LMFDB - Embedded newform 2254.2.a.v.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2254,2,Mod(1,2254)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2254, 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("2254.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2254 = 2 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2254.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:	$17.9982806156$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.14013.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 6x + 3 $ x^4 - x^3 - 6x^2 + 6x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 322)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.37167$ of defining polynomial
Character	$\chi$	$=$	2254.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.62484 q^{3} +1.00000 q^{4} +3.37167 q^{5} -2.62484 q^{6} -1.00000 q^{8} +3.88977 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.62484 q^{3} +1.00000 q^{4} +3.37167 q^{5} -2.62484 q^{6} -1.00000 q^{8} +3.88977 q^{9} -3.37167 q^{10} -2.22875 q^{11} +2.62484 q^{12} -3.10674 q^{13} +8.85009 q^{15} +1.00000 q^{16} +6.37167 q^{17} -3.88977 q^{18} +0.914183 q^{19} +3.37167 q^{20} +2.22875 q^{22} +1.00000 q^{23} -2.62484 q^{24} +6.36818 q^{25} +3.10674 q^{26} +2.33549 q^{27} -4.22526 q^{29} -8.85009 q^{30} -3.47842 q^{31} -1.00000 q^{32} -5.85009 q^{33} -6.37167 q^{34} +3.88977 q^{36} +9.41782 q^{37} -0.914183 q^{38} -8.15470 q^{39} -3.37167 q^{40} -5.85009 q^{41} +12.7643 q^{43} -2.22875 q^{44} +13.1150 q^{45} -1.00000 q^{46} +6.56423 q^{47} +2.62484 q^{48} -6.36818 q^{50} +16.7246 q^{51} -3.10674 q^{52} +11.1477 q^{53} -2.33549 q^{54} -7.51460 q^{55} +2.39958 q^{57} +4.22526 q^{58} -2.97209 q^{59} +8.85009 q^{60} +6.80563 q^{61} +3.47842 q^{62} +1.00000 q^{64} -10.4749 q^{65} +5.85009 q^{66} +6.87451 q^{67} +6.37167 q^{68} +2.62484 q^{69} +1.61307 q^{71} -3.88977 q^{72} +5.93591 q^{73} -9.41782 q^{74} +16.7154 q^{75} +0.914183 q^{76} +8.15470 q^{78} -14.7498 q^{79} +3.37167 q^{80} -5.53902 q^{81} +5.85009 q^{82} -6.51111 q^{83} +21.4832 q^{85} -12.7643 q^{86} -11.0906 q^{87} +2.22875 q^{88} -1.58516 q^{89} -13.1150 q^{90} +1.00000 q^{92} -9.13028 q^{93} -6.56423 q^{94} +3.08233 q^{95} -2.62484 q^{96} +13.7970 q^{97} -8.66930 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + q^{3} + 4 q^{4} + 3 q^{5} - q^{6} - 4 q^{8} + 7 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + q^3 + 4 * q^4 + 3 * q^5 - q^6 - 4 * q^8 + 7 * q^9	$ 4 q - 4 q^{2} + q^{3} + 4 q^{4} + 3 q^{5} - q^{6} - 4 q^{8} + 7 q^{9} - 3 q^{10} - 6 q^{11} + q^{12} - q^{13} + 3 q^{15} + 4 q^{16} + 15 q^{17} - 7 q^{18} - q^{19} + 3 q^{20} + 6 q^{22} + 4 q^{23} - q^{24} - 5 q^{25} + q^{26} - 5 q^{27} + 6 q^{29} - 3 q^{30} + 8 q^{31} - 4 q^{32} + 9 q^{33} - 15 q^{34} + 7 q^{36} + 8 q^{37} + q^{38} - 25 q^{39} - 3 q^{40} + 9 q^{41} + 14 q^{43} - 6 q^{44} + 21 q^{45} - 4 q^{46} + 9 q^{47} + q^{48} + 5 q^{50} + 6 q^{51} - q^{52} - 3 q^{53} + 5 q^{54} - 12 q^{55} + 23 q^{57} - 6 q^{58} + 12 q^{59} + 3 q^{60} + 11 q^{61} - 8 q^{62} + 4 q^{64} - 9 q^{66} - q^{67} + 15 q^{68} + q^{69} - 3 q^{71} - 7 q^{72} - 4 q^{73} - 8 q^{74} + 22 q^{75} - q^{76} + 25 q^{78} + 5 q^{79} + 3 q^{80} - 8 q^{81} - 9 q^{82} + 12 q^{83} + 24 q^{85} - 14 q^{86} - 9 q^{87} + 6 q^{88} + 27 q^{89} - 21 q^{90} + 4 q^{92} - 25 q^{93} - 9 q^{94} - 3 q^{95} - q^{96} + 2 q^{97} - 9 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + q^3 + 4 * q^4 + 3 * q^5 - q^6 - 4 * q^8 + 7 * q^9 - 3 * q^10 - 6 * q^11 + q^12 - q^13 + 3 * q^15 + 4 * q^16 + 15 * q^17 - 7 * q^18 - q^19 + 3 * q^20 + 6 * q^22 + 4 * q^23 - q^24 - 5 * q^25 + q^26 - 5 * q^27 + 6 * q^29 - 3 * q^30 + 8 * q^31 - 4 * q^32 + 9 * q^33 - 15 * q^34 + 7 * q^36 + 8 * q^37 + q^38 - 25 * q^39 - 3 * q^40 + 9 * q^41 + 14 * q^43 - 6 * q^44 + 21 * q^45 - 4 * q^46 + 9 * q^47 + q^48 + 5 * q^50 + 6 * q^51 - q^52 - 3 * q^53 + 5 * q^54 - 12 * q^55 + 23 * q^57 - 6 * q^58 + 12 * q^59 + 3 * q^60 + 11 * q^61 - 8 * q^62 + 4 * q^64 - 9 * q^66 - q^67 + 15 * q^68 + q^69 - 3 * q^71 - 7 * q^72 - 4 * q^73 - 8 * q^74 + 22 * q^75 - q^76 + 25 * q^78 + 5 * q^79 + 3 * q^80 - 8 * q^81 - 9 * q^82 + 12 * q^83 + 24 * q^85 - 14 * q^86 - 9 * q^87 + 6 * q^88 + 27 * q^89 - 21 * q^90 + 4 * q^92 - 25 * q^93 - 9 * q^94 - 3 * q^95 - q^96 + 2 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.62484	1.51545	0.757725	−	0.652574i	$-0.226311\pi$
$3$	2.62484	1.51545	0.757725	+	0.652574i	$0.226311\pi$
$4$	1.00000	0.500000
$5$	3.37167	1.50786	0.753929	−	0.656956i	$-0.228156\pi$
$5$	3.37167	1.50786	0.753929	+	0.656956i	$0.228156\pi$
$6$	−2.62484	−1.07158
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	3.88977	1.29659
$10$	−3.37167	−1.06622
$11$	−2.22875	−0.671992	−0.335996	−	0.941863i	$-0.609073\pi$
$11$	−2.22875	−0.671992	−0.335996	+	0.941863i	$0.609073\pi$
$12$	2.62484	0.757725
$13$	−3.10674	−0.861656	−0.430828	−	0.902434i	$-0.641778\pi$
$13$	−3.10674	−0.861656	−0.430828	+	0.902434i	$0.641778\pi$
$14$	0	0
$15$	8.85009	2.28508
$16$	1.00000	0.250000
$17$	6.37167	1.54536	0.772679	−	0.634797i	$-0.218916\pi$
$17$	6.37167	1.54536	0.772679	+	0.634797i	$0.218916\pi$
$18$	−3.88977	−0.916827
$19$	0.914183	0.209728	0.104864	−	0.994487i	$-0.466559\pi$
$19$	0.914183	0.209728	0.104864	+	0.994487i	$0.466559\pi$
$20$	3.37167	0.753929
$21$	0	0
$22$	2.22875	0.475170
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.62484	−0.535792
$25$	6.36818	1.27364
$26$	3.10674	0.609283
$27$	2.33549	0.449465
$28$	0	0
$29$	−4.22526	−0.784610	−0.392305	−	0.919835i	$-0.628322\pi$
$29$	−4.22526	−0.784610	−0.392305	+	0.919835i	$0.628322\pi$
$30$	−8.85009	−1.61580
$31$	−3.47842	−0.624742	−0.312371	−	0.949960i	$-0.601123\pi$
$31$	−3.47842	−0.624742	−0.312371	+	0.949960i	$0.601123\pi$
$32$	−1.00000	−0.176777
$33$	−5.85009	−1.01837
$34$	−6.37167	−1.09273
$35$	0	0
$36$	3.88977	0.648294
$37$	9.41782	1.54828	0.774140	−	0.633015i	$-0.218183\pi$
$37$	9.41782	1.54828	0.774140	+	0.633015i	$0.218183\pi$
$38$	−0.914183	−0.148300
$39$	−8.15470	−1.30580
$40$	−3.37167	−0.533108
$41$	−5.85009	−0.913631	−0.456815	−	0.889562i	$-0.651010\pi$
$41$	−5.85009	−0.913631	−0.456815	+	0.889562i	$0.651010\pi$
$42$	0	0
$43$	12.7643	1.94653	0.973267	−	0.229677i	$-0.0737671\pi$
$43$	12.7643	1.94653	0.973267	+	0.229677i	$0.0737671\pi$
$44$	−2.22875	−0.335996
$45$	13.1150	1.95507
$46$	−1.00000	−0.147442
$47$	6.56423	0.957492	0.478746	−	0.877953i	$-0.341091\pi$
$47$	6.56423	0.957492	0.478746	+	0.877953i	$0.341091\pi$
$48$	2.62484	0.378862
$49$	0	0
$50$	−6.36818	−0.900597
$51$	16.7246	2.34191
$52$	−3.10674	−0.430828
$53$	11.1477	1.53126	0.765628	−	0.643283i	$-0.222428\pi$
$53$	11.1477	1.53126	0.765628	+	0.643283i	$0.222428\pi$
$54$	−2.33549	−0.317820
$55$	−7.51460	−1.01327
$56$	0	0
$57$	2.39958	0.317832
$58$	4.22526	0.554803
$59$	−2.97209	−0.386934	−0.193467	−	0.981107i	$-0.561973\pi$
$59$	−2.97209	−0.386934	−0.193467	+	0.981107i	$0.561973\pi$
$60$	8.85009	1.14254
$61$	6.80563	0.871372	0.435686	−	0.900099i	$-0.356506\pi$
$61$	6.80563	0.871372	0.435686	+	0.900099i	$0.356506\pi$
$62$	3.47842	0.441760
$63$	0	0
$64$	1.00000	0.125000
$65$	−10.4749	−1.29925
$66$	5.85009	0.720097
$67$	6.87451	0.839855	0.419927	−	0.907558i	$-0.362056\pi$
$67$	6.87451	0.839855	0.419927	+	0.907558i	$0.362056\pi$
$68$	6.37167	0.772679
$69$	2.62484	0.315993
$70$	0	0
$71$	1.61307	0.191436	0.0957181	−	0.995408i	$-0.469485\pi$
$71$	1.61307	0.191436	0.0957181	+	0.995408i	$0.469485\pi$
$72$	−3.88977	−0.458413
$73$	5.93591	0.694746	0.347373	−	0.937727i	$-0.387074\pi$
$73$	5.93591	0.694746	0.347373	+	0.937727i	$0.387074\pi$
$74$	−9.41782	−1.09480
$75$	16.7154	1.93013
$76$	0.914183	0.104864
$77$	0	0
$78$	8.15470	0.923337
$79$	−14.7498	−1.65948	−0.829742	−	0.558147i	$-0.811512\pi$
$79$	−14.7498	−1.65948	−0.829742	+	0.558147i	$0.811512\pi$
$80$	3.37167	0.376965
$81$	−5.53902	−0.615447
$82$	5.85009	0.646035
$83$	−6.51111	−0.714687	−0.357344	−	0.933973i	$-0.616318\pi$
$83$	−6.51111	−0.714687	−0.357344	+	0.933973i	$0.616318\pi$
$84$	0	0
$85$	21.4832	2.33018
$86$	−12.7643	−1.37641
$87$	−11.0906	−1.18904
$88$	2.22875	0.237585
$89$	−1.58516	−0.168027	−0.0840134	−	0.996465i	$-0.526774\pi$
$89$	−1.58516	−0.168027	−0.0840134	+	0.996465i	$0.526774\pi$
$90$	−13.1150	−1.38244
$91$	0	0
$92$	1.00000	0.104257
$93$	−9.13028	−0.946766
$94$	−6.56423	−0.677049
$95$	3.08233	0.316240
$96$	−2.62484	−0.267896
$97$	13.7970	1.40087	0.700435	−	0.713716i	$-0.252989\pi$
$97$	13.7970	1.40087	0.700435	+	0.713716i	$0.252989\pi$
$98$	0	0
$99$	−8.66930	−0.871297
$100$	6.36818	0.636818
$101$	−7.07535	−0.704023	−0.352012	−	0.935996i	$-0.614502\pi$
$101$	−7.07535	−0.704023	−0.352012	+	0.935996i	$0.614502\pi$
$102$	−16.7246	−1.65598
$103$	−15.7516	−1.55205	−0.776027	−	0.630700i	$-0.782768\pi$
$103$	−15.7516	−1.55205	−0.776027	+	0.630700i	$0.782768\pi$
$104$	3.10674	0.304641
$105$	0	0
$106$	−11.1477	−1.08276
$107$	5.76776	0.557591	0.278795	−	0.960351i	$-0.410065\pi$
$107$	5.76776	0.557591	0.278795	+	0.960351i	$0.410065\pi$
$108$	2.33549	0.224733
$109$	−18.9207	−1.81227	−0.906135	−	0.422989i	$-0.860981\pi$
$109$	−18.9207	−1.81227	−0.906135	+	0.422989i	$0.860981\pi$
$110$	7.51460	0.716489
$111$	24.7202	2.34634
$112$	0	0
$113$	−11.2697	−1.06017	−0.530083	−	0.847946i	$-0.677839\pi$
$113$	−11.2697	−1.06017	−0.530083	+	0.847946i	$0.677839\pi$
$114$	−2.39958	−0.224741
$115$	3.37167	0.314410
$116$	−4.22526	−0.392305
$117$	−12.0845	−1.11721
$118$	2.97209	0.273603
$119$	0	0
$120$	−8.85009	−0.807899
$121$	−6.03269	−0.548427
$122$	−6.80563	−0.616153
$123$	−15.3555	−1.38456
$124$	−3.47842	−0.312371
$125$	4.61307	0.412605
$126$	0	0
$127$	−20.9743	−1.86117	−0.930583	−	0.366081i	$-0.880699\pi$
$127$	−20.9743	−1.86117	−0.930583	+	0.366081i	$0.880699\pi$
$128$	−1.00000	−0.0883883
$129$	33.5041	2.94987
$130$	10.4749	0.918712
$131$	3.27590	0.286217	0.143108	−	0.989707i	$-0.454290\pi$
$131$	3.27590	0.286217	0.143108	+	0.989707i	$0.454290\pi$
$132$	−5.85009	−0.509185
$133$	0	0
$134$	−6.87451	−0.593867
$135$	7.87451	0.677730
$136$	−6.37167	−0.546367
$137$	1.09758	0.0937729	0.0468865	−	0.998900i	$-0.485070\pi$
$137$	1.09758	0.0937729	0.0468865	+	0.998900i	$0.485070\pi$
$138$	−2.62484	−0.223441
$139$	−2.44572	−0.207444	−0.103722	−	0.994606i	$-0.533075\pi$
$139$	−2.44572	−0.207444	−0.103722	+	0.994606i	$0.533075\pi$
$140$	0	0
$141$	17.2300	1.45103
$142$	−1.61307	−0.135366
$143$	6.92414	0.579026
$144$	3.88977	0.324147
$145$	−14.2462	−1.18308
$146$	−5.93591	−0.491259
$147$	0	0
$148$	9.41782	0.774140
$149$	18.6875	1.53094	0.765471	−	0.643470i	$-0.222506\pi$
$149$	18.6875	1.53094	0.765471	+	0.643470i	$0.222506\pi$
$150$	−16.7154	−1.36481
$151$	−0.535529	−0.0435808	−0.0217904	−	0.999763i	$-0.506937\pi$
$151$	−0.535529	−0.0435808	−0.0217904	+	0.999763i	$0.506937\pi$
$152$	−0.914183	−0.0741500
$153$	24.7843	2.00369
$154$	0	0
$155$	−11.7281	−0.942023
$156$	−8.15470	−0.652898
$157$	−10.4406	−0.833247	−0.416623	−	0.909079i	$-0.636787\pi$
$157$	−10.4406	−0.833247	−0.416623	+	0.909079i	$0.636787\pi$
$158$	14.7498	1.17343
$159$	29.2609	2.32054
$160$	−3.37167	−0.266554
$161$	0	0
$162$	5.53902	0.435186
$163$	4.17562	0.327060	0.163530	−	0.986538i	$-0.447712\pi$
$163$	4.17562	0.327060	0.163530	+	0.986538i	$0.447712\pi$
$164$	−5.85009	−0.456815
$165$	−19.7246	−1.53556
$166$	6.51111	0.505360
$167$	−7.26623	−0.562277	−0.281139	−	0.959667i	$-0.590712\pi$
$167$	−7.26623	−0.562277	−0.281139	+	0.959667i	$0.590712\pi$
$168$	0	0
$169$	−3.34814	−0.257549
$170$	−21.4832	−1.64769
$171$	3.55596	0.271931
$172$	12.7643	0.973267
$173$	−2.42530	−0.184392	−0.0921959	−	0.995741i	$-0.529389\pi$
$173$	−2.42530	−0.184392	−0.0921959	+	0.995741i	$0.529389\pi$
$174$	11.0906	0.840777
$175$	0	0
$176$	−2.22875	−0.167998
$177$	−7.80126	−0.586378
$178$	1.58516	0.118813
$179$	−13.8701	−1.03670	−0.518351	−	0.855168i	$-0.673454\pi$
$179$	−13.8701	−1.03670	−0.518351	+	0.855168i	$0.673454\pi$
$180$	13.1150	0.977536
$181$	3.48271	0.258868	0.129434	−	0.991588i	$-0.458684\pi$
$181$	3.48271	0.258868	0.129434	+	0.991588i	$0.458684\pi$
$182$	0	0
$183$	17.8637	1.32052
$184$	−1.00000	−0.0737210
$185$	31.7538	2.33459
$186$	9.13028	0.669464
$187$	−14.2008	−1.03847
$188$	6.56423	0.478746
$189$	0	0
$190$	−3.08233	−0.223616
$191$	−14.8423	−1.07395	−0.536976	−	0.843597i	$-0.680433\pi$
$191$	−14.8423	−1.07395	−0.536976	+	0.843597i	$0.680433\pi$
$192$	2.62484	0.189431
$193$	−15.9895	−1.15095	−0.575476	−	0.817819i	$-0.695183\pi$
$193$	−15.9895	−1.15095	−0.575476	+	0.817819i	$0.695183\pi$
$194$	−13.7970	−0.990565
$195$	−27.4950	−1.96896
$196$	0	0
$197$	−14.8954	−1.06126	−0.530628	−	0.847605i	$-0.678044\pi$
$197$	−14.8954	−1.06126	−0.530628	+	0.847605i	$0.678044\pi$
$198$	8.66930	0.616100
$199$	−24.1255	−1.71021	−0.855105	−	0.518455i	$-0.826507\pi$
$199$	−24.1255	−1.71021	−0.855105	+	0.518455i	$0.826507\pi$
$200$	−6.36818	−0.450299
$201$	18.0445	1.27276
$202$	7.07535	0.497820
$203$	0	0
$204$	16.7246	1.17096
$205$	−19.7246	−1.37763
$206$	15.7516	1.09747
$207$	3.88977	0.270357
$208$	−3.10674	−0.215414
$209$	−2.03748	−0.140936
$210$	0	0
$211$	−18.1067	−1.24652	−0.623260	−	0.782015i	$-0.714192\pi$
$211$	−18.1067	−1.24652	−0.623260	+	0.782015i	$0.714192\pi$
$212$	11.1477	0.765628
$213$	4.23404	0.290112
$214$	−5.76776	−0.394276
$215$	43.0370	2.93510
$216$	−2.33549	−0.158910
$217$	0	0
$218$	18.9207	1.28147
$219$	15.5808	1.05285
$220$	−7.51460	−0.506634
$221$	−19.7952	−1.33157
$222$	−24.7202	−1.65911
$223$	20.1922	1.35217	0.676084	−	0.736824i	$-0.263676\pi$
$223$	20.1922	1.35217	0.676084	+	0.736824i	$0.263676\pi$
$224$	0	0
$225$	24.7707	1.65138
$226$	11.2697	0.749650
$227$	−19.8187	−1.31541	−0.657706	−	0.753274i	$-0.728473\pi$
$227$	−19.8187	−1.31541	−0.657706	+	0.753274i	$0.728473\pi$
$228$	2.39958	0.158916
$229$	18.1604	1.20007	0.600035	−	0.799973i	$-0.295153\pi$
$229$	18.1604	1.20007	0.600035	+	0.799973i	$0.295153\pi$
$230$	−3.37167	−0.222322
$231$	0	0
$232$	4.22526	0.277402
$233$	12.4113	0.813094	0.406547	−	0.913630i	$-0.366733\pi$
$233$	12.4113	0.813094	0.406547	+	0.913630i	$0.366733\pi$
$234$	12.0845	0.789989
$235$	22.1325	1.44376
$236$	−2.97209	−0.193467
$237$	−38.7159	−2.51486
$238$	0	0
$239$	−0.868040	−0.0561489	−0.0280744	−	0.999606i	$-0.508938\pi$
$239$	−0.868040	−0.0561489	−0.0280744	+	0.999606i	$0.508938\pi$
$240$	8.85009	0.571271
$241$	1.58697	0.102226	0.0511129	−	0.998693i	$-0.483723\pi$
$241$	1.58697	0.102226	0.0511129	+	0.998693i	$0.483723\pi$
$242$	6.03269	0.387796
$243$	−21.5455	−1.38214
$244$	6.80563	0.435686
$245$	0	0
$246$	15.3555	0.979033
$247$	−2.84013	−0.180713
$248$	3.47842	0.220880
$249$	−17.0906	−1.08307
$250$	−4.61307	−0.291756
$251$	−3.09976	−0.195655	−0.0978277	−	0.995203i	$-0.531189\pi$
$251$	−3.09976	−0.195655	−0.0978277	+	0.995203i	$0.531189\pi$
$252$	0	0
$253$	−2.22875	−0.140120
$254$	20.9743	1.31604
$255$	56.3899	3.53127
$256$	1.00000	0.0625000
$257$	−6.97390	−0.435020	−0.217510	−	0.976058i	$-0.569793\pi$
$257$	−6.97390	−0.435020	−0.217510	+	0.976058i	$0.569793\pi$
$258$	−33.5041	−2.08588
$259$	0	0
$260$	−10.4749	−0.649627
$261$	−16.4353	−1.01732
$262$	−3.27590	−0.202386
$263$	4.56902	0.281738	0.140869	−	0.990028i	$-0.455010\pi$
$263$	4.56902	0.281738	0.140869	+	0.990028i	$0.455010\pi$
$264$	5.85009	0.360048
$265$	37.5865	2.30892
$266$	0	0
$267$	−4.16079	−0.254636
$268$	6.87451	0.419927
$269$	29.7516	1.81399	0.906994	−	0.421143i	$-0.138371\pi$
$269$	29.7516	1.81399	0.906994	+	0.421143i	$0.138371\pi$
$270$	−7.87451	−0.479227
$271$	−5.38991	−0.327414	−0.163707	−	0.986509i	$-0.552345\pi$
$271$	−5.38991	−0.327414	−0.163707	+	0.986509i	$0.552345\pi$
$272$	6.37167	0.386339
$273$	0	0
$274$	−1.09758	−0.0663075
$275$	−14.1931	−0.855874
$276$	2.62484	0.157997
$277$	1.56852	0.0942434	0.0471217	−	0.998889i	$-0.484995\pi$
$277$	1.56852	0.0942434	0.0471217	+	0.998889i	$0.484995\pi$
$278$	2.44572	0.146685
$279$	−13.5302	−0.810034
$280$	0	0
$281$	15.4009	0.918739	0.459370	−	0.888245i	$-0.348075\pi$
$281$	15.4009	0.918739	0.459370	+	0.888245i	$0.348075\pi$
$282$	−17.2300	−1.02603
$283$	−15.9882	−0.950402	−0.475201	−	0.879877i	$-0.657625\pi$
$283$	−15.9882	−0.950402	−0.475201	+	0.879877i	$0.657625\pi$
$284$	1.61307	0.0957181
$285$	8.09060	0.479246
$286$	−6.92414	−0.409433
$287$	0	0
$288$	−3.88977	−0.229207
$289$	23.5982	1.38813
$290$	14.2462	0.836565
$291$	36.2148	2.12295
$292$	5.93591	0.347373
$293$	12.8179	0.748830	0.374415	−	0.927261i	$-0.377844\pi$
$293$	12.8179	0.748830	0.374415	+	0.927261i	$0.377844\pi$
$294$	0	0
$295$	−10.0209	−0.583441
$296$	−9.41782	−0.547399
$297$	−5.20521	−0.302037
$298$	−18.6875	−1.08254
$299$	−3.10674	−0.179668
$300$	16.7154	0.965066
$301$	0	0
$302$	0.535529	0.0308163
$303$	−18.5716	−1.06691
$304$	0.914183	0.0524320
$305$	22.9464	1.31391
$306$	−24.7843	−1.41683
$307$	−0.501952	−0.0286479	−0.0143239	−	0.999897i	$-0.504560\pi$
$307$	−0.501952	−0.0286479	−0.0143239	+	0.999897i	$0.504560\pi$
$308$	0	0
$309$	−41.3454	−2.35206
$310$	11.7281	0.666111
$311$	15.3673	0.871400	0.435700	−	0.900092i	$-0.356501\pi$
$311$	15.3673	0.871400	0.435700	+	0.900092i	$0.356501\pi$
$312$	8.15470	0.461669
$313$	−7.61966	−0.430689	−0.215344	−	0.976538i	$-0.569087\pi$
$313$	−7.61966	−0.430689	−0.215344	+	0.976538i	$0.569087\pi$
$314$	10.4406	0.589194
$315$	0	0
$316$	−14.7498	−0.829742
$317$	−18.2984	−1.02774	−0.513871	−	0.857868i	$-0.671789\pi$
$317$	−18.2984	−1.02774	−0.513871	+	0.857868i	$0.671789\pi$
$318$	−29.2609	−1.64087
$319$	9.41702	0.527252
$320$	3.37167	0.188482
$321$	15.1394	0.845001
$322$	0	0
$323$	5.82488	0.324105
$324$	−5.53902	−0.307723
$325$	−19.7843	−1.09744
$326$	−4.17562	−0.231266
$327$	−49.6636	−2.74640
$328$	5.85009	0.323017
$329$	0	0
$330$	19.7246	1.08580
$331$	11.6728	0.641594	0.320797	−	0.947148i	$-0.396049\pi$
$331$	11.6728	0.641594	0.320797	+	0.947148i	$0.396049\pi$
$332$	−6.51111	−0.357344
$333$	36.6331	2.00748
$334$	7.26623	0.397590
$335$	23.1786	1.26638
$336$	0	0
$337$	−24.1242	−1.31413	−0.657064	−	0.753835i	$-0.728202\pi$
$337$	−24.1242	−1.31413	−0.657064	+	0.753835i	$0.728202\pi$
$338$	3.34814	0.182115
$339$	−29.5812	−1.60663
$340$	21.4832	1.16509
$341$	7.75251	0.419822
$342$	−3.55596	−0.192284
$343$	0	0
$344$	−12.7643	−0.688204
$345$	8.85009	0.476473
$346$	2.42530	0.130385
$347$	22.3260	1.19852	0.599262	−	0.800553i	$-0.295461\pi$
$347$	22.3260	1.19852	0.599262	+	0.800553i	$0.295461\pi$
$348$	−11.0906	−0.594519
$349$	−8.64837	−0.462937	−0.231468	−	0.972842i	$-0.574353\pi$
$349$	−8.64837	−0.462937	−0.231468	+	0.972842i	$0.574353\pi$
$350$	0	0
$351$	−7.25577	−0.387284
$352$	2.22875	0.118793
$353$	31.5690	1.68025	0.840125	−	0.542393i	$-0.182482\pi$
$353$	31.5690	1.68025	0.840125	+	0.542393i	$0.182482\pi$
$354$	7.80126	0.414632
$355$	5.43874	0.288659
$356$	−1.58516	−0.0840134
$357$	0	0
$358$	13.8701	0.733059
$359$	15.0279	0.793143	0.396571	−	0.918004i	$-0.370200\pi$
$359$	15.0279	0.793143	0.396571	+	0.918004i	$0.370200\pi$
$360$	−13.1150	−0.691222
$361$	−18.1643	−0.956014
$362$	−3.48271	−0.183047
$363$	−15.8348	−0.831113
$364$	0	0
$365$	20.0139	1.04758
$366$	−17.8637	−0.933749
$367$	−34.9869	−1.82630	−0.913151	−	0.407621i	$-0.866359\pi$
$367$	−34.9869	−1.82630	−0.913151	+	0.407621i	$0.866359\pi$
$368$	1.00000	0.0521286
$369$	−22.7555	−1.18460
$370$	−31.7538	−1.65080
$371$	0	0
$372$	−9.13028	−0.473383
$373$	−14.8540	−0.769111	−0.384555	−	0.923102i	$-0.625645\pi$
$373$	−14.8540	−0.769111	−0.384555	+	0.923102i	$0.625645\pi$
$374$	14.2008	0.734308
$375$	12.1086	0.625283
$376$	−6.56423	−0.338525
$377$	13.1268	0.676064
$378$	0	0
$379$	3.30019	0.169519	0.0847597	−	0.996401i	$-0.472988\pi$
$379$	3.30019	0.169519	0.0847597	+	0.996401i	$0.472988\pi$
$380$	3.08233	0.158120
$381$	−55.0540	−2.82050
$382$	14.8423	0.759399
$383$	11.4985	0.587548	0.293774	−	0.955875i	$-0.405089\pi$
$383$	11.4985	0.587548	0.293774	+	0.955875i	$0.405089\pi$
$384$	−2.62484	−0.133948
$385$	0	0
$386$	15.9895	0.813846
$387$	49.6500	2.52385
$388$	13.7970	0.700435
$389$	12.4422	0.630846	0.315423	−	0.948951i	$-0.397854\pi$
$389$	12.4422	0.630846	0.315423	+	0.948951i	$0.397854\pi$
$390$	27.4950	1.39226
$391$	6.37167	0.322229
$392$	0	0
$393$	8.59870	0.433747
$394$	14.8954	0.750421
$395$	−49.7316	−2.50227
$396$	−8.66930	−0.435649
$397$	24.1678	1.21295	0.606473	−	0.795104i	$-0.292584\pi$
$397$	24.1678	1.21295	0.606473	+	0.795104i	$0.292584\pi$
$398$	24.1255	1.20930
$399$	0	0
$400$	6.36818	0.318409
$401$	4.08313	0.203902	0.101951	−	0.994789i	$-0.467492\pi$
$401$	4.08313	0.203902	0.101951	+	0.994789i	$0.467492\pi$
$402$	−18.0445	−0.899976
$403$	10.8066	0.538313
$404$	−7.07535	−0.352012
$405$	−18.6758	−0.928006
$406$	0	0
$407$	−20.9899	−1.04043
$408$	−16.7246	−0.827991
$409$	14.2234	0.703304	0.351652	−	0.936131i	$-0.385620\pi$
$409$	14.2234	0.703304	0.351652	+	0.936131i	$0.385620\pi$
$410$	19.7246	0.974129
$411$	2.88098	0.142108
$412$	−15.7516	−0.776027
$413$	0	0
$414$	−3.88977	−0.191172
$415$	−21.9533	−1.07765
$416$	3.10674	0.152321
$417$	−6.41962	−0.314370
$418$	2.03748	0.0996565
$419$	13.2679	0.648180	0.324090	−	0.946026i	$-0.394942\pi$
$419$	13.2679	0.648180	0.324090	+	0.946026i	$0.394942\pi$
$420$	0	0
$421$	−37.5460	−1.82988	−0.914940	−	0.403591i	$-0.867762\pi$
$421$	−37.5460	−1.82988	−0.914940	+	0.403591i	$0.867762\pi$
$422$	18.1067	0.881423
$423$	25.5333	1.24147
$424$	−11.1477	−0.541381
$425$	40.5760	1.96822
$426$	−4.23404	−0.205140
$427$	0	0
$428$	5.76776	0.278795
$429$	18.1747	0.877485
$430$	−43.0370	−2.07543
$431$	9.29233	0.447596	0.223798	−	0.974636i	$-0.428154\pi$
$431$	9.29233	0.447596	0.223798	+	0.974636i	$0.428154\pi$
$432$	2.33549	0.112366
$433$	−14.1033	−0.677759	−0.338880	−	0.940830i	$-0.610048\pi$
$433$	−14.1033	−0.677759	−0.338880	+	0.940830i	$0.610048\pi$
$434$	0	0
$435$	−37.3939	−1.79290
$436$	−18.9207	−0.906135
$437$	0.914183	0.0437313
$438$	−15.5808	−0.744479
$439$	19.4770	0.929588	0.464794	−	0.885419i	$-0.346128\pi$
$439$	19.4770	0.929588	0.464794	+	0.885419i	$0.346128\pi$
$440$	7.51460	0.358245
$441$	0	0
$442$	19.7952	0.941560
$443$	−5.93242	−0.281858	−0.140929	−	0.990020i	$-0.545009\pi$
$443$	−5.93242	−0.281858	−0.140929	+	0.990020i	$0.545009\pi$
$444$	24.7202	1.17317
$445$	−5.34465	−0.253361
$446$	−20.1922	−0.956127
$447$	49.0517	2.32007
$448$	0	0
$449$	−5.13864	−0.242507	−0.121254	−	0.992622i	$-0.538691\pi$
$449$	−5.13864	−0.242507	−0.121254	+	0.992622i	$0.538691\pi$
$450$	−24.7707	−1.16770
$451$	13.0384	0.613953
$452$	−11.2697	−0.530083
$453$	−1.40568	−0.0660445
$454$	19.8187	0.930137
$455$	0	0
$456$	−2.39958	−0.112371
$457$	36.6304	1.71350	0.856749	−	0.515733i	$-0.172480\pi$
$457$	36.6304	1.71350	0.856749	+	0.515733i	$0.172480\pi$
$458$	−18.1604	−0.848578
$459$	14.8810	0.694585
$460$	3.37167	0.157205
$461$	−16.0663	−0.748281	−0.374140	−	0.927372i	$-0.622062\pi$
$461$	−16.0663	−0.748281	−0.374140	+	0.927372i	$0.622062\pi$
$462$	0	0
$463$	14.7503	0.685505	0.342753	−	0.939426i	$-0.388641\pi$
$463$	14.7503	0.685505	0.342753	+	0.939426i	$0.388641\pi$
$464$	−4.22526	−0.196153
$465$	−30.7843	−1.42759
$466$	−12.4113	−0.574945
$467$	29.7028	1.37448	0.687240	−	0.726430i	$-0.258822\pi$
$467$	29.7028	1.37448	0.687240	+	0.726430i	$0.258822\pi$
$468$	−12.0845	−0.558607
$469$	0	0
$470$	−22.1325	−1.02089
$471$	−27.4047	−1.26274
$472$	2.97209	0.136802
$473$	−28.4483	−1.30806
$474$	38.7159	1.77828
$475$	5.82169	0.267117
$476$	0	0
$477$	43.3620	1.98541
$478$	0.868040	0.0397032
$479$	−12.0466	−0.550425	−0.275213	−	0.961383i	$-0.588748\pi$
$479$	−12.0466	−0.550425	−0.275213	+	0.961383i	$0.588748\pi$
$480$	−8.85009	−0.403950
$481$	−29.2587	−1.33408
$482$	−1.58697	−0.0722845
$483$	0	0
$484$	−6.03269	−0.274213
$485$	46.5189	2.11231
$486$	21.5455	0.977323
$487$	33.9316	1.53759	0.768794	−	0.639496i	$-0.220857\pi$
$487$	33.9316	1.53759	0.768794	+	0.639496i	$0.220857\pi$
$488$	−6.80563	−0.308076
$489$	10.9603	0.495643
$490$	0	0
$491$	−23.1813	−1.04616	−0.523079	−	0.852284i	$-0.675217\pi$
$491$	−23.1813	−1.04616	−0.523079	+	0.852284i	$0.675217\pi$
$492$	−15.3555	−0.692281
$493$	−26.9219	−1.21250
$494$	2.84013	0.127784
$495$	−29.2300	−1.31379
$496$	−3.47842	−0.156186
$497$	0	0
$498$	17.0906	0.765848
$499$	8.80214	0.394038	0.197019	−	0.980400i	$-0.436874\pi$
$499$	8.80214	0.394038	0.197019	+	0.980400i	$0.436874\pi$
$500$	4.61307	0.206303
$501$	−19.0727	−0.852103
$502$	3.09976	0.138349
$503$	−31.0653	−1.38513	−0.692566	−	0.721355i	$-0.743520\pi$
$503$	−31.0653	−1.38513	−0.692566	+	0.721355i	$0.743520\pi$
$504$	0	0
$505$	−23.8558	−1.06157
$506$	2.22875	0.0990798
$507$	−8.78832	−0.390303
$508$	−20.9743	−0.930583
$509$	−14.7560	−0.654048	−0.327024	−	0.945016i	$-0.606046\pi$
$509$	−14.7560	−0.654048	−0.327024	+	0.945016i	$0.606046\pi$
$510$	−56.3899	−2.49699
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	2.13507	0.0942654
$514$	6.97390	0.307606
$515$	−53.1093	−2.34028
$516$	33.5041	1.47494
$517$	−14.6300	−0.643427
$518$	0	0
$519$	−6.36600	−0.279437
$520$	10.4749	0.459356
$521$	−19.3895	−0.849471	−0.424735	−	0.905318i	$-0.639633\pi$
$521$	−19.3895	−0.849471	−0.424735	+	0.905318i	$0.639633\pi$
$522$	16.4353	0.719352
$523$	−5.30730	−0.232072	−0.116036	−	0.993245i	$-0.537019\pi$
$523$	−5.30730	−0.232072	−0.116036	+	0.993245i	$0.537019\pi$
$524$	3.27590	0.143108
$525$	0	0
$526$	−4.56902	−0.199219
$527$	−22.1633	−0.965450
$528$	−5.85009	−0.254593
$529$	1.00000	0.0434783
$530$	−37.5865	−1.63265
$531$	−11.5607	−0.501694
$532$	0	0
$533$	18.1747	0.787235
$534$	4.16079	0.180055
$535$	19.4470	0.840768
$536$	−6.87451	−0.296934
$537$	−36.4068	−1.57107
$538$	−29.7516	−1.28268
$539$	0	0
$540$	7.87451	0.338865
$541$	−42.8191	−1.84094	−0.920468	−	0.390819i	$-0.872192\pi$
$541$	−42.8191	−1.84094	−0.920468	+	0.390819i	$0.872192\pi$
$542$	5.38991	0.231516
$543$	9.14153	0.392301
$544$	−6.37167	−0.273183
$545$	−63.7943	−2.73265
$546$	0	0
$547$	1.51910	0.0649521	0.0324761	−	0.999473i	$-0.489661\pi$
$547$	1.51910	0.0649521	0.0324761	+	0.999473i	$0.489661\pi$
$548$	1.09758	0.0468865
$549$	26.4723	1.12981
$550$	14.1931	0.605194
$551$	−3.86266	−0.164555
$552$	−2.62484	−0.111720
$553$	0	0
$554$	−1.56852	−0.0666402
$555$	83.3485	3.53795
$556$	−2.44572	−0.103722
$557$	−12.5770	−0.532905	−0.266453	−	0.963848i	$-0.585852\pi$
$557$	−12.5770	−0.532905	−0.266453	+	0.963848i	$0.585852\pi$
$558$	13.5302	0.572780
$559$	−39.6553	−1.67724
$560$	0	0
$561$	−37.2749	−1.57375
$562$	−15.4009	−0.649647
$563$	−10.9102	−0.459810	−0.229905	−	0.973213i	$-0.573842\pi$
$563$	−10.9102	−0.459810	−0.229905	+	0.973213i	$0.573842\pi$
$564$	17.2300	0.725516
$565$	−37.9978	−1.59858
$566$	15.9882	0.672036
$567$	0	0
$568$	−1.61307	−0.0676829
$569$	32.4864	1.36190	0.680950	−	0.732330i	$-0.261567\pi$
$569$	32.4864	1.36190	0.680950	+	0.732330i	$0.261567\pi$
$570$	−8.09060	−0.338878
$571$	10.8182	0.452727	0.226364	−	0.974043i	$-0.427316\pi$
$571$	10.8182	0.452727	0.226364	+	0.974043i	$0.427316\pi$
$572$	6.92414	0.289513
$573$	−38.9586	−1.62752
$574$	0	0
$575$	6.36818	0.265572
$576$	3.88977	0.162074
$577$	−7.86434	−0.327397	−0.163698	−	0.986510i	$-0.552342\pi$
$577$	−7.86434	−0.327397	−0.163698	+	0.986510i	$0.552342\pi$
$578$	−23.5982	−0.981557
$579$	−41.9699	−1.74421
$580$	−14.2462	−0.591541
$581$	0	0
$582$	−36.2148	−1.50115
$583$	−24.8454	−1.02899
$584$	−5.93591	−0.245630
$585$	−40.7450	−1.68460
$586$	−12.8179	−0.529502
$587$	31.4964	1.29999	0.649997	−	0.759937i	$-0.274770\pi$
$587$	31.4964	1.29999	0.649997	+	0.759937i	$0.274770\pi$
$588$	0	0
$589$	−3.17991	−0.131026
$590$	10.0209	0.412555
$591$	−39.0981	−1.60828
$592$	9.41782	0.387070
$593$	5.35852	0.220048	0.110024	−	0.993929i	$-0.464907\pi$
$593$	5.35852	0.220048	0.110024	+	0.993929i	$0.464907\pi$
$594$	5.20521	0.213572
$595$	0	0
$596$	18.6875	0.765471
$597$	−63.3254	−2.59174
$598$	3.10674	0.127044
$599$	−19.0915	−0.780057	−0.390029	−	0.920803i	$-0.627535\pi$
$599$	−19.0915	−0.780057	−0.390029	+	0.920803i	$0.627535\pi$
$600$	−16.7154	−0.682405
$601$	32.3703	1.32041	0.660206	−	0.751085i	$-0.270469\pi$
$601$	32.3703	1.32041	0.660206	+	0.751085i	$0.270469\pi$
$602$	0	0
$603$	26.7402	1.08895
$604$	−0.535529	−0.0217904
$605$	−20.3403	−0.826950
$606$	18.5716	0.754421
$607$	−33.8810	−1.37519	−0.687593	−	0.726096i	$-0.741333\pi$
$607$	−33.8810	−1.37519	−0.687593	+	0.726096i	$0.741333\pi$
$608$	−0.914183	−0.0370750
$609$	0	0
$610$	−22.9464	−0.929071
$611$	−20.3934	−0.825029
$612$	24.7843	1.00185
$613$	16.9442	0.684369	0.342185	−	0.939633i	$-0.388833\pi$
$613$	16.9442	0.684369	0.342185	+	0.939633i	$0.388833\pi$
$614$	0.501952	0.0202571
$615$	−51.7738	−2.08772
$616$	0	0
$617$	−4.06228	−0.163541	−0.0817707	−	0.996651i	$-0.526058\pi$
$617$	−4.06228	−0.163541	−0.0817707	+	0.996651i	$0.526058\pi$
$618$	41.3454	1.66316
$619$	6.66710	0.267974	0.133987	−	0.990983i	$-0.457222\pi$
$619$	6.66710	0.267974	0.133987	+	0.990983i	$0.457222\pi$
$620$	−11.7281	−0.471011
$621$	2.33549	0.0937200
$622$	−15.3673	−0.616173
$623$	0	0
$624$	−8.15470	−0.326449
$625$	−16.2872	−0.651486
$626$	7.61966	0.304543
$627$	−5.34805	−0.213581
$628$	−10.4406	−0.416623
$629$	60.0073	2.39265
$630$	0	0
$631$	−11.8611	−0.472181	−0.236091	−	0.971731i	$-0.575866\pi$
$631$	−11.8611	−0.472181	−0.236091	+	0.971731i	$0.575866\pi$
$632$	14.7498	0.586716
$633$	−47.5272	−1.88904
$634$	18.2984	0.726723
$635$	−70.7184	−2.80637
$636$	29.2609	1.16027
$637$	0	0
$638$	−9.41702	−0.372823
$639$	6.27446	0.248214
$640$	−3.37167	−0.133277
$641$	21.9181	0.865712	0.432856	−	0.901463i	$-0.357506\pi$
$641$	21.9181	0.865712	0.432856	+	0.901463i	$0.357506\pi$
$642$	−15.1394	−0.597506
$643$	11.9456	0.471087	0.235544	−	0.971864i	$-0.424313\pi$
$643$	11.9456	0.471087	0.235544	+	0.971864i	$0.424313\pi$
$644$	0	0
$645$	112.965	4.44799
$646$	−5.82488	−0.229177
$647$	43.0810	1.69369	0.846845	−	0.531840i	$-0.178499\pi$
$647$	43.0810	1.69369	0.846845	+	0.531840i	$0.178499\pi$
$648$	5.53902	0.217593
$649$	6.62404	0.260016
$650$	19.7843	0.776005
$651$	0	0
$652$	4.17562	0.163530
$653$	36.5259	1.42937	0.714684	−	0.699448i	$-0.246571\pi$
$653$	36.5259	1.42937	0.714684	+	0.699448i	$0.246571\pi$
$654$	49.6636	1.94200
$655$	11.0453	0.431574
$656$	−5.85009	−0.228408
$657$	23.0893	0.900799
$658$	0	0
$659$	49.2823	1.91976	0.959882	−	0.280403i	$-0.0904681\pi$
$659$	49.2823	1.91976	0.959882	+	0.280403i	$0.0904681\pi$
$660$	−19.7246	−0.767779
$661$	33.7367	1.31220	0.656102	−	0.754672i	$-0.272204\pi$
$661$	33.7367	1.31220	0.656102	+	0.754672i	$0.272204\pi$
$662$	−11.6728	−0.453676
$663$	−51.9591	−2.01792
$664$	6.51111	0.252680
$665$	0	0
$666$	−36.6331	−1.41950
$667$	−4.22526	−0.163603
$668$	−7.26623	−0.281139
$669$	53.0012	2.04914
$670$	−23.1786	−0.895468
$671$	−15.1680	−0.585555
$672$	0	0
$673$	1.47443	0.0568351	0.0284175	−	0.999596i	$-0.490953\pi$
$673$	1.47443	0.0568351	0.0284175	+	0.999596i	$0.490953\pi$
$674$	24.1242	0.929229
$675$	14.8728	0.572455
$676$	−3.34814	−0.128775
$677$	28.3765	1.09060	0.545298	−	0.838242i	$-0.316417\pi$
$677$	28.3765	1.09060	0.545298	+	0.838242i	$0.316417\pi$
$678$	29.5812	1.13606
$679$	0	0
$680$	−21.4832	−0.823843
$681$	−52.0208	−1.99344
$682$	−7.75251	−0.296859
$683$	−38.1564	−1.46001	−0.730006	−	0.683440i	$-0.760483\pi$
$683$	−38.1564	−1.46001	−0.730006	+	0.683440i	$0.760483\pi$
$684$	3.55596	0.135965
$685$	3.70069	0.141396
$686$	0	0
$687$	47.6680	1.81865
$688$	12.7643	0.486633
$689$	−34.6331	−1.31942
$690$	−8.85009	−0.336917
$691$	24.1080	0.917110	0.458555	−	0.888666i	$-0.348367\pi$
$691$	24.1080	0.917110	0.458555	+	0.888666i	$0.348367\pi$
$692$	−2.42530	−0.0921959
$693$	0	0
$694$	−22.3260	−0.847484
$695$	−8.24618	−0.312796
$696$	11.0906	0.420388
$697$	−37.2749	−1.41189
$698$	8.64837	0.327346
$699$	32.5778	1.23220
$700$	0	0
$701$	−13.3899	−0.505730	−0.252865	−	0.967502i	$-0.581373\pi$
$701$	−13.3899	−0.505730	−0.252865	+	0.967502i	$0.581373\pi$
$702$	7.25577	0.273851
$703$	8.60961	0.324718
$704$	−2.22875	−0.0839990
$705$	58.0941	2.18795
$706$	−31.5690	−1.18812
$707$	0	0
$708$	−7.80126	−0.293189
$709$	−30.2824	−1.13728	−0.568639	−	0.822587i	$-0.692530\pi$
$709$	−30.2824	−1.13728	−0.568639	+	0.822587i	$0.692530\pi$
$710$	−5.43874	−0.204112
$711$	−57.3733	−2.15167
$712$	1.58516	0.0594065
$713$	−3.47842	−0.130268
$714$	0	0
$715$	23.3459	0.873089
$716$	−13.8701	−0.518351
$717$	−2.27846	−0.0850908
$718$	−15.0279	−0.560837
$719$	1.03140	0.0384646	0.0192323	−	0.999815i	$-0.493878\pi$
$719$	1.03140	0.0384646	0.0192323	+	0.999815i	$0.493878\pi$
$720$	13.1150	0.488768
$721$	0	0
$722$	18.1643	0.676004
$723$	4.16554	0.154918
$724$	3.48271	0.129434
$725$	−26.9072	−0.999308
$726$	15.8348	0.587686
$727$	−19.4291	−0.720584	−0.360292	−	0.932839i	$-0.617323\pi$
$727$	−19.4291	−0.720584	−0.360292	+	0.932839i	$0.617323\pi$
$728$	0	0
$729$	−39.9363	−1.47912
$730$	−20.0139	−0.740749
$731$	81.3298	3.00809
$732$	17.8637	0.660260
$733$	−6.80302	−0.251275	−0.125638	−	0.992076i	$-0.540098\pi$
$733$	−6.80302	−0.251275	−0.125638	+	0.992076i	$0.540098\pi$
$734$	34.9869	1.29139
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	−15.3215	−0.564376
$738$	22.7555	0.837641
$739$	24.7683	0.911115	0.455558	−	0.890206i	$-0.349440\pi$
$739$	24.7683	0.911115	0.455558	+	0.890206i	$0.349440\pi$
$740$	31.7538	1.16729
$741$	−7.45488	−0.273862
$742$	0	0
$743$	−46.9124	−1.72105	−0.860524	−	0.509410i	$-0.829864\pi$
$743$	−46.9124	−1.72105	−0.860524	+	0.509410i	$0.829864\pi$
$744$	9.13028	0.334732
$745$	63.0083	2.30844
$746$	14.8540	0.543843
$747$	−25.3267	−0.926656
$748$	−14.2008	−0.519234
$749$	0	0
$750$	−12.1086	−0.442142
$751$	7.67837	0.280188	0.140094	−	0.990138i	$-0.455260\pi$
$751$	7.67837	0.280188	0.140094	+	0.990138i	$0.455260\pi$
$752$	6.56423	0.239373
$753$	−8.13637	−0.296506
$754$	−13.1268	−0.478049
$755$	−1.80563	−0.0657136
$756$	0	0
$757$	−11.3250	−0.411615	−0.205807	−	0.978593i	$-0.565982\pi$
$757$	−11.3250	−0.411615	−0.205807	+	0.978593i	$0.565982\pi$
$758$	−3.30019	−0.119868
$759$	−5.85009	−0.212345
$760$	−3.08233	−0.111808
$761$	−18.1155	−0.656687	−0.328344	−	0.944558i	$-0.606490\pi$
$761$	−18.1155	−0.656687	−0.328344	+	0.944558i	$0.606490\pi$
$762$	55.0540	1.99440
$763$	0	0
$764$	−14.8423	−0.536976
$765$	83.5646	3.02129
$766$	−11.4985	−0.415459
$767$	9.23353	0.333404
$768$	2.62484	0.0947156
$769$	−37.2805	−1.34437	−0.672184	−	0.740384i	$-0.734644\pi$
$769$	−37.2805	−1.34437	−0.672184	+	0.740384i	$0.734644\pi$
$770$	0	0
$771$	−18.3053	−0.659251
$772$	−15.9895	−0.575476
$773$	7.43266	0.267334	0.133667	−	0.991026i	$-0.457325\pi$
$773$	7.43266	0.267334	0.133667	+	0.991026i	$0.457325\pi$
$774$	−49.6500	−1.78463
$775$	−22.1512	−0.795695
$776$	−13.7970	−0.495282
$777$	0	0
$778$	−12.4422	−0.446076
$779$	−5.34805	−0.191614
$780$	−27.4950	−0.984478
$781$	−3.59512	−0.128644
$782$	−6.37167	−0.227851
$783$	−9.86804	−0.352655
$784$	0	0
$785$	−35.2021	−1.25642
$786$	−8.59870	−0.306705
$787$	6.58079	0.234580	0.117290	−	0.993098i	$-0.462579\pi$
$787$	6.58079	0.234580	0.117290	+	0.993098i	$0.462579\pi$
$788$	−14.8954	−0.530628
$789$	11.9929	0.426960
$790$	49.7316	1.76937
$791$	0	0
$792$	8.66930	0.308050
$793$	−21.1434	−0.750823
$794$	−24.1678	−0.857682
$795$	98.6583	3.49905
$796$	−24.1255	−0.855105
$797$	38.8340	1.37557	0.687785	−	0.725915i	$-0.258583\pi$
$797$	38.8340	1.37557	0.687785	+	0.725915i	$0.258583\pi$
$798$	0	0
$799$	41.8252	1.47967
$800$	−6.36818	−0.225149
$801$	−6.16591	−0.217862
$802$	−4.08313	−0.144180
$803$	−13.2296	−0.466863
$804$	18.0445	0.636379
$805$	0	0
$806$	−10.8066	−0.380645
$807$	78.0931	2.74901
$808$	7.07535	0.248910
$809$	0.912375	0.0320774	0.0160387	−	0.999871i	$-0.494895\pi$
$809$	0.912375	0.0320774	0.0160387	+	0.999871i	$0.494895\pi$
$810$	18.6758	0.656200
$811$	−33.0771	−1.16149	−0.580746	−	0.814085i	$-0.697239\pi$
$811$	−33.0771	−1.16149	−0.580746	+	0.814085i	$0.697239\pi$
$812$	0	0
$813$	−14.1476	−0.496179
$814$	20.9899	0.735696
$815$	14.0788	0.493160
$816$	16.7246	0.585478
$817$	11.6689	0.408243
$818$	−14.2234	−0.497311
$819$	0	0
$820$	−19.7246	−0.688813
$821$	−7.90242	−0.275796	−0.137898	−	0.990446i	$-0.544035\pi$
$821$	−7.90242	−0.275796	−0.137898	+	0.990446i	$0.544035\pi$
$822$	−2.88098	−0.100486
$823$	−11.5068	−0.401103	−0.200551	−	0.979683i	$-0.564273\pi$
$823$	−11.5068	−0.401103	−0.200551	+	0.979683i	$0.564273\pi$
$824$	15.7516	0.548734
$825$	−37.2545	−1.29703
$826$	0	0
$827$	−2.63501	−0.0916282	−0.0458141	−	0.998950i	$-0.514588\pi$
$827$	−2.63501	−0.0916282	−0.0458141	+	0.998950i	$0.514588\pi$
$828$	3.88977	0.135179
$829$	−10.5381	−0.366002	−0.183001	−	0.983113i	$-0.558581\pi$
$829$	−10.5381	−0.366002	−0.183001	+	0.983113i	$0.558581\pi$
$830$	21.9533	0.762012
$831$	4.11712	0.142821
$832$	−3.10674	−0.107707
$833$	0	0
$834$	6.41962	0.222293
$835$	−24.4993	−0.847835
$836$	−2.03748	−0.0704678
$837$	−8.12381	−0.280800
$838$	−13.2679	−0.458332
$839$	6.65434	0.229733	0.114867	−	0.993381i	$-0.463356\pi$
$839$	6.65434	0.229733	0.114867	+	0.993381i	$0.463356\pi$
$840$	0	0
$841$	−11.1472	−0.384387
$842$	37.5460	1.29392
$843$	40.4248	1.39230
$844$	−18.1067	−0.623260
$845$	−11.2888	−0.388348
$846$	−25.5333	−0.877854
$847$	0	0
$848$	11.1477	0.382814
$849$	−41.9665	−1.44029
$850$	−40.5760	−1.39174
$851$	9.41782	0.322839
$852$	4.23404	0.145056
$853$	10.4535	0.357921	0.178960	−	0.983856i	$-0.442727\pi$
$853$	10.4535	0.357921	0.178960	+	0.983856i	$0.442727\pi$
$854$	0	0
$855$	11.9895	0.410033
$856$	−5.76776	−0.197138
$857$	11.8253	0.403943	0.201972	−	0.979391i	$-0.435265\pi$
$857$	11.8253	0.403943	0.201972	+	0.979391i	$0.435265\pi$
$858$	−18.1747	−0.620475
$859$	−2.94780	−0.100578	−0.0502889	−	0.998735i	$-0.516014\pi$
$859$	−2.94780	−0.100578	−0.0502889	+	0.998735i	$0.516014\pi$
$860$	43.0370	1.46755
$861$	0	0
$862$	−9.29233	−0.316498
$863$	13.7441	0.467856	0.233928	−	0.972254i	$-0.424842\pi$
$863$	13.7441	0.467856	0.233928	+	0.972254i	$0.424842\pi$
$864$	−2.33549	−0.0794550
$865$	−8.17730	−0.278037
$866$	14.1033	0.479248
$867$	61.9415	2.10364
$868$	0	0
$869$	32.8736	1.11516
$870$	37.3939	1.26777
$871$	−21.3573	−0.723666
$872$	18.9207	0.640734
$873$	53.6670	1.81635
$874$	−0.914183	−0.0309227
$875$	0	0
$876$	15.5808	0.526426
$877$	12.9225	0.436363	0.218182	−	0.975908i	$-0.429987\pi$
$877$	12.9225	0.436363	0.218182	+	0.975908i	$0.429987\pi$
$878$	−19.4770	−0.657318
$879$	33.6449	1.13481
$880$	−7.51460	−0.253317
$881$	39.5393	1.33211	0.666057	−	0.745901i	$-0.267981\pi$
$881$	39.5393	1.33211	0.666057	+	0.745901i	$0.267981\pi$
$882$	0	0
$883$	−43.8065	−1.47420	−0.737102	−	0.675781i	$-0.763806\pi$
$883$	−43.8065	−1.47420	−0.737102	+	0.675781i	$0.763806\pi$
$884$	−19.7952	−0.665783
$885$	−26.3033	−0.884176
$886$	5.93242	0.199304
$887$	−22.3237	−0.749557	−0.374779	−	0.927114i	$-0.622281\pi$
$887$	−22.3237	−0.749557	−0.374779	+	0.927114i	$0.622281\pi$
$888$	−24.7202	−0.829557
$889$	0	0
$890$	5.34465	0.179153
$891$	12.3451	0.413575
$892$	20.1922	0.676084
$893$	6.00091	0.200813
$894$	−49.0517	−1.64053
$895$	−46.7656	−1.56320
$896$	0	0
$897$	−8.15470	−0.272277
$898$	5.13864	0.171479
$899$	14.6972	0.490179
$900$	24.7707	0.825691
$901$	71.0296	2.36634
$902$	−13.0384	−0.434130
$903$	0	0
$904$	11.2697	0.374825
$905$	11.7425	0.390336
$906$	1.40568	0.0467005
$907$	−18.0728	−0.600097	−0.300048	−	0.953924i	$-0.597003\pi$
$907$	−18.0728	−0.600097	−0.300048	+	0.953924i	$0.597003\pi$
$908$	−19.8187	−0.657706
$909$	−27.5214	−0.912829
$910$	0	0
$911$	46.0819	1.52676	0.763381	−	0.645948i	$-0.223538\pi$
$911$	46.0819	1.52676	0.763381	+	0.645948i	$0.223538\pi$
$912$	2.39958	0.0794581
$913$	14.5116	0.480264
$914$	−36.6304	−1.21163
$915$	60.2305	1.99116
$916$	18.1604	0.600035
$917$	0	0
$918$	−14.8810	−0.491145
$919$	−29.8392	−0.984305	−0.492152	−	0.870509i	$-0.663790\pi$
$919$	−29.8392	−0.984305	−0.492152	+	0.870509i	$0.663790\pi$
$920$	−3.37167	−0.111161
$921$	−1.31754	−0.0434145
$922$	16.0663	0.529114
$923$	−5.01139	−0.164952
$924$	0	0
$925$	59.9744	1.97195
$926$	−14.7503	−0.484725
$927$	−61.2701	−2.01238
$928$	4.22526	0.138701
$929$	45.2789	1.48555	0.742776	−	0.669540i	$-0.233509\pi$
$929$	45.2789	1.48555	0.742776	+	0.669540i	$0.233509\pi$
$930$	30.7843	1.00946
$931$	0	0
$932$	12.4113	0.406547
$933$	40.3366	1.32056
$934$	−29.7028	−0.971905
$935$	−47.8806	−1.56586
$936$	12.0845	0.394994
$937$	59.2418	1.93535	0.967673	−	0.252210i	$-0.0811573\pi$
$937$	59.2418	1.93535	0.967673	+	0.252210i	$0.0811573\pi$
$938$	0	0
$939$	−20.0004	−0.652687
$940$	22.1325	0.721881
$941$	37.1115	1.20980	0.604900	−	0.796301i	$-0.293213\pi$
$941$	37.1115	1.20980	0.604900	+	0.796301i	$0.293213\pi$
$942$	27.4047	0.892895
$943$	−5.85009	−0.190505
$944$	−2.97209	−0.0967334
$945$	0	0
$946$	28.4483	0.924935
$947$	−34.1254	−1.10893	−0.554463	−	0.832208i	$-0.687076\pi$
$947$	−34.1254	−1.10893	−0.554463	+	0.832208i	$0.687076\pi$
$948$	−38.7159	−1.25743
$949$	−18.4414	−0.598632
$950$	−5.82169	−0.188880
$951$	−48.0304	−1.55749
$952$	0	0
$953$	59.6326	1.93169	0.965845	−	0.259121i	$-0.0834330\pi$
$953$	59.6326	1.93169	0.965845	+	0.259121i	$0.0834330\pi$
$954$	−43.3620	−1.40390
$955$	−50.0434	−1.61937
$956$	−0.868040	−0.0280744
$957$	24.7181	0.799024
$958$	12.0466	0.389209
$959$	0	0
$960$	8.85009	0.285635
$961$	−18.9006	−0.609697
$962$	29.2587	0.943340
$963$	22.4353	0.722966
$964$	1.58697	0.0511129
$965$	−53.9115	−1.73547
$966$	0	0
$967$	−18.2061	−0.585469	−0.292735	−	0.956194i	$-0.594565\pi$
$967$	−18.2061	−0.585469	−0.292735	+	0.956194i	$0.594565\pi$
$968$	6.03269	0.193898
$969$	15.2893	0.491165
$970$	−46.5189	−1.49363
$971$	−1.01925	−0.0327091	−0.0163546	−	0.999866i	$-0.505206\pi$
$971$	−1.01925	−0.0327091	−0.0163546	+	0.999866i	$0.505206\pi$
$972$	−21.5455	−0.691072
$973$	0	0
$974$	−33.9316	−1.08724
$975$	−51.9306	−1.66311
$976$	6.80563	0.217843
$977$	−27.1672	−0.869157	−0.434579	−	0.900634i	$-0.643103\pi$
$977$	−27.1672	−0.869157	−0.434579	+	0.900634i	$0.643103\pi$
$978$	−10.9603	−0.350473
$979$	3.53292	0.112913
$980$	0	0
$981$	−73.5969	−2.34977
$982$	23.1813	0.739745
$983$	−21.6902	−0.691811	−0.345905	−	0.938269i	$-0.612428\pi$
$983$	−21.6902	−0.691811	−0.345905	+	0.938269i	$0.612428\pi$
$984$	15.3555	0.489517
$985$	−50.2226	−1.60022
$986$	26.9219	0.857370
$987$	0	0
$988$	−2.84013	−0.0903567
$989$	12.7643	0.405880
$990$	29.2300	0.928992
$991$	−48.9686	−1.55554	−0.777770	−	0.628549i	$-0.783649\pi$
$991$	−48.9686	−1.55554	−0.777770	+	0.628549i	$0.783649\pi$
$992$	3.47842	0.110440
$993$	30.6392	0.972304
$994$	0	0
$995$	−81.3432	−2.57875
$996$	−17.0906	−0.541537
$997$	5.36937	0.170050	0.0850248	−	0.996379i	$-0.472903\pi$
$997$	5.36937	0.170050	0.0850248	+	0.996379i	$0.472903\pi$
$998$	−8.80214	−0.278627
$999$	21.9952	0.695898

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2254.2.a.v.1.4		4
7.2	even	3		322.2.e.c.277.1	yes	8
7.4	even	3		322.2.e.c.93.1	✓	8
7.6	odd	2		2254.2.a.q.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.e.c.93.1	✓	8	7.4	even	3
322.2.e.c.277.1	yes	8	7.2	even	3
2254.2.a.q.1.1		4	7.6	odd	2
2254.2.a.v.1.4		4	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:	\( N \)	\(=\)	\( 2254 = 2 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2254.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.62484 q^{3} +1.00000 q^{4} +3.37167 q^{5} -2.62484 q^{6} -1.00000 q^{8} +3.88977 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.62484 q^{3} +1.00000 q^{4} +3.37167 q^{5} -2.62484 q^{6} -1.00000 q^{8} +3.88977 q^{9} -3.37167 q^{10} -2.22875 q^{11} +2.62484 q^{12} -3.10674 q^{13} +8.85009 q^{15} +1.00000 q^{16} +6.37167 q^{17} -3.88977 q^{18} +0.914183 q^{19} +3.37167 q^{20} +2.22875 q^{22} +1.00000 q^{23} -2.62484 q^{24} +6.36818 q^{25} +3.10674 q^{26} +2.33549 q^{27} -4.22526 q^{29} -8.85009 q^{30} -3.47842 q^{31} -1.00000 q^{32} -5.85009 q^{33} -6.37167 q^{34} +3.88977 q^{36} +9.41782 q^{37} -0.914183 q^{38} -8.15470 q^{39} -3.37167 q^{40} -5.85009 q^{41} +12.7643 q^{43} -2.22875 q^{44} +13.1150 q^{45} -1.00000 q^{46} +6.56423 q^{47} +2.62484 q^{48} -6.36818 q^{50} +16.7246 q^{51} -3.10674 q^{52} +11.1477 q^{53} -2.33549 q^{54} -7.51460 q^{55} +2.39958 q^{57} +4.22526 q^{58} -2.97209 q^{59} +8.85009 q^{60} +6.80563 q^{61} +3.47842 q^{62} +1.00000 q^{64} -10.4749 q^{65} +5.85009 q^{66} +6.87451 q^{67} +6.37167 q^{68} +2.62484 q^{69} +1.61307 q^{71} -3.88977 q^{72} +5.93591 q^{73} -9.41782 q^{74} +16.7154 q^{75} +0.914183 q^{76} +8.15470 q^{78} -14.7498 q^{79} +3.37167 q^{80} -5.53902 q^{81} +5.85009 q^{82} -6.51111 q^{83} +21.4832 q^{85} -12.7643 q^{86} -11.0906 q^{87} +2.22875 q^{88} -1.58516 q^{89} -13.1150 q^{90} +1.00000 q^{92} -9.13028 q^{93} -6.56423 q^{94} +3.08233 q^{95} -2.62484 q^{96} +13.7970 q^{97} -8.66930 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + q^{3} + 4 q^{4} + 3 q^{5} - q^{6} - 4 q^{8} + 7 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + q^3 + 4 * q^4 + 3 * q^5 - q^6 - 4 * q^8 + 7 * q^9	\( 4 q - 4 q^{2} + q^{3} + 4 q^{4} + 3 q^{5} - q^{6} - 4 q^{8} + 7 q^{9} - 3 q^{10} - 6 q^{11} + q^{12} - q^{13} + 3 q^{15} + 4 q^{16} + 15 q^{17} - 7 q^{18} - q^{19} + 3 q^{20} + 6 q^{22} + 4 q^{23} - q^{24} - 5 q^{25} + q^{26} - 5 q^{27} + 6 q^{29} - 3 q^{30} + 8 q^{31} - 4 q^{32} + 9 q^{33} - 15 q^{34} + 7 q^{36} + 8 q^{37} + q^{38} - 25 q^{39} - 3 q^{40} + 9 q^{41} + 14 q^{43} - 6 q^{44} + 21 q^{45} - 4 q^{46} + 9 q^{47} + q^{48} + 5 q^{50} + 6 q^{51} - q^{52} - 3 q^{53} + 5 q^{54} - 12 q^{55} + 23 q^{57} - 6 q^{58} + 12 q^{59} + 3 q^{60} + 11 q^{61} - 8 q^{62} + 4 q^{64} - 9 q^{66} - q^{67} + 15 q^{68} + q^{69} - 3 q^{71} - 7 q^{72} - 4 q^{73} - 8 q^{74} + 22 q^{75} - q^{76} + 25 q^{78} + 5 q^{79} + 3 q^{80} - 8 q^{81} - 9 q^{82} + 12 q^{83} + 24 q^{85} - 14 q^{86} - 9 q^{87} + 6 q^{88} + 27 q^{89} - 21 q^{90} + 4 q^{92} - 25 q^{93} - 9 q^{94} - 3 q^{95} - q^{96} + 2 q^{97} - 9 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + q^3 + 4 * q^4 + 3 * q^5 - q^6 - 4 * q^8 + 7 * q^9 - 3 * q^10 - 6 * q^11 + q^12 - q^13 + 3 * q^15 + 4 * q^16 + 15 * q^17 - 7 * q^18 - q^19 + 3 * q^20 + 6 * q^22 + 4 * q^23 - q^24 - 5 * q^25 + q^26 - 5 * q^27 + 6 * q^29 - 3 * q^30 + 8 * q^31 - 4 * q^32 + 9 * q^33 - 15 * q^34 + 7 * q^36 + 8 * q^37 + q^38 - 25 * q^39 - 3 * q^40 + 9 * q^41 + 14 * q^43 - 6 * q^44 + 21 * q^45 - 4 * q^46 + 9 * q^47 + q^48 + 5 * q^50 + 6 * q^51 - q^52 - 3 * q^53 + 5 * q^54 - 12 * q^55 + 23 * q^57 - 6 * q^58 + 12 * q^59 + 3 * q^60 + 11 * q^61 - 8 * q^62 + 4 * q^64 - 9 * q^66 - q^67 + 15 * q^68 + q^69 - 3 * q^71 - 7 * q^72 - 4 * q^73 - 8 * q^74 + 22 * q^75 - q^76 + 25 * q^78 + 5 * q^79 + 3 * q^80 - 8 * q^81 - 9 * q^82 + 12 * q^83 + 24 * q^85 - 14 * q^86 - 9 * q^87 + 6 * q^88 + 27 * q^89 - 21 * q^90 + 4 * q^92 - 25 * q^93 - 9 * q^94 - 3 * q^95 - q^96 + 2 * q^97 - 9 * q^99

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