LMFDB - Embedded newform 2550.2.a.bm.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2550,2,Mod(1,2550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2550, 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("2550.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2550.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:	$20.3618525154$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{33}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 8 $ x^2 - x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.37228$ of defining polynomial
Character	$\chi$	$=$	2550.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.37228 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.37228 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.37228 q^{11} +1.00000 q^{12} +2.00000 q^{13} -2.37228 q^{14} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -2.37228 q^{19} -2.37228 q^{21} +4.37228 q^{22} -1.37228 q^{23} +1.00000 q^{24} +2.00000 q^{26} +1.00000 q^{27} -2.37228 q^{28} +8.74456 q^{29} +9.11684 q^{31} +1.00000 q^{32} +4.37228 q^{33} -1.00000 q^{34} +1.00000 q^{36} -1.00000 q^{37} -2.37228 q^{38} +2.00000 q^{39} -1.37228 q^{41} -2.37228 q^{42} +3.62772 q^{43} +4.37228 q^{44} -1.37228 q^{46} -1.62772 q^{47} +1.00000 q^{48} -1.37228 q^{49} -1.00000 q^{51} +2.00000 q^{52} +5.74456 q^{53} +1.00000 q^{54} -2.37228 q^{56} -2.37228 q^{57} +8.74456 q^{58} +10.1168 q^{59} -8.11684 q^{61} +9.11684 q^{62} -2.37228 q^{63} +1.00000 q^{64} +4.37228 q^{66} +0.372281 q^{67} -1.00000 q^{68} -1.37228 q^{69} -1.37228 q^{71} +1.00000 q^{72} +8.00000 q^{73} -1.00000 q^{74} -2.37228 q^{76} -10.3723 q^{77} +2.00000 q^{78} -11.1168 q^{79} +1.00000 q^{81} -1.37228 q^{82} +1.37228 q^{83} -2.37228 q^{84} +3.62772 q^{86} +8.74456 q^{87} +4.37228 q^{88} -2.74456 q^{89} -4.74456 q^{91} -1.37228 q^{92} +9.11684 q^{93} -1.62772 q^{94} +1.00000 q^{96} -12.7446 q^{97} -1.37228 q^{98} +4.37228 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + q^{7} + 2 q^{8} + 2 q^{9} + 3 q^{11} + 2 q^{12} + 4 q^{13} + q^{14} + 2 q^{16} - 2 q^{17} + 2 q^{18} + q^{19} + q^{21} + 3 q^{22} + 3 q^{23} + 2 q^{24} + 4 q^{26} + 2 q^{27} + q^{28} + 6 q^{29} + q^{31} + 2 q^{32} + 3 q^{33} - 2 q^{34} + 2 q^{36} - 2 q^{37} + q^{38} + 4 q^{39} + 3 q^{41} + q^{42} + 13 q^{43} + 3 q^{44} + 3 q^{46} - 9 q^{47} + 2 q^{48} + 3 q^{49} - 2 q^{51} + 4 q^{52} + 2 q^{54} + q^{56} + q^{57} + 6 q^{58} + 3 q^{59} + q^{61} + q^{62} + q^{63} + 2 q^{64} + 3 q^{66} - 5 q^{67} - 2 q^{68} + 3 q^{69} + 3 q^{71} + 2 q^{72} + 16 q^{73} - 2 q^{74} + q^{76} - 15 q^{77} + 4 q^{78} - 5 q^{79} + 2 q^{81} + 3 q^{82} - 3 q^{83} + q^{84} + 13 q^{86} + 6 q^{87} + 3 q^{88} + 6 q^{89} + 2 q^{91} + 3 q^{92} + q^{93} - 9 q^{94} + 2 q^{96} - 14 q^{97} + 3 q^{98} + 3 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + q^7 + 2 * q^8 + 2 * q^9 + 3 * q^11 + 2 * q^12 + 4 * q^13 + q^14 + 2 * q^16 - 2 * q^17 + 2 * q^18 + q^19 + q^21 + 3 * q^22 + 3 * q^23 + 2 * q^24 + 4 * q^26 + 2 * q^27 + q^28 + 6 * q^29 + q^31 + 2 * q^32 + 3 * q^33 - 2 * q^34 + 2 * q^36 - 2 * q^37 + q^38 + 4 * q^39 + 3 * q^41 + q^42 + 13 * q^43 + 3 * q^44 + 3 * q^46 - 9 * q^47 + 2 * q^48 + 3 * q^49 - 2 * q^51 + 4 * q^52 + 2 * q^54 + q^56 + q^57 + 6 * q^58 + 3 * q^59 + q^61 + q^62 + q^63 + 2 * q^64 + 3 * q^66 - 5 * q^67 - 2 * q^68 + 3 * q^69 + 3 * q^71 + 2 * q^72 + 16 * q^73 - 2 * q^74 + q^76 - 15 * q^77 + 4 * q^78 - 5 * q^79 + 2 * q^81 + 3 * q^82 - 3 * q^83 + q^84 + 13 * q^86 + 6 * q^87 + 3 * q^88 + 6 * q^89 + 2 * q^91 + 3 * q^92 + q^93 - 9 * q^94 + 2 * q^96 - 14 * q^97 + 3 * q^98 + 3 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	−2.37228	−0.896638	−0.448319	−	0.893874i	$-0.647977\pi$
$7$	−2.37228	−0.896638	−0.448319	+	0.893874i	$0.647977\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	4.37228	1.31829	0.659146	−	0.752015i	$-0.270918\pi$
$11$	4.37228	1.31829	0.659146	+	0.752015i	$0.270918\pi$
$12$	1.00000	0.288675
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	−2.37228	−0.634019
$15$	0	0
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−2.37228	−0.544239	−0.272119	−	0.962264i	$-0.587725\pi$
$19$	−2.37228	−0.544239	−0.272119	+	0.962264i	$0.587725\pi$
$20$	0	0
$21$	−2.37228	−0.517674
$22$	4.37228	0.932174
$23$	−1.37228	−0.286140	−0.143070	−	0.989713i	$-0.545697\pi$
$23$	−1.37228	−0.286140	−0.143070	+	0.989713i	$0.545697\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	2.00000	0.392232
$27$	1.00000	0.192450
$28$	−2.37228	−0.448319
$29$	8.74456	1.62382	0.811912	−	0.583779i	$-0.198427\pi$
$29$	8.74456	1.62382	0.811912	+	0.583779i	$0.198427\pi$
$30$	0	0
$31$	9.11684	1.63743	0.818717	−	0.574198i	$-0.194686\pi$
$31$	9.11684	1.63743	0.818717	+	0.574198i	$0.194686\pi$
$32$	1.00000	0.176777
$33$	4.37228	0.761116
$34$	−1.00000	−0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	−1.00000	−0.164399	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000	−0.164399	−0.0821995	+	0.996616i	$0.526194\pi$
$38$	−2.37228	−0.384835
$39$	2.00000	0.320256
$40$	0	0
$41$	−1.37228	−0.214314	−0.107157	−	0.994242i	$-0.534175\pi$
$41$	−1.37228	−0.214314	−0.107157	+	0.994242i	$0.534175\pi$
$42$	−2.37228	−0.366051
$43$	3.62772	0.553222	0.276611	−	0.960982i	$-0.410789\pi$
$43$	3.62772	0.553222	0.276611	+	0.960982i	$0.410789\pi$
$44$	4.37228	0.659146
$45$	0	0
$46$	−1.37228	−0.202332
$47$	−1.62772	−0.237427	−0.118714	−	0.992929i	$-0.537877\pi$
$47$	−1.62772	−0.237427	−0.118714	+	0.992929i	$0.537877\pi$
$48$	1.00000	0.144338
$49$	−1.37228	−0.196040
$50$	0	0
$51$	−1.00000	−0.140028
$52$	2.00000	0.277350
$53$	5.74456	0.789076	0.394538	−	0.918880i	$-0.370905\pi$
$53$	5.74456	0.789076	0.394538	+	0.918880i	$0.370905\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−2.37228	−0.317009
$57$	−2.37228	−0.314216
$58$	8.74456	1.14822
$59$	10.1168	1.31710	0.658550	−	0.752537i	$-0.271170\pi$
$59$	10.1168	1.31710	0.658550	+	0.752537i	$0.271170\pi$
$60$	0	0
$61$	−8.11684	−1.03926	−0.519628	−	0.854393i	$-0.673929\pi$
$61$	−8.11684	−1.03926	−0.519628	+	0.854393i	$0.673929\pi$
$62$	9.11684	1.15784
$63$	−2.37228	−0.298879
$64$	1.00000	0.125000
$65$	0	0
$66$	4.37228	0.538191
$67$	0.372281	0.0454814	0.0227407	−	0.999741i	$-0.492761\pi$
$67$	0.372281	0.0454814	0.0227407	+	0.999741i	$0.492761\pi$
$68$	−1.00000	−0.121268
$69$	−1.37228	−0.165203
$70$	0	0
$71$	−1.37228	−0.162860	−0.0814299	−	0.996679i	$-0.525949\pi$
$71$	−1.37228	−0.162860	−0.0814299	+	0.996679i	$0.525949\pi$
$72$	1.00000	0.117851
$73$	8.00000	0.936329	0.468165	−	0.883641i	$-0.344915\pi$
$73$	8.00000	0.936329	0.468165	+	0.883641i	$0.344915\pi$
$74$	−1.00000	−0.116248
$75$	0	0
$76$	−2.37228	−0.272119
$77$	−10.3723	−1.18203
$78$	2.00000	0.226455
$79$	−11.1168	−1.25074	−0.625371	−	0.780327i	$-0.715052\pi$
$79$	−11.1168	−1.25074	−0.625371	+	0.780327i	$0.715052\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−1.37228	−0.151543
$83$	1.37228	0.150627	0.0753137	−	0.997160i	$-0.476004\pi$
$83$	1.37228	0.150627	0.0753137	+	0.997160i	$0.476004\pi$
$84$	−2.37228	−0.258837
$85$	0	0
$86$	3.62772	0.391187
$87$	8.74456	0.937516
$88$	4.37228	0.466087
$89$	−2.74456	−0.290923	−0.145462	−	0.989364i	$-0.546467\pi$
$89$	−2.74456	−0.290923	−0.145462	+	0.989364i	$0.546467\pi$
$90$	0	0
$91$	−4.74456	−0.497365
$92$	−1.37228	−0.143070
$93$	9.11684	0.945373
$94$	−1.62772	−0.167886
$95$	0	0
$96$	1.00000	0.102062
$97$	−12.7446	−1.29401	−0.647007	−	0.762484i	$-0.723980\pi$
$97$	−12.7446	−1.29401	−0.647007	+	0.762484i	$0.723980\pi$
$98$	−1.37228	−0.138621
$99$	4.37228	0.439431
$100$	0	0
$101$	13.1168	1.30517	0.652587	−	0.757713i	$-0.273684\pi$
$101$	13.1168	1.30517	0.652587	+	0.757713i	$0.273684\pi$
$102$	−1.00000	−0.0990148
$103$	15.3723	1.51468	0.757338	−	0.653023i	$-0.226500\pi$
$103$	15.3723	1.51468	0.757338	+	0.653023i	$0.226500\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	5.74456	0.557961
$107$	−10.3723	−1.00273	−0.501363	−	0.865237i	$-0.667168\pi$
$107$	−10.3723	−1.00273	−0.501363	+	0.865237i	$0.667168\pi$
$108$	1.00000	0.0962250
$109$	9.11684	0.873235	0.436618	−	0.899647i	$-0.356176\pi$
$109$	9.11684	0.873235	0.436618	+	0.899647i	$0.356176\pi$
$110$	0	0
$111$	−1.00000	−0.0949158
$112$	−2.37228	−0.224160
$113$	−11.7446	−1.10484	−0.552418	−	0.833567i	$-0.686295\pi$
$113$	−11.7446	−1.10484	−0.552418	+	0.833567i	$0.686295\pi$
$114$	−2.37228	−0.222185
$115$	0	0
$116$	8.74456	0.811912
$117$	2.00000	0.184900
$118$	10.1168	0.931331
$119$	2.37228	0.217467
$120$	0	0
$121$	8.11684	0.737895
$122$	−8.11684	−0.734865
$123$	−1.37228	−0.123734
$124$	9.11684	0.818717
$125$	0	0
$126$	−2.37228	−0.211340
$127$	1.48913	0.132139	0.0660693	−	0.997815i	$-0.478954\pi$
$127$	1.48913	0.132139	0.0660693	+	0.997815i	$0.478954\pi$
$128$	1.00000	0.0883883
$129$	3.62772	0.319403
$130$	0	0
$131$	17.4891	1.52803	0.764016	−	0.645197i	$-0.223225\pi$
$131$	17.4891	1.52803	0.764016	+	0.645197i	$0.223225\pi$
$132$	4.37228	0.380558
$133$	5.62772	0.487985
$134$	0.372281	0.0321602
$135$	0	0
$136$	−1.00000	−0.0857493
$137$	5.48913	0.468968	0.234484	−	0.972120i	$-0.424660\pi$
$137$	5.48913	0.468968	0.234484	+	0.972120i	$0.424660\pi$
$138$	−1.37228	−0.116816
$139$	18.1168	1.53665	0.768325	−	0.640060i	$-0.221090\pi$
$139$	18.1168	1.53665	0.768325	+	0.640060i	$0.221090\pi$
$140$	0	0
$141$	−1.62772	−0.137079
$142$	−1.37228	−0.115159
$143$	8.74456	0.731257
$144$	1.00000	0.0833333
$145$	0	0
$146$	8.00000	0.662085
$147$	−1.37228	−0.113184
$148$	−1.00000	−0.0821995
$149$	−6.86141	−0.562108	−0.281054	−	0.959692i	$-0.590684\pi$
$149$	−6.86141	−0.562108	−0.281054	+	0.959692i	$0.590684\pi$
$150$	0	0
$151$	−14.1168	−1.14881	−0.574406	−	0.818570i	$-0.694767\pi$
$151$	−14.1168	−1.14881	−0.574406	+	0.818570i	$0.694767\pi$
$152$	−2.37228	−0.192417
$153$	−1.00000	−0.0808452
$154$	−10.3723	−0.835822
$155$	0	0
$156$	2.00000	0.160128
$157$	−18.7446	−1.49598	−0.747989	−	0.663711i	$-0.768981\pi$
$157$	−18.7446	−1.49598	−0.747989	+	0.663711i	$0.768981\pi$
$158$	−11.1168	−0.884409
$159$	5.74456	0.455573
$160$	0	0
$161$	3.25544	0.256564
$162$	1.00000	0.0785674
$163$	−2.11684	−0.165804	−0.0829020	−	0.996558i	$-0.526419\pi$
$163$	−2.11684	−0.165804	−0.0829020	+	0.996558i	$0.526419\pi$
$164$	−1.37228	−0.107157
$165$	0	0
$166$	1.37228	0.106510
$167$	−20.7446	−1.60526	−0.802631	−	0.596476i	$-0.796567\pi$
$167$	−20.7446	−1.60526	−0.802631	+	0.596476i	$0.796567\pi$
$168$	−2.37228	−0.183025
$169$	−9.00000	−0.692308
$170$	0	0
$171$	−2.37228	−0.181413
$172$	3.62772	0.276611
$173$	−12.0000	−0.912343	−0.456172	−	0.889892i	$-0.650780\pi$
$173$	−12.0000	−0.912343	−0.456172	+	0.889892i	$0.650780\pi$
$174$	8.74456	0.662924
$175$	0	0
$176$	4.37228	0.329573
$177$	10.1168	0.760429
$178$	−2.74456	−0.205714
$179$	−10.1168	−0.756168	−0.378084	−	0.925771i	$-0.623417\pi$
$179$	−10.1168	−0.756168	−0.378084	+	0.925771i	$0.623417\pi$
$180$	0	0
$181$	−0.489125	−0.0363564	−0.0181782	−	0.999835i	$-0.505787\pi$
$181$	−0.489125	−0.0363564	−0.0181782	+	0.999835i	$0.505787\pi$
$182$	−4.74456	−0.351690
$183$	−8.11684	−0.600014
$184$	−1.37228	−0.101166
$185$	0	0
$186$	9.11684	0.668479
$187$	−4.37228	−0.319733
$188$	−1.62772	−0.118714
$189$	−2.37228	−0.172558
$190$	0	0
$191$	−27.3505	−1.97902	−0.989508	−	0.144481i	$-0.953849\pi$
$191$	−27.3505	−1.97902	−0.989508	+	0.144481i	$0.953849\pi$
$192$	1.00000	0.0721688
$193$	8.00000	0.575853	0.287926	−	0.957653i	$-0.407034\pi$
$193$	8.00000	0.575853	0.287926	+	0.957653i	$0.407034\pi$
$194$	−12.7446	−0.915006
$195$	0	0
$196$	−1.37228	−0.0980201
$197$	−9.25544	−0.659423	−0.329711	−	0.944082i	$-0.606951\pi$
$197$	−9.25544	−0.659423	−0.329711	+	0.944082i	$0.606951\pi$
$198$	4.37228	0.310725
$199$	21.1168	1.49693	0.748467	−	0.663172i	$-0.230790\pi$
$199$	21.1168	1.49693	0.748467	+	0.663172i	$0.230790\pi$
$200$	0	0
$201$	0.372281	0.0262587
$202$	13.1168	0.922898
$203$	−20.7446	−1.45598
$204$	−1.00000	−0.0700140
$205$	0	0
$206$	15.3723	1.07104
$207$	−1.37228	−0.0953801
$208$	2.00000	0.138675
$209$	−10.3723	−0.717466
$210$	0	0
$211$	10.2337	0.704516	0.352258	−	0.935903i	$-0.385414\pi$
$211$	10.2337	0.704516	0.352258	+	0.935903i	$0.385414\pi$
$212$	5.74456	0.394538
$213$	−1.37228	−0.0940272
$214$	−10.3723	−0.709035
$215$	0	0
$216$	1.00000	0.0680414
$217$	−21.6277	−1.46819
$218$	9.11684	0.617471
$219$	8.00000	0.540590
$220$	0	0
$221$	−2.00000	−0.134535
$222$	−1.00000	−0.0671156
$223$	−8.11684	−0.543544	−0.271772	−	0.962362i	$-0.587610\pi$
$223$	−8.11684	−0.543544	−0.271772	+	0.962362i	$0.587610\pi$
$224$	−2.37228	−0.158505
$225$	0	0
$226$	−11.7446	−0.781237
$227$	−4.37228	−0.290199	−0.145099	−	0.989417i	$-0.546350\pi$
$227$	−4.37228	−0.290199	−0.145099	+	0.989417i	$0.546350\pi$
$228$	−2.37228	−0.157108
$229$	−12.2337	−0.808425	−0.404212	−	0.914665i	$-0.632454\pi$
$229$	−12.2337	−0.808425	−0.404212	+	0.914665i	$0.632454\pi$
$230$	0	0
$231$	−10.3723	−0.682446
$232$	8.74456	0.574109
$233$	−10.6277	−0.696245	−0.348122	−	0.937449i	$-0.613181\pi$
$233$	−10.6277	−0.696245	−0.348122	+	0.937449i	$0.613181\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	10.1168	0.658550
$237$	−11.1168	−0.722117
$238$	2.37228	0.153772
$239$	−13.1168	−0.848458	−0.424229	−	0.905555i	$-0.639455\pi$
$239$	−13.1168	−0.848458	−0.424229	+	0.905555i	$0.639455\pi$
$240$	0	0
$241$	28.2337	1.81869	0.909346	−	0.416041i	$-0.136583\pi$
$241$	28.2337	1.81869	0.909346	+	0.416041i	$0.136583\pi$
$242$	8.11684	0.521770
$243$	1.00000	0.0641500
$244$	−8.11684	−0.519628
$245$	0	0
$246$	−1.37228	−0.0874935
$247$	−4.74456	−0.301889
$248$	9.11684	0.578920
$249$	1.37228	0.0869648
$250$	0	0
$251$	8.74456	0.551952	0.275976	−	0.961165i	$-0.410999\pi$
$251$	8.74456	0.551952	0.275976	+	0.961165i	$0.410999\pi$
$252$	−2.37228	−0.149440
$253$	−6.00000	−0.377217
$254$	1.48913	0.0934360
$255$	0	0
$256$	1.00000	0.0625000
$257$	−14.2337	−0.887873	−0.443937	−	0.896058i	$-0.646418\pi$
$257$	−14.2337	−0.887873	−0.443937	+	0.896058i	$0.646418\pi$
$258$	3.62772	0.225852
$259$	2.37228	0.147406
$260$	0	0
$261$	8.74456	0.541275
$262$	17.4891	1.08048
$263$	−25.6277	−1.58027	−0.790136	−	0.612931i	$-0.789990\pi$
$263$	−25.6277	−1.58027	−0.790136	+	0.612931i	$0.789990\pi$
$264$	4.37228	0.269095
$265$	0	0
$266$	5.62772	0.345058
$267$	−2.74456	−0.167965
$268$	0.372281	0.0227407
$269$	11.4891	0.700504	0.350252	−	0.936655i	$-0.386096\pi$
$269$	11.4891	0.700504	0.350252	+	0.936655i	$0.386096\pi$
$270$	0	0
$271$	−2.62772	−0.159623	−0.0798113	−	0.996810i	$-0.525432\pi$
$271$	−2.62772	−0.159623	−0.0798113	+	0.996810i	$0.525432\pi$
$272$	−1.00000	−0.0606339
$273$	−4.74456	−0.287154
$274$	5.48913	0.331610
$275$	0	0
$276$	−1.37228	−0.0826016
$277$	−13.0000	−0.781094	−0.390547	−	0.920583i	$-0.627714\pi$
$277$	−13.0000	−0.781094	−0.390547	+	0.920583i	$0.627714\pi$
$278$	18.1168	1.08658
$279$	9.11684	0.545811
$280$	0	0
$281$	0.510875	0.0304762	0.0152381	−	0.999884i	$-0.495149\pi$
$281$	0.510875	0.0304762	0.0152381	+	0.999884i	$0.495149\pi$
$282$	−1.62772	−0.0969292
$283$	12.1168	0.720272	0.360136	−	0.932900i	$-0.382730\pi$
$283$	12.1168	0.720272	0.360136	+	0.932900i	$0.382730\pi$
$284$	−1.37228	−0.0814299
$285$	0	0
$286$	8.74456	0.517077
$287$	3.25544	0.192162
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	0	0
$291$	−12.7446	−0.747099
$292$	8.00000	0.468165
$293$	−28.1168	−1.64260	−0.821302	−	0.570494i	$-0.806752\pi$
$293$	−28.1168	−1.64260	−0.821302	+	0.570494i	$0.806752\pi$
$294$	−1.37228	−0.0800331
$295$	0	0
$296$	−1.00000	−0.0581238
$297$	4.37228	0.253705
$298$	−6.86141	−0.397471
$299$	−2.74456	−0.158722
$300$	0	0
$301$	−8.60597	−0.496040
$302$	−14.1168	−0.812333
$303$	13.1168	0.753543
$304$	−2.37228	−0.136060
$305$	0	0
$306$	−1.00000	−0.0571662
$307$	16.2337	0.926506	0.463253	−	0.886226i	$-0.346682\pi$
$307$	16.2337	0.926506	0.463253	+	0.886226i	$0.346682\pi$
$308$	−10.3723	−0.591016
$309$	15.3723	0.874499
$310$	0	0
$311$	−28.1168	−1.59436	−0.797180	−	0.603742i	$-0.793676\pi$
$311$	−28.1168	−1.59436	−0.797180	+	0.603742i	$0.793676\pi$
$312$	2.00000	0.113228
$313$	4.74456	0.268179	0.134089	−	0.990969i	$-0.457189\pi$
$313$	4.74456	0.268179	0.134089	+	0.990969i	$0.457189\pi$
$314$	−18.7446	−1.05782
$315$	0	0
$316$	−11.1168	−0.625371
$317$	14.7446	0.828137	0.414069	−	0.910246i	$-0.364107\pi$
$317$	14.7446	0.828137	0.414069	+	0.910246i	$0.364107\pi$
$318$	5.74456	0.322139
$319$	38.2337	2.14068
$320$	0	0
$321$	−10.3723	−0.578924
$322$	3.25544	0.181418
$323$	2.37228	0.131997
$324$	1.00000	0.0555556
$325$	0	0
$326$	−2.11684	−0.117241
$327$	9.11684	0.504163
$328$	−1.37228	−0.0757716
$329$	3.86141	0.212886
$330$	0	0
$331$	14.6060	0.802817	0.401408	−	0.915899i	$-0.368521\pi$
$331$	14.6060	0.802817	0.401408	+	0.915899i	$0.368521\pi$
$332$	1.37228	0.0753137
$333$	−1.00000	−0.0547997
$334$	−20.7446	−1.13509
$335$	0	0
$336$	−2.37228	−0.129419
$337$	−24.2337	−1.32009	−0.660047	−	0.751225i	$-0.729463\pi$
$337$	−24.2337	−1.32009	−0.660047	+	0.751225i	$0.729463\pi$
$338$	−9.00000	−0.489535
$339$	−11.7446	−0.637877
$340$	0	0
$341$	39.8614	2.15862
$342$	−2.37228	−0.128278
$343$	19.8614	1.07242
$344$	3.62772	0.195593
$345$	0	0
$346$	−12.0000	−0.645124
$347$	22.3723	1.20101	0.600503	−	0.799622i	$-0.294967\pi$
$347$	22.3723	1.20101	0.600503	+	0.799622i	$0.294967\pi$
$348$	8.74456	0.468758
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	0	0
$351$	2.00000	0.106752
$352$	4.37228	0.233043
$353$	−15.2554	−0.811965	−0.405983	−	0.913881i	$-0.633071\pi$
$353$	−15.2554	−0.811965	−0.405983	+	0.913881i	$0.633071\pi$
$354$	10.1168	0.537704
$355$	0	0
$356$	−2.74456	−0.145462
$357$	2.37228	0.125554
$358$	−10.1168	−0.534692
$359$	−13.6277	−0.719243	−0.359622	−	0.933098i	$-0.617094\pi$
$359$	−13.6277	−0.719243	−0.359622	+	0.933098i	$0.617094\pi$
$360$	0	0
$361$	−13.3723	−0.703804
$362$	−0.489125	−0.0257079
$363$	8.11684	0.426024
$364$	−4.74456	−0.248683
$365$	0	0
$366$	−8.11684	−0.424274
$367$	14.6060	0.762425	0.381213	−	0.924487i	$-0.375507\pi$
$367$	14.6060	0.762425	0.381213	+	0.924487i	$0.375507\pi$
$368$	−1.37228	−0.0715351
$369$	−1.37228	−0.0714381
$370$	0	0
$371$	−13.6277	−0.707516
$372$	9.11684	0.472686
$373$	−1.76631	−0.0914562	−0.0457281	−	0.998954i	$-0.514561\pi$
$373$	−1.76631	−0.0914562	−0.0457281	+	0.998954i	$0.514561\pi$
$374$	−4.37228	−0.226085
$375$	0	0
$376$	−1.62772	−0.0839432
$377$	17.4891	0.900736
$378$	−2.37228	−0.122017
$379$	−19.6060	−1.00709	−0.503545	−	0.863969i	$-0.667971\pi$
$379$	−19.6060	−1.00709	−0.503545	+	0.863969i	$0.667971\pi$
$380$	0	0
$381$	1.48913	0.0762902
$382$	−27.3505	−1.39937
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	8.00000	0.407189
$387$	3.62772	0.184407
$388$	−12.7446	−0.647007
$389$	17.7446	0.899685	0.449843	−	0.893108i	$-0.351480\pi$
$389$	17.7446	0.899685	0.449843	+	0.893108i	$0.351480\pi$
$390$	0	0
$391$	1.37228	0.0693992
$392$	−1.37228	−0.0693107
$393$	17.4891	0.882210
$394$	−9.25544	−0.466282
$395$	0	0
$396$	4.37228	0.219715
$397$	−1.00000	−0.0501886	−0.0250943	−	0.999685i	$-0.507989\pi$
$397$	−1.00000	−0.0501886	−0.0250943	+	0.999685i	$0.507989\pi$
$398$	21.1168	1.05849
$399$	5.62772	0.281738
$400$	0	0
$401$	4.11684	0.205585	0.102793	−	0.994703i	$-0.467222\pi$
$401$	4.11684	0.205585	0.102793	+	0.994703i	$0.467222\pi$
$402$	0.372281	0.0185677
$403$	18.2337	0.908285
$404$	13.1168	0.652587
$405$	0	0
$406$	−20.7446	−1.02954
$407$	−4.37228	−0.216726
$408$	−1.00000	−0.0495074
$409$	14.8614	0.734849	0.367425	−	0.930053i	$-0.380240\pi$
$409$	14.8614	0.734849	0.367425	+	0.930053i	$0.380240\pi$
$410$	0	0
$411$	5.48913	0.270759
$412$	15.3723	0.757338
$413$	−24.0000	−1.18096
$414$	−1.37228	−0.0674439
$415$	0	0
$416$	2.00000	0.0980581
$417$	18.1168	0.887186
$418$	−10.3723	−0.507325
$419$	10.9783	0.536323	0.268161	−	0.963374i	$-0.413584\pi$
$419$	10.9783	0.536323	0.268161	+	0.963374i	$0.413584\pi$
$420$	0	0
$421$	−18.2337	−0.888656	−0.444328	−	0.895864i	$-0.646557\pi$
$421$	−18.2337	−0.888656	−0.444328	+	0.895864i	$0.646557\pi$
$422$	10.2337	0.498168
$423$	−1.62772	−0.0791424
$424$	5.74456	0.278981
$425$	0	0
$426$	−1.37228	−0.0664872
$427$	19.2554	0.931836
$428$	−10.3723	−0.501363
$429$	8.74456	0.422191
$430$	0	0
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	1.00000	0.0481125
$433$	−40.0951	−1.92685	−0.963424	−	0.267983i	$-0.913643\pi$
$433$	−40.0951	−1.92685	−0.963424	+	0.267983i	$0.913643\pi$
$434$	−21.6277	−1.03816
$435$	0	0
$436$	9.11684	0.436618
$437$	3.25544	0.155729
$438$	8.00000	0.382255
$439$	2.51087	0.119838	0.0599188	−	0.998203i	$-0.480916\pi$
$439$	2.51087	0.119838	0.0599188	+	0.998203i	$0.480916\pi$
$440$	0	0
$441$	−1.37228	−0.0653467
$442$	−2.00000	−0.0951303
$443$	−7.37228	−0.350268	−0.175134	−	0.984545i	$-0.556036\pi$
$443$	−7.37228	−0.350268	−0.175134	+	0.984545i	$0.556036\pi$
$444$	−1.00000	−0.0474579
$445$	0	0
$446$	−8.11684	−0.384344
$447$	−6.86141	−0.324533
$448$	−2.37228	−0.112080
$449$	−33.8614	−1.59802	−0.799009	−	0.601319i	$-0.794642\pi$
$449$	−33.8614	−1.59802	−0.799009	+	0.601319i	$0.794642\pi$
$450$	0	0
$451$	−6.00000	−0.282529
$452$	−11.7446	−0.552418
$453$	−14.1168	−0.663267
$454$	−4.37228	−0.205201
$455$	0	0
$456$	−2.37228	−0.111092
$457$	23.0000	1.07589	0.537947	−	0.842978i	$-0.319200\pi$
$457$	23.0000	1.07589	0.537947	+	0.842978i	$0.319200\pi$
$458$	−12.2337	−0.571643
$459$	−1.00000	−0.0466760
$460$	0	0
$461$	34.7228	1.61720	0.808601	−	0.588357i	$-0.200225\pi$
$461$	34.7228	1.61720	0.808601	+	0.588357i	$0.200225\pi$
$462$	−10.3723	−0.482562
$463$	−19.6060	−0.911167	−0.455583	−	0.890193i	$-0.650569\pi$
$463$	−19.6060	−0.911167	−0.455583	+	0.890193i	$0.650569\pi$
$464$	8.74456	0.405956
$465$	0	0
$466$	−10.6277	−0.492320
$467$	16.1168	0.745799	0.372899	−	0.927872i	$-0.378364\pi$
$467$	16.1168	0.745799	0.372899	+	0.927872i	$0.378364\pi$
$468$	2.00000	0.0924500
$469$	−0.883156	−0.0407804
$470$	0	0
$471$	−18.7446	−0.863704
$472$	10.1168	0.465665
$473$	15.8614	0.729308
$474$	−11.1168	−0.510614
$475$	0	0
$476$	2.37228	0.108733
$477$	5.74456	0.263025
$478$	−13.1168	−0.599950
$479$	−31.7228	−1.44945	−0.724726	−	0.689037i	$-0.758034\pi$
$479$	−31.7228	−1.44945	−0.724726	+	0.689037i	$0.758034\pi$
$480$	0	0
$481$	−2.00000	−0.0911922
$482$	28.2337	1.28601
$483$	3.25544	0.148128
$484$	8.11684	0.368947
$485$	0	0
$486$	1.00000	0.0453609
$487$	−12.2337	−0.554361	−0.277181	−	0.960818i	$-0.589400\pi$
$487$	−12.2337	−0.554361	−0.277181	+	0.960818i	$0.589400\pi$
$488$	−8.11684	−0.367432
$489$	−2.11684	−0.0957270
$490$	0	0
$491$	−31.3723	−1.41581	−0.707906	−	0.706307i	$-0.750360\pi$
$491$	−31.3723	−1.41581	−0.707906	+	0.706307i	$0.750360\pi$
$492$	−1.37228	−0.0618672
$493$	−8.74456	−0.393835
$494$	−4.74456	−0.213468
$495$	0	0
$496$	9.11684	0.409358
$497$	3.25544	0.146026
$498$	1.37228	0.0614934
$499$	18.6277	0.833891	0.416946	−	0.908931i	$-0.363101\pi$
$499$	18.6277	0.833891	0.416946	+	0.908931i	$0.363101\pi$
$500$	0	0
$501$	−20.7446	−0.926799
$502$	8.74456	0.390289
$503$	−9.60597	−0.428309	−0.214154	−	0.976800i	$-0.568700\pi$
$503$	−9.60597	−0.428309	−0.214154	+	0.976800i	$0.568700\pi$
$504$	−2.37228	−0.105670
$505$	0	0
$506$	−6.00000	−0.266733
$507$	−9.00000	−0.399704
$508$	1.48913	0.0660693
$509$	−19.6277	−0.869983	−0.434992	−	0.900434i	$-0.643249\pi$
$509$	−19.6277	−0.869983	−0.434992	+	0.900434i	$0.643249\pi$
$510$	0	0
$511$	−18.9783	−0.839548
$512$	1.00000	0.0441942
$513$	−2.37228	−0.104739
$514$	−14.2337	−0.627821
$515$	0	0
$516$	3.62772	0.159701
$517$	−7.11684	−0.312998
$518$	2.37228	0.104232
$519$	−12.0000	−0.526742
$520$	0	0
$521$	−27.3505	−1.19825	−0.599124	−	0.800656i	$-0.704484\pi$
$521$	−27.3505	−1.19825	−0.599124	+	0.800656i	$0.704484\pi$
$522$	8.74456	0.382739
$523$	16.2337	0.709850	0.354925	−	0.934895i	$-0.384506\pi$
$523$	16.2337	0.709850	0.354925	+	0.934895i	$0.384506\pi$
$524$	17.4891	0.764016
$525$	0	0
$526$	−25.6277	−1.11742
$527$	−9.11684	−0.397136
$528$	4.37228	0.190279
$529$	−21.1168	−0.918124
$530$	0	0
$531$	10.1168	0.439034
$532$	5.62772	0.243993
$533$	−2.74456	−0.118880
$534$	−2.74456	−0.118769
$535$	0	0
$536$	0.372281	0.0160801
$537$	−10.1168	−0.436574
$538$	11.4891	0.495331
$539$	−6.00000	−0.258438
$540$	0	0
$541$	5.00000	0.214967	0.107483	−	0.994207i	$-0.465721\pi$
$541$	5.00000	0.214967	0.107483	+	0.994207i	$0.465721\pi$
$542$	−2.62772	−0.112870
$543$	−0.489125	−0.0209904
$544$	−1.00000	−0.0428746
$545$	0	0
$546$	−4.74456	−0.203049
$547$	30.6277	1.30955	0.654773	−	0.755825i	$-0.272764\pi$
$547$	30.6277	1.30955	0.654773	+	0.755825i	$0.272764\pi$
$548$	5.48913	0.234484
$549$	−8.11684	−0.346418
$550$	0	0
$551$	−20.7446	−0.883748
$552$	−1.37228	−0.0584082
$553$	26.3723	1.12146
$554$	−13.0000	−0.552317
$555$	0	0
$556$	18.1168	0.768325
$557$	−24.2554	−1.02774	−0.513868	−	0.857869i	$-0.671788\pi$
$557$	−24.2554	−1.02774	−0.513868	+	0.857869i	$0.671788\pi$
$558$	9.11684	0.385947
$559$	7.25544	0.306872
$560$	0	0
$561$	−4.37228	−0.184598
$562$	0.510875	0.0215499
$563$	18.3505	0.773383	0.386691	−	0.922209i	$-0.373618\pi$
$563$	18.3505	0.773383	0.386691	+	0.922209i	$0.373618\pi$
$564$	−1.62772	−0.0685393
$565$	0	0
$566$	12.1168	0.509309
$567$	−2.37228	−0.0996265
$568$	−1.37228	−0.0575796
$569$	−9.25544	−0.388008	−0.194004	−	0.981001i	$-0.562147\pi$
$569$	−9.25544	−0.388008	−0.194004	+	0.981001i	$0.562147\pi$
$570$	0	0
$571$	−32.6277	−1.36543	−0.682714	−	0.730686i	$-0.739200\pi$
$571$	−32.6277	−1.36543	−0.682714	+	0.730686i	$0.739200\pi$
$572$	8.74456	0.365629
$573$	−27.3505	−1.14258
$574$	3.25544	0.135879
$575$	0	0
$576$	1.00000	0.0416667
$577$	−7.00000	−0.291414	−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000	−0.291414	−0.145707	+	0.989328i	$0.546546\pi$
$578$	1.00000	0.0415945
$579$	8.00000	0.332469
$580$	0	0
$581$	−3.25544	−0.135058
$582$	−12.7446	−0.528279
$583$	25.1168	1.04023
$584$	8.00000	0.331042
$585$	0	0
$586$	−28.1168	−1.16150
$587$	30.8614	1.27379	0.636893	−	0.770952i	$-0.280219\pi$
$587$	30.8614	1.27379	0.636893	+	0.770952i	$0.280219\pi$
$588$	−1.37228	−0.0565919
$589$	−21.6277	−0.891155
$590$	0	0
$591$	−9.25544	−0.380718
$592$	−1.00000	−0.0410997
$593$	−40.4674	−1.66180	−0.830898	−	0.556425i	$-0.812173\pi$
$593$	−40.4674	−1.66180	−0.830898	+	0.556425i	$0.812173\pi$
$594$	4.37228	0.179397
$595$	0	0
$596$	−6.86141	−0.281054
$597$	21.1168	0.864255
$598$	−2.74456	−0.112234
$599$	−1.62772	−0.0665068	−0.0332534	−	0.999447i	$-0.510587\pi$
$599$	−1.62772	−0.0665068	−0.0332534	+	0.999447i	$0.510587\pi$
$600$	0	0
$601$	36.9783	1.50837	0.754187	−	0.656660i	$-0.228031\pi$
$601$	36.9783	1.50837	0.754187	+	0.656660i	$0.228031\pi$
$602$	−8.60597	−0.350753
$603$	0.372281	0.0151605
$604$	−14.1168	−0.574406
$605$	0	0
$606$	13.1168	0.532835
$607$	40.2337	1.63304	0.816518	−	0.577321i	$-0.195902\pi$
$607$	40.2337	1.63304	0.816518	+	0.577321i	$0.195902\pi$
$608$	−2.37228	−0.0962087
$609$	−20.7446	−0.840612
$610$	0	0
$611$	−3.25544	−0.131701
$612$	−1.00000	−0.0404226
$613$	−3.48913	−0.140924	−0.0704622	−	0.997514i	$-0.522447\pi$
$613$	−3.48913	−0.140924	−0.0704622	+	0.997514i	$0.522447\pi$
$614$	16.2337	0.655138
$615$	0	0
$616$	−10.3723	−0.417911
$617$	44.8397	1.80518	0.902588	−	0.430505i	$-0.141664\pi$
$617$	44.8397	1.80518	0.902588	+	0.430505i	$0.141664\pi$
$618$	15.3723	0.618364
$619$	−4.00000	−0.160774	−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000	−0.160774	−0.0803868	+	0.996764i	$0.525616\pi$
$620$	0	0
$621$	−1.37228	−0.0550678
$622$	−28.1168	−1.12738
$623$	6.51087	0.260853
$624$	2.00000	0.0800641
$625$	0	0
$626$	4.74456	0.189631
$627$	−10.3723	−0.414229
$628$	−18.7446	−0.747989
$629$	1.00000	0.0398726
$630$	0	0
$631$	−34.8614	−1.38781	−0.693905	−	0.720066i	$-0.744111\pi$
$631$	−34.8614	−1.38781	−0.693905	+	0.720066i	$0.744111\pi$
$632$	−11.1168	−0.442204
$633$	10.2337	0.406753
$634$	14.7446	0.585581
$635$	0	0
$636$	5.74456	0.227787
$637$	−2.74456	−0.108744
$638$	38.2337	1.51369
$639$	−1.37228	−0.0542866
$640$	0	0
$641$	40.9783	1.61854	0.809272	−	0.587434i	$-0.199862\pi$
$641$	40.9783	1.61854	0.809272	+	0.587434i	$0.199862\pi$
$642$	−10.3723	−0.409361
$643$	24.1168	0.951075	0.475538	−	0.879695i	$-0.342254\pi$
$643$	24.1168	0.951075	0.475538	+	0.879695i	$0.342254\pi$
$644$	3.25544	0.128282
$645$	0	0
$646$	2.37228	0.0933362
$647$	−25.7228	−1.01127	−0.505634	−	0.862748i	$-0.668741\pi$
$647$	−25.7228	−1.01127	−0.505634	+	0.862748i	$0.668741\pi$
$648$	1.00000	0.0392837
$649$	44.2337	1.73632
$650$	0	0
$651$	−21.6277	−0.847657
$652$	−2.11684	−0.0829020
$653$	−22.9783	−0.899208	−0.449604	−	0.893228i	$-0.648435\pi$
$653$	−22.9783	−0.899208	−0.449604	+	0.893228i	$0.648435\pi$
$654$	9.11684	0.356497
$655$	0	0
$656$	−1.37228	−0.0535786
$657$	8.00000	0.312110
$658$	3.86141	0.150533
$659$	6.51087	0.253628	0.126814	−	0.991927i	$-0.459525\pi$
$659$	6.51087	0.253628	0.126814	+	0.991927i	$0.459525\pi$
$660$	0	0
$661$	−13.2554	−0.515577	−0.257788	−	0.966201i	$-0.582994\pi$
$661$	−13.2554	−0.515577	−0.257788	+	0.966201i	$0.582994\pi$
$662$	14.6060	0.567677
$663$	−2.00000	−0.0776736
$664$	1.37228	0.0532548
$665$	0	0
$666$	−1.00000	−0.0387492
$667$	−12.0000	−0.464642
$668$	−20.7446	−0.802631
$669$	−8.11684	−0.313815
$670$	0	0
$671$	−35.4891	−1.37004
$672$	−2.37228	−0.0915127
$673$	39.7228	1.53120	0.765601	−	0.643316i	$-0.222442\pi$
$673$	39.7228	1.53120	0.765601	+	0.643316i	$0.222442\pi$
$674$	−24.2337	−0.933447
$675$	0	0
$676$	−9.00000	−0.346154
$677$	−24.0000	−0.922395	−0.461197	−	0.887298i	$-0.652580\pi$
$677$	−24.0000	−0.922395	−0.461197	+	0.887298i	$0.652580\pi$
$678$	−11.7446	−0.451047
$679$	30.2337	1.16026
$680$	0	0
$681$	−4.37228	−0.167546
$682$	39.8614	1.52637
$683$	9.25544	0.354149	0.177075	−	0.984197i	$-0.443337\pi$
$683$	9.25544	0.354149	0.177075	+	0.984197i	$0.443337\pi$
$684$	−2.37228	−0.0907064
$685$	0	0
$686$	19.8614	0.758312
$687$	−12.2337	−0.466744
$688$	3.62772	0.138305
$689$	11.4891	0.437701
$690$	0	0
$691$	39.3723	1.49779	0.748896	−	0.662687i	$-0.230584\pi$
$691$	39.3723	1.49779	0.748896	+	0.662687i	$0.230584\pi$
$692$	−12.0000	−0.456172
$693$	−10.3723	−0.394010
$694$	22.3723	0.849240
$695$	0	0
$696$	8.74456	0.331462
$697$	1.37228	0.0519789
$698$	−10.0000	−0.378506
$699$	−10.6277	−0.401977
$700$	0	0
$701$	9.60597	0.362812	0.181406	−	0.983408i	$-0.441935\pi$
$701$	9.60597	0.362812	0.181406	+	0.983408i	$0.441935\pi$
$702$	2.00000	0.0754851
$703$	2.37228	0.0894723
$704$	4.37228	0.164787
$705$	0	0
$706$	−15.2554	−0.574146
$707$	−31.1168	−1.17027
$708$	10.1168	0.380214
$709$	−8.37228	−0.314428	−0.157214	−	0.987565i	$-0.550251\pi$
$709$	−8.37228	−0.314428	−0.157214	+	0.987565i	$0.550251\pi$
$710$	0	0
$711$	−11.1168	−0.416914
$712$	−2.74456	−0.102857
$713$	−12.5109	−0.468536
$714$	2.37228	0.0887804
$715$	0	0
$716$	−10.1168	−0.378084
$717$	−13.1168	−0.489858
$718$	−13.6277	−0.508582
$719$	−27.2554	−1.01646	−0.508228	−	0.861222i	$-0.669699\pi$
$719$	−27.2554	−1.01646	−0.508228	+	0.861222i	$0.669699\pi$
$720$	0	0
$721$	−36.4674	−1.35812
$722$	−13.3723	−0.497665
$723$	28.2337	1.05002
$724$	−0.489125	−0.0181782
$725$	0	0
$726$	8.11684	0.301244
$727$	−31.2554	−1.15920	−0.579600	−	0.814901i	$-0.696791\pi$
$727$	−31.2554	−1.15920	−0.579600	+	0.814901i	$0.696791\pi$
$728$	−4.74456	−0.175845
$729$	1.00000	0.0370370
$730$	0	0
$731$	−3.62772	−0.134176
$732$	−8.11684	−0.300007
$733$	−1.25544	−0.0463706	−0.0231853	−	0.999731i	$-0.507381\pi$
$733$	−1.25544	−0.0463706	−0.0231853	+	0.999731i	$0.507381\pi$
$734$	14.6060	0.539116
$735$	0	0
$736$	−1.37228	−0.0505830
$737$	1.62772	0.0599578
$738$	−1.37228	−0.0505144
$739$	33.6277	1.23702	0.618508	−	0.785779i	$-0.287738\pi$
$739$	33.6277	1.23702	0.618508	+	0.785779i	$0.287738\pi$
$740$	0	0
$741$	−4.74456	−0.174296
$742$	−13.6277	−0.500289
$743$	22.6277	0.830130	0.415065	−	0.909792i	$-0.363759\pi$
$743$	22.6277	0.830130	0.415065	+	0.909792i	$0.363759\pi$
$744$	9.11684	0.334240
$745$	0	0
$746$	−1.76631	−0.0646693
$747$	1.37228	0.0502091
$748$	−4.37228	−0.159866
$749$	24.6060	0.899083
$750$	0	0
$751$	−32.4674	−1.18475	−0.592376	−	0.805662i	$-0.701810\pi$
$751$	−32.4674	−1.18475	−0.592376	+	0.805662i	$0.701810\pi$
$752$	−1.62772	−0.0593568
$753$	8.74456	0.318670
$754$	17.4891	0.636916
$755$	0	0
$756$	−2.37228	−0.0862790
$757$	34.2337	1.24424	0.622122	−	0.782920i	$-0.286271\pi$
$757$	34.2337	1.24424	0.622122	+	0.782920i	$0.286271\pi$
$758$	−19.6060	−0.712121
$759$	−6.00000	−0.217786
$760$	0	0
$761$	−17.4891	−0.633980	−0.316990	−	0.948429i	$-0.602672\pi$
$761$	−17.4891	−0.633980	−0.316990	+	0.948429i	$0.602672\pi$
$762$	1.48913	0.0539453
$763$	−21.6277	−0.782976
$764$	−27.3505	−0.989508
$765$	0	0
$766$	0	0
$767$	20.2337	0.730596
$768$	1.00000	0.0360844
$769$	−13.0000	−0.468792	−0.234396	−	0.972141i	$-0.575311\pi$
$769$	−13.0000	−0.468792	−0.234396	+	0.972141i	$0.575311\pi$
$770$	0	0
$771$	−14.2337	−0.512614
$772$	8.00000	0.287926
$773$	−17.1386	−0.616432	−0.308216	−	0.951316i	$-0.599732\pi$
$773$	−17.1386	−0.616432	−0.308216	+	0.951316i	$0.599732\pi$
$774$	3.62772	0.130396
$775$	0	0
$776$	−12.7446	−0.457503
$777$	2.37228	0.0851051
$778$	17.7446	0.636173
$779$	3.25544	0.116638
$780$	0	0
$781$	−6.00000	−0.214697
$782$	1.37228	0.0490727
$783$	8.74456	0.312505
$784$	−1.37228	−0.0490100
$785$	0	0
$786$	17.4891	0.623816
$787$	44.3505	1.58093	0.790463	−	0.612510i	$-0.209840\pi$
$787$	44.3505	1.58093	0.790463	+	0.612510i	$0.209840\pi$
$788$	−9.25544	−0.329711
$789$	−25.6277	−0.912371
$790$	0	0
$791$	27.8614	0.990638
$792$	4.37228	0.155362
$793$	−16.2337	−0.576475
$794$	−1.00000	−0.0354887
$795$	0	0
$796$	21.1168	0.748467
$797$	6.25544	0.221579	0.110789	−	0.993844i	$-0.464662\pi$
$797$	6.25544	0.221579	0.110789	+	0.993844i	$0.464662\pi$
$798$	5.62772	0.199219
$799$	1.62772	0.0575845
$800$	0	0
$801$	−2.74456	−0.0969744
$802$	4.11684	0.145371
$803$	34.9783	1.23436
$804$	0.372281	0.0131293
$805$	0	0
$806$	18.2337	0.642254
$807$	11.4891	0.404436
$808$	13.1168	0.461449
$809$	18.6060	0.654151	0.327076	−	0.944998i	$-0.393937\pi$
$809$	18.6060	0.654151	0.327076	+	0.944998i	$0.393937\pi$
$810$	0	0
$811$	44.0000	1.54505	0.772524	−	0.634985i	$-0.218994\pi$
$811$	44.0000	1.54505	0.772524	+	0.634985i	$0.218994\pi$
$812$	−20.7446	−0.727991
$813$	−2.62772	−0.0921581
$814$	−4.37228	−0.153248
$815$	0	0
$816$	−1.00000	−0.0350070
$817$	−8.60597	−0.301085
$818$	14.8614	0.519617
$819$	−4.74456	−0.165788
$820$	0	0
$821$	−44.7446	−1.56160	−0.780798	−	0.624784i	$-0.785187\pi$
$821$	−44.7446	−1.56160	−0.780798	+	0.624784i	$0.785187\pi$
$822$	5.48913	0.191455
$823$	−20.4674	−0.713448	−0.356724	−	0.934210i	$-0.616106\pi$
$823$	−20.4674	−0.713448	−0.356724	+	0.934210i	$0.616106\pi$
$824$	15.3723	0.535519
$825$	0	0
$826$	−24.0000	−0.835067
$827$	−12.0951	−0.420588	−0.210294	−	0.977638i	$-0.567442\pi$
$827$	−12.0951	−0.420588	−0.210294	+	0.977638i	$0.567442\pi$
$828$	−1.37228	−0.0476901
$829$	40.7446	1.41512	0.707559	−	0.706655i	$-0.249797\pi$
$829$	40.7446	1.41512	0.707559	+	0.706655i	$0.249797\pi$
$830$	0	0
$831$	−13.0000	−0.450965
$832$	2.00000	0.0693375
$833$	1.37228	0.0475467
$834$	18.1168	0.627335
$835$	0	0
$836$	−10.3723	−0.358733
$837$	9.11684	0.315124
$838$	10.9783	0.379237
$839$	7.37228	0.254519	0.127260	−	0.991869i	$-0.459382\pi$
$839$	7.37228	0.254519	0.127260	+	0.991869i	$0.459382\pi$
$840$	0	0
$841$	47.4674	1.63681
$842$	−18.2337	−0.628374
$843$	0.510875	0.0175955
$844$	10.2337	0.352258
$845$	0	0
$846$	−1.62772	−0.0559621
$847$	−19.2554	−0.661625
$848$	5.74456	0.197269
$849$	12.1168	0.415849
$850$	0	0
$851$	1.37228	0.0470412
$852$	−1.37228	−0.0470136
$853$	17.8614	0.611563	0.305781	−	0.952102i	$-0.401082\pi$
$853$	17.8614	0.611563	0.305781	+	0.952102i	$0.401082\pi$
$854$	19.2554	0.658908
$855$	0	0
$856$	−10.3723	−0.354517
$857$	18.2554	0.623594	0.311797	−	0.950149i	$-0.399069\pi$
$857$	18.2554	0.623594	0.311797	+	0.950149i	$0.399069\pi$
$858$	8.74456	0.298534
$859$	−13.3505	−0.455514	−0.227757	−	0.973718i	$-0.573139\pi$
$859$	−13.3505	−0.455514	−0.227757	+	0.973718i	$0.573139\pi$
$860$	0	0
$861$	3.25544	0.110945
$862$	12.0000	0.408722
$863$	−13.6277	−0.463893	−0.231946	−	0.972729i	$-0.574509\pi$
$863$	−13.6277	−0.463893	−0.231946	+	0.972729i	$0.574509\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	−40.0951	−1.36249
$867$	1.00000	0.0339618
$868$	−21.6277	−0.734093
$869$	−48.6060	−1.64884
$870$	0	0
$871$	0.744563	0.0252285
$872$	9.11684	0.308735
$873$	−12.7446	−0.431338
$874$	3.25544	0.110117
$875$	0	0
$876$	8.00000	0.270295
$877$	−46.0000	−1.55331	−0.776655	−	0.629926i	$-0.783085\pi$
$877$	−46.0000	−1.55331	−0.776655	+	0.629926i	$0.783085\pi$
$878$	2.51087	0.0847379
$879$	−28.1168	−0.948358
$880$	0	0
$881$	−34.2119	−1.15263	−0.576315	−	0.817228i	$-0.695510\pi$
$881$	−34.2119	−1.15263	−0.576315	+	0.817228i	$0.695510\pi$
$882$	−1.37228	−0.0462071
$883$	−7.76631	−0.261357	−0.130679	−	0.991425i	$-0.541716\pi$
$883$	−7.76631	−0.261357	−0.130679	+	0.991425i	$0.541716\pi$
$884$	−2.00000	−0.0672673
$885$	0	0
$886$	−7.37228	−0.247677
$887$	39.6060	1.32984	0.664919	−	0.746915i	$-0.268466\pi$
$887$	39.6060	1.32984	0.664919	+	0.746915i	$0.268466\pi$
$888$	−1.00000	−0.0335578
$889$	−3.53262	−0.118480
$890$	0	0
$891$	4.37228	0.146477
$892$	−8.11684	−0.271772
$893$	3.86141	0.129217
$894$	−6.86141	−0.229480
$895$	0	0
$896$	−2.37228	−0.0792524
$897$	−2.74456	−0.0916383
$898$	−33.8614	−1.12997
$899$	79.7228	2.65890
$900$	0	0
$901$	−5.74456	−0.191379
$902$	−6.00000	−0.199778
$903$	−8.60597	−0.286389
$904$	−11.7446	−0.390618
$905$	0	0
$906$	−14.1168	−0.469001
$907$	10.3940	0.345128	0.172564	−	0.984998i	$-0.444795\pi$
$907$	10.3940	0.345128	0.172564	+	0.984998i	$0.444795\pi$
$908$	−4.37228	−0.145099
$909$	13.1168	0.435058
$910$	0	0
$911$	−6.51087	−0.215715	−0.107857	−	0.994166i	$-0.534399\pi$
$911$	−6.51087	−0.215715	−0.107857	+	0.994166i	$0.534399\pi$
$912$	−2.37228	−0.0785541
$913$	6.00000	0.198571
$914$	23.0000	0.760772
$915$	0	0
$916$	−12.2337	−0.404212
$917$	−41.4891	−1.37009
$918$	−1.00000	−0.0330049
$919$	−42.5842	−1.40472	−0.702362	−	0.711820i	$-0.747871\pi$
$919$	−42.5842	−1.40472	−0.702362	+	0.711820i	$0.747871\pi$
$920$	0	0
$921$	16.2337	0.534918
$922$	34.7228	1.14353
$923$	−2.74456	−0.0903384
$924$	−10.3723	−0.341223
$925$	0	0
$926$	−19.6060	−0.644292
$927$	15.3723	0.504892
$928$	8.74456	0.287054
$929$	−40.7228	−1.33607	−0.668036	−	0.744129i	$-0.732865\pi$
$929$	−40.7228	−1.33607	−0.668036	+	0.744129i	$0.732865\pi$
$930$	0	0
$931$	3.25544	0.106693
$932$	−10.6277	−0.348122
$933$	−28.1168	−0.920504
$934$	16.1168	0.527359
$935$	0	0
$936$	2.00000	0.0653720
$937$	41.6060	1.35921	0.679604	−	0.733579i	$-0.262152\pi$
$937$	41.6060	1.35921	0.679604	+	0.733579i	$0.262152\pi$
$938$	−0.883156	−0.0288361
$939$	4.74456	0.154833
$940$	0	0
$941$	−22.4674	−0.732416	−0.366208	−	0.930533i	$-0.619344\pi$
$941$	−22.4674	−0.732416	−0.366208	+	0.930533i	$0.619344\pi$
$942$	−18.7446	−0.610731
$943$	1.88316	0.0613240
$944$	10.1168	0.329275
$945$	0	0
$946$	15.8614	0.515699
$947$	34.3723	1.11695	0.558475	−	0.829522i	$-0.311387\pi$
$947$	34.3723	1.11695	0.558475	+	0.829522i	$0.311387\pi$
$948$	−11.1168	−0.361058
$949$	16.0000	0.519382
$950$	0	0
$951$	14.7446	0.478125
$952$	2.37228	0.0768861
$953$	40.9783	1.32742	0.663708	−	0.747992i	$-0.268982\pi$
$953$	40.9783	1.32742	0.663708	+	0.747992i	$0.268982\pi$
$954$	5.74456	0.185987
$955$	0	0
$956$	−13.1168	−0.424229
$957$	38.2337	1.23592
$958$	−31.7228	−1.02492
$959$	−13.0217	−0.420494
$960$	0	0
$961$	52.1168	1.68119
$962$	−2.00000	−0.0644826
$963$	−10.3723	−0.334242
$964$	28.2337	0.909346
$965$	0	0
$966$	3.25544	0.104742
$967$	−22.3505	−0.718745	−0.359372	−	0.933194i	$-0.617009\pi$
$967$	−22.3505	−0.718745	−0.359372	+	0.933194i	$0.617009\pi$
$968$	8.11684	0.260885
$969$	2.37228	0.0762087
$970$	0	0
$971$	−6.86141	−0.220193	−0.110097	−	0.993921i	$-0.535116\pi$
$971$	−6.86141	−0.220193	−0.110097	+	0.993921i	$0.535116\pi$
$972$	1.00000	0.0320750
$973$	−42.9783	−1.37782
$974$	−12.2337	−0.391993
$975$	0	0
$976$	−8.11684	−0.259814
$977$	6.00000	0.191957	0.0959785	−	0.995383i	$-0.469402\pi$
$977$	6.00000	0.191957	0.0959785	+	0.995383i	$0.469402\pi$
$978$	−2.11684	−0.0676892
$979$	−12.0000	−0.383522
$980$	0	0
$981$	9.11684	0.291078
$982$	−31.3723	−1.00113
$983$	9.76631	0.311497	0.155748	−	0.987797i	$-0.450221\pi$
$983$	9.76631	0.311497	0.155748	+	0.987797i	$0.450221\pi$
$984$	−1.37228	−0.0437467
$985$	0	0
$986$	−8.74456	−0.278484
$987$	3.86141	0.122910
$988$	−4.74456	−0.150945
$989$	−4.97825	−0.158299
$990$	0	0
$991$	60.4674	1.92081	0.960405	−	0.278609i	$-0.0898732\pi$
$991$	60.4674	1.92081	0.960405	+	0.278609i	$0.0898732\pi$
$992$	9.11684	0.289460
$993$	14.6060	0.463506
$994$	3.25544	0.103256
$995$	0	0
$996$	1.37228	0.0434824
$997$	33.1168	1.04882	0.524410	−	0.851466i	$-0.324286\pi$
$997$	33.1168	1.04882	0.524410	+	0.851466i	$0.324286\pi$
$998$	18.6277	0.589650
$999$	−1.00000	−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2550.2.a.bm.1.1	yes	2
3.2	odd	2		7650.2.a.cv.1.1		2
5.2	odd	4		2550.2.d.v.2449.3		4
5.3	odd	4		2550.2.d.v.2449.2		4
5.4	even	2		2550.2.a.bg.1.2	✓	2
15.14	odd	2		7650.2.a.df.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2550.2.a.bg.1.2	✓	2	5.4	even	2
2550.2.a.bm.1.1	yes	2	1.1	even	1	trivial
2550.2.d.v.2449.2		4	5.3	odd	4
2550.2.d.v.2449.3		4	5.2	odd	4
7650.2.a.cv.1.1		2	3.2	odd	2
7650.2.a.df.1.2		2	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2550.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.37228 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.37228 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.37228 q^{11} +1.00000 q^{12} +2.00000 q^{13} -2.37228 q^{14} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -2.37228 q^{19} -2.37228 q^{21} +4.37228 q^{22} -1.37228 q^{23} +1.00000 q^{24} +2.00000 q^{26} +1.00000 q^{27} -2.37228 q^{28} +8.74456 q^{29} +9.11684 q^{31} +1.00000 q^{32} +4.37228 q^{33} -1.00000 q^{34} +1.00000 q^{36} -1.00000 q^{37} -2.37228 q^{38} +2.00000 q^{39} -1.37228 q^{41} -2.37228 q^{42} +3.62772 q^{43} +4.37228 q^{44} -1.37228 q^{46} -1.62772 q^{47} +1.00000 q^{48} -1.37228 q^{49} -1.00000 q^{51} +2.00000 q^{52} +5.74456 q^{53} +1.00000 q^{54} -2.37228 q^{56} -2.37228 q^{57} +8.74456 q^{58} +10.1168 q^{59} -8.11684 q^{61} +9.11684 q^{62} -2.37228 q^{63} +1.00000 q^{64} +4.37228 q^{66} +0.372281 q^{67} -1.00000 q^{68} -1.37228 q^{69} -1.37228 q^{71} +1.00000 q^{72} +8.00000 q^{73} -1.00000 q^{74} -2.37228 q^{76} -10.3723 q^{77} +2.00000 q^{78} -11.1168 q^{79} +1.00000 q^{81} -1.37228 q^{82} +1.37228 q^{83} -2.37228 q^{84} +3.62772 q^{86} +8.74456 q^{87} +4.37228 q^{88} -2.74456 q^{89} -4.74456 q^{91} -1.37228 q^{92} +9.11684 q^{93} -1.62772 q^{94} +1.00000 q^{96} -12.7446 q^{97} -1.37228 q^{98} +4.37228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + q^{7} + 2 q^{8} + 2 q^{9} + 3 q^{11} + 2 q^{12} + 4 q^{13} + q^{14} + 2 q^{16} - 2 q^{17} + 2 q^{18} + q^{19} + q^{21} + 3 q^{22} + 3 q^{23} + 2 q^{24} + 4 q^{26} + 2 q^{27} + q^{28} + 6 q^{29} + q^{31} + 2 q^{32} + 3 q^{33} - 2 q^{34} + 2 q^{36} - 2 q^{37} + q^{38} + 4 q^{39} + 3 q^{41} + q^{42} + 13 q^{43} + 3 q^{44} + 3 q^{46} - 9 q^{47} + 2 q^{48} + 3 q^{49} - 2 q^{51} + 4 q^{52} + 2 q^{54} + q^{56} + q^{57} + 6 q^{58} + 3 q^{59} + q^{61} + q^{62} + q^{63} + 2 q^{64} + 3 q^{66} - 5 q^{67} - 2 q^{68} + 3 q^{69} + 3 q^{71} + 2 q^{72} + 16 q^{73} - 2 q^{74} + q^{76} - 15 q^{77} + 4 q^{78} - 5 q^{79} + 2 q^{81} + 3 q^{82} - 3 q^{83} + q^{84} + 13 q^{86} + 6 q^{87} + 3 q^{88} + 6 q^{89} + 2 q^{91} + 3 q^{92} + q^{93} - 9 q^{94} + 2 q^{96} - 14 q^{97} + 3 q^{98} + 3 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + q^7 + 2 * q^8 + 2 * q^9 + 3 * q^11 + 2 * q^12 + 4 * q^13 + q^14 + 2 * q^16 - 2 * q^17 + 2 * q^18 + q^19 + q^21 + 3 * q^22 + 3 * q^23 + 2 * q^24 + 4 * q^26 + 2 * q^27 + q^28 + 6 * q^29 + q^31 + 2 * q^32 + 3 * q^33 - 2 * q^34 + 2 * q^36 - 2 * q^37 + q^38 + 4 * q^39 + 3 * q^41 + q^42 + 13 * q^43 + 3 * q^44 + 3 * q^46 - 9 * q^47 + 2 * q^48 + 3 * q^49 - 2 * q^51 + 4 * q^52 + 2 * q^54 + q^56 + q^57 + 6 * q^58 + 3 * q^59 + q^61 + q^62 + q^63 + 2 * q^64 + 3 * q^66 - 5 * q^67 - 2 * q^68 + 3 * q^69 + 3 * q^71 + 2 * q^72 + 16 * q^73 - 2 * q^74 + q^76 - 15 * q^77 + 4 * q^78 - 5 * q^79 + 2 * q^81 + 3 * q^82 - 3 * q^83 + q^84 + 13 * q^86 + 6 * q^87 + 3 * q^88 + 6 * q^89 + 2 * q^91 + 3 * q^92 + q^93 - 9 * q^94 + 2 * q^96 - 14 * q^97 + 3 * q^98 + 3 * q^99

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