LMFDB - Embedded newform 6045.2.a.bd.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6045,2,Mod(1,6045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6045, 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("6045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6045 = 3 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6045.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:	$48.2695680219$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 18 x^{12} + 35 x^{11} + 120 x^{10} - 226 x^{9} - 367 x^{8} + 658 x^{7} + 527 x^{6} + \cdots - 16 $ x^14 - 2x^13 - 18x^12 + 35x^11 + 120x^10 - 226x^9 - 367x^8 + 658x^7 + 527x^6 - 849x^5 - 345x^4 + 402x^3 + 122x^2 - 56*x - 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.72465$ of defining polynomial
Character	$\chi$	$=$	6045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.72465 q^{2} -1.00000 q^{3} +5.42372 q^{4} +1.00000 q^{5} +2.72465 q^{6} +4.13479 q^{7} -9.32843 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.72465 q^{2} -1.00000 q^{3} +5.42372 q^{4} +1.00000 q^{5} +2.72465 q^{6} +4.13479 q^{7} -9.32843 q^{8} +1.00000 q^{9} -2.72465 q^{10} -3.04118 q^{11} -5.42372 q^{12} -1.00000 q^{13} -11.2658 q^{14} -1.00000 q^{15} +14.5693 q^{16} +6.28725 q^{17} -2.72465 q^{18} +3.02151 q^{19} +5.42372 q^{20} -4.13479 q^{21} +8.28615 q^{22} +3.35212 q^{23} +9.32843 q^{24} +1.00000 q^{25} +2.72465 q^{26} -1.00000 q^{27} +22.4259 q^{28} +2.21912 q^{29} +2.72465 q^{30} -1.00000 q^{31} -21.0393 q^{32} +3.04118 q^{33} -17.1306 q^{34} +4.13479 q^{35} +5.42372 q^{36} +0.515213 q^{37} -8.23256 q^{38} +1.00000 q^{39} -9.32843 q^{40} -0.324239 q^{41} +11.2658 q^{42} +9.05972 q^{43} -16.4945 q^{44} +1.00000 q^{45} -9.13337 q^{46} -0.903459 q^{47} -14.5693 q^{48} +10.0965 q^{49} -2.72465 q^{50} -6.28725 q^{51} -5.42372 q^{52} -5.47286 q^{53} +2.72465 q^{54} -3.04118 q^{55} -38.5711 q^{56} -3.02151 q^{57} -6.04632 q^{58} -1.76817 q^{59} -5.42372 q^{60} +7.13595 q^{61} +2.72465 q^{62} +4.13479 q^{63} +28.1862 q^{64} -1.00000 q^{65} -8.28615 q^{66} +1.68811 q^{67} +34.1003 q^{68} -3.35212 q^{69} -11.2658 q^{70} -12.1379 q^{71} -9.32843 q^{72} +4.18111 q^{73} -1.40377 q^{74} -1.00000 q^{75} +16.3878 q^{76} -12.5746 q^{77} -2.72465 q^{78} -9.29393 q^{79} +14.5693 q^{80} +1.00000 q^{81} +0.883438 q^{82} +15.6482 q^{83} -22.4259 q^{84} +6.28725 q^{85} -24.6846 q^{86} -2.21912 q^{87} +28.3694 q^{88} -9.84969 q^{89} -2.72465 q^{90} -4.13479 q^{91} +18.1810 q^{92} +1.00000 q^{93} +2.46161 q^{94} +3.02151 q^{95} +21.0393 q^{96} -5.63685 q^{97} -27.5093 q^{98} -3.04118 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} + 14 q^{5} + 2 q^{6} + 5 q^{7} - 3 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 - 14 * q^3 + 12 * q^4 + 14 * q^5 + 2 * q^6 + 5 * q^7 - 3 * q^8 + 14 * q^9	\( 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} + 14 q^{5} + 2 q^{6} + 5 q^{7} - 3 q^{8} + 14 q^{9} - 2 q^{10} + 4 q^{11} - 12 q^{12} - 14 q^{13} - 7 q^{14} - 14 q^{15} + 8 q^{16} + 7 q^{17} - 2 q^{18} + 2 q^{19} + 12 q^{20} - 5 q^{21} + 21 q^{22} + 31 q^{23} + 3 q^{24} + 14 q^{25} + 2 q^{26} - 14 q^{27} + 8 q^{28} - 5 q^{29} + 2 q^{30} - 14 q^{31} - 8 q^{32} - 4 q^{33} - 11 q^{34} + 5 q^{35} + 12 q^{36} + 15 q^{37} + 2 q^{38} + 14 q^{39} - 3 q^{40} + 7 q^{41} + 7 q^{42} + 30 q^{43} + q^{44} + 14 q^{45} + 2 q^{46} + 23 q^{47} - 8 q^{48} + 11 q^{49} - 2 q^{50} - 7 q^{51} - 12 q^{52} + 14 q^{53} + 2 q^{54} + 4 q^{55} - 23 q^{56} - 2 q^{57} + 22 q^{58} + 10 q^{59} - 12 q^{60} + 2 q^{62} + 5 q^{63} - 3 q^{64} - 14 q^{65} - 21 q^{66} + 28 q^{67} + 23 q^{68} - 31 q^{69} - 7 q^{70} - 35 q^{71} - 3 q^{72} + 27 q^{73} - 12 q^{74} - 14 q^{75} + 26 q^{76} + 24 q^{77} - 2 q^{78} + 9 q^{79} + 8 q^{80} + 14 q^{81} + 45 q^{82} + 49 q^{83} - 8 q^{84} + 7 q^{85} + 4 q^{86} + 5 q^{87} + 49 q^{88} + 5 q^{89} - 2 q^{90} - 5 q^{91} + 107 q^{92} + 14 q^{93} + 26 q^{94} + 2 q^{95} + 8 q^{96} + 9 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 - 14 * q^3 + 12 * q^4 + 14 * q^5 + 2 * q^6 + 5 * q^7 - 3 * q^8 + 14 * q^9 - 2 * q^10 + 4 * q^11 - 12 * q^12 - 14 * q^13 - 7 * q^14 - 14 * q^15 + 8 * q^16 + 7 * q^17 - 2 * q^18 + 2 * q^19 + 12 * q^20 - 5 * q^21 + 21 * q^22 + 31 * q^23 + 3 * q^24 + 14 * q^25 + 2 * q^26 - 14 * q^27 + 8 * q^28 - 5 * q^29 + 2 * q^30 - 14 * q^31 - 8 * q^32 - 4 * q^33 - 11 * q^34 + 5 * q^35 + 12 * q^36 + 15 * q^37 + 2 * q^38 + 14 * q^39 - 3 * q^40 + 7 * q^41 + 7 * q^42 + 30 * q^43 + q^44 + 14 * q^45 + 2 * q^46 + 23 * q^47 - 8 * q^48 + 11 * q^49 - 2 * q^50 - 7 * q^51 - 12 * q^52 + 14 * q^53 + 2 * q^54 + 4 * q^55 - 23 * q^56 - 2 * q^57 + 22 * q^58 + 10 * q^59 - 12 * q^60 + 2 * q^62 + 5 * q^63 - 3 * q^64 - 14 * q^65 - 21 * q^66 + 28 * q^67 + 23 * q^68 - 31 * q^69 - 7 * q^70 - 35 * q^71 - 3 * q^72 + 27 * q^73 - 12 * q^74 - 14 * q^75 + 26 * q^76 + 24 * q^77 - 2 * q^78 + 9 * q^79 + 8 * q^80 + 14 * q^81 + 45 * q^82 + 49 * q^83 - 8 * q^84 + 7 * q^85 + 4 * q^86 + 5 * q^87 + 49 * q^88 + 5 * q^89 - 2 * q^90 - 5 * q^91 + 107 * q^92 + 14 * q^93 + 26 * q^94 + 2 * q^95 + 8 * q^96 + 9 * q^97 - 6 * q^98 + 4 * 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 $

$2$	−2.72465	−1.92662	−0.963309	−	0.268394i	$-0.913507\pi$
$2$	−2.72465	−1.92662	−0.963309	+	0.268394i	$0.913507\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.42372	2.71186
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.72465	1.11233
$7$	4.13479	1.56280	0.781401	−	0.624029i	$-0.214505\pi$
$7$	4.13479	1.56280	0.781401	+	0.624029i	$0.214505\pi$
$8$	−9.32843	−3.29810
$9$	1.00000	0.333333
$10$	−2.72465	−0.861610
$11$	−3.04118	−0.916950	−0.458475	−	0.888707i	$-0.651604\pi$
$11$	−3.04118	−0.916950	−0.458475	+	0.888707i	$0.651604\pi$
$12$	−5.42372	−1.56569
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−11.2658	−3.01092
$15$	−1.00000	−0.258199
$16$	14.5693	3.64232
$17$	6.28725	1.52488	0.762441	−	0.647057i	$-0.224001\pi$
$17$	6.28725	1.52488	0.762441	+	0.647057i	$0.224001\pi$
$18$	−2.72465	−0.642206
$19$	3.02151	0.693182	0.346591	−	0.938016i	$-0.387339\pi$
$19$	3.02151	0.693182	0.346591	+	0.938016i	$0.387339\pi$
$20$	5.42372	1.21278
$21$	−4.13479	−0.902284
$22$	8.28615	1.76661
$23$	3.35212	0.698966	0.349483	−	0.936943i	$-0.386357\pi$
$23$	3.35212	0.698966	0.349483	+	0.936943i	$0.386357\pi$
$24$	9.32843	1.90416
$25$	1.00000	0.200000
$26$	2.72465	0.534348
$27$	−1.00000	−0.192450
$28$	22.4259	4.23810
$29$	2.21912	0.412080	0.206040	−	0.978544i	$-0.433942\pi$
$29$	2.21912	0.412080	0.206040	+	0.978544i	$0.433942\pi$
$30$	2.72465	0.497451
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−21.0393	−3.71926
$33$	3.04118	0.529401
$34$	−17.1306	−2.93787
$35$	4.13479	0.698906
$36$	5.42372	0.903953
$37$	0.515213	0.0847005	0.0423502	−	0.999103i	$-0.486515\pi$
$37$	0.515213	0.0847005	0.0423502	+	0.999103i	$0.486515\pi$
$38$	−8.23256	−1.33550
$39$	1.00000	0.160128
$40$	−9.32843	−1.47495
$41$	−0.324239	−0.0506377	−0.0253188	−	0.999679i	$-0.508060\pi$
$41$	−0.324239	−0.0506377	−0.0253188	+	0.999679i	$0.508060\pi$
$42$	11.2658	1.73836
$43$	9.05972	1.38159	0.690797	−	0.723049i	$-0.257260\pi$
$43$	9.05972	1.38159	0.690797	+	0.723049i	$0.257260\pi$
$44$	−16.4945	−2.48664
$45$	1.00000	0.149071
$46$	−9.13337	−1.34664
$47$	−0.903459	−0.131783	−0.0658915	−	0.997827i	$-0.520989\pi$
$47$	−0.903459	−0.131783	−0.0658915	+	0.997827i	$0.520989\pi$
$48$	−14.5693	−2.10289
$49$	10.0965	1.44235
$50$	−2.72465	−0.385324
$51$	−6.28725	−0.880391
$52$	−5.42372	−0.752134
$53$	−5.47286	−0.751756	−0.375878	−	0.926669i	$-0.622659\pi$
$53$	−5.47286	−0.751756	−0.375878	+	0.926669i	$0.622659\pi$
$54$	2.72465	0.370778
$55$	−3.04118	−0.410073
$56$	−38.5711	−5.15428
$57$	−3.02151	−0.400209
$58$	−6.04632	−0.793921
$59$	−1.76817	−0.230196	−0.115098	−	0.993354i	$-0.536718\pi$
$59$	−1.76817	−0.230196	−0.115098	+	0.993354i	$0.536718\pi$
$60$	−5.42372	−0.700199
$61$	7.13595	0.913664	0.456832	−	0.889553i	$-0.348984\pi$
$61$	7.13595	0.913664	0.456832	+	0.889553i	$0.348984\pi$
$62$	2.72465	0.346031
$63$	4.13479	0.520934
$64$	28.1862	3.52328
$65$	−1.00000	−0.124035
$66$	−8.28615	−1.01995
$67$	1.68811	0.206236	0.103118	−	0.994669i	$-0.467118\pi$
$67$	1.68811	0.206236	0.103118	+	0.994669i	$0.467118\pi$
$68$	34.1003	4.13527
$69$	−3.35212	−0.403548
$70$	−11.2658	−1.34653
$71$	−12.1379	−1.44051	−0.720254	−	0.693711i	$-0.755975\pi$
$71$	−12.1379	−1.44051	−0.720254	+	0.693711i	$0.755975\pi$
$72$	−9.32843	−1.09937
$73$	4.18111	0.489362	0.244681	−	0.969604i	$-0.421317\pi$
$73$	4.18111	0.489362	0.244681	+	0.969604i	$0.421317\pi$
$74$	−1.40377	−0.163186
$75$	−1.00000	−0.115470
$76$	16.3878	1.87981
$77$	−12.5746	−1.43301
$78$	−2.72465	−0.308506
$79$	−9.29393	−1.04565	−0.522825	−	0.852440i	$-0.675122\pi$
$79$	−9.29393	−1.04565	−0.522825	+	0.852440i	$0.675122\pi$
$80$	14.5693	1.62889
$81$	1.00000	0.111111
$82$	0.883438	0.0975594
$83$	15.6482	1.71761	0.858806	−	0.512301i	$-0.171207\pi$
$83$	15.6482	1.71761	0.858806	+	0.512301i	$0.171207\pi$
$84$	−22.4259	−2.44687
$85$	6.28725	0.681948
$86$	−24.6846	−2.66180
$87$	−2.21912	−0.237914
$88$	28.3694	3.02419
$89$	−9.84969	−1.04406	−0.522032	−	0.852926i	$-0.674826\pi$
$89$	−9.84969	−1.04406	−0.522032	+	0.852926i	$0.674826\pi$
$90$	−2.72465	−0.287203
$91$	−4.13479	−0.433443
$92$	18.1810	1.89550
$93$	1.00000	0.103695
$94$	2.46161	0.253896
$95$	3.02151	0.310001
$96$	21.0393	2.14732
$97$	−5.63685	−0.572335	−0.286168	−	0.958180i	$-0.592381\pi$
$97$	−5.63685	−0.572335	−0.286168	+	0.958180i	$0.592381\pi$
$98$	−27.5093	−2.77886
$99$	−3.04118	−0.305650
$100$	5.42372	0.542372
$101$	0.405880	0.0403865	0.0201933	−	0.999796i	$-0.493572\pi$
$101$	0.405880	0.0403865	0.0201933	+	0.999796i	$0.493572\pi$
$102$	17.1306	1.69618
$103$	11.1261	1.09629	0.548145	−	0.836383i	$-0.315334\pi$
$103$	11.1261	1.09629	0.548145	+	0.836383i	$0.315334\pi$
$104$	9.32843	0.914728
$105$	−4.13479	−0.403514
$106$	14.9116	1.44835
$107$	6.71328	0.648997	0.324498	−	0.945886i	$-0.394804\pi$
$107$	6.71328	0.648997	0.324498	+	0.945886i	$0.394804\pi$
$108$	−5.42372	−0.521897
$109$	15.1769	1.45368	0.726841	−	0.686806i	$-0.240988\pi$
$109$	15.1769	1.45368	0.726841	+	0.686806i	$0.240988\pi$
$110$	8.28615	0.790053
$111$	−0.515213	−0.0489018
$112$	60.2408	5.69222
$113$	−5.27773	−0.496487	−0.248244	−	0.968698i	$-0.579853\pi$
$113$	−5.27773	−0.496487	−0.248244	+	0.968698i	$0.579853\pi$
$114$	8.23256	0.771050
$115$	3.35212	0.312587
$116$	12.0359	1.11750
$117$	−1.00000	−0.0924500
$118$	4.81764	0.443499
$119$	25.9964	2.38309
$120$	9.32843	0.851565
$121$	−1.75123	−0.159202
$122$	−19.4430	−1.76028
$123$	0.324239	0.0292357
$124$	−5.42372	−0.487064
$125$	1.00000	0.0894427
$126$	−11.2658	−1.00364
$127$	16.8491	1.49511	0.747557	−	0.664198i	$-0.231227\pi$
$127$	16.8491	1.49511	0.747557	+	0.664198i	$0.231227\pi$
$128$	−34.7190	−3.06875
$129$	−9.05972	−0.797664
$130$	2.72465	0.238968
$131$	−2.59849	−0.227031	−0.113515	−	0.993536i	$-0.536211\pi$
$131$	−2.59849	−0.227031	−0.113515	+	0.993536i	$0.536211\pi$
$132$	16.4945	1.43566
$133$	12.4933	1.08331
$134$	−4.59951	−0.397337
$135$	−1.00000	−0.0860663
$136$	−58.6502	−5.02921
$137$	19.9446	1.70398	0.851992	−	0.523555i	$-0.175394\pi$
$137$	19.9446	1.70398	0.851992	+	0.523555i	$0.175394\pi$
$138$	9.13337	0.777484
$139$	10.3894	0.881219	0.440610	−	0.897699i	$-0.354762\pi$
$139$	10.3894	0.881219	0.440610	+	0.897699i	$0.354762\pi$
$140$	22.4259	1.89534
$141$	0.903459	0.0760850
$142$	33.0716	2.77531
$143$	3.04118	0.254316
$144$	14.5693	1.21411
$145$	2.21912	0.184288
$146$	−11.3921	−0.942814
$147$	−10.0965	−0.832741
$148$	2.79437	0.229696
$149$	5.19787	0.425826	0.212913	−	0.977071i	$-0.431705\pi$
$149$	5.19787	0.425826	0.212913	+	0.977071i	$0.431705\pi$
$150$	2.72465	0.222467
$151$	−9.54563	−0.776812	−0.388406	−	0.921488i	$-0.626974\pi$
$151$	−9.54563	−0.776812	−0.388406	+	0.921488i	$0.626974\pi$
$152$	−28.1860	−2.28618
$153$	6.28725	0.508294
$154$	34.2615	2.76087
$155$	−1.00000	−0.0803219
$156$	5.42372	0.434245
$157$	3.78478	0.302058	0.151029	−	0.988529i	$-0.451741\pi$
$157$	3.78478	0.302058	0.151029	+	0.988529i	$0.451741\pi$
$158$	25.3227	2.01457
$159$	5.47286	0.434026
$160$	−21.0393	−1.66330
$161$	13.8603	1.09235
$162$	−2.72465	−0.214069
$163$	4.07053	0.318828	0.159414	−	0.987212i	$-0.449039\pi$
$163$	4.07053	0.318828	0.159414	+	0.987212i	$0.449039\pi$
$164$	−1.75858	−0.137322
$165$	3.04118	0.236756
$166$	−42.6358	−3.30918
$167$	−12.2220	−0.945770	−0.472885	−	0.881124i	$-0.656787\pi$
$167$	−12.2220	−0.945770	−0.472885	+	0.881124i	$0.656787\pi$
$168$	38.5711	2.97582
$169$	1.00000	0.0769231
$170$	−17.1306	−1.31385
$171$	3.02151	0.231061
$172$	49.1373	3.74669
$173$	3.29183	0.250273	0.125137	−	0.992140i	$-0.460063\pi$
$173$	3.29183	0.250273	0.125137	+	0.992140i	$0.460063\pi$
$174$	6.04632	0.458370
$175$	4.13479	0.312560
$176$	−44.3078	−3.33983
$177$	1.76817	0.132904
$178$	26.8369	2.01151
$179$	23.1353	1.72922	0.864608	−	0.502447i	$-0.167567\pi$
$179$	23.1353	1.72922	0.864608	+	0.502447i	$0.167567\pi$
$180$	5.42372	0.404260
$181$	−24.9847	−1.85709	−0.928547	−	0.371214i	$-0.878942\pi$
$181$	−24.9847	−1.85709	−0.928547	+	0.371214i	$0.878942\pi$
$182$	11.2658	0.835080
$183$	−7.13595	−0.527504
$184$	−31.2701	−2.30526
$185$	0.515213	0.0378792
$186$	−2.72465	−0.199781
$187$	−19.1207	−1.39824
$188$	−4.90011	−0.357377
$189$	−4.13479	−0.300761
$190$	−8.23256	−0.597253
$191$	−20.2733	−1.46693	−0.733463	−	0.679730i	$-0.762097\pi$
$191$	−20.2733	−1.46693	−0.733463	+	0.679730i	$0.762097\pi$
$192$	−28.1862	−2.03417
$193$	−20.8799	−1.50297	−0.751484	−	0.659751i	$-0.770662\pi$
$193$	−20.8799	−1.50297	−0.751484	+	0.659751i	$0.770662\pi$
$194$	15.3584	1.10267
$195$	1.00000	0.0716115
$196$	54.7603	3.91145
$197$	−22.3569	−1.59287	−0.796433	−	0.604727i	$-0.793282\pi$
$197$	−22.3569	−1.59287	−0.796433	+	0.604727i	$0.793282\pi$
$198$	8.28615	0.588871
$199$	−15.0463	−1.06661	−0.533304	−	0.845924i	$-0.679050\pi$
$199$	−15.0463	−1.06661	−0.533304	+	0.845924i	$0.679050\pi$
$200$	−9.32843	−0.659620
$201$	−1.68811	−0.119070
$202$	−1.10588	−0.0778094
$203$	9.17558	0.643999
$204$	−34.1003	−2.38750
$205$	−0.324239	−0.0226458
$206$	−30.3148	−2.11213
$207$	3.35212	0.232989
$208$	−14.5693	−1.01020
$209$	−9.18896	−0.635614
$210$	11.2658	0.777417
$211$	−7.33223	−0.504771	−0.252386	−	0.967627i	$-0.581215\pi$
$211$	−7.33223	−0.504771	−0.252386	+	0.967627i	$0.581215\pi$
$212$	−29.6833	−2.03866
$213$	12.1379	0.831678
$214$	−18.2913	−1.25037
$215$	9.05972	0.617868
$216$	9.32843	0.634719
$217$	−4.13479	−0.280688
$218$	−41.3517	−2.80069
$219$	−4.18111	−0.282533
$220$	−16.4945	−1.11206
$221$	−6.28725	−0.422926
$222$	1.40377	0.0942152
$223$	26.9052	1.80171	0.900853	−	0.434125i	$-0.142942\pi$
$223$	26.9052	1.80171	0.900853	+	0.434125i	$0.142942\pi$
$224$	−86.9931	−5.81247
$225$	1.00000	0.0666667
$226$	14.3800	0.956542
$227$	21.0580	1.39767	0.698835	−	0.715283i	$-0.253702\pi$
$227$	21.0580	1.39767	0.698835	+	0.715283i	$0.253702\pi$
$228$	−16.3878	−1.08531
$229$	−6.64594	−0.439176	−0.219588	−	0.975593i	$-0.570471\pi$
$229$	−6.64594	−0.439176	−0.219588	+	0.975593i	$0.570471\pi$
$230$	−9.13337	−0.602236
$231$	12.5746	0.827350
$232$	−20.7009	−1.35908
$233$	11.7172	0.767620	0.383810	−	0.923412i	$-0.374612\pi$
$233$	11.7172	0.767620	0.383810	+	0.923412i	$0.374612\pi$
$234$	2.72465	0.178116
$235$	−0.903459	−0.0589352
$236$	−9.59004	−0.624258
$237$	9.29393	0.603706
$238$	−70.8312	−4.59130
$239$	−9.34994	−0.604797	−0.302399	−	0.953182i	$-0.597787\pi$
$239$	−9.34994	−0.604797	−0.302399	+	0.953182i	$0.597787\pi$
$240$	−14.5693	−0.940443
$241$	−11.5311	−0.742781	−0.371391	−	0.928477i	$-0.621119\pi$
$241$	−11.5311	−0.742781	−0.371391	+	0.928477i	$0.621119\pi$
$242$	4.77148	0.306722
$243$	−1.00000	−0.0641500
$244$	38.7034	2.47773
$245$	10.0965	0.645039
$246$	−0.883438	−0.0563260
$247$	−3.02151	−0.192254
$248$	9.32843	0.592356
$249$	−15.6482	−0.991664
$250$	−2.72465	−0.172322
$251$	1.62765	0.102737	0.0513683	−	0.998680i	$-0.483642\pi$
$251$	1.62765	0.102737	0.0513683	+	0.998680i	$0.483642\pi$
$252$	22.4259	1.41270
$253$	−10.1944	−0.640917
$254$	−45.9078	−2.88051
$255$	−6.28725	−0.393723
$256$	38.2246	2.38904
$257$	−3.02392	−0.188627	−0.0943134	−	0.995543i	$-0.530066\pi$
$257$	−3.02392	−0.188627	−0.0943134	+	0.995543i	$0.530066\pi$
$258$	24.6846	1.53679
$259$	2.13029	0.132370
$260$	−5.42372	−0.336365
$261$	2.21912	0.137360
$262$	7.07997	0.437402
$263$	−16.5116	−1.01815	−0.509076	−	0.860722i	$-0.670013\pi$
$263$	−16.5116	−1.01815	−0.509076	+	0.860722i	$0.670013\pi$
$264$	−28.3694	−1.74602
$265$	−5.47286	−0.336195
$266$	−34.0399	−2.08712
$267$	9.84969	0.602791
$268$	9.15584	0.559282
$269$	23.6880	1.44428	0.722142	−	0.691745i	$-0.243158\pi$
$269$	23.6880	1.44428	0.722142	+	0.691745i	$0.243158\pi$
$270$	2.72465	0.165817
$271$	9.98151	0.606334	0.303167	−	0.952937i	$-0.401956\pi$
$271$	9.98151	0.606334	0.303167	+	0.952937i	$0.401956\pi$
$272$	91.6007	5.55411
$273$	4.13479	0.250249
$274$	−54.3421	−3.28293
$275$	−3.04118	−0.183390
$276$	−18.1810	−1.09437
$277$	9.19122	0.552247	0.276123	−	0.961122i	$-0.410950\pi$
$277$	9.19122	0.552247	0.276123	+	0.961122i	$0.410950\pi$
$278$	−28.3075	−1.69777
$279$	−1.00000	−0.0598684
$280$	−38.5711	−2.30506
$281$	30.6451	1.82814	0.914068	−	0.405562i	$-0.132924\pi$
$281$	30.6451	1.82814	0.914068	+	0.405562i	$0.132924\pi$
$282$	−2.46161	−0.146587
$283$	−0.434850	−0.0258492	−0.0129246	−	0.999916i	$-0.504114\pi$
$283$	−0.434850	−0.0258492	−0.0129246	+	0.999916i	$0.504114\pi$
$284$	−65.8327	−3.90645
$285$	−3.02151	−0.178979
$286$	−8.28615	−0.489970
$287$	−1.34066	−0.0791366
$288$	−21.0393	−1.23975
$289$	22.5295	1.32527
$290$	−6.04632	−0.355052
$291$	5.63685	0.330438
$292$	22.6772	1.32708
$293$	−13.1502	−0.768243	−0.384122	−	0.923283i	$-0.625496\pi$
$293$	−13.1502	−0.768243	−0.384122	+	0.923283i	$0.625496\pi$
$294$	27.5093	1.60437
$295$	−1.76817	−0.102947
$296$	−4.80613	−0.279351
$297$	3.04118	0.176467
$298$	−14.1624	−0.820405
$299$	−3.35212	−0.193858
$300$	−5.42372	−0.313138
$301$	37.4600	2.15916
$302$	26.0085	1.49662
$303$	−0.405880	−0.0233172
$304$	44.0213	2.52479
$305$	7.13595	0.408603
$306$	−17.1306	−0.979289
$307$	−11.5990	−0.661992	−0.330996	−	0.943632i	$-0.607385\pi$
$307$	−11.5990	−0.661992	−0.330996	+	0.943632i	$0.607385\pi$
$308$	−68.2012	−3.88613
$309$	−11.1261	−0.632944
$310$	2.72465	0.154750
$311$	10.9296	0.619763	0.309882	−	0.950775i	$-0.399711\pi$
$311$	10.9296	0.619763	0.309882	+	0.950775i	$0.399711\pi$
$312$	−9.32843	−0.528118
$313$	−28.8933	−1.63315	−0.816573	−	0.577242i	$-0.804129\pi$
$313$	−28.8933	−1.63315	−0.816573	+	0.577242i	$0.804129\pi$
$314$	−10.3122	−0.581951
$315$	4.13479	0.232969
$316$	−50.4077	−2.83565
$317$	−27.5341	−1.54647	−0.773234	−	0.634121i	$-0.781362\pi$
$317$	−27.5341	−1.54647	−0.773234	+	0.634121i	$0.781362\pi$
$318$	−14.9116	−0.836203
$319$	−6.74874	−0.377857
$320$	28.1862	1.57566
$321$	−6.71328	−0.374699
$322$	−37.7645	−2.10453
$323$	18.9970	1.05702
$324$	5.42372	0.301318
$325$	−1.00000	−0.0554700
$326$	−11.0908	−0.614261
$327$	−15.1769	−0.839284
$328$	3.02464	0.167008
$329$	−3.73561	−0.205951
$330$	−8.28615	−0.456138
$331$	−24.6750	−1.35626	−0.678131	−	0.734941i	$-0.737210\pi$
$331$	−24.6750	−1.35626	−0.678131	+	0.734941i	$0.737210\pi$
$332$	84.8713	4.65792
$333$	0.515213	0.0282335
$334$	33.3008	1.82214
$335$	1.68811	0.0922313
$336$	−60.2408	−3.28641
$337$	−1.33155	−0.0725341	−0.0362670	−	0.999342i	$-0.511547\pi$
$337$	−1.33155	−0.0725341	−0.0362670	+	0.999342i	$0.511547\pi$
$338$	−2.72465	−0.148201
$339$	5.27773	0.286647
$340$	34.1003	1.84935
$341$	3.04118	0.164689
$342$	−8.23256	−0.445166
$343$	12.8032	0.691306
$344$	−84.5130	−4.55663
$345$	−3.35212	−0.180472
$346$	−8.96909	−0.482181
$347$	18.9176	1.01555	0.507774	−	0.861490i	$-0.330468\pi$
$347$	18.9176	1.01555	0.507774	+	0.861490i	$0.330468\pi$
$348$	−12.0359	−0.645190
$349$	−23.6852	−1.26784	−0.633920	−	0.773399i	$-0.718555\pi$
$349$	−23.6852	−1.26784	−0.633920	+	0.773399i	$0.718555\pi$
$350$	−11.2658	−0.602185
$351$	1.00000	0.0533761
$352$	63.9844	3.41038
$353$	26.1813	1.39349	0.696744	−	0.717320i	$-0.254631\pi$
$353$	26.1813	1.39349	0.696744	+	0.717320i	$0.254631\pi$
$354$	−4.81764	−0.256054
$355$	−12.1379	−0.644215
$356$	−53.4219	−2.83136
$357$	−25.9964	−1.37588
$358$	−63.0357	−3.33154
$359$	−20.2570	−1.06912	−0.534562	−	0.845129i	$-0.679523\pi$
$359$	−20.2570	−1.06912	−0.534562	+	0.845129i	$0.679523\pi$
$360$	−9.32843	−0.491652
$361$	−9.87046	−0.519498
$362$	68.0744	3.57791
$363$	1.75123	0.0919155
$364$	−22.4259	−1.17544
$365$	4.18111	0.218849
$366$	19.4430	1.01630
$367$	−31.4261	−1.64043	−0.820214	−	0.572057i	$-0.806146\pi$
$367$	−31.4261	−1.64043	−0.820214	+	0.572057i	$0.806146\pi$
$368$	48.8380	2.54586
$369$	−0.324239	−0.0168792
$370$	−1.40377	−0.0729788
$371$	−22.6291	−1.17485
$372$	5.42372	0.281207
$373$	27.4819	1.42296	0.711479	−	0.702707i	$-0.248025\pi$
$373$	27.4819	1.42296	0.711479	+	0.702707i	$0.248025\pi$
$374$	52.0971	2.69388
$375$	−1.00000	−0.0516398
$376$	8.42786	0.434634
$377$	−2.21912	−0.114290
$378$	11.2658	0.579452
$379$	8.32019	0.427380	0.213690	−	0.976902i	$-0.431452\pi$
$379$	8.32019	0.427380	0.213690	+	0.976902i	$0.431452\pi$
$380$	16.3878	0.840678
$381$	−16.8491	−0.863205
$382$	55.2377	2.82621
$383$	25.6975	1.31308	0.656541	−	0.754290i	$-0.272019\pi$
$383$	25.6975	1.31308	0.656541	+	0.754290i	$0.272019\pi$
$384$	34.7190	1.77174
$385$	−12.5746	−0.640862
$386$	56.8904	2.89565
$387$	9.05972	0.460531
$388$	−30.5727	−1.55209
$389$	−20.1612	−1.02221	−0.511107	−	0.859517i	$-0.670764\pi$
$389$	−20.1612	−1.02221	−0.511107	+	0.859517i	$0.670764\pi$
$390$	−2.72465	−0.137968
$391$	21.0757	1.06584
$392$	−94.1841	−4.75701
$393$	2.59849	0.131076
$394$	60.9148	3.06884
$395$	−9.29393	−0.467629
$396$	−16.4945	−0.828880
$397$	−19.2711	−0.967191	−0.483595	−	0.875292i	$-0.660669\pi$
$397$	−19.2711	−0.967191	−0.483595	+	0.875292i	$0.660669\pi$
$398$	40.9960	2.05494
$399$	−12.4933	−0.625448
$400$	14.5693	0.728464
$401$	17.9470	0.896232	0.448116	−	0.893975i	$-0.352095\pi$
$401$	17.9470	0.896232	0.448116	+	0.893975i	$0.352095\pi$
$402$	4.59951	0.229403
$403$	1.00000	0.0498135
$404$	2.20138	0.109523
$405$	1.00000	0.0496904
$406$	−25.0002	−1.24074
$407$	−1.56686	−0.0776661
$408$	58.6502	2.90362
$409$	3.23018	0.159722	0.0798611	−	0.996806i	$-0.474552\pi$
$409$	3.23018	0.159722	0.0798611	+	0.996806i	$0.474552\pi$
$410$	0.883438	0.0436299
$411$	−19.9446	−0.983796
$412$	60.3450	2.97299
$413$	−7.31099	−0.359750
$414$	−9.13337	−0.448881
$415$	15.6482	0.768139
$416$	21.0393	1.03154
$417$	−10.3894	−0.508772
$418$	25.0367	1.22459
$419$	31.0325	1.51604	0.758018	−	0.652233i	$-0.226168\pi$
$419$	31.0325	1.51604	0.758018	+	0.652233i	$0.226168\pi$
$420$	−22.4259	−1.09427
$421$	24.2492	1.18183	0.590917	−	0.806732i	$-0.298766\pi$
$421$	24.2492	1.18183	0.590917	+	0.806732i	$0.298766\pi$
$422$	19.9778	0.972502
$423$	−0.903459	−0.0439277
$424$	51.0532	2.47936
$425$	6.28725	0.304977
$426$	−33.0716	−1.60233
$427$	29.5056	1.42788
$428$	36.4109	1.75999
$429$	−3.04118	−0.146830
$430$	−24.6846	−1.19040
$431$	18.5148	0.891829	0.445914	−	0.895076i	$-0.352879\pi$
$431$	18.5148	0.891829	0.445914	+	0.895076i	$0.352879\pi$
$432$	−14.5693	−0.700965
$433$	5.08660	0.244447	0.122223	−	0.992503i	$-0.460998\pi$
$433$	5.08660	0.244447	0.122223	+	0.992503i	$0.460998\pi$
$434$	11.2658	0.540778
$435$	−2.21912	−0.106399
$436$	82.3152	3.94218
$437$	10.1285	0.484511
$438$	11.3921	0.544334
$439$	−12.7663	−0.609300	−0.304650	−	0.952464i	$-0.598539\pi$
$439$	−12.7663	−0.609300	−0.304650	+	0.952464i	$0.598539\pi$
$440$	28.3694	1.35246
$441$	10.0965	0.480783
$442$	17.1306	0.814818
$443$	30.4670	1.44753	0.723766	−	0.690046i	$-0.242410\pi$
$443$	30.4670	1.44753	0.723766	+	0.690046i	$0.242410\pi$
$444$	−2.79437	−0.132615
$445$	−9.84969	−0.466920
$446$	−73.3072	−3.47120
$447$	−5.19787	−0.245851
$448$	116.544	5.50619
$449$	3.84735	0.181568	0.0907839	−	0.995871i	$-0.471063\pi$
$449$	3.84735	0.181568	0.0907839	+	0.995871i	$0.471063\pi$
$450$	−2.72465	−0.128441
$451$	0.986070	0.0464322
$452$	−28.6249	−1.34640
$453$	9.54563	0.448493
$454$	−57.3757	−2.69278
$455$	−4.13479	−0.193842
$456$	28.1860	1.31993
$457$	26.3618	1.23315	0.616575	−	0.787296i	$-0.288520\pi$
$457$	26.3618	1.23315	0.616575	+	0.787296i	$0.288520\pi$
$458$	18.1079	0.846125
$459$	−6.28725	−0.293464
$460$	18.1810	0.847693
$461$	−5.28542	−0.246166	−0.123083	−	0.992396i	$-0.539278\pi$
$461$	−5.28542	−0.246166	−0.123083	+	0.992396i	$0.539278\pi$
$462$	−34.2615	−1.59399
$463$	−36.5652	−1.69933	−0.849664	−	0.527324i	$-0.823196\pi$
$463$	−36.5652	−1.69933	−0.849664	+	0.527324i	$0.823196\pi$
$464$	32.3309	1.50093
$465$	1.00000	0.0463739
$466$	−31.9253	−1.47891
$467$	−25.1637	−1.16444	−0.582219	−	0.813032i	$-0.697815\pi$
$467$	−25.1637	−1.16444	−0.582219	+	0.813032i	$0.697815\pi$
$468$	−5.42372	−0.250711
$469$	6.97998	0.322305
$470$	2.46161	0.113546
$471$	−3.78478	−0.174393
$472$	16.4942	0.759208
$473$	−27.5522	−1.26685
$474$	−25.3227	−1.16311
$475$	3.02151	0.138636
$476$	140.997	6.46260
$477$	−5.47286	−0.250585
$478$	25.4753	1.16521
$479$	−32.6195	−1.49042	−0.745211	−	0.666829i	$-0.767651\pi$
$479$	−32.6195	−1.49042	−0.745211	+	0.666829i	$0.767651\pi$
$480$	21.0393	0.960309
$481$	−0.515213	−0.0234917
$482$	31.4181	1.43106
$483$	−13.8603	−0.630666
$484$	−9.49815	−0.431734
$485$	−5.63685	−0.255956
$486$	2.72465	0.123593
$487$	15.5045	0.702575	0.351288	−	0.936268i	$-0.385744\pi$
$487$	15.5045	0.702575	0.351288	+	0.936268i	$0.385744\pi$
$488$	−66.5672	−3.01336
$489$	−4.07053	−0.184076
$490$	−27.5093	−1.24274
$491$	2.33169	0.105228	0.0526139	−	0.998615i	$-0.483245\pi$
$491$	2.33169	0.105228	0.0526139	+	0.998615i	$0.483245\pi$
$492$	1.75858	0.0792830
$493$	13.9522	0.628373
$494$	8.23256	0.370401
$495$	−3.04118	−0.136691
$496$	−14.5693	−0.654180
$497$	−50.1878	−2.25123
$498$	42.6358	1.91056
$499$	−9.69291	−0.433914	−0.216957	−	0.976181i	$-0.569613\pi$
$499$	−9.69291	−0.433914	−0.216957	+	0.976181i	$0.569613\pi$
$500$	5.42372	0.242556
$501$	12.2220	0.546041
$502$	−4.43479	−0.197934
$503$	−32.1873	−1.43516	−0.717581	−	0.696475i	$-0.754751\pi$
$503$	−32.1873	−1.43516	−0.717581	+	0.696475i	$0.754751\pi$
$504$	−38.5711	−1.71809
$505$	0.405880	0.0180614
$506$	27.7762	1.23480
$507$	−1.00000	−0.0444116
$508$	91.3847	4.05454
$509$	31.1641	1.38133	0.690663	−	0.723177i	$-0.257319\pi$
$509$	31.1641	1.38133	0.690663	+	0.723177i	$0.257319\pi$
$510$	17.1306	0.758554
$511$	17.2880	0.764776
$512$	−34.7106	−1.53401
$513$	−3.02151	−0.133403
$514$	8.23912	0.363412
$515$	11.1261	0.490276
$516$	−49.1373	−2.16315
$517$	2.74758	0.120839
$518$	−5.80431	−0.255027
$519$	−3.29183	−0.144495
$520$	9.32843	0.409079
$521$	27.8636	1.22073	0.610363	−	0.792122i	$-0.291024\pi$
$521$	27.8636	1.22073	0.610363	+	0.792122i	$0.291024\pi$
$522$	−6.04632	−0.264640
$523$	−2.04539	−0.0894388	−0.0447194	−	0.999000i	$-0.514239\pi$
$523$	−2.04539	−0.0894388	−0.0447194	+	0.999000i	$0.514239\pi$
$524$	−14.0935	−0.615676
$525$	−4.13479	−0.180457
$526$	44.9885	1.96159
$527$	−6.28725	−0.273877
$528$	44.3078	1.92825
$529$	−11.7633	−0.511446
$530$	14.9116	0.647720
$531$	−1.76817	−0.0767319
$532$	67.7602	2.93778
$533$	0.324239	0.0140444
$534$	−26.8369	−1.16135
$535$	6.71328	0.290240
$536$	−15.7474	−0.680185
$537$	−23.1353	−0.998363
$538$	−64.5415	−2.78258
$539$	−30.7051	−1.32256
$540$	−5.42372	−0.233400
$541$	2.35281	0.101155	0.0505776	−	0.998720i	$-0.483894\pi$
$541$	2.35281	0.101155	0.0505776	+	0.998720i	$0.483894\pi$
$542$	−27.1961	−1.16817
$543$	24.9847	1.07219
$544$	−132.280	−5.67144
$545$	15.1769	0.650106
$546$	−11.2658	−0.482134
$547$	29.5702	1.26433	0.632164	−	0.774834i	$-0.282167\pi$
$547$	29.5702	1.26433	0.632164	+	0.774834i	$0.282167\pi$
$548$	108.174	4.62096
$549$	7.13595	0.304555
$550$	8.28615	0.353323
$551$	6.70509	0.285646
$552$	31.2701	1.33094
$553$	−38.4284	−1.63414
$554$	−25.0428	−1.06397
$555$	−0.515213	−0.0218696
$556$	56.3493	2.38974
$557$	−8.59668	−0.364253	−0.182127	−	0.983275i	$-0.558298\pi$
$557$	−8.59668	−0.364253	−0.182127	+	0.983275i	$0.558298\pi$
$558$	2.72465	0.115344
$559$	−9.05972	−0.383185
$560$	60.2408	2.54564
$561$	19.1207	0.807275
$562$	−83.4973	−3.52212
$563$	30.4022	1.28130	0.640651	−	0.767832i	$-0.278665\pi$
$563$	30.4022	1.28130	0.640651	+	0.767832i	$0.278665\pi$
$564$	4.90011	0.206332
$565$	−5.27773	−0.222036
$566$	1.18481	0.0498015
$567$	4.13479	0.173645
$568$	113.228	4.75094
$569$	1.00850	0.0422786	0.0211393	−	0.999777i	$-0.493271\pi$
$569$	1.00850	0.0422786	0.0211393	+	0.999777i	$0.493271\pi$
$570$	8.23256	0.344824
$571$	25.4479	1.06496	0.532480	−	0.846442i	$-0.321260\pi$
$571$	25.4479	1.06496	0.532480	+	0.846442i	$0.321260\pi$
$572$	16.4945	0.689670
$573$	20.2733	0.846930
$574$	3.65283	0.152466
$575$	3.35212	0.139793
$576$	28.1862	1.17443
$577$	−10.8008	−0.449644	−0.224822	−	0.974400i	$-0.572180\pi$
$577$	−10.8008	−0.449644	−0.224822	+	0.974400i	$0.572180\pi$
$578$	−61.3851	−2.55328
$579$	20.8799	0.867739
$580$	12.0359	0.499762
$581$	64.7019	2.68429
$582$	−15.3584	−0.636628
$583$	16.6440	0.689322
$584$	−39.0032	−1.61397
$585$	−1.00000	−0.0413449
$586$	35.8297	1.48011
$587$	−40.6278	−1.67689	−0.838445	−	0.544986i	$-0.816535\pi$
$587$	−40.6278	−1.67689	−0.838445	+	0.544986i	$0.816535\pi$
$588$	−54.7603	−2.25828
$589$	−3.02151	−0.124499
$590$	4.81764	0.198339
$591$	22.3569	0.919642
$592$	7.50628	0.308506
$593$	−26.9858	−1.10817	−0.554087	−	0.832459i	$-0.686932\pi$
$593$	−26.9858	−1.10817	−0.554087	+	0.832459i	$0.686932\pi$
$594$	−8.28615	−0.339985
$595$	25.9964	1.06575
$596$	28.1918	1.15478
$597$	15.0463	0.615806
$598$	9.13337	0.373491
$599$	−0.383375	−0.0156643	−0.00783215	−	0.999969i	$-0.502493\pi$
$599$	−0.383375	−0.0156643	−0.00783215	+	0.999969i	$0.502493\pi$
$600$	9.32843	0.380832
$601$	−25.0873	−1.02333	−0.511666	−	0.859184i	$-0.670971\pi$
$601$	−25.0873	−1.02333	−0.511666	+	0.859184i	$0.670971\pi$
$602$	−102.065	−4.15987
$603$	1.68811	0.0687452
$604$	−51.7728	−2.10661
$605$	−1.75123	−0.0711974
$606$	1.10588	0.0449233
$607$	−17.9641	−0.729142	−0.364571	−	0.931176i	$-0.618784\pi$
$607$	−17.9641	−0.729142	−0.364571	+	0.931176i	$0.618784\pi$
$608$	−63.5706	−2.57813
$609$	−9.17558	−0.371813
$610$	−19.4430	−0.787222
$611$	0.903459	0.0365501
$612$	34.1003	1.37842
$613$	−32.8686	−1.32755	−0.663776	−	0.747932i	$-0.731047\pi$
$613$	−32.8686	−1.32755	−0.663776	+	0.747932i	$0.731047\pi$
$614$	31.6033	1.27541
$615$	0.324239	0.0130746
$616$	117.302	4.72621
$617$	3.36616	0.135517	0.0677583	−	0.997702i	$-0.478415\pi$
$617$	3.36616	0.135517	0.0677583	+	0.997702i	$0.478415\pi$
$618$	30.3148	1.21944
$619$	20.6945	0.831784	0.415892	−	0.909414i	$-0.363470\pi$
$619$	20.6945	0.831784	0.415892	+	0.909414i	$0.363470\pi$
$620$	−5.42372	−0.217822
$621$	−3.35212	−0.134516
$622$	−29.7795	−1.19405
$623$	−40.7263	−1.63167
$624$	14.5693	0.583238
$625$	1.00000	0.0400000
$626$	78.7242	3.14645
$627$	9.18896	0.366972
$628$	20.5276	0.819139
$629$	3.23927	0.129158
$630$	−11.2658	−0.448842
$631$	−2.24822	−0.0895004	−0.0447502	−	0.998998i	$-0.514249\pi$
$631$	−2.24822	−0.0895004	−0.0447502	+	0.998998i	$0.514249\pi$
$632$	86.6978	3.44865
$633$	7.33223	0.291430
$634$	75.0207	2.97945
$635$	16.8491	0.668635
$636$	29.6833	1.17702
$637$	−10.0965	−0.400036
$638$	18.3879	0.727986
$639$	−12.1379	−0.480169
$640$	−34.7190	−1.37239
$641$	35.2223	1.39120	0.695599	−	0.718430i	$-0.255139\pi$
$641$	35.2223	1.39120	0.695599	+	0.718430i	$0.255139\pi$
$642$	18.2913	0.721901
$643$	44.3814	1.75023	0.875115	−	0.483915i	$-0.160786\pi$
$643$	44.3814	1.75023	0.875115	+	0.483915i	$0.160786\pi$
$644$	75.1744	2.96229
$645$	−9.05972	−0.356726
$646$	−51.7602	−2.03648
$647$	−14.4919	−0.569736	−0.284868	−	0.958567i	$-0.591950\pi$
$647$	−14.4919	−0.569736	−0.284868	+	0.958567i	$0.591950\pi$
$648$	−9.32843	−0.366455
$649$	5.37731	0.211078
$650$	2.72465	0.106870
$651$	4.13479	0.162055
$652$	22.0774	0.864618
$653$	29.5611	1.15682	0.578408	−	0.815748i	$-0.303674\pi$
$653$	29.5611	1.15682	0.578408	+	0.815748i	$0.303674\pi$
$654$	41.3517	1.61698
$655$	−2.59849	−0.101531
$656$	−4.72393	−0.184439
$657$	4.18111	0.163121
$658$	10.1782	0.396789
$659$	−26.7331	−1.04137	−0.520686	−	0.853748i	$-0.674324\pi$
$659$	−26.7331	−1.04137	−0.520686	+	0.853748i	$0.674324\pi$
$660$	16.4945	0.642048
$661$	−41.2294	−1.60364	−0.801819	−	0.597567i	$-0.796134\pi$
$661$	−41.2294	−1.60364	−0.801819	+	0.597567i	$0.796134\pi$
$662$	67.2308	2.61300
$663$	6.28725	0.244177
$664$	−145.973	−5.66485
$665$	12.4933	0.484470
$666$	−1.40377	−0.0543952
$667$	7.43876	0.288030
$668$	−66.2889	−2.56480
$669$	−26.9052	−1.04021
$670$	−4.59951	−0.177695
$671$	−21.7017	−0.837785
$672$	86.9931	3.35583
$673$	36.3433	1.40093	0.700466	−	0.713686i	$-0.252976\pi$
$673$	36.3433	1.40093	0.700466	+	0.713686i	$0.252976\pi$
$674$	3.62800	0.139745
$675$	−1.00000	−0.0384900
$676$	5.42372	0.208605
$677$	−18.8973	−0.726282	−0.363141	−	0.931734i	$-0.618296\pi$
$677$	−18.8973	−0.726282	−0.363141	+	0.931734i	$0.618296\pi$
$678$	−14.3800	−0.552260
$679$	−23.3072	−0.894447
$680$	−58.6502	−2.24913
$681$	−21.0580	−0.806945
$682$	−8.28615	−0.317293
$683$	−44.8226	−1.71509	−0.857545	−	0.514409i	$-0.828011\pi$
$683$	−44.8226	−1.71509	−0.857545	+	0.514409i	$0.828011\pi$
$684$	16.3878	0.626604
$685$	19.9446	0.762045
$686$	−34.8841	−1.33188
$687$	6.64594	0.253559
$688$	131.994	5.03221
$689$	5.47286	0.208499
$690$	9.13337	0.347701
$691$	27.2863	1.03802	0.519010	−	0.854768i	$-0.326301\pi$
$691$	27.2863	1.03802	0.519010	+	0.854768i	$0.326301\pi$
$692$	17.8540	0.678706
$693$	−12.5746	−0.477671
$694$	−51.5438	−1.95657
$695$	10.3894	0.394093
$696$	20.7009	0.784665
$697$	−2.03857	−0.0772165
$698$	64.5338	2.44264
$699$	−11.7172	−0.443185
$700$	22.4259	0.847620
$701$	30.5470	1.15375	0.576873	−	0.816834i	$-0.304273\pi$
$701$	30.5470	1.15375	0.576873	+	0.816834i	$0.304273\pi$
$702$	−2.72465	−0.102835
$703$	1.55672	0.0587129
$704$	−85.7194	−3.23067
$705$	0.903459	0.0340262
$706$	−71.3348	−2.68472
$707$	1.67823	0.0631162
$708$	9.59004	0.360416
$709$	10.8863	0.408843	0.204421	−	0.978883i	$-0.434469\pi$
$709$	10.8863	0.408843	0.204421	+	0.978883i	$0.434469\pi$
$710$	33.0716	1.24116
$711$	−9.29393	−0.348550
$712$	91.8821	3.44343
$713$	−3.35212	−0.125538
$714$	70.8312	2.65079
$715$	3.04118	0.113734
$716$	125.479	4.68939
$717$	9.34994	0.349180
$718$	55.1933	2.05979
$719$	26.7398	0.997226	0.498613	−	0.866825i	$-0.333843\pi$
$719$	26.7398	0.997226	0.498613	+	0.866825i	$0.333843\pi$
$720$	14.5693	0.542965
$721$	46.0042	1.71329
$722$	26.8936	1.00087
$723$	11.5311	0.428845
$724$	−135.510	−5.03618
$725$	2.21912	0.0824160
$726$	−4.77148	−0.177086
$727$	23.3778	0.867034	0.433517	−	0.901145i	$-0.357272\pi$
$727$	23.3778	0.867034	0.433517	+	0.901145i	$0.357272\pi$
$728$	38.5711	1.42954
$729$	1.00000	0.0370370
$730$	−11.3921	−0.421639
$731$	56.9607	2.10677
$732$	−38.7034	−1.43052
$733$	−1.76203	−0.0650819	−0.0325410	−	0.999470i	$-0.510360\pi$
$733$	−1.76203	−0.0650819	−0.0325410	+	0.999470i	$0.510360\pi$
$734$	85.6251	3.16048
$735$	−10.0965	−0.372413
$736$	−70.5264	−2.59964
$737$	−5.13385	−0.189108
$738$	0.883438	0.0325198
$739$	27.2340	1.00182	0.500910	−	0.865499i	$-0.332999\pi$
$739$	27.2340	1.00182	0.500910	+	0.865499i	$0.332999\pi$
$740$	2.79437	0.102723
$741$	3.02151	0.110998
$742$	61.6564	2.26348
$743$	−3.96009	−0.145282	−0.0726408	−	0.997358i	$-0.523143\pi$
$743$	−3.96009	−0.145282	−0.0726408	+	0.997358i	$0.523143\pi$
$744$	−9.32843	−0.341997
$745$	5.19787	0.190435
$746$	−74.8786	−2.74150
$747$	15.6482	0.572537
$748$	−103.705	−3.79183
$749$	27.7580	1.01425
$750$	2.72465	0.0994902
$751$	24.1090	0.879750	0.439875	−	0.898059i	$-0.355023\pi$
$751$	24.1090	0.879750	0.439875	+	0.898059i	$0.355023\pi$
$752$	−13.1627	−0.479996
$753$	−1.62765	−0.0593150
$754$	6.04632	0.220194
$755$	−9.54563	−0.347401
$756$	−22.4259	−0.815622
$757$	−2.02498	−0.0735993	−0.0367996	−	0.999323i	$-0.511716\pi$
$757$	−2.02498	−0.0735993	−0.0367996	+	0.999323i	$0.511716\pi$
$758$	−22.6696	−0.823398
$759$	10.1944	0.370034
$760$	−28.1860	−1.02241
$761$	39.9141	1.44688	0.723442	−	0.690385i	$-0.242559\pi$
$761$	39.9141	1.44688	0.723442	+	0.690385i	$0.242559\pi$
$762$	45.9078	1.66307
$763$	62.7532	2.27182
$764$	−109.957	−3.97809
$765$	6.28725	0.227316
$766$	−70.0168	−2.52981
$767$	1.76817	0.0638448
$768$	−38.2246	−1.37931
$769$	−7.59895	−0.274025	−0.137013	−	0.990569i	$-0.543750\pi$
$769$	−7.59895	−0.274025	−0.137013	+	0.990569i	$0.543750\pi$
$770$	34.2615	1.23470
$771$	3.02392	0.108904
$772$	−113.247	−4.07584
$773$	−27.1865	−0.977832	−0.488916	−	0.872331i	$-0.662608\pi$
$773$	−27.1865	−0.977832	−0.488916	+	0.872331i	$0.662608\pi$
$774$	−24.6846	−0.887268
$775$	−1.00000	−0.0359211
$776$	52.5830	1.88762
$777$	−2.13029	−0.0764239
$778$	54.9322	1.96942
$779$	−0.979693	−0.0351011
$780$	5.42372	0.194200
$781$	36.9136	1.32087
$782$	−57.4238	−2.05347
$783$	−2.21912	−0.0793048
$784$	147.098	5.25350
$785$	3.78478	0.135085
$786$	−7.07997	−0.252534
$787$	29.5935	1.05489	0.527447	−	0.849588i	$-0.323149\pi$
$787$	29.5935	1.05489	0.527447	+	0.849588i	$0.323149\pi$
$788$	−121.258	−4.31963
$789$	16.5116	0.587830
$790$	25.3227	0.900942
$791$	−21.8223	−0.775911
$792$	28.3694	1.00806
$793$	−7.13595	−0.253405
$794$	52.5071	1.86341
$795$	5.47286	0.194102
$796$	−81.6071	−2.89249
$797$	41.1610	1.45800	0.728998	−	0.684516i	$-0.239986\pi$
$797$	41.1610	1.45800	0.728998	+	0.684516i	$0.239986\pi$
$798$	34.0399	1.20500
$799$	−5.68028	−0.200954
$800$	−21.0393	−0.743852
$801$	−9.84969	−0.348022
$802$	−48.8994	−1.72670
$803$	−12.7155	−0.448721
$804$	−9.15584	−0.322901
$805$	13.8603	0.488512
$806$	−2.72465	−0.0959717
$807$	−23.6880	−0.833857
$808$	−3.78622	−0.133199
$809$	−16.5525	−0.581955	−0.290977	−	0.956730i	$-0.593980\pi$
$809$	−16.5525	−0.581955	−0.290977	+	0.956730i	$0.593980\pi$
$810$	−2.72465	−0.0957344
$811$	47.8407	1.67992	0.839958	−	0.542652i	$-0.182580\pi$
$811$	47.8407	1.67992	0.839958	+	0.542652i	$0.182580\pi$
$812$	49.7657	1.74643
$813$	−9.98151	−0.350067
$814$	4.26913	0.149633
$815$	4.07053	0.142584
$816$	−91.6007	−3.20667
$817$	27.3740	0.957697
$818$	−8.80111	−0.307724
$819$	−4.13479	−0.144481
$820$	−1.75858	−0.0614123
$821$	−28.3673	−0.990026	−0.495013	−	0.868886i	$-0.664837\pi$
$821$	−28.3673	−0.990026	−0.495013	+	0.868886i	$0.664837\pi$
$822$	54.3421	1.89540
$823$	−2.87974	−0.100381	−0.0501907	−	0.998740i	$-0.515983\pi$
$823$	−2.87974	−0.100381	−0.0501907	+	0.998740i	$0.515983\pi$
$824$	−103.789	−3.61567
$825$	3.04118	0.105880
$826$	19.9199	0.693102
$827$	27.0699	0.941314	0.470657	−	0.882316i	$-0.344017\pi$
$827$	27.0699	0.941314	0.470657	+	0.882316i	$0.344017\pi$
$828$	18.1810	0.631833
$829$	−47.0797	−1.63515	−0.817573	−	0.575826i	$-0.804681\pi$
$829$	−47.0797	−1.63515	−0.817573	+	0.575826i	$0.804681\pi$
$830$	−42.6358	−1.47991
$831$	−9.19122	−0.318840
$832$	−28.1862	−0.977182
$833$	63.4789	2.19941
$834$	28.3075	0.980210
$835$	−12.2220	−0.422961
$836$	−49.8383	−1.72369
$837$	1.00000	0.0345651
$838$	−84.5527	−2.92082
$839$	−24.6785	−0.851996	−0.425998	−	0.904724i	$-0.640077\pi$
$839$	−24.6785	−0.851996	−0.425998	+	0.904724i	$0.640077\pi$
$840$	38.5711	1.33083
$841$	−24.0755	−0.830190
$842$	−66.0706	−2.27694
$843$	−30.6451	−1.05547
$844$	−39.7679	−1.36887
$845$	1.00000	0.0344010
$846$	2.46161	0.0846319
$847$	−7.24094	−0.248802
$848$	−79.7357	−2.73813
$849$	0.434850	0.0149240
$850$	−17.1306	−0.587573
$851$	1.72706	0.0592028
$852$	65.8327	2.25539
$853$	−45.7178	−1.56535	−0.782673	−	0.622433i	$-0.786144\pi$
$853$	−45.7178	−1.56535	−0.782673	+	0.622433i	$0.786144\pi$
$854$	−80.3925	−2.75097
$855$	3.02151	0.103334
$856$	−62.6244	−2.14046
$857$	−51.0083	−1.74241	−0.871205	−	0.490919i	$-0.836661\pi$
$857$	−51.0083	−1.74241	−0.871205	+	0.490919i	$0.836661\pi$
$858$	8.28615	0.282885
$859$	41.6768	1.42199	0.710997	−	0.703196i	$-0.248244\pi$
$859$	41.6768	1.42199	0.710997	+	0.703196i	$0.248244\pi$
$860$	49.1373	1.67557
$861$	1.34066	0.0456896
$862$	−50.4465	−1.71821
$863$	−21.7352	−0.739875	−0.369937	−	0.929057i	$-0.620621\pi$
$863$	−21.7352	−0.739875	−0.369937	+	0.929057i	$0.620621\pi$
$864$	21.0393	0.715772
$865$	3.29183	0.111926
$866$	−13.8592	−0.470955
$867$	−22.5295	−0.765143
$868$	−22.4259	−0.761185
$869$	28.2645	0.958808
$870$	6.04632	0.204989
$871$	−1.68811	−0.0571995
$872$	−141.577	−4.79439
$873$	−5.63685	−0.190778
$874$	−27.5966	−0.933468
$875$	4.13479	0.139781
$876$	−22.6772	−0.766191
$877$	−6.29860	−0.212689	−0.106344	−	0.994329i	$-0.533915\pi$
$877$	−6.29860	−0.212689	−0.106344	+	0.994329i	$0.533915\pi$
$878$	34.7836	1.17389
$879$	13.1502	0.443545
$880$	−44.3078	−1.49362
$881$	28.3791	0.956116	0.478058	−	0.878328i	$-0.341341\pi$
$881$	28.3791	0.956116	0.478058	+	0.878328i	$0.341341\pi$
$882$	−27.5093	−0.926286
$883$	20.4716	0.688924	0.344462	−	0.938800i	$-0.388061\pi$
$883$	20.4716	0.688924	0.344462	+	0.938800i	$0.388061\pi$
$884$	−34.1003	−1.14692
$885$	1.76817	0.0594363
$886$	−83.0119	−2.78884
$887$	32.7627	1.10006	0.550031	−	0.835144i	$-0.314616\pi$
$887$	32.7627	1.10006	0.550031	+	0.835144i	$0.314616\pi$
$888$	4.80613	0.161283
$889$	69.6673	2.33657
$890$	26.8369	0.899577
$891$	−3.04118	−0.101883
$892$	145.926	4.88597
$893$	−2.72981	−0.0913497
$894$	14.1624	0.473661
$895$	23.1353	0.773329
$896$	−143.555	−4.79585
$897$	3.35212	0.111924
$898$	−10.4827	−0.349812
$899$	−2.21912	−0.0740117
$900$	5.42372	0.180791
$901$	−34.4093	−1.14634
$902$	−2.68669	−0.0894572
$903$	−37.4600	−1.24659
$904$	49.2330	1.63746
$905$	−24.9847	−0.830518
$906$	−26.0085	−0.864075
$907$	19.6456	0.652322	0.326161	−	0.945314i	$-0.394245\pi$
$907$	19.6456	0.652322	0.326161	+	0.945314i	$0.394245\pi$
$908$	114.213	3.79028
$909$	0.405880	0.0134622
$910$	11.2658	0.373459
$911$	55.5626	1.84087	0.920436	−	0.390894i	$-0.127834\pi$
$911$	55.5626	1.84087	0.920436	+	0.390894i	$0.127834\pi$
$912$	−44.0213	−1.45769
$913$	−47.5890	−1.57496
$914$	−71.8266	−2.37581
$915$	−7.13595	−0.235907
$916$	−36.0457	−1.19098
$917$	−10.7442	−0.354804
$918$	17.1306	0.565393
$919$	51.5442	1.70029	0.850143	−	0.526552i	$-0.176515\pi$
$919$	51.5442	1.70029	0.850143	+	0.526552i	$0.176515\pi$
$920$	−31.2701	−1.03094
$921$	11.5990	0.382201
$922$	14.4009	0.474269
$923$	12.1379	0.399525
$924$	68.2012	2.24366
$925$	0.515213	0.0169401
$926$	99.6274	3.27396
$927$	11.1261	0.365430
$928$	−46.6887	−1.53263
$929$	−41.1221	−1.34917	−0.674586	−	0.738196i	$-0.735678\pi$
$929$	−41.1221	−1.34917	−0.674586	+	0.738196i	$0.735678\pi$
$930$	−2.72465	−0.0893448
$931$	30.5065	0.999812
$932$	63.5508	2.08168
$933$	−10.9296	−0.357820
$934$	68.5623	2.24343
$935$	−19.1207	−0.625313
$936$	9.32843	0.304909
$937$	−9.06576	−0.296165	−0.148083	−	0.988975i	$-0.547310\pi$
$937$	−9.06576	−0.296165	−0.148083	+	0.988975i	$0.547310\pi$
$938$	−19.0180	−0.620959
$939$	28.8933	0.942898
$940$	−4.90011	−0.159824
$941$	37.3566	1.21779	0.608894	−	0.793251i	$-0.291613\pi$
$941$	37.3566	1.21779	0.608894	+	0.793251i	$0.291613\pi$
$942$	10.3122	0.335990
$943$	−1.08689	−0.0353940
$944$	−25.7609	−0.838446
$945$	−4.13479	−0.134505
$946$	75.0702	2.44074
$947$	9.67228	0.314307	0.157153	−	0.987574i	$-0.449768\pi$
$947$	9.67228	0.314307	0.157153	+	0.987574i	$0.449768\pi$
$948$	50.4077	1.63717
$949$	−4.18111	−0.135725
$950$	−8.23256	−0.267100
$951$	27.5341	0.892853
$952$	−242.506	−7.85967
$953$	16.8616	0.546200	0.273100	−	0.961986i	$-0.411951\pi$
$953$	16.8616	0.546200	0.273100	+	0.961986i	$0.411951\pi$
$954$	14.9116	0.482782
$955$	−20.2733	−0.656029
$956$	−50.7114	−1.64012
$957$	6.74874	0.218156
$958$	88.8766	2.87147
$959$	82.4667	2.66299
$960$	−28.1862	−0.909706
$961$	1.00000	0.0322581
$962$	1.40377	0.0452595
$963$	6.71328	0.216332
$964$	−62.5413	−2.01432
$965$	−20.8799	−0.672148
$966$	37.7645	1.21505
$967$	19.8200	0.637368	0.318684	−	0.947861i	$-0.396759\pi$
$967$	19.8200	0.637368	0.318684	+	0.947861i	$0.396759\pi$
$968$	16.3362	0.525065
$969$	−18.9970	−0.610272
$970$	15.3584	0.493130
$971$	27.9805	0.897937	0.448968	−	0.893548i	$-0.351792\pi$
$971$	27.9805	0.897937	0.448968	+	0.893548i	$0.351792\pi$
$972$	−5.42372	−0.173966
$973$	42.9580	1.37717
$974$	−42.2443	−1.35359
$975$	1.00000	0.0320256
$976$	103.966	3.32786
$977$	−46.6927	−1.49383	−0.746915	−	0.664919i	$-0.768466\pi$
$977$	−46.6927	−1.49383	−0.746915	+	0.664919i	$0.768466\pi$
$978$	11.0908	0.354644
$979$	29.9547	0.957355
$980$	54.7603	1.74925
$981$	15.1769	0.484561
$982$	−6.35304	−0.202734
$983$	53.0196	1.69106	0.845531	−	0.533927i	$-0.179284\pi$
$983$	53.0196	1.69106	0.845531	+	0.533927i	$0.179284\pi$
$984$	−3.02464	−0.0964221
$985$	−22.3569	−0.712351
$986$	−38.0147	−1.21064
$987$	3.73561	0.118906
$988$	−16.3878	−0.521366
$989$	30.3693	0.965688
$990$	8.28615	0.263351
$991$	−5.94856	−0.188962	−0.0944812	−	0.995527i	$-0.530119\pi$
$991$	−5.94856	−0.188962	−0.0944812	+	0.995527i	$0.530119\pi$
$992$	21.0393	0.667999
$993$	24.6750	0.783038
$994$	136.744	4.33726
$995$	−15.0463	−0.477001
$996$	−84.8713	−2.68925
$997$	20.0561	0.635184	0.317592	−	0.948228i	$-0.397126\pi$
$997$	20.0561	0.635184	0.317592	+	0.948228i	$0.397126\pi$
$998$	26.4098	0.835987
$999$	−0.515213	−0.0163006

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.bd.1.1	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.bd.1.1	✓	14	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:	\( N \)	\(=\)	\( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.72465 q^{2} -1.00000 q^{3} +5.42372 q^{4} +1.00000 q^{5} +2.72465 q^{6} +4.13479 q^{7} -9.32843 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.72465 q^{2} -1.00000 q^{3} +5.42372 q^{4} +1.00000 q^{5} +2.72465 q^{6} +4.13479 q^{7} -9.32843 q^{8} +1.00000 q^{9} -2.72465 q^{10} -3.04118 q^{11} -5.42372 q^{12} -1.00000 q^{13} -11.2658 q^{14} -1.00000 q^{15} +14.5693 q^{16} +6.28725 q^{17} -2.72465 q^{18} +3.02151 q^{19} +5.42372 q^{20} -4.13479 q^{21} +8.28615 q^{22} +3.35212 q^{23} +9.32843 q^{24} +1.00000 q^{25} +2.72465 q^{26} -1.00000 q^{27} +22.4259 q^{28} +2.21912 q^{29} +2.72465 q^{30} -1.00000 q^{31} -21.0393 q^{32} +3.04118 q^{33} -17.1306 q^{34} +4.13479 q^{35} +5.42372 q^{36} +0.515213 q^{37} -8.23256 q^{38} +1.00000 q^{39} -9.32843 q^{40} -0.324239 q^{41} +11.2658 q^{42} +9.05972 q^{43} -16.4945 q^{44} +1.00000 q^{45} -9.13337 q^{46} -0.903459 q^{47} -14.5693 q^{48} +10.0965 q^{49} -2.72465 q^{50} -6.28725 q^{51} -5.42372 q^{52} -5.47286 q^{53} +2.72465 q^{54} -3.04118 q^{55} -38.5711 q^{56} -3.02151 q^{57} -6.04632 q^{58} -1.76817 q^{59} -5.42372 q^{60} +7.13595 q^{61} +2.72465 q^{62} +4.13479 q^{63} +28.1862 q^{64} -1.00000 q^{65} -8.28615 q^{66} +1.68811 q^{67} +34.1003 q^{68} -3.35212 q^{69} -11.2658 q^{70} -12.1379 q^{71} -9.32843 q^{72} +4.18111 q^{73} -1.40377 q^{74} -1.00000 q^{75} +16.3878 q^{76} -12.5746 q^{77} -2.72465 q^{78} -9.29393 q^{79} +14.5693 q^{80} +1.00000 q^{81} +0.883438 q^{82} +15.6482 q^{83} -22.4259 q^{84} +6.28725 q^{85} -24.6846 q^{86} -2.21912 q^{87} +28.3694 q^{88} -9.84969 q^{89} -2.72465 q^{90} -4.13479 q^{91} +18.1810 q^{92} +1.00000 q^{93} +2.46161 q^{94} +3.02151 q^{95} +21.0393 q^{96} -5.63685 q^{97} -27.5093 q^{98} -3.04118 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} + 14 q^{5} + 2 q^{6} + 5 q^{7} - 3 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 - 14 * q^3 + 12 * q^4 + 14 * q^5 + 2 * q^6 + 5 * q^7 - 3 * q^8 + 14 * q^9	\( 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} + 14 q^{5} + 2 q^{6} + 5 q^{7} - 3 q^{8} + 14 q^{9} - 2 q^{10} + 4 q^{11} - 12 q^{12} - 14 q^{13} - 7 q^{14} - 14 q^{15} + 8 q^{16} + 7 q^{17} - 2 q^{18} + 2 q^{19} + 12 q^{20} - 5 q^{21} + 21 q^{22} + 31 q^{23} + 3 q^{24} + 14 q^{25} + 2 q^{26} - 14 q^{27} + 8 q^{28} - 5 q^{29} + 2 q^{30} - 14 q^{31} - 8 q^{32} - 4 q^{33} - 11 q^{34} + 5 q^{35} + 12 q^{36} + 15 q^{37} + 2 q^{38} + 14 q^{39} - 3 q^{40} + 7 q^{41} + 7 q^{42} + 30 q^{43} + q^{44} + 14 q^{45} + 2 q^{46} + 23 q^{47} - 8 q^{48} + 11 q^{49} - 2 q^{50} - 7 q^{51} - 12 q^{52} + 14 q^{53} + 2 q^{54} + 4 q^{55} - 23 q^{56} - 2 q^{57} + 22 q^{58} + 10 q^{59} - 12 q^{60} + 2 q^{62} + 5 q^{63} - 3 q^{64} - 14 q^{65} - 21 q^{66} + 28 q^{67} + 23 q^{68} - 31 q^{69} - 7 q^{70} - 35 q^{71} - 3 q^{72} + 27 q^{73} - 12 q^{74} - 14 q^{75} + 26 q^{76} + 24 q^{77} - 2 q^{78} + 9 q^{79} + 8 q^{80} + 14 q^{81} + 45 q^{82} + 49 q^{83} - 8 q^{84} + 7 q^{85} + 4 q^{86} + 5 q^{87} + 49 q^{88} + 5 q^{89} - 2 q^{90} - 5 q^{91} + 107 q^{92} + 14 q^{93} + 26 q^{94} + 2 q^{95} + 8 q^{96} + 9 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 - 14 * q^3 + 12 * q^4 + 14 * q^5 + 2 * q^6 + 5 * q^7 - 3 * q^8 + 14 * q^9 - 2 * q^10 + 4 * q^11 - 12 * q^12 - 14 * q^13 - 7 * q^14 - 14 * q^15 + 8 * q^16 + 7 * q^17 - 2 * q^18 + 2 * q^19 + 12 * q^20 - 5 * q^21 + 21 * q^22 + 31 * q^23 + 3 * q^24 + 14 * q^25 + 2 * q^26 - 14 * q^27 + 8 * q^28 - 5 * q^29 + 2 * q^30 - 14 * q^31 - 8 * q^32 - 4 * q^33 - 11 * q^34 + 5 * q^35 + 12 * q^36 + 15 * q^37 + 2 * q^38 + 14 * q^39 - 3 * q^40 + 7 * q^41 + 7 * q^42 + 30 * q^43 + q^44 + 14 * q^45 + 2 * q^46 + 23 * q^47 - 8 * q^48 + 11 * q^49 - 2 * q^50 - 7 * q^51 - 12 * q^52 + 14 * q^53 + 2 * q^54 + 4 * q^55 - 23 * q^56 - 2 * q^57 + 22 * q^58 + 10 * q^59 - 12 * q^60 + 2 * q^62 + 5 * q^63 - 3 * q^64 - 14 * q^65 - 21 * q^66 + 28 * q^67 + 23 * q^68 - 31 * q^69 - 7 * q^70 - 35 * q^71 - 3 * q^72 + 27 * q^73 - 12 * q^74 - 14 * q^75 + 26 * q^76 + 24 * q^77 - 2 * q^78 + 9 * q^79 + 8 * q^80 + 14 * q^81 + 45 * q^82 + 49 * q^83 - 8 * q^84 + 7 * q^85 + 4 * q^86 + 5 * q^87 + 49 * q^88 + 5 * q^89 - 2 * q^90 - 5 * q^91 + 107 * q^92 + 14 * q^93 + 26 * q^94 + 2 * q^95 + 8 * q^96 + 9 * q^97 - 6 * q^98 + 4 * q^99

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