LMFDB - Embedded newform 4017.2.a.j.1.18

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			1.18
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.59660 q^{2} -1.00000 q^{3} +0.549133 q^{4} -3.22334 q^{5} -1.59660 q^{6} +2.57812 q^{7} -2.31645 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.59660 q^{2} -1.00000 q^{3} +0.549133 q^{4} -3.22334 q^{5} -1.59660 q^{6} +2.57812 q^{7} -2.31645 q^{8} +1.00000 q^{9} -5.14639 q^{10} -3.57802 q^{11} -0.549133 q^{12} +1.00000 q^{13} +4.11623 q^{14} +3.22334 q^{15} -4.79672 q^{16} +6.66029 q^{17} +1.59660 q^{18} -5.80781 q^{19} -1.77005 q^{20} -2.57812 q^{21} -5.71266 q^{22} -1.56970 q^{23} +2.31645 q^{24} +5.38994 q^{25} +1.59660 q^{26} -1.00000 q^{27} +1.41573 q^{28} -3.85916 q^{29} +5.14639 q^{30} -2.09496 q^{31} -3.02554 q^{32} +3.57802 q^{33} +10.6338 q^{34} -8.31016 q^{35} +0.549133 q^{36} -3.49607 q^{37} -9.27276 q^{38} -1.00000 q^{39} +7.46673 q^{40} +8.46980 q^{41} -4.11623 q^{42} -4.32621 q^{43} -1.96481 q^{44} -3.22334 q^{45} -2.50619 q^{46} +8.30395 q^{47} +4.79672 q^{48} -0.353301 q^{49} +8.60558 q^{50} -6.66029 q^{51} +0.549133 q^{52} +5.20081 q^{53} -1.59660 q^{54} +11.5332 q^{55} -5.97210 q^{56} +5.80781 q^{57} -6.16153 q^{58} +7.94515 q^{59} +1.77005 q^{60} -0.135083 q^{61} -3.34481 q^{62} +2.57812 q^{63} +4.76287 q^{64} -3.22334 q^{65} +5.71266 q^{66} +6.03238 q^{67} +3.65739 q^{68} +1.56970 q^{69} -13.2680 q^{70} +6.61908 q^{71} -2.31645 q^{72} -6.56636 q^{73} -5.58183 q^{74} -5.38994 q^{75} -3.18926 q^{76} -9.22455 q^{77} -1.59660 q^{78} +10.9360 q^{79} +15.4615 q^{80} +1.00000 q^{81} +13.5229 q^{82} +3.61033 q^{83} -1.41573 q^{84} -21.4684 q^{85} -6.90723 q^{86} +3.85916 q^{87} +8.28831 q^{88} +1.01165 q^{89} -5.14639 q^{90} +2.57812 q^{91} -0.861976 q^{92} +2.09496 q^{93} +13.2581 q^{94} +18.7206 q^{95} +3.02554 q^{96} +7.20505 q^{97} -0.564081 q^{98} -3.57802 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.59660	1.12897	0.564484	−	0.825444i	$-0.309075\pi$
$2$	1.59660	1.12897	0.564484	+	0.825444i	$0.309075\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.549133	0.274567
$5$	−3.22334	−1.44152	−0.720761	−	0.693183i	$-0.756208\pi$
$5$	−3.22334	−1.44152	−0.720761	+	0.693183i	$0.756208\pi$
$6$	−1.59660	−0.651809
$7$	2.57812	0.974437	0.487219	−	0.873280i	$-0.338011\pi$
$7$	2.57812	0.974437	0.487219	+	0.873280i	$0.338011\pi$
$8$	−2.31645	−0.818990
$9$	1.00000	0.333333
$10$	−5.14639	−1.62743
$11$	−3.57802	−1.07881	−0.539406	−	0.842046i	$-0.681351\pi$
$11$	−3.57802	−1.07881	−0.539406	+	0.842046i	$0.681351\pi$
$12$	−0.549133	−0.158521
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	4.11623	1.10011
$15$	3.22334	0.832264
$16$	−4.79672	−1.19918
$17$	6.66029	1.61536	0.807679	−	0.589623i	$-0.200724\pi$
$17$	6.66029	1.61536	0.807679	+	0.589623i	$0.200724\pi$
$18$	1.59660	0.376322
$19$	−5.80781	−1.33240	−0.666202	−	0.745772i	$-0.732081\pi$
$19$	−5.80781	−1.33240	−0.666202	+	0.745772i	$0.732081\pi$
$20$	−1.77005	−0.395794
$21$	−2.57812	−0.562592
$22$	−5.71266	−1.21794
$23$	−1.56970	−0.327305	−0.163653	−	0.986518i	$-0.552328\pi$
$23$	−1.56970	−0.327305	−0.163653	+	0.986518i	$0.552328\pi$
$24$	2.31645	0.472844
$25$	5.38994	1.07799
$26$	1.59660	0.313119
$27$	−1.00000	−0.192450
$28$	1.41573	0.267548
$29$	−3.85916	−0.716627	−0.358314	−	0.933601i	$-0.616648\pi$
$29$	−3.85916	−0.716627	−0.358314	+	0.933601i	$0.616648\pi$
$30$	5.14639	0.939598
$31$	−2.09496	−0.376266	−0.188133	−	0.982144i	$-0.560244\pi$
$31$	−2.09496	−0.376266	−0.188133	+	0.982144i	$0.560244\pi$
$32$	−3.02554	−0.534844
$33$	3.57802	0.622853
$34$	10.6338	1.82369
$35$	−8.31016	−1.40467
$36$	0.549133	0.0915222
$37$	−3.49607	−0.574751	−0.287375	−	0.957818i	$-0.592783\pi$
$37$	−3.49607	−0.574751	−0.287375	+	0.957818i	$0.592783\pi$
$38$	−9.27276	−1.50424
$39$	−1.00000	−0.160128
$40$	7.46673	1.18059
$41$	8.46980	1.32276	0.661380	−	0.750051i	$-0.269971\pi$
$41$	8.46980	1.32276	0.661380	+	0.750051i	$0.269971\pi$
$42$	−4.11623	−0.635148
$43$	−4.32621	−0.659741	−0.329871	−	0.944026i	$-0.607005\pi$
$43$	−4.32621	−0.659741	−0.329871	+	0.944026i	$0.607005\pi$
$44$	−1.96481	−0.296206
$45$	−3.22334	−0.480508
$46$	−2.50619	−0.369517
$47$	8.30395	1.21126	0.605628	−	0.795748i	$-0.292922\pi$
$47$	8.30395	1.21126	0.605628	+	0.795748i	$0.292922\pi$
$48$	4.79672	0.692347
$49$	−0.353301	−0.0504716
$50$	8.60558	1.21701
$51$	−6.66029	−0.932627
$52$	0.549133	0.0761511
$53$	5.20081	0.714387	0.357193	−	0.934030i	$-0.383734\pi$
$53$	5.20081	0.714387	0.357193	+	0.934030i	$0.383734\pi$
$54$	−1.59660	−0.217270
$55$	11.5332	1.55513
$56$	−5.97210	−0.798055
$57$	5.80781	0.769264
$58$	−6.16153	−0.809048
$59$	7.94515	1.03437	0.517185	−	0.855874i	$-0.326980\pi$
$59$	7.94515	1.03437	0.517185	+	0.855874i	$0.326980\pi$
$60$	1.77005	0.228512
$61$	−0.135083	−0.0172957	−0.00864783	−	0.999963i	$-0.502753\pi$
$61$	−0.135083	−0.0172957	−0.00864783	+	0.999963i	$0.502753\pi$
$62$	−3.34481	−0.424792
$63$	2.57812	0.324812
$64$	4.76287	0.595358
$65$	−3.22334	−0.399806
$66$	5.71266	0.703180
$67$	6.03238	0.736972	0.368486	−	0.929633i	$-0.379876\pi$
$67$	6.03238	0.736972	0.368486	+	0.929633i	$0.379876\pi$
$68$	3.65739	0.443523
$69$	1.56970	0.188970
$70$	−13.2680	−1.58583
$71$	6.61908	0.785540	0.392770	−	0.919637i	$-0.371517\pi$
$71$	6.61908	0.785540	0.392770	+	0.919637i	$0.371517\pi$
$72$	−2.31645	−0.272997
$73$	−6.56636	−0.768534	−0.384267	−	0.923222i	$-0.625546\pi$
$73$	−6.56636	−0.768534	−0.384267	+	0.923222i	$0.625546\pi$
$74$	−5.58183	−0.648875
$75$	−5.38994	−0.622377
$76$	−3.18926	−0.365834
$77$	−9.22455	−1.05124
$78$	−1.59660	−0.180779
$79$	10.9360	1.23040	0.615198	−	0.788372i	$-0.289076\pi$
$79$	10.9360	1.23040	0.615198	+	0.788372i	$0.289076\pi$
$80$	15.4615	1.72865
$81$	1.00000	0.111111
$82$	13.5229	1.49335
$83$	3.61033	0.396285	0.198142	−	0.980173i	$-0.436509\pi$
$83$	3.61033	0.396285	0.198142	+	0.980173i	$0.436509\pi$
$84$	−1.41573	−0.154469
$85$	−21.4684	−2.32857
$86$	−6.90723	−0.744826
$87$	3.85916	0.413745
$88$	8.28831	0.883537
$89$	1.01165	0.107234	0.0536171	−	0.998562i	$-0.482925\pi$
$89$	1.01165	0.107234	0.0536171	+	0.998562i	$0.482925\pi$
$90$	−5.14639	−0.542477
$91$	2.57812	0.270260
$92$	−0.861976	−0.0898672
$93$	2.09496	0.217237
$94$	13.2581	1.36747
$95$	18.7206	1.92069
$96$	3.02554	0.308792
$97$	7.20505	0.731562	0.365781	−	0.930701i	$-0.380802\pi$
$97$	7.20505	0.731562	0.365781	+	0.930701i	$0.380802\pi$
$98$	−0.564081	−0.0569807
$99$	−3.57802	−0.359604
$100$	2.95980	0.295980
$101$	−1.41011	−0.140311	−0.0701557	−	0.997536i	$-0.522350\pi$
$101$	−1.41011	−0.140311	−0.0701557	+	0.997536i	$0.522350\pi$
$102$	−10.6338	−1.05291
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−2.31645	−0.227147
$105$	8.31016	0.810989
$106$	8.30362	0.806519
$107$	9.96774	0.963618	0.481809	−	0.876276i	$-0.339980\pi$
$107$	9.96774	0.963618	0.481809	+	0.876276i	$0.339980\pi$
$108$	−0.549133	−0.0528404
$109$	−2.14955	−0.205889	−0.102945	−	0.994687i	$-0.532826\pi$
$109$	−2.14955	−0.205889	−0.102945	+	0.994687i	$0.532826\pi$
$110$	18.4139	1.75569
$111$	3.49607	0.331833
$112$	−12.3665	−1.16853
$113$	6.79670	0.639380	0.319690	−	0.947522i	$-0.396421\pi$
$113$	6.79670	0.639380	0.319690	+	0.947522i	$0.396421\pi$
$114$	9.27276	0.868473
$115$	5.05969	0.471818
$116$	−2.11919	−0.196762
$117$	1.00000	0.0924500
$118$	12.6852	1.16777
$119$	17.1710	1.57407
$120$	−7.46673	−0.681616
$121$	1.80219	0.163836
$122$	−0.215674	−0.0195262
$123$	−8.46980	−0.763696
$124$	−1.15041	−0.103310
$125$	−1.25691	−0.112422
$126$	4.11623	0.366703
$127$	9.75142	0.865299	0.432649	−	0.901562i	$-0.357579\pi$
$127$	9.75142	0.865299	0.432649	+	0.901562i	$0.357579\pi$
$128$	13.6555	1.20698
$129$	4.32621	0.380902
$130$	−5.14639	−0.451368
$131$	16.1198	1.40839	0.704196	−	0.710005i	$-0.251308\pi$
$131$	16.1198	1.40839	0.704196	+	0.710005i	$0.251308\pi$
$132$	1.96481	0.171015
$133$	−14.9732	−1.29834
$134$	9.63130	0.832017
$135$	3.22334	0.277421
$136$	−15.4283	−1.32296
$137$	−13.4521	−1.14929	−0.574645	−	0.818403i	$-0.694860\pi$
$137$	−13.4521	−1.14929	−0.574645	+	0.818403i	$0.694860\pi$
$138$	2.50619	0.213341
$139$	−3.42243	−0.290287	−0.145143	−	0.989411i	$-0.546364\pi$
$139$	−3.42243	−0.290287	−0.145143	+	0.989411i	$0.546364\pi$
$140$	−4.56339	−0.385677
$141$	−8.30395	−0.699319
$142$	10.5680	0.886849
$143$	−3.57802	−0.299209
$144$	−4.79672	−0.399727
$145$	12.4394	1.03303
$146$	−10.4838	−0.867649
$147$	0.353301	0.0291398
$148$	−1.91981	−0.157807
$149$	10.8433	0.888317	0.444159	−	0.895948i	$-0.353503\pi$
$149$	10.8433	0.888317	0.444159	+	0.895948i	$0.353503\pi$
$150$	−8.60558	−0.702643
$151$	8.34496	0.679103	0.339552	−	0.940587i	$-0.389725\pi$
$151$	8.34496	0.679103	0.339552	+	0.940587i	$0.389725\pi$
$152$	13.4535	1.09123
$153$	6.66029	0.538453
$154$	−14.7279	−1.18681
$155$	6.75277	0.542396
$156$	−0.549133	−0.0439659
$157$	−16.8485	−1.34466	−0.672330	−	0.740252i	$-0.734706\pi$
$157$	−16.8485	−1.34466	−0.672330	+	0.740252i	$0.734706\pi$
$158$	17.4604	1.38908
$159$	−5.20081	−0.412451
$160$	9.75234	0.770990
$161$	−4.04688	−0.318939
$162$	1.59660	0.125441
$163$	−4.67365	−0.366068	−0.183034	−	0.983107i	$-0.558592\pi$
$163$	−4.67365	−0.366068	−0.183034	+	0.983107i	$0.558592\pi$
$164$	4.65105	0.363186
$165$	−11.5332	−0.897856
$166$	5.76425	0.447393
$167$	22.9189	1.77352	0.886760	−	0.462231i	$-0.152951\pi$
$167$	22.9189	1.77352	0.886760	+	0.462231i	$0.152951\pi$
$168$	5.97210	0.460757
$169$	1.00000	0.0769231
$170$	−34.2765	−2.62888
$171$	−5.80781	−0.444134
$172$	−2.37567	−0.181143
$173$	14.7285	1.11979	0.559893	−	0.828565i	$-0.310842\pi$
$173$	14.7285	1.11979	0.559893	+	0.828565i	$0.310842\pi$
$174$	6.16153	0.467104
$175$	13.8959	1.05043
$176$	17.1627	1.29369
$177$	−7.94515	−0.597194
$178$	1.61519	0.121064
$179$	17.5602	1.31251	0.656256	−	0.754538i	$-0.272139\pi$
$179$	17.5602	1.31251	0.656256	+	0.754538i	$0.272139\pi$
$180$	−1.77005	−0.131931
$181$	−15.4511	−1.14847	−0.574236	−	0.818690i	$-0.694701\pi$
$181$	−15.4511	−1.14847	−0.574236	+	0.818690i	$0.694701\pi$
$182$	4.11623	0.305115
$183$	0.135083	0.00998565
$184$	3.63614	0.268060
$185$	11.2690	0.828516
$186$	3.34481	0.245254
$187$	−23.8306	−1.74267
$188$	4.55998	0.332571
$189$	−2.57812	−0.187531
$190$	29.8893	2.16840
$191$	0.231028	0.0167166	0.00835828	−	0.999965i	$-0.497339\pi$
$191$	0.231028	0.0167166	0.00835828	+	0.999965i	$0.497339\pi$
$192$	−4.76287	−0.343730
$193$	21.8826	1.57514	0.787571	−	0.616224i	$-0.211338\pi$
$193$	21.8826	1.57514	0.787571	+	0.616224i	$0.211338\pi$
$194$	11.5036	0.825909
$195$	3.22334	0.230828
$196$	−0.194009	−0.0138578
$197$	13.7099	0.976788	0.488394	−	0.872623i	$-0.337583\pi$
$197$	13.7099	0.976788	0.488394	+	0.872623i	$0.337583\pi$
$198$	−5.71266	−0.405981
$199$	−8.14665	−0.577501	−0.288750	−	0.957404i	$-0.593240\pi$
$199$	−8.14665	−0.577501	−0.288750	+	0.957404i	$0.593240\pi$
$200$	−12.4856	−0.882862
$201$	−6.03238	−0.425491
$202$	−2.25139	−0.158407
$203$	−9.94936	−0.698308
$204$	−3.65739	−0.256068
$205$	−27.3011	−1.90679
$206$	−1.59660	−0.111240
$207$	−1.56970	−0.109102
$208$	−4.79672	−0.332593
$209$	20.7804	1.43741
$210$	13.2680	0.915580
$211$	−24.5469	−1.68988	−0.844940	−	0.534860i	$-0.820364\pi$
$211$	−24.5469	−1.68988	−0.844940	+	0.534860i	$0.820364\pi$
$212$	2.85594	0.196147
$213$	−6.61908	−0.453532
$214$	15.9145	1.08789
$215$	13.9449	0.951032
$216$	2.31645	0.157615
$217$	−5.40106	−0.366648
$218$	−3.43197	−0.232442
$219$	6.56636	0.443713
$220$	6.33325	0.426988
$221$	6.66029	0.448020
$222$	5.58183	0.374628
$223$	−5.62517	−0.376689	−0.188345	−	0.982103i	$-0.560312\pi$
$223$	−5.62517	−0.376689	−0.188345	+	0.982103i	$0.560312\pi$
$224$	−7.80019	−0.521172
$225$	5.38994	0.359329
$226$	10.8516	0.721839
$227$	6.41165	0.425556	0.212778	−	0.977101i	$-0.431749\pi$
$227$	6.41165	0.425556	0.212778	+	0.977101i	$0.431749\pi$
$228$	3.18926	0.211214
$229$	−3.01587	−0.199295	−0.0996473	−	0.995023i	$-0.531771\pi$
$229$	−3.01587	−0.199295	−0.0996473	+	0.995023i	$0.531771\pi$
$230$	8.07830	0.532667
$231$	9.22455	0.606931
$232$	8.93956	0.586911
$233$	−14.0535	−0.920679	−0.460339	−	0.887743i	$-0.652272\pi$
$233$	−14.0535	−0.920679	−0.460339	+	0.887743i	$0.652272\pi$
$234$	1.59660	0.104373
$235$	−26.7665	−1.74605
$236$	4.36295	0.284004
$237$	−10.9360	−0.710370
$238$	27.4153	1.77707
$239$	0.749192	0.0484612	0.0242306	−	0.999706i	$-0.492286\pi$
$239$	0.749192	0.0484612	0.0242306	+	0.999706i	$0.492286\pi$
$240$	−15.4615	−0.998034
$241$	−7.65457	−0.493074	−0.246537	−	0.969133i	$-0.579293\pi$
$241$	−7.65457	−0.493074	−0.246537	+	0.969133i	$0.579293\pi$
$242$	2.87738	0.184965
$243$	−1.00000	−0.0641500
$244$	−0.0741788	−0.00474881
$245$	1.13881	0.0727559
$246$	−13.5229	−0.862188
$247$	−5.80781	−0.369542
$248$	4.85288	0.308158
$249$	−3.61033	−0.228795
$250$	−2.00678	−0.126920
$251$	14.2662	0.900475	0.450237	−	0.892909i	$-0.351339\pi$
$251$	14.2662	0.900475	0.450237	+	0.892909i	$0.351339\pi$
$252$	1.41573	0.0891827
$253$	5.61642	0.353101
$254$	15.5691	0.976894
$255$	21.4684	1.34440
$256$	12.2766	0.767287
$257$	−30.8369	−1.92356	−0.961778	−	0.273831i	$-0.911709\pi$
$257$	−30.8369	−1.92356	−0.961778	+	0.273831i	$0.911709\pi$
$258$	6.90723	0.430026
$259$	−9.01329	−0.560059
$260$	−1.77005	−0.109774
$261$	−3.85916	−0.238876
$262$	25.7369	1.59003
$263$	−23.5911	−1.45469	−0.727345	−	0.686272i	$-0.759246\pi$
$263$	−23.5911	−1.45469	−0.727345	+	0.686272i	$0.759246\pi$
$264$	−8.28831	−0.510110
$265$	−16.7640	−1.02980
$266$	−23.9063	−1.46579
$267$	−1.01165	−0.0619117
$268$	3.31258	0.202348
$269$	−1.96246	−0.119654	−0.0598268	−	0.998209i	$-0.519055\pi$
$269$	−1.96246	−0.119654	−0.0598268	+	0.998209i	$0.519055\pi$
$270$	5.14639	0.313199
$271$	23.6062	1.43398	0.716989	−	0.697085i	$-0.245520\pi$
$271$	23.6062	1.43398	0.716989	+	0.697085i	$0.245520\pi$
$272$	−31.9475	−1.93710
$273$	−2.57812	−0.156035
$274$	−21.4776	−1.29751
$275$	−19.2853	−1.16295
$276$	0.861976	0.0518848
$277$	−10.4327	−0.626839	−0.313420	−	0.949615i	$-0.601475\pi$
$277$	−10.4327	−0.626839	−0.313420	+	0.949615i	$0.601475\pi$
$278$	−5.46426	−0.327724
$279$	−2.09496	−0.125422
$280$	19.2501	1.15041
$281$	−12.7137	−0.758434	−0.379217	−	0.925308i	$-0.623807\pi$
$281$	−12.7137	−0.758434	−0.379217	+	0.925308i	$0.623807\pi$
$282$	−13.2581	−0.789508
$283$	−26.7437	−1.58975	−0.794875	−	0.606773i	$-0.792464\pi$
$283$	−26.7437	−1.58975	−0.794875	+	0.606773i	$0.792464\pi$
$284$	3.63476	0.215683
$285$	−18.7206	−1.10891
$286$	−5.71266	−0.337797
$287$	21.8362	1.28895
$288$	−3.02554	−0.178281
$289$	27.3595	1.60938
$290$	19.8607	1.16626
$291$	−7.20505	−0.422367
$292$	−3.60581	−0.211014
$293$	−17.6685	−1.03221	−0.516104	−	0.856526i	$-0.672618\pi$
$293$	−17.6685	−1.03221	−0.516104	+	0.856526i	$0.672618\pi$
$294$	0.564081	0.0328978
$295$	−25.6099	−1.49107
$296$	8.09849	0.470715
$297$	3.57802	0.207618
$298$	17.3124	1.00288
$299$	−1.56970	−0.0907782
$300$	−2.95980	−0.170884
$301$	−11.1535	−0.642877
$302$	13.3236	0.766685
$303$	1.41011	0.0810088
$304$	27.8584	1.59779
$305$	0.435420	0.0249321
$306$	10.6338	0.607895
$307$	31.5625	1.80137	0.900683	−	0.434476i	$-0.143066\pi$
$307$	31.5625	1.80137	0.900683	+	0.434476i	$0.143066\pi$
$308$	−5.06551	−0.288634
$309$	1.00000	0.0568880
$310$	10.7815	0.612347
$311$	−28.3939	−1.61007	−0.805035	−	0.593227i	$-0.797854\pi$
$311$	−28.3939	−1.61007	−0.805035	+	0.593227i	$0.797854\pi$
$312$	2.31645	0.131143
$313$	16.8316	0.951376	0.475688	−	0.879614i	$-0.342199\pi$
$313$	16.8316	0.951376	0.475688	+	0.879614i	$0.342199\pi$
$314$	−26.9004	−1.51808
$315$	−8.31016	−0.468225
$316$	6.00532	0.337826
$317$	5.44697	0.305932	0.152966	−	0.988231i	$-0.451117\pi$
$317$	5.44697	0.305932	0.152966	+	0.988231i	$0.451117\pi$
$318$	−8.30362	−0.465644
$319$	13.8081	0.773106
$320$	−15.3524	−0.858223
$321$	−9.96774	−0.556345
$322$	−6.46125	−0.360071
$323$	−38.6817	−2.15231
$324$	0.549133	0.0305074
$325$	5.38994	0.298980
$326$	−7.46194	−0.413279
$327$	2.14955	0.118870
$328$	−19.6199	−1.08333
$329$	21.4086	1.18029
$330$	−18.4139	−1.01365
$331$	7.06715	0.388445	0.194223	−	0.980957i	$-0.437782\pi$
$331$	7.06715	0.388445	0.194223	+	0.980957i	$0.437782\pi$
$332$	1.98255	0.108807
$333$	−3.49607	−0.191584
$334$	36.5924	2.00224
$335$	−19.4444	−1.06236
$336$	12.3665	0.674649
$337$	1.23801	0.0674389	0.0337195	−	0.999431i	$-0.489265\pi$
$337$	1.23801	0.0674389	0.0337195	+	0.999431i	$0.489265\pi$
$338$	1.59660	0.0868436
$339$	−6.79670	−0.369146
$340$	−11.7890	−0.639349
$341$	7.49580	0.405920
$342$	−9.27276	−0.501413
$343$	−18.9577	−1.02362
$344$	10.0215	0.540322
$345$	−5.05969	−0.272404
$346$	23.5155	1.26420
$347$	6.32481	0.339533	0.169767	−	0.985484i	$-0.445699\pi$
$347$	6.32481	0.339533	0.169767	+	0.985484i	$0.445699\pi$
$348$	2.11919	0.113601
$349$	33.6754	1.80260	0.901301	−	0.433194i	$-0.142614\pi$
$349$	33.6754	1.80260	0.901301	+	0.433194i	$0.142614\pi$
$350$	22.1862	1.18590
$351$	−1.00000	−0.0533761
$352$	10.8254	0.576996
$353$	11.7523	0.625510	0.312755	−	0.949834i	$-0.398748\pi$
$353$	11.7523	0.625510	0.312755	+	0.949834i	$0.398748\pi$
$354$	−12.6852	−0.674212
$355$	−21.3356	−1.13237
$356$	0.555528	0.0294429
$357$	−17.1710	−0.908787
$358$	28.0367	1.48178
$359$	−18.6150	−0.982461	−0.491230	−	0.871030i	$-0.663453\pi$
$359$	−18.6150	−0.982461	−0.491230	+	0.871030i	$0.663453\pi$
$360$	7.46673	0.393531
$361$	14.7307	0.775299
$362$	−24.6692	−1.29659
$363$	−1.80219	−0.0945906
$364$	1.41573	0.0742045
$365$	21.1656	1.10786
$366$	0.215674	0.0112735
$367$	−11.1980	−0.584531	−0.292265	−	0.956337i	$-0.594409\pi$
$367$	−11.1980	−0.584531	−0.292265	+	0.956337i	$0.594409\pi$
$368$	7.52942	0.392498
$369$	8.46980	0.440920
$370$	17.9922	0.935368
$371$	13.4083	0.696125
$372$	1.15041	0.0596461
$373$	29.1863	1.51121	0.755605	−	0.655027i	$-0.227343\pi$
$373$	29.1863	1.51121	0.755605	+	0.655027i	$0.227343\pi$
$374$	−38.0480	−1.96741
$375$	1.25691	0.0649066
$376$	−19.2357	−0.992007
$377$	−3.85916	−0.198757
$378$	−4.11623	−0.211716
$379$	24.9563	1.28192	0.640960	−	0.767574i	$-0.278537\pi$
$379$	24.9563	1.28192	0.640960	+	0.767574i	$0.278537\pi$
$380$	10.2801	0.527357
$381$	−9.75142	−0.499580
$382$	0.368859	0.0188725
$383$	7.05811	0.360653	0.180326	−	0.983607i	$-0.442285\pi$
$383$	7.05811	0.360653	0.180326	+	0.983607i	$0.442285\pi$
$384$	−13.6555	−0.696853
$385$	29.7339	1.51538
$386$	34.9377	1.77828
$387$	−4.32621	−0.219914
$388$	3.95653	0.200863
$389$	−20.7027	−1.04967	−0.524833	−	0.851205i	$-0.675872\pi$
$389$	−20.7027	−1.04967	−0.524833	+	0.851205i	$0.675872\pi$
$390$	5.14639	0.260598
$391$	−10.4547	−0.528715
$392$	0.818406	0.0413357
$393$	−16.1198	−0.813136
$394$	21.8892	1.10276
$395$	−35.2505	−1.77364
$396$	−1.96481	−0.0987353
$397$	0.775127	0.0389025	0.0194513	−	0.999811i	$-0.493808\pi$
$397$	0.775127	0.0389025	0.0194513	+	0.999811i	$0.493808\pi$
$398$	−13.0069	−0.651979
$399$	14.9732	0.749599
$400$	−25.8540	−1.29270
$401$	7.14144	0.356627	0.178313	−	0.983974i	$-0.442936\pi$
$401$	7.14144	0.356627	0.178313	+	0.983974i	$0.442936\pi$
$402$	−9.63130	−0.480365
$403$	−2.09496	−0.104357
$404$	−0.774340	−0.0385248
$405$	−3.22334	−0.160169
$406$	−15.8852	−0.788367
$407$	12.5090	0.620048
$408$	15.4283	0.763813
$409$	3.01082	0.148875	0.0744377	−	0.997226i	$-0.476284\pi$
$409$	3.01082	0.148875	0.0744377	+	0.997226i	$0.476284\pi$
$410$	−43.5889	−2.15270
$411$	13.4521	0.663542
$412$	−0.549133	−0.0270539
$413$	20.4835	1.00793
$414$	−2.50619	−0.123172
$415$	−11.6373	−0.571254
$416$	−3.02554	−0.148339
$417$	3.42243	0.167597
$418$	33.1781	1.62279
$419$	−3.59360	−0.175559	−0.0877794	−	0.996140i	$-0.527977\pi$
$419$	−3.59360	−0.175559	−0.0877794	+	0.996140i	$0.527977\pi$
$420$	4.56339	0.222671
$421$	4.05623	0.197688	0.0988442	−	0.995103i	$-0.468485\pi$
$421$	4.05623	0.197688	0.0988442	+	0.995103i	$0.468485\pi$
$422$	−39.1917	−1.90782
$423$	8.30395	0.403752
$424$	−12.0474	−0.585076
$425$	35.8986	1.74134
$426$	−10.5680	−0.512023
$427$	−0.348261	−0.0168535
$428$	5.47362	0.264577
$429$	3.57802	0.172748
$430$	22.2644	1.07368
$431$	7.57357	0.364806	0.182403	−	0.983224i	$-0.441612\pi$
$431$	7.57357	0.364806	0.182403	+	0.983224i	$0.441612\pi$
$432$	4.79672	0.230782
$433$	−8.51732	−0.409316	−0.204658	−	0.978834i	$-0.565608\pi$
$433$	−8.51732	−0.409316	−0.204658	+	0.978834i	$0.565608\pi$
$434$	−8.62333	−0.413933
$435$	−12.4394	−0.596423
$436$	−1.18039	−0.0565303
$437$	9.11653	0.436103
$438$	10.4838	0.500938
$439$	39.2208	1.87191	0.935954	−	0.352122i	$-0.114540\pi$
$439$	39.2208	1.87191	0.935954	+	0.352122i	$0.114540\pi$
$440$	−26.7161	−1.27364
$441$	−0.353301	−0.0168239
$442$	10.6338	0.505799
$443$	−16.7432	−0.795491	−0.397746	−	0.917496i	$-0.630207\pi$
$443$	−16.7432	−0.795491	−0.397746	+	0.917496i	$0.630207\pi$
$444$	1.91981	0.0911102
$445$	−3.26088	−0.154581
$446$	−8.98115	−0.425270
$447$	−10.8433	−0.512870
$448$	12.2792	0.580139
$449$	35.5172	1.67616	0.838080	−	0.545548i	$-0.183678\pi$
$449$	35.5172	1.67616	0.838080	+	0.545548i	$0.183678\pi$
$450$	8.60558	0.405671
$451$	−30.3051	−1.42701
$452$	3.73230	0.175552
$453$	−8.34496	−0.392080
$454$	10.2368	0.480439
$455$	−8.31016	−0.389586
$456$	−13.4535	−0.630019
$457$	−13.7067	−0.641174	−0.320587	−	0.947219i	$-0.603880\pi$
$457$	−13.7067	−0.641174	−0.320587	+	0.947219i	$0.603880\pi$
$458$	−4.81515	−0.224997
$459$	−6.66029	−0.310876
$460$	2.77844	0.129546
$461$	3.90957	0.182087	0.0910435	−	0.995847i	$-0.470980\pi$
$461$	3.90957	0.182087	0.0910435	+	0.995847i	$0.470980\pi$
$462$	14.7279	0.685205
$463$	−9.73352	−0.452355	−0.226178	−	0.974086i	$-0.572623\pi$
$463$	−9.73352	−0.452355	−0.226178	+	0.974086i	$0.572623\pi$
$464$	18.5113	0.859365
$465$	−6.75277	−0.313152
$466$	−22.4379	−1.03942
$467$	9.33894	0.432155	0.216077	−	0.976376i	$-0.430674\pi$
$467$	9.33894	0.432155	0.216077	+	0.976376i	$0.430674\pi$
$468$	0.549133	0.0253837
$469$	15.5522	0.718133
$470$	−42.7354	−1.97124
$471$	16.8485	0.776340
$472$	−18.4046	−0.847139
$473$	15.4793	0.711737
$474$	−17.4604	−0.801984
$475$	−31.3038	−1.43632
$476$	9.42918	0.432186
$477$	5.20081	0.238129
$478$	1.19616	0.0547111
$479$	−0.416598	−0.0190349	−0.00951743	−	0.999955i	$-0.503030\pi$
$479$	−0.416598	−0.0190349	−0.00951743	+	0.999955i	$0.503030\pi$
$480$	−9.75234	−0.445131
$481$	−3.49607	−0.159407
$482$	−12.2213	−0.556665
$483$	4.04688	0.184139
$484$	0.989645	0.0449838
$485$	−23.2243	−1.05456
$486$	−1.59660	−0.0724233
$487$	24.9793	1.13192	0.565960	−	0.824433i	$-0.308506\pi$
$487$	24.9793	1.13192	0.565960	+	0.824433i	$0.308506\pi$
$488$	0.312914	0.0141650
$489$	4.67365	0.211350
$490$	1.81823	0.0821390
$491$	3.95448	0.178463	0.0892315	−	0.996011i	$-0.471559\pi$
$491$	3.95448	0.178463	0.0892315	+	0.996011i	$0.471559\pi$
$492$	−4.65105	−0.209686
$493$	−25.7031	−1.15761
$494$	−9.27276	−0.417201
$495$	11.5332	0.518377
$496$	10.0489	0.451210
$497$	17.0648	0.765460
$498$	−5.76425	−0.258302
$499$	23.5092	1.05241	0.526207	−	0.850356i	$-0.323614\pi$
$499$	23.5092	1.05241	0.526207	+	0.850356i	$0.323614\pi$
$500$	−0.690212	−0.0308672
$501$	−22.9189	−1.02394
$502$	22.7774	1.01661
$503$	−3.54033	−0.157856	−0.0789278	−	0.996880i	$-0.525150\pi$
$503$	−3.54033	−0.157856	−0.0789278	+	0.996880i	$0.525150\pi$
$504$	−5.97210	−0.266018
$505$	4.54527	0.202262
$506$	8.96717	0.398640
$507$	−1.00000	−0.0444116
$508$	5.35483	0.237582
$509$	−9.55862	−0.423679	−0.211839	−	0.977305i	$-0.567945\pi$
$509$	−9.55862	−0.423679	−0.211839	+	0.977305i	$0.567945\pi$
$510$	34.2765	1.51779
$511$	−16.9288	−0.748888
$512$	−7.71012	−0.340742
$513$	5.80781	0.256421
$514$	−49.2343	−2.17163
$515$	3.22334	0.142037
$516$	2.37567	0.104583
$517$	−29.7117	−1.30672
$518$	−14.3906	−0.632288
$519$	−14.7285	−0.646509
$520$	7.46673	0.327438
$521$	−22.9877	−1.00711	−0.503554	−	0.863964i	$-0.667975\pi$
$521$	−22.9877	−1.00711	−0.503554	+	0.863964i	$0.667975\pi$
$522$	−6.16153	−0.269683
$523$	−3.41642	−0.149390	−0.0746948	−	0.997206i	$-0.523798\pi$
$523$	−3.41642	−0.149390	−0.0746948	+	0.997206i	$0.523798\pi$
$524$	8.85191	0.386698
$525$	−13.8959	−0.606467
$526$	−37.6656	−1.64230
$527$	−13.9530	−0.607804
$528$	−17.1627	−0.746912
$529$	−20.5360	−0.892871
$530$	−26.7654	−1.16262
$531$	7.94515	0.344790
$532$	−8.22230	−0.356482
$533$	8.46980	0.366868
$534$	−1.61519	−0.0698963
$535$	−32.1295	−1.38908
$536$	−13.9737	−0.603573
$537$	−17.5602	−0.757780
$538$	−3.13327	−0.135085
$539$	1.26412	0.0544493
$540$	1.77005	0.0761706
$541$	−11.8510	−0.509514	−0.254757	−	0.967005i	$-0.581996\pi$
$541$	−11.8510	−0.509514	−0.254757	+	0.967005i	$0.581996\pi$
$542$	37.6897	1.61891
$543$	15.4511	0.663070
$544$	−20.1509	−0.863965
$545$	6.92872	0.296794
$546$	−4.11623	−0.176158
$547$	10.4548	0.447015	0.223507	−	0.974702i	$-0.428249\pi$
$547$	10.4548	0.447015	0.223507	+	0.974702i	$0.428249\pi$
$548$	−7.38699	−0.315557
$549$	−0.135083	−0.00576522
$550$	−30.7909	−1.31293
$551$	22.4132	0.954836
$552$	−3.63614	−0.154765
$553$	28.1943	1.19894
$554$	−16.6568	−0.707681
$555$	−11.2690	−0.478344
$556$	−1.87937	−0.0797031
$557$	−29.1013	−1.23306	−0.616530	−	0.787331i	$-0.711462\pi$
$557$	−29.1013	−1.23306	−0.616530	+	0.787331i	$0.711462\pi$
$558$	−3.34481	−0.141597
$559$	−4.32621	−0.182979
$560$	39.8615	1.68446
$561$	23.8306	1.00613
$562$	−20.2986	−0.856247
$563$	−29.4468	−1.24103	−0.620517	−	0.784193i	$-0.713077\pi$
$563$	−29.4468	−1.24103	−0.620517	+	0.784193i	$0.713077\pi$
$564$	−4.55998	−0.192010
$565$	−21.9081	−0.921681
$566$	−42.6991	−1.79478
$567$	2.57812	0.108271
$568$	−15.3328	−0.643350
$569$	1.01936	0.0427336	0.0213668	−	0.999772i	$-0.493198\pi$
$569$	1.01936	0.0427336	0.0213668	+	0.999772i	$0.493198\pi$
$570$	−29.8893	−1.25192
$571$	−2.07941	−0.0870206	−0.0435103	−	0.999053i	$-0.513854\pi$
$571$	−2.07941	−0.0870206	−0.0435103	+	0.999053i	$0.513854\pi$
$572$	−1.96481	−0.0821527
$573$	−0.231028	−0.00965131
$574$	34.8636	1.45518
$575$	−8.46060	−0.352831
$576$	4.76287	0.198453
$577$	−42.8261	−1.78287	−0.891437	−	0.453145i	$-0.850302\pi$
$577$	−42.8261	−1.78287	−0.891437	+	0.453145i	$0.850302\pi$
$578$	43.6821	1.81694
$579$	−21.8826	−0.909409
$580$	6.83088	0.283637
$581$	9.30786	0.386155
$582$	−11.5036	−0.476839
$583$	−18.6086	−0.770689
$584$	15.2107	0.629422
$585$	−3.22334	−0.133269
$586$	−28.2096	−1.16533
$587$	−9.35303	−0.386041	−0.193020	−	0.981195i	$-0.561828\pi$
$587$	−9.35303	−0.386041	−0.193020	+	0.981195i	$0.561828\pi$
$588$	0.194009	0.00800081
$589$	12.1671	0.501338
$590$	−40.8888	−1.68337
$591$	−13.7099	−0.563949
$592$	16.7697	0.689230
$593$	0.260122	0.0106819	0.00534096	−	0.999986i	$-0.498300\pi$
$593$	0.260122	0.0106819	0.00534096	+	0.999986i	$0.498300\pi$
$594$	5.71266	0.234393
$595$	−55.3481	−2.26905
$596$	5.95441	0.243902
$597$	8.14665	0.333420
$598$	−2.50619	−0.102486
$599$	10.6170	0.433798	0.216899	−	0.976194i	$-0.430406\pi$
$599$	10.6170	0.433798	0.216899	+	0.976194i	$0.430406\pi$
$600$	12.4856	0.509720
$601$	35.8306	1.46156	0.730780	−	0.682613i	$-0.239157\pi$
$601$	35.8306	1.46156	0.730780	+	0.682613i	$0.239157\pi$
$602$	−17.8077	−0.725787
$603$	6.03238	0.245657
$604$	4.58249	0.186459
$605$	−5.80909	−0.236173
$606$	2.25139	0.0914563
$607$	−27.2341	−1.10540	−0.552699	−	0.833381i	$-0.686402\pi$
$607$	−27.2341	−1.10540	−0.552699	+	0.833381i	$0.686402\pi$
$608$	17.5717	0.712628
$609$	9.94936	0.403169
$610$	0.695192	0.0281475
$611$	8.30395	0.335942
$612$	3.65739	0.147841
$613$	15.5878	0.629587	0.314793	−	0.949160i	$-0.398065\pi$
$613$	15.5878	0.629587	0.314793	+	0.949160i	$0.398065\pi$
$614$	50.3927	2.03368
$615$	27.3011	1.10089
$616$	21.3683	0.860951
$617$	−7.16142	−0.288308	−0.144154	−	0.989555i	$-0.546046\pi$
$617$	−7.16142	−0.288308	−0.144154	+	0.989555i	$0.546046\pi$
$618$	1.59660	0.0642247
$619$	41.2809	1.65922	0.829610	−	0.558343i	$-0.188563\pi$
$619$	41.2809	1.65922	0.829610	+	0.558343i	$0.188563\pi$
$620$	3.70817	0.148924
$621$	1.56970	0.0629900
$622$	−45.3337	−1.81772
$623$	2.60814	0.104493
$624$	4.79672	0.192022
$625$	−22.8982	−0.915930
$626$	26.8733	1.07407
$627$	−20.7804	−0.829891
$628$	−9.25210	−0.369199
$629$	−23.2849	−0.928428
$630$	−13.2680	−0.528610
$631$	7.14149	0.284298	0.142149	−	0.989845i	$-0.454599\pi$
$631$	7.14149	0.284298	0.142149	+	0.989845i	$0.454599\pi$
$632$	−25.3328	−1.00768
$633$	24.5469	0.975653
$634$	8.69663	0.345387
$635$	−31.4322	−1.24735
$636$	−2.85594	−0.113245
$637$	−0.353301	−0.0139983
$638$	22.0460	0.872811
$639$	6.61908	0.261847
$640$	−44.0163	−1.73990
$641$	−4.34844	−0.171753	−0.0858765	−	0.996306i	$-0.527369\pi$
$641$	−4.34844	−0.171753	−0.0858765	+	0.996306i	$0.527369\pi$
$642$	−15.9145	−0.628095
$643$	−29.0148	−1.14423	−0.572117	−	0.820172i	$-0.693878\pi$
$643$	−29.0148	−1.14423	−0.572117	+	0.820172i	$0.693878\pi$
$644$	−2.22228	−0.0875699
$645$	−13.9449	−0.549079
$646$	−61.7592	−2.42988
$647$	−11.5206	−0.452922	−0.226461	−	0.974020i	$-0.572716\pi$
$647$	−11.5206	−0.452922	−0.226461	+	0.974020i	$0.572716\pi$
$648$	−2.31645	−0.0909989
$649$	−28.4279	−1.11589
$650$	8.60558	0.337539
$651$	5.40106	0.211684
$652$	−2.56645	−0.100510
$653$	3.87607	0.151682	0.0758411	−	0.997120i	$-0.475836\pi$
$653$	3.87607	0.151682	0.0758411	+	0.997120i	$0.475836\pi$
$654$	3.43197	0.134200
$655$	−51.9596	−2.03023
$656$	−40.6273	−1.58623
$657$	−6.56636	−0.256178
$658$	34.1810	1.33251
$659$	29.7929	1.16057	0.580284	−	0.814414i	$-0.302942\pi$
$659$	29.7929	1.16057	0.580284	+	0.814414i	$0.302942\pi$
$660$	−6.33325	−0.246521
$661$	19.9665	0.776607	0.388303	−	0.921532i	$-0.373061\pi$
$661$	19.9665	0.776607	0.388303	+	0.921532i	$0.373061\pi$
$662$	11.2834	0.438542
$663$	−6.66029	−0.258664
$664$	−8.36316	−0.324554
$665$	48.2639	1.87159
$666$	−5.58183	−0.216292
$667$	6.05772	0.234556
$668$	12.5855	0.486949
$669$	5.62517	0.217482
$670$	−31.0450	−1.19937
$671$	0.483330	0.0186588
$672$	7.80019	0.300899
$673$	−39.5360	−1.52400	−0.762001	−	0.647576i	$-0.775783\pi$
$673$	−39.5360	−1.52400	−0.762001	+	0.647576i	$0.775783\pi$
$674$	1.97661	0.0761363
$675$	−5.38994	−0.207459
$676$	0.549133	0.0211205
$677$	−10.6400	−0.408928	−0.204464	−	0.978874i	$-0.565545\pi$
$677$	−10.6400	−0.408928	−0.204464	+	0.978874i	$0.565545\pi$
$678$	−10.8516	−0.416754
$679$	18.5755	0.712861
$680$	49.7306	1.90708
$681$	−6.41165	−0.245695
$682$	11.9678	0.458271
$683$	17.6970	0.677158	0.338579	−	0.940938i	$-0.390054\pi$
$683$	17.6970	0.677158	0.338579	+	0.940938i	$0.390054\pi$
$684$	−3.18926	−0.121945
$685$	43.3607	1.65673
$686$	−30.2679	−1.15563
$687$	3.01587	0.115063
$688$	20.7516	0.791149
$689$	5.20081	0.198135
$690$	−8.07830	−0.307536
$691$	−33.3799	−1.26983	−0.634916	−	0.772581i	$-0.718965\pi$
$691$	−33.3799	−1.26983	−0.634916	+	0.772581i	$0.718965\pi$
$692$	8.08791	0.307456
$693$	−9.22455	−0.350412
$694$	10.0982	0.383322
$695$	11.0317	0.418455
$696$	−8.93956	−0.338853
$697$	56.4113	2.13673
$698$	53.7661	2.03508
$699$	14.0535	0.531554
$700$	7.63071	0.288414
$701$	44.5997	1.68451	0.842254	−	0.539080i	$-0.181228\pi$
$701$	44.5997	1.68451	0.842254	+	0.539080i	$0.181228\pi$
$702$	−1.59660	−0.0602598
$703$	20.3045	0.765800
$704$	−17.0416	−0.642280
$705$	26.7665	1.00808
$706$	18.7637	0.706181
$707$	−3.63544	−0.136725
$708$	−4.36295	−0.163970
$709$	39.5936	1.48697	0.743485	−	0.668753i	$-0.233172\pi$
$709$	39.5936	1.48697	0.743485	+	0.668753i	$0.233172\pi$
$710$	−34.0644	−1.27841
$711$	10.9360	0.410132
$712$	−2.34343	−0.0878238
$713$	3.28846	0.123154
$714$	−27.4153	−1.02599
$715$	11.5332	0.431316
$716$	9.64291	0.360372
$717$	−0.749192	−0.0279791
$718$	−29.7207	−1.10917
$719$	−43.7690	−1.63231	−0.816155	−	0.577834i	$-0.803898\pi$
$719$	−43.7690	−1.63231	−0.816155	+	0.577834i	$0.803898\pi$
$720$	15.4615	0.576215
$721$	−2.57812	−0.0960142
$722$	23.5190	0.875287
$723$	7.65457	0.284677
$724$	−8.48472	−0.315332
$725$	−20.8006	−0.772515
$726$	−2.87738	−0.106790
$727$	19.3339	0.717054	0.358527	−	0.933519i	$-0.383279\pi$
$727$	19.3339	0.717054	0.358527	+	0.933519i	$0.383279\pi$
$728$	−5.97210	−0.221341
$729$	1.00000	0.0370370
$730$	33.7930	1.25074
$731$	−28.8138	−1.06572
$732$	0.0741788	0.00274173
$733$	−44.5155	−1.64422	−0.822109	−	0.569331i	$-0.807202\pi$
$733$	−44.5155	−1.64422	−0.822109	+	0.569331i	$0.807202\pi$
$734$	−17.8787	−0.659916
$735$	−1.13881	−0.0420056
$736$	4.74919	0.175057
$737$	−21.5839	−0.795055
$738$	13.5229	0.497785
$739$	36.4258	1.33995	0.669973	−	0.742386i	$-0.266306\pi$
$739$	36.4258	1.33995	0.669973	+	0.742386i	$0.266306\pi$
$740$	6.18821	0.227483
$741$	5.80781	0.213355
$742$	21.4077	0.785902
$743$	18.2327	0.668893	0.334446	−	0.942415i	$-0.391451\pi$
$743$	18.2327	0.668893	0.334446	+	0.942415i	$0.391451\pi$
$744$	−4.85288	−0.177915
$745$	−34.9517	−1.28053
$746$	46.5989	1.70611
$747$	3.61033	0.132095
$748$	−13.0862	−0.478478
$749$	25.6980	0.938986
$750$	2.00678	0.0732774
$751$	49.1586	1.79382	0.896911	−	0.442212i	$-0.145806\pi$
$751$	49.1586	1.79382	0.896911	+	0.442212i	$0.145806\pi$
$752$	−39.8317	−1.45251
$753$	−14.2662	−0.519889
$754$	−6.16153	−0.224390
$755$	−26.8987	−0.978943
$756$	−1.41573	−0.0514897
$757$	36.2067	1.31596	0.657978	−	0.753038i	$-0.271412\pi$
$757$	36.2067	1.31596	0.657978	+	0.753038i	$0.271412\pi$
$758$	39.8453	1.44725
$759$	−5.61642	−0.203863
$760$	−43.3653	−1.57303
$761$	−9.92457	−0.359766	−0.179883	−	0.983688i	$-0.557572\pi$
$761$	−9.92457	−0.359766	−0.179883	+	0.983688i	$0.557572\pi$
$762$	−15.5691	−0.564010
$763$	−5.54179	−0.200626
$764$	0.126865	0.00458981
$765$	−21.4684	−0.776192
$766$	11.2690	0.407165
$767$	7.94515	0.286883
$768$	−12.2766	−0.442993
$769$	17.7053	0.638469	0.319234	−	0.947676i	$-0.396574\pi$
$769$	17.7053	0.638469	0.319234	+	0.947676i	$0.396574\pi$
$770$	47.4731	1.71081
$771$	30.8369	1.11057
$772$	12.0165	0.432482
$773$	−10.7427	−0.386389	−0.193194	−	0.981160i	$-0.561885\pi$
$773$	−10.7427	−0.386389	−0.193194	+	0.981160i	$0.561885\pi$
$774$	−6.90723	−0.248275
$775$	−11.2917	−0.405610
$776$	−16.6902	−0.599142
$777$	9.01329	0.323350
$778$	−33.0539	−1.18504
$779$	−49.1910	−1.76245
$780$	1.77005	0.0633778
$781$	−23.6832	−0.847450
$782$	−16.6919	−0.596902
$783$	3.85916	0.137915
$784$	1.69469	0.0605245
$785$	54.3086	1.93836
$786$	−25.7369	−0.918004
$787$	50.1564	1.78788	0.893941	−	0.448184i	$-0.147929\pi$
$787$	50.1564	1.78788	0.893941	+	0.448184i	$0.147929\pi$
$788$	7.52855	0.268193
$789$	23.5911	0.839865
$790$	−56.2810	−2.00239
$791$	17.5227	0.623036
$792$	8.28831	0.294512
$793$	−0.135083	−0.00479695
$794$	1.23757	0.0439197
$795$	16.7640	0.594558
$796$	−4.47360	−0.158562
$797$	−17.6046	−0.623586	−0.311793	−	0.950150i	$-0.600930\pi$
$797$	−17.6046	−0.623586	−0.311793	+	0.950150i	$0.600930\pi$
$798$	23.9063	0.846273
$799$	55.3067	1.95661
$800$	−16.3075	−0.576556
$801$	1.01165	0.0357447
$802$	11.4020	0.402620
$803$	23.4945	0.829104
$804$	−3.31258	−0.116826
$805$	13.0445	0.459757
$806$	−3.34481	−0.117816
$807$	1.96246	0.0690820
$808$	3.26646	0.114914
$809$	32.4891	1.14225	0.571127	−	0.820862i	$-0.306506\pi$
$809$	32.4891	1.14225	0.571127	+	0.820862i	$0.306506\pi$
$810$	−5.14639	−0.180826
$811$	−12.1576	−0.426911	−0.213456	−	0.976953i	$-0.568472\pi$
$811$	−12.1576	−0.426911	−0.213456	+	0.976953i	$0.568472\pi$
$812$	−5.46353	−0.191732
$813$	−23.6062	−0.827907
$814$	19.9719	0.700014
$815$	15.0648	0.527696
$816$	31.9475	1.11839
$817$	25.1258	0.879042
$818$	4.80707	0.168075
$819$	2.57812	0.0900868
$820$	−14.9919	−0.523541
$821$	−8.88825	−0.310202	−0.155101	−	0.987899i	$-0.549570\pi$
$821$	−8.88825	−0.310202	−0.155101	+	0.987899i	$0.549570\pi$
$822$	21.4776	0.749118
$823$	27.7821	0.968424	0.484212	−	0.874951i	$-0.339106\pi$
$823$	27.7821	0.968424	0.484212	+	0.874951i	$0.339106\pi$
$824$	2.31645	0.0806975
$825$	19.2853	0.671428
$826$	32.7040	1.13792
$827$	−9.07084	−0.315424	−0.157712	−	0.987485i	$-0.550412\pi$
$827$	−9.07084	−0.315424	−0.157712	+	0.987485i	$0.550412\pi$
$828$	−0.861976	−0.0299557
$829$	11.9161	0.413864	0.206932	−	0.978355i	$-0.433652\pi$
$829$	11.9161	0.413864	0.206932	+	0.978355i	$0.433652\pi$
$830$	−18.5802	−0.644927
$831$	10.4327	0.361906
$832$	4.76287	0.165123
$833$	−2.35309	−0.0815296
$834$	5.46426	0.189212
$835$	−73.8755	−2.55657
$836$	11.4112	0.394666
$837$	2.09496	0.0724124
$838$	−5.73754	−0.198200
$839$	46.7223	1.61303	0.806516	−	0.591212i	$-0.201350\pi$
$839$	46.7223	1.61303	0.806516	+	0.591212i	$0.201350\pi$
$840$	−19.2501	−0.664192
$841$	−14.1069	−0.486446
$842$	6.47617	0.223184
$843$	12.7137	0.437882
$844$	−13.4795	−0.463985
$845$	−3.22334	−0.110886
$846$	13.2581	0.455823
$847$	4.64627	0.159648
$848$	−24.9468	−0.856678
$849$	26.7437	0.917843
$850$	57.3157	1.96591
$851$	5.48779	0.188119
$852$	−3.63476	−0.124525
$853$	6.58574	0.225491	0.112746	−	0.993624i	$-0.464035\pi$
$853$	6.58574	0.225491	0.112746	+	0.993624i	$0.464035\pi$
$854$	−0.556034	−0.0190271
$855$	18.7206	0.640230
$856$	−23.0898	−0.789194
$857$	2.26160	0.0772547	0.0386274	−	0.999254i	$-0.487701\pi$
$857$	2.26160	0.0772547	0.0386274	+	0.999254i	$0.487701\pi$
$858$	5.71266	0.195027
$859$	−26.8486	−0.916064	−0.458032	−	0.888936i	$-0.651445\pi$
$859$	−26.8486	−0.916064	−0.458032	+	0.888936i	$0.651445\pi$
$860$	7.65759	0.261122
$861$	−21.8362	−0.744174
$862$	12.0920	0.411854
$863$	47.5016	1.61697	0.808487	−	0.588515i	$-0.200287\pi$
$863$	47.5016	1.61697	0.808487	+	0.588515i	$0.200287\pi$
$864$	3.02554	0.102931
$865$	−47.4750	−1.61420
$866$	−13.5988	−0.462104
$867$	−27.3595	−0.929176
$868$	−2.96590	−0.100669
$869$	−39.1292	−1.32737
$870$	−19.8607	−0.673342
$871$	6.03238	0.204399
$872$	4.97933	0.168621
$873$	7.20505	0.243854
$874$	14.5555	0.492346
$875$	−3.24047	−0.109548
$876$	3.60581	0.121829
$877$	−15.2072	−0.513512	−0.256756	−	0.966476i	$-0.582654\pi$
$877$	−15.2072	−0.513512	−0.256756	+	0.966476i	$0.582654\pi$
$878$	62.6200	2.11332
$879$	17.6685	0.595945
$880$	−55.3214	−1.86488
$881$	34.6385	1.16700	0.583501	−	0.812113i	$-0.301683\pi$
$881$	34.6385	1.16700	0.583501	+	0.812113i	$0.301683\pi$
$882$	−0.564081	−0.0189936
$883$	11.1299	0.374551	0.187276	−	0.982307i	$-0.440034\pi$
$883$	11.1299	0.374551	0.187276	+	0.982307i	$0.440034\pi$
$884$	3.65739	0.123011
$885$	25.6099	0.860869
$886$	−26.7321	−0.898084
$887$	−14.1441	−0.474912	−0.237456	−	0.971398i	$-0.576313\pi$
$887$	−14.1441	−0.474912	−0.237456	+	0.971398i	$0.576313\pi$
$888$	−8.09849	−0.271768
$889$	25.1403	0.843179
$890$	−5.20632	−0.174516
$891$	−3.57802	−0.119868
$892$	−3.08897	−0.103426
$893$	−48.2278	−1.61388
$894$	−17.3124	−0.579014
$895$	−56.6026	−1.89202
$896$	35.2054	1.17613
$897$	1.56970	0.0524108
$898$	56.7068	1.89233
$899$	8.08477	0.269642
$900$	2.95980	0.0986599
$901$	34.6389	1.15399
$902$	−48.3851	−1.61105
$903$	11.1535	0.371165
$904$	−15.7443	−0.523646
$905$	49.8042	1.65555
$906$	−13.3236	−0.442646
$907$	2.69785	0.0895808	0.0447904	−	0.998996i	$-0.485738\pi$
$907$	2.69785	0.0895808	0.0447904	+	0.998996i	$0.485738\pi$
$908$	3.52085	0.116844
$909$	−1.41011	−0.0467705
$910$	−13.2680	−0.439830
$911$	54.5279	1.80659	0.903295	−	0.429019i	$-0.141141\pi$
$911$	54.5279	1.80659	0.903295	+	0.429019i	$0.141141\pi$
$912$	−27.8584	−0.922485
$913$	−12.9178	−0.427517
$914$	−21.8842	−0.723864
$915$	−0.435420	−0.0143945
$916$	−1.65612	−0.0547196
$917$	41.5587	1.37239
$918$	−10.6338	−0.350968
$919$	56.2695	1.85616	0.928079	−	0.372383i	$-0.121459\pi$
$919$	56.2695	1.85616	0.928079	+	0.372383i	$0.121459\pi$
$920$	−11.7205	−0.386415
$921$	−31.5625	−1.04002
$922$	6.24203	0.205570
$923$	6.61908	0.217870
$924$	5.06551	0.166643
$925$	−18.8436	−0.619574
$926$	−15.5406	−0.510694
$927$	−1.00000	−0.0328443
$928$	11.6760	0.383284
$929$	−45.0044	−1.47655	−0.738273	−	0.674503i	$-0.764358\pi$
$929$	−45.0044	−1.47655	−0.738273	+	0.674503i	$0.764358\pi$
$930$	−10.7815	−0.353539
$931$	2.05191	0.0672485
$932$	−7.71727	−0.252788
$933$	28.3939	0.929575
$934$	14.9106	0.487889
$935$	76.8143	2.51209
$936$	−2.31645	−0.0757157
$937$	−33.4371	−1.09234	−0.546171	−	0.837674i	$-0.683915\pi$
$937$	−33.4371	−1.09234	−0.546171	+	0.837674i	$0.683915\pi$
$938$	24.8306	0.810749
$939$	−16.8316	−0.549277
$940$	−14.6984	−0.479408
$941$	−26.7502	−0.872031	−0.436016	−	0.899939i	$-0.643611\pi$
$941$	−26.7502	−0.872031	−0.436016	+	0.899939i	$0.643611\pi$
$942$	26.9004	0.876462
$943$	−13.2951	−0.432947
$944$	−38.1106	−1.24040
$945$	8.31016	0.270330
$946$	24.7142	0.803528
$947$	−7.84123	−0.254806	−0.127403	−	0.991851i	$-0.540664\pi$
$947$	−7.84123	−0.254806	−0.127403	+	0.991851i	$0.540664\pi$
$948$	−6.00532	−0.195044
$949$	−6.56636	−0.213153
$950$	−49.9796	−1.62155
$951$	−5.44697	−0.176630
$952$	−39.7759	−1.28914
$953$	52.2893	1.69382	0.846909	−	0.531739i	$-0.178461\pi$
$953$	52.2893	1.69382	0.846909	+	0.531739i	$0.178461\pi$
$954$	8.30362	0.268840
$955$	−0.744681	−0.0240973
$956$	0.411406	0.0133058
$957$	−13.8081	−0.446353
$958$	−0.665141	−0.0214897
$959$	−34.6811	−1.11991
$960$	15.3524	0.495495
$961$	−26.6111	−0.858424
$962$	−5.58183	−0.179965
$963$	9.96774	0.321206
$964$	−4.20338	−0.135382
$965$	−70.5350	−2.27060
$966$	6.46125	0.207887
$967$	−14.6150	−0.469988	−0.234994	−	0.971997i	$-0.575507\pi$
$967$	−14.6150	−0.469988	−0.234994	+	0.971997i	$0.575507\pi$
$968$	−4.17470	−0.134180
$969$	38.6817	1.24264
$970$	−37.0800	−1.19057
$971$	−29.8225	−0.957050	−0.478525	−	0.878074i	$-0.658828\pi$
$971$	−29.8225	−0.957050	−0.478525	+	0.878074i	$0.658828\pi$
$972$	−0.549133	−0.0176135
$973$	−8.82344	−0.282866
$974$	39.8819	1.27790
$975$	−5.38994	−0.172616
$976$	0.647957	0.0207406
$977$	14.0118	0.448276	0.224138	−	0.974557i	$-0.428043\pi$
$977$	14.0118	0.448276	0.224138	+	0.974557i	$0.428043\pi$
$978$	7.46194	0.238607
$979$	−3.61968	−0.115686
$980$	0.625359	0.0199764
$981$	−2.14955	−0.0686297
$982$	6.31372	0.201479
$983$	35.4476	1.13060	0.565302	−	0.824884i	$-0.308760\pi$
$983$	35.4476	1.13060	0.565302	+	0.824884i	$0.308760\pi$
$984$	19.6199	0.625460
$985$	−44.1916	−1.40806
$986$	−41.0376	−1.30690
$987$	−21.4086	−0.681443
$988$	−3.18926	−0.101464
$989$	6.79087	0.215937
$990$	18.4139	0.585231
$991$	−61.6821	−1.95940	−0.979698	−	0.200478i	$-0.935751\pi$
$991$	−61.6821	−1.95940	−0.979698	+	0.200478i	$0.935751\pi$
$992$	6.33837	0.201244
$993$	−7.06715	−0.224269
$994$	27.2456	0.864179
$995$	26.2595	0.832481
$996$	−1.98255	−0.0628196
$997$	−46.2017	−1.46322	−0.731611	−	0.681722i	$-0.761231\pi$
$997$	−46.2017	−1.46322	−0.731611	+	0.681722i	$0.761231\pi$
$998$	37.5347	1.18814
$999$	3.49607	0.110611

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.j.1.18	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.j.1.18	✓	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)

\(f(q)\)	\(=\)	\(q+1.59660 q^{2} -1.00000 q^{3} +0.549133 q^{4} -3.22334 q^{5} -1.59660 q^{6} +2.57812 q^{7} -2.31645 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.59660 q^{2} -1.00000 q^{3} +0.549133 q^{4} -3.22334 q^{5} -1.59660 q^{6} +2.57812 q^{7} -2.31645 q^{8} +1.00000 q^{9} -5.14639 q^{10} -3.57802 q^{11} -0.549133 q^{12} +1.00000 q^{13} +4.11623 q^{14} +3.22334 q^{15} -4.79672 q^{16} +6.66029 q^{17} +1.59660 q^{18} -5.80781 q^{19} -1.77005 q^{20} -2.57812 q^{21} -5.71266 q^{22} -1.56970 q^{23} +2.31645 q^{24} +5.38994 q^{25} +1.59660 q^{26} -1.00000 q^{27} +1.41573 q^{28} -3.85916 q^{29} +5.14639 q^{30} -2.09496 q^{31} -3.02554 q^{32} +3.57802 q^{33} +10.6338 q^{34} -8.31016 q^{35} +0.549133 q^{36} -3.49607 q^{37} -9.27276 q^{38} -1.00000 q^{39} +7.46673 q^{40} +8.46980 q^{41} -4.11623 q^{42} -4.32621 q^{43} -1.96481 q^{44} -3.22334 q^{45} -2.50619 q^{46} +8.30395 q^{47} +4.79672 q^{48} -0.353301 q^{49} +8.60558 q^{50} -6.66029 q^{51} +0.549133 q^{52} +5.20081 q^{53} -1.59660 q^{54} +11.5332 q^{55} -5.97210 q^{56} +5.80781 q^{57} -6.16153 q^{58} +7.94515 q^{59} +1.77005 q^{60} -0.135083 q^{61} -3.34481 q^{62} +2.57812 q^{63} +4.76287 q^{64} -3.22334 q^{65} +5.71266 q^{66} +6.03238 q^{67} +3.65739 q^{68} +1.56970 q^{69} -13.2680 q^{70} +6.61908 q^{71} -2.31645 q^{72} -6.56636 q^{73} -5.58183 q^{74} -5.38994 q^{75} -3.18926 q^{76} -9.22455 q^{77} -1.59660 q^{78} +10.9360 q^{79} +15.4615 q^{80} +1.00000 q^{81} +13.5229 q^{82} +3.61033 q^{83} -1.41573 q^{84} -21.4684 q^{85} -6.90723 q^{86} +3.85916 q^{87} +8.28831 q^{88} +1.01165 q^{89} -5.14639 q^{90} +2.57812 q^{91} -0.861976 q^{92} +2.09496 q^{93} +13.2581 q^{94} +18.7206 q^{95} +3.02554 q^{96} +7.20505 q^{97} -0.564081 q^{98} -3.57802 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) \) 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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