LMFDB - Embedded newform 349.2.a.b.1.4

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			1.4
Root			$-1.82251$ 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)

$f(q)$	$=$	$q-1.82251 q^{2} -0.490735 q^{3} +1.32154 q^{4} +3.61587 q^{5} +0.894370 q^{6} +2.81440 q^{7} +1.23649 q^{8} -2.75918 q^{9} +O(q^{10})$	\(q-1.82251 q^{2} -0.490735 q^{3} +1.32154 q^{4} +3.61587 q^{5} +0.894370 q^{6} +2.81440 q^{7} +1.23649 q^{8} -2.75918 q^{9} -6.58995 q^{10} +0.311769 q^{11} -0.648528 q^{12} -0.272273 q^{13} -5.12928 q^{14} -1.77443 q^{15} -4.89661 q^{16} -1.85179 q^{17} +5.02863 q^{18} +4.42517 q^{19} +4.77853 q^{20} -1.38113 q^{21} -0.568203 q^{22} +1.16470 q^{23} -0.606791 q^{24} +8.07449 q^{25} +0.496221 q^{26} +2.82623 q^{27} +3.71936 q^{28} +5.84596 q^{29} +3.23392 q^{30} -2.18402 q^{31} +6.45113 q^{32} -0.152996 q^{33} +3.37490 q^{34} +10.1765 q^{35} -3.64637 q^{36} -0.111045 q^{37} -8.06492 q^{38} +0.133614 q^{39} +4.47100 q^{40} +5.02225 q^{41} +2.51712 q^{42} -9.29272 q^{43} +0.412017 q^{44} -9.97682 q^{45} -2.12268 q^{46} +13.5485 q^{47} +2.40294 q^{48} +0.920867 q^{49} -14.7158 q^{50} +0.908737 q^{51} -0.359821 q^{52} -0.614386 q^{53} -5.15084 q^{54} +1.12732 q^{55} +3.47999 q^{56} -2.17159 q^{57} -10.6543 q^{58} +5.55774 q^{59} -2.34499 q^{60} -7.62317 q^{61} +3.98039 q^{62} -7.76544 q^{63} -1.96404 q^{64} -0.984504 q^{65} +0.278837 q^{66} -9.59207 q^{67} -2.44722 q^{68} -0.571560 q^{69} -18.5468 q^{70} +6.06291 q^{71} -3.41171 q^{72} -4.33583 q^{73} +0.202380 q^{74} -3.96244 q^{75} +5.84806 q^{76} +0.877444 q^{77} -0.243513 q^{78} +14.3483 q^{79} -17.7055 q^{80} +6.89061 q^{81} -9.15311 q^{82} -0.466802 q^{83} -1.82522 q^{84} -6.69581 q^{85} +16.9361 q^{86} -2.86882 q^{87} +0.385501 q^{88} -2.75356 q^{89} +18.1829 q^{90} -0.766287 q^{91} +1.53920 q^{92} +1.07177 q^{93} -24.6923 q^{94} +16.0008 q^{95} -3.16580 q^{96} -16.4060 q^{97} -1.67829 q^{98} -0.860227 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.82251	−1.28871	−0.644355	−	0.764727i	$-0.722874\pi$
$2$	−1.82251	−1.28871	−0.644355	+	0.764727i	$0.722874\pi$
$3$	−0.490735	−0.283326	−0.141663	−	0.989915i	$-0.545245\pi$
$3$	−0.490735	−0.283326	−0.141663	+	0.989915i	$0.545245\pi$
$4$	1.32154	0.660772
$5$	3.61587	1.61706	0.808532	−	0.588452i	$-0.200262\pi$
$5$	3.61587	1.61706	0.808532	+	0.588452i	$0.200262\pi$
$6$	0.894370	0.365125
$7$	2.81440	1.06374	0.531872	−	0.846825i	$-0.321489\pi$
$7$	2.81440	1.06374	0.531872	+	0.846825i	$0.321489\pi$
$8$	1.23649	0.437167
$9$	−2.75918	−0.919726
$10$	−6.58995	−2.08393
$11$	0.311769	0.0940020	0.0470010	−	0.998895i	$-0.485034\pi$
$11$	0.311769	0.0940020	0.0470010	+	0.998895i	$0.485034\pi$
$12$	−0.648528	−0.187214
$13$	−0.272273	−0.0755150	−0.0377575	−	0.999287i	$-0.512021\pi$
$13$	−0.272273	−0.0755150	−0.0377575	+	0.999287i	$0.512021\pi$
$14$	−5.12928	−1.37086
$15$	−1.77443	−0.458157
$16$	−4.89661	−1.22415
$17$	−1.85179	−0.449124	−0.224562	−	0.974460i	$-0.572095\pi$
$17$	−1.85179	−0.449124	−0.224562	+	0.974460i	$0.572095\pi$
$18$	5.02863	1.18526
$19$	4.42517	1.01520	0.507602	−	0.861592i	$-0.330532\pi$
$19$	4.42517	1.01520	0.507602	+	0.861592i	$0.330532\pi$
$20$	4.77853	1.06851
$21$	−1.38113	−0.301387
$22$	−0.568203	−0.121141
$23$	1.16470	0.242857	0.121429	−	0.992600i	$-0.461252\pi$
$23$	1.16470	0.242857	0.121429	+	0.992600i	$0.461252\pi$
$24$	−0.606791	−0.123861
$25$	8.07449	1.61490
$26$	0.496221	0.0973169
$27$	2.82623	0.543909
$28$	3.71936	0.702892
$29$	5.84596	1.08557	0.542783	−	0.839873i	$-0.317370\pi$
$29$	5.84596	1.08557	0.542783	+	0.839873i	$0.317370\pi$
$30$	3.23392	0.590431
$31$	−2.18402	−0.392261	−0.196130	−	0.980578i	$-0.562838\pi$
$31$	−2.18402	−0.392261	−0.196130	+	0.980578i	$0.562838\pi$
$32$	6.45113	1.14041
$33$	−0.152996	−0.0266332
$34$	3.37490	0.578790
$35$	10.1765	1.72014
$36$	−3.64637	−0.607729
$37$	−0.111045	−0.0182556	−0.00912782	−	0.999958i	$-0.502906\pi$
$37$	−0.111045	−0.0182556	−0.00912782	+	0.999958i	$0.502906\pi$
$38$	−8.06492	−1.30830
$39$	0.133614	0.0213954
$40$	4.47100	0.706927
$41$	5.02225	0.784344	0.392172	−	0.919892i	$-0.371724\pi$
$41$	5.02225	0.784344	0.392172	+	0.919892i	$0.371724\pi$
$42$	2.51712	0.388400
$43$	−9.29272	−1.41713	−0.708563	−	0.705647i	$-0.750656\pi$
$43$	−9.29272	−1.41713	−0.708563	+	0.705647i	$0.750656\pi$
$44$	0.412017	0.0621138
$45$	−9.97682	−1.48726
$46$	−2.12268	−0.312972
$47$	13.5485	1.97625	0.988127	−	0.153640i	$-0.0490996\pi$
$47$	13.5485	1.97625	0.988127	+	0.153640i	$0.0490996\pi$
$48$	2.40294	0.346834
$49$	0.920867	0.131552
$50$	−14.7158	−2.08114
$51$	0.908737	0.127249
$52$	−0.359821	−0.0498982
$53$	−0.614386	−0.0843924	−0.0421962	−	0.999109i	$-0.513435\pi$
$53$	−0.614386	−0.0843924	−0.0421962	+	0.999109i	$0.513435\pi$
$54$	−5.15084	−0.700940
$55$	1.12732	0.152007
$56$	3.47999	0.465034
$57$	−2.17159	−0.287634
$58$	−10.6543	−1.39898
$59$	5.55774	0.723556	0.361778	−	0.932264i	$-0.382170\pi$
$59$	5.55774	0.723556	0.361778	+	0.932264i	$0.382170\pi$
$60$	−2.34499	−0.302737
$61$	−7.62317	−0.976047	−0.488024	−	0.872830i	$-0.662282\pi$
$61$	−7.62317	−0.976047	−0.488024	+	0.872830i	$0.662282\pi$
$62$	3.98039	0.505510
$63$	−7.76544	−0.978354
$64$	−1.96404	−0.245505
$65$	−0.984504	−0.122113
$66$	0.278837	0.0343225
$67$	−9.59207	−1.17186	−0.585929	−	0.810363i	$-0.699270\pi$
$67$	−9.59207	−1.17186	−0.585929	+	0.810363i	$0.699270\pi$
$68$	−2.44722	−0.296769
$69$	−0.571560	−0.0688077
$70$	−18.5468	−2.21677
$71$	6.06291	0.719535	0.359768	−	0.933042i	$-0.382856\pi$
$71$	6.06291	0.719535	0.359768	+	0.933042i	$0.382856\pi$
$72$	−3.41171	−0.402074
$73$	−4.33583	−0.507470	−0.253735	−	0.967274i	$-0.581659\pi$
$73$	−4.33583	−0.507470	−0.253735	+	0.967274i	$0.581659\pi$
$74$	0.202380	0.0235262
$75$	−3.96244	−0.457543
$76$	5.84806	0.670818
$77$	0.877444	0.0999941
$78$	−0.243513	−0.0275724
$79$	14.3483	1.61431	0.807156	−	0.590339i	$-0.201006\pi$
$79$	14.3483	1.61431	0.807156	+	0.590339i	$0.201006\pi$
$80$	−17.7055	−1.97953
$81$	6.89061	0.765623
$82$	−9.15311	−1.01079
$83$	−0.466802	−0.0512382	−0.0256191	−	0.999672i	$-0.508156\pi$
$83$	−0.466802	−0.0512382	−0.0256191	+	0.999672i	$0.508156\pi$
$84$	−1.82522	−0.199148
$85$	−6.69581	−0.726263
$86$	16.9361	1.82626
$87$	−2.86882	−0.307569
$88$	0.385501	0.0410945
$89$	−2.75356	−0.291876	−0.145938	−	0.989294i	$-0.546620\pi$
$89$	−2.75356	−0.291876	−0.145938	+	0.989294i	$0.546620\pi$
$90$	18.1829	1.91664
$91$	−0.766287	−0.0803287
$92$	1.53920	0.160473
$93$	1.07177	0.111138
$94$	−24.6923	−2.54682
$95$	16.0008	1.64165
$96$	−3.16580	−0.323108
$97$	−16.4060	−1.66578	−0.832891	−	0.553437i	$-0.813316\pi$
$97$	−16.4060	−1.66578	−0.832891	+	0.553437i	$0.813316\pi$
$98$	−1.67829	−0.169533
$99$	−0.860227	−0.0864561
$100$	10.6708	1.06708
$101$	−4.38995	−0.436816	−0.218408	−	0.975857i	$-0.570086\pi$
$101$	−4.38995	−0.436816	−0.218408	+	0.975857i	$0.570086\pi$
$102$	−1.65618	−0.163986
$103$	3.86801	0.381126	0.190563	−	0.981675i	$-0.438969\pi$
$103$	3.86801	0.381126	0.190563	+	0.981675i	$0.438969\pi$
$104$	−0.336664	−0.0330126
$105$	−4.99397	−0.487362
$106$	1.11972	0.108757
$107$	−5.93924	−0.574168	−0.287084	−	0.957905i	$-0.592686\pi$
$107$	−5.93924	−0.574168	−0.287084	+	0.957905i	$0.592686\pi$
$108$	3.73499	0.359399
$109$	−8.68554	−0.831924	−0.415962	−	0.909382i	$-0.636555\pi$
$109$	−8.68554	−0.831924	−0.415962	+	0.909382i	$0.636555\pi$
$110$	−2.05455	−0.195893
$111$	0.0544936	0.00517230
$112$	−13.7810	−1.30219
$113$	−15.6083	−1.46831	−0.734153	−	0.678984i	$-0.762420\pi$
$113$	−15.6083	−1.46831	−0.734153	+	0.678984i	$0.762420\pi$
$114$	3.95774	0.370676
$115$	4.21141	0.392716
$116$	7.72569	0.717312
$117$	0.751250	0.0694531
$118$	−10.1290	−0.932453
$119$	−5.21167	−0.477753
$120$	−2.19408	−0.200291
$121$	−10.9028	−0.991164
$122$	13.8933	1.25784
$123$	−2.46460	−0.222225
$124$	−2.88627	−0.259195
$125$	11.1170	0.994331
$126$	14.1526	1.26081
$127$	21.1019	1.87249	0.936244	−	0.351349i	$-0.114277\pi$
$127$	21.1019	1.87249	0.936244	+	0.351349i	$0.114277\pi$
$128$	−9.32279	−0.824026
$129$	4.56027	0.401509
$130$	1.79427	0.157368
$131$	4.05559	0.354338	0.177169	−	0.984180i	$-0.443306\pi$
$131$	4.05559	0.354338	0.177169	+	0.984180i	$0.443306\pi$
$132$	−0.202191	−0.0175985
$133$	12.4542	1.07992
$134$	17.4816	1.51018
$135$	10.2193	0.879535
$136$	−2.28972	−0.196342
$137$	−13.9045	−1.18794	−0.593969	−	0.804488i	$-0.702440\pi$
$137$	−13.9045	−1.18794	−0.593969	+	0.804488i	$0.702440\pi$
$138$	1.04167	0.0886732
$139$	16.5086	1.40024	0.700121	−	0.714024i	$-0.253129\pi$
$139$	16.5086	1.40024	0.700121	+	0.714024i	$0.253129\pi$
$140$	13.4487	1.13662
$141$	−6.64873	−0.559924
$142$	−11.0497	−0.927272
$143$	−0.0848864	−0.00709856
$144$	13.5106	1.12589
$145$	21.1382	1.75543
$146$	7.90209	0.653982
$147$	−0.451902	−0.0372722
$148$	−0.146750	−0.0120628
$149$	9.63385	0.789235	0.394618	−	0.918845i	$-0.370877\pi$
$149$	9.63385	0.789235	0.394618	+	0.918845i	$0.370877\pi$
$150$	7.22158	0.589640
$151$	−6.56527	−0.534274	−0.267137	−	0.963659i	$-0.586078\pi$
$151$	−6.56527	−0.534274	−0.267137	+	0.963659i	$0.586078\pi$
$152$	5.47170	0.443813
$153$	5.10941	0.413071
$154$	−1.59915	−0.128863
$155$	−7.89711	−0.634311
$156$	0.176577	0.0141375
$157$	0.0552634	0.00441050	0.00220525	−	0.999998i	$-0.499298\pi$
$157$	0.0552634	0.00441050	0.00220525	+	0.999998i	$0.499298\pi$
$158$	−26.1499	−2.08038
$159$	0.301501	0.0239106
$160$	23.3264	1.84412
$161$	3.27794	0.258338
$162$	−12.5582	−0.986665
$163$	−15.9518	−1.24944	−0.624719	−	0.780850i	$-0.714786\pi$
$163$	−15.9518	−1.24944	−0.624719	+	0.780850i	$0.714786\pi$
$164$	6.63713	0.518272
$165$	−0.553214	−0.0430676
$166$	0.850752	0.0660312
$167$	−7.55542	−0.584656	−0.292328	−	0.956318i	$-0.594430\pi$
$167$	−7.55542	−0.584656	−0.292328	+	0.956318i	$0.594430\pi$
$168$	−1.70776	−0.131756
$169$	−12.9259	−0.994297
$170$	12.2032	0.935942
$171$	−12.2098	−0.933710
$172$	−12.2807	−0.936397
$173$	−17.4849	−1.32935	−0.664676	−	0.747132i	$-0.731430\pi$
$173$	−17.4849	−1.32935	−0.664676	+	0.747132i	$0.731430\pi$
$174$	5.22845	0.396368
$175$	22.7249	1.71784
$176$	−1.52661	−0.115073
$177$	−2.72738	−0.205002
$178$	5.01838	0.376144
$179$	13.2332	0.989095	0.494548	−	0.869151i	$-0.335334\pi$
$179$	13.2332	0.989095	0.494548	+	0.869151i	$0.335334\pi$
$180$	−13.1848	−0.982737
$181$	22.6000	1.67985	0.839924	−	0.542704i	$-0.182600\pi$
$181$	22.6000	1.67985	0.839924	+	0.542704i	$0.182600\pi$
$182$	1.39657	0.103520
$183$	3.74096	0.276540
$184$	1.44015	0.106169
$185$	−0.401523	−0.0295206
$186$	−1.95332	−0.143224
$187$	−0.577330	−0.0422185
$188$	17.9049	1.30585
$189$	7.95416	0.578580
$190$	−29.1617	−2.11561
$191$	−9.25688	−0.669805	−0.334902	−	0.942253i	$-0.608703\pi$
$191$	−9.25688	−0.669805	−0.334902	+	0.942253i	$0.608703\pi$
$192$	0.963822	0.0695579
$193$	−20.3374	−1.46392	−0.731958	−	0.681349i	$-0.761393\pi$
$193$	−20.3374	−1.46392	−0.731958	+	0.681349i	$0.761393\pi$
$194$	29.9002	2.14671
$195$	0.483131	0.0345977
$196$	1.21697	0.0869261
$197$	3.90195	0.278003	0.139001	−	0.990292i	$-0.455611\pi$
$197$	3.90195	0.278003	0.139001	+	0.990292i	$0.455611\pi$
$198$	1.56777	0.111417
$199$	16.3736	1.16070	0.580348	−	0.814368i	$-0.302916\pi$
$199$	16.3736	1.16070	0.580348	+	0.814368i	$0.302916\pi$
$200$	9.98406	0.705980
$201$	4.70716	0.332018
$202$	8.00073	0.562929
$203$	16.4529	1.15477
$204$	1.20093	0.0840823
$205$	18.1598	1.26834
$206$	−7.04948	−0.491161
$207$	−3.21362	−0.223362
$208$	1.33322	0.0924419
$209$	1.37963	0.0954312
$210$	9.10156	0.628068
$211$	−23.2926	−1.60353	−0.801765	−	0.597639i	$-0.796106\pi$
$211$	−23.2926	−1.60353	−0.801765	+	0.597639i	$0.796106\pi$
$212$	−0.811937	−0.0557641
$213$	−2.97528	−0.203863
$214$	10.8243	0.739936
$215$	−33.6012	−2.29159
$216$	3.49462	0.237779
$217$	−6.14670	−0.417265
$218$	15.8295	1.07211
$219$	2.12774	0.143780
$220$	1.48980	0.100442
$221$	0.504192	0.0339156
$222$	−0.0993151	−0.00666559
$223$	−9.98648	−0.668744	−0.334372	−	0.942441i	$-0.608524\pi$
$223$	−9.98648	−0.668744	−0.334372	+	0.942441i	$0.608524\pi$
$224$	18.1561	1.21310
$225$	−22.2790	−1.48526
$226$	28.4463	1.89222
$227$	−4.39218	−0.291519	−0.145760	−	0.989320i	$-0.546563\pi$
$227$	−4.39218	−0.291519	−0.145760	+	0.989320i	$0.546563\pi$
$228$	−2.86985	−0.190060
$229$	−6.44441	−0.425858	−0.212929	−	0.977068i	$-0.568300\pi$
$229$	−6.44441	−0.425858	−0.212929	+	0.977068i	$0.568300\pi$
$230$	−7.67533	−0.506096
$231$	−0.430593	−0.0283309
$232$	7.22849	0.474574
$233$	−14.4014	−0.943467	−0.471734	−	0.881741i	$-0.656372\pi$
$233$	−14.4014	−0.943467	−0.471734	+	0.881741i	$0.656372\pi$
$234$	−1.36916	−0.0895049
$235$	48.9896	3.19573
$236$	7.34479	0.478105
$237$	−7.04122	−0.457377
$238$	9.49833	0.615685
$239$	−6.72701	−0.435134	−0.217567	−	0.976045i	$-0.569812\pi$
$239$	−6.72701	−0.435134	−0.217567	+	0.976045i	$0.569812\pi$
$240$	8.68871	0.560854
$241$	−20.5159	−1.32154	−0.660772	−	0.750587i	$-0.729771\pi$
$241$	−20.5159	−1.32154	−0.660772	+	0.750587i	$0.729771\pi$
$242$	19.8705	1.27732
$243$	−11.8602	−0.760830
$244$	−10.0744	−0.644945
$245$	3.32973	0.212729
$246$	4.49175	0.286384
$247$	−1.20486	−0.0766631
$248$	−2.70052	−0.171483
$249$	0.229076	0.0145171
$250$	−20.2608	−1.28140
$251$	−23.9375	−1.51092	−0.755460	−	0.655195i	$-0.772586\pi$
$251$	−23.9375	−1.51092	−0.755460	+	0.655195i	$0.772586\pi$
$252$	−10.2624	−0.646469
$253$	0.363118	0.0228290
$254$	−38.4584	−2.41309
$255$	3.28587	0.205769
$256$	20.9190	1.30743
$257$	27.5380	1.71778	0.858888	−	0.512164i	$-0.171156\pi$
$257$	27.5380	1.71778	0.858888	+	0.512164i	$0.171156\pi$
$258$	−8.31113	−0.517428
$259$	−0.312525	−0.0194193
$260$	−1.30106	−0.0806886
$261$	−16.1300	−0.998424
$262$	−7.39135	−0.456639
$263$	−22.5508	−1.39054	−0.695272	−	0.718746i	$-0.744716\pi$
$263$	−22.5508	−1.39054	−0.695272	+	0.718746i	$0.744716\pi$
$264$	−0.189179	−0.0116432
$265$	−2.22154	−0.136468
$266$	−22.6979	−1.39170
$267$	1.35127	0.0826962
$268$	−12.6763	−0.774330
$269$	15.6894	0.956599	0.478300	−	0.878197i	$-0.341253\pi$
$269$	15.6894	0.956599	0.478300	+	0.878197i	$0.341253\pi$
$270$	−18.6247	−1.13347
$271$	4.86714	0.295658	0.147829	−	0.989013i	$-0.452771\pi$
$271$	4.86714	0.295658	0.147829	+	0.989013i	$0.452771\pi$
$272$	9.06747	0.549796
$273$	0.376044	0.0227592
$274$	25.3410	1.53091
$275$	2.51738	0.151804
$276$	−0.755341	−0.0454662
$277$	−30.5435	−1.83518	−0.917590	−	0.397528i	$-0.869868\pi$
$277$	−30.5435	−1.83518	−0.917590	+	0.397528i	$0.869868\pi$
$278$	−30.0871	−1.80451
$279$	6.02609	0.360773
$280$	12.5832	0.751990
$281$	1.58577	0.0945990	0.0472995	−	0.998881i	$-0.484938\pi$
$281$	1.58577	0.0945990	0.0472995	+	0.998881i	$0.484938\pi$
$282$	12.1174	0.721580
$283$	−19.3873	−1.15245	−0.576226	−	0.817290i	$-0.695475\pi$
$283$	−19.3873	−1.15245	−0.576226	+	0.817290i	$0.695475\pi$
$284$	8.01240	0.475448
$285$	−7.85217	−0.465123
$286$	0.154706	0.00914798
$287$	14.1346	0.834342
$288$	−17.7998	−1.04887
$289$	−13.5709	−0.798288
$290$	−38.5246	−2.26224
$291$	8.05103	0.471959
$292$	−5.72999	−0.335322
$293$	24.3455	1.42228	0.711139	−	0.703052i	$-0.248180\pi$
$293$	24.3455	1.42228	0.711139	+	0.703052i	$0.248180\pi$
$294$	0.823596	0.0480331
$295$	20.0960	1.17004
$296$	−0.137306	−0.00798076
$297$	0.881132	0.0511285
$298$	−17.5578	−1.01710
$299$	−0.317117	−0.0183393
$300$	−5.23653	−0.302331
$301$	−26.1535	−1.50746
$302$	11.9653	0.688524
$303$	2.15430	0.123762
$304$	−21.6683	−1.24276
$305$	−27.5644	−1.57833
$306$	−9.31195	−0.532329
$307$	−20.4092	−1.16482	−0.582408	−	0.812897i	$-0.697889\pi$
$307$	−20.4092	−1.16482	−0.582408	+	0.812897i	$0.697889\pi$
$308$	1.15958	0.0660733
$309$	−1.89817	−0.107983
$310$	14.3926	0.817443
$311$	−4.87763	−0.276585	−0.138292	−	0.990391i	$-0.544161\pi$
$311$	−4.87763	−0.276585	−0.138292	+	0.990391i	$0.544161\pi$
$312$	0.165213	0.00935334
$313$	30.1452	1.70391	0.851955	−	0.523616i	$-0.175417\pi$
$313$	30.1452	1.70391	0.851955	+	0.523616i	$0.175417\pi$
$314$	−0.100718	−0.00568385
$315$	−28.0788	−1.58206
$316$	18.9619	1.06669
$317$	26.3133	1.47790	0.738952	−	0.673758i	$-0.235321\pi$
$317$	26.3133	1.47790	0.738952	+	0.673758i	$0.235321\pi$
$318$	−0.549488	−0.0308138
$319$	1.82259	0.102045
$320$	−7.10170	−0.396997
$321$	2.91459	0.162677
$322$	−5.97408	−0.332922
$323$	−8.19447	−0.455953
$324$	9.10623	0.505902
$325$	−2.19847	−0.121949
$326$	29.0722	1.61016
$327$	4.26230	0.235706
$328$	6.20999	0.342889
$329$	38.1310	2.10223
$330$	1.00824	0.0555017
$331$	22.3828	1.23027	0.615134	−	0.788423i	$-0.289102\pi$
$331$	22.3828	1.23027	0.615134	+	0.788423i	$0.289102\pi$
$332$	−0.616899	−0.0338568
$333$	0.306392	0.0167902
$334$	13.7698	0.753452
$335$	−34.6836	−1.89497
$336$	6.76284	0.368943
$337$	−9.80227	−0.533964	−0.266982	−	0.963702i	$-0.586026\pi$
$337$	−9.80227	−0.533964	−0.266982	+	0.963702i	$0.586026\pi$
$338$	23.5575	1.28136
$339$	7.65954	0.416009
$340$	−8.84881	−0.479894
$341$	−0.680909	−0.0368733
$342$	22.2526	1.20328
$343$	−17.1091	−0.923806
$344$	−11.4904	−0.619521
$345$	−2.06668	−0.111267
$346$	31.8664	1.71315
$347$	−0.0291015	−0.00156225	−0.000781126	−	1.00000i	$-0.500249\pi$
$347$	−0.0291015	−0.00156225	−0.000781126		1.00000i	$0.500249\pi$
$348$	−3.79127	−0.203233
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	−41.4163	−2.21380
$351$	−0.769507	−0.0410732
$352$	2.01127	0.107201
$353$	−25.6106	−1.36311	−0.681557	−	0.731765i	$-0.738697\pi$
$353$	−25.6106	−1.36311	−0.681557	+	0.731765i	$0.738697\pi$
$354$	4.97067	0.264188
$355$	21.9227	1.16354
$356$	−3.63894	−0.192864
$357$	2.55755	0.135360
$358$	−24.1176	−1.27466
$359$	−4.70856	−0.248508	−0.124254	−	0.992250i	$-0.539654\pi$
$359$	−4.70856	−0.248508	−0.124254	+	0.992250i	$0.539654\pi$
$360$	−12.3363	−0.650179
$361$	0.582157	0.0306398
$362$	−41.1888	−2.16484
$363$	5.35039	0.280823
$364$	−1.01268	−0.0530789
$365$	−15.6778	−0.820613
$366$	−6.81794	−0.356379
$367$	16.5423	0.863500	0.431750	−	0.901993i	$-0.357896\pi$
$367$	16.5423	0.863500	0.431750	+	0.901993i	$0.357896\pi$
$368$	−5.70309	−0.297294
$369$	−13.8573	−0.721382
$370$	0.731780	0.0380434
$371$	−1.72913	−0.0897719
$372$	1.41640	0.0734367
$373$	37.5060	1.94199	0.970993	−	0.239108i	$-0.0768550\pi$
$373$	37.5060	1.94199	0.970993	+	0.239108i	$0.0768550\pi$
$374$	1.05219	0.0544074
$375$	−5.45548	−0.281720
$376$	16.7527	0.863952
$377$	−1.59170	−0.0819766
$378$	−14.4965	−0.745621
$379$	−13.4274	−0.689719	−0.344860	−	0.938654i	$-0.612074\pi$
$379$	−13.4274	−0.689719	−0.344860	+	0.938654i	$0.612074\pi$
$380$	21.1458	1.08476
$381$	−10.3554	−0.530525
$382$	16.8708	0.863183
$383$	27.8295	1.42202	0.711010	−	0.703182i	$-0.248238\pi$
$383$	27.8295	1.42202	0.711010	+	0.703182i	$0.248238\pi$
$384$	4.57502	0.233468
$385$	3.17272	0.161697
$386$	37.0651	1.88656
$387$	25.6403	1.30337
$388$	−21.6813	−1.10070
$389$	−17.3719	−0.880791	−0.440396	−	0.897804i	$-0.645162\pi$
$389$	−17.3719	−0.880791	−0.440396	+	0.897804i	$0.645162\pi$
$390$	−0.880510	−0.0445864
$391$	−2.15678	−0.109073
$392$	1.13865	0.0575103
$393$	−1.99022	−0.100393
$394$	−7.11135	−0.358264
$395$	51.8816	2.61045
$396$	−1.13683	−0.0571277
$397$	35.0355	1.75838	0.879190	−	0.476472i	$-0.158085\pi$
$397$	35.0355	1.75838	0.879190	+	0.476472i	$0.158085\pi$
$398$	−29.8411	−1.49580
$399$	−6.11173	−0.305969
$400$	−39.5376	−1.97688
$401$	22.1054	1.10389	0.551944	−	0.833881i	$-0.313886\pi$
$401$	22.1054	1.10389	0.551944	+	0.833881i	$0.313886\pi$
$402$	−8.57886	−0.427874
$403$	0.594649	0.0296216
$404$	−5.80151	−0.288636
$405$	24.9155	1.23806
$406$	−29.9855	−1.48816
$407$	−0.0346203	−0.00171607
$408$	1.12365	0.0556288
$409$	18.6308	0.921232	0.460616	−	0.887600i	$-0.347629\pi$
$409$	18.6308	0.921232	0.460616	+	0.887600i	$0.347629\pi$
$410$	−33.0964	−1.63452
$411$	6.82341	0.336574
$412$	5.11174	0.251837
$413$	15.6417	0.769679
$414$	5.85685	0.287849
$415$	−1.68789	−0.0828555
$416$	−1.75647	−0.0861180
$417$	−8.10136	−0.396725
$418$	−2.51440	−0.122983
$419$	−6.82714	−0.333528	−0.166764	−	0.985997i	$-0.553332\pi$
$419$	−6.82714	−0.333528	−0.166764	+	0.985997i	$0.553332\pi$
$420$	−6.59975	−0.322035
$421$	−4.17712	−0.203580	−0.101790	−	0.994806i	$-0.532457\pi$
$421$	−4.17712	−0.203580	−0.101790	+	0.994806i	$0.532457\pi$
$422$	42.4511	2.06649
$423$	−37.3828	−1.81761
$424$	−0.759684	−0.0368935
$425$	−14.9522	−0.725290
$426$	5.42249	0.262720
$427$	−21.4547	−1.03827
$428$	−7.84896	−0.379394
$429$	0.0416567	0.00201121
$430$	61.2386	2.95319
$431$	−23.7799	−1.14544	−0.572718	−	0.819752i	$-0.694111\pi$
$431$	−23.7799	−1.14544	−0.572718	+	0.819752i	$0.694111\pi$
$432$	−13.8390	−0.665827
$433$	33.1758	1.59432	0.797162	−	0.603765i	$-0.206333\pi$
$433$	33.1758	1.59432	0.797162	+	0.603765i	$0.206333\pi$
$434$	11.2024	0.537734
$435$	−10.3733	−0.497360
$436$	−11.4783	−0.549712
$437$	5.15401	0.246550
$438$	−3.87784	−0.185290
$439$	16.4580	0.785496	0.392748	−	0.919646i	$-0.371524\pi$
$439$	16.4580	0.785496	0.392748	+	0.919646i	$0.371524\pi$
$440$	1.39392	0.0664525
$441$	−2.54084	−0.120992
$442$	−0.918894	−0.0437074
$443$	12.2526	0.582137	0.291068	−	0.956702i	$-0.405989\pi$
$443$	12.2526	0.582137	0.291068	+	0.956702i	$0.405989\pi$
$444$	0.0720156	0.00341771
$445$	−9.95649	−0.471983
$446$	18.2005	0.861817
$447$	−4.72767	−0.223611
$448$	−5.52759	−0.261154
$449$	23.1535	1.09268	0.546341	−	0.837563i	$-0.316020\pi$
$449$	23.1535	1.09268	0.546341	+	0.837563i	$0.316020\pi$
$450$	40.6037	1.91407
$451$	1.56578	0.0737299
$452$	−20.6270	−0.970215
$453$	3.22181	0.151374
$454$	8.00480	0.375684
$455$	−2.77079	−0.129897
$456$	−2.68516	−0.125744
$457$	12.4954	0.584511	0.292256	−	0.956340i	$-0.405594\pi$
$457$	12.4954	0.584511	0.292256	+	0.956340i	$0.405594\pi$
$458$	11.7450	0.548808
$459$	−5.23358	−0.244282
$460$	5.56556	0.259495
$461$	−35.2441	−1.64148	−0.820741	−	0.571300i	$-0.806439\pi$
$461$	−35.2441	−1.64148	−0.820741	+	0.571300i	$0.806439\pi$
$462$	0.784760	0.0365103
$463$	4.78339	0.222303	0.111152	−	0.993803i	$-0.464546\pi$
$463$	4.78339	0.222303	0.111152	+	0.993803i	$0.464546\pi$
$464$	−28.6254	−1.32890
$465$	3.87539	0.179717
$466$	26.2467	1.21586
$467$	9.54087	0.441499	0.220749	−	0.975331i	$-0.429150\pi$
$467$	9.54087	0.441499	0.220749	+	0.975331i	$0.429150\pi$
$468$	0.992810	0.0458927
$469$	−26.9959	−1.24656
$470$	−89.2841	−4.11837
$471$	−0.0271197	−0.00124961
$472$	6.87211	0.316314
$473$	−2.89718	−0.133213
$474$	12.8327	0.589425
$475$	35.7310	1.63945
$476$	−6.88745	−0.315686
$477$	1.69520	0.0776179
$478$	12.2601	0.560762
$479$	−16.6412	−0.760357	−0.380179	−	0.924913i	$-0.624137\pi$
$479$	−16.6412	−0.760357	−0.380179	+	0.924913i	$0.624137\pi$
$480$	−11.4471	−0.522487
$481$	0.0302345	0.00137857
$482$	37.3904	1.70308
$483$	−1.60860	−0.0731939
$484$	−14.4085	−0.654933
$485$	−59.3221	−2.69368
$486$	21.6153	0.980488
$487$	33.0927	1.49957	0.749787	−	0.661679i	$-0.230156\pi$
$487$	33.0927	1.49957	0.749787	+	0.661679i	$0.230156\pi$
$488$	−9.42601	−0.426695
$489$	7.82809	0.353998
$490$	−6.06847	−0.274146
$491$	5.19156	0.234292	0.117146	−	0.993115i	$-0.462626\pi$
$491$	5.19156	0.234292	0.117146	+	0.993115i	$0.462626\pi$
$492$	−3.25707	−0.146840
$493$	−10.8255	−0.487554
$494$	2.19586	0.0987965
$495$	−3.11047	−0.139805
$496$	10.6943	0.480187
$497$	17.0635	0.765402
$498$	−0.417494	−0.0187083
$499$	8.59090	0.384582	0.192291	−	0.981338i	$-0.438408\pi$
$499$	8.59090	0.384582	0.192291	+	0.981338i	$0.438408\pi$
$500$	14.6915	0.657026
$501$	3.70771	0.165648
$502$	43.6263	1.94714
$503$	−35.8265	−1.59742	−0.798711	−	0.601714i	$-0.794485\pi$
$503$	−35.8265	−1.59742	−0.798711	+	0.601714i	$0.794485\pi$
$504$	−9.60192	−0.427704
$505$	−15.8735	−0.706361
$506$	−0.661786	−0.0294200
$507$	6.34318	0.281710
$508$	27.8870	1.23729
$509$	12.2068	0.541058	0.270529	−	0.962712i	$-0.412801\pi$
$509$	12.2068	0.541058	0.270529	+	0.962712i	$0.412801\pi$
$510$	−5.98853	−0.265177
$511$	−12.2028	−0.539819
$512$	−19.4794	−0.860877
$513$	12.5066	0.552178
$514$	−50.1884	−2.21371
$515$	13.9862	0.616305
$516$	6.02659	0.265306
$517$	4.22401	0.185772
$518$	0.569579	0.0250259
$519$	8.58045	0.376640
$520$	−1.21733	−0.0533836
$521$	26.8151	1.17479	0.587396	−	0.809299i	$-0.300153\pi$
$521$	26.8151	1.17479	0.587396	+	0.809299i	$0.300153\pi$
$522$	29.3972	1.28668
$523$	10.0025	0.437377	0.218689	−	0.975795i	$-0.429822\pi$
$523$	10.0025	0.437377	0.218689	+	0.975795i	$0.429822\pi$
$524$	5.35964	0.234137
$525$	−11.1519	−0.486709
$526$	41.0991	1.79201
$527$	4.04433	0.176174
$528$	0.749162	0.0326031
$529$	−21.6435	−0.941020
$530$	4.04877	0.175868
$531$	−15.3348	−0.665473
$532$	16.4588	0.713579
$533$	−1.36742	−0.0592297
$534$	−2.46270	−0.106571
$535$	−21.4755	−0.928467
$536$	−11.8605	−0.512297
$537$	−6.49399	−0.280237
$538$	−28.5941	−1.23278
$539$	0.287098	0.0123662
$540$	13.5052	0.581172
$541$	8.25484	0.354903	0.177452	−	0.984130i	$-0.443215\pi$
$541$	8.25484	0.354903	0.177452	+	0.984130i	$0.443215\pi$
$542$	−8.87042	−0.381017
$543$	−11.0906	−0.475945
$544$	−11.9461	−0.512186
$545$	−31.4058	−1.34527
$546$	−0.685344	−0.0293300
$547$	−29.6395	−1.26729	−0.633646	−	0.773623i	$-0.718443\pi$
$547$	−29.6395	−1.26729	−0.633646	+	0.773623i	$0.718443\pi$
$548$	−18.3754	−0.784956
$549$	21.0337	0.897697
$550$	−4.58795	−0.195631
$551$	25.8694	1.10207
$552$	−0.706730	−0.0300804
$553$	40.3819	1.71721
$554$	55.6658	2.36501
$555$	0.197041	0.00836395
$556$	21.8168	0.925240
$557$	33.6606	1.42625	0.713123	−	0.701039i	$-0.247280\pi$
$557$	33.6606	1.42625	0.713123	+	0.701039i	$0.247280\pi$
$558$	−10.9826	−0.464931
$559$	2.53016	0.107014
$560$	−49.8304	−2.10572
$561$	0.283316	0.0119616
$562$	−2.89008	−0.121911
$563$	−10.0927	−0.425356	−0.212678	−	0.977122i	$-0.568219\pi$
$563$	−10.0927	−0.425356	−0.212678	+	0.977122i	$0.568219\pi$
$564$	−8.78659	−0.369982
$565$	−56.4375	−2.37435
$566$	35.3335	1.48518
$567$	19.3929	0.814427
$568$	7.49675	0.314557
$569$	−20.3255	−0.852088	−0.426044	−	0.904702i	$-0.640093\pi$
$569$	−20.3255	−0.852088	−0.426044	+	0.904702i	$0.640093\pi$
$570$	14.3107	0.599408
$571$	35.0869	1.46834	0.734170	−	0.678966i	$-0.237572\pi$
$571$	35.0869	1.46834	0.734170	+	0.678966i	$0.237572\pi$
$572$	−0.112181	−0.00469053
$573$	4.54268	0.189773
$574$	−25.7605	−1.07522
$575$	9.40437	0.392190
$576$	5.41913	0.225797
$577$	−46.2132	−1.92388	−0.961940	−	0.273262i	$-0.911898\pi$
$577$	−46.2132	−1.92388	−0.961940	+	0.273262i	$0.911898\pi$
$578$	24.7331	1.02876
$579$	9.98027	0.414766
$580$	27.9351	1.15994
$581$	−1.31377	−0.0545044
$582$	−14.6731	−0.608219
$583$	−0.191547	−0.00793305
$584$	−5.36123	−0.221849
$585$	2.71642	0.112310
$586$	−44.3699	−1.83290
$587$	−2.22373	−0.0917831	−0.0458915	−	0.998946i	$-0.514613\pi$
$587$	−2.22373	−0.0917831	−0.0458915	+	0.998946i	$0.514613\pi$
$588$	−0.597208	−0.0246284
$589$	−9.66465	−0.398225
$590$	−36.6252	−1.50784
$591$	−1.91482	−0.0787654
$592$	0.543743	0.0223477
$593$	−29.9269	−1.22895	−0.614474	−	0.788937i	$-0.710632\pi$
$593$	−29.9269	−1.22895	−0.614474	+	0.788937i	$0.710632\pi$
$594$	−1.60587	−0.0658897
$595$	−18.8447	−0.772558
$596$	12.7315	0.521504
$597$	−8.03512	−0.328856
$598$	0.577949	0.0236341
$599$	16.6734	0.681258	0.340629	−	0.940198i	$-0.389360\pi$
$599$	16.6734	0.681258	0.340629	+	0.940198i	$0.389360\pi$
$600$	−4.89953	−0.200023
$601$	10.4498	0.426255	0.213128	−	0.977024i	$-0.431635\pi$
$601$	10.4498	0.426255	0.213128	+	0.977024i	$0.431635\pi$
$602$	47.6650	1.94268
$603$	26.4662	1.07779
$604$	−8.67628	−0.353033
$605$	−39.4231	−1.60278
$606$	−3.92624	−0.159493
$607$	−25.6586	−1.04145	−0.520725	−	0.853724i	$-0.674338\pi$
$607$	−25.6586	−1.04145	−0.520725	+	0.853724i	$0.674338\pi$
$608$	28.5474	1.15775
$609$	−8.07401	−0.327175
$610$	50.2364	2.03401
$611$	−3.68890	−0.149237
$612$	6.75231	0.272946
$613$	−34.8451	−1.40738	−0.703690	−	0.710507i	$-0.748466\pi$
$613$	−34.8451	−1.40738	−0.703690	+	0.710507i	$0.748466\pi$
$614$	37.1960	1.50111
$615$	−8.91165	−0.359353
$616$	1.08495	0.0437141
$617$	−2.10853	−0.0848861	−0.0424431	−	0.999099i	$-0.513514\pi$
$617$	−2.10853	−0.0848861	−0.0424431	+	0.999099i	$0.513514\pi$
$618$	3.45943	0.139159
$619$	−1.81522	−0.0729599	−0.0364800	−	0.999334i	$-0.511615\pi$
$619$	−1.81522	−0.0729599	−0.0364800	+	0.999334i	$0.511615\pi$
$620$	−10.4364	−0.419135
$621$	3.29172	0.132092
$622$	8.88953	0.356438
$623$	−7.74962	−0.310482
$624$	−0.654256	−0.0261912
$625$	−0.175014	−0.00700056
$626$	−54.9400	−2.19584
$627$	−0.677034	−0.0270382
$628$	0.0730330	0.00291433
$629$	0.205631	0.00819905
$630$	51.1739	2.03882
$631$	−16.6499	−0.662820	−0.331410	−	0.943487i	$-0.607524\pi$
$631$	−16.6499	−0.662820	−0.331410	+	0.943487i	$0.607524\pi$
$632$	17.7416	0.705723
$633$	11.4305	0.454322
$634$	−47.9563	−1.90459
$635$	76.3016	3.02794
$636$	0.398446	0.0157994
$637$	−0.250727	−0.00993418
$638$	−3.32169	−0.131507
$639$	−16.7287	−0.661775
$640$	−33.7100	−1.33250
$641$	−33.2676	−1.31399	−0.656997	−	0.753894i	$-0.728173\pi$
$641$	−33.2676	−1.31399	−0.656997	+	0.753894i	$0.728173\pi$
$642$	−5.31188	−0.209643
$643$	29.4152	1.16002	0.580011	−	0.814608i	$-0.303048\pi$
$643$	29.4152	1.16002	0.580011	+	0.814608i	$0.303048\pi$
$644$	4.33194	0.170702
$645$	16.4893	0.649266
$646$	14.9345	0.587591
$647$	24.8539	0.977108	0.488554	−	0.872534i	$-0.337525\pi$
$647$	24.8539	0.977108	0.488554	+	0.872534i	$0.337525\pi$
$648$	8.52019	0.334705
$649$	1.73273	0.0680157
$650$	4.00673	0.157157
$651$	3.01640	0.118222
$652$	−21.0809	−0.825593
$653$	23.5565	0.921838	0.460919	−	0.887442i	$-0.347520\pi$
$653$	23.5565	0.921838	0.460919	+	0.887442i	$0.347520\pi$
$654$	−7.76808	−0.303756
$655$	14.6645	0.572988
$656$	−24.5920	−0.960157
$657$	11.9633	0.466734
$658$	−69.4941	−2.70916
$659$	45.9537	1.79010	0.895051	−	0.445964i	$-0.147139\pi$
$659$	45.9537	1.79010	0.895051	+	0.445964i	$0.147139\pi$
$660$	−0.731096	−0.0284579
$661$	1.44653	0.0562635	0.0281318	−	0.999604i	$-0.491044\pi$
$661$	1.44653	0.0562635	0.0281318	+	0.999604i	$0.491044\pi$
$662$	−40.7928	−1.58546
$663$	−0.247425	−0.00960918
$664$	−0.577198	−0.0223996
$665$	45.0328	1.74630
$666$	−0.558403	−0.0216377
$667$	6.80879	0.263638
$668$	−9.98482	−0.386324
$669$	4.90072	0.189473
$670$	63.2113	2.44206
$671$	−2.37667	−0.0917504
$672$	−8.90983	−0.343704
$673$	−35.6344	−1.37360	−0.686802	−	0.726844i	$-0.740986\pi$
$673$	−35.6344	−1.37360	−0.686802	+	0.726844i	$0.740986\pi$
$674$	17.8647	0.688124
$675$	22.8204	0.878357
$676$	−17.0821	−0.657004
$677$	−7.11266	−0.273362	−0.136681	−	0.990615i	$-0.543644\pi$
$677$	−7.11266	−0.273362	−0.136681	+	0.990615i	$0.543644\pi$
$678$	−13.9596	−0.536115
$679$	−46.1732	−1.77197
$680$	−8.27933	−0.317498
$681$	2.15540	0.0825950
$682$	1.24096	0.0475190
$683$	32.6512	1.24936	0.624682	−	0.780879i	$-0.285228\pi$
$683$	32.6512	1.24936	0.624682	+	0.780879i	$0.285228\pi$
$684$	−16.1358	−0.616969
$685$	−50.2767	−1.92097
$686$	31.1816	1.19052
$687$	3.16250	0.120657
$688$	45.5028	1.73478
$689$	0.167281	0.00637289
$690$	3.76655	0.143390
$691$	14.1061	0.536621	0.268311	−	0.963332i	$-0.413535\pi$
$691$	14.1061	0.536621	0.268311	+	0.963332i	$0.413535\pi$
$692$	−23.1070	−0.878398
$693$	−2.42103	−0.0919672
$694$	0.0530378	0.00201329
$695$	59.6929	2.26428
$696$	−3.54727	−0.134459
$697$	−9.30014	−0.352268
$698$	−1.82251	−0.0689830
$699$	7.06728	0.267309
$700$	30.0319	1.13510
$701$	23.5785	0.890550	0.445275	−	0.895394i	$-0.353106\pi$
$701$	23.5785	0.890550	0.445275	+	0.895394i	$0.353106\pi$
$702$	1.40243	0.0529315
$703$	−0.491392	−0.0185332
$704$	−0.612326	−0.0230779
$705$	−24.0409	−0.905434
$706$	46.6755	1.75666
$707$	−12.3551	−0.464661
$708$	−3.60435	−0.135460
$709$	4.28751	0.161021	0.0805105	−	0.996754i	$-0.474345\pi$
$709$	4.28751	0.161021	0.0805105	+	0.996754i	$0.474345\pi$
$710$	−39.9543	−1.49946
$711$	−39.5896	−1.48472
$712$	−3.40475	−0.127599
$713$	−2.54373	−0.0952633
$714$	−4.66116	−0.174440
$715$	−0.306938	−0.0114788
$716$	17.4882	0.653566
$717$	3.30118	0.123285
$718$	8.58140	0.320255
$719$	−50.4410	−1.88113	−0.940566	−	0.339612i	$-0.889704\pi$
$719$	−50.4410	−1.88113	−0.940566	+	0.339612i	$0.889704\pi$
$720$	48.8526	1.82063
$721$	10.8861	0.405421
$722$	−1.06099	−0.0394859
$723$	10.0679	0.374428
$724$	29.8669	1.11000
$725$	47.2031	1.75308
$726$	−9.75114	−0.361899
$727$	10.3079	0.382298	0.191149	−	0.981561i	$-0.438779\pi$
$727$	10.3079	0.382298	0.191149	+	0.981561i	$0.438779\pi$
$728$	−0.947509	−0.0351170
$729$	−14.8516	−0.550060
$730$	28.5729	1.05753
$731$	17.2081	0.636466
$732$	4.94384	0.182730
$733$	−26.2018	−0.967784	−0.483892	−	0.875128i	$-0.660777\pi$
$733$	−26.2018	−0.967784	−0.483892	+	0.875128i	$0.660777\pi$
$734$	−30.1485	−1.11280
$735$	−1.63402	−0.0602716
$736$	7.51364	0.276957
$737$	−2.99051	−0.110157
$738$	25.2551	0.929652
$739$	−8.75491	−0.322054	−0.161027	−	0.986950i	$-0.551481\pi$
$739$	−8.75491	−0.322054	−0.161027	+	0.986950i	$0.551481\pi$
$740$	−0.530630	−0.0195064
$741$	0.591265	0.0217207
$742$	3.15136	0.115690
$743$	−16.9892	−0.623273	−0.311636	−	0.950201i	$-0.600877\pi$
$743$	−16.9892	−0.623273	−0.311636	+	0.950201i	$0.600877\pi$
$744$	1.32524	0.0485857
$745$	34.8347	1.27624
$746$	−68.3550	−2.50266
$747$	1.28799	0.0471251
$748$	−0.762967	−0.0278968
$749$	−16.7154	−0.610768
$750$	9.94268	0.363055
$751$	−9.80653	−0.357845	−0.178923	−	0.983863i	$-0.557261\pi$
$751$	−9.80653	−0.357845	−0.178923	+	0.983863i	$0.557261\pi$
$752$	−66.3418	−2.41924
$753$	11.7470	0.428083
$754$	2.90088	0.105644
$755$	−23.7391	−0.863955
$756$	10.5118	0.382309
$757$	24.7143	0.898255	0.449127	−	0.893468i	$-0.351735\pi$
$757$	24.7143	0.898255	0.449127	+	0.893468i	$0.351735\pi$
$758$	24.4716	0.888848
$759$	−0.178195	−0.00646806
$760$	19.7849	0.717675
$761$	35.8391	1.29917	0.649584	−	0.760290i	$-0.274943\pi$
$761$	35.8391	1.29917	0.649584	+	0.760290i	$0.274943\pi$
$762$	18.8729	0.683692
$763$	−24.4446	−0.884954
$764$	−12.2334	−0.442588
$765$	18.4749	0.667963
$766$	−50.7195	−1.83257
$767$	−1.51322	−0.0546393
$768$	−10.2657	−0.370430
$769$	−2.15983	−0.0778854	−0.0389427	−	0.999241i	$-0.512399\pi$
$769$	−2.15983	−0.0778854	−0.0389427	+	0.999241i	$0.512399\pi$
$770$	−5.78232	−0.208380
$771$	−13.5139	−0.486691
$772$	−26.8767	−0.967315
$773$	−8.81916	−0.317203	−0.158602	−	0.987343i	$-0.550699\pi$
$773$	−8.81916	−0.317203	−0.158602	+	0.987343i	$0.550699\pi$
$774$	−46.7297	−1.67966
$775$	−17.6348	−0.633462
$776$	−20.2860	−0.728224
$777$	0.153367	0.00550201
$778$	31.6605	1.13508
$779$	22.2243	0.796270
$780$	0.638478	0.0228612
$781$	1.89023	0.0676377
$782$	3.93075	0.140563
$783$	16.5220	0.590449
$784$	−4.50913	−0.161040
$785$	0.199825	0.00713206
$786$	3.62720	0.129378
$787$	21.2850	0.758728	0.379364	−	0.925248i	$-0.376143\pi$
$787$	21.2850	0.758728	0.379364	+	0.925248i	$0.376143\pi$
$788$	5.15660	0.183696
$789$	11.0665	0.393978
$790$	−94.5547	−3.36411
$791$	−43.9281	−1.56190
$792$	−1.06367	−0.0377957
$793$	2.07559	0.0737062
$794$	−63.8525	−2.26604
$795$	1.09019	0.0386649
$796$	21.6385	0.766956
$797$	−25.9151	−0.917960	−0.458980	−	0.888447i	$-0.651785\pi$
$797$	−25.9151	−0.917960	−0.458980	+	0.888447i	$0.651785\pi$
$798$	11.1387	0.394305
$799$	−25.0889	−0.887583
$800$	52.0896	1.84165
$801$	7.59755	0.268446
$802$	−40.2872	−1.42259
$803$	−1.35178	−0.0477032
$804$	6.22072	0.219388
$805$	11.8526	0.417749
$806$	−1.08375	−0.0381736
$807$	−7.69934	−0.271030
$808$	−5.42815	−0.190962
$809$	−8.93605	−0.314175	−0.157087	−	0.987585i	$-0.550210\pi$
$809$	−8.93605	−0.314175	−0.157087	+	0.987585i	$0.550210\pi$
$810$	−45.4088	−1.59550
$811$	−25.9873	−0.912539	−0.456269	−	0.889842i	$-0.650815\pi$
$811$	−25.9873	−0.912539	−0.456269	+	0.889842i	$0.650815\pi$
$812$	21.7432	0.763037
$813$	−2.38848	−0.0837676
$814$	0.0630959	0.00221151
$815$	−57.6794	−2.02042
$816$	−4.44973	−0.155772
$817$	−41.1219	−1.43867
$818$	−33.9548	−1.18720
$819$	2.11432	0.0738804
$820$	23.9990	0.838080
$821$	10.9558	0.382360	0.191180	−	0.981555i	$-0.438769\pi$
$821$	10.9558	0.382360	0.191180	+	0.981555i	$0.438769\pi$
$822$	−12.4357	−0.433746
$823$	−7.24280	−0.252468	−0.126234	−	0.992000i	$-0.540289\pi$
$823$	−7.24280	−0.252468	−0.126234	+	0.992000i	$0.540289\pi$
$824$	4.78277	0.166616
$825$	−1.23537	−0.0430099
$826$	−28.5072	−0.991892
$827$	6.42484	0.223413	0.111707	−	0.993741i	$-0.464368\pi$
$827$	6.42484	0.223413	0.111707	+	0.993741i	$0.464368\pi$
$828$	−4.24694	−0.147591
$829$	28.8458	1.00186	0.500928	−	0.865489i	$-0.332992\pi$
$829$	28.8458	1.00186	0.500928	+	0.865489i	$0.332992\pi$
$830$	3.07621	0.106777
$831$	14.9888	0.519954
$832$	0.534754	0.0185393
$833$	−1.70525	−0.0590834
$834$	14.7648	0.511263
$835$	−27.3194	−0.945427
$836$	1.82324	0.0630582
$837$	−6.17254	−0.213354
$838$	12.4425	0.429820
$839$	22.5301	0.777825	0.388913	−	0.921275i	$-0.372851\pi$
$839$	22.5301	0.777825	0.388913	+	0.921275i	$0.372851\pi$
$840$	−6.17502	−0.213058
$841$	5.17521	0.178455
$842$	7.61284	0.262356
$843$	−0.778193	−0.0268024
$844$	−30.7822	−1.05957
$845$	−46.7382	−1.60784
$846$	68.1305	2.34237
$847$	−30.6849	−1.05434
$848$	3.00841	0.103309
$849$	9.51401	0.326520
$850$	27.2506	0.934688
$851$	−0.129334	−0.00443351
$852$	−3.93197	−0.134707
$853$	31.4641	1.07731	0.538654	−	0.842527i	$-0.318933\pi$
$853$	31.4641	1.07731	0.538654	+	0.842527i	$0.318933\pi$
$854$	39.1014	1.33802
$855$	−44.1492	−1.50987
$856$	−7.34383	−0.251007
$857$	6.72237	0.229632	0.114816	−	0.993387i	$-0.463372\pi$
$857$	6.72237	0.229632	0.114816	+	0.993387i	$0.463372\pi$
$858$	−0.0759198	−0.00259186
$859$	−9.99514	−0.341030	−0.170515	−	0.985355i	$-0.554543\pi$
$859$	−9.99514	−0.341030	−0.170515	+	0.985355i	$0.554543\pi$
$860$	−44.4055	−1.51422
$861$	−6.93637	−0.236391
$862$	43.3391	1.47613
$863$	−3.49537	−0.118984	−0.0594919	−	0.998229i	$-0.518948\pi$
$863$	−3.49537	−0.118984	−0.0594919	+	0.998229i	$0.518948\pi$
$864$	18.2324	0.620279
$865$	−63.2230	−2.14965
$866$	−60.4631	−2.05462
$867$	6.65971	0.226176
$868$	−8.12314	−0.275717
$869$	4.47336	0.151748
$870$	18.9054	0.640952
$871$	2.61166	0.0884928
$872$	−10.7396	−0.363689
$873$	45.2672	1.53206
$874$	−9.39323	−0.317731
$875$	31.2876	1.05771
$876$	2.81191	0.0950055
$877$	12.5442	0.423587	0.211793	−	0.977314i	$-0.432070\pi$
$877$	12.5442	0.423587	0.211793	+	0.977314i	$0.432070\pi$
$878$	−29.9948	−1.01228
$879$	−11.9472	−0.402968
$880$	−5.52003	−0.186080
$881$	−28.2916	−0.953167	−0.476584	−	0.879129i	$-0.658125\pi$
$881$	−28.2916	−0.953167	−0.476584	+	0.879129i	$0.658125\pi$
$882$	4.63070	0.155924
$883$	−31.9432	−1.07498	−0.537488	−	0.843271i	$-0.680627\pi$
$883$	−31.9432	−1.07498	−0.537488	+	0.843271i	$0.680627\pi$
$884$	0.666311	0.0224105
$885$	−9.86183	−0.331502
$886$	−22.3304	−0.750205
$887$	−27.3278	−0.917577	−0.458789	−	0.888545i	$-0.651717\pi$
$887$	−27.3278	−0.917577	−0.458789	+	0.888545i	$0.651717\pi$
$888$	0.0673810	0.00226116
$889$	59.3892	1.99185
$890$	18.1458	0.608249
$891$	2.14828	0.0719701
$892$	−13.1976	−0.441887
$893$	59.9545	2.00630
$894$	8.61622	0.288170
$895$	47.8495	1.59943
$896$	−26.2381	−0.876553
$897$	0.155620	0.00519602
$898$	−42.1976	−1.40815
$899$	−12.7677	−0.425826
$900$	−29.4426	−0.981421
$901$	1.13771	0.0379026
$902$	−2.85366	−0.0950164
$903$	12.8344	0.427103
$904$	−19.2996	−0.641894
$905$	81.7187	2.71642
$906$	−5.87178	−0.195077
$907$	−12.5279	−0.415983	−0.207991	−	0.978131i	$-0.566693\pi$
$907$	−12.5279	−0.415983	−0.207991	+	0.978131i	$0.566693\pi$
$908$	−5.80446	−0.192628
$909$	12.1127	0.401752
$910$	5.04979	0.167399
$911$	44.5657	1.47653	0.738264	−	0.674512i	$-0.235646\pi$
$911$	44.5657	1.47653	0.738264	+	0.674512i	$0.235646\pi$
$912$	10.6334	0.352108
$913$	−0.145535	−0.00481649
$914$	−22.7730	−0.753265
$915$	13.5268	0.447183
$916$	−8.51656	−0.281395
$917$	11.4141	0.376925
$918$	9.53825	0.314809
$919$	−29.8021	−0.983080	−0.491540	−	0.870855i	$-0.663566\pi$
$919$	−29.8021	−0.983080	−0.491540	+	0.870855i	$0.663566\pi$
$920$	5.20738	0.171682
$921$	10.0155	0.330023
$922$	64.2328	2.11539
$923$	−1.65077	−0.0543357
$924$	−0.569047	−0.0187203
$925$	−0.896630	−0.0294810
$926$	−8.71778	−0.286484
$927$	−10.6725	−0.350532
$928$	37.7130	1.23799
$929$	−0.506662	−0.0166231	−0.00831153	−	0.999965i	$-0.502646\pi$
$929$	−0.506662	−0.0166231	−0.00831153	+	0.999965i	$0.502646\pi$
$930$	−7.06294	−0.231603
$931$	4.07500	0.133553
$932$	−19.0321	−0.623417
$933$	2.39362	0.0783637
$934$	−17.3883	−0.568963
$935$	−2.08755	−0.0682701
$936$	0.928917	0.0303626
$937$	44.2460	1.44545	0.722727	−	0.691133i	$-0.242888\pi$
$937$	44.2460	1.44545	0.722727	+	0.691133i	$0.242888\pi$
$938$	49.2004	1.60645
$939$	−14.7933	−0.482762
$940$	64.7419	2.11165
$941$	−2.85417	−0.0930433	−0.0465217	−	0.998917i	$-0.514814\pi$
$941$	−2.85417	−0.0930433	−0.0465217	+	0.998917i	$0.514814\pi$
$942$	0.0494259	0.00161038
$943$	5.84943	0.190483
$944$	−27.2141	−0.885743
$945$	28.7612	0.935601
$946$	5.28015	0.171672
$947$	43.1447	1.40201	0.701007	−	0.713154i	$-0.252734\pi$
$947$	43.1447	1.40201	0.701007	+	0.713154i	$0.252734\pi$
$948$	−9.30528	−0.302221
$949$	1.18053	0.0383216
$950$	−65.1202	−2.11278
$951$	−12.9129	−0.418729
$952$	−6.44420	−0.208858
$953$	7.73163	0.250452	0.125226	−	0.992128i	$-0.460034\pi$
$953$	7.73163	0.250452	0.125226	+	0.992128i	$0.460034\pi$
$954$	−3.08952	−0.100027
$955$	−33.4717	−1.08312
$956$	−8.89004	−0.287524
$957$	−0.894409	−0.0289121
$958$	30.3288	0.979880
$959$	−39.1328	−1.26366
$960$	3.48505	0.112480
$961$	−26.2301	−0.846131
$962$	−0.0551027	−0.00177658
$963$	16.3874	0.528077
$964$	−27.1126	−0.873238
$965$	−73.5373	−2.36725
$966$	2.93169	0.0943256
$967$	42.7728	1.37548	0.687740	−	0.725957i	$-0.258603\pi$
$967$	42.7728	1.37548	0.687740	+	0.725957i	$0.258603\pi$
$968$	−13.4812	−0.433304
$969$	4.02132	0.129183
$970$	108.115	3.47137
$971$	15.1038	0.484703	0.242352	−	0.970189i	$-0.422081\pi$
$971$	15.1038	0.484703	0.242352	+	0.970189i	$0.422081\pi$
$972$	−15.6737	−0.502735
$973$	46.4619	1.48950
$974$	−60.3118	−1.93252
$975$	1.07887	0.0345514
$976$	37.3277	1.19483
$977$	−28.9371	−0.925780	−0.462890	−	0.886416i	$-0.653188\pi$
$977$	−28.9371	−0.925780	−0.462890	+	0.886416i	$0.653188\pi$
$978$	−14.2668	−0.456201
$979$	−0.858474	−0.0274369
$980$	4.40039	0.140565
$981$	23.9650	0.765142
$982$	−9.46166	−0.301934
$983$	−49.2962	−1.57231	−0.786153	−	0.618032i	$-0.787930\pi$
$983$	−49.2962	−1.57231	−0.786153	+	0.618032i	$0.787930\pi$
$984$	−3.04746	−0.0971494
$985$	14.1089	0.449548
$986$	19.7295	0.628316
$987$	−18.7122	−0.595616
$988$	−1.59227	−0.0506568
$989$	−10.8232	−0.344159
$990$	5.66886	0.180168
$991$	37.6633	1.19642	0.598208	−	0.801341i	$-0.295880\pi$
$991$	37.6633	1.19642	0.598208	+	0.801341i	$0.295880\pi$
$992$	−14.0894	−0.447338
$993$	−10.9840	−0.348567
$994$	−31.0984	−0.986380
$995$	59.2049	1.87692
$996$	0.302734	0.00959250
$997$	−20.1504	−0.638170	−0.319085	−	0.947726i	$-0.603376\pi$
$997$	−20.1504	−0.638170	−0.319085	+	0.947726i	$0.603376\pi$
$998$	−15.6570	−0.495614
$999$	−0.313838	−0.00992940

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.a.b.1.4	✓	17
3.2	odd	2		3141.2.a.e.1.14		17
4.3	odd	2		5584.2.a.m.1.11		17
5.4	even	2		8725.2.a.m.1.14		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.a.b.1.4	✓	17	1.1	even	1	trivial
3141.2.a.e.1.14		17	3.2	odd	2
5584.2.a.m.1.11		17	4.3	odd	2
8725.2.a.m.1.14		17	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.a (trivial)

\(f(q)\)	\(=\)	\(q-1.82251 q^{2} -0.490735 q^{3} +1.32154 q^{4} +3.61587 q^{5} +0.894370 q^{6} +2.81440 q^{7} +1.23649 q^{8} -2.75918 q^{9} +O(q^{10})\)	\(q-1.82251 q^{2} -0.490735 q^{3} +1.32154 q^{4} +3.61587 q^{5} +0.894370 q^{6} +2.81440 q^{7} +1.23649 q^{8} -2.75918 q^{9} -6.58995 q^{10} +0.311769 q^{11} -0.648528 q^{12} -0.272273 q^{13} -5.12928 q^{14} -1.77443 q^{15} -4.89661 q^{16} -1.85179 q^{17} +5.02863 q^{18} +4.42517 q^{19} +4.77853 q^{20} -1.38113 q^{21} -0.568203 q^{22} +1.16470 q^{23} -0.606791 q^{24} +8.07449 q^{25} +0.496221 q^{26} +2.82623 q^{27} +3.71936 q^{28} +5.84596 q^{29} +3.23392 q^{30} -2.18402 q^{31} +6.45113 q^{32} -0.152996 q^{33} +3.37490 q^{34} +10.1765 q^{35} -3.64637 q^{36} -0.111045 q^{37} -8.06492 q^{38} +0.133614 q^{39} +4.47100 q^{40} +5.02225 q^{41} +2.51712 q^{42} -9.29272 q^{43} +0.412017 q^{44} -9.97682 q^{45} -2.12268 q^{46} +13.5485 q^{47} +2.40294 q^{48} +0.920867 q^{49} -14.7158 q^{50} +0.908737 q^{51} -0.359821 q^{52} -0.614386 q^{53} -5.15084 q^{54} +1.12732 q^{55} +3.47999 q^{56} -2.17159 q^{57} -10.6543 q^{58} +5.55774 q^{59} -2.34499 q^{60} -7.62317 q^{61} +3.98039 q^{62} -7.76544 q^{63} -1.96404 q^{64} -0.984504 q^{65} +0.278837 q^{66} -9.59207 q^{67} -2.44722 q^{68} -0.571560 q^{69} -18.5468 q^{70} +6.06291 q^{71} -3.41171 q^{72} -4.33583 q^{73} +0.202380 q^{74} -3.96244 q^{75} +5.84806 q^{76} +0.877444 q^{77} -0.243513 q^{78} +14.3483 q^{79} -17.7055 q^{80} +6.89061 q^{81} -9.15311 q^{82} -0.466802 q^{83} -1.82522 q^{84} -6.69581 q^{85} +16.9361 q^{86} -2.86882 q^{87} +0.385501 q^{88} -2.75356 q^{89} +18.1829 q^{90} -0.766287 q^{91} +1.53920 q^{92} +1.07177 q^{93} -24.6923 q^{94} +16.0008 q^{95} -3.16580 q^{96} -16.4060 q^{97} -1.67829 q^{98} -0.860227 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9}+O(q^{10}) \) 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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