LMFDB - Embedded newform 4017.2.a.j.1.25

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:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.25
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)

$f(q)$	$=$	$q+2.73802 q^{2} -1.00000 q^{3} +5.49677 q^{4} +2.25213 q^{5} -2.73802 q^{6} -2.23039 q^{7} +9.57422 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.73802 q^{2} -1.00000 q^{3} +5.49677 q^{4} +2.25213 q^{5} -2.73802 q^{6} -2.23039 q^{7} +9.57422 q^{8} +1.00000 q^{9} +6.16638 q^{10} +4.01232 q^{11} -5.49677 q^{12} +1.00000 q^{13} -6.10685 q^{14} -2.25213 q^{15} +15.2209 q^{16} +1.93575 q^{17} +2.73802 q^{18} -3.89952 q^{19} +12.3794 q^{20} +2.23039 q^{21} +10.9858 q^{22} +1.46506 q^{23} -9.57422 q^{24} +0.0720843 q^{25} +2.73802 q^{26} -1.00000 q^{27} -12.2599 q^{28} -0.0392005 q^{29} -6.16638 q^{30} -0.286582 q^{31} +22.5267 q^{32} -4.01232 q^{33} +5.30011 q^{34} -5.02312 q^{35} +5.49677 q^{36} +0.862130 q^{37} -10.6770 q^{38} -1.00000 q^{39} +21.5624 q^{40} -6.36427 q^{41} +6.10685 q^{42} +2.68261 q^{43} +22.0548 q^{44} +2.25213 q^{45} +4.01136 q^{46} +3.27883 q^{47} -15.2209 q^{48} -2.02537 q^{49} +0.197368 q^{50} -1.93575 q^{51} +5.49677 q^{52} -11.3322 q^{53} -2.73802 q^{54} +9.03626 q^{55} -21.3542 q^{56} +3.89952 q^{57} -0.107332 q^{58} +12.5156 q^{59} -12.3794 q^{60} +1.47526 q^{61} -0.784668 q^{62} -2.23039 q^{63} +31.2369 q^{64} +2.25213 q^{65} -10.9858 q^{66} +3.33628 q^{67} +10.6403 q^{68} -1.46506 q^{69} -13.7534 q^{70} -4.53598 q^{71} +9.57422 q^{72} +7.69775 q^{73} +2.36053 q^{74} -0.0720843 q^{75} -21.4347 q^{76} -8.94903 q^{77} -2.73802 q^{78} +3.50200 q^{79} +34.2794 q^{80} +1.00000 q^{81} -17.4255 q^{82} -6.37677 q^{83} +12.2599 q^{84} +4.35955 q^{85} +7.34504 q^{86} +0.0392005 q^{87} +38.4148 q^{88} -9.23478 q^{89} +6.16638 q^{90} -2.23039 q^{91} +8.05309 q^{92} +0.286582 q^{93} +8.97752 q^{94} -8.78222 q^{95} -22.5267 q^{96} -17.3424 q^{97} -5.54550 q^{98} +4.01232 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * 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 $

$2$	2.73802	1.93607	0.968037	−	0.250807i	$-0.0806960\pi$
$2$	2.73802	1.93607	0.968037	+	0.250807i	$0.0806960\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.49677	2.74838
$5$	2.25213	1.00718	0.503591	−	0.863942i	$-0.332012\pi$
$5$	2.25213	1.00718	0.503591	+	0.863942i	$0.332012\pi$
$6$	−2.73802	−1.11779
$7$	−2.23039	−0.843008	−0.421504	−	0.906827i	$-0.638498\pi$
$7$	−2.23039	−0.843008	−0.421504	+	0.906827i	$0.638498\pi$
$8$	9.57422	3.38500
$9$	1.00000	0.333333
$10$	6.16638	1.94998
$11$	4.01232	1.20976	0.604880	−	0.796317i	$-0.293221\pi$
$11$	4.01232	1.20976	0.604880	+	0.796317i	$0.293221\pi$
$12$	−5.49677	−1.58678
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−6.10685	−1.63213
$15$	−2.25213	−0.581497
$16$	15.2209	3.80523
$17$	1.93575	0.469487	0.234744	−	0.972057i	$-0.424575\pi$
$17$	1.93575	0.469487	0.234744	+	0.972057i	$0.424575\pi$
$18$	2.73802	0.645358
$19$	−3.89952	−0.894611	−0.447306	−	0.894381i	$-0.647616\pi$
$19$	−3.89952	−0.894611	−0.447306	+	0.894381i	$0.647616\pi$
$20$	12.3794	2.76812
$21$	2.23039	0.486711
$22$	10.9858	2.34218
$23$	1.46506	0.305486	0.152743	−	0.988266i	$-0.451189\pi$
$23$	1.46506	0.305486	0.152743	+	0.988266i	$0.451189\pi$
$24$	−9.57422	−1.95433
$25$	0.0720843	0.0144169
$26$	2.73802	0.536970
$27$	−1.00000	−0.192450
$28$	−12.2599	−2.31691
$29$	−0.0392005	−0.00727935	−0.00363968	−	0.999993i	$-0.501159\pi$
$29$	−0.0392005	−0.00727935	−0.00363968	+	0.999993i	$0.501159\pi$
$30$	−6.16638	−1.12582
$31$	−0.286582	−0.0514716	−0.0257358	−	0.999669i	$-0.508193\pi$
$31$	−0.286582	−0.0514716	−0.0257358	+	0.999669i	$0.508193\pi$
$32$	22.5267	3.98220
$33$	−4.01232	−0.698455
$34$	5.30011	0.908962
$35$	−5.02312	−0.849063
$36$	5.49677	0.916128
$37$	0.862130	0.141733	0.0708667	−	0.997486i	$-0.477424\pi$
$37$	0.862130	0.141733	0.0708667	+	0.997486i	$0.477424\pi$
$38$	−10.6770	−1.73203
$39$	−1.00000	−0.160128
$40$	21.5624	3.40931
$41$	−6.36427	−0.993932	−0.496966	−	0.867770i	$-0.665553\pi$
$41$	−6.36427	−0.993932	−0.496966	+	0.867770i	$0.665553\pi$
$42$	6.10685	0.942308
$43$	2.68261	0.409094	0.204547	−	0.978857i	$-0.434428\pi$
$43$	2.68261	0.409094	0.204547	+	0.978857i	$0.434428\pi$
$44$	22.0548	3.32488
$45$	2.25213	0.335728
$46$	4.01136	0.591443
$47$	3.27883	0.478267	0.239133	−	0.970987i	$-0.423137\pi$
$47$	3.27883	0.478267	0.239133	+	0.970987i	$0.423137\pi$
$48$	−15.2209	−2.19695
$49$	−2.02537	−0.289338
$50$	0.197368	0.0279121
$51$	−1.93575	−0.271059
$52$	5.49677	0.762264
$53$	−11.3322	−1.55660	−0.778298	−	0.627895i	$-0.783917\pi$
$53$	−11.3322	−1.55660	−0.778298	+	0.627895i	$0.783917\pi$
$54$	−2.73802	−0.372598
$55$	9.03626	1.21845
$56$	−21.3542	−2.85358
$57$	3.89952	0.516504
$58$	−0.107332	−0.0140934
$59$	12.5156	1.62940	0.814698	−	0.579886i	$-0.196903\pi$
$59$	12.5156	1.62940	0.814698	+	0.579886i	$0.196903\pi$
$60$	−12.3794	−1.59818
$61$	1.47526	0.188888	0.0944439	−	0.995530i	$-0.469893\pi$
$61$	1.47526	0.188888	0.0944439	+	0.995530i	$0.469893\pi$
$62$	−0.784668	−0.0996529
$63$	−2.23039	−0.281003
$64$	31.2369	3.90461
$65$	2.25213	0.279342
$66$	−10.9858	−1.35226
$67$	3.33628	0.407591	0.203796	−	0.979013i	$-0.434672\pi$
$67$	3.33628	0.407591	0.203796	+	0.979013i	$0.434672\pi$
$68$	10.6403	1.29033
$69$	−1.46506	−0.176372
$70$	−13.7534	−1.64385
$71$	−4.53598	−0.538321	−0.269161	−	0.963095i	$-0.586746\pi$
$71$	−4.53598	−0.538321	−0.269161	+	0.963095i	$0.586746\pi$
$72$	9.57422	1.12833
$73$	7.69775	0.900954	0.450477	−	0.892788i	$-0.351254\pi$
$73$	7.69775	0.900954	0.450477	+	0.892788i	$0.351254\pi$
$74$	2.36053	0.274406
$75$	−0.0720843	−0.00832358
$76$	−21.4347	−2.45873
$77$	−8.94903	−1.01984
$78$	−2.73802	−0.310020
$79$	3.50200	0.394005	0.197003	−	0.980403i	$-0.436879\pi$
$79$	3.50200	0.394005	0.197003	+	0.980403i	$0.436879\pi$
$80$	34.2794	3.83256
$81$	1.00000	0.111111
$82$	−17.4255	−1.92433
$83$	−6.37677	−0.699941	−0.349970	−	0.936761i	$-0.613808\pi$
$83$	−6.37677	−0.699941	−0.349970	+	0.936761i	$0.613808\pi$
$84$	12.2599	1.33767
$85$	4.35955	0.472859
$86$	7.34504	0.792036
$87$	0.0392005	0.00420274
$88$	38.4148	4.09503
$89$	−9.23478	−0.978885	−0.489442	−	0.872036i	$-0.662800\pi$
$89$	−9.23478	−0.978885	−0.489442	+	0.872036i	$0.662800\pi$
$90$	6.16638	0.649993
$91$	−2.23039	−0.233808
$92$	8.05309	0.839592
$93$	0.286582	0.0297172
$94$	8.97752	0.925960
$95$	−8.78222	−0.901037
$96$	−22.5267	−2.29912
$97$	−17.3424	−1.76086	−0.880428	−	0.474180i	$-0.842744\pi$
$97$	−17.3424	−1.76086	−0.880428	+	0.474180i	$0.842744\pi$
$98$	−5.54550	−0.560180
$99$	4.01232	0.403253
$100$	0.396230	0.0396230
$101$	−2.92744	−0.291291	−0.145646	−	0.989337i	$-0.546526\pi$
$101$	−2.92744	−0.291291	−0.145646	+	0.989337i	$0.546526\pi$
$102$	−5.30011	−0.524789
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	9.57422	0.938830
$105$	5.02312	0.490207
$106$	−31.0278	−3.01369
$107$	−6.90978	−0.667994	−0.333997	−	0.942574i	$-0.608398\pi$
$107$	−6.90978	−0.667994	−0.333997	+	0.942574i	$0.608398\pi$
$108$	−5.49677	−0.528927
$109$	1.29481	0.124020	0.0620100	−	0.998076i	$-0.480249\pi$
$109$	1.29481	0.124020	0.0620100	+	0.998076i	$0.480249\pi$
$110$	24.7415	2.35901
$111$	−0.862130	−0.0818298
$112$	−33.9485	−3.20783
$113$	13.8148	1.29959	0.649795	−	0.760109i	$-0.274855\pi$
$113$	13.8148	1.29959	0.649795	+	0.760109i	$0.274855\pi$
$114$	10.6770	0.999990
$115$	3.29950	0.307680
$116$	−0.215476	−0.0200064
$117$	1.00000	0.0924500
$118$	34.2681	3.15463
$119$	−4.31746	−0.395781
$120$	−21.5624	−1.96837
$121$	5.09870	0.463518
$122$	4.03930	0.365701
$123$	6.36427	0.573847
$124$	−1.57527	−0.141464
$125$	−11.0983	−0.992662
$126$	−6.10685	−0.544042
$127$	18.7055	1.65984	0.829922	−	0.557879i	$-0.188385\pi$
$127$	18.7055	1.65984	0.829922	+	0.557879i	$0.188385\pi$
$128$	40.4738	3.57741
$129$	−2.68261	−0.236190
$130$	6.16638	0.540827
$131$	16.8203	1.46959	0.734797	−	0.678287i	$-0.237277\pi$
$131$	16.8203	1.46959	0.734797	+	0.678287i	$0.237277\pi$
$132$	−22.0548	−1.91962
$133$	8.69744	0.754164
$134$	9.13481	0.789127
$135$	−2.25213	−0.193832
$136$	18.5333	1.58921
$137$	−5.88521	−0.502808	−0.251404	−	0.967882i	$-0.580892\pi$
$137$	−5.88521	−0.502808	−0.251404	+	0.967882i	$0.580892\pi$
$138$	−4.01136	−0.341470
$139$	−4.02739	−0.341599	−0.170799	−	0.985306i	$-0.554635\pi$
$139$	−4.02739	−0.341599	−0.170799	+	0.985306i	$0.554635\pi$
$140$	−27.6109	−2.33355
$141$	−3.27883	−0.276127
$142$	−12.4196	−1.04223
$143$	4.01232	0.335527
$144$	15.2209	1.26841
$145$	−0.0882846	−0.00733164
$146$	21.0766	1.74431
$147$	2.02537	0.167050
$148$	4.73893	0.389537
$149$	19.3486	1.58510	0.792549	−	0.609809i	$-0.208754\pi$
$149$	19.3486	1.58510	0.792549	+	0.609809i	$0.208754\pi$
$150$	−0.197368	−0.0161151
$151$	7.51787	0.611796	0.305898	−	0.952064i	$-0.401043\pi$
$151$	7.51787	0.611796	0.305898	+	0.952064i	$0.401043\pi$
$152$	−37.3349	−3.02826
$153$	1.93575	0.156496
$154$	−24.5026	−1.97448
$155$	−0.645420	−0.0518414
$156$	−5.49677	−0.440093
$157$	6.80666	0.543231	0.271615	−	0.962406i	$-0.412442\pi$
$157$	6.80666	0.543231	0.271615	+	0.962406i	$0.412442\pi$
$158$	9.58854	0.762823
$159$	11.3322	0.898701
$160$	50.7331	4.01080
$161$	−3.26765	−0.257527
$162$	2.73802	0.215119
$163$	25.0489	1.96198	0.980989	−	0.194064i	$-0.0621671\pi$
$163$	25.0489	1.96198	0.980989	+	0.194064i	$0.0621671\pi$
$164$	−34.9829	−2.73171
$165$	−9.03626	−0.703472
$166$	−17.4597	−1.35514
$167$	−12.1377	−0.939241	−0.469620	−	0.882868i	$-0.655609\pi$
$167$	−12.1377	−0.939241	−0.469620	+	0.882868i	$0.655609\pi$
$168$	21.3542	1.64751
$169$	1.00000	0.0769231
$170$	11.9365	0.915491
$171$	−3.89952	−0.298204
$172$	14.7457	1.12435
$173$	−10.3059	−0.783545	−0.391773	−	0.920062i	$-0.628138\pi$
$173$	−10.3059	−0.783545	−0.391773	+	0.920062i	$0.628138\pi$
$174$	0.107332	0.00813681
$175$	−0.160776	−0.0121535
$176$	61.0711	4.60341
$177$	−12.5156	−0.940732
$178$	−25.2850	−1.89519
$179$	−24.9691	−1.86628	−0.933140	−	0.359514i	$-0.882943\pi$
$179$	−24.9691	−1.86628	−0.933140	+	0.359514i	$0.882943\pi$
$180$	12.3794	0.922708
$181$	−19.6972	−1.46408	−0.732042	−	0.681260i	$-0.761433\pi$
$181$	−19.6972	−1.46408	−0.732042	+	0.681260i	$0.761433\pi$
$182$	−6.10685	−0.452670
$183$	−1.47526	−0.109054
$184$	14.0268	1.03407
$185$	1.94163	0.142751
$186$	0.784668	0.0575346
$187$	7.76683	0.567967
$188$	18.0230	1.31446
$189$	2.23039	0.162237
$190$	−24.0459	−1.74447
$191$	−16.8097	−1.21631	−0.608153	−	0.793820i	$-0.708089\pi$
$191$	−16.8097	−1.21631	−0.608153	+	0.793820i	$0.708089\pi$
$192$	−31.2369	−2.25433
$193$	−13.7159	−0.987292	−0.493646	−	0.869663i	$-0.664336\pi$
$193$	−13.7159	−0.987292	−0.493646	+	0.869663i	$0.664336\pi$
$194$	−47.4839	−3.40915
$195$	−2.25213	−0.161278
$196$	−11.1330	−0.795212
$197$	−3.72352	−0.265290	−0.132645	−	0.991164i	$-0.542347\pi$
$197$	−3.72352	−0.265290	−0.132645	+	0.991164i	$0.542347\pi$
$198$	10.9858	0.780728
$199$	21.3145	1.51094	0.755472	−	0.655181i	$-0.227408\pi$
$199$	21.3145	1.51094	0.755472	+	0.655181i	$0.227408\pi$
$200$	0.690151	0.0488010
$201$	−3.33628	−0.235323
$202$	−8.01540	−0.563961
$203$	0.0874324	0.00613655
$204$	−10.6403	−0.744973
$205$	−14.3332	−1.00107
$206$	−2.73802	−0.190767
$207$	1.46506	0.101829
$208$	15.2209	1.05538
$209$	−15.6461	−1.08226
$210$	13.7534	0.949076
$211$	−0.347438	−0.0239186	−0.0119593	−	0.999928i	$-0.503807\pi$
$211$	−0.347438	−0.0239186	−0.0119593	+	0.999928i	$0.503807\pi$
$212$	−62.2904	−4.27812
$213$	4.53598	0.310800
$214$	−18.9191	−1.29329
$215$	6.04158	0.412032
$216$	−9.57422	−0.651443
$217$	0.639189	0.0433910
$218$	3.54521	0.240112
$219$	−7.69775	−0.520166
$220$	49.6702	3.34876
$221$	1.93575	0.130212
$222$	−2.36053	−0.158429
$223$	−8.88346	−0.594880	−0.297440	−	0.954740i	$-0.596133\pi$
$223$	−8.88346	−0.594880	−0.297440	+	0.954740i	$0.596133\pi$
$224$	−50.2433	−3.35702
$225$	0.0720843	0.00480562
$226$	37.8253	2.51610
$227$	−15.3482	−1.01870	−0.509349	−	0.860560i	$-0.670114\pi$
$227$	−15.3482	−1.01870	−0.509349	+	0.860560i	$0.670114\pi$
$228$	21.4347	1.41955
$229$	−11.4562	−0.757044	−0.378522	−	0.925592i	$-0.623568\pi$
$229$	−11.4562	−0.757044	−0.378522	+	0.925592i	$0.623568\pi$
$230$	9.03411	0.595692
$231$	8.94903	0.588803
$232$	−0.375314	−0.0246406
$233$	10.4366	0.683724	0.341862	−	0.939750i	$-0.388942\pi$
$233$	10.4366	0.683724	0.341862	+	0.939750i	$0.388942\pi$
$234$	2.73802	0.178990
$235$	7.38435	0.481702
$236$	68.7955	4.47820
$237$	−3.50200	−0.227479
$238$	−11.8213	−0.766262
$239$	4.27431	0.276482	0.138241	−	0.990399i	$-0.455855\pi$
$239$	4.27431	0.276482	0.138241	+	0.990399i	$0.455855\pi$
$240$	−34.2794	−2.21273
$241$	−15.5365	−1.00080	−0.500398	−	0.865796i	$-0.666813\pi$
$241$	−15.5365	−1.00080	−0.500398	+	0.865796i	$0.666813\pi$
$242$	13.9603	0.897405
$243$	−1.00000	−0.0641500
$244$	8.10916	0.519136
$245$	−4.56139	−0.291416
$246$	17.4255	1.11101
$247$	−3.89952	−0.248121
$248$	−2.74380	−0.174231
$249$	6.37677	0.404111
$250$	−30.3874	−1.92187
$251$	−3.10336	−0.195882	−0.0979412	−	0.995192i	$-0.531226\pi$
$251$	−3.10336	−0.195882	−0.0979412	+	0.995192i	$0.531226\pi$
$252$	−12.2599	−0.772303
$253$	5.87828	0.369565
$254$	51.2161	3.21358
$255$	−4.35955	−0.273005
$256$	48.3444	3.02152
$257$	−17.7908	−1.10976	−0.554879	−	0.831931i	$-0.687236\pi$
$257$	−17.7908	−1.10976	−0.554879	+	0.831931i	$0.687236\pi$
$258$	−7.34504	−0.457282
$259$	−1.92289	−0.119482
$260$	12.3794	0.767739
$261$	−0.0392005	−0.00242645
$262$	46.0543	2.84524
$263$	−6.04045	−0.372470	−0.186235	−	0.982505i	$-0.559629\pi$
$263$	−6.04045	−0.372470	−0.186235	+	0.982505i	$0.559629\pi$
$264$	−38.4148	−2.36427
$265$	−25.5216	−1.56778
$266$	23.8138	1.46012
$267$	9.23478	0.565159
$268$	18.3387	1.12022
$269$	−16.9184	−1.03153	−0.515766	−	0.856729i	$-0.672493\pi$
$269$	−16.9184	−1.03153	−0.515766	+	0.856729i	$0.672493\pi$
$270$	−6.16638	−0.375274
$271$	−16.4202	−0.997456	−0.498728	−	0.866758i	$-0.666199\pi$
$271$	−16.4202	−0.997456	−0.498728	+	0.866758i	$0.666199\pi$
$272$	29.4638	1.78650
$273$	2.23039	0.134989
$274$	−16.1138	−0.973473
$275$	0.289225	0.0174409
$276$	−8.05309	−0.484739
$277$	−7.13667	−0.428801	−0.214401	−	0.976746i	$-0.568780\pi$
$277$	−7.13667	−0.428801	−0.214401	+	0.976746i	$0.568780\pi$
$278$	−11.0271	−0.661360
$279$	−0.286582	−0.0171572
$280$	−48.0925	−2.87408
$281$	−8.08608	−0.482375	−0.241188	−	0.970479i	$-0.577537\pi$
$281$	−8.08608	−0.482375	−0.241188	+	0.970479i	$0.577537\pi$
$282$	−8.97752	−0.534603
$283$	1.86933	0.111120	0.0555600	−	0.998455i	$-0.482306\pi$
$283$	1.86933	0.111120	0.0555600	+	0.998455i	$0.482306\pi$
$284$	−24.9332	−1.47951
$285$	8.78222	0.520214
$286$	10.9858	0.649605
$287$	14.1948	0.837893
$288$	22.5267	1.32740
$289$	−13.2529	−0.779582
$290$	−0.241725	−0.0141946
$291$	17.3424	1.01663
$292$	42.3127	2.47617
$293$	−2.61365	−0.152691	−0.0763455	−	0.997081i	$-0.524325\pi$
$293$	−2.61365	−0.152691	−0.0763455	+	0.997081i	$0.524325\pi$
$294$	5.54550	0.323420
$295$	28.1868	1.64110
$296$	8.25423	0.479767
$297$	−4.01232	−0.232818
$298$	52.9768	3.06887
$299$	1.46506	0.0847266
$300$	−0.396230	−0.0228764
$301$	−5.98325	−0.344869
$302$	20.5841	1.18448
$303$	2.92744	0.168177
$304$	−59.3542	−3.40420
$305$	3.32248	0.190244
$306$	5.30011	0.302987
$307$	13.8308	0.789366	0.394683	−	0.918817i	$-0.370854\pi$
$307$	13.8308	0.789366	0.394683	+	0.918817i	$0.370854\pi$
$308$	−49.1907	−2.80290
$309$	1.00000	0.0568880
$310$	−1.76717	−0.100369
$311$	1.27395	0.0722389	0.0361195	−	0.999347i	$-0.488500\pi$
$311$	1.27395	0.0722389	0.0361195	+	0.999347i	$0.488500\pi$
$312$	−9.57422	−0.542034
$313$	2.55357	0.144336	0.0721681	−	0.997392i	$-0.477008\pi$
$313$	2.55357	0.144336	0.0721681	+	0.997392i	$0.477008\pi$
$314$	18.6368	1.05173
$315$	−5.02312	−0.283021
$316$	19.2496	1.08288
$317$	17.1973	0.965894	0.482947	−	0.875649i	$-0.339566\pi$
$317$	17.1973	0.965894	0.482947	+	0.875649i	$0.339566\pi$
$318$	31.0278	1.73995
$319$	−0.157285	−0.00880627
$320$	70.3494	3.93265
$321$	6.90978	0.385666
$322$	−8.94690	−0.498591
$323$	−7.54848	−0.420009
$324$	5.49677	0.305376
$325$	0.0720843	0.00399852
$326$	68.5843	3.79853
$327$	−1.29481	−0.0716029
$328$	−60.9330	−3.36446
$329$	−7.31307	−0.403183
$330$	−24.7415	−1.36197
$331$	6.63238	0.364548	0.182274	−	0.983248i	$-0.441654\pi$
$331$	6.63238	0.364548	0.182274	+	0.983248i	$0.441654\pi$
$332$	−35.0516	−1.92371
$333$	0.862130	0.0472444
$334$	−33.2332	−1.81844
$335$	7.51373	0.410519
$336$	33.9485	1.85204
$337$	8.19212	0.446253	0.223127	−	0.974789i	$-0.428374\pi$
$337$	8.19212	0.446253	0.223127	+	0.974789i	$0.428374\pi$
$338$	2.73802	0.148929
$339$	−13.8148	−0.750319
$340$	23.9634	1.29960
$341$	−1.14986	−0.0622683
$342$	−10.6770	−0.577345
$343$	20.1301	1.08692
$344$	25.6839	1.38478
$345$	−3.29950	−0.177639
$346$	−28.2179	−1.51700
$347$	14.9052	0.800153	0.400076	−	0.916482i	$-0.368984\pi$
$347$	14.9052	0.800153	0.400076	+	0.916482i	$0.368984\pi$
$348$	0.215476	0.0115507
$349$	−0.206241	−0.0110398	−0.00551990	−	0.999985i	$-0.501757\pi$
$349$	−0.206241	−0.0110398	−0.00551990	+	0.999985i	$0.501757\pi$
$350$	−0.440208	−0.0235301
$351$	−1.00000	−0.0533761
$352$	90.3844	4.81750
$353$	15.8088	0.841416	0.420708	−	0.907196i	$-0.361782\pi$
$353$	15.8088	0.841416	0.420708	+	0.907196i	$0.361782\pi$
$354$	−34.2681	−1.82133
$355$	−10.2156	−0.542188
$356$	−50.7614	−2.69035
$357$	4.31746	0.228504
$358$	−68.3660	−3.61326
$359$	22.9336	1.21039	0.605195	−	0.796077i	$-0.293095\pi$
$359$	22.9336	1.21039	0.605195	+	0.796077i	$0.293095\pi$
$360$	21.5624	1.13644
$361$	−3.79375	−0.199671
$362$	−53.9315	−2.83457
$363$	−5.09870	−0.267612
$364$	−12.2599	−0.642595
$365$	17.3363	0.907425
$366$	−4.03930	−0.211137
$367$	−21.8950	−1.14291	−0.571455	−	0.820633i	$-0.693621\pi$
$367$	−21.8950	−1.14291	−0.571455	+	0.820633i	$0.693621\pi$
$368$	22.2995	1.16244
$369$	−6.36427	−0.331311
$370$	5.31622	0.276377
$371$	25.2752	1.31222
$372$	1.57527	0.0816742
$373$	−28.3129	−1.46599	−0.732994	−	0.680235i	$-0.761878\pi$
$373$	−28.3129	−1.46599	−0.732994	+	0.680235i	$0.761878\pi$
$374$	21.2657	1.09963
$375$	11.0983	0.573114
$376$	31.3923	1.61893
$377$	−0.0392005	−0.00201893
$378$	6.10685	0.314103
$379$	−4.66157	−0.239449	−0.119724	−	0.992807i	$-0.538201\pi$
$379$	−4.66157	−0.239449	−0.119724	+	0.992807i	$0.538201\pi$
$380$	−48.2738	−2.47639
$381$	−18.7055	−0.958312
$382$	−46.0253	−2.35486
$383$	−25.4152	−1.29866	−0.649328	−	0.760509i	$-0.724950\pi$
$383$	−25.4152	−1.29866	−0.649328	+	0.760509i	$0.724950\pi$
$384$	−40.4738	−2.06542
$385$	−20.1544	−1.02716
$386$	−37.5544	−1.91147
$387$	2.68261	0.136365
$388$	−95.3272	−4.83950
$389$	22.8812	1.16012	0.580060	−	0.814573i	$-0.303029\pi$
$389$	22.8812	1.16012	0.580060	+	0.814573i	$0.303029\pi$
$390$	−6.16638	−0.312247
$391$	2.83598	0.143422
$392$	−19.3913	−0.979410
$393$	−16.8203	−0.848471
$394$	−10.1951	−0.513621
$395$	7.88694	0.396835
$396$	22.0548	1.10829
$397$	8.76949	0.440128	0.220064	−	0.975485i	$-0.429373\pi$
$397$	8.76949	0.440128	0.220064	+	0.975485i	$0.429373\pi$
$398$	58.3596	2.92530
$399$	−8.69744	−0.435417
$400$	1.09719	0.0548594
$401$	−10.3080	−0.514757	−0.257379	−	0.966311i	$-0.582859\pi$
$401$	−10.3080	−0.514757	−0.257379	+	0.966311i	$0.582859\pi$
$402$	−9.13481	−0.455603
$403$	−0.286582	−0.0142757
$404$	−16.0915	−0.800580
$405$	2.25213	0.111909
$406$	0.239392	0.0118808
$407$	3.45914	0.171463
$408$	−18.5333	−0.917533
$409$	−30.9929	−1.53250	−0.766250	−	0.642543i	$-0.777879\pi$
$409$	−30.9929	−1.53250	−0.766250	+	0.642543i	$0.777879\pi$
$410$	−39.2445	−1.93815
$411$	5.88521	0.290296
$412$	−5.49677	−0.270806
$413$	−27.9147	−1.37359
$414$	4.01136	0.197148
$415$	−14.3613	−0.704968
$416$	22.5267	1.10446
$417$	4.02739	0.197222
$418$	−42.8394	−2.09534
$419$	26.0310	1.27170	0.635850	−	0.771813i	$-0.280650\pi$
$419$	26.0310	1.27170	0.635850	+	0.771813i	$0.280650\pi$
$420$	27.6109	1.34728
$421$	5.86010	0.285604	0.142802	−	0.989751i	$-0.454389\pi$
$421$	5.86010	0.285604	0.142802	+	0.989751i	$0.454389\pi$
$422$	−0.951293	−0.0463082
$423$	3.27883	0.159422
$424$	−108.497	−5.26908
$425$	0.139537	0.00676853
$426$	12.4196	0.601732
$427$	−3.29040	−0.159234
$428$	−37.9815	−1.83590
$429$	−4.01232	−0.193717
$430$	16.5420	0.797725
$431$	22.3070	1.07449	0.537244	−	0.843427i	$-0.319465\pi$
$431$	22.3070	1.07449	0.537244	+	0.843427i	$0.319465\pi$
$432$	−15.2209	−0.732316
$433$	12.5592	0.603559	0.301779	−	0.953378i	$-0.402419\pi$
$433$	12.5592	0.603559	0.301779	+	0.953378i	$0.402419\pi$
$434$	1.75011	0.0840082
$435$	0.0882846	0.00423292
$436$	7.11724	0.340854
$437$	−5.71303	−0.273291
$438$	−21.0766	−1.00708
$439$	20.4122	0.974223	0.487112	−	0.873340i	$-0.338050\pi$
$439$	20.4122	0.974223	0.487112	+	0.873340i	$0.338050\pi$
$440$	86.5151	4.12445
$441$	−2.02537	−0.0964461
$442$	5.30011	0.252101
$443$	−6.84950	−0.325430	−0.162715	−	0.986673i	$-0.552025\pi$
$443$	−6.84950	−0.325430	−0.162715	+	0.986673i	$0.552025\pi$
$444$	−4.73893	−0.224900
$445$	−20.7979	−0.985916
$446$	−24.3231	−1.15173
$447$	−19.3486	−0.915156
$448$	−69.6703	−3.29161
$449$	19.0147	0.897359	0.448679	−	0.893693i	$-0.351894\pi$
$449$	19.0147	0.897359	0.448679	+	0.893693i	$0.351894\pi$
$450$	0.197368	0.00930403
$451$	−25.5355	−1.20242
$452$	75.9369	3.57177
$453$	−7.51787	−0.353220
$454$	−42.0238	−1.97227
$455$	−5.02312	−0.235488
$456$	37.3349	1.74837
$457$	29.2712	1.36925	0.684624	−	0.728897i	$-0.259967\pi$
$457$	29.2712	1.36925	0.684624	+	0.728897i	$0.259967\pi$
$458$	−31.3672	−1.46569
$459$	−1.93575	−0.0903529
$460$	18.1366	0.845623
$461$	−31.9394	−1.48757	−0.743784	−	0.668420i	$-0.766971\pi$
$461$	−31.9394	−1.48757	−0.743784	+	0.668420i	$0.766971\pi$
$462$	24.5026	1.13997
$463$	7.27286	0.337998	0.168999	−	0.985616i	$-0.445946\pi$
$463$	7.27286	0.337998	0.168999	+	0.985616i	$0.445946\pi$
$464$	−0.596667	−0.0276996
$465$	0.645420	0.0299306
$466$	28.5756	1.32374
$467$	19.9052	0.921101	0.460551	−	0.887633i	$-0.347652\pi$
$467$	19.9052	0.921101	0.460551	+	0.887633i	$0.347652\pi$
$468$	5.49677	0.254088
$469$	−7.44120	−0.343603
$470$	20.2185	0.932611
$471$	−6.80666	−0.313634
$472$	119.827	5.51550
$473$	10.7635	0.494905
$474$	−9.58854	−0.440416
$475$	−0.281094	−0.0128975
$476$	−23.7321	−1.08776
$477$	−11.3322	−0.518866
$478$	11.7032	0.535290
$479$	−42.0670	−1.92209	−0.961046	−	0.276389i	$-0.910862\pi$
$479$	−42.0670	−1.92209	−0.961046	+	0.276389i	$0.910862\pi$
$480$	−50.7331	−2.31564
$481$	0.862130	0.0393098
$482$	−42.5394	−1.93761
$483$	3.26765	0.148683
$484$	28.0263	1.27392
$485$	−39.0574	−1.77350
$486$	−2.73802	−0.124199
$487$	−31.9367	−1.44719	−0.723596	−	0.690224i	$-0.757512\pi$
$487$	−31.9367	−1.44719	−0.723596	+	0.690224i	$0.757512\pi$
$488$	14.1245	0.639385
$489$	−25.0489	−1.13275
$490$	−12.4892	−0.564204
$491$	−12.9039	−0.582347	−0.291173	−	0.956670i	$-0.594046\pi$
$491$	−12.9039	−0.582347	−0.291173	+	0.956670i	$0.594046\pi$
$492$	34.9829	1.57715
$493$	−0.0758822	−0.00341756
$494$	−10.6770	−0.480380
$495$	9.03626	0.406150
$496$	−4.36204	−0.195861
$497$	10.1170	0.453809
$498$	17.4597	0.782389
$499$	34.8983	1.56226	0.781130	−	0.624368i	$-0.214643\pi$
$499$	34.8983	1.56226	0.781130	+	0.624368i	$0.214643\pi$
$500$	−61.0048	−2.72822
$501$	12.1377	0.542271
$502$	−8.49707	−0.379243
$503$	−23.7413	−1.05857	−0.529287	−	0.848443i	$-0.677540\pi$
$503$	−23.7413	−1.05857	−0.529287	+	0.848443i	$0.677540\pi$
$504$	−21.3542	−0.951193
$505$	−6.59297	−0.293383
$506$	16.0949	0.715504
$507$	−1.00000	−0.0444116
$508$	102.820	4.56189
$509$	20.9102	0.926828	0.463414	−	0.886142i	$-0.346624\pi$
$509$	20.9102	0.926828	0.463414	+	0.886142i	$0.346624\pi$
$510$	−11.9365	−0.528559
$511$	−17.1690	−0.759511
$512$	51.4204	2.27248
$513$	3.89952	0.172168
$514$	−48.7116	−2.14857
$515$	−2.25213	−0.0992407
$516$	−14.7457	−0.649141
$517$	13.1557	0.578588
$518$	−5.26490	−0.231327
$519$	10.3059	0.452380
$520$	21.5624	0.945573
$521$	11.4309	0.500799	0.250399	−	0.968143i	$-0.419438\pi$
$521$	11.4309	0.500799	0.250399	+	0.968143i	$0.419438\pi$
$522$	−0.107332	−0.00469779
$523$	−26.2467	−1.14769	−0.573844	−	0.818965i	$-0.694548\pi$
$523$	−26.2467	−1.14769	−0.573844	+	0.818965i	$0.694548\pi$
$524$	92.4571	4.03901
$525$	0.160776	0.00701684
$526$	−16.5389	−0.721130
$527$	−0.554750	−0.0241653
$528$	−61.0711	−2.65778
$529$	−20.8536	−0.906678
$530$	−69.8786	−3.03533
$531$	12.5156	0.543132
$532$	47.8078	2.07273
$533$	−6.36427	−0.275667
$534$	25.2850	1.09419
$535$	−15.5617	−0.672792
$536$	31.9423	1.37970
$537$	24.9691	1.07750
$538$	−46.3229	−1.99712
$539$	−8.12642	−0.350030
$540$	−12.3794	−0.532726
$541$	−6.81108	−0.292831	−0.146416	−	0.989223i	$-0.546774\pi$
$541$	−6.81108	−0.292831	−0.146416	+	0.989223i	$0.546774\pi$
$542$	−44.9589	−1.93115
$543$	19.6972	0.845289
$544$	43.6060	1.86959
$545$	2.91607	0.124911
$546$	6.10685	0.261349
$547$	14.1543	0.605193	0.302597	−	0.953119i	$-0.402146\pi$
$547$	14.1543	0.605193	0.302597	+	0.953119i	$0.402146\pi$
$548$	−32.3496	−1.38191
$549$	1.47526	0.0629626
$550$	0.791905	0.0337669
$551$	0.152863	0.00651219
$552$	−14.0268	−0.597020
$553$	−7.81081	−0.332149
$554$	−19.5404	−0.830191
$555$	−1.94163	−0.0824175
$556$	−22.1376	−0.938843
$557$	−23.5680	−0.998608	−0.499304	−	0.866427i	$-0.666411\pi$
$557$	−23.5680	−0.998608	−0.499304	+	0.866427i	$0.666411\pi$
$558$	−0.784668	−0.0332176
$559$	2.68261	0.113462
$560$	−76.4564	−3.23087
$561$	−7.76683	−0.327916
$562$	−22.1399	−0.933914
$563$	−2.79150	−0.117648	−0.0588239	−	0.998268i	$-0.518735\pi$
$563$	−2.79150	−0.117648	−0.0588239	+	0.998268i	$0.518735\pi$
$564$	−18.0230	−0.758904
$565$	31.1128	1.30893
$566$	5.11826	0.215137
$567$	−2.23039	−0.0936675
$568$	−43.4284	−1.82222
$569$	−0.812193	−0.0340489	−0.0170245	−	0.999855i	$-0.505419\pi$
$569$	−0.812193	−0.0340489	−0.0170245	+	0.999855i	$0.505419\pi$
$570$	24.0459	1.00717
$571$	−12.4909	−0.522729	−0.261365	−	0.965240i	$-0.584172\pi$
$571$	−12.4909	−0.522729	−0.261365	+	0.965240i	$0.584172\pi$
$572$	22.0548	0.922156
$573$	16.8097	0.702235
$574$	38.8657	1.62222
$575$	0.105608	0.00440415
$576$	31.2369	1.30154
$577$	−12.8212	−0.533756	−0.266878	−	0.963730i	$-0.585992\pi$
$577$	−12.8212	−0.533756	−0.266878	+	0.963730i	$0.585992\pi$
$578$	−36.2867	−1.50933
$579$	13.7159	0.570013
$580$	−0.485280	−0.0201501
$581$	14.2227	0.590056
$582$	47.4839	1.96827
$583$	−45.4684	−1.88311
$584$	73.7000	3.04973
$585$	2.25213	0.0931141
$586$	−7.15623	−0.295621
$587$	27.6397	1.14081	0.570405	−	0.821363i	$-0.306786\pi$
$587$	27.6397	1.14081	0.570405	+	0.821363i	$0.306786\pi$
$588$	11.1330	0.459116
$589$	1.11753	0.0460471
$590$	77.1761	3.17729
$591$	3.72352	0.153165
$592$	13.1224	0.539327
$593$	29.5963	1.21538	0.607688	−	0.794176i	$-0.292097\pi$
$593$	29.5963	1.21538	0.607688	+	0.794176i	$0.292097\pi$
$594$	−10.9858	−0.450753
$595$	−9.72349	−0.398624
$596$	106.355	4.35645
$597$	−21.3145	−0.872344
$598$	4.01136	0.164037
$599$	−30.6489	−1.25228	−0.626141	−	0.779710i	$-0.715367\pi$
$599$	−30.6489	−1.25228	−0.626141	+	0.779710i	$0.715367\pi$
$600$	−0.690151	−0.0281753
$601$	12.0523	0.491623	0.245811	−	0.969318i	$-0.420946\pi$
$601$	12.0523	0.491623	0.245811	+	0.969318i	$0.420946\pi$
$602$	−16.3823	−0.667692
$603$	3.33628	0.135864
$604$	41.3240	1.68145
$605$	11.4829	0.466847
$606$	8.01540	0.325603
$607$	33.6940	1.36760	0.683799	−	0.729671i	$-0.260327\pi$
$607$	33.6940	1.36760	0.683799	+	0.729671i	$0.260327\pi$
$608$	−87.8434	−3.56252
$609$	−0.0874324	−0.00354294
$610$	9.09702	0.368327
$611$	3.27883	0.132647
$612$	10.6403	0.430110
$613$	−1.33551	−0.0539407	−0.0269704	−	0.999636i	$-0.508586\pi$
$613$	−1.33551	−0.0539407	−0.0269704	+	0.999636i	$0.508586\pi$
$614$	37.8691	1.52827
$615$	14.3332	0.577969
$616$	−85.6800	−3.45214
$617$	−32.8870	−1.32398	−0.661991	−	0.749512i	$-0.730288\pi$
$617$	−32.8870	−1.32398	−0.661991	+	0.749512i	$0.730288\pi$
$618$	2.73802	0.110139
$619$	−20.5063	−0.824217	−0.412108	−	0.911135i	$-0.635208\pi$
$619$	−20.5063	−0.824217	−0.412108	+	0.911135i	$0.635208\pi$
$620$	−3.54772	−0.142480
$621$	−1.46506	−0.0587908
$622$	3.48810	0.139860
$623$	20.5971	0.825207
$624$	−15.2209	−0.609324
$625$	−25.3552	−1.01421
$626$	6.99173	0.279446
$627$	15.6461	0.624846
$628$	37.4146	1.49301
$629$	1.66886	0.0665420
$630$	−13.7534	−0.547949
$631$	39.4988	1.57242	0.786211	−	0.617958i	$-0.212040\pi$
$631$	39.4988	1.57242	0.786211	+	0.617958i	$0.212040\pi$
$632$	33.5289	1.33371
$633$	0.347438	0.0138094
$634$	47.0865	1.87004
$635$	42.1272	1.67177
$636$	62.2904	2.46998
$637$	−2.02537	−0.0802480
$638$	−0.430650	−0.0170496
$639$	−4.53598	−0.179440
$640$	91.1522	3.60311
$641$	−42.0904	−1.66247	−0.831236	−	0.555919i	$-0.812366\pi$
$641$	−42.0904	−1.66247	−0.831236	+	0.555919i	$0.812366\pi$
$642$	18.9191	0.746679
$643$	36.5921	1.44305	0.721525	−	0.692388i	$-0.243441\pi$
$643$	36.5921	1.44305	0.721525	+	0.692388i	$0.243441\pi$
$644$	−17.9615	−0.707783
$645$	−6.04158	−0.237887
$646$	−20.6679	−0.813168
$647$	0.150619	0.00592144	0.00296072	−	0.999996i	$-0.499058\pi$
$647$	0.150619	0.00592144	0.00296072	+	0.999996i	$0.499058\pi$
$648$	9.57422	0.376111
$649$	50.2167	1.97118
$650$	0.197368	0.00774142
$651$	−0.639189	−0.0250518
$652$	137.688	5.39227
$653$	7.77619	0.304306	0.152153	−	0.988357i	$-0.451379\pi$
$653$	7.77619	0.304306	0.152153	+	0.988357i	$0.451379\pi$
$654$	−3.54521	−0.138629
$655$	37.8814	1.48015
$656$	−96.8700	−3.78214
$657$	7.69775	0.300318
$658$	−20.0233	−0.780591
$659$	−10.7563	−0.419004	−0.209502	−	0.977808i	$-0.567184\pi$
$659$	−10.7563	−0.419004	−0.209502	+	0.977808i	$0.567184\pi$
$660$	−49.6702	−1.93341
$661$	32.8404	1.27734	0.638671	−	0.769480i	$-0.279485\pi$
$661$	32.8404	1.27734	0.638671	+	0.769480i	$0.279485\pi$
$662$	18.1596	0.705793
$663$	−1.93575	−0.0751781
$664$	−61.0526	−2.36930
$665$	19.5878	0.759581
$666$	2.36053	0.0914687
$667$	−0.0574311	−0.00222374
$668$	−66.7179	−2.58139
$669$	8.88346	0.343454
$670$	20.5728	0.794795
$671$	5.91921	0.228509
$672$	50.2433	1.93818
$673$	14.0879	0.543047	0.271523	−	0.962432i	$-0.412473\pi$
$673$	14.0879	0.543047	0.271523	+	0.962432i	$0.412473\pi$
$674$	22.4302	0.863979
$675$	−0.0720843	−0.00277453
$676$	5.49677	0.211414
$677$	31.2527	1.20114	0.600569	−	0.799573i	$-0.294941\pi$
$677$	31.2527	1.20114	0.600569	+	0.799573i	$0.294941\pi$
$678$	−37.8253	−1.45267
$679$	38.6803	1.48441
$680$	41.7393	1.60063
$681$	15.3482	0.588145
$682$	−3.14834	−0.120556
$683$	−45.8345	−1.75381	−0.876904	−	0.480665i	$-0.840395\pi$
$683$	−45.8345	−1.75381	−0.876904	+	0.480665i	$0.840395\pi$
$684$	−21.4347	−0.819578
$685$	−13.2543	−0.506419
$686$	55.1166	2.10436
$687$	11.4562	0.437080
$688$	40.8317	1.55669
$689$	−11.3322	−0.431722
$690$	−9.03411	−0.343923
$691$	−43.0759	−1.63869	−0.819343	−	0.573304i	$-0.805661\pi$
$691$	−43.0759	−1.63869	−0.819343	+	0.573304i	$0.805661\pi$
$692$	−56.6493	−2.15348
$693$	−8.94903	−0.339945
$694$	40.8107	1.54915
$695$	−9.07019	−0.344052
$696$	0.375314	0.0142263
$697$	−12.3196	−0.466639
$698$	−0.564691	−0.0213739
$699$	−10.4366	−0.394748
$700$	−0.883748	−0.0334025
$701$	30.4099	1.14857	0.574283	−	0.818657i	$-0.305281\pi$
$701$	30.4099	1.14857	0.574283	+	0.818657i	$0.305281\pi$
$702$	−2.73802	−0.103340
$703$	−3.36189	−0.126796
$704$	125.332	4.72364
$705$	−7.38435	−0.278111
$706$	43.2848	1.62904
$707$	6.52933	0.245561
$708$	−68.7955	−2.58549
$709$	8.91063	0.334646	0.167323	−	0.985902i	$-0.446488\pi$
$709$	8.91063	0.334646	0.167323	+	0.985902i	$0.446488\pi$
$710$	−27.9705	−1.04972
$711$	3.50200	0.131335
$712$	−88.4158	−3.31352
$713$	−0.419860	−0.0157239
$714$	11.8213	0.442401
$715$	9.03626	0.337937
$716$	−137.249	−5.12925
$717$	−4.27431	−0.159627
$718$	62.7928	2.34341
$719$	4.70263	0.175379	0.0876893	−	0.996148i	$-0.472052\pi$
$719$	4.70263	0.175379	0.0876893	+	0.996148i	$0.472052\pi$
$720$	34.2794	1.27752
$721$	2.23039	0.0830640
$722$	−10.3874	−0.386577
$723$	15.5365	0.577810
$724$	−108.271	−4.02386
$725$	−0.00282574	−0.000104945 0
$726$	−13.9603	−0.518117
$727$	−41.4810	−1.53844	−0.769222	−	0.638981i	$-0.779356\pi$
$727$	−41.4810	−1.53844	−0.769222	+	0.638981i	$0.779356\pi$
$728$	−21.3542	−0.791441
$729$	1.00000	0.0370370
$730$	47.4673	1.75684
$731$	5.19284	0.192064
$732$	−8.10916	−0.299723
$733$	−24.8936	−0.919465	−0.459733	−	0.888057i	$-0.652055\pi$
$733$	−24.8936	−0.919465	−0.459733	+	0.888057i	$0.652055\pi$
$734$	−59.9491	−2.21276
$735$	4.56139	0.168249
$736$	33.0030	1.21651
$737$	13.3862	0.493088
$738$	−17.4255	−0.641442
$739$	−11.6467	−0.428431	−0.214216	−	0.976786i	$-0.568720\pi$
$739$	−11.6467	−0.428431	−0.214216	+	0.976786i	$0.568720\pi$
$740$	10.6727	0.392335
$741$	3.89952	0.143252
$742$	69.2040	2.54056
$743$	−30.6055	−1.12281	−0.561403	−	0.827543i	$-0.689738\pi$
$743$	−30.6055	−1.12281	−0.561403	+	0.827543i	$0.689738\pi$
$744$	2.74380	0.100593
$745$	43.5755	1.59648
$746$	−77.5214	−2.83826
$747$	−6.37677	−0.233314
$748$	42.6924	1.56099
$749$	15.4115	0.563124
$750$	30.3874	1.10959
$751$	−29.1830	−1.06490	−0.532451	−	0.846461i	$-0.678729\pi$
$751$	−29.1830	−1.06490	−0.532451	+	0.846461i	$0.678729\pi$
$752$	49.9068	1.81991
$753$	3.10336	0.113093
$754$	−0.107332	−0.00390880
$755$	16.9312	0.616190
$756$	12.2599	0.445889
$757$	15.0268	0.546158	0.273079	−	0.961992i	$-0.411958\pi$
$757$	15.0268	0.546158	0.273079	+	0.961992i	$0.411958\pi$
$758$	−12.7635	−0.463590
$759$	−5.87828	−0.213368
$760$	−84.0829	−3.05001
$761$	12.0306	0.436111	0.218055	−	0.975936i	$-0.430029\pi$
$761$	12.0306	0.436111	0.218055	+	0.975936i	$0.430029\pi$
$762$	−51.2161	−1.85536
$763$	−2.88792	−0.104550
$764$	−92.3989	−3.34287
$765$	4.35955	0.157620
$766$	−69.5873	−2.51429
$767$	12.5156	0.451913
$768$	−48.3444	−1.74448
$769$	−3.09469	−0.111598	−0.0557988	−	0.998442i	$-0.517771\pi$
$769$	−3.09469	−0.111598	−0.0557988	+	0.998442i	$0.517771\pi$
$770$	−55.1831	−1.98866
$771$	17.7908	0.640719
$772$	−75.3931	−2.71346
$773$	−34.2136	−1.23058	−0.615289	−	0.788301i	$-0.710961\pi$
$773$	−34.2136	−1.23058	−0.615289	+	0.788301i	$0.710961\pi$
$774$	7.34504	0.264012
$775$	−0.0206581	−0.000742059 0
$776$	−166.040	−5.96049
$777$	1.92289	0.0689831
$778$	62.6491	2.24608
$779$	24.8176	0.889183
$780$	−12.3794	−0.443254
$781$	−18.1998	−0.651239
$782$	7.76498	0.277675
$783$	0.0392005	0.00140091
$784$	−30.8279	−1.10100
$785$	15.3295	0.547132
$786$	−46.0543	−1.64270
$787$	37.0412	1.32038	0.660188	−	0.751101i	$-0.270477\pi$
$787$	37.0412	1.32038	0.660188	+	0.751101i	$0.270477\pi$
$788$	−20.4673	−0.729118
$789$	6.04045	0.215046
$790$	21.5946	0.768302
$791$	−30.8125	−1.09556
$792$	38.4148	1.36501
$793$	1.47526	0.0523880
$794$	24.0111	0.852120
$795$	25.5216	0.905157
$796$	117.161	4.15265
$797$	35.2454	1.24846	0.624228	−	0.781242i	$-0.285414\pi$
$797$	35.2454	1.24846	0.624228	+	0.781242i	$0.285414\pi$
$798$	−23.8138	−0.842999
$799$	6.34698	0.224540
$800$	1.62382	0.0574108
$801$	−9.23478	−0.326295
$802$	−28.2235	−0.996608
$803$	30.8858	1.08994
$804$	−18.3387	−0.646758
$805$	−7.35917	−0.259377
$806$	−0.784668	−0.0276387
$807$	16.9184	0.595556
$808$	−28.0280	−0.986020
$809$	27.9356	0.982163	0.491082	−	0.871114i	$-0.336602\pi$
$809$	27.9356	0.982163	0.491082	+	0.871114i	$0.336602\pi$
$810$	6.16638	0.216664
$811$	−15.2507	−0.535524	−0.267762	−	0.963485i	$-0.586284\pi$
$811$	−15.2507	−0.535524	−0.267762	+	0.963485i	$0.586284\pi$
$812$	0.480595	0.0168656
$813$	16.4202	0.575882
$814$	9.47120	0.331966
$815$	56.4132	1.97607
$816$	−29.4638	−1.03144
$817$	−10.4609	−0.365980
$818$	−84.8592	−2.96703
$819$	−2.23039	−0.0779361
$820$	−78.7860	−2.75133
$821$	5.78489	0.201894	0.100947	−	0.994892i	$-0.467813\pi$
$821$	5.78489	0.201894	0.100947	+	0.994892i	$0.467813\pi$
$822$	16.1138	0.562035
$823$	49.3605	1.72060	0.860299	−	0.509790i	$-0.170277\pi$
$823$	49.3605	1.72060	0.860299	+	0.509790i	$0.170277\pi$
$824$	−9.57422	−0.333534
$825$	−0.289225	−0.0100695
$826$	−76.4311	−2.65938
$827$	−29.1946	−1.01519	−0.507597	−	0.861594i	$-0.669466\pi$
$827$	−29.1946	−1.01519	−0.507597	+	0.861594i	$0.669466\pi$
$828$	8.05309	0.279864
$829$	7.10218	0.246669	0.123335	−	0.992365i	$-0.460641\pi$
$829$	7.10218	0.246669	0.123335	+	0.992365i	$0.460641\pi$
$830$	−39.3216	−1.36487
$831$	7.13667	0.247568
$832$	31.2369	1.08294
$833$	−3.92060	−0.135841
$834$	11.0271	0.381836
$835$	−27.3356	−0.945987
$836$	−86.0030	−2.97448
$837$	0.286582	0.00990572
$838$	71.2736	2.46211
$839$	−13.2473	−0.457346	−0.228673	−	0.973503i	$-0.573439\pi$
$839$	−13.2473	−0.457346	−0.228673	+	0.973503i	$0.573439\pi$
$840$	48.0925	1.65935
$841$	−28.9985	−0.999947
$842$	16.0451	0.552950
$843$	8.08608	0.278499
$844$	−1.90978	−0.0657375
$845$	2.25213	0.0774756
$846$	8.97752	0.308653
$847$	−11.3721	−0.390749
$848$	−172.486	−5.92320
$849$	−1.86933	−0.0641552
$850$	0.382055	0.0131044
$851$	1.26307	0.0432975
$852$	24.9332	0.854197
$853$	33.7902	1.15695	0.578477	−	0.815698i	$-0.303647\pi$
$853$	33.7902	1.15695	0.578477	+	0.815698i	$0.303647\pi$
$854$	−9.00920	−0.308288
$855$	−8.78222	−0.300346
$856$	−66.1558	−2.26116
$857$	0.434238	0.0148333	0.00741664	−	0.999972i	$-0.497639\pi$
$857$	0.434238	0.0148333	0.00741664	+	0.999972i	$0.497639\pi$
$858$	−10.9858	−0.375050
$859$	−28.5717	−0.974855	−0.487427	−	0.873164i	$-0.662065\pi$
$859$	−28.5717	−0.974855	−0.487427	+	0.873164i	$0.662065\pi$
$860$	33.2091	1.13242
$861$	−14.1948	−0.483757
$862$	61.0770	2.08029
$863$	48.2336	1.64189	0.820946	−	0.571007i	$-0.193447\pi$
$863$	48.2336	1.64189	0.820946	+	0.571007i	$0.193447\pi$
$864$	−22.5267	−0.766375
$865$	−23.2103	−0.789173
$866$	34.3875	1.16853
$867$	13.2529	0.450092
$868$	3.51347	0.119255
$869$	14.0511	0.476652
$870$	0.241725	0.00819525
$871$	3.33628	0.113046
$872$	12.3968	0.419807
$873$	−17.3424	−0.586952
$874$	−15.6424	−0.529112
$875$	24.7535	0.836822
$876$	−42.3127	−1.42962
$877$	−3.21501	−0.108563	−0.0542817	−	0.998526i	$-0.517287\pi$
$877$	−3.21501	−0.108563	−0.0542817	+	0.998526i	$0.517287\pi$
$878$	55.8892	1.88617
$879$	2.61365	0.0881562
$880$	137.540	4.63647
$881$	36.9025	1.24328	0.621639	−	0.783304i	$-0.286467\pi$
$881$	36.9025	1.24328	0.621639	+	0.783304i	$0.286467\pi$
$882$	−5.54550	−0.186727
$883$	22.2626	0.749196	0.374598	−	0.927187i	$-0.377781\pi$
$883$	22.2626	0.749196	0.374598	+	0.927187i	$0.377781\pi$
$884$	10.6403	0.357873
$885$	−28.1868	−0.947489
$886$	−18.7541	−0.630056
$887$	−18.7149	−0.628383	−0.314192	−	0.949360i	$-0.601733\pi$
$887$	−18.7149	−0.628383	−0.314192	+	0.949360i	$0.601733\pi$
$888$	−8.25423	−0.276994
$889$	−41.7205	−1.39926
$890$	−56.9451	−1.90881
$891$	4.01232	0.134418
$892$	−48.8303	−1.63496
$893$	−12.7859	−0.427863
$894$	−52.9768	−1.77181
$895$	−56.2337	−1.87968
$896$	−90.2722	−3.01578
$897$	−1.46506	−0.0489169
$898$	52.0627	1.73735
$899$	0.0112342	0.000374680 0
$900$	0.396230	0.0132077
$901$	−21.9362	−0.730802
$902$	−69.9167	−2.32797
$903$	5.98325	0.199110
$904$	132.266	4.39911
$905$	−44.3607	−1.47460
$906$	−20.5841	−0.683861
$907$	27.6472	0.918009	0.459005	−	0.888434i	$-0.348206\pi$
$907$	27.6472	0.918009	0.459005	+	0.888434i	$0.348206\pi$
$908$	−84.3656	−2.79977
$909$	−2.92744	−0.0970971
$910$	−13.7534	−0.455921
$911$	−56.2268	−1.86288	−0.931438	−	0.363899i	$-0.881445\pi$
$911$	−56.2268	−1.86288	−0.931438	+	0.363899i	$0.881445\pi$
$912$	59.3542	1.96541
$913$	−25.5856	−0.846760
$914$	80.1451	2.65096
$915$	−3.32248	−0.109838
$916$	−62.9718	−2.08065
$917$	−37.5157	−1.23888
$918$	−5.30011	−0.174930
$919$	49.4192	1.63019	0.815095	−	0.579327i	$-0.196685\pi$
$919$	49.4192	1.63019	0.815095	+	0.579327i	$0.196685\pi$
$920$	31.5902	1.04150
$921$	−13.8308	−0.455741
$922$	−87.4509	−2.88004
$923$	−4.53598	−0.149303
$924$	49.1907	1.61826
$925$	0.0621460	0.00204335
$926$	19.9132	0.654390
$927$	−1.00000	−0.0328443
$928$	−0.883059	−0.0289878
$929$	−6.98607	−0.229206	−0.114603	−	0.993411i	$-0.536560\pi$
$929$	−6.98607	−0.229206	−0.114603	+	0.993411i	$0.536560\pi$
$930$	1.76717	0.0579479
$931$	7.89796	0.258845
$932$	57.3675	1.87914
$933$	−1.27395	−0.0417072
$934$	54.5008	1.78332
$935$	17.4919	0.572046
$936$	9.57422	0.312943
$937$	−53.0486	−1.73302	−0.866511	−	0.499158i	$-0.833643\pi$
$937$	−53.0486	−1.73302	−0.866511	+	0.499158i	$0.833643\pi$
$938$	−20.3742	−0.665240
$939$	−2.55357	−0.0833326
$940$	40.5901	1.32390
$941$	60.1422	1.96058	0.980290	−	0.197563i	$-0.0633028\pi$
$941$	60.1422	1.96058	0.980290	+	0.197563i	$0.0633028\pi$
$942$	−18.6368	−0.607219
$943$	−9.32404	−0.303632
$944$	190.499	6.20022
$945$	5.02312	0.163402
$946$	29.4706	0.958173
$947$	43.9056	1.42674	0.713370	−	0.700787i	$-0.247168\pi$
$947$	43.9056	1.42674	0.713370	+	0.700787i	$0.247168\pi$
$948$	−19.2496	−0.625199
$949$	7.69775	0.249880
$950$	−0.769642	−0.0249705
$951$	−17.1973	−0.557659
$952$	−41.3364	−1.33972
$953$	−19.5581	−0.633548	−0.316774	−	0.948501i	$-0.602600\pi$
$953$	−19.5581	−0.633548	−0.316774	+	0.948501i	$0.602600\pi$
$954$	−31.0278	−1.00456
$955$	−37.8576	−1.22504
$956$	23.4949	0.759879
$957$	0.157285	0.00508430
$958$	−115.180	−3.72131
$959$	13.1263	0.423871
$960$	−70.3494	−2.27052
$961$	−30.9179	−0.997351
$962$	2.36053	0.0761066
$963$	−6.90978	−0.222665
$964$	−85.4006	−2.75057
$965$	−30.8900	−0.994383
$966$	8.94690	0.287862
$967$	−8.97958	−0.288764	−0.144382	−	0.989522i	$-0.546119\pi$
$967$	−8.97958	−0.288764	−0.144382	+	0.989522i	$0.546119\pi$
$968$	48.8160	1.56901
$969$	7.54848	0.242492
$970$	−106.940	−3.43363
$971$	−42.9997	−1.37992	−0.689962	−	0.723845i	$-0.742373\pi$
$971$	−42.9997	−1.37992	−0.689962	+	0.723845i	$0.742373\pi$
$972$	−5.49677	−0.176309
$973$	8.98264	0.287970
$974$	−87.4435	−2.80187
$975$	−0.0720843	−0.00230854
$976$	22.4548	0.718760
$977$	45.3026	1.44936	0.724680	−	0.689086i	$-0.241988\pi$
$977$	45.3026	1.44936	0.724680	+	0.689086i	$0.241988\pi$
$978$	−68.5843	−2.19308
$979$	−37.0529	−1.18421
$980$	−25.0729	−0.800924
$981$	1.29481	0.0413400
$982$	−35.3313	−1.12747
$983$	36.6821	1.16998	0.584988	−	0.811042i	$-0.301099\pi$
$983$	36.6821	1.16998	0.584988	+	0.811042i	$0.301099\pi$
$984$	60.9330	1.94247
$985$	−8.38585	−0.267195
$986$	−0.207767	−0.00661666
$987$	7.31307	0.232778
$988$	−21.4347	−0.681930
$989$	3.93018	0.124972
$990$	24.7415	0.786336
$991$	−8.80711	−0.279767	−0.139884	−	0.990168i	$-0.544673\pi$
$991$	−8.80711	−0.279767	−0.139884	+	0.990168i	$0.544673\pi$
$992$	−6.45575	−0.204970
$993$	−6.63238	−0.210472
$994$	27.7005	0.878608
$995$	48.0030	1.52180
$996$	35.0516	1.11065
$997$	−16.2359	−0.514195	−0.257098	−	0.966385i	$-0.582766\pi$
$997$	−16.2359	−0.514195	−0.257098	+	0.966385i	$0.582766\pi$
$998$	95.5522	3.02465
$999$	−0.862130	−0.0272766

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.j.1.25	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.j.1.25	✓	25	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)

\(f(q)\)	\(=\)	\(q+2.73802 q^{2} -1.00000 q^{3} +5.49677 q^{4} +2.25213 q^{5} -2.73802 q^{6} -2.23039 q^{7} +9.57422 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.73802 q^{2} -1.00000 q^{3} +5.49677 q^{4} +2.25213 q^{5} -2.73802 q^{6} -2.23039 q^{7} +9.57422 q^{8} +1.00000 q^{9} +6.16638 q^{10} +4.01232 q^{11} -5.49677 q^{12} +1.00000 q^{13} -6.10685 q^{14} -2.25213 q^{15} +15.2209 q^{16} +1.93575 q^{17} +2.73802 q^{18} -3.89952 q^{19} +12.3794 q^{20} +2.23039 q^{21} +10.9858 q^{22} +1.46506 q^{23} -9.57422 q^{24} +0.0720843 q^{25} +2.73802 q^{26} -1.00000 q^{27} -12.2599 q^{28} -0.0392005 q^{29} -6.16638 q^{30} -0.286582 q^{31} +22.5267 q^{32} -4.01232 q^{33} +5.30011 q^{34} -5.02312 q^{35} +5.49677 q^{36} +0.862130 q^{37} -10.6770 q^{38} -1.00000 q^{39} +21.5624 q^{40} -6.36427 q^{41} +6.10685 q^{42} +2.68261 q^{43} +22.0548 q^{44} +2.25213 q^{45} +4.01136 q^{46} +3.27883 q^{47} -15.2209 q^{48} -2.02537 q^{49} +0.197368 q^{50} -1.93575 q^{51} +5.49677 q^{52} -11.3322 q^{53} -2.73802 q^{54} +9.03626 q^{55} -21.3542 q^{56} +3.89952 q^{57} -0.107332 q^{58} +12.5156 q^{59} -12.3794 q^{60} +1.47526 q^{61} -0.784668 q^{62} -2.23039 q^{63} +31.2369 q^{64} +2.25213 q^{65} -10.9858 q^{66} +3.33628 q^{67} +10.6403 q^{68} -1.46506 q^{69} -13.7534 q^{70} -4.53598 q^{71} +9.57422 q^{72} +7.69775 q^{73} +2.36053 q^{74} -0.0720843 q^{75} -21.4347 q^{76} -8.94903 q^{77} -2.73802 q^{78} +3.50200 q^{79} +34.2794 q^{80} +1.00000 q^{81} -17.4255 q^{82} -6.37677 q^{83} +12.2599 q^{84} +4.35955 q^{85} +7.34504 q^{86} +0.0392005 q^{87} +38.4148 q^{88} -9.23478 q^{89} +6.16638 q^{90} -2.23039 q^{91} +8.05309 q^{92} +0.286582 q^{93} +8.97752 q^{94} -8.78222 q^{95} -22.5267 q^{96} -17.3424 q^{97} -5.54550 q^{98} +4.01232 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * q^99

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