LMFDB - Embedded newform 649.2.a.f.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [649,2,Mod(1,649)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(649, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("649.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 649 = 11 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	649.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:	$5.18229109118$
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} - 3 x^{16} - 24 x^{15} + 74 x^{14} + 224 x^{13} - 719 x^{12} - 1025 x^{11} + 3506 x^{10} + \cdots + 56 $ x^17 - 3x^16 - 24x^15 + 74x^14 + 224x^13 - 719x^12 - 1025x^11 + 3506x^10 + 2357x^9 - 9053x^8 - 2358x^7 + 12050x^6 + 122x^5 - 7537x^4 + 1399x^3 + 1682x^2 - 656x + 56
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			1.5
Root			$-1.21582$ of defining polynomial
Character	$\chi$	$=$	649.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.21582 q^{2} +3.28544 q^{3} -0.521790 q^{4} -2.54257 q^{5} -3.99449 q^{6} -0.741538 q^{7} +3.06603 q^{8} +7.79410 q^{9} +O(q^{10})$	\(q-1.21582 q^{2} +3.28544 q^{3} -0.521790 q^{4} -2.54257 q^{5} -3.99449 q^{6} -0.741538 q^{7} +3.06603 q^{8} +7.79410 q^{9} +3.09130 q^{10} +1.00000 q^{11} -1.71431 q^{12} +5.31662 q^{13} +0.901574 q^{14} -8.35345 q^{15} -2.68415 q^{16} +0.0374924 q^{17} -9.47619 q^{18} -8.05879 q^{19} +1.32669 q^{20} -2.43628 q^{21} -1.21582 q^{22} +7.90567 q^{23} +10.0733 q^{24} +1.46466 q^{25} -6.46404 q^{26} +15.7507 q^{27} +0.386927 q^{28} +2.64197 q^{29} +10.1563 q^{30} +5.44177 q^{31} -2.86863 q^{32} +3.28544 q^{33} -0.0455839 q^{34} +1.88541 q^{35} -4.06689 q^{36} +3.24546 q^{37} +9.79801 q^{38} +17.4674 q^{39} -7.79560 q^{40} +0.357926 q^{41} +2.96206 q^{42} +8.62626 q^{43} -0.521790 q^{44} -19.8170 q^{45} -9.61185 q^{46} +6.77433 q^{47} -8.81862 q^{48} -6.45012 q^{49} -1.78076 q^{50} +0.123179 q^{51} -2.77416 q^{52} +11.9690 q^{53} -19.1500 q^{54} -2.54257 q^{55} -2.27358 q^{56} -26.4766 q^{57} -3.21215 q^{58} -1.00000 q^{59} +4.35875 q^{60} -9.78002 q^{61} -6.61619 q^{62} -5.77962 q^{63} +8.85604 q^{64} -13.5179 q^{65} -3.99449 q^{66} -13.4313 q^{67} -0.0195632 q^{68} +25.9736 q^{69} -2.29231 q^{70} -0.219360 q^{71} +23.8970 q^{72} -0.402118 q^{73} -3.94589 q^{74} +4.81204 q^{75} +4.20500 q^{76} -0.741538 q^{77} -21.2372 q^{78} -0.236355 q^{79} +6.82465 q^{80} +28.3657 q^{81} -0.435172 q^{82} -2.26479 q^{83} +1.27123 q^{84} -0.0953271 q^{85} -10.4880 q^{86} +8.68002 q^{87} +3.06603 q^{88} -1.54698 q^{89} +24.0939 q^{90} -3.94248 q^{91} -4.12511 q^{92} +17.8786 q^{93} -8.23634 q^{94} +20.4900 q^{95} -9.42470 q^{96} -1.36672 q^{97} +7.84216 q^{98} +7.79410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 3 q^{2} + 4 q^{3} + 23 q^{4} + 7 q^{5} - 5 q^{6} + 4 q^{7} + 9 q^{8} + 29 q^{9}+O(q^{10}) $ 17 * q + 3 * q^2 + 4 * q^3 + 23 * q^4 + 7 * q^5 - 5 * q^6 + 4 * q^7 + 9 * q^8 + 29 * q^9	\( 17 q + 3 q^{2} + 4 q^{3} + 23 q^{4} + 7 q^{5} - 5 q^{6} + 4 q^{7} + 9 q^{8} + 29 q^{9} - 4 q^{10} + 17 q^{11} + 2 q^{12} - 11 q^{13} + 16 q^{14} + 20 q^{15} + 39 q^{16} + 6 q^{17} - 15 q^{18} - 4 q^{19} - q^{20} - 11 q^{21} + 3 q^{22} + 36 q^{23} + 4 q^{24} + 22 q^{25} + 28 q^{26} + 13 q^{27} + 13 q^{29} - 34 q^{30} + 6 q^{31} + 16 q^{32} + 4 q^{33} - 5 q^{34} + 16 q^{35} + 34 q^{36} + 14 q^{37} + 12 q^{38} + 41 q^{39} - 54 q^{40} + 6 q^{41} - 57 q^{42} - 11 q^{43} + 23 q^{44} + 5 q^{45} + q^{46} + 25 q^{47} + 14 q^{48} + 23 q^{49} + 15 q^{50} - 4 q^{51} - 64 q^{52} - 2 q^{54} + 7 q^{55} + 43 q^{56} - 9 q^{57} - 21 q^{58} - 17 q^{59} + 15 q^{60} - 38 q^{61} - 21 q^{62} + 2 q^{63} + 43 q^{64} - 13 q^{65} - 5 q^{66} + q^{67} + 34 q^{68} - 13 q^{69} + 5 q^{70} + 89 q^{71} + 15 q^{72} - 16 q^{73} + 17 q^{74} + 2 q^{75} - q^{76} + 4 q^{77} - 58 q^{78} + 34 q^{79} - 64 q^{80} + 29 q^{81} - 17 q^{82} - 12 q^{83} - 111 q^{84} - 15 q^{85} - 21 q^{86} - 4 q^{87} + 9 q^{88} - 5 q^{89} + 7 q^{90} - 12 q^{91} + 80 q^{92} + 32 q^{93} - 25 q^{94} + 103 q^{95} - 48 q^{96} - 15 q^{97} + 8 q^{98} + 29 q^{99}+O(q^{100}) \) 17 * q + 3 * q^2 + 4 * q^3 + 23 * q^4 + 7 * q^5 - 5 * q^6 + 4 * q^7 + 9 * q^8 + 29 * q^9 - 4 * q^10 + 17 * q^11 + 2 * q^12 - 11 * q^13 + 16 * q^14 + 20 * q^15 + 39 * q^16 + 6 * q^17 - 15 * q^18 - 4 * q^19 - q^20 - 11 * q^21 + 3 * q^22 + 36 * q^23 + 4 * q^24 + 22 * q^25 + 28 * q^26 + 13 * q^27 + 13 * q^29 - 34 * q^30 + 6 * q^31 + 16 * q^32 + 4 * q^33 - 5 * q^34 + 16 * q^35 + 34 * q^36 + 14 * q^37 + 12 * q^38 + 41 * q^39 - 54 * q^40 + 6 * q^41 - 57 * q^42 - 11 * q^43 + 23 * q^44 + 5 * q^45 + q^46 + 25 * q^47 + 14 * q^48 + 23 * q^49 + 15 * q^50 - 4 * q^51 - 64 * q^52 - 2 * q^54 + 7 * q^55 + 43 * q^56 - 9 * q^57 - 21 * q^58 - 17 * q^59 + 15 * q^60 - 38 * q^61 - 21 * q^62 + 2 * q^63 + 43 * q^64 - 13 * q^65 - 5 * q^66 + q^67 + 34 * q^68 - 13 * q^69 + 5 * q^70 + 89 * q^71 + 15 * q^72 - 16 * q^73 + 17 * q^74 + 2 * q^75 - q^76 + 4 * q^77 - 58 * q^78 + 34 * q^79 - 64 * q^80 + 29 * q^81 - 17 * q^82 - 12 * q^83 - 111 * q^84 - 15 * q^85 - 21 * q^86 - 4 * q^87 + 9 * q^88 - 5 * q^89 + 7 * q^90 - 12 * q^91 + 80 * q^92 + 32 * q^93 - 25 * q^94 + 103 * q^95 - 48 * q^96 - 15 * q^97 + 8 * q^98 + 29 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.21582	−0.859712	−0.429856	−	0.902897i	$-0.641436\pi$
$2$	−1.21582	−0.859712	−0.429856	+	0.902897i	$0.641436\pi$
$3$	3.28544	1.89685	0.948424	−	0.317005i	$-0.102677\pi$
$3$	3.28544	1.89685	0.948424	+	0.317005i	$0.102677\pi$
$4$	−0.521790	−0.260895
$5$	−2.54257	−1.13707	−0.568536	−	0.822659i	$-0.692490\pi$
$5$	−2.54257	−1.13707	−0.568536	+	0.822659i	$0.692490\pi$
$6$	−3.99449	−1.63074
$7$	−0.741538	−0.280275	−0.140137	−	0.990132i	$-0.544754\pi$
$7$	−0.741538	−0.280275	−0.140137	+	0.990132i	$0.544754\pi$
$8$	3.06603	1.08401
$9$	7.79410	2.59803
$10$	3.09130	0.977554
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.71431	−0.494879
$13$	5.31662	1.47457	0.737283	−	0.675584i	$-0.236108\pi$
$13$	5.31662	1.47457	0.737283	+	0.675584i	$0.236108\pi$
$14$	0.901574	0.240956
$15$	−8.35345	−2.15685
$16$	−2.68415	−0.671038
$17$	0.0374924	0.00909325	0.00454662	−	0.999990i	$-0.498553\pi$
$17$	0.0374924	0.00909325	0.00454662	+	0.999990i	$0.498553\pi$
$18$	−9.47619	−2.23356
$19$	−8.05879	−1.84881	−0.924406	−	0.381409i	$-0.875439\pi$
$19$	−8.05879	−1.84881	−0.924406	+	0.381409i	$0.875439\pi$
$20$	1.32669	0.296657
$21$	−2.43628	−0.531639
$22$	−1.21582	−0.259213
$23$	7.90567	1.64845	0.824224	−	0.566265i	$-0.191612\pi$
$23$	7.90567	1.64845	0.824224	+	0.566265i	$0.191612\pi$
$24$	10.0733	2.05620
$25$	1.46466	0.292932
$26$	−6.46404	−1.26770
$27$	15.7507	3.03122
$28$	0.386927	0.0731224
$29$	2.64197	0.490601	0.245301	−	0.969447i	$-0.421113\pi$
$29$	2.64197	0.490601	0.245301	+	0.969447i	$0.421113\pi$
$30$	10.1563	1.85427
$31$	5.44177	0.977371	0.488685	−	0.872460i	$-0.337477\pi$
$31$	5.44177	0.977371	0.488685	+	0.872460i	$0.337477\pi$
$32$	−2.86863	−0.507107
$33$	3.28544	0.571921
$34$	−0.0455839	−0.00781757
$35$	1.88541	0.318693
$36$	−4.06689	−0.677814
$37$	3.24546	0.533551	0.266775	−	0.963759i	$-0.414042\pi$
$37$	3.24546	0.533551	0.266775	+	0.963759i	$0.414042\pi$
$38$	9.79801	1.58945
$39$	17.4674	2.79703
$40$	−7.79560	−1.23259
$41$	0.357926	0.0558986	0.0279493	−	0.999609i	$-0.491102\pi$
$41$	0.357926	0.0558986	0.0279493	+	0.999609i	$0.491102\pi$
$42$	2.96206	0.457056
$43$	8.62626	1.31549	0.657746	−	0.753239i	$-0.271510\pi$
$43$	8.62626	1.31549	0.657746	+	0.753239i	$0.271510\pi$
$44$	−0.521790	−0.0786629
$45$	−19.8170	−2.95415
$46$	−9.61185	−1.41719
$47$	6.77433	0.988137	0.494069	−	0.869423i	$-0.335509\pi$
$47$	6.77433	0.988137	0.494069	+	0.869423i	$0.335509\pi$
$48$	−8.81862	−1.27286
$49$	−6.45012	−0.921446
$50$	−1.78076	−0.251837
$51$	0.123179	0.0172485
$52$	−2.77416	−0.384707
$53$	11.9690	1.64407	0.822033	−	0.569441i	$-0.192840\pi$
$53$	11.9690	1.64407	0.822033	+	0.569441i	$0.192840\pi$
$54$	−19.1500	−2.60598
$55$	−2.54257	−0.342840
$56$	−2.27358	−0.303820
$57$	−26.4766	−3.50692
$58$	−3.21215	−0.421776
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	4.35875	0.562712
$61$	−9.78002	−1.25220	−0.626101	−	0.779742i	$-0.715350\pi$
$61$	−9.78002	−1.25220	−0.626101	+	0.779742i	$0.715350\pi$
$62$	−6.61619	−0.840257
$63$	−5.77962	−0.728163
$64$	8.85604	1.10700
$65$	−13.5179	−1.67669
$66$	−3.99449	−0.491688
$67$	−13.4313	−1.64090	−0.820449	−	0.571719i	$-0.806277\pi$
$67$	−13.4313	−1.64090	−0.820449	+	0.571719i	$0.806277\pi$
$68$	−0.0195632	−0.00237239
$69$	25.9736	3.12685
$70$	−2.29231	−0.273984
$71$	−0.219360	−0.0260333	−0.0130166	−	0.999915i	$-0.504143\pi$
$71$	−0.219360	−0.0260333	−0.0130166	+	0.999915i	$0.504143\pi$
$72$	23.8970	2.81628
$73$	−0.402118	−0.0470644	−0.0235322	−	0.999723i	$-0.507491\pi$
$73$	−0.402118	−0.0470644	−0.0235322	+	0.999723i	$0.507491\pi$
$74$	−3.94589	−0.458700
$75$	4.81204	0.555647
$76$	4.20500	0.482346
$77$	−0.741538	−0.0845061
$78$	−21.2372	−2.40464
$79$	−0.236355	−0.0265921	−0.0132960	−	0.999912i	$-0.504232\pi$
$79$	−0.236355	−0.0265921	−0.0132960	+	0.999912i	$0.504232\pi$
$80$	6.82465	0.763019
$81$	28.3657	3.15174
$82$	−0.435172	−0.0480567
$83$	−2.26479	−0.248593	−0.124296	−	0.992245i	$-0.539667\pi$
$83$	−2.26479	−0.248593	−0.124296	+	0.992245i	$0.539667\pi$
$84$	1.27123	0.138702
$85$	−0.0953271	−0.0103397
$86$	−10.4880	−1.13095
$87$	8.68002	0.930596
$88$	3.06603	0.326840
$89$	−1.54698	−0.163980	−0.0819899	−	0.996633i	$-0.526128\pi$
$89$	−1.54698	−0.163980	−0.0819899	+	0.996633i	$0.526128\pi$
$90$	24.0939	2.53972
$91$	−3.94248	−0.413284
$92$	−4.12511	−0.430072
$93$	17.8786	1.85392
$94$	−8.23634	−0.849513
$95$	20.4900	2.10223
$96$	−9.42470	−0.961905
$97$	−1.36672	−0.138770	−0.0693848	−	0.997590i	$-0.522104\pi$
$97$	−1.36672	−0.138770	−0.0693848	+	0.997590i	$0.522104\pi$
$98$	7.84216	0.792178
$99$	7.79410	0.783336
$100$	−0.764244	−0.0764244
$101$	−12.9317	−1.28676	−0.643378	−	0.765549i	$-0.722468\pi$
$101$	−12.9317	−1.28676	−0.643378	+	0.765549i	$0.722468\pi$
$102$	−0.149763	−0.0148288
$103$	−6.30951	−0.621694	−0.310847	−	0.950460i	$-0.600613\pi$
$103$	−6.30951	−0.621694	−0.310847	+	0.950460i	$0.600613\pi$
$104$	16.3010	1.59844
$105$	6.19440	0.604511
$106$	−14.5521	−1.41342
$107$	−4.32126	−0.417752	−0.208876	−	0.977942i	$-0.566980\pi$
$107$	−4.32126	−0.417752	−0.208876	+	0.977942i	$0.566980\pi$
$108$	−8.21857	−0.790832
$109$	−17.3252	−1.65945	−0.829726	−	0.558171i	$-0.811503\pi$
$109$	−17.3252	−1.65945	−0.829726	+	0.558171i	$0.811503\pi$
$110$	3.09130	0.294744
$111$	10.6628	1.01206
$112$	1.99040	0.188075
$113$	−6.78242	−0.638037	−0.319018	−	0.947749i	$-0.603353\pi$
$113$	−6.78242	−0.638037	−0.319018	+	0.947749i	$0.603353\pi$
$114$	32.1907	3.01494
$115$	−20.1007	−1.87440
$116$	−1.37855	−0.127996
$117$	41.4383	3.83097
$118$	1.21582	0.111925
$119$	−0.0278020	−0.00254861
$120$	−25.6120	−2.33804
$121$	1.00000	0.0909091
$122$	11.8907	1.07653
$123$	1.17594	0.106031
$124$	−2.83946	−0.254991
$125$	8.98885	0.803987
$126$	7.02695	0.626011
$127$	−2.83179	−0.251281	−0.125641	−	0.992076i	$-0.540099\pi$
$127$	−2.83179	−0.251281	−0.125641	+	0.992076i	$0.540099\pi$
$128$	−5.03005	−0.444598
$129$	28.3410	2.49529
$130$	16.4353	1.44147
$131$	−11.6587	−1.01863	−0.509314	−	0.860581i	$-0.670101\pi$
$131$	−11.6587	−1.01863	−0.509314	+	0.860581i	$0.670101\pi$
$132$	−1.71431	−0.149212
$133$	5.97590	0.518176
$134$	16.3300	1.41070
$135$	−40.0473	−3.44672
$136$	0.114953	0.00985714
$137$	5.15212	0.440175	0.220088	−	0.975480i	$-0.429366\pi$
$137$	5.15212	0.440175	0.220088	+	0.975480i	$0.429366\pi$
$138$	−31.5791	−2.68819
$139$	−9.90192	−0.839870	−0.419935	−	0.907554i	$-0.637947\pi$
$139$	−9.90192	−0.839870	−0.419935	+	0.907554i	$0.637947\pi$
$140$	−0.983789	−0.0831454
$141$	22.2566	1.87435
$142$	0.266702	0.0223811
$143$	5.31662	0.444598
$144$	−20.9206	−1.74338
$145$	−6.71739	−0.557849
$146$	0.488902	0.0404618
$147$	−21.1915	−1.74784
$148$	−1.69345	−0.139201
$149$	−17.9123	−1.46744	−0.733718	−	0.679454i	$-0.762217\pi$
$149$	−17.9123	−1.46744	−0.733718	+	0.679454i	$0.762217\pi$
$150$	−5.85056	−0.477696
$151$	−14.0903	−1.14665	−0.573327	−	0.819326i	$-0.694348\pi$
$151$	−14.0903	−1.14665	−0.573327	+	0.819326i	$0.694348\pi$
$152$	−24.7085	−2.00413
$153$	0.292220	0.0236246
$154$	0.901574	0.0726509
$155$	−13.8361	−1.11134
$156$	−9.11434	−0.729731
$157$	19.7597	1.57699	0.788497	−	0.615038i	$-0.210860\pi$
$157$	19.7597	1.57699	0.788497	+	0.615038i	$0.210860\pi$
$158$	0.287365	0.0228615
$159$	39.3233	3.11854
$160$	7.29369	0.576617
$161$	−5.86236	−0.462018
$162$	−34.4874	−2.70959
$163$	−1.74950	−0.137031	−0.0685155	−	0.997650i	$-0.521826\pi$
$163$	−1.74950	−0.137031	−0.0685155	+	0.997650i	$0.521826\pi$
$164$	−0.186762	−0.0145837
$165$	−8.35345	−0.650315
$166$	2.75357	0.213718
$167$	−8.03975	−0.622134	−0.311067	−	0.950388i	$-0.600686\pi$
$167$	−8.03975	−0.622134	−0.311067	+	0.950388i	$0.600686\pi$
$168$	−7.46970	−0.576300
$169$	15.2665	1.17435
$170$	0.115900	0.00888914
$171$	−62.8110	−4.80328
$172$	−4.50110	−0.343206
$173$	7.99640	0.607955	0.303977	−	0.952679i	$-0.401685\pi$
$173$	7.99640	0.607955	0.303977	+	0.952679i	$0.401685\pi$
$174$	−10.5533	−0.800044
$175$	−1.08610	−0.0821014
$176$	−2.68415	−0.202326
$177$	−3.28544	−0.246949
$178$	1.88085	0.140975
$179$	15.1366	1.13136	0.565682	−	0.824624i	$-0.308613\pi$
$179$	15.1366	1.13136	0.565682	+	0.824624i	$0.308613\pi$
$180$	10.3403	0.770723
$181$	−9.76663	−0.725948	−0.362974	−	0.931799i	$-0.618239\pi$
$181$	−9.76663	−0.725948	−0.362974	+	0.931799i	$0.618239\pi$
$182$	4.79333	0.355305
$183$	−32.1316	−2.37524
$184$	24.2391	1.78693
$185$	−8.25181	−0.606685
$186$	−21.7371	−1.59384
$187$	0.0374924	0.00274172
$188$	−3.53478	−0.257800
$189$	−11.6797	−0.849576
$190$	−24.9121	−1.80731
$191$	7.64423	0.553117	0.276559	−	0.960997i	$-0.410806\pi$
$191$	7.64423	0.553117	0.276559	+	0.960997i	$0.410806\pi$
$192$	29.0959	2.09982
$193$	−10.8763	−0.782890	−0.391445	−	0.920202i	$-0.628025\pi$
$193$	−10.8763	−0.782890	−0.391445	+	0.920202i	$0.628025\pi$
$194$	1.66168	0.119302
$195$	−44.4122	−3.18042
$196$	3.36561	0.240401
$197$	25.2783	1.80100	0.900502	−	0.434853i	$-0.143200\pi$
$197$	25.2783	1.80100	0.900502	+	0.434853i	$0.143200\pi$
$198$	−9.47619	−0.673444
$199$	−16.4838	−1.16851	−0.584254	−	0.811571i	$-0.698613\pi$
$199$	−16.4838	−1.16851	−0.584254	+	0.811571i	$0.698613\pi$
$200$	4.49069	0.317540
$201$	−44.1278	−3.11254
$202$	15.7226	1.10624
$203$	−1.95912	−0.137503
$204$	−0.0642736	−0.00450005
$205$	−0.910051	−0.0635607
$206$	7.67120	0.534478
$207$	61.6176	4.28272
$208$	−14.2706	−0.989491
$209$	−8.05879	−0.557438
$210$	−7.53125	−0.519706
$211$	15.4126	1.06105	0.530524	−	0.847670i	$-0.321995\pi$
$211$	15.4126	1.06105	0.530524	+	0.847670i	$0.321995\pi$
$212$	−6.24530	−0.428929
$213$	−0.720695	−0.0493812
$214$	5.25386	0.359146
$215$	−21.9329	−1.49581
$216$	48.2922	3.28587
$217$	−4.03528	−0.273933
$218$	21.0643	1.42665
$219$	−1.32113	−0.0892740
$220$	1.32669	0.0894453
$221$	0.199333	0.0134086
$222$	−12.9640	−0.870084
$223$	24.5742	1.64561	0.822804	−	0.568325i	$-0.192408\pi$
$223$	24.5742	1.64561	0.822804	+	0.568325i	$0.192408\pi$
$224$	2.12720	0.142129
$225$	11.4157	0.761046
$226$	8.24618	0.548528
$227$	15.7894	1.04798	0.523989	−	0.851725i	$-0.324443\pi$
$227$	15.7894	1.04798	0.523989	+	0.851725i	$0.324443\pi$
$228$	13.8153	0.914938
$229$	−15.8855	−1.04974	−0.524871	−	0.851182i	$-0.675886\pi$
$229$	−15.8855	−1.04974	−0.524871	+	0.851182i	$0.675886\pi$
$230$	24.4388	1.61145
$231$	−2.43628	−0.160295
$232$	8.10036	0.531815
$233$	7.92907	0.519451	0.259725	−	0.965682i	$-0.416368\pi$
$233$	7.92907	0.519451	0.259725	+	0.965682i	$0.416368\pi$
$234$	−50.3813	−3.29353
$235$	−17.2242	−1.12358
$236$	0.521790	0.0339657
$237$	−0.776531	−0.0504411
$238$	0.0338022	0.00219107
$239$	12.2136	0.790029	0.395014	−	0.918675i	$-0.370740\pi$
$239$	12.2136	0.790029	0.395014	+	0.918675i	$0.370740\pi$
$240$	22.4219	1.44733
$241$	6.78153	0.436837	0.218418	−	0.975855i	$-0.429910\pi$
$241$	6.78153	0.436837	0.218418	+	0.975855i	$0.429910\pi$
$242$	−1.21582	−0.0781556
$243$	45.9415	2.94715
$244$	5.10312	0.326694
$245$	16.3999	1.04775
$246$	−1.42973	−0.0911562
$247$	−42.8455	−2.72620
$248$	16.6847	1.05948
$249$	−7.44082	−0.471543
$250$	−10.9288	−0.691198
$251$	−21.2162	−1.33916	−0.669578	−	0.742742i	$-0.733525\pi$
$251$	−21.2162	−1.33916	−0.669578	+	0.742742i	$0.733525\pi$
$252$	3.01575	0.189974
$253$	7.90567	0.497025
$254$	3.44294	0.216029
$255$	−0.313191	−0.0196128
$256$	−11.5964	−0.724778
$257$	−10.1080	−0.630519	−0.315260	−	0.949005i	$-0.602092\pi$
$257$	−10.1080	−0.630519	−0.315260	+	0.949005i	$0.602092\pi$
$258$	−34.4575	−2.14523
$259$	−2.40663	−0.149541
$260$	7.05350	0.437440
$261$	20.5918	1.27460
$262$	14.1749	0.875727
$263$	13.5571	0.835964	0.417982	−	0.908455i	$-0.362738\pi$
$263$	13.5571	0.835964	0.417982	+	0.908455i	$0.362738\pi$
$264$	10.0733	0.619966
$265$	−30.4319	−1.86942
$266$	−7.26559	−0.445482
$267$	−5.08251	−0.311045
$268$	7.00834	0.428103
$269$	−22.6966	−1.38384	−0.691919	−	0.721975i	$-0.743234\pi$
$269$	−22.6966	−1.38384	−0.691919	+	0.721975i	$0.743234\pi$
$270$	48.6901	2.96319
$271$	−11.6160	−0.705619	−0.352810	−	0.935695i	$-0.614774\pi$
$271$	−11.6160	−0.705619	−0.352810	+	0.935695i	$0.614774\pi$
$272$	−0.100635	−0.00610192
$273$	−12.9528	−0.783937
$274$	−6.26403	−0.378424
$275$	1.46466	0.0883222
$276$	−13.5528	−0.815781
$277$	8.71012	0.523341	0.261670	−	0.965157i	$-0.415727\pi$
$277$	8.71012	0.523341	0.261670	+	0.965157i	$0.415727\pi$
$278$	12.0389	0.722046
$279$	42.4137	2.53924
$280$	5.78073	0.345465
$281$	11.9741	0.714314	0.357157	−	0.934044i	$-0.383746\pi$
$281$	11.9741	0.714314	0.357157	+	0.934044i	$0.383746\pi$
$282$	−27.0600	−1.61140
$283$	−14.5693	−0.866058	−0.433029	−	0.901380i	$-0.642555\pi$
$283$	−14.5693	−0.866058	−0.433029	+	0.901380i	$0.642555\pi$
$284$	0.114460	0.00679196
$285$	67.3187	3.98762
$286$	−6.46404	−0.382227
$287$	−0.265415	−0.0156670
$288$	−22.3584	−1.31748
$289$	−16.9986	−0.999917
$290$	8.16711	0.479589
$291$	−4.49028	−0.263225
$292$	0.209822	0.0122789
$293$	−5.69046	−0.332440	−0.166220	−	0.986089i	$-0.553156\pi$
$293$	−5.69046	−0.332440	−0.166220	+	0.986089i	$0.553156\pi$
$294$	25.7649	1.50264
$295$	2.54257	0.148034
$296$	9.95070	0.578373
$297$	15.7507	0.913949
$298$	21.7781	1.26157
$299$	42.0315	2.43074
$300$	−2.51088	−0.144966
$301$	−6.39670	−0.368700
$302$	17.1313	0.985793
$303$	−42.4864	−2.44078
$304$	21.6310	1.24062
$305$	24.8664	1.42384
$306$	−0.355285	−0.0203103
$307$	−15.0971	−0.861639	−0.430820	−	0.902438i	$-0.641776\pi$
$307$	−15.0971	−0.861639	−0.430820	+	0.902438i	$0.641776\pi$
$308$	0.386927	0.0220472
$309$	−20.7295	−1.17926
$310$	16.8221	0.955433
$311$	22.2044	1.25909	0.629547	−	0.776962i	$-0.283241\pi$
$311$	22.2044	1.25909	0.629547	+	0.776962i	$0.283241\pi$
$312$	53.5557	3.03200
$313$	12.4333	0.702774	0.351387	−	0.936230i	$-0.385710\pi$
$313$	12.4333	0.702774	0.351387	+	0.936230i	$0.385710\pi$
$314$	−24.0241	−1.35576
$315$	14.6951	0.827974
$316$	0.123328	0.00693774
$317$	−23.4100	−1.31484	−0.657419	−	0.753526i	$-0.728352\pi$
$317$	−23.4100	−1.31484	−0.657419	+	0.753526i	$0.728352\pi$
$318$	−47.8099	−2.68105
$319$	2.64197	0.147922
$320$	−22.5171	−1.25874
$321$	−14.1972	−0.792412
$322$	7.12755	0.397203
$323$	−0.302144	−0.0168117
$324$	−14.8009	−0.822274
$325$	7.78703	0.431947
$326$	2.12707	0.117807
$327$	−56.9208	−3.14773
$328$	1.09741	0.0605944
$329$	−5.02342	−0.276950
$330$	10.1563	0.559084
$331$	−3.07138	−0.168818	−0.0844092	−	0.996431i	$-0.526900\pi$
$331$	−3.07138	−0.168818	−0.0844092	+	0.996431i	$0.526900\pi$
$332$	1.18174	0.0648567
$333$	25.2955	1.38618
$334$	9.77486	0.534856
$335$	34.1501	1.86582
$336$	6.53934	0.356750
$337$	28.1246	1.53204	0.766022	−	0.642815i	$-0.222233\pi$
$337$	28.1246	1.53204	0.766022	+	0.642815i	$0.222233\pi$
$338$	−18.5612	−1.00960
$339$	−22.2832	−1.21026
$340$	0.0497408	0.00269757
$341$	5.44177	0.294688
$342$	76.3666	4.12943
$343$	9.97377	0.538533
$344$	26.4484	1.42600
$345$	−66.0397	−3.55546
$346$	−9.72215	−0.522666
$347$	16.5636	0.889180	0.444590	−	0.895734i	$-0.353349\pi$
$347$	16.5636	0.889180	0.444590	+	0.895734i	$0.353349\pi$
$348$	−4.52915	−0.242788
$349$	8.43616	0.451577	0.225789	−	0.974176i	$-0.427504\pi$
$349$	8.43616	0.451577	0.225789	+	0.974176i	$0.427504\pi$
$350$	1.32050	0.0705835
$351$	83.7406	4.46974
$352$	−2.86863	−0.152898
$353$	−4.98746	−0.265456	−0.132728	−	0.991153i	$-0.542374\pi$
$353$	−4.98746	−0.265456	−0.132728	+	0.991153i	$0.542374\pi$
$354$	3.99449	0.212305
$355$	0.557739	0.0296017
$356$	0.807201	0.0427816
$357$	−0.0913419	−0.00483432
$358$	−18.4033	−0.972647
$359$	13.8234	0.729573	0.364787	−	0.931091i	$-0.381142\pi$
$359$	13.8234	0.729573	0.364787	+	0.931091i	$0.381142\pi$
$360$	−60.7597	−3.20232
$361$	45.9441	2.41811
$362$	11.8744	0.624106
$363$	3.28544	0.172441
$364$	2.05715	0.107824
$365$	1.02241	0.0535156
$366$	39.0662	2.04202
$367$	−14.0583	−0.733838	−0.366919	−	0.930253i	$-0.619587\pi$
$367$	−14.0583	−0.733838	−0.366919	+	0.930253i	$0.619587\pi$
$368$	−21.2200	−1.10617
$369$	2.78971	0.145226
$370$	10.0327	0.521575
$371$	−8.87545	−0.460790
$372$	−9.32888	−0.483680
$373$	−7.87779	−0.407897	−0.203948	−	0.978982i	$-0.565377\pi$
$373$	−7.87779	−0.407897	−0.203948	+	0.978982i	$0.565377\pi$
$374$	−0.0455839	−0.00235709
$375$	29.5323	1.52504
$376$	20.7703	1.07115
$377$	14.0464	0.723424
$378$	14.2004	0.730391
$379$	−2.59001	−0.133040	−0.0665198	−	0.997785i	$-0.521190\pi$
$379$	−2.59001	−0.133040	−0.0665198	+	0.997785i	$0.521190\pi$
$380$	−10.6915	−0.548462
$381$	−9.30368	−0.476642
$382$	−9.29398	−0.475521
$383$	−23.1206	−1.18141	−0.590704	−	0.806888i	$-0.701150\pi$
$383$	−23.1206	−1.18141	−0.590704	+	0.806888i	$0.701150\pi$
$384$	−16.5259	−0.843335
$385$	1.88541	0.0960894
$386$	13.2235	0.673060
$387$	67.2339	3.41769
$388$	0.713142	0.0362043
$389$	−13.7274	−0.696005	−0.348002	−	0.937494i	$-0.613140\pi$
$389$	−13.7274	−0.696005	−0.348002	+	0.937494i	$0.613140\pi$
$390$	53.9970	2.73425
$391$	0.296403	0.0149897
$392$	−19.7763	−0.998854
$393$	−38.3040	−1.93218
$394$	−30.7338	−1.54834
$395$	0.600950	0.0302371
$396$	−4.06689	−0.204369
$397$	−12.5508	−0.629909	−0.314954	−	0.949107i	$-0.601989\pi$
$397$	−12.5508	−0.629909	−0.314954	+	0.949107i	$0.601989\pi$
$398$	20.0413	1.00458
$399$	19.6334	0.982901
$400$	−3.93137	−0.196568
$401$	−25.2128	−1.25907	−0.629533	−	0.776974i	$-0.716754\pi$
$401$	−25.2128	−1.25907	−0.629533	+	0.776974i	$0.716754\pi$
$402$	53.6513	2.67588
$403$	28.9318	1.44120
$404$	6.74766	0.335708
$405$	−72.1216	−3.58375
$406$	2.38193	0.118213
$407$	3.24546	0.160872
$408$	0.377671	0.0186975
$409$	−12.2437	−0.605413	−0.302706	−	0.953084i	$-0.597890\pi$
$409$	−12.2437	−0.605413	−0.302706	+	0.953084i	$0.597890\pi$
$410$	1.10645	0.0546439
$411$	16.9270	0.834946
$412$	3.29224	0.162197
$413$	0.741538	0.0364887
$414$	−74.9157	−3.68190
$415$	5.75838	0.282668
$416$	−15.2514	−0.747763
$417$	−32.5321	−1.59311
$418$	9.79801	0.479236
$419$	1.78104	0.0870097	0.0435049	−	0.999053i	$-0.486148\pi$
$419$	1.78104	0.0870097	0.0435049	+	0.999053i	$0.486148\pi$
$420$	−3.23218	−0.157714
$421$	37.7060	1.83768	0.918838	−	0.394634i	$-0.129129\pi$
$421$	37.7060	1.83768	0.918838	+	0.394634i	$0.129129\pi$
$422$	−18.7389	−0.912195
$423$	52.7998	2.56721
$424$	36.6973	1.78218
$425$	0.0549136	0.00266370
$426$	0.876232	0.0424536
$427$	7.25225	0.350961
$428$	2.25479	0.108989
$429$	17.4674	0.843336
$430$	26.6663	1.28597
$431$	−3.37203	−0.162425	−0.0812125	−	0.996697i	$-0.525879\pi$
$431$	−3.37203	−0.162425	−0.0812125	+	0.996697i	$0.525879\pi$
$432$	−42.2773	−2.03407
$433$	−37.9856	−1.82547	−0.912735	−	0.408553i	$-0.866034\pi$
$433$	−37.9856	−1.82547	−0.912735	+	0.408553i	$0.866034\pi$
$434$	4.90616	0.235503
$435$	−22.0696	−1.05815
$436$	9.04012	0.432943
$437$	−63.7102	−3.04767
$438$	1.60626	0.0767499
$439$	−7.78616	−0.371613	−0.185806	−	0.982586i	$-0.559490\pi$
$439$	−7.78616	−0.371613	−0.185806	+	0.982586i	$0.559490\pi$
$440$	−7.79560	−0.371641
$441$	−50.2729	−2.39395
$442$	−0.242352	−0.0115275
$443$	−7.39437	−0.351317	−0.175659	−	0.984451i	$-0.556205\pi$
$443$	−7.39437	−0.351317	−0.175659	+	0.984451i	$0.556205\pi$
$444$	−5.56373	−0.264043
$445$	3.93331	0.186457
$446$	−29.8777	−1.41475
$447$	−58.8499	−2.78350
$448$	−6.56708	−0.310266
$449$	−35.9107	−1.69473	−0.847366	−	0.531009i	$-0.821813\pi$
$449$	−35.9107	−1.69473	−0.847366	+	0.531009i	$0.821813\pi$
$450$	−13.8794	−0.654280
$451$	0.357926	0.0168541
$452$	3.53900	0.166461
$453$	−46.2929	−2.17503
$454$	−19.1970	−0.900960
$455$	10.0240	0.469933
$456$	−81.1783	−3.80152
$457$	36.4629	1.70566	0.852832	−	0.522185i	$-0.174883\pi$
$457$	36.4629	1.70566	0.852832	+	0.522185i	$0.174883\pi$
$458$	19.3138	0.902475
$459$	0.590532	0.0275637
$460$	10.4884	0.489023
$461$	25.4895	1.18717	0.593583	−	0.804773i	$-0.297713\pi$
$461$	25.4895	1.18717	0.593583	+	0.804773i	$0.297713\pi$
$462$	2.96206	0.137808
$463$	−7.65107	−0.355575	−0.177788	−	0.984069i	$-0.556894\pi$
$463$	−7.65107	−0.355575	−0.177788	+	0.984069i	$0.556894\pi$
$464$	−7.09145	−0.329212
$465$	−45.4576	−2.10804
$466$	−9.64030	−0.446578
$467$	22.2103	1.02777	0.513886	−	0.857859i	$-0.328206\pi$
$467$	22.2103	1.02777	0.513886	+	0.857859i	$0.328206\pi$
$468$	−21.6221	−0.999482
$469$	9.95984	0.459903
$470$	20.9415	0.965957
$471$	64.9192	2.99132
$472$	−3.06603	−0.141126
$473$	8.62626	0.396636
$474$	0.944119	0.0433648
$475$	−11.8034	−0.541576
$476$	0.0145068	0.000664920 0
$477$	93.2873	4.27133
$478$	−14.8494	−0.679197
$479$	25.5651	1.16810	0.584049	−	0.811719i	$-0.301468\pi$
$479$	25.5651	1.16810	0.584049	+	0.811719i	$0.301468\pi$
$480$	23.9630	1.09375
$481$	17.2549	0.786756
$482$	−8.24510	−0.375554
$483$	−19.2604	−0.876379
$484$	−0.521790	−0.0237177
$485$	3.47498	0.157791
$486$	−55.8564	−2.53370
$487$	1.39929	0.0634081	0.0317040	−	0.999497i	$-0.489907\pi$
$487$	1.39929	0.0634081	0.0317040	+	0.999497i	$0.489907\pi$
$488$	−29.9859	−1.35740
$489$	−5.74786	−0.259927
$490$	−19.9392	−0.900763
$491$	−22.0307	−0.994232	−0.497116	−	0.867684i	$-0.665608\pi$
$491$	−22.0307	−0.994232	−0.497116	+	0.867684i	$0.665608\pi$
$492$	−0.613595	−0.0276630
$493$	0.0990538	0.00446116
$494$	52.0923	2.34374
$495$	−19.8170	−0.890709
$496$	−14.6065	−0.655853
$497$	0.162664	0.00729648
$498$	9.04667	0.405391
$499$	−13.2699	−0.594044	−0.297022	−	0.954871i	$-0.595993\pi$
$499$	−13.2699	−0.594044	−0.297022	+	0.954871i	$0.595993\pi$
$500$	−4.69030	−0.209756
$501$	−26.4141	−1.18009
$502$	25.7950	1.15129
$503$	−4.29994	−0.191725	−0.0958623	−	0.995395i	$-0.530561\pi$
$503$	−4.29994	−0.191725	−0.0958623	+	0.995395i	$0.530561\pi$
$504$	−17.7205	−0.789334
$505$	32.8798	1.46313
$506$	−9.61185	−0.427299
$507$	50.1571	2.22755
$508$	1.47760	0.0655580
$509$	−13.7000	−0.607243	−0.303622	−	0.952793i	$-0.598196\pi$
$509$	−13.7000	−0.607243	−0.303622	+	0.952793i	$0.598196\pi$
$510$	0.380783	0.0168614
$511$	0.298186	0.0131910
$512$	24.1593	1.06770
$513$	−126.932	−5.60417
$514$	12.2895	0.542065
$515$	16.0424	0.706911
$516$	−14.7881	−0.651009
$517$	6.77433	0.297935
$518$	2.92602	0.128562
$519$	26.2717	1.15320
$520$	−41.4463	−1.81754
$521$	16.4630	0.721256	0.360628	−	0.932710i	$-0.382562\pi$
$521$	16.4630	0.721256	0.360628	+	0.932710i	$0.382562\pi$
$522$	−25.0358	−1.09579
$523$	−26.5880	−1.16261	−0.581306	−	0.813685i	$-0.697458\pi$
$523$	−26.5880	−1.16261	−0.581306	+	0.813685i	$0.697458\pi$
$524$	6.08341	0.265755
$525$	−3.56831	−0.155734
$526$	−16.4829	−0.718688
$527$	0.204025	0.00888748
$528$	−8.81862	−0.383781
$529$	39.4997	1.71738
$530$	36.9997	1.60716
$531$	−7.79410	−0.338235
$532$	−3.11817	−0.135190
$533$	1.90296	0.0824262
$534$	6.17940	0.267409
$535$	10.9871	0.475014
$536$	−41.1809	−1.77875
$537$	49.7304	2.14602
$538$	27.5949	1.18970
$539$	−6.45012	−0.277826
$540$	20.8963	0.899233
$541$	39.2055	1.68558	0.842789	−	0.538245i	$-0.180912\pi$
$541$	39.2055	1.68558	0.842789	+	0.538245i	$0.180912\pi$
$542$	14.1229	0.606629
$543$	−32.0876	−1.37701
$544$	−0.107552	−0.00461125
$545$	44.0505	1.88692
$546$	15.7482	0.673960
$547$	−21.1003	−0.902184	−0.451092	−	0.892477i	$-0.648965\pi$
$547$	−21.1003	−0.902184	−0.451092	+	0.892477i	$0.648965\pi$
$548$	−2.68833	−0.114840
$549$	−76.2264	−3.25326
$550$	−1.78076	−0.0759317
$551$	−21.2911	−0.907030
$552$	79.6359	3.38953
$553$	0.175266	0.00745309
$554$	−10.5899	−0.449922
$555$	−27.1108	−1.15079
$556$	5.16673	0.219118
$557$	−32.6337	−1.38274	−0.691368	−	0.722503i	$-0.742992\pi$
$557$	−32.6337	−1.38274	−0.691368	+	0.722503i	$0.742992\pi$
$558$	−51.5673	−2.18302
$559$	45.8626	1.93978
$560$	−5.06073	−0.213855
$561$	0.123179	0.00520062
$562$	−14.5583	−0.614104
$563$	10.8486	0.457212	0.228606	−	0.973519i	$-0.426583\pi$
$563$	10.8486	0.457212	0.228606	+	0.973519i	$0.426583\pi$
$564$	−11.6133	−0.489008
$565$	17.2448	0.725493
$566$	17.7136	0.744560
$567$	−21.0342	−0.883354
$568$	−0.672566	−0.0282203
$569$	−46.6176	−1.95431	−0.977156	−	0.212524i	$-0.931831\pi$
$569$	−46.6176	−1.95431	−0.977156	+	0.212524i	$0.931831\pi$
$570$	−81.8472	−3.42820
$571$	21.4579	0.897986	0.448993	−	0.893535i	$-0.351783\pi$
$571$	21.4579	0.897986	0.448993	+	0.893535i	$0.351783\pi$
$572$	−2.77416	−0.115994
$573$	25.1146	1.04918
$574$	0.322696	0.0134691
$575$	11.5791	0.482882
$576$	69.0248	2.87603
$577$	35.6708	1.48499	0.742497	−	0.669850i	$-0.233641\pi$
$577$	35.6708	1.48499	0.742497	+	0.669850i	$0.233641\pi$
$578$	20.6672	0.859641
$579$	−35.7332	−1.48502
$580$	3.50507	0.145540
$581$	1.67943	0.0696743
$582$	5.45935	0.226297
$583$	11.9690	0.495704
$584$	−1.23291	−0.0510181
$585$	−105.360	−4.35609
$586$	6.91856	0.285803
$587$	11.6420	0.480517	0.240259	−	0.970709i	$-0.422768\pi$
$587$	11.6420	0.480517	0.240259	+	0.970709i	$0.422768\pi$
$588$	11.0575	0.456004
$589$	−43.8541	−1.80698
$590$	−3.09130	−0.127267
$591$	83.0502	3.41623
$592$	−8.71132	−0.358033
$593$	11.0099	0.452123	0.226062	−	0.974113i	$-0.427415\pi$
$593$	11.0099	0.452123	0.226062	+	0.974113i	$0.427415\pi$
$594$	−19.1500	−0.785733
$595$	0.0706886	0.00289795
$596$	9.34649	0.382847
$597$	−54.1566	−2.21648
$598$	−51.1026	−2.08974
$599$	27.7254	1.13283	0.566415	−	0.824120i	$-0.308330\pi$
$599$	27.7254	1.13283	0.566415	+	0.824120i	$0.308330\pi$
$600$	14.7539	0.602325
$601$	−31.2267	−1.27376	−0.636882	−	0.770961i	$-0.719776\pi$
$601$	−31.2267	−1.27376	−0.636882	+	0.770961i	$0.719776\pi$
$602$	7.77721	0.316976
$603$	−104.685	−4.26311
$604$	7.35220	0.299157
$605$	−2.54257	−0.103370
$606$	51.6557	2.09837
$607$	4.91168	0.199359	0.0996795	−	0.995020i	$-0.468218\pi$
$607$	4.91168	0.199359	0.0996795	+	0.995020i	$0.468218\pi$
$608$	23.1177	0.937546
$609$	−6.43656	−0.260823
$610$	−30.2329	−1.22410
$611$	36.0165	1.45707
$612$	−0.152477	−0.00616353
$613$	−12.2366	−0.494231	−0.247115	−	0.968986i	$-0.579483\pi$
$613$	−12.2366	−0.494231	−0.247115	+	0.968986i	$0.579483\pi$
$614$	18.3554	0.740762
$615$	−2.98991	−0.120565
$616$	−2.27358	−0.0916051
$617$	−22.3887	−0.901337	−0.450668	−	0.892691i	$-0.648814\pi$
$617$	−22.3887	−0.901337	−0.450668	+	0.892691i	$0.648814\pi$
$618$	25.2032	1.01382
$619$	35.4394	1.42443	0.712215	−	0.701961i	$-0.247692\pi$
$619$	35.4394	1.42443	0.712215	+	0.701961i	$0.247692\pi$
$620$	7.21953	0.289943
$621$	124.520	4.99681
$622$	−26.9964	−1.08246
$623$	1.14715	0.0459594
$624$	−46.8853	−1.87691
$625$	−30.1781	−1.20712
$626$	−15.1167	−0.604184
$627$	−26.4766	−1.05738
$628$	−10.3104	−0.411430
$629$	0.121680	0.00485171
$630$	−17.8665	−0.711819
$631$	39.0027	1.55267	0.776336	−	0.630319i	$-0.217076\pi$
$631$	39.0027	1.55267	0.776336	+	0.630319i	$0.217076\pi$
$632$	−0.724674	−0.0288260
$633$	50.6371	2.01265
$634$	28.4623	1.13038
$635$	7.20003	0.285725
$636$	−20.5185	−0.813613
$637$	−34.2929	−1.35873
$638$	−3.21215	−0.127170
$639$	−1.70972	−0.0676353
$640$	12.7893	0.505540
$641$	0.159628	0.00630492	0.00315246	−	0.999995i	$-0.498997\pi$
$641$	0.159628	0.00630492	0.00315246	+	0.999995i	$0.498997\pi$
$642$	17.2612	0.681246
$643$	−38.2224	−1.50734	−0.753672	−	0.657250i	$-0.771719\pi$
$643$	−38.2224	−1.50734	−0.753672	+	0.657250i	$0.771719\pi$
$644$	3.05892	0.120538
$645$	−72.0591	−2.83732
$646$	0.367351	0.0144532
$647$	7.85819	0.308937	0.154469	−	0.987998i	$-0.450633\pi$
$647$	7.85819	0.308937	0.154469	+	0.987998i	$0.450633\pi$
$648$	86.9701	3.41651
$649$	−1.00000	−0.0392534
$650$	−9.46760	−0.371350
$651$	−13.2577	−0.519608
$652$	0.912870	0.0357507
$653$	−15.1175	−0.591593	−0.295796	−	0.955251i	$-0.595585\pi$
$653$	−15.1175	−0.591593	−0.295796	+	0.955251i	$0.595585\pi$
$654$	69.2053	2.70614
$655$	29.6431	1.15825
$656$	−0.960727	−0.0375101
$657$	−3.13415	−0.122275
$658$	6.10756	0.238097
$659$	−19.2800	−0.751043	−0.375522	−	0.926814i	$-0.622536\pi$
$659$	−19.2800	−0.751043	−0.375522	+	0.926814i	$0.622536\pi$
$660$	4.35875	0.169664
$661$	−16.0443	−0.624049	−0.312025	−	0.950074i	$-0.601007\pi$
$661$	−16.0443	−0.624049	−0.312025	+	0.950074i	$0.601007\pi$
$662$	3.73424	0.145135
$663$	0.654896	0.0254341
$664$	−6.94392	−0.269476
$665$	−15.1941	−0.589203
$666$	−30.7546	−1.19172
$667$	20.8865	0.808730
$668$	4.19506	0.162312
$669$	80.7369	3.12147
$670$	−41.5202	−1.60407
$671$	−9.78002	−0.377553
$672$	6.98877	0.269598
$673$	20.9897	0.809092	0.404546	−	0.914518i	$-0.367429\pi$
$673$	20.9897	0.809092	0.404546	+	0.914518i	$0.367429\pi$
$674$	−34.1943	−1.31712
$675$	23.0694	0.887941
$676$	−7.96591	−0.306381
$677$	28.0814	1.07925	0.539627	−	0.841904i	$-0.318565\pi$
$677$	28.0814	1.07925	0.539627	+	0.841904i	$0.318565\pi$
$678$	27.0923	1.04047
$679$	1.01348	0.0388936
$680$	−0.292276	−0.0112083
$681$	51.8751	1.98786
$682$	−6.61619	−0.253347
$683$	10.5828	0.404940	0.202470	−	0.979288i	$-0.435103\pi$
$683$	10.5828	0.404940	0.202470	+	0.979288i	$0.435103\pi$
$684$	32.7742	1.25315
$685$	−13.0996	−0.500511
$686$	−12.1263	−0.462983
$687$	−52.1907	−1.99120
$688$	−23.1542	−0.882746
$689$	63.6345	2.42428
$690$	80.2921	3.05667
$691$	−1.97560	−0.0751555	−0.0375777	−	0.999294i	$-0.511964\pi$
$691$	−1.97560	−0.0751555	−0.0375777	+	0.999294i	$0.511964\pi$
$692$	−4.17244	−0.158612
$693$	−5.77962	−0.219549
$694$	−20.1383	−0.764439
$695$	25.1763	0.954992
$696$	26.6132	1.00877
$697$	0.0134195	0.000508300 0
$698$	−10.2568	−0.388226
$699$	26.0505	0.985319
$700$	0.566716	0.0214199
$701$	26.5930	1.00441	0.502203	−	0.864750i	$-0.332523\pi$
$701$	26.5930	1.00441	0.502203	+	0.864750i	$0.332523\pi$
$702$	−101.813	−3.84269
$703$	−26.1545	−0.986436
$704$	8.85604	0.333774
$705$	−56.5890	−2.13127
$706$	6.06384	0.228215
$707$	9.58937	0.360645
$708$	1.71431	0.0644277
$709$	8.78513	0.329932	0.164966	−	0.986299i	$-0.447249\pi$
$709$	8.78513	0.329932	0.164966	+	0.986299i	$0.447249\pi$
$710$	−0.678108	−0.0254489
$711$	−1.84218	−0.0690870
$712$	−4.74310	−0.177755
$713$	43.0209	1.61114
$714$	0.111055	0.00415613
$715$	−13.5179	−0.505540
$716$	−7.89814	−0.295167
$717$	40.1269	1.49856
$718$	−16.8068	−0.627223
$719$	−20.9871	−0.782685	−0.391343	−	0.920245i	$-0.627989\pi$
$719$	−20.9871	−0.782685	−0.391343	+	0.920245i	$0.627989\pi$
$720$	53.1920	1.98235
$721$	4.67874	0.174245
$722$	−55.8596	−2.07888
$723$	22.2803	0.828613
$724$	5.09613	0.189396
$725$	3.86958	0.143713
$726$	−3.99449	−0.148249
$727$	0.818122	0.0303425	0.0151712	−	0.999885i	$-0.495171\pi$
$727$	0.818122	0.0303425	0.0151712	+	0.999885i	$0.495171\pi$
$728$	−12.0878	−0.448003
$729$	65.8409	2.43855
$730$	−1.24307	−0.0460080
$731$	0.323420	0.0119621
$732$	16.7660	0.619688
$733$	−0.345628	−0.0127661	−0.00638304	−	0.999980i	$-0.502032\pi$
$733$	−0.345628	−0.0127661	−0.00638304	+	0.999980i	$0.502032\pi$
$734$	17.0923	0.630889
$735$	53.8808	1.98742
$736$	−22.6785	−0.835939
$737$	−13.4313	−0.494750
$738$	−3.39177	−0.124853
$739$	−4.02947	−0.148226	−0.0741132	−	0.997250i	$-0.523613\pi$
$739$	−4.02947	−0.148226	−0.0741132	+	0.997250i	$0.523613\pi$
$740$	4.30572	0.158281
$741$	−140.766	−5.17118
$742$	10.7909	0.396147
$743$	−31.1642	−1.14331	−0.571653	−	0.820496i	$-0.693697\pi$
$743$	−31.1642	−1.14331	−0.571653	+	0.820496i	$0.693697\pi$
$744$	54.8164	2.00967
$745$	45.5434	1.66858
$746$	9.57795	0.350674
$747$	−17.6520	−0.645852
$748$	−0.0195632	−0.000715301 0
$749$	3.20438	0.117085
$750$	−35.9059	−1.31110
$751$	29.9276	1.09207	0.546036	−	0.837762i	$-0.316136\pi$
$751$	29.9276	1.09207	0.546036	+	0.837762i	$0.316136\pi$
$752$	−18.1833	−0.663078
$753$	−69.7045	−2.54017
$754$	−17.0778	−0.621936
$755$	35.8256	1.30383
$756$	6.09438	0.221650
$757$	−15.8955	−0.577731	−0.288865	−	0.957370i	$-0.593278\pi$
$757$	−15.8955	−0.577731	−0.288865	+	0.957370i	$0.593278\pi$
$758$	3.14897	0.114376
$759$	25.9736	0.942782
$760$	62.8231	2.27883
$761$	6.26545	0.227122	0.113561	−	0.993531i	$-0.463774\pi$
$761$	6.26545	0.227122	0.113561	+	0.993531i	$0.463774\pi$
$762$	11.3116	0.409775
$763$	12.8473	0.465103
$764$	−3.98869	−0.144306
$765$	−0.742989	−0.0268628
$766$	28.1104	1.01567
$767$	−5.31662	−0.191972
$768$	−38.0994	−1.37479
$769$	−16.1826	−0.583561	−0.291780	−	0.956485i	$-0.594248\pi$
$769$	−16.1826	−0.583561	−0.291780	+	0.956485i	$0.594248\pi$
$770$	−2.29231	−0.0826092
$771$	−33.2092	−1.19600
$772$	5.67512	0.204252
$773$	−34.4263	−1.23823	−0.619114	−	0.785301i	$-0.712508\pi$
$773$	−34.4263	−1.23823	−0.619114	+	0.785301i	$0.712508\pi$
$774$	−81.7441	−2.93823
$775$	7.97033	0.286303
$776$	−4.19041	−0.150427
$777$	−7.90684	−0.283656
$778$	16.6899	0.598363
$779$	−2.88445	−0.103346
$780$	23.1738	0.829757
$781$	−0.219360	−0.00784933
$782$	−0.360372	−0.0128869
$783$	41.6129	1.48712
$784$	17.3131	0.618326
$785$	−50.2404	−1.79316
$786$	46.5707	1.66112
$787$	−19.2096	−0.684749	−0.342374	−	0.939564i	$-0.611231\pi$
$787$	−19.2096	−0.684749	−0.342374	+	0.939564i	$0.611231\pi$
$788$	−13.1900	−0.469873
$789$	44.5408	1.58570
$790$	−0.730645	−0.0259952
$791$	5.02942	0.178826
$792$	23.8970	0.849142
$793$	−51.9967	−1.84646
$794$	15.2595	0.541540
$795$	−99.9822	−3.54600
$796$	8.60110	0.304858
$797$	12.2383	0.433503	0.216752	−	0.976227i	$-0.430454\pi$
$797$	12.2383	0.433503	0.216752	+	0.976227i	$0.430454\pi$
$798$	−23.8706	−0.845012
$799$	0.253986	0.00898538
$800$	−4.20156	−0.148548
$801$	−12.0573	−0.426025
$802$	30.6541	1.08243
$803$	−0.402118	−0.0141904
$804$	23.0255	0.812046
$805$	14.9054	0.525348
$806$	−35.1758	−1.23902
$807$	−74.5683	−2.62493
$808$	−39.6491	−1.39485
$809$	−26.7445	−0.940287	−0.470143	−	0.882590i	$-0.655798\pi$
$809$	−26.7445	−0.940287	−0.470143	+	0.882590i	$0.655798\pi$
$810$	87.6867	3.08100
$811$	−21.5044	−0.755123	−0.377561	−	0.925985i	$-0.623237\pi$
$811$	−21.5044	−0.755123	−0.377561	+	0.925985i	$0.623237\pi$
$812$	1.02225	0.0358739
$813$	−38.1635	−1.33845
$814$	−3.94589	−0.138303
$815$	4.44821	0.155814
$816$	−0.330631	−0.0115744
$817$	−69.5172	−2.43210
$818$	14.8861	0.520480
$819$	−30.7280	−1.07372
$820$	0.474856	0.0165827
$821$	−24.7059	−0.862243	−0.431121	−	0.902294i	$-0.641882\pi$
$821$	−24.7059	−0.862243	−0.431121	+	0.902294i	$0.641882\pi$
$822$	−20.5801	−0.717813
$823$	0.318348	0.0110969	0.00554846	−	0.999985i	$-0.498234\pi$
$823$	0.318348	0.0110969	0.00554846	+	0.999985i	$0.498234\pi$
$824$	−19.3452	−0.673921
$825$	4.81204	0.167534
$826$	−0.901574	−0.0313698
$827$	2.31817	0.0806108	0.0403054	−	0.999187i	$-0.487167\pi$
$827$	2.31817	0.0806108	0.0403054	+	0.999187i	$0.487167\pi$
$828$	−32.1515	−1.11734
$829$	42.8841	1.48943	0.744713	−	0.667385i	$-0.232586\pi$
$829$	42.8841	1.48943	0.744713	+	0.667385i	$0.232586\pi$
$830$	−7.00113	−0.243013
$831$	28.6166	0.992698
$832$	47.0842	1.63235
$833$	−0.241831	−0.00837894
$834$	39.5531	1.36961
$835$	20.4416	0.707411
$836$	4.20500	0.145433
$837$	85.7117	2.96263
$838$	−2.16542	−0.0748033
$839$	−12.4719	−0.430577	−0.215289	−	0.976550i	$-0.569069\pi$
$839$	−12.4719	−0.430577	−0.215289	+	0.976550i	$0.569069\pi$
$840$	18.9922	0.655295
$841$	−22.0200	−0.759310
$842$	−45.8435	−1.57987
$843$	39.3401	1.35495
$844$	−8.04215	−0.276822
$845$	−38.8161	−1.33531
$846$	−64.1948	−2.20706
$847$	−0.741538	−0.0254795
$848$	−32.1266	−1.10323
$849$	−47.8667	−1.64278
$850$	−0.0667648	−0.00229001
$851$	25.6576	0.879530
$852$	0.376052	0.0128833
$853$	20.4006	0.698505	0.349252	−	0.937029i	$-0.386436\pi$
$853$	20.4006	0.698505	0.349252	+	0.937029i	$0.386436\pi$
$854$	−8.81741	−0.301725
$855$	159.701	5.46167
$856$	−13.2491	−0.452846
$857$	5.51114	0.188257	0.0941285	−	0.995560i	$-0.469994\pi$
$857$	5.51114	0.188257	0.0941285	+	0.995560i	$0.469994\pi$
$858$	−21.2372	−0.725026
$859$	27.1039	0.924773	0.462386	−	0.886679i	$-0.346993\pi$
$859$	27.1039	0.924773	0.462386	+	0.886679i	$0.346993\pi$
$860$	11.4444	0.390250
$861$	−0.872005	−0.0297179
$862$	4.09977	0.139639
$863$	−8.14048	−0.277105	−0.138553	−	0.990355i	$-0.544245\pi$
$863$	−8.14048	−0.277105	−0.138553	+	0.990355i	$0.544245\pi$
$864$	−45.1829	−1.53716
$865$	−20.3314	−0.691288
$866$	46.1835	1.56938
$867$	−55.8478	−1.89669
$868$	2.10557	0.0714677
$869$	−0.236355	−0.00801781
$870$	26.8325	0.909708
$871$	−71.4093	−2.41961
$872$	−53.1196	−1.79886
$873$	−10.6524	−0.360528
$874$	77.4599	2.62012
$875$	−6.66557	−0.225337
$876$	0.689355	0.0232912
$877$	−45.8512	−1.54829	−0.774143	−	0.633010i	$-0.781819\pi$
$877$	−45.8512	−1.54829	−0.774143	+	0.633010i	$0.781819\pi$
$878$	9.46654	0.319480
$879$	−18.6957	−0.630589
$880$	6.82465	0.230059
$881$	−17.1852	−0.578983	−0.289491	−	0.957181i	$-0.593486\pi$
$881$	−17.1852	−0.578983	−0.289491	+	0.957181i	$0.593486\pi$
$882$	61.1226	2.05810
$883$	26.5779	0.894419	0.447210	−	0.894429i	$-0.352418\pi$
$883$	26.5779	0.894419	0.447210	+	0.894429i	$0.352418\pi$
$884$	−0.104010	−0.00349824
$885$	8.35345	0.280798
$886$	8.99019	0.302032
$887$	3.87491	0.130107	0.0650533	−	0.997882i	$-0.479278\pi$
$887$	3.87491	0.130107	0.0650533	+	0.997882i	$0.479278\pi$
$888$	32.6924	1.09709
$889$	2.09988	0.0704278
$890$	−4.78218	−0.160299
$891$	28.3657	0.950285
$892$	−12.8226	−0.429331
$893$	−54.5929	−1.82688
$894$	71.5507	2.39301
$895$	−38.4859	−1.28644
$896$	3.72997	0.124610
$897$	138.092	4.61075
$898$	43.6609	1.45698
$899$	14.3770	0.479499
$900$	−5.95660	−0.198553
$901$	0.448746	0.0149499
$902$	−0.435172	−0.0144896
$903$	−21.0160	−0.699367
$904$	−20.7951	−0.691636
$905$	24.8323	0.825454
$906$	56.2836	1.86990
$907$	26.5023	0.879995	0.439998	−	0.897999i	$-0.354979\pi$
$907$	26.5023	0.879995	0.439998	+	0.897999i	$0.354979\pi$
$908$	−8.23875	−0.273413
$909$	−100.791	−3.34303
$910$	−12.1874	−0.404007
$911$	−19.4498	−0.644401	−0.322201	−	0.946671i	$-0.604423\pi$
$911$	−19.4498	−0.644401	−0.322201	+	0.946671i	$0.604423\pi$
$912$	71.0674	2.35328
$913$	−2.26479	−0.0749536
$914$	−44.3322	−1.46638
$915$	81.6969	2.70082
$916$	8.28889	0.273873
$917$	8.64539	0.285496
$918$	−0.717979	−0.0236968
$919$	−34.8294	−1.14891	−0.574457	−	0.818534i	$-0.694787\pi$
$919$	−34.8294	−1.14891	−0.574457	+	0.818534i	$0.694787\pi$
$920$	−61.6295	−2.03186
$921$	−49.6007	−1.63440
$922$	−30.9906	−1.02062
$923$	−1.16626	−0.0383878
$924$	1.27123	0.0418202
$925$	4.75349	0.156294
$926$	9.30230	0.305693
$927$	−49.1769	−1.61518
$928$	−7.57883	−0.248787
$929$	−19.5698	−0.642065	−0.321032	−	0.947068i	$-0.604030\pi$
$929$	−19.5698	−0.642065	−0.321032	+	0.947068i	$0.604030\pi$
$930$	55.2681	1.81231
$931$	51.9802	1.70358
$932$	−4.13732	−0.135522
$933$	72.9510	2.38831
$934$	−27.0037	−0.883587
$935$	−0.0953271	−0.00311753
$936$	127.051	4.15280
$937$	−1.13802	−0.0371775	−0.0185888	−	0.999827i	$-0.505917\pi$
$937$	−1.13802	−0.0371775	−0.0185888	+	0.999827i	$0.505917\pi$
$938$	−12.1093	−0.395384
$939$	40.8490	1.33306
$940$	8.98742	0.293137
$941$	−31.1541	−1.01559	−0.507797	−	0.861477i	$-0.669540\pi$
$941$	−31.1541	−1.01559	−0.507797	+	0.861477i	$0.669540\pi$
$942$	−78.9298	−2.57167
$943$	2.82964	0.0921459
$944$	2.68415	0.0873618
$945$	29.6966	0.966029
$946$	−10.4880	−0.340993
$947$	31.7301	1.03109	0.515544	−	0.856863i	$-0.327590\pi$
$947$	31.7301	1.03109	0.515544	+	0.856863i	$0.327590\pi$
$948$	0.405186	0.0131598
$949$	−2.13791	−0.0693996
$950$	14.3507	0.465599
$951$	−76.9121	−2.49405
$952$	−0.0852420	−0.00276271
$953$	−27.4682	−0.889783	−0.444892	−	0.895584i	$-0.646758\pi$
$953$	−27.4682	−0.889783	−0.444892	+	0.895584i	$0.646758\pi$
$954$	−113.420	−3.67212
$955$	−19.4360	−0.628934
$956$	−6.37291	−0.206115
$957$	8.68002	0.280585
$958$	−31.0824	−1.00423
$959$	−3.82049	−0.123370
$960$	−73.9785	−2.38764
$961$	−1.38713	−0.0447462
$962$	−20.9788	−0.676384
$963$	−33.6803	−1.08533
$964$	−3.53854	−0.113969
$965$	27.6536	0.890202
$966$	23.4171	0.753433
$967$	−18.2061	−0.585468	−0.292734	−	0.956194i	$-0.594565\pi$
$967$	−18.2061	−0.585468	−0.292734	+	0.956194i	$0.594565\pi$
$968$	3.06603	0.0985461
$969$	−0.992673	−0.0318893
$970$	−4.22494	−0.135655
$971$	−47.6830	−1.53022	−0.765111	−	0.643899i	$-0.777316\pi$
$971$	−47.6830	−1.53022	−0.765111	+	0.643899i	$0.777316\pi$
$972$	−23.9718	−0.768897
$973$	7.34265	0.235394
$974$	−1.70128	−0.0545127
$975$	25.5838	0.819338
$976$	26.2511	0.840276
$977$	−32.8451	−1.05081	−0.525403	−	0.850853i	$-0.676086\pi$
$977$	−32.8451	−1.05081	−0.525403	+	0.850853i	$0.676086\pi$
$978$	6.98834	0.223462
$979$	−1.54698	−0.0494418
$980$	−8.55730	−0.273353
$981$	−135.034	−4.31131
$982$	26.7853	0.854753
$983$	32.7803	1.04553	0.522765	−	0.852477i	$-0.324901\pi$
$983$	32.7803	1.04553	0.522765	+	0.852477i	$0.324901\pi$
$984$	3.60548	0.114938
$985$	−64.2718	−2.04787
$986$	−0.120431	−0.00383531
$987$	−16.5041	−0.525332
$988$	22.3564	0.711252
$989$	68.1964	2.16852
$990$	24.0939	0.765754
$991$	46.7176	1.48403	0.742016	−	0.670382i	$-0.233870\pi$
$991$	46.7176	1.48403	0.742016	+	0.670382i	$0.233870\pi$
$992$	−15.6104	−0.495632
$993$	−10.0908	−0.320223
$994$	−0.197770	−0.00627287
$995$	41.9113	1.32868
$996$	3.88255	0.123023
$997$	−21.7327	−0.688280	−0.344140	−	0.938918i	$-0.611830\pi$
$997$	−21.7327	−0.688280	−0.344140	+	0.938918i	$0.611830\pi$
$998$	16.1338	0.510707
$999$	51.1183	1.61731

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	649.2.a.f.1.5	✓	17
3.2	odd	2		5841.2.a.z.1.13		17
11.10	odd	2		7139.2.a.r.1.13		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
649.2.a.f.1.5	✓	17	1.1	even	1	trivial
5841.2.a.z.1.13		17	3.2	odd	2
7139.2.a.r.1.13		17	11.10	odd	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:	\( N \)	\(=\)	\( 649 = 11 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	649.a (trivial)

\(f(q)\)	\(=\)	\(q-1.21582 q^{2} +3.28544 q^{3} -0.521790 q^{4} -2.54257 q^{5} -3.99449 q^{6} -0.741538 q^{7} +3.06603 q^{8} +7.79410 q^{9} +O(q^{10})\)	\(q-1.21582 q^{2} +3.28544 q^{3} -0.521790 q^{4} -2.54257 q^{5} -3.99449 q^{6} -0.741538 q^{7} +3.06603 q^{8} +7.79410 q^{9} +3.09130 q^{10} +1.00000 q^{11} -1.71431 q^{12} +5.31662 q^{13} +0.901574 q^{14} -8.35345 q^{15} -2.68415 q^{16} +0.0374924 q^{17} -9.47619 q^{18} -8.05879 q^{19} +1.32669 q^{20} -2.43628 q^{21} -1.21582 q^{22} +7.90567 q^{23} +10.0733 q^{24} +1.46466 q^{25} -6.46404 q^{26} +15.7507 q^{27} +0.386927 q^{28} +2.64197 q^{29} +10.1563 q^{30} +5.44177 q^{31} -2.86863 q^{32} +3.28544 q^{33} -0.0455839 q^{34} +1.88541 q^{35} -4.06689 q^{36} +3.24546 q^{37} +9.79801 q^{38} +17.4674 q^{39} -7.79560 q^{40} +0.357926 q^{41} +2.96206 q^{42} +8.62626 q^{43} -0.521790 q^{44} -19.8170 q^{45} -9.61185 q^{46} +6.77433 q^{47} -8.81862 q^{48} -6.45012 q^{49} -1.78076 q^{50} +0.123179 q^{51} -2.77416 q^{52} +11.9690 q^{53} -19.1500 q^{54} -2.54257 q^{55} -2.27358 q^{56} -26.4766 q^{57} -3.21215 q^{58} -1.00000 q^{59} +4.35875 q^{60} -9.78002 q^{61} -6.61619 q^{62} -5.77962 q^{63} +8.85604 q^{64} -13.5179 q^{65} -3.99449 q^{66} -13.4313 q^{67} -0.0195632 q^{68} +25.9736 q^{69} -2.29231 q^{70} -0.219360 q^{71} +23.8970 q^{72} -0.402118 q^{73} -3.94589 q^{74} +4.81204 q^{75} +4.20500 q^{76} -0.741538 q^{77} -21.2372 q^{78} -0.236355 q^{79} +6.82465 q^{80} +28.3657 q^{81} -0.435172 q^{82} -2.26479 q^{83} +1.27123 q^{84} -0.0953271 q^{85} -10.4880 q^{86} +8.68002 q^{87} +3.06603 q^{88} -1.54698 q^{89} +24.0939 q^{90} -3.94248 q^{91} -4.12511 q^{92} +17.8786 q^{93} -8.23634 q^{94} +20.4900 q^{95} -9.42470 q^{96} -1.36672 q^{97} +7.84216 q^{98} +7.79410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 3 q^{2} + 4 q^{3} + 23 q^{4} + 7 q^{5} - 5 q^{6} + 4 q^{7} + 9 q^{8} + 29 q^{9}+O(q^{10}) \) 17 * q + 3 * q^2 + 4 * q^3 + 23 * q^4 + 7 * q^5 - 5 * q^6 + 4 * q^7 + 9 * q^8 + 29 * q^9	\( 17 q + 3 q^{2} + 4 q^{3} + 23 q^{4} + 7 q^{5} - 5 q^{6} + 4 q^{7} + 9 q^{8} + 29 q^{9} - 4 q^{10} + 17 q^{11} + 2 q^{12} - 11 q^{13} + 16 q^{14} + 20 q^{15} + 39 q^{16} + 6 q^{17} - 15 q^{18} - 4 q^{19} - q^{20} - 11 q^{21} + 3 q^{22} + 36 q^{23} + 4 q^{24} + 22 q^{25} + 28 q^{26} + 13 q^{27} + 13 q^{29} - 34 q^{30} + 6 q^{31} + 16 q^{32} + 4 q^{33} - 5 q^{34} + 16 q^{35} + 34 q^{36} + 14 q^{37} + 12 q^{38} + 41 q^{39} - 54 q^{40} + 6 q^{41} - 57 q^{42} - 11 q^{43} + 23 q^{44} + 5 q^{45} + q^{46} + 25 q^{47} + 14 q^{48} + 23 q^{49} + 15 q^{50} - 4 q^{51} - 64 q^{52} - 2 q^{54} + 7 q^{55} + 43 q^{56} - 9 q^{57} - 21 q^{58} - 17 q^{59} + 15 q^{60} - 38 q^{61} - 21 q^{62} + 2 q^{63} + 43 q^{64} - 13 q^{65} - 5 q^{66} + q^{67} + 34 q^{68} - 13 q^{69} + 5 q^{70} + 89 q^{71} + 15 q^{72} - 16 q^{73} + 17 q^{74} + 2 q^{75} - q^{76} + 4 q^{77} - 58 q^{78} + 34 q^{79} - 64 q^{80} + 29 q^{81} - 17 q^{82} - 12 q^{83} - 111 q^{84} - 15 q^{85} - 21 q^{86} - 4 q^{87} + 9 q^{88} - 5 q^{89} + 7 q^{90} - 12 q^{91} + 80 q^{92} + 32 q^{93} - 25 q^{94} + 103 q^{95} - 48 q^{96} - 15 q^{97} + 8 q^{98} + 29 q^{99}+O(q^{100}) \) 17 * q + 3 * q^2 + 4 * q^3 + 23 * q^4 + 7 * q^5 - 5 * q^6 + 4 * q^7 + 9 * q^8 + 29 * q^9 - 4 * q^10 + 17 * q^11 + 2 * q^12 - 11 * q^13 + 16 * q^14 + 20 * q^15 + 39 * q^16 + 6 * q^17 - 15 * q^18 - 4 * q^19 - q^20 - 11 * q^21 + 3 * q^22 + 36 * q^23 + 4 * q^24 + 22 * q^25 + 28 * q^26 + 13 * q^27 + 13 * q^29 - 34 * q^30 + 6 * q^31 + 16 * q^32 + 4 * q^33 - 5 * q^34 + 16 * q^35 + 34 * q^36 + 14 * q^37 + 12 * q^38 + 41 * q^39 - 54 * q^40 + 6 * q^41 - 57 * q^42 - 11 * q^43 + 23 * q^44 + 5 * q^45 + q^46 + 25 * q^47 + 14 * q^48 + 23 * q^49 + 15 * q^50 - 4 * q^51 - 64 * q^52 - 2 * q^54 + 7 * q^55 + 43 * q^56 - 9 * q^57 - 21 * q^58 - 17 * q^59 + 15 * q^60 - 38 * q^61 - 21 * q^62 + 2 * q^63 + 43 * q^64 - 13 * q^65 - 5 * q^66 + q^67 + 34 * q^68 - 13 * q^69 + 5 * q^70 + 89 * q^71 + 15 * q^72 - 16 * q^73 + 17 * q^74 + 2 * q^75 - q^76 + 4 * q^77 - 58 * q^78 + 34 * q^79 - 64 * q^80 + 29 * q^81 - 17 * q^82 - 12 * q^83 - 111 * q^84 - 15 * q^85 - 21 * q^86 - 4 * q^87 + 9 * q^88 - 5 * q^89 + 7 * q^90 - 12 * q^91 + 80 * q^92 + 32 * q^93 - 25 * q^94 + 103 * q^95 - 48 * q^96 - 15 * q^97 + 8 * q^98 + 29 * q^99

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