LMFDB - Embedded newform 2695.2.a.t.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2695,2,Mod(1,2695)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2695, 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("2695.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2695 = 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2695.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:	$21.5196833447$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 8x^{6} + 26x^{5} + 15x^{4} - 60x^{3} - 2x^{2} + 37x - 9 $ x^8 - 3x^7 - 8x^6 + 26x^5 + 15x^4 - 60x^3 - 2x^2 + 37*x - 9
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$2.51872$ of defining polynomial
Character	$\chi$	$=$	2695.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.51872 q^{2} -3.29098 q^{3} +4.34396 q^{4} +1.00000 q^{5} -8.28906 q^{6} +5.90377 q^{8} +7.83055 q^{9} +O(q^{10})$	\(q+2.51872 q^{2} -3.29098 q^{3} +4.34396 q^{4} +1.00000 q^{5} -8.28906 q^{6} +5.90377 q^{8} +7.83055 q^{9} +2.51872 q^{10} -1.00000 q^{11} -14.2959 q^{12} +5.30061 q^{13} -3.29098 q^{15} +6.18204 q^{16} +1.79311 q^{17} +19.7230 q^{18} -5.49034 q^{19} +4.34396 q^{20} -2.51872 q^{22} -0.509528 q^{23} -19.4292 q^{24} +1.00000 q^{25} +13.3508 q^{26} -15.8972 q^{27} +4.77451 q^{29} -8.28906 q^{30} +5.61984 q^{31} +3.76329 q^{32} +3.29098 q^{33} +4.51634 q^{34} +34.0156 q^{36} -6.19498 q^{37} -13.8286 q^{38} -17.4442 q^{39} +5.90377 q^{40} +1.28221 q^{41} +6.22470 q^{43} -4.34396 q^{44} +7.83055 q^{45} -1.28336 q^{46} +11.1724 q^{47} -20.3450 q^{48} +2.51872 q^{50} -5.90108 q^{51} +23.0256 q^{52} +1.88528 q^{53} -40.0407 q^{54} -1.00000 q^{55} +18.0686 q^{57} +12.0257 q^{58} -5.80252 q^{59} -14.2959 q^{60} +1.94382 q^{61} +14.1548 q^{62} -2.88540 q^{64} +5.30061 q^{65} +8.28906 q^{66} +1.77944 q^{67} +7.78918 q^{68} +1.67685 q^{69} -3.97341 q^{71} +46.2298 q^{72} +2.99761 q^{73} -15.6034 q^{74} -3.29098 q^{75} -23.8498 q^{76} -43.9371 q^{78} +4.63677 q^{79} +6.18204 q^{80} +28.8259 q^{81} +3.22953 q^{82} +4.07571 q^{83} +1.79311 q^{85} +15.6783 q^{86} -15.7128 q^{87} -5.90377 q^{88} +3.11717 q^{89} +19.7230 q^{90} -2.21337 q^{92} -18.4948 q^{93} +28.1402 q^{94} -5.49034 q^{95} -12.3849 q^{96} +12.0725 q^{97} -7.83055 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} + q^{3} + 9 q^{4} + 8 q^{5} - 3 q^{6} + 9 q^{8} + 19 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 + q^3 + 9 * q^4 + 8 * q^5 - 3 * q^6 + 9 * q^8 + 19 * q^9	$ 8 q + 3 q^{2} + q^{3} + 9 q^{4} + 8 q^{5} - 3 q^{6} + 9 q^{8} + 19 q^{9} + 3 q^{10} - 8 q^{11} + 9 q^{12} + 14 q^{13} + q^{15} + 7 q^{16} + 5 q^{17} + 27 q^{18} + q^{19} + 9 q^{20} - 3 q^{22} - 2 q^{23} - 24 q^{24} + 8 q^{25} + 21 q^{26} - 5 q^{27} + 26 q^{29} - 3 q^{30} + 2 q^{31} + 16 q^{32} - q^{33} - 26 q^{34} + 54 q^{36} - q^{37} - 31 q^{38} + 19 q^{39} + 9 q^{40} - 3 q^{41} + 4 q^{43} - 9 q^{44} + 19 q^{45} + 10 q^{46} + q^{47} - 21 q^{48} + 3 q^{50} + 3 q^{51} + 37 q^{52} + 26 q^{53} - 5 q^{54} - 8 q^{55} + 20 q^{57} - q^{58} - 19 q^{59} + 9 q^{60} - 26 q^{62} + q^{64} + 14 q^{65} + 3 q^{66} - 13 q^{67} + 15 q^{68} - 14 q^{69} - 9 q^{71} + 32 q^{72} + 11 q^{73} + 24 q^{74} + q^{75} - 18 q^{76} - 33 q^{78} - 8 q^{79} + 7 q^{80} + 52 q^{81} + 41 q^{82} + 32 q^{83} + 5 q^{85} + 28 q^{86} - 16 q^{87} - 9 q^{88} + 5 q^{89} + 27 q^{90} + 30 q^{92} - 14 q^{93} - 5 q^{94} + q^{95} + q^{96} + 9 q^{97} - 19 q^{99}+O(q^{100}) $ 8 * q + 3 * q^2 + q^3 + 9 * q^4 + 8 * q^5 - 3 * q^6 + 9 * q^8 + 19 * q^9 + 3 * q^10 - 8 * q^11 + 9 * q^12 + 14 * q^13 + q^15 + 7 * q^16 + 5 * q^17 + 27 * q^18 + q^19 + 9 * q^20 - 3 * q^22 - 2 * q^23 - 24 * q^24 + 8 * q^25 + 21 * q^26 - 5 * q^27 + 26 * q^29 - 3 * q^30 + 2 * q^31 + 16 * q^32 - q^33 - 26 * q^34 + 54 * q^36 - q^37 - 31 * q^38 + 19 * q^39 + 9 * q^40 - 3 * q^41 + 4 * q^43 - 9 * q^44 + 19 * q^45 + 10 * q^46 + q^47 - 21 * q^48 + 3 * q^50 + 3 * q^51 + 37 * q^52 + 26 * q^53 - 5 * q^54 - 8 * q^55 + 20 * q^57 - q^58 - 19 * q^59 + 9 * q^60 - 26 * q^62 + q^64 + 14 * q^65 + 3 * q^66 - 13 * q^67 + 15 * q^68 - 14 * q^69 - 9 * q^71 + 32 * q^72 + 11 * q^73 + 24 * q^74 + q^75 - 18 * q^76 - 33 * q^78 - 8 * q^79 + 7 * q^80 + 52 * q^81 + 41 * q^82 + 32 * q^83 + 5 * q^85 + 28 * q^86 - 16 * q^87 - 9 * q^88 + 5 * q^89 + 27 * q^90 + 30 * q^92 - 14 * q^93 - 5 * q^94 + q^95 + q^96 + 9 * q^97 - 19 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.51872	1.78100	0.890502	−	0.454979i	$-0.150353\pi$
$2$	2.51872	1.78100	0.890502	+	0.454979i	$0.150353\pi$
$3$	−3.29098	−1.90005	−0.950024	−	0.312177i	$-0.898942\pi$
$3$	−3.29098	−1.90005	−0.950024	+	0.312177i	$0.898942\pi$
$4$	4.34396	2.17198
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−8.28906	−3.38399
$7$	0	0
$7$	0	0
$8$	5.90377	2.08730
$9$	7.83055	2.61018
$10$	2.51872	0.796490
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−14.2959	−4.12686
$13$	5.30061	1.47013	0.735063	−	0.677999i	$-0.237153\pi$
$13$	5.30061	1.47013	0.735063	+	0.677999i	$0.237153\pi$
$14$	0	0
$15$	−3.29098	−0.849727
$16$	6.18204	1.54551
$17$	1.79311	0.434893	0.217446	−	0.976072i	$-0.430227\pi$
$17$	1.79311	0.434893	0.217446	+	0.976072i	$0.430227\pi$
$18$	19.7230	4.64875
$19$	−5.49034	−1.25957	−0.629785	−	0.776770i	$-0.716857\pi$
$19$	−5.49034	−1.25957	−0.629785	+	0.776770i	$0.716857\pi$
$20$	4.34396	0.971338
$21$	0	0
$22$	−2.51872	−0.536993
$23$	−0.509528	−0.106244	−0.0531219	−	0.998588i	$-0.516917\pi$
$23$	−0.509528	−0.106244	−0.0531219	+	0.998588i	$0.516917\pi$
$24$	−19.4292	−3.96597
$25$	1.00000	0.200000
$26$	13.3508	2.61830
$27$	−15.8972	−3.05943
$28$	0	0
$29$	4.77451	0.886604	0.443302	−	0.896372i	$-0.353807\pi$
$29$	4.77451	0.886604	0.443302	+	0.896372i	$0.353807\pi$
$30$	−8.28906	−1.51337
$31$	5.61984	1.00935	0.504676	−	0.863309i	$-0.331612\pi$
$31$	5.61984	1.00935	0.504676	+	0.863309i	$0.331612\pi$
$32$	3.76329	0.665262
$33$	3.29098	0.572886
$34$	4.51634	0.774546
$35$	0	0
$36$	34.0156	5.66926
$37$	−6.19498	−1.01845	−0.509224	−	0.860634i	$-0.670067\pi$
$37$	−6.19498	−1.01845	−0.509224	+	0.860634i	$0.670067\pi$
$38$	−13.8286	−2.24330
$39$	−17.4442	−2.79331
$40$	5.90377	0.933468
$41$	1.28221	0.200248	0.100124	−	0.994975i	$-0.468076\pi$
$41$	1.28221	0.200248	0.100124	+	0.994975i	$0.468076\pi$
$42$	0	0
$43$	6.22470	0.949259	0.474629	−	0.880186i	$-0.342582\pi$
$43$	6.22470	0.949259	0.474629	+	0.880186i	$0.342582\pi$
$44$	−4.34396	−0.654876
$45$	7.83055	1.16731
$46$	−1.28336	−0.189221
$47$	11.1724	1.62967	0.814833	−	0.579696i	$-0.196829\pi$
$47$	11.1724	1.62967	0.814833	+	0.579696i	$0.196829\pi$
$48$	−20.3450	−2.93654
$49$	0	0
$50$	2.51872	0.356201
$51$	−5.90108	−0.826317
$52$	23.0256	3.19308
$53$	1.88528	0.258963	0.129482	−	0.991582i	$-0.458669\pi$
$53$	1.88528	0.258963	0.129482	+	0.991582i	$0.458669\pi$
$54$	−40.0407	−5.44885
$55$	−1.00000	−0.134840
$56$	0	0
$57$	18.0686	2.39324
$58$	12.0257	1.57905
$59$	−5.80252	−0.755423	−0.377712	−	0.925923i	$-0.623289\pi$
$59$	−5.80252	−0.755423	−0.377712	+	0.925923i	$0.623289\pi$
$60$	−14.2959	−1.84559
$61$	1.94382	0.248881	0.124441	−	0.992227i	$-0.460286\pi$
$61$	1.94382	0.248881	0.124441	+	0.992227i	$0.460286\pi$
$62$	14.1548	1.79766
$63$	0	0
$64$	−2.88540	−0.360675
$65$	5.30061	0.657460
$66$	8.28906	1.02031
$67$	1.77944	0.217394	0.108697	−	0.994075i	$-0.465332\pi$
$67$	1.77944	0.217394	0.108697	+	0.994075i	$0.465332\pi$
$68$	7.78918	0.944577
$69$	1.67685	0.201868
$70$	0	0
$71$	−3.97341	−0.471557	−0.235779	−	0.971807i	$-0.575764\pi$
$71$	−3.97341	−0.471557	−0.235779	+	0.971807i	$0.575764\pi$
$72$	46.2298	5.44823
$73$	2.99761	0.350844	0.175422	−	0.984493i	$-0.443871\pi$
$73$	2.99761	0.350844	0.175422	+	0.984493i	$0.443871\pi$
$74$	−15.6034	−1.81386
$75$	−3.29098	−0.380010
$76$	−23.8498	−2.73576
$77$	0	0
$78$	−43.9371	−4.97490
$79$	4.63677	0.521677	0.260839	−	0.965382i	$-0.416001\pi$
$79$	4.63677	0.521677	0.260839	+	0.965382i	$0.416001\pi$
$80$	6.18204	0.691173
$81$	28.8259	3.20287
$82$	3.22953	0.356642
$83$	4.07571	0.447367	0.223684	−	0.974662i	$-0.428192\pi$
$83$	4.07571	0.447367	0.223684	+	0.974662i	$0.428192\pi$
$84$	0	0
$85$	1.79311	0.194490
$86$	15.6783	1.69063
$87$	−15.7128	−1.68459
$88$	−5.90377	−0.629344
$89$	3.11717	0.330419	0.165210	−	0.986258i	$-0.447170\pi$
$89$	3.11717	0.330419	0.165210	+	0.986258i	$0.447170\pi$
$90$	19.7230	2.07898
$91$	0	0
$92$	−2.21337	−0.230759
$93$	−18.4948	−1.91782
$94$	28.1402	2.90244
$95$	−5.49034	−0.563297
$96$	−12.3849	−1.26403
$97$	12.0725	1.22578	0.612891	−	0.790168i	$-0.290007\pi$
$97$	12.0725	1.22578	0.612891	+	0.790168i	$0.290007\pi$
$98$	0	0
$99$	−7.83055	−0.787000
$100$	4.34396	0.434396
$101$	7.80420	0.776547	0.388274	−	0.921544i	$-0.373072\pi$
$101$	7.80420	0.776547	0.388274	+	0.921544i	$0.373072\pi$
$102$	−14.8632	−1.47167
$103$	9.60169	0.946083	0.473041	−	0.881040i	$-0.343156\pi$
$103$	9.60169	0.946083	0.473041	+	0.881040i	$0.343156\pi$
$104$	31.2936	3.06859
$105$	0	0
$106$	4.74850	0.461215
$107$	11.4503	1.10694	0.553471	−	0.832868i	$-0.313303\pi$
$107$	11.4503	1.10694	0.553471	+	0.832868i	$0.313303\pi$
$108$	−69.0569	−6.64501
$109$	7.64051	0.731828	0.365914	−	0.930649i	$-0.380756\pi$
$109$	7.64051	0.731828	0.365914	+	0.930649i	$0.380756\pi$
$110$	−2.51872	−0.240151
$111$	20.3875	1.93510
$112$	0	0
$113$	−2.21984	−0.208825	−0.104413	−	0.994534i	$-0.533296\pi$
$113$	−2.21984	−0.208825	−0.104413	+	0.994534i	$0.533296\pi$
$114$	45.5097	4.26238
$115$	−0.509528	−0.0475137
$116$	20.7402	1.92568
$117$	41.5067	3.83730
$118$	−14.6149	−1.34541
$119$	0	0
$120$	−19.4292	−1.77363
$121$	1.00000	0.0909091
$122$	4.89595	0.443258
$123$	−4.21973	−0.380481
$124$	24.4123	2.19229
$125$	1.00000	0.0894427
$126$	0	0
$127$	−2.58387	−0.229281	−0.114641	−	0.993407i	$-0.536572\pi$
$127$	−2.58387	−0.229281	−0.114641	+	0.993407i	$0.536572\pi$
$128$	−14.7941	−1.30763
$129$	−20.4854	−1.80364
$130$	13.3508	1.17094
$131$	−15.9960	−1.39758	−0.698790	−	0.715327i	$-0.746278\pi$
$131$	−15.9960	−1.39758	−0.698790	+	0.715327i	$0.746278\pi$
$132$	14.2959	1.24430
$133$	0	0
$134$	4.48193	0.387179
$135$	−15.8972	−1.36822
$136$	10.5861	0.907750
$137$	5.08468	0.434413	0.217207	−	0.976126i	$-0.430305\pi$
$137$	5.08468	0.434413	0.217207	+	0.976126i	$0.430305\pi$
$138$	4.22350	0.359529
$139$	−5.27535	−0.447450	−0.223725	−	0.974652i	$-0.571822\pi$
$139$	−5.27535	−0.447450	−0.223725	+	0.974652i	$0.571822\pi$
$140$	0	0
$141$	−36.7682	−3.09644
$142$	−10.0079	−0.839845
$143$	−5.30061	−0.443260
$144$	48.4088	4.03406
$145$	4.77451	0.396501
$146$	7.55015	0.624855
$147$	0	0
$148$	−26.9107	−2.21205
$149$	−12.7844	−1.04734	−0.523670	−	0.851921i	$-0.675438\pi$
$149$	−12.7844	−1.04734	−0.523670	+	0.851921i	$0.675438\pi$
$150$	−8.28906	−0.676799
$151$	−5.84536	−0.475688	−0.237844	−	0.971303i	$-0.576441\pi$
$151$	−5.84536	−0.475688	−0.237844	+	0.971303i	$0.576441\pi$
$152$	−32.4137	−2.62910
$153$	14.0410	1.13515
$154$	0	0
$155$	5.61984	0.451396
$156$	−75.7769	−6.06701
$157$	9.77817	0.780383	0.390191	−	0.920734i	$-0.372409\pi$
$157$	9.77817	0.780383	0.390191	+	0.920734i	$0.372409\pi$
$158$	11.6787	0.929110
$159$	−6.20442	−0.492043
$160$	3.76329	0.297514
$161$	0	0
$162$	72.6043	5.70433
$163$	−17.2557	−1.35157	−0.675784	−	0.737100i	$-0.736195\pi$
$163$	−17.2557	−1.35157	−0.675784	+	0.737100i	$0.736195\pi$
$164$	5.56987	0.434934
$165$	3.29098	0.256202
$166$	10.2656	0.796763
$167$	−9.48832	−0.734228	−0.367114	−	0.930176i	$-0.619654\pi$
$167$	−9.48832	−0.734228	−0.367114	+	0.930176i	$0.619654\pi$
$168$	0	0
$169$	15.0965	1.16127
$170$	4.51634	0.346387
$171$	−42.9924	−3.28771
$172$	27.0398	2.06177
$173$	−0.694844	−0.0528280	−0.0264140	−	0.999651i	$-0.508409\pi$
$173$	−0.694844	−0.0528280	−0.0264140	+	0.999651i	$0.508409\pi$
$174$	−39.5762	−3.00026
$175$	0	0
$176$	−6.18204	−0.465989
$177$	19.0960	1.43534
$178$	7.85127	0.588478
$179$	3.01189	0.225119	0.112560	−	0.993645i	$-0.464095\pi$
$179$	3.01189	0.225119	0.112560	+	0.993645i	$0.464095\pi$
$180$	34.0156	2.53537
$181$	−22.1739	−1.64817	−0.824085	−	0.566466i	$-0.808310\pi$
$181$	−22.1739	−1.64817	−0.824085	+	0.566466i	$0.808310\pi$
$182$	0	0
$183$	−6.39708	−0.472886
$184$	−3.00813	−0.221763
$185$	−6.19498	−0.455464
$186$	−46.5832	−3.41564
$187$	−1.79311	−0.131125
$188$	48.5325	3.53960
$189$	0	0
$190$	−13.8286	−1.00323
$191$	20.6363	1.49319	0.746595	−	0.665278i	$-0.231687\pi$
$191$	20.6363	1.49319	0.746595	+	0.665278i	$0.231687\pi$
$192$	9.49578	0.685299
$193$	−4.52408	−0.325650	−0.162825	−	0.986655i	$-0.552061\pi$
$193$	−4.52408	−0.325650	−0.162825	+	0.986655i	$0.552061\pi$
$194$	30.4074	2.18312
$195$	−17.4442	−1.24921
$196$	0	0
$197$	10.9741	0.781871	0.390935	−	0.920418i	$-0.372152\pi$
$197$	10.9741	0.781871	0.390935	+	0.920418i	$0.372152\pi$
$198$	−19.7230	−1.40165
$199$	−11.4372	−0.810759	−0.405379	−	0.914149i	$-0.632861\pi$
$199$	−11.4372	−0.810759	−0.405379	+	0.914149i	$0.632861\pi$
$200$	5.90377	0.417460
$201$	−5.85612	−0.413059
$202$	19.6566	1.38303
$203$	0	0
$204$	−25.6340	−1.79474
$205$	1.28221	0.0895536
$206$	24.1840	1.68498
$207$	−3.98988	−0.277316
$208$	32.7686	2.27209
$209$	5.49034	0.379775
$210$	0	0
$211$	20.3863	1.40345	0.701724	−	0.712449i	$-0.252414\pi$
$211$	20.3863	1.40345	0.701724	+	0.712449i	$0.252414\pi$
$212$	8.18958	0.562462
$213$	13.0764	0.895981
$214$	28.8401	1.97147
$215$	6.22470	0.424521
$216$	−93.8537	−6.38593
$217$	0	0
$218$	19.2443	1.30339
$219$	−9.86509	−0.666621
$220$	−4.34396	−0.292869
$221$	9.50457	0.639347
$222$	51.3505	3.44642
$223$	15.0377	1.00700	0.503501	−	0.863995i	$-0.332045\pi$
$223$	15.0377	1.00700	0.503501	+	0.863995i	$0.332045\pi$
$224$	0	0
$225$	7.83055	0.522037
$226$	−5.59116	−0.371919
$227$	−20.6340	−1.36953	−0.684763	−	0.728766i	$-0.740094\pi$
$227$	−20.6340	−1.36953	−0.684763	+	0.728766i	$0.740094\pi$
$228$	78.4892	5.19807
$229$	−22.1780	−1.46556	−0.732781	−	0.680465i	$-0.761778\pi$
$229$	−22.1780	−1.46556	−0.732781	+	0.680465i	$0.761778\pi$
$230$	−1.28336	−0.0846221
$231$	0	0
$232$	28.1876	1.85061
$233$	−25.6499	−1.68038	−0.840190	−	0.542292i	$-0.817557\pi$
$233$	−25.6499	−1.68038	−0.840190	+	0.542292i	$0.817557\pi$
$234$	104.544	6.83424
$235$	11.1724	0.728808
$236$	−25.2059	−1.64076
$237$	−15.2595	−0.991212
$238$	0	0
$239$	−27.3883	−1.77160	−0.885799	−	0.464068i	$-0.846389\pi$
$239$	−27.3883	−1.77160	−0.885799	+	0.464068i	$0.846389\pi$
$240$	−20.3450	−1.31326
$241$	−23.6951	−1.52634	−0.763169	−	0.646199i	$-0.776357\pi$
$241$	−23.6951	−1.52634	−0.763169	+	0.646199i	$0.776357\pi$
$242$	2.51872	0.161910
$243$	−47.1736	−3.02619
$244$	8.44388	0.540564
$245$	0	0
$246$	−10.6283	−0.677638
$247$	−29.1022	−1.85173
$248$	33.1782	2.10682
$249$	−13.4131	−0.850019
$250$	2.51872	0.159298
$251$	21.5663	1.36125	0.680626	−	0.732631i	$-0.261708\pi$
$251$	21.5663	1.36125	0.680626	+	0.732631i	$0.261708\pi$
$252$	0	0
$253$	0.509528	0.0320337
$254$	−6.50804	−0.408351
$255$	−5.90108	−0.369540
$256$	−31.4914	−1.96821
$257$	4.32048	0.269504	0.134752	−	0.990879i	$-0.456976\pi$
$257$	4.32048	0.269504	0.134752	+	0.990879i	$0.456976\pi$
$258$	−51.5970	−3.21229
$259$	0	0
$260$	23.0256	1.42799
$261$	37.3870	2.31420
$262$	−40.2895	−2.48910
$263$	14.7079	0.906928	0.453464	−	0.891275i	$-0.350188\pi$
$263$	14.7079	0.906928	0.453464	+	0.891275i	$0.350188\pi$
$264$	19.4292	1.19578
$265$	1.88528	0.115812
$266$	0	0
$267$	−10.2585	−0.627812
$268$	7.72983	0.472174
$269$	−16.8557	−1.02771	−0.513855	−	0.857877i	$-0.671783\pi$
$269$	−16.8557	−1.02771	−0.513855	+	0.857877i	$0.671783\pi$
$270$	−40.0407	−2.43680
$271$	−20.5416	−1.24781	−0.623907	−	0.781498i	$-0.714456\pi$
$271$	−20.5416	−1.24781	−0.623907	+	0.781498i	$0.714456\pi$
$272$	11.0851	0.672131
$273$	0	0
$274$	12.8069	0.773692
$275$	−1.00000	−0.0603023
$276$	7.28414	0.438454
$277$	11.1339	0.668970	0.334485	−	0.942401i	$-0.391438\pi$
$277$	11.1339	0.668970	0.334485	+	0.942401i	$0.391438\pi$
$278$	−13.2871	−0.796910
$279$	44.0064	2.63460
$280$	0	0
$281$	10.6506	0.635364	0.317682	−	0.948197i	$-0.397096\pi$
$281$	10.6506	0.635364	0.317682	+	0.948197i	$0.397096\pi$
$282$	−92.6089	−5.51478
$283$	−25.4396	−1.51223	−0.756113	−	0.654441i	$-0.772904\pi$
$283$	−25.4396	−1.51223	−0.756113	+	0.654441i	$0.772904\pi$
$284$	−17.2603	−1.02421
$285$	18.0686	1.07029
$286$	−13.3508	−0.789447
$287$	0	0
$288$	29.4686	1.73646
$289$	−13.7848	−0.810868
$290$	12.0257	0.706171
$291$	−39.7305	−2.32904
$292$	13.0215	0.762026
$293$	−4.15823	−0.242926	−0.121463	−	0.992596i	$-0.538759\pi$
$293$	−4.15823	−0.242926	−0.121463	+	0.992596i	$0.538759\pi$
$294$	0	0
$295$	−5.80252	−0.337836
$296$	−36.5737	−2.12580
$297$	15.8972	0.922452
$298$	−32.2004	−1.86532
$299$	−2.70081	−0.156192
$300$	−14.2959	−0.825373
$301$	0	0
$302$	−14.7228	−0.847203
$303$	−25.6835	−1.47548
$304$	−33.9415	−1.94668
$305$	1.94382	0.111303
$306$	35.3654	2.02171
$307$	16.8008	0.958872	0.479436	−	0.877577i	$-0.340841\pi$
$307$	16.8008	0.958872	0.479436	+	0.877577i	$0.340841\pi$
$308$	0	0
$309$	−31.5990	−1.79760
$310$	14.1548	0.803939
$311$	4.82496	0.273599	0.136799	−	0.990599i	$-0.456318\pi$
$311$	4.82496	0.273599	0.136799	+	0.990599i	$0.456318\pi$
$312$	−102.987	−5.83047
$313$	25.8645	1.46195	0.730973	−	0.682406i	$-0.239066\pi$
$313$	25.8645	1.46195	0.730973	+	0.682406i	$0.239066\pi$
$314$	24.6285	1.38986
$315$	0	0
$316$	20.1419	1.13307
$317$	−8.99975	−0.505477	−0.252738	−	0.967535i	$-0.581331\pi$
$317$	−8.99975	−0.505477	−0.252738	+	0.967535i	$0.581331\pi$
$318$	−15.6272	−0.876330
$319$	−4.77451	−0.267321
$320$	−2.88540	−0.161299
$321$	−37.6827	−2.10324
$322$	0	0
$323$	−9.84477	−0.547778
$324$	125.218	6.95657
$325$	5.30061	0.294025
$326$	−43.4622	−2.40715
$327$	−25.1448	−1.39051
$328$	7.56989	0.417977
$329$	0	0
$330$	8.28906	0.456298
$331$	−25.0938	−1.37928	−0.689639	−	0.724154i	$-0.742231\pi$
$331$	−25.0938	−1.37928	−0.689639	+	0.724154i	$0.742231\pi$
$332$	17.7047	0.971672
$333$	−48.5101	−2.65834
$334$	−23.8984	−1.30766
$335$	1.77944	0.0972215
$336$	0	0
$337$	−23.0416	−1.25516	−0.627578	−	0.778554i	$-0.715954\pi$
$337$	−23.0416	−1.25516	−0.627578	+	0.778554i	$0.715954\pi$
$338$	38.0239	2.06823
$339$	7.30545	0.396778
$340$	7.78918	0.422428
$341$	−5.61984	−0.304331
$342$	−108.286	−5.85542
$343$	0	0
$344$	36.7492	1.98139
$345$	1.67685	0.0902783
$346$	−1.75012	−0.0940869
$347$	11.0119	0.591147	0.295574	−	0.955320i	$-0.404489\pi$
$347$	11.0119	0.591147	0.295574	+	0.955320i	$0.404489\pi$
$348$	−68.2557	−3.65889
$349$	−34.2561	−1.83369	−0.916844	−	0.399245i	$-0.869272\pi$
$349$	−34.2561	−1.83369	−0.916844	+	0.399245i	$0.869272\pi$
$350$	0	0
$351$	−84.2651	−4.49774
$352$	−3.76329	−0.200584
$353$	−1.49467	−0.0795533	−0.0397767	−	0.999209i	$-0.512665\pi$
$353$	−1.49467	−0.0795533	−0.0397767	+	0.999209i	$0.512665\pi$
$354$	48.0974	2.55635
$355$	−3.97341	−0.210887
$356$	13.5408	0.717663
$357$	0	0
$358$	7.58612	0.400939
$359$	18.9831	1.00189	0.500945	−	0.865479i	$-0.332986\pi$
$359$	18.9831	1.00189	0.500945	+	0.865479i	$0.332986\pi$
$360$	46.2298	2.43652
$361$	11.1438	0.586517
$362$	−55.8498	−2.93540
$363$	−3.29098	−0.172732
$364$	0	0
$365$	2.99761	0.156902
$366$	−16.1125	−0.842212
$367$	−14.6557	−0.765019	−0.382509	−	0.923952i	$-0.624940\pi$
$367$	−14.6557	−0.765019	−0.382509	+	0.923952i	$0.624940\pi$
$368$	−3.14992	−0.164201
$369$	10.0404	0.522684
$370$	−15.6034	−0.811183
$371$	0	0
$372$	−80.3405	−4.16546
$373$	25.5616	1.32353	0.661765	−	0.749711i	$-0.269808\pi$
$373$	25.5616	1.32353	0.661765	+	0.749711i	$0.269808\pi$
$374$	−4.51634	−0.233534
$375$	−3.29098	−0.169945
$376$	65.9594	3.40160
$377$	25.3078	1.30342
$378$	0	0
$379$	−30.9775	−1.59121	−0.795604	−	0.605817i	$-0.792846\pi$
$379$	−30.9775	−1.59121	−0.795604	+	0.605817i	$0.792846\pi$
$380$	−23.8498	−1.22347
$381$	8.50346	0.435645
$382$	51.9771	2.65938
$383$	−34.4431	−1.75996	−0.879980	−	0.475010i	$-0.842444\pi$
$383$	−34.4431	−1.75996	−0.879980	+	0.475010i	$0.842444\pi$
$384$	48.6871	2.48455
$385$	0	0
$386$	−11.3949	−0.579984
$387$	48.7429	2.47774
$388$	52.4426	2.66237
$389$	−5.43130	−0.275378	−0.137689	−	0.990476i	$-0.543967\pi$
$389$	−5.43130	−0.275378	−0.137689	+	0.990476i	$0.543967\pi$
$390$	−43.9371	−2.22484
$391$	−0.913638	−0.0462047
$392$	0	0
$393$	52.6426	2.65547
$394$	27.6406	1.39252
$395$	4.63677	0.233301
$396$	−34.0156	−1.70935
$397$	30.2090	1.51614	0.758072	−	0.652171i	$-0.226141\pi$
$397$	30.2090	1.51614	0.758072	+	0.652171i	$0.226141\pi$
$398$	−28.8070	−1.44397
$399$	0	0
$400$	6.18204	0.309102
$401$	−6.48893	−0.324042	−0.162021	−	0.986787i	$-0.551801\pi$
$401$	−6.48893	−0.324042	−0.162021	+	0.986787i	$0.551801\pi$
$402$	−14.7499	−0.735659
$403$	29.7886	1.48388
$404$	33.9011	1.68664
$405$	28.8259	1.43237
$406$	0	0
$407$	6.19498	0.307074
$408$	−34.8386	−1.72477
$409$	3.73320	0.184595	0.0922974	−	0.995731i	$-0.470579\pi$
$409$	3.73320	0.184595	0.0922974	+	0.995731i	$0.470579\pi$
$410$	3.22953	0.159495
$411$	−16.7336	−0.825406
$412$	41.7093	2.05487
$413$	0	0
$414$	−10.0494	−0.493901
$415$	4.07571	0.200069
$416$	19.9478	0.978019
$417$	17.3611	0.850176
$418$	13.8286	0.676380
$419$	−24.0207	−1.17349	−0.586744	−	0.809773i	$-0.699590\pi$
$419$	−24.0207	−1.17349	−0.586744	+	0.809773i	$0.699590\pi$
$420$	0	0
$421$	32.8926	1.60309	0.801544	−	0.597935i	$-0.204012\pi$
$421$	32.8926	1.60309	0.801544	+	0.597935i	$0.204012\pi$
$422$	51.3473	2.49955
$423$	87.4862	4.25373
$424$	11.1303	0.540533
$425$	1.79311	0.0869785
$426$	32.9358	1.59575
$427$	0	0
$428$	49.7396	2.40425
$429$	17.4442	0.842215
$430$	15.6783	0.756074
$431$	20.8731	1.00542	0.502711	−	0.864455i	$-0.332336\pi$
$431$	20.8731	1.00542	0.502711	+	0.864455i	$0.332336\pi$
$432$	−98.2774	−4.72837
$433$	−26.2218	−1.26014	−0.630069	−	0.776539i	$-0.716973\pi$
$433$	−26.2218	−1.26014	−0.630069	+	0.776539i	$0.716973\pi$
$434$	0	0
$435$	−15.7128	−0.753372
$436$	33.1900	1.58951
$437$	2.79748	0.133822
$438$	−24.8474	−1.18725
$439$	25.8288	1.23274	0.616371	−	0.787456i	$-0.288602\pi$
$439$	25.8288	1.23274	0.616371	+	0.787456i	$0.288602\pi$
$440$	−5.90377	−0.281451
$441$	0	0
$442$	23.9394	1.13868
$443$	16.5853	0.787989	0.393995	−	0.919113i	$-0.371093\pi$
$443$	16.5853	0.787989	0.393995	+	0.919113i	$0.371093\pi$
$444$	88.5626	4.20299
$445$	3.11717	0.147768
$446$	37.8759	1.79347
$447$	42.0733	1.99000
$448$	0	0
$449$	−36.6076	−1.72762	−0.863810	−	0.503818i	$-0.831928\pi$
$449$	−36.6076	−1.72762	−0.863810	+	0.503818i	$0.831928\pi$
$450$	19.7230	0.929750
$451$	−1.28221	−0.0603770
$452$	−9.64289	−0.453564
$453$	19.2370	0.903831
$454$	−51.9712	−2.43913
$455$	0	0
$456$	106.673	4.99541
$457$	−23.4400	−1.09648	−0.548240	−	0.836321i	$-0.684702\pi$
$457$	−23.4400	−1.09648	−0.548240	+	0.836321i	$0.684702\pi$
$458$	−55.8601	−2.61017
$459$	−28.5055	−1.33052
$460$	−2.21337	−0.103199
$461$	−24.2805	−1.13086	−0.565428	−	0.824798i	$-0.691289\pi$
$461$	−24.2805	−1.13086	−0.565428	+	0.824798i	$0.691289\pi$
$462$	0	0
$463$	31.0998	1.44533	0.722665	−	0.691198i	$-0.242917\pi$
$463$	31.0998	1.44533	0.722665	+	0.691198i	$0.242917\pi$
$464$	29.5162	1.37025
$465$	−18.4948	−0.857675
$466$	−64.6049	−2.99277
$467$	−7.63952	−0.353515	−0.176757	−	0.984254i	$-0.556561\pi$
$467$	−7.63952	−0.353515	−0.176757	+	0.984254i	$0.556561\pi$
$468$	180.303	8.33452
$469$	0	0
$470$	28.1402	1.29801
$471$	−32.1797	−1.48276
$472$	−34.2567	−1.57679
$473$	−6.22470	−0.286212
$474$	−38.4345	−1.76535
$475$	−5.49034	−0.251914
$476$	0	0
$477$	14.7628	0.675942
$478$	−68.9834	−3.15523
$479$	33.9113	1.54945	0.774723	−	0.632301i	$-0.217889\pi$
$479$	33.9113	1.54945	0.774723	+	0.632301i	$0.217889\pi$
$480$	−12.3849	−0.565292
$481$	−32.8372	−1.49725
$482$	−59.6814	−2.71841
$483$	0	0
$484$	4.34396	0.197453
$485$	12.0725	0.548186
$486$	−118.817	−5.38966
$487$	22.6745	1.02748	0.513739	−	0.857947i	$-0.328260\pi$
$487$	22.6745	1.02748	0.513739	+	0.857947i	$0.328260\pi$
$488$	11.4759	0.519489
$489$	56.7881	2.56804
$490$	0	0
$491$	18.6463	0.841498	0.420749	−	0.907177i	$-0.361767\pi$
$491$	18.6463	0.841498	0.420749	+	0.907177i	$0.361767\pi$
$492$	−18.3303	−0.826396
$493$	8.56121	0.385577
$494$	−73.3002	−3.29793
$495$	−7.83055	−0.351957
$496$	34.7421	1.55996
$497$	0	0
$498$	−33.7838	−1.51389
$499$	−33.3506	−1.49298	−0.746489	−	0.665397i	$-0.768262\pi$
$499$	−33.3506	−1.49298	−0.746489	+	0.665397i	$0.768262\pi$
$500$	4.34396	0.194268
$501$	31.2259	1.39507
$502$	54.3194	2.42440
$503$	21.1300	0.942142	0.471071	−	0.882095i	$-0.343868\pi$
$503$	21.1300	0.942142	0.471071	+	0.882095i	$0.343868\pi$
$504$	0	0
$505$	7.80420	0.347282
$506$	1.28336	0.0570522
$507$	−49.6823	−2.20647
$508$	−11.2242	−0.497994
$509$	5.68320	0.251904	0.125952	−	0.992036i	$-0.459802\pi$
$509$	5.68320	0.251904	0.125952	+	0.992036i	$0.459802\pi$
$510$	−14.8632	−0.658153
$511$	0	0
$512$	−49.7299	−2.19777
$513$	87.2812	3.85356
$514$	10.8821	0.479988
$515$	9.60169	0.423101
$516$	−88.9876	−3.91746
$517$	−11.1724	−0.491363
$518$	0	0
$519$	2.28672	0.100376
$520$	31.2936	1.37232
$521$	2.82106	0.123593	0.0617964	−	0.998089i	$-0.480317\pi$
$521$	2.82106	0.123593	0.0617964	+	0.998089i	$0.480317\pi$
$522$	94.1675	4.12160
$523$	25.3575	1.10881	0.554403	−	0.832248i	$-0.312947\pi$
$523$	25.3575	1.10881	0.554403	+	0.832248i	$0.312947\pi$
$524$	−69.4860	−3.03551
$525$	0	0
$526$	37.0451	1.61524
$527$	10.0770	0.438960
$528$	20.3450	0.885401
$529$	−22.7404	−0.988712
$530$	4.74850	0.206262
$531$	−45.4369	−1.97179
$532$	0	0
$533$	6.79651	0.294390
$534$	−25.8384	−1.11814
$535$	11.4503	0.495040
$536$	10.5054	0.453766
$537$	−9.91208	−0.427738
$538$	−42.4548	−1.83036
$539$	0	0
$540$	−69.0569	−2.97174
$541$	−31.0080	−1.33314	−0.666568	−	0.745444i	$-0.732237\pi$
$541$	−31.0080	−1.33314	−0.666568	+	0.745444i	$0.732237\pi$
$542$	−51.7386	−2.22236
$543$	72.9737	3.13160
$544$	6.74799	0.289318
$545$	7.64051	0.327284
$546$	0	0
$547$	20.2066	0.863971	0.431986	−	0.901880i	$-0.357813\pi$
$547$	20.2066	0.863971	0.431986	+	0.901880i	$0.357813\pi$
$548$	22.0876	0.943536
$549$	15.2212	0.649625
$550$	−2.51872	−0.107399
$551$	−26.2137	−1.11674
$552$	9.89971	0.421360
$553$	0	0
$554$	28.0431	1.19144
$555$	20.3875	0.865403
$556$	−22.9159	−0.971850
$557$	4.86546	0.206156	0.103078	−	0.994673i	$-0.467131\pi$
$557$	4.86546	0.206156	0.103078	+	0.994673i	$0.467131\pi$
$558$	110.840	4.69223
$559$	32.9948	1.39553
$560$	0	0
$561$	5.90108	0.249144
$562$	26.8260	1.13159
$563$	−33.1632	−1.39766	−0.698831	−	0.715287i	$-0.746296\pi$
$563$	−33.1632	−1.39766	−0.698831	+	0.715287i	$0.746296\pi$
$564$	−159.720	−6.72540
$565$	−2.21984	−0.0933894
$566$	−64.0752	−2.69328
$567$	0	0
$568$	−23.4581	−0.984280
$569$	−36.5092	−1.53055	−0.765273	−	0.643706i	$-0.777396\pi$
$569$	−36.5092	−1.53055	−0.765273	+	0.643706i	$0.777396\pi$
$570$	45.5097	1.90619
$571$	1.77175	0.0741453	0.0370727	−	0.999313i	$-0.488197\pi$
$571$	1.77175	0.0741453	0.0370727	+	0.999313i	$0.488197\pi$
$572$	−23.0256	−0.962750
$573$	−67.9137	−2.83713
$574$	0	0
$575$	−0.509528	−0.0212488
$576$	−22.5942	−0.941427
$577$	−7.59095	−0.316015	−0.158008	−	0.987438i	$-0.550507\pi$
$577$	−7.59095	−0.316015	−0.158008	+	0.987438i	$0.550507\pi$
$578$	−34.7200	−1.44416
$579$	14.8886	0.618751
$580$	20.7402	0.861192
$581$	0	0
$582$	−100.070	−4.14804
$583$	−1.88528	−0.0780804
$584$	17.6972	0.732316
$585$	41.5067	1.71609
$586$	−10.4734	−0.432653
$587$	−18.3651	−0.758009	−0.379004	−	0.925395i	$-0.623733\pi$
$587$	−18.3651	−0.758009	−0.379004	+	0.925395i	$0.623733\pi$
$588$	0	0
$589$	−30.8548	−1.27135
$590$	−14.6149	−0.601687
$591$	−36.1155	−1.48559
$592$	−38.2976	−1.57402
$593$	−32.1374	−1.31973	−0.659863	−	0.751386i	$-0.729386\pi$
$593$	−32.1374	−1.31973	−0.659863	+	0.751386i	$0.729386\pi$
$594$	40.0407	1.64289
$595$	0	0
$596$	−55.5350	−2.27480
$597$	37.6395	1.54048
$598$	−6.80258	−0.278178
$599$	40.2341	1.64392	0.821961	−	0.569544i	$-0.192880\pi$
$599$	40.2341	1.64392	0.821961	+	0.569544i	$0.192880\pi$
$600$	−19.4292	−0.793193
$601$	12.5052	0.510099	0.255049	−	0.966928i	$-0.417908\pi$
$601$	12.5052	0.510099	0.255049	+	0.966928i	$0.417908\pi$
$602$	0	0
$603$	13.9340	0.567438
$604$	−25.3920	−1.03318
$605$	1.00000	0.0406558
$606$	−64.6895	−2.62783
$607$	2.61044	0.105955	0.0529773	−	0.998596i	$-0.483129\pi$
$607$	2.61044	0.105955	0.0529773	+	0.998596i	$0.483129\pi$
$608$	−20.6617	−0.837944
$609$	0	0
$610$	4.89595	0.198231
$611$	59.2207	2.39581
$612$	60.9936	2.46552
$613$	−14.1046	−0.569681	−0.284840	−	0.958575i	$-0.591941\pi$
$613$	−14.1046	−0.569681	−0.284840	+	0.958575i	$0.591941\pi$
$614$	42.3165	1.70775
$615$	−4.21973	−0.170156
$616$	0	0
$617$	14.3444	0.577483	0.288742	−	0.957407i	$-0.406763\pi$
$617$	14.3444	0.577483	0.288742	+	0.957407i	$0.406763\pi$
$618$	−79.5890	−3.20154
$619$	−42.7165	−1.71692	−0.858461	−	0.512878i	$-0.828579\pi$
$619$	−42.7165	−1.71692	−0.858461	+	0.512878i	$0.828579\pi$
$620$	24.4123	0.980423
$621$	8.10008	0.325045
$622$	12.1527	0.487280
$623$	0	0
$624$	−107.841	−4.31709
$625$	1.00000	0.0400000
$626$	65.1454	2.60373
$627$	−18.0686	−0.721590
$628$	42.4759	1.69497
$629$	−11.1083	−0.442915
$630$	0	0
$631$	−24.9795	−0.994417	−0.497209	−	0.867631i	$-0.665642\pi$
$631$	−24.9795	−0.994417	−0.497209	+	0.867631i	$0.665642\pi$
$632$	27.3744	1.08890
$633$	−67.0907	−2.66662
$634$	−22.6679	−0.900256
$635$	−2.58387	−0.102538
$636$	−26.9517	−1.06871
$637$	0	0
$638$	−12.0257	−0.476100
$639$	−31.1140	−1.23085
$640$	−14.7941	−0.584788
$641$	42.5765	1.68167	0.840836	−	0.541290i	$-0.182064\pi$
$641$	42.5765	1.68167	0.840836	+	0.541290i	$0.182064\pi$
$642$	−94.9122	−3.74589
$643$	24.9393	0.983508	0.491754	−	0.870734i	$-0.336356\pi$
$643$	24.9393	0.983508	0.491754	+	0.870734i	$0.336356\pi$
$644$	0	0
$645$	−20.4854	−0.806611
$646$	−24.7962	−0.975594
$647$	−20.1401	−0.791791	−0.395895	−	0.918296i	$-0.629566\pi$
$647$	−20.1401	−0.791791	−0.395895	+	0.918296i	$0.629566\pi$
$648$	170.181	6.68535
$649$	5.80252	0.227769
$650$	13.3508	0.523660
$651$	0	0
$652$	−74.9579	−2.93558
$653$	4.47581	0.175152	0.0875759	−	0.996158i	$-0.472088\pi$
$653$	4.47581	0.175152	0.0875759	+	0.996158i	$0.472088\pi$
$654$	−63.3327	−2.47650
$655$	−15.9960	−0.625017
$656$	7.92669	0.309485
$657$	23.4730	0.915767
$658$	0	0
$659$	9.01118	0.351026	0.175513	−	0.984477i	$-0.443842\pi$
$659$	9.01118	0.351026	0.175513	+	0.984477i	$0.443842\pi$
$660$	14.2959	0.556466
$661$	33.9508	1.32053	0.660266	−	0.751032i	$-0.270443\pi$
$661$	33.9508	1.32053	0.660266	+	0.751032i	$0.270443\pi$
$662$	−63.2042	−2.45650
$663$	−31.2794	−1.21479
$664$	24.0621	0.933789
$665$	0	0
$666$	−122.183	−4.73451
$667$	−2.43274	−0.0941962
$668$	−41.2168	−1.59473
$669$	−49.4889	−1.91335
$670$	4.48193	0.173152
$671$	−1.94382	−0.0750405
$672$	0	0
$673$	−7.57324	−0.291927	−0.145963	−	0.989290i	$-0.546628\pi$
$673$	−7.57324	−0.291927	−0.145963	+	0.989290i	$0.546628\pi$
$674$	−58.0354	−2.23544
$675$	−15.8972	−0.611885
$676$	65.5785	2.52225
$677$	39.0298	1.50004	0.750019	−	0.661417i	$-0.230045\pi$
$677$	39.0298	1.50004	0.750019	+	0.661417i	$0.230045\pi$
$678$	18.4004	0.706663
$679$	0	0
$680$	10.5861	0.405958
$681$	67.9060	2.60216
$682$	−14.1548	−0.542015
$683$	−30.8531	−1.18056	−0.590281	−	0.807198i	$-0.700983\pi$
$683$	−30.8531	−1.18056	−0.590281	+	0.807198i	$0.700983\pi$
$684$	−186.757	−7.14083
$685$	5.08468	0.194276
$686$	0	0
$687$	72.9873	2.78464
$688$	38.4814	1.46709
$689$	9.99314	0.380709
$690$	4.22350	0.160786
$691$	9.36677	0.356329	0.178164	−	0.984001i	$-0.442984\pi$
$691$	9.36677	0.356329	0.178164	+	0.984001i	$0.442984\pi$
$692$	−3.01837	−0.114741
$693$	0	0
$694$	27.7358	1.05284
$695$	−5.27535	−0.200106
$696$	−92.7648	−3.51624
$697$	2.29914	0.0870863
$698$	−86.2816	−3.26581
$699$	84.4133	3.19280
$700$	0	0
$701$	−23.8625	−0.901276	−0.450638	−	0.892707i	$-0.648803\pi$
$701$	−23.8625	−0.901276	−0.450638	+	0.892707i	$0.648803\pi$
$702$	−212.240	−8.01050
$703$	34.0125	1.28281
$704$	2.88540	0.108747
$705$	−36.7682	−1.38477
$706$	−3.76466	−0.141685
$707$	0	0
$708$	82.9520	3.11753
$709$	−17.6792	−0.663958	−0.331979	−	0.943287i	$-0.607716\pi$
$709$	−17.6792	−0.663958	−0.331979	+	0.943287i	$0.607716\pi$
$710$	−10.0079	−0.375590
$711$	36.3084	1.36167
$712$	18.4030	0.689683
$713$	−2.86346	−0.107238
$714$	0	0
$715$	−5.30061	−0.198232
$716$	13.0835	0.488954
$717$	90.1342	3.36612
$718$	47.8131	1.78437
$719$	25.1127	0.936545	0.468273	−	0.883584i	$-0.344876\pi$
$719$	25.1127	0.936545	0.468273	+	0.883584i	$0.344876\pi$
$720$	48.4088	1.80409
$721$	0	0
$722$	28.0682	1.04459
$723$	77.9802	2.90011
$724$	−96.3223	−3.57979
$725$	4.77451	0.177321
$726$	−8.28906	−0.307636
$727$	−34.6511	−1.28514	−0.642570	−	0.766227i	$-0.722132\pi$
$727$	−34.6511	−1.28514	−0.642570	+	0.766227i	$0.722132\pi$
$728$	0	0
$729$	68.7698	2.54703
$730$	7.55015	0.279444
$731$	11.1616	0.412825
$732$	−27.7887	−1.02710
$733$	−0.425302	−0.0157089	−0.00785444	−	0.999969i	$-0.502500\pi$
$733$	−0.425302	−0.0157089	−0.00785444	+	0.999969i	$0.502500\pi$
$734$	−36.9135	−1.36250
$735$	0	0
$736$	−1.91750	−0.0706800
$737$	−1.77944	−0.0655467
$738$	25.2890	0.930902
$739$	−17.5003	−0.643760	−0.321880	−	0.946780i	$-0.604315\pi$
$739$	−17.5003	−0.643760	−0.321880	+	0.946780i	$0.604315\pi$
$740$	−26.9107	−0.989257
$741$	95.7746	3.51837
$742$	0	0
$743$	−15.1702	−0.556540	−0.278270	−	0.960503i	$-0.589761\pi$
$743$	−15.1702	−0.556540	−0.278270	+	0.960503i	$0.589761\pi$
$744$	−109.189	−4.00306
$745$	−12.7844	−0.468385
$746$	64.3826	2.35721
$747$	31.9151	1.16771
$748$	−7.78918	−0.284801
$749$	0	0
$750$	−8.28906	−0.302674
$751$	−8.02546	−0.292853	−0.146427	−	0.989222i	$-0.546777\pi$
$751$	−8.02546	−0.292853	−0.146427	+	0.989222i	$0.546777\pi$
$752$	69.0684	2.51866
$753$	−70.9742	−2.58644
$754$	63.7433	2.32140
$755$	−5.84536	−0.212734
$756$	0	0
$757$	4.81301	0.174932	0.0874658	−	0.996168i	$-0.472123\pi$
$757$	4.81301	0.174932	0.0874658	+	0.996168i	$0.472123\pi$
$758$	−78.0237	−2.83395
$759$	−1.67685	−0.0608656
$760$	−32.4137	−1.17577
$761$	4.43442	0.160747	0.0803737	−	0.996765i	$-0.474389\pi$
$761$	4.43442	0.160747	0.0803737	+	0.996765i	$0.474389\pi$
$762$	21.4178	0.775887
$763$	0	0
$764$	89.6432	3.24318
$765$	14.0410	0.507654
$766$	−86.7526	−3.13450
$767$	−30.7569	−1.11057
$768$	103.638	3.73970
$769$	−3.82639	−0.137983	−0.0689915	−	0.997617i	$-0.521978\pi$
$769$	−3.82639	−0.137983	−0.0689915	+	0.997617i	$0.521978\pi$
$770$	0	0
$771$	−14.2186	−0.512071
$772$	−19.6524	−0.707305
$773$	2.19875	0.0790835	0.0395417	−	0.999218i	$-0.487410\pi$
$773$	2.19875	0.0790835	0.0395417	+	0.999218i	$0.487410\pi$
$774$	122.770	4.41286
$775$	5.61984	0.201871
$776$	71.2736	2.55857
$777$	0	0
$778$	−13.6799	−0.490449
$779$	−7.03978	−0.252226
$780$	−75.7769	−2.71325
$781$	3.97341	0.142180
$782$	−2.30120	−0.0822907
$783$	−75.9015	−2.71250
$784$	0	0
$785$	9.77817	0.348998
$786$	132.592	4.72940
$787$	−15.3999	−0.548949	−0.274474	−	0.961594i	$-0.588504\pi$
$787$	−15.3999	−0.548949	−0.274474	+	0.961594i	$0.588504\pi$
$788$	47.6709	1.69821
$789$	−48.4034	−1.72321
$790$	11.6787	0.415510
$791$	0	0
$792$	−46.2298	−1.64270
$793$	10.3035	0.365886
$794$	76.0880	2.70026
$795$	−6.20442	−0.220048
$796$	−49.6825	−1.76095
$797$	19.3677	0.686039	0.343019	−	0.939328i	$-0.388550\pi$
$797$	19.3677	0.686039	0.343019	+	0.939328i	$0.388550\pi$
$798$	0	0
$799$	20.0334	0.708729
$800$	3.76329	0.133052
$801$	24.4091	0.862454
$802$	−16.3438	−0.577120
$803$	−2.99761	−0.105783
$804$	−25.4387	−0.897154
$805$	0	0
$806$	75.0291	2.64279
$807$	55.4718	1.95270
$808$	46.0742	1.62089
$809$	7.32378	0.257490	0.128745	−	0.991678i	$-0.458905\pi$
$809$	7.32378	0.257490	0.128745	+	0.991678i	$0.458905\pi$
$810$	72.6043	2.55106
$811$	−31.3236	−1.09992	−0.549960	−	0.835191i	$-0.685357\pi$
$811$	−31.3236	−1.09992	−0.549960	+	0.835191i	$0.685357\pi$
$812$	0	0
$813$	67.6021	2.37091
$814$	15.6034	0.546899
$815$	−17.2557	−0.604440
$816$	−36.4807	−1.27708
$817$	−34.1757	−1.19566
$818$	9.40289	0.328764
$819$	0	0
$820$	5.56987	0.194508
$821$	−47.1818	−1.64666	−0.823328	−	0.567566i	$-0.807885\pi$
$821$	−47.1818	−1.64666	−0.823328	+	0.567566i	$0.807885\pi$
$822$	−42.1472	−1.47005
$823$	−50.2150	−1.75039	−0.875193	−	0.483775i	$-0.839265\pi$
$823$	−50.2150	−1.75039	−0.875193	+	0.483775i	$0.839265\pi$
$824$	56.6862	1.97476
$825$	3.29098	0.114577
$826$	0	0
$827$	0.0456538	0.00158754	0.000793769	−	1.00000i	$-0.499747\pi$
$827$	0.0456538	0.00158754	0.000793769		1.00000i	$0.499747\pi$
$828$	−17.3319	−0.602324
$829$	24.3624	0.846142	0.423071	−	0.906097i	$-0.360952\pi$
$829$	24.3624	0.846142	0.423071	+	0.906097i	$0.360952\pi$
$830$	10.2656	0.356323
$831$	−36.6414	−1.27107
$832$	−15.2944	−0.530237
$833$	0	0
$834$	43.7277	1.51417
$835$	−9.48832	−0.328357
$836$	23.8498	0.824862
$837$	−89.3399	−3.08804
$838$	−60.5014	−2.08999
$839$	−13.2346	−0.456908	−0.228454	−	0.973555i	$-0.573367\pi$
$839$	−13.2346	−0.456908	−0.228454	+	0.973555i	$0.573367\pi$
$840$	0	0
$841$	−6.20408	−0.213934
$842$	82.8474	2.85511
$843$	−35.0510	−1.20722
$844$	88.5570	3.04826
$845$	15.0965	0.519335
$846$	220.353	7.57590
$847$	0	0
$848$	11.6549	0.400230
$849$	83.7212	2.87330
$850$	4.51634	0.154909
$851$	3.15651	0.108204
$852$	56.8034	1.94605
$853$	−17.6903	−0.605704	−0.302852	−	0.953038i	$-0.597939\pi$
$853$	−17.6903	−0.605704	−0.302852	+	0.953038i	$0.597939\pi$
$854$	0	0
$855$	−42.9924	−1.47031
$856$	67.5999	2.31052
$857$	40.7050	1.39045	0.695227	−	0.718790i	$-0.255304\pi$
$857$	40.7050	1.39045	0.695227	+	0.718790i	$0.255304\pi$
$858$	43.9371	1.49999
$859$	26.4437	0.902248	0.451124	−	0.892461i	$-0.351023\pi$
$859$	26.4437	0.902248	0.451124	+	0.892461i	$0.351023\pi$
$860$	27.0398	0.922051
$861$	0	0
$862$	52.5735	1.79066
$863$	22.8211	0.776838	0.388419	−	0.921483i	$-0.373021\pi$
$863$	22.8211	0.776838	0.388419	+	0.921483i	$0.373021\pi$
$864$	−59.8260	−2.03532
$865$	−0.694844	−0.0236254
$866$	−66.0453	−2.24431
$867$	45.3654	1.54069
$868$	0	0
$869$	−4.63677	−0.157292
$870$	−39.5762	−1.34176
$871$	9.43215	0.319596
$872$	45.1078	1.52754
$873$	94.5347	3.19951
$874$	7.04607	0.238337
$875$	0	0
$876$	−42.8535	−1.44789
$877$	−18.2285	−0.615532	−0.307766	−	0.951462i	$-0.599581\pi$
$877$	−18.2285	−0.615532	−0.307766	+	0.951462i	$0.599581\pi$
$878$	65.0555	2.19552
$879$	13.6846	0.461571
$880$	−6.18204	−0.208397
$881$	49.1054	1.65440	0.827201	−	0.561906i	$-0.189932\pi$
$881$	49.1054	1.65440	0.827201	+	0.561906i	$0.189932\pi$
$882$	0	0
$883$	−14.4898	−0.487619	−0.243810	−	0.969823i	$-0.578397\pi$
$883$	−14.4898	−0.487619	−0.243810	+	0.969823i	$0.578397\pi$
$884$	41.2874	1.38865
$885$	19.0960	0.641904
$886$	41.7736	1.40341
$887$	11.9125	0.399983	0.199992	−	0.979798i	$-0.435909\pi$
$887$	11.9125	0.399983	0.199992	+	0.979798i	$0.435909\pi$
$888$	120.363	4.03913
$889$	0	0
$890$	7.85127	0.263175
$891$	−28.8259	−0.965703
$892$	65.3232	2.18718
$893$	−61.3404	−2.05268
$894$	105.971	3.54420
$895$	3.01189	0.100676
$896$	0	0
$897$	8.88831	0.296772
$898$	−92.2043	−3.07690
$899$	26.8320	0.894896
$900$	34.0156	1.13385
$901$	3.38051	0.112621
$902$	−3.22953	−0.107532
$903$	0	0
$904$	−13.1054	−0.435880
$905$	−22.1739	−0.737084
$906$	48.4525	1.60973
$907$	−17.7613	−0.589753	−0.294877	−	0.955535i	$-0.595279\pi$
$907$	−17.7613	−0.589753	−0.294877	+	0.955535i	$0.595279\pi$
$908$	−89.6331	−2.97458
$909$	61.1112	2.02693
$910$	0	0
$911$	5.00677	0.165882	0.0829408	−	0.996554i	$-0.473569\pi$
$911$	5.00677	0.165882	0.0829408	+	0.996554i	$0.473569\pi$
$912$	111.701	3.69878
$913$	−4.07571	−0.134886
$914$	−59.0389	−1.95283
$915$	−6.39708	−0.211481
$916$	−96.3401	−3.18317
$917$	0	0
$918$	−71.7973	−2.36967
$919$	10.9683	0.361810	0.180905	−	0.983501i	$-0.442097\pi$
$919$	10.9683	0.361810	0.180905	+	0.983501i	$0.442097\pi$
$920$	−3.00813	−0.0991752
$921$	−55.2911	−1.82190
$922$	−61.1558	−2.01406
$923$	−21.0615	−0.693248
$924$	0	0
$925$	−6.19498	−0.203690
$926$	78.3317	2.57414
$927$	75.1865	2.46945
$928$	17.9679	0.589824
$929$	−18.4795	−0.606291	−0.303146	−	0.952944i	$-0.598037\pi$
$929$	−18.4795	−0.606291	−0.303146	+	0.952944i	$0.598037\pi$
$930$	−46.5832	−1.52752
$931$	0	0
$932$	−111.422	−3.64975
$933$	−15.8789	−0.519850
$934$	−19.2418	−0.629611
$935$	−1.79311	−0.0586409
$936$	245.046	8.00958
$937$	42.7809	1.39759	0.698795	−	0.715322i	$-0.253720\pi$
$937$	42.7809	1.39759	0.698795	+	0.715322i	$0.253720\pi$
$938$	0	0
$939$	−85.1195	−2.77777
$940$	48.5325	1.58296
$941$	−31.0248	−1.01138	−0.505691	−	0.862715i	$-0.668762\pi$
$941$	−31.0248	−1.01138	−0.505691	+	0.862715i	$0.668762\pi$
$942$	−81.0518	−2.64081
$943$	−0.653322	−0.0212751
$944$	−35.8714	−1.16751
$945$	0	0
$946$	−15.6783	−0.509745
$947$	6.19791	0.201405	0.100703	−	0.994917i	$-0.467891\pi$
$947$	6.19791	0.201405	0.100703	+	0.994917i	$0.467891\pi$
$948$	−66.2866	−2.15289
$949$	15.8892	0.515785
$950$	−13.8286	−0.448660
$951$	29.6180	0.960430
$952$	0	0
$953$	−2.74266	−0.0888435	−0.0444217	−	0.999013i	$-0.514145\pi$
$953$	−2.74266	−0.0888435	−0.0444217	+	0.999013i	$0.514145\pi$
$954$	37.1833	1.20386
$955$	20.6363	0.667775
$956$	−118.973	−3.84787
$957$	15.7128	0.507923
$958$	85.4130	2.75957
$959$	0	0
$960$	9.49578	0.306475
$961$	0.582579	0.0187929
$962$	−82.7077	−2.66660
$963$	89.6621	2.88932
$964$	−102.931	−3.31517
$965$	−4.52408	−0.145635
$966$	0	0
$967$	16.4386	0.528629	0.264315	−	0.964437i	$-0.414854\pi$
$967$	16.4386	0.528629	0.264315	+	0.964437i	$0.414854\pi$
$968$	5.90377	0.189754
$969$	32.3989	1.04080
$970$	30.4074	0.976322
$971$	10.0406	0.322218	0.161109	−	0.986937i	$-0.448493\pi$
$971$	10.0406	0.322218	0.161109	+	0.986937i	$0.448493\pi$
$972$	−204.920	−6.57281
$973$	0	0
$974$	57.1106	1.82994
$975$	−17.4442	−0.558662
$976$	12.0168	0.384648
$977$	53.6843	1.71751	0.858756	−	0.512385i	$-0.171238\pi$
$977$	53.6843	1.71751	0.858756	+	0.512385i	$0.171238\pi$
$978$	143.033	4.57370
$979$	−3.11717	−0.0996251
$980$	0	0
$981$	59.8294	1.91021
$982$	46.9649	1.49871
$983$	11.8084	0.376628	0.188314	−	0.982109i	$-0.439698\pi$
$983$	11.8084	0.376628	0.188314	+	0.982109i	$0.439698\pi$
$984$	−24.9123	−0.794177
$985$	10.9741	0.349663
$986$	21.5633	0.686715
$987$	0	0
$988$	−126.418	−4.02191
$989$	−3.17166	−0.100853
$990$	−19.7230	−0.626837
$991$	2.78053	0.0883266	0.0441633	−	0.999024i	$-0.485938\pi$
$991$	2.78053	0.0883266	0.0441633	+	0.999024i	$0.485938\pi$
$992$	21.1491	0.671484
$993$	82.5830	2.62069
$994$	0	0
$995$	−11.4372	−0.362582
$996$	−58.2658	−1.84622
$997$	5.06526	0.160419	0.0802093	−	0.996778i	$-0.474441\pi$
$997$	5.06526	0.160419	0.0802093	+	0.996778i	$0.474441\pi$
$998$	−84.0009	−2.65900
$999$	98.4830	3.11587

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.t.1.7		8
7.2	even	3		385.2.i.c.221.2	✓	16
7.4	even	3		385.2.i.c.331.2	yes	16
7.6	odd	2		2695.2.a.s.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.c.221.2	✓	16	7.2	even	3
385.2.i.c.331.2	yes	16	7.4	even	3
2695.2.a.s.1.7		8	7.6	odd	2
2695.2.a.t.1.7		8	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:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2695.a (trivial)

\(f(q)\)	\(=\)	\(q+2.51872 q^{2} -3.29098 q^{3} +4.34396 q^{4} +1.00000 q^{5} -8.28906 q^{6} +5.90377 q^{8} +7.83055 q^{9} +O(q^{10})\)	\(q+2.51872 q^{2} -3.29098 q^{3} +4.34396 q^{4} +1.00000 q^{5} -8.28906 q^{6} +5.90377 q^{8} +7.83055 q^{9} +2.51872 q^{10} -1.00000 q^{11} -14.2959 q^{12} +5.30061 q^{13} -3.29098 q^{15} +6.18204 q^{16} +1.79311 q^{17} +19.7230 q^{18} -5.49034 q^{19} +4.34396 q^{20} -2.51872 q^{22} -0.509528 q^{23} -19.4292 q^{24} +1.00000 q^{25} +13.3508 q^{26} -15.8972 q^{27} +4.77451 q^{29} -8.28906 q^{30} +5.61984 q^{31} +3.76329 q^{32} +3.29098 q^{33} +4.51634 q^{34} +34.0156 q^{36} -6.19498 q^{37} -13.8286 q^{38} -17.4442 q^{39} +5.90377 q^{40} +1.28221 q^{41} +6.22470 q^{43} -4.34396 q^{44} +7.83055 q^{45} -1.28336 q^{46} +11.1724 q^{47} -20.3450 q^{48} +2.51872 q^{50} -5.90108 q^{51} +23.0256 q^{52} +1.88528 q^{53} -40.0407 q^{54} -1.00000 q^{55} +18.0686 q^{57} +12.0257 q^{58} -5.80252 q^{59} -14.2959 q^{60} +1.94382 q^{61} +14.1548 q^{62} -2.88540 q^{64} +5.30061 q^{65} +8.28906 q^{66} +1.77944 q^{67} +7.78918 q^{68} +1.67685 q^{69} -3.97341 q^{71} +46.2298 q^{72} +2.99761 q^{73} -15.6034 q^{74} -3.29098 q^{75} -23.8498 q^{76} -43.9371 q^{78} +4.63677 q^{79} +6.18204 q^{80} +28.8259 q^{81} +3.22953 q^{82} +4.07571 q^{83} +1.79311 q^{85} +15.6783 q^{86} -15.7128 q^{87} -5.90377 q^{88} +3.11717 q^{89} +19.7230 q^{90} -2.21337 q^{92} -18.4948 q^{93} +28.1402 q^{94} -5.49034 q^{95} -12.3849 q^{96} +12.0725 q^{97} -7.83055 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + q^{3} + 9 q^{4} + 8 q^{5} - 3 q^{6} + 9 q^{8} + 19 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 + q^3 + 9 * q^4 + 8 * q^5 - 3 * q^6 + 9 * q^8 + 19 * q^9	\( 8 q + 3 q^{2} + q^{3} + 9 q^{4} + 8 q^{5} - 3 q^{6} + 9 q^{8} + 19 q^{9} + 3 q^{10} - 8 q^{11} + 9 q^{12} + 14 q^{13} + q^{15} + 7 q^{16} + 5 q^{17} + 27 q^{18} + q^{19} + 9 q^{20} - 3 q^{22} - 2 q^{23} - 24 q^{24} + 8 q^{25} + 21 q^{26} - 5 q^{27} + 26 q^{29} - 3 q^{30} + 2 q^{31} + 16 q^{32} - q^{33} - 26 q^{34} + 54 q^{36} - q^{37} - 31 q^{38} + 19 q^{39} + 9 q^{40} - 3 q^{41} + 4 q^{43} - 9 q^{44} + 19 q^{45} + 10 q^{46} + q^{47} - 21 q^{48} + 3 q^{50} + 3 q^{51} + 37 q^{52} + 26 q^{53} - 5 q^{54} - 8 q^{55} + 20 q^{57} - q^{58} - 19 q^{59} + 9 q^{60} - 26 q^{62} + q^{64} + 14 q^{65} + 3 q^{66} - 13 q^{67} + 15 q^{68} - 14 q^{69} - 9 q^{71} + 32 q^{72} + 11 q^{73} + 24 q^{74} + q^{75} - 18 q^{76} - 33 q^{78} - 8 q^{79} + 7 q^{80} + 52 q^{81} + 41 q^{82} + 32 q^{83} + 5 q^{85} + 28 q^{86} - 16 q^{87} - 9 q^{88} + 5 q^{89} + 27 q^{90} + 30 q^{92} - 14 q^{93} - 5 q^{94} + q^{95} + q^{96} + 9 q^{97} - 19 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 + q^3 + 9 * q^4 + 8 * q^5 - 3 * q^6 + 9 * q^8 + 19 * q^9 + 3 * q^10 - 8 * q^11 + 9 * q^12 + 14 * q^13 + q^15 + 7 * q^16 + 5 * q^17 + 27 * q^18 + q^19 + 9 * q^20 - 3 * q^22 - 2 * q^23 - 24 * q^24 + 8 * q^25 + 21 * q^26 - 5 * q^27 + 26 * q^29 - 3 * q^30 + 2 * q^31 + 16 * q^32 - q^33 - 26 * q^34 + 54 * q^36 - q^37 - 31 * q^38 + 19 * q^39 + 9 * q^40 - 3 * q^41 + 4 * q^43 - 9 * q^44 + 19 * q^45 + 10 * q^46 + q^47 - 21 * q^48 + 3 * q^50 + 3 * q^51 + 37 * q^52 + 26 * q^53 - 5 * q^54 - 8 * q^55 + 20 * q^57 - q^58 - 19 * q^59 + 9 * q^60 - 26 * q^62 + q^64 + 14 * q^65 + 3 * q^66 - 13 * q^67 + 15 * q^68 - 14 * q^69 - 9 * q^71 + 32 * q^72 + 11 * q^73 + 24 * q^74 + q^75 - 18 * q^76 - 33 * q^78 - 8 * q^79 + 7 * q^80 + 52 * q^81 + 41 * q^82 + 32 * q^83 + 5 * q^85 + 28 * q^86 - 16 * q^87 - 9 * q^88 + 5 * q^89 + 27 * q^90 + 30 * q^92 - 14 * q^93 - 5 * q^94 + q^95 + q^96 + 9 * q^97 - 19 * q^99

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