LMFDB - Embedded newform 349.2.a.b.1.14

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			1.14
Root			$2.18773$ 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)

$f(q)$	$=$	$q+2.18773 q^{2} +1.16554 q^{3} +2.78617 q^{4} +0.568409 q^{5} +2.54988 q^{6} +0.610781 q^{7} +1.71993 q^{8} -1.64153 q^{9} +O(q^{10})$	\(q+2.18773 q^{2} +1.16554 q^{3} +2.78617 q^{4} +0.568409 q^{5} +2.54988 q^{6} +0.610781 q^{7} +1.71993 q^{8} -1.64153 q^{9} +1.24353 q^{10} -2.93934 q^{11} +3.24738 q^{12} -0.274046 q^{13} +1.33622 q^{14} +0.662500 q^{15} -1.80960 q^{16} +0.122536 q^{17} -3.59122 q^{18} +1.54031 q^{19} +1.58368 q^{20} +0.711886 q^{21} -6.43048 q^{22} +0.331969 q^{23} +2.00464 q^{24} -4.67691 q^{25} -0.599539 q^{26} -5.40986 q^{27} +1.70174 q^{28} +8.59295 q^{29} +1.44937 q^{30} +5.79433 q^{31} -7.39877 q^{32} -3.42590 q^{33} +0.268076 q^{34} +0.347173 q^{35} -4.57358 q^{36} -3.66019 q^{37} +3.36978 q^{38} -0.319410 q^{39} +0.977623 q^{40} +8.17001 q^{41} +1.55742 q^{42} +1.77982 q^{43} -8.18949 q^{44} -0.933059 q^{45} +0.726259 q^{46} +1.23528 q^{47} -2.10915 q^{48} -6.62695 q^{49} -10.2318 q^{50} +0.142820 q^{51} -0.763539 q^{52} +3.59972 q^{53} -11.8353 q^{54} -1.67075 q^{55} +1.05050 q^{56} +1.79528 q^{57} +18.7991 q^{58} -5.50814 q^{59} +1.84584 q^{60} -4.74598 q^{61} +12.6764 q^{62} -1.00261 q^{63} -12.5673 q^{64} -0.155770 q^{65} -7.49495 q^{66} +5.95564 q^{67} +0.341406 q^{68} +0.386922 q^{69} +0.759522 q^{70} -1.76887 q^{71} -2.82331 q^{72} -1.64166 q^{73} -8.00751 q^{74} -5.45110 q^{75} +4.29156 q^{76} -1.79529 q^{77} -0.698784 q^{78} +4.55765 q^{79} -1.02859 q^{80} -1.38080 q^{81} +17.8738 q^{82} +2.82122 q^{83} +1.98344 q^{84} +0.0696505 q^{85} +3.89376 q^{86} +10.0154 q^{87} -5.05545 q^{88} -4.83085 q^{89} -2.04128 q^{90} -0.167382 q^{91} +0.924922 q^{92} +6.75349 q^{93} +2.70245 q^{94} +0.875525 q^{95} -8.62353 q^{96} +0.739640 q^{97} -14.4980 q^{98} +4.82500 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.18773	1.54696	0.773480	−	0.633821i	$-0.218514\pi$
$2$	2.18773	1.54696	0.773480	+	0.633821i	$0.218514\pi$
$3$	1.16554	0.672922	0.336461	−	0.941697i	$-0.390770\pi$
$3$	1.16554	0.672922	0.336461	+	0.941697i	$0.390770\pi$
$4$	2.78617	1.39309
$5$	0.568409	0.254200	0.127100	−	0.991890i	$-0.459433\pi$
$5$	0.568409	0.254200	0.127100	+	0.991890i	$0.459433\pi$
$6$	2.54988	1.04098
$7$	0.610781	0.230853	0.115427	−	0.993316i	$-0.463176\pi$
$7$	0.610781	0.230853	0.115427	+	0.993316i	$0.463176\pi$
$8$	1.71993	0.608087
$9$	−1.64153	−0.547176
$10$	1.24353	0.393237
$11$	−2.93934	−0.886243	−0.443122	−	0.896461i	$-0.646129\pi$
$11$	−2.93934	−0.886243	−0.443122	+	0.896461i	$0.646129\pi$
$12$	3.24738	0.937438
$13$	−0.274046	−0.0760067	−0.0380033	−	0.999278i	$-0.512100\pi$
$13$	−0.274046	−0.0760067	−0.0380033	+	0.999278i	$0.512100\pi$
$14$	1.33622	0.357121
$15$	0.662500	0.171057
$16$	−1.80960	−0.452399
$17$	0.122536	0.0297193	0.0148597	−	0.999890i	$-0.495270\pi$
$17$	0.122536	0.0297193	0.0148597	+	0.999890i	$0.495270\pi$
$18$	−3.59122	−0.846459
$19$	1.54031	0.353371	0.176686	−	0.984267i	$-0.443462\pi$
$19$	1.54031	0.353371	0.176686	+	0.984267i	$0.443462\pi$
$20$	1.58368	0.354122
$21$	0.711886	0.155346
$22$	−6.43048	−1.37098
$23$	0.331969	0.0692203	0.0346102	−	0.999401i	$-0.488981\pi$
$23$	0.331969	0.0692203	0.0346102	+	0.999401i	$0.488981\pi$
$24$	2.00464	0.409195
$25$	−4.67691	−0.935382
$26$	−0.599539	−0.117579
$27$	−5.40986	−1.04113
$28$	1.70174	0.321598
$29$	8.59295	1.59567	0.797836	−	0.602875i	$-0.205978\pi$
$29$	8.59295	1.59567	0.797836	+	0.602875i	$0.205978\pi$
$30$	1.44937	0.264618
$31$	5.79433	1.04069	0.520346	−	0.853955i	$-0.325803\pi$
$31$	5.79433	1.04069	0.520346	+	0.853955i	$0.325803\pi$
$32$	−7.39877	−1.30793
$33$	−3.42590	−0.596373
$34$	0.268076	0.0459746
$35$	0.347173	0.0586830
$36$	−4.57358	−0.762263
$37$	−3.66019	−0.601731	−0.300866	−	0.953667i	$-0.597276\pi$
$37$	−3.66019	−0.601731	−0.300866	+	0.953667i	$0.597276\pi$
$38$	3.36978	0.546651
$39$	−0.319410	−0.0511466
$40$	0.977623	0.154576
$41$	8.17001	1.27594	0.637970	−	0.770061i	$-0.279774\pi$
$41$	8.17001	1.27594	0.637970	+	0.770061i	$0.279774\pi$
$42$	1.55742	0.240314
$43$	1.77982	0.271419	0.135710	−	0.990749i	$-0.456669\pi$
$43$	1.77982	0.271419	0.135710	+	0.990749i	$0.456669\pi$
$44$	−8.18949	−1.23461
$45$	−0.933059	−0.139092
$46$	0.726259	0.107081
$47$	1.23528	0.180183	0.0900917	−	0.995933i	$-0.471284\pi$
$47$	1.23528	0.180183	0.0900917	+	0.995933i	$0.471284\pi$
$48$	−2.10915	−0.304429
$49$	−6.62695	−0.946707
$50$	−10.2318	−1.44700
$51$	0.142820	0.0199988
$52$	−0.763539	−0.105884
$53$	3.59972	0.494459	0.247230	−	0.968957i	$-0.420480\pi$
$53$	3.59972	0.494459	0.247230	+	0.968957i	$0.420480\pi$
$54$	−11.8353	−1.61058
$55$	−1.67075	−0.225283
$56$	1.05050	0.140379
$57$	1.79528	0.237791
$58$	18.7991	2.46844
$59$	−5.50814	−0.717099	−0.358550	−	0.933511i	$-0.616729\pi$
$59$	−5.50814	−0.717099	−0.358550	+	0.933511i	$0.616729\pi$
$60$	1.84584	0.238297
$61$	−4.74598	−0.607661	−0.303831	−	0.952726i	$-0.598266\pi$
$61$	−4.74598	−0.607661	−0.303831	+	0.952726i	$0.598266\pi$
$62$	12.6764	1.60991
$63$	−1.00261	−0.126317
$64$	−12.5673	−1.57092
$65$	−0.155770	−0.0193209
$66$	−7.49495	−0.922565
$67$	5.95564	0.727597	0.363799	−	0.931478i	$-0.381480\pi$
$67$	5.95564	0.727597	0.363799	+	0.931478i	$0.381480\pi$
$68$	0.341406	0.0414016
$69$	0.386922	0.0465799
$70$	0.759522	0.0907802
$71$	−1.76887	−0.209926	−0.104963	−	0.994476i	$-0.533472\pi$
$71$	−1.76887	−0.209926	−0.104963	+	0.994476i	$0.533472\pi$
$72$	−2.82331	−0.332731
$73$	−1.64166	−0.192142	−0.0960711	−	0.995374i	$-0.530628\pi$
$73$	−1.64166	−0.192142	−0.0960711	+	0.995374i	$0.530628\pi$
$74$	−8.00751	−0.930854
$75$	−5.45110	−0.629439
$76$	4.29156	0.492276
$77$	−1.79529	−0.204592
$78$	−0.698784	−0.0791217
$79$	4.55765	0.512776	0.256388	−	0.966574i	$-0.417467\pi$
$79$	4.55765	0.512776	0.256388	+	0.966574i	$0.417467\pi$
$80$	−1.02859	−0.115000
$81$	−1.38080	−0.153422
$82$	17.8738	1.97383
$83$	2.82122	0.309669	0.154835	−	0.987940i	$-0.450516\pi$
$83$	2.82122	0.309669	0.154835	+	0.987940i	$0.450516\pi$
$84$	1.98344	0.216411
$85$	0.0696505	0.00755466
$86$	3.89376	0.419875
$87$	10.0154	1.07376
$88$	−5.05545	−0.538913
$89$	−4.83085	−0.512069	−0.256035	−	0.966668i	$-0.582416\pi$
$89$	−4.83085	−0.512069	−0.256035	+	0.966668i	$0.582416\pi$
$90$	−2.04128	−0.215170
$91$	−0.167382	−0.0175464
$92$	0.924922	0.0964298
$93$	6.75349	0.700305
$94$	2.70245	0.278737
$95$	0.875525	0.0898270
$96$	−8.62353	−0.880135
$97$	0.739640	0.0750991	0.0375496	−	0.999295i	$-0.488045\pi$
$97$	0.739640	0.0750991	0.0375496	+	0.999295i	$0.488045\pi$
$98$	−14.4980	−1.46452
$99$	4.82500	0.484931
$100$	−13.0307	−1.30307
$101$	3.02952	0.301449	0.150724	−	0.988576i	$-0.451839\pi$
$101$	3.02952	0.301449	0.150724	+	0.988576i	$0.451839\pi$
$102$	0.312452	0.0309373
$103$	−7.12181	−0.701733	−0.350866	−	0.936426i	$-0.614113\pi$
$103$	−7.12181	−0.701733	−0.350866	+	0.936426i	$0.614113\pi$
$104$	−0.471340	−0.0462187
$105$	0.404642	0.0394891
$106$	7.87522	0.764909
$107$	−1.31358	−0.126989	−0.0634944	−	0.997982i	$-0.520224\pi$
$107$	−1.31358	−0.126989	−0.0634944	+	0.997982i	$0.520224\pi$
$108$	−15.0728	−1.45038
$109$	−5.30432	−0.508062	−0.254031	−	0.967196i	$-0.581756\pi$
$109$	−5.30432	−0.508062	−0.254031	+	0.967196i	$0.581756\pi$
$110$	−3.65514	−0.348504
$111$	−4.26608	−0.404918
$112$	−1.10527	−0.104438
$113$	19.4364	1.82842	0.914211	−	0.405237i	$-0.132811\pi$
$113$	19.4364	1.82842	0.914211	+	0.405237i	$0.132811\pi$
$114$	3.92760	0.367853
$115$	0.188694	0.0175958
$116$	23.9414	2.22291
$117$	0.449854	0.0415890
$118$	−12.0503	−1.10932
$119$	0.0748426	0.00686081
$120$	1.13945	0.104017
$121$	−2.36030	−0.214573
$122$	−10.3829	−0.940027
$123$	9.52243	0.858609
$124$	16.1440	1.44977
$125$	−5.50044	−0.491975
$126$	−2.19345	−0.195408
$127$	10.9845	0.974717	0.487359	−	0.873202i	$-0.337960\pi$
$127$	10.9845	0.974717	0.487359	+	0.873202i	$0.337960\pi$
$128$	−12.6964	−1.12221
$129$	2.07444	0.182644
$130$	−0.340783	−0.0298887
$131$	17.4022	1.52043	0.760217	−	0.649669i	$-0.225093\pi$
$131$	17.4022	1.52043	0.760217	+	0.649669i	$0.225093\pi$
$132$	−9.54514	−0.830798
$133$	0.940791	0.0815769
$134$	13.0293	1.12556
$135$	−3.07501	−0.264655
$136$	0.210753	0.0180719
$137$	−7.72993	−0.660413	−0.330206	−	0.943909i	$-0.607118\pi$
$137$	−7.72993	−0.660413	−0.330206	+	0.943909i	$0.607118\pi$
$138$	0.846481	0.0720572
$139$	0.807533	0.0684941	0.0342470	−	0.999413i	$-0.489097\pi$
$139$	0.807533	0.0684941	0.0342470	+	0.999413i	$0.489097\pi$
$140$	0.967283	0.0817504
$141$	1.43976	0.121249
$142$	−3.86982	−0.324748
$143$	0.805513	0.0673604
$144$	2.97050	0.247542
$145$	4.88431	0.405620
$146$	−3.59152	−0.297236
$147$	−7.72394	−0.637060
$148$	−10.1979	−0.838263
$149$	−4.49628	−0.368349	−0.184175	−	0.982894i	$-0.558961\pi$
$149$	−4.49628	−0.368349	−0.184175	+	0.982894i	$0.558961\pi$
$150$	−11.9256	−0.973717
$151$	6.98052	0.568066	0.284033	−	0.958814i	$-0.408327\pi$
$151$	6.98052	0.568066	0.284033	+	0.958814i	$0.408327\pi$
$152$	2.64922	0.214880
$153$	−0.201146	−0.0162617
$154$	−3.92761	−0.316496
$155$	3.29355	0.264544
$156$	−0.889931	−0.0712515
$157$	5.17705	0.413173	0.206587	−	0.978428i	$-0.433764\pi$
$157$	5.17705	0.413173	0.206587	+	0.978428i	$0.433764\pi$
$158$	9.97093	0.793244
$159$	4.19560	0.332733
$160$	−4.20553	−0.332476
$161$	0.202760	0.0159797
$162$	−3.02082	−0.237338
$163$	8.26637	0.647472	0.323736	−	0.946147i	$-0.395061\pi$
$163$	8.26637	0.647472	0.323736	+	0.946147i	$0.395061\pi$
$164$	22.7630	1.77749
$165$	−1.94731	−0.151598
$166$	6.17207	0.479046
$167$	−15.9874	−1.23714	−0.618571	−	0.785729i	$-0.712288\pi$
$167$	−15.9874	−1.23714	−0.618571	+	0.785729i	$0.712288\pi$
$168$	1.22439	0.0944641
$169$	−12.9249	−0.994223
$170$	0.152377	0.0116868
$171$	−2.52846	−0.193356
$172$	4.95887	0.378110
$173$	−10.1851	−0.774356	−0.387178	−	0.922005i	$-0.626550\pi$
$173$	−10.1851	−0.774356	−0.387178	+	0.922005i	$0.626550\pi$
$174$	21.9110	1.66107
$175$	−2.85657	−0.215936
$176$	5.31901	0.400936
$177$	−6.41993	−0.482552
$178$	−10.5686	−0.792150
$179$	−7.53150	−0.562931	−0.281465	−	0.959571i	$-0.590820\pi$
$179$	−7.53150	−0.562931	−0.281465	+	0.959571i	$0.590820\pi$
$180$	−2.59966	−0.193767
$181$	−17.2252	−1.28034	−0.640169	−	0.768234i	$-0.721136\pi$
$181$	−17.2252	−1.28034	−0.640169	+	0.768234i	$0.721136\pi$
$182$	−0.366187	−0.0271436
$183$	−5.53161	−0.408908
$184$	0.570964	0.0420920
$185$	−2.08048	−0.152960
$186$	14.7748	1.08334
$187$	−0.360175	−0.0263386
$188$	3.44169	0.251011
$189$	−3.30424	−0.240348
$190$	1.91541	0.138959
$191$	18.4045	1.33170	0.665850	−	0.746086i	$-0.268069\pi$
$191$	18.4045	1.33170	0.665850	+	0.746086i	$0.268069\pi$
$192$	−14.6477	−1.05710
$193$	18.1546	1.30680	0.653399	−	0.757013i	$-0.273342\pi$
$193$	18.1546	1.30680	0.653399	+	0.757013i	$0.273342\pi$
$194$	1.61814	0.116175
$195$	−0.181556	−0.0130015
$196$	−18.4638	−1.31884
$197$	9.68699	0.690170	0.345085	−	0.938571i	$-0.387850\pi$
$197$	9.68699	0.690170	0.345085	+	0.938571i	$0.387850\pi$
$198$	10.5558	0.750169
$199$	−1.49407	−0.105912	−0.0529559	−	0.998597i	$-0.516864\pi$
$199$	−1.49407	−0.105912	−0.0529559	+	0.998597i	$0.516864\pi$
$200$	−8.04396	−0.568794
$201$	6.94151	0.489616
$202$	6.62778	0.466329
$203$	5.24841	0.368366
$204$	0.397921	0.0278600
$205$	4.64390	0.324344
$206$	−15.5806	−1.08555
$207$	−0.544937	−0.0378757
$208$	0.495912	0.0343853
$209$	−4.52749	−0.313173
$210$	0.885249	0.0610880
$211$	10.7164	0.737749	0.368875	−	0.929479i	$-0.379743\pi$
$211$	10.7164	0.737749	0.368875	+	0.929479i	$0.379743\pi$
$212$	10.0294	0.688824
$213$	−2.06168	−0.141264
$214$	−2.87377	−0.196447
$215$	1.01166	0.0689949
$216$	−9.30459	−0.633097
$217$	3.53906	0.240247
$218$	−11.6044	−0.785951
$219$	−1.91342	−0.129297
$220$	−4.65498	−0.313839
$221$	−0.0335805	−0.00225887
$222$	−9.33304	−0.626392
$223$	−16.5557	−1.10865	−0.554327	−	0.832299i	$-0.687024\pi$
$223$	−16.5557	−1.10865	−0.554327	+	0.832299i	$0.687024\pi$
$224$	−4.51902	−0.301940
$225$	7.67728	0.511819
$226$	42.5216	2.82850
$227$	19.2658	1.27872	0.639359	−	0.768908i	$-0.279200\pi$
$227$	19.2658	1.27872	0.639359	+	0.768908i	$0.279200\pi$
$228$	5.00197	0.331263
$229$	1.00065	0.0661249	0.0330625	−	0.999453i	$-0.489474\pi$
$229$	1.00065	0.0661249	0.0330625	+	0.999453i	$0.489474\pi$
$230$	0.412812	0.0272200
$231$	−2.09247	−0.137675
$232$	14.7793	0.970307
$233$	−3.89548	−0.255201	−0.127601	−	0.991826i	$-0.540728\pi$
$233$	−3.89548	−0.255201	−0.127601	+	0.991826i	$0.540728\pi$
$234$	0.984160	0.0643365
$235$	0.702142	0.0458027
$236$	−15.3466	−0.998980
$237$	5.31211	0.345058
$238$	0.163735	0.0106134
$239$	−9.90993	−0.641020	−0.320510	−	0.947245i	$-0.603854\pi$
$239$	−9.90993	−0.641020	−0.320510	+	0.947245i	$0.603854\pi$
$240$	−1.19886	−0.0773859
$241$	−21.4379	−1.38094	−0.690469	−	0.723362i	$-0.742596\pi$
$241$	−21.4379	−1.38094	−0.690469	+	0.723362i	$0.742596\pi$
$242$	−5.16370	−0.331935
$243$	14.6202	0.937887
$244$	−13.2231	−0.846524
$245$	−3.76682	−0.240653
$246$	20.8325	1.32823
$247$	−0.422115	−0.0268586
$248$	9.96584	0.632831
$249$	3.28823	0.208383
$250$	−12.0335	−0.761065
$251$	24.5026	1.54659	0.773295	−	0.634047i	$-0.218607\pi$
$251$	24.5026	1.54659	0.773295	+	0.634047i	$0.218607\pi$
$252$	−2.79345	−0.175971
$253$	−0.975769	−0.0613461
$254$	24.0312	1.50785
$255$	0.0811801	0.00508370
$256$	−2.64168	−0.165105
$257$	−5.10312	−0.318324	−0.159162	−	0.987252i	$-0.550879\pi$
$257$	−5.10312	−0.318324	−0.159162	+	0.987252i	$0.550879\pi$
$258$	4.53831	0.282543
$259$	−2.23557	−0.138912
$260$	−0.434002	−0.0269157
$261$	−14.1056	−0.873113
$262$	38.0713	2.35205
$263$	17.6978	1.09129	0.545645	−	0.838016i	$-0.316285\pi$
$263$	17.6978	1.09129	0.545645	+	0.838016i	$0.316285\pi$
$264$	−5.89231	−0.362647
$265$	2.04611	0.125692
$266$	2.05820	0.126196
$267$	−5.63053	−0.344583
$268$	16.5934	1.01361
$269$	−12.8072	−0.780868	−0.390434	−	0.920631i	$-0.627675\pi$
$269$	−12.8072	−0.780868	−0.390434	+	0.920631i	$0.627675\pi$
$270$	−6.72731	−0.409411
$271$	6.97193	0.423514	0.211757	−	0.977322i	$-0.432081\pi$
$271$	6.97193	0.423514	0.211757	+	0.977322i	$0.432081\pi$
$272$	−0.221741	−0.0134450
$273$	−0.195089	−0.0118074
$274$	−16.9110	−1.02163
$275$	13.7470	0.828976
$276$	1.07803	0.0648898
$277$	−20.8796	−1.25453	−0.627266	−	0.778805i	$-0.715826\pi$
$277$	−20.8796	−1.25453	−0.627266	+	0.778805i	$0.715826\pi$
$278$	1.76667	0.105958
$279$	−9.51155	−0.569442
$280$	0.597113	0.0356843
$281$	25.6429	1.52973	0.764864	−	0.644191i	$-0.222806\pi$
$281$	25.6429	1.52973	0.764864	+	0.644191i	$0.222806\pi$
$282$	3.14980	0.187568
$283$	−3.57072	−0.212257	−0.106129	−	0.994352i	$-0.533846\pi$
$283$	−3.57072	−0.212257	−0.106129	+	0.994352i	$0.533846\pi$
$284$	−4.92838	−0.292445
$285$	1.02046	0.0604466
$286$	1.76225	0.104204
$287$	4.99008	0.294555
$288$	12.1453	0.715668
$289$	−16.9850	−0.999117
$290$	10.6856	0.627478
$291$	0.862077	0.0505358
$292$	−4.57395	−0.267670
$293$	−28.6780	−1.67539	−0.837694	−	0.546140i	$-0.816097\pi$
$293$	−28.6780	−1.67539	−0.837694	+	0.546140i	$0.816097\pi$
$294$	−16.8979	−0.985506
$295$	−3.13088	−0.182287
$296$	−6.29527	−0.365905
$297$	15.9014	0.922694
$298$	−9.83665	−0.569822
$299$	−0.0909748	−0.00526121
$300$	−15.1877	−0.876863
$301$	1.08708	0.0626581
$302$	15.2715	0.878776
$303$	3.53101	0.202851
$304$	−2.78734	−0.159865
$305$	−2.69766	−0.154468
$306$	−0.440054	−0.0251562
$307$	−26.6106	−1.51874	−0.759372	−	0.650656i	$-0.774494\pi$
$307$	−26.6106	−1.51874	−0.759372	+	0.650656i	$0.774494\pi$
$308$	−5.00198	−0.285014
$309$	−8.30072	−0.472211
$310$	7.20540	0.409239
$311$	14.4297	0.818233	0.409116	−	0.912482i	$-0.365837\pi$
$311$	14.4297	0.818233	0.409116	+	0.912482i	$0.365837\pi$
$312$	−0.549363	−0.0311016
$313$	−0.470669	−0.0266038	−0.0133019	−	0.999912i	$-0.504234\pi$
$313$	−0.470669	−0.0266038	−0.0133019	+	0.999912i	$0.504234\pi$
$314$	11.3260	0.639163
$315$	−0.569894	−0.0321099
$316$	12.6984	0.714341
$317$	5.96206	0.334863	0.167431	−	0.985884i	$-0.446453\pi$
$317$	5.96206	0.334863	0.167431	+	0.985884i	$0.446453\pi$
$318$	9.17884	0.514724
$319$	−25.2576	−1.41415
$320$	−7.14338	−0.399327
$321$	−1.53103	−0.0854535
$322$	0.443585	0.0247200
$323$	0.188743	0.0105020
$324$	−3.84715	−0.213731
$325$	1.28169	0.0710953
$326$	18.0846	1.00161
$327$	−6.18237	−0.341886
$328$	14.0518	0.775883
$329$	0.754482	0.0415959
$330$	−4.26020	−0.234516
$331$	−15.2929	−0.840573	−0.420287	−	0.907391i	$-0.638070\pi$
$331$	−15.2929	−0.840573	−0.420287	+	0.907391i	$0.638070\pi$
$332$	7.86040	0.431396
$333$	6.00830	0.329253
$334$	−34.9761	−1.91381
$335$	3.38524	0.184955
$336$	−1.28823	−0.0702785
$337$	−31.6983	−1.72672	−0.863358	−	0.504591i	$-0.831643\pi$
$337$	−31.6983	−1.72672	−0.863358	+	0.504591i	$0.831643\pi$
$338$	−28.2762	−1.53802
$339$	22.6538	1.23039
$340$	0.194058	0.0105243
$341$	−17.0315	−0.922307
$342$	−5.53159	−0.299114
$343$	−8.32307	−0.449404
$344$	3.06116	0.165047
$345$	0.219930	0.0118406
$346$	−22.2822	−1.19790
$347$	−5.70089	−0.306040	−0.153020	−	0.988223i	$-0.548900\pi$
$347$	−5.70089	−0.306040	−0.153020	+	0.988223i	$0.548900\pi$
$348$	27.9046	1.49584
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	−6.24940	−0.334045
$351$	1.48255	0.0791327
$352$	21.7475	1.15914
$353$	−18.0462	−0.960501	−0.480251	−	0.877131i	$-0.659454\pi$
$353$	−18.0462	−0.960501	−0.480251	+	0.877131i	$0.659454\pi$
$354$	−14.0451	−0.746488
$355$	−1.00544	−0.0533633
$356$	−13.4596	−0.713356
$357$	0.0872317	0.00461679
$358$	−16.4769	−0.870831
$359$	−18.4905	−0.975890	−0.487945	−	0.872874i	$-0.662253\pi$
$359$	−18.4905	−0.975890	−0.487945	+	0.872874i	$0.662253\pi$
$360$	−1.60480	−0.0845802
$361$	−16.6274	−0.875129
$362$	−37.6841	−1.98063
$363$	−2.75101	−0.144391
$364$	−0.466354	−0.0244436
$365$	−0.933136	−0.0488426
$366$	−12.1017	−0.632565
$367$	−13.7619	−0.718364	−0.359182	−	0.933267i	$-0.616944\pi$
$367$	−13.7619	−0.718364	−0.359182	+	0.933267i	$0.616944\pi$
$368$	−0.600730	−0.0313152
$369$	−13.4113	−0.698164
$370$	−4.55154	−0.236623
$371$	2.19864	0.114148
$372$	18.8164	0.975584
$373$	−17.2993	−0.895722	−0.447861	−	0.894103i	$-0.647814\pi$
$373$	−17.2993	−0.895722	−0.447861	+	0.894103i	$0.647814\pi$
$374$	−0.787965	−0.0407447
$375$	−6.41096	−0.331060
$376$	2.12459	0.109567
$377$	−2.35486	−0.121282
$378$	−7.22879	−0.371809
$379$	3.79756	0.195068	0.0975338	−	0.995232i	$-0.468905\pi$
$379$	3.79756	0.195068	0.0975338	+	0.995232i	$0.468905\pi$
$380$	2.43936	0.125137
$381$	12.8028	0.655909
$382$	40.2640	2.06009
$383$	3.49718	0.178697	0.0893487	−	0.996000i	$-0.471521\pi$
$383$	3.49718	0.178697	0.0893487	+	0.996000i	$0.471521\pi$
$384$	−14.7981	−0.755163
$385$	−1.02046	−0.0520074
$386$	39.7175	2.02157
$387$	−2.92162	−0.148514
$388$	2.06076	0.104619
$389$	8.39300	0.425542	0.212771	−	0.977102i	$-0.431751\pi$
$389$	8.39300	0.425542	0.212771	+	0.977102i	$0.431751\pi$
$390$	−0.397195	−0.0201127
$391$	0.0406782	0.00205718
$392$	−11.3979	−0.575680
$393$	20.2828	1.02313
$394$	21.1925	1.06766
$395$	2.59061	0.130348
$396$	13.4433	0.675550
$397$	−23.5711	−1.18300	−0.591501	−	0.806305i	$-0.701464\pi$
$397$	−23.5711	−1.18300	−0.591501	+	0.806305i	$0.701464\pi$
$398$	−3.26863	−0.163841
$399$	1.09652	0.0548949
$400$	8.46332	0.423166
$401$	−28.9986	−1.44812	−0.724061	−	0.689736i	$-0.757727\pi$
$401$	−28.9986	−1.44812	−0.724061	+	0.689736i	$0.757727\pi$
$402$	15.1862	0.757417
$403$	−1.58791	−0.0790995
$404$	8.44076	0.419943
$405$	−0.784860	−0.0390000
$406$	11.4821	0.569847
$407$	10.7585	0.533281
$408$	0.245640	0.0121610
$409$	−35.8552	−1.77293	−0.886464	−	0.462798i	$-0.846846\pi$
$409$	−35.8552	−1.77293	−0.886464	+	0.462798i	$0.846846\pi$
$410$	10.1596	0.501748
$411$	−9.00951	−0.444406
$412$	−19.8426	−0.977573
$413$	−3.36427	−0.165545
$414$	−1.19218	−0.0585922
$415$	1.60361	0.0787180
$416$	2.02760	0.0994114
$417$	0.941208	0.0460912
$418$	−9.90493	−0.484466
$419$	−28.2474	−1.37998	−0.689988	−	0.723821i	$-0.742384\pi$
$419$	−28.2474	−1.37998	−0.689988	+	0.723821i	$0.742384\pi$
$420$	1.12740	0.0550116
$421$	−8.63453	−0.420821	−0.210411	−	0.977613i	$-0.567480\pi$
$421$	−8.63453	−0.420821	−0.210411	+	0.977613i	$0.567480\pi$
$422$	23.4447	1.14127
$423$	−2.02774	−0.0985921
$424$	6.19126	0.300674
$425$	−0.573090	−0.0277989
$426$	−4.51041	−0.218530
$427$	−2.89875	−0.140281
$428$	−3.65986	−0.176906
$429$	0.938854	0.0453283
$430$	2.21325	0.106732
$431$	21.4810	1.03470	0.517351	−	0.855773i	$-0.326918\pi$
$431$	21.4810	1.03470	0.517351	+	0.855773i	$0.326918\pi$
$432$	9.78967	0.471005
$433$	15.4989	0.744831	0.372415	−	0.928066i	$-0.378530\pi$
$433$	15.4989	0.744831	0.372415	+	0.928066i	$0.378530\pi$
$434$	7.74252	0.371653
$435$	5.69283	0.272951
$436$	−14.7787	−0.707773
$437$	0.511335	0.0244605
$438$	−4.18604	−0.200017
$439$	−36.2997	−1.73249	−0.866245	−	0.499620i	$-0.833473\pi$
$439$	−36.2997	−1.73249	−0.866245	+	0.499620i	$0.833473\pi$
$440$	−2.87356	−0.136992
$441$	10.8783	0.518015
$442$	−0.0734651	−0.00349438
$443$	15.3466	0.729141	0.364571	−	0.931176i	$-0.381216\pi$
$443$	15.3466	0.729141	0.364571	+	0.931176i	$0.381216\pi$
$444$	−11.8860	−0.564086
$445$	−2.74590	−0.130168
$446$	−36.2195	−1.71504
$447$	−5.24057	−0.247870
$448$	−7.67588	−0.362651
$449$	30.0773	1.41944	0.709719	−	0.704485i	$-0.248822\pi$
$449$	30.0773	1.41944	0.709719	+	0.704485i	$0.248822\pi$
$450$	16.7958	0.791763
$451$	−24.0144	−1.13079
$452$	54.1531	2.54715
$453$	8.13604	0.382264
$454$	42.1485	1.97813
$455$	−0.0951414	−0.00446030
$456$	3.08776	0.144598
$457$	32.5593	1.52306	0.761531	−	0.648129i	$-0.224448\pi$
$457$	32.5593	1.52306	0.761531	+	0.648129i	$0.224448\pi$
$458$	2.18916	0.102293
$459$	−0.662903	−0.0309417
$460$	0.525734	0.0245125
$461$	22.4698	1.04652	0.523262	−	0.852172i	$-0.324715\pi$
$461$	22.4698	1.04652	0.523262	+	0.852172i	$0.324715\pi$
$462$	−4.57777	−0.212977
$463$	24.6082	1.14364	0.571820	−	0.820379i	$-0.306238\pi$
$463$	24.6082	1.14364	0.571820	+	0.820379i	$0.306238\pi$
$464$	−15.5498	−0.721880
$465$	3.83875	0.178018
$466$	−8.52225	−0.394786
$467$	22.8742	1.05849	0.529247	−	0.848468i	$-0.322475\pi$
$467$	22.8742	1.05849	0.529247	+	0.848468i	$0.322475\pi$
$468$	1.25337	0.0579370
$469$	3.63759	0.167968
$470$	1.53610	0.0708549
$471$	6.03403	0.278033
$472$	−9.47362	−0.436059
$473$	−5.23148	−0.240544
$474$	11.6215	0.533792
$475$	−7.20389	−0.330537
$476$	0.208524	0.00955769
$477$	−5.90904	−0.270556
$478$	−21.6803	−0.991632
$479$	35.9176	1.64112	0.820559	−	0.571562i	$-0.193662\pi$
$479$	35.9176	1.64112	0.820559	+	0.571562i	$0.193662\pi$
$480$	−4.90169	−0.223730
$481$	1.00306	0.0457356
$482$	−46.9004	−2.13626
$483$	0.236324	0.0107531
$484$	−6.57619	−0.298918
$485$	0.420418	0.0190902
$486$	31.9851	1.45087
$487$	28.8461	1.30714	0.653572	−	0.756865i	$-0.273270\pi$
$487$	28.8461	1.30714	0.653572	+	0.756865i	$0.273270\pi$
$488$	−8.16276	−0.369511
$489$	9.63475	0.435698
$490$	−8.24078	−0.372281
$491$	21.7733	0.982614	0.491307	−	0.870987i	$-0.336519\pi$
$491$	21.7733	0.982614	0.491307	+	0.870987i	$0.336519\pi$
$492$	26.5311	1.19611
$493$	1.05295	0.0474223
$494$	−0.923475	−0.0415491
$495$	2.74258	0.123270
$496$	−10.4854	−0.470808
$497$	−1.08039	−0.0484622
$498$	7.19377	0.322361
$499$	12.7455	0.570566	0.285283	−	0.958443i	$-0.407912\pi$
$499$	12.7455	0.570566	0.285283	+	0.958443i	$0.407912\pi$
$500$	−15.3252	−0.685362
$501$	−18.6339	−0.832500
$502$	53.6051	2.39251
$503$	−44.1651	−1.96923	−0.984613	−	0.174749i	$-0.944089\pi$
$503$	−44.1651	−1.96923	−0.984613	+	0.174749i	$0.944089\pi$
$504$	−1.72442	−0.0768120
$505$	1.72201	0.0766283
$506$	−2.13472	−0.0948999
$507$	−15.0644	−0.669035
$508$	30.6047	1.35786
$509$	2.31475	0.102600	0.0512998	−	0.998683i	$-0.483664\pi$
$509$	2.31475	0.102600	0.0512998	+	0.998683i	$0.483664\pi$
$510$	0.177600	0.00786428
$511$	−1.00270	−0.0443567
$512$	19.6135	0.866804
$513$	−8.33286	−0.367905
$514$	−11.1643	−0.492434
$515$	−4.04810	−0.178381
$516$	5.77974	0.254439
$517$	−3.63089	−0.159686
$518$	−4.89083	−0.214891
$519$	−11.8711	−0.521081
$520$	−0.267914	−0.0117488
$521$	32.7846	1.43632	0.718159	−	0.695879i	$-0.244985\pi$
$521$	32.7846	1.43632	0.718159	+	0.695879i	$0.244985\pi$
$522$	−30.8592	−1.35067
$523$	−1.40118	−0.0612692	−0.0306346	−	0.999531i	$-0.509753\pi$
$523$	−1.40118	−0.0612692	−0.0306346	+	0.999531i	$0.509753\pi$
$524$	48.4854	2.11809
$525$	−3.32943	−0.145308
$526$	38.7179	1.68818
$527$	0.710014	0.0309287
$528$	6.19949	0.269798
$529$	−22.8898	−0.995209
$530$	4.47634	0.194440
$531$	9.04177	0.392379
$532$	2.62120	0.113644
$533$	−2.23896	−0.0969800
$534$	−12.3181	−0.533055
$535$	−0.746652	−0.0322806
$536$	10.2433	0.442443
$537$	−8.77823	−0.378809
$538$	−28.0187	−1.20797
$539$	19.4788	0.839013
$540$	−8.56751	−0.368687
$541$	−19.1007	−0.821201	−0.410601	−	0.911815i	$-0.634681\pi$
$541$	−19.1007	−0.821201	−0.410601	+	0.911815i	$0.634681\pi$
$542$	15.2527	0.655160
$543$	−20.0766	−0.861567
$544$	−0.906615	−0.0388708
$545$	−3.01502	−0.129149
$546$	−0.426803	−0.0182655
$547$	12.5254	0.535546	0.267773	−	0.963482i	$-0.413712\pi$
$547$	12.5254	0.535546	0.267773	+	0.963482i	$0.413712\pi$
$548$	−21.5369	−0.920011
$549$	7.79067	0.332498
$550$	30.0748	1.28239
$551$	13.2358	0.563864
$552$	0.665478	0.0283246
$553$	2.78373	0.118376
$554$	−45.6789	−1.94071
$555$	−2.42488	−0.102930
$556$	2.24992	0.0954181
$557$	−17.5697	−0.744452	−0.372226	−	0.928142i	$-0.621405\pi$
$557$	−17.5697	−0.744452	−0.372226	+	0.928142i	$0.621405\pi$
$558$	−20.8087	−0.880904
$559$	−0.487751	−0.0206297
$560$	−0.628243	−0.0265481
$561$	−0.419796	−0.0177238
$562$	56.0999	2.36643
$563$	28.1001	1.18428	0.592140	−	0.805835i	$-0.298283\pi$
$563$	28.1001	1.18428	0.592140	+	0.805835i	$0.298283\pi$
$564$	4.01141	0.168911
$565$	11.0478	0.464785
$566$	−7.81178	−0.328354
$567$	−0.843367	−0.0354181
$568$	−3.04233	−0.127653
$569$	15.2513	0.639367	0.319684	−	0.947524i	$-0.396423\pi$
$569$	15.2513	0.639367	0.319684	+	0.947524i	$0.396423\pi$
$570$	2.23248	0.0935084
$571$	24.6464	1.03142	0.515710	−	0.856763i	$-0.327528\pi$
$571$	24.6464	1.03142	0.515710	+	0.856763i	$0.327528\pi$
$572$	2.24430	0.0938388
$573$	21.4510	0.896130
$574$	10.9170	0.455665
$575$	−1.55259	−0.0647475
$576$	20.6296	0.859568
$577$	2.81322	0.117116	0.0585580	−	0.998284i	$-0.481350\pi$
$577$	2.81322	0.117116	0.0585580	+	0.998284i	$0.481350\pi$
$578$	−37.1586	−1.54559
$579$	21.1599	0.879374
$580$	13.6085	0.565063
$581$	1.72315	0.0714882
$582$	1.88599	0.0781769
$583$	−10.5808	−0.438211
$584$	−2.82355	−0.116839
$585$	0.255701	0.0105719
$586$	−62.7398	−2.59176
$587$	31.6204	1.30511	0.652557	−	0.757739i	$-0.273696\pi$
$587$	31.6204	1.30511	0.652557	+	0.757739i	$0.273696\pi$
$588$	−21.5202	−0.887479
$589$	8.92506	0.367750
$590$	−6.84952	−0.281990
$591$	11.2905	0.464430
$592$	6.62346	0.272223
$593$	−8.02592	−0.329585	−0.164793	−	0.986328i	$-0.552695\pi$
$593$	−8.02592	−0.329585	−0.164793	+	0.986328i	$0.552695\pi$
$594$	34.7880	1.42737
$595$	0.0425412	0.00174402
$596$	−12.5274	−0.513142
$597$	−1.74139	−0.0712704
$598$	−0.199028	−0.00813888
$599$	−29.4007	−1.20128	−0.600639	−	0.799520i	$-0.705087\pi$
$599$	−29.4007	−1.20128	−0.600639	+	0.799520i	$0.705087\pi$
$600$	−9.37552	−0.382754
$601$	40.4751	1.65102	0.825508	−	0.564391i	$-0.190889\pi$
$601$	40.4751	1.65102	0.825508	+	0.564391i	$0.190889\pi$
$602$	2.37823	0.0969295
$603$	−9.77635	−0.398124
$604$	19.4489	0.791365
$605$	−1.34161	−0.0545444
$606$	7.72491	0.313803
$607$	−11.3392	−0.460244	−0.230122	−	0.973162i	$-0.573912\pi$
$607$	−11.3392	−0.460244	−0.230122	+	0.973162i	$0.573912\pi$
$608$	−11.3964	−0.462185
$609$	6.11720	0.247882
$610$	−5.90176	−0.238955
$611$	−0.338522	−0.0136951
$612$	−0.560428	−0.0226539
$613$	15.6548	0.632292	0.316146	−	0.948711i	$-0.397611\pi$
$613$	15.6548	0.632292	0.316146	+	0.948711i	$0.397611\pi$
$614$	−58.2168	−2.34944
$615$	5.41263	0.218258
$616$	−3.08777	−0.124410
$617$	−10.4716	−0.421572	−0.210786	−	0.977532i	$-0.567602\pi$
$617$	−10.4716	−0.421572	−0.210786	+	0.977532i	$0.567602\pi$
$618$	−18.1597	−0.730492
$619$	27.1415	1.09091	0.545455	−	0.838140i	$-0.316357\pi$
$619$	27.1415	1.09091	0.545455	+	0.838140i	$0.316357\pi$
$620$	9.17639	0.368532
$621$	−1.79591	−0.0720673
$622$	31.5683	1.26577
$623$	−2.95059	−0.118213
$624$	0.578003	0.0231386
$625$	20.2581	0.810322
$626$	−1.02970	−0.0411550
$627$	−5.27694	−0.210741
$628$	14.4241	0.575586
$629$	−0.448505	−0.0178831
$630$	−1.24678	−0.0496727
$631$	26.7876	1.06640	0.533199	−	0.845990i	$-0.320990\pi$
$631$	26.7876	1.06640	0.533199	+	0.845990i	$0.320990\pi$
$632$	7.83885	0.311813
$633$	12.4904	0.496448
$634$	13.0434	0.518019
$635$	6.24369	0.247773
$636$	11.6897	0.463525
$637$	1.81609	0.0719560
$638$	−55.2568	−2.18764
$639$	2.90365	0.114867
$640$	−7.21675	−0.285267
$641$	−1.31730	−0.0520301	−0.0260151	−	0.999662i	$-0.508282\pi$
$641$	−1.31730	−0.0520301	−0.0260151	+	0.999662i	$0.508282\pi$
$642$	−3.34947	−0.132193
$643$	11.8389	0.466881	0.233441	−	0.972371i	$-0.425002\pi$
$643$	11.8389	0.466881	0.233441	+	0.972371i	$0.425002\pi$
$644$	0.564925	0.0222611
$645$	1.17913	0.0464282
$646$	0.412920	0.0162461
$647$	−22.3982	−0.880563	−0.440281	−	0.897860i	$-0.645121\pi$
$647$	−22.3982	−0.880563	−0.440281	+	0.897860i	$0.645121\pi$
$648$	−2.37488	−0.0932942
$649$	16.1903	0.635524
$650$	2.80399	0.109982
$651$	4.12490	0.161668
$652$	23.0315	0.901984
$653$	−20.5895	−0.805729	−0.402865	−	0.915260i	$-0.631985\pi$
$653$	−20.5895	−0.805729	−0.402865	+	0.915260i	$0.631985\pi$
$654$	−13.5254	−0.528884
$655$	9.89154	0.386495
$656$	−14.7844	−0.577234
$657$	2.69484	0.105136
$658$	1.65060	0.0643473
$659$	13.5074	0.526174	0.263087	−	0.964772i	$-0.415259\pi$
$659$	13.5074	0.526174	0.263087	+	0.964772i	$0.415259\pi$
$660$	−5.42554	−0.211189
$661$	−15.4481	−0.600863	−0.300432	−	0.953803i	$-0.597131\pi$
$661$	−15.4481	−0.600863	−0.300432	+	0.953803i	$0.597131\pi$
$662$	−33.4567	−1.30033
$663$	−0.0391392	−0.00152004
$664$	4.85230	0.188306
$665$	0.534754	0.0207369
$666$	13.1446	0.509341
$667$	2.85259	0.110453
$668$	−44.5436	−1.72344
$669$	−19.2963	−0.746038
$670$	7.40600	0.286119
$671$	13.9500	0.538536
$672$	−5.26708	−0.203182
$673$	−35.1314	−1.35422	−0.677108	−	0.735884i	$-0.736767\pi$
$673$	−35.1314	−1.35422	−0.677108	+	0.735884i	$0.736767\pi$
$674$	−69.3474	−2.67116
$675$	25.3015	0.973853
$676$	−36.0110	−1.38504
$677$	−20.4506	−0.785981	−0.392990	−	0.919543i	$-0.628559\pi$
$677$	−20.4506	−0.785981	−0.392990	+	0.919543i	$0.628559\pi$
$678$	49.5605	1.90336
$679$	0.451758	0.0173369
$680$	0.119794	0.00459389
$681$	22.4550	0.860477
$682$	−37.2603	−1.42677
$683$	−26.7212	−1.02246	−0.511229	−	0.859444i	$-0.670810\pi$
$683$	−26.7212	−1.02246	−0.511229	+	0.859444i	$0.670810\pi$
$684$	−7.04472	−0.269362
$685$	−4.39376	−0.167877
$686$	−18.2087	−0.695210
$687$	1.16629	0.0444969
$688$	−3.22075	−0.122790
$689$	−0.986488	−0.0375822
$690$	0.481147	0.0183170
$691$	−6.24678	−0.237639	−0.118819	−	0.992916i	$-0.537911\pi$
$691$	−6.24678	−0.237639	−0.118819	+	0.992916i	$0.537911\pi$
$692$	−28.3773	−1.07874
$693$	2.94702	0.111948
$694$	−12.4720	−0.473432
$695$	0.459009	0.0174112
$696$	17.2258	0.652941
$697$	1.00112	0.0379201
$698$	2.18773	0.0828069
$699$	−4.54031	−0.171730
$700$	−7.95888	−0.300817
$701$	20.9270	0.790401	0.395201	−	0.918595i	$-0.370675\pi$
$701$	20.9270	0.790401	0.395201	+	0.918595i	$0.370675\pi$
$702$	3.24342	0.122415
$703$	−5.63782	−0.212634
$704$	36.9396	1.39221
$705$	0.818371	0.0308216
$706$	−39.4802	−1.48586
$707$	1.85037	0.0695904
$708$	−17.8870	−0.672236
$709$	26.0326	0.977676	0.488838	−	0.872375i	$-0.337421\pi$
$709$	26.0326	0.977676	0.488838	+	0.872375i	$0.337421\pi$
$710$	−2.19964	−0.0825509
$711$	−7.48152	−0.280579
$712$	−8.30872	−0.311383
$713$	1.92354	0.0720371
$714$	0.190839	0.00714199
$715$	0.457861	0.0171230
$716$	−20.9840	−0.784211
$717$	−11.5504	−0.431356
$718$	−40.4522	−1.50966
$719$	−22.9846	−0.857181	−0.428590	−	0.903499i	$-0.640990\pi$
$719$	−22.9846	−0.857181	−0.428590	+	0.903499i	$0.640990\pi$
$720$	1.68846	0.0629252
$721$	−4.34986	−0.161997
$722$	−36.3764	−1.35379
$723$	−24.9867	−0.929264
$724$	−47.9923	−1.78362
$725$	−40.1885	−1.49256
$726$	−6.01847	−0.223366
$727$	2.65683	0.0985364	0.0492682	−	0.998786i	$-0.484311\pi$
$727$	2.65683	0.0985364	0.0492682	+	0.998786i	$0.484311\pi$
$728$	−0.287885	−0.0106697
$729$	21.1828	0.784548
$730$	−2.04145	−0.0755575
$731$	0.218092	0.00806641
$732$	−15.4120	−0.569644
$733$	−19.4823	−0.719594	−0.359797	−	0.933031i	$-0.617154\pi$
$733$	−19.4823	−0.719594	−0.359797	+	0.933031i	$0.617154\pi$
$734$	−30.1073	−1.11128
$735$	−4.39036	−0.161941
$736$	−2.45616	−0.0905354
$737$	−17.5056	−0.644828
$738$	−29.3403	−1.08003
$739$	26.6883	0.981745	0.490873	−	0.871231i	$-0.336678\pi$
$739$	26.6883	0.981745	0.490873	+	0.871231i	$0.336678\pi$
$740$	−5.79658	−0.213087
$741$	−0.491990	−0.0180737
$742$	4.81003	0.176582
$743$	−34.3972	−1.26191	−0.630956	−	0.775819i	$-0.717337\pi$
$743$	−34.3972	−1.26191	−0.630956	+	0.775819i	$0.717337\pi$
$744$	11.6155	0.425846
$745$	−2.55572	−0.0936345
$746$	−37.8462	−1.38565
$747$	−4.63111	−0.169444
$748$	−1.00351	−0.0366919
$749$	−0.802310	−0.0293158
$750$	−14.0255	−0.512137
$751$	31.8111	1.16080	0.580401	−	0.814331i	$-0.302896\pi$
$751$	31.8111	1.16080	0.580401	+	0.814331i	$0.302896\pi$
$752$	−2.23535	−0.0815148
$753$	28.5586	1.04073
$754$	−5.15181	−0.187618
$755$	3.96779	0.144403
$756$	−9.20617	−0.334825
$757$	13.3398	0.484843	0.242421	−	0.970171i	$-0.422058\pi$
$757$	13.3398	0.484843	0.242421	+	0.970171i	$0.422058\pi$
$758$	8.30805	0.301762
$759$	−1.13729	−0.0412811
$760$	1.50584	0.0546226
$761$	−39.3547	−1.42661	−0.713303	−	0.700855i	$-0.752802\pi$
$761$	−39.3547	−1.42661	−0.713303	+	0.700855i	$0.752802\pi$
$762$	28.0091	1.01466
$763$	−3.23977	−0.117288
$764$	51.2780	1.85517
$765$	−0.114333	−0.00413373
$766$	7.65089	0.276438
$767$	1.50948	0.0545043
$768$	−3.07897	−0.111103
$769$	18.2914	0.659605	0.329803	−	0.944050i	$-0.393018\pi$
$769$	18.2914	0.659605	0.329803	+	0.944050i	$0.393018\pi$
$770$	−2.23249	−0.0804533
$771$	−5.94787	−0.214207
$772$	50.5819	1.82048
$773$	53.5659	1.92663	0.963316	−	0.268369i	$-0.0864847\pi$
$773$	53.5659	1.92663	0.963316	+	0.268369i	$0.0864847\pi$
$774$	−6.39172	−0.229746
$775$	−27.0996	−0.973445
$776$	1.27213	0.0456668
$777$	−2.60564	−0.0934767
$778$	18.3616	0.658297
$779$	12.5843	0.450881
$780$	−0.505845	−0.0181121
$781$	5.19931	0.186046
$782$	0.0889929	0.00318238
$783$	−46.4867	−1.66130
$784$	11.9921	0.428289
$785$	2.94268	0.105029
$786$	44.3734	1.58275
$787$	15.9898	0.569976	0.284988	−	0.958531i	$-0.408010\pi$
$787$	15.9898	0.569976	0.284988	+	0.958531i	$0.408010\pi$
$788$	26.9896	0.961465
$789$	20.6274	0.734353
$790$	5.66756	0.201643
$791$	11.8714	0.422098
$792$	8.29867	0.294880
$793$	1.30062	0.0461863
$794$	−51.5673	−1.83006
$795$	2.38482	0.0845807
$796$	−4.16274	−0.147544
$797$	−0.524636	−0.0185836	−0.00929178	−	0.999957i	$-0.502958\pi$
$797$	−0.524636	−0.0185836	−0.00929178	+	0.999957i	$0.502958\pi$
$798$	2.39890	0.0849202
$799$	0.151366	0.00535493
$800$	34.6034	1.22341
$801$	7.92998	0.280192
$802$	−63.4412	−2.24019
$803$	4.82540	0.170285
$804$	19.3402	0.682077
$805$	0.115251	0.00406205
$806$	−3.47393	−0.122364
$807$	−14.9272	−0.525464
$808$	5.21056	0.183307
$809$	−9.21770	−0.324077	−0.162039	−	0.986784i	$-0.551807\pi$
$809$	−9.21770	−0.324077	−0.162039	+	0.986784i	$0.551807\pi$
$810$	−1.71706	−0.0603315
$811$	12.7036	0.446085	0.223042	−	0.974809i	$-0.428401\pi$
$811$	12.7036	0.446085	0.223042	+	0.974809i	$0.428401\pi$
$812$	14.6230	0.513165
$813$	8.12602	0.284992
$814$	23.5368	0.824964
$815$	4.69868	0.164588
$816$	−0.258446	−0.00904743
$817$	2.74147	0.0959118
$818$	−78.4417	−2.74265
$819$	0.274762	0.00960096
$820$	12.9387	0.451839
$821$	37.9925	1.32595	0.662975	−	0.748642i	$-0.269294\pi$
$821$	37.9925	1.32595	0.662975	+	0.748642i	$0.269294\pi$
$822$	−19.7104	−0.687479
$823$	−22.4886	−0.783903	−0.391952	−	0.919986i	$-0.628200\pi$
$823$	−22.4886	−0.783903	−0.391952	+	0.919986i	$0.628200\pi$
$824$	−12.2490	−0.426714
$825$	16.0226	0.557836
$826$	−7.36011	−0.256091
$827$	33.0467	1.14915	0.574573	−	0.818453i	$-0.305168\pi$
$827$	33.0467	1.14915	0.574573	+	0.818453i	$0.305168\pi$
$828$	−1.51829	−0.0527641
$829$	51.8342	1.80028	0.900138	−	0.435604i	$-0.143465\pi$
$829$	51.8342	1.80028	0.900138	+	0.435604i	$0.143465\pi$
$830$	3.50826	0.121774
$831$	−24.3359	−0.844202
$832$	3.44403	0.119400
$833$	−0.812039	−0.0281355
$834$	2.05911	0.0713012
$835$	−9.08738	−0.314482
$836$	−12.6143	−0.436276
$837$	−31.3465	−1.08349
$838$	−61.7977	−2.13477
$839$	35.2277	1.21619	0.608097	−	0.793863i	$-0.291933\pi$
$839$	35.2277	1.21619	0.608097	+	0.793863i	$0.291933\pi$
$840$	0.695956	0.0240128
$841$	44.8388	1.54617
$842$	−18.8900	−0.650994
$843$	29.8877	1.02939
$844$	29.8578	1.02775
$845$	−7.34663	−0.252732
$846$	−4.43615	−0.152518
$847$	−1.44162	−0.0495348
$848$	−6.51404	−0.223693
$849$	−4.16180	−0.142833
$850$	−1.25377	−0.0430039
$851$	−1.21507	−0.0416521
$852$	−5.74419	−0.196793
$853$	41.5244	1.42177	0.710884	−	0.703309i	$-0.248295\pi$
$853$	41.5244	1.42177	0.710884	+	0.703309i	$0.248295\pi$
$854$	−6.34170	−0.217008
$855$	−1.43720	−0.0491512
$856$	−2.25927	−0.0772202
$857$	0.240250	0.00820678	0.00410339	−	0.999992i	$-0.498694\pi$
$857$	0.240250	0.00820678	0.00410339	+	0.999992i	$0.498694\pi$
$858$	2.05396	0.0701211
$859$	7.97052	0.271951	0.135975	−	0.990712i	$-0.456583\pi$
$859$	7.97052	0.271951	0.135975	+	0.990712i	$0.456583\pi$
$860$	2.81867	0.0961157
$861$	5.81611	0.198213
$862$	46.9946	1.60064
$863$	−50.0497	−1.70371	−0.851856	−	0.523777i	$-0.824523\pi$
$863$	−50.0497	−1.70371	−0.851856	+	0.523777i	$0.824523\pi$
$864$	40.0263	1.36172
$865$	−5.78928	−0.196841
$866$	33.9075	1.15222
$867$	−19.7966	−0.672328
$868$	9.86043	0.334685
$869$	−13.3965	−0.454445
$870$	12.4544	0.422244
$871$	−1.63212	−0.0553022
$872$	−9.12306	−0.308946
$873$	−1.21414	−0.0410924
$874$	1.11866	0.0378394
$875$	−3.35956	−0.113574
$876$	−5.33110	−0.180121
$877$	3.73218	0.126027	0.0630134	−	0.998013i	$-0.479929\pi$
$877$	3.73218	0.126027	0.0630134	+	0.998013i	$0.479929\pi$
$878$	−79.4140	−2.68009
$879$	−33.4252	−1.12741
$880$	3.02337	0.101918
$881$	50.5621	1.70348	0.851740	−	0.523965i	$-0.175548\pi$
$881$	50.5621	1.70348	0.851740	+	0.523965i	$0.175548\pi$
$882$	23.7988	0.801349
$883$	34.6897	1.16740	0.583701	−	0.811968i	$-0.301604\pi$
$883$	34.6897	1.16740	0.583701	+	0.811968i	$0.301604\pi$
$884$	−0.0935609	−0.00314679
$885$	−3.64915	−0.122665
$886$	33.5743	1.12795
$887$	−41.7349	−1.40132	−0.700661	−	0.713495i	$-0.747111\pi$
$887$	−41.7349	−1.40132	−0.700661	+	0.713495i	$0.747111\pi$
$888$	−7.33736	−0.246226
$889$	6.70912	0.225017
$890$	−6.00729	−0.201365
$891$	4.05864	0.135970
$892$	−46.1271	−1.54445
$893$	1.90271	0.0636716
$894$	−11.4650	−0.383446
$895$	−4.28097	−0.143097
$896$	−7.75472	−0.259067
$897$	−0.106034	−0.00354038
$898$	65.8012	2.19581
$899$	49.7904	1.66060
$900$	21.3902	0.713007
$901$	0.441095	0.0146950
$902$	−52.5371	−1.74929
$903$	1.26703	0.0421640
$904$	33.4292	1.11184
$905$	−9.79095	−0.325462
$906$	17.7995	0.591348
$907$	−40.8225	−1.35549	−0.677745	−	0.735297i	$-0.737043\pi$
$907$	−40.8225	−1.35549	−0.677745	+	0.735297i	$0.737043\pi$
$908$	53.6779	1.78136
$909$	−4.97304	−0.164945
$910$	−0.208144	−0.00689990
$911$	11.3921	0.377438	0.188719	−	0.982031i	$-0.439566\pi$
$911$	11.3921	0.377438	0.188719	+	0.982031i	$0.439566\pi$
$912$	−3.24874	−0.107576
$913$	−8.29252	−0.274442
$914$	71.2311	2.35611
$915$	−3.14422	−0.103945
$916$	2.78799	0.0921177
$917$	10.6289	0.350997
$918$	−1.45025	−0.0478655
$919$	6.23381	0.205634	0.102817	−	0.994700i	$-0.467214\pi$
$919$	6.23381	0.205634	0.102817	+	0.994700i	$0.467214\pi$
$920$	0.324541	0.0106998
$921$	−31.0155	−1.02200
$922$	49.1579	1.61893
$923$	0.484752	0.0159558
$924$	−5.82999	−0.191792
$925$	17.1184	0.562849
$926$	53.8361	1.76916
$927$	11.6906	0.383971
$928$	−63.5773	−2.08703
$929$	4.98043	0.163403	0.0817013	−	0.996657i	$-0.473965\pi$
$929$	4.98043	0.163403	0.0817013	+	0.996657i	$0.473965\pi$
$930$	8.39815	0.275386
$931$	−10.2075	−0.334539
$932$	−10.8535	−0.355517
$933$	16.8183	0.550607
$934$	50.0427	1.63745
$935$	−0.204726	−0.00669527
$936$	0.773717	0.0252897
$937$	−15.6557	−0.511450	−0.255725	−	0.966750i	$-0.582314\pi$
$937$	−15.6557	−0.511450	−0.255725	+	0.966750i	$0.582314\pi$
$938$	7.95807	0.259840
$939$	−0.548582	−0.0179023
$940$	1.95629	0.0638070
$941$	8.22961	0.268278	0.134139	−	0.990963i	$-0.457173\pi$
$941$	8.22961	0.268278	0.134139	+	0.990963i	$0.457173\pi$
$942$	13.2008	0.430107
$943$	2.71219	0.0883211
$944$	9.96751	0.324415
$945$	−1.87816	−0.0610965
$946$	−11.4451	−0.372111
$947$	−7.72634	−0.251072	−0.125536	−	0.992089i	$-0.540065\pi$
$947$	−7.72634	−0.251072	−0.125536	+	0.992089i	$0.540065\pi$
$948$	14.8004	0.480696
$949$	0.449891	0.0146041
$950$	−15.7602	−0.511328
$951$	6.94899	0.225336
$952$	0.128724	0.00417197
$953$	24.0314	0.778454	0.389227	−	0.921142i	$-0.372742\pi$
$953$	24.0314	0.778454	0.389227	+	0.921142i	$0.372742\pi$
$954$	−12.9274	−0.418540
$955$	10.4613	0.338518
$956$	−27.6107	−0.892995
$957$	−29.4386	−0.951615
$958$	78.5781	2.53874
$959$	−4.72129	−0.152458
$960$	−8.32586	−0.268716
$961$	2.57425	0.0830402
$962$	2.19443	0.0707511
$963$	2.15628	0.0694852
$964$	−59.7297	−1.92376
$965$	10.3193	0.332188
$966$	0.517014	0.0166347
$967$	−54.6016	−1.75587	−0.877934	−	0.478781i	$-0.841079\pi$
$967$	−54.6016	−1.75587	−0.877934	+	0.478781i	$0.841079\pi$
$968$	−4.05955	−0.130479
$969$	0.219987	0.00706700
$970$	0.919762	0.0295318
$971$	−8.00894	−0.257019	−0.128510	−	0.991708i	$-0.541019\pi$
$971$	−8.00894	−0.257019	−0.128510	+	0.991708i	$0.541019\pi$
$972$	40.7344	1.30656
$973$	0.493225	0.0158121
$974$	63.1076	2.02210
$975$	1.49385	0.0478416
$976$	8.58831	0.274905
$977$	45.3569	1.45110	0.725548	−	0.688172i	$-0.241586\pi$
$977$	45.3569	1.45110	0.725548	+	0.688172i	$0.241586\pi$
$978$	21.0782	0.674008
$979$	14.1995	0.453818
$980$	−10.4950	−0.335250
$981$	8.70719	0.277999
$982$	47.6341	1.52006
$983$	−24.8470	−0.792496	−0.396248	−	0.918144i	$-0.629688\pi$
$983$	−24.8470	−0.792496	−0.396248	+	0.918144i	$0.629688\pi$
$984$	16.3779	0.522109
$985$	5.50617	0.175441
$986$	2.30356	0.0733604
$987$	0.879375	0.0279908
$988$	−1.17609	−0.0374163
$989$	0.590844	0.0187877
$990$	6.00002	0.190693
$991$	−30.9557	−0.983342	−0.491671	−	0.870781i	$-0.663614\pi$
$991$	−30.9557	−0.983342	−0.491671	+	0.870781i	$0.663614\pi$
$992$	−42.8709	−1.36115
$993$	−17.8244	−0.565640
$994$	−2.36361	−0.0749691
$995$	−0.849243	−0.0269228
$996$	9.16157	0.290296
$997$	−27.8997	−0.883592	−0.441796	−	0.897116i	$-0.645658\pi$
$997$	−27.8997	−0.883592	−0.441796	+	0.897116i	$0.645658\pi$
$998$	27.8837	0.882643
$999$	19.8011	0.626480

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.a.b.1.14	✓	17
3.2	odd	2		3141.2.a.e.1.4		17
4.3	odd	2		5584.2.a.m.1.8		17
5.4	even	2		8725.2.a.m.1.4		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.a.b.1.14	✓	17	1.1	even	1	trivial
3141.2.a.e.1.4		17	3.2	odd	2
5584.2.a.m.1.8		17	4.3	odd	2
8725.2.a.m.1.4		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)

\(f(q)\)	\(=\)	\(q+2.18773 q^{2} +1.16554 q^{3} +2.78617 q^{4} +0.568409 q^{5} +2.54988 q^{6} +0.610781 q^{7} +1.71993 q^{8} -1.64153 q^{9} +O(q^{10})\)	\(q+2.18773 q^{2} +1.16554 q^{3} +2.78617 q^{4} +0.568409 q^{5} +2.54988 q^{6} +0.610781 q^{7} +1.71993 q^{8} -1.64153 q^{9} +1.24353 q^{10} -2.93934 q^{11} +3.24738 q^{12} -0.274046 q^{13} +1.33622 q^{14} +0.662500 q^{15} -1.80960 q^{16} +0.122536 q^{17} -3.59122 q^{18} +1.54031 q^{19} +1.58368 q^{20} +0.711886 q^{21} -6.43048 q^{22} +0.331969 q^{23} +2.00464 q^{24} -4.67691 q^{25} -0.599539 q^{26} -5.40986 q^{27} +1.70174 q^{28} +8.59295 q^{29} +1.44937 q^{30} +5.79433 q^{31} -7.39877 q^{32} -3.42590 q^{33} +0.268076 q^{34} +0.347173 q^{35} -4.57358 q^{36} -3.66019 q^{37} +3.36978 q^{38} -0.319410 q^{39} +0.977623 q^{40} +8.17001 q^{41} +1.55742 q^{42} +1.77982 q^{43} -8.18949 q^{44} -0.933059 q^{45} +0.726259 q^{46} +1.23528 q^{47} -2.10915 q^{48} -6.62695 q^{49} -10.2318 q^{50} +0.142820 q^{51} -0.763539 q^{52} +3.59972 q^{53} -11.8353 q^{54} -1.67075 q^{55} +1.05050 q^{56} +1.79528 q^{57} +18.7991 q^{58} -5.50814 q^{59} +1.84584 q^{60} -4.74598 q^{61} +12.6764 q^{62} -1.00261 q^{63} -12.5673 q^{64} -0.155770 q^{65} -7.49495 q^{66} +5.95564 q^{67} +0.341406 q^{68} +0.386922 q^{69} +0.759522 q^{70} -1.76887 q^{71} -2.82331 q^{72} -1.64166 q^{73} -8.00751 q^{74} -5.45110 q^{75} +4.29156 q^{76} -1.79529 q^{77} -0.698784 q^{78} +4.55765 q^{79} -1.02859 q^{80} -1.38080 q^{81} +17.8738 q^{82} +2.82122 q^{83} +1.98344 q^{84} +0.0696505 q^{85} +3.89376 q^{86} +10.0154 q^{87} -5.05545 q^{88} -4.83085 q^{89} -2.04128 q^{90} -0.167382 q^{91} +0.924922 q^{92} +6.75349 q^{93} +2.70245 q^{94} +0.875525 q^{95} -8.62353 q^{96} +0.739640 q^{97} -14.4980 q^{98} +4.82500 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9}+O(q^{10}) \) 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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