LMFDB - Embedded newform 4017.2.a.h.1.13

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

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-0.451110 q^{2} -1.00000 q^{3} -1.79650 q^{4} -1.20422 q^{5} +0.451110 q^{6} +5.19076 q^{7} +1.71264 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.451110 q^{2} -1.00000 q^{3} -1.79650 q^{4} -1.20422 q^{5} +0.451110 q^{6} +5.19076 q^{7} +1.71264 q^{8} +1.00000 q^{9} +0.543237 q^{10} +1.40876 q^{11} +1.79650 q^{12} +1.00000 q^{13} -2.34160 q^{14} +1.20422 q^{15} +2.82041 q^{16} -1.28094 q^{17} -0.451110 q^{18} -7.00349 q^{19} +2.16339 q^{20} -5.19076 q^{21} -0.635504 q^{22} -1.60507 q^{23} -1.71264 q^{24} -3.54984 q^{25} -0.451110 q^{26} -1.00000 q^{27} -9.32520 q^{28} -2.24806 q^{29} -0.543237 q^{30} -4.40457 q^{31} -4.69759 q^{32} -1.40876 q^{33} +0.577846 q^{34} -6.25084 q^{35} -1.79650 q^{36} +2.58387 q^{37} +3.15934 q^{38} -1.00000 q^{39} -2.06240 q^{40} +8.22366 q^{41} +2.34160 q^{42} -6.24816 q^{43} -2.53083 q^{44} -1.20422 q^{45} +0.724064 q^{46} -9.77534 q^{47} -2.82041 q^{48} +19.9440 q^{49} +1.60137 q^{50} +1.28094 q^{51} -1.79650 q^{52} -5.58587 q^{53} +0.451110 q^{54} -1.69646 q^{55} +8.88989 q^{56} +7.00349 q^{57} +1.01412 q^{58} +13.4433 q^{59} -2.16339 q^{60} +13.2465 q^{61} +1.98694 q^{62} +5.19076 q^{63} -3.52170 q^{64} -1.20422 q^{65} +0.635504 q^{66} +8.40617 q^{67} +2.30121 q^{68} +1.60507 q^{69} +2.81981 q^{70} -12.1576 q^{71} +1.71264 q^{72} -7.50071 q^{73} -1.16561 q^{74} +3.54984 q^{75} +12.5818 q^{76} +7.31252 q^{77} +0.451110 q^{78} +12.6899 q^{79} -3.39641 q^{80} +1.00000 q^{81} -3.70977 q^{82} -4.71567 q^{83} +9.32520 q^{84} +1.54254 q^{85} +2.81861 q^{86} +2.24806 q^{87} +2.41269 q^{88} -14.1823 q^{89} +0.543237 q^{90} +5.19076 q^{91} +2.88351 q^{92} +4.40457 q^{93} +4.40975 q^{94} +8.43377 q^{95} +4.69759 q^{96} -3.15507 q^{97} -8.99691 q^{98} +1.40876 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9} - 12 q^{10} - 23 q^{11} - 28 q^{12} + 25 q^{13} + 5 q^{15} + 26 q^{16} - 14 q^{17} - 4 q^{18} - 4 q^{19} - 12 q^{20} + 7 q^{21} - 7 q^{22} - 47 q^{23} + 9 q^{24} + 26 q^{25} - 4 q^{26} - 25 q^{27} - 38 q^{28} + 6 q^{29} + 12 q^{30} - 8 q^{31} - 62 q^{32} + 23 q^{33} + 25 q^{34} + 28 q^{36} - 20 q^{37} - 2 q^{38} - 25 q^{39} - 8 q^{40} - 33 q^{41} - 13 q^{43} - 13 q^{44} - 5 q^{45} - 21 q^{46} - 48 q^{47} - 26 q^{48} + 40 q^{49} - 9 q^{50} + 14 q^{51} + 28 q^{52} - 24 q^{53} + 4 q^{54} - 2 q^{55} - 14 q^{56} + 4 q^{57} - 31 q^{58} - 36 q^{59} + 12 q^{60} + 25 q^{61} - 7 q^{62} - 7 q^{63} + 45 q^{64} - 5 q^{65} + 7 q^{66} - 2 q^{67} - 32 q^{68} + 47 q^{69} - 13 q^{70} - 60 q^{71} - 9 q^{72} + 28 q^{73} - 16 q^{74} - 26 q^{75} - 12 q^{76} - 17 q^{77} + 4 q^{78} - 29 q^{79} - 88 q^{80} + 25 q^{81} - 22 q^{82} - 71 q^{83} + 38 q^{84} + 3 q^{85} - 3 q^{86} - 6 q^{87} + 23 q^{88} - 46 q^{89} - 12 q^{90} - 7 q^{91} - 69 q^{92} + 8 q^{93} + 4 q^{94} - 47 q^{95} + 62 q^{96} - 14 q^{97} - 71 q^{98} - 23 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9 - 12 * q^10 - 23 * q^11 - 28 * q^12 + 25 * q^13 + 5 * q^15 + 26 * q^16 - 14 * q^17 - 4 * q^18 - 4 * q^19 - 12 * q^20 + 7 * q^21 - 7 * q^22 - 47 * q^23 + 9 * q^24 + 26 * q^25 - 4 * q^26 - 25 * q^27 - 38 * q^28 + 6 * q^29 + 12 * q^30 - 8 * q^31 - 62 * q^32 + 23 * q^33 + 25 * q^34 + 28 * q^36 - 20 * q^37 - 2 * q^38 - 25 * q^39 - 8 * q^40 - 33 * q^41 - 13 * q^43 - 13 * q^44 - 5 * q^45 - 21 * q^46 - 48 * q^47 - 26 * q^48 + 40 * q^49 - 9 * q^50 + 14 * q^51 + 28 * q^52 - 24 * q^53 + 4 * q^54 - 2 * q^55 - 14 * q^56 + 4 * q^57 - 31 * q^58 - 36 * q^59 + 12 * q^60 + 25 * q^61 - 7 * q^62 - 7 * q^63 + 45 * q^64 - 5 * q^65 + 7 * q^66 - 2 * q^67 - 32 * q^68 + 47 * q^69 - 13 * q^70 - 60 * q^71 - 9 * q^72 + 28 * q^73 - 16 * q^74 - 26 * q^75 - 12 * q^76 - 17 * q^77 + 4 * q^78 - 29 * q^79 - 88 * q^80 + 25 * q^81 - 22 * q^82 - 71 * q^83 + 38 * q^84 + 3 * q^85 - 3 * q^86 - 6 * q^87 + 23 * q^88 - 46 * q^89 - 12 * q^90 - 7 * q^91 - 69 * q^92 + 8 * q^93 + 4 * q^94 - 47 * q^95 + 62 * q^96 - 14 * q^97 - 71 * q^98 - 23 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.451110	−0.318983	−0.159491	−	0.987199i	$-0.550985\pi$
$2$	−0.451110	−0.318983	−0.159491	+	0.987199i	$0.550985\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.79650	−0.898250
$5$	−1.20422	−0.538546	−0.269273	−	0.963064i	$-0.586783\pi$
$5$	−1.20422	−0.538546	−0.269273	+	0.963064i	$0.586783\pi$
$6$	0.451110	0.184165
$7$	5.19076	1.96192	0.980961	−	0.194205i	$-0.0622129\pi$
$7$	5.19076	1.96192	0.980961	+	0.194205i	$0.0622129\pi$
$8$	1.71264	0.605509
$9$	1.00000	0.333333
$10$	0.543237	0.171787
$11$	1.40876	0.424757	0.212378	−	0.977188i	$-0.431879\pi$
$11$	1.40876	0.424757	0.212378	+	0.977188i	$0.431879\pi$
$12$	1.79650	0.518605
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.34160	−0.625819
$15$	1.20422	0.310929
$16$	2.82041	0.705103
$17$	−1.28094	−0.310674	−0.155337	−	0.987862i	$-0.549646\pi$
$17$	−1.28094	−0.310674	−0.155337	+	0.987862i	$0.549646\pi$
$18$	−0.451110	−0.106328
$19$	−7.00349	−1.60671	−0.803355	−	0.595500i	$-0.796954\pi$
$19$	−7.00349	−1.60671	−0.803355	+	0.595500i	$0.796954\pi$
$20$	2.16339	0.483749
$21$	−5.19076	−1.13272
$22$	−0.635504	−0.135490
$23$	−1.60507	−0.334681	−0.167340	−	0.985899i	$-0.553518\pi$
$23$	−1.60507	−0.334681	−0.167340	+	0.985899i	$0.553518\pi$
$24$	−1.71264	−0.349591
$25$	−3.54984	−0.709969
$26$	−0.451110	−0.0884699
$27$	−1.00000	−0.192450
$28$	−9.32520	−1.76230
$29$	−2.24806	−0.417455	−0.208728	−	0.977974i	$-0.566932\pi$
$29$	−2.24806	−0.417455	−0.208728	+	0.977974i	$0.566932\pi$
$30$	−0.543237	−0.0991811
$31$	−4.40457	−0.791084	−0.395542	−	0.918448i	$-0.629443\pi$
$31$	−4.40457	−0.791084	−0.395542	+	0.918448i	$0.629443\pi$
$32$	−4.69759	−0.830425
$33$	−1.40876	−0.245233
$34$	0.577846	0.0990997
$35$	−6.25084	−1.05658
$36$	−1.79650	−0.299417
$37$	2.58387	0.424786	0.212393	−	0.977184i	$-0.431874\pi$
$37$	2.58387	0.424786	0.212393	+	0.977184i	$0.431874\pi$
$38$	3.15934	0.512513
$39$	−1.00000	−0.160128
$40$	−2.06240	−0.326094
$41$	8.22366	1.28432	0.642160	−	0.766570i	$-0.278038\pi$
$41$	8.22366	1.28432	0.642160	+	0.766570i	$0.278038\pi$
$42$	2.34160	0.361317
$43$	−6.24816	−0.952836	−0.476418	−	0.879219i	$-0.658065\pi$
$43$	−6.24816	−0.952836	−0.476418	+	0.879219i	$0.658065\pi$
$44$	−2.53083	−0.381538
$45$	−1.20422	−0.179515
$46$	0.724064	0.106757
$47$	−9.77534	−1.42588	−0.712940	−	0.701225i	$-0.752637\pi$
$47$	−9.77534	−1.42588	−0.712940	+	0.701225i	$0.752637\pi$
$48$	−2.82041	−0.407091
$49$	19.9440	2.84914
$50$	1.60137	0.226468
$51$	1.28094	0.179368
$52$	−1.79650	−0.249130
$53$	−5.58587	−0.767279	−0.383639	−	0.923483i	$-0.625329\pi$
$53$	−5.58587	−0.767279	−0.383639	+	0.923483i	$0.625329\pi$
$54$	0.451110	0.0613883
$55$	−1.69646	−0.228751
$56$	8.88989	1.18796
$57$	7.00349	0.927635
$58$	1.01412	0.133161
$59$	13.4433	1.75016	0.875082	−	0.483974i	$-0.160807\pi$
$59$	13.4433	1.75016	0.875082	+	0.483974i	$0.160807\pi$
$60$	−2.16339	−0.279292
$61$	13.2465	1.69604	0.848019	−	0.529967i	$-0.177796\pi$
$61$	13.2465	1.69604	0.848019	+	0.529967i	$0.177796\pi$
$62$	1.98694	0.252342
$63$	5.19076	0.653974
$64$	−3.52170	−0.440212
$65$	−1.20422	−0.149366
$66$	0.635504	0.0782252
$67$	8.40617	1.02698	0.513488	−	0.858097i	$-0.328353\pi$
$67$	8.40617	1.02698	0.513488	+	0.858097i	$0.328353\pi$
$68$	2.30121	0.279063
$69$	1.60507	0.193228
$70$	2.81981	0.337032
$71$	−12.1576	−1.44284	−0.721421	−	0.692496i	$-0.756511\pi$
$71$	−12.1576	−1.44284	−0.721421	+	0.692496i	$0.756511\pi$
$72$	1.71264	0.201836
$73$	−7.50071	−0.877891	−0.438946	−	0.898514i	$-0.644648\pi$
$73$	−7.50071	−0.877891	−0.438946	+	0.898514i	$0.644648\pi$
$74$	−1.16561	−0.135499
$75$	3.54984	0.409901
$76$	12.5818	1.44323
$77$	7.31252	0.833339
$78$	0.451110	0.0510781
$79$	12.6899	1.42773	0.713863	−	0.700285i	$-0.246944\pi$
$79$	12.6899	1.42773	0.713863	+	0.700285i	$0.246944\pi$
$80$	−3.39641	−0.379730
$81$	1.00000	0.111111
$82$	−3.70977	−0.409676
$83$	−4.71567	−0.517612	−0.258806	−	0.965929i	$-0.583329\pi$
$83$	−4.71567	−0.517612	−0.258806	+	0.965929i	$0.583329\pi$
$84$	9.32520	1.01746
$85$	1.54254	0.167312
$86$	2.81861	0.303938
$87$	2.24806	0.241018
$88$	2.41269	0.257194
$89$	−14.1823	−1.50332	−0.751658	−	0.659553i	$-0.770746\pi$
$89$	−14.1823	−1.50332	−0.751658	+	0.659553i	$0.770746\pi$
$90$	0.543237	0.0572622
$91$	5.19076	0.544139
$92$	2.88351	0.300627
$93$	4.40457	0.456733
$94$	4.40975	0.454831
$95$	8.43377	0.865287
$96$	4.69759	0.479446
$97$	−3.15507	−0.320349	−0.160174	−	0.987089i	$-0.551206\pi$
$97$	−3.15507	−0.320349	−0.160174	+	0.987089i	$0.551206\pi$
$98$	−8.99691	−0.908825
$99$	1.40876	0.141586
$100$	6.37729	0.637729
$101$	−13.7278	−1.36597	−0.682984	−	0.730433i	$-0.739318\pi$
$101$	−13.7278	−1.36597	−0.682984	+	0.730433i	$0.739318\pi$
$102$	−0.577846	−0.0572152
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.71264	0.167938
$105$	6.25084	0.610019
$106$	2.51984	0.244749
$107$	2.80368	0.271042	0.135521	−	0.990774i	$-0.456729\pi$
$107$	2.80368	0.271042	0.135521	+	0.990774i	$0.456729\pi$
$108$	1.79650	0.172868
$109$	−2.52496	−0.241847	−0.120924	−	0.992662i	$-0.538586\pi$
$109$	−2.52496	−0.241847	−0.120924	+	0.992662i	$0.538586\pi$
$110$	0.765290	0.0729675
$111$	−2.58387	−0.245250
$112$	14.6401	1.38336
$113$	−20.3068	−1.91030	−0.955150	−	0.296124i	$-0.904306\pi$
$113$	−20.3068	−1.91030	−0.955150	+	0.296124i	$0.904306\pi$
$114$	−3.15934	−0.295899
$115$	1.93287	0.180241
$116$	4.03865	0.374979
$117$	1.00000	0.0924500
$118$	−6.06439	−0.558272
$119$	−6.64906	−0.609519
$120$	2.06240	0.188271
$121$	−9.01540	−0.819582
$122$	−5.97561	−0.541007
$123$	−8.22366	−0.741503
$124$	7.91281	0.710591
$125$	10.2959	0.920896
$126$	−2.34160	−0.208606
$127$	−13.6492	−1.21117	−0.605585	−	0.795781i	$-0.707061\pi$
$127$	−13.6492	−1.21117	−0.605585	+	0.795781i	$0.707061\pi$
$128$	10.9839	0.970845
$129$	6.24816	0.550120
$130$	0.543237	0.0476451
$131$	−11.4138	−0.997230	−0.498615	−	0.866824i	$-0.666158\pi$
$131$	−11.4138	−0.997230	−0.498615	+	0.866824i	$0.666158\pi$
$132$	2.53083	0.220281
$133$	−36.3534	−3.15224
$134$	−3.79210	−0.327588
$135$	1.20422	0.103643
$136$	−2.19379	−0.188116
$137$	18.6226	1.59104	0.795519	−	0.605928i	$-0.207198\pi$
$137$	18.6226	1.59104	0.795519	+	0.605928i	$0.207198\pi$
$138$	−0.724064	−0.0616364
$139$	−4.09694	−0.347498	−0.173749	−	0.984790i	$-0.555588\pi$
$139$	−4.09694	−0.347498	−0.173749	+	0.984790i	$0.555588\pi$
$140$	11.2296	0.949077
$141$	9.77534	0.823232
$142$	5.48442	0.460242
$143$	1.40876	0.117806
$144$	2.82041	0.235034
$145$	2.70717	0.224819
$146$	3.38364	0.280032
$147$	−19.9440	−1.64495
$148$	−4.64193	−0.381564
$149$	−16.4347	−1.34639	−0.673193	−	0.739467i	$-0.735078\pi$
$149$	−16.4347	−1.34639	−0.673193	+	0.739467i	$0.735078\pi$
$150$	−1.60137	−0.130751
$151$	−2.96867	−0.241587	−0.120793	−	0.992678i	$-0.538544\pi$
$151$	−2.96867	−0.241587	−0.120793	+	0.992678i	$0.538544\pi$
$152$	−11.9944	−0.972878
$153$	−1.28094	−0.103558
$154$	−3.29875	−0.265821
$155$	5.30409	0.426035
$156$	1.79650	0.143835
$157$	14.4272	1.15142	0.575709	−	0.817655i	$-0.304726\pi$
$157$	14.4272	1.15142	0.575709	+	0.817655i	$0.304726\pi$
$158$	−5.72454	−0.455420
$159$	5.58587	0.442989
$160$	5.65695	0.447222
$161$	−8.33155	−0.656618
$162$	−0.451110	−0.0354425
$163$	12.4950	0.978680	0.489340	−	0.872093i	$-0.337238\pi$
$163$	12.4950	0.978680	0.489340	+	0.872093i	$0.337238\pi$
$164$	−14.7738	−1.15364
$165$	1.69646	0.132069
$166$	2.12729	0.165109
$167$	−16.8245	−1.30192	−0.650958	−	0.759114i	$-0.725633\pi$
$167$	−16.8245	−1.30192	−0.650958	+	0.759114i	$0.725633\pi$
$168$	−8.88989	−0.685870
$169$	1.00000	0.0769231
$170$	−0.695856	−0.0533697
$171$	−7.00349	−0.535570
$172$	11.2248	0.855885
$173$	12.1267	0.921974	0.460987	−	0.887407i	$-0.347496\pi$
$173$	12.1267	0.921974	0.460987	+	0.887407i	$0.347496\pi$
$174$	−1.01412	−0.0768805
$175$	−18.4264	−1.39290
$176$	3.97328	0.299497
$177$	−13.4433	−1.01046
$178$	6.39775	0.479532
$179$	1.23296	0.0921556	0.0460778	−	0.998938i	$-0.485328\pi$
$179$	1.23296	0.0921556	0.0460778	+	0.998938i	$0.485328\pi$
$180$	2.16339	0.161250
$181$	−4.13907	−0.307655	−0.153827	−	0.988098i	$-0.549160\pi$
$181$	−4.13907	−0.307655	−0.153827	+	0.988098i	$0.549160\pi$
$182$	−2.34160	−0.173571
$183$	−13.2465	−0.979207
$184$	−2.74891	−0.202652
$185$	−3.11156	−0.228767
$186$	−1.98694	−0.145690
$187$	−1.80454	−0.131961
$188$	17.5614	1.28080
$189$	−5.19076	−0.377572
$190$	−3.80456	−0.276012
$191$	−18.9726	−1.37281	−0.686403	−	0.727221i	$-0.740811\pi$
$191$	−18.9726	−1.37281	−0.686403	+	0.727221i	$0.740811\pi$
$192$	3.52170	0.254157
$193$	18.1333	1.30526	0.652631	−	0.757676i	$-0.273665\pi$
$193$	18.1333	1.30526	0.652631	+	0.757676i	$0.273665\pi$
$194$	1.42328	0.102186
$195$	1.20422	0.0862363
$196$	−35.8293	−2.55924
$197$	−12.6402	−0.900580	−0.450290	−	0.892882i	$-0.648679\pi$
$197$	−12.6402	−0.900580	−0.450290	+	0.892882i	$0.648679\pi$
$198$	−0.635504	−0.0451633
$199$	0.811146	0.0575006	0.0287503	−	0.999587i	$-0.490847\pi$
$199$	0.811146	0.0575006	0.0287503	+	0.999587i	$0.490847\pi$
$200$	−6.07960	−0.429892
$201$	−8.40617	−0.592925
$202$	6.19275	0.435720
$203$	−11.6692	−0.819014
$204$	−2.30121	−0.161117
$205$	−9.90314	−0.691665
$206$	−0.451110	−0.0314303
$207$	−1.60507	−0.111560
$208$	2.82041	0.195560
$209$	−9.86622	−0.682461
$210$	−2.81981	−0.194586
$211$	−19.9286	−1.37194	−0.685970	−	0.727630i	$-0.740622\pi$
$211$	−19.9286	−1.37194	−0.685970	+	0.727630i	$0.740622\pi$
$212$	10.0350	0.689208
$213$	12.1576	0.833026
$214$	−1.26477	−0.0864576
$215$	7.52419	0.513146
$216$	−1.71264	−0.116530
$217$	−22.8631	−1.55205
$218$	1.13903	0.0771451
$219$	7.50071	0.506851
$220$	3.04769	0.205475
$221$	−1.28094	−0.0861655
$222$	1.16561	0.0782306
$223$	0.748342	0.0501127	0.0250563	−	0.999686i	$-0.492023\pi$
$223$	0.748342	0.0501127	0.0250563	+	0.999686i	$0.492023\pi$
$224$	−24.3841	−1.62923
$225$	−3.54984	−0.236656
$226$	9.16058	0.609352
$227$	24.5069	1.62658	0.813289	−	0.581860i	$-0.197675\pi$
$227$	24.5069	1.62658	0.813289	+	0.581860i	$0.197675\pi$
$228$	−12.5818	−0.833248
$229$	26.6448	1.76074	0.880369	−	0.474290i	$-0.157295\pi$
$229$	26.6448	1.76074	0.880369	+	0.474290i	$0.157295\pi$
$230$	−0.871936	−0.0574938
$231$	−7.31252	−0.481129
$232$	−3.85012	−0.252773
$233$	16.6668	1.09188	0.545938	−	0.837826i	$-0.316174\pi$
$233$	16.6668	1.09188	0.545938	+	0.837826i	$0.316174\pi$
$234$	−0.451110	−0.0294900
$235$	11.7717	0.767901
$236$	−24.1508	−1.57209
$237$	−12.6899	−0.824298
$238$	2.99946	0.194426
$239$	−2.46660	−0.159551	−0.0797757	−	0.996813i	$-0.525420\pi$
$239$	−2.46660	−0.159551	−0.0797757	+	0.996813i	$0.525420\pi$
$240$	3.39641	0.219237
$241$	−12.8649	−0.828704	−0.414352	−	0.910117i	$-0.635992\pi$
$241$	−12.8649	−0.828704	−0.414352	+	0.910117i	$0.635992\pi$
$242$	4.06693	0.261432
$243$	−1.00000	−0.0641500
$244$	−23.7973	−1.52347
$245$	−24.0170	−1.53439
$246$	3.70977	0.236527
$247$	−7.00349	−0.445621
$248$	−7.54344	−0.479009
$249$	4.71567	0.298844
$250$	−4.64459	−0.293750
$251$	7.49259	0.472928	0.236464	−	0.971640i	$-0.424011\pi$
$251$	7.49259	0.472928	0.236464	+	0.971640i	$0.424011\pi$
$252$	−9.32520	−0.587432
$253$	−2.26116	−0.142158
$254$	6.15728	0.386342
$255$	−1.54254	−0.0965978
$256$	2.08847	0.130529
$257$	−8.68166	−0.541547	−0.270774	−	0.962643i	$-0.587279\pi$
$257$	−8.68166	−0.541547	−0.270774	+	0.962643i	$0.587279\pi$
$258$	−2.81861	−0.175479
$259$	13.4123	0.833397
$260$	2.16339	0.134168
$261$	−2.24806	−0.139152
$262$	5.14888	0.318099
$263$	−1.59625	−0.0984291	−0.0492146	−	0.998788i	$-0.515672\pi$
$263$	−1.59625	−0.0984291	−0.0492146	+	0.998788i	$0.515672\pi$
$264$	−2.41269	−0.148491
$265$	6.72665	0.413215
$266$	16.3994	1.00551
$267$	14.1823	0.867940
$268$	−15.1017	−0.922482
$269$	−9.20110	−0.561001	−0.280500	−	0.959854i	$-0.590500\pi$
$269$	−9.20110	−0.561001	−0.280500	+	0.959854i	$0.590500\pi$
$270$	−0.543237	−0.0330604
$271$	−23.5641	−1.43142	−0.715710	−	0.698398i	$-0.753897\pi$
$271$	−23.5641	−1.43142	−0.715710	+	0.698398i	$0.753897\pi$
$272$	−3.61279	−0.219057
$273$	−5.19076	−0.314159
$274$	−8.40085	−0.507514
$275$	−5.00087	−0.301564
$276$	−2.88351	−0.173567
$277$	18.0171	1.08254	0.541271	−	0.840848i	$-0.317943\pi$
$277$	18.0171	1.08254	0.541271	+	0.840848i	$0.317943\pi$
$278$	1.84817	0.110846
$279$	−4.40457	−0.263695
$280$	−10.7054	−0.639771
$281$	−6.39568	−0.381535	−0.190767	−	0.981635i	$-0.561098\pi$
$281$	−6.39568	−0.381535	−0.190767	+	0.981635i	$0.561098\pi$
$282$	−4.40975	−0.262597
$283$	−9.67921	−0.575370	−0.287685	−	0.957725i	$-0.592886\pi$
$283$	−9.67921	−0.575370	−0.287685	+	0.957725i	$0.592886\pi$
$284$	21.8411	1.29603
$285$	−8.43377	−0.499574
$286$	−0.635504	−0.0375782
$287$	42.6870	2.51974
$288$	−4.69759	−0.276808
$289$	−15.3592	−0.903482
$290$	−1.22123	−0.0717132
$291$	3.15507	0.184954
$292$	13.4750	0.788566
$293$	5.14444	0.300541	0.150271	−	0.988645i	$-0.451986\pi$
$293$	5.14444	0.300541	0.150271	+	0.988645i	$0.451986\pi$
$294$	8.99691	0.524711
$295$	−16.1887	−0.942543
$296$	4.42524	0.257212
$297$	−1.40876	−0.0817444
$298$	7.41386	0.429474
$299$	−1.60507	−0.0928238
$300$	−6.37729	−0.368193
$301$	−32.4327	−1.86939
$302$	1.33920	0.0770621
$303$	13.7278	0.788642
$304$	−19.7527	−1.13290
$305$	−15.9517	−0.913393
$306$	0.577846	0.0330332
$307$	8.99105	0.513146	0.256573	−	0.966525i	$-0.417407\pi$
$307$	8.99105	0.513146	0.256573	+	0.966525i	$0.417407\pi$
$308$	−13.1369	−0.748547
$309$	−1.00000	−0.0568880
$310$	−2.39273	−0.135898
$311$	19.2166	1.08967	0.544837	−	0.838542i	$-0.316591\pi$
$311$	19.2166	1.08967	0.544837	+	0.838542i	$0.316591\pi$
$312$	−1.71264	−0.0969590
$313$	−19.9453	−1.12738	−0.563688	−	0.825988i	$-0.690618\pi$
$313$	−19.9453	−1.12738	−0.563688	+	0.825988i	$0.690618\pi$
$314$	−6.50826	−0.367282
$315$	−6.25084	−0.352195
$316$	−22.7974	−1.28246
$317$	−28.1591	−1.58157	−0.790785	−	0.612094i	$-0.790327\pi$
$317$	−28.1591	−1.58157	−0.790785	+	0.612094i	$0.790327\pi$
$318$	−2.51984	−0.141306
$319$	−3.16698	−0.177317
$320$	4.24091	0.237074
$321$	−2.80368	−0.156486
$322$	3.75844	0.209450
$323$	8.97107	0.499164
$324$	−1.79650	−0.0998056
$325$	−3.54984	−0.196910
$326$	−5.63659	−0.312182
$327$	2.52496	0.139631
$328$	14.0842	0.777668
$329$	−50.7414	−2.79746
$330$	−0.765290	−0.0421278
$331$	11.5315	0.633830	0.316915	−	0.948454i	$-0.397353\pi$
$331$	11.5315	0.633830	0.316915	+	0.948454i	$0.397353\pi$
$332$	8.47170	0.464945
$333$	2.58387	0.141595
$334$	7.58968	0.415289
$335$	−10.1229	−0.553074
$336$	−14.6401	−0.798682
$337$	−14.4858	−0.789094	−0.394547	−	0.918876i	$-0.629099\pi$
$337$	−14.4858	−0.789094	−0.394547	+	0.918876i	$0.629099\pi$
$338$	−0.451110	−0.0245371
$339$	20.3068	1.10291
$340$	−2.77118	−0.150288
$341$	−6.20497	−0.336018
$342$	3.15934	0.170838
$343$	67.1889	3.62786
$344$	−10.7008	−0.576951
$345$	−1.93287	−0.104062
$346$	−5.47046	−0.294094
$347$	−14.9549	−0.802822	−0.401411	−	0.915898i	$-0.631480\pi$
$347$	−14.9549	−0.802822	−0.401411	+	0.915898i	$0.631480\pi$
$348$	−4.03865	−0.216494
$349$	3.97972	0.213030	0.106515	−	0.994311i	$-0.466031\pi$
$349$	3.97972	0.213030	0.106515	+	0.994311i	$0.466031\pi$
$350$	8.31232	0.444312
$351$	−1.00000	−0.0533761
$352$	−6.61777	−0.352728
$353$	−32.9820	−1.75545	−0.877727	−	0.479161i	$-0.840941\pi$
$353$	−32.9820	−1.75545	−0.877727	+	0.479161i	$0.840941\pi$
$354$	6.06439	0.322319
$355$	14.6405	0.777037
$356$	25.4784	1.35035
$357$	6.64906	0.351906
$358$	−0.556199	−0.0293961
$359$	7.87825	0.415798	0.207899	−	0.978150i	$-0.433337\pi$
$359$	7.87825	0.415798	0.207899	+	0.978150i	$0.433337\pi$
$360$	−2.06240	−0.108698
$361$	30.0489	1.58152
$362$	1.86717	0.0981365
$363$	9.01540	0.473186
$364$	−9.32520	−0.488773
$365$	9.03253	0.472784
$366$	5.97561	0.312350
$367$	1.72897	0.0902515	0.0451258	−	0.998981i	$-0.485631\pi$
$367$	1.72897	0.0902515	0.0451258	+	0.998981i	$0.485631\pi$
$368$	−4.52697	−0.235985
$369$	8.22366	0.428107
$370$	1.40366	0.0729726
$371$	−28.9949	−1.50534
$372$	−7.91281	−0.410260
$373$	−12.5646	−0.650572	−0.325286	−	0.945616i	$-0.605461\pi$
$373$	−12.5646	−0.650572	−0.325286	+	0.945616i	$0.605461\pi$
$374$	0.814045	0.0420933
$375$	−10.2959	−0.531680
$376$	−16.7416	−0.863383
$377$	−2.24806	−0.115781
$378$	2.34160	0.120439
$379$	26.4468	1.35848	0.679240	−	0.733917i	$-0.262310\pi$
$379$	26.4468	1.35848	0.679240	+	0.733917i	$0.262310\pi$
$380$	−15.1513	−0.777244
$381$	13.6492	0.699269
$382$	8.55871	0.437902
$383$	−22.4566	−1.14748	−0.573740	−	0.819038i	$-0.694508\pi$
$383$	−22.4566	−1.14748	−0.573740	+	0.819038i	$0.694508\pi$
$384$	−10.9839	−0.560517
$385$	−8.80592	−0.448791
$386$	−8.18010	−0.416356
$387$	−6.24816	−0.317612
$388$	5.66809	0.287753
$389$	−29.4309	−1.49221	−0.746103	−	0.665830i	$-0.768077\pi$
$389$	−29.4309	−1.49221	−0.746103	+	0.665830i	$0.768077\pi$
$390$	−0.543237	−0.0275079
$391$	2.05601	0.103977
$392$	34.1568	1.72518
$393$	11.4138	0.575751
$394$	5.70213	0.287269
$395$	−15.2815	−0.768896
$396$	−2.53083	−0.127179
$397$	16.0117	0.803606	0.401803	−	0.915726i	$-0.368384\pi$
$397$	16.0117	0.803606	0.401803	+	0.915726i	$0.368384\pi$
$398$	−0.365916	−0.0183417
$399$	36.3534	1.81995
$400$	−10.0120	−0.500601
$401$	−21.1160	−1.05448	−0.527240	−	0.849716i	$-0.676773\pi$
$401$	−21.1160	−1.05448	−0.527240	+	0.849716i	$0.676773\pi$
$402$	3.79210	0.189133
$403$	−4.40457	−0.219407
$404$	24.6620	1.22698
$405$	−1.20422	−0.0598384
$406$	5.26407	0.261251
$407$	3.64005	0.180431
$408$	2.19379	0.108609
$409$	21.2609	1.05128	0.525641	−	0.850706i	$-0.323825\pi$
$409$	21.2609	1.05128	0.525641	+	0.850706i	$0.323825\pi$
$410$	4.46740	0.220629
$411$	−18.6226	−0.918586
$412$	−1.79650	−0.0885072
$413$	69.7807	3.43369
$414$	0.724064	0.0355858
$415$	5.67873	0.278758
$416$	−4.69759	−0.230318
$417$	4.09694	0.200628
$418$	4.45075	0.217693
$419$	−8.68767	−0.424420	−0.212210	−	0.977224i	$-0.568066\pi$
$419$	−8.68767	−0.424420	−0.212210	+	0.977224i	$0.568066\pi$
$420$	−11.2296	−0.547950
$421$	−20.7452	−1.01106	−0.505531	−	0.862809i	$-0.668703\pi$
$421$	−20.7452	−1.01106	−0.505531	+	0.862809i	$0.668703\pi$
$422$	8.98997	0.437625
$423$	−9.77534	−0.475293
$424$	−9.56658	−0.464594
$425$	4.54715	0.220569
$426$	−5.48442	−0.265721
$427$	68.7592	3.32749
$428$	−5.03681	−0.243463
$429$	−1.40876	−0.0680155
$430$	−3.39424	−0.163685
$431$	31.9984	1.54131	0.770655	−	0.637253i	$-0.219929\pi$
$431$	31.9984	1.54131	0.770655	+	0.637253i	$0.219929\pi$
$432$	−2.82041	−0.135697
$433$	−32.7140	−1.57213	−0.786067	−	0.618142i	$-0.787886\pi$
$433$	−32.7140	−1.57213	−0.786067	+	0.618142i	$0.787886\pi$
$434$	10.3137	0.495076
$435$	−2.70717	−0.129799
$436$	4.53609	0.217239
$437$	11.2411	0.537735
$438$	−3.38364	−0.161677
$439$	−21.5293	−1.02754	−0.513770	−	0.857928i	$-0.671751\pi$
$439$	−21.5293	−1.02754	−0.513770	+	0.857928i	$0.671751\pi$
$440$	−2.90542	−0.138511
$441$	19.9440	0.949712
$442$	0.577846	0.0274853
$443$	−12.6140	−0.599307	−0.299653	−	0.954048i	$-0.596871\pi$
$443$	−12.6140	−0.599307	−0.299653	+	0.954048i	$0.596871\pi$
$444$	4.64193	0.220296
$445$	17.0786	0.809604
$446$	−0.337584	−0.0159851
$447$	16.4347	0.777336
$448$	−18.2803	−0.863662
$449$	9.79104	0.462068	0.231034	−	0.972946i	$-0.425789\pi$
$449$	9.79104	0.462068	0.231034	+	0.972946i	$0.425789\pi$
$450$	1.60137	0.0754892
$451$	11.5852	0.545524
$452$	36.4811	1.71593
$453$	2.96867	0.139480
$454$	−11.0553	−0.518850
$455$	−6.25084	−0.293044
$456$	11.9944	0.561691
$457$	16.8077	0.786231	0.393116	−	0.919489i	$-0.371397\pi$
$457$	16.8077	0.786231	0.393116	+	0.919489i	$0.371397\pi$
$458$	−12.0197	−0.561645
$459$	1.28094	0.0597893
$460$	−3.47240	−0.161901
$461$	−32.4914	−1.51328	−0.756638	−	0.653834i	$-0.773160\pi$
$461$	−32.4914	−1.51328	−0.756638	+	0.653834i	$0.773160\pi$
$462$	3.29875	0.153472
$463$	−36.2492	−1.68464	−0.842322	−	0.538974i	$-0.818812\pi$
$463$	−36.2492	−1.68464	−0.842322	+	0.538974i	$0.818812\pi$
$464$	−6.34047	−0.294349
$465$	−5.30409	−0.245971
$466$	−7.51853	−0.348289
$467$	4.99752	0.231257	0.115629	−	0.993293i	$-0.463112\pi$
$467$	4.99752	0.231257	0.115629	+	0.993293i	$0.463112\pi$
$468$	−1.79650	−0.0830432
$469$	43.6344	2.01485
$470$	−5.31033	−0.244947
$471$	−14.4272	−0.664771
$472$	23.0235	1.05974
$473$	−8.80215	−0.404723
$474$	5.72454	0.262937
$475$	24.8613	1.14071
$476$	11.9450	0.547500
$477$	−5.58587	−0.255760
$478$	1.11271	0.0508941
$479$	21.4085	0.978179	0.489089	−	0.872234i	$-0.337329\pi$
$479$	21.4085	0.978179	0.489089	+	0.872234i	$0.337329\pi$
$480$	−5.65695	−0.258203
$481$	2.58387	0.117814
$482$	5.80350	0.264342
$483$	8.33155	0.379098
$484$	16.1962	0.736189
$485$	3.79941	0.172523
$486$	0.451110	0.0204628
$487$	−16.1314	−0.730982	−0.365491	−	0.930815i	$-0.619099\pi$
$487$	−16.1314	−0.730982	−0.365491	+	0.930815i	$0.619099\pi$
$488$	22.6864	1.02697
$489$	−12.4950	−0.565041
$490$	10.8343	0.489444
$491$	10.6709	0.481573	0.240786	−	0.970578i	$-0.422595\pi$
$491$	10.6709	0.481573	0.240786	+	0.970578i	$0.422595\pi$
$492$	14.7738	0.666055
$493$	2.87964	0.129693
$494$	3.15934	0.142146
$495$	−1.69646	−0.0762503
$496$	−12.4227	−0.557796
$497$	−63.1072	−2.83074
$498$	−2.12729	−0.0953259
$499$	−16.8144	−0.752714	−0.376357	−	0.926475i	$-0.622823\pi$
$499$	−16.8144	−0.752714	−0.376357	+	0.926475i	$0.622823\pi$
$500$	−18.4966	−0.827195
$501$	16.8245	0.751662
$502$	−3.37998	−0.150856
$503$	−20.4855	−0.913403	−0.456702	−	0.889620i	$-0.650969\pi$
$503$	−20.4855	−0.913403	−0.456702	+	0.889620i	$0.650969\pi$
$504$	8.88989	0.395987
$505$	16.5314	0.735636
$506$	1.02003	0.0453459
$507$	−1.00000	−0.0444116
$508$	24.5208	1.08793
$509$	−29.4003	−1.30315	−0.651573	−	0.758586i	$-0.725891\pi$
$509$	−29.4003	−1.30315	−0.651573	+	0.758586i	$0.725891\pi$
$510$	0.695856	0.0308130
$511$	−38.9343	−1.72235
$512$	−22.9098	−1.01248
$513$	7.00349	0.309212
$514$	3.91638	0.172744
$515$	−1.20422	−0.0530645
$516$	−11.2248	−0.494145
$517$	−13.7711	−0.605652
$518$	−6.05040	−0.265839
$519$	−12.1267	−0.532302
$520$	−2.06240	−0.0904423
$521$	−10.0572	−0.440615	−0.220308	−	0.975430i	$-0.570706\pi$
$521$	−10.0572	−0.440615	−0.220308	+	0.975430i	$0.570706\pi$
$522$	1.01412	0.0443870
$523$	−7.64651	−0.334359	−0.167179	−	0.985927i	$-0.553466\pi$
$523$	−7.64651	−0.334359	−0.167179	+	0.985927i	$0.553466\pi$
$524$	20.5049	0.895762
$525$	18.4264	0.804193
$526$	0.720085	0.0313972
$527$	5.64200	0.245770
$528$	−3.97328	−0.172915
$529$	−20.4237	−0.887989
$530$	−3.03446	−0.131808
$531$	13.4433	0.583388
$532$	65.3089	2.83150
$533$	8.22366	0.356206
$534$	−6.39775	−0.276858
$535$	−3.37626	−0.145968
$536$	14.3967	0.621844
$537$	−1.23296	−0.0532061
$538$	4.15070	0.178950
$539$	28.0962	1.21019
$540$	−2.16339	−0.0930975
$541$	7.79711	0.335224	0.167612	−	0.985853i	$-0.446394\pi$
$541$	7.79711	0.335224	0.167612	+	0.985853i	$0.446394\pi$
$542$	10.6300	0.456598
$543$	4.13907	0.177624
$544$	6.01735	0.257992
$545$	3.04062	0.130246
$546$	2.34160	0.100211
$547$	16.1129	0.688939	0.344470	−	0.938798i	$-0.388059\pi$
$547$	16.1129	0.688939	0.344470	+	0.938798i	$0.388059\pi$
$548$	−33.4556	−1.42915
$549$	13.2465	0.565346
$550$	2.25594	0.0961936
$551$	15.7443	0.670729
$552$	2.74891	0.117001
$553$	65.8702	2.80109
$554$	−8.12769	−0.345312
$555$	3.11156	0.132079
$556$	7.36015	0.312140
$557$	−0.359735	−0.0152424	−0.00762122	−	0.999971i	$-0.502426\pi$
$557$	−0.359735	−0.0152424	−0.00762122	+	0.999971i	$0.502426\pi$
$558$	1.98694	0.0841141
$559$	−6.24816	−0.264269
$560$	−17.6299	−0.745001
$561$	1.80454	0.0761877
$562$	2.88516	0.121703
$563$	−30.8029	−1.29819	−0.649093	−	0.760709i	$-0.724851\pi$
$563$	−30.8029	−1.29819	−0.649093	+	0.760709i	$0.724851\pi$
$564$	−17.5614	−0.739468
$565$	24.4539	1.02878
$566$	4.36639	0.183533
$567$	5.19076	0.217991
$568$	−20.8216	−0.873654
$569$	10.5731	0.443247	0.221624	−	0.975132i	$-0.428864\pi$
$569$	10.5731	0.443247	0.221624	+	0.975132i	$0.428864\pi$
$570$	3.80456	0.159355
$571$	−5.69834	−0.238468	−0.119234	−	0.992866i	$-0.538044\pi$
$571$	−5.69834	−0.238468	−0.119234	+	0.992866i	$0.538044\pi$
$572$	−2.53083	−0.105819
$573$	18.9726	0.792590
$574$	−19.2565	−0.803752
$575$	5.69776	0.237613
$576$	−3.52170	−0.146737
$577$	22.5264	0.937786	0.468893	−	0.883255i	$-0.344653\pi$
$577$	22.5264	0.937786	0.468893	+	0.883255i	$0.344653\pi$
$578$	6.92868	0.288195
$579$	−18.1333	−0.753593
$580$	−4.86344	−0.201943
$581$	−24.4779	−1.01551
$582$	−1.42328	−0.0589970
$583$	−7.86914	−0.325907
$584$	−12.8460	−0.531571
$585$	−1.20422	−0.0497886
$586$	−2.32071	−0.0958675
$587$	10.6435	0.439306	0.219653	−	0.975578i	$-0.429507\pi$
$587$	10.6435	0.439306	0.219653	+	0.975578i	$0.429507\pi$
$588$	35.8293	1.47758
$589$	30.8474	1.27104
$590$	7.30289	0.300655
$591$	12.6402	0.519950
$592$	7.28759	0.299518
$593$	12.3429	0.506861	0.253430	−	0.967354i	$-0.418441\pi$
$593$	12.3429	0.506861	0.253430	+	0.967354i	$0.418441\pi$
$594$	0.635504	0.0260751
$595$	8.00696	0.328254
$596$	29.5250	1.20939
$597$	−0.811146	−0.0331980
$598$	0.724064	0.0296092
$599$	24.1154	0.985329	0.492665	−	0.870219i	$-0.336023\pi$
$599$	24.1154	0.985329	0.492665	+	0.870219i	$0.336023\pi$
$600$	6.07960	0.248198
$601$	−23.7392	−0.968341	−0.484170	−	0.874974i	$-0.660878\pi$
$601$	−23.7392	−0.968341	−0.484170	+	0.874974i	$0.660878\pi$
$602$	14.6307	0.596303
$603$	8.40617	0.342326
$604$	5.33322	0.217005
$605$	10.8566	0.441382
$606$	−6.19275	−0.251563
$607$	29.2612	1.18768	0.593838	−	0.804585i	$-0.297612\pi$
$607$	29.2612	1.18768	0.593838	+	0.804585i	$0.297612\pi$
$608$	32.8995	1.33425
$609$	11.6692	0.472858
$610$	7.19598	0.291357
$611$	−9.77534	−0.395468
$612$	2.30121	0.0930211
$613$	−20.1318	−0.813115	−0.406558	−	0.913625i	$-0.633271\pi$
$613$	−20.1318	−0.813115	−0.406558	+	0.913625i	$0.633271\pi$
$614$	−4.05595	−0.163685
$615$	9.90314	0.399333
$616$	12.5237	0.504594
$617$	35.2917	1.42079	0.710396	−	0.703803i	$-0.248516\pi$
$617$	35.2917	1.42079	0.710396	+	0.703803i	$0.248516\pi$
$618$	0.451110	0.0181463
$619$	−7.17260	−0.288291	−0.144146	−	0.989556i	$-0.546043\pi$
$619$	−7.17260	−0.288291	−0.144146	+	0.989556i	$0.546043\pi$
$620$	−9.52880	−0.382686
$621$	1.60507	0.0644094
$622$	−8.66881	−0.347587
$623$	−73.6166	−2.94939
$624$	−2.82041	−0.112907
$625$	5.35060	0.214024
$626$	8.99753	0.359614
$627$	9.86622	0.394019
$628$	−25.9185	−1.03426
$629$	−3.30979	−0.131970
$630$	2.81981	0.112344
$631$	−10.4443	−0.415781	−0.207890	−	0.978152i	$-0.566660\pi$
$631$	−10.4443	−0.415781	−0.207890	+	0.978152i	$0.566660\pi$
$632$	21.7332	0.864501
$633$	19.9286	0.792090
$634$	12.7028	0.504494
$635$	16.4367	0.652270
$636$	−10.0350	−0.397914
$637$	19.9440	0.790208
$638$	1.42865	0.0565610
$639$	−12.1576	−0.480948
$640$	−13.2270	−0.522844
$641$	−0.115264	−0.00455266	−0.00227633	−	0.999997i	$-0.500725\pi$
$641$	−0.115264	−0.00455266	−0.00227633	+	0.999997i	$0.500725\pi$
$642$	1.26477	0.0499163
$643$	42.2551	1.66638	0.833190	−	0.552987i	$-0.186512\pi$
$643$	42.2551	1.66638	0.833190	+	0.552987i	$0.186512\pi$
$644$	14.9676	0.589807
$645$	−7.52419	−0.296265
$646$	−4.04694	−0.159225
$647$	−33.8057	−1.32904	−0.664519	−	0.747271i	$-0.731364\pi$
$647$	−33.8057	−1.32904	−0.664519	+	0.747271i	$0.731364\pi$
$648$	1.71264	0.0672788
$649$	18.9383	0.743394
$650$	1.60137	0.0628108
$651$	22.8631	0.896074
$652$	−22.4472	−0.879100
$653$	−7.73692	−0.302769	−0.151385	−	0.988475i	$-0.548373\pi$
$653$	−7.73692	−0.302769	−0.151385	+	0.988475i	$0.548373\pi$
$654$	−1.13903	−0.0445398
$655$	13.7448	0.537054
$656$	23.1941	0.905578
$657$	−7.50071	−0.292630
$658$	22.8899	0.892343
$659$	−16.2285	−0.632172	−0.316086	−	0.948731i	$-0.602369\pi$
$659$	−16.2285	−0.632172	−0.316086	+	0.948731i	$0.602369\pi$
$660$	−3.04769	−0.118631
$661$	14.8663	0.578232	0.289116	−	0.957294i	$-0.406639\pi$
$661$	14.8663	0.578232	0.289116	+	0.957294i	$0.406639\pi$
$662$	−5.20199	−0.202181
$663$	1.28094	0.0497477
$664$	−8.07624	−0.313419
$665$	43.7777	1.69763
$666$	−1.16561	−0.0451665
$667$	3.60831	0.139714
$668$	30.2251	1.16945
$669$	−0.748342	−0.0289326
$670$	4.56654	0.176421
$671$	18.6611	0.720403
$672$	24.3841	0.940635
$673$	−47.8919	−1.84610	−0.923049	−	0.384681i	$-0.874311\pi$
$673$	−47.8919	−1.84610	−0.923049	+	0.384681i	$0.874311\pi$
$674$	6.53471	0.251707
$675$	3.54984	0.136634
$676$	−1.79650	−0.0690962
$677$	27.2890	1.04880	0.524401	−	0.851471i	$-0.324289\pi$
$677$	27.2890	1.04880	0.524401	+	0.851471i	$0.324289\pi$
$678$	−9.16058	−0.351810
$679$	−16.3772	−0.628500
$680$	2.64182	0.101309
$681$	−24.5069	−0.939105
$682$	2.79912	0.107184
$683$	−25.5034	−0.975860	−0.487930	−	0.872883i	$-0.662248\pi$
$683$	−25.5034	−0.975860	−0.487930	+	0.872883i	$0.662248\pi$
$684$	12.5818	0.481076
$685$	−22.4258	−0.856847
$686$	−30.3096	−1.15723
$687$	−26.6448	−1.01656
$688$	−17.6224	−0.671847
$689$	−5.58587	−0.212805
$690$	0.871936	0.0331940
$691$	−3.94614	−0.150118	−0.0750590	−	0.997179i	$-0.523915\pi$
$691$	−3.94614	−0.150118	−0.0750590	+	0.997179i	$0.523915\pi$
$692$	−21.7856	−0.828163
$693$	7.31252	0.277780
$694$	6.74631	0.256086
$695$	4.93363	0.187143
$696$	3.85012	0.145938
$697$	−10.5340	−0.399005
$698$	−1.79529	−0.0679528
$699$	−16.6668	−0.630395
$700$	33.1030	1.25118
$701$	22.8048	0.861324	0.430662	−	0.902513i	$-0.358280\pi$
$701$	22.8048	0.861324	0.430662	+	0.902513i	$0.358280\pi$
$702$	0.451110	0.0170260
$703$	−18.0961	−0.682509
$704$	−4.96122	−0.186983
$705$	−11.7717	−0.443348
$706$	14.8785	0.559960
$707$	−71.2577	−2.67992
$708$	24.1508	0.907644
$709$	−21.4962	−0.807306	−0.403653	−	0.914912i	$-0.632260\pi$
$709$	−21.4962	−0.807306	−0.403653	+	0.914912i	$0.632260\pi$
$710$	−6.60447	−0.247861
$711$	12.6899	0.475909
$712$	−24.2891	−0.910271
$713$	7.06966	0.264761
$714$	−2.99946	−0.112252
$715$	−1.69646	−0.0634440
$716$	−2.21501	−0.0827788
$717$	2.46660	0.0921170
$718$	−3.55396	−0.132632
$719$	−33.0388	−1.23214	−0.616071	−	0.787691i	$-0.711276\pi$
$719$	−33.0388	−1.23214	−0.616071	+	0.787691i	$0.711276\pi$
$720$	−3.39641	−0.126577
$721$	5.19076	0.193314
$722$	−13.5553	−0.504477
$723$	12.8649	0.478452
$724$	7.43584	0.276351
$725$	7.98028	0.296380
$726$	−4.06693	−0.150938
$727$	40.7623	1.51179	0.755895	−	0.654692i	$-0.227202\pi$
$727$	40.7623	1.51179	0.755895	+	0.654692i	$0.227202\pi$
$728$	8.88989	0.329481
$729$	1.00000	0.0370370
$730$	−4.07466	−0.150810
$731$	8.00354	0.296022
$732$	23.7973	0.879573
$733$	23.9818	0.885789	0.442894	−	0.896574i	$-0.353952\pi$
$733$	23.9818	0.885789	0.442894	+	0.896574i	$0.353952\pi$
$734$	−0.779955	−0.0287887
$735$	24.0170	0.885881
$736$	7.53998	0.277927
$737$	11.8423	0.436215
$738$	−3.70977	−0.136559
$739$	−29.6248	−1.08976	−0.544882	−	0.838513i	$-0.683426\pi$
$739$	−29.6248	−1.08976	−0.544882	+	0.838513i	$0.683426\pi$
$740$	5.58993	0.205490
$741$	7.00349	0.257280
$742$	13.0799	0.480178
$743$	−29.9849	−1.10004	−0.550020	−	0.835151i	$-0.685380\pi$
$743$	−29.9849	−1.10004	−0.550020	+	0.835151i	$0.685380\pi$
$744$	7.54344	0.276556
$745$	19.7911	0.725090
$746$	5.66803	0.207521
$747$	−4.71567	−0.172537
$748$	3.24185	0.118534
$749$	14.5532	0.531763
$750$	4.64459	0.169597
$751$	−33.2270	−1.21247	−0.606235	−	0.795286i	$-0.707321\pi$
$751$	−33.2270	−1.21247	−0.606235	+	0.795286i	$0.707321\pi$
$752$	−27.5705	−1.00539
$753$	−7.49259	−0.273045
$754$	1.01412	0.0369322
$755$	3.57494	0.130106
$756$	9.32520	0.339154
$757$	−45.4816	−1.65306	−0.826529	−	0.562894i	$-0.809688\pi$
$757$	−45.4816	−1.65306	−0.826529	+	0.562894i	$0.809688\pi$
$758$	−11.9304	−0.433331
$759$	2.26116	0.0820749
$760$	14.4440	0.523939
$761$	−14.8286	−0.537537	−0.268769	−	0.963205i	$-0.586617\pi$
$761$	−14.8286	−0.537537	−0.268769	+	0.963205i	$0.586617\pi$
$762$	−6.15728	−0.223055
$763$	−13.1065	−0.474486
$764$	34.0842	1.23312
$765$	1.54254	0.0557708
$766$	10.1304	0.366026
$767$	13.4433	0.485408
$768$	−2.08847	−0.0753611
$769$	−11.2574	−0.405952	−0.202976	−	0.979184i	$-0.565061\pi$
$769$	−11.2574	−0.405952	−0.202976	+	0.979184i	$0.565061\pi$
$770$	3.97243	0.143157
$771$	8.68166	0.312662
$772$	−32.5764	−1.17245
$773$	16.5074	0.593731	0.296865	−	0.954919i	$-0.404059\pi$
$773$	16.5074	0.593731	0.296865	+	0.954919i	$0.404059\pi$
$774$	2.81861	0.101313
$775$	15.6355	0.561645
$776$	−5.40349	−0.193974
$777$	−13.4123	−0.481162
$778$	13.2766	0.475988
$779$	−57.5943	−2.06353
$780$	−2.16339	−0.0774618
$781$	−17.1271	−0.612857
$782$	−0.927485	−0.0331668
$783$	2.24806	0.0803393
$784$	56.2502	2.00894
$785$	−17.3736	−0.620091
$786$	−5.14888	−0.183655
$787$	13.0019	0.463467	0.231733	−	0.972779i	$-0.425560\pi$
$787$	13.0019	0.463467	0.231733	+	0.972779i	$0.425560\pi$
$788$	22.7082	0.808946
$789$	1.59625	0.0568281
$790$	6.89363	0.245264
$791$	−105.407	−3.74786
$792$	2.41269	0.0857313
$793$	13.2465	0.470396
$794$	−7.22305	−0.256336
$795$	−6.72665	−0.238570
$796$	−1.45722	−0.0516499
$797$	−30.9463	−1.09618	−0.548088	−	0.836421i	$-0.684644\pi$
$797$	−30.9463	−1.09618	−0.548088	+	0.836421i	$0.684644\pi$
$798$	−16.3994	−0.580532
$799$	12.5216	0.442984
$800$	16.6757	0.589575
$801$	−14.1823	−0.501105
$802$	9.52561	0.336361
$803$	−10.5667	−0.372890
$804$	15.1017	0.532595
$805$	10.0331	0.353619
$806$	1.98694	0.0699871
$807$	9.20110	0.323894
$808$	−23.5108	−0.827106
$809$	−12.1502	−0.427180	−0.213590	−	0.976923i	$-0.568516\pi$
$809$	−12.1502	−0.427180	−0.213590	+	0.976923i	$0.568516\pi$
$810$	0.543237	0.0190874
$811$	−10.6688	−0.374632	−0.187316	−	0.982300i	$-0.559979\pi$
$811$	−10.6688	−0.374632	−0.187316	+	0.982300i	$0.559979\pi$
$812$	20.9636	0.735679
$813$	23.5641	0.826431
$814$	−1.64206	−0.0575543
$815$	−15.0467	−0.527064
$816$	3.61279	0.126473
$817$	43.7589	1.53093
$818$	−9.59098	−0.335341
$819$	5.19076	0.181380
$820$	17.7910	0.621288
$821$	40.6726	1.41948	0.709741	−	0.704462i	$-0.248812\pi$
$821$	40.6726	1.41948	0.709741	+	0.704462i	$0.248812\pi$
$822$	8.40085	0.293013
$823$	−45.7883	−1.59608	−0.798040	−	0.602605i	$-0.794130\pi$
$823$	−45.7883	−1.59608	−0.798040	+	0.602605i	$0.794130\pi$
$824$	1.71264	0.0596626
$825$	5.00087	0.174108
$826$	−31.4788	−1.09529
$827$	−40.9114	−1.42263	−0.711315	−	0.702874i	$-0.751900\pi$
$827$	−40.9114	−1.42263	−0.711315	+	0.702874i	$0.751900\pi$
$828$	2.88351	0.100209
$829$	49.4050	1.71590	0.857952	−	0.513729i	$-0.171736\pi$
$829$	49.4050	1.71590	0.857952	+	0.513729i	$0.171736\pi$
$830$	−2.56173	−0.0889189
$831$	−18.0171	−0.625006
$832$	−3.52170	−0.122093
$833$	−25.5471	−0.885153
$834$	−1.84817	−0.0639968
$835$	20.2604	0.701141
$836$	17.7247	0.613020
$837$	4.40457	0.152244
$838$	3.91909	0.135383
$839$	−41.0445	−1.41701	−0.708506	−	0.705704i	$-0.750631\pi$
$839$	−41.0445	−1.41701	−0.708506	+	0.705704i	$0.750631\pi$
$840$	10.7054	0.369372
$841$	−23.9462	−0.825731
$842$	9.35838	0.322511
$843$	6.39568	0.220279
$844$	35.8017	1.23234
$845$	−1.20422	−0.0414266
$846$	4.40975	0.151610
$847$	−46.7968	−1.60796
$848$	−15.7545	−0.541011
$849$	9.67921	0.332190
$850$	−2.05126	−0.0703577
$851$	−4.14731	−0.142168
$852$	−21.8411	−0.748265
$853$	0.110952	0.00379894	0.00189947	−	0.999998i	$-0.499395\pi$
$853$	0.110952	0.00379894	0.00189947	+	0.999998i	$0.499395\pi$
$854$	−31.0180	−1.06141
$855$	8.43377	0.288429
$856$	4.80168	0.164118
$857$	18.5982	0.635302	0.317651	−	0.948208i	$-0.397106\pi$
$857$	18.5982	0.635302	0.317651	+	0.948208i	$0.397106\pi$
$858$	0.635504	0.0216958
$859$	1.15366	0.0393622	0.0196811	−	0.999806i	$-0.493735\pi$
$859$	1.15366	0.0393622	0.0196811	+	0.999806i	$0.493735\pi$
$860$	−13.5172	−0.460933
$861$	−42.6870	−1.45477
$862$	−14.4348	−0.491651
$863$	6.09660	0.207531	0.103765	−	0.994602i	$-0.466911\pi$
$863$	6.09660	0.207531	0.103765	+	0.994602i	$0.466911\pi$
$864$	4.69759	0.159815
$865$	−14.6032	−0.496525
$866$	14.7576	0.501483
$867$	15.3592	0.521625
$868$	41.0735	1.39412
$869$	17.8770	0.606436
$870$	1.22123	0.0414037
$871$	8.40617	0.284832
$872$	−4.32434	−0.146441
$873$	−3.15507	−0.106783
$874$	−5.07098	−0.171528
$875$	53.4437	1.80673
$876$	−13.4750	−0.455279
$877$	24.1387	0.815106	0.407553	−	0.913182i	$-0.366382\pi$
$877$	24.1387	0.815106	0.407553	+	0.913182i	$0.366382\pi$
$878$	9.71210	0.327767
$879$	−5.14444	−0.173518
$880$	−4.78472	−0.161293
$881$	10.4092	0.350696	0.175348	−	0.984506i	$-0.443895\pi$
$881$	10.4092	0.350696	0.175348	+	0.984506i	$0.443895\pi$
$882$	−8.99691	−0.302942
$883$	38.2969	1.28879	0.644397	−	0.764691i	$-0.277109\pi$
$883$	38.2969	1.28879	0.644397	+	0.764691i	$0.277109\pi$
$884$	2.30121	0.0773982
$885$	16.1887	0.544178
$886$	5.69028	0.191169
$887$	−22.2868	−0.748318	−0.374159	−	0.927365i	$-0.622069\pi$
$887$	−22.2868	−0.748318	−0.374159	+	0.927365i	$0.622069\pi$
$888$	−4.42524	−0.148501
$889$	−70.8496	−2.37622
$890$	−7.70433	−0.258250
$891$	1.40876	0.0471952
$892$	−1.34440	−0.0450137
$893$	68.4615	2.29098
$894$	−7.41386	−0.247957
$895$	−1.48476	−0.0496300
$896$	57.0145	1.90472
$897$	1.60507	0.0535918
$898$	−4.41683	−0.147392
$899$	9.90176	0.330242
$900$	6.37729	0.212576
$901$	7.15518	0.238374
$902$	−5.22617	−0.174013
$903$	32.4327	1.07929
$904$	−34.7781	−1.15670
$905$	4.98437	0.165686
$906$	−1.33920	−0.0444918
$907$	8.03929	0.266940	0.133470	−	0.991053i	$-0.457388\pi$
$907$	8.03929	0.266940	0.133470	+	0.991053i	$0.457388\pi$
$908$	−44.0266	−1.46107
$909$	−13.7278	−0.455323
$910$	2.81981	0.0934759
$911$	9.97208	0.330390	0.165195	−	0.986261i	$-0.447175\pi$
$911$	9.97208	0.330390	0.165195	+	0.986261i	$0.447175\pi$
$912$	19.7527	0.654078
$913$	−6.64324	−0.219859
$914$	−7.58212	−0.250794
$915$	15.9517	0.527348
$916$	−47.8674	−1.58158
$917$	−59.2463	−1.95649
$918$	−0.577846	−0.0190717
$919$	25.6484	0.846063	0.423031	−	0.906115i	$-0.360966\pi$
$919$	25.6484	0.846063	0.423031	+	0.906115i	$0.360966\pi$
$920$	3.31030	0.109138
$921$	−8.99105	−0.296265
$922$	14.6572	0.482709
$923$	−12.1576	−0.400173
$924$	13.1369	0.432174
$925$	−9.17235	−0.301585
$926$	16.3524	0.537373
$927$	1.00000	0.0328443
$928$	10.5605	0.346665
$929$	4.14490	0.135990	0.0679949	−	0.997686i	$-0.478340\pi$
$929$	4.14490	0.135990	0.0679949	+	0.997686i	$0.478340\pi$
$930$	2.39273	0.0784606
$931$	−139.677	−4.57774
$932$	−29.9418	−0.980777
$933$	−19.2166	−0.629124
$934$	−2.25443	−0.0737671
$935$	2.17307	0.0710670
$936$	1.71264	0.0559793
$937$	−23.6512	−0.772652	−0.386326	−	0.922362i	$-0.626256\pi$
$937$	−23.6512	−0.772652	−0.386326	+	0.922362i	$0.626256\pi$
$938$	−19.6839	−0.642702
$939$	19.9453	0.650891
$940$	−21.1479	−0.689767
$941$	28.2400	0.920598	0.460299	−	0.887764i	$-0.347742\pi$
$941$	28.2400	0.920598	0.460299	+	0.887764i	$0.347742\pi$
$942$	6.50826	0.212050
$943$	−13.1996	−0.429838
$944$	37.9156	1.23405
$945$	6.25084	0.203340
$946$	3.97073	0.129100
$947$	−11.1874	−0.363543	−0.181772	−	0.983341i	$-0.558183\pi$
$947$	−11.1874	−0.363543	−0.181772	+	0.983341i	$0.558183\pi$
$948$	22.7974	0.740426
$949$	−7.50071	−0.243483
$950$	−11.2152	−0.363868
$951$	28.1591	0.913120
$952$	−11.3874	−0.369069
$953$	−23.9187	−0.774802	−0.387401	−	0.921911i	$-0.626627\pi$
$953$	−23.9187	−0.774802	−0.387401	+	0.921911i	$0.626627\pi$
$954$	2.51984	0.0815829
$955$	22.8472	0.739319
$956$	4.43125	0.143317
$957$	3.16698	0.102374
$958$	−9.65757	−0.312022
$959$	96.6655	3.12149
$960$	−4.24091	−0.136875
$961$	−11.5998	−0.374186
$962$	−1.16561	−0.0375808
$963$	2.80368	0.0903472
$964$	23.1119	0.744383
$965$	−21.8365	−0.702943
$966$	−3.75844	−0.120926
$967$	−15.8872	−0.510899	−0.255450	−	0.966822i	$-0.582224\pi$
$967$	−15.8872	−0.510899	−0.255450	+	0.966822i	$0.582224\pi$
$968$	−15.4401	−0.496264
$969$	−8.97107	−0.288192
$970$	−1.71395	−0.0550317
$971$	5.12868	0.164587	0.0822937	−	0.996608i	$-0.473775\pi$
$971$	5.12868	0.164587	0.0822937	+	0.996608i	$0.473775\pi$
$972$	1.79650	0.0576228
$973$	−21.2662	−0.681763
$974$	7.27701	0.233171
$975$	3.54984	0.113686
$976$	37.3605	1.19588
$977$	−48.4294	−1.54939	−0.774696	−	0.632334i	$-0.782097\pi$
$977$	−48.4294	−1.54939	−0.774696	+	0.632334i	$0.782097\pi$
$978$	5.63659	0.180238
$979$	−19.9794	−0.638543
$980$	43.1465	1.37827
$981$	−2.52496	−0.0806158
$982$	−4.81377	−0.153613
$983$	−48.5655	−1.54900	−0.774499	−	0.632575i	$-0.781998\pi$
$983$	−48.5655	−1.54900	−0.774499	+	0.632575i	$0.781998\pi$
$984$	−14.0842	−0.448987
$985$	15.2217	0.485003
$986$	−1.29903	−0.0413697
$987$	50.7414	1.61512
$988$	12.5818	0.400279
$989$	10.0288	0.318896
$990$	0.765290	0.0243225
$991$	44.9851	1.42900	0.714500	−	0.699635i	$-0.246654\pi$
$991$	44.9851	1.42900	0.714500	+	0.699635i	$0.246654\pi$
$992$	20.6909	0.656936
$993$	−11.5315	−0.365942
$994$	28.4683	0.902959
$995$	−0.976802	−0.0309667
$996$	−8.47170	−0.268436
$997$	55.7165	1.76456	0.882280	−	0.470724i	$-0.156007\pi$
$997$	55.7165	1.76456	0.882280	+	0.470724i	$0.156007\pi$
$998$	7.58512	0.240103
$999$	−2.58387	−0.0817501

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.h.1.13	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.h.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-0.451110 q^{2} -1.00000 q^{3} -1.79650 q^{4} -1.20422 q^{5} +0.451110 q^{6} +5.19076 q^{7} +1.71264 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.451110 q^{2} -1.00000 q^{3} -1.79650 q^{4} -1.20422 q^{5} +0.451110 q^{6} +5.19076 q^{7} +1.71264 q^{8} +1.00000 q^{9} +0.543237 q^{10} +1.40876 q^{11} +1.79650 q^{12} +1.00000 q^{13} -2.34160 q^{14} +1.20422 q^{15} +2.82041 q^{16} -1.28094 q^{17} -0.451110 q^{18} -7.00349 q^{19} +2.16339 q^{20} -5.19076 q^{21} -0.635504 q^{22} -1.60507 q^{23} -1.71264 q^{24} -3.54984 q^{25} -0.451110 q^{26} -1.00000 q^{27} -9.32520 q^{28} -2.24806 q^{29} -0.543237 q^{30} -4.40457 q^{31} -4.69759 q^{32} -1.40876 q^{33} +0.577846 q^{34} -6.25084 q^{35} -1.79650 q^{36} +2.58387 q^{37} +3.15934 q^{38} -1.00000 q^{39} -2.06240 q^{40} +8.22366 q^{41} +2.34160 q^{42} -6.24816 q^{43} -2.53083 q^{44} -1.20422 q^{45} +0.724064 q^{46} -9.77534 q^{47} -2.82041 q^{48} +19.9440 q^{49} +1.60137 q^{50} +1.28094 q^{51} -1.79650 q^{52} -5.58587 q^{53} +0.451110 q^{54} -1.69646 q^{55} +8.88989 q^{56} +7.00349 q^{57} +1.01412 q^{58} +13.4433 q^{59} -2.16339 q^{60} +13.2465 q^{61} +1.98694 q^{62} +5.19076 q^{63} -3.52170 q^{64} -1.20422 q^{65} +0.635504 q^{66} +8.40617 q^{67} +2.30121 q^{68} +1.60507 q^{69} +2.81981 q^{70} -12.1576 q^{71} +1.71264 q^{72} -7.50071 q^{73} -1.16561 q^{74} +3.54984 q^{75} +12.5818 q^{76} +7.31252 q^{77} +0.451110 q^{78} +12.6899 q^{79} -3.39641 q^{80} +1.00000 q^{81} -3.70977 q^{82} -4.71567 q^{83} +9.32520 q^{84} +1.54254 q^{85} +2.81861 q^{86} +2.24806 q^{87} +2.41269 q^{88} -14.1823 q^{89} +0.543237 q^{90} +5.19076 q^{91} +2.88351 q^{92} +4.40457 q^{93} +4.40975 q^{94} +8.43377 q^{95} +4.69759 q^{96} -3.15507 q^{97} -8.99691 q^{98} +1.40876 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9} - 12 q^{10} - 23 q^{11} - 28 q^{12} + 25 q^{13} + 5 q^{15} + 26 q^{16} - 14 q^{17} - 4 q^{18} - 4 q^{19} - 12 q^{20} + 7 q^{21} - 7 q^{22} - 47 q^{23} + 9 q^{24} + 26 q^{25} - 4 q^{26} - 25 q^{27} - 38 q^{28} + 6 q^{29} + 12 q^{30} - 8 q^{31} - 62 q^{32} + 23 q^{33} + 25 q^{34} + 28 q^{36} - 20 q^{37} - 2 q^{38} - 25 q^{39} - 8 q^{40} - 33 q^{41} - 13 q^{43} - 13 q^{44} - 5 q^{45} - 21 q^{46} - 48 q^{47} - 26 q^{48} + 40 q^{49} - 9 q^{50} + 14 q^{51} + 28 q^{52} - 24 q^{53} + 4 q^{54} - 2 q^{55} - 14 q^{56} + 4 q^{57} - 31 q^{58} - 36 q^{59} + 12 q^{60} + 25 q^{61} - 7 q^{62} - 7 q^{63} + 45 q^{64} - 5 q^{65} + 7 q^{66} - 2 q^{67} - 32 q^{68} + 47 q^{69} - 13 q^{70} - 60 q^{71} - 9 q^{72} + 28 q^{73} - 16 q^{74} - 26 q^{75} - 12 q^{76} - 17 q^{77} + 4 q^{78} - 29 q^{79} - 88 q^{80} + 25 q^{81} - 22 q^{82} - 71 q^{83} + 38 q^{84} + 3 q^{85} - 3 q^{86} - 6 q^{87} + 23 q^{88} - 46 q^{89} - 12 q^{90} - 7 q^{91} - 69 q^{92} + 8 q^{93} + 4 q^{94} - 47 q^{95} + 62 q^{96} - 14 q^{97} - 71 q^{98} - 23 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9 - 12 * q^10 - 23 * q^11 - 28 * q^12 + 25 * q^13 + 5 * q^15 + 26 * q^16 - 14 * q^17 - 4 * q^18 - 4 * q^19 - 12 * q^20 + 7 * q^21 - 7 * q^22 - 47 * q^23 + 9 * q^24 + 26 * q^25 - 4 * q^26 - 25 * q^27 - 38 * q^28 + 6 * q^29 + 12 * q^30 - 8 * q^31 - 62 * q^32 + 23 * q^33 + 25 * q^34 + 28 * q^36 - 20 * q^37 - 2 * q^38 - 25 * q^39 - 8 * q^40 - 33 * q^41 - 13 * q^43 - 13 * q^44 - 5 * q^45 - 21 * q^46 - 48 * q^47 - 26 * q^48 + 40 * q^49 - 9 * q^50 + 14 * q^51 + 28 * q^52 - 24 * q^53 + 4 * q^54 - 2 * q^55 - 14 * q^56 + 4 * q^57 - 31 * q^58 - 36 * q^59 + 12 * q^60 + 25 * q^61 - 7 * q^62 - 7 * q^63 + 45 * q^64 - 5 * q^65 + 7 * q^66 - 2 * q^67 - 32 * q^68 + 47 * q^69 - 13 * q^70 - 60 * q^71 - 9 * q^72 + 28 * q^73 - 16 * q^74 - 26 * q^75 - 12 * q^76 - 17 * q^77 + 4 * q^78 - 29 * q^79 - 88 * q^80 + 25 * q^81 - 22 * q^82 - 71 * q^83 + 38 * q^84 + 3 * q^85 - 3 * q^86 - 6 * q^87 + 23 * q^88 - 46 * q^89 - 12 * q^90 - 7 * q^91 - 69 * q^92 + 8 * q^93 + 4 * q^94 - 47 * q^95 + 62 * q^96 - 14 * q^97 - 71 * q^98 - 23 * q^99

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