LMFDB - Embedded newform 3381.2.a.s.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, 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("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.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:	$26.9974209234$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 483)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.56155 q^{2} +1.00000 q^{3} +4.56155 q^{4} -2.56155 q^{5} -2.56155 q^{6} -6.56155 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.56155 q^{2} +1.00000 q^{3} +4.56155 q^{4} -2.56155 q^{5} -2.56155 q^{6} -6.56155 q^{8} +1.00000 q^{9} +6.56155 q^{10} -2.00000 q^{11} +4.56155 q^{12} +2.12311 q^{13} -2.56155 q^{15} +7.68466 q^{16} -3.43845 q^{17} -2.56155 q^{18} +5.56155 q^{19} -11.6847 q^{20} +5.12311 q^{22} +1.00000 q^{23} -6.56155 q^{24} +1.56155 q^{25} -5.43845 q^{26} +1.00000 q^{27} -0.876894 q^{29} +6.56155 q^{30} -6.68466 q^{31} -6.56155 q^{32} -2.00000 q^{33} +8.80776 q^{34} +4.56155 q^{36} +7.56155 q^{37} -14.2462 q^{38} +2.12311 q^{39} +16.8078 q^{40} +6.24621 q^{41} -12.6847 q^{43} -9.12311 q^{44} -2.56155 q^{45} -2.56155 q^{46} -5.68466 q^{47} +7.68466 q^{48} -4.00000 q^{50} -3.43845 q^{51} +9.68466 q^{52} +12.8078 q^{53} -2.56155 q^{54} +5.12311 q^{55} +5.56155 q^{57} +2.24621 q^{58} +0.876894 q^{59} -11.6847 q^{60} +6.00000 q^{61} +17.1231 q^{62} +1.43845 q^{64} -5.43845 q^{65} +5.12311 q^{66} -5.87689 q^{67} -15.6847 q^{68} +1.00000 q^{69} -6.80776 q^{71} -6.56155 q^{72} +14.1231 q^{73} -19.3693 q^{74} +1.56155 q^{75} +25.3693 q^{76} -5.43845 q^{78} -9.56155 q^{79} -19.6847 q^{80} +1.00000 q^{81} -16.0000 q^{82} +13.1231 q^{83} +8.80776 q^{85} +32.4924 q^{86} -0.876894 q^{87} +13.1231 q^{88} -10.0000 q^{89} +6.56155 q^{90} +4.56155 q^{92} -6.68466 q^{93} +14.5616 q^{94} -14.2462 q^{95} -6.56155 q^{96} -9.36932 q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 2 q^{3} + 5 q^{4} - q^{5} - q^{6} - 9 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 + 2 * q^3 + 5 * q^4 - q^5 - q^6 - 9 * q^8 + 2 * q^9	$ 2 q - q^{2} + 2 q^{3} + 5 q^{4} - q^{5} - q^{6} - 9 q^{8} + 2 q^{9} + 9 q^{10} - 4 q^{11} + 5 q^{12} - 4 q^{13} - q^{15} + 3 q^{16} - 11 q^{17} - q^{18} + 7 q^{19} - 11 q^{20} + 2 q^{22} + 2 q^{23} - 9 q^{24} - q^{25} - 15 q^{26} + 2 q^{27} - 10 q^{29} + 9 q^{30} - q^{31} - 9 q^{32} - 4 q^{33} - 3 q^{34} + 5 q^{36} + 11 q^{37} - 12 q^{38} - 4 q^{39} + 13 q^{40} - 4 q^{41} - 13 q^{43} - 10 q^{44} - q^{45} - q^{46} + q^{47} + 3 q^{48} - 8 q^{50} - 11 q^{51} + 7 q^{52} + 5 q^{53} - q^{54} + 2 q^{55} + 7 q^{57} - 12 q^{58} + 10 q^{59} - 11 q^{60} + 12 q^{61} + 26 q^{62} + 7 q^{64} - 15 q^{65} + 2 q^{66} - 20 q^{67} - 19 q^{68} + 2 q^{69} + 7 q^{71} - 9 q^{72} + 20 q^{73} - 14 q^{74} - q^{75} + 26 q^{76} - 15 q^{78} - 15 q^{79} - 27 q^{80} + 2 q^{81} - 32 q^{82} + 18 q^{83} - 3 q^{85} + 32 q^{86} - 10 q^{87} + 18 q^{88} - 20 q^{89} + 9 q^{90} + 5 q^{92} - q^{93} + 25 q^{94} - 12 q^{95} - 9 q^{96} + 6 q^{97} - 4 q^{99}+O(q^{100}) $ 2 * q - q^2 + 2 * q^3 + 5 * q^4 - q^5 - q^6 - 9 * q^8 + 2 * q^9 + 9 * q^10 - 4 * q^11 + 5 * q^12 - 4 * q^13 - q^15 + 3 * q^16 - 11 * q^17 - q^18 + 7 * q^19 - 11 * q^20 + 2 * q^22 + 2 * q^23 - 9 * q^24 - q^25 - 15 * q^26 + 2 * q^27 - 10 * q^29 + 9 * q^30 - q^31 - 9 * q^32 - 4 * q^33 - 3 * q^34 + 5 * q^36 + 11 * q^37 - 12 * q^38 - 4 * q^39 + 13 * q^40 - 4 * q^41 - 13 * q^43 - 10 * q^44 - q^45 - q^46 + q^47 + 3 * q^48 - 8 * q^50 - 11 * q^51 + 7 * q^52 + 5 * q^53 - q^54 + 2 * q^55 + 7 * q^57 - 12 * q^58 + 10 * q^59 - 11 * q^60 + 12 * q^61 + 26 * q^62 + 7 * q^64 - 15 * q^65 + 2 * q^66 - 20 * q^67 - 19 * q^68 + 2 * q^69 + 7 * q^71 - 9 * q^72 + 20 * q^73 - 14 * q^74 - q^75 + 26 * q^76 - 15 * q^78 - 15 * q^79 - 27 * q^80 + 2 * q^81 - 32 * q^82 + 18 * q^83 - 3 * q^85 + 32 * q^86 - 10 * q^87 + 18 * q^88 - 20 * q^89 + 9 * q^90 + 5 * q^92 - q^93 + 25 * q^94 - 12 * q^95 - 9 * q^96 + 6 * q^97 - 4 * 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 $

$2$	−2.56155	−1.81129	−0.905646	−	0.424035i	$-0.860613\pi$
$2$	−2.56155	−1.81129	−0.905646	+	0.424035i	$0.860613\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.56155	2.28078
$5$	−2.56155	−1.14556	−0.572781	−	0.819709i	$-0.694135\pi$
$5$	−2.56155	−1.14556	−0.572781	+	0.819709i	$0.694135\pi$
$6$	−2.56155	−1.04575
$7$	0	0
$7$	0	0
$8$	−6.56155	−2.31986
$9$	1.00000	0.333333
$10$	6.56155	2.07495
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	4.56155	1.31681
$13$	2.12311	0.588844	0.294422	−	0.955676i	$-0.404873\pi$
$13$	2.12311	0.588844	0.294422	+	0.955676i	$0.404873\pi$
$14$	0	0
$15$	−2.56155	−0.661390
$16$	7.68466	1.92116
$17$	−3.43845	−0.833946	−0.416973	−	0.908919i	$-0.636909\pi$
$17$	−3.43845	−0.833946	−0.416973	+	0.908919i	$0.636909\pi$
$18$	−2.56155	−0.603764
$19$	5.56155	1.27591	0.637954	−	0.770075i	$-0.279781\pi$
$19$	5.56155	1.27591	0.637954	+	0.770075i	$0.279781\pi$
$20$	−11.6847	−2.61277
$21$	0	0
$22$	5.12311	1.09225
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−6.56155	−1.33937
$25$	1.56155	0.312311
$26$	−5.43845	−1.06657
$27$	1.00000	0.192450
$28$	0	0
$29$	−0.876894	−0.162835	−0.0814176	−	0.996680i	$-0.525945\pi$
$29$	−0.876894	−0.162835	−0.0814176	+	0.996680i	$0.525945\pi$
$30$	6.56155	1.19797
$31$	−6.68466	−1.20060	−0.600300	−	0.799775i	$-0.704952\pi$
$31$	−6.68466	−1.20060	−0.600300	+	0.799775i	$0.704952\pi$
$32$	−6.56155	−1.15993
$33$	−2.00000	−0.348155
$34$	8.80776	1.51052
$35$	0	0
$36$	4.56155	0.760259
$37$	7.56155	1.24311	0.621556	−	0.783370i	$-0.286501\pi$
$37$	7.56155	1.24311	0.621556	+	0.783370i	$0.286501\pi$
$38$	−14.2462	−2.31104
$39$	2.12311	0.339969
$40$	16.8078	2.65754
$41$	6.24621	0.975494	0.487747	−	0.872985i	$-0.337819\pi$
$41$	6.24621	0.975494	0.487747	+	0.872985i	$0.337819\pi$
$42$	0	0
$43$	−12.6847	−1.93439	−0.967196	−	0.254031i	$-0.918244\pi$
$43$	−12.6847	−1.93439	−0.967196	+	0.254031i	$0.918244\pi$
$44$	−9.12311	−1.37536
$45$	−2.56155	−0.381854
$46$	−2.56155	−0.377680
$47$	−5.68466	−0.829193	−0.414596	−	0.910005i	$-0.636077\pi$
$47$	−5.68466	−0.829193	−0.414596	+	0.910005i	$0.636077\pi$
$48$	7.68466	1.10918
$49$	0	0
$50$	−4.00000	−0.565685
$51$	−3.43845	−0.481479
$52$	9.68466	1.34302
$53$	12.8078	1.75928	0.879641	−	0.475638i	$-0.157783\pi$
$53$	12.8078	1.75928	0.879641	+	0.475638i	$0.157783\pi$
$54$	−2.56155	−0.348583
$55$	5.12311	0.690799
$56$	0	0
$57$	5.56155	0.736646
$58$	2.24621	0.294942
$59$	0.876894	0.114162	0.0570810	−	0.998370i	$-0.481821\pi$
$59$	0.876894	0.114162	0.0570810	+	0.998370i	$0.481821\pi$
$60$	−11.6847	−1.50848
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	17.1231	2.17464
$63$	0	0
$64$	1.43845	0.179806
$65$	−5.43845	−0.674556
$66$	5.12311	0.630611
$67$	−5.87689	−0.717977	−0.358988	−	0.933342i	$-0.616878\pi$
$67$	−5.87689	−0.717977	−0.358988	+	0.933342i	$0.616878\pi$
$68$	−15.6847	−1.90204
$69$	1.00000	0.120386
$70$	0	0
$71$	−6.80776	−0.807933	−0.403966	−	0.914774i	$-0.632369\pi$
$71$	−6.80776	−0.807933	−0.403966	+	0.914774i	$0.632369\pi$
$72$	−6.56155	−0.773286
$73$	14.1231	1.65298	0.826492	−	0.562948i	$-0.190333\pi$
$73$	14.1231	1.65298	0.826492	+	0.562948i	$0.190333\pi$
$74$	−19.3693	−2.25164
$75$	1.56155	0.180313
$76$	25.3693	2.91006
$77$	0	0
$78$	−5.43845	−0.615783
$79$	−9.56155	−1.07576	−0.537879	−	0.843022i	$-0.680774\pi$
$79$	−9.56155	−1.07576	−0.537879	+	0.843022i	$0.680774\pi$
$80$	−19.6847	−2.20081
$81$	1.00000	0.111111
$82$	−16.0000	−1.76690
$83$	13.1231	1.44045	0.720224	−	0.693742i	$-0.244039\pi$
$83$	13.1231	1.44045	0.720224	+	0.693742i	$0.244039\pi$
$84$	0	0
$85$	8.80776	0.955336
$86$	32.4924	3.50375
$87$	−0.876894	−0.0940129
$88$	13.1231	1.39893
$89$	−10.0000	−1.06000	−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000	−1.06000	−0.529999	+	0.847998i	$0.677808\pi$
$90$	6.56155	0.691648
$91$	0	0
$92$	4.56155	0.475575
$93$	−6.68466	−0.693167
$94$	14.5616	1.50191
$95$	−14.2462	−1.46163
$96$	−6.56155	−0.669686
$97$	−9.36932	−0.951310	−0.475655	−	0.879632i	$-0.657789\pi$
$97$	−9.36932	−0.951310	−0.475655	+	0.879632i	$0.657789\pi$
$98$	0	0
$99$	−2.00000	−0.201008
$100$	7.12311	0.712311
$101$	−9.12311	−0.907783	−0.453891	−	0.891057i	$-0.649965\pi$
$101$	−9.12311	−0.907783	−0.453891	+	0.891057i	$0.649965\pi$
$102$	8.80776	0.872099
$103$	5.87689	0.579068	0.289534	−	0.957168i	$-0.406500\pi$
$103$	5.87689	0.579068	0.289534	+	0.957168i	$0.406500\pi$
$104$	−13.9309	−1.36603
$105$	0	0
$106$	−32.8078	−3.18657
$107$	10.2462	0.990539	0.495269	−	0.868739i	$-0.335069\pi$
$107$	10.2462	0.990539	0.495269	+	0.868739i	$0.335069\pi$
$108$	4.56155	0.438936
$109$	−6.43845	−0.616691	−0.308346	−	0.951274i	$-0.599775\pi$
$109$	−6.43845	−0.616691	−0.308346	+	0.951274i	$0.599775\pi$
$110$	−13.1231	−1.25124
$111$	7.56155	0.717711
$112$	0	0
$113$	−10.8078	−1.01671	−0.508354	−	0.861148i	$-0.669746\pi$
$113$	−10.8078	−1.01671	−0.508354	+	0.861148i	$0.669746\pi$
$114$	−14.2462	−1.33428
$115$	−2.56155	−0.238866
$116$	−4.00000	−0.371391
$117$	2.12311	0.196281
$118$	−2.24621	−0.206781
$119$	0	0
$120$	16.8078	1.53433
$121$	−7.00000	−0.636364
$122$	−15.3693	−1.39147
$123$	6.24621	0.563202
$124$	−30.4924	−2.73830
$125$	8.80776	0.787790
$126$	0	0
$127$	−10.6847	−0.948110	−0.474055	−	0.880495i	$-0.657210\pi$
$127$	−10.6847	−0.948110	−0.474055	+	0.880495i	$0.657210\pi$
$128$	9.43845	0.834249
$129$	−12.6847	−1.11682
$130$	13.9309	1.22182
$131$	0.315342	0.0275515	0.0137758	−	0.999905i	$-0.495615\pi$
$131$	0.315342	0.0275515	0.0137758	+	0.999905i	$0.495615\pi$
$132$	−9.12311	−0.794064
$133$	0	0
$134$	15.0540	1.30047
$135$	−2.56155	−0.220463
$136$	22.5616	1.93464
$137$	12.8078	1.09424	0.547121	−	0.837054i	$-0.315724\pi$
$137$	12.8078	1.09424	0.547121	+	0.837054i	$0.315724\pi$
$138$	−2.56155	−0.218054
$139$	−16.9309	−1.43606	−0.718029	−	0.696013i	$-0.754955\pi$
$139$	−16.9309	−1.43606	−0.718029	+	0.696013i	$0.754955\pi$
$140$	0	0
$141$	−5.68466	−0.478735
$142$	17.4384	1.46340
$143$	−4.24621	−0.355086
$144$	7.68466	0.640388
$145$	2.24621	0.186538
$146$	−36.1771	−2.99404
$147$	0	0
$148$	34.4924	2.83526
$149$	−13.6847	−1.12109	−0.560545	−	0.828124i	$-0.689408\pi$
$149$	−13.6847	−1.12109	−0.560545	+	0.828124i	$0.689408\pi$
$150$	−4.00000	−0.326599
$151$	−1.75379	−0.142721	−0.0713607	−	0.997451i	$-0.522734\pi$
$151$	−1.75379	−0.142721	−0.0713607	+	0.997451i	$0.522734\pi$
$152$	−36.4924	−2.95993
$153$	−3.43845	−0.277982
$154$	0	0
$155$	17.1231	1.37536
$156$	9.68466	0.775393
$157$	−12.2462	−0.977354	−0.488677	−	0.872465i	$-0.662520\pi$
$157$	−12.2462	−0.977354	−0.488677	+	0.872465i	$0.662520\pi$
$158$	24.4924	1.94851
$159$	12.8078	1.01572
$160$	16.8078	1.32877
$161$	0	0
$162$	−2.56155	−0.201255
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	28.4924	2.22488
$165$	5.12311	0.398833
$166$	−33.6155	−2.60907
$167$	−15.6847	−1.21372	−0.606858	−	0.794811i	$-0.707570\pi$
$167$	−15.6847	−1.21372	−0.606858	+	0.794811i	$0.707570\pi$
$168$	0	0
$169$	−8.49242	−0.653263
$170$	−22.5616	−1.73039
$171$	5.56155	0.425303
$172$	−57.8617	−4.41192
$173$	1.36932	0.104107	0.0520536	−	0.998644i	$-0.483423\pi$
$173$	1.36932	0.104107	0.0520536	+	0.998644i	$0.483423\pi$
$174$	2.24621	0.170285
$175$	0	0
$176$	−15.3693	−1.15851
$177$	0.876894	0.0659114
$178$	25.6155	1.91997
$179$	−21.9309	−1.63919	−0.819595	−	0.572943i	$-0.805802\pi$
$179$	−21.9309	−1.63919	−0.819595	+	0.572943i	$0.805802\pi$
$180$	−11.6847	−0.870923
$181$	20.9309	1.55578	0.777890	−	0.628401i	$-0.216290\pi$
$181$	20.9309	1.55578	0.777890	+	0.628401i	$0.216290\pi$
$182$	0	0
$183$	6.00000	0.443533
$184$	−6.56155	−0.483724
$185$	−19.3693	−1.42406
$186$	17.1231	1.25553
$187$	6.87689	0.502888
$188$	−25.9309	−1.89120
$189$	0	0
$190$	36.4924	2.64744
$191$	7.12311	0.515410	0.257705	−	0.966224i	$-0.417034\pi$
$191$	7.12311	0.515410	0.257705	+	0.966224i	$0.417034\pi$
$192$	1.43845	0.103811
$193$	16.1231	1.16057	0.580283	−	0.814415i	$-0.302942\pi$
$193$	16.1231	1.16057	0.580283	+	0.814415i	$0.302942\pi$
$194$	24.0000	1.72310
$195$	−5.43845	−0.389455
$196$	0	0
$197$	3.36932	0.240054	0.120027	−	0.992771i	$-0.461702\pi$
$197$	3.36932	0.240054	0.120027	+	0.992771i	$0.461702\pi$
$198$	5.12311	0.364083
$199$	−8.00000	−0.567105	−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000	−0.567105	−0.283552	+	0.958957i	$0.591513\pi$
$200$	−10.2462	−0.724517
$201$	−5.87689	−0.414524
$202$	23.3693	1.64426
$203$	0	0
$204$	−15.6847	−1.09815
$205$	−16.0000	−1.11749
$206$	−15.0540	−1.04886
$207$	1.00000	0.0695048
$208$	16.3153	1.13127
$209$	−11.1231	−0.769401
$210$	0	0
$211$	1.12311	0.0773178	0.0386589	−	0.999252i	$-0.487691\pi$
$211$	1.12311	0.0773178	0.0386589	+	0.999252i	$0.487691\pi$
$212$	58.4233	4.01253
$213$	−6.80776	−0.466460
$214$	−26.2462	−1.79415
$215$	32.4924	2.21596
$216$	−6.56155	−0.446457
$217$	0	0
$218$	16.4924	1.11701
$219$	14.1231	0.954351
$220$	23.3693	1.57556
$221$	−7.30019	−0.491064
$222$	−19.3693	−1.29998
$223$	12.4924	0.836554	0.418277	−	0.908319i	$-0.362634\pi$
$223$	12.4924	0.836554	0.418277	+	0.908319i	$0.362634\pi$
$224$	0	0
$225$	1.56155	0.104104
$226$	27.6847	1.84156
$227$	2.00000	0.132745	0.0663723	−	0.997795i	$-0.478857\pi$
$227$	2.00000	0.132745	0.0663723	+	0.997795i	$0.478857\pi$
$228$	25.3693	1.68012
$229$	24.3002	1.60580	0.802901	−	0.596113i	$-0.203289\pi$
$229$	24.3002	1.60580	0.802901	+	0.596113i	$0.203289\pi$
$230$	6.56155	0.432656
$231$	0	0
$232$	5.75379	0.377755
$233$	−19.1231	−1.25280	−0.626398	−	0.779503i	$-0.715472\pi$
$233$	−19.1231	−1.25280	−0.626398	+	0.779503i	$0.715472\pi$
$234$	−5.43845	−0.355522
$235$	14.5616	0.949891
$236$	4.00000	0.260378
$237$	−9.56155	−0.621090
$238$	0	0
$239$	−1.75379	−0.113443	−0.0567216	−	0.998390i	$-0.518065\pi$
$239$	−1.75379	−0.113443	−0.0567216	+	0.998390i	$0.518065\pi$
$240$	−19.6847	−1.27064
$241$	2.00000	0.128831	0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000	0.128831	0.0644157	+	0.997923i	$0.479482\pi$
$242$	17.9309	1.15264
$243$	1.00000	0.0641500
$244$	27.3693	1.75214
$245$	0	0
$246$	−16.0000	−1.02012
$247$	11.8078	0.751310
$248$	43.8617	2.78522
$249$	13.1231	0.831643
$250$	−22.5616	−1.42692
$251$	2.00000	0.126239	0.0631194	−	0.998006i	$-0.479895\pi$
$251$	2.00000	0.126239	0.0631194	+	0.998006i	$0.479895\pi$
$252$	0	0
$253$	−2.00000	−0.125739
$254$	27.3693	1.71730
$255$	8.80776	0.551564
$256$	−27.0540	−1.69087
$257$	−31.3693	−1.95676	−0.978382	−	0.206805i	$-0.933693\pi$
$257$	−31.3693	−1.95676	−0.978382	+	0.206805i	$0.933693\pi$
$258$	32.4924	2.02289
$259$	0	0
$260$	−24.8078	−1.53851
$261$	−0.876894	−0.0542784
$262$	−0.807764	−0.0499038
$263$	−28.4924	−1.75692	−0.878459	−	0.477818i	$-0.841428\pi$
$263$	−28.4924	−1.75692	−0.878459	+	0.477818i	$0.841428\pi$
$264$	13.1231	0.807671
$265$	−32.8078	−2.01536
$266$	0	0
$267$	−10.0000	−0.611990
$268$	−26.8078	−1.63754
$269$	24.4924	1.49333	0.746665	−	0.665201i	$-0.231654\pi$
$269$	24.4924	1.49333	0.746665	+	0.665201i	$0.231654\pi$
$270$	6.56155	0.399323
$271$	21.6155	1.31305	0.656525	−	0.754304i	$-0.272026\pi$
$271$	21.6155	1.31305	0.656525	+	0.754304i	$0.272026\pi$
$272$	−26.4233	−1.60215
$273$	0	0
$274$	−32.8078	−1.98199
$275$	−3.12311	−0.188330
$276$	4.56155	0.274573
$277$	−12.7538	−0.766301	−0.383150	−	0.923686i	$-0.625161\pi$
$277$	−12.7538	−0.766301	−0.383150	+	0.923686i	$0.625161\pi$
$278$	43.3693	2.60112
$279$	−6.68466	−0.400200
$280$	0	0
$281$	15.4384	0.920981	0.460490	−	0.887665i	$-0.347674\pi$
$281$	15.4384	0.920981	0.460490	+	0.887665i	$0.347674\pi$
$282$	14.5616	0.867128
$283$	−15.8769	−0.943783	−0.471892	−	0.881657i	$-0.656429\pi$
$283$	−15.8769	−0.943783	−0.471892	+	0.881657i	$0.656429\pi$
$284$	−31.0540	−1.84271
$285$	−14.2462	−0.843873
$286$	10.8769	0.643164
$287$	0	0
$288$	−6.56155	−0.386643
$289$	−5.17708	−0.304534
$290$	−5.75379	−0.337874
$291$	−9.36932	−0.549239
$292$	64.4233	3.77009
$293$	−13.0540	−0.762621	−0.381311	−	0.924447i	$-0.624527\pi$
$293$	−13.0540	−0.762621	−0.381311	+	0.924447i	$0.624527\pi$
$294$	0	0
$295$	−2.24621	−0.130779
$296$	−49.6155	−2.88384
$297$	−2.00000	−0.116052
$298$	35.0540	2.03062
$299$	2.12311	0.122782
$300$	7.12311	0.411253
$301$	0	0
$302$	4.49242	0.258510
$303$	−9.12311	−0.524109
$304$	42.7386	2.45123
$305$	−15.3693	−0.880045
$306$	8.80776	0.503506
$307$	−0.684658	−0.0390755	−0.0195378	−	0.999809i	$-0.506219\pi$
$307$	−0.684658	−0.0390755	−0.0195378	+	0.999809i	$0.506219\pi$
$308$	0	0
$309$	5.87689	0.334325
$310$	−43.8617	−2.49118
$311$	3.43845	0.194976	0.0974882	−	0.995237i	$-0.468919\pi$
$311$	3.43845	0.194976	0.0974882	+	0.995237i	$0.468919\pi$
$312$	−13.9309	−0.788680
$313$	−24.3002	−1.37353	−0.686764	−	0.726881i	$-0.740969\pi$
$313$	−24.3002	−1.37353	−0.686764	+	0.726881i	$0.740969\pi$
$314$	31.3693	1.77027
$315$	0	0
$316$	−43.6155	−2.45357
$317$	−28.2462	−1.58647	−0.793233	−	0.608919i	$-0.791604\pi$
$317$	−28.2462	−1.58647	−0.793233	+	0.608919i	$0.791604\pi$
$318$	−32.8078	−1.83977
$319$	1.75379	0.0981933
$320$	−3.68466	−0.205979
$321$	10.2462	0.571888
$322$	0	0
$323$	−19.1231	−1.06404
$324$	4.56155	0.253420
$325$	3.31534	0.183902
$326$	−10.2462	−0.567485
$327$	−6.43845	−0.356047
$328$	−40.9848	−2.26301
$329$	0	0
$330$	−13.1231	−0.722403
$331$	−19.5616	−1.07520	−0.537600	−	0.843200i	$-0.680669\pi$
$331$	−19.5616	−1.07520	−0.537600	+	0.843200i	$0.680669\pi$
$332$	59.8617	3.28534
$333$	7.56155	0.414371
$334$	40.1771	2.19839
$335$	15.0540	0.822487
$336$	0	0
$337$	−0.192236	−0.0104718	−0.00523588	−	0.999986i	$-0.501667\pi$
$337$	−0.192236	−0.0104718	−0.00523588	+	0.999986i	$0.501667\pi$
$338$	21.7538	1.18325
$339$	−10.8078	−0.586997
$340$	40.1771	2.17891
$341$	13.3693	0.723989
$342$	−14.2462	−0.770347
$343$	0	0
$344$	83.2311	4.48752
$345$	−2.56155	−0.137909
$346$	−3.50758	−0.188569
$347$	−0.315342	−0.0169284	−0.00846421	−	0.999964i	$-0.502694\pi$
$347$	−0.315342	−0.0169284	−0.00846421	+	0.999964i	$0.502694\pi$
$348$	−4.00000	−0.214423
$349$	−27.9309	−1.49511	−0.747553	−	0.664203i	$-0.768771\pi$
$349$	−27.9309	−1.49511	−0.747553	+	0.664203i	$0.768771\pi$
$350$	0	0
$351$	2.12311	0.113323
$352$	13.1231	0.699464
$353$	17.3693	0.924475	0.462238	−	0.886756i	$-0.347047\pi$
$353$	17.3693	0.924475	0.462238	+	0.886756i	$0.347047\pi$
$354$	−2.24621	−0.119385
$355$	17.4384	0.925537
$356$	−45.6155	−2.41762
$357$	0	0
$358$	56.1771	2.96905
$359$	−36.7386	−1.93899	−0.969495	−	0.245109i	$-0.921176\pi$
$359$	−36.7386	−1.93899	−0.969495	+	0.245109i	$0.921176\pi$
$360$	16.8078	0.885847
$361$	11.9309	0.627941
$362$	−53.6155	−2.81797
$363$	−7.00000	−0.367405
$364$	0	0
$365$	−36.1771	−1.89359
$366$	−15.3693	−0.803367
$367$	16.3693	0.854471	0.427236	−	0.904140i	$-0.359487\pi$
$367$	16.3693	0.854471	0.427236	+	0.904140i	$0.359487\pi$
$368$	7.68466	0.400591
$369$	6.24621	0.325165
$370$	49.6155	2.57939
$371$	0	0
$372$	−30.4924	−1.58096
$373$	−2.68466	−0.139006	−0.0695032	−	0.997582i	$-0.522141\pi$
$373$	−2.68466	−0.139006	−0.0695032	+	0.997582i	$0.522141\pi$
$374$	−17.6155	−0.910877
$375$	8.80776	0.454831
$376$	37.3002	1.92361
$377$	−1.86174	−0.0958845
$378$	0	0
$379$	−32.6155	−1.67535	−0.837674	−	0.546171i	$-0.816085\pi$
$379$	−32.6155	−1.67535	−0.837674	+	0.546171i	$0.816085\pi$
$380$	−64.9848	−3.33365
$381$	−10.6847	−0.547392
$382$	−18.2462	−0.933557
$383$	−12.2462	−0.625752	−0.312876	−	0.949794i	$-0.601292\pi$
$383$	−12.2462	−0.625752	−0.312876	+	0.949794i	$0.601292\pi$
$384$	9.43845	0.481654
$385$	0	0
$386$	−41.3002	−2.10212
$387$	−12.6847	−0.644797
$388$	−42.7386	−2.16973
$389$	−25.6155	−1.29876	−0.649379	−	0.760465i	$-0.724971\pi$
$389$	−25.6155	−1.29876	−0.649379	+	0.760465i	$0.724971\pi$
$390$	13.9309	0.705417
$391$	−3.43845	−0.173890
$392$	0	0
$393$	0.315342	0.0159069
$394$	−8.63068	−0.434808
$395$	24.4924	1.23235
$396$	−9.12311	−0.458453
$397$	−18.6155	−0.934287	−0.467143	−	0.884182i	$-0.654717\pi$
$397$	−18.6155	−0.934287	−0.467143	+	0.884182i	$0.654717\pi$
$398$	20.4924	1.02719
$399$	0	0
$400$	12.0000	0.600000
$401$	11.6847	0.583504	0.291752	−	0.956494i	$-0.405762\pi$
$401$	11.6847	0.583504	0.291752	+	0.956494i	$0.405762\pi$
$402$	15.0540	0.750824
$403$	−14.1922	−0.706966
$404$	−41.6155	−2.07045
$405$	−2.56155	−0.127285
$406$	0	0
$407$	−15.1231	−0.749625
$408$	22.5616	1.11696
$409$	−38.8617	−1.92159	−0.960795	−	0.277261i	$-0.910573\pi$
$409$	−38.8617	−1.92159	−0.960795	+	0.277261i	$0.910573\pi$
$410$	40.9848	2.02410
$411$	12.8078	0.631760
$412$	26.8078	1.32072
$413$	0	0
$414$	−2.56155	−0.125893
$415$	−33.6155	−1.65012
$416$	−13.9309	−0.683017
$417$	−16.9309	−0.829108
$418$	28.4924	1.39361
$419$	4.49242	0.219469	0.109735	−	0.993961i	$-0.465000\pi$
$419$	4.49242	0.219469	0.109735	+	0.993961i	$0.465000\pi$
$420$	0	0
$421$	−16.6847	−0.813160	−0.406580	−	0.913615i	$-0.633279\pi$
$421$	−16.6847	−0.813160	−0.406580	+	0.913615i	$0.633279\pi$
$422$	−2.87689	−0.140045
$423$	−5.68466	−0.276398
$424$	−84.0388	−4.08129
$425$	−5.36932	−0.260450
$426$	17.4384	0.844896
$427$	0	0
$428$	46.7386	2.25920
$429$	−4.24621	−0.205009
$430$	−83.2311	−4.01376
$431$	8.00000	0.385346	0.192673	−	0.981263i	$-0.438284\pi$
$431$	8.00000	0.385346	0.192673	+	0.981263i	$0.438284\pi$
$432$	7.68466	0.369728
$433$	13.8078	0.663559	0.331779	−	0.943357i	$-0.392351\pi$
$433$	13.8078	0.663559	0.331779	+	0.943357i	$0.392351\pi$
$434$	0	0
$435$	2.24621	0.107698
$436$	−29.3693	−1.40654
$437$	5.56155	0.266045
$438$	−36.1771	−1.72861
$439$	−25.6155	−1.22256	−0.611281	−	0.791413i	$-0.709346\pi$
$439$	−25.6155	−1.22256	−0.611281	+	0.791413i	$0.709346\pi$
$440$	−33.6155	−1.60256
$441$	0	0
$442$	18.6998	0.889459
$443$	25.6847	1.22031	0.610157	−	0.792280i	$-0.291106\pi$
$443$	25.6847	1.22031	0.610157	+	0.792280i	$0.291106\pi$
$444$	34.4924	1.63694
$445$	25.6155	1.21429
$446$	−32.0000	−1.51524
$447$	−13.6847	−0.647262
$448$	0	0
$449$	−14.0000	−0.660701	−0.330350	−	0.943858i	$-0.607167\pi$
$449$	−14.0000	−0.660701	−0.330350	+	0.943858i	$0.607167\pi$
$450$	−4.00000	−0.188562
$451$	−12.4924	−0.588245
$452$	−49.3002	−2.31889
$453$	−1.75379	−0.0824002
$454$	−5.12311	−0.240439
$455$	0	0
$456$	−36.4924	−1.70891
$457$	5.56155	0.260158	0.130079	−	0.991504i	$-0.458477\pi$
$457$	5.56155	0.260158	0.130079	+	0.991504i	$0.458477\pi$
$458$	−62.2462	−2.90857
$459$	−3.43845	−0.160493
$460$	−11.6847	−0.544800
$461$	12.2462	0.570363	0.285181	−	0.958474i	$-0.407946\pi$
$461$	12.2462	0.570363	0.285181	+	0.958474i	$0.407946\pi$
$462$	0	0
$463$	7.31534	0.339973	0.169986	−	0.985446i	$-0.445628\pi$
$463$	7.31534	0.339973	0.169986	+	0.985446i	$0.445628\pi$
$464$	−6.73863	−0.312833
$465$	17.1231	0.794065
$466$	48.9848	2.26918
$467$	−7.12311	−0.329618	−0.164809	−	0.986325i	$-0.552701\pi$
$467$	−7.12311	−0.329618	−0.164809	+	0.986325i	$0.552701\pi$
$468$	9.68466	0.447673
$469$	0	0
$470$	−37.3002	−1.72053
$471$	−12.2462	−0.564276
$472$	−5.75379	−0.264840
$473$	25.3693	1.16648
$474$	24.4924	1.12497
$475$	8.68466	0.398479
$476$	0	0
$477$	12.8078	0.586427
$478$	4.49242	0.205479
$479$	5.36932	0.245330	0.122665	−	0.992448i	$-0.460856\pi$
$479$	5.36932	0.245330	0.122665	+	0.992448i	$0.460856\pi$
$480$	16.8078	0.767166
$481$	16.0540	0.731998
$482$	−5.12311	−0.233351
$483$	0	0
$484$	−31.9309	−1.45140
$485$	24.0000	1.08978
$486$	−2.56155	−0.116194
$487$	−39.4233	−1.78644	−0.893220	−	0.449620i	$-0.851559\pi$
$487$	−39.4233	−1.78644	−0.893220	+	0.449620i	$0.851559\pi$
$488$	−39.3693	−1.78217
$489$	4.00000	0.180886
$490$	0	0
$491$	−18.3153	−0.826560	−0.413280	−	0.910604i	$-0.635617\pi$
$491$	−18.3153	−0.826560	−0.413280	+	0.910604i	$0.635617\pi$
$492$	28.4924	1.28454
$493$	3.01515	0.135796
$494$	−30.2462	−1.36084
$495$	5.12311	0.230266
$496$	−51.3693	−2.30655
$497$	0	0
$498$	−33.6155	−1.50635
$499$	−23.3153	−1.04374	−0.521869	−	0.853026i	$-0.674765\pi$
$499$	−23.3153	−1.04374	−0.521869	+	0.853026i	$0.674765\pi$
$500$	40.1771	1.79677
$501$	−15.6847	−0.700739
$502$	−5.12311	−0.228655
$503$	−15.3693	−0.685284	−0.342642	−	0.939466i	$-0.611322\pi$
$503$	−15.3693	−0.685284	−0.342642	+	0.939466i	$0.611322\pi$
$504$	0	0
$505$	23.3693	1.03992
$506$	5.12311	0.227750
$507$	−8.49242	−0.377162
$508$	−48.7386	−2.16243
$509$	13.1231	0.581671	0.290836	−	0.956773i	$-0.406067\pi$
$509$	13.1231	0.581671	0.290836	+	0.956773i	$0.406067\pi$
$510$	−22.5616	−0.999042
$511$	0	0
$512$	50.4233	2.22842
$513$	5.56155	0.245549
$514$	80.3542	3.54427
$515$	−15.0540	−0.663357
$516$	−57.8617	−2.54722
$517$	11.3693	0.500022
$518$	0	0
$519$	1.36932	0.0601063
$520$	35.6847	1.56488
$521$	−18.3153	−0.802410	−0.401205	−	0.915988i	$-0.631408\pi$
$521$	−18.3153	−0.802410	−0.401205	+	0.915988i	$0.631408\pi$
$522$	2.24621	0.0983140
$523$	−6.36932	−0.278511	−0.139255	−	0.990257i	$-0.544471\pi$
$523$	−6.36932	−0.278511	−0.139255	+	0.990257i	$0.544471\pi$
$524$	1.43845	0.0628389
$525$	0	0
$526$	72.9848	3.18229
$527$	22.9848	1.00124
$528$	−15.3693	−0.668864
$529$	1.00000	0.0434783
$530$	84.0388	3.65041
$531$	0.876894	0.0380540
$532$	0	0
$533$	13.2614	0.574414
$534$	25.6155	1.10849
$535$	−26.2462	−1.13472
$536$	38.5616	1.66561
$537$	−21.9309	−0.946387
$538$	−62.7386	−2.70485
$539$	0	0
$540$	−11.6847	−0.502828
$541$	−45.7386	−1.96646	−0.983229	−	0.182377i	$-0.941621\pi$
$541$	−45.7386	−1.96646	−0.983229	+	0.182377i	$0.941621\pi$
$542$	−55.3693	−2.37832
$543$	20.9309	0.898230
$544$	22.5616	0.967319
$545$	16.4924	0.706458
$546$	0	0
$547$	4.63068	0.197994	0.0989969	−	0.995088i	$-0.468437\pi$
$547$	4.63068	0.197994	0.0989969	+	0.995088i	$0.468437\pi$
$548$	58.4233	2.49572
$549$	6.00000	0.256074
$550$	8.00000	0.341121
$551$	−4.87689	−0.207763
$552$	−6.56155	−0.279278
$553$	0	0
$554$	32.6695	1.38799
$555$	−19.3693	−0.822182
$556$	−77.2311	−3.27533
$557$	15.7538	0.667509	0.333755	−	0.942660i	$-0.391684\pi$
$557$	15.7538	0.667509	0.333755	+	0.942660i	$0.391684\pi$
$558$	17.1231	0.724879
$559$	−26.9309	−1.13905
$560$	0	0
$561$	6.87689	0.290343
$562$	−39.5464	−1.66816
$563$	2.24621	0.0946665	0.0473333	−	0.998879i	$-0.484928\pi$
$563$	2.24621	0.0946665	0.0473333	+	0.998879i	$0.484928\pi$
$564$	−25.9309	−1.09189
$565$	27.6847	1.16470
$566$	40.6695	1.70947
$567$	0	0
$568$	44.6695	1.87429
$569$	20.1771	0.845867	0.422934	−	0.906161i	$-0.361000\pi$
$569$	20.1771	0.845867	0.422934	+	0.906161i	$0.361000\pi$
$570$	36.4924	1.52850
$571$	−16.8617	−0.705642	−0.352821	−	0.935691i	$-0.614778\pi$
$571$	−16.8617	−0.705642	−0.352821	+	0.935691i	$0.614778\pi$
$572$	−19.3693	−0.809872
$573$	7.12311	0.297572
$574$	0	0
$575$	1.56155	0.0651213
$576$	1.43845	0.0599353
$577$	22.6847	0.944375	0.472187	−	0.881498i	$-0.343465\pi$
$577$	22.6847	0.944375	0.472187	+	0.881498i	$0.343465\pi$
$578$	13.2614	0.551600
$579$	16.1231	0.670053
$580$	10.2462	0.425451
$581$	0	0
$582$	24.0000	0.994832
$583$	−25.6155	−1.06089
$584$	−92.6695	−3.83469
$585$	−5.43845	−0.224852
$586$	33.4384	1.38133
$587$	4.56155	0.188275	0.0941377	−	0.995559i	$-0.469991\pi$
$587$	4.56155	0.188275	0.0941377	+	0.995559i	$0.469991\pi$
$588$	0	0
$589$	−37.1771	−1.53185
$590$	5.75379	0.236880
$591$	3.36932	0.138595
$592$	58.1080	2.38822
$593$	−10.0000	−0.410651	−0.205325	−	0.978694i	$-0.565825\pi$
$593$	−10.0000	−0.410651	−0.205325	+	0.978694i	$0.565825\pi$
$594$	5.12311	0.210204
$595$	0	0
$596$	−62.4233	−2.55696
$597$	−8.00000	−0.327418
$598$	−5.43845	−0.222395
$599$	8.17708	0.334106	0.167053	−	0.985948i	$-0.446575\pi$
$599$	8.17708	0.334106	0.167053	+	0.985948i	$0.446575\pi$
$600$	−10.2462	−0.418300
$601$	−32.0540	−1.30751	−0.653754	−	0.756707i	$-0.726807\pi$
$601$	−32.0540	−1.30751	−0.653754	+	0.756707i	$0.726807\pi$
$602$	0	0
$603$	−5.87689	−0.239326
$604$	−8.00000	−0.325515
$605$	17.9309	0.728994
$606$	23.3693	0.949314
$607$	22.1922	0.900755	0.450378	−	0.892838i	$-0.351289\pi$
$607$	22.1922	0.900755	0.450378	+	0.892838i	$0.351289\pi$
$608$	−36.4924	−1.47996
$609$	0	0
$610$	39.3693	1.59402
$611$	−12.0691	−0.488265
$612$	−15.6847	−0.634015
$613$	26.0000	1.05013	0.525065	−	0.851062i	$-0.324041\pi$
$613$	26.0000	1.05013	0.525065	+	0.851062i	$0.324041\pi$
$614$	1.75379	0.0707772
$615$	−16.0000	−0.645182
$616$	0	0
$617$	27.9309	1.12445	0.562227	−	0.826983i	$-0.309945\pi$
$617$	27.9309	1.12445	0.562227	+	0.826983i	$0.309945\pi$
$618$	−15.0540	−0.605560
$619$	−13.8769	−0.557759	−0.278880	−	0.960326i	$-0.589963\pi$
$619$	−13.8769	−0.557759	−0.278880	+	0.960326i	$0.589963\pi$
$620$	78.1080	3.13689
$621$	1.00000	0.0401286
$622$	−8.80776	−0.353159
$623$	0	0
$624$	16.3153	0.653136
$625$	−30.3693	−1.21477
$626$	62.2462	2.48786
$627$	−11.1231	−0.444214
$628$	−55.8617	−2.22913
$629$	−26.0000	−1.03669
$630$	0	0
$631$	43.0540	1.71395	0.856976	−	0.515357i	$-0.172341\pi$
$631$	43.0540	1.71395	0.856976	+	0.515357i	$0.172341\pi$
$632$	62.7386	2.49561
$633$	1.12311	0.0446394
$634$	72.3542	2.87355
$635$	27.3693	1.08612
$636$	58.4233	2.31663
$637$	0	0
$638$	−4.49242	−0.177857
$639$	−6.80776	−0.269311
$640$	−24.1771	−0.955683
$641$	−38.5616	−1.52309	−0.761545	−	0.648112i	$-0.775559\pi$
$641$	−38.5616	−1.52309	−0.761545	+	0.648112i	$0.775559\pi$
$642$	−26.2462	−1.03586
$643$	41.5616	1.63903	0.819514	−	0.573059i	$-0.194244\pi$
$643$	41.5616	1.63903	0.819514	+	0.573059i	$0.194244\pi$
$644$	0	0
$645$	32.4924	1.27939
$646$	48.9848	1.92728
$647$	25.3693	0.997371	0.498685	−	0.866783i	$-0.333816\pi$
$647$	25.3693	0.997371	0.498685	+	0.866783i	$0.333816\pi$
$648$	−6.56155	−0.257762
$649$	−1.75379	−0.0688422
$650$	−8.49242	−0.333100
$651$	0	0
$652$	18.2462	0.714577
$653$	−22.4924	−0.880197	−0.440098	−	0.897950i	$-0.645056\pi$
$653$	−22.4924	−0.880197	−0.440098	+	0.897950i	$0.645056\pi$
$654$	16.4924	0.644905
$655$	−0.807764	−0.0315620
$656$	48.0000	1.87409
$657$	14.1231	0.550995
$658$	0	0
$659$	−41.6155	−1.62111	−0.810555	−	0.585662i	$-0.800835\pi$
$659$	−41.6155	−1.62111	−0.810555	+	0.585662i	$0.800835\pi$
$660$	23.3693	0.909649
$661$	8.19224	0.318641	0.159321	−	0.987227i	$-0.449070\pi$
$661$	8.19224	0.318641	0.159321	+	0.987227i	$0.449070\pi$
$662$	50.1080	1.94750
$663$	−7.30019	−0.283516
$664$	−86.1080	−3.34164
$665$	0	0
$666$	−19.3693	−0.750546
$667$	−0.876894	−0.0339535
$668$	−71.5464	−2.76821
$669$	12.4924	0.482985
$670$	−38.5616	−1.48976
$671$	−12.0000	−0.463255
$672$	0	0
$673$	10.6847	0.411863	0.205932	−	0.978566i	$-0.433978\pi$
$673$	10.6847	0.411863	0.205932	+	0.978566i	$0.433978\pi$
$674$	0.492423	0.0189674
$675$	1.56155	0.0601042
$676$	−38.7386	−1.48995
$677$	12.0691	0.463854	0.231927	−	0.972733i	$-0.425497\pi$
$677$	12.0691	0.463854	0.231927	+	0.972733i	$0.425497\pi$
$678$	27.6847	1.06322
$679$	0	0
$680$	−57.7926	−2.21625
$681$	2.00000	0.0766402
$682$	−34.2462	−1.31136
$683$	23.0540	0.882136	0.441068	−	0.897474i	$-0.354600\pi$
$683$	23.0540	0.882136	0.441068	+	0.897474i	$0.354600\pi$
$684$	25.3693	0.970020
$685$	−32.8078	−1.25352
$686$	0	0
$687$	24.3002	0.927110
$688$	−97.4773	−3.71629
$689$	27.1922	1.03594
$690$	6.56155	0.249794
$691$	−5.80776	−0.220938	−0.110469	−	0.993880i	$-0.535235\pi$
$691$	−5.80776	−0.220938	−0.110469	+	0.993880i	$0.535235\pi$
$692$	6.24621	0.237445
$693$	0	0
$694$	0.807764	0.0306623
$695$	43.3693	1.64509
$696$	5.75379	0.218097
$697$	−21.4773	−0.813510
$698$	71.5464	2.70807
$699$	−19.1231	−0.723302
$700$	0	0
$701$	−38.1771	−1.44193	−0.720964	−	0.692972i	$-0.756301\pi$
$701$	−38.1771	−1.44193	−0.720964	+	0.692972i	$0.756301\pi$
$702$	−5.43845	−0.205261
$703$	42.0540	1.58610
$704$	−2.87689	−0.108427
$705$	14.5616	0.548420
$706$	−44.4924	−1.67449
$707$	0	0
$708$	4.00000	0.150329
$709$	45.3693	1.70388	0.851940	−	0.523639i	$-0.175426\pi$
$709$	45.3693	1.70388	0.851940	+	0.523639i	$0.175426\pi$
$710$	−44.6695	−1.67642
$711$	−9.56155	−0.358586
$712$	65.6155	2.45905
$713$	−6.68466	−0.250342
$714$	0	0
$715$	10.8769	0.406773
$716$	−100.039	−3.73863
$717$	−1.75379	−0.0654964
$718$	94.1080	3.51208
$719$	33.5464	1.25107	0.625535	−	0.780196i	$-0.284881\pi$
$719$	33.5464	1.25107	0.625535	+	0.780196i	$0.284881\pi$
$720$	−19.6847	−0.733604
$721$	0	0
$722$	−30.5616	−1.13738
$723$	2.00000	0.0743808
$724$	95.4773	3.54838
$725$	−1.36932	−0.0508552
$726$	17.9309	0.665477
$727$	40.6847	1.50891	0.754455	−	0.656352i	$-0.227901\pi$
$727$	40.6847	1.50891	0.754455	+	0.656352i	$0.227901\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	92.6695	3.42985
$731$	43.6155	1.61318
$732$	27.3693	1.01160
$733$	52.3002	1.93175	0.965876	−	0.259006i	$-0.0833949\pi$
$733$	52.3002	1.93175	0.965876	+	0.259006i	$0.0833949\pi$
$734$	−41.9309	−1.54770
$735$	0	0
$736$	−6.56155	−0.241862
$737$	11.7538	0.432956
$738$	−16.0000	−0.588968
$739$	49.6695	1.82712	0.913561	−	0.406701i	$-0.133321\pi$
$739$	49.6695	1.82712	0.913561	+	0.406701i	$0.133321\pi$
$740$	−88.3542	−3.24796
$741$	11.8078	0.433769
$742$	0	0
$743$	−13.6155	−0.499505	−0.249753	−	0.968310i	$-0.580349\pi$
$743$	−13.6155	−0.499505	−0.249753	+	0.968310i	$0.580349\pi$
$744$	43.8617	1.60805
$745$	35.0540	1.28428
$746$	6.87689	0.251781
$747$	13.1231	0.480149
$748$	31.3693	1.14698
$749$	0	0
$750$	−22.5616	−0.823831
$751$	1.06913	0.0390131	0.0195066	−	0.999810i	$-0.493790\pi$
$751$	1.06913	0.0390131	0.0195066	+	0.999810i	$0.493790\pi$
$752$	−43.6847	−1.59302
$753$	2.00000	0.0728841
$754$	4.76894	0.173675
$755$	4.49242	0.163496
$756$	0	0
$757$	19.6155	0.712938	0.356469	−	0.934307i	$-0.383980\pi$
$757$	19.6155	0.712938	0.356469	+	0.934307i	$0.383980\pi$
$758$	83.5464	3.03454
$759$	−2.00000	−0.0725954
$760$	93.4773	3.39078
$761$	−47.6155	−1.72606	−0.863031	−	0.505151i	$-0.831437\pi$
$761$	−47.6155	−1.72606	−0.863031	+	0.505151i	$0.831437\pi$
$762$	27.3693	0.991486
$763$	0	0
$764$	32.4924	1.17553
$765$	8.80776	0.318445
$766$	31.3693	1.13342
$767$	1.86174	0.0672235
$768$	−27.0540	−0.976226
$769$	1.80776	0.0651896	0.0325948	−	0.999469i	$-0.489623\pi$
$769$	1.80776	0.0651896	0.0325948	+	0.999469i	$0.489623\pi$
$770$	0	0
$771$	−31.3693	−1.12974
$772$	73.5464	2.64699
$773$	23.3002	0.838049	0.419025	−	0.907975i	$-0.362372\pi$
$773$	23.3002	0.838049	0.419025	+	0.907975i	$0.362372\pi$
$774$	32.4924	1.16792
$775$	−10.4384	−0.374960
$776$	61.4773	2.20691
$777$	0	0
$778$	65.6155	2.35243
$779$	34.7386	1.24464
$780$	−24.8078	−0.888260
$781$	13.6155	0.487202
$782$	8.80776	0.314965
$783$	−0.876894	−0.0313376
$784$	0	0
$785$	31.3693	1.11962
$786$	−0.807764	−0.0288120
$787$	−41.4384	−1.47712	−0.738561	−	0.674187i	$-0.764494\pi$
$787$	−41.4384	−1.47712	−0.738561	+	0.674187i	$0.764494\pi$
$788$	15.3693	0.547509
$789$	−28.4924	−1.01436
$790$	−62.7386	−2.23214
$791$	0	0
$792$	13.1231	0.466309
$793$	12.7386	0.452362
$794$	47.6847	1.69227
$795$	−32.8078	−1.16357
$796$	−36.4924	−1.29344
$797$	7.05398	0.249865	0.124932	−	0.992165i	$-0.460129\pi$
$797$	7.05398	0.249865	0.124932	+	0.992165i	$0.460129\pi$
$798$	0	0
$799$	19.5464	0.691502
$800$	−10.2462	−0.362258
$801$	−10.0000	−0.353333
$802$	−29.9309	−1.05690
$803$	−28.2462	−0.996787
$804$	−26.8078	−0.945437
$805$	0	0
$806$	36.3542	1.28052
$807$	24.4924	0.862174
$808$	59.8617	2.10593
$809$	−43.3693	−1.52478	−0.762392	−	0.647115i	$-0.775975\pi$
$809$	−43.3693	−1.52478	−0.762392	+	0.647115i	$0.775975\pi$
$810$	6.56155	0.230549
$811$	21.6155	0.759024	0.379512	−	0.925187i	$-0.376092\pi$
$811$	21.6155	0.759024	0.379512	+	0.925187i	$0.376092\pi$
$812$	0	0
$813$	21.6155	0.758090
$814$	38.7386	1.35779
$815$	−10.2462	−0.358909
$816$	−26.4233	−0.925000
$817$	−70.5464	−2.46811
$818$	99.5464	3.48056
$819$	0	0
$820$	−72.9848	−2.54874
$821$	36.7386	1.28219	0.641094	−	0.767463i	$-0.278481\pi$
$821$	36.7386	1.28219	0.641094	+	0.767463i	$0.278481\pi$
$822$	−32.8078	−1.14430
$823$	−27.8617	−0.971199	−0.485600	−	0.874181i	$-0.661399\pi$
$823$	−27.8617	−0.971199	−0.485600	+	0.874181i	$0.661399\pi$
$824$	−38.5616	−1.34336
$825$	−3.12311	−0.108733
$826$	0	0
$827$	−26.7386	−0.929793	−0.464897	−	0.885365i	$-0.653909\pi$
$827$	−26.7386	−0.929793	−0.464897	+	0.885365i	$0.653909\pi$
$828$	4.56155	0.158525
$829$	−31.4924	−1.09378	−0.546889	−	0.837205i	$-0.684188\pi$
$829$	−31.4924	−1.09378	−0.546889	+	0.837205i	$0.684188\pi$
$830$	86.1080	2.98885
$831$	−12.7538	−0.442424
$832$	3.05398	0.105878
$833$	0	0
$834$	43.3693	1.50176
$835$	40.1771	1.39039
$836$	−50.7386	−1.75483
$837$	−6.68466	−0.231056
$838$	−11.5076	−0.397523
$839$	−45.3693	−1.56632	−0.783161	−	0.621819i	$-0.786394\pi$
$839$	−45.3693	−1.56632	−0.783161	+	0.621819i	$0.786394\pi$
$840$	0	0
$841$	−28.2311	−0.973485
$842$	42.7386	1.47287
$843$	15.4384	0.531728
$844$	5.12311	0.176345
$845$	21.7538	0.748353
$846$	14.5616	0.500636
$847$	0	0
$848$	98.4233	3.37987
$849$	−15.8769	−0.544894
$850$	13.7538	0.471751
$851$	7.56155	0.259207
$852$	−31.0540	−1.06389
$853$	−3.06913	−0.105085	−0.0525425	−	0.998619i	$-0.516733\pi$
$853$	−3.06913	−0.105085	−0.0525425	+	0.998619i	$0.516733\pi$
$854$	0	0
$855$	−14.2462	−0.487210
$856$	−67.2311	−2.29791
$857$	−7.36932	−0.251731	−0.125866	−	0.992047i	$-0.540171\pi$
$857$	−7.36932	−0.251731	−0.125866	+	0.992047i	$0.540171\pi$
$858$	10.8769	0.371331
$859$	−9.75379	−0.332795	−0.166397	−	0.986059i	$-0.553213\pi$
$859$	−9.75379	−0.332795	−0.166397	+	0.986059i	$0.553213\pi$
$860$	148.216	5.05412
$861$	0	0
$862$	−20.4924	−0.697975
$863$	47.3002	1.61012	0.805059	−	0.593195i	$-0.202134\pi$
$863$	47.3002	1.61012	0.805059	+	0.593195i	$0.202134\pi$
$864$	−6.56155	−0.223229
$865$	−3.50758	−0.119261
$866$	−35.3693	−1.20190
$867$	−5.17708	−0.175823
$868$	0	0
$869$	19.1231	0.648707
$870$	−5.75379	−0.195072
$871$	−12.4773	−0.422776
$872$	42.2462	1.43064
$873$	−9.36932	−0.317103
$874$	−14.2462	−0.481885
$875$	0	0
$876$	64.4233	2.17666
$877$	13.0540	0.440801	0.220401	−	0.975409i	$-0.429264\pi$
$877$	13.0540	0.440801	0.220401	+	0.975409i	$0.429264\pi$
$878$	65.6155	2.21442
$879$	−13.0540	−0.440300
$880$	39.3693	1.32714
$881$	17.6847	0.595811	0.297906	−	0.954595i	$-0.403712\pi$
$881$	17.6847	0.595811	0.297906	+	0.954595i	$0.403712\pi$
$882$	0	0
$883$	−30.9309	−1.04091	−0.520453	−	0.853890i	$-0.674237\pi$
$883$	−30.9309	−1.04091	−0.520453	+	0.853890i	$0.674237\pi$
$884$	−33.3002	−1.12001
$885$	−2.24621	−0.0755056
$886$	−65.7926	−2.21035
$887$	25.3693	0.851818	0.425909	−	0.904766i	$-0.359954\pi$
$887$	25.3693	0.851818	0.425909	+	0.904766i	$0.359954\pi$
$888$	−49.6155	−1.66499
$889$	0	0
$890$	−65.6155	−2.19944
$891$	−2.00000	−0.0670025
$892$	56.9848	1.90799
$893$	−31.6155	−1.05797
$894$	35.0540	1.17238
$895$	56.1771	1.87779
$896$	0	0
$897$	2.12311	0.0708884
$898$	35.8617	1.19672
$899$	5.86174	0.195500
$900$	7.12311	0.237437
$901$	−44.0388	−1.46715
$902$	32.0000	1.06548
$903$	0	0
$904$	70.9157	2.35862
$905$	−53.6155	−1.78224
$906$	4.49242	0.149251
$907$	−41.7386	−1.38591	−0.692954	−	0.720982i	$-0.743691\pi$
$907$	−41.7386	−1.38591	−0.692954	+	0.720982i	$0.743691\pi$
$908$	9.12311	0.302761
$909$	−9.12311	−0.302594
$910$	0	0
$911$	7.50758	0.248737	0.124369	−	0.992236i	$-0.460309\pi$
$911$	7.50758	0.248737	0.124369	+	0.992236i	$0.460309\pi$
$912$	42.7386	1.41522
$913$	−26.2462	−0.868623
$914$	−14.2462	−0.471223
$915$	−15.3693	−0.508094
$916$	110.847	3.66247
$917$	0	0
$918$	8.80776	0.290700
$919$	−6.50758	−0.214665	−0.107333	−	0.994223i	$-0.534231\pi$
$919$	−6.50758	−0.214665	−0.107333	+	0.994223i	$0.534231\pi$
$920$	16.8078	0.554136
$921$	−0.684658	−0.0225603
$922$	−31.3693	−1.03309
$923$	−14.4536	−0.475746
$924$	0	0
$925$	11.8078	0.388237
$926$	−18.7386	−0.615790
$927$	5.87689	0.193023
$928$	5.75379	0.188877
$929$	36.4924	1.19728	0.598639	−	0.801019i	$-0.295709\pi$
$929$	36.4924	1.19728	0.598639	+	0.801019i	$0.295709\pi$
$930$	−43.8617	−1.43828
$931$	0	0
$932$	−87.2311	−2.85735
$933$	3.43845	0.112570
$934$	18.2462	0.597034
$935$	−17.6155	−0.576089
$936$	−13.9309	−0.455345
$937$	26.9309	0.879793	0.439897	−	0.898048i	$-0.355015\pi$
$937$	26.9309	0.879793	0.439897	+	0.898048i	$0.355015\pi$
$938$	0	0
$939$	−24.3002	−0.793007
$940$	66.4233	2.16649
$941$	−6.87689	−0.224180	−0.112090	−	0.993698i	$-0.535755\pi$
$941$	−6.87689	−0.224180	−0.112090	+	0.993698i	$0.535755\pi$
$942$	31.3693	1.02207
$943$	6.24621	0.203405
$944$	6.73863	0.219324
$945$	0	0
$946$	−64.9848	−2.11284
$947$	−29.6847	−0.964622	−0.482311	−	0.876000i	$-0.660202\pi$
$947$	−29.6847	−0.964622	−0.482311	+	0.876000i	$0.660202\pi$
$948$	−43.6155	−1.41657
$949$	29.9848	0.973349
$950$	−22.2462	−0.721762
$951$	−28.2462	−0.915946
$952$	0	0
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	−32.8078	−1.06219
$955$	−18.2462	−0.590434
$956$	−8.00000	−0.258738
$957$	1.75379	0.0566919
$958$	−13.7538	−0.444365
$959$	0	0
$960$	−3.68466	−0.118922
$961$	13.6847	0.441441
$962$	−41.1231	−1.32586
$963$	10.2462	0.330180
$964$	9.12311	0.293835
$965$	−41.3002	−1.32950
$966$	0	0
$967$	−20.1922	−0.649339	−0.324669	−	0.945828i	$-0.605253\pi$
$967$	−20.1922	−0.649339	−0.324669	+	0.945828i	$0.605253\pi$
$968$	45.9309	1.47627
$969$	−19.1231	−0.614323
$970$	−61.4773	−1.97392
$971$	−0.876894	−0.0281409	−0.0140704	−	0.999901i	$-0.504479\pi$
$971$	−0.876894	−0.0281409	−0.0140704	+	0.999901i	$0.504479\pi$
$972$	4.56155	0.146312
$973$	0	0
$974$	100.985	3.23576
$975$	3.31534	0.106176
$976$	46.1080	1.47588
$977$	−12.5616	−0.401880	−0.200940	−	0.979604i	$-0.564400\pi$
$977$	−12.5616	−0.401880	−0.200940	+	0.979604i	$0.564400\pi$
$978$	−10.2462	−0.327638
$979$	20.0000	0.639203
$980$	0	0
$981$	−6.43845	−0.205564
$982$	46.9157	1.49714
$983$	−19.3693	−0.617785	−0.308893	−	0.951097i	$-0.599958\pi$
$983$	−19.3693	−0.617785	−0.308893	+	0.951097i	$0.599958\pi$
$984$	−40.9848	−1.30655
$985$	−8.63068	−0.274996
$986$	−7.72348	−0.245966
$987$	0	0
$988$	53.8617	1.71357
$989$	−12.6847	−0.403349
$990$	−13.1231	−0.417080
$991$	46.3002	1.47077	0.735387	−	0.677647i	$-0.237000\pi$
$991$	46.3002	1.47077	0.735387	+	0.677647i	$0.237000\pi$
$992$	43.8617	1.39261
$993$	−19.5616	−0.620767
$994$	0	0
$995$	20.4924	0.649653
$996$	59.8617	1.89679
$997$	−22.3002	−0.706254	−0.353127	−	0.935575i	$-0.614882\pi$
$997$	−22.3002	−0.706254	−0.353127	+	0.935575i	$0.614882\pi$
$998$	59.7235	1.89051
$999$	7.56155	0.239237

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.s.1.1		2
7.2	even	3		483.2.i.e.277.2	✓	4
7.4	even	3		483.2.i.e.415.2	yes	4
7.6	odd	2		3381.2.a.q.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.e.277.2	✓	4	7.2	even	3
483.2.i.e.415.2	yes	4	7.4	even	3
3381.2.a.q.1.1		2	7.6	odd	2
3381.2.a.s.1.1		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q-2.56155 q^{2} +1.00000 q^{3} +4.56155 q^{4} -2.56155 q^{5} -2.56155 q^{6} -6.56155 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.56155 q^{2} +1.00000 q^{3} +4.56155 q^{4} -2.56155 q^{5} -2.56155 q^{6} -6.56155 q^{8} +1.00000 q^{9} +6.56155 q^{10} -2.00000 q^{11} +4.56155 q^{12} +2.12311 q^{13} -2.56155 q^{15} +7.68466 q^{16} -3.43845 q^{17} -2.56155 q^{18} +5.56155 q^{19} -11.6847 q^{20} +5.12311 q^{22} +1.00000 q^{23} -6.56155 q^{24} +1.56155 q^{25} -5.43845 q^{26} +1.00000 q^{27} -0.876894 q^{29} +6.56155 q^{30} -6.68466 q^{31} -6.56155 q^{32} -2.00000 q^{33} +8.80776 q^{34} +4.56155 q^{36} +7.56155 q^{37} -14.2462 q^{38} +2.12311 q^{39} +16.8078 q^{40} +6.24621 q^{41} -12.6847 q^{43} -9.12311 q^{44} -2.56155 q^{45} -2.56155 q^{46} -5.68466 q^{47} +7.68466 q^{48} -4.00000 q^{50} -3.43845 q^{51} +9.68466 q^{52} +12.8078 q^{53} -2.56155 q^{54} +5.12311 q^{55} +5.56155 q^{57} +2.24621 q^{58} +0.876894 q^{59} -11.6847 q^{60} +6.00000 q^{61} +17.1231 q^{62} +1.43845 q^{64} -5.43845 q^{65} +5.12311 q^{66} -5.87689 q^{67} -15.6847 q^{68} +1.00000 q^{69} -6.80776 q^{71} -6.56155 q^{72} +14.1231 q^{73} -19.3693 q^{74} +1.56155 q^{75} +25.3693 q^{76} -5.43845 q^{78} -9.56155 q^{79} -19.6847 q^{80} +1.00000 q^{81} -16.0000 q^{82} +13.1231 q^{83} +8.80776 q^{85} +32.4924 q^{86} -0.876894 q^{87} +13.1231 q^{88} -10.0000 q^{89} +6.56155 q^{90} +4.56155 q^{92} -6.68466 q^{93} +14.5616 q^{94} -14.2462 q^{95} -6.56155 q^{96} -9.36932 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 2 q^{3} + 5 q^{4} - q^{5} - q^{6} - 9 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 + 2 * q^3 + 5 * q^4 - q^5 - q^6 - 9 * q^8 + 2 * q^9	\( 2 q - q^{2} + 2 q^{3} + 5 q^{4} - q^{5} - q^{6} - 9 q^{8} + 2 q^{9} + 9 q^{10} - 4 q^{11} + 5 q^{12} - 4 q^{13} - q^{15} + 3 q^{16} - 11 q^{17} - q^{18} + 7 q^{19} - 11 q^{20} + 2 q^{22} + 2 q^{23} - 9 q^{24} - q^{25} - 15 q^{26} + 2 q^{27} - 10 q^{29} + 9 q^{30} - q^{31} - 9 q^{32} - 4 q^{33} - 3 q^{34} + 5 q^{36} + 11 q^{37} - 12 q^{38} - 4 q^{39} + 13 q^{40} - 4 q^{41} - 13 q^{43} - 10 q^{44} - q^{45} - q^{46} + q^{47} + 3 q^{48} - 8 q^{50} - 11 q^{51} + 7 q^{52} + 5 q^{53} - q^{54} + 2 q^{55} + 7 q^{57} - 12 q^{58} + 10 q^{59} - 11 q^{60} + 12 q^{61} + 26 q^{62} + 7 q^{64} - 15 q^{65} + 2 q^{66} - 20 q^{67} - 19 q^{68} + 2 q^{69} + 7 q^{71} - 9 q^{72} + 20 q^{73} - 14 q^{74} - q^{75} + 26 q^{76} - 15 q^{78} - 15 q^{79} - 27 q^{80} + 2 q^{81} - 32 q^{82} + 18 q^{83} - 3 q^{85} + 32 q^{86} - 10 q^{87} + 18 q^{88} - 20 q^{89} + 9 q^{90} + 5 q^{92} - q^{93} + 25 q^{94} - 12 q^{95} - 9 q^{96} + 6 q^{97} - 4 q^{99}+O(q^{100}) \) 2 * q - q^2 + 2 * q^3 + 5 * q^4 - q^5 - q^6 - 9 * q^8 + 2 * q^9 + 9 * q^10 - 4 * q^11 + 5 * q^12 - 4 * q^13 - q^15 + 3 * q^16 - 11 * q^17 - q^18 + 7 * q^19 - 11 * q^20 + 2 * q^22 + 2 * q^23 - 9 * q^24 - q^25 - 15 * q^26 + 2 * q^27 - 10 * q^29 + 9 * q^30 - q^31 - 9 * q^32 - 4 * q^33 - 3 * q^34 + 5 * q^36 + 11 * q^37 - 12 * q^38 - 4 * q^39 + 13 * q^40 - 4 * q^41 - 13 * q^43 - 10 * q^44 - q^45 - q^46 + q^47 + 3 * q^48 - 8 * q^50 - 11 * q^51 + 7 * q^52 + 5 * q^53 - q^54 + 2 * q^55 + 7 * q^57 - 12 * q^58 + 10 * q^59 - 11 * q^60 + 12 * q^61 + 26 * q^62 + 7 * q^64 - 15 * q^65 + 2 * q^66 - 20 * q^67 - 19 * q^68 + 2 * q^69 + 7 * q^71 - 9 * q^72 + 20 * q^73 - 14 * q^74 - q^75 + 26 * q^76 - 15 * q^78 - 15 * q^79 - 27 * q^80 + 2 * q^81 - 32 * q^82 + 18 * q^83 - 3 * q^85 + 32 * q^86 - 10 * q^87 + 18 * q^88 - 20 * q^89 + 9 * q^90 + 5 * q^92 - q^93 + 25 * q^94 - 12 * q^95 - 9 * q^96 + 6 * q^97 - 4 * q^99

Introduction

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