LMFDB - Embedded newform 4029.2.a.e.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
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} - 6 x^{17} - 10 x^{16} + 120 x^{15} - 56 x^{14} - 921 x^{13} + 1181 x^{12} + 3316 x^{11} + \cdots + 138 $ x^18 - 6x^17 - 10x^16 + 120x^15 - 56x^14 - 921x^13 + 1181x^12 + 3316x^11 - 6280x^10 - 5249x^9 + 15005x^8 + 1809x^7 - 16711x^6 + 2434x^5 + 8758x^4 - 1858x^3 - 1942x^2 + 318*x + 138
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			1.6
Root			$1.59625$ of defining polynomial
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.59625 q^{2} +1.00000 q^{3} +0.548008 q^{4} -4.15667 q^{5} -1.59625 q^{6} -4.26341 q^{7} +2.31774 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.59625 q^{2} +1.00000 q^{3} +0.548008 q^{4} -4.15667 q^{5} -1.59625 q^{6} -4.26341 q^{7} +2.31774 q^{8} +1.00000 q^{9} +6.63507 q^{10} -3.96232 q^{11} +0.548008 q^{12} +5.96783 q^{13} +6.80546 q^{14} -4.15667 q^{15} -4.79570 q^{16} +1.00000 q^{17} -1.59625 q^{18} -3.39274 q^{19} -2.27789 q^{20} -4.26341 q^{21} +6.32485 q^{22} -1.77015 q^{23} +2.31774 q^{24} +12.2779 q^{25} -9.52613 q^{26} +1.00000 q^{27} -2.33638 q^{28} -1.91377 q^{29} +6.63507 q^{30} +7.60328 q^{31} +3.01965 q^{32} -3.96232 q^{33} -1.59625 q^{34} +17.7216 q^{35} +0.548008 q^{36} +4.78864 q^{37} +5.41565 q^{38} +5.96783 q^{39} -9.63408 q^{40} +0.393873 q^{41} +6.80546 q^{42} -9.34742 q^{43} -2.17138 q^{44} -4.15667 q^{45} +2.82560 q^{46} +3.81846 q^{47} -4.79570 q^{48} +11.1767 q^{49} -19.5986 q^{50} +1.00000 q^{51} +3.27042 q^{52} -6.91150 q^{53} -1.59625 q^{54} +16.4701 q^{55} -9.88147 q^{56} -3.39274 q^{57} +3.05484 q^{58} +7.28917 q^{59} -2.27789 q^{60} -3.33905 q^{61} -12.1367 q^{62} -4.26341 q^{63} +4.77129 q^{64} -24.8063 q^{65} +6.32485 q^{66} +11.7822 q^{67} +0.548008 q^{68} -1.77015 q^{69} -28.2880 q^{70} +14.0914 q^{71} +2.31774 q^{72} +3.83452 q^{73} -7.64386 q^{74} +12.2779 q^{75} -1.85925 q^{76} +16.8930 q^{77} -9.52613 q^{78} -1.00000 q^{79} +19.9341 q^{80} +1.00000 q^{81} -0.628719 q^{82} -2.25707 q^{83} -2.33638 q^{84} -4.15667 q^{85} +14.9208 q^{86} -1.91377 q^{87} -9.18364 q^{88} +13.0851 q^{89} +6.63507 q^{90} -25.4433 q^{91} -0.970055 q^{92} +7.60328 q^{93} -6.09521 q^{94} +14.1025 q^{95} +3.01965 q^{96} -2.41881 q^{97} -17.8407 q^{98} -3.96232 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * 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 $

$2$	−1.59625	−1.12872	−0.564359	−	0.825530i	$-0.690877\pi$
$2$	−1.59625	−1.12872	−0.564359	+	0.825530i	$0.690877\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.548008	0.274004
$5$	−4.15667	−1.85892	−0.929459	−	0.368925i	$-0.879726\pi$
$5$	−4.15667	−1.85892	−0.929459	+	0.368925i	$0.879726\pi$
$6$	−1.59625	−0.651666
$7$	−4.26341	−1.61142	−0.805709	−	0.592312i	$-0.798215\pi$
$7$	−4.26341	−1.61142	−0.805709	+	0.592312i	$0.798215\pi$
$8$	2.31774	0.819445
$9$	1.00000	0.333333
$10$	6.63507	2.09819
$11$	−3.96232	−1.19469	−0.597343	−	0.801986i	$-0.703777\pi$
$11$	−3.96232	−1.19469	−0.597343	+	0.801986i	$0.703777\pi$
$12$	0.548008	0.158196
$13$	5.96783	1.65518	0.827589	−	0.561335i	$-0.189712\pi$
$13$	5.96783	1.65518	0.827589	+	0.561335i	$0.189712\pi$
$14$	6.80546	1.81884
$15$	−4.15667	−1.07325
$16$	−4.79570	−1.19893
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.59625	−0.376239
$19$	−3.39274	−0.778347	−0.389174	−	0.921164i	$-0.627239\pi$
$19$	−3.39274	−0.778347	−0.389174	+	0.921164i	$0.627239\pi$
$20$	−2.27789	−0.509351
$21$	−4.26341	−0.930352
$22$	6.32485	1.34846
$23$	−1.77015	−0.369102	−0.184551	−	0.982823i	$-0.559083\pi$
$23$	−1.77015	−0.369102	−0.184551	+	0.982823i	$0.559083\pi$
$24$	2.31774	0.473107
$25$	12.2779	2.45558
$26$	−9.52613	−1.86823
$27$	1.00000	0.192450
$28$	−2.33638	−0.441535
$29$	−1.91377	−0.355377	−0.177689	−	0.984087i	$-0.556862\pi$
$29$	−1.91377	−0.355377	−0.177689	+	0.984087i	$0.556862\pi$
$30$	6.63507	1.21139
$31$	7.60328	1.36559	0.682795	−	0.730610i	$-0.260764\pi$
$31$	7.60328	1.36559	0.682795	+	0.730610i	$0.260764\pi$
$32$	3.01965	0.533804
$33$	−3.96232	−0.689752
$34$	−1.59625	−0.273754
$35$	17.7216	2.99549
$36$	0.548008	0.0913346
$37$	4.78864	0.787248	0.393624	−	0.919271i	$-0.371221\pi$
$37$	4.78864	0.787248	0.393624	+	0.919271i	$0.371221\pi$
$38$	5.41565	0.878535
$39$	5.96783	0.955617
$40$	−9.63408	−1.52328
$41$	0.393873	0.0615127	0.0307563	−	0.999527i	$-0.490208\pi$
$41$	0.393873	0.0615127	0.0307563	+	0.999527i	$0.490208\pi$
$42$	6.80546	1.05011
$43$	−9.34742	−1.42547	−0.712734	−	0.701434i	$-0.752544\pi$
$43$	−9.34742	−1.42547	−0.712734	+	0.701434i	$0.752544\pi$
$44$	−2.17138	−0.327349
$45$	−4.15667	−0.619640
$46$	2.82560	0.416612
$47$	3.81846	0.556980	0.278490	−	0.960439i	$-0.410166\pi$
$47$	3.81846	0.556980	0.278490	+	0.960439i	$0.410166\pi$
$48$	−4.79570	−0.692200
$49$	11.1767	1.59667
$50$	−19.5986	−2.77166
$51$	1.00000	0.140028
$52$	3.27042	0.453525
$53$	−6.91150	−0.949367	−0.474684	−	0.880157i	$-0.657438\pi$
$53$	−6.91150	−0.949367	−0.474684	+	0.880157i	$0.657438\pi$
$54$	−1.59625	−0.217222
$55$	16.4701	2.22082
$56$	−9.88147	−1.32047
$57$	−3.39274	−0.449379
$58$	3.05484	0.401121
$59$	7.28917	0.948970	0.474485	−	0.880264i	$-0.342634\pi$
$59$	7.28917	0.948970	0.474485	+	0.880264i	$0.342634\pi$
$60$	−2.27789	−0.294074
$61$	−3.33905	−0.427522	−0.213761	−	0.976886i	$-0.568571\pi$
$61$	−3.33905	−0.427522	−0.213761	+	0.976886i	$0.568571\pi$
$62$	−12.1367	−1.54137
$63$	−4.26341	−0.537139
$64$	4.77129	0.596412
$65$	−24.8063	−3.07684
$66$	6.32485	0.778536
$67$	11.7822	1.43942	0.719710	−	0.694274i	$-0.244275\pi$
$67$	11.7822	1.43942	0.719710	+	0.694274i	$0.244275\pi$
$68$	0.548008	0.0664557
$69$	−1.77015	−0.213101
$70$	−28.2880	−3.38107
$71$	14.0914	1.67234	0.836171	−	0.548469i	$-0.184789\pi$
$71$	14.0914	1.67234	0.836171	+	0.548469i	$0.184789\pi$
$72$	2.31774	0.273148
$73$	3.83452	0.448797	0.224398	−	0.974497i	$-0.427958\pi$
$73$	3.83452	0.448797	0.224398	+	0.974497i	$0.427958\pi$
$74$	−7.64386	−0.888581
$75$	12.2779	1.41773
$76$	−1.85925	−0.213270
$77$	16.8930	1.92514
$78$	−9.52613	−1.07862
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	19.9341	2.22871
$81$	1.00000	0.111111
$82$	−0.628719	−0.0694304
$83$	−2.25707	−0.247746	−0.123873	−	0.992298i	$-0.539532\pi$
$83$	−2.25707	−0.247746	−0.123873	+	0.992298i	$0.539532\pi$
$84$	−2.33638	−0.254920
$85$	−4.15667	−0.450854
$86$	14.9208	1.60895
$87$	−1.91377	−0.205177
$88$	−9.18364	−0.978979
$89$	13.0851	1.38701	0.693507	−	0.720450i	$-0.256065\pi$
$89$	13.0851	1.38701	0.693507	+	0.720450i	$0.256065\pi$
$90$	6.63507	0.699398
$91$	−25.4433	−2.66718
$92$	−0.970055	−0.101135
$93$	7.60328	0.788424
$94$	−6.09521	−0.628673
$95$	14.1025	1.44688
$96$	3.01965	0.308192
$97$	−2.41881	−0.245592	−0.122796	−	0.992432i	$-0.539186\pi$
$97$	−2.41881	−0.245592	−0.122796	+	0.992432i	$0.539186\pi$
$98$	−17.8407	−1.80218
$99$	−3.96232	−0.398229
$100$	6.72838	0.672838
$101$	−8.39736	−0.835569	−0.417784	−	0.908546i	$-0.637193\pi$
$101$	−8.39736	−0.835569	−0.417784	+	0.908546i	$0.637193\pi$
$102$	−1.59625	−0.158052
$103$	7.46747	0.735792	0.367896	−	0.929867i	$-0.380078\pi$
$103$	7.46747	0.735792	0.367896	+	0.929867i	$0.380078\pi$
$104$	13.8319	1.35633
$105$	17.7216	1.72945
$106$	11.0325	1.07157
$107$	−13.9703	−1.35056	−0.675280	−	0.737561i	$-0.735977\pi$
$107$	−13.9703	−1.35056	−0.675280	+	0.737561i	$0.735977\pi$
$108$	0.548008	0.0527321
$109$	7.68304	0.735901	0.367951	−	0.929845i	$-0.380060\pi$
$109$	7.68304	0.735901	0.367951	+	0.929845i	$0.380060\pi$
$110$	−26.2903	−2.50668
$111$	4.78864	0.454518
$112$	20.4460	1.93197
$113$	0.305026	0.0286945	0.0143472	−	0.999897i	$-0.495433\pi$
$113$	0.305026	0.0286945	0.0143472	+	0.999897i	$0.495433\pi$
$114$	5.41565	0.507222
$115$	7.35792	0.686130
$116$	−1.04876	−0.0973748
$117$	5.96783	0.551726
$118$	−11.6353	−1.07112
$119$	−4.26341	−0.390826
$120$	−9.63408	−0.879467
$121$	4.70002	0.427274
$122$	5.32995	0.482551
$123$	0.393873	0.0355143
$124$	4.16666	0.374177
$125$	−30.2518	−2.70580
$126$	6.80546	0.606278
$127$	5.90499	0.523983	0.261991	−	0.965070i	$-0.415621\pi$
$127$	5.90499	0.523983	0.261991	+	0.965070i	$0.415621\pi$
$128$	−13.6555	−1.20698
$129$	−9.34742	−0.822995
$130$	39.5970	3.47288
$131$	−4.64141	−0.405522	−0.202761	−	0.979228i	$-0.564991\pi$
$131$	−4.64141	−0.405522	−0.202761	+	0.979228i	$0.564991\pi$
$132$	−2.17138	−0.188995
$133$	14.4646	1.25424
$134$	−18.8073	−1.62470
$135$	−4.15667	−0.357749
$136$	2.31774	0.198745
$137$	6.67907	0.570631	0.285316	−	0.958434i	$-0.407902\pi$
$137$	6.67907	0.570631	0.285316	+	0.958434i	$0.407902\pi$
$138$	2.82560	0.240531
$139$	−15.6676	−1.32891	−0.664454	−	0.747329i	$-0.731336\pi$
$139$	−15.6676	−1.32891	−0.664454	+	0.747329i	$0.731336\pi$
$140$	9.71156	0.820777
$141$	3.81846	0.321572
$142$	−22.4934	−1.88760
$143$	−23.6465	−1.97742
$144$	−4.79570	−0.399642
$145$	7.95489	0.660618
$146$	−6.12085	−0.506565
$147$	11.1767	0.921835
$148$	2.62421	0.215709
$149$	−22.2186	−1.82022	−0.910110	−	0.414368i	$-0.864003\pi$
$149$	−22.2186	−1.82022	−0.910110	+	0.414368i	$0.864003\pi$
$150$	−19.5986	−1.60022
$151$	18.3134	1.49032	0.745161	−	0.666884i	$-0.232373\pi$
$151$	18.3134	1.49032	0.745161	+	0.666884i	$0.232373\pi$
$152$	−7.86348	−0.637813
$153$	1.00000	0.0808452
$154$	−26.9654	−2.17294
$155$	−31.6043	−2.53852
$156$	3.27042	0.261843
$157$	3.68675	0.294234	0.147117	−	0.989119i	$-0.453001\pi$
$157$	3.68675	0.294234	0.147117	+	0.989119i	$0.453001\pi$
$158$	1.59625	0.126991
$159$	−6.91150	−0.548117
$160$	−12.5517	−0.992298
$161$	7.54687	0.594777
$162$	−1.59625	−0.125413
$163$	−8.03803	−0.629587	−0.314794	−	0.949160i	$-0.601935\pi$
$163$	−8.03803	−0.629587	−0.314794	+	0.949160i	$0.601935\pi$
$164$	0.215846	0.0168547
$165$	16.4701	1.28219
$166$	3.60285	0.279635
$167$	−16.2762	−1.25949	−0.629745	−	0.776802i	$-0.716841\pi$
$167$	−16.2762	−1.25949	−0.629745	+	0.776802i	$0.716841\pi$
$168$	−9.88147	−0.762372
$169$	22.6150	1.73961
$170$	6.63507	0.508887
$171$	−3.39274	−0.259449
$172$	−5.12246	−0.390584
$173$	−5.09091	−0.387054	−0.193527	−	0.981095i	$-0.561993\pi$
$173$	−5.09091	−0.387054	−0.193527	+	0.981095i	$0.561993\pi$
$174$	3.05484	0.231587
$175$	−52.3457	−3.95696
$176$	19.0021	1.43234
$177$	7.28917	0.547888
$178$	−20.8870	−1.56555
$179$	−18.0546	−1.34947	−0.674733	−	0.738062i	$-0.735741\pi$
$179$	−18.0546	−1.34947	−0.674733	+	0.738062i	$0.735741\pi$
$180$	−2.27789	−0.169784
$181$	−21.7056	−1.61336	−0.806682	−	0.590986i	$-0.798739\pi$
$181$	−21.7056	−1.61336	−0.806682	+	0.590986i	$0.798739\pi$
$182$	40.6138	3.01050
$183$	−3.33905	−0.246830
$184$	−4.10274	−0.302458
$185$	−19.9048	−1.46343
$186$	−12.1367	−0.889908
$187$	−3.96232	−0.289754
$188$	2.09255	0.152615
$189$	−4.26341	−0.310117
$190$	−22.5111	−1.63312
$191$	−8.58891	−0.621471	−0.310736	−	0.950496i	$-0.600575\pi$
$191$	−8.58891	−0.621471	−0.310736	+	0.950496i	$0.600575\pi$
$192$	4.77129	0.344338
$193$	−9.32666	−0.671347	−0.335674	−	0.941978i	$-0.608964\pi$
$193$	−9.32666	−0.671347	−0.335674	+	0.941978i	$0.608964\pi$
$194$	3.86101	0.277205
$195$	−24.8063	−1.77641
$196$	6.12490	0.437493
$197$	−5.99071	−0.426821	−0.213410	−	0.976963i	$-0.568457\pi$
$197$	−5.99071	−0.426821	−0.213410	+	0.976963i	$0.568457\pi$
$198$	6.32485	0.449488
$199$	3.84352	0.272460	0.136230	−	0.990677i	$-0.456501\pi$
$199$	3.84352	0.272460	0.136230	+	0.990677i	$0.456501\pi$
$200$	28.4570	2.01221
$201$	11.7822	0.831050
$202$	13.4043	0.943121
$203$	8.15916	0.572661
$204$	0.548008	0.0383682
$205$	−1.63720	−0.114347
$206$	−11.9199	−0.830501
$207$	−1.77015	−0.123034
$208$	−28.6199	−1.98443
$209$	13.4431	0.929881
$210$	−28.2880	−1.95206
$211$	−9.01206	−0.620416	−0.310208	−	0.950669i	$-0.600399\pi$
$211$	−9.01206	−0.620416	−0.310208	+	0.950669i	$0.600399\pi$
$212$	−3.78755	−0.260130
$213$	14.0914	0.965527
$214$	22.3001	1.52440
$215$	38.8541	2.64983
$216$	2.31774	0.157702
$217$	−32.4159	−2.20053
$218$	−12.2640	−0.830625
$219$	3.83452	0.259113
$220$	9.02573	0.608514
$221$	5.96783	0.401440
$222$	−7.64386	−0.513023
$223$	−21.5850	−1.44544	−0.722718	−	0.691143i	$-0.757108\pi$
$223$	−21.5850	−1.44544	−0.722718	+	0.691143i	$0.757108\pi$
$224$	−12.8740	−0.860181
$225$	12.2779	0.818526
$226$	−0.486898	−0.0323879
$227$	−2.14853	−0.142603	−0.0713015	−	0.997455i	$-0.522715\pi$
$227$	−2.14853	−0.142603	−0.0713015	+	0.997455i	$0.522715\pi$
$228$	−1.85925	−0.123132
$229$	8.60576	0.568685	0.284342	−	0.958723i	$-0.408225\pi$
$229$	8.60576	0.568685	0.284342	+	0.958723i	$0.408225\pi$
$230$	−11.7451	−0.774447
$231$	16.8930	1.11148
$232$	−4.43561	−0.291212
$233$	−23.0101	−1.50744	−0.753720	−	0.657195i	$-0.771743\pi$
$233$	−23.0101	−1.50744	−0.753720	+	0.657195i	$0.771743\pi$
$234$	−9.52613	−0.622743
$235$	−15.8721	−1.03538
$236$	3.99452	0.260021
$237$	−1.00000	−0.0649570
$238$	6.80546	0.441132
$239$	−7.72552	−0.499722	−0.249861	−	0.968282i	$-0.580385\pi$
$239$	−7.72552	−0.499722	−0.249861	+	0.968282i	$0.580385\pi$
$240$	19.9341	1.28674
$241$	24.9474	1.60701	0.803503	−	0.595301i	$-0.202967\pi$
$241$	24.9474	1.60701	0.803503	+	0.595301i	$0.202967\pi$
$242$	−7.50240	−0.482272
$243$	1.00000	0.0641500
$244$	−1.82983	−0.117143
$245$	−46.4577	−2.96807
$246$	−0.628719	−0.0400857
$247$	−20.2473	−1.28830
$248$	17.6224	1.11903
$249$	−2.25707	−0.143036
$250$	48.2894	3.05409
$251$	7.04128	0.444442	0.222221	−	0.974996i	$-0.428669\pi$
$251$	7.04128	0.444442	0.222221	+	0.974996i	$0.428669\pi$
$252$	−2.33638	−0.147178
$253$	7.01391	0.440960
$254$	−9.42582	−0.591429
$255$	−4.15667	−0.260301
$256$	12.2549	0.765933
$257$	23.1709	1.44536	0.722680	−	0.691183i	$-0.242910\pi$
$257$	23.1709	1.44536	0.722680	+	0.691183i	$0.242910\pi$
$258$	14.9208	0.928929
$259$	−20.4160	−1.26859
$260$	−13.5940	−0.843066
$261$	−1.91377	−0.118459
$262$	7.40884	0.457720
$263$	−12.5178	−0.771880	−0.385940	−	0.922524i	$-0.626123\pi$
$263$	−12.5178	−0.771880	−0.385940	+	0.922524i	$0.626123\pi$
$264$	−9.18364	−0.565214
$265$	28.7288	1.76480
$266$	−23.0891	−1.41569
$267$	13.0851	0.800793
$268$	6.45672	0.394407
$269$	7.17854	0.437683	0.218842	−	0.975760i	$-0.429772\pi$
$269$	7.17854	0.437683	0.218842	+	0.975760i	$0.429772\pi$
$270$	6.63507	0.403798
$271$	29.4071	1.78635	0.893177	−	0.449705i	$-0.148471\pi$
$271$	29.4071	1.78635	0.893177	+	0.449705i	$0.148471\pi$
$272$	−4.79570	−0.290782
$273$	−25.4433	−1.53990
$274$	−10.6614	−0.644082
$275$	−48.6490	−2.93365
$276$	−0.970055	−0.0583905
$277$	14.8982	0.895143	0.447572	−	0.894248i	$-0.352289\pi$
$277$	14.8982	0.895143	0.447572	+	0.894248i	$0.352289\pi$
$278$	25.0094	1.49996
$279$	7.60328	0.455197
$280$	41.0740	2.45464
$281$	−21.5979	−1.28842	−0.644210	−	0.764848i	$-0.722814\pi$
$281$	−21.5979	−1.28842	−0.644210	+	0.764848i	$0.722814\pi$
$282$	−6.09521	−0.362965
$283$	−26.4570	−1.57271	−0.786354	−	0.617776i	$-0.788034\pi$
$283$	−26.4570	−1.57271	−0.786354	+	0.617776i	$0.788034\pi$
$284$	7.72220	0.458228
$285$	14.1025	0.835359
$286$	37.7456	2.23195
$287$	−1.67924	−0.0991225
$288$	3.01965	0.177935
$289$	1.00000	0.0588235
$290$	−12.6980	−0.745651
$291$	−2.41881	−0.141793
$292$	2.10135	0.122972
$293$	21.0376	1.22903	0.614516	−	0.788905i	$-0.289351\pi$
$293$	21.0376	1.22903	0.614516	+	0.788905i	$0.289351\pi$
$294$	−17.8407	−1.04049
$295$	−30.2987	−1.76406
$296$	11.0988	0.645106
$297$	−3.96232	−0.229917
$298$	35.4664	2.05451
$299$	−10.5639	−0.610929
$300$	6.72838	0.388463
$301$	39.8519	2.29702
$302$	−29.2327	−1.68215
$303$	−8.39736	−0.482416
$304$	16.2706	0.933181
$305$	13.8793	0.794728
$306$	−1.59625	−0.0912514
$307$	−30.0126	−1.71291	−0.856455	−	0.516221i	$-0.827338\pi$
$307$	−30.0126	−1.71291	−0.856455	+	0.516221i	$0.827338\pi$
$308$	9.25750	0.527495
$309$	7.46747	0.424809
$310$	50.4483	2.86527
$311$	−2.19918	−0.124704	−0.0623520	−	0.998054i	$-0.519860\pi$
$311$	−2.19918	−0.124704	−0.0623520	+	0.998054i	$0.519860\pi$
$312$	13.8319	0.783075
$313$	29.3593	1.65949	0.829743	−	0.558146i	$-0.188487\pi$
$313$	29.3593	1.65949	0.829743	+	0.558146i	$0.188487\pi$
$314$	−5.88496	−0.332108
$315$	17.7216	0.998498
$316$	−0.548008	−0.0308278
$317$	17.5501	0.985713	0.492856	−	0.870111i	$-0.335953\pi$
$317$	17.5501	0.985713	0.492856	+	0.870111i	$0.335953\pi$
$318$	11.0325	0.618670
$319$	7.58296	0.424564
$320$	−19.8327	−1.10868
$321$	−13.9703	−0.779746
$322$	−12.0467	−0.671335
$323$	−3.39274	−0.188777
$324$	0.548008	0.0304449
$325$	73.2723	4.06442
$326$	12.8307	0.710626
$327$	7.68304	0.424873
$328$	0.912895	0.0504062
$329$	−16.2797	−0.897527
$330$	−26.2903	−1.44723
$331$	1.14543	0.0629583	0.0314792	−	0.999504i	$-0.489978\pi$
$331$	1.14543	0.0629583	0.0314792	+	0.999504i	$0.489978\pi$
$332$	−1.23689	−0.0678833
$333$	4.78864	0.262416
$334$	25.9809	1.42161
$335$	−48.9746	−2.67577
$336$	20.4460	1.11542
$337$	−4.73030	−0.257676	−0.128838	−	0.991666i	$-0.541125\pi$
$337$	−4.73030	−0.257676	−0.128838	+	0.991666i	$0.541125\pi$
$338$	−36.0991	−1.96353
$339$	0.305026	0.0165668
$340$	−2.27789	−0.123536
$341$	−30.1267	−1.63145
$342$	5.41565	0.292845
$343$	−17.8068	−0.961477
$344$	−21.6649	−1.16809
$345$	7.35792	0.396137
$346$	8.12635	0.436875
$347$	20.1981	1.08429	0.542144	−	0.840285i	$-0.317613\pi$
$347$	20.1981	1.08429	0.542144	+	0.840285i	$0.317613\pi$
$348$	−1.04876	−0.0562193
$349$	−14.4684	−0.774477	−0.387239	−	0.921980i	$-0.626571\pi$
$349$	−14.4684	−0.774477	−0.387239	+	0.921980i	$0.626571\pi$
$350$	83.5567	4.46629
$351$	5.96783	0.318539
$352$	−11.9648	−0.637728
$353$	−23.5638	−1.25418	−0.627088	−	0.778948i	$-0.715754\pi$
$353$	−23.5638	−1.25418	−0.627088	+	0.778948i	$0.715754\pi$
$354$	−11.6353	−0.618411
$355$	−58.5733	−3.10875
$356$	7.17072	0.380047
$357$	−4.26341	−0.225644
$358$	28.8197	1.52317
$359$	−9.34581	−0.493253	−0.246627	−	0.969111i	$-0.579322\pi$
$359$	−9.34581	−0.493253	−0.246627	+	0.969111i	$0.579322\pi$
$360$	−9.63408	−0.507760
$361$	−7.48933	−0.394175
$362$	34.6475	1.82103
$363$	4.70002	0.246687
$364$	−13.9431	−0.730818
$365$	−15.9388	−0.834277
$366$	5.32995	0.278601
$367$	9.69079	0.505855	0.252928	−	0.967485i	$-0.418607\pi$
$367$	9.69079	0.505855	0.252928	+	0.967485i	$0.418607\pi$
$368$	8.48911	0.442525
$369$	0.393873	0.0205042
$370$	31.7730	1.65180
$371$	29.4665	1.52983
$372$	4.16666	0.216031
$373$	−17.5690	−0.909689	−0.454845	−	0.890571i	$-0.650305\pi$
$373$	−17.5690	−0.909689	−0.454845	+	0.890571i	$0.650305\pi$
$374$	6.32485	0.327050
$375$	−30.2518	−1.56220
$376$	8.85020	0.456414
$377$	−11.4210	−0.588213
$378$	6.80546	0.350035
$379$	16.0946	0.826725	0.413363	−	0.910566i	$-0.364354\pi$
$379$	16.0946	0.826725	0.413363	+	0.910566i	$0.364354\pi$
$380$	7.72827	0.396452
$381$	5.90499	0.302522
$382$	13.7100	0.701466
$383$	−9.00626	−0.460198	−0.230099	−	0.973167i	$-0.573905\pi$
$383$	−9.00626	−0.460198	−0.230099	+	0.973167i	$0.573905\pi$
$384$	−13.6555	−0.696853
$385$	−70.2187	−3.57867
$386$	14.8877	0.757762
$387$	−9.34742	−0.475156
$388$	−1.32552	−0.0672933
$389$	19.9738	1.01271	0.506357	−	0.862324i	$-0.330992\pi$
$389$	19.9738	1.01271	0.506357	+	0.862324i	$0.330992\pi$
$390$	39.5970	2.00507
$391$	−1.77015	−0.0895203
$392$	25.9046	1.30838
$393$	−4.64141	−0.234128
$394$	9.56266	0.481760
$395$	4.15667	0.209145
$396$	−2.17138	−0.109116
$397$	19.9790	1.00272	0.501358	−	0.865240i	$-0.332834\pi$
$397$	19.9790	1.00272	0.501358	+	0.865240i	$0.332834\pi$
$398$	−6.13520	−0.307530
$399$	14.4646	0.724137
$400$	−58.8811	−2.94406
$401$	−11.0030	−0.549461	−0.274731	−	0.961521i	$-0.588589\pi$
$401$	−11.0030	−0.549461	−0.274731	+	0.961521i	$0.588589\pi$
$402$	−18.8073	−0.938021
$403$	45.3751	2.26029
$404$	−4.60182	−0.228949
$405$	−4.15667	−0.206547
$406$	−13.0241	−0.646373
$407$	−18.9742	−0.940514
$408$	2.31774	0.114745
$409$	22.6782	1.12137	0.560683	−	0.828031i	$-0.310539\pi$
$409$	22.6782	1.12137	0.560683	+	0.828031i	$0.310539\pi$
$410$	2.61338	0.129066
$411$	6.67907	0.329454
$412$	4.09223	0.201610
$413$	−31.0767	−1.52919
$414$	2.82560	0.138871
$415$	9.38190	0.460539
$416$	18.0208	0.883541
$417$	−15.6676	−0.767246
$418$	−21.4586	−1.04957
$419$	34.5466	1.68771	0.843857	−	0.536568i	$-0.180280\pi$
$419$	34.5466	1.68771	0.843857	+	0.536568i	$0.180280\pi$
$420$	9.71156	0.473876
$421$	32.1608	1.56742	0.783712	−	0.621125i	$-0.213324\pi$
$421$	32.1608	1.56742	0.783712	+	0.621125i	$0.213324\pi$
$422$	14.3855	0.700275
$423$	3.81846	0.185660
$424$	−16.0191	−0.777954
$425$	12.2779	0.595565
$426$	−22.4934	−1.08981
$427$	14.2357	0.688916
$428$	−7.65584	−0.370059
$429$	−23.6465	−1.14166
$430$	−62.0208	−2.99091
$431$	−17.9279	−0.863558	−0.431779	−	0.901979i	$-0.642114\pi$
$431$	−17.9279	−0.863558	−0.431779	+	0.901979i	$0.642114\pi$
$432$	−4.79570	−0.230733
$433$	−8.35999	−0.401756	−0.200878	−	0.979616i	$-0.564379\pi$
$433$	−8.35999	−0.401756	−0.200878	+	0.979616i	$0.564379\pi$
$434$	51.7438	2.48378
$435$	7.95489	0.381408
$436$	4.21036	0.201640
$437$	6.00565	0.287289
$438$	−6.12085	−0.292465
$439$	−27.9269	−1.33288	−0.666439	−	0.745559i	$-0.732182\pi$
$439$	−27.9269	−1.33288	−0.666439	+	0.745559i	$0.732182\pi$
$440$	38.1733	1.81984
$441$	11.1767	0.532222
$442$	−9.52613	−0.453112
$443$	−2.48221	−0.117934	−0.0589668	−	0.998260i	$-0.518781\pi$
$443$	−2.48221	−0.117934	−0.0589668	+	0.998260i	$0.518781\pi$
$444$	2.62421	0.124540
$445$	−54.3903	−2.57835
$446$	34.4550	1.63149
$447$	−22.2186	−1.05090
$448$	−20.3420	−0.961068
$449$	−14.1565	−0.668084	−0.334042	−	0.942558i	$-0.608413\pi$
$449$	−14.1565	−0.668084	−0.334042	+	0.942558i	$0.608413\pi$
$450$	−19.5986	−0.923885
$451$	−1.56065	−0.0734883
$452$	0.167157	0.00786239
$453$	18.3134	0.860438
$454$	3.42959	0.160959
$455$	105.759	4.95807
$456$	−7.86348	−0.368241
$457$	14.9408	0.698903	0.349451	−	0.936954i	$-0.386368\pi$
$457$	14.9408	0.698903	0.349451	+	0.936954i	$0.386368\pi$
$458$	−13.7369	−0.641885
$459$	1.00000	0.0466760
$460$	4.03220	0.188002
$461$	34.0688	1.58674	0.793371	−	0.608738i	$-0.208324\pi$
$461$	34.0688	1.58674	0.793371	+	0.608738i	$0.208324\pi$
$462$	−26.9654	−1.25455
$463$	25.4896	1.18460	0.592301	−	0.805717i	$-0.298220\pi$
$463$	25.4896	1.18460	0.592301	+	0.805717i	$0.298220\pi$
$464$	9.17785	0.426071
$465$	−31.6043	−1.46562
$466$	36.7298	1.70147
$467$	20.4151	0.944699	0.472350	−	0.881411i	$-0.343406\pi$
$467$	20.4151	0.944699	0.472350	+	0.881411i	$0.343406\pi$
$468$	3.27042	0.151175
$469$	−50.2322	−2.31951
$470$	25.3358	1.16865
$471$	3.68675	0.169876
$472$	16.8944	0.777628
$473$	37.0375	1.70299
$474$	1.59625	0.0733181
$475$	−41.6557	−1.91129
$476$	−2.33638	−0.107088
$477$	−6.91150	−0.316456
$478$	12.3318	0.564045
$479$	0.905247	0.0413618	0.0206809	−	0.999786i	$-0.493417\pi$
$479$	0.905247	0.0413618	0.0206809	+	0.999786i	$0.493417\pi$
$480$	−12.5517	−0.572904
$481$	28.5778	1.30304
$482$	−39.8223	−1.81386
$483$	7.54687	0.343394
$484$	2.57565	0.117075
$485$	10.0542	0.456536
$486$	−1.59625	−0.0724073
$487$	−25.3324	−1.14792	−0.573960	−	0.818883i	$-0.694594\pi$
$487$	−25.3324	−1.14792	−0.573960	+	0.818883i	$0.694594\pi$
$488$	−7.73905	−0.350330
$489$	−8.03803	−0.363492
$490$	74.1579	3.35011
$491$	−10.0882	−0.455276	−0.227638	−	0.973746i	$-0.573100\pi$
$491$	−10.0882	−0.455276	−0.227638	+	0.973746i	$0.573100\pi$
$492$	0.215846	0.00973107
$493$	−1.91377	−0.0861917
$494$	32.3197	1.45413
$495$	16.4701	0.740275
$496$	−36.4631	−1.63724
$497$	−60.0774	−2.69484
$498$	3.60285	0.161447
$499$	−35.7509	−1.60043	−0.800216	−	0.599712i	$-0.795282\pi$
$499$	−35.7509	−1.60043	−0.800216	+	0.599712i	$0.795282\pi$
$500$	−16.5782	−0.741400
$501$	−16.2762	−0.727167
$502$	−11.2396	−0.501649
$503$	−25.8937	−1.15454	−0.577271	−	0.816553i	$-0.695882\pi$
$503$	−25.8937	−1.15454	−0.577271	+	0.816553i	$0.695882\pi$
$504$	−9.88147	−0.440156
$505$	34.9051	1.55325
$506$	−11.1959	−0.497720
$507$	22.6150	1.00437
$508$	3.23598	0.143573
$509$	−36.1289	−1.60138	−0.800692	−	0.599076i	$-0.795535\pi$
$509$	−36.1289	−1.60138	−0.800692	+	0.599076i	$0.795535\pi$
$510$	6.63507	0.293806
$511$	−16.3481	−0.723199
$512$	7.74903	0.342462
$513$	−3.39274	−0.149793
$514$	−36.9865	−1.63140
$515$	−31.0398	−1.36778
$516$	−5.12246	−0.225504
$517$	−15.1300	−0.665416
$518$	32.5889	1.43188
$519$	−5.09091	−0.223466
$520$	−57.4945	−2.52130
$521$	−5.73665	−0.251327	−0.125664	−	0.992073i	$-0.540106\pi$
$521$	−5.73665	−0.251327	−0.125664	+	0.992073i	$0.540106\pi$
$522$	3.05484	0.133707
$523$	−24.6806	−1.07921	−0.539604	−	0.841919i	$-0.681426\pi$
$523$	−24.6806	−1.07921	−0.539604	+	0.841919i	$0.681426\pi$
$524$	−2.54353	−0.111115
$525$	−52.3457	−2.28455
$526$	19.9815	0.871235
$527$	7.60328	0.331204
$528$	19.0021	0.826962
$529$	−19.8666	−0.863764
$530$	−45.8583	−1.99196
$531$	7.28917	0.316323
$532$	7.92673	0.343667
$533$	2.35057	0.101814
$534$	−20.8870	−0.903869
$535$	58.0699	2.51058
$536$	27.3080	1.17953
$537$	−18.0546	−0.779115
$538$	−11.4587	−0.494021
$539$	−44.2855	−1.90751
$540$	−2.27789	−0.0980246
$541$	12.3627	0.531513	0.265756	−	0.964040i	$-0.414378\pi$
$541$	12.3627	0.531513	0.265756	+	0.964040i	$0.414378\pi$
$542$	−46.9410	−2.01629
$543$	−21.7056	−0.931476
$544$	3.01965	0.129467
$545$	−31.9358	−1.36798
$546$	40.6138	1.73811
$547$	−27.2169	−1.16371	−0.581856	−	0.813292i	$-0.697673\pi$
$547$	−27.2169	−1.16371	−0.581856	+	0.813292i	$0.697673\pi$
$548$	3.66018	0.156355
$549$	−3.33905	−0.142507
$550$	77.6559	3.31126
$551$	6.49290	0.276607
$552$	−4.10274	−0.174624
$553$	4.26341	0.181299
$554$	−23.7811	−1.01036
$555$	−19.9048	−0.844912
$556$	−8.58597	−0.364126
$557$	−25.5750	−1.08365	−0.541824	−	0.840492i	$-0.682266\pi$
$557$	−25.5750	−1.08365	−0.541824	+	0.840492i	$0.682266\pi$
$558$	−12.1367	−0.513788
$559$	−55.7838	−2.35940
$560$	−84.9874	−3.59137
$561$	−3.96232	−0.167289
$562$	34.4755	1.45426
$563$	13.9178	0.586567	0.293283	−	0.956026i	$-0.405252\pi$
$563$	13.9178	0.586567	0.293283	+	0.956026i	$0.405252\pi$
$564$	2.09255	0.0881121
$565$	−1.26789	−0.0533407
$566$	42.2320	1.77514
$567$	−4.26341	−0.179046
$568$	32.6602	1.37039
$569$	−7.47325	−0.313295	−0.156647	−	0.987655i	$-0.550069\pi$
$569$	−7.47325	−0.313295	−0.156647	+	0.987655i	$0.550069\pi$
$570$	−22.5111	−0.942885
$571$	24.7495	1.03574	0.517868	−	0.855461i	$-0.326726\pi$
$571$	24.7495	1.03574	0.517868	+	0.855461i	$0.326726\pi$
$572$	−12.9585	−0.541820
$573$	−8.58891	−0.358807
$574$	2.68049	0.111881
$575$	−21.7337	−0.906358
$576$	4.77129	0.198804
$577$	−22.5104	−0.937121	−0.468561	−	0.883431i	$-0.655227\pi$
$577$	−22.5104	−0.937121	−0.468561	+	0.883431i	$0.655227\pi$
$578$	−1.59625	−0.0663952
$579$	−9.32666	−0.387603
$580$	4.35934	0.181012
$581$	9.62282	0.399222
$582$	3.86101	0.160044
$583$	27.3856	1.13420
$584$	8.88742	0.367764
$585$	−24.8063	−1.02561
$586$	−33.5813	−1.38723
$587$	34.1615	1.41000	0.704999	−	0.709209i	$-0.250948\pi$
$587$	34.1615	1.41000	0.704999	+	0.709209i	$0.250948\pi$
$588$	6.12490	0.252586
$589$	−25.7959	−1.06290
$590$	48.3642	1.99112
$591$	−5.99071	−0.246425
$592$	−22.9649	−0.943852
$593$	16.0519	0.659173	0.329587	−	0.944125i	$-0.393091\pi$
$593$	16.0519	0.659173	0.329587	+	0.944125i	$0.393091\pi$
$594$	6.32485	0.259512
$595$	17.7216	0.726514
$596$	−12.1760	−0.498747
$597$	3.84352	0.157305
$598$	16.8627	0.689566
$599$	25.7868	1.05362	0.526811	−	0.849983i	$-0.323388\pi$
$599$	25.7868	1.05362	0.526811	+	0.849983i	$0.323388\pi$
$600$	28.4570	1.16175
$601$	2.46717	0.100638	0.0503190	−	0.998733i	$-0.483976\pi$
$601$	2.46717	0.100638	0.0503190	+	0.998733i	$0.483976\pi$
$602$	−63.6135	−2.59269
$603$	11.7822	0.479807
$604$	10.0359	0.408354
$605$	−19.5364	−0.794268
$606$	13.4043	0.544511
$607$	23.7825	0.965300	0.482650	−	0.875813i	$-0.339674\pi$
$607$	23.7825	0.965300	0.482650	+	0.875813i	$0.339674\pi$
$608$	−10.2449	−0.415485
$609$	8.15916	0.330626
$610$	−22.1548	−0.897024
$611$	22.7879	0.921900
$612$	0.548008	0.0221519
$613$	38.7969	1.56699	0.783496	−	0.621397i	$-0.213435\pi$
$613$	38.7969	1.56699	0.783496	+	0.621397i	$0.213435\pi$
$614$	47.9076	1.93339
$615$	−1.63720	−0.0660183
$616$	39.1536	1.57754
$617$	43.4241	1.74819	0.874095	−	0.485755i	$-0.161455\pi$
$617$	43.4241	1.74819	0.874095	+	0.485755i	$0.161455\pi$
$618$	−11.9199	−0.479490
$619$	−17.1316	−0.688578	−0.344289	−	0.938864i	$-0.611880\pi$
$619$	−17.1316	−0.688578	−0.344289	+	0.938864i	$0.611880\pi$
$620$	−17.3194	−0.695564
$621$	−1.77015	−0.0710336
$622$	3.51043	0.140756
$623$	−55.7870	−2.23506
$624$	−28.6199	−1.14571
$625$	64.3572	2.57429
$626$	−46.8647	−1.87309
$627$	13.4431	0.536867
$628$	2.02037	0.0806214
$629$	4.78864	0.190936
$630$	−28.2880	−1.12702
$631$	12.4997	0.497605	0.248803	−	0.968554i	$-0.419963\pi$
$631$	12.4997	0.497605	0.248803	+	0.968554i	$0.419963\pi$
$632$	−2.31774	−0.0921947
$633$	−9.01206	−0.358197
$634$	−28.0143	−1.11259
$635$	−24.5451	−0.974041
$636$	−3.78755	−0.150186
$637$	66.7004	2.64276
$638$	−12.1043	−0.479213
$639$	14.0914	0.557447
$640$	56.7613	2.24369
$641$	−1.07776	−0.0425690	−0.0212845	−	0.999773i	$-0.506776\pi$
$641$	−1.07776	−0.0425690	−0.0212845	+	0.999773i	$0.506776\pi$
$642$	22.3001	0.880114
$643$	−14.4401	−0.569464	−0.284732	−	0.958607i	$-0.591905\pi$
$643$	−14.4401	−0.569464	−0.284732	+	0.958607i	$0.591905\pi$
$644$	4.13574	0.162971
$645$	38.8541	1.52988
$646$	5.41565	0.213076
$647$	35.8344	1.40880	0.704398	−	0.709806i	$-0.251217\pi$
$647$	35.8344	1.40880	0.704398	+	0.709806i	$0.251217\pi$
$648$	2.31774	0.0910494
$649$	−28.8821	−1.13372
$650$	−116.961	−4.58758
$651$	−32.4159	−1.27048
$652$	−4.40490	−0.172509
$653$	34.5779	1.35314	0.676570	−	0.736379i	$-0.263466\pi$
$653$	34.5779	1.35314	0.676570	+	0.736379i	$0.263466\pi$
$654$	−12.2640	−0.479562
$655$	19.2928	0.753832
$656$	−1.88890	−0.0737491
$657$	3.83452	0.149599
$658$	25.9864	1.01305
$659$	−45.9677	−1.79065	−0.895323	−	0.445417i	$-0.853055\pi$
$659$	−45.9677	−1.79065	−0.895323	+	0.445417i	$0.853055\pi$
$660$	9.02573	0.351326
$661$	−39.4290	−1.53361	−0.766806	−	0.641879i	$-0.778155\pi$
$661$	−39.4290	−1.53361	−0.766806	+	0.641879i	$0.778155\pi$
$662$	−1.82838	−0.0710622
$663$	5.96783	0.231771
$664$	−5.23130	−0.203014
$665$	−60.1247	−2.33153
$666$	−7.64386	−0.296194
$667$	3.38765	0.131170
$668$	−8.91949	−0.345105
$669$	−21.5850	−0.834523
$670$	78.1755	3.02018
$671$	13.2304	0.510754
$672$	−12.8740	−0.496626
$673$	−22.9884	−0.886139	−0.443069	−	0.896487i	$-0.646110\pi$
$673$	−22.9884	−0.886139	−0.443069	+	0.896487i	$0.646110\pi$
$674$	7.55073	0.290843
$675$	12.2779	0.472576
$676$	12.3932	0.476661
$677$	30.3612	1.16688	0.583439	−	0.812157i	$-0.301707\pi$
$677$	30.3612	1.16688	0.583439	+	0.812157i	$0.301707\pi$
$678$	−0.486898	−0.0186992
$679$	10.3124	0.395752
$680$	−9.63408	−0.369450
$681$	−2.14853	−0.0823319
$682$	48.0896	1.84145
$683$	−35.1631	−1.34548	−0.672739	−	0.739880i	$-0.734882\pi$
$683$	−35.1631	−1.34548	−0.672739	+	0.739880i	$0.734882\pi$
$684$	−1.85925	−0.0710901
$685$	−27.7627	−1.06076
$686$	28.4241	1.08524
$687$	8.60576	0.328330
$688$	44.8275	1.70903
$689$	−41.2466	−1.57137
$690$	−11.7451	−0.447127
$691$	−35.9579	−1.36790	−0.683951	−	0.729528i	$-0.739740\pi$
$691$	−35.9579	−1.36790	−0.683951	+	0.729528i	$0.739740\pi$
$692$	−2.78986	−0.106054
$693$	16.8930	0.641712
$694$	−32.2411	−1.22386
$695$	65.1250	2.47033
$696$	−4.43561	−0.168131
$697$	0.393873	0.0149190
$698$	23.0952	0.874166
$699$	−23.0101	−0.870321
$700$	−28.6858	−1.08422
$701$	44.6026	1.68462	0.842308	−	0.538997i	$-0.181197\pi$
$701$	44.6026	1.68462	0.842308	+	0.538997i	$0.181197\pi$
$702$	−9.52613	−0.359541
$703$	−16.2466	−0.612753
$704$	−18.9054	−0.712524
$705$	−15.8721	−0.597777
$706$	37.6137	1.41561
$707$	35.8014	1.34645
$708$	3.99452	0.150123
$709$	−43.0226	−1.61575	−0.807873	−	0.589357i	$-0.799381\pi$
$709$	−43.0226	−1.61575	−0.807873	+	0.589357i	$0.799381\pi$
$710$	93.4975	3.50890
$711$	−1.00000	−0.0375029
$712$	30.3278	1.13658
$713$	−13.4589	−0.504041
$714$	6.80546	0.254688
$715$	98.2905	3.67586
$716$	−9.89408	−0.369759
$717$	−7.72552	−0.288515
$718$	14.9182	0.556744
$719$	−0.122633	−0.00457346	−0.00228673	−	0.999997i	$-0.500728\pi$
$719$	−0.122633	−0.00457346	−0.00228673	+	0.999997i	$0.500728\pi$
$720$	19.9341	0.742902
$721$	−31.8369	−1.18567
$722$	11.9548	0.444913
$723$	24.9474	0.927805
$724$	−11.8948	−0.442068
$725$	−23.4970	−0.872657
$726$	−7.50240	−0.278440
$727$	−21.7640	−0.807180	−0.403590	−	0.914940i	$-0.632238\pi$
$727$	−21.7640	−0.807180	−0.403590	+	0.914940i	$0.632238\pi$
$728$	−58.9709	−2.18561
$729$	1.00000	0.0370370
$730$	25.4423	0.941663
$731$	−9.34742	−0.345727
$732$	−1.82983	−0.0676323
$733$	5.85752	0.216352	0.108176	−	0.994132i	$-0.465499\pi$
$733$	5.85752	0.216352	0.108176	+	0.994132i	$0.465499\pi$
$734$	−15.4689	−0.570968
$735$	−46.4577	−1.71362
$736$	−5.34523	−0.197028
$737$	−46.6848	−1.71966
$738$	−0.628719	−0.0231435
$739$	−6.40198	−0.235501	−0.117750	−	0.993043i	$-0.537568\pi$
$739$	−6.40198	−0.235501	−0.117750	+	0.993043i	$0.537568\pi$
$740$	−10.9080	−0.400986
$741$	−20.2473	−0.743802
$742$	−47.0359	−1.72674
$743$	27.9656	1.02596	0.512979	−	0.858401i	$-0.328542\pi$
$743$	27.9656	1.02596	0.512979	+	0.858401i	$0.328542\pi$
$744$	17.6224	0.646070
$745$	92.3554	3.38364
$746$	28.0445	1.02678
$747$	−2.25707	−0.0825819
$748$	−2.17138	−0.0793937
$749$	59.5611	2.17632
$750$	48.2894	1.76328
$751$	16.3481	0.596552	0.298276	−	0.954480i	$-0.403588\pi$
$751$	16.3481	0.596552	0.298276	+	0.954480i	$0.403588\pi$
$752$	−18.3122	−0.667777
$753$	7.04128	0.256599
$754$	18.2308	0.663926
$755$	−76.1227	−2.77039
$756$	−2.33638	−0.0849734
$757$	−48.9524	−1.77921	−0.889603	−	0.456735i	$-0.849019\pi$
$757$	−48.9524	−1.77921	−0.889603	+	0.456735i	$0.849019\pi$
$758$	−25.6910	−0.933140
$759$	7.01391	0.254589
$760$	32.6859	1.18564
$761$	−34.0379	−1.23387	−0.616936	−	0.787013i	$-0.711626\pi$
$761$	−34.0379	−1.23387	−0.616936	+	0.787013i	$0.711626\pi$
$762$	−9.42582	−0.341461
$763$	−32.7559	−1.18584
$764$	−4.70679	−0.170286
$765$	−4.15667	−0.150285
$766$	14.3762	0.519434
$767$	43.5005	1.57071
$768$	12.2549	0.442212
$769$	−46.5739	−1.67950	−0.839750	−	0.542974i	$-0.817298\pi$
$769$	−46.5739	−1.67950	−0.839750	+	0.542974i	$0.817298\pi$
$770$	112.086	4.03931
$771$	23.1709	0.834479
$772$	−5.11108	−0.183952
$773$	−2.86291	−0.102972	−0.0514859	−	0.998674i	$-0.516396\pi$
$773$	−2.86291	−0.102972	−0.0514859	+	0.998674i	$0.516396\pi$
$774$	14.9208	0.536317
$775$	93.3523	3.35331
$776$	−5.60616	−0.201249
$777$	−20.4160	−0.732418
$778$	−31.8832	−1.14307
$779$	−1.33631	−0.0478782
$780$	−13.5940	−0.486745
$781$	−55.8347	−1.99792
$782$	2.82560	0.101043
$783$	−1.91377	−0.0683924
$784$	−53.5999	−1.91428
$785$	−15.3246	−0.546958
$786$	7.40884	0.264265
$787$	−40.8427	−1.45588	−0.727942	−	0.685638i	$-0.759523\pi$
$787$	−40.8427	−1.45588	−0.727942	+	0.685638i	$0.759523\pi$
$788$	−3.28296	−0.116951
$789$	−12.5178	−0.445645
$790$	−6.63507	−0.236065
$791$	−1.30045	−0.0462387
$792$	−9.18364	−0.326326
$793$	−19.9269	−0.707624
$794$	−31.8914	−1.13178
$795$	28.7288	1.01891
$796$	2.10628	0.0746550
$797$	49.8255	1.76491	0.882456	−	0.470396i	$-0.155889\pi$
$797$	49.8255	1.76491	0.882456	+	0.470396i	$0.155889\pi$
$798$	−23.0891	−0.817347
$799$	3.81846	0.135087
$800$	37.0750	1.31080
$801$	13.0851	0.462338
$802$	17.5634	0.620187
$803$	−15.1936	−0.536171
$804$	6.45672	0.227711
$805$	−31.3698	−1.10564
$806$	−72.4299	−2.55123
$807$	7.17854	0.252697
$808$	−19.4629	−0.684702
$809$	13.1579	0.462607	0.231304	−	0.972882i	$-0.425701\pi$
$809$	13.1579	0.462607	0.231304	+	0.972882i	$0.425701\pi$
$810$	6.63507	0.233133
$811$	1.77516	0.0623342	0.0311671	−	0.999514i	$-0.490078\pi$
$811$	1.77516	0.0623342	0.0311671	+	0.999514i	$0.490078\pi$
$812$	4.47129	0.156911
$813$	29.4071	1.03135
$814$	30.2875	1.06158
$815$	33.4114	1.17035
$816$	−4.79570	−0.167883
$817$	31.7134	1.10951
$818$	−36.2000	−1.26570
$819$	−25.4433	−0.889061
$820$	−0.897198	−0.0313315
$821$	−49.6539	−1.73293	−0.866466	−	0.499237i	$-0.833614\pi$
$821$	−49.6539	−1.73293	−0.866466	+	0.499237i	$0.833614\pi$
$822$	−10.6614	−0.371861
$823$	44.5406	1.55259	0.776294	−	0.630371i	$-0.217097\pi$
$823$	44.5406	1.55259	0.776294	+	0.630371i	$0.217097\pi$
$824$	17.3076	0.602941
$825$	−48.6490	−1.69374
$826$	49.6062	1.72602
$827$	5.73724	0.199503	0.0997516	−	0.995012i	$-0.468195\pi$
$827$	5.73724	0.199503	0.0997516	+	0.995012i	$0.468195\pi$
$828$	−0.970055	−0.0337118
$829$	24.8564	0.863299	0.431649	−	0.902041i	$-0.357932\pi$
$829$	24.8564	0.863299	0.431649	+	0.902041i	$0.357932\pi$
$830$	−14.9758	−0.519819
$831$	14.8982	0.516811
$832$	28.4742	0.987167
$833$	11.1767	0.387248
$834$	25.0094	0.866004
$835$	67.6548	2.34129
$836$	7.36694	0.254791
$837$	7.60328	0.262808
$838$	−55.1450	−1.90495
$839$	−9.17829	−0.316870	−0.158435	−	0.987369i	$-0.550645\pi$
$839$	−9.17829	−0.316870	−0.158435	+	0.987369i	$0.550645\pi$
$840$	41.0740	1.41719
$841$	−25.3375	−0.873707
$842$	−51.3367	−1.76918
$843$	−21.5979	−0.743870
$844$	−4.93868	−0.169996
$845$	−94.0029	−3.23380
$846$	−6.09521	−0.209558
$847$	−20.0381	−0.688517
$848$	33.1455	1.13822
$849$	−26.4570	−0.908004
$850$	−19.5986	−0.672225
$851$	−8.47661	−0.290575
$852$	7.72220	0.264558
$853$	44.4403	1.52161	0.760803	−	0.648983i	$-0.224805\pi$
$853$	44.4403	1.52161	0.760803	+	0.648983i	$0.224805\pi$
$854$	−22.7238	−0.777591
$855$	14.1025	0.482295
$856$	−32.3795	−1.10671
$857$	−9.52424	−0.325342	−0.162671	−	0.986680i	$-0.552011\pi$
$857$	−9.52424	−0.325342	−0.162671	+	0.986680i	$0.552011\pi$
$858$	37.7456	1.28861
$859$	−50.4885	−1.72265	−0.861323	−	0.508058i	$-0.830364\pi$
$859$	−50.4885	−1.72265	−0.861323	+	0.508058i	$0.830364\pi$
$860$	21.2924	0.726064
$861$	−1.67924	−0.0572284
$862$	28.6174	0.974714
$863$	−53.3641	−1.81654	−0.908268	−	0.418389i	$-0.862595\pi$
$863$	−53.3641	−1.81654	−0.908268	+	0.418389i	$0.862595\pi$
$864$	3.01965	0.102731
$865$	21.1612	0.719503
$866$	13.3446	0.453469
$867$	1.00000	0.0339618
$868$	−17.7642	−0.602955
$869$	3.96232	0.134413
$870$	−12.6980	−0.430502
$871$	70.3139	2.38250
$872$	17.8073	0.603030
$873$	−2.41881	−0.0818642
$874$	−9.58651	−0.324269
$875$	128.976	4.36018
$876$	2.10135	0.0709979
$877$	−38.7198	−1.30748	−0.653738	−	0.756721i	$-0.726800\pi$
$877$	−38.7198	−1.30748	−0.653738	+	0.756721i	$0.726800\pi$
$878$	44.5783	1.50444
$879$	21.0376	0.709582
$880$	−78.9856	−2.66260
$881$	−11.1427	−0.375408	−0.187704	−	0.982226i	$-0.560105\pi$
$881$	−11.1427	−0.375408	−0.187704	+	0.982226i	$0.560105\pi$
$882$	−17.8407	−0.600728
$883$	−26.2879	−0.884660	−0.442330	−	0.896852i	$-0.645848\pi$
$883$	−26.2879	−0.884660	−0.442330	+	0.896852i	$0.645848\pi$
$884$	3.27042	0.109996
$885$	−30.2987	−1.01848
$886$	3.96223	0.133114
$887$	36.6632	1.23103	0.615515	−	0.788125i	$-0.288948\pi$
$887$	36.6632	1.23103	0.615515	+	0.788125i	$0.288948\pi$
$888$	11.0988	0.372452
$889$	−25.1754	−0.844355
$890$	86.8203	2.91022
$891$	−3.96232	−0.132743
$892$	−11.8287	−0.396055
$893$	−12.9550	−0.433524
$894$	35.4664	1.18617
$895$	75.0471	2.50855
$896$	58.2189	1.94496
$897$	−10.5639	−0.352720
$898$	22.5972	0.754079
$899$	−14.5509	−0.485300
$900$	6.72838	0.224279
$901$	−6.91150	−0.230255
$902$	2.49119	0.0829476
$903$	39.8519	1.32619
$904$	0.706971	0.0235135
$905$	90.2229	2.99911
$906$	−29.2327	−0.971192
$907$	−50.2535	−1.66864	−0.834320	−	0.551281i	$-0.814139\pi$
$907$	−50.2535	−1.66864	−0.834320	+	0.551281i	$0.814139\pi$
$908$	−1.17741	−0.0390738
$909$	−8.39736	−0.278523
$910$	−168.818	−5.59627
$911$	−17.8003	−0.589751	−0.294876	−	0.955536i	$-0.595278\pi$
$911$	−17.8003	−0.589751	−0.294876	+	0.955536i	$0.595278\pi$
$912$	16.2706	0.538772
$913$	8.94325	0.295978
$914$	−23.8493	−0.788864
$915$	13.8793	0.458836
$916$	4.71602	0.155822
$917$	19.7882	0.653465
$918$	−1.59625	−0.0526840
$919$	−22.0773	−0.728264	−0.364132	−	0.931347i	$-0.618634\pi$
$919$	−22.0773	−0.728264	−0.364132	+	0.931347i	$0.618634\pi$
$920$	17.0538	0.562245
$921$	−30.0126	−0.988949
$922$	−54.3823	−1.79098
$923$	84.0951	2.76802
$924$	9.25750	0.304549
$925$	58.7945	1.93315
$926$	−40.6877	−1.33708
$927$	7.46747	0.245264
$928$	−5.77891	−0.189702
$929$	−24.7231	−0.811138	−0.405569	−	0.914064i	$-0.632927\pi$
$929$	−24.7231	−0.811138	−0.405569	+	0.914064i	$0.632927\pi$
$930$	50.4483	1.65427
$931$	−37.9195	−1.24276
$932$	−12.6097	−0.413045
$933$	−2.19918	−0.0719978
$934$	−32.5876	−1.06630
$935$	16.4701	0.538629
$936$	13.8319	0.452109
$937$	4.84184	0.158176	0.0790880	−	0.996868i	$-0.474799\pi$
$937$	4.84184	0.158176	0.0790880	+	0.996868i	$0.474799\pi$
$938$	80.1830	2.61807
$939$	29.3593	0.958104
$940$	−8.69802	−0.283698
$941$	51.7516	1.68705	0.843527	−	0.537086i	$-0.180475\pi$
$941$	51.7516	1.68705	0.843527	+	0.537086i	$0.180475\pi$
$942$	−5.88496	−0.191742
$943$	−0.697214	−0.0227044
$944$	−34.9567	−1.13774
$945$	17.7216	0.576483
$946$	−59.1211	−1.92219
$947$	−28.9478	−0.940676	−0.470338	−	0.882486i	$-0.655868\pi$
$947$	−28.9478	−0.940676	−0.470338	+	0.882486i	$0.655868\pi$
$948$	−0.548008	−0.0177985
$949$	22.8838	0.742838
$950$	66.4928	2.15731
$951$	17.5501	0.569102
$952$	−9.88147	−0.320260
$953$	−18.2519	−0.591236	−0.295618	−	0.955306i	$-0.595526\pi$
$953$	−18.2519	−0.591236	−0.295618	+	0.955306i	$0.595526\pi$
$954$	11.0325	0.357189
$955$	35.7012	1.15526
$956$	−4.23364	−0.136926
$957$	7.58296	0.245122
$958$	−1.44500	−0.0466858
$959$	−28.4756	−0.919525
$960$	−19.8327	−0.640097
$961$	26.8099	0.864835
$962$	−45.6173	−1.47076
$963$	−13.9703	−0.450187
$964$	13.6714	0.440326
$965$	38.7678	1.24798
$966$	−12.0467	−0.387595
$967$	−30.2945	−0.974204	−0.487102	−	0.873345i	$-0.661946\pi$
$967$	−30.2945	−0.974204	−0.487102	+	0.873345i	$0.661946\pi$
$968$	10.8934	0.350128
$969$	−3.39274	−0.108990
$970$	−16.0490	−0.515301
$971$	2.18036	0.0699710	0.0349855	−	0.999388i	$-0.488861\pi$
$971$	2.18036	0.0699710	0.0349855	+	0.999388i	$0.488861\pi$
$972$	0.548008	0.0175774
$973$	66.7974	2.14143
$974$	40.4368	1.29568
$975$	73.2723	2.34659
$976$	16.0131	0.512567
$977$	−15.4316	−0.493702	−0.246851	−	0.969053i	$-0.579396\pi$
$977$	−15.4316	−0.493702	−0.246851	+	0.969053i	$0.579396\pi$
$978$	12.8307	0.410280
$979$	−51.8473	−1.65705
$980$	−25.4592	−0.813263
$981$	7.68304	0.245300
$982$	16.1033	0.513878
$983$	−31.6956	−1.01093	−0.505467	−	0.862846i	$-0.668680\pi$
$983$	−31.6956	−1.01093	−0.505467	+	0.862846i	$0.668680\pi$
$984$	0.912895	0.0291020
$985$	24.9014	0.793425
$986$	3.05484	0.0972861
$987$	−16.2797	−0.518187
$988$	−11.0957	−0.353000
$989$	16.5463	0.526143
$990$	−26.2903	−0.835561
$991$	−37.0238	−1.17610	−0.588050	−	0.808824i	$-0.700104\pi$
$991$	−37.0238	−1.17610	−0.588050	+	0.808824i	$0.700104\pi$
$992$	22.9593	0.728957
$993$	1.14543	0.0363490
$994$	95.8985	3.04171
$995$	−15.9762	−0.506480
$996$	−1.23689	−0.0391924
$997$	60.3970	1.91279	0.956397	−	0.292071i	$-0.0943445\pi$
$997$	60.3970	1.91279	0.956397	+	0.292071i	$0.0943445\pi$
$998$	57.0674	1.80644
$999$	4.78864	0.151506

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.e.1.6	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.e.1.6	✓	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.59625 q^{2} +1.00000 q^{3} +0.548008 q^{4} -4.15667 q^{5} -1.59625 q^{6} -4.26341 q^{7} +2.31774 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.59625 q^{2} +1.00000 q^{3} +0.548008 q^{4} -4.15667 q^{5} -1.59625 q^{6} -4.26341 q^{7} +2.31774 q^{8} +1.00000 q^{9} +6.63507 q^{10} -3.96232 q^{11} +0.548008 q^{12} +5.96783 q^{13} +6.80546 q^{14} -4.15667 q^{15} -4.79570 q^{16} +1.00000 q^{17} -1.59625 q^{18} -3.39274 q^{19} -2.27789 q^{20} -4.26341 q^{21} +6.32485 q^{22} -1.77015 q^{23} +2.31774 q^{24} +12.2779 q^{25} -9.52613 q^{26} +1.00000 q^{27} -2.33638 q^{28} -1.91377 q^{29} +6.63507 q^{30} +7.60328 q^{31} +3.01965 q^{32} -3.96232 q^{33} -1.59625 q^{34} +17.7216 q^{35} +0.548008 q^{36} +4.78864 q^{37} +5.41565 q^{38} +5.96783 q^{39} -9.63408 q^{40} +0.393873 q^{41} +6.80546 q^{42} -9.34742 q^{43} -2.17138 q^{44} -4.15667 q^{45} +2.82560 q^{46} +3.81846 q^{47} -4.79570 q^{48} +11.1767 q^{49} -19.5986 q^{50} +1.00000 q^{51} +3.27042 q^{52} -6.91150 q^{53} -1.59625 q^{54} +16.4701 q^{55} -9.88147 q^{56} -3.39274 q^{57} +3.05484 q^{58} +7.28917 q^{59} -2.27789 q^{60} -3.33905 q^{61} -12.1367 q^{62} -4.26341 q^{63} +4.77129 q^{64} -24.8063 q^{65} +6.32485 q^{66} +11.7822 q^{67} +0.548008 q^{68} -1.77015 q^{69} -28.2880 q^{70} +14.0914 q^{71} +2.31774 q^{72} +3.83452 q^{73} -7.64386 q^{74} +12.2779 q^{75} -1.85925 q^{76} +16.8930 q^{77} -9.52613 q^{78} -1.00000 q^{79} +19.9341 q^{80} +1.00000 q^{81} -0.628719 q^{82} -2.25707 q^{83} -2.33638 q^{84} -4.15667 q^{85} +14.9208 q^{86} -1.91377 q^{87} -9.18364 q^{88} +13.0851 q^{89} +6.63507 q^{90} -25.4433 q^{91} -0.970055 q^{92} +7.60328 q^{93} -6.09521 q^{94} +14.1025 q^{95} +3.01965 q^{96} -2.41881 q^{97} -17.8407 q^{98} -3.96232 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * q^99

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