LMFDB - Embedded newform 8085.2.a.bb.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8085,2,Mod(1,8085)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8085, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8085.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8085.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:	$64.5590500342$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1155)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.56155$ of defining polynomial
Character	$\chi$	$=$	8085.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.56155 q^{2} +1.00000 q^{3} +0.438447 q^{4} -1.00000 q^{5} +1.56155 q^{6} -2.43845 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.56155 q^{2} +1.00000 q^{3} +0.438447 q^{4} -1.00000 q^{5} +1.56155 q^{6} -2.43845 q^{8} +1.00000 q^{9} -1.56155 q^{10} +1.00000 q^{11} +0.438447 q^{12} +7.12311 q^{13} -1.00000 q^{15} -4.68466 q^{16} -0.561553 q^{17} +1.56155 q^{18} +2.56155 q^{19} -0.438447 q^{20} +1.56155 q^{22} -1.43845 q^{23} -2.43845 q^{24} +1.00000 q^{25} +11.1231 q^{26} +1.00000 q^{27} +1.68466 q^{29} -1.56155 q^{30} +5.12311 q^{31} -2.43845 q^{32} +1.00000 q^{33} -0.876894 q^{34} +0.438447 q^{36} -7.12311 q^{37} +4.00000 q^{38} +7.12311 q^{39} +2.43845 q^{40} -2.00000 q^{41} +2.56155 q^{43} +0.438447 q^{44} -1.00000 q^{45} -2.24621 q^{46} +5.12311 q^{47} -4.68466 q^{48} +1.56155 q^{50} -0.561553 q^{51} +3.12311 q^{52} -13.6847 q^{53} +1.56155 q^{54} -1.00000 q^{55} +2.56155 q^{57} +2.63068 q^{58} -10.5616 q^{59} -0.438447 q^{60} +3.43845 q^{61} +8.00000 q^{62} +5.56155 q^{64} -7.12311 q^{65} +1.56155 q^{66} +6.87689 q^{67} -0.246211 q^{68} -1.43845 q^{69} +5.12311 q^{71} -2.43845 q^{72} +11.1231 q^{73} -11.1231 q^{74} +1.00000 q^{75} +1.12311 q^{76} +11.1231 q^{78} -10.2462 q^{79} +4.68466 q^{80} +1.00000 q^{81} -3.12311 q^{82} +5.43845 q^{83} +0.561553 q^{85} +4.00000 q^{86} +1.68466 q^{87} -2.43845 q^{88} +2.31534 q^{89} -1.56155 q^{90} -0.630683 q^{92} +5.12311 q^{93} +8.00000 q^{94} -2.56155 q^{95} -2.43845 q^{96} -2.80776 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 2 q^{3} + 5 q^{4} - 2 q^{5} - q^{6} - 9 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 + 2 * q^3 + 5 * q^4 - 2 * q^5 - q^6 - 9 * q^8 + 2 * q^9	$ 2 q - q^{2} + 2 q^{3} + 5 q^{4} - 2 q^{5} - q^{6} - 9 q^{8} + 2 q^{9} + q^{10} + 2 q^{11} + 5 q^{12} + 6 q^{13} - 2 q^{15} + 3 q^{16} + 3 q^{17} - q^{18} + q^{19} - 5 q^{20} - q^{22} - 7 q^{23} - 9 q^{24} + 2 q^{25} + 14 q^{26} + 2 q^{27} - 9 q^{29} + q^{30} + 2 q^{31} - 9 q^{32} + 2 q^{33} - 10 q^{34} + 5 q^{36} - 6 q^{37} + 8 q^{38} + 6 q^{39} + 9 q^{40} - 4 q^{41} + q^{43} + 5 q^{44} - 2 q^{45} + 12 q^{46} + 2 q^{47} + 3 q^{48} - q^{50} + 3 q^{51} - 2 q^{52} - 15 q^{53} - q^{54} - 2 q^{55} + q^{57} + 30 q^{58} - 17 q^{59} - 5 q^{60} + 11 q^{61} + 16 q^{62} + 7 q^{64} - 6 q^{65} - q^{66} + 22 q^{67} + 16 q^{68} - 7 q^{69} + 2 q^{71} - 9 q^{72} + 14 q^{73} - 14 q^{74} + 2 q^{75} - 6 q^{76} + 14 q^{78} - 4 q^{79} - 3 q^{80} + 2 q^{81} + 2 q^{82} + 15 q^{83} - 3 q^{85} + 8 q^{86} - 9 q^{87} - 9 q^{88} + 17 q^{89} + q^{90} - 26 q^{92} + 2 q^{93} + 16 q^{94} - q^{95} - 9 q^{96} + 15 q^{97} + 2 q^{99}+O(q^{100}) $ 2 * q - q^2 + 2 * q^3 + 5 * q^4 - 2 * q^5 - q^6 - 9 * q^8 + 2 * q^9 + q^10 + 2 * q^11 + 5 * q^12 + 6 * q^13 - 2 * q^15 + 3 * q^16 + 3 * q^17 - q^18 + q^19 - 5 * q^20 - q^22 - 7 * q^23 - 9 * q^24 + 2 * q^25 + 14 * q^26 + 2 * q^27 - 9 * q^29 + q^30 + 2 * q^31 - 9 * q^32 + 2 * q^33 - 10 * q^34 + 5 * q^36 - 6 * q^37 + 8 * q^38 + 6 * q^39 + 9 * q^40 - 4 * q^41 + q^43 + 5 * q^44 - 2 * q^45 + 12 * q^46 + 2 * q^47 + 3 * q^48 - q^50 + 3 * q^51 - 2 * q^52 - 15 * q^53 - q^54 - 2 * q^55 + q^57 + 30 * q^58 - 17 * q^59 - 5 * q^60 + 11 * q^61 + 16 * q^62 + 7 * q^64 - 6 * q^65 - q^66 + 22 * q^67 + 16 * q^68 - 7 * q^69 + 2 * q^71 - 9 * q^72 + 14 * q^73 - 14 * q^74 + 2 * q^75 - 6 * q^76 + 14 * q^78 - 4 * q^79 - 3 * q^80 + 2 * q^81 + 2 * q^82 + 15 * q^83 - 3 * q^85 + 8 * q^86 - 9 * q^87 - 9 * q^88 + 17 * q^89 + q^90 - 26 * q^92 + 2 * q^93 + 16 * q^94 - q^95 - 9 * q^96 + 15 * q^97 + 2 * 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 $

$2$	1.56155	1.10418	0.552092	−	0.833783i	$-0.313830\pi$
$2$	1.56155	1.10418	0.552092	+	0.833783i	$0.313830\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.438447	0.219224
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.56155	0.637501
$7$	0	0
$7$	0	0
$8$	−2.43845	−0.862121
$9$	1.00000	0.333333
$10$	−1.56155	−0.493806
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.438447	0.126569
$13$	7.12311	1.97559	0.987797	−	0.155747i	$-0.0497784\pi$
$13$	7.12311	1.97559	0.987797	+	0.155747i	$0.0497784\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	−4.68466	−1.17116
$17$	−0.561553	−0.136197	−0.0680983	−	0.997679i	$-0.521693\pi$
$17$	−0.561553	−0.136197	−0.0680983	+	0.997679i	$0.521693\pi$
$18$	1.56155	0.368062
$19$	2.56155	0.587661	0.293830	−	0.955858i	$-0.405070\pi$
$19$	2.56155	0.587661	0.293830	+	0.955858i	$0.405070\pi$
$20$	−0.438447	−0.0980398
$21$	0	0
$22$	1.56155	0.332924
$23$	−1.43845	−0.299937	−0.149968	−	0.988691i	$-0.547917\pi$
$23$	−1.43845	−0.299937	−0.149968	+	0.988691i	$0.547917\pi$
$24$	−2.43845	−0.497746
$25$	1.00000	0.200000
$26$	11.1231	2.18142
$27$	1.00000	0.192450
$28$	0	0
$29$	1.68466	0.312833	0.156417	−	0.987691i	$-0.450006\pi$
$29$	1.68466	0.312833	0.156417	+	0.987691i	$0.450006\pi$
$30$	−1.56155	−0.285099
$31$	5.12311	0.920137	0.460068	−	0.887883i	$-0.347825\pi$
$31$	5.12311	0.920137	0.460068	+	0.887883i	$0.347825\pi$
$32$	−2.43845	−0.431061
$33$	1.00000	0.174078
$34$	−0.876894	−0.150386
$35$	0	0
$36$	0.438447	0.0730745
$37$	−7.12311	−1.17103	−0.585516	−	0.810661i	$-0.699108\pi$
$37$	−7.12311	−1.17103	−0.585516	+	0.810661i	$0.699108\pi$
$38$	4.00000	0.648886
$39$	7.12311	1.14061
$40$	2.43845	0.385552
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	0	0
$43$	2.56155	0.390633	0.195317	−	0.980740i	$-0.437427\pi$
$43$	2.56155	0.390633	0.195317	+	0.980740i	$0.437427\pi$
$44$	0.438447	0.0660984
$45$	−1.00000	−0.149071
$46$	−2.24621	−0.331186
$47$	5.12311	0.747282	0.373641	−	0.927573i	$-0.378109\pi$
$47$	5.12311	0.747282	0.373641	+	0.927573i	$0.378109\pi$
$48$	−4.68466	−0.676172
$49$	0	0
$50$	1.56155	0.220837
$51$	−0.561553	−0.0786331
$52$	3.12311	0.433097
$53$	−13.6847	−1.87973	−0.939866	−	0.341543i	$-0.889051\pi$
$53$	−13.6847	−1.87973	−0.939866	+	0.341543i	$0.889051\pi$
$54$	1.56155	0.212500
$55$	−1.00000	−0.134840
$56$	0	0
$57$	2.56155	0.339286
$58$	2.63068	0.345426
$59$	−10.5616	−1.37500	−0.687499	−	0.726186i	$-0.741291\pi$
$59$	−10.5616	−1.37500	−0.687499	+	0.726186i	$0.741291\pi$
$60$	−0.438447	−0.0566033
$61$	3.43845	0.440248	0.220124	−	0.975472i	$-0.429354\pi$
$61$	3.43845	0.440248	0.220124	+	0.975472i	$0.429354\pi$
$62$	8.00000	1.01600
$63$	0	0
$64$	5.56155	0.695194
$65$	−7.12311	−0.883513
$66$	1.56155	0.192214
$67$	6.87689	0.840146	0.420073	−	0.907490i	$-0.362004\pi$
$67$	6.87689	0.840146	0.420073	+	0.907490i	$0.362004\pi$
$68$	−0.246211	−0.0298575
$69$	−1.43845	−0.173169
$70$	0	0
$71$	5.12311	0.608001	0.304000	−	0.952672i	$-0.401678\pi$
$71$	5.12311	0.608001	0.304000	+	0.952672i	$0.401678\pi$
$72$	−2.43845	−0.287374
$73$	11.1231	1.30186	0.650931	−	0.759137i	$-0.274379\pi$
$73$	11.1231	1.30186	0.650931	+	0.759137i	$0.274379\pi$
$74$	−11.1231	−1.29303
$75$	1.00000	0.115470
$76$	1.12311	0.128829
$77$	0	0
$78$	11.1231	1.25944
$79$	−10.2462	−1.15279	−0.576394	−	0.817172i	$-0.695541\pi$
$79$	−10.2462	−1.15279	−0.576394	+	0.817172i	$0.695541\pi$
$80$	4.68466	0.523761
$81$	1.00000	0.111111
$82$	−3.12311	−0.344889
$83$	5.43845	0.596947	0.298474	−	0.954418i	$-0.403523\pi$
$83$	5.43845	0.596947	0.298474	+	0.954418i	$0.403523\pi$
$84$	0	0
$85$	0.561553	0.0609090
$86$	4.00000	0.431331
$87$	1.68466	0.180614
$88$	−2.43845	−0.259939
$89$	2.31534	0.245426	0.122713	−	0.992442i	$-0.460841\pi$
$89$	2.31534	0.245426	0.122713	+	0.992442i	$0.460841\pi$
$90$	−1.56155	−0.164602
$91$	0	0
$92$	−0.630683	−0.0657533
$93$	5.12311	0.531241
$94$	8.00000	0.825137
$95$	−2.56155	−0.262810
$96$	−2.43845	−0.248873
$97$	−2.80776	−0.285085	−0.142543	−	0.989789i	$-0.545528\pi$
$97$	−2.80776	−0.285085	−0.142543	+	0.989789i	$0.545528\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	0.438447	0.0438447
$101$	12.2462	1.21854	0.609272	−	0.792961i	$-0.291462\pi$
$101$	12.2462	1.21854	0.609272	+	0.792961i	$0.291462\pi$
$102$	−0.876894	−0.0868255
$103$	−3.68466	−0.363060	−0.181530	−	0.983385i	$-0.558105\pi$
$103$	−3.68466	−0.363060	−0.181530	+	0.983385i	$0.558105\pi$
$104$	−17.3693	−1.70320
$105$	0	0
$106$	−21.3693	−2.07557
$107$	19.3693	1.87250	0.936251	−	0.351331i	$-0.114271\pi$
$107$	19.3693	1.87250	0.936251	+	0.351331i	$0.114271\pi$
$108$	0.438447	0.0421896
$109$	18.4924	1.77125	0.885626	−	0.464398i	$-0.153729\pi$
$109$	18.4924	1.77125	0.885626	+	0.464398i	$0.153729\pi$
$110$	−1.56155	−0.148888
$111$	−7.12311	−0.676095
$112$	0	0
$113$	8.56155	0.805403	0.402702	−	0.915331i	$-0.368071\pi$
$113$	8.56155	0.805403	0.402702	+	0.915331i	$0.368071\pi$
$114$	4.00000	0.374634
$115$	1.43845	0.134136
$116$	0.738634	0.0685804
$117$	7.12311	0.658531
$118$	−16.4924	−1.51825
$119$	0	0
$120$	2.43845	0.222599
$121$	1.00000	0.0909091
$122$	5.36932	0.486115
$123$	−2.00000	−0.180334
$124$	2.24621	0.201716
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	0.807764	0.0716775	0.0358387	−	0.999358i	$-0.488590\pi$
$127$	0.807764	0.0716775	0.0358387	+	0.999358i	$0.488590\pi$
$128$	13.5616	1.19868
$129$	2.56155	0.225532
$130$	−11.1231	−0.975561
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	0.438447	0.0381619
$133$	0	0
$134$	10.7386	0.927677
$135$	−1.00000	−0.0860663
$136$	1.36932	0.117418
$137$	10.0000	0.854358	0.427179	−	0.904167i	$-0.359507\pi$
$137$	10.0000	0.854358	0.427179	+	0.904167i	$0.359507\pi$
$138$	−2.24621	−0.191210
$139$	20.0000	1.69638	0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000	1.69638	0.848189	+	0.529694i	$0.177693\pi$
$140$	0	0
$141$	5.12311	0.431443
$142$	8.00000	0.671345
$143$	7.12311	0.595664
$144$	−4.68466	−0.390388
$145$	−1.68466	−0.139903
$146$	17.3693	1.43749
$147$	0	0
$148$	−3.12311	−0.256718
$149$	0.246211	0.0201704	0.0100852	−	0.999949i	$-0.496790\pi$
$149$	0.246211	0.0201704	0.0100852	+	0.999949i	$0.496790\pi$
$150$	1.56155	0.127500
$151$	5.12311	0.416912	0.208456	−	0.978032i	$-0.433156\pi$
$151$	5.12311	0.416912	0.208456	+	0.978032i	$0.433156\pi$
$152$	−6.24621	−0.506635
$153$	−0.561553	−0.0453989
$154$	0	0
$155$	−5.12311	−0.411498
$156$	3.12311	0.250049
$157$	11.4384	0.912887	0.456444	−	0.889752i	$-0.349123\pi$
$157$	11.4384	0.912887	0.456444	+	0.889752i	$0.349123\pi$
$158$	−16.0000	−1.27289
$159$	−13.6847	−1.08526
$160$	2.43845	0.192776
$161$	0	0
$162$	1.56155	0.122687
$163$	20.0000	1.56652	0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000	1.56652	0.783260	+	0.621694i	$0.213555\pi$
$164$	−0.876894	−0.0684739
$165$	−1.00000	−0.0778499
$166$	8.49242	0.659140
$167$	−2.24621	−0.173817	−0.0869085	−	0.996216i	$-0.527699\pi$
$167$	−2.24621	−0.173817	−0.0869085	+	0.996216i	$0.527699\pi$
$168$	0	0
$169$	37.7386	2.90297
$170$	0.876894	0.0672547
$171$	2.56155	0.195887
$172$	1.12311	0.0856360
$173$	4.24621	0.322833	0.161417	−	0.986886i	$-0.448394\pi$
$173$	4.24621	0.322833	0.161417	+	0.986886i	$0.448394\pi$
$174$	2.63068	0.199432
$175$	0	0
$176$	−4.68466	−0.353119
$177$	−10.5616	−0.793855
$178$	3.61553	0.270995
$179$	−19.3693	−1.44773	−0.723865	−	0.689941i	$-0.757636\pi$
$179$	−19.3693	−1.44773	−0.723865	+	0.689941i	$0.757636\pi$
$180$	−0.438447	−0.0326799
$181$	20.2462	1.50489	0.752445	−	0.658656i	$-0.228875\pi$
$181$	20.2462	1.50489	0.752445	+	0.658656i	$0.228875\pi$
$182$	0	0
$183$	3.43845	0.254177
$184$	3.50758	0.258582
$185$	7.12311	0.523701
$186$	8.00000	0.586588
$187$	−0.561553	−0.0410648
$188$	2.24621	0.163822
$189$	0	0
$190$	−4.00000	−0.290191
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	5.56155	0.401371
$193$	22.4924	1.61904	0.809520	−	0.587092i	$-0.199727\pi$
$193$	22.4924	1.61904	0.809520	+	0.587092i	$0.199727\pi$
$194$	−4.38447	−0.314787
$195$	−7.12311	−0.510096
$196$	0	0
$197$	−23.1231	−1.64745	−0.823727	−	0.566987i	$-0.808109\pi$
$197$	−23.1231	−1.64745	−0.823727	+	0.566987i	$0.808109\pi$
$198$	1.56155	0.110975
$199$	−20.4924	−1.45267	−0.726335	−	0.687341i	$-0.758778\pi$
$199$	−20.4924	−1.45267	−0.726335	+	0.687341i	$0.758778\pi$
$200$	−2.43845	−0.172424
$201$	6.87689	0.485059
$202$	19.1231	1.34550
$203$	0	0
$204$	−0.246211	−0.0172382
$205$	2.00000	0.139686
$206$	−5.75379	−0.400885
$207$	−1.43845	−0.0999790
$208$	−33.3693	−2.31375
$209$	2.56155	0.177186
$210$	0	0
$211$	−3.36932	−0.231953	−0.115977	−	0.993252i	$-0.537000\pi$
$211$	−3.36932	−0.231953	−0.115977	+	0.993252i	$0.537000\pi$
$212$	−6.00000	−0.412082
$213$	5.12311	0.351029
$214$	30.2462	2.06759
$215$	−2.56155	−0.174696
$216$	−2.43845	−0.165915
$217$	0	0
$218$	28.8769	1.95579
$219$	11.1231	0.751630
$220$	−0.438447	−0.0295601
$221$	−4.00000	−0.269069
$222$	−11.1231	−0.746534
$223$	−14.5616	−0.975114	−0.487557	−	0.873091i	$-0.662112\pi$
$223$	−14.5616	−0.975114	−0.487557	+	0.873091i	$0.662112\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	13.3693	0.889314
$227$	25.9309	1.72109	0.860546	−	0.509373i	$-0.170122\pi$
$227$	25.9309	1.72109	0.860546	+	0.509373i	$0.170122\pi$
$228$	1.12311	0.0743795
$229$	−10.4924	−0.693359	−0.346679	−	0.937984i	$-0.612691\pi$
$229$	−10.4924	−0.693359	−0.346679	+	0.937984i	$0.612691\pi$
$230$	2.24621	0.148111
$231$	0	0
$232$	−4.10795	−0.269700
$233$	−23.6155	−1.54710	−0.773552	−	0.633732i	$-0.781522\pi$
$233$	−23.6155	−1.54710	−0.773552	+	0.633732i	$0.781522\pi$
$234$	11.1231	0.727140
$235$	−5.12311	−0.334195
$236$	−4.63068	−0.301432
$237$	−10.2462	−0.665563
$238$	0	0
$239$	19.6847	1.27329	0.636647	−	0.771155i	$-0.280321\pi$
$239$	19.6847	1.27329	0.636647	+	0.771155i	$0.280321\pi$
$240$	4.68466	0.302393
$241$	0.246211	0.0158599	0.00792993	−	0.999969i	$-0.497476\pi$
$241$	0.246211	0.0158599	0.00792993	+	0.999969i	$0.497476\pi$
$242$	1.56155	0.100380
$243$	1.00000	0.0641500
$244$	1.50758	0.0965128
$245$	0	0
$246$	−3.12311	−0.199122
$247$	18.2462	1.16098
$248$	−12.4924	−0.793270
$249$	5.43845	0.344648
$250$	−1.56155	−0.0987613
$251$	−24.4924	−1.54595	−0.772974	−	0.634438i	$-0.781232\pi$
$251$	−24.4924	−1.54595	−0.772974	+	0.634438i	$0.781232\pi$
$252$	0	0
$253$	−1.43845	−0.0904344
$254$	1.26137	0.0791452
$255$	0.561553	0.0351658
$256$	10.0540	0.628373
$257$	−9.36932	−0.584442	−0.292221	−	0.956351i	$-0.594394\pi$
$257$	−9.36932	−0.584442	−0.292221	+	0.956351i	$0.594394\pi$
$258$	4.00000	0.249029
$259$	0	0
$260$	−3.12311	−0.193687
$261$	1.68466	0.104278
$262$	−6.24621	−0.385892
$263$	−18.2462	−1.12511	−0.562555	−	0.826760i	$-0.690181\pi$
$263$	−18.2462	−1.12511	−0.562555	+	0.826760i	$0.690181\pi$
$264$	−2.43845	−0.150076
$265$	13.6847	0.840642
$266$	0	0
$267$	2.31534	0.141697
$268$	3.01515	0.184180
$269$	−1.68466	−0.102715	−0.0513577	−	0.998680i	$-0.516355\pi$
$269$	−1.68466	−0.102715	−0.0513577	+	0.998680i	$0.516355\pi$
$270$	−1.56155	−0.0950331
$271$	13.9309	0.846240	0.423120	−	0.906074i	$-0.360935\pi$
$271$	13.9309	0.846240	0.423120	+	0.906074i	$0.360935\pi$
$272$	2.63068	0.159509
$273$	0	0
$274$	15.6155	0.943369
$275$	1.00000	0.0603023
$276$	−0.630683	−0.0379627
$277$	−24.7386	−1.48640	−0.743200	−	0.669069i	$-0.766693\pi$
$277$	−24.7386	−1.48640	−0.743200	+	0.669069i	$0.766693\pi$
$278$	31.2311	1.87311
$279$	5.12311	0.306712
$280$	0	0
$281$	14.4924	0.864545	0.432273	−	0.901743i	$-0.357712\pi$
$281$	14.4924	0.864545	0.432273	+	0.901743i	$0.357712\pi$
$282$	8.00000	0.476393
$283$	−6.24621	−0.371299	−0.185649	−	0.982616i	$-0.559439\pi$
$283$	−6.24621	−0.371299	−0.185649	+	0.982616i	$0.559439\pi$
$284$	2.24621	0.133288
$285$	−2.56155	−0.151733
$286$	11.1231	0.657723
$287$	0	0
$288$	−2.43845	−0.143687
$289$	−16.6847	−0.981450
$290$	−2.63068	−0.154479
$291$	−2.80776	−0.164594
$292$	4.87689	0.285399
$293$	26.1771	1.52928	0.764641	−	0.644457i	$-0.222916\pi$
$293$	26.1771	1.52928	0.764641	+	0.644457i	$0.222916\pi$
$294$	0	0
$295$	10.5616	0.614917
$296$	17.3693	1.00957
$297$	1.00000	0.0580259
$298$	0.384472	0.0222719
$299$	−10.2462	−0.592554
$300$	0.438447	0.0253138
$301$	0	0
$302$	8.00000	0.460348
$303$	12.2462	0.703526
$304$	−12.0000	−0.688247
$305$	−3.43845	−0.196885
$306$	−0.876894	−0.0501287
$307$	−11.3693	−0.648881	−0.324441	−	0.945906i	$-0.605176\pi$
$307$	−11.3693	−0.648881	−0.324441	+	0.945906i	$0.605176\pi$
$308$	0	0
$309$	−3.68466	−0.209613
$310$	−8.00000	−0.454369
$311$	16.0000	0.907277	0.453638	−	0.891186i	$-0.350126\pi$
$311$	16.0000	0.907277	0.453638	+	0.891186i	$0.350126\pi$
$312$	−17.3693	−0.983344
$313$	2.31534	0.130871	0.0654354	−	0.997857i	$-0.479156\pi$
$313$	2.31534	0.130871	0.0654354	+	0.997857i	$0.479156\pi$
$314$	17.8617	1.00800
$315$	0	0
$316$	−4.49242	−0.252719
$317$	−22.4924	−1.26330	−0.631650	−	0.775254i	$-0.717622\pi$
$317$	−22.4924	−1.26330	−0.631650	+	0.775254i	$0.717622\pi$
$318$	−21.3693	−1.19833
$319$	1.68466	0.0943228
$320$	−5.56155	−0.310900
$321$	19.3693	1.08109
$322$	0	0
$323$	−1.43845	−0.0800373
$324$	0.438447	0.0243582
$325$	7.12311	0.395119
$326$	31.2311	1.72973
$327$	18.4924	1.02263
$328$	4.87689	0.269281
$329$	0	0
$330$	−1.56155	−0.0859607
$331$	−23.6847	−1.30183	−0.650913	−	0.759152i	$-0.725614\pi$
$331$	−23.6847	−1.30183	−0.650913	+	0.759152i	$0.725614\pi$
$332$	2.38447	0.130865
$333$	−7.12311	−0.390344
$334$	−3.50758	−0.191926
$335$	−6.87689	−0.375725
$336$	0	0
$337$	−9.05398	−0.493201	−0.246601	−	0.969117i	$-0.579314\pi$
$337$	−9.05398	−0.493201	−0.246601	+	0.969117i	$0.579314\pi$
$338$	58.9309	3.20542
$339$	8.56155	0.465000
$340$	0.246211	0.0133527
$341$	5.12311	0.277432
$342$	4.00000	0.216295
$343$	0	0
$344$	−6.24621	−0.336773
$345$	1.43845	0.0774434
$346$	6.63068	0.356468
$347$	−14.2462	−0.764777	−0.382388	−	0.924002i	$-0.624898\pi$
$347$	−14.2462	−0.764777	−0.382388	+	0.924002i	$0.624898\pi$
$348$	0.738634	0.0395949
$349$	9.19224	0.492049	0.246025	−	0.969264i	$-0.420876\pi$
$349$	9.19224	0.492049	0.246025	+	0.969264i	$0.420876\pi$
$350$	0	0
$351$	7.12311	0.380203
$352$	−2.43845	−0.129970
$353$	30.0000	1.59674	0.798369	−	0.602168i	$-0.205696\pi$
$353$	30.0000	1.59674	0.798369	+	0.602168i	$0.205696\pi$
$354$	−16.4924	−0.876562
$355$	−5.12311	−0.271906
$356$	1.01515	0.0538031
$357$	0	0
$358$	−30.2462	−1.59856
$359$	−4.31534	−0.227755	−0.113878	−	0.993495i	$-0.536327\pi$
$359$	−4.31534	−0.227755	−0.113878	+	0.993495i	$0.536327\pi$
$360$	2.43845	0.128517
$361$	−12.4384	−0.654655
$362$	31.6155	1.66168
$363$	1.00000	0.0524864
$364$	0	0
$365$	−11.1231	−0.582210
$366$	5.36932	0.280659
$367$	−17.4384	−0.910280	−0.455140	−	0.890420i	$-0.650411\pi$
$367$	−17.4384	−0.910280	−0.455140	+	0.890420i	$0.650411\pi$
$368$	6.73863	0.351276
$369$	−2.00000	−0.104116
$370$	11.1231	0.578263
$371$	0	0
$372$	2.24621	0.116461
$373$	−0.561553	−0.0290761	−0.0145381	−	0.999894i	$-0.504628\pi$
$373$	−0.561553	−0.0290761	−0.0145381	+	0.999894i	$0.504628\pi$
$374$	−0.876894	−0.0453431
$375$	−1.00000	−0.0516398
$376$	−12.4924	−0.644247
$377$	12.0000	0.618031
$378$	0	0
$379$	23.0540	1.18420	0.592102	−	0.805863i	$-0.298298\pi$
$379$	23.0540	1.18420	0.592102	+	0.805863i	$0.298298\pi$
$380$	−1.12311	−0.0576141
$381$	0.807764	0.0413830
$382$	0	0
$383$	12.4924	0.638333	0.319166	−	0.947699i	$-0.396597\pi$
$383$	12.4924	0.638333	0.319166	+	0.947699i	$0.396597\pi$
$384$	13.5616	0.692060
$385$	0	0
$386$	35.1231	1.78772
$387$	2.56155	0.130211
$388$	−1.23106	−0.0624974
$389$	−21.8617	−1.10843	−0.554217	−	0.832372i	$-0.686982\pi$
$389$	−21.8617	−1.10843	−0.554217	+	0.832372i	$0.686982\pi$
$390$	−11.1231	−0.563240
$391$	0.807764	0.0408504
$392$	0	0
$393$	−4.00000	−0.201773
$394$	−36.1080	−1.81909
$395$	10.2462	0.515543
$396$	0.438447	0.0220328
$397$	−14.0000	−0.702640	−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000	−0.702640	−0.351320	+	0.936255i	$0.614267\pi$
$398$	−32.0000	−1.60402
$399$	0	0
$400$	−4.68466	−0.234233
$401$	−34.4924	−1.72247	−0.861235	−	0.508207i	$-0.830308\pi$
$401$	−34.4924	−1.72247	−0.861235	+	0.508207i	$0.830308\pi$
$402$	10.7386	0.535594
$403$	36.4924	1.81782
$404$	5.36932	0.267133
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	−7.12311	−0.353079
$408$	1.36932	0.0677913
$409$	8.24621	0.407749	0.203874	−	0.978997i	$-0.434647\pi$
$409$	8.24621	0.407749	0.203874	+	0.978997i	$0.434647\pi$
$410$	3.12311	0.154239
$411$	10.0000	0.493264
$412$	−1.61553	−0.0795914
$413$	0	0
$414$	−2.24621	−0.110395
$415$	−5.43845	−0.266963
$416$	−17.3693	−0.851601
$417$	20.0000	0.979404
$418$	4.00000	0.195646
$419$	−11.1922	−0.546777	−0.273388	−	0.961904i	$-0.588144\pi$
$419$	−11.1922	−0.546777	−0.273388	+	0.961904i	$0.588144\pi$
$420$	0	0
$421$	30.1771	1.47074	0.735370	−	0.677665i	$-0.237008\pi$
$421$	30.1771	1.47074	0.735370	+	0.677665i	$0.237008\pi$
$422$	−5.26137	−0.256119
$423$	5.12311	0.249094
$424$	33.3693	1.62056
$425$	−0.561553	−0.0272393
$426$	8.00000	0.387601
$427$	0	0
$428$	8.49242	0.410497
$429$	7.12311	0.343907
$430$	−4.00000	−0.192897
$431$	−14.7386	−0.709935	−0.354968	−	0.934879i	$-0.615508\pi$
$431$	−14.7386	−0.709935	−0.354968	+	0.934879i	$0.615508\pi$
$432$	−4.68466	−0.225391
$433$	12.7386	0.612180	0.306090	−	0.952003i	$-0.400979\pi$
$433$	12.7386	0.612180	0.306090	+	0.952003i	$0.400979\pi$
$434$	0	0
$435$	−1.68466	−0.0807732
$436$	8.10795	0.388300
$437$	−3.68466	−0.176261
$438$	17.3693	0.829938
$439$	−21.9309	−1.04670	−0.523352	−	0.852117i	$-0.675319\pi$
$439$	−21.9309	−1.04670	−0.523352	+	0.852117i	$0.675319\pi$
$440$	2.43845	0.116248
$441$	0	0
$442$	−6.24621	−0.297102
$443$	−18.7386	−0.890299	−0.445150	−	0.895456i	$-0.646850\pi$
$443$	−18.7386	−0.890299	−0.445150	+	0.895456i	$0.646850\pi$
$444$	−3.12311	−0.148216
$445$	−2.31534	−0.109758
$446$	−22.7386	−1.07671
$447$	0.246211	0.0116454
$448$	0	0
$449$	2.00000	0.0943858	0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000	0.0943858	0.0471929	+	0.998886i	$0.484972\pi$
$450$	1.56155	0.0736123
$451$	−2.00000	−0.0941763
$452$	3.75379	0.176563
$453$	5.12311	0.240704
$454$	40.4924	1.90040
$455$	0	0
$456$	−6.24621	−0.292506
$457$	−18.3153	−0.856756	−0.428378	−	0.903600i	$-0.640915\pi$
$457$	−18.3153	−0.856756	−0.428378	+	0.903600i	$0.640915\pi$
$458$	−16.3845	−0.765596
$459$	−0.561553	−0.0262110
$460$	0.630683	0.0294058
$461$	−32.2462	−1.50186	−0.750928	−	0.660384i	$-0.770393\pi$
$461$	−32.2462	−1.50186	−0.750928	+	0.660384i	$0.770393\pi$
$462$	0	0
$463$	27.8617	1.29484	0.647422	−	0.762131i	$-0.275847\pi$
$463$	27.8617	1.29484	0.647422	+	0.762131i	$0.275847\pi$
$464$	−7.89205	−0.366379
$465$	−5.12311	−0.237578
$466$	−36.8769	−1.70829
$467$	−16.4924	−0.763178	−0.381589	−	0.924332i	$-0.624623\pi$
$467$	−16.4924	−0.763178	−0.381589	+	0.924332i	$0.624623\pi$
$468$	3.12311	0.144366
$469$	0	0
$470$	−8.00000	−0.369012
$471$	11.4384	0.527056
$472$	25.7538	1.18541
$473$	2.56155	0.117780
$474$	−16.0000	−0.734904
$475$	2.56155	0.117532
$476$	0	0
$477$	−13.6847	−0.626577
$478$	30.7386	1.40595
$479$	36.4924	1.66738	0.833691	−	0.552232i	$-0.186224\pi$
$479$	36.4924	1.66738	0.833691	+	0.552232i	$0.186224\pi$
$480$	2.43845	0.111299
$481$	−50.7386	−2.31348
$482$	0.384472	0.0175122
$483$	0	0
$484$	0.438447	0.0199294
$485$	2.80776	0.127494
$486$	1.56155	0.0708335
$487$	−9.61553	−0.435721	−0.217861	−	0.975980i	$-0.569908\pi$
$487$	−9.61553	−0.435721	−0.217861	+	0.975980i	$0.569908\pi$
$488$	−8.38447	−0.379547
$489$	20.0000	0.904431
$490$	0	0
$491$	33.3002	1.50282	0.751408	−	0.659838i	$-0.229375\pi$
$491$	33.3002	1.50282	0.751408	+	0.659838i	$0.229375\pi$
$492$	−0.876894	−0.0395335
$493$	−0.946025	−0.0426068
$494$	28.4924	1.28193
$495$	−1.00000	−0.0449467
$496$	−24.0000	−1.07763
$497$	0	0
$498$	8.49242	0.380555
$499$	−7.05398	−0.315779	−0.157890	−	0.987457i	$-0.550469\pi$
$499$	−7.05398	−0.315779	−0.157890	+	0.987457i	$0.550469\pi$
$500$	−0.438447	−0.0196080
$501$	−2.24621	−0.100353
$502$	−38.2462	−1.70701
$503$	40.8078	1.81953	0.909764	−	0.415126i	$-0.136262\pi$
$503$	40.8078	1.81953	0.909764	+	0.415126i	$0.136262\pi$
$504$	0	0
$505$	−12.2462	−0.544949
$506$	−2.24621	−0.0998563
$507$	37.7386	1.67603
$508$	0.354162	0.0157134
$509$	1.19224	0.0528449	0.0264225	−	0.999651i	$-0.491588\pi$
$509$	1.19224	0.0528449	0.0264225	+	0.999651i	$0.491588\pi$
$510$	0.876894	0.0388295
$511$	0	0
$512$	−11.4233	−0.504843
$513$	2.56155	0.113095
$514$	−14.6307	−0.645332
$515$	3.68466	0.162365
$516$	1.12311	0.0494420
$517$	5.12311	0.225314
$518$	0	0
$519$	4.24621	0.186388
$520$	17.3693	0.761695
$521$	3.93087	0.172215	0.0861073	−	0.996286i	$-0.472557\pi$
$521$	3.93087	0.172215	0.0861073	+	0.996286i	$0.472557\pi$
$522$	2.63068	0.115142
$523$	30.2462	1.32257	0.661287	−	0.750133i	$-0.270010\pi$
$523$	30.2462	1.32257	0.661287	+	0.750133i	$0.270010\pi$
$524$	−1.75379	−0.0766146
$525$	0	0
$526$	−28.4924	−1.24233
$527$	−2.87689	−0.125319
$528$	−4.68466	−0.203874
$529$	−20.9309	−0.910038
$530$	21.3693	0.928224
$531$	−10.5616	−0.458332
$532$	0	0
$533$	−14.2462	−0.617072
$534$	3.61553	0.156459
$535$	−19.3693	−0.837409
$536$	−16.7689	−0.724308
$537$	−19.3693	−0.835848
$538$	−2.63068	−0.113417
$539$	0	0
$540$	−0.438447	−0.0188678
$541$	−22.4924	−0.967025	−0.483512	−	0.875338i	$-0.660639\pi$
$541$	−22.4924	−0.967025	−0.483512	+	0.875338i	$0.660639\pi$
$542$	21.7538	0.934405
$543$	20.2462	0.868848
$544$	1.36932	0.0587090
$545$	−18.4924	−0.792128
$546$	0	0
$547$	−23.0540	−0.985717	−0.492858	−	0.870110i	$-0.664048\pi$
$547$	−23.0540	−0.985717	−0.492858	+	0.870110i	$0.664048\pi$
$548$	4.38447	0.187295
$549$	3.43845	0.146749
$550$	1.56155	0.0665848
$551$	4.31534	0.183840
$552$	3.50758	0.149292
$553$	0	0
$554$	−38.6307	−1.64126
$555$	7.12311	0.302359
$556$	8.76894	0.371886
$557$	18.4924	0.783549	0.391775	−	0.920061i	$-0.371861\pi$
$557$	18.4924	0.783549	0.391775	+	0.920061i	$0.371861\pi$
$558$	8.00000	0.338667
$559$	18.2462	0.771733
$560$	0	0
$561$	−0.561553	−0.0237088
$562$	22.6307	0.954618
$563$	−24.4924	−1.03223	−0.516116	−	0.856519i	$-0.672623\pi$
$563$	−24.4924	−1.03223	−0.516116	+	0.856519i	$0.672623\pi$
$564$	2.24621	0.0945826
$565$	−8.56155	−0.360187
$566$	−9.75379	−0.409982
$567$	0	0
$568$	−12.4924	−0.524170
$569$	−22.8078	−0.956151	−0.478076	−	0.878319i	$-0.658666\pi$
$569$	−22.8078	−0.956151	−0.478076	+	0.878319i	$0.658666\pi$
$570$	−4.00000	−0.167542
$571$	−14.2462	−0.596185	−0.298093	−	0.954537i	$-0.596350\pi$
$571$	−14.2462	−0.596185	−0.298093	+	0.954537i	$0.596350\pi$
$572$	3.12311	0.130584
$573$	0	0
$574$	0	0
$575$	−1.43845	−0.0599874
$576$	5.56155	0.231731
$577$	−26.9848	−1.12339	−0.561697	−	0.827343i	$-0.689851\pi$
$577$	−26.9848	−1.12339	−0.561697	+	0.827343i	$0.689851\pi$
$578$	−26.0540	−1.08370
$579$	22.4924	0.934753
$580$	−0.738634	−0.0306701
$581$	0	0
$582$	−4.38447	−0.181742
$583$	−13.6847	−0.566761
$584$	−27.1231	−1.12236
$585$	−7.12311	−0.294504
$586$	40.8769	1.68861
$587$	−28.9848	−1.19633	−0.598166	−	0.801372i	$-0.704104\pi$
$587$	−28.9848	−1.19633	−0.598166	+	0.801372i	$0.704104\pi$
$588$	0	0
$589$	13.1231	0.540728
$590$	16.4924	0.678982
$591$	−23.1231	−0.951157
$592$	33.3693	1.37147
$593$	0.246211	0.0101107	0.00505534	−	0.999987i	$-0.498391\pi$
$593$	0.246211	0.0101107	0.00505534	+	0.999987i	$0.498391\pi$
$594$	1.56155	0.0640713
$595$	0	0
$596$	0.107951	0.00442183
$597$	−20.4924	−0.838699
$598$	−16.0000	−0.654289
$599$	0.630683	0.0257690	0.0128845	−	0.999917i	$-0.495899\pi$
$599$	0.630683	0.0257690	0.0128845	+	0.999917i	$0.495899\pi$
$600$	−2.43845	−0.0995492
$601$	9.05398	0.369319	0.184660	−	0.982803i	$-0.440882\pi$
$601$	9.05398	0.369319	0.184660	+	0.982803i	$0.440882\pi$
$602$	0	0
$603$	6.87689	0.280049
$604$	2.24621	0.0913970
$605$	−1.00000	−0.0406558
$606$	19.1231	0.776823
$607$	−23.3693	−0.948531	−0.474266	−	0.880382i	$-0.657286\pi$
$607$	−23.3693	−0.948531	−0.474266	+	0.880382i	$0.657286\pi$
$608$	−6.24621	−0.253317
$609$	0	0
$610$	−5.36932	−0.217397
$611$	36.4924	1.47633
$612$	−0.246211	−0.00995250
$613$	−10.0000	−0.403896	−0.201948	−	0.979396i	$-0.564727\pi$
$613$	−10.0000	−0.403896	−0.201948	+	0.979396i	$0.564727\pi$
$614$	−17.7538	−0.716485
$615$	2.00000	0.0806478
$616$	0	0
$617$	4.24621	0.170946	0.0854730	−	0.996340i	$-0.472760\pi$
$617$	4.24621	0.170946	0.0854730	+	0.996340i	$0.472760\pi$
$618$	−5.75379	−0.231451
$619$	−1.12311	−0.0451414	−0.0225707	−	0.999745i	$-0.507185\pi$
$619$	−1.12311	−0.0451414	−0.0225707	+	0.999745i	$0.507185\pi$
$620$	−2.24621	−0.0902100
$621$	−1.43845	−0.0577229
$622$	24.9848	1.00180
$623$	0	0
$624$	−33.3693	−1.33584
$625$	1.00000	0.0400000
$626$	3.61553	0.144506
$627$	2.56155	0.102299
$628$	5.01515	0.200126
$629$	4.00000	0.159490
$630$	0	0
$631$	29.3002	1.16642	0.583211	−	0.812321i	$-0.301796\pi$
$631$	29.3002	1.16642	0.583211	+	0.812321i	$0.301796\pi$
$632$	24.9848	0.993844
$633$	−3.36932	−0.133918
$634$	−35.1231	−1.39492
$635$	−0.807764	−0.0320551
$636$	−6.00000	−0.237915
$637$	0	0
$638$	2.63068	0.104150
$639$	5.12311	0.202667
$640$	−13.5616	−0.536067
$641$	−12.7386	−0.503146	−0.251573	−	0.967838i	$-0.580948\pi$
$641$	−12.7386	−0.503146	−0.251573	+	0.967838i	$0.580948\pi$
$642$	30.2462	1.19372
$643$	25.3002	0.997742	0.498871	−	0.866676i	$-0.333748\pi$
$643$	25.3002	0.997742	0.498871	+	0.866676i	$0.333748\pi$
$644$	0	0
$645$	−2.56155	−0.100861
$646$	−2.24621	−0.0883760
$647$	10.2462	0.402820	0.201410	−	0.979507i	$-0.435448\pi$
$647$	10.2462	0.402820	0.201410	+	0.979507i	$0.435448\pi$
$648$	−2.43845	−0.0957913
$649$	−10.5616	−0.414577
$650$	11.1231	0.436284
$651$	0	0
$652$	8.76894	0.343418
$653$	6.17708	0.241728	0.120864	−	0.992669i	$-0.461434\pi$
$653$	6.17708	0.241728	0.120864	+	0.992669i	$0.461434\pi$
$654$	28.8769	1.12918
$655$	4.00000	0.156293
$656$	9.36932	0.365810
$657$	11.1231	0.433954
$658$	0	0
$659$	0.315342	0.0122840	0.00614198	−	0.999981i	$-0.498045\pi$
$659$	0.315342	0.0122840	0.00614198	+	0.999981i	$0.498045\pi$
$660$	−0.438447	−0.0170665
$661$	−10.4924	−0.408108	−0.204054	−	0.978960i	$-0.565412\pi$
$661$	−10.4924	−0.408108	−0.204054	+	0.978960i	$0.565412\pi$
$662$	−36.9848	−1.43746
$663$	−4.00000	−0.155347
$664$	−13.2614	−0.514641
$665$	0	0
$666$	−11.1231	−0.431012
$667$	−2.42329	−0.0938302
$668$	−0.984845	−0.0381048
$669$	−14.5616	−0.562982
$670$	−10.7386	−0.414870
$671$	3.43845	0.132740
$672$	0	0
$673$	8.56155	0.330024	0.165012	−	0.986292i	$-0.447234\pi$
$673$	8.56155	0.330024	0.165012	+	0.986292i	$0.447234\pi$
$674$	−14.1383	−0.544585
$675$	1.00000	0.0384900
$676$	16.5464	0.636400
$677$	−16.0691	−0.617587	−0.308793	−	0.951129i	$-0.599925\pi$
$677$	−16.0691	−0.617587	−0.308793	+	0.951129i	$0.599925\pi$
$678$	13.3693	0.513446
$679$	0	0
$680$	−1.36932	−0.0525109
$681$	25.9309	0.993673
$682$	8.00000	0.306336
$683$	−40.4924	−1.54940	−0.774700	−	0.632329i	$-0.782099\pi$
$683$	−40.4924	−1.54940	−0.774700	+	0.632329i	$0.782099\pi$
$684$	1.12311	0.0429430
$685$	−10.0000	−0.382080
$686$	0	0
$687$	−10.4924	−0.400311
$688$	−12.0000	−0.457496
$689$	−97.4773	−3.71359
$690$	2.24621	0.0855118
$691$	−30.8769	−1.17461	−0.587306	−	0.809365i	$-0.699812\pi$
$691$	−30.8769	−1.17461	−0.587306	+	0.809365i	$0.699812\pi$
$692$	1.86174	0.0707727
$693$	0	0
$694$	−22.2462	−0.844455
$695$	−20.0000	−0.758643
$696$	−4.10795	−0.155711
$697$	1.12311	0.0425407
$698$	14.3542	0.543313
$699$	−23.6155	−0.893221
$700$	0	0
$701$	26.3153	0.993917	0.496958	−	0.867774i	$-0.334450\pi$
$701$	26.3153	0.993917	0.496958	+	0.867774i	$0.334450\pi$
$702$	11.1231	0.419815
$703$	−18.2462	−0.688169
$704$	5.56155	0.209609
$705$	−5.12311	−0.192947
$706$	46.8466	1.76309
$707$	0	0
$708$	−4.63068	−0.174032
$709$	−42.8078	−1.60768	−0.803840	−	0.594846i	$-0.797213\pi$
$709$	−42.8078	−1.60768	−0.803840	+	0.594846i	$0.797213\pi$
$710$	−8.00000	−0.300235
$711$	−10.2462	−0.384263
$712$	−5.64584	−0.211587
$713$	−7.36932	−0.275983
$714$	0	0
$715$	−7.12311	−0.266389
$716$	−8.49242	−0.317377
$717$	19.6847	0.735137
$718$	−6.73863	−0.251484
$719$	−23.5464	−0.878132	−0.439066	−	0.898455i	$-0.644691\pi$
$719$	−23.5464	−0.878132	−0.439066	+	0.898455i	$0.644691\pi$
$720$	4.68466	0.174587
$721$	0	0
$722$	−19.4233	−0.722860
$723$	0.246211	0.00915669
$724$	8.87689	0.329907
$725$	1.68466	0.0625666
$726$	1.56155	0.0579547
$727$	−22.5616	−0.836762	−0.418381	−	0.908272i	$-0.637402\pi$
$727$	−22.5616	−0.836762	−0.418381	+	0.908272i	$0.637402\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−17.3693	−0.642867
$731$	−1.43845	−0.0532029
$732$	1.50758	0.0557217
$733$	52.2462	1.92976	0.964879	−	0.262695i	$-0.0846113\pi$
$733$	52.2462	1.92976	0.964879	+	0.262695i	$0.0846113\pi$
$734$	−27.2311	−1.00512
$735$	0	0
$736$	3.50758	0.129291
$737$	6.87689	0.253314
$738$	−3.12311	−0.114963
$739$	−4.63068	−0.170342	−0.0851712	−	0.996366i	$-0.527144\pi$
$739$	−4.63068	−0.170342	−0.0851712	+	0.996366i	$0.527144\pi$
$740$	3.12311	0.114808
$741$	18.2462	0.670291
$742$	0	0
$743$	6.38447	0.234224	0.117112	−	0.993119i	$-0.462636\pi$
$743$	6.38447	0.234224	0.117112	+	0.993119i	$0.462636\pi$
$744$	−12.4924	−0.457994
$745$	−0.246211	−0.00902048
$746$	−0.876894	−0.0321054
$747$	5.43845	0.198982
$748$	−0.246211	−0.00900237
$749$	0	0
$750$	−1.56155	−0.0570198
$751$	−3.68466	−0.134455	−0.0672275	−	0.997738i	$-0.521415\pi$
$751$	−3.68466	−0.134455	−0.0672275	+	0.997738i	$0.521415\pi$
$752$	−24.0000	−0.875190
$753$	−24.4924	−0.892553
$754$	18.7386	0.682421
$755$	−5.12311	−0.186449
$756$	0	0
$757$	1.50758	0.0547938	0.0273969	−	0.999625i	$-0.491278\pi$
$757$	1.50758	0.0547938	0.0273969	+	0.999625i	$0.491278\pi$
$758$	36.0000	1.30758
$759$	−1.43845	−0.0522123
$760$	6.24621	0.226574
$761$	3.75379	0.136075	0.0680374	−	0.997683i	$-0.478326\pi$
$761$	3.75379	0.136075	0.0680374	+	0.997683i	$0.478326\pi$
$762$	1.26137	0.0456945
$763$	0	0
$764$	0	0
$765$	0.561553	0.0203030
$766$	19.5076	0.704837
$767$	−75.2311	−2.71644
$768$	10.0540	0.362792
$769$	−1.82292	−0.0657361	−0.0328681	−	0.999460i	$-0.510464\pi$
$769$	−1.82292	−0.0657361	−0.0328681	+	0.999460i	$0.510464\pi$
$770$	0	0
$771$	−9.36932	−0.337428
$772$	9.86174	0.354932
$773$	24.7386	0.889787	0.444893	−	0.895584i	$-0.353242\pi$
$773$	24.7386	0.889787	0.444893	+	0.895584i	$0.353242\pi$
$774$	4.00000	0.143777
$775$	5.12311	0.184027
$776$	6.84658	0.245778
$777$	0	0
$778$	−34.1383	−1.22392
$779$	−5.12311	−0.183554
$780$	−3.12311	−0.111825
$781$	5.12311	0.183319
$782$	1.26137	0.0451064
$783$	1.68466	0.0602048
$784$	0	0
$785$	−11.4384	−0.408256
$786$	−6.24621	−0.222795
$787$	32.4924	1.15823	0.579115	−	0.815246i	$-0.303398\pi$
$787$	32.4924	1.15823	0.579115	+	0.815246i	$0.303398\pi$
$788$	−10.1383	−0.361161
$789$	−18.2462	−0.649582
$790$	16.0000	0.569254
$791$	0	0
$792$	−2.43845	−0.0866464
$793$	24.4924	0.869751
$794$	−21.8617	−0.775844
$795$	13.6847	0.485345
$796$	−8.98485	−0.318459
$797$	−12.7386	−0.451226	−0.225613	−	0.974217i	$-0.572438\pi$
$797$	−12.7386	−0.451226	−0.225613	+	0.974217i	$0.572438\pi$
$798$	0	0
$799$	−2.87689	−0.101777
$800$	−2.43845	−0.0862121
$801$	2.31534	0.0818086
$802$	−53.8617	−1.90192
$803$	11.1231	0.392526
$804$	3.01515	0.106336
$805$	0	0
$806$	56.9848	2.00721
$807$	−1.68466	−0.0593028
$808$	−29.8617	−1.05053
$809$	26.0000	0.914111	0.457056	−	0.889438i	$-0.348904\pi$
$809$	26.0000	0.914111	0.457056	+	0.889438i	$0.348904\pi$
$810$	−1.56155	−0.0548674
$811$	4.00000	0.140459	0.0702295	−	0.997531i	$-0.477627\pi$
$811$	4.00000	0.140459	0.0702295	+	0.997531i	$0.477627\pi$
$812$	0	0
$813$	13.9309	0.488577
$814$	−11.1231	−0.389865
$815$	−20.0000	−0.700569
$816$	2.63068	0.0920923
$817$	6.56155	0.229560
$818$	12.8769	0.450230
$819$	0	0
$820$	0.876894	0.0306225
$821$	37.5464	1.31038	0.655189	−	0.755465i	$-0.272589\pi$
$821$	37.5464	1.31038	0.655189	+	0.755465i	$0.272589\pi$
$822$	15.6155	0.544654
$823$	−22.7386	−0.792619	−0.396309	−	0.918117i	$-0.629709\pi$
$823$	−22.7386	−0.792619	−0.396309	+	0.918117i	$0.629709\pi$
$824$	8.98485	0.313002
$825$	1.00000	0.0348155
$826$	0	0
$827$	−2.73863	−0.0952316	−0.0476158	−	0.998866i	$-0.515162\pi$
$827$	−2.73863	−0.0952316	−0.0476158	+	0.998866i	$0.515162\pi$
$828$	−0.630683	−0.0219178
$829$	−33.2311	−1.15416	−0.577081	−	0.816687i	$-0.695808\pi$
$829$	−33.2311	−1.15416	−0.577081	+	0.816687i	$0.695808\pi$
$830$	−8.49242	−0.294776
$831$	−24.7386	−0.858174
$832$	39.6155	1.37342
$833$	0	0
$834$	31.2311	1.08144
$835$	2.24621	0.0777333
$836$	1.12311	0.0388434
$837$	5.12311	0.177080
$838$	−17.4773	−0.603742
$839$	34.4233	1.18842	0.594212	−	0.804308i	$-0.297464\pi$
$839$	34.4233	1.18842	0.594212	+	0.804308i	$0.297464\pi$
$840$	0	0
$841$	−26.1619	−0.902135
$842$	47.1231	1.62397
$843$	14.4924	0.499146
$844$	−1.47727	−0.0508496
$845$	−37.7386	−1.29825
$846$	8.00000	0.275046
$847$	0	0
$848$	64.1080	2.20148
$849$	−6.24621	−0.214369
$850$	−0.876894	−0.0300772
$851$	10.2462	0.351236
$852$	2.24621	0.0769539
$853$	−2.49242	−0.0853389	−0.0426695	−	0.999089i	$-0.513586\pi$
$853$	−2.49242	−0.0853389	−0.0426695	+	0.999089i	$0.513586\pi$
$854$	0	0
$855$	−2.56155	−0.0876033
$856$	−47.2311	−1.61432
$857$	−13.5076	−0.461410	−0.230705	−	0.973024i	$-0.574103\pi$
$857$	−13.5076	−0.461410	−0.230705	+	0.973024i	$0.574103\pi$
$858$	11.1231	0.379737
$859$	41.1231	1.40310	0.701551	−	0.712619i	$-0.252491\pi$
$859$	41.1231	1.40310	0.701551	+	0.712619i	$0.252491\pi$
$860$	−1.12311	−0.0382976
$861$	0	0
$862$	−23.0152	−0.783899
$863$	31.5464	1.07385	0.536926	−	0.843629i	$-0.319585\pi$
$863$	31.5464	1.07385	0.536926	+	0.843629i	$0.319585\pi$
$864$	−2.43845	−0.0829577
$865$	−4.24621	−0.144376
$866$	19.8920	0.675959
$867$	−16.6847	−0.566641
$868$	0	0
$869$	−10.2462	−0.347579
$870$	−2.63068	−0.0891885
$871$	48.9848	1.65979
$872$	−45.0928	−1.52703
$873$	−2.80776	−0.0950284
$874$	−5.75379	−0.194625
$875$	0	0
$876$	4.87689	0.164775
$877$	−46.6695	−1.57592	−0.787959	−	0.615728i	$-0.788862\pi$
$877$	−46.6695	−1.57592	−0.787959	+	0.615728i	$0.788862\pi$
$878$	−34.2462	−1.15575
$879$	26.1771	0.882931
$880$	4.68466	0.157920
$881$	−31.9309	−1.07578	−0.537889	−	0.843016i	$-0.680778\pi$
$881$	−31.9309	−1.07578	−0.537889	+	0.843016i	$0.680778\pi$
$882$	0	0
$883$	−44.0000	−1.48072	−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000	−1.48072	−0.740359	+	0.672212i	$0.765344\pi$
$884$	−1.75379	−0.0589863
$885$	10.5616	0.355023
$886$	−29.2614	−0.983055
$887$	33.4384	1.12275	0.561377	−	0.827560i	$-0.310272\pi$
$887$	33.4384	1.12275	0.561377	+	0.827560i	$0.310272\pi$
$888$	17.3693	0.582876
$889$	0	0
$890$	−3.61553	−0.121193
$891$	1.00000	0.0335013
$892$	−6.38447	−0.213768
$893$	13.1231	0.439148
$894$	0.384472	0.0128587
$895$	19.3693	0.647445
$896$	0	0
$897$	−10.2462	−0.342111
$898$	3.12311	0.104219
$899$	8.63068	0.287849
$900$	0.438447	0.0146149
$901$	7.68466	0.256013
$902$	−3.12311	−0.103988
$903$	0	0
$904$	−20.8769	−0.694355
$905$	−20.2462	−0.673007
$906$	8.00000	0.265782
$907$	57.4773	1.90850	0.954251	−	0.299008i	$-0.0966557\pi$
$907$	57.4773	1.90850	0.954251	+	0.299008i	$0.0966557\pi$
$908$	11.3693	0.377304
$909$	12.2462	0.406181
$910$	0	0
$911$	20.4924	0.678944	0.339472	−	0.940616i	$-0.389752\pi$
$911$	20.4924	0.678944	0.339472	+	0.940616i	$0.389752\pi$
$912$	−12.0000	−0.397360
$913$	5.43845	0.179986
$914$	−28.6004	−0.946016
$915$	−3.43845	−0.113672
$916$	−4.60037	−0.152001
$917$	0	0
$918$	−0.876894	−0.0289418
$919$	−19.8617	−0.655178	−0.327589	−	0.944820i	$-0.606236\pi$
$919$	−19.8617	−0.655178	−0.327589	+	0.944820i	$0.606236\pi$
$920$	−3.50758	−0.115641
$921$	−11.3693	−0.374632
$922$	−50.3542	−1.65833
$923$	36.4924	1.20116
$924$	0	0
$925$	−7.12311	−0.234206
$926$	43.5076	1.42975
$927$	−3.68466	−0.121020
$928$	−4.10795	−0.134850
$929$	22.9848	0.754108	0.377054	−	0.926191i	$-0.376937\pi$
$929$	22.9848	0.754108	0.377054	+	0.926191i	$0.376937\pi$
$930$	−8.00000	−0.262330
$931$	0	0
$932$	−10.3542	−0.339162
$933$	16.0000	0.523816
$934$	−25.7538	−0.842690
$935$	0.561553	0.0183647
$936$	−17.3693	−0.567734
$937$	−2.00000	−0.0653372	−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000	−0.0653372	−0.0326686	+	0.999466i	$0.510401\pi$
$938$	0	0
$939$	2.31534	0.0755583
$940$	−2.24621	−0.0732633
$941$	−7.61553	−0.248259	−0.124130	−	0.992266i	$-0.539614\pi$
$941$	−7.61553	−0.248259	−0.124130	+	0.992266i	$0.539614\pi$
$942$	17.8617	0.581967
$943$	2.87689	0.0936846
$944$	49.4773	1.61035
$945$	0	0
$946$	4.00000	0.130051
$947$	31.0540	1.00912	0.504559	−	0.863377i	$-0.331655\pi$
$947$	31.0540	1.00912	0.504559	+	0.863377i	$0.331655\pi$
$948$	−4.49242	−0.145907
$949$	79.2311	2.57195
$950$	4.00000	0.129777
$951$	−22.4924	−0.729367
$952$	0	0
$953$	15.7538	0.510315	0.255158	−	0.966899i	$-0.417873\pi$
$953$	15.7538	0.510315	0.255158	+	0.966899i	$0.417873\pi$
$954$	−21.3693	−0.691857
$955$	0	0
$956$	8.63068	0.279136
$957$	1.68466	0.0544573
$958$	56.9848	1.84110
$959$	0	0
$960$	−5.56155	−0.179498
$961$	−4.75379	−0.153348
$962$	−79.2311	−2.55451
$963$	19.3693	0.624168
$964$	0.107951	0.00347686
$965$	−22.4924	−0.724057
$966$	0	0
$967$	30.5616	0.982793	0.491397	−	0.870936i	$-0.336487\pi$
$967$	30.5616	0.982793	0.491397	+	0.870936i	$0.336487\pi$
$968$	−2.43845	−0.0783747
$969$	−1.43845	−0.0462096
$970$	4.38447	0.140777
$971$	−4.80776	−0.154288	−0.0771442	−	0.997020i	$-0.524580\pi$
$971$	−4.80776	−0.154288	−0.0771442	+	0.997020i	$0.524580\pi$
$972$	0.438447	0.0140632
$973$	0	0
$974$	−15.0152	−0.481117
$975$	7.12311	0.228122
$976$	−16.1080	−0.515603
$977$	−6.17708	−0.197622	−0.0988112	−	0.995106i	$-0.531504\pi$
$977$	−6.17708	−0.197622	−0.0988112	+	0.995106i	$0.531504\pi$
$978$	31.2311	0.998659
$979$	2.31534	0.0739986
$980$	0	0
$981$	18.4924	0.590418
$982$	52.0000	1.65939
$983$	−49.6155	−1.58249	−0.791245	−	0.611500i	$-0.790567\pi$
$983$	−49.6155	−1.58249	−0.791245	+	0.611500i	$0.790567\pi$
$984$	4.87689	0.155470
$985$	23.1231	0.736763
$986$	−1.47727	−0.0470458
$987$	0	0
$988$	8.00000	0.254514
$989$	−3.68466	−0.117165
$990$	−1.56155	−0.0496294
$991$	57.4384	1.82459	0.912296	−	0.409531i	$-0.134308\pi$
$991$	57.4384	1.82459	0.912296	+	0.409531i	$0.134308\pi$
$992$	−12.4924	−0.396635
$993$	−23.6847	−0.751610
$994$	0	0
$995$	20.4924	0.649653
$996$	2.38447	0.0755549
$997$	2.00000	0.0633406	0.0316703	−	0.999498i	$-0.489917\pi$
$997$	2.00000	0.0633406	0.0316703	+	0.999498i	$0.489917\pi$
$998$	−11.0152	−0.348679
$999$	−7.12311	−0.225365

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8085.2.a.bb.1.2		2
7.6	odd	2		1155.2.a.o.1.2	✓	2
21.20	even	2		3465.2.a.z.1.1		2
35.34	odd	2		5775.2.a.bm.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.a.o.1.2	✓	2	7.6	odd	2
3465.2.a.z.1.1		2	21.20	even	2
5775.2.a.bm.1.1		2	35.34	odd	2
8085.2.a.bb.1.2		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8085.a (trivial)

\(f(q)\)	\(=\)	\(q+1.56155 q^{2} +1.00000 q^{3} +0.438447 q^{4} -1.00000 q^{5} +1.56155 q^{6} -2.43845 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.56155 q^{2} +1.00000 q^{3} +0.438447 q^{4} -1.00000 q^{5} +1.56155 q^{6} -2.43845 q^{8} +1.00000 q^{9} -1.56155 q^{10} +1.00000 q^{11} +0.438447 q^{12} +7.12311 q^{13} -1.00000 q^{15} -4.68466 q^{16} -0.561553 q^{17} +1.56155 q^{18} +2.56155 q^{19} -0.438447 q^{20} +1.56155 q^{22} -1.43845 q^{23} -2.43845 q^{24} +1.00000 q^{25} +11.1231 q^{26} +1.00000 q^{27} +1.68466 q^{29} -1.56155 q^{30} +5.12311 q^{31} -2.43845 q^{32} +1.00000 q^{33} -0.876894 q^{34} +0.438447 q^{36} -7.12311 q^{37} +4.00000 q^{38} +7.12311 q^{39} +2.43845 q^{40} -2.00000 q^{41} +2.56155 q^{43} +0.438447 q^{44} -1.00000 q^{45} -2.24621 q^{46} +5.12311 q^{47} -4.68466 q^{48} +1.56155 q^{50} -0.561553 q^{51} +3.12311 q^{52} -13.6847 q^{53} +1.56155 q^{54} -1.00000 q^{55} +2.56155 q^{57} +2.63068 q^{58} -10.5616 q^{59} -0.438447 q^{60} +3.43845 q^{61} +8.00000 q^{62} +5.56155 q^{64} -7.12311 q^{65} +1.56155 q^{66} +6.87689 q^{67} -0.246211 q^{68} -1.43845 q^{69} +5.12311 q^{71} -2.43845 q^{72} +11.1231 q^{73} -11.1231 q^{74} +1.00000 q^{75} +1.12311 q^{76} +11.1231 q^{78} -10.2462 q^{79} +4.68466 q^{80} +1.00000 q^{81} -3.12311 q^{82} +5.43845 q^{83} +0.561553 q^{85} +4.00000 q^{86} +1.68466 q^{87} -2.43845 q^{88} +2.31534 q^{89} -1.56155 q^{90} -0.630683 q^{92} +5.12311 q^{93} +8.00000 q^{94} -2.56155 q^{95} -2.43845 q^{96} -2.80776 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 2 q^{3} + 5 q^{4} - 2 q^{5} - q^{6} - 9 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 + 2 * q^3 + 5 * q^4 - 2 * q^5 - q^6 - 9 * q^8 + 2 * q^9	\( 2 q - q^{2} + 2 q^{3} + 5 q^{4} - 2 q^{5} - q^{6} - 9 q^{8} + 2 q^{9} + q^{10} + 2 q^{11} + 5 q^{12} + 6 q^{13} - 2 q^{15} + 3 q^{16} + 3 q^{17} - q^{18} + q^{19} - 5 q^{20} - q^{22} - 7 q^{23} - 9 q^{24} + 2 q^{25} + 14 q^{26} + 2 q^{27} - 9 q^{29} + q^{30} + 2 q^{31} - 9 q^{32} + 2 q^{33} - 10 q^{34} + 5 q^{36} - 6 q^{37} + 8 q^{38} + 6 q^{39} + 9 q^{40} - 4 q^{41} + q^{43} + 5 q^{44} - 2 q^{45} + 12 q^{46} + 2 q^{47} + 3 q^{48} - q^{50} + 3 q^{51} - 2 q^{52} - 15 q^{53} - q^{54} - 2 q^{55} + q^{57} + 30 q^{58} - 17 q^{59} - 5 q^{60} + 11 q^{61} + 16 q^{62} + 7 q^{64} - 6 q^{65} - q^{66} + 22 q^{67} + 16 q^{68} - 7 q^{69} + 2 q^{71} - 9 q^{72} + 14 q^{73} - 14 q^{74} + 2 q^{75} - 6 q^{76} + 14 q^{78} - 4 q^{79} - 3 q^{80} + 2 q^{81} + 2 q^{82} + 15 q^{83} - 3 q^{85} + 8 q^{86} - 9 q^{87} - 9 q^{88} + 17 q^{89} + q^{90} - 26 q^{92} + 2 q^{93} + 16 q^{94} - q^{95} - 9 q^{96} + 15 q^{97} + 2 q^{99}+O(q^{100}) \) 2 * q - q^2 + 2 * q^3 + 5 * q^4 - 2 * q^5 - q^6 - 9 * q^8 + 2 * q^9 + q^10 + 2 * q^11 + 5 * q^12 + 6 * q^13 - 2 * q^15 + 3 * q^16 + 3 * q^17 - q^18 + q^19 - 5 * q^20 - q^22 - 7 * q^23 - 9 * q^24 + 2 * q^25 + 14 * q^26 + 2 * q^27 - 9 * q^29 + q^30 + 2 * q^31 - 9 * q^32 + 2 * q^33 - 10 * q^34 + 5 * q^36 - 6 * q^37 + 8 * q^38 + 6 * q^39 + 9 * q^40 - 4 * q^41 + q^43 + 5 * q^44 - 2 * q^45 + 12 * q^46 + 2 * q^47 + 3 * q^48 - q^50 + 3 * q^51 - 2 * q^52 - 15 * q^53 - q^54 - 2 * q^55 + q^57 + 30 * q^58 - 17 * q^59 - 5 * q^60 + 11 * q^61 + 16 * q^62 + 7 * q^64 - 6 * q^65 - q^66 + 22 * q^67 + 16 * q^68 - 7 * q^69 + 2 * q^71 - 9 * q^72 + 14 * q^73 - 14 * q^74 + 2 * q^75 - 6 * q^76 + 14 * q^78 - 4 * q^79 - 3 * q^80 + 2 * q^81 + 2 * q^82 + 15 * q^83 - 3 * q^85 + 8 * q^86 - 9 * q^87 - 9 * q^88 + 17 * q^89 + q^90 - 26 * q^92 + 2 * q^93 + 16 * q^94 - q^95 - 9 * q^96 + 15 * q^97 + 2 * q^99

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