LMFDB - Embedded newform 6650.2.a.bq.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6650,2,Mod(1,6650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6650, 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("6650.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6650 = 2 \cdot 5^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6650.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:	$53.1005173442$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	6650.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.61803 q^{3} +1.00000 q^{4} -2.61803 q^{6} -1.00000 q^{7} +1.00000 q^{8} +3.85410 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.61803 q^{3} +1.00000 q^{4} -2.61803 q^{6} -1.00000 q^{7} +1.00000 q^{8} +3.85410 q^{9} +4.61803 q^{11} -2.61803 q^{12} -5.23607 q^{13} -1.00000 q^{14} +1.00000 q^{16} -2.47214 q^{17} +3.85410 q^{18} -1.00000 q^{19} +2.61803 q^{21} +4.61803 q^{22} +5.70820 q^{23} -2.61803 q^{24} -5.23607 q^{26} -2.23607 q^{27} -1.00000 q^{28} -8.85410 q^{29} -0.472136 q^{31} +1.00000 q^{32} -12.0902 q^{33} -2.47214 q^{34} +3.85410 q^{36} -4.85410 q^{37} -1.00000 q^{38} +13.7082 q^{39} +5.32624 q^{41} +2.61803 q^{42} +7.61803 q^{43} +4.61803 q^{44} +5.70820 q^{46} +3.85410 q^{47} -2.61803 q^{48} +1.00000 q^{49} +6.47214 q^{51} -5.23607 q^{52} +11.3820 q^{53} -2.23607 q^{54} -1.00000 q^{56} +2.61803 q^{57} -8.85410 q^{58} -8.85410 q^{59} -2.32624 q^{61} -0.472136 q^{62} -3.85410 q^{63} +1.00000 q^{64} -12.0902 q^{66} -10.9443 q^{67} -2.47214 q^{68} -14.9443 q^{69} +16.0344 q^{71} +3.85410 q^{72} +7.23607 q^{73} -4.85410 q^{74} -1.00000 q^{76} -4.61803 q^{77} +13.7082 q^{78} -13.3262 q^{79} -5.70820 q^{81} +5.32624 q^{82} -8.94427 q^{83} +2.61803 q^{84} +7.61803 q^{86} +23.1803 q^{87} +4.61803 q^{88} -1.38197 q^{89} +5.23607 q^{91} +5.70820 q^{92} +1.23607 q^{93} +3.85410 q^{94} -2.61803 q^{96} -3.85410 q^{97} +1.00000 q^{98} +17.7984 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{6} - 2 q^{7} + 2 q^{8} + q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^6 - 2 * q^7 + 2 * q^8 + q^9	$ 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{6} - 2 q^{7} + 2 q^{8} + q^{9} + 7 q^{11} - 3 q^{12} - 6 q^{13} - 2 q^{14} + 2 q^{16} + 4 q^{17} + q^{18} - 2 q^{19} + 3 q^{21} + 7 q^{22} - 2 q^{23} - 3 q^{24} - 6 q^{26} - 2 q^{28} - 11 q^{29} + 8 q^{31} + 2 q^{32} - 13 q^{33} + 4 q^{34} + q^{36} - 3 q^{37} - 2 q^{38} + 14 q^{39} - 5 q^{41} + 3 q^{42} + 13 q^{43} + 7 q^{44} - 2 q^{46} + q^{47} - 3 q^{48} + 2 q^{49} + 4 q^{51} - 6 q^{52} + 25 q^{53} - 2 q^{56} + 3 q^{57} - 11 q^{58} - 11 q^{59} + 11 q^{61} + 8 q^{62} - q^{63} + 2 q^{64} - 13 q^{66} - 4 q^{67} + 4 q^{68} - 12 q^{69} + 3 q^{71} + q^{72} + 10 q^{73} - 3 q^{74} - 2 q^{76} - 7 q^{77} + 14 q^{78} - 11 q^{79} + 2 q^{81} - 5 q^{82} + 3 q^{84} + 13 q^{86} + 24 q^{87} + 7 q^{88} - 5 q^{89} + 6 q^{91} - 2 q^{92} - 2 q^{93} + q^{94} - 3 q^{96} - q^{97} + 2 q^{98} + 11 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^6 - 2 * q^7 + 2 * q^8 + q^9 + 7 * q^11 - 3 * q^12 - 6 * q^13 - 2 * q^14 + 2 * q^16 + 4 * q^17 + q^18 - 2 * q^19 + 3 * q^21 + 7 * q^22 - 2 * q^23 - 3 * q^24 - 6 * q^26 - 2 * q^28 - 11 * q^29 + 8 * q^31 + 2 * q^32 - 13 * q^33 + 4 * q^34 + q^36 - 3 * q^37 - 2 * q^38 + 14 * q^39 - 5 * q^41 + 3 * q^42 + 13 * q^43 + 7 * q^44 - 2 * q^46 + q^47 - 3 * q^48 + 2 * q^49 + 4 * q^51 - 6 * q^52 + 25 * q^53 - 2 * q^56 + 3 * q^57 - 11 * q^58 - 11 * q^59 + 11 * q^61 + 8 * q^62 - q^63 + 2 * q^64 - 13 * q^66 - 4 * q^67 + 4 * q^68 - 12 * q^69 + 3 * q^71 + q^72 + 10 * q^73 - 3 * q^74 - 2 * q^76 - 7 * q^77 + 14 * q^78 - 11 * q^79 + 2 * q^81 - 5 * q^82 + 3 * q^84 + 13 * q^86 + 24 * q^87 + 7 * q^88 - 5 * q^89 + 6 * q^91 - 2 * q^92 - 2 * q^93 + q^94 - 3 * q^96 - q^97 + 2 * q^98 + 11 * 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
$3$	−2.61803	−1.51152	−0.755761	−	0.654847i	$-0.772733\pi$
$3$	−2.61803	−1.51152	−0.755761	+	0.654847i	$0.772733\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−2.61803	−1.06881
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	3.85410	1.28470
$10$	0	0
$11$	4.61803	1.39239	0.696195	−	0.717853i	$-0.254875\pi$
$11$	4.61803	1.39239	0.696195	+	0.717853i	$0.254875\pi$
$12$	−2.61803	−0.755761
$13$	−5.23607	−1.45222	−0.726112	−	0.687576i	$-0.758675\pi$
$13$	−5.23607	−1.45222	−0.726112	+	0.687576i	$0.758675\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−2.47214	−0.599581	−0.299791	−	0.954005i	$-0.596917\pi$
$17$	−2.47214	−0.599581	−0.299791	+	0.954005i	$0.596917\pi$
$18$	3.85410	0.908421
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0	0
$21$	2.61803	0.571302
$22$	4.61803	0.984568
$23$	5.70820	1.19024	0.595121	−	0.803636i	$-0.297104\pi$
$23$	5.70820	1.19024	0.595121	+	0.803636i	$0.297104\pi$
$24$	−2.61803	−0.534404
$25$	0	0
$26$	−5.23607	−1.02688
$27$	−2.23607	−0.430331
$28$	−1.00000	−0.188982
$29$	−8.85410	−1.64417	−0.822083	−	0.569368i	$-0.807188\pi$
$29$	−8.85410	−1.64417	−0.822083	+	0.569368i	$0.807188\pi$
$30$	0	0
$31$	−0.472136	−0.0847981	−0.0423991	−	0.999101i	$-0.513500\pi$
$31$	−0.472136	−0.0847981	−0.0423991	+	0.999101i	$0.513500\pi$
$32$	1.00000	0.176777
$33$	−12.0902	−2.10463
$34$	−2.47214	−0.423968
$35$	0	0
$36$	3.85410	0.642350
$37$	−4.85410	−0.798009	−0.399005	−	0.916949i	$-0.630644\pi$
$37$	−4.85410	−0.798009	−0.399005	+	0.916949i	$0.630644\pi$
$38$	−1.00000	−0.162221
$39$	13.7082	2.19507
$40$	0	0
$41$	5.32624	0.831819	0.415909	−	0.909406i	$-0.363463\pi$
$41$	5.32624	0.831819	0.415909	+	0.909406i	$0.363463\pi$
$42$	2.61803	0.403971
$43$	7.61803	1.16174	0.580870	−	0.813997i	$-0.302713\pi$
$43$	7.61803	1.16174	0.580870	+	0.813997i	$0.302713\pi$
$44$	4.61803	0.696195
$45$	0	0
$46$	5.70820	0.841629
$47$	3.85410	0.562179	0.281089	−	0.959682i	$-0.409304\pi$
$47$	3.85410	0.562179	0.281089	+	0.959682i	$0.409304\pi$
$48$	−2.61803	−0.377881
$49$	1.00000	0.142857
$50$	0	0
$51$	6.47214	0.906280
$52$	−5.23607	−0.726112
$53$	11.3820	1.56343	0.781717	−	0.623634i	$-0.214344\pi$
$53$	11.3820	1.56343	0.781717	+	0.623634i	$0.214344\pi$
$54$	−2.23607	−0.304290
$55$	0	0
$56$	−1.00000	−0.133631
$57$	2.61803	0.346767
$58$	−8.85410	−1.16260
$59$	−8.85410	−1.15271	−0.576353	−	0.817201i	$-0.695525\pi$
$59$	−8.85410	−1.15271	−0.576353	+	0.817201i	$0.695525\pi$
$60$	0	0
$61$	−2.32624	−0.297844	−0.148922	−	0.988849i	$-0.547580\pi$
$61$	−2.32624	−0.297844	−0.148922	+	0.988849i	$0.547580\pi$
$62$	−0.472136	−0.0599613
$63$	−3.85410	−0.485571
$64$	1.00000	0.125000
$65$	0	0
$66$	−12.0902	−1.48820
$67$	−10.9443	−1.33706	−0.668528	−	0.743687i	$-0.733075\pi$
$67$	−10.9443	−1.33706	−0.668528	+	0.743687i	$0.733075\pi$
$68$	−2.47214	−0.299791
$69$	−14.9443	−1.79908
$70$	0	0
$71$	16.0344	1.90294	0.951469	−	0.307744i	$-0.0995742\pi$
$71$	16.0344	1.90294	0.951469	+	0.307744i	$0.0995742\pi$
$72$	3.85410	0.454210
$73$	7.23607	0.846918	0.423459	−	0.905915i	$-0.360816\pi$
$73$	7.23607	0.846918	0.423459	+	0.905915i	$0.360816\pi$
$74$	−4.85410	−0.564278
$75$	0	0
$76$	−1.00000	−0.114708
$77$	−4.61803	−0.526274
$78$	13.7082	1.55215
$79$	−13.3262	−1.49932	−0.749659	−	0.661824i	$-0.769783\pi$
$79$	−13.3262	−1.49932	−0.749659	+	0.661824i	$0.769783\pi$
$80$	0	0
$81$	−5.70820	−0.634245
$82$	5.32624	0.588185
$83$	−8.94427	−0.981761	−0.490881	−	0.871227i	$-0.663325\pi$
$83$	−8.94427	−0.981761	−0.490881	+	0.871227i	$0.663325\pi$
$84$	2.61803	0.285651
$85$	0	0
$86$	7.61803	0.821474
$87$	23.1803	2.48519
$88$	4.61803	0.492284
$89$	−1.38197	−0.146488	−0.0732441	−	0.997314i	$-0.523335\pi$
$89$	−1.38197	−0.146488	−0.0732441	+	0.997314i	$0.523335\pi$
$90$	0	0
$91$	5.23607	0.548889
$92$	5.70820	0.595121
$93$	1.23607	0.128174
$94$	3.85410	0.397520
$95$	0	0
$96$	−2.61803	−0.267202
$97$	−3.85410	−0.391325	−0.195662	−	0.980671i	$-0.562686\pi$
$97$	−3.85410	−0.391325	−0.195662	+	0.980671i	$0.562686\pi$
$98$	1.00000	0.101015
$99$	17.7984	1.78880
$100$	0	0
$101$	14.9443	1.48701	0.743505	−	0.668730i	$-0.233162\pi$
$101$	14.9443	1.48701	0.743505	+	0.668730i	$0.233162\pi$
$102$	6.47214	0.640837
$103$	−8.76393	−0.863536	−0.431768	−	0.901985i	$-0.642110\pi$
$103$	−8.76393	−0.863536	−0.431768	+	0.901985i	$0.642110\pi$
$104$	−5.23607	−0.513439
$105$	0	0
$106$	11.3820	1.10551
$107$	0.763932	0.0738521	0.0369260	−	0.999318i	$-0.488243\pi$
$107$	0.763932	0.0738521	0.0369260	+	0.999318i	$0.488243\pi$
$108$	−2.23607	−0.215166
$109$	−8.32624	−0.797509	−0.398754	−	0.917058i	$-0.630557\pi$
$109$	−8.32624	−0.797509	−0.398754	+	0.917058i	$0.630557\pi$
$110$	0	0
$111$	12.7082	1.20621
$112$	−1.00000	−0.0944911
$113$	8.94427	0.841406	0.420703	−	0.907198i	$-0.361783\pi$
$113$	8.94427	0.841406	0.420703	+	0.907198i	$0.361783\pi$
$114$	2.61803	0.245201
$115$	0	0
$116$	−8.85410	−0.822083
$117$	−20.1803	−1.86567
$118$	−8.85410	−0.815086
$119$	2.47214	0.226620
$120$	0	0
$121$	10.3262	0.938749
$122$	−2.32624	−0.210608
$123$	−13.9443	−1.25731
$124$	−0.472136	−0.0423991
$125$	0	0
$126$	−3.85410	−0.343351
$127$	11.3820	1.00999	0.504993	−	0.863123i	$-0.331495\pi$
$127$	11.3820	1.00999	0.504993	+	0.863123i	$0.331495\pi$
$128$	1.00000	0.0883883
$129$	−19.9443	−1.75600
$130$	0	0
$131$	−6.18034	−0.539979	−0.269989	−	0.962863i	$-0.587020\pi$
$131$	−6.18034	−0.539979	−0.269989	+	0.962863i	$0.587020\pi$
$132$	−12.0902	−1.05231
$133$	1.00000	0.0867110
$134$	−10.9443	−0.945441
$135$	0	0
$136$	−2.47214	−0.211984
$137$	10.3820	0.886991	0.443496	−	0.896277i	$-0.353738\pi$
$137$	10.3820	0.886991	0.443496	+	0.896277i	$0.353738\pi$
$138$	−14.9443	−1.27214
$139$	10.4721	0.888235	0.444117	−	0.895969i	$-0.353517\pi$
$139$	10.4721	0.888235	0.444117	+	0.895969i	$0.353517\pi$
$140$	0	0
$141$	−10.0902	−0.849746
$142$	16.0344	1.34558
$143$	−24.1803	−2.02206
$144$	3.85410	0.321175
$145$	0	0
$146$	7.23607	0.598861
$147$	−2.61803	−0.215932
$148$	−4.85410	−0.399005
$149$	4.00000	0.327693	0.163846	−	0.986486i	$-0.447610\pi$
$149$	4.00000	0.327693	0.163846	+	0.986486i	$0.447610\pi$
$150$	0	0
$151$	−21.8885	−1.78126	−0.890632	−	0.454724i	$-0.849738\pi$
$151$	−21.8885	−1.78126	−0.890632	+	0.454724i	$0.849738\pi$
$152$	−1.00000	−0.0811107
$153$	−9.52786	−0.770282
$154$	−4.61803	−0.372132
$155$	0	0
$156$	13.7082	1.09753
$157$	2.90983	0.232230	0.116115	−	0.993236i	$-0.462956\pi$
$157$	2.90983	0.232230	0.116115	+	0.993236i	$0.462956\pi$
$158$	−13.3262	−1.06018
$159$	−29.7984	−2.36316
$160$	0	0
$161$	−5.70820	−0.449869
$162$	−5.70820	−0.448479
$163$	−7.09017	−0.555345	−0.277672	−	0.960676i	$-0.589563\pi$
$163$	−7.09017	−0.555345	−0.277672	+	0.960676i	$0.589563\pi$
$164$	5.32624	0.415909
$165$	0	0
$166$	−8.94427	−0.694210
$167$	−2.94427	−0.227835	−0.113917	−	0.993490i	$-0.536340\pi$
$167$	−2.94427	−0.227835	−0.113917	+	0.993490i	$0.536340\pi$
$168$	2.61803	0.201986
$169$	14.4164	1.10895
$170$	0	0
$171$	−3.85410	−0.294731
$172$	7.61803	0.580870
$173$	17.7082	1.34633	0.673165	−	0.739492i	$-0.264934\pi$
$173$	17.7082	1.34633	0.673165	+	0.739492i	$0.264934\pi$
$174$	23.1803	1.75730
$175$	0	0
$176$	4.61803	0.348097
$177$	23.1803	1.74234
$178$	−1.38197	−0.103583
$179$	19.2361	1.43777	0.718886	−	0.695128i	$-0.244652\pi$
$179$	19.2361	1.43777	0.718886	+	0.695128i	$0.244652\pi$
$180$	0	0
$181$	−4.18034	−0.310722	−0.155361	−	0.987858i	$-0.549654\pi$
$181$	−4.18034	−0.310722	−0.155361	+	0.987858i	$0.549654\pi$
$182$	5.23607	0.388123
$183$	6.09017	0.450198
$184$	5.70820	0.420814
$185$	0	0
$186$	1.23607	0.0906329
$187$	−11.4164	−0.834850
$188$	3.85410	0.281089
$189$	2.23607	0.162650
$190$	0	0
$191$	22.6525	1.63908	0.819538	−	0.573025i	$-0.194230\pi$
$191$	22.6525	1.63908	0.819538	+	0.573025i	$0.194230\pi$
$192$	−2.61803	−0.188940
$193$	13.7082	0.986738	0.493369	−	0.869820i	$-0.335765\pi$
$193$	13.7082	0.986738	0.493369	+	0.869820i	$0.335765\pi$
$194$	−3.85410	−0.276708
$195$	0	0
$196$	1.00000	0.0714286
$197$	10.9443	0.779747	0.389874	−	0.920868i	$-0.372519\pi$
$197$	10.9443	0.779747	0.389874	+	0.920868i	$0.372519\pi$
$198$	17.7984	1.26488
$199$	25.0344	1.77464	0.887322	−	0.461150i	$-0.152563\pi$
$199$	25.0344	1.77464	0.887322	+	0.461150i	$0.152563\pi$
$200$	0	0
$201$	28.6525	2.02099
$202$	14.9443	1.05148
$203$	8.85410	0.621436
$204$	6.47214	0.453140
$205$	0	0
$206$	−8.76393	−0.610612
$207$	22.0000	1.52911
$208$	−5.23607	−0.363056
$209$	−4.61803	−0.319436
$210$	0	0
$211$	−4.00000	−0.275371	−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000	−0.275371	−0.137686	+	0.990476i	$0.543966\pi$
$212$	11.3820	0.781717
$213$	−41.9787	−2.87633
$214$	0.763932	0.0522213
$215$	0	0
$216$	−2.23607	−0.152145
$217$	0.472136	0.0320507
$218$	−8.32624	−0.563924
$219$	−18.9443	−1.28014
$220$	0	0
$221$	12.9443	0.870726
$222$	12.7082	0.852919
$223$	12.6525	0.847272	0.423636	−	0.905832i	$-0.360753\pi$
$223$	12.6525	0.847272	0.423636	+	0.905832i	$0.360753\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	8.94427	0.594964
$227$	−3.05573	−0.202816	−0.101408	−	0.994845i	$-0.532335\pi$
$227$	−3.05573	−0.202816	−0.101408	+	0.994845i	$0.532335\pi$
$228$	2.61803	0.173384
$229$	23.0344	1.52216	0.761079	−	0.648659i	$-0.224670\pi$
$229$	23.0344	1.52216	0.761079	+	0.648659i	$0.224670\pi$
$230$	0	0
$231$	12.0902	0.795475
$232$	−8.85410	−0.581300
$233$	−15.7426	−1.03134	−0.515668	−	0.856789i	$-0.672456\pi$
$233$	−15.7426	−1.03134	−0.515668	+	0.856789i	$0.672456\pi$
$234$	−20.1803	−1.31923
$235$	0	0
$236$	−8.85410	−0.576353
$237$	34.8885	2.26625
$238$	2.47214	0.160245
$239$	−15.1246	−0.978330	−0.489165	−	0.872191i	$-0.662698\pi$
$239$	−15.1246	−0.978330	−0.489165	+	0.872191i	$0.662698\pi$
$240$	0	0
$241$	9.14590	0.589139	0.294570	−	0.955630i	$-0.404824\pi$
$241$	9.14590	0.589139	0.294570	+	0.955630i	$0.404824\pi$
$242$	10.3262	0.663796
$243$	21.6525	1.38901
$244$	−2.32624	−0.148922
$245$	0	0
$246$	−13.9443	−0.889054
$247$	5.23607	0.333163
$248$	−0.472136	−0.0299807
$249$	23.4164	1.48395
$250$	0	0
$251$	13.2361	0.835453	0.417727	−	0.908573i	$-0.362827\pi$
$251$	13.2361	0.835453	0.417727	+	0.908573i	$0.362827\pi$
$252$	−3.85410	−0.242786
$253$	26.3607	1.65728
$254$	11.3820	0.714168
$255$	0	0
$256$	1.00000	0.0625000
$257$	23.9787	1.49575	0.747876	−	0.663839i	$-0.231074\pi$
$257$	23.9787	1.49575	0.747876	+	0.663839i	$0.231074\pi$
$258$	−19.9443	−1.24168
$259$	4.85410	0.301619
$260$	0	0
$261$	−34.1246	−2.11226
$262$	−6.18034	−0.381823
$263$	9.23607	0.569520	0.284760	−	0.958599i	$-0.408086\pi$
$263$	9.23607	0.569520	0.284760	+	0.958599i	$0.408086\pi$
$264$	−12.0902	−0.744099
$265$	0	0
$266$	1.00000	0.0613139
$267$	3.61803	0.221420
$268$	−10.9443	−0.668528
$269$	28.4721	1.73598	0.867988	−	0.496584i	$-0.165413\pi$
$269$	28.4721	1.73598	0.867988	+	0.496584i	$0.165413\pi$
$270$	0	0
$271$	8.85410	0.537848	0.268924	−	0.963161i	$-0.413332\pi$
$271$	8.85410	0.537848	0.268924	+	0.963161i	$0.413332\pi$
$272$	−2.47214	−0.149895
$273$	−13.7082	−0.829658
$274$	10.3820	0.627198
$275$	0	0
$276$	−14.9443	−0.899539
$277$	−10.6525	−0.640045	−0.320023	−	0.947410i	$-0.603691\pi$
$277$	−10.6525	−0.640045	−0.320023	+	0.947410i	$0.603691\pi$
$278$	10.4721	0.628077
$279$	−1.81966	−0.108940
$280$	0	0
$281$	16.0000	0.954480	0.477240	−	0.878773i	$-0.341637\pi$
$281$	16.0000	0.954480	0.477240	+	0.878773i	$0.341637\pi$
$282$	−10.0902	−0.600861
$283$	−18.4721	−1.09805	−0.549027	−	0.835804i	$-0.685002\pi$
$283$	−18.4721	−1.09805	−0.549027	+	0.835804i	$0.685002\pi$
$284$	16.0344	0.951469
$285$	0	0
$286$	−24.1803	−1.42981
$287$	−5.32624	−0.314398
$288$	3.85410	0.227105
$289$	−10.8885	−0.640503
$290$	0	0
$291$	10.0902	0.591496
$292$	7.23607	0.423459
$293$	−26.1803	−1.52947	−0.764736	−	0.644344i	$-0.777131\pi$
$293$	−26.1803	−1.52947	−0.764736	+	0.644344i	$0.777131\pi$
$294$	−2.61803	−0.152687
$295$	0	0
$296$	−4.85410	−0.282139
$297$	−10.3262	−0.599189
$298$	4.00000	0.231714
$299$	−29.8885	−1.72850
$300$	0	0
$301$	−7.61803	−0.439096
$302$	−21.8885	−1.25954
$303$	−39.1246	−2.24765
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	−9.52786	−0.544672
$307$	25.0344	1.42879	0.714396	−	0.699742i	$-0.246702\pi$
$307$	25.0344	1.42879	0.714396	+	0.699742i	$0.246702\pi$
$308$	−4.61803	−0.263137
$309$	22.9443	1.30525
$310$	0	0
$311$	2.61803	0.148455	0.0742275	−	0.997241i	$-0.476351\pi$
$311$	2.61803	0.148455	0.0742275	+	0.997241i	$0.476351\pi$
$312$	13.7082	0.776074
$313$	17.8885	1.01112	0.505560	−	0.862791i	$-0.331286\pi$
$313$	17.8885	1.01112	0.505560	+	0.862791i	$0.331286\pi$
$314$	2.90983	0.164211
$315$	0	0
$316$	−13.3262	−0.749659
$317$	20.6180	1.15802	0.579012	−	0.815319i	$-0.303438\pi$
$317$	20.6180	1.15802	0.579012	+	0.815319i	$0.303438\pi$
$318$	−29.7984	−1.67101
$319$	−40.8885	−2.28932
$320$	0	0
$321$	−2.00000	−0.111629
$322$	−5.70820	−0.318106
$323$	2.47214	0.137553
$324$	−5.70820	−0.317122
$325$	0	0
$326$	−7.09017	−0.392688
$327$	21.7984	1.20545
$328$	5.32624	0.294092
$329$	−3.85410	−0.212484
$330$	0	0
$331$	−2.58359	−0.142007	−0.0710035	−	0.997476i	$-0.522620\pi$
$331$	−2.58359	−0.142007	−0.0710035	+	0.997476i	$0.522620\pi$
$332$	−8.94427	−0.490881
$333$	−18.7082	−1.02520
$334$	−2.94427	−0.161103
$335$	0	0
$336$	2.61803	0.142825
$337$	17.2361	0.938908	0.469454	−	0.882957i	$-0.344451\pi$
$337$	17.2361	0.938908	0.469454	+	0.882957i	$0.344451\pi$
$338$	14.4164	0.784149
$339$	−23.4164	−1.27180
$340$	0	0
$341$	−2.18034	−0.118072
$342$	−3.85410	−0.208406
$343$	−1.00000	−0.0539949
$344$	7.61803	0.410737
$345$	0	0
$346$	17.7082	0.951999
$347$	−31.4164	−1.68652	−0.843261	−	0.537505i	$-0.819367\pi$
$347$	−31.4164	−1.68652	−0.843261	+	0.537505i	$0.819367\pi$
$348$	23.1803	1.24260
$349$	−6.00000	−0.321173	−0.160586	−	0.987022i	$-0.551338\pi$
$349$	−6.00000	−0.321173	−0.160586	+	0.987022i	$0.551338\pi$
$350$	0	0
$351$	11.7082	0.624938
$352$	4.61803	0.246142
$353$	8.36068	0.444994	0.222497	−	0.974933i	$-0.428579\pi$
$353$	8.36068	0.444994	0.222497	+	0.974933i	$0.428579\pi$
$354$	23.1803	1.23202
$355$	0	0
$356$	−1.38197	−0.0732441
$357$	−6.47214	−0.342542
$358$	19.2361	1.01666
$359$	14.2918	0.754292	0.377146	−	0.926154i	$-0.376905\pi$
$359$	14.2918	0.754292	0.377146	+	0.926154i	$0.376905\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	−4.18034	−0.219714
$363$	−27.0344	−1.41894
$364$	5.23607	0.274445
$365$	0	0
$366$	6.09017	0.318338
$367$	2.32624	0.121429	0.0607143	−	0.998155i	$-0.480662\pi$
$367$	2.32624	0.121429	0.0607143	+	0.998155i	$0.480662\pi$
$368$	5.70820	0.297561
$369$	20.5279	1.06864
$370$	0	0
$371$	−11.3820	−0.590922
$372$	1.23607	0.0640871
$373$	18.7426	0.970457	0.485229	−	0.874387i	$-0.338736\pi$
$373$	18.7426	0.970457	0.485229	+	0.874387i	$0.338736\pi$
$374$	−11.4164	−0.590328
$375$	0	0
$376$	3.85410	0.198760
$377$	46.3607	2.38770
$378$	2.23607	0.115011
$379$	7.34752	0.377417	0.188708	−	0.982033i	$-0.439570\pi$
$379$	7.34752	0.377417	0.188708	+	0.982033i	$0.439570\pi$
$380$	0	0
$381$	−29.7984	−1.52662
$382$	22.6525	1.15900
$383$	20.7639	1.06099	0.530494	−	0.847689i	$-0.322007\pi$
$383$	20.7639	1.06099	0.530494	+	0.847689i	$0.322007\pi$
$384$	−2.61803	−0.133601
$385$	0	0
$386$	13.7082	0.697729
$387$	29.3607	1.49249
$388$	−3.85410	−0.195662
$389$	22.3607	1.13373	0.566866	−	0.823810i	$-0.308156\pi$
$389$	22.3607	1.13373	0.566866	+	0.823810i	$0.308156\pi$
$390$	0	0
$391$	−14.1115	−0.713647
$392$	1.00000	0.0505076
$393$	16.1803	0.816190
$394$	10.9443	0.551364
$395$	0	0
$396$	17.7984	0.894402
$397$	−21.0902	−1.05849	−0.529243	−	0.848471i	$-0.677524\pi$
$397$	−21.0902	−1.05849	−0.529243	+	0.848471i	$0.677524\pi$
$398$	25.0344	1.25486
$399$	−2.61803	−0.131066
$400$	0	0
$401$	11.0557	0.552097	0.276048	−	0.961144i	$-0.410975\pi$
$401$	11.0557	0.552097	0.276048	+	0.961144i	$0.410975\pi$
$402$	28.6525	1.42906
$403$	2.47214	0.123146
$404$	14.9443	0.743505
$405$	0	0
$406$	8.85410	0.439422
$407$	−22.4164	−1.11114
$408$	6.47214	0.320418
$409$	−27.5623	−1.36287	−0.681434	−	0.731879i	$-0.738643\pi$
$409$	−27.5623	−1.36287	−0.681434	+	0.731879i	$0.738643\pi$
$410$	0	0
$411$	−27.1803	−1.34071
$412$	−8.76393	−0.431768
$413$	8.85410	0.435682
$414$	22.0000	1.08124
$415$	0	0
$416$	−5.23607	−0.256719
$417$	−27.4164	−1.34259
$418$	−4.61803	−0.225875
$419$	17.4164	0.850847	0.425424	−	0.904994i	$-0.360125\pi$
$419$	17.4164	0.850847	0.425424	+	0.904994i	$0.360125\pi$
$420$	0	0
$421$	−14.3607	−0.699897	−0.349948	−	0.936769i	$-0.613801\pi$
$421$	−14.3607	−0.699897	−0.349948	+	0.936769i	$0.613801\pi$
$422$	−4.00000	−0.194717
$423$	14.8541	0.722231
$424$	11.3820	0.552757
$425$	0	0
$426$	−41.9787	−2.03388
$427$	2.32624	0.112575
$428$	0.763932	0.0369260
$429$	63.3050	3.05639
$430$	0	0
$431$	5.27051	0.253872	0.126936	−	0.991911i	$-0.459486\pi$
$431$	5.27051	0.253872	0.126936	+	0.991911i	$0.459486\pi$
$432$	−2.23607	−0.107583
$433$	−22.0902	−1.06159	−0.530793	−	0.847502i	$-0.678106\pi$
$433$	−22.0902	−1.06159	−0.530793	+	0.847502i	$0.678106\pi$
$434$	0.472136	0.0226633
$435$	0	0
$436$	−8.32624	−0.398754
$437$	−5.70820	−0.273060
$438$	−18.9443	−0.905192
$439$	4.47214	0.213443	0.106722	−	0.994289i	$-0.465965\pi$
$439$	4.47214	0.213443	0.106722	+	0.994289i	$0.465965\pi$
$440$	0	0
$441$	3.85410	0.183529
$442$	12.9443	0.615696
$443$	7.79837	0.370512	0.185256	−	0.982690i	$-0.440689\pi$
$443$	7.79837	0.370512	0.185256	+	0.982690i	$0.440689\pi$
$444$	12.7082	0.603105
$445$	0	0
$446$	12.6525	0.599112
$447$	−10.4721	−0.495315
$448$	−1.00000	−0.0472456
$449$	28.0689	1.32465	0.662326	−	0.749216i	$-0.269569\pi$
$449$	28.0689	1.32465	0.662326	+	0.749216i	$0.269569\pi$
$450$	0	0
$451$	24.5967	1.15822
$452$	8.94427	0.420703
$453$	57.3050	2.69242
$454$	−3.05573	−0.143412
$455$	0	0
$456$	2.61803	0.122601
$457$	22.5066	1.05281	0.526407	−	0.850233i	$-0.323539\pi$
$457$	22.5066	1.05281	0.526407	+	0.850233i	$0.323539\pi$
$458$	23.0344	1.07633
$459$	5.52786	0.258019
$460$	0	0
$461$	−5.38197	−0.250663	−0.125332	−	0.992115i	$-0.539999\pi$
$461$	−5.38197	−0.250663	−0.125332	+	0.992115i	$0.539999\pi$
$462$	12.0902	0.562486
$463$	2.76393	0.128451	0.0642254	−	0.997935i	$-0.479542\pi$
$463$	2.76393	0.128451	0.0642254	+	0.997935i	$0.479542\pi$
$464$	−8.85410	−0.411041
$465$	0	0
$466$	−15.7426	−0.729264
$467$	−21.7082	−1.00454	−0.502268	−	0.864712i	$-0.667501\pi$
$467$	−21.7082	−1.00454	−0.502268	+	0.864712i	$0.667501\pi$
$468$	−20.1803	−0.932837
$469$	10.9443	0.505360
$470$	0	0
$471$	−7.61803	−0.351020
$472$	−8.85410	−0.407543
$473$	35.1803	1.61759
$474$	34.8885	1.60248
$475$	0	0
$476$	2.47214	0.113310
$477$	43.8673	2.00854
$478$	−15.1246	−0.691784
$479$	0.270510	0.0123599	0.00617995	−	0.999981i	$-0.498033\pi$
$479$	0.270510	0.0123599	0.00617995	+	0.999981i	$0.498033\pi$
$480$	0	0
$481$	25.4164	1.15889
$482$	9.14590	0.416584
$483$	14.9443	0.679988
$484$	10.3262	0.469374
$485$	0	0
$486$	21.6525	0.982176
$487$	−36.5623	−1.65680	−0.828398	−	0.560140i	$-0.810747\pi$
$487$	−36.5623	−1.65680	−0.828398	+	0.560140i	$0.810747\pi$
$488$	−2.32624	−0.105304
$489$	18.5623	0.839416
$490$	0	0
$491$	2.11146	0.0952887	0.0476443	−	0.998864i	$-0.484829\pi$
$491$	2.11146	0.0952887	0.0476443	+	0.998864i	$0.484829\pi$
$492$	−13.9443	−0.628656
$493$	21.8885	0.985810
$494$	5.23607	0.235582
$495$	0	0
$496$	−0.472136	−0.0211995
$497$	−16.0344	−0.719243
$498$	23.4164	1.04931
$499$	−25.3262	−1.13376	−0.566879	−	0.823801i	$-0.691849\pi$
$499$	−25.3262	−1.13376	−0.566879	+	0.823801i	$0.691849\pi$
$500$	0	0
$501$	7.70820	0.344377
$502$	13.2361	0.590755
$503$	12.0902	0.539074	0.269537	−	0.962990i	$-0.413129\pi$
$503$	12.0902	0.539074	0.269537	+	0.962990i	$0.413129\pi$
$504$	−3.85410	−0.171675
$505$	0	0
$506$	26.3607	1.17188
$507$	−37.7426	−1.67621
$508$	11.3820	0.504993
$509$	41.7082	1.84868	0.924342	−	0.381565i	$-0.124615\pi$
$509$	41.7082	1.84868	0.924342	+	0.381565i	$0.124615\pi$
$510$	0	0
$511$	−7.23607	−0.320105
$512$	1.00000	0.0441942
$513$	2.23607	0.0987248
$514$	23.9787	1.05766
$515$	0	0
$516$	−19.9443	−0.877998
$517$	17.7984	0.782772
$518$	4.85410	0.213277
$519$	−46.3607	−2.03501
$520$	0	0
$521$	−12.4721	−0.546414	−0.273207	−	0.961955i	$-0.588084\pi$
$521$	−12.4721	−0.546414	−0.273207	+	0.961955i	$0.588084\pi$
$522$	−34.1246	−1.49359
$523$	−24.0000	−1.04945	−0.524723	−	0.851273i	$-0.675831\pi$
$523$	−24.0000	−1.04945	−0.524723	+	0.851273i	$0.675831\pi$
$524$	−6.18034	−0.269989
$525$	0	0
$526$	9.23607	0.402712
$527$	1.16718	0.0508433
$528$	−12.0902	−0.526157
$529$	9.58359	0.416678
$530$	0	0
$531$	−34.1246	−1.48088
$532$	1.00000	0.0433555
$533$	−27.8885	−1.20799
$534$	3.61803	0.156568
$535$	0	0
$536$	−10.9443	−0.472721
$537$	−50.3607	−2.17322
$538$	28.4721	1.22752
$539$	4.61803	0.198913
$540$	0	0
$541$	21.7082	0.933309	0.466654	−	0.884440i	$-0.345459\pi$
$541$	21.7082	0.933309	0.466654	+	0.884440i	$0.345459\pi$
$542$	8.85410	0.380316
$543$	10.9443	0.469664
$544$	−2.47214	−0.105992
$545$	0	0
$546$	−13.7082	−0.586657
$547$	4.76393	0.203691	0.101846	−	0.994800i	$-0.467525\pi$
$547$	4.76393	0.203691	0.101846	+	0.994800i	$0.467525\pi$
$548$	10.3820	0.443496
$549$	−8.96556	−0.382641
$550$	0	0
$551$	8.85410	0.377197
$552$	−14.9443	−0.636070
$553$	13.3262	0.566689
$554$	−10.6525	−0.452580
$555$	0	0
$556$	10.4721	0.444117
$557$	25.2361	1.06929	0.534643	−	0.845078i	$-0.320446\pi$
$557$	25.2361	1.06929	0.534643	+	0.845078i	$0.320446\pi$
$558$	−1.81966	−0.0770324
$559$	−39.8885	−1.68711
$560$	0	0
$561$	29.8885	1.26190
$562$	16.0000	0.674919
$563$	0.145898	0.00614887	0.00307443	−	0.999995i	$-0.499021\pi$
$563$	0.145898	0.00614887	0.00307443	+	0.999995i	$0.499021\pi$
$564$	−10.0902	−0.424873
$565$	0	0
$566$	−18.4721	−0.776442
$567$	5.70820	0.239722
$568$	16.0344	0.672790
$569$	−10.2918	−0.431455	−0.215727	−	0.976454i	$-0.569212\pi$
$569$	−10.2918	−0.431455	−0.215727	+	0.976454i	$0.569212\pi$
$570$	0	0
$571$	−28.0344	−1.17320	−0.586602	−	0.809875i	$-0.699535\pi$
$571$	−28.0344	−1.17320	−0.586602	+	0.809875i	$0.699535\pi$
$572$	−24.1803	−1.01103
$573$	−59.3050	−2.47750
$574$	−5.32624	−0.222313
$575$	0	0
$576$	3.85410	0.160588
$577$	34.9443	1.45475	0.727375	−	0.686241i	$-0.240740\pi$
$577$	34.9443	1.45475	0.727375	+	0.686241i	$0.240740\pi$
$578$	−10.8885	−0.452904
$579$	−35.8885	−1.49148
$580$	0	0
$581$	8.94427	0.371071
$582$	10.0902	0.418251
$583$	52.5623	2.17691
$584$	7.23607	0.299431
$585$	0	0
$586$	−26.1803	−1.08150
$587$	−11.2361	−0.463762	−0.231881	−	0.972744i	$-0.574488\pi$
$587$	−11.2361	−0.463762	−0.231881	+	0.972744i	$0.574488\pi$
$588$	−2.61803	−0.107966
$589$	0.472136	0.0194540
$590$	0	0
$591$	−28.6525	−1.17861
$592$	−4.85410	−0.199502
$593$	22.2918	0.915414	0.457707	−	0.889103i	$-0.348671\pi$
$593$	22.2918	0.915414	0.457707	+	0.889103i	$0.348671\pi$
$594$	−10.3262	−0.423691
$595$	0	0
$596$	4.00000	0.163846
$597$	−65.5410	−2.68242
$598$	−29.8885	−1.22223
$599$	17.5623	0.717576	0.358788	−	0.933419i	$-0.383190\pi$
$599$	17.5623	0.717576	0.358788	+	0.933419i	$0.383190\pi$
$600$	0	0
$601$	−18.0000	−0.734235	−0.367118	−	0.930175i	$-0.619655\pi$
$601$	−18.0000	−0.734235	−0.367118	+	0.930175i	$0.619655\pi$
$602$	−7.61803	−0.310488
$603$	−42.1803	−1.71772
$604$	−21.8885	−0.890632
$605$	0	0
$606$	−39.1246	−1.58933
$607$	9.81966	0.398568	0.199284	−	0.979942i	$-0.436138\pi$
$607$	9.81966	0.398568	0.199284	+	0.979942i	$0.436138\pi$
$608$	−1.00000	−0.0405554
$609$	−23.1803	−0.939315
$610$	0	0
$611$	−20.1803	−0.816409
$612$	−9.52786	−0.385141
$613$	−39.7771	−1.60658	−0.803291	−	0.595587i	$-0.796919\pi$
$613$	−39.7771	−1.60658	−0.803291	+	0.595587i	$0.796919\pi$
$614$	25.0344	1.01031
$615$	0	0
$616$	−4.61803	−0.186066
$617$	35.1459	1.41492	0.707460	−	0.706753i	$-0.249841\pi$
$617$	35.1459	1.41492	0.707460	+	0.706753i	$0.249841\pi$
$618$	22.9443	0.922954
$619$	14.0689	0.565476	0.282738	−	0.959197i	$-0.408757\pi$
$619$	14.0689	0.565476	0.282738	+	0.959197i	$0.408757\pi$
$620$	0	0
$621$	−12.7639	−0.512199
$622$	2.61803	0.104974
$623$	1.38197	0.0553673
$624$	13.7082	0.548767
$625$	0	0
$626$	17.8885	0.714970
$627$	12.0902	0.482835
$628$	2.90983	0.116115
$629$	12.0000	0.478471
$630$	0	0
$631$	32.3607	1.28826	0.644129	−	0.764917i	$-0.277220\pi$
$631$	32.3607	1.28826	0.644129	+	0.764917i	$0.277220\pi$
$632$	−13.3262	−0.530089
$633$	10.4721	0.416230
$634$	20.6180	0.818847
$635$	0	0
$636$	−29.7984	−1.18158
$637$	−5.23607	−0.207461
$638$	−40.8885	−1.61879
$639$	61.7984	2.44471
$640$	0	0
$641$	−15.8197	−0.624839	−0.312420	−	0.949944i	$-0.601139\pi$
$641$	−15.8197	−0.624839	−0.312420	+	0.949944i	$0.601139\pi$
$642$	−2.00000	−0.0789337
$643$	−10.4721	−0.412981	−0.206490	−	0.978449i	$-0.566204\pi$
$643$	−10.4721	−0.412981	−0.206490	+	0.978449i	$0.566204\pi$
$644$	−5.70820	−0.224935
$645$	0	0
$646$	2.47214	0.0972649
$647$	−32.6738	−1.28454	−0.642269	−	0.766479i	$-0.722007\pi$
$647$	−32.6738	−1.28454	−0.642269	+	0.766479i	$0.722007\pi$
$648$	−5.70820	−0.224239
$649$	−40.8885	−1.60502
$650$	0	0
$651$	−1.23607	−0.0484453
$652$	−7.09017	−0.277672
$653$	−12.2918	−0.481015	−0.240508	−	0.970647i	$-0.577314\pi$
$653$	−12.2918	−0.481015	−0.240508	+	0.970647i	$0.577314\pi$
$654$	21.7984	0.852384
$655$	0	0
$656$	5.32624	0.207955
$657$	27.8885	1.08804
$658$	−3.85410	−0.150249
$659$	5.88854	0.229385	0.114693	−	0.993401i	$-0.463412\pi$
$659$	5.88854	0.229385	0.114693	+	0.993401i	$0.463412\pi$
$660$	0	0
$661$	−3.88854	−0.151247	−0.0756234	−	0.997136i	$-0.524095\pi$
$661$	−3.88854	−0.151247	−0.0756234	+	0.997136i	$0.524095\pi$
$662$	−2.58359	−0.100414
$663$	−33.8885	−1.31612
$664$	−8.94427	−0.347105
$665$	0	0
$666$	−18.7082	−0.724928
$667$	−50.5410	−1.95696
$668$	−2.94427	−0.113917
$669$	−33.1246	−1.28067
$670$	0	0
$671$	−10.7426	−0.414715
$672$	2.61803	0.100993
$673$	−24.6525	−0.950283	−0.475142	−	0.879909i	$-0.657603\pi$
$673$	−24.6525	−0.950283	−0.475142	+	0.879909i	$0.657603\pi$
$674$	17.2361	0.663909
$675$	0	0
$676$	14.4164	0.554477
$677$	19.8885	0.764379	0.382189	−	0.924084i	$-0.375170\pi$
$677$	19.8885	0.764379	0.382189	+	0.924084i	$0.375170\pi$
$678$	−23.4164	−0.899302
$679$	3.85410	0.147907
$680$	0	0
$681$	8.00000	0.306561
$682$	−2.18034	−0.0834895
$683$	34.0000	1.30097	0.650487	−	0.759517i	$-0.274565\pi$
$683$	34.0000	1.30097	0.650487	+	0.759517i	$0.274565\pi$
$684$	−3.85410	−0.147365
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	−60.3050	−2.30078
$688$	7.61803	0.290435
$689$	−59.5967	−2.27046
$690$	0	0
$691$	37.1246	1.41229	0.706143	−	0.708069i	$-0.250433\pi$
$691$	37.1246	1.41229	0.706143	+	0.708069i	$0.250433\pi$
$692$	17.7082	0.673165
$693$	−17.7984	−0.676104
$694$	−31.4164	−1.19255
$695$	0	0
$696$	23.1803	0.878649
$697$	−13.1672	−0.498743
$698$	−6.00000	−0.227103
$699$	41.2148	1.55889
$700$	0	0
$701$	−2.65248	−0.100183	−0.0500913	−	0.998745i	$-0.515951\pi$
$701$	−2.65248	−0.100183	−0.0500913	+	0.998745i	$0.515951\pi$
$702$	11.7082	0.441898
$703$	4.85410	0.183076
$704$	4.61803	0.174049
$705$	0	0
$706$	8.36068	0.314658
$707$	−14.9443	−0.562037
$708$	23.1803	0.871171
$709$	−7.70820	−0.289488	−0.144744	−	0.989469i	$-0.546236\pi$
$709$	−7.70820	−0.289488	−0.144744	+	0.989469i	$0.546236\pi$
$710$	0	0
$711$	−51.3607	−1.92618
$712$	−1.38197	−0.0517914
$713$	−2.69505	−0.100930
$714$	−6.47214	−0.242214
$715$	0	0
$716$	19.2361	0.718886
$717$	39.5967	1.47877
$718$	14.2918	0.533365
$719$	41.8885	1.56218	0.781090	−	0.624419i	$-0.214664\pi$
$719$	41.8885	1.56218	0.781090	+	0.624419i	$0.214664\pi$
$720$	0	0
$721$	8.76393	0.326386
$722$	1.00000	0.0372161
$723$	−23.9443	−0.890497
$724$	−4.18034	−0.155361
$725$	0	0
$726$	−27.0344	−1.00334
$727$	−12.5066	−0.463843	−0.231922	−	0.972734i	$-0.574501\pi$
$727$	−12.5066	−0.463843	−0.231922	+	0.972734i	$0.574501\pi$
$728$	5.23607	0.194062
$729$	−39.5623	−1.46527
$730$	0	0
$731$	−18.8328	−0.696557
$732$	6.09017	0.225099
$733$	−1.14590	−0.0423247	−0.0211624	−	0.999776i	$-0.506737\pi$
$733$	−1.14590	−0.0423247	−0.0211624	+	0.999776i	$0.506737\pi$
$734$	2.32624	0.0858630
$735$	0	0
$736$	5.70820	0.210407
$737$	−50.5410	−1.86170
$738$	20.5279	0.755641
$739$	23.7984	0.875437	0.437719	−	0.899112i	$-0.355787\pi$
$739$	23.7984	0.875437	0.437719	+	0.899112i	$0.355787\pi$
$740$	0	0
$741$	−13.7082	−0.503583
$742$	−11.3820	−0.417845
$743$	−45.3262	−1.66286	−0.831429	−	0.555631i	$-0.812477\pi$
$743$	−45.3262	−1.66286	−0.831429	+	0.555631i	$0.812477\pi$
$744$	1.23607	0.0453165
$745$	0	0
$746$	18.7426	0.686217
$747$	−34.4721	−1.26127
$748$	−11.4164	−0.417425
$749$	−0.763932	−0.0279135
$750$	0	0
$751$	−11.6180	−0.423948	−0.211974	−	0.977275i	$-0.567989\pi$
$751$	−11.6180	−0.423948	−0.211974	+	0.977275i	$0.567989\pi$
$752$	3.85410	0.140545
$753$	−34.6525	−1.26281
$754$	46.3607	1.68836
$755$	0	0
$756$	2.23607	0.0813250
$757$	8.58359	0.311976	0.155988	−	0.987759i	$-0.450144\pi$
$757$	8.58359	0.311976	0.155988	+	0.987759i	$0.450144\pi$
$758$	7.34752	0.266874
$759$	−69.0132	−2.50502
$760$	0	0
$761$	−47.8885	−1.73596	−0.867979	−	0.496601i	$-0.834581\pi$
$761$	−47.8885	−1.73596	−0.867979	+	0.496601i	$0.834581\pi$
$762$	−29.7984	−1.07948
$763$	8.32624	0.301430
$764$	22.6525	0.819538
$765$	0	0
$766$	20.7639	0.750231
$767$	46.3607	1.67399
$768$	−2.61803	−0.0944702
$769$	−32.1803	−1.16045	−0.580226	−	0.814455i	$-0.697036\pi$
$769$	−32.1803	−1.16045	−0.580226	+	0.814455i	$0.697036\pi$
$770$	0	0
$771$	−62.7771	−2.26086
$772$	13.7082	0.493369
$773$	−18.2918	−0.657910	−0.328955	−	0.944346i	$-0.606696\pi$
$773$	−18.2918	−0.657910	−0.328955	+	0.944346i	$0.606696\pi$
$774$	29.3607	1.05535
$775$	0	0
$776$	−3.85410	−0.138354
$777$	−12.7082	−0.455904
$778$	22.3607	0.801669
$779$	−5.32624	−0.190832
$780$	0	0
$781$	74.0476	2.64963
$782$	−14.1115	−0.504625
$783$	19.7984	0.707536
$784$	1.00000	0.0357143
$785$	0	0
$786$	16.1803	0.577134
$787$	16.4508	0.586409	0.293205	−	0.956050i	$-0.405278\pi$
$787$	16.4508	0.586409	0.293205	+	0.956050i	$0.405278\pi$
$788$	10.9443	0.389874
$789$	−24.1803	−0.860843
$790$	0	0
$791$	−8.94427	−0.318022
$792$	17.7984	0.632438
$793$	12.1803	0.432537
$794$	−21.0902	−0.748462
$795$	0	0
$796$	25.0344	0.887322
$797$	51.9574	1.84043	0.920213	−	0.391417i	$-0.128015\pi$
$797$	51.9574	1.84043	0.920213	+	0.391417i	$0.128015\pi$
$798$	−2.61803	−0.0926774
$799$	−9.52786	−0.337072
$800$	0	0
$801$	−5.32624	−0.188193
$802$	11.0557	0.390391
$803$	33.4164	1.17924
$804$	28.6525	1.01049
$805$	0	0
$806$	2.47214	0.0870773
$807$	−74.5410	−2.62397
$808$	14.9443	0.525738
$809$	−26.7426	−0.940221	−0.470111	−	0.882607i	$-0.655786\pi$
$809$	−26.7426	−0.940221	−0.470111	+	0.882607i	$0.655786\pi$
$810$	0	0
$811$	41.3820	1.45312	0.726559	−	0.687104i	$-0.241119\pi$
$811$	41.3820	1.45312	0.726559	+	0.687104i	$0.241119\pi$
$812$	8.85410	0.310718
$813$	−23.1803	−0.812970
$814$	−22.4164	−0.785695
$815$	0	0
$816$	6.47214	0.226570
$817$	−7.61803	−0.266521
$818$	−27.5623	−0.963693
$819$	20.1803	0.705158
$820$	0	0
$821$	17.4164	0.607837	0.303918	−	0.952698i	$-0.401705\pi$
$821$	17.4164	0.607837	0.303918	+	0.952698i	$0.401705\pi$
$822$	−27.1803	−0.948023
$823$	−30.3607	−1.05831	−0.529153	−	0.848526i	$-0.677490\pi$
$823$	−30.3607	−1.05831	−0.529153	+	0.848526i	$0.677490\pi$
$824$	−8.76393	−0.305306
$825$	0	0
$826$	8.85410	0.308074
$827$	−32.1803	−1.11902	−0.559510	−	0.828824i	$-0.689011\pi$
$827$	−32.1803	−1.11902	−0.559510	+	0.828824i	$0.689011\pi$
$828$	22.0000	0.764553
$829$	0.583592	0.0202690	0.0101345	−	0.999949i	$-0.496774\pi$
$829$	0.583592	0.0202690	0.0101345	+	0.999949i	$0.496774\pi$
$830$	0	0
$831$	27.8885	0.967443
$832$	−5.23607	−0.181528
$833$	−2.47214	−0.0856544
$834$	−27.4164	−0.949353
$835$	0	0
$836$	−4.61803	−0.159718
$837$	1.05573	0.0364913
$838$	17.4164	0.601640
$839$	4.11146	0.141943	0.0709716	−	0.997478i	$-0.477390\pi$
$839$	4.11146	0.141943	0.0709716	+	0.997478i	$0.477390\pi$
$840$	0	0
$841$	49.3951	1.70328
$842$	−14.3607	−0.494902
$843$	−41.8885	−1.44272
$844$	−4.00000	−0.137686
$845$	0	0
$846$	14.8541	0.510695
$847$	−10.3262	−0.354814
$848$	11.3820	0.390858
$849$	48.3607	1.65973
$850$	0	0
$851$	−27.7082	−0.949825
$852$	−41.9787	−1.43817
$853$	−44.1591	−1.51198	−0.755989	−	0.654585i	$-0.772843\pi$
$853$	−44.1591	−1.51198	−0.755989	+	0.654585i	$0.772843\pi$
$854$	2.32624	0.0796022
$855$	0	0
$856$	0.763932	0.0261107
$857$	−11.8885	−0.406105	−0.203052	−	0.979168i	$-0.565086\pi$
$857$	−11.8885	−0.406105	−0.203052	+	0.979168i	$0.565086\pi$
$858$	63.3050	2.16120
$859$	9.12461	0.311328	0.155664	−	0.987810i	$-0.450248\pi$
$859$	9.12461	0.311328	0.155664	+	0.987810i	$0.450248\pi$
$860$	0	0
$861$	13.9443	0.475220
$862$	5.27051	0.179514
$863$	7.03444	0.239455	0.119728	−	0.992807i	$-0.461798\pi$
$863$	7.03444	0.239455	0.119728	+	0.992807i	$0.461798\pi$
$864$	−2.23607	−0.0760726
$865$	0	0
$866$	−22.0902	−0.750655
$867$	28.5066	0.968134
$868$	0.472136	0.0160253
$869$	−61.5410	−2.08764
$870$	0	0
$871$	57.3050	1.94170
$872$	−8.32624	−0.281962
$873$	−14.8541	−0.502735
$874$	−5.70820	−0.193083
$875$	0	0
$876$	−18.9443	−0.640068
$877$	25.2705	0.853324	0.426662	−	0.904411i	$-0.359689\pi$
$877$	25.2705	0.853324	0.426662	+	0.904411i	$0.359689\pi$
$878$	4.47214	0.150927
$879$	68.5410	2.31183
$880$	0	0
$881$	2.76393	0.0931192	0.0465596	−	0.998916i	$-0.485174\pi$
$881$	2.76393	0.0931192	0.0465596	+	0.998916i	$0.485174\pi$
$882$	3.85410	0.129774
$883$	−17.5623	−0.591019	−0.295509	−	0.955340i	$-0.595489\pi$
$883$	−17.5623	−0.591019	−0.295509	+	0.955340i	$0.595489\pi$
$884$	12.9443	0.435363
$885$	0	0
$886$	7.79837	0.261991
$887$	48.2492	1.62005	0.810025	−	0.586395i	$-0.199453\pi$
$887$	48.2492	1.62005	0.810025	+	0.586395i	$0.199453\pi$
$888$	12.7082	0.426459
$889$	−11.3820	−0.381739
$890$	0	0
$891$	−26.3607	−0.883116
$892$	12.6525	0.423636
$893$	−3.85410	−0.128973
$894$	−10.4721	−0.350241
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	78.2492	2.61267
$898$	28.0689	0.936671
$899$	4.18034	0.139422
$900$	0	0
$901$	−28.1378	−0.937405
$902$	24.5967	0.818982
$903$	19.9443	0.663704
$904$	8.94427	0.297482
$905$	0	0
$906$	57.3050	1.90383
$907$	−32.0689	−1.06483	−0.532415	−	0.846484i	$-0.678715\pi$
$907$	−32.0689	−1.06483	−0.532415	+	0.846484i	$0.678715\pi$
$908$	−3.05573	−0.101408
$909$	57.5967	1.91036
$910$	0	0
$911$	11.2148	0.371562	0.185781	−	0.982591i	$-0.440518\pi$
$911$	11.2148	0.371562	0.185781	+	0.982591i	$0.440518\pi$
$912$	2.61803	0.0866918
$913$	−41.3050	−1.36699
$914$	22.5066	0.744451
$915$	0	0
$916$	23.0344	0.761079
$917$	6.18034	0.204093
$918$	5.52786	0.182447
$919$	24.7639	0.816887	0.408443	−	0.912784i	$-0.366072\pi$
$919$	24.7639	0.816887	0.408443	+	0.912784i	$0.366072\pi$
$920$	0	0
$921$	−65.5410	−2.15965
$922$	−5.38197	−0.177246
$923$	−83.9574	−2.76349
$924$	12.0902	0.397737
$925$	0	0
$926$	2.76393	0.0908284
$927$	−33.7771	−1.10939
$928$	−8.85410	−0.290650
$929$	0.291796	0.00957352	0.00478676	−	0.999989i	$-0.498476\pi$
$929$	0.291796	0.00957352	0.00478676	+	0.999989i	$0.498476\pi$
$930$	0	0
$931$	−1.00000	−0.0327737
$932$	−15.7426	−0.515668
$933$	−6.85410	−0.224393
$934$	−21.7082	−0.710314
$935$	0	0
$936$	−20.1803	−0.659615
$937$	−46.8328	−1.52996	−0.764981	−	0.644053i	$-0.777252\pi$
$937$	−46.8328	−1.52996	−0.764981	+	0.644053i	$0.777252\pi$
$938$	10.9443	0.357343
$939$	−46.8328	−1.52833
$940$	0	0
$941$	8.06888	0.263038	0.131519	−	0.991314i	$-0.458015\pi$
$941$	8.06888	0.263038	0.131519	+	0.991314i	$0.458015\pi$
$942$	−7.61803	−0.248209
$943$	30.4033	0.990066
$944$	−8.85410	−0.288176
$945$	0	0
$946$	35.1803	1.14381
$947$	−19.3820	−0.629829	−0.314915	−	0.949120i	$-0.601976\pi$
$947$	−19.3820	−0.629829	−0.314915	+	0.949120i	$0.601976\pi$
$948$	34.8885	1.13313
$949$	−37.8885	−1.22991
$950$	0	0
$951$	−53.9787	−1.75038
$952$	2.47214	0.0801224
$953$	−8.47214	−0.274439	−0.137220	−	0.990541i	$-0.543817\pi$
$953$	−8.47214	−0.274439	−0.137220	+	0.990541i	$0.543817\pi$
$954$	43.8673	1.42025
$955$	0	0
$956$	−15.1246	−0.489165
$957$	107.048	3.46036
$958$	0.270510	0.00873978
$959$	−10.3820	−0.335251
$960$	0	0
$961$	−30.7771	−0.992809
$962$	25.4164	0.819458
$963$	2.94427	0.0948778
$964$	9.14590	0.294570
$965$	0	0
$966$	14.9443	0.480824
$967$	9.30495	0.299227	0.149614	−	0.988745i	$-0.452197\pi$
$967$	9.30495	0.299227	0.149614	+	0.988745i	$0.452197\pi$
$968$	10.3262	0.331898
$969$	−6.47214	−0.207915
$970$	0	0
$971$	−15.4934	−0.497208	−0.248604	−	0.968605i	$-0.579972\pi$
$971$	−15.4934	−0.497208	−0.248604	+	0.968605i	$0.579972\pi$
$972$	21.6525	0.694503
$973$	−10.4721	−0.335721
$974$	−36.5623	−1.17153
$975$	0	0
$976$	−2.32624	−0.0744611
$977$	−28.7639	−0.920240	−0.460120	−	0.887857i	$-0.652194\pi$
$977$	−28.7639	−0.920240	−0.460120	+	0.887857i	$0.652194\pi$
$978$	18.5623	0.593557
$979$	−6.38197	−0.203969
$980$	0	0
$981$	−32.0902	−1.02456
$982$	2.11146	0.0673793
$983$	−0.944272	−0.0301176	−0.0150588	−	0.999887i	$-0.504794\pi$
$983$	−0.944272	−0.0301176	−0.0150588	+	0.999887i	$0.504794\pi$
$984$	−13.9443	−0.444527
$985$	0	0
$986$	21.8885	0.697073
$987$	10.0902	0.321174
$988$	5.23607	0.166582
$989$	43.4853	1.38275
$990$	0	0
$991$	−52.6869	−1.67366	−0.836828	−	0.547467i	$-0.815592\pi$
$991$	−52.6869	−1.67366	−0.836828	+	0.547467i	$0.815592\pi$
$992$	−0.472136	−0.0149903
$993$	6.76393	0.214647
$994$	−16.0344	−0.508582
$995$	0	0
$996$	23.4164	0.741977
$997$	−17.9098	−0.567210	−0.283605	−	0.958941i	$-0.591530\pi$
$997$	−17.9098	−0.567210	−0.283605	+	0.958941i	$0.591530\pi$
$998$	−25.3262	−0.801688
$999$	10.8541	0.343409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6650.2.a.bq.1.1		2
5.4	even	2		266.2.a.b.1.2	✓	2
15.14	odd	2		2394.2.a.w.1.2		2
20.19	odd	2		2128.2.a.b.1.1		2
35.34	odd	2		1862.2.a.g.1.1		2
40.19	odd	2		8512.2.a.bc.1.2		2
40.29	even	2		8512.2.a.h.1.1		2
95.94	odd	2		5054.2.a.k.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.a.b.1.2	✓	2	5.4	even	2
1862.2.a.g.1.1		2	35.34	odd	2
2128.2.a.b.1.1		2	20.19	odd	2
2394.2.a.w.1.2		2	15.14	odd	2
5054.2.a.k.1.1		2	95.94	odd	2
6650.2.a.bq.1.1		2	1.1	even	1	trivial
8512.2.a.h.1.1		2	40.29	even	2
8512.2.a.bc.1.2		2	40.19	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:	\( N \)	\(=\)	\( 6650 = 2 \cdot 5^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6650.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.61803 q^{3} +1.00000 q^{4} -2.61803 q^{6} -1.00000 q^{7} +1.00000 q^{8} +3.85410 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.61803 q^{3} +1.00000 q^{4} -2.61803 q^{6} -1.00000 q^{7} +1.00000 q^{8} +3.85410 q^{9} +4.61803 q^{11} -2.61803 q^{12} -5.23607 q^{13} -1.00000 q^{14} +1.00000 q^{16} -2.47214 q^{17} +3.85410 q^{18} -1.00000 q^{19} +2.61803 q^{21} +4.61803 q^{22} +5.70820 q^{23} -2.61803 q^{24} -5.23607 q^{26} -2.23607 q^{27} -1.00000 q^{28} -8.85410 q^{29} -0.472136 q^{31} +1.00000 q^{32} -12.0902 q^{33} -2.47214 q^{34} +3.85410 q^{36} -4.85410 q^{37} -1.00000 q^{38} +13.7082 q^{39} +5.32624 q^{41} +2.61803 q^{42} +7.61803 q^{43} +4.61803 q^{44} +5.70820 q^{46} +3.85410 q^{47} -2.61803 q^{48} +1.00000 q^{49} +6.47214 q^{51} -5.23607 q^{52} +11.3820 q^{53} -2.23607 q^{54} -1.00000 q^{56} +2.61803 q^{57} -8.85410 q^{58} -8.85410 q^{59} -2.32624 q^{61} -0.472136 q^{62} -3.85410 q^{63} +1.00000 q^{64} -12.0902 q^{66} -10.9443 q^{67} -2.47214 q^{68} -14.9443 q^{69} +16.0344 q^{71} +3.85410 q^{72} +7.23607 q^{73} -4.85410 q^{74} -1.00000 q^{76} -4.61803 q^{77} +13.7082 q^{78} -13.3262 q^{79} -5.70820 q^{81} +5.32624 q^{82} -8.94427 q^{83} +2.61803 q^{84} +7.61803 q^{86} +23.1803 q^{87} +4.61803 q^{88} -1.38197 q^{89} +5.23607 q^{91} +5.70820 q^{92} +1.23607 q^{93} +3.85410 q^{94} -2.61803 q^{96} -3.85410 q^{97} +1.00000 q^{98} +17.7984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{6} - 2 q^{7} + 2 q^{8} + q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^6 - 2 * q^7 + 2 * q^8 + q^9	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{6} - 2 q^{7} + 2 q^{8} + q^{9} + 7 q^{11} - 3 q^{12} - 6 q^{13} - 2 q^{14} + 2 q^{16} + 4 q^{17} + q^{18} - 2 q^{19} + 3 q^{21} + 7 q^{22} - 2 q^{23} - 3 q^{24} - 6 q^{26} - 2 q^{28} - 11 q^{29} + 8 q^{31} + 2 q^{32} - 13 q^{33} + 4 q^{34} + q^{36} - 3 q^{37} - 2 q^{38} + 14 q^{39} - 5 q^{41} + 3 q^{42} + 13 q^{43} + 7 q^{44} - 2 q^{46} + q^{47} - 3 q^{48} + 2 q^{49} + 4 q^{51} - 6 q^{52} + 25 q^{53} - 2 q^{56} + 3 q^{57} - 11 q^{58} - 11 q^{59} + 11 q^{61} + 8 q^{62} - q^{63} + 2 q^{64} - 13 q^{66} - 4 q^{67} + 4 q^{68} - 12 q^{69} + 3 q^{71} + q^{72} + 10 q^{73} - 3 q^{74} - 2 q^{76} - 7 q^{77} + 14 q^{78} - 11 q^{79} + 2 q^{81} - 5 q^{82} + 3 q^{84} + 13 q^{86} + 24 q^{87} + 7 q^{88} - 5 q^{89} + 6 q^{91} - 2 q^{92} - 2 q^{93} + q^{94} - 3 q^{96} - q^{97} + 2 q^{98} + 11 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^6 - 2 * q^7 + 2 * q^8 + q^9 + 7 * q^11 - 3 * q^12 - 6 * q^13 - 2 * q^14 + 2 * q^16 + 4 * q^17 + q^18 - 2 * q^19 + 3 * q^21 + 7 * q^22 - 2 * q^23 - 3 * q^24 - 6 * q^26 - 2 * q^28 - 11 * q^29 + 8 * q^31 + 2 * q^32 - 13 * q^33 + 4 * q^34 + q^36 - 3 * q^37 - 2 * q^38 + 14 * q^39 - 5 * q^41 + 3 * q^42 + 13 * q^43 + 7 * q^44 - 2 * q^46 + q^47 - 3 * q^48 + 2 * q^49 + 4 * q^51 - 6 * q^52 + 25 * q^53 - 2 * q^56 + 3 * q^57 - 11 * q^58 - 11 * q^59 + 11 * q^61 + 8 * q^62 - q^63 + 2 * q^64 - 13 * q^66 - 4 * q^67 + 4 * q^68 - 12 * q^69 + 3 * q^71 + q^72 + 10 * q^73 - 3 * q^74 - 2 * q^76 - 7 * q^77 + 14 * q^78 - 11 * q^79 + 2 * q^81 - 5 * q^82 + 3 * q^84 + 13 * q^86 + 24 * q^87 + 7 * q^88 - 5 * q^89 + 6 * q^91 - 2 * q^92 - 2 * q^93 + q^94 - 3 * q^96 - q^97 + 2 * q^98 + 11 * q^99

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