LMFDB - Embedded newform 6046.2.a.e.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6046,2,Mod(1,6046)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6046, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6046.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6046 = 2 \cdot 3023 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6046.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:	$48.2775530621$
Analytic rank:	$1$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6046.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.97472 q^{3} +1.00000 q^{4} -3.51408 q^{5} -1.97472 q^{6} +4.87260 q^{7} +1.00000 q^{8} +0.899523 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.97472 q^{3} +1.00000 q^{4} -3.51408 q^{5} -1.97472 q^{6} +4.87260 q^{7} +1.00000 q^{8} +0.899523 q^{9} -3.51408 q^{10} -1.47578 q^{11} -1.97472 q^{12} -2.61189 q^{13} +4.87260 q^{14} +6.93932 q^{15} +1.00000 q^{16} +1.59217 q^{17} +0.899523 q^{18} +1.74056 q^{19} -3.51408 q^{20} -9.62203 q^{21} -1.47578 q^{22} -5.13851 q^{23} -1.97472 q^{24} +7.34874 q^{25} -2.61189 q^{26} +4.14786 q^{27} +4.87260 q^{28} -0.369928 q^{29} +6.93932 q^{30} +1.95718 q^{31} +1.00000 q^{32} +2.91426 q^{33} +1.59217 q^{34} -17.1227 q^{35} +0.899523 q^{36} -5.92193 q^{37} +1.74056 q^{38} +5.15775 q^{39} -3.51408 q^{40} -5.91710 q^{41} -9.62203 q^{42} +8.03912 q^{43} -1.47578 q^{44} -3.16099 q^{45} -5.13851 q^{46} +6.55289 q^{47} -1.97472 q^{48} +16.7423 q^{49} +7.34874 q^{50} -3.14410 q^{51} -2.61189 q^{52} -6.60780 q^{53} +4.14786 q^{54} +5.18602 q^{55} +4.87260 q^{56} -3.43711 q^{57} -0.369928 q^{58} -0.526124 q^{59} +6.93932 q^{60} -4.21582 q^{61} +1.95718 q^{62} +4.38302 q^{63} +1.00000 q^{64} +9.17839 q^{65} +2.91426 q^{66} -0.936292 q^{67} +1.59217 q^{68} +10.1471 q^{69} -17.1227 q^{70} -9.67414 q^{71} +0.899523 q^{72} -3.75817 q^{73} -5.92193 q^{74} -14.5117 q^{75} +1.74056 q^{76} -7.19091 q^{77} +5.15775 q^{78} +12.5352 q^{79} -3.51408 q^{80} -10.8894 q^{81} -5.91710 q^{82} +1.28573 q^{83} -9.62203 q^{84} -5.59503 q^{85} +8.03912 q^{86} +0.730504 q^{87} -1.47578 q^{88} -1.27476 q^{89} -3.16099 q^{90} -12.7267 q^{91} -5.13851 q^{92} -3.86488 q^{93} +6.55289 q^{94} -6.11645 q^{95} -1.97472 q^{96} +6.71023 q^{97} +16.7423 q^{98} -1.32750 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9}+O(q^{10}) $ 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9} - 17 q^{10} - 53 q^{11} - 18 q^{12} - 21 q^{13} - 35 q^{14} - 36 q^{15} + 56 q^{16} - 22 q^{17} + 34 q^{18} - 31 q^{19} - 17 q^{20} - 23 q^{21} - 53 q^{22} - 59 q^{23} - 18 q^{24} + 41 q^{25} - 21 q^{26} - 63 q^{27} - 35 q^{28} - 88 q^{29} - 36 q^{30} - 44 q^{31} + 56 q^{32} + 4 q^{33} - 22 q^{34} - 51 q^{35} + 34 q^{36} - 60 q^{37} - 31 q^{38} - 62 q^{39} - 17 q^{40} - 39 q^{41} - 23 q^{42} - 66 q^{43} - 53 q^{44} - 34 q^{45} - 59 q^{46} - 51 q^{47} - 18 q^{48} + 41 q^{49} + 41 q^{50} - 48 q^{51} - 21 q^{52} - 75 q^{53} - 63 q^{54} - 41 q^{55} - 35 q^{56} - 12 q^{57} - 88 q^{58} - 77 q^{59} - 36 q^{60} - 43 q^{61} - 44 q^{62} - 88 q^{63} + 56 q^{64} - 54 q^{65} + 4 q^{66} - 62 q^{67} - 22 q^{68} - 48 q^{69} - 51 q^{70} - 122 q^{71} + 34 q^{72} - 7 q^{73} - 60 q^{74} - 63 q^{75} - 31 q^{76} - 39 q^{77} - 62 q^{78} - 91 q^{79} - 17 q^{80} + 8 q^{81} - 39 q^{82} - 51 q^{83} - 23 q^{84} - 72 q^{85} - 66 q^{86} - 19 q^{87} - 53 q^{88} - 62 q^{89} - 34 q^{90} - 48 q^{91} - 59 q^{92} - 41 q^{93} - 51 q^{94} - 120 q^{95} - 18 q^{96} + 6 q^{97} + 41 q^{98} - 128 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9 - 17 * q^10 - 53 * q^11 - 18 * q^12 - 21 * q^13 - 35 * q^14 - 36 * q^15 + 56 * q^16 - 22 * q^17 + 34 * q^18 - 31 * q^19 - 17 * q^20 - 23 * q^21 - 53 * q^22 - 59 * q^23 - 18 * q^24 + 41 * q^25 - 21 * q^26 - 63 * q^27 - 35 * q^28 - 88 * q^29 - 36 * q^30 - 44 * q^31 + 56 * q^32 + 4 * q^33 - 22 * q^34 - 51 * q^35 + 34 * q^36 - 60 * q^37 - 31 * q^38 - 62 * q^39 - 17 * q^40 - 39 * q^41 - 23 * q^42 - 66 * q^43 - 53 * q^44 - 34 * q^45 - 59 * q^46 - 51 * q^47 - 18 * q^48 + 41 * q^49 + 41 * q^50 - 48 * q^51 - 21 * q^52 - 75 * q^53 - 63 * q^54 - 41 * q^55 - 35 * q^56 - 12 * q^57 - 88 * q^58 - 77 * q^59 - 36 * q^60 - 43 * q^61 - 44 * q^62 - 88 * q^63 + 56 * q^64 - 54 * q^65 + 4 * q^66 - 62 * q^67 - 22 * q^68 - 48 * q^69 - 51 * q^70 - 122 * q^71 + 34 * q^72 - 7 * q^73 - 60 * q^74 - 63 * q^75 - 31 * q^76 - 39 * q^77 - 62 * q^78 - 91 * q^79 - 17 * q^80 + 8 * q^81 - 39 * q^82 - 51 * q^83 - 23 * q^84 - 72 * q^85 - 66 * q^86 - 19 * q^87 - 53 * q^88 - 62 * q^89 - 34 * q^90 - 48 * q^91 - 59 * q^92 - 41 * q^93 - 51 * q^94 - 120 * q^95 - 18 * q^96 + 6 * q^97 + 41 * q^98 - 128 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.97472	−1.14011	−0.570053	−	0.821608i	$-0.693077\pi$
$3$	−1.97472	−1.14011	−0.570053	+	0.821608i	$0.693077\pi$
$4$	1.00000	0.500000
$5$	−3.51408	−1.57154	−0.785772	−	0.618517i	$-0.787734\pi$
$5$	−3.51408	−1.57154	−0.785772	+	0.618517i	$0.787734\pi$
$6$	−1.97472	−0.806176
$7$	4.87260	1.84167	0.920835	−	0.389952i	$-0.127508\pi$
$7$	4.87260	1.84167	0.920835	+	0.389952i	$0.127508\pi$
$8$	1.00000	0.353553
$9$	0.899523	0.299841
$10$	−3.51408	−1.11125
$11$	−1.47578	−0.444966	−0.222483	−	0.974937i	$-0.571416\pi$
$11$	−1.47578	−0.444966	−0.222483	+	0.974937i	$0.571416\pi$
$12$	−1.97472	−0.570053
$13$	−2.61189	−0.724408	−0.362204	−	0.932099i	$-0.617976\pi$
$13$	−2.61189	−0.724408	−0.362204	+	0.932099i	$0.617976\pi$
$14$	4.87260	1.30226
$15$	6.93932	1.79173
$16$	1.00000	0.250000
$17$	1.59217	0.386159	0.193080	−	0.981183i	$-0.438152\pi$
$17$	1.59217	0.386159	0.193080	+	0.981183i	$0.438152\pi$
$18$	0.899523	0.212020
$19$	1.74056	0.399311	0.199655	−	0.979866i	$-0.436018\pi$
$19$	1.74056	0.399311	0.199655	+	0.979866i	$0.436018\pi$
$20$	−3.51408	−0.785772
$21$	−9.62203	−2.09970
$22$	−1.47578	−0.314638
$23$	−5.13851	−1.07145	−0.535727	−	0.844391i	$-0.679962\pi$
$23$	−5.13851	−1.07145	−0.535727	+	0.844391i	$0.679962\pi$
$24$	−1.97472	−0.403088
$25$	7.34874	1.46975
$26$	−2.61189	−0.512234
$27$	4.14786	0.798255
$28$	4.87260	0.920835
$29$	−0.369928	−0.0686939	−0.0343469	−	0.999410i	$-0.510935\pi$
$29$	−0.369928	−0.0686939	−0.0343469	+	0.999410i	$0.510935\pi$
$30$	6.93932	1.26694
$31$	1.95718	0.351520	0.175760	−	0.984433i	$-0.443762\pi$
$31$	1.95718	0.351520	0.175760	+	0.984433i	$0.443762\pi$
$32$	1.00000	0.176777
$33$	2.91426	0.507308
$34$	1.59217	0.273056
$35$	−17.1227	−2.89427
$36$	0.899523	0.149920
$37$	−5.92193	−0.973560	−0.486780	−	0.873525i	$-0.661829\pi$
$37$	−5.92193	−0.973560	−0.486780	+	0.873525i	$0.661829\pi$
$38$	1.74056	0.282356
$39$	5.15775	0.825902
$40$	−3.51408	−0.555624
$41$	−5.91710	−0.924096	−0.462048	−	0.886855i	$-0.652885\pi$
$41$	−5.91710	−0.924096	−0.462048	+	0.886855i	$0.652885\pi$
$42$	−9.62203	−1.48471
$43$	8.03912	1.22595	0.612977	−	0.790100i	$-0.289972\pi$
$43$	8.03912	1.22595	0.612977	+	0.790100i	$0.289972\pi$
$44$	−1.47578	−0.222483
$45$	−3.16099	−0.471213
$46$	−5.13851	−0.757632
$47$	6.55289	0.955838	0.477919	−	0.878404i	$-0.341391\pi$
$47$	6.55289	0.955838	0.477919	+	0.878404i	$0.341391\pi$
$48$	−1.97472	−0.285026
$49$	16.7423	2.39175
$50$	7.34874	1.03927
$51$	−3.14410	−0.440262
$52$	−2.61189	−0.362204
$53$	−6.60780	−0.907651	−0.453826	−	0.891090i	$-0.649941\pi$
$53$	−6.60780	−0.907651	−0.453826	+	0.891090i	$0.649941\pi$
$54$	4.14786	0.564452
$55$	5.18602	0.699283
$56$	4.87260	0.651129
$57$	−3.43711	−0.455257
$58$	−0.369928	−0.0485739
$59$	−0.526124	−0.0684956	−0.0342478	−	0.999413i	$-0.510904\pi$
$59$	−0.526124	−0.0684956	−0.0342478	+	0.999413i	$0.510904\pi$
$60$	6.93932	0.895863
$61$	−4.21582	−0.539781	−0.269891	−	0.962891i	$-0.586988\pi$
$61$	−4.21582	−0.539781	−0.269891	+	0.962891i	$0.586988\pi$
$62$	1.95718	0.248562
$63$	4.38302	0.552208
$64$	1.00000	0.125000
$65$	9.17839	1.13844
$66$	2.91426	0.358721
$67$	−0.936292	−0.114386	−0.0571931	−	0.998363i	$-0.518215\pi$
$67$	−0.936292	−0.114386	−0.0571931	+	0.998363i	$0.518215\pi$
$68$	1.59217	0.193080
$69$	10.1471	1.22157
$70$	−17.1227	−2.04655
$71$	−9.67414	−1.14811	−0.574054	−	0.818817i	$-0.694630\pi$
$71$	−9.67414	−1.14811	−0.574054	+	0.818817i	$0.694630\pi$
$72$	0.899523	0.106010
$73$	−3.75817	−0.439861	−0.219930	−	0.975516i	$-0.570583\pi$
$73$	−3.75817	−0.439861	−0.219930	+	0.975516i	$0.570583\pi$
$74$	−5.92193	−0.688411
$75$	−14.5117	−1.67567
$76$	1.74056	0.199655
$77$	−7.19091	−0.819480
$78$	5.15775	0.584001
$79$	12.5352	1.41032	0.705158	−	0.709050i	$-0.250876\pi$
$79$	12.5352	1.41032	0.705158	+	0.709050i	$0.250876\pi$
$80$	−3.51408	−0.392886
$81$	−10.8894	−1.20994
$82$	−5.91710	−0.653435
$83$	1.28573	0.141128	0.0705638	−	0.997507i	$-0.477520\pi$
$83$	1.28573	0.141128	0.0705638	+	0.997507i	$0.477520\pi$
$84$	−9.62203	−1.04985
$85$	−5.59503	−0.606866
$86$	8.03912	0.866881
$87$	0.730504	0.0783183
$88$	−1.47578	−0.157319
$89$	−1.27476	−0.135125	−0.0675623	−	0.997715i	$-0.521522\pi$
$89$	−1.27476	−0.135125	−0.0675623	+	0.997715i	$0.521522\pi$
$90$	−3.16099	−0.333198
$91$	−12.7267	−1.33412
$92$	−5.13851	−0.535727
$93$	−3.86488	−0.400770
$94$	6.55289	0.675879
$95$	−6.11645	−0.627534
$96$	−1.97472	−0.201544
$97$	6.71023	0.681320	0.340660	−	0.940186i	$-0.389349\pi$
$97$	6.71023	0.681320	0.340660	+	0.940186i	$0.389349\pi$
$98$	16.7423	1.69122
$99$	−1.32750	−0.133419
$100$	7.34874	0.734874
$101$	1.82876	0.181969	0.0909843	−	0.995852i	$-0.470999\pi$
$101$	1.82876	0.181969	0.0909843	+	0.995852i	$0.470999\pi$
$102$	−3.14410	−0.311312
$103$	10.4099	1.02572	0.512860	−	0.858472i	$-0.328586\pi$
$103$	10.4099	1.02572	0.512860	+	0.858472i	$0.328586\pi$
$104$	−2.61189	−0.256117
$105$	33.8126	3.29977
$106$	−6.60780	−0.641806
$107$	−7.61879	−0.736536	−0.368268	−	0.929720i	$-0.620049\pi$
$107$	−7.61879	−0.736536	−0.368268	+	0.929720i	$0.620049\pi$
$108$	4.14786	0.399128
$109$	−4.32693	−0.414445	−0.207223	−	0.978294i	$-0.566442\pi$
$109$	−4.32693	−0.414445	−0.207223	+	0.978294i	$0.566442\pi$
$110$	5.18602	0.494467
$111$	11.6942	1.10996
$112$	4.87260	0.460418
$113$	2.33924	0.220057	0.110029	−	0.993928i	$-0.464906\pi$
$113$	2.33924	0.220057	0.110029	+	0.993928i	$0.464906\pi$
$114$	−3.43711	−0.321915
$115$	18.0571	1.68384
$116$	−0.369928	−0.0343469
$117$	−2.34945	−0.217207
$118$	−0.526124	−0.0484337
$119$	7.75804	0.711178
$120$	6.93932	0.633471
$121$	−8.82206	−0.802006
$122$	−4.21582	−0.381683
$123$	11.6846	1.05357
$124$	1.95718	0.175760
$125$	−8.25366	−0.738229
$126$	4.38302	0.390470
$127$	4.04431	0.358875	0.179437	−	0.983769i	$-0.442572\pi$
$127$	4.04431	0.358875	0.179437	+	0.983769i	$0.442572\pi$
$128$	1.00000	0.0883883
$129$	−15.8750	−1.39772
$130$	9.17839	0.804998
$131$	−3.16815	−0.276803	−0.138401	−	0.990376i	$-0.544196\pi$
$131$	−3.16815	−0.276803	−0.138401	+	0.990376i	$0.544196\pi$
$132$	2.91426	0.253654
$133$	8.48104	0.735399
$134$	−0.936292	−0.0808833
$135$	−14.5759	−1.25449
$136$	1.59217	0.136528
$137$	−13.3102	−1.13717	−0.568583	−	0.822626i	$-0.692508\pi$
$137$	−13.3102	−1.13717	−0.568583	+	0.822626i	$0.692508\pi$
$138$	10.1471	0.863781
$139$	10.4050	0.882542	0.441271	−	0.897374i	$-0.354528\pi$
$139$	10.4050	0.882542	0.441271	+	0.897374i	$0.354528\pi$
$140$	−17.1227	−1.44713
$141$	−12.9401	−1.08976
$142$	−9.67414	−0.811836
$143$	3.85459	0.322337
$144$	0.899523	0.0749602
$145$	1.29995	0.107955
$146$	−3.75817	−0.311029
$147$	−33.0613	−2.72685
$148$	−5.92193	−0.486780
$149$	−11.4804	−0.940512	−0.470256	−	0.882530i	$-0.655838\pi$
$149$	−11.4804	−0.940512	−0.470256	+	0.882530i	$0.655838\pi$
$150$	−14.5117	−1.18488
$151$	10.4489	0.850320	0.425160	−	0.905118i	$-0.360218\pi$
$151$	10.4489	0.850320	0.425160	+	0.905118i	$0.360218\pi$
$152$	1.74056	0.141178
$153$	1.43220	0.115786
$154$	−7.19091	−0.579460
$155$	−6.87768	−0.552429
$156$	5.15775	0.412951
$157$	−12.8774	−1.02773	−0.513863	−	0.857872i	$-0.671786\pi$
$157$	−12.8774	−1.02773	−0.513863	+	0.857872i	$0.671786\pi$
$158$	12.5352	0.997244
$159$	13.0486	1.03482
$160$	−3.51408	−0.277812
$161$	−25.0379	−1.97326
$162$	−10.8894	−0.855554
$163$	−15.6838	−1.22845	−0.614227	−	0.789130i	$-0.710532\pi$
$163$	−15.6838	−1.22845	−0.614227	+	0.789130i	$0.710532\pi$
$164$	−5.91710	−0.462048
$165$	−10.2409	−0.797256
$166$	1.28573	0.0997923
$167$	−11.9870	−0.927585	−0.463792	−	0.885944i	$-0.653512\pi$
$167$	−11.9870	−0.927585	−0.463792	+	0.885944i	$0.653512\pi$
$168$	−9.62203	−0.742356
$169$	−6.17803	−0.475233
$170$	−5.59503	−0.429119
$171$	1.56567	0.119730
$172$	8.03912	0.612977
$173$	−15.4443	−1.17421	−0.587105	−	0.809511i	$-0.699733\pi$
$173$	−15.4443	−1.17421	−0.587105	+	0.809511i	$0.699733\pi$
$174$	0.730504	0.0553794
$175$	35.8075	2.70679
$176$	−1.47578	−0.111241
$177$	1.03895	0.0780922
$178$	−1.27476	−0.0955475
$179$	19.4101	1.45078	0.725388	−	0.688340i	$-0.241660\pi$
$179$	19.4101	1.45078	0.725388	+	0.688340i	$0.241660\pi$
$180$	−3.16099	−0.235606
$181$	−25.4619	−1.89257	−0.946283	−	0.323338i	$-0.895195\pi$
$181$	−25.4619	−1.89257	−0.946283	+	0.323338i	$0.895195\pi$
$182$	−12.7267	−0.943366
$183$	8.32508	0.615407
$184$	−5.13851	−0.378816
$185$	20.8101	1.52999
$186$	−3.86488	−0.283387
$187$	−2.34971	−0.171828
$188$	6.55289	0.477919
$189$	20.2109	1.47012
$190$	−6.11645	−0.443734
$191$	2.14410	0.155142	0.0775709	−	0.996987i	$-0.475284\pi$
$191$	2.14410	0.155142	0.0775709	+	0.996987i	$0.475284\pi$
$192$	−1.97472	−0.142513
$193$	−9.05142	−0.651535	−0.325768	−	0.945450i	$-0.605623\pi$
$193$	−9.05142	−0.651535	−0.325768	+	0.945450i	$0.605623\pi$
$194$	6.71023	0.481766
$195$	−18.1247	−1.29794
$196$	16.7423	1.19588
$197$	−19.6593	−1.40067	−0.700334	−	0.713815i	$-0.746966\pi$
$197$	−19.6593	−1.40067	−0.700334	+	0.713815i	$0.746966\pi$
$198$	−1.32750	−0.0943414
$199$	−0.228087	−0.0161687	−0.00808433	−	0.999967i	$-0.502573\pi$
$199$	−0.228087	−0.0161687	−0.00808433	+	0.999967i	$0.502573\pi$
$200$	7.34874	0.519634
$201$	1.84892	0.130412
$202$	1.82876	0.128671
$203$	−1.80251	−0.126511
$204$	−3.14410	−0.220131
$205$	20.7932	1.45226
$206$	10.4099	0.725293
$207$	−4.62221	−0.321266
$208$	−2.61189	−0.181102
$209$	−2.56868	−0.177680
$210$	33.8126	2.33329
$211$	7.57063	0.521184	0.260592	−	0.965449i	$-0.416082\pi$
$211$	7.57063	0.521184	0.260592	+	0.965449i	$0.416082\pi$
$212$	−6.60780	−0.453826
$213$	19.1037	1.30897
$214$	−7.61879	−0.520810
$215$	−28.2501	−1.92664
$216$	4.14786	0.282226
$217$	9.53656	0.647384
$218$	−4.32693	−0.293057
$219$	7.42134	0.501488
$220$	5.18602	0.349641
$221$	−4.15859	−0.279737
$222$	11.6942	0.784861
$223$	2.64730	0.177276	0.0886382	−	0.996064i	$-0.471748\pi$
$223$	2.64730	0.177276	0.0886382	+	0.996064i	$0.471748\pi$
$224$	4.87260	0.325564
$225$	6.61036	0.440691
$226$	2.33924	0.155604
$227$	−6.89786	−0.457827	−0.228913	−	0.973447i	$-0.573517\pi$
$227$	−6.89786	−0.457827	−0.228913	+	0.973447i	$0.573517\pi$
$228$	−3.43711	−0.227628
$229$	−13.8437	−0.914815	−0.457407	−	0.889257i	$-0.651222\pi$
$229$	−13.8437	−0.914815	−0.457407	+	0.889257i	$0.651222\pi$
$230$	18.0571	1.19065
$231$	14.2000	0.934294
$232$	−0.369928	−0.0242869
$233$	−7.73376	−0.506656	−0.253328	−	0.967380i	$-0.581525\pi$
$233$	−7.73376	−0.506656	−0.253328	+	0.967380i	$0.581525\pi$
$234$	−2.34945	−0.153589
$235$	−23.0274	−1.50214
$236$	−0.526124	−0.0342478
$237$	−24.7534	−1.60791
$238$	7.75804	0.502879
$239$	−15.8628	−1.02608	−0.513041	−	0.858364i	$-0.671481\pi$
$239$	−15.8628	−1.02608	−0.513041	+	0.858364i	$0.671481\pi$
$240$	6.93932	0.447931
$241$	−13.2217	−0.851681	−0.425841	−	0.904798i	$-0.640022\pi$
$241$	−13.2217	−0.851681	−0.425841	+	0.904798i	$0.640022\pi$
$242$	−8.82206	−0.567104
$243$	9.06001	0.581200
$244$	−4.21582	−0.269891
$245$	−58.8336	−3.75874
$246$	11.6846	0.744985
$247$	−4.54614	−0.289264
$248$	1.95718	0.124281
$249$	−2.53896	−0.160900
$250$	−8.25366	−0.522007
$251$	14.3155	0.903587	0.451793	−	0.892123i	$-0.350784\pi$
$251$	14.3155	0.903587	0.451793	+	0.892123i	$0.350784\pi$
$252$	4.38302	0.276104
$253$	7.58333	0.476760
$254$	4.04431	0.253763
$255$	11.0486	0.691891
$256$	1.00000	0.0625000
$257$	25.1955	1.57165	0.785825	−	0.618448i	$-0.212238\pi$
$257$	25.1955	1.57165	0.785825	+	0.618448i	$0.212238\pi$
$258$	−15.8750	−0.988336
$259$	−28.8552	−1.79298
$260$	9.17839	0.569219
$261$	−0.332758	−0.0205972
$262$	−3.16815	−0.195729
$263$	−9.88538	−0.609559	−0.304779	−	0.952423i	$-0.598583\pi$
$263$	−9.88538	−0.609559	−0.304779	+	0.952423i	$0.598583\pi$
$264$	2.91426	0.179360
$265$	23.2203	1.42641
$266$	8.48104	0.520006
$267$	2.51730	0.154056
$268$	−0.936292	−0.0571931
$269$	−20.7402	−1.26455	−0.632276	−	0.774743i	$-0.717879\pi$
$269$	−20.7402	−1.26455	−0.632276	+	0.774743i	$0.717879\pi$
$270$	−14.5759	−0.887060
$271$	−12.1185	−0.736144	−0.368072	−	0.929797i	$-0.619982\pi$
$271$	−12.1185	−0.736144	−0.368072	+	0.929797i	$0.619982\pi$
$272$	1.59217	0.0965398
$273$	25.1317	1.52104
$274$	−13.3102	−0.804097
$275$	−10.8452	−0.653987
$276$	10.1471	0.610785
$277$	−21.6799	−1.30262	−0.651309	−	0.758813i	$-0.725780\pi$
$277$	−21.6799	−1.30262	−0.651309	+	0.758813i	$0.725780\pi$
$278$	10.4050	0.624052
$279$	1.76053	0.105400
$280$	−17.1227	−1.02328
$281$	7.60750	0.453825	0.226913	−	0.973915i	$-0.427137\pi$
$281$	7.60750	0.453825	0.226913	+	0.973915i	$0.427137\pi$
$282$	−12.9401	−0.770574
$283$	−13.4520	−0.799639	−0.399820	−	0.916594i	$-0.630927\pi$
$283$	−13.4520	−0.799639	−0.399820	+	0.916594i	$0.630927\pi$
$284$	−9.67414	−0.574054
$285$	12.0783	0.715456
$286$	3.85459	0.227926
$287$	−28.8317	−1.70188
$288$	0.899523	0.0530049
$289$	−14.4650	−0.850881
$290$	1.29995	0.0763360
$291$	−13.2508	−0.776777
$292$	−3.75817	−0.219930
$293$	−4.11505	−0.240403	−0.120202	−	0.992749i	$-0.538354\pi$
$293$	−4.11505	−0.240403	−0.120202	+	0.992749i	$0.538354\pi$
$294$	−33.0613	−1.92817
$295$	1.84884	0.107644
$296$	−5.92193	−0.344205
$297$	−6.12134	−0.355196
$298$	−11.4804	−0.665042
$299$	13.4212	0.776170
$300$	−14.5117	−0.837834
$301$	39.1715	2.25781
$302$	10.4489	0.601267
$303$	−3.61130	−0.207464
$304$	1.74056	0.0998277
$305$	14.8147	0.848289
$306$	1.43220	0.0818733
$307$	−4.72181	−0.269488	−0.134744	−	0.990880i	$-0.543021\pi$
$307$	−4.72181	−0.269488	−0.134744	+	0.990880i	$0.543021\pi$
$308$	−7.19091	−0.409740
$309$	−20.5567	−1.16943
$310$	−6.87768	−0.390626
$311$	−12.1993	−0.691760	−0.345880	−	0.938279i	$-0.612420\pi$
$311$	−12.1993	−0.691760	−0.345880	+	0.938279i	$0.612420\pi$
$312$	5.15775	0.292000
$313$	−32.9605	−1.86304	−0.931518	−	0.363695i	$-0.881515\pi$
$313$	−32.9605	−1.86304	−0.931518	+	0.363695i	$0.881515\pi$
$314$	−12.8774	−0.726713
$315$	−15.4023	−0.867819
$316$	12.5352	0.705158
$317$	10.0023	0.561785	0.280893	−	0.959739i	$-0.409370\pi$
$317$	10.0023	0.561785	0.280893	+	0.959739i	$0.409370\pi$
$318$	13.0486	0.731727
$319$	0.545933	0.0305664
$320$	−3.51408	−0.196443
$321$	15.0450	0.839729
$322$	−25.0379	−1.39531
$323$	2.77127	0.154198
$324$	−10.8894	−0.604968
$325$	−19.1941	−1.06470
$326$	−15.6838	−0.868648
$327$	8.54449	0.472511
$328$	−5.91710	−0.326717
$329$	31.9296	1.76034
$330$	−10.2409	−0.563745
$331$	−15.2506	−0.838251	−0.419126	−	0.907928i	$-0.637663\pi$
$331$	−15.2506	−0.838251	−0.419126	+	0.907928i	$0.637663\pi$
$332$	1.28573	0.0705638
$333$	−5.32691	−0.291913
$334$	−11.9870	−0.655901
$335$	3.29020	0.179763
$336$	−9.62203	−0.524925
$337$	7.33844	0.399750	0.199875	−	0.979821i	$-0.435946\pi$
$337$	7.33844	0.399750	0.199875	+	0.979821i	$0.435946\pi$
$338$	−6.17803	−0.336040
$339$	−4.61935	−0.250889
$340$	−5.59503	−0.303433
$341$	−2.88837	−0.156414
$342$	1.56567	0.0846617
$343$	47.4701	2.56315
$344$	8.03912	0.433441
$345$	−35.6578	−1.91975
$346$	−15.4443	−0.830292
$347$	19.2796	1.03498	0.517492	−	0.855688i	$-0.326866\pi$
$347$	19.2796	1.03498	0.517492	+	0.855688i	$0.326866\pi$
$348$	0.730504	0.0391591
$349$	−1.35991	−0.0727941	−0.0363971	−	0.999337i	$-0.511588\pi$
$349$	−1.35991	−0.0727941	−0.0363971	+	0.999337i	$0.511588\pi$
$350$	35.8075	1.91399
$351$	−10.8337	−0.578263
$352$	−1.47578	−0.0786595
$353$	20.4620	1.08908	0.544542	−	0.838734i	$-0.316704\pi$
$353$	20.4620	1.08908	0.544542	+	0.838734i	$0.316704\pi$
$354$	1.03895	0.0552195
$355$	33.9957	1.80430
$356$	−1.27476	−0.0675623
$357$	−15.3200	−0.810818
$358$	19.4101	1.02585
$359$	10.1701	0.536760	0.268380	−	0.963313i	$-0.413512\pi$
$359$	10.1701	0.536760	0.268380	+	0.963313i	$0.413512\pi$
$360$	−3.16099	−0.166599
$361$	−15.9705	−0.840551
$362$	−25.4619	−1.33825
$363$	17.4211	0.914371
$364$	−12.7267	−0.667061
$365$	13.2065	0.691260
$366$	8.32508	0.435159
$367$	12.6495	0.660298	0.330149	−	0.943929i	$-0.392901\pi$
$367$	12.6495	0.660298	0.330149	+	0.943929i	$0.392901\pi$
$368$	−5.13851	−0.267863
$369$	−5.32257	−0.277082
$370$	20.8101	1.08187
$371$	−32.1972	−1.67159
$372$	−3.86488	−0.200385
$373$	−28.0744	−1.45364	−0.726818	−	0.686830i	$-0.759002\pi$
$373$	−28.0744	−1.45364	−0.726818	+	0.686830i	$0.759002\pi$
$374$	−2.34971	−0.121500
$375$	16.2987	0.841660
$376$	6.55289	0.337940
$377$	0.966211	0.0497624
$378$	20.2109	1.03953
$379$	0.847183	0.0435168	0.0217584	−	0.999763i	$-0.493074\pi$
$379$	0.847183	0.0435168	0.0217584	+	0.999763i	$0.493074\pi$
$380$	−6.11645	−0.313767
$381$	−7.98639	−0.409155
$382$	2.14410	0.109702
$383$	−25.7614	−1.31635	−0.658174	−	0.752866i	$-0.728671\pi$
$383$	−25.7614	−1.31635	−0.658174	+	0.752866i	$0.728671\pi$
$384$	−1.97472	−0.100772
$385$	25.2694	1.28785
$386$	−9.05142	−0.460705
$387$	7.23137	0.367591
$388$	6.71023	0.340660
$389$	−9.24327	−0.468652	−0.234326	−	0.972158i	$-0.575288\pi$
$389$	−9.24327	−0.468652	−0.234326	+	0.972158i	$0.575288\pi$
$390$	−18.1247	−0.917782
$391$	−8.18141	−0.413752
$392$	16.7423	0.845612
$393$	6.25622	0.315585
$394$	−19.6593	−0.990422
$395$	−44.0495	−2.21637
$396$	−1.32750	−0.0667094
$397$	4.91497	0.246675	0.123338	−	0.992365i	$-0.460640\pi$
$397$	4.91497	0.246675	0.123338	+	0.992365i	$0.460640\pi$
$398$	−0.228087	−0.0114330
$399$	−16.7477	−0.838433
$400$	7.34874	0.367437
$401$	23.2804	1.16257	0.581284	−	0.813701i	$-0.302551\pi$
$401$	23.2804	1.16257	0.581284	+	0.813701i	$0.302551\pi$
$402$	1.84892	0.0922155
$403$	−5.11194	−0.254644
$404$	1.82876	0.0909843
$405$	38.2663	1.90147
$406$	−1.80251	−0.0894571
$407$	8.73949	0.433201
$408$	−3.14410	−0.155656
$409$	33.4814	1.65555	0.827774	−	0.561062i	$-0.189607\pi$
$409$	33.4814	1.65555	0.827774	+	0.561062i	$0.189607\pi$
$410$	20.7932	1.02690
$411$	26.2839	1.29649
$412$	10.4099	0.512860
$413$	−2.56360	−0.126146
$414$	−4.62221	−0.227169
$415$	−4.51817	−0.221788
$416$	−2.61189	−0.128058
$417$	−20.5470	−1.00619
$418$	−2.56868	−0.125638
$419$	27.9013	1.36307	0.681535	−	0.731786i	$-0.261313\pi$
$419$	27.9013	1.36307	0.681535	+	0.731786i	$0.261313\pi$
$420$	33.8126	1.64988
$421$	−27.9515	−1.36227	−0.681136	−	0.732157i	$-0.738514\pi$
$421$	−27.9515	−1.36227	−0.681136	+	0.732157i	$0.738514\pi$
$422$	7.57063	0.368532
$423$	5.89447	0.286599
$424$	−6.60780	−0.320903
$425$	11.7005	0.567557
$426$	19.1037	0.925578
$427$	−20.5420	−0.994099
$428$	−7.61879	−0.368268
$429$	−7.61173	−0.367498
$430$	−28.2501	−1.36234
$431$	−31.9920	−1.54100	−0.770500	−	0.637440i	$-0.779994\pi$
$431$	−31.9920	−1.54100	−0.770500	+	0.637440i	$0.779994\pi$
$432$	4.14786	0.199564
$433$	2.27753	0.109451	0.0547256	−	0.998501i	$-0.482572\pi$
$433$	2.27753	0.109451	0.0547256	+	0.998501i	$0.482572\pi$
$434$	9.53656	0.457769
$435$	−2.56705	−0.123081
$436$	−4.32693	−0.207223
$437$	−8.94387	−0.427843
$438$	7.42134	0.354605
$439$	−25.0275	−1.19450	−0.597248	−	0.802057i	$-0.703739\pi$
$439$	−25.0275	−1.19450	−0.597248	+	0.802057i	$0.703739\pi$
$440$	5.18602	0.247234
$441$	15.0600	0.717145
$442$	−4.15859	−0.197804
$443$	0.146187	0.00694557	0.00347279	−	0.999994i	$-0.498895\pi$
$443$	0.146187	0.00694557	0.00347279	+	0.999994i	$0.498895\pi$
$444$	11.6942	0.554981
$445$	4.47962	0.212354
$446$	2.64730	0.125353
$447$	22.6706	1.07228
$448$	4.87260	0.230209
$449$	1.31597	0.0621043	0.0310521	−	0.999518i	$-0.490114\pi$
$449$	1.31597	0.0621043	0.0310521	+	0.999518i	$0.490114\pi$
$450$	6.61036	0.311615
$451$	8.73237	0.411191
$452$	2.33924	0.110029
$453$	−20.6337	−0.969454
$454$	−6.89786	−0.323732
$455$	44.7226	2.09663
$456$	−3.43711	−0.160958
$457$	−22.7607	−1.06470	−0.532350	−	0.846524i	$-0.678691\pi$
$457$	−22.7607	−1.06470	−0.532350	+	0.846524i	$0.678691\pi$
$458$	−13.8437	−0.646872
$459$	6.60411	0.308254
$460$	18.0571	0.841918
$461$	10.7250	0.499514	0.249757	−	0.968309i	$-0.419649\pi$
$461$	10.7250	0.499514	0.249757	+	0.968309i	$0.419649\pi$
$462$	14.2000	0.660645
$463$	29.5722	1.37434	0.687168	−	0.726499i	$-0.258854\pi$
$463$	29.5722	1.37434	0.687168	+	0.726499i	$0.258854\pi$
$464$	−0.369928	−0.0171735
$465$	13.5815	0.629827
$466$	−7.73376	−0.358260
$467$	0.0909172	0.00420715	0.00210357	−	0.999998i	$-0.499330\pi$
$467$	0.0909172	0.00420715	0.00210357	+	0.999998i	$0.499330\pi$
$468$	−2.34945	−0.108604
$469$	−4.56218	−0.210662
$470$	−23.0274	−1.06217
$471$	25.4292	1.17172
$472$	−0.526124	−0.0242168
$473$	−11.8640	−0.545508
$474$	−24.7534	−1.13696
$475$	12.7909	0.586887
$476$	7.75804	0.355589
$477$	−5.94387	−0.272151
$478$	−15.8628	−0.725550
$479$	14.8975	0.680685	0.340342	−	0.940302i	$-0.389457\pi$
$479$	14.8975	0.680685	0.340342	+	0.940302i	$0.389457\pi$
$480$	6.93932	0.316735
$481$	15.4674	0.705255
$482$	−13.2217	−0.602230
$483$	49.4429	2.24973
$484$	−8.82206	−0.401003
$485$	−23.5803	−1.07072
$486$	9.06001	0.410970
$487$	−21.6717	−0.982038	−0.491019	−	0.871149i	$-0.663375\pi$
$487$	−21.6717	−0.982038	−0.491019	+	0.871149i	$0.663375\pi$
$488$	−4.21582	−0.190841
$489$	30.9712	1.40057
$490$	−58.8336	−2.65783
$491$	−38.6320	−1.74344	−0.871719	−	0.490006i	$-0.836995\pi$
$491$	−38.6320	−1.74344	−0.871719	+	0.490006i	$0.836995\pi$
$492$	11.6846	0.526784
$493$	−0.588990	−0.0265268
$494$	−4.54614	−0.204541
$495$	4.66494	0.209674
$496$	1.95718	0.0878800
$497$	−47.1382	−2.11444
$498$	−2.53896	−0.113774
$499$	−17.9210	−0.802256	−0.401128	−	0.916022i	$-0.631382\pi$
$499$	−17.9210	−0.802256	−0.401128	+	0.916022i	$0.631382\pi$
$500$	−8.25366	−0.369115
$501$	23.6710	1.05754
$502$	14.3155	0.638932
$503$	4.67831	0.208596	0.104298	−	0.994546i	$-0.466741\pi$
$503$	4.67831	0.208596	0.104298	+	0.994546i	$0.466741\pi$
$504$	4.38302	0.195235
$505$	−6.42641	−0.285972
$506$	7.58333	0.337120
$507$	12.1999	0.541816
$508$	4.04431	0.179437
$509$	16.0194	0.710049	0.355024	−	0.934857i	$-0.384473\pi$
$509$	16.0194	0.710049	0.355024	+	0.934857i	$0.384473\pi$
$510$	11.0486	0.489241
$511$	−18.3121	−0.810079
$512$	1.00000	0.0441942
$513$	7.21958	0.318752
$514$	25.1955	1.11132
$515$	−36.5812	−1.61196
$516$	−15.8750	−0.698859
$517$	−9.67065	−0.425315
$518$	−28.8552	−1.26783
$519$	30.4982	1.33872
$520$	9.17839	0.402499
$521$	10.2550	0.449278	0.224639	−	0.974442i	$-0.427880\pi$
$521$	10.2550	0.449278	0.224639	+	0.974442i	$0.427880\pi$
$522$	−0.332758	−0.0145644
$523$	−14.6078	−0.638757	−0.319378	−	0.947627i	$-0.603474\pi$
$523$	−14.6078	−0.638757	−0.319378	+	0.947627i	$0.603474\pi$
$524$	−3.16815	−0.138401
$525$	−70.7098	−3.08603
$526$	−9.88538	−0.431023
$527$	3.11617	0.135743
$528$	2.91426	0.126827
$529$	3.40429	0.148013
$530$	23.2203	1.00863
$531$	−0.473261	−0.0205378
$532$	8.48104	0.367700
$533$	15.4548	0.669423
$534$	2.51730	0.108934
$535$	26.7730	1.15750
$536$	−0.936292	−0.0404417
$537$	−38.3295	−1.65404
$538$	−20.7402	−0.894173
$539$	−24.7080	−1.06425
$540$	−14.5759	−0.627246
$541$	31.9891	1.37532	0.687659	−	0.726034i	$-0.258638\pi$
$541$	31.9891	1.37532	0.687659	+	0.726034i	$0.258638\pi$
$542$	−12.1185	−0.520532
$543$	50.2801	2.15773
$544$	1.59217	0.0682639
$545$	15.2052	0.651319
$546$	25.1317	1.07554
$547$	15.3193	0.655005	0.327502	−	0.944850i	$-0.393793\pi$
$547$	15.3193	0.655005	0.327502	+	0.944850i	$0.393793\pi$
$548$	−13.3102	−0.568583
$549$	−3.79223	−0.161848
$550$	−10.8452	−0.462439
$551$	−0.643880	−0.0274302
$552$	10.1471	0.431890
$553$	61.0789	2.59734
$554$	−21.6799	−0.921090
$555$	−41.0942	−1.74435
$556$	10.4050	0.441271
$557$	7.53624	0.319321	0.159660	−	0.987172i	$-0.448960\pi$
$557$	7.53624	0.319321	0.159660	+	0.987172i	$0.448960\pi$
$558$	1.76053	0.0745291
$559$	−20.9973	−0.888092
$560$	−17.1227	−0.723566
$561$	4.64001	0.195902
$562$	7.60750	0.320903
$563$	32.8790	1.38569	0.692843	−	0.721088i	$-0.256358\pi$
$563$	32.8790	1.38569	0.692843	+	0.721088i	$0.256358\pi$
$564$	−12.9401	−0.544878
$565$	−8.22028	−0.345830
$566$	−13.4520	−0.565430
$567$	−53.0599	−2.22830
$568$	−9.67414	−0.405918
$569$	−16.8706	−0.707253	−0.353627	−	0.935387i	$-0.615052\pi$
$569$	−16.8706	−0.707253	−0.353627	+	0.935387i	$0.615052\pi$
$570$	12.0783	0.505904
$571$	−40.1586	−1.68058	−0.840292	−	0.542134i	$-0.817617\pi$
$571$	−40.1586	−1.68058	−0.840292	+	0.542134i	$0.817617\pi$
$572$	3.85459	0.161168
$573$	−4.23400	−0.176878
$574$	−28.8317	−1.20341
$575$	−37.7616	−1.57477
$576$	0.899523	0.0374801
$577$	−18.1693	−0.756398	−0.378199	−	0.925724i	$-0.623457\pi$
$577$	−18.1693	−0.756398	−0.378199	+	0.925724i	$0.623457\pi$
$578$	−14.4650	−0.601664
$579$	17.8740	0.742819
$580$	1.29995	0.0539777
$581$	6.26487	0.259911
$582$	−13.2508	−0.549264
$583$	9.75169	0.403874
$584$	−3.75817	−0.155514
$585$	8.25616	0.341350
$586$	−4.11505	−0.169991
$587$	6.10464	0.251966	0.125983	−	0.992032i	$-0.459792\pi$
$587$	6.10464	0.251966	0.125983	+	0.992032i	$0.459792\pi$
$588$	−33.0613	−1.36342
$589$	3.40658	0.140366
$590$	1.84884	0.0761156
$591$	38.8217	1.59691
$592$	−5.92193	−0.243390
$593$	26.2168	1.07660	0.538298	−	0.842754i	$-0.319067\pi$
$593$	26.2168	1.07660	0.538298	+	0.842754i	$0.319067\pi$
$594$	−6.12134	−0.251162
$595$	−27.2623	−1.11765
$596$	−11.4804	−0.470256
$597$	0.450408	0.0184340
$598$	13.4212	0.548835
$599$	−35.8055	−1.46297	−0.731486	−	0.681857i	$-0.761173\pi$
$599$	−35.8055	−1.46297	−0.731486	+	0.681857i	$0.761173\pi$
$600$	−14.5117	−0.592438
$601$	23.9639	0.977508	0.488754	−	0.872422i	$-0.337452\pi$
$601$	23.9639	0.977508	0.488754	+	0.872422i	$0.337452\pi$
$602$	39.1715	1.59651
$603$	−0.842216	−0.0342977
$604$	10.4489	0.425160
$605$	31.0014	1.26039
$606$	−3.61130	−0.146699
$607$	−34.9822	−1.41989	−0.709943	−	0.704260i	$-0.751279\pi$
$607$	−34.9822	−1.41989	−0.709943	+	0.704260i	$0.751279\pi$
$608$	1.74056	0.0705889
$609$	3.55946	0.144236
$610$	14.8147	0.599831
$611$	−17.1154	−0.692416
$612$	1.43220	0.0578931
$613$	−21.9878	−0.888079	−0.444039	−	0.896007i	$-0.646455\pi$
$613$	−21.9878	−0.888079	−0.444039	+	0.896007i	$0.646455\pi$
$614$	−4.72181	−0.190557
$615$	−41.0607	−1.65573
$616$	−7.19091	−0.289730
$617$	−11.9458	−0.480918	−0.240459	−	0.970659i	$-0.577298\pi$
$617$	−11.9458	−0.480918	−0.240459	+	0.970659i	$0.577298\pi$
$618$	−20.5567	−0.826911
$619$	49.2814	1.98079	0.990393	−	0.138284i	$-0.0441587\pi$
$619$	49.2814	1.98079	0.990393	+	0.138284i	$0.0441587\pi$
$620$	−6.87768	−0.276214
$621$	−21.3138	−0.855294
$622$	−12.1993	−0.489148
$623$	−6.21141	−0.248855
$624$	5.15775	0.206475
$625$	−7.73972	−0.309589
$626$	−32.9605	−1.31737
$627$	5.07244	0.202574
$628$	−12.8774	−0.513863
$629$	−9.42875	−0.375949
$630$	−15.4023	−0.613641
$631$	32.5116	1.29427	0.647133	−	0.762377i	$-0.275968\pi$
$631$	32.5116	1.29427	0.647133	+	0.762377i	$0.275968\pi$
$632$	12.5352	0.498622
$633$	−14.9499	−0.594204
$634$	10.0023	0.397242
$635$	−14.2120	−0.563987
$636$	13.0486	0.517409
$637$	−43.7289	−1.73260
$638$	0.545933	0.0216137
$639$	−8.70211	−0.344250
$640$	−3.51408	−0.138906
$641$	19.9214	0.786846	0.393423	−	0.919358i	$-0.371291\pi$
$641$	19.9214	0.786846	0.393423	+	0.919358i	$0.371291\pi$
$642$	15.0450	0.593778
$643$	−1.47410	−0.0581330	−0.0290665	−	0.999577i	$-0.509253\pi$
$643$	−1.47410	−0.0581330	−0.0290665	+	0.999577i	$0.509253\pi$
$644$	−25.0379	−0.986632
$645$	55.7861	2.19657
$646$	2.77127	0.109034
$647$	−4.28820	−0.168586	−0.0842932	−	0.996441i	$-0.526863\pi$
$647$	−4.28820	−0.168586	−0.0842932	+	0.996441i	$0.526863\pi$
$648$	−10.8894	−0.427777
$649$	0.776446	0.0304782
$650$	−19.1941	−0.752855
$651$	−18.8320	−0.738086
$652$	−15.6838	−0.614227
$653$	21.6565	0.847486	0.423743	−	0.905782i	$-0.360716\pi$
$653$	21.6565	0.847486	0.423743	+	0.905782i	$0.360716\pi$
$654$	8.54449	0.334116
$655$	11.1331	0.435008
$656$	−5.91710	−0.231024
$657$	−3.38056	−0.131888
$658$	31.9296	1.24475
$659$	−7.08833	−0.276122	−0.138061	−	0.990424i	$-0.544087\pi$
$659$	−7.08833	−0.276122	−0.138061	+	0.990424i	$0.544087\pi$
$660$	−10.2409	−0.398628
$661$	7.71754	0.300177	0.150089	−	0.988673i	$-0.452044\pi$
$661$	7.71754	0.300177	0.150089	+	0.988673i	$0.452044\pi$
$662$	−15.2506	−0.592733
$663$	8.21205	0.318929
$664$	1.28573	0.0498961
$665$	−29.8030	−1.15571
$666$	−5.32691	−0.206414
$667$	1.90088	0.0736023
$668$	−11.9870	−0.463792
$669$	−5.22768	−0.202114
$670$	3.29020	0.127112
$671$	6.22165	0.240184
$672$	−9.62203	−0.371178
$673$	5.89585	0.227268	0.113634	−	0.993523i	$-0.463751\pi$
$673$	5.89585	0.227268	0.113634	+	0.993523i	$0.463751\pi$
$674$	7.33844	0.282666
$675$	30.4815	1.17323
$676$	−6.17803	−0.237616
$677$	5.68398	0.218453	0.109226	−	0.994017i	$-0.465163\pi$
$677$	5.68398	0.218453	0.109226	+	0.994017i	$0.465163\pi$
$678$	−4.61935	−0.177405
$679$	32.6963	1.25477
$680$	−5.59503	−0.214559
$681$	13.6213	0.521971
$682$	−2.88837	−0.110602
$683$	−38.2737	−1.46450	−0.732252	−	0.681034i	$-0.761530\pi$
$683$	−38.2737	−1.46450	−0.732252	+	0.681034i	$0.761530\pi$
$684$	1.56567	0.0598649
$685$	46.7730	1.78710
$686$	47.4701	1.81242
$687$	27.3374	1.04299
$688$	8.03912	0.306489
$689$	17.2589	0.657510
$690$	−35.6578	−1.35747
$691$	2.37597	0.0903860	0.0451930	−	0.998978i	$-0.485610\pi$
$691$	2.37597	0.0903860	0.0451930	+	0.998978i	$0.485610\pi$
$692$	−15.4443	−0.587105
$693$	−6.46838	−0.245714
$694$	19.2796	0.731844
$695$	−36.5640	−1.38695
$696$	0.730504	0.0276897
$697$	−9.42107	−0.356848
$698$	−1.35991	−0.0514732
$699$	15.2720	0.577641
$700$	35.8075	1.35340
$701$	−6.96897	−0.263214	−0.131607	−	0.991302i	$-0.542014\pi$
$701$	−6.96897	−0.263214	−0.131607	+	0.991302i	$0.542014\pi$
$702$	−10.8337	−0.408893
$703$	−10.3075	−0.388753
$704$	−1.47578	−0.0556207
$705$	45.4726	1.71260
$706$	20.4620	0.770099
$707$	8.91083	0.335126
$708$	1.03895	0.0390461
$709$	7.51184	0.282113	0.141057	−	0.990002i	$-0.454950\pi$
$709$	7.51184	0.282113	0.141057	+	0.990002i	$0.454950\pi$
$710$	33.9957	1.27583
$711$	11.2757	0.422870
$712$	−1.27476	−0.0477738
$713$	−10.0570	−0.376637
$714$	−15.3200	−0.573335
$715$	−13.5453	−0.506566
$716$	19.4101	0.725388
$717$	31.3247	1.16984
$718$	10.1701	0.379547
$719$	1.12755	0.0420505	0.0210253	−	0.999779i	$-0.493307\pi$
$719$	1.12755	0.0420505	0.0210253	+	0.999779i	$0.493307\pi$
$720$	−3.16099	−0.117803
$721$	50.7234	1.88904
$722$	−15.9705	−0.594359
$723$	26.1091	0.971007
$724$	−25.4619	−0.946283
$725$	−2.71850	−0.100963
$726$	17.4211	0.646558
$727$	22.1325	0.820850	0.410425	−	0.911894i	$-0.365380\pi$
$727$	22.1325	0.820850	0.410425	+	0.911894i	$0.365380\pi$
$728$	−12.7267	−0.471683
$729$	14.7773	0.547307
$730$	13.2065	0.488795
$731$	12.7997	0.473414
$732$	8.32508	0.307704
$733$	26.4644	0.977487	0.488743	−	0.872428i	$-0.337455\pi$
$733$	26.4644	0.977487	0.488743	+	0.872428i	$0.337455\pi$
$734$	12.6495	0.466901
$735$	116.180	4.28536
$736$	−5.13851	−0.189408
$737$	1.38176	0.0508980
$738$	−5.32257	−0.195926
$739$	19.8423	0.729910	0.364955	−	0.931025i	$-0.381084\pi$
$739$	19.8423	0.729910	0.364955	+	0.931025i	$0.381084\pi$
$740$	20.8101	0.764996
$741$	8.97736	0.329792
$742$	−32.1972	−1.18200
$743$	−24.6127	−0.902953	−0.451477	−	0.892283i	$-0.649103\pi$
$743$	−24.6127	−0.902953	−0.451477	+	0.892283i	$0.649103\pi$
$744$	−3.86488	−0.141694
$745$	40.3431	1.47806
$746$	−28.0744	−1.02788
$747$	1.15655	0.0423158
$748$	−2.34971	−0.0859138
$749$	−37.1233	−1.35646
$750$	16.2987	0.595143
$751$	39.6532	1.44697	0.723483	−	0.690342i	$-0.242540\pi$
$751$	39.6532	1.44697	0.723483	+	0.690342i	$0.242540\pi$
$752$	6.55289	0.238959
$753$	−28.2691	−1.03018
$754$	0.966211	0.0351873
$755$	−36.7183	−1.33631
$756$	20.2109	0.735062
$757$	−6.51156	−0.236667	−0.118333	−	0.992974i	$-0.537755\pi$
$757$	−6.51156	−0.236667	−0.118333	+	0.992974i	$0.537755\pi$
$758$	0.847183	0.0307711
$759$	−14.9750	−0.543557
$760$	−6.11645	−0.221867
$761$	0.799414	0.0289788	0.0144894	−	0.999895i	$-0.495388\pi$
$761$	0.799414	0.0289788	0.0144894	+	0.999895i	$0.495388\pi$
$762$	−7.98639	−0.289316
$763$	−21.0834	−0.763272
$764$	2.14410	0.0775709
$765$	−5.03285	−0.181963
$766$	−25.7614	−0.930798
$767$	1.37418	0.0496187
$768$	−1.97472	−0.0712566
$769$	52.3347	1.88724	0.943619	−	0.331034i	$-0.107397\pi$
$769$	52.3347	1.88724	0.943619	+	0.331034i	$0.107397\pi$
$770$	25.2694	0.910646
$771$	−49.7540	−1.79185
$772$	−9.05142	−0.325768
$773$	−7.73872	−0.278342	−0.139171	−	0.990268i	$-0.544444\pi$
$773$	−7.73872	−0.278342	−0.139171	+	0.990268i	$0.544444\pi$
$774$	7.23137	0.259926
$775$	14.3828	0.516646
$776$	6.71023	0.240883
$777$	56.9810	2.04418
$778$	−9.24327	−0.331387
$779$	−10.2991	−0.369002
$780$	−18.1247	−0.648970
$781$	14.2769	0.510869
$782$	−8.18141	−0.292567
$783$	−1.53441	−0.0548352
$784$	16.7423	0.597938
$785$	45.2521	1.61512
$786$	6.25622	0.223152
$787$	40.0482	1.42756	0.713782	−	0.700368i	$-0.246981\pi$
$787$	40.0482	1.42756	0.713782	+	0.700368i	$0.246981\pi$
$788$	−19.6593	−0.700334
$789$	19.5209	0.694961
$790$	−44.0495	−1.56721
$791$	11.3982	0.405273
$792$	−1.32750	−0.0471707
$793$	11.0113	0.391022
$794$	4.91497	0.174426
$795$	−45.8537	−1.62626
$796$	−0.228087	−0.00808433
$797$	40.5501	1.43636	0.718179	−	0.695859i	$-0.244976\pi$
$797$	40.5501	1.43636	0.718179	+	0.695859i	$0.244976\pi$
$798$	−16.7477	−0.592862
$799$	10.4334	0.369105
$800$	7.34874	0.259817
$801$	−1.14668	−0.0405159
$802$	23.2804	0.822059
$803$	5.54625	0.195723
$804$	1.84892	0.0652062
$805$	87.9852	3.10107
$806$	−5.11194	−0.180060
$807$	40.9561	1.44172
$808$	1.82876	0.0643356
$809$	−35.2141	−1.23806	−0.619032	−	0.785366i	$-0.712475\pi$
$809$	−35.2141	−1.23806	−0.619032	+	0.785366i	$0.712475\pi$
$810$	38.2663	1.34454
$811$	54.5581	1.91579	0.957897	−	0.287113i	$-0.0926956\pi$
$811$	54.5581	1.91579	0.957897	+	0.287113i	$0.0926956\pi$
$812$	−1.80251	−0.0632557
$813$	23.9306	0.839281
$814$	8.73949	0.306319
$815$	55.1142	1.93057
$816$	−3.14410	−0.110066
$817$	13.9925	0.489537
$818$	33.4814	1.17065
$819$	−11.4480	−0.400024
$820$	20.7932	0.726129
$821$	48.0984	1.67865	0.839323	−	0.543633i	$-0.182952\pi$
$821$	48.0984	1.67865	0.839323	+	0.543633i	$0.182952\pi$
$822$	26.2839	0.916756
$823$	30.3935	1.05945	0.529725	−	0.848169i	$-0.322295\pi$
$823$	30.3935	1.05945	0.529725	+	0.848169i	$0.322295\pi$
$824$	10.4099	0.362647
$825$	21.4161	0.745615
$826$	−2.56360	−0.0891989
$827$	24.5400	0.853340	0.426670	−	0.904407i	$-0.359687\pi$
$827$	24.5400	0.853340	0.426670	+	0.904407i	$0.359687\pi$
$828$	−4.62221	−0.160633
$829$	1.39163	0.0483334	0.0241667	−	0.999708i	$-0.492307\pi$
$829$	1.39163	0.0483334	0.0241667	+	0.999708i	$0.492307\pi$
$830$	−4.51817	−0.156828
$831$	42.8117	1.48512
$832$	−2.61189	−0.0905510
$833$	26.6566	0.923597
$834$	−20.5470	−0.711485
$835$	42.1234	1.45774
$836$	−2.56868	−0.0888398
$837$	8.11810	0.280603
$838$	27.9013	0.963835
$839$	−30.1224	−1.03994	−0.519971	−	0.854184i	$-0.674057\pi$
$839$	−30.1224	−1.03994	−0.519971	+	0.854184i	$0.674057\pi$
$840$	33.8126	1.16664
$841$	−28.8632	−0.995281
$842$	−27.9515	−0.963272
$843$	−15.0227	−0.517409
$844$	7.57063	0.260592
$845$	21.7101	0.746849
$846$	5.89447	0.202656
$847$	−42.9864	−1.47703
$848$	−6.60780	−0.226913
$849$	26.5640	0.911673
$850$	11.7005	0.401323
$851$	30.4299	1.04312
$852$	19.1037	0.654483
$853$	39.5525	1.35425	0.677126	−	0.735867i	$-0.263225\pi$
$853$	39.5525	1.35425	0.677126	+	0.735867i	$0.263225\pi$
$854$	−20.5420	−0.702934
$855$	−5.50188	−0.188160
$856$	−7.61879	−0.260405
$857$	27.2126	0.929565	0.464783	−	0.885425i	$-0.346132\pi$
$857$	27.2126	0.929565	0.464783	+	0.885425i	$0.346132\pi$
$858$	−7.61173	−0.259860
$859$	−6.43113	−0.219427	−0.109714	−	0.993963i	$-0.534993\pi$
$859$	−6.43113	−0.219427	−0.109714	+	0.993963i	$0.534993\pi$
$860$	−28.2501	−0.963321
$861$	56.9346	1.94032
$862$	−31.9920	−1.08965
$863$	−17.0326	−0.579798	−0.289899	−	0.957057i	$-0.593622\pi$
$863$	−17.0326	−0.579798	−0.289899	+	0.957057i	$0.593622\pi$
$864$	4.14786	0.141113
$865$	54.2726	1.84532
$866$	2.27753	0.0773936
$867$	28.5643	0.970094
$868$	9.53656	0.323692
$869$	−18.4992	−0.627542
$870$	−2.56705	−0.0870311
$871$	2.44549	0.0828623
$872$	−4.32693	−0.146529
$873$	6.03600	0.204288
$874$	−8.94387	−0.302531
$875$	−40.2168	−1.35958
$876$	7.42134	0.250744
$877$	−13.7263	−0.463503	−0.231752	−	0.972775i	$-0.574446\pi$
$877$	−13.7263	−0.463503	−0.231752	+	0.972775i	$0.574446\pi$
$878$	−25.0275	−0.844636
$879$	8.12607	0.274085
$880$	5.18602	0.174821
$881$	17.1543	0.577942	0.288971	−	0.957338i	$-0.406687\pi$
$881$	17.1543	0.577942	0.288971	+	0.957338i	$0.406687\pi$
$882$	15.0600	0.507098
$883$	−56.8249	−1.91231	−0.956154	−	0.292863i	$-0.905392\pi$
$883$	−56.8249	−1.91231	−0.956154	+	0.292863i	$0.905392\pi$
$884$	−4.15859	−0.139868
$885$	−3.65095	−0.122725
$886$	0.146187	0.00491126
$887$	34.7884	1.16808	0.584039	−	0.811725i	$-0.301471\pi$
$887$	34.7884	1.16808	0.584039	+	0.811725i	$0.301471\pi$
$888$	11.6942	0.392431
$889$	19.7063	0.660929
$890$	4.47962	0.150157
$891$	16.0704	0.538380
$892$	2.64730	0.0886382
$893$	11.4057	0.381676
$894$	22.6706	0.758219
$895$	−68.2085	−2.27996
$896$	4.87260	0.162782
$897$	−26.5032	−0.884915
$898$	1.31597	0.0439144
$899$	−0.724015	−0.0241473
$900$	6.61036	0.220345
$901$	−10.5208	−0.350498
$902$	8.73237	0.290756
$903$	−77.3527	−2.57414
$904$	2.33924	0.0778020
$905$	89.4750	2.97425
$906$	−20.6337	−0.685508
$907$	−22.7209	−0.754434	−0.377217	−	0.926125i	$-0.623119\pi$
$907$	−22.7209	−0.754434	−0.377217	+	0.926125i	$0.623119\pi$
$908$	−6.89786	−0.228913
$909$	1.64501	0.0545616
$910$	44.7226	1.48254
$911$	−3.67469	−0.121748	−0.0608740	−	0.998145i	$-0.519389\pi$
$911$	−3.67469	−0.121748	−0.0608740	+	0.998145i	$0.519389\pi$
$912$	−3.43711	−0.113814
$913$	−1.89746	−0.0627969
$914$	−22.7607	−0.752857
$915$	−29.2550	−0.967139
$916$	−13.8437	−0.457407
$917$	−15.4372	−0.509780
$918$	6.60411	0.217968
$919$	22.8787	0.754697	0.377349	−	0.926071i	$-0.376836\pi$
$919$	22.8787	0.754697	0.377349	+	0.926071i	$0.376836\pi$
$920$	18.0571	0.595326
$921$	9.32425	0.307245
$922$	10.7250	0.353210
$923$	25.2678	0.831699
$924$	14.2000	0.467147
$925$	−43.5188	−1.43089
$926$	29.5722	0.971802
$927$	9.36395	0.307553
$928$	−0.369928	−0.0121435
$929$	−20.3361	−0.667206	−0.333603	−	0.942714i	$-0.608264\pi$
$929$	−20.3361	−0.667206	−0.333603	+	0.942714i	$0.608264\pi$
$930$	13.5815	0.445355
$931$	29.1408	0.955052
$932$	−7.73376	−0.253328
$933$	24.0902	0.788679
$934$	0.0909172	0.00297490
$935$	8.25705	0.270034
$936$	−2.34945	−0.0767943
$937$	9.27462	0.302989	0.151494	−	0.988458i	$-0.451591\pi$
$937$	9.27462	0.302989	0.151494	+	0.988458i	$0.451591\pi$
$938$	−4.56218	−0.148960
$939$	65.0877	2.12406
$940$	−23.0274	−0.751070
$941$	−42.8268	−1.39611	−0.698057	−	0.716042i	$-0.745952\pi$
$941$	−42.8268	−1.39611	−0.698057	+	0.716042i	$0.745952\pi$
$942$	25.4292	0.828529
$943$	30.4051	0.990126
$944$	−0.526124	−0.0171239
$945$	−71.0225	−2.31036
$946$	−11.8640	−0.385732
$947$	−4.40003	−0.142982	−0.0714909	−	0.997441i	$-0.522776\pi$
$947$	−4.40003	−0.142982	−0.0714909	+	0.997441i	$0.522776\pi$
$948$	−24.7534	−0.803955
$949$	9.81593	0.318639
$950$	12.7909	0.414991
$951$	−19.7518	−0.640494
$952$	7.75804	0.251439
$953$	27.5565	0.892642	0.446321	−	0.894873i	$-0.352734\pi$
$953$	27.5565	0.892642	0.446321	+	0.894873i	$0.352734\pi$
$954$	−5.94387	−0.192440
$955$	−7.53454	−0.243812
$956$	−15.8628	−0.513041
$957$	−1.07807	−0.0348489
$958$	14.8975	0.481317
$959$	−64.8552	−2.09428
$960$	6.93932	0.223966
$961$	−27.1694	−0.876434
$962$	15.4674	0.498690
$963$	−6.85328	−0.220844
$964$	−13.2217	−0.425841
$965$	31.8074	1.02392
$966$	49.4429	1.59080
$967$	−30.4855	−0.980348	−0.490174	−	0.871624i	$-0.663067\pi$
$967$	−30.4855	−0.980348	−0.490174	+	0.871624i	$0.663067\pi$
$968$	−8.82206	−0.283552
$969$	−5.47248	−0.175802
$970$	−23.5803	−0.757117
$971$	37.8366	1.21423	0.607117	−	0.794612i	$-0.292326\pi$
$971$	37.8366	1.21423	0.607117	+	0.794612i	$0.292326\pi$
$972$	9.06001	0.290600
$973$	50.6995	1.62535
$974$	−21.6717	−0.694405
$975$	37.9030	1.21387
$976$	−4.21582	−0.134945
$977$	−36.0630	−1.15376	−0.576880	−	0.816829i	$-0.695730\pi$
$977$	−36.0630	−1.15376	−0.576880	+	0.816829i	$0.695730\pi$
$978$	30.9712	0.990350
$979$	1.88127	0.0601258
$980$	−58.8336	−1.87937
$981$	−3.89218	−0.124268
$982$	−38.6320	−1.23280
$983$	28.1470	0.897749	0.448874	−	0.893595i	$-0.351825\pi$
$983$	28.1470	0.897749	0.448874	+	0.893595i	$0.351825\pi$
$984$	11.6846	0.372492
$985$	69.0844	2.20121
$986$	−0.588990	−0.0187573
$987$	−63.0521	−2.00697
$988$	−4.54614	−0.144632
$989$	−41.3091	−1.31355
$990$	4.66494	0.148262
$991$	31.5228	1.00136	0.500678	−	0.865634i	$-0.333084\pi$
$991$	31.5228	1.00136	0.500678	+	0.865634i	$0.333084\pi$
$992$	1.95718	0.0621405
$993$	30.1158	0.955695
$994$	−47.1382	−1.49513
$995$	0.801515	0.0254097
$996$	−2.53896	−0.0804502
$997$	−6.05575	−0.191788	−0.0958938	−	0.995392i	$-0.530571\pi$
$997$	−6.05575	−0.191788	−0.0958938	+	0.995392i	$0.530571\pi$
$998$	−17.9210	−0.567281
$999$	−24.5633	−0.777149

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.e.1.15	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.e.1.15	✓	56	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:	\( N \)	\(=\)	\( 6046 = 2 \cdot 3023 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6046.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.97472 q^{3} +1.00000 q^{4} -3.51408 q^{5} -1.97472 q^{6} +4.87260 q^{7} +1.00000 q^{8} +0.899523 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.97472 q^{3} +1.00000 q^{4} -3.51408 q^{5} -1.97472 q^{6} +4.87260 q^{7} +1.00000 q^{8} +0.899523 q^{9} -3.51408 q^{10} -1.47578 q^{11} -1.97472 q^{12} -2.61189 q^{13} +4.87260 q^{14} +6.93932 q^{15} +1.00000 q^{16} +1.59217 q^{17} +0.899523 q^{18} +1.74056 q^{19} -3.51408 q^{20} -9.62203 q^{21} -1.47578 q^{22} -5.13851 q^{23} -1.97472 q^{24} +7.34874 q^{25} -2.61189 q^{26} +4.14786 q^{27} +4.87260 q^{28} -0.369928 q^{29} +6.93932 q^{30} +1.95718 q^{31} +1.00000 q^{32} +2.91426 q^{33} +1.59217 q^{34} -17.1227 q^{35} +0.899523 q^{36} -5.92193 q^{37} +1.74056 q^{38} +5.15775 q^{39} -3.51408 q^{40} -5.91710 q^{41} -9.62203 q^{42} +8.03912 q^{43} -1.47578 q^{44} -3.16099 q^{45} -5.13851 q^{46} +6.55289 q^{47} -1.97472 q^{48} +16.7423 q^{49} +7.34874 q^{50} -3.14410 q^{51} -2.61189 q^{52} -6.60780 q^{53} +4.14786 q^{54} +5.18602 q^{55} +4.87260 q^{56} -3.43711 q^{57} -0.369928 q^{58} -0.526124 q^{59} +6.93932 q^{60} -4.21582 q^{61} +1.95718 q^{62} +4.38302 q^{63} +1.00000 q^{64} +9.17839 q^{65} +2.91426 q^{66} -0.936292 q^{67} +1.59217 q^{68} +10.1471 q^{69} -17.1227 q^{70} -9.67414 q^{71} +0.899523 q^{72} -3.75817 q^{73} -5.92193 q^{74} -14.5117 q^{75} +1.74056 q^{76} -7.19091 q^{77} +5.15775 q^{78} +12.5352 q^{79} -3.51408 q^{80} -10.8894 q^{81} -5.91710 q^{82} +1.28573 q^{83} -9.62203 q^{84} -5.59503 q^{85} +8.03912 q^{86} +0.730504 q^{87} -1.47578 q^{88} -1.27476 q^{89} -3.16099 q^{90} -12.7267 q^{91} -5.13851 q^{92} -3.86488 q^{93} +6.55289 q^{94} -6.11645 q^{95} -1.97472 q^{96} +6.71023 q^{97} +16.7423 q^{98} -1.32750 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9}+O(q^{10}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9} - 17 q^{10} - 53 q^{11} - 18 q^{12} - 21 q^{13} - 35 q^{14} - 36 q^{15} + 56 q^{16} - 22 q^{17} + 34 q^{18} - 31 q^{19} - 17 q^{20} - 23 q^{21} - 53 q^{22} - 59 q^{23} - 18 q^{24} + 41 q^{25} - 21 q^{26} - 63 q^{27} - 35 q^{28} - 88 q^{29} - 36 q^{30} - 44 q^{31} + 56 q^{32} + 4 q^{33} - 22 q^{34} - 51 q^{35} + 34 q^{36} - 60 q^{37} - 31 q^{38} - 62 q^{39} - 17 q^{40} - 39 q^{41} - 23 q^{42} - 66 q^{43} - 53 q^{44} - 34 q^{45} - 59 q^{46} - 51 q^{47} - 18 q^{48} + 41 q^{49} + 41 q^{50} - 48 q^{51} - 21 q^{52} - 75 q^{53} - 63 q^{54} - 41 q^{55} - 35 q^{56} - 12 q^{57} - 88 q^{58} - 77 q^{59} - 36 q^{60} - 43 q^{61} - 44 q^{62} - 88 q^{63} + 56 q^{64} - 54 q^{65} + 4 q^{66} - 62 q^{67} - 22 q^{68} - 48 q^{69} - 51 q^{70} - 122 q^{71} + 34 q^{72} - 7 q^{73} - 60 q^{74} - 63 q^{75} - 31 q^{76} - 39 q^{77} - 62 q^{78} - 91 q^{79} - 17 q^{80} + 8 q^{81} - 39 q^{82} - 51 q^{83} - 23 q^{84} - 72 q^{85} - 66 q^{86} - 19 q^{87} - 53 q^{88} - 62 q^{89} - 34 q^{90} - 48 q^{91} - 59 q^{92} - 41 q^{93} - 51 q^{94} - 120 q^{95} - 18 q^{96} + 6 q^{97} + 41 q^{98} - 128 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9 - 17 * q^10 - 53 * q^11 - 18 * q^12 - 21 * q^13 - 35 * q^14 - 36 * q^15 + 56 * q^16 - 22 * q^17 + 34 * q^18 - 31 * q^19 - 17 * q^20 - 23 * q^21 - 53 * q^22 - 59 * q^23 - 18 * q^24 + 41 * q^25 - 21 * q^26 - 63 * q^27 - 35 * q^28 - 88 * q^29 - 36 * q^30 - 44 * q^31 + 56 * q^32 + 4 * q^33 - 22 * q^34 - 51 * q^35 + 34 * q^36 - 60 * q^37 - 31 * q^38 - 62 * q^39 - 17 * q^40 - 39 * q^41 - 23 * q^42 - 66 * q^43 - 53 * q^44 - 34 * q^45 - 59 * q^46 - 51 * q^47 - 18 * q^48 + 41 * q^49 + 41 * q^50 - 48 * q^51 - 21 * q^52 - 75 * q^53 - 63 * q^54 - 41 * q^55 - 35 * q^56 - 12 * q^57 - 88 * q^58 - 77 * q^59 - 36 * q^60 - 43 * q^61 - 44 * q^62 - 88 * q^63 + 56 * q^64 - 54 * q^65 + 4 * q^66 - 62 * q^67 - 22 * q^68 - 48 * q^69 - 51 * q^70 - 122 * q^71 + 34 * q^72 - 7 * q^73 - 60 * q^74 - 63 * q^75 - 31 * q^76 - 39 * q^77 - 62 * q^78 - 91 * q^79 - 17 * q^80 + 8 * q^81 - 39 * q^82 - 51 * q^83 - 23 * q^84 - 72 * q^85 - 66 * q^86 - 19 * q^87 - 53 * q^88 - 62 * q^89 - 34 * q^90 - 48 * q^91 - 59 * q^92 - 41 * q^93 - 51 * q^94 - 120 * q^95 - 18 * q^96 + 6 * q^97 + 41 * q^98 - 128 * q^99

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