LMFDB - Embedded newform 6045.2.a.bi.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6045,2,Mod(1,6045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6045 = 3 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6045.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:	$48.2695680219$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 4 x^{17} - 21 x^{16} + 97 x^{15} + 156 x^{14} - 935 x^{13} - 411 x^{12} + 4582 x^{11} + \cdots - 112 $ x^18 - 4x^17 - 21x^16 + 97x^15 + 156x^14 - 935x^13 - 411x^12 + 4582x^11 - 446x^10 - 12159x^9 + 4398x^8 + 17347x^7 - 7839x^6 - 12832x^5 + 4744x^4 + 5064x^3 - 746x^2 - 892*x - 112
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$0.844677$ of defining polynomial
Character	$\chi$	$=$	6045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.844677 q^{2} +1.00000 q^{3} -1.28652 q^{4} +1.00000 q^{5} +0.844677 q^{6} -2.49791 q^{7} -2.77605 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.844677 q^{2} +1.00000 q^{3} -1.28652 q^{4} +1.00000 q^{5} +0.844677 q^{6} -2.49791 q^{7} -2.77605 q^{8} +1.00000 q^{9} +0.844677 q^{10} +0.589102 q^{11} -1.28652 q^{12} -1.00000 q^{13} -2.10993 q^{14} +1.00000 q^{15} +0.228180 q^{16} -7.59404 q^{17} +0.844677 q^{18} +0.806944 q^{19} -1.28652 q^{20} -2.49791 q^{21} +0.497601 q^{22} +6.24354 q^{23} -2.77605 q^{24} +1.00000 q^{25} -0.844677 q^{26} +1.00000 q^{27} +3.21362 q^{28} +3.14473 q^{29} +0.844677 q^{30} +1.00000 q^{31} +5.74483 q^{32} +0.589102 q^{33} -6.41451 q^{34} -2.49791 q^{35} -1.28652 q^{36} -3.66879 q^{37} +0.681607 q^{38} -1.00000 q^{39} -2.77605 q^{40} +5.40311 q^{41} -2.10993 q^{42} +1.91079 q^{43} -0.757893 q^{44} +1.00000 q^{45} +5.27377 q^{46} -4.74710 q^{47} +0.228180 q^{48} -0.760441 q^{49} +0.844677 q^{50} -7.59404 q^{51} +1.28652 q^{52} +11.3043 q^{53} +0.844677 q^{54} +0.589102 q^{55} +6.93432 q^{56} +0.806944 q^{57} +2.65628 q^{58} -12.9434 q^{59} -1.28652 q^{60} +11.5460 q^{61} +0.844677 q^{62} -2.49791 q^{63} +4.39617 q^{64} -1.00000 q^{65} +0.497601 q^{66} +0.320783 q^{67} +9.76989 q^{68} +6.24354 q^{69} -2.10993 q^{70} -1.69109 q^{71} -2.77605 q^{72} +0.0347964 q^{73} -3.09894 q^{74} +1.00000 q^{75} -1.03815 q^{76} -1.47153 q^{77} -0.844677 q^{78} +14.3989 q^{79} +0.228180 q^{80} +1.00000 q^{81} +4.56388 q^{82} +4.49210 q^{83} +3.21362 q^{84} -7.59404 q^{85} +1.61400 q^{86} +3.14473 q^{87} -1.63538 q^{88} +5.40483 q^{89} +0.844677 q^{90} +2.49791 q^{91} -8.03244 q^{92} +1.00000 q^{93} -4.00976 q^{94} +0.806944 q^{95} +5.74483 q^{96} +0.220681 q^{97} -0.642327 q^{98} +0.589102 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9	\( 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9} + 4 q^{10} + 6 q^{11} + 22 q^{12} - 18 q^{13} + 5 q^{14} + 18 q^{15} + 30 q^{16} + 18 q^{17} + 4 q^{18} + 12 q^{19} + 22 q^{20} + 8 q^{21} + 7 q^{22} + 32 q^{23} + 9 q^{24} + 18 q^{25} - 4 q^{26} + 18 q^{27} + 10 q^{28} + 7 q^{29} + 4 q^{30} + 18 q^{31} + 22 q^{32} + 6 q^{33} + 15 q^{34} + 8 q^{35} + 22 q^{36} + 3 q^{37} + 32 q^{38} - 18 q^{39} + 9 q^{40} + 4 q^{41} + 5 q^{42} + 14 q^{43} - 5 q^{44} + 18 q^{45} + 10 q^{46} + 23 q^{47} + 30 q^{48} + 28 q^{49} + 4 q^{50} + 18 q^{51} - 22 q^{52} + 35 q^{53} + 4 q^{54} + 6 q^{55} - 7 q^{56} + 12 q^{57} - 6 q^{58} + 28 q^{59} + 22 q^{60} + 19 q^{61} + 4 q^{62} + 8 q^{63} + 43 q^{64} - 18 q^{65} + 7 q^{66} + 34 q^{67} + 55 q^{68} + 32 q^{69} + 5 q^{70} - 8 q^{71} + 9 q^{72} + 22 q^{74} + 18 q^{75} + 2 q^{76} + 21 q^{77} - 4 q^{78} + 4 q^{79} + 30 q^{80} + 18 q^{81} + 29 q^{82} + 11 q^{83} + 10 q^{84} + 18 q^{85} - 22 q^{86} + 7 q^{87} - 31 q^{88} + 17 q^{89} + 4 q^{90} - 8 q^{91} + 33 q^{92} + 18 q^{93} - 14 q^{94} + 12 q^{95} + 22 q^{96} + 32 q^{97} + 20 q^{98} + 6 q^{99}+O(q^{100}) \) 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9 + 4 * q^10 + 6 * q^11 + 22 * q^12 - 18 * q^13 + 5 * q^14 + 18 * q^15 + 30 * q^16 + 18 * q^17 + 4 * q^18 + 12 * q^19 + 22 * q^20 + 8 * q^21 + 7 * q^22 + 32 * q^23 + 9 * q^24 + 18 * q^25 - 4 * q^26 + 18 * q^27 + 10 * q^28 + 7 * q^29 + 4 * q^30 + 18 * q^31 + 22 * q^32 + 6 * q^33 + 15 * q^34 + 8 * q^35 + 22 * q^36 + 3 * q^37 + 32 * q^38 - 18 * q^39 + 9 * q^40 + 4 * q^41 + 5 * q^42 + 14 * q^43 - 5 * q^44 + 18 * q^45 + 10 * q^46 + 23 * q^47 + 30 * q^48 + 28 * q^49 + 4 * q^50 + 18 * q^51 - 22 * q^52 + 35 * q^53 + 4 * q^54 + 6 * q^55 - 7 * q^56 + 12 * q^57 - 6 * q^58 + 28 * q^59 + 22 * q^60 + 19 * q^61 + 4 * q^62 + 8 * q^63 + 43 * q^64 - 18 * q^65 + 7 * q^66 + 34 * q^67 + 55 * q^68 + 32 * q^69 + 5 * q^70 - 8 * q^71 + 9 * q^72 + 22 * q^74 + 18 * q^75 + 2 * q^76 + 21 * q^77 - 4 * q^78 + 4 * q^79 + 30 * q^80 + 18 * q^81 + 29 * q^82 + 11 * q^83 + 10 * q^84 + 18 * q^85 - 22 * q^86 + 7 * q^87 - 31 * q^88 + 17 * q^89 + 4 * q^90 - 8 * q^91 + 33 * q^92 + 18 * q^93 - 14 * q^94 + 12 * q^95 + 22 * q^96 + 32 * q^97 + 20 * q^98 + 6 * 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 $

$2$	0.844677	0.597277	0.298638	−	0.954366i	$-0.403468\pi$
$2$	0.844677	0.597277	0.298638	+	0.954366i	$0.403468\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.28652	−0.643261
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.844677	0.344838
$7$	−2.49791	−0.944122	−0.472061	−	0.881566i	$-0.656490\pi$
$7$	−2.49791	−0.944122	−0.472061	+	0.881566i	$0.656490\pi$
$8$	−2.77605	−0.981481
$9$	1.00000	0.333333
$10$	0.844677	0.267110
$11$	0.589102	0.177621	0.0888105	−	0.996049i	$-0.471693\pi$
$11$	0.589102	0.177621	0.0888105	+	0.996049i	$0.471693\pi$
$12$	−1.28652	−0.371387
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−2.10993	−0.563902
$15$	1.00000	0.258199
$16$	0.228180	0.0570449
$17$	−7.59404	−1.84183	−0.920913	−	0.389769i	$-0.872555\pi$
$17$	−7.59404	−1.84183	−0.920913	+	0.389769i	$0.872555\pi$
$18$	0.844677	0.199092
$19$	0.806944	0.185126	0.0925629	−	0.995707i	$-0.470494\pi$
$19$	0.806944	0.185126	0.0925629	+	0.995707i	$0.470494\pi$
$20$	−1.28652	−0.287675
$21$	−2.49791	−0.545089
$22$	0.497601	0.106089
$23$	6.24354	1.30187	0.650934	−	0.759135i	$-0.274378\pi$
$23$	6.24354	1.30187	0.650934	+	0.759135i	$0.274378\pi$
$24$	−2.77605	−0.566658
$25$	1.00000	0.200000
$26$	−0.844677	−0.165655
$27$	1.00000	0.192450
$28$	3.21362	0.607316
$29$	3.14473	0.583962	0.291981	−	0.956424i	$-0.405686\pi$
$29$	3.14473	0.583962	0.291981	+	0.956424i	$0.405686\pi$
$30$	0.844677	0.154216
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	5.74483	1.01555
$33$	0.589102	0.102550
$34$	−6.41451	−1.10008
$35$	−2.49791	−0.422224
$36$	−1.28652	−0.214420
$37$	−3.66879	−0.603145	−0.301573	−	0.953443i	$-0.597512\pi$
$37$	−3.66879	−0.603145	−0.301573	+	0.953443i	$0.597512\pi$
$38$	0.681607	0.110571
$39$	−1.00000	−0.160128
$40$	−2.77605	−0.438932
$41$	5.40311	0.843824	0.421912	−	0.906637i	$-0.361359\pi$
$41$	5.40311	0.843824	0.421912	+	0.906637i	$0.361359\pi$
$42$	−2.10993	−0.325569
$43$	1.91079	0.291393	0.145697	−	0.989329i	$-0.453458\pi$
$43$	1.91079	0.291393	0.145697	+	0.989329i	$0.453458\pi$
$44$	−0.757893	−0.114257
$45$	1.00000	0.149071
$46$	5.27377	0.777575
$47$	−4.74710	−0.692435	−0.346218	−	0.938154i	$-0.612534\pi$
$47$	−4.74710	−0.692435	−0.346218	+	0.938154i	$0.612534\pi$
$48$	0.228180	0.0329349
$49$	−0.760441	−0.108634
$50$	0.844677	0.119455
$51$	−7.59404	−1.06338
$52$	1.28652	0.178408
$53$	11.3043	1.55277	0.776385	−	0.630259i	$-0.217051\pi$
$53$	11.3043	1.55277	0.776385	+	0.630259i	$0.217051\pi$
$54$	0.844677	0.114946
$55$	0.589102	0.0794345
$56$	6.93432	0.926638
$57$	0.806944	0.106882
$58$	2.65628	0.348787
$59$	−12.9434	−1.68508	−0.842541	−	0.538632i	$-0.818941\pi$
$59$	−12.9434	−1.68508	−0.842541	+	0.538632i	$0.818941\pi$
$60$	−1.28652	−0.166089
$61$	11.5460	1.47832	0.739159	−	0.673531i	$-0.235223\pi$
$61$	11.5460	1.47832	0.739159	+	0.673531i	$0.235223\pi$
$62$	0.844677	0.107274
$63$	−2.49791	−0.314707
$64$	4.39617	0.549521
$65$	−1.00000	−0.124035
$66$	0.497601	0.0612504
$67$	0.320783	0.0391899	0.0195950	−	0.999808i	$-0.493762\pi$
$67$	0.320783	0.0391899	0.0195950	+	0.999808i	$0.493762\pi$
$68$	9.76989	1.18477
$69$	6.24354	0.751634
$70$	−2.10993	−0.252185
$71$	−1.69109	−0.200696	−0.100348	−	0.994952i	$-0.531996\pi$
$71$	−1.69109	−0.200696	−0.100348	+	0.994952i	$0.531996\pi$
$72$	−2.77605	−0.327160
$73$	0.0347964	0.00407261	0.00203631	−	0.999998i	$-0.499352\pi$
$73$	0.0347964	0.00407261	0.00203631	+	0.999998i	$0.499352\pi$
$74$	−3.09894	−0.360244
$75$	1.00000	0.115470
$76$	−1.03815	−0.119084
$77$	−1.47153	−0.167696
$78$	−0.844677	−0.0956408
$79$	14.3989	1.62000	0.810001	−	0.586429i	$-0.199467\pi$
$79$	14.3989	1.62000	0.810001	+	0.586429i	$0.199467\pi$
$80$	0.228180	0.0255113
$81$	1.00000	0.111111
$82$	4.56388	0.503996
$83$	4.49210	0.493072	0.246536	−	0.969134i	$-0.420708\pi$
$83$	4.49210	0.493072	0.246536	+	0.969134i	$0.420708\pi$
$84$	3.21362	0.350634
$85$	−7.59404	−0.823689
$86$	1.61400	0.174042
$87$	3.14473	0.337150
$88$	−1.63538	−0.174332
$89$	5.40483	0.572911	0.286456	−	0.958094i	$-0.407523\pi$
$89$	5.40483	0.572911	0.286456	+	0.958094i	$0.407523\pi$
$90$	0.844677	0.0890367
$91$	2.49791	0.261852
$92$	−8.03244	−0.837440
$93$	1.00000	0.103695
$94$	−4.00976	−0.413575
$95$	0.806944	0.0827907
$96$	5.74483	0.586330
$97$	0.220681	0.0224067	0.0112034	−	0.999937i	$-0.496434\pi$
$97$	0.220681	0.0224067	0.0112034	+	0.999937i	$0.496434\pi$
$98$	−0.642327	−0.0648848
$99$	0.589102	0.0592070
$100$	−1.28652	−0.128652
$101$	−2.32449	−0.231295	−0.115647	−	0.993290i	$-0.536894\pi$
$101$	−2.32449	−0.231295	−0.115647	+	0.993290i	$0.536894\pi$
$102$	−6.41451	−0.635131
$103$	3.57840	0.352590	0.176295	−	0.984337i	$-0.443589\pi$
$103$	3.57840	0.352590	0.176295	+	0.984337i	$0.443589\pi$
$104$	2.77605	0.272214
$105$	−2.49791	−0.243771
$106$	9.54851	0.927433
$107$	15.0943	1.45922	0.729612	−	0.683862i	$-0.239701\pi$
$107$	15.0943	1.45922	0.729612	+	0.683862i	$0.239701\pi$
$108$	−1.28652	−0.123796
$109$	6.31200	0.604580	0.302290	−	0.953216i	$-0.402249\pi$
$109$	6.31200	0.604580	0.302290	+	0.953216i	$0.402249\pi$
$110$	0.497601	0.0474444
$111$	−3.66879	−0.348226
$112$	−0.569972	−0.0538573
$113$	11.5685	1.08827	0.544135	−	0.838997i	$-0.316858\pi$
$113$	11.5685	1.08827	0.544135	+	0.838997i	$0.316858\pi$
$114$	0.681607	0.0638383
$115$	6.24354	0.582213
$116$	−4.04576	−0.375639
$117$	−1.00000	−0.0924500
$118$	−10.9330	−1.00646
$119$	18.9692	1.73891
$120$	−2.77605	−0.253417
$121$	−10.6530	−0.968451
$122$	9.75267	0.882965
$123$	5.40311	0.487182
$124$	−1.28652	−0.115533
$125$	1.00000	0.0894427
$126$	−2.10993	−0.187967
$127$	17.9075	1.58903	0.794516	−	0.607243i	$-0.207725\pi$
$127$	17.9075	1.58903	0.794516	+	0.607243i	$0.207725\pi$
$128$	−7.77633	−0.687337
$129$	1.91079	0.168236
$130$	−0.844677	−0.0740830
$131$	13.1602	1.14981	0.574907	−	0.818219i	$-0.305038\pi$
$131$	13.1602	1.14981	0.574907	+	0.818219i	$0.305038\pi$
$132$	−0.757893	−0.0659661
$133$	−2.01567	−0.174781
$134$	0.270958	0.0234072
$135$	1.00000	0.0860663
$136$	21.0814	1.80772
$137$	12.9745	1.10849	0.554244	−	0.832354i	$-0.313008\pi$
$137$	12.9745	1.10849	0.554244	+	0.832354i	$0.313008\pi$
$138$	5.27377	0.448933
$139$	−11.7800	−0.999170	−0.499585	−	0.866265i	$-0.666514\pi$
$139$	−11.7800	−0.999170	−0.499585	+	0.866265i	$0.666514\pi$
$140$	3.21362	0.271600
$141$	−4.74710	−0.399778
$142$	−1.42843	−0.119871
$143$	−0.589102	−0.0492632
$144$	0.228180	0.0190150
$145$	3.14473	0.261156
$146$	0.0293917	0.00243248
$147$	−0.760441	−0.0627201
$148$	4.71997	0.387979
$149$	−14.6411	−1.19945	−0.599724	−	0.800207i	$-0.704723\pi$
$149$	−14.6411	−1.19945	−0.599724	+	0.800207i	$0.704723\pi$
$150$	0.844677	0.0689676
$151$	−20.4000	−1.66013	−0.830063	−	0.557669i	$-0.811696\pi$
$151$	−20.4000	−1.66013	−0.830063	+	0.557669i	$0.811696\pi$
$152$	−2.24012	−0.181697
$153$	−7.59404	−0.613942
$154$	−1.24296	−0.100161
$155$	1.00000	0.0803219
$156$	1.28652	0.103004
$157$	24.0263	1.91750	0.958752	−	0.284243i	$-0.0917421\pi$
$157$	24.0263	1.91750	0.958752	+	0.284243i	$0.0917421\pi$
$158$	12.1624	0.967589
$159$	11.3043	0.896492
$160$	5.74483	0.454169
$161$	−15.5958	−1.22912
$162$	0.844677	0.0663641
$163$	17.9820	1.40846	0.704229	−	0.709973i	$-0.251293\pi$
$163$	17.9820	1.40846	0.704229	+	0.709973i	$0.251293\pi$
$164$	−6.95121	−0.542799
$165$	0.589102	0.0458616
$166$	3.79437	0.294500
$167$	22.4539	1.73754	0.868768	−	0.495219i	$-0.164912\pi$
$167$	22.4539	1.73754	0.868768	+	0.495219i	$0.164912\pi$
$168$	6.93432	0.534994
$169$	1.00000	0.0769231
$170$	−6.41451	−0.491970
$171$	0.806944	0.0617086
$172$	−2.45827	−0.187442
$173$	−7.86719	−0.598131	−0.299066	−	0.954233i	$-0.596675\pi$
$173$	−7.86719	−0.598131	−0.299066	+	0.954233i	$0.596675\pi$
$174$	2.65628	0.201372
$175$	−2.49791	−0.188824
$176$	0.134421	0.0101324
$177$	−12.9434	−0.972883
$178$	4.56534	0.342186
$179$	7.49597	0.560275	0.280137	−	0.959960i	$-0.409620\pi$
$179$	7.49597	0.560275	0.280137	+	0.959960i	$0.409620\pi$
$180$	−1.28652	−0.0958916
$181$	−11.8855	−0.883440	−0.441720	−	0.897153i	$-0.645631\pi$
$181$	−11.8855	−0.883440	−0.441720	+	0.897153i	$0.645631\pi$
$182$	2.10993	0.156398
$183$	11.5460	0.853508
$184$	−17.3324	−1.27776
$185$	−3.66879	−0.269735
$186$	0.844677	0.0619347
$187$	−4.47367	−0.327147
$188$	6.10724	0.445416
$189$	−2.49791	−0.181696
$190$	0.681607	0.0494490
$191$	−18.3046	−1.32447	−0.662236	−	0.749295i	$-0.730393\pi$
$191$	−18.3046	−1.32447	−0.662236	+	0.749295i	$0.730393\pi$
$192$	4.39617	0.317266
$193$	16.4411	1.18345	0.591727	−	0.806138i	$-0.298446\pi$
$193$	16.4411	1.18345	0.591727	+	0.806138i	$0.298446\pi$
$194$	0.186404	0.0133830
$195$	−1.00000	−0.0716115
$196$	0.978324	0.0698803
$197$	−3.98133	−0.283658	−0.141829	−	0.989891i	$-0.545298\pi$
$197$	−3.98133	−0.283658	−0.141829	+	0.989891i	$0.545298\pi$
$198$	0.497601	0.0353630
$199$	−8.49412	−0.602132	−0.301066	−	0.953603i	$-0.597342\pi$
$199$	−8.49412	−0.602132	−0.301066	+	0.953603i	$0.597342\pi$
$200$	−2.77605	−0.196296
$201$	0.320783	0.0226263
$202$	−1.96344	−0.138147
$203$	−7.85525	−0.551331
$204$	9.76989	0.684029
$205$	5.40311	0.377369
$206$	3.02259	0.210594
$207$	6.24354	0.433956
$208$	−0.228180	−0.0158214
$209$	0.475373	0.0328822
$210$	−2.10993	−0.145599
$211$	−12.2615	−0.844116	−0.422058	−	0.906569i	$-0.638692\pi$
$211$	−12.2615	−0.844116	−0.422058	+	0.906569i	$0.638692\pi$
$212$	−14.5433	−0.998836
$213$	−1.69109	−0.115872
$214$	12.7498	0.871560
$215$	1.91079	0.130315
$216$	−2.77605	−0.188886
$217$	−2.49791	−0.169569
$218$	5.33160	0.361102
$219$	0.0347964	0.00235132
$220$	−0.757893	−0.0510971
$221$	7.59404	0.510830
$222$	−3.09894	−0.207987
$223$	21.3643	1.43066	0.715331	−	0.698785i	$-0.246276\pi$
$223$	21.3643	1.43066	0.715331	+	0.698785i	$0.246276\pi$
$224$	−14.3501	−0.958805
$225$	1.00000	0.0666667
$226$	9.77162	0.649999
$227$	−21.8054	−1.44728	−0.723639	−	0.690178i	$-0.757532\pi$
$227$	−21.8054	−1.44728	−0.723639	+	0.690178i	$0.757532\pi$
$228$	−1.03815	−0.0687532
$229$	8.43808	0.557604	0.278802	−	0.960349i	$-0.410063\pi$
$229$	8.43808	0.557604	0.278802	+	0.960349i	$0.410063\pi$
$230$	5.27377	0.347742
$231$	−1.47153	−0.0968192
$232$	−8.72992	−0.573147
$233$	−20.8801	−1.36790	−0.683952	−	0.729527i	$-0.739740\pi$
$233$	−20.8801	−1.36790	−0.683952	+	0.729527i	$0.739740\pi$
$234$	−0.844677	−0.0552182
$235$	−4.74710	−0.309666
$236$	16.6519	1.08395
$237$	14.3989	0.935309
$238$	16.0229	1.03861
$239$	−26.9739	−1.74480	−0.872398	−	0.488796i	$-0.837436\pi$
$239$	−26.9739	−1.74480	−0.872398	+	0.488796i	$0.837436\pi$
$240$	0.228180	0.0147289
$241$	10.9691	0.706583	0.353292	−	0.935513i	$-0.385062\pi$
$241$	10.9691	0.706583	0.353292	+	0.935513i	$0.385062\pi$
$242$	−8.99831	−0.578433
$243$	1.00000	0.0641500
$244$	−14.8542	−0.950944
$245$	−0.760441	−0.0485828
$246$	4.56388	0.290982
$247$	−0.806944	−0.0513446
$248$	−2.77605	−0.176279
$249$	4.49210	0.284675
$250$	0.844677	0.0534220
$251$	23.2478	1.46739	0.733694	−	0.679480i	$-0.237795\pi$
$251$	23.2478	1.46739	0.733694	+	0.679480i	$0.237795\pi$
$252$	3.21362	0.202439
$253$	3.67808	0.231239
$254$	15.1260	0.949092
$255$	−7.59404	−0.475557
$256$	−15.3608	−0.960051
$257$	−2.24669	−0.140144	−0.0700722	−	0.997542i	$-0.522323\pi$
$257$	−2.24669	−0.140144	−0.0700722	+	0.997542i	$0.522323\pi$
$258$	1.61400	0.100483
$259$	9.16431	0.569442
$260$	1.28652	0.0797867
$261$	3.14473	0.194654
$262$	11.1161	0.686756
$263$	−3.47965	−0.214565	−0.107282	−	0.994229i	$-0.534215\pi$
$263$	−3.47965	−0.214565	−0.107282	+	0.994229i	$0.534215\pi$
$264$	−1.63538	−0.100650
$265$	11.3043	0.694420
$266$	−1.70259	−0.104393
$267$	5.40483	0.330770
$268$	−0.412695	−0.0252093
$269$	−4.61310	−0.281266	−0.140633	−	0.990062i	$-0.544914\pi$
$269$	−4.61310	−0.281266	−0.140633	+	0.990062i	$0.544914\pi$
$270$	0.844677	0.0514054
$271$	−4.96666	−0.301703	−0.150851	−	0.988556i	$-0.548202\pi$
$271$	−4.96666	−0.301703	−0.150851	+	0.988556i	$0.548202\pi$
$272$	−1.73280	−0.105067
$273$	2.49791	0.151180
$274$	10.9593	0.662074
$275$	0.589102	0.0355242
$276$	−8.03244	−0.483496
$277$	21.5468	1.29462	0.647312	−	0.762225i	$-0.275893\pi$
$277$	21.5468	1.29462	0.647312	+	0.762225i	$0.275893\pi$
$278$	−9.95033	−0.596781
$279$	1.00000	0.0598684
$280$	6.93432	0.414405
$281$	−19.9255	−1.18866	−0.594328	−	0.804223i	$-0.702582\pi$
$281$	−19.9255	−1.18866	−0.594328	+	0.804223i	$0.702582\pi$
$282$	−4.00976	−0.238778
$283$	6.81140	0.404896	0.202448	−	0.979293i	$-0.435110\pi$
$283$	6.81140	0.404896	0.202448	+	0.979293i	$0.435110\pi$
$284$	2.17563	0.129100
$285$	0.806944	0.0477993
$286$	−0.497601	−0.0294238
$287$	−13.4965	−0.796672
$288$	5.74483	0.338518
$289$	40.6694	2.39232
$290$	2.65628	0.155982
$291$	0.220681	0.0129365
$292$	−0.0447663	−0.00261975
$293$	16.3516	0.955273	0.477636	−	0.878558i	$-0.341494\pi$
$293$	16.3516	0.955273	0.477636	+	0.878558i	$0.341494\pi$
$294$	−0.642327	−0.0374613
$295$	−12.9434	−0.753592
$296$	10.1847	0.591975
$297$	0.589102	0.0341832
$298$	−12.3670	−0.716403
$299$	−6.24354	−0.361073
$300$	−1.28652	−0.0742773
$301$	−4.77299	−0.275110
$302$	−17.2314	−0.991555
$303$	−2.32449	−0.133538
$304$	0.184128	0.0105605
$305$	11.5460	0.661124
$306$	−6.41451	−0.366693
$307$	−14.2485	−0.813206	−0.406603	−	0.913605i	$-0.633287\pi$
$307$	−14.2485	−0.813206	−0.406603	+	0.913605i	$0.633287\pi$
$308$	1.89315	0.107872
$309$	3.57840	0.203568
$310$	0.844677	0.0479744
$311$	−17.4438	−0.989144	−0.494572	−	0.869137i	$-0.664675\pi$
$311$	−17.4438	−0.989144	−0.494572	+	0.869137i	$0.664675\pi$
$312$	2.77605	0.157163
$313$	20.8058	1.17601	0.588006	−	0.808857i	$-0.299913\pi$
$313$	20.8058	1.17601	0.588006	+	0.808857i	$0.299913\pi$
$314$	20.2944	1.14528
$315$	−2.49791	−0.140741
$316$	−18.5245	−1.04208
$317$	20.1635	1.13249	0.566246	−	0.824236i	$-0.308395\pi$
$317$	20.1635	1.13249	0.566246	+	0.824236i	$0.308395\pi$
$318$	9.54851	0.535454
$319$	1.85257	0.103724
$320$	4.39617	0.245753
$321$	15.0943	0.842483
$322$	−13.1734	−0.734125
$323$	−6.12797	−0.340969
$324$	−1.28652	−0.0714734
$325$	−1.00000	−0.0554700
$326$	15.1890	0.841239
$327$	6.31200	0.349055
$328$	−14.9993	−0.828197
$329$	11.8578	0.653743
$330$	0.497601	0.0273920
$331$	9.75634	0.536257	0.268128	−	0.963383i	$-0.413595\pi$
$331$	9.75634	0.536257	0.268128	+	0.963383i	$0.413595\pi$
$332$	−5.77918	−0.317174
$333$	−3.66879	−0.201048
$334$	18.9663	1.03779
$335$	0.320783	0.0175263
$336$	−0.569972	−0.0310945
$337$	−31.0899	−1.69358	−0.846788	−	0.531931i	$-0.821467\pi$
$337$	−31.0899	−1.69358	−0.846788	+	0.531931i	$0.821467\pi$
$338$	0.844677	0.0459444
$339$	11.5685	0.628313
$340$	9.76989	0.529847
$341$	0.589102	0.0319017
$342$	0.681607	0.0368571
$343$	19.3849	1.04669
$344$	−5.30445	−0.285997
$345$	6.24354	0.336141
$346$	−6.64523	−0.357250
$347$	3.12425	0.167718	0.0838592	−	0.996478i	$-0.473275\pi$
$347$	3.12425	0.167718	0.0838592	+	0.996478i	$0.473275\pi$
$348$	−4.04576	−0.216876
$349$	24.1222	1.29123	0.645615	−	0.763663i	$-0.276601\pi$
$349$	24.1222	1.29123	0.645615	+	0.763663i	$0.276601\pi$
$350$	−2.10993	−0.112780
$351$	−1.00000	−0.0533761
$352$	3.38429	0.180384
$353$	9.37511	0.498987	0.249493	−	0.968376i	$-0.419736\pi$
$353$	9.37511	0.498987	0.249493	+	0.968376i	$0.419736\pi$
$354$	−10.9330	−0.581080
$355$	−1.69109	−0.0897539
$356$	−6.95343	−0.368531
$357$	18.9692	1.00396
$358$	6.33167	0.334639
$359$	12.1226	0.639808	0.319904	−	0.947450i	$-0.396349\pi$
$359$	12.1226	0.639808	0.319904	+	0.947450i	$0.396349\pi$
$360$	−2.77605	−0.146311
$361$	−18.3488	−0.965728
$362$	−10.0394	−0.527658
$363$	−10.6530	−0.559135
$364$	−3.21362	−0.168439
$365$	0.0347964	0.00182133
$366$	9.75267	0.509780
$367$	11.2633	0.587941	0.293970	−	0.955815i	$-0.405023\pi$
$367$	11.2633	0.587941	0.293970	+	0.955815i	$0.405023\pi$
$368$	1.42465	0.0742649
$369$	5.40311	0.281275
$370$	−3.09894	−0.161106
$371$	−28.2372	−1.46600
$372$	−1.28652	−0.0667030
$373$	−16.3330	−0.845692	−0.422846	−	0.906202i	$-0.638969\pi$
$373$	−16.3330	−0.845692	−0.422846	+	0.906202i	$0.638969\pi$
$374$	−3.77880	−0.195397
$375$	1.00000	0.0516398
$376$	13.1782	0.679612
$377$	−3.14473	−0.161962
$378$	−2.10993	−0.108523
$379$	10.5771	0.543307	0.271653	−	0.962395i	$-0.412430\pi$
$379$	10.5771	0.543307	0.271653	+	0.962395i	$0.412430\pi$
$380$	−1.03815	−0.0532560
$381$	17.9075	0.917428
$382$	−15.4615	−0.791077
$383$	33.3685	1.70505	0.852524	−	0.522687i	$-0.175070\pi$
$383$	33.3685	1.70505	0.852524	+	0.522687i	$0.175070\pi$
$384$	−7.77633	−0.396834
$385$	−1.47153	−0.0749959
$386$	13.8874	0.706850
$387$	1.91079	0.0971310
$388$	−0.283911	−0.0144134
$389$	15.1691	0.769103	0.384551	−	0.923104i	$-0.374356\pi$
$389$	15.1691	0.769103	0.384551	+	0.923104i	$0.374356\pi$
$390$	−0.844677	−0.0427719
$391$	−47.4137	−2.39781
$392$	2.11102	0.106623
$393$	13.1602	0.663845
$394$	−3.36294	−0.169422
$395$	14.3989	0.724487
$396$	−0.757893	−0.0380855
$397$	9.23445	0.463464	0.231732	−	0.972780i	$-0.425561\pi$
$397$	9.23445	0.463464	0.231732	+	0.972780i	$0.425561\pi$
$398$	−7.17478	−0.359639
$399$	−2.01567	−0.100910
$400$	0.228180	0.0114090
$401$	−2.17904	−0.108816	−0.0544081	−	0.998519i	$-0.517327\pi$
$401$	−2.17904	−0.108816	−0.0544081	+	0.998519i	$0.517327\pi$
$402$	0.270958	0.0135142
$403$	−1.00000	−0.0498135
$404$	2.99050	0.148783
$405$	1.00000	0.0496904
$406$	−6.63515	−0.329297
$407$	−2.16129	−0.107131
$408$	21.0814	1.04369
$409$	13.8468	0.684682	0.342341	−	0.939576i	$-0.388780\pi$
$409$	13.8468	0.684682	0.342341	+	0.939576i	$0.388780\pi$
$410$	4.56388	0.225394
$411$	12.9745	0.639986
$412$	−4.60369	−0.226807
$413$	32.3314	1.59092
$414$	5.27377	0.259192
$415$	4.49210	0.220509
$416$	−5.74483	−0.281664
$417$	−11.7800	−0.576871
$418$	0.401536	0.0196398
$419$	−34.9983	−1.70978	−0.854891	−	0.518808i	$-0.826376\pi$
$419$	−34.9983	−1.70978	−0.854891	+	0.518808i	$0.826376\pi$
$420$	3.21362	0.156808
$421$	8.14184	0.396809	0.198404	−	0.980120i	$-0.436424\pi$
$421$	8.14184	0.396809	0.198404	+	0.980120i	$0.436424\pi$
$422$	−10.3570	−0.504171
$423$	−4.74710	−0.230812
$424$	−31.3814	−1.52401
$425$	−7.59404	−0.368365
$426$	−1.42843	−0.0692075
$427$	−28.8410	−1.39571
$428$	−19.4192	−0.938661
$429$	−0.589102	−0.0284421
$430$	1.61400	0.0778341
$431$	−2.80823	−0.135268	−0.0676338	−	0.997710i	$-0.521545\pi$
$431$	−2.80823	−0.135268	−0.0676338	+	0.997710i	$0.521545\pi$
$432$	0.228180	0.0109783
$433$	11.6053	0.557714	0.278857	−	0.960333i	$-0.410045\pi$
$433$	11.6053	0.557714	0.278857	+	0.960333i	$0.410045\pi$
$434$	−2.10993	−0.101280
$435$	3.14473	0.150778
$436$	−8.12053	−0.388903
$437$	5.03819	0.241009
$438$	0.0293917	0.00140439
$439$	5.19988	0.248177	0.124088	−	0.992271i	$-0.460399\pi$
$439$	5.19988	0.248177	0.124088	+	0.992271i	$0.460399\pi$
$440$	−1.63538	−0.0779635
$441$	−0.760441	−0.0362115
$442$	6.41451	0.305107
$443$	−36.0824	−1.71433	−0.857164	−	0.515043i	$-0.827776\pi$
$443$	−36.0824	−1.71433	−0.857164	+	0.515043i	$0.827776\pi$
$444$	4.71997	0.224000
$445$	5.40483	0.256214
$446$	18.0460	0.854501
$447$	−14.6411	−0.692502
$448$	−10.9812	−0.518815
$449$	−7.73416	−0.364998	−0.182499	−	0.983206i	$-0.558419\pi$
$449$	−7.73416	−0.364998	−0.182499	+	0.983206i	$0.558419\pi$
$450$	0.844677	0.0398184
$451$	3.18298	0.149881
$452$	−14.8831	−0.700042
$453$	−20.4000	−0.958475
$454$	−18.4186	−0.864426
$455$	2.49791	0.117104
$456$	−2.24012	−0.104903
$457$	−35.4882	−1.66007	−0.830034	−	0.557713i	$-0.811679\pi$
$457$	−35.4882	−1.66007	−0.830034	+	0.557713i	$0.811679\pi$
$458$	7.12745	0.333044
$459$	−7.59404	−0.354459
$460$	−8.03244	−0.374515
$461$	−34.4361	−1.60385	−0.801924	−	0.597426i	$-0.796190\pi$
$461$	−34.4361	−1.60385	−0.801924	+	0.597426i	$0.796190\pi$
$462$	−1.24296	−0.0578279
$463$	2.65489	0.123383	0.0616917	−	0.998095i	$-0.480350\pi$
$463$	2.65489	0.123383	0.0616917	+	0.998095i	$0.480350\pi$
$464$	0.717563	0.0333120
$465$	1.00000	0.0463739
$466$	−17.6370	−0.817017
$467$	30.6268	1.41724	0.708621	−	0.705590i	$-0.249318\pi$
$467$	30.6268	1.41724	0.708621	+	0.705590i	$0.249318\pi$
$468$	1.28652	0.0594695
$469$	−0.801288	−0.0370001
$470$	−4.00976	−0.184956
$471$	24.0263	1.10707
$472$	35.9314	1.65388
$473$	1.12565	0.0517575
$474$	12.1624	0.558638
$475$	0.806944	0.0370251
$476$	−24.4043	−1.11857
$477$	11.3043	0.517590
$478$	−22.7842	−1.04213
$479$	36.6753	1.67574	0.837870	−	0.545871i	$-0.183801\pi$
$479$	36.6753	1.67574	0.837870	+	0.545871i	$0.183801\pi$
$480$	5.74483	0.262215
$481$	3.66879	0.167282
$482$	9.26536	0.422026
$483$	−15.5958	−0.709633
$484$	13.7053	0.622966
$485$	0.220681	0.0100206
$486$	0.844677	0.0383153
$487$	−29.2597	−1.32588	−0.662942	−	0.748671i	$-0.730692\pi$
$487$	−29.2597	−1.32588	−0.662942	+	0.748671i	$0.730692\pi$
$488$	−32.0524	−1.45094
$489$	17.9820	0.813173
$490$	−0.642327	−0.0290174
$491$	0.0869136	0.00392235	0.00196118	−	0.999998i	$-0.499376\pi$
$491$	0.0869136	0.00392235	0.00196118	+	0.999998i	$0.499376\pi$
$492$	−6.95121	−0.313385
$493$	−23.8812	−1.07556
$494$	−0.681607	−0.0306669
$495$	0.589102	0.0264782
$496$	0.228180	0.0102456
$497$	4.22420	0.189481
$498$	3.79437	0.170030
$499$	−41.6437	−1.86423	−0.932114	−	0.362165i	$-0.882038\pi$
$499$	−41.6437	−1.86423	−0.932114	+	0.362165i	$0.882038\pi$
$500$	−1.28652	−0.0575350
$501$	22.4539	1.00317
$502$	19.6369	0.876436
$503$	11.6881	0.521145	0.260573	−	0.965454i	$-0.416089\pi$
$503$	11.6881	0.521145	0.260573	+	0.965454i	$0.416089\pi$
$504$	6.93432	0.308879
$505$	−2.32449	−0.103438
$506$	3.10679	0.138114
$507$	1.00000	0.0444116
$508$	−23.0384	−1.02216
$509$	−9.34402	−0.414166	−0.207083	−	0.978323i	$-0.566397\pi$
$509$	−9.34402	−0.414166	−0.207083	+	0.978323i	$0.566397\pi$
$510$	−6.41451	−0.284039
$511$	−0.0869184	−0.00384504
$512$	2.57773	0.113921
$513$	0.806944	0.0356275
$514$	−1.89772	−0.0837050
$515$	3.57840	0.157683
$516$	−2.45827	−0.108220
$517$	−2.79653	−0.122991
$518$	7.74087	0.340115
$519$	−7.86719	−0.345331
$520$	2.77605	0.121738
$521$	34.1043	1.49414	0.747068	−	0.664747i	$-0.231461\pi$
$521$	34.1043	1.49414	0.747068	+	0.664747i	$0.231461\pi$
$522$	2.65628	0.116262
$523$	11.8634	0.518752	0.259376	−	0.965776i	$-0.416483\pi$
$523$	11.8634	0.518752	0.259376	+	0.965776i	$0.416483\pi$
$524$	−16.9309	−0.739630
$525$	−2.49791	−0.109018
$526$	−2.93918	−0.128154
$527$	−7.59404	−0.330802
$528$	0.134421	0.00584993
$529$	15.9818	0.694859
$530$	9.54851	0.414761
$531$	−12.9434	−0.561694
$532$	2.59321	0.112430
$533$	−5.40311	−0.234035
$534$	4.56534	0.197561
$535$	15.0943	0.652584
$536$	−0.890510	−0.0384642
$537$	7.49597	0.323475
$538$	−3.89658	−0.167993
$539$	−0.447978	−0.0192958
$540$	−1.28652	−0.0553631
$541$	14.3143	0.615422	0.307711	−	0.951480i	$-0.400437\pi$
$541$	14.3143	0.615422	0.307711	+	0.951480i	$0.400437\pi$
$542$	−4.19522	−0.180200
$543$	−11.8855	−0.510054
$544$	−43.6265	−1.87047
$545$	6.31200	0.270377
$546$	2.10993	0.0902965
$547$	−35.6551	−1.52450	−0.762250	−	0.647282i	$-0.775905\pi$
$547$	−35.6551	−1.52450	−0.762250	+	0.647282i	$0.775905\pi$
$548$	−16.6920	−0.713046
$549$	11.5460	0.492773
$550$	0.497601	0.0212178
$551$	2.53762	0.108106
$552$	−17.3324	−0.737714
$553$	−35.9672	−1.52948
$554$	18.2001	0.773249
$555$	−3.66879	−0.155731
$556$	15.1553	0.642727
$557$	−43.4347	−1.84039	−0.920193	−	0.391466i	$-0.871968\pi$
$557$	−43.4347	−1.84039	−0.920193	+	0.391466i	$0.871968\pi$
$558$	0.844677	0.0357580
$559$	−1.91079	−0.0808179
$560$	−0.569972	−0.0240857
$561$	−4.47367	−0.188878
$562$	−16.8306	−0.709956
$563$	37.7737	1.59197	0.795986	−	0.605315i	$-0.206953\pi$
$563$	37.7737	1.59197	0.795986	+	0.605315i	$0.206953\pi$
$564$	6.10724	0.257161
$565$	11.5685	0.486689
$566$	5.75343	0.241835
$567$	−2.49791	−0.104902
$568$	4.69456	0.196979
$569$	11.6238	0.487294	0.243647	−	0.969864i	$-0.421656\pi$
$569$	11.6238	0.487294	0.243647	+	0.969864i	$0.421656\pi$
$570$	0.681607	0.0285494
$571$	−22.5729	−0.944646	−0.472323	−	0.881426i	$-0.656584\pi$
$571$	−22.5729	−0.944646	−0.472323	+	0.881426i	$0.656584\pi$
$572$	0.757893	0.0316891
$573$	−18.3046	−0.764685
$574$	−11.4002	−0.475834
$575$	6.24354	0.260373
$576$	4.39617	0.183174
$577$	−25.1557	−1.04724	−0.523622	−	0.851951i	$-0.675419\pi$
$577$	−25.1557	−1.04724	−0.523622	+	0.851951i	$0.675419\pi$
$578$	34.3525	1.42888
$579$	16.4411	0.683268
$580$	−4.04576	−0.167991
$581$	−11.2209	−0.465520
$582$	0.186404	0.00772669
$583$	6.65941	0.275805
$584$	−0.0965965	−0.00399719
$585$	−1.00000	−0.0413449
$586$	13.8118	0.570562
$587$	19.5579	0.807239	0.403620	−	0.914927i	$-0.367752\pi$
$587$	19.5579	0.807239	0.403620	+	0.914927i	$0.367752\pi$
$588$	0.978324	0.0403454
$589$	0.806944	0.0332496
$590$	−10.9330	−0.450103
$591$	−3.98133	−0.163770
$592$	−0.837143	−0.0344063
$593$	−5.05825	−0.207717	−0.103859	−	0.994592i	$-0.533119\pi$
$593$	−5.05825	−0.207717	−0.103859	+	0.994592i	$0.533119\pi$
$594$	0.497601	0.0204168
$595$	18.9692	0.777663
$596$	18.8361	0.771558
$597$	−8.49412	−0.347641
$598$	−5.27377	−0.215660
$599$	10.4596	0.427370	0.213685	−	0.976903i	$-0.431453\pi$
$599$	10.4596	0.427370	0.213685	+	0.976903i	$0.431453\pi$
$600$	−2.77605	−0.113332
$601$	−37.9179	−1.54670	−0.773352	−	0.633976i	$-0.781422\pi$
$601$	−37.9179	−1.54670	−0.773352	+	0.633976i	$0.781422\pi$
$602$	−4.03163	−0.164317
$603$	0.320783	0.0130633
$604$	26.2450	1.06789
$605$	−10.6530	−0.433104
$606$	−1.96344	−0.0797593
$607$	−18.8576	−0.765406	−0.382703	−	0.923871i	$-0.625007\pi$
$607$	−18.8576	−0.765406	−0.382703	+	0.923871i	$0.625007\pi$
$608$	4.63576	0.188005
$609$	−7.85525	−0.318311
$610$	9.75267	0.394874
$611$	4.74710	0.192047
$612$	9.76989	0.394925
$613$	−12.2225	−0.493663	−0.246831	−	0.969058i	$-0.579389\pi$
$613$	−12.2225	−0.493663	−0.246831	+	0.969058i	$0.579389\pi$
$614$	−12.0354	−0.485709
$615$	5.40311	0.217874
$616$	4.08502	0.164590
$617$	10.6298	0.427939	0.213970	−	0.976840i	$-0.431361\pi$
$617$	10.6298	0.427939	0.213970	+	0.976840i	$0.431361\pi$
$618$	3.02259	0.121586
$619$	35.1439	1.41255	0.706276	−	0.707937i	$-0.250374\pi$
$619$	35.1439	1.41255	0.706276	+	0.707937i	$0.250374\pi$
$620$	−1.28652	−0.0516679
$621$	6.24354	0.250545
$622$	−14.7343	−0.590793
$623$	−13.5008	−0.540898
$624$	−0.228180	−0.00913449
$625$	1.00000	0.0400000
$626$	17.5741	0.702404
$627$	0.475373	0.0189846
$628$	−30.9103	−1.23346
$629$	27.8609	1.11089
$630$	−2.10993	−0.0840615
$631$	0.377752	0.0150381	0.00751903	−	0.999972i	$-0.497607\pi$
$631$	0.377752	0.0150381	0.00751903	+	0.999972i	$0.497607\pi$
$632$	−39.9720	−1.59000
$633$	−12.2615	−0.487351
$634$	17.0316	0.676411
$635$	17.9075	0.710637
$636$	−14.5433	−0.576678
$637$	0.760441	0.0301298
$638$	1.56482	0.0619518
$639$	−1.69109	−0.0668986
$640$	−7.77633	−0.307386
$641$	−24.5156	−0.968307	−0.484154	−	0.874983i	$-0.660872\pi$
$641$	−24.5156	−0.968307	−0.484154	+	0.874983i	$0.660872\pi$
$642$	12.7498	0.503195
$643$	27.9042	1.10044	0.550218	−	0.835021i	$-0.314545\pi$
$643$	27.9042	1.10044	0.550218	+	0.835021i	$0.314545\pi$
$644$	20.0643	0.790645
$645$	1.91079	0.0752374
$646$	−5.17615	−0.203653
$647$	44.4132	1.74606	0.873032	−	0.487662i	$-0.162150\pi$
$647$	44.4132	1.74606	0.873032	+	0.487662i	$0.162150\pi$
$648$	−2.77605	−0.109053
$649$	−7.62497	−0.299306
$650$	−0.844677	−0.0331309
$651$	−2.49791	−0.0979008
$652$	−23.1342	−0.906005
$653$	−7.30619	−0.285913	−0.142957	−	0.989729i	$-0.545661\pi$
$653$	−7.30619	−0.285913	−0.142957	+	0.989729i	$0.545661\pi$
$654$	5.33160	0.208482
$655$	13.1602	0.514212
$656$	1.23288	0.0481358
$657$	0.0347964	0.00135754
$658$	10.0160	0.390465
$659$	8.76305	0.341360	0.170680	−	0.985327i	$-0.445404\pi$
$659$	8.76305	0.341360	0.170680	+	0.985327i	$0.445404\pi$
$660$	−0.757893	−0.0295009
$661$	−22.7867	−0.886299	−0.443150	−	0.896448i	$-0.646139\pi$
$661$	−22.7867	−0.886299	−0.443150	+	0.896448i	$0.646139\pi$
$662$	8.24095	0.320294
$663$	7.59404	0.294928
$664$	−12.4703	−0.483941
$665$	−2.01567	−0.0781645
$666$	−3.09894	−0.120081
$667$	19.6342	0.760241
$668$	−28.8874	−1.11769
$669$	21.3643	0.825993
$670$	0.270958	0.0104680
$671$	6.80180	0.262580
$672$	−14.3501	−0.553566
$673$	33.9589	1.30902	0.654509	−	0.756054i	$-0.272875\pi$
$673$	33.9589	1.30902	0.654509	+	0.756054i	$0.272875\pi$
$674$	−26.2609	−1.01153
$675$	1.00000	0.0384900
$676$	−1.28652	−0.0494816
$677$	34.1153	1.31116	0.655579	−	0.755127i	$-0.272425\pi$
$677$	34.1153	1.31116	0.655579	+	0.755127i	$0.272425\pi$
$678$	9.77162	0.375277
$679$	−0.551241	−0.0211547
$680$	21.0814	0.808436
$681$	−21.8054	−0.835587
$682$	0.497601	0.0190541
$683$	−19.7603	−0.756108	−0.378054	−	0.925784i	$-0.623407\pi$
$683$	−19.7603	−0.756108	−0.378054	+	0.925784i	$0.623407\pi$
$684$	−1.03815	−0.0396947
$685$	12.9745	0.495731
$686$	16.3740	0.625161
$687$	8.43808	0.321933
$688$	0.436004	0.0166225
$689$	−11.3043	−0.430661
$690$	5.27377	0.200769
$691$	6.11177	0.232503	0.116251	−	0.993220i	$-0.462912\pi$
$691$	6.11177	0.232503	0.116251	+	0.993220i	$0.462912\pi$
$692$	10.1213	0.384754
$693$	−1.47153	−0.0558986
$694$	2.63898	0.100174
$695$	−11.7800	−0.446842
$696$	−8.72992	−0.330907
$697$	−41.0314	−1.55418
$698$	20.3754	0.771222
$699$	−20.8801	−0.789759
$700$	3.21362	0.121463
$701$	30.2224	1.14148	0.570742	−	0.821129i	$-0.306656\pi$
$701$	30.2224	1.14148	0.570742	+	0.821129i	$0.306656\pi$
$702$	−0.844677	−0.0318803
$703$	−2.96051	−0.111658
$704$	2.58979	0.0976065
$705$	−4.74710	−0.178786
$706$	7.91894	0.298033
$707$	5.80636	0.218371
$708$	16.6519	0.625817
$709$	−51.0459	−1.91707	−0.958534	−	0.284979i	$-0.908013\pi$
$709$	−51.0459	−1.91707	−0.958534	+	0.284979i	$0.908013\pi$
$710$	−1.42843	−0.0536079
$711$	14.3989	0.540001
$712$	−15.0041	−0.562302
$713$	6.24354	0.233822
$714$	16.0229	0.599641
$715$	−0.589102	−0.0220312
$716$	−9.64372	−0.360403
$717$	−26.9739	−1.00736
$718$	10.2397	0.382142
$719$	−40.0801	−1.49474	−0.747368	−	0.664410i	$-0.768683\pi$
$719$	−40.0801	−1.49474	−0.747368	+	0.664410i	$0.768683\pi$
$720$	0.228180	0.00850375
$721$	−8.93852	−0.332888
$722$	−15.4988	−0.576807
$723$	10.9691	0.407946
$724$	15.2909	0.568282
$725$	3.14473	0.116792
$726$	−8.99831	−0.333958
$727$	34.2514	1.27031	0.635157	−	0.772383i	$-0.280936\pi$
$727$	34.2514	1.27031	0.635157	+	0.772383i	$0.280936\pi$
$728$	−6.93432	−0.257003
$729$	1.00000	0.0370370
$730$	0.0293917	0.00108784
$731$	−14.5106	−0.536695
$732$	−14.8542	−0.549028
$733$	−8.59363	−0.317413	−0.158706	−	0.987326i	$-0.550732\pi$
$733$	−8.59363	−0.317413	−0.158706	+	0.987326i	$0.550732\pi$
$734$	9.51386	0.351163
$735$	−0.760441	−0.0280493
$736$	35.8681	1.32212
$737$	0.188974	0.00696095
$738$	4.56388	0.167999
$739$	−2.13153	−0.0784096	−0.0392048	−	0.999231i	$-0.512482\pi$
$739$	−2.13153	−0.0784096	−0.0392048	+	0.999231i	$0.512482\pi$
$740$	4.71997	0.173510
$741$	−0.806944	−0.0296438
$742$	−23.8513	−0.875610
$743$	−13.4994	−0.495245	−0.247622	−	0.968857i	$-0.579649\pi$
$743$	−13.4994	−0.495245	−0.247622	+	0.968857i	$0.579649\pi$
$744$	−2.77605	−0.101775
$745$	−14.6411	−0.536410
$746$	−13.7961	−0.505112
$747$	4.49210	0.164357
$748$	5.75547	0.210441
$749$	−37.7043	−1.37768
$750$	0.844677	0.0308432
$751$	29.3938	1.07260	0.536298	−	0.844029i	$-0.319822\pi$
$751$	29.3938	1.07260	0.536298	+	0.844029i	$0.319822\pi$
$752$	−1.08319	−0.0394999
$753$	23.2478	0.847197
$754$	−2.65628	−0.0967360
$755$	−20.4000	−0.742431
$756$	3.21362	0.116878
$757$	−44.5916	−1.62071	−0.810355	−	0.585939i	$-0.800726\pi$
$757$	−44.5916	−1.62071	−0.810355	+	0.585939i	$0.800726\pi$
$758$	8.93419	0.324504
$759$	3.67808	0.133506
$760$	−2.24012	−0.0812575
$761$	37.7300	1.36771	0.683856	−	0.729617i	$-0.260302\pi$
$761$	37.7300	1.36771	0.683856	+	0.729617i	$0.260302\pi$
$762$	15.1260	0.547958
$763$	−15.7668	−0.570797
$764$	23.5492	0.851981
$765$	−7.59404	−0.274563
$766$	28.1856	1.01839
$767$	12.9434	0.467358
$768$	−15.3608	−0.554286
$769$	18.8848	0.681004	0.340502	−	0.940244i	$-0.389403\pi$
$769$	18.8848	0.681004	0.340502	+	0.940244i	$0.389403\pi$
$770$	−1.24296	−0.0447933
$771$	−2.24669	−0.0809124
$772$	−21.1518	−0.761270
$773$	−6.28987	−0.226231	−0.113116	−	0.993582i	$-0.536083\pi$
$773$	−6.28987	−0.226231	−0.113116	+	0.993582i	$0.536083\pi$
$774$	1.61400	0.0580141
$775$	1.00000	0.0359211
$776$	−0.612621	−0.0219918
$777$	9.16431	0.328768
$778$	12.8130	0.459367
$779$	4.36001	0.156213
$780$	1.28652	0.0460649
$781$	−0.996227	−0.0356478
$782$	−40.0492	−1.43216
$783$	3.14473	0.112383
$784$	−0.173517	−0.00619704
$785$	24.0263	0.857534
$786$	11.1161	0.396499
$787$	−2.64796	−0.0943895	−0.0471948	−	0.998886i	$-0.515028\pi$
$787$	−2.64796	−0.0943895	−0.0471948	+	0.998886i	$0.515028\pi$
$788$	5.12207	0.182466
$789$	−3.47965	−0.123879
$790$	12.1624	0.432719
$791$	−28.8970	−1.02746
$792$	−1.63538	−0.0581106
$793$	−11.5460	−0.410012
$794$	7.80012	0.276816
$795$	11.3043	0.400924
$796$	10.9279	0.387328
$797$	31.4978	1.11571	0.557855	−	0.829938i	$-0.311624\pi$
$797$	31.4978	1.11571	0.557855	+	0.829938i	$0.311624\pi$
$798$	−1.70259	−0.0602712
$799$	36.0496	1.27534
$800$	5.74483	0.203111
$801$	5.40483	0.190970
$802$	−1.84059	−0.0649934
$803$	0.0204987	0.000723382 0
$804$	−0.412695	−0.0145546
$805$	−15.5958	−0.549680
$806$	−0.844677	−0.0297525
$807$	−4.61310	−0.162389
$808$	6.45288	0.227012
$809$	28.6176	1.00614	0.503071	−	0.864245i	$-0.332204\pi$
$809$	28.6176	1.00614	0.503071	+	0.864245i	$0.332204\pi$
$810$	0.844677	0.0296789
$811$	14.8123	0.520130	0.260065	−	0.965591i	$-0.416256\pi$
$811$	14.8123	0.520130	0.260065	+	0.965591i	$0.416256\pi$
$812$	10.1060	0.354649
$813$	−4.96666	−0.174188
$814$	−1.82559	−0.0639870
$815$	17.9820	0.629881
$816$	−1.73280	−0.0606603
$817$	1.54190	0.0539444
$818$	11.6961	0.408945
$819$	2.49791	0.0872841
$820$	−6.95121	−0.242747
$821$	2.44692	0.0853982	0.0426991	−	0.999088i	$-0.486404\pi$
$821$	2.44692	0.0853982	0.0426991	+	0.999088i	$0.486404\pi$
$822$	10.9593	0.382248
$823$	−50.8509	−1.77255	−0.886276	−	0.463157i	$-0.846717\pi$
$823$	−50.8509	−1.77255	−0.886276	+	0.463157i	$0.846717\pi$
$824$	−9.93381	−0.346061
$825$	0.589102	0.0205099
$826$	27.3096	0.950221
$827$	−48.5594	−1.68858	−0.844288	−	0.535889i	$-0.819976\pi$
$827$	−48.5594	−1.68858	−0.844288	+	0.535889i	$0.819976\pi$
$828$	−8.03244	−0.279147
$829$	−41.6528	−1.44666	−0.723331	−	0.690502i	$-0.757390\pi$
$829$	−41.6528	−1.44666	−0.723331	+	0.690502i	$0.757390\pi$
$830$	3.79437	0.131705
$831$	21.5468	0.747452
$832$	−4.39617	−0.152410
$833$	5.77482	0.200086
$834$	−9.95033	−0.344552
$835$	22.4539	0.777050
$836$	−0.611577	−0.0211518
$837$	1.00000	0.0345651
$838$	−29.5623	−1.02121
$839$	−32.4901	−1.12168	−0.560841	−	0.827924i	$-0.689522\pi$
$839$	−32.4901	−1.12168	−0.560841	+	0.827924i	$0.689522\pi$
$840$	6.93432	0.239257
$841$	−19.1107	−0.658989
$842$	6.87722	0.237005
$843$	−19.9255	−0.686271
$844$	15.7747	0.542987
$845$	1.00000	0.0344010
$846$	−4.00976	−0.137858
$847$	26.6101	0.914335
$848$	2.57942	0.0885776
$849$	6.81140	0.233767
$850$	−6.41451	−0.220016
$851$	−22.9062	−0.785215
$852$	2.17563	0.0745358
$853$	−33.4997	−1.14701	−0.573504	−	0.819203i	$-0.694416\pi$
$853$	−33.4997	−1.14701	−0.573504	+	0.819203i	$0.694416\pi$
$854$	−24.3613	−0.833626
$855$	0.806944	0.0275969
$856$	−41.9026	−1.43220
$857$	−11.9483	−0.408146	−0.204073	−	0.978956i	$-0.565418\pi$
$857$	−11.9483	−0.408146	−0.204073	+	0.978956i	$0.565418\pi$
$858$	−0.497601	−0.0169878
$859$	36.6337	1.24993	0.624963	−	0.780654i	$-0.285114\pi$
$859$	36.6337	1.24993	0.624963	+	0.780654i	$0.285114\pi$
$860$	−2.45827	−0.0838265
$861$	−13.4965	−0.459959
$862$	−2.37204	−0.0807922
$863$	39.2602	1.33643	0.668216	−	0.743967i	$-0.267058\pi$
$863$	39.2602	1.33643	0.668216	+	0.743967i	$0.267058\pi$
$864$	5.74483	0.195443
$865$	−7.86719	−0.267492
$866$	9.80270	0.333109
$867$	40.6694	1.38121
$868$	3.21362	0.109077
$869$	8.48242	0.287746
$870$	2.65628	0.0900563
$871$	−0.320783	−0.0108693
$872$	−17.5224	−0.593384
$873$	0.220681	0.00746891
$874$	4.25564	0.143949
$875$	−2.49791	−0.0844448
$876$	−0.0447663	−0.00151251
$877$	0.0812476	0.00274354	0.00137177	−	0.999999i	$-0.499563\pi$
$877$	0.0812476	0.00274354	0.00137177	+	0.999999i	$0.499563\pi$
$878$	4.39222	0.148230
$879$	16.3516	0.551527
$880$	0.134421	0.00453133
$881$	39.9317	1.34533	0.672667	−	0.739946i	$-0.265149\pi$
$881$	39.9317	1.34533	0.672667	+	0.739946i	$0.265149\pi$
$882$	−0.642327	−0.0216283
$883$	27.9950	0.942105	0.471053	−	0.882105i	$-0.343874\pi$
$883$	27.9950	0.942105	0.471053	+	0.882105i	$0.343874\pi$
$884$	−9.76989	−0.328597
$885$	−12.9434	−0.435087
$886$	−30.4780	−1.02393
$887$	−4.70885	−0.158108	−0.0790539	−	0.996870i	$-0.525190\pi$
$887$	−4.70885	−0.158108	−0.0790539	+	0.996870i	$0.525190\pi$
$888$	10.1847	0.341777
$889$	−44.7313	−1.50024
$890$	4.56534	0.153030
$891$	0.589102	0.0197357
$892$	−27.4857	−0.920289
$893$	−3.83064	−0.128188
$894$	−12.3670	−0.413615
$895$	7.49597	0.250562
$896$	19.4246	0.648929
$897$	−6.24354	−0.208466
$898$	−6.53286	−0.218005
$899$	3.14473	0.104883
$900$	−1.28652	−0.0428840
$901$	−85.8456	−2.85993
$902$	2.68859	0.0895203
$903$	−4.77299	−0.158835
$904$	−32.1146	−1.06812
$905$	−11.8855	−0.395086
$906$	−17.2314	−0.572475
$907$	−19.5012	−0.647527	−0.323763	−	0.946138i	$-0.604948\pi$
$907$	−19.5012	−0.647527	−0.323763	+	0.946138i	$0.604948\pi$
$908$	28.0532	0.930977
$909$	−2.32449	−0.0770983
$910$	2.10993	0.0699434
$911$	4.37347	0.144900	0.0724498	−	0.997372i	$-0.476918\pi$
$911$	4.37347	0.144900	0.0724498	+	0.997372i	$0.476918\pi$
$912$	0.184128	0.00609709
$913$	2.64631	0.0875800
$914$	−29.9761	−0.991520
$915$	11.5460	0.381700
$916$	−10.8558	−0.358685
$917$	−32.8730	−1.08556
$918$	−6.41451	−0.211710
$919$	34.9717	1.15361	0.576805	−	0.816882i	$-0.304299\pi$
$919$	34.9717	1.15361	0.576805	+	0.816882i	$0.304299\pi$
$920$	−17.3324	−0.571431
$921$	−14.2485	−0.469505
$922$	−29.0873	−0.957941
$923$	1.69109	0.0556630
$924$	1.89315	0.0622800
$925$	−3.66879	−0.120629
$926$	2.24253	0.0736940
$927$	3.57840	0.117530
$928$	18.0659	0.593044
$929$	−21.3751	−0.701295	−0.350647	−	0.936508i	$-0.614038\pi$
$929$	−21.3751	−0.701295	−0.350647	+	0.936508i	$0.614038\pi$
$930$	0.844677	0.0276980
$931$	−0.613634	−0.0201110
$932$	26.8627	0.879918
$933$	−17.4438	−0.571083
$934$	25.8698	0.846485
$935$	−4.47367	−0.146305
$936$	2.77605	0.0907380
$937$	−58.0910	−1.89775	−0.948875	−	0.315653i	$-0.897776\pi$
$937$	−58.0910	−1.89775	−0.948875	+	0.315653i	$0.897776\pi$
$938$	−0.676829	−0.0220993
$939$	20.8058	0.678970
$940$	6.10724	0.199196
$941$	32.6648	1.06484	0.532420	−	0.846480i	$-0.321283\pi$
$941$	32.6648	1.06484	0.532420	+	0.846480i	$0.321283\pi$
$942$	20.2944	0.661228
$943$	33.7345	1.09855
$944$	−2.95341	−0.0961254
$945$	−2.49791	−0.0812570
$946$	0.950812	0.0309136
$947$	44.0437	1.43123	0.715614	−	0.698496i	$-0.246147\pi$
$947$	44.0437	1.43123	0.715614	+	0.698496i	$0.246147\pi$
$948$	−18.5245	−0.601647
$949$	−0.0347964	−0.00112954
$950$	0.681607	0.0221143
$951$	20.1635	0.653845
$952$	−52.6595	−1.70670
$953$	−30.8185	−0.998309	−0.499154	−	0.866513i	$-0.666356\pi$
$953$	−30.8185	−0.998309	−0.499154	+	0.866513i	$0.666356\pi$
$954$	9.54851	0.309144
$955$	−18.3046	−0.592322
$956$	34.7025	1.12236
$957$	1.85257	0.0598850
$958$	30.9788	1.00088
$959$	−32.4092	−1.04655
$960$	4.39617	0.141886
$961$	1.00000	0.0322581
$962$	3.09894	0.0999138
$963$	15.0943	0.486408
$964$	−14.1120	−0.454517
$965$	16.4411	0.529257
$966$	−13.1734	−0.423847
$967$	−28.0327	−0.901472	−0.450736	−	0.892657i	$-0.648838\pi$
$967$	−28.0327	−0.901472	−0.450736	+	0.892657i	$0.648838\pi$
$968$	29.5731	0.950516
$969$	−6.12797	−0.196859
$970$	0.186404	0.00598507
$971$	4.17538	0.133994	0.0669971	−	0.997753i	$-0.478658\pi$
$971$	4.17538	0.133994	0.0669971	+	0.997753i	$0.478658\pi$
$972$	−1.28652	−0.0412652
$973$	29.4255	0.943338
$974$	−24.7150	−0.791919
$975$	−1.00000	−0.0320256
$976$	2.63457	0.0843305
$977$	−10.0338	−0.321011	−0.160506	−	0.987035i	$-0.551312\pi$
$977$	−10.0338	−0.321011	−0.160506	+	0.987035i	$0.551312\pi$
$978$	15.1890	0.485689
$979$	3.18400	0.101761
$980$	0.978324	0.0312514
$981$	6.31200	0.201527
$982$	0.0734139	0.00234273
$983$	29.1177	0.928711	0.464355	−	0.885649i	$-0.346286\pi$
$983$	29.1177	0.928711	0.464355	+	0.885649i	$0.346286\pi$
$984$	−14.9993	−0.478160
$985$	−3.98133	−0.126856
$986$	−20.1719	−0.642404
$987$	11.8578	0.377439
$988$	1.03815	0.0330280
$989$	11.9301	0.379355
$990$	0.497601	0.0158148
$991$	56.8604	1.80623	0.903116	−	0.429397i	$-0.141274\pi$
$991$	56.8604	1.80623	0.903116	+	0.429397i	$0.141274\pi$
$992$	5.74483	0.182399
$993$	9.75634	0.309608
$994$	3.56808	0.113173
$995$	−8.49412	−0.269282
$996$	−5.77918	−0.183120
$997$	−2.22287	−0.0703990	−0.0351995	−	0.999380i	$-0.511207\pi$
$997$	−2.22287	−0.0703990	−0.0351995	+	0.999380i	$0.511207\pi$
$998$	−35.1755	−1.11346
$999$	−3.66879	−0.116075

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.bi.1.10	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.bi.1.10	✓	18	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:	\( N \)	\(=\)	\( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6045.a (trivial)

\(f(q)\)	\(=\)	\(q+0.844677 q^{2} +1.00000 q^{3} -1.28652 q^{4} +1.00000 q^{5} +0.844677 q^{6} -2.49791 q^{7} -2.77605 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.844677 q^{2} +1.00000 q^{3} -1.28652 q^{4} +1.00000 q^{5} +0.844677 q^{6} -2.49791 q^{7} -2.77605 q^{8} +1.00000 q^{9} +0.844677 q^{10} +0.589102 q^{11} -1.28652 q^{12} -1.00000 q^{13} -2.10993 q^{14} +1.00000 q^{15} +0.228180 q^{16} -7.59404 q^{17} +0.844677 q^{18} +0.806944 q^{19} -1.28652 q^{20} -2.49791 q^{21} +0.497601 q^{22} +6.24354 q^{23} -2.77605 q^{24} +1.00000 q^{25} -0.844677 q^{26} +1.00000 q^{27} +3.21362 q^{28} +3.14473 q^{29} +0.844677 q^{30} +1.00000 q^{31} +5.74483 q^{32} +0.589102 q^{33} -6.41451 q^{34} -2.49791 q^{35} -1.28652 q^{36} -3.66879 q^{37} +0.681607 q^{38} -1.00000 q^{39} -2.77605 q^{40} +5.40311 q^{41} -2.10993 q^{42} +1.91079 q^{43} -0.757893 q^{44} +1.00000 q^{45} +5.27377 q^{46} -4.74710 q^{47} +0.228180 q^{48} -0.760441 q^{49} +0.844677 q^{50} -7.59404 q^{51} +1.28652 q^{52} +11.3043 q^{53} +0.844677 q^{54} +0.589102 q^{55} +6.93432 q^{56} +0.806944 q^{57} +2.65628 q^{58} -12.9434 q^{59} -1.28652 q^{60} +11.5460 q^{61} +0.844677 q^{62} -2.49791 q^{63} +4.39617 q^{64} -1.00000 q^{65} +0.497601 q^{66} +0.320783 q^{67} +9.76989 q^{68} +6.24354 q^{69} -2.10993 q^{70} -1.69109 q^{71} -2.77605 q^{72} +0.0347964 q^{73} -3.09894 q^{74} +1.00000 q^{75} -1.03815 q^{76} -1.47153 q^{77} -0.844677 q^{78} +14.3989 q^{79} +0.228180 q^{80} +1.00000 q^{81} +4.56388 q^{82} +4.49210 q^{83} +3.21362 q^{84} -7.59404 q^{85} +1.61400 q^{86} +3.14473 q^{87} -1.63538 q^{88} +5.40483 q^{89} +0.844677 q^{90} +2.49791 q^{91} -8.03244 q^{92} +1.00000 q^{93} -4.00976 q^{94} +0.806944 q^{95} +5.74483 q^{96} +0.220681 q^{97} -0.642327 q^{98} +0.589102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9	\( 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9} + 4 q^{10} + 6 q^{11} + 22 q^{12} - 18 q^{13} + 5 q^{14} + 18 q^{15} + 30 q^{16} + 18 q^{17} + 4 q^{18} + 12 q^{19} + 22 q^{20} + 8 q^{21} + 7 q^{22} + 32 q^{23} + 9 q^{24} + 18 q^{25} - 4 q^{26} + 18 q^{27} + 10 q^{28} + 7 q^{29} + 4 q^{30} + 18 q^{31} + 22 q^{32} + 6 q^{33} + 15 q^{34} + 8 q^{35} + 22 q^{36} + 3 q^{37} + 32 q^{38} - 18 q^{39} + 9 q^{40} + 4 q^{41} + 5 q^{42} + 14 q^{43} - 5 q^{44} + 18 q^{45} + 10 q^{46} + 23 q^{47} + 30 q^{48} + 28 q^{49} + 4 q^{50} + 18 q^{51} - 22 q^{52} + 35 q^{53} + 4 q^{54} + 6 q^{55} - 7 q^{56} + 12 q^{57} - 6 q^{58} + 28 q^{59} + 22 q^{60} + 19 q^{61} + 4 q^{62} + 8 q^{63} + 43 q^{64} - 18 q^{65} + 7 q^{66} + 34 q^{67} + 55 q^{68} + 32 q^{69} + 5 q^{70} - 8 q^{71} + 9 q^{72} + 22 q^{74} + 18 q^{75} + 2 q^{76} + 21 q^{77} - 4 q^{78} + 4 q^{79} + 30 q^{80} + 18 q^{81} + 29 q^{82} + 11 q^{83} + 10 q^{84} + 18 q^{85} - 22 q^{86} + 7 q^{87} - 31 q^{88} + 17 q^{89} + 4 q^{90} - 8 q^{91} + 33 q^{92} + 18 q^{93} - 14 q^{94} + 12 q^{95} + 22 q^{96} + 32 q^{97} + 20 q^{98} + 6 q^{99}+O(q^{100}) \) 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9 + 4 * q^10 + 6 * q^11 + 22 * q^12 - 18 * q^13 + 5 * q^14 + 18 * q^15 + 30 * q^16 + 18 * q^17 + 4 * q^18 + 12 * q^19 + 22 * q^20 + 8 * q^21 + 7 * q^22 + 32 * q^23 + 9 * q^24 + 18 * q^25 - 4 * q^26 + 18 * q^27 + 10 * q^28 + 7 * q^29 + 4 * q^30 + 18 * q^31 + 22 * q^32 + 6 * q^33 + 15 * q^34 + 8 * q^35 + 22 * q^36 + 3 * q^37 + 32 * q^38 - 18 * q^39 + 9 * q^40 + 4 * q^41 + 5 * q^42 + 14 * q^43 - 5 * q^44 + 18 * q^45 + 10 * q^46 + 23 * q^47 + 30 * q^48 + 28 * q^49 + 4 * q^50 + 18 * q^51 - 22 * q^52 + 35 * q^53 + 4 * q^54 + 6 * q^55 - 7 * q^56 + 12 * q^57 - 6 * q^58 + 28 * q^59 + 22 * q^60 + 19 * q^61 + 4 * q^62 + 8 * q^63 + 43 * q^64 - 18 * q^65 + 7 * q^66 + 34 * q^67 + 55 * q^68 + 32 * q^69 + 5 * q^70 - 8 * q^71 + 9 * q^72 + 22 * q^74 + 18 * q^75 + 2 * q^76 + 21 * q^77 - 4 * q^78 + 4 * q^79 + 30 * q^80 + 18 * q^81 + 29 * q^82 + 11 * q^83 + 10 * q^84 + 18 * q^85 - 22 * q^86 + 7 * q^87 - 31 * q^88 + 17 * q^89 + 4 * q^90 - 8 * q^91 + 33 * q^92 + 18 * q^93 - 14 * q^94 + 12 * q^95 + 22 * q^96 + 32 * q^97 + 20 * q^98 + 6 * q^99

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