LMFDB - Embedded newform 349.2.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(1,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, 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("349.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.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:	$2.78677903054$
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} - 5 x^{16} - 14 x^{15} + 102 x^{14} + 26 x^{13} - 792 x^{12} + 474 x^{11} + 2887 x^{10} + \cdots - 4 $ x^17 - 5x^16 - 14x^15 + 102x^14 + 26x^13 - 792x^12 + 474x^11 + 2887x^10 - 3021x^9 - 4835x^8 + 6673x^7 + 2880x^6 - 5373x^5 - 164x^4 + 1075x^3 + 75x^2 - 41x - 4
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			$-1.09071$ of defining polynomial
Character	$\chi$	$=$	349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.09071 q^{2} +2.75693 q^{3} -0.810342 q^{4} +1.35282 q^{5} -3.00702 q^{6} +0.0387215 q^{7} +3.06528 q^{8} +4.60064 q^{9} +O(q^{10})$	\(q-1.09071 q^{2} +2.75693 q^{3} -0.810342 q^{4} +1.35282 q^{5} -3.00702 q^{6} +0.0387215 q^{7} +3.06528 q^{8} +4.60064 q^{9} -1.47554 q^{10} -2.52544 q^{11} -2.23405 q^{12} +3.42579 q^{13} -0.0422341 q^{14} +3.72962 q^{15} -1.72266 q^{16} +0.349950 q^{17} -5.01798 q^{18} +0.797001 q^{19} -1.09625 q^{20} +0.106752 q^{21} +2.75453 q^{22} +7.33792 q^{23} +8.45075 q^{24} -3.16988 q^{25} -3.73656 q^{26} +4.41285 q^{27} -0.0313777 q^{28} -4.43160 q^{29} -4.06796 q^{30} -3.02716 q^{31} -4.25163 q^{32} -6.96245 q^{33} -0.381696 q^{34} +0.0523833 q^{35} -3.72809 q^{36} +2.34285 q^{37} -0.869300 q^{38} +9.44466 q^{39} +4.14677 q^{40} +1.21384 q^{41} -0.116436 q^{42} +4.67252 q^{43} +2.04647 q^{44} +6.22384 q^{45} -8.00358 q^{46} +6.08599 q^{47} -4.74925 q^{48} -6.99850 q^{49} +3.45743 q^{50} +0.964787 q^{51} -2.77607 q^{52} +1.83205 q^{53} -4.81315 q^{54} -3.41647 q^{55} +0.118692 q^{56} +2.19727 q^{57} +4.83361 q^{58} +5.73115 q^{59} -3.02227 q^{60} -14.1922 q^{61} +3.30177 q^{62} +0.178144 q^{63} +8.08264 q^{64} +4.63448 q^{65} +7.59405 q^{66} -5.42047 q^{67} -0.283579 q^{68} +20.2301 q^{69} -0.0571352 q^{70} -9.26457 q^{71} +14.1023 q^{72} -1.57837 q^{73} -2.55538 q^{74} -8.73912 q^{75} -0.645843 q^{76} -0.0977889 q^{77} -10.3014 q^{78} -12.1896 q^{79} -2.33045 q^{80} -1.63603 q^{81} -1.32395 q^{82} -6.51564 q^{83} -0.0865059 q^{84} +0.473420 q^{85} -5.09639 q^{86} -12.2176 q^{87} -7.74118 q^{88} -0.0481816 q^{89} -6.78843 q^{90} +0.132652 q^{91} -5.94623 q^{92} -8.34565 q^{93} -6.63808 q^{94} +1.07820 q^{95} -11.7214 q^{96} -0.0462142 q^{97} +7.63337 q^{98} -11.6186 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9}+O(q^{10}) $ 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9} - 6 q^{10} + 39 q^{11} + 4 q^{12} - 6 q^{13} + 11 q^{14} + 12 q^{15} + 23 q^{16} + q^{17} + 7 q^{19} + 8 q^{20} - 3 q^{21} - q^{22} + 8 q^{23} - 21 q^{24} + 14 q^{25} + q^{26} + 9 q^{27} - 23 q^{28} + 9 q^{29} - 27 q^{30} - 2 q^{31} + 23 q^{32} - 5 q^{33} - 12 q^{34} + 16 q^{35} + 10 q^{36} - 7 q^{37} - 8 q^{38} - 39 q^{40} + 3 q^{41} - 30 q^{42} + q^{43} + 56 q^{44} - 21 q^{45} - q^{46} + 16 q^{47} - 31 q^{48} + 6 q^{49} - 5 q^{50} + 29 q^{51} - 37 q^{52} + 27 q^{53} - 36 q^{54} - 16 q^{55} + 14 q^{56} - 21 q^{57} - 44 q^{58} + 74 q^{59} - 27 q^{60} - 30 q^{61} - 18 q^{62} - 9 q^{63} - 17 q^{64} - 3 q^{65} - 66 q^{66} + 9 q^{67} - 51 q^{68} - 23 q^{69} - 77 q^{70} + 70 q^{71} - 55 q^{72} - 38 q^{73} + 26 q^{74} + 22 q^{75} - 50 q^{76} - 38 q^{77} - 75 q^{78} + 7 q^{79} - 28 q^{80} + 5 q^{81} - 56 q^{82} + 47 q^{83} - 69 q^{84} - 49 q^{85} + 17 q^{86} - 37 q^{87} - 30 q^{88} + 23 q^{89} - 64 q^{90} + 6 q^{91} + 17 q^{92} - 31 q^{93} - 40 q^{94} - 11 q^{95} - 49 q^{96} - 14 q^{97} + 5 q^{98} + 79 q^{99}+O(q^{100}) \) 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9 - 6 * q^10 + 39 * q^11 + 4 * q^12 - 6 * q^13 + 11 * q^14 + 12 * q^15 + 23 * q^16 + q^17 + 7 * q^19 + 8 * q^20 - 3 * q^21 - q^22 + 8 * q^23 - 21 * q^24 + 14 * q^25 + q^26 + 9 * q^27 - 23 * q^28 + 9 * q^29 - 27 * q^30 - 2 * q^31 + 23 * q^32 - 5 * q^33 - 12 * q^34 + 16 * q^35 + 10 * q^36 - 7 * q^37 - 8 * q^38 - 39 * q^40 + 3 * q^41 - 30 * q^42 + q^43 + 56 * q^44 - 21 * q^45 - q^46 + 16 * q^47 - 31 * q^48 + 6 * q^49 - 5 * q^50 + 29 * q^51 - 37 * q^52 + 27 * q^53 - 36 * q^54 - 16 * q^55 + 14 * q^56 - 21 * q^57 - 44 * q^58 + 74 * q^59 - 27 * q^60 - 30 * q^61 - 18 * q^62 - 9 * q^63 - 17 * q^64 - 3 * q^65 - 66 * q^66 + 9 * q^67 - 51 * q^68 - 23 * q^69 - 77 * q^70 + 70 * q^71 - 55 * q^72 - 38 * q^73 + 26 * q^74 + 22 * q^75 - 50 * q^76 - 38 * q^77 - 75 * q^78 + 7 * q^79 - 28 * q^80 + 5 * q^81 - 56 * q^82 + 47 * q^83 - 69 * q^84 - 49 * q^85 + 17 * q^86 - 37 * q^87 - 30 * q^88 + 23 * q^89 - 64 * q^90 + 6 * q^91 + 17 * q^92 - 31 * q^93 - 40 * q^94 - 11 * q^95 - 49 * q^96 - 14 * q^97 + 5 * q^98 + 79 * 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 $

$2$	−1.09071	−0.771252	−0.385626	−	0.922655i	$-0.626014\pi$
$2$	−1.09071	−0.771252	−0.385626	+	0.922655i	$0.626014\pi$
$3$	2.75693	1.59171	0.795856	−	0.605486i	$-0.207021\pi$
$3$	2.75693	1.59171	0.795856	+	0.605486i	$0.207021\pi$
$4$	−0.810342	−0.405171
$5$	1.35282	0.605000	0.302500	−	0.953149i	$-0.402179\pi$
$5$	1.35282	0.605000	0.302500	+	0.953149i	$0.402179\pi$
$6$	−3.00702	−1.22761
$7$	0.0387215	0.0146354	0.00731768	−	0.999973i	$-0.497671\pi$
$7$	0.0387215	0.0146354	0.00731768	+	0.999973i	$0.497671\pi$
$8$	3.06528	1.08374
$9$	4.60064	1.53355
$10$	−1.47554	−0.466607
$11$	−2.52544	−0.761449	−0.380724	−	0.924689i	$-0.624325\pi$
$11$	−2.52544	−0.761449	−0.380724	+	0.924689i	$0.624325\pi$
$12$	−2.23405	−0.644915
$13$	3.42579	0.950145	0.475072	−	0.879947i	$-0.342422\pi$
$13$	3.42579	0.950145	0.475072	+	0.879947i	$0.342422\pi$
$14$	−0.0422341	−0.0112875
$15$	3.72962	0.962985
$16$	−1.72266	−0.430666
$17$	0.349950	0.0848754	0.0424377	−	0.999099i	$-0.486488\pi$
$17$	0.349950	0.0848754	0.0424377	+	0.999099i	$0.486488\pi$
$18$	−5.01798	−1.18275
$19$	0.797001	0.182845	0.0914223	−	0.995812i	$-0.470859\pi$
$19$	0.797001	0.182845	0.0914223	+	0.995812i	$0.470859\pi$
$20$	−1.09625	−0.245128
$21$	0.106752	0.0232953
$22$	2.75453	0.587269
$23$	7.33792	1.53006	0.765031	−	0.643993i	$-0.222723\pi$
$23$	7.33792	1.53006	0.765031	+	0.643993i	$0.222723\pi$
$24$	8.45075	1.72500
$25$	−3.16988	−0.633976
$26$	−3.73656	−0.732801
$27$	4.41285	0.849252
$28$	−0.0313777	−0.00592982
$29$	−4.43160	−0.822927	−0.411463	−	0.911426i	$-0.634982\pi$
$29$	−4.43160	−0.822927	−0.411463	+	0.911426i	$0.634982\pi$
$30$	−4.06796	−0.742704
$31$	−3.02716	−0.543694	−0.271847	−	0.962341i	$-0.587634\pi$
$31$	−3.02716	−0.543694	−0.271847	+	0.962341i	$0.587634\pi$
$32$	−4.25163	−0.751589
$33$	−6.96245	−1.21201
$34$	−0.381696	−0.0654603
$35$	0.0523833	0.00885439
$36$	−3.72809	−0.621349
$37$	2.34285	0.385162	0.192581	−	0.981281i	$-0.438314\pi$
$37$	2.34285	0.385162	0.192581	+	0.981281i	$0.438314\pi$
$38$	−0.869300	−0.141019
$39$	9.44466	1.51236
$40$	4.14677	0.655662
$41$	1.21384	0.189570	0.0947849	−	0.995498i	$-0.469784\pi$
$41$	1.21384	0.189570	0.0947849	+	0.995498i	$0.469784\pi$
$42$	−0.116436	−0.0179665
$43$	4.67252	0.712553	0.356277	−	0.934381i	$-0.384046\pi$
$43$	4.67252	0.712553	0.356277	+	0.934381i	$0.384046\pi$
$44$	2.04647	0.308517
$45$	6.22384	0.927795
$46$	−8.00358	−1.18006
$47$	6.08599	0.887733	0.443866	−	0.896093i	$-0.353606\pi$
$47$	6.08599	0.887733	0.443866	+	0.896093i	$0.353606\pi$
$48$	−4.74925	−0.685495
$49$	−6.99850	−0.999786
$50$	3.45743	0.488955
$51$	0.964787	0.135097
$52$	−2.77607	−0.384971
$53$	1.83205	0.251651	0.125826	−	0.992052i	$-0.459842\pi$
$53$	1.83205	0.251651	0.125826	+	0.992052i	$0.459842\pi$
$54$	−4.81315	−0.654987
$55$	−3.41647	−0.460676
$56$	0.118692	0.0158609
$57$	2.19727	0.291036
$58$	4.83361	0.634684
$59$	5.73115	0.746133	0.373066	−	0.927805i	$-0.378306\pi$
$59$	5.73115	0.746133	0.373066	+	0.927805i	$0.378306\pi$
$60$	−3.02227	−0.390174
$61$	−14.1922	−1.81712	−0.908560	−	0.417755i	$-0.862817\pi$
$61$	−14.1922	−1.81712	−0.908560	+	0.417755i	$0.862817\pi$
$62$	3.30177	0.419325
$63$	0.178144	0.0224440
$64$	8.08264	1.01033
$65$	4.63448	0.574837
$66$	7.59405	0.934762
$67$	−5.42047	−0.662215	−0.331108	−	0.943593i	$-0.607422\pi$
$67$	−5.42047	−0.662215	−0.331108	+	0.943593i	$0.607422\pi$
$68$	−0.283579	−0.0343890
$69$	20.2301	2.43542
$70$	−0.0571352	−0.00682896
$71$	−9.26457	−1.09950	−0.549751	−	0.835328i	$-0.685277\pi$
$71$	−9.26457	−1.09950	−0.549751	+	0.835328i	$0.685277\pi$
$72$	14.1023	1.66197
$73$	−1.57837	−0.184734	−0.0923672	−	0.995725i	$-0.529443\pi$
$73$	−1.57837	−0.184734	−0.0923672	+	0.995725i	$0.529443\pi$
$74$	−2.55538	−0.297057
$75$	−8.73912	−1.00911
$76$	−0.645843	−0.0740833
$77$	−0.0977889	−0.0111441
$78$	−10.3014	−1.16641
$79$	−12.1896	−1.37144	−0.685718	−	0.727867i	$-0.740512\pi$
$79$	−12.1896	−1.37144	−0.685718	+	0.727867i	$0.740512\pi$
$80$	−2.33045	−0.260552
$81$	−1.63603	−0.181781
$82$	−1.32395	−0.146206
$83$	−6.51564	−0.715185	−0.357592	−	0.933878i	$-0.616402\pi$
$83$	−6.51564	−0.715185	−0.357592	+	0.933878i	$0.616402\pi$
$84$	−0.0865059	−0.00943857
$85$	0.473420	0.0513496
$86$	−5.09639	−0.549558
$87$	−12.2176	−1.30986
$88$	−7.74118	−0.825213
$89$	−0.0481816	−0.00510724	−0.00255362	−	0.999997i	$-0.500813\pi$
$89$	−0.0481816	−0.00510724	−0.00255362	+	0.999997i	$0.500813\pi$
$90$	−6.78843	−0.715563
$91$	0.132652	0.0139057
$92$	−5.94623	−0.619937
$93$	−8.34565	−0.865404
$94$	−6.63808	−0.684665
$95$	1.07820	0.110621
$96$	−11.7214	−1.19631
$97$	−0.0462142	−0.00469234	−0.00234617	−	0.999997i	$-0.500747\pi$
$97$	−0.0462142	−0.00469234	−0.00234617	+	0.999997i	$0.500747\pi$
$98$	7.63337	0.771086
$99$	−11.6186	−1.16772
$100$	2.56868	0.256868
$101$	−15.5165	−1.54395	−0.771973	−	0.635656i	$-0.780730\pi$
$101$	−15.5165	−1.54395	−0.771973	+	0.635656i	$0.780730\pi$
$102$	−1.05231	−0.104194
$103$	−12.1548	−1.19765	−0.598824	−	0.800881i	$-0.704365\pi$
$103$	−12.1548	−1.19765	−0.598824	+	0.800881i	$0.704365\pi$
$104$	10.5010	1.02971
$105$	0.144417	0.0140936
$106$	−1.99824	−0.194086
$107$	15.4919	1.49765	0.748827	−	0.662765i	$-0.230617\pi$
$107$	15.4919	1.49765	0.748827	+	0.662765i	$0.230617\pi$
$108$	−3.57591	−0.344092
$109$	−9.41409	−0.901707	−0.450853	−	0.892598i	$-0.648880\pi$
$109$	−9.41409	−0.901707	−0.450853	+	0.892598i	$0.648880\pi$
$110$	3.72639	0.355297
$111$	6.45906	0.613067
$112$	−0.0667041	−0.00630295
$113$	14.1869	1.33459	0.667294	−	0.744794i	$-0.267452\pi$
$113$	14.1869	1.33459	0.667294	+	0.744794i	$0.267452\pi$
$114$	−2.39660	−0.224462
$115$	9.92689	0.925687
$116$	3.59111	0.333426
$117$	15.7608	1.45709
$118$	−6.25105	−0.575456
$119$	0.0135506	0.00124218
$120$	11.4323	1.04363
$121$	−4.62215	−0.420196
$122$	15.4796	1.40146
$123$	3.34646	0.301740
$124$	2.45303	0.220289
$125$	−11.0524	−0.988554
$126$	−0.194304	−0.0173100
$127$	−18.0392	−1.60072	−0.800359	−	0.599521i	$-0.795358\pi$
$127$	−18.0392	−1.60072	−0.800359	+	0.599521i	$0.795358\pi$
$128$	−0.312593	−0.0276295
$129$	12.8818	1.13418
$130$	−5.05490	−0.443344
$131$	8.94960	0.781930	0.390965	−	0.920406i	$-0.372141\pi$
$131$	8.94960	0.781930	0.390965	+	0.920406i	$0.372141\pi$
$132$	5.64197	0.491070
$133$	0.0308611	0.00267600
$134$	5.91218	0.510735
$135$	5.96979	0.513797
$136$	1.07270	0.0919829
$137$	11.2254	0.959049	0.479524	−	0.877529i	$-0.340809\pi$
$137$	11.2254	0.959049	0.479524	+	0.877529i	$0.340809\pi$
$138$	−22.0653	−1.87832
$139$	−6.64598	−0.563705	−0.281852	−	0.959458i	$-0.590949\pi$
$139$	−6.64598	−0.563705	−0.281852	+	0.959458i	$0.590949\pi$
$140$	−0.0424483	−0.00358754
$141$	16.7786	1.41302
$142$	10.1050	0.847993
$143$	−8.65164	−0.723486
$144$	−7.92535	−0.660446
$145$	−5.99515	−0.497870
$146$	1.72155	0.142477
$147$	−19.2943	−1.59137
$148$	−1.89851	−0.156056
$149$	5.65306	0.463116	0.231558	−	0.972821i	$-0.425618\pi$
$149$	5.65306	0.463116	0.231558	+	0.972821i	$0.425618\pi$
$150$	9.53188	0.778275
$151$	1.22246	0.0994824	0.0497412	−	0.998762i	$-0.484160\pi$
$151$	1.22246	0.0994824	0.0497412	+	0.998762i	$0.484160\pi$
$152$	2.44303	0.198156
$153$	1.61000	0.130160
$154$	0.106660	0.00859489
$155$	−4.09520	−0.328934
$156$	−7.65341	−0.612763
$157$	2.61794	0.208934	0.104467	−	0.994528i	$-0.466686\pi$
$157$	2.61794	0.208934	0.104467	+	0.994528i	$0.466686\pi$
$158$	13.2954	1.05772
$159$	5.05082	0.400556
$160$	−5.75169	−0.454711
$161$	0.284136	0.0223930
$162$	1.78444	0.140199
$163$	17.7600	1.39107	0.695535	−	0.718492i	$-0.255167\pi$
$163$	17.7600	1.39107	0.695535	+	0.718492i	$0.255167\pi$
$164$	−0.983624	−0.0768081
$165$	−9.41894	−0.733264
$166$	7.10670	0.551587
$167$	12.0908	0.935610	0.467805	−	0.883832i	$-0.345045\pi$
$167$	12.0908	0.935610	0.467805	+	0.883832i	$0.345045\pi$
$168$	0.327226	0.0252460
$169$	−1.26393	−0.0972253
$170$	−0.516366	−0.0396034
$171$	3.66671	0.280401
$172$	−3.78634	−0.288706
$173$	2.62524	0.199593	0.0997966	−	0.995008i	$-0.468181\pi$
$173$	2.62524	0.199593	0.0997966	+	0.995008i	$0.468181\pi$
$174$	13.3259	1.01023
$175$	−0.122743	−0.00927846
$176$	4.35048	0.327930
$177$	15.8004	1.18763
$178$	0.0525524	0.00393897
$179$	10.4691	0.782501	0.391250	−	0.920284i	$-0.372043\pi$
$179$	10.4691	0.782501	0.391250	+	0.920284i	$0.372043\pi$
$180$	−5.04344	−0.375916
$181$	6.23267	0.463271	0.231635	−	0.972803i	$-0.425592\pi$
$181$	6.23267	0.463271	0.231635	+	0.972803i	$0.425592\pi$
$182$	−0.144685	−0.0107248
$183$	−39.1267	−2.89233
$184$	22.4928	1.65819
$185$	3.16945	0.233023
$186$	9.10272	0.667444
$187$	−0.883778	−0.0646283
$188$	−4.93173	−0.359684
$189$	0.170872	0.0124291
$190$	−1.17601	−0.0853165
$191$	19.6696	1.42324	0.711622	−	0.702563i	$-0.247961\pi$
$191$	19.6696	1.42324	0.711622	+	0.702563i	$0.247961\pi$
$192$	22.2832	1.60815
$193$	16.8057	1.20970	0.604851	−	0.796339i	$-0.293233\pi$
$193$	16.8057	1.20970	0.604851	+	0.796339i	$0.293233\pi$
$194$	0.0504065	0.00361897
$195$	12.7769	0.914975
$196$	5.67118	0.405084
$197$	−23.2824	−1.65880	−0.829402	−	0.558652i	$-0.811319\pi$
$197$	−23.2824	−1.65880	−0.829402	+	0.558652i	$0.811319\pi$
$198$	12.6726	0.900604
$199$	7.74945	0.549344	0.274672	−	0.961538i	$-0.411431\pi$
$199$	7.74945	0.549344	0.274672	+	0.961538i	$0.411431\pi$
$200$	−9.71657	−0.687065
$201$	−14.9438	−1.05406
$202$	16.9240	1.19077
$203$	−0.171598	−0.0120438
$204$	−0.781807	−0.0547375
$205$	1.64211	0.114690
$206$	13.2574	0.923688
$207$	33.7591	2.34642
$208$	−5.90149	−0.409195
$209$	−2.01278	−0.139227
$210$	−0.157517	−0.0108697
$211$	11.9992	0.826059	0.413030	−	0.910718i	$-0.364471\pi$
$211$	11.9992	0.826059	0.413030	+	0.910718i	$0.364471\pi$
$212$	−1.48459	−0.101962
$213$	−25.5417	−1.75009
$214$	−16.8972	−1.15507
$215$	6.32108	0.431094
$216$	13.5266	0.920369
$217$	−0.117216	−0.00795715
$218$	10.2681	0.695443
$219$	−4.35145	−0.294044
$220$	2.76851	0.186653
$221$	1.19886	0.0806439
$222$	−7.04499	−0.472829
$223$	11.0373	0.739115	0.369557	−	0.929208i	$-0.379509\pi$
$223$	11.0373	0.739115	0.369557	+	0.929208i	$0.379509\pi$
$224$	−0.164630	−0.0109998
$225$	−14.5835	−0.972231
$226$	−15.4738	−1.02930
$227$	13.7433	0.912176	0.456088	−	0.889935i	$-0.349250\pi$
$227$	13.7433	0.912176	0.456088	+	0.889935i	$0.349250\pi$
$228$	−1.78054	−0.117919
$229$	6.07797	0.401643	0.200822	−	0.979628i	$-0.435639\pi$
$229$	6.07797	0.401643	0.200822	+	0.979628i	$0.435639\pi$
$230$	−10.8274	−0.713938
$231$	−0.269597	−0.0177382
$232$	−13.5841	−0.891839
$233$	−1.92732	−0.126263	−0.0631314	−	0.998005i	$-0.520109\pi$
$233$	−1.92732	−0.126263	−0.0631314	+	0.998005i	$0.520109\pi$
$234$	−17.1906	−1.12378
$235$	8.23325	0.537078
$236$	−4.64419	−0.302311
$237$	−33.6058	−2.18293
$238$	−0.0147798	−0.000958035 0
$239$	−12.0785	−0.781290	−0.390645	−	0.920541i	$-0.627748\pi$
$239$	−12.0785	−0.781290	−0.390645	+	0.920541i	$0.627748\pi$
$240$	−6.42488	−0.414724
$241$	2.68122	0.172712	0.0863562	−	0.996264i	$-0.472478\pi$
$241$	2.68122	0.172712	0.0863562	+	0.996264i	$0.472478\pi$
$242$	5.04145	0.324077
$243$	−17.7490	−1.13860
$244$	11.5005	0.736244
$245$	−9.46771	−0.604870
$246$	−3.65004	−0.232718
$247$	2.73036	0.173729
$248$	−9.27909	−0.589223
$249$	−17.9631	−1.13837
$250$	12.0550	0.762424
$251$	−15.8710	−1.00177	−0.500884	−	0.865515i	$-0.666992\pi$
$251$	−15.8710	−1.00177	−0.500884	+	0.865515i	$0.666992\pi$
$252$	−0.144357	−0.00909366
$253$	−18.5315	−1.16506
$254$	19.6756	1.23456
$255$	1.30518	0.0817337
$256$	−15.8243	−0.989020
$257$	18.8695	1.17705	0.588524	−	0.808480i	$-0.299709\pi$
$257$	18.8695	1.17705	0.588524	+	0.808480i	$0.299709\pi$
$258$	−14.0504	−0.874738
$259$	0.0907186	0.00563698
$260$	−3.75552	−0.232907
$261$	−20.3882	−1.26200
$262$	−9.76146	−0.603065
$263$	−24.2982	−1.49829	−0.749145	−	0.662406i	$-0.769535\pi$
$263$	−24.2982	−1.49829	−0.749145	+	0.662406i	$0.769535\pi$
$264$	−21.3419	−1.31350
$265$	2.47843	0.152249
$266$	−0.0336606	−0.00206387
$267$	−0.132833	−0.00812926
$268$	4.39243	0.268310
$269$	11.0375	0.672970	0.336485	−	0.941689i	$-0.390762\pi$
$269$	11.0375	0.672970	0.336485	+	0.941689i	$0.390762\pi$
$270$	−6.51133	−0.396267
$271$	26.5146	1.61065	0.805325	−	0.592834i	$-0.201991\pi$
$271$	26.5146	1.61065	0.805325	+	0.592834i	$0.201991\pi$
$272$	−0.602846	−0.0365529
$273$	0.365712	0.0221339
$274$	−12.2437	−0.739668
$275$	8.00534	0.482740
$276$	−16.3933	−0.986761
$277$	25.0782	1.50680	0.753401	−	0.657562i	$-0.228412\pi$
$277$	25.0782	1.50680	0.753401	+	0.657562i	$0.228412\pi$
$278$	7.24887	0.434758
$279$	−13.9269	−0.833780
$280$	0.160569	0.00959586
$281$	−9.33195	−0.556697	−0.278349	−	0.960480i	$-0.589787\pi$
$281$	−9.33195	−0.556697	−0.278349	+	0.960480i	$0.589787\pi$
$282$	−18.3007	−1.08979
$283$	−10.6182	−0.631185	−0.315593	−	0.948895i	$-0.602203\pi$
$283$	−10.6182	−0.631185	−0.315593	+	0.948895i	$0.602203\pi$
$284$	7.50747	0.445486
$285$	2.97251	0.176076
$286$	9.43647	0.557990
$287$	0.0470017	0.00277442
$288$	−19.5602	−1.15260
$289$	−16.8775	−0.992796
$290$	6.53900	0.383983
$291$	−0.127409	−0.00746885
$292$	1.27902	0.0748490
$293$	−31.1009	−1.81693	−0.908467	−	0.417956i	$-0.862747\pi$
$293$	−31.1009	−1.81693	−0.908467	+	0.417956i	$0.862747\pi$
$294$	21.0446	1.22735
$295$	7.75322	0.451410
$296$	7.18149	0.417415
$297$	−11.1444	−0.646662
$298$	−6.16587	−0.357179
$299$	25.1382	1.45378
$300$	7.08167	0.408861
$301$	0.180927	0.0104285
$302$	−1.33335	−0.0767259
$303$	−42.7777	−2.45752
$304$	−1.37296	−0.0787448
$305$	−19.1994	−1.09936
$306$	−1.75605	−0.100386
$307$	14.6154	0.834148	0.417074	−	0.908873i	$-0.363056\pi$
$307$	14.6154	0.834148	0.417074	+	0.908873i	$0.363056\pi$
$308$	0.0792424	0.00451526
$309$	−33.5099	−1.90631
$310$	4.46669	0.253691
$311$	24.0649	1.36459	0.682297	−	0.731075i	$-0.260981\pi$
$311$	24.0649	1.36459	0.682297	+	0.731075i	$0.260981\pi$
$312$	28.9505	1.63900
$313$	8.99735	0.508560	0.254280	−	0.967131i	$-0.418161\pi$
$313$	8.99735	0.508560	0.254280	+	0.967131i	$0.418161\pi$
$314$	−2.85543	−0.161141
$315$	0.240996	0.0135786
$316$	9.87774	0.555666
$317$	−22.1657	−1.24495	−0.622475	−	0.782640i	$-0.713873\pi$
$317$	−22.1657	−1.24495	−0.622475	+	0.782640i	$0.713873\pi$
$318$	−5.50900	−0.308930
$319$	11.1917	0.626617
$320$	10.9344	0.611249
$321$	42.7099	2.38383
$322$	−0.309911	−0.0172707
$323$	0.278911	0.0155190
$324$	1.32575	0.0736526
$325$	−10.8594	−0.602368
$326$	−19.3711	−1.07287
$327$	−25.9540	−1.43526
$328$	3.72076	0.205444
$329$	0.235659	0.0129923
$330$	10.2734	0.565531
$331$	32.2705	1.77375	0.886875	−	0.462010i	$-0.152872\pi$
$331$	32.2705	1.77375	0.886875	+	0.462010i	$0.152872\pi$
$332$	5.27990	0.289772
$333$	10.7786	0.590664
$334$	−13.1876	−0.721591
$335$	−7.33292	−0.400640
$336$	−0.183898	−0.0100325
$337$	−14.4513	−0.787211	−0.393605	−	0.919279i	$-0.628772\pi$
$337$	−14.4513	−0.787211	−0.393605	+	0.919279i	$0.628772\pi$
$338$	1.37859	0.0749852
$339$	39.1121	2.12428
$340$	−0.383632	−0.0208054
$341$	7.64491	0.413995
$342$	−3.99934	−0.216259
$343$	−0.542043	−0.0292676
$344$	14.3226	0.772223
$345$	27.3677	1.47343
$346$	−2.86339	−0.153937
$347$	−26.4572	−1.42030	−0.710148	−	0.704052i	$-0.751372\pi$
$347$	−26.4572	−1.42030	−0.710148	+	0.704052i	$0.751372\pi$
$348$	9.90042	0.530718
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	0.133877	0.00715603
$351$	15.1175	0.806913
$352$	10.7372	0.572296
$353$	13.8482	0.737067	0.368534	−	0.929614i	$-0.379860\pi$
$353$	13.8482	0.737067	0.368534	+	0.929614i	$0.379860\pi$
$354$	−17.2337	−0.915960
$355$	−12.5333	−0.665198
$356$	0.0390436	0.00206931
$357$	0.0373580	0.00197720
$358$	−11.4189	−0.603505
$359$	25.4455	1.34296	0.671482	−	0.741021i	$-0.265658\pi$
$359$	25.4455	1.34296	0.671482	+	0.741021i	$0.265658\pi$
$360$	19.0778	1.00549
$361$	−18.3648	−0.966568
$362$	−6.79807	−0.357298
$363$	−12.7429	−0.668830
$364$	−0.107493	−0.00563419
$365$	−2.13525	−0.111764
$366$	42.6761	2.23071
$367$	27.6581	1.44374	0.721869	−	0.692029i	$-0.243283\pi$
$367$	27.6581	1.44374	0.721869	+	0.692029i	$0.243283\pi$
$368$	−12.6408	−0.658945
$369$	5.58443	0.290714
$370$	−3.45697	−0.179719
$371$	0.0709397	0.00368300
$372$	6.76283	0.350636
$373$	−19.9861	−1.03484	−0.517419	−	0.855732i	$-0.673107\pi$
$373$	−19.9861	−1.03484	−0.517419	+	0.855732i	$0.673107\pi$
$374$	0.963950	0.0498447
$375$	−30.4706	−1.57349
$376$	18.6553	0.962072
$377$	−15.1817	−0.781899
$378$	−0.186373	−0.00958598
$379$	0.204570	0.0105080	0.00525402	−	0.999986i	$-0.498328\pi$
$379$	0.204570	0.0105080	0.00525402	+	0.999986i	$0.498328\pi$
$380$	−0.873709	−0.0448203
$381$	−49.7326	−2.54788
$382$	−21.4539	−1.09768
$383$	35.0565	1.79131	0.895653	−	0.444754i	$-0.146709\pi$
$383$	35.0565	1.79131	0.895653	+	0.444754i	$0.146709\pi$
$384$	−0.861794	−0.0439783
$385$	−0.132291	−0.00674216
$386$	−18.3302	−0.932984
$387$	21.4966	1.09273
$388$	0.0374493	0.00190120
$389$	9.50268	0.481805	0.240902	−	0.970549i	$-0.422557\pi$
$389$	9.50268	0.481805	0.240902	+	0.970549i	$0.422557\pi$
$390$	−13.9360	−0.705676
$391$	2.56791	0.129865
$392$	−21.4524	−1.08351
$393$	24.6734	1.24461
$394$	25.3945	1.27936
$395$	−16.4903	−0.829718
$396$	9.41507	0.473125
$397$	16.3138	0.818767	0.409383	−	0.912362i	$-0.365744\pi$
$397$	16.3138	0.818767	0.409383	+	0.912362i	$0.365744\pi$
$398$	−8.45243	−0.423682
$399$	0.0850817	0.00425941
$400$	5.46063	0.273031
$401$	8.56261	0.427596	0.213798	−	0.976878i	$-0.431417\pi$
$401$	8.56261	0.427596	0.213798	+	0.976878i	$0.431417\pi$
$402$	16.2994	0.812943
$403$	−10.3704	−0.516588
$404$	12.5736	0.625562
$405$	−2.21326	−0.109978
$406$	0.187165	0.00928882
$407$	−5.91672	−0.293281
$408$	2.95734	0.146410
$409$	18.7315	0.926213	0.463107	−	0.886303i	$-0.346735\pi$
$409$	18.7315	0.926213	0.463107	+	0.886303i	$0.346735\pi$
$410$	−1.79107	−0.0884545
$411$	30.9475	1.52653
$412$	9.84954	0.485252
$413$	0.221919	0.0109199
$414$	−36.8216	−1.80968
$415$	−8.81449	−0.432686
$416$	−14.5652	−0.714118
$417$	−18.3225	−0.897256
$418$	2.19537	0.107379
$419$	25.6171	1.25148	0.625739	−	0.780032i	$-0.284797\pi$
$419$	25.6171	1.25148	0.625739	+	0.780032i	$0.284797\pi$
$420$	−0.117027	−0.00571033
$421$	−29.1083	−1.41865	−0.709326	−	0.704881i	$-0.751000\pi$
$421$	−29.1083	−1.41865	−0.709326	+	0.704881i	$0.751000\pi$
$422$	−13.0877	−0.637100
$423$	27.9995	1.36138
$424$	5.61574	0.272724
$425$	−1.10930	−0.0538089
$426$	27.8587	1.34976
$427$	−0.549542	−0.0265942
$428$	−12.5537	−0.606806
$429$	−23.8519	−1.15158
$430$	−6.89450	−0.332482
$431$	−22.8305	−1.09970	−0.549852	−	0.835262i	$-0.685316\pi$
$431$	−22.8305	−1.09970	−0.549852	+	0.835262i	$0.685316\pi$
$432$	−7.60184	−0.365744
$433$	−36.5699	−1.75744	−0.878719	−	0.477340i	$-0.841601\pi$
$433$	−36.5699	−1.75744	−0.878719	+	0.477340i	$0.841601\pi$
$434$	0.127849	0.00613697
$435$	−16.5282	−0.792466
$436$	7.62863	0.365345
$437$	5.84833	0.279764
$438$	4.74619	0.226782
$439$	−30.7581	−1.46801	−0.734003	−	0.679146i	$-0.762350\pi$
$439$	−30.7581	−1.46801	−0.734003	+	0.679146i	$0.762350\pi$
$440$	−10.4724	−0.499253
$441$	−32.1976	−1.53322
$442$	−1.30761	−0.0621967
$443$	−25.0439	−1.18987	−0.594936	−	0.803773i	$-0.702823\pi$
$443$	−25.0439	−1.18987	−0.594936	+	0.803773i	$0.702823\pi$
$444$	−5.23404	−0.248397
$445$	−0.0651811	−0.00308988
$446$	−12.0386	−0.570044
$447$	15.5851	0.737148
$448$	0.312972	0.0147865
$449$	14.4519	0.682025	0.341012	−	0.940059i	$-0.389230\pi$
$449$	14.4519	0.682025	0.341012	+	0.940059i	$0.389230\pi$
$450$	15.9064	0.749835
$451$	−3.06548	−0.144348
$452$	−11.4962	−0.540736
$453$	3.37023	0.158347
$454$	−14.9900	−0.703517
$455$	0.179454	0.00841295
$456$	6.73525	0.315407
$457$	6.86842	0.321291	0.160646	−	0.987012i	$-0.448642\pi$
$457$	6.86842	0.321291	0.160646	+	0.987012i	$0.448642\pi$
$458$	−6.62933	−0.309768
$459$	1.54428	0.0720806
$460$	−8.04418	−0.375062
$461$	16.9413	0.789037	0.394519	−	0.918888i	$-0.370911\pi$
$461$	16.9413	0.789037	0.394519	+	0.918888i	$0.370911\pi$
$462$	0.294053	0.0136806
$463$	19.8411	0.922094	0.461047	−	0.887376i	$-0.347474\pi$
$463$	19.8411	0.922094	0.461047	+	0.887376i	$0.347474\pi$
$464$	7.63414	0.354406
$465$	−11.2902	−0.523569
$466$	2.10215	0.0973804
$467$	−14.3809	−0.665469	−0.332735	−	0.943021i	$-0.607971\pi$
$467$	−14.3809	−0.665469	−0.332735	+	0.943021i	$0.607971\pi$
$468$	−12.7717	−0.590371
$469$	−0.209889	−0.00969176
$470$	−8.98013	−0.414222
$471$	7.21747	0.332563
$472$	17.5676	0.808614
$473$	−11.8002	−0.542573
$474$	36.6543	1.68359
$475$	−2.52639	−0.115919
$476$	−0.0109806	−0.000503296 0
$477$	8.42859	0.385919
$478$	13.1741	0.602572
$479$	−15.3411	−0.700951	−0.350476	−	0.936572i	$-0.613980\pi$
$479$	−15.3411	−0.700951	−0.350476	+	0.936572i	$0.613980\pi$
$480$	−15.8570	−0.723769
$481$	8.02612	0.365959
$482$	−2.92444	−0.133205
$483$	0.783341	0.0356432
$484$	3.74552	0.170251
$485$	−0.0625195	−0.00283886
$486$	19.3590	0.878144
$487$	−37.8081	−1.71325	−0.856625	−	0.515939i	$-0.827443\pi$
$487$	−37.8081	−1.71325	−0.856625	+	0.515939i	$0.827443\pi$
$488$	−43.5029	−1.96929
$489$	48.9630	2.21418
$490$	10.3266	0.466507
$491$	5.26778	0.237731	0.118866	−	0.992910i	$-0.462074\pi$
$491$	5.26778	0.237731	0.118866	+	0.992910i	$0.462074\pi$
$492$	−2.71178	−0.122256
$493$	−1.55084	−0.0698462
$494$	−2.97804	−0.133989
$495$	−15.7179	−0.706468
$496$	5.21477	0.234150
$497$	−0.358738	−0.0160916
$498$	19.5927	0.877968
$499$	26.9094	1.20463	0.602316	−	0.798258i	$-0.294245\pi$
$499$	26.9094	1.20463	0.602316	+	0.798258i	$0.294245\pi$
$500$	8.95620	0.400534
$501$	33.3333	1.48922
$502$	17.3107	0.772614
$503$	31.1411	1.38851	0.694257	−	0.719727i	$-0.255733\pi$
$503$	31.1411	1.38851	0.694257	+	0.719727i	$0.255733\pi$
$504$	0.546061	0.0243235
$505$	−20.9910	−0.934086
$506$	20.2126	0.898558
$507$	−3.48456	−0.154755
$508$	14.6179	0.648564
$509$	−25.1512	−1.11481	−0.557404	−	0.830242i	$-0.688202\pi$
$509$	−25.1512	−1.11481	−0.557404	+	0.830242i	$0.688202\pi$
$510$	−1.42358	−0.0630373
$511$	−0.0611169	−0.00270365
$512$	17.8850	0.790413
$513$	3.51704	0.155281
$514$	−20.5813	−0.907800
$515$	−16.4433	−0.724576
$516$	−10.4387	−0.459537
$517$	−15.3698	−0.675963
$518$	−0.0989481	−0.00434753
$519$	7.23759	0.317695
$520$	14.2060	0.622974
$521$	−1.30073	−0.0569862	−0.0284931	−	0.999594i	$-0.509071\pi$
$521$	−1.30073	−0.0569862	−0.0284931	+	0.999594i	$0.509071\pi$
$522$	22.2377	0.973317
$523$	−7.02745	−0.307289	−0.153644	−	0.988126i	$-0.549101\pi$
$523$	−7.02745	−0.307289	−0.153644	+	0.988126i	$0.549101\pi$
$524$	−7.25224	−0.316815
$525$	−0.338392	−0.0147686
$526$	26.5024	1.15556
$527$	−1.05935	−0.0461462
$528$	11.9940	0.521970
$529$	30.8451	1.34109
$530$	−2.70326	−0.117422
$531$	26.3670	1.14423
$532$	−0.0250080	−0.00108424
$533$	4.15836	0.180119
$534$	0.144883	0.00626970
$535$	20.9577	0.906080
$536$	−16.6153	−0.717670
$537$	28.8627	1.24552
$538$	−12.0388	−0.519029
$539$	17.6743	0.761286
$540$	−4.83757	−0.208176
$541$	−28.5841	−1.22893	−0.614464	−	0.788945i	$-0.710627\pi$
$541$	−28.5841	−1.22893	−0.614464	+	0.788945i	$0.710627\pi$
$542$	−28.9199	−1.24222
$543$	17.1830	0.737394
$544$	−1.48786	−0.0637914
$545$	−12.7356	−0.545532
$546$	−0.398887	−0.0170708
$547$	4.04299	0.172866	0.0864330	−	0.996258i	$-0.472453\pi$
$547$	4.04299	0.172866	0.0864330	+	0.996258i	$0.472453\pi$
$548$	−9.09639	−0.388579
$549$	−65.2930	−2.78664
$550$	−8.73154	−0.372314
$551$	−3.53199	−0.150468
$552$	62.0110	2.63936
$553$	−0.472000	−0.0200715
$554$	−27.3531	−1.16212
$555$	8.73794	0.370905
$556$	5.38552	0.228397
$557$	−19.3600	−0.820308	−0.410154	−	0.912016i	$-0.634525\pi$
$557$	−19.3600	−0.820308	−0.410154	+	0.912016i	$0.634525\pi$
$558$	15.1902	0.643054
$559$	16.0071	0.677029
$560$	−0.0902387	−0.00381328
$561$	−2.43651	−0.102870
$562$	10.1785	0.429354
$563$	26.2875	1.10789	0.553944	−	0.832554i	$-0.313122\pi$
$563$	26.2875	1.10789	0.553944	+	0.832554i	$0.313122\pi$
$564$	−13.5964	−0.572513
$565$	19.1923	0.807425
$566$	11.5814	0.486803
$567$	−0.0633497	−0.00266044
$568$	−28.3985	−1.19158
$569$	31.9316	1.33864	0.669322	−	0.742973i	$-0.266585\pi$
$569$	31.9316	1.33864	0.669322	+	0.742973i	$0.266585\pi$
$570$	−3.24216	−0.135799
$571$	3.81070	0.159473	0.0797363	−	0.996816i	$-0.474592\pi$
$571$	3.81070	0.159473	0.0797363	+	0.996816i	$0.474592\pi$
$572$	7.01079	0.293136
$573$	54.2277	2.26539
$574$	−0.0512654	−0.00213978
$575$	−23.2603	−0.970023
$576$	37.1853	1.54939
$577$	−22.8247	−0.950203	−0.475102	−	0.879931i	$-0.657589\pi$
$577$	−22.8247	−0.950203	−0.475102	+	0.879931i	$0.657589\pi$
$578$	18.4086	0.765696
$579$	46.3321	1.92550
$580$	4.85812	0.201723
$581$	−0.252296	−0.0104670
$582$	0.138967	0.00576036
$583$	−4.62673	−0.191619
$584$	−4.83815	−0.200204
$585$	21.3216	0.881539
$586$	33.9222	1.40131
$587$	−14.9870	−0.618580	−0.309290	−	0.950968i	$-0.600091\pi$
$587$	−14.9870	−0.618580	−0.309290	+	0.950968i	$0.600091\pi$
$588$	15.6350	0.644777
$589$	−2.41265	−0.0994114
$590$	−8.45655	−0.348151
$591$	−64.1880	−2.64034
$592$	−4.03594	−0.165876
$593$	18.0250	0.740200	0.370100	−	0.928992i	$-0.379323\pi$
$593$	18.0250	0.740200	0.370100	+	0.928992i	$0.379323\pi$
$594$	12.1553	0.498739
$595$	0.0183315	0.000751520 0
$596$	−4.58091	−0.187641
$597$	21.3647	0.874397
$598$	−27.4186	−1.12123
$599$	−17.3166	−0.707537	−0.353769	−	0.935333i	$-0.615100\pi$
$599$	−17.3166	−0.707537	−0.353769	+	0.935333i	$0.615100\pi$
$600$	−26.7878	−1.09361
$601$	−38.0096	−1.55045	−0.775223	−	0.631688i	$-0.782362\pi$
$601$	−38.0096	−1.55045	−0.775223	+	0.631688i	$0.782362\pi$
$602$	−0.197340	−0.00804298
$603$	−24.9376	−1.01554
$604$	−0.990611	−0.0403074
$605$	−6.25294	−0.254218
$606$	46.6583	1.89536
$607$	−16.3355	−0.663039	−0.331519	−	0.943448i	$-0.607561\pi$
$607$	−16.3355	−0.663039	−0.331519	+	0.943448i	$0.607561\pi$
$608$	−3.38855	−0.137424
$609$	−0.473083	−0.0191703
$610$	20.9411	0.847880
$611$	20.8494	0.843475
$612$	−1.30465	−0.0527372
$613$	−14.0167	−0.566130	−0.283065	−	0.959101i	$-0.591351\pi$
$613$	−14.0167	−0.566130	−0.283065	+	0.959101i	$0.591351\pi$
$614$	−15.9413	−0.643338
$615$	4.52716	0.182553
$616$	−0.299750	−0.0120773
$617$	3.46481	0.139488	0.0697439	−	0.997565i	$-0.477782\pi$
$617$	3.46481	0.139488	0.0697439	+	0.997565i	$0.477782\pi$
$618$	36.5497	1.47025
$619$	−37.6697	−1.51407	−0.757037	−	0.653372i	$-0.773354\pi$
$619$	−37.6697	−1.51407	−0.757037	+	0.653372i	$0.773354\pi$
$620$	3.31851	0.133275
$621$	32.3811	1.29941
$622$	−26.2479	−1.05245
$623$	−0.00186567	−7.47463e−5 0
$624$	−16.2700	−0.651320
$625$	0.897516	0.0359006
$626$	−9.81354	−0.392228
$627$	−5.54908	−0.221609
$628$	−2.12143	−0.0846541
$629$	0.819880	0.0326908
$630$	−0.262858	−0.0104725
$631$	27.4376	1.09227	0.546137	−	0.837696i	$-0.316098\pi$
$631$	27.4376	1.09227	0.546137	+	0.837696i	$0.316098\pi$
$632$	−37.3645	−1.48628
$633$	33.0809	1.31485
$634$	24.1764	0.960169
$635$	−24.4037	−0.968433
$636$	−4.09289	−0.162294
$637$	−23.9754	−0.949941
$638$	−12.2070	−0.483279
$639$	−42.6230	−1.68614
$640$	−0.422881	−0.0167159
$641$	−31.1942	−1.23210	−0.616048	−	0.787709i	$-0.711267\pi$
$641$	−31.1942	−1.23210	−0.616048	+	0.787709i	$0.711267\pi$
$642$	−46.5843	−1.83854
$643$	47.1640	1.85997	0.929984	−	0.367601i	$-0.119821\pi$
$643$	47.1640	1.85997	0.929984	+	0.367601i	$0.119821\pi$
$644$	−0.230247	−0.00907300
$645$	17.4268	0.686178
$646$	−0.304212	−0.0119691
$647$	−0.314143	−0.0123502	−0.00617512	−	0.999981i	$-0.501966\pi$
$647$	−0.314143	−0.0123502	−0.00617512	+	0.999981i	$0.501966\pi$
$648$	−5.01490	−0.197004
$649$	−14.4737	−0.568142
$650$	11.8445	0.464578
$651$	−0.323156	−0.0126655
$652$	−14.3917	−0.563621
$653$	−42.4013	−1.65929	−0.829645	−	0.558292i	$-0.811457\pi$
$653$	−42.4013	−1.65929	−0.829645	+	0.558292i	$0.811457\pi$
$654$	28.3084	1.10694
$655$	12.1072	0.473067
$656$	−2.09103	−0.0816411
$657$	−7.26152	−0.283299
$658$	−0.257037	−0.0100203
$659$	22.2905	0.868316	0.434158	−	0.900837i	$-0.357046\pi$
$659$	22.2905	0.868316	0.434158	+	0.900837i	$0.357046\pi$
$660$	7.63256	0.297097
$661$	47.8018	1.85927	0.929637	−	0.368477i	$-0.120121\pi$
$661$	47.8018	1.85927	0.929637	+	0.368477i	$0.120121\pi$
$662$	−35.1980	−1.36801
$663$	3.30516	0.128362
$664$	−19.9723	−0.775074
$665$	0.0417495	0.00161898
$666$	−11.7564	−0.455550
$667$	−32.5187	−1.25913
$668$	−9.79764	−0.379082
$669$	30.4291	1.17646
$670$	7.99812	0.308994
$671$	35.8414	1.38364
$672$	−0.453871	−0.0175085
$673$	10.4837	0.404118	0.202059	−	0.979373i	$-0.435237\pi$
$673$	10.4837	0.404118	0.202059	+	0.979373i	$0.435237\pi$
$674$	15.7622	0.607138
$675$	−13.9882	−0.538405
$676$	1.02421	0.0393929
$677$	6.69615	0.257354	0.128677	−	0.991687i	$-0.458927\pi$
$677$	6.69615	0.257354	0.128677	+	0.991687i	$0.458927\pi$
$678$	−42.6602	−1.63835
$679$	−0.00178948	−6.86741e−5 0
$680$	1.45116	0.0556496
$681$	37.8893	1.45192
$682$	−8.33841	−0.319294
$683$	27.5839	1.05547	0.527734	−	0.849410i	$-0.323042\pi$
$683$	27.5839	1.05547	0.527734	+	0.849410i	$0.323042\pi$
$684$	−2.97129	−0.113610
$685$	15.1859	0.580224
$686$	0.591214	0.0225727
$687$	16.7565	0.639301
$688$	−8.04918	−0.306872
$689$	6.27622	0.239105
$690$	−29.8503	−1.13638
$691$	41.6672	1.58510	0.792548	−	0.609809i	$-0.208754\pi$
$691$	41.6672	1.58510	0.792548	+	0.609809i	$0.208754\pi$
$692$	−2.12734	−0.0808693
$693$	−0.449891	−0.0170900
$694$	28.8572	1.09541
$695$	−8.99082	−0.341041
$696$	−37.4503	−1.41955
$697$	0.424783	0.0160898
$698$	−1.09071	−0.0412842
$699$	−5.31347	−0.200974
$700$	0.0994634	0.00375936
$701$	−5.03648	−0.190225	−0.0951125	−	0.995467i	$-0.530321\pi$
$701$	−5.03648	−0.190225	−0.0951125	+	0.995467i	$0.530321\pi$
$702$	−16.4889	−0.622333
$703$	1.86725	0.0704247
$704$	−20.4122	−0.769314
$705$	22.6985	0.854873
$706$	−15.1045	−0.568464
$707$	−0.600821	−0.0225962
$708$	−12.8037	−0.481192
$709$	13.7487	0.516342	0.258171	−	0.966099i	$-0.416880\pi$
$709$	13.7487	0.516342	0.258171	+	0.966099i	$0.416880\pi$
$710$	13.6702	0.513035
$711$	−56.0799	−2.10316
$712$	−0.147690	−0.00553492
$713$	−22.2131	−0.831886
$714$	−0.0407469	−0.00152492
$715$	−11.7041	−0.437709
$716$	−8.48359	−0.317047
$717$	−33.2994	−1.24359
$718$	−27.7538	−1.03576
$719$	29.3766	1.09556	0.547781	−	0.836622i	$-0.315473\pi$
$719$	29.3766	1.09556	0.547781	+	0.836622i	$0.315473\pi$
$720$	−10.7216	−0.399569
$721$	−0.470652	−0.0175280
$722$	20.0307	0.745467
$723$	7.39191	0.274908
$724$	−5.05060	−0.187704
$725$	14.0476	0.521715
$726$	13.8989	0.515837
$727$	−16.2108	−0.601227	−0.300613	−	0.953746i	$-0.597191\pi$
$727$	−16.2108	−0.601227	−0.300613	+	0.953746i	$0.597191\pi$
$728$	0.406616	0.0150702
$729$	−44.0245	−1.63054
$730$	2.32895	0.0861983
$731$	1.63515	0.0604782
$732$	31.7060	1.17189
$733$	40.4449	1.49387	0.746933	−	0.664899i	$-0.231526\pi$
$733$	40.4449	1.49387	0.746933	+	0.664899i	$0.231526\pi$
$734$	−30.1670	−1.11349
$735$	−26.1018	−0.962779
$736$	−31.1981	−1.14998
$737$	13.6891	0.504243
$738$	−6.09102	−0.224214
$739$	−21.9408	−0.807106	−0.403553	−	0.914956i	$-0.632225\pi$
$739$	−21.9408	−0.807106	−0.403553	+	0.914956i	$0.632225\pi$
$740$	−2.56834	−0.0944140
$741$	7.52740	0.276526
$742$	−0.0773749	−0.00284052
$743$	47.1912	1.73128	0.865639	−	0.500668i	$-0.166912\pi$
$743$	47.1912	1.73128	0.865639	+	0.500668i	$0.166912\pi$
$744$	−25.5818	−0.937873
$745$	7.64757	0.280185
$746$	21.7991	0.798121
$747$	−29.9761	−1.09677
$748$	0.716163	0.0261855
$749$	0.599868	0.0219187
$750$	33.2347	1.21356
$751$	−4.98219	−0.181803	−0.0909013	−	0.995860i	$-0.528975\pi$
$751$	−4.98219	−0.181803	−0.0909013	+	0.995860i	$0.528975\pi$
$752$	−10.4841	−0.382316
$753$	−43.7551	−1.59452
$754$	16.5589	0.603041
$755$	1.65377	0.0601868
$756$	−0.138465	−0.00503592
$757$	43.8266	1.59290	0.796452	−	0.604702i	$-0.206708\pi$
$757$	43.8266	1.59290	0.796452	+	0.604702i	$0.206708\pi$
$758$	−0.223127	−0.00810434
$759$	−51.0899	−1.85445
$760$	3.30498	0.119884
$761$	52.8508	1.91584	0.957920	−	0.287035i	$-0.0926695\pi$
$761$	52.8508	1.91584	0.957920	+	0.287035i	$0.0926695\pi$
$762$	54.2441	1.96506
$763$	−0.364528	−0.0131968
$764$	−15.9391	−0.576657
$765$	2.17803	0.0787470
$766$	−38.2367	−1.38155
$767$	19.6338	0.708934
$768$	−43.6265	−1.57424
$769$	6.83975	0.246648	0.123324	−	0.992366i	$-0.460645\pi$
$769$	6.83975	0.246648	0.123324	+	0.992366i	$0.460645\pi$
$770$	0.144291	0.00519990
$771$	52.0219	1.87352
$772$	−13.6184	−0.490136
$773$	27.0532	0.973034	0.486517	−	0.873671i	$-0.338267\pi$
$773$	27.0532	0.973034	0.486517	+	0.873671i	$0.338267\pi$
$774$	−23.4467	−0.842772
$775$	9.59572	0.344689
$776$	−0.141659	−0.00508528
$777$	0.250105	0.00897245
$778$	−10.3647	−0.371593
$779$	0.967430	0.0346618
$780$	−10.3537	−0.370721
$781$	23.3971	0.837215
$782$	−2.80086	−0.100158
$783$	−19.5559	−0.698873
$784$	12.0561	0.430573
$785$	3.54160	0.126405
$786$	−26.9116	−0.959906
$787$	−46.4839	−1.65697	−0.828486	−	0.560010i	$-0.810797\pi$
$787$	−46.4839	−1.65697	−0.828486	+	0.560010i	$0.810797\pi$
$788$	18.8667	0.672100
$789$	−66.9883	−2.38485
$790$	17.9862	0.639922
$791$	0.549337	0.0195322
$792$	−35.6144	−1.26550
$793$	−48.6194	−1.72653
$794$	−17.7937	−0.631475
$795$	6.83285	0.242336
$796$	−6.27970	−0.222578
$797$	0.951060	0.0336883	0.0168441	−	0.999858i	$-0.494638\pi$
$797$	0.951060	0.0336883	0.0168441	+	0.999858i	$0.494638\pi$
$798$	−0.0927999	−0.00328508
$799$	2.12979	0.0753467
$800$	13.4771	0.476489
$801$	−0.221666	−0.00783219
$802$	−9.33936	−0.329784
$803$	3.98608	0.140666
$804$	12.1096	0.427073
$805$	0.384384	0.0135478
$806$	11.3112	0.398419
$807$	30.4297	1.07117
$808$	−47.5623	−1.67324
$809$	−54.2923	−1.90881	−0.954407	−	0.298507i	$-0.903511\pi$
$809$	−54.2923	−1.90881	−0.954407	+	0.298507i	$0.903511\pi$
$810$	2.41403	0.0848205
$811$	−39.6326	−1.39169	−0.695844	−	0.718193i	$-0.744970\pi$
$811$	−39.6326	−1.39169	−0.695844	+	0.718193i	$0.744970\pi$
$812$	0.139053	0.00487981
$813$	73.0989	2.56369
$814$	6.45345	0.226193
$815$	24.0261	0.841597
$816$	−1.66200	−0.0581817
$817$	3.72400	0.130286
$818$	−20.4307	−0.714344
$819$	0.610284	0.0213251
$820$	−1.33067	−0.0464689
$821$	−20.6885	−0.722032	−0.361016	−	0.932560i	$-0.617570\pi$
$821$	−20.6885	−0.722032	−0.361016	+	0.932560i	$0.617570\pi$
$822$	−33.7549	−1.17734
$823$	−25.9870	−0.905850	−0.452925	−	0.891549i	$-0.649620\pi$
$823$	−25.9870	−0.905850	−0.452925	+	0.891549i	$0.649620\pi$
$824$	−37.2579	−1.29794
$825$	22.0701	0.768383
$826$	−0.242050	−0.00842200
$827$	20.9851	0.729725	0.364862	−	0.931062i	$-0.381116\pi$
$827$	20.9851	0.729725	0.364862	+	0.931062i	$0.381116\pi$
$828$	−27.3565	−0.950702
$829$	−36.0721	−1.25284	−0.626418	−	0.779487i	$-0.715480\pi$
$829$	−36.0721	−1.25284	−0.626418	+	0.779487i	$0.715480\pi$
$830$	9.61409	0.333710
$831$	69.1387	2.39839
$832$	27.6895	0.959959
$833$	−2.44913	−0.0848572
$834$	19.9846	0.692010
$835$	16.3566	0.566044
$836$	1.63104	0.0564106
$837$	−13.3584	−0.461733
$838$	−27.9410	−0.965205
$839$	−2.77402	−0.0957698	−0.0478849	−	0.998853i	$-0.515248\pi$
$839$	−2.77402	−0.0957698	−0.0478849	+	0.998853i	$0.515248\pi$
$840$	0.442678	0.0152738
$841$	−9.36096	−0.322792
$842$	31.7488	1.09414
$843$	−25.7275	−0.886102
$844$	−9.72346	−0.334695
$845$	−1.70987	−0.0588213
$846$	−30.5394	−1.04997
$847$	−0.178977	−0.00614971
$848$	−3.15600	−0.108377
$849$	−29.2735	−1.00467
$850$	1.20993	0.0415002
$851$	17.1916	0.589322
$852$	20.6975	0.709086
$853$	−11.2688	−0.385838	−0.192919	−	0.981215i	$-0.561795\pi$
$853$	−11.2688	−0.385838	−0.192919	+	0.981215i	$0.561795\pi$
$854$	0.599393	0.0205108
$855$	4.96040	0.169642
$856$	47.4869	1.62307
$857$	−14.2951	−0.488311	−0.244156	−	0.969736i	$-0.578511\pi$
$857$	−14.2951	−0.488311	−0.244156	+	0.969736i	$0.578511\pi$
$858$	26.0156	0.888159
$859$	10.4946	0.358070	0.179035	−	0.983843i	$-0.442702\pi$
$859$	10.4946	0.358070	0.179035	+	0.983843i	$0.442702\pi$
$860$	−5.12224	−0.174667
$861$	0.129580	0.00441608
$862$	24.9015	0.848149
$863$	41.4464	1.41085	0.705426	−	0.708783i	$-0.250756\pi$
$863$	41.4464	1.41085	0.705426	+	0.708783i	$0.250756\pi$
$864$	−18.7618	−0.638289
$865$	3.55147	0.120754
$866$	39.8873	1.35543
$867$	−46.5301	−1.58025
$868$	0.0949852	0.00322401
$869$	30.7841	1.04428
$870$	18.0275	0.611191
$871$	−18.5694	−0.629200
$872$	−28.8568	−0.977216
$873$	−0.212615	−0.00719592
$874$	−6.37886	−0.215768
$875$	−0.427965	−0.0144679
$876$	3.52616	0.119138
$877$	43.0640	1.45417	0.727084	−	0.686549i	$-0.240875\pi$
$877$	43.0640	1.45417	0.727084	+	0.686549i	$0.240875\pi$
$878$	33.5484	1.13220
$879$	−85.7429	−2.89204
$880$	5.88542	0.198397
$881$	−31.3397	−1.05586	−0.527931	−	0.849287i	$-0.677032\pi$
$881$	−31.3397	−1.05586	−0.527931	+	0.849287i	$0.677032\pi$
$882$	35.1184	1.18250
$883$	5.78397	0.194646	0.0973230	−	0.995253i	$-0.468972\pi$
$883$	5.78397	0.194646	0.0973230	+	0.995253i	$0.468972\pi$
$884$	−0.971485	−0.0326746
$885$	21.3750	0.718514
$886$	27.3158	0.917691
$887$	−23.3160	−0.782873	−0.391437	−	0.920205i	$-0.628022\pi$
$887$	−23.3160	−0.782873	−0.391437	+	0.920205i	$0.628022\pi$
$888$	19.7988	0.664405
$889$	−0.698504	−0.0234271
$890$	0.0710939	0.00238307
$891$	4.13170	0.138417
$892$	−8.94402	−0.299468
$893$	4.85054	0.162317
$894$	−16.9988	−0.568526
$895$	14.1629	0.473413
$896$	−0.0121041	−0.000404368 0
$897$	69.3042	2.31400
$898$	−15.7628	−0.526013
$899$	13.4151	0.447420
$900$	11.8176	0.393920
$901$	0.641126	0.0213590
$902$	3.34356	0.111328
$903$	0.498803	0.0165991
$904$	43.4867	1.44635
$905$	8.43168	0.280279
$906$	−3.67596	−0.122126
$907$	38.2886	1.27135	0.635676	−	0.771956i	$-0.280722\pi$
$907$	38.2886	1.27135	0.635676	+	0.771956i	$0.280722\pi$
$908$	−11.1368	−0.369587
$909$	−71.3856	−2.36771
$910$	−0.195733	−0.00648850
$911$	−14.7550	−0.488853	−0.244427	−	0.969668i	$-0.578600\pi$
$911$	−14.7550	−0.488853	−0.244427	+	0.969668i	$0.578600\pi$
$912$	−3.78516	−0.125339
$913$	16.4549	0.544576
$914$	−7.49149	−0.247796
$915$	−52.9314	−1.74986
$916$	−4.92523	−0.162734
$917$	0.346542	0.0114438
$918$	−1.68436	−0.0555923
$919$	0.848311	0.0279832	0.0139916	−	0.999902i	$-0.495546\pi$
$919$	0.848311	0.0279832	0.0139916	+	0.999902i	$0.495546\pi$
$920$	30.4287	1.00320
$921$	40.2937	1.32772
$922$	−18.4782	−0.608546
$923$	−31.7385	−1.04469
$924$	0.218466	0.00718699
$925$	−7.42654	−0.244183
$926$	−21.6410	−0.711166
$927$	−55.9199	−1.83665
$928$	18.8415	0.618503
$929$	−22.4040	−0.735052	−0.367526	−	0.930013i	$-0.619795\pi$
$929$	−22.4040	−0.735052	−0.367526	+	0.930013i	$0.619795\pi$
$930$	12.3143	0.403803
$931$	−5.57781	−0.182805
$932$	1.56179	0.0511580
$933$	66.3451	2.17204
$934$	15.6855	0.513244
$935$	−1.19559	−0.0391001
$936$	48.3114	1.57911
$937$	48.2000	1.57462	0.787312	−	0.616554i	$-0.211472\pi$
$937$	48.2000	1.57462	0.787312	+	0.616554i	$0.211472\pi$
$938$	0.228929	0.00747479
$939$	24.8050	0.809481
$940$	−6.67175	−0.217608
$941$	−43.0919	−1.40476	−0.702379	−	0.711803i	$-0.747879\pi$
$941$	−43.0919	−1.40476	−0.702379	+	0.711803i	$0.747879\pi$
$942$	−7.87220	−0.256490
$943$	8.90705	0.290054
$944$	−9.87284	−0.321334
$945$	0.231159	0.00751961
$946$	12.8706	0.418460
$947$	−35.8037	−1.16346	−0.581732	−	0.813381i	$-0.697625\pi$
$947$	−35.8037	−1.16346	−0.581732	+	0.813381i	$0.697625\pi$
$948$	27.2322	0.884460
$949$	−5.40718	−0.175524
$950$	2.75558	0.0894027
$951$	−61.1092	−1.98160
$952$	0.0415364	0.00134620
$953$	−11.1213	−0.360256	−0.180128	−	0.983643i	$-0.557651\pi$
$953$	−11.1213	−0.360256	−0.180128	+	0.983643i	$0.557651\pi$
$954$	−9.19319	−0.297640
$955$	26.6094	0.861061
$956$	9.78768	0.316556
$957$	30.8548	0.997393
$958$	16.7327	0.540610
$959$	0.434664	0.0140360
$960$	30.1452	0.972932
$961$	−21.8363	−0.704397
$962$	−8.75420	−0.282247
$963$	71.2725	2.29672
$964$	−2.17270	−0.0699780
$965$	22.7351	0.731869
$966$	−0.854401	−0.0274899
$967$	−38.3634	−1.23368	−0.616842	−	0.787087i	$-0.711588\pi$
$967$	−38.3634	−1.23368	−0.616842	+	0.787087i	$0.711588\pi$
$968$	−14.1682	−0.455383
$969$	0.768936	0.0247018
$970$	0.0681909	0.00218948
$971$	−32.4519	−1.04143	−0.520715	−	0.853730i	$-0.674335\pi$
$971$	−32.4519	−1.04143	−0.520715	+	0.853730i	$0.674335\pi$
$972$	14.3827	0.461326
$973$	−0.257343	−0.00825002
$974$	41.2379	1.32135
$975$	−29.9384	−0.958797
$976$	24.4483	0.782571
$977$	−4.09532	−0.131021	−0.0655104	−	0.997852i	$-0.520868\pi$
$977$	−4.09532	−0.131021	−0.0655104	+	0.997852i	$0.520868\pi$
$978$	−53.4046	−1.70769
$979$	0.121680	0.00388890
$980$	7.67208	0.245076
$981$	−43.3109	−1.38281
$982$	−5.74564	−0.183351
$983$	−47.8897	−1.52744	−0.763722	−	0.645546i	$-0.776630\pi$
$983$	−47.8897	−1.52744	−0.763722	+	0.645546i	$0.776630\pi$
$984$	10.2578	0.327008
$985$	−31.4969	−1.00358
$986$	1.69152	0.0538690
$987$	0.649694	0.0206800
$988$	−2.21253	−0.0703898
$989$	34.2866	1.09025
$990$	17.1438	0.544865
$991$	0.564451	0.0179304	0.00896519	−	0.999960i	$-0.497146\pi$
$991$	0.564451	0.0179304	0.00896519	+	0.999960i	$0.497146\pi$
$992$	12.8704	0.408634
$993$	88.9675	2.82330
$994$	0.391281	0.0124107
$995$	10.4836	0.332353
$996$	14.5563	0.461234
$997$	16.0474	0.508225	0.254112	−	0.967175i	$-0.418217\pi$
$997$	16.0474	0.508225	0.254112	+	0.967175i	$0.418217\pi$
$998$	−29.3505	−0.929074
$999$	10.3386	0.327100

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.a.b.1.5	✓	17
3.2	odd	2		3141.2.a.e.1.13		17
4.3	odd	2		5584.2.a.m.1.3		17
5.4	even	2		8725.2.a.m.1.13		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.a.b.1.5	✓	17	1.1	even	1	trivial
3141.2.a.e.1.13		17	3.2	odd	2
5584.2.a.m.1.3		17	4.3	odd	2
8725.2.a.m.1.13		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:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.a (trivial)

\(f(q)\)	\(=\)	\(q-1.09071 q^{2} +2.75693 q^{3} -0.810342 q^{4} +1.35282 q^{5} -3.00702 q^{6} +0.0387215 q^{7} +3.06528 q^{8} +4.60064 q^{9} +O(q^{10})\)	\(q-1.09071 q^{2} +2.75693 q^{3} -0.810342 q^{4} +1.35282 q^{5} -3.00702 q^{6} +0.0387215 q^{7} +3.06528 q^{8} +4.60064 q^{9} -1.47554 q^{10} -2.52544 q^{11} -2.23405 q^{12} +3.42579 q^{13} -0.0422341 q^{14} +3.72962 q^{15} -1.72266 q^{16} +0.349950 q^{17} -5.01798 q^{18} +0.797001 q^{19} -1.09625 q^{20} +0.106752 q^{21} +2.75453 q^{22} +7.33792 q^{23} +8.45075 q^{24} -3.16988 q^{25} -3.73656 q^{26} +4.41285 q^{27} -0.0313777 q^{28} -4.43160 q^{29} -4.06796 q^{30} -3.02716 q^{31} -4.25163 q^{32} -6.96245 q^{33} -0.381696 q^{34} +0.0523833 q^{35} -3.72809 q^{36} +2.34285 q^{37} -0.869300 q^{38} +9.44466 q^{39} +4.14677 q^{40} +1.21384 q^{41} -0.116436 q^{42} +4.67252 q^{43} +2.04647 q^{44} +6.22384 q^{45} -8.00358 q^{46} +6.08599 q^{47} -4.74925 q^{48} -6.99850 q^{49} +3.45743 q^{50} +0.964787 q^{51} -2.77607 q^{52} +1.83205 q^{53} -4.81315 q^{54} -3.41647 q^{55} +0.118692 q^{56} +2.19727 q^{57} +4.83361 q^{58} +5.73115 q^{59} -3.02227 q^{60} -14.1922 q^{61} +3.30177 q^{62} +0.178144 q^{63} +8.08264 q^{64} +4.63448 q^{65} +7.59405 q^{66} -5.42047 q^{67} -0.283579 q^{68} +20.2301 q^{69} -0.0571352 q^{70} -9.26457 q^{71} +14.1023 q^{72} -1.57837 q^{73} -2.55538 q^{74} -8.73912 q^{75} -0.645843 q^{76} -0.0977889 q^{77} -10.3014 q^{78} -12.1896 q^{79} -2.33045 q^{80} -1.63603 q^{81} -1.32395 q^{82} -6.51564 q^{83} -0.0865059 q^{84} +0.473420 q^{85} -5.09639 q^{86} -12.2176 q^{87} -7.74118 q^{88} -0.0481816 q^{89} -6.78843 q^{90} +0.132652 q^{91} -5.94623 q^{92} -8.34565 q^{93} -6.63808 q^{94} +1.07820 q^{95} -11.7214 q^{96} -0.0462142 q^{97} +7.63337 q^{98} -11.6186 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9}+O(q^{10}) \) 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9} - 6 q^{10} + 39 q^{11} + 4 q^{12} - 6 q^{13} + 11 q^{14} + 12 q^{15} + 23 q^{16} + q^{17} + 7 q^{19} + 8 q^{20} - 3 q^{21} - q^{22} + 8 q^{23} - 21 q^{24} + 14 q^{25} + q^{26} + 9 q^{27} - 23 q^{28} + 9 q^{29} - 27 q^{30} - 2 q^{31} + 23 q^{32} - 5 q^{33} - 12 q^{34} + 16 q^{35} + 10 q^{36} - 7 q^{37} - 8 q^{38} - 39 q^{40} + 3 q^{41} - 30 q^{42} + q^{43} + 56 q^{44} - 21 q^{45} - q^{46} + 16 q^{47} - 31 q^{48} + 6 q^{49} - 5 q^{50} + 29 q^{51} - 37 q^{52} + 27 q^{53} - 36 q^{54} - 16 q^{55} + 14 q^{56} - 21 q^{57} - 44 q^{58} + 74 q^{59} - 27 q^{60} - 30 q^{61} - 18 q^{62} - 9 q^{63} - 17 q^{64} - 3 q^{65} - 66 q^{66} + 9 q^{67} - 51 q^{68} - 23 q^{69} - 77 q^{70} + 70 q^{71} - 55 q^{72} - 38 q^{73} + 26 q^{74} + 22 q^{75} - 50 q^{76} - 38 q^{77} - 75 q^{78} + 7 q^{79} - 28 q^{80} + 5 q^{81} - 56 q^{82} + 47 q^{83} - 69 q^{84} - 49 q^{85} + 17 q^{86} - 37 q^{87} - 30 q^{88} + 23 q^{89} - 64 q^{90} + 6 q^{91} + 17 q^{92} - 31 q^{93} - 40 q^{94} - 11 q^{95} - 49 q^{96} - 14 q^{97} + 5 q^{98} + 79 q^{99}+O(q^{100}) \) 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9 - 6 * q^10 + 39 * q^11 + 4 * q^12 - 6 * q^13 + 11 * q^14 + 12 * q^15 + 23 * q^16 + q^17 + 7 * q^19 + 8 * q^20 - 3 * q^21 - q^22 + 8 * q^23 - 21 * q^24 + 14 * q^25 + q^26 + 9 * q^27 - 23 * q^28 + 9 * q^29 - 27 * q^30 - 2 * q^31 + 23 * q^32 - 5 * q^33 - 12 * q^34 + 16 * q^35 + 10 * q^36 - 7 * q^37 - 8 * q^38 - 39 * q^40 + 3 * q^41 - 30 * q^42 + q^43 + 56 * q^44 - 21 * q^45 - q^46 + 16 * q^47 - 31 * q^48 + 6 * q^49 - 5 * q^50 + 29 * q^51 - 37 * q^52 + 27 * q^53 - 36 * q^54 - 16 * q^55 + 14 * q^56 - 21 * q^57 - 44 * q^58 + 74 * q^59 - 27 * q^60 - 30 * q^61 - 18 * q^62 - 9 * q^63 - 17 * q^64 - 3 * q^65 - 66 * q^66 + 9 * q^67 - 51 * q^68 - 23 * q^69 - 77 * q^70 + 70 * q^71 - 55 * q^72 - 38 * q^73 + 26 * q^74 + 22 * q^75 - 50 * q^76 - 38 * q^77 - 75 * q^78 + 7 * q^79 - 28 * q^80 + 5 * q^81 - 56 * q^82 + 47 * q^83 - 69 * q^84 - 49 * q^85 + 17 * q^86 - 37 * q^87 - 30 * q^88 + 23 * q^89 - 64 * q^90 + 6 * q^91 + 17 * q^92 - 31 * q^93 - 40 * q^94 - 11 * q^95 - 49 * q^96 - 14 * q^97 + 5 * q^98 + 79 * q^99

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