LMFDB - Embedded newform 2415.2.a.p.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2415,2,Mod(1,2415)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2415, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2415.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2415 = 3 \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2415.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:	$19.2838720881$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.42978136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 6x^{3} + 16x^{2} - 7x - 9 $ x^6 - x^5 - 8x^4 + 6x^3 + 16x^2 - 7x - 9
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.50731$ of defining polynomial
Character	$\chi$	$=$	2415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.50731 q^{2} -1.00000 q^{3} +0.271970 q^{4} -1.00000 q^{5} -1.50731 q^{6} -1.00000 q^{7} -2.60467 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.50731 q^{2} -1.00000 q^{3} +0.271970 q^{4} -1.00000 q^{5} -1.50731 q^{6} -1.00000 q^{7} -2.60467 q^{8} +1.00000 q^{9} -1.50731 q^{10} +2.60724 q^{11} -0.271970 q^{12} -2.83255 q^{13} -1.50731 q^{14} +1.00000 q^{15} -4.46997 q^{16} +4.57882 q^{17} +1.50731 q^{18} -0.659697 q^{19} -0.271970 q^{20} +1.00000 q^{21} +3.92991 q^{22} +1.00000 q^{23} +2.60467 q^{24} +1.00000 q^{25} -4.26951 q^{26} -1.00000 q^{27} -0.271970 q^{28} -10.5404 q^{29} +1.50731 q^{30} +8.42598 q^{31} -1.52827 q^{32} -2.60724 q^{33} +6.90168 q^{34} +1.00000 q^{35} +0.271970 q^{36} -3.37649 q^{37} -0.994366 q^{38} +2.83255 q^{39} +2.60467 q^{40} +7.83365 q^{41} +1.50731 q^{42} +12.0478 q^{43} +0.709091 q^{44} -1.00000 q^{45} +1.50731 q^{46} +9.01461 q^{47} +4.46997 q^{48} +1.00000 q^{49} +1.50731 q^{50} -4.57882 q^{51} -0.770367 q^{52} -5.60749 q^{53} -1.50731 q^{54} -2.60724 q^{55} +2.60467 q^{56} +0.659697 q^{57} -15.8876 q^{58} -8.77434 q^{59} +0.271970 q^{60} +7.51361 q^{61} +12.7005 q^{62} -1.00000 q^{63} +6.63637 q^{64} +2.83255 q^{65} -3.92991 q^{66} +7.98943 q^{67} +1.24530 q^{68} -1.00000 q^{69} +1.50731 q^{70} +6.63001 q^{71} -2.60467 q^{72} +16.1279 q^{73} -5.08940 q^{74} -1.00000 q^{75} -0.179418 q^{76} -2.60724 q^{77} +4.26951 q^{78} -4.25373 q^{79} +4.46997 q^{80} +1.00000 q^{81} +11.8077 q^{82} +10.0043 q^{83} +0.271970 q^{84} -4.57882 q^{85} +18.1598 q^{86} +10.5404 q^{87} -6.79101 q^{88} +8.61510 q^{89} -1.50731 q^{90} +2.83255 q^{91} +0.271970 q^{92} -8.42598 q^{93} +13.5878 q^{94} +0.659697 q^{95} +1.52827 q^{96} +8.49335 q^{97} +1.50731 q^{98} +2.60724 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 6 q^{3} + 5 q^{4} - 6 q^{5} - q^{6} - 6 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + q^2 - 6 * q^3 + 5 * q^4 - 6 * q^5 - q^6 - 6 * q^7 + 3 * q^8 + 6 * q^9	\( 6 q + q^{2} - 6 q^{3} + 5 q^{4} - 6 q^{5} - q^{6} - 6 q^{7} + 3 q^{8} + 6 q^{9} - q^{10} - 6 q^{11} - 5 q^{12} + 6 q^{13} - q^{14} + 6 q^{15} - 5 q^{16} + 16 q^{17} + q^{18} - 5 q^{20} + 6 q^{21} - 10 q^{22} + 6 q^{23} - 3 q^{24} + 6 q^{25} + 3 q^{26} - 6 q^{27} - 5 q^{28} - 4 q^{29} + q^{30} + 2 q^{32} + 6 q^{33} - 3 q^{34} + 6 q^{35} + 5 q^{36} - 4 q^{37} + 22 q^{38} - 6 q^{39} - 3 q^{40} + 4 q^{41} + q^{42} - 16 q^{43} - 13 q^{44} - 6 q^{45} + q^{46} + 38 q^{47} + 5 q^{48} + 6 q^{49} + q^{50} - 16 q^{51} + 24 q^{52} + 24 q^{53} - q^{54} + 6 q^{55} - 3 q^{56} + 2 q^{58} + 2 q^{59} + 5 q^{60} - 4 q^{61} + 26 q^{62} - 6 q^{63} + 7 q^{64} - 6 q^{65} + 10 q^{66} - 30 q^{67} + 54 q^{68} - 6 q^{69} + q^{70} - 6 q^{71} + 3 q^{72} + 38 q^{73} - 7 q^{74} - 6 q^{75} + 3 q^{76} + 6 q^{77} - 3 q^{78} - 14 q^{79} + 5 q^{80} + 6 q^{81} + 56 q^{82} + 22 q^{83} + 5 q^{84} - 16 q^{85} + 48 q^{86} + 4 q^{87} - 21 q^{88} + 20 q^{89} - q^{90} - 6 q^{91} + 5 q^{92} + 40 q^{94} - 2 q^{96} + 4 q^{97} + q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q + q^2 - 6 * q^3 + 5 * q^4 - 6 * q^5 - q^6 - 6 * q^7 + 3 * q^8 + 6 * q^9 - q^10 - 6 * q^11 - 5 * q^12 + 6 * q^13 - q^14 + 6 * q^15 - 5 * q^16 + 16 * q^17 + q^18 - 5 * q^20 + 6 * q^21 - 10 * q^22 + 6 * q^23 - 3 * q^24 + 6 * q^25 + 3 * q^26 - 6 * q^27 - 5 * q^28 - 4 * q^29 + q^30 + 2 * q^32 + 6 * q^33 - 3 * q^34 + 6 * q^35 + 5 * q^36 - 4 * q^37 + 22 * q^38 - 6 * q^39 - 3 * q^40 + 4 * q^41 + q^42 - 16 * q^43 - 13 * q^44 - 6 * q^45 + q^46 + 38 * q^47 + 5 * q^48 + 6 * q^49 + q^50 - 16 * q^51 + 24 * q^52 + 24 * q^53 - q^54 + 6 * q^55 - 3 * q^56 + 2 * q^58 + 2 * q^59 + 5 * q^60 - 4 * q^61 + 26 * q^62 - 6 * q^63 + 7 * q^64 - 6 * q^65 + 10 * q^66 - 30 * q^67 + 54 * q^68 - 6 * q^69 + q^70 - 6 * q^71 + 3 * q^72 + 38 * q^73 - 7 * q^74 - 6 * q^75 + 3 * q^76 + 6 * q^77 - 3 * q^78 - 14 * q^79 + 5 * q^80 + 6 * q^81 + 56 * q^82 + 22 * q^83 + 5 * q^84 - 16 * q^85 + 48 * q^86 + 4 * q^87 - 21 * q^88 + 20 * q^89 - q^90 - 6 * q^91 + 5 * q^92 + 40 * q^94 - 2 * q^96 + 4 * q^97 + q^98 - 6 * 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 $

$2$	1.50731	1.06583	0.532913	−	0.846170i	$-0.321097\pi$
$2$	1.50731	1.06583	0.532913	+	0.846170i	$0.321097\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.271970	0.135985
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.50731	−0.615355
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.60467	−0.920890
$9$	1.00000	0.333333
$10$	−1.50731	−0.476652
$11$	2.60724	0.786113	0.393057	−	0.919514i	$-0.371418\pi$
$11$	2.60724	0.786113	0.393057	+	0.919514i	$0.371418\pi$
$12$	−0.271970	−0.0785109
$13$	−2.83255	−0.785607	−0.392804	−	0.919622i	$-0.628495\pi$
$13$	−2.83255	−0.785607	−0.392804	+	0.919622i	$0.628495\pi$
$14$	−1.50731	−0.402844
$15$	1.00000	0.258199
$16$	−4.46997	−1.11749
$17$	4.57882	1.11053	0.555263	−	0.831675i	$-0.312618\pi$
$17$	4.57882	1.11053	0.555263	+	0.831675i	$0.312618\pi$
$18$	1.50731	0.355275
$19$	−0.659697	−0.151345	−0.0756725	−	0.997133i	$-0.524110\pi$
$19$	−0.659697	−0.151345	−0.0756725	+	0.997133i	$0.524110\pi$
$20$	−0.271970	−0.0608142
$21$	1.00000	0.218218
$22$	3.92991	0.837860
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.60467	0.531676
$25$	1.00000	0.200000
$26$	−4.26951	−0.837321
$27$	−1.00000	−0.192450
$28$	−0.271970	−0.0513974
$29$	−10.5404	−1.95731	−0.978654	−	0.205514i	$-0.934114\pi$
$29$	−10.5404	−1.95731	−0.978654	+	0.205514i	$0.934114\pi$
$30$	1.50731	0.275195
$31$	8.42598	1.51335	0.756675	−	0.653791i	$-0.226823\pi$
$31$	8.42598	1.51335	0.756675	+	0.653791i	$0.226823\pi$
$32$	−1.52827	−0.270163
$33$	−2.60724	−0.453863
$34$	6.90168	1.18363
$35$	1.00000	0.169031
$36$	0.271970	0.0453283
$37$	−3.37649	−0.555091	−0.277546	−	0.960712i	$-0.589521\pi$
$37$	−3.37649	−0.555091	−0.277546	+	0.960712i	$0.589521\pi$
$38$	−0.994366	−0.161307
$39$	2.83255	0.453571
$40$	2.60467	0.411834
$41$	7.83365	1.22341	0.611705	−	0.791086i	$-0.290484\pi$
$41$	7.83365	1.22341	0.611705	+	0.791086i	$0.290484\pi$
$42$	1.50731	0.232582
$43$	12.0478	1.83728	0.918638	−	0.395099i	$-0.129290\pi$
$43$	12.0478	1.83728	0.918638	+	0.395099i	$0.129290\pi$
$44$	0.709091	0.106899
$45$	−1.00000	−0.149071
$46$	1.50731	0.222240
$47$	9.01461	1.31492	0.657458	−	0.753491i	$-0.271632\pi$
$47$	9.01461	1.31492	0.657458	+	0.753491i	$0.271632\pi$
$48$	4.46997	0.645185
$49$	1.00000	0.142857
$50$	1.50731	0.213165
$51$	−4.57882	−0.641163
$52$	−0.770367	−0.106831
$53$	−5.60749	−0.770249	−0.385124	−	0.922865i	$-0.625841\pi$
$53$	−5.60749	−0.770249	−0.385124	+	0.922865i	$0.625841\pi$
$54$	−1.50731	−0.205118
$55$	−2.60724	−0.351561
$56$	2.60467	0.348064
$57$	0.659697	0.0873791
$58$	−15.8876	−2.08615
$59$	−8.77434	−1.14232	−0.571161	−	0.820838i	$-0.693507\pi$
$59$	−8.77434	−1.14232	−0.571161	+	0.820838i	$0.693507\pi$
$60$	0.271970	0.0351111
$61$	7.51361	0.962020	0.481010	−	0.876715i	$-0.340270\pi$
$61$	7.51361	0.962020	0.481010	+	0.876715i	$0.340270\pi$
$62$	12.7005	1.61297
$63$	−1.00000	−0.125988
$64$	6.63637	0.829546
$65$	2.83255	0.351334
$66$	−3.92991	−0.483739
$67$	7.98943	0.976065	0.488032	−	0.872826i	$-0.337715\pi$
$67$	7.98943	0.976065	0.488032	+	0.872826i	$0.337715\pi$
$68$	1.24530	0.151015
$69$	−1.00000	−0.120386
$70$	1.50731	0.180157
$71$	6.63001	0.786838	0.393419	−	0.919359i	$-0.371292\pi$
$71$	6.63001	0.786838	0.393419	+	0.919359i	$0.371292\pi$
$72$	−2.60467	−0.306963
$73$	16.1279	1.88763	0.943815	−	0.330475i	$-0.107209\pi$
$73$	16.1279	1.88763	0.943815	+	0.330475i	$0.107209\pi$
$74$	−5.08940	−0.591630
$75$	−1.00000	−0.115470
$76$	−0.179418	−0.0205806
$77$	−2.60724	−0.297123
$78$	4.26951	0.483427
$79$	−4.25373	−0.478582	−0.239291	−	0.970948i	$-0.576915\pi$
$79$	−4.25373	−0.478582	−0.239291	+	0.970948i	$0.576915\pi$
$80$	4.46997	0.499758
$81$	1.00000	0.111111
$82$	11.8077	1.30394
$83$	10.0043	1.09811	0.549057	−	0.835785i	$-0.314987\pi$
$83$	10.0043	1.09811	0.549057	+	0.835785i	$0.314987\pi$
$84$	0.271970	0.0296743
$85$	−4.57882	−0.496643
$86$	18.1598	1.95822
$87$	10.5404	1.13005
$88$	−6.79101	−0.723924
$89$	8.61510	0.913198	0.456599	−	0.889673i	$-0.349067\pi$
$89$	8.61510	0.913198	0.456599	+	0.889673i	$0.349067\pi$
$90$	−1.50731	−0.158884
$91$	2.83255	0.296932
$92$	0.271970	0.0283548
$93$	−8.42598	−0.873733
$94$	13.5878	1.40147
$95$	0.659697	0.0676835
$96$	1.52827	0.155979
$97$	8.49335	0.862369	0.431184	−	0.902264i	$-0.358096\pi$
$97$	8.49335	0.862369	0.431184	+	0.902264i	$0.358096\pi$
$98$	1.50731	0.152261
$99$	2.60724	0.262038
$100$	0.271970	0.0271970
$101$	−9.55555	−0.950813	−0.475406	−	0.879766i	$-0.657699\pi$
$101$	−9.55555	−0.950813	−0.475406	+	0.879766i	$0.657699\pi$
$102$	−6.90168	−0.683368
$103$	−5.07006	−0.499568	−0.249784	−	0.968302i	$-0.580360\pi$
$103$	−5.07006	−0.499568	−0.249784	+	0.968302i	$0.580360\pi$
$104$	7.37785	0.723458
$105$	−1.00000	−0.0975900
$106$	−8.45221	−0.820951
$107$	4.63758	0.448332	0.224166	−	0.974551i	$-0.428034\pi$
$107$	4.63758	0.448332	0.224166	+	0.974551i	$0.428034\pi$
$108$	−0.271970	−0.0261703
$109$	−11.2236	−1.07503	−0.537515	−	0.843254i	$-0.680637\pi$
$109$	−11.2236	−1.07503	−0.537515	+	0.843254i	$0.680637\pi$
$110$	−3.92991	−0.374702
$111$	3.37649	0.320482
$112$	4.46997	0.422373
$113$	13.0119	1.22405	0.612026	−	0.790838i	$-0.290355\pi$
$113$	13.0119	1.22405	0.612026	+	0.790838i	$0.290355\pi$
$114$	0.994366	0.0931309
$115$	−1.00000	−0.0932505
$116$	−2.86668	−0.266164
$117$	−2.83255	−0.261869
$118$	−13.2256	−1.21752
$119$	−4.57882	−0.419740
$120$	−2.60467	−0.237773
$121$	−4.20228	−0.382026
$122$	11.3253	1.02535
$123$	−7.83365	−0.706336
$124$	2.29161	0.205793
$125$	−1.00000	−0.0894427
$126$	−1.50731	−0.134281
$127$	−20.7546	−1.84167	−0.920837	−	0.389948i	$-0.872493\pi$
$127$	−20.7546	−1.84167	−0.920837	+	0.389948i	$0.872493\pi$
$128$	13.0596	1.15431
$129$	−12.0478	−1.06075
$130$	4.26951	0.374461
$131$	−1.37649	−0.120264	−0.0601321	−	0.998190i	$-0.519152\pi$
$131$	−1.37649	−0.120264	−0.0601321	+	0.998190i	$0.519152\pi$
$132$	−0.709091	−0.0617184
$133$	0.659697	0.0572030
$134$	12.0425	1.04031
$135$	1.00000	0.0860663
$136$	−11.9263	−1.02267
$137$	21.0687	1.80002	0.900010	−	0.435869i	$-0.143559\pi$
$137$	21.0687	1.80002	0.900010	+	0.435869i	$0.143559\pi$
$138$	−1.50731	−0.128310
$139$	−6.49149	−0.550601	−0.275300	−	0.961358i	$-0.588777\pi$
$139$	−6.49149	−0.550601	−0.275300	+	0.961358i	$0.588777\pi$
$140$	0.271970	0.0229856
$141$	−9.01461	−0.759167
$142$	9.99345	0.838632
$143$	−7.38514	−0.617577
$144$	−4.46997	−0.372498
$145$	10.5404	0.875335
$146$	24.3097	2.01188
$147$	−1.00000	−0.0824786
$148$	−0.918302	−0.0754839
$149$	−3.31889	−0.271894	−0.135947	−	0.990716i	$-0.543408\pi$
$149$	−3.31889	−0.271894	−0.135947	+	0.990716i	$0.543408\pi$
$150$	−1.50731	−0.123071
$151$	−5.07091	−0.412665	−0.206332	−	0.978482i	$-0.566153\pi$
$151$	−5.07091	−0.412665	−0.206332	+	0.978482i	$0.566153\pi$
$152$	1.71829	0.139372
$153$	4.57882	0.370175
$154$	−3.92991	−0.316681
$155$	−8.42598	−0.676791
$156$	0.770367	0.0616787
$157$	0.847512	0.0676388	0.0338194	−	0.999428i	$-0.489233\pi$
$157$	0.847512	0.0676388	0.0338194	+	0.999428i	$0.489233\pi$
$158$	−6.41167	−0.510085
$159$	5.60749	0.444703
$160$	1.52827	0.120821
$161$	−1.00000	−0.0788110
$162$	1.50731	0.118425
$163$	18.2319	1.42804	0.714018	−	0.700127i	$-0.246873\pi$
$163$	18.2319	1.42804	0.714018	+	0.700127i	$0.246873\pi$
$164$	2.13051	0.166365
$165$	2.60724	0.202974
$166$	15.0795	1.17040
$167$	−4.29371	−0.332257	−0.166129	−	0.986104i	$-0.553127\pi$
$167$	−4.29371	−0.332257	−0.166129	+	0.986104i	$0.553127\pi$
$168$	−2.60467	−0.200955
$169$	−4.97667	−0.382821
$170$	−6.90168	−0.529334
$171$	−0.659697	−0.0504483
$172$	3.27664	0.249842
$173$	11.5656	0.879313	0.439657	−	0.898166i	$-0.355100\pi$
$173$	11.5656	0.879313	0.439657	+	0.898166i	$0.355100\pi$
$174$	15.8876	1.20444
$175$	−1.00000	−0.0755929
$176$	−11.6543	−0.878476
$177$	8.77434	0.659520
$178$	12.9856	0.973310
$179$	−12.9614	−0.968781	−0.484390	−	0.874852i	$-0.660959\pi$
$179$	−12.9614	−0.968781	−0.484390	+	0.874852i	$0.660959\pi$
$180$	−0.271970	−0.0202714
$181$	9.85170	0.732271	0.366136	−	0.930561i	$-0.380681\pi$
$181$	9.85170	0.732271	0.366136	+	0.930561i	$0.380681\pi$
$182$	4.26951	0.316477
$183$	−7.51361	−0.555422
$184$	−2.60467	−0.192019
$185$	3.37649	0.248244
$186$	−12.7005	−0.931247
$187$	11.9381	0.873000
$188$	2.45170	0.178809
$189$	1.00000	0.0727393
$190$	0.994366	0.0721389
$191$	1.70133	0.123104	0.0615521	−	0.998104i	$-0.480395\pi$
$191$	1.70133	0.123104	0.0615521	+	0.998104i	$0.480395\pi$
$192$	−6.63637	−0.478939
$193$	0.556845	0.0400826	0.0200413	−	0.999799i	$-0.493620\pi$
$193$	0.556845	0.0400826	0.0200413	+	0.999799i	$0.493620\pi$
$194$	12.8021	0.919135
$195$	−2.83255	−0.202843
$196$	0.271970	0.0194264
$197$	−14.2569	−1.01576	−0.507882	−	0.861427i	$-0.669571\pi$
$197$	−14.2569	−1.01576	−0.507882	+	0.861427i	$0.669571\pi$
$198$	3.92991	0.279287
$199$	7.38915	0.523803	0.261902	−	0.965095i	$-0.415650\pi$
$199$	7.38915	0.523803	0.261902	+	0.965095i	$0.415650\pi$
$200$	−2.60467	−0.184178
$201$	−7.98943	−0.563531
$202$	−14.4031	−1.01340
$203$	10.5404	0.739793
$204$	−1.24530	−0.0871884
$205$	−7.83365	−0.547126
$206$	−7.64213	−0.532453
$207$	1.00000	0.0695048
$208$	12.6614	0.877911
$209$	−1.71999	−0.118974
$210$	−1.50731	−0.104014
$211$	−25.8784	−1.78154	−0.890772	−	0.454450i	$-0.849836\pi$
$211$	−25.8784	−1.78154	−0.890772	+	0.454450i	$0.849836\pi$
$212$	−1.52507	−0.104742
$213$	−6.63001	−0.454281
$214$	6.99025	0.477843
$215$	−12.0478	−0.821655
$216$	2.60467	0.177225
$217$	−8.42598	−0.571993
$218$	−16.9175	−1.14580
$219$	−16.1279	−1.08982
$220$	−0.709091	−0.0478069
$221$	−12.9697	−0.872438
$222$	5.08940	0.341578
$223$	−24.9678	−1.67196	−0.835982	−	0.548756i	$-0.815101\pi$
$223$	−24.9678	−1.67196	−0.835982	+	0.548756i	$0.815101\pi$
$224$	1.52827	0.102112
$225$	1.00000	0.0666667
$226$	19.6128	1.30463
$227$	−14.5650	−0.966714	−0.483357	−	0.875423i	$-0.660583\pi$
$227$	−14.5650	−0.966714	−0.483357	+	0.875423i	$0.660583\pi$
$228$	0.179418	0.0118822
$229$	1.58188	0.104533	0.0522667	−	0.998633i	$-0.483355\pi$
$229$	1.58188	0.104533	0.0522667	+	0.998633i	$0.483355\pi$
$230$	−1.50731	−0.0993888
$231$	2.60724	0.171544
$232$	27.4543	1.80247
$233$	−16.3778	−1.07295	−0.536473	−	0.843917i	$-0.680244\pi$
$233$	−16.3778	−1.07295	−0.536473	+	0.843917i	$0.680244\pi$
$234$	−4.26951	−0.279107
$235$	−9.01461	−0.588048
$236$	−2.38635	−0.155338
$237$	4.25373	0.276309
$238$	−6.90168	−0.447369
$239$	26.4886	1.71341	0.856703	−	0.515809i	$-0.172509\pi$
$239$	26.4886	1.71341	0.856703	+	0.515809i	$0.172509\pi$
$240$	−4.46997	−0.288535
$241$	5.23767	0.337388	0.168694	−	0.985668i	$-0.446045\pi$
$241$	5.23767	0.337388	0.168694	+	0.985668i	$0.446045\pi$
$242$	−6.33412	−0.407173
$243$	−1.00000	−0.0641500
$244$	2.04347	0.130820
$245$	−1.00000	−0.0638877
$246$	−11.8077	−0.752831
$247$	1.86862	0.118898
$248$	−21.9469	−1.39363
$249$	−10.0043	−0.633997
$250$	−1.50731	−0.0953304
$251$	−12.8115	−0.808652	−0.404326	−	0.914615i	$-0.632494\pi$
$251$	−12.8115	−0.808652	−0.404326	+	0.914615i	$0.632494\pi$
$252$	−0.271970	−0.0171325
$253$	2.60724	0.163916
$254$	−31.2835	−1.96290
$255$	4.57882	0.286737
$256$	6.41204	0.400752
$257$	28.1574	1.75641	0.878205	−	0.478285i	$-0.158741\pi$
$257$	28.1574	1.75641	0.878205	+	0.478285i	$0.158741\pi$
$258$	−18.1598	−1.13058
$259$	3.37649	0.209805
$260$	0.770367	0.0477761
$261$	−10.5404	−0.652436
$262$	−2.07479	−0.128181
$263$	−1.60189	−0.0987765	−0.0493882	−	0.998780i	$-0.515727\pi$
$263$	−1.60189	−0.0987765	−0.0493882	+	0.998780i	$0.515727\pi$
$264$	6.79101	0.417958
$265$	5.60749	0.344466
$266$	0.994366	0.0609685
$267$	−8.61510	−0.527235
$268$	2.17288	0.132730
$269$	5.72756	0.349215	0.174608	−	0.984638i	$-0.444134\pi$
$269$	5.72756	0.349215	0.174608	+	0.984638i	$0.444134\pi$
$270$	1.50731	0.0917317
$271$	19.9653	1.21281	0.606403	−	0.795157i	$-0.292612\pi$
$271$	19.9653	1.21281	0.606403	+	0.795157i	$0.292612\pi$
$272$	−20.4672	−1.24101
$273$	−2.83255	−0.171434
$274$	31.7570	1.91851
$275$	2.60724	0.157223
$276$	−0.271970	−0.0163706
$277$	21.5223	1.29315	0.646574	−	0.762852i	$-0.276201\pi$
$277$	21.5223	1.29315	0.646574	+	0.762852i	$0.276201\pi$
$278$	−9.78465	−0.586844
$279$	8.42598	0.504450
$280$	−2.60467	−0.155659
$281$	27.0198	1.61187	0.805934	−	0.592005i	$-0.201663\pi$
$281$	27.0198	1.61187	0.805934	+	0.592005i	$0.201663\pi$
$282$	−13.5878	−0.809140
$283$	−23.0332	−1.36918	−0.684590	−	0.728929i	$-0.740019\pi$
$283$	−23.0332	−1.36918	−0.684590	+	0.728929i	$0.740019\pi$
$284$	1.80316	0.106998
$285$	−0.659697	−0.0390771
$286$	−11.1317	−0.658229
$287$	−7.83365	−0.462406
$288$	−1.52827	−0.0900544
$289$	3.96557	0.233269
$290$	15.8876	0.932955
$291$	−8.49335	−0.497889
$292$	4.38630	0.256689
$293$	8.54945	0.499464	0.249732	−	0.968315i	$-0.419657\pi$
$293$	8.54945	0.499464	0.249732	+	0.968315i	$0.419657\pi$
$294$	−1.50731	−0.0879078
$295$	8.77434	0.510862
$296$	8.79463	0.511178
$297$	−2.60724	−0.151288
$298$	−5.00257	−0.289791
$299$	−2.83255	−0.163810
$300$	−0.271970	−0.0157022
$301$	−12.0478	−0.694425
$302$	−7.64341	−0.439829
$303$	9.55555	0.548952
$304$	2.94883	0.169127
$305$	−7.51361	−0.430228
$306$	6.90168	0.394543
$307$	−11.8379	−0.675624	−0.337812	−	0.941214i	$-0.609687\pi$
$307$	−11.8379	−0.675624	−0.337812	+	0.941214i	$0.609687\pi$
$308$	−0.709091	−0.0404042
$309$	5.07006	0.288426
$310$	−12.7005	−0.721341
$311$	8.93405	0.506603	0.253302	−	0.967387i	$-0.418483\pi$
$311$	8.93405	0.506603	0.253302	+	0.967387i	$0.418483\pi$
$312$	−7.37785	−0.417689
$313$	−16.1598	−0.913408	−0.456704	−	0.889619i	$-0.650970\pi$
$313$	−16.1598	−0.913408	−0.456704	+	0.889619i	$0.650970\pi$
$314$	1.27746	0.0720912
$315$	1.00000	0.0563436
$316$	−1.15689	−0.0650799
$317$	13.5605	0.761631	0.380816	−	0.924651i	$-0.375643\pi$
$317$	13.5605	0.761631	0.380816	+	0.924651i	$0.375643\pi$
$318$	8.45221	0.473976
$319$	−27.4815	−1.53867
$320$	−6.63637	−0.370984
$321$	−4.63758	−0.258844
$322$	−1.50731	−0.0839988
$323$	−3.02063	−0.168073
$324$	0.271970	0.0151094
$325$	−2.83255	−0.157121
$326$	27.4811	1.52204
$327$	11.2236	0.620669
$328$	−20.4041	−1.12663
$329$	−9.01461	−0.496992
$330$	3.92991	0.216335
$331$	−9.66561	−0.531270	−0.265635	−	0.964074i	$-0.585582\pi$
$331$	−9.66561	−0.531270	−0.265635	+	0.964074i	$0.585582\pi$
$332$	2.72087	0.149327
$333$	−3.37649	−0.185030
$334$	−6.47193	−0.354128
$335$	−7.98943	−0.436509
$336$	−4.46997	−0.243857
$337$	7.99533	0.435533	0.217767	−	0.976001i	$-0.430123\pi$
$337$	7.99533	0.435533	0.217767	+	0.976001i	$0.430123\pi$
$338$	−7.50137	−0.408021
$339$	−13.0119	−0.706707
$340$	−1.24530	−0.0675358
$341$	21.9686	1.18966
$342$	−0.994366	−0.0537691
$343$	−1.00000	−0.0539949
$344$	−31.3806	−1.69193
$345$	1.00000	0.0538382
$346$	17.4328	0.937195
$347$	4.26889	0.229166	0.114583	−	0.993414i	$-0.463447\pi$
$347$	4.26889	0.229166	0.114583	+	0.993414i	$0.463447\pi$
$348$	2.86668	0.153670
$349$	21.5326	1.15261	0.576306	−	0.817234i	$-0.304494\pi$
$349$	21.5326	1.15261	0.576306	+	0.817234i	$0.304494\pi$
$350$	−1.50731	−0.0805689
$351$	2.83255	0.151190
$352$	−3.98458	−0.212379
$353$	0.396563	0.0211069	0.0105534	−	0.999944i	$-0.496641\pi$
$353$	0.396563	0.0211069	0.0105534	+	0.999944i	$0.496641\pi$
$354$	13.2256	0.702933
$355$	−6.63001	−0.351884
$356$	2.34304	0.124181
$357$	4.57882	0.242337
$358$	−19.5368	−1.03255
$359$	10.3343	0.545423	0.272712	−	0.962096i	$-0.412080\pi$
$359$	10.3343	0.545423	0.272712	+	0.962096i	$0.412080\pi$
$360$	2.60467	0.137278
$361$	−18.5648	−0.977095
$362$	14.8495	0.780474
$363$	4.20228	0.220563
$364$	0.770367	0.0403782
$365$	−16.1279	−0.844174
$366$	−11.3253	−0.591983
$367$	−1.78030	−0.0929308	−0.0464654	−	0.998920i	$-0.514796\pi$
$367$	−1.78030	−0.0929308	−0.0464654	+	0.998920i	$0.514796\pi$
$368$	−4.46997	−0.233013
$369$	7.83365	0.407803
$370$	5.08940	0.264585
$371$	5.60749	0.291127
$372$	−2.29161	−0.118814
$373$	−22.0213	−1.14022	−0.570110	−	0.821568i	$-0.693100\pi$
$373$	−22.0213	−1.14022	−0.570110	+	0.821568i	$0.693100\pi$
$374$	17.9944	0.930466
$375$	1.00000	0.0516398
$376$	−23.4801	−1.21089
$377$	29.8563	1.53768
$378$	1.50731	0.0775274
$379$	36.6615	1.88318	0.941588	−	0.336767i	$-0.109333\pi$
$379$	36.6615	1.88318	0.941588	+	0.336767i	$0.109333\pi$
$380$	0.179418	0.00920393
$381$	20.7546	1.06329
$382$	2.56443	0.131208
$383$	13.3900	0.684199	0.342100	−	0.939664i	$-0.388862\pi$
$383$	13.3900	0.684199	0.342100	+	0.939664i	$0.388862\pi$
$384$	−13.0596	−0.666444
$385$	2.60724	0.132877
$386$	0.839336	0.0427211
$387$	12.0478	0.612426
$388$	2.30993	0.117269
$389$	−7.58192	−0.384419	−0.192209	−	0.981354i	$-0.561565\pi$
$389$	−7.58192	−0.384419	−0.192209	+	0.981354i	$0.561565\pi$
$390$	−4.26951	−0.216195
$391$	4.57882	0.231561
$392$	−2.60467	−0.131556
$393$	1.37649	0.0694346
$394$	−21.4895	−1.08263
$395$	4.25373	0.214028
$396$	0.709091	0.0356332
$397$	37.2245	1.86824	0.934122	−	0.356955i	$-0.116185\pi$
$397$	37.2245	1.86824	0.934122	+	0.356955i	$0.116185\pi$
$398$	11.1377	0.558283
$399$	−0.659697	−0.0330262
$400$	−4.46997	−0.223499
$401$	25.6647	1.28163	0.640817	−	0.767694i	$-0.278596\pi$
$401$	25.6647	1.28163	0.640817	+	0.767694i	$0.278596\pi$
$402$	−12.0425	−0.600626
$403$	−23.8670	−1.18890
$404$	−2.59882	−0.129296
$405$	−1.00000	−0.0496904
$406$	15.8876	0.788491
$407$	−8.80332	−0.436365
$408$	11.9263	0.590440
$409$	27.9005	1.37959	0.689794	−	0.724005i	$-0.257701\pi$
$409$	27.9005	1.37959	0.689794	+	0.724005i	$0.257701\pi$
$410$	−11.8077	−0.583141
$411$	−21.0687	−1.03924
$412$	−1.37890	−0.0679337
$413$	8.77434	0.431757
$414$	1.50731	0.0740800
$415$	−10.0043	−0.491092
$416$	4.32891	0.212242
$417$	6.49149	0.317889
$418$	−2.59255	−0.126806
$419$	−30.9621	−1.51260	−0.756299	−	0.654226i	$-0.772994\pi$
$419$	−30.9621	−1.51260	−0.756299	+	0.654226i	$0.772994\pi$
$420$	−0.271970	−0.0132708
$421$	−25.5884	−1.24710	−0.623552	−	0.781782i	$-0.714311\pi$
$421$	−25.5884	−1.24710	−0.623552	+	0.781782i	$0.714311\pi$
$422$	−39.0067	−1.89882
$423$	9.01461	0.438305
$424$	14.6057	0.709314
$425$	4.57882	0.222105
$426$	−9.99345	−0.484184
$427$	−7.51361	−0.363609
$428$	1.26128	0.0609663
$429$	7.38514	0.356558
$430$	−18.1598	−0.875741
$431$	−39.7680	−1.91556	−0.957778	−	0.287510i	$-0.907173\pi$
$431$	−39.7680	−1.91556	−0.957778	+	0.287510i	$0.907173\pi$
$432$	4.46997	0.215062
$433$	−21.3781	−1.02736	−0.513682	−	0.857980i	$-0.671719\pi$
$433$	−21.3781	−1.02736	−0.513682	+	0.857980i	$0.671719\pi$
$434$	−12.7005	−0.609644
$435$	−10.5404	−0.505375
$436$	−3.05249	−0.146188
$437$	−0.659697	−0.0315576
$438$	−24.3097	−1.16156
$439$	−6.43767	−0.307253	−0.153627	−	0.988129i	$-0.549095\pi$
$439$	−6.43767	−0.307253	−0.153627	+	0.988129i	$0.549095\pi$
$440$	6.79101	0.323749
$441$	1.00000	0.0476190
$442$	−19.5493	−0.929867
$443$	40.2070	1.91029	0.955145	−	0.296137i	$-0.0956985\pi$
$443$	40.2070	1.91029	0.955145	+	0.296137i	$0.0956985\pi$
$444$	0.918302	0.0435807
$445$	−8.61510	−0.408395
$446$	−37.6340	−1.78202
$447$	3.31889	0.156978
$448$	−6.63637	−0.313539
$449$	−1.39921	−0.0660328	−0.0330164	−	0.999455i	$-0.510511\pi$
$449$	−1.39921	−0.0660328	−0.0330164	+	0.999455i	$0.510511\pi$
$450$	1.50731	0.0710551
$451$	20.4242	0.961739
$452$	3.53883	0.166452
$453$	5.07091	0.238252
$454$	−21.9539	−1.03035
$455$	−2.83255	−0.132792
$456$	−1.71829	−0.0804665
$457$	−41.3336	−1.93350	−0.966751	−	0.255718i	$-0.917688\pi$
$457$	−41.3336	−1.93350	−0.966751	+	0.255718i	$0.917688\pi$
$458$	2.38437	0.111414
$459$	−4.57882	−0.213721
$460$	−0.271970	−0.0126806
$461$	−16.7284	−0.779119	−0.389559	−	0.921001i	$-0.627373\pi$
$461$	−16.7284	−0.779119	−0.389559	+	0.921001i	$0.627373\pi$
$462$	3.92991	0.182836
$463$	−29.1287	−1.35373	−0.676864	−	0.736108i	$-0.736661\pi$
$463$	−29.1287	−1.35373	−0.676864	+	0.736108i	$0.736661\pi$
$464$	47.1154	2.18728
$465$	8.42598	0.390745
$466$	−24.6864	−1.14357
$467$	7.14093	0.330443	0.165221	−	0.986257i	$-0.447166\pi$
$467$	7.14093	0.330443	0.165221	+	0.986257i	$0.447166\pi$
$468$	−0.770367	−0.0356102
$469$	−7.98943	−0.368918
$470$	−13.5878	−0.626757
$471$	−0.847512	−0.0390513
$472$	22.8543	1.05195
$473$	31.4116	1.44431
$474$	6.41167	0.294498
$475$	−0.659697	−0.0302690
$476$	−1.24530	−0.0570782
$477$	−5.60749	−0.256750
$478$	39.9265	1.82619
$479$	−8.30941	−0.379667	−0.189833	−	0.981816i	$-0.560795\pi$
$479$	−8.30941	−0.379667	−0.189833	+	0.981816i	$0.560795\pi$
$480$	−1.52827	−0.0697558
$481$	9.56406	0.436084
$482$	7.89477	0.359597
$483$	1.00000	0.0455016
$484$	−1.14289	−0.0519497
$485$	−8.49335	−0.385663
$486$	−1.50731	−0.0683728
$487$	−8.39891	−0.380591	−0.190295	−	0.981727i	$-0.560945\pi$
$487$	−8.39891	−0.380591	−0.190295	+	0.981727i	$0.560945\pi$
$488$	−19.5705	−0.885914
$489$	−18.2319	−0.824477
$490$	−1.50731	−0.0680931
$491$	14.2434	0.642796	0.321398	−	0.946944i	$-0.395847\pi$
$491$	14.2434	0.642796	0.321398	+	0.946944i	$0.395847\pi$
$492$	−2.13051	−0.0960510
$493$	−48.2627	−2.17364
$494$	2.81659	0.126724
$495$	−2.60724	−0.117187
$496$	−37.6639	−1.69116
$497$	−6.63001	−0.297397
$498$	−15.0795	−0.675730
$499$	33.7456	1.51066	0.755329	−	0.655345i	$-0.227477\pi$
$499$	33.7456	1.51066	0.755329	+	0.655345i	$0.227477\pi$
$500$	−0.271970	−0.0121628
$501$	4.29371	0.191829
$502$	−19.3108	−0.861883
$503$	12.2256	0.545112	0.272556	−	0.962140i	$-0.412131\pi$
$503$	12.2256	0.545112	0.272556	+	0.962140i	$0.412131\pi$
$504$	2.60467	0.116021
$505$	9.55555	0.425216
$506$	3.92991	0.174706
$507$	4.97667	0.221022
$508$	−5.64462	−0.250440
$509$	11.6972	0.518468	0.259234	−	0.965815i	$-0.416530\pi$
$509$	11.6972	0.518468	0.259234	+	0.965815i	$0.416530\pi$
$510$	6.90168	0.305611
$511$	−16.1279	−0.713457
$512$	−16.4543	−0.727182
$513$	0.659697	0.0291264
$514$	42.4418	1.87203
$515$	5.07006	0.223414
$516$	−3.27664	−0.144246
$517$	23.5033	1.03367
$518$	5.08940	0.223615
$519$	−11.5656	−0.507672
$520$	−7.37785	−0.323540
$521$	−23.2234	−1.01743	−0.508717	−	0.860934i	$-0.669880\pi$
$521$	−23.2234	−1.01743	−0.508717	+	0.860934i	$0.669880\pi$
$522$	−15.8876	−0.695383
$523$	9.65074	0.421998	0.210999	−	0.977486i	$-0.432328\pi$
$523$	9.65074	0.421998	0.210999	+	0.977486i	$0.432328\pi$
$524$	−0.374363	−0.0163541
$525$	1.00000	0.0436436
$526$	−2.41453	−0.105279
$527$	38.5810	1.68062
$528$	11.6543	0.507188
$529$	1.00000	0.0434783
$530$	8.45221	0.367140
$531$	−8.77434	−0.380774
$532$	0.179418	0.00777874
$533$	−22.1892	−0.961120
$534$	−12.9856	−0.561941
$535$	−4.63758	−0.200500
$536$	−20.8098	−0.898848
$537$	12.9614	0.559326
$538$	8.63318	0.372203
$539$	2.60724	0.112302
$540$	0.271970	0.0117037
$541$	2.36782	0.101801	0.0509003	−	0.998704i	$-0.483791\pi$
$541$	2.36782	0.101801	0.0509003	+	0.998704i	$0.483791\pi$
$542$	30.0938	1.29264
$543$	−9.85170	−0.422777
$544$	−6.99768	−0.300023
$545$	11.2236	0.480768
$546$	−4.26951	−0.182718
$547$	20.9788	0.896987	0.448493	−	0.893786i	$-0.351961\pi$
$547$	20.9788	0.896987	0.448493	+	0.893786i	$0.351961\pi$
$548$	5.73005	0.244775
$549$	7.51361	0.320673
$550$	3.92991	0.167572
$551$	6.95349	0.296229
$552$	2.60467	0.110862
$553$	4.25373	0.180887
$554$	32.4406	1.37827
$555$	−3.37649	−0.143324
$556$	−1.76549	−0.0748733
$557$	−6.58924	−0.279195	−0.139597	−	0.990208i	$-0.544581\pi$
$557$	−6.58924	−0.279195	−0.139597	+	0.990208i	$0.544581\pi$
$558$	12.7005	0.537656
$559$	−34.1261	−1.44338
$560$	−4.46997	−0.188891
$561$	−11.9381	−0.504027
$562$	40.7272	1.71797
$563$	43.1657	1.81922	0.909609	−	0.415465i	$-0.136381\pi$
$563$	43.1657	1.81922	0.909609	+	0.415465i	$0.136381\pi$
$564$	−2.45170	−0.103235
$565$	−13.0119	−0.547413
$566$	−34.7180	−1.45931
$567$	−1.00000	−0.0419961
$568$	−17.2690	−0.724591
$569$	−13.8518	−0.580699	−0.290349	−	0.956921i	$-0.593771\pi$
$569$	−13.8518	−0.580699	−0.290349	+	0.956921i	$0.593771\pi$
$570$	−0.994366	−0.0416494
$571$	−32.4439	−1.35774	−0.678868	−	0.734260i	$-0.737529\pi$
$571$	−32.4439	−1.35774	−0.678868	+	0.734260i	$0.737529\pi$
$572$	−2.00853	−0.0839810
$573$	−1.70133	−0.0710742
$574$	−11.8077	−0.492844
$575$	1.00000	0.0417029
$576$	6.63637	0.276515
$577$	7.83046	0.325986	0.162993	−	0.986627i	$-0.447885\pi$
$577$	7.83046	0.325986	0.162993	+	0.986627i	$0.447885\pi$
$578$	5.97733	0.248624
$579$	−0.556845	−0.0231417
$580$	2.86668	0.119032
$581$	−10.0043	−0.415048
$582$	−12.8021	−0.530663
$583$	−14.6201	−0.605503
$584$	−42.0079	−1.73830
$585$	2.83255	0.117111
$586$	12.8866	0.532342
$587$	30.8505	1.27333	0.636667	−	0.771139i	$-0.280312\pi$
$587$	30.8505	1.27333	0.636667	+	0.771139i	$0.280312\pi$
$588$	−0.271970	−0.0112158
$589$	−5.55860	−0.229038
$590$	13.2256	0.544490
$591$	14.2569	0.586451
$592$	15.0928	0.620310
$593$	4.02282	0.165198	0.0825988	−	0.996583i	$-0.473678\pi$
$593$	4.02282	0.165198	0.0825988	+	0.996583i	$0.473678\pi$
$594$	−3.92991	−0.161246
$595$	4.57882	0.187713
$596$	−0.902636	−0.0369734
$597$	−7.38915	−0.302418
$598$	−4.26951	−0.174593
$599$	31.3148	1.27949	0.639743	−	0.768589i	$-0.279041\pi$
$599$	31.3148	1.27949	0.639743	+	0.768589i	$0.279041\pi$
$600$	2.60467	0.106335
$601$	15.4310	0.629444	0.314722	−	0.949184i	$-0.398089\pi$
$601$	15.4310	0.629444	0.314722	+	0.949184i	$0.398089\pi$
$602$	−18.1598	−0.740137
$603$	7.98943	0.325355
$604$	−1.37913	−0.0561161
$605$	4.20228	0.170847
$606$	14.4031	0.585087
$607$	12.7815	0.518785	0.259392	−	0.965772i	$-0.416478\pi$
$607$	12.7815	0.518785	0.259392	+	0.965772i	$0.416478\pi$
$608$	1.00820	0.0408878
$609$	−10.5404	−0.427120
$610$	−11.3253	−0.458548
$611$	−25.5343	−1.03301
$612$	1.24530	0.0503382
$613$	−33.7533	−1.36328	−0.681642	−	0.731686i	$-0.738734\pi$
$613$	−33.7533	−1.36328	−0.681642	+	0.731686i	$0.738734\pi$
$614$	−17.8433	−0.720098
$615$	7.83365	0.315883
$616$	6.79101	0.273617
$617$	15.7812	0.635329	0.317664	−	0.948203i	$-0.397101\pi$
$617$	15.7812	0.635329	0.317664	+	0.948203i	$0.397101\pi$
$618$	7.64213	0.307412
$619$	−15.5491	−0.624973	−0.312486	−	0.949922i	$-0.601162\pi$
$619$	−15.5491	−0.624973	−0.312486	+	0.949922i	$0.601162\pi$
$620$	−2.29161	−0.0920332
$621$	−1.00000	−0.0401286
$622$	13.4663	0.539951
$623$	−8.61510	−0.345157
$624$	−12.6614	−0.506862
$625$	1.00000	0.0400000
$626$	−24.3578	−0.973534
$627$	1.71999	0.0686899
$628$	0.230497	0.00919785
$629$	−15.4603	−0.616443
$630$	1.50731	0.0600525
$631$	−0.509012	−0.0202634	−0.0101317	−	0.999949i	$-0.503225\pi$
$631$	−0.509012	−0.0202634	−0.0101317	+	0.999949i	$0.503225\pi$
$632$	11.0796	0.440721
$633$	25.8784	1.02858
$634$	20.4398	0.811766
$635$	20.7546	0.823622
$636$	1.52507	0.0604729
$637$	−2.83255	−0.112230
$638$	−41.4230	−1.63995
$639$	6.63001	0.262279
$640$	−13.0596	−0.516225
$641$	−47.9733	−1.89483	−0.947415	−	0.320008i	$-0.896314\pi$
$641$	−47.9733	−1.89483	−0.947415	+	0.320008i	$0.896314\pi$
$642$	−6.99025	−0.275883
$643$	45.9834	1.81341	0.906704	−	0.421767i	$-0.138590\pi$
$643$	45.9834	1.81341	0.906704	+	0.421767i	$0.138590\pi$
$644$	−0.271970	−0.0107171
$645$	12.0478	0.474383
$646$	−4.55302	−0.179136
$647$	30.8035	1.21101	0.605506	−	0.795841i	$-0.292971\pi$
$647$	30.8035	1.21101	0.605506	+	0.795841i	$0.292971\pi$
$648$	−2.60467	−0.102321
$649$	−22.8768	−0.897995
$650$	−4.26951	−0.167464
$651$	8.42598	0.330240
$652$	4.95853	0.194191
$653$	8.98072	0.351443	0.175721	−	0.984440i	$-0.443774\pi$
$653$	8.98072	0.351443	0.175721	+	0.984440i	$0.443774\pi$
$654$	16.9175	0.661525
$655$	1.37649	0.0537838
$656$	−35.0162	−1.36715
$657$	16.1279	0.629210
$658$	−13.5878	−0.529706
$659$	4.51377	0.175832	0.0879159	−	0.996128i	$-0.471979\pi$
$659$	4.51377	0.175832	0.0879159	+	0.996128i	$0.471979\pi$
$660$	0.709091	0.0276013
$661$	14.1677	0.551060	0.275530	−	0.961293i	$-0.411147\pi$
$661$	14.1677	0.551060	0.275530	+	0.961293i	$0.411147\pi$
$662$	−14.5690	−0.566241
$663$	12.9697	0.503702
$664$	−26.0579	−1.01124
$665$	−0.659697	−0.0255820
$666$	−5.08940	−0.197210
$667$	−10.5404	−0.408127
$668$	−1.16776	−0.0451819
$669$	24.9678	0.965309
$670$	−12.0425	−0.465243
$671$	19.5898	0.756257
$672$	−1.52827	−0.0589544
$673$	13.1387	0.506459	0.253230	−	0.967406i	$-0.418507\pi$
$673$	13.1387	0.506459	0.253230	+	0.967406i	$0.418507\pi$
$674$	12.0514	0.464203
$675$	−1.00000	−0.0384900
$676$	−1.35350	−0.0520578
$677$	29.4218	1.13077	0.565385	−	0.824827i	$-0.308727\pi$
$677$	29.4218	1.13077	0.565385	+	0.824827i	$0.308727\pi$
$678$	−19.6128	−0.753226
$679$	−8.49335	−0.325945
$680$	11.9263	0.457353
$681$	14.5650	0.558133
$682$	33.1133	1.26798
$683$	−19.8227	−0.758494	−0.379247	−	0.925295i	$-0.623817\pi$
$683$	−19.8227	−0.758494	−0.379247	+	0.925295i	$0.623817\pi$
$684$	−0.179418	−0.00686020
$685$	−21.0687	−0.804994
$686$	−1.50731	−0.0575492
$687$	−1.58188	−0.0603524
$688$	−53.8535	−2.05314
$689$	15.8835	0.605113
$690$	1.50731	0.0573821
$691$	−20.8430	−0.792906	−0.396453	−	0.918055i	$-0.629759\pi$
$691$	−20.8430	−0.792906	−0.396453	+	0.918055i	$0.629759\pi$
$692$	3.14548	0.119573
$693$	−2.60724	−0.0990410
$694$	6.43452	0.244251
$695$	6.49149	0.246236
$696$	−27.4543	−1.04065
$697$	35.8688	1.35863
$698$	32.4561	1.22848
$699$	16.3778	0.619466
$700$	−0.271970	−0.0102795
$701$	47.8761	1.80825	0.904127	−	0.427264i	$-0.140523\pi$
$701$	47.8761	1.80825	0.904127	+	0.427264i	$0.140523\pi$
$702$	4.26951	0.161142
$703$	2.22746	0.0840102
$704$	17.3026	0.652117
$705$	9.01461	0.339510
$706$	0.597741	0.0224963
$707$	9.55555	0.359373
$708$	2.38635	0.0896847
$709$	51.2456	1.92457	0.962284	−	0.272048i	$-0.0877010\pi$
$709$	51.2456	1.92457	0.962284	+	0.272048i	$0.0877010\pi$
$710$	−9.99345	−0.375048
$711$	−4.25373	−0.159527
$712$	−22.4395	−0.840955
$713$	8.42598	0.315555
$714$	6.90168	0.258289
$715$	7.38514	0.276189
$716$	−3.52511	−0.131739
$717$	−26.4886	−0.989236
$718$	15.5769	0.581326
$719$	−27.0297	−1.00804	−0.504018	−	0.863693i	$-0.668146\pi$
$719$	−27.0297	−1.00804	−0.504018	+	0.863693i	$0.668146\pi$
$720$	4.46997	0.166586
$721$	5.07006	0.188819
$722$	−27.9828	−1.04141
$723$	−5.23767	−0.194791
$724$	2.67936	0.0995777
$725$	−10.5404	−0.391462
$726$	6.33412	0.235081
$727$	−50.8974	−1.88768	−0.943840	−	0.330402i	$-0.892816\pi$
$727$	−50.8974	−1.88768	−0.943840	+	0.330402i	$0.892816\pi$
$728$	−7.37785	−0.273441
$729$	1.00000	0.0370370
$730$	−24.3097	−0.899742
$731$	55.1648	2.04034
$732$	−2.04347	−0.0755290
$733$	9.02139	0.333213	0.166606	−	0.986024i	$-0.446719\pi$
$733$	9.02139	0.333213	0.166606	+	0.986024i	$0.446719\pi$
$734$	−2.68345	−0.0990481
$735$	1.00000	0.0368856
$736$	−1.52827	−0.0563329
$737$	20.8304	0.767297
$738$	11.8077	0.434647
$739$	−27.5951	−1.01510	−0.507550	−	0.861622i	$-0.669449\pi$
$739$	−27.5951	−1.01510	−0.507550	+	0.861622i	$0.669449\pi$
$740$	0.918302	0.0337574
$741$	−1.86862	−0.0686456
$742$	8.45221	0.310290
$743$	29.0878	1.06713	0.533564	−	0.845760i	$-0.320853\pi$
$743$	29.0878	1.06713	0.533564	+	0.845760i	$0.320853\pi$
$744$	21.9469	0.804612
$745$	3.31889	0.121595
$746$	−33.1928	−1.21528
$747$	10.0043	0.366038
$748$	3.24680	0.118715
$749$	−4.63758	−0.169453
$750$	1.50731	0.0550390
$751$	−51.4522	−1.87752	−0.938759	−	0.344574i	$-0.888023\pi$
$751$	−51.4522	−1.87752	−0.938759	+	0.344574i	$0.888023\pi$
$752$	−40.2951	−1.46941
$753$	12.8115	0.466876
$754$	45.0025	1.63889
$755$	5.07091	0.184549
$756$	0.271970	0.00989144
$757$	−26.1007	−0.948647	−0.474323	−	0.880351i	$-0.657307\pi$
$757$	−26.1007	−0.948647	−0.474323	+	0.880351i	$0.657307\pi$
$758$	55.2601	2.00714
$759$	−2.60724	−0.0946369
$760$	−1.71829	−0.0623291
$761$	38.3819	1.39134	0.695671	−	0.718360i	$-0.255107\pi$
$761$	38.3819	1.39134	0.695671	+	0.718360i	$0.255107\pi$
$762$	31.2835	1.13328
$763$	11.2236	0.406323
$764$	0.462711	0.0167403
$765$	−4.57882	−0.165548
$766$	20.1829	0.729237
$767$	24.8537	0.897417
$768$	−6.41204	−0.231375
$769$	−13.4271	−0.484195	−0.242097	−	0.970252i	$-0.577835\pi$
$769$	−13.4271	−0.484195	−0.242097	+	0.970252i	$0.577835\pi$
$770$	3.92991	0.141624
$771$	−28.1574	−1.01406
$772$	0.151445	0.00545063
$773$	22.1400	0.796321	0.398161	−	0.917316i	$-0.369649\pi$
$773$	22.1400	0.796321	0.398161	+	0.917316i	$0.369649\pi$
$774$	18.1598	0.652739
$775$	8.42598	0.302670
$776$	−22.1224	−0.794146
$777$	−3.37649	−0.121131
$778$	−11.4283	−0.409723
$779$	−5.16784	−0.185157
$780$	−0.770367	−0.0275836
$781$	17.2861	0.618544
$782$	6.90168	0.246803
$783$	10.5404	0.376684
$784$	−4.46997	−0.159642
$785$	−0.847512	−0.0302490
$786$	2.07479	0.0740052
$787$	−54.1749	−1.93113	−0.965564	−	0.260166i	$-0.916223\pi$
$787$	−54.1749	−1.93113	−0.965564	+	0.260166i	$0.916223\pi$
$788$	−3.87745	−0.138128
$789$	1.60189	0.0570286
$790$	6.41167	0.228117
$791$	−13.0119	−0.462648
$792$	−6.79101	−0.241308
$793$	−21.2827	−0.755770
$794$	56.1087	1.99122
$795$	−5.60749	−0.198877
$796$	2.00962	0.0712293
$797$	−10.2718	−0.363845	−0.181923	−	0.983313i	$-0.558232\pi$
$797$	−10.2718	−0.363845	−0.181923	+	0.983313i	$0.558232\pi$
$798$	−0.994366	−0.0352002
$799$	41.2763	1.46025
$800$	−1.52827	−0.0540326
$801$	8.61510	0.304399
$802$	38.6845	1.36600
$803$	42.0494	1.48389
$804$	−2.17288	−0.0766317
$805$	1.00000	0.0352454
$806$	−35.9748	−1.26716
$807$	−5.72756	−0.201620
$808$	24.8890	0.875594
$809$	3.93370	0.138302	0.0691508	−	0.997606i	$-0.477971\pi$
$809$	3.93370	0.138302	0.0691508	+	0.997606i	$0.477971\pi$
$810$	−1.50731	−0.0529613
$811$	−7.98021	−0.280223	−0.140112	−	0.990136i	$-0.544746\pi$
$811$	−7.98021	−0.280223	−0.140112	+	0.990136i	$0.544746\pi$
$812$	2.86668	0.100601
$813$	−19.9653	−0.700214
$814$	−13.2693	−0.465089
$815$	−18.2319	−0.638637
$816$	20.4672	0.716495
$817$	−7.94792	−0.278063
$818$	42.0545	1.47040
$819$	2.83255	0.0989772
$820$	−2.13051	−0.0744008
$821$	4.48259	0.156443	0.0782217	−	0.996936i	$-0.475076\pi$
$821$	4.48259	0.156443	0.0782217	+	0.996936i	$0.475076\pi$
$822$	−31.7570	−1.10765
$823$	−5.36920	−0.187158	−0.0935792	−	0.995612i	$-0.529831\pi$
$823$	−5.36920	−0.187158	−0.0935792	+	0.995612i	$0.529831\pi$
$824$	13.2058	0.460047
$825$	−2.60724	−0.0907726
$826$	13.2256	0.460178
$827$	−4.28703	−0.149075	−0.0745373	−	0.997218i	$-0.523748\pi$
$827$	−4.28703	−0.149075	−0.0745373	+	0.997218i	$0.523748\pi$
$828$	0.271970	0.00945160
$829$	11.1615	0.387653	0.193827	−	0.981036i	$-0.437910\pi$
$829$	11.1615	0.387653	0.193827	+	0.981036i	$0.437910\pi$
$830$	−15.0795	−0.523418
$831$	−21.5223	−0.746599
$832$	−18.7978	−0.651698
$833$	4.57882	0.158647
$834$	9.78465	0.338815
$835$	4.29371	0.148590
$836$	−0.467785	−0.0161787
$837$	−8.42598	−0.291244
$838$	−46.6693	−1.61217
$839$	4.91807	0.169791	0.0848953	−	0.996390i	$-0.472944\pi$
$839$	4.91807	0.169791	0.0848953	+	0.996390i	$0.472944\pi$
$840$	2.60467	0.0898696
$841$	82.1006	2.83106
$842$	−38.5696	−1.32919
$843$	−27.0198	−0.930613
$844$	−7.03815	−0.242263
$845$	4.97667	0.171203
$846$	13.5878	0.467157
$847$	4.20228	0.144392
$848$	25.0653	0.860747
$849$	23.0332	0.790496
$850$	6.90168	0.236726
$851$	−3.37649	−0.115744
$852$	−1.80316	−0.0617753
$853$	3.79831	0.130052	0.0650259	−	0.997884i	$-0.479287\pi$
$853$	3.79831	0.130052	0.0650259	+	0.997884i	$0.479287\pi$
$854$	−11.3253	−0.387544
$855$	0.659697	0.0225612
$856$	−12.0794	−0.412864
$857$	−50.7591	−1.73390	−0.866949	−	0.498397i	$-0.833922\pi$
$857$	−50.7591	−1.73390	−0.866949	+	0.498397i	$0.833922\pi$
$858$	11.1317	0.380029
$859$	3.96730	0.135363	0.0676813	−	0.997707i	$-0.478440\pi$
$859$	3.96730	0.135363	0.0676813	+	0.997707i	$0.478440\pi$
$860$	−3.27664	−0.111733
$861$	7.83365	0.266970
$862$	−59.9425	−2.04165
$863$	9.02537	0.307227	0.153614	−	0.988131i	$-0.450909\pi$
$863$	9.02537	0.307227	0.153614	+	0.988131i	$0.450909\pi$
$864$	1.52827	0.0519929
$865$	−11.5656	−0.393241
$866$	−32.2233	−1.09499
$867$	−3.96557	−0.134678
$868$	−2.29161	−0.0777823
$869$	−11.0905	−0.376220
$870$	−15.8876	−0.538642
$871$	−22.6305	−0.766804
$872$	29.2339	0.989984
$873$	8.49335	0.287456
$874$	−0.994366	−0.0336349
$875$	1.00000	0.0338062
$876$	−4.38630	−0.148199
$877$	37.5075	1.26654	0.633269	−	0.773932i	$-0.281713\pi$
$877$	37.5075	1.26654	0.633269	+	0.773932i	$0.281713\pi$
$878$	−9.70354	−0.327479
$879$	−8.54945	−0.288366
$880$	11.6543	0.392867
$881$	25.3676	0.854656	0.427328	−	0.904097i	$-0.359455\pi$
$881$	25.3676	0.854656	0.427328	+	0.904097i	$0.359455\pi$
$882$	1.50731	0.0507536
$883$	3.89232	0.130987	0.0654935	−	0.997853i	$-0.479138\pi$
$883$	3.89232	0.130987	0.0654935	+	0.997853i	$0.479138\pi$
$884$	−3.52737	−0.118638
$885$	−8.77434	−0.294946
$886$	60.6042	2.03604
$887$	8.51481	0.285899	0.142950	−	0.989730i	$-0.454341\pi$
$887$	8.51481	0.285899	0.142950	+	0.989730i	$0.454341\pi$
$888$	−8.79463	−0.295129
$889$	20.7546	0.696087
$890$	−12.9856	−0.435278
$891$	2.60724	0.0873459
$892$	−6.79047	−0.227362
$893$	−5.94692	−0.199006
$894$	5.00257	0.167311
$895$	12.9614	0.433252
$896$	−13.0596	−0.436290
$897$	2.83255	0.0945760
$898$	−2.10904	−0.0703795
$899$	−88.8134	−2.96209
$900$	0.271970	0.00906565
$901$	−25.6757	−0.855381
$902$	30.7855	1.02505
$903$	12.0478	0.400927
$904$	−33.8916	−1.12722
$905$	−9.85170	−0.327482
$906$	7.64341	0.253935
$907$	−32.3107	−1.07286	−0.536429	−	0.843945i	$-0.680227\pi$
$907$	−32.3107	−1.07286	−0.536429	+	0.843945i	$0.680227\pi$
$908$	−3.96124	−0.131458
$909$	−9.55555	−0.316938
$910$	−4.26951	−0.141533
$911$	−17.9673	−0.595282	−0.297641	−	0.954678i	$-0.596200\pi$
$911$	−17.9673	−0.595282	−0.297641	+	0.954678i	$0.596200\pi$
$912$	−2.94883	−0.0976455
$913$	26.0837	0.863243
$914$	−62.3023	−2.06078
$915$	7.51361	0.248392
$916$	0.430222	0.0142149
$917$	1.37649	0.0454556
$918$	−6.90168	−0.227789
$919$	−43.3285	−1.42927	−0.714637	−	0.699495i	$-0.753408\pi$
$919$	−43.3285	−1.42927	−0.714637	+	0.699495i	$0.753408\pi$
$920$	2.60467	0.0858734
$921$	11.8379	0.390072
$922$	−25.2148	−0.830405
$923$	−18.7798	−0.618145
$924$	0.709091	0.0233274
$925$	−3.37649	−0.111018
$926$	−43.9059	−1.44284
$927$	−5.07006	−0.166523
$928$	16.1087	0.528793
$929$	−4.45738	−0.146242	−0.0731209	−	0.997323i	$-0.523296\pi$
$929$	−4.45738	−0.146242	−0.0731209	+	0.997323i	$0.523296\pi$
$930$	12.7005	0.416466
$931$	−0.659697	−0.0216207
$932$	−4.45427	−0.145904
$933$	−8.93405	−0.292488
$934$	10.7636	0.352194
$935$	−11.9381	−0.390417
$936$	7.37785	0.241153
$937$	−6.46047	−0.211054	−0.105527	−	0.994416i	$-0.533653\pi$
$937$	−6.46047	−0.211054	−0.105527	+	0.994416i	$0.533653\pi$
$938$	−12.0425	−0.393202
$939$	16.1598	0.527356
$940$	−2.45170	−0.0799656
$941$	31.2557	1.01891	0.509454	−	0.860498i	$-0.329848\pi$
$941$	31.2557	1.01891	0.509454	+	0.860498i	$0.329848\pi$
$942$	−1.27746	−0.0416219
$943$	7.83365	0.255099
$944$	39.2211	1.27654
$945$	−1.00000	−0.0325300
$946$	47.3469	1.53938
$947$	35.5606	1.15556	0.577781	−	0.816192i	$-0.303919\pi$
$947$	35.5606	1.15556	0.577781	+	0.816192i	$0.303919\pi$
$948$	1.15689	0.0375739
$949$	−45.6831	−1.48294
$950$	−0.994366	−0.0322615
$951$	−13.5605	−0.439728
$952$	11.9263	0.386534
$953$	40.9741	1.32728	0.663640	−	0.748052i	$-0.269011\pi$
$953$	40.9741	1.32728	0.663640	+	0.748052i	$0.269011\pi$
$954$	−8.45221	−0.273650
$955$	−1.70133	−0.0550539
$956$	7.20410	0.232997
$957$	27.4815	0.888350
$958$	−12.5248	−0.404659
$959$	−21.0687	−0.680344
$960$	6.63637	0.214188
$961$	39.9971	1.29023
$962$	14.4160	0.464789
$963$	4.63758	0.149444
$964$	1.42449	0.0458796
$965$	−0.556845	−0.0179255
$966$	1.50731	0.0484968
$967$	24.4248	0.785449	0.392725	−	0.919656i	$-0.371533\pi$
$967$	24.4248	0.785449	0.392725	+	0.919656i	$0.371533\pi$
$968$	10.9456	0.351804
$969$	3.02063	0.0970368
$970$	−12.8021	−0.411050
$971$	−38.3606	−1.23105	−0.615525	−	0.788118i	$-0.711056\pi$
$971$	−38.3606	−1.23105	−0.615525	+	0.788118i	$0.711056\pi$
$972$	−0.271970	−0.00872343
$973$	6.49149	0.208107
$974$	−12.6597	−0.405643
$975$	2.83255	0.0907141
$976$	−33.5856	−1.07505
$977$	−22.4869	−0.719419	−0.359710	−	0.933064i	$-0.617124\pi$
$977$	−22.4869	−0.719419	−0.359710	+	0.933064i	$0.617124\pi$
$978$	−27.4811	−0.878749
$979$	22.4617	0.717878
$980$	−0.271970	−0.00868775
$981$	−11.2236	−0.358343
$982$	21.4692	0.685108
$983$	−3.35782	−0.107098	−0.0535489	−	0.998565i	$-0.517053\pi$
$983$	−3.35782	−0.107098	−0.0535489	+	0.998565i	$0.517053\pi$
$984$	20.4041	0.650458
$985$	14.2569	0.454263
$986$	−72.7466	−2.31672
$987$	9.01461	0.286938
$988$	0.508209	0.0161683
$989$	12.0478	0.383099
$990$	−3.92991	−0.124901
$991$	−37.9636	−1.20595	−0.602977	−	0.797758i	$-0.706019\pi$
$991$	−37.9636	−1.20595	−0.602977	+	0.797758i	$0.706019\pi$
$992$	−12.8772	−0.408851
$993$	9.66561	0.306729
$994$	−9.99345	−0.316973
$995$	−7.38915	−0.234252
$996$	−2.72087	−0.0862139
$997$	35.7572	1.13244	0.566220	−	0.824254i	$-0.308405\pi$
$997$	35.7572	1.13244	0.566220	+	0.824254i	$0.308405\pi$
$998$	50.8649	1.61010
$999$	3.37649	0.106827

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2415.2.a.p.1.5	✓	6
3.2	odd	2		7245.2.a.bk.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2415.2.a.p.1.5	✓	6	1.1	even	1	trivial
7245.2.a.bk.1.2		6	3.2	odd	2

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:	\( N \)	\(=\)	\( 2415 = 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2415.a (trivial)

\(f(q)\)	\(=\)	\(q+1.50731 q^{2} -1.00000 q^{3} +0.271970 q^{4} -1.00000 q^{5} -1.50731 q^{6} -1.00000 q^{7} -2.60467 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.50731 q^{2} -1.00000 q^{3} +0.271970 q^{4} -1.00000 q^{5} -1.50731 q^{6} -1.00000 q^{7} -2.60467 q^{8} +1.00000 q^{9} -1.50731 q^{10} +2.60724 q^{11} -0.271970 q^{12} -2.83255 q^{13} -1.50731 q^{14} +1.00000 q^{15} -4.46997 q^{16} +4.57882 q^{17} +1.50731 q^{18} -0.659697 q^{19} -0.271970 q^{20} +1.00000 q^{21} +3.92991 q^{22} +1.00000 q^{23} +2.60467 q^{24} +1.00000 q^{25} -4.26951 q^{26} -1.00000 q^{27} -0.271970 q^{28} -10.5404 q^{29} +1.50731 q^{30} +8.42598 q^{31} -1.52827 q^{32} -2.60724 q^{33} +6.90168 q^{34} +1.00000 q^{35} +0.271970 q^{36} -3.37649 q^{37} -0.994366 q^{38} +2.83255 q^{39} +2.60467 q^{40} +7.83365 q^{41} +1.50731 q^{42} +12.0478 q^{43} +0.709091 q^{44} -1.00000 q^{45} +1.50731 q^{46} +9.01461 q^{47} +4.46997 q^{48} +1.00000 q^{49} +1.50731 q^{50} -4.57882 q^{51} -0.770367 q^{52} -5.60749 q^{53} -1.50731 q^{54} -2.60724 q^{55} +2.60467 q^{56} +0.659697 q^{57} -15.8876 q^{58} -8.77434 q^{59} +0.271970 q^{60} +7.51361 q^{61} +12.7005 q^{62} -1.00000 q^{63} +6.63637 q^{64} +2.83255 q^{65} -3.92991 q^{66} +7.98943 q^{67} +1.24530 q^{68} -1.00000 q^{69} +1.50731 q^{70} +6.63001 q^{71} -2.60467 q^{72} +16.1279 q^{73} -5.08940 q^{74} -1.00000 q^{75} -0.179418 q^{76} -2.60724 q^{77} +4.26951 q^{78} -4.25373 q^{79} +4.46997 q^{80} +1.00000 q^{81} +11.8077 q^{82} +10.0043 q^{83} +0.271970 q^{84} -4.57882 q^{85} +18.1598 q^{86} +10.5404 q^{87} -6.79101 q^{88} +8.61510 q^{89} -1.50731 q^{90} +2.83255 q^{91} +0.271970 q^{92} -8.42598 q^{93} +13.5878 q^{94} +0.659697 q^{95} +1.52827 q^{96} +8.49335 q^{97} +1.50731 q^{98} +2.60724 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 6 q^{3} + 5 q^{4} - 6 q^{5} - q^{6} - 6 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + q^2 - 6 * q^3 + 5 * q^4 - 6 * q^5 - q^6 - 6 * q^7 + 3 * q^8 + 6 * q^9	\( 6 q + q^{2} - 6 q^{3} + 5 q^{4} - 6 q^{5} - q^{6} - 6 q^{7} + 3 q^{8} + 6 q^{9} - q^{10} - 6 q^{11} - 5 q^{12} + 6 q^{13} - q^{14} + 6 q^{15} - 5 q^{16} + 16 q^{17} + q^{18} - 5 q^{20} + 6 q^{21} - 10 q^{22} + 6 q^{23} - 3 q^{24} + 6 q^{25} + 3 q^{26} - 6 q^{27} - 5 q^{28} - 4 q^{29} + q^{30} + 2 q^{32} + 6 q^{33} - 3 q^{34} + 6 q^{35} + 5 q^{36} - 4 q^{37} + 22 q^{38} - 6 q^{39} - 3 q^{40} + 4 q^{41} + q^{42} - 16 q^{43} - 13 q^{44} - 6 q^{45} + q^{46} + 38 q^{47} + 5 q^{48} + 6 q^{49} + q^{50} - 16 q^{51} + 24 q^{52} + 24 q^{53} - q^{54} + 6 q^{55} - 3 q^{56} + 2 q^{58} + 2 q^{59} + 5 q^{60} - 4 q^{61} + 26 q^{62} - 6 q^{63} + 7 q^{64} - 6 q^{65} + 10 q^{66} - 30 q^{67} + 54 q^{68} - 6 q^{69} + q^{70} - 6 q^{71} + 3 q^{72} + 38 q^{73} - 7 q^{74} - 6 q^{75} + 3 q^{76} + 6 q^{77} - 3 q^{78} - 14 q^{79} + 5 q^{80} + 6 q^{81} + 56 q^{82} + 22 q^{83} + 5 q^{84} - 16 q^{85} + 48 q^{86} + 4 q^{87} - 21 q^{88} + 20 q^{89} - q^{90} - 6 q^{91} + 5 q^{92} + 40 q^{94} - 2 q^{96} + 4 q^{97} + q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q + q^2 - 6 * q^3 + 5 * q^4 - 6 * q^5 - q^6 - 6 * q^7 + 3 * q^8 + 6 * q^9 - q^10 - 6 * q^11 - 5 * q^12 + 6 * q^13 - q^14 + 6 * q^15 - 5 * q^16 + 16 * q^17 + q^18 - 5 * q^20 + 6 * q^21 - 10 * q^22 + 6 * q^23 - 3 * q^24 + 6 * q^25 + 3 * q^26 - 6 * q^27 - 5 * q^28 - 4 * q^29 + q^30 + 2 * q^32 + 6 * q^33 - 3 * q^34 + 6 * q^35 + 5 * q^36 - 4 * q^37 + 22 * q^38 - 6 * q^39 - 3 * q^40 + 4 * q^41 + q^42 - 16 * q^43 - 13 * q^44 - 6 * q^45 + q^46 + 38 * q^47 + 5 * q^48 + 6 * q^49 + q^50 - 16 * q^51 + 24 * q^52 + 24 * q^53 - q^54 + 6 * q^55 - 3 * q^56 + 2 * q^58 + 2 * q^59 + 5 * q^60 - 4 * q^61 + 26 * q^62 - 6 * q^63 + 7 * q^64 - 6 * q^65 + 10 * q^66 - 30 * q^67 + 54 * q^68 - 6 * q^69 + q^70 - 6 * q^71 + 3 * q^72 + 38 * q^73 - 7 * q^74 - 6 * q^75 + 3 * q^76 + 6 * q^77 - 3 * q^78 - 14 * q^79 + 5 * q^80 + 6 * q^81 + 56 * q^82 + 22 * q^83 + 5 * q^84 - 16 * q^85 + 48 * q^86 + 4 * q^87 - 21 * q^88 + 20 * q^89 - q^90 - 6 * q^91 + 5 * q^92 + 40 * q^94 - 2 * q^96 + 4 * q^97 + q^98 - 6 * q^99

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