LMFDB - Embedded newform 6017.2.a.c.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$1$
Dimension:	$106$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57284 q^{2} +2.82606 q^{3} +4.61950 q^{4} +1.34186 q^{5} -7.27099 q^{6} -3.61511 q^{7} -6.73954 q^{8} +4.98661 q^{9} +O(q^{10})$	\(q-2.57284 q^{2} +2.82606 q^{3} +4.61950 q^{4} +1.34186 q^{5} -7.27099 q^{6} -3.61511 q^{7} -6.73954 q^{8} +4.98661 q^{9} -3.45239 q^{10} +1.00000 q^{11} +13.0550 q^{12} -0.296690 q^{13} +9.30109 q^{14} +3.79217 q^{15} +8.10076 q^{16} -4.19377 q^{17} -12.8297 q^{18} +0.592754 q^{19} +6.19872 q^{20} -10.2165 q^{21} -2.57284 q^{22} +1.33653 q^{23} -19.0464 q^{24} -3.19941 q^{25} +0.763336 q^{26} +5.61428 q^{27} -16.7000 q^{28} +5.99718 q^{29} -9.75665 q^{30} +7.96398 q^{31} -7.36287 q^{32} +2.82606 q^{33} +10.7899 q^{34} -4.85097 q^{35} +23.0356 q^{36} -7.24254 q^{37} -1.52506 q^{38} -0.838464 q^{39} -9.04352 q^{40} -10.4646 q^{41} +26.2854 q^{42} -3.89021 q^{43} +4.61950 q^{44} +6.69133 q^{45} -3.43868 q^{46} -5.62283 q^{47} +22.8932 q^{48} +6.06900 q^{49} +8.23157 q^{50} -11.8518 q^{51} -1.37056 q^{52} -11.7607 q^{53} -14.4446 q^{54} +1.34186 q^{55} +24.3642 q^{56} +1.67516 q^{57} -15.4298 q^{58} -6.98866 q^{59} +17.5179 q^{60} -1.94629 q^{61} -20.4900 q^{62} -18.0271 q^{63} +2.74194 q^{64} -0.398117 q^{65} -7.27099 q^{66} -8.97316 q^{67} -19.3731 q^{68} +3.77711 q^{69} +12.4808 q^{70} +2.79874 q^{71} -33.6075 q^{72} +1.22988 q^{73} +18.6339 q^{74} -9.04173 q^{75} +2.73822 q^{76} -3.61511 q^{77} +2.15723 q^{78} +12.7100 q^{79} +10.8701 q^{80} +0.906459 q^{81} +26.9238 q^{82} -16.2683 q^{83} -47.1951 q^{84} -5.62745 q^{85} +10.0089 q^{86} +16.9484 q^{87} -6.73954 q^{88} +4.80932 q^{89} -17.2157 q^{90} +1.07257 q^{91} +6.17410 q^{92} +22.5067 q^{93} +14.4666 q^{94} +0.795392 q^{95} -20.8079 q^{96} +3.11996 q^{97} -15.6146 q^{98} +4.98661 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) $ 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * 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 $

$2$	−2.57284	−1.81927	−0.909636	−	0.415407i	$-0.863639\pi$
$2$	−2.57284	−1.81927	−0.909636	+	0.415407i	$0.863639\pi$
$3$	2.82606	1.63163	0.815813	−	0.578316i	$-0.196290\pi$
$3$	2.82606	1.63163	0.815813	+	0.578316i	$0.196290\pi$
$4$	4.61950	2.30975
$5$	1.34186	0.600098	0.300049	−	0.953924i	$-0.402997\pi$
$5$	1.34186	0.600098	0.300049	+	0.953924i	$0.402997\pi$
$6$	−7.27099	−2.96837
$7$	−3.61511	−1.36638	−0.683191	−	0.730240i	$-0.739408\pi$
$7$	−3.61511	−1.36638	−0.683191	+	0.730240i	$0.739408\pi$
$8$	−6.73954	−2.38279
$9$	4.98661	1.66220
$10$	−3.45239	−1.09174
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	13.0550	3.76865
$13$	−0.296690	−0.0822871	−0.0411435	−	0.999153i	$-0.513100\pi$
$13$	−0.296690	−0.0822871	−0.0411435	+	0.999153i	$0.513100\pi$
$14$	9.30109	2.48582
$15$	3.79217	0.979135
$16$	8.10076	2.02519
$17$	−4.19377	−1.01714	−0.508569	−	0.861021i	$-0.669825\pi$
$17$	−4.19377	−1.01714	−0.508569	+	0.861021i	$0.669825\pi$
$18$	−12.8297	−3.02400
$19$	0.592754	0.135987	0.0679935	−	0.997686i	$-0.478340\pi$
$19$	0.592754	0.135987	0.0679935	+	0.997686i	$0.478340\pi$
$20$	6.19872	1.38608
$21$	−10.2165	−2.22942
$22$	−2.57284	−0.548531
$23$	1.33653	0.278686	0.139343	−	0.990244i	$-0.455501\pi$
$23$	1.33653	0.278686	0.139343	+	0.990244i	$0.455501\pi$
$24$	−19.0464	−3.88782
$25$	−3.19941	−0.639883
$26$	0.763336	0.149703
$27$	5.61428	1.08047
$28$	−16.7000	−3.15600
$29$	5.99718	1.11365	0.556824	−	0.830631i	$-0.312020\pi$
$29$	5.99718	1.11365	0.556824	+	0.830631i	$0.312020\pi$
$30$	−9.75665	−1.78131
$31$	7.96398	1.43037	0.715187	−	0.698933i	$-0.246342\pi$
$31$	7.96398	1.43037	0.715187	+	0.698933i	$0.246342\pi$
$32$	−7.36287	−1.30158
$33$	2.82606	0.491954
$34$	10.7899	1.85045
$35$	−4.85097	−0.819963
$36$	23.0356	3.83927
$37$	−7.24254	−1.19067	−0.595333	−	0.803479i	$-0.702980\pi$
$37$	−7.24254	−1.19067	−0.595333	+	0.803479i	$0.702980\pi$
$38$	−1.52506	−0.247397
$39$	−0.838464	−0.134262
$40$	−9.04352	−1.42991
$41$	−10.4646	−1.63430	−0.817151	−	0.576424i	$-0.804448\pi$
$41$	−10.4646	−1.63430	−0.817151	+	0.576424i	$0.804448\pi$
$42$	26.2854	4.05593
$43$	−3.89021	−0.593252	−0.296626	−	0.954994i	$-0.595861\pi$
$43$	−3.89021	−0.593252	−0.296626	+	0.954994i	$0.595861\pi$
$44$	4.61950	0.696415
$45$	6.69133	0.997485
$46$	−3.43868	−0.507005
$47$	−5.62283	−0.820175	−0.410087	−	0.912046i	$-0.634502\pi$
$47$	−5.62283	−0.820175	−0.410087	+	0.912046i	$0.634502\pi$
$48$	22.8932	3.30435
$49$	6.06900	0.867000
$50$	8.23157	1.16412
$51$	−11.8518	−1.65959
$52$	−1.37056	−0.190063
$53$	−11.7607	−1.61545	−0.807725	−	0.589559i	$-0.799301\pi$
$53$	−11.7607	−1.61545	−0.807725	+	0.589559i	$0.799301\pi$
$54$	−14.4446	−1.96567
$55$	1.34186	0.180936
$56$	24.3642	3.25580
$57$	1.67516	0.221880
$58$	−15.4298	−2.02603
$59$	−6.98866	−0.909846	−0.454923	−	0.890531i	$-0.650333\pi$
$59$	−6.98866	−0.909846	−0.454923	+	0.890531i	$0.650333\pi$
$60$	17.5179	2.26156
$61$	−1.94629	−0.249196	−0.124598	−	0.992207i	$-0.539764\pi$
$61$	−1.94629	−0.249196	−0.124598	+	0.992207i	$0.539764\pi$
$62$	−20.4900	−2.60224
$63$	−18.0271	−2.27121
$64$	2.74194	0.342743
$65$	−0.398117	−0.0493803
$66$	−7.27099	−0.894998
$67$	−8.97316	−1.09625	−0.548123	−	0.836398i	$-0.684657\pi$
$67$	−8.97316	−1.09625	−0.548123	+	0.836398i	$0.684657\pi$
$68$	−19.3731	−2.34934
$69$	3.77711	0.454711
$70$	12.4808	1.49174
$71$	2.79874	0.332150	0.166075	−	0.986113i	$-0.446891\pi$
$71$	2.79874	0.332150	0.166075	+	0.986113i	$0.446891\pi$
$72$	−33.6075	−3.96068
$73$	1.22988	0.143947	0.0719734	−	0.997407i	$-0.477070\pi$
$73$	1.22988	0.143947	0.0719734	+	0.997407i	$0.477070\pi$
$74$	18.6339	2.16615
$75$	−9.04173	−1.04405
$76$	2.73822	0.314096
$77$	−3.61511	−0.411980
$78$	2.15723	0.244259
$79$	12.7100	1.42998	0.714991	−	0.699134i	$-0.246431\pi$
$79$	12.7100	1.42998	0.714991	+	0.699134i	$0.246431\pi$
$80$	10.8701	1.21531
$81$	0.906459	0.100718
$82$	26.9238	2.97324
$83$	−16.2683	−1.78568	−0.892838	−	0.450379i	$-0.851289\pi$
$83$	−16.2683	−1.78568	−0.892838	+	0.450379i	$0.851289\pi$
$84$	−47.1951	−5.14941
$85$	−5.62745	−0.610383
$86$	10.0089	1.07929
$87$	16.9484	1.81706
$88$	−6.73954	−0.718438
$89$	4.80932	0.509787	0.254894	−	0.966969i	$-0.417960\pi$
$89$	4.80932	0.509787	0.254894	+	0.966969i	$0.417960\pi$
$90$	−17.2157	−1.81470
$91$	1.07257	0.112436
$92$	6.17410	0.643694
$93$	22.5067	2.33384
$94$	14.4666	1.49212
$95$	0.795392	0.0816055
$96$	−20.8079	−2.12370
$97$	3.11996	0.316784	0.158392	−	0.987376i	$-0.449369\pi$
$97$	3.11996	0.316784	0.158392	+	0.987376i	$0.449369\pi$
$98$	−15.6146	−1.57731
$99$	4.98661	0.501173
$100$	−14.7797	−1.47797
$101$	14.1519	1.40817	0.704085	−	0.710116i	$-0.251358\pi$
$101$	14.1519	1.40817	0.704085	+	0.710116i	$0.251358\pi$
$102$	30.4929	3.01925
$103$	−4.84287	−0.477182	−0.238591	−	0.971120i	$-0.576686\pi$
$103$	−4.84287	−0.477182	−0.238591	+	0.971120i	$0.576686\pi$
$104$	1.99956	0.196073
$105$	−13.7091	−1.33787
$106$	30.2583	2.93894
$107$	10.4934	1.01444	0.507219	−	0.861817i	$-0.330674\pi$
$107$	10.4934	1.01444	0.507219	+	0.861817i	$0.330674\pi$
$108$	25.9352	2.49561
$109$	−1.86581	−0.178712	−0.0893562	−	0.996000i	$-0.528481\pi$
$109$	−1.86581	−0.178712	−0.0893562	+	0.996000i	$0.528481\pi$
$110$	−3.45239	−0.329172
$111$	−20.4679	−1.94272
$112$	−29.2851	−2.76719
$113$	1.70563	0.160452	0.0802261	−	0.996777i	$-0.474436\pi$
$113$	1.70563	0.160452	0.0802261	+	0.996777i	$0.474436\pi$
$114$	−4.30991	−0.403660
$115$	1.79344	0.167239
$116$	27.7039	2.57225
$117$	−1.47948	−0.136778
$118$	17.9807	1.65526
$119$	15.1609	1.38980
$120$	−25.5575	−2.33307
$121$	1.00000	0.0909091
$122$	5.00748	0.453356
$123$	−29.5737	−2.66657
$124$	36.7896	3.30380
$125$	−11.0025	−0.984090
$126$	46.3809	4.13194
$127$	−8.06490	−0.715644	−0.357822	−	0.933790i	$-0.616481\pi$
$127$	−8.06490	−0.715644	−0.357822	+	0.933790i	$0.616481\pi$
$128$	7.67116	0.678041
$129$	−10.9940	−0.967965
$130$	1.02429	0.0898362
$131$	6.62646	0.578956	0.289478	−	0.957185i	$-0.406518\pi$
$131$	6.62646	0.578956	0.289478	+	0.957185i	$0.406518\pi$
$132$	13.0550	1.13629
$133$	−2.14287	−0.185810
$134$	23.0865	1.99437
$135$	7.53358	0.648387
$136$	28.2641	2.42363
$137$	12.2385	1.04561	0.522804	−	0.852453i	$-0.324886\pi$
$137$	12.2385	1.04561	0.522804	+	0.852453i	$0.324886\pi$
$138$	−9.71790	−0.827243
$139$	−10.3449	−0.877440	−0.438720	−	0.898624i	$-0.644568\pi$
$139$	−10.3449	−0.877440	−0.438720	+	0.898624i	$0.644568\pi$
$140$	−22.4090	−1.89391
$141$	−15.8905	−1.33822
$142$	−7.20071	−0.604270
$143$	−0.296690	−0.0248105
$144$	40.3954	3.36628
$145$	8.04737	0.668297
$146$	−3.16429	−0.261878
$147$	17.1514	1.41462
$148$	−33.4569	−2.75014
$149$	−1.88470	−0.154401	−0.0772005	−	0.997016i	$-0.524598\pi$
$149$	−1.88470	−0.154401	−0.0772005	+	0.997016i	$0.524598\pi$
$150$	23.2629	1.89941
$151$	−20.1164	−1.63705	−0.818524	−	0.574472i	$-0.805207\pi$
$151$	−20.1164	−1.63705	−0.818524	+	0.574472i	$0.805207\pi$
$152$	−3.99489	−0.324028
$153$	−20.9127	−1.69069
$154$	9.30109	0.749503
$155$	10.6865	0.858364
$156$	−3.87328	−0.310111
$157$	−8.53604	−0.681250	−0.340625	−	0.940199i	$-0.610639\pi$
$157$	−8.53604	−0.681250	−0.340625	+	0.940199i	$0.610639\pi$
$158$	−32.7007	−2.60152
$159$	−33.2363	−2.63581
$160$	−9.87993	−0.781077
$161$	−4.83170	−0.380791
$162$	−2.33217	−0.183233
$163$	20.3708	1.59557	0.797783	−	0.602945i	$-0.206006\pi$
$163$	20.3708	1.59557	0.797783	+	0.602945i	$0.206006\pi$
$164$	−48.3414	−3.77483
$165$	3.79217	0.295220
$166$	41.8556	3.24863
$167$	3.25170	0.251624	0.125812	−	0.992054i	$-0.459846\pi$
$167$	3.25170	0.251624	0.125812	+	0.992054i	$0.459846\pi$
$168$	68.8546	5.31225
$169$	−12.9120	−0.993229
$170$	14.4785	1.11045
$171$	2.95583	0.226038
$172$	−17.9708	−1.37026
$173$	−13.6488	−1.03770	−0.518851	−	0.854865i	$-0.673640\pi$
$173$	−13.6488	−1.03770	−0.518851	+	0.854865i	$0.673640\pi$
$174$	−43.6054	−3.30572
$175$	11.5662	0.874324
$176$	8.10076	0.610618
$177$	−19.7504	−1.48453
$178$	−12.3736	−0.927441
$179$	23.5873	1.76300	0.881499	−	0.472187i	$-0.156535\pi$
$179$	23.5873	1.76300	0.881499	+	0.472187i	$0.156535\pi$
$180$	30.9106	2.30394
$181$	8.79771	0.653929	0.326964	−	0.945037i	$-0.393974\pi$
$181$	8.79771	0.653929	0.326964	+	0.945037i	$0.393974\pi$
$182$	−2.75954	−0.204551
$183$	−5.50032	−0.406595
$184$	−9.00760	−0.664049
$185$	−9.71847	−0.714516
$186$	−57.9061	−4.24588
$187$	−4.19377	−0.306679
$188$	−25.9747	−1.89440
$189$	−20.2962	−1.47633
$190$	−2.04641	−0.148463
$191$	0.340337	0.0246259	0.0123130	−	0.999924i	$-0.496081\pi$
$191$	0.340337	0.0246259	0.0123130	+	0.999924i	$0.496081\pi$
$192$	7.74889	0.559228
$193$	1.18589	0.0853623	0.0426812	−	0.999089i	$-0.486410\pi$
$193$	1.18589	0.0853623	0.0426812	+	0.999089i	$0.486410\pi$
$194$	−8.02715	−0.576316
$195$	−1.12510	−0.0805702
$196$	28.0357	2.00255
$197$	−21.7604	−1.55036	−0.775182	−	0.631739i	$-0.782342\pi$
$197$	−21.7604	−1.55036	−0.775182	+	0.631739i	$0.782342\pi$
$198$	−12.8297	−0.911770
$199$	0.440890	0.0312539	0.0156269	−	0.999878i	$-0.495026\pi$
$199$	0.440890	0.0312539	0.0156269	+	0.999878i	$0.495026\pi$
$200$	21.5626	1.52471
$201$	−25.3587	−1.78866
$202$	−36.4106	−2.56184
$203$	−21.6804	−1.52167
$204$	−54.7496	−3.83324
$205$	−14.0421	−0.980741
$206$	12.4599	0.868124
$207$	6.66476	0.463233
$208$	−2.40342	−0.166647
$209$	0.592754	0.0410016
$210$	35.2713	2.43395
$211$	−26.3894	−1.81672	−0.908362	−	0.418186i	$-0.862666\pi$
$211$	−26.3894	−1.81672	−0.908362	+	0.418186i	$0.862666\pi$
$212$	−54.3283	−3.73128
$213$	7.90941	0.541944
$214$	−26.9979	−1.84554
$215$	−5.22012	−0.356009
$216$	−37.8377	−2.57453
$217$	−28.7907	−1.95444
$218$	4.80044	0.325127
$219$	3.47572	0.234867
$220$	6.19872	0.417917
$221$	1.24425	0.0836974
$222$	52.6605	3.53434
$223$	−17.1999	−1.15179	−0.575896	−	0.817523i	$-0.695347\pi$
$223$	−17.1999	−1.15179	−0.575896	+	0.817523i	$0.695347\pi$
$224$	26.6176	1.77846
$225$	−15.9542	−1.06362
$226$	−4.38831	−0.291906
$227$	6.51454	0.432385	0.216193	−	0.976351i	$-0.430636\pi$
$227$	6.51454	0.432385	0.216193	+	0.976351i	$0.430636\pi$
$228$	7.73838	0.512487
$229$	−0.972276	−0.0642498	−0.0321249	−	0.999484i	$-0.510227\pi$
$229$	−0.972276	−0.0642498	−0.0321249	+	0.999484i	$0.510227\pi$
$230$	−4.61422	−0.304253
$231$	−10.2165	−0.672197
$232$	−40.4182	−2.65359
$233$	25.0558	1.64146	0.820732	−	0.571314i	$-0.193566\pi$
$233$	25.0558	1.64146	0.820732	+	0.571314i	$0.193566\pi$
$234$	3.80646	0.248836
$235$	−7.54505	−0.492185
$236$	−32.2841	−2.10152
$237$	35.9191	2.33320
$238$	−39.0066	−2.52842
$239$	2.80758	0.181607	0.0908037	−	0.995869i	$-0.471056\pi$
$239$	2.80758	0.181607	0.0908037	+	0.995869i	$0.471056\pi$
$240$	30.7195	1.98294
$241$	−16.3796	−1.05510	−0.527551	−	0.849523i	$-0.676890\pi$
$241$	−16.3796	−1.05510	−0.527551	+	0.849523i	$0.676890\pi$
$242$	−2.57284	−0.165388
$243$	−14.2811	−0.916135
$244$	−8.99086	−0.575581
$245$	8.14375	0.520285
$246$	76.0883	4.85121
$247$	−0.175864	−0.0111900
$248$	−53.6736	−3.40828
$249$	−45.9751	−2.91355
$250$	28.3076	1.79033
$251$	−9.40382	−0.593564	−0.296782	−	0.954945i	$-0.595913\pi$
$251$	−9.40382	−0.593564	−0.296782	+	0.954945i	$0.595913\pi$
$252$	−83.2763	−5.24592
$253$	1.33653	0.0840269
$254$	20.7497	1.30195
$255$	−15.9035	−0.995916
$256$	−25.2205	−1.57628
$257$	2.15675	0.134534	0.0672671	−	0.997735i	$-0.478572\pi$
$257$	2.15675	0.134534	0.0672671	+	0.997735i	$0.478572\pi$
$258$	28.2857	1.76099
$259$	26.1826	1.62691
$260$	−1.83910	−0.114056
$261$	29.9056	1.85111
$262$	−17.0488	−1.05328
$263$	−6.74037	−0.415629	−0.207815	−	0.978168i	$-0.566635\pi$
$263$	−6.74037	−0.415629	−0.207815	+	0.978168i	$0.566635\pi$
$264$	−19.0464	−1.17222
$265$	−15.7811	−0.969428
$266$	5.51325	0.338039
$267$	13.5914	0.831782
$268$	−41.4515	−2.53205
$269$	9.58429	0.584365	0.292182	−	0.956363i	$-0.405619\pi$
$269$	9.58429	0.584365	0.292182	+	0.956363i	$0.405619\pi$
$270$	−19.3827	−1.17959
$271$	9.70651	0.589629	0.294814	−	0.955555i	$-0.404742\pi$
$271$	9.70651	0.589629	0.294814	+	0.955555i	$0.404742\pi$
$272$	−33.9728	−2.05990
$273$	3.03114	0.183453
$274$	−31.4877	−1.90224
$275$	−3.19941	−0.192932
$276$	17.4484	1.05027
$277$	5.63887	0.338807	0.169404	−	0.985547i	$-0.445816\pi$
$277$	5.63887	0.338807	0.169404	+	0.985547i	$0.445816\pi$
$278$	26.6157	1.59630
$279$	39.7133	2.37757
$280$	32.6933	1.95380
$281$	1.62335	0.0968409	0.0484205	−	0.998827i	$-0.484581\pi$
$281$	1.62335	0.0968409	0.0484205	+	0.998827i	$0.484581\pi$
$282$	40.8836	2.43458
$283$	−13.8259	−0.821864	−0.410932	−	0.911666i	$-0.634797\pi$
$283$	−13.8259	−0.821864	−0.410932	+	0.911666i	$0.634797\pi$
$284$	12.9288	0.767182
$285$	2.24782	0.133150
$286$	0.763336	0.0451370
$287$	37.8308	2.23308
$288$	−36.7158	−2.16350
$289$	0.587717	0.0345716
$290$	−20.7046	−1.21581
$291$	8.81719	0.516873
$292$	5.68144	0.332481
$293$	−19.6258	−1.14655	−0.573277	−	0.819362i	$-0.694328\pi$
$293$	−19.6258	−1.14655	−0.573277	+	0.819362i	$0.694328\pi$
$294$	−44.1277	−2.57358
$295$	−9.37780	−0.545996
$296$	48.8114	2.83711
$297$	5.61428	0.325774
$298$	4.84904	0.280897
$299$	−0.396535	−0.0229322
$300$	−41.7683	−2.41149
$301$	14.0635	0.810609
$302$	51.7562	2.97824
$303$	39.9942	2.29761
$304$	4.80176	0.275400
$305$	−2.61164	−0.149542
$306$	53.8050	3.07583
$307$	28.8752	1.64799	0.823997	−	0.566594i	$-0.191739\pi$
$307$	28.8752	1.64799	0.823997	+	0.566594i	$0.191739\pi$
$308$	−16.7000	−0.951570
$309$	−13.6862	−0.778583
$310$	−27.4948	−1.56160
$311$	−19.4470	−1.10274	−0.551370	−	0.834261i	$-0.685895\pi$
$311$	−19.4470	−1.10274	−0.551370	+	0.834261i	$0.685895\pi$
$312$	5.65087	0.319917
$313$	−23.7564	−1.34279	−0.671396	−	0.741099i	$-0.734305\pi$
$313$	−23.7564	−1.34279	−0.671396	+	0.741099i	$0.734305\pi$
$314$	21.9618	1.23938
$315$	−24.1899	−1.36295
$316$	58.7136	3.30290
$317$	9.72984	0.546482	0.273241	−	0.961946i	$-0.411904\pi$
$317$	9.72984	0.546482	0.273241	+	0.961946i	$0.411904\pi$
$318$	85.5116	4.79526
$319$	5.99718	0.335777
$320$	3.67930	0.205679
$321$	29.6550	1.65518
$322$	12.4312	0.692763
$323$	−2.48587	−0.138318
$324$	4.18739	0.232633
$325$	0.949235	0.0526541
$326$	−52.4108	−2.90277
$327$	−5.27290	−0.291592
$328$	70.5269	3.89420
$329$	20.3272	1.12067
$330$	−9.75665	−0.537086
$331$	8.72398	0.479514	0.239757	−	0.970833i	$-0.422932\pi$
$331$	8.72398	0.479514	0.239757	+	0.970833i	$0.422932\pi$
$332$	−75.1513	−4.12446
$333$	−36.1157	−1.97913
$334$	−8.36611	−0.457773
$335$	−12.0407	−0.657854
$336$	−82.7615	−4.51501
$337$	31.8345	1.73413	0.867067	−	0.498191i	$-0.166002\pi$
$337$	31.8345	1.73413	0.867067	+	0.498191i	$0.166002\pi$
$338$	33.2204	1.80695
$339$	4.82021	0.261798
$340$	−25.9960	−1.40983
$341$	7.96398	0.431274
$342$	−7.60488	−0.411225
$343$	3.36565	0.181728
$344$	26.2183	1.41359
$345$	5.06835	0.272871
$346$	35.1162	1.88786
$347$	29.2943	1.57260	0.786300	−	0.617845i	$-0.211994\pi$
$347$	29.2943	1.57260	0.786300	+	0.617845i	$0.211994\pi$
$348$	78.2930	4.19694
$349$	−27.2253	−1.45734	−0.728669	−	0.684866i	$-0.759861\pi$
$349$	−27.2253	−1.45734	−0.728669	+	0.684866i	$0.759861\pi$
$350$	−29.7580	−1.59063
$351$	−1.66570	−0.0889086
$352$	−7.36287	−0.392442
$353$	−31.1453	−1.65770	−0.828849	−	0.559473i	$-0.811004\pi$
$353$	−31.1453	−1.65770	−0.828849	+	0.559473i	$0.811004\pi$
$354$	50.8145	2.70076
$355$	3.75552	0.199322
$356$	22.2167	1.17748
$357$	42.8457	2.26763
$358$	−60.6863	−3.20737
$359$	18.5386	0.978432	0.489216	−	0.872163i	$-0.337283\pi$
$359$	18.5386	0.978432	0.489216	+	0.872163i	$0.337283\pi$
$360$	−45.0965	−2.37680
$361$	−18.6486	−0.981508
$362$	−22.6351	−1.18967
$363$	2.82606	0.148330
$364$	4.95472	0.259698
$365$	1.65033	0.0863821
$366$	14.1514	0.739707
$367$	−9.18248	−0.479322	−0.239661	−	0.970857i	$-0.577036\pi$
$367$	−9.18248	−0.479322	−0.239661	+	0.970857i	$0.577036\pi$
$368$	10.8269	0.564392
$369$	−52.1831	−2.71654
$370$	25.0041	1.29990
$371$	42.5160	2.20732
$372$	103.970	5.39057
$373$	−22.2419	−1.15164	−0.575820	−	0.817576i	$-0.695317\pi$
$373$	−22.2419	−1.15164	−0.575820	+	0.817576i	$0.695317\pi$
$374$	10.7899	0.557932
$375$	−31.0936	−1.60567
$376$	37.8953	1.95430
$377$	−1.77930	−0.0916388
$378$	52.2189	2.68585
$379$	−19.5353	−1.00346	−0.501731	−	0.865024i	$-0.667303\pi$
$379$	−19.5353	−1.00346	−0.501731	+	0.865024i	$0.667303\pi$
$380$	3.67431	0.188488
$381$	−22.7919	−1.16766
$382$	−0.875633	−0.0448013
$383$	3.99204	0.203983	0.101992	−	0.994785i	$-0.467478\pi$
$383$	3.99204	0.203983	0.101992	+	0.994785i	$0.467478\pi$
$384$	21.6792	1.10631
$385$	−4.85097	−0.247228
$386$	−3.05111	−0.155297
$387$	−19.3990	−0.986106
$388$	14.4126	0.731691
$389$	24.8590	1.26040	0.630201	−	0.776432i	$-0.282973\pi$
$389$	24.8590	1.26040	0.630201	+	0.776432i	$0.282973\pi$
$390$	2.89470	0.146579
$391$	−5.60510	−0.283462
$392$	−40.9023	−2.06588
$393$	18.7268	0.944640
$394$	55.9859	2.82053
$395$	17.0550	0.858129
$396$	23.0356	1.15758
$397$	−35.2361	−1.76845	−0.884225	−	0.467060i	$-0.845313\pi$
$397$	−35.2361	−1.76845	−0.884225	+	0.467060i	$0.845313\pi$
$398$	−1.13434	−0.0568593
$399$	−6.05587	−0.303173
$400$	−25.9177	−1.29588
$401$	−12.8493	−0.641661	−0.320831	−	0.947137i	$-0.603962\pi$
$401$	−12.8493	−0.641661	−0.320831	+	0.947137i	$0.603962\pi$
$402$	65.2438	3.25406
$403$	−2.36284	−0.117701
$404$	65.3748	3.25252
$405$	1.21634	0.0604404
$406$	55.7803	2.76833
$407$	−7.24254	−0.359000
$408$	79.8760	3.95445
$409$	−8.68451	−0.429421	−0.214711	−	0.976678i	$-0.568881\pi$
$409$	−8.68451	−0.429421	−0.214711	+	0.976678i	$0.568881\pi$
$410$	36.1280	1.78423
$411$	34.5868	1.70604
$412$	−22.3716	−1.10217
$413$	25.2648	1.24320
$414$	−17.1473	−0.842746
$415$	−21.8297	−1.07158
$416$	2.18449	0.107104
$417$	−29.2352	−1.43165
$418$	−1.52506	−0.0745931
$419$	3.27758	0.160120	0.0800602	−	0.996790i	$-0.474489\pi$
$419$	3.27758	0.160120	0.0800602	+	0.996790i	$0.474489\pi$
$420$	−63.3292	−3.09015
$421$	0.278301	0.0135635	0.00678177	−	0.999977i	$-0.497841\pi$
$421$	0.278301	0.0135635	0.00678177	+	0.999977i	$0.497841\pi$
$422$	67.8957	3.30511
$423$	−28.0389	−1.36330
$424$	79.2615	3.84928
$425$	13.4176	0.650850
$426$	−20.3496	−0.985943
$427$	7.03603	0.340498
$428$	48.4743	2.34310
$429$	−0.838464	−0.0404814
$430$	13.4305	0.647677
$431$	−0.925609	−0.0445850	−0.0222925	−	0.999751i	$-0.507097\pi$
$431$	−0.925609	−0.0445850	−0.0222925	+	0.999751i	$0.507097\pi$
$432$	45.4800	2.18816
$433$	5.68063	0.272993	0.136497	−	0.990641i	$-0.456416\pi$
$433$	5.68063	0.272993	0.136497	+	0.990641i	$0.456416\pi$
$434$	74.0737	3.55565
$435$	22.7423	1.09041
$436$	−8.61912	−0.412781
$437$	0.792233	0.0378976
$438$	−8.94246	−0.427287
$439$	−16.2552	−0.775818	−0.387909	−	0.921698i	$-0.626803\pi$
$439$	−16.2552	−0.775818	−0.387909	+	0.921698i	$0.626803\pi$
$440$	−9.04352	−0.431133
$441$	30.2638	1.44113
$442$	−3.20126	−0.152268
$443$	36.8367	1.75016	0.875082	−	0.483975i	$-0.160807\pi$
$443$	36.8367	1.75016	0.875082	+	0.483975i	$0.160807\pi$
$444$	−94.5512	−4.48720
$445$	6.45343	0.305922
$446$	44.2526	2.09542
$447$	−5.32628	−0.251925
$448$	−9.91242	−0.468318
$449$	−37.4233	−1.76612	−0.883058	−	0.469263i	$-0.844520\pi$
$449$	−37.4233	−1.76612	−0.883058	+	0.469263i	$0.844520\pi$
$450$	41.0477	1.93501
$451$	−10.4646	−0.492760
$452$	7.87916	0.370604
$453$	−56.8501	−2.67105
$454$	−16.7609	−0.786626
$455$	1.43923	0.0674724
$456$	−11.2898	−0.528693
$457$	28.2903	1.32336	0.661682	−	0.749784i	$-0.269843\pi$
$457$	28.2903	1.32336	0.661682	+	0.749784i	$0.269843\pi$
$458$	2.50151	0.116888
$459$	−23.5450	−1.09899
$460$	8.28477	0.386279
$461$	12.0127	0.559488	0.279744	−	0.960075i	$-0.409750\pi$
$461$	12.0127	0.559488	0.279744	+	0.960075i	$0.409750\pi$
$462$	26.2854	1.22291
$463$	−35.8562	−1.66638	−0.833189	−	0.552988i	$-0.813488\pi$
$463$	−35.8562	−1.66638	−0.833189	+	0.552988i	$0.813488\pi$
$464$	48.5817	2.25535
$465$	30.2008	1.40053
$466$	−64.4647	−2.98627
$467$	1.77727	0.0822424	0.0411212	−	0.999154i	$-0.486907\pi$
$467$	1.77727	0.0822424	0.0411212	+	0.999154i	$0.486907\pi$
$468$	−6.83445	−0.315923
$469$	32.4389	1.49789
$470$	19.4122	0.895418
$471$	−24.1233	−1.11155
$472$	47.1004	2.16797
$473$	−3.89021	−0.178872
$474$	−92.4140	−4.24472
$475$	−1.89646	−0.0870157
$476$	70.0359	3.21009
$477$	−58.6458	−2.68521
$478$	−7.22346	−0.330393
$479$	−16.8139	−0.768247	−0.384123	−	0.923282i	$-0.625496\pi$
$479$	−16.8139	−0.768247	−0.384123	+	0.923282i	$0.625496\pi$
$480$	−27.9213	−1.27443
$481$	2.14879	0.0979765
$482$	42.1420	1.91952
$483$	−13.6547	−0.621309
$484$	4.61950	0.209977
$485$	4.18655	0.190101
$486$	36.7431	1.66670
$487$	−16.0847	−0.728868	−0.364434	−	0.931229i	$-0.618737\pi$
$487$	−16.0847	−0.728868	−0.364434	+	0.931229i	$0.618737\pi$
$488$	13.1171	0.593782
$489$	57.5692	2.60337
$490$	−20.9525	−0.946540
$491$	12.0568	0.544118	0.272059	−	0.962281i	$-0.412295\pi$
$491$	12.0568	0.544118	0.272059	+	0.962281i	$0.412295\pi$
$492$	−136.616	−6.15911
$493$	−25.1508	−1.13273
$494$	0.452470	0.0203576
$495$	6.69133	0.300753
$496$	64.5144	2.89678
$497$	−10.1178	−0.453843
$498$	118.287	5.30055
$499$	−11.7110	−0.524257	−0.262128	−	0.965033i	$-0.584424\pi$
$499$	−11.7110	−0.524257	−0.262128	+	0.965033i	$0.584424\pi$
$500$	−50.8258	−2.27300
$501$	9.18950	0.410557
$502$	24.1945	1.07985
$503$	26.1561	1.16624	0.583122	−	0.812385i	$-0.301831\pi$
$503$	26.1561	1.16624	0.583122	+	0.812385i	$0.301831\pi$
$504$	121.495	5.41180
$505$	18.9899	0.845039
$506$	−3.43868	−0.152868
$507$	−36.4900	−1.62058
$508$	−37.2558	−1.65296
$509$	−25.7948	−1.14333	−0.571667	−	0.820486i	$-0.693703\pi$
$509$	−25.7948	−1.14333	−0.571667	+	0.820486i	$0.693703\pi$
$510$	40.9172	1.81184
$511$	−4.44615	−0.196686
$512$	49.5461	2.18965
$513$	3.32789	0.146930
$514$	−5.54896	−0.244754
$515$	−6.49845	−0.286356
$516$	−50.7866	−2.23576
$517$	−5.62283	−0.247292
$518$	−67.3635	−2.95978
$519$	−38.5724	−1.69314
$520$	2.68312	0.117663
$521$	8.81247	0.386081	0.193041	−	0.981191i	$-0.438165\pi$
$521$	8.81247	0.386081	0.193041	+	0.981191i	$0.438165\pi$
$522$	−76.9422	−3.36767
$523$	22.4392	0.981200	0.490600	−	0.871385i	$-0.336778\pi$
$523$	22.4392	0.981200	0.490600	+	0.871385i	$0.336778\pi$
$524$	30.6109	1.33724
$525$	32.6868	1.42657
$526$	17.3419	0.756142
$527$	−33.3991	−1.45489
$528$	22.8932	0.996300
$529$	−21.2137	−0.922334
$530$	40.6023	1.76365
$531$	−34.8497	−1.51235
$532$	−9.89897	−0.429175
$533$	3.10476	0.134482
$534$	−34.9686	−1.51324
$535$	14.0807	0.608762
$536$	60.4750	2.61212
$537$	66.6591	2.87655
$538$	−24.6588	−1.06312
$539$	6.06900	0.261410
$540$	34.8013	1.49761
$541$	16.6249	0.714759	0.357379	−	0.933959i	$-0.383670\pi$
$541$	16.6249	0.714759	0.357379	+	0.933959i	$0.383670\pi$
$542$	−24.9733	−1.07269
$543$	24.8628	1.06697
$544$	30.8782	1.32389
$545$	−2.50366	−0.107245
$546$	−7.79863	−0.333751
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	56.5358	2.41509
$549$	−9.70537	−0.414215
$550$	8.23157	0.350996
$551$	3.55485	0.151442
$552$	−25.4560	−1.08348
$553$	−45.9479	−1.95390
$554$	−14.5079	−0.616382
$555$	−27.4650	−1.16582
$556$	−47.7881	−2.02667
$557$	13.2525	0.561526	0.280763	−	0.959777i	$-0.409413\pi$
$557$	13.2525	0.561526	0.280763	+	0.959777i	$0.409413\pi$
$558$	−102.176	−4.32545
$559$	1.15419	0.0488170
$560$	−39.2965	−1.66058
$561$	−11.8518	−0.500385
$562$	−4.17662	−0.176180
$563$	−8.96867	−0.377984	−0.188992	−	0.981979i	$-0.560522\pi$
$563$	−8.96867	−0.377984	−0.188992	+	0.981979i	$0.560522\pi$
$564$	−73.4060	−3.09095
$565$	2.28872	0.0962870
$566$	35.5718	1.49519
$567$	−3.27695	−0.137619
$568$	−18.8623	−0.791442
$569$	29.4542	1.23478	0.617392	−	0.786655i	$-0.288189\pi$
$569$	29.4542	1.23478	0.617392	+	0.786655i	$0.288189\pi$
$570$	−5.78329	−0.242235
$571$	−14.3825	−0.601891	−0.300945	−	0.953641i	$-0.597302\pi$
$571$	−14.3825	−0.601891	−0.300945	+	0.953641i	$0.597302\pi$
$572$	−1.37056	−0.0573060
$573$	0.961813	0.0401803
$574$	−97.3325	−4.06258
$575$	−4.27611	−0.178326
$576$	13.6730	0.569709
$577$	32.8631	1.36811	0.684054	−	0.729431i	$-0.260215\pi$
$577$	32.8631	1.36811	0.684054	+	0.729431i	$0.260215\pi$
$578$	−1.51210	−0.0628951
$579$	3.35140	0.139279
$580$	37.1748	1.54360
$581$	58.8116	2.43991
$582$	−22.6852	−0.940332
$583$	−11.7607	−0.487077
$584$	−8.28884	−0.342995
$585$	−1.98525	−0.0820801
$586$	50.4941	2.08589
$587$	−7.18025	−0.296361	−0.148180	−	0.988960i	$-0.547342\pi$
$587$	−7.18025	−0.296361	−0.148180	+	0.988960i	$0.547342\pi$
$588$	79.2307	3.26742
$589$	4.72068	0.194512
$590$	24.1276	0.993316
$591$	−61.4961	−2.52961
$592$	−58.6701	−2.41133
$593$	−35.2885	−1.44912	−0.724562	−	0.689210i	$-0.757958\pi$
$593$	−35.2885	−1.44912	−0.724562	+	0.689210i	$0.757958\pi$
$594$	−14.4446	−0.592671
$595$	20.3438	0.834016
$596$	−8.70638	−0.356627
$597$	1.24598	0.0509946
$598$	1.02022	0.0417200
$599$	−29.7188	−1.21428	−0.607138	−	0.794597i	$-0.707682\pi$
$599$	−29.7188	−1.21428	−0.607138	+	0.794597i	$0.707682\pi$
$600$	60.9372	2.48775
$601$	8.84367	0.360741	0.180370	−	0.983599i	$-0.442270\pi$
$601$	8.84367	0.360741	0.180370	+	0.983599i	$0.442270\pi$
$602$	−36.1832	−1.47472
$603$	−44.7456	−1.82218
$604$	−92.9276	−3.78117
$605$	1.34186	0.0545543
$606$	−102.899	−4.17997
$607$	−18.5685	−0.753671	−0.376836	−	0.926280i	$-0.622988\pi$
$607$	−18.5685	−0.753671	−0.376836	+	0.926280i	$0.622988\pi$
$608$	−4.36437	−0.176998
$609$	−61.2702	−2.48279
$610$	6.71933	0.272058
$611$	1.66824	0.0674898
$612$	−96.6062	−3.90507
$613$	−9.85988	−0.398237	−0.199118	−	0.979975i	$-0.563808\pi$
$613$	−9.85988	−0.398237	−0.199118	+	0.979975i	$0.563808\pi$
$614$	−74.2912	−2.99815
$615$	−39.6837	−1.60020
$616$	24.3642	0.981661
$617$	28.3609	1.14177	0.570884	−	0.821030i	$-0.306600\pi$
$617$	28.3609	1.14177	0.570884	+	0.821030i	$0.306600\pi$
$618$	35.2125	1.41645
$619$	−3.90217	−0.156841	−0.0784207	−	0.996920i	$-0.524988\pi$
$619$	−3.90217	−0.156841	−0.0784207	+	0.996920i	$0.524988\pi$
$620$	49.3665	1.98261
$621$	7.50366	0.301111
$622$	50.0341	2.00619
$623$	−17.3862	−0.696564
$624$	−6.79220	−0.271906
$625$	1.23332	0.0493327
$626$	61.1214	2.44290
$627$	1.67516	0.0668993
$628$	−39.4322	−1.57352
$629$	30.3736	1.21107
$630$	62.2367	2.47957
$631$	13.8419	0.551038	0.275519	−	0.961296i	$-0.411150\pi$
$631$	13.8419	0.551038	0.275519	+	0.961296i	$0.411150\pi$
$632$	−85.6593	−3.40734
$633$	−74.5781	−2.96421
$634$	−25.0333	−0.994200
$635$	−10.8220	−0.429456
$636$	−153.535	−6.08806
$637$	−1.80061	−0.0713429
$638$	−15.4298	−0.610870
$639$	13.9562	0.552100
$640$	10.2936	0.406891
$641$	15.0054	0.592678	0.296339	−	0.955083i	$-0.404234\pi$
$641$	15.0054	0.592678	0.296339	+	0.955083i	$0.404234\pi$
$642$	−76.2976	−3.01123
$643$	42.4178	1.67279	0.836396	−	0.548125i	$-0.184658\pi$
$643$	42.4178	1.67279	0.836396	+	0.548125i	$0.184658\pi$
$644$	−22.3200	−0.879532
$645$	−14.7524	−0.580874
$646$	6.39575	0.251637
$647$	29.6448	1.16546	0.582728	−	0.812667i	$-0.301985\pi$
$647$	29.6448	1.16546	0.582728	+	0.812667i	$0.301985\pi$
$648$	−6.10912	−0.239989
$649$	−6.98866	−0.274329
$650$	−2.44223	−0.0957921
$651$	−81.3641	−3.18891
$652$	94.1030	3.68536
$653$	30.7970	1.20518	0.602590	−	0.798051i	$-0.294135\pi$
$653$	30.7970	1.20518	0.602590	+	0.798051i	$0.294135\pi$
$654$	13.5663	0.530485
$655$	8.89177	0.347430
$656$	−84.7716	−3.30977
$657$	6.13294	0.239269
$658$	−52.2985	−2.03881
$659$	−11.3759	−0.443143	−0.221572	−	0.975144i	$-0.571119\pi$
$659$	−11.3759	−0.443143	−0.221572	+	0.975144i	$0.571119\pi$
$660$	17.5179	0.681885
$661$	12.9902	0.505259	0.252630	−	0.967563i	$-0.418705\pi$
$661$	12.9902	0.505259	0.252630	+	0.967563i	$0.418705\pi$
$662$	−22.4454	−0.872365
$663$	3.51633	0.136563
$664$	109.641	4.25489
$665$	−2.87543	−0.111504
$666$	92.9200	3.60058
$667$	8.01541	0.310358
$668$	15.0212	0.581189
$669$	−48.6080	−1.87929
$670$	30.9788	1.19682
$671$	−1.94629	−0.0751355
$672$	75.2228	2.90178
$673$	−19.7802	−0.762470	−0.381235	−	0.924478i	$-0.624501\pi$
$673$	−19.7802	−0.762470	−0.381235	+	0.924478i	$0.624501\pi$
$674$	−81.9050	−3.15486
$675$	−17.9624	−0.691373
$676$	−59.6468	−2.29411
$677$	37.5273	1.44229	0.721146	−	0.692783i	$-0.243616\pi$
$677$	37.5273	1.44229	0.721146	+	0.692783i	$0.243616\pi$
$678$	−12.4016	−0.476282
$679$	−11.2790	−0.432848
$680$	37.9265	1.45441
$681$	18.4105	0.705491
$682$	−20.4900	−0.784604
$683$	−24.7681	−0.947726	−0.473863	−	0.880598i	$-0.657141\pi$
$683$	−24.7681	−0.947726	−0.473863	+	0.880598i	$0.657141\pi$
$684$	13.6545	0.522091
$685$	16.4224	0.627467
$686$	−8.65928	−0.330613
$687$	−2.74771	−0.104832
$688$	−31.5137	−1.20145
$689$	3.48927	0.132931
$690$	−13.0401	−0.496426
$691$	15.7083	0.597574	0.298787	−	0.954320i	$-0.403418\pi$
$691$	15.7083	0.597574	0.298787	+	0.954320i	$0.403418\pi$
$692$	−63.0507	−2.39683
$693$	−18.0271	−0.684794
$694$	−75.3695	−2.86099
$695$	−13.8813	−0.526550
$696$	−114.224	−4.32966
$697$	43.8863	1.66231
$698$	70.0464	2.65129
$699$	70.8093	2.67825
$700$	53.4302	2.01947
$701$	−4.45779	−0.168369	−0.0841843	−	0.996450i	$-0.526828\pi$
$701$	−4.45779	−0.168369	−0.0841843	+	0.996450i	$0.526828\pi$
$702$	4.28558	0.161749
$703$	−4.29304	−0.161915
$704$	2.74194	0.103341
$705$	−21.3228	−0.803062
$706$	80.1318	3.01580
$707$	−51.1607	−1.92410
$708$	−91.2368	−3.42889
$709$	−3.44233	−0.129280	−0.0646398	−	0.997909i	$-0.520590\pi$
$709$	−3.44233	−0.129280	−0.0646398	+	0.997909i	$0.520590\pi$
$710$	−9.66234	−0.362621
$711$	63.3796	2.37692
$712$	−32.4126	−1.21472
$713$	10.6441	0.398625
$714$	−110.235	−4.12544
$715$	−0.398117	−0.0148887
$716$	108.961	4.07208
$717$	7.93439	0.296315
$718$	−47.6969	−1.78003
$719$	1.84667	0.0688693	0.0344347	−	0.999407i	$-0.489037\pi$
$719$	1.84667	0.0688693	0.0344347	+	0.999407i	$0.489037\pi$
$720$	54.2049	2.02010
$721$	17.5075	0.652013
$722$	47.9799	1.78563
$723$	−46.2897	−1.72153
$724$	40.6410	1.51041
$725$	−19.1874	−0.712604
$726$	−7.27099	−0.269852
$727$	−39.2268	−1.45484	−0.727421	−	0.686191i	$-0.759281\pi$
$727$	−39.2268	−1.45484	−0.727421	+	0.686191i	$0.759281\pi$
$728$	−7.22862	−0.267910
$729$	−43.0787	−1.59551
$730$	−4.24603	−0.157153
$731$	16.3147	0.603420
$732$	−25.4087	−0.939133
$733$	25.1196	0.927814	0.463907	−	0.885884i	$-0.346447\pi$
$733$	25.1196	0.927814	0.463907	+	0.885884i	$0.346447\pi$
$734$	23.6250	0.872016
$735$	23.0147	0.848911
$736$	−9.84070	−0.362733
$737$	−8.97316	−0.330530
$738$	134.259	4.94213
$739$	−2.20942	−0.0812748	−0.0406374	−	0.999174i	$-0.512939\pi$
$739$	−2.20942	−0.0812748	−0.0406374	+	0.999174i	$0.512939\pi$
$740$	−44.8945	−1.65035
$741$	−0.497003	−0.0182579
$742$	−109.387	−4.01572
$743$	3.99593	0.146596	0.0732982	−	0.997310i	$-0.476648\pi$
$743$	3.99593	0.146596	0.0732982	+	0.997310i	$0.476648\pi$
$744$	−151.685	−5.56104
$745$	−2.52901	−0.0926556
$746$	57.2248	2.09515
$747$	−81.1236	−2.96816
$748$	−19.3731	−0.708351
$749$	−37.9349	−1.38611
$750$	79.9988	2.92114
$751$	14.6502	0.534594	0.267297	−	0.963614i	$-0.413869\pi$
$751$	14.6502	0.534594	0.267297	+	0.963614i	$0.413869\pi$
$752$	−45.5493	−1.66101
$753$	−26.5757	−0.968474
$754$	4.57786	0.166716
$755$	−26.9934	−0.982389
$756$	−93.7584	−3.40996
$757$	−23.0916	−0.839278	−0.419639	−	0.907691i	$-0.637843\pi$
$757$	−23.0916	−0.839278	−0.419639	+	0.907691i	$0.637843\pi$
$758$	50.2612	1.82557
$759$	3.77711	0.137101
$760$	−5.36058	−0.194449
$761$	10.0058	0.362709	0.181354	−	0.983418i	$-0.441952\pi$
$761$	10.0058	0.362709	0.181354	+	0.983418i	$0.441952\pi$
$762$	58.6398	2.12430
$763$	6.74512	0.244190
$764$	1.57219	0.0568797
$765$	−28.0619	−1.01458
$766$	−10.2709	−0.371101
$767$	2.07347	0.0748686
$768$	−71.2748	−2.57191
$769$	20.8232	0.750905	0.375452	−	0.926842i	$-0.377487\pi$
$769$	20.8232	0.750905	0.375452	+	0.926842i	$0.377487\pi$
$770$	12.4808	0.449775
$771$	6.09510	0.219510
$772$	5.47822	0.197165
$773$	−0.517597	−0.0186167	−0.00930834	−	0.999957i	$-0.502963\pi$
$773$	−0.517597	−0.0186167	−0.00930834	+	0.999957i	$0.502963\pi$
$774$	49.9104	1.79399
$775$	−25.4801	−0.915271
$776$	−21.0271	−0.754829
$777$	73.9935	2.65450
$778$	−63.9582	−2.29301
$779$	−6.20295	−0.222244
$780$	−5.19740	−0.186097
$781$	2.79874	0.100147
$782$	14.4210	0.515695
$783$	33.6698	1.20326
$784$	49.1636	1.75584
$785$	−11.4542	−0.408816
$786$	−48.1809	−1.71856
$787$	−50.8626	−1.81305	−0.906527	−	0.422147i	$-0.861277\pi$
$787$	−50.8626	−1.81305	−0.906527	+	0.422147i	$0.861277\pi$
$788$	−100.522	−3.58095
$789$	−19.0487	−0.678151
$790$	−43.8797	−1.56117
$791$	−6.16604	−0.219239
$792$	−33.6075	−1.19419
$793$	0.577444	0.0205056
$794$	90.6569	3.21729
$795$	−44.5984	−1.58174
$796$	2.03669	0.0721886
$797$	−7.05967	−0.250066	−0.125033	−	0.992153i	$-0.539904\pi$
$797$	−7.05967	−0.250066	−0.125033	+	0.992153i	$0.539904\pi$
$798$	15.5808	0.551554
$799$	23.5809	0.834232
$800$	23.5569	0.832861
$801$	23.9822	0.847370
$802$	33.0591	1.16736
$803$	1.22988	0.0434016
$804$	−117.144	−4.13136
$805$	−6.48346	−0.228512
$806$	6.07920	0.214131
$807$	27.0858	0.953464
$808$	−95.3775	−3.35537
$809$	25.4973	0.896437	0.448219	−	0.893924i	$-0.352059\pi$
$809$	25.4973	0.896437	0.448219	+	0.893924i	$0.352059\pi$
$810$	−3.12945	−0.109958
$811$	4.69577	0.164891	0.0824454	−	0.996596i	$-0.473727\pi$
$811$	4.69577	0.164891	0.0824454	+	0.996596i	$0.473727\pi$
$812$	−100.153	−3.51467
$813$	27.4312	0.962054
$814$	18.6339	0.653118
$815$	27.3348	0.957495
$816$	−96.0090	−3.36099
$817$	−2.30594	−0.0806745
$818$	22.3438	0.781234
$819$	5.34848	0.186891
$820$	−64.8673	−2.26526
$821$	−16.5015	−0.575906	−0.287953	−	0.957645i	$-0.592975\pi$
$821$	−16.5015	−0.575906	−0.287953	+	0.957645i	$0.592975\pi$
$822$	−88.9862	−3.10375
$823$	4.93114	0.171889	0.0859444	−	0.996300i	$-0.472609\pi$
$823$	4.93114	0.171889	0.0859444	+	0.996300i	$0.472609\pi$
$824$	32.6387	1.13702
$825$	−9.04173	−0.314793
$826$	−65.0021	−2.26171
$827$	16.6829	0.580122	0.290061	−	0.957008i	$-0.406324\pi$
$827$	16.6829	0.580122	0.290061	+	0.957008i	$0.406324\pi$
$828$	30.7878	1.06995
$829$	42.7677	1.48538	0.742691	−	0.669634i	$-0.233549\pi$
$829$	42.7677	1.48538	0.742691	+	0.669634i	$0.233549\pi$
$830$	56.1644	1.94949
$831$	15.9358	0.552806
$832$	−0.813508	−0.0282033
$833$	−25.4520	−0.881860
$834$	75.2174	2.60457
$835$	4.36333	0.150999
$836$	2.73822	0.0947034
$837$	44.7121	1.54547
$838$	−8.43269	−0.291302
$839$	−16.9024	−0.583537	−0.291768	−	0.956489i	$-0.594244\pi$
$839$	−16.9024	−0.583537	−0.291768	+	0.956489i	$0.594244\pi$
$840$	92.3932	3.18787
$841$	6.96611	0.240211
$842$	−0.716023	−0.0246758
$843$	4.58768	0.158008
$844$	−121.906	−4.19617
$845$	−17.3261	−0.596034
$846$	72.1395	2.48021
$847$	−3.61511	−0.124217
$848$	−95.2703	−3.27160
$849$	−39.0728	−1.34098
$850$	−34.5213	−1.18407
$851$	−9.67988	−0.331822
$852$	36.5375	1.25175
$853$	−51.0685	−1.74855	−0.874277	−	0.485428i	$-0.838664\pi$
$853$	−51.0685	−1.74855	−0.874277	+	0.485428i	$0.838664\pi$
$854$	−18.1026	−0.619458
$855$	3.96631	0.135645
$856$	−70.7209	−2.41719
$857$	−7.49913	−0.256165	−0.128083	−	0.991763i	$-0.540882\pi$
$857$	−7.49913	−0.256165	−0.128083	+	0.991763i	$0.540882\pi$
$858$	2.15723	0.0736467
$859$	−10.5597	−0.360291	−0.180145	−	0.983640i	$-0.557657\pi$
$859$	−10.5597	−0.360291	−0.180145	+	0.983640i	$0.557657\pi$
$860$	−24.1143	−0.822292
$861$	106.912	3.64355
$862$	2.38144	0.0811122
$863$	−24.1987	−0.823734	−0.411867	−	0.911244i	$-0.635123\pi$
$863$	−24.1987	−0.823734	−0.411867	+	0.911244i	$0.635123\pi$
$864$	−41.3372	−1.40632
$865$	−18.3148	−0.622722
$866$	−14.6153	−0.496649
$867$	1.66092	0.0564079
$868$	−132.998	−4.51426
$869$	12.7100	0.431156
$870$	−58.5123	−1.98375
$871$	2.66225	0.0902068
$872$	12.5747	0.425834
$873$	15.5580	0.526559
$874$	−2.03829	−0.0689461
$875$	39.7751	1.34464
$876$	16.0561	0.542484
$877$	31.0382	1.04808	0.524042	−	0.851692i	$-0.324423\pi$
$877$	31.0382	1.04808	0.524042	+	0.851692i	$0.324423\pi$
$878$	41.8220	1.41142
$879$	−55.4638	−1.87075
$880$	10.8701	0.366431
$881$	15.0579	0.507315	0.253657	−	0.967294i	$-0.418366\pi$
$881$	15.0579	0.507315	0.253657	+	0.967294i	$0.418366\pi$
$882$	−77.8638	−2.62181
$883$	46.0845	1.55087	0.775433	−	0.631429i	$-0.217531\pi$
$883$	46.0845	1.55087	0.775433	+	0.631429i	$0.217531\pi$
$884$	5.74782	0.193320
$885$	−26.5022	−0.890862
$886$	−94.7748	−3.18402
$887$	−27.5919	−0.926445	−0.463223	−	0.886242i	$-0.653307\pi$
$887$	−27.5919	−0.926445	−0.463223	+	0.886242i	$0.653307\pi$
$888$	137.944	4.62910
$889$	29.1555	0.977843
$890$	−16.6036	−0.556555
$891$	0.906459	0.0303675
$892$	−79.4549	−2.66035
$893$	−3.33296	−0.111533
$894$	13.7037	0.458319
$895$	31.6508	1.05797
$896$	−27.7321	−0.926463
$897$	−1.12063	−0.0374168
$898$	96.2842	3.21305
$899$	47.7614	1.59293
$900$	−73.7005	−2.45668
$901$	49.3215	1.64314
$902$	26.9238	0.896465
$903$	39.7444	1.32261
$904$	−11.4952	−0.382324
$905$	11.8053	0.392421
$906$	146.266	4.85937
$907$	28.0669	0.931946	0.465973	−	0.884799i	$-0.345704\pi$
$907$	28.0669	0.931946	0.465973	+	0.884799i	$0.345704\pi$
$908$	30.0939	0.998701
$909$	70.5702	2.34066
$910$	−3.70292	−0.122751
$911$	16.7853	0.556123	0.278061	−	0.960563i	$-0.410308\pi$
$911$	16.7853	0.556123	0.278061	+	0.960563i	$0.410308\pi$
$912$	13.5700	0.449349
$913$	−16.2683	−0.538401
$914$	−72.7864	−2.40756
$915$	−7.38066	−0.243997
$916$	−4.49143	−0.148401
$917$	−23.9553	−0.791075
$918$	60.5775	1.99936
$919$	−55.6147	−1.83456	−0.917281	−	0.398242i	$-0.869621\pi$
$919$	−55.6147	−1.83456	−0.917281	+	0.398242i	$0.869621\pi$
$920$	−12.0869	−0.398495
$921$	81.6030	2.68891
$922$	−30.9068	−1.01786
$923$	−0.830360	−0.0273316
$924$	−47.1951	−1.55261
$925$	23.1719	0.761887
$926$	92.2522	3.03160
$927$	−24.1495	−0.793174
$928$	−44.1564	−1.44951
$929$	−38.8290	−1.27394	−0.636968	−	0.770890i	$-0.719812\pi$
$929$	−38.8290	−1.27394	−0.636968	+	0.770890i	$0.719812\pi$
$930$	−77.7018	−2.54794
$931$	3.59742	0.117901
$932$	115.745	3.79137
$933$	−54.9585	−1.79926
$934$	−4.57264	−0.149621
$935$	−5.62745	−0.184037
$936$	9.97102	0.325913
$937$	−24.2020	−0.790643	−0.395322	−	0.918543i	$-0.629367\pi$
$937$	−24.2020	−0.790643	−0.395322	+	0.918543i	$0.629367\pi$
$938$	−83.4601	−2.72507
$939$	−67.1370	−2.19093
$940$	−34.8544	−1.13682
$941$	−24.0444	−0.783826	−0.391913	−	0.920002i	$-0.628187\pi$
$941$	−24.0444	−0.783826	−0.391913	+	0.920002i	$0.628187\pi$
$942$	62.0655	2.02220
$943$	−13.9863	−0.455457
$944$	−56.6135	−1.84261
$945$	−27.2347	−0.885944
$946$	10.0089	0.325417
$947$	−41.1051	−1.33574	−0.667868	−	0.744280i	$-0.732793\pi$
$947$	−41.1051	−1.33574	−0.667868	+	0.744280i	$0.732793\pi$
$948$	165.928	5.38910
$949$	−0.364894	−0.0118450
$950$	4.87930	0.158305
$951$	27.4971	0.891655
$952$	−102.178	−3.31160
$953$	5.03137	0.162982	0.0814910	−	0.996674i	$-0.474032\pi$
$953$	5.03137	0.162982	0.0814910	+	0.996674i	$0.474032\pi$
$954$	150.886	4.88512
$955$	0.456685	0.0147780
$956$	12.9696	0.419467
$957$	16.9484	0.547863
$958$	43.2595	1.39765
$959$	−44.2436	−1.42870
$960$	10.3979	0.335592
$961$	32.4250	1.04597
$962$	−5.52850	−0.178246
$963$	52.3266	1.68620
$964$	−75.6655	−2.43702
$965$	1.59130	0.0512257
$966$	35.1313	1.13033
$967$	−27.0486	−0.869823	−0.434912	−	0.900473i	$-0.643220\pi$
$967$	−27.0486	−0.869823	−0.434912	+	0.900473i	$0.643220\pi$
$968$	−6.73954	−0.216617
$969$	−7.02522	−0.225683
$970$	−10.7713	−0.345846
$971$	−30.6423	−0.983360	−0.491680	−	0.870776i	$-0.663617\pi$
$971$	−30.6423	−0.983360	−0.491680	+	0.870776i	$0.663617\pi$
$972$	−65.9717	−2.11604
$973$	37.3978	1.19892
$974$	41.3834	1.32601
$975$	2.68259	0.0859118
$976$	−15.7664	−0.504670
$977$	40.3902	1.29220	0.646098	−	0.763254i	$-0.276400\pi$
$977$	40.3902	1.29220	0.646098	+	0.763254i	$0.276400\pi$
$978$	−148.116	−4.73623
$979$	4.80932	0.153707
$980$	37.6200	1.20173
$981$	−9.30409	−0.297057
$982$	−31.0203	−0.989898
$983$	51.7403	1.65026	0.825130	−	0.564943i	$-0.191102\pi$
$983$	51.7403	1.65026	0.825130	+	0.564943i	$0.191102\pi$
$984$	199.313	6.35387
$985$	−29.1994	−0.930369
$986$	64.7089	2.06075
$987$	57.4457	1.82852
$988$	−0.812404	−0.0258460
$989$	−5.19939	−0.165331
$990$	−17.2157	−0.547151
$991$	7.94887	0.252504	0.126252	−	0.991998i	$-0.459705\pi$
$991$	7.94887	0.252504	0.126252	+	0.991998i	$0.459705\pi$
$992$	−58.6378	−1.86175
$993$	24.6545	0.782387
$994$	26.0314	0.825664
$995$	0.591612	0.0187554
$996$	−212.382	−6.72958
$997$	−26.1909	−0.829475	−0.414738	−	0.909941i	$-0.636127\pi$
$997$	−26.1909	−0.829475	−0.414738	+	0.909941i	$0.636127\pi$
$998$	30.1305	0.953766
$999$	−40.6617	−1.28648

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.c.1.8	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.c.1.8	✓	106	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57284 q^{2} +2.82606 q^{3} +4.61950 q^{4} +1.34186 q^{5} -7.27099 q^{6} -3.61511 q^{7} -6.73954 q^{8} +4.98661 q^{9} +O(q^{10})\)	\(q-2.57284 q^{2} +2.82606 q^{3} +4.61950 q^{4} +1.34186 q^{5} -7.27099 q^{6} -3.61511 q^{7} -6.73954 q^{8} +4.98661 q^{9} -3.45239 q^{10} +1.00000 q^{11} +13.0550 q^{12} -0.296690 q^{13} +9.30109 q^{14} +3.79217 q^{15} +8.10076 q^{16} -4.19377 q^{17} -12.8297 q^{18} +0.592754 q^{19} +6.19872 q^{20} -10.2165 q^{21} -2.57284 q^{22} +1.33653 q^{23} -19.0464 q^{24} -3.19941 q^{25} +0.763336 q^{26} +5.61428 q^{27} -16.7000 q^{28} +5.99718 q^{29} -9.75665 q^{30} +7.96398 q^{31} -7.36287 q^{32} +2.82606 q^{33} +10.7899 q^{34} -4.85097 q^{35} +23.0356 q^{36} -7.24254 q^{37} -1.52506 q^{38} -0.838464 q^{39} -9.04352 q^{40} -10.4646 q^{41} +26.2854 q^{42} -3.89021 q^{43} +4.61950 q^{44} +6.69133 q^{45} -3.43868 q^{46} -5.62283 q^{47} +22.8932 q^{48} +6.06900 q^{49} +8.23157 q^{50} -11.8518 q^{51} -1.37056 q^{52} -11.7607 q^{53} -14.4446 q^{54} +1.34186 q^{55} +24.3642 q^{56} +1.67516 q^{57} -15.4298 q^{58} -6.98866 q^{59} +17.5179 q^{60} -1.94629 q^{61} -20.4900 q^{62} -18.0271 q^{63} +2.74194 q^{64} -0.398117 q^{65} -7.27099 q^{66} -8.97316 q^{67} -19.3731 q^{68} +3.77711 q^{69} +12.4808 q^{70} +2.79874 q^{71} -33.6075 q^{72} +1.22988 q^{73} +18.6339 q^{74} -9.04173 q^{75} +2.73822 q^{76} -3.61511 q^{77} +2.15723 q^{78} +12.7100 q^{79} +10.8701 q^{80} +0.906459 q^{81} +26.9238 q^{82} -16.2683 q^{83} -47.1951 q^{84} -5.62745 q^{85} +10.0089 q^{86} +16.9484 q^{87} -6.73954 q^{88} +4.80932 q^{89} -17.2157 q^{90} +1.07257 q^{91} +6.17410 q^{92} +22.5067 q^{93} +14.4666 q^{94} +0.795392 q^{95} -20.8079 q^{96} +3.11996 q^{97} -15.6146 q^{98} +4.98661 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * q^99

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