LMFDB - Embedded newform 6017.2.a.e.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$0$
Dimension:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37466 q^{2} +0.769590 q^{3} +3.63899 q^{4} -2.34020 q^{5} -1.82751 q^{6} -2.65740 q^{7} -3.89204 q^{8} -2.40773 q^{9} +O(q^{10})$	\(q-2.37466 q^{2} +0.769590 q^{3} +3.63899 q^{4} -2.34020 q^{5} -1.82751 q^{6} -2.65740 q^{7} -3.89204 q^{8} -2.40773 q^{9} +5.55717 q^{10} +1.00000 q^{11} +2.80053 q^{12} -3.14079 q^{13} +6.31040 q^{14} -1.80099 q^{15} +1.96428 q^{16} -0.557539 q^{17} +5.71753 q^{18} +0.143556 q^{19} -8.51596 q^{20} -2.04511 q^{21} -2.37466 q^{22} +2.65168 q^{23} -2.99528 q^{24} +0.476528 q^{25} +7.45830 q^{26} -4.16174 q^{27} -9.67024 q^{28} -5.75611 q^{29} +4.27674 q^{30} -1.62645 q^{31} +3.11959 q^{32} +0.769590 q^{33} +1.32396 q^{34} +6.21883 q^{35} -8.76172 q^{36} -6.38330 q^{37} -0.340896 q^{38} -2.41712 q^{39} +9.10815 q^{40} -3.76072 q^{41} +4.85642 q^{42} +3.54715 q^{43} +3.63899 q^{44} +5.63457 q^{45} -6.29683 q^{46} -1.18118 q^{47} +1.51169 q^{48} +0.0617514 q^{49} -1.13159 q^{50} -0.429077 q^{51} -11.4293 q^{52} -1.49876 q^{53} +9.88269 q^{54} -2.34020 q^{55} +10.3427 q^{56} +0.110479 q^{57} +13.6688 q^{58} +1.68341 q^{59} -6.55380 q^{60} -11.4533 q^{61} +3.86227 q^{62} +6.39829 q^{63} -11.3365 q^{64} +7.35008 q^{65} -1.82751 q^{66} -8.38172 q^{67} -2.02888 q^{68} +2.04071 q^{69} -14.7676 q^{70} -14.1088 q^{71} +9.37100 q^{72} +7.21200 q^{73} +15.1581 q^{74} +0.366731 q^{75} +0.522399 q^{76} -2.65740 q^{77} +5.73984 q^{78} +13.6103 q^{79} -4.59681 q^{80} +4.02036 q^{81} +8.93041 q^{82} -12.3046 q^{83} -7.44212 q^{84} +1.30475 q^{85} -8.42327 q^{86} -4.42984 q^{87} -3.89204 q^{88} -15.3582 q^{89} -13.3802 q^{90} +8.34633 q^{91} +9.64945 q^{92} -1.25170 q^{93} +2.80490 q^{94} -0.335949 q^{95} +2.40081 q^{96} +2.61597 q^{97} -0.146638 q^{98} -2.40773 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) $ 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * 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 $

$2$	−2.37466	−1.67914	−0.839568	−	0.543255i	$-0.817192\pi$
$2$	−2.37466	−1.67914	−0.839568	+	0.543255i	$0.817192\pi$
$3$	0.769590	0.444323	0.222162	−	0.975010i	$-0.428689\pi$
$3$	0.769590	0.444323	0.222162	+	0.975010i	$0.428689\pi$
$4$	3.63899	1.81950
$5$	−2.34020	−1.04657	−0.523284	−	0.852158i	$-0.675293\pi$
$5$	−2.34020	−1.04657	−0.523284	+	0.852158i	$0.675293\pi$
$6$	−1.82751	−0.746079
$7$	−2.65740	−1.00440	−0.502201	−	0.864751i	$-0.667476\pi$
$7$	−2.65740	−1.00440	−0.502201	+	0.864751i	$0.667476\pi$
$8$	−3.89204	−1.37605
$9$	−2.40773	−0.802577
$10$	5.55717	1.75733
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.80053	0.808444
$13$	−3.14079	−0.871099	−0.435550	−	0.900165i	$-0.643446\pi$
$13$	−3.14079	−0.871099	−0.435550	+	0.900165i	$0.643446\pi$
$14$	6.31040	1.68653
$15$	−1.80099	−0.465015
$16$	1.96428	0.491071
$17$	−0.557539	−0.135223	−0.0676116	−	0.997712i	$-0.521538\pi$
$17$	−0.557539	−0.135223	−0.0676116	+	0.997712i	$0.521538\pi$
$18$	5.71753	1.34764
$19$	0.143556	0.0329340	0.0164670	−	0.999864i	$-0.494758\pi$
$19$	0.143556	0.0329340	0.0164670	+	0.999864i	$0.494758\pi$
$20$	−8.51596	−1.90423
$21$	−2.04511	−0.446279
$22$	−2.37466	−0.506278
$23$	2.65168	0.552914	0.276457	−	0.961026i	$-0.410840\pi$
$23$	2.65168	0.552914	0.276457	+	0.961026i	$0.410840\pi$
$24$	−2.99528	−0.611409
$25$	0.476528	0.0953055
$26$	7.45830	1.46269
$27$	−4.16174	−0.800927
$28$	−9.67024	−1.82750
$29$	−5.75611	−1.06888	−0.534441	−	0.845206i	$-0.679478\pi$
$29$	−5.75611	−1.06888	−0.534441	+	0.845206i	$0.679478\pi$
$30$	4.27674	0.780822
$31$	−1.62645	−0.292120	−0.146060	−	0.989276i	$-0.546659\pi$
$31$	−1.62645	−0.292120	−0.146060	+	0.989276i	$0.546659\pi$
$32$	3.11959	0.551471
$33$	0.769590	0.133968
$34$	1.32396	0.227058
$35$	6.21883	1.05117
$36$	−8.76172	−1.46029
$37$	−6.38330	−1.04941	−0.524704	−	0.851285i	$-0.675824\pi$
$37$	−6.38330	−1.04941	−0.524704	+	0.851285i	$0.675824\pi$
$38$	−0.340896	−0.0553006
$39$	−2.41712	−0.387050
$40$	9.10815	1.44013
$41$	−3.76072	−0.587325	−0.293663	−	0.955909i	$-0.594874\pi$
$41$	−3.76072	−0.587325	−0.293663	+	0.955909i	$0.594874\pi$
$42$	4.85642	0.749362
$43$	3.54715	0.540936	0.270468	−	0.962729i	$-0.412822\pi$
$43$	3.54715	0.540936	0.270468	+	0.962729i	$0.412822\pi$
$44$	3.63899	0.548599
$45$	5.63457	0.839952
$46$	−6.29683	−0.928417
$47$	−1.18118	−0.172293	−0.0861466	−	0.996282i	$-0.527455\pi$
$47$	−1.18118	−0.172293	−0.0861466	+	0.996282i	$0.527455\pi$
$48$	1.51169	0.218194
$49$	0.0617514	0.00882163
$50$	−1.13159	−0.160031
$51$	−0.429077	−0.0600828
$52$	−11.4293	−1.58496
$53$	−1.49876	−0.205871	−0.102936	−	0.994688i	$-0.532824\pi$
$53$	−1.49876	−0.205871	−0.102936	+	0.994688i	$0.532824\pi$
$54$	9.88269	1.34486
$55$	−2.34020	−0.315552
$56$	10.3427	1.38210
$57$	0.110479	0.0146333
$58$	13.6688	1.79480
$59$	1.68341	0.219162	0.109581	−	0.993978i	$-0.465049\pi$
$59$	1.68341	0.219162	0.109581	+	0.993978i	$0.465049\pi$
$60$	−6.55380	−0.846092
$61$	−11.4533	−1.46644	−0.733222	−	0.679989i	$-0.761984\pi$
$61$	−11.4533	−1.46644	−0.733222	+	0.679989i	$0.761984\pi$
$62$	3.86227	0.490508
$63$	6.39829	0.806109
$64$	−11.3365	−1.41707
$65$	7.35008	0.911665
$66$	−1.82751	−0.224951
$67$	−8.38172	−1.02399	−0.511995	−	0.858988i	$-0.671093\pi$
$67$	−8.38172	−1.02399	−0.511995	+	0.858988i	$0.671093\pi$
$68$	−2.02888	−0.246038
$69$	2.04071	0.245672
$70$	−14.7676	−1.76506
$71$	−14.1088	−1.67441	−0.837205	−	0.546890i	$-0.815812\pi$
$71$	−14.1088	−1.67441	−0.837205	+	0.546890i	$0.815812\pi$
$72$	9.37100	1.10438
$73$	7.21200	0.844101	0.422050	−	0.906572i	$-0.361311\pi$
$73$	7.21200	0.844101	0.422050	+	0.906572i	$0.361311\pi$
$74$	15.1581	1.76210
$75$	0.366731	0.0423464
$76$	0.522399	0.0599232
$77$	−2.65740	−0.302838
$78$	5.73984	0.649909
$79$	13.6103	1.53128	0.765639	−	0.643270i	$-0.222423\pi$
$79$	13.6103	1.53128	0.765639	+	0.643270i	$0.222423\pi$
$80$	−4.59681	−0.513939
$81$	4.02036	0.446707
$82$	8.93041	0.986198
$83$	−12.3046	−1.35060	−0.675301	−	0.737542i	$-0.735986\pi$
$83$	−12.3046	−1.35060	−0.675301	+	0.737542i	$0.735986\pi$
$84$	−7.44212	−0.812002
$85$	1.30475	0.141520
$86$	−8.42327	−0.908304
$87$	−4.42984	−0.474929
$88$	−3.89204	−0.414893
$89$	−15.3582	−1.62797	−0.813983	−	0.580889i	$-0.802705\pi$
$89$	−15.3582	−1.62797	−0.813983	+	0.580889i	$0.802705\pi$
$90$	−13.3802	−1.41039
$91$	8.34633	0.874933
$92$	9.64945	1.00602
$93$	−1.25170	−0.129796
$94$	2.80490	0.289304
$95$	−0.335949	−0.0344677
$96$	2.40081	0.245031
$97$	2.61597	0.265611	0.132806	−	0.991142i	$-0.457601\pi$
$97$	2.61597	0.265611	0.132806	+	0.991142i	$0.457601\pi$
$98$	−0.146638	−0.0148127
$99$	−2.40773	−0.241986
$100$	1.73408	0.173408
$101$	−12.0520	−1.19922	−0.599608	−	0.800294i	$-0.704677\pi$
$101$	−12.0520	−1.19922	−0.599608	+	0.800294i	$0.704677\pi$
$102$	1.01891	0.100887
$103$	−17.8795	−1.76172	−0.880859	−	0.473379i	$-0.843034\pi$
$103$	−17.8795	−1.76172	−0.880859	+	0.473379i	$0.843034\pi$
$104$	12.2241	1.19867
$105$	4.78595	0.467061
$106$	3.55905	0.345686
$107$	−14.2684	−1.37937	−0.689687	−	0.724108i	$-0.742252\pi$
$107$	−14.2684	−1.37937	−0.689687	+	0.724108i	$0.742252\pi$
$108$	−15.1445	−1.45728
$109$	15.1971	1.45562	0.727811	−	0.685778i	$-0.240538\pi$
$109$	15.1971	1.45562	0.727811	+	0.685778i	$0.240538\pi$
$110$	5.55717	0.529855
$111$	−4.91252	−0.466276
$112$	−5.21987	−0.493232
$113$	−10.7650	−1.01268	−0.506341	−	0.862333i	$-0.669002\pi$
$113$	−10.7650	−1.01268	−0.506341	+	0.862333i	$0.669002\pi$
$114$	−0.262350	−0.0245713
$115$	−6.20546	−0.578662
$116$	−20.9464	−1.94483
$117$	7.56219	0.699124
$118$	−3.99753	−0.368002
$119$	1.48160	0.135818
$120$	7.00955	0.639881
$121$	1.00000	0.0909091
$122$	27.1976	2.46236
$123$	−2.89421	−0.260962
$124$	−5.91865	−0.531511
$125$	10.5858	0.946825
$126$	−15.1937	−1.35357
$127$	10.7998	0.958329	0.479164	−	0.877725i	$-0.340940\pi$
$127$	10.7998	0.958329	0.479164	+	0.877725i	$0.340940\pi$
$128$	20.6812	1.82797
$129$	2.72985	0.240350
$130$	−17.4539	−1.53081
$131$	−13.6805	−1.19527	−0.597635	−	0.801769i	$-0.703893\pi$
$131$	−13.6805	−1.19527	−0.597635	+	0.801769i	$0.703893\pi$
$132$	2.80053	0.243755
$133$	−0.381485	−0.0330789
$134$	19.9037	1.71942
$135$	9.73929	0.838224
$136$	2.16997	0.186073
$137$	−2.64492	−0.225971	−0.112986	−	0.993597i	$-0.536041\pi$
$137$	−2.64492	−0.225971	−0.112986	+	0.993597i	$0.536041\pi$
$138$	−4.84598	−0.412517
$139$	−10.9853	−0.931762	−0.465881	−	0.884847i	$-0.654263\pi$
$139$	−10.9853	−0.931762	−0.465881	+	0.884847i	$0.654263\pi$
$140$	22.6303	1.91261
$141$	−0.909027	−0.0765539
$142$	33.5036	2.81156
$143$	−3.14079	−0.262646
$144$	−4.72946	−0.394122
$145$	13.4704	1.11866
$146$	−17.1260	−1.41736
$147$	0.0475233	0.00391966
$148$	−23.2288	−1.90939
$149$	9.55090	0.782440	0.391220	−	0.920297i	$-0.372053\pi$
$149$	9.55090	0.782440	0.391220	+	0.920297i	$0.372053\pi$
$150$	−0.870860	−0.0711054
$151$	9.93174	0.808234	0.404117	−	0.914707i	$-0.367579\pi$
$151$	9.93174	0.808234	0.404117	+	0.914707i	$0.367579\pi$
$152$	−0.558726	−0.0453186
$153$	1.34240	0.108527
$154$	6.31040	0.508507
$155$	3.80622	0.305723
$156$	−8.79590	−0.704235
$157$	17.3930	1.38812	0.694058	−	0.719919i	$-0.255821\pi$
$157$	17.3930	1.38812	0.694058	+	0.719919i	$0.255821\pi$
$158$	−32.3198	−2.57122
$159$	−1.15343	−0.0914733
$160$	−7.30047	−0.577153
$161$	−7.04656	−0.555347
$162$	−9.54698	−0.750081
$163$	−1.50620	−0.117975	−0.0589873	−	0.998259i	$-0.518787\pi$
$163$	−1.50620	−0.117975	−0.0589873	+	0.998259i	$0.518787\pi$
$164$	−13.6852	−1.06864
$165$	−1.80099	−0.140207
$166$	29.2191	2.26784
$167$	−23.2458	−1.79881	−0.899406	−	0.437113i	$-0.856001\pi$
$167$	−23.2458	−1.79881	−0.899406	+	0.437113i	$0.856001\pi$
$168$	7.95964	0.614100
$169$	−3.13542	−0.241186
$170$	−3.09834	−0.237632
$171$	−0.345644	−0.0264320
$172$	12.9081	0.984230
$173$	14.1430	1.07527	0.537636	−	0.843177i	$-0.319317\pi$
$173$	14.1430	1.07527	0.537636	+	0.843177i	$0.319317\pi$
$174$	10.5194	0.797470
$175$	−1.26632	−0.0957250
$176$	1.96428	0.148063
$177$	1.29554	0.0973787
$178$	36.4704	2.73358
$179$	−1.15597	−0.0864009	−0.0432004	−	0.999066i	$-0.513755\pi$
$179$	−1.15597	−0.0864009	−0.0432004	+	0.999066i	$0.513755\pi$
$180$	20.5042	1.52829
$181$	13.8049	1.02611	0.513054	−	0.858356i	$-0.328514\pi$
$181$	13.8049	1.02611	0.513054	+	0.858356i	$0.328514\pi$
$182$	−19.8197	−1.46913
$183$	−8.81434	−0.651575
$184$	−10.3205	−0.760834
$185$	14.9382	1.09828
$186$	2.97236	0.217944
$187$	−0.557539	−0.0407713
$188$	−4.29832	−0.313487
$189$	11.0594	0.804452
$190$	0.797764	0.0578759
$191$	−6.38322	−0.461874	−0.230937	−	0.972969i	$-0.574179\pi$
$191$	−6.38322	−0.461874	−0.230937	+	0.972969i	$0.574179\pi$
$192$	−8.72448	−0.629635
$193$	−3.32615	−0.239421	−0.119711	−	0.992809i	$-0.538197\pi$
$193$	−3.32615	−0.239421	−0.119711	+	0.992809i	$0.538197\pi$
$194$	−6.21202	−0.445997
$195$	5.65655	0.405074
$196$	0.224713	0.0160509
$197$	−5.37766	−0.383143	−0.191571	−	0.981479i	$-0.561358\pi$
$197$	−5.37766	−0.383143	−0.191571	+	0.981479i	$0.561358\pi$
$198$	5.71753	0.406327
$199$	−18.9031	−1.34000	−0.670002	−	0.742359i	$-0.733707\pi$
$199$	−18.9031	−1.34000	−0.670002	+	0.742359i	$0.733707\pi$
$200$	−1.85467	−0.131145
$201$	−6.45049	−0.454983
$202$	28.6193	2.01365
$203$	15.2963	1.07359
$204$	−1.56141	−0.109320
$205$	8.80082	0.614676
$206$	42.4576	2.95816
$207$	−6.38453	−0.443756
$208$	−6.16940	−0.427771
$209$	0.143556	0.00992997
$210$	−11.3650	−0.784259
$211$	7.71172	0.530897	0.265448	−	0.964125i	$-0.414480\pi$
$211$	7.71172	0.530897	0.265448	+	0.964125i	$0.414480\pi$
$212$	−5.45399	−0.374582
$213$	−10.8580	−0.743979
$214$	33.8824	2.31616
$215$	−8.30104	−0.566126
$216$	16.1977	1.10211
$217$	4.32213	0.293405
$218$	−36.0880	−2.44419
$219$	5.55028	0.375053
$220$	−8.51596	−0.574146
$221$	1.75112	0.117793
$222$	11.6656	0.782941
$223$	25.9823	1.73990	0.869951	−	0.493139i	$-0.164151\pi$
$223$	25.9823	1.73990	0.869951	+	0.493139i	$0.164151\pi$
$224$	−8.28999	−0.553899
$225$	−1.14735	−0.0764900
$226$	25.5631	1.70043
$227$	10.6777	0.708706	0.354353	−	0.935112i	$-0.384701\pi$
$227$	10.6777	0.708706	0.354353	+	0.935112i	$0.384701\pi$
$228$	0.402033	0.0266253
$229$	20.2118	1.33563	0.667816	−	0.744327i	$-0.267229\pi$
$229$	20.2118	1.33563	0.667816	+	0.744327i	$0.267229\pi$
$230$	14.7358	0.971652
$231$	−2.04511	−0.134558
$232$	22.4030	1.47083
$233$	−1.53537	−0.100586	−0.0502928	−	0.998735i	$-0.516015\pi$
$233$	−1.53537	−0.100586	−0.0502928	+	0.998735i	$0.516015\pi$
$234$	−17.9576	−1.17392
$235$	2.76420	0.180317
$236$	6.12593	0.398764
$237$	10.4744	0.680382
$238$	−3.51830	−0.228057
$239$	7.81339	0.505406	0.252703	−	0.967544i	$-0.418680\pi$
$239$	7.81339	0.505406	0.252703	+	0.967544i	$0.418680\pi$
$240$	−3.53766	−0.228355
$241$	6.46997	0.416768	0.208384	−	0.978047i	$-0.433180\pi$
$241$	6.46997	0.416768	0.208384	+	0.978047i	$0.433180\pi$
$242$	−2.37466	−0.152649
$243$	15.5792	0.999409
$244$	−41.6784	−2.66819
$245$	−0.144511	−0.00923244
$246$	6.87275	0.438191
$247$	−0.450879	−0.0286888
$248$	6.33023	0.401970
$249$	−9.46948	−0.600104
$250$	−25.1377	−1.58985
$251$	−13.7574	−0.868361	−0.434181	−	0.900826i	$-0.642962\pi$
$251$	−13.7574	−0.868361	−0.434181	+	0.900826i	$0.642962\pi$
$252$	23.2833	1.46671
$253$	2.65168	0.166710
$254$	−25.6459	−1.60916
$255$	1.00412	0.0628807
$256$	−26.4376	−1.65235
$257$	15.6173	0.974183	0.487092	−	0.873351i	$-0.338058\pi$
$257$	15.6173	0.974183	0.487092	+	0.873351i	$0.338058\pi$
$258$	−6.48246	−0.403581
$259$	16.9629	1.05403
$260$	26.7469	1.65877
$261$	13.8592	0.857860
$262$	32.4864	2.00702
$263$	16.0636	0.990526	0.495263	−	0.868743i	$-0.335072\pi$
$263$	16.0636	0.990526	0.495263	+	0.868743i	$0.335072\pi$
$264$	−2.99528	−0.184347
$265$	3.50741	0.215458
$266$	0.905895	0.0555440
$267$	−11.8195	−0.723343
$268$	−30.5010	−1.86315
$269$	−14.1787	−0.864490	−0.432245	−	0.901756i	$-0.642278\pi$
$269$	−14.1787	−0.864490	−0.432245	+	0.901756i	$0.642278\pi$
$270$	−23.1275	−1.40749
$271$	18.3761	1.11627	0.558134	−	0.829751i	$-0.311517\pi$
$271$	18.3761	1.11627	0.558134	+	0.829751i	$0.311517\pi$
$272$	−1.09516	−0.0664041
$273$	6.42325	0.388753
$274$	6.28078	0.379436
$275$	0.476528	0.0287357
$276$	7.42612	0.447000
$277$	20.8189	1.25088	0.625442	−	0.780270i	$-0.284918\pi$
$277$	20.8189	1.25088	0.625442	+	0.780270i	$0.284918\pi$
$278$	26.0864	1.56456
$279$	3.91606	0.234449
$280$	−24.2040	−1.44646
$281$	−26.4328	−1.57685	−0.788425	−	0.615131i	$-0.789103\pi$
$281$	−26.4328	−1.57685	−0.788425	+	0.615131i	$0.789103\pi$
$282$	2.15863	0.128544
$283$	3.51250	0.208796	0.104398	−	0.994536i	$-0.466708\pi$
$283$	3.51250	0.208796	0.104398	+	0.994536i	$0.466708\pi$
$284$	−51.3419	−3.04658
$285$	−0.258543	−0.0153148
$286$	7.45830	0.441019
$287$	9.99371	0.589910
$288$	−7.51114	−0.442598
$289$	−16.6891	−0.981715
$290$	−31.9876	−1.87838
$291$	2.01322	0.118017
$292$	26.2444	1.53584
$293$	20.8402	1.21750	0.608749	−	0.793363i	$-0.291672\pi$
$293$	20.8402	1.21750	0.608749	+	0.793363i	$0.291672\pi$
$294$	−0.112851	−0.00658163
$295$	−3.93952	−0.229368
$296$	24.8441	1.44403
$297$	−4.16174	−0.241488
$298$	−22.6801	−1.31382
$299$	−8.32838	−0.481643
$300$	1.33453	0.0770492
$301$	−9.42619	−0.543316
$302$	−23.5845	−1.35713
$303$	−9.27508	−0.532840
$304$	0.281984	0.0161729
$305$	26.8030	1.53473
$306$	−3.18775	−0.182232
$307$	−12.2545	−0.699401	−0.349700	−	0.936862i	$-0.613717\pi$
$307$	−12.2545	−0.699401	−0.349700	+	0.936862i	$0.613717\pi$
$308$	−9.67024	−0.551013
$309$	−13.7599	−0.782772
$310$	−9.03847	−0.513351
$311$	−6.59021	−0.373696	−0.186848	−	0.982389i	$-0.559827\pi$
$311$	−6.59021	−0.373696	−0.186848	+	0.982389i	$0.559827\pi$
$312$	9.40755	0.532598
$313$	15.6452	0.884320	0.442160	−	0.896936i	$-0.354212\pi$
$313$	15.6452	0.884320	0.442160	+	0.896936i	$0.354212\pi$
$314$	−41.3025	−2.33084
$315$	−14.9733	−0.843649
$316$	49.5278	2.78616
$317$	−29.8598	−1.67709	−0.838546	−	0.544831i	$-0.816594\pi$
$317$	−29.8598	−1.67709	−0.838546	+	0.544831i	$0.816594\pi$
$318$	2.73901	0.153596
$319$	−5.75611	−0.322280
$320$	26.5297	1.48306
$321$	−10.9808	−0.612888
$322$	16.7332	0.932503
$323$	−0.0800380	−0.00445344
$324$	14.6301	0.812781
$325$	−1.49667	−0.0830206
$326$	3.57671	0.198095
$327$	11.6956	0.646766
$328$	14.6369	0.808186
$329$	3.13887	0.173052
$330$	4.27674	0.235427
$331$	−7.77301	−0.427243	−0.213622	−	0.976916i	$-0.568526\pi$
$331$	−7.77301	−0.427243	−0.213622	+	0.976916i	$0.568526\pi$
$332$	−44.7763	−2.45742
$333$	15.3693	0.842230
$334$	55.2008	3.02045
$335$	19.6149	1.07168
$336$	−4.01716	−0.219154
$337$	3.97050	0.216287	0.108143	−	0.994135i	$-0.465509\pi$
$337$	3.97050	0.216287	0.108143	+	0.994135i	$0.465509\pi$
$338$	7.44554	0.404984
$339$	−8.28461	−0.449958
$340$	4.74798	0.257496
$341$	−1.62645	−0.0880774
$342$	0.820785	0.0443830
$343$	18.4377	0.995541
$344$	−13.8057	−0.744352
$345$	−4.77566	−0.257113
$346$	−33.5848	−1.80553
$347$	−35.9894	−1.93201	−0.966007	−	0.258516i	$-0.916766\pi$
$347$	−35.9894	−1.93201	−0.966007	+	0.258516i	$0.916766\pi$
$348$	−16.1202	−0.864132
$349$	−10.6475	−0.569948	−0.284974	−	0.958535i	$-0.591985\pi$
$349$	−10.6475	−0.569948	−0.284974	+	0.958535i	$0.591985\pi$
$350$	3.00708	0.160735
$351$	13.0712	0.697687
$352$	3.11959	0.166275
$353$	22.6129	1.20356	0.601782	−	0.798660i	$-0.294457\pi$
$353$	22.6129	1.20356	0.601782	+	0.798660i	$0.294457\pi$
$354$	−3.07646	−0.163512
$355$	33.0174	1.75238
$356$	−55.8884	−2.96208
$357$	1.14023	0.0603472
$358$	2.74502	0.145079
$359$	34.7627	1.83470	0.917351	−	0.398078i	$-0.130323\pi$
$359$	34.7627	1.83470	0.917351	+	0.398078i	$0.130323\pi$
$360$	−21.9300	−1.15581
$361$	−18.9794	−0.998915
$362$	−32.7818	−1.72298
$363$	0.769590	0.0403930
$364$	30.3722	1.59194
$365$	−16.8775	−0.883409
$366$	20.9310	1.09408
$367$	−5.50295	−0.287252	−0.143626	−	0.989632i	$-0.545876\pi$
$367$	−5.50295	−0.287252	−0.143626	+	0.989632i	$0.545876\pi$
$368$	5.20865	0.271520
$369$	9.05479	0.471374
$370$	−35.4730	−1.84416
$371$	3.98281	0.206777
$372$	−4.55494	−0.236162
$373$	−37.9241	−1.96364	−0.981819	−	0.189822i	$-0.939209\pi$
$373$	−37.9241	−1.96364	−0.981819	+	0.189822i	$0.939209\pi$
$374$	1.32396	0.0684606
$375$	8.14674	0.420696
$376$	4.59722	0.237083
$377$	18.0787	0.931103
$378$	−26.2622	−1.35078
$379$	−23.6403	−1.21432	−0.607160	−	0.794579i	$-0.707691\pi$
$379$	−23.6403	−1.21432	−0.607160	+	0.794579i	$0.707691\pi$
$380$	−1.22252	−0.0627138
$381$	8.31143	0.425808
$382$	15.1580	0.775548
$383$	6.41627	0.327856	0.163928	−	0.986472i	$-0.447584\pi$
$383$	6.41627	0.327856	0.163928	+	0.986472i	$0.447584\pi$
$384$	15.9160	0.812211
$385$	6.21883	0.316941
$386$	7.89846	0.402021
$387$	−8.54059	−0.434142
$388$	9.51948	0.483278
$389$	−12.6096	−0.639330	−0.319665	−	0.947531i	$-0.603570\pi$
$389$	−12.6096	−0.639330	−0.319665	+	0.947531i	$0.603570\pi$
$390$	−13.4324	−0.680174
$391$	−1.47842	−0.0747667
$392$	−0.240339	−0.0121390
$393$	−10.5284	−0.531086
$394$	12.7701	0.643348
$395$	−31.8508	−1.60259
$396$	−8.76172	−0.440293
$397$	16.2059	0.813351	0.406675	−	0.913573i	$-0.366688\pi$
$397$	16.2059	0.813351	0.406675	+	0.913573i	$0.366688\pi$
$398$	44.8883	2.25005
$399$	−0.293587	−0.0146977
$400$	0.936035	0.0468017
$401$	31.4923	1.57265	0.786326	−	0.617812i	$-0.211981\pi$
$401$	31.4923	1.57265	0.786326	+	0.617812i	$0.211981\pi$
$402$	15.3177	0.763978
$403$	5.10835	0.254465
$404$	−43.8571	−2.18197
$405$	−9.40844	−0.467509
$406$	−36.3233	−1.80270
$407$	−6.38330	−0.316408
$408$	1.66999	0.0826766
$409$	−23.9333	−1.18343	−0.591713	−	0.806149i	$-0.701548\pi$
$409$	−23.9333	−1.18343	−0.591713	+	0.806149i	$0.701548\pi$
$410$	−20.8989	−1.03212
$411$	−2.03551	−0.100404
$412$	−65.0633	−3.20544
$413$	−4.47350	−0.220126
$414$	15.1611	0.745126
$415$	28.7951	1.41350
$416$	−9.79800	−0.480386
$417$	−8.45419	−0.414004
$418$	−0.340896	−0.0166738
$419$	−31.5693	−1.54226	−0.771131	−	0.636677i	$-0.780309\pi$
$419$	−31.5693	−1.54226	−0.771131	+	0.636677i	$0.780309\pi$
$420$	17.4160	0.849816
$421$	−8.18945	−0.399130	−0.199565	−	0.979885i	$-0.563953\pi$
$421$	−8.18945	−0.399130	−0.199565	+	0.979885i	$0.563953\pi$
$422$	−18.3127	−0.891448
$423$	2.84397	0.138279
$424$	5.83326	0.283288
$425$	−0.265683	−0.0128875
$426$	25.7840	1.24924
$427$	30.4359	1.47290
$428$	−51.9224	−2.50977
$429$	−2.41712	−0.116700
$430$	19.7121	0.950603
$431$	−20.6342	−0.993916	−0.496958	−	0.867775i	$-0.665550\pi$
$431$	−20.6342	−0.993916	−0.496958	+	0.867775i	$0.665550\pi$
$432$	−8.17482	−0.393311
$433$	−6.91950	−0.332530	−0.166265	−	0.986081i	$-0.553171\pi$
$433$	−6.91950	−0.332530	−0.166265	+	0.986081i	$0.553171\pi$
$434$	−10.2636	−0.492667
$435$	10.3667	0.497046
$436$	55.3023	2.64850
$437$	0.380664	0.0182096
$438$	−13.1800	−0.629766
$439$	36.5389	1.74391	0.871954	−	0.489589i	$-0.162853\pi$
$439$	36.5389	1.74391	0.871954	+	0.489589i	$0.162853\pi$
$440$	9.10815	0.434214
$441$	−0.148681	−0.00708004
$442$	−4.15830	−0.197790
$443$	−7.26275	−0.345064	−0.172532	−	0.985004i	$-0.555195\pi$
$443$	−7.26275	−0.345064	−0.172532	+	0.985004i	$0.555195\pi$
$444$	−17.8766	−0.848387
$445$	35.9412	1.70378
$446$	−61.6990	−2.92153
$447$	7.35028	0.347656
$448$	30.1256	1.42330
$449$	−14.9796	−0.706929	−0.353465	−	0.935448i	$-0.614997\pi$
$449$	−14.9796	−0.706929	−0.353465	+	0.935448i	$0.614997\pi$
$450$	2.72456	0.128437
$451$	−3.76072	−0.177085
$452$	−39.1736	−1.84257
$453$	7.64337	0.359117
$454$	−25.3559	−1.19001
$455$	−19.5321	−0.915677
$456$	−0.429990	−0.0201361
$457$	6.71103	0.313929	0.156964	−	0.987604i	$-0.449829\pi$
$457$	6.71103	0.313929	0.156964	+	0.987604i	$0.449829\pi$
$458$	−47.9960	−2.24271
$459$	2.32033	0.108304
$460$	−22.5816	−1.05287
$461$	28.6933	1.33638	0.668191	−	0.743990i	$-0.267069\pi$
$461$	28.6933	1.33638	0.668191	+	0.743990i	$0.267069\pi$
$462$	4.85642	0.225941
$463$	−7.44396	−0.345950	−0.172975	−	0.984926i	$-0.555338\pi$
$463$	−7.44396	−0.345950	−0.172975	+	0.984926i	$0.555338\pi$
$464$	−11.3066	−0.524897
$465$	2.92923	0.135840
$466$	3.64598	0.168897
$467$	42.5188	1.96753	0.983767	−	0.179448i	$-0.0574313\pi$
$467$	42.5188	1.96753	0.983767	+	0.179448i	$0.0574313\pi$
$468$	27.5187	1.27205
$469$	22.2736	1.02850
$470$	−6.56403	−0.302776
$471$	13.3855	0.616772
$472$	−6.55192	−0.301577
$473$	3.54715	0.163098
$474$	−24.8730	−1.14245
$475$	0.0684083	0.00313879
$476$	5.39154	0.247121
$477$	3.60862	0.165227
$478$	−18.5541	−0.848645
$479$	34.9207	1.59557	0.797783	−	0.602945i	$-0.206006\pi$
$479$	34.9207	1.59557	0.797783	+	0.602945i	$0.206006\pi$
$480$	−5.61837	−0.256442
$481$	20.0486	0.914138
$482$	−15.3640	−0.699809
$483$	−5.42297	−0.246754
$484$	3.63899	0.165409
$485$	−6.12188	−0.277980
$486$	−36.9953	−1.67814
$487$	1.48400	0.0672465	0.0336232	−	0.999435i	$-0.489295\pi$
$487$	1.48400	0.0672465	0.0336232	+	0.999435i	$0.489295\pi$
$488$	44.5767	2.01789
$489$	−1.15916	−0.0524188
$490$	0.343163	0.0155025
$491$	−17.4502	−0.787517	−0.393759	−	0.919214i	$-0.628825\pi$
$491$	−17.4502	−0.787517	−0.393759	+	0.919214i	$0.628825\pi$
$492$	−10.5320	−0.474820
$493$	3.20926	0.144538
$494$	1.07068	0.0481723
$495$	5.63457	0.253255
$496$	−3.19481	−0.143451
$497$	37.4927	1.68178
$498$	22.4868	1.00766
$499$	−42.5462	−1.90463	−0.952314	−	0.305120i	$-0.901303\pi$
$499$	−42.5462	−1.90463	−0.952314	+	0.305120i	$0.901303\pi$
$500$	38.5217	1.72274
$501$	−17.8897	−0.799254
$502$	32.6692	1.45810
$503$	−5.29145	−0.235934	−0.117967	−	0.993018i	$-0.537638\pi$
$503$	−5.29145	−0.235934	−0.117967	+	0.993018i	$0.537638\pi$
$504$	−24.9024	−1.10924
$505$	28.2040	1.25506
$506$	−6.29683	−0.279928
$507$	−2.41299	−0.107164
$508$	39.3005	1.74368
$509$	6.34182	0.281096	0.140548	−	0.990074i	$-0.455114\pi$
$509$	6.34182	0.281096	0.140548	+	0.990074i	$0.455114\pi$
$510$	−2.38445	−0.105585
$511$	−19.1651	−0.847816
$512$	21.4179	0.946547
$513$	−0.597442	−0.0263777
$514$	−37.0858	−1.63579
$515$	41.8415	1.84376
$516$	9.93392	0.437316
$517$	−1.18118	−0.0519484
$518$	−40.2812	−1.76985
$519$	10.8843	0.477768
$520$	−28.6068	−1.25449
$521$	−15.6932	−0.687530	−0.343765	−	0.939056i	$-0.611702\pi$
$521$	−15.6932	−0.687530	−0.343765	+	0.939056i	$0.611702\pi$
$522$	−32.9107	−1.44046
$523$	9.38577	0.410411	0.205206	−	0.978719i	$-0.434214\pi$
$523$	9.38577	0.410411	0.205206	+	0.978719i	$0.434214\pi$
$524$	−49.7832	−2.17479
$525$	−0.974549	−0.0425328
$526$	−38.1456	−1.66323
$527$	0.906812	0.0395013
$528$	1.51169	0.0657880
$529$	−15.9686	−0.694287
$530$	−8.32888	−0.361784
$531$	−4.05321	−0.175894
$532$	−1.38822	−0.0601870
$533$	11.8116	0.511618
$534$	28.0673	1.21459
$535$	33.3908	1.44361
$536$	32.6220	1.40906
$537$	−0.889619	−0.0383899
$538$	33.6695	1.45160
$539$	0.0617514	0.00265982
$540$	35.4412	1.52515
$541$	−37.9526	−1.63171	−0.815855	−	0.578256i	$-0.803733\pi$
$541$	−37.9526	−1.63171	−0.815855	+	0.578256i	$0.803733\pi$
$542$	−43.6369	−1.87437
$543$	10.6241	0.455924
$544$	−1.73930	−0.0745717
$545$	−35.5643	−1.52341
$546$	−15.2530	−0.652769
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−9.62485	−0.411153
$549$	27.5764	1.17693
$550$	−1.13159	−0.0482511
$551$	−0.826323	−0.0352025
$552$	−7.94252	−0.338056
$553$	−36.1679	−1.53802
$554$	−49.4377	−2.10041
$555$	11.4963	0.487990
$556$	−39.9755	−1.69534
$557$	41.4952	1.75821	0.879105	−	0.476629i	$-0.158141\pi$
$557$	41.4952	1.75821	0.879105	+	0.476629i	$0.158141\pi$
$558$	−9.29930	−0.393671
$559$	−11.1409	−0.471209
$560$	12.2155	0.516201
$561$	−0.429077	−0.0181156
$562$	62.7689	2.64775
$563$	−33.7721	−1.42332	−0.711662	−	0.702522i	$-0.752057\pi$
$563$	−33.7721	−1.42332	−0.711662	+	0.702522i	$0.752057\pi$
$564$	−3.30794	−0.139289
$565$	25.1921	1.05984
$566$	−8.34097	−0.350597
$567$	−10.6837	−0.448673
$568$	54.9122	2.30406
$569$	27.7879	1.16493	0.582465	−	0.812856i	$-0.302088\pi$
$569$	27.7879	1.16493	0.582465	+	0.812856i	$0.302088\pi$
$570$	0.613951	0.0257156
$571$	−6.93310	−0.290141	−0.145070	−	0.989421i	$-0.546341\pi$
$571$	−6.93310	−0.290141	−0.145070	+	0.989421i	$0.546341\pi$
$572$	−11.4293	−0.477884
$573$	−4.91246	−0.205221
$574$	−23.7316	−0.990539
$575$	1.26360	0.0526957
$576$	27.2953	1.13730
$577$	42.0947	1.75243	0.876213	−	0.481923i	$-0.160062\pi$
$577$	42.0947	1.75243	0.876213	+	0.481923i	$0.160062\pi$
$578$	39.6310	1.64843
$579$	−2.55977	−0.106380
$580$	49.0188	2.03539
$581$	32.6981	1.35655
$582$	−4.78071	−0.198167
$583$	−1.49876	−0.0620725
$584$	−28.0694	−1.16152
$585$	−17.6970	−0.731681
$586$	−49.4883	−2.04434
$587$	−3.40406	−0.140501	−0.0702504	−	0.997529i	$-0.522380\pi$
$587$	−3.40406	−0.140501	−0.0702504	+	0.997529i	$0.522380\pi$
$588$	0.172937	0.00713180
$589$	−0.233487	−0.00962066
$590$	9.35501	0.385140
$591$	−4.13860	−0.170239
$592$	−12.5386	−0.515333
$593$	13.2246	0.543070	0.271535	−	0.962429i	$-0.412469\pi$
$593$	13.2246	0.543070	0.271535	+	0.962429i	$0.412469\pi$
$594$	9.88269	0.405492
$595$	−3.46724	−0.142143
$596$	34.7556	1.42365
$597$	−14.5476	−0.595395
$598$	19.7770	0.808743
$599$	22.2722	0.910019	0.455010	−	0.890487i	$-0.349636\pi$
$599$	22.2722	0.910019	0.455010	+	0.890487i	$0.349636\pi$
$600$	−1.42733	−0.0582706
$601$	−15.8428	−0.646243	−0.323122	−	0.946357i	$-0.604732\pi$
$601$	−15.8428	−0.646243	−0.323122	+	0.946357i	$0.604732\pi$
$602$	22.3840	0.912302
$603$	20.1809	0.821831
$604$	36.1415	1.47058
$605$	−2.34020	−0.0951426
$606$	22.0251	0.894710
$607$	13.6126	0.552518	0.276259	−	0.961083i	$-0.410905\pi$
$607$	13.6126	0.552518	0.276259	+	0.961083i	$0.410905\pi$
$608$	0.447836	0.0181621
$609$	11.7718	0.477019
$610$	−63.6479	−2.57703
$611$	3.70985	0.150085
$612$	4.88500	0.197464
$613$	9.84384	0.397589	0.198794	−	0.980041i	$-0.436297\pi$
$613$	9.84384	0.397589	0.198794	+	0.980041i	$0.436297\pi$
$614$	29.1002	1.17439
$615$	6.77302	0.273115
$616$	10.3427	0.416719
$617$	37.6977	1.51765	0.758827	−	0.651292i	$-0.225773\pi$
$617$	37.6977	1.51765	0.758827	+	0.651292i	$0.225773\pi$
$618$	32.6750	1.31438
$619$	21.1157	0.848711	0.424355	−	0.905496i	$-0.360501\pi$
$619$	21.1157	0.848711	0.424355	+	0.905496i	$0.360501\pi$
$620$	13.8508	0.556262
$621$	−11.0356	−0.442843
$622$	15.6495	0.627487
$623$	40.8128	1.63513
$624$	−4.74791	−0.190069
$625$	−27.1556	−1.08622
$626$	−37.1520	−1.48489
$627$	0.110479	0.00441211
$628$	63.2932	2.52567
$629$	3.55894	0.141904
$630$	35.5564	1.41660
$631$	−28.6968	−1.14240	−0.571201	−	0.820810i	$-0.693522\pi$
$631$	−28.6968	−1.14240	−0.571201	+	0.820810i	$0.693522\pi$
$632$	−52.9719	−2.10711
$633$	5.93486	0.235890
$634$	70.9067	2.81606
$635$	−25.2737	−1.00296
$636$	−4.19734	−0.166435
$637$	−0.193948	−0.00768452
$638$	13.6688	0.541152
$639$	33.9702	1.34384
$640$	−48.3980	−1.91310
$641$	−9.85381	−0.389202	−0.194601	−	0.980882i	$-0.562341\pi$
$641$	−9.85381	−0.389202	−0.194601	+	0.980882i	$0.562341\pi$
$642$	26.0756	1.02912
$643$	9.18077	0.362054	0.181027	−	0.983478i	$-0.442058\pi$
$643$	9.18077	0.362054	0.181027	+	0.983478i	$0.442058\pi$
$644$	−25.6424	−1.01045
$645$	−6.38840	−0.251543
$646$	0.190063	0.00747792
$647$	14.9328	0.587071	0.293535	−	0.955948i	$-0.405168\pi$
$647$	14.9328	0.587071	0.293535	+	0.955948i	$0.405168\pi$
$648$	−15.6474	−0.614689
$649$	1.68341	0.0660798
$650$	3.55409	0.139403
$651$	3.32627	0.130367
$652$	−5.48105	−0.214654
$653$	−28.0147	−1.09630	−0.548149	−	0.836380i	$-0.684667\pi$
$653$	−28.0147	−1.09630	−0.548149	+	0.836380i	$0.684667\pi$
$654$	−27.7730	−1.08601
$655$	32.0150	1.25093
$656$	−7.38711	−0.288418
$657$	−17.3646	−0.677456
$658$	−7.45374	−0.290577
$659$	20.1201	0.783769	0.391885	−	0.920014i	$-0.371823\pi$
$659$	20.1201	0.783769	0.391885	+	0.920014i	$0.371823\pi$
$660$	−6.55380	−0.255106
$661$	−35.4985	−1.38073	−0.690366	−	0.723460i	$-0.742550\pi$
$661$	−35.4985	−1.38073	−0.690366	+	0.723460i	$0.742550\pi$
$662$	18.4582	0.717399
$663$	1.34764	0.0523381
$664$	47.8899	1.85849
$665$	0.892750	0.0346194
$666$	−36.4967	−1.41422
$667$	−15.2634	−0.591000
$668$	−84.5912	−3.27293
$669$	19.9957	0.773078
$670$	−46.5786	−1.79949
$671$	−11.4533	−0.442149
$672$	−6.37990	−0.246110
$673$	29.3182	1.13014	0.565068	−	0.825045i	$-0.308850\pi$
$673$	29.3182	1.13014	0.565068	+	0.825045i	$0.308850\pi$
$674$	−9.42857	−0.363175
$675$	−1.98318	−0.0763327
$676$	−11.4098	−0.438837
$677$	19.7711	0.759864	0.379932	−	0.925014i	$-0.375947\pi$
$677$	19.7711	0.759864	0.379932	+	0.925014i	$0.375947\pi$
$678$	19.6731	0.755541
$679$	−6.95166	−0.266780
$680$	−5.07815	−0.194738
$681$	8.21748	0.314894
$682$	3.86227	0.147894
$683$	0.755115	0.0288937	0.0144468	−	0.999896i	$-0.495401\pi$
$683$	0.755115	0.0288937	0.0144468	+	0.999896i	$0.495401\pi$
$684$	−1.25780	−0.0480930
$685$	6.18964	0.236494
$686$	−43.7831	−1.67165
$687$	15.5548	0.593452
$688$	6.96761	0.265638
$689$	4.70731	0.179334
$690$	11.3406	0.431727
$691$	−17.9024	−0.681041	−0.340520	−	0.940237i	$-0.610603\pi$
$691$	−17.9024	−0.681041	−0.340520	+	0.940237i	$0.610603\pi$
$692$	51.4663	1.95645
$693$	6.39829	0.243051
$694$	85.4625	3.24411
$695$	25.7078	0.975153
$696$	17.2411	0.653524
$697$	2.09675	0.0794199
$698$	25.2842	0.957020
$699$	−1.18161	−0.0446925
$700$	−4.60814	−0.174171
$701$	29.0701	1.09796	0.548982	−	0.835834i	$-0.315016\pi$
$701$	29.0701	1.09796	0.548982	+	0.835834i	$0.315016\pi$
$702$	−31.0395	−1.17151
$703$	−0.916360	−0.0345612
$704$	−11.3365	−0.427261
$705$	2.12730	0.0801189
$706$	−53.6979	−2.02095
$707$	32.0269	1.20449
$708$	4.71446	0.177180
$709$	−2.72540	−0.102355	−0.0511773	−	0.998690i	$-0.516297\pi$
$709$	−2.72540	−0.102355	−0.0511773	+	0.998690i	$0.516297\pi$
$710$	−78.4051	−2.94249
$711$	−32.7699	−1.22897
$712$	59.7748	2.24016
$713$	−4.31283	−0.161517
$714$	−2.70765	−0.101331
$715$	7.35008	0.274877
$716$	−4.20655	−0.157206
$717$	6.01311	0.224564
$718$	−82.5494	−3.08071
$719$	23.7066	0.884107	0.442053	−	0.896989i	$-0.354250\pi$
$719$	23.7066	0.884107	0.442053	+	0.896989i	$0.354250\pi$
$720$	11.0679	0.412476
$721$	47.5129	1.76947
$722$	45.0695	1.67731
$723$	4.97923	0.185179
$724$	50.2359	1.86700
$725$	−2.74294	−0.101870
$726$	−1.82751	−0.0678253
$727$	3.11543	0.115545	0.0577724	−	0.998330i	$-0.481600\pi$
$727$	3.11543	0.115545	0.0577724	+	0.998330i	$0.481600\pi$
$728$	−32.4843	−1.20395
$729$	−0.0714542	−0.00264645
$730$	40.0783	1.48336
$731$	−1.97768	−0.0731470
$732$	−32.0753	−1.18554
$733$	24.1082	0.890456	0.445228	−	0.895417i	$-0.353123\pi$
$733$	24.1082	0.890456	0.445228	+	0.895417i	$0.353123\pi$
$734$	13.0676	0.482335
$735$	−0.111214	−0.00410219
$736$	8.27217	0.304916
$737$	−8.38172	−0.308745
$738$	−21.5020	−0.791500
$739$	38.7133	1.42409	0.712046	−	0.702133i	$-0.247769\pi$
$739$	38.7133	1.42409	0.712046	+	0.702133i	$0.247769\pi$
$740$	54.3599	1.99831
$741$	−0.346992	−0.0127471
$742$	−9.45780	−0.347207
$743$	8.77372	0.321876	0.160938	−	0.986964i	$-0.448548\pi$
$743$	8.77372	0.321876	0.160938	+	0.986964i	$0.448548\pi$
$744$	4.87168	0.178605
$745$	−22.3510	−0.818877
$746$	90.0568	3.29721
$747$	29.6261	1.08396
$748$	−2.02888	−0.0741833
$749$	37.9167	1.38544
$750$	−19.3457	−0.706406
$751$	8.70445	0.317630	0.158815	−	0.987308i	$-0.449233\pi$
$751$	8.70445	0.317630	0.158815	+	0.987308i	$0.449233\pi$
$752$	−2.32018	−0.0846081
$753$	−10.5876	−0.385833
$754$	−42.9308	−1.56345
$755$	−23.2422	−0.845872
$756$	40.2450	1.46370
$757$	36.5038	1.32675	0.663377	−	0.748285i	$-0.269123\pi$
$757$	36.5038	1.32675	0.663377	+	0.748285i	$0.269123\pi$
$758$	56.1376	2.03901
$759$	2.04071	0.0740730
$760$	1.30753	0.0474291
$761$	40.2210	1.45801	0.729005	−	0.684508i	$-0.239983\pi$
$761$	40.2210	1.45801	0.729005	+	0.684508i	$0.239983\pi$
$762$	−19.7368	−0.714989
$763$	−40.3848	−1.46203
$764$	−23.2285	−0.840377
$765$	−3.14149	−0.113581
$766$	−15.2364	−0.550515
$767$	−5.28726	−0.190912
$768$	−20.3461	−0.734178
$769$	10.9061	0.393283	0.196642	−	0.980475i	$-0.436996\pi$
$769$	10.9061	0.393283	0.196642	+	0.980475i	$0.436996\pi$
$770$	−14.7676	−0.532187
$771$	12.0190	0.432852
$772$	−12.1038	−0.435627
$773$	−2.76866	−0.0995818	−0.0497909	−	0.998760i	$-0.515855\pi$
$773$	−2.76866	−0.0995818	−0.0497909	+	0.998760i	$0.515855\pi$
$774$	20.2810	0.728984
$775$	−0.775050	−0.0278406
$776$	−10.1815	−0.365493
$777$	13.0545	0.468328
$778$	29.9434	1.07352
$779$	−0.539873	−0.0193429
$780$	20.5841	0.737030
$781$	−14.1088	−0.504853
$782$	3.51073	0.125543
$783$	23.9554	0.856096
$784$	0.121297	0.00433204
$785$	−40.7032	−1.45276
$786$	25.0012	0.891765
$787$	−28.3803	−1.01165	−0.505824	−	0.862637i	$-0.668811\pi$
$787$	−28.3803	−1.01165	−0.505824	+	0.862637i	$0.668811\pi$
$788$	−19.5693	−0.697127
$789$	12.3624	0.440113
$790$	75.6347	2.69096
$791$	28.6068	1.01714
$792$	9.37100	0.332984
$793$	35.9724	1.27742
$794$	−38.4834	−1.36573
$795$	2.69926	0.0957331
$796$	−68.7882	−2.43813
$797$	−21.9758	−0.778422	−0.389211	−	0.921149i	$-0.627252\pi$
$797$	−21.9758	−0.778422	−0.389211	+	0.921149i	$0.627252\pi$
$798$	0.697168	0.0246795
$799$	0.658556	0.0232980
$800$	1.48657	0.0525583
$801$	36.9784	1.30657
$802$	−74.7835	−2.64070
$803$	7.21200	0.254506
$804$	−23.4733	−0.827839
$805$	16.4904	0.581209
$806$	−12.1306	−0.427282
$807$	−10.9118	−0.384113
$808$	46.9068	1.65018
$809$	−20.6468	−0.725902	−0.362951	−	0.931808i	$-0.618231\pi$
$809$	−20.6468	−0.725902	−0.362951	+	0.931808i	$0.618231\pi$
$810$	22.3418	0.785011
$811$	42.2323	1.48298	0.741489	−	0.670966i	$-0.234120\pi$
$811$	42.2323	1.48298	0.741489	+	0.670966i	$0.234120\pi$
$812$	55.6630	1.95339
$813$	14.1421	0.495984
$814$	15.1581	0.531292
$815$	3.52480	0.123469
$816$	−0.842828	−0.0295049
$817$	0.509214	0.0178152
$818$	56.8333	1.98713
$819$	−20.0957	−0.702201
$820$	32.0261	1.11840
$821$	0.792698	0.0276654	0.0138327	−	0.999904i	$-0.495597\pi$
$821$	0.792698	0.0276654	0.0138327	+	0.999904i	$0.495597\pi$
$822$	4.83363	0.168592
$823$	11.7878	0.410896	0.205448	−	0.978668i	$-0.434135\pi$
$823$	11.7878	0.410896	0.205448	+	0.978668i	$0.434135\pi$
$824$	69.5877	2.42420
$825$	0.366731	0.0127679
$826$	10.6230	0.369622
$827$	−48.5944	−1.68979	−0.844897	−	0.534929i	$-0.820338\pi$
$827$	−48.5944	−1.68979	−0.844897	+	0.534929i	$0.820338\pi$
$828$	−23.2333	−0.807412
$829$	0.977348	0.0339447	0.0169724	−	0.999856i	$-0.494597\pi$
$829$	0.977348	0.0339447	0.0169724	+	0.999856i	$0.494597\pi$
$830$	−68.3786	−2.37345
$831$	16.0220	0.555797
$832$	35.6057	1.23441
$833$	−0.0344289	−0.00119289
$834$	20.0758	0.695168
$835$	54.3997	1.88258
$836$	0.522399	0.0180675
$837$	6.76887	0.233966
$838$	74.9663	2.58967
$839$	−9.54785	−0.329628	−0.164814	−	0.986325i	$-0.552702\pi$
$839$	−9.54785	−0.329628	−0.164814	+	0.986325i	$0.552702\pi$
$840$	−18.6271	−0.642697
$841$	4.13276	0.142509
$842$	19.4471	0.670193
$843$	−20.3424	−0.700631
$844$	28.0629	0.965965
$845$	7.33750	0.252418
$846$	−6.75345	−0.232188
$847$	−2.65740	−0.0913092
$848$	−2.94400	−0.101097
$849$	2.70318	0.0927730
$850$	0.630906	0.0216399
$851$	−16.9265	−0.580232
$852$	−39.5122	−1.35367
$853$	41.0319	1.40490	0.702452	−	0.711731i	$-0.252088\pi$
$853$	41.0319	1.40490	0.702452	+	0.711731i	$0.252088\pi$
$854$	−72.2749	−2.47320
$855$	0.808875	0.0276629
$856$	55.5331	1.89808
$857$	−18.6317	−0.636446	−0.318223	−	0.948016i	$-0.603086\pi$
$857$	−18.6317	−0.636446	−0.318223	+	0.948016i	$0.603086\pi$
$858$	5.73984	0.195955
$859$	1.72642	0.0589048	0.0294524	−	0.999566i	$-0.490624\pi$
$859$	1.72642	0.0589048	0.0294524	+	0.999566i	$0.490624\pi$
$860$	−30.2074	−1.03006
$861$	7.69106	0.262111
$862$	48.9992	1.66892
$863$	−37.2236	−1.26711	−0.633553	−	0.773699i	$-0.718404\pi$
$863$	−37.2236	−1.26711	−0.633553	+	0.773699i	$0.718404\pi$
$864$	−12.9829	−0.441688
$865$	−33.0974	−1.12535
$866$	16.4314	0.558362
$867$	−12.8438	−0.436199
$868$	15.7282	0.533850
$869$	13.6103	0.461698
$870$	−24.6174	−0.834607
$871$	26.3253	0.891998
$872$	−59.1479	−2.00300
$873$	−6.29854	−0.213173
$874$	−0.903947	−0.0305765
$875$	−28.1307	−0.950992
$876$	20.1974	0.682408
$877$	−29.1251	−0.983484	−0.491742	−	0.870741i	$-0.663640\pi$
$877$	−29.1251	−0.983484	−0.491742	+	0.870741i	$0.663640\pi$
$878$	−86.7674	−2.92826
$879$	16.0384	0.540962
$880$	−4.59681	−0.154958
$881$	−29.4059	−0.990709	−0.495354	−	0.868691i	$-0.664962\pi$
$881$	−29.4059	−0.990709	−0.495354	+	0.868691i	$0.664962\pi$
$882$	0.353066	0.0118883
$883$	48.0054	1.61551	0.807756	−	0.589517i	$-0.200682\pi$
$883$	48.0054	1.61551	0.807756	+	0.589517i	$0.200682\pi$
$884$	6.37230	0.214324
$885$	−3.03182	−0.101913
$886$	17.2465	0.579409
$887$	0.828135	0.0278060	0.0139030	−	0.999903i	$-0.495574\pi$
$887$	0.828135	0.0278060	0.0139030	+	0.999903i	$0.495574\pi$
$888$	19.1198	0.641617
$889$	−28.6994	−0.962547
$890$	−85.3481	−2.86087
$891$	4.02036	0.134687
$892$	94.5493	3.16574
$893$	−0.169566	−0.00567430
$894$	−17.4544	−0.583762
$895$	2.70519	0.0904244
$896$	−54.9580	−1.83602
$897$	−6.40944	−0.214005
$898$	35.5713	1.18703
$899$	9.36204	0.312241
$900$	−4.17520	−0.139173
$901$	0.835620	0.0278385
$902$	8.93041	0.297350
$903$	−7.25430	−0.241408
$904$	41.8977	1.39350
$905$	−32.3062	−1.07389
$906$	−18.1504	−0.603006
$907$	−12.9836	−0.431115	−0.215557	−	0.976491i	$-0.569157\pi$
$907$	−12.9836	−0.431115	−0.215557	+	0.976491i	$0.569157\pi$
$908$	38.8562	1.28949
$909$	29.0179	0.962464
$910$	46.3819	1.53755
$911$	−15.7499	−0.521817	−0.260908	−	0.965364i	$-0.584022\pi$
$911$	−15.7499	−0.521817	−0.260908	+	0.965364i	$0.584022\pi$
$912$	0.217012	0.00718599
$913$	−12.3046	−0.407222
$914$	−15.9364	−0.527129
$915$	20.6273	0.681918
$916$	73.5505	2.43018
$917$	36.3544	1.20053
$918$	−5.50999	−0.181857
$919$	51.6966	1.70531	0.852657	−	0.522471i	$-0.174990\pi$
$919$	51.6966	1.70531	0.852657	+	0.522471i	$0.174990\pi$
$920$	24.1519	0.796265
$921$	−9.43093	−0.310760
$922$	−68.1368	−2.24397
$923$	44.3129	1.45858
$924$	−7.44212	−0.244828
$925$	−3.04182	−0.100014
$926$	17.6768	0.580897
$927$	43.0490	1.41391
$928$	−17.9567	−0.589458
$929$	−52.5917	−1.72548	−0.862739	−	0.505649i	$-0.831253\pi$
$929$	−52.5917	−1.72548	−0.862739	+	0.505649i	$0.831253\pi$
$930$	−6.95592	−0.228094
$931$	0.00886478	0.000290531 0
$932$	−5.58721	−0.183015
$933$	−5.07176	−0.166042
$934$	−100.968	−3.30376
$935$	1.30475	0.0426700
$936$	−29.4324	−0.962027
$937$	27.1678	0.887534	0.443767	−	0.896142i	$-0.353642\pi$
$937$	27.1678	0.887534	0.443767	+	0.896142i	$0.353642\pi$
$938$	−52.8920	−1.72699
$939$	12.0404	0.392924
$940$	10.0589	0.328086
$941$	24.0598	0.784326	0.392163	−	0.919896i	$-0.371727\pi$
$941$	24.0598	0.784326	0.392163	+	0.919896i	$0.371727\pi$
$942$	−31.7860	−1.03564
$943$	−9.97222	−0.324740
$944$	3.30670	0.107624
$945$	−25.8811	−0.841914
$946$	−8.42327	−0.273864
$947$	43.2531	1.40554	0.702769	−	0.711418i	$-0.251947\pi$
$947$	43.2531	1.40554	0.702769	+	0.711418i	$0.251947\pi$
$948$	38.1161	1.23795
$949$	−22.6514	−0.735296
$950$	−0.162446	−0.00527045
$951$	−22.9798	−0.745170
$952$	−5.76646	−0.186892
$953$	−16.2801	−0.527363	−0.263681	−	0.964610i	$-0.584937\pi$
$953$	−16.2801	−0.527363	−0.263681	+	0.964610i	$0.584937\pi$
$954$	−8.56924	−0.277439
$955$	14.9380	0.483382
$956$	28.4329	0.919585
$957$	−4.42984	−0.143196
$958$	−82.9246	−2.67917
$959$	7.02861	0.226966
$960$	20.4170	0.658956
$961$	−28.3546	−0.914666
$962$	−47.6086	−1.53496
$963$	34.3544	1.10705
$964$	23.5442	0.758307
$965$	7.78385	0.250571
$966$	12.8777	0.414333
$967$	−32.0206	−1.02971	−0.514856	−	0.857277i	$-0.672155\pi$
$967$	−32.0206	−1.02971	−0.514856	+	0.857277i	$0.672155\pi$
$968$	−3.89204	−0.125095
$969$	−0.0615965	−0.00197876
$970$	14.5374	0.466766
$971$	−21.9083	−0.703070	−0.351535	−	0.936175i	$-0.614340\pi$
$971$	−21.9083	−0.703070	−0.351535	+	0.936175i	$0.614340\pi$
$972$	56.6927	1.81842
$973$	29.1923	0.935863
$974$	−3.52399	−0.112916
$975$	−1.15183	−0.0368880
$976$	−22.4975	−0.720127
$977$	−57.2897	−1.83286	−0.916430	−	0.400196i	$-0.868942\pi$
$977$	−57.2897	−1.83286	−0.916430	+	0.400196i	$0.868942\pi$
$978$	2.75260	0.0880184
$979$	−15.3582	−0.490850
$980$	−0.525873	−0.0167984
$981$	−36.5906	−1.16825
$982$	41.4383	1.32235
$983$	−47.9486	−1.52932	−0.764661	−	0.644432i	$-0.777094\pi$
$983$	−47.9486	−1.52932	−0.764661	+	0.644432i	$0.777094\pi$
$984$	11.2644	0.359096
$985$	12.5848	0.400985
$986$	−7.62088	−0.242698
$987$	2.41564	0.0768908
$988$	−1.64075	−0.0521991
$989$	9.40591	0.299091
$990$	−13.3802	−0.425249
$991$	11.5702	0.367539	0.183770	−	0.982969i	$-0.441170\pi$
$991$	11.5702	0.367539	0.183770	+	0.982969i	$0.441170\pi$
$992$	−5.07387	−0.161096
$993$	−5.98203	−0.189834
$994$	−89.0323	−2.82393
$995$	44.2370	1.40241
$996$	−34.4594	−1.09189
$997$	−18.8910	−0.598283	−0.299141	−	0.954209i	$-0.596700\pi$
$997$	−18.8910	−0.598283	−0.299141	+	0.954209i	$0.596700\pi$
$998$	101.032	3.19813
$999$	26.5656	0.840498

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.e.1.11	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.e.1.11	✓	119	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37466 q^{2} +0.769590 q^{3} +3.63899 q^{4} -2.34020 q^{5} -1.82751 q^{6} -2.65740 q^{7} -3.89204 q^{8} -2.40773 q^{9} +O(q^{10})\)	\(q-2.37466 q^{2} +0.769590 q^{3} +3.63899 q^{4} -2.34020 q^{5} -1.82751 q^{6} -2.65740 q^{7} -3.89204 q^{8} -2.40773 q^{9} +5.55717 q^{10} +1.00000 q^{11} +2.80053 q^{12} -3.14079 q^{13} +6.31040 q^{14} -1.80099 q^{15} +1.96428 q^{16} -0.557539 q^{17} +5.71753 q^{18} +0.143556 q^{19} -8.51596 q^{20} -2.04511 q^{21} -2.37466 q^{22} +2.65168 q^{23} -2.99528 q^{24} +0.476528 q^{25} +7.45830 q^{26} -4.16174 q^{27} -9.67024 q^{28} -5.75611 q^{29} +4.27674 q^{30} -1.62645 q^{31} +3.11959 q^{32} +0.769590 q^{33} +1.32396 q^{34} +6.21883 q^{35} -8.76172 q^{36} -6.38330 q^{37} -0.340896 q^{38} -2.41712 q^{39} +9.10815 q^{40} -3.76072 q^{41} +4.85642 q^{42} +3.54715 q^{43} +3.63899 q^{44} +5.63457 q^{45} -6.29683 q^{46} -1.18118 q^{47} +1.51169 q^{48} +0.0617514 q^{49} -1.13159 q^{50} -0.429077 q^{51} -11.4293 q^{52} -1.49876 q^{53} +9.88269 q^{54} -2.34020 q^{55} +10.3427 q^{56} +0.110479 q^{57} +13.6688 q^{58} +1.68341 q^{59} -6.55380 q^{60} -11.4533 q^{61} +3.86227 q^{62} +6.39829 q^{63} -11.3365 q^{64} +7.35008 q^{65} -1.82751 q^{66} -8.38172 q^{67} -2.02888 q^{68} +2.04071 q^{69} -14.7676 q^{70} -14.1088 q^{71} +9.37100 q^{72} +7.21200 q^{73} +15.1581 q^{74} +0.366731 q^{75} +0.522399 q^{76} -2.65740 q^{77} +5.73984 q^{78} +13.6103 q^{79} -4.59681 q^{80} +4.02036 q^{81} +8.93041 q^{82} -12.3046 q^{83} -7.44212 q^{84} +1.30475 q^{85} -8.42327 q^{86} -4.42984 q^{87} -3.89204 q^{88} -15.3582 q^{89} -13.3802 q^{90} +8.34633 q^{91} +9.64945 q^{92} -1.25170 q^{93} +2.80490 q^{94} -0.335949 q^{95} +2.40081 q^{96} +2.61597 q^{97} -0.146638 q^{98} -2.40773 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * q^99

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