LMFDB - Embedded newform 251.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [251,2,Mod(1,251)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(251, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("251.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 251 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	251.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:	$2.00424509073$
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} - 2 x^{16} - 28 x^{15} + 54 x^{14} + 317 x^{13} - 582 x^{12} - 1867 x^{11} + 3178 x^{10} + \cdots + 256 $ x^17 - 2x^16 - 28x^15 + 54x^14 + 317x^13 - 582x^12 - 1867x^11 + 3178x^10 + 6186x^9 - 9216x^8 - 11921x^7 + 13680x^6 + 13752x^5 - 9400x^4 - 8800x^3 + 1920x^2 + 2240x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.27410$ of defining polynomial
Character	$\chi$	$=$	251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.27410 q^{2} +0.935470 q^{3} +3.17152 q^{4} +3.41593 q^{5} -2.12735 q^{6} +3.69332 q^{7} -2.66415 q^{8} -2.12490 q^{9} +O(q^{10})$	\(q-2.27410 q^{2} +0.935470 q^{3} +3.17152 q^{4} +3.41593 q^{5} -2.12735 q^{6} +3.69332 q^{7} -2.66415 q^{8} -2.12490 q^{9} -7.76816 q^{10} -1.09538 q^{11} +2.96686 q^{12} +0.0975293 q^{13} -8.39896 q^{14} +3.19550 q^{15} -0.284494 q^{16} -4.03572 q^{17} +4.83222 q^{18} +5.04841 q^{19} +10.8337 q^{20} +3.45499 q^{21} +2.49100 q^{22} -0.592256 q^{23} -2.49224 q^{24} +6.66859 q^{25} -0.221791 q^{26} -4.79419 q^{27} +11.7134 q^{28} -3.45917 q^{29} -7.26688 q^{30} -0.372983 q^{31} +5.97528 q^{32} -1.02469 q^{33} +9.17763 q^{34} +12.6161 q^{35} -6.73915 q^{36} +6.18783 q^{37} -11.4806 q^{38} +0.0912357 q^{39} -9.10057 q^{40} +11.3439 q^{41} -7.85698 q^{42} -5.37250 q^{43} -3.47402 q^{44} -7.25850 q^{45} +1.34685 q^{46} -10.3815 q^{47} -0.266136 q^{48} +6.64059 q^{49} -15.1650 q^{50} -3.77530 q^{51} +0.309316 q^{52} -11.2337 q^{53} +10.9024 q^{54} -3.74174 q^{55} -9.83957 q^{56} +4.72264 q^{57} +7.86649 q^{58} -7.25509 q^{59} +10.1346 q^{60} +0.601444 q^{61} +0.848199 q^{62} -7.84791 q^{63} -13.0194 q^{64} +0.333153 q^{65} +2.33026 q^{66} +11.6371 q^{67} -12.7994 q^{68} -0.554038 q^{69} -28.6903 q^{70} -0.624713 q^{71} +5.66105 q^{72} +9.71599 q^{73} -14.0717 q^{74} +6.23827 q^{75} +16.0112 q^{76} -4.04558 q^{77} -0.207479 q^{78} -6.82487 q^{79} -0.971814 q^{80} +1.88987 q^{81} -25.7971 q^{82} -15.5486 q^{83} +10.9576 q^{84} -13.7858 q^{85} +12.2176 q^{86} -3.23595 q^{87} +2.91826 q^{88} +15.9119 q^{89} +16.5065 q^{90} +0.360206 q^{91} -1.87835 q^{92} -0.348914 q^{93} +23.6087 q^{94} +17.2450 q^{95} +5.58969 q^{96} -7.70534 q^{97} -15.1013 q^{98} +2.32757 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 2 q^{2} + 26 q^{4} + 3 q^{5} + q^{6} + 3 q^{7} + 6 q^{8} + 25 q^{9}+O(q^{10}) $ 17 * q + 2 * q^2 + 26 * q^4 + 3 * q^5 + q^6 + 3 * q^7 + 6 * q^8 + 25 * q^9	\( 17 q + 2 q^{2} + 26 q^{4} + 3 q^{5} + q^{6} + 3 q^{7} + 6 q^{8} + 25 q^{9} + 7 q^{10} - q^{11} - 9 q^{12} + 22 q^{13} - 7 q^{14} - 8 q^{15} + 40 q^{16} - q^{17} - 7 q^{18} + 13 q^{19} - 14 q^{20} + 25 q^{21} + 4 q^{22} - 2 q^{23} - 24 q^{24} + 32 q^{25} - 9 q^{26} - 15 q^{27} - 10 q^{28} + 28 q^{29} - 34 q^{30} + 12 q^{31} + 4 q^{32} - 16 q^{33} - 21 q^{34} - 15 q^{35} + 21 q^{36} + 27 q^{37} - 37 q^{38} + 13 q^{39} - 7 q^{40} - q^{41} - 56 q^{42} + 9 q^{43} - 43 q^{44} - 7 q^{45} + 4 q^{46} - 20 q^{47} - 79 q^{48} + 32 q^{49} - 28 q^{50} - 2 q^{51} - q^{52} + q^{53} - 65 q^{54} - 11 q^{55} - 61 q^{56} - 24 q^{57} - 46 q^{58} - 20 q^{59} - 106 q^{60} + 59 q^{61} - 73 q^{62} - 41 q^{63} + 54 q^{64} - 14 q^{65} - 43 q^{66} + 15 q^{67} - 20 q^{68} + 38 q^{69} - 11 q^{70} - 26 q^{71} - 2 q^{72} + 8 q^{73} + 2 q^{74} - 20 q^{75} + 38 q^{76} + 33 q^{79} - 29 q^{80} + 29 q^{81} + 10 q^{82} + 63 q^{84} + 67 q^{85} + 11 q^{86} - 11 q^{87} + 27 q^{88} + 11 q^{89} + 72 q^{90} - 2 q^{91} + 28 q^{92} + 28 q^{93} + 29 q^{94} - 8 q^{95} - 17 q^{96} - 10 q^{97} + 22 q^{98} - 36 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 + 26 * q^4 + 3 * q^5 + q^6 + 3 * q^7 + 6 * q^8 + 25 * q^9 + 7 * q^10 - q^11 - 9 * q^12 + 22 * q^13 - 7 * q^14 - 8 * q^15 + 40 * q^16 - q^17 - 7 * q^18 + 13 * q^19 - 14 * q^20 + 25 * q^21 + 4 * q^22 - 2 * q^23 - 24 * q^24 + 32 * q^25 - 9 * q^26 - 15 * q^27 - 10 * q^28 + 28 * q^29 - 34 * q^30 + 12 * q^31 + 4 * q^32 - 16 * q^33 - 21 * q^34 - 15 * q^35 + 21 * q^36 + 27 * q^37 - 37 * q^38 + 13 * q^39 - 7 * q^40 - q^41 - 56 * q^42 + 9 * q^43 - 43 * q^44 - 7 * q^45 + 4 * q^46 - 20 * q^47 - 79 * q^48 + 32 * q^49 - 28 * q^50 - 2 * q^51 - q^52 + q^53 - 65 * q^54 - 11 * q^55 - 61 * q^56 - 24 * q^57 - 46 * q^58 - 20 * q^59 - 106 * q^60 + 59 * q^61 - 73 * q^62 - 41 * q^63 + 54 * q^64 - 14 * q^65 - 43 * q^66 + 15 * q^67 - 20 * q^68 + 38 * q^69 - 11 * q^70 - 26 * q^71 - 2 * q^72 + 8 * q^73 + 2 * q^74 - 20 * q^75 + 38 * q^76 + 33 * q^79 - 29 * q^80 + 29 * q^81 + 10 * q^82 + 63 * q^84 + 67 * q^85 + 11 * q^86 - 11 * q^87 + 27 * q^88 + 11 * q^89 + 72 * q^90 - 2 * q^91 + 28 * q^92 + 28 * q^93 + 29 * q^94 - 8 * q^95 - 17 * q^96 - 10 * q^97 + 22 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.27410	−1.60803	−0.804015	−	0.594609i	$-0.797307\pi$
$2$	−2.27410	−1.60803	−0.804015	+	0.594609i	$0.797307\pi$
$3$	0.935470	0.540094	0.270047	−	0.962847i	$-0.412961\pi$
$3$	0.935470	0.540094	0.270047	+	0.962847i	$0.412961\pi$
$4$	3.17152	1.58576
$5$	3.41593	1.52765	0.763826	−	0.645423i	$-0.223319\pi$
$5$	3.41593	1.52765	0.763826	+	0.645423i	$0.223319\pi$
$6$	−2.12735	−0.868487
$7$	3.69332	1.39594	0.697971	−	0.716126i	$-0.254086\pi$
$7$	3.69332	1.39594	0.697971	+	0.716126i	$0.254086\pi$
$8$	−2.66415	−0.941921
$9$	−2.12490	−0.708299
$10$	−7.76816	−2.45651
$11$	−1.09538	−0.330269	−0.165135	−	0.986271i	$-0.552806\pi$
$11$	−1.09538	−0.330269	−0.165135	+	0.986271i	$0.552806\pi$
$12$	2.96686	0.856459
$13$	0.0975293	0.0270498	0.0135249	−	0.999909i	$-0.495695\pi$
$13$	0.0975293	0.0270498	0.0135249	+	0.999909i	$0.495695\pi$
$14$	−8.39896	−2.24472
$15$	3.19550	0.825075
$16$	−0.284494	−0.0711236
$17$	−4.03572	−0.978807	−0.489403	−	0.872057i	$-0.662785\pi$
$17$	−4.03572	−0.978807	−0.489403	+	0.872057i	$0.662785\pi$
$18$	4.83222	1.13897
$19$	5.04841	1.15819	0.579093	−	0.815262i	$-0.303407\pi$
$19$	5.04841	1.15819	0.579093	+	0.815262i	$0.303407\pi$
$20$	10.8337	2.42249
$21$	3.45499	0.753940
$22$	2.49100	0.531083
$23$	−0.592256	−0.123494	−0.0617469	−	0.998092i	$-0.519667\pi$
$23$	−0.592256	−0.123494	−0.0617469	+	0.998092i	$0.519667\pi$
$24$	−2.49224	−0.508726
$25$	6.66859	1.33372
$26$	−0.221791	−0.0434968
$27$	−4.79419	−0.922641
$28$	11.7134	2.21363
$29$	−3.45917	−0.642352	−0.321176	−	0.947020i	$-0.604078\pi$
$29$	−3.45917	−0.642352	−0.321176	+	0.947020i	$0.604078\pi$
$30$	−7.26688	−1.32675
$31$	−0.372983	−0.0669897	−0.0334948	−	0.999439i	$-0.510664\pi$
$31$	−0.372983	−0.0669897	−0.0334948	+	0.999439i	$0.510664\pi$
$32$	5.97528	1.05629
$33$	−1.02469	−0.178376
$34$	9.17763	1.57395
$35$	12.6161	2.13251
$36$	−6.73915	−1.12319
$37$	6.18783	1.01727	0.508636	−	0.860981i	$-0.330150\pi$
$37$	6.18783	1.01727	0.508636	+	0.860981i	$0.330150\pi$
$38$	−11.4806	−1.86240
$39$	0.0912357	0.0146094
$40$	−9.10057	−1.43893
$41$	11.3439	1.77161	0.885807	−	0.464054i	$-0.153605\pi$
$41$	11.3439	1.77161	0.885807	+	0.464054i	$0.153605\pi$
$42$	−7.85698	−1.21236
$43$	−5.37250	−0.819298	−0.409649	−	0.912243i	$-0.634349\pi$
$43$	−5.37250	−0.819298	−0.409649	+	0.912243i	$0.634349\pi$
$44$	−3.47402	−0.523728
$45$	−7.25850	−1.08203
$46$	1.34685	0.198582
$47$	−10.3815	−1.51430	−0.757152	−	0.653239i	$-0.773410\pi$
$47$	−10.3815	−1.51430	−0.757152	+	0.653239i	$0.773410\pi$
$48$	−0.266136	−0.0384134
$49$	6.64059	0.948655
$50$	−15.1650	−2.14466
$51$	−3.77530	−0.528647
$52$	0.309316	0.0428944
$53$	−11.2337	−1.54306	−0.771531	−	0.636192i	$-0.780508\pi$
$53$	−11.2337	−1.54306	−0.771531	+	0.636192i	$0.780508\pi$
$54$	10.9024	1.48364
$55$	−3.74174	−0.504537
$56$	−9.83957	−1.31487
$57$	4.72264	0.625529
$58$	7.86649	1.03292
$59$	−7.25509	−0.944533	−0.472266	−	0.881456i	$-0.656564\pi$
$59$	−7.25509	−0.944533	−0.472266	+	0.881456i	$0.656564\pi$
$60$	10.1346	1.30837
$61$	0.601444	0.0770070	0.0385035	−	0.999258i	$-0.487741\pi$
$61$	0.601444	0.0770070	0.0385035	+	0.999258i	$0.487741\pi$
$62$	0.848199	0.107721
$63$	−7.84791	−0.988744
$64$	−13.0194	−1.62742
$65$	0.333153	0.0413226
$66$	2.33026	0.286835
$67$	11.6371	1.42170	0.710848	−	0.703346i	$-0.248311\pi$
$67$	11.6371	1.42170	0.710848	+	0.703346i	$0.248311\pi$
$68$	−12.7994	−1.55215
$69$	−0.554038	−0.0666983
$70$	−28.6903	−3.42915
$71$	−0.624713	−0.0741397	−0.0370699	−	0.999313i	$-0.511802\pi$
$71$	−0.624713	−0.0741397	−0.0370699	+	0.999313i	$0.511802\pi$
$72$	5.66105	0.667161
$73$	9.71599	1.13717	0.568585	−	0.822624i	$-0.307491\pi$
$73$	9.71599	1.13717	0.568585	+	0.822624i	$0.307491\pi$
$74$	−14.0717	−1.63581
$75$	6.23827	0.720333
$76$	16.0112	1.83661
$77$	−4.04558	−0.461037
$78$	−0.207479	−0.0234924
$79$	−6.82487	−0.767858	−0.383929	−	0.923363i	$-0.625429\pi$
$79$	−6.82487	−0.767858	−0.383929	+	0.923363i	$0.625429\pi$
$80$	−0.971814	−0.108652
$81$	1.88987	0.209986
$82$	−25.7971	−2.84881
$83$	−15.5486	−1.70668	−0.853341	−	0.521353i	$-0.825428\pi$
$83$	−15.5486	−1.70668	−0.853341	+	0.521353i	$0.825428\pi$
$84$	10.9576	1.19557
$85$	−13.7858	−1.49528
$86$	12.2176	1.31746
$87$	−3.23595	−0.346930
$88$	2.91826	0.311088
$89$	15.9119	1.68665	0.843327	−	0.537401i	$-0.180594\pi$
$89$	15.9119	1.68665	0.843327	+	0.537401i	$0.180594\pi$
$90$	16.5065	1.73994
$91$	0.360206	0.0377599
$92$	−1.87835	−0.195832
$93$	−0.348914	−0.0361807
$94$	23.6087	2.43505
$95$	17.2450	1.76930
$96$	5.58969	0.570495
$97$	−7.70534	−0.782359	−0.391179	−	0.920314i	$-0.627933\pi$
$97$	−7.70534	−0.782359	−0.391179	+	0.920314i	$0.627933\pi$
$98$	−15.1013	−1.52547
$99$	2.32757	0.233929
$100$	21.1496	2.11496
$101$	18.0872	1.79975	0.899873	−	0.436153i	$-0.143659\pi$
$101$	18.0872	1.79975	0.899873	+	0.436153i	$0.143659\pi$
$102$	8.58540	0.850081
$103$	−7.78184	−0.766767	−0.383384	−	0.923589i	$-0.625241\pi$
$103$	−7.78184	−0.766767	−0.383384	+	0.923589i	$0.625241\pi$
$104$	−0.259833	−0.0254787
$105$	11.8020	1.15176
$106$	25.5464	2.48129
$107$	−2.56314	−0.247788	−0.123894	−	0.992295i	$-0.539538\pi$
$107$	−2.56314	−0.247788	−0.123894	+	0.992295i	$0.539538\pi$
$108$	−15.2049	−1.46309
$109$	0.411462	0.0394109	0.0197054	−	0.999806i	$-0.493727\pi$
$109$	0.411462	0.0394109	0.0197054	+	0.999806i	$0.493727\pi$
$110$	8.50909	0.811310
$111$	5.78853	0.549423
$112$	−1.05073	−0.0992845
$113$	−4.12662	−0.388200	−0.194100	−	0.980982i	$-0.562179\pi$
$113$	−4.12662	−0.388200	−0.194100	+	0.980982i	$0.562179\pi$
$114$	−10.7397	−1.00587
$115$	−2.02311	−0.188656
$116$	−10.9708	−1.01862
$117$	−0.207240	−0.0191593
$118$	16.4988	1.51884
$119$	−14.9052	−1.36636
$120$	−8.51331	−0.777155
$121$	−9.80014	−0.890922
$122$	−1.36774	−0.123830
$123$	10.6118	0.956838
$124$	−1.18292	−0.106230
$125$	5.69980	0.509805
$126$	17.8469	1.58993
$127$	−11.8625	−1.05263	−0.526316	−	0.850289i	$-0.676427\pi$
$127$	−11.8625	−1.05263	−0.526316	+	0.850289i	$0.676427\pi$
$128$	17.6568	1.56065
$129$	−5.02581	−0.442498
$130$	−0.757623	−0.0664480
$131$	22.4352	1.96017	0.980087	−	0.198570i	$-0.0636298\pi$
$131$	22.4352	1.96017	0.980087	+	0.198570i	$0.0636298\pi$
$132$	−3.24984	−0.282862
$133$	18.6454	1.61676
$134$	−26.4639	−2.28613
$135$	−16.3766	−1.40947
$136$	10.7518	0.921959
$137$	−10.6248	−0.907740	−0.453870	−	0.891068i	$-0.649957\pi$
$137$	−10.6248	−0.907740	−0.453870	+	0.891068i	$0.649957\pi$
$138$	1.25994	0.107253
$139$	−17.7360	−1.50435	−0.752175	−	0.658964i	$-0.770995\pi$
$139$	−17.7360	−1.50435	−0.752175	+	0.658964i	$0.770995\pi$
$140$	40.0123	3.38166
$141$	−9.71162	−0.817866
$142$	1.42066	0.119219
$143$	−0.106832	−0.00893371
$144$	0.604521	0.0503768
$145$	−11.8163	−0.981290
$146$	−22.0951	−1.82860
$147$	6.21207	0.512363
$148$	19.6248	1.61315
$149$	10.3371	0.846844	0.423422	−	0.905933i	$-0.360829\pi$
$149$	10.3371	0.846844	0.423422	+	0.905933i	$0.360829\pi$
$150$	−14.1864	−1.15832
$151$	11.0755	0.901312	0.450656	−	0.892698i	$-0.351190\pi$
$151$	11.0755	0.901312	0.450656	+	0.892698i	$0.351190\pi$
$152$	−13.4498	−1.09092
$153$	8.57550	0.693288
$154$	9.20005	0.741362
$155$	−1.27408	−0.102337
$156$	0.289356	0.0231670
$157$	−24.3028	−1.93957	−0.969787	−	0.243955i	$-0.921555\pi$
$157$	−24.3028	−1.93957	−0.969787	+	0.243955i	$0.921555\pi$
$158$	15.5204	1.23474
$159$	−10.5087	−0.833398
$160$	20.4111	1.61364
$161$	−2.18739	−0.172390
$162$	−4.29776	−0.337664
$163$	−12.6767	−0.992913	−0.496456	−	0.868062i	$-0.665366\pi$
$163$	−12.6767	−0.992913	−0.496456	+	0.868062i	$0.665366\pi$
$164$	35.9773	2.80936
$165$	−3.50029	−0.272497
$166$	35.3591	2.74440
$167$	8.35277	0.646357	0.323178	−	0.946338i	$-0.395249\pi$
$167$	8.35277	0.646357	0.323178	+	0.946338i	$0.395249\pi$
$168$	−9.20462	−0.710152
$169$	−12.9905	−0.999268
$170$	31.3502	2.40445
$171$	−10.7274	−0.820342
$172$	−17.0390	−1.29921
$173$	12.8831	0.979487	0.489744	−	0.871866i	$-0.337090\pi$
$173$	12.8831	0.979487	0.489744	+	0.871866i	$0.337090\pi$
$174$	7.35887	0.557874
$175$	24.6292	1.86179
$176$	0.311629	0.0234900
$177$	−6.78692	−0.510136
$178$	−36.1851	−2.71219
$179$	−26.3530	−1.96971	−0.984856	−	0.173373i	$-0.944533\pi$
$179$	−26.3530	−1.96971	−0.984856	+	0.173373i	$0.944533\pi$
$180$	−23.0205	−1.71585
$181$	−16.9891	−1.26279	−0.631396	−	0.775461i	$-0.717518\pi$
$181$	−16.9891	−1.26279	−0.631396	+	0.775461i	$0.717518\pi$
$182$	−0.819145	−0.0607191
$183$	0.562633	0.0415910
$184$	1.57786	0.116321
$185$	21.1372	1.55404
$186$	0.793465	0.0581797
$187$	4.42065	0.323270
$188$	−32.9253	−2.40132
$189$	−17.7064	−1.28795
$190$	−39.2169	−2.84509
$191$	7.24390	0.524151	0.262075	−	0.965047i	$-0.415593\pi$
$191$	7.24390	0.524151	0.262075	+	0.965047i	$0.415593\pi$
$192$	−12.1792	−0.878960
$193$	2.35410	0.169452	0.0847259	−	0.996404i	$-0.472999\pi$
$193$	2.35410	0.169452	0.0847259	+	0.996404i	$0.472999\pi$
$194$	17.5227	1.25806
$195$	0.311655	0.0223181
$196$	21.0608	1.50434
$197$	−12.2704	−0.874233	−0.437117	−	0.899405i	$-0.644000\pi$
$197$	−12.2704	−0.874233	−0.437117	+	0.899405i	$0.644000\pi$
$198$	−5.29312	−0.376166
$199$	1.62720	0.115349	0.0576745	−	0.998335i	$-0.481631\pi$
$199$	1.62720	0.115349	0.0576745	+	0.998335i	$0.481631\pi$
$200$	−17.7662	−1.25626
$201$	10.8861	0.767849
$202$	−41.1321	−2.89404
$203$	−12.7758	−0.896686
$204$	−11.9734	−0.838308
$205$	38.7499	2.70641
$206$	17.6967	1.23298
$207$	1.25848	0.0874706
$208$	−0.0277465	−0.00192388
$209$	−5.52993	−0.382513
$210$	−26.8389	−1.85206
$211$	12.7353	0.876736	0.438368	−	0.898796i	$-0.355557\pi$
$211$	12.7353	0.876736	0.438368	+	0.898796i	$0.355557\pi$
$212$	−35.6278	−2.44693
$213$	−0.584400	−0.0400424
$214$	5.82883	0.398451
$215$	−18.3521	−1.25160
$216$	12.7725	0.869055
$217$	−1.37754	−0.0935137
$218$	−0.935704	−0.0633739
$219$	9.08901	0.614179
$220$	−11.8670	−0.800074
$221$	−0.393601	−0.0264765
$222$	−13.1637	−0.883488
$223$	22.4100	1.50069	0.750343	−	0.661048i	$-0.229888\pi$
$223$	22.4100	1.50069	0.750343	+	0.661048i	$0.229888\pi$
$224$	22.0686	1.47452
$225$	−14.1701	−0.944671
$226$	9.38433	0.624237
$227$	−9.39073	−0.623285	−0.311642	−	0.950199i	$-0.600879\pi$
$227$	−9.39073	−0.623285	−0.311642	+	0.950199i	$0.600879\pi$
$228$	14.9780	0.991939
$229$	14.8143	0.978957	0.489478	−	0.872015i	$-0.337187\pi$
$229$	14.8143	0.978957	0.489478	+	0.872015i	$0.337187\pi$
$230$	4.60074	0.303364
$231$	−3.78452	−0.249003
$232$	9.21577	0.605045
$233$	11.7123	0.767297	0.383648	−	0.923479i	$-0.374667\pi$
$233$	11.7123	0.767297	0.383648	+	0.923479i	$0.374667\pi$
$234$	0.471283	0.0308087
$235$	−35.4627	−2.31333
$236$	−23.0097	−1.49780
$237$	−6.38446	−0.414715
$238$	33.8959	2.19714
$239$	−25.8228	−1.67034	−0.835168	−	0.549995i	$-0.814629\pi$
$239$	−25.8228	−1.67034	−0.835168	+	0.549995i	$0.814629\pi$
$240$	−0.909102	−0.0586823
$241$	5.23762	0.337385	0.168692	−	0.985669i	$-0.446046\pi$
$241$	5.23762	0.337385	0.168692	+	0.985669i	$0.446046\pi$
$242$	22.2865	1.43263
$243$	16.1505	1.03605
$244$	1.90749	0.122115
$245$	22.6838	1.44921
$246$	−24.1324	−1.53862
$247$	0.492368	0.0313286
$248$	0.993684	0.0630990
$249$	−14.5453	−0.921768
$250$	−12.9619	−0.819782
$251$	1.00000	0.0631194
$251$	1.00000	0.0631194
$252$	−24.8898	−1.56791
$253$	0.648745	0.0407863
$254$	26.9766	1.69266
$255$	−12.8962	−0.807589
$256$	−14.1145	−0.882156
$257$	25.3189	1.57935	0.789675	−	0.613525i	$-0.210249\pi$
$257$	25.3189	1.57935	0.789675	+	0.613525i	$0.210249\pi$
$258$	11.4292	0.711550
$259$	22.8536	1.42005
$260$	1.05660	0.0655277
$261$	7.35038	0.454977
$262$	−51.0199	−3.15202
$263$	−10.9977	−0.678147	−0.339074	−	0.940760i	$-0.610114\pi$
$263$	−10.9977	−0.678147	−0.339074	+	0.940760i	$0.610114\pi$
$264$	2.72994	0.168016
$265$	−38.3734	−2.35726
$266$	−42.4014	−2.59980
$267$	14.8851	0.910951
$268$	36.9073	2.25447
$269$	24.8062	1.51246	0.756230	−	0.654305i	$-0.227039\pi$
$269$	24.8062	1.51246	0.756230	+	0.654305i	$0.227039\pi$
$270$	37.2420	2.26648
$271$	−5.48722	−0.333325	−0.166662	−	0.986014i	$-0.553299\pi$
$271$	−5.48722	−0.333325	−0.166662	+	0.986014i	$0.553299\pi$
$272$	1.14814	0.0696163
$273$	0.336962	0.0203939
$274$	24.1619	1.45967
$275$	−7.30464	−0.440486
$276$	−1.75714	−0.105768
$277$	5.78730	0.347725	0.173862	−	0.984770i	$-0.444375\pi$
$277$	5.78730	0.347725	0.173862	+	0.984770i	$0.444375\pi$
$278$	40.3334	2.41904
$279$	0.792550	0.0474487
$280$	−33.6113	−2.00866
$281$	12.7109	0.758266	0.379133	−	0.925342i	$-0.376222\pi$
$281$	12.7109	0.758266	0.379133	+	0.925342i	$0.376222\pi$
$282$	22.0852	1.31515
$283$	8.50578	0.505616	0.252808	−	0.967516i	$-0.418646\pi$
$283$	8.50578	0.505616	0.252808	+	0.967516i	$0.418646\pi$
$284$	−1.98129	−0.117568
$285$	16.1322	0.955590
$286$	0.242945	0.0143657
$287$	41.8965	2.47307
$288$	−12.6968	−0.748169
$289$	−0.712929	−0.0419370
$290$	26.8714	1.57794
$291$	−7.20811	−0.422547
$292$	30.8145	1.80328
$293$	19.2686	1.12569	0.562843	−	0.826564i	$-0.309708\pi$
$293$	19.2686	1.12569	0.562843	+	0.826564i	$0.309708\pi$
$294$	−14.1269	−0.823895
$295$	−24.7829	−1.44292
$296$	−16.4853	−0.958191
$297$	5.25145	0.304720
$298$	−23.5075	−1.36175
$299$	−0.0577623	−0.00334048
$300$	19.7848	1.14228
$301$	−19.8423	−1.14369
$302$	−25.1868	−1.44934
$303$	16.9200	0.972031
$304$	−1.43625	−0.0823744
$305$	2.05449	0.117640
$306$	−19.5015	−1.11483
$307$	−0.292654	−0.0167026	−0.00835132	−	0.999965i	$-0.502658\pi$
$307$	−0.292654	−0.0167026	−0.00835132	+	0.999965i	$0.502658\pi$
$308$	−12.8307	−0.731095
$309$	−7.27967	−0.414126
$310$	2.89739	0.164561
$311$	5.10705	0.289594	0.144797	−	0.989461i	$-0.453747\pi$
$311$	5.10705	0.289594	0.144797	+	0.989461i	$0.453747\pi$
$312$	−0.243066	−0.0137609
$313$	−7.20479	−0.407239	−0.203619	−	0.979050i	$-0.565271\pi$
$313$	−7.20479	−0.407239	−0.203619	+	0.979050i	$0.565271\pi$
$314$	55.2669	3.11889
$315$	−26.8079	−1.51046
$316$	−21.6452	−1.21764
$317$	−10.6486	−0.598086	−0.299043	−	0.954240i	$-0.596667\pi$
$317$	−10.6486	−0.598086	−0.299043	+	0.954240i	$0.596667\pi$
$318$	23.8979	1.34013
$319$	3.78911	0.212149
$320$	−44.4733	−2.48613
$321$	−2.39774	−0.133829
$322$	4.97434	0.277209
$323$	−20.3740	−1.13364
$324$	5.99377	0.332987
$325$	0.650383	0.0360768
$326$	28.8280	1.59663
$327$	0.384910	0.0212856
$328$	−30.2218	−1.66872
$329$	−38.3423	−2.11388
$330$	7.96000	0.438183
$331$	16.4433	0.903804	0.451902	−	0.892068i	$-0.350746\pi$
$331$	16.4433	0.903804	0.451902	+	0.892068i	$0.350746\pi$
$332$	−49.3128	−2.70639
$333$	−13.1485	−0.720533
$334$	−18.9950	−1.03936
$335$	39.7515	2.17186
$336$	−0.982924	−0.0536229
$337$	14.0936	0.767728	0.383864	−	0.923390i	$-0.374593\pi$
$337$	14.0936	0.767728	0.383864	+	0.923390i	$0.374593\pi$
$338$	29.5416	1.60685
$339$	−3.86033	−0.209664
$340$	−43.7218	−2.37115
$341$	0.408558	0.0221246
$342$	24.3951	1.31913
$343$	−1.32743	−0.0716743
$344$	14.3132	0.771714
$345$	−1.89255	−0.101892
$346$	−29.2975	−1.57505
$347$	10.7871	0.579084	0.289542	−	0.957165i	$-0.406497\pi$
$347$	10.7871	0.579084	0.289542	+	0.957165i	$0.406497\pi$
$348$	−10.2629	−0.550148
$349$	7.97572	0.426930	0.213465	−	0.976951i	$-0.431525\pi$
$349$	7.97572	0.426930	0.213465	+	0.976951i	$0.431525\pi$
$350$	−56.0093	−2.99382
$351$	−0.467573	−0.0249572
$352$	−6.54520	−0.348860
$353$	11.2749	0.600104	0.300052	−	0.953923i	$-0.402996\pi$
$353$	11.2749	0.600104	0.300052	+	0.953923i	$0.402996\pi$
$354$	15.4341	0.820314
$355$	−2.13398	−0.113260
$356$	50.4648	2.67463
$357$	−13.9434	−0.737961
$358$	59.9292	3.16736
$359$	13.1558	0.694339	0.347169	−	0.937802i	$-0.387143\pi$
$359$	13.1558	0.694339	0.347169	+	0.937802i	$0.387143\pi$
$360$	19.3378	1.01919
$361$	6.48649	0.341394
$362$	38.6349	2.03061
$363$	−9.16774	−0.481181
$364$	1.14240	0.0598782
$365$	33.1892	1.73720
$366$	−1.27948	−0.0668796
$367$	10.6315	0.554961	0.277481	−	0.960731i	$-0.410501\pi$
$367$	10.6315	0.554961	0.277481	+	0.960731i	$0.410501\pi$
$368$	0.168494	0.00878333
$369$	−24.1045	−1.25483
$370$	−48.0681	−2.49894
$371$	−41.4894	−2.15402
$372$	−1.10659	−0.0573739
$373$	−12.1705	−0.630163	−0.315082	−	0.949065i	$-0.602032\pi$
$373$	−12.1705	−0.630163	−0.315082	+	0.949065i	$0.602032\pi$
$374$	−10.0530	−0.519828
$375$	5.33199	0.275343
$376$	27.6580	1.42635
$377$	−0.337370	−0.0173755
$378$	40.2662	2.07107
$379$	−2.32877	−0.119621	−0.0598103	−	0.998210i	$-0.519050\pi$
$379$	−2.32877	−0.119621	−0.0598103	+	0.998210i	$0.519050\pi$
$380$	54.6930	2.80569
$381$	−11.0971	−0.568519
$382$	−16.4733	−0.842850
$383$	0.235563	0.0120367	0.00601835	−	0.999982i	$-0.498084\pi$
$383$	0.235563	0.0120367	0.00601835	+	0.999982i	$0.498084\pi$
$384$	16.5174	0.842899
$385$	−13.8194	−0.704304
$386$	−5.35345	−0.272484
$387$	11.4160	0.580308
$388$	−24.4376	−1.24063
$389$	−22.8102	−1.15652	−0.578261	−	0.815852i	$-0.696268\pi$
$389$	−22.8102	−1.15652	−0.578261	+	0.815852i	$0.696268\pi$
$390$	−0.708734	−0.0358881
$391$	2.39018	0.120877
$392$	−17.6915	−0.893558
$393$	20.9875	1.05868
$394$	27.9042	1.40579
$395$	−23.3133	−1.17302
$396$	7.38193	0.370956
$397$	23.5310	1.18099	0.590493	−	0.807043i	$-0.298933\pi$
$397$	23.5310	1.18099	0.590493	+	0.807043i	$0.298933\pi$
$398$	−3.70041	−0.185485
$399$	17.4422	0.873202
$400$	−1.89718	−0.0948589
$401$	−0.765035	−0.0382040	−0.0191020	−	0.999818i	$-0.506081\pi$
$401$	−0.765035	−0.0382040	−0.0191020	+	0.999818i	$0.506081\pi$
$402$	−24.7561	−1.23472
$403$	−0.0363767	−0.00181205
$404$	57.3640	2.85397
$405$	6.45568	0.320785
$406$	29.0535	1.44190
$407$	−6.77802	−0.335974
$408$	10.0580	0.497944
$409$	−5.60286	−0.277044	−0.138522	−	0.990359i	$-0.544235\pi$
$409$	−5.60286	−0.277044	−0.138522	+	0.990359i	$0.544235\pi$
$410$	−88.1210	−4.35199
$411$	−9.93920	−0.490265
$412$	−24.6803	−1.21591
$413$	−26.7954	−1.31851
$414$	−2.86191	−0.140655
$415$	−53.1130	−2.60722
$416$	0.582764	0.0285724
$417$	−16.5915	−0.812490
$418$	12.5756	0.615093
$419$	−24.8299	−1.21302	−0.606509	−	0.795077i	$-0.707431\pi$
$419$	−24.8299	−1.21302	−0.606509	+	0.795077i	$0.707431\pi$
$420$	37.4303	1.82641
$421$	12.2521	0.597133	0.298566	−	0.954389i	$-0.403492\pi$
$421$	12.2521	0.597133	0.298566	+	0.954389i	$0.403492\pi$
$422$	−28.9614	−1.40982
$423$	22.0597	1.07258
$424$	29.9282	1.45344
$425$	−26.9126	−1.30545
$426$	1.32898	0.0643894
$427$	2.22132	0.107497
$428$	−8.12906	−0.392933
$429$	−0.0999377	−0.00482504
$430$	41.7344	2.01261
$431$	−24.3396	−1.17240	−0.586199	−	0.810167i	$-0.699376\pi$
$431$	−24.3396	−1.17240	−0.586199	+	0.810167i	$0.699376\pi$
$432$	1.36392	0.0656216
$433$	8.35633	0.401580	0.200790	−	0.979634i	$-0.435649\pi$
$433$	8.35633	0.401580	0.200790	+	0.979634i	$0.435649\pi$
$434$	3.13267	0.150373
$435$	−11.0538	−0.529988
$436$	1.30496	0.0624962
$437$	−2.98995	−0.143029
$438$	−20.6693	−0.987618
$439$	−5.67395	−0.270803	−0.135402	−	0.990791i	$-0.543232\pi$
$439$	−5.67395	−0.270803	−0.135402	+	0.990791i	$0.543232\pi$
$440$	9.96858	0.475233
$441$	−14.1106	−0.671931
$442$	0.895088	0.0425750
$443$	3.55735	0.169015	0.0845073	−	0.996423i	$-0.473068\pi$
$443$	3.55735	0.169015	0.0845073	+	0.996423i	$0.473068\pi$
$444$	18.3584	0.871253
$445$	54.3538	2.57662
$446$	−50.9626	−2.41315
$447$	9.67000	0.457375
$448$	−48.0847	−2.27179
$449$	27.9540	1.31923	0.659616	−	0.751603i	$-0.270719\pi$
$449$	27.9540	1.31923	0.659616	+	0.751603i	$0.270719\pi$
$450$	32.2241	1.51906
$451$	−12.4258	−0.585110
$452$	−13.0877	−0.615592
$453$	10.3608	0.486793
$454$	21.3554	1.00226
$455$	1.23044	0.0576840
$456$	−12.5818	−0.589199
$457$	11.2752	0.527430	0.263715	−	0.964601i	$-0.415052\pi$
$457$	11.2752	0.527430	0.263715	+	0.964601i	$0.415052\pi$
$458$	−33.6892	−1.57419
$459$	19.3480	0.903088
$460$	−6.41632	−0.299163
$461$	20.2942	0.945193	0.472597	−	0.881279i	$-0.343317\pi$
$461$	20.2942	0.945193	0.472597	+	0.881279i	$0.343317\pi$
$462$	8.60637	0.400405
$463$	−25.6264	−1.19096	−0.595481	−	0.803370i	$-0.703038\pi$
$463$	−25.6264	−1.19096	−0.595481	+	0.803370i	$0.703038\pi$
$464$	0.984115	0.0456864
$465$	−1.19187	−0.0552715
$466$	−26.6349	−1.23384
$467$	19.0460	0.881345	0.440673	−	0.897668i	$-0.354740\pi$
$467$	19.0460	0.881345	0.440673	+	0.897668i	$0.354740\pi$
$468$	−0.657265	−0.0303821
$469$	42.9794	1.98461
$470$	80.6456	3.71990
$471$	−22.7345	−1.04755
$472$	19.3287	0.889675
$473$	5.88492	0.270589
$474$	14.5189	0.666875
$475$	33.6658	1.54469
$476$	−47.2722	−2.16672
$477$	23.8704	1.09295
$478$	58.7235	2.68595
$479$	0.620088	0.0283326	0.0141663	−	0.999900i	$-0.495491\pi$
$479$	0.620088	0.0283326	0.0141663	+	0.999900i	$0.495491\pi$
$480$	19.0940	0.871518
$481$	0.603495	0.0275170
$482$	−11.9109	−0.542525
$483$	−2.04624	−0.0931070
$484$	−31.0814	−1.41279
$485$	−26.3209	−1.19517
$486$	−36.7278	−1.66601
$487$	3.10719	0.140800	0.0704000	−	0.997519i	$-0.477572\pi$
$487$	3.10719	0.140800	0.0704000	+	0.997519i	$0.477572\pi$
$488$	−1.60234	−0.0725345
$489$	−11.8586	−0.536266
$490$	−51.5852	−2.33038
$491$	−1.67757	−0.0757079	−0.0378539	−	0.999283i	$-0.512052\pi$
$491$	−1.67757	−0.0757079	−0.0378539	+	0.999283i	$0.512052\pi$
$492$	33.6557	1.51732
$493$	13.9603	0.628739
$494$	−1.11969	−0.0503774
$495$	7.95082	0.357363
$496$	0.106112	0.00476455
$497$	−2.30726	−0.103495
$498$	33.0773	1.48223
$499$	−18.6142	−0.833284	−0.416642	−	0.909071i	$-0.636793\pi$
$499$	−18.6142	−0.833284	−0.416642	+	0.909071i	$0.636793\pi$
$500$	18.0770	0.808429
$501$	7.81376	0.349093
$502$	−2.27410	−0.101498
$503$	−29.5856	−1.31915	−0.659577	−	0.751637i	$-0.729265\pi$
$503$	−29.5856	−1.31915	−0.659577	+	0.751637i	$0.729265\pi$
$504$	20.9081	0.931319
$505$	61.7847	2.74938
$506$	−1.47531	−0.0655855
$507$	−12.1522	−0.539699
$508$	−37.6223	−1.66922
$509$	25.2807	1.12055	0.560274	−	0.828307i	$-0.310696\pi$
$509$	25.2807	1.12055	0.560274	+	0.828307i	$0.310696\pi$
$510$	29.3271	1.29863
$511$	35.8842	1.58742
$512$	−3.21581	−0.142120
$513$	−24.2030	−1.06859
$514$	−57.5777	−2.53964
$515$	−26.5822	−1.17135
$516$	−15.9395	−0.701696
$517$	11.3717	0.500128
$518$	−51.9714	−2.28349
$519$	12.0518	0.529015
$520$	−0.887572	−0.0389226
$521$	31.4315	1.37704	0.688520	−	0.725217i	$-0.258261\pi$
$521$	31.4315	1.37704	0.688520	+	0.725217i	$0.258261\pi$
$522$	−16.7155	−0.731617
$523$	2.72046	0.118957	0.0594786	−	0.998230i	$-0.481056\pi$
$523$	2.72046	0.118957	0.0594786	+	0.998230i	$0.481056\pi$
$524$	71.1537	3.10837
$525$	23.0399	1.00554
$526$	25.0098	1.09048
$527$	1.50526	0.0655699
$528$	0.291520	0.0126868
$529$	−22.6492	−0.984749
$530$	87.2649	3.79054
$531$	15.4163	0.669011
$532$	59.1343	2.56380
$533$	1.10636	0.0479217
$534$	−33.8501	−1.46484
$535$	−8.75551	−0.378534
$536$	−31.0030	−1.33912
$537$	−24.6524	−1.06383
$538$	−56.4117	−2.43208
$539$	−7.27396	−0.313312
$540$	−51.9388	−2.23509
$541$	33.7433	1.45074	0.725369	−	0.688360i	$-0.241669\pi$
$541$	33.7433	1.45074	0.725369	+	0.688360i	$0.241669\pi$
$542$	12.4785	0.535996
$543$	−15.8928	−0.682026
$544$	−24.1146	−1.03390
$545$	1.40553	0.0602061
$546$	−0.766285	−0.0327940
$547$	1.51530	0.0647894	0.0323947	−	0.999475i	$-0.489687\pi$
$547$	1.51530	0.0647894	0.0323947	+	0.999475i	$0.489687\pi$
$548$	−33.6969	−1.43946
$549$	−1.27801	−0.0545440
$550$	16.6115	0.708315
$551$	−17.4633	−0.743963
$552$	1.47604	0.0628245
$553$	−25.2064	−1.07189
$554$	−13.1609	−0.559152
$555$	19.7732	0.839326
$556$	−56.2502	−2.38554
$557$	−4.08594	−0.173127	−0.0865633	−	0.996246i	$-0.527588\pi$
$557$	−4.08594	−0.173127	−0.0865633	+	0.996246i	$0.527588\pi$
$558$	−1.80234	−0.0762989
$559$	−0.523976	−0.0221618
$560$	−3.58922	−0.151672
$561$	4.13539	0.174596
$562$	−28.9057	−1.21932
$563$	4.30244	0.181326	0.0906631	−	0.995882i	$-0.471101\pi$
$563$	4.30244	0.181326	0.0906631	+	0.995882i	$0.471101\pi$
$564$	−30.8006	−1.29694
$565$	−14.0962	−0.593034
$566$	−19.3430	−0.813046
$567$	6.97990	0.293128
$568$	1.66433	0.0698338
$569$	−25.8210	−1.08247	−0.541236	−	0.840871i	$-0.682043\pi$
$569$	−25.8210	−1.08247	−0.541236	+	0.840871i	$0.682043\pi$
$570$	−36.6862	−1.53662
$571$	26.3752	1.10377	0.551884	−	0.833921i	$-0.313909\pi$
$571$	26.3752	1.10377	0.551884	+	0.833921i	$0.313909\pi$
$572$	−0.338819	−0.0141667
$573$	6.77645	0.283090
$574$	−95.2767	−3.97677
$575$	−3.94951	−0.164706
$576$	27.6648	1.15270
$577$	−28.3402	−1.17982	−0.589909	−	0.807470i	$-0.700836\pi$
$577$	−28.3402	−1.17982	−0.589909	+	0.807470i	$0.700836\pi$
$578$	1.62127	0.0674359
$579$	2.20219	0.0915199
$580$	−37.4756	−1.55609
$581$	−57.4260	−2.38243
$582$	16.3920	0.679468
$583$	12.3051	0.509626
$584$	−25.8849	−1.07112
$585$	−0.707916	−0.0292687
$586$	−43.8187	−1.81014
$587$	21.1726	0.873885	0.436942	−	0.899489i	$-0.356061\pi$
$587$	21.1726	0.873885	0.436942	+	0.899489i	$0.356061\pi$
$588$	19.7017	0.812485
$589$	−1.88297	−0.0775865
$590$	56.3588	2.32025
$591$	−11.4786	−0.472168
$592$	−1.76040	−0.0723521
$593$	−34.9627	−1.43575	−0.717873	−	0.696174i	$-0.754884\pi$
$593$	−34.9627	−1.43575	−0.717873	+	0.696174i	$0.754884\pi$
$594$	−11.9423	−0.489999
$595$	−50.9152	−2.08732
$596$	32.7842	1.34289
$597$	1.52219	0.0622993
$598$	0.131357	0.00537159
$599$	36.2409	1.48076	0.740381	−	0.672188i	$-0.234645\pi$
$599$	36.2409	1.48076	0.740381	+	0.672188i	$0.234645\pi$
$600$	−16.6197	−0.678497
$601$	−26.6251	−1.08606	−0.543030	−	0.839713i	$-0.682723\pi$
$601$	−26.6251	−1.08606	−0.543030	+	0.839713i	$0.682723\pi$
$602$	45.1234	1.83909
$603$	−24.7276	−1.00699
$604$	35.1262	1.42926
$605$	−33.4766	−1.36102
$606$	−38.4778	−1.56306
$607$	37.0123	1.50228	0.751142	−	0.660140i	$-0.229503\pi$
$607$	37.0123	1.50228	0.751142	+	0.660140i	$0.229503\pi$
$608$	30.1657	1.22338
$609$	−11.9514	−0.484295
$610$	−4.67212	−0.189168
$611$	−1.01250	−0.0409616
$612$	27.1974	1.09939
$613$	13.4713	0.544100	0.272050	−	0.962283i	$-0.412298\pi$
$613$	13.4713	0.544100	0.272050	+	0.962283i	$0.412298\pi$
$614$	0.665524	0.0268583
$615$	36.2493	1.46171
$616$	10.7781	0.434260
$617$	−34.0747	−1.37180	−0.685899	−	0.727697i	$-0.740591\pi$
$617$	−34.0747	−1.37180	−0.685899	+	0.727697i	$0.740591\pi$
$618$	16.5547	0.665927
$619$	14.1852	0.570150	0.285075	−	0.958505i	$-0.407981\pi$
$619$	14.1852	0.570150	0.285075	+	0.958505i	$0.407981\pi$
$620$	−4.04078	−0.162282
$621$	2.83938	0.113941
$622$	−11.6139	−0.465676
$623$	58.7675	2.35447
$624$	−0.0259560	−0.00103907
$625$	−13.8728	−0.554914
$626$	16.3844	0.654852
$627$	−5.17308	−0.206593
$628$	−77.0768	−3.07570
$629$	−24.9724	−0.995714
$630$	60.9639	2.42886
$631$	−27.9613	−1.11312	−0.556560	−	0.830807i	$-0.687879\pi$
$631$	−27.9613	−1.11312	−0.556560	+	0.830807i	$0.687879\pi$
$632$	18.1825	0.723262
$633$	11.9135	0.473520
$634$	24.2160	0.961740
$635$	−40.5217	−1.60805
$636$	−33.3287	−1.32157
$637$	0.647652	0.0256609
$638$	−8.61680	−0.341142
$639$	1.32745	0.0525131
$640$	60.3144	2.38414
$641$	32.4718	1.28256	0.641279	−	0.767308i	$-0.278404\pi$
$641$	32.4718	1.28256	0.641279	+	0.767308i	$0.278404\pi$
$642$	5.45270	0.215201
$643$	28.4307	1.12120	0.560599	−	0.828087i	$-0.310571\pi$
$643$	28.4307	1.12120	0.560599	+	0.828087i	$0.310571\pi$
$644$	−6.93735	−0.273370
$645$	−17.1678	−0.675982
$646$	46.3325	1.82293
$647$	−12.0028	−0.471877	−0.235938	−	0.971768i	$-0.575816\pi$
$647$	−12.0028	−0.471877	−0.235938	+	0.971768i	$0.575816\pi$
$648$	−5.03491	−0.197790
$649$	7.94708	0.311950
$650$	−1.47903	−0.0580125
$651$	−1.28865	−0.0505062
$652$	−40.2043	−1.57452
$653$	−10.9544	−0.428677	−0.214338	−	0.976759i	$-0.568760\pi$
$653$	−10.9544	−0.428677	−0.214338	+	0.976759i	$0.568760\pi$
$654$	−0.875323	−0.0342278
$655$	76.6372	2.99446
$656$	−3.22727	−0.126004
$657$	−20.6455	−0.805456
$658$	87.1942	3.39919
$659$	7.12266	0.277460	0.138730	−	0.990330i	$-0.455698\pi$
$659$	7.12266	0.277460	0.138730	+	0.990330i	$0.455698\pi$
$660$	−11.1012	−0.432115
$661$	30.5505	1.18828	0.594138	−	0.804363i	$-0.297493\pi$
$661$	30.5505	1.18828	0.594138	+	0.804363i	$0.297493\pi$
$662$	−37.3936	−1.45334
$663$	−0.368202	−0.0142998
$664$	41.4239	1.60756
$665$	63.6914	2.46985
$666$	29.9010	1.15864
$667$	2.04871	0.0793266
$668$	26.4910	1.02497
$669$	20.9639	0.810511
$670$	−90.3988	−3.49241
$671$	−0.658810	−0.0254331
$672$	20.6445	0.796379
$673$	−17.8945	−0.689782	−0.344891	−	0.938643i	$-0.612084\pi$
$673$	−17.8945	−0.689782	−0.344891	+	0.938643i	$0.612084\pi$
$674$	−32.0502	−1.23453
$675$	−31.9705	−1.23054
$676$	−41.1996	−1.58460
$677$	18.2603	0.701802	0.350901	−	0.936413i	$-0.385875\pi$
$677$	18.2603	0.701802	0.350901	+	0.936413i	$0.385875\pi$
$678$	8.77876	0.337146
$679$	−28.4583	−1.09213
$680$	36.7274	1.40843
$681$	−8.78474	−0.336632
$682$	−0.929100	−0.0355771
$683$	36.9531	1.41397	0.706985	−	0.707229i	$-0.250055\pi$
$683$	36.9531	1.41397	0.706985	+	0.707229i	$0.250055\pi$
$684$	−34.0220	−1.30087
$685$	−36.2937	−1.38671
$686$	3.01870	0.115255
$687$	13.8583	0.528728
$688$	1.52845	0.0582714
$689$	−1.09561	−0.0417394
$690$	4.30385	0.163845
$691$	30.4630	1.15887	0.579434	−	0.815019i	$-0.303274\pi$
$691$	30.4630	1.15887	0.579434	+	0.815019i	$0.303274\pi$
$692$	40.8592	1.55323
$693$	8.59645	0.326552
$694$	−24.5310	−0.931185
$695$	−60.5850	−2.29812
$696$	8.62107	0.326781
$697$	−45.7807	−1.73407
$698$	−18.1376	−0.686517
$699$	10.9565	0.414412
$700$	78.1121	2.95236
$701$	23.1239	0.873376	0.436688	−	0.899613i	$-0.356151\pi$
$701$	23.1239	0.873376	0.436688	+	0.899613i	$0.356151\pi$
$702$	1.06331	0.0401320
$703$	31.2387	1.17819
$704$	14.2612	0.537488
$705$	−33.1742	−1.24941
$706$	−25.6403	−0.964986
$707$	66.8018	2.51234
$708$	−21.5249	−0.808954
$709$	33.4421	1.25595	0.627973	−	0.778235i	$-0.283885\pi$
$709$	33.4421	1.25595	0.627973	+	0.778235i	$0.283885\pi$
$710$	4.85287	0.182125
$711$	14.5021	0.543873
$712$	−42.3916	−1.58869
$713$	0.220901	0.00827281
$714$	31.7086	1.18666
$715$	−0.364929	−0.0136476
$716$	−83.5790	−3.12349
$717$	−24.1564	−0.902138
$718$	−29.9177	−1.11652
$719$	32.2243	1.20176	0.600882	−	0.799338i	$-0.294816\pi$
$719$	32.2243	1.20176	0.600882	+	0.799338i	$0.294816\pi$
$720$	2.06500	0.0769581
$721$	−28.7408	−1.07036
$722$	−14.7509	−0.548972
$723$	4.89964	0.182219
$724$	−53.8814	−2.00249
$725$	−23.0678	−0.856717
$726$	20.8483	0.773754
$727$	−15.5274	−0.575881	−0.287940	−	0.957648i	$-0.592970\pi$
$727$	−15.5274	−0.575881	−0.287940	+	0.957648i	$0.592970\pi$
$728$	−0.959646	−0.0355668
$729$	9.43866	0.349580
$730$	−75.4754	−2.79347
$731$	21.6819	0.801935
$732$	1.78440	0.0659534
$733$	11.3519	0.419293	0.209646	−	0.977777i	$-0.432769\pi$
$733$	11.3519	0.419293	0.209646	+	0.977777i	$0.432769\pi$
$734$	−24.1771	−0.892394
$735$	21.2200	0.782712
$736$	−3.53889	−0.130445
$737$	−12.7470	−0.469543
$738$	54.8161	2.01781
$739$	−34.6988	−1.27641	−0.638207	−	0.769864i	$-0.720324\pi$
$739$	−34.6988	−1.27641	−0.638207	+	0.769864i	$0.720324\pi$
$740$	67.0371	2.46433
$741$	0.460596	0.0169204
$742$	94.3511	3.46374
$743$	−17.1702	−0.629912	−0.314956	−	0.949106i	$-0.601990\pi$
$743$	−17.1702	−0.629912	−0.314956	+	0.949106i	$0.601990\pi$
$744$	0.929561	0.0340794
$745$	35.3107	1.29368
$746$	27.6769	1.01332
$747$	33.0392	1.20884
$748$	14.0202	0.512629
$749$	−9.46649	−0.345898
$750$	−12.1255	−0.442759
$751$	18.5379	0.676457	0.338229	−	0.941064i	$-0.390172\pi$
$751$	18.5379	0.676457	0.338229	+	0.941064i	$0.390172\pi$
$752$	2.95349	0.107703
$753$	0.935470	0.0340904
$754$	0.767213	0.0279403
$755$	37.8332	1.37689
$756$	−56.1564	−2.04239
$757$	19.1921	0.697550	0.348775	−	0.937207i	$-0.386598\pi$
$757$	19.1921	0.697550	0.348775	+	0.937207i	$0.386598\pi$
$758$	5.29584	0.192354
$759$	0.606881	0.0220284
$760$	−45.9435	−1.66654
$761$	44.6608	1.61895	0.809477	−	0.587152i	$-0.199751\pi$
$761$	44.6608	1.61895	0.809477	+	0.587152i	$0.199751\pi$
$762$	25.2358	0.914196
$763$	1.51966	0.0550153
$764$	22.9742	0.831177
$765$	29.2933	1.05910
$766$	−0.535693	−0.0193554
$767$	−0.707584	−0.0255494
$768$	−13.2037	−0.476447
$769$	11.1082	0.400572	0.200286	−	0.979737i	$-0.435813\pi$
$769$	11.1082	0.400572	0.200286	+	0.979737i	$0.435813\pi$
$770$	31.4268	1.13254
$771$	23.6851	0.852997
$772$	7.46608	0.268710
$773$	−54.3686	−1.95550	−0.977751	−	0.209769i	$-0.932729\pi$
$773$	−54.3686	−1.95550	−0.977751	+	0.209769i	$0.932729\pi$
$774$	−25.9611	−0.933152
$775$	−2.48727	−0.0893454
$776$	20.5282	0.736920
$777$	21.3789	0.766963
$778$	51.8725	1.85972
$779$	57.2685	2.05186
$780$	0.988420	0.0353911
$781$	0.684298	0.0244861
$782$	−5.43551	−0.194373
$783$	16.5839	0.592661
$784$	−1.88921	−0.0674718
$785$	−83.0167	−2.96299
$786$	−47.7275	−1.70238
$787$	0.0428803	0.00152852	0.000764259	−	1.00000i	$-0.499757\pi$
$787$	0.0428803	0.00152852	0.000764259		1.00000i	$0.499757\pi$
$788$	−38.9160	−1.38632
$789$	−10.2880	−0.366263
$790$	53.0167	1.88625
$791$	−15.2409	−0.541904
$792$	−6.20100	−0.220343
$793$	0.0586584	0.00208302
$794$	−53.5117	−1.89906
$795$	−35.8972	−1.27314
$796$	5.16069	0.182916
$797$	−42.0336	−1.48891	−0.744454	−	0.667674i	$-0.767290\pi$
$797$	−42.0336	−1.48891	−0.744454	+	0.667674i	$0.767290\pi$
$798$	−39.6653	−1.40414
$799$	41.8971	1.48221
$800$	39.8467	1.40879
$801$	−33.8110	−1.19465
$802$	1.73976	0.0614332
$803$	−10.6427	−0.375573
$804$	34.5256	1.21762
$805$	−7.47197	−0.263352
$806$	0.0827242	0.00291384
$807$	23.2055	0.816871
$808$	−48.1871	−1.69522
$809$	−35.3621	−1.24327	−0.621633	−	0.783309i	$-0.713530\pi$
$809$	−35.3621	−1.24327	−0.621633	+	0.783309i	$0.713530\pi$
$810$	−14.6808	−0.515832
$811$	−44.0189	−1.54571	−0.772856	−	0.634582i	$-0.781172\pi$
$811$	−44.0189	−1.54571	−0.772856	+	0.634582i	$0.781172\pi$
$812$	−40.5188	−1.42193
$813$	−5.13313	−0.180027
$814$	15.4139	0.540257
$815$	−43.3026	−1.51682
$816$	1.07405	0.0375993
$817$	−27.1226	−0.948899
$818$	12.7415	0.445494
$819$	−0.765401	−0.0267453
$820$	122.896	4.29172
$821$	3.78216	0.131998	0.0659991	−	0.997820i	$-0.478977\pi$
$821$	3.78216	0.131998	0.0659991	+	0.997820i	$0.478977\pi$
$822$	22.6027	0.788360
$823$	−41.0108	−1.42955	−0.714774	−	0.699356i	$-0.753470\pi$
$823$	−41.0108	−1.42955	−0.714774	+	0.699356i	$0.753470\pi$
$824$	20.7320	0.722234
$825$	−6.83327	−0.237904
$826$	60.9353	2.12021
$827$	43.0262	1.49617	0.748083	−	0.663605i	$-0.230974\pi$
$827$	43.0262	1.49617	0.748083	+	0.663605i	$0.230974\pi$
$828$	3.99130	0.138707
$829$	22.6915	0.788108	0.394054	−	0.919087i	$-0.371072\pi$
$829$	22.6915	0.788108	0.394054	+	0.919087i	$0.371072\pi$
$830$	120.784	4.19248
$831$	5.41384	0.187804
$832$	−1.26977	−0.0440214
$833$	−26.7996	−0.928550
$834$	37.7307	1.30651
$835$	28.5325	0.987407
$836$	−17.5383	−0.606575
$837$	1.78815	0.0618074
$838$	56.4655	1.95057
$839$	49.4834	1.70835	0.854177	−	0.519982i	$-0.174061\pi$
$839$	49.4834	1.70835	0.854177	+	0.519982i	$0.174061\pi$
$840$	−31.4423	−1.08486
$841$	−17.0341	−0.587384
$842$	−27.8626	−0.960207
$843$	11.8906	0.409535
$844$	40.3904	1.39029
$845$	−44.3746	−1.52653
$846$	−50.1659	−1.72474
$847$	−36.1950	−1.24368
$848$	3.19591	0.109748
$849$	7.95690	0.273080
$850$	61.2019	2.09921
$851$	−3.66478	−0.125627
$852$	−1.85344	−0.0634977
$853$	23.5427	0.806087	0.403043	−	0.915181i	$-0.367952\pi$
$853$	23.5427	0.806087	0.403043	+	0.915181i	$0.367952\pi$
$854$	−5.05151	−0.172859
$855$	−36.6439	−1.25320
$856$	6.82860	0.233397
$857$	−28.5719	−0.975996	−0.487998	−	0.872845i	$-0.662273\pi$
$857$	−28.5719	−0.975996	−0.487998	+	0.872845i	$0.662273\pi$
$858$	0.227268	0.00775881
$859$	−30.5642	−1.04284	−0.521418	−	0.853301i	$-0.674597\pi$
$859$	−30.5642	−1.04284	−0.521418	+	0.853301i	$0.674597\pi$
$860$	−58.2040	−1.98474
$861$	39.1929	1.33569
$862$	55.3506	1.88525
$863$	−20.3242	−0.691845	−0.345922	−	0.938263i	$-0.612434\pi$
$863$	−20.3242	−0.691845	−0.345922	+	0.938263i	$0.612434\pi$
$864$	−28.6466	−0.974577
$865$	44.0079	1.49632
$866$	−19.0031	−0.645752
$867$	−0.666923	−0.0226499
$868$	−4.36891	−0.148290
$869$	7.47583	0.253600
$870$	25.1374	0.852237
$871$	1.13496	0.0384565
$872$	−1.09620	−0.0371219
$873$	16.3730	0.554144
$874$	6.79945	0.229995
$875$	21.0512	0.711659
$876$	28.8260	0.973940
$877$	15.6408	0.528152	0.264076	−	0.964502i	$-0.414933\pi$
$877$	15.6408	0.528152	0.264076	+	0.964502i	$0.414933\pi$
$878$	12.9031	0.435460
$879$	18.0252	0.607975
$880$	1.06451	0.0358845
$881$	−46.2975	−1.55980	−0.779901	−	0.625902i	$-0.784731\pi$
$881$	−46.2975	−1.55980	−0.779901	+	0.625902i	$0.784731\pi$
$882$	32.0888	1.08049
$883$	23.7796	0.800246	0.400123	−	0.916461i	$-0.368967\pi$
$883$	23.7796	0.800246	0.400123	+	0.916461i	$0.368967\pi$
$884$	−1.24831	−0.0419854
$885$	−23.1837	−0.779310
$886$	−8.08976	−0.271781
$887$	4.44067	0.149103	0.0745515	−	0.997217i	$-0.476247\pi$
$887$	4.44067	0.149103	0.0745515	+	0.997217i	$0.476247\pi$
$888$	−15.4215	−0.517513
$889$	−43.8121	−1.46941
$890$	−123.606	−4.14328
$891$	−2.07013	−0.0693519
$892$	71.0739	2.37973
$893$	−52.4104	−1.75385
$894$	−21.9905	−0.735473
$895$	−90.0199	−3.00903
$896$	65.2121	2.17858
$897$	−0.0540349	−0.00180417
$898$	−63.5702	−2.12136
$899$	1.29021	0.0430309
$900$	−44.9407	−1.49802
$901$	45.3359	1.51036
$902$	28.2576	0.940875
$903$	−18.5619	−0.617701
$904$	10.9939	0.365653
$905$	−58.0337	−1.92911
$906$	−23.5615	−0.782777
$907$	14.8394	0.492735	0.246368	−	0.969176i	$-0.420763\pi$
$907$	14.8394	0.492735	0.246368	+	0.969176i	$0.420763\pi$
$908$	−29.7829	−0.988380
$909$	−38.4335	−1.27476
$910$	−2.79814	−0.0927575
$911$	36.2128	1.19978	0.599892	−	0.800081i	$-0.295210\pi$
$911$	36.2128	1.19978	0.599892	+	0.800081i	$0.295210\pi$
$912$	−1.34356	−0.0444899
$913$	17.0316	0.563665
$914$	−25.6408	−0.848123
$915$	1.92192	0.0635366
$916$	46.9839	1.55239
$917$	82.8603	2.73629
$918$	−43.9993	−1.45219
$919$	45.1422	1.48910	0.744551	−	0.667565i	$-0.232663\pi$
$919$	45.1422	1.48910	0.744551	+	0.667565i	$0.232663\pi$
$920$	5.38987	0.177699
$921$	−0.273769	−0.00902099
$922$	−46.1509	−1.51990
$923$	−0.0609278	−0.00200546
$924$	−12.0027	−0.394860
$925$	41.2641	1.35676
$926$	58.2770	1.91510
$927$	16.5356	0.543100
$928$	−20.6695	−0.678510
$929$	47.1799	1.54792	0.773961	−	0.633233i	$-0.218273\pi$
$929$	47.1799	1.54792	0.773961	+	0.633233i	$0.218273\pi$
$930$	2.71042	0.0888782
$931$	33.5244	1.09872
$932$	37.1457	1.21675
$933$	4.77749	0.156408
$934$	−43.3125	−1.41723
$935$	15.1006	0.493844
$936$	0.552118	0.0180466
$937$	−44.0230	−1.43817	−0.719084	−	0.694923i	$-0.755439\pi$
$937$	−44.0230	−1.43817	−0.719084	+	0.694923i	$0.755439\pi$
$938$	−97.7394	−3.19131
$939$	−6.73987	−0.219947
$940$	−112.471	−3.66839
$941$	35.1353	1.14538	0.572688	−	0.819773i	$-0.305900\pi$
$941$	35.1353	1.14538	0.572688	+	0.819773i	$0.305900\pi$
$942$	51.7005	1.68449
$943$	−6.71847	−0.218784
$944$	2.06403	0.0671786
$945$	−60.4840	−1.96755
$946$	−13.3829	−0.435115
$947$	18.6892	0.607316	0.303658	−	0.952781i	$-0.401792\pi$
$947$	18.6892	0.607316	0.303658	+	0.952781i	$0.401792\pi$
$948$	−20.2485	−0.657639
$949$	0.947593	0.0307602
$950$	−76.5594	−2.48391
$951$	−9.96146	−0.323022
$952$	39.7098	1.28700
$953$	−9.80725	−0.317688	−0.158844	−	0.987304i	$-0.550777\pi$
$953$	−9.80725	−0.317688	−0.158844	+	0.987304i	$0.550777\pi$
$954$	−54.2835	−1.75749
$955$	24.7447	0.800719
$956$	−81.8974	−2.64875
$957$	3.54459	0.114580
$958$	−1.41014	−0.0455596
$959$	−39.2408	−1.26715
$960$	−41.6034	−1.34275
$961$	−30.8609	−0.995512
$962$	−1.37241	−0.0442481
$963$	5.44641	0.175508
$964$	16.6112	0.535012
$965$	8.04145	0.258863
$966$	4.65334	0.149719
$967$	−10.4028	−0.334533	−0.167266	−	0.985912i	$-0.553494\pi$
$967$	−10.4028	−0.334533	−0.167266	+	0.985912i	$0.553494\pi$
$968$	26.1091	0.839178
$969$	−19.0593	−0.612272
$970$	59.8563	1.92187
$971$	−36.5079	−1.17159	−0.585797	−	0.810458i	$-0.699218\pi$
$971$	−36.5079	−1.17159	−0.585797	+	0.810458i	$0.699218\pi$
$972$	51.2216	1.64293
$973$	−65.5047	−2.09999
$974$	−7.06605	−0.226411
$975$	0.608414	0.0194848
$976$	−0.171108	−0.00547702
$977$	−2.60773	−0.0834288	−0.0417144	−	0.999130i	$-0.513282\pi$
$977$	−2.60773	−0.0834288	−0.0417144	+	0.999130i	$0.513282\pi$
$978$	26.9677	0.862332
$979$	−17.4295	−0.557050
$980$	71.9421	2.29811
$981$	−0.874314	−0.0279147
$982$	3.81497	0.121741
$983$	−14.7408	−0.470160	−0.235080	−	0.971976i	$-0.575535\pi$
$983$	−14.7408	−0.470160	−0.235080	+	0.971976i	$0.575535\pi$
$984$	−28.2716	−0.901265
$985$	−41.9150	−1.33552
$986$	−31.7470	−1.01103
$987$	−35.8681	−1.14169
$988$	1.56156	0.0496797
$989$	3.18189	0.101178
$990$	−18.0809	−0.574650
$991$	−22.1779	−0.704505	−0.352252	−	0.935905i	$-0.614584\pi$
$991$	−22.1779	−0.704505	−0.352252	+	0.935905i	$0.614584\pi$
$992$	−2.22867	−0.0707605
$993$	15.3822	0.488139
$994$	5.24694	0.166423
$995$	5.55840	0.176213
$996$	−46.1306	−1.46170
$997$	−34.6820	−1.09839	−0.549194	−	0.835695i	$-0.685065\pi$
$997$	−34.6820	−1.09839	−0.549194	+	0.835695i	$0.685065\pi$
$998$	42.3304	1.33995
$999$	−29.6656	−0.938578

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	251.2.a.b.1.4	✓	17
3.2	odd	2		2259.2.a.k.1.14		17
4.3	odd	2		4016.2.a.k.1.7		17
5.4	even	2		6275.2.a.e.1.14		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
251.2.a.b.1.4	✓	17	1.1	even	1	trivial
2259.2.a.k.1.14		17	3.2	odd	2
4016.2.a.k.1.7		17	4.3	odd	2
6275.2.a.e.1.14		17	5.4	even	2

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:	\( N \)	\(=\)	\( 251 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	251.a (trivial)

\(f(q)\)	\(=\)	\(q-2.27410 q^{2} +0.935470 q^{3} +3.17152 q^{4} +3.41593 q^{5} -2.12735 q^{6} +3.69332 q^{7} -2.66415 q^{8} -2.12490 q^{9} +O(q^{10})\)	\(q-2.27410 q^{2} +0.935470 q^{3} +3.17152 q^{4} +3.41593 q^{5} -2.12735 q^{6} +3.69332 q^{7} -2.66415 q^{8} -2.12490 q^{9} -7.76816 q^{10} -1.09538 q^{11} +2.96686 q^{12} +0.0975293 q^{13} -8.39896 q^{14} +3.19550 q^{15} -0.284494 q^{16} -4.03572 q^{17} +4.83222 q^{18} +5.04841 q^{19} +10.8337 q^{20} +3.45499 q^{21} +2.49100 q^{22} -0.592256 q^{23} -2.49224 q^{24} +6.66859 q^{25} -0.221791 q^{26} -4.79419 q^{27} +11.7134 q^{28} -3.45917 q^{29} -7.26688 q^{30} -0.372983 q^{31} +5.97528 q^{32} -1.02469 q^{33} +9.17763 q^{34} +12.6161 q^{35} -6.73915 q^{36} +6.18783 q^{37} -11.4806 q^{38} +0.0912357 q^{39} -9.10057 q^{40} +11.3439 q^{41} -7.85698 q^{42} -5.37250 q^{43} -3.47402 q^{44} -7.25850 q^{45} +1.34685 q^{46} -10.3815 q^{47} -0.266136 q^{48} +6.64059 q^{49} -15.1650 q^{50} -3.77530 q^{51} +0.309316 q^{52} -11.2337 q^{53} +10.9024 q^{54} -3.74174 q^{55} -9.83957 q^{56} +4.72264 q^{57} +7.86649 q^{58} -7.25509 q^{59} +10.1346 q^{60} +0.601444 q^{61} +0.848199 q^{62} -7.84791 q^{63} -13.0194 q^{64} +0.333153 q^{65} +2.33026 q^{66} +11.6371 q^{67} -12.7994 q^{68} -0.554038 q^{69} -28.6903 q^{70} -0.624713 q^{71} +5.66105 q^{72} +9.71599 q^{73} -14.0717 q^{74} +6.23827 q^{75} +16.0112 q^{76} -4.04558 q^{77} -0.207479 q^{78} -6.82487 q^{79} -0.971814 q^{80} +1.88987 q^{81} -25.7971 q^{82} -15.5486 q^{83} +10.9576 q^{84} -13.7858 q^{85} +12.2176 q^{86} -3.23595 q^{87} +2.91826 q^{88} +15.9119 q^{89} +16.5065 q^{90} +0.360206 q^{91} -1.87835 q^{92} -0.348914 q^{93} +23.6087 q^{94} +17.2450 q^{95} +5.58969 q^{96} -7.70534 q^{97} -15.1013 q^{98} +2.32757 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 2 q^{2} + 26 q^{4} + 3 q^{5} + q^{6} + 3 q^{7} + 6 q^{8} + 25 q^{9}+O(q^{10}) \) 17 * q + 2 * q^2 + 26 * q^4 + 3 * q^5 + q^6 + 3 * q^7 + 6 * q^8 + 25 * q^9	\( 17 q + 2 q^{2} + 26 q^{4} + 3 q^{5} + q^{6} + 3 q^{7} + 6 q^{8} + 25 q^{9} + 7 q^{10} - q^{11} - 9 q^{12} + 22 q^{13} - 7 q^{14} - 8 q^{15} + 40 q^{16} - q^{17} - 7 q^{18} + 13 q^{19} - 14 q^{20} + 25 q^{21} + 4 q^{22} - 2 q^{23} - 24 q^{24} + 32 q^{25} - 9 q^{26} - 15 q^{27} - 10 q^{28} + 28 q^{29} - 34 q^{30} + 12 q^{31} + 4 q^{32} - 16 q^{33} - 21 q^{34} - 15 q^{35} + 21 q^{36} + 27 q^{37} - 37 q^{38} + 13 q^{39} - 7 q^{40} - q^{41} - 56 q^{42} + 9 q^{43} - 43 q^{44} - 7 q^{45} + 4 q^{46} - 20 q^{47} - 79 q^{48} + 32 q^{49} - 28 q^{50} - 2 q^{51} - q^{52} + q^{53} - 65 q^{54} - 11 q^{55} - 61 q^{56} - 24 q^{57} - 46 q^{58} - 20 q^{59} - 106 q^{60} + 59 q^{61} - 73 q^{62} - 41 q^{63} + 54 q^{64} - 14 q^{65} - 43 q^{66} + 15 q^{67} - 20 q^{68} + 38 q^{69} - 11 q^{70} - 26 q^{71} - 2 q^{72} + 8 q^{73} + 2 q^{74} - 20 q^{75} + 38 q^{76} + 33 q^{79} - 29 q^{80} + 29 q^{81} + 10 q^{82} + 63 q^{84} + 67 q^{85} + 11 q^{86} - 11 q^{87} + 27 q^{88} + 11 q^{89} + 72 q^{90} - 2 q^{91} + 28 q^{92} + 28 q^{93} + 29 q^{94} - 8 q^{95} - 17 q^{96} - 10 q^{97} + 22 q^{98} - 36 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 + 26 * q^4 + 3 * q^5 + q^6 + 3 * q^7 + 6 * q^8 + 25 * q^9 + 7 * q^10 - q^11 - 9 * q^12 + 22 * q^13 - 7 * q^14 - 8 * q^15 + 40 * q^16 - q^17 - 7 * q^18 + 13 * q^19 - 14 * q^20 + 25 * q^21 + 4 * q^22 - 2 * q^23 - 24 * q^24 + 32 * q^25 - 9 * q^26 - 15 * q^27 - 10 * q^28 + 28 * q^29 - 34 * q^30 + 12 * q^31 + 4 * q^32 - 16 * q^33 - 21 * q^34 - 15 * q^35 + 21 * q^36 + 27 * q^37 - 37 * q^38 + 13 * q^39 - 7 * q^40 - q^41 - 56 * q^42 + 9 * q^43 - 43 * q^44 - 7 * q^45 + 4 * q^46 - 20 * q^47 - 79 * q^48 + 32 * q^49 - 28 * q^50 - 2 * q^51 - q^52 + q^53 - 65 * q^54 - 11 * q^55 - 61 * q^56 - 24 * q^57 - 46 * q^58 - 20 * q^59 - 106 * q^60 + 59 * q^61 - 73 * q^62 - 41 * q^63 + 54 * q^64 - 14 * q^65 - 43 * q^66 + 15 * q^67 - 20 * q^68 + 38 * q^69 - 11 * q^70 - 26 * q^71 - 2 * q^72 + 8 * q^73 + 2 * q^74 - 20 * q^75 + 38 * q^76 + 33 * q^79 - 29 * q^80 + 29 * q^81 + 10 * q^82 + 63 * q^84 + 67 * q^85 + 11 * q^86 - 11 * q^87 + 27 * q^88 + 11 * q^89 + 72 * q^90 - 2 * q^91 + 28 * q^92 + 28 * q^93 + 29 * q^94 - 8 * q^95 - 17 * q^96 - 10 * q^97 + 22 * q^98 - 36 * q^99

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