LMFDB - Embedded newform 4017.2.a.g.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.32626 q^{2} -1.00000 q^{3} -0.241032 q^{4} -0.192408 q^{5} +1.32626 q^{6} +3.16535 q^{7} +2.97219 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.32626 q^{2} -1.00000 q^{3} -0.241032 q^{4} -0.192408 q^{5} +1.32626 q^{6} +3.16535 q^{7} +2.97219 q^{8} +1.00000 q^{9} +0.255184 q^{10} -4.14335 q^{11} +0.241032 q^{12} -1.00000 q^{13} -4.19809 q^{14} +0.192408 q^{15} -3.45984 q^{16} +1.73632 q^{17} -1.32626 q^{18} -5.98156 q^{19} +0.0463766 q^{20} -3.16535 q^{21} +5.49516 q^{22} +0.169342 q^{23} -2.97219 q^{24} -4.96298 q^{25} +1.32626 q^{26} -1.00000 q^{27} -0.762953 q^{28} +0.935080 q^{29} -0.255184 q^{30} +10.5446 q^{31} -1.35574 q^{32} +4.14335 q^{33} -2.30282 q^{34} -0.609040 q^{35} -0.241032 q^{36} -2.98142 q^{37} +7.93310 q^{38} +1.00000 q^{39} -0.571875 q^{40} +9.00768 q^{41} +4.19809 q^{42} -0.399904 q^{43} +0.998681 q^{44} -0.192408 q^{45} -0.224591 q^{46} +11.9952 q^{47} +3.45984 q^{48} +3.01947 q^{49} +6.58220 q^{50} -1.73632 q^{51} +0.241032 q^{52} +4.74559 q^{53} +1.32626 q^{54} +0.797215 q^{55} +9.40804 q^{56} +5.98156 q^{57} -1.24016 q^{58} -10.9706 q^{59} -0.0463766 q^{60} -0.590445 q^{61} -13.9849 q^{62} +3.16535 q^{63} +8.71774 q^{64} +0.192408 q^{65} -5.49516 q^{66} -9.87749 q^{67} -0.418510 q^{68} -0.169342 q^{69} +0.807747 q^{70} -6.57275 q^{71} +2.97219 q^{72} -7.85326 q^{73} +3.95414 q^{74} +4.96298 q^{75} +1.44175 q^{76} -13.1152 q^{77} -1.32626 q^{78} -0.0866763 q^{79} +0.665702 q^{80} +1.00000 q^{81} -11.9465 q^{82} +8.46725 q^{83} +0.762953 q^{84} -0.334083 q^{85} +0.530378 q^{86} -0.935080 q^{87} -12.3148 q^{88} +0.647549 q^{89} +0.255184 q^{90} -3.16535 q^{91} -0.0408168 q^{92} -10.5446 q^{93} -15.9087 q^{94} +1.15090 q^{95} +1.35574 q^{96} -11.4983 q^{97} -4.00460 q^{98} -4.14335 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * 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 $

$2$	−1.32626	−0.937808	−0.468904	−	0.883249i	$-0.655351\pi$
$2$	−1.32626	−0.937808	−0.468904	+	0.883249i	$0.655351\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.241032	−0.120516
$5$	−0.192408	−0.0860476	−0.0430238	−	0.999074i	$-0.513699\pi$
$5$	−0.192408	−0.0860476	−0.0430238	+	0.999074i	$0.513699\pi$
$6$	1.32626	0.541444
$7$	3.16535	1.19639	0.598196	−	0.801350i	$-0.295885\pi$
$7$	3.16535	1.19639	0.598196	+	0.801350i	$0.295885\pi$
$8$	2.97219	1.05083
$9$	1.00000	0.333333
$10$	0.255184	0.0806961
$11$	−4.14335	−1.24927	−0.624633	−	0.780918i	$-0.714752\pi$
$11$	−4.14335	−1.24927	−0.624633	+	0.780918i	$0.714752\pi$
$12$	0.241032	0.0695800
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−4.19809	−1.12199
$15$	0.192408	0.0496796
$16$	−3.45984	−0.864960
$17$	1.73632	0.421120	0.210560	−	0.977581i	$-0.432471\pi$
$17$	1.73632	0.421120	0.210560	+	0.977581i	$0.432471\pi$
$18$	−1.32626	−0.312603
$19$	−5.98156	−1.37226	−0.686132	−	0.727478i	$-0.740693\pi$
$19$	−5.98156	−1.37226	−0.686132	+	0.727478i	$0.740693\pi$
$20$	0.0463766	0.0103701
$21$	−3.16535	−0.690737
$22$	5.49516	1.17157
$23$	0.169342	0.0353102	0.0176551	−	0.999844i	$-0.494380\pi$
$23$	0.169342	0.0353102	0.0176551	+	0.999844i	$0.494380\pi$
$24$	−2.97219	−0.606696
$25$	−4.96298	−0.992596
$26$	1.32626	0.260101
$27$	−1.00000	−0.192450
$28$	−0.762953	−0.144185
$29$	0.935080	0.173640	0.0868200	−	0.996224i	$-0.472329\pi$
$29$	0.935080	0.173640	0.0868200	+	0.996224i	$0.472329\pi$
$30$	−0.255184	−0.0465899
$31$	10.5446	1.89387	0.946934	−	0.321428i	$-0.104163\pi$
$31$	10.5446	1.89387	0.946934	+	0.321428i	$0.104163\pi$
$32$	−1.35574	−0.239663
$33$	4.14335	0.721264
$34$	−2.30282	−0.394930
$35$	−0.609040	−0.102947
$36$	−0.241032	−0.0401721
$37$	−2.98142	−0.490143	−0.245071	−	0.969505i	$-0.578811\pi$
$37$	−2.98142	−0.490143	−0.245071	+	0.969505i	$0.578811\pi$
$38$	7.93310	1.28692
$39$	1.00000	0.160128
$40$	−0.571875	−0.0904213
$41$	9.00768	1.40676	0.703381	−	0.710813i	$-0.251673\pi$
$41$	9.00768	1.40676	0.703381	+	0.710813i	$0.251673\pi$
$42$	4.19809	0.647779
$43$	−0.399904	−0.0609849	−0.0304924	−	0.999535i	$-0.509708\pi$
$43$	−0.399904	−0.0609849	−0.0304924	+	0.999535i	$0.509708\pi$
$44$	0.998681	0.150557
$45$	−0.192408	−0.0286825
$46$	−0.224591	−0.0331142
$47$	11.9952	1.74968	0.874838	−	0.484415i	$-0.160968\pi$
$47$	11.9952	1.74968	0.874838	+	0.484415i	$0.160968\pi$
$48$	3.45984	0.499385
$49$	3.01947	0.431352
$50$	6.58220	0.930864
$51$	−1.73632	−0.243134
$52$	0.241032	0.0334252
$53$	4.74559	0.651856	0.325928	−	0.945395i	$-0.394323\pi$
$53$	4.74559	0.651856	0.325928	+	0.945395i	$0.394323\pi$
$54$	1.32626	0.180481
$55$	0.797215	0.107496
$56$	9.40804	1.25720
$57$	5.98156	0.792276
$58$	−1.24016	−0.162841
$59$	−10.9706	−1.42825	−0.714127	−	0.700016i	$-0.753176\pi$
$59$	−10.9706	−1.42825	−0.714127	+	0.700016i	$0.753176\pi$
$60$	−0.0463766	−0.00598720
$61$	−0.590445	−0.0755988	−0.0377994	−	0.999285i	$-0.512035\pi$
$61$	−0.590445	−0.0755988	−0.0377994	+	0.999285i	$0.512035\pi$
$62$	−13.9849	−1.77608
$63$	3.16535	0.398797
$64$	8.71774	1.08972
$65$	0.192408	0.0238653
$66$	−5.49516	−0.676408
$67$	−9.87749	−1.20673	−0.603364	−	0.797466i	$-0.706173\pi$
$67$	−9.87749	−1.20673	−0.603364	+	0.797466i	$0.706173\pi$
$68$	−0.418510	−0.0507518
$69$	−0.169342	−0.0203864
$70$	0.807747	0.0965442
$71$	−6.57275	−0.780041	−0.390021	−	0.920806i	$-0.627532\pi$
$71$	−6.57275	−0.780041	−0.390021	+	0.920806i	$0.627532\pi$
$72$	2.97219	0.350276
$73$	−7.85326	−0.919154	−0.459577	−	0.888138i	$-0.651999\pi$
$73$	−7.85326	−0.919154	−0.459577	+	0.888138i	$0.651999\pi$
$74$	3.95414	0.459660
$75$	4.96298	0.573075
$76$	1.44175	0.165380
$77$	−13.1152	−1.49461
$78$	−1.32626	−0.150169
$79$	−0.0866763	−0.00975184	−0.00487592	−	0.999988i	$-0.501552\pi$
$79$	−0.0866763	−0.00975184	−0.00487592	+	0.999988i	$0.501552\pi$
$80$	0.665702	0.0744277
$81$	1.00000	0.111111
$82$	−11.9465	−1.31927
$83$	8.46725	0.929402	0.464701	−	0.885468i	$-0.346162\pi$
$83$	8.46725	0.929402	0.464701	+	0.885468i	$0.346162\pi$
$84$	0.762953	0.0832450
$85$	−0.334083	−0.0362364
$86$	0.530378	0.0571921
$87$	−0.935080	−0.100251
$88$	−12.3148	−1.31277
$89$	0.647549	0.0686400	0.0343200	−	0.999411i	$-0.489073\pi$
$89$	0.647549	0.0686400	0.0343200	+	0.999411i	$0.489073\pi$
$90$	0.255184	0.0268987
$91$	−3.16535	−0.331819
$92$	−0.0408168	−0.00425545
$93$	−10.5446	−1.09343
$94$	−15.9087	−1.64086
$95$	1.15090	0.118080
$96$	1.35574	0.138369
$97$	−11.4983	−1.16748	−0.583740	−	0.811941i	$-0.698411\pi$
$97$	−11.4983	−1.16748	−0.583740	+	0.811941i	$0.698411\pi$
$98$	−4.00460	−0.404526
$99$	−4.14335	−0.416422
$100$	1.19624	0.119624
$101$	11.7977	1.17391	0.586957	−	0.809618i	$-0.300326\pi$
$101$	11.7977	1.17391	0.586957	+	0.809618i	$0.300326\pi$
$102$	2.30282	0.228013
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−2.97219	−0.291448
$105$	0.609040	0.0594363
$106$	−6.29388	−0.611316
$107$	11.6731	1.12848	0.564242	−	0.825609i	$-0.309169\pi$
$107$	11.6731	1.12848	0.564242	+	0.825609i	$0.309169\pi$
$108$	0.241032	0.0231933
$109$	10.4367	0.999655	0.499828	−	0.866125i	$-0.333397\pi$
$109$	10.4367	0.999655	0.499828	+	0.866125i	$0.333397\pi$
$110$	−1.05731	−0.100811
$111$	2.98142	0.282984
$112$	−10.9516	−1.03483
$113$	−14.4395	−1.35836	−0.679178	−	0.733973i	$-0.737664\pi$
$113$	−14.4395	−1.35836	−0.679178	+	0.733973i	$0.737664\pi$
$114$	−7.93310	−0.743003
$115$	−0.0325828	−0.00303836
$116$	−0.225385	−0.0209264
$117$	−1.00000	−0.0924500
$118$	14.5499	1.33943
$119$	5.49607	0.503824
$120$	0.571875	0.0522048
$121$	6.16734	0.560667
$122$	0.783084	0.0708971
$123$	−9.00768	−0.812195
$124$	−2.54159	−0.228242
$125$	1.91696	0.171458
$126$	−4.19809	−0.373995
$127$	−6.72564	−0.596804	−0.298402	−	0.954440i	$-0.596454\pi$
$127$	−6.72564	−0.596804	−0.298402	+	0.954440i	$0.596454\pi$
$128$	−8.85052	−0.782283
$129$	0.399904	0.0352096
$130$	−0.255184	−0.0223811
$131$	5.09100	0.444803	0.222402	−	0.974955i	$-0.428610\pi$
$131$	5.09100	0.444803	0.222402	+	0.974955i	$0.428610\pi$
$132$	−0.998681	−0.0869240
$133$	−18.9337	−1.64176
$134$	13.1001	1.13168
$135$	0.192408	0.0165599
$136$	5.16068	0.442525
$137$	−0.822792	−0.0702958	−0.0351479	−	0.999382i	$-0.511190\pi$
$137$	−0.822792	−0.0702958	−0.0351479	+	0.999382i	$0.511190\pi$
$138$	0.224591	0.0191185
$139$	1.29312	0.109681	0.0548404	−	0.998495i	$-0.482535\pi$
$139$	1.29312	0.109681	0.0548404	+	0.998495i	$0.482535\pi$
$140$	0.146798	0.0124067
$141$	−11.9952	−1.01018
$142$	8.71718	0.731529
$143$	4.14335	0.346484
$144$	−3.45984	−0.288320
$145$	−0.179917	−0.0149413
$146$	10.4155	0.861990
$147$	−3.01947	−0.249041
$148$	0.718619	0.0590701
$149$	−2.83204	−0.232010	−0.116005	−	0.993249i	$-0.537009\pi$
$149$	−2.83204	−0.232010	−0.116005	+	0.993249i	$0.537009\pi$
$150$	−6.58220	−0.537435
$151$	0.707133	0.0575457	0.0287728	−	0.999586i	$-0.490840\pi$
$151$	0.707133	0.0575457	0.0287728	+	0.999586i	$0.490840\pi$
$152$	−17.7783	−1.44201
$153$	1.73632	0.140373
$154$	17.3941	1.40166
$155$	−2.02887	−0.162963
$156$	−0.241032	−0.0192980
$157$	−7.40971	−0.591359	−0.295680	−	0.955287i	$-0.595546\pi$
$157$	−7.40971	−0.591359	−0.295680	+	0.955287i	$0.595546\pi$
$158$	0.114955	0.00914536
$159$	−4.74559	−0.376349
$160$	0.260855	0.0206224
$161$	0.536027	0.0422448
$162$	−1.32626	−0.104201
$163$	16.2137	1.26996	0.634978	−	0.772530i	$-0.281009\pi$
$163$	16.2137	1.26996	0.634978	+	0.772530i	$0.281009\pi$
$164$	−2.17114	−0.169538
$165$	−0.797215	−0.0620631
$166$	−11.2298	−0.871600
$167$	18.6345	1.44198	0.720991	−	0.692944i	$-0.243687\pi$
$167$	18.6345	1.44198	0.720991	+	0.692944i	$0.243687\pi$
$168$	−9.40804	−0.725846
$169$	1.00000	0.0769231
$170$	0.443081	0.0339828
$171$	−5.98156	−0.457421
$172$	0.0963899	0.00734966
$173$	−19.9918	−1.51995	−0.759974	−	0.649954i	$-0.774788\pi$
$173$	−19.9918	−1.51995	−0.759974	+	0.649954i	$0.774788\pi$
$174$	1.24016	0.0940163
$175$	−15.7096	−1.18753
$176$	14.3353	1.08057
$177$	10.9706	0.824603
$178$	−0.858819	−0.0643712
$179$	13.0783	0.977520	0.488760	−	0.872418i	$-0.337449\pi$
$179$	13.0783	0.977520	0.488760	+	0.872418i	$0.337449\pi$
$180$	0.0463766	0.00345671
$181$	18.8711	1.40268	0.701338	−	0.712829i	$-0.252587\pi$
$181$	18.8711	1.40268	0.701338	+	0.712829i	$0.252587\pi$
$182$	4.19809	0.311183
$183$	0.590445	0.0436470
$184$	0.503316	0.0371050
$185$	0.573650	0.0421756
$186$	13.9849	1.02542
$187$	−7.19419	−0.526091
$188$	−2.89123	−0.210864
$189$	−3.16535	−0.230246
$190$	−1.52639	−0.110736
$191$	9.11256	0.659362	0.329681	−	0.944092i	$-0.393059\pi$
$191$	9.11256	0.659362	0.329681	+	0.944092i	$0.393059\pi$
$192$	−8.71774	−0.629149
$193$	24.3986	1.75625	0.878124	−	0.478432i	$-0.158795\pi$
$193$	24.3986	1.75625	0.878124	+	0.478432i	$0.158795\pi$
$194$	15.2498	1.09487
$195$	−0.192408	−0.0137786
$196$	−0.727789	−0.0519849
$197$	−23.9888	−1.70913	−0.854565	−	0.519345i	$-0.826176\pi$
$197$	−23.9888	−1.70913	−0.854565	+	0.519345i	$0.826176\pi$
$198$	5.49516	0.390524
$199$	−21.3197	−1.51131	−0.755656	−	0.654969i	$-0.772682\pi$
$199$	−21.3197	−1.51131	−0.755656	+	0.654969i	$0.772682\pi$
$200$	−14.7509	−1.04305
$201$	9.87749	0.696704
$202$	−15.6468	−1.10091
$203$	2.95986	0.207741
$204$	0.418510	0.0293015
$205$	−1.73315	−0.121049
$206$	−1.32626	−0.0924050
$207$	0.169342	0.0117701
$208$	3.45984	0.239897
$209$	24.7837	1.71432
$210$	−0.807747	−0.0557398
$211$	2.64146	0.181845	0.0909227	−	0.995858i	$-0.471018\pi$
$211$	2.64146	0.181845	0.0909227	+	0.995858i	$0.471018\pi$
$212$	−1.14384	−0.0785592
$213$	6.57275	0.450357
$214$	−15.4816	−1.05830
$215$	0.0769449	0.00524760
$216$	−2.97219	−0.202232
$217$	33.3774	2.26581
$218$	−13.8418	−0.937485
$219$	7.85326	0.530674
$220$	−0.192155	−0.0129551
$221$	−1.73632	−0.116798
$222$	−3.95414	−0.265385
$223$	8.98854	0.601917	0.300958	−	0.953637i	$-0.402693\pi$
$223$	8.98854	0.601917	0.300958	+	0.953637i	$0.402693\pi$
$224$	−4.29139	−0.286731
$225$	−4.96298	−0.330865
$226$	19.1506	1.27388
$227$	9.03483	0.599663	0.299831	−	0.953992i	$-0.403070\pi$
$227$	9.03483	0.599663	0.299831	+	0.953992i	$0.403070\pi$
$228$	−1.44175	−0.0954821
$229$	13.6582	0.902562	0.451281	−	0.892382i	$-0.350967\pi$
$229$	13.6582	0.902562	0.451281	+	0.892382i	$0.350967\pi$
$230$	0.0432132	0.00284940
$231$	13.1152	0.862915
$232$	2.77924	0.182466
$233$	26.3895	1.72883	0.864416	−	0.502777i	$-0.167688\pi$
$233$	26.3895	1.72883	0.864416	+	0.502777i	$0.167688\pi$
$234$	1.32626	0.0867004
$235$	−2.30797	−0.150556
$236$	2.64428	0.172128
$237$	0.0866763	0.00563023
$238$	−7.28923	−0.472490
$239$	21.0550	1.36194	0.680969	−	0.732313i	$-0.261559\pi$
$239$	21.0550	1.36194	0.680969	+	0.732313i	$0.261559\pi$
$240$	−0.665702	−0.0429709
$241$	6.68009	0.430302	0.215151	−	0.976581i	$-0.430976\pi$
$241$	6.68009	0.430302	0.215151	+	0.976581i	$0.430976\pi$
$242$	−8.17950	−0.525798
$243$	−1.00000	−0.0641500
$244$	0.142316	0.00911087
$245$	−0.580971	−0.0371168
$246$	11.9465	0.761683
$247$	5.98156	0.380597
$248$	31.3406	1.99013
$249$	−8.46725	−0.536590
$250$	−2.54239	−0.160795
$251$	30.7591	1.94150	0.970750	−	0.240093i	$-0.0771779\pi$
$251$	30.7591	1.94150	0.970750	+	0.240093i	$0.0771779\pi$
$252$	−0.762953	−0.0480615
$253$	−0.701642	−0.0441119
$254$	8.91995	0.559688
$255$	0.334083	0.0209211
$256$	−5.69738	−0.356086
$257$	14.2938	0.891622	0.445811	−	0.895127i	$-0.352915\pi$
$257$	14.2938	0.891622	0.445811	+	0.895127i	$0.352915\pi$
$258$	−0.530378	−0.0330199
$259$	−9.43726	−0.586403
$260$	−0.0463766	−0.00287616
$261$	0.935080	0.0578800
$262$	−6.75200	−0.417140
$263$	−24.4022	−1.50470	−0.752352	−	0.658761i	$-0.771081\pi$
$263$	−24.4022	−1.50470	−0.752352	+	0.658761i	$0.771081\pi$
$264$	12.3148	0.757926
$265$	−0.913090	−0.0560907
$266$	25.1111	1.53966
$267$	−0.647549	−0.0396293
$268$	2.38079	0.145430
$269$	−0.524784	−0.0319967	−0.0159983	−	0.999872i	$-0.505093\pi$
$269$	−0.524784	−0.0319967	−0.0159983	+	0.999872i	$0.505093\pi$
$270$	−0.255184	−0.0155300
$271$	−1.52972	−0.0929241	−0.0464621	−	0.998920i	$-0.514795\pi$
$271$	−1.52972	−0.0929241	−0.0464621	+	0.998920i	$0.514795\pi$
$272$	−6.00739	−0.364252
$273$	3.16535	0.191576
$274$	1.09124	0.0659240
$275$	20.5634	1.24002
$276$	0.0408168	0.00245689
$277$	−32.1329	−1.93068	−0.965340	−	0.260997i	$-0.915949\pi$
$277$	−32.1329	−1.93068	−0.965340	+	0.260997i	$0.915949\pi$
$278$	−1.71501	−0.102860
$279$	10.5446	0.631289
$280$	−1.81019	−0.108179
$281$	17.6938	1.05552	0.527762	−	0.849393i	$-0.323031\pi$
$281$	17.6938	1.05552	0.527762	+	0.849393i	$0.323031\pi$
$282$	15.9087	0.947351
$283$	15.7618	0.936939	0.468469	−	0.883480i	$-0.344806\pi$
$283$	15.7618	0.936939	0.468469	+	0.883480i	$0.344806\pi$
$284$	1.58424	0.0940076
$285$	−1.15090	−0.0681735
$286$	−5.49516	−0.324936
$287$	28.5125	1.68304
$288$	−1.35574	−0.0798876
$289$	−13.9852	−0.822658
$290$	0.238617	0.0140121
$291$	11.4983	0.674045
$292$	1.89289	0.110773
$293$	11.2127	0.655053	0.327526	−	0.944842i	$-0.393785\pi$
$293$	11.2127	0.655053	0.327526	+	0.944842i	$0.393785\pi$
$294$	4.00460	0.233553
$295$	2.11084	0.122898
$296$	−8.86136	−0.515056
$297$	4.14335	0.240421
$298$	3.75603	0.217581
$299$	−0.169342	−0.00979329
$300$	−1.19624	−0.0690649
$301$	−1.26584	−0.0729618
$302$	−0.937843	−0.0539668
$303$	−11.7977	−0.677760
$304$	20.6952	1.18695
$305$	0.113607	0.00650509
$306$	−2.30282	−0.131643
$307$	−14.3622	−0.819694	−0.409847	−	0.912154i	$-0.634418\pi$
$307$	−14.3622	−0.819694	−0.409847	+	0.912154i	$0.634418\pi$
$308$	3.16118	0.180125
$309$	−1.00000	−0.0568880
$310$	2.69081	0.152828
$311$	−4.37207	−0.247918	−0.123959	−	0.992287i	$-0.539559\pi$
$311$	−4.37207	−0.247918	−0.123959	+	0.992287i	$0.539559\pi$
$312$	2.97219	0.168267
$313$	25.8291	1.45995	0.729974	−	0.683475i	$-0.239532\pi$
$313$	25.8291	1.45995	0.729974	+	0.683475i	$0.239532\pi$
$314$	9.82721	0.554581
$315$	−0.609040	−0.0343155
$316$	0.0208918	0.00117525
$317$	−8.10495	−0.455220	−0.227610	−	0.973752i	$-0.573091\pi$
$317$	−8.10495	−0.455220	−0.227610	+	0.973752i	$0.573091\pi$
$318$	6.29388	0.352944
$319$	−3.87436	−0.216923
$320$	−1.67737	−0.0937676
$321$	−11.6731	−0.651530
$322$	−0.710911	−0.0396175
$323$	−10.3859	−0.577887
$324$	−0.241032	−0.0133907
$325$	4.96298	0.275297
$326$	−21.5036	−1.19098
$327$	−10.4367	−0.577151
$328$	26.7726	1.47827
$329$	37.9690	2.09330
$330$	1.05731	0.0582033
$331$	−6.59177	−0.362316	−0.181158	−	0.983454i	$-0.557985\pi$
$331$	−6.59177	−0.362316	−0.181158	+	0.983454i	$0.557985\pi$
$332$	−2.04088	−0.112008
$333$	−2.98142	−0.163381
$334$	−24.7142	−1.35230
$335$	1.90051	0.103836
$336$	10.9516	0.597460
$337$	−0.311739	−0.0169815	−0.00849075	−	0.999964i	$-0.502703\pi$
$337$	−0.311739	−0.0169815	−0.00849075	+	0.999964i	$0.502703\pi$
$338$	−1.32626	−0.0721391
$339$	14.4395	0.784247
$340$	0.0805248	0.00436707
$341$	−43.6900	−2.36595
$342$	7.93310	0.428973
$343$	−12.5998	−0.680325
$344$	−1.18859	−0.0640847
$345$	0.0325828	0.00175420
$346$	26.5143	1.42542
$347$	−10.2217	−0.548731	−0.274366	−	0.961625i	$-0.588468\pi$
$347$	−10.2217	−0.548731	−0.274366	+	0.961625i	$0.588468\pi$
$348$	0.225385	0.0120819
$349$	13.1673	0.704831	0.352416	−	0.935844i	$-0.385360\pi$
$349$	13.1673	0.704831	0.352416	+	0.935844i	$0.385360\pi$
$350$	20.8350	1.11368
$351$	1.00000	0.0533761
$352$	5.61730	0.299403
$353$	11.0733	0.589375	0.294687	−	0.955594i	$-0.404784\pi$
$353$	11.0733	0.589375	0.294687	+	0.955594i	$0.404784\pi$
$354$	−14.5499	−0.773319
$355$	1.26465	0.0671207
$356$	−0.156080	−0.00827223
$357$	−5.49607	−0.290883
$358$	−17.3453	−0.916726
$359$	13.7928	0.727958	0.363979	−	0.931407i	$-0.381418\pi$
$359$	13.7928	0.727958	0.363979	+	0.931407i	$0.381418\pi$
$360$	−0.571875	−0.0301404
$361$	16.7790	0.883106
$362$	−25.0280	−1.31544
$363$	−6.16734	−0.323701
$364$	0.762953	0.0399896
$365$	1.51103	0.0790910
$366$	−0.783084	−0.0409325
$367$	7.88356	0.411519	0.205759	−	0.978603i	$-0.434034\pi$
$367$	7.88356	0.411519	0.205759	+	0.978603i	$0.434034\pi$
$368$	−0.585895	−0.0305419
$369$	9.00768	0.468921
$370$	−0.760810	−0.0395526
$371$	15.0215	0.779875
$372$	2.54159	0.131775
$373$	11.4031	0.590429	0.295215	−	0.955431i	$-0.404609\pi$
$373$	11.4031	0.590429	0.295215	+	0.955431i	$0.404609\pi$
$374$	9.54137	0.493372
$375$	−1.91696	−0.0989914
$376$	35.6520	1.83861
$377$	−0.935080	−0.0481591
$378$	4.19809	0.215926
$379$	−12.4875	−0.641441	−0.320721	−	0.947174i	$-0.603925\pi$
$379$	−12.4875	−0.641441	−0.320721	+	0.947174i	$0.603925\pi$
$380$	−0.277404	−0.0142305
$381$	6.72564	0.344565
$382$	−12.0856	−0.618355
$383$	12.1254	0.619581	0.309790	−	0.950805i	$-0.399741\pi$
$383$	12.1254	0.619581	0.309790	+	0.950805i	$0.399741\pi$
$384$	8.85052	0.451651
$385$	2.52347	0.128608
$386$	−32.3589	−1.64702
$387$	−0.399904	−0.0203283
$388$	2.77147	0.140700
$389$	4.91490	0.249195	0.124598	−	0.992207i	$-0.460236\pi$
$389$	4.91490	0.249195	0.124598	+	0.992207i	$0.460236\pi$
$390$	0.255184	0.0129217
$391$	0.294032	0.0148698
$392$	8.97444	0.453278
$393$	−5.09100	−0.256807
$394$	31.8154	1.60284
$395$	0.0166772	0.000839123 0
$396$	0.998681	0.0501856
$397$	21.6567	1.08692	0.543458	−	0.839436i	$-0.317115\pi$
$397$	21.6567	1.08692	0.543458	+	0.839436i	$0.317115\pi$
$398$	28.2754	1.41732
$399$	18.9337	0.947873
$400$	17.1711	0.858555
$401$	20.8666	1.04203	0.521014	−	0.853548i	$-0.325554\pi$
$401$	20.8666	1.04203	0.521014	+	0.853548i	$0.325554\pi$
$402$	−13.1001	−0.653375
$403$	−10.5446	−0.525265
$404$	−2.84363	−0.141476
$405$	−0.192408	−0.00956085
$406$	−3.92555	−0.194822
$407$	12.3531	0.612319
$408$	−5.16068	−0.255492
$409$	−26.8098	−1.32566	−0.662830	−	0.748770i	$-0.730645\pi$
$409$	−26.8098	−1.32566	−0.662830	+	0.748770i	$0.730645\pi$
$410$	2.29861	0.113520
$411$	0.822792	0.0405853
$412$	−0.241032	−0.0118748
$413$	−34.7259	−1.70875
$414$	−0.224591	−0.0110381
$415$	−1.62917	−0.0799728
$416$	1.35574	0.0664705
$417$	−1.29312	−0.0633243
$418$	−32.8696	−1.60771
$419$	18.1526	0.886810	0.443405	−	0.896321i	$-0.353770\pi$
$419$	18.1526	0.886810	0.443405	+	0.896321i	$0.353770\pi$
$420$	−0.146798	−0.00716303
$421$	−37.6786	−1.83634	−0.918172	−	0.396183i	$-0.870335\pi$
$421$	−37.6786	−1.83634	−0.918172	+	0.396183i	$0.870335\pi$
$422$	−3.50326	−0.170536
$423$	11.9952	0.583226
$424$	14.1048	0.684990
$425$	−8.61733	−0.418002
$426$	−8.71718	−0.422349
$427$	−1.86897	−0.0904457
$428$	−2.81360	−0.136001
$429$	−4.14335	−0.200043
$430$	−0.102049	−0.00492124
$431$	−23.2562	−1.12021	−0.560105	−	0.828422i	$-0.689239\pi$
$431$	−23.2562	−1.12021	−0.560105	+	0.828422i	$0.689239\pi$
$432$	3.45984	0.166462
$433$	18.5374	0.890850	0.445425	−	0.895319i	$-0.353053\pi$
$433$	18.5374	0.890850	0.445425	+	0.895319i	$0.353053\pi$
$434$	−44.2672	−2.12489
$435$	0.179917	0.00862637
$436$	−2.51558	−0.120475
$437$	−1.01293	−0.0484549
$438$	−10.4155	−0.497670
$439$	11.4118	0.544656	0.272328	−	0.962204i	$-0.412206\pi$
$439$	11.4118	0.544656	0.272328	+	0.962204i	$0.412206\pi$
$440$	2.36948	0.112960
$441$	3.01947	0.143784
$442$	2.30282	0.109534
$443$	−7.56911	−0.359619	−0.179810	−	0.983701i	$-0.557548\pi$
$443$	−7.56911	−0.359619	−0.179810	+	0.983701i	$0.557548\pi$
$444$	−0.718619	−0.0341042
$445$	−0.124594	−0.00590631
$446$	−11.9211	−0.564482
$447$	2.83204	0.133951
$448$	27.5947	1.30373
$449$	−12.0793	−0.570057	−0.285028	−	0.958519i	$-0.592003\pi$
$449$	−12.0793	−0.570057	−0.285028	+	0.958519i	$0.592003\pi$
$450$	6.58220	0.310288
$451$	−37.3219	−1.75742
$452$	3.48039	0.163704
$453$	−0.707133	−0.0332240
$454$	−11.9825	−0.562368
$455$	0.609040	0.0285523
$456$	17.7783	0.832547
$457$	9.54114	0.446316	0.223158	−	0.974782i	$-0.428363\pi$
$457$	9.54114	0.446316	0.223158	+	0.974782i	$0.428363\pi$
$458$	−18.1144	−0.846430
$459$	−1.73632	−0.0810446
$460$	0.00785350	0.000366171 0
$461$	1.12753	0.0525142	0.0262571	−	0.999655i	$-0.491641\pi$
$461$	1.12753	0.0525142	0.0262571	+	0.999655i	$0.491641\pi$
$462$	−17.3941	−0.809248
$463$	20.5689	0.955918	0.477959	−	0.878382i	$-0.341377\pi$
$463$	20.5689	0.955918	0.477959	+	0.878382i	$0.341377\pi$
$464$	−3.23523	−0.150192
$465$	2.02887	0.0940866
$466$	−34.9993	−1.62131
$467$	−18.0569	−0.835572	−0.417786	−	0.908545i	$-0.637194\pi$
$467$	−18.0569	−0.835572	−0.417786	+	0.908545i	$0.637194\pi$
$468$	0.241032	0.0111417
$469$	−31.2657	−1.44372
$470$	3.06097	0.141192
$471$	7.40971	0.341421
$472$	−32.6068	−1.50085
$473$	1.65694	0.0761863
$474$	−0.114955	−0.00528007
$475$	29.6863	1.36210
$476$	−1.32473	−0.0607190
$477$	4.74559	0.217285
$478$	−27.9245	−1.27724
$479$	33.4017	1.52616	0.763081	−	0.646303i	$-0.223686\pi$
$479$	33.4017	1.52616	0.763081	+	0.646303i	$0.223686\pi$
$480$	−0.260855	−0.0119064
$481$	2.98142	0.135941
$482$	−8.85954	−0.403541
$483$	−0.536027	−0.0243901
$484$	−1.48653	−0.0675694
$485$	2.21238	0.100459
$486$	1.32626	0.0601604
$487$	37.9964	1.72178	0.860891	−	0.508790i	$-0.169907\pi$
$487$	37.9964	1.72178	0.860891	+	0.508790i	$0.169907\pi$
$488$	−1.75492	−0.0794414
$489$	−16.2137	−0.733210
$490$	0.770518	0.0348085
$491$	16.1996	0.731077	0.365539	−	0.930796i	$-0.380885\pi$
$491$	16.1996	0.731077	0.365539	+	0.930796i	$0.380885\pi$
$492$	2.17114	0.0978826
$493$	1.62360	0.0731233
$494$	−7.93310	−0.356927
$495$	0.797215	0.0358321
$496$	−36.4827	−1.63812
$497$	−20.8051	−0.933235
$498$	11.2298	0.503219
$499$	−15.3267	−0.686116	−0.343058	−	0.939314i	$-0.611463\pi$
$499$	−15.3267	−0.686116	−0.343058	+	0.939314i	$0.611463\pi$
$500$	−0.462049	−0.0206635
$501$	−18.6345	−0.832529
$502$	−40.7946	−1.82075
$503$	16.1619	0.720623	0.360311	−	0.932832i	$-0.382670\pi$
$503$	16.1619	0.720623	0.360311	+	0.932832i	$0.382670\pi$
$504$	9.40804	0.419068
$505$	−2.26998	−0.101013
$506$	0.930560	0.0413684
$507$	−1.00000	−0.0444116
$508$	1.62110	0.0719245
$509$	29.2323	1.29570	0.647849	−	0.761769i	$-0.275669\pi$
$509$	29.2323	1.29570	0.647849	+	0.761769i	$0.275669\pi$
$510$	−0.443081	−0.0196200
$511$	−24.8583	−1.09967
$512$	25.2573	1.11622
$513$	5.98156	0.264092
$514$	−18.9573	−0.836170
$515$	−0.192408	−0.00847852
$516$	−0.0963899	−0.00424333
$517$	−49.7002	−2.18581
$518$	12.5163	0.549933
$519$	19.9918	0.877542
$520$	0.571875	0.0250784
$521$	7.24547	0.317430	0.158715	−	0.987324i	$-0.449265\pi$
$521$	7.24547	0.317430	0.158715	+	0.987324i	$0.449265\pi$
$522$	−1.24016	−0.0542803
$523$	−5.35969	−0.234363	−0.117181	−	0.993111i	$-0.537386\pi$
$523$	−5.35969	−0.234363	−0.117181	+	0.993111i	$0.537386\pi$
$524$	−1.22710	−0.0536060
$525$	15.7096	0.685623
$526$	32.3637	1.41112
$527$	18.3088	0.797546
$528$	−14.3353	−0.623865
$529$	−22.9713	−0.998753
$530$	1.21100	0.0526023
$531$	−10.9706	−0.476085
$532$	4.56364	0.197859
$533$	−9.00768	−0.390166
$534$	0.858819	0.0371647
$535$	−2.24601	−0.0971033
$536$	−29.3578	−1.26806
$537$	−13.0783	−0.564371
$538$	0.696001	0.0300067
$539$	−12.5107	−0.538874
$540$	−0.0463766	−0.00199573
$541$	28.4956	1.22512	0.612561	−	0.790423i	$-0.290139\pi$
$541$	28.4956	1.22512	0.612561	+	0.790423i	$0.290139\pi$
$542$	2.02881	0.0871450
$543$	−18.8711	−0.809835
$544$	−2.35400	−0.100927
$545$	−2.00811	−0.0860180
$546$	−4.19809	−0.179661
$547$	7.49207	0.320338	0.160169	−	0.987090i	$-0.448796\pi$
$547$	7.49207	0.320338	0.160169	+	0.987090i	$0.448796\pi$
$548$	0.198319	0.00847178
$549$	−0.590445	−0.0251996
$550$	−27.2724	−1.16290
$551$	−5.59323	−0.238280
$552$	−0.503316	−0.0214226
$553$	−0.274361	−0.0116670
$554$	42.6166	1.81061
$555$	−0.573650	−0.0243501
$556$	−0.311683	−0.0132183
$557$	6.80581	0.288372	0.144186	−	0.989551i	$-0.453944\pi$
$557$	6.80581	0.288372	0.144186	+	0.989551i	$0.453944\pi$
$558$	−13.9849	−0.592028
$559$	0.399904	0.0169142
$560$	2.10718	0.0890447
$561$	7.19419	0.303739
$562$	−23.4666	−0.989878
$563$	42.8700	1.80676	0.903378	−	0.428844i	$-0.141079\pi$
$563$	42.8700	1.80676	0.903378	+	0.428844i	$0.141079\pi$
$564$	2.89123	0.121743
$565$	2.77828	0.116883
$566$	−20.9042	−0.878669
$567$	3.16535	0.132932
$568$	−19.5355	−0.819690
$569$	12.7015	0.532474	0.266237	−	0.963908i	$-0.414220\pi$
$569$	12.7015	0.532474	0.266237	+	0.963908i	$0.414220\pi$
$570$	1.52639	0.0639337
$571$	12.1574	0.508770	0.254385	−	0.967103i	$-0.418127\pi$
$571$	12.1574	0.508770	0.254385	+	0.967103i	$0.418127\pi$
$572$	−0.998681	−0.0417569
$573$	−9.11256	−0.380683
$574$	−37.8150	−1.57837
$575$	−0.840440	−0.0350488
$576$	8.71774	0.363239
$577$	−35.2221	−1.46632	−0.733159	−	0.680058i	$-0.761955\pi$
$577$	−35.2221	−1.46632	−0.733159	+	0.680058i	$0.761955\pi$
$578$	18.5480	0.771495
$579$	−24.3986	−1.01397
$580$	0.0433659	0.00180067
$581$	26.8018	1.11193
$582$	−15.2498	−0.632124
$583$	−19.6626	−0.814342
$584$	−23.3414	−0.965874
$585$	0.192408	0.00795510
$586$	−14.8710	−0.614314
$587$	20.3580	0.840265	0.420133	−	0.907463i	$-0.361984\pi$
$587$	20.3580	0.840265	0.420133	+	0.907463i	$0.361984\pi$
$588$	0.727789	0.0300135
$589$	−63.0732	−2.59889
$590$	−2.79952	−0.115255
$591$	23.9888	0.986766
$592$	10.3152	0.423954
$593$	−12.8068	−0.525910	−0.262955	−	0.964808i	$-0.584697\pi$
$593$	−12.8068	−0.525910	−0.262955	+	0.964808i	$0.584697\pi$
$594$	−5.49516	−0.225469
$595$	−1.05749	−0.0433529
$596$	0.682614	0.0279610
$597$	21.3197	0.872556
$598$	0.224591	0.00918422
$599$	21.9931	0.898613	0.449307	−	0.893378i	$-0.351671\pi$
$599$	21.9931	0.898613	0.449307	+	0.893378i	$0.351671\pi$
$600$	14.7509	0.602204
$601$	22.5867	0.921329	0.460664	−	0.887574i	$-0.347611\pi$
$601$	22.5867	0.921329	0.460664	+	0.887574i	$0.347611\pi$
$602$	1.67883	0.0684241
$603$	−9.87749	−0.402242
$604$	−0.170442	−0.00693519
$605$	−1.18665	−0.0482441
$606$	15.6468	0.635609
$607$	46.2656	1.87786	0.938931	−	0.344105i	$-0.111818\pi$
$607$	46.2656	1.87786	0.938931	+	0.344105i	$0.111818\pi$
$608$	8.10942	0.328881
$609$	−2.95986	−0.119940
$610$	−0.150672	−0.00610053
$611$	−11.9952	−0.485273
$612$	−0.418510	−0.0169173
$613$	−28.9804	−1.17051	−0.585253	−	0.810851i	$-0.699005\pi$
$613$	−28.9804	−1.17051	−0.585253	+	0.810851i	$0.699005\pi$
$614$	19.0480	0.768715
$615$	1.73315	0.0698874
$616$	−38.9808	−1.57058
$617$	13.6322	0.548812	0.274406	−	0.961614i	$-0.411519\pi$
$617$	13.6322	0.548812	0.274406	+	0.961614i	$0.411519\pi$
$618$	1.32626	0.0533500
$619$	−32.8611	−1.32080	−0.660400	−	0.750914i	$-0.729613\pi$
$619$	−32.8611	−1.32080	−0.660400	+	0.750914i	$0.729613\pi$
$620$	0.489024	0.0196397
$621$	−0.169342	−0.00679545
$622$	5.79851	0.232499
$623$	2.04972	0.0821204
$624$	−3.45984	−0.138504
$625$	24.4461	0.977842
$626$	−34.2562	−1.36915
$627$	−24.7837	−0.989764
$628$	1.78598	0.0712683
$629$	−5.17671	−0.206409
$630$	0.807747	0.0321814
$631$	22.8113	0.908102	0.454051	−	0.890976i	$-0.349978\pi$
$631$	22.8113	0.908102	0.454051	+	0.890976i	$0.349978\pi$
$632$	−0.257619	−0.0102475
$633$	−2.64146	−0.104988
$634$	10.7493	0.426909
$635$	1.29407	0.0513536
$636$	1.14384	0.0453562
$637$	−3.01947	−0.119636
$638$	5.13842	0.203432
$639$	−6.57275	−0.260014
$640$	1.70291	0.0673136
$641$	2.70587	0.106875	0.0534377	−	0.998571i	$-0.482982\pi$
$641$	2.70587	0.106875	0.0534377	+	0.998571i	$0.482982\pi$
$642$	15.4816	0.611010
$643$	1.69269	0.0667531	0.0333765	−	0.999443i	$-0.489374\pi$
$643$	1.69269	0.0667531	0.0333765	+	0.999443i	$0.489374\pi$
$644$	−0.129200	−0.00509118
$645$	−0.0769449	−0.00302970
$646$	13.7744	0.541947
$647$	−32.5016	−1.27777	−0.638886	−	0.769302i	$-0.720604\pi$
$647$	−32.5016	−1.27777	−0.638886	+	0.769302i	$0.720604\pi$
$648$	2.97219	0.116759
$649$	45.4551	1.78427
$650$	−6.58220	−0.258175
$651$	−33.3774	−1.30816
$652$	−3.90803	−0.153050
$653$	−5.91451	−0.231453	−0.115726	−	0.993281i	$-0.536920\pi$
$653$	−5.91451	−0.231453	−0.115726	+	0.993281i	$0.536920\pi$
$654$	13.8418	0.541257
$655$	−0.979552	−0.0382742
$656$	−31.1651	−1.21679
$657$	−7.85326	−0.306385
$658$	−50.3568	−1.96311
$659$	−3.19163	−0.124328	−0.0621641	−	0.998066i	$-0.519800\pi$
$659$	−3.19163	−0.124328	−0.0621641	+	0.998066i	$0.519800\pi$
$660$	0.192155	0.00747960
$661$	−14.4559	−0.562269	−0.281134	−	0.959668i	$-0.590711\pi$
$661$	−14.4559	−0.562269	−0.281134	+	0.959668i	$0.590711\pi$
$662$	8.74240	0.339783
$663$	1.73632	0.0674332
$664$	25.1663	0.976642
$665$	3.64301	0.141270
$666$	3.95414	0.153220
$667$	0.158348	0.00613126
$668$	−4.49152	−0.173782
$669$	−8.98854	−0.347517
$670$	−2.52057	−0.0973782
$671$	2.44642	0.0944430
$672$	4.29139	0.165544
$673$	24.0344	0.926457	0.463228	−	0.886239i	$-0.346691\pi$
$673$	24.0344	0.926457	0.463228	+	0.886239i	$0.346691\pi$
$674$	0.413447	0.0159254
$675$	4.96298	0.191025
$676$	−0.241032	−0.00927047
$677$	7.02747	0.270088	0.135044	−	0.990840i	$-0.456882\pi$
$677$	7.02747	0.270088	0.135044	+	0.990840i	$0.456882\pi$
$678$	−19.1506	−0.735473
$679$	−36.3963	−1.39676
$680$	−0.992959	−0.0380782
$681$	−9.03483	−0.346215
$682$	57.9443	2.21880
$683$	10.0088	0.382976	0.191488	−	0.981495i	$-0.438669\pi$
$683$	10.0088	0.382976	0.191488	+	0.981495i	$0.438669\pi$
$684$	1.44175	0.0551266
$685$	0.158312	0.00604879
$686$	16.7106	0.638014
$687$	−13.6582	−0.521095
$688$	1.38360	0.0527494
$689$	−4.74559	−0.180792
$690$	−0.0432132	−0.00164510
$691$	24.2579	0.922813	0.461406	−	0.887189i	$-0.347345\pi$
$691$	24.2579	0.922813	0.461406	+	0.887189i	$0.347345\pi$
$692$	4.81867	0.183178
$693$	−13.1152	−0.498204
$694$	13.5567	0.514604
$695$	−0.248807	−0.00943778
$696$	−2.77924	−0.105347
$697$	15.6402	0.592416
$698$	−17.4633	−0.660996
$699$	−26.3895	−0.998142
$700$	3.78652	0.143117
$701$	14.7724	0.557944	0.278972	−	0.960299i	$-0.410006\pi$
$701$	14.7724	0.557944	0.278972	+	0.960299i	$0.410006\pi$
$702$	−1.32626	−0.0500565
$703$	17.8335	0.672605
$704$	−36.1206	−1.36135
$705$	2.30797	0.0869233
$706$	−14.6861	−0.552721
$707$	37.3439	1.40446
$708$	−2.64428	−0.0993780
$709$	5.00308	0.187894	0.0939472	−	0.995577i	$-0.470052\pi$
$709$	5.00308	0.187894	0.0939472	+	0.995577i	$0.470052\pi$
$710$	−1.67726	−0.0629463
$711$	−0.0866763	−0.00325061
$712$	1.92464	0.0721289
$713$	1.78564	0.0668729
$714$	7.28923	0.272792
$715$	−0.797215	−0.0298141
$716$	−3.15230	−0.117807
$717$	−21.0550	−0.786315
$718$	−18.2929	−0.682684
$719$	48.5400	1.81024	0.905118	−	0.425161i	$-0.139782\pi$
$719$	48.5400	1.81024	0.905118	+	0.425161i	$0.139782\pi$
$720$	0.665702	0.0248092
$721$	3.16535	0.117884
$722$	−22.2533	−0.828184
$723$	−6.68009	−0.248435
$724$	−4.54854	−0.169045
$725$	−4.64078	−0.172354
$726$	8.17950	0.303570
$727$	−4.95491	−0.183767	−0.0918837	−	0.995770i	$-0.529289\pi$
$727$	−4.95491	−0.183767	−0.0918837	+	0.995770i	$0.529289\pi$
$728$	−9.40804	−0.348685
$729$	1.00000	0.0370370
$730$	−2.00402	−0.0741722
$731$	−0.694363	−0.0256819
$732$	−0.142316	−0.00526017
$733$	1.74217	0.0643485	0.0321743	−	0.999482i	$-0.489757\pi$
$733$	1.74217	0.0643485	0.0321743	+	0.999482i	$0.489757\pi$
$734$	−10.4557	−0.385925
$735$	0.580971	0.0214294
$736$	−0.229583	−0.00846255
$737$	40.9259	1.50752
$738$	−11.9465	−0.439758
$739$	−24.2749	−0.892966	−0.446483	−	0.894792i	$-0.647324\pi$
$739$	−24.2749	−0.892966	−0.446483	+	0.894792i	$0.647324\pi$
$740$	−0.138268	−0.00508284
$741$	−5.98156	−0.219738
$742$	−19.9224	−0.731373
$743$	45.9547	1.68592	0.842958	−	0.537980i	$-0.180812\pi$
$743$	45.9547	1.68592	0.842958	+	0.537980i	$0.180812\pi$
$744$	−31.3406	−1.14900
$745$	0.544909	0.0199639
$746$	−15.1235	−0.553709
$747$	8.46725	0.309801
$748$	1.73403	0.0634025
$749$	36.9496	1.35011
$750$	2.54239	0.0928349
$751$	10.2225	0.373024	0.186512	−	0.982453i	$-0.440282\pi$
$751$	10.2225	0.373024	0.186512	+	0.982453i	$0.440282\pi$
$752$	−41.5014	−1.51340
$753$	−30.7591	−1.12093
$754$	1.24016	0.0451640
$755$	−0.136058	−0.00495167
$756$	0.762953	0.0277483
$757$	−15.0163	−0.545777	−0.272888	−	0.962046i	$-0.587979\pi$
$757$	−15.0163	−0.545777	−0.272888	+	0.962046i	$0.587979\pi$
$758$	16.5617	0.601549
$759$	0.701642	0.0254680
$760$	3.42070	0.124082
$761$	8.05883	0.292132	0.146066	−	0.989275i	$-0.453339\pi$
$761$	8.05883	0.292132	0.146066	+	0.989275i	$0.453339\pi$
$762$	−8.91995	−0.323136
$763$	33.0359	1.19598
$764$	−2.19642	−0.0794638
$765$	−0.334083	−0.0120788
$766$	−16.0815	−0.581048
$767$	10.9706	0.396126
$768$	5.69738	0.205587
$769$	25.4398	0.917382	0.458691	−	0.888596i	$-0.348319\pi$
$769$	25.4398	0.917382	0.458691	+	0.888596i	$0.348319\pi$
$770$	−3.34678	−0.120609
$771$	−14.2938	−0.514778
$772$	−5.88085	−0.211656
$773$	16.9199	0.608566	0.304283	−	0.952582i	$-0.401583\pi$
$773$	16.9199	0.608566	0.304283	+	0.952582i	$0.401583\pi$
$774$	0.530378	0.0190640
$775$	−52.3327	−1.87985
$776$	−34.1753	−1.22682
$777$	9.43726	0.338560
$778$	−6.51844	−0.233697
$779$	−53.8799	−1.93045
$780$	0.0463766	0.00166055
$781$	27.2332	0.974480
$782$	−0.389963	−0.0139450
$783$	−0.935080	−0.0334170
$784$	−10.4469	−0.373102
$785$	1.42569	0.0508850
$786$	6.75200	0.240836
$787$	40.7352	1.45205	0.726027	−	0.687667i	$-0.241365\pi$
$787$	40.7352	1.45205	0.726027	+	0.687667i	$0.241365\pi$
$788$	5.78207	0.205978
$789$	24.4022	0.868742
$790$	−0.0221184	−0.000786936 0
$791$	−45.7062	−1.62513
$792$	−12.3148	−0.437589
$793$	0.590445	0.0209673
$794$	−28.7224	−1.01932
$795$	0.913090	0.0323840
$796$	5.13873	0.182137
$797$	−24.2583	−0.859272	−0.429636	−	0.903002i	$-0.641358\pi$
$797$	−24.2583	−0.859272	−0.429636	+	0.903002i	$0.641358\pi$
$798$	−25.1111	−0.888923
$799$	20.8275	0.736824
$800$	6.72850	0.237888
$801$	0.647549	0.0228800
$802$	−27.6746	−0.977223
$803$	32.5388	1.14827
$804$	−2.38079	−0.0839641
$805$	−0.103136	−0.00363507
$806$	13.9849	0.492597
$807$	0.524784	0.0184733
$808$	35.0650	1.23358
$809$	−24.7408	−0.869840	−0.434920	−	0.900469i	$-0.643223\pi$
$809$	−24.7408	−0.869840	−0.434920	+	0.900469i	$0.643223\pi$
$810$	0.255184	0.00896624
$811$	−53.4560	−1.87709	−0.938547	−	0.345150i	$-0.887828\pi$
$811$	−53.4560	−1.87709	−0.938547	+	0.345150i	$0.887828\pi$
$812$	−0.713422	−0.0250362
$813$	1.52972	0.0536498
$814$	−16.3834	−0.574238
$815$	−3.11965	−0.109277
$816$	6.00739	0.210301
$817$	2.39205	0.0836873
$818$	35.5568	1.24322
$819$	−3.16535	−0.110606
$820$	0.417746	0.0145883
$821$	−17.3147	−0.604287	−0.302143	−	0.953263i	$-0.597702\pi$
$821$	−17.3147	−0.604287	−0.302143	+	0.953263i	$0.597702\pi$
$822$	−1.09124	−0.0380612
$823$	7.73179	0.269513	0.134757	−	0.990879i	$-0.456975\pi$
$823$	7.73179	0.269513	0.134757	+	0.990879i	$0.456975\pi$
$824$	2.97219	0.103541
$825$	−20.5634	−0.715924
$826$	46.0556	1.60248
$827$	2.87085	0.0998292	0.0499146	−	0.998753i	$-0.484105\pi$
$827$	2.87085	0.0998292	0.0499146	+	0.998753i	$0.484105\pi$
$828$	−0.0408168	−0.00141848
$829$	5.18541	0.180097	0.0900484	−	0.995937i	$-0.471298\pi$
$829$	5.18541	0.180097	0.0900484	+	0.995937i	$0.471298\pi$
$830$	2.16070	0.0749991
$831$	32.1329	1.11468
$832$	−8.71774	−0.302233
$833$	5.24277	0.181651
$834$	1.71501	0.0593860
$835$	−3.58544	−0.124079
$836$	−5.97367	−0.206604
$837$	−10.5446	−0.364475
$838$	−24.0750	−0.831658
$839$	6.08881	0.210209	0.105105	−	0.994461i	$-0.466482\pi$
$839$	6.08881	0.210209	0.105105	+	0.994461i	$0.466482\pi$
$840$	1.81019	0.0624574
$841$	−28.1256	−0.969849
$842$	49.9717	1.72214
$843$	−17.6938	−0.609407
$844$	−0.636676	−0.0219153
$845$	−0.192408	−0.00661905
$846$	−15.9087	−0.546954
$847$	19.5218	0.670777
$848$	−16.4190	−0.563829
$849$	−15.7618	−0.540942
$850$	11.4288	0.392005
$851$	−0.504879	−0.0173070
$852$	−1.58424	−0.0542753
$853$	−20.7073	−0.709005	−0.354503	−	0.935055i	$-0.615350\pi$
$853$	−20.7073	−0.709005	−0.354503	+	0.935055i	$0.615350\pi$
$854$	2.47874	0.0848207
$855$	1.15090	0.0393600
$856$	34.6948	1.18584
$857$	45.7058	1.56128	0.780639	−	0.624982i	$-0.214894\pi$
$857$	45.7058	1.56128	0.780639	+	0.624982i	$0.214894\pi$
$858$	5.49516	0.187602
$859$	47.1522	1.60881	0.804406	−	0.594079i	$-0.202484\pi$
$859$	47.1522	1.60881	0.804406	+	0.594079i	$0.202484\pi$
$860$	−0.0185462	−0.000632421 0
$861$	−28.5125	−0.971703
$862$	30.8437	1.05054
$863$	−13.1766	−0.448536	−0.224268	−	0.974528i	$-0.571999\pi$
$863$	−13.1766	−0.448536	−0.224268	+	0.974528i	$0.571999\pi$
$864$	1.35574	0.0461231
$865$	3.84659	0.130788
$866$	−24.5854	−0.835446
$867$	13.9852	0.474962
$868$	−8.04504	−0.273066
$869$	0.359130	0.0121826
$870$	−0.238617	−0.00808988
$871$	9.87749	0.334686
$872$	31.0199	1.05047
$873$	−11.4983	−0.389160
$874$	1.34341	0.0454414
$875$	6.06786	0.205131
$876$	−1.89289	−0.0639548
$877$	−23.7807	−0.803016	−0.401508	−	0.915855i	$-0.631514\pi$
$877$	−23.7807	−0.803016	−0.401508	+	0.915855i	$0.631514\pi$
$878$	−15.1350	−0.510783
$879$	−11.2127	−0.378195
$880$	−2.75823	−0.0929801
$881$	29.7843	1.00346	0.501729	−	0.865025i	$-0.332697\pi$
$881$	29.7843	1.00346	0.501729	+	0.865025i	$0.332697\pi$
$882$	−4.00460	−0.134842
$883$	−6.10129	−0.205325	−0.102662	−	0.994716i	$-0.532736\pi$
$883$	−6.10129	−0.205325	−0.102662	+	0.994716i	$0.532736\pi$
$884$	0.418510	0.0140760
$885$	−2.11084	−0.0709551
$886$	10.0386	0.337254
$887$	−53.5063	−1.79657	−0.898283	−	0.439417i	$-0.855185\pi$
$887$	−53.5063	−1.79657	−0.898283	+	0.439417i	$0.855185\pi$
$888$	8.86136	0.297368
$889$	−21.2890	−0.714011
$890$	0.165244	0.00553899
$891$	−4.14335	−0.138807
$892$	−2.16653	−0.0725407
$893$	−71.7498	−2.40102
$894$	−3.75603	−0.125620
$895$	−2.51638	−0.0841132
$896$	−28.0150	−0.935916
$897$	0.169342	0.00565416
$898$	16.0203	0.534604
$899$	9.86006	0.328851
$900$	1.19624	0.0398746
$901$	8.23986	0.274510
$902$	49.4986	1.64812
$903$	1.26584	0.0421245
$904$	−42.9171	−1.42740
$905$	−3.63095	−0.120697
$906$	0.937843	0.0311578
$907$	35.6178	1.18267	0.591335	−	0.806426i	$-0.298601\pi$
$907$	35.6178	1.18267	0.591335	+	0.806426i	$0.298601\pi$
$908$	−2.17769	−0.0722690
$909$	11.7977	0.391305
$910$	−0.807747	−0.0267765
$911$	−46.1467	−1.52891	−0.764455	−	0.644677i	$-0.776992\pi$
$911$	−46.1467	−1.52891	−0.764455	+	0.644677i	$0.776992\pi$
$912$	−20.6952	−0.685287
$913$	−35.0828	−1.16107
$914$	−12.6540	−0.418558
$915$	−0.113607	−0.00375572
$916$	−3.29208	−0.108773
$917$	16.1148	0.532159
$918$	2.30282	0.0760042
$919$	13.2790	0.438035	0.219018	−	0.975721i	$-0.429715\pi$
$919$	13.2790	0.438035	0.219018	+	0.975721i	$0.429715\pi$
$920$	−0.0968423	−0.00319280
$921$	14.3622	0.473250
$922$	−1.49540	−0.0492483
$923$	6.57275	0.216345
$924$	−3.16118	−0.103995
$925$	14.7967	0.486514
$926$	−27.2797	−0.896468
$927$	1.00000	0.0328443
$928$	−1.26772	−0.0416151
$929$	−33.9761	−1.11472	−0.557360	−	0.830271i	$-0.688186\pi$
$929$	−33.9761	−1.11472	−0.557360	+	0.830271i	$0.688186\pi$
$930$	−2.69081	−0.0882352
$931$	−18.0611	−0.591929
$932$	−6.36072	−0.208352
$933$	4.37207	0.143135
$934$	23.9481	0.783606
$935$	1.38422	0.0452689
$936$	−2.97219	−0.0971492
$937$	5.06376	0.165426	0.0827129	−	0.996573i	$-0.473642\pi$
$937$	5.06376	0.165426	0.0827129	+	0.996573i	$0.473642\pi$
$938$	41.4665	1.35393
$939$	−25.8291	−0.842902
$940$	0.556296	0.0181444
$941$	−27.2773	−0.889216	−0.444608	−	0.895725i	$-0.646657\pi$
$941$	−27.2773	−0.889216	−0.444608	+	0.895725i	$0.646657\pi$
$942$	−9.82721	−0.320188
$943$	1.52538	0.0496731
$944$	37.9566	1.23538
$945$	0.609040	0.0198121
$946$	−2.19754	−0.0714482
$947$	25.0855	0.815170	0.407585	−	0.913167i	$-0.366371\pi$
$947$	25.0855	0.815170	0.407585	+	0.913167i	$0.366371\pi$
$948$	−0.0208918	−0.000678534 0
$949$	7.85326	0.254927
$950$	−39.3718	−1.27739
$951$	8.10495	0.262821
$952$	16.3354	0.529433
$953$	−42.2304	−1.36798	−0.683988	−	0.729493i	$-0.739756\pi$
$953$	−42.2304	−1.36798	−0.683988	+	0.729493i	$0.739756\pi$
$954$	−6.29388	−0.203772
$955$	−1.75333	−0.0567365
$956$	−5.07495	−0.164135
$957$	3.87436	0.125240
$958$	−44.2993	−1.43125
$959$	−2.60443	−0.0841013
$960$	1.67737	0.0541367
$961$	80.1888	2.58674
$962$	−3.95414	−0.127487
$963$	11.6731	0.376161
$964$	−1.61012	−0.0518584
$965$	−4.69449	−0.151121
$966$	0.710911	0.0228732
$967$	36.2140	1.16456	0.582282	−	0.812987i	$-0.302160\pi$
$967$	36.2140	1.16456	0.582282	+	0.812987i	$0.302160\pi$
$968$	18.3305	0.589165
$969$	10.3859	0.333643
$970$	−2.93419	−0.0942111
$971$	25.2842	0.811410	0.405705	−	0.914004i	$-0.367026\pi$
$971$	25.2842	0.811410	0.405705	+	0.914004i	$0.367026\pi$
$972$	0.241032	0.00773112
$973$	4.09318	0.131221
$974$	−50.3931	−1.61470
$975$	−4.96298	−0.158943
$976$	2.04285	0.0653899
$977$	−20.3272	−0.650323	−0.325162	−	0.945658i	$-0.605419\pi$
$977$	−20.3272	−0.650323	−0.325162	+	0.945658i	$0.605419\pi$
$978$	21.5036	0.687610
$979$	−2.68302	−0.0857497
$980$	0.140033	0.00447318
$981$	10.4367	0.333218
$982$	−21.4849	−0.685610
$983$	−1.82185	−0.0581080	−0.0290540	−	0.999578i	$-0.509249\pi$
$983$	−1.82185	−0.0581080	−0.0290540	+	0.999578i	$0.509249\pi$
$984$	−26.7726	−0.853478
$985$	4.61564	0.147067
$986$	−2.15332	−0.0685756
$987$	−37.9690	−1.20857
$988$	−1.44175	−0.0458681
$989$	−0.0677205	−0.00215339
$990$	−1.05731	−0.0336037
$991$	−33.0178	−1.04885	−0.524423	−	0.851458i	$-0.675719\pi$
$991$	−33.0178	−1.04885	−0.524423	+	0.851458i	$0.675719\pi$
$992$	−14.2957	−0.453890
$993$	6.59177	0.209183
$994$	27.5929	0.875195
$995$	4.10208	0.130045
$996$	2.04088	0.0646678
$997$	15.6665	0.496164	0.248082	−	0.968739i	$-0.420200\pi$
$997$	15.6665	0.496164	0.248082	+	0.968739i	$0.420200\pi$
$998$	20.3272	0.643445
$999$	2.98142	0.0943280

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.g.1.7	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.g.1.7	✓	24	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-1.32626 q^{2} -1.00000 q^{3} -0.241032 q^{4} -0.192408 q^{5} +1.32626 q^{6} +3.16535 q^{7} +2.97219 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.32626 q^{2} -1.00000 q^{3} -0.241032 q^{4} -0.192408 q^{5} +1.32626 q^{6} +3.16535 q^{7} +2.97219 q^{8} +1.00000 q^{9} +0.255184 q^{10} -4.14335 q^{11} +0.241032 q^{12} -1.00000 q^{13} -4.19809 q^{14} +0.192408 q^{15} -3.45984 q^{16} +1.73632 q^{17} -1.32626 q^{18} -5.98156 q^{19} +0.0463766 q^{20} -3.16535 q^{21} +5.49516 q^{22} +0.169342 q^{23} -2.97219 q^{24} -4.96298 q^{25} +1.32626 q^{26} -1.00000 q^{27} -0.762953 q^{28} +0.935080 q^{29} -0.255184 q^{30} +10.5446 q^{31} -1.35574 q^{32} +4.14335 q^{33} -2.30282 q^{34} -0.609040 q^{35} -0.241032 q^{36} -2.98142 q^{37} +7.93310 q^{38} +1.00000 q^{39} -0.571875 q^{40} +9.00768 q^{41} +4.19809 q^{42} -0.399904 q^{43} +0.998681 q^{44} -0.192408 q^{45} -0.224591 q^{46} +11.9952 q^{47} +3.45984 q^{48} +3.01947 q^{49} +6.58220 q^{50} -1.73632 q^{51} +0.241032 q^{52} +4.74559 q^{53} +1.32626 q^{54} +0.797215 q^{55} +9.40804 q^{56} +5.98156 q^{57} -1.24016 q^{58} -10.9706 q^{59} -0.0463766 q^{60} -0.590445 q^{61} -13.9849 q^{62} +3.16535 q^{63} +8.71774 q^{64} +0.192408 q^{65} -5.49516 q^{66} -9.87749 q^{67} -0.418510 q^{68} -0.169342 q^{69} +0.807747 q^{70} -6.57275 q^{71} +2.97219 q^{72} -7.85326 q^{73} +3.95414 q^{74} +4.96298 q^{75} +1.44175 q^{76} -13.1152 q^{77} -1.32626 q^{78} -0.0866763 q^{79} +0.665702 q^{80} +1.00000 q^{81} -11.9465 q^{82} +8.46725 q^{83} +0.762953 q^{84} -0.334083 q^{85} +0.530378 q^{86} -0.935080 q^{87} -12.3148 q^{88} +0.647549 q^{89} +0.255184 q^{90} -3.16535 q^{91} -0.0408168 q^{92} -10.5446 q^{93} -15.9087 q^{94} +1.15090 q^{95} +1.35574 q^{96} -11.4983 q^{97} -4.00460 q^{98} -4.14335 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * q^99

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