LMFDB - Embedded newform 4018.2.a.bn.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, 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("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0838915322$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.52046292.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 10x^{4} + 9x^{3} + 24x^{2} - 18x + 1 $ x^6 - x^5 - 10x^4 + 9x^3 + 24x^2 - 18x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 574)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.0605469$ of defining polynomial
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.302513 q^{3} +1.00000 q^{4} +2.67551 q^{5} +0.302513 q^{6} -1.00000 q^{8} -2.90849 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.302513 q^{3} +1.00000 q^{4} +2.67551 q^{5} +0.302513 q^{6} -1.00000 q^{8} -2.90849 q^{9} -2.67551 q^{10} -4.53183 q^{11} -0.302513 q^{12} +5.61129 q^{13} -0.809374 q^{15} +1.00000 q^{16} +1.23298 q^{17} +2.90849 q^{18} +5.44398 q^{19} +2.67551 q^{20} +4.53183 q^{22} +4.32083 q^{23} +0.302513 q^{24} +2.15833 q^{25} -5.61129 q^{26} +1.78739 q^{27} -2.63327 q^{29} +0.809374 q^{30} +0.837499 q^{31} -1.00000 q^{32} +1.37094 q^{33} -1.23298 q^{34} -2.90849 q^{36} -10.6865 q^{37} -5.44398 q^{38} -1.69749 q^{39} -2.67551 q^{40} -1.00000 q^{41} -0.192081 q^{43} -4.53183 q^{44} -7.78167 q^{45} -4.32083 q^{46} +9.24823 q^{47} -0.302513 q^{48} -2.15833 q^{50} -0.372992 q^{51} +5.61129 q^{52} +7.10771 q^{53} -1.78739 q^{54} -12.1249 q^{55} -1.64687 q^{57} +2.63327 q^{58} +5.34162 q^{59} -0.809374 q^{60} +1.85948 q^{61} -0.837499 q^{62} +1.00000 q^{64} +15.0130 q^{65} -1.37094 q^{66} -15.8741 q^{67} +1.23298 q^{68} -1.30711 q^{69} +11.9802 q^{71} +2.90849 q^{72} -8.70958 q^{73} +10.6865 q^{74} -0.652922 q^{75} +5.44398 q^{76} +1.69749 q^{78} +10.7417 q^{79} +2.67551 q^{80} +8.18475 q^{81} +1.00000 q^{82} -8.34120 q^{83} +3.29885 q^{85} +0.192081 q^{86} +0.796599 q^{87} +4.53183 q^{88} -2.04328 q^{89} +7.78167 q^{90} +4.32083 q^{92} -0.253354 q^{93} -9.24823 q^{94} +14.5654 q^{95} +0.302513 q^{96} +2.40675 q^{97} +13.1808 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - q^{3} + 6 q^{4} + q^{6} - 6 q^{8} + 5 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - q^3 + 6 * q^4 + q^6 - 6 * q^8 + 5 * q^9	$ 6 q - 6 q^{2} - q^{3} + 6 q^{4} + q^{6} - 6 q^{8} + 5 q^{9} + q^{11} - q^{12} - 4 q^{13} + 2 q^{15} + 6 q^{16} + q^{17} - 5 q^{18} + 3 q^{19} - q^{22} + 21 q^{23} + q^{24} + 4 q^{26} - 13 q^{27} + 5 q^{29} - 2 q^{30} - 3 q^{31} - 6 q^{32} + 19 q^{33} - q^{34} + 5 q^{36} - 2 q^{37} - 3 q^{38} - 11 q^{39} - 6 q^{41} + 12 q^{43} + q^{44} - 28 q^{45} - 21 q^{46} + 18 q^{47} - q^{48} + 13 q^{51} - 4 q^{52} + 14 q^{53} + 13 q^{54} + 7 q^{55} + 5 q^{57} - 5 q^{58} - 16 q^{59} + 2 q^{60} + 20 q^{61} + 3 q^{62} + 6 q^{64} + 18 q^{65} - 19 q^{66} - 13 q^{67} + q^{68} - 15 q^{69} + 11 q^{71} - 5 q^{72} - q^{73} + 2 q^{74} + 23 q^{75} + 3 q^{76} + 11 q^{78} + 19 q^{79} - 6 q^{81} + 6 q^{82} - 15 q^{83} - 2 q^{85} - 12 q^{86} - 10 q^{87} - q^{88} + 14 q^{89} + 28 q^{90} + 21 q^{92} + 35 q^{93} - 18 q^{94} + 24 q^{95} + q^{96} - q^{97} + 10 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 - q^3 + 6 * q^4 + q^6 - 6 * q^8 + 5 * q^9 + q^11 - q^12 - 4 * q^13 + 2 * q^15 + 6 * q^16 + q^17 - 5 * q^18 + 3 * q^19 - q^22 + 21 * q^23 + q^24 + 4 * q^26 - 13 * q^27 + 5 * q^29 - 2 * q^30 - 3 * q^31 - 6 * q^32 + 19 * q^33 - q^34 + 5 * q^36 - 2 * q^37 - 3 * q^38 - 11 * q^39 - 6 * q^41 + 12 * q^43 + q^44 - 28 * q^45 - 21 * q^46 + 18 * q^47 - q^48 + 13 * q^51 - 4 * q^52 + 14 * q^53 + 13 * q^54 + 7 * q^55 + 5 * q^57 - 5 * q^58 - 16 * q^59 + 2 * q^60 + 20 * q^61 + 3 * q^62 + 6 * q^64 + 18 * q^65 - 19 * q^66 - 13 * q^67 + q^68 - 15 * q^69 + 11 * q^71 - 5 * q^72 - q^73 + 2 * q^74 + 23 * q^75 + 3 * q^76 + 11 * q^78 + 19 * q^79 - 6 * q^81 + 6 * q^82 - 15 * q^83 - 2 * q^85 - 12 * q^86 - 10 * q^87 - q^88 + 14 * q^89 + 28 * q^90 + 21 * q^92 + 35 * q^93 - 18 * q^94 + 24 * q^95 + q^96 - q^97 + 10 * 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
$3$	−0.302513	−0.174656	−0.0873279	−	0.996180i	$-0.527833\pi$
$3$	−0.302513	−0.174656	−0.0873279	+	0.996180i	$0.527833\pi$
$4$	1.00000	0.500000
$5$	2.67551	1.19652	0.598261	−	0.801301i	$-0.295859\pi$
$5$	2.67551	1.19652	0.598261	+	0.801301i	$0.295859\pi$
$6$	0.302513	0.123500
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	−2.90849	−0.969495
$10$	−2.67551	−0.846069
$11$	−4.53183	−1.36640	−0.683199	−	0.730232i	$-0.739412\pi$
$11$	−4.53183	−1.36640	−0.683199	+	0.730232i	$0.739412\pi$
$12$	−0.302513	−0.0873279
$13$	5.61129	1.55629	0.778146	−	0.628083i	$-0.216160\pi$
$13$	5.61129	1.55629	0.778146	+	0.628083i	$0.216160\pi$
$14$	0	0
$15$	−0.809374	−0.208980
$16$	1.00000	0.250000
$17$	1.23298	0.299042	0.149521	−	0.988759i	$-0.452227\pi$
$17$	1.23298	0.299042	0.149521	+	0.988759i	$0.452227\pi$
$18$	2.90849	0.685537
$19$	5.44398	1.24893	0.624467	−	0.781051i	$-0.285316\pi$
$19$	5.44398	1.24893	0.624467	+	0.781051i	$0.285316\pi$
$20$	2.67551	0.598261
$21$	0	0
$22$	4.53183	0.966189
$23$	4.32083	0.900955	0.450478	−	0.892788i	$-0.351254\pi$
$23$	4.32083	0.900955	0.450478	+	0.892788i	$0.351254\pi$
$24$	0.302513	0.0617502
$25$	2.15833	0.431666
$26$	−5.61129	−1.10046
$27$	1.78739	0.343984
$28$	0	0
$29$	−2.63327	−0.488987	−0.244493	−	0.969651i	$-0.578622\pi$
$29$	−2.63327	−0.488987	−0.244493	+	0.969651i	$0.578622\pi$
$30$	0.809374	0.147771
$31$	0.837499	0.150419	0.0752096	−	0.997168i	$-0.476037\pi$
$31$	0.837499	0.150419	0.0752096	+	0.997168i	$0.476037\pi$
$32$	−1.00000	−0.176777
$33$	1.37094	0.238649
$34$	−1.23298	−0.211454
$35$	0	0
$36$	−2.90849	−0.484748
$37$	−10.6865	−1.75685	−0.878424	−	0.477882i	$-0.841405\pi$
$37$	−10.6865	−1.75685	−0.878424	+	0.477882i	$0.841405\pi$
$38$	−5.44398	−0.883130
$39$	−1.69749	−0.271816
$40$	−2.67551	−0.423035
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−0.192081	−0.0292921	−0.0146461	−	0.999893i	$-0.504662\pi$
$43$	−0.192081	−0.0292921	−0.0146461	+	0.999893i	$0.504662\pi$
$44$	−4.53183	−0.683199
$45$	−7.78167	−1.16002
$46$	−4.32083	−0.637071
$47$	9.24823	1.34899	0.674497	−	0.738278i	$-0.264361\pi$
$47$	9.24823	1.34899	0.674497	+	0.738278i	$0.264361\pi$
$48$	−0.302513	−0.0436639
$49$	0	0
$50$	−2.15833	−0.305234
$51$	−0.372992	−0.0522294
$52$	5.61129	0.778146
$53$	7.10771	0.976320	0.488160	−	0.872754i	$-0.337668\pi$
$53$	7.10771	0.976320	0.488160	+	0.872754i	$0.337668\pi$
$54$	−1.78739	−0.243233
$55$	−12.1249	−1.63492
$56$	0	0
$57$	−1.64687	−0.218134
$58$	2.63327	0.345766
$59$	5.34162	0.695420	0.347710	−	0.937602i	$-0.386959\pi$
$59$	5.34162	0.695420	0.347710	+	0.937602i	$0.386959\pi$
$60$	−0.809374	−0.104490
$61$	1.85948	0.238082	0.119041	−	0.992889i	$-0.462018\pi$
$61$	1.85948	0.238082	0.119041	+	0.992889i	$0.462018\pi$
$62$	−0.837499	−0.106362
$63$	0	0
$64$	1.00000	0.125000
$65$	15.0130	1.86214
$66$	−1.37094	−0.168750
$67$	−15.8741	−1.93932	−0.969662	−	0.244450i	$-0.921393\pi$
$67$	−15.8741	−1.93932	−0.969662	+	0.244450i	$0.921393\pi$
$68$	1.23298	0.149521
$69$	−1.30711	−0.157357
$70$	0	0
$71$	11.9802	1.42179	0.710894	−	0.703299i	$-0.248291\pi$
$71$	11.9802	1.42179	0.710894	+	0.703299i	$0.248291\pi$
$72$	2.90849	0.342768
$73$	−8.70958	−1.01938	−0.509690	−	0.860358i	$-0.670240\pi$
$73$	−8.70958	−1.01938	−0.509690	+	0.860358i	$0.670240\pi$
$74$	10.6865	1.24228
$75$	−0.652922	−0.0753929
$76$	5.44398	0.624467
$77$	0	0
$78$	1.69749	0.192203
$79$	10.7417	1.20854	0.604269	−	0.796781i	$-0.293465\pi$
$79$	10.7417	1.20854	0.604269	+	0.796781i	$0.293465\pi$
$80$	2.67551	0.299131
$81$	8.18475	0.909417
$82$	1.00000	0.110432
$83$	−8.34120	−0.915566	−0.457783	−	0.889064i	$-0.651356\pi$
$83$	−8.34120	−0.915566	−0.457783	+	0.889064i	$0.651356\pi$
$84$	0	0
$85$	3.29885	0.357810
$86$	0.192081	0.0207126
$87$	0.796599	0.0854044
$88$	4.53183	0.483094
$89$	−2.04328	−0.216587	−0.108294	−	0.994119i	$-0.534539\pi$
$89$	−2.04328	−0.216587	−0.108294	+	0.994119i	$0.534539\pi$
$90$	7.78167	0.820260
$91$	0	0
$92$	4.32083	0.450478
$93$	−0.253354	−0.0262716
$94$	−9.24823	−0.953882
$95$	14.5654	1.49438
$96$	0.302513	0.0308751
$97$	2.40675	0.244368	0.122184	−	0.992507i	$-0.461010\pi$
$97$	2.40675	0.244368	0.122184	+	0.992507i	$0.461010\pi$
$98$	0	0
$99$	13.1808	1.32472
$100$	2.15833	0.215833
$101$	14.2320	1.41614	0.708070	−	0.706142i	$-0.249566\pi$
$101$	14.2320	1.41614	0.708070	+	0.706142i	$0.249566\pi$
$102$	0.372992	0.0369318
$103$	12.4403	1.22578	0.612890	−	0.790168i	$-0.290007\pi$
$103$	12.4403	1.22578	0.612890	+	0.790168i	$0.290007\pi$
$104$	−5.61129	−0.550232
$105$	0	0
$106$	−7.10771	−0.690362
$107$	6.75937	0.653452	0.326726	−	0.945119i	$-0.394054\pi$
$107$	6.75937	0.653452	0.326726	+	0.945119i	$0.394054\pi$
$108$	1.78739	0.171992
$109$	−8.19117	−0.784572	−0.392286	−	0.919843i	$-0.628316\pi$
$109$	−8.19117	−0.784572	−0.392286	+	0.919843i	$0.628316\pi$
$110$	12.1249	1.15607
$111$	3.23280	0.306844
$112$	0	0
$113$	12.2861	1.15578	0.577888	−	0.816116i	$-0.303877\pi$
$113$	12.2861	1.15578	0.577888	+	0.816116i	$0.303877\pi$
$114$	1.64687	0.154244
$115$	11.5604	1.07801
$116$	−2.63327	−0.244493
$117$	−16.3204	−1.50882
$118$	−5.34162	−0.491736
$119$	0	0
$120$	0.809374	0.0738854
$121$	9.53746	0.867042
$122$	−1.85948	−0.168349
$123$	0.302513	0.0272767
$124$	0.837499	0.0752096
$125$	−7.60291	−0.680025
$126$	0	0
$127$	2.23213	0.198069	0.0990346	−	0.995084i	$-0.468425\pi$
$127$	2.23213	0.198069	0.0990346	+	0.995084i	$0.468425\pi$
$128$	−1.00000	−0.0883883
$129$	0.0581070	0.00511604
$130$	−15.0130	−1.31673
$131$	21.0340	1.83775	0.918875	−	0.394548i	$-0.129099\pi$
$131$	21.0340	1.83775	0.918875	+	0.394548i	$0.129099\pi$
$132$	1.37094	0.119325
$133$	0	0
$134$	15.8741	1.37131
$135$	4.78218	0.411584
$136$	−1.23298	−0.105727
$137$	−3.54818	−0.303142	−0.151571	−	0.988446i	$-0.548433\pi$
$137$	−3.54818	−0.303142	−0.151571	+	0.988446i	$0.548433\pi$
$138$	1.30711	0.111268
$139$	2.80375	0.237811	0.118905	−	0.992906i	$-0.462062\pi$
$139$	2.80375	0.237811	0.118905	+	0.992906i	$0.462062\pi$
$140$	0	0
$141$	−2.79771	−0.235610
$142$	−11.9802	−1.00536
$143$	−25.4294	−2.12651
$144$	−2.90849	−0.242374
$145$	−7.04534	−0.585084
$146$	8.70958	0.720810
$147$	0	0
$148$	−10.6865	−0.878424
$149$	−0.0302850	−0.00248105	−0.00124052	−	0.999999i	$-0.500395\pi$
$149$	−0.0302850	−0.00248105	−0.00124052	+	0.999999i	$0.500395\pi$
$150$	0.652922	0.0533108
$151$	−17.2199	−1.40134	−0.700669	−	0.713487i	$-0.747115\pi$
$151$	−17.2199	−1.40134	−0.700669	+	0.713487i	$0.747115\pi$
$152$	−5.44398	−0.441565
$153$	−3.58611	−0.289920
$154$	0	0
$155$	2.24073	0.179980
$156$	−1.69749	−0.135908
$157$	−18.3765	−1.46661	−0.733303	−	0.679902i	$-0.762022\pi$
$157$	−18.3765	−1.46661	−0.733303	+	0.679902i	$0.762022\pi$
$158$	−10.7417	−0.854565
$159$	−2.15017	−0.170520
$160$	−2.67551	−0.211517
$161$	0	0
$162$	−8.18475	−0.643055
$163$	−3.05903	−0.239602	−0.119801	−	0.992798i	$-0.538226\pi$
$163$	−3.05903	−0.239602	−0.119801	+	0.992798i	$0.538226\pi$
$164$	−1.00000	−0.0780869
$165$	3.66795	0.285549
$166$	8.34120	0.647403
$167$	9.88049	0.764575	0.382287	−	0.924043i	$-0.375136\pi$
$167$	9.88049	0.764575	0.382287	+	0.924043i	$0.375136\pi$
$168$	0	0
$169$	18.4866	1.42205
$170$	−3.29885	−0.253010
$171$	−15.8337	−1.21084
$172$	−0.192081	−0.0146461
$173$	11.6774	0.887815	0.443907	−	0.896073i	$-0.353592\pi$
$173$	11.6774	0.887815	0.443907	+	0.896073i	$0.353592\pi$
$174$	−0.796599	−0.0603900
$175$	0	0
$176$	−4.53183	−0.341599
$177$	−1.61591	−0.121459
$178$	2.04328	0.153150
$179$	7.20884	0.538814	0.269407	−	0.963026i	$-0.413172\pi$
$179$	7.20884	0.538814	0.269407	+	0.963026i	$0.413172\pi$
$180$	−7.78167	−0.580011
$181$	17.2003	1.27849	0.639246	−	0.769002i	$-0.279247\pi$
$181$	17.2003	1.27849	0.639246	+	0.769002i	$0.279247\pi$
$182$	0	0
$183$	−0.562517	−0.0415824
$184$	−4.32083	−0.318536
$185$	−28.5918	−2.10211
$186$	0.253354	0.0185768
$187$	−5.58766	−0.408610
$188$	9.24823	0.674497
$189$	0	0
$190$	−14.5654	−1.05668
$191$	9.14524	0.661726	0.330863	−	0.943679i	$-0.392660\pi$
$191$	9.14524	0.661726	0.330863	+	0.943679i	$0.392660\pi$
$192$	−0.302513	−0.0218320
$193$	−13.4178	−0.965837	−0.482918	−	0.875665i	$-0.660423\pi$
$193$	−13.4178	−0.965837	−0.482918	+	0.875665i	$0.660423\pi$
$194$	−2.40675	−0.172794
$195$	−4.54164	−0.325233
$196$	0	0
$197$	−16.3793	−1.16698	−0.583489	−	0.812121i	$-0.698313\pi$
$197$	−16.3793	−1.16698	−0.583489	+	0.812121i	$0.698313\pi$
$198$	−13.1808	−0.936716
$199$	11.7741	0.834645	0.417322	−	0.908758i	$-0.362969\pi$
$199$	11.7741	0.834645	0.417322	+	0.908758i	$0.362969\pi$
$200$	−2.15833	−0.152617
$201$	4.80210	0.338714
$202$	−14.2320	−1.00136
$203$	0	0
$204$	−0.372992	−0.0261147
$205$	−2.67551	−0.186865
$206$	−12.4403	−0.866758
$207$	−12.5671	−0.873472
$208$	5.61129	0.389073
$209$	−24.6712	−1.70654
$210$	0	0
$211$	18.3313	1.26198	0.630990	−	0.775791i	$-0.282649\pi$
$211$	18.3313	1.26198	0.630990	+	0.775791i	$0.282649\pi$
$212$	7.10771	0.488160
$213$	−3.62416	−0.248324
$214$	−6.75937	−0.462061
$215$	−0.513914	−0.0350487
$216$	−1.78739	−0.121617
$217$	0	0
$218$	8.19117	0.554776
$219$	2.63476	0.178041
$220$	−12.1249	−0.817462
$221$	6.91862	0.465396
$222$	−3.23280	−0.216971
$223$	19.6446	1.31550	0.657749	−	0.753237i	$-0.271509\pi$
$223$	19.6446	1.31550	0.657749	+	0.753237i	$0.271509\pi$
$224$	0	0
$225$	−6.27747	−0.418498
$226$	−12.2861	−0.817257
$227$	8.78493	0.583076	0.291538	−	0.956559i	$-0.405833\pi$
$227$	8.78493	0.583076	0.291538	+	0.956559i	$0.405833\pi$
$228$	−1.64687	−0.109067
$229$	−6.89649	−0.455733	−0.227867	−	0.973692i	$-0.573175\pi$
$229$	−6.89649	−0.455733	−0.227867	+	0.973692i	$0.573175\pi$
$230$	−11.5604	−0.762270
$231$	0	0
$232$	2.63327	0.172883
$233$	30.4233	1.99309	0.996547	−	0.0830274i	$-0.0264589\pi$
$233$	30.4233	1.99309	0.996547	+	0.0830274i	$0.0264589\pi$
$234$	16.3204	1.06690
$235$	24.7437	1.61410
$236$	5.34162	0.347710
$237$	−3.24951	−0.211078
$238$	0	0
$239$	6.29887	0.407440	0.203720	−	0.979029i	$-0.434697\pi$
$239$	6.29887	0.407440	0.203720	+	0.979029i	$0.434697\pi$
$240$	−0.809374	−0.0522449
$241$	−9.49953	−0.611919	−0.305959	−	0.952045i	$-0.598977\pi$
$241$	−9.49953	−0.611919	−0.305959	+	0.952045i	$0.598977\pi$
$242$	−9.53746	−0.613091
$243$	−7.83817	−0.502819
$244$	1.85948	0.119041
$245$	0	0
$246$	−0.302513	−0.0192875
$247$	30.5478	1.94371
$248$	−0.837499	−0.0531812
$249$	2.52332	0.159909
$250$	7.60291	0.480850
$251$	11.1562	0.704173	0.352087	−	0.935967i	$-0.385472\pi$
$251$	11.1562	0.704173	0.352087	+	0.935967i	$0.385472\pi$
$252$	0	0
$253$	−19.5813	−1.23106
$254$	−2.23213	−0.140056
$255$	−0.997943	−0.0624936
$256$	1.00000	0.0625000
$257$	−13.6549	−0.851769	−0.425884	−	0.904778i	$-0.640037\pi$
$257$	−13.6549	−0.851769	−0.425884	+	0.904778i	$0.640037\pi$
$258$	−0.0581070	−0.00361758
$259$	0	0
$260$	15.0130	0.931069
$261$	7.65884	0.474070
$262$	−21.0340	−1.29949
$263$	5.43132	0.334910	0.167455	−	0.985880i	$-0.446445\pi$
$263$	5.43132	0.334910	0.167455	+	0.985880i	$0.446445\pi$
$264$	−1.37094	−0.0843752
$265$	19.0167	1.16819
$266$	0	0
$267$	0.618119	0.0378283
$268$	−15.8741	−0.969662
$269$	−19.3636	−1.18062	−0.590311	−	0.807176i	$-0.700995\pi$
$269$	−19.3636	−1.18062	−0.590311	+	0.807176i	$0.700995\pi$
$270$	−4.78218	−0.291034
$271$	−15.6578	−0.951142	−0.475571	−	0.879677i	$-0.657758\pi$
$271$	−15.6578	−0.951142	−0.475571	+	0.879677i	$0.657758\pi$
$272$	1.23298	0.0747604
$273$	0	0
$274$	3.54818	0.214353
$275$	−9.78117	−0.589827
$276$	−1.30711	−0.0786785
$277$	1.44438	0.0867845	0.0433923	−	0.999058i	$-0.486183\pi$
$277$	1.44438	0.0867845	0.0433923	+	0.999058i	$0.486183\pi$
$278$	−2.80375	−0.168157
$279$	−2.43585	−0.145831
$280$	0	0
$281$	−9.76875	−0.582755	−0.291377	−	0.956608i	$-0.594113\pi$
$281$	−9.76875	−0.582755	−0.291377	+	0.956608i	$0.594113\pi$
$282$	2.79771	0.166601
$283$	18.8705	1.12174	0.560869	−	0.827905i	$-0.310467\pi$
$283$	18.8705	1.12174	0.560869	+	0.827905i	$0.310467\pi$
$284$	11.9802	0.710894
$285$	−4.40622	−0.261002
$286$	25.4294	1.50367
$287$	0	0
$288$	2.90849	0.171384
$289$	−15.4798	−0.910574
$290$	7.04534	0.413717
$291$	−0.728071	−0.0426803
$292$	−8.70958	−0.509690
$293$	−7.66092	−0.447556	−0.223778	−	0.974640i	$-0.571839\pi$
$293$	−7.66092	−0.447556	−0.223778	+	0.974640i	$0.571839\pi$
$294$	0	0
$295$	14.2915	0.832085
$296$	10.6865	0.621140
$297$	−8.10015	−0.470019
$298$	0.0302850	0.00175436
$299$	24.2454	1.40215
$300$	−0.652922	−0.0376964
$301$	0	0
$302$	17.2199	0.990895
$303$	−4.30537	−0.247337
$304$	5.44398	0.312234
$305$	4.97505	0.284871
$306$	3.58611	0.205004
$307$	3.85361	0.219937	0.109969	−	0.993935i	$-0.464925\pi$
$307$	3.85361	0.219937	0.109969	+	0.993935i	$0.464925\pi$
$308$	0	0
$309$	−3.76335	−0.214090
$310$	−2.24073	−0.127265
$311$	0.951906	0.0539777	0.0269888	−	0.999636i	$-0.491408\pi$
$311$	0.951906	0.0539777	0.0269888	+	0.999636i	$0.491408\pi$
$312$	1.69749	0.0961013
$313$	23.7853	1.34443	0.672213	−	0.740358i	$-0.265344\pi$
$313$	23.7853	1.34443	0.672213	+	0.740358i	$0.265344\pi$
$314$	18.3765	1.03705
$315$	0	0
$316$	10.7417	0.604269
$317$	−7.44237	−0.418005	−0.209003	−	0.977915i	$-0.567022\pi$
$317$	−7.44237	−0.418005	−0.209003	+	0.977915i	$0.567022\pi$
$318$	2.15017	0.120576
$319$	11.9335	0.668150
$320$	2.67551	0.149565
$321$	−2.04479	−0.114129
$322$	0	0
$323$	6.71232	0.373484
$324$	8.18475	0.454708
$325$	12.1110	0.671798
$326$	3.05903	0.169424
$327$	2.47793	0.137030
$328$	1.00000	0.0552158
$329$	0	0
$330$	−3.66795	−0.201914
$331$	20.3269	1.11727	0.558634	−	0.829414i	$-0.311326\pi$
$331$	20.3269	1.11727	0.558634	+	0.829414i	$0.311326\pi$
$332$	−8.34120	−0.457783
$333$	31.0815	1.70326
$334$	−9.88049	−0.540636
$335$	−42.4711	−2.32044
$336$	0	0
$337$	−32.6366	−1.77783	−0.888914	−	0.458075i	$-0.848539\pi$
$337$	−32.6366	−1.77783	−0.888914	+	0.458075i	$0.848539\pi$
$338$	−18.4866	−1.00554
$339$	−3.71669	−0.201863
$340$	3.29885	0.178905
$341$	−3.79540	−0.205532
$342$	15.8337	0.856191
$343$	0	0
$344$	0.192081	0.0103563
$345$	−3.49717	−0.188281
$346$	−11.6774	−0.627780
$347$	34.9767	1.87765	0.938824	−	0.344398i	$-0.111917\pi$
$347$	34.9767	1.87765	0.938824	+	0.344398i	$0.111917\pi$
$348$	0.796599	0.0427022
$349$	2.25155	0.120523	0.0602614	−	0.998183i	$-0.480807\pi$
$349$	2.25155	0.120523	0.0602614	+	0.998183i	$0.480807\pi$
$350$	0	0
$351$	10.0296	0.535339
$352$	4.53183	0.241547
$353$	30.6220	1.62984	0.814921	−	0.579571i	$-0.196780\pi$
$353$	30.6220	1.62984	0.814921	+	0.579571i	$0.196780\pi$
$354$	1.61591	0.0858846
$355$	32.0531	1.70120
$356$	−2.04328	−0.108294
$357$	0	0
$358$	−7.20884	−0.380999
$359$	−19.1701	−1.01176	−0.505879	−	0.862604i	$-0.668832\pi$
$359$	−19.1701	−1.01176	−0.505879	+	0.862604i	$0.668832\pi$
$360$	7.78167	0.410130
$361$	10.6369	0.559838
$362$	−17.2003	−0.904030
$363$	−2.88520	−0.151434
$364$	0	0
$365$	−23.3025	−1.21971
$366$	0.562517	0.0294032
$367$	30.3024	1.58177	0.790887	−	0.611963i	$-0.209620\pi$
$367$	30.3024	1.58177	0.790887	+	0.611963i	$0.209620\pi$
$368$	4.32083	0.225239
$369$	2.90849	0.151410
$370$	28.5918	1.48641
$371$	0	0
$372$	−0.253354	−0.0131358
$373$	28.5671	1.47915	0.739575	−	0.673074i	$-0.235026\pi$
$373$	28.5671	1.47915	0.739575	+	0.673074i	$0.235026\pi$
$374$	5.58766	0.288931
$375$	2.29998	0.118770
$376$	−9.24823	−0.476941
$377$	−14.7761	−0.761006
$378$	0	0
$379$	−33.0736	−1.69888	−0.849439	−	0.527687i	$-0.823060\pi$
$379$	−33.0736	−1.69888	−0.849439	+	0.527687i	$0.823060\pi$
$380$	14.5654	0.747189
$381$	−0.675247	−0.0345939
$382$	−9.14524	−0.467911
$383$	−17.0073	−0.869032	−0.434516	−	0.900664i	$-0.643081\pi$
$383$	−17.0073	−0.869032	−0.434516	+	0.900664i	$0.643081\pi$
$384$	0.302513	0.0154375
$385$	0	0
$386$	13.4178	0.682950
$387$	0.558665	0.0283986
$388$	2.40675	0.122184
$389$	20.2684	1.02765	0.513824	−	0.857896i	$-0.328228\pi$
$389$	20.2684	1.02765	0.513824	+	0.857896i	$0.328228\pi$
$390$	4.54164	0.229975
$391$	5.32750	0.269423
$392$	0	0
$393$	−6.36306	−0.320974
$394$	16.3793	0.825177
$395$	28.7395	1.44604
$396$	13.1808	0.662358
$397$	10.9200	0.548060	0.274030	−	0.961721i	$-0.411643\pi$
$397$	10.9200	0.548060	0.274030	+	0.961721i	$0.411643\pi$
$398$	−11.7741	−0.590183
$399$	0	0
$400$	2.15833	0.107916
$401$	−13.3283	−0.665586	−0.332793	−	0.943000i	$-0.607991\pi$
$401$	−13.3283	−0.665586	−0.332793	+	0.943000i	$0.607991\pi$
$402$	−4.80210	−0.239507
$403$	4.69945	0.234096
$404$	14.2320	0.708070
$405$	21.8983	1.08814
$406$	0	0
$407$	48.4293	2.40055
$408$	0.372992	0.0184659
$409$	18.8109	0.930139	0.465070	−	0.885274i	$-0.346029\pi$
$409$	18.8109	0.930139	0.465070	+	0.885274i	$0.346029\pi$
$410$	2.67551	0.132134
$411$	1.07337	0.0529454
$412$	12.4403	0.612890
$413$	0	0
$414$	12.5671	0.617638
$415$	−22.3169	−1.09549
$416$	−5.61129	−0.275116
$417$	−0.848169	−0.0415350
$418$	24.6712	1.20671
$419$	−8.19107	−0.400160	−0.200080	−	0.979780i	$-0.564120\pi$
$419$	−8.19107	−0.400160	−0.200080	+	0.979780i	$0.564120\pi$
$420$	0	0
$421$	40.6667	1.98198	0.990988	−	0.133951i	$-0.0427665\pi$
$421$	40.6667	1.98198	0.990988	+	0.133951i	$0.0427665\pi$
$422$	−18.3313	−0.892354
$423$	−26.8984	−1.30784
$424$	−7.10771	−0.345181
$425$	2.66118	0.129086
$426$	3.62416	0.175591
$427$	0	0
$428$	6.75937	0.326726
$429$	7.69272	0.371408
$430$	0.513914	0.0247831
$431$	−10.8454	−0.522402	−0.261201	−	0.965284i	$-0.584119\pi$
$431$	−10.8454	−0.522402	−0.261201	+	0.965284i	$0.584119\pi$
$432$	1.78739	0.0859959
$433$	12.5834	0.604719	0.302360	−	0.953194i	$-0.402226\pi$
$433$	12.5834	0.604719	0.302360	+	0.953194i	$0.402226\pi$
$434$	0	0
$435$	2.13130	0.102188
$436$	−8.19117	−0.392286
$437$	23.5225	1.12523
$438$	−2.63476	−0.125894
$439$	−30.3023	−1.44625	−0.723126	−	0.690716i	$-0.757295\pi$
$439$	−30.3023	−1.44625	−0.723126	+	0.690716i	$0.757295\pi$
$440$	12.1249	0.578033
$441$	0	0
$442$	−6.91862	−0.329085
$443$	−20.0561	−0.952893	−0.476447	−	0.879203i	$-0.658075\pi$
$443$	−20.0561	−0.952893	−0.476447	+	0.879203i	$0.658075\pi$
$444$	3.23280	0.153422
$445$	−5.46681	−0.259152
$446$	−19.6446	−0.930198
$447$	0.00916161	0.000433329 0
$448$	0	0
$449$	35.2349	1.66284	0.831420	−	0.555645i	$-0.187529\pi$
$449$	35.2349	1.66284	0.831420	+	0.555645i	$0.187529\pi$
$450$	6.27747	0.295923
$451$	4.53183	0.213395
$452$	12.2861	0.577888
$453$	5.20925	0.244752
$454$	−8.78493	−0.412297
$455$	0	0
$456$	1.64687	0.0771219
$457$	33.9064	1.58607	0.793036	−	0.609174i	$-0.208499\pi$
$457$	33.9064	1.58607	0.793036	+	0.609174i	$0.208499\pi$
$458$	6.89649	0.322252
$459$	2.20382	0.102866
$460$	11.5604	0.539006
$461$	−12.2136	−0.568845	−0.284423	−	0.958699i	$-0.591802\pi$
$461$	−12.2136	−0.568845	−0.284423	+	0.958699i	$0.591802\pi$
$462$	0	0
$463$	−9.17302	−0.426306	−0.213153	−	0.977019i	$-0.568373\pi$
$463$	−9.17302	−0.426306	−0.213153	+	0.977019i	$0.568373\pi$
$464$	−2.63327	−0.122247
$465$	−0.677850	−0.0314345
$466$	−30.4233	−1.40933
$467$	−17.3031	−0.800693	−0.400346	−	0.916364i	$-0.631110\pi$
$467$	−17.3031	−0.800693	−0.400346	+	0.916364i	$0.631110\pi$
$468$	−16.3204	−0.754409
$469$	0	0
$470$	−24.7437	−1.14134
$471$	5.55913	0.256151
$472$	−5.34162	−0.245868
$473$	0.870479	0.0400247
$474$	3.24951	0.149255
$475$	11.7499	0.539122
$476$	0	0
$477$	−20.6727	−0.946537
$478$	−6.29887	−0.288103
$479$	−38.6426	−1.76563	−0.882813	−	0.469724i	$-0.844353\pi$
$479$	−38.6426	−1.76563	−0.882813	+	0.469724i	$0.844353\pi$
$480$	0.809374	0.0369427
$481$	−59.9650	−2.73417
$482$	9.49953	0.432692
$483$	0	0
$484$	9.53746	0.433521
$485$	6.43926	0.292392
$486$	7.83817	0.355546
$487$	−15.0759	−0.683156	−0.341578	−	0.939853i	$-0.610961\pi$
$487$	−15.0759	−0.683156	−0.341578	+	0.939853i	$0.610961\pi$
$488$	−1.85948	−0.0841747
$489$	0.925397	0.0418479
$490$	0	0
$491$	−2.05333	−0.0926653	−0.0463327	−	0.998926i	$-0.514753\pi$
$491$	−2.05333	−0.0926653	−0.0463327	+	0.998926i	$0.514753\pi$
$492$	0.302513	0.0136383
$493$	−3.24678	−0.146227
$494$	−30.5478	−1.37441
$495$	35.2652	1.58505
$496$	0.837499	0.0376048
$497$	0	0
$498$	−2.52332	−0.113073
$499$	−6.89466	−0.308647	−0.154324	−	0.988020i	$-0.549320\pi$
$499$	−6.89466	−0.308647	−0.154324	+	0.988020i	$0.549320\pi$
$500$	−7.60291	−0.340012
$501$	−2.98897	−0.133537
$502$	−11.1562	−0.497926
$503$	29.2548	1.30441	0.652204	−	0.758043i	$-0.273844\pi$
$503$	29.2548	1.30441	0.652204	+	0.758043i	$0.273844\pi$
$504$	0	0
$505$	38.0779	1.69444
$506$	19.5813	0.870493
$507$	−5.59243	−0.248369
$508$	2.23213	0.0990346
$509$	16.1722	0.716819	0.358409	−	0.933565i	$-0.383319\pi$
$509$	16.1722	0.716819	0.358409	+	0.933565i	$0.383319\pi$
$510$	0.997943	0.0441897
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	9.73053	0.429613
$514$	13.6549	0.602291
$515$	33.2841	1.46667
$516$	0.0581070	0.00255802
$517$	−41.9114	−1.84326
$518$	0	0
$519$	−3.53256	−0.155062
$520$	−15.0130	−0.658365
$521$	12.1289	0.531379	0.265689	−	0.964059i	$-0.414400\pi$
$521$	12.1289	0.531379	0.265689	+	0.964059i	$0.414400\pi$
$522$	−7.65884	−0.335218
$523$	−2.15169	−0.0940868	−0.0470434	−	0.998893i	$-0.514980\pi$
$523$	−2.15169	−0.0940868	−0.0470434	+	0.998893i	$0.514980\pi$
$524$	21.0340	0.918875
$525$	0	0
$526$	−5.43132	−0.236817
$527$	1.03262	0.0449816
$528$	1.37094	0.0596623
$529$	−4.33044	−0.188280
$530$	−19.0167	−0.826034
$531$	−15.5360	−0.674206
$532$	0	0
$533$	−5.61129	−0.243052
$534$	−0.618119	−0.0267486
$535$	18.0847	0.781870
$536$	15.8741	0.685655
$537$	−2.18077	−0.0941070
$538$	19.3636	0.834826
$539$	0	0
$540$	4.78218	0.205792
$541$	−14.8636	−0.639035	−0.319517	−	0.947580i	$-0.603521\pi$
$541$	−14.8636	−0.639035	−0.319517	+	0.947580i	$0.603521\pi$
$542$	15.6578	0.672559
$543$	−5.20332	−0.223296
$544$	−1.23298	−0.0528636
$545$	−21.9155	−0.938758
$546$	0	0
$547$	−6.71360	−0.287053	−0.143526	−	0.989646i	$-0.545844\pi$
$547$	−6.71360	−0.287053	−0.143526	+	0.989646i	$0.545844\pi$
$548$	−3.54818	−0.151571
$549$	−5.40827	−0.230820
$550$	9.78117	0.417070
$551$	−14.3355	−0.610713
$552$	1.30711	0.0556341
$553$	0	0
$554$	−1.44438	−0.0613659
$555$	8.64937	0.367145
$556$	2.80375	0.118905
$557$	25.8666	1.09600	0.548002	−	0.836477i	$-0.315389\pi$
$557$	25.8666	1.09600	0.548002	+	0.836477i	$0.315389\pi$
$558$	2.43585	0.103118
$559$	−1.07782	−0.0455871
$560$	0	0
$561$	1.69034	0.0713661
$562$	9.76875	0.412070
$563$	9.18039	0.386907	0.193454	−	0.981109i	$-0.438031\pi$
$563$	9.18039	0.386907	0.193454	+	0.981109i	$0.438031\pi$
$564$	−2.79771	−0.117805
$565$	32.8714	1.38291
$566$	−18.8705	−0.793188
$567$	0	0
$568$	−11.9802	−0.502678
$569$	4.68175	0.196269	0.0981346	−	0.995173i	$-0.468712\pi$
$569$	4.68175	0.196269	0.0981346	+	0.995173i	$0.468712\pi$
$570$	4.40622	0.184556
$571$	−35.7090	−1.49438	−0.747188	−	0.664613i	$-0.768597\pi$
$571$	−35.7090	−1.49438	−0.747188	+	0.664613i	$0.768597\pi$
$572$	−25.4294	−1.06326
$573$	−2.76655	−0.115574
$574$	0	0
$575$	9.32576	0.388911
$576$	−2.90849	−0.121187
$577$	−20.7675	−0.864562	−0.432281	−	0.901739i	$-0.642291\pi$
$577$	−20.7675	−0.864562	−0.432281	+	0.901739i	$0.642291\pi$
$578$	15.4798	0.643873
$579$	4.05906	0.168689
$580$	−7.04534	−0.292542
$581$	0	0
$582$	0.728071	0.0301795
$583$	−32.2109	−1.33404
$584$	8.70958	0.360405
$585$	−43.6652	−1.80533
$586$	7.66092	0.316470
$587$	3.24039	0.133745	0.0668727	−	0.997762i	$-0.478698\pi$
$587$	3.24039	0.133745	0.0668727	+	0.997762i	$0.478698\pi$
$588$	0	0
$589$	4.55933	0.187864
$590$	−14.2915	−0.588373
$591$	4.95495	0.203819
$592$	−10.6865	−0.439212
$593$	6.41962	0.263622	0.131811	−	0.991275i	$-0.457921\pi$
$593$	6.41962	0.263622	0.131811	+	0.991275i	$0.457921\pi$
$594$	8.10015	0.332353
$595$	0	0
$596$	−0.0302850	−0.00124052
$597$	−3.56182	−0.145776
$598$	−24.2454	−0.991470
$599$	−18.8108	−0.768590	−0.384295	−	0.923210i	$-0.625555\pi$
$599$	−18.8108	−0.768590	−0.384295	+	0.923210i	$0.625555\pi$
$600$	0.652922	0.0266554
$601$	−25.4939	−1.03992	−0.519959	−	0.854191i	$-0.674053\pi$
$601$	−25.4939	−1.03992	−0.519959	+	0.854191i	$0.674053\pi$
$602$	0	0
$603$	46.1695	1.88017
$604$	−17.2199	−0.700669
$605$	25.5175	1.03744
$606$	4.30537	0.174894
$607$	−35.3309	−1.43404	−0.717018	−	0.697054i	$-0.754494\pi$
$607$	−35.3309	−1.43404	−0.717018	+	0.697054i	$0.754494\pi$
$608$	−5.44398	−0.220783
$609$	0	0
$610$	−4.97505	−0.201434
$611$	51.8945	2.09943
$612$	−3.58611	−0.144960
$613$	−8.34101	−0.336890	−0.168445	−	0.985711i	$-0.553875\pi$
$613$	−8.34101	−0.336890	−0.168445	+	0.985711i	$0.553875\pi$
$614$	−3.85361	−0.155519
$615$	0.809374	0.0326371
$616$	0	0
$617$	18.8143	0.757435	0.378717	−	0.925512i	$-0.376365\pi$
$617$	18.8143	0.757435	0.378717	+	0.925512i	$0.376365\pi$
$618$	3.76335	0.151384
$619$	30.9426	1.24369	0.621844	−	0.783141i	$-0.286384\pi$
$619$	30.9426	1.24369	0.621844	+	0.783141i	$0.286384\pi$
$620$	2.24073	0.0899900
$621$	7.72302	0.309914
$622$	−0.951906	−0.0381680
$623$	0	0
$624$	−1.69749	−0.0679539
$625$	−31.1333	−1.24533
$626$	−23.7853	−0.950653
$627$	7.46335	0.298057
$628$	−18.3765	−0.733303
$629$	−13.1762	−0.525371
$630$	0	0
$631$	−14.4094	−0.573629	−0.286815	−	0.957986i	$-0.592596\pi$
$631$	−14.4094	−0.573629	−0.286815	+	0.957986i	$0.592596\pi$
$632$	−10.7417	−0.427283
$633$	−5.54546	−0.220412
$634$	7.44237	0.295574
$635$	5.97207	0.236994
$636$	−2.15017	−0.0852599
$637$	0	0
$638$	−11.9335	−0.472454
$639$	−34.8442	−1.37842
$640$	−2.67551	−0.105759
$641$	−49.4030	−1.95130	−0.975650	−	0.219335i	$-0.929611\pi$
$641$	−49.4030	−1.95130	−0.975650	+	0.219335i	$0.929611\pi$
$642$	2.04479	0.0807016
$643$	0.960171	0.0378655	0.0189327	−	0.999821i	$-0.493973\pi$
$643$	0.960171	0.0378655	0.0189327	+	0.999821i	$0.493973\pi$
$644$	0	0
$645$	0.155466	0.00612145
$646$	−6.71232	−0.264093
$647$	28.4291	1.11767	0.558833	−	0.829280i	$-0.311249\pi$
$647$	28.4291	1.11767	0.558833	+	0.829280i	$0.311249\pi$
$648$	−8.18475	−0.321527
$649$	−24.2073	−0.950220
$650$	−12.1110	−0.475033
$651$	0	0
$652$	−3.05903	−0.119801
$653$	−45.5729	−1.78341	−0.891703	−	0.452621i	$-0.850489\pi$
$653$	−45.5729	−1.78341	−0.891703	+	0.452621i	$0.850489\pi$
$654$	−2.47793	−0.0968948
$655$	56.2766	2.19891
$656$	−1.00000	−0.0390434
$657$	25.3317	0.988284
$658$	0	0
$659$	−27.5301	−1.07242	−0.536211	−	0.844084i	$-0.680145\pi$
$659$	−27.5301	−1.07242	−0.536211	+	0.844084i	$0.680145\pi$
$660$	3.66795	0.142775
$661$	36.5640	1.42217	0.711087	−	0.703104i	$-0.248203\pi$
$661$	36.5640	1.42217	0.711087	+	0.703104i	$0.248203\pi$
$662$	−20.3269	−0.790028
$663$	−2.09297	−0.0812842
$664$	8.34120	0.323701
$665$	0	0
$666$	−31.0815	−1.20438
$667$	−11.3779	−0.440555
$668$	9.88049	0.382287
$669$	−5.94274	−0.229759
$670$	42.4711	1.64080
$671$	−8.42685	−0.325315
$672$	0	0
$673$	18.2388	0.703053	0.351526	−	0.936178i	$-0.385663\pi$
$673$	18.2388	0.703053	0.351526	+	0.936178i	$0.385663\pi$
$674$	32.6366	1.25711
$675$	3.85778	0.148486
$676$	18.4866	0.711023
$677$	−6.40683	−0.246234	−0.123117	−	0.992392i	$-0.539289\pi$
$677$	−6.40683	−0.246234	−0.123117	+	0.992392i	$0.539289\pi$
$678$	3.71669	0.142739
$679$	0	0
$680$	−3.29885	−0.126505
$681$	−2.65755	−0.101838
$682$	3.79540	0.145333
$683$	21.4613	0.821195	0.410598	−	0.911817i	$-0.365320\pi$
$683$	21.4613	0.821195	0.410598	+	0.911817i	$0.365320\pi$
$684$	−15.8337	−0.605418
$685$	−9.49318	−0.362716
$686$	0	0
$687$	2.08628	0.0795964
$688$	−0.192081	−0.00732303
$689$	39.8835	1.51944
$690$	3.49717	0.133135
$691$	−23.4540	−0.892231	−0.446115	−	0.894975i	$-0.647193\pi$
$691$	−23.4540	−0.892231	−0.446115	+	0.894975i	$0.647193\pi$
$692$	11.6774	0.443907
$693$	0	0
$694$	−34.9767	−1.32770
$695$	7.50143	0.284546
$696$	−0.796599	−0.0301950
$697$	−1.23298	−0.0467025
$698$	−2.25155	−0.0852225
$699$	−9.20343	−0.348106
$700$	0	0
$701$	−28.1862	−1.06458	−0.532290	−	0.846562i	$-0.678668\pi$
$701$	−28.1862	−1.06458	−0.532290	+	0.846562i	$0.678668\pi$
$702$	−10.0296	−0.378542
$703$	−58.1770	−2.19419
$704$	−4.53183	−0.170800
$705$	−7.48528	−0.281912
$706$	−30.6220	−1.15247
$707$	0	0
$708$	−1.61591	−0.0607296
$709$	−5.90510	−0.221771	−0.110885	−	0.993833i	$-0.535369\pi$
$709$	−5.90510	−0.221771	−0.110885	+	0.993833i	$0.535369\pi$
$710$	−32.0531	−1.20293
$711$	−31.2421	−1.17167
$712$	2.04328	0.0765752
$713$	3.61869	0.135521
$714$	0	0
$715$	−68.0365	−2.54442
$716$	7.20884	0.269407
$717$	−1.90549	−0.0711617
$718$	19.1701	0.715421
$719$	−34.0146	−1.26853	−0.634265	−	0.773115i	$-0.718697\pi$
$719$	−34.0146	−1.26853	−0.634265	+	0.773115i	$0.718697\pi$
$720$	−7.78167	−0.290006
$721$	0	0
$722$	−10.6369	−0.395865
$723$	2.87373	0.106875
$724$	17.2003	0.639246
$725$	−5.68347	−0.211079
$726$	2.88520	0.107080
$727$	−24.5472	−0.910405	−0.455202	−	0.890388i	$-0.650433\pi$
$727$	−24.5472	−0.910405	−0.455202	+	0.890388i	$0.650433\pi$
$728$	0	0
$729$	−22.1831	−0.821596
$730$	23.3025	0.862465
$731$	−0.236832	−0.00875956
$732$	−0.562517	−0.0207912
$733$	−38.3455	−1.41632	−0.708162	−	0.706050i	$-0.750475\pi$
$733$	−38.3455	−1.41632	−0.708162	+	0.706050i	$0.750475\pi$
$734$	−30.3024	−1.11848
$735$	0	0
$736$	−4.32083	−0.159268
$737$	71.9385	2.64989
$738$	−2.90849	−0.107063
$739$	22.2910	0.819986	0.409993	−	0.912089i	$-0.365531\pi$
$739$	22.2910	0.819986	0.409993	+	0.912089i	$0.365531\pi$
$740$	−28.5918	−1.05105
$741$	−9.24109	−0.339480
$742$	0	0
$743$	23.7524	0.871392	0.435696	−	0.900094i	$-0.356502\pi$
$743$	23.7524	0.871392	0.435696	+	0.900094i	$0.356502\pi$
$744$	0.253354	0.00928841
$745$	−0.0810277	−0.00296863
$746$	−28.5671	−1.04592
$747$	24.2603	0.887637
$748$	−5.58766	−0.204305
$749$	0	0
$750$	−2.29998	−0.0839833
$751$	32.5879	1.18915	0.594574	−	0.804041i	$-0.297321\pi$
$751$	32.5879	1.18915	0.594574	+	0.804041i	$0.297321\pi$
$752$	9.24823	0.337248
$753$	−3.37489	−0.122988
$754$	14.7761	0.538113
$755$	−46.0720	−1.67673
$756$	0	0
$757$	−22.8281	−0.829702	−0.414851	−	0.909889i	$-0.636166\pi$
$757$	−22.8281	−0.829702	−0.414851	+	0.909889i	$0.636166\pi$
$758$	33.0736	1.20129
$759$	5.92358	0.215012
$760$	−14.5654	−0.528342
$761$	48.7280	1.76639	0.883195	−	0.469007i	$-0.155388\pi$
$761$	48.7280	1.76639	0.883195	+	0.469007i	$0.155388\pi$
$762$	0.675247	0.0244616
$763$	0	0
$764$	9.14524	0.330863
$765$	−9.59465	−0.346895
$766$	17.0073	0.614498
$767$	29.9734	1.08228
$768$	−0.302513	−0.0109160
$769$	−21.9943	−0.793135	−0.396568	−	0.918006i	$-0.629799\pi$
$769$	−21.9943	−0.793135	−0.396568	+	0.918006i	$0.629799\pi$
$770$	0	0
$771$	4.13078	0.148766
$772$	−13.4178	−0.482918
$773$	−51.8024	−1.86320	−0.931602	−	0.363481i	$-0.881588\pi$
$773$	−51.8024	−1.86320	−0.931602	+	0.363481i	$0.881588\pi$
$774$	−0.558665	−0.0200808
$775$	1.80760	0.0649308
$776$	−2.40675	−0.0863971
$777$	0	0
$778$	−20.2684	−0.726657
$779$	−5.44398	−0.195051
$780$	−4.54164	−0.162617
$781$	−54.2922	−1.94273
$782$	−5.32750	−0.190511
$783$	−4.70669	−0.168204
$784$	0	0
$785$	−49.1665	−1.75483
$786$	6.36306	0.226963
$787$	−37.1629	−1.32471	−0.662357	−	0.749188i	$-0.730444\pi$
$787$	−37.1629	−1.32471	−0.662357	+	0.749188i	$0.730444\pi$
$788$	−16.3793	−0.583489
$789$	−1.64304	−0.0584939
$790$	−28.7395	−1.02251
$791$	0	0
$792$	−13.1808	−0.468358
$793$	10.4341	0.370525
$794$	−10.9200	−0.387537
$795$	−5.75280	−0.204031
$796$	11.7741	0.417322
$797$	−18.7534	−0.664279	−0.332139	−	0.943230i	$-0.607770\pi$
$797$	−18.7534	−0.664279	−0.332139	+	0.943230i	$0.607770\pi$
$798$	0	0
$799$	11.4029	0.403405
$800$	−2.15833	−0.0763084
$801$	5.94286	0.209981
$802$	13.3283	0.470640
$803$	39.4703	1.39288
$804$	4.80210	0.169357
$805$	0	0
$806$	−4.69945	−0.165531
$807$	5.85775	0.206202
$808$	−14.2320	−0.500681
$809$	13.0276	0.458028	0.229014	−	0.973423i	$-0.426450\pi$
$809$	13.0276	0.458028	0.229014	+	0.973423i	$0.426450\pi$
$810$	−21.8983	−0.769429
$811$	35.4164	1.24364	0.621819	−	0.783161i	$-0.286394\pi$
$811$	35.4164	1.24364	0.621819	+	0.783161i	$0.286394\pi$
$812$	0	0
$813$	4.73667	0.166122
$814$	−48.4293	−1.69745
$815$	−8.18446	−0.286689
$816$	−0.372992	−0.0130573
$817$	−1.04569	−0.0365839
$818$	−18.8109	−0.657708
$819$	0	0
$820$	−2.67551	−0.0934327
$821$	−43.7803	−1.52794	−0.763972	−	0.645250i	$-0.776753\pi$
$821$	−43.7803	−1.52794	−0.763972	+	0.645250i	$0.776753\pi$
$822$	−1.07337	−0.0374381
$823$	32.2317	1.12353	0.561764	−	0.827298i	$-0.310123\pi$
$823$	32.2317	1.12353	0.561764	+	0.827298i	$0.310123\pi$
$824$	−12.4403	−0.433379
$825$	2.95893	0.103017
$826$	0	0
$827$	12.4846	0.434132	0.217066	−	0.976157i	$-0.430351\pi$
$827$	12.4846	0.434132	0.217066	+	0.976157i	$0.430351\pi$
$828$	−12.5671	−0.436736
$829$	21.3862	0.742774	0.371387	−	0.928478i	$-0.378882\pi$
$829$	21.3862	0.742774	0.371387	+	0.928478i	$0.378882\pi$
$830$	22.3169	0.774632
$831$	−0.436944	−0.0151574
$832$	5.61129	0.194537
$833$	0	0
$834$	0.848169	0.0293697
$835$	26.4353	0.914831
$836$	−24.6712	−0.853271
$837$	1.49694	0.0517418
$838$	8.19107	0.282956
$839$	48.9609	1.69032	0.845159	−	0.534515i	$-0.179506\pi$
$839$	48.9609	1.69032	0.845159	+	0.534515i	$0.179506\pi$
$840$	0	0
$841$	−22.0659	−0.760892
$842$	−40.6667	−1.40147
$843$	2.95517	0.101781
$844$	18.3313	0.630990
$845$	49.4610	1.70151
$846$	26.8984	0.924785
$847$	0	0
$848$	7.10771	0.244080
$849$	−5.70858	−0.195918
$850$	−2.66118	−0.0912776
$851$	−46.1745	−1.58284
$852$	−3.62416	−0.124162
$853$	24.1910	0.828284	0.414142	−	0.910212i	$-0.364082\pi$
$853$	24.1910	0.828284	0.414142	+	0.910212i	$0.364082\pi$
$854$	0	0
$855$	−42.3633	−1.44879
$856$	−6.75937	−0.231030
$857$	47.5547	1.62444	0.812218	−	0.583353i	$-0.198260\pi$
$857$	47.5547	1.62444	0.812218	+	0.583353i	$0.198260\pi$
$858$	−7.69272	−0.262625
$859$	27.7055	0.945299	0.472649	−	0.881251i	$-0.343298\pi$
$859$	27.7055	0.945299	0.472649	+	0.881251i	$0.343298\pi$
$860$	−0.513914	−0.0175243
$861$	0	0
$862$	10.8454	0.369394
$863$	−4.05610	−0.138071	−0.0690355	−	0.997614i	$-0.521992\pi$
$863$	−4.05610	−0.138071	−0.0690355	+	0.997614i	$0.521992\pi$
$864$	−1.78739	−0.0608083
$865$	31.2429	1.06229
$866$	−12.5834	−0.427601
$867$	4.68282	0.159037
$868$	0	0
$869$	−48.6796	−1.65134
$870$	−2.13130	−0.0722580
$871$	−89.0739	−3.01816
$872$	8.19117	0.277388
$873$	−6.99999	−0.236914
$874$	−23.5225	−0.795661
$875$	0	0
$876$	2.63476	0.0890203
$877$	−35.6867	−1.20505	−0.602527	−	0.798098i	$-0.705840\pi$
$877$	−35.6867	−1.20505	−0.602527	+	0.798098i	$0.705840\pi$
$878$	30.3023	1.02265
$879$	2.31753	0.0781682
$880$	−12.1249	−0.408731
$881$	53.2845	1.79520	0.897601	−	0.440809i	$-0.145308\pi$
$881$	53.2845	1.79520	0.897601	+	0.440809i	$0.145308\pi$
$882$	0	0
$883$	29.6827	0.998902	0.499451	−	0.866342i	$-0.333535\pi$
$883$	29.6827	0.998902	0.499451	+	0.866342i	$0.333535\pi$
$884$	6.91862	0.232698
$885$	−4.32337	−0.145329
$886$	20.0561	0.673797
$887$	−14.9807	−0.503001	−0.251501	−	0.967857i	$-0.580924\pi$
$887$	−14.9807	−0.503001	−0.251501	+	0.967857i	$0.580924\pi$
$888$	−3.23280	−0.108486
$889$	0	0
$890$	5.46681	0.183248
$891$	−37.0919	−1.24262
$892$	19.6446	0.657749
$893$	50.3472	1.68480
$894$	−0.00916161	−0.000306410 0
$895$	19.2873	0.644703
$896$	0	0
$897$	−7.33455	−0.244894
$898$	−35.2349	−1.17581
$899$	−2.20536	−0.0735530
$900$	−6.27747	−0.209249
$901$	8.76368	0.291960
$902$	−4.53183	−0.150893
$903$	0	0
$904$	−12.2861	−0.408629
$905$	46.0196	1.52974
$906$	−5.20925	−0.173066
$907$	26.2259	0.870818	0.435409	−	0.900233i	$-0.356604\pi$
$907$	26.2259	0.870818	0.435409	+	0.900233i	$0.356604\pi$
$908$	8.78493	0.291538
$909$	−41.3937	−1.37294
$910$	0	0
$911$	−10.6221	−0.351926	−0.175963	−	0.984397i	$-0.556304\pi$
$911$	−10.6221	−0.351926	−0.175963	+	0.984397i	$0.556304\pi$
$912$	−1.64687	−0.0545334
$913$	37.8009	1.25103
$914$	−33.9064	−1.12152
$915$	−1.50502	−0.0497543
$916$	−6.89649	−0.227867
$917$	0	0
$918$	−2.20382	−0.0727369
$919$	18.8892	0.623099	0.311549	−	0.950230i	$-0.399152\pi$
$919$	18.8892	0.623099	0.311549	+	0.950230i	$0.399152\pi$
$920$	−11.5604	−0.381135
$921$	−1.16577	−0.0384133
$922$	12.2136	0.402234
$923$	67.2244	2.21272
$924$	0	0
$925$	−23.0649	−0.758371
$926$	9.17302	0.301444
$927$	−36.1825	−1.18839
$928$	2.63327	0.0864415
$929$	−9.37707	−0.307652	−0.153826	−	0.988098i	$-0.549159\pi$
$929$	−9.37707	−0.307652	−0.153826	+	0.988098i	$0.549159\pi$
$930$	0.677850	0.0222276
$931$	0	0
$932$	30.4233	0.996547
$933$	−0.287964	−0.00942751
$934$	17.3031	0.566175
$935$	−14.9498	−0.488911
$936$	16.3204	0.533448
$937$	48.0417	1.56945	0.784727	−	0.619841i	$-0.212803\pi$
$937$	48.0417	1.56945	0.784727	+	0.619841i	$0.212803\pi$
$938$	0	0
$939$	−7.19536	−0.234812
$940$	24.7437	0.807050
$941$	−6.62455	−0.215954	−0.107977	−	0.994153i	$-0.534437\pi$
$941$	−6.62455	−0.215954	−0.107977	+	0.994153i	$0.534437\pi$
$942$	−5.55913	−0.181126
$943$	−4.32083	−0.140706
$944$	5.34162	0.173855
$945$	0	0
$946$	−0.870479	−0.0283017
$947$	38.1609	1.24006	0.620032	−	0.784577i	$-0.287120\pi$
$947$	38.1609	1.24006	0.620032	+	0.784577i	$0.287120\pi$
$948$	−3.24951	−0.105539
$949$	−48.8720	−1.58645
$950$	−11.7499	−0.381217
$951$	2.25141	0.0730070
$952$	0	0
$953$	−5.36423	−0.173765	−0.0868823	−	0.996219i	$-0.527690\pi$
$953$	−5.36423	−0.173765	−0.0868823	+	0.996219i	$0.527690\pi$
$954$	20.6727	0.669303
$955$	24.4681	0.791770
$956$	6.29887	0.203720
$957$	−3.61005	−0.116696
$958$	38.6426	1.24849
$959$	0	0
$960$	−0.809374	−0.0261224
$961$	−30.2986	−0.977374
$962$	59.9650	1.93335
$963$	−19.6595	−0.633519
$964$	−9.49953	−0.305959
$965$	−35.8995	−1.15565
$966$	0	0
$967$	−17.2209	−0.553786	−0.276893	−	0.960901i	$-0.589305\pi$
$967$	−17.2209	−0.553786	−0.276893	+	0.960901i	$0.589305\pi$
$968$	−9.53746	−0.306546
$969$	−2.03056	−0.0652311
$970$	−6.43926	−0.206752
$971$	45.3102	1.45407	0.727037	−	0.686598i	$-0.240897\pi$
$971$	45.3102	1.45407	0.727037	+	0.686598i	$0.240897\pi$
$972$	−7.83817	−0.251409
$973$	0	0
$974$	15.0759	0.483064
$975$	−3.66373	−0.117333
$976$	1.85948	0.0595205
$977$	−38.2813	−1.22473	−0.612364	−	0.790576i	$-0.709781\pi$
$977$	−38.2813	−1.22473	−0.612364	+	0.790576i	$0.709781\pi$
$978$	−0.925397	−0.0295909
$979$	9.25980	0.295945
$980$	0	0
$981$	23.8239	0.760639
$982$	2.05333	0.0655243
$983$	−12.4157	−0.395998	−0.197999	−	0.980202i	$-0.563444\pi$
$983$	−12.4157	−0.395998	−0.197999	+	0.980202i	$0.563444\pi$
$984$	−0.302513	−0.00964375
$985$	−43.8229	−1.39631
$986$	3.24678	0.103398
$987$	0	0
$988$	30.5478	0.971854
$989$	−0.829950	−0.0263909
$990$	−35.2652	−1.12080
$991$	−23.3035	−0.740260	−0.370130	−	0.928980i	$-0.620687\pi$
$991$	−23.3035	−0.740260	−0.370130	+	0.928980i	$0.620687\pi$
$992$	−0.837499	−0.0265906
$993$	−6.14915	−0.195137
$994$	0	0
$995$	31.5017	0.998671
$996$	2.52332	0.0799544
$997$	32.5685	1.03145	0.515727	−	0.856753i	$-0.327522\pi$
$997$	32.5685	1.03145	0.515727	+	0.856753i	$0.327522\pi$
$998$	6.89466	0.218247
$999$	−19.1009	−0.604327

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bn.1.3		6
7.3	odd	6		574.2.e.g.247.3	yes	12
7.5	odd	6		574.2.e.g.165.3	✓	12
7.6	odd	2		4018.2.a.bo.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.g.165.3	✓	12	7.5	odd	6
574.2.e.g.247.3	yes	12	7.3	odd	6
4018.2.a.bn.1.3		6	1.1	even	1	trivial
4018.2.a.bo.1.4		6	7.6	odd	2

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:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.302513 q^{3} +1.00000 q^{4} +2.67551 q^{5} +0.302513 q^{6} -1.00000 q^{8} -2.90849 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.302513 q^{3} +1.00000 q^{4} +2.67551 q^{5} +0.302513 q^{6} -1.00000 q^{8} -2.90849 q^{9} -2.67551 q^{10} -4.53183 q^{11} -0.302513 q^{12} +5.61129 q^{13} -0.809374 q^{15} +1.00000 q^{16} +1.23298 q^{17} +2.90849 q^{18} +5.44398 q^{19} +2.67551 q^{20} +4.53183 q^{22} +4.32083 q^{23} +0.302513 q^{24} +2.15833 q^{25} -5.61129 q^{26} +1.78739 q^{27} -2.63327 q^{29} +0.809374 q^{30} +0.837499 q^{31} -1.00000 q^{32} +1.37094 q^{33} -1.23298 q^{34} -2.90849 q^{36} -10.6865 q^{37} -5.44398 q^{38} -1.69749 q^{39} -2.67551 q^{40} -1.00000 q^{41} -0.192081 q^{43} -4.53183 q^{44} -7.78167 q^{45} -4.32083 q^{46} +9.24823 q^{47} -0.302513 q^{48} -2.15833 q^{50} -0.372992 q^{51} +5.61129 q^{52} +7.10771 q^{53} -1.78739 q^{54} -12.1249 q^{55} -1.64687 q^{57} +2.63327 q^{58} +5.34162 q^{59} -0.809374 q^{60} +1.85948 q^{61} -0.837499 q^{62} +1.00000 q^{64} +15.0130 q^{65} -1.37094 q^{66} -15.8741 q^{67} +1.23298 q^{68} -1.30711 q^{69} +11.9802 q^{71} +2.90849 q^{72} -8.70958 q^{73} +10.6865 q^{74} -0.652922 q^{75} +5.44398 q^{76} +1.69749 q^{78} +10.7417 q^{79} +2.67551 q^{80} +8.18475 q^{81} +1.00000 q^{82} -8.34120 q^{83} +3.29885 q^{85} +0.192081 q^{86} +0.796599 q^{87} +4.53183 q^{88} -2.04328 q^{89} +7.78167 q^{90} +4.32083 q^{92} -0.253354 q^{93} -9.24823 q^{94} +14.5654 q^{95} +0.302513 q^{96} +2.40675 q^{97} +13.1808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} + q^{6} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 + q^6 - 6 * q^8 + 5 * q^9	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} + q^{6} - 6 q^{8} + 5 q^{9} + q^{11} - q^{12} - 4 q^{13} + 2 q^{15} + 6 q^{16} + q^{17} - 5 q^{18} + 3 q^{19} - q^{22} + 21 q^{23} + q^{24} + 4 q^{26} - 13 q^{27} + 5 q^{29} - 2 q^{30} - 3 q^{31} - 6 q^{32} + 19 q^{33} - q^{34} + 5 q^{36} - 2 q^{37} - 3 q^{38} - 11 q^{39} - 6 q^{41} + 12 q^{43} + q^{44} - 28 q^{45} - 21 q^{46} + 18 q^{47} - q^{48} + 13 q^{51} - 4 q^{52} + 14 q^{53} + 13 q^{54} + 7 q^{55} + 5 q^{57} - 5 q^{58} - 16 q^{59} + 2 q^{60} + 20 q^{61} + 3 q^{62} + 6 q^{64} + 18 q^{65} - 19 q^{66} - 13 q^{67} + q^{68} - 15 q^{69} + 11 q^{71} - 5 q^{72} - q^{73} + 2 q^{74} + 23 q^{75} + 3 q^{76} + 11 q^{78} + 19 q^{79} - 6 q^{81} + 6 q^{82} - 15 q^{83} - 2 q^{85} - 12 q^{86} - 10 q^{87} - q^{88} + 14 q^{89} + 28 q^{90} + 21 q^{92} + 35 q^{93} - 18 q^{94} + 24 q^{95} + q^{96} - q^{97} + 10 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 + q^6 - 6 * q^8 + 5 * q^9 + q^11 - q^12 - 4 * q^13 + 2 * q^15 + 6 * q^16 + q^17 - 5 * q^18 + 3 * q^19 - q^22 + 21 * q^23 + q^24 + 4 * q^26 - 13 * q^27 + 5 * q^29 - 2 * q^30 - 3 * q^31 - 6 * q^32 + 19 * q^33 - q^34 + 5 * q^36 - 2 * q^37 - 3 * q^38 - 11 * q^39 - 6 * q^41 + 12 * q^43 + q^44 - 28 * q^45 - 21 * q^46 + 18 * q^47 - q^48 + 13 * q^51 - 4 * q^52 + 14 * q^53 + 13 * q^54 + 7 * q^55 + 5 * q^57 - 5 * q^58 - 16 * q^59 + 2 * q^60 + 20 * q^61 + 3 * q^62 + 6 * q^64 + 18 * q^65 - 19 * q^66 - 13 * q^67 + q^68 - 15 * q^69 + 11 * q^71 - 5 * q^72 - q^73 + 2 * q^74 + 23 * q^75 + 3 * q^76 + 11 * q^78 + 19 * q^79 - 6 * q^81 + 6 * q^82 - 15 * q^83 - 2 * q^85 - 12 * q^86 - 10 * q^87 - q^88 + 14 * q^89 + 28 * q^90 + 21 * q^92 + 35 * q^93 - 18 * q^94 + 24 * q^95 + q^96 - q^97 + 10 * q^99

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