LMFDB - Embedded newform 6046.2.a.e.1.12

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			1.12
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.37532 q^{3} +1.00000 q^{4} -4.29598 q^{5} -2.37532 q^{6} -4.13959 q^{7} +1.00000 q^{8} +2.64215 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.37532 q^{3} +1.00000 q^{4} -4.29598 q^{5} -2.37532 q^{6} -4.13959 q^{7} +1.00000 q^{8} +2.64215 q^{9} -4.29598 q^{10} -4.77640 q^{11} -2.37532 q^{12} -3.98414 q^{13} -4.13959 q^{14} +10.2043 q^{15} +1.00000 q^{16} +6.95682 q^{17} +2.64215 q^{18} +6.18372 q^{19} -4.29598 q^{20} +9.83285 q^{21} -4.77640 q^{22} +1.81455 q^{23} -2.37532 q^{24} +13.4554 q^{25} -3.98414 q^{26} +0.850001 q^{27} -4.13959 q^{28} -9.39839 q^{29} +10.2043 q^{30} +1.34878 q^{31} +1.00000 q^{32} +11.3455 q^{33} +6.95682 q^{34} +17.7836 q^{35} +2.64215 q^{36} +3.33633 q^{37} +6.18372 q^{38} +9.46361 q^{39} -4.29598 q^{40} +6.78627 q^{41} +9.83285 q^{42} +11.4679 q^{43} -4.77640 q^{44} -11.3506 q^{45} +1.81455 q^{46} -8.13733 q^{47} -2.37532 q^{48} +10.1362 q^{49} +13.4554 q^{50} -16.5247 q^{51} -3.98414 q^{52} -9.88577 q^{53} +0.850001 q^{54} +20.5193 q^{55} -4.13959 q^{56} -14.6883 q^{57} -9.39839 q^{58} -4.10917 q^{59} +10.2043 q^{60} -5.06837 q^{61} +1.34878 q^{62} -10.9374 q^{63} +1.00000 q^{64} +17.1158 q^{65} +11.3455 q^{66} +0.781290 q^{67} +6.95682 q^{68} -4.31015 q^{69} +17.7836 q^{70} -4.60291 q^{71} +2.64215 q^{72} -3.36966 q^{73} +3.33633 q^{74} -31.9609 q^{75} +6.18372 q^{76} +19.7723 q^{77} +9.46361 q^{78} +1.30201 q^{79} -4.29598 q^{80} -9.94549 q^{81} +6.78627 q^{82} -1.11886 q^{83} +9.83285 q^{84} -29.8863 q^{85} +11.4679 q^{86} +22.3242 q^{87} -4.77640 q^{88} +14.7694 q^{89} -11.3506 q^{90} +16.4927 q^{91} +1.81455 q^{92} -3.20379 q^{93} -8.13733 q^{94} -26.5651 q^{95} -2.37532 q^{96} -9.10575 q^{97} +10.1362 q^{98} -12.6200 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.37532	−1.37139	−0.685696	−	0.727888i	$-0.740502\pi$
$3$	−2.37532	−1.37139	−0.685696	+	0.727888i	$0.740502\pi$
$4$	1.00000	0.500000
$5$	−4.29598	−1.92122	−0.960609	−	0.277902i	$-0.910361\pi$
$5$	−4.29598	−1.92122	−0.960609	+	0.277902i	$0.910361\pi$
$6$	−2.37532	−0.969721
$7$	−4.13959	−1.56462	−0.782308	−	0.622892i	$-0.785958\pi$
$7$	−4.13959	−1.56462	−0.782308	+	0.622892i	$0.785958\pi$
$8$	1.00000	0.353553
$9$	2.64215	0.880718
$10$	−4.29598	−1.35851
$11$	−4.77640	−1.44014	−0.720070	−	0.693902i	$-0.755890\pi$
$11$	−4.77640	−1.44014	−0.720070	+	0.693902i	$0.755890\pi$
$12$	−2.37532	−0.685696
$13$	−3.98414	−1.10500	−0.552501	−	0.833512i	$-0.686326\pi$
$13$	−3.98414	−1.10500	−0.552501	+	0.833512i	$0.686326\pi$
$14$	−4.13959	−1.10635
$15$	10.2043	2.63475
$16$	1.00000	0.250000
$17$	6.95682	1.68728	0.843639	−	0.536911i	$-0.180409\pi$
$17$	6.95682	1.68728	0.843639	+	0.536911i	$0.180409\pi$
$18$	2.64215	0.622762
$19$	6.18372	1.41864	0.709322	−	0.704885i	$-0.249001\pi$
$19$	6.18372	1.41864	0.709322	+	0.704885i	$0.249001\pi$
$20$	−4.29598	−0.960609
$21$	9.83285	2.14570
$22$	−4.77640	−1.01833
$23$	1.81455	0.378360	0.189180	−	0.981942i	$-0.439417\pi$
$23$	1.81455	0.378360	0.189180	+	0.981942i	$0.439417\pi$
$24$	−2.37532	−0.484861
$25$	13.4554	2.69108
$26$	−3.98414	−0.781354
$27$	0.850001	0.163583
$28$	−4.13959	−0.782308
$29$	−9.39839	−1.74524	−0.872618	−	0.488403i	$-0.837580\pi$
$29$	−9.39839	−1.74524	−0.872618	+	0.488403i	$0.837580\pi$
$30$	10.2043	1.86305
$31$	1.34878	0.242248	0.121124	−	0.992637i	$-0.461350\pi$
$31$	1.34878	0.242248	0.121124	+	0.992637i	$0.461350\pi$
$32$	1.00000	0.176777
$33$	11.3455	1.97500
$34$	6.95682	1.19309
$35$	17.7836	3.00597
$36$	2.64215	0.440359
$37$	3.33633	0.548490	0.274245	−	0.961660i	$-0.411572\pi$
$37$	3.33633	0.548490	0.274245	+	0.961660i	$0.411572\pi$
$38$	6.18372	1.00313
$39$	9.46361	1.51539
$40$	−4.29598	−0.679253
$41$	6.78627	1.05984	0.529919	−	0.848048i	$-0.322222\pi$
$41$	6.78627	1.05984	0.529919	+	0.848048i	$0.322222\pi$
$42$	9.83285	1.51724
$43$	11.4679	1.74884	0.874420	−	0.485170i	$-0.161242\pi$
$43$	11.4679	1.74884	0.874420	+	0.485170i	$0.161242\pi$
$44$	−4.77640	−0.720070
$45$	−11.3506	−1.69205
$46$	1.81455	0.267541
$47$	−8.13733	−1.18695	−0.593476	−	0.804852i	$-0.702245\pi$
$47$	−8.13733	−1.18695	−0.593476	+	0.804852i	$0.702245\pi$
$48$	−2.37532	−0.342848
$49$	10.1362	1.44802
$50$	13.4554	1.90288
$51$	−16.5247	−2.31392
$52$	−3.98414	−0.552501
$53$	−9.88577	−1.35791	−0.678957	−	0.734178i	$-0.737568\pi$
$53$	−9.88577	−1.35791	−0.678957	+	0.734178i	$0.737568\pi$
$54$	0.850001	0.115670
$55$	20.5193	2.76682
$56$	−4.13959	−0.553175
$57$	−14.6883	−1.94552
$58$	−9.39839	−1.23407
$59$	−4.10917	−0.534968	−0.267484	−	0.963562i	$-0.586192\pi$
$59$	−4.10917	−0.534968	−0.267484	+	0.963562i	$0.586192\pi$
$60$	10.2043	1.31737
$61$	−5.06837	−0.648938	−0.324469	−	0.945896i	$-0.605186\pi$
$61$	−5.06837	−0.648938	−0.324469	+	0.945896i	$0.605186\pi$
$62$	1.34878	0.171295
$63$	−10.9374	−1.37799
$64$	1.00000	0.125000
$65$	17.1158	2.12295
$66$	11.3455	1.39653
$67$	0.781290	0.0954498	0.0477249	−	0.998861i	$-0.484803\pi$
$67$	0.781290	0.0954498	0.0477249	+	0.998861i	$0.484803\pi$
$68$	6.95682	0.843639
$69$	−4.31015	−0.518881
$70$	17.7836	2.12554
$71$	−4.60291	−0.546265	−0.273133	−	0.961976i	$-0.588060\pi$
$71$	−4.60291	−0.546265	−0.273133	+	0.961976i	$0.588060\pi$
$72$	2.64215	0.311381
$73$	−3.36966	−0.394389	−0.197194	−	0.980364i	$-0.563183\pi$
$73$	−3.36966	−0.394389	−0.197194	+	0.980364i	$0.563183\pi$
$74$	3.33633	0.387841
$75$	−31.9609	−3.69053
$76$	6.18372	0.709322
$77$	19.7723	2.25326
$78$	9.46361	1.07154
$79$	1.30201	0.146487	0.0732437	−	0.997314i	$-0.476665\pi$
$79$	1.30201	0.146487	0.0732437	+	0.997314i	$0.476665\pi$
$80$	−4.29598	−0.480305
$81$	−9.94549	−1.10505
$82$	6.78627	0.749418
$83$	−1.11886	−0.122811	−0.0614055	−	0.998113i	$-0.519558\pi$
$83$	−1.11886	−0.122811	−0.0614055	+	0.998113i	$0.519558\pi$
$84$	9.83285	1.07285
$85$	−29.8863	−3.24163
$86$	11.4679	1.23662
$87$	22.3242	2.39340
$88$	−4.77640	−0.509166
$89$	14.7694	1.56555	0.782775	−	0.622305i	$-0.213804\pi$
$89$	14.7694	1.56555	0.782775	+	0.622305i	$0.213804\pi$
$90$	−11.3506	−1.19646
$91$	16.4927	1.72890
$92$	1.81455	0.189180
$93$	−3.20379	−0.332217
$94$	−8.13733	−0.839302
$95$	−26.5651	−2.72552
$96$	−2.37532	−0.242430
$97$	−9.10575	−0.924549	−0.462274	−	0.886737i	$-0.652966\pi$
$97$	−9.10575	−0.924549	−0.462274	+	0.886737i	$0.652966\pi$
$98$	10.1362	1.02391
$99$	−12.6200	−1.26836
$100$	13.4554	1.34554
$101$	5.98885	0.595913	0.297956	−	0.954579i	$-0.403695\pi$
$101$	5.98885	0.595913	0.297956	+	0.954579i	$0.403695\pi$
$102$	−16.5247	−1.63619
$103$	−4.90197	−0.483005	−0.241503	−	0.970400i	$-0.577640\pi$
$103$	−4.90197	−0.483005	−0.241503	+	0.970400i	$0.577640\pi$
$104$	−3.98414	−0.390677
$105$	−42.2417	−4.12237
$106$	−9.88577	−0.960191
$107$	−16.0304	−1.54972	−0.774860	−	0.632133i	$-0.782180\pi$
$107$	−16.0304	−1.54972	−0.774860	+	0.632133i	$0.782180\pi$
$108$	0.850001	0.0817913
$109$	18.9173	1.81195	0.905973	−	0.423335i	$-0.139141\pi$
$109$	18.9173	1.81195	0.905973	+	0.423335i	$0.139141\pi$
$110$	20.5193	1.95644
$111$	−7.92487	−0.752195
$112$	−4.13959	−0.391154
$113$	−6.41382	−0.603362	−0.301681	−	0.953409i	$-0.597548\pi$
$113$	−6.41382	−0.603362	−0.301681	+	0.953409i	$0.597548\pi$
$114$	−14.6883	−1.37569
$115$	−7.79528	−0.726913
$116$	−9.39839	−0.872618
$117$	−10.5267	−0.973194
$118$	−4.10917	−0.378280
$119$	−28.7984	−2.63994
$120$	10.2043	0.931523
$121$	11.8140	1.07400
$122$	−5.06837	−0.458869
$123$	−16.1196	−1.45345
$124$	1.34878	0.121124
$125$	−36.3242	−3.24894
$126$	−10.9374	−0.974383
$127$	13.4330	1.19199	0.595995	−	0.802989i	$-0.296758\pi$
$127$	13.4330	1.19199	0.595995	+	0.802989i	$0.296758\pi$
$128$	1.00000	0.0883883
$129$	−27.2400	−2.39835
$130$	17.1158	1.50115
$131$	2.88203	0.251804	0.125902	−	0.992043i	$-0.459817\pi$
$131$	2.88203	0.251804	0.125902	+	0.992043i	$0.459817\pi$
$132$	11.3455	0.987498
$133$	−25.5980	−2.21963
$134$	0.781290	0.0674932
$135$	−3.65158	−0.314278
$136$	6.95682	0.596543
$137$	8.70248	0.743503	0.371752	−	0.928332i	$-0.378757\pi$
$137$	8.70248	0.743503	0.371752	+	0.928332i	$0.378757\pi$
$138$	−4.31015	−0.366904
$139$	−9.64284	−0.817895	−0.408947	−	0.912558i	$-0.634104\pi$
$139$	−9.64284	−0.817895	−0.408947	+	0.912558i	$0.634104\pi$
$140$	17.7836	1.50299
$141$	19.3288	1.62778
$142$	−4.60291	−0.386268
$143$	19.0298	1.59136
$144$	2.64215	0.220179
$145$	40.3752	3.35298
$146$	−3.36966	−0.278875
$147$	−24.0767	−1.98581
$148$	3.33633	0.274245
$149$	−0.462774	−0.0379120	−0.0189560	−	0.999820i	$-0.506034\pi$
$149$	−0.462774	−0.0379120	−0.0189560	+	0.999820i	$0.506034\pi$
$150$	−31.9609	−2.60960
$151$	−9.33301	−0.759510	−0.379755	−	0.925087i	$-0.623992\pi$
$151$	−9.33301	−0.759510	−0.379755	+	0.925087i	$0.623992\pi$
$152$	6.18372	0.501566
$153$	18.3810	1.48602
$154$	19.7723	1.59330
$155$	−5.79433	−0.465411
$156$	9.46361	0.757695
$157$	4.61070	0.367974	0.183987	−	0.982929i	$-0.441100\pi$
$157$	4.61070	0.367974	0.183987	+	0.982929i	$0.441100\pi$
$158$	1.30201	0.103582
$159$	23.4819	1.86223
$160$	−4.29598	−0.339627
$161$	−7.51150	−0.591989
$162$	−9.94549	−0.781391
$163$	12.4158	0.972479	0.486240	−	0.873826i	$-0.338368\pi$
$163$	12.4158	0.972479	0.486240	+	0.873826i	$0.338368\pi$
$164$	6.78627	0.529919
$165$	−48.7400	−3.79440
$166$	−1.11886	−0.0868405
$167$	16.9404	1.31088	0.655442	−	0.755245i	$-0.272482\pi$
$167$	16.9404	1.31088	0.655442	+	0.755245i	$0.272482\pi$
$168$	9.83285	0.758621
$169$	2.87336	0.221028
$170$	−29.8863	−2.29218
$171$	16.3383	1.24942
$172$	11.4679	0.874420
$173$	12.5446	0.953752	0.476876	−	0.878971i	$-0.341769\pi$
$173$	12.5446	0.953752	0.476876	+	0.878971i	$0.341769\pi$
$174$	22.3242	1.69239
$175$	−55.6998	−4.21051
$176$	−4.77640	−0.360035
$177$	9.76060	0.733651
$178$	14.7694	1.10701
$179$	−12.3957	−0.926498	−0.463249	−	0.886228i	$-0.653316\pi$
$179$	−12.3957	−0.926498	−0.463249	+	0.886228i	$0.653316\pi$
$180$	−11.3506	−0.846026
$181$	15.0158	1.11612	0.558060	−	0.829801i	$-0.311546\pi$
$181$	15.0158	1.11612	0.558060	+	0.829801i	$0.311546\pi$
$182$	16.4927	1.22252
$183$	12.0390	0.889949
$184$	1.81455	0.133771
$185$	−14.3328	−1.05377
$186$	−3.20379	−0.234913
$187$	−33.2286	−2.42991
$188$	−8.13733	−0.593476
$189$	−3.51865	−0.255944
$190$	−26.5651	−1.92724
$191$	−9.55539	−0.691404	−0.345702	−	0.938344i	$-0.612359\pi$
$191$	−9.55539	−0.691404	−0.345702	+	0.938344i	$0.612359\pi$
$192$	−2.37532	−0.171424
$193$	12.3145	0.886416	0.443208	−	0.896419i	$-0.353840\pi$
$193$	12.3145	0.886416	0.443208	+	0.896419i	$0.353840\pi$
$194$	−9.10575	−0.653755
$195$	−40.6555	−2.91140
$196$	10.1362	0.724012
$197$	27.2001	1.93793	0.968965	−	0.247198i	$-0.0795097\pi$
$197$	27.2001	1.93793	0.968965	+	0.247198i	$0.0795097\pi$
$198$	−12.6200	−0.896863
$199$	−10.6742	−0.756671	−0.378335	−	0.925669i	$-0.623503\pi$
$199$	−10.6742	−0.756671	−0.378335	+	0.925669i	$0.623503\pi$
$200$	13.4554	0.951441
$201$	−1.85582	−0.130899
$202$	5.98885	0.421374
$203$	38.9054	2.73063
$204$	−16.5247	−1.15696
$205$	−29.1537	−2.03618
$206$	−4.90197	−0.341536
$207$	4.79433	0.333229
$208$	−3.98414	−0.276250
$209$	−29.5359	−2.04304
$210$	−42.2417	−2.91495
$211$	−19.4169	−1.33671	−0.668357	−	0.743841i	$-0.733002\pi$
$211$	−19.4169	−1.33671	−0.668357	+	0.743841i	$0.733002\pi$
$212$	−9.88577	−0.678957
$213$	10.9334	0.749144
$214$	−16.0304	−1.09582
$215$	−49.2659	−3.35990
$216$	0.850001	0.0578352
$217$	−5.58339	−0.379025
$218$	18.9173	1.28124
$219$	8.00402	0.540862
$220$	20.5193	1.38341
$221$	−27.7169	−1.86444
$222$	−7.92487	−0.531882
$223$	21.5021	1.43989	0.719945	−	0.694031i	$-0.244167\pi$
$223$	21.5021	1.43989	0.719945	+	0.694031i	$0.244167\pi$
$224$	−4.13959	−0.276588
$225$	35.5513	2.37008
$226$	−6.41382	−0.426641
$227$	20.3408	1.35007	0.675034	−	0.737787i	$-0.264129\pi$
$227$	20.3408	1.35007	0.675034	+	0.737787i	$0.264129\pi$
$228$	−14.6883	−0.972758
$229$	−4.61892	−0.305227	−0.152614	−	0.988286i	$-0.548769\pi$
$229$	−4.61892	−0.305227	−0.152614	+	0.988286i	$0.548769\pi$
$230$	−7.79528	−0.514005
$231$	−46.9656	−3.09011
$232$	−9.39839	−0.617034
$233$	−1.34168	−0.0878967	−0.0439483	−	0.999034i	$-0.513994\pi$
$233$	−1.34168	−0.0878967	−0.0439483	+	0.999034i	$0.513994\pi$
$234$	−10.5267	−0.688152
$235$	34.9578	2.28040
$236$	−4.10917	−0.267484
$237$	−3.09269	−0.200892
$238$	−28.7984	−1.86672
$239$	9.40757	0.608525	0.304262	−	0.952588i	$-0.401590\pi$
$239$	9.40757	0.608525	0.304262	+	0.952588i	$0.401590\pi$
$240$	10.2043	0.658686
$241$	15.5459	1.00140	0.500700	−	0.865621i	$-0.333076\pi$
$241$	15.5459	1.00140	0.500700	+	0.865621i	$0.333076\pi$
$242$	11.8140	0.759433
$243$	21.0737	1.35188
$244$	−5.06837	−0.324469
$245$	−43.5447	−2.78197
$246$	−16.1196	−1.02775
$247$	−24.6368	−1.56760
$248$	1.34878	0.0856476
$249$	2.65766	0.168422
$250$	−36.3242	−2.29735
$251$	2.31031	0.145826	0.0729129	−	0.997338i	$-0.476770\pi$
$251$	2.31031	0.145826	0.0729129	+	0.997338i	$0.476770\pi$
$252$	−10.9374	−0.688993
$253$	−8.66703	−0.544892
$254$	13.4330	0.842864
$255$	70.9897	4.44555
$256$	1.00000	0.0625000
$257$	23.4072	1.46010	0.730051	−	0.683392i	$-0.239496\pi$
$257$	23.4072	1.46010	0.730051	+	0.683392i	$0.239496\pi$
$258$	−27.2400	−1.69589
$259$	−13.8110	−0.858176
$260$	17.1158	1.06147
$261$	−24.8320	−1.53706
$262$	2.88203	0.178053
$263$	−3.60324	−0.222185	−0.111093	−	0.993810i	$-0.535435\pi$
$263$	−3.60324	−0.222185	−0.111093	+	0.993810i	$0.535435\pi$
$264$	11.3455	0.698267
$265$	42.4690	2.60885
$266$	−25.5980	−1.56952
$267$	−35.0820	−2.14698
$268$	0.781290	0.0477249
$269$	6.54235	0.398894	0.199447	−	0.979909i	$-0.436085\pi$
$269$	6.54235	0.398894	0.199447	+	0.979909i	$0.436085\pi$
$270$	−3.65158	−0.222228
$271$	20.6475	1.25425	0.627123	−	0.778920i	$-0.284232\pi$
$271$	20.6475	1.25425	0.627123	+	0.778920i	$0.284232\pi$
$272$	6.95682	0.421819
$273$	−39.1754	−2.37101
$274$	8.70248	0.525736
$275$	−64.2684	−3.87553
$276$	−4.31015	−0.259440
$277$	2.64937	0.159185	0.0795927	−	0.996827i	$-0.474638\pi$
$277$	2.64937	0.159185	0.0795927	+	0.996827i	$0.474638\pi$
$278$	−9.64284	−0.578339
$279$	3.56368	0.213352
$280$	17.7836	1.06277
$281$	−22.2785	−1.32903	−0.664513	−	0.747277i	$-0.731361\pi$
$281$	−22.2785	−1.32903	−0.664513	+	0.747277i	$0.731361\pi$
$282$	19.3288	1.15101
$283$	−28.5843	−1.69916	−0.849581	−	0.527458i	$-0.823145\pi$
$283$	−28.5843	−1.69916	−0.849581	+	0.527458i	$0.823145\pi$
$284$	−4.60291	−0.273133
$285$	63.1007	3.73776
$286$	19.0298	1.12526
$287$	−28.0923	−1.65824
$288$	2.64215	0.155690
$289$	31.3974	1.84690
$290$	40.3752	2.37092
$291$	21.6291	1.26792
$292$	−3.36966	−0.197194
$293$	15.5867	0.910586	0.455293	−	0.890342i	$-0.349535\pi$
$293$	15.5867	0.910586	0.455293	+	0.890342i	$0.349535\pi$
$294$	−24.0767	−1.40418
$295$	17.6529	1.02779
$296$	3.33633	0.193920
$297$	−4.05994	−0.235582
$298$	−0.462774	−0.0268078
$299$	−7.22943	−0.418089
$300$	−31.9609	−1.84527
$301$	−47.4724	−2.73626
$302$	−9.33301	−0.537054
$303$	−14.2254	−0.817230
$304$	6.18372	0.354661
$305$	21.7736	1.24675
$306$	18.3810	1.05077
$307$	−14.5021	−0.827679	−0.413839	−	0.910350i	$-0.635812\pi$
$307$	−14.5021	−0.827679	−0.413839	+	0.910350i	$0.635812\pi$
$308$	19.7723	1.12663
$309$	11.6438	0.662390
$310$	−5.79433	−0.329096
$311$	−27.9650	−1.58575	−0.792874	−	0.609386i	$-0.791416\pi$
$311$	−27.9650	−1.58575	−0.792874	+	0.609386i	$0.791416\pi$
$312$	9.46361	0.535772
$313$	27.9377	1.57913	0.789566	−	0.613666i	$-0.210306\pi$
$313$	27.9377	1.57913	0.789566	+	0.613666i	$0.210306\pi$
$314$	4.61070	0.260197
$315$	46.9869	2.64741
$316$	1.30201	0.0732437
$317$	−25.0265	−1.40563	−0.702815	−	0.711373i	$-0.748074\pi$
$317$	−25.0265	−1.40563	−0.702815	+	0.711373i	$0.748074\pi$
$318$	23.4819	1.31680
$319$	44.8905	2.51338
$320$	−4.29598	−0.240152
$321$	38.0774	2.12527
$322$	−7.51150	−0.418599
$323$	43.0191	2.39364
$324$	−9.94549	−0.552527
$325$	−53.6082	−2.97365
$326$	12.4158	0.687647
$327$	−44.9346	−2.48489
$328$	6.78627	0.374709
$329$	33.6852	1.85712
$330$	−48.7400	−2.68305
$331$	−13.1269	−0.721518	−0.360759	−	0.932659i	$-0.617482\pi$
$331$	−13.1269	−0.721518	−0.360759	+	0.932659i	$0.617482\pi$
$332$	−1.11886	−0.0614055
$333$	8.81511	0.483065
$334$	16.9404	0.926935
$335$	−3.35640	−0.183380
$336$	9.83285	0.536426
$337$	−8.98777	−0.489595	−0.244798	−	0.969574i	$-0.578721\pi$
$337$	−8.98777	−0.489595	−0.244798	+	0.969574i	$0.578721\pi$
$338$	2.87336	0.156290
$339$	15.2349	0.827446
$340$	−29.8863	−1.62081
$341$	−6.44231	−0.348871
$342$	16.3383	0.883476
$343$	−12.9824	−0.700986
$344$	11.4679	0.618308
$345$	18.5163	0.996883
$346$	12.5446	0.674404
$347$	11.3684	0.610286	0.305143	−	0.952307i	$-0.401296\pi$
$347$	11.3684	0.610286	0.305143	+	0.952307i	$0.401296\pi$
$348$	22.3242	1.19670
$349$	4.78531	0.256152	0.128076	−	0.991764i	$-0.459120\pi$
$349$	4.78531	0.256152	0.128076	+	0.991764i	$0.459120\pi$
$350$	−55.6998	−2.97728
$351$	−3.38652	−0.180759
$352$	−4.77640	−0.254583
$353$	9.97946	0.531153	0.265577	−	0.964090i	$-0.414438\pi$
$353$	9.97946	0.531153	0.265577	+	0.964090i	$0.414438\pi$
$354$	9.76060	0.518770
$355$	19.7740	1.04949
$356$	14.7694	0.782775
$357$	68.4054	3.62040
$358$	−12.3957	−0.655133
$359$	3.10338	0.163790	0.0818950	−	0.996641i	$-0.473903\pi$
$359$	3.10338	0.163790	0.0818950	+	0.996641i	$0.473903\pi$
$360$	−11.3506	−0.598231
$361$	19.2384	1.01255
$362$	15.0158	0.789215
$363$	−28.0621	−1.47288
$364$	16.4927	0.864452
$365$	14.4760	0.757707
$366$	12.0390	0.629289
$367$	−23.1661	−1.20926	−0.604631	−	0.796506i	$-0.706680\pi$
$367$	−23.1661	−1.20926	−0.604631	+	0.796506i	$0.706680\pi$
$368$	1.81455	0.0945901
$369$	17.9304	0.933418
$370$	−14.3328	−0.745127
$371$	40.9230	2.12462
$372$	−3.20379	−0.166109
$373$	−13.4004	−0.693844	−0.346922	−	0.937894i	$-0.612773\pi$
$373$	−13.4004	−0.693844	−0.346922	+	0.937894i	$0.612773\pi$
$374$	−33.2286	−1.71821
$375$	86.2818	4.45557
$376$	−8.13733	−0.419651
$377$	37.4445	1.92849
$378$	−3.51865	−0.180980
$379$	−13.4284	−0.689773	−0.344886	−	0.938644i	$-0.612083\pi$
$379$	−13.4284	−0.689773	−0.344886	+	0.938644i	$0.612083\pi$
$380$	−26.5651	−1.36276
$381$	−31.9078	−1.63468
$382$	−9.55539	−0.488897
$383$	7.22497	0.369179	0.184589	−	0.982816i	$-0.440904\pi$
$383$	7.22497	0.369179	0.184589	+	0.982816i	$0.440904\pi$
$384$	−2.37532	−0.121215
$385$	−84.9414	−4.32902
$386$	12.3145	0.626791
$387$	30.3000	1.54023
$388$	−9.10575	−0.462274
$389$	−20.3368	−1.03112	−0.515558	−	0.856855i	$-0.672415\pi$
$389$	−20.3368	−1.03112	−0.515558	+	0.856855i	$0.672415\pi$
$390$	−40.6555	−2.05867
$391$	12.6235	0.638399
$392$	10.1362	0.511954
$393$	−6.84576	−0.345323
$394$	27.2001	1.37032
$395$	−5.59339	−0.281434
$396$	−12.6200	−0.634178
$397$	−19.7742	−0.992441	−0.496220	−	0.868197i	$-0.665279\pi$
$397$	−19.7742	−0.992441	−0.496220	+	0.868197i	$0.665279\pi$
$398$	−10.6742	−0.535047
$399$	60.8036	3.04399
$400$	13.4554	0.672771
$401$	11.2480	0.561698	0.280849	−	0.959752i	$-0.409384\pi$
$401$	11.2480	0.561698	0.280849	+	0.959752i	$0.409384\pi$
$402$	−1.85582	−0.0925597
$403$	−5.37373	−0.267684
$404$	5.98885	0.297956
$405$	42.7256	2.12305
$406$	38.9054	1.93084
$407$	−15.9357	−0.789902
$408$	−16.5247	−0.818094
$409$	29.8879	1.47786	0.738931	−	0.673781i	$-0.235331\pi$
$409$	29.8879	1.47786	0.738931	+	0.673781i	$0.235331\pi$
$410$	−29.1537	−1.43980
$411$	−20.6712	−1.01963
$412$	−4.90197	−0.241503
$413$	17.0103	0.837020
$414$	4.79433	0.235628
$415$	4.80660	0.235947
$416$	−3.98414	−0.195338
$417$	22.9048	1.12165
$418$	−29.5359	−1.44465
$419$	−17.5989	−0.859761	−0.429881	−	0.902886i	$-0.641444\pi$
$419$	−17.5989	−0.859761	−0.429881	+	0.902886i	$0.641444\pi$
$420$	−42.2417	−2.06118
$421$	−17.3497	−0.845572	−0.422786	−	0.906230i	$-0.638948\pi$
$421$	−17.3497	−0.845572	−0.422786	+	0.906230i	$0.638948\pi$
$422$	−19.4169	−0.945200
$423$	−21.5001	−1.04537
$424$	−9.88577	−0.480095
$425$	93.6069	4.54060
$426$	10.9334	0.529725
$427$	20.9810	1.01534
$428$	−16.0304	−0.774860
$429$	−45.2020	−2.18237
$430$	−49.2659	−2.37581
$431$	17.0949	0.823430	0.411715	−	0.911313i	$-0.364930\pi$
$431$	17.0949	0.823430	0.411715	+	0.911313i	$0.364930\pi$
$432$	0.850001	0.0408957
$433$	27.8055	1.33625	0.668124	−	0.744050i	$-0.267098\pi$
$433$	27.8055	1.33625	0.668124	+	0.744050i	$0.267098\pi$
$434$	−5.58339	−0.268011
$435$	−95.9042	−4.59825
$436$	18.9173	0.905973
$437$	11.2207	0.536758
$438$	8.00402	0.382447
$439$	−13.5981	−0.649004	−0.324502	−	0.945885i	$-0.605197\pi$
$439$	−13.5981	−0.649004	−0.324502	+	0.945885i	$0.605197\pi$
$440$	20.5193	0.978219
$441$	26.7813	1.27530
$442$	−27.7169	−1.31836
$443$	−22.7488	−1.08083	−0.540415	−	0.841399i	$-0.681733\pi$
$443$	−22.7488	−1.08083	−0.540415	+	0.841399i	$0.681733\pi$
$444$	−7.92487	−0.376098
$445$	−63.4488	−3.00776
$446$	21.5021	1.01816
$447$	1.09924	0.0519922
$448$	−4.13959	−0.195577
$449$	6.05669	0.285833	0.142916	−	0.989735i	$-0.454352\pi$
$449$	6.05669	0.285833	0.142916	+	0.989735i	$0.454352\pi$
$450$	35.5513	1.67590
$451$	−32.4139	−1.52631
$452$	−6.41382	−0.301681
$453$	22.1689	1.04159
$454$	20.3408	0.954642
$455$	−70.8522	−3.32160
$456$	−14.6883	−0.687844
$457$	−22.9951	−1.07567	−0.537833	−	0.843051i	$-0.680757\pi$
$457$	−22.9951	−1.07567	−0.537833	+	0.843051i	$0.680757\pi$
$458$	−4.61892	−0.215828
$459$	5.91330	0.276009
$460$	−7.79528	−0.363457
$461$	−12.8118	−0.596704	−0.298352	−	0.954456i	$-0.596437\pi$
$461$	−12.8118	−0.596704	−0.298352	+	0.954456i	$0.596437\pi$
$462$	−46.9656	−2.18504
$463$	−34.2067	−1.58972	−0.794860	−	0.606793i	$-0.792456\pi$
$463$	−34.2067	−1.58972	−0.794860	+	0.606793i	$0.792456\pi$
$464$	−9.39839	−0.436309
$465$	13.7634	0.638262
$466$	−1.34168	−0.0621523
$467$	2.71143	0.125470	0.0627350	−	0.998030i	$-0.480018\pi$
$467$	2.71143	0.125470	0.0627350	+	0.998030i	$0.480018\pi$
$468$	−10.5267	−0.486597
$469$	−3.23422	−0.149342
$470$	34.9578	1.61248
$471$	−10.9519	−0.504637
$472$	−4.10917	−0.189140
$473$	−54.7753	−2.51857
$474$	−3.09269	−0.142052
$475$	83.2045	3.81769
$476$	−28.7984	−1.31997
$477$	−26.1197	−1.19594
$478$	9.40757	0.430292
$479$	−10.3446	−0.472656	−0.236328	−	0.971673i	$-0.575944\pi$
$479$	−10.3446	−0.472656	−0.236328	+	0.971673i	$0.575944\pi$
$480$	10.2043	0.465762
$481$	−13.2924	−0.606082
$482$	15.5459	0.708097
$483$	17.8422	0.811849
$484$	11.8140	0.537000
$485$	39.1181	1.77626
$486$	21.0737	0.955924
$487$	−18.3140	−0.829886	−0.414943	−	0.909847i	$-0.636198\pi$
$487$	−18.3140	−0.829886	−0.414943	+	0.909847i	$0.636198\pi$
$488$	−5.06837	−0.229434
$489$	−29.4915	−1.33365
$490$	−43.5447	−1.96715
$491$	−24.3370	−1.09831	−0.549156	−	0.835720i	$-0.685051\pi$
$491$	−24.3370	−1.09831	−0.549156	+	0.835720i	$0.685051\pi$
$492$	−16.1196	−0.726727
$493$	−65.3829	−2.94470
$494$	−24.6368	−1.10846
$495$	54.2152	2.43679
$496$	1.34878	0.0605620
$497$	19.0541	0.854695
$498$	2.65766	0.119092
$499$	22.0160	0.985572	0.492786	−	0.870151i	$-0.335979\pi$
$499$	22.0160	0.985572	0.492786	+	0.870151i	$0.335979\pi$
$500$	−36.3242	−1.62447
$501$	−40.2388	−1.79774
$502$	2.31031	0.103114
$503$	−31.7541	−1.41584	−0.707922	−	0.706290i	$-0.750367\pi$
$503$	−31.7541	−1.41584	−0.707922	+	0.706290i	$0.750367\pi$
$504$	−10.9374	−0.487191
$505$	−25.7280	−1.14488
$506$	−8.66703	−0.385297
$507$	−6.82517	−0.303116
$508$	13.4330	0.595995
$509$	12.7192	0.563769	0.281884	−	0.959448i	$-0.409041\pi$
$509$	12.7192	0.563769	0.281884	+	0.959448i	$0.409041\pi$
$510$	70.9897	3.14348
$511$	13.9490	0.617067
$512$	1.00000	0.0441942
$513$	5.25617	0.232065
$514$	23.4072	1.03245
$515$	21.0587	0.927959
$516$	−27.2400	−1.19917
$517$	38.8672	1.70938
$518$	−13.8110	−0.606822
$519$	−29.7976	−1.30797
$520$	17.1158	0.750576
$521$	−0.106214	−0.00465331	−0.00232665	−	0.999997i	$-0.500741\pi$
$521$	−0.106214	−0.00465331	−0.00232665	+	0.999997i	$0.500741\pi$
$522$	−24.8320	−1.08687
$523$	17.5353	0.766766	0.383383	−	0.923589i	$-0.374759\pi$
$523$	17.5353	0.766766	0.383383	+	0.923589i	$0.374759\pi$
$524$	2.88203	0.125902
$525$	132.305	5.77426
$526$	−3.60324	−0.157109
$527$	9.38322	0.408740
$528$	11.3455	0.493749
$529$	−19.7074	−0.856843
$530$	42.4690	1.84474
$531$	−10.8571	−0.471156
$532$	−25.5980	−1.10982
$533$	−27.0374	−1.17112
$534$	−35.0820	−1.51815
$535$	68.8663	2.97735
$536$	0.781290	0.0337466
$537$	29.4438	1.27059
$538$	6.54235	0.282061
$539$	−48.4144	−2.08536
$540$	−3.65158	−0.157139
$541$	−29.3425	−1.26153	−0.630766	−	0.775973i	$-0.717259\pi$
$541$	−29.3425	−1.26153	−0.630766	+	0.775973i	$0.717259\pi$
$542$	20.6475	0.886886
$543$	−35.6675	−1.53064
$544$	6.95682	0.298271
$545$	−81.2682	−3.48115
$546$	−39.1754	−1.67655
$547$	−11.7519	−0.502474	−0.251237	−	0.967926i	$-0.580837\pi$
$547$	−11.7519	−0.502474	−0.251237	+	0.967926i	$0.580837\pi$
$548$	8.70248	0.371752
$549$	−13.3914	−0.571532
$550$	−64.2684	−2.74042
$551$	−58.1170	−2.47587
$552$	−4.31015	−0.183452
$553$	−5.38977	−0.229196
$554$	2.64937	0.112561
$555$	34.0450	1.44513
$556$	−9.64284	−0.408947
$557$	−44.8804	−1.90164	−0.950821	−	0.309740i	$-0.899758\pi$
$557$	−44.8804	−1.90164	−0.950821	+	0.309740i	$0.899758\pi$
$558$	3.56368	0.150863
$559$	−45.6898	−1.93247
$560$	17.7836	0.751493
$561$	78.9286	3.33237
$562$	−22.2785	−0.939763
$563$	14.6056	0.615551	0.307776	−	0.951459i	$-0.400415\pi$
$563$	14.6056	0.615551	0.307776	+	0.951459i	$0.400415\pi$
$564$	19.3288	0.813889
$565$	27.5536	1.15919
$566$	−28.5843	−1.20149
$567$	41.1702	1.72899
$568$	−4.60291	−0.193134
$569$	−21.1512	−0.886703	−0.443351	−	0.896348i	$-0.646211\pi$
$569$	−21.1512	−0.886703	−0.443351	+	0.896348i	$0.646211\pi$
$570$	63.1007	2.64300
$571$	23.4200	0.980098	0.490049	−	0.871695i	$-0.336979\pi$
$571$	23.4200	0.980098	0.490049	+	0.871695i	$0.336979\pi$
$572$	19.0298	0.795678
$573$	22.6971	0.948186
$574$	−28.0923	−1.17255
$575$	24.4156	1.01820
$576$	2.64215	0.110090
$577$	−0.503005	−0.0209404	−0.0104702	−	0.999945i	$-0.503333\pi$
$577$	−0.503005	−0.0209404	−0.0104702	+	0.999945i	$0.503333\pi$
$578$	31.3974	1.30596
$579$	−29.2509	−1.21562
$580$	40.3752	1.67649
$581$	4.63162	0.192152
$582$	21.6291	0.896554
$583$	47.2184	1.95559
$584$	−3.36966	−0.139437
$585$	45.2225	1.86972
$586$	15.5867	0.643882
$587$	−14.9494	−0.617027	−0.308513	−	0.951220i	$-0.599831\pi$
$587$	−14.9494	−0.617027	−0.308513	+	0.951220i	$0.599831\pi$
$588$	−24.0767	−0.992905
$589$	8.34048	0.343663
$590$	17.6529	0.726758
$591$	−64.6091	−2.65766
$592$	3.33633	0.137122
$593$	−18.3485	−0.753481	−0.376740	−	0.926319i	$-0.622955\pi$
$593$	−18.3485	−0.753481	−0.376740	+	0.926319i	$0.622955\pi$
$594$	−4.05994	−0.166581
$595$	123.717	5.07191
$596$	−0.462774	−0.0189560
$597$	25.3545	1.03769
$598$	−7.22943	−0.295633
$599$	36.8449	1.50544	0.752720	−	0.658341i	$-0.228741\pi$
$599$	36.8449	1.50544	0.752720	+	0.658341i	$0.228741\pi$
$600$	−31.9609	−1.30480
$601$	−38.2871	−1.56176	−0.780882	−	0.624678i	$-0.785230\pi$
$601$	−38.2871	−1.56176	−0.780882	+	0.624678i	$0.785230\pi$
$602$	−47.4724	−1.93483
$603$	2.06429	0.0840643
$604$	−9.33301	−0.379755
$605$	−50.7527	−2.06339
$606$	−14.2254	−0.577869
$607$	−26.0911	−1.05901	−0.529503	−	0.848308i	$-0.677622\pi$
$607$	−26.0911	−1.05901	−0.529503	+	0.848308i	$0.677622\pi$
$608$	6.18372	0.250783
$609$	−92.4129	−3.74476
$610$	21.7736	0.881587
$611$	32.4203	1.31158
$612$	18.3810	0.743008
$613$	−17.5050	−0.707020	−0.353510	−	0.935431i	$-0.615012\pi$
$613$	−17.5050	−0.707020	−0.353510	+	0.935431i	$0.615012\pi$
$614$	−14.5021	−0.585257
$615$	69.2493	2.79240
$616$	19.7723	0.796649
$617$	24.4092	0.982676	0.491338	−	0.870969i	$-0.336508\pi$
$617$	24.4092	0.982676	0.491338	+	0.870969i	$0.336508\pi$
$618$	11.6438	0.468381
$619$	−13.6797	−0.549833	−0.274916	−	0.961468i	$-0.588650\pi$
$619$	−13.6797	−0.549833	−0.274916	+	0.961468i	$0.588650\pi$
$620$	−5.79433	−0.232706
$621$	1.54237	0.0618932
$622$	−27.9650	−1.12129
$623$	−61.1390	−2.44948
$624$	9.46361	0.378848
$625$	88.7710	3.55084
$626$	27.9377	1.11661
$627$	70.1573	2.80181
$628$	4.61070	0.183987
$629$	23.2103	0.925455
$630$	46.9869	1.87200
$631$	−15.9167	−0.633635	−0.316817	−	0.948487i	$-0.602614\pi$
$631$	−15.9167	−0.633635	−0.316817	+	0.948487i	$0.602614\pi$
$632$	1.30201	0.0517911
$633$	46.1214	1.83316
$634$	−25.0265	−0.993930
$635$	−57.7080	−2.29007
$636$	23.4819	0.931117
$637$	−40.3839	−1.60007
$638$	44.8905	1.77723
$639$	−12.1616	−0.481105
$640$	−4.29598	−0.169813
$641$	−48.6484	−1.92149	−0.960747	−	0.277426i	$-0.910519\pi$
$641$	−48.6484	−1.92149	−0.960747	+	0.277426i	$0.910519\pi$
$642$	38.0774	1.50280
$643$	16.0558	0.633180	0.316590	−	0.948563i	$-0.397462\pi$
$643$	16.0558	0.633180	0.316590	+	0.948563i	$0.397462\pi$
$644$	−7.51150	−0.295994
$645$	117.022	4.60775
$646$	43.0191	1.69256
$647$	9.06451	0.356363	0.178181	−	0.983998i	$-0.442979\pi$
$647$	9.06451	0.356363	0.178181	+	0.983998i	$0.442979\pi$
$648$	−9.94549	−0.390696
$649$	19.6270	0.770428
$650$	−53.6082	−2.10269
$651$	13.2623	0.519792
$652$	12.4158	0.486240
$653$	−25.5304	−0.999081	−0.499540	−	0.866291i	$-0.666498\pi$
$653$	−25.5304	−0.999081	−0.499540	+	0.866291i	$0.666498\pi$
$654$	−44.9346	−1.75708
$655$	−12.3812	−0.483772
$656$	6.78627	0.264959
$657$	−8.90316	−0.347345
$658$	33.6852	1.31319
$659$	−9.33289	−0.363558	−0.181779	−	0.983339i	$-0.558186\pi$
$659$	−9.33289	−0.363558	−0.181779	+	0.983339i	$0.558186\pi$
$660$	−48.7400	−1.89720
$661$	−5.50675	−0.214188	−0.107094	−	0.994249i	$-0.534155\pi$
$661$	−5.50675	−0.214188	−0.107094	+	0.994249i	$0.534155\pi$
$662$	−13.1269	−0.510191
$663$	65.8367	2.55688
$664$	−1.11886	−0.0434203
$665$	109.969	4.26440
$666$	8.81511	0.341578
$667$	−17.0539	−0.660328
$668$	16.9404	0.655442
$669$	−51.0745	−1.97465
$670$	−3.35640	−0.129669
$671$	24.2086	0.934561
$672$	9.83285	0.379310
$673$	31.5208	1.21504	0.607519	−	0.794305i	$-0.292165\pi$
$673$	31.5208	1.21504	0.607519	+	0.794305i	$0.292165\pi$
$674$	−8.98777	−0.346196
$675$	11.4371	0.440214
$676$	2.87336	0.110514
$677$	10.8491	0.416963	0.208482	−	0.978026i	$-0.433148\pi$
$677$	10.8491	0.416963	0.208482	+	0.978026i	$0.433148\pi$
$678$	15.2349	0.585093
$679$	37.6940	1.44656
$680$	−29.8863	−1.14609
$681$	−48.3160	−1.85147
$682$	−6.44231	−0.246689
$683$	−46.0040	−1.76030	−0.880148	−	0.474700i	$-0.842557\pi$
$683$	−46.0040	−1.76030	−0.880148	+	0.474700i	$0.842557\pi$
$684$	16.3383	0.624712
$685$	−37.3857	−1.42843
$686$	−12.9824	−0.495672
$687$	10.9714	0.418586
$688$	11.4679	0.437210
$689$	39.3863	1.50050
$690$	18.5163	0.704903
$691$	40.3434	1.53473	0.767367	−	0.641208i	$-0.221567\pi$
$691$	40.3434	1.53473	0.767367	+	0.641208i	$0.221567\pi$
$692$	12.5446	0.476876
$693$	52.2415	1.98449
$694$	11.3684	0.431537
$695$	41.4254	1.57135
$696$	22.3242	0.846196
$697$	47.2109	1.78824
$698$	4.78531	0.181127
$699$	3.18693	0.120541
$700$	−55.6998	−2.10526
$701$	−42.1697	−1.59273	−0.796363	−	0.604818i	$-0.793246\pi$
$701$	−42.1697	−1.59273	−0.796363	+	0.604818i	$0.793246\pi$
$702$	−3.38652	−0.127816
$703$	20.6310	0.778111
$704$	−4.77640	−0.180017
$705$	−83.0360	−3.12732
$706$	9.97946	0.375582
$707$	−24.7914	−0.932375
$708$	9.76060	0.366826
$709$	21.2082	0.796490	0.398245	−	0.917279i	$-0.369619\pi$
$709$	21.2082	0.796490	0.398245	+	0.917279i	$0.369619\pi$
$710$	19.7740	0.742105
$711$	3.44010	0.129014
$712$	14.7694	0.553505
$713$	2.44743	0.0916571
$714$	68.4054	2.56001
$715$	−81.7518	−3.05734
$716$	−12.3957	−0.463249
$717$	−22.3460	−0.834527
$718$	3.10338	0.115817
$719$	39.7170	1.48120	0.740598	−	0.671949i	$-0.234543\pi$
$719$	39.7170	1.48120	0.740598	+	0.671949i	$0.234543\pi$
$720$	−11.3506	−0.423013
$721$	20.2921	0.755718
$722$	19.2384	0.715980
$723$	−36.9265	−1.37331
$724$	15.0158	0.558060
$725$	−126.459	−4.69658
$726$	−28.0621	−1.04148
$727$	1.66280	0.0616700	0.0308350	−	0.999524i	$-0.490183\pi$
$727$	1.66280	0.0616700	0.0308350	+	0.999524i	$0.490183\pi$
$728$	16.4927	0.611260
$729$	−20.2204	−0.748905
$730$	14.4760	0.535780
$731$	79.7802	2.95078
$732$	12.0390	0.444975
$733$	−4.12031	−0.152187	−0.0760936	−	0.997101i	$-0.524245\pi$
$733$	−4.12031	−0.152187	−0.0760936	+	0.997101i	$0.524245\pi$
$734$	−23.1661	−0.855078
$735$	103.433	3.81517
$736$	1.81455	0.0668853
$737$	−3.73176	−0.137461
$738$	17.9304	0.660026
$739$	−44.8290	−1.64906	−0.824531	−	0.565817i	$-0.808561\pi$
$739$	−44.8290	−1.64906	−0.824531	+	0.565817i	$0.808561\pi$
$740$	−14.3328	−0.526885
$741$	58.5203	2.14980
$742$	40.9230	1.50233
$743$	3.00801	0.110353	0.0551766	−	0.998477i	$-0.482428\pi$
$743$	3.00801	0.110353	0.0551766	+	0.998477i	$0.482428\pi$
$744$	−3.20379	−0.117457
$745$	1.98807	0.0728372
$746$	−13.4004	−0.490622
$747$	−2.95621	−0.108162
$748$	−33.2286	−1.21496
$749$	66.3593	2.42472
$750$	86.2818	3.15056
$751$	−6.29529	−0.229718	−0.114859	−	0.993382i	$-0.536642\pi$
$751$	−6.29529	−0.229718	−0.114859	+	0.993382i	$0.536642\pi$
$752$	−8.13733	−0.296738
$753$	−5.48774	−0.199984
$754$	37.4445	1.36365
$755$	40.0944	1.45918
$756$	−3.51865	−0.127972
$757$	29.3048	1.06510	0.532550	−	0.846399i	$-0.321234\pi$
$757$	29.3048	1.06510	0.532550	+	0.846399i	$0.321234\pi$
$758$	−13.4284	−0.487743
$759$	20.5870	0.747260
$760$	−26.5651	−0.963618
$761$	−21.1530	−0.766795	−0.383398	−	0.923583i	$-0.625246\pi$
$761$	−21.1530	−0.766795	−0.383398	+	0.923583i	$0.625246\pi$
$762$	−31.9078	−1.15590
$763$	−78.3097	−2.83500
$764$	−9.55539	−0.345702
$765$	−78.9643	−2.85496
$766$	7.22497	0.261049
$767$	16.3715	0.591140
$768$	−2.37532	−0.0857120
$769$	−25.1664	−0.907525	−0.453762	−	0.891123i	$-0.649919\pi$
$769$	−25.1664	−0.907525	−0.453762	+	0.891123i	$0.649919\pi$
$770$	−84.9414	−3.06108
$771$	−55.5997	−2.00237
$772$	12.3145	0.443208
$773$	54.2582	1.95153	0.975766	−	0.218817i	$-0.0702198\pi$
$773$	54.2582	1.95153	0.975766	+	0.218817i	$0.0702198\pi$
$774$	30.3000	1.08911
$775$	18.1484	0.651909
$776$	−9.10575	−0.326877
$777$	32.8057	1.17690
$778$	−20.3368	−0.729109
$779$	41.9644	1.50353
$780$	−40.6555	−1.45570
$781$	21.9854	0.786698
$782$	12.6235	0.451416
$783$	−7.98863	−0.285490
$784$	10.1362	0.362006
$785$	−19.8075	−0.706959
$786$	−6.84576	−0.244180
$787$	−13.5948	−0.484602	−0.242301	−	0.970201i	$-0.577902\pi$
$787$	−13.5948	−0.484602	−0.242301	+	0.970201i	$0.577902\pi$
$788$	27.2001	0.968965
$789$	8.55886	0.304704
$790$	−5.59339	−0.199004
$791$	26.5506	0.944030
$792$	−12.6200	−0.448432
$793$	20.1931	0.717078
$794$	−19.7742	−0.701762
$795$	−100.878	−3.57776
$796$	−10.6742	−0.378335
$797$	22.1333	0.784002	0.392001	−	0.919965i	$-0.371783\pi$
$797$	22.1333	0.784002	0.392001	+	0.919965i	$0.371783\pi$
$798$	60.8036	2.15242
$799$	−56.6100	−2.00272
$800$	13.4554	0.475721
$801$	39.0229	1.37881
$802$	11.2480	0.397181
$803$	16.0948	0.567975
$804$	−1.85582	−0.0654496
$805$	32.2692	1.13734
$806$	−5.37373	−0.189281
$807$	−15.5402	−0.547040
$808$	5.98885	0.210687
$809$	6.33017	0.222557	0.111279	−	0.993789i	$-0.464505\pi$
$809$	6.33017	0.222557	0.111279	+	0.993789i	$0.464505\pi$
$810$	42.7256	1.50122
$811$	−3.90667	−0.137182	−0.0685909	−	0.997645i	$-0.521850\pi$
$811$	−3.90667	−0.137182	−0.0685909	+	0.997645i	$0.521850\pi$
$812$	38.9054	1.36531
$813$	−49.0445	−1.72006
$814$	−15.9357	−0.558545
$815$	−53.3379	−1.86835
$816$	−16.5247	−0.578480
$817$	70.9144	2.48098
$818$	29.8879	1.04501
$819$	43.5762	1.52268
$820$	−29.1537	−1.01809
$821$	−0.814360	−0.0284214	−0.0142107	−	0.999899i	$-0.504524\pi$
$821$	−0.814360	−0.0284214	−0.0142107	+	0.999899i	$0.504524\pi$
$822$	−20.6712	−0.720991
$823$	−7.07179	−0.246507	−0.123253	−	0.992375i	$-0.539333\pi$
$823$	−7.07179	−0.246507	−0.123253	+	0.992375i	$0.539333\pi$
$824$	−4.90197	−0.170768
$825$	152.658	5.31488
$826$	17.0103	0.591862
$827$	24.0992	0.838012	0.419006	−	0.907983i	$-0.362379\pi$
$827$	24.0992	0.838012	0.419006	+	0.907983i	$0.362379\pi$
$828$	4.79433	0.166614
$829$	43.0419	1.49491	0.747453	−	0.664314i	$-0.231276\pi$
$829$	43.0419	1.49491	0.747453	+	0.664314i	$0.231276\pi$
$830$	4.80660	0.166840
$831$	−6.29311	−0.218306
$832$	−3.98414	−0.138125
$833$	70.5155	2.44322
$834$	22.9048	0.793130
$835$	−72.7754	−2.51850
$836$	−29.5359	−1.02152
$837$	1.14646	0.0396276
$838$	−17.5989	−0.607943
$839$	−11.6372	−0.401760	−0.200880	−	0.979616i	$-0.564380\pi$
$839$	−11.6372	−0.401760	−0.200880	+	0.979616i	$0.564380\pi$
$840$	−42.2417	−1.45748
$841$	59.3297	2.04585
$842$	−17.3497	−0.597910
$843$	52.9187	1.82262
$844$	−19.4169	−0.668357
$845$	−12.3439	−0.424643
$846$	−21.5001	−0.739188
$847$	−48.9051	−1.68040
$848$	−9.88577	−0.339479
$849$	67.8970	2.33022
$850$	93.6069	3.21069
$851$	6.05395	0.207527
$852$	10.9334	0.374572
$853$	48.4145	1.65768	0.828841	−	0.559484i	$-0.189001\pi$
$853$	48.4145	1.65768	0.828841	+	0.559484i	$0.189001\pi$
$854$	20.9810	0.717953
$855$	−70.1891	−2.40042
$856$	−16.0304	−0.547909
$857$	−15.7300	−0.537328	−0.268664	−	0.963234i	$-0.586582\pi$
$857$	−15.7300	−0.537328	−0.268664	+	0.963234i	$0.586582\pi$
$858$	−45.2020	−1.54317
$859$	0.182180	0.00621589	0.00310795	−	0.999995i	$-0.499011\pi$
$859$	0.182180	0.00621589	0.00310795	+	0.999995i	$0.499011\pi$
$860$	−49.2659	−1.67995
$861$	66.7284	2.27410
$862$	17.0949	0.582253
$863$	−51.6006	−1.75650	−0.878252	−	0.478198i	$-0.841290\pi$
$863$	−51.6006	−1.75650	−0.878252	+	0.478198i	$0.841290\pi$
$864$	0.850001	0.0289176
$865$	−53.8915	−1.83237
$866$	27.8055	0.944869
$867$	−74.5789	−2.53283
$868$	−5.58339	−0.189513
$869$	−6.21891	−0.210962
$870$	−95.9042	−3.25146
$871$	−3.11277	−0.105472
$872$	18.9173	0.640620
$873$	−24.0588	−0.814267
$874$	11.2207	0.379545
$875$	150.367	5.08334
$876$	8.00402	0.270431
$877$	20.0808	0.678079	0.339040	−	0.940772i	$-0.389898\pi$
$877$	20.0808	0.678079	0.339040	+	0.940772i	$0.389898\pi$
$878$	−13.5981	−0.458915
$879$	−37.0235	−1.24877
$880$	20.5193	0.691706
$881$	−30.6252	−1.03179	−0.515894	−	0.856652i	$-0.672540\pi$
$881$	−30.6252	−1.03179	−0.515894	+	0.856652i	$0.672540\pi$
$882$	26.7813	0.901774
$883$	20.2189	0.680421	0.340210	−	0.940349i	$-0.389502\pi$
$883$	20.2189	0.680421	0.340210	+	0.940349i	$0.389502\pi$
$884$	−27.7169	−0.932222
$885$	−41.9313	−1.40950
$886$	−22.7488	−0.764262
$887$	9.25590	0.310783	0.155391	−	0.987853i	$-0.450336\pi$
$887$	9.25590	0.310783	0.155391	+	0.987853i	$0.450336\pi$
$888$	−7.92487	−0.265941
$889$	−55.6072	−1.86501
$890$	−63.4488	−2.12681
$891$	47.5036	1.59143
$892$	21.5021	0.719945
$893$	−50.3190	−1.68386
$894$	1.09924	0.0367640
$895$	53.2516	1.78000
$896$	−4.13959	−0.138294
$897$	17.1722	0.573364
$898$	6.05669	0.202114
$899$	−12.6764	−0.422780
$900$	35.5513	1.18504
$901$	−68.7735	−2.29118
$902$	−32.4139	−1.07927
$903$	112.762	3.75249
$904$	−6.41382	−0.213321
$905$	−64.5077	−2.14431
$906$	22.1689	0.736512
$907$	−13.5049	−0.448421	−0.224211	−	0.974541i	$-0.571980\pi$
$907$	−13.5049	−0.448421	−0.224211	+	0.974541i	$0.571980\pi$
$908$	20.3408	0.675034
$909$	15.8235	0.524831
$910$	−70.8522	−2.34873
$911$	7.09476	0.235060	0.117530	−	0.993069i	$-0.462502\pi$
$911$	7.09476	0.235060	0.117530	+	0.993069i	$0.462502\pi$
$912$	−14.6883	−0.486379
$913$	5.34413	0.176865
$914$	−22.9951	−0.760611
$915$	−51.7193	−1.70979
$916$	−4.61892	−0.152614
$917$	−11.9304	−0.393977
$918$	5.91330	0.195168
$919$	−46.2906	−1.52699	−0.763493	−	0.645816i	$-0.776517\pi$
$919$	−46.2906	−1.52699	−0.763493	+	0.645816i	$0.776517\pi$
$920$	−7.79528	−0.257003
$921$	34.4472	1.13507
$922$	−12.8118	−0.421934
$923$	18.3386	0.603624
$924$	−46.9656	−1.54506
$925$	44.8917	1.47603
$926$	−34.2067	−1.12410
$927$	−12.9518	−0.425392
$928$	−9.39839	−0.308517
$929$	−19.4114	−0.636869	−0.318434	−	0.947945i	$-0.603157\pi$
$929$	−19.4114	−0.636869	−0.318434	+	0.947945i	$0.603157\pi$
$930$	13.7634	0.451319
$931$	62.6792	2.05423
$932$	−1.34168	−0.0439483
$933$	66.4258	2.17468
$934$	2.71143	0.0887207
$935$	142.749	4.66840
$936$	−10.5267	−0.344076
$937$	−46.6867	−1.52519	−0.762595	−	0.646876i	$-0.776075\pi$
$937$	−46.6867	−1.52519	−0.762595	+	0.646876i	$0.776075\pi$
$938$	−3.23422	−0.105601
$939$	−66.3610	−2.16561
$940$	34.9578	1.14020
$941$	21.5896	0.703800	0.351900	−	0.936038i	$-0.385536\pi$
$941$	21.5896	0.703800	0.351900	+	0.936038i	$0.385536\pi$
$942$	−10.9519	−0.356832
$943$	12.3140	0.401000
$944$	−4.10917	−0.133742
$945$	15.1160	0.491725
$946$	−54.7753	−1.78090
$947$	−6.25457	−0.203246	−0.101623	−	0.994823i	$-0.532404\pi$
$947$	−6.25457	−0.203246	−0.101623	+	0.994823i	$0.532404\pi$
$948$	−3.09269	−0.100446
$949$	13.4252	0.435800
$950$	83.2045	2.69951
$951$	59.4460	1.92767
$952$	−28.7984	−0.933360
$953$	35.9635	1.16497	0.582486	−	0.812841i	$-0.302080\pi$
$953$	35.9635	1.16497	0.582486	+	0.812841i	$0.302080\pi$
$954$	−26.1197	−0.845657
$955$	41.0497	1.32834
$956$	9.40757	0.304262
$957$	−106.629	−3.44684
$958$	−10.3446	−0.334218
$959$	−36.0247	−1.16330
$960$	10.2043	0.329343
$961$	−29.1808	−0.941316
$962$	−13.2924	−0.428565
$963$	−42.3548	−1.36487
$964$	15.5459	0.500700
$965$	−52.9027	−1.70300
$966$	17.8422	0.574064
$967$	18.4969	0.594821	0.297411	−	0.954750i	$-0.403877\pi$
$967$	18.4969	0.594821	0.297411	+	0.954750i	$0.403877\pi$
$968$	11.8140	0.379717
$969$	−102.184	−3.28263
$970$	39.1181	1.25601
$971$	−14.6674	−0.470699	−0.235349	−	0.971911i	$-0.575623\pi$
$971$	−14.6674	−0.470699	−0.235349	+	0.971911i	$0.575623\pi$
$972$	21.0737	0.675940
$973$	39.9173	1.27969
$974$	−18.3140	−0.586818
$975$	127.337	4.07804
$976$	−5.06837	−0.162235
$977$	19.8464	0.634944	0.317472	−	0.948268i	$-0.397166\pi$
$977$	19.8464	0.634944	0.317472	+	0.948268i	$0.397166\pi$
$978$	−29.4915	−0.943033
$979$	−70.5444	−2.25461
$980$	−43.5447	−1.39099
$981$	49.9824	1.59581
$982$	−24.3370	−0.776624
$983$	−2.22037	−0.0708189	−0.0354095	−	0.999373i	$-0.511274\pi$
$983$	−2.22037	−0.0708189	−0.0354095	+	0.999373i	$0.511274\pi$
$984$	−16.1196	−0.513873
$985$	−116.851	−3.72319
$986$	−65.3829	−2.08222
$987$	−80.0132	−2.54685
$988$	−24.6368	−0.783801
$989$	20.8091	0.661692
$990$	54.2152	1.72307
$991$	16.4824	0.523581	0.261790	−	0.965125i	$-0.415687\pi$
$991$	16.4824	0.523581	0.261790	+	0.965125i	$0.415687\pi$
$992$	1.34878	0.0428238
$993$	31.1806	0.989485
$994$	19.0541	0.604361
$995$	45.8559	1.45373
$996$	2.65766	0.0842111
$997$	−11.9134	−0.377302	−0.188651	−	0.982044i	$-0.560412\pi$
$997$	−11.9134	−0.377302	−0.188651	+	0.982044i	$0.560412\pi$
$998$	22.0160	0.696904
$999$	2.83589	0.0897234

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.e.1.12	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.e.1.12	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.37532 q^{3} +1.00000 q^{4} -4.29598 q^{5} -2.37532 q^{6} -4.13959 q^{7} +1.00000 q^{8} +2.64215 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.37532 q^{3} +1.00000 q^{4} -4.29598 q^{5} -2.37532 q^{6} -4.13959 q^{7} +1.00000 q^{8} +2.64215 q^{9} -4.29598 q^{10} -4.77640 q^{11} -2.37532 q^{12} -3.98414 q^{13} -4.13959 q^{14} +10.2043 q^{15} +1.00000 q^{16} +6.95682 q^{17} +2.64215 q^{18} +6.18372 q^{19} -4.29598 q^{20} +9.83285 q^{21} -4.77640 q^{22} +1.81455 q^{23} -2.37532 q^{24} +13.4554 q^{25} -3.98414 q^{26} +0.850001 q^{27} -4.13959 q^{28} -9.39839 q^{29} +10.2043 q^{30} +1.34878 q^{31} +1.00000 q^{32} +11.3455 q^{33} +6.95682 q^{34} +17.7836 q^{35} +2.64215 q^{36} +3.33633 q^{37} +6.18372 q^{38} +9.46361 q^{39} -4.29598 q^{40} +6.78627 q^{41} +9.83285 q^{42} +11.4679 q^{43} -4.77640 q^{44} -11.3506 q^{45} +1.81455 q^{46} -8.13733 q^{47} -2.37532 q^{48} +10.1362 q^{49} +13.4554 q^{50} -16.5247 q^{51} -3.98414 q^{52} -9.88577 q^{53} +0.850001 q^{54} +20.5193 q^{55} -4.13959 q^{56} -14.6883 q^{57} -9.39839 q^{58} -4.10917 q^{59} +10.2043 q^{60} -5.06837 q^{61} +1.34878 q^{62} -10.9374 q^{63} +1.00000 q^{64} +17.1158 q^{65} +11.3455 q^{66} +0.781290 q^{67} +6.95682 q^{68} -4.31015 q^{69} +17.7836 q^{70} -4.60291 q^{71} +2.64215 q^{72} -3.36966 q^{73} +3.33633 q^{74} -31.9609 q^{75} +6.18372 q^{76} +19.7723 q^{77} +9.46361 q^{78} +1.30201 q^{79} -4.29598 q^{80} -9.94549 q^{81} +6.78627 q^{82} -1.11886 q^{83} +9.83285 q^{84} -29.8863 q^{85} +11.4679 q^{86} +22.3242 q^{87} -4.77640 q^{88} +14.7694 q^{89} -11.3506 q^{90} +16.4927 q^{91} +1.81455 q^{92} -3.20379 q^{93} -8.13733 q^{94} -26.5651 q^{95} -2.37532 q^{96} -9.10575 q^{97} +10.1362 q^{98} -12.6200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9}+O(q^{10}) \) 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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