LMFDB - Embedded newform 349.2.a.b.1.13

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			1.13
Root			$1.93329$ 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)

$f(q)$	$=$	$q+1.93329 q^{2} -3.25199 q^{3} +1.73762 q^{4} +0.302138 q^{5} -6.28704 q^{6} +2.99039 q^{7} -0.507260 q^{8} +7.57541 q^{9} +O(q^{10})$	\(q+1.93329 q^{2} -3.25199 q^{3} +1.73762 q^{4} +0.302138 q^{5} -6.28704 q^{6} +2.99039 q^{7} -0.507260 q^{8} +7.57541 q^{9} +0.584120 q^{10} +5.06531 q^{11} -5.65071 q^{12} +1.94169 q^{13} +5.78130 q^{14} -0.982547 q^{15} -4.45592 q^{16} -4.04520 q^{17} +14.6455 q^{18} +4.56410 q^{19} +0.525000 q^{20} -9.72470 q^{21} +9.79273 q^{22} +5.84252 q^{23} +1.64960 q^{24} -4.90871 q^{25} +3.75386 q^{26} -14.8792 q^{27} +5.19616 q^{28} +6.55966 q^{29} -1.89955 q^{30} +2.32359 q^{31} -7.60007 q^{32} -16.4723 q^{33} -7.82055 q^{34} +0.903509 q^{35} +13.1632 q^{36} -4.10389 q^{37} +8.82375 q^{38} -6.31435 q^{39} -0.153262 q^{40} -10.2078 q^{41} -18.8007 q^{42} -9.88756 q^{43} +8.80158 q^{44} +2.28882 q^{45} +11.2953 q^{46} -3.91383 q^{47} +14.4906 q^{48} +1.94243 q^{49} -9.48998 q^{50} +13.1549 q^{51} +3.37392 q^{52} +11.2380 q^{53} -28.7658 q^{54} +1.53042 q^{55} -1.51691 q^{56} -14.8424 q^{57} +12.6817 q^{58} +7.81051 q^{59} -1.70729 q^{60} -2.89733 q^{61} +4.49217 q^{62} +22.6534 q^{63} -5.78132 q^{64} +0.586658 q^{65} -31.8458 q^{66} +8.71157 q^{67} -7.02901 q^{68} -18.9998 q^{69} +1.74675 q^{70} +2.51270 q^{71} -3.84270 q^{72} -13.3105 q^{73} -7.93403 q^{74} +15.9631 q^{75} +7.93067 q^{76} +15.1473 q^{77} -12.2075 q^{78} -2.31976 q^{79} -1.34630 q^{80} +25.6606 q^{81} -19.7346 q^{82} +3.71146 q^{83} -16.8978 q^{84} -1.22221 q^{85} -19.1155 q^{86} -21.3319 q^{87} -2.56943 q^{88} -2.30883 q^{89} +4.42495 q^{90} +5.80641 q^{91} +10.1521 q^{92} -7.55628 q^{93} -7.56658 q^{94} +1.37899 q^{95} +24.7153 q^{96} +0.690661 q^{97} +3.75528 q^{98} +38.3718 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.93329	1.36704	0.683522	−	0.729930i	$-0.260447\pi$
$2$	1.93329	1.36704	0.683522	+	0.729930i	$0.260447\pi$
$3$	−3.25199	−1.87753	−0.938767	−	0.344551i	$-0.888031\pi$
$3$	−3.25199	−1.87753	−0.938767	+	0.344551i	$0.888031\pi$
$4$	1.73762	0.868809
$5$	0.302138	0.135120	0.0675600	−	0.997715i	$-0.478479\pi$
$5$	0.302138	0.135120	0.0675600	+	0.997715i	$0.478479\pi$
$6$	−6.28704	−2.56667
$7$	2.99039	1.13026	0.565131	−	0.825002i	$-0.308826\pi$
$7$	2.99039	1.13026	0.565131	+	0.825002i	$0.308826\pi$
$8$	−0.507260	−0.179344
$9$	7.57541	2.52514
$10$	0.584120	0.184715
$11$	5.06531	1.52725	0.763625	−	0.645660i	$-0.223418\pi$
$11$	5.06531	1.52725	0.763625	+	0.645660i	$0.223418\pi$
$12$	−5.65071	−1.63122
$13$	1.94169	0.538528	0.269264	−	0.963066i	$-0.413220\pi$
$13$	1.94169	0.538528	0.269264	+	0.963066i	$0.413220\pi$
$14$	5.78130	1.54512
$15$	−0.982547	−0.253693
$16$	−4.45592	−1.11398
$17$	−4.04520	−0.981104	−0.490552	−	0.871412i	$-0.663205\pi$
$17$	−4.04520	−0.981104	−0.490552	+	0.871412i	$0.663205\pi$
$18$	14.6455	3.45197
$19$	4.56410	1.04708	0.523539	−	0.852002i	$-0.324612\pi$
$19$	4.56410	1.04708	0.523539	+	0.852002i	$0.324612\pi$
$20$	0.525000	0.117394
$21$	−9.72470	−2.12210
$22$	9.79273	2.08782
$23$	5.84252	1.21825	0.609125	−	0.793074i	$-0.291521\pi$
$23$	5.84252	1.21825	0.609125	+	0.793074i	$0.291521\pi$
$24$	1.64960	0.336724
$25$	−4.90871	−0.981743
$26$	3.75386	0.736192
$27$	−14.8792	−2.86350
$28$	5.19616	0.981981
$29$	6.55966	1.21810	0.609049	−	0.793132i	$-0.291551\pi$
$29$	6.55966	1.21810	0.609049	+	0.793132i	$0.291551\pi$
$30$	−1.89955	−0.346809
$31$	2.32359	0.417329	0.208664	−	0.977987i	$-0.433088\pi$
$31$	2.32359	0.417329	0.208664	+	0.977987i	$0.433088\pi$
$32$	−7.60007	−1.34352
$33$	−16.4723	−2.86746
$34$	−7.82055	−1.34121
$35$	0.903509	0.152721
$36$	13.1632	2.19386
$37$	−4.10389	−0.674676	−0.337338	−	0.941384i	$-0.609527\pi$
$37$	−4.10389	−0.674676	−0.337338	+	0.941384i	$0.609527\pi$
$38$	8.82375	1.43140
$39$	−6.31435	−1.01111
$40$	−0.153262	−0.0242329
$41$	−10.2078	−1.59418	−0.797092	−	0.603857i	$-0.793630\pi$
$41$	−10.2078	−1.59418	−0.797092	+	0.603857i	$0.793630\pi$
$42$	−18.8007	−2.90101
$43$	−9.88756	−1.50784	−0.753920	−	0.656967i	$-0.771839\pi$
$43$	−9.88756	−1.50784	−0.753920	+	0.656967i	$0.771839\pi$
$44$	8.80158	1.32689
$45$	2.28882	0.341197
$46$	11.2953	1.66540
$47$	−3.91383	−0.570891	−0.285446	−	0.958395i	$-0.592142\pi$
$47$	−3.91383	−0.570891	−0.285446	+	0.958395i	$0.592142\pi$
$48$	14.4906	2.09154
$49$	1.94243	0.277490
$50$	−9.48998	−1.34209
$51$	13.1549	1.84206
$52$	3.37392	0.467878
$53$	11.2380	1.54365	0.771827	−	0.635832i	$-0.219343\pi$
$53$	11.2380	1.54365	0.771827	+	0.635832i	$0.219343\pi$
$54$	−28.7658	−3.91453
$55$	1.53042	0.206362
$56$	−1.51691	−0.202705
$57$	−14.8424	−1.96592
$58$	12.6817	1.66519
$59$	7.81051	1.01684	0.508421	−	0.861109i	$-0.330229\pi$
$59$	7.81051	1.01684	0.508421	+	0.861109i	$0.330229\pi$
$60$	−1.70729	−0.220410
$61$	−2.89733	−0.370965	−0.185482	−	0.982648i	$-0.559385\pi$
$61$	−2.89733	−0.370965	−0.185482	+	0.982648i	$0.559385\pi$
$62$	4.49217	0.570507
$63$	22.6534	2.85406
$64$	−5.78132	−0.722665
$65$	0.586658	0.0727659
$66$	−31.8458	−3.91995
$67$	8.71157	1.06429	0.532144	−	0.846654i	$-0.321387\pi$
$67$	8.71157	1.06429	0.532144	+	0.846654i	$0.321387\pi$
$68$	−7.02901	−0.852393
$69$	−18.9998	−2.28731
$70$	1.74675	0.208776
$71$	2.51270	0.298202	0.149101	−	0.988822i	$-0.452362\pi$
$71$	2.51270	0.298202	0.149101	+	0.988822i	$0.452362\pi$
$72$	−3.84270	−0.452867
$73$	−13.3105	−1.55788	−0.778941	−	0.627098i	$-0.784243\pi$
$73$	−13.3105	−1.55788	−0.778941	+	0.627098i	$0.784243\pi$
$74$	−7.93403	−0.922312
$75$	15.9631	1.84326
$76$	7.93067	0.909710
$77$	15.1473	1.72619
$78$	−12.2075	−1.38223
$79$	−2.31976	−0.260993	−0.130497	−	0.991449i	$-0.541657\pi$
$79$	−2.31976	−0.260993	−0.130497	+	0.991449i	$0.541657\pi$
$80$	−1.34630	−0.150521
$81$	25.6606	2.85118
$82$	−19.7346	−2.17932
$83$	3.71146	0.407386	0.203693	−	0.979035i	$-0.434706\pi$
$83$	3.71146	0.407386	0.203693	+	0.979035i	$0.434706\pi$
$84$	−16.8978	−1.84370
$85$	−1.22221	−0.132567
$86$	−19.1155	−2.06128
$87$	−21.3319	−2.28702
$88$	−2.56943	−0.273902
$89$	−2.30883	−0.244736	−0.122368	−	0.992485i	$-0.539049\pi$
$89$	−2.30883	−0.244736	−0.122368	+	0.992485i	$0.539049\pi$
$90$	4.42495	0.466431
$91$	5.80641	0.608677
$92$	10.1521	1.05843
$93$	−7.55628	−0.783549
$94$	−7.56658	−0.780433
$95$	1.37899	0.141481
$96$	24.7153	2.52250
$97$	0.690661	0.0701259	0.0350630	−	0.999385i	$-0.488837\pi$
$97$	0.690661	0.0701259	0.0350630	+	0.999385i	$0.488837\pi$
$98$	3.75528	0.379341
$99$	38.3718	3.85651
$100$	−8.52947	−0.852947
$101$	−7.04295	−0.700800	−0.350400	−	0.936600i	$-0.613954\pi$
$101$	−7.04295	−0.700800	−0.350400	+	0.936600i	$0.613954\pi$
$102$	25.4323	2.51817
$103$	2.41375	0.237834	0.118917	−	0.992904i	$-0.462058\pi$
$103$	2.41375	0.237834	0.118917	+	0.992904i	$0.462058\pi$
$104$	−0.984942	−0.0965815
$105$	−2.93820	−0.286739
$106$	21.7263	2.11024
$107$	−7.30272	−0.705981	−0.352991	−	0.935627i	$-0.614835\pi$
$107$	−7.30272	−0.705981	−0.352991	+	0.935627i	$0.614835\pi$
$108$	−25.8543	−2.48783
$109$	9.89722	0.947982	0.473991	−	0.880530i	$-0.342813\pi$
$109$	9.89722	0.947982	0.473991	+	0.880530i	$0.342813\pi$
$110$	2.95875	0.282106
$111$	13.3458	1.26673
$112$	−13.3249	−1.25909
$113$	−14.7975	−1.39203	−0.696015	−	0.718027i	$-0.745045\pi$
$113$	−14.7975	−1.39203	−0.696015	+	0.718027i	$0.745045\pi$
$114$	−28.6947	−2.68751
$115$	1.76524	0.164610
$116$	11.3982	1.05830
$117$	14.7091	1.35986
$118$	15.1000	1.39007
$119$	−12.0967	−1.10890
$120$	0.498407	0.0454981
$121$	14.6574	1.33249
$122$	−5.60138	−0.507125
$123$	33.1955	2.99314
$124$	4.03751	0.362579
$125$	−2.99379	−0.267773
$126$	43.7957	3.90163
$127$	−6.67672	−0.592463	−0.296231	−	0.955116i	$-0.595730\pi$
$127$	−6.67672	−0.592463	−0.296231	+	0.955116i	$0.595730\pi$
$128$	4.02316	0.355600
$129$	32.1542	2.83102
$130$	1.13418	0.0994742
$131$	2.88533	0.252092	0.126046	−	0.992024i	$-0.459771\pi$
$131$	2.88533	0.252092	0.126046	+	0.992024i	$0.459771\pi$
$132$	−28.6226	−2.49128
$133$	13.6485	1.18347
$134$	16.8420	1.45493
$135$	−4.49556	−0.386916
$136$	2.05197	0.175955
$137$	3.50589	0.299529	0.149764	−	0.988722i	$-0.452148\pi$
$137$	3.50589	0.299529	0.149764	+	0.988722i	$0.452148\pi$
$138$	−36.7322	−3.12685
$139$	−21.1069	−1.79027	−0.895133	−	0.445799i	$-0.852920\pi$
$139$	−21.1069	−1.79027	−0.895133	+	0.445799i	$0.852920\pi$
$140$	1.56995	0.132685
$141$	12.7277	1.07187
$142$	4.85778	0.407655
$143$	9.83527	0.822467
$144$	−33.7554	−2.81295
$145$	1.98192	0.164590
$146$	−25.7332	−2.12969
$147$	−6.31675	−0.520997
$148$	−7.13100	−0.586165
$149$	−16.6283	−1.36224	−0.681120	−	0.732172i	$-0.738507\pi$
$149$	−16.6283	−1.36224	−0.681120	+	0.732172i	$0.738507\pi$
$150$	30.8613	2.51981
$151$	−2.22496	−0.181065	−0.0905325	−	0.995893i	$-0.528857\pi$
$151$	−2.22496	−0.181065	−0.0905325	+	0.995893i	$0.528857\pi$
$152$	−2.31519	−0.187787
$153$	−30.6440	−2.47742
$154$	29.2841	2.35978
$155$	0.702043	0.0563895
$156$	−10.9719	−0.878458
$157$	−19.1450	−1.52794	−0.763968	−	0.645254i	$-0.776751\pi$
$157$	−19.1450	−1.52794	−0.763968	+	0.645254i	$0.776751\pi$
$158$	−4.48477	−0.356789
$159$	−36.5457	−2.89827
$160$	−2.29627	−0.181536
$161$	17.4714	1.37694
$162$	49.6095	3.89769
$163$	−8.22036	−0.643868	−0.321934	−	0.946762i	$-0.604333\pi$
$163$	−8.22036	−0.643868	−0.321934	+	0.946762i	$0.604333\pi$
$164$	−17.7372	−1.38504
$165$	−4.97691	−0.387452
$166$	7.17534	0.556915
$167$	−3.58701	−0.277571	−0.138785	−	0.990322i	$-0.544320\pi$
$167$	−3.58701	−0.277571	−0.138785	+	0.990322i	$0.544320\pi$
$168$	4.93296	0.380586
$169$	−9.22984	−0.709988
$170$	−2.36288	−0.181225
$171$	34.5750	2.64401
$172$	−17.1808	−1.31002
$173$	9.28858	0.706198	0.353099	−	0.935586i	$-0.385128\pi$
$173$	9.28858	0.706198	0.353099	+	0.935586i	$0.385128\pi$
$174$	−41.2409	−3.12646
$175$	−14.6790	−1.10963
$176$	−22.5706	−1.70132
$177$	−25.3997	−1.90916
$178$	−4.46365	−0.334564
$179$	16.3227	1.22002	0.610008	−	0.792395i	$-0.291166\pi$
$179$	16.3227	1.22002	0.610008	+	0.792395i	$0.291166\pi$
$180$	3.97709	0.296435
$181$	17.9890	1.33711	0.668555	−	0.743662i	$-0.266913\pi$
$181$	17.9890	1.33711	0.668555	+	0.743662i	$0.266913\pi$
$182$	11.2255	0.832089
$183$	9.42206	0.696499
$184$	−2.96368	−0.218485
$185$	−1.23994	−0.0911622
$186$	−14.6085	−1.07115
$187$	−20.4902	−1.49839
$188$	−6.80075	−0.495996
$189$	−44.4945	−3.23650
$190$	2.66599	0.193411
$191$	−17.2611	−1.24897	−0.624486	−	0.781036i	$-0.714691\pi$
$191$	−17.2611	−1.24897	−0.624486	+	0.781036i	$0.714691\pi$
$192$	18.8008	1.35683
$193$	0.901135	0.0648651	0.0324326	−	0.999474i	$-0.489675\pi$
$193$	0.901135	0.0648651	0.0324326	+	0.999474i	$0.489675\pi$
$194$	1.33525	0.0958653
$195$	−1.90780	−0.136621
$196$	3.37520	0.241086
$197$	10.8059	0.769891	0.384945	−	0.922939i	$-0.374220\pi$
$197$	10.8059	0.769891	0.384945	+	0.922939i	$0.374220\pi$
$198$	74.1840	5.27203
$199$	7.15768	0.507394	0.253697	−	0.967284i	$-0.418353\pi$
$199$	7.15768	0.507394	0.253697	+	0.967284i	$0.418353\pi$
$200$	2.48999	0.176069
$201$	−28.3299	−1.99824
$202$	−13.6161	−0.958024
$203$	19.6159	1.37677
$204$	22.8582	1.60040
$205$	−3.08415	−0.215406
$206$	4.66648	0.325129
$207$	44.2595	3.07625
$208$	−8.65202	−0.599909
$209$	23.1186	1.59915
$210$	−5.68040	−0.391985
$211$	−26.1676	−1.80145	−0.900724	−	0.434391i	$-0.856964\pi$
$211$	−26.1676	−1.80145	−0.900724	+	0.434391i	$0.856964\pi$
$212$	19.5273	1.34114
$213$	−8.17125	−0.559885
$214$	−14.1183	−0.965107
$215$	−2.98740	−0.203739
$216$	7.54761	0.513550
$217$	6.94843	0.471690
$218$	19.1342	1.29593
$219$	43.2857	2.92498
$220$	2.65929	0.179289
$221$	−7.85452	−0.528352
$222$	25.8013	1.73167
$223$	26.6893	1.78725	0.893625	−	0.448815i	$-0.148154\pi$
$223$	26.6893	1.78725	0.893625	+	0.448815i	$0.148154\pi$
$224$	−22.7272	−1.51852
$225$	−37.1855	−2.47903
$226$	−28.6079	−1.90297
$227$	−4.08162	−0.270906	−0.135453	−	0.990784i	$-0.543249\pi$
$227$	−4.08162	−0.270906	−0.135453	+	0.990784i	$0.543249\pi$
$228$	−25.7904	−1.70801
$229$	8.76318	0.579087	0.289544	−	0.957165i	$-0.406496\pi$
$229$	8.76318	0.579087	0.289544	+	0.957165i	$0.406496\pi$
$230$	3.41273	0.225029
$231$	−49.2587	−3.24098
$232$	−3.32746	−0.218458
$233$	−14.8713	−0.974250	−0.487125	−	0.873332i	$-0.661954\pi$
$233$	−14.8713	−0.974250	−0.487125	+	0.873332i	$0.661954\pi$
$234$	28.4370	1.85898
$235$	−1.18252	−0.0771388
$236$	13.5717	0.883441
$237$	7.54382	0.490024
$238$	−23.3865	−1.51592
$239$	0.386269	0.0249857	0.0124928	−	0.999922i	$-0.496023\pi$
$239$	0.386269	0.0249857	0.0124928	+	0.999922i	$0.496023\pi$
$240$	4.37815	0.282608
$241$	1.79304	0.115500	0.0577501	−	0.998331i	$-0.481607\pi$
$241$	1.79304	0.115500	0.0577501	+	0.998331i	$0.481607\pi$
$242$	28.3370	1.82157
$243$	−38.8105	−2.48969
$244$	−5.03445	−0.322297
$245$	0.586881	0.0374944
$246$	64.1766	4.09175
$247$	8.86208	0.563881
$248$	−1.17866	−0.0748452
$249$	−12.0696	−0.764882
$250$	−5.78788	−0.366058
$251$	11.6314	0.734166	0.367083	−	0.930188i	$-0.380356\pi$
$251$	11.6314	0.734166	0.367083	+	0.930188i	$0.380356\pi$
$252$	39.3630	2.47964
$253$	29.5942	1.86057
$254$	−12.9080	−0.809923
$255$	3.97460	0.248899
$256$	19.3406	1.20879
$257$	19.3238	1.20539	0.602693	−	0.797974i	$-0.294095\pi$
$257$	19.3238	1.20539	0.602693	+	0.797974i	$0.294095\pi$
$258$	62.1635	3.87013
$259$	−12.2722	−0.762560
$260$	1.01939	0.0632197
$261$	49.6921	3.07587
$262$	5.57818	0.344621
$263$	20.0179	1.23436	0.617180	−	0.786822i	$-0.288275\pi$
$263$	20.0179	1.23436	0.617180	+	0.786822i	$0.288275\pi$
$264$	8.35576	0.514261
$265$	3.39541	0.208579
$266$	26.3864	1.61786
$267$	7.50829	0.459500
$268$	15.1374	0.924663
$269$	19.2607	1.17434	0.587172	−	0.809462i	$-0.300241\pi$
$269$	19.2607	1.17434	0.587172	+	0.809462i	$0.300241\pi$
$270$	−8.69123	−0.528931
$271$	−24.0200	−1.45911	−0.729557	−	0.683920i	$-0.760274\pi$
$271$	−24.0200	−1.45911	−0.729557	+	0.683920i	$0.760274\pi$
$272$	18.0251	1.09293
$273$	−18.8824	−1.14281
$274$	6.77792	0.409469
$275$	−24.8642	−1.49937
$276$	−33.0144	−1.98723
$277$	−26.3049	−1.58051	−0.790254	−	0.612779i	$-0.790052\pi$
$277$	−26.3049	−1.58051	−0.790254	+	0.612779i	$0.790052\pi$
$278$	−40.8059	−2.44737
$279$	17.6021	1.05381
$280$	−0.458314	−0.0273895
$281$	−0.521682	−0.0311209	−0.0155605	−	0.999879i	$-0.504953\pi$
$281$	−0.521682	−0.0311209	−0.0155605	+	0.999879i	$0.504953\pi$
$282$	24.6064	1.46529
$283$	−20.6047	−1.22482	−0.612412	−	0.790539i	$-0.709801\pi$
$283$	−20.6047	−1.22482	−0.612412	+	0.790539i	$0.709801\pi$
$284$	4.36611	0.259081
$285$	−4.48445	−0.265636
$286$	19.0145	1.12435
$287$	−30.5252	−1.80185
$288$	−57.5737	−3.39256
$289$	−0.636381	−0.0374342
$290$	3.83163	0.225001
$291$	−2.24602	−0.131664
$292$	−23.1286	−1.35350
$293$	9.73847	0.568927	0.284464	−	0.958687i	$-0.408184\pi$
$293$	9.73847	0.568927	0.284464	+	0.958687i	$0.408184\pi$
$294$	−12.2121	−0.712226
$295$	2.35985	0.137396
$296$	2.08174	0.120999
$297$	−75.3677	−4.37328
$298$	−32.1473	−1.86224
$299$	11.3444	0.656062
$300$	27.7377	1.60144
$301$	−29.5677	−1.70425
$302$	−4.30151	−0.247524
$303$	22.9036	1.31578
$304$	−20.3373	−1.16642
$305$	−0.875391	−0.0501247
$306$	−59.2439	−3.38675
$307$	−5.79214	−0.330575	−0.165287	−	0.986245i	$-0.552855\pi$
$307$	−5.79214	−0.330575	−0.165287	+	0.986245i	$0.552855\pi$
$308$	26.3202	1.49973
$309$	−7.84947	−0.446541
$310$	1.35725	0.0770869
$311$	27.9876	1.58703	0.793517	−	0.608548i	$-0.208248\pi$
$311$	27.9876	1.58703	0.793517	+	0.608548i	$0.208248\pi$
$312$	3.20302	0.181335
$313$	−23.2772	−1.31571	−0.657853	−	0.753146i	$-0.728535\pi$
$313$	−23.2772	−1.31571	−0.657853	+	0.753146i	$0.728535\pi$
$314$	−37.0128	−2.08876
$315$	6.84445	0.385641
$316$	−4.03086	−0.226753
$317$	−18.8226	−1.05718	−0.528590	−	0.848877i	$-0.677279\pi$
$317$	−18.8226	−1.05718	−0.528590	+	0.848877i	$0.677279\pi$
$318$	−70.6536	−3.96206
$319$	33.2267	1.86034
$320$	−1.74675	−0.0976465
$321$	23.7484	1.32550
$322$	33.7773	1.88234
$323$	−18.4627	−1.02729
$324$	44.5884	2.47713
$325$	−9.53120	−0.528696
$326$	−15.8924	−0.880196
$327$	−32.1856	−1.77987
$328$	5.17799	0.285907
$329$	−11.7039	−0.645256
$330$	−9.62182	−0.529664
$331$	6.86988	0.377603	0.188801	−	0.982015i	$-0.439540\pi$
$331$	6.86988	0.377603	0.188801	+	0.982015i	$0.439540\pi$
$332$	6.44911	0.353941
$333$	−31.0887	−1.70365
$334$	−6.93473	−0.379452
$335$	2.63209	0.143807
$336$	43.3325	2.36398
$337$	6.08455	0.331446	0.165723	−	0.986172i	$-0.447004\pi$
$337$	6.08455	0.331446	0.165723	+	0.986172i	$0.447004\pi$
$338$	−17.8440	−0.970584
$339$	48.1212	2.61358
$340$	−2.12373	−0.115175
$341$	11.7697	0.637365
$342$	66.8435	3.61448
$343$	−15.1241	−0.816625
$344$	5.01557	0.270421
$345$	−5.74055	−0.309061
$346$	17.9575	0.965403
$347$	4.83799	0.259717	0.129858	−	0.991533i	$-0.458548\pi$
$347$	4.83799	0.259717	0.129858	+	0.991533i	$0.458548\pi$
$348$	−37.0668	−1.98699
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	−28.3787	−1.51691
$351$	−28.8908	−1.54207
$352$	−38.4967	−2.05188
$353$	6.80328	0.362102	0.181051	−	0.983474i	$-0.442050\pi$
$353$	6.80328	0.362102	0.181051	+	0.983474i	$0.442050\pi$
$354$	−49.1050	−2.60990
$355$	0.759180	0.0402931
$356$	−4.01187	−0.212629
$357$	39.3383	2.08201
$358$	31.5566	1.66782
$359$	27.5339	1.45318	0.726591	−	0.687071i	$-0.241104\pi$
$359$	27.5339	1.45318	0.726591	+	0.687071i	$0.241104\pi$
$360$	−1.16103	−0.0611914
$361$	1.83105	0.0963710
$362$	34.7780	1.82789
$363$	−47.6656	−2.50180
$364$	10.0893	0.528824
$365$	−4.02161	−0.210501
$366$	18.2156	0.952145
$367$	10.7700	0.562192	0.281096	−	0.959680i	$-0.409302\pi$
$367$	10.7700	0.562192	0.281096	+	0.959680i	$0.409302\pi$
$368$	−26.0338	−1.35711
$369$	−77.3280	−4.02554
$370$	−2.39717	−0.124623
$371$	33.6059	1.74473
$372$	−13.1299	−0.680755
$373$	6.76887	0.350479	0.175240	−	0.984526i	$-0.443930\pi$
$373$	6.76887	0.350479	0.175240	+	0.984526i	$0.443930\pi$
$374$	−39.6135	−2.04837
$375$	9.73578	0.502753
$376$	1.98533	0.102386
$377$	12.7368	0.655980
$378$	−86.0209	−4.42444
$379$	27.5045	1.41281	0.706406	−	0.707807i	$-0.250315\pi$
$379$	27.5045	1.41281	0.706406	+	0.707807i	$0.250315\pi$
$380$	2.39615	0.122920
$381$	21.7126	1.11237
$382$	−33.3708	−1.70740
$383$	−6.58002	−0.336223	−0.168112	−	0.985768i	$-0.553767\pi$
$383$	−6.58002	−0.336223	−0.168112	+	0.985768i	$0.553767\pi$
$384$	−13.0833	−0.667652
$385$	4.57656	0.233243
$386$	1.74216	0.0886735
$387$	−74.9024	−3.80750
$388$	1.20010	0.0609261
$389$	38.0631	1.92987	0.964937	−	0.262481i	$-0.0845407\pi$
$389$	38.0631	1.92987	0.964937	+	0.262481i	$0.0845407\pi$
$390$	−3.68834	−0.186766
$391$	−23.6341	−1.19523
$392$	−0.985317	−0.0497660
$393$	−9.38304	−0.473312
$394$	20.8910	1.05247
$395$	−0.700886	−0.0352654
$396$	66.6756	3.35058
$397$	21.9052	1.09939	0.549695	−	0.835366i	$-0.314744\pi$
$397$	21.9052	1.09939	0.549695	+	0.835366i	$0.314744\pi$
$398$	13.8379	0.693630
$399$	−44.3846	−2.22201
$400$	21.8728	1.09364
$401$	−13.3371	−0.666022	−0.333011	−	0.942923i	$-0.608065\pi$
$401$	−13.3371	−0.666022	−0.333011	+	0.942923i	$0.608065\pi$
$402$	−54.7700	−2.73168
$403$	4.51169	0.224743
$404$	−12.2380	−0.608861
$405$	7.75304	0.385252
$406$	37.9234	1.88210
$407$	−20.7875	−1.03040
$408$	−6.67297	−0.330361
$409$	3.76676	0.186254	0.0931271	−	0.995654i	$-0.470314\pi$
$409$	3.76676	0.186254	0.0931271	+	0.995654i	$0.470314\pi$
$410$	−5.96256	−0.294470
$411$	−11.4011	−0.562376
$412$	4.19417	0.206632
$413$	23.3565	1.14930
$414$	85.5665	4.20537
$415$	1.12137	0.0550460
$416$	−14.7570	−0.723521
$417$	68.6394	3.36129
$418$	44.6950	2.18611
$419$	−30.2985	−1.48018	−0.740089	−	0.672509i	$-0.765217\pi$
$419$	−30.2985	−1.48018	−0.740089	+	0.672509i	$0.765217\pi$
$420$	−5.10547	−0.249121
$421$	−6.51439	−0.317492	−0.158746	−	0.987319i	$-0.550745\pi$
$421$	−6.51439	−0.317492	−0.158746	+	0.987319i	$0.550745\pi$
$422$	−50.5895	−2.46266
$423$	−29.6489	−1.44158
$424$	−5.70058	−0.276844
$425$	19.8567	0.963192
$426$	−15.7974	−0.765387
$427$	−8.66413	−0.419287
$428$	−12.6893	−0.613363
$429$	−31.9842	−1.54421
$430$	−5.77552	−0.278521
$431$	−16.0206	−0.771683	−0.385842	−	0.922565i	$-0.626089\pi$
$431$	−16.0206	−0.771683	−0.385842	+	0.922565i	$0.626089\pi$
$432$	66.3004	3.18988
$433$	−27.0478	−1.29983	−0.649916	−	0.760006i	$-0.725196\pi$
$433$	−27.0478	−1.29983	−0.649916	+	0.760006i	$0.725196\pi$
$434$	13.4334	0.644822
$435$	−6.44518	−0.309023
$436$	17.1976	0.823616
$437$	26.6659	1.27560
$438$	83.6839	3.99857
$439$	−15.7921	−0.753714	−0.376857	−	0.926272i	$-0.622995\pi$
$439$	−15.7921	−0.753714	−0.376857	+	0.926272i	$0.622995\pi$
$440$	−0.776322	−0.0370097
$441$	14.7147	0.700700
$442$	−15.1851	−0.722281
$443$	15.6214	0.742194	0.371097	−	0.928594i	$-0.378982\pi$
$443$	15.6214	0.742194	0.371097	+	0.928594i	$0.378982\pi$
$444$	23.1899	1.10055
$445$	−0.697585	−0.0330687
$446$	51.5983	2.44325
$447$	54.0749	2.55765
$448$	−17.2884	−0.816800
$449$	22.2468	1.04989	0.524945	−	0.851136i	$-0.324086\pi$
$449$	22.2468	1.04989	0.524945	+	0.851136i	$0.324086\pi$
$450$	−71.8905	−3.38895
$451$	−51.7055	−2.43472
$452$	−25.7124	−1.20941
$453$	7.23555	0.339956
$454$	−7.89095	−0.370341
$455$	1.75433	0.0822445
$456$	7.52896	0.352576
$457$	13.2410	0.619389	0.309694	−	0.950836i	$-0.399773\pi$
$457$	13.2410	0.619389	0.309694	+	0.950836i	$0.399773\pi$
$458$	16.9418	0.791638
$459$	60.1892	2.80939
$460$	3.06732	0.143015
$461$	33.7197	1.57048	0.785242	−	0.619189i	$-0.212539\pi$
$461$	33.7197	1.57048	0.785242	+	0.619189i	$0.212539\pi$
$462$	−95.2314	−4.43057
$463$	−4.53570	−0.210792	−0.105396	−	0.994430i	$-0.533611\pi$
$463$	−4.53570	−0.210792	−0.105396	+	0.994430i	$0.533611\pi$
$464$	−29.2293	−1.35694
$465$	−2.28303	−0.105873
$466$	−28.7505	−1.33184
$467$	21.0411	0.973665	0.486832	−	0.873495i	$-0.338152\pi$
$467$	21.0411	0.973665	0.486832	+	0.873495i	$0.338152\pi$
$468$	25.5588	1.18146
$469$	26.0510	1.20292
$470$	−2.28615	−0.105452
$471$	62.2592	2.86875
$472$	−3.96196	−0.182364
$473$	−50.0836	−2.30285
$474$	14.5844	0.669884
$475$	−22.4039	−1.02796
$476$	−21.0195	−0.963426
$477$	85.1323	3.89794
$478$	0.746771	0.0341565
$479$	−19.4252	−0.887558	−0.443779	−	0.896136i	$-0.646363\pi$
$479$	−19.4252	−0.887558	−0.443779	+	0.896136i	$0.646363\pi$
$480$	7.46743	0.340840
$481$	−7.96849	−0.363332
$482$	3.46648	0.157894
$483$	−56.8168	−2.58525
$484$	25.4690	1.15768
$485$	0.208674	0.00947542
$486$	−75.0320	−3.40352
$487$	−29.6846	−1.34514	−0.672568	−	0.740036i	$-0.734809\pi$
$487$	−29.6846	−1.34514	−0.672568	+	0.740036i	$0.734809\pi$
$488$	1.46970	0.0665301
$489$	26.7325	1.20889
$490$	1.13461	0.0512566
$491$	5.64801	0.254891	0.127445	−	0.991846i	$-0.459322\pi$
$491$	5.64801	0.254891	0.127445	+	0.991846i	$0.459322\pi$
$492$	57.6811	2.60047
$493$	−26.5351	−1.19508
$494$	17.1330	0.770850
$495$	11.5936	0.521092
$496$	−10.3537	−0.464896
$497$	7.51394	0.337046
$498$	−23.3341	−1.04563
$499$	36.9827	1.65557	0.827786	−	0.561043i	$-0.189600\pi$
$499$	36.9827	1.65557	0.827786	+	0.561043i	$0.189600\pi$
$500$	−5.20207	−0.232644
$501$	11.6649	0.521149
$502$	22.4869	1.00364
$503$	28.4186	1.26712	0.633560	−	0.773693i	$-0.281593\pi$
$503$	28.4186	1.26712	0.633560	+	0.773693i	$0.281593\pi$
$504$	−11.4912	−0.511858
$505$	−2.12794	−0.0946920
$506$	57.2142	2.54348
$507$	30.0153	1.33303
$508$	−11.6016	−0.514737
$509$	35.1699	1.55888	0.779439	−	0.626478i	$-0.215504\pi$
$509$	35.1699	1.55888	0.779439	+	0.626478i	$0.215504\pi$
$510$	7.68406	0.340256
$511$	−39.8037	−1.76081
$512$	29.3447	1.29686
$513$	−67.9101	−2.99830
$514$	37.3585	1.64781
$515$	0.729284	0.0321361
$516$	55.8718	2.45962
$517$	−19.8248	−0.871893
$518$	−23.7258	−1.04245
$519$	−30.2063	−1.32591
$520$	−0.297588	−0.0130501
$521$	−22.2816	−0.976174	−0.488087	−	0.872795i	$-0.662305\pi$
$521$	−22.2816	−0.976174	−0.488087	+	0.872795i	$0.662305\pi$
$522$	96.0694	4.20485
$523$	34.5723	1.51174	0.755871	−	0.654721i	$-0.227214\pi$
$523$	34.5723	1.51174	0.755871	+	0.654721i	$0.227214\pi$
$524$	5.01360	0.219020
$525$	47.7358	2.08336
$526$	38.7005	1.68742
$527$	−9.39937	−0.409443
$528$	73.3994	3.19430
$529$	11.1350	0.484132
$530$	6.56433	0.285136
$531$	59.1678	2.56767
$532$	23.7158	1.02821
$533$	−19.8203	−0.858513
$534$	14.5157	0.628156
$535$	−2.20643	−0.0953922
$536$	−4.41903	−0.190873
$537$	−53.0812	−2.29062
$538$	37.2365	1.60538
$539$	9.83901	0.423796
$540$	−7.81156	−0.336156
$541$	−15.2389	−0.655173	−0.327586	−	0.944821i	$-0.606235\pi$
$541$	−15.2389	−0.655173	−0.327586	+	0.944821i	$0.606235\pi$
$542$	−46.4378	−1.99467
$543$	−58.4999	−2.51047
$544$	30.7438	1.31813
$545$	2.99032	0.128091
$546$	−36.5051	−1.56228
$547$	−31.2127	−1.33456	−0.667279	−	0.744808i	$-0.732541\pi$
$547$	−31.2127	−1.33456	−0.667279	+	0.744808i	$0.732541\pi$
$548$	6.09191	0.260233
$549$	−21.9484	−0.936737
$550$	−48.0697	−2.04970
$551$	29.9390	1.27544
$552$	9.63784	0.410214
$553$	−6.93698	−0.294991
$554$	−50.8551	−2.16063
$555$	4.03227	0.171160
$556$	−36.6758	−1.55540
$557$	−41.3224	−1.75088	−0.875442	−	0.483322i	$-0.839430\pi$
$557$	−41.3224	−1.75088	−0.875442	+	0.483322i	$0.839430\pi$
$558$	34.0301	1.44061
$559$	−19.1986	−0.812014
$560$	−4.02596	−0.170128
$561$	66.6338	2.81328
$562$	−1.00856	−0.0425437
$563$	7.88952	0.332504	0.166252	−	0.986083i	$-0.446834\pi$
$563$	7.88952	0.332504	0.166252	+	0.986083i	$0.446834\pi$
$564$	22.1159	0.931249
$565$	−4.47087	−0.188091
$566$	−39.8350	−1.67439
$567$	76.7353	3.22258
$568$	−1.27459	−0.0534806
$569$	−17.8790	−0.749526	−0.374763	−	0.927121i	$-0.622276\pi$
$569$	−17.8790	−0.749526	−0.374763	+	0.927121i	$0.622276\pi$
$570$	−8.66975	−0.363136
$571$	−24.6298	−1.03073	−0.515363	−	0.856972i	$-0.672343\pi$
$571$	−24.6298	−1.03073	−0.515363	+	0.856972i	$0.672343\pi$
$572$	17.0899	0.714567
$573$	56.1330	2.34499
$574$	−59.0141	−2.46320
$575$	−28.6793	−1.19601
$576$	−43.7959	−1.82483
$577$	25.7448	1.07177	0.535884	−	0.844291i	$-0.319978\pi$
$577$	25.7448	1.07177	0.535884	+	0.844291i	$0.319978\pi$
$578$	−1.23031	−0.0511742
$579$	−2.93048	−0.121787
$580$	3.44382	0.142997
$581$	11.0987	0.460453
$582$	−4.34221	−0.179990
$583$	56.9239	2.35755
$584$	6.75191	0.279396
$585$	4.44417	0.183744
$586$	18.8273	0.777749
$587$	−38.5409	−1.59076	−0.795378	−	0.606114i	$-0.792727\pi$
$587$	−38.5409	−1.59076	−0.795378	+	0.606114i	$0.792727\pi$
$588$	−10.9761	−0.452647
$589$	10.6051	0.436976
$590$	4.56228	0.187826
$591$	−35.1407	−1.44550
$592$	18.2866	0.751576
$593$	−2.52872	−0.103842	−0.0519211	−	0.998651i	$-0.516534\pi$
$593$	−2.52872	−0.103842	−0.0519211	+	0.998651i	$0.516534\pi$
$594$	−145.708	−5.97846
$595$	−3.65487	−0.149835
$596$	−28.8936	−1.18353
$597$	−23.2767	−0.952650
$598$	21.9320	0.896865
$599$	40.0133	1.63490	0.817449	−	0.576000i	$-0.195387\pi$
$599$	40.0133	1.63490	0.817449	+	0.576000i	$0.195387\pi$
$600$	−8.09743	−0.330576
$601$	13.6174	0.555466	0.277733	−	0.960658i	$-0.410417\pi$
$601$	13.6174	0.555466	0.277733	+	0.960658i	$0.410417\pi$
$602$	−57.1629	−2.32979
$603$	65.9938	2.68747
$604$	−3.86614	−0.157311
$605$	4.42855	0.180046
$606$	44.2793	1.79872
$607$	7.52266	0.305335	0.152668	−	0.988278i	$-0.451214\pi$
$607$	7.52266	0.305335	0.152668	+	0.988278i	$0.451214\pi$
$608$	−34.6875	−1.40676
$609$	−63.7908	−2.58493
$610$	−1.69239	−0.0685227
$611$	−7.59945	−0.307441
$612$	−53.2476	−2.15241
$613$	−13.7644	−0.555938	−0.277969	−	0.960590i	$-0.589661\pi$
$613$	−13.7644	−0.555938	−0.277969	+	0.960590i	$0.589661\pi$
$614$	−11.1979	−0.451910
$615$	10.0296	0.404433
$616$	−7.68360	−0.309581
$617$	−11.9599	−0.481488	−0.240744	−	0.970589i	$-0.577391\pi$
$617$	−11.9599	−0.481488	−0.240744	+	0.970589i	$0.577391\pi$
$618$	−15.1753	−0.610441
$619$	−1.00764	−0.0405006	−0.0202503	−	0.999795i	$-0.506446\pi$
$619$	−1.00764	−0.0405006	−0.0202503	+	0.999795i	$0.506446\pi$
$620$	1.21988	0.0489917
$621$	−86.9319	−3.48846
$622$	54.1083	2.16954
$623$	−6.90431	−0.276615
$624$	28.1362	1.12635
$625$	23.6390	0.945561
$626$	−45.0017	−1.79863
$627$	−75.1814	−3.00246
$628$	−33.2667	−1.32748
$629$	16.6011	0.661928
$630$	13.2323	0.527188
$631$	17.2606	0.687135	0.343567	−	0.939128i	$-0.388365\pi$
$631$	17.2606	0.687135	0.343567	+	0.939128i	$0.388365\pi$
$632$	1.17672	0.0468075
$633$	85.0965	3.38228
$634$	−36.3895	−1.44521
$635$	−2.01729	−0.0800536
$636$	−63.5025	−2.51804
$637$	3.77160	0.149436
$638$	64.2370	2.54317
$639$	19.0347	0.753001
$640$	1.21555	0.0480487
$641$	−3.29584	−0.130178	−0.0650890	−	0.997879i	$-0.520733\pi$
$641$	−3.29584	−0.130178	−0.0650890	+	0.997879i	$0.520733\pi$
$642$	45.9125	1.81202
$643$	11.1087	0.438084	0.219042	−	0.975715i	$-0.429707\pi$
$643$	11.1087	0.438084	0.219042	+	0.975715i	$0.429707\pi$
$644$	30.3586	1.19630
$645$	9.71500	0.382528
$646$	−35.6938	−1.40435
$647$	6.17668	0.242830	0.121415	−	0.992602i	$-0.461257\pi$
$647$	6.17668	0.242830	0.121415	+	0.992602i	$0.461257\pi$
$648$	−13.0166	−0.511341
$649$	39.5627	1.55297
$650$	−18.4266	−0.722751
$651$	−22.5962	−0.885615
$652$	−14.2839	−0.559399
$653$	−19.8744	−0.777747	−0.388873	−	0.921291i	$-0.627136\pi$
$653$	−19.8744	−0.777747	−0.388873	+	0.921291i	$0.627136\pi$
$654$	−62.2242	−2.43316
$655$	0.871765	0.0340627
$656$	45.4850	1.77589
$657$	−100.833	−3.93386
$658$	−22.6270	−0.882094
$659$	−27.9526	−1.08888	−0.544439	−	0.838800i	$-0.683257\pi$
$659$	−27.9526	−1.08888	−0.544439	+	0.838800i	$0.683257\pi$
$660$	−8.64797	−0.336622
$661$	8.49351	0.330359	0.165180	−	0.986263i	$-0.447180\pi$
$661$	8.49351	0.330359	0.165180	+	0.986263i	$0.447180\pi$
$662$	13.2815	0.516200
$663$	25.5428	0.992000
$664$	−1.88268	−0.0730621
$665$	4.12371	0.159911
$666$	−60.1035	−2.32896
$667$	38.3250	1.48395
$668$	−6.23285	−0.241156
$669$	−86.7933	−3.35562
$670$	5.08860	0.196590
$671$	−14.6759	−0.566555
$672$	73.9085	2.85108
$673$	40.6380	1.56648	0.783240	−	0.621719i	$-0.213565\pi$
$673$	40.6380	1.56648	0.783240	+	0.621719i	$0.213565\pi$
$674$	11.7632	0.453102
$675$	73.0376	2.81122
$676$	−16.0379	−0.616844
$677$	−20.9542	−0.805335	−0.402667	−	0.915346i	$-0.631917\pi$
$677$	−20.9542	−0.805335	−0.402667	+	0.915346i	$0.631917\pi$
$678$	93.0323	3.57289
$679$	2.06534	0.0792606
$680$	0.619976	0.0237750
$681$	13.2734	0.508636
$682$	22.7543	0.871306
$683$	22.7047	0.868771	0.434385	−	0.900727i	$-0.356966\pi$
$683$	22.7047	0.868771	0.434385	+	0.900727i	$0.356966\pi$
$684$	60.0781	2.29714
$685$	1.05926	0.0404723
$686$	−29.2393	−1.11636
$687$	−28.4977	−1.08726
$688$	44.0582	1.67970
$689$	21.8207	0.831301
$690$	−11.0982	−0.422500
$691$	−14.1391	−0.537877	−0.268938	−	0.963157i	$-0.586673\pi$
$691$	−14.1391	−0.537877	−0.268938	+	0.963157i	$0.586673\pi$
$692$	16.1400	0.613551
$693$	114.747	4.35887
$694$	9.35325	0.355044
$695$	−6.37719	−0.241901
$696$	10.8208	0.410163
$697$	41.2924	1.56406
$698$	1.93329	0.0731762
$699$	48.3612	1.82919
$700$	−25.5064	−0.964053
$701$	−33.4603	−1.26378	−0.631890	−	0.775058i	$-0.717721\pi$
$701$	−33.4603	−1.26378	−0.631890	+	0.775058i	$0.717721\pi$
$702$	−55.8543	−2.10808
$703$	−18.7306	−0.706438
$704$	−29.2842	−1.10369
$705$	3.84553	0.144831
$706$	13.1527	0.495009
$707$	−21.0612	−0.792086
$708$	−44.1349	−1.65869
$709$	−11.9786	−0.449867	−0.224933	−	0.974374i	$-0.572216\pi$
$709$	−11.9786	−0.449867	−0.224933	+	0.974374i	$0.572216\pi$
$710$	1.46772	0.0550824
$711$	−17.5731	−0.659044
$712$	1.17118	0.0438918
$713$	13.5756	0.508411
$714$	76.0525	2.84619
$715$	2.97160	0.111132
$716$	28.3626	1.05996
$717$	−1.25614	−0.0469115
$718$	53.2310	1.98656
$719$	36.6491	1.36678	0.683391	−	0.730052i	$-0.260504\pi$
$719$	36.6491	1.36678	0.683391	+	0.730052i	$0.260504\pi$
$720$	−10.1988	−0.380086
$721$	7.21804	0.268814
$722$	3.53995	0.131743
$723$	−5.83096	−0.216856
$724$	31.2580	1.16169
$725$	−32.1995	−1.19586
$726$	−92.1516	−3.42007
$727$	26.9589	0.999851	0.499926	−	0.866068i	$-0.333361\pi$
$727$	26.9589	0.999851	0.499926	+	0.866068i	$0.333361\pi$
$728$	−2.94536	−0.109162
$729$	49.2293	1.82331
$730$	−7.77496	−0.287764
$731$	39.9971	1.47935
$732$	16.3720	0.605125
$733$	8.01416	0.296010	0.148005	−	0.988987i	$-0.452715\pi$
$733$	8.01416	0.296010	0.148005	+	0.988987i	$0.452715\pi$
$734$	20.8216	0.768541
$735$	−1.90853	−0.0703971
$736$	−44.4036	−1.63674
$737$	44.1268	1.62543
$738$	−149.498	−5.50308
$739$	12.9449	0.476188	0.238094	−	0.971242i	$-0.423477\pi$
$739$	12.9449	0.476188	0.238094	+	0.971242i	$0.423477\pi$
$740$	−2.15454	−0.0792026
$741$	−28.8194	−1.05871
$742$	64.9701	2.38513
$743$	9.22356	0.338380	0.169190	−	0.985583i	$-0.445885\pi$
$743$	9.22356	0.338380	0.169190	+	0.985583i	$0.445885\pi$
$744$	3.83300	0.140525
$745$	−5.02402	−0.184066
$746$	13.0862	0.479120
$747$	28.1159	1.02871
$748$	−35.6041	−1.30182
$749$	−21.8380	−0.797943
$750$	18.8221	0.687286
$751$	−9.24590	−0.337388	−0.168694	−	0.985668i	$-0.553955\pi$
$751$	−9.24590	−0.337388	−0.168694	+	0.985668i	$0.553955\pi$
$752$	17.4397	0.635961
$753$	−37.8251	−1.37842
$754$	24.6240	0.896754
$755$	−0.672245	−0.0244655
$756$	−77.3145	−2.81190
$757$	−1.28037	−0.0465359	−0.0232679	−	0.999729i	$-0.507407\pi$
$757$	−1.28037	−0.0465359	−0.0232679	+	0.999729i	$0.507407\pi$
$758$	53.1743	1.93138
$759$	−96.2399	−3.49329
$760$	−0.699505	−0.0253737
$761$	3.08913	0.111981	0.0559904	−	0.998431i	$-0.482168\pi$
$761$	3.08913	0.111981	0.0559904	+	0.998431i	$0.482168\pi$
$762$	41.9768	1.52066
$763$	29.5966	1.07147
$764$	−29.9933	−1.08512
$765$	−9.25871	−0.334749
$766$	−12.7211	−0.459632
$767$	15.1656	0.547598
$768$	−62.8953	−2.26954
$769$	15.1151	0.545065	0.272533	−	0.962147i	$-0.412139\pi$
$769$	15.1151	0.545065	0.272533	+	0.962147i	$0.412139\pi$
$770$	8.84782	0.318853
$771$	−62.8407	−2.26315
$772$	1.56583	0.0563554
$773$	−48.8534	−1.75713	−0.878567	−	0.477620i	$-0.841500\pi$
$773$	−48.8534	−1.75713	−0.878567	+	0.477620i	$0.841500\pi$
$774$	−144.808	−5.20502
$775$	−11.4058	−0.409709
$776$	−0.350345	−0.0125766
$777$	39.9092	1.43173
$778$	73.5870	2.63822
$779$	−46.5893	−1.66924
$780$	−3.31503	−0.118697
$781$	12.7276	0.455429
$782$	−45.6917	−1.63393
$783$	−97.6024	−3.48802
$784$	−8.65531	−0.309118
$785$	−5.78442	−0.206455
$786$	−18.1402	−0.647038
$787$	33.0618	1.17853	0.589263	−	0.807942i	$-0.299418\pi$
$787$	33.0618	1.17853	0.589263	+	0.807942i	$0.299418\pi$
$788$	18.7766	0.668888
$789$	−65.0981	−2.31755
$790$	−1.35502	−0.0482094
$791$	−44.2502	−1.57336
$792$	−19.4645	−0.691641
$793$	−5.62571	−0.199775
$794$	42.3491	1.50291
$795$	−11.0418	−0.391614
$796$	12.4373	0.440829
$797$	21.8440	0.773755	0.386878	−	0.922131i	$-0.373554\pi$
$797$	21.8440	0.773755	0.386878	+	0.922131i	$0.373554\pi$
$798$	−85.8083	−3.03758
$799$	15.8322	0.560104
$800$	37.3066	1.31899
$801$	−17.4904	−0.617991
$802$	−25.7845	−0.910481
$803$	−67.4221	−2.37927
$804$	−49.2266	−1.73609
$805$	5.27877	0.186052
$806$	8.72241	0.307234
$807$	−62.6354	−2.20487
$808$	3.57261	0.125684
$809$	9.29926	0.326945	0.163472	−	0.986548i	$-0.447731\pi$
$809$	9.29926	0.326945	0.163472	+	0.986548i	$0.447731\pi$
$810$	14.9889	0.526656
$811$	−14.3706	−0.504620	−0.252310	−	0.967646i	$-0.581190\pi$
$811$	−14.3706	−0.504620	−0.252310	+	0.967646i	$0.581190\pi$
$812$	34.0850	1.19615
$813$	78.1129	2.73954
$814$	−40.1883	−1.40860
$815$	−2.48368	−0.0869995
$816$	−58.6173	−2.05202
$817$	−45.1279	−1.57882
$818$	7.28225	0.254618
$819$	43.9860	1.53699
$820$	−5.35907	−0.187147
$821$	25.9028	0.904015	0.452008	−	0.892014i	$-0.350708\pi$
$821$	25.9028	0.904015	0.452008	+	0.892014i	$0.350708\pi$
$822$	−22.0417	−0.768792
$823$	−6.35832	−0.221637	−0.110819	−	0.993841i	$-0.535347\pi$
$823$	−6.35832	−0.221637	−0.110819	+	0.993841i	$0.535347\pi$
$824$	−1.22440	−0.0426539
$825$	80.8579	2.81511
$826$	45.1549	1.57114
$827$	−17.3424	−0.603055	−0.301528	−	0.953457i	$-0.597497\pi$
$827$	−17.3424	−0.603055	−0.301528	+	0.953457i	$0.597497\pi$
$828$	76.9061	2.67267
$829$	−19.6646	−0.682979	−0.341490	−	0.939886i	$-0.610931\pi$
$829$	−19.6646	−0.682979	−0.341490	+	0.939886i	$0.610931\pi$
$830$	2.16794	0.0752503
$831$	85.5432	2.96746
$832$	−11.2255	−0.389176
$833$	−7.85751	−0.272247
$834$	132.700	4.59503
$835$	−1.08377	−0.0375054
$836$	40.1713	1.38935
$837$	−34.5731	−1.19502
$838$	−58.5759	−2.02347
$839$	30.8195	1.06401	0.532004	−	0.846742i	$-0.321439\pi$
$839$	30.8195	1.06401	0.532004	+	0.846742i	$0.321439\pi$
$840$	1.49043	0.0514247
$841$	14.0292	0.483765
$842$	−12.5942	−0.434025
$843$	1.69650	0.0584306
$844$	−45.4692	−1.56512
$845$	−2.78868	−0.0959335
$846$	−57.3200	−1.97070
$847$	43.8313	1.50606
$848$	−50.0755	−1.71960
$849$	67.0063	2.29965
$850$	38.3888	1.31673
$851$	−23.9771	−0.821924
$852$	−14.1985	−0.486433
$853$	4.88184	0.167151	0.0835755	−	0.996501i	$-0.473366\pi$
$853$	4.88184	0.167151	0.0835755	+	0.996501i	$0.473366\pi$
$854$	−16.7503	−0.573184
$855$	10.4464	0.357259
$856$	3.70438	0.126613
$857$	15.0808	0.515149	0.257575	−	0.966258i	$-0.417077\pi$
$857$	15.0808	0.515149	0.257575	+	0.966258i	$0.417077\pi$
$858$	−61.8347	−2.11100
$859$	−26.2744	−0.896469	−0.448235	−	0.893916i	$-0.647947\pi$
$859$	−26.2744	−0.896469	−0.448235	+	0.893916i	$0.647947\pi$
$860$	−5.19097	−0.177011
$861$	99.2675	3.38303
$862$	−30.9724	−1.05493
$863$	−28.7015	−0.977010	−0.488505	−	0.872561i	$-0.662458\pi$
$863$	−28.7015	−0.977010	−0.488505	+	0.872561i	$0.662458\pi$
$864$	113.083	3.84716
$865$	2.80643	0.0954214
$866$	−52.2912	−1.77693
$867$	2.06950	0.0702840
$868$	12.0737	0.409809
$869$	−11.7503	−0.398602
$870$	−12.4604	−0.422447
$871$	16.9152	0.573149
$872$	−5.02047	−0.170014
$873$	5.23204	0.177078
$874$	51.5529	1.74380
$875$	−8.95261	−0.302653
$876$	75.2140	2.54125
$877$	−2.70892	−0.0914736	−0.0457368	−	0.998954i	$-0.514564\pi$
$877$	−2.70892	−0.0914736	−0.0457368	+	0.998954i	$0.514564\pi$
$878$	−30.5307	−1.03036
$879$	−31.6694	−1.06818
$880$	−6.81943	−0.229883
$881$	−53.5581	−1.80442	−0.902209	−	0.431299i	$-0.858055\pi$
$881$	−53.5581	−1.80442	−0.902209	+	0.431299i	$0.858055\pi$
$882$	28.4478	0.957888
$883$	23.3499	0.785787	0.392894	−	0.919584i	$-0.371474\pi$
$883$	23.3499	0.785787	0.392894	+	0.919584i	$0.371474\pi$
$884$	−13.6482	−0.459037
$885$	−7.67419	−0.257965
$886$	30.2007	1.01461
$887$	−40.8895	−1.37293	−0.686467	−	0.727161i	$-0.740840\pi$
$887$	−40.8895	−1.37293	−0.686467	+	0.727161i	$0.740840\pi$
$888$	−6.76980	−0.227180
$889$	−19.9660	−0.669638
$890$	−1.34863	−0.0452063
$891$	129.979	4.35447
$892$	46.3759	1.55278
$893$	−17.8631	−0.597767
$894$	104.543	3.49643
$895$	4.93170	0.164849
$896$	12.0308	0.401921
$897$	−36.8917	−1.23178
$898$	43.0095	1.43525
$899$	15.2420	0.508348
$900$	−64.6143	−2.15381
$901$	−45.4598	−1.51449
$902$	−99.9619	−3.32837
$903$	96.1536	3.19979
$904$	7.50617	0.249652
$905$	5.43515	0.180670
$906$	13.9884	0.464735
$907$	21.0031	0.697396	0.348698	−	0.937235i	$-0.386624\pi$
$907$	21.0031	0.697396	0.348698	+	0.937235i	$0.386624\pi$
$908$	−7.09229	−0.235366
$909$	−53.3532	−1.76962
$910$	3.39164	0.112432
$911$	−26.3055	−0.871539	−0.435770	−	0.900058i	$-0.643524\pi$
$911$	−26.3055	−0.871539	−0.435770	+	0.900058i	$0.643524\pi$
$912$	66.1365	2.19000
$913$	18.7997	0.622180
$914$	25.5988	0.846732
$915$	2.84676	0.0941110
$916$	15.2271	0.503116
$917$	8.62825	0.284930
$918$	116.363	3.84056
$919$	25.2817	0.833965	0.416983	−	0.908914i	$-0.363088\pi$
$919$	25.2817	0.833965	0.416983	+	0.908914i	$0.363088\pi$
$920$	−0.895438	−0.0295217
$921$	18.8360	0.620666
$922$	65.1900	2.14692
$923$	4.87888	0.160590
$924$	−85.5928	−2.81580
$925$	20.1448	0.662358
$926$	−8.76884	−0.288162
$927$	18.2851	0.600562
$928$	−49.8539	−1.63653
$929$	32.3403	1.06105	0.530526	−	0.847669i	$-0.321994\pi$
$929$	32.3403	1.06105	0.530526	+	0.847669i	$0.321994\pi$
$930$	−4.41377	−0.144733
$931$	8.86545	0.290553
$932$	−25.8406	−0.846438
$933$	−91.0154	−2.97971
$934$	40.6785	1.33104
$935$	−6.19085	−0.202463
$936$	−7.46134	−0.243882
$937$	−35.8979	−1.17273	−0.586367	−	0.810046i	$-0.699442\pi$
$937$	−35.8979	−1.17273	−0.586367	+	0.810046i	$0.699442\pi$
$938$	50.3642	1.64445
$939$	75.6972	2.47028
$940$	−2.05476	−0.0670189
$941$	−45.1295	−1.47118	−0.735591	−	0.677426i	$-0.763095\pi$
$941$	−45.1295	−1.47118	−0.735591	+	0.677426i	$0.763095\pi$
$942$	120.365	3.92171
$943$	−59.6391	−1.94212
$944$	−34.8030	−1.13274
$945$	−13.4435	−0.437316
$946$	−96.8262	−3.14809
$947$	13.6843	0.444679	0.222339	−	0.974969i	$-0.428631\pi$
$947$	13.6843	0.444679	0.222339	+	0.974969i	$0.428631\pi$
$948$	13.1083	0.425737
$949$	−25.8450	−0.838963
$950$	−43.3132	−1.40527
$951$	61.2107	1.98489
$952$	6.13618	0.198875
$953$	48.4986	1.57102	0.785512	−	0.618847i	$-0.212400\pi$
$953$	48.4986	1.57102	0.785512	+	0.618847i	$0.212400\pi$
$954$	164.586	5.32865
$955$	−5.21524	−0.168761
$956$	0.671189	0.0217078
$957$	−108.053	−3.49285
$958$	−37.5545	−1.21333
$959$	10.4840	0.338546
$960$	5.68042	0.183335
$961$	−25.6009	−0.825837
$962$	−15.4054	−0.496691
$963$	−55.3212	−1.78270
$964$	3.11563	0.100348
$965$	0.272267	0.00876457
$966$	−109.843	−3.53415
$967$	−46.6246	−1.49935	−0.749674	−	0.661808i	$-0.769790\pi$
$967$	−46.6246	−1.49935	−0.749674	+	0.661808i	$0.769790\pi$
$968$	−7.43511	−0.238974
$969$	60.0404	1.92878
$970$	0.403429	0.0129533
$971$	−18.9025	−0.606611	−0.303305	−	0.952893i	$-0.598090\pi$
$971$	−18.9025	−0.606611	−0.303305	+	0.952893i	$0.598090\pi$
$972$	−67.4378	−2.16307
$973$	−63.1179	−2.02347
$974$	−57.3889	−1.83886
$975$	30.9953	0.992645
$976$	12.9103	0.413247
$977$	−47.6595	−1.52476	−0.762381	−	0.647128i	$-0.775970\pi$
$977$	−47.6595	−1.52476	−0.762381	+	0.647128i	$0.775970\pi$
$978$	51.6817	1.65260
$979$	−11.6950	−0.373772
$980$	1.01978	0.0325755
$981$	74.9755	2.39378
$982$	10.9192	0.348447
$983$	2.46549	0.0786370	0.0393185	−	0.999227i	$-0.487481\pi$
$983$	2.46549	0.0786370	0.0393185	+	0.999227i	$0.487481\pi$
$984$	−16.8388	−0.536800
$985$	3.26488	0.104028
$986$	−51.3002	−1.63373
$987$	38.0609	1.21149
$988$	15.3989	0.489905
$989$	−57.7683	−1.83692
$990$	22.4138	0.712356
$991$	−9.08033	−0.288446	−0.144223	−	0.989545i	$-0.546068\pi$
$991$	−9.08033	−0.288446	−0.144223	+	0.989545i	$0.546068\pi$
$992$	−17.6594	−0.560688
$993$	−22.3408	−0.708963
$994$	14.5266	0.460757
$995$	2.16260	0.0685591
$996$	−20.9724	−0.664536
$997$	37.1590	1.17684	0.588418	−	0.808557i	$-0.299751\pi$
$997$	37.1590	1.17684	0.588418	+	0.808557i	$0.299751\pi$
$998$	71.4984	2.26324
$999$	61.0626	1.93193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.a.b.1.13	✓	17
3.2	odd	2		3141.2.a.e.1.5		17
4.3	odd	2		5584.2.a.m.1.17		17
5.4	even	2		8725.2.a.m.1.5		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.a.b.1.13	✓	17	1.1	even	1	trivial
3141.2.a.e.1.5		17	3.2	odd	2
5584.2.a.m.1.17		17	4.3	odd	2
8725.2.a.m.1.5		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)

\(f(q)\)	\(=\)	\(q+1.93329 q^{2} -3.25199 q^{3} +1.73762 q^{4} +0.302138 q^{5} -6.28704 q^{6} +2.99039 q^{7} -0.507260 q^{8} +7.57541 q^{9} +O(q^{10})\)	\(q+1.93329 q^{2} -3.25199 q^{3} +1.73762 q^{4} +0.302138 q^{5} -6.28704 q^{6} +2.99039 q^{7} -0.507260 q^{8} +7.57541 q^{9} +0.584120 q^{10} +5.06531 q^{11} -5.65071 q^{12} +1.94169 q^{13} +5.78130 q^{14} -0.982547 q^{15} -4.45592 q^{16} -4.04520 q^{17} +14.6455 q^{18} +4.56410 q^{19} +0.525000 q^{20} -9.72470 q^{21} +9.79273 q^{22} +5.84252 q^{23} +1.64960 q^{24} -4.90871 q^{25} +3.75386 q^{26} -14.8792 q^{27} +5.19616 q^{28} +6.55966 q^{29} -1.89955 q^{30} +2.32359 q^{31} -7.60007 q^{32} -16.4723 q^{33} -7.82055 q^{34} +0.903509 q^{35} +13.1632 q^{36} -4.10389 q^{37} +8.82375 q^{38} -6.31435 q^{39} -0.153262 q^{40} -10.2078 q^{41} -18.8007 q^{42} -9.88756 q^{43} +8.80158 q^{44} +2.28882 q^{45} +11.2953 q^{46} -3.91383 q^{47} +14.4906 q^{48} +1.94243 q^{49} -9.48998 q^{50} +13.1549 q^{51} +3.37392 q^{52} +11.2380 q^{53} -28.7658 q^{54} +1.53042 q^{55} -1.51691 q^{56} -14.8424 q^{57} +12.6817 q^{58} +7.81051 q^{59} -1.70729 q^{60} -2.89733 q^{61} +4.49217 q^{62} +22.6534 q^{63} -5.78132 q^{64} +0.586658 q^{65} -31.8458 q^{66} +8.71157 q^{67} -7.02901 q^{68} -18.9998 q^{69} +1.74675 q^{70} +2.51270 q^{71} -3.84270 q^{72} -13.3105 q^{73} -7.93403 q^{74} +15.9631 q^{75} +7.93067 q^{76} +15.1473 q^{77} -12.2075 q^{78} -2.31976 q^{79} -1.34630 q^{80} +25.6606 q^{81} -19.7346 q^{82} +3.71146 q^{83} -16.8978 q^{84} -1.22221 q^{85} -19.1155 q^{86} -21.3319 q^{87} -2.56943 q^{88} -2.30883 q^{89} +4.42495 q^{90} +5.80641 q^{91} +10.1521 q^{92} -7.55628 q^{93} -7.56658 q^{94} +1.37899 q^{95} +24.7153 q^{96} +0.690661 q^{97} +3.75528 q^{98} +38.3718 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9}+O(q^{10}) \) 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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