LMFDB - Embedded newform 6045.2.a.bd.1.3

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			1.3
Root			$1.95655$ 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)

$f(q)$	$=$	$q-1.95655 q^{2} -1.00000 q^{3} +1.82809 q^{4} +1.00000 q^{5} +1.95655 q^{6} -1.02534 q^{7} +0.336358 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.95655 q^{2} -1.00000 q^{3} +1.82809 q^{4} +1.00000 q^{5} +1.95655 q^{6} -1.02534 q^{7} +0.336358 q^{8} +1.00000 q^{9} -1.95655 q^{10} +2.02003 q^{11} -1.82809 q^{12} -1.00000 q^{13} +2.00612 q^{14} -1.00000 q^{15} -4.31427 q^{16} +1.68368 q^{17} -1.95655 q^{18} +1.28184 q^{19} +1.82809 q^{20} +1.02534 q^{21} -3.95229 q^{22} +7.89696 q^{23} -0.336358 q^{24} +1.00000 q^{25} +1.95655 q^{26} -1.00000 q^{27} -1.87440 q^{28} +7.29349 q^{29} +1.95655 q^{30} -1.00000 q^{31} +7.76837 q^{32} -2.02003 q^{33} -3.29419 q^{34} -1.02534 q^{35} +1.82809 q^{36} +3.99368 q^{37} -2.50798 q^{38} +1.00000 q^{39} +0.336358 q^{40} -11.2311 q^{41} -2.00612 q^{42} +0.405533 q^{43} +3.69279 q^{44} +1.00000 q^{45} -15.4508 q^{46} +11.1077 q^{47} +4.31427 q^{48} -5.94869 q^{49} -1.95655 q^{50} -1.68368 q^{51} -1.82809 q^{52} -4.73719 q^{53} +1.95655 q^{54} +2.02003 q^{55} -0.344879 q^{56} -1.28184 q^{57} -14.2701 q^{58} -10.9594 q^{59} -1.82809 q^{60} +11.9130 q^{61} +1.95655 q^{62} -1.02534 q^{63} -6.57066 q^{64} -1.00000 q^{65} +3.95229 q^{66} +11.7295 q^{67} +3.07790 q^{68} -7.89696 q^{69} +2.00612 q^{70} +8.21187 q^{71} +0.336358 q^{72} +11.4048 q^{73} -7.81383 q^{74} -1.00000 q^{75} +2.34331 q^{76} -2.07121 q^{77} -1.95655 q^{78} -5.99899 q^{79} -4.31427 q^{80} +1.00000 q^{81} +21.9742 q^{82} -10.9309 q^{83} +1.87440 q^{84} +1.68368 q^{85} -0.793446 q^{86} -7.29349 q^{87} +0.679454 q^{88} -6.09497 q^{89} -1.95655 q^{90} +1.02534 q^{91} +14.4363 q^{92} +1.00000 q^{93} -21.7327 q^{94} +1.28184 q^{95} -7.76837 q^{96} +0.783630 q^{97} +11.6389 q^{98} +2.02003 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.95655	−1.38349	−0.691745	−	0.722142i	$-0.743158\pi$
$2$	−1.95655	−1.38349	−0.691745	+	0.722142i	$0.743158\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.82809	0.914043
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.95655	0.798758
$7$	−1.02534	−0.387540	−0.193770	−	0.981047i	$-0.562072\pi$
$7$	−1.02534	−0.387540	−0.193770	+	0.981047i	$0.562072\pi$
$8$	0.336358	0.118920
$9$	1.00000	0.333333
$10$	−1.95655	−0.618715
$11$	2.02003	0.609063	0.304531	−	0.952502i	$-0.401500\pi$
$11$	2.02003	0.609063	0.304531	+	0.952502i	$0.401500\pi$
$12$	−1.82809	−0.527723
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.00612	0.536158
$15$	−1.00000	−0.258199
$16$	−4.31427	−1.07857
$17$	1.68368	0.408351	0.204176	−	0.978934i	$-0.434549\pi$
$17$	1.68368	0.408351	0.204176	+	0.978934i	$0.434549\pi$
$18$	−1.95655	−0.461163
$19$	1.28184	0.294074	0.147037	−	0.989131i	$-0.453026\pi$
$19$	1.28184	0.294074	0.147037	+	0.989131i	$0.453026\pi$
$20$	1.82809	0.408773
$21$	1.02534	0.223747
$22$	−3.95229	−0.842632
$23$	7.89696	1.64663	0.823315	−	0.567585i	$-0.192122\pi$
$23$	7.89696	1.64663	0.823315	+	0.567585i	$0.192122\pi$
$24$	−0.336358	−0.0686587
$25$	1.00000	0.200000
$26$	1.95655	0.383711
$27$	−1.00000	−0.192450
$28$	−1.87440	−0.354229
$29$	7.29349	1.35437	0.677184	−	0.735814i	$-0.263200\pi$
$29$	7.29349	1.35437	0.677184	+	0.735814i	$0.263200\pi$
$30$	1.95655	0.357215
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	7.76837	1.37327
$33$	−2.02003	−0.351643
$34$	−3.29419	−0.564950
$35$	−1.02534	−0.173313
$36$	1.82809	0.304681
$37$	3.99368	0.656557	0.328278	−	0.944581i	$-0.393532\pi$
$37$	3.99368	0.656557	0.328278	+	0.944581i	$0.393532\pi$
$38$	−2.50798	−0.406848
$39$	1.00000	0.160128
$40$	0.336358	0.0531828
$41$	−11.2311	−1.75400	−0.877001	−	0.480489i	$-0.840459\pi$
$41$	−11.2311	−1.75400	−0.877001	+	0.480489i	$0.840459\pi$
$42$	−2.00612	−0.309551
$43$	0.405533	0.0618433	0.0309216	−	0.999522i	$-0.490156\pi$
$43$	0.405533	0.0618433	0.0309216	+	0.999522i	$0.490156\pi$
$44$	3.69279	0.556710
$45$	1.00000	0.149071
$46$	−15.4508	−2.27810
$47$	11.1077	1.62022	0.810109	−	0.586279i	$-0.199408\pi$
$47$	11.1077	1.62022	0.810109	+	0.586279i	$0.199408\pi$
$48$	4.31427	0.622712
$49$	−5.94869	−0.849812
$50$	−1.95655	−0.276698
$51$	−1.68368	−0.235762
$52$	−1.82809	−0.253510
$53$	−4.73719	−0.650703	−0.325351	−	0.945593i	$-0.605483\pi$
$53$	−4.73719	−0.650703	−0.325351	+	0.945593i	$0.605483\pi$
$54$	1.95655	0.266253
$55$	2.02003	0.272381
$56$	−0.344879	−0.0460864
$57$	−1.28184	−0.169783
$58$	−14.2701	−1.87375
$59$	−10.9594	−1.42679	−0.713397	−	0.700760i	$-0.752844\pi$
$59$	−10.9594	−1.42679	−0.713397	+	0.700760i	$0.752844\pi$
$60$	−1.82809	−0.236005
$61$	11.9130	1.52530	0.762649	−	0.646813i	$-0.223898\pi$
$61$	11.9130	1.52530	0.762649	+	0.646813i	$0.223898\pi$
$62$	1.95655	0.248482
$63$	−1.02534	−0.129180
$64$	−6.57066	−0.821333
$65$	−1.00000	−0.124035
$66$	3.95229	0.486494
$67$	11.7295	1.43298	0.716492	−	0.697596i	$-0.245747\pi$
$67$	11.7295	1.43298	0.716492	+	0.697596i	$0.245747\pi$
$68$	3.07790	0.373251
$69$	−7.89696	−0.950682
$70$	2.00612	0.239777
$71$	8.21187	0.974570	0.487285	−	0.873243i	$-0.337987\pi$
$71$	8.21187	0.974570	0.487285	+	0.873243i	$0.337987\pi$
$72$	0.336358	0.0396401
$73$	11.4048	1.33483	0.667414	−	0.744687i	$-0.267401\pi$
$73$	11.4048	1.33483	0.667414	+	0.744687i	$0.267401\pi$
$74$	−7.81383	−0.908340
$75$	−1.00000	−0.115470
$76$	2.34331	0.268796
$77$	−2.07121	−0.236036
$78$	−1.95655	−0.221536
$79$	−5.99899	−0.674939	−0.337470	−	0.941336i	$-0.609571\pi$
$79$	−5.99899	−0.674939	−0.337470	+	0.941336i	$0.609571\pi$
$80$	−4.31427	−0.482350
$81$	1.00000	0.111111
$82$	21.9742	2.42664
$83$	−10.9309	−1.19982	−0.599912	−	0.800066i	$-0.704798\pi$
$83$	−10.9309	−1.19982	−0.599912	+	0.800066i	$0.704798\pi$
$84$	1.87440	0.204514
$85$	1.68368	0.182620
$86$	−0.793446	−0.0855595
$87$	−7.29349	−0.781944
$88$	0.679454	0.0724300
$89$	−6.09497	−0.646065	−0.323033	−	0.946388i	$-0.604702\pi$
$89$	−6.09497	−0.646065	−0.323033	+	0.946388i	$0.604702\pi$
$90$	−1.95655	−0.206238
$91$	1.02534	0.107484
$92$	14.4363	1.50509
$93$	1.00000	0.103695
$94$	−21.7327	−2.24156
$95$	1.28184	0.131514
$96$	−7.76837	−0.792856
$97$	0.783630	0.0795656	0.0397828	−	0.999208i	$-0.487333\pi$
$97$	0.783630	0.0795656	0.0397828	+	0.999208i	$0.487333\pi$
$98$	11.6389	1.17571
$99$	2.02003	0.203021
$100$	1.82809	0.182809
$101$	14.0352	1.39656	0.698278	−	0.715827i	$-0.253950\pi$
$101$	14.0352	1.39656	0.698278	+	0.715827i	$0.253950\pi$
$102$	3.29419	0.326174
$103$	7.39750	0.728897	0.364449	−	0.931224i	$-0.381258\pi$
$103$	7.39750	0.728897	0.364449	+	0.931224i	$0.381258\pi$
$104$	−0.336358	−0.0329826
$105$	1.02534	0.100062
$106$	9.26854	0.900240
$107$	8.97518	0.867663	0.433832	−	0.900994i	$-0.357161\pi$
$107$	8.97518	0.867663	0.433832	+	0.900994i	$0.357161\pi$
$108$	−1.82809	−0.175908
$109$	3.60854	0.345636	0.172818	−	0.984954i	$-0.444713\pi$
$109$	3.60854	0.345636	0.172818	+	0.984954i	$0.444713\pi$
$110$	−3.95229	−0.376837
$111$	−3.99368	−0.379063
$112$	4.42358	0.417989
$113$	11.9895	1.12787	0.563937	−	0.825818i	$-0.309286\pi$
$113$	11.9895	1.12787	0.563937	+	0.825818i	$0.309286\pi$
$114$	2.50798	0.234894
$115$	7.89696	0.736395
$116$	13.3331	1.23795
$117$	−1.00000	−0.0924500
$118$	21.4426	1.97395
$119$	−1.72633	−0.158253
$120$	−0.336358	−0.0307051
$121$	−6.91947	−0.629042
$122$	−23.3083	−2.11023
$123$	11.2311	1.01267
$124$	−1.82809	−0.164167
$125$	1.00000	0.0894427
$126$	2.00612	0.178719
$127$	−20.5863	−1.82674	−0.913368	−	0.407134i	$-0.866528\pi$
$127$	−20.5863	−1.82674	−0.913368	+	0.407134i	$0.866528\pi$
$128$	−2.68092	−0.236962
$129$	−0.405533	−0.0357052
$130$	1.95655	0.171601
$131$	−10.8842	−0.950953	−0.475477	−	0.879728i	$-0.657724\pi$
$131$	−10.8842	−0.950953	−0.475477	+	0.879728i	$0.657724\pi$
$132$	−3.69279	−0.321417
$133$	−1.31431	−0.113965
$134$	−22.9493	−1.98252
$135$	−1.00000	−0.0860663
$136$	0.566317	0.0485613
$137$	−2.12215	−0.181307	−0.0906537	−	0.995882i	$-0.528896\pi$
$137$	−2.12215	−0.181307	−0.0906537	+	0.995882i	$0.528896\pi$
$138$	15.4508	1.31526
$139$	6.41933	0.544481	0.272240	−	0.962229i	$-0.412235\pi$
$139$	6.41933	0.544481	0.272240	+	0.962229i	$0.412235\pi$
$140$	−1.87440	−0.158416
$141$	−11.1077	−0.935434
$142$	−16.0669	−1.34831
$143$	−2.02003	−0.168924
$144$	−4.31427	−0.359523
$145$	7.29349	0.605691
$146$	−22.3140	−1.84672
$147$	5.94869	0.490639
$148$	7.30079	0.600121
$149$	−12.5262	−1.02619	−0.513094	−	0.858332i	$-0.671501\pi$
$149$	−12.5262	−1.02619	−0.513094	+	0.858332i	$0.671501\pi$
$150$	1.95655	0.159752
$151$	12.0571	0.981194	0.490597	−	0.871387i	$-0.336779\pi$
$151$	12.0571	0.981194	0.490597	+	0.871387i	$0.336779\pi$
$152$	0.431156	0.0349713
$153$	1.68368	0.136117
$154$	4.05243	0.326554
$155$	−1.00000	−0.0803219
$156$	1.82809	0.146364
$157$	23.8222	1.90121	0.950607	−	0.310396i	$-0.100462\pi$
$157$	23.8222	1.90121	0.950607	+	0.310396i	$0.100462\pi$
$158$	11.7373	0.933771
$159$	4.73719	0.375683
$160$	7.76837	0.614144
$161$	−8.09703	−0.638136
$162$	−1.95655	−0.153721
$163$	−10.6459	−0.833852	−0.416926	−	0.908940i	$-0.636893\pi$
$163$	−10.6459	−0.833852	−0.416926	+	0.908940i	$0.636893\pi$
$164$	−20.5314	−1.60323
$165$	−2.02003	−0.157259
$166$	21.3869	1.65994
$167$	−10.8731	−0.841388	−0.420694	−	0.907203i	$-0.638213\pi$
$167$	−10.8731	−0.841388	−0.420694	+	0.907203i	$0.638213\pi$
$168$	0.344879	0.0266080
$169$	1.00000	0.0769231
$170$	−3.29419	−0.252653
$171$	1.28184	0.0980245
$172$	0.741350	0.0565274
$173$	−7.06835	−0.537397	−0.268698	−	0.963224i	$-0.586593\pi$
$173$	−7.06835	−0.537397	−0.268698	+	0.963224i	$0.586593\pi$
$174$	14.2701	1.08181
$175$	−1.02534	−0.0775081
$176$	−8.71497	−0.656916
$177$	10.9594	0.823760
$178$	11.9251	0.893825
$179$	−14.8383	−1.10907	−0.554533	−	0.832161i	$-0.687103\pi$
$179$	−14.8383	−1.10907	−0.554533	+	0.832161i	$0.687103\pi$
$180$	1.82809	0.136258
$181$	−5.76824	−0.428750	−0.214375	−	0.976751i	$-0.568771\pi$
$181$	−5.76824	−0.428750	−0.214375	+	0.976751i	$0.568771\pi$
$182$	−2.00612	−0.148703
$183$	−11.9130	−0.880631
$184$	2.65620	0.195818
$185$	3.99368	0.293621
$186$	−1.95655	−0.143461
$187$	3.40108	0.248712
$188$	20.3058	1.48095
$189$	1.02534	0.0745822
$190$	−2.50798	−0.181948
$191$	−9.77567	−0.707342	−0.353671	−	0.935370i	$-0.615067\pi$
$191$	−9.77567	−0.707342	−0.353671	+	0.935370i	$0.615067\pi$
$192$	6.57066	0.474197
$193$	17.5483	1.26315	0.631577	−	0.775313i	$-0.282408\pi$
$193$	17.5483	1.26315	0.631577	+	0.775313i	$0.282408\pi$
$194$	−1.53321	−0.110078
$195$	1.00000	0.0716115
$196$	−10.8747	−0.776765
$197$	−14.0243	−0.999193	−0.499596	−	0.866258i	$-0.666518\pi$
$197$	−14.0243	−0.999193	−0.499596	+	0.866258i	$0.666518\pi$
$198$	−3.95229	−0.280877
$199$	−5.04763	−0.357817	−0.178909	−	0.983866i	$-0.557257\pi$
$199$	−5.04763	−0.357817	−0.178909	+	0.983866i	$0.557257\pi$
$200$	0.336358	0.0237841
$201$	−11.7295	−0.827333
$202$	−27.4606	−1.93212
$203$	−7.47827	−0.524872
$204$	−3.07790	−0.215496
$205$	−11.2311	−0.784413
$206$	−14.4736	−1.00842
$207$	7.89696	0.548877
$208$	4.31427	0.299141
$209$	2.58935	0.179109
$210$	−2.00612	−0.138435
$211$	−16.6476	−1.14607	−0.573035	−	0.819531i	$-0.694234\pi$
$211$	−16.6476	−1.14607	−0.573035	+	0.819531i	$0.694234\pi$
$212$	−8.65999	−0.594770
$213$	−8.21187	−0.562668
$214$	−17.5604	−1.20040
$215$	0.405533	0.0276571
$216$	−0.336358	−0.0228862
$217$	1.02534	0.0696043
$218$	−7.06030	−0.478184
$219$	−11.4048	−0.770663
$220$	3.69279	0.248968
$221$	−1.68368	−0.113256
$222$	7.81383	0.524430
$223$	−2.35711	−0.157844	−0.0789218	−	0.996881i	$-0.525148\pi$
$223$	−2.35711	−0.157844	−0.0789218	+	0.996881i	$0.525148\pi$
$224$	−7.96519	−0.532197
$225$	1.00000	0.0666667
$226$	−23.4580	−1.56040
$227$	−17.0902	−1.13431	−0.567157	−	0.823610i	$-0.691957\pi$
$227$	−17.0902	−1.13431	−0.567157	+	0.823610i	$0.691957\pi$
$228$	−2.34331	−0.155189
$229$	0.766365	0.0506429	0.0253214	−	0.999679i	$-0.491939\pi$
$229$	0.766365	0.0506429	0.0253214	+	0.999679i	$0.491939\pi$
$230$	−15.4508	−1.01880
$231$	2.07121	0.136276
$232$	2.45322	0.161062
$233$	−1.88258	−0.123332	−0.0616660	−	0.998097i	$-0.519641\pi$
$233$	−1.88258	−0.123332	−0.0616660	+	0.998097i	$0.519641\pi$
$234$	1.95655	0.127904
$235$	11.1077	0.724584
$236$	−20.0347	−1.30415
$237$	5.99899	0.389676
$238$	3.37765	0.218941
$239$	22.1805	1.43474	0.717369	−	0.696693i	$-0.245346\pi$
$239$	22.1805	1.43474	0.717369	+	0.696693i	$0.245346\pi$
$240$	4.31427	0.278485
$241$	1.33837	0.0862118	0.0431059	−	0.999071i	$-0.486275\pi$
$241$	1.33837	0.0862118	0.0431059	+	0.999071i	$0.486275\pi$
$242$	13.5383	0.870274
$243$	−1.00000	−0.0641500
$244$	21.7779	1.39419
$245$	−5.94869	−0.380048
$246$	−21.9742	−1.40102
$247$	−1.28184	−0.0815613
$248$	−0.336358	−0.0213587
$249$	10.9309	0.692719
$250$	−1.95655	−0.123743
$251$	27.7834	1.75367	0.876837	−	0.480788i	$-0.159649\pi$
$251$	27.7834	1.75367	0.876837	+	0.480788i	$0.159649\pi$
$252$	−1.87440	−0.118076
$253$	15.9521	1.00290
$254$	40.2781	2.52727
$255$	−1.68368	−0.105436
$256$	18.3867	1.14917
$257$	−10.1707	−0.634433	−0.317216	−	0.948353i	$-0.602748\pi$
$257$	−10.1707	−0.634433	−0.317216	+	0.948353i	$0.602748\pi$
$258$	0.793446	0.0493978
$259$	−4.09486	−0.254442
$260$	−1.82809	−0.113373
$261$	7.29349	0.451456
$262$	21.2954	1.31563
$263$	25.4289	1.56802	0.784008	−	0.620751i	$-0.213172\pi$
$263$	25.4289	1.56802	0.784008	+	0.620751i	$0.213172\pi$
$264$	−0.679454	−0.0418175
$265$	−4.73719	−0.291003
$266$	2.57152	0.157670
$267$	6.09497	0.373006
$268$	21.4425	1.30981
$269$	−9.84853	−0.600475	−0.300238	−	0.953864i	$-0.597066\pi$
$269$	−9.84853	−0.600475	−0.300238	+	0.953864i	$0.597066\pi$
$270$	1.95655	0.119072
$271$	−16.8031	−1.02071	−0.510357	−	0.859963i	$-0.670487\pi$
$271$	−16.8031	−1.02071	−0.510357	+	0.859963i	$0.670487\pi$
$272$	−7.26383	−0.440435
$273$	−1.02534	−0.0620561
$274$	4.15209	0.250837
$275$	2.02003	0.121813
$276$	−14.4363	−0.868965
$277$	−32.8960	−1.97653	−0.988265	−	0.152748i	$-0.951188\pi$
$277$	−32.8960	−1.97653	−0.988265	+	0.152748i	$0.951188\pi$
$278$	−12.5597	−0.753283
$279$	−1.00000	−0.0598684
$280$	−0.344879	−0.0206105
$281$	−6.98727	−0.416825	−0.208413	−	0.978041i	$-0.566830\pi$
$281$	−6.98727	−0.416825	−0.208413	+	0.978041i	$0.566830\pi$
$282$	21.7327	1.29416
$283$	15.5280	0.923046	0.461523	−	0.887128i	$-0.347303\pi$
$283$	15.5280	0.923046	0.461523	+	0.887128i	$0.347303\pi$
$284$	15.0120	0.890799
$285$	−1.28184	−0.0759295
$286$	3.95229	0.233704
$287$	11.5156	0.679746
$288$	7.76837	0.457756
$289$	−14.1652	−0.833249
$290$	−14.2701	−0.837968
$291$	−0.783630	−0.0459372
$292$	20.8489	1.22009
$293$	−2.15734	−0.126033	−0.0630164	−	0.998012i	$-0.520072\pi$
$293$	−2.15734	−0.126033	−0.0630164	+	0.998012i	$0.520072\pi$
$294$	−11.6389	−0.678795
$295$	−10.9594	−0.638081
$296$	1.34330	0.0780780
$297$	−2.02003	−0.117214
$298$	24.5082	1.41972
$299$	−7.89696	−0.456693
$300$	−1.82809	−0.105545
$301$	−0.415808	−0.0239668
$302$	−23.5903	−1.35747
$303$	−14.0352	−0.806302
$304$	−5.53019	−0.317178
$305$	11.9130	0.682134
$306$	−3.29419	−0.188317
$307$	20.8418	1.18951	0.594753	−	0.803909i	$-0.297250\pi$
$307$	20.8418	1.18951	0.594753	+	0.803909i	$0.297250\pi$
$308$	−3.78635	−0.215747
$309$	−7.39750	−0.420829
$310$	1.95655	0.111125
$311$	34.3500	1.94781	0.973906	−	0.226951i	$-0.0728758\pi$
$311$	34.3500	1.94781	0.973906	+	0.226951i	$0.0728758\pi$
$312$	0.336358	0.0190425
$313$	1.73371	0.0979949	0.0489975	−	0.998799i	$-0.484397\pi$
$313$	1.73371	0.0979949	0.0489975	+	0.998799i	$0.484397\pi$
$314$	−46.6092	−2.63031
$315$	−1.02534	−0.0577711
$316$	−10.9667	−0.616924
$317$	17.7318	0.995916	0.497958	−	0.867201i	$-0.334083\pi$
$317$	17.7318	0.995916	0.497958	+	0.867201i	$0.334083\pi$
$318$	−9.26854	−0.519754
$319$	14.7331	0.824895
$320$	−6.57066	−0.367311
$321$	−8.97518	−0.500946
$322$	15.8422	0.882854
$323$	2.15820	0.120085
$324$	1.82809	0.101560
$325$	−1.00000	−0.0554700
$326$	20.8292	1.15363
$327$	−3.60854	−0.199553
$328$	−3.77766	−0.208587
$329$	−11.3891	−0.627900
$330$	3.95229	0.217567
$331$	3.08885	0.169779	0.0848893	−	0.996390i	$-0.472946\pi$
$331$	3.08885	0.169779	0.0848893	+	0.996390i	$0.472946\pi$
$332$	−19.9827	−1.09669
$333$	3.99368	0.218852
$334$	21.2738	1.16405
$335$	11.7295	0.640850
$336$	−4.42358	−0.241326
$337$	3.99932	0.217857	0.108928	−	0.994050i	$-0.465258\pi$
$337$	3.99932	0.217857	0.108928	+	0.994050i	$0.465258\pi$
$338$	−1.95655	−0.106422
$339$	−11.9895	−0.651178
$340$	3.07790	0.166923
$341$	−2.02003	−0.109391
$342$	−2.50798	−0.135616
$343$	13.2767	0.716877
$344$	0.136404	0.00735442
$345$	−7.89696	−0.425158
$346$	13.8296	0.743483
$347$	−27.0596	−1.45263	−0.726317	−	0.687360i	$-0.758769\pi$
$347$	−27.0596	−1.45263	−0.726317	+	0.687360i	$0.758769\pi$
$348$	−13.3331	−0.714731
$349$	4.78841	0.256318	0.128159	−	0.991754i	$-0.459093\pi$
$349$	4.78841	0.256318	0.128159	+	0.991754i	$0.459093\pi$
$350$	2.00612	0.107232
$351$	1.00000	0.0533761
$352$	15.6924	0.836406
$353$	−14.6711	−0.780866	−0.390433	−	0.920631i	$-0.627675\pi$
$353$	−14.6711	−0.780866	−0.390433	+	0.920631i	$0.627675\pi$
$354$	−21.4426	−1.13966
$355$	8.21187	0.435841
$356$	−11.1421	−0.590532
$357$	1.72633	0.0913672
$358$	29.0319	1.53438
$359$	−5.33329	−0.281480	−0.140740	−	0.990047i	$-0.544948\pi$
$359$	−5.33329	−0.281480	−0.140740	+	0.990047i	$0.544948\pi$
$360$	0.336358	0.0177276
$361$	−17.3569	−0.913521
$362$	11.2858	0.593171
$363$	6.91947	0.363178
$364$	1.87440	0.0982453
$365$	11.4048	0.596953
$366$	23.3083	1.21834
$367$	34.1926	1.78484	0.892419	−	0.451208i	$-0.149007\pi$
$367$	34.1926	1.78484	0.892419	+	0.451208i	$0.149007\pi$
$368$	−34.0696	−1.77600
$369$	−11.2311	−0.584667
$370$	−7.81383	−0.406222
$371$	4.85721	0.252174
$372$	1.82809	0.0947819
$373$	4.31627	0.223488	0.111744	−	0.993737i	$-0.464356\pi$
$373$	4.31627	0.223488	0.111744	+	0.993737i	$0.464356\pi$
$374$	−6.65438	−0.344090
$375$	−1.00000	−0.0516398
$376$	3.73615	0.192677
$377$	−7.29349	−0.375634
$378$	−2.00612	−0.103184
$379$	−29.5557	−1.51818	−0.759088	−	0.650988i	$-0.774355\pi$
$379$	−29.5557	−1.51818	−0.759088	+	0.650988i	$0.774355\pi$
$380$	2.34331	0.120209
$381$	20.5863	1.05467
$382$	19.1266	0.978601
$383$	5.98442	0.305790	0.152895	−	0.988242i	$-0.451140\pi$
$383$	5.98442	0.305790	0.152895	+	0.988242i	$0.451140\pi$
$384$	2.68092	0.136810
$385$	−2.07121	−0.105559
$386$	−34.3341	−1.74756
$387$	0.405533	0.0206144
$388$	1.43254	0.0727264
$389$	−12.8251	−0.650256	−0.325128	−	0.945670i	$-0.605407\pi$
$389$	−12.8251	−0.650256	−0.325128	+	0.945670i	$0.605407\pi$
$390$	−1.95655	−0.0990737
$391$	13.2959	0.672403
$392$	−2.00089	−0.101060
$393$	10.8842	0.549033
$394$	27.4393	1.38237
$395$	−5.99899	−0.301842
$396$	3.69279	0.185570
$397$	−2.16721	−0.108769	−0.0543846	−	0.998520i	$-0.517320\pi$
$397$	−2.16721	−0.108769	−0.0543846	+	0.998520i	$0.517320\pi$
$398$	9.87594	0.495036
$399$	1.31431	0.0657979
$400$	−4.31427	−0.215714
$401$	18.5628	0.926981	0.463490	−	0.886102i	$-0.346597\pi$
$401$	18.5628	0.926981	0.463490	+	0.886102i	$0.346597\pi$
$402$	22.9493	1.14461
$403$	1.00000	0.0498135
$404$	25.6576	1.27651
$405$	1.00000	0.0496904
$406$	14.6316	0.726155
$407$	8.06736	0.399884
$408$	−0.566317	−0.0280369
$409$	25.0472	1.23850	0.619252	−	0.785192i	$-0.287436\pi$
$409$	25.0472	1.23850	0.619252	+	0.785192i	$0.287436\pi$
$410$	21.9742	1.08523
$411$	2.12215	0.104678
$412$	13.5233	0.666243
$413$	11.2371	0.552940
$414$	−15.4508	−0.759365
$415$	−10.9309	−0.536578
$416$	−7.76837	−0.380876
$417$	−6.41933	−0.314356
$418$	−5.06620	−0.247796
$419$	−23.9986	−1.17241	−0.586205	−	0.810163i	$-0.699379\pi$
$419$	−23.9986	−1.17241	−0.586205	+	0.810163i	$0.699379\pi$
$420$	1.87440	0.0914614
$421$	31.3013	1.52553	0.762765	−	0.646676i	$-0.223841\pi$
$421$	31.3013	1.52553	0.762765	+	0.646676i	$0.223841\pi$
$422$	32.5719	1.58557
$423$	11.1077	0.540073
$424$	−1.59339	−0.0773818
$425$	1.68368	0.0816702
$426$	16.0669	0.778446
$427$	−12.2148	−0.591114
$428$	16.4074	0.793082
$429$	2.02003	0.0975281
$430$	−0.793446	−0.0382634
$431$	−6.38933	−0.307763	−0.153882	−	0.988089i	$-0.549177\pi$
$431$	−6.38933	−0.307763	−0.153882	+	0.988089i	$0.549177\pi$
$432$	4.31427	0.207571
$433$	−28.8822	−1.38799	−0.693996	−	0.719979i	$-0.744151\pi$
$433$	−28.8822	−1.38799	−0.693996	+	0.719979i	$0.744151\pi$
$434$	−2.00612	−0.0962968
$435$	−7.29349	−0.349696
$436$	6.59673	0.315926
$437$	10.1226	0.484230
$438$	22.3140	1.06620
$439$	40.6687	1.94101	0.970505	−	0.241080i	$-0.0775017\pi$
$439$	40.6687	1.94101	0.970505	+	0.241080i	$0.0775017\pi$
$440$	0.679454	0.0323917
$441$	−5.94869	−0.283271
$442$	3.29419	0.156689
$443$	12.7695	0.606699	0.303350	−	0.952879i	$-0.401895\pi$
$443$	12.7695	0.606699	0.303350	+	0.952879i	$0.401895\pi$
$444$	−7.30079	−0.346480
$445$	−6.09497	−0.288929
$446$	4.61180	0.218375
$447$	12.5262	0.592470
$448$	6.73713	0.318300
$449$	−27.5704	−1.30113	−0.650564	−	0.759452i	$-0.725467\pi$
$449$	−27.5704	−1.30113	−0.650564	+	0.759452i	$0.725467\pi$
$450$	−1.95655	−0.0922326
$451$	−22.6872	−1.06830
$452$	21.9178	1.03093
$453$	−12.0571	−0.566492
$454$	33.4377	1.56931
$455$	1.02534	0.0480685
$456$	−0.431156	−0.0201907
$457$	−27.4817	−1.28554	−0.642771	−	0.766058i	$-0.722215\pi$
$457$	−27.4817	−1.28554	−0.642771	+	0.766058i	$0.722215\pi$
$458$	−1.49943	−0.0700639
$459$	−1.68368	−0.0785872
$460$	14.4363	0.673097
$461$	2.77609	0.129295	0.0646477	−	0.997908i	$-0.479408\pi$
$461$	2.77609	0.129295	0.0646477	+	0.997908i	$0.479408\pi$
$462$	−4.05243	−0.188536
$463$	34.3108	1.59456	0.797280	−	0.603610i	$-0.206272\pi$
$463$	34.3108	1.59456	0.797280	+	0.603610i	$0.206272\pi$
$464$	−31.4661	−1.46078
$465$	1.00000	0.0463739
$466$	3.68337	0.170629
$467$	10.6134	0.491128	0.245564	−	0.969380i	$-0.421027\pi$
$467$	10.6134	0.491128	0.245564	+	0.969380i	$0.421027\pi$
$468$	−1.82809	−0.0845033
$469$	−12.0266	−0.555339
$470$	−21.7327	−1.00245
$471$	−23.8222	−1.09767
$472$	−3.68628	−0.169675
$473$	0.819191	0.0376664
$474$	−11.7373	−0.539113
$475$	1.28184	0.0588147
$476$	−3.15588	−0.144650
$477$	−4.73719	−0.216901
$478$	−43.3973	−1.98495
$479$	28.3354	1.29468	0.647338	−	0.762203i	$-0.275882\pi$
$479$	28.3354	1.29468	0.647338	+	0.762203i	$0.275882\pi$
$480$	−7.76837	−0.354576
$481$	−3.99368	−0.182096
$482$	−2.61858	−0.119273
$483$	8.09703	0.368428
$484$	−12.6494	−0.574972
$485$	0.783630	0.0355828
$486$	1.95655	0.0887509
$487$	−24.7697	−1.12242	−0.561210	−	0.827673i	$-0.689664\pi$
$487$	−24.7697	−1.12242	−0.561210	+	0.827673i	$0.689664\pi$
$488$	4.00701	0.181389
$489$	10.6459	0.481425
$490$	11.6389	0.525792
$491$	14.0303	0.633180	0.316590	−	0.948563i	$-0.397462\pi$
$491$	14.0303	0.633180	0.316590	+	0.948563i	$0.397462\pi$
$492$	20.5314	0.925627
$493$	12.2799	0.553057
$494$	2.50798	0.112839
$495$	2.02003	0.0907937
$496$	4.31427	0.193717
$497$	−8.41992	−0.377685
$498$	−21.3869	−0.958369
$499$	−6.05754	−0.271173	−0.135586	−	0.990766i	$-0.543292\pi$
$499$	−6.05754	−0.271173	−0.135586	+	0.990766i	$0.543292\pi$
$500$	1.82809	0.0817545
$501$	10.8731	0.485775
$502$	−54.3596	−2.42619
$503$	30.5789	1.36344	0.681722	−	0.731611i	$-0.261231\pi$
$503$	30.5789	1.36344	0.681722	+	0.731611i	$0.261231\pi$
$504$	−0.344879	−0.0153621
$505$	14.0352	0.624559
$506$	−31.2111	−1.38750
$507$	−1.00000	−0.0444116
$508$	−37.6335	−1.66972
$509$	24.2552	1.07509	0.537546	−	0.843234i	$-0.319351\pi$
$509$	24.2552	1.07509	0.537546	+	0.843234i	$0.319351\pi$
$510$	3.29419	0.145869
$511$	−11.6937	−0.517300
$512$	−30.6126	−1.35290
$513$	−1.28184	−0.0565945
$514$	19.8995	0.877731
$515$	7.39750	0.325973
$516$	−0.741350	−0.0326361
$517$	22.4378	0.986815
$518$	8.01180	0.352018
$519$	7.06835	0.310266
$520$	−0.336358	−0.0147503
$521$	−1.07475	−0.0470858	−0.0235429	−	0.999723i	$-0.507495\pi$
$521$	−1.07475	−0.0470858	−0.0235429	+	0.999723i	$0.507495\pi$
$522$	−14.2701	−0.624584
$523$	30.1537	1.31853	0.659265	−	0.751911i	$-0.270868\pi$
$523$	30.1537	1.31853	0.659265	+	0.751911i	$0.270868\pi$
$524$	−19.8972	−0.869212
$525$	1.02534	0.0447493
$526$	−49.7530	−2.16933
$527$	−1.68368	−0.0733420
$528$	8.71497	0.379271
$529$	39.3620	1.71139
$530$	9.26854	0.402600
$531$	−10.9594	−0.475598
$532$	−2.40268	−0.104169
$533$	11.2311	0.486473
$534$	−11.9251	−0.516050
$535$	8.97518	0.388031
$536$	3.94530	0.170411
$537$	14.8383	0.640320
$538$	19.2691	0.830751
$539$	−12.0165	−0.517589
$540$	−1.82809	−0.0786683
$541$	26.7276	1.14911	0.574554	−	0.818467i	$-0.305176\pi$
$541$	26.7276	1.14911	0.574554	+	0.818467i	$0.305176\pi$
$542$	32.8760	1.41215
$543$	5.76824	0.247539
$544$	13.0794	0.560775
$545$	3.60854	0.154573
$546$	2.00612	0.0858540
$547$	31.3604	1.34087	0.670436	−	0.741967i	$-0.266107\pi$
$547$	31.3604	1.34087	0.670436	+	0.741967i	$0.266107\pi$
$548$	−3.87947	−0.165723
$549$	11.9130	0.508433
$550$	−3.95229	−0.168526
$551$	9.34906	0.398283
$552$	−2.65620	−0.113056
$553$	6.15098	0.261566
$554$	64.3627	2.73451
$555$	−3.99368	−0.169522
$556$	11.7351	0.497679
$557$	−32.5566	−1.37947	−0.689733	−	0.724064i	$-0.742272\pi$
$557$	−32.5566	−1.37947	−0.689733	+	0.724064i	$0.742272\pi$
$558$	1.95655	0.0828273
$559$	−0.405533	−0.0171522
$560$	4.42358	0.186930
$561$	−3.40108	−0.143594
$562$	13.6709	0.576673
$563$	−7.42567	−0.312955	−0.156477	−	0.987682i	$-0.550014\pi$
$563$	−7.42567	−0.312955	−0.156477	+	0.987682i	$0.550014\pi$
$564$	−20.3058	−0.855027
$565$	11.9895	0.504400
$566$	−30.3814	−1.27702
$567$	−1.02534	−0.0430600
$568$	2.76213	0.115896
$569$	−34.8156	−1.45955	−0.729774	−	0.683689i	$-0.760375\pi$
$569$	−34.8156	−1.45955	−0.729774	+	0.683689i	$0.760375\pi$
$570$	2.50798	0.105048
$571$	23.1305	0.967980	0.483990	−	0.875073i	$-0.339187\pi$
$571$	23.1305	0.967980	0.483990	+	0.875073i	$0.339187\pi$
$572$	−3.69279	−0.154403
$573$	9.77567	0.408384
$574$	−22.5309	−0.940422
$575$	7.89696	0.329326
$576$	−6.57066	−0.273778
$577$	12.0868	0.503179	0.251590	−	0.967834i	$-0.419047\pi$
$577$	12.0868	0.503179	0.251590	+	0.967834i	$0.419047\pi$
$578$	27.7150	1.15279
$579$	−17.5483	−0.729282
$580$	13.3331	0.553628
$581$	11.2079	0.464980
$582$	1.53321	0.0635537
$583$	−9.56927	−0.396319
$584$	3.83608	0.158738
$585$	−1.00000	−0.0413449
$586$	4.22093	0.174365
$587$	39.2888	1.62162	0.810811	−	0.585308i	$-0.199027\pi$
$587$	39.2888	1.62162	0.810811	+	0.585308i	$0.199027\pi$
$588$	10.8747	0.448466
$589$	−1.28184	−0.0528172
$590$	21.4426	0.882779
$591$	14.0243	0.576884
$592$	−17.2298	−0.708141
$593$	−18.6050	−0.764016	−0.382008	−	0.924159i	$-0.624767\pi$
$593$	−18.6050	−0.764016	−0.382008	+	0.924159i	$0.624767\pi$
$594$	3.95229	0.162165
$595$	−1.72633	−0.0707727
$596$	−22.8990	−0.937981
$597$	5.04763	0.206586
$598$	15.4508	0.631830
$599$	14.0756	0.575115	0.287558	−	0.957763i	$-0.407157\pi$
$599$	14.0756	0.575115	0.287558	+	0.957763i	$0.407157\pi$
$600$	−0.336358	−0.0137317
$601$	−11.1723	−0.455726	−0.227863	−	0.973693i	$-0.573174\pi$
$601$	−11.1723	−0.455726	−0.227863	+	0.973693i	$0.573174\pi$
$602$	0.813548	0.0331578
$603$	11.7295	0.477661
$604$	22.0414	0.896853
$605$	−6.91947	−0.281316
$606$	27.4606	1.11551
$607$	41.6787	1.69169	0.845844	−	0.533431i	$-0.179098\pi$
$607$	41.6787	1.69169	0.845844	+	0.533431i	$0.179098\pi$
$608$	9.95779	0.403842
$609$	7.47827	0.303035
$610$	−23.3083	−0.943725
$611$	−11.1077	−0.449368
$612$	3.07790	0.124417
$613$	17.4639	0.705362	0.352681	−	0.935744i	$-0.385270\pi$
$613$	17.4639	0.705362	0.352681	+	0.935744i	$0.385270\pi$
$614$	−40.7781	−1.64567
$615$	11.2311	0.452881
$616$	−0.696668	−0.0280695
$617$	−10.5751	−0.425739	−0.212869	−	0.977081i	$-0.568281\pi$
$617$	−10.5751	−0.425739	−0.212869	+	0.977081i	$0.568281\pi$
$618$	14.4736	0.582212
$619$	19.5784	0.786922	0.393461	−	0.919341i	$-0.371278\pi$
$619$	19.5784	0.786922	0.393461	+	0.919341i	$0.371278\pi$
$620$	−1.82809	−0.0734177
$621$	−7.89696	−0.316894
$622$	−67.2076	−2.69478
$623$	6.24939	0.250376
$624$	−4.31427	−0.172709
$625$	1.00000	0.0400000
$626$	−3.39208	−0.135575
$627$	−2.58935	−0.103409
$628$	43.5490	1.73779
$629$	6.72406	0.268106
$630$	2.00612	0.0799257
$631$	−28.3908	−1.13022	−0.565110	−	0.825016i	$-0.691166\pi$
$631$	−28.3908	−1.13022	−0.565110	+	0.825016i	$0.691166\pi$
$632$	−2.01781	−0.0802640
$633$	16.6476	0.661683
$634$	−34.6931	−1.37784
$635$	−20.5863	−0.816942
$636$	8.65999	0.343391
$637$	5.94869	0.235696
$638$	−28.8260	−1.14123
$639$	8.21187	0.324857
$640$	−2.68092	−0.105973
$641$	−6.70308	−0.264756	−0.132378	−	0.991199i	$-0.542261\pi$
$641$	−6.70308	−0.264756	−0.132378	+	0.991199i	$0.542261\pi$
$642$	17.5604	0.693053
$643$	25.0516	0.987937	0.493969	−	0.869480i	$-0.335546\pi$
$643$	25.0516	0.987937	0.493969	+	0.869480i	$0.335546\pi$
$644$	−14.8021	−0.583283
$645$	−0.405533	−0.0159679
$646$	−4.22262	−0.166137
$647$	21.4715	0.844133	0.422067	−	0.906565i	$-0.361305\pi$
$647$	21.4715	0.844133	0.422067	+	0.906565i	$0.361305\pi$
$648$	0.336358	0.0132134
$649$	−22.1384	−0.869007
$650$	1.95655	0.0767422
$651$	−1.02534	−0.0401861
$652$	−19.4616	−0.762177
$653$	20.8201	0.814752	0.407376	−	0.913261i	$-0.366444\pi$
$653$	20.8201	0.814752	0.407376	+	0.913261i	$0.366444\pi$
$654$	7.06030	0.276079
$655$	−10.8842	−0.425279
$656$	48.4540	1.89181
$657$	11.4048	0.444943
$658$	22.2833	0.868693
$659$	−9.39023	−0.365791	−0.182896	−	0.983132i	$-0.558547\pi$
$659$	−9.39023	−0.365791	−0.182896	+	0.983132i	$0.558547\pi$
$660$	−3.69279	−0.143742
$661$	5.55534	0.216078	0.108039	−	0.994147i	$-0.465543\pi$
$661$	5.55534	0.216078	0.108039	+	0.994147i	$0.465543\pi$
$662$	−6.04349	−0.234887
$663$	1.68368	0.0653885
$664$	−3.67670	−0.142684
$665$	−1.31431	−0.0509669
$666$	−7.81383	−0.302780
$667$	57.5964	2.23014
$668$	−19.8770	−0.769065
$669$	2.35711	0.0911311
$670$	−22.9493	−0.886609
$671$	24.0646	0.929002
$672$	7.96519	0.307264
$673$	37.4514	1.44365	0.721823	−	0.692078i	$-0.243304\pi$
$673$	37.4514	1.44365	0.721823	+	0.692078i	$0.243304\pi$
$674$	−7.82487	−0.301403
$675$	−1.00000	−0.0384900
$676$	1.82809	0.0703110
$677$	−26.3770	−1.01375	−0.506875	−	0.862020i	$-0.669199\pi$
$677$	−26.3770	−1.01375	−0.506875	+	0.862020i	$0.669199\pi$
$678$	23.4580	0.900898
$679$	−0.803484	−0.0308349
$680$	0.566317	0.0217173
$681$	17.0902	0.654896
$682$	3.95229	0.151341
$683$	2.86062	0.109458	0.0547292	−	0.998501i	$-0.482570\pi$
$683$	2.86062	0.109458	0.0547292	+	0.998501i	$0.482570\pi$
$684$	2.34331	0.0895986
$685$	−2.12215	−0.0810831
$686$	−25.9766	−0.991792
$687$	−0.766365	−0.0292387
$688$	−1.74958	−0.0667022
$689$	4.73719	0.180472
$690$	15.4508	0.588202
$691$	11.1276	0.423312	0.211656	−	0.977344i	$-0.432114\pi$
$691$	11.1276	0.423312	0.211656	+	0.977344i	$0.432114\pi$
$692$	−12.9216	−0.491204
$693$	−2.07121	−0.0786788
$694$	52.9434	2.00970
$695$	6.41933	0.243499
$696$	−2.45322	−0.0929891
$697$	−18.9095	−0.716249
$698$	−9.36876	−0.354613
$699$	1.88258	0.0712058
$700$	−1.87440	−0.0708457
$701$	−1.53199	−0.0578626	−0.0289313	−	0.999581i	$-0.509210\pi$
$701$	−1.53199	−0.0578626	−0.0289313	+	0.999581i	$0.509210\pi$
$702$	−1.95655	−0.0738452
$703$	5.11925	0.193076
$704$	−13.2730	−0.500243
$705$	−11.1077	−0.418339
$706$	28.7048	1.08032
$707$	−14.3908	−0.541222
$708$	20.0347	0.752952
$709$	−19.5782	−0.735273	−0.367637	−	0.929970i	$-0.619833\pi$
$709$	−19.5782	−0.735273	−0.367637	+	0.929970i	$0.619833\pi$
$710$	−16.0669	−0.602981
$711$	−5.99899	−0.224980
$712$	−2.05009	−0.0768304
$713$	−7.89696	−0.295743
$714$	−3.37765	−0.126406
$715$	−2.02003	−0.0755449
$716$	−27.1257	−1.01374
$717$	−22.1805	−0.828347
$718$	10.4348	0.389425
$719$	27.9136	1.04100	0.520501	−	0.853861i	$-0.325745\pi$
$719$	27.9136	1.04100	0.520501	+	0.853861i	$0.325745\pi$
$720$	−4.31427	−0.160783
$721$	−7.58492	−0.282477
$722$	33.9596	1.26385
$723$	−1.33837	−0.0497744
$724$	−10.5448	−0.391896
$725$	7.29349	0.270873
$726$	−13.5383	−0.502453
$727$	−5.81093	−0.215515	−0.107758	−	0.994177i	$-0.534367\pi$
$727$	−5.81093	−0.215515	−0.107758	+	0.994177i	$0.534367\pi$
$728$	0.344879	0.0127821
$729$	1.00000	0.0370370
$730$	−22.3140	−0.825878
$731$	0.682786	0.0252538
$732$	−21.7779	−0.804935
$733$	42.3738	1.56511	0.782555	−	0.622581i	$-0.213916\pi$
$733$	42.3738	1.56511	0.782555	+	0.622581i	$0.213916\pi$
$734$	−66.8994	−2.46930
$735$	5.94869	0.219421
$736$	61.3465	2.26126
$737$	23.6939	0.872777
$738$	21.9742	0.808881
$739$	−11.0024	−0.404731	−0.202365	−	0.979310i	$-0.564863\pi$
$739$	−11.0024	−0.404731	−0.202365	+	0.979310i	$0.564863\pi$
$740$	7.30079	0.268382
$741$	1.28184	0.0470894
$742$	−9.50336	−0.348879
$743$	47.0191	1.72496	0.862482	−	0.506088i	$-0.168909\pi$
$743$	47.0191	1.72496	0.862482	+	0.506088i	$0.168909\pi$
$744$	0.336358	0.0123315
$745$	−12.5262	−0.458926
$746$	−8.44501	−0.309194
$747$	−10.9309	−0.399941
$748$	6.21747	0.227333
$749$	−9.20257	−0.336254
$750$	1.95655	0.0714431
$751$	35.8710	1.30895	0.654475	−	0.756083i	$-0.272890\pi$
$751$	35.8710	1.30895	0.654475	+	0.756083i	$0.272890\pi$
$752$	−47.9215	−1.74752
$753$	−27.7834	−1.01248
$754$	14.2701	0.519685
$755$	12.0571	0.438803
$756$	1.87440	0.0681713
$757$	2.19324	0.0797148	0.0398574	−	0.999205i	$-0.487310\pi$
$757$	2.19324	0.0797148	0.0398574	+	0.999205i	$0.487310\pi$
$758$	57.8273	2.10038
$759$	−15.9521	−0.579025
$760$	0.431156	0.0156397
$761$	−3.33077	−0.120740	−0.0603702	−	0.998176i	$-0.519228\pi$
$761$	−3.33077	−0.120740	−0.0603702	+	0.998176i	$0.519228\pi$
$762$	−40.2781	−1.45912
$763$	−3.69997	−0.133948
$764$	−17.8708	−0.646541
$765$	1.68368	0.0608734
$766$	−11.7088	−0.423057
$767$	10.9594	0.395721
$768$	−18.3867	−0.663472
$769$	14.0618	0.507082	0.253541	−	0.967325i	$-0.418405\pi$
$769$	14.0618	0.507082	0.253541	+	0.967325i	$0.418405\pi$
$770$	4.05243	0.146039
$771$	10.1707	0.366290
$772$	32.0798	1.15458
$773$	−25.7367	−0.925683	−0.462842	−	0.886441i	$-0.653170\pi$
$773$	−25.7367	−0.925683	−0.462842	+	0.886441i	$0.653170\pi$
$774$	−0.793446	−0.0285198
$775$	−1.00000	−0.0359211
$776$	0.263580	0.00946197
$777$	4.09486	0.146902
$778$	25.0929	0.899623
$779$	−14.3964	−0.515805
$780$	1.82809	0.0654560
$781$	16.5883	0.593574
$782$	−26.0141	−0.930263
$783$	−7.29349	−0.260648
$784$	25.6643	0.916581
$785$	23.8222	0.850249
$786$	−21.2954	−0.759582
$787$	38.0354	1.35582	0.677908	−	0.735146i	$-0.262887\pi$
$787$	38.0354	1.35582	0.677908	+	0.735146i	$0.262887\pi$
$788$	−25.6377	−0.913305
$789$	−25.4289	−0.905294
$790$	11.7373	0.417595
$791$	−12.2932	−0.437097
$792$	0.679454	0.0241433
$793$	−11.9130	−0.423042
$794$	4.24026	0.150481
$795$	4.73719	0.168011
$796$	−9.22751	−0.327060
$797$	31.2603	1.10730	0.553648	−	0.832751i	$-0.313235\pi$
$797$	31.2603	1.10730	0.553648	+	0.832751i	$0.313235\pi$
$798$	−2.57152	−0.0910307
$799$	18.7017	0.661618
$800$	7.76837	0.274653
$801$	−6.09497	−0.215355
$802$	−36.3190	−1.28247
$803$	23.0380	0.812994
$804$	−21.4425	−0.756218
$805$	−8.09703	−0.285383
$806$	−1.95655	−0.0689165
$807$	9.84853	0.346685
$808$	4.72085	0.166079
$809$	−32.1565	−1.13056	−0.565282	−	0.824898i	$-0.691233\pi$
$809$	−32.1565	−1.13056	−0.565282	+	0.824898i	$0.691233\pi$
$810$	−1.95655	−0.0687461
$811$	−47.5610	−1.67009	−0.835047	−	0.550179i	$-0.814559\pi$
$811$	−47.5610	−1.67009	−0.835047	+	0.550179i	$0.814559\pi$
$812$	−13.6709	−0.479756
$813$	16.8031	0.589309
$814$	−15.7842	−0.553236
$815$	−10.6459	−0.372910
$816$	7.26383	0.254285
$817$	0.519828	0.0181865
$818$	−49.0061	−1.71346
$819$	1.02534	0.0358281
$820$	−20.5314	−0.716988
$821$	8.69474	0.303448	0.151724	−	0.988423i	$-0.451517\pi$
$821$	8.69474	0.303448	0.151724	+	0.988423i	$0.451517\pi$
$822$	−4.15209	−0.144821
$823$	−31.7062	−1.10521	−0.552605	−	0.833443i	$-0.686366\pi$
$823$	−31.7062	−1.10521	−0.552605	+	0.833443i	$0.686366\pi$
$824$	2.48821	0.0866807
$825$	−2.02003	−0.0703285
$826$	−21.9859	−0.764987
$827$	43.1328	1.49987	0.749937	−	0.661509i	$-0.230084\pi$
$827$	43.1328	1.49987	0.749937	+	0.661509i	$0.230084\pi$
$828$	14.4363	0.501697
$829$	−6.27871	−0.218069	−0.109034	−	0.994038i	$-0.534776\pi$
$829$	−6.27871	−0.218069	−0.109034	+	0.994038i	$0.534776\pi$
$830$	21.3869	0.742349
$831$	32.8960	1.14115
$832$	6.57066	0.227797
$833$	−10.0157	−0.347022
$834$	12.5597	0.434908
$835$	−10.8731	−0.376280
$836$	4.73356	0.163714
$837$	1.00000	0.0345651
$838$	46.9545	1.62202
$839$	−11.0570	−0.381729	−0.190864	−	0.981616i	$-0.561129\pi$
$839$	−11.0570	−0.381729	−0.190864	+	0.981616i	$0.561129\pi$
$840$	0.344879	0.0118995
$841$	24.1950	0.834310
$842$	−61.2425	−2.11055
$843$	6.98727	0.240654
$844$	−30.4333	−1.04756
$845$	1.00000	0.0344010
$846$	−21.7327	−0.747185
$847$	7.09477	0.243779
$848$	20.4375	0.701827
$849$	−15.5280	−0.532921
$850$	−3.29419	−0.112990
$851$	31.5379	1.08111
$852$	−15.0120	−0.514303
$853$	14.5197	0.497145	0.248572	−	0.968613i	$-0.420039\pi$
$853$	14.5197	0.497145	0.248572	+	0.968613i	$0.420039\pi$
$854$	23.8988	0.817801
$855$	1.28184	0.0438379
$856$	3.01887	0.103183
$857$	22.7671	0.777708	0.388854	−	0.921299i	$-0.372871\pi$
$857$	22.7671	0.777708	0.388854	+	0.921299i	$0.372871\pi$
$858$	−3.95229	−0.134929
$859$	45.9313	1.56715	0.783577	−	0.621294i	$-0.213393\pi$
$859$	45.9313	1.56715	0.783577	+	0.621294i	$0.213393\pi$
$860$	0.741350	0.0252798
$861$	−11.5156	−0.392452
$862$	12.5010	0.425787
$863$	−18.7085	−0.636846	−0.318423	−	0.947949i	$-0.603153\pi$
$863$	−18.7085	−0.636846	−0.318423	+	0.947949i	$0.603153\pi$
$864$	−7.76837	−0.264285
$865$	−7.06835	−0.240331
$866$	56.5095	1.92027
$867$	14.1652	0.481077
$868$	1.87440	0.0636213
$869$	−12.1182	−0.411080
$870$	14.2701	0.483801
$871$	−11.7295	−0.397438
$872$	1.21376	0.0411032
$873$	0.783630	0.0265219
$874$	−19.8054	−0.669927
$875$	−1.02534	−0.0346627
$876$	−20.8489	−0.704419
$877$	−30.3802	−1.02587	−0.512933	−	0.858429i	$-0.671441\pi$
$877$	−30.3802	−1.02587	−0.512933	+	0.858429i	$0.671441\pi$
$878$	−79.5703	−2.68537
$879$	2.15734	0.0727651
$880$	−8.71497	−0.293782
$881$	4.37072	0.147253	0.0736267	−	0.997286i	$-0.476543\pi$
$881$	4.37072	0.147253	0.0736267	+	0.997286i	$0.476543\pi$
$882$	11.6389	0.391902
$883$	20.0849	0.675910	0.337955	−	0.941162i	$-0.390265\pi$
$883$	20.0849	0.675910	0.337955	+	0.941162i	$0.390265\pi$
$884$	−3.07790	−0.103521
$885$	10.9594	0.368397
$886$	−24.9842	−0.839362
$887$	−5.62736	−0.188948	−0.0944741	−	0.995527i	$-0.530117\pi$
$887$	−5.62736	−0.188948	−0.0944741	+	0.995527i	$0.530117\pi$
$888$	−1.34330	−0.0450784
$889$	21.1078	0.707934
$890$	11.9251	0.399731
$891$	2.02003	0.0676736
$892$	−4.30900	−0.144276
$893$	14.2382	0.476463
$894$	−24.5082	−0.819677
$895$	−14.8383	−0.495990
$896$	2.74884	0.0918324
$897$	7.89696	0.263672
$898$	53.9429	1.80010
$899$	−7.29349	−0.243252
$900$	1.82809	0.0609362
$901$	−7.97589	−0.265715
$902$	44.3886	1.47798
$903$	0.415808	0.0138372
$904$	4.03275	0.134127
$905$	−5.76824	−0.191743
$906$	23.5903	0.783736
$907$	28.1852	0.935873	0.467936	−	0.883762i	$-0.344998\pi$
$907$	28.1852	0.935873	0.467936	+	0.883762i	$0.344998\pi$
$908$	−31.2423	−1.03681
$909$	14.0352	0.465519
$910$	−2.00612	−0.0665022
$911$	22.8078	0.755657	0.377829	−	0.925876i	$-0.376671\pi$
$911$	22.8078	0.755657	0.377829	+	0.925876i	$0.376671\pi$
$912$	5.53019	0.183123
$913$	−22.0808	−0.730768
$914$	53.7694	1.77853
$915$	−11.9130	−0.393830
$916$	1.40098	0.0462898
$917$	11.1599	0.368533
$918$	3.29419	0.108725
$919$	−49.2161	−1.62349	−0.811744	−	0.584013i	$-0.801482\pi$
$919$	−49.2161	−1.62349	−0.811744	+	0.584013i	$0.801482\pi$
$920$	2.65620	0.0875724
$921$	−20.8418	−0.686762
$922$	−5.43156	−0.178879
$923$	−8.21187	−0.270297
$924$	3.78635	0.124562
$925$	3.99368	0.131311
$926$	−67.1308	−2.20606
$927$	7.39750	0.242966
$928$	56.6586	1.85991
$929$	29.2424	0.959413	0.479706	−	0.877429i	$-0.340743\pi$
$929$	29.2424	0.959413	0.479706	+	0.877429i	$0.340743\pi$
$930$	−1.95655	−0.0641578
$931$	−7.62525	−0.249907
$932$	−3.44152	−0.112731
$933$	−34.3500	−1.12457
$934$	−20.7656	−0.679471
$935$	3.40108	0.111227
$936$	−0.336358	−0.0109942
$937$	29.6504	0.968636	0.484318	−	0.874892i	$-0.339068\pi$
$937$	29.6504	0.968636	0.484318	+	0.874892i	$0.339068\pi$
$938$	23.5307	0.768306
$939$	−1.73371	−0.0565774
$940$	20.3058	0.662301
$941$	−2.14723	−0.0699978	−0.0349989	−	0.999387i	$-0.511143\pi$
$941$	−2.14723	−0.0699978	−0.0349989	+	0.999387i	$0.511143\pi$
$942$	46.6092	1.51861
$943$	−88.6915	−2.88819
$944$	47.2819	1.53889
$945$	1.02534	0.0333542
$946$	−1.60279	−0.0521111
$947$	−42.1588	−1.36998	−0.684988	−	0.728555i	$-0.740192\pi$
$947$	−42.1588	−1.36998	−0.684988	+	0.728555i	$0.740192\pi$
$948$	10.9667	0.356181
$949$	−11.4048	−0.370215
$950$	−2.50798	−0.0813695
$951$	−17.7318	−0.574992
$952$	−0.580665	−0.0188195
$953$	37.7202	1.22188	0.610939	−	0.791678i	$-0.290792\pi$
$953$	37.7202	1.22188	0.610939	+	0.791678i	$0.290792\pi$
$954$	9.26854	0.300080
$955$	−9.77567	−0.316333
$956$	40.5479	1.31141
$957$	−14.7331	−0.476253
$958$	−55.4396	−1.79117
$959$	2.17591	0.0702639
$960$	6.57066	0.212067
$961$	1.00000	0.0322581
$962$	7.81383	0.251928
$963$	8.97518	0.289221
$964$	2.44665	0.0788013
$965$	17.5483	0.564899
$966$	−15.8422	−0.509716
$967$	2.34193	0.0753114	0.0376557	−	0.999291i	$-0.488011\pi$
$967$	2.34193	0.0753114	0.0376557	+	0.999291i	$0.488011\pi$
$968$	−2.32742	−0.0748060
$969$	−2.15820	−0.0693313
$970$	−1.53321	−0.0492285
$971$	36.4251	1.16894	0.584468	−	0.811417i	$-0.301303\pi$
$971$	36.4251	1.16894	0.584468	+	0.811417i	$0.301303\pi$
$972$	−1.82809	−0.0586359
$973$	−6.58197	−0.211008
$974$	48.4631	1.55286
$975$	1.00000	0.0320256
$976$	−51.3958	−1.64514
$977$	−57.2305	−1.83096	−0.915482	−	0.402358i	$-0.868191\pi$
$977$	−57.2305	−1.83096	−0.915482	+	0.402358i	$0.868191\pi$
$978$	−20.8292	−0.666046
$979$	−12.3120	−0.393494
$980$	−10.8747	−0.347380
$981$	3.60854	0.115212
$982$	−27.4510	−0.875997
$983$	−26.6914	−0.851322	−0.425661	−	0.904883i	$-0.639958\pi$
$983$	−26.6914	−0.851322	−0.425661	+	0.904883i	$0.639958\pi$
$984$	3.77766	0.120428
$985$	−14.0243	−0.446853
$986$	−24.0262	−0.765149
$987$	11.3891	0.362518
$988$	−2.34331	−0.0745506
$989$	3.20248	0.101833
$990$	−3.95229	−0.125612
$991$	−13.3185	−0.423077	−0.211539	−	0.977370i	$-0.567847\pi$
$991$	−13.3185	−0.423077	−0.211539	+	0.977370i	$0.567847\pi$
$992$	−7.76837	−0.246646
$993$	−3.08885	−0.0980217
$994$	16.4740	0.522524
$995$	−5.04763	−0.160021
$996$	19.9827	0.633175
$997$	−5.56195	−0.176149	−0.0880744	−	0.996114i	$-0.528071\pi$
$997$	−5.56195	−0.176149	−0.0880744	+	0.996114i	$0.528071\pi$
$998$	11.8519	0.375164
$999$	−3.99368	−0.126354

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.bd.1.3	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.bd.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-1.95655 q^{2} -1.00000 q^{3} +1.82809 q^{4} +1.00000 q^{5} +1.95655 q^{6} -1.02534 q^{7} +0.336358 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.95655 q^{2} -1.00000 q^{3} +1.82809 q^{4} +1.00000 q^{5} +1.95655 q^{6} -1.02534 q^{7} +0.336358 q^{8} +1.00000 q^{9} -1.95655 q^{10} +2.02003 q^{11} -1.82809 q^{12} -1.00000 q^{13} +2.00612 q^{14} -1.00000 q^{15} -4.31427 q^{16} +1.68368 q^{17} -1.95655 q^{18} +1.28184 q^{19} +1.82809 q^{20} +1.02534 q^{21} -3.95229 q^{22} +7.89696 q^{23} -0.336358 q^{24} +1.00000 q^{25} +1.95655 q^{26} -1.00000 q^{27} -1.87440 q^{28} +7.29349 q^{29} +1.95655 q^{30} -1.00000 q^{31} +7.76837 q^{32} -2.02003 q^{33} -3.29419 q^{34} -1.02534 q^{35} +1.82809 q^{36} +3.99368 q^{37} -2.50798 q^{38} +1.00000 q^{39} +0.336358 q^{40} -11.2311 q^{41} -2.00612 q^{42} +0.405533 q^{43} +3.69279 q^{44} +1.00000 q^{45} -15.4508 q^{46} +11.1077 q^{47} +4.31427 q^{48} -5.94869 q^{49} -1.95655 q^{50} -1.68368 q^{51} -1.82809 q^{52} -4.73719 q^{53} +1.95655 q^{54} +2.02003 q^{55} -0.344879 q^{56} -1.28184 q^{57} -14.2701 q^{58} -10.9594 q^{59} -1.82809 q^{60} +11.9130 q^{61} +1.95655 q^{62} -1.02534 q^{63} -6.57066 q^{64} -1.00000 q^{65} +3.95229 q^{66} +11.7295 q^{67} +3.07790 q^{68} -7.89696 q^{69} +2.00612 q^{70} +8.21187 q^{71} +0.336358 q^{72} +11.4048 q^{73} -7.81383 q^{74} -1.00000 q^{75} +2.34331 q^{76} -2.07121 q^{77} -1.95655 q^{78} -5.99899 q^{79} -4.31427 q^{80} +1.00000 q^{81} +21.9742 q^{82} -10.9309 q^{83} +1.87440 q^{84} +1.68368 q^{85} -0.793446 q^{86} -7.29349 q^{87} +0.679454 q^{88} -6.09497 q^{89} -1.95655 q^{90} +1.02534 q^{91} +14.4363 q^{92} +1.00000 q^{93} -21.7327 q^{94} +1.28184 q^{95} -7.76837 q^{96} +0.783630 q^{97} +11.6389 q^{98} +2.02003 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} + 14 q^{5} + 2 q^{6} + 5 q^{7} - 3 q^{8} + 14 q^{9}+O(q^{10}) \) 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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