LMFDB - Embedded newform 4641.2.a.ba.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4641,2,Mod(1,4641)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4641, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4641.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4641 = 3 \cdot 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4641.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:	$37.0585715781$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - x^{16} - 29 x^{15} + 26 x^{14} + 339 x^{13} - 266 x^{12} - 2047 x^{11} + 1356 x^{10} + \cdots + 18 $ x^17 - x^16 - 29x^15 + 26x^14 + 339x^13 - 266x^12 - 2047x^11 + 1356x^10 + 6792x^9 - 3573x^8 - 12125x^7 + 4456x^6 + 10521x^5 - 1858x^4 - 3551x^3 + 34x^2 + 323*x + 18
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$0.744396$ of defining polynomial
Character	$\chi$	$=$	4641.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.744396 q^{2} -1.00000 q^{3} -1.44587 q^{4} -1.18048 q^{5} -0.744396 q^{6} -1.00000 q^{7} -2.56510 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.744396 q^{2} -1.00000 q^{3} -1.44587 q^{4} -1.18048 q^{5} -0.744396 q^{6} -1.00000 q^{7} -2.56510 q^{8} +1.00000 q^{9} -0.878746 q^{10} -6.27171 q^{11} +1.44587 q^{12} +1.00000 q^{13} -0.744396 q^{14} +1.18048 q^{15} +0.982303 q^{16} -1.00000 q^{17} +0.744396 q^{18} -1.31201 q^{19} +1.70683 q^{20} +1.00000 q^{21} -4.66863 q^{22} +0.460825 q^{23} +2.56510 q^{24} -3.60646 q^{25} +0.744396 q^{26} -1.00000 q^{27} +1.44587 q^{28} -7.69176 q^{29} +0.878746 q^{30} -1.78367 q^{31} +5.86141 q^{32} +6.27171 q^{33} -0.744396 q^{34} +1.18048 q^{35} -1.44587 q^{36} -10.5278 q^{37} -0.976654 q^{38} -1.00000 q^{39} +3.02805 q^{40} -3.80452 q^{41} +0.744396 q^{42} +5.96073 q^{43} +9.06810 q^{44} -1.18048 q^{45} +0.343036 q^{46} -12.5400 q^{47} -0.982303 q^{48} +1.00000 q^{49} -2.68464 q^{50} +1.00000 q^{51} -1.44587 q^{52} -8.11622 q^{53} -0.744396 q^{54} +7.40364 q^{55} +2.56510 q^{56} +1.31201 q^{57} -5.72571 q^{58} -10.9399 q^{59} -1.70683 q^{60} +5.06772 q^{61} -1.32776 q^{62} -1.00000 q^{63} +2.39860 q^{64} -1.18048 q^{65} +4.66863 q^{66} -10.2881 q^{67} +1.44587 q^{68} -0.460825 q^{69} +0.878746 q^{70} +9.69952 q^{71} -2.56510 q^{72} +4.12330 q^{73} -7.83682 q^{74} +3.60646 q^{75} +1.89700 q^{76} +6.27171 q^{77} -0.744396 q^{78} +16.4197 q^{79} -1.15959 q^{80} +1.00000 q^{81} -2.83207 q^{82} +16.8207 q^{83} -1.44587 q^{84} +1.18048 q^{85} +4.43714 q^{86} +7.69176 q^{87} +16.0875 q^{88} +13.5138 q^{89} -0.878746 q^{90} -1.00000 q^{91} -0.666295 q^{92} +1.78367 q^{93} -9.33475 q^{94} +1.54880 q^{95} -5.86141 q^{96} +2.33389 q^{97} +0.744396 q^{98} -6.27171 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9}+O(q^{10}) $ 17 * q + q^2 - 17 * q^3 + 25 * q^4 - 4 * q^5 - q^6 - 17 * q^7 + 6 * q^8 + 17 * q^9	\( 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9} - q^{10} + 4 q^{11} - 25 q^{12} + 17 q^{13} - q^{14} + 4 q^{15} + 53 q^{16} - 17 q^{17} + q^{18} + 13 q^{19} - 5 q^{20} + 17 q^{21} + 4 q^{22} + 8 q^{23} - 6 q^{24} + 37 q^{25} + q^{26} - 17 q^{27} - 25 q^{28} - 3 q^{29} + q^{30} + 10 q^{31} + 18 q^{32} - 4 q^{33} - q^{34} + 4 q^{35} + 25 q^{36} - 25 q^{38} - 17 q^{39} - 12 q^{41} + q^{42} + 29 q^{43} + 12 q^{44} - 4 q^{45} + 19 q^{46} - 4 q^{47} - 53 q^{48} + 17 q^{49} + 9 q^{50} + 17 q^{51} + 25 q^{52} - 8 q^{53} - q^{54} + 27 q^{55} - 6 q^{56} - 13 q^{57} + 2 q^{58} + 25 q^{59} + 5 q^{60} - 5 q^{61} - 37 q^{62} - 17 q^{63} + 94 q^{64} - 4 q^{65} - 4 q^{66} + 15 q^{67} - 25 q^{68} - 8 q^{69} + q^{70} + 32 q^{71} + 6 q^{72} - 15 q^{73} + 16 q^{74} - 37 q^{75} + 3 q^{76} - 4 q^{77} - q^{78} + 27 q^{79} + 41 q^{80} + 17 q^{81} - 8 q^{82} - 24 q^{83} + 25 q^{84} + 4 q^{85} + 53 q^{86} + 3 q^{87} - 9 q^{88} - 8 q^{89} - q^{90} - 17 q^{91} + 14 q^{92} - 10 q^{93} + 51 q^{94} - 9 q^{95} - 18 q^{96} - 22 q^{97} + q^{98} + 4 q^{99}+O(q^{100}) \) 17 * q + q^2 - 17 * q^3 + 25 * q^4 - 4 * q^5 - q^6 - 17 * q^7 + 6 * q^8 + 17 * q^9 - q^10 + 4 * q^11 - 25 * q^12 + 17 * q^13 - q^14 + 4 * q^15 + 53 * q^16 - 17 * q^17 + q^18 + 13 * q^19 - 5 * q^20 + 17 * q^21 + 4 * q^22 + 8 * q^23 - 6 * q^24 + 37 * q^25 + q^26 - 17 * q^27 - 25 * q^28 - 3 * q^29 + q^30 + 10 * q^31 + 18 * q^32 - 4 * q^33 - q^34 + 4 * q^35 + 25 * q^36 - 25 * q^38 - 17 * q^39 - 12 * q^41 + q^42 + 29 * q^43 + 12 * q^44 - 4 * q^45 + 19 * q^46 - 4 * q^47 - 53 * q^48 + 17 * q^49 + 9 * q^50 + 17 * q^51 + 25 * q^52 - 8 * q^53 - q^54 + 27 * q^55 - 6 * q^56 - 13 * q^57 + 2 * q^58 + 25 * q^59 + 5 * q^60 - 5 * q^61 - 37 * q^62 - 17 * q^63 + 94 * q^64 - 4 * q^65 - 4 * q^66 + 15 * q^67 - 25 * q^68 - 8 * q^69 + q^70 + 32 * q^71 + 6 * q^72 - 15 * q^73 + 16 * q^74 - 37 * q^75 + 3 * q^76 - 4 * q^77 - q^78 + 27 * q^79 + 41 * q^80 + 17 * q^81 - 8 * q^82 - 24 * q^83 + 25 * q^84 + 4 * q^85 + 53 * q^86 + 3 * q^87 - 9 * q^88 - 8 * q^89 - q^90 - 17 * q^91 + 14 * q^92 - 10 * q^93 + 51 * q^94 - 9 * q^95 - 18 * q^96 - 22 * q^97 + q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.744396	0.526367	0.263184	−	0.964746i	$-0.415227\pi$
$2$	0.744396	0.526367	0.263184	+	0.964746i	$0.415227\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.44587	−0.722937
$5$	−1.18048	−0.527928	−0.263964	−	0.964533i	$-0.585030\pi$
$5$	−1.18048	−0.527928	−0.263964	+	0.964533i	$0.585030\pi$
$6$	−0.744396	−0.303898
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.56510	−0.906898
$9$	1.00000	0.333333
$10$	−0.878746	−0.277884
$11$	−6.27171	−1.89099	−0.945496	−	0.325635i	$-0.894422\pi$
$11$	−6.27171	−1.89099	−0.945496	+	0.325635i	$0.894422\pi$
$12$	1.44587	0.417388
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.744396	−0.198948
$15$	1.18048	0.304799
$16$	0.982303	0.245576
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.744396	0.175456
$19$	−1.31201	−0.300995	−0.150498	−	0.988610i	$-0.548088\pi$
$19$	−1.31201	−0.300995	−0.150498	+	0.988610i	$0.548088\pi$
$20$	1.70683	0.381659
$21$	1.00000	0.218218
$22$	−4.66863	−0.995356
$23$	0.460825	0.0960886	0.0480443	−	0.998845i	$-0.484701\pi$
$23$	0.460825	0.0960886	0.0480443	+	0.998845i	$0.484701\pi$
$24$	2.56510	0.523598
$25$	−3.60646	−0.721292
$26$	0.744396	0.145988
$27$	−1.00000	−0.192450
$28$	1.44587	0.273245
$29$	−7.69176	−1.42832	−0.714162	−	0.699981i	$-0.753192\pi$
$29$	−7.69176	−1.42832	−0.714162	+	0.699981i	$0.753192\pi$
$30$	0.878746	0.160436
$31$	−1.78367	−0.320357	−0.160178	−	0.987088i	$-0.551207\pi$
$31$	−1.78367	−0.320357	−0.160178	+	0.987088i	$0.551207\pi$
$32$	5.86141	1.03616
$33$	6.27171	1.09176
$34$	−0.744396	−0.127663
$35$	1.18048	0.199538
$36$	−1.44587	−0.240979
$37$	−10.5278	−1.73075	−0.865376	−	0.501123i	$-0.832920\pi$
$37$	−10.5278	−1.73075	−0.865376	+	0.501123i	$0.832920\pi$
$38$	−0.976654	−0.158434
$39$	−1.00000	−0.160128
$40$	3.02805	0.478777
$41$	−3.80452	−0.594166	−0.297083	−	0.954852i	$-0.596014\pi$
$41$	−3.80452	−0.594166	−0.297083	+	0.954852i	$0.596014\pi$
$42$	0.744396	0.114863
$43$	5.96073	0.909002	0.454501	−	0.890746i	$-0.349818\pi$
$43$	5.96073	0.909002	0.454501	+	0.890746i	$0.349818\pi$
$44$	9.06810	1.36707
$45$	−1.18048	−0.175976
$46$	0.343036	0.0505779
$47$	−12.5400	−1.82915	−0.914576	−	0.404414i	$-0.867476\pi$
$47$	−12.5400	−1.82915	−0.914576	+	0.404414i	$0.867476\pi$
$48$	−0.982303	−0.141783
$49$	1.00000	0.142857
$50$	−2.68464	−0.379665
$51$	1.00000	0.140028
$52$	−1.44587	−0.200507
$53$	−8.11622	−1.11485	−0.557424	−	0.830228i	$-0.688210\pi$
$53$	−8.11622	−1.11485	−0.557424	+	0.830228i	$0.688210\pi$
$54$	−0.744396	−0.101299
$55$	7.40364	0.998306
$56$	2.56510	0.342775
$57$	1.31201	0.173780
$58$	−5.72571	−0.751823
$59$	−10.9399	−1.42426	−0.712129	−	0.702049i	$-0.752269\pi$
$59$	−10.9399	−1.42426	−0.712129	+	0.702049i	$0.752269\pi$
$60$	−1.70683	−0.220351
$61$	5.06772	0.648855	0.324428	−	0.945911i	$-0.394828\pi$
$61$	5.06772	0.648855	0.324428	+	0.945911i	$0.394828\pi$
$62$	−1.32776	−0.168625
$63$	−1.00000	−0.125988
$64$	2.39860	0.299826
$65$	−1.18048	−0.146421
$66$	4.66863	0.574669
$67$	−10.2881	−1.25689	−0.628447	−	0.777852i	$-0.716309\pi$
$67$	−10.2881	−1.25689	−0.628447	+	0.777852i	$0.716309\pi$
$68$	1.44587	0.175338
$69$	−0.460825	−0.0554768
$70$	0.878746	0.105030
$71$	9.69952	1.15112	0.575560	−	0.817759i	$-0.304784\pi$
$71$	9.69952	1.15112	0.575560	+	0.817759i	$0.304784\pi$
$72$	−2.56510	−0.302299
$73$	4.12330	0.482596	0.241298	−	0.970451i	$-0.422427\pi$
$73$	4.12330	0.482596	0.241298	+	0.970451i	$0.422427\pi$
$74$	−7.83682	−0.911011
$75$	3.60646	0.416438
$76$	1.89700	0.217601
$77$	6.27171	0.714728
$78$	−0.744396	−0.0842862
$79$	16.4197	1.84736	0.923679	−	0.383167i	$-0.125166\pi$
$79$	16.4197	1.84736	0.923679	+	0.383167i	$0.125166\pi$
$80$	−1.15959	−0.129646
$81$	1.00000	0.111111
$82$	−2.83207	−0.312749
$83$	16.8207	1.84631	0.923157	−	0.384423i	$-0.125600\pi$
$83$	16.8207	1.84631	0.923157	+	0.384423i	$0.125600\pi$
$84$	−1.44587	−0.157758
$85$	1.18048	0.128041
$86$	4.43714	0.478469
$87$	7.69176	0.824643
$88$	16.0875	1.71494
$89$	13.5138	1.43246	0.716231	−	0.697863i	$-0.245866\pi$
$89$	13.5138	1.43246	0.716231	+	0.697863i	$0.245866\pi$
$90$	−0.878746	−0.0926280
$91$	−1.00000	−0.104828
$92$	−0.666295	−0.0694660
$93$	1.78367	0.184958
$94$	−9.33475	−0.962806
$95$	1.54880	0.158904
$96$	−5.86141	−0.598228
$97$	2.33389	0.236971	0.118486	−	0.992956i	$-0.462196\pi$
$97$	2.33389	0.236971	0.118486	+	0.992956i	$0.462196\pi$
$98$	0.744396	0.0751953
$99$	−6.27171	−0.630330
$100$	5.21449	0.521449
$101$	6.06056	0.603048	0.301524	−	0.953459i	$-0.402505\pi$
$101$	6.06056	0.603048	0.301524	+	0.953459i	$0.402505\pi$
$102$	0.744396	0.0737062
$103$	−0.783469	−0.0771975	−0.0385987	−	0.999255i	$-0.512289\pi$
$103$	−0.783469	−0.0771975	−0.0385987	+	0.999255i	$0.512289\pi$
$104$	−2.56510	−0.251528
$105$	−1.18048	−0.115203
$106$	−6.04168	−0.586820
$107$	−14.6112	−1.41252	−0.706261	−	0.707952i	$-0.749619\pi$
$107$	−14.6112	−1.41252	−0.706261	+	0.707952i	$0.749619\pi$
$108$	1.44587	0.139129
$109$	−11.0990	−1.06310	−0.531548	−	0.847028i	$-0.678389\pi$
$109$	−11.0990	−1.06310	−0.531548	+	0.847028i	$0.678389\pi$
$110$	5.51124	0.525476
$111$	10.5278	0.999250
$112$	−0.982303	−0.0928189
$113$	−8.85807	−0.833297	−0.416648	−	0.909068i	$-0.636795\pi$
$113$	−8.85807	−0.833297	−0.416648	+	0.909068i	$0.636795\pi$
$114$	0.976654	0.0914720
$115$	−0.543995	−0.0507278
$116$	11.1213	1.03259
$117$	1.00000	0.0924500
$118$	−8.14364	−0.749683
$119$	1.00000	0.0916698
$120$	−3.02805	−0.276422
$121$	28.3343	2.57585
$122$	3.77239	0.341536
$123$	3.80452	0.343042
$124$	2.57897	0.231598
$125$	10.1598	0.908718
$126$	−0.744396	−0.0663161
$127$	12.6979	1.12676	0.563380	−	0.826198i	$-0.309501\pi$
$127$	12.6979	1.12676	0.563380	+	0.826198i	$0.309501\pi$
$128$	−9.93731	−0.878343
$129$	−5.96073	−0.524813
$130$	−0.878746	−0.0770711
$131$	−18.6214	−1.62696	−0.813479	−	0.581594i	$-0.802429\pi$
$131$	−18.6214	−1.62696	−0.813479	+	0.581594i	$0.802429\pi$
$132$	−9.06810	−0.789277
$133$	1.31201	0.113766
$134$	−7.65844	−0.661588
$135$	1.18048	0.101600
$136$	2.56510	0.219955
$137$	−7.61513	−0.650604	−0.325302	−	0.945610i	$-0.605466\pi$
$137$	−7.61513	−0.650604	−0.325302	+	0.945610i	$0.605466\pi$
$138$	−0.343036	−0.0292012
$139$	13.1654	1.11667	0.558337	−	0.829614i	$-0.311440\pi$
$139$	13.1654	1.11667	0.558337	+	0.829614i	$0.311440\pi$
$140$	−1.70683	−0.144253
$141$	12.5400	1.05606
$142$	7.22028	0.605912
$143$	−6.27171	−0.524467
$144$	0.982303	0.0818586
$145$	9.07998	0.754051
$146$	3.06937	0.254023
$147$	−1.00000	−0.0824786
$148$	15.2218	1.25123
$149$	−1.13409	−0.0929087	−0.0464543	−	0.998920i	$-0.514792\pi$
$149$	−1.13409	−0.0929087	−0.0464543	+	0.998920i	$0.514792\pi$
$150$	2.68464	0.219200
$151$	5.91099	0.481030	0.240515	−	0.970645i	$-0.422684\pi$
$151$	5.91099	0.481030	0.240515	+	0.970645i	$0.422684\pi$
$152$	3.36543	0.272972
$153$	−1.00000	−0.0808452
$154$	4.66863	0.376209
$155$	2.10559	0.169125
$156$	1.44587	0.115763
$157$	6.23902	0.497928	0.248964	−	0.968513i	$-0.419910\pi$
$157$	6.23902	0.497928	0.248964	+	0.968513i	$0.419910\pi$
$158$	12.2227	0.972389
$159$	8.11622	0.643658
$160$	−6.91929	−0.547018
$161$	−0.460825	−0.0363181
$162$	0.744396	0.0584853
$163$	14.6918	1.15075	0.575374	−	0.817890i	$-0.304856\pi$
$163$	14.6918	1.15075	0.575374	+	0.817890i	$0.304856\pi$
$164$	5.50085	0.429545
$165$	−7.40364	−0.576373
$166$	12.5213	0.971839
$167$	13.4860	1.04357	0.521787	−	0.853076i	$-0.325265\pi$
$167$	13.4860	1.04357	0.521787	+	0.853076i	$0.325265\pi$
$168$	−2.56510	−0.197901
$169$	1.00000	0.0769231
$170$	0.878746	0.0673967
$171$	−1.31201	−0.100332
$172$	−8.61846	−0.657152
$173$	−15.1146	−1.14914	−0.574571	−	0.818455i	$-0.694831\pi$
$173$	−15.1146	−1.14914	−0.574571	+	0.818455i	$0.694831\pi$
$174$	5.72571	0.434065
$175$	3.60646	0.272623
$176$	−6.16072	−0.464382
$177$	10.9399	0.822295
$178$	10.0596	0.754002
$179$	12.2013	0.911968	0.455984	−	0.889988i	$-0.349288\pi$
$179$	12.2013	0.911968	0.455984	+	0.889988i	$0.349288\pi$
$180$	1.70683	0.127220
$181$	−13.2827	−0.987294	−0.493647	−	0.869663i	$-0.664336\pi$
$181$	−13.2827	−0.987294	−0.493647	+	0.869663i	$0.664336\pi$
$182$	−0.744396	−0.0551783
$183$	−5.06772	−0.374617
$184$	−1.18206	−0.0871426
$185$	12.4278	0.913712
$186$	1.32776	0.0973560
$187$	6.27171	0.458633
$188$	18.1313	1.32236
$189$	1.00000	0.0727393
$190$	1.15292	0.0836418
$191$	24.3164	1.75947	0.879737	−	0.475462i	$-0.157719\pi$
$191$	24.3164	1.75947	0.879737	+	0.475462i	$0.157719\pi$
$192$	−2.39860	−0.173104
$193$	−16.9799	−1.22224	−0.611119	−	0.791539i	$-0.709280\pi$
$193$	−16.9799	−1.22224	−0.611119	+	0.791539i	$0.709280\pi$
$194$	1.73734	0.124734
$195$	1.18048	0.0845361
$196$	−1.44587	−0.103277
$197$	4.76410	0.339428	0.169714	−	0.985493i	$-0.445716\pi$
$197$	4.76410	0.339428	0.169714	+	0.985493i	$0.445716\pi$
$198$	−4.66863	−0.331785
$199$	−17.8095	−1.26248	−0.631240	−	0.775588i	$-0.717454\pi$
$199$	−17.8095	−1.26248	−0.631240	+	0.775588i	$0.717454\pi$
$200$	9.25092	0.654139
$201$	10.2881	0.725668
$202$	4.51146	0.317425
$203$	7.69176	0.539855
$204$	−1.44587	−0.101231
$205$	4.49116	0.313676
$206$	−0.583211	−0.0406342
$207$	0.460825	0.0320295
$208$	0.982303	0.0681105
$209$	8.22854	0.569180
$210$	−0.878746	−0.0606392
$211$	−28.7436	−1.97879	−0.989396	−	0.145241i	$-0.953604\pi$
$211$	−28.7436	−1.97879	−0.989396	+	0.145241i	$0.953604\pi$
$212$	11.7350	0.805965
$213$	−9.69952	−0.664600
$214$	−10.8765	−0.743505
$215$	−7.03653	−0.479887
$216$	2.56510	0.174533
$217$	1.78367	0.121084
$218$	−8.26208	−0.559579
$219$	−4.12330	−0.278627
$220$	−10.7047	−0.721713
$221$	−1.00000	−0.0672673
$222$	7.83682	0.525973
$223$	−6.11119	−0.409235	−0.204618	−	0.978842i	$-0.565595\pi$
$223$	−6.11119	−0.409235	−0.204618	+	0.978842i	$0.565595\pi$
$224$	−5.86141	−0.391632
$225$	−3.60646	−0.240431
$226$	−6.59391	−0.438620
$227$	−0.369834	−0.0245467	−0.0122734	−	0.999925i	$-0.503907\pi$
$227$	−0.369834	−0.0245467	−0.0122734	+	0.999925i	$0.503907\pi$
$228$	−1.89700	−0.125632
$229$	−2.82260	−0.186523	−0.0932614	−	0.995642i	$-0.529729\pi$
$229$	−2.82260	−0.186523	−0.0932614	+	0.995642i	$0.529729\pi$
$230$	−0.404948	−0.0267015
$231$	−6.27171	−0.412648
$232$	19.7301	1.29534
$233$	8.71883	0.571190	0.285595	−	0.958350i	$-0.407809\pi$
$233$	8.71883	0.571190	0.285595	+	0.958350i	$0.407809\pi$
$234$	0.744396	0.0486627
$235$	14.8033	0.965660
$236$	15.8178	1.02965
$237$	−16.4197	−1.06657
$238$	0.744396	0.0482520
$239$	−11.8641	−0.767428	−0.383714	−	0.923452i	$-0.625355\pi$
$239$	−11.8641	−0.767428	−0.383714	+	0.923452i	$0.625355\pi$
$240$	1.15959	0.0748513
$241$	−14.3989	−0.927515	−0.463757	−	0.885962i	$-0.653499\pi$
$241$	−14.3989	−0.927515	−0.463757	+	0.885962i	$0.653499\pi$
$242$	21.0920	1.35584
$243$	−1.00000	−0.0641500
$244$	−7.32729	−0.469082
$245$	−1.18048	−0.0754182
$246$	2.83207	0.180566
$247$	−1.31201	−0.0834811
$248$	4.57529	0.290531
$249$	−16.8207	−1.06597
$250$	7.56289	0.478319
$251$	2.18877	0.138154	0.0690768	−	0.997611i	$-0.477995\pi$
$251$	2.18877	0.138154	0.0690768	+	0.997611i	$0.477995\pi$
$252$	1.44587	0.0910815
$253$	−2.89016	−0.181703
$254$	9.45229	0.593090
$255$	−1.18048	−0.0739247
$256$	−12.1945	−0.762157
$257$	24.1729	1.50786	0.753932	−	0.656953i	$-0.228155\pi$
$257$	24.1729	1.50786	0.753932	+	0.656953i	$0.228155\pi$
$258$	−4.43714	−0.276244
$259$	10.5278	0.654163
$260$	1.70683	0.105853
$261$	−7.69176	−0.476108
$262$	−13.8617	−0.856378
$263$	17.8113	1.09829	0.549146	−	0.835727i	$-0.314953\pi$
$263$	17.8113	1.09829	0.549146	+	0.835727i	$0.314953\pi$
$264$	−16.0875	−0.990119
$265$	9.58105	0.588559
$266$	0.976654	0.0598825
$267$	−13.5138	−0.827033
$268$	14.8753	0.908656
$269$	−8.92777	−0.544336	−0.272168	−	0.962250i	$-0.587741\pi$
$269$	−8.92777	−0.544336	−0.272168	+	0.962250i	$0.587741\pi$
$270$	0.878746	0.0534788
$271$	4.78201	0.290486	0.145243	−	0.989396i	$-0.453604\pi$
$271$	4.78201	0.290486	0.145243	+	0.989396i	$0.453604\pi$
$272$	−0.982303	−0.0595609
$273$	1.00000	0.0605228
$274$	−5.66867	−0.342457
$275$	22.6187	1.36396
$276$	0.666295	0.0401062
$277$	26.7296	1.60603	0.803013	−	0.595961i	$-0.203229\pi$
$277$	26.7296	1.60603	0.803013	+	0.595961i	$0.203229\pi$
$278$	9.80026	0.587780
$279$	−1.78367	−0.106786
$280$	−3.02805	−0.180961
$281$	−21.4698	−1.28078	−0.640391	−	0.768049i	$-0.721228\pi$
$281$	−21.4698	−1.28078	−0.640391	+	0.768049i	$0.721228\pi$
$282$	9.33475	0.555876
$283$	10.8532	0.645153	0.322577	−	0.946543i	$-0.395451\pi$
$283$	10.8532	0.645153	0.322577	+	0.946543i	$0.395451\pi$
$284$	−14.0243	−0.832188
$285$	−1.54880	−0.0917432
$286$	−4.66863	−0.276062
$287$	3.80452	0.224573
$288$	5.86141	0.345387
$289$	1.00000	0.0588235
$290$	6.75910	0.396908
$291$	−2.33389	−0.136815
$292$	−5.96178	−0.348887
$293$	−28.2104	−1.64807	−0.824035	−	0.566538i	$-0.808282\pi$
$293$	−28.2104	−1.64807	−0.824035	+	0.566538i	$0.808282\pi$
$294$	−0.744396	−0.0434141
$295$	12.9144	0.751905
$296$	27.0047	1.56962
$297$	6.27171	0.363921
$298$	−0.844216	−0.0489041
$299$	0.460825	0.0266502
$300$	−5.21449	−0.301059
$301$	−5.96073	−0.343570
$302$	4.40012	0.253198
$303$	−6.06056	−0.348170
$304$	−1.28879	−0.0739172
$305$	−5.98235	−0.342549
$306$	−0.744396	−0.0425543
$307$	9.42262	0.537777	0.268889	−	0.963171i	$-0.413344\pi$
$307$	9.42262	0.537777	0.268889	+	0.963171i	$0.413344\pi$
$308$	−9.06810	−0.516703
$309$	0.783469	0.0445700
$310$	1.56739	0.0890220
$311$	−27.1444	−1.53922	−0.769609	−	0.638515i	$-0.779549\pi$
$311$	−27.1444	−1.53922	−0.769609	+	0.638515i	$0.779549\pi$
$312$	2.56510	0.145220
$313$	−16.5603	−0.936041	−0.468021	−	0.883718i	$-0.655033\pi$
$313$	−16.5603	−0.936041	−0.468021	+	0.883718i	$0.655033\pi$
$314$	4.64430	0.262093
$315$	1.18048	0.0665126
$316$	−23.7408	−1.33552
$317$	4.05783	0.227910	0.113955	−	0.993486i	$-0.463648\pi$
$317$	4.05783	0.227910	0.113955	+	0.993486i	$0.463648\pi$
$318$	6.04168	0.338801
$319$	48.2405	2.70095
$320$	−2.83151	−0.158286
$321$	14.6112	0.815520
$322$	−0.343036	−0.0191167
$323$	1.31201	0.0730021
$324$	−1.44587	−0.0803264
$325$	−3.60646	−0.200051
$326$	10.9365	0.605717
$327$	11.0990	0.613778
$328$	9.75895	0.538848
$329$	12.5400	0.691355
$330$	−5.51124	−0.303384
$331$	−12.8623	−0.706974	−0.353487	−	0.935439i	$-0.615004\pi$
$331$	−12.8623	−0.706974	−0.353487	+	0.935439i	$0.615004\pi$
$332$	−24.3207	−1.33477
$333$	−10.5278	−0.576917
$334$	10.0389	0.549304
$335$	12.1449	0.663549
$336$	0.982303	0.0535890
$337$	−3.78835	−0.206365	−0.103182	−	0.994662i	$-0.532902\pi$
$337$	−3.78835	−0.206365	−0.103182	+	0.994662i	$0.532902\pi$
$338$	0.744396	0.0404898
$339$	8.85807	0.481104
$340$	−1.70683	−0.0925658
$341$	11.1867	0.605792
$342$	−0.976654	−0.0528114
$343$	−1.00000	−0.0539949
$344$	−15.2898	−0.824372
$345$	0.543995	0.0292877
$346$	−11.2512	−0.604871
$347$	24.4582	1.31298	0.656492	−	0.754333i	$-0.272040\pi$
$347$	24.4582	1.31298	0.656492	+	0.754333i	$0.272040\pi$
$348$	−11.1213	−0.596165
$349$	−24.4995	−1.31143	−0.655713	−	0.755010i	$-0.727632\pi$
$349$	−24.4995	−1.31143	−0.655713	+	0.755010i	$0.727632\pi$
$350$	2.68464	0.143500
$351$	−1.00000	−0.0533761
$352$	−36.7611	−1.95937
$353$	−1.51570	−0.0806726	−0.0403363	−	0.999186i	$-0.512843\pi$
$353$	−1.51570	−0.0806726	−0.0403363	+	0.999186i	$0.512843\pi$
$354$	8.14364	0.432829
$355$	−11.4501	−0.607708
$356$	−19.5393	−1.03558
$357$	−1.00000	−0.0529256
$358$	9.08259	0.480030
$359$	8.07436	0.426149	0.213074	−	0.977036i	$-0.431652\pi$
$359$	8.07436	0.426149	0.213074	+	0.977036i	$0.431652\pi$
$360$	3.02805	0.159592
$361$	−17.2786	−0.909402
$362$	−9.88757	−0.519679
$363$	−28.3343	−1.48717
$364$	1.44587	0.0757844
$365$	−4.86749	−0.254776
$366$	−3.77239	−0.197186
$367$	1.10357	0.0576060	0.0288030	−	0.999585i	$-0.490830\pi$
$367$	1.10357	0.0576060	0.0288030	+	0.999585i	$0.490830\pi$
$368$	0.452670	0.0235970
$369$	−3.80452	−0.198055
$370$	9.25122	0.480948
$371$	8.11622	0.421373
$372$	−2.57897	−0.133713
$373$	36.2574	1.87734	0.938669	−	0.344820i	$-0.112060\pi$
$373$	36.2574	1.87734	0.938669	+	0.344820i	$0.112060\pi$
$374$	4.66863	0.241409
$375$	−10.1598	−0.524648
$376$	32.1664	1.65885
$377$	−7.69176	−0.396146
$378$	0.744396	0.0382876
$379$	29.0975	1.49464	0.747319	−	0.664466i	$-0.231341\pi$
$379$	29.0975	1.49464	0.747319	+	0.664466i	$0.231341\pi$
$380$	−2.23937	−0.114878
$381$	−12.6979	−0.650535
$382$	18.1010	0.926129
$383$	−7.28514	−0.372253	−0.186127	−	0.982526i	$-0.559593\pi$
$383$	−7.28514	−0.372253	−0.186127	+	0.982526i	$0.559593\pi$
$384$	9.93731	0.507111
$385$	−7.40364	−0.377324
$386$	−12.6397	−0.643346
$387$	5.96073	0.303001
$388$	−3.37452	−0.171315
$389$	11.9213	0.604436	0.302218	−	0.953239i	$-0.402273\pi$
$389$	11.9213	0.604436	0.302218	+	0.953239i	$0.402273\pi$
$390$	0.878746	0.0444970
$391$	−0.460825	−0.0233049
$392$	−2.56510	−0.129557
$393$	18.6214	0.939325
$394$	3.54638	0.178664
$395$	−19.3831	−0.975272
$396$	9.06810	0.455689
$397$	−14.9806	−0.751854	−0.375927	−	0.926649i	$-0.622676\pi$
$397$	−14.9806	−0.751854	−0.375927	+	0.926649i	$0.622676\pi$
$398$	−13.2573	−0.664528
$399$	−1.31201	−0.0656826
$400$	−3.54264	−0.177132
$401$	29.7184	1.48407	0.742034	−	0.670363i	$-0.233861\pi$
$401$	29.7184	1.48407	0.742034	+	0.670363i	$0.233861\pi$
$402$	7.65844	0.381968
$403$	−1.78367	−0.0888510
$404$	−8.76281	−0.435966
$405$	−1.18048	−0.0586586
$406$	5.72571	0.284162
$407$	66.0270	3.27284
$408$	−2.56510	−0.126991
$409$	6.64081	0.328367	0.164183	−	0.986430i	$-0.447501\pi$
$409$	6.64081	0.328367	0.164183	+	0.986430i	$0.447501\pi$
$410$	3.34320	0.165109
$411$	7.61513	0.375627
$412$	1.13280	0.0558089
$413$	10.9399	0.538319
$414$	0.343036	0.0168593
$415$	−19.8566	−0.974720
$416$	5.86141	0.287379
$417$	−13.1654	−0.644712
$418$	6.12529	0.299598
$419$	1.41144	0.0689533	0.0344766	−	0.999406i	$-0.489024\pi$
$419$	1.41144	0.0689533	0.0344766	+	0.999406i	$0.489024\pi$
$420$	1.70683	0.0832847
$421$	−15.7298	−0.766623	−0.383311	−	0.923619i	$-0.625216\pi$
$421$	−15.7298	−0.766623	−0.383311	+	0.923619i	$0.625216\pi$
$422$	−21.3966	−1.04157
$423$	−12.5400	−0.609717
$424$	20.8189	1.01105
$425$	3.60646	0.174939
$426$	−7.22028	−0.349824
$427$	−5.06772	−0.245244
$428$	21.1260	1.02116
$429$	6.27171	0.302801
$430$	−5.23796	−0.252597
$431$	−9.61321	−0.463052	−0.231526	−	0.972829i	$-0.574372\pi$
$431$	−9.61321	−0.463052	−0.231526	+	0.972829i	$0.574372\pi$
$432$	−0.982303	−0.0472611
$433$	31.2386	1.50123	0.750615	−	0.660740i	$-0.229757\pi$
$433$	31.2386	1.50123	0.750615	+	0.660740i	$0.229757\pi$
$434$	1.32776	0.0637344
$435$	−9.07998	−0.435352
$436$	16.0478	0.768551
$437$	−0.604606	−0.0289222
$438$	−3.06937	−0.146660
$439$	20.0197	0.955489	0.477744	−	0.878499i	$-0.341454\pi$
$439$	20.0197	0.955489	0.477744	+	0.878499i	$0.341454\pi$
$440$	−18.9910	−0.905362
$441$	1.00000	0.0476190
$442$	−0.744396	−0.0354073
$443$	−4.82537	−0.229260	−0.114630	−	0.993408i	$-0.536568\pi$
$443$	−4.82537	−0.229260	−0.114630	+	0.993408i	$0.536568\pi$
$444$	−15.2218	−0.722395
$445$	−15.9528	−0.756237
$446$	−4.54914	−0.215408
$447$	1.13409	0.0536408
$448$	−2.39860	−0.113323
$449$	4.60545	0.217345	0.108672	−	0.994078i	$-0.465340\pi$
$449$	4.60545	0.217345	0.108672	+	0.994078i	$0.465340\pi$
$450$	−2.68464	−0.126555
$451$	23.8608	1.12356
$452$	12.8077	0.602421
$453$	−5.91099	−0.277723
$454$	−0.275303	−0.0129206
$455$	1.18048	0.0553418
$456$	−3.36543	−0.157601
$457$	−9.69881	−0.453691	−0.226846	−	0.973931i	$-0.572841\pi$
$457$	−9.69881	−0.453691	−0.226846	+	0.973931i	$0.572841\pi$
$458$	−2.10113	−0.0981795
$459$	1.00000	0.0466760
$460$	0.786549	0.0366730
$461$	−20.1610	−0.938993	−0.469496	−	0.882934i	$-0.655565\pi$
$461$	−20.1610	−0.938993	−0.469496	+	0.882934i	$0.655565\pi$
$462$	−4.66863	−0.217205
$463$	14.8896	0.691980	0.345990	−	0.938238i	$-0.387543\pi$
$463$	14.8896	0.691980	0.345990	+	0.938238i	$0.387543\pi$
$464$	−7.55564	−0.350762
$465$	−2.10559	−0.0976445
$466$	6.49026	0.300656
$467$	−32.7974	−1.51768	−0.758841	−	0.651276i	$-0.774234\pi$
$467$	−32.7974	−1.51768	−0.758841	+	0.651276i	$0.774234\pi$
$468$	−1.44587	−0.0668356
$469$	10.2881	0.475061
$470$	11.0195	0.508292
$471$	−6.23902	−0.287479
$472$	28.0620	1.29166
$473$	−37.3839	−1.71891
$474$	−12.2227	−0.561409
$475$	4.73171	0.217106
$476$	−1.44587	−0.0662716
$477$	−8.11622	−0.371616
$478$	−8.83162	−0.403949
$479$	23.1048	1.05569	0.527843	−	0.849342i	$-0.323001\pi$
$479$	23.1048	1.05569	0.527843	+	0.849342i	$0.323001\pi$
$480$	6.91929	0.315821
$481$	−10.5278	−0.480024
$482$	−10.7185	−0.488214
$483$	0.460825	0.0209683
$484$	−40.9679	−1.86218
$485$	−2.75512	−0.125104
$486$	−0.744396	−0.0337665
$487$	7.60658	0.344687	0.172344	−	0.985037i	$-0.444866\pi$
$487$	7.60658	0.344687	0.172344	+	0.985037i	$0.444866\pi$
$488$	−12.9992	−0.588446
$489$	−14.6918	−0.664385
$490$	−0.878746	−0.0396977
$491$	29.8496	1.34709	0.673547	−	0.739144i	$-0.264770\pi$
$491$	29.8496	1.34709	0.673547	+	0.739144i	$0.264770\pi$
$492$	−5.50085	−0.247998
$493$	7.69176	0.346419
$494$	−0.976654	−0.0439417
$495$	7.40364	0.332769
$496$	−1.75211	−0.0786719
$497$	−9.69952	−0.435083
$498$	−12.5213	−0.561092
$499$	−23.8202	−1.06634	−0.533168	−	0.846009i	$-0.678999\pi$
$499$	−23.8202	−1.06634	−0.533168	+	0.846009i	$0.678999\pi$
$500$	−14.6898	−0.656946
$501$	−13.4860	−0.602508
$502$	1.62931	0.0727196
$503$	−42.0243	−1.87377	−0.936884	−	0.349639i	$-0.886304\pi$
$503$	−42.0243	−1.87377	−0.936884	+	0.349639i	$0.886304\pi$
$504$	2.56510	0.114258
$505$	−7.15438	−0.318366
$506$	−2.15142	−0.0956424
$507$	−1.00000	−0.0444116
$508$	−18.3596	−0.814577
$509$	−32.9458	−1.46030	−0.730149	−	0.683288i	$-0.760549\pi$
$509$	−32.9458	−1.46030	−0.730149	+	0.683288i	$0.760549\pi$
$510$	−0.878746	−0.0389115
$511$	−4.12330	−0.182404
$512$	10.7971	0.477168
$513$	1.31201	0.0579266
$514$	17.9942	0.793690
$515$	0.924871	0.0407547
$516$	8.61846	0.379407
$517$	78.6475	3.45891
$518$	7.83682	0.344330
$519$	15.1146	0.663457
$520$	3.02805	0.132789
$521$	−22.5114	−0.986241	−0.493121	−	0.869961i	$-0.664144\pi$
$521$	−22.5114	−0.986241	−0.493121	+	0.869961i	$0.664144\pi$
$522$	−5.72571	−0.250608
$523$	3.81516	0.166825	0.0834127	−	0.996515i	$-0.473418\pi$
$523$	3.81516	0.166825	0.0834127	+	0.996515i	$0.473418\pi$
$524$	26.9242	1.17619
$525$	−3.60646	−0.157399
$526$	13.2587	0.578105
$527$	1.78367	0.0776980
$528$	6.16072	0.268111
$529$	−22.7876	−0.990767
$530$	7.13209	0.309798
$531$	−10.9399	−0.474752
$532$	−1.89700	−0.0822454
$533$	−3.80452	−0.164792
$534$	−10.0596	−0.435323
$535$	17.2483	0.745709
$536$	26.3900	1.13988
$537$	−12.2013	−0.526525
$538$	−6.64580	−0.286521
$539$	−6.27171	−0.270142
$540$	−1.70683	−0.0734502
$541$	14.7838	0.635605	0.317802	−	0.948157i	$-0.397055\pi$
$541$	14.7838	0.635605	0.317802	+	0.948157i	$0.397055\pi$
$542$	3.55971	0.152902
$543$	13.2827	0.570014
$544$	−5.86141	−0.251306
$545$	13.1022	0.561237
$546$	0.744396	0.0318572
$547$	42.6776	1.82476	0.912381	−	0.409342i	$-0.134242\pi$
$547$	42.6776	1.82476	0.912381	+	0.409342i	$0.134242\pi$
$548$	11.0105	0.470346
$549$	5.06772	0.216285
$550$	16.8373	0.717943
$551$	10.0917	0.429919
$552$	1.18206	0.0503118
$553$	−16.4197	−0.698236
$554$	19.8974	0.845360
$555$	−12.4278	−0.527532
$556$	−19.0355	−0.807285
$557$	8.19316	0.347155	0.173578	−	0.984820i	$-0.444467\pi$
$557$	8.19316	0.347155	0.173578	+	0.984820i	$0.444467\pi$
$558$	−1.32776	−0.0562085
$559$	5.96073	0.252112
$560$	1.15959	0.0490017
$561$	−6.27171	−0.264792
$562$	−15.9820	−0.674161
$563$	0.875188	0.0368848	0.0184424	−	0.999830i	$-0.494129\pi$
$563$	0.875188	0.0368848	0.0184424	+	0.999830i	$0.494129\pi$
$564$	−18.1313	−0.763466
$565$	10.4568	0.439920
$566$	8.07904	0.339588
$567$	−1.00000	−0.0419961
$568$	−24.8802	−1.04395
$569$	−37.6629	−1.57891	−0.789455	−	0.613808i	$-0.789637\pi$
$569$	−37.6629	−1.57891	−0.789455	+	0.613808i	$0.789637\pi$
$570$	−1.15292	−0.0482906
$571$	−20.6094	−0.862474	−0.431237	−	0.902239i	$-0.641923\pi$
$571$	−20.6094	−0.862474	−0.431237	+	0.902239i	$0.641923\pi$
$572$	9.06810	0.379157
$573$	−24.3164	−1.01583
$574$	2.83207	0.118208
$575$	−1.66195	−0.0693080
$576$	2.39860	0.0999419
$577$	−30.3064	−1.26167	−0.630837	−	0.775915i	$-0.717288\pi$
$577$	−30.3064	−1.26167	−0.630837	+	0.775915i	$0.717288\pi$
$578$	0.744396	0.0309628
$579$	16.9799	0.705659
$580$	−13.1285	−0.545132
$581$	−16.8207	−0.697841
$582$	−1.73734	−0.0720151
$583$	50.9025	2.10817
$584$	−10.5767	−0.437666
$585$	−1.18048	−0.0488069
$586$	−20.9997	−0.867491
$587$	−16.4178	−0.677634	−0.338817	−	0.940852i	$-0.610027\pi$
$587$	−16.4178	−0.677634	−0.338817	+	0.940852i	$0.610027\pi$
$588$	1.44587	0.0596269
$589$	2.34019	0.0964260
$590$	9.61342	0.395778
$591$	−4.76410	−0.195969
$592$	−10.3414	−0.425031
$593$	−22.3724	−0.918723	−0.459362	−	0.888249i	$-0.651922\pi$
$593$	−22.3724	−0.918723	−0.459362	+	0.888249i	$0.651922\pi$
$594$	4.66863	0.191556
$595$	−1.18048	−0.0483950
$596$	1.63976	0.0671672
$597$	17.8095	0.728893
$598$	0.343036	0.0140278
$599$	21.7707	0.889525	0.444763	−	0.895648i	$-0.353288\pi$
$599$	21.7707	0.889525	0.444763	+	0.895648i	$0.353288\pi$
$600$	−9.25092	−0.377667
$601$	−1.72916	−0.0705338	−0.0352669	−	0.999378i	$-0.511228\pi$
$601$	−1.72916	−0.0705338	−0.0352669	+	0.999378i	$0.511228\pi$
$602$	−4.43714	−0.180844
$603$	−10.2881	−0.418965
$604$	−8.54655	−0.347754
$605$	−33.4482	−1.35986
$606$	−4.51146	−0.183265
$607$	−29.1194	−1.18192	−0.590959	−	0.806701i	$-0.701251\pi$
$607$	−29.1194	−1.18192	−0.590959	+	0.806701i	$0.701251\pi$
$608$	−7.69023	−0.311880
$609$	−7.69176	−0.311686
$610$	−4.45324	−0.180306
$611$	−12.5400	−0.507316
$612$	1.44587	0.0584460
$613$	34.2908	1.38499	0.692496	−	0.721422i	$-0.256511\pi$
$613$	34.2908	1.38499	0.692496	+	0.721422i	$0.256511\pi$
$614$	7.01416	0.283068
$615$	−4.49116	−0.181101
$616$	−16.0875	−0.648185
$617$	−37.0929	−1.49331	−0.746653	−	0.665214i	$-0.768340\pi$
$617$	−37.0929	−1.49331	−0.746653	+	0.665214i	$0.768340\pi$
$618$	0.583211	0.0234602
$619$	−31.8853	−1.28158	−0.640788	−	0.767718i	$-0.721392\pi$
$619$	−31.8853	−1.28158	−0.640788	+	0.767718i	$0.721392\pi$
$620$	−3.04442	−0.122267
$621$	−0.460825	−0.0184923
$622$	−20.2062	−0.810194
$623$	−13.5138	−0.541420
$624$	−0.982303	−0.0393236
$625$	6.03888	0.241555
$626$	−12.3274	−0.492702
$627$	−8.22854	−0.328616
$628$	−9.02084	−0.359971
$629$	10.5278	0.419769
$630$	0.878746	0.0350101
$631$	−17.4082	−0.693011	−0.346506	−	0.938048i	$-0.612632\pi$
$631$	−17.4082	−0.693011	−0.346506	+	0.938048i	$0.612632\pi$
$632$	−42.1180	−1.67537
$633$	28.7436	1.14246
$634$	3.02063	0.119964
$635$	−14.9897	−0.594848
$636$	−11.7350	−0.465324
$637$	1.00000	0.0396214
$638$	35.9100	1.42169
$639$	9.69952	0.383707
$640$	11.7308	0.463701
$641$	−6.57820	−0.259823	−0.129912	−	0.991526i	$-0.541469\pi$
$641$	−6.57820	−0.259823	−0.129912	+	0.991526i	$0.541469\pi$
$642$	10.8765	0.429263
$643$	9.54725	0.376507	0.188253	−	0.982120i	$-0.439717\pi$
$643$	9.54725	0.376507	0.188253	+	0.982120i	$0.439717\pi$
$644$	0.666295	0.0262557
$645$	7.03653	0.277063
$646$	0.976654	0.0384259
$647$	−0.295810	−0.0116295	−0.00581474	−	0.999983i	$-0.501851\pi$
$647$	−0.295810	−0.0116295	−0.00581474	+	0.999983i	$0.501851\pi$
$648$	−2.56510	−0.100766
$649$	68.6120	2.69326
$650$	−2.68464	−0.105300
$651$	−1.78367	−0.0699076
$652$	−21.2425	−0.831919
$653$	−33.3988	−1.30700	−0.653499	−	0.756928i	$-0.726699\pi$
$653$	−33.3988	−1.30700	−0.653499	+	0.756928i	$0.726699\pi$
$654$	8.26208	0.323073
$655$	21.9822	0.858916
$656$	−3.73719	−0.145913
$657$	4.12330	0.160865
$658$	9.33475	0.363907
$659$	3.07696	0.119861	0.0599307	−	0.998203i	$-0.480912\pi$
$659$	3.07696	0.119861	0.0599307	+	0.998203i	$0.480912\pi$
$660$	10.7047	0.416681
$661$	−26.4074	−1.02713	−0.513564	−	0.858052i	$-0.671675\pi$
$661$	−26.4074	−1.02713	−0.513564	+	0.858052i	$0.671675\pi$
$662$	−9.57462	−0.372128
$663$	1.00000	0.0388368
$664$	−43.1467	−1.67442
$665$	−1.54880	−0.0600600
$666$	−7.83682	−0.303670
$667$	−3.54455	−0.137246
$668$	−19.4990	−0.754439
$669$	6.11119	0.236272
$670$	9.04065	0.349271
$671$	−31.7833	−1.22698
$672$	5.86141	0.226109
$673$	24.8228	0.956850	0.478425	−	0.878129i	$-0.341208\pi$
$673$	24.8228	0.956850	0.478425	+	0.878129i	$0.341208\pi$
$674$	−2.82003	−0.108624
$675$	3.60646	0.138813
$676$	−1.44587	−0.0556106
$677$	30.4640	1.17082	0.585412	−	0.810736i	$-0.300933\pi$
$677$	30.4640	1.17082	0.585412	+	0.810736i	$0.300933\pi$
$678$	6.59391	0.253238
$679$	−2.33389	−0.0895666
$680$	−3.02805	−0.116120
$681$	0.369834	0.0141721
$682$	8.32731	0.318869
$683$	−20.7291	−0.793175	−0.396588	−	0.917997i	$-0.629806\pi$
$683$	−20.7291	−0.793175	−0.396588	+	0.917997i	$0.629806\pi$
$684$	1.89700	0.0725336
$685$	8.98952	0.343472
$686$	−0.744396	−0.0284212
$687$	2.82260	0.107689
$688$	5.85524	0.223229
$689$	−8.11622	−0.309203
$690$	0.404948	0.0154161
$691$	−10.1272	−0.385256	−0.192628	−	0.981272i	$-0.561701\pi$
$691$	−10.1272	−0.385256	−0.192628	+	0.981272i	$0.561701\pi$
$692$	21.8538	0.830757
$693$	6.27171	0.238243
$694$	18.2066	0.691111
$695$	−15.5415	−0.589523
$696$	−19.7301	−0.747867
$697$	3.80452	0.144106
$698$	−18.2373	−0.690292
$699$	−8.71883	−0.329777
$700$	−5.21449	−0.197089
$701$	−27.3737	−1.03389	−0.516946	−	0.856018i	$-0.672931\pi$
$701$	−27.3737	−1.03389	−0.516946	+	0.856018i	$0.672931\pi$
$702$	−0.744396	−0.0280954
$703$	13.8125	0.520949
$704$	−15.0434	−0.566968
$705$	−14.8033	−0.557524
$706$	−1.12828	−0.0424635
$707$	−6.06056	−0.227931
$708$	−15.8178	−0.594468
$709$	−23.8770	−0.896718	−0.448359	−	0.893854i	$-0.647991\pi$
$709$	−23.8770	−0.896718	−0.448359	+	0.893854i	$0.647991\pi$
$710$	−8.52341	−0.319878
$711$	16.4197	0.615786
$712$	−34.6642	−1.29910
$713$	−0.821960	−0.0307827
$714$	−0.744396	−0.0278583
$715$	7.40364	0.276880
$716$	−17.6415	−0.659295
$717$	11.8641	0.443075
$718$	6.01052	0.224311
$719$	41.0624	1.53137	0.765685	−	0.643216i	$-0.222400\pi$
$719$	41.0624	1.53137	0.765685	+	0.643216i	$0.222400\pi$
$720$	−1.15959	−0.0432154
$721$	0.783469	0.0291779
$722$	−12.8621	−0.478679
$723$	14.3989	0.535501
$724$	19.2051	0.713751
$725$	27.7400	1.03024
$726$	−21.0920	−0.782796
$727$	−18.7807	−0.696539	−0.348269	−	0.937394i	$-0.613231\pi$
$727$	−18.7807	−0.696539	−0.348269	+	0.937394i	$0.613231\pi$
$728$	2.56510	0.0950687
$729$	1.00000	0.0370370
$730$	−3.62334	−0.134106
$731$	−5.96073	−0.220465
$732$	7.32729	0.270824
$733$	35.3013	1.30388	0.651942	−	0.758269i	$-0.273955\pi$
$733$	35.3013	1.30388	0.651942	+	0.758269i	$0.273955\pi$
$734$	0.821495	0.0303219
$735$	1.18048	0.0435427
$736$	2.70108	0.0995633
$737$	64.5241	2.37678
$738$	−2.83207	−0.104250
$739$	17.9948	0.661948	0.330974	−	0.943640i	$-0.392623\pi$
$739$	17.9948	0.661948	0.330974	+	0.943640i	$0.392623\pi$
$740$	−17.9691	−0.660556
$741$	1.31201	0.0481978
$742$	6.04168	0.221797
$743$	−27.5894	−1.01216	−0.506078	−	0.862488i	$-0.668905\pi$
$743$	−27.5894	−1.01216	−0.506078	+	0.862488i	$0.668905\pi$
$744$	−4.57529	−0.167738
$745$	1.33878	0.0490491
$746$	26.9899	0.988169
$747$	16.8207	0.615438
$748$	−9.06810	−0.331563
$749$	14.6112	0.533883
$750$	−7.56289	−0.276158
$751$	−25.0575	−0.914361	−0.457181	−	0.889374i	$-0.651141\pi$
$751$	−25.0575	−0.914361	−0.457181	+	0.889374i	$0.651141\pi$
$752$	−12.3181	−0.449196
$753$	−2.18877	−0.0797630
$754$	−5.72571	−0.208518
$755$	−6.97782	−0.253949
$756$	−1.44587	−0.0525860
$757$	−1.29306	−0.0469970	−0.0234985	−	0.999724i	$-0.507480\pi$
$757$	−1.29306	−0.0469970	−0.0234985	+	0.999724i	$0.507480\pi$
$758$	21.6600	0.786728
$759$	2.89016	0.104906
$760$	−3.97283	−0.144110
$761$	−13.7888	−0.499843	−0.249921	−	0.968266i	$-0.580405\pi$
$761$	−13.7888	−0.499843	−0.249921	+	0.968266i	$0.580405\pi$
$762$	−9.45229	−0.342420
$763$	11.0990	0.401812
$764$	−35.1585	−1.27199
$765$	1.18048	0.0426804
$766$	−5.42303	−0.195942
$767$	−10.9399	−0.395018
$768$	12.1945	0.440031
$769$	−5.35772	−0.193204	−0.0966022	−	0.995323i	$-0.530797\pi$
$769$	−5.35772	−0.193204	−0.0966022	+	0.995323i	$0.530797\pi$
$770$	−5.51124	−0.198611
$771$	−24.1729	−0.870565
$772$	24.5508	0.883601
$773$	−5.37297	−0.193252	−0.0966261	−	0.995321i	$-0.530805\pi$
$773$	−5.37297	−0.193252	−0.0966261	+	0.995321i	$0.530805\pi$
$774$	4.43714	0.159490
$775$	6.43275	0.231071
$776$	−5.98666	−0.214909
$777$	−10.5278	−0.377681
$778$	8.87420	0.318156
$779$	4.99156	0.178841
$780$	−1.70683	−0.0611143
$781$	−60.8325	−2.17676
$782$	−0.343036	−0.0122669
$783$	7.69176	0.274881
$784$	0.982303	0.0350823
$785$	−7.36505	−0.262870
$786$	13.8617	0.494430
$787$	19.6300	0.699733	0.349867	−	0.936800i	$-0.386227\pi$
$787$	19.6300	0.699733	0.349867	+	0.936800i	$0.386227\pi$
$788$	−6.88829	−0.245385
$789$	−17.8113	−0.634099
$790$	−14.4287	−0.513351
$791$	8.85807	0.314957
$792$	16.0875	0.571645
$793$	5.06772	0.179960
$794$	−11.1515	−0.395751
$795$	−9.58105	−0.339805
$796$	25.7503	0.912694
$797$	−33.1005	−1.17248	−0.586240	−	0.810138i	$-0.699392\pi$
$797$	−33.1005	−1.17248	−0.586240	+	0.810138i	$0.699392\pi$
$798$	−0.976654	−0.0345732
$799$	12.5400	0.443635
$800$	−21.1390	−0.747375
$801$	13.5138	0.477488
$802$	22.1223	0.781165
$803$	−25.8602	−0.912585
$804$	−14.8753	−0.524613
$805$	0.543995	0.0191733
$806$	−1.32776	−0.0467683
$807$	8.92777	0.314272
$808$	−15.5459	−0.546903
$809$	−37.9409	−1.33393	−0.666966	−	0.745088i	$-0.732407\pi$
$809$	−37.9409	−1.33393	−0.666966	+	0.745088i	$0.732407\pi$
$810$	−0.878746	−0.0308760
$811$	38.2159	1.34194	0.670971	−	0.741484i	$-0.265878\pi$
$811$	38.2159	1.34194	0.670971	+	0.741484i	$0.265878\pi$
$812$	−11.1213	−0.390282
$813$	−4.78201	−0.167712
$814$	49.1502	1.72271
$815$	−17.3434	−0.607512
$816$	0.982303	0.0343875
$817$	−7.82052	−0.273606
$818$	4.94339	0.172842
$819$	−1.00000	−0.0349428
$820$	−6.49366	−0.226768
$821$	23.2184	0.810328	0.405164	−	0.914244i	$-0.367214\pi$
$821$	23.2184	0.810328	0.405164	+	0.914244i	$0.367214\pi$
$822$	5.66867	0.197718
$823$	0.126807	0.00442023	0.00221011	−	0.999998i	$-0.499296\pi$
$823$	0.126807	0.00442023	0.00221011	+	0.999998i	$0.499296\pi$
$824$	2.00967	0.0700102
$825$	−22.6187	−0.787481
$826$	8.14364	0.283353
$827$	30.8689	1.07342	0.536708	−	0.843768i	$-0.319668\pi$
$827$	30.8689	1.07342	0.536708	+	0.843768i	$0.319668\pi$
$828$	−0.666295	−0.0231553
$829$	18.9726	0.658946	0.329473	−	0.944165i	$-0.393129\pi$
$829$	18.9726	0.658946	0.329473	+	0.944165i	$0.393129\pi$
$830$	−14.7811	−0.513061
$831$	−26.7296	−0.927240
$832$	2.39860	0.0831567
$833$	−1.00000	−0.0346479
$834$	−9.80026	−0.339355
$835$	−15.9199	−0.550932
$836$	−11.8974	−0.411481
$837$	1.78367	0.0616527
$838$	1.05067	0.0362947
$839$	33.9079	1.17063	0.585315	−	0.810806i	$-0.300971\pi$
$839$	33.9079	1.17063	0.585315	+	0.810806i	$0.300971\pi$
$840$	3.02805	0.104478
$841$	30.1631	1.04011
$842$	−11.7092	−0.403525
$843$	21.4698	0.739459
$844$	41.5597	1.43054
$845$	−1.18048	−0.0406098
$846$	−9.33475	−0.320935
$847$	−28.3343	−0.973579
$848$	−7.97259	−0.273780
$849$	−10.8532	−0.372479
$850$	2.68464	0.0920822
$851$	−4.85145	−0.166306
$852$	14.0243	0.480464
$853$	−43.4439	−1.48749	−0.743745	−	0.668464i	$-0.766952\pi$
$853$	−43.4439	−1.48749	−0.743745	+	0.668464i	$0.766952\pi$
$854$	−3.77239	−0.129089
$855$	1.54880	0.0529679
$856$	37.4792	1.28101
$857$	−17.7917	−0.607752	−0.303876	−	0.952712i	$-0.598281\pi$
$857$	−17.7917	−0.607752	−0.303876	+	0.952712i	$0.598281\pi$
$858$	4.66863	0.159385
$859$	28.4334	0.970136	0.485068	−	0.874476i	$-0.338795\pi$
$859$	28.4334	0.970136	0.485068	+	0.874476i	$0.338795\pi$
$860$	10.1739	0.346928
$861$	−3.80452	−0.129658
$862$	−7.15603	−0.243735
$863$	14.8029	0.503896	0.251948	−	0.967741i	$-0.418929\pi$
$863$	14.8029	0.503896	0.251948	+	0.967741i	$0.418929\pi$
$864$	−5.86141	−0.199409
$865$	17.8425	0.606664
$866$	23.2539	0.790199
$867$	−1.00000	−0.0339618
$868$	−2.57897	−0.0875358
$869$	−102.979	−3.49334
$870$	−6.75910	−0.229155
$871$	−10.2881	−0.348600
$872$	28.4701	0.964119
$873$	2.33389	0.0789904
$874$	−0.450066	−0.0152237
$875$	−10.1598	−0.343463
$876$	5.96178	0.201430
$877$	−25.0175	−0.844782	−0.422391	−	0.906414i	$-0.638809\pi$
$877$	−25.0175	−0.844782	−0.422391	+	0.906414i	$0.638809\pi$
$878$	14.9026	0.502938
$879$	28.2104	0.951514
$880$	7.27262	0.245160
$881$	48.3671	1.62953	0.814764	−	0.579793i	$-0.196867\pi$
$881$	48.3671	1.62953	0.814764	+	0.579793i	$0.196867\pi$
$882$	0.744396	0.0250651
$883$	−16.7955	−0.565212	−0.282606	−	0.959236i	$-0.591199\pi$
$883$	−16.7955	−0.565212	−0.282606	+	0.959236i	$0.591199\pi$
$884$	1.44587	0.0486300
$885$	−12.9144	−0.434112
$886$	−3.59198	−0.120675
$887$	−54.5074	−1.83018	−0.915090	−	0.403250i	$-0.867881\pi$
$887$	−54.5074	−1.83018	−0.915090	+	0.403250i	$0.867881\pi$
$888$	−27.0047	−0.906218
$889$	−12.6979	−0.425875
$890$	−11.8752	−0.398058
$891$	−6.27171	−0.210110
$892$	8.83601	0.295852
$893$	16.4526	0.550567
$894$	0.844216	0.0282348
$895$	−14.4034	−0.481453
$896$	9.93731	0.331982
$897$	−0.460825	−0.0153865
$898$	3.42828	0.114403
$899$	13.7196	0.457573
$900$	5.21449	0.173816
$901$	8.11622	0.270390
$902$	17.7619	0.591406
$903$	5.96073	0.198361
$904$	22.7218	0.755715
$905$	15.6800	0.521219
$906$	−4.40012	−0.146184
$907$	21.2330	0.705031	0.352515	−	0.935806i	$-0.385326\pi$
$907$	21.2330	0.705031	0.352515	+	0.935806i	$0.385326\pi$
$908$	0.534734	0.0177458
$909$	6.06056	0.201016
$910$	0.878746	0.0291301
$911$	−55.6491	−1.84374	−0.921868	−	0.387503i	$-0.873338\pi$
$911$	−55.6491	−1.84374	−0.921868	+	0.387503i	$0.873338\pi$
$912$	1.28879	0.0426761
$913$	−105.495	−3.49136
$914$	−7.21975	−0.238808
$915$	5.98235	0.197771
$916$	4.08113	0.134844
$917$	18.6214	0.614932
$918$	0.744396	0.0245687
$919$	40.1035	1.32289	0.661446	−	0.749992i	$-0.269943\pi$
$919$	40.1035	1.32289	0.661446	+	0.749992i	$0.269943\pi$
$920$	1.39540	0.0460050
$921$	−9.42262	−0.310486
$922$	−15.0078	−0.494255
$923$	9.69952	0.319263
$924$	9.06810	0.298319
$925$	37.9679	1.24838
$926$	11.0838	0.364236
$927$	−0.783469	−0.0257325
$928$	−45.0846	−1.47997
$929$	−36.5058	−1.19772	−0.598858	−	0.800856i	$-0.704378\pi$
$929$	−36.5058	−1.19772	−0.598858	+	0.800856i	$0.704378\pi$
$930$	−1.56739	−0.0513969
$931$	−1.31201	−0.0429994
$932$	−12.6063	−0.412934
$933$	27.1444	0.888668
$934$	−24.4142	−0.798859
$935$	−7.40364	−0.242125
$936$	−2.56510	−0.0838428
$937$	−12.8282	−0.419077	−0.209539	−	0.977800i	$-0.567196\pi$
$937$	−12.8282	−0.419077	−0.209539	+	0.977800i	$0.567196\pi$
$938$	7.65844	0.250057
$939$	16.5603	0.540424
$940$	−21.4037	−0.698112
$941$	57.9680	1.88970	0.944852	−	0.327497i	$-0.106205\pi$
$941$	57.9680	1.88970	0.944852	+	0.327497i	$0.106205\pi$
$942$	−4.64430	−0.151319
$943$	−1.75322	−0.0570925
$944$	−10.7463	−0.349763
$945$	−1.18048	−0.0384011
$946$	−27.8284	−0.904781
$947$	−15.5931	−0.506707	−0.253353	−	0.967374i	$-0.581534\pi$
$947$	−15.5931	−0.506707	−0.253353	+	0.967374i	$0.581534\pi$
$948$	23.7408	0.771065
$949$	4.12330	0.133848
$950$	3.52227	0.114277
$951$	−4.05783	−0.131584
$952$	−2.56510	−0.0831352
$953$	38.4745	1.24631	0.623155	−	0.782098i	$-0.285851\pi$
$953$	38.4745	1.24631	0.623155	+	0.782098i	$0.285851\pi$
$954$	−6.04168	−0.195607
$955$	−28.7051	−0.928874
$956$	17.1541	0.554802
$957$	−48.2405	−1.55939
$958$	17.1991	0.555679
$959$	7.61513	0.245905
$960$	2.83151	0.0913866
$961$	−27.8185	−0.897371
$962$	−7.83682	−0.252669
$963$	−14.6112	−0.470840
$964$	20.8190	0.670535
$965$	20.0444	0.645253
$966$	0.343036	0.0110370
$967$	27.5065	0.884550	0.442275	−	0.896880i	$-0.354172\pi$
$967$	27.5065	0.884550	0.442275	+	0.896880i	$0.354172\pi$
$968$	−72.6802	−2.33603
$969$	−1.31201	−0.0421478
$970$	−2.05090	−0.0658504
$971$	48.0095	1.54070	0.770349	−	0.637622i	$-0.220082\pi$
$971$	48.0095	1.54070	0.770349	+	0.637622i	$0.220082\pi$
$972$	1.44587	0.0463765
$973$	−13.1654	−0.422063
$974$	5.66231	0.181432
$975$	3.60646	0.115499
$976$	4.97804	0.159343
$977$	24.3512	0.779064	0.389532	−	0.921013i	$-0.372637\pi$
$977$	24.3512	0.779064	0.389532	+	0.921013i	$0.372637\pi$
$978$	−10.9365	−0.349711
$979$	−84.7548	−2.70877
$980$	1.70683	0.0545227
$981$	−11.0990	−0.354365
$982$	22.2199	0.709066
$983$	−9.97236	−0.318069	−0.159034	−	0.987273i	$-0.550838\pi$
$983$	−9.97236	−0.318069	−0.159034	+	0.987273i	$0.550838\pi$
$984$	−9.75895	−0.311104
$985$	−5.62393	−0.179193
$986$	5.72571	0.182344
$987$	−12.5400	−0.399154
$988$	1.89700	0.0603516
$989$	2.74685	0.0873447
$990$	5.51124	0.175159
$991$	21.7606	0.691249	0.345624	−	0.938373i	$-0.387667\pi$
$991$	21.7606	0.691249	0.345624	+	0.938373i	$0.387667\pi$
$992$	−10.4548	−0.331941
$993$	12.8623	0.408172
$994$	−7.22028	−0.229013
$995$	21.0238	0.666498
$996$	24.3207	0.770629
$997$	47.5565	1.50613	0.753065	−	0.657946i	$-0.228575\pi$
$997$	47.5565	1.50613	0.753065	+	0.657946i	$0.228575\pi$
$998$	−17.7316	−0.561285
$999$	10.5278	0.333083

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4641.2.a.ba.1.11	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4641.2.a.ba.1.11	✓	17	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:	\( N \)	\(=\)	\( 4641 = 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4641.a (trivial)

\(f(q)\)	\(=\)	\(q+0.744396 q^{2} -1.00000 q^{3} -1.44587 q^{4} -1.18048 q^{5} -0.744396 q^{6} -1.00000 q^{7} -2.56510 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.744396 q^{2} -1.00000 q^{3} -1.44587 q^{4} -1.18048 q^{5} -0.744396 q^{6} -1.00000 q^{7} -2.56510 q^{8} +1.00000 q^{9} -0.878746 q^{10} -6.27171 q^{11} +1.44587 q^{12} +1.00000 q^{13} -0.744396 q^{14} +1.18048 q^{15} +0.982303 q^{16} -1.00000 q^{17} +0.744396 q^{18} -1.31201 q^{19} +1.70683 q^{20} +1.00000 q^{21} -4.66863 q^{22} +0.460825 q^{23} +2.56510 q^{24} -3.60646 q^{25} +0.744396 q^{26} -1.00000 q^{27} +1.44587 q^{28} -7.69176 q^{29} +0.878746 q^{30} -1.78367 q^{31} +5.86141 q^{32} +6.27171 q^{33} -0.744396 q^{34} +1.18048 q^{35} -1.44587 q^{36} -10.5278 q^{37} -0.976654 q^{38} -1.00000 q^{39} +3.02805 q^{40} -3.80452 q^{41} +0.744396 q^{42} +5.96073 q^{43} +9.06810 q^{44} -1.18048 q^{45} +0.343036 q^{46} -12.5400 q^{47} -0.982303 q^{48} +1.00000 q^{49} -2.68464 q^{50} +1.00000 q^{51} -1.44587 q^{52} -8.11622 q^{53} -0.744396 q^{54} +7.40364 q^{55} +2.56510 q^{56} +1.31201 q^{57} -5.72571 q^{58} -10.9399 q^{59} -1.70683 q^{60} +5.06772 q^{61} -1.32776 q^{62} -1.00000 q^{63} +2.39860 q^{64} -1.18048 q^{65} +4.66863 q^{66} -10.2881 q^{67} +1.44587 q^{68} -0.460825 q^{69} +0.878746 q^{70} +9.69952 q^{71} -2.56510 q^{72} +4.12330 q^{73} -7.83682 q^{74} +3.60646 q^{75} +1.89700 q^{76} +6.27171 q^{77} -0.744396 q^{78} +16.4197 q^{79} -1.15959 q^{80} +1.00000 q^{81} -2.83207 q^{82} +16.8207 q^{83} -1.44587 q^{84} +1.18048 q^{85} +4.43714 q^{86} +7.69176 q^{87} +16.0875 q^{88} +13.5138 q^{89} -0.878746 q^{90} -1.00000 q^{91} -0.666295 q^{92} +1.78367 q^{93} -9.33475 q^{94} +1.54880 q^{95} -5.86141 q^{96} +2.33389 q^{97} +0.744396 q^{98} -6.27171 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9}+O(q^{10}) \) 17 * q + q^2 - 17 * q^3 + 25 * q^4 - 4 * q^5 - q^6 - 17 * q^7 + 6 * q^8 + 17 * q^9	\( 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9} - q^{10} + 4 q^{11} - 25 q^{12} + 17 q^{13} - q^{14} + 4 q^{15} + 53 q^{16} - 17 q^{17} + q^{18} + 13 q^{19} - 5 q^{20} + 17 q^{21} + 4 q^{22} + 8 q^{23} - 6 q^{24} + 37 q^{25} + q^{26} - 17 q^{27} - 25 q^{28} - 3 q^{29} + q^{30} + 10 q^{31} + 18 q^{32} - 4 q^{33} - q^{34} + 4 q^{35} + 25 q^{36} - 25 q^{38} - 17 q^{39} - 12 q^{41} + q^{42} + 29 q^{43} + 12 q^{44} - 4 q^{45} + 19 q^{46} - 4 q^{47} - 53 q^{48} + 17 q^{49} + 9 q^{50} + 17 q^{51} + 25 q^{52} - 8 q^{53} - q^{54} + 27 q^{55} - 6 q^{56} - 13 q^{57} + 2 q^{58} + 25 q^{59} + 5 q^{60} - 5 q^{61} - 37 q^{62} - 17 q^{63} + 94 q^{64} - 4 q^{65} - 4 q^{66} + 15 q^{67} - 25 q^{68} - 8 q^{69} + q^{70} + 32 q^{71} + 6 q^{72} - 15 q^{73} + 16 q^{74} - 37 q^{75} + 3 q^{76} - 4 q^{77} - q^{78} + 27 q^{79} + 41 q^{80} + 17 q^{81} - 8 q^{82} - 24 q^{83} + 25 q^{84} + 4 q^{85} + 53 q^{86} + 3 q^{87} - 9 q^{88} - 8 q^{89} - q^{90} - 17 q^{91} + 14 q^{92} - 10 q^{93} + 51 q^{94} - 9 q^{95} - 18 q^{96} - 22 q^{97} + q^{98} + 4 q^{99}+O(q^{100}) \) 17 * q + q^2 - 17 * q^3 + 25 * q^4 - 4 * q^5 - q^6 - 17 * q^7 + 6 * q^8 + 17 * q^9 - q^10 + 4 * q^11 - 25 * q^12 + 17 * q^13 - q^14 + 4 * q^15 + 53 * q^16 - 17 * q^17 + q^18 + 13 * q^19 - 5 * q^20 + 17 * q^21 + 4 * q^22 + 8 * q^23 - 6 * q^24 + 37 * q^25 + q^26 - 17 * q^27 - 25 * q^28 - 3 * q^29 + q^30 + 10 * q^31 + 18 * q^32 - 4 * q^33 - q^34 + 4 * q^35 + 25 * q^36 - 25 * q^38 - 17 * q^39 - 12 * q^41 + q^42 + 29 * q^43 + 12 * q^44 - 4 * q^45 + 19 * q^46 - 4 * q^47 - 53 * q^48 + 17 * q^49 + 9 * q^50 + 17 * q^51 + 25 * q^52 - 8 * q^53 - q^54 + 27 * q^55 - 6 * q^56 - 13 * q^57 + 2 * q^58 + 25 * q^59 + 5 * q^60 - 5 * q^61 - 37 * q^62 - 17 * q^63 + 94 * q^64 - 4 * q^65 - 4 * q^66 + 15 * q^67 - 25 * q^68 - 8 * q^69 + q^70 + 32 * q^71 + 6 * q^72 - 15 * q^73 + 16 * q^74 - 37 * q^75 + 3 * q^76 - 4 * q^77 - q^78 + 27 * q^79 + 41 * q^80 + 17 * q^81 - 8 * q^82 - 24 * q^83 + 25 * q^84 + 4 * q^85 + 53 * q^86 + 3 * q^87 - 9 * q^88 - 8 * q^89 - q^90 - 17 * q^91 + 14 * q^92 - 10 * q^93 + 51 * q^94 - 9 * q^95 - 18 * q^96 - 22 * q^97 + q^98 + 4 * q^99

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