LMFDB - Embedded newform 6018.2.a.v.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 21x^{7} + 42x^{6} + 121x^{5} - 127x^{4} - 141x^{3} + 27x^{2} + 26x - 1 $ x^9 - 3x^8 - 21x^7 + 42x^6 + 121x^5 - 127x^4 - 141x^3 + 27x^2 + 26x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-2.43329$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.43329 q^{5} +1.00000 q^{6} -0.177683 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.43329 q^{5} +1.00000 q^{6} -0.177683 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.43329 q^{10} -4.21857 q^{11} -1.00000 q^{12} +6.72581 q^{13} +0.177683 q^{14} -3.43329 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -6.85710 q^{19} +3.43329 q^{20} +0.177683 q^{21} +4.21857 q^{22} +3.46595 q^{23} +1.00000 q^{24} +6.78745 q^{25} -6.72581 q^{26} -1.00000 q^{27} -0.177683 q^{28} -4.28222 q^{29} +3.43329 q^{30} -8.07950 q^{31} -1.00000 q^{32} +4.21857 q^{33} +1.00000 q^{34} -0.610038 q^{35} +1.00000 q^{36} -8.31114 q^{37} +6.85710 q^{38} -6.72581 q^{39} -3.43329 q^{40} +4.55318 q^{41} -0.177683 q^{42} +7.07506 q^{43} -4.21857 q^{44} +3.43329 q^{45} -3.46595 q^{46} +3.46487 q^{47} -1.00000 q^{48} -6.96843 q^{49} -6.78745 q^{50} +1.00000 q^{51} +6.72581 q^{52} -1.92919 q^{53} +1.00000 q^{54} -14.4835 q^{55} +0.177683 q^{56} +6.85710 q^{57} +4.28222 q^{58} -1.00000 q^{59} -3.43329 q^{60} -11.3137 q^{61} +8.07950 q^{62} -0.177683 q^{63} +1.00000 q^{64} +23.0916 q^{65} -4.21857 q^{66} +2.33800 q^{67} -1.00000 q^{68} -3.46595 q^{69} +0.610038 q^{70} -6.54749 q^{71} -1.00000 q^{72} +1.67935 q^{73} +8.31114 q^{74} -6.78745 q^{75} -6.85710 q^{76} +0.749569 q^{77} +6.72581 q^{78} -12.9674 q^{79} +3.43329 q^{80} +1.00000 q^{81} -4.55318 q^{82} -5.52235 q^{83} +0.177683 q^{84} -3.43329 q^{85} -7.07506 q^{86} +4.28222 q^{87} +4.21857 q^{88} -3.84979 q^{89} -3.43329 q^{90} -1.19506 q^{91} +3.46595 q^{92} +8.07950 q^{93} -3.46487 q^{94} -23.5424 q^{95} +1.00000 q^{96} -4.92259 q^{97} +6.96843 q^{98} -4.21857 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} + 9 q^{6} - 11 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 + 9 * q^6 - 11 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} + 9 q^{6} - 11 q^{7} - 9 q^{8} + 9 q^{9} - 6 q^{10} + q^{11} - 9 q^{12} + 4 q^{13} + 11 q^{14} - 6 q^{15} + 9 q^{16} - 9 q^{17} - 9 q^{18} - 13 q^{19} + 6 q^{20} + 11 q^{21} - q^{22} - 6 q^{23} + 9 q^{24} + 9 q^{25} - 4 q^{26} - 9 q^{27} - 11 q^{28} + 10 q^{29} + 6 q^{30} + q^{31} - 9 q^{32} - q^{33} + 9 q^{34} + 6 q^{35} + 9 q^{36} - 2 q^{37} + 13 q^{38} - 4 q^{39} - 6 q^{40} + 20 q^{41} - 11 q^{42} - 17 q^{43} + q^{44} + 6 q^{45} + 6 q^{46} + 4 q^{47} - 9 q^{48} + 2 q^{49} - 9 q^{50} + 9 q^{51} + 4 q^{52} + 16 q^{53} + 9 q^{54} - 17 q^{55} + 11 q^{56} + 13 q^{57} - 10 q^{58} - 9 q^{59} - 6 q^{60} - 9 q^{61} - q^{62} - 11 q^{63} + 9 q^{64} + q^{66} - 8 q^{67} - 9 q^{68} + 6 q^{69} - 6 q^{70} - 8 q^{71} - 9 q^{72} - 20 q^{73} + 2 q^{74} - 9 q^{75} - 13 q^{76} - 32 q^{77} + 4 q^{78} - 29 q^{79} + 6 q^{80} + 9 q^{81} - 20 q^{82} - 16 q^{83} + 11 q^{84} - 6 q^{85} + 17 q^{86} - 10 q^{87} - q^{88} + 11 q^{89} - 6 q^{90} - 13 q^{91} - 6 q^{92} - q^{93} - 4 q^{94} + 5 q^{95} + 9 q^{96} + 17 q^{97} - 2 q^{98} + q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 + 9 * q^6 - 11 * q^7 - 9 * q^8 + 9 * q^9 - 6 * q^10 + q^11 - 9 * q^12 + 4 * q^13 + 11 * q^14 - 6 * q^15 + 9 * q^16 - 9 * q^17 - 9 * q^18 - 13 * q^19 + 6 * q^20 + 11 * q^21 - q^22 - 6 * q^23 + 9 * q^24 + 9 * q^25 - 4 * q^26 - 9 * q^27 - 11 * q^28 + 10 * q^29 + 6 * q^30 + q^31 - 9 * q^32 - q^33 + 9 * q^34 + 6 * q^35 + 9 * q^36 - 2 * q^37 + 13 * q^38 - 4 * q^39 - 6 * q^40 + 20 * q^41 - 11 * q^42 - 17 * q^43 + q^44 + 6 * q^45 + 6 * q^46 + 4 * q^47 - 9 * q^48 + 2 * q^49 - 9 * q^50 + 9 * q^51 + 4 * q^52 + 16 * q^53 + 9 * q^54 - 17 * q^55 + 11 * q^56 + 13 * q^57 - 10 * q^58 - 9 * q^59 - 6 * q^60 - 9 * q^61 - q^62 - 11 * q^63 + 9 * q^64 + q^66 - 8 * q^67 - 9 * q^68 + 6 * q^69 - 6 * q^70 - 8 * q^71 - 9 * q^72 - 20 * q^73 + 2 * q^74 - 9 * q^75 - 13 * q^76 - 32 * q^77 + 4 * q^78 - 29 * q^79 + 6 * q^80 + 9 * q^81 - 20 * q^82 - 16 * q^83 + 11 * q^84 - 6 * q^85 + 17 * q^86 - 10 * q^87 - q^88 + 11 * q^89 - 6 * q^90 - 13 * q^91 - 6 * q^92 - q^93 - 4 * q^94 + 5 * q^95 + 9 * q^96 + 17 * q^97 - 2 * q^98 + 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	3.43329	1.53541	0.767706	−	0.640802i	$-0.221398\pi$
$5$	3.43329	1.53541	0.767706	+	0.640802i	$0.221398\pi$
$6$	1.00000	0.408248
$7$	−0.177683	−0.0671580	−0.0335790	−	0.999436i	$-0.510691\pi$
$7$	−0.177683	−0.0671580	−0.0335790	+	0.999436i	$0.510691\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.43329	−1.08570
$11$	−4.21857	−1.27195	−0.635973	−	0.771711i	$-0.719401\pi$
$11$	−4.21857	−1.27195	−0.635973	+	0.771711i	$0.719401\pi$
$12$	−1.00000	−0.288675
$13$	6.72581	1.86540	0.932701	−	0.360649i	$-0.117445\pi$
$13$	6.72581	1.86540	0.932701	+	0.360649i	$0.117445\pi$
$14$	0.177683	0.0474879
$15$	−3.43329	−0.886471
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	−6.85710	−1.57313	−0.786563	−	0.617509i	$-0.788142\pi$
$19$	−6.85710	−1.57313	−0.786563	+	0.617509i	$0.788142\pi$
$20$	3.43329	0.767706
$21$	0.177683	0.0387737
$22$	4.21857	0.899401
$23$	3.46595	0.722701	0.361350	−	0.932430i	$-0.382316\pi$
$23$	3.46595	0.722701	0.361350	+	0.932430i	$0.382316\pi$
$24$	1.00000	0.204124
$25$	6.78745	1.35749
$26$	−6.72581	−1.31904
$27$	−1.00000	−0.192450
$28$	−0.177683	−0.0335790
$29$	−4.28222	−0.795188	−0.397594	−	0.917561i	$-0.630155\pi$
$29$	−4.28222	−0.795188	−0.397594	+	0.917561i	$0.630155\pi$
$30$	3.43329	0.626829
$31$	−8.07950	−1.45112	−0.725560	−	0.688159i	$-0.758419\pi$
$31$	−8.07950	−1.45112	−0.725560	+	0.688159i	$0.758419\pi$
$32$	−1.00000	−0.176777
$33$	4.21857	0.734358
$34$	1.00000	0.171499
$35$	−0.610038	−0.103115
$36$	1.00000	0.166667
$37$	−8.31114	−1.36634	−0.683171	−	0.730258i	$-0.739400\pi$
$37$	−8.31114	−1.36634	−0.683171	+	0.730258i	$0.739400\pi$
$38$	6.85710	1.11237
$39$	−6.72581	−1.07699
$40$	−3.43329	−0.542850
$41$	4.55318	0.711087	0.355544	−	0.934660i	$-0.384296\pi$
$41$	4.55318	0.711087	0.355544	+	0.934660i	$0.384296\pi$
$42$	−0.177683	−0.0274171
$43$	7.07506	1.07894	0.539468	−	0.842006i	$-0.318625\pi$
$43$	7.07506	1.07894	0.539468	+	0.842006i	$0.318625\pi$
$44$	−4.21857	−0.635973
$45$	3.43329	0.511804
$46$	−3.46595	−0.511027
$47$	3.46487	0.505404	0.252702	−	0.967544i	$-0.418681\pi$
$47$	3.46487	0.505404	0.252702	+	0.967544i	$0.418681\pi$
$48$	−1.00000	−0.144338
$49$	−6.96843	−0.995490
$50$	−6.78745	−0.959891
$51$	1.00000	0.140028
$52$	6.72581	0.932701
$53$	−1.92919	−0.264995	−0.132497	−	0.991183i	$-0.542300\pi$
$53$	−1.92919	−0.264995	−0.132497	+	0.991183i	$0.542300\pi$
$54$	1.00000	0.136083
$55$	−14.4835	−1.95296
$56$	0.177683	0.0237439
$57$	6.85710	0.908245
$58$	4.28222	0.562283
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−3.43329	−0.443235
$61$	−11.3137	−1.44857	−0.724287	−	0.689498i	$-0.757831\pi$
$61$	−11.3137	−1.44857	−0.724287	+	0.689498i	$0.757831\pi$
$62$	8.07950	1.02610
$63$	−0.177683	−0.0223860
$64$	1.00000	0.125000
$65$	23.0916	2.86416
$66$	−4.21857	−0.519270
$67$	2.33800	0.285632	0.142816	−	0.989749i	$-0.454384\pi$
$67$	2.33800	0.285632	0.142816	+	0.989749i	$0.454384\pi$
$68$	−1.00000	−0.121268
$69$	−3.46595	−0.417251
$70$	0.610038	0.0729134
$71$	−6.54749	−0.777044	−0.388522	−	0.921440i	$-0.627014\pi$
$71$	−6.54749	−0.777044	−0.388522	+	0.921440i	$0.627014\pi$
$72$	−1.00000	−0.117851
$73$	1.67935	0.196553	0.0982765	−	0.995159i	$-0.468667\pi$
$73$	1.67935	0.196553	0.0982765	+	0.995159i	$0.468667\pi$
$74$	8.31114	0.966150
$75$	−6.78745	−0.783747
$76$	−6.85710	−0.786563
$77$	0.749569	0.0854213
$78$	6.72581	0.761548
$79$	−12.9674	−1.45895	−0.729473	−	0.684009i	$-0.760235\pi$
$79$	−12.9674	−1.45895	−0.729473	+	0.684009i	$0.760235\pi$
$80$	3.43329	0.383853
$81$	1.00000	0.111111
$82$	−4.55318	−0.502815
$83$	−5.52235	−0.606157	−0.303078	−	0.952966i	$-0.598014\pi$
$83$	−5.52235	−0.606157	−0.303078	+	0.952966i	$0.598014\pi$
$84$	0.177683	0.0193868
$85$	−3.43329	−0.372392
$86$	−7.07506	−0.762923
$87$	4.28222	0.459102
$88$	4.21857	0.449701
$89$	−3.84979	−0.408077	−0.204038	−	0.978963i	$-0.565407\pi$
$89$	−3.84979	−0.408077	−0.204038	+	0.978963i	$0.565407\pi$
$90$	−3.43329	−0.361900
$91$	−1.19506	−0.125277
$92$	3.46595	0.361350
$93$	8.07950	0.837805
$94$	−3.46487	−0.357374
$95$	−23.5424	−2.41540
$96$	1.00000	0.102062
$97$	−4.92259	−0.499814	−0.249907	−	0.968270i	$-0.580400\pi$
$97$	−4.92259	−0.499814	−0.249907	+	0.968270i	$0.580400\pi$
$98$	6.96843	0.703918
$99$	−4.21857	−0.423982
$100$	6.78745	0.678745
$101$	−2.85227	−0.283811	−0.141906	−	0.989880i	$-0.545323\pi$
$101$	−2.85227	−0.283811	−0.141906	+	0.989880i	$0.545323\pi$
$102$	−1.00000	−0.0990148
$103$	4.39930	0.433476	0.216738	−	0.976230i	$-0.430458\pi$
$103$	4.39930	0.433476	0.216738	+	0.976230i	$0.430458\pi$
$104$	−6.72581	−0.659520
$105$	0.610038	0.0595336
$106$	1.92919	0.187380
$107$	2.72992	0.263911	0.131956	−	0.991256i	$-0.457874\pi$
$107$	2.72992	0.263911	0.131956	+	0.991256i	$0.457874\pi$
$108$	−1.00000	−0.0962250
$109$	4.86495	0.465978	0.232989	−	0.972479i	$-0.425149\pi$
$109$	4.86495	0.465978	0.232989	+	0.972479i	$0.425149\pi$
$110$	14.4835	1.38095
$111$	8.31114	0.788858
$112$	−0.177683	−0.0167895
$113$	−16.7112	−1.57206	−0.786028	−	0.618191i	$-0.787866\pi$
$113$	−16.7112	−1.57206	−0.786028	+	0.618191i	$0.787866\pi$
$114$	−6.85710	−0.642226
$115$	11.8996	1.10964
$116$	−4.28222	−0.397594
$117$	6.72581	0.621801
$118$	1.00000	0.0920575
$119$	0.177683	0.0162882
$120$	3.43329	0.313415
$121$	6.79630	0.617846
$122$	11.3137	1.02430
$123$	−4.55318	−0.410546
$124$	−8.07950	−0.725560
$125$	6.13683	0.548895
$126$	0.177683	0.0158293
$127$	1.29791	0.115171	0.0575855	−	0.998341i	$-0.481660\pi$
$127$	1.29791	0.115171	0.0575855	+	0.998341i	$0.481660\pi$
$128$	−1.00000	−0.0883883
$129$	−7.07506	−0.622924
$130$	−23.0916	−2.02527
$131$	9.11877	0.796711	0.398355	−	0.917231i	$-0.369581\pi$
$131$	9.11877	0.796711	0.398355	+	0.917231i	$0.369581\pi$
$132$	4.21857	0.367179
$133$	1.21839	0.105648
$134$	−2.33800	−0.201972
$135$	−3.43329	−0.295490
$136$	1.00000	0.0857493
$137$	21.3710	1.82585	0.912926	−	0.408126i	$-0.133817\pi$
$137$	21.3710	1.82585	0.912926	+	0.408126i	$0.133817\pi$
$138$	3.46595	0.295041
$139$	−18.1244	−1.53730	−0.768648	−	0.639672i	$-0.779070\pi$
$139$	−18.1244	−1.53730	−0.768648	+	0.639672i	$0.779070\pi$
$140$	−0.610038	−0.0515576
$141$	−3.46487	−0.291795
$142$	6.54749	0.549453
$143$	−28.3733	−2.37269
$144$	1.00000	0.0833333
$145$	−14.7021	−1.22094
$146$	−1.67935	−0.138984
$147$	6.96843	0.574746
$148$	−8.31114	−0.683171
$149$	−19.3670	−1.58660	−0.793302	−	0.608828i	$-0.791640\pi$
$149$	−19.3670	−1.58660	−0.793302	+	0.608828i	$0.791640\pi$
$150$	6.78745	0.554193
$151$	−16.7380	−1.36212	−0.681058	−	0.732230i	$-0.738480\pi$
$151$	−16.7380	−1.36212	−0.681058	+	0.732230i	$0.738480\pi$
$152$	6.85710	0.556184
$153$	−1.00000	−0.0808452
$154$	−0.749569	−0.0604020
$155$	−27.7392	−2.22807
$156$	−6.72581	−0.538495
$157$	13.9462	1.11303	0.556514	−	0.830838i	$-0.312139\pi$
$157$	13.9462	1.11303	0.556514	+	0.830838i	$0.312139\pi$
$158$	12.9674	1.03163
$159$	1.92919	0.152995
$160$	−3.43329	−0.271425
$161$	−0.615842	−0.0485351
$162$	−1.00000	−0.0785674
$163$	−21.6925	−1.69909	−0.849546	−	0.527515i	$-0.823124\pi$
$163$	−21.6925	−1.69909	−0.849546	+	0.527515i	$0.823124\pi$
$164$	4.55318	0.355544
$165$	14.4835	1.12754
$166$	5.52235	0.428617
$167$	−15.0938	−1.16799	−0.583995	−	0.811757i	$-0.698511\pi$
$167$	−15.0938	−1.16799	−0.583995	+	0.811757i	$0.698511\pi$
$168$	−0.177683	−0.0137086
$169$	32.2365	2.47973
$170$	3.43329	0.263321
$171$	−6.85710	−0.524376
$172$	7.07506	0.539468
$173$	2.15207	0.163619	0.0818094	−	0.996648i	$-0.473930\pi$
$173$	2.15207	0.163619	0.0818094	+	0.996648i	$0.473930\pi$
$174$	−4.28222	−0.324634
$175$	−1.20602	−0.0911663
$176$	−4.21857	−0.317986
$177$	1.00000	0.0751646
$178$	3.84979	0.288554
$179$	18.6454	1.39362	0.696811	−	0.717255i	$-0.254602\pi$
$179$	18.6454	1.39362	0.696811	+	0.717255i	$0.254602\pi$
$180$	3.43329	0.255902
$181$	12.7948	0.951028	0.475514	−	0.879708i	$-0.342262\pi$
$181$	12.7948	0.951028	0.475514	+	0.879708i	$0.342262\pi$
$182$	1.19506	0.0885840
$183$	11.3137	0.836335
$184$	−3.46595	−0.255513
$185$	−28.5345	−2.09790
$186$	−8.07950	−0.592418
$187$	4.21857	0.308492
$188$	3.46487	0.252702
$189$	0.177683	0.0129246
$190$	23.5424	1.70794
$191$	−18.6662	−1.35064	−0.675320	−	0.737525i	$-0.735994\pi$
$191$	−18.6662	−1.35064	−0.675320	+	0.737525i	$0.735994\pi$
$192$	−1.00000	−0.0721688
$193$	8.91501	0.641717	0.320858	−	0.947127i	$-0.396029\pi$
$193$	8.91501	0.641717	0.320858	+	0.947127i	$0.396029\pi$
$194$	4.92259	0.353422
$195$	−23.0916	−1.65362
$196$	−6.96843	−0.497745
$197$	20.2481	1.44262	0.721308	−	0.692615i	$-0.243541\pi$
$197$	20.2481	1.44262	0.721308	+	0.692615i	$0.243541\pi$
$198$	4.21857	0.299800
$199$	−1.83823	−0.130309	−0.0651543	−	0.997875i	$-0.520754\pi$
$199$	−1.83823	−0.130309	−0.0651543	+	0.997875i	$0.520754\pi$
$200$	−6.78745	−0.479945
$201$	−2.33800	−0.164910
$202$	2.85227	0.200685
$203$	0.760879	0.0534032
$204$	1.00000	0.0700140
$205$	15.6324	1.09181
$206$	−4.39930	−0.306514
$207$	3.46595	0.240900
$208$	6.72581	0.466351
$209$	28.9271	2.00093
$210$	−0.610038	−0.0420966
$211$	12.1185	0.834272	0.417136	−	0.908844i	$-0.363034\pi$
$211$	12.1185	0.834272	0.417136	+	0.908844i	$0.363034\pi$
$212$	−1.92919	−0.132497
$213$	6.54749	0.448626
$214$	−2.72992	−0.186613
$215$	24.2907	1.65661
$216$	1.00000	0.0680414
$217$	1.43559	0.0974543
$218$	−4.86495	−0.329496
$219$	−1.67935	−0.113480
$220$	−14.4835	−0.976480
$221$	−6.72581	−0.452427
$222$	−8.31114	−0.557807
$223$	7.95696	0.532838	0.266419	−	0.963857i	$-0.414160\pi$
$223$	7.95696	0.532838	0.266419	+	0.963857i	$0.414160\pi$
$224$	0.177683	0.0118720
$225$	6.78745	0.452497
$226$	16.7112	1.11161
$227$	25.0974	1.66577	0.832887	−	0.553443i	$-0.186686\pi$
$227$	25.0974	1.66577	0.832887	+	0.553443i	$0.186686\pi$
$228$	6.85710	0.454123
$229$	−24.3719	−1.61054	−0.805269	−	0.592910i	$-0.797979\pi$
$229$	−24.3719	−1.61054	−0.805269	+	0.592910i	$0.797979\pi$
$230$	−11.8996	−0.784636
$231$	−0.749569	−0.0493180
$232$	4.28222	0.281142
$233$	−20.1082	−1.31733	−0.658666	−	0.752436i	$-0.728879\pi$
$233$	−20.1082	−1.31733	−0.658666	+	0.752436i	$0.728879\pi$
$234$	−6.72581	−0.439680
$235$	11.8959	0.776003
$236$	−1.00000	−0.0650945
$237$	12.9674	0.842323
$238$	−0.177683	−0.0115175
$239$	−0.720065	−0.0465771	−0.0232886	−	0.999729i	$-0.507414\pi$
$239$	−0.720065	−0.0465771	−0.0232886	+	0.999729i	$0.507414\pi$
$240$	−3.43329	−0.221618
$241$	25.5539	1.64607	0.823037	−	0.567987i	$-0.192278\pi$
$241$	25.5539	1.64607	0.823037	+	0.567987i	$0.192278\pi$
$242$	−6.79630	−0.436883
$243$	−1.00000	−0.0641500
$244$	−11.3137	−0.724287
$245$	−23.9246	−1.52849
$246$	4.55318	0.290300
$247$	−46.1195	−2.93452
$248$	8.07950	0.513049
$249$	5.52235	0.349965
$250$	−6.13683	−0.388127
$251$	14.9432	0.943208	0.471604	−	0.881810i	$-0.343675\pi$
$251$	14.9432	0.943208	0.471604	+	0.881810i	$0.343675\pi$
$252$	−0.177683	−0.0111930
$253$	−14.6213	−0.919236
$254$	−1.29791	−0.0814383
$255$	3.43329	0.215001
$256$	1.00000	0.0625000
$257$	28.9281	1.80449	0.902243	−	0.431227i	$-0.141919\pi$
$257$	28.9281	1.80449	0.902243	+	0.431227i	$0.141919\pi$
$258$	7.07506	0.440474
$259$	1.47675	0.0917608
$260$	23.0916	1.43208
$261$	−4.28222	−0.265063
$262$	−9.11877	−0.563360
$263$	−1.32264	−0.0815574	−0.0407787	−	0.999168i	$-0.512984\pi$
$263$	−1.32264	−0.0815574	−0.0407787	+	0.999168i	$0.512984\pi$
$264$	−4.21857	−0.259635
$265$	−6.62347	−0.406876
$266$	−1.21839	−0.0747044
$267$	3.84979	0.235603
$268$	2.33800	0.142816
$269$	−3.01175	−0.183630	−0.0918149	−	0.995776i	$-0.529267\pi$
$269$	−3.01175	−0.183630	−0.0918149	+	0.995776i	$0.529267\pi$
$270$	3.43329	0.208943
$271$	3.86074	0.234523	0.117262	−	0.993101i	$-0.462588\pi$
$271$	3.86074	0.234523	0.117262	+	0.993101i	$0.462588\pi$
$272$	−1.00000	−0.0606339
$273$	1.19506	0.0723285
$274$	−21.3710	−1.29107
$275$	−28.6333	−1.72665
$276$	−3.46595	−0.208626
$277$	−26.4074	−1.58667	−0.793335	−	0.608785i	$-0.791657\pi$
$277$	−26.4074	−1.58667	−0.793335	+	0.608785i	$0.791657\pi$
$278$	18.1244	1.08703
$279$	−8.07950	−0.483707
$280$	0.610038	0.0364567
$281$	22.0628	1.31615	0.658077	−	0.752951i	$-0.271370\pi$
$281$	22.0628	1.31615	0.658077	+	0.752951i	$0.271370\pi$
$282$	3.46487	0.206330
$283$	−27.7366	−1.64877	−0.824386	−	0.566029i	$-0.808479\pi$
$283$	−27.7366	−1.64877	−0.824386	+	0.566029i	$0.808479\pi$
$284$	−6.54749	−0.388522
$285$	23.5424	1.39453
$286$	28.3733	1.67775
$287$	−0.809024	−0.0477552
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	14.7021	0.863336
$291$	4.92259	0.288568
$292$	1.67935	0.0982765
$293$	1.55991	0.0911308	0.0455654	−	0.998961i	$-0.485491\pi$
$293$	1.55991	0.0911308	0.0455654	+	0.998961i	$0.485491\pi$
$294$	−6.96843	−0.406407
$295$	−3.43329	−0.199894
$296$	8.31114	0.483075
$297$	4.21857	0.244786
$298$	19.3670	1.12190
$299$	23.3113	1.34813
$300$	−6.78745	−0.391874
$301$	−1.25712	−0.0724592
$302$	16.7380	0.963161
$303$	2.85227	0.163859
$304$	−6.85710	−0.393282
$305$	−38.8433	−2.22416
$306$	1.00000	0.0571662
$307$	−9.59670	−0.547713	−0.273856	−	0.961771i	$-0.588299\pi$
$307$	−9.59670	−0.547713	−0.273856	+	0.961771i	$0.588299\pi$
$308$	0.749569	0.0427107
$309$	−4.39930	−0.250267
$310$	27.7392	1.57548
$311$	−7.57970	−0.429805	−0.214903	−	0.976635i	$-0.568943\pi$
$311$	−7.57970	−0.429805	−0.214903	+	0.976635i	$0.568943\pi$
$312$	6.72581	0.380774
$313$	−24.2800	−1.37239	−0.686193	−	0.727420i	$-0.740719\pi$
$313$	−24.2800	−1.37239	−0.686193	+	0.727420i	$0.740719\pi$
$314$	−13.9462	−0.787029
$315$	−0.610038	−0.0343717
$316$	−12.9674	−0.729473
$317$	26.4122	1.48346	0.741730	−	0.670699i	$-0.234006\pi$
$317$	26.4122	1.48346	0.741730	+	0.670699i	$0.234006\pi$
$318$	−1.92919	−0.108184
$319$	18.0648	1.01144
$320$	3.43329	0.191927
$321$	−2.72992	−0.152369
$322$	0.615842	0.0343195
$323$	6.85710	0.381539
$324$	1.00000	0.0555556
$325$	45.6511	2.53227
$326$	21.6925	1.20144
$327$	−4.86495	−0.269033
$328$	−4.55318	−0.251407
$329$	−0.615650	−0.0339419
$330$	−14.4835	−0.797293
$331$	−6.78865	−0.373138	−0.186569	−	0.982442i	$-0.559737\pi$
$331$	−6.78865	−0.373138	−0.186569	+	0.982442i	$0.559737\pi$
$332$	−5.52235	−0.303078
$333$	−8.31114	−0.455448
$334$	15.0938	0.825894
$335$	8.02702	0.438563
$336$	0.177683	0.00969342
$337$	−0.0987220	−0.00537773	−0.00268887	−	0.999996i	$-0.500856\pi$
$337$	−0.0987220	−0.00537773	−0.00268887	+	0.999996i	$0.500856\pi$
$338$	−32.2365	−1.75343
$339$	16.7112	0.907627
$340$	−3.43329	−0.186196
$341$	34.0839	1.84575
$342$	6.85710	0.370790
$343$	2.48196	0.134013
$344$	−7.07506	−0.381462
$345$	−11.8996	−0.640653
$346$	−2.15207	−0.115696
$347$	9.27118	0.497703	0.248851	−	0.968542i	$-0.419947\pi$
$347$	9.27118	0.497703	0.248851	+	0.968542i	$0.419947\pi$
$348$	4.28222	0.229551
$349$	−8.45154	−0.452400	−0.226200	−	0.974081i	$-0.572630\pi$
$349$	−8.45154	−0.452400	−0.226200	+	0.974081i	$0.572630\pi$
$350$	1.20602	0.0644643
$351$	−6.72581	−0.358997
$352$	4.21857	0.224850
$353$	13.3770	0.711984	0.355992	−	0.934489i	$-0.384143\pi$
$353$	13.3770	0.711984	0.355992	+	0.934489i	$0.384143\pi$
$354$	−1.00000	−0.0531494
$355$	−22.4794	−1.19308
$356$	−3.84979	−0.204038
$357$	−0.177683	−0.00940400
$358$	−18.6454	−0.985439
$359$	−21.4768	−1.13350	−0.566751	−	0.823889i	$-0.691800\pi$
$359$	−21.4768	−1.13350	−0.566751	+	0.823889i	$0.691800\pi$
$360$	−3.43329	−0.180950
$361$	28.0198	1.47473
$362$	−12.7948	−0.672478
$363$	−6.79630	−0.356713
$364$	−1.19506	−0.0626383
$365$	5.76569	0.301790
$366$	−11.3137	−0.591378
$367$	−30.4973	−1.59194	−0.795972	−	0.605333i	$-0.793040\pi$
$367$	−30.4973	−1.59194	−0.795972	+	0.605333i	$0.793040\pi$
$368$	3.46595	0.180675
$369$	4.55318	0.237029
$370$	28.5345	1.48344
$371$	0.342785	0.0177965
$372$	8.07950	0.418902
$373$	−13.6516	−0.706852	−0.353426	−	0.935462i	$-0.614983\pi$
$373$	−13.6516	−0.706852	−0.353426	+	0.935462i	$0.614983\pi$
$374$	−4.21857	−0.218137
$375$	−6.13683	−0.316905
$376$	−3.46487	−0.178687
$377$	−28.8014	−1.48335
$378$	−0.177683	−0.00913904
$379$	11.7190	0.601964	0.300982	−	0.953630i	$-0.402686\pi$
$379$	11.7190	0.601964	0.300982	+	0.953630i	$0.402686\pi$
$380$	−23.5424	−1.20770
$381$	−1.29791	−0.0664941
$382$	18.6662	0.955046
$383$	−7.57651	−0.387142	−0.193571	−	0.981086i	$-0.562007\pi$
$383$	−7.57651	−0.387142	−0.193571	+	0.981086i	$0.562007\pi$
$384$	1.00000	0.0510310
$385$	2.57348	0.131157
$386$	−8.91501	−0.453762
$387$	7.07506	0.359645
$388$	−4.92259	−0.249907
$389$	0.499048	0.0253028	0.0126514	−	0.999920i	$-0.495973\pi$
$389$	0.499048	0.0253028	0.0126514	+	0.999920i	$0.495973\pi$
$390$	23.0916	1.16929
$391$	−3.46595	−0.175281
$392$	6.96843	0.351959
$393$	−9.11877	−0.459981
$394$	−20.2481	−1.02008
$395$	−44.5208	−2.24008
$396$	−4.21857	−0.211991
$397$	30.6620	1.53888	0.769440	−	0.638719i	$-0.220535\pi$
$397$	30.6620	1.53888	0.769440	+	0.638719i	$0.220535\pi$
$398$	1.83823	0.0921420
$399$	−1.21839	−0.0609959
$400$	6.78745	0.339373
$401$	−11.7173	−0.585134	−0.292567	−	0.956245i	$-0.594509\pi$
$401$	−11.7173	−0.585134	−0.292567	+	0.956245i	$0.594509\pi$
$402$	2.33800	0.116609
$403$	−54.3411	−2.70692
$404$	−2.85227	−0.141906
$405$	3.43329	0.170601
$406$	−0.760879	−0.0377618
$407$	35.0611	1.73791
$408$	−1.00000	−0.0495074
$409$	25.1167	1.24194	0.620970	−	0.783835i	$-0.286739\pi$
$409$	25.1167	1.24194	0.620970	+	0.783835i	$0.286739\pi$
$410$	−15.6324	−0.772028
$411$	−21.3710	−1.05416
$412$	4.39930	0.216738
$413$	0.177683	0.00874322
$414$	−3.46595	−0.170342
$415$	−18.9598	−0.930700
$416$	−6.72581	−0.329760
$417$	18.1244	0.887558
$418$	−28.9271	−1.41487
$419$	21.7118	1.06069	0.530345	−	0.847782i	$-0.322062\pi$
$419$	21.7118	1.06069	0.530345	+	0.847782i	$0.322062\pi$
$420$	0.610038	0.0297668
$421$	7.71516	0.376014	0.188007	−	0.982168i	$-0.439797\pi$
$421$	7.71516	0.376014	0.188007	+	0.982168i	$0.439797\pi$
$422$	−12.1185	−0.589920
$423$	3.46487	0.168468
$424$	1.92919	0.0936898
$425$	−6.78745	−0.329240
$426$	−6.54749	−0.317227
$427$	2.01026	0.0972834
$428$	2.72992	0.131956
$429$	28.3733	1.36987
$430$	−24.2907	−1.17140
$431$	−2.04332	−0.0984232	−0.0492116	−	0.998788i	$-0.515671\pi$
$431$	−2.04332	−0.0984232	−0.0492116	+	0.998788i	$0.515671\pi$
$432$	−1.00000	−0.0481125
$433$	−27.6943	−1.33090	−0.665452	−	0.746441i	$-0.731761\pi$
$433$	−27.6943	−1.33090	−0.665452	+	0.746441i	$0.731761\pi$
$434$	−1.43559	−0.0689106
$435$	14.7021	0.704911
$436$	4.86495	0.232989
$437$	−23.7664	−1.13690
$438$	1.67935	0.0802424
$439$	−13.1167	−0.626026	−0.313013	−	0.949749i	$-0.601338\pi$
$439$	−13.1167	−0.626026	−0.313013	+	0.949749i	$0.601338\pi$
$440$	14.4835	0.690476
$441$	−6.96843	−0.331830
$442$	6.72581	0.319914
$443$	16.4314	0.780680	0.390340	−	0.920671i	$-0.372357\pi$
$443$	16.4314	0.780680	0.390340	+	0.920671i	$0.372357\pi$
$444$	8.31114	0.394429
$445$	−13.2174	−0.626566
$446$	−7.95696	−0.376773
$447$	19.3670	0.916027
$448$	−0.177683	−0.00839475
$449$	−13.1504	−0.620606	−0.310303	−	0.950638i	$-0.600430\pi$
$449$	−13.1504	−0.620606	−0.310303	+	0.950638i	$0.600430\pi$
$450$	−6.78745	−0.319964
$451$	−19.2079	−0.904464
$452$	−16.7112	−0.786028
$453$	16.7380	0.786418
$454$	−25.0974	−1.17788
$455$	−4.10299	−0.192351
$456$	−6.85710	−0.321113
$457$	16.5629	0.774778	0.387389	−	0.921916i	$-0.373377\pi$
$457$	16.5629	0.774778	0.387389	+	0.921916i	$0.373377\pi$
$458$	24.3719	1.13882
$459$	1.00000	0.0466760
$460$	11.8996	0.554822
$461$	4.29392	0.199988	0.0999939	−	0.994988i	$-0.468118\pi$
$461$	4.29392	0.199988	0.0999939	+	0.994988i	$0.468118\pi$
$462$	0.749569	0.0348731
$463$	−26.6139	−1.23685	−0.618426	−	0.785843i	$-0.712229\pi$
$463$	−26.6139	−1.23685	−0.618426	+	0.785843i	$0.712229\pi$
$464$	−4.28222	−0.198797
$465$	27.7392	1.28638
$466$	20.1082	0.931494
$467$	24.6031	1.13850	0.569248	−	0.822166i	$-0.307234\pi$
$467$	24.6031	1.13850	0.569248	+	0.822166i	$0.307234\pi$
$468$	6.72581	0.310900
$469$	−0.415424	−0.0191825
$470$	−11.8959	−0.548717
$471$	−13.9462	−0.642607
$472$	1.00000	0.0460287
$473$	−29.8466	−1.37235
$474$	−12.9674	−0.595612
$475$	−46.5422	−2.13550
$476$	0.177683	0.00814410
$477$	−1.92919	−0.0883316
$478$	0.720065	0.0329350
$479$	−26.5182	−1.21165	−0.605825	−	0.795598i	$-0.707157\pi$
$479$	−26.5182	−1.21165	−0.605825	+	0.795598i	$0.707157\pi$
$480$	3.43329	0.156707
$481$	−55.8991	−2.54878
$482$	−25.5539	−1.16395
$483$	0.615842	0.0280218
$484$	6.79630	0.308923
$485$	−16.9007	−0.767420
$486$	1.00000	0.0453609
$487$	−13.0331	−0.590587	−0.295293	−	0.955407i	$-0.595417\pi$
$487$	−13.0331	−0.590587	−0.295293	+	0.955407i	$0.595417\pi$
$488$	11.3137	0.512148
$489$	21.6925	0.980971
$490$	23.9246	1.08080
$491$	−19.4218	−0.876492	−0.438246	−	0.898855i	$-0.644400\pi$
$491$	−19.4218	−0.876492	−0.438246	+	0.898855i	$0.644400\pi$
$492$	−4.55318	−0.205273
$493$	4.28222	0.192862
$494$	46.1195	2.07502
$495$	−14.4835	−0.650987
$496$	−8.07950	−0.362780
$497$	1.16338	0.0521847
$498$	−5.52235	−0.247462
$499$	−0.552423	−0.0247299	−0.0123649	−	0.999924i	$-0.503936\pi$
$499$	−0.552423	−0.0247299	−0.0123649	+	0.999924i	$0.503936\pi$
$500$	6.13683	0.274447
$501$	15.0938	0.674339
$502$	−14.9432	−0.666949
$503$	21.3141	0.950348	0.475174	−	0.879892i	$-0.342385\pi$
$503$	21.3141	0.950348	0.475174	+	0.879892i	$0.342385\pi$
$504$	0.177683	0.00791464
$505$	−9.79266	−0.435767
$506$	14.6213	0.649998
$507$	−32.2365	−1.43167
$508$	1.29791	0.0575855
$509$	−17.3206	−0.767724	−0.383862	−	0.923390i	$-0.625406\pi$
$509$	−17.3206	−0.767724	−0.383862	+	0.923390i	$0.625406\pi$
$510$	−3.43329	−0.152028
$511$	−0.298392	−0.0132001
$512$	−1.00000	−0.0441942
$513$	6.85710	0.302748
$514$	−28.9281	−1.27596
$515$	15.1041	0.665564
$516$	−7.07506	−0.311462
$517$	−14.6168	−0.642846
$518$	−1.47675	−0.0648847
$519$	−2.15207	−0.0944654
$520$	−23.0916	−1.01263
$521$	−23.3522	−1.02308	−0.511539	−	0.859260i	$-0.670924\pi$
$521$	−23.3522	−1.02308	−0.511539	+	0.859260i	$0.670924\pi$
$522$	4.28222	0.187428
$523$	−1.74366	−0.0762450	−0.0381225	−	0.999273i	$-0.512138\pi$
$523$	−1.74366	−0.0762450	−0.0381225	+	0.999273i	$0.512138\pi$
$524$	9.11877	0.398355
$525$	1.20602	0.0526349
$526$	1.32264	0.0576698
$527$	8.07950	0.351948
$528$	4.21857	0.183590
$529$	−10.9872	−0.477704
$530$	6.62347	0.287705
$531$	−1.00000	−0.0433963
$532$	1.21839	0.0528240
$533$	30.6238	1.32646
$534$	−3.84979	−0.166597
$535$	9.37260	0.405213
$536$	−2.33800	−0.100986
$537$	−18.6454	−0.804608
$538$	3.01175	0.129846
$539$	29.3968	1.26621
$540$	−3.43329	−0.147745
$541$	−36.3987	−1.56490	−0.782452	−	0.622711i	$-0.786031\pi$
$541$	−36.3987	−1.56490	−0.782452	+	0.622711i	$0.786031\pi$
$542$	−3.86074	−0.165833
$543$	−12.7948	−0.549076
$544$	1.00000	0.0428746
$545$	16.7028	0.715468
$546$	−1.19506	−0.0511440
$547$	−7.32211	−0.313071	−0.156535	−	0.987672i	$-0.550033\pi$
$547$	−7.32211	−0.313071	−0.156535	+	0.987672i	$0.550033\pi$
$548$	21.3710	0.912926
$549$	−11.3137	−0.482858
$550$	28.6333	1.22093
$551$	29.3636	1.25093
$552$	3.46595	0.147521
$553$	2.30409	0.0979799
$554$	26.4074	1.12194
$555$	28.5345	1.21122
$556$	−18.1244	−0.768648
$557$	−11.7051	−0.495962	−0.247981	−	0.968765i	$-0.579767\pi$
$557$	−11.7051	−0.495962	−0.247981	+	0.968765i	$0.579767\pi$
$558$	8.07950	0.342032
$559$	47.5855	2.01265
$560$	−0.610038	−0.0257788
$561$	−4.21857	−0.178108
$562$	−22.0628	−0.930661
$563$	−12.2722	−0.517212	−0.258606	−	0.965983i	$-0.583263\pi$
$563$	−12.2722	−0.517212	−0.258606	+	0.965983i	$0.583263\pi$
$564$	−3.46487	−0.145898
$565$	−57.3743	−2.41375
$566$	27.7366	1.16586
$567$	−0.177683	−0.00746200
$568$	6.54749	0.274726
$569$	−2.64311	−0.110805	−0.0554024	−	0.998464i	$-0.517644\pi$
$569$	−2.64311	−0.110805	−0.0554024	+	0.998464i	$0.517644\pi$
$570$	−23.5424	−0.986082
$571$	23.2543	0.973163	0.486581	−	0.873635i	$-0.338244\pi$
$571$	23.2543	0.973163	0.486581	+	0.873635i	$0.338244\pi$
$572$	−28.3733	−1.18635
$573$	18.6662	0.779792
$574$	0.809024	0.0337680
$575$	23.5250	0.981059
$576$	1.00000	0.0416667
$577$	−4.38631	−0.182605	−0.0913023	−	0.995823i	$-0.529103\pi$
$577$	−4.38631	−0.182605	−0.0913023	+	0.995823i	$0.529103\pi$
$578$	−1.00000	−0.0415945
$579$	−8.91501	−0.370495
$580$	−14.7021	−0.610471
$581$	0.981229	0.0407083
$582$	−4.92259	−0.204048
$583$	8.13842	0.337059
$584$	−1.67935	−0.0694920
$585$	23.0916	0.954721
$586$	−1.55991	−0.0644392
$587$	−20.1990	−0.833704	−0.416852	−	0.908974i	$-0.636867\pi$
$587$	−20.1990	−0.833704	−0.416852	+	0.908974i	$0.636867\pi$
$588$	6.96843	0.287373
$589$	55.4019	2.28280
$590$	3.43329	0.141346
$591$	−20.2481	−0.832894
$592$	−8.31114	−0.341586
$593$	−4.82281	−0.198049	−0.0990245	−	0.995085i	$-0.531572\pi$
$593$	−4.82281	−0.198049	−0.0990245	+	0.995085i	$0.531572\pi$
$594$	−4.21857	−0.173090
$595$	0.610038	0.0250091
$596$	−19.3670	−0.793302
$597$	1.83823	0.0752337
$598$	−23.3113	−0.953270
$599$	−41.9256	−1.71303	−0.856517	−	0.516118i	$-0.827377\pi$
$599$	−41.9256	−1.71303	−0.856517	+	0.516118i	$0.827377\pi$
$600$	6.78745	0.277097
$601$	−27.0419	−1.10306	−0.551531	−	0.834154i	$-0.685956\pi$
$601$	−27.0419	−1.10306	−0.551531	+	0.834154i	$0.685956\pi$
$602$	1.25712	0.0512364
$603$	2.33800	0.0952107
$604$	−16.7380	−0.681058
$605$	23.3336	0.948648
$606$	−2.85227	−0.115866
$607$	−27.0271	−1.09700	−0.548498	−	0.836152i	$-0.684800\pi$
$607$	−27.0271	−1.09700	−0.548498	+	0.836152i	$0.684800\pi$
$608$	6.85710	0.278092
$609$	−0.760879	−0.0308324
$610$	38.8433	1.57272
$611$	23.3041	0.942782
$612$	−1.00000	−0.0404226
$613$	7.24948	0.292804	0.146402	−	0.989225i	$-0.453231\pi$
$613$	7.24948	0.292804	0.146402	+	0.989225i	$0.453231\pi$
$614$	9.59670	0.387291
$615$	−15.6324	−0.630358
$616$	−0.749569	−0.0302010
$617$	−30.2136	−1.21635	−0.608177	−	0.793802i	$-0.708099\pi$
$617$	−30.2136	−1.21635	−0.608177	+	0.793802i	$0.708099\pi$
$618$	4.39930	0.176966
$619$	−10.5917	−0.425717	−0.212859	−	0.977083i	$-0.568277\pi$
$619$	−10.5917	−0.425717	−0.212859	+	0.977083i	$0.568277\pi$
$620$	−27.7392	−1.11403
$621$	−3.46595	−0.139084
$622$	7.57970	0.303918
$623$	0.684043	0.0274056
$624$	−6.72581	−0.269248
$625$	−12.8678	−0.514710
$626$	24.2800	0.970423
$627$	−28.9271	−1.15524
$628$	13.9462	0.556514
$629$	8.31114	0.331387
$630$	0.610038	0.0243045
$631$	19.2974	0.768219	0.384110	−	0.923288i	$-0.374508\pi$
$631$	19.2974	0.768219	0.384110	+	0.923288i	$0.374508\pi$
$632$	12.9674	0.515815
$633$	−12.1185	−0.481667
$634$	−26.4122	−1.04896
$635$	4.45610	0.176835
$636$	1.92919	0.0764974
$637$	−46.8683	−1.85699
$638$	−18.0648	−0.715194
$639$	−6.54749	−0.259015
$640$	−3.43329	−0.135713
$641$	−10.2922	−0.406516	−0.203258	−	0.979125i	$-0.565153\pi$
$641$	−10.2922	−0.406516	−0.203258	+	0.979125i	$0.565153\pi$
$642$	2.72992	0.107741
$643$	−20.7388	−0.817860	−0.408930	−	0.912566i	$-0.634098\pi$
$643$	−20.7388	−0.817860	−0.408930	+	0.912566i	$0.634098\pi$
$644$	−0.615842	−0.0242676
$645$	−24.2907	−0.956445
$646$	−6.85710	−0.269789
$647$	23.4244	0.920907	0.460453	−	0.887684i	$-0.347687\pi$
$647$	23.4244	0.920907	0.460453	+	0.887684i	$0.347687\pi$
$648$	−1.00000	−0.0392837
$649$	4.21857	0.165593
$650$	−45.6511	−1.79058
$651$	−1.43559	−0.0562653
$652$	−21.6925	−0.849546
$653$	−18.8130	−0.736211	−0.368105	−	0.929784i	$-0.619993\pi$
$653$	−18.8130	−0.736211	−0.368105	+	0.929784i	$0.619993\pi$
$654$	4.86495	0.190235
$655$	31.3073	1.22328
$656$	4.55318	0.177772
$657$	1.67935	0.0655177
$658$	0.615650	0.0240005
$659$	8.66074	0.337374	0.168687	−	0.985670i	$-0.446047\pi$
$659$	8.66074	0.337374	0.168687	+	0.985670i	$0.446047\pi$
$660$	14.4835	0.563771
$661$	−25.5367	−0.993264	−0.496632	−	0.867961i	$-0.665430\pi$
$661$	−25.5367	−0.993264	−0.496632	+	0.867961i	$0.665430\pi$
$662$	6.78865	0.263848
$663$	6.72581	0.261209
$664$	5.52235	0.214309
$665$	4.18309	0.162213
$666$	8.31114	0.322050
$667$	−14.8420	−0.574683
$668$	−15.0938	−0.583995
$669$	−7.95696	−0.307634
$670$	−8.02702	−0.310111
$671$	47.7277	1.84251
$672$	−0.177683	−0.00685428
$673$	−39.3787	−1.51794	−0.758968	−	0.651128i	$-0.774296\pi$
$673$	−39.3787	−1.51794	−0.758968	+	0.651128i	$0.774296\pi$
$674$	0.0987220	0.00380263
$675$	−6.78745	−0.261249
$676$	32.2365	1.23986
$677$	−49.8822	−1.91713	−0.958563	−	0.284879i	$-0.908047\pi$
$677$	−49.8822	−1.91713	−0.958563	+	0.284879i	$0.908047\pi$
$678$	−16.7112	−0.641789
$679$	0.874663	0.0335665
$680$	3.43329	0.131661
$681$	−25.0974	−0.961735
$682$	−34.0839	−1.30514
$683$	−21.9811	−0.841084	−0.420542	−	0.907273i	$-0.638160\pi$
$683$	−21.9811	−0.841084	−0.420542	+	0.907273i	$0.638160\pi$
$684$	−6.85710	−0.262188
$685$	73.3729	2.80343
$686$	−2.48196	−0.0947616
$687$	24.3719	0.929844
$688$	7.07506	0.269734
$689$	−12.9754	−0.494322
$690$	11.8996	0.453010
$691$	−8.88562	−0.338025	−0.169013	−	0.985614i	$-0.554058\pi$
$691$	−8.88562	−0.338025	−0.169013	+	0.985614i	$0.554058\pi$
$692$	2.15207	0.0818094
$693$	0.749569	0.0284738
$694$	−9.27118	−0.351929
$695$	−62.2264	−2.36038
$696$	−4.28222	−0.162317
$697$	−4.55318	−0.172464
$698$	8.45154	0.319895
$699$	20.1082	0.760562
$700$	−1.20602	−0.0455832
$701$	23.7444	0.896814	0.448407	−	0.893829i	$-0.351991\pi$
$701$	23.7444	0.896814	0.448407	+	0.893829i	$0.351991\pi$
$702$	6.72581	0.253849
$703$	56.9903	2.14943
$704$	−4.21857	−0.158993
$705$	−11.8959	−0.448026
$706$	−13.3770	−0.503449
$707$	0.506801	0.0190602
$708$	1.00000	0.0375823
$709$	−17.9186	−0.672949	−0.336474	−	0.941693i	$-0.609235\pi$
$709$	−17.9186	−0.672949	−0.336474	+	0.941693i	$0.609235\pi$
$710$	22.4794	0.843637
$711$	−12.9674	−0.486315
$712$	3.84979	0.144277
$713$	−28.0031	−1.04873
$714$	0.177683	0.00664963
$715$	−97.4135	−3.64306
$716$	18.6454	0.696811
$717$	0.720065	0.0268913
$718$	21.4768	0.801507
$719$	21.6578	0.807700	0.403850	−	0.914825i	$-0.367672\pi$
$719$	21.6578	0.807700	0.403850	+	0.914825i	$0.367672\pi$
$720$	3.43329	0.127951
$721$	−0.781682	−0.0291114
$722$	−28.0198	−1.04279
$723$	−25.5539	−0.950362
$724$	12.7948	0.475514
$725$	−29.0654	−1.07946
$726$	6.79630	0.252234
$727$	46.2196	1.71419	0.857095	−	0.515158i	$-0.172267\pi$
$727$	46.2196	1.71419	0.857095	+	0.515158i	$0.172267\pi$
$728$	1.19506	0.0442920
$729$	1.00000	0.0370370
$730$	−5.76569	−0.213398
$731$	−7.07506	−0.261680
$732$	11.3137	0.418167
$733$	−33.3657	−1.23239	−0.616195	−	0.787594i	$-0.711327\pi$
$733$	−33.3657	−1.23239	−0.616195	+	0.787594i	$0.711327\pi$
$734$	30.4973	1.12567
$735$	23.9246	0.882472
$736$	−3.46595	−0.127757
$737$	−9.86301	−0.363309
$738$	−4.55318	−0.167605
$739$	−38.2501	−1.40705	−0.703526	−	0.710669i	$-0.748392\pi$
$739$	−38.2501	−1.40705	−0.703526	+	0.710669i	$0.748392\pi$
$740$	−28.5345	−1.04895
$741$	46.1195	1.69424
$742$	−0.342785	−0.0125840
$743$	45.2513	1.66011	0.830055	−	0.557682i	$-0.188309\pi$
$743$	45.2513	1.66011	0.830055	+	0.557682i	$0.188309\pi$
$744$	−8.07950	−0.296209
$745$	−66.4924	−2.43609
$746$	13.6516	0.499820
$747$	−5.52235	−0.202052
$748$	4.21857	0.154246
$749$	−0.485061	−0.0177238
$750$	6.13683	0.224085
$751$	54.4950	1.98855	0.994275	−	0.106847i	$-0.0340756\pi$
$751$	54.4950	1.98855	0.994275	+	0.106847i	$0.0340756\pi$
$752$	3.46487	0.126351
$753$	−14.9432	−0.544562
$754$	28.8014	1.04888
$755$	−57.4662	−2.09141
$756$	0.177683	0.00646228
$757$	−14.5546	−0.528996	−0.264498	−	0.964386i	$-0.585206\pi$
$757$	−14.5546	−0.528996	−0.264498	+	0.964386i	$0.585206\pi$
$758$	−11.7190	−0.425653
$759$	14.6213	0.530721
$760$	23.5424	0.853972
$761$	−1.63752	−0.0593599	−0.0296800	−	0.999559i	$-0.509449\pi$
$761$	−1.63752	−0.0593599	−0.0296800	+	0.999559i	$0.509449\pi$
$762$	1.29791	0.0470184
$763$	−0.864421	−0.0312941
$764$	−18.6662	−0.675320
$765$	−3.43329	−0.124131
$766$	7.57651	0.273750
$767$	−6.72581	−0.242855
$768$	−1.00000	−0.0360844
$769$	−14.6689	−0.528973	−0.264486	−	0.964389i	$-0.585202\pi$
$769$	−14.6689	−0.528973	−0.264486	+	0.964389i	$0.585202\pi$
$770$	−2.57348	−0.0927419
$771$	−28.9281	−1.04182
$772$	8.91501	0.320858
$773$	6.21724	0.223618	0.111809	−	0.993730i	$-0.464335\pi$
$773$	6.21724	0.223618	0.111809	+	0.993730i	$0.464335\pi$
$774$	−7.07506	−0.254308
$775$	−54.8392	−1.96988
$776$	4.92259	0.176711
$777$	−1.47675	−0.0529781
$778$	−0.499048	−0.0178917
$779$	−31.2216	−1.11863
$780$	−23.0916	−0.826812
$781$	27.6210	0.988357
$782$	3.46595	0.123942
$783$	4.28222	0.153034
$784$	−6.96843	−0.248872
$785$	47.8813	1.70896
$786$	9.11877	0.325256
$787$	−31.7227	−1.13079	−0.565395	−	0.824820i	$-0.691276\pi$
$787$	−31.7227	−1.13079	−0.565395	+	0.824820i	$0.691276\pi$
$788$	20.2481	0.721308
$789$	1.32264	0.0470872
$790$	44.5208	1.58398
$791$	2.96930	0.105576
$792$	4.21857	0.149900
$793$	−76.0939	−2.70218
$794$	−30.6620	−1.08815
$795$	6.62347	0.234910
$796$	−1.83823	−0.0651543
$797$	22.4471	0.795117	0.397558	−	0.917577i	$-0.369858\pi$
$797$	22.4471	0.795117	0.397558	+	0.917577i	$0.369858\pi$
$798$	1.21839	0.0431306
$799$	−3.46487	−0.122578
$800$	−6.78745	−0.239973
$801$	−3.84979	−0.136026
$802$	11.7173	0.413752
$803$	−7.08445	−0.250005
$804$	−2.33800	−0.0824549
$805$	−2.11436	−0.0745214
$806$	54.3411	1.91408
$807$	3.01175	0.106019
$808$	2.85227	0.100342
$809$	47.3819	1.66586	0.832930	−	0.553378i	$-0.186662\pi$
$809$	47.3819	1.66586	0.832930	+	0.553378i	$0.186662\pi$
$810$	−3.43329	−0.120633
$811$	13.1092	0.460326	0.230163	−	0.973152i	$-0.426074\pi$
$811$	13.1092	0.460326	0.230163	+	0.973152i	$0.426074\pi$
$812$	0.760879	0.0267016
$813$	−3.86074	−0.135402
$814$	−35.0611	−1.22889
$815$	−74.4767	−2.60881
$816$	1.00000	0.0350070
$817$	−48.5144	−1.69730
$818$	−25.1167	−0.878184
$819$	−1.19506	−0.0417589
$820$	15.6324	0.545906
$821$	22.7890	0.795342	0.397671	−	0.917528i	$-0.369819\pi$
$821$	22.7890	0.795342	0.397671	+	0.917528i	$0.369819\pi$
$822$	21.3710	0.745401
$823$	5.54626	0.193330	0.0966652	−	0.995317i	$-0.469182\pi$
$823$	5.54626	0.193330	0.0966652	+	0.995317i	$0.469182\pi$
$824$	−4.39930	−0.153257
$825$	28.6333	0.996884
$826$	−0.177683	−0.00618239
$827$	49.1311	1.70846	0.854228	−	0.519898i	$-0.174030\pi$
$827$	49.1311	1.70846	0.854228	+	0.519898i	$0.174030\pi$
$828$	3.46595	0.120450
$829$	−4.05955	−0.140994	−0.0704971	−	0.997512i	$-0.522459\pi$
$829$	−4.05955	−0.140994	−0.0704971	+	0.997512i	$0.522459\pi$
$830$	18.9598	0.658104
$831$	26.4074	0.916064
$832$	6.72581	0.233175
$833$	6.96843	0.241442
$834$	−18.1244	−0.627598
$835$	−51.8212	−1.79335
$836$	28.9271	1.00047
$837$	8.07950	0.279268
$838$	−21.7118	−0.750021
$839$	22.3144	0.770379	0.385189	−	0.922838i	$-0.374136\pi$
$839$	22.3144	0.770379	0.385189	+	0.922838i	$0.374136\pi$
$840$	−0.610038	−0.0210483
$841$	−10.6626	−0.367675
$842$	−7.71516	−0.265882
$843$	−22.0628	−0.759882
$844$	12.1185	0.417136
$845$	110.677	3.80740
$846$	−3.46487	−0.119125
$847$	−1.20759	−0.0414933
$848$	−1.92919	−0.0662487
$849$	27.7366	0.951919
$850$	6.78745	0.232808
$851$	−28.8060	−0.987457
$852$	6.54749	0.224313
$853$	58.1566	1.99125	0.995623	−	0.0934616i	$-0.0297932\pi$
$853$	58.1566	1.99125	0.995623	+	0.0934616i	$0.0297932\pi$
$854$	−2.01026	−0.0687897
$855$	−23.5424	−0.805133
$856$	−2.72992	−0.0933067
$857$	35.9296	1.22733	0.613665	−	0.789566i	$-0.289695\pi$
$857$	35.9296	1.22733	0.613665	+	0.789566i	$0.289695\pi$
$858$	−28.3733	−0.968647
$859$	−15.6376	−0.533549	−0.266775	−	0.963759i	$-0.585958\pi$
$859$	−15.6376	−0.533549	−0.266775	+	0.963759i	$0.585958\pi$
$860$	24.2907	0.828306
$861$	0.809024	0.0275715
$862$	2.04332	0.0695957
$863$	1.57209	0.0535145	0.0267572	−	0.999642i	$-0.491482\pi$
$863$	1.57209	0.0535145	0.0267572	+	0.999642i	$0.491482\pi$
$864$	1.00000	0.0340207
$865$	7.38867	0.251222
$866$	27.6943	0.941091
$867$	−1.00000	−0.0339618
$868$	1.43559	0.0487272
$869$	54.7038	1.85570
$870$	−14.7021	−0.498447
$871$	15.7249	0.532819
$872$	−4.86495	−0.164748
$873$	−4.92259	−0.166605
$874$	23.7664	0.803910
$875$	−1.09041	−0.0368627
$876$	−1.67935	−0.0567399
$877$	52.1597	1.76131	0.880654	−	0.473761i	$-0.157104\pi$
$877$	52.1597	1.76131	0.880654	+	0.473761i	$0.157104\pi$
$878$	13.1167	0.442667
$879$	−1.55991	−0.0526144
$880$	−14.4835	−0.488240
$881$	−16.2891	−0.548795	−0.274397	−	0.961616i	$-0.588478\pi$
$881$	−16.2891	−0.548795	−0.274397	+	0.961616i	$0.588478\pi$
$882$	6.96843	0.234639
$883$	28.4206	0.956431	0.478215	−	0.878243i	$-0.341284\pi$
$883$	28.4206	0.956431	0.478215	+	0.878243i	$0.341284\pi$
$884$	−6.72581	−0.226213
$885$	3.43329	0.115409
$886$	−16.4314	−0.552024
$887$	12.4029	0.416448	0.208224	−	0.978081i	$-0.433232\pi$
$887$	12.4029	0.416448	0.208224	+	0.978081i	$0.433232\pi$
$888$	−8.31114	−0.278904
$889$	−0.230617	−0.00773466
$890$	13.2174	0.443049
$891$	−4.21857	−0.141327
$892$	7.95696	0.266419
$893$	−23.7590	−0.795064
$894$	−19.3670	−0.647729
$895$	64.0149	2.13978
$896$	0.177683	0.00593598
$897$	−23.3113	−0.778342
$898$	13.1504	0.438834
$899$	34.5982	1.15391
$900$	6.78745	0.226248
$901$	1.92919	0.0642707
$902$	19.2079	0.639553
$903$	1.25712	0.0418343
$904$	16.7112	0.555806
$905$	43.9281	1.46022
$906$	−16.7380	−0.556081
$907$	8.97389	0.297973	0.148987	−	0.988839i	$-0.452399\pi$
$907$	8.97389	0.297973	0.148987	+	0.988839i	$0.452399\pi$
$908$	25.0974	0.832887
$909$	−2.85227	−0.0946038
$910$	4.10299	0.136013
$911$	−31.8070	−1.05381	−0.526906	−	0.849923i	$-0.676648\pi$
$911$	−31.8070	−1.05381	−0.526906	+	0.849923i	$0.676648\pi$
$912$	6.85710	0.227061
$913$	23.2964	0.770998
$914$	−16.5629	−0.547850
$915$	38.8433	1.28412
$916$	−24.3719	−0.805269
$917$	−1.62025	−0.0535055
$918$	−1.00000	−0.0330049
$919$	−45.7956	−1.51066	−0.755330	−	0.655345i	$-0.772523\pi$
$919$	−45.7956	−1.51066	−0.755330	+	0.655345i	$0.772523\pi$
$920$	−11.8996	−0.392318
$921$	9.59670	0.316222
$922$	−4.29392	−0.141413
$923$	−44.0371	−1.44950
$924$	−0.749569	−0.0246590
$925$	−56.4115	−1.85480
$926$	26.6139	0.874586
$927$	4.39930	0.144492
$928$	4.28222	0.140571
$929$	−15.7318	−0.516143	−0.258071	−	0.966126i	$-0.583087\pi$
$929$	−15.7318	−0.516143	−0.258071	+	0.966126i	$0.583087\pi$
$930$	−27.7392	−0.909605
$931$	47.7832	1.56603
$932$	−20.1082	−0.658666
$933$	7.57970	0.248148
$934$	−24.6031	−0.805039
$935$	14.4835	0.473663
$936$	−6.72581	−0.219840
$937$	−49.2734	−1.60969	−0.804847	−	0.593483i	$-0.797752\pi$
$937$	−49.2734	−1.60969	−0.804847	+	0.593483i	$0.797752\pi$
$938$	0.415424	0.0135641
$939$	24.2800	0.792347
$940$	11.8959	0.388002
$941$	−22.4388	−0.731484	−0.365742	−	0.930716i	$-0.619185\pi$
$941$	−22.4388	−0.731484	−0.365742	+	0.930716i	$0.619185\pi$
$942$	13.9462	0.454391
$943$	15.7811	0.513903
$944$	−1.00000	−0.0325472
$945$	0.610038	0.0198445
$946$	29.8466	0.970397
$947$	−0.290698	−0.00944641	−0.00472320	−	0.999989i	$-0.501503\pi$
$947$	−0.290698	−0.00944641	−0.00472320	+	0.999989i	$0.501503\pi$
$948$	12.9674	0.421162
$949$	11.2950	0.366650
$950$	46.5422	1.51003
$951$	−26.4122	−0.856475
$952$	−0.177683	−0.00575875
$953$	−13.6648	−0.442647	−0.221323	−	0.975200i	$-0.571038\pi$
$953$	−13.6648	−0.442647	−0.221323	+	0.975200i	$0.571038\pi$
$954$	1.92919	0.0624599
$955$	−64.0864	−2.07379
$956$	−0.720065	−0.0232886
$957$	−18.0648	−0.583953
$958$	26.5182	0.856766
$959$	−3.79728	−0.122621
$960$	−3.43329	−0.110809
$961$	34.2783	1.10575
$962$	55.8991	1.80226
$963$	2.72992	0.0879704
$964$	25.5539	0.823037
$965$	30.6078	0.985300
$966$	−0.615842	−0.0198144
$967$	29.9504	0.963138	0.481569	−	0.876408i	$-0.340067\pi$
$967$	29.9504	0.963138	0.481569	+	0.876408i	$0.340067\pi$
$968$	−6.79630	−0.218441
$969$	−6.85710	−0.220282
$970$	16.9007	0.542648
$971$	8.03399	0.257823	0.128911	−	0.991656i	$-0.458852\pi$
$971$	8.03399	0.257823	0.128911	+	0.991656i	$0.458852\pi$
$972$	−1.00000	−0.0320750
$973$	3.22041	0.103242
$974$	13.0331	0.417608
$975$	−45.6511	−1.46200
$976$	−11.3137	−0.362144
$977$	42.3664	1.35542	0.677711	−	0.735328i	$-0.262972\pi$
$977$	42.3664	1.35542	0.677711	+	0.735328i	$0.262972\pi$
$978$	−21.6925	−0.693651
$979$	16.2406	0.519051
$980$	−23.9246	−0.764244
$981$	4.86495	0.155326
$982$	19.4218	0.619774
$983$	59.2810	1.89077	0.945385	−	0.325956i	$-0.105686\pi$
$983$	59.2810	1.89077	0.945385	+	0.325956i	$0.105686\pi$
$984$	4.55318	0.145150
$985$	69.5174	2.21501
$986$	−4.28222	−0.136374
$987$	0.615650	0.0195964
$988$	−46.1195	−1.46726
$989$	24.5218	0.779748
$990$	14.4835	0.460317
$991$	39.2274	1.24610	0.623049	−	0.782183i	$-0.285894\pi$
$991$	39.2274	1.24610	0.623049	+	0.782183i	$0.285894\pi$
$992$	8.07950	0.256524
$993$	6.78865	0.215431
$994$	−1.16338	−0.0369001
$995$	−6.31116	−0.200077
$996$	5.52235	0.174982
$997$	−52.0546	−1.64859	−0.824293	−	0.566164i	$-0.808427\pi$
$997$	−52.0546	−1.64859	−0.824293	+	0.566164i	$0.808427\pi$
$998$	0.552423	0.0174867
$999$	8.31114	0.262953

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.v.1.8	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.v.1.8	✓	9	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.43329 q^{5} +1.00000 q^{6} -0.177683 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.43329 q^{5} +1.00000 q^{6} -0.177683 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.43329 q^{10} -4.21857 q^{11} -1.00000 q^{12} +6.72581 q^{13} +0.177683 q^{14} -3.43329 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -6.85710 q^{19} +3.43329 q^{20} +0.177683 q^{21} +4.21857 q^{22} +3.46595 q^{23} +1.00000 q^{24} +6.78745 q^{25} -6.72581 q^{26} -1.00000 q^{27} -0.177683 q^{28} -4.28222 q^{29} +3.43329 q^{30} -8.07950 q^{31} -1.00000 q^{32} +4.21857 q^{33} +1.00000 q^{34} -0.610038 q^{35} +1.00000 q^{36} -8.31114 q^{37} +6.85710 q^{38} -6.72581 q^{39} -3.43329 q^{40} +4.55318 q^{41} -0.177683 q^{42} +7.07506 q^{43} -4.21857 q^{44} +3.43329 q^{45} -3.46595 q^{46} +3.46487 q^{47} -1.00000 q^{48} -6.96843 q^{49} -6.78745 q^{50} +1.00000 q^{51} +6.72581 q^{52} -1.92919 q^{53} +1.00000 q^{54} -14.4835 q^{55} +0.177683 q^{56} +6.85710 q^{57} +4.28222 q^{58} -1.00000 q^{59} -3.43329 q^{60} -11.3137 q^{61} +8.07950 q^{62} -0.177683 q^{63} +1.00000 q^{64} +23.0916 q^{65} -4.21857 q^{66} +2.33800 q^{67} -1.00000 q^{68} -3.46595 q^{69} +0.610038 q^{70} -6.54749 q^{71} -1.00000 q^{72} +1.67935 q^{73} +8.31114 q^{74} -6.78745 q^{75} -6.85710 q^{76} +0.749569 q^{77} +6.72581 q^{78} -12.9674 q^{79} +3.43329 q^{80} +1.00000 q^{81} -4.55318 q^{82} -5.52235 q^{83} +0.177683 q^{84} -3.43329 q^{85} -7.07506 q^{86} +4.28222 q^{87} +4.21857 q^{88} -3.84979 q^{89} -3.43329 q^{90} -1.19506 q^{91} +3.46595 q^{92} +8.07950 q^{93} -3.46487 q^{94} -23.5424 q^{95} +1.00000 q^{96} -4.92259 q^{97} +6.96843 q^{98} -4.21857 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} + 9 q^{6} - 11 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 + 9 * q^6 - 11 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 6 q^{5} + 9 q^{6} - 11 q^{7} - 9 q^{8} + 9 q^{9} - 6 q^{10} + q^{11} - 9 q^{12} + 4 q^{13} + 11 q^{14} - 6 q^{15} + 9 q^{16} - 9 q^{17} - 9 q^{18} - 13 q^{19} + 6 q^{20} + 11 q^{21} - q^{22} - 6 q^{23} + 9 q^{24} + 9 q^{25} - 4 q^{26} - 9 q^{27} - 11 q^{28} + 10 q^{29} + 6 q^{30} + q^{31} - 9 q^{32} - q^{33} + 9 q^{34} + 6 q^{35} + 9 q^{36} - 2 q^{37} + 13 q^{38} - 4 q^{39} - 6 q^{40} + 20 q^{41} - 11 q^{42} - 17 q^{43} + q^{44} + 6 q^{45} + 6 q^{46} + 4 q^{47} - 9 q^{48} + 2 q^{49} - 9 q^{50} + 9 q^{51} + 4 q^{52} + 16 q^{53} + 9 q^{54} - 17 q^{55} + 11 q^{56} + 13 q^{57} - 10 q^{58} - 9 q^{59} - 6 q^{60} - 9 q^{61} - q^{62} - 11 q^{63} + 9 q^{64} + q^{66} - 8 q^{67} - 9 q^{68} + 6 q^{69} - 6 q^{70} - 8 q^{71} - 9 q^{72} - 20 q^{73} + 2 q^{74} - 9 q^{75} - 13 q^{76} - 32 q^{77} + 4 q^{78} - 29 q^{79} + 6 q^{80} + 9 q^{81} - 20 q^{82} - 16 q^{83} + 11 q^{84} - 6 q^{85} + 17 q^{86} - 10 q^{87} - q^{88} + 11 q^{89} - 6 q^{90} - 13 q^{91} - 6 q^{92} - q^{93} - 4 q^{94} + 5 q^{95} + 9 q^{96} + 17 q^{97} - 2 q^{98} + q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 6 * q^5 + 9 * q^6 - 11 * q^7 - 9 * q^8 + 9 * q^9 - 6 * q^10 + q^11 - 9 * q^12 + 4 * q^13 + 11 * q^14 - 6 * q^15 + 9 * q^16 - 9 * q^17 - 9 * q^18 - 13 * q^19 + 6 * q^20 + 11 * q^21 - q^22 - 6 * q^23 + 9 * q^24 + 9 * q^25 - 4 * q^26 - 9 * q^27 - 11 * q^28 + 10 * q^29 + 6 * q^30 + q^31 - 9 * q^32 - q^33 + 9 * q^34 + 6 * q^35 + 9 * q^36 - 2 * q^37 + 13 * q^38 - 4 * q^39 - 6 * q^40 + 20 * q^41 - 11 * q^42 - 17 * q^43 + q^44 + 6 * q^45 + 6 * q^46 + 4 * q^47 - 9 * q^48 + 2 * q^49 - 9 * q^50 + 9 * q^51 + 4 * q^52 + 16 * q^53 + 9 * q^54 - 17 * q^55 + 11 * q^56 + 13 * q^57 - 10 * q^58 - 9 * q^59 - 6 * q^60 - 9 * q^61 - q^62 - 11 * q^63 + 9 * q^64 + q^66 - 8 * q^67 - 9 * q^68 + 6 * q^69 - 6 * q^70 - 8 * q^71 - 9 * q^72 - 20 * q^73 + 2 * q^74 - 9 * q^75 - 13 * q^76 - 32 * q^77 + 4 * q^78 - 29 * q^79 + 6 * q^80 + 9 * q^81 - 20 * q^82 - 16 * q^83 + 11 * q^84 - 6 * q^85 + 17 * q^86 - 10 * q^87 - q^88 + 11 * q^89 - 6 * q^90 - 13 * q^91 - 6 * q^92 - q^93 - 4 * q^94 + 5 * q^95 + 9 * q^96 + 17 * q^97 - 2 * q^98 + q^99

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