LMFDB - Embedded newform 6035.2.a.h.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, 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("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$0$
Dimension:	$59$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.71705 q^{2} -3.23330 q^{3} +0.948270 q^{4} +1.00000 q^{5} +5.55174 q^{6} +4.30663 q^{7} +1.80588 q^{8} +7.45420 q^{9} +O(q^{10})$	\(q-1.71705 q^{2} -3.23330 q^{3} +0.948270 q^{4} +1.00000 q^{5} +5.55174 q^{6} +4.30663 q^{7} +1.80588 q^{8} +7.45420 q^{9} -1.71705 q^{10} +5.53210 q^{11} -3.06604 q^{12} -4.12392 q^{13} -7.39471 q^{14} -3.23330 q^{15} -4.99732 q^{16} -1.00000 q^{17} -12.7993 q^{18} +8.25238 q^{19} +0.948270 q^{20} -13.9246 q^{21} -9.49891 q^{22} -4.74680 q^{23} -5.83893 q^{24} +1.00000 q^{25} +7.08100 q^{26} -14.4017 q^{27} +4.08385 q^{28} -8.71206 q^{29} +5.55174 q^{30} +5.60910 q^{31} +4.96892 q^{32} -17.8869 q^{33} +1.71705 q^{34} +4.30663 q^{35} +7.06859 q^{36} +0.462809 q^{37} -14.1698 q^{38} +13.3339 q^{39} +1.80588 q^{40} +8.70359 q^{41} +23.9093 q^{42} +0.856473 q^{43} +5.24592 q^{44} +7.45420 q^{45} +8.15051 q^{46} +9.13969 q^{47} +16.1578 q^{48} +11.5471 q^{49} -1.71705 q^{50} +3.23330 q^{51} -3.91059 q^{52} +7.07434 q^{53} +24.7286 q^{54} +5.53210 q^{55} +7.77724 q^{56} -26.6824 q^{57} +14.9591 q^{58} -1.35014 q^{59} -3.06604 q^{60} -4.37132 q^{61} -9.63113 q^{62} +32.1025 q^{63} +1.46276 q^{64} -4.12392 q^{65} +30.7128 q^{66} +11.7507 q^{67} -0.948270 q^{68} +15.3478 q^{69} -7.39471 q^{70} -1.00000 q^{71} +13.4614 q^{72} -14.3985 q^{73} -0.794667 q^{74} -3.23330 q^{75} +7.82548 q^{76} +23.8247 q^{77} -22.8949 q^{78} -2.74615 q^{79} -4.99732 q^{80} +24.2025 q^{81} -14.9445 q^{82} -1.08854 q^{83} -13.2043 q^{84} -1.00000 q^{85} -1.47061 q^{86} +28.1687 q^{87} +9.99029 q^{88} -14.0676 q^{89} -12.7993 q^{90} -17.7602 q^{91} -4.50125 q^{92} -18.1359 q^{93} -15.6933 q^{94} +8.25238 q^{95} -16.0660 q^{96} +9.18526 q^{97} -19.8269 q^{98} +41.2374 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9}+O(q^{10}) $ 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9} + 2 q^{10} + 6 q^{11} + 16 q^{12} + 25 q^{13} + 8 q^{14} + 6 q^{15} + 114 q^{16} - 59 q^{17} + 3 q^{18} + 35 q^{19} + 76 q^{20} + 41 q^{21} + 13 q^{22} - 2 q^{23} + 35 q^{24} + 59 q^{25} + 10 q^{26} + 27 q^{27} + 28 q^{28} + 10 q^{29} + 14 q^{30} + 15 q^{31} + 19 q^{32} - 3 q^{33} - 2 q^{34} + 9 q^{35} + 160 q^{36} + 56 q^{37} + 17 q^{38} + 25 q^{39} + 6 q^{40} + 47 q^{41} + 46 q^{42} + 27 q^{43} + 39 q^{44} + 97 q^{45} + 4 q^{46} - 8 q^{47} + 58 q^{48} + 174 q^{49} + 2 q^{50} - 6 q^{51} + 13 q^{52} + 17 q^{53} + 48 q^{54} + 6 q^{55} + 33 q^{56} + 6 q^{57} + 32 q^{58} + 30 q^{59} + 16 q^{60} + 85 q^{61} - 3 q^{62} + 14 q^{63} + 168 q^{64} + 25 q^{65} + 87 q^{66} + 21 q^{67} - 76 q^{68} + 111 q^{69} + 8 q^{70} - 59 q^{71} - 52 q^{72} + 41 q^{73} + 11 q^{74} + 6 q^{75} + 118 q^{76} + 55 q^{77} - 54 q^{78} + 43 q^{79} + 114 q^{80} + 207 q^{81} + 45 q^{82} + 10 q^{83} + 62 q^{84} - 59 q^{85} + 19 q^{86} + 8 q^{87} + 35 q^{88} + 86 q^{89} + 3 q^{90} + 47 q^{91} - 98 q^{92} + 41 q^{93} + 30 q^{94} + 35 q^{95} + 69 q^{96} + 72 q^{97} + 14 q^{98} + 25 q^{99}+O(q^{100}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9 + 2 * q^10 + 6 * q^11 + 16 * q^12 + 25 * q^13 + 8 * q^14 + 6 * q^15 + 114 * q^16 - 59 * q^17 + 3 * q^18 + 35 * q^19 + 76 * q^20 + 41 * q^21 + 13 * q^22 - 2 * q^23 + 35 * q^24 + 59 * q^25 + 10 * q^26 + 27 * q^27 + 28 * q^28 + 10 * q^29 + 14 * q^30 + 15 * q^31 + 19 * q^32 - 3 * q^33 - 2 * q^34 + 9 * q^35 + 160 * q^36 + 56 * q^37 + 17 * q^38 + 25 * q^39 + 6 * q^40 + 47 * q^41 + 46 * q^42 + 27 * q^43 + 39 * q^44 + 97 * q^45 + 4 * q^46 - 8 * q^47 + 58 * q^48 + 174 * q^49 + 2 * q^50 - 6 * q^51 + 13 * q^52 + 17 * q^53 + 48 * q^54 + 6 * q^55 + 33 * q^56 + 6 * q^57 + 32 * q^58 + 30 * q^59 + 16 * q^60 + 85 * q^61 - 3 * q^62 + 14 * q^63 + 168 * q^64 + 25 * q^65 + 87 * q^66 + 21 * q^67 - 76 * q^68 + 111 * q^69 + 8 * q^70 - 59 * q^71 - 52 * q^72 + 41 * q^73 + 11 * q^74 + 6 * q^75 + 118 * q^76 + 55 * q^77 - 54 * q^78 + 43 * q^79 + 114 * q^80 + 207 * q^81 + 45 * q^82 + 10 * q^83 + 62 * q^84 - 59 * q^85 + 19 * q^86 + 8 * q^87 + 35 * q^88 + 86 * q^89 + 3 * q^90 + 47 * q^91 - 98 * q^92 + 41 * q^93 + 30 * q^94 + 35 * q^95 + 69 * q^96 + 72 * q^97 + 14 * q^98 + 25 * 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 $

$2$	−1.71705	−1.21414	−0.607070	−	0.794649i	$-0.707655\pi$
$2$	−1.71705	−1.21414	−0.607070	+	0.794649i	$0.707655\pi$
$3$	−3.23330	−1.86674	−0.933372	−	0.358910i	$-0.883148\pi$
$3$	−3.23330	−1.86674	−0.933372	+	0.358910i	$0.883148\pi$
$4$	0.948270	0.474135
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	5.55174	2.26649
$7$	4.30663	1.62775	0.813877	−	0.581038i	$-0.197353\pi$
$7$	4.30663	1.62775	0.813877	+	0.581038i	$0.197353\pi$
$8$	1.80588	0.638474
$9$	7.45420	2.48473
$10$	−1.71705	−0.542980
$11$	5.53210	1.66799	0.833996	−	0.551771i	$-0.186048\pi$
$11$	5.53210	1.66799	0.833996	+	0.551771i	$0.186048\pi$
$12$	−3.06604	−0.885088
$13$	−4.12392	−1.14377	−0.571885	−	0.820334i	$-0.693788\pi$
$13$	−4.12392	−1.14377	−0.571885	+	0.820334i	$0.693788\pi$
$14$	−7.39471	−1.97632
$15$	−3.23330	−0.834833
$16$	−4.99732	−1.24933
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−12.7993	−3.01681
$19$	8.25238	1.89323	0.946613	−	0.322373i	$-0.104481\pi$
$19$	8.25238	1.89323	0.946613	+	0.322373i	$0.104481\pi$
$20$	0.948270	0.212040
$21$	−13.9246	−3.03860
$22$	−9.49891	−2.02517
$23$	−4.74680	−0.989776	−0.494888	−	0.868957i	$-0.664791\pi$
$23$	−4.74680	−0.989776	−0.494888	+	0.868957i	$0.664791\pi$
$24$	−5.83893	−1.19187
$25$	1.00000	0.200000
$26$	7.08100	1.38870
$27$	−14.4017	−2.77162
$28$	4.08385	0.771775
$29$	−8.71206	−1.61779	−0.808895	−	0.587953i	$-0.799934\pi$
$29$	−8.71206	−1.61779	−0.808895	+	0.587953i	$0.799934\pi$
$30$	5.55174	1.01360
$31$	5.60910	1.00742	0.503712	−	0.863871i	$-0.331967\pi$
$31$	5.60910	1.00742	0.503712	+	0.863871i	$0.331967\pi$
$32$	4.96892	0.878388
$33$	−17.8869	−3.11371
$34$	1.71705	0.294472
$35$	4.30663	0.727953
$36$	7.06859	1.17810
$37$	0.462809	0.0760853	0.0380426	−	0.999276i	$-0.487888\pi$
$37$	0.462809	0.0760853	0.0380426	+	0.999276i	$0.487888\pi$
$38$	−14.1698	−2.29864
$39$	13.3339	2.13513
$40$	1.80588	0.285534
$41$	8.70359	1.35927	0.679636	−	0.733550i	$-0.262138\pi$
$41$	8.70359	1.35927	0.679636	+	0.733550i	$0.262138\pi$
$42$	23.9093	3.68928
$43$	0.856473	0.130611	0.0653054	−	0.997865i	$-0.479198\pi$
$43$	0.856473	0.130611	0.0653054	+	0.997865i	$0.479198\pi$
$44$	5.24592	0.790853
$45$	7.45420	1.11121
$46$	8.15051	1.20173
$47$	9.13969	1.33316	0.666580	−	0.745433i	$-0.267757\pi$
$47$	9.13969	1.33316	0.666580	+	0.745433i	$0.267757\pi$
$48$	16.1578	2.33218
$49$	11.5471	1.64958
$50$	−1.71705	−0.242828
$51$	3.23330	0.452752
$52$	−3.91059	−0.542302
$53$	7.07434	0.971735	0.485868	−	0.874032i	$-0.338504\pi$
$53$	7.07434	0.971735	0.485868	+	0.874032i	$0.338504\pi$
$54$	24.7286	3.36513
$55$	5.53210	0.745948
$56$	7.77724	1.03928
$57$	−26.6824	−3.53417
$58$	14.9591	1.96422
$59$	−1.35014	−0.175774	−0.0878868	−	0.996130i	$-0.528011\pi$
$59$	−1.35014	−0.175774	−0.0878868	+	0.996130i	$0.528011\pi$
$60$	−3.06604	−0.395824
$61$	−4.37132	−0.559690	−0.279845	−	0.960045i	$-0.590283\pi$
$61$	−4.37132	−0.559690	−0.279845	+	0.960045i	$0.590283\pi$
$62$	−9.63113	−1.22315
$63$	32.1025	4.04453
$64$	1.46276	0.182845
$65$	−4.12392	−0.511510
$66$	30.7128	3.78048
$67$	11.7507	1.43558	0.717788	−	0.696262i	$-0.245155\pi$
$67$	11.7507	1.43558	0.717788	+	0.696262i	$0.245155\pi$
$68$	−0.948270	−0.114995
$69$	15.3478	1.84766
$70$	−7.39471	−0.883837
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	13.4614	1.58644
$73$	−14.3985	−1.68521	−0.842606	−	0.538531i	$-0.818980\pi$
$73$	−14.3985	−1.68521	−0.842606	+	0.538531i	$0.818980\pi$
$74$	−0.794667	−0.0923782
$75$	−3.23330	−0.373349
$76$	7.82548	0.897644
$77$	23.8247	2.71508
$78$	−22.8949	−2.59234
$79$	−2.74615	−0.308966	−0.154483	−	0.987995i	$-0.549371\pi$
$79$	−2.74615	−0.308966	−0.154483	+	0.987995i	$0.549371\pi$
$80$	−4.99732	−0.558718
$81$	24.2025	2.68917
$82$	−14.9445	−1.65035
$83$	−1.08854	−0.119483	−0.0597413	−	0.998214i	$-0.519028\pi$
$83$	−1.08854	−0.119483	−0.0597413	+	0.998214i	$0.519028\pi$
$84$	−13.2043	−1.44071
$85$	−1.00000	−0.108465
$86$	−1.47061	−0.158580
$87$	28.1687	3.02000
$88$	9.99029	1.06497
$89$	−14.0676	−1.49116	−0.745581	−	0.666415i	$-0.767828\pi$
$89$	−14.0676	−1.49116	−0.745581	+	0.666415i	$0.767828\pi$
$90$	−12.7993	−1.34916
$91$	−17.7602	−1.86178
$92$	−4.50125	−0.469287
$93$	−18.1359	−1.88060
$94$	−15.6933	−1.61864
$95$	8.25238	0.846676
$96$	−16.0660	−1.63973
$97$	9.18526	0.932622	0.466311	−	0.884621i	$-0.345583\pi$
$97$	9.18526	0.932622	0.466311	+	0.884621i	$0.345583\pi$
$98$	−19.8269	−2.00282
$99$	41.2374	4.14451
$100$	0.948270	0.0948270
$101$	8.97141	0.892688	0.446344	−	0.894861i	$-0.352726\pi$
$101$	8.97141	0.892688	0.446344	+	0.894861i	$0.352726\pi$
$102$	−5.55174	−0.549704
$103$	−1.05275	−0.103731	−0.0518653	−	0.998654i	$-0.516517\pi$
$103$	−1.05275	−0.103731	−0.0518653	+	0.998654i	$0.516517\pi$
$104$	−7.44730	−0.730268
$105$	−13.9246	−1.35890
$106$	−12.1470	−1.17982
$107$	7.83512	0.757449	0.378725	−	0.925509i	$-0.376363\pi$
$107$	7.83512	0.757449	0.378725	+	0.925509i	$0.376363\pi$
$108$	−13.6567	−1.31412
$109$	−0.0431254	−0.00413066	−0.00206533	−	0.999998i	$-0.500657\pi$
$109$	−0.0431254	−0.00413066	−0.00206533	+	0.999998i	$0.500657\pi$
$110$	−9.49891	−0.905686
$111$	−1.49640	−0.142032
$112$	−21.5216	−2.03360
$113$	−8.86002	−0.833480	−0.416740	−	0.909026i	$-0.636827\pi$
$113$	−8.86002	−0.833480	−0.416740	+	0.909026i	$0.636827\pi$
$114$	45.8150	4.29097
$115$	−4.74680	−0.442641
$116$	−8.26139	−0.767050
$117$	−30.7406	−2.84197
$118$	2.31826	0.213414
$119$	−4.30663	−0.394788
$120$	−5.83893	−0.533019
$121$	19.6042	1.78220
$122$	7.50579	0.679542
$123$	−28.1413	−2.53741
$124$	5.31894	0.477655
$125$	1.00000	0.0894427
$126$	−55.1217	−4.91063
$127$	−17.8836	−1.58692	−0.793459	−	0.608624i	$-0.791722\pi$
$127$	−17.8836	−1.58692	−0.793459	+	0.608624i	$0.791722\pi$
$128$	−12.4495	−1.10039
$129$	−2.76923	−0.243817
$130$	7.08100	0.621044
$131$	5.45196	0.476340	0.238170	−	0.971223i	$-0.423452\pi$
$131$	5.45196	0.476340	0.238170	+	0.971223i	$0.423452\pi$
$132$	−16.9616	−1.47632
$133$	35.5399	3.08170
$134$	−20.1766	−1.74299
$135$	−14.4017	−1.23950
$136$	−1.80588	−0.154853
$137$	3.83123	0.327324	0.163662	−	0.986516i	$-0.447669\pi$
$137$	3.83123	0.327324	0.163662	+	0.986516i	$0.447669\pi$
$138$	−26.3530	−2.24332
$139$	5.09033	0.431756	0.215878	−	0.976420i	$-0.430739\pi$
$139$	5.09033	0.431756	0.215878	+	0.976420i	$0.430739\pi$
$140$	4.08385	0.345148
$141$	−29.5513	−2.48867
$142$	1.71705	0.144092
$143$	−22.8140	−1.90780
$144$	−37.2510	−3.10425
$145$	−8.71206	−0.723498
$146$	24.7229	2.04608
$147$	−37.3351	−3.07935
$148$	0.438867	0.0360747
$149$	12.3403	1.01096	0.505480	−	0.862838i	$-0.331315\pi$
$149$	12.3403	1.01096	0.505480	+	0.862838i	$0.331315\pi$
$150$	5.55174	0.453298
$151$	13.9463	1.13493	0.567467	−	0.823396i	$-0.307923\pi$
$151$	13.9463	1.13493	0.567467	+	0.823396i	$0.307923\pi$
$152$	14.9028	1.20877
$153$	−7.45420	−0.602636
$154$	−40.9083	−3.29648
$155$	5.60910	0.450534
$156$	12.6441	1.01234
$157$	9.28085	0.740692	0.370346	−	0.928894i	$-0.379239\pi$
$157$	9.28085	0.740692	0.370346	+	0.928894i	$0.379239\pi$
$158$	4.71528	0.375128
$159$	−22.8734	−1.81398
$160$	4.96892	0.392827
$161$	−20.4427	−1.61111
$162$	−41.5570	−3.26502
$163$	23.5557	1.84502	0.922511	−	0.385970i	$-0.126133\pi$
$163$	23.5557	1.84502	0.922511	+	0.385970i	$0.126133\pi$
$164$	8.25335	0.644478
$165$	−17.8869	−1.39249
$166$	1.86908	0.145069
$167$	12.4756	0.965392	0.482696	−	0.875788i	$-0.339658\pi$
$167$	12.4756	0.965392	0.482696	+	0.875788i	$0.339658\pi$
$168$	−25.1461	−1.94007
$169$	4.00675	0.308212
$170$	1.71705	0.131692
$171$	61.5149	4.70416
$172$	0.812167	0.0619271
$173$	−7.63585	−0.580543	−0.290272	−	0.956944i	$-0.593746\pi$
$173$	−7.63585	−0.580543	−0.290272	+	0.956944i	$0.593746\pi$
$174$	−48.3671	−3.66670
$175$	4.30663	0.325551
$176$	−27.6457	−2.08387
$177$	4.36541	0.328124
$178$	24.1548	1.81048
$179$	19.7023	1.47262	0.736311	−	0.676643i	$-0.236566\pi$
$179$	19.7023	1.47262	0.736311	+	0.676643i	$0.236566\pi$
$180$	7.06859	0.526862
$181$	13.6516	1.01472	0.507358	−	0.861736i	$-0.330622\pi$
$181$	13.6516	1.01472	0.507358	+	0.861736i	$0.330622\pi$
$182$	30.4952	2.26046
$183$	14.1338	1.04480
$184$	−8.57213	−0.631946
$185$	0.462809	0.0340264
$186$	31.1403	2.28332
$187$	−5.53210	−0.404547
$188$	8.66689	0.632098
$189$	−62.0230	−4.51151
$190$	−14.1698	−1.02798
$191$	−12.3639	−0.894622	−0.447311	−	0.894379i	$-0.647618\pi$
$191$	−12.3639	−0.894622	−0.447311	+	0.894379i	$0.647618\pi$
$192$	−4.72953	−0.341325
$193$	−16.4564	−1.18456	−0.592279	−	0.805733i	$-0.701772\pi$
$193$	−16.4564	−1.18456	−0.592279	+	0.805733i	$0.701772\pi$
$194$	−15.7716	−1.13233
$195$	13.3339	0.954858
$196$	10.9497	0.782124
$197$	4.53939	0.323418	0.161709	−	0.986839i	$-0.448299\pi$
$197$	4.53939	0.323418	0.161709	+	0.986839i	$0.448299\pi$
$198$	−70.8068	−5.03202
$199$	−3.65135	−0.258838	−0.129419	−	0.991590i	$-0.541311\pi$
$199$	−3.65135	−0.258838	−0.129419	+	0.991590i	$0.541311\pi$
$200$	1.80588	0.127695
$201$	−37.9935	−2.67985
$202$	−15.4044	−1.08385
$203$	−37.5196	−2.63336
$204$	3.06604	0.214665
$205$	8.70359	0.607885
$206$	1.80763	0.125943
$207$	−35.3836	−2.45933
$208$	20.6086	1.42895
$209$	45.6530	3.15788
$210$	23.9093	1.64990
$211$	2.45699	0.169146	0.0845731	−	0.996417i	$-0.473047\pi$
$211$	2.45699	0.169146	0.0845731	+	0.996417i	$0.473047\pi$
$212$	6.70838	0.460734
$213$	3.23330	0.221542
$214$	−13.4533	−0.919649
$215$	0.856473	0.0584109
$216$	−26.0078	−1.76960
$217$	24.1563	1.63984
$218$	0.0740486	0.00501520
$219$	46.5545	3.14586
$220$	5.24592	0.353680
$221$	4.12392	0.277405
$222$	2.56939	0.172446
$223$	−1.15287	−0.0772020	−0.0386010	−	0.999255i	$-0.512290\pi$
$223$	−1.15287	−0.0772020	−0.0386010	+	0.999255i	$0.512290\pi$
$224$	21.3993	1.42980
$225$	7.45420	0.496947
$226$	15.2131	1.01196
$227$	−13.1107	−0.870188	−0.435094	−	0.900385i	$-0.643285\pi$
$227$	−13.1107	−0.870188	−0.435094	+	0.900385i	$0.643285\pi$
$228$	−25.3021	−1.67567
$229$	23.4652	1.55063	0.775313	−	0.631577i	$-0.217592\pi$
$229$	23.4652	1.55063	0.775313	+	0.631577i	$0.217592\pi$
$230$	8.15051	0.537428
$231$	−77.0324	−5.06836
$232$	−15.7329	−1.03292
$233$	−15.7298	−1.03049	−0.515247	−	0.857042i	$-0.672300\pi$
$233$	−15.7298	−1.03049	−0.515247	+	0.857042i	$0.672300\pi$
$234$	52.7832	3.45054
$235$	9.13969	0.596208
$236$	−1.28030	−0.0833403
$237$	8.87912	0.576761
$238$	7.39471	0.479328
$239$	−16.3331	−1.05650	−0.528251	−	0.849088i	$-0.677152\pi$
$239$	−16.3331	−1.05650	−0.528251	+	0.849088i	$0.677152\pi$
$240$	16.1578	1.04298
$241$	−8.36976	−0.539143	−0.269572	−	0.962980i	$-0.586882\pi$
$241$	−8.36976	−0.539143	−0.269572	+	0.962980i	$0.586882\pi$
$242$	−33.6614	−2.16383
$243$	−35.0486	−2.24837
$244$	−4.14519	−0.265369
$245$	11.5471	0.737715
$246$	48.3200	3.08077
$247$	−34.0322	−2.16542
$248$	10.1293	0.643214
$249$	3.51957	0.223044
$250$	−1.71705	−0.108596
$251$	−15.1622	−0.957030	−0.478515	−	0.878079i	$-0.658825\pi$
$251$	−15.1622	−0.957030	−0.478515	+	0.878079i	$0.658825\pi$
$252$	30.4418	1.91765
$253$	−26.2598	−1.65094
$254$	30.7072	1.92674
$255$	3.23330	0.202477
$256$	18.4509	1.15318
$257$	13.4510	0.839049	0.419524	−	0.907744i	$-0.362197\pi$
$257$	13.4510	0.839049	0.419524	+	0.907744i	$0.362197\pi$
$258$	4.75491	0.296028
$259$	1.99315	0.123848
$260$	−3.91059	−0.242525
$261$	−64.9415	−4.01978
$262$	−9.36131	−0.578344
$263$	28.1959	1.73864	0.869318	−	0.494253i	$-0.164558\pi$
$263$	28.1959	1.73864	0.869318	+	0.494253i	$0.164558\pi$
$264$	−32.3016	−1.98802
$265$	7.07434	0.434573
$266$	−61.0239	−3.74162
$267$	45.4847	2.78362
$268$	11.1428	0.680656
$269$	10.2726	0.626330	0.313165	−	0.949699i	$-0.398611\pi$
$269$	10.2726	0.626330	0.313165	+	0.949699i	$0.398611\pi$
$270$	24.7286	1.50493
$271$	−10.9636	−0.665993	−0.332997	−	0.942928i	$-0.608060\pi$
$271$	−10.9636	−0.665993	−0.332997	+	0.942928i	$0.608060\pi$
$272$	4.99732	0.303007
$273$	57.4240	3.47546
$274$	−6.57842	−0.397417
$275$	5.53210	0.333598
$276$	14.5539	0.876039
$277$	1.82504	0.109656	0.0548279	−	0.998496i	$-0.482539\pi$
$277$	1.82504	0.109656	0.0548279	+	0.998496i	$0.482539\pi$
$278$	−8.74036	−0.524212
$279$	41.8114	2.50318
$280$	7.77724	0.464779
$281$	−14.1441	−0.843765	−0.421882	−	0.906651i	$-0.638630\pi$
$281$	−14.1441	−0.843765	−0.421882	+	0.906651i	$0.638630\pi$
$282$	50.7412	3.02159
$283$	−1.86370	−0.110786	−0.0553928	−	0.998465i	$-0.517641\pi$
$283$	−1.86370	−0.110786	−0.0553928	+	0.998465i	$0.517641\pi$
$284$	−0.948270	−0.0562694
$285$	−26.6824	−1.58053
$286$	39.1728	2.31634
$287$	37.4831	2.21256
$288$	37.0393	2.18256
$289$	1.00000	0.0588235
$290$	14.9591	0.878427
$291$	−29.6987	−1.74097
$292$	−13.6536	−0.799018
$293$	−12.3321	−0.720449	−0.360224	−	0.932866i	$-0.617300\pi$
$293$	−12.3321	−0.720449	−0.360224	+	0.932866i	$0.617300\pi$
$294$	64.1063	3.73875
$295$	−1.35014	−0.0786083
$296$	0.835775	0.0485785
$297$	−79.6719	−4.62303
$298$	−21.1890	−1.22745
$299$	19.5754	1.13208
$300$	−3.06604	−0.177018
$301$	3.68851	0.212602
$302$	−23.9466	−1.37797
$303$	−29.0072	−1.66642
$304$	−41.2398	−2.36527
$305$	−4.37132	−0.250301
$306$	12.7993	0.731685
$307$	−23.0050	−1.31296	−0.656482	−	0.754342i	$-0.727956\pi$
$307$	−23.0050	−1.31296	−0.656482	+	0.754342i	$0.727956\pi$
$308$	22.5923	1.28731
$309$	3.40385	0.193638
$310$	−9.63113	−0.547011
$311$	11.1572	0.632666	0.316333	−	0.948648i	$-0.397548\pi$
$311$	11.1572	0.632666	0.316333	+	0.948648i	$0.397548\pi$
$312$	24.0793	1.36322
$313$	−8.75516	−0.494871	−0.247435	−	0.968904i	$-0.579588\pi$
$313$	−8.75516	−0.494871	−0.247435	+	0.968904i	$0.579588\pi$
$314$	−15.9357	−0.899304
$315$	32.1025	1.80877
$316$	−2.60409	−0.146492
$317$	−33.4341	−1.87784	−0.938922	−	0.344130i	$-0.888174\pi$
$317$	−33.4341	−1.87784	−0.938922	+	0.344130i	$0.888174\pi$
$318$	39.2749	2.20243
$319$	−48.1960	−2.69846
$320$	1.46276	0.0817707
$321$	−25.3332	−1.41396
$322$	35.1012	1.95611
$323$	−8.25238	−0.459175
$324$	22.9505	1.27503
$325$	−4.12392	−0.228754
$326$	−40.4463	−2.24011
$327$	0.139437	0.00771089
$328$	15.7176	0.867859
$329$	39.3613	2.17006
$330$	30.7128	1.69068
$331$	−13.8848	−0.763179	−0.381590	−	0.924332i	$-0.624623\pi$
$331$	−13.8848	−0.763179	−0.381590	+	0.924332i	$0.624623\pi$
$332$	−1.03223	−0.0566509
$333$	3.44987	0.189052
$334$	−21.4213	−1.17212
$335$	11.7507	0.642009
$336$	69.5858	3.79622
$337$	2.44240	0.133046	0.0665231	−	0.997785i	$-0.478809\pi$
$337$	2.44240	0.133046	0.0665231	+	0.997785i	$0.478809\pi$
$338$	−6.87981	−0.374212
$339$	28.6471	1.55589
$340$	−0.948270	−0.0514271
$341$	31.0301	1.68038
$342$	−105.624	−5.71151
$343$	19.5825	1.05736
$344$	1.54668	0.0833916
$345$	15.3478	0.826298
$346$	13.1112	0.704860
$347$	−21.7663	−1.16847	−0.584237	−	0.811583i	$-0.698606\pi$
$347$	−21.7663	−1.16847	−0.584237	+	0.811583i	$0.698606\pi$
$348$	26.7115	1.43189
$349$	6.39026	0.342063	0.171032	−	0.985266i	$-0.445290\pi$
$349$	6.39026	0.342063	0.171032	+	0.985266i	$0.445290\pi$
$350$	−7.39471	−0.395264
$351$	59.3917	3.17009
$352$	27.4885	1.46514
$353$	0.606624	0.0322874	0.0161437	−	0.999870i	$-0.494861\pi$
$353$	0.606624	0.0322874	0.0161437	+	0.999870i	$0.494861\pi$
$354$	−7.49563	−0.398389
$355$	−1.00000	−0.0530745
$356$	−13.3399	−0.707012
$357$	13.9246	0.736968
$358$	−33.8300	−1.78797
$359$	−25.2494	−1.33261	−0.666307	−	0.745677i	$-0.732126\pi$
$359$	−25.2494	−1.33261	−0.666307	+	0.745677i	$0.732126\pi$
$360$	13.4614	0.709476
$361$	49.1017	2.58430
$362$	−23.4405	−1.23201
$363$	−63.3860	−3.32690
$364$	−16.8415	−0.882733
$365$	−14.3985	−0.753650
$366$	−24.2684	−1.26853
$367$	15.8299	0.826314	0.413157	−	0.910660i	$-0.364426\pi$
$367$	15.8299	0.826314	0.413157	+	0.910660i	$0.364426\pi$
$368$	23.7213	1.23656
$369$	64.8783	3.37743
$370$	−0.794667	−0.0413128
$371$	30.4666	1.58175
$372$	−17.1977	−0.891660
$373$	−17.4932	−0.905763	−0.452881	−	0.891571i	$-0.649604\pi$
$373$	−17.4932	−0.905763	−0.452881	+	0.891571i	$0.649604\pi$
$374$	9.49891	0.491177
$375$	−3.23330	−0.166967
$376$	16.5051	0.851188
$377$	35.9279	1.85038
$378$	106.497	5.47760
$379$	20.2402	1.03967	0.519834	−	0.854267i	$-0.325994\pi$
$379$	20.2402	1.03967	0.519834	+	0.854267i	$0.325994\pi$
$380$	7.82548	0.401439
$381$	57.8231	2.96237
$382$	21.2295	1.08620
$383$	−14.7124	−0.751767	−0.375883	−	0.926667i	$-0.622661\pi$
$383$	−14.7124	−0.751767	−0.375883	+	0.926667i	$0.622661\pi$
$384$	40.2528	2.05414
$385$	23.8247	1.21422
$386$	28.2565	1.43822
$387$	6.38432	0.324533
$388$	8.71010	0.442189
$389$	14.4239	0.731319	0.365660	−	0.930749i	$-0.380843\pi$
$389$	14.4239	0.731319	0.365660	+	0.930749i	$0.380843\pi$
$390$	−22.8949	−1.15933
$391$	4.74680	0.240056
$392$	20.8526	1.05321
$393$	−17.6278	−0.889205
$394$	−7.79436	−0.392674
$395$	−2.74615	−0.138174
$396$	39.1042	1.96506
$397$	39.3243	1.97363	0.986815	−	0.161855i	$-0.0517476\pi$
$397$	39.3243	1.97363	0.986815	+	0.161855i	$0.0517476\pi$
$398$	6.26957	0.314265
$399$	−114.911	−5.75275
$400$	−4.99732	−0.249866
$401$	26.6351	1.33009	0.665046	−	0.746802i	$-0.268412\pi$
$401$	26.6351	1.33009	0.665046	+	0.746802i	$0.268412\pi$
$402$	65.2368	3.25371
$403$	−23.1315	−1.15226
$404$	8.50731	0.423255
$405$	24.2025	1.20263
$406$	64.4232	3.19727
$407$	2.56030	0.126910
$408$	5.83893	0.289070
$409$	−20.1721	−0.997446	−0.498723	−	0.866761i	$-0.666197\pi$
$409$	−20.1721	−0.997446	−0.498723	+	0.866761i	$0.666197\pi$
$410$	−14.9445	−0.738057
$411$	−12.3875	−0.611030
$412$	−0.998291	−0.0491822
$413$	−5.81456	−0.286116
$414$	60.7555	2.98597
$415$	−1.08854	−0.0534343
$416$	−20.4914	−1.00468
$417$	−16.4585	−0.805978
$418$	−78.3886	−3.83411
$419$	−0.141426	−0.00690910	−0.00345455	−	0.999994i	$-0.501100\pi$
$419$	−0.141426	−0.00690910	−0.00345455	+	0.999994i	$0.501100\pi$
$420$	−13.2043	−0.644303
$421$	−20.5697	−1.00251	−0.501253	−	0.865301i	$-0.667127\pi$
$421$	−20.5697	−1.00251	−0.501253	+	0.865301i	$0.667127\pi$
$422$	−4.21878	−0.205367
$423$	68.1291	3.31255
$424$	12.7754	0.620427
$425$	−1.00000	−0.0485071
$426$	−5.55174	−0.268983
$427$	−18.8257	−0.911038
$428$	7.42980	0.359133
$429$	73.7643	3.56137
$430$	−1.47061	−0.0709190
$431$	4.80958	0.231669	0.115835	−	0.993269i	$-0.463046\pi$
$431$	4.80958	0.231669	0.115835	+	0.993269i	$0.463046\pi$
$432$	71.9702	3.46267
$433$	21.4637	1.03148	0.515740	−	0.856745i	$-0.327517\pi$
$433$	21.4637	1.03148	0.515740	+	0.856745i	$0.327517\pi$
$434$	−41.4777	−1.99099
$435$	28.1687	1.35058
$436$	−0.0408945	−0.00195849
$437$	−39.1724	−1.87387
$438$	−79.9365	−3.81951
$439$	−3.27835	−0.156467	−0.0782334	−	0.996935i	$-0.524928\pi$
$439$	−3.27835	−0.156467	−0.0782334	+	0.996935i	$0.524928\pi$
$440$	9.99029	0.476268
$441$	86.0741	4.09877
$442$	−7.08100	−0.336809
$443$	2.02231	0.0960829	0.0480414	−	0.998845i	$-0.484702\pi$
$443$	2.02231	0.0960829	0.0480414	+	0.998845i	$0.484702\pi$
$444$	−1.41899	−0.0673422
$445$	−14.0676	−0.666868
$446$	1.97954	0.0937339
$447$	−39.9000	−1.88720
$448$	6.29956	0.297626
$449$	32.3137	1.52498	0.762489	−	0.647002i	$-0.223977\pi$
$449$	32.3137	1.52498	0.762489	+	0.647002i	$0.223977\pi$
$450$	−12.7993	−0.603363
$451$	48.1491	2.26725
$452$	−8.40168	−0.395182
$453$	−45.0925	−2.11863
$454$	22.5118	1.05653
$455$	−17.7602	−0.832612
$456$	−48.1851	−2.25647
$457$	−11.3317	−0.530076	−0.265038	−	0.964238i	$-0.585384\pi$
$457$	−11.3317	−0.530076	−0.265038	+	0.964238i	$0.585384\pi$
$458$	−40.2910	−1.88268
$459$	14.4017	0.672216
$460$	−4.50125	−0.209872
$461$	1.36553	0.0635990	0.0317995	−	0.999494i	$-0.489876\pi$
$461$	1.36553	0.0635990	0.0317995	+	0.999494i	$0.489876\pi$
$462$	132.269	6.15369
$463$	25.4259	1.18164	0.590820	−	0.806804i	$-0.298804\pi$
$463$	25.4259	1.18164	0.590820	+	0.806804i	$0.298804\pi$
$464$	43.5370	2.02115
$465$	−18.1359	−0.841032
$466$	27.0089	1.25116
$467$	−9.17702	−0.424662	−0.212331	−	0.977198i	$-0.568106\pi$
$467$	−9.17702	−0.424662	−0.212331	+	0.977198i	$0.568106\pi$
$468$	−29.1503	−1.34747
$469$	50.6059	2.33676
$470$	−15.6933	−0.723879
$471$	−30.0077	−1.38268
$472$	−2.43819	−0.112227
$473$	4.73809	0.217858
$474$	−15.2459	−0.700268
$475$	8.25238	0.378645
$476$	−4.08385	−0.187183
$477$	52.7335	2.41450
$478$	28.0448	1.28274
$479$	−27.0210	−1.23462	−0.617310	−	0.786720i	$-0.711777\pi$
$479$	−27.0210	−1.23462	−0.617310	+	0.786720i	$0.711777\pi$
$480$	−16.0660	−0.733308
$481$	−1.90859	−0.0870241
$482$	14.3713	0.654595
$483$	66.0973	3.00753
$484$	18.5900	0.845001
$485$	9.18526	0.417081
$486$	60.1803	2.72983
$487$	−37.7106	−1.70883	−0.854416	−	0.519589i	$-0.826085\pi$
$487$	−37.7106	−1.70883	−0.854416	+	0.519589i	$0.826085\pi$
$488$	−7.89407	−0.357348
$489$	−76.1624	−3.44418
$490$	−19.8269	−0.895689
$491$	8.54760	0.385748	0.192874	−	0.981224i	$-0.438219\pi$
$491$	8.54760	0.385748	0.192874	+	0.981224i	$0.438219\pi$
$492$	−26.6855	−1.20308
$493$	8.71206	0.392372
$494$	58.4350	2.62912
$495$	41.2374	1.85348
$496$	−28.0305	−1.25861
$497$	−4.30663	−0.193179
$498$	−6.04328	−0.270806
$499$	16.8927	0.756223	0.378111	−	0.925760i	$-0.376574\pi$
$499$	16.8927	0.756223	0.378111	+	0.925760i	$0.376574\pi$
$500$	0.948270	0.0424079
$501$	−40.3373	−1.80214
$502$	26.0343	1.16197
$503$	−11.4975	−0.512647	−0.256324	−	0.966591i	$-0.582511\pi$
$503$	−11.4975	−0.512647	−0.256324	+	0.966591i	$0.582511\pi$
$504$	57.9731	2.58233
$505$	8.97141	0.399222
$506$	45.0894	2.00447
$507$	−12.9550	−0.575352
$508$	−16.9585	−0.752413
$509$	6.44898	0.285846	0.142923	−	0.989734i	$-0.454350\pi$
$509$	6.44898	0.285846	0.142923	+	0.989734i	$0.454350\pi$
$510$	−5.55174	−0.245835
$511$	−62.0088	−2.74311
$512$	−6.78218	−0.299733
$513$	−118.849	−5.24729
$514$	−23.0960	−1.01872
$515$	−1.05275	−0.0463897
$516$	−2.62598	−0.115602
$517$	50.5617	2.22370
$518$	−3.42234	−0.150369
$519$	24.6890	1.08373
$520$	−7.44730	−0.326586
$521$	−30.1947	−1.32285	−0.661427	−	0.750010i	$-0.730049\pi$
$521$	−30.1947	−1.32285	−0.661427	+	0.750010i	$0.730049\pi$
$522$	111.508	4.88057
$523$	20.6033	0.900921	0.450460	−	0.892796i	$-0.351260\pi$
$523$	20.6033	0.900921	0.450460	+	0.892796i	$0.351260\pi$
$524$	5.16993	0.225850
$525$	−13.9246	−0.607720
$526$	−48.4139	−2.11095
$527$	−5.60910	−0.244336
$528$	89.3867	3.89006
$529$	−0.467890	−0.0203431
$530$	−12.1470	−0.527633
$531$	−10.0642	−0.436750
$532$	33.7014	1.46114
$533$	−35.8929	−1.55470
$534$	−78.0996	−3.37970
$535$	7.83512	0.338742
$536$	21.2203	0.916577
$537$	−63.7035	−2.74901
$538$	−17.6386	−0.760452
$539$	63.8795	2.75149
$540$	−13.6567	−0.587692
$541$	−25.7593	−1.10748	−0.553740	−	0.832689i	$-0.686800\pi$
$541$	−25.7593	−1.10748	−0.553740	+	0.832689i	$0.686800\pi$
$542$	18.8251	0.808609
$543$	−44.1396	−1.89421
$544$	−4.96892	−0.213040
$545$	−0.0431254	−0.00184729
$546$	−98.6001	−4.21969
$547$	22.3685	0.956407	0.478204	−	0.878249i	$-0.341288\pi$
$547$	22.3685	0.956407	0.478204	+	0.878249i	$0.341288\pi$
$548$	3.63304	0.155196
$549$	−32.5847	−1.39068
$550$	−9.49891	−0.405035
$551$	−71.8952	−3.06284
$552$	27.7162	1.17968
$553$	−11.8267	−0.502921
$554$	−3.13368	−0.133137
$555$	−1.49640	−0.0635185
$556$	4.82701	0.204711
$557$	2.99082	0.126725	0.0633625	−	0.997991i	$-0.479818\pi$
$557$	2.99082	0.126725	0.0633625	+	0.997991i	$0.479818\pi$
$558$	−71.7923	−3.03921
$559$	−3.53203	−0.149389
$560$	−21.5216	−0.909455
$561$	17.8869	0.755186
$562$	24.2861	1.02445
$563$	−33.3896	−1.40720	−0.703602	−	0.710594i	$-0.748426\pi$
$563$	−33.3896	−1.40720	−0.703602	+	0.710594i	$0.748426\pi$
$564$	−28.0226	−1.17996
$565$	−8.86002	−0.372744
$566$	3.20008	0.134509
$567$	104.231	4.37730
$568$	−1.80588	−0.0757729
$569$	−11.0840	−0.464663	−0.232332	−	0.972637i	$-0.574635\pi$
$569$	−11.0840	−0.464663	−0.232332	+	0.972637i	$0.574635\pi$
$570$	45.8150	1.91898
$571$	−28.9863	−1.21304	−0.606520	−	0.795068i	$-0.707435\pi$
$571$	−28.9863	−1.21304	−0.606520	+	0.795068i	$0.707435\pi$
$572$	−21.6338	−0.904554
$573$	39.9762	1.67003
$574$	−64.3605	−2.68636
$575$	−4.74680	−0.197955
$576$	10.9037	0.454321
$577$	8.23533	0.342841	0.171421	−	0.985198i	$-0.445164\pi$
$577$	8.23533	0.342841	0.171421	+	0.985198i	$0.445164\pi$
$578$	−1.71705	−0.0714200
$579$	53.2085	2.21127
$580$	−8.26139	−0.343035
$581$	−4.68793	−0.194488
$582$	50.9942	2.11378
$583$	39.1360	1.62085
$584$	−26.0018	−1.07596
$585$	−30.7406	−1.27097
$586$	21.1749	0.874725
$587$	−21.0401	−0.868417	−0.434209	−	0.900812i	$-0.642972\pi$
$587$	−21.0401	−0.868417	−0.434209	+	0.900812i	$0.642972\pi$
$588$	−35.4037	−1.46002
$589$	46.2884	1.90728
$590$	2.31826	0.0954415
$591$	−14.6772	−0.603738
$592$	−2.31281	−0.0950557
$593$	1.19135	0.0489228	0.0244614	−	0.999701i	$-0.492213\pi$
$593$	1.19135	0.0489228	0.0244614	+	0.999701i	$0.492213\pi$
$594$	136.801	5.61301
$595$	−4.30663	−0.176555
$596$	11.7020	0.479331
$597$	11.8059	0.483183
$598$	−33.6121	−1.37450
$599$	−40.0265	−1.63544	−0.817718	−	0.575618i	$-0.804761\pi$
$599$	−40.0265	−1.63544	−0.817718	+	0.575618i	$0.804761\pi$
$600$	−5.83893	−0.238373
$601$	27.3570	1.11591	0.557957	−	0.829870i	$-0.311585\pi$
$601$	27.3570	1.11591	0.557957	+	0.829870i	$0.311585\pi$
$602$	−6.33337	−0.258129
$603$	87.5920	3.56702
$604$	13.2249	0.538112
$605$	19.6042	0.797022
$606$	49.8069	2.02327
$607$	41.6642	1.69110	0.845549	−	0.533897i	$-0.179273\pi$
$607$	41.6642	1.69110	0.845549	+	0.533897i	$0.179273\pi$
$608$	41.0054	1.66299
$609$	121.312	4.91581
$610$	7.50579	0.303900
$611$	−37.6914	−1.52483
$612$	−7.06859	−0.285731
$613$	8.66315	0.349901	0.174951	−	0.984577i	$-0.444023\pi$
$613$	8.66315	0.349901	0.174951	+	0.984577i	$0.444023\pi$
$614$	39.5008	1.59412
$615$	−28.1413	−1.13477
$616$	43.0245	1.73351
$617$	−19.0256	−0.765941	−0.382970	−	0.923761i	$-0.625099\pi$
$617$	−19.0256	−0.765941	−0.382970	+	0.923761i	$0.625099\pi$
$618$	−5.84459	−0.235104
$619$	−0.102595	−0.00412364	−0.00206182	−	0.999998i	$-0.500656\pi$
$619$	−0.102595	−0.00412364	−0.00206182	+	0.999998i	$0.500656\pi$
$620$	5.31894	0.213614
$621$	68.3622	2.74328
$622$	−19.1575	−0.768145
$623$	−60.5839	−2.42724
$624$	−66.6336	−2.66748
$625$	1.00000	0.0400000
$626$	15.0331	0.600842
$627$	−147.610	−5.89496
$628$	8.80075	0.351188
$629$	−0.462809	−0.0184534
$630$	−55.1217	−2.19610
$631$	42.7966	1.70371	0.851854	−	0.523780i	$-0.175478\pi$
$631$	42.7966	1.70371	0.851854	+	0.523780i	$0.175478\pi$
$632$	−4.95921	−0.197267
$633$	−7.94418	−0.315753
$634$	57.4080	2.27996
$635$	−17.8836	−0.709691
$636$	−21.6902	−0.860072
$637$	−47.6192	−1.88674
$638$	82.7551	3.27631
$639$	−7.45420	−0.294884
$640$	−12.4495	−0.492108
$641$	−21.5917	−0.852821	−0.426411	−	0.904530i	$-0.640222\pi$
$641$	−21.5917	−0.852821	−0.426411	+	0.904530i	$0.640222\pi$
$642$	43.4985	1.71675
$643$	35.9218	1.41662	0.708308	−	0.705904i	$-0.249459\pi$
$643$	35.9218	1.41662	0.708308	+	0.705904i	$0.249459\pi$
$644$	−19.3852	−0.763884
$645$	−2.76923	−0.109038
$646$	14.1698	0.557502
$647$	2.60860	0.102554	0.0512772	−	0.998684i	$-0.483671\pi$
$647$	2.60860	0.102554	0.0512772	+	0.998684i	$0.483671\pi$
$648$	43.7067	1.71696
$649$	−7.46912	−0.293189
$650$	7.08100	0.277739
$651$	−78.1046	−3.06116
$652$	22.3371	0.874789
$653$	40.5180	1.58559	0.792796	−	0.609486i	$-0.208624\pi$
$653$	40.5180	1.58559	0.792796	+	0.609486i	$0.208624\pi$
$654$	−0.239421	−0.00936210
$655$	5.45196	0.213026
$656$	−43.4946	−1.69818
$657$	−107.329	−4.18730
$658$	−67.5854	−2.63475
$659$	−26.6690	−1.03888	−0.519439	−	0.854508i	$-0.673859\pi$
$659$	−26.6690	−1.03888	−0.519439	+	0.854508i	$0.673859\pi$
$660$	−16.9616	−0.660230
$661$	12.1870	0.474020	0.237010	−	0.971507i	$-0.423833\pi$
$661$	12.1870	0.474020	0.237010	+	0.971507i	$0.423833\pi$
$662$	23.8410	0.926606
$663$	−13.3339	−0.517844
$664$	−1.96577	−0.0762865
$665$	35.5399	1.37818
$666$	−5.92361	−0.229535
$667$	41.3544	1.60125
$668$	11.8302	0.457726
$669$	3.72757	0.144116
$670$	−20.1766	−0.779489
$671$	−24.1826	−0.933559
$672$	−69.1902	−2.66907
$673$	35.3265	1.36174	0.680869	−	0.732405i	$-0.261602\pi$
$673$	35.3265	1.36174	0.680869	+	0.732405i	$0.261602\pi$
$674$	−4.19373	−0.161537
$675$	−14.4017	−0.554323
$676$	3.79948	0.146134
$677$	−9.74849	−0.374665	−0.187333	−	0.982297i	$-0.559984\pi$
$677$	−9.74849	−0.374665	−0.187333	+	0.982297i	$0.559984\pi$
$678$	−49.1885	−1.88907
$679$	39.5575	1.51808
$680$	−1.80588	−0.0692522
$681$	42.3908	1.62442
$682$	−53.2804	−2.04021
$683$	−6.13991	−0.234937	−0.117469	−	0.993077i	$-0.537478\pi$
$683$	−6.13991	−0.234937	−0.117469	+	0.993077i	$0.537478\pi$
$684$	58.3327	2.23041
$685$	3.83123	0.146384
$686$	−33.6242	−1.28378
$687$	−75.8700	−2.89462
$688$	−4.28007	−0.163176
$689$	−29.1740	−1.11144
$690$	−26.3530	−1.00324
$691$	45.1667	1.71822	0.859110	−	0.511790i	$-0.171018\pi$
$691$	45.1667	1.71822	0.859110	+	0.511790i	$0.171018\pi$
$692$	−7.24085	−0.275256
$693$	177.594	6.74625
$694$	37.3738	1.41869
$695$	5.09033	0.193087
$696$	50.8691	1.92819
$697$	−8.70359	−0.329672
$698$	−10.9724	−0.415312
$699$	50.8591	1.92367
$700$	4.08385	0.154355
$701$	15.8553	0.598846	0.299423	−	0.954120i	$-0.403206\pi$
$701$	15.8553	0.598846	0.299423	+	0.954120i	$0.403206\pi$
$702$	−101.979	−3.84894
$703$	3.81927	0.144047
$704$	8.09213	0.304984
$705$	−29.5513	−1.11297
$706$	−1.04161	−0.0392014
$707$	38.6365	1.45308
$708$	4.13958	0.155575
$709$	−49.5247	−1.85994	−0.929969	−	0.367637i	$-0.880167\pi$
$709$	−49.5247	−1.85994	−0.929969	+	0.367637i	$0.880167\pi$
$710$	1.71705	0.0644398
$711$	−20.4704	−0.767698
$712$	−25.4043	−0.952068
$713$	−26.6253	−0.997125
$714$	−23.9093	−0.894783
$715$	−22.8140	−0.853194
$716$	18.6831	0.698222
$717$	52.8098	1.97222
$718$	43.3546	1.61798
$719$	−30.3962	−1.13359	−0.566794	−	0.823859i	$-0.691817\pi$
$719$	−30.3962	−1.13359	−0.566794	+	0.823859i	$0.691817\pi$
$720$	−37.2510	−1.38826
$721$	−4.53380	−0.168848
$722$	−84.3103	−3.13770
$723$	27.0619	1.00644
$724$	12.9454	0.481112
$725$	−8.71206	−0.323558
$726$	108.837	4.03932
$727$	−0.908020	−0.0336766	−0.0168383	−	0.999858i	$-0.505360\pi$
$727$	−0.908020	−0.0336766	−0.0168383	+	0.999858i	$0.505360\pi$
$728$	−32.0728	−1.18870
$729$	40.7149	1.50796
$730$	24.7229	0.915036
$731$	−0.856473	−0.0316778
$732$	13.4026	0.495375
$733$	38.6624	1.42803	0.714013	−	0.700132i	$-0.246876\pi$
$733$	38.6624	1.42803	0.714013	+	0.700132i	$0.246876\pi$
$734$	−27.1808	−1.00326
$735$	−37.3351	−1.37713
$736$	−23.5864	−0.869408
$737$	65.0060	2.39453
$738$	−111.399	−4.10067
$739$	29.1567	1.07255	0.536273	−	0.844044i	$-0.319832\pi$
$739$	29.1567	1.07255	0.536273	+	0.844044i	$0.319832\pi$
$740$	0.438867	0.0161331
$741$	110.036	4.04228
$742$	−52.3127	−1.92046
$743$	−52.1270	−1.91235	−0.956177	−	0.292788i	$-0.905417\pi$
$743$	−52.1270	−1.91235	−0.956177	+	0.292788i	$0.905417\pi$
$744$	−32.7512	−1.20072
$745$	12.3403	0.452115
$746$	30.0367	1.09972
$747$	−8.11419	−0.296883
$748$	−5.24592	−0.191810
$749$	33.7430	1.23294
$750$	5.55174	0.202721
$751$	−42.9538	−1.56741	−0.783704	−	0.621135i	$-0.786672\pi$
$751$	−42.9538	−1.56741	−0.783704	+	0.621135i	$0.786672\pi$
$752$	−45.6740	−1.66556
$753$	49.0239	1.78653
$754$	−61.6901	−2.24662
$755$	13.9463	0.507558
$756$	−58.8145	−2.13906
$757$	47.7083	1.73399	0.866995	−	0.498317i	$-0.166049\pi$
$757$	47.7083	1.73399	0.866995	+	0.498317i	$0.166049\pi$
$758$	−34.7534	−1.26230
$759$	84.9056	3.08188
$760$	14.9028	0.540580
$761$	−21.5965	−0.782872	−0.391436	−	0.920205i	$-0.628022\pi$
$761$	−21.5965	−0.782872	−0.391436	+	0.920205i	$0.628022\pi$
$762$	−99.2853	−3.59673
$763$	−0.185725	−0.00672370
$764$	−11.7243	−0.424171
$765$	−7.45420	−0.269507
$766$	25.2619	0.912749
$767$	5.56788	0.201045
$768$	−59.6571	−2.15269
$769$	−12.3008	−0.443577	−0.221789	−	0.975095i	$-0.571190\pi$
$769$	−12.3008	−0.443577	−0.221789	+	0.975095i	$0.571190\pi$
$770$	−40.9083	−1.47423
$771$	−43.4910	−1.56629
$772$	−15.6051	−0.561640
$773$	29.2853	1.05332	0.526660	−	0.850076i	$-0.323444\pi$
$773$	29.2853	1.05332	0.526660	+	0.850076i	$0.323444\pi$
$774$	−10.9622	−0.394028
$775$	5.60910	0.201485
$776$	16.5874	0.595455
$777$	−6.44443	−0.231193
$778$	−24.7665	−0.887924
$779$	71.8253	2.57341
$780$	12.6441	0.452731
$781$	−5.53210	−0.197954
$782$	−8.15051	−0.291461
$783$	125.469	4.48389
$784$	−57.7044	−2.06087
$785$	9.28085	0.331248
$786$	30.2679	1.07962
$787$	−33.5112	−1.19454	−0.597272	−	0.802038i	$-0.703749\pi$
$787$	−33.5112	−1.19454	−0.597272	+	0.802038i	$0.703749\pi$
$788$	4.30456	0.153344
$789$	−91.1658	−3.24559
$790$	4.71528	0.167762
$791$	−38.1568	−1.35670
$792$	74.4696	2.64616
$793$	18.0270	0.640157
$794$	−67.5219	−2.39626
$795$	−22.8734	−0.811237
$796$	−3.46247	−0.122724
$797$	−45.8562	−1.62431	−0.812155	−	0.583441i	$-0.801706\pi$
$797$	−45.8562	−1.62431	−0.812155	+	0.583441i	$0.801706\pi$
$798$	197.308	6.98464
$799$	−9.13969	−0.323339
$800$	4.96892	0.175678
$801$	−104.863	−3.70514
$802$	−45.7338	−1.61492
$803$	−79.6537	−2.81092
$804$	−36.0281	−1.27061
$805$	−20.4427	−0.720511
$806$	39.7180	1.39901
$807$	−33.2143	−1.16920
$808$	16.2012	0.569958
$809$	−19.7849	−0.695599	−0.347800	−	0.937569i	$-0.613071\pi$
$809$	−19.7849	−0.695599	−0.347800	+	0.937569i	$0.613071\pi$
$810$	−41.5570	−1.46016
$811$	−40.9872	−1.43925	−0.719627	−	0.694360i	$-0.755687\pi$
$811$	−40.9872	−1.43925	−0.719627	+	0.694360i	$0.755687\pi$
$812$	−35.5787	−1.24857
$813$	35.4487	1.24324
$814$	−4.39618	−0.154086
$815$	23.5557	0.825119
$816$	−16.1578	−0.565637
$817$	7.06793	0.247276
$818$	34.6365	1.21104
$819$	−132.388	−4.62602
$820$	8.25335	0.288219
$821$	0.141390	0.00493456	0.00246728	−	0.999997i	$-0.499215\pi$
$821$	0.141390	0.00493456	0.00246728	+	0.999997i	$0.499215\pi$
$822$	21.2700	0.741876
$823$	20.2324	0.705256	0.352628	−	0.935764i	$-0.385288\pi$
$823$	20.2324	0.705256	0.352628	+	0.935764i	$0.385288\pi$
$824$	−1.90114	−0.0662292
$825$	−17.8869	−0.622743
$826$	9.98391	0.347385
$827$	31.2245	1.08578	0.542892	−	0.839803i	$-0.317329\pi$
$827$	31.2245	1.08578	0.542892	+	0.839803i	$0.317329\pi$
$828$	−33.5532	−1.16605
$829$	37.3315	1.29658	0.648288	−	0.761395i	$-0.275485\pi$
$829$	37.3315	1.29658	0.648288	+	0.761395i	$0.275485\pi$
$830$	1.86908	0.0648767
$831$	−5.90088	−0.204699
$832$	−6.03231	−0.209133
$833$	−11.5471	−0.400082
$834$	28.2602	0.978570
$835$	12.4756	0.431736
$836$	43.2913	1.49726
$837$	−80.7809	−2.79220
$838$	0.242836	0.00838862
$839$	41.3332	1.42698	0.713491	−	0.700664i	$-0.247113\pi$
$839$	41.3332	1.42698	0.713491	+	0.700664i	$0.247113\pi$
$840$	−25.1461	−0.867624
$841$	46.9001	1.61724
$842$	35.3193	1.21718
$843$	45.7320	1.57509
$844$	2.32989	0.0801981
$845$	4.00675	0.137836
$846$	−116.981	−4.02190
$847$	84.4278	2.90097
$848$	−35.3528	−1.21402
$849$	6.02590	0.206808
$850$	1.71705	0.0588944
$851$	−2.19686	−0.0753074
$852$	3.06604	0.105041
$853$	35.6812	1.22170	0.610851	−	0.791746i	$-0.290827\pi$
$853$	35.6812	1.22170	0.610851	+	0.791746i	$0.290827\pi$
$854$	32.3247	1.10613
$855$	61.5149	2.10376
$856$	14.1493	0.483611
$857$	−40.3088	−1.37692	−0.688462	−	0.725273i	$-0.741714\pi$
$857$	−40.3088	−1.37692	−0.688462	+	0.725273i	$0.741714\pi$
$858$	−126.657	−4.32401
$859$	8.52249	0.290784	0.145392	−	0.989374i	$-0.453556\pi$
$859$	8.52249	0.290784	0.145392	+	0.989374i	$0.453556\pi$
$860$	0.812167	0.0276947
$861$	−121.194	−4.13028
$862$	−8.25831	−0.281279
$863$	−2.02569	−0.0689553	−0.0344776	−	0.999405i	$-0.510977\pi$
$863$	−2.02569	−0.0689553	−0.0344776	+	0.999405i	$0.510977\pi$
$864$	−71.5610	−2.43456
$865$	−7.63585	−0.259627
$866$	−36.8543	−1.25236
$867$	−3.23330	−0.109808
$868$	22.9067	0.777505
$869$	−15.1920	−0.515353
$870$	−48.3671	−1.63980
$871$	−48.4590	−1.64197
$872$	−0.0778791	−0.00263732
$873$	68.4688	2.31732
$874$	67.2610	2.27514
$875$	4.30663	0.145591
$876$	44.1462	1.49156
$877$	−28.6510	−0.967475	−0.483738	−	0.875213i	$-0.660721\pi$
$877$	−28.6510	−0.967475	−0.483738	+	0.875213i	$0.660721\pi$
$878$	5.62909	0.189973
$879$	39.8733	1.34489
$880$	−27.6457	−0.931937
$881$	27.3498	0.921438	0.460719	−	0.887546i	$-0.347592\pi$
$881$	27.3498	0.921438	0.460719	+	0.887546i	$0.347592\pi$
$882$	−147.794	−4.97648
$883$	3.53927	0.119106	0.0595529	−	0.998225i	$-0.481032\pi$
$883$	3.53927	0.119106	0.0595529	+	0.998225i	$0.481032\pi$
$884$	3.91059	0.131527
$885$	4.36541	0.146742
$886$	−3.47241	−0.116658
$887$	−14.5669	−0.489109	−0.244554	−	0.969636i	$-0.578642\pi$
$887$	−14.5669	−0.489109	−0.244554	+	0.969636i	$0.578642\pi$
$888$	−2.70231	−0.0906835
$889$	−77.0183	−2.58311
$890$	24.1548	0.809671
$891$	133.891	4.48551
$892$	−1.09323	−0.0366041
$893$	75.4242	2.52397
$894$	68.5103	2.29133
$895$	19.7023	0.658577
$896$	−53.6152	−1.79116
$897$	−63.2932	−2.11330
$898$	−55.4843	−1.85154
$899$	−48.8669	−1.62980
$900$	7.06859	0.235620
$901$	−7.07434	−0.235680
$902$	−82.6746	−2.75276
$903$	−11.9260	−0.396874
$904$	−16.0001	−0.532155
$905$	13.6516	0.453794
$906$	77.4263	2.57232
$907$	−5.86414	−0.194715	−0.0973577	−	0.995249i	$-0.531039\pi$
$907$	−5.86414	−0.194715	−0.0973577	+	0.995249i	$0.531039\pi$
$908$	−12.4325	−0.412587
$909$	66.8746	2.21809
$910$	30.4952	1.01091
$911$	13.7141	0.454369	0.227185	−	0.973852i	$-0.427048\pi$
$911$	13.7141	0.454369	0.227185	+	0.973852i	$0.427048\pi$
$912$	133.340	4.41534
$913$	−6.02191	−0.199296
$914$	19.4572	0.643586
$915$	14.1338	0.467248
$916$	22.2514	0.735206
$917$	23.4796	0.775364
$918$	−24.7286	−0.816164
$919$	20.2019	0.666398	0.333199	−	0.942857i	$-0.391872\pi$
$919$	20.2019	0.666398	0.333199	+	0.942857i	$0.391872\pi$
$920$	−8.57213	−0.282615
$921$	74.3819	2.45097
$922$	−2.34469	−0.0772181
$923$	4.12392	0.135741
$924$	−73.0474	−2.40308
$925$	0.462809	0.0152171
$926$	−43.6575	−1.43468
$927$	−7.84741	−0.257743
$928$	−43.2895	−1.42105
$929$	18.2400	0.598434	0.299217	−	0.954185i	$-0.403274\pi$
$929$	18.2400	0.598434	0.299217	+	0.954185i	$0.403274\pi$
$930$	31.1403	1.02113
$931$	95.2908	3.12303
$932$	−14.9161	−0.488593
$933$	−36.0745	−1.18103
$934$	15.7574	0.515599
$935$	−5.53210	−0.180919
$936$	−55.5136	−1.81452
$937$	2.21580	0.0723869	0.0361935	−	0.999345i	$-0.488477\pi$
$937$	2.21580	0.0723869	0.0361935	+	0.999345i	$0.488477\pi$
$938$	−86.8930	−2.83716
$939$	28.3080	0.923797
$940$	8.66689	0.282683
$941$	45.1328	1.47129	0.735644	−	0.677369i	$-0.236880\pi$
$941$	45.1328	1.47129	0.735644	+	0.677369i	$0.236880\pi$
$942$	51.5248	1.67877
$943$	−41.3142	−1.34537
$944$	6.74710	0.219599
$945$	−62.0230	−2.01761
$946$	−8.13556	−0.264510
$947$	54.1546	1.75979	0.879894	−	0.475170i	$-0.157613\pi$
$947$	54.1546	1.75979	0.879894	+	0.475170i	$0.157613\pi$
$948$	8.41980	0.273462
$949$	59.3781	1.92750
$950$	−14.1698	−0.459728
$951$	108.102	3.50545
$952$	−7.77724	−0.252062
$953$	17.7375	0.574574	0.287287	−	0.957845i	$-0.407247\pi$
$953$	17.7375	0.574574	0.287287	+	0.957845i	$0.407247\pi$
$954$	−90.5463	−2.93154
$955$	−12.3639	−0.400087
$956$	−15.4882	−0.500925
$957$	155.832	5.03733
$958$	46.3964	1.49900
$959$	16.4997	0.532803
$960$	−4.72953	−0.152645
$961$	0.462041	0.0149046
$962$	3.27715	0.105659
$963$	58.4045	1.88206
$964$	−7.93678	−0.255627
$965$	−16.4564	−0.529751
$966$	−113.493	−3.65156
$967$	16.0935	0.517533	0.258766	−	0.965940i	$-0.416684\pi$
$967$	16.0935	0.517533	0.258766	+	0.965940i	$0.416684\pi$
$968$	35.4027	1.13789
$969$	26.6824	0.857161
$970$	−15.7716	−0.506395
$971$	−4.91363	−0.157686	−0.0788430	−	0.996887i	$-0.525123\pi$
$971$	−4.91363	−0.157686	−0.0788430	+	0.996887i	$0.525123\pi$
$972$	−33.2355	−1.06603
$973$	21.9222	0.702793
$974$	64.7512	2.07476
$975$	13.3339	0.427025
$976$	21.8449	0.699238
$977$	6.95529	0.222520	0.111260	−	0.993791i	$-0.464511\pi$
$977$	6.95529	0.222520	0.111260	+	0.993791i	$0.464511\pi$
$978$	130.775	4.18172
$979$	−77.8234	−2.48725
$980$	10.9497	0.349776
$981$	−0.321465	−0.0102636
$982$	−14.6767	−0.468352
$983$	25.2910	0.806657	0.403329	−	0.915055i	$-0.367853\pi$
$983$	25.2910	0.806657	0.403329	+	0.915055i	$0.367853\pi$
$984$	−50.8197	−1.62007
$985$	4.53939	0.144637
$986$	−14.9591	−0.476394
$987$	−127.267	−4.05094
$988$	−32.2717	−1.02670
$989$	−4.06550	−0.129275
$990$	−70.8068	−2.25039
$991$	29.7187	0.944044	0.472022	−	0.881587i	$-0.343524\pi$
$991$	29.7187	0.944044	0.472022	+	0.881587i	$0.343524\pi$
$992$	27.8712	0.884910
$993$	44.8938	1.42466
$994$	7.39471	0.234546
$995$	−3.65135	−0.115756
$996$	3.33750	0.105753
$997$	−48.0854	−1.52288	−0.761441	−	0.648235i	$-0.775508\pi$
$997$	−48.0854	−1.52288	−0.761441	+	0.648235i	$0.775508\pi$
$998$	−29.0057	−0.918160
$999$	−6.66525	−0.210879

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.h.1.15	✓	59

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.h.1.15	✓	59	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-1.71705 q^{2} -3.23330 q^{3} +0.948270 q^{4} +1.00000 q^{5} +5.55174 q^{6} +4.30663 q^{7} +1.80588 q^{8} +7.45420 q^{9} +O(q^{10})\)	\(q-1.71705 q^{2} -3.23330 q^{3} +0.948270 q^{4} +1.00000 q^{5} +5.55174 q^{6} +4.30663 q^{7} +1.80588 q^{8} +7.45420 q^{9} -1.71705 q^{10} +5.53210 q^{11} -3.06604 q^{12} -4.12392 q^{13} -7.39471 q^{14} -3.23330 q^{15} -4.99732 q^{16} -1.00000 q^{17} -12.7993 q^{18} +8.25238 q^{19} +0.948270 q^{20} -13.9246 q^{21} -9.49891 q^{22} -4.74680 q^{23} -5.83893 q^{24} +1.00000 q^{25} +7.08100 q^{26} -14.4017 q^{27} +4.08385 q^{28} -8.71206 q^{29} +5.55174 q^{30} +5.60910 q^{31} +4.96892 q^{32} -17.8869 q^{33} +1.71705 q^{34} +4.30663 q^{35} +7.06859 q^{36} +0.462809 q^{37} -14.1698 q^{38} +13.3339 q^{39} +1.80588 q^{40} +8.70359 q^{41} +23.9093 q^{42} +0.856473 q^{43} +5.24592 q^{44} +7.45420 q^{45} +8.15051 q^{46} +9.13969 q^{47} +16.1578 q^{48} +11.5471 q^{49} -1.71705 q^{50} +3.23330 q^{51} -3.91059 q^{52} +7.07434 q^{53} +24.7286 q^{54} +5.53210 q^{55} +7.77724 q^{56} -26.6824 q^{57} +14.9591 q^{58} -1.35014 q^{59} -3.06604 q^{60} -4.37132 q^{61} -9.63113 q^{62} +32.1025 q^{63} +1.46276 q^{64} -4.12392 q^{65} +30.7128 q^{66} +11.7507 q^{67} -0.948270 q^{68} +15.3478 q^{69} -7.39471 q^{70} -1.00000 q^{71} +13.4614 q^{72} -14.3985 q^{73} -0.794667 q^{74} -3.23330 q^{75} +7.82548 q^{76} +23.8247 q^{77} -22.8949 q^{78} -2.74615 q^{79} -4.99732 q^{80} +24.2025 q^{81} -14.9445 q^{82} -1.08854 q^{83} -13.2043 q^{84} -1.00000 q^{85} -1.47061 q^{86} +28.1687 q^{87} +9.99029 q^{88} -14.0676 q^{89} -12.7993 q^{90} -17.7602 q^{91} -4.50125 q^{92} -18.1359 q^{93} -15.6933 q^{94} +8.25238 q^{95} -16.0660 q^{96} +9.18526 q^{97} -19.8269 q^{98} +41.2374 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9}+O(q^{10}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9} + 2 q^{10} + 6 q^{11} + 16 q^{12} + 25 q^{13} + 8 q^{14} + 6 q^{15} + 114 q^{16} - 59 q^{17} + 3 q^{18} + 35 q^{19} + 76 q^{20} + 41 q^{21} + 13 q^{22} - 2 q^{23} + 35 q^{24} + 59 q^{25} + 10 q^{26} + 27 q^{27} + 28 q^{28} + 10 q^{29} + 14 q^{30} + 15 q^{31} + 19 q^{32} - 3 q^{33} - 2 q^{34} + 9 q^{35} + 160 q^{36} + 56 q^{37} + 17 q^{38} + 25 q^{39} + 6 q^{40} + 47 q^{41} + 46 q^{42} + 27 q^{43} + 39 q^{44} + 97 q^{45} + 4 q^{46} - 8 q^{47} + 58 q^{48} + 174 q^{49} + 2 q^{50} - 6 q^{51} + 13 q^{52} + 17 q^{53} + 48 q^{54} + 6 q^{55} + 33 q^{56} + 6 q^{57} + 32 q^{58} + 30 q^{59} + 16 q^{60} + 85 q^{61} - 3 q^{62} + 14 q^{63} + 168 q^{64} + 25 q^{65} + 87 q^{66} + 21 q^{67} - 76 q^{68} + 111 q^{69} + 8 q^{70} - 59 q^{71} - 52 q^{72} + 41 q^{73} + 11 q^{74} + 6 q^{75} + 118 q^{76} + 55 q^{77} - 54 q^{78} + 43 q^{79} + 114 q^{80} + 207 q^{81} + 45 q^{82} + 10 q^{83} + 62 q^{84} - 59 q^{85} + 19 q^{86} + 8 q^{87} + 35 q^{88} + 86 q^{89} + 3 q^{90} + 47 q^{91} - 98 q^{92} + 41 q^{93} + 30 q^{94} + 35 q^{95} + 69 q^{96} + 72 q^{97} + 14 q^{98} + 25 q^{99}+O(q^{100}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9 + 2 * q^10 + 6 * q^11 + 16 * q^12 + 25 * q^13 + 8 * q^14 + 6 * q^15 + 114 * q^16 - 59 * q^17 + 3 * q^18 + 35 * q^19 + 76 * q^20 + 41 * q^21 + 13 * q^22 - 2 * q^23 + 35 * q^24 + 59 * q^25 + 10 * q^26 + 27 * q^27 + 28 * q^28 + 10 * q^29 + 14 * q^30 + 15 * q^31 + 19 * q^32 - 3 * q^33 - 2 * q^34 + 9 * q^35 + 160 * q^36 + 56 * q^37 + 17 * q^38 + 25 * q^39 + 6 * q^40 + 47 * q^41 + 46 * q^42 + 27 * q^43 + 39 * q^44 + 97 * q^45 + 4 * q^46 - 8 * q^47 + 58 * q^48 + 174 * q^49 + 2 * q^50 - 6 * q^51 + 13 * q^52 + 17 * q^53 + 48 * q^54 + 6 * q^55 + 33 * q^56 + 6 * q^57 + 32 * q^58 + 30 * q^59 + 16 * q^60 + 85 * q^61 - 3 * q^62 + 14 * q^63 + 168 * q^64 + 25 * q^65 + 87 * q^66 + 21 * q^67 - 76 * q^68 + 111 * q^69 + 8 * q^70 - 59 * q^71 - 52 * q^72 + 41 * q^73 + 11 * q^74 + 6 * q^75 + 118 * q^76 + 55 * q^77 - 54 * q^78 + 43 * q^79 + 114 * q^80 + 207 * q^81 + 45 * q^82 + 10 * q^83 + 62 * q^84 - 59 * q^85 + 19 * q^86 + 8 * q^87 + 35 * q^88 + 86 * q^89 + 3 * q^90 + 47 * q^91 - 98 * q^92 + 41 * q^93 + 30 * q^94 + 35 * q^95 + 69 * q^96 + 72 * q^97 + 14 * q^98 + 25 * q^99

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