 + 140 * q^81 + 36 * q^82 - 60 * q^83 + 9 * q^84 - 7 * q^85 - 27 * q^86 + 24 * q^87 + 175 * q^88 + 19 * q^89 - 39 * q^90 + 15 * q^91 + 75 * q^92 + 37 * q^93 + 11 * q^94 - 20 * q^95 + 15 * q^96 + 96 * q^97 + 9 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.76919	−1.95811	−0.979056	−	0.203592i	$-0.934739\pi$
$2$	−2.76919	−1.95811	−0.979056	+	0.203592i	$0.934739\pi$
$3$	2.35151	1.35765	0.678823	−	0.734302i	$-0.262491\pi$
$3$	2.35151	1.35765	0.678823	+	0.734302i	$0.262491\pi$
$4$	5.66840	2.83420
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−6.51177	−2.65842
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−10.1585	−3.59157
$9$	2.52960	0.843200
$10$	2.76919	0.875694
$11$	−2.01218	−0.606695	−0.303347	−	0.952880i	$-0.598104\pi$
$11$	−2.01218	−0.606695	−0.303347	+	0.952880i	$0.598104\pi$
$12$	13.3293	3.84784
$13$	1.38072	0.382944	0.191472	−	0.981498i	$-0.438674\pi$
$13$	1.38072	0.382944	0.191472	+	0.981498i	$0.438674\pi$
$14$	−2.76919	−0.740097
$15$	−2.35151	−0.607157
$16$	16.7940	4.19850
$17$	−2.26399	−0.549097	−0.274549	−	0.961573i	$-0.588528\pi$
$17$	−2.26399	−0.549097	−0.274549	+	0.961573i	$0.588528\pi$
$18$	−7.00494	−1.65108
$19$	5.32055	1.22062	0.610309	−	0.792164i	$-0.291045\pi$
$19$	5.32055	1.22062	0.610309	+	0.792164i	$0.291045\pi$
$20$	−5.66840	−1.26749
$21$	2.35151	0.513142
$22$	5.57210	1.18798
$23$	1.27982	0.266861	0.133431	−	0.991058i	$-0.457401\pi$
$23$	1.27982	0.266861	0.133431	+	0.991058i	$0.457401\pi$
$24$	−23.8878	−4.87608
$25$	1.00000	0.200000
$26$	−3.82349	−0.749847
$27$	−1.10615	−0.212878
$28$	5.66840	1.07123
$29$	−6.62969	−1.23110	−0.615551	−	0.788097i	$-0.711066\pi$
$29$	−6.62969	−1.23110	−0.615551	+	0.788097i	$0.711066\pi$
$30$	6.51177	1.18888
$31$	−5.76408	−1.03526	−0.517630	−	0.855605i	$-0.673186\pi$
$31$	−5.76408	−1.03526	−0.517630	+	0.855605i	$0.673186\pi$
$32$	−26.1887	−4.62956
$33$	−4.73166	−0.823676
$34$	6.26940	1.07519
$35$	−1.00000	−0.169031
$36$	14.3388	2.38980
$37$	6.34746	1.04352	0.521758	−	0.853094i	$-0.325277\pi$
$37$	6.34746	1.04352	0.521758	+	0.853094i	$0.325277\pi$
$38$	−14.7336	−2.39011
$39$	3.24679	0.519902
$40$	10.1585	1.60620
$41$	−6.28995	−0.982326	−0.491163	−	0.871068i	$-0.663428\pi$
$41$	−6.28995	−0.982326	−0.491163	+	0.871068i	$0.663428\pi$
$42$	−6.51177	−1.00479
$43$	−0.270250	−0.0412128	−0.0206064	−	0.999788i	$-0.506560\pi$
$43$	−0.270250	−0.0412128	−0.0206064	+	0.999788i	$0.506560\pi$
$44$	−11.4058	−1.71950
$45$	−2.52960	−0.377091
$46$	−3.54407	−0.522544
$47$	3.63872	0.530762	0.265381	−	0.964144i	$-0.414502\pi$
$47$	3.63872	0.530762	0.265381	+	0.964144i	$0.414502\pi$
$48$	39.4912	5.70007
$49$	1.00000	0.142857
$50$	−2.76919	−0.391622
$51$	−5.32379	−0.745479
$52$	7.82650	1.08534
$53$	−1.02330	−0.140561	−0.0702805	−	0.997527i	$-0.522389\pi$
$53$	−1.02330	−0.140561	−0.0702805	+	0.997527i	$0.522389\pi$
$54$	3.06313	0.416840
$55$	2.01218	0.271322
$56$	−10.1585	−1.35749
$57$	12.5113	1.65717
$58$	18.3589	2.41064
$59$	14.3051	1.86236	0.931181	−	0.364557i	$-0.118780\pi$
$59$	14.3051	1.86236	0.931181	+	0.364557i	$0.118780\pi$
$60$	−13.3293	−1.72081
$61$	3.80840	0.487616	0.243808	−	0.969824i	$-0.421603\pi$
$61$	3.80840	0.487616	0.243808	+	0.969824i	$0.421603\pi$
$62$	15.9618	2.02715
$63$	2.52960	0.318700
$64$	38.9335	4.86669
$65$	−1.38072	−0.171258
$66$	13.1029	1.61285
$67$	3.60369	0.440261	0.220130	−	0.975470i	$-0.429352\pi$
$67$	3.60369	0.440261	0.220130	+	0.975470i	$0.429352\pi$
$68$	−12.8332	−1.55625
$69$	3.00951	0.362303
$70$	2.76919	0.330981
$71$	−5.49633	−0.652294	−0.326147	−	0.945319i	$-0.605750\pi$
$71$	−5.49633	−0.652294	−0.326147	+	0.945319i	$0.605750\pi$
$72$	−25.6969	−3.02841
$73$	−6.18791	−0.724240	−0.362120	−	0.932131i	$-0.617947\pi$
$73$	−6.18791	−0.724240	−0.362120	+	0.932131i	$0.617947\pi$
$74$	−17.5773	−2.04332
$75$	2.35151	0.271529
$76$	30.1590	3.45948
$77$	−2.01218	−0.229309
$78$	−8.99097	−1.01803
$79$	−3.54552	−0.398903	−0.199451	−	0.979908i	$-0.563916\pi$
$79$	−3.54552	−0.398903	−0.199451	+	0.979908i	$0.563916\pi$
$80$	−16.7940	−1.87763
$81$	−10.1899	−1.13221
$82$	17.4181	1.92350
$83$	13.2517	1.45456	0.727282	−	0.686339i	$-0.240783\pi$
$83$	13.2517	1.45456	0.727282	+	0.686339i	$0.240783\pi$
$84$	13.3293	1.45435
$85$	2.26399	0.245564
$86$	0.748374	0.0806993
$87$	−15.5898	−1.67140
$88$	20.4407	2.17899
$89$	15.5323	1.64642	0.823208	−	0.567740i	$-0.192182\pi$
$89$	15.5323	1.64642	0.823208	+	0.567740i	$0.192182\pi$
$90$	7.00494	0.738386
$91$	1.38072	0.144739
$92$	7.25455	0.756339
$93$	−13.5543	−1.40552
$94$	−10.0763	−1.03929
$95$	−5.32055	−0.545877
$96$	−61.5831	−6.28530
$97$	10.2806	1.04384	0.521920	−	0.852994i	$-0.325216\pi$
$97$	10.2806	1.04384	0.521920	+	0.852994i	$0.325216\pi$
$98$	−2.76919	−0.279730
$99$	−5.09001	−0.511565
$100$	5.66840	0.566840
$101$	14.0861	1.40162	0.700810	−	0.713348i	$-0.252822\pi$
$101$	14.0861	1.40162	0.700810	+	0.713348i	$0.252822\pi$
$102$	14.7426	1.45973
$103$	1.06710	0.105145	0.0525723	−	0.998617i	$-0.483258\pi$
$103$	1.06710	0.105145	0.0525723	+	0.998617i	$0.483258\pi$
$104$	−14.0261	−1.37537
$105$	−2.35151	−0.229484
$106$	2.83371	0.275234
$107$	11.0163	1.06498	0.532491	−	0.846436i	$-0.321256\pi$
$107$	11.0163	1.06498	0.532491	+	0.846436i	$0.321256\pi$
$108$	−6.27010	−0.603341
$109$	0.585386	0.0560698	0.0280349	−	0.999607i	$-0.491075\pi$
$109$	0.585386	0.0560698	0.0280349	+	0.999607i	$0.491075\pi$
$110$	−5.57210	−0.531279
$111$	14.9261	1.41672
$112$	16.7940	1.58688
$113$	0.541306	0.0509218	0.0254609	−	0.999676i	$-0.491895\pi$
$113$	0.541306	0.0509218	0.0254609	+	0.999676i	$0.491895\pi$
$114$	−34.6462	−3.24492
$115$	−1.27982	−0.119344
$116$	−37.5797	−3.48919
$117$	3.49268	0.322899
$118$	−39.6134	−3.64671
$119$	−2.26399	−0.207539
$120$	23.8878	2.18065
$121$	−6.95114	−0.631921
$122$	−10.5462	−0.954807
$123$	−14.7909	−1.33365
$124$	−32.6731	−2.93413
$125$	−1.00000	−0.0894427
$126$	−7.00494	−0.624050
$127$	0.982343	0.0871689	0.0435844	−	0.999050i	$-0.486122\pi$
$127$	0.982343	0.0871689	0.0435844	+	0.999050i	$0.486122\pi$
$128$	−55.4368	−4.89997
$129$	−0.635497	−0.0559524
$130$	3.82349	0.335342
$131$	−0.953130	−0.0832754	−0.0416377	−	0.999133i	$-0.513258\pi$
$131$	−0.953130	−0.0832754	−0.0416377	+	0.999133i	$0.513258\pi$
$132$	−26.8210	−2.33446
$133$	5.32055	0.461350
$134$	−9.97929	−0.862080
$135$	1.10615	0.0952021
$136$	22.9987	1.97212
$137$	6.62358	0.565891	0.282945	−	0.959136i	$-0.408688\pi$
$137$	6.62358	0.565891	0.282945	+	0.959136i	$0.408688\pi$
$138$	−8.33391	−0.709430
$139$	5.51586	0.467849	0.233924	−	0.972255i	$-0.424843\pi$
$139$	5.51586	0.467849	0.233924	+	0.972255i	$0.424843\pi$
$140$	−5.66840	−0.479068
$141$	8.55649	0.720586
$142$	15.2204	1.27727
$143$	−2.77827	−0.232330
$144$	42.4821	3.54017
$145$	6.62969	0.550566
$146$	17.1355	1.41814
$147$	2.35151	0.193949
$148$	35.9799	2.95753
$149$	−16.2504	−1.33128	−0.665641	−	0.746272i	$-0.731842\pi$
$149$	−16.2504	−1.33128	−0.665641	+	0.746272i	$0.731842\pi$
$150$	−6.51177	−0.531684
$151$	2.98179	0.242654	0.121327	−	0.992613i	$-0.461285\pi$
$151$	2.98179	0.242654	0.121327	+	0.992613i	$0.461285\pi$
$152$	−54.0488	−4.38394
$153$	−5.72698	−0.462999
$154$	5.57210	0.449013
$155$	5.76408	0.462982
$156$	18.4041	1.47351
$157$	23.6031	1.88373	0.941867	−	0.335985i	$-0.109069\pi$
$157$	23.6031	1.88373	0.941867	+	0.335985i	$0.109069\pi$
$158$	9.81822	0.781096
$159$	−2.40630	−0.190832
$160$	26.1887	2.07040
$161$	1.27982	0.100864
$162$	28.2178	2.21700
$163$	13.2579	1.03844	0.519218	−	0.854642i	$-0.326223\pi$
$163$	13.2579	1.03844	0.519218	+	0.854642i	$0.326223\pi$
$164$	−35.6540	−2.78411
$165$	4.73166	0.368359
$166$	−36.6965	−2.84820
$167$	−5.60693	−0.433878	−0.216939	−	0.976185i	$-0.569607\pi$
$167$	−5.60693	−0.433878	−0.216939	+	0.976185i	$0.569607\pi$
$168$	−23.8878	−1.84299
$169$	−11.0936	−0.853354
$170$	−6.26940	−0.480841
$171$	13.4589	1.02922
$172$	−1.53189	−0.116805
$173$	−13.0246	−0.990242	−0.495121	−	0.868824i	$-0.664876\pi$
$173$	−13.0246	−0.990242	−0.495121	+	0.868824i	$0.664876\pi$
$174$	43.1710	3.27279
$175$	1.00000	0.0755929
$176$	−33.7925	−2.54721
$177$	33.6385	2.52843
$178$	−43.0117	−3.22387
$179$	8.68570	0.649200	0.324600	−	0.945851i	$-0.394770\pi$
$179$	8.68570	0.649200	0.324600	+	0.945851i	$0.394770\pi$
$180$	−14.3388	−1.06875
$181$	0.956005	0.0710593	0.0355296	−	0.999369i	$-0.488688\pi$
$181$	0.956005	0.0710593	0.0355296	+	0.999369i	$0.488688\pi$
$182$	−3.82349	−0.283416
$183$	8.95550	0.662009
$184$	−13.0011	−0.958452
$185$	−6.34746	−0.466674
$186$	37.5344	2.75216
$187$	4.55554	0.333134
$188$	20.6257	1.50429
$189$	−1.10615	−0.0804605
$190$	14.7336	1.06889
$191$	−16.7279	−1.21039	−0.605193	−	0.796079i	$-0.706904\pi$
$191$	−16.7279	−1.21039	−0.605193	+	0.796079i	$0.706904\pi$
$192$	91.5526	6.60724
$193$	−6.62160	−0.476633	−0.238317	−	0.971187i	$-0.576596\pi$
$193$	−6.62160	−0.476633	−0.238317	+	0.971187i	$0.576596\pi$
$194$	−28.4690	−2.04396
$195$	−3.24679	−0.232507
$196$	5.66840	0.404886
$197$	9.38540	0.668682	0.334341	−	0.942452i	$-0.391486\pi$
$197$	9.38540	0.668682	0.334341	+	0.942452i	$0.391486\pi$
$198$	14.0952	1.00170
$199$	−18.3566	−1.30127	−0.650633	−	0.759393i	$-0.725496\pi$
$199$	−18.3566	−1.30127	−0.650633	+	0.759393i	$0.725496\pi$
$200$	−10.1585	−0.718314
$201$	8.47411	0.597718
$202$	−39.0071	−2.74453
$203$	−6.62969	−0.465313
$204$	−30.1774	−2.11284
$205$	6.28995	0.439309
$206$	−2.95500	−0.205885
$207$	3.23744	0.225018
$208$	23.1879	1.60779
$209$	−10.7059	−0.740542
$210$	6.51177	0.449355
$211$	11.7587	0.809501	0.404751	−	0.914427i	$-0.367358\pi$
$211$	11.7587	0.809501	0.404751	+	0.914427i	$0.367358\pi$
$212$	−5.80048	−0.398378
$213$	−12.9247	−0.885584
$214$	−30.5061	−2.08535
$215$	0.270250	0.0184309
$216$	11.2368	0.764568
$217$	−5.76408	−0.391291
$218$	−1.62104	−0.109791
$219$	−14.5509	−0.983261
$220$	11.4058	0.768982
$221$	−3.12594	−0.210274
$222$	−41.3332	−2.77410
$223$	17.0102	1.13909	0.569544	−	0.821961i	$-0.307120\pi$
$223$	17.0102	1.13909	0.569544	+	0.821961i	$0.307120\pi$
$224$	−26.1887	−1.74981
$225$	2.52960	0.168640
$226$	−1.49898	−0.0997105
$227$	21.1963	1.40685	0.703424	−	0.710770i	$-0.251653\pi$
$227$	21.1963	1.40685	0.703424	+	0.710770i	$0.251653\pi$
$228$	70.9192	4.69674
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	3.54407	0.233689
$231$	−4.73166	−0.311320
$232$	67.3477	4.42159
$233$	3.39130	0.222171	0.111086	−	0.993811i	$-0.464567\pi$
$233$	3.39130	0.222171	0.111086	+	0.993811i	$0.464567\pi$
$234$	−9.67189	−0.632271
$235$	−3.63872	−0.237364
$236$	81.0869	5.27831
$237$	−8.33734	−0.541568
$238$	6.26940	0.406385
$239$	25.8668	1.67319	0.836593	−	0.547825i	$-0.184544\pi$
$239$	25.8668	1.67319	0.836593	+	0.547825i	$0.184544\pi$
$240$	−39.4912	−2.54915
$241$	8.54509	0.550438	0.275219	−	0.961382i	$-0.411250\pi$
$241$	8.54509	0.550438	0.275219	+	0.961382i	$0.411250\pi$
$242$	19.2490	1.23737
$243$	−20.6433	−1.32427
$244$	21.5876	1.38200
$245$	−1.00000	−0.0638877
$246$	40.9588	2.61144
$247$	7.34621	0.467428
$248$	58.5544	3.71821
$249$	31.1615	1.97478
$250$	2.76919	0.175139
$251$	20.8646	1.31696	0.658481	−	0.752598i	$-0.271199\pi$
$251$	20.8646	1.31696	0.658481	+	0.752598i	$0.271199\pi$
$252$	14.3388	0.903259
$253$	−2.57523	−0.161903
$254$	−2.72029	−0.170686
$255$	5.32379	0.333388
$256$	75.6480	4.72800
$257$	−25.0713	−1.56391	−0.781953	−	0.623337i	$-0.785777\pi$
$257$	−25.0713	−1.56391	−0.781953	+	0.623337i	$0.785777\pi$
$258$	1.75981	0.109561
$259$	6.34746	0.394412
$260$	−7.82650	−0.485379
$261$	−16.7705	−1.03807
$262$	2.63940	0.163063
$263$	14.7081	0.906937	0.453469	−	0.891272i	$-0.350186\pi$
$263$	14.7081	0.906937	0.453469	+	0.891272i	$0.350186\pi$
$264$	48.0666	2.95829
$265$	1.02330	0.0628608
$266$	−14.7336	−0.903375
$267$	36.5243	2.23525
$268$	20.4272	1.24779
$269$	17.6154	1.07403	0.537015	−	0.843573i	$-0.319552\pi$
$269$	17.6154	1.07403	0.537015	+	0.843573i	$0.319552\pi$
$270$	−3.06313	−0.186416
$271$	−30.4163	−1.84766	−0.923830	−	0.382802i	$-0.874959\pi$
$271$	−30.4163	−1.84766	−0.923830	+	0.382802i	$0.874959\pi$
$272$	−38.0214	−2.30538
$273$	3.24679	0.196505
$274$	−18.3419	−1.10808
$275$	−2.01218	−0.121339
$276$	17.0591	1.02684
$277$	−9.53986	−0.573195	−0.286597	−	0.958051i	$-0.592524\pi$
$277$	−9.53986	−0.573195	−0.286597	+	0.958051i	$0.592524\pi$
$278$	−15.2745	−0.916101
$279$	−14.5808	−0.872931
$280$	10.1585	0.607087
$281$	1.48472	0.0885711	0.0442856	−	0.999019i	$-0.485899\pi$
$281$	1.48472	0.0885711	0.0442856	+	0.999019i	$0.485899\pi$
$282$	−23.6945	−1.41099
$283$	25.8574	1.53706	0.768530	−	0.639814i	$-0.220989\pi$
$283$	25.8574	1.53706	0.768530	+	0.639814i	$0.220989\pi$
$284$	−31.1554	−1.84873
$285$	−12.5113	−0.741107
$286$	7.69354	0.454928
$287$	−6.28995	−0.371284
$288$	−66.2470	−3.90364
$289$	−11.8744	−0.698492
$290$	−18.3589	−1.07807
$291$	24.1750	1.41717
$292$	−35.0756	−2.05264
$293$	−0.579308	−0.0338435	−0.0169218	−	0.999857i	$-0.505387\pi$
$293$	−0.579308	−0.0338435	−0.0169218	+	0.999857i	$0.505387\pi$
$294$	−6.51177	−0.379774
$295$	−14.3051	−0.832874
$296$	−64.4806	−3.74786
$297$	2.22577	0.129152
$298$	45.0003	2.60680
$299$	1.76708	0.102193
$300$	13.3293	0.769568
$301$	−0.270250	−0.0155770
$302$	−8.25713	−0.475144
$303$	33.1236	1.90290
$304$	89.3533	5.12476
$305$	−3.80840	−0.218068
$306$	15.8591	0.906604
$307$	−18.9583	−1.08201	−0.541003	−	0.841021i	$-0.681955\pi$
$307$	−18.9583	−1.08201	−0.541003	+	0.841021i	$0.681955\pi$
$308$	−11.4058	−0.649908
$309$	2.50930	0.142749
$310$	−15.9618	−0.906571
$311$	29.8745	1.69403	0.847013	−	0.531573i	$-0.178399\pi$
$311$	29.8745	1.69403	0.847013	+	0.531573i	$0.178399\pi$
$312$	−32.9825	−1.86727
$313$	0.314395	0.0177707	0.00888533	−	0.999961i	$-0.497172\pi$
$313$	0.314395	0.0177707	0.00888533	+	0.999961i	$0.497172\pi$
$314$	−65.3615	−3.68856
$315$	−2.52960	−0.142527
$316$	−20.0975	−1.13057
$317$	28.9708	1.62716	0.813581	−	0.581452i	$-0.197515\pi$
$317$	28.9708	1.62716	0.813581	+	0.581452i	$0.197515\pi$
$318$	6.66350	0.373670
$319$	13.3401	0.746903
$320$	−38.9335	−2.17645
$321$	25.9048	1.44587
$322$	−3.54407	−0.197503
$323$	−12.0456	−0.670238
$324$	−57.7606	−3.20892
$325$	1.38072	0.0765888
$326$	−36.7135	−2.03337
$327$	1.37654	0.0761229
$328$	63.8965	3.52809
$329$	3.63872	0.200609
$330$	−13.1029	−0.721288
$331$	19.8828	1.09286	0.546429	−	0.837505i	$-0.315987\pi$
$331$	19.8828	1.09286	0.546429	+	0.837505i	$0.315987\pi$
$332$	75.1160	4.12253
$333$	16.0565	0.879892
$334$	15.5267	0.849581
$335$	−3.60369	−0.196891
$336$	39.4912	2.15442
$337$	0.207525	0.0113046	0.00565230	−	0.999984i	$-0.498201\pi$
$337$	0.207525	0.0113046	0.00565230	+	0.999984i	$0.498201\pi$
$338$	30.7203	1.67096
$339$	1.27289	0.0691337
$340$	12.8332	0.695977
$341$	11.5984	0.628087
$342$	−37.2701	−2.01534
$343$	1.00000	0.0539949
$344$	2.74534	0.148019
$345$	−3.00951	−0.162027
$346$	36.0676	1.93900
$347$	1.41175	0.0757865	0.0378933	−	0.999282i	$-0.487935\pi$
$347$	1.41175	0.0757865	0.0378933	+	0.999282i	$0.487935\pi$
$348$	−88.3691	−4.73708
$349$	−4.63095	−0.247889	−0.123945	−	0.992289i	$-0.539555\pi$
$349$	−4.63095	−0.247889	−0.123945	+	0.992289i	$0.539555\pi$
$350$	−2.76919	−0.148019
$351$	−1.52729	−0.0815206
$352$	52.6964	2.80873
$353$	1.71665	0.0913681	0.0456840	−	0.998956i	$-0.485453\pi$
$353$	1.71665	0.0913681	0.0456840	+	0.998956i	$0.485453\pi$
$354$	−93.1514	−4.95094
$355$	5.49633	0.291715
$356$	88.0431	4.66627
$357$	−5.32379	−0.281765
$358$	−24.0523	−1.27121
$359$	23.7318	1.25252	0.626258	−	0.779615i	$-0.284585\pi$
$359$	23.7318	1.25252	0.626258	+	0.779615i	$0.284585\pi$
$360$	25.6969	1.35435
$361$	9.30824	0.489907
$362$	−2.64736	−0.139142
$363$	−16.3457	−0.857925
$364$	7.82650	0.410220
$365$	6.18791	0.323890
$366$	−24.7995	−1.29629
$367$	−29.7067	−1.55068	−0.775338	−	0.631546i	$-0.782421\pi$
$367$	−29.7067	−1.55068	−0.775338	+	0.631546i	$0.782421\pi$
$368$	21.4933	1.12042
$369$	−15.9111	−0.828297
$370$	17.5773	0.913800
$371$	−1.02330	−0.0531271
$372$	−76.8312	−3.98351
$373$	11.0651	0.572929	0.286465	−	0.958091i	$-0.407520\pi$
$373$	11.0651	0.572929	0.286465	+	0.958091i	$0.407520\pi$
$374$	−12.6152	−0.652314
$375$	−2.35151	−0.121431
$376$	−36.9639	−1.90627
$377$	−9.15377	−0.471443
$378$	3.06313	0.157551
$379$	−7.70031	−0.395538	−0.197769	−	0.980249i	$-0.563370\pi$
$379$	−7.70031	−0.395538	−0.197769	+	0.980249i	$0.563370\pi$
$380$	−30.1590	−1.54712
$381$	2.30999	0.118344
$382$	46.3226	2.37007
$383$	20.4278	1.04381	0.521906	−	0.853003i	$-0.325221\pi$
$383$	20.4278	1.04381	0.521906	+	0.853003i	$0.325221\pi$
$384$	−130.360	−6.65242
$385$	2.01218	0.102550
$386$	18.3365	0.933302
$387$	−0.683626	−0.0347507
$388$	58.2748	2.95845
$389$	−8.41681	−0.426749	−0.213374	−	0.976970i	$-0.568445\pi$
$389$	−8.41681	−0.426749	−0.213374	+	0.976970i	$0.568445\pi$
$390$	8.99097	0.455275
$391$	−2.89750	−0.146533
$392$	−10.1585	−0.513082
$393$	−2.24130	−0.113058
$394$	−25.9899	−1.30935
$395$	3.54552	0.178395
$396$	−28.8522	−1.44988
$397$	18.3561	0.921268	0.460634	−	0.887590i	$-0.347622\pi$
$397$	18.3561	0.921268	0.460634	+	0.887590i	$0.347622\pi$
$398$	50.8329	2.54802
$399$	12.5113	0.626350
$400$	16.7940	0.839700
$401$	−6.66346	−0.332758	−0.166379	−	0.986062i	$-0.553207\pi$
$401$	−6.66346	−0.332758	−0.166379	+	0.986062i	$0.553207\pi$
$402$	−23.4664	−1.17040
$403$	−7.95861	−0.396447
$404$	79.8458	3.97248
$405$	10.1899	0.506341
$406$	18.3589	0.911134
$407$	−12.7722	−0.633095
$408$	54.0817	2.67744
$409$	−31.5561	−1.56035	−0.780175	−	0.625561i	$-0.784870\pi$
$409$	−31.5561	−1.56035	−0.780175	+	0.625561i	$0.784870\pi$
$410$	−17.4181	−0.860217
$411$	15.5754	0.768279
$412$	6.04876	0.298001
$413$	14.3051	0.703907
$414$	−8.96508	−0.440609
$415$	−13.2517	−0.650501
$416$	−36.1594	−1.77286
$417$	12.9706	0.635173
$418$	29.6466	1.45006
$419$	−38.7001	−1.89063	−0.945313	−	0.326165i	$-0.894244\pi$
$419$	−38.7001	−1.89063	−0.945313	+	0.326165i	$0.894244\pi$
$420$	−13.3293	−0.650404
$421$	2.44887	0.119351	0.0596754	−	0.998218i	$-0.480993\pi$
$421$	2.44887	0.119351	0.0596754	+	0.998218i	$0.480993\pi$
$422$	−32.5620	−1.58509
$423$	9.20451	0.447538
$424$	10.3952	0.504835
$425$	−2.26399	−0.109819
$426$	35.7909	1.73407
$427$	3.80840	0.184302
$428$	62.4446	3.01837
$429$	−6.53312	−0.315422
$430$	−0.748374	−0.0360898
$431$	−6.75338	−0.325299	−0.162649	−	0.986684i	$-0.552004\pi$
$431$	−6.75338	−0.325299	−0.162649	+	0.986684i	$0.552004\pi$
$432$	−18.5767	−0.893770
$433$	22.2350	1.06855	0.534273	−	0.845312i	$-0.320586\pi$
$433$	22.2350	1.06855	0.534273	+	0.845312i	$0.320586\pi$
$434$	15.9618	0.766192
$435$	15.5898	0.747473
$436$	3.31821	0.158913
$437$	6.80936	0.325736
$438$	40.2943	1.92533
$439$	−16.5155	−0.788240	−0.394120	−	0.919059i	$-0.628950\pi$
$439$	−16.5155	−0.788240	−0.394120	+	0.919059i	$0.628950\pi$
$440$	−20.4407	−0.974473
$441$	2.52960	0.120457
$442$	8.65632	0.411739
$443$	0.172893	0.00821441	0.00410720	−	0.999992i	$-0.498693\pi$
$443$	0.172893	0.00821441	0.00410720	+	0.999992i	$0.498693\pi$
$444$	84.6072	4.01528
$445$	−15.5323	−0.736300
$446$	−47.1045	−2.23046
$447$	−38.2129	−1.80741
$448$	38.9335	1.83944
$449$	3.25807	0.153758	0.0768790	−	0.997040i	$-0.475504\pi$
$449$	3.25807	0.153758	0.0768790	+	0.997040i	$0.475504\pi$
$450$	−7.00494	−0.330216
$451$	12.6565	0.595972
$452$	3.06834	0.144323
$453$	7.01170	0.329438
$454$	−58.6966	−2.75477
$455$	−1.38072	−0.0647294
$456$	−127.096	−5.95183
$457$	31.4980	1.47341	0.736707	−	0.676213i	$-0.236380\pi$
$457$	31.4980	1.47341	0.736707	+	0.676213i	$0.236380\pi$
$458$	2.76919	0.129396
$459$	2.50431	0.116891
$460$	−7.25455	−0.338245
$461$	26.7077	1.24390	0.621950	−	0.783057i	$-0.286341\pi$
$461$	26.7077	1.24390	0.621950	+	0.783057i	$0.286341\pi$
$462$	13.1029	0.609600
$463$	−17.2011	−0.799403	−0.399702	−	0.916645i	$-0.630886\pi$
$463$	−17.2011	−0.799403	−0.399702	+	0.916645i	$0.630886\pi$
$464$	−111.339	−5.16878
$465$	13.5543	0.628565
$466$	−9.39115	−0.435036
$467$	−0.880842	−0.0407605	−0.0203803	−	0.999792i	$-0.506488\pi$
$467$	−0.880842	−0.0407605	−0.0203803	+	0.999792i	$0.506488\pi$
$468$	19.7979	0.915160
$469$	3.60369	0.166403
$470$	10.0763	0.464785
$471$	55.5030	2.55744
$472$	−145.318	−6.68881
$473$	0.543792	0.0250036
$474$	23.0877	1.06045
$475$	5.32055	0.244124
$476$	−12.8332	−0.588208
$477$	−2.58854	−0.118521
$478$	−71.6301	−3.27628
$479$	−13.7055	−0.626220	−0.313110	−	0.949717i	$-0.601371\pi$
$479$	−13.7055	−0.626220	−0.313110	+	0.949717i	$0.601371\pi$
$480$	61.5831	2.81087
$481$	8.76409	0.399608
$482$	−23.6630	−1.07782
$483$	3.00951	0.136938
$484$	−39.4018	−1.79099
$485$	−10.2806	−0.466820
$486$	57.1651	2.59306
$487$	−20.7125	−0.938574	−0.469287	−	0.883046i	$-0.655489\pi$
$487$	−20.7125	−0.938574	−0.469287	+	0.883046i	$0.655489\pi$
$488$	−38.6877	−1.75131
$489$	31.1760	1.40983
$490$	2.76919	0.125099
$491$	−8.44481	−0.381109	−0.190555	−	0.981677i	$-0.561029\pi$
$491$	−8.44481	−0.381109	−0.190555	+	0.981677i	$0.561029\pi$
$492$	−83.8407	−3.77983
$493$	15.0095	0.675995
$494$	−20.3430	−0.915277
$495$	5.09001	0.228779
$496$	−96.8019	−4.34654
$497$	−5.49633	−0.246544
$498$	−86.2921	−3.86684
$499$	17.4641	0.781801	0.390901	−	0.920433i	$-0.372164\pi$
$499$	17.4641	0.781801	0.390901	+	0.920433i	$0.372164\pi$
$500$	−5.66840	−0.253499
$501$	−13.1848	−0.589052
$502$	−57.7780	−2.57876
$503$	25.3808	1.13167	0.565836	−	0.824518i	$-0.308553\pi$
$503$	25.3808	1.13167	0.565836	+	0.824518i	$0.308553\pi$
$504$	−25.6969	−1.14463
$505$	−14.0861	−0.626824
$506$	7.13130	0.317025
$507$	−26.0867	−1.15855
$508$	5.56832	0.247054
$509$	35.5547	1.57593	0.787967	−	0.615718i	$-0.211134\pi$
$509$	35.5547	1.57593	0.787967	+	0.615718i	$0.211134\pi$
$510$	−14.7426	−0.652812
$511$	−6.18791	−0.273737
$512$	−98.6098	−4.35798
$513$	−5.88532	−0.259843
$514$	69.4272	3.06230
$515$	−1.06710	−0.0470221
$516$	−3.60225	−0.158580
$517$	−7.32175	−0.322010
$518$	−17.5773	−0.772302
$519$	−30.6275	−1.34440
$520$	14.0261	0.615085
$521$	0.0652412	0.00285827	0.00142913	−	0.999999i	$-0.499545\pi$
$521$	0.0652412	0.00285827	0.00142913	+	0.999999i	$0.499545\pi$
$522$	46.4406	2.03265
$523$	−15.4423	−0.675244	−0.337622	−	0.941282i	$-0.609623\pi$
$523$	−15.4423	−0.675244	−0.337622	+	0.941282i	$0.609623\pi$
$524$	−5.40273	−0.236019
$525$	2.35151	0.102628
$526$	−40.7294	−1.77588
$527$	13.0498	0.568458
$528$	−79.4635	−3.45820
$529$	−21.3621	−0.928785
$530$	−2.83371	−0.123088
$531$	36.1861	1.57034
$532$	30.1590	1.30756
$533$	−8.68469	−0.376176
$534$	−101.143	−4.37687
$535$	−11.0163	−0.476274
$536$	−36.6081	−1.58123
$537$	20.4245	0.881383
$538$	−48.7804	−2.10307
$539$	−2.01218	−0.0866707
$540$	6.27010	0.269822
$541$	−12.6792	−0.545123	−0.272562	−	0.962138i	$-0.587871\pi$
$541$	−12.6792	−0.545123	−0.272562	+	0.962138i	$0.587871\pi$
$542$	84.2286	3.61793
$543$	2.24805	0.0964733
$544$	59.2909	2.54208
$545$	−0.585386	−0.0250752
$546$	−8.99097	−0.384778
$547$	−34.7862	−1.48735	−0.743675	−	0.668541i	$-0.766919\pi$
$547$	−34.7862	−1.48735	−0.743675	+	0.668541i	$0.766919\pi$
$548$	37.5451	1.60385
$549$	9.63374	0.411158
$550$	5.57210	0.237595
$551$	−35.2736	−1.50270
$552$	−30.5722	−1.30124
$553$	−3.54552	−0.150771
$554$	26.4177	1.12238
$555$	−14.9261	−0.633578
$556$	31.2661	1.32598
$557$	34.8405	1.47624	0.738121	−	0.674669i	$-0.235713\pi$
$557$	34.8405	1.47624	0.738121	+	0.674669i	$0.235713\pi$
$558$	40.3770	1.70930
$559$	−0.373141	−0.0157822
$560$	−16.7940	−0.709676
$561$	10.7124	0.452278
$562$	−4.11148	−0.173432
$563$	12.7893	0.539005	0.269502	−	0.963000i	$-0.413141\pi$
$563$	12.7893	0.539005	0.269502	+	0.963000i	$0.413141\pi$
$564$	48.5016	2.04229
$565$	−0.541306	−0.0227729
$566$	−71.6039	−3.00974
$567$	−10.1899	−0.427937
$568$	55.8345	2.34276
$569$	−23.6318	−0.990697	−0.495348	−	0.868694i	$-0.664960\pi$
$569$	−23.6318	−0.990697	−0.495348	+	0.868694i	$0.664960\pi$
$570$	34.6462	1.45117
$571$	−9.33208	−0.390535	−0.195268	−	0.980750i	$-0.562558\pi$
$571$	−9.33208	−0.390535	−0.195268	+	0.980750i	$0.562558\pi$
$572$	−15.7483	−0.658471
$573$	−39.3358	−1.64328
$574$	17.4181	0.727016
$575$	1.27982	0.0533723
$576$	98.4863	4.10360
$577$	10.3463	0.430723	0.215361	−	0.976534i	$-0.430907\pi$
$577$	10.3463	0.430723	0.215361	+	0.976534i	$0.430907\pi$
$578$	32.8824	1.36773
$579$	−15.5708	−0.647099
$580$	37.5797	1.56041
$581$	13.2517	0.549773
$582$	−66.9452	−2.77497
$583$	2.05906	0.0852776
$584$	62.8599	2.60116
$585$	−3.49268	−0.144405
$586$	1.60421	0.0662694
$587$	3.89888	0.160924	0.0804621	−	0.996758i	$-0.474360\pi$
$587$	3.89888	0.160924	0.0804621	+	0.996758i	$0.474360\pi$
$588$	13.3293	0.549691
$589$	−30.6681	−1.26366
$590$	39.6134	1.63086
$591$	22.0699	0.907833
$592$	106.599	4.38120
$593$	−22.8066	−0.936556	−0.468278	−	0.883581i	$-0.655125\pi$
$593$	−22.8066	−0.936556	−0.468278	+	0.883581i	$0.655125\pi$
$594$	−6.16358	−0.252895
$595$	2.26399	0.0928144
$596$	−92.1137	−3.77312
$597$	−43.1657	−1.76666
$598$	−4.89338	−0.200105
$599$	−14.1186	−0.576872	−0.288436	−	0.957499i	$-0.593135\pi$
$599$	−14.1186	−0.576872	−0.288436	+	0.957499i	$0.593135\pi$
$600$	−23.8878	−0.975216
$601$	2.51125	0.102436	0.0512180	−	0.998687i	$-0.483690\pi$
$601$	2.51125	0.102436	0.0512180	+	0.998687i	$0.483690\pi$
$602$	0.748374	0.0305015
$603$	9.11589	0.371228
$604$	16.9020	0.687731
$605$	6.95114	0.282604
$606$	−91.7256	−3.72610
$607$	−9.68268	−0.393008	−0.196504	−	0.980503i	$-0.562959\pi$
$607$	−9.68268	−0.393008	−0.196504	+	0.980503i	$0.562959\pi$
$608$	−139.338	−5.65092
$609$	−15.5898	−0.631730
$610$	10.5462	0.427002
$611$	5.02407	0.203252
$612$	−32.4628	−1.31223
$613$	−24.5428	−0.991275	−0.495637	−	0.868530i	$-0.665065\pi$
$613$	−24.5428	−0.991275	−0.495637	+	0.868530i	$0.665065\pi$
$614$	52.4990	2.11869
$615$	14.7909	0.596426
$616$	20.4407	0.823580
$617$	−31.5853	−1.27158	−0.635789	−	0.771863i	$-0.719325\pi$
$617$	−31.5853	−1.27158	−0.635789	+	0.771863i	$0.719325\pi$
$618$	−6.94872	−0.279519
$619$	4.51921	0.181642	0.0908211	−	0.995867i	$-0.471051\pi$
$619$	4.51921	0.181642	0.0908211	+	0.995867i	$0.471051\pi$
$620$	32.6731	1.31218
$621$	−1.41567	−0.0568090
$622$	−82.7280	−3.31709
$623$	15.5323	0.622287
$624$	54.5265	2.18281
$625$	1.00000	0.0400000
$626$	−0.870619	−0.0347969
$627$	−25.1750	−1.00539
$628$	133.792	5.33889
$629$	−14.3706	−0.572991
$630$	7.00494	0.279084
$631$	40.6995	1.62022	0.810110	−	0.586278i	$-0.199407\pi$
$631$	40.6995	1.62022	0.810110	+	0.586278i	$0.199407\pi$
$632$	36.0172	1.43269
$633$	27.6507	1.09902
$634$	−80.2256	−3.18616
$635$	−0.982343	−0.0389831
$636$	−13.6399	−0.540856
$637$	1.38072	0.0547063
$638$	−36.9413	−1.46252
$639$	−13.9035	−0.550015
$640$	55.4368	2.19133
$641$	−13.3048	−0.525507	−0.262754	−	0.964863i	$-0.584631\pi$
$641$	−13.3048	−0.525507	−0.262754	+	0.964863i	$0.584631\pi$
$642$	−71.7354	−2.83117
$643$	33.0287	1.30253	0.651263	−	0.758853i	$-0.274240\pi$
$643$	33.0287	1.30253	0.651263	+	0.758853i	$0.274240\pi$
$644$	7.25455	0.285869
$645$	0.635497	0.0250227
$646$	33.3567	1.31240
$647$	27.3229	1.07417	0.537086	−	0.843527i	$-0.319525\pi$
$647$	27.3229	1.07417	0.537086	+	0.843527i	$0.319525\pi$
$648$	103.514	4.06643
$649$	−28.7844	−1.12989
$650$	−3.82349	−0.149969
$651$	−13.5543	−0.531235
$652$	75.1509	2.94314
$653$	−35.6055	−1.39335	−0.696676	−	0.717386i	$-0.745338\pi$
$653$	−35.6055	−1.39335	−0.696676	+	0.717386i	$0.745338\pi$
$654$	−3.81190	−0.149057
$655$	0.953130	0.0372419
$656$	−105.633	−4.12429
$657$	−15.6529	−0.610679
$658$	−10.0763	−0.392815
$659$	10.2065	0.397588	0.198794	−	0.980041i	$-0.436298\pi$
$659$	10.2065	0.397588	0.198794	+	0.980041i	$0.436298\pi$
$660$	26.8210	1.04400
$661$	13.6740	0.531858	0.265929	−	0.963993i	$-0.414321\pi$
$661$	13.6740	0.531858	0.265929	+	0.963993i	$0.414321\pi$
$662$	−55.0592	−2.13994
$663$	−7.35068	−0.285477
$664$	−134.617	−5.22417
$665$	−5.32055	−0.206322
$666$	−44.4636	−1.72293
$667$	−8.48482	−0.328534
$668$	−31.7824	−1.22970
$669$	39.9997	1.54648
$670$	9.97929	0.385534
$671$	−7.66319	−0.295834
$672$	−61.5831	−2.37562
$673$	14.1085	0.543842	0.271921	−	0.962320i	$-0.412341\pi$
$673$	14.1085	0.543842	0.271921	+	0.962320i	$0.412341\pi$
$674$	−0.574676	−0.0221357
$675$	−1.10615	−0.0425757
$676$	−62.8830	−2.41858
$677$	−4.21436	−0.161971	−0.0809856	−	0.996715i	$-0.525807\pi$
$677$	−4.21436	−0.161971	−0.0809856	+	0.996715i	$0.525807\pi$
$678$	−3.52486	−0.135371
$679$	10.2806	0.394535
$680$	−22.9987	−0.881960
$681$	49.8433	1.91000
$682$	−32.1181	−1.22986
$683$	−0.523688	−0.0200383	−0.0100192	−	0.999950i	$-0.503189\pi$
$683$	−0.523688	−0.0200383	−0.0100192	+	0.999950i	$0.503189\pi$
$684$	76.2903	2.91703
$685$	−6.62358	−0.253074
$686$	−2.76919	−0.105728
$687$	−2.35151	−0.0897157
$688$	−4.53858	−0.173032
$689$	−1.41290	−0.0538270
$690$	8.33391	0.317267
$691$	0.947841	0.0360576	0.0180288	−	0.999837i	$-0.494261\pi$
$691$	0.947841	0.0360576	0.0180288	+	0.999837i	$0.494261\pi$
$692$	−73.8287	−2.80655
$693$	−5.09001	−0.193353
$694$	−3.90939	−0.148399
$695$	−5.51586	−0.209228
$696$	158.369	6.00295
$697$	14.2404	0.539392
$698$	12.8240	0.485395
$699$	7.97467	0.301630
$700$	5.66840	0.214246
$701$	−32.7750	−1.23790	−0.618948	−	0.785432i	$-0.712441\pi$
$701$	−32.7750	−1.23790	−0.618948	+	0.785432i	$0.712441\pi$
$702$	4.22935	0.159626
$703$	33.7720	1.27373
$704$	−78.3412	−2.95260
$705$	−8.55649	−0.322256
$706$	−4.75373	−0.178909
$707$	14.0861	0.529763
$708$	190.677	7.16607
$709$	23.0590	0.866000	0.433000	−	0.901394i	$-0.357455\pi$
$709$	23.0590	0.866000	0.433000	+	0.901394i	$0.357455\pi$
$710$	−15.2204	−0.571210
$711$	−8.96876	−0.336355
$712$	−157.784	−5.91322
$713$	−7.37700	−0.276271
$714$	14.7426	0.551727
$715$	2.77827	0.103901
$716$	49.2341	1.83996
$717$	60.8261	2.27159
$718$	−65.7178	−2.45257
$719$	−43.5422	−1.62385	−0.811926	−	0.583761i	$-0.801581\pi$
$719$	−43.5422	−1.62385	−0.811926	+	0.583761i	$0.801581\pi$
$720$	−42.4821	−1.58321
$721$	1.06710	0.0397409
$722$	−25.7763	−0.959293
$723$	20.0939	0.747299
$724$	5.41902	0.201396
$725$	−6.62969	−0.246220
$726$	45.2642	1.67991
$727$	30.1293	1.11743	0.558717	−	0.829359i	$-0.311294\pi$
$727$	30.1293	1.11743	0.558717	+	0.829359i	$0.311294\pi$
$728$	−14.0261	−0.519842
$729$	−17.9731	−0.665669
$730$	−17.1355	−0.634213
$731$	0.611843	0.0226298
$732$	50.7634	1.87627
$733$	41.8344	1.54519	0.772594	−	0.634900i	$-0.218959\pi$
$733$	41.8344	1.54519	0.772594	+	0.634900i	$0.218959\pi$
$734$	82.2634	3.03640
$735$	−2.35151	−0.0867368
$736$	−33.5169	−1.23545
$737$	−7.25127	−0.267104
$738$	44.0608	1.62190
$739$	16.7502	0.616165	0.308082	−	0.951360i	$-0.400313\pi$
$739$	16.7502	0.616165	0.308082	+	0.951360i	$0.400313\pi$
$740$	−35.9799	−1.32265
$741$	17.2747	0.634602
$742$	2.83371	0.104029
$743$	38.9323	1.42829	0.714143	−	0.699999i	$-0.246816\pi$
$743$	38.9323	1.42829	0.714143	+	0.699999i	$0.246816\pi$
$744$	137.691	5.04801
$745$	16.2504	0.595367
$746$	−30.6413	−1.12186
$747$	33.5215	1.22649
$748$	25.8227	0.944170
$749$	11.0163	0.402525
$750$	6.51177	0.237776
$751$	−15.4954	−0.565434	−0.282717	−	0.959203i	$-0.591236\pi$
$751$	−15.4954	−0.565434	−0.282717	+	0.959203i	$0.591236\pi$
$752$	61.1086	2.22840
$753$	49.0633	1.78797
$754$	25.3485	0.923139
$755$	−2.98179	−0.108518
$756$	−6.27010	−0.228041
$757$	44.4178	1.61439	0.807197	−	0.590282i	$-0.200984\pi$
$757$	44.4178	1.61439	0.807197	+	0.590282i	$0.200984\pi$
$758$	21.3236	0.774508
$759$	−6.05568	−0.219807
$760$	54.0488	1.96056
$761$	−19.7587	−0.716253	−0.358127	−	0.933673i	$-0.616584\pi$
$761$	−19.7587	−0.716253	−0.358127	+	0.933673i	$0.616584\pi$
$762$	−6.39680	−0.231731
$763$	0.585386	0.0211924
$764$	−94.8204	−3.43048
$765$	5.72698	0.207059
$766$	−56.5684	−2.04390
$767$	19.7514	0.713181
$768$	177.887	6.41894
$769$	−9.07151	−0.327127	−0.163564	−	0.986533i	$-0.552299\pi$
$769$	−9.07151	−0.327127	−0.163564	+	0.986533i	$0.552299\pi$
$770$	−5.57210	−0.200805
$771$	−58.9555	−2.12323
$772$	−37.5339	−1.35088
$773$	25.8745	0.930641	0.465320	−	0.885142i	$-0.345939\pi$
$773$	25.8745	0.930641	0.465320	+	0.885142i	$0.345939\pi$
$774$	1.89309	0.0680457
$775$	−5.76408	−0.207052
$776$	−104.436	−3.74903
$777$	14.9261	0.535471
$778$	23.3077	0.835622
$779$	−33.4660	−1.19904
$780$	−18.4041	−0.658973
$781$	11.0596	0.395744
$782$	8.02372	0.286928
$783$	7.33342	0.262075
$784$	16.7940	0.599785
$785$	−23.6031	−0.842432
$786$	6.20657	0.221381
$787$	36.2276	1.29138	0.645688	−	0.763602i	$-0.276571\pi$
$787$	36.2276	1.29138	0.645688	+	0.763602i	$0.276571\pi$
$788$	53.2002	1.89518
$789$	34.5861	1.23130
$790$	−9.81822	−0.349317
$791$	0.541306	0.0192466
$792$	51.7069	1.83732
$793$	5.25836	0.186730
$794$	−50.8316	−1.80395
$795$	2.40630	0.0853427
$796$	−104.053	−3.68805
$797$	−28.5522	−1.01137	−0.505685	−	0.862718i	$-0.668760\pi$
$797$	−28.5522	−1.01137	−0.505685	+	0.862718i	$0.668760\pi$
$798$	−34.6462	−1.22646
$799$	−8.23801	−0.291440
$800$	−26.1887	−0.925911
$801$	39.2904	1.38826
$802$	18.4524	0.651577
$803$	12.4512	0.439393
$804$	48.0347	1.69405
$805$	−1.27982	−0.0451078
$806$	22.0389	0.776287
$807$	41.4228	1.45815
$808$	−143.094	−5.03402
$809$	−39.6362	−1.39354	−0.696768	−	0.717297i	$-0.745379\pi$
$809$	−39.6362	−1.39354	−0.696768	+	0.717297i	$0.745379\pi$
$810$	−28.2178	−0.991473
$811$	13.9143	0.488598	0.244299	−	0.969700i	$-0.421442\pi$
$811$	13.9143	0.488598	0.244299	+	0.969700i	$0.421442\pi$
$812$	−37.5797	−1.31879
$813$	−71.5243	−2.50847
$814$	35.3687	1.23967
$815$	−13.2579	−0.464402
$816$	−89.4076	−3.12989
$817$	−1.43788	−0.0503051
$818$	87.3849	3.05534
$819$	3.49268	0.122044
$820$	35.6540	1.24509
$821$	−37.7795	−1.31851	−0.659256	−	0.751918i	$-0.729129\pi$
$821$	−37.7795	−1.31851	−0.659256	+	0.751918i	$0.729129\pi$
$822$	−43.1313	−1.50438
$823$	19.4065	0.676469	0.338234	−	0.941062i	$-0.390170\pi$
$823$	19.4065	0.676469	0.338234	+	0.941062i	$0.390170\pi$
$824$	−10.8401	−0.377634
$825$	−4.73166	−0.164735
$826$	−39.6134	−1.37833
$827$	19.1152	0.664700	0.332350	−	0.943156i	$-0.392158\pi$
$827$	19.1152	0.664700	0.332350	+	0.943156i	$0.392158\pi$
$828$	18.3511	0.637745
$829$	38.3634	1.33242	0.666208	−	0.745766i	$-0.267916\pi$
$829$	38.3634	1.33242	0.666208	+	0.745766i	$0.267916\pi$
$830$	36.6965	1.27375
$831$	−22.4331	−0.778195
$832$	53.7565	1.86367
$833$	−2.26399	−0.0784425
$834$	−35.9180	−1.24374
$835$	5.60693	0.194036
$836$	−60.6853	−2.09885
$837$	6.37593	0.220384
$838$	107.168	3.70206
$839$	−10.3291	−0.356601	−0.178300	−	0.983976i	$-0.557060\pi$
$839$	−10.3291	−0.356601	−0.178300	+	0.983976i	$0.557060\pi$
$840$	23.8878	0.824208
$841$	14.9527	0.515612
$842$	−6.78139	−0.233702
$843$	3.49134	0.120248
$844$	66.6530	2.29429
$845$	11.0936	0.381631
$846$	−25.4890	−0.876330
$847$	−6.95114	−0.238844
$848$	−17.1853	−0.590145
$849$	60.8038	2.08678
$850$	6.26940	0.215039
$851$	8.12361	0.278474
$852$	−73.2623	−2.50992
$853$	16.8780	0.577893	0.288947	−	0.957345i	$-0.406695\pi$
$853$	16.8780	0.577893	0.288947	+	0.957345i	$0.406695\pi$
$854$	−10.5462	−0.360883
$855$	−13.4589	−0.460283
$856$	−111.909	−3.82496
$857$	22.2789	0.761033	0.380516	−	0.924774i	$-0.375746\pi$
$857$	22.2789	0.761033	0.380516	+	0.924774i	$0.375746\pi$
$858$	18.0914	0.617631
$859$	−18.5010	−0.631246	−0.315623	−	0.948885i	$-0.602213\pi$
$859$	−18.5010	−0.631246	−0.315623	+	0.948885i	$0.602213\pi$
$860$	1.53189	0.0522370
$861$	−14.7909	−0.504072
$862$	18.7014	0.636972
$863$	5.70698	0.194268	0.0971340	−	0.995271i	$-0.469032\pi$
$863$	5.70698	0.194268	0.0971340	+	0.995271i	$0.469032\pi$
$864$	28.9686	0.985533
$865$	13.0246	0.442850
$866$	−61.5729	−2.09233
$867$	−27.9227	−0.948305
$868$	−32.6731	−1.10900
$869$	7.13423	0.242012
$870$	−43.1710	−1.46363
$871$	4.97570	0.168595
$872$	−5.94665	−0.201379
$873$	26.0059	0.880167
$874$	−18.8564	−0.637827
$875$	−1.00000	−0.0338062
$876$	−82.4806	−2.78676
$877$	12.8712	0.434630	0.217315	−	0.976102i	$-0.430270\pi$
$877$	12.8712	0.434630	0.217315	+	0.976102i	$0.430270\pi$
$878$	45.7344	1.54346
$879$	−1.36225	−0.0459475
$880$	33.7925	1.13915
$881$	41.6313	1.40260	0.701298	−	0.712868i	$-0.252604\pi$
$881$	41.6313	1.40260	0.701298	+	0.712868i	$0.252604\pi$
$882$	−7.00494	−0.235869
$883$	−25.6113	−0.861888	−0.430944	−	0.902379i	$-0.641819\pi$
$883$	−25.6113	−0.861888	−0.430944	+	0.902379i	$0.641819\pi$
$884$	−17.7191	−0.595958
$885$	−33.6385	−1.13075
$886$	−0.478774	−0.0160847
$887$	10.4262	0.350078	0.175039	−	0.984562i	$-0.443995\pi$
$887$	10.4262	0.350078	0.175039	+	0.984562i	$0.443995\pi$
$888$	−151.627	−5.08827
$889$	0.982343	0.0329467
$890$	43.0117	1.44176
$891$	20.5039	0.686908
$892$	96.4208	3.22841
$893$	19.3600	0.647857
$894$	105.819	3.53911
$895$	−8.68570	−0.290331
$896$	−55.4368	−1.85201
$897$	4.15531	0.138742
$898$	−9.02222	−0.301075
$899$	38.2141	1.27451
$900$	14.3388	0.477960
$901$	2.31674	0.0771817
$902$	−35.0483	−1.16698
$903$	−0.635497	−0.0211480
$904$	−5.49886	−0.182889
$905$	−0.956005	−0.0317787
$906$	−19.4167	−0.645077
$907$	49.3486	1.63859	0.819296	−	0.573371i	$-0.194365\pi$
$907$	49.3486	1.63859	0.819296	+	0.573371i	$0.194365\pi$
$908$	120.149	3.98729
$909$	35.6322	1.18185
$910$	3.82349	0.126747
$911$	37.8304	1.25338	0.626689	−	0.779269i	$-0.284410\pi$
$911$	37.8304	1.25338	0.626689	+	0.779269i	$0.284410\pi$
$912$	210.115	6.95761
$913$	−26.6648	−0.882476
$914$	−87.2238	−2.88511
$915$	−8.95550	−0.296060
$916$	−5.66840	−0.187289
$917$	−0.953130	−0.0314751
$918$	−6.93489	−0.228886
$919$	6.87590	0.226815	0.113407	−	0.993549i	$-0.463823\pi$
$919$	6.87590	0.226815	0.113407	+	0.993549i	$0.463823\pi$
$920$	13.0011	0.428633
$921$	−44.5806	−1.46898
$922$	−73.9586	−2.43570
$923$	−7.58892	−0.249792
$924$	−26.8210	−0.882345
$925$	6.34746	0.208703
$926$	47.6331	1.56532
$927$	2.69934	0.0886579
$928$	173.623	5.69946
$929$	−17.4987	−0.574114	−0.287057	−	0.957913i	$-0.592677\pi$
$929$	−17.4987	−0.574114	−0.287057	+	0.957913i	$0.592677\pi$
$930$	−37.5344	−1.23080
$931$	5.32055	0.174374
$932$	19.2233	0.629679
$933$	70.2501	2.29989
$934$	2.43922	0.0798137
$935$	−4.55554	−0.148982
$936$	−35.4804	−1.15971
$937$	31.9830	1.04484	0.522419	−	0.852689i	$-0.325030\pi$
$937$	31.9830	1.04484	0.522419	+	0.852689i	$0.325030\pi$
$938$	−9.97929	−0.325835
$939$	0.739303	0.0241262
$940$	−20.6257	−0.672737
$941$	−24.1295	−0.786598	−0.393299	−	0.919411i	$-0.628666\pi$
$941$	−24.1295	−0.786598	−0.393299	+	0.919411i	$0.628666\pi$
$942$	−153.698	−5.00776
$943$	−8.05002	−0.262145
$944$	240.239	7.81912
$945$	1.10615	0.0359830
$946$	−1.50586	−0.0489598
$947$	46.9113	1.52441	0.762206	−	0.647334i	$-0.224116\pi$
$947$	46.9113	1.52441	0.762206	+	0.647334i	$0.224116\pi$
$948$	−47.2594	−1.53491
$949$	−8.54380	−0.277343
$950$	−14.7336	−0.478021
$951$	68.1251	2.20911
$952$	22.9987	0.745392
$953$	21.2605	0.688695	0.344347	−	0.938842i	$-0.388100\pi$
$953$	21.2605	0.688695	0.344347	+	0.938842i	$0.388100\pi$
$954$	7.16815	0.232078
$955$	16.7279	0.541301
$956$	146.624	4.74215
$957$	31.3694	1.01403
$958$	37.9531	1.22621
$959$	6.62358	0.213887
$960$	−91.5526	−2.95485
$961$	2.22463	0.0717624
$962$	−24.2694	−0.782477
$963$	27.8667	0.897993
$964$	48.4370	1.56005
$965$	6.62160	0.213157
$966$	−8.33391	−0.268139
$967$	−24.5416	−0.789204	−0.394602	−	0.918852i	$-0.629117\pi$
$967$	−24.5416	−0.789204	−0.394602	+	0.918852i	$0.629117\pi$
$968$	70.6131	2.26959
$969$	−28.3255	−0.909945
$970$	28.4690	0.914085
$971$	−1.30780	−0.0419694	−0.0209847	−	0.999780i	$-0.506680\pi$
$971$	−1.30780	−0.0419694	−0.0209847	+	0.999780i	$0.506680\pi$
$972$	−117.014	−3.75324
$973$	5.51586	0.176830
$974$	57.3569	1.83783
$975$	3.24679	0.103980
$976$	63.9583	2.04725
$977$	12.2205	0.390968	0.195484	−	0.980707i	$-0.437372\pi$
$977$	12.2205	0.390968	0.195484	+	0.980707i	$0.437372\pi$
$978$	−86.3322	−2.76060
$979$	−31.2537	−0.998872
$980$	−5.66840	−0.181071
$981$	1.48079	0.0472781
$982$	23.3853	0.746254
$983$	6.42199	0.204830	0.102415	−	0.994742i	$-0.467343\pi$
$983$	6.42199	0.204830	0.102415	+	0.994742i	$0.467343\pi$
$984$	150.253	4.78990
$985$	−9.38540	−0.299044
$986$	−41.5642	−1.32367
$987$	8.55649	0.272356
$988$	41.6413	1.32479
$989$	−0.345873	−0.0109981
$990$	−14.0952	−0.447975
$991$	8.59631	0.273071	0.136535	−	0.990635i	$-0.456403\pi$
$991$	8.59631	0.273071	0.136535	+	0.990635i	$0.456403\pi$
$992$	150.954	4.79279
$993$	46.7546	1.48371
$994$	15.2204	0.482761
$995$	18.3566	0.581943
$996$	176.636	5.59693
$997$	−44.6557	−1.41426	−0.707130	−	0.707084i	$-0.750010\pi$
$997$	−44.6557	−1.41426	−0.707130	+	0.707084i	$0.750010\pi$
$998$	−48.3614	−1.53085
$999$	−7.02123	−0.222142

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.76919 q^{2} +2.35151 q^{3} +5.66840 q^{4} -1.00000 q^{5} -6.51177 q^{6} +1.00000 q^{7} -10.1585 q^{8} +2.52960 q^{9} +O(q^{10})\)	\(q-2.76919 q^{2} +2.35151 q^{3} +5.66840 q^{4} -1.00000 q^{5} -6.51177 q^{6} +1.00000 q^{7} -10.1585 q^{8} +2.52960 q^{9} +2.76919 q^{10} -2.01218 q^{11} +13.3293 q^{12} +1.38072 q^{13} -2.76919 q^{14} -2.35151 q^{15} +16.7940 q^{16} -2.26399 q^{17} -7.00494 q^{18} +5.32055 q^{19} -5.66840 q^{20} +2.35151 q^{21} +5.57210 q^{22} +1.27982 q^{23} -23.8878 q^{24} +1.00000 q^{25} -3.82349 q^{26} -1.10615 q^{27} +5.66840 q^{28} -6.62969 q^{29} +6.51177 q^{30} -5.76408 q^{31} -26.1887 q^{32} -4.73166 q^{33} +6.26940 q^{34} -1.00000 q^{35} +14.3388 q^{36} +6.34746 q^{37} -14.7336 q^{38} +3.24679 q^{39} +10.1585 q^{40} -6.28995 q^{41} -6.51177 q^{42} -0.270250 q^{43} -11.4058 q^{44} -2.52960 q^{45} -3.54407 q^{46} +3.63872 q^{47} +39.4912 q^{48} +1.00000 q^{49} -2.76919 q^{50} -5.32379 q^{51} +7.82650 q^{52} -1.02330 q^{53} +3.06313 q^{54} +2.01218 q^{55} -10.1585 q^{56} +12.5113 q^{57} +18.3589 q^{58} +14.3051 q^{59} -13.3293 q^{60} +3.80840 q^{61} +15.9618 q^{62} +2.52960 q^{63} +38.9335 q^{64} -1.38072 q^{65} +13.1029 q^{66} +3.60369 q^{67} -12.8332 q^{68} +3.00951 q^{69} +2.76919 q^{70} -5.49633 q^{71} -25.6969 q^{72} -6.18791 q^{73} -17.5773 q^{74} +2.35151 q^{75} +30.1590 q^{76} -2.01218 q^{77} -8.99097 q^{78} -3.54552 q^{79} -16.7940 q^{80} -10.1899 q^{81} +17.4181 q^{82} +13.2517 q^{83} +13.3293 q^{84} +2.26399 q^{85} +0.748374 q^{86} -15.5898 q^{87} +20.4407 q^{88} +15.5323 q^{89} +7.00494 q^{90} +1.38072 q^{91} +7.25455 q^{92} -13.5543 q^{93} -10.0763 q^{94} -5.32055 q^{95} -61.5831 q^{96} +10.2806 q^{97} -2.76919 q^{98} -5.09001 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9}+O(q^{10}) \) 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9} - 9 q^{10} + 5 q^{11} + 9 q^{12} + 15 q^{13} + 9 q^{14} + 109 q^{16} + 7 q^{17} + 39 q^{18} + 20 q^{19} - 83 q^{20} + 56 q^{22} + 36 q^{23} + q^{24} + 68 q^{25} + q^{26} + 12 q^{27} + 83 q^{28} - 16 q^{29} - 5 q^{30} + 31 q^{31} + 79 q^{32} + 45 q^{33} + 31 q^{34} - 68 q^{35} + 114 q^{36} + 72 q^{37} + 8 q^{38} + 47 q^{39} - 30 q^{40} + 6 q^{41} + 5 q^{42} + 75 q^{43} + 15 q^{44} - 86 q^{45} + 29 q^{46} - 10 q^{47} + 44 q^{48} + 68 q^{49} + 9 q^{50} + 23 q^{51} + 37 q^{52} + 41 q^{53} + 4 q^{54} - 5 q^{55} + 30 q^{56} + 55 q^{57} + 66 q^{58} - 5 q^{59} - 9 q^{60} - 2 q^{61} + 3 q^{62} + 86 q^{63} + 162 q^{64} - 15 q^{65} - 23 q^{66} + 92 q^{67} + 35 q^{68} - 25 q^{69} - 9 q^{70} - 2 q^{71} + 128 q^{72} + 80 q^{73} + 18 q^{74} + 71 q^{76} + 5 q^{77} + 20 q^{78} + 100 q^{79} - 109 q^{80} + 140 q^{81} + 36 q^{82} - 60 q^{83} + 9 q^{84} - 7 q^{85} - 27 q^{86} + 24 q^{87} + 175 q^{88} + 19 q^{89} - 39 q^{90} + 15 q^{91} + 75 q^{92} + 37 q^{93} + 11 q^{94} - 20 q^{95} + 15 q^{96} + 96 q^{97} + 9 q^{98} + 3 q^{99}+O(q^{100}) \) 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9 - 9 * q^10 + 5 * q^11 + 9 * q^12 + 15 * q^13 + 9 * q^14 + 109 * q^16 + 7 * q^17 + 39 * q^18 + 20 * q^19 - 83 * q^20 + 56 * q^22 + 36 * q^23 + q^24 + 68 * q^25 + q^26 + 12 * q^27 + 83 * q^28 - 16 * q^29 - 5 * q^30 + 31 * q^31 + 79 * q^32 + 45 * q^33 + 31 * q^34 - 68 * q^35 + 114 * q^36 + 72 * q^37 + 8 * q^38 + 47 * q^39 - 30 * q^40 + 6 * q^41 + 5 * q^42 + 75 * q^43 + 15 * q^44 - 86 * q^45 + 29 * q^46 - 10 * q^47 + 44 * q^48 + 68 * q^49 + 9 * q^50 + 23 * q^51 + 37 * q^52 + 41 * q^53 + 4 * q^54 - 5 * q^55 + 30 * q^56 + 55 * q^57 + 66 * q^58 - 5 * q^59 - 9 * q^60 - 2 * q^61 + 3 * q^62 + 86 * q^63 + 162 * q^64 - 15 * q^65 - 23 * q^66 + 92 * q^67 + 35 * q^68 - 25 * q^69 - 9 * q^70 - 2 * q^71 + 128 * q^72 + 80 * q^73 + 18 * q^74 + 71 * q^76 + 5 * q^77 + 20 * q^78 + 100 * q^79 - 109 * q^80 + 140 * q^81 + 36 * q^82 - 60 * q^83 + 9 * q^84 - 7 * q^85 - 27 * q^86 + 24 * q^87 + 175 * q^88 + 19 * q^89 - 39 * q^90 + 15 * q^91 + 75 * q^92 + 37 * q^93 + 11 * q^94 - 20 * q^95 + 15 * q^96 + 96 * q^97 + 9 * q^98 + 3 * q^99

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