LMFDB - Embedded newform 6025.2.a.h.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 14 x^{10} + 44 x^{9} + 65 x^{8} - 219 x^{7} - 123 x^{6} + 444 x^{5} + 105 x^{4} + \cdots - 1 $ x^12 - 3x^11 - 14x^10 + 44x^9 + 65x^8 - 219x^7 - 123x^6 + 444x^5 + 105x^4 - 328x^3 - 45x^2 + 18*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 241)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.54879$ of defining polynomial
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.54879 q^{2} -2.81087 q^{3} +0.398765 q^{4} +4.35346 q^{6} +4.24623 q^{7} +2.47998 q^{8} +4.90098 q^{9} +O(q^{10})$	\(q-1.54879 q^{2} -2.81087 q^{3} +0.398765 q^{4} +4.35346 q^{6} +4.24623 q^{7} +2.47998 q^{8} +4.90098 q^{9} +0.915418 q^{11} -1.12088 q^{12} -4.81392 q^{13} -6.57654 q^{14} -4.63852 q^{16} +5.38915 q^{17} -7.59061 q^{18} -4.34799 q^{19} -11.9356 q^{21} -1.41779 q^{22} -8.10534 q^{23} -6.97091 q^{24} +7.45578 q^{26} -5.34340 q^{27} +1.69325 q^{28} -6.45221 q^{29} +10.7804 q^{31} +2.22414 q^{32} -2.57312 q^{33} -8.34668 q^{34} +1.95434 q^{36} -5.16908 q^{37} +6.73415 q^{38} +13.5313 q^{39} -0.612344 q^{41} +18.4858 q^{42} +1.85213 q^{43} +0.365036 q^{44} +12.5535 q^{46} +2.21116 q^{47} +13.0383 q^{48} +11.0305 q^{49} -15.1482 q^{51} -1.91962 q^{52} -0.00846193 q^{53} +8.27584 q^{54} +10.5306 q^{56} +12.2216 q^{57} +9.99315 q^{58} +8.85799 q^{59} +3.78644 q^{61} -16.6967 q^{62} +20.8107 q^{63} +5.83230 q^{64} +3.98523 q^{66} -4.67684 q^{67} +2.14900 q^{68} +22.7830 q^{69} +1.48694 q^{71} +12.1544 q^{72} +10.3630 q^{73} +8.00585 q^{74} -1.73383 q^{76} +3.88708 q^{77} -20.9572 q^{78} -17.6786 q^{79} +0.316666 q^{81} +0.948396 q^{82} -7.45731 q^{83} -4.75950 q^{84} -2.86857 q^{86} +18.1363 q^{87} +2.27022 q^{88} -0.520713 q^{89} -20.4410 q^{91} -3.23212 q^{92} -30.3024 q^{93} -3.42463 q^{94} -6.25177 q^{96} +6.33494 q^{97} -17.0840 q^{98} +4.48644 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - q^3 + 13 * q^4 - q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9	$ 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9} + 22 q^{11} + 7 q^{12} + 5 q^{13} + 6 q^{14} + 15 q^{16} + 4 q^{17} + q^{18} - 6 q^{19} - 14 q^{21} + 12 q^{22} - 32 q^{23} - 15 q^{24} + 8 q^{26} + 5 q^{27} + 11 q^{28} + 6 q^{29} + 8 q^{31} - q^{32} + 24 q^{33} - 19 q^{34} - 8 q^{36} + 8 q^{37} + 10 q^{38} + 31 q^{39} - q^{41} + 49 q^{42} + 2 q^{43} + 42 q^{44} - 25 q^{46} - 34 q^{47} + 49 q^{48} - 9 q^{49} - 3 q^{51} + 41 q^{52} - 5 q^{53} - 40 q^{54} + q^{56} + 22 q^{57} + 33 q^{58} + 26 q^{59} - 26 q^{61} + 17 q^{62} + 4 q^{63} + 13 q^{64} - 2 q^{66} - 6 q^{67} + 35 q^{68} - 2 q^{69} + 94 q^{71} - 17 q^{72} + 22 q^{73} + 26 q^{74} - 20 q^{76} + 7 q^{77} - 54 q^{78} + 9 q^{79} + 4 q^{81} - 15 q^{82} + 8 q^{83} + 2 q^{84} + 9 q^{86} - 4 q^{87} - 6 q^{88} - 3 q^{89} - 20 q^{91} - 36 q^{92} - 12 q^{93} + 48 q^{94} - 23 q^{96} + 29 q^{97} - 28 q^{98} + 36 q^{99}+O(q^{100}) $ 12 * q - 3 * q^2 - q^3 + 13 * q^4 - q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9 + 22 * q^11 + 7 * q^12 + 5 * q^13 + 6 * q^14 + 15 * q^16 + 4 * q^17 + q^18 - 6 * q^19 - 14 * q^21 + 12 * q^22 - 32 * q^23 - 15 * q^24 + 8 * q^26 + 5 * q^27 + 11 * q^28 + 6 * q^29 + 8 * q^31 - q^32 + 24 * q^33 - 19 * q^34 - 8 * q^36 + 8 * q^37 + 10 * q^38 + 31 * q^39 - q^41 + 49 * q^42 + 2 * q^43 + 42 * q^44 - 25 * q^46 - 34 * q^47 + 49 * q^48 - 9 * q^49 - 3 * q^51 + 41 * q^52 - 5 * q^53 - 40 * q^54 + q^56 + 22 * q^57 + 33 * q^58 + 26 * q^59 - 26 * q^61 + 17 * q^62 + 4 * q^63 + 13 * q^64 - 2 * q^66 - 6 * q^67 + 35 * q^68 - 2 * q^69 + 94 * q^71 - 17 * q^72 + 22 * q^73 + 26 * q^74 - 20 * q^76 + 7 * q^77 - 54 * q^78 + 9 * q^79 + 4 * q^81 - 15 * q^82 + 8 * q^83 + 2 * q^84 + 9 * q^86 - 4 * q^87 - 6 * q^88 - 3 * q^89 - 20 * q^91 - 36 * q^92 - 12 * q^93 + 48 * q^94 - 23 * q^96 + 29 * q^97 - 28 * q^98 + 36 * 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 $

$2$	−1.54879	−1.09516	−0.547582	−	0.836752i	$-0.684451\pi$
$2$	−1.54879	−1.09516	−0.547582	+	0.836752i	$0.684451\pi$
$3$	−2.81087	−1.62286	−0.811428	−	0.584453i	$-0.801309\pi$
$3$	−2.81087	−1.62286	−0.811428	+	0.584453i	$0.801309\pi$
$4$	0.398765	0.199382
$5$	0	0
$5$	0	0
$6$	4.35346	1.77729
$7$	4.24623	1.60493	0.802463	−	0.596702i	$-0.203523\pi$
$7$	4.24623	1.60493	0.802463	+	0.596702i	$0.203523\pi$
$8$	2.47998	0.876807
$9$	4.90098	1.63366
$10$	0	0
$11$	0.915418	0.276009	0.138004	−	0.990432i	$-0.455931\pi$
$11$	0.915418	0.276009	0.138004	+	0.990432i	$0.455931\pi$
$12$	−1.12088	−0.323569
$13$	−4.81392	−1.33514	−0.667571	−	0.744546i	$-0.732666\pi$
$13$	−4.81392	−1.33514	−0.667571	+	0.744546i	$0.732666\pi$
$14$	−6.57654	−1.75766
$15$	0	0
$16$	−4.63852	−1.15963
$17$	5.38915	1.30706	0.653530	−	0.756901i	$-0.273287\pi$
$17$	5.38915	1.30706	0.653530	+	0.756901i	$0.273287\pi$
$18$	−7.59061	−1.78912
$19$	−4.34799	−0.997498	−0.498749	−	0.866747i	$-0.666207\pi$
$19$	−4.34799	−0.997498	−0.498749	+	0.866747i	$0.666207\pi$
$20$	0	0
$21$	−11.9356	−2.60456
$22$	−1.41779	−0.302275
$23$	−8.10534	−1.69008	−0.845040	−	0.534703i	$-0.820423\pi$
$23$	−8.10534	−1.69008	−0.845040	+	0.534703i	$0.820423\pi$
$24$	−6.97091	−1.42293
$25$	0	0
$26$	7.45578	1.46220
$27$	−5.34340	−1.02834
$28$	1.69325	0.319994
$29$	−6.45221	−1.19815	−0.599073	−	0.800695i	$-0.704464\pi$
$29$	−6.45221	−1.19815	−0.599073	+	0.800695i	$0.704464\pi$
$30$	0	0
$31$	10.7804	1.93623	0.968113	−	0.250515i	$-0.0806000\pi$
$31$	10.7804	1.93623	0.968113	+	0.250515i	$0.0806000\pi$
$32$	2.22414	0.393176
$33$	−2.57312	−0.447922
$34$	−8.34668	−1.43144
$35$	0	0
$36$	1.95434	0.325723
$37$	−5.16908	−0.849792	−0.424896	−	0.905242i	$-0.639689\pi$
$37$	−5.16908	−0.849792	−0.424896	+	0.905242i	$0.639689\pi$
$38$	6.73415	1.09242
$39$	13.5313	2.16674
$40$	0	0
$41$	−0.612344	−0.0956321	−0.0478161	−	0.998856i	$-0.515226\pi$
$41$	−0.612344	−0.0956321	−0.0478161	+	0.998856i	$0.515226\pi$
$42$	18.4858	2.85242
$43$	1.85213	0.282447	0.141223	−	0.989978i	$-0.454896\pi$
$43$	1.85213	0.282447	0.141223	+	0.989978i	$0.454896\pi$
$44$	0.365036	0.0550313
$45$	0	0
$46$	12.5535	1.85091
$47$	2.21116	0.322531	0.161265	−	0.986911i	$-0.448443\pi$
$47$	2.21116	0.322531	0.161265	+	0.986911i	$0.448443\pi$
$48$	13.0383	1.88191
$49$	11.0305	1.57579
$50$	0	0
$51$	−15.1482	−2.12117
$52$	−1.91962	−0.266204
$53$	−0.00846193	−0.00116234	−0.000581168	−	1.00000i	$-0.500185\pi$
$53$	−0.00846193	−0.00116234	−0.000581168		1.00000i	$0.500185\pi$
$54$	8.27584	1.12620
$55$	0	0
$56$	10.5306	1.40721
$57$	12.2216	1.61879
$58$	9.99315	1.31216
$59$	8.85799	1.15321	0.576606	−	0.817022i	$-0.304377\pi$
$59$	8.85799	1.15321	0.576606	+	0.817022i	$0.304377\pi$
$60$	0	0
$61$	3.78644	0.484805	0.242402	−	0.970176i	$-0.422065\pi$
$61$	3.78644	0.484805	0.242402	+	0.970176i	$0.422065\pi$
$62$	−16.6967	−2.12048
$63$	20.8107	2.62190
$64$	5.83230	0.729037
$65$	0	0
$66$	3.98523	0.490548
$67$	−4.67684	−0.571367	−0.285683	−	0.958324i	$-0.592221\pi$
$67$	−4.67684	−0.571367	−0.285683	+	0.958324i	$0.592221\pi$
$68$	2.14900	0.260605
$69$	22.7830	2.74276
$70$	0	0
$71$	1.48694	0.176467	0.0882334	−	0.996100i	$-0.471878\pi$
$71$	1.48694	0.176467	0.0882334	+	0.996100i	$0.471878\pi$
$72$	12.1544	1.43240
$73$	10.3630	1.21290	0.606449	−	0.795122i	$-0.292593\pi$
$73$	10.3630	1.21290	0.606449	+	0.795122i	$0.292593\pi$
$74$	8.00585	0.930661
$75$	0	0
$76$	−1.73383	−0.198884
$77$	3.88708	0.442974
$78$	−20.9572	−2.37294
$79$	−17.6786	−1.98900	−0.994499	−	0.104743i	$-0.966598\pi$
$79$	−17.6786	−1.98900	−0.994499	+	0.104743i	$0.966598\pi$
$80$	0	0
$81$	0.316666	0.0351851
$82$	0.948396	0.104733
$83$	−7.45731	−0.818546	−0.409273	−	0.912412i	$-0.634218\pi$
$83$	−7.45731	−0.818546	−0.409273	+	0.912412i	$0.634218\pi$
$84$	−4.75950	−0.519304
$85$	0	0
$86$	−2.86857	−0.309325
$87$	18.1363	1.94442
$88$	2.27022	0.242006
$89$	−0.520713	−0.0551955	−0.0275978	−	0.999619i	$-0.508786\pi$
$89$	−0.520713	−0.0551955	−0.0275978	+	0.999619i	$0.508786\pi$
$90$	0	0
$91$	−20.4410	−2.14280
$92$	−3.23212	−0.336972
$93$	−30.3024	−3.14221
$94$	−3.42463	−0.353224
$95$	0	0
$96$	−6.25177	−0.638068
$97$	6.33494	0.643216	0.321608	−	0.946873i	$-0.395777\pi$
$97$	6.33494	0.643216	0.321608	+	0.946873i	$0.395777\pi$
$98$	−17.0840	−1.72574
$99$	4.48644	0.450904
$100$	0	0
$101$	7.20652	0.717076	0.358538	−	0.933515i	$-0.383275\pi$
$101$	7.20652	0.717076	0.358538	+	0.933515i	$0.383275\pi$
$102$	23.4614	2.32303
$103$	−7.82738	−0.771255	−0.385627	−	0.922655i	$-0.626015\pi$
$103$	−7.82738	−0.771255	−0.385627	+	0.922655i	$0.626015\pi$
$104$	−11.9385	−1.17066
$105$	0	0
$106$	0.0131058	0.00127295
$107$	−3.28176	−0.317260	−0.158630	−	0.987338i	$-0.550708\pi$
$107$	−3.28176	−0.317260	−0.158630	+	0.987338i	$0.550708\pi$
$108$	−2.13076	−0.205033
$109$	6.89529	0.660449	0.330224	−	0.943902i	$-0.392876\pi$
$109$	6.89529	0.660449	0.330224	+	0.943902i	$0.392876\pi$
$110$	0	0
$111$	14.5296	1.37909
$112$	−19.6962	−1.86112
$113$	14.4737	1.36157	0.680787	−	0.732481i	$-0.261638\pi$
$113$	14.4737	1.36157	0.680787	+	0.732481i	$0.261638\pi$
$114$	−18.9288	−1.77284
$115$	0	0
$116$	−2.57292	−0.238889
$117$	−23.5929	−2.18117
$118$	−13.7192	−1.26296
$119$	22.8836	2.09773
$120$	0	0
$121$	−10.1620	−0.923819
$122$	−5.86443	−0.530940
$123$	1.72122	0.155197
$124$	4.29886	0.386049
$125$	0	0
$126$	−32.2315	−2.87141
$127$	−6.96745	−0.618261	−0.309130	−	0.951020i	$-0.600038\pi$
$127$	−6.96745	−0.618261	−0.309130	+	0.951020i	$0.600038\pi$
$128$	−13.4813	−1.19159
$129$	−5.20609	−0.458370
$130$	0	0
$131$	7.02108	0.613434	0.306717	−	0.951801i	$-0.400769\pi$
$131$	7.02108	0.613434	0.306717	+	0.951801i	$0.400769\pi$
$132$	−1.02607	−0.0893079
$133$	−18.4626	−1.60091
$134$	7.24346	0.625740
$135$	0	0
$136$	13.3650	1.14604
$137$	−5.78101	−0.493905	−0.246953	−	0.969028i	$-0.579429\pi$
$137$	−5.78101	−0.493905	−0.246953	+	0.969028i	$0.579429\pi$
$138$	−35.2862	−3.00376
$139$	2.34939	0.199272	0.0996362	−	0.995024i	$-0.468232\pi$
$139$	2.34939	0.199272	0.0996362	+	0.995024i	$0.468232\pi$
$140$	0	0
$141$	−6.21527	−0.523421
$142$	−2.30296	−0.193260
$143$	−4.40675	−0.368511
$144$	−22.7333	−1.89444
$145$	0	0
$146$	−16.0502	−1.32832
$147$	−31.0053	−2.55727
$148$	−2.06125	−0.169434
$149$	4.44128	0.363844	0.181922	−	0.983313i	$-0.441768\pi$
$149$	4.44128	0.363844	0.181922	+	0.983313i	$0.441768\pi$
$150$	0	0
$151$	−5.33629	−0.434261	−0.217130	−	0.976143i	$-0.569670\pi$
$151$	−5.33629	−0.434261	−0.217130	+	0.976143i	$0.569670\pi$
$152$	−10.7830	−0.874613
$153$	26.4121	2.13529
$154$	−6.02028	−0.485128
$155$	0	0
$156$	5.39581	0.432010
$157$	21.6127	1.72488	0.862442	−	0.506157i	$-0.168934\pi$
$157$	21.6127	1.72488	0.862442	+	0.506157i	$0.168934\pi$
$158$	27.3805	2.17828
$159$	0.0237854	0.00188630
$160$	0	0
$161$	−34.4172	−2.71245
$162$	−0.490451	−0.0385334
$163$	22.0999	1.73100	0.865500	−	0.500909i	$-0.167001\pi$
$163$	22.0999	1.73100	0.865500	+	0.500909i	$0.167001\pi$
$164$	−0.244181	−0.0190674
$165$	0	0
$166$	11.5498	0.896442
$167$	2.58299	0.199877	0.0999387	−	0.994994i	$-0.468135\pi$
$167$	2.58299	0.199877	0.0999387	+	0.994994i	$0.468135\pi$
$168$	−29.6001	−2.28370
$169$	10.1739	0.782604
$170$	0	0
$171$	−21.3094	−1.62957
$172$	0.738564	0.0563149
$173$	−9.53817	−0.725174	−0.362587	−	0.931950i	$-0.618106\pi$
$173$	−9.53817	−0.725174	−0.362587	+	0.931950i	$0.618106\pi$
$174$	−28.0894	−2.12945
$175$	0	0
$176$	−4.24618	−0.320068
$177$	−24.8986	−1.87150
$178$	0.806478	0.0604481
$179$	11.6661	0.871963	0.435981	−	0.899956i	$-0.356401\pi$
$179$	11.6661	0.871963	0.435981	+	0.899956i	$0.356401\pi$
$180$	0	0
$181$	−6.78106	−0.504032	−0.252016	−	0.967723i	$-0.581094\pi$
$181$	−6.78106	−0.504032	−0.252016	+	0.967723i	$0.581094\pi$
$182$	31.6590	2.34672
$183$	−10.6432	−0.786768
$184$	−20.1011	−1.48187
$185$	0	0
$186$	46.9322	3.44124
$187$	4.93332	0.360760
$188$	0.881732	0.0643069
$189$	−22.6893	−1.65041
$190$	0	0
$191$	9.30072	0.672976	0.336488	−	0.941688i	$-0.390761\pi$
$191$	9.30072	0.672976	0.336488	+	0.941688i	$0.390761\pi$
$192$	−16.3938	−1.18312
$193$	1.27177	0.0915440	0.0457720	−	0.998952i	$-0.485425\pi$
$193$	1.27177	0.0915440	0.0457720	+	0.998952i	$0.485425\pi$
$194$	−9.81153	−0.704427
$195$	0	0
$196$	4.39858	0.314184
$197$	−9.51222	−0.677718	−0.338859	−	0.940837i	$-0.610041\pi$
$197$	−9.51222	−0.677718	−0.338859	+	0.940837i	$0.610041\pi$
$198$	−6.94858	−0.493814
$199$	−18.4776	−1.30984	−0.654922	−	0.755696i	$-0.727299\pi$
$199$	−18.4776	−1.30984	−0.654922	+	0.755696i	$0.727299\pi$
$200$	0	0
$201$	13.1460	0.927246
$202$	−11.1614	−0.785315
$203$	−27.3976	−1.92293
$204$	−6.04056	−0.422924
$205$	0	0
$206$	12.1230	0.844650
$207$	−39.7241	−2.76102
$208$	22.3295	1.54827
$209$	−3.98023	−0.275318
$210$	0	0
$211$	5.54459	0.381705	0.190853	−	0.981619i	$-0.438875\pi$
$211$	5.54459	0.381705	0.190853	+	0.981619i	$0.438875\pi$
$212$	−0.00337432	−0.000231749 0
$213$	−4.17958	−0.286380
$214$	5.08278	0.347451
$215$	0	0
$216$	−13.2516	−0.901654
$217$	45.7763	3.10750
$218$	−10.6794	−0.723299
$219$	−29.1290	−1.96836
$220$	0	0
$221$	−25.9429	−1.74511
$222$	−22.5034	−1.51033
$223$	12.8984	0.863744	0.431872	−	0.901935i	$-0.357853\pi$
$223$	12.8984	0.863744	0.431872	+	0.901935i	$0.357853\pi$
$224$	9.44422	0.631019
$225$	0	0
$226$	−22.4169	−1.49115
$227$	−2.85469	−0.189473	−0.0947364	−	0.995502i	$-0.530201\pi$
$227$	−2.85469	−0.189473	−0.0947364	+	0.995502i	$0.530201\pi$
$228$	4.87356	0.322759
$229$	−16.1705	−1.06857	−0.534287	−	0.845303i	$-0.679420\pi$
$229$	−16.1705	−1.06857	−0.534287	+	0.845303i	$0.679420\pi$
$230$	0	0
$231$	−10.9261	−0.718882
$232$	−16.0014	−1.05054
$233$	−11.3792	−0.745476	−0.372738	−	0.927937i	$-0.621581\pi$
$233$	−11.3792	−0.745476	−0.372738	+	0.927937i	$0.621581\pi$
$234$	36.5406	2.38874
$235$	0	0
$236$	3.53226	0.229930
$237$	49.6922	3.22786
$238$	−35.4420	−2.29736
$239$	27.0358	1.74880	0.874400	−	0.485206i	$-0.161255\pi$
$239$	27.0358	1.74880	0.874400	+	0.485206i	$0.161255\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	15.7389	1.01173
$243$	15.1401	0.971238
$244$	1.50990	0.0966615
$245$	0	0
$246$	−2.66582	−0.169966
$247$	20.9309	1.33180
$248$	26.7353	1.69770
$249$	20.9615	1.32838
$250$	0	0
$251$	−16.5147	−1.04240	−0.521199	−	0.853435i	$-0.674515\pi$
$251$	−16.5147	−1.04240	−0.521199	+	0.853435i	$0.674515\pi$
$252$	8.29858	0.522761
$253$	−7.41977	−0.466477
$254$	10.7911	0.677097
$255$	0	0
$256$	9.21519	0.575949
$257$	9.88138	0.616383	0.308192	−	0.951324i	$-0.400276\pi$
$257$	9.88138	0.616383	0.308192	+	0.951324i	$0.400276\pi$
$258$	8.06316	0.501990
$259$	−21.9491	−1.36385
$260$	0	0
$261$	−31.6222	−1.95736
$262$	−10.8742	−0.671811
$263$	31.5776	1.94716	0.973579	−	0.228351i	$-0.0733335\pi$
$263$	31.5776	1.94716	0.973579	+	0.228351i	$0.0733335\pi$
$264$	−6.38129	−0.392741
$265$	0	0
$266$	28.5948	1.75326
$267$	1.46366	0.0895744
$268$	−1.86496	−0.113921
$269$	4.21527	0.257010	0.128505	−	0.991709i	$-0.458982\pi$
$269$	4.21527	0.257010	0.128505	+	0.991709i	$0.458982\pi$
$270$	0	0
$271$	11.8060	0.717162	0.358581	−	0.933499i	$-0.383261\pi$
$271$	11.8060	0.717162	0.358581	+	0.933499i	$0.383261\pi$
$272$	−24.9976	−1.51570
$273$	57.4571	3.47746
$274$	8.95360	0.540907
$275$	0	0
$276$	9.08508	0.546857
$277$	−8.01314	−0.481463	−0.240731	−	0.970592i	$-0.577387\pi$
$277$	−8.01314	−0.481463	−0.240731	+	0.970592i	$0.577387\pi$
$278$	−3.63872	−0.218236
$279$	52.8348	3.16313
$280$	0	0
$281$	−21.6719	−1.29284	−0.646419	−	0.762982i	$-0.723734\pi$
$281$	−21.6719	−1.29284	−0.646419	+	0.762982i	$0.723734\pi$
$282$	9.62618	0.573231
$283$	−2.15646	−0.128188	−0.0640941	−	0.997944i	$-0.520416\pi$
$283$	−2.15646	−0.128188	−0.0640941	+	0.997944i	$0.520416\pi$
$284$	0.592938	0.0351844
$285$	0	0
$286$	6.82515	0.403580
$287$	−2.60016	−0.153482
$288$	10.9005	0.642316
$289$	12.0429	0.708406
$290$	0	0
$291$	−17.8067	−1.04385
$292$	4.13240	0.241831
$293$	−26.9520	−1.57455	−0.787276	−	0.616601i	$-0.788509\pi$
$293$	−26.9520	−1.57455	−0.787276	+	0.616601i	$0.788509\pi$
$294$	48.0208	2.80063
$295$	0	0
$296$	−12.8192	−0.745103
$297$	−4.89145	−0.283830
$298$	−6.87863	−0.398469
$299$	39.0185	2.25650
$300$	0	0
$301$	7.86457	0.453306
$302$	8.26481	0.475586
$303$	−20.2566	−1.16371
$304$	20.1682	1.15673
$305$	0	0
$306$	−40.9069	−2.33849
$307$	−16.6282	−0.949020	−0.474510	−	0.880250i	$-0.657375\pi$
$307$	−16.6282	−0.949020	−0.474510	+	0.880250i	$0.657375\pi$
$308$	1.55003	0.0883211
$309$	22.0017	1.25163
$310$	0	0
$311$	−10.1432	−0.575167	−0.287584	−	0.957756i	$-0.592852\pi$
$311$	−10.1432	−0.575167	−0.287584	+	0.957756i	$0.592852\pi$
$312$	33.5574	1.89981
$313$	26.7382	1.51133	0.755667	−	0.654956i	$-0.227313\pi$
$313$	26.7382	1.51133	0.755667	+	0.654956i	$0.227313\pi$
$314$	−33.4737	−1.88903
$315$	0	0
$316$	−7.04961	−0.396571
$317$	25.6438	1.44030	0.720151	−	0.693817i	$-0.244072\pi$
$317$	25.6438	1.44030	0.720151	+	0.693817i	$0.244072\pi$
$318$	−0.0368387	−0.00206581
$319$	−5.90647	−0.330699
$320$	0	0
$321$	9.22460	0.514867
$322$	53.3051	2.97058
$323$	−23.4320	−1.30379
$324$	0.126275	0.00701529
$325$	0	0
$326$	−34.2282	−1.89573
$327$	−19.3817	−1.07181
$328$	−1.51860	−0.0838509
$329$	9.38910	0.517638
$330$	0	0
$331$	21.9178	1.20471	0.602356	−	0.798228i	$-0.294229\pi$
$331$	21.9178	1.20471	0.602356	+	0.798228i	$0.294229\pi$
$332$	−2.97371	−0.163204
$333$	−25.3336	−1.38827
$334$	−4.00052	−0.218898
$335$	0	0
$336$	55.3635	3.02033
$337$	−5.64948	−0.307747	−0.153873	−	0.988091i	$-0.549175\pi$
$337$	−5.64948	−0.307747	−0.153873	+	0.988091i	$0.549175\pi$
$338$	−15.7572	−0.857079
$339$	−40.6838	−2.20964
$340$	0	0
$341$	9.86861	0.534415
$342$	33.0039	1.78465
$343$	17.1144	0.924093
$344$	4.59325	0.247651
$345$	0	0
$346$	14.7727	0.794184
$347$	−19.7057	−1.05786	−0.528928	−	0.848667i	$-0.677406\pi$
$347$	−19.7057	−1.05786	−0.528928	+	0.848667i	$0.677406\pi$
$348$	7.23213	0.387683
$349$	−31.5930	−1.69113	−0.845567	−	0.533869i	$-0.820738\pi$
$349$	−31.5930	−1.69113	−0.845567	+	0.533869i	$0.820738\pi$
$350$	0	0
$351$	25.7227	1.37298
$352$	2.03602	0.108520
$353$	−12.7948	−0.680999	−0.340499	−	0.940245i	$-0.610596\pi$
$353$	−12.7948	−0.680999	−0.340499	+	0.940245i	$0.610596\pi$
$354$	38.5629	2.04959
$355$	0	0
$356$	−0.207642	−0.0110050
$357$	−64.3227	−3.40432
$358$	−18.0683	−0.954942
$359$	27.2866	1.44013	0.720066	−	0.693906i	$-0.244112\pi$
$359$	27.2866	1.44013	0.720066	+	0.693906i	$0.244112\pi$
$360$	0	0
$361$	−0.0949647	−0.00499814
$362$	10.5025	0.551998
$363$	28.5641	1.49923
$364$	−8.15117	−0.427237
$365$	0	0
$366$	16.4841	0.861639
$367$	−25.9541	−1.35479	−0.677396	−	0.735619i	$-0.736891\pi$
$367$	−25.9541	−1.35479	−0.677396	+	0.735619i	$0.736891\pi$
$368$	37.5967	1.95987
$369$	−3.00109	−0.156230
$370$	0	0
$371$	−0.0359313	−0.00186546
$372$	−12.0835	−0.626502
$373$	−1.94963	−0.100948	−0.0504740	−	0.998725i	$-0.516073\pi$
$373$	−1.94963	−0.100948	−0.0504740	+	0.998725i	$0.516073\pi$
$374$	−7.64070	−0.395091
$375$	0	0
$376$	5.48364	0.282797
$377$	31.0604	1.59969
$378$	35.1411	1.80747
$379$	22.0885	1.13461	0.567305	−	0.823508i	$-0.307986\pi$
$379$	22.0885	1.13461	0.567305	+	0.823508i	$0.307986\pi$
$380$	0	0
$381$	19.5846	1.00335
$382$	−14.4049	−0.737019
$383$	32.6589	1.66879	0.834396	−	0.551166i	$-0.185817\pi$
$383$	32.6589	1.66879	0.834396	+	0.551166i	$0.185817\pi$
$384$	37.8942	1.93378
$385$	0	0
$386$	−1.96971	−0.100256
$387$	9.07724	0.461422
$388$	2.52615	0.128246
$389$	−1.59569	−0.0809045	−0.0404522	−	0.999181i	$-0.512880\pi$
$389$	−1.59569	−0.0809045	−0.0404522	+	0.999181i	$0.512880\pi$
$390$	0	0
$391$	−43.6809	−2.20904
$392$	27.3555	1.38166
$393$	−19.7353	−0.995515
$394$	14.7325	0.742212
$395$	0	0
$396$	1.78904	0.0899024
$397$	20.5064	1.02919	0.514593	−	0.857434i	$-0.327943\pi$
$397$	20.5064	1.02919	0.514593	+	0.857434i	$0.327943\pi$
$398$	28.6181	1.43449
$399$	51.8959	2.59805
$400$	0	0
$401$	2.51432	0.125559	0.0627795	−	0.998027i	$-0.480004\pi$
$401$	2.51432	0.125559	0.0627795	+	0.998027i	$0.480004\pi$
$402$	−20.3604	−1.01549
$403$	−51.8962	−2.58514
$404$	2.87371	0.142972
$405$	0	0
$406$	42.4333	2.10593
$407$	−4.73187	−0.234550
$408$	−37.5672	−1.85986
$409$	−3.99904	−0.197740	−0.0988698	−	0.995100i	$-0.531523\pi$
$409$	−3.99904	−0.197740	−0.0988698	+	0.995100i	$0.531523\pi$
$410$	0	0
$411$	16.2497	0.801537
$412$	−3.12128	−0.153775
$413$	37.6131	1.85082
$414$	61.5245	3.02376
$415$	0	0
$416$	−10.7068	−0.524946
$417$	−6.60382	−0.323390
$418$	6.16456	0.301518
$419$	19.3567	0.945635	0.472818	−	0.881160i	$-0.343237\pi$
$419$	19.3567	0.945635	0.472818	+	0.881160i	$0.343237\pi$
$420$	0	0
$421$	−4.81504	−0.234671	−0.117335	−	0.993092i	$-0.537435\pi$
$421$	−4.81504	−0.234671	−0.117335	+	0.993092i	$0.537435\pi$
$422$	−8.58743	−0.418029
$423$	10.8368	0.526905
$424$	−0.0209855	−0.00101914
$425$	0	0
$426$	6.47331	0.313633
$427$	16.0781	0.778075
$428$	−1.30865	−0.0632561
$429$	12.3868	0.598040
$430$	0	0
$431$	26.8254	1.29213	0.646067	−	0.763281i	$-0.276413\pi$
$431$	26.8254	1.29213	0.646067	+	0.763281i	$0.276413\pi$
$432$	24.7855	1.19249
$433$	−1.59224	−0.0765181	−0.0382591	−	0.999268i	$-0.512181\pi$
$433$	−1.59224	−0.0765181	−0.0382591	+	0.999268i	$0.512181\pi$
$434$	−70.8981	−3.40322
$435$	0	0
$436$	2.74960	0.131682
$437$	35.2419	1.68585
$438$	45.1149	2.15567
$439$	−36.5165	−1.74284	−0.871418	−	0.490541i	$-0.836799\pi$
$439$	−36.5165	−1.74284	−0.871418	+	0.490541i	$0.836799\pi$
$440$	0	0
$441$	54.0603	2.57430
$442$	40.1803	1.91118
$443$	1.27451	0.0605540	0.0302770	−	0.999542i	$-0.490361\pi$
$443$	1.27451	0.0605540	0.0302770	+	0.999542i	$0.490361\pi$
$444$	5.79390	0.274966
$445$	0	0
$446$	−19.9770	−0.945940
$447$	−12.4839	−0.590466
$448$	24.7653	1.17005
$449$	31.9473	1.50768	0.753842	−	0.657055i	$-0.228198\pi$
$449$	31.9473	1.50768	0.753842	+	0.657055i	$0.228198\pi$
$450$	0	0
$451$	−0.560551	−0.0263953
$452$	5.77162	0.271474
$453$	14.9996	0.704742
$454$	4.42133	0.207504
$455$	0	0
$456$	30.3095	1.41937
$457$	−12.8561	−0.601384	−0.300692	−	0.953721i	$-0.597218\pi$
$457$	−12.8561	−0.601384	−0.300692	+	0.953721i	$0.597218\pi$
$458$	25.0447	1.17026
$459$	−28.7964	−1.34410
$460$	0	0
$461$	35.6691	1.66127	0.830637	−	0.556814i	$-0.187976\pi$
$461$	35.6691	1.66127	0.830637	+	0.556814i	$0.187976\pi$
$462$	16.9222	0.787293
$463$	−2.74466	−0.127555	−0.0637776	−	0.997964i	$-0.520315\pi$
$463$	−2.74466	−0.127555	−0.0637776	+	0.997964i	$0.520315\pi$
$464$	29.9287	1.38940
$465$	0	0
$466$	17.6240	0.816418
$467$	25.5934	1.18432	0.592160	−	0.805821i	$-0.298275\pi$
$467$	25.5934	1.18432	0.592160	+	0.805821i	$0.298275\pi$
$468$	−9.40804	−0.434887
$469$	−19.8590	−0.917001
$470$	0	0
$471$	−60.7505	−2.79924
$472$	21.9677	1.01114
$473$	1.69547	0.0779578
$474$	−76.9631	−3.53503
$475$	0	0
$476$	9.12517	0.418251
$477$	−0.0414718	−0.00189886
$478$	−41.8729	−1.91522
$479$	−0.610882	−0.0279119	−0.0139560	−	0.999903i	$-0.504442\pi$
$479$	−0.610882	−0.0279119	−0.0139560	+	0.999903i	$0.504442\pi$
$480$	0	0
$481$	24.8836	1.13459
$482$	−1.54879	−0.0705457
$483$	96.7421	4.40192
$484$	−4.05225	−0.184193
$485$	0	0
$486$	−23.4489	−1.06366
$487$	−26.6270	−1.20658	−0.603291	−	0.797521i	$-0.706144\pi$
$487$	−26.6270	−1.20658	−0.603291	+	0.797521i	$0.706144\pi$
$488$	9.39032	0.425080
$489$	−62.1200	−2.80916
$490$	0	0
$491$	−31.7856	−1.43447	−0.717233	−	0.696833i	$-0.754592\pi$
$491$	−31.7856	−1.43447	−0.717233	+	0.696833i	$0.754592\pi$
$492$	0.686362	0.0309436
$493$	−34.7719	−1.56605
$494$	−32.4177	−1.45854
$495$	0	0
$496$	−50.0053	−2.24530
$497$	6.31387	0.283216
$498$	−32.4651	−1.45480
$499$	−17.2468	−0.772074	−0.386037	−	0.922483i	$-0.626156\pi$
$499$	−17.2468	−0.772074	−0.386037	+	0.922483i	$0.626156\pi$
$500$	0	0
$501$	−7.26043	−0.324372
$502$	25.5779	1.14160
$503$	23.6924	1.05639	0.528196	−	0.849122i	$-0.322868\pi$
$503$	23.6924	1.05639	0.528196	+	0.849122i	$0.322868\pi$
$504$	51.6102	2.29890
$505$	0	0
$506$	11.4917	0.510868
$507$	−28.5974	−1.27005
$508$	−2.77837	−0.123270
$509$	20.3227	0.900787	0.450394	−	0.892830i	$-0.351284\pi$
$509$	20.3227	0.900787	0.450394	+	0.892830i	$0.351284\pi$
$510$	0	0
$511$	44.0037	1.94661
$512$	12.6902	0.560832
$513$	23.2331	1.02577
$514$	−15.3042	−0.675040
$515$	0	0
$516$	−2.07600	−0.0913910
$517$	2.02413	0.0890213
$518$	33.9947	1.49364
$519$	26.8106	1.17685
$520$	0	0
$521$	16.3912	0.718112	0.359056	−	0.933316i	$-0.383099\pi$
$521$	16.3912	0.718112	0.359056	+	0.933316i	$0.383099\pi$
$522$	48.9762	2.14363
$523$	−0.258754	−0.0113145	−0.00565727	−	0.999984i	$-0.501801\pi$
$523$	−0.258754	−0.0113145	−0.00565727	+	0.999984i	$0.501801\pi$
$524$	2.79976	0.122308
$525$	0	0
$526$	−48.9072	−2.13246
$527$	58.0974	2.53076
$528$	11.9354	0.519424
$529$	42.6965	1.85637
$530$	0	0
$531$	43.4128	1.88396
$532$	−7.36223	−0.319193
$533$	2.94778	0.127682
$534$	−2.26690	−0.0980985
$535$	0	0
$536$	−11.5985	−0.500978
$537$	−32.7918	−1.41507
$538$	−6.52859	−0.281468
$539$	10.0975	0.434931
$540$	0	0
$541$	−17.9084	−0.769941	−0.384970	−	0.922929i	$-0.625788\pi$
$541$	−17.9084	−0.769941	−0.384970	+	0.922929i	$0.625788\pi$
$542$	−18.2850	−0.785410
$543$	19.0607	0.817971
$544$	11.9862	0.513905
$545$	0	0
$546$	−88.9892	−3.80839
$547$	−12.2295	−0.522897	−0.261448	−	0.965217i	$-0.584200\pi$
$547$	−12.2295	−0.522897	−0.261448	+	0.965217i	$0.584200\pi$
$548$	−2.30526	−0.0984760
$549$	18.5573	0.792006
$550$	0	0
$551$	28.0542	1.19515
$552$	56.5016	2.40487
$553$	−75.0675	−3.19219
$554$	12.4107	0.527280
$555$	0	0
$556$	0.936853	0.0397314
$557$	−25.2541	−1.07005	−0.535024	−	0.844837i	$-0.679698\pi$
$557$	−25.2541	−1.07005	−0.535024	+	0.844837i	$0.679698\pi$
$558$	−81.8302	−3.46415
$559$	−8.91600	−0.377107
$560$	0	0
$561$	−13.8669	−0.585461
$562$	33.5654	1.41587
$563$	10.4115	0.438794	0.219397	−	0.975636i	$-0.429591\pi$
$563$	10.4115	0.438794	0.219397	+	0.975636i	$0.429591\pi$
$564$	−2.47843	−0.104361
$565$	0	0
$566$	3.33991	0.140387
$567$	1.34464	0.0564695
$568$	3.68758	0.154727
$569$	−28.5127	−1.19532	−0.597658	−	0.801751i	$-0.703902\pi$
$569$	−28.5127	−1.19532	−0.597658	+	0.801751i	$0.703902\pi$
$570$	0	0
$571$	35.8278	1.49935	0.749674	−	0.661807i	$-0.230210\pi$
$571$	35.8278	1.49935	0.749674	+	0.661807i	$0.230210\pi$
$572$	−1.75726	−0.0734746
$573$	−26.1431	−1.09214
$574$	4.02711	0.168088
$575$	0	0
$576$	28.5840	1.19100
$577$	−1.00615	−0.0418864	−0.0209432	−	0.999781i	$-0.506667\pi$
$577$	−1.00615	−0.0418864	−0.0209432	+	0.999781i	$0.506667\pi$
$578$	−18.6520	−0.775820
$579$	−3.57478	−0.148563
$580$	0	0
$581$	−31.6655	−1.31371
$582$	27.5789	1.14318
$583$	−0.00774620	−0.000320815 0
$584$	25.7001	1.06348
$585$	0	0
$586$	41.7431	1.72439
$587$	7.69459	0.317590	0.158795	−	0.987312i	$-0.449239\pi$
$587$	7.69459	0.317590	0.158795	+	0.987312i	$0.449239\pi$
$588$	−12.3638	−0.509875
$589$	−46.8733	−1.93138
$590$	0	0
$591$	26.7376	1.09984
$592$	23.9769	0.985443
$593$	27.9165	1.14639	0.573197	−	0.819418i	$-0.305703\pi$
$593$	27.9165	1.14639	0.573197	+	0.819418i	$0.305703\pi$
$594$	7.57585	0.310841
$595$	0	0
$596$	1.77103	0.0725441
$597$	51.9382	2.12569
$598$	−60.4316	−2.47123
$599$	43.2997	1.76918	0.884588	−	0.466372i	$-0.154439\pi$
$599$	43.2997	1.76918	0.884588	+	0.466372i	$0.154439\pi$
$600$	0	0
$601$	−25.4104	−1.03651	−0.518255	−	0.855226i	$-0.673418\pi$
$601$	−25.4104	−1.03651	−0.518255	+	0.855226i	$0.673418\pi$
$602$	−12.1806	−0.496444
$603$	−22.9211	−0.933419
$604$	−2.12792	−0.0865840
$605$	0	0
$606$	31.3733	1.27445
$607$	2.58042	0.104736	0.0523679	−	0.998628i	$-0.483323\pi$
$607$	2.58042	0.104736	0.0523679	+	0.998628i	$0.483323\pi$
$608$	−9.67055	−0.392192
$609$	77.0110	3.12064
$610$	0	0
$611$	−10.6443	−0.430624
$612$	10.5322	0.425740
$613$	−24.6593	−0.995980	−0.497990	−	0.867183i	$-0.665928\pi$
$613$	−24.6593	−0.995980	−0.497990	+	0.867183i	$0.665928\pi$
$614$	25.7536	1.03933
$615$	0	0
$616$	9.63989	0.388402
$617$	17.2509	0.694497	0.347248	−	0.937773i	$-0.387116\pi$
$617$	17.2509	0.694497	0.347248	+	0.937773i	$0.387116\pi$
$618$	−34.0762	−1.37074
$619$	−0.0379403	−0.00152495	−0.000762475	−	1.00000i	$-0.500243\pi$
$619$	−0.0379403	−0.00152495	−0.000762475		1.00000i	$0.500243\pi$
$620$	0	0
$621$	43.3101	1.73797
$622$	15.7097	0.629902
$623$	−2.21107	−0.0885847
$624$	−62.7652	−2.51262
$625$	0	0
$626$	−41.4120	−1.65516
$627$	11.1879	0.446802
$628$	8.61840	0.343911
$629$	−27.8569	−1.11073
$630$	0	0
$631$	39.8274	1.58551	0.792753	−	0.609544i	$-0.208647\pi$
$631$	39.8274	1.58551	0.792753	+	0.609544i	$0.208647\pi$
$632$	−43.8427	−1.74397
$633$	−15.5851	−0.619452
$634$	−39.7171	−1.57737
$635$	0	0
$636$	0.00948477	0.000376096 0
$637$	−53.1000	−2.10390
$638$	9.14790	0.362169
$639$	7.28744	0.288287
$640$	0	0
$641$	17.4965	0.691071	0.345536	−	0.938406i	$-0.387697\pi$
$641$	17.4965	0.691071	0.345536	+	0.938406i	$0.387697\pi$
$642$	−14.2870	−0.563863
$643$	−19.8884	−0.784323	−0.392162	−	0.919896i	$-0.628273\pi$
$643$	−19.8884	−0.784323	−0.392162	+	0.919896i	$0.628273\pi$
$644$	−13.7244	−0.540815
$645$	0	0
$646$	36.2913	1.42786
$647$	39.9620	1.57107	0.785535	−	0.618817i	$-0.212388\pi$
$647$	39.9620	1.57107	0.785535	+	0.618817i	$0.212388\pi$
$648$	0.785327	0.0308506
$649$	8.10876	0.318297
$650$	0	0
$651$	−128.671	−5.04302
$652$	8.81267	0.345131
$653$	45.0393	1.76252	0.881262	−	0.472629i	$-0.156695\pi$
$653$	45.0393	1.76252	0.881262	+	0.472629i	$0.156695\pi$
$654$	30.0183	1.17381
$655$	0	0
$656$	2.84037	0.110898
$657$	50.7889	1.98146
$658$	−14.5418	−0.566898
$659$	−28.6163	−1.11473	−0.557367	−	0.830266i	$-0.688188\pi$
$659$	−28.6163	−1.11473	−0.557367	+	0.830266i	$0.688188\pi$
$660$	0	0
$661$	−21.0849	−0.820106	−0.410053	−	0.912062i	$-0.634490\pi$
$661$	−21.0849	−0.820106	−0.410053	+	0.912062i	$0.634490\pi$
$662$	−33.9462	−1.31936
$663$	72.9222	2.83206
$664$	−18.4940	−0.717707
$665$	0	0
$666$	39.2365	1.52038
$667$	52.2974	2.02496
$668$	1.03000	0.0398521
$669$	−36.2558	−1.40173
$670$	0	0
$671$	3.46618	0.133810
$672$	−26.5465	−1.02405
$673$	−11.9180	−0.459406	−0.229703	−	0.973261i	$-0.573776\pi$
$673$	−11.9180	−0.459406	−0.229703	+	0.973261i	$0.573776\pi$
$674$	8.74988	0.337033
$675$	0	0
$676$	4.05698	0.156038
$677$	−46.0077	−1.76822	−0.884111	−	0.467278i	$-0.845235\pi$
$677$	−46.0077	−1.76822	−0.884111	+	0.467278i	$0.845235\pi$
$678$	63.0108	2.41992
$679$	26.8997	1.03231
$680$	0	0
$681$	8.02417	0.307487
$682$	−15.2844	−0.585272
$683$	−41.5189	−1.58868	−0.794338	−	0.607477i	$-0.792182\pi$
$683$	−41.5189	−1.58868	−0.794338	+	0.607477i	$0.792182\pi$
$684$	−8.49745	−0.324908
$685$	0	0
$686$	−26.5068	−1.01203
$687$	45.4531	1.73414
$688$	−8.59113	−0.327534
$689$	0.0407351	0.00155188
$690$	0	0
$691$	28.5903	1.08763	0.543814	−	0.839206i	$-0.316980\pi$
$691$	28.5903	1.08763	0.543814	+	0.839206i	$0.316980\pi$
$692$	−3.80349	−0.144587
$693$	19.0505	0.723668
$694$	30.5200	1.15852
$695$	0	0
$696$	44.9778	1.70488
$697$	−3.30001	−0.124997
$698$	48.9311	1.85207
$699$	31.9854	1.20980
$700$	0	0
$701$	19.2033	0.725298	0.362649	−	0.931926i	$-0.381872\pi$
$701$	19.2033	0.725298	0.362649	+	0.931926i	$0.381872\pi$
$702$	−39.8392	−1.50364
$703$	22.4751	0.847665
$704$	5.33899	0.201221
$705$	0	0
$706$	19.8165	0.745805
$707$	30.6006	1.15085
$708$	−9.92870	−0.373144
$709$	4.05386	0.152246	0.0761229	−	0.997098i	$-0.475746\pi$
$709$	4.05386	0.152246	0.0761229	+	0.997098i	$0.475746\pi$
$710$	0	0
$711$	−86.6425	−3.24935
$712$	−1.29136	−0.0483958
$713$	−87.3792	−3.27238
$714$	99.6227	3.72828
$715$	0	0
$716$	4.65202	0.173854
$717$	−75.9940	−2.83805
$718$	−42.2613	−1.57718
$719$	13.0438	0.486452	0.243226	−	0.969970i	$-0.421794\pi$
$719$	13.0438	0.486452	0.243226	+	0.969970i	$0.421794\pi$
$720$	0	0
$721$	−33.2369	−1.23781
$722$	0.147081	0.00547378
$723$	−2.81087	−0.104537
$724$	−2.70405	−0.100495
$725$	0	0
$726$	−44.2399	−1.64190
$727$	43.3367	1.60727	0.803635	−	0.595123i	$-0.202897\pi$
$727$	43.3367	1.60727	0.803635	+	0.595123i	$0.202897\pi$
$728$	−50.6935	−1.87882
$729$	−43.5068	−1.61136
$730$	0	0
$731$	9.98139	0.369175
$732$	−4.24413	−0.156868
$733$	6.99674	0.258431	0.129215	−	0.991617i	$-0.458754\pi$
$733$	6.99674	0.258431	0.129215	+	0.991617i	$0.458754\pi$
$734$	40.1975	1.48372
$735$	0	0
$736$	−18.0274	−0.664499
$737$	−4.28126	−0.157702
$738$	4.64807	0.171098
$739$	−1.44307	−0.0530842	−0.0265421	−	0.999648i	$-0.508450\pi$
$739$	−1.44307	−0.0530842	−0.0265421	+	0.999648i	$0.508450\pi$
$740$	0	0
$741$	−58.8340	−2.16132
$742$	0.0556503	0.00204299
$743$	4.24266	0.155648	0.0778240	−	0.996967i	$-0.475203\pi$
$743$	4.24266	0.155648	0.0778240	+	0.996967i	$0.475203\pi$
$744$	−75.1495	−2.75511
$745$	0	0
$746$	3.01958	0.110555
$747$	−36.5481	−1.33723
$748$	1.96723	0.0719292
$749$	−13.9351	−0.509179
$750$	0	0
$751$	19.0193	0.694024	0.347012	−	0.937861i	$-0.387196\pi$
$751$	19.0193	0.694024	0.347012	+	0.937861i	$0.387196\pi$
$752$	−10.2565	−0.374016
$753$	46.4206	1.69166
$754$	−48.1063	−1.75193
$755$	0	0
$756$	−9.04771	−0.329062
$757$	−0.151878	−0.00552010	−0.00276005	−	0.999996i	$-0.500879\pi$
$757$	−0.151878	−0.00552010	−0.00276005	+	0.999996i	$0.500879\pi$
$758$	−34.2105	−1.24258
$759$	20.8560	0.757025
$760$	0	0
$761$	−16.2184	−0.587916	−0.293958	−	0.955818i	$-0.594973\pi$
$761$	−16.2184	−0.587916	−0.293958	+	0.955818i	$0.594973\pi$
$762$	−30.3325	−1.09883
$763$	29.2790	1.05997
$764$	3.70880	0.134180
$765$	0	0
$766$	−50.5819	−1.82760
$767$	−42.6417	−1.53970
$768$	−25.9027	−0.934682
$769$	5.32816	0.192138	0.0960691	−	0.995375i	$-0.469373\pi$
$769$	5.32816	0.192138	0.0960691	+	0.995375i	$0.469373\pi$
$770$	0	0
$771$	−27.7752	−1.00030
$772$	0.507137	0.0182523
$773$	6.19612	0.222859	0.111430	−	0.993772i	$-0.464457\pi$
$773$	6.19612	0.222859	0.111430	+	0.993772i	$0.464457\pi$
$774$	−14.0588	−0.505333
$775$	0	0
$776$	15.7106	0.563976
$777$	61.6961	2.21334
$778$	2.47139	0.0886036
$779$	2.66247	0.0953929
$780$	0	0
$781$	1.36117	0.0487064
$782$	67.6527	2.41925
$783$	34.4768	1.23210
$784$	−51.1652	−1.82733
$785$	0	0
$786$	30.5660	1.09025
$787$	−26.4924	−0.944351	−0.472176	−	0.881504i	$-0.656531\pi$
$787$	−26.4924	−0.944351	−0.472176	+	0.881504i	$0.656531\pi$
$788$	−3.79314	−0.135125
$789$	−88.7604	−3.15996
$790$	0	0
$791$	61.4589	2.18523
$792$	11.1263	0.395356
$793$	−18.2277	−0.647283
$794$	−31.7602	−1.12713
$795$	0	0
$796$	−7.36823	−0.261160
$797$	−41.8090	−1.48095	−0.740476	−	0.672083i	$-0.765400\pi$
$797$	−41.8090	−1.48095	−0.740476	+	0.672083i	$0.765400\pi$
$798$	−80.3761	−2.84528
$799$	11.9163	0.421567
$800$	0	0
$801$	−2.55201	−0.0901707
$802$	−3.89416	−0.137508
$803$	9.48648	0.334770
$804$	5.24215	0.184877
$805$	0	0
$806$	80.3766	2.83115
$807$	−11.8486	−0.417090
$808$	17.8721	0.628737
$809$	1.66235	0.0584451	0.0292226	−	0.999573i	$-0.490697\pi$
$809$	1.66235	0.0584451	0.0292226	+	0.999573i	$0.490697\pi$
$810$	0	0
$811$	−13.4156	−0.471085	−0.235542	−	0.971864i	$-0.575687\pi$
$811$	−13.4156	−0.471085	−0.235542	+	0.971864i	$0.575687\pi$
$812$	−10.9252	−0.383399
$813$	−33.1851	−1.16385
$814$	7.32869	0.256870
$815$	0	0
$816$	70.2651	2.45977
$817$	−8.05304	−0.281740
$818$	6.19369	0.216557
$819$	−100.181	−3.50061
$820$	0	0
$821$	23.1210	0.806930	0.403465	−	0.914995i	$-0.367806\pi$
$821$	23.1210	0.806930	0.403465	+	0.914995i	$0.367806\pi$
$822$	−25.1674	−0.877814
$823$	−20.7084	−0.721849	−0.360924	−	0.932595i	$-0.617539\pi$
$823$	−20.7084	−0.721849	−0.360924	+	0.932595i	$0.617539\pi$
$824$	−19.4118	−0.676241
$825$	0	0
$826$	−58.2550	−2.02695
$827$	1.22288	0.0425235	0.0212618	−	0.999774i	$-0.493232\pi$
$827$	1.22288	0.0425235	0.0212618	+	0.999774i	$0.493232\pi$
$828$	−15.8406	−0.550498
$829$	26.5008	0.920411	0.460205	−	0.887813i	$-0.347776\pi$
$829$	26.5008	0.920411	0.460205	+	0.887813i	$0.347776\pi$
$830$	0	0
$831$	22.5239	0.781344
$832$	−28.0762	−0.973368
$833$	59.4450	2.05965
$834$	10.2280	0.354165
$835$	0	0
$836$	−1.58718	−0.0548936
$837$	−57.6043	−1.99110
$838$	−29.9795	−1.03562
$839$	27.5572	0.951380	0.475690	−	0.879613i	$-0.342198\pi$
$839$	27.5572	0.951380	0.475690	+	0.879613i	$0.342198\pi$
$840$	0	0
$841$	12.6310	0.435553
$842$	7.45750	0.257003
$843$	60.9169	2.09809
$844$	2.21099	0.0761053
$845$	0	0
$846$	−16.7840	−0.577047
$847$	−43.1503	−1.48266
$848$	0.0392508	0.00134788
$849$	6.06152	0.208031
$850$	0	0
$851$	41.8972	1.43622
$852$	−1.66667	−0.0570992
$853$	−14.3366	−0.490875	−0.245437	−	0.969412i	$-0.578932\pi$
$853$	−14.3366	−0.490875	−0.245437	+	0.969412i	$0.578932\pi$
$854$	−24.9017	−0.852119
$855$	0	0
$856$	−8.13872	−0.278176
$857$	−33.5953	−1.14759	−0.573796	−	0.818998i	$-0.694530\pi$
$857$	−33.5953	−1.14759	−0.573796	+	0.818998i	$0.694530\pi$
$858$	−19.1846	−0.654951
$859$	−31.1946	−1.06435	−0.532173	−	0.846635i	$-0.678625\pi$
$859$	−31.1946	−1.06435	−0.532173	+	0.846635i	$0.678625\pi$
$860$	0	0
$861$	7.30870	0.249080
$862$	−41.5470	−1.41510
$863$	−23.3830	−0.795965	−0.397983	−	0.917393i	$-0.630290\pi$
$863$	−23.3830	−0.795965	−0.397983	+	0.917393i	$0.630290\pi$
$864$	−11.8845	−0.404318
$865$	0	0
$866$	2.46605	0.0837999
$867$	−33.8510	−1.14964
$868$	18.2540	0.619580
$869$	−16.1833	−0.548981
$870$	0	0
$871$	22.5139	0.762856
$872$	17.1002	0.579086
$873$	31.0474	1.05080
$874$	−54.5825	−1.84628
$875$	0	0
$876$	−11.6156	−0.392456
$877$	35.6526	1.20390	0.601951	−	0.798533i	$-0.294390\pi$
$877$	35.6526	1.20390	0.601951	+	0.798533i	$0.294390\pi$
$878$	56.5565	1.90869
$879$	75.7585	2.55527
$880$	0	0
$881$	29.7222	1.00137	0.500683	−	0.865631i	$-0.333082\pi$
$881$	29.7222	1.00137	0.500683	+	0.865631i	$0.333082\pi$
$882$	−83.7283	−2.81928
$883$	41.7428	1.40476	0.702379	−	0.711803i	$-0.252121\pi$
$883$	41.7428	1.40476	0.702379	+	0.711803i	$0.252121\pi$
$884$	−10.3451	−0.347944
$885$	0	0
$886$	−1.97396	−0.0663165
$887$	2.72462	0.0914838	0.0457419	−	0.998953i	$-0.485435\pi$
$887$	2.72462	0.0914838	0.0457419	+	0.998953i	$0.485435\pi$
$888$	36.0332	1.20919
$889$	−29.5854	−0.992263
$890$	0	0
$891$	0.289882	0.00971140
$892$	5.14345	0.172215
$893$	−9.61410	−0.321724
$894$	19.3349	0.646657
$895$	0	0
$896$	−57.2448	−1.91241
$897$	−109.676	−3.66197
$898$	−49.4797	−1.65116
$899$	−69.5577	−2.31988
$900$	0	0
$901$	−0.0456026	−0.00151924
$902$	0.868178	0.0289072
$903$	−22.1063	−0.735650
$904$	35.8946	1.19384
$905$	0	0
$906$	−23.2313	−0.771808
$907$	19.4428	0.645587	0.322794	−	0.946469i	$-0.395378\pi$
$907$	19.4428	0.645587	0.322794	+	0.946469i	$0.395378\pi$
$908$	−1.13835	−0.0377775
$909$	35.3190	1.17146
$910$	0	0
$911$	35.4707	1.17520	0.587598	−	0.809153i	$-0.300074\pi$
$911$	35.4707	1.17520	0.587598	+	0.809153i	$0.300074\pi$
$912$	−56.6902	−1.87720
$913$	−6.82655	−0.225926
$914$	19.9115	0.658614
$915$	0	0
$916$	−6.44821	−0.213055
$917$	29.8131	0.984516
$918$	44.5997	1.47201
$919$	30.5669	1.00831	0.504154	−	0.863614i	$-0.331804\pi$
$919$	30.5669	1.00831	0.504154	+	0.863614i	$0.331804\pi$
$920$	0	0
$921$	46.7396	1.54012
$922$	−55.2441	−1.81937
$923$	−7.15799	−0.235608
$924$	−4.35693	−0.143332
$925$	0	0
$926$	4.25092	0.139694
$927$	−38.3618	−1.25997
$928$	−14.3506	−0.471082
$929$	−59.7630	−1.96076	−0.980380	−	0.197116i	$-0.936842\pi$
$929$	−59.7630	−1.96076	−0.980380	+	0.197116i	$0.936842\pi$
$930$	0	0
$931$	−47.9605	−1.57184
$932$	−4.53762	−0.148635
$933$	28.5111	0.933413
$934$	−39.6389	−1.29702
$935$	0	0
$936$	−58.5101	−1.91246
$937$	−29.4112	−0.960824	−0.480412	−	0.877043i	$-0.659513\pi$
$937$	−29.4112	−0.960824	−0.480412	+	0.877043i	$0.659513\pi$
$938$	30.7574	1.00427
$939$	−75.1577	−2.45268
$940$	0	0
$941$	45.0066	1.46717	0.733587	−	0.679595i	$-0.237845\pi$
$941$	45.0066	1.46717	0.733587	+	0.679595i	$0.237845\pi$
$942$	94.0901	3.06562
$943$	4.96326	0.161626
$944$	−41.0879	−1.33730
$945$	0	0
$946$	−2.62594	−0.0853765
$947$	10.4456	0.339437	0.169719	−	0.985493i	$-0.445714\pi$
$947$	10.4456	0.339437	0.169719	+	0.985493i	$0.445714\pi$
$948$	19.8155	0.643578
$949$	−49.8867	−1.61939
$950$	0	0
$951$	−72.0815	−2.33740
$952$	56.7509	1.83931
$953$	48.6114	1.57468	0.787339	−	0.616521i	$-0.211458\pi$
$953$	48.6114	1.57468	0.787339	+	0.616521i	$0.211458\pi$
$954$	0.0642313	0.00207956
$955$	0	0
$956$	10.7809	0.348680
$957$	16.6023	0.536676
$958$	0.946131	0.0305681
$959$	−24.5475	−0.792681
$960$	0	0
$961$	85.2180	2.74897
$962$	−38.5395	−1.24256
$963$	−16.0839	−0.518295
$964$	0.398765	0.0128434
$965$	0	0
$966$	−149.834	−4.82082
$967$	28.8087	0.926426	0.463213	−	0.886247i	$-0.346697\pi$
$967$	28.8087	0.926426	0.463213	+	0.886247i	$0.346697\pi$
$968$	−25.2016	−0.810011
$969$	65.8642	2.11586
$970$	0	0
$971$	−4.01498	−0.128847	−0.0644234	−	0.997923i	$-0.520521\pi$
$971$	−4.01498	−0.128847	−0.0644234	+	0.997923i	$0.520521\pi$
$972$	6.03734	0.193648
$973$	9.97605	0.319817
$974$	41.2397	1.32140
$975$	0	0
$976$	−17.5635	−0.562193
$977$	−4.44163	−0.142100	−0.0710501	−	0.997473i	$-0.522635\pi$
$977$	−4.44163	−0.142100	−0.0710501	+	0.997473i	$0.522635\pi$
$978$	96.2111	3.07649
$979$	−0.476670	−0.0152344
$980$	0	0
$981$	33.7937	1.07895
$982$	49.2294	1.57097
$983$	16.5283	0.527172	0.263586	−	0.964636i	$-0.415095\pi$
$983$	16.5283	0.527172	0.263586	+	0.964636i	$0.415095\pi$
$984$	4.26860	0.136078
$985$	0	0
$986$	53.8545	1.71508
$987$	−26.3915	−0.840051
$988$	8.34651	0.265538
$989$	−15.0121	−0.477358
$990$	0	0
$991$	34.8094	1.10576	0.552878	−	0.833262i	$-0.313530\pi$
$991$	34.8094	1.10576	0.552878	+	0.833262i	$0.313530\pi$
$992$	23.9772	0.761278
$993$	−61.6081	−1.95507
$994$	−9.77890	−0.310168
$995$	0	0
$996$	8.35872	0.264856
$997$	14.7239	0.466312	0.233156	−	0.972439i	$-0.425095\pi$
$997$	14.7239	0.466312	0.233156	+	0.972439i	$0.425095\pi$
$998$	26.7118	0.845547
$999$	27.6205	0.873874

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.h.1.5		12
5.4	even	2		241.2.a.b.1.8	✓	12
15.14	odd	2		2169.2.a.h.1.5		12
20.19	odd	2		3856.2.a.n.1.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.b.1.8	✓	12	5.4	even	2
2169.2.a.h.1.5		12	15.14	odd	2
3856.2.a.n.1.2		12	20.19	odd	2
6025.2.a.h.1.5		12	1.1	even	1	trivial

Overview	Random
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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:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.54879 q^{2} -2.81087 q^{3} +0.398765 q^{4} +4.35346 q^{6} +4.24623 q^{7} +2.47998 q^{8} +4.90098 q^{9} +O(q^{10})\)	\(q-1.54879 q^{2} -2.81087 q^{3} +0.398765 q^{4} +4.35346 q^{6} +4.24623 q^{7} +2.47998 q^{8} +4.90098 q^{9} +0.915418 q^{11} -1.12088 q^{12} -4.81392 q^{13} -6.57654 q^{14} -4.63852 q^{16} +5.38915 q^{17} -7.59061 q^{18} -4.34799 q^{19} -11.9356 q^{21} -1.41779 q^{22} -8.10534 q^{23} -6.97091 q^{24} +7.45578 q^{26} -5.34340 q^{27} +1.69325 q^{28} -6.45221 q^{29} +10.7804 q^{31} +2.22414 q^{32} -2.57312 q^{33} -8.34668 q^{34} +1.95434 q^{36} -5.16908 q^{37} +6.73415 q^{38} +13.5313 q^{39} -0.612344 q^{41} +18.4858 q^{42} +1.85213 q^{43} +0.365036 q^{44} +12.5535 q^{46} +2.21116 q^{47} +13.0383 q^{48} +11.0305 q^{49} -15.1482 q^{51} -1.91962 q^{52} -0.00846193 q^{53} +8.27584 q^{54} +10.5306 q^{56} +12.2216 q^{57} +9.99315 q^{58} +8.85799 q^{59} +3.78644 q^{61} -16.6967 q^{62} +20.8107 q^{63} +5.83230 q^{64} +3.98523 q^{66} -4.67684 q^{67} +2.14900 q^{68} +22.7830 q^{69} +1.48694 q^{71} +12.1544 q^{72} +10.3630 q^{73} +8.00585 q^{74} -1.73383 q^{76} +3.88708 q^{77} -20.9572 q^{78} -17.6786 q^{79} +0.316666 q^{81} +0.948396 q^{82} -7.45731 q^{83} -4.75950 q^{84} -2.86857 q^{86} +18.1363 q^{87} +2.27022 q^{88} -0.520713 q^{89} -20.4410 q^{91} -3.23212 q^{92} -30.3024 q^{93} -3.42463 q^{94} -6.25177 q^{96} +6.33494 q^{97} -17.0840 q^{98} +4.48644 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - q^3 + 13 * q^4 - q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9	\( 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9} + 22 q^{11} + 7 q^{12} + 5 q^{13} + 6 q^{14} + 15 q^{16} + 4 q^{17} + q^{18} - 6 q^{19} - 14 q^{21} + 12 q^{22} - 32 q^{23} - 15 q^{24} + 8 q^{26} + 5 q^{27} + 11 q^{28} + 6 q^{29} + 8 q^{31} - q^{32} + 24 q^{33} - 19 q^{34} - 8 q^{36} + 8 q^{37} + 10 q^{38} + 31 q^{39} - q^{41} + 49 q^{42} + 2 q^{43} + 42 q^{44} - 25 q^{46} - 34 q^{47} + 49 q^{48} - 9 q^{49} - 3 q^{51} + 41 q^{52} - 5 q^{53} - 40 q^{54} + q^{56} + 22 q^{57} + 33 q^{58} + 26 q^{59} - 26 q^{61} + 17 q^{62} + 4 q^{63} + 13 q^{64} - 2 q^{66} - 6 q^{67} + 35 q^{68} - 2 q^{69} + 94 q^{71} - 17 q^{72} + 22 q^{73} + 26 q^{74} - 20 q^{76} + 7 q^{77} - 54 q^{78} + 9 q^{79} + 4 q^{81} - 15 q^{82} + 8 q^{83} + 2 q^{84} + 9 q^{86} - 4 q^{87} - 6 q^{88} - 3 q^{89} - 20 q^{91} - 36 q^{92} - 12 q^{93} + 48 q^{94} - 23 q^{96} + 29 q^{97} - 28 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - q^3 + 13 * q^4 - q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9 + 22 * q^11 + 7 * q^12 + 5 * q^13 + 6 * q^14 + 15 * q^16 + 4 * q^17 + q^18 - 6 * q^19 - 14 * q^21 + 12 * q^22 - 32 * q^23 - 15 * q^24 + 8 * q^26 + 5 * q^27 + 11 * q^28 + 6 * q^29 + 8 * q^31 - q^32 + 24 * q^33 - 19 * q^34 - 8 * q^36 + 8 * q^37 + 10 * q^38 + 31 * q^39 - q^41 + 49 * q^42 + 2 * q^43 + 42 * q^44 - 25 * q^46 - 34 * q^47 + 49 * q^48 - 9 * q^49 - 3 * q^51 + 41 * q^52 - 5 * q^53 - 40 * q^54 + q^56 + 22 * q^57 + 33 * q^58 + 26 * q^59 - 26 * q^61 + 17 * q^62 + 4 * q^63 + 13 * q^64 - 2 * q^66 - 6 * q^67 + 35 * q^68 - 2 * q^69 + 94 * q^71 - 17 * q^72 + 22 * q^73 + 26 * q^74 - 20 * q^76 + 7 * q^77 - 54 * q^78 + 9 * q^79 + 4 * q^81 - 15 * q^82 + 8 * q^83 + 2 * q^84 + 9 * q^86 - 4 * q^87 - 6 * q^88 - 3 * q^89 - 20 * q^91 - 36 * q^92 - 12 * q^93 + 48 * q^94 - 23 * q^96 + 29 * q^97 - 28 * q^98 + 36 * q^99

Introduction

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