LMFDB - Embedded newform 1911.2.a.w.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1911,2,Mod(1,1911)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1911, 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("1911.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1911 = 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1911.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:	$15.2594118263$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.2196544.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 6x^{3} + 10x^{2} + 7x - 8 $ x^5 - 2x^4 - 6x^3 + 10x^2 + 7x - 8
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.755150$ of defining polynomial
Character	$\chi$	$=$	1911.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.755150 q^{2} +1.00000 q^{3} -1.42975 q^{4} -3.73850 q^{5} +0.755150 q^{6} -2.58997 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.755150 q^{2} +1.00000 q^{3} -1.42975 q^{4} -3.73850 q^{5} +0.755150 q^{6} -2.58997 q^{8} +1.00000 q^{9} -2.82313 q^{10} +3.02467 q^{11} -1.42975 q^{12} +1.00000 q^{13} -3.73850 q^{15} +0.903680 q^{16} -4.32045 q^{17} +0.755150 q^{18} +0.0963195 q^{19} +5.34512 q^{20} +2.28408 q^{22} -5.25288 q^{23} -2.58997 q^{24} +8.97642 q^{25} +0.755150 q^{26} +1.00000 q^{27} +2.88308 q^{29} -2.82313 q^{30} +2.71383 q^{31} +5.86236 q^{32} +3.02467 q^{33} -3.26259 q^{34} -1.42975 q^{36} +3.83075 q^{37} +0.0727357 q^{38} +1.00000 q^{39} +9.68263 q^{40} +9.88417 q^{41} +7.57333 q^{43} -4.32452 q^{44} -3.73850 q^{45} -3.96671 q^{46} -7.49079 q^{47} +0.903680 q^{48} +6.77854 q^{50} -4.32045 q^{51} -1.42975 q^{52} +12.5939 q^{53} +0.755150 q^{54} -11.3078 q^{55} +0.0963195 q^{57} +2.17716 q^{58} +9.80153 q^{59} +5.34512 q^{60} -5.02060 q^{61} +2.04935 q^{62} +2.61960 q^{64} -3.73850 q^{65} +2.28408 q^{66} +6.61751 q^{67} +6.17716 q^{68} -5.25288 q^{69} -11.4729 q^{71} -2.58997 q^{72} +10.7632 q^{73} +2.89279 q^{74} +8.97642 q^{75} -0.137713 q^{76} +0.755150 q^{78} +17.0503 q^{79} -3.37841 q^{80} +1.00000 q^{81} +7.46403 q^{82} -0.800544 q^{83} +16.1520 q^{85} +5.71900 q^{86} +2.88308 q^{87} -7.83383 q^{88} -1.24090 q^{89} -2.82313 q^{90} +7.51030 q^{92} +2.71383 q^{93} -5.65667 q^{94} -0.360091 q^{95} +5.86236 q^{96} -14.3129 q^{97} +3.02467 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{2} + 5 q^{3} + 6 q^{4} + 3 q^{5} + 2 q^{6} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 2 * q^2 + 5 * q^3 + 6 * q^4 + 3 * q^5 + 2 * q^6 + 6 * q^8 + 5 * q^9	$ 5 q + 2 q^{2} + 5 q^{3} + 6 q^{4} + 3 q^{5} + 2 q^{6} + 6 q^{8} + 5 q^{9} + 6 q^{11} + 6 q^{12} + 5 q^{13} + 3 q^{15} - 10 q^{17} + 2 q^{18} + 5 q^{19} + 6 q^{20} + 12 q^{22} + q^{23} + 6 q^{24} + 16 q^{25} + 2 q^{26} + 5 q^{27} + 17 q^{29} + q^{31} + 14 q^{32} + 6 q^{33} + 6 q^{36} + 4 q^{37} - 24 q^{38} + 5 q^{39} + 8 q^{40} + 14 q^{41} - q^{43} - 8 q^{44} + 3 q^{45} + 20 q^{46} - 3 q^{47} + 26 q^{50} - 10 q^{51} + 6 q^{52} + 17 q^{53} + 2 q^{54} + 2 q^{55} + 5 q^{57} - 28 q^{58} - 8 q^{59} + 6 q^{60} - 18 q^{61} - 8 q^{62} + 8 q^{64} + 3 q^{65} + 12 q^{66} + 16 q^{67} - 8 q^{68} + q^{69} - 16 q^{71} + 6 q^{72} + 23 q^{73} + 28 q^{74} + 16 q^{75} - 26 q^{76} + 2 q^{78} + 3 q^{79} - 36 q^{80} + 5 q^{81} - 11 q^{83} - 2 q^{85} - 24 q^{86} + 17 q^{87} + 28 q^{88} - 35 q^{89} + 34 q^{92} + q^{93} + 39 q^{95} + 14 q^{96} + 27 q^{97} + 6 q^{99}+O(q^{100}) $ 5 * q + 2 * q^2 + 5 * q^3 + 6 * q^4 + 3 * q^5 + 2 * q^6 + 6 * q^8 + 5 * q^9 + 6 * q^11 + 6 * q^12 + 5 * q^13 + 3 * q^15 - 10 * q^17 + 2 * q^18 + 5 * q^19 + 6 * q^20 + 12 * q^22 + q^23 + 6 * q^24 + 16 * q^25 + 2 * q^26 + 5 * q^27 + 17 * q^29 + q^31 + 14 * q^32 + 6 * q^33 + 6 * q^36 + 4 * q^37 - 24 * q^38 + 5 * q^39 + 8 * q^40 + 14 * q^41 - q^43 - 8 * q^44 + 3 * q^45 + 20 * q^46 - 3 * q^47 + 26 * q^50 - 10 * q^51 + 6 * q^52 + 17 * q^53 + 2 * q^54 + 2 * q^55 + 5 * q^57 - 28 * q^58 - 8 * q^59 + 6 * q^60 - 18 * q^61 - 8 * q^62 + 8 * q^64 + 3 * q^65 + 12 * q^66 + 16 * q^67 - 8 * q^68 + q^69 - 16 * q^71 + 6 * q^72 + 23 * q^73 + 28 * q^74 + 16 * q^75 - 26 * q^76 + 2 * q^78 + 3 * q^79 - 36 * q^80 + 5 * q^81 - 11 * q^83 - 2 * q^85 - 24 * q^86 + 17 * q^87 + 28 * q^88 - 35 * q^89 + 34 * q^92 + q^93 + 39 * q^95 + 14 * q^96 + 27 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.755150	0.533971	0.266986	−	0.963700i	$-0.413972\pi$
$2$	0.755150	0.533971	0.266986	+	0.963700i	$0.413972\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.42975	−0.714875
$5$	−3.73850	−1.67191	−0.835955	−	0.548798i	$-0.815086\pi$
$5$	−3.73850	−1.67191	−0.835955	+	0.548798i	$0.815086\pi$
$6$	0.755150	0.308289
$7$	0	0
$7$	0	0
$8$	−2.58997	−0.915694
$9$	1.00000	0.333333
$10$	−2.82313	−0.892752
$11$	3.02467	0.911974	0.455987	−	0.889987i	$-0.349286\pi$
$11$	3.02467	0.911974	0.455987	+	0.889987i	$0.349286\pi$
$12$	−1.42975	−0.412733
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	−3.73850	−0.965278
$16$	0.903680	0.225920
$17$	−4.32045	−1.04786	−0.523931	−	0.851760i	$-0.675535\pi$
$17$	−4.32045	−1.04786	−0.523931	+	0.851760i	$0.675535\pi$
$18$	0.755150	0.177990
$19$	0.0963195	0.0220972	0.0110486	−	0.999939i	$-0.496483\pi$
$19$	0.0963195	0.0220972	0.0110486	+	0.999939i	$0.496483\pi$
$20$	5.34512	1.19521
$21$	0	0
$22$	2.28408	0.486968
$23$	−5.25288	−1.09530	−0.547651	−	0.836707i	$-0.684478\pi$
$23$	−5.25288	−1.09530	−0.547651	+	0.836707i	$0.684478\pi$
$24$	−2.58997	−0.528676
$25$	8.97642	1.79528
$26$	0.755150	0.148097
$27$	1.00000	0.192450
$28$	0	0
$29$	2.88308	0.535375	0.267687	−	0.963506i	$-0.413741\pi$
$29$	2.88308	0.535375	0.267687	+	0.963506i	$0.413741\pi$
$30$	−2.82313	−0.515431
$31$	2.71383	0.487418	0.243709	−	0.969848i	$-0.421636\pi$
$31$	2.71383	0.487418	0.243709	+	0.969848i	$0.421636\pi$
$32$	5.86236	1.03633
$33$	3.02467	0.526528
$34$	−3.26259	−0.559529
$35$	0	0
$36$	−1.42975	−0.238292
$37$	3.83075	0.629771	0.314886	−	0.949130i	$-0.398034\pi$
$37$	3.83075	0.629771	0.314886	+	0.949130i	$0.398034\pi$
$38$	0.0727357	0.0117993
$39$	1.00000	0.160128
$40$	9.68263	1.53096
$41$	9.88417	1.54365	0.771824	−	0.635836i	$-0.219345\pi$
$41$	9.88417	1.54365	0.771824	+	0.635836i	$0.219345\pi$
$42$	0	0
$43$	7.57333	1.15492	0.577461	−	0.816418i	$-0.304044\pi$
$43$	7.57333	1.15492	0.577461	+	0.816418i	$0.304044\pi$
$44$	−4.32452	−0.651947
$45$	−3.73850	−0.557303
$46$	−3.96671	−0.584859
$47$	−7.49079	−1.09264	−0.546322	−	0.837575i	$-0.683973\pi$
$47$	−7.49079	−1.09264	−0.546322	+	0.837575i	$0.683973\pi$
$48$	0.903680	0.130435
$49$	0	0
$50$	6.77854	0.958630
$51$	−4.32045	−0.604984
$52$	−1.42975	−0.198271
$53$	12.5939	1.72991	0.864954	−	0.501850i	$-0.167347\pi$
$53$	12.5939	1.72991	0.864954	+	0.501850i	$0.167347\pi$
$54$	0.755150	0.102763
$55$	−11.3078	−1.52474
$56$	0	0
$57$	0.0963195	0.0127578
$58$	2.17716	0.285875
$59$	9.80153	1.27605	0.638026	−	0.770015i	$-0.279751\pi$
$59$	9.80153	1.27605	0.638026	+	0.770015i	$0.279751\pi$
$60$	5.34512	0.690052
$61$	−5.02060	−0.642822	−0.321411	−	0.946940i	$-0.604157\pi$
$61$	−5.02060	−0.642822	−0.321411	+	0.946940i	$0.604157\pi$
$62$	2.04935	0.260267
$63$	0	0
$64$	2.61960	0.327450
$65$	−3.73850	−0.463704
$66$	2.28408	0.281151
$67$	6.61751	0.808458	0.404229	−	0.914658i	$-0.367540\pi$
$67$	6.61751	0.808458	0.404229	+	0.914658i	$0.367540\pi$
$68$	6.17716	0.749090
$69$	−5.25288	−0.632372
$70$	0	0
$71$	−11.4729	−1.36159	−0.680793	−	0.732476i	$-0.738365\pi$
$71$	−11.4729	−1.36159	−0.680793	+	0.732476i	$0.738365\pi$
$72$	−2.58997	−0.305231
$73$	10.7632	1.25973	0.629867	−	0.776703i	$-0.283109\pi$
$73$	10.7632	1.25973	0.629867	+	0.776703i	$0.283109\pi$
$74$	2.89279	0.336280
$75$	8.97642	1.03651
$76$	−0.137713	−0.0157967
$77$	0	0
$78$	0.755150	0.0855039
$79$	17.0503	1.91831	0.959156	−	0.282876i	$-0.0912886\pi$
$79$	17.0503	1.91831	0.959156	+	0.282876i	$0.0912886\pi$
$80$	−3.37841	−0.377718
$81$	1.00000	0.111111
$82$	7.46403	0.824264
$83$	−0.800544	−0.0878712	−0.0439356	−	0.999034i	$-0.513990\pi$
$83$	−0.800544	−0.0878712	−0.0439356	+	0.999034i	$0.513990\pi$
$84$	0	0
$85$	16.1520	1.75193
$86$	5.71900	0.616695
$87$	2.88308	0.309099
$88$	−7.83383	−0.835089
$89$	−1.24090	−0.131535	−0.0657674	−	0.997835i	$-0.520950\pi$
$89$	−1.24090	−0.131535	−0.0657674	+	0.997835i	$0.520950\pi$
$90$	−2.82313	−0.297584
$91$	0	0
$92$	7.51030	0.783003
$93$	2.71383	0.281411
$94$	−5.65667	−0.583441
$95$	−0.360091	−0.0369446
$96$	5.86236	0.598325
$97$	−14.3129	−1.45326	−0.726629	−	0.687030i	$-0.758914\pi$
$97$	−14.3129	−1.45326	−0.726629	+	0.687030i	$0.758914\pi$
$98$	0	0
$99$	3.02467	0.303991
$100$	−12.8340	−1.28340
$101$	−10.3698	−1.03183	−0.515917	−	0.856639i	$-0.672549\pi$
$101$	−10.3698	−1.03183	−0.515917	+	0.856639i	$0.672549\pi$
$102$	−3.26259	−0.323044
$103$	−2.85950	−0.281755	−0.140877	−	0.990027i	$-0.544992\pi$
$103$	−2.85950	−0.281755	−0.140877	+	0.990027i	$0.544992\pi$
$104$	−2.58997	−0.253968
$105$	0	0
$106$	9.51030	0.923722
$107$	7.39855	0.715245	0.357622	−	0.933866i	$-0.383588\pi$
$107$	7.39855	0.715245	0.357622	+	0.933866i	$0.383588\pi$
$108$	−1.42975	−0.137578
$109$	14.4564	1.38467	0.692337	−	0.721575i	$-0.256581\pi$
$109$	14.4564	1.38467	0.692337	+	0.721575i	$0.256581\pi$
$110$	−8.53905	−0.814166
$111$	3.83075	0.363599
$112$	0	0
$113$	10.8359	1.01936	0.509679	−	0.860365i	$-0.329764\pi$
$113$	10.8359	1.01936	0.509679	+	0.860365i	$0.329764\pi$
$114$	0.0727357	0.00681232
$115$	19.6379	1.83124
$116$	−4.12208	−0.382726
$117$	1.00000	0.0924500
$118$	7.40162	0.681375
$119$	0	0
$120$	9.68263	0.883899
$121$	−1.85135	−0.168304
$122$	−3.79130	−0.343248
$123$	9.88417	0.891226
$124$	−3.88010	−0.348443
$125$	−14.8658	−1.32964
$126$	0	0
$127$	−8.83611	−0.784078	−0.392039	−	0.919949i	$-0.628230\pi$
$127$	−8.83611	−0.784078	−0.392039	+	0.919949i	$0.628230\pi$
$128$	−9.74653	−0.861480
$129$	7.57333	0.666794
$130$	−2.82313	−0.247605
$131$	−2.73741	−0.239169	−0.119585	−	0.992824i	$-0.538156\pi$
$131$	−2.73741	−0.239169	−0.119585	+	0.992824i	$0.538156\pi$
$132$	−4.32452	−0.376402
$133$	0	0
$134$	4.99721	0.431693
$135$	−3.73850	−0.321759
$136$	11.1898	0.959522
$137$	−17.7310	−1.51486	−0.757430	−	0.652917i	$-0.773545\pi$
$137$	−17.7310	−1.51486	−0.757430	+	0.652917i	$0.773545\pi$
$138$	−3.96671	−0.337669
$139$	16.3859	1.38983	0.694915	−	0.719092i	$-0.255442\pi$
$139$	16.3859	1.38983	0.694915	+	0.719092i	$0.255442\pi$
$140$	0	0
$141$	−7.49079	−0.630838
$142$	−8.66378	−0.727048
$143$	3.02467	0.252936
$144$	0.903680	0.0753067
$145$	−10.7784	−0.895099
$146$	8.12781	0.672662
$147$	0	0
$148$	−5.47701	−0.450207
$149$	8.36970	0.685672	0.342836	−	0.939395i	$-0.388612\pi$
$149$	8.36970	0.685672	0.342836	+	0.939395i	$0.388612\pi$
$150$	6.77854	0.553465
$151$	12.6669	1.03081	0.515407	−	0.856945i	$-0.327641\pi$
$151$	12.6669	1.03081	0.515407	+	0.856945i	$0.327641\pi$
$152$	−0.249465	−0.0202343
$153$	−4.32045	−0.349288
$154$	0	0
$155$	−10.1457	−0.814920
$156$	−1.42975	−0.114472
$157$	−15.1467	−1.20883	−0.604417	−	0.796668i	$-0.706594\pi$
$157$	−15.1467	−1.20883	−0.604417	+	0.796668i	$0.706594\pi$
$158$	12.8756	1.02432
$159$	12.5939	0.998763
$160$	−21.9165	−1.73265
$161$	0	0
$162$	0.755150	0.0593302
$163$	−20.8575	−1.63369	−0.816843	−	0.576860i	$-0.804278\pi$
$163$	−20.8575	−1.63369	−0.816843	+	0.576860i	$0.804278\pi$
$164$	−14.1319	−1.10351
$165$	−11.3078	−0.880308
$166$	−0.604531	−0.0469207
$167$	15.4242	1.19356	0.596781	−	0.802404i	$-0.296446\pi$
$167$	15.4242	1.19356	0.596781	+	0.802404i	$0.296446\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	12.1972	0.935482
$171$	0.0963195	0.00736574
$172$	−10.8280	−0.825624
$173$	−15.1566	−1.15233	−0.576166	−	0.817333i	$-0.695452\pi$
$173$	−15.1566	−1.15233	−0.576166	+	0.817333i	$0.695452\pi$
$174$	2.17716	0.165050
$175$	0	0
$176$	2.73334	0.206033
$177$	9.80153	0.736728
$178$	−0.937063	−0.0702358
$179$	16.1358	1.20604	0.603022	−	0.797725i	$-0.293963\pi$
$179$	16.1358	1.20604	0.603022	+	0.797725i	$0.293963\pi$
$180$	5.34512	0.398402
$181$	6.40706	0.476233	0.238117	−	0.971237i	$-0.423470\pi$
$181$	6.40706	0.476233	0.238117	+	0.971237i	$0.423470\pi$
$182$	0	0
$183$	−5.02060	−0.371133
$184$	13.6048	1.00296
$185$	−14.3213	−1.05292
$186$	2.04935	0.150265
$187$	−13.0680	−0.955623
$188$	10.7100	0.781103
$189$	0	0
$190$	−0.271923	−0.0197273
$191$	−22.3444	−1.61679	−0.808393	−	0.588644i	$-0.799662\pi$
$191$	−22.3444	−1.61679	−0.808393	+	0.588644i	$0.799662\pi$
$192$	2.61960	0.189053
$193$	−3.83075	−0.275743	−0.137872	−	0.990450i	$-0.544026\pi$
$193$	−3.83075	−0.275743	−0.137872	+	0.990450i	$0.544026\pi$
$194$	−10.8084	−0.775998
$195$	−3.73850	−0.267720
$196$	0	0
$197$	−8.79874	−0.626885	−0.313442	−	0.949607i	$-0.601482\pi$
$197$	−8.79874	−0.626885	−0.313442	+	0.949607i	$0.601482\pi$
$198$	2.28408	0.162323
$199$	−16.1261	−1.14315	−0.571573	−	0.820551i	$-0.693667\pi$
$199$	−16.1261	−1.14315	−0.571573	+	0.820551i	$0.693667\pi$
$200$	−23.2487	−1.64393
$201$	6.61751	0.466763
$202$	−7.83075	−0.550970
$203$	0	0
$204$	6.17716	0.432488
$205$	−36.9520	−2.58084
$206$	−2.15935	−0.150449
$207$	−5.25288	−0.365100
$208$	0.903680	0.0626590
$209$	0.291335	0.0201521
$210$	0	0
$211$	−0.924279	−0.0636300	−0.0318150	−	0.999494i	$-0.510129\pi$
$211$	−0.924279	−0.0636300	−0.0318150	+	0.999494i	$0.510129\pi$
$212$	−18.0062	−1.23667
$213$	−11.4729	−0.786112
$214$	5.58701	0.381920
$215$	−28.3129	−1.93093
$216$	−2.58997	−0.176225
$217$	0	0
$218$	10.9168	0.739376
$219$	10.7632	0.727308
$220$	16.1673	1.09000
$221$	−4.32045	−0.290625
$222$	2.89279	0.194151
$223$	11.5652	0.774462	0.387231	−	0.921983i	$-0.373432\pi$
$223$	11.5652	0.774462	0.387231	+	0.921983i	$0.373432\pi$
$224$	0	0
$225$	8.97642	0.598428
$226$	8.18274	0.544308
$227$	2.47039	0.163965	0.0819827	−	0.996634i	$-0.473875\pi$
$227$	2.47039	0.163965	0.0819827	+	0.996634i	$0.473875\pi$
$228$	−0.137713	−0.00912025
$229$	17.2584	1.14047	0.570234	−	0.821482i	$-0.306853\pi$
$229$	17.2584	1.14047	0.570234	+	0.821482i	$0.306853\pi$
$230$	14.8296	0.977832
$231$	0	0
$232$	−7.46711	−0.490240
$233$	9.90368	0.648812	0.324406	−	0.945918i	$-0.394836\pi$
$233$	9.90368	0.648812	0.324406	+	0.945918i	$0.394836\pi$
$234$	0.755150	0.0493657
$235$	28.0044	1.82680
$236$	−14.0137	−0.912216
$237$	17.0503	1.10754
$238$	0	0
$239$	5.23910	0.338889	0.169445	−	0.985540i	$-0.445803\pi$
$239$	5.23910	0.338889	0.169445	+	0.985540i	$0.445803\pi$
$240$	−3.37841	−0.218076
$241$	−2.47184	−0.159225	−0.0796127	−	0.996826i	$-0.525368\pi$
$241$	−2.47184	−0.159225	−0.0796127	+	0.996826i	$0.525368\pi$
$242$	−1.39804	−0.0898697
$243$	1.00000	0.0641500
$244$	7.17820	0.459537
$245$	0	0
$246$	7.46403	0.475889
$247$	0.0963195	0.00612867
$248$	−7.02875	−0.446326
$249$	−0.800544	−0.0507324
$250$	−11.2259	−0.709991
$251$	−9.90348	−0.625102	−0.312551	−	0.949901i	$-0.601184\pi$
$251$	−9.90348	−0.625102	−0.312551	+	0.949901i	$0.601184\pi$
$252$	0	0
$253$	−15.8882	−0.998886
$254$	−6.67259	−0.418675
$255$	16.1520	1.01148
$256$	−12.5993	−0.787456
$257$	23.3650	1.45747	0.728735	−	0.684796i	$-0.240109\pi$
$257$	23.3650	1.45747	0.728735	+	0.684796i	$0.240109\pi$
$258$	5.71900	0.356049
$259$	0	0
$260$	5.34512	0.331490
$261$	2.88308	0.178458
$262$	−2.06716	−0.127709
$263$	−18.4407	−1.13710	−0.568552	−	0.822647i	$-0.692496\pi$
$263$	−18.4407	−1.13710	−0.568552	+	0.822647i	$0.692496\pi$
$264$	−7.83383	−0.482139
$265$	−47.0825	−2.89225
$266$	0	0
$267$	−1.24090	−0.0759417
$268$	−9.46138	−0.577946
$269$	−30.0634	−1.83300	−0.916499	−	0.400036i	$-0.868997\pi$
$269$	−30.0634	−1.83300	−0.916499	+	0.400036i	$0.868997\pi$
$270$	−2.82313	−0.171810
$271$	18.8617	1.14577	0.572883	−	0.819637i	$-0.305825\pi$
$271$	18.8617	1.14577	0.572883	+	0.819637i	$0.305825\pi$
$272$	−3.90431	−0.236733
$273$	0	0
$274$	−13.3895	−0.808892
$275$	27.1507	1.63725
$276$	7.51030	0.452067
$277$	−22.4588	−1.34942	−0.674709	−	0.738084i	$-0.735731\pi$
$277$	−22.4588	−1.34942	−0.674709	+	0.738084i	$0.735731\pi$
$278$	12.3738	0.742130
$279$	2.71383	0.162473
$280$	0	0
$281$	14.9420	0.891367	0.445684	−	0.895191i	$-0.352961\pi$
$281$	14.9420	0.891367	0.445684	+	0.895191i	$0.352961\pi$
$282$	−5.65667	−0.336850
$283$	8.25562	0.490746	0.245373	−	0.969429i	$-0.421090\pi$
$283$	8.25562	0.490746	0.245373	+	0.969429i	$0.421090\pi$
$284$	16.4034	0.973364
$285$	−0.360091	−0.0213300
$286$	2.28408	0.135061
$287$	0	0
$288$	5.86236	0.345443
$289$	1.66628	0.0980166
$290$	−8.13932	−0.477957
$291$	−14.3129	−0.839038
$292$	−15.3886	−0.900552
$293$	24.1949	1.41348	0.706741	−	0.707472i	$-0.250165\pi$
$293$	24.1949	1.41348	0.706741	+	0.707472i	$0.250165\pi$
$294$	0	0
$295$	−36.6431	−2.13344
$296$	−9.92154	−0.576678
$297$	3.02467	0.175509
$298$	6.32037	0.366129
$299$	−5.25288	−0.303782
$300$	−12.8340	−0.740973
$301$	0	0
$302$	9.56537	0.550425
$303$	−10.3698	−0.595729
$304$	0.0870421	0.00499221
$305$	18.7695	1.07474
$306$	−3.26259	−0.186510
$307$	27.9276	1.59391	0.796957	−	0.604035i	$-0.206441\pi$
$307$	27.9276	1.59391	0.796957	+	0.604035i	$0.206441\pi$
$308$	0	0
$309$	−2.85950	−0.162671
$310$	−7.66150	−0.435144
$311$	14.9459	0.847502	0.423751	−	0.905779i	$-0.360713\pi$
$311$	14.9459	0.847502	0.423751	+	0.905779i	$0.360713\pi$
$312$	−2.58997	−0.146628
$313$	17.5949	0.994523	0.497262	−	0.867601i	$-0.334339\pi$
$313$	17.5949	0.994523	0.497262	+	0.867601i	$0.334339\pi$
$314$	−11.4380	−0.645483
$315$	0	0
$316$	−24.3777	−1.37135
$317$	−1.18402	−0.0665014	−0.0332507	−	0.999447i	$-0.510586\pi$
$317$	−1.18402	−0.0665014	−0.0332507	+	0.999447i	$0.510586\pi$
$318$	9.51030	0.533311
$319$	8.72038	0.488248
$320$	−9.79338	−0.547467
$321$	7.39855	0.412947
$322$	0	0
$323$	−0.416144	−0.0231549
$324$	−1.42975	−0.0794305
$325$	8.97642	0.497922
$326$	−15.7505	−0.872341
$327$	14.4564	0.799441
$328$	−25.5997	−1.41351
$329$	0	0
$330$	−8.53905	−0.470059
$331$	30.9069	1.69879	0.849397	−	0.527754i	$-0.176966\pi$
$331$	30.9069	1.69879	0.849397	+	0.527754i	$0.176966\pi$
$332$	1.14458	0.0628168
$333$	3.83075	0.209924
$334$	11.6476	0.637328
$335$	−24.7396	−1.35167
$336$	0	0
$337$	−7.17024	−0.390588	−0.195294	−	0.980745i	$-0.562566\pi$
$337$	−7.17024	−0.390588	−0.195294	+	0.980745i	$0.562566\pi$
$338$	0.755150	0.0410747
$339$	10.8359	0.588526
$340$	−23.0933	−1.25241
$341$	8.20845	0.444513
$342$	0.0727357	0.00393309
$343$	0	0
$344$	−19.6147	−1.05755
$345$	19.6379	1.05727
$346$	−11.4455	−0.615312
$347$	−22.7297	−1.22019	−0.610097	−	0.792327i	$-0.708869\pi$
$347$	−22.7297	−1.22019	−0.610097	+	0.792327i	$0.708869\pi$
$348$	−4.12208	−0.220967
$349$	11.1744	0.598153	0.299076	−	0.954229i	$-0.403321\pi$
$349$	11.1744	0.598153	0.299076	+	0.954229i	$0.403321\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	17.7317	0.945104
$353$	−1.86787	−0.0994167	−0.0497083	−	0.998764i	$-0.515829\pi$
$353$	−1.86787	−0.0994167	−0.0497083	+	0.998764i	$0.515829\pi$
$354$	7.40162	0.393392
$355$	42.8916	2.27645
$356$	1.77417	0.0940309
$357$	0	0
$358$	12.1849	0.643993
$359$	17.8800	0.943670	0.471835	−	0.881687i	$-0.343592\pi$
$359$	17.8800	0.943670	0.471835	+	0.881687i	$0.343592\pi$
$360$	9.68263	0.510319
$361$	−18.9907	−0.999512
$362$	4.83829	0.254295
$363$	−1.85135	−0.0971705
$364$	0	0
$365$	−40.2382	−2.10616
$366$	−3.79130	−0.198175
$367$	35.7881	1.86813	0.934063	−	0.357109i	$-0.116238\pi$
$367$	35.7881	1.86813	0.934063	+	0.357109i	$0.116238\pi$
$368$	−4.74692	−0.247451
$369$	9.88417	0.514549
$370$	−10.8147	−0.562230
$371$	0	0
$372$	−3.88010	−0.201174
$373$	3.14865	0.163031	0.0815155	−	0.996672i	$-0.474024\pi$
$373$	3.14865	0.163031	0.0815155	+	0.996672i	$0.474024\pi$
$374$	−9.86826	−0.510275
$375$	−14.8658	−0.767669
$376$	19.4010	1.00053
$377$	2.88308	0.148486
$378$	0	0
$379$	−8.05332	−0.413671	−0.206836	−	0.978376i	$-0.566317\pi$
$379$	−8.05332	−0.413671	−0.206836	+	0.978376i	$0.566317\pi$
$380$	0.514840	0.0264107
$381$	−8.83611	−0.452688
$382$	−16.8734	−0.863317
$383$	−4.46782	−0.228295	−0.114147	−	0.993464i	$-0.536414\pi$
$383$	−4.46782	−0.228295	−0.114147	+	0.993464i	$0.536414\pi$
$384$	−9.74653	−0.497376
$385$	0	0
$386$	−2.89279	−0.147239
$387$	7.57333	0.384974
$388$	20.4639	1.03890
$389$	−2.91282	−0.147686	−0.0738429	−	0.997270i	$-0.523526\pi$
$389$	−2.91282	−0.147686	−0.0738429	+	0.997270i	$0.523526\pi$
$390$	−2.82313	−0.142955
$391$	22.6948	1.14773
$392$	0	0
$393$	−2.73741	−0.138084
$394$	−6.64437	−0.334738
$395$	−63.7428	−3.20725
$396$	−4.32452	−0.217316
$397$	10.4328	0.523609	0.261804	−	0.965121i	$-0.415683\pi$
$397$	10.4328	0.523609	0.261804	+	0.965121i	$0.415683\pi$
$398$	−12.1776	−0.610407
$399$	0	0
$400$	8.11181	0.405591
$401$	23.8275	1.18989	0.594944	−	0.803767i	$-0.297174\pi$
$401$	23.8275	1.18989	0.594944	+	0.803767i	$0.297174\pi$
$402$	4.99721	0.249238
$403$	2.71383	0.135186
$404$	14.8262	0.737631
$405$	−3.73850	−0.185768
$406$	0	0
$407$	11.5868	0.574335
$408$	11.1898	0.553980
$409$	27.4021	1.35495	0.677473	−	0.735548i	$-0.263075\pi$
$409$	27.4021	1.35495	0.677473	+	0.735548i	$0.263075\pi$
$410$	−27.9043	−1.37810
$411$	−17.7310	−0.874605
$412$	4.08836	0.201419
$413$	0	0
$414$	−3.96671	−0.194953
$415$	2.99284	0.146913
$416$	5.86236	0.287426
$417$	16.3859	0.802419
$418$	0.220002	0.0107606
$419$	−11.6423	−0.568763	−0.284381	−	0.958711i	$-0.591788\pi$
$419$	−11.6423	−0.568763	−0.284381	+	0.958711i	$0.591788\pi$
$420$	0	0
$421$	4.62566	0.225441	0.112720	−	0.993627i	$-0.464044\pi$
$421$	4.62566	0.225441	0.112720	+	0.993627i	$0.464044\pi$
$422$	−0.697969	−0.0339766
$423$	−7.49079	−0.364215
$424$	−32.6179	−1.58407
$425$	−38.7822	−1.88121
$426$	−8.66378	−0.419762
$427$	0	0
$428$	−10.5781	−0.511310
$429$	3.02467	0.146033
$430$	−21.3805	−1.03106
$431$	24.0667	1.15925	0.579625	−	0.814883i	$-0.303199\pi$
$431$	24.0667	1.15925	0.579625	+	0.814883i	$0.303199\pi$
$432$	0.903680	0.0434783
$433$	37.4538	1.79992	0.899958	−	0.435978i	$-0.143597\pi$
$433$	37.4538	1.79992	0.899958	+	0.435978i	$0.143597\pi$
$434$	0	0
$435$	−10.7784	−0.516785
$436$	−20.6690	−0.989867
$437$	−0.505955	−0.0242031
$438$	8.12781	0.388362
$439$	29.3490	1.40075	0.700375	−	0.713775i	$-0.253016\pi$
$439$	29.3490	1.40075	0.700375	+	0.713775i	$0.253016\pi$
$440$	29.2868	1.39619
$441$	0	0
$442$	−3.26259	−0.155185
$443$	−20.1082	−0.955369	−0.477685	−	0.878531i	$-0.658524\pi$
$443$	−20.1082	−0.955369	−0.477685	+	0.878531i	$0.658524\pi$
$444$	−5.47701	−0.259927
$445$	4.63910	0.219914
$446$	8.73344	0.413540
$447$	8.36970	0.395873
$448$	0	0
$449$	−25.2161	−1.19002	−0.595012	−	0.803717i	$-0.702853\pi$
$449$	−25.2161	−1.19002	−0.595012	+	0.803717i	$0.702853\pi$
$450$	6.77854	0.319543
$451$	29.8964	1.40777
$452$	−15.4926	−0.728712
$453$	12.6669	0.595141
$454$	1.86551	0.0875529
$455$	0	0
$456$	−0.249465	−0.0116823
$457$	9.44965	0.442036	0.221018	−	0.975270i	$-0.429062\pi$
$457$	9.44965	0.442036	0.221018	+	0.975270i	$0.429062\pi$
$458$	13.0327	0.608977
$459$	−4.32045	−0.201661
$460$	−28.0773	−1.30911
$461$	32.2441	1.50176	0.750878	−	0.660441i	$-0.229631\pi$
$461$	32.2441	1.50176	0.750878	+	0.660441i	$0.229631\pi$
$462$	0	0
$463$	29.0095	1.34819	0.674093	−	0.738646i	$-0.264535\pi$
$463$	29.0095	1.34819	0.674093	+	0.738646i	$0.264535\pi$
$464$	2.60538	0.120952
$465$	−10.1457	−0.470494
$466$	7.47876	0.346447
$467$	−14.1480	−0.654693	−0.327347	−	0.944904i	$-0.606155\pi$
$467$	−14.1480	−0.654693	−0.327347	+	0.944904i	$0.606155\pi$
$468$	−1.42975	−0.0660902
$469$	0	0
$470$	21.1475	0.975460
$471$	−15.1467	−0.697921
$472$	−25.3857	−1.16847
$473$	22.9069	1.05326
$474$	12.8756	0.591394
$475$	0.864604	0.0396708
$476$	0	0
$477$	12.5939	0.576636
$478$	3.95630	0.180957
$479$	17.4333	0.796547	0.398274	−	0.917267i	$-0.369609\pi$
$479$	17.4333	0.796547	0.398274	+	0.917267i	$0.369609\pi$
$480$	−21.9165	−1.00035
$481$	3.83075	0.174667
$482$	−1.86661	−0.0850218
$483$	0	0
$484$	2.64696	0.120316
$485$	53.5089	2.42972
$486$	0.755150	0.0342543
$487$	−12.6197	−0.571853	−0.285926	−	0.958252i	$-0.592301\pi$
$487$	−12.6197	−0.571853	−0.285926	+	0.958252i	$0.592301\pi$
$488$	13.0032	0.588628
$489$	−20.8575	−0.943209
$490$	0	0
$491$	−25.9819	−1.17255	−0.586274	−	0.810113i	$-0.699406\pi$
$491$	−25.9819	−1.17255	−0.586274	+	0.810113i	$0.699406\pi$
$492$	−14.1319	−0.637115
$493$	−12.4562	−0.560999
$494$	0.0727357	0.00327253
$495$	−11.3078	−0.508246
$496$	2.45244	0.110118
$497$	0	0
$498$	−0.604531	−0.0270897
$499$	26.9069	1.20452	0.602258	−	0.798301i	$-0.294268\pi$
$499$	26.9069	1.20452	0.602258	+	0.798301i	$0.294268\pi$
$500$	21.2544	0.950527
$501$	15.4242	0.689103
$502$	−7.47861	−0.333787
$503$	−2.09652	−0.0934790	−0.0467395	−	0.998907i	$-0.514883\pi$
$503$	−2.09652	−0.0934790	−0.0467395	+	0.998907i	$0.514883\pi$
$504$	0	0
$505$	38.7675	1.72513
$506$	−11.9980	−0.533376
$507$	1.00000	0.0444116
$508$	12.6334	0.560517
$509$	−30.7912	−1.36480	−0.682398	−	0.730980i	$-0.739063\pi$
$509$	−30.7912	−1.36480	−0.682398	+	0.730980i	$0.739063\pi$
$510$	12.1972	0.540101
$511$	0	0
$512$	9.97872	0.441001
$513$	0.0963195	0.00425261
$514$	17.6441	0.778247
$515$	10.6902	0.471069
$516$	−10.8280	−0.476674
$517$	−22.6572	−0.996463
$518$	0	0
$519$	−15.1566	−0.665299
$520$	9.68263	0.424611
$521$	0.391582	0.0171555	0.00857775	−	0.999963i	$-0.497270\pi$
$521$	0.391582	0.0171555	0.00857775	+	0.999963i	$0.497270\pi$
$522$	2.17716	0.0952916
$523$	−25.2000	−1.10192	−0.550959	−	0.834532i	$-0.685738\pi$
$523$	−25.2000	−1.10192	−0.550959	+	0.834532i	$0.685738\pi$
$524$	3.91382	0.170976
$525$	0	0
$526$	−13.9255	−0.607181
$527$	−11.7250	−0.510748
$528$	2.73334	0.118953
$529$	4.59274	0.199684
$530$	−35.5543	−1.54438
$531$	9.80153	0.425350
$532$	0	0
$533$	9.88417	0.428131
$534$	−0.937063	−0.0405507
$535$	−27.6595	−1.19582
$536$	−17.1392	−0.740300
$537$	16.1358	0.696310
$538$	−22.7024	−0.978769
$539$	0	0
$540$	5.34512	0.230017
$541$	28.9994	1.24678	0.623391	−	0.781911i	$-0.285755\pi$
$541$	28.9994	1.24678	0.623391	+	0.781911i	$0.285755\pi$
$542$	14.2434	0.611806
$543$	6.40706	0.274953
$544$	−25.3280	−1.08593
$545$	−54.0454	−2.31505
$546$	0	0
$547$	10.8690	0.464723	0.232362	−	0.972629i	$-0.425355\pi$
$547$	10.8690	0.464723	0.232362	+	0.972629i	$0.425355\pi$
$548$	25.3508	1.08293
$549$	−5.02060	−0.214274
$550$	20.5029	0.874245
$551$	0.277697	0.0118303
$552$	13.6048	0.579060
$553$	0	0
$554$	−16.9597	−0.720551
$555$	−14.3213	−0.607904
$556$	−23.4277	−0.993554
$557$	−36.3973	−1.54220	−0.771101	−	0.636713i	$-0.780294\pi$
$557$	−36.3973	−1.54220	−0.771101	+	0.636713i	$0.780294\pi$
$558$	2.04935	0.0867558
$559$	7.57333	0.320318
$560$	0	0
$561$	−13.0680	−0.551729
$562$	11.2835	0.475965
$563$	−1.83274	−0.0772410	−0.0386205	−	0.999254i	$-0.512296\pi$
$563$	−1.83274	−0.0772410	−0.0386205	+	0.999254i	$0.512296\pi$
$564$	10.7100	0.450970
$565$	−40.5101	−1.70427
$566$	6.23423	0.262044
$567$	0	0
$568$	29.7146	1.24680
$569$	21.4083	0.897481	0.448740	−	0.893662i	$-0.351873\pi$
$569$	21.4083	0.897481	0.448740	+	0.893662i	$0.351873\pi$
$570$	−0.271923	−0.0113896
$571$	14.8941	0.623300	0.311650	−	0.950197i	$-0.399118\pi$
$571$	14.8941	0.623300	0.311650	+	0.950197i	$0.399118\pi$
$572$	−4.32452	−0.180817
$573$	−22.3444	−0.933451
$574$	0	0
$575$	−47.1520	−1.96638
$576$	2.61960	0.109150
$577$	−35.8904	−1.49414	−0.747069	−	0.664746i	$-0.768540\pi$
$577$	−35.8904	−1.49414	−0.747069	+	0.664746i	$0.768540\pi$
$578$	1.25829	0.0523381
$579$	−3.83075	−0.159200
$580$	15.4104	0.639883
$581$	0	0
$582$	−10.8084	−0.448023
$583$	38.0925	1.57763
$584$	−27.8763	−1.15353
$585$	−3.73850	−0.154568
$586$	18.2708	0.754759
$587$	5.98840	0.247168	0.123584	−	0.992334i	$-0.460561\pi$
$587$	5.98840	0.247168	0.123584	+	0.992334i	$0.460561\pi$
$588$	0	0
$589$	0.261395	0.0107706
$590$	−27.6710	−1.13920
$591$	−8.79874	−0.361932
$592$	3.46177	0.142278
$593$	−12.8830	−0.529041	−0.264520	−	0.964380i	$-0.585214\pi$
$593$	−12.8830	−0.529041	−0.264520	+	0.964380i	$0.585214\pi$
$594$	2.28408	0.0937170
$595$	0	0
$596$	−11.9666	−0.490170
$597$	−16.1261	−0.659996
$598$	−3.96671	−0.162211
$599$	−33.1585	−1.35482	−0.677411	−	0.735605i	$-0.736898\pi$
$599$	−33.1585	−1.35482	−0.677411	+	0.735605i	$0.736898\pi$
$600$	−23.2487	−0.949123
$601$	−45.2775	−1.84691	−0.923453	−	0.383711i	$-0.874646\pi$
$601$	−45.2775	−1.84691	−0.923453	+	0.383711i	$0.874646\pi$
$602$	0	0
$603$	6.61751	0.269486
$604$	−18.1104	−0.736903
$605$	6.92127	0.281390
$606$	−7.83075	−0.318102
$607$	−40.3030	−1.63585	−0.817924	−	0.575327i	$-0.804875\pi$
$607$	−40.3030	−1.63585	−0.817924	+	0.575327i	$0.804875\pi$
$608$	0.564660	0.0229000
$609$	0	0
$610$	14.1738	0.573881
$611$	−7.49079	−0.303045
$612$	6.17716	0.249697
$613$	−26.0903	−1.05378	−0.526890	−	0.849934i	$-0.676642\pi$
$613$	−26.0903	−1.05378	−0.526890	+	0.849934i	$0.676642\pi$
$614$	21.0896	0.851105
$615$	−36.9520	−1.49005
$616$	0	0
$617$	30.0338	1.20911	0.604557	−	0.796562i	$-0.293350\pi$
$617$	30.0338	1.20911	0.604557	+	0.796562i	$0.293350\pi$
$618$	−2.15935	−0.0868618
$619$	−9.04399	−0.363508	−0.181754	−	0.983344i	$-0.558178\pi$
$619$	−9.04399	−0.363508	−0.181754	+	0.983344i	$0.558178\pi$
$620$	14.5058	0.582565
$621$	−5.25288	−0.210791
$622$	11.2864	0.452542
$623$	0	0
$624$	0.903680	0.0361762
$625$	10.6940	0.427759
$626$	13.2868	0.531047
$627$	0.291335	0.0116348
$628$	21.6559	0.864165
$629$	−16.5506	−0.659914
$630$	0	0
$631$	−46.9974	−1.87094	−0.935468	−	0.353410i	$-0.885022\pi$
$631$	−46.9974	−1.87094	−0.935468	+	0.353410i	$0.885022\pi$
$632$	−44.1599	−1.75659
$633$	−0.924279	−0.0367368
$634$	−0.894114	−0.0355098
$635$	33.0338	1.31091
$636$	−18.0062	−0.713991
$637$	0	0
$638$	6.58519	0.260710
$639$	−11.4729	−0.453862
$640$	36.4375	1.44032
$641$	10.8119	0.427046	0.213523	−	0.976938i	$-0.431506\pi$
$641$	10.8119	0.427046	0.213523	+	0.976938i	$0.431506\pi$
$642$	5.58701	0.220502
$643$	33.3805	1.31640	0.658199	−	0.752844i	$-0.271319\pi$
$643$	33.3805	1.31640	0.658199	+	0.752844i	$0.271319\pi$
$644$	0	0
$645$	−28.3129	−1.11482
$646$	−0.314251	−0.0123640
$647$	9.12487	0.358736	0.179368	−	0.983782i	$-0.442595\pi$
$647$	9.12487	0.358736	0.179368	+	0.983782i	$0.442595\pi$
$648$	−2.58997	−0.101744
$649$	29.6464	1.16372
$650$	6.77854	0.265876
$651$	0	0
$652$	29.8210	1.16788
$653$	16.5916	0.649278	0.324639	−	0.945838i	$-0.394757\pi$
$653$	16.5916	0.649278	0.324639	+	0.945838i	$0.394757\pi$
$654$	10.9168	0.426879
$655$	10.2338	0.399869
$656$	8.93213	0.348741
$657$	10.7632	0.419912
$658$	0	0
$659$	−0.714075	−0.0278164	−0.0139082	−	0.999903i	$-0.504427\pi$
$659$	−0.714075	−0.0278164	−0.0139082	+	0.999903i	$0.504427\pi$
$660$	16.1673	0.629310
$661$	−13.8839	−0.540020	−0.270010	−	0.962857i	$-0.587027\pi$
$661$	−13.8839	−0.540020	−0.270010	+	0.962857i	$0.587027\pi$
$662$	23.3393	0.907108
$663$	−4.32045	−0.167792
$664$	2.07339	0.0804631
$665$	0	0
$666$	2.89279	0.112093
$667$	−15.1445	−0.586397
$668$	−22.0528	−0.853247
$669$	11.5652	0.447136
$670$	−18.6821	−0.721752
$671$	−15.1857	−0.586236
$672$	0	0
$673$	−25.4596	−0.981395	−0.490697	−	0.871330i	$-0.663258\pi$
$673$	−25.4596	−0.981395	−0.490697	+	0.871330i	$0.663258\pi$
$674$	−5.41460	−0.208563
$675$	8.97642	0.345502
$676$	−1.42975	−0.0549903
$677$	−51.4829	−1.97865	−0.989325	−	0.145728i	$-0.953448\pi$
$677$	−51.4829	−1.97865	−0.989325	+	0.145728i	$0.953448\pi$
$678$	8.18274	0.314256
$679$	0	0
$680$	−41.8333	−1.60423
$681$	2.47039	0.0946655
$682$	6.19861	0.237357
$683$	2.25752	0.0863814	0.0431907	−	0.999067i	$-0.486248\pi$
$683$	2.25752	0.0863814	0.0431907	+	0.999067i	$0.486248\pi$
$684$	−0.137713	−0.00526558
$685$	66.2873	2.53271
$686$	0	0
$687$	17.2584	0.658449
$688$	6.84387	0.260920
$689$	12.5939	0.479790
$690$	14.8296	0.564552
$691$	5.78975	0.220252	0.110126	−	0.993918i	$-0.464874\pi$
$691$	5.78975	0.220252	0.110126	+	0.993918i	$0.464874\pi$
$692$	21.6701	0.823773
$693$	0	0
$694$	−17.1643	−0.651549
$695$	−61.2586	−2.32367
$696$	−7.46711	−0.283040
$697$	−42.7041	−1.61753
$698$	8.43836	0.319397
$699$	9.90368	0.374592
$700$	0	0
$701$	−1.67202	−0.0631515	−0.0315758	−	0.999501i	$-0.510053\pi$
$701$	−1.67202	−0.0631515	−0.0315758	+	0.999501i	$0.510053\pi$
$702$	0.755150	0.0285013
$703$	0.368976	0.0139162
$704$	7.92343	0.298626
$705$	28.0044	1.05471
$706$	−1.41052	−0.0530857
$707$	0	0
$708$	−14.0137	−0.526668
$709$	17.7362	0.666098	0.333049	−	0.942910i	$-0.391923\pi$
$709$	17.7362	0.666098	0.333049	+	0.942910i	$0.391923\pi$
$710$	32.3896	1.21556
$711$	17.0503	0.639438
$712$	3.21389	0.120446
$713$	−14.2554	−0.533870
$714$	0	0
$715$	−11.3078	−0.422886
$716$	−23.0701	−0.862170
$717$	5.23910	0.195658
$718$	13.5021	0.503893
$719$	4.07473	0.151962	0.0759809	−	0.997109i	$-0.475791\pi$
$719$	4.07473	0.151962	0.0759809	+	0.997109i	$0.475791\pi$
$720$	−3.37841	−0.125906
$721$	0	0
$722$	−14.3408	−0.533711
$723$	−2.47184	−0.0919288
$724$	−9.16049	−0.340447
$725$	25.8797	0.961150
$726$	−1.39804	−0.0518863
$727$	5.14468	0.190806	0.0954028	−	0.995439i	$-0.469586\pi$
$727$	5.14468	0.190806	0.0954028	+	0.995439i	$0.469586\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−30.3859	−1.12463
$731$	−32.7202	−1.21020
$732$	7.17820	0.265314
$733$	15.4870	0.572024	0.286012	−	0.958226i	$-0.407670\pi$
$733$	15.4870	0.572024	0.286012	+	0.958226i	$0.407670\pi$
$734$	27.0254	0.997526
$735$	0	0
$736$	−30.7943	−1.13509
$737$	20.0158	0.737292
$738$	7.46403	0.274755
$739$	−2.52357	−0.0928309	−0.0464155	−	0.998922i	$-0.514780\pi$
$739$	−2.52357	−0.0928309	−0.0464155	+	0.998922i	$0.514780\pi$
$740$	20.4758	0.752706
$741$	0.0963195	0.00353839
$742$	0	0
$743$	−28.6368	−1.05058	−0.525292	−	0.850922i	$-0.676044\pi$
$743$	−28.6368	−1.05058	−0.525292	+	0.850922i	$0.676044\pi$
$744$	−7.02875	−0.257686
$745$	−31.2901	−1.14638
$746$	2.37770	0.0870539
$747$	−0.800544	−0.0292904
$748$	18.6839	0.683151
$749$	0	0
$750$	−11.2259	−0.409913
$751$	−6.95184	−0.253676	−0.126838	−	0.991923i	$-0.540483\pi$
$751$	−6.95184	−0.253676	−0.126838	+	0.991923i	$0.540483\pi$
$752$	−6.76928	−0.246850
$753$	−9.90348	−0.360903
$754$	2.17716	0.0792874
$755$	−47.3551	−1.72343
$756$	0	0
$757$	39.6427	1.44084	0.720419	−	0.693539i	$-0.243950\pi$
$757$	39.6427	1.44084	0.720419	+	0.693539i	$0.243950\pi$
$758$	−6.08146	−0.220889
$759$	−15.8882	−0.576707
$760$	0.932626	0.0338299
$761$	−0.198514	−0.00719613	−0.00359807	−	0.999994i	$-0.501145\pi$
$761$	−0.198514	−0.00719613	−0.00359807	+	0.999994i	$0.501145\pi$
$762$	−6.67259	−0.241722
$763$	0	0
$764$	31.9469	1.15580
$765$	16.1520	0.583977
$766$	−3.37387	−0.121903
$767$	9.80153	0.353913
$768$	−12.5993	−0.454638
$769$	−20.0872	−0.724364	−0.362182	−	0.932107i	$-0.617968\pi$
$769$	−20.0872	−0.724364	−0.362182	+	0.932107i	$0.617968\pi$
$770$	0	0
$771$	23.3650	0.841470
$772$	5.47701	0.197122
$773$	54.6121	1.96426	0.982131	−	0.188201i	$-0.0602656\pi$
$773$	54.6121	1.96426	0.982131	+	0.188201i	$0.0602656\pi$
$774$	5.71900	0.205565
$775$	24.3605	0.875054
$776$	37.0701	1.33074
$777$	0	0
$778$	−2.19962	−0.0788600
$779$	0.952039	0.0341103
$780$	5.34512	0.191386
$781$	−34.7019	−1.24173
$782$	17.1380	0.612853
$783$	2.88308	0.103033
$784$	0	0
$785$	56.6258	2.02106
$786$	−2.06716	−0.0737331
$787$	−23.3676	−0.832966	−0.416483	−	0.909143i	$-0.636737\pi$
$787$	−23.3676	−0.832966	−0.416483	+	0.909143i	$0.636737\pi$
$788$	12.5800	0.448144
$789$	−18.4407	−0.656507
$790$	−48.1353	−1.71258
$791$	0	0
$792$	−7.83383	−0.278363
$793$	−5.02060	−0.178287
$794$	7.87835	0.279592
$795$	−47.0825	−1.66984
$796$	23.0562	0.817206
$797$	−53.6070	−1.89886	−0.949429	−	0.313983i	$-0.898337\pi$
$797$	−53.6070	−1.89886	−0.949429	+	0.313983i	$0.898337\pi$
$798$	0	0
$799$	32.3636	1.14494
$800$	52.6230	1.86050
$801$	−1.24090	−0.0438449
$802$	17.9933	0.635366
$803$	32.5551	1.14884
$804$	−9.46138	−0.333677
$805$	0	0
$806$	2.04935	0.0721852
$807$	−30.0634	−1.05828
$808$	26.8575	0.944844
$809$	46.9263	1.64984	0.824920	−	0.565250i	$-0.191220\pi$
$809$	46.9263	1.64984	0.824920	+	0.565250i	$0.191220\pi$
$810$	−2.82313	−0.0991947
$811$	−43.9233	−1.54235	−0.771177	−	0.636620i	$-0.780332\pi$
$811$	−43.9233	−1.54235	−0.771177	+	0.636620i	$0.780332\pi$
$812$	0	0
$813$	18.8617	0.661508
$814$	8.74974	0.306678
$815$	77.9759	2.73138
$816$	−3.90431	−0.136678
$817$	0.729460	0.0255206
$818$	20.6927	0.723502
$819$	0	0
$820$	52.8321	1.84498
$821$	−14.6275	−0.510503	−0.255252	−	0.966875i	$-0.582158\pi$
$821$	−14.6275	−0.510503	−0.255252	+	0.966875i	$0.582158\pi$
$822$	−13.3895	−0.467014
$823$	−2.74868	−0.0958128	−0.0479064	−	0.998852i	$-0.515255\pi$
$823$	−2.74868	−0.0958128	−0.0479064	+	0.998852i	$0.515255\pi$
$824$	7.40602	0.258001
$825$	27.1507	0.945267
$826$	0	0
$827$	40.6222	1.41257	0.706286	−	0.707927i	$-0.250369\pi$
$827$	40.6222	1.41257	0.706286	+	0.707927i	$0.250369\pi$
$828$	7.51030	0.261001
$829$	−26.7202	−0.928030	−0.464015	−	0.885827i	$-0.653592\pi$
$829$	−26.7202	−0.928030	−0.464015	+	0.885827i	$0.653592\pi$
$830$	2.26004	0.0784472
$831$	−22.4588	−0.779087
$832$	2.61960	0.0908183
$833$	0	0
$834$	12.3738	0.428469
$835$	−57.6635	−1.99553
$836$	−0.416536	−0.0144062
$837$	2.71383	0.0938037
$838$	−8.79167	−0.303703
$839$	−7.01259	−0.242102	−0.121051	−	0.992646i	$-0.538626\pi$
$839$	−7.01259	−0.242102	−0.121051	+	0.992646i	$0.538626\pi$
$840$	0	0
$841$	−20.6878	−0.713374
$842$	3.49307	0.120379
$843$	14.9420	0.514631
$844$	1.32149	0.0454875
$845$	−3.73850	−0.128608
$846$	−5.65667	−0.194480
$847$	0	0
$848$	11.3809	0.390821
$849$	8.25562	0.283332
$850$	−29.2863	−1.00451
$851$	−20.1225	−0.689789
$852$	16.4034	0.561972
$853$	50.8969	1.74268	0.871338	−	0.490683i	$-0.163253\pi$
$853$	50.8969	1.74268	0.871338	+	0.490683i	$0.163253\pi$
$854$	0	0
$855$	−0.360091	−0.0123149
$856$	−19.1620	−0.654945
$857$	48.4431	1.65479	0.827393	−	0.561624i	$-0.189823\pi$
$857$	48.4431	1.65479	0.827393	+	0.561624i	$0.189823\pi$
$858$	2.28408	0.0779773
$859$	58.2267	1.98667	0.993335	−	0.115261i	$-0.0367704\pi$
$859$	58.2267	1.98667	0.993335	+	0.115261i	$0.0367704\pi$
$860$	40.4804	1.38037
$861$	0	0
$862$	18.1739	0.619007
$863$	−43.8436	−1.49245	−0.746226	−	0.665693i	$-0.768136\pi$
$863$	−43.8436	−1.49245	−0.746226	+	0.665693i	$0.768136\pi$
$864$	5.86236	0.199442
$865$	56.6629	1.92660
$866$	28.2832	0.961103
$867$	1.66628	0.0565899
$868$	0	0
$869$	51.5717	1.74945
$870$	−8.13932	−0.275949
$871$	6.61751	0.224226
$872$	−37.4417	−1.26794
$873$	−14.3129	−0.484419
$874$	−0.382072	−0.0129238
$875$	0	0
$876$	−15.3886	−0.519934
$877$	−18.9128	−0.638641	−0.319320	−	0.947647i	$-0.603455\pi$
$877$	−18.9128	−0.638641	−0.319320	+	0.947647i	$0.603455\pi$
$878$	22.1629	0.747960
$879$	24.1949	0.816074
$880$	−10.2186	−0.344469
$881$	−7.66829	−0.258351	−0.129176	−	0.991622i	$-0.541233\pi$
$881$	−7.66829	−0.258351	−0.129176	+	0.991622i	$0.541233\pi$
$882$	0	0
$883$	−14.3735	−0.483708	−0.241854	−	0.970313i	$-0.577755\pi$
$883$	−14.3735	−0.483708	−0.241854	+	0.970313i	$0.577755\pi$
$884$	6.17716	0.207760
$885$	−36.6431	−1.23174
$886$	−15.1847	−0.510140
$887$	31.3745	1.05345	0.526727	−	0.850035i	$-0.323419\pi$
$887$	31.3745	1.05345	0.526727	+	0.850035i	$0.323419\pi$
$888$	−9.92154	−0.332945
$889$	0	0
$890$	3.50321	0.117428
$891$	3.02467	0.101330
$892$	−16.5353	−0.553643
$893$	−0.721510	−0.0241444
$894$	6.32037	0.211385
$895$	−60.3236	−2.01640
$896$	0	0
$897$	−5.25288	−0.175389
$898$	−19.0420	−0.635438
$899$	7.82420	0.260952
$900$	−12.8340	−0.427801
$901$	−54.4114	−1.81271
$902$	22.5763	0.751707
$903$	0	0
$904$	−28.0647	−0.933419
$905$	−23.9528	−0.796219
$906$	9.56537	0.317788
$907$	6.73722	0.223706	0.111853	−	0.993725i	$-0.464321\pi$
$907$	6.73722	0.223706	0.111853	+	0.993725i	$0.464321\pi$
$908$	−3.53204	−0.117215
$909$	−10.3698	−0.343944
$910$	0	0
$911$	7.21983	0.239204	0.119602	−	0.992822i	$-0.461838\pi$
$911$	7.21983	0.239204	0.119602	+	0.992822i	$0.461838\pi$
$912$	0.0870421	0.00288225
$913$	−2.42139	−0.0801362
$914$	7.13590	0.236034
$915$	18.7695	0.620502
$916$	−24.6752	−0.815291
$917$	0	0
$918$	−3.26259	−0.107681
$919$	49.9265	1.64692	0.823462	−	0.567372i	$-0.192040\pi$
$919$	49.9265	1.64692	0.823462	+	0.567372i	$0.192040\pi$
$920$	−50.8617	−1.67686
$921$	27.9276	0.920247
$922$	24.3491	0.801895
$923$	−11.4729	−0.377636
$924$	0	0
$925$	34.3864	1.13062
$926$	21.9065	0.719893
$927$	−2.85950	−0.0939182
$928$	16.9017	0.554824
$929$	2.79462	0.0916884	0.0458442	−	0.998949i	$-0.485402\pi$
$929$	2.79462	0.0916884	0.0458442	+	0.998949i	$0.485402\pi$
$930$	−7.66150	−0.251230
$931$	0	0
$932$	−14.1598	−0.463819
$933$	14.9459	0.489306
$934$	−10.6839	−0.349588
$935$	48.8546	1.59772
$936$	−2.58997	−0.0846559
$937$	26.9322	0.879838	0.439919	−	0.898038i	$-0.355007\pi$
$937$	26.9322	0.879838	0.439919	+	0.898038i	$0.355007\pi$
$938$	0	0
$939$	17.5949	0.574188
$940$	−40.0392	−1.30593
$941$	6.11005	0.199182	0.0995910	−	0.995028i	$-0.468247\pi$
$941$	6.11005	0.199182	0.0995910	+	0.995028i	$0.468247\pi$
$942$	−11.4380	−0.372670
$943$	−51.9204	−1.69076
$944$	8.85745	0.288286
$945$	0	0
$946$	17.2981	0.562410
$947$	−15.3242	−0.497968	−0.248984	−	0.968508i	$-0.580097\pi$
$947$	−15.3242	−0.497968	−0.248984	+	0.968508i	$0.580097\pi$
$948$	−24.3777	−0.791751
$949$	10.7632	0.349388
$950$	0.652906	0.0211831
$951$	−1.18402	−0.0383946
$952$	0	0
$953$	−2.92986	−0.0949074	−0.0474537	−	0.998873i	$-0.515111\pi$
$953$	−2.92986	−0.0949074	−0.0474537	+	0.998873i	$0.515111\pi$
$954$	9.51030	0.307907
$955$	83.5347	2.70312
$956$	−7.49059	−0.242263
$957$	8.72038	0.281890
$958$	13.1647	0.425334
$959$	0	0
$960$	−9.79338	−0.316080
$961$	−23.6351	−0.762423
$962$	2.89279	0.0932672
$963$	7.39855	0.238415
$964$	3.53412	0.113826
$965$	14.3213	0.461018
$966$	0	0
$967$	−34.0101	−1.09369	−0.546846	−	0.837233i	$-0.684172\pi$
$967$	−34.0101	−1.09369	−0.546846	+	0.837233i	$0.684172\pi$
$968$	4.79494	0.154115
$969$	−0.416144	−0.0133685
$970$	40.4072	1.29740
$971$	−24.6373	−0.790649	−0.395324	−	0.918542i	$-0.629368\pi$
$971$	−24.6373	−0.790649	−0.395324	+	0.918542i	$0.629368\pi$
$972$	−1.42975	−0.0458592
$973$	0	0
$974$	−9.52976	−0.305353
$975$	8.97642	0.287475
$976$	−4.53702	−0.145226
$977$	24.2128	0.774635	0.387318	−	0.921946i	$-0.373402\pi$
$977$	24.2128	0.774635	0.387318	+	0.921946i	$0.373402\pi$
$978$	−15.7505	−0.503647
$979$	−3.75331	−0.119956
$980$	0	0
$981$	14.4564	0.461558
$982$	−19.6203	−0.626108
$983$	−22.6130	−0.721243	−0.360621	−	0.932712i	$-0.617435\pi$
$983$	−22.6130	−0.721243	−0.360621	+	0.932712i	$0.617435\pi$
$984$	−25.5997	−0.816090
$985$	32.8941	1.04809
$986$	−9.40630	−0.299558
$987$	0	0
$988$	−0.137713	−0.00438123
$989$	−39.7818	−1.26499
$990$	−8.53905	−0.271389
$991$	−1.73045	−0.0549695	−0.0274848	−	0.999622i	$-0.508750\pi$
$991$	−1.73045	−0.0549695	−0.0274848	+	0.999622i	$0.508750\pi$
$992$	15.9095	0.505126
$993$	30.9069	0.980799
$994$	0	0
$995$	60.2873	1.91124
$996$	1.14458	0.0362673
$997$	8.57432	0.271551	0.135776	−	0.990740i	$-0.456647\pi$
$997$	8.57432	0.271551	0.135776	+	0.990740i	$0.456647\pi$
$998$	20.3187	0.643177
$999$	3.83075	0.121200

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1911.2.a.w.1.3	yes	5
3.2	odd	2		5733.2.a.bn.1.3		5
7.6	odd	2		1911.2.a.v.1.3	✓	5
21.20	even	2		5733.2.a.bo.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1911.2.a.v.1.3	✓	5	7.6	odd	2
1911.2.a.w.1.3	yes	5	1.1	even	1	trivial
5733.2.a.bn.1.3		5	3.2	odd	2
5733.2.a.bo.1.3		5	21.20	even	2

Overview	Random
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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:	\( N \)	\(=\)	\( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1911.a (trivial)

\(f(q)\)	\(=\)	\(q+0.755150 q^{2} +1.00000 q^{3} -1.42975 q^{4} -3.73850 q^{5} +0.755150 q^{6} -2.58997 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.755150 q^{2} +1.00000 q^{3} -1.42975 q^{4} -3.73850 q^{5} +0.755150 q^{6} -2.58997 q^{8} +1.00000 q^{9} -2.82313 q^{10} +3.02467 q^{11} -1.42975 q^{12} +1.00000 q^{13} -3.73850 q^{15} +0.903680 q^{16} -4.32045 q^{17} +0.755150 q^{18} +0.0963195 q^{19} +5.34512 q^{20} +2.28408 q^{22} -5.25288 q^{23} -2.58997 q^{24} +8.97642 q^{25} +0.755150 q^{26} +1.00000 q^{27} +2.88308 q^{29} -2.82313 q^{30} +2.71383 q^{31} +5.86236 q^{32} +3.02467 q^{33} -3.26259 q^{34} -1.42975 q^{36} +3.83075 q^{37} +0.0727357 q^{38} +1.00000 q^{39} +9.68263 q^{40} +9.88417 q^{41} +7.57333 q^{43} -4.32452 q^{44} -3.73850 q^{45} -3.96671 q^{46} -7.49079 q^{47} +0.903680 q^{48} +6.77854 q^{50} -4.32045 q^{51} -1.42975 q^{52} +12.5939 q^{53} +0.755150 q^{54} -11.3078 q^{55} +0.0963195 q^{57} +2.17716 q^{58} +9.80153 q^{59} +5.34512 q^{60} -5.02060 q^{61} +2.04935 q^{62} +2.61960 q^{64} -3.73850 q^{65} +2.28408 q^{66} +6.61751 q^{67} +6.17716 q^{68} -5.25288 q^{69} -11.4729 q^{71} -2.58997 q^{72} +10.7632 q^{73} +2.89279 q^{74} +8.97642 q^{75} -0.137713 q^{76} +0.755150 q^{78} +17.0503 q^{79} -3.37841 q^{80} +1.00000 q^{81} +7.46403 q^{82} -0.800544 q^{83} +16.1520 q^{85} +5.71900 q^{86} +2.88308 q^{87} -7.83383 q^{88} -1.24090 q^{89} -2.82313 q^{90} +7.51030 q^{92} +2.71383 q^{93} -5.65667 q^{94} -0.360091 q^{95} +5.86236 q^{96} -14.3129 q^{97} +3.02467 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} + 5 q^{3} + 6 q^{4} + 3 q^{5} + 2 q^{6} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 2 * q^2 + 5 * q^3 + 6 * q^4 + 3 * q^5 + 2 * q^6 + 6 * q^8 + 5 * q^9	\( 5 q + 2 q^{2} + 5 q^{3} + 6 q^{4} + 3 q^{5} + 2 q^{6} + 6 q^{8} + 5 q^{9} + 6 q^{11} + 6 q^{12} + 5 q^{13} + 3 q^{15} - 10 q^{17} + 2 q^{18} + 5 q^{19} + 6 q^{20} + 12 q^{22} + q^{23} + 6 q^{24} + 16 q^{25} + 2 q^{26} + 5 q^{27} + 17 q^{29} + q^{31} + 14 q^{32} + 6 q^{33} + 6 q^{36} + 4 q^{37} - 24 q^{38} + 5 q^{39} + 8 q^{40} + 14 q^{41} - q^{43} - 8 q^{44} + 3 q^{45} + 20 q^{46} - 3 q^{47} + 26 q^{50} - 10 q^{51} + 6 q^{52} + 17 q^{53} + 2 q^{54} + 2 q^{55} + 5 q^{57} - 28 q^{58} - 8 q^{59} + 6 q^{60} - 18 q^{61} - 8 q^{62} + 8 q^{64} + 3 q^{65} + 12 q^{66} + 16 q^{67} - 8 q^{68} + q^{69} - 16 q^{71} + 6 q^{72} + 23 q^{73} + 28 q^{74} + 16 q^{75} - 26 q^{76} + 2 q^{78} + 3 q^{79} - 36 q^{80} + 5 q^{81} - 11 q^{83} - 2 q^{85} - 24 q^{86} + 17 q^{87} + 28 q^{88} - 35 q^{89} + 34 q^{92} + q^{93} + 39 q^{95} + 14 q^{96} + 27 q^{97} + 6 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 + 5 * q^3 + 6 * q^4 + 3 * q^5 + 2 * q^6 + 6 * q^8 + 5 * q^9 + 6 * q^11 + 6 * q^12 + 5 * q^13 + 3 * q^15 - 10 * q^17 + 2 * q^18 + 5 * q^19 + 6 * q^20 + 12 * q^22 + q^23 + 6 * q^24 + 16 * q^25 + 2 * q^26 + 5 * q^27 + 17 * q^29 + q^31 + 14 * q^32 + 6 * q^33 + 6 * q^36 + 4 * q^37 - 24 * q^38 + 5 * q^39 + 8 * q^40 + 14 * q^41 - q^43 - 8 * q^44 + 3 * q^45 + 20 * q^46 - 3 * q^47 + 26 * q^50 - 10 * q^51 + 6 * q^52 + 17 * q^53 + 2 * q^54 + 2 * q^55 + 5 * q^57 - 28 * q^58 - 8 * q^59 + 6 * q^60 - 18 * q^61 - 8 * q^62 + 8 * q^64 + 3 * q^65 + 12 * q^66 + 16 * q^67 - 8 * q^68 + q^69 - 16 * q^71 + 6 * q^72 + 23 * q^73 + 28 * q^74 + 16 * q^75 - 26 * q^76 + 2 * q^78 + 3 * q^79 - 36 * q^80 + 5 * q^81 - 11 * q^83 - 2 * q^85 - 24 * q^86 + 17 * q^87 + 28 * q^88 - 35 * q^89 + 34 * q^92 + q^93 + 39 * q^95 + 14 * q^96 + 27 * q^97 + 6 * q^99

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