LMFDB - Embedded newform 2678.2.a.w.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2678,2,Mod(1,2678)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2678, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2678.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2678 = 2 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2678.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:	$21.3839376613$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 6 x^{18} - 25 x^{17} + 203 x^{16} + 149 x^{15} - 2691 x^{14} + 997 x^{13} + 17945 x^{12} + \cdots - 992 $ x^19 - 6x^18 - 25x^17 + 203x^16 + 149x^15 - 2691x^14 + 997x^13 + 17945x^12 - 16121x^11 - 64301x^10 + 77853x^9 + 121033x^8 - 174824x^7 - 105553x^6 + 182160x^5 + 27788x^4 - 76124x^3 + 6952x^2 + 7152x - 992
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.15456$ of defining polynomial
Character	$\chi$	$=$	2678.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.15456 q^{3} +1.00000 q^{4} -0.187336 q^{5} -2.15456 q^{6} -4.59782 q^{7} +1.00000 q^{8} +1.64213 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.15456 q^{3} +1.00000 q^{4} -0.187336 q^{5} -2.15456 q^{6} -4.59782 q^{7} +1.00000 q^{8} +1.64213 q^{9} -0.187336 q^{10} +0.328880 q^{11} -2.15456 q^{12} +1.00000 q^{13} -4.59782 q^{14} +0.403628 q^{15} +1.00000 q^{16} -3.70849 q^{17} +1.64213 q^{18} +3.68044 q^{19} -0.187336 q^{20} +9.90629 q^{21} +0.328880 q^{22} -0.497084 q^{23} -2.15456 q^{24} -4.96491 q^{25} +1.00000 q^{26} +2.92562 q^{27} -4.59782 q^{28} -10.1557 q^{29} +0.403628 q^{30} -2.20858 q^{31} +1.00000 q^{32} -0.708591 q^{33} -3.70849 q^{34} +0.861340 q^{35} +1.64213 q^{36} +8.18502 q^{37} +3.68044 q^{38} -2.15456 q^{39} -0.187336 q^{40} -4.14775 q^{41} +9.90629 q^{42} +9.41221 q^{43} +0.328880 q^{44} -0.307631 q^{45} -0.497084 q^{46} +8.47174 q^{47} -2.15456 q^{48} +14.1400 q^{49} -4.96491 q^{50} +7.99017 q^{51} +1.00000 q^{52} -7.92357 q^{53} +2.92562 q^{54} -0.0616112 q^{55} -4.59782 q^{56} -7.92973 q^{57} -10.1557 q^{58} -9.67420 q^{59} +0.403628 q^{60} +4.27086 q^{61} -2.20858 q^{62} -7.55022 q^{63} +1.00000 q^{64} -0.187336 q^{65} -0.708591 q^{66} +15.0598 q^{67} -3.70849 q^{68} +1.07100 q^{69} +0.861340 q^{70} +6.49844 q^{71} +1.64213 q^{72} +3.70401 q^{73} +8.18502 q^{74} +10.6972 q^{75} +3.68044 q^{76} -1.51213 q^{77} -2.15456 q^{78} -0.0945017 q^{79} -0.187336 q^{80} -11.2298 q^{81} -4.14775 q^{82} +12.9907 q^{83} +9.90629 q^{84} +0.694736 q^{85} +9.41221 q^{86} +21.8811 q^{87} +0.328880 q^{88} +15.2319 q^{89} -0.307631 q^{90} -4.59782 q^{91} -0.497084 q^{92} +4.75851 q^{93} +8.47174 q^{94} -0.689480 q^{95} -2.15456 q^{96} -7.17216 q^{97} +14.1400 q^{98} +0.540063 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 19 q^{2} + 6 q^{3} + 19 q^{4} + q^{5} + 6 q^{6} + 13 q^{7} + 19 q^{8} + 29 q^{9}+O(q^{10}) $ 19 * q + 19 * q^2 + 6 * q^3 + 19 * q^4 + q^5 + 6 * q^6 + 13 * q^7 + 19 * q^8 + 29 * q^9	\( 19 q + 19 q^{2} + 6 q^{3} + 19 q^{4} + q^{5} + 6 q^{6} + 13 q^{7} + 19 q^{8} + 29 q^{9} + q^{10} + 7 q^{11} + 6 q^{12} + 19 q^{13} + 13 q^{14} + 3 q^{15} + 19 q^{16} + 15 q^{17} + 29 q^{18} + 22 q^{19} + q^{20} - 2 q^{21} + 7 q^{22} + 9 q^{23} + 6 q^{24} + 34 q^{25} + 19 q^{26} + 21 q^{27} + 13 q^{28} - 5 q^{29} + 3 q^{30} + 15 q^{31} + 19 q^{32} + 15 q^{34} + 6 q^{35} + 29 q^{36} + 3 q^{37} + 22 q^{38} + 6 q^{39} + q^{40} + 2 q^{41} - 2 q^{42} + 23 q^{43} + 7 q^{44} - 18 q^{45} + 9 q^{46} + 28 q^{47} + 6 q^{48} + 50 q^{49} + 34 q^{50} - 6 q^{51} + 19 q^{52} - 11 q^{53} + 21 q^{54} + 46 q^{55} + 13 q^{56} + 8 q^{57} - 5 q^{58} + 34 q^{59} + 3 q^{60} + 17 q^{61} + 15 q^{62} + 33 q^{63} + 19 q^{64} + q^{65} + 13 q^{67} + 15 q^{68} - 42 q^{69} + 6 q^{70} + 15 q^{71} + 29 q^{72} + 27 q^{73} + 3 q^{74} + 63 q^{75} + 22 q^{76} - 45 q^{77} + 6 q^{78} + 31 q^{79} + q^{80} + 75 q^{81} + 2 q^{82} + 46 q^{83} - 2 q^{84} - 13 q^{85} + 23 q^{86} + 53 q^{87} + 7 q^{88} + 4 q^{89} - 18 q^{90} + 13 q^{91} + 9 q^{92} - 12 q^{93} + 28 q^{94} - 47 q^{95} + 6 q^{96} + 2 q^{97} + 50 q^{98} - 25 q^{99}+O(q^{100}) \) 19 * q + 19 * q^2 + 6 * q^3 + 19 * q^4 + q^5 + 6 * q^6 + 13 * q^7 + 19 * q^8 + 29 * q^9 + q^10 + 7 * q^11 + 6 * q^12 + 19 * q^13 + 13 * q^14 + 3 * q^15 + 19 * q^16 + 15 * q^17 + 29 * q^18 + 22 * q^19 + q^20 - 2 * q^21 + 7 * q^22 + 9 * q^23 + 6 * q^24 + 34 * q^25 + 19 * q^26 + 21 * q^27 + 13 * q^28 - 5 * q^29 + 3 * q^30 + 15 * q^31 + 19 * q^32 + 15 * q^34 + 6 * q^35 + 29 * q^36 + 3 * q^37 + 22 * q^38 + 6 * q^39 + q^40 + 2 * q^41 - 2 * q^42 + 23 * q^43 + 7 * q^44 - 18 * q^45 + 9 * q^46 + 28 * q^47 + 6 * q^48 + 50 * q^49 + 34 * q^50 - 6 * q^51 + 19 * q^52 - 11 * q^53 + 21 * q^54 + 46 * q^55 + 13 * q^56 + 8 * q^57 - 5 * q^58 + 34 * q^59 + 3 * q^60 + 17 * q^61 + 15 * q^62 + 33 * q^63 + 19 * q^64 + q^65 + 13 * q^67 + 15 * q^68 - 42 * q^69 + 6 * q^70 + 15 * q^71 + 29 * q^72 + 27 * q^73 + 3 * q^74 + 63 * q^75 + 22 * q^76 - 45 * q^77 + 6 * q^78 + 31 * q^79 + q^80 + 75 * q^81 + 2 * q^82 + 46 * q^83 - 2 * q^84 - 13 * q^85 + 23 * q^86 + 53 * q^87 + 7 * q^88 + 4 * q^89 - 18 * q^90 + 13 * q^91 + 9 * q^92 - 12 * q^93 + 28 * q^94 - 47 * q^95 + 6 * q^96 + 2 * q^97 + 50 * q^98 - 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.15456	−1.24394	−0.621968	−	0.783043i	$-0.713667\pi$
$3$	−2.15456	−1.24394	−0.621968	+	0.783043i	$0.713667\pi$
$4$	1.00000	0.500000
$5$	−0.187336	−0.0837794	−0.0418897	−	0.999122i	$-0.513338\pi$
$5$	−0.187336	−0.0837794	−0.0418897	+	0.999122i	$0.513338\pi$
$6$	−2.15456	−0.879595
$7$	−4.59782	−1.73781	−0.868907	−	0.494975i	$-0.835177\pi$
$7$	−4.59782	−1.73781	−0.868907	+	0.494975i	$0.835177\pi$
$8$	1.00000	0.353553
$9$	1.64213	0.547376
$10$	−0.187336	−0.0592410
$11$	0.328880	0.0991609	0.0495805	−	0.998770i	$-0.484212\pi$
$11$	0.328880	0.0991609	0.0495805	+	0.998770i	$0.484212\pi$
$12$	−2.15456	−0.621968
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−4.59782	−1.22882
$15$	0.403628	0.104216
$16$	1.00000	0.250000
$17$	−3.70849	−0.899442	−0.449721	−	0.893169i	$-0.648477\pi$
$17$	−3.70849	−0.899442	−0.449721	+	0.893169i	$0.648477\pi$
$18$	1.64213	0.387053
$19$	3.68044	0.844351	0.422175	−	0.906514i	$-0.361267\pi$
$19$	3.68044	0.844351	0.422175	+	0.906514i	$0.361267\pi$
$20$	−0.187336	−0.0418897
$21$	9.90629	2.16173
$22$	0.328880	0.0701174
$23$	−0.497084	−0.103649	−0.0518246	−	0.998656i	$-0.516504\pi$
$23$	−0.497084	−0.103649	−0.0518246	+	0.998656i	$0.516504\pi$
$24$	−2.15456	−0.439798
$25$	−4.96491	−0.992981
$26$	1.00000	0.196116
$27$	2.92562	0.563035
$28$	−4.59782	−0.868907
$29$	−10.1557	−1.88587	−0.942936	−	0.332973i	$-0.891948\pi$
$29$	−10.1557	−1.88587	−0.942936	+	0.332973i	$0.891948\pi$
$30$	0.403628	0.0736920
$31$	−2.20858	−0.396672	−0.198336	−	0.980134i	$-0.563554\pi$
$31$	−2.20858	−0.396672	−0.198336	+	0.980134i	$0.563554\pi$
$32$	1.00000	0.176777
$33$	−0.708591	−0.123350
$34$	−3.70849	−0.636001
$35$	0.861340	0.145593
$36$	1.64213	0.273688
$37$	8.18502	1.34561	0.672805	−	0.739820i	$-0.265089\pi$
$37$	8.18502	1.34561	0.672805	+	0.739820i	$0.265089\pi$
$38$	3.68044	0.597046
$39$	−2.15456	−0.345006
$40$	−0.187336	−0.0296205
$41$	−4.14775	−0.647770	−0.323885	−	0.946096i	$-0.604989\pi$
$41$	−4.14775	−0.647770	−0.323885	+	0.946096i	$0.604989\pi$
$42$	9.90629	1.52857
$43$	9.41221	1.43535	0.717674	−	0.696379i	$-0.245207\pi$
$43$	9.41221	1.43535	0.717674	+	0.696379i	$0.245207\pi$
$44$	0.328880	0.0495805
$45$	−0.307631	−0.0458589
$46$	−0.497084	−0.0732910
$47$	8.47174	1.23573	0.617865	−	0.786284i	$-0.287998\pi$
$47$	8.47174	1.23573	0.617865	+	0.786284i	$0.287998\pi$
$48$	−2.15456	−0.310984
$49$	14.1400	2.02000
$50$	−4.96491	−0.702144
$51$	7.99017	1.11885
$52$	1.00000	0.138675
$53$	−7.92357	−1.08839	−0.544193	−	0.838960i	$-0.683164\pi$
$53$	−7.92357	−1.08839	−0.544193	+	0.838960i	$0.683164\pi$
$54$	2.92562	0.398126
$55$	−0.0616112	−0.00830765
$56$	−4.59782	−0.614410
$57$	−7.92973	−1.05032
$58$	−10.1557	−1.33351
$59$	−9.67420	−1.25947	−0.629737	−	0.776808i	$-0.716837\pi$
$59$	−9.67420	−1.25947	−0.629737	+	0.776808i	$0.716837\pi$
$60$	0.403628	0.0521081
$61$	4.27086	0.546828	0.273414	−	0.961897i	$-0.411847\pi$
$61$	4.27086	0.546828	0.273414	+	0.961897i	$0.411847\pi$
$62$	−2.20858	−0.280490
$63$	−7.55022	−0.951238
$64$	1.00000	0.125000
$65$	−0.187336	−0.0232362
$66$	−0.708591	−0.0872215
$67$	15.0598	1.83985	0.919926	−	0.392093i	$-0.128249\pi$
$67$	15.0598	1.83985	0.919926	+	0.392093i	$0.128249\pi$
$68$	−3.70849	−0.449721
$69$	1.07100	0.128933
$70$	0.861340	0.102950
$71$	6.49844	0.771223	0.385612	−	0.922661i	$-0.373990\pi$
$71$	6.49844	0.771223	0.385612	+	0.922661i	$0.373990\pi$
$72$	1.64213	0.193527
$73$	3.70401	0.433522	0.216761	−	0.976225i	$-0.430451\pi$
$73$	3.70401	0.433522	0.216761	+	0.976225i	$0.430451\pi$
$74$	8.18502	0.951490
$75$	10.6972	1.23520
$76$	3.68044	0.422175
$77$	−1.51213	−0.172323
$78$	−2.15456	−0.243956
$79$	−0.0945017	−0.0106323	−0.00531613	−	0.999986i	$-0.501692\pi$
$79$	−0.0945017	−0.0106323	−0.00531613	+	0.999986i	$0.501692\pi$
$80$	−0.187336	−0.0209449
$81$	−11.2298	−1.24776
$82$	−4.14775	−0.458043
$83$	12.9907	1.42591	0.712957	−	0.701207i	$-0.247355\pi$
$83$	12.9907	1.42591	0.712957	+	0.701207i	$0.247355\pi$
$84$	9.90629	1.08086
$85$	0.694736	0.0753547
$86$	9.41221	1.01494
$87$	21.8811	2.34590
$88$	0.328880	0.0350587
$89$	15.2319	1.61458	0.807290	−	0.590155i	$-0.200933\pi$
$89$	15.2319	1.61458	0.807290	+	0.590155i	$0.200933\pi$
$90$	−0.307631	−0.0324271
$91$	−4.59782	−0.481983
$92$	−0.497084	−0.0518246
$93$	4.75851	0.493435
$94$	8.47174	0.873793
$95$	−0.689480	−0.0707392
$96$	−2.15456	−0.219899
$97$	−7.17216	−0.728222	−0.364111	−	0.931356i	$-0.618627\pi$
$97$	−7.17216	−0.728222	−0.364111	+	0.931356i	$0.618627\pi$
$98$	14.1400	1.42835
$99$	0.540063	0.0542783
$100$	−4.96491	−0.496491
$101$	11.8169	1.17583	0.587914	−	0.808923i	$-0.299949\pi$
$101$	11.8169	1.17583	0.587914	+	0.808923i	$0.299949\pi$
$102$	7.99017	0.791145
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	−1.85581	−0.181108
$106$	−7.92357	−0.769605
$107$	18.7936	1.81684	0.908421	−	0.418057i	$-0.137289\pi$
$107$	18.7936	1.81684	0.908421	+	0.418057i	$0.137289\pi$
$108$	2.92562	0.281517
$109$	8.76714	0.839740	0.419870	−	0.907584i	$-0.362076\pi$
$109$	8.76714	0.839740	0.419870	+	0.907584i	$0.362076\pi$
$110$	−0.0616112	−0.00587439
$111$	−17.6351	−1.67385
$112$	−4.59782	−0.434453
$113$	−7.73767	−0.727898	−0.363949	−	0.931419i	$-0.618572\pi$
$113$	−7.73767	−0.727898	−0.363949	+	0.931419i	$0.618572\pi$
$114$	−7.92973	−0.742687
$115$	0.0931220	0.00868367
$116$	−10.1557	−0.942936
$117$	1.64213	0.151815
$118$	−9.67420	−0.890583
$119$	17.0510	1.56306
$120$	0.403628	0.0368460
$121$	−10.8918	−0.990167
$122$	4.27086	0.386666
$123$	8.93658	0.805785
$124$	−2.20858	−0.198336
$125$	1.86679	0.166971
$126$	−7.55022	−0.672627
$127$	−10.3904	−0.922001	−0.461000	−	0.887400i	$-0.652509\pi$
$127$	−10.3904	−0.922001	−0.461000	+	0.887400i	$0.652509\pi$
$128$	1.00000	0.0883883
$129$	−20.2792	−1.78548
$130$	−0.187336	−0.0164305
$131$	9.57345	0.836437	0.418218	−	0.908347i	$-0.362655\pi$
$131$	9.57345	0.836437	0.418218	+	0.908347i	$0.362655\pi$
$132$	−0.708591	−0.0616749
$133$	−16.9220	−1.46732
$134$	15.0598	1.30097
$135$	−0.548075	−0.0471707
$136$	−3.70849	−0.318001
$137$	2.96154	0.253021	0.126511	−	0.991965i	$-0.459622\pi$
$137$	2.96154	0.253021	0.126511	+	0.991965i	$0.459622\pi$
$138$	1.07100	0.0911693
$139$	−2.45151	−0.207934	−0.103967	−	0.994581i	$-0.533154\pi$
$139$	−2.45151	−0.207934	−0.103967	+	0.994581i	$0.533154\pi$
$140$	0.861340	0.0727965
$141$	−18.2529	−1.53717
$142$	6.49844	0.545337
$143$	0.328880	0.0275023
$144$	1.64213	0.136844
$145$	1.90254	0.157997
$146$	3.70401	0.306546
$147$	−30.4654	−2.51275
$148$	8.18502	0.672805
$149$	−3.86857	−0.316925	−0.158463	−	0.987365i	$-0.550654\pi$
$149$	−3.86857	−0.316925	−0.158463	+	0.987365i	$0.550654\pi$
$150$	10.6972	0.873422
$151$	−0.122913	−0.0100025	−0.00500124	−	0.999987i	$-0.501592\pi$
$151$	−0.122913	−0.0100025	−0.00500124	+	0.999987i	$0.501592\pi$
$152$	3.68044	0.298523
$153$	−6.08982	−0.492333
$154$	−1.51213	−0.121851
$155$	0.413747	0.0332330
$156$	−2.15456	−0.172503
$157$	9.12275	0.728074	0.364037	−	0.931384i	$-0.381398\pi$
$157$	9.12275	0.728074	0.364037	+	0.931384i	$0.381398\pi$
$158$	−0.0945017	−0.00751815
$159$	17.0718	1.35388
$160$	−0.187336	−0.0148102
$161$	2.28550	0.180123
$162$	−11.2298	−0.882296
$163$	13.4625	1.05447	0.527234	−	0.849720i	$-0.323229\pi$
$163$	13.4625	1.05447	0.527234	+	0.849720i	$0.323229\pi$
$164$	−4.14775	−0.323885
$165$	0.132745	0.0103342
$166$	12.9907	1.00827
$167$	−11.1699	−0.864354	−0.432177	−	0.901789i	$-0.642254\pi$
$167$	−11.1699	−0.864354	−0.432177	+	0.901789i	$0.642254\pi$
$168$	9.90629	0.764287
$169$	1.00000	0.0769231
$170$	0.694736	0.0532838
$171$	6.04375	0.462177
$172$	9.41221	0.717674
$173$	−9.59704	−0.729649	−0.364825	−	0.931076i	$-0.618871\pi$
$173$	−9.59704	−0.729649	−0.364825	+	0.931076i	$0.618871\pi$
$174$	21.8811	1.65881
$175$	22.8278	1.72562
$176$	0.328880	0.0247902
$177$	20.8437	1.56670
$178$	15.2319	1.14168
$179$	−1.30621	−0.0976305	−0.0488153	−	0.998808i	$-0.515545\pi$
$179$	−1.30621	−0.0976305	−0.0488153	+	0.998808i	$0.515545\pi$
$180$	−0.307631	−0.0229294
$181$	−5.74427	−0.426968	−0.213484	−	0.976947i	$-0.568481\pi$
$181$	−5.74427	−0.426968	−0.213484	+	0.976947i	$0.568481\pi$
$182$	−4.59782	−0.340813
$183$	−9.20182	−0.680218
$184$	−0.497084	−0.0366455
$185$	−1.53335	−0.112734
$186$	4.75851	0.348911
$187$	−1.21965	−0.0891895
$188$	8.47174	0.617865
$189$	−13.4515	−0.978450
$190$	−0.689480	−0.0500202
$191$	−8.98678	−0.650261	−0.325130	−	0.945669i	$-0.605408\pi$
$191$	−8.98678	−0.650261	−0.325130	+	0.945669i	$0.605408\pi$
$192$	−2.15456	−0.155492
$193$	12.8072	0.921879	0.460939	−	0.887432i	$-0.347513\pi$
$193$	12.8072	0.921879	0.460939	+	0.887432i	$0.347513\pi$
$194$	−7.17216	−0.514931
$195$	0.403628	0.0289044
$196$	14.1400	1.01000
$197$	5.40914	0.385385	0.192693	−	0.981259i	$-0.438278\pi$
$197$	5.40914	0.385385	0.192693	+	0.981259i	$0.438278\pi$
$198$	0.540063	0.0383806
$199$	14.2126	1.00750	0.503751	−	0.863849i	$-0.331953\pi$
$199$	14.2126	1.00750	0.503751	+	0.863849i	$0.331953\pi$
$200$	−4.96491	−0.351072
$201$	−32.4473	−2.28866
$202$	11.8169	0.831436
$203$	46.6943	3.27730
$204$	7.99017	0.559424
$205$	0.777026	0.0542698
$206$	1.00000	0.0696733
$207$	−0.816276	−0.0567351
$208$	1.00000	0.0693375
$209$	1.21042	0.0837266
$210$	−1.85581	−0.128063
$211$	−3.04328	−0.209508	−0.104754	−	0.994498i	$-0.533406\pi$
$211$	−3.04328	−0.209508	−0.104754	+	0.994498i	$0.533406\pi$
$212$	−7.92357	−0.544193
$213$	−14.0013	−0.959352
$214$	18.7936	1.28470
$215$	−1.76325	−0.120253
$216$	2.92562	0.199063
$217$	10.1547	0.689343
$218$	8.76714	0.593786
$219$	−7.98051	−0.539273
$220$	−0.0616112	−0.00415382
$221$	−3.70849	−0.249460
$222$	−17.6351	−1.18359
$223$	−26.7244	−1.78960	−0.894798	−	0.446470i	$-0.852681\pi$
$223$	−26.7244	−1.78960	−0.894798	+	0.446470i	$0.852681\pi$
$224$	−4.59782	−0.307205
$225$	−8.15301	−0.543534
$226$	−7.73767	−0.514702
$227$	−8.87811	−0.589261	−0.294630	−	0.955611i	$-0.595197\pi$
$227$	−8.87811	−0.589261	−0.294630	+	0.955611i	$0.595197\pi$
$228$	−7.92973	−0.525159
$229$	6.75198	0.446183	0.223092	−	0.974797i	$-0.428385\pi$
$229$	6.75198	0.446183	0.223092	+	0.974797i	$0.428385\pi$
$230$	0.0931220	0.00614028
$231$	3.25798	0.214359
$232$	−10.1557	−0.666757
$233$	−27.6393	−1.81071	−0.905355	−	0.424656i	$-0.860395\pi$
$233$	−27.6393	−1.81071	−0.905355	+	0.424656i	$0.860395\pi$
$234$	1.64213	0.107349
$235$	−1.58707	−0.103529
$236$	−9.67420	−0.629737
$237$	0.203610	0.0132259
$238$	17.0510	1.10525
$239$	13.3371	0.862702	0.431351	−	0.902184i	$-0.358037\pi$
$239$	13.3371	0.862702	0.431351	+	0.902184i	$0.358037\pi$
$240$	0.403628	0.0260541
$241$	−15.9739	−1.02897	−0.514484	−	0.857500i	$-0.672016\pi$
$241$	−15.9739	−1.02897	−0.514484	+	0.857500i	$0.672016\pi$
$242$	−10.8918	−0.700154
$243$	15.4184	0.989093
$244$	4.27086	0.273414
$245$	−2.64893	−0.169234
$246$	8.93658	0.569776
$247$	3.68044	0.234181
$248$	−2.20858	−0.140245
$249$	−27.9892	−1.77375
$250$	1.86679	0.118066
$251$	15.9111	1.00430	0.502150	−	0.864781i	$-0.332543\pi$
$251$	15.9111	1.00430	0.502150	+	0.864781i	$0.332543\pi$
$252$	−7.55022	−0.475619
$253$	−0.163481	−0.0102779
$254$	−10.3904	−0.651953
$255$	−1.49685	−0.0937364
$256$	1.00000	0.0625000
$257$	16.9167	1.05524	0.527618	−	0.849482i	$-0.323085\pi$
$257$	16.9167	1.05524	0.527618	+	0.849482i	$0.323085\pi$
$258$	−20.2792	−1.26253
$259$	−37.6333	−2.33842
$260$	−0.187336	−0.0116181
$261$	−16.6770	−1.03228
$262$	9.57345	0.591450
$263$	2.29915	0.141772	0.0708858	−	0.997484i	$-0.477417\pi$
$263$	2.29915	0.141772	0.0708858	+	0.997484i	$0.477417\pi$
$264$	−0.708591	−0.0436108
$265$	1.48437	0.0911844
$266$	−16.9220	−1.03755
$267$	−32.8181	−2.00843
$268$	15.0598	0.919926
$269$	−10.0131	−0.610507	−0.305254	−	0.952271i	$-0.598741\pi$
$269$	−10.0131	−0.610507	−0.305254	+	0.952271i	$0.598741\pi$
$270$	−0.548075	−0.0333548
$271$	−1.35828	−0.0825095	−0.0412547	−	0.999149i	$-0.513136\pi$
$271$	−1.35828	−0.0825095	−0.0412547	+	0.999149i	$0.513136\pi$
$272$	−3.70849	−0.224860
$273$	9.90629	0.599556
$274$	2.96154	0.178913
$275$	−1.63286	−0.0984649
$276$	1.07100	0.0644665
$277$	−4.52131	−0.271659	−0.135830	−	0.990732i	$-0.543370\pi$
$277$	−4.52131	−0.271659	−0.135830	+	0.990732i	$0.543370\pi$
$278$	−2.45151	−0.147032
$279$	−3.62677	−0.217129
$280$	0.861340	0.0514749
$281$	11.3414	0.676572	0.338286	−	0.941043i	$-0.390153\pi$
$281$	11.3414	0.676572	0.338286	+	0.941043i	$0.390153\pi$
$282$	−18.2529	−1.08694
$283$	33.5185	1.99247	0.996235	−	0.0866909i	$-0.0276292\pi$
$283$	33.5185	1.99247	0.996235	+	0.0866909i	$0.0276292\pi$
$284$	6.49844	0.385612
$285$	1.48553	0.0879950
$286$	0.328880	0.0194471
$287$	19.0706	1.12570
$288$	1.64213	0.0967634
$289$	−3.24708	−0.191005
$290$	1.90254	0.111721
$291$	15.4528	0.905861
$292$	3.70401	0.216761
$293$	31.7204	1.85313	0.926564	−	0.376138i	$-0.122748\pi$
$293$	31.7204	1.85313	0.926564	+	0.376138i	$0.122748\pi$
$294$	−30.4654	−1.77678
$295$	1.81233	0.105518
$296$	8.18502	0.475745
$297$	0.962175	0.0558311
$298$	−3.86857	−0.224100
$299$	−0.497084	−0.0287471
$300$	10.6972	0.617602
$301$	−43.2757	−2.49437
$302$	−0.122913	−0.00707283
$303$	−25.4603	−1.46265
$304$	3.68044	0.211088
$305$	−0.800088	−0.0458129
$306$	−6.08982	−0.348132
$307$	−20.6580	−1.17901	−0.589506	−	0.807764i	$-0.700678\pi$
$307$	−20.6580	−1.17901	−0.589506	+	0.807764i	$0.700678\pi$
$308$	−1.51213	−0.0861616
$309$	−2.15456	−0.122569
$310$	0.413747	0.0234993
$311$	22.1023	1.25330	0.626652	−	0.779299i	$-0.284425\pi$
$311$	22.1023	1.25330	0.626652	+	0.779299i	$0.284425\pi$
$312$	−2.15456	−0.121978
$313$	29.5927	1.67268	0.836340	−	0.548211i	$-0.184691\pi$
$313$	29.5927	1.67268	0.836340	+	0.548211i	$0.184691\pi$
$314$	9.12275	0.514826
$315$	1.41443	0.0796942
$316$	−0.0945017	−0.00531613
$317$	−5.91200	−0.332051	−0.166025	−	0.986121i	$-0.553093\pi$
$317$	−5.91200	−0.332051	−0.166025	+	0.986121i	$0.553093\pi$
$318$	17.0718	0.957340
$319$	−3.34001	−0.187005
$320$	−0.187336	−0.0104724
$321$	−40.4918	−2.26003
$322$	2.28550	0.127366
$323$	−13.6489	−0.759444
$324$	−11.2298	−0.623878
$325$	−4.96491	−0.275403
$326$	13.4625	0.745621
$327$	−18.8893	−1.04458
$328$	−4.14775	−0.229021
$329$	−38.9516	−2.14747
$330$	0.132745	0.00730737
$331$	−31.3956	−1.72566	−0.862829	−	0.505496i	$-0.831310\pi$
$331$	−31.3956	−1.72566	−0.862829	+	0.505496i	$0.831310\pi$
$332$	12.9907	0.712957
$333$	13.4409	0.736555
$334$	−11.1699	−0.611191
$335$	−2.82126	−0.154142
$336$	9.90629	0.540432
$337$	1.33581	0.0727661	0.0363831	−	0.999338i	$-0.488416\pi$
$337$	1.33581	0.0727661	0.0363831	+	0.999338i	$0.488416\pi$
$338$	1.00000	0.0543928
$339$	16.6713	0.905459
$340$	0.694736	0.0376774
$341$	−0.726356	−0.0393344
$342$	6.04375	0.326809
$343$	−32.8284	−1.77257
$344$	9.41221	0.507472
$345$	−0.200637	−0.0108019
$346$	−9.59704	−0.515940
$347$	4.75075	0.255034	0.127517	−	0.991836i	$-0.459299\pi$
$347$	4.75075	0.255034	0.127517	+	0.991836i	$0.459299\pi$
$348$	21.8811	1.17295
$349$	14.9577	0.800665	0.400332	−	0.916370i	$-0.368895\pi$
$349$	14.9577	0.800665	0.400332	+	0.916370i	$0.368895\pi$
$350$	22.8278	1.22019
$351$	2.92562	0.156158
$352$	0.328880	0.0175293
$353$	4.30807	0.229295	0.114648	−	0.993406i	$-0.463426\pi$
$353$	4.30807	0.229295	0.114648	+	0.993406i	$0.463426\pi$
$354$	20.8437	1.10783
$355$	−1.21740	−0.0646126
$356$	15.2319	0.807290
$357$	−36.7374	−1.94435
$358$	−1.30621	−0.0690352
$359$	19.2207	1.01443	0.507215	−	0.861819i	$-0.330675\pi$
$359$	19.2207	1.01443	0.507215	+	0.861819i	$0.330675\pi$
$360$	−0.307631	−0.0162136
$361$	−5.45437	−0.287072
$362$	−5.74427	−0.301912
$363$	23.4671	1.23170
$364$	−4.59782	−0.240991
$365$	−0.693896	−0.0363202
$366$	−9.20182	−0.480987
$367$	36.0377	1.88115	0.940576	−	0.339584i	$-0.110286\pi$
$367$	36.0377	1.88115	0.940576	+	0.339584i	$0.110286\pi$
$368$	−0.497084	−0.0259123
$369$	−6.81114	−0.354574
$370$	−1.53335	−0.0797152
$371$	36.4312	1.89141
$372$	4.75851	0.246717
$373$	5.69784	0.295023	0.147512	−	0.989060i	$-0.452874\pi$
$373$	5.69784	0.295023	0.147512	+	0.989060i	$0.452874\pi$
$374$	−1.21965	−0.0630665
$375$	−4.02211	−0.207701
$376$	8.47174	0.436897
$377$	−10.1557	−0.523047
$378$	−13.4515	−0.691869
$379$	−17.2353	−0.885317	−0.442658	−	0.896690i	$-0.645965\pi$
$379$	−17.2353	−0.885317	−0.442658	+	0.896690i	$0.645965\pi$
$380$	−0.689480	−0.0353696
$381$	22.3868	1.14691
$382$	−8.98678	−0.459804
$383$	−35.2519	−1.80129	−0.900644	−	0.434558i	$-0.856905\pi$
$383$	−35.2519	−1.80129	−0.900644	+	0.434558i	$0.856905\pi$
$384$	−2.15456	−0.109949
$385$	0.283277	0.0144371
$386$	12.8072	0.651867
$387$	15.4561	0.785675
$388$	−7.17216	−0.364111
$389$	−16.9738	−0.860606	−0.430303	−	0.902684i	$-0.641593\pi$
$389$	−16.9738	−0.860606	−0.430303	+	0.902684i	$0.641593\pi$
$390$	0.403628	0.0204385
$391$	1.84343	0.0932264
$392$	14.1400	0.714177
$393$	−20.6266	−1.04047
$394$	5.40914	0.272508
$395$	0.0177036	0.000890765 0
$396$	0.540063	0.0271392
$397$	25.6994	1.28981	0.644907	−	0.764261i	$-0.276896\pi$
$397$	25.6994	1.28981	0.644907	+	0.764261i	$0.276896\pi$
$398$	14.2126	0.712411
$399$	36.4595	1.82526
$400$	−4.96491	−0.248245
$401$	−14.5941	−0.728796	−0.364398	−	0.931243i	$-0.618725\pi$
$401$	−14.5941	−0.728796	−0.364398	+	0.931243i	$0.618725\pi$
$402$	−32.4473	−1.61832
$403$	−2.20858	−0.110017
$404$	11.8169	0.587914
$405$	2.10375	0.104536
$406$	46.6943	2.31740
$407$	2.69189	0.133432
$408$	7.99017	0.395572
$409$	−7.35012	−0.363440	−0.181720	−	0.983350i	$-0.558166\pi$
$409$	−7.35012	−0.363440	−0.181720	+	0.983350i	$0.558166\pi$
$410$	0.777026	0.0383746
$411$	−6.38080	−0.314742
$412$	1.00000	0.0492665
$413$	44.4803	2.18873
$414$	−0.816276	−0.0401178
$415$	−2.43363	−0.119462
$416$	1.00000	0.0490290
$417$	5.28193	0.258657
$418$	1.21042	0.0592036
$419$	−22.2191	−1.08547	−0.542737	−	0.839903i	$-0.682612\pi$
$419$	−22.2191	−1.08547	−0.542737	+	0.839903i	$0.682612\pi$
$420$	−1.85581	−0.0905542
$421$	6.26332	0.305255	0.152628	−	0.988284i	$-0.451226\pi$
$421$	6.26332	0.305255	0.152628	+	0.988284i	$0.451226\pi$
$422$	−3.04328	−0.148145
$423$	13.9117	0.676409
$424$	−7.92357	−0.384803
$425$	18.4123	0.893128
$426$	−14.0013	−0.678364
$427$	−19.6367	−0.950285
$428$	18.7936	0.908421
$429$	−0.708591	−0.0342111
$430$	−1.76325	−0.0850315
$431$	−28.8020	−1.38734	−0.693671	−	0.720292i	$-0.744008\pi$
$431$	−28.8020	−1.38734	−0.693671	+	0.720292i	$0.744008\pi$
$432$	2.92562	0.140759
$433$	35.2289	1.69299	0.846497	−	0.532394i	$-0.178708\pi$
$433$	35.2289	1.69299	0.846497	+	0.532394i	$0.178708\pi$
$434$	10.1547	0.487439
$435$	−4.09914	−0.196539
$436$	8.76714	0.419870
$437$	−1.82949	−0.0875162
$438$	−7.98051	−0.381324
$439$	26.1807	1.24954	0.624769	−	0.780810i	$-0.285193\pi$
$439$	26.1807	1.24954	0.624769	+	0.780810i	$0.285193\pi$
$440$	−0.0616112	−0.00293720
$441$	23.2197	1.10570
$442$	−3.70849	−0.176395
$443$	4.73550	0.224990	0.112495	−	0.993652i	$-0.464116\pi$
$443$	4.73550	0.224990	0.112495	+	0.993652i	$0.464116\pi$
$444$	−17.6351	−0.836926
$445$	−2.85349	−0.135269
$446$	−26.7244	−1.26544
$447$	8.33506	0.394235
$448$	−4.59782	−0.217227
$449$	−32.9613	−1.55554	−0.777770	−	0.628549i	$-0.783649\pi$
$449$	−32.9613	−1.55554	−0.777770	+	0.628549i	$0.783649\pi$
$450$	−8.15301	−0.384337
$451$	−1.36411	−0.0642335
$452$	−7.73767	−0.363949
$453$	0.264823	0.0124425
$454$	−8.87811	−0.416670
$455$	0.861340	0.0403802
$456$	−7.92973	−0.371343
$457$	15.6050	0.729971	0.364986	−	0.931013i	$-0.381074\pi$
$457$	15.6050	0.729971	0.364986	+	0.931013i	$0.381074\pi$
$458$	6.75198	0.315499
$459$	−10.8496	−0.506417
$460$	0.0931220	0.00434183
$461$	−36.9590	−1.72135	−0.860675	−	0.509154i	$-0.829958\pi$
$461$	−36.9590	−1.72135	−0.860675	+	0.509154i	$0.829958\pi$
$462$	3.25798	0.151575
$463$	−26.6148	−1.23689	−0.618446	−	0.785827i	$-0.712238\pi$
$463$	−26.6148	−1.23689	−0.618446	+	0.785827i	$0.712238\pi$
$464$	−10.1557	−0.471468
$465$	−0.891443	−0.0413397
$466$	−27.6393	−1.28037
$467$	8.05853	0.372904	0.186452	−	0.982464i	$-0.440301\pi$
$467$	8.05853	0.372904	0.186452	+	0.982464i	$0.440301\pi$
$468$	1.64213	0.0759074
$469$	−69.2425	−3.19732
$470$	−1.58707	−0.0732059
$471$	−19.6555	−0.905678
$472$	−9.67420	−0.445291
$473$	3.09548	0.142330
$474$	0.203610	0.00935210
$475$	−18.2730	−0.838424
$476$	17.0510	0.781531
$477$	−13.0115	−0.595757
$478$	13.3371	0.610023
$479$	−36.1507	−1.65177	−0.825883	−	0.563841i	$-0.809323\pi$
$479$	−36.1507	−1.65177	−0.825883	+	0.563841i	$0.809323\pi$
$480$	0.403628	0.0184230
$481$	8.18502	0.373205
$482$	−15.9739	−0.727590
$483$	−4.92426	−0.224061
$484$	−10.8918	−0.495084
$485$	1.34361	0.0610100
$486$	15.4184	0.699394
$487$	14.3866	0.651918	0.325959	−	0.945384i	$-0.394313\pi$
$487$	14.3866	0.651918	0.325959	+	0.945384i	$0.394313\pi$
$488$	4.27086	0.193333
$489$	−29.0059	−1.31169
$490$	−2.64893	−0.119667
$491$	4.33866	0.195801	0.0979004	−	0.995196i	$-0.468787\pi$
$491$	4.33866	0.195801	0.0979004	+	0.995196i	$0.468787\pi$
$492$	8.93658	0.402892
$493$	37.6625	1.69623
$494$	3.68044	0.165591
$495$	−0.101173	−0.00454741
$496$	−2.20858	−0.0991681
$497$	−29.8787	−1.34024
$498$	−27.9892	−1.25423
$499$	−11.8309	−0.529625	−0.264813	−	0.964300i	$-0.585310\pi$
$499$	−11.8309	−0.529625	−0.264813	+	0.964300i	$0.585310\pi$
$500$	1.86679	0.0834854
$501$	24.0663	1.07520
$502$	15.9111	0.710147
$503$	−16.8006	−0.749100	−0.374550	−	0.927207i	$-0.622203\pi$
$503$	−16.8006	−0.749100	−0.374550	+	0.927207i	$0.622203\pi$
$504$	−7.55022	−0.336313
$505$	−2.21374	−0.0985102
$506$	−0.163481	−0.00726761
$507$	−2.15456	−0.0956874
$508$	−10.3904	−0.461000
$509$	28.4521	1.26112	0.630558	−	0.776142i	$-0.282826\pi$
$509$	28.4521	1.26112	0.630558	+	0.776142i	$0.282826\pi$
$510$	−1.49685	−0.0662817
$511$	−17.0304	−0.753380
$512$	1.00000	0.0441942
$513$	10.7675	0.475399
$514$	16.9167	0.746164
$515$	−0.187336	−0.00825503
$516$	−20.2792	−0.892740
$517$	2.78618	0.122536
$518$	−37.6333	−1.65351
$519$	20.6774	0.907637
$520$	−0.187336	−0.00821525
$521$	5.60116	0.245391	0.122696	−	0.992444i	$-0.460846\pi$
$521$	5.60116	0.245391	0.122696	+	0.992444i	$0.460846\pi$
$522$	−16.6770	−0.729934
$523$	44.6180	1.95101	0.975503	−	0.219984i	$-0.0706006\pi$
$523$	44.6180	1.95101	0.975503	+	0.219984i	$0.0706006\pi$
$524$	9.57345	0.418218
$525$	−49.1838	−2.14656
$526$	2.29915	0.100248
$527$	8.19050	0.356784
$528$	−0.708591	−0.0308375
$529$	−22.7529	−0.989257
$530$	1.48437	0.0644771
$531$	−15.8863	−0.689406
$532$	−16.9220	−0.733662
$533$	−4.14775	−0.179659
$534$	−32.8181	−1.42018
$535$	−3.52072	−0.152214
$536$	15.0598	0.650486
$537$	2.81430	0.121446
$538$	−10.0131	−0.431694
$539$	4.65035	0.200305
$540$	−0.548075	−0.0235854
$541$	−41.8854	−1.80079	−0.900396	−	0.435070i	$-0.856723\pi$
$541$	−41.8854	−1.80079	−0.900396	+	0.435070i	$0.856723\pi$
$542$	−1.35828	−0.0583430
$543$	12.3764	0.531121
$544$	−3.70849	−0.159000
$545$	−1.64241	−0.0703529
$546$	9.90629	0.423950
$547$	−3.81681	−0.163195	−0.0815975	−	0.996665i	$-0.526002\pi$
$547$	−3.81681	−0.163195	−0.0815975	+	0.996665i	$0.526002\pi$
$548$	2.96154	0.126511
$549$	7.01330	0.299320
$550$	−1.63286	−0.0696252
$551$	−37.3776	−1.59234
$552$	1.07100	0.0455847
$553$	0.434502	0.0184769
$554$	−4.52131	−0.192092
$555$	3.30370	0.140234
$556$	−2.45151	−0.103967
$557$	29.2526	1.23947	0.619736	−	0.784810i	$-0.287240\pi$
$557$	29.2526	1.23947	0.619736	+	0.784810i	$0.287240\pi$
$558$	−3.62677	−0.153533
$559$	9.41221	0.398094
$560$	0.861340	0.0363983
$561$	2.62780	0.110946
$562$	11.3414	0.478408
$563$	−35.6139	−1.50095	−0.750474	−	0.660900i	$-0.770175\pi$
$563$	−35.6139	−1.50095	−0.750474	+	0.660900i	$0.770175\pi$
$564$	−18.2529	−0.768585
$565$	1.44955	0.0609829
$566$	33.5185	1.40889
$567$	51.6326	2.16837
$568$	6.49844	0.272669
$569$	3.19351	0.133879	0.0669394	−	0.997757i	$-0.478677\pi$
$569$	3.19351	0.133879	0.0669394	+	0.997757i	$0.478677\pi$
$570$	1.48553	0.0622219
$571$	−25.5638	−1.06981	−0.534907	−	0.844911i	$-0.679653\pi$
$571$	−25.5638	−1.06981	−0.534907	+	0.844911i	$0.679653\pi$
$572$	0.328880	0.0137511
$573$	19.3626	0.808883
$574$	19.0706	0.795993
$575$	2.46797	0.102922
$576$	1.64213	0.0684220
$577$	25.1518	1.04708	0.523541	−	0.852000i	$-0.324611\pi$
$577$	25.1518	1.04708	0.523541	+	0.852000i	$0.324611\pi$
$578$	−3.24708	−0.135061
$579$	−27.5938	−1.14676
$580$	1.90254	0.0789987
$581$	−59.7289	−2.47797
$582$	15.4528	0.640541
$583$	−2.60590	−0.107925
$584$	3.70401	0.153273
$585$	−0.307631	−0.0127190
$586$	31.7204	1.31036
$587$	42.2887	1.74544	0.872721	−	0.488220i	$-0.162354\pi$
$587$	42.2887	1.74544	0.872721	+	0.488220i	$0.162354\pi$
$588$	−30.4654	−1.25637
$589$	−8.12854	−0.334930
$590$	1.81233	0.0746125
$591$	−11.6543	−0.479394
$592$	8.18502	0.336402
$593$	22.5234	0.924924	0.462462	−	0.886639i	$-0.346966\pi$
$593$	22.5234	0.924924	0.462462	+	0.886639i	$0.346966\pi$
$594$	0.962175	0.0394785
$595$	−3.19427	−0.130952
$596$	−3.86857	−0.158463
$597$	−30.6218	−1.25327
$598$	−0.497084	−0.0203273
$599$	−23.1683	−0.946629	−0.473315	−	0.880893i	$-0.656943\pi$
$599$	−23.1683	−0.946629	−0.473315	+	0.880893i	$0.656943\pi$
$600$	10.6972	0.436711
$601$	29.8704	1.21844	0.609219	−	0.793002i	$-0.291483\pi$
$601$	29.8704	1.21844	0.609219	+	0.793002i	$0.291483\pi$
$602$	−43.2757	−1.76378
$603$	24.7302	1.00709
$604$	−0.122913	−0.00500124
$605$	2.04044	0.0829556
$606$	−25.4603	−1.03425
$607$	−12.9979	−0.527567	−0.263783	−	0.964582i	$-0.584970\pi$
$607$	−12.9979	−0.527567	−0.263783	+	0.964582i	$0.584970\pi$
$608$	3.68044	0.149261
$609$	−100.606	−4.07675
$610$	−0.800088	−0.0323946
$611$	8.47174	0.342730
$612$	−6.08982	−0.246166
$613$	−10.1764	−0.411022	−0.205511	−	0.978655i	$-0.565886\pi$
$613$	−10.1764	−0.411022	−0.205511	+	0.978655i	$0.565886\pi$
$614$	−20.6580	−0.833687
$615$	−1.67415	−0.0675082
$616$	−1.51213	−0.0609255
$617$	−30.6160	−1.23256	−0.616278	−	0.787529i	$-0.711360\pi$
$617$	−30.6160	−1.23256	−0.616278	+	0.787529i	$0.711360\pi$
$618$	−2.15456	−0.0866691
$619$	−18.6436	−0.749351	−0.374676	−	0.927156i	$-0.622246\pi$
$619$	−18.6436	−0.749351	−0.374676	+	0.927156i	$0.622246\pi$
$620$	0.413747	0.0166165
$621$	−1.45428	−0.0583581
$622$	22.1023	0.886220
$623$	−70.0337	−2.80584
$624$	−2.15456	−0.0862514
$625$	24.4748	0.978992
$626$	29.5927	1.18276
$627$	−2.60793	−0.104150
$628$	9.12275	0.364037
$629$	−30.3541	−1.21030
$630$	1.41443	0.0563523
$631$	41.5059	1.65232	0.826162	−	0.563432i	$-0.190519\pi$
$631$	41.5059	1.65232	0.826162	+	0.563432i	$0.190519\pi$
$632$	−0.0945017	−0.00375907
$633$	6.55693	0.260615
$634$	−5.91200	−0.234795
$635$	1.94650	0.0772447
$636$	17.0718	0.676941
$637$	14.1400	0.560246
$638$	−3.34001	−0.132232
$639$	10.6713	0.422149
$640$	−0.187336	−0.00740512
$641$	20.8448	0.823322	0.411661	−	0.911337i	$-0.364949\pi$
$641$	20.8448	0.823322	0.411661	+	0.911337i	$0.364949\pi$
$642$	−40.4918	−1.59809
$643$	−14.2935	−0.563682	−0.281841	−	0.959461i	$-0.590945\pi$
$643$	−14.2935	−0.563682	−0.281841	+	0.959461i	$0.590945\pi$
$644$	2.28550	0.0900615
$645$	3.79903	0.149587
$646$	−13.6489	−0.537008
$647$	30.7053	1.20715	0.603575	−	0.797306i	$-0.293742\pi$
$647$	30.7053	1.20715	0.603575	+	0.797306i	$0.293742\pi$
$648$	−11.2298	−0.441148
$649$	−3.18165	−0.124891
$650$	−4.96491	−0.194740
$651$	−21.8788	−0.857498
$652$	13.4625	0.527234
$653$	−34.9722	−1.36857	−0.684283	−	0.729216i	$-0.739885\pi$
$653$	−34.9722	−1.36857	−0.684283	+	0.729216i	$0.739885\pi$
$654$	−18.8893	−0.738631
$655$	−1.79346	−0.0700762
$656$	−4.14775	−0.161943
$657$	6.08246	0.237299
$658$	−38.9516	−1.51849
$659$	28.3618	1.10482	0.552409	−	0.833573i	$-0.313709\pi$
$659$	28.3618	1.10482	0.552409	+	0.833573i	$0.313709\pi$
$660$	0.132745	0.00516709
$661$	−12.7956	−0.497693	−0.248846	−	0.968543i	$-0.580051\pi$
$661$	−12.7956	−0.497693	−0.248846	+	0.968543i	$0.580051\pi$
$662$	−31.3956	−1.22022
$663$	7.99017	0.310313
$664$	12.9907	0.504137
$665$	3.17011	0.122932
$666$	13.4409	0.520823
$667$	5.04825	0.195469
$668$	−11.1699	−0.432177
$669$	57.5793	2.22614
$670$	−2.82126	−0.108995
$671$	1.40460	0.0542239
$672$	9.90629	0.382143
$673$	3.96159	0.152708	0.0763541	−	0.997081i	$-0.475672\pi$
$673$	3.96159	0.152708	0.0763541	+	0.997081i	$0.475672\pi$
$674$	1.33581	0.0514534
$675$	−14.5254	−0.559083
$676$	1.00000	0.0384615
$677$	−31.3026	−1.20306	−0.601529	−	0.798851i	$-0.705442\pi$
$677$	−31.3026	−1.20306	−0.601529	+	0.798851i	$0.705442\pi$
$678$	16.6713	0.640256
$679$	32.9763	1.26551
$680$	0.694736	0.0266419
$681$	19.1284	0.733003
$682$	−0.726356	−0.0278136
$683$	0.615750	0.0235610	0.0117805	−	0.999931i	$-0.496250\pi$
$683$	0.615750	0.0235610	0.0117805	+	0.999931i	$0.496250\pi$
$684$	6.04375	0.231089
$685$	−0.554804	−0.0211980
$686$	−32.8284	−1.25339
$687$	−14.5475	−0.555023
$688$	9.41221	0.358837
$689$	−7.92357	−0.301864
$690$	−0.200637	−0.00763812
$691$	15.4896	0.589252	0.294626	−	0.955613i	$-0.404805\pi$
$691$	15.4896	0.589252	0.294626	+	0.955613i	$0.404805\pi$
$692$	−9.59704	−0.364825
$693$	−2.48311	−0.0943256
$694$	4.75075	0.180336
$695$	0.459257	0.0174206
$696$	21.8811	0.829403
$697$	15.3819	0.582632
$698$	14.9577	0.566156
$699$	59.5505	2.25241
$700$	22.8278	0.862808
$701$	−5.07456	−0.191663	−0.0958316	−	0.995398i	$-0.530551\pi$
$701$	−5.07456	−0.191663	−0.0958316	+	0.995398i	$0.530551\pi$
$702$	2.92562	0.110420
$703$	30.1245	1.13617
$704$	0.328880	0.0123951
$705$	3.41943	0.128783
$706$	4.30807	0.162136
$707$	−54.3321	−2.04337
$708$	20.8437	0.783352
$709$	−13.0778	−0.491146	−0.245573	−	0.969378i	$-0.578976\pi$
$709$	−13.0778	−0.491146	−0.245573	+	0.969378i	$0.578976\pi$
$710$	−1.21740	−0.0456880
$711$	−0.155184	−0.00581985
$712$	15.2319	0.570840
$713$	1.09785	0.0411148
$714$	−36.7374	−1.37486
$715$	−0.0616112	−0.00230413
$716$	−1.30621	−0.0488153
$717$	−28.7355	−1.07315
$718$	19.2207	0.717311
$719$	−37.2698	−1.38993	−0.694965	−	0.719043i	$-0.744580\pi$
$719$	−37.2698	−1.38993	−0.694965	+	0.719043i	$0.744580\pi$
$720$	−0.307631	−0.0114647
$721$	−4.59782	−0.171232
$722$	−5.45437	−0.202991
$723$	34.4167	1.27997
$724$	−5.74427	−0.213484
$725$	50.4223	1.87264
$726$	23.4671	0.870946
$727$	−8.90769	−0.330368	−0.165184	−	0.986263i	$-0.552822\pi$
$727$	−8.90769	−0.330368	−0.165184	+	0.986263i	$0.552822\pi$
$728$	−4.59782	−0.170407
$729$	0.469467	0.0173877
$730$	−0.693896	−0.0256823
$731$	−34.9051	−1.29101
$732$	−9.20182	−0.340109
$733$	9.44560	0.348881	0.174441	−	0.984668i	$-0.444188\pi$
$733$	9.44560	0.348881	0.174441	+	0.984668i	$0.444188\pi$
$734$	36.0377	1.33017
$735$	5.70729	0.210516
$736$	−0.497084	−0.0183228
$737$	4.95287	0.182441
$738$	−6.81114	−0.250722
$739$	40.3881	1.48570	0.742849	−	0.669459i	$-0.233474\pi$
$739$	40.3881	1.48570	0.742849	+	0.669459i	$0.233474\pi$
$740$	−1.53335	−0.0563672
$741$	−7.92973	−0.291306
$742$	36.4312	1.33743
$743$	0.104634	0.00383865	0.00191932	−	0.999998i	$-0.499389\pi$
$743$	0.104634	0.00383865	0.00191932	+	0.999998i	$0.499389\pi$
$744$	4.75851	0.174456
$745$	0.724723	0.0265518
$746$	5.69784	0.208613
$747$	21.3324	0.780512
$748$	−1.21965	−0.0445947
$749$	−86.4095	−3.15733
$750$	−4.02211	−0.146867
$751$	0.967963	0.0353215	0.0176607	−	0.999844i	$-0.494378\pi$
$751$	0.967963	0.0353215	0.0176607	+	0.999844i	$0.494378\pi$
$752$	8.47174	0.308933
$753$	−34.2814	−1.24928
$754$	−10.1557	−0.369850
$755$	0.0230260	0.000838003 0
$756$	−13.4515	−0.489225
$757$	−5.67696	−0.206333	−0.103166	−	0.994664i	$-0.532897\pi$
$757$	−5.67696	−0.206333	−0.103166	+	0.994664i	$0.532897\pi$
$758$	−17.2353	−0.626014
$759$	0.352229	0.0127851
$760$	−0.689480	−0.0250101
$761$	40.2870	1.46040	0.730201	−	0.683233i	$-0.239426\pi$
$761$	40.2870	1.46040	0.730201	+	0.683233i	$0.239426\pi$
$762$	22.3868	0.810987
$763$	−40.3098	−1.45931
$764$	−8.98678	−0.325130
$765$	1.14085	0.0412474
$766$	−35.2519	−1.27370
$767$	−9.67420	−0.349315
$768$	−2.15456	−0.0777460
$769$	49.6800	1.79151	0.895753	−	0.444552i	$-0.146637\pi$
$769$	49.6800	1.79151	0.895753	+	0.444552i	$0.146637\pi$
$770$	0.283277	0.0102086
$771$	−36.4481	−1.31265
$772$	12.8072	0.460939
$773$	−6.83763	−0.245932	−0.122966	−	0.992411i	$-0.539241\pi$
$773$	−6.83763	−0.245932	−0.122966	+	0.992411i	$0.539241\pi$
$774$	15.4561	0.555556
$775$	10.9654	0.393888
$776$	−7.17216	−0.257465
$777$	81.0832	2.90884
$778$	−16.9738	−0.608540
$779$	−15.2656	−0.546945
$780$	0.403628	0.0144522
$781$	2.13720	0.0764752
$782$	1.84343	0.0659210
$783$	−29.7118	−1.06181
$784$	14.1400	0.504999
$785$	−1.70902	−0.0609977
$786$	−20.6266	−0.735726
$787$	4.84804	0.172814	0.0864070	−	0.996260i	$-0.472461\pi$
$787$	4.84804	0.172814	0.0864070	+	0.996260i	$0.472461\pi$
$788$	5.40914	0.192693
$789$	−4.95366	−0.176355
$790$	0.0177036	0.000629866 0
$791$	35.5764	1.26495
$792$	0.540063	0.0191903
$793$	4.27086	0.151663
$794$	25.6994	0.912036
$795$	−3.19817	−0.113428
$796$	14.2126	0.503751
$797$	−26.5459	−0.940303	−0.470152	−	0.882586i	$-0.655801\pi$
$797$	−26.5459	−0.940303	−0.470152	+	0.882586i	$0.655801\pi$
$798$	36.4595	1.29065
$799$	−31.4174	−1.11147
$800$	−4.96491	−0.175536
$801$	25.0128	0.883783
$802$	−14.5941	−0.515337
$803$	1.21817	0.0429884
$804$	−32.4473	−1.14433
$805$	−0.428158	−0.0150906
$806$	−2.20858	−0.0777938
$807$	21.5737	0.759432
$808$	11.8169	0.415718
$809$	31.2608	1.09907	0.549535	−	0.835471i	$-0.314805\pi$
$809$	31.2608	1.09907	0.549535	+	0.835471i	$0.314805\pi$
$810$	2.10375	0.0739183
$811$	−33.3551	−1.17126	−0.585628	−	0.810580i	$-0.699152\pi$
$811$	−33.3551	−1.17126	−0.585628	+	0.810580i	$0.699152\pi$
$812$	46.6943	1.63865
$813$	2.92649	0.102636
$814$	2.69189	0.0943506
$815$	−2.52203	−0.0883427
$816$	7.99017	0.279712
$817$	34.6411	1.21194
$818$	−7.35012	−0.256991
$819$	−7.55022	−0.263826
$820$	0.777026	0.0271349
$821$	38.1783	1.33243	0.666215	−	0.745759i	$-0.267913\pi$
$821$	38.1783	1.33243	0.666215	+	0.745759i	$0.267913\pi$
$822$	−6.38080	−0.222556
$823$	−25.8944	−0.902624	−0.451312	−	0.892366i	$-0.649044\pi$
$823$	−25.8944	−0.902624	−0.451312	+	0.892366i	$0.649044\pi$
$824$	1.00000	0.0348367
$825$	3.51809	0.122484
$826$	44.4803	1.54767
$827$	18.2580	0.634893	0.317447	−	0.948276i	$-0.397175\pi$
$827$	18.2580	0.634893	0.317447	+	0.948276i	$0.397175\pi$
$828$	−0.816276	−0.0283675
$829$	1.24322	0.0431787	0.0215894	−	0.999767i	$-0.493127\pi$
$829$	1.24322	0.0431787	0.0215894	+	0.999767i	$0.493127\pi$
$830$	−2.43363	−0.0844726
$831$	9.74143	0.337927
$832$	1.00000	0.0346688
$833$	−52.4380	−1.81687
$834$	5.28193	0.182898
$835$	2.09253	0.0724151
$836$	1.21042	0.0418633
$837$	−6.46145	−0.223340
$838$	−22.2191	−0.767546
$839$	27.2945	0.942311	0.471155	−	0.882050i	$-0.343837\pi$
$839$	27.2945	0.942311	0.471155	+	0.882050i	$0.343837\pi$
$840$	−1.85581	−0.0640315
$841$	74.1390	2.55652
$842$	6.26332	0.215848
$843$	−24.4357	−0.841612
$844$	−3.04328	−0.104754
$845$	−0.187336	−0.00644457
$846$	13.9117	0.478294
$847$	50.0788	1.72073
$848$	−7.92357	−0.272097
$849$	−72.2177	−2.47851
$850$	18.4123	0.631537
$851$	−4.06864	−0.139471
$852$	−14.0013	−0.479676
$853$	8.63303	0.295589	0.147795	−	0.989018i	$-0.452783\pi$
$853$	8.63303	0.295589	0.147795	+	0.989018i	$0.452783\pi$
$854$	−19.6367	−0.671953
$855$	−1.13222	−0.0387210
$856$	18.7936	0.642351
$857$	55.4151	1.89294	0.946472	−	0.322786i	$-0.104619\pi$
$857$	55.4151	1.89294	0.946472	+	0.322786i	$0.104619\pi$
$858$	−0.708591	−0.0241909
$859$	39.1845	1.33696	0.668479	−	0.743731i	$-0.266946\pi$
$859$	39.1845	1.33696	0.668479	+	0.743731i	$0.266946\pi$
$860$	−1.76325	−0.0601263
$861$	−41.0888	−1.40030
$862$	−28.8020	−0.980999
$863$	6.95890	0.236884	0.118442	−	0.992961i	$-0.462210\pi$
$863$	6.95890	0.236884	0.118442	+	0.992961i	$0.462210\pi$
$864$	2.92562	0.0995315
$865$	1.79788	0.0611296
$866$	35.2289	1.19713
$867$	6.99603	0.237598
$868$	10.1547	0.344671
$869$	−0.0310797	−0.00105431
$870$	−4.09914	−0.138974
$871$	15.0598	0.510283
$872$	8.76714	0.296893
$873$	−11.7776	−0.398611
$874$	−1.82949	−0.0618833
$875$	−8.58317	−0.290164
$876$	−7.98051	−0.269636
$877$	−5.99722	−0.202512	−0.101256	−	0.994860i	$-0.532286\pi$
$877$	−5.99722	−0.202512	−0.101256	+	0.994860i	$0.532286\pi$
$878$	26.1807	0.883557
$879$	−68.3436	−2.30517
$880$	−0.0616112	−0.00207691
$881$	19.7291	0.664689	0.332345	−	0.943158i	$-0.392160\pi$
$881$	19.7291	0.664689	0.332345	+	0.943158i	$0.392160\pi$
$882$	23.2197	0.781847
$883$	−2.57736	−0.0867350	−0.0433675	−	0.999059i	$-0.513809\pi$
$883$	−2.57736	−0.0867350	−0.0433675	+	0.999059i	$0.513809\pi$
$884$	−3.70849	−0.124730
$885$	−3.90478	−0.131258
$886$	4.73550	0.159092
$887$	12.3840	0.415814	0.207907	−	0.978149i	$-0.433335\pi$
$887$	12.3840	0.415814	0.207907	+	0.978149i	$0.433335\pi$
$888$	−17.6351	−0.591796
$889$	47.7733	1.60227
$890$	−2.85349	−0.0956494
$891$	−3.69325	−0.123729
$892$	−26.7244	−0.894798
$893$	31.1797	1.04339
$894$	8.33506	0.278766
$895$	0.244700	0.00817943
$896$	−4.59782	−0.153603
$897$	1.07100	0.0357596
$898$	−32.9613	−1.09993
$899$	22.4297	0.748074
$900$	−8.15301	−0.271767
$901$	29.3845	0.978940
$902$	−1.36411	−0.0454199
$903$	93.2400	3.10283
$904$	−7.73767	−0.257351
$905$	1.07611	0.0357711
$906$	0.264823	0.00879814
$907$	−5.37220	−0.178381	−0.0891905	−	0.996015i	$-0.528428\pi$
$907$	−5.37220	−0.178381	−0.0891905	+	0.996015i	$0.528428\pi$
$908$	−8.87811	−0.294630
$909$	19.4049	0.643620
$910$	0.861340	0.0285531
$911$	46.1363	1.52856	0.764281	−	0.644883i	$-0.223094\pi$
$911$	46.1363	1.52856	0.764281	+	0.644883i	$0.223094\pi$
$912$	−7.92973	−0.262579
$913$	4.27238	0.141395
$914$	15.6050	0.516168
$915$	1.72384	0.0569883
$916$	6.75198	0.223092
$917$	−44.0171	−1.45357
$918$	−10.8496	−0.358091
$919$	24.5590	0.810128	0.405064	−	0.914288i	$-0.367249\pi$
$919$	24.5590	0.810128	0.405064	+	0.914288i	$0.367249\pi$
$920$	0.0931220	0.00307014
$921$	44.5088	1.46662
$922$	−36.9590	−1.21718
$923$	6.49844	0.213899
$924$	3.25798	0.107180
$925$	−40.6379	−1.33616
$926$	−26.6148	−0.874615
$927$	1.64213	0.0539346
$928$	−10.1557	−0.333378
$929$	−22.2818	−0.731043	−0.365522	−	0.930803i	$-0.619109\pi$
$929$	−22.2818	−0.731043	−0.365522	+	0.930803i	$0.619109\pi$
$930$	−0.891443	−0.0292316
$931$	52.0413	1.70559
$932$	−27.6393	−0.905355
$933$	−47.6207	−1.55903
$934$	8.05853	0.263683
$935$	0.228485	0.00747224
$936$	1.64213	0.0536747
$937$	45.9426	1.50088	0.750440	−	0.660939i	$-0.229842\pi$
$937$	45.9426	1.50088	0.750440	+	0.660939i	$0.229842\pi$
$938$	−69.2425	−2.26085
$939$	−63.7593	−2.08071
$940$	−1.58707	−0.0517644
$941$	50.4572	1.64486	0.822429	−	0.568868i	$-0.192618\pi$
$941$	50.4572	1.64486	0.822429	+	0.568868i	$0.192618\pi$
$942$	−19.6555	−0.640411
$943$	2.06178	0.0671409
$944$	−9.67420	−0.314869
$945$	2.51995	0.0819740
$946$	3.09548	0.100643
$947$	20.7657	0.674795	0.337398	−	0.941362i	$-0.390453\pi$
$947$	20.7657	0.674795	0.337398	+	0.941362i	$0.390453\pi$
$948$	0.203610	0.00661293
$949$	3.70401	0.120237
$950$	−18.2730	−0.592855
$951$	12.7378	0.413050
$952$	17.0510	0.552626
$953$	57.1058	1.84984	0.924920	−	0.380162i	$-0.124132\pi$
$953$	57.1058	1.84984	0.924920	+	0.380162i	$0.124132\pi$
$954$	−13.0115	−0.421264
$955$	1.68355	0.0544785
$956$	13.3371	0.431351
$957$	7.19626	0.232622
$958$	−36.1507	−1.16798
$959$	−13.6166	−0.439703
$960$	0.403628	0.0130270
$961$	−26.1222	−0.842651
$962$	8.18502	0.263896
$963$	30.8614	0.994496
$964$	−15.9739	−0.514484
$965$	−2.39925	−0.0772345
$966$	−4.92426	−0.158435
$967$	51.8080	1.66603	0.833016	−	0.553249i	$-0.186612\pi$
$967$	51.8080	1.66603	0.833016	+	0.553249i	$0.186612\pi$
$968$	−10.8918	−0.350077
$969$	29.4073	0.944700
$970$	1.34361	0.0431406
$971$	29.8729	0.958666	0.479333	−	0.877633i	$-0.340879\pi$
$971$	29.8729	0.958666	0.479333	+	0.877633i	$0.340879\pi$
$972$	15.4184	0.494546
$973$	11.2716	0.361351
$974$	14.3866	0.460976
$975$	10.6972	0.342584
$976$	4.27086	0.136707
$977$	−23.5489	−0.753395	−0.376698	−	0.926336i	$-0.622940\pi$
$977$	−23.5489	−0.753395	−0.376698	+	0.926336i	$0.622940\pi$
$978$	−29.0059	−0.927505
$979$	5.00947	0.160103
$980$	−2.64893	−0.0846171
$981$	14.3968	0.459654
$982$	4.33866	0.138452
$983$	−7.68245	−0.245032	−0.122516	−	0.992467i	$-0.539096\pi$
$983$	−7.68245	−0.245032	−0.122516	+	0.992467i	$0.539096\pi$
$984$	8.93658	0.284888
$985$	−1.01333	−0.0322873
$986$	37.6625	1.19942
$987$	83.9235	2.67131
$988$	3.68044	0.117090
$989$	−4.67866	−0.148773
$990$	−0.101173	−0.00321550
$991$	37.3831	1.18751	0.593756	−	0.804645i	$-0.297644\pi$
$991$	37.3831	1.18751	0.593756	+	0.804645i	$0.297644\pi$
$992$	−2.20858	−0.0701224
$993$	67.6437	2.14661
$994$	−29.8787	−0.947694
$995$	−2.66253	−0.0844079
$996$	−27.9892	−0.886873
$997$	16.2622	0.515028	0.257514	−	0.966275i	$-0.417097\pi$
$997$	16.2622	0.515028	0.257514	+	0.966275i	$0.417097\pi$
$998$	−11.8309	−0.374502
$999$	23.9462	0.757625

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2678.2.a.w.1.3	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2678.2.a.w.1.3	✓	19	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:	\( N \)	\(=\)	\( 2678 = 2 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2678.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.15456 q^{3} +1.00000 q^{4} -0.187336 q^{5} -2.15456 q^{6} -4.59782 q^{7} +1.00000 q^{8} +1.64213 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.15456 q^{3} +1.00000 q^{4} -0.187336 q^{5} -2.15456 q^{6} -4.59782 q^{7} +1.00000 q^{8} +1.64213 q^{9} -0.187336 q^{10} +0.328880 q^{11} -2.15456 q^{12} +1.00000 q^{13} -4.59782 q^{14} +0.403628 q^{15} +1.00000 q^{16} -3.70849 q^{17} +1.64213 q^{18} +3.68044 q^{19} -0.187336 q^{20} +9.90629 q^{21} +0.328880 q^{22} -0.497084 q^{23} -2.15456 q^{24} -4.96491 q^{25} +1.00000 q^{26} +2.92562 q^{27} -4.59782 q^{28} -10.1557 q^{29} +0.403628 q^{30} -2.20858 q^{31} +1.00000 q^{32} -0.708591 q^{33} -3.70849 q^{34} +0.861340 q^{35} +1.64213 q^{36} +8.18502 q^{37} +3.68044 q^{38} -2.15456 q^{39} -0.187336 q^{40} -4.14775 q^{41} +9.90629 q^{42} +9.41221 q^{43} +0.328880 q^{44} -0.307631 q^{45} -0.497084 q^{46} +8.47174 q^{47} -2.15456 q^{48} +14.1400 q^{49} -4.96491 q^{50} +7.99017 q^{51} +1.00000 q^{52} -7.92357 q^{53} +2.92562 q^{54} -0.0616112 q^{55} -4.59782 q^{56} -7.92973 q^{57} -10.1557 q^{58} -9.67420 q^{59} +0.403628 q^{60} +4.27086 q^{61} -2.20858 q^{62} -7.55022 q^{63} +1.00000 q^{64} -0.187336 q^{65} -0.708591 q^{66} +15.0598 q^{67} -3.70849 q^{68} +1.07100 q^{69} +0.861340 q^{70} +6.49844 q^{71} +1.64213 q^{72} +3.70401 q^{73} +8.18502 q^{74} +10.6972 q^{75} +3.68044 q^{76} -1.51213 q^{77} -2.15456 q^{78} -0.0945017 q^{79} -0.187336 q^{80} -11.2298 q^{81} -4.14775 q^{82} +12.9907 q^{83} +9.90629 q^{84} +0.694736 q^{85} +9.41221 q^{86} +21.8811 q^{87} +0.328880 q^{88} +15.2319 q^{89} -0.307631 q^{90} -4.59782 q^{91} -0.497084 q^{92} +4.75851 q^{93} +8.47174 q^{94} -0.689480 q^{95} -2.15456 q^{96} -7.17216 q^{97} +14.1400 q^{98} +0.540063 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 19 q^{2} + 6 q^{3} + 19 q^{4} + q^{5} + 6 q^{6} + 13 q^{7} + 19 q^{8} + 29 q^{9}+O(q^{10}) \) 19 * q + 19 * q^2 + 6 * q^3 + 19 * q^4 + q^5 + 6 * q^6 + 13 * q^7 + 19 * q^8 + 29 * q^9	\( 19 q + 19 q^{2} + 6 q^{3} + 19 q^{4} + q^{5} + 6 q^{6} + 13 q^{7} + 19 q^{8} + 29 q^{9} + q^{10} + 7 q^{11} + 6 q^{12} + 19 q^{13} + 13 q^{14} + 3 q^{15} + 19 q^{16} + 15 q^{17} + 29 q^{18} + 22 q^{19} + q^{20} - 2 q^{21} + 7 q^{22} + 9 q^{23} + 6 q^{24} + 34 q^{25} + 19 q^{26} + 21 q^{27} + 13 q^{28} - 5 q^{29} + 3 q^{30} + 15 q^{31} + 19 q^{32} + 15 q^{34} + 6 q^{35} + 29 q^{36} + 3 q^{37} + 22 q^{38} + 6 q^{39} + q^{40} + 2 q^{41} - 2 q^{42} + 23 q^{43} + 7 q^{44} - 18 q^{45} + 9 q^{46} + 28 q^{47} + 6 q^{48} + 50 q^{49} + 34 q^{50} - 6 q^{51} + 19 q^{52} - 11 q^{53} + 21 q^{54} + 46 q^{55} + 13 q^{56} + 8 q^{57} - 5 q^{58} + 34 q^{59} + 3 q^{60} + 17 q^{61} + 15 q^{62} + 33 q^{63} + 19 q^{64} + q^{65} + 13 q^{67} + 15 q^{68} - 42 q^{69} + 6 q^{70} + 15 q^{71} + 29 q^{72} + 27 q^{73} + 3 q^{74} + 63 q^{75} + 22 q^{76} - 45 q^{77} + 6 q^{78} + 31 q^{79} + q^{80} + 75 q^{81} + 2 q^{82} + 46 q^{83} - 2 q^{84} - 13 q^{85} + 23 q^{86} + 53 q^{87} + 7 q^{88} + 4 q^{89} - 18 q^{90} + 13 q^{91} + 9 q^{92} - 12 q^{93} + 28 q^{94} - 47 q^{95} + 6 q^{96} + 2 q^{97} + 50 q^{98} - 25 q^{99}+O(q^{100}) \) 19 * q + 19 * q^2 + 6 * q^3 + 19 * q^4 + q^5 + 6 * q^6 + 13 * q^7 + 19 * q^8 + 29 * q^9 + q^10 + 7 * q^11 + 6 * q^12 + 19 * q^13 + 13 * q^14 + 3 * q^15 + 19 * q^16 + 15 * q^17 + 29 * q^18 + 22 * q^19 + q^20 - 2 * q^21 + 7 * q^22 + 9 * q^23 + 6 * q^24 + 34 * q^25 + 19 * q^26 + 21 * q^27 + 13 * q^28 - 5 * q^29 + 3 * q^30 + 15 * q^31 + 19 * q^32 + 15 * q^34 + 6 * q^35 + 29 * q^36 + 3 * q^37 + 22 * q^38 + 6 * q^39 + q^40 + 2 * q^41 - 2 * q^42 + 23 * q^43 + 7 * q^44 - 18 * q^45 + 9 * q^46 + 28 * q^47 + 6 * q^48 + 50 * q^49 + 34 * q^50 - 6 * q^51 + 19 * q^52 - 11 * q^53 + 21 * q^54 + 46 * q^55 + 13 * q^56 + 8 * q^57 - 5 * q^58 + 34 * q^59 + 3 * q^60 + 17 * q^61 + 15 * q^62 + 33 * q^63 + 19 * q^64 + q^65 + 13 * q^67 + 15 * q^68 - 42 * q^69 + 6 * q^70 + 15 * q^71 + 29 * q^72 + 27 * q^73 + 3 * q^74 + 63 * q^75 + 22 * q^76 - 45 * q^77 + 6 * q^78 + 31 * q^79 + q^80 + 75 * q^81 + 2 * q^82 + 46 * q^83 - 2 * q^84 - 13 * q^85 + 23 * q^86 + 53 * q^87 + 7 * q^88 + 4 * q^89 - 18 * q^90 + 13 * q^91 + 9 * q^92 - 12 * q^93 + 28 * q^94 - 47 * q^95 + 6 * q^96 + 2 * q^97 + 50 * q^98 - 25 * q^99

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