LMFDB - Embedded newform 5239.2.a.l.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5239,2,Mod(1,5239)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5239, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5239.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5239 = 13^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5239.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:	$41.8336256189$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 17 x^{14} + 80 x^{13} + 98 x^{12} - 628 x^{11} - 158 x^{10} + 2458 x^{9} + \cdots - 147 $ x^16 - 4x^15 - 17x^14 + 80x^13 + 98x^12 - 628x^11 - 158x^10 + 2458x^9 - 510x^8 - 5030x^7 + 2318x^6 + 5112x^5 - 3154x^4 - 2086x^3 + 1542x^2 + 124*x - 147
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 403)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$1.01245$ of defining polynomial
Character	$\chi$	$=$	5239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.01245 q^{2} -1.05136 q^{3} -0.974950 q^{4} +3.24438 q^{5} -1.06445 q^{6} -1.79572 q^{7} -3.01198 q^{8} -1.89463 q^{9} +O(q^{10})$	\(q+1.01245 q^{2} -1.05136 q^{3} -0.974950 q^{4} +3.24438 q^{5} -1.06445 q^{6} -1.79572 q^{7} -3.01198 q^{8} -1.89463 q^{9} +3.28477 q^{10} +6.09683 q^{11} +1.02503 q^{12} -1.81807 q^{14} -3.41103 q^{15} -1.09957 q^{16} -4.79598 q^{17} -1.91821 q^{18} +1.84875 q^{19} -3.16311 q^{20} +1.88796 q^{21} +6.17272 q^{22} +7.94273 q^{23} +3.16669 q^{24} +5.52601 q^{25} +5.14604 q^{27} +1.75074 q^{28} -2.23287 q^{29} -3.45349 q^{30} -1.00000 q^{31} +4.91070 q^{32} -6.40999 q^{33} -4.85568 q^{34} -5.82601 q^{35} +1.84717 q^{36} -8.64644 q^{37} +1.87176 q^{38} -9.77201 q^{40} +0.0498113 q^{41} +1.91146 q^{42} -4.76573 q^{43} -5.94410 q^{44} -6.14691 q^{45} +8.04159 q^{46} +4.00376 q^{47} +1.15605 q^{48} -3.77538 q^{49} +5.59480 q^{50} +5.04233 q^{51} +0.588394 q^{53} +5.21010 q^{54} +19.7804 q^{55} +5.40868 q^{56} -1.94371 q^{57} -2.26066 q^{58} -3.49014 q^{59} +3.32558 q^{60} +12.1590 q^{61} -1.01245 q^{62} +3.40223 q^{63} +7.17097 q^{64} -6.48978 q^{66} -1.72095 q^{67} +4.67585 q^{68} -8.35070 q^{69} -5.89852 q^{70} +10.3643 q^{71} +5.70659 q^{72} -2.28292 q^{73} -8.75406 q^{74} -5.80985 q^{75} -1.80244 q^{76} -10.9482 q^{77} +16.1812 q^{79} -3.56743 q^{80} +0.273525 q^{81} +0.0504314 q^{82} -10.2561 q^{83} -1.84067 q^{84} -15.5600 q^{85} -4.82505 q^{86} +2.34756 q^{87} -18.3635 q^{88} +7.99914 q^{89} -6.22342 q^{90} -7.74376 q^{92} +1.05136 q^{93} +4.05360 q^{94} +5.99805 q^{95} -5.16294 q^{96} +10.1745 q^{97} -3.82238 q^{98} -11.5512 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 2 q^{3} + 18 q^{4} + 4 q^{5} + 6 q^{6} + 2 q^{7} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 - 2 * q^3 + 18 * q^4 + 4 * q^5 + 6 * q^6 + 2 * q^7 + 12 * q^8 + 10 * q^9	$ 16 q + 4 q^{2} - 2 q^{3} + 18 q^{4} + 4 q^{5} + 6 q^{6} + 2 q^{7} + 12 q^{8} + 10 q^{9} - 2 q^{10} + 14 q^{11} + 8 q^{12} - 8 q^{14} + 14 q^{16} + 4 q^{17} - 28 q^{18} + 22 q^{19} + 28 q^{20} + 12 q^{21} - 8 q^{22} + 4 q^{23} - 8 q^{24} - 2 q^{25} + 10 q^{27} + 16 q^{28} - 8 q^{29} - 20 q^{30} - 16 q^{31} + 48 q^{32} + 10 q^{33} + 8 q^{34} - 2 q^{35} + 22 q^{36} + 16 q^{37} - 6 q^{38} + 14 q^{40} + 44 q^{41} + 14 q^{42} + 16 q^{43} + 4 q^{44} + 56 q^{45} + 10 q^{47} + 32 q^{49} + 2 q^{50} - 6 q^{53} + 24 q^{54} + 22 q^{55} - 4 q^{56} - 8 q^{57} + 74 q^{58} + 2 q^{59} + 40 q^{60} + 8 q^{61} - 4 q^{62} + 56 q^{63} + 38 q^{64} - 34 q^{66} - 8 q^{67} + 32 q^{68} - 10 q^{69} - 108 q^{70} + 50 q^{71} - 44 q^{72} + 14 q^{73} + 8 q^{74} + 44 q^{76} + 16 q^{77} + 32 q^{79} + 68 q^{80} - 8 q^{81} - 6 q^{82} - 20 q^{83} + 136 q^{84} - 32 q^{85} + 8 q^{86} - 36 q^{87} - 40 q^{88} + 52 q^{89} - 34 q^{90} + 14 q^{92} + 2 q^{93} + 44 q^{94} - 2 q^{95} - 80 q^{96} + 18 q^{97} + 12 q^{98} + 38 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 2 * q^3 + 18 * q^4 + 4 * q^5 + 6 * q^6 + 2 * q^7 + 12 * q^8 + 10 * q^9 - 2 * q^10 + 14 * q^11 + 8 * q^12 - 8 * q^14 + 14 * q^16 + 4 * q^17 - 28 * q^18 + 22 * q^19 + 28 * q^20 + 12 * q^21 - 8 * q^22 + 4 * q^23 - 8 * q^24 - 2 * q^25 + 10 * q^27 + 16 * q^28 - 8 * q^29 - 20 * q^30 - 16 * q^31 + 48 * q^32 + 10 * q^33 + 8 * q^34 - 2 * q^35 + 22 * q^36 + 16 * q^37 - 6 * q^38 + 14 * q^40 + 44 * q^41 + 14 * q^42 + 16 * q^43 + 4 * q^44 + 56 * q^45 + 10 * q^47 + 32 * q^49 + 2 * q^50 - 6 * q^53 + 24 * q^54 + 22 * q^55 - 4 * q^56 - 8 * q^57 + 74 * q^58 + 2 * q^59 + 40 * q^60 + 8 * q^61 - 4 * q^62 + 56 * q^63 + 38 * q^64 - 34 * q^66 - 8 * q^67 + 32 * q^68 - 10 * q^69 - 108 * q^70 + 50 * q^71 - 44 * q^72 + 14 * q^73 + 8 * q^74 + 44 * q^76 + 16 * q^77 + 32 * q^79 + 68 * q^80 - 8 * q^81 - 6 * q^82 - 20 * q^83 + 136 * q^84 - 32 * q^85 + 8 * q^86 - 36 * q^87 - 40 * q^88 + 52 * q^89 - 34 * q^90 + 14 * q^92 + 2 * q^93 + 44 * q^94 - 2 * q^95 - 80 * q^96 + 18 * q^97 + 12 * q^98 + 38 * 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 $

$2$	1.01245	0.715908	0.357954	−	0.933739i	$-0.383474\pi$
$2$	1.01245	0.715908	0.357954	+	0.933739i	$0.383474\pi$
$3$	−1.05136	−0.607006	−0.303503	−	0.952831i	$-0.598156\pi$
$3$	−1.05136	−0.607006	−0.303503	+	0.952831i	$0.598156\pi$
$4$	−0.974950	−0.487475
$5$	3.24438	1.45093	0.725466	−	0.688258i	$-0.241624\pi$
$5$	3.24438	1.45093	0.725466	+	0.688258i	$0.241624\pi$
$6$	−1.06445	−0.434561
$7$	−1.79572	−0.678719	−0.339360	−	0.940657i	$-0.610210\pi$
$7$	−1.79572	−0.678719	−0.339360	+	0.940657i	$0.610210\pi$
$8$	−3.01198	−1.06490
$9$	−1.89463	−0.631544
$10$	3.28477	1.03873
$11$	6.09683	1.83826	0.919131	−	0.393951i	$-0.128892\pi$
$11$	6.09683	1.83826	0.919131	+	0.393951i	$0.128892\pi$
$12$	1.02503	0.295900
$13$	0	0
$13$	0	0
$14$	−1.81807	−0.485901
$15$	−3.41103	−0.880724
$16$	−1.09957	−0.274893
$17$	−4.79598	−1.16320	−0.581598	−	0.813476i	$-0.697572\pi$
$17$	−4.79598	−1.16320	−0.581598	+	0.813476i	$0.697572\pi$
$18$	−1.91821	−0.452128
$19$	1.84875	0.424133	0.212066	−	0.977255i	$-0.431981\pi$
$19$	1.84875	0.424133	0.212066	+	0.977255i	$0.431981\pi$
$20$	−3.16311	−0.707293
$21$	1.88796	0.411986
$22$	6.17272	1.31603
$23$	7.94273	1.65617	0.828086	−	0.560600i	$-0.189430\pi$
$23$	7.94273	1.65617	0.828086	+	0.560600i	$0.189430\pi$
$24$	3.16669	0.646398
$25$	5.52601	1.10520
$26$	0	0
$27$	5.14604	0.990357
$28$	1.75074	0.330859
$29$	−2.23287	−0.414633	−0.207317	−	0.978274i	$-0.566473\pi$
$29$	−2.23287	−0.414633	−0.207317	+	0.978274i	$0.566473\pi$
$30$	−3.45349	−0.630518
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	4.91070	0.868098
$33$	−6.40999	−1.11584
$34$	−4.85568	−0.832742
$35$	−5.82601	−0.984775
$36$	1.84717	0.307862
$37$	−8.64644	−1.42147	−0.710733	−	0.703462i	$-0.751636\pi$
$37$	−8.64644	−1.42147	−0.710733	+	0.703462i	$0.751636\pi$
$38$	1.87176	0.303640
$39$	0	0
$40$	−9.77201	−1.54509
$41$	0.0498113	0.00777923	0.00388961	−	0.999992i	$-0.498762\pi$
$41$	0.0498113	0.00777923	0.00388961	+	0.999992i	$0.498762\pi$
$42$	1.91146	0.294945
$43$	−4.76573	−0.726767	−0.363384	−	0.931640i	$-0.618379\pi$
$43$	−4.76573	−0.726767	−0.363384	+	0.931640i	$0.618379\pi$
$44$	−5.94410	−0.896107
$45$	−6.14691	−0.916327
$46$	8.04159	1.18567
$47$	4.00376	0.584008	0.292004	−	0.956417i	$-0.405678\pi$
$47$	4.00376	0.584008	0.292004	+	0.956417i	$0.405678\pi$
$48$	1.15605	0.166862
$49$	−3.77538	−0.539341
$50$	5.59480	0.791224
$51$	5.04233	0.706067
$52$	0	0
$53$	0.588394	0.0808221	0.0404111	−	0.999183i	$-0.487133\pi$
$53$	0.588394	0.0808221	0.0404111	+	0.999183i	$0.487133\pi$
$54$	5.21010	0.709005
$55$	19.7804	2.66719
$56$	5.40868	0.722765
$57$	−1.94371	−0.257451
$58$	−2.26066	−0.296840
$59$	−3.49014	−0.454377	−0.227189	−	0.973851i	$-0.572953\pi$
$59$	−3.49014	−0.454377	−0.227189	+	0.973851i	$0.572953\pi$
$60$	3.32558	0.429331
$61$	12.1590	1.55680	0.778400	−	0.627769i	$-0.216032\pi$
$61$	12.1590	1.55680	0.778400	+	0.627769i	$0.216032\pi$
$62$	−1.01245	−0.128581
$63$	3.40223	0.428641
$64$	7.17097	0.896371
$65$	0	0
$66$	−6.48978	−0.798836
$67$	−1.72095	−0.210247	−0.105124	−	0.994459i	$-0.533524\pi$
$67$	−1.72095	−0.210247	−0.105124	+	0.994459i	$0.533524\pi$
$68$	4.67585	0.567029
$69$	−8.35070	−1.00531
$70$	−5.89852	−0.705009
$71$	10.3643	1.23002	0.615011	−	0.788519i	$-0.289152\pi$
$71$	10.3643	1.23002	0.615011	+	0.788519i	$0.289152\pi$
$72$	5.70659	0.672529
$73$	−2.28292	−0.267196	−0.133598	−	0.991036i	$-0.542653\pi$
$73$	−2.28292	−0.267196	−0.133598	+	0.991036i	$0.542653\pi$
$74$	−8.75406	−1.01764
$75$	−5.80985	−0.670864
$76$	−1.80244	−0.206754
$77$	−10.9482	−1.24766
$78$	0	0
$79$	16.1812	1.82053	0.910265	−	0.414027i	$-0.135878\pi$
$79$	16.1812	1.82053	0.910265	+	0.414027i	$0.135878\pi$
$80$	−3.56743	−0.398851
$81$	0.273525	0.0303917
$82$	0.0504314	0.00556921
$83$	−10.2561	−1.12575	−0.562877	−	0.826541i	$-0.690306\pi$
$83$	−10.2561	−1.12575	−0.562877	+	0.826541i	$0.690306\pi$
$84$	−1.84067	−0.200833
$85$	−15.5600	−1.68772
$86$	−4.82505	−0.520299
$87$	2.34756	0.251685
$88$	−18.3635	−1.95756
$89$	7.99914	0.847907	0.423953	−	0.905684i	$-0.360642\pi$
$89$	7.99914	0.847907	0.423953	+	0.905684i	$0.360642\pi$
$90$	−6.22342	−0.656006
$91$	0	0
$92$	−7.74376	−0.807343
$93$	1.05136	0.109021
$94$	4.05360	0.418097
$95$	5.99805	0.615387
$96$	−5.16294	−0.526940
$97$	10.1745	1.03307	0.516533	−	0.856268i	$-0.327223\pi$
$97$	10.1745	1.03307	0.516533	+	0.856268i	$0.327223\pi$
$98$	−3.82238	−0.386118
$99$	−11.5512	−1.16094
$100$	−5.38759	−0.538759
$101$	10.3806	1.03291	0.516454	−	0.856315i	$-0.327252\pi$
$101$	10.3806	1.03291	0.516454	+	0.856315i	$0.327252\pi$
$102$	5.10509	0.505479
$103$	−7.56287	−0.745191	−0.372596	−	0.927994i	$-0.621532\pi$
$103$	−7.56287	−0.745191	−0.372596	+	0.927994i	$0.621532\pi$
$104$	0	0
$105$	6.12526	0.597764
$106$	0.595718	0.0578612
$107$	9.88355	0.955478	0.477739	−	0.878502i	$-0.341456\pi$
$107$	9.88355	0.955478	0.477739	+	0.878502i	$0.341456\pi$
$108$	−5.01714	−0.482774
$109$	−5.97227	−0.572040	−0.286020	−	0.958224i	$-0.592332\pi$
$109$	−5.97227	−0.572040	−0.286020	+	0.958224i	$0.592332\pi$
$110$	20.0266	1.90947
$111$	9.09056	0.862838
$112$	1.97452	0.186575
$113$	5.83695	0.549094	0.274547	−	0.961574i	$-0.411472\pi$
$113$	5.83695	0.549094	0.274547	+	0.961574i	$0.411472\pi$
$114$	−1.96791	−0.184311
$115$	25.7692	2.40299
$116$	2.17694	0.202123
$117$	0	0
$118$	−3.53358	−0.325292
$119$	8.61225	0.789484
$120$	10.2740	0.937879
$121$	26.1713	2.37921
$122$	12.3103	1.11453
$123$	−0.0523699	−0.00472204
$124$	0.974950	0.0875531
$125$	1.70658	0.152641
$126$	3.44458	0.306868
$127$	−1.76344	−0.156480	−0.0782399	−	0.996935i	$-0.524930\pi$
$127$	−1.76344	−0.156480	−0.0782399	+	0.996935i	$0.524930\pi$
$128$	−2.56118	−0.226378
$129$	5.01052	0.441152
$130$	0	0
$131$	15.7996	1.38042	0.690209	−	0.723610i	$-0.257518\pi$
$131$	15.7996	1.38042	0.690209	+	0.723610i	$0.257518\pi$
$132$	6.24942	0.543942
$133$	−3.31984	−0.287867
$134$	−1.74237	−0.150518
$135$	16.6957	1.43694
$136$	14.4454	1.23868
$137$	14.0263	1.19835	0.599174	−	0.800619i	$-0.295496\pi$
$137$	14.0263	1.19835	0.599174	+	0.800619i	$0.295496\pi$
$138$	−8.45465	−0.719707
$139$	−8.87486	−0.752756	−0.376378	−	0.926466i	$-0.622831\pi$
$139$	−8.87486	−0.752756	−0.376378	+	0.926466i	$0.622831\pi$
$140$	5.68007	0.480053
$141$	−4.20941	−0.354497
$142$	10.4934	0.880583
$143$	0	0
$144$	2.08328	0.173607
$145$	−7.24428	−0.601605
$146$	−2.31134	−0.191288
$147$	3.96931	0.327383
$148$	8.42985	0.692929
$149$	0.896489	0.0734432	0.0367216	−	0.999326i	$-0.488309\pi$
$149$	0.896489	0.0734432	0.0367216	+	0.999326i	$0.488309\pi$
$150$	−5.88217	−0.480277
$151$	−0.221338	−0.0180122	−0.00900611	−	0.999959i	$-0.502867\pi$
$151$	−0.221338	−0.0180122	−0.00900611	+	0.999959i	$0.502867\pi$
$152$	−5.56840	−0.451657
$153$	9.08662	0.734610
$154$	−11.0845	−0.893213
$155$	−3.24438	−0.260595
$156$	0	0
$157$	8.52165	0.680102	0.340051	−	0.940407i	$-0.389556\pi$
$157$	8.52165	0.680102	0.340051	+	0.940407i	$0.389556\pi$
$158$	16.3826	1.30333
$159$	−0.618617	−0.0490595
$160$	15.9322	1.25955
$161$	−14.2629	−1.12408
$162$	0.276930	0.0217576
$163$	0.474988	0.0372039	0.0186019	−	0.999827i	$-0.494078\pi$
$163$	0.474988	0.0372039	0.0186019	+	0.999827i	$0.494078\pi$
$164$	−0.0485636	−0.00379218
$165$	−20.7965	−1.61900
$166$	−10.3838	−0.805937
$167$	5.99300	0.463752	0.231876	−	0.972745i	$-0.425514\pi$
$167$	5.99300	0.463752	0.231876	+	0.972745i	$0.425514\pi$
$168$	−5.68650	−0.438723
$169$	0	0
$170$	−15.7537	−1.20825
$171$	−3.50270	−0.267858
$172$	4.64635	0.354281
$173$	−0.0189761	−0.00144272	−0.000721362	−	1.00000i	$-0.500230\pi$
$173$	−0.0189761	−0.00144272	−0.000721362		1.00000i	$0.500230\pi$
$174$	2.37678	0.180183
$175$	−9.92318	−0.750122
$176$	−6.70390	−0.505325
$177$	3.66941	0.275810
$178$	8.09870	0.607024
$179$	−5.66716	−0.423583	−0.211792	−	0.977315i	$-0.567930\pi$
$179$	−5.66716	−0.423583	−0.211792	+	0.977315i	$0.567930\pi$
$180$	5.99293	0.446687
$181$	15.5416	1.15520	0.577598	−	0.816322i	$-0.303990\pi$
$181$	15.5416	1.15520	0.577598	+	0.816322i	$0.303990\pi$
$182$	0	0
$183$	−12.7835	−0.944986
$184$	−23.9233	−1.76365
$185$	−28.0523	−2.06245
$186$	1.06445	0.0780494
$187$	−29.2403	−2.13826
$188$	−3.90347	−0.284690
$189$	−9.24086	−0.672174
$190$	6.07271	0.440561
$191$	−7.38826	−0.534596	−0.267298	−	0.963614i	$-0.586131\pi$
$191$	−7.38826	−0.534596	−0.267298	+	0.963614i	$0.586131\pi$
$192$	−7.53931	−0.544103
$193$	4.22194	0.303902	0.151951	−	0.988388i	$-0.451444\pi$
$193$	4.22194	0.303902	0.151951	+	0.988388i	$0.451444\pi$
$194$	10.3012	0.739580
$195$	0	0
$196$	3.68081	0.262915
$197$	7.13939	0.508660	0.254330	−	0.967117i	$-0.418145\pi$
$197$	7.13939	0.508660	0.254330	+	0.967117i	$0.418145\pi$
$198$	−11.6950	−0.831129
$199$	17.5333	1.24290	0.621452	−	0.783453i	$-0.286543\pi$
$199$	17.5333	1.24290	0.621452	+	0.783453i	$0.286543\pi$
$200$	−16.6442	−1.17693
$201$	1.80934	0.127621
$202$	10.5098	0.739467
$203$	4.00961	0.281420
$204$	−4.91602	−0.344190
$205$	0.161607	0.0112871
$206$	−7.65701	−0.533489
$207$	−15.0485	−1.04595
$208$	0	0
$209$	11.2715	0.779667
$210$	6.20150	0.427944
$211$	12.5199	0.861905	0.430952	−	0.902375i	$-0.358178\pi$
$211$	12.5199	0.861905	0.430952	+	0.902375i	$0.358178\pi$
$212$	−0.573655	−0.0393988
$213$	−10.8967	−0.746630
$214$	10.0066	0.684035
$215$	−15.4619	−1.05449
$216$	−15.4998	−1.05463
$217$	1.79572	0.121902
$218$	−6.04661	−0.409528
$219$	2.40019	0.162190
$220$	−19.2849	−1.30019
$221$	0	0
$222$	9.20371	0.617713
$223$	13.4782	0.902565	0.451282	−	0.892381i	$-0.350967\pi$
$223$	13.4782	0.902565	0.451282	+	0.892381i	$0.350967\pi$
$224$	−8.81826	−0.589195
$225$	−10.4698	−0.697984
$226$	5.90961	0.393101
$227$	−21.7487	−1.44351	−0.721755	−	0.692149i	$-0.756664\pi$
$227$	−21.7487	−1.44351	−0.721755	+	0.692149i	$0.756664\pi$
$228$	1.89502	0.125501
$229$	−4.82129	−0.318600	−0.159300	−	0.987230i	$-0.550924\pi$
$229$	−4.82129	−0.318600	−0.159300	+	0.987230i	$0.550924\pi$
$230$	26.0900	1.72032
$231$	11.5106	0.757339
$232$	6.72536	0.441541
$233$	29.1203	1.90774	0.953868	−	0.300227i	$-0.0970623\pi$
$233$	29.1203	1.90774	0.953868	+	0.300227i	$0.0970623\pi$
$234$	0	0
$235$	12.9897	0.847356
$236$	3.40271	0.221498
$237$	−17.0124	−1.10507
$238$	8.71945	0.565198
$239$	27.1826	1.75829	0.879147	−	0.476552i	$-0.158113\pi$
$239$	27.1826	1.75829	0.879147	+	0.476552i	$0.158113\pi$
$240$	3.75067	0.242105
$241$	−21.6242	−1.39294	−0.696468	−	0.717588i	$-0.745246\pi$
$241$	−21.6242	−1.39294	−0.696468	+	0.717588i	$0.745246\pi$
$242$	26.4971	1.70330
$243$	−15.7257	−1.00880
$244$	−11.8544	−0.758901
$245$	−12.2488	−0.782546
$246$	−0.0530218	−0.00338054
$247$	0	0
$248$	3.01198	0.191261
$249$	10.7829	0.683339
$250$	1.72782	0.109277
$251$	−23.7774	−1.50082	−0.750410	−	0.660973i	$-0.770144\pi$
$251$	−23.7774	−1.50082	−0.750410	+	0.660973i	$0.770144\pi$
$252$	−3.31701	−0.208952
$253$	48.4254	3.04448
$254$	−1.78539	−0.112025
$255$	16.3592	1.02446
$256$	−16.9350	−1.05844
$257$	−3.84862	−0.240070	−0.120035	−	0.992770i	$-0.538301\pi$
$257$	−3.84862	−0.240070	−0.120035	+	0.992770i	$0.538301\pi$
$258$	5.07289	0.315824
$259$	15.5266	0.964776
$260$	0	0
$261$	4.23046	0.261859
$262$	15.9963	0.988253
$263$	−27.4393	−1.69198	−0.845991	−	0.533198i	$-0.820990\pi$
$263$	−27.4393	−1.69198	−0.845991	+	0.533198i	$0.820990\pi$
$264$	19.3068	1.18825
$265$	1.90897	0.117267
$266$	−3.36117	−0.206086
$267$	−8.41001	−0.514684
$268$	1.67784	0.102490
$269$	4.99431	0.304508	0.152254	−	0.988341i	$-0.451347\pi$
$269$	4.99431	0.304508	0.152254	+	0.988341i	$0.451347\pi$
$270$	16.9035	1.02872
$271$	27.8192	1.68990	0.844948	−	0.534848i	$-0.179631\pi$
$271$	27.8192	1.68990	0.844948	+	0.534848i	$0.179631\pi$
$272$	5.27353	0.319754
$273$	0	0
$274$	14.2009	0.857908
$275$	33.6911	2.03165
$276$	8.14152	0.490062
$277$	−19.5970	−1.17747	−0.588734	−	0.808327i	$-0.700373\pi$
$277$	−19.5970	−1.17747	−0.588734	+	0.808327i	$0.700373\pi$
$278$	−8.98533	−0.538904
$279$	1.89463	0.113429
$280$	17.5478	1.04868
$281$	9.44497	0.563440	0.281720	−	0.959497i	$-0.409095\pi$
$281$	9.44497	0.563440	0.281720	+	0.959497i	$0.409095\pi$
$282$	−4.26181	−0.253787
$283$	−11.1656	−0.663726	−0.331863	−	0.943328i	$-0.607677\pi$
$283$	−11.1656	−0.663726	−0.331863	+	0.943328i	$0.607677\pi$
$284$	−10.1047	−0.599605
$285$	−6.30614	−0.373544
$286$	0	0
$287$	−0.0894473	−0.00527991
$288$	−9.30397	−0.548242
$289$	6.00145	0.353027
$290$	−7.33445	−0.430694
$291$	−10.6971	−0.627077
$292$	2.22574	0.130251
$293$	19.3914	1.13286	0.566429	−	0.824110i	$-0.308324\pi$
$293$	19.3914	1.13286	0.566429	+	0.824110i	$0.308324\pi$
$294$	4.01871	0.234376
$295$	−11.3233	−0.659270
$296$	26.0429	1.51371
$297$	31.3745	1.82054
$298$	0.907647	0.0525786
$299$	0	0
$300$	5.66432	0.327030
$301$	8.55793	0.493271
$302$	−0.224093	−0.0128951
$303$	−10.9138	−0.626981
$304$	−2.03283	−0.116591
$305$	39.4484	2.25881
$306$	9.19973	0.525913
$307$	−2.97843	−0.169988	−0.0849939	−	0.996381i	$-0.527087\pi$
$307$	−2.97843	−0.169988	−0.0849939	+	0.996381i	$0.527087\pi$
$308$	10.6740	0.608205
$309$	7.95133	0.452336
$310$	−3.28477	−0.186562
$311$	15.2149	0.862756	0.431378	−	0.902171i	$-0.358028\pi$
$311$	15.2149	0.862756	0.431378	+	0.902171i	$0.358028\pi$
$312$	0	0
$313$	−6.83949	−0.386591	−0.193295	−	0.981141i	$-0.561918\pi$
$313$	−6.83949	−0.386591	−0.193295	+	0.981141i	$0.561918\pi$
$314$	8.62773	0.486891
$315$	11.0381	0.621929
$316$	−15.7759	−0.887463
$317$	17.3492	0.974431	0.487215	−	0.873282i	$-0.338013\pi$
$317$	17.3492	0.974431	0.487215	+	0.873282i	$0.338013\pi$
$318$	−0.626317	−0.0351221
$319$	−13.6134	−0.762205
$320$	23.2654	1.30057
$321$	−10.3912	−0.579981
$322$	−14.4405	−0.804735
$323$	−8.86658	−0.493350
$324$	−0.266673	−0.0148152
$325$	0	0
$326$	0.480900	0.0266346
$327$	6.27904	0.347231
$328$	−0.150031	−0.00828407
$329$	−7.18964	−0.396378
$330$	−21.0553	−1.15906
$331$	5.82160	0.319984	0.159992	−	0.987118i	$-0.448853\pi$
$331$	5.82160	0.319984	0.159992	+	0.987118i	$0.448853\pi$
$332$	9.99920	0.548777
$333$	16.3818	0.897718
$334$	6.06760	0.332004
$335$	−5.58341	−0.305054
$336$	−2.07595	−0.113252
$337$	30.6724	1.67083	0.835415	−	0.549620i	$-0.185227\pi$
$337$	30.6724	1.67083	0.835415	+	0.549620i	$0.185227\pi$
$338$	0	0
$339$	−6.13677	−0.333303
$340$	15.1702	0.822721
$341$	−6.09683	−0.330162
$342$	−3.54630	−0.191762
$343$	19.3496	1.04478
$344$	14.3543	0.773932
$345$	−27.0929	−1.45863
$346$	−0.0192123	−0.00103286
$347$	−24.5555	−1.31821	−0.659103	−	0.752053i	$-0.729064\pi$
$347$	−24.5555	−1.31821	−0.659103	+	0.752053i	$0.729064\pi$
$348$	−2.28875	−0.122690
$349$	27.8390	1.49019	0.745094	−	0.666959i	$-0.232404\pi$
$349$	27.8390	1.49019	0.745094	+	0.666959i	$0.232404\pi$
$350$	−10.0467	−0.537018
$351$	0	0
$352$	29.9397	1.59579
$353$	−7.01905	−0.373586	−0.186793	−	0.982399i	$-0.559809\pi$
$353$	−7.01905	−0.373586	−0.186793	+	0.982399i	$0.559809\pi$
$354$	3.71508	0.197454
$355$	33.6259	1.78468
$356$	−7.79876	−0.413333
$357$	−9.05462	−0.479221
$358$	−5.73770	−0.303247
$359$	15.7950	0.833628	0.416814	−	0.908992i	$-0.363147\pi$
$359$	15.7950	0.833628	0.416814	+	0.908992i	$0.363147\pi$
$360$	18.5144	0.975793
$361$	−15.5821	−0.820112
$362$	15.7350	0.827014
$363$	−27.5156	−1.44419
$364$	0	0
$365$	−7.40667	−0.387683
$366$	−12.9427	−0.676523
$367$	10.2880	0.537029	0.268515	−	0.963276i	$-0.413467\pi$
$367$	10.2880	0.537029	0.268515	+	0.963276i	$0.413467\pi$
$368$	−8.73359	−0.455270
$369$	−0.0943742	−0.00491292
$370$	−28.4015	−1.47652
$371$	−1.05659	−0.0548555
$372$	−1.02503	−0.0531453
$373$	33.4821	1.73364	0.866820	−	0.498622i	$-0.166160\pi$
$373$	33.4821	1.73364	0.866820	+	0.498622i	$0.166160\pi$
$374$	−29.6042	−1.53080
$375$	−1.79424	−0.0926541
$376$	−12.0592	−0.621908
$377$	0	0
$378$	−9.35589	−0.481215
$379$	−31.2200	−1.60367	−0.801833	−	0.597548i	$-0.796142\pi$
$379$	−31.2200	−1.60367	−0.801833	+	0.597548i	$0.796142\pi$
$380$	−5.84781	−0.299986
$381$	1.85402	0.0949841
$382$	−7.48023	−0.382722
$383$	−8.55469	−0.437124	−0.218562	−	0.975823i	$-0.570137\pi$
$383$	−8.55469	−0.437124	−0.218562	+	0.975823i	$0.570137\pi$
$384$	2.69273	0.137413
$385$	−35.5202	−1.81027
$386$	4.27450	0.217566
$387$	9.02931	0.458985
$388$	−9.91964	−0.503594
$389$	−38.2805	−1.94090	−0.970450	−	0.241303i	$-0.922425\pi$
$389$	−38.2805	−1.94090	−0.970450	+	0.241303i	$0.922425\pi$
$390$	0	0
$391$	−38.0932	−1.92645
$392$	11.3714	0.574342
$393$	−16.6112	−0.837922
$394$	7.22825	0.364154
$395$	52.4980	2.64146
$396$	11.2619	0.565931
$397$	18.1469	0.910767	0.455383	−	0.890295i	$-0.349502\pi$
$397$	18.1469	0.910767	0.455383	+	0.890295i	$0.349502\pi$
$398$	17.7515	0.889805
$399$	3.49037	0.174737
$400$	−6.07624	−0.303812
$401$	23.7338	1.18521	0.592605	−	0.805493i	$-0.298100\pi$
$401$	23.7338	1.18521	0.592605	+	0.805493i	$0.298100\pi$
$402$	1.83187	0.0913651
$403$	0	0
$404$	−10.1206	−0.503517
$405$	0.887419	0.0440962
$406$	4.05952	0.201471
$407$	−52.7158	−2.61303
$408$	−15.1874	−0.751888
$409$	−29.4641	−1.45691	−0.728453	−	0.685096i	$-0.759760\pi$
$409$	−29.4641	−1.45691	−0.728453	+	0.685096i	$0.759760\pi$
$410$	0.163619	0.00808055
$411$	−14.7468	−0.727404
$412$	7.37342	0.363262
$413$	6.26731	0.308394
$414$	−15.2359	−0.748801
$415$	−33.2747	−1.63339
$416$	0	0
$417$	9.33071	0.456927
$418$	11.4118	0.558170
$419$	24.8096	1.21203	0.606014	−	0.795454i	$-0.292768\pi$
$419$	24.8096	1.21203	0.606014	+	0.795454i	$0.292768\pi$
$420$	−5.97182	−0.291395
$421$	0.191902	0.00935275	0.00467637	−	0.999989i	$-0.498511\pi$
$421$	0.191902	0.00935275	0.00467637	+	0.999989i	$0.498511\pi$
$422$	12.6757	0.617045
$423$	−7.58565	−0.368827
$424$	−1.77223	−0.0860672
$425$	−26.5027	−1.28557
$426$	−11.0323	−0.534519
$427$	−21.8342	−1.05663
$428$	−9.63597	−0.465772
$429$	0	0
$430$	−15.6543	−0.754918
$431$	−15.0633	−0.725574	−0.362787	−	0.931872i	$-0.618175\pi$
$431$	−15.0633	−0.725574	−0.362787	+	0.931872i	$0.618175\pi$
$432$	−5.65844	−0.272242
$433$	−12.8565	−0.617844	−0.308922	−	0.951087i	$-0.599968\pi$
$433$	−12.8565	−0.617844	−0.308922	+	0.951087i	$0.599968\pi$
$434$	1.81807	0.0872703
$435$	7.61638	0.365178
$436$	5.82267	0.278855
$437$	14.6841	0.702437
$438$	2.43006	0.116113
$439$	0.561664	0.0268068	0.0134034	−	0.999910i	$-0.495733\pi$
$439$	0.561664	0.0268068	0.0134034	+	0.999910i	$0.495733\pi$
$440$	−59.5783	−2.84028
$441$	7.15296	0.340617
$442$	0	0
$443$	−10.0558	−0.477765	−0.238883	−	0.971048i	$-0.576781\pi$
$443$	−10.0558	−0.477765	−0.238883	+	0.971048i	$0.576781\pi$
$444$	−8.86284	−0.420612
$445$	25.9522	1.23025
$446$	13.6459	0.646154
$447$	−0.942537	−0.0445805
$448$	−12.8771	−0.608384
$449$	15.4936	0.731187	0.365594	−	0.930775i	$-0.380866\pi$
$449$	15.4936	0.731187	0.365594	+	0.930775i	$0.380866\pi$
$450$	−10.6001	−0.499692
$451$	0.303691	0.0143003
$452$	−5.69074	−0.267670
$453$	0.232707	0.0109335
$454$	−22.0194	−1.03342
$455$	0	0
$456$	5.85442	0.274159
$457$	22.5213	1.05350	0.526751	−	0.850020i	$-0.323410\pi$
$457$	22.5213	1.05350	0.526751	+	0.850020i	$0.323410\pi$
$458$	−4.88131	−0.228088
$459$	−24.6803	−1.15198
$460$	−25.1237	−1.17140
$461$	11.9714	0.557563	0.278782	−	0.960354i	$-0.410069\pi$
$461$	11.9714	0.557563	0.278782	+	0.960354i	$0.410069\pi$
$462$	11.6538	0.542186
$463$	42.4947	1.97489	0.987447	−	0.157950i	$-0.0504886\pi$
$463$	42.4947	1.97489	0.987447	+	0.157950i	$0.0504886\pi$
$464$	2.45520	0.113980
$465$	3.41103	0.158183
$466$	29.4828	1.36576
$467$	−35.2701	−1.63211	−0.816053	−	0.577977i	$-0.803842\pi$
$467$	−35.2701	−1.63211	−0.816053	+	0.577977i	$0.803842\pi$
$468$	0	0
$469$	3.09034	0.142699
$470$	13.1514	0.606629
$471$	−8.95937	−0.412826
$472$	10.5122	0.483864
$473$	−29.0558	−1.33599
$474$	−17.2241	−0.791130
$475$	10.2162	0.468752
$476$	−8.39652	−0.384854
$477$	−1.11479	−0.0510427
$478$	27.5209	1.25878
$479$	−17.0249	−0.777888	−0.388944	−	0.921261i	$-0.627160\pi$
$479$	−17.0249	−0.777888	−0.388944	+	0.921261i	$0.627160\pi$
$480$	−16.7506	−0.764555
$481$	0	0
$482$	−21.8933	−0.997214
$483$	14.9955	0.682321
$484$	−25.5157	−1.15981
$485$	33.0100	1.49891
$486$	−15.9215	−0.722212
$487$	3.52549	0.159755	0.0798776	−	0.996805i	$-0.474547\pi$
$487$	3.52549	0.159755	0.0798776	+	0.996805i	$0.474547\pi$
$488$	−36.6226	−1.65783
$489$	−0.499385	−0.0225830
$490$	−12.4012	−0.560231
$491$	29.9606	1.35210	0.676051	−	0.736855i	$-0.263690\pi$
$491$	29.9606	1.35210	0.676051	+	0.736855i	$0.263690\pi$
$492$	0.0510581	0.00230187
$493$	10.7088	0.482300
$494$	0	0
$495$	−37.4766	−1.68445
$496$	1.09957	0.0493722
$497$	−18.6115	−0.834839
$498$	10.9171	0.489208
$499$	−9.74284	−0.436149	−0.218075	−	0.975932i	$-0.569978\pi$
$499$	−9.74284	−0.436149	−0.218075	+	0.975932i	$0.569978\pi$
$500$	−1.66383	−0.0744088
$501$	−6.30083	−0.281500
$502$	−24.0734	−1.07445
$503$	15.7364	0.701651	0.350825	−	0.936441i	$-0.385901\pi$
$503$	15.7364	0.701651	0.350825	+	0.936441i	$0.385901\pi$
$504$	−10.2475	−0.456458
$505$	33.6786	1.49868
$506$	49.0282	2.17957
$507$	0	0
$508$	1.71926	0.0762800
$509$	−30.5793	−1.35541	−0.677703	−	0.735336i	$-0.737024\pi$
$509$	−30.5793	−1.35541	−0.677703	+	0.735336i	$0.737024\pi$
$510$	16.5629	0.733416
$511$	4.09950	0.181351
$512$	−12.0234	−0.531366
$513$	9.51376	0.420043
$514$	−3.89652	−0.171868
$515$	−24.5368	−1.08122
$516$	−4.88501	−0.215051
$517$	24.4102	1.07356
$518$	15.7199	0.690691
$519$	0.0199508	0.000875742 0
$520$	0	0
$521$	−36.3668	−1.59326	−0.796628	−	0.604469i	$-0.793385\pi$
$521$	−36.3668	−1.59326	−0.796628	+	0.604469i	$0.793385\pi$
$522$	4.28312	0.187467
$523$	−12.1385	−0.530780	−0.265390	−	0.964141i	$-0.585501\pi$
$523$	−12.1385	−0.530780	−0.265390	+	0.964141i	$0.585501\pi$
$524$	−15.4038	−0.672920
$525$	10.4329	0.455328
$526$	−27.7809	−1.21130
$527$	4.79598	0.208916
$528$	7.04824	0.306735
$529$	40.0869	1.74291
$530$	1.93274	0.0839527
$531$	6.61252	0.286959
$532$	3.23668	0.140328
$533$	0	0
$534$	−8.51469	−0.368467
$535$	32.0660	1.38633
$536$	5.18346	0.223891
$537$	5.95825	0.257118
$538$	5.05648	0.218000
$539$	−23.0179	−0.991450
$540$	−16.2775	−0.700472
$541$	−36.2301	−1.55765	−0.778826	−	0.627240i	$-0.784184\pi$
$541$	−36.2301	−1.55765	−0.778826	+	0.627240i	$0.784184\pi$
$542$	28.1655	1.20981
$543$	−16.3399	−0.701210
$544$	−23.5516	−1.00977
$545$	−19.3763	−0.829991
$546$	0	0
$547$	−4.85710	−0.207675	−0.103837	−	0.994594i	$-0.533112\pi$
$547$	−4.85710	−0.207675	−0.103837	+	0.994594i	$0.533112\pi$
$548$	−13.6750	−0.584165
$549$	−23.0368	−0.983187
$550$	34.1105	1.45448
$551$	−4.12802	−0.175860
$552$	25.1522	1.07055
$553$	−29.0570	−1.23563
$554$	−19.8409	−0.842959
$555$	29.4932	1.25192
$556$	8.65254	0.366950
$557$	−41.4847	−1.75776	−0.878882	−	0.477040i	$-0.841710\pi$
$557$	−41.4847	−1.75776	−0.878882	+	0.477040i	$0.841710\pi$
$558$	1.91821	0.0812045
$559$	0	0
$560$	6.40611	0.270708
$561$	30.7422	1.29794
$562$	9.56254	0.403371
$563$	5.12904	0.216163	0.108082	−	0.994142i	$-0.465529\pi$
$563$	5.12904	0.216163	0.108082	+	0.994142i	$0.465529\pi$
$564$	4.10397	0.172808
$565$	18.9373	0.796698
$566$	−11.3046	−0.475167
$567$	−0.491175	−0.0206274
$568$	−31.2172	−1.30984
$569$	20.7637	0.870458	0.435229	−	0.900320i	$-0.356667\pi$
$569$	20.7637	0.870458	0.435229	+	0.900320i	$0.356667\pi$
$570$	−6.38464	−0.267423
$571$	29.8037	1.24725	0.623623	−	0.781726i	$-0.285660\pi$
$571$	29.8037	1.24725	0.623623	+	0.781726i	$0.285660\pi$
$572$	0	0
$573$	7.76776	0.324503
$574$	−0.0905607	−0.00377993
$575$	43.8916	1.83041
$576$	−13.5863	−0.566098
$577$	31.5439	1.31319	0.656596	−	0.754243i	$-0.271996\pi$
$577$	31.5439	1.31319	0.656596	+	0.754243i	$0.271996\pi$
$578$	6.07615	0.252735
$579$	−4.43880	−0.184470
$580$	7.06281	0.293267
$581$	18.4171	0.764071
$582$	−10.8303	−0.448929
$583$	3.58734	0.148572
$584$	6.87612	0.284536
$585$	0	0
$586$	19.6328	0.811023
$587$	−32.0469	−1.32272	−0.661358	−	0.750071i	$-0.730019\pi$
$587$	−32.0469	−1.32272	−0.661358	+	0.750071i	$0.730019\pi$
$588$	−3.86988	−0.159591
$589$	−1.84875	−0.0761765
$590$	−11.4643	−0.471977
$591$	−7.50610	−0.308760
$592$	9.50737	0.390751
$593$	−30.8314	−1.26609	−0.633046	−	0.774114i	$-0.718196\pi$
$593$	−30.8314	−1.26609	−0.633046	+	0.774114i	$0.718196\pi$
$594$	31.7651	1.30334
$595$	27.9414	1.14549
$596$	−0.874032	−0.0358017
$597$	−18.4339	−0.754449
$598$	0	0
$599$	−29.6376	−1.21096	−0.605479	−	0.795861i	$-0.707018\pi$
$599$	−29.6376	−1.21096	−0.605479	+	0.795861i	$0.707018\pi$
$600$	17.4992	0.714401
$601$	29.7503	1.21354	0.606769	−	0.794878i	$-0.292465\pi$
$601$	29.7503	1.21354	0.606769	+	0.794878i	$0.292465\pi$
$602$	8.66445	0.353137
$603$	3.26056	0.132780
$604$	0.215793	0.00878051
$605$	84.9097	3.45207
$606$	−11.0496	−0.448861
$607$	−34.1070	−1.38436	−0.692181	−	0.721724i	$-0.743350\pi$
$607$	−34.1070	−1.38436	−0.692181	+	0.721724i	$0.743350\pi$
$608$	9.07867	0.368189
$609$	−4.21556	−0.170823
$610$	39.9394	1.61710
$611$	0	0
$612$	−8.85900	−0.358104
$613$	−23.4986	−0.949100	−0.474550	−	0.880228i	$-0.657389\pi$
$613$	−23.4986	−0.949100	−0.474550	+	0.880228i	$0.657389\pi$
$614$	−3.01550	−0.121696
$615$	−0.169908	−0.00685135
$616$	32.9758	1.32863
$617$	−13.5012	−0.543539	−0.271770	−	0.962362i	$-0.587609\pi$
$617$	−13.5012	−0.543539	−0.271770	+	0.962362i	$0.587609\pi$
$618$	8.05031	0.323831
$619$	15.3528	0.617080	0.308540	−	0.951211i	$-0.400160\pi$
$619$	15.3528	0.617080	0.308540	+	0.951211i	$0.400160\pi$
$620$	3.16311	0.127034
$621$	40.8736	1.64020
$622$	15.4043	0.617654
$623$	−14.3642	−0.575490
$624$	0	0
$625$	−22.0933	−0.883730
$626$	−6.92463	−0.276764
$627$	−11.8505	−0.473263
$628$	−8.30819	−0.331533
$629$	41.4682	1.65344
$630$	11.1755	0.445244
$631$	12.9193	0.514310	0.257155	−	0.966370i	$-0.417215\pi$
$631$	12.9193	0.514310	0.257155	+	0.966370i	$0.417215\pi$
$632$	−48.7375	−1.93867
$633$	−13.1630	−0.523181
$634$	17.5652	0.697603
$635$	−5.72126	−0.227041
$636$	0.603121	0.0239153
$637$	0	0
$638$	−13.7829	−0.545669
$639$	−19.6366	−0.776813
$640$	−8.30943	−0.328459
$641$	−37.2265	−1.47036	−0.735180	−	0.677872i	$-0.762902\pi$
$641$	−37.2265	−1.47036	−0.735180	+	0.677872i	$0.762902\pi$
$642$	−10.5206	−0.415213
$643$	24.3497	0.960259	0.480130	−	0.877198i	$-0.340590\pi$
$643$	24.3497	0.960259	0.480130	+	0.877198i	$0.340590\pi$
$644$	13.9056	0.547959
$645$	16.2560	0.640081
$646$	−8.97695	−0.353193
$647$	−24.9639	−0.981433	−0.490717	−	0.871319i	$-0.663265\pi$
$647$	−24.9639	−0.981433	−0.490717	+	0.871319i	$0.663265\pi$
$648$	−0.823852	−0.0323640
$649$	−21.2788	−0.835264
$650$	0	0
$651$	−1.88796	−0.0739949
$652$	−0.463089	−0.0181360
$653$	−2.17194	−0.0849947	−0.0424974	−	0.999097i	$-0.513531\pi$
$653$	−2.17194	−0.0849947	−0.0424974	+	0.999097i	$0.513531\pi$
$654$	6.35719	0.248586
$655$	51.2600	2.00289
$656$	−0.0547711	−0.00213845
$657$	4.32530	0.168746
$658$	−7.27913	−0.283770
$659$	3.53137	0.137563	0.0687814	−	0.997632i	$-0.478089\pi$
$659$	3.53137	0.137563	0.0687814	+	0.997632i	$0.478089\pi$
$660$	20.2755	0.789223
$661$	0.781774	0.0304075	0.0152037	−	0.999884i	$-0.495160\pi$
$661$	0.781774	0.0304075	0.0152037	+	0.999884i	$0.495160\pi$
$662$	5.89407	0.229079
$663$	0	0
$664$	30.8912	1.19881
$665$	−10.7708	−0.417675
$666$	16.5857	0.642684
$667$	−17.7351	−0.686705
$668$	−5.84288	−0.226068
$669$	−14.1705	−0.547862
$670$	−5.65291	−0.218391
$671$	74.1313	2.86181
$672$	9.27121	0.357645
$673$	39.4571	1.52096	0.760479	−	0.649362i	$-0.224964\pi$
$673$	39.4571	1.52096	0.760479	+	0.649362i	$0.224964\pi$
$674$	31.0541	1.19616
$675$	28.4371	1.09454
$676$	0	0
$677$	44.1582	1.69714	0.848569	−	0.529085i	$-0.177465\pi$
$677$	44.1582	1.69714	0.848569	+	0.529085i	$0.177465\pi$
$678$	−6.21315	−0.238615
$679$	−18.2706	−0.701161
$680$	46.8664	1.79724
$681$	22.8658	0.876219
$682$	−6.17272	−0.236366
$683$	−49.3853	−1.88967	−0.944837	−	0.327540i	$-0.893781\pi$
$683$	−49.3853	−1.88967	−0.944837	+	0.327540i	$0.893781\pi$
$684$	3.41496	0.130574
$685$	45.5067	1.73872
$686$	19.5904	0.747967
$687$	5.06894	0.193392
$688$	5.24026	0.199783
$689$	0	0
$690$	−27.4301	−1.04425
$691$	12.4149	0.472284	0.236142	−	0.971719i	$-0.424117\pi$
$691$	12.4149	0.472284	0.236142	+	0.971719i	$0.424117\pi$
$692$	0.0185007	0.000703292 0
$693$	20.7428	0.787955
$694$	−24.8611	−0.943715
$695$	−28.7934	−1.09220
$696$	−7.07081	−0.268018
$697$	−0.238894	−0.00904877
$698$	28.1855	1.06684
$699$	−30.6161	−1.15801
$700$	9.67461	0.365666
$701$	−27.1200	−1.02431	−0.512155	−	0.858893i	$-0.671153\pi$
$701$	−27.1200	−1.02431	−0.512155	+	0.858893i	$0.671153\pi$
$702$	0	0
$703$	−15.9851	−0.602890
$704$	43.7202	1.64777
$705$	−13.6569	−0.514350
$706$	−7.10642	−0.267454
$707$	−18.6406	−0.701054
$708$	−3.57749	−0.134450
$709$	9.01510	0.338569	0.169285	−	0.985567i	$-0.445854\pi$
$709$	9.01510	0.338569	0.169285	+	0.985567i	$0.445854\pi$
$710$	34.0444	1.27767
$711$	−30.6574	−1.14974
$712$	−24.0932	−0.902932
$713$	−7.94273	−0.297457
$714$	−9.16732	−0.343078
$715$	0	0
$716$	5.52520	0.206486
$717$	−28.5788	−1.06729
$718$	15.9916	0.596801
$719$	−2.03502	−0.0758934	−0.0379467	−	0.999280i	$-0.512082\pi$
$719$	−2.03502	−0.0758934	−0.0379467	+	0.999280i	$0.512082\pi$
$720$	6.75896	0.251892
$721$	13.5808	0.505776
$722$	−15.7761	−0.587125
$723$	22.7349	0.845520
$724$	−15.1523	−0.563129
$725$	−12.3389	−0.458254
$726$	−27.8581	−1.03391
$727$	−6.51447	−0.241608	−0.120804	−	0.992676i	$-0.538547\pi$
$727$	−6.51447	−0.241608	−0.120804	+	0.992676i	$0.538547\pi$
$728$	0	0
$729$	15.7129	0.581959
$730$	−7.49887	−0.277546
$731$	22.8564	0.845373
$732$	12.4633	0.460657
$733$	−3.11568	−0.115080	−0.0575402	−	0.998343i	$-0.518326\pi$
$733$	−3.11568	−0.115080	−0.0575402	+	0.998343i	$0.518326\pi$
$734$	10.4161	0.384464
$735$	12.8779	0.475010
$736$	39.0044	1.43772
$737$	−10.4923	−0.386490
$738$	−0.0955489	−0.00351720
$739$	39.1735	1.44102	0.720510	−	0.693444i	$-0.243908\pi$
$739$	39.1735	1.44102	0.720510	+	0.693444i	$0.243908\pi$
$740$	27.3496	1.00539
$741$	0	0
$742$	−1.06974	−0.0392715
$743$	−30.6791	−1.12551	−0.562753	−	0.826625i	$-0.690258\pi$
$743$	−30.6791	−1.12551	−0.562753	+	0.826625i	$0.690258\pi$
$744$	−3.16669	−0.116097
$745$	2.90855	0.106561
$746$	33.8989	1.24113
$747$	19.4315	0.710963
$748$	28.5078	1.04235
$749$	−17.7481	−0.648501
$750$	−1.81657	−0.0663318
$751$	25.5019	0.930578	0.465289	−	0.885159i	$-0.345950\pi$
$751$	25.5019	0.930578	0.465289	+	0.885159i	$0.345950\pi$
$752$	−4.40242	−0.160540
$753$	24.9988	0.911006
$754$	0	0
$755$	−0.718105	−0.0261345
$756$	9.00938	0.327668
$757$	−8.04879	−0.292538	−0.146269	−	0.989245i	$-0.546727\pi$
$757$	−8.04879	−0.292538	−0.146269	+	0.989245i	$0.546727\pi$
$758$	−31.6087	−1.14808
$759$	−50.9128	−1.84802
$760$	−18.0660	−0.655324
$761$	−52.1296	−1.88970	−0.944848	−	0.327508i	$-0.893791\pi$
$761$	−52.1296	−1.88970	−0.944848	+	0.327508i	$0.893791\pi$
$762$	1.87709	0.0679999
$763$	10.7245	0.388254
$764$	7.20319	0.260602
$765$	29.4805	1.06587
$766$	−8.66117	−0.312941
$767$	0	0
$768$	17.8049	0.642478
$769$	−3.62057	−0.130561	−0.0652806	−	0.997867i	$-0.520794\pi$
$769$	−3.62057	−0.130561	−0.0652806	+	0.997867i	$0.520794\pi$
$770$	−35.9623	−1.29599
$771$	4.04630	0.145724
$772$	−4.11619	−0.148145
$773$	−32.4020	−1.16542	−0.582710	−	0.812680i	$-0.698008\pi$
$773$	−32.4020	−1.16542	−0.582710	+	0.812680i	$0.698008\pi$
$774$	9.14170	0.328592
$775$	−5.52601	−0.198500
$776$	−30.6454	−1.10011
$777$	−16.3241	−0.585624
$778$	−38.7570	−1.38951
$779$	0.0920888	0.00329942
$780$	0	0
$781$	63.1896	2.26110
$782$	−38.5673	−1.37917
$783$	−11.4904	−0.410635
$784$	4.15130	0.148261
$785$	27.6475	0.986781
$786$	−16.8179	−0.599876
$787$	13.0411	0.464866	0.232433	−	0.972612i	$-0.425331\pi$
$787$	13.0411	0.464866	0.232433	+	0.972612i	$0.425331\pi$
$788$	−6.96055	−0.247959
$789$	28.8487	1.02704
$790$	53.1515	1.89105
$791$	−10.4815	−0.372681
$792$	34.7921	1.23628
$793$	0	0
$794$	18.3728	0.652026
$795$	−2.00703	−0.0711820
$796$	−17.0941	−0.605884
$797$	−1.44802	−0.0512914	−0.0256457	−	0.999671i	$-0.508164\pi$
$797$	−1.44802	−0.0512914	−0.0256457	+	0.999671i	$0.508164\pi$
$798$	3.53381	0.125096
$799$	−19.2020	−0.679317
$800$	27.1366	0.959424
$801$	−15.1554	−0.535490
$802$	24.0292	0.848501
$803$	−13.9186	−0.491176
$804$	−1.76402	−0.0622122
$805$	−46.2744	−1.63096
$806$	0	0
$807$	−5.25084	−0.184838
$808$	−31.2661	−1.09994
$809$	−21.8771	−0.769156	−0.384578	−	0.923092i	$-0.625653\pi$
$809$	−21.8771	−0.769156	−0.384578	+	0.923092i	$0.625653\pi$
$810$	0.898465	0.0315689
$811$	−25.9895	−0.912614	−0.456307	−	0.889822i	$-0.650828\pi$
$811$	−25.9895	−0.912614	−0.456307	+	0.889822i	$0.650828\pi$
$812$	−3.90917	−0.137185
$813$	−29.2481	−1.02578
$814$	−53.3720	−1.87069
$815$	1.54104	0.0539803
$816$	−5.54440	−0.194093
$817$	−8.81065	−0.308246
$818$	−29.8309	−1.04301
$819$	0	0
$820$	−0.157559	−0.00550219
$821$	10.0098	0.349345	0.174672	−	0.984627i	$-0.444113\pi$
$821$	10.0098	0.349345	0.174672	+	0.984627i	$0.444113\pi$
$822$	−14.9303	−0.520755
$823$	27.5363	0.959857	0.479928	−	0.877308i	$-0.340663\pi$
$823$	27.5363	0.959857	0.479928	+	0.877308i	$0.340663\pi$
$824$	22.7792	0.793551
$825$	−35.4217	−1.23322
$826$	6.34533	0.220782
$827$	−6.20407	−0.215737	−0.107868	−	0.994165i	$-0.534402\pi$
$827$	−6.20407	−0.215737	−0.107868	+	0.994165i	$0.534402\pi$
$828$	14.6716	0.509873
$829$	−47.6602	−1.65531	−0.827654	−	0.561239i	$-0.810325\pi$
$829$	−47.6602	−1.65531	−0.827654	+	0.561239i	$0.810325\pi$
$830$	−33.6889	−1.16936
$831$	20.6036	0.714729
$832$	0	0
$833$	18.1067	0.627359
$834$	9.44686	0.327118
$835$	19.4436	0.672873
$836$	−10.9892	−0.380068
$837$	−5.14604	−0.177873
$838$	25.1184	0.867701
$839$	−49.1966	−1.69846	−0.849228	−	0.528026i	$-0.822932\pi$
$839$	−49.1966	−1.69846	−0.849228	+	0.528026i	$0.822932\pi$
$840$	−18.4492	−0.636557
$841$	−24.0143	−0.828079
$842$	0.194291	0.00669571
$843$	−9.93011	−0.342011
$844$	−12.2063	−0.420157
$845$	0	0
$846$	−7.68007	−0.264046
$847$	−46.9964	−1.61481
$848$	−0.646981	−0.0222174
$849$	11.7391	0.402885
$850$	−26.8325	−0.920349
$851$	−68.6763	−2.35419
$852$	10.6237	0.363964
$853$	−38.1893	−1.30758	−0.653789	−	0.756677i	$-0.726821\pi$
$853$	−38.1893	−1.30758	−0.653789	+	0.756677i	$0.726821\pi$
$854$	−22.1059	−0.756450
$855$	−11.3641	−0.388644
$856$	−29.7690	−1.01749
$857$	18.2224	0.622466	0.311233	−	0.950334i	$-0.399258\pi$
$857$	18.2224	0.622466	0.311233	+	0.950334i	$0.399258\pi$
$858$	0	0
$859$	22.2461	0.759028	0.379514	−	0.925186i	$-0.376091\pi$
$859$	22.2461	0.759028	0.379514	+	0.925186i	$0.376091\pi$
$860$	15.0745	0.514037
$861$	0.0940418	0.00320494
$862$	−15.2508	−0.519444
$863$	−9.63571	−0.328003	−0.164002	−	0.986460i	$-0.552440\pi$
$863$	−9.63571	−0.328003	−0.164002	+	0.986460i	$0.552440\pi$
$864$	25.2707	0.859727
$865$	−0.0615656	−0.00209329
$866$	−13.0165	−0.442319
$867$	−6.30972	−0.214289
$868$	−1.75074	−0.0594240
$869$	98.6541	3.34661
$870$	7.71118	0.261434
$871$	0	0
$872$	17.9884	0.609163
$873$	−19.2770	−0.652426
$874$	14.8669	0.502881
$875$	−3.06454	−0.103600
$876$	−2.34006	−0.0790634
$877$	29.0418	0.980672	0.490336	−	0.871534i	$-0.336874\pi$
$877$	29.0418	0.980672	0.490336	+	0.871534i	$0.336874\pi$
$878$	0.568656	0.0191912
$879$	−20.3875	−0.687652
$880$	−21.7500	−0.733192
$881$	−24.1421	−0.813368	−0.406684	−	0.913569i	$-0.633315\pi$
$881$	−24.1421	−0.813368	−0.406684	+	0.913569i	$0.633315\pi$
$882$	7.24200	0.243851
$883$	−6.46930	−0.217709	−0.108855	−	0.994058i	$-0.534718\pi$
$883$	−6.46930	−0.217709	−0.108855	+	0.994058i	$0.534718\pi$
$884$	0	0
$885$	11.9050	0.400181
$886$	−10.1810	−0.342036
$887$	−14.4837	−0.486315	−0.243158	−	0.969987i	$-0.578183\pi$
$887$	−14.4837	−0.486315	−0.243158	+	0.969987i	$0.578183\pi$
$888$	−27.3806	−0.918832
$889$	3.16664	0.106206
$890$	26.2753	0.880750
$891$	1.66763	0.0558679
$892$	−13.1405	−0.439978
$893$	7.40196	0.247697
$894$	−0.954269	−0.0319155
$895$	−18.3864	−0.614590
$896$	4.59916	0.153647
$897$	0	0
$898$	15.6864	0.523463
$899$	2.23287	0.0744704
$900$	10.2075	0.340250
$901$	−2.82193	−0.0940120
$902$	0.307471	0.0102377
$903$	−8.99751	−0.299418
$904$	−17.5808	−0.584728
$905$	50.4228	1.67611
$906$	0.235604	0.00782740
$907$	−33.0392	−1.09705	−0.548525	−	0.836134i	$-0.684810\pi$
$907$	−33.0392	−1.09705	−0.548525	+	0.836134i	$0.684810\pi$
$908$	21.2039	0.703675
$909$	−19.6674	−0.652326
$910$	0	0
$911$	−42.4959	−1.40795	−0.703975	−	0.710225i	$-0.748593\pi$
$911$	−42.4959	−1.40795	−0.703975	+	0.710225i	$0.748593\pi$
$912$	2.13725	0.0707714
$913$	−62.5297	−2.06943
$914$	22.8016	0.754211
$915$	−41.4747	−1.37111
$916$	4.70052	0.155310
$917$	−28.3717	−0.936916
$918$	−24.9875	−0.824712
$919$	5.17140	0.170589	0.0852944	−	0.996356i	$-0.472817\pi$
$919$	5.17140	0.170589	0.0852944	+	0.996356i	$0.472817\pi$
$920$	−77.6164	−2.55894
$921$	3.13141	0.103184
$922$	12.1204	0.399164
$923$	0	0
$924$	−11.2222	−0.369184
$925$	−47.7803	−1.57101
$926$	43.0236	1.41384
$927$	14.3288	0.470621
$928$	−10.9650	−0.359942
$929$	4.37621	0.143579	0.0717894	−	0.997420i	$-0.477129\pi$
$929$	4.37621	0.143579	0.0717894	+	0.997420i	$0.477129\pi$
$930$	3.45349	0.113244
$931$	−6.97975	−0.228752
$932$	−28.3909	−0.929974
$933$	−15.9964	−0.523698
$934$	−35.7091	−1.16844
$935$	−94.8666	−3.10247
$936$	0	0
$937$	2.77193	0.0905550	0.0452775	−	0.998974i	$-0.485583\pi$
$937$	2.77193	0.0905550	0.0452775	+	0.998974i	$0.485583\pi$
$938$	3.12881	0.102159
$939$	7.19080	0.234663
$940$	−12.6643	−0.413065
$941$	36.3782	1.18589	0.592947	−	0.805241i	$-0.297964\pi$
$941$	36.3782	1.18589	0.592947	+	0.805241i	$0.297964\pi$
$942$	−9.07089	−0.295545
$943$	0.395638	0.0128837
$944$	3.83765	0.124905
$945$	−29.9809	−0.975278
$946$	−29.4175	−0.956446
$947$	−28.0675	−0.912071	−0.456035	−	0.889962i	$-0.650731\pi$
$947$	−28.0675	−0.912071	−0.456035	+	0.889962i	$0.650731\pi$
$948$	16.5862	0.538695
$949$	0	0
$950$	10.3434	0.335584
$951$	−18.2404	−0.591485
$952$	−25.9399	−0.840718
$953$	−47.1931	−1.52874	−0.764368	−	0.644781i	$-0.776949\pi$
$953$	−47.1931	−1.52874	−0.764368	+	0.644781i	$0.776949\pi$
$954$	−1.12867	−0.0365419
$955$	−23.9703	−0.775662
$956$	−26.5016	−0.857124
$957$	14.3127	0.462663
$958$	−17.2368	−0.556896
$959$	−25.1873	−0.813342
$960$	−24.4604	−0.789456
$961$	1.00000	0.0322581
$962$	0	0
$963$	−18.7257	−0.603427
$964$	21.0825	0.679022
$965$	13.6976	0.440941
$966$	15.1822	0.488479
$967$	−19.0739	−0.613375	−0.306688	−	0.951810i	$-0.599221\pi$
$967$	−19.0739	−0.613375	−0.306688	+	0.951810i	$0.599221\pi$
$968$	−78.8275	−2.53361
$969$	9.32201	0.299466
$970$	33.4209	1.07308
$971$	56.9080	1.82626	0.913132	−	0.407664i	$-0.133656\pi$
$971$	56.9080	1.82626	0.913132	+	0.407664i	$0.133656\pi$
$972$	15.3318	0.491767
$973$	15.9368	0.510909
$974$	3.56937	0.114370
$975$	0	0
$976$	−13.3697	−0.427953
$977$	34.4785	1.10307	0.551533	−	0.834153i	$-0.314043\pi$
$977$	34.4785	1.10307	0.551533	+	0.834153i	$0.314043\pi$
$978$	−0.505601	−0.0161673
$979$	48.7694	1.55868
$980$	11.9420	0.381472
$981$	11.3153	0.361268
$982$	30.3335	0.967981
$983$	33.5510	1.07011	0.535056	−	0.844817i	$-0.320291\pi$
$983$	33.5510	1.07011	0.535056	+	0.844817i	$0.320291\pi$
$984$	0.157737	0.00502848
$985$	23.1629	0.738031
$986$	10.8421	0.345283
$987$	7.55893	0.240604
$988$	0	0
$989$	−37.8529	−1.20365
$990$	−37.9431	−1.20591
$991$	0.204273	0.00648894	0.00324447	−	0.999995i	$-0.498967\pi$
$991$	0.204273	0.00648894	0.00324447	+	0.999995i	$0.498967\pi$
$992$	−4.91070	−0.155915
$993$	−6.12063	−0.194232
$994$	−18.8431	−0.597668
$995$	56.8847	1.80337
$996$	−10.5128	−0.333111
$997$	−36.7937	−1.16527	−0.582634	−	0.812735i	$-0.697978\pi$
$997$	−36.7937	−1.16527	−0.582634	+	0.812735i	$0.697978\pi$
$998$	−9.86411	−0.312243
$999$	−44.4949	−1.40776

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.l.1.10		16
13.5	odd	4		403.2.c.b.311.12	✓	32
13.8	odd	4		403.2.c.b.311.21	yes	32
13.12	even	2		5239.2.a.k.1.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.c.b.311.12	✓	32	13.5	odd	4
403.2.c.b.311.21	yes	32	13.8	odd	4
5239.2.a.k.1.7		16	13.12	even	2
5239.2.a.l.1.10		16	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:	\( N \)	\(=\)	\( 5239 = 13^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5239.a (trivial)

\(f(q)\)	\(=\)	\(q+1.01245 q^{2} -1.05136 q^{3} -0.974950 q^{4} +3.24438 q^{5} -1.06445 q^{6} -1.79572 q^{7} -3.01198 q^{8} -1.89463 q^{9} +O(q^{10})\)	\(q+1.01245 q^{2} -1.05136 q^{3} -0.974950 q^{4} +3.24438 q^{5} -1.06445 q^{6} -1.79572 q^{7} -3.01198 q^{8} -1.89463 q^{9} +3.28477 q^{10} +6.09683 q^{11} +1.02503 q^{12} -1.81807 q^{14} -3.41103 q^{15} -1.09957 q^{16} -4.79598 q^{17} -1.91821 q^{18} +1.84875 q^{19} -3.16311 q^{20} +1.88796 q^{21} +6.17272 q^{22} +7.94273 q^{23} +3.16669 q^{24} +5.52601 q^{25} +5.14604 q^{27} +1.75074 q^{28} -2.23287 q^{29} -3.45349 q^{30} -1.00000 q^{31} +4.91070 q^{32} -6.40999 q^{33} -4.85568 q^{34} -5.82601 q^{35} +1.84717 q^{36} -8.64644 q^{37} +1.87176 q^{38} -9.77201 q^{40} +0.0498113 q^{41} +1.91146 q^{42} -4.76573 q^{43} -5.94410 q^{44} -6.14691 q^{45} +8.04159 q^{46} +4.00376 q^{47} +1.15605 q^{48} -3.77538 q^{49} +5.59480 q^{50} +5.04233 q^{51} +0.588394 q^{53} +5.21010 q^{54} +19.7804 q^{55} +5.40868 q^{56} -1.94371 q^{57} -2.26066 q^{58} -3.49014 q^{59} +3.32558 q^{60} +12.1590 q^{61} -1.01245 q^{62} +3.40223 q^{63} +7.17097 q^{64} -6.48978 q^{66} -1.72095 q^{67} +4.67585 q^{68} -8.35070 q^{69} -5.89852 q^{70} +10.3643 q^{71} +5.70659 q^{72} -2.28292 q^{73} -8.75406 q^{74} -5.80985 q^{75} -1.80244 q^{76} -10.9482 q^{77} +16.1812 q^{79} -3.56743 q^{80} +0.273525 q^{81} +0.0504314 q^{82} -10.2561 q^{83} -1.84067 q^{84} -15.5600 q^{85} -4.82505 q^{86} +2.34756 q^{87} -18.3635 q^{88} +7.99914 q^{89} -6.22342 q^{90} -7.74376 q^{92} +1.05136 q^{93} +4.05360 q^{94} +5.99805 q^{95} -5.16294 q^{96} +10.1745 q^{97} -3.82238 q^{98} -11.5512 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 2 q^{3} + 18 q^{4} + 4 q^{5} + 6 q^{6} + 2 q^{7} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 2 * q^3 + 18 * q^4 + 4 * q^5 + 6 * q^6 + 2 * q^7 + 12 * q^8 + 10 * q^9	\( 16 q + 4 q^{2} - 2 q^{3} + 18 q^{4} + 4 q^{5} + 6 q^{6} + 2 q^{7} + 12 q^{8} + 10 q^{9} - 2 q^{10} + 14 q^{11} + 8 q^{12} - 8 q^{14} + 14 q^{16} + 4 q^{17} - 28 q^{18} + 22 q^{19} + 28 q^{20} + 12 q^{21} - 8 q^{22} + 4 q^{23} - 8 q^{24} - 2 q^{25} + 10 q^{27} + 16 q^{28} - 8 q^{29} - 20 q^{30} - 16 q^{31} + 48 q^{32} + 10 q^{33} + 8 q^{34} - 2 q^{35} + 22 q^{36} + 16 q^{37} - 6 q^{38} + 14 q^{40} + 44 q^{41} + 14 q^{42} + 16 q^{43} + 4 q^{44} + 56 q^{45} + 10 q^{47} + 32 q^{49} + 2 q^{50} - 6 q^{53} + 24 q^{54} + 22 q^{55} - 4 q^{56} - 8 q^{57} + 74 q^{58} + 2 q^{59} + 40 q^{60} + 8 q^{61} - 4 q^{62} + 56 q^{63} + 38 q^{64} - 34 q^{66} - 8 q^{67} + 32 q^{68} - 10 q^{69} - 108 q^{70} + 50 q^{71} - 44 q^{72} + 14 q^{73} + 8 q^{74} + 44 q^{76} + 16 q^{77} + 32 q^{79} + 68 q^{80} - 8 q^{81} - 6 q^{82} - 20 q^{83} + 136 q^{84} - 32 q^{85} + 8 q^{86} - 36 q^{87} - 40 q^{88} + 52 q^{89} - 34 q^{90} + 14 q^{92} + 2 q^{93} + 44 q^{94} - 2 q^{95} - 80 q^{96} + 18 q^{97} + 12 q^{98} + 38 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 2 * q^3 + 18 * q^4 + 4 * q^5 + 6 * q^6 + 2 * q^7 + 12 * q^8 + 10 * q^9 - 2 * q^10 + 14 * q^11 + 8 * q^12 - 8 * q^14 + 14 * q^16 + 4 * q^17 - 28 * q^18 + 22 * q^19 + 28 * q^20 + 12 * q^21 - 8 * q^22 + 4 * q^23 - 8 * q^24 - 2 * q^25 + 10 * q^27 + 16 * q^28 - 8 * q^29 - 20 * q^30 - 16 * q^31 + 48 * q^32 + 10 * q^33 + 8 * q^34 - 2 * q^35 + 22 * q^36 + 16 * q^37 - 6 * q^38 + 14 * q^40 + 44 * q^41 + 14 * q^42 + 16 * q^43 + 4 * q^44 + 56 * q^45 + 10 * q^47 + 32 * q^49 + 2 * q^50 - 6 * q^53 + 24 * q^54 + 22 * q^55 - 4 * q^56 - 8 * q^57 + 74 * q^58 + 2 * q^59 + 40 * q^60 + 8 * q^61 - 4 * q^62 + 56 * q^63 + 38 * q^64 - 34 * q^66 - 8 * q^67 + 32 * q^68 - 10 * q^69 - 108 * q^70 + 50 * q^71 - 44 * q^72 + 14 * q^73 + 8 * q^74 + 44 * q^76 + 16 * q^77 + 32 * q^79 + 68 * q^80 - 8 * q^81 - 6 * q^82 - 20 * q^83 + 136 * q^84 - 32 * q^85 + 8 * q^86 - 36 * q^87 - 40 * q^88 + 52 * q^89 - 34 * q^90 + 14 * q^92 + 2 * q^93 + 44 * q^94 - 2 * q^95 - 80 * q^96 + 18 * q^97 + 12 * q^98 + 38 * q^99

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