LMFDB - Embedded newform 4015.2.a.f.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.403680 q^{2} +1.58032 q^{3} -1.83704 q^{4} -1.00000 q^{5} -0.637944 q^{6} +3.59112 q^{7} +1.54894 q^{8} -0.502579 q^{9} +O(q^{10})$	\(q-0.403680 q^{2} +1.58032 q^{3} -1.83704 q^{4} -1.00000 q^{5} -0.637944 q^{6} +3.59112 q^{7} +1.54894 q^{8} -0.502579 q^{9} +0.403680 q^{10} +1.00000 q^{11} -2.90312 q^{12} -2.34485 q^{13} -1.44966 q^{14} -1.58032 q^{15} +3.04881 q^{16} -1.11784 q^{17} +0.202881 q^{18} +3.68423 q^{19} +1.83704 q^{20} +5.67513 q^{21} -0.403680 q^{22} -8.55398 q^{23} +2.44782 q^{24} +1.00000 q^{25} +0.946568 q^{26} -5.53521 q^{27} -6.59704 q^{28} -7.37617 q^{29} +0.637944 q^{30} +1.70809 q^{31} -4.32861 q^{32} +1.58032 q^{33} +0.451251 q^{34} -3.59112 q^{35} +0.923259 q^{36} -6.91406 q^{37} -1.48725 q^{38} -3.70562 q^{39} -1.54894 q^{40} -2.30729 q^{41} -2.29093 q^{42} +2.37582 q^{43} -1.83704 q^{44} +0.502579 q^{45} +3.45307 q^{46} -9.18261 q^{47} +4.81811 q^{48} +5.89615 q^{49} -0.403680 q^{50} -1.76656 q^{51} +4.30759 q^{52} -0.155573 q^{53} +2.23445 q^{54} -1.00000 q^{55} +5.56241 q^{56} +5.82227 q^{57} +2.97761 q^{58} +8.63307 q^{59} +2.90312 q^{60} +12.1257 q^{61} -0.689521 q^{62} -1.80482 q^{63} -4.35025 q^{64} +2.34485 q^{65} -0.637944 q^{66} +10.0365 q^{67} +2.05353 q^{68} -13.5181 q^{69} +1.44966 q^{70} +0.586776 q^{71} -0.778463 q^{72} +1.00000 q^{73} +2.79106 q^{74} +1.58032 q^{75} -6.76809 q^{76} +3.59112 q^{77} +1.49588 q^{78} +10.1020 q^{79} -3.04881 q^{80} -7.23968 q^{81} +0.931405 q^{82} +2.90982 q^{83} -10.4255 q^{84} +1.11784 q^{85} -0.959071 q^{86} -11.6567 q^{87} +1.54894 q^{88} -16.2056 q^{89} -0.202881 q^{90} -8.42064 q^{91} +15.7140 q^{92} +2.69933 q^{93} +3.70683 q^{94} -3.68423 q^{95} -6.84061 q^{96} -19.5500 q^{97} -2.38015 q^{98} -0.502579 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9} + 7 q^{10} + 31 q^{11} - 4 q^{12} - 24 q^{13} - 9 q^{14} + 4 q^{15} + 43 q^{16} - 49 q^{17} - 35 q^{18} - 22 q^{19} - 39 q^{20} - 8 q^{21} - 7 q^{22} - q^{23} - 13 q^{24} + 31 q^{25} - 9 q^{26} - 22 q^{27} - 34 q^{28} - 12 q^{29} + 5 q^{30} + 4 q^{31} - 45 q^{32} - 4 q^{33} + 2 q^{34} + 11 q^{35} + 34 q^{36} - 18 q^{37} - 7 q^{38} - q^{39} + 24 q^{40} - 58 q^{41} - 21 q^{42} - 41 q^{43} + 39 q^{44} - 31 q^{45} + 23 q^{46} - 31 q^{47} - 29 q^{48} + 44 q^{49} - 7 q^{50} + 8 q^{51} - 89 q^{52} - 46 q^{53} - 47 q^{54} - 31 q^{55} + 10 q^{56} - 47 q^{57} - 34 q^{58} - 9 q^{59} + 4 q^{60} - 5 q^{61} - 50 q^{62} - 61 q^{63} + 78 q^{64} + 24 q^{65} - 5 q^{66} + q^{67} - 115 q^{68} - 19 q^{69} + 9 q^{70} - 8 q^{71} - 93 q^{72} + 31 q^{73} - 19 q^{74} - 4 q^{75} - 7 q^{76} - 11 q^{77} + 57 q^{78} - 43 q^{80} + 43 q^{81} + 20 q^{82} - 29 q^{83} - 32 q^{84} + 49 q^{85} + 25 q^{86} - 62 q^{87} - 24 q^{88} - 77 q^{89} + 35 q^{90} - 11 q^{91} - 25 q^{92} - 38 q^{94} + 22 q^{95} - 23 q^{96} - 39 q^{97} - 65 q^{98} + 31 q^{99}+O(q^{100}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9 + 7 * q^10 + 31 * q^11 - 4 * q^12 - 24 * q^13 - 9 * q^14 + 4 * q^15 + 43 * q^16 - 49 * q^17 - 35 * q^18 - 22 * q^19 - 39 * q^20 - 8 * q^21 - 7 * q^22 - q^23 - 13 * q^24 + 31 * q^25 - 9 * q^26 - 22 * q^27 - 34 * q^28 - 12 * q^29 + 5 * q^30 + 4 * q^31 - 45 * q^32 - 4 * q^33 + 2 * q^34 + 11 * q^35 + 34 * q^36 - 18 * q^37 - 7 * q^38 - q^39 + 24 * q^40 - 58 * q^41 - 21 * q^42 - 41 * q^43 + 39 * q^44 - 31 * q^45 + 23 * q^46 - 31 * q^47 - 29 * q^48 + 44 * q^49 - 7 * q^50 + 8 * q^51 - 89 * q^52 - 46 * q^53 - 47 * q^54 - 31 * q^55 + 10 * q^56 - 47 * q^57 - 34 * q^58 - 9 * q^59 + 4 * q^60 - 5 * q^61 - 50 * q^62 - 61 * q^63 + 78 * q^64 + 24 * q^65 - 5 * q^66 + q^67 - 115 * q^68 - 19 * q^69 + 9 * q^70 - 8 * q^71 - 93 * q^72 + 31 * q^73 - 19 * q^74 - 4 * q^75 - 7 * q^76 - 11 * q^77 + 57 * q^78 - 43 * q^80 + 43 * q^81 + 20 * q^82 - 29 * q^83 - 32 * q^84 + 49 * q^85 + 25 * q^86 - 62 * q^87 - 24 * q^88 - 77 * q^89 + 35 * q^90 - 11 * q^91 - 25 * q^92 - 38 * q^94 + 22 * q^95 - 23 * q^96 - 39 * q^97 - 65 * q^98 + 31 * 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 $

$2$	−0.403680	−0.285445	−0.142722	−	0.989763i	$-0.545586\pi$
$2$	−0.403680	−0.285445	−0.142722	+	0.989763i	$0.545586\pi$
$3$	1.58032	0.912400	0.456200	−	0.889877i	$-0.349210\pi$
$3$	1.58032	0.912400	0.456200	+	0.889877i	$0.349210\pi$
$4$	−1.83704	−0.918521
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.637944	−0.260440
$7$	3.59112	1.35732	0.678658	−	0.734454i	$-0.262562\pi$
$7$	3.59112	1.35732	0.678658	+	0.734454i	$0.262562\pi$
$8$	1.54894	0.547631
$9$	−0.502579	−0.167526
$10$	0.403680	0.127655
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.90312	−0.838059
$13$	−2.34485	−0.650345	−0.325172	−	0.945655i	$-0.605422\pi$
$13$	−2.34485	−0.650345	−0.325172	+	0.945655i	$0.605422\pi$
$14$	−1.44966	−0.387438
$15$	−1.58032	−0.408038
$16$	3.04881	0.762203
$17$	−1.11784	−0.271117	−0.135559	−	0.990769i	$-0.543283\pi$
$17$	−1.11784	−0.271117	−0.135559	+	0.990769i	$0.543283\pi$
$18$	0.202881	0.0478195
$19$	3.68423	0.845220	0.422610	−	0.906312i	$-0.361114\pi$
$19$	3.68423	0.845220	0.422610	+	0.906312i	$0.361114\pi$
$20$	1.83704	0.410775
$21$	5.67513	1.23841
$22$	−0.403680	−0.0860648
$23$	−8.55398	−1.78363	−0.891814	−	0.452402i	$-0.850567\pi$
$23$	−8.55398	−1.78363	−0.891814	+	0.452402i	$0.850567\pi$
$24$	2.44782	0.499659
$25$	1.00000	0.200000
$26$	0.946568	0.185637
$27$	−5.53521	−1.06525
$28$	−6.59704	−1.24672
$29$	−7.37617	−1.36972	−0.684860	−	0.728675i	$-0.740137\pi$
$29$	−7.37617	−1.36972	−0.684860	+	0.728675i	$0.740137\pi$
$30$	0.637944	0.116472
$31$	1.70809	0.306782	0.153391	−	0.988166i	$-0.450981\pi$
$31$	1.70809	0.306782	0.153391	+	0.988166i	$0.450981\pi$
$32$	−4.32861	−0.765198
$33$	1.58032	0.275099
$34$	0.451251	0.0773889
$35$	−3.59112	−0.607010
$36$	0.923259	0.153877
$37$	−6.91406	−1.13666	−0.568332	−	0.822799i	$-0.692411\pi$
$37$	−6.91406	−1.13666	−0.568332	+	0.822799i	$0.692411\pi$
$38$	−1.48725	−0.241263
$39$	−3.70562	−0.593375
$40$	−1.54894	−0.244908
$41$	−2.30729	−0.360338	−0.180169	−	0.983636i	$-0.557664\pi$
$41$	−2.30729	−0.360338	−0.180169	+	0.983636i	$0.557664\pi$
$42$	−2.29093	−0.353499
$43$	2.37582	0.362310	0.181155	−	0.983455i	$-0.442017\pi$
$43$	2.37582	0.362310	0.181155	+	0.983455i	$0.442017\pi$
$44$	−1.83704	−0.276945
$45$	0.502579	0.0749201
$46$	3.45307	0.509127
$47$	−9.18261	−1.33942	−0.669711	−	0.742622i	$-0.733582\pi$
$47$	−9.18261	−1.33942	−0.669711	+	0.742622i	$0.733582\pi$
$48$	4.81811	0.695434
$49$	5.89615	0.842306
$50$	−0.403680	−0.0570889
$51$	−1.76656	−0.247367
$52$	4.30759	0.597356
$53$	−0.155573	−0.0213696	−0.0106848	−	0.999943i	$-0.503401\pi$
$53$	−0.155573	−0.0213696	−0.0106848	+	0.999943i	$0.503401\pi$
$54$	2.23445	0.304070
$55$	−1.00000	−0.134840
$56$	5.56241	0.743309
$57$	5.82227	0.771179
$58$	2.97761	0.390979
$59$	8.63307	1.12393	0.561965	−	0.827161i	$-0.310046\pi$
$59$	8.63307	1.12393	0.561965	+	0.827161i	$0.310046\pi$
$60$	2.90312	0.374791
$61$	12.1257	1.55254	0.776271	−	0.630399i	$-0.217109\pi$
$61$	12.1257	1.55254	0.776271	+	0.630399i	$0.217109\pi$
$62$	−0.689521	−0.0875692
$63$	−1.80482	−0.227386
$64$	−4.35025	−0.543781
$65$	2.34485	0.290843
$66$	−0.637944	−0.0785255
$67$	10.0365	1.22615	0.613076	−	0.790024i	$-0.289932\pi$
$67$	10.0365	1.22615	0.613076	+	0.790024i	$0.289932\pi$
$68$	2.05353	0.249027
$69$	−13.5181	−1.62738
$70$	1.44966	0.173268
$71$	0.586776	0.0696375	0.0348188	−	0.999394i	$-0.488915\pi$
$71$	0.586776	0.0696375	0.0348188	+	0.999394i	$0.488915\pi$
$72$	−0.778463	−0.0917427
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	2.79106	0.324455
$75$	1.58032	0.182480
$76$	−6.76809	−0.776353
$77$	3.59112	0.409246
$78$	1.49588	0.169376
$79$	10.1020	1.13657	0.568283	−	0.822833i	$-0.307608\pi$
$79$	10.1020	1.13657	0.568283	+	0.822833i	$0.307608\pi$
$80$	−3.04881	−0.340868
$81$	−7.23968	−0.804409
$82$	0.931405	0.102856
$83$	2.90982	0.319395	0.159697	−	0.987166i	$-0.448948\pi$
$83$	2.90982	0.319395	0.159697	+	0.987166i	$0.448948\pi$
$84$	−10.4255	−1.13751
$85$	1.11784	0.121247
$86$	−0.959071	−0.103419
$87$	−11.6567	−1.24973
$88$	1.54894	0.165117
$89$	−16.2056	−1.71779	−0.858896	−	0.512150i	$-0.828849\pi$
$89$	−16.2056	−1.71779	−0.858896	+	0.512150i	$0.828849\pi$
$90$	−0.202881	−0.0213855
$91$	−8.42064	−0.882723
$92$	15.7140	1.63830
$93$	2.69933	0.279908
$94$	3.70683	0.382331
$95$	−3.68423	−0.377994
$96$	−6.84061	−0.698167
$97$	−19.5500	−1.98500	−0.992502	−	0.122231i	$-0.960995\pi$
$97$	−19.5500	−1.98500	−0.992502	+	0.122231i	$0.960995\pi$
$98$	−2.38015	−0.240432
$99$	−0.502579	−0.0505111
$100$	−1.83704	−0.183704
$101$	4.91410	0.488972	0.244486	−	0.969653i	$-0.421381\pi$
$101$	4.91410	0.488972	0.244486	+	0.969653i	$0.421381\pi$
$102$	0.713122	0.0706096
$103$	−10.3977	−1.02452	−0.512259	−	0.858831i	$-0.671191\pi$
$103$	−10.3977	−1.02452	−0.512259	+	0.858831i	$0.671191\pi$
$104$	−3.63202	−0.356149
$105$	−5.67513	−0.553836
$106$	0.0628016	0.00609983
$107$	−17.9247	−1.73285	−0.866425	−	0.499307i	$-0.833588\pi$
$107$	−17.9247	−1.73285	−0.866425	+	0.499307i	$0.833588\pi$
$108$	10.1684	0.978456
$109$	−8.91913	−0.854298	−0.427149	−	0.904181i	$-0.640482\pi$
$109$	−8.91913	−0.854298	−0.427149	+	0.904181i	$0.640482\pi$
$110$	0.403680	0.0384893
$111$	−10.9265	−1.03709
$112$	10.9487	1.03455
$113$	−6.41099	−0.603096	−0.301548	−	0.953451i	$-0.597503\pi$
$113$	−6.41099	−0.603096	−0.301548	+	0.953451i	$0.597503\pi$
$114$	−2.35033	−0.220129
$115$	8.55398	0.797663
$116$	13.5503	1.25812
$117$	1.17847	0.108950
$118$	−3.48499	−0.320820
$119$	−4.01431	−0.367992
$120$	−2.44782	−0.223454
$121$	1.00000	0.0909091
$122$	−4.89491	−0.443165
$123$	−3.64626	−0.328772
$124$	−3.13783	−0.281786
$125$	−1.00000	−0.0894427
$126$	0.728570	0.0649061
$127$	18.0801	1.60435	0.802174	−	0.597090i	$-0.203677\pi$
$127$	18.0801	1.60435	0.802174	+	0.597090i	$0.203677\pi$
$128$	10.4133	0.920418
$129$	3.75457	0.330571
$130$	−0.946568	−0.0830195
$131$	−13.3109	−1.16298	−0.581488	−	0.813555i	$-0.697529\pi$
$131$	−13.3109	−1.16298	−0.581488	+	0.813555i	$0.697529\pi$
$132$	−2.90312	−0.252684
$133$	13.2305	1.14723
$134$	−4.05152	−0.349998
$135$	5.53521	0.476395
$136$	−1.73147	−0.148472
$137$	−0.249930	−0.0213530	−0.0106765	−	0.999943i	$-0.503398\pi$
$137$	−0.249930	−0.0213530	−0.0106765	+	0.999943i	$0.503398\pi$
$138$	5.45696	0.464527
$139$	−21.9756	−1.86395	−0.931973	−	0.362528i	$-0.881914\pi$
$139$	−21.9756	−1.86395	−0.931973	+	0.362528i	$0.881914\pi$
$140$	6.59704	0.557552
$141$	−14.5115	−1.22209
$142$	−0.236870	−0.0198777
$143$	−2.34485	−0.196086
$144$	−1.53227	−0.127689
$145$	7.37617	0.612557
$146$	−0.403680	−0.0334088
$147$	9.31781	0.768520
$148$	12.7014	1.04405
$149$	0.0683002	0.00559537	0.00279769	−	0.999996i	$-0.499109\pi$
$149$	0.0683002	0.00559537	0.00279769	+	0.999996i	$0.499109\pi$
$150$	−0.637944	−0.0520879
$151$	16.4648	1.33988	0.669942	−	0.742414i	$-0.266319\pi$
$151$	16.4648	1.33988	0.669942	+	0.742414i	$0.266319\pi$
$152$	5.70663	0.462869
$153$	0.561805	0.0454192
$154$	−1.44966	−0.116817
$155$	−1.70809	−0.137197
$156$	6.80739	0.545027
$157$	−9.09333	−0.725727	−0.362863	−	0.931842i	$-0.618201\pi$
$157$	−9.09333	−0.725727	−0.362863	+	0.931842i	$0.618201\pi$
$158$	−4.07798	−0.324427
$159$	−0.245856	−0.0194976
$160$	4.32861	0.342207
$161$	−30.7184	−2.42095
$162$	2.92251	0.229614
$163$	−22.7131	−1.77903	−0.889514	−	0.456908i	$-0.848957\pi$
$163$	−22.7131	−1.77903	−0.889514	+	0.456908i	$0.848957\pi$
$164$	4.23859	0.330978
$165$	−1.58032	−0.123028
$166$	−1.17464	−0.0911695
$167$	14.3354	1.10931	0.554655	−	0.832081i	$-0.312850\pi$
$167$	14.3354	1.10931	0.554655	+	0.832081i	$0.312850\pi$
$168$	8.79041	0.678195
$169$	−7.50167	−0.577052
$170$	−0.451251	−0.0346094
$171$	−1.85162	−0.141597
$172$	−4.36449	−0.332789
$173$	−2.99074	−0.227382	−0.113691	−	0.993516i	$-0.536267\pi$
$173$	−2.99074	−0.227382	−0.113691	+	0.993516i	$0.536267\pi$
$174$	4.70558	0.356729
$175$	3.59112	0.271463
$176$	3.04881	0.229813
$177$	13.6430	1.02547
$178$	6.54188	0.490334
$179$	7.60622	0.568516	0.284258	−	0.958748i	$-0.408253\pi$
$179$	7.60622	0.568516	0.284258	+	0.958748i	$0.408253\pi$
$180$	−0.923259	−0.0688157
$181$	2.10306	0.156319	0.0781597	−	0.996941i	$-0.475096\pi$
$181$	2.10306	0.156319	0.0781597	+	0.996941i	$0.475096\pi$
$182$	3.39924	0.251969
$183$	19.1626	1.41654
$184$	−13.2496	−0.976771
$185$	6.91406	0.508332
$186$	−1.08967	−0.0798981
$187$	−1.11784	−0.0817449
$188$	16.8689	1.23029
$189$	−19.8776	−1.44588
$190$	1.48725	0.107896
$191$	−16.4990	−1.19383	−0.596914	−	0.802305i	$-0.703607\pi$
$191$	−16.4990	−1.19383	−0.596914	+	0.802305i	$0.703607\pi$
$192$	−6.87480	−0.496146
$193$	−10.5532	−0.759634	−0.379817	−	0.925062i	$-0.624013\pi$
$193$	−10.5532	−0.759634	−0.379817	+	0.925062i	$0.624013\pi$
$194$	7.89194	0.566608
$195$	3.70562	0.265365
$196$	−10.8315	−0.773677
$197$	10.3521	0.737559	0.368779	−	0.929517i	$-0.379776\pi$
$197$	10.3521	0.737559	0.368779	+	0.929517i	$0.379776\pi$
$198$	0.202881	0.0144181
$199$	−12.1721	−0.862860	−0.431430	−	0.902147i	$-0.641991\pi$
$199$	−12.1721	−0.862860	−0.431430	+	0.902147i	$0.641991\pi$
$200$	1.54894	0.109526
$201$	15.8609	1.11874
$202$	−1.98372	−0.139574
$203$	−26.4887	−1.85914
$204$	3.24524	0.227212
$205$	2.30729	0.161148
$206$	4.19735	0.292443
$207$	4.29905	0.298805
$208$	−7.14901	−0.495695
$209$	3.68423	0.254843
$210$	2.29093	0.158089
$211$	−6.53751	−0.450061	−0.225030	−	0.974352i	$-0.572248\pi$
$211$	−6.53751	−0.450061	−0.225030	+	0.974352i	$0.572248\pi$
$212$	0.285794	0.0196284
$213$	0.927296	0.0635373
$214$	7.23585	0.494632
$215$	−2.37582	−0.162030
$216$	−8.57368	−0.583365
$217$	6.13395	0.416400
$218$	3.60047	0.243855
$219$	1.58032	0.106788
$220$	1.83704	0.123853
$221$	2.62118	0.176320
$222$	4.41078	0.296032
$223$	6.54373	0.438201	0.219100	−	0.975702i	$-0.429688\pi$
$223$	6.54373	0.438201	0.219100	+	0.975702i	$0.429688\pi$
$224$	−15.5446	−1.03862
$225$	−0.502579	−0.0335053
$226$	2.58799	0.172150
$227$	−18.3589	−1.21853	−0.609263	−	0.792968i	$-0.708535\pi$
$227$	−18.3589	−1.21853	−0.609263	+	0.792968i	$0.708535\pi$
$228$	−10.6958	−0.708344
$229$	−27.2759	−1.80244	−0.901221	−	0.433359i	$-0.857328\pi$
$229$	−27.2759	−1.80244	−0.901221	+	0.433359i	$0.857328\pi$
$230$	−3.45307	−0.227689
$231$	5.67513	0.373396
$232$	−11.4252	−0.750102
$233$	4.14708	0.271684	0.135842	−	0.990731i	$-0.456626\pi$
$233$	4.14708	0.271684	0.135842	+	0.990731i	$0.456626\pi$
$234$	−0.475725	−0.0310991
$235$	9.18261	0.599008
$236$	−15.8593	−1.03235
$237$	15.9645	1.03700
$238$	1.62050	0.105041
$239$	−13.9915	−0.905035	−0.452517	−	0.891756i	$-0.649474\pi$
$239$	−13.9915	−0.905035	−0.452517	+	0.891756i	$0.649474\pi$
$240$	−4.81811	−0.311008
$241$	27.6436	1.78068	0.890341	−	0.455294i	$-0.150466\pi$
$241$	27.6436	1.78068	0.890341	+	0.455294i	$0.150466\pi$
$242$	−0.403680	−0.0259495
$243$	5.16459	0.331309
$244$	−22.2755	−1.42604
$245$	−5.89615	−0.376691
$246$	1.47192	0.0938462
$247$	−8.63897	−0.549684
$248$	2.64572	0.168003
$249$	4.59846	0.291416
$250$	0.403680	0.0255309
$251$	−19.5347	−1.23302	−0.616509	−	0.787348i	$-0.711454\pi$
$251$	−19.5347	−1.23302	−0.616509	+	0.787348i	$0.711454\pi$
$252$	3.31553	0.208859
$253$	−8.55398	−0.537784
$254$	−7.29856	−0.457952
$255$	1.76656	0.110626
$256$	4.49685	0.281053
$257$	20.7066	1.29164	0.645821	−	0.763488i	$-0.276515\pi$
$257$	20.7066	1.29164	0.645821	+	0.763488i	$0.276515\pi$
$258$	−1.51564	−0.0943597
$259$	−24.8292	−1.54281
$260$	−4.30759	−0.267146
$261$	3.70711	0.229464
$262$	5.37333	0.331965
$263$	−3.46405	−0.213602	−0.106801	−	0.994280i	$-0.534061\pi$
$263$	−3.46405	−0.213602	−0.106801	+	0.994280i	$0.534061\pi$
$264$	2.44782	0.150653
$265$	0.155573	0.00955677
$266$	−5.34089	−0.327471
$267$	−25.6101	−1.56731
$268$	−18.4374	−1.12625
$269$	18.3825	1.12080	0.560401	−	0.828221i	$-0.310647\pi$
$269$	18.3825	1.12080	0.560401	+	0.828221i	$0.310647\pi$
$270$	−2.23445	−0.135984
$271$	20.7047	1.25772	0.628862	−	0.777517i	$-0.283521\pi$
$271$	20.7047	1.25772	0.628862	+	0.777517i	$0.283521\pi$
$272$	−3.40810	−0.206646
$273$	−13.3073	−0.805397
$274$	0.100892	0.00609509
$275$	1.00000	0.0603023
$276$	24.8332	1.49479
$277$	15.4127	0.926060	0.463030	−	0.886343i	$-0.346762\pi$
$277$	15.4127	0.926060	0.463030	+	0.886343i	$0.346762\pi$
$278$	8.87110	0.532053
$279$	−0.858450	−0.0513940
$280$	−5.56241	−0.332418
$281$	19.2882	1.15064	0.575318	−	0.817930i	$-0.304878\pi$
$281$	19.2882	1.15064	0.575318	+	0.817930i	$0.304878\pi$
$282$	5.85799	0.348838
$283$	−32.2243	−1.91554	−0.957768	−	0.287541i	$-0.907162\pi$
$283$	−32.2243	−1.91554	−0.957768	+	0.287541i	$0.907162\pi$
$284$	−1.07793	−0.0639636
$285$	−5.82227	−0.344882
$286$	0.946568	0.0559718
$287$	−8.28575	−0.489092
$288$	2.17547	0.128191
$289$	−15.7504	−0.926496
$290$	−2.97761	−0.174851
$291$	−30.8953	−1.81112
$292$	−1.83704	−0.107505
$293$	−10.1067	−0.590437	−0.295218	−	0.955430i	$-0.595392\pi$
$293$	−10.1067	−0.590437	−0.295218	+	0.955430i	$0.595392\pi$
$294$	−3.76141	−0.219370
$295$	−8.63307	−0.502637
$296$	−10.7094	−0.622473
$297$	−5.53521	−0.321185
$298$	−0.0275714	−0.00159717
$299$	20.0578	1.15997
$300$	−2.90312	−0.167612
$301$	8.53186	0.491768
$302$	−6.64649	−0.382462
$303$	7.76587	0.446138
$304$	11.2325	0.644229
$305$	−12.1257	−0.694318
$306$	−0.226789	−0.0129647
$307$	17.1227	0.977243	0.488622	−	0.872496i	$-0.337500\pi$
$307$	17.1227	0.977243	0.488622	+	0.872496i	$0.337500\pi$
$308$	−6.59704	−0.375901
$309$	−16.4318	−0.934770
$310$	0.689521	0.0391621
$311$	7.91805	0.448991	0.224496	−	0.974475i	$-0.427927\pi$
$311$	7.91805	0.448991	0.224496	+	0.974475i	$0.427927\pi$
$312$	−5.73977	−0.324951
$313$	15.5197	0.877224	0.438612	−	0.898677i	$-0.355470\pi$
$313$	15.5197	0.877224	0.438612	+	0.898677i	$0.355470\pi$
$314$	3.67079	0.207155
$315$	1.80482	0.101690
$316$	−18.5579	−1.04396
$317$	18.6093	1.04520	0.522600	−	0.852578i	$-0.324962\pi$
$317$	18.6093	1.04520	0.522600	+	0.852578i	$0.324962\pi$
$318$	0.0992469	0.00556549
$319$	−7.37617	−0.412986
$320$	4.35025	0.243186
$321$	−28.3269	−1.58105
$322$	12.4004	0.691046
$323$	−4.11839	−0.229154
$324$	13.2996	0.738867
$325$	−2.34485	−0.130069
$326$	9.16881	0.507814
$327$	−14.0951	−0.779461
$328$	−3.57384	−0.197332
$329$	−32.9759	−1.81802
$330$	0.637944	0.0351177
$331$	−26.8476	−1.47568	−0.737838	−	0.674978i	$-0.764153\pi$
$331$	−26.8476	−1.47568	−0.737838	+	0.674978i	$0.764153\pi$
$332$	−5.34547	−0.293371
$333$	3.47486	0.190421
$334$	−5.78692	−0.316646
$335$	−10.0365	−0.548351
$336$	17.3024	0.943924
$337$	−21.4037	−1.16593	−0.582967	−	0.812496i	$-0.698108\pi$
$337$	−21.4037	−1.16593	−0.582967	+	0.812496i	$0.698108\pi$
$338$	3.02827	0.164716
$339$	−10.1314	−0.550264
$340$	−2.05353	−0.111368
$341$	1.70809	0.0924982
$342$	0.747460	0.0404180
$343$	−3.96408	−0.214040
$344$	3.68000	0.198412
$345$	13.5181	0.727788
$346$	1.20730	0.0649049
$347$	−0.790957	−0.0424608	−0.0212304	−	0.999775i	$-0.506758\pi$
$347$	−0.790957	−0.0424608	−0.0212304	+	0.999775i	$0.506758\pi$
$348$	21.4139	1.14791
$349$	17.9399	0.960303	0.480151	−	0.877186i	$-0.340582\pi$
$349$	17.9399	0.960303	0.480151	+	0.877186i	$0.340582\pi$
$350$	−1.44966	−0.0774877
$351$	12.9792	0.692780
$352$	−4.32861	−0.230716
$353$	−20.2859	−1.07971	−0.539856	−	0.841758i	$-0.681521\pi$
$353$	−20.2859	−1.07971	−0.539856	+	0.841758i	$0.681521\pi$
$354$	−5.50742	−0.292716
$355$	−0.586776	−0.0311429
$356$	29.7704	1.57783
$357$	−6.34391	−0.335755
$358$	−3.07048	−0.162280
$359$	−25.3617	−1.33854	−0.669269	−	0.743020i	$-0.733393\pi$
$359$	−25.3617	−1.33854	−0.669269	+	0.743020i	$0.733393\pi$
$360$	0.778463	0.0410286
$361$	−5.42645	−0.285603
$362$	−0.848964	−0.0446205
$363$	1.58032	0.0829454
$364$	15.4691	0.810800
$365$	−1.00000	−0.0523424
$366$	−7.73555	−0.404343
$367$	2.34489	0.122402	0.0612010	−	0.998125i	$-0.480507\pi$
$367$	2.34489	0.122402	0.0612010	+	0.998125i	$0.480507\pi$
$368$	−26.0795	−1.35949
$369$	1.15959	0.0603661
$370$	−2.79106	−0.145101
$371$	−0.558681	−0.0290053
$372$	−4.95879	−0.257101
$373$	−14.5925	−0.755571	−0.377786	−	0.925893i	$-0.623314\pi$
$373$	−14.5925	−0.755571	−0.377786	+	0.925893i	$0.623314\pi$
$374$	0.451251	0.0233336
$375$	−1.58032	−0.0816075
$376$	−14.2233	−0.733509
$377$	17.2960	0.890790
$378$	8.02418	0.412719
$379$	29.6441	1.52272	0.761358	−	0.648332i	$-0.224533\pi$
$379$	29.6441	1.52272	0.761358	+	0.648332i	$0.224533\pi$
$380$	6.76809	0.347196
$381$	28.5724	1.46381
$382$	6.66032	0.340772
$383$	7.43307	0.379812	0.189906	−	0.981802i	$-0.439182\pi$
$383$	7.43307	0.379812	0.189906	+	0.981802i	$0.439182\pi$
$384$	16.4564	0.839789
$385$	−3.59112	−0.183020
$386$	4.26010	0.216833
$387$	−1.19404	−0.0606964
$388$	35.9142	1.82327
$389$	−28.0702	−1.42322	−0.711609	−	0.702576i	$-0.752033\pi$
$389$	−28.0702	−1.42322	−0.711609	+	0.702576i	$0.752033\pi$
$390$	−1.49588	−0.0757470
$391$	9.56202	0.483572
$392$	9.13275	0.461273
$393$	−21.0355	−1.06110
$394$	−4.17894	−0.210532
$395$	−10.1020	−0.508288
$396$	0.923259	0.0463955
$397$	−19.9562	−1.00157	−0.500786	−	0.865571i	$-0.666956\pi$
$397$	−19.9562	−1.00157	−0.500786	+	0.865571i	$0.666956\pi$
$398$	4.91364	0.246299
$399$	20.9085	1.04673
$400$	3.04881	0.152441
$401$	18.8481	0.941229	0.470615	−	0.882339i	$-0.344032\pi$
$401$	18.8481	0.941229	0.470615	+	0.882339i	$0.344032\pi$
$402$	−6.40271	−0.319338
$403$	−4.00522	−0.199514
$404$	−9.02742	−0.449131
$405$	7.23968	0.359742
$406$	10.6929	0.530682
$407$	−6.91406	−0.342717
$408$	−2.73628	−0.135466
$409$	11.8921	0.588027	0.294013	−	0.955801i	$-0.405009\pi$
$409$	11.8921	0.588027	0.294013	+	0.955801i	$0.405009\pi$
$410$	−0.931405	−0.0459988
$411$	−0.394970	−0.0194824
$412$	19.1011	0.941041
$413$	31.0024	1.52553
$414$	−1.73544	−0.0852922
$415$	−2.90982	−0.142838
$416$	10.1500	0.497643
$417$	−34.7285	−1.70066
$418$	−1.48725	−0.0727437
$419$	−20.0879	−0.981357	−0.490678	−	0.871341i	$-0.663251\pi$
$419$	−20.0879	−0.981357	−0.490678	+	0.871341i	$0.663251\pi$
$420$	10.4255	0.508710
$421$	8.22646	0.400933	0.200467	−	0.979701i	$-0.435754\pi$
$421$	8.22646	0.400933	0.200467	+	0.979701i	$0.435754\pi$
$422$	2.63906	0.128467
$423$	4.61499	0.224388
$424$	−0.240973	−0.0117027
$425$	−1.11784	−0.0542234
$426$	−0.374330	−0.0181364
$427$	43.5450	2.10729
$428$	32.9285	1.59166
$429$	−3.70562	−0.178909
$430$	0.959071	0.0462505
$431$	3.41237	0.164368	0.0821841	−	0.996617i	$-0.473810\pi$
$431$	3.41237	0.164368	0.0821841	+	0.996617i	$0.473810\pi$
$432$	−16.8758	−0.811938
$433$	40.5939	1.95082	0.975408	−	0.220405i	$-0.0707380\pi$
$433$	40.5939	1.95082	0.975408	+	0.220405i	$0.0707380\pi$
$434$	−2.47615	−0.118859
$435$	11.6567	0.558897
$436$	16.3848	0.784691
$437$	−31.5148	−1.50756
$438$	−0.637944	−0.0304821
$439$	28.5456	1.36241	0.681204	−	0.732094i	$-0.261457\pi$
$439$	28.5456	1.36241	0.681204	+	0.732094i	$0.261457\pi$
$440$	−1.54894	−0.0738426
$441$	−2.96328	−0.141109
$442$	−1.05812	−0.0503295
$443$	7.78211	0.369739	0.184870	−	0.982763i	$-0.440814\pi$
$443$	7.78211	0.369739	0.184870	+	0.982763i	$0.440814\pi$
$444$	20.0724	0.952592
$445$	16.2056	0.768220
$446$	−2.64157	−0.125082
$447$	0.107936	0.00510522
$448$	−15.6223	−0.738083
$449$	8.80725	0.415640	0.207820	−	0.978167i	$-0.433363\pi$
$449$	8.80725	0.415640	0.207820	+	0.978167i	$0.433363\pi$
$450$	0.202881	0.00956389
$451$	−2.30729	−0.108646
$452$	11.7773	0.553956
$453$	26.0196	1.22251
$454$	7.41113	0.347821
$455$	8.42064	0.394766
$456$	9.01833	0.422322
$457$	30.5163	1.42749	0.713746	−	0.700405i	$-0.246997\pi$
$457$	30.5163	1.42749	0.713746	+	0.700405i	$0.246997\pi$
$458$	11.0107	0.514497
$459$	6.18750	0.288808
$460$	−15.7140	−0.732671
$461$	33.6170	1.56570	0.782851	−	0.622210i	$-0.213765\pi$
$461$	33.6170	1.56570	0.782851	+	0.622210i	$0.213765\pi$
$462$	−2.29093	−0.106584
$463$	−11.2551	−0.523070	−0.261535	−	0.965194i	$-0.584229\pi$
$463$	−11.2551	−0.523070	−0.261535	+	0.965194i	$0.584229\pi$
$464$	−22.4885	−1.04400
$465$	−2.69933	−0.125179
$466$	−1.67409	−0.0775507
$467$	−26.9442	−1.24683	−0.623415	−	0.781891i	$-0.714255\pi$
$467$	−26.9442	−1.24683	−0.623415	+	0.781891i	$0.714255\pi$
$468$	−2.16491	−0.100073
$469$	36.0422	1.66427
$470$	−3.70683	−0.170983
$471$	−14.3704	−0.662153
$472$	13.3721	0.615499
$473$	2.37582	0.109240
$474$	−6.44453	−0.296007
$475$	3.68423	0.169044
$476$	7.37447	0.338008
$477$	0.0781877	0.00357997
$478$	5.64808	0.258337
$479$	−1.07188	−0.0489752	−0.0244876	−	0.999700i	$-0.507795\pi$
$479$	−1.07188	−0.0489752	−0.0244876	+	0.999700i	$0.507795\pi$
$480$	6.84061	0.312230
$481$	16.2124	0.739224
$482$	−11.1592	−0.508286
$483$	−48.5450	−2.20887
$484$	−1.83704	−0.0835019
$485$	19.5500	0.887721
$486$	−2.08484	−0.0945702
$487$	9.99892	0.453094	0.226547	−	0.974000i	$-0.427256\pi$
$487$	9.99892	0.453094	0.226547	+	0.974000i	$0.427256\pi$
$488$	18.7820	0.850221
$489$	−35.8940	−1.62318
$490$	2.38015	0.107524
$491$	12.1813	0.549734	0.274867	−	0.961482i	$-0.411366\pi$
$491$	12.1813	0.549734	0.274867	+	0.961482i	$0.411366\pi$
$492$	6.69833	0.301984
$493$	8.24541	0.371354
$494$	3.48738	0.156904
$495$	0.502579	0.0225892
$496$	5.20764	0.233830
$497$	2.10718	0.0945201
$498$	−1.85630	−0.0831830
$499$	−6.15678	−0.275615	−0.137808	−	0.990459i	$-0.544006\pi$
$499$	−6.15678	−0.275615	−0.137808	+	0.990459i	$0.544006\pi$
$500$	1.83704	0.0821551
$501$	22.6546	1.01213
$502$	7.88575	0.351958
$503$	−2.83916	−0.126592	−0.0632960	−	0.997995i	$-0.520161\pi$
$503$	−2.83916	−0.126592	−0.0632960	+	0.997995i	$0.520161\pi$
$504$	−2.79555	−0.124524
$505$	−4.91410	−0.218675
$506$	3.45307	0.153508
$507$	−11.8551	−0.526502
$508$	−33.2139	−1.47363
$509$	38.2572	1.69572	0.847861	−	0.530218i	$-0.177890\pi$
$509$	38.2572	1.69572	0.847861	+	0.530218i	$0.177890\pi$
$510$	−0.713122	−0.0315776
$511$	3.59112	0.158862
$512$	−22.6420	−1.00064
$513$	−20.3930	−0.900372
$514$	−8.35883	−0.368692
$515$	10.3977	0.458178
$516$	−6.89730	−0.303637
$517$	−9.18261	−0.403851
$518$	10.0230	0.440388
$519$	−4.72633	−0.207463
$520$	3.63202	0.159275
$521$	13.5332	0.592900	0.296450	−	0.955048i	$-0.404197\pi$
$521$	13.5332	0.592900	0.296450	+	0.955048i	$0.404197\pi$
$522$	−1.49648	−0.0654993
$523$	−44.9913	−1.96733	−0.983667	−	0.180000i	$-0.942390\pi$
$523$	−44.9913	−1.96733	−0.983667	+	0.180000i	$0.942390\pi$
$524$	24.4527	1.06822
$525$	5.67513	0.247683
$526$	1.39836	0.0609716
$527$	−1.90938	−0.0831738
$528$	4.81811	0.209681
$529$	50.1706	2.18133
$530$	−0.0628016	−0.00272793
$531$	−4.33880	−0.188288
$532$	−24.3050	−1.05376
$533$	5.41025	0.234344
$534$	10.3383	0.447381
$535$	17.9247	0.774954
$536$	15.5459	0.671479
$537$	12.0203	0.518714
$538$	−7.42065	−0.319927
$539$	5.89615	0.253965
$540$	−10.1684	−0.437579
$541$	14.8447	0.638224	0.319112	−	0.947717i	$-0.396615\pi$
$541$	14.8447	0.638224	0.319112	+	0.947717i	$0.396615\pi$
$542$	−8.35808	−0.359010
$543$	3.32352	0.142626
$544$	4.83872	0.207458
$545$	8.91913	0.382054
$546$	5.37190	0.229896
$547$	−34.9644	−1.49497	−0.747485	−	0.664278i	$-0.768739\pi$
$547$	−34.9644	−1.49497	−0.747485	+	0.664278i	$0.768739\pi$
$548$	0.459132	0.0196132
$549$	−6.09414	−0.260092
$550$	−0.403680	−0.0172130
$551$	−27.1755	−1.15771
$552$	−20.9386	−0.891206
$553$	36.2776	1.54268
$554$	−6.22179	−0.264339
$555$	10.9265	0.463802
$556$	40.3701	1.71207
$557$	−12.2969	−0.521034	−0.260517	−	0.965469i	$-0.583893\pi$
$557$	−12.2969	−0.521034	−0.260517	+	0.965469i	$0.583893\pi$
$558$	0.346539	0.0146701
$559$	−5.57095	−0.235626
$560$	−10.9487	−0.462665
$561$	−1.76656	−0.0745840
$562$	−7.78624	−0.328443
$563$	15.6543	0.659752	0.329876	−	0.944024i	$-0.392993\pi$
$563$	15.6543	0.659752	0.329876	+	0.944024i	$0.392993\pi$
$564$	26.6582	1.12251
$565$	6.41099	0.269713
$566$	13.0083	0.546779
$567$	−25.9986	−1.09184
$568$	0.908879	0.0381357
$569$	−13.0605	−0.547526	−0.273763	−	0.961797i	$-0.588268\pi$
$569$	−13.0605	−0.547526	−0.273763	+	0.961797i	$0.588268\pi$
$570$	2.35033	0.0984446
$571$	−1.70695	−0.0714335	−0.0357168	−	0.999362i	$-0.511371\pi$
$571$	−1.70695	−0.0714335	−0.0357168	+	0.999362i	$0.511371\pi$
$572$	4.30759	0.180109
$573$	−26.0738	−1.08925
$574$	3.34479	0.139609
$575$	−8.55398	−0.356726
$576$	2.18635	0.0910977
$577$	−21.2045	−0.882755	−0.441378	−	0.897321i	$-0.645510\pi$
$577$	−21.2045	−0.882755	−0.441378	+	0.897321i	$0.645510\pi$
$578$	6.35812	0.264463
$579$	−16.6774	−0.693090
$580$	−13.5503	−0.562647
$581$	10.4495	0.433519
$582$	12.4718	0.516973
$583$	−0.155573	−0.00644317
$584$	1.54894	0.0640954
$585$	−1.17847	−0.0487239
$586$	4.07985	0.168537
$587$	3.02998	0.125061	0.0625303	−	0.998043i	$-0.480083\pi$
$587$	3.02998	0.125061	0.0625303	+	0.998043i	$0.480083\pi$
$588$	−17.1172	−0.705902
$589$	6.29299	0.259298
$590$	3.48499	0.143475
$591$	16.3597	0.672948
$592$	−21.0797	−0.866369
$593$	−17.6554	−0.725019	−0.362510	−	0.931980i	$-0.618080\pi$
$593$	−17.6554	−0.725019	−0.362510	+	0.931980i	$0.618080\pi$
$594$	2.23445	0.0916806
$595$	4.01431	0.164571
$596$	−0.125470	−0.00513947
$597$	−19.2359	−0.787273
$598$	−8.09693	−0.331108
$599$	18.7673	0.766811	0.383406	−	0.923580i	$-0.374751\pi$
$599$	18.7673	0.766811	0.383406	+	0.923580i	$0.374751\pi$
$600$	2.44782	0.0999318
$601$	−32.9693	−1.34485	−0.672423	−	0.740167i	$-0.734746\pi$
$601$	−32.9693	−1.34485	−0.672423	+	0.740167i	$0.734746\pi$
$602$	−3.44414	−0.140373
$603$	−5.04412	−0.205413
$604$	−30.2465	−1.23071
$605$	−1.00000	−0.0406558
$606$	−3.13492	−0.127348
$607$	34.5391	1.40190	0.700949	−	0.713211i	$-0.252760\pi$
$607$	34.5391	1.40190	0.700949	+	0.713211i	$0.252760\pi$
$608$	−15.9476	−0.646761
$609$	−41.8607	−1.69628
$610$	4.89491	0.198189
$611$	21.5319	0.871086
$612$	−1.03206	−0.0417186
$613$	−27.5179	−1.11144	−0.555718	−	0.831371i	$-0.687557\pi$
$613$	−27.5179	−1.11144	−0.555718	+	0.831371i	$0.687557\pi$
$614$	−6.91208	−0.278949
$615$	3.64626	0.147031
$616$	5.56241	0.224116
$617$	29.4285	1.18475	0.592374	−	0.805663i	$-0.298191\pi$
$617$	29.4285	1.18475	0.592374	+	0.805663i	$0.298191\pi$
$618$	6.63316	0.266825
$619$	−4.72318	−0.189841	−0.0949204	−	0.995485i	$-0.530260\pi$
$619$	−4.72318	−0.189841	−0.0949204	+	0.995485i	$0.530260\pi$
$620$	3.13783	0.126018
$621$	47.3481	1.90001
$622$	−3.19636	−0.128162
$623$	−58.1963	−2.33159
$624$	−11.2977	−0.452272
$625$	1.00000	0.0400000
$626$	−6.26498	−0.250399
$627$	5.82227	0.232519
$628$	16.7048	0.666595
$629$	7.72884	0.308169
$630$	−0.728570	−0.0290269
$631$	−15.0256	−0.598160	−0.299080	−	0.954228i	$-0.596680\pi$
$631$	−15.0256	−0.598160	−0.299080	+	0.954228i	$0.596680\pi$
$632$	15.6474	0.622420
$633$	−10.3314	−0.410636
$634$	−7.51218	−0.298347
$635$	−18.0801	−0.717486
$636$	0.451647	0.0179090
$637$	−13.8256	−0.547790
$638$	2.97761	0.117885
$639$	−0.294901	−0.0116661
$640$	−10.4133	−0.411623
$641$	−32.9449	−1.30124	−0.650622	−	0.759402i	$-0.725492\pi$
$641$	−32.9449	−1.30124	−0.650622	+	0.759402i	$0.725492\pi$
$642$	11.4350	0.451303
$643$	−36.9294	−1.45635	−0.728177	−	0.685389i	$-0.759632\pi$
$643$	−36.9294	−1.45635	−0.728177	+	0.685389i	$0.759632\pi$
$644$	56.4310	2.22369
$645$	−3.75457	−0.147836
$646$	1.66251	0.0654106
$647$	−4.88299	−0.191970	−0.0959850	−	0.995383i	$-0.530600\pi$
$647$	−4.88299	−0.191970	−0.0959850	+	0.995383i	$0.530600\pi$
$648$	−11.2138	−0.440519
$649$	8.63307	0.338878
$650$	0.946568	0.0371275
$651$	9.69363	0.379923
$652$	41.7249	1.63407
$653$	9.97601	0.390391	0.195196	−	0.980764i	$-0.437466\pi$
$653$	9.97601	0.390391	0.195196	+	0.980764i	$0.437466\pi$
$654$	5.68991	0.222493
$655$	13.3109	0.520099
$656$	−7.03449	−0.274651
$657$	−0.502579	−0.0196075
$658$	13.3117	0.518943
$659$	−33.4565	−1.30328	−0.651640	−	0.758528i	$-0.725919\pi$
$659$	−33.4565	−1.30328	−0.651640	+	0.758528i	$0.725919\pi$
$660$	2.90312	0.113004
$661$	24.9573	0.970728	0.485364	−	0.874312i	$-0.338687\pi$
$661$	24.9573	0.970728	0.485364	+	0.874312i	$0.338687\pi$
$662$	10.8378	0.421224
$663$	4.14231	0.160874
$664$	4.50713	0.174911
$665$	−13.2305	−0.513057
$666$	−1.40273	−0.0543547
$667$	63.0956	2.44307
$668$	−26.3348	−1.01892
$669$	10.3412	0.399814
$670$	4.05152	0.156524
$671$	12.1257	0.468109
$672$	−24.5654	−0.947633
$673$	−23.9502	−0.923211	−0.461605	−	0.887085i	$-0.652726\pi$
$673$	−23.9502	−0.923211	−0.461605	+	0.887085i	$0.652726\pi$
$674$	8.64023	0.332809
$675$	−5.53521	−0.213050
$676$	13.7809	0.530034
$677$	19.5849	0.752707	0.376353	−	0.926476i	$-0.377178\pi$
$677$	19.5849	0.752707	0.376353	+	0.926476i	$0.377178\pi$
$678$	4.08986	0.157070
$679$	−70.2065	−2.69428
$680$	1.73147	0.0663988
$681$	−29.0131	−1.11178
$682$	−0.689521	−0.0264031
$683$	23.1929	0.887451	0.443725	−	0.896163i	$-0.353657\pi$
$683$	23.1929	0.887451	0.443725	+	0.896163i	$0.353657\pi$
$684$	3.40150	0.130060
$685$	0.249930	0.00954934
$686$	1.60022	0.0610965
$687$	−43.1047	−1.64455
$688$	7.24344	0.276153
$689$	0.364796	0.0138976
$690$	−5.45696	−0.207743
$691$	46.2072	1.75781	0.878903	−	0.477000i	$-0.158276\pi$
$691$	46.2072	1.75781	0.878903	+	0.477000i	$0.158276\pi$
$692$	5.49412	0.208855
$693$	−1.80482	−0.0685595
$694$	0.319293	0.0121202
$695$	21.9756	0.833582
$696$	−18.0555	−0.684393
$697$	2.57919	0.0976937
$698$	−7.24198	−0.274113
$699$	6.55372	0.247885
$700$	−6.59704	−0.249345
$701$	−19.6169	−0.740921	−0.370460	−	0.928848i	$-0.620800\pi$
$701$	−19.6169	−0.740921	−0.370460	+	0.928848i	$0.620800\pi$
$702$	−5.23945	−0.197750
$703$	−25.4730	−0.960732
$704$	−4.35025	−0.163956
$705$	14.5115	0.546534
$706$	8.18901	0.308198
$707$	17.6471	0.663689
$708$	−25.0628	−0.941919
$709$	−7.62086	−0.286208	−0.143104	−	0.989708i	$-0.545708\pi$
$709$	−7.62086	−0.286208	−0.143104	+	0.989708i	$0.545708\pi$
$710$	0.236870	0.00888956
$711$	−5.07707	−0.190405
$712$	−25.1015	−0.940717
$713$	−14.6110	−0.547185
$714$	2.56091	0.0958395
$715$	2.34485	0.0876925
$716$	−13.9730	−0.522194
$717$	−22.1111	−0.825754
$718$	10.2380	0.382078
$719$	27.5396	1.02705	0.513527	−	0.858074i	$-0.328339\pi$
$719$	27.5396	1.02705	0.513527	+	0.858074i	$0.328339\pi$
$720$	1.53227	0.0571043
$721$	−37.3395	−1.39059
$722$	2.19055	0.0815238
$723$	43.6859	1.62469
$724$	−3.86342	−0.143583
$725$	−7.37617	−0.273944
$726$	−0.637944	−0.0236763
$727$	7.81246	0.289748	0.144874	−	0.989450i	$-0.453722\pi$
$727$	7.81246	0.289748	0.144874	+	0.989450i	$0.453722\pi$
$728$	−13.0430	−0.483407
$729$	29.8808	1.10669
$730$	0.403680	0.0149408
$731$	−2.65580	−0.0982283
$732$	−35.2025	−1.30112
$733$	37.2390	1.37545	0.687727	−	0.725970i	$-0.258609\pi$
$733$	37.2390	1.37545	0.687727	+	0.725970i	$0.258609\pi$
$734$	−0.946582	−0.0349390
$735$	−9.31781	−0.343693
$736$	37.0269	1.36483
$737$	10.0365	0.369698
$738$	−0.468104	−0.0172312
$739$	7.15334	0.263140	0.131570	−	0.991307i	$-0.457998\pi$
$739$	7.15334	0.263140	0.131570	+	0.991307i	$0.457998\pi$
$740$	−12.7014	−0.466914
$741$	−13.6524	−0.501532
$742$	0.225528	0.00827940
$743$	−34.0580	−1.24947	−0.624733	−	0.780838i	$-0.714792\pi$
$743$	−34.0580	−1.24947	−0.624733	+	0.780838i	$0.714792\pi$
$744$	4.18109	0.153286
$745$	−0.0683002	−0.00250233
$746$	5.89070	0.215674
$747$	−1.46242	−0.0535070
$748$	2.05353	0.0750844
$749$	−64.3699	−2.35202
$750$	0.637944	0.0232944
$751$	−11.5657	−0.422038	−0.211019	−	0.977482i	$-0.567678\pi$
$751$	−11.5657	−0.422038	−0.211019	+	0.977482i	$0.567678\pi$
$752$	−27.9961	−1.02091
$753$	−30.8711	−1.12501
$754$	−6.98205	−0.254271
$755$	−16.4648	−0.599214
$756$	36.5160	1.32807
$757$	41.0313	1.49131	0.745654	−	0.666333i	$-0.232137\pi$
$757$	41.0313	1.49131	0.745654	+	0.666333i	$0.232137\pi$
$758$	−11.9667	−0.434651
$759$	−13.5181	−0.490674
$760$	−5.70663	−0.207001
$761$	18.8158	0.682072	0.341036	−	0.940050i	$-0.389222\pi$
$761$	18.8158	0.682072	0.341036	+	0.940050i	$0.389222\pi$
$762$	−11.5341	−0.417836
$763$	−32.0297	−1.15955
$764$	30.3094	1.09656
$765$	−0.561805	−0.0203121
$766$	−3.00058	−0.108415
$767$	−20.2433	−0.730942
$768$	7.10648	0.256433
$769$	3.85204	0.138908	0.0694541	−	0.997585i	$-0.477874\pi$
$769$	3.85204	0.138908	0.0694541	+	0.997585i	$0.477874\pi$
$770$	1.44966	0.0522422
$771$	32.7231	1.17849
$772$	19.3866	0.697740
$773$	15.0449	0.541127	0.270563	−	0.962702i	$-0.412790\pi$
$773$	15.0449	0.541127	0.270563	+	0.962702i	$0.412790\pi$
$774$	0.482009	0.0173255
$775$	1.70809	0.0613564
$776$	−30.2817	−1.08705
$777$	−39.2382	−1.40766
$778$	11.3314	0.406250
$779$	−8.50058	−0.304565
$780$	−6.80739	−0.243744
$781$	0.586776	0.0209965
$782$	−3.85999	−0.138033
$783$	40.8286	1.45910
$784$	17.9762	0.642009
$785$	9.09333	0.324555
$786$	8.49160	0.302885
$787$	34.7480	1.23863	0.619315	−	0.785142i	$-0.287410\pi$
$787$	34.7480	1.23863	0.619315	+	0.785142i	$0.287410\pi$
$788$	−19.0173	−0.677463
$789$	−5.47431	−0.194891
$790$	4.07798	0.145088
$791$	−23.0226	−0.818591
$792$	−0.778463	−0.0276615
$793$	−28.4331	−1.00969
$794$	8.05591	0.285894
$795$	0.245856	0.00871960
$796$	22.3607	0.792555
$797$	52.4763	1.85881	0.929403	−	0.369068i	$-0.120323\pi$
$797$	52.4763	1.85881	0.929403	+	0.369068i	$0.120323\pi$
$798$	−8.44033	−0.298784
$799$	10.2647	0.363140
$800$	−4.32861	−0.153040
$801$	8.14460	0.287775
$802$	−7.60859	−0.268669
$803$	1.00000	0.0352892
$804$	−29.1371	−1.02759
$805$	30.7184	1.08268
$806$	1.61682	0.0569502
$807$	29.0503	1.02262
$808$	7.61163	0.267776
$809$	1.98557	0.0698090	0.0349045	−	0.999391i	$-0.488887\pi$
$809$	1.98557	0.0698090	0.0349045	+	0.999391i	$0.488887\pi$
$810$	−2.92251	−0.102687
$811$	18.8199	0.660856	0.330428	−	0.943831i	$-0.392807\pi$
$811$	18.8199	0.660856	0.330428	+	0.943831i	$0.392807\pi$
$812$	48.6609	1.70766
$813$	32.7202	1.14755
$814$	2.79106	0.0978268
$815$	22.7131	0.795605
$816$	−5.38589	−0.188544
$817$	8.75307	0.306231
$818$	−4.80060	−0.167849
$819$	4.23204	0.147879
$820$	−4.23859	−0.148018
$821$	45.5341	1.58915	0.794576	−	0.607165i	$-0.207693\pi$
$821$	45.5341	1.58915	0.794576	+	0.607165i	$0.207693\pi$
$822$	0.159441	0.00556116
$823$	43.5015	1.51637	0.758184	−	0.652041i	$-0.226087\pi$
$823$	43.5015	1.51637	0.758184	+	0.652041i	$0.226087\pi$
$824$	−16.1054	−0.561058
$825$	1.58032	0.0550198
$826$	−12.5150	−0.435454
$827$	−1.55981	−0.0542399	−0.0271199	−	0.999632i	$-0.508634\pi$
$827$	−1.55981	−0.0542399	−0.0271199	+	0.999632i	$0.508634\pi$
$828$	−7.89754	−0.274459
$829$	−48.8301	−1.69594	−0.847969	−	0.530045i	$-0.822175\pi$
$829$	−48.8301	−1.69594	−0.847969	+	0.530045i	$0.822175\pi$
$830$	1.17464	0.0407722
$831$	24.3571	0.844937
$832$	10.2007	0.353645
$833$	−6.59097	−0.228364
$834$	14.0192	0.485445
$835$	−14.3354	−0.496098
$836$	−6.76809	−0.234079
$837$	−9.45463	−0.326800
$838$	8.10906	0.280123
$839$	−19.4375	−0.671057	−0.335529	−	0.942030i	$-0.608915\pi$
$839$	−19.4375	−0.671057	−0.335529	+	0.942030i	$0.608915\pi$
$840$	−8.79041	−0.303298
$841$	25.4078	0.876132
$842$	−3.32085	−0.114444
$843$	30.4816	1.04984
$844$	12.0097	0.413391
$845$	7.50167	0.258065
$846$	−1.86298	−0.0640504
$847$	3.59112	0.123392
$848$	−0.474313	−0.0162880
$849$	−50.9248	−1.74774
$850$	0.451251	0.0154778
$851$	59.1428	2.02739
$852$	−1.70348	−0.0583604
$853$	−18.8436	−0.645192	−0.322596	−	0.946537i	$-0.604555\pi$
$853$	−18.8436	−0.645192	−0.322596	+	0.946537i	$0.604555\pi$
$854$	−17.5782	−0.601514
$855$	1.85162	0.0633239
$856$	−27.7643	−0.948963
$857$	−43.8336	−1.49733	−0.748663	−	0.662950i	$-0.769304\pi$
$857$	−43.8336	−1.49733	−0.748663	+	0.662950i	$0.769304\pi$
$858$	1.49588	0.0510686
$859$	−1.79386	−0.0612058	−0.0306029	−	0.999532i	$-0.509743\pi$
$859$	−1.79386	−0.0612058	−0.0306029	+	0.999532i	$0.509743\pi$
$860$	4.36449	0.148828
$861$	−13.0942	−0.446248
$862$	−1.37751	−0.0469180
$863$	−25.1226	−0.855184	−0.427592	−	0.903972i	$-0.640638\pi$
$863$	−25.1226	−0.855184	−0.427592	+	0.903972i	$0.640638\pi$
$864$	23.9598	0.815128
$865$	2.99074	0.101688
$866$	−16.3869	−0.556850
$867$	−24.8908	−0.845334
$868$	−11.2683	−0.382472
$869$	10.1020	0.342688
$870$	−4.70558	−0.159534
$871$	−23.5341	−0.797421
$872$	−13.8152	−0.467840
$873$	9.82543	0.332540
$874$	12.7219	0.430324
$875$	−3.59112	−0.121402
$876$	−2.90312	−0.0980874
$877$	−16.0247	−0.541116	−0.270558	−	0.962704i	$-0.587208\pi$
$877$	−16.0247	−0.541116	−0.270558	+	0.962704i	$0.587208\pi$
$878$	−11.5233	−0.388892
$879$	−15.9718	−0.538715
$880$	−3.04881	−0.102775
$881$	−39.7518	−1.33927	−0.669636	−	0.742689i	$-0.733550\pi$
$881$	−39.7518	−1.33927	−0.669636	+	0.742689i	$0.733550\pi$
$882$	1.19621	0.0402787
$883$	−1.72260	−0.0579700	−0.0289850	−	0.999580i	$-0.509227\pi$
$883$	−1.72260	−0.0579700	−0.0289850	+	0.999580i	$0.509227\pi$
$884$	−4.81522	−0.161953
$885$	−13.6430	−0.458606
$886$	−3.14148	−0.105540
$887$	−55.6260	−1.86774	−0.933870	−	0.357613i	$-0.883591\pi$
$887$	−55.6260	−1.86774	−0.933870	+	0.357613i	$0.883591\pi$
$888$	−16.9244	−0.567945
$889$	64.9278	2.17761
$890$	−6.54188	−0.219284
$891$	−7.23968	−0.242538
$892$	−12.0211	−0.402497
$893$	−33.8308	−1.13211
$894$	−0.0435717	−0.00145726
$895$	−7.60622	−0.254248
$896$	37.3955	1.24930
$897$	31.6978	1.05836
$898$	−3.55530	−0.118642
$899$	−12.5992	−0.420205
$900$	0.923259	0.0307753
$901$	0.173906	0.00579366
$902$	0.931405	0.0310124
$903$	13.4831	0.448690
$904$	−9.93022	−0.330274
$905$	−2.10306	−0.0699082
$906$	−10.5036	−0.348959
$907$	46.8880	1.55689	0.778445	−	0.627713i	$-0.216009\pi$
$907$	46.8880	1.55689	0.778445	+	0.627713i	$0.216009\pi$
$908$	33.7262	1.11924
$909$	−2.46973	−0.0819156
$910$	−3.39924	−0.112684
$911$	−42.2955	−1.40131	−0.700657	−	0.713499i	$-0.747110\pi$
$911$	−42.2955	−1.40131	−0.700657	+	0.713499i	$0.747110\pi$
$912$	17.7510	0.587795
$913$	2.90982	0.0963011
$914$	−12.3188	−0.407470
$915$	−19.1626	−0.633496
$916$	50.1070	1.65558
$917$	−47.8010	−1.57853
$918$	−2.49777	−0.0824386
$919$	−6.40501	−0.211282	−0.105641	−	0.994404i	$-0.533689\pi$
$919$	−6.40501	−0.211282	−0.105641	+	0.994404i	$0.533689\pi$
$920$	13.2496	0.436825
$921$	27.0594	0.891637
$922$	−13.5705	−0.446921
$923$	−1.37590	−0.0452884
$924$	−10.4255	−0.342972
$925$	−6.91406	−0.227333
$926$	4.54346	0.149307
$927$	5.22567	0.171634
$928$	31.9286	1.04811
$929$	24.1195	0.791334	0.395667	−	0.918394i	$-0.370513\pi$
$929$	24.1195	0.791334	0.395667	+	0.918394i	$0.370513\pi$
$930$	1.08967	0.0357315
$931$	21.7228	0.711934
$932$	−7.61836	−0.249548
$933$	12.5131	0.409660
$934$	10.8768	0.355901
$935$	1.11784	0.0365574
$936$	1.82538	0.0596644
$937$	−44.0765	−1.43992	−0.719958	−	0.694018i	$-0.755839\pi$
$937$	−44.0765	−1.43992	−0.719958	+	0.694018i	$0.755839\pi$
$938$	−14.5495	−0.475058
$939$	24.5261	0.800379
$940$	−16.8689	−0.550201
$941$	44.3607	1.44612	0.723058	−	0.690787i	$-0.242736\pi$
$941$	44.3607	1.44612	0.723058	+	0.690787i	$0.242736\pi$
$942$	5.80103	0.189008
$943$	19.7365	0.642709
$944$	26.3206	0.856663
$945$	19.8776	0.646618
$946$	−0.959071	−0.0311821
$947$	−7.42055	−0.241135	−0.120568	−	0.992705i	$-0.538471\pi$
$947$	−7.42055	−0.241135	−0.120568	+	0.992705i	$0.538471\pi$
$948$	−29.3274	−0.952510
$949$	−2.34485	−0.0761171
$950$	−1.48725	−0.0482527
$951$	29.4086	0.953641
$952$	−6.21791	−0.201524
$953$	35.5120	1.15035	0.575173	−	0.818032i	$-0.304935\pi$
$953$	35.5120	1.15035	0.575173	+	0.818032i	$0.304935\pi$
$954$	−0.0315628	−0.00102188
$955$	16.4990	0.533896
$956$	25.7030	0.831294
$957$	−11.6567	−0.376808
$958$	0.432694	0.0139797
$959$	−0.897529	−0.0289827
$960$	6.87480	0.221883
$961$	−28.0824	−0.905885
$962$	−6.54463	−0.211007
$963$	9.00860	0.290298
$964$	−50.7825	−1.63559
$965$	10.5532	0.339719
$966$	19.5966	0.630511
$967$	−11.0891	−0.356602	−0.178301	−	0.983976i	$-0.557060\pi$
$967$	−11.0891	−0.356602	−0.178301	+	0.983976i	$0.557060\pi$
$968$	1.54894	0.0497847
$969$	−6.50839	−0.209080
$970$	−7.89194	−0.253395
$971$	−12.4897	−0.400813	−0.200407	−	0.979713i	$-0.564226\pi$
$971$	−12.4897	−0.400813	−0.200407	+	0.979713i	$0.564226\pi$
$972$	−9.48757	−0.304314
$973$	−78.9170	−2.52996
$974$	−4.03636	−0.129333
$975$	−3.70562	−0.118675
$976$	36.9691	1.18335
$977$	−3.99837	−0.127919	−0.0639595	−	0.997952i	$-0.520373\pi$
$977$	−3.99837	−0.127919	−0.0639595	+	0.997952i	$0.520373\pi$
$978$	14.4897	0.463329
$979$	−16.2056	−0.517934
$980$	10.8315	0.345999
$981$	4.48257	0.143117
$982$	−4.91734	−0.156919
$983$	47.3734	1.51098	0.755489	−	0.655162i	$-0.227400\pi$
$983$	47.3734	1.51098	0.755489	+	0.655162i	$0.227400\pi$
$984$	−5.64782	−0.180046
$985$	−10.3521	−0.329846
$986$	−3.32850	−0.106001
$987$	−52.1125	−1.65876
$988$	15.8702	0.504897
$989$	−20.3227	−0.646226
$990$	−0.202881	−0.00644798
$991$	−49.8568	−1.58375	−0.791877	−	0.610680i	$-0.790896\pi$
$991$	−49.8568	−1.58375	−0.791877	+	0.610680i	$0.790896\pi$
$992$	−7.39366	−0.234749
$993$	−42.4278	−1.34641
$994$	−0.850627	−0.0269803
$995$	12.1721	0.385883
$996$	−8.44757	−0.267672
$997$	−9.24530	−0.292802	−0.146401	−	0.989225i	$-0.546769\pi$
$997$	−9.24530	−0.292802	−0.146401	+	0.989225i	$0.546769\pi$
$998$	2.48537	0.0786729
$999$	38.2708	1.21083

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.f.1.17	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.f.1.17	✓	31	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.403680 q^{2} +1.58032 q^{3} -1.83704 q^{4} -1.00000 q^{5} -0.637944 q^{6} +3.59112 q^{7} +1.54894 q^{8} -0.502579 q^{9} +O(q^{10})\)	\(q-0.403680 q^{2} +1.58032 q^{3} -1.83704 q^{4} -1.00000 q^{5} -0.637944 q^{6} +3.59112 q^{7} +1.54894 q^{8} -0.502579 q^{9} +0.403680 q^{10} +1.00000 q^{11} -2.90312 q^{12} -2.34485 q^{13} -1.44966 q^{14} -1.58032 q^{15} +3.04881 q^{16} -1.11784 q^{17} +0.202881 q^{18} +3.68423 q^{19} +1.83704 q^{20} +5.67513 q^{21} -0.403680 q^{22} -8.55398 q^{23} +2.44782 q^{24} +1.00000 q^{25} +0.946568 q^{26} -5.53521 q^{27} -6.59704 q^{28} -7.37617 q^{29} +0.637944 q^{30} +1.70809 q^{31} -4.32861 q^{32} +1.58032 q^{33} +0.451251 q^{34} -3.59112 q^{35} +0.923259 q^{36} -6.91406 q^{37} -1.48725 q^{38} -3.70562 q^{39} -1.54894 q^{40} -2.30729 q^{41} -2.29093 q^{42} +2.37582 q^{43} -1.83704 q^{44} +0.502579 q^{45} +3.45307 q^{46} -9.18261 q^{47} +4.81811 q^{48} +5.89615 q^{49} -0.403680 q^{50} -1.76656 q^{51} +4.30759 q^{52} -0.155573 q^{53} +2.23445 q^{54} -1.00000 q^{55} +5.56241 q^{56} +5.82227 q^{57} +2.97761 q^{58} +8.63307 q^{59} +2.90312 q^{60} +12.1257 q^{61} -0.689521 q^{62} -1.80482 q^{63} -4.35025 q^{64} +2.34485 q^{65} -0.637944 q^{66} +10.0365 q^{67} +2.05353 q^{68} -13.5181 q^{69} +1.44966 q^{70} +0.586776 q^{71} -0.778463 q^{72} +1.00000 q^{73} +2.79106 q^{74} +1.58032 q^{75} -6.76809 q^{76} +3.59112 q^{77} +1.49588 q^{78} +10.1020 q^{79} -3.04881 q^{80} -7.23968 q^{81} +0.931405 q^{82} +2.90982 q^{83} -10.4255 q^{84} +1.11784 q^{85} -0.959071 q^{86} -11.6567 q^{87} +1.54894 q^{88} -16.2056 q^{89} -0.202881 q^{90} -8.42064 q^{91} +15.7140 q^{92} +2.69933 q^{93} +3.70683 q^{94} -3.68423 q^{95} -6.84061 q^{96} -19.5500 q^{97} -2.38015 q^{98} -0.502579 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9} + 7 q^{10} + 31 q^{11} - 4 q^{12} - 24 q^{13} - 9 q^{14} + 4 q^{15} + 43 q^{16} - 49 q^{17} - 35 q^{18} - 22 q^{19} - 39 q^{20} - 8 q^{21} - 7 q^{22} - q^{23} - 13 q^{24} + 31 q^{25} - 9 q^{26} - 22 q^{27} - 34 q^{28} - 12 q^{29} + 5 q^{30} + 4 q^{31} - 45 q^{32} - 4 q^{33} + 2 q^{34} + 11 q^{35} + 34 q^{36} - 18 q^{37} - 7 q^{38} - q^{39} + 24 q^{40} - 58 q^{41} - 21 q^{42} - 41 q^{43} + 39 q^{44} - 31 q^{45} + 23 q^{46} - 31 q^{47} - 29 q^{48} + 44 q^{49} - 7 q^{50} + 8 q^{51} - 89 q^{52} - 46 q^{53} - 47 q^{54} - 31 q^{55} + 10 q^{56} - 47 q^{57} - 34 q^{58} - 9 q^{59} + 4 q^{60} - 5 q^{61} - 50 q^{62} - 61 q^{63} + 78 q^{64} + 24 q^{65} - 5 q^{66} + q^{67} - 115 q^{68} - 19 q^{69} + 9 q^{70} - 8 q^{71} - 93 q^{72} + 31 q^{73} - 19 q^{74} - 4 q^{75} - 7 q^{76} - 11 q^{77} + 57 q^{78} - 43 q^{80} + 43 q^{81} + 20 q^{82} - 29 q^{83} - 32 q^{84} + 49 q^{85} + 25 q^{86} - 62 q^{87} - 24 q^{88} - 77 q^{89} + 35 q^{90} - 11 q^{91} - 25 q^{92} - 38 q^{94} + 22 q^{95} - 23 q^{96} - 39 q^{97} - 65 q^{98} + 31 q^{99}+O(q^{100}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9 + 7 * q^10 + 31 * q^11 - 4 * q^12 - 24 * q^13 - 9 * q^14 + 4 * q^15 + 43 * q^16 - 49 * q^17 - 35 * q^18 - 22 * q^19 - 39 * q^20 - 8 * q^21 - 7 * q^22 - q^23 - 13 * q^24 + 31 * q^25 - 9 * q^26 - 22 * q^27 - 34 * q^28 - 12 * q^29 + 5 * q^30 + 4 * q^31 - 45 * q^32 - 4 * q^33 + 2 * q^34 + 11 * q^35 + 34 * q^36 - 18 * q^37 - 7 * q^38 - q^39 + 24 * q^40 - 58 * q^41 - 21 * q^42 - 41 * q^43 + 39 * q^44 - 31 * q^45 + 23 * q^46 - 31 * q^47 - 29 * q^48 + 44 * q^49 - 7 * q^50 + 8 * q^51 - 89 * q^52 - 46 * q^53 - 47 * q^54 - 31 * q^55 + 10 * q^56 - 47 * q^57 - 34 * q^58 - 9 * q^59 + 4 * q^60 - 5 * q^61 - 50 * q^62 - 61 * q^63 + 78 * q^64 + 24 * q^65 - 5 * q^66 + q^67 - 115 * q^68 - 19 * q^69 + 9 * q^70 - 8 * q^71 - 93 * q^72 + 31 * q^73 - 19 * q^74 - 4 * q^75 - 7 * q^76 - 11 * q^77 + 57 * q^78 - 43 * q^80 + 43 * q^81 + 20 * q^82 - 29 * q^83 - 32 * q^84 + 49 * q^85 + 25 * q^86 - 62 * q^87 - 24 * q^88 - 77 * q^89 + 35 * q^90 - 11 * q^91 - 25 * q^92 - 38 * q^94 + 22 * q^95 - 23 * q^96 - 39 * q^97 - 65 * q^98 + 31 * q^99

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