LMFDB - Embedded newform 3775.2.a.p.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3775,2,Mod(1,3775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3775, 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("3775.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3775 = 5^{2} \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3775.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:	$30.1435267630$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.4838537.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 7x^{4} + 3x^{3} + 13x^{2} + 3x - 1 $ x^6 - x^5 - 7x^4 + 3x^3 + 13x^2 + 3x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 151)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.183668$ of defining polynomial
Character	$\chi$	$=$	3775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.183668 q^{2} +3.29466 q^{3} -1.96627 q^{4} -0.605125 q^{6} -3.65107 q^{7} +0.728478 q^{8} +7.85477 q^{9} +O(q^{10})$	\(q-0.183668 q^{2} +3.29466 q^{3} -1.96627 q^{4} -0.605125 q^{6} -3.65107 q^{7} +0.728478 q^{8} +7.85477 q^{9} -0.912147 q^{11} -6.47817 q^{12} +1.27865 q^{13} +0.670586 q^{14} +3.79873 q^{16} -1.65822 q^{17} -1.44267 q^{18} +3.74742 q^{19} -12.0290 q^{21} +0.167533 q^{22} +0.248713 q^{23} +2.40009 q^{24} -0.234848 q^{26} +15.9948 q^{27} +7.17897 q^{28} +1.93860 q^{29} -5.44267 q^{31} -2.15466 q^{32} -3.00521 q^{33} +0.304563 q^{34} -15.4446 q^{36} +4.41526 q^{37} -0.688284 q^{38} +4.21272 q^{39} +8.64880 q^{41} +2.20935 q^{42} -1.41210 q^{43} +1.79352 q^{44} -0.0456807 q^{46} -2.19095 q^{47} +12.5155 q^{48} +6.33031 q^{49} -5.46328 q^{51} -2.51417 q^{52} +10.4493 q^{53} -2.93774 q^{54} -2.65972 q^{56} +12.3465 q^{57} -0.356059 q^{58} -0.862276 q^{59} -2.48235 q^{61} +0.999648 q^{62} -28.6783 q^{63} -7.20172 q^{64} +0.551962 q^{66} +13.4435 q^{67} +3.26051 q^{68} +0.819424 q^{69} +8.78436 q^{71} +5.72203 q^{72} +14.3562 q^{73} -0.810944 q^{74} -7.36843 q^{76} +3.33031 q^{77} -0.773744 q^{78} -10.1620 q^{79} +29.1331 q^{81} -1.58851 q^{82} -7.06074 q^{83} +23.6523 q^{84} +0.259358 q^{86} +6.38702 q^{87} -0.664479 q^{88} +11.7770 q^{89} -4.66844 q^{91} -0.489036 q^{92} -17.9317 q^{93} +0.402409 q^{94} -7.09888 q^{96} +0.860838 q^{97} -1.16268 q^{98} -7.16470 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} + 5 q^{3} + 3 q^{4} - 2 q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) $ 6 * q - q^2 + 5 * q^3 + 3 * q^4 - 2 * q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9	$ 6 q - q^{2} + 5 q^{3} + 3 q^{4} - 2 q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9} + 8 q^{11} + 11 q^{12} + q^{13} + 6 q^{14} - 3 q^{16} - 9 q^{17} + 16 q^{18} - 6 q^{19} + 13 q^{21} + 12 q^{22} + 4 q^{23} + q^{24} - 7 q^{26} + 2 q^{27} + 24 q^{28} - 2 q^{29} - 8 q^{31} + 11 q^{32} - 3 q^{33} - 9 q^{34} - 25 q^{36} + 12 q^{37} + 3 q^{38} - 22 q^{39} + 41 q^{41} + 24 q^{42} - q^{43} - 17 q^{46} - 28 q^{47} - 9 q^{48} + 33 q^{49} - 31 q^{51} - 15 q^{52} - 14 q^{53} + 27 q^{54} - 9 q^{56} + 28 q^{57} - q^{58} + 12 q^{59} + 5 q^{61} + 9 q^{62} - 4 q^{63} - 27 q^{64} + 8 q^{66} + 15 q^{67} - 11 q^{68} + 33 q^{69} - 2 q^{71} - q^{72} + 7 q^{73} + 53 q^{74} - 3 q^{76} + 15 q^{77} - 16 q^{78} - 9 q^{79} + 66 q^{81} - 10 q^{82} + 11 q^{83} + 49 q^{84} - 26 q^{86} + 26 q^{87} - 24 q^{88} + 36 q^{89} - 35 q^{91} + 38 q^{92} + q^{93} + 42 q^{94} - 34 q^{96} - 11 q^{97} - 15 q^{98} + 17 q^{99}+O(q^{100}) $ 6 * q - q^2 + 5 * q^3 + 3 * q^4 - 2 * q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9 + 8 * q^11 + 11 * q^12 + q^13 + 6 * q^14 - 3 * q^16 - 9 * q^17 + 16 * q^18 - 6 * q^19 + 13 * q^21 + 12 * q^22 + 4 * q^23 + q^24 - 7 * q^26 + 2 * q^27 + 24 * q^28 - 2 * q^29 - 8 * q^31 + 11 * q^32 - 3 * q^33 - 9 * q^34 - 25 * q^36 + 12 * q^37 + 3 * q^38 - 22 * q^39 + 41 * q^41 + 24 * q^42 - q^43 - 17 * q^46 - 28 * q^47 - 9 * q^48 + 33 * q^49 - 31 * q^51 - 15 * q^52 - 14 * q^53 + 27 * q^54 - 9 * q^56 + 28 * q^57 - q^58 + 12 * q^59 + 5 * q^61 + 9 * q^62 - 4 * q^63 - 27 * q^64 + 8 * q^66 + 15 * q^67 - 11 * q^68 + 33 * q^69 - 2 * q^71 - q^72 + 7 * q^73 + 53 * q^74 - 3 * q^76 + 15 * q^77 - 16 * q^78 - 9 * q^79 + 66 * q^81 - 10 * q^82 + 11 * q^83 + 49 * q^84 - 26 * q^86 + 26 * q^87 - 24 * q^88 + 36 * q^89 - 35 * q^91 + 38 * q^92 + q^93 + 42 * q^94 - 34 * q^96 - 11 * q^97 - 15 * q^98 + 17 * 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 $

$2$	−0.183668	−0.129873	−0.0649366	−	0.997889i	$-0.520685\pi$
$2$	−0.183668	−0.129873	−0.0649366	+	0.997889i	$0.520685\pi$
$3$	3.29466	1.90217	0.951086	−	0.308927i	$-0.0999698\pi$
$3$	3.29466	1.90217	0.951086	+	0.308927i	$0.0999698\pi$
$4$	−1.96627	−0.983133
$5$	0	0
$5$	0	0
$6$	−0.605125	−0.247041
$7$	−3.65107	−1.37997	−0.689987	−	0.723821i	$-0.742384\pi$
$7$	−3.65107	−1.37997	−0.689987	+	0.723821i	$0.742384\pi$
$8$	0.728478	0.257556
$9$	7.85477	2.61826
$10$	0	0
$11$	−0.912147	−0.275023	−0.137511	−	0.990500i	$-0.543910\pi$
$11$	−0.912147	−0.275023	−0.137511	+	0.990500i	$0.543910\pi$
$12$	−6.47817	−1.87009
$13$	1.27865	0.354634	0.177317	−	0.984154i	$-0.443258\pi$
$13$	1.27865	0.354634	0.177317	+	0.984154i	$0.443258\pi$
$14$	0.670586	0.179222
$15$	0	0
$16$	3.79873	0.949683
$17$	−1.65822	−0.402178	−0.201089	−	0.979573i	$-0.564448\pi$
$17$	−1.65822	−0.402178	−0.201089	+	0.979573i	$0.564448\pi$
$18$	−1.44267	−0.340041
$19$	3.74742	0.859718	0.429859	−	0.902896i	$-0.358563\pi$
$19$	3.74742	0.859718	0.429859	+	0.902896i	$0.358563\pi$
$20$	0	0
$21$	−12.0290	−2.62495
$22$	0.167533	0.0357181
$23$	0.248713	0.0518602	0.0259301	−	0.999664i	$-0.491745\pi$
$23$	0.248713	0.0518602	0.0259301	+	0.999664i	$0.491745\pi$
$24$	2.40009	0.489915
$25$	0	0
$26$	−0.234848	−0.0460575
$27$	15.9948	3.07820
$28$	7.17897	1.35670
$29$	1.93860	0.359989	0.179994	−	0.983668i	$-0.442392\pi$
$29$	1.93860	0.359989	0.179994	+	0.983668i	$0.442392\pi$
$30$	0	0
$31$	−5.44267	−0.977533	−0.488767	−	0.872415i	$-0.662553\pi$
$31$	−5.44267	−0.977533	−0.488767	+	0.872415i	$0.662553\pi$
$32$	−2.15466	−0.380894
$33$	−3.00521	−0.523140
$34$	0.304563	0.0522322
$35$	0	0
$36$	−15.4446	−2.57409
$37$	4.41526	0.725864	0.362932	−	0.931816i	$-0.381776\pi$
$37$	4.41526	0.725864	0.362932	+	0.931816i	$0.381776\pi$
$38$	−0.688284	−0.111654
$39$	4.21272	0.674575
$40$	0	0
$41$	8.64880	1.35072	0.675358	−	0.737490i	$-0.263989\pi$
$41$	8.64880	1.35072	0.675358	+	0.737490i	$0.263989\pi$
$42$	2.20935	0.340911
$43$	−1.41210	−0.215343	−0.107671	−	0.994187i	$-0.534339\pi$
$43$	−1.41210	−0.215343	−0.107671	+	0.994187i	$0.534339\pi$
$44$	1.79352	0.270384
$45$	0	0
$46$	−0.0456807	−0.00673526
$47$	−2.19095	−0.319583	−0.159791	−	0.987151i	$-0.551082\pi$
$47$	−2.19095	−0.319583	−0.159791	+	0.987151i	$0.551082\pi$
$48$	12.5155	1.80646
$49$	6.33031	0.904330
$50$	0	0
$51$	−5.46328	−0.765012
$52$	−2.51417	−0.348652
$53$	10.4493	1.43532	0.717661	−	0.696393i	$-0.245213\pi$
$53$	10.4493	1.43532	0.717661	+	0.696393i	$0.245213\pi$
$54$	−2.93774	−0.399776
$55$	0	0
$56$	−2.65972	−0.355421
$57$	12.3465	1.63533
$58$	−0.356059	−0.0467529
$59$	−0.862276	−0.112259	−0.0561294	−	0.998424i	$-0.517876\pi$
$59$	−0.862276	−0.112259	−0.0561294	+	0.998424i	$0.517876\pi$
$60$	0	0
$61$	−2.48235	−0.317833	−0.158916	−	0.987292i	$-0.550800\pi$
$61$	−2.48235	−0.317833	−0.158916	+	0.987292i	$0.550800\pi$
$62$	0.999648	0.126955
$63$	−28.6783	−3.61313
$64$	−7.20172	−0.900215
$65$	0	0
$66$	0.551962	0.0679419
$67$	13.4435	1.64239	0.821195	−	0.570647i	$-0.193308\pi$
$67$	13.4435	1.64239	0.821195	+	0.570647i	$0.193308\pi$
$68$	3.26051	0.395395
$69$	0.819424	0.0986471
$70$	0	0
$71$	8.78436	1.04251	0.521256	−	0.853400i	$-0.325464\pi$
$71$	8.78436	1.04251	0.521256	+	0.853400i	$0.325464\pi$
$72$	5.72203	0.674347
$73$	14.3562	1.68026	0.840131	−	0.542383i	$-0.182478\pi$
$73$	14.3562	1.68026	0.840131	+	0.542383i	$0.182478\pi$
$74$	−0.810944	−0.0942703
$75$	0	0
$76$	−7.36843	−0.845217
$77$	3.33031	0.379524
$78$	−0.773744	−0.0876092
$79$	−10.1620	−1.14331	−0.571655	−	0.820494i	$-0.693698\pi$
$79$	−10.1620	−1.14331	−0.571655	+	0.820494i	$0.693698\pi$
$80$	0	0
$81$	29.1331	3.23701
$82$	−1.58851	−0.175422
$83$	−7.06074	−0.775017	−0.387509	−	0.921866i	$-0.626664\pi$
$83$	−7.06074	−0.775017	−0.387509	+	0.921866i	$0.626664\pi$
$84$	23.6523	2.58067
$85$	0	0
$86$	0.259358	0.0279673
$87$	6.38702	0.684760
$88$	−0.664479	−0.0708337
$89$	11.7770	1.24836	0.624180	−	0.781280i	$-0.285433\pi$
$89$	11.7770	1.24836	0.624180	+	0.781280i	$0.285433\pi$
$90$	0	0
$91$	−4.66844	−0.489386
$92$	−0.489036	−0.0509855
$93$	−17.9317	−1.85944
$94$	0.402409	0.0415053
$95$	0	0
$96$	−7.09888	−0.724526
$97$	0.860838	0.0874048	0.0437024	−	0.999045i	$-0.486085\pi$
$97$	0.860838	0.0874048	0.0437024	+	0.999045i	$0.486085\pi$
$98$	−1.16268	−0.117448
$99$	−7.16470	−0.720080
$100$	0	0
$101$	−7.72970	−0.769134	−0.384567	−	0.923097i	$-0.625649\pi$
$101$	−7.72970	−0.769134	−0.384567	+	0.923097i	$0.625649\pi$
$102$	1.00343	0.0993545
$103$	−1.97534	−0.194636	−0.0973179	−	0.995253i	$-0.531026\pi$
$103$	−1.97534	−0.194636	−0.0973179	+	0.995253i	$0.531026\pi$
$104$	0.931469	0.0913381
$105$	0	0
$106$	−1.91921	−0.186410
$107$	0.319598	0.0308967	0.0154484	−	0.999881i	$-0.495082\pi$
$107$	0.319598	0.0308967	0.0154484	+	0.999881i	$0.495082\pi$
$108$	−31.4501	−3.02628
$109$	12.6271	1.20945	0.604727	−	0.796433i	$-0.293282\pi$
$109$	12.6271	1.20945	0.604727	+	0.796433i	$0.293282\pi$
$110$	0	0
$111$	14.5468	1.38072
$112$	−13.8694	−1.31054
$113$	13.1810	1.23997	0.619984	−	0.784615i	$-0.287139\pi$
$113$	13.1810	1.23997	0.619984	+	0.784615i	$0.287139\pi$
$114$	−2.26766	−0.212386
$115$	0	0
$116$	−3.81180	−0.353917
$117$	10.0435	0.928523
$118$	0.158373	0.0145794
$119$	6.05429	0.554996
$120$	0	0
$121$	−10.1680	−0.924363
$122$	0.455930	0.0412780
$123$	28.4948	2.56929
$124$	10.7017	0.961045
$125$	0	0
$126$	5.26730	0.469249
$127$	−0.830524	−0.0736971	−0.0368485	−	0.999321i	$-0.511732\pi$
$127$	−0.830524	−0.0736971	−0.0368485	+	0.999321i	$0.511732\pi$
$128$	5.63206	0.497808
$129$	−4.65238	−0.409619
$130$	0	0
$131$	9.31948	0.814247	0.407124	−	0.913373i	$-0.366532\pi$
$131$	9.31948	0.814247	0.407124	+	0.913373i	$0.366532\pi$
$132$	5.90904	0.514316
$133$	−13.6821	−1.18639
$134$	−2.46916	−0.213303
$135$	0	0
$136$	−1.20798	−0.103583
$137$	−4.27610	−0.365332	−0.182666	−	0.983175i	$-0.558473\pi$
$137$	−4.27610	−0.365332	−0.182666	+	0.983175i	$0.558473\pi$
$138$	−0.150502	−0.0128116
$139$	11.8522	1.00529	0.502645	−	0.864493i	$-0.332360\pi$
$139$	11.8522	1.00529	0.502645	+	0.864493i	$0.332360\pi$
$140$	0	0
$141$	−7.21843	−0.607902
$142$	−1.61341	−0.135394
$143$	−1.16632	−0.0975323
$144$	29.8382	2.48652
$145$	0	0
$146$	−2.63678	−0.218221
$147$	20.8562	1.72019
$148$	−8.68158	−0.713621
$149$	−21.2817	−1.74347	−0.871734	−	0.489979i	$-0.837004\pi$
$149$	−21.2817	−1.74347	−0.871734	+	0.489979i	$0.837004\pi$
$150$	0	0
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	2.72992	0.221425
$153$	−13.0250	−1.05301
$154$	−0.611673	−0.0492900
$155$	0	0
$156$	−8.28332	−0.663197
$157$	15.8157	1.26223	0.631115	−	0.775689i	$-0.282597\pi$
$157$	15.8157	1.26223	0.631115	+	0.775689i	$0.282597\pi$
$158$	1.86643	0.148485
$159$	34.4269	2.73023
$160$	0	0
$161$	−0.908069	−0.0715658
$162$	−5.35084	−0.420401
$163$	13.1212	1.02773	0.513866	−	0.857871i	$-0.328213\pi$
$163$	13.1212	1.02773	0.513866	+	0.857871i	$0.328213\pi$
$164$	−17.0058	−1.32793
$165$	0	0
$166$	1.29684	0.100654
$167$	−20.1890	−1.56227	−0.781134	−	0.624363i	$-0.785359\pi$
$167$	−20.1890	−1.56227	−0.781134	+	0.624363i	$0.785359\pi$
$168$	−8.76288	−0.676071
$169$	−11.3651	−0.874235
$170$	0	0
$171$	29.4352	2.25096
$172$	2.77656	0.211711
$173$	−0.672028	−0.0510933	−0.0255467	−	0.999674i	$-0.508133\pi$
$173$	−0.672028	−0.0510933	−0.0255467	+	0.999674i	$0.508133\pi$
$174$	−1.17309	−0.0889320
$175$	0	0
$176$	−3.46500	−0.261184
$177$	−2.84091	−0.213536
$178$	−2.16307	−0.162129
$179$	−2.07329	−0.154965	−0.0774823	−	0.996994i	$-0.524688\pi$
$179$	−2.07329	−0.154965	−0.0774823	+	0.996994i	$0.524688\pi$
$180$	0	0
$181$	2.78471	0.206985	0.103493	−	0.994630i	$-0.466998\pi$
$181$	2.78471	0.206985	0.103493	+	0.994630i	$0.466998\pi$
$182$	0.857446	0.0635581
$183$	−8.17850	−0.604572
$184$	0.181182	0.0133569
$185$	0	0
$186$	3.29350	0.241491
$187$	1.51254	0.110608
$188$	4.30799	0.314193
$189$	−58.3982	−4.24784
$190$	0	0
$191$	12.6722	0.916930	0.458465	−	0.888712i	$-0.348399\pi$
$191$	12.6722	0.916930	0.458465	+	0.888712i	$0.348399\pi$
$192$	−23.7272	−1.71236
$193$	6.20943	0.446964	0.223482	−	0.974708i	$-0.428258\pi$
$193$	6.20943	0.446964	0.223482	+	0.974708i	$0.428258\pi$
$194$	−0.158109	−0.0113515
$195$	0	0
$196$	−12.4471	−0.889077
$197$	14.8505	1.05805	0.529027	−	0.848605i	$-0.322557\pi$
$197$	14.8505	1.05805	0.529027	+	0.848605i	$0.322557\pi$
$198$	1.31593	0.0935191
$199$	15.0571	1.06737	0.533685	−	0.845683i	$-0.320807\pi$
$199$	15.0571	1.06737	0.533685	+	0.845683i	$0.320807\pi$
$200$	0	0
$201$	44.2919	3.12411
$202$	1.41970	0.0998899
$203$	−7.07796	−0.496775
$204$	10.7423	0.752108
$205$	0	0
$206$	0.362807	0.0252780
$207$	1.95358	0.135783
$208$	4.85725	0.336790
$209$	−3.41820	−0.236442
$210$	0	0
$211$	−14.1331	−0.972961	−0.486481	−	0.873691i	$-0.661720\pi$
$211$	−14.1331	−0.972961	−0.486481	+	0.873691i	$0.661720\pi$
$212$	−20.5461	−1.41111
$213$	28.9415	1.98304
$214$	−0.0587001	−0.00401266
$215$	0	0
$216$	11.6519	0.792809
$217$	19.8716	1.34897
$218$	−2.31919	−0.157076
$219$	47.2987	3.19615
$220$	0	0
$221$	−2.12029	−0.142626
$222$	−2.67178	−0.179318
$223$	9.31277	0.623629	0.311815	−	0.950143i	$-0.399063\pi$
$223$	9.31277	0.623629	0.311815	+	0.950143i	$0.399063\pi$
$224$	7.86683	0.525625
$225$	0	0
$226$	−2.42094	−0.161039
$227$	−0.485548	−0.0322270	−0.0161135	−	0.999870i	$-0.505129\pi$
$227$	−0.485548	−0.0322270	−0.0161135	+	0.999870i	$0.505129\pi$
$228$	−24.2765	−1.60775
$229$	15.3956	1.01737	0.508685	−	0.860953i	$-0.330132\pi$
$229$	15.3956	1.01737	0.508685	+	0.860953i	$0.330132\pi$
$230$	0	0
$231$	10.9722	0.721920
$232$	1.41223	0.0927172
$233$	20.5505	1.34631	0.673154	−	0.739502i	$-0.264939\pi$
$233$	20.5505	1.34631	0.673154	+	0.739502i	$0.264939\pi$
$234$	−1.84468	−0.120590
$235$	0	0
$236$	1.69546	0.110365
$237$	−33.4802	−2.17477
$238$	−1.11198	−0.0720791
$239$	−2.85049	−0.184383	−0.0921915	−	0.995741i	$-0.529387\pi$
$239$	−2.85049	−0.184383	−0.0921915	+	0.995741i	$0.529387\pi$
$240$	0	0
$241$	11.0331	0.710707	0.355354	−	0.934732i	$-0.384360\pi$
$241$	11.0331	0.710707	0.355354	+	0.934732i	$0.384360\pi$
$242$	1.86754	0.120050
$243$	47.9992	3.07915
$244$	4.88097	0.312472
$245$	0	0
$246$	−5.23360	−0.333682
$247$	4.79165	0.304885
$248$	−3.96487	−0.251769
$249$	−23.2627	−1.47422
$250$	0	0
$251$	−14.4565	−0.912486	−0.456243	−	0.889855i	$-0.650805\pi$
$251$	−14.4565	−0.912486	−0.456243	+	0.889855i	$0.650805\pi$
$252$	56.3892	3.55219
$253$	−0.226863	−0.0142627
$254$	0.152541	0.00957127
$255$	0	0
$256$	13.3690	0.835563
$257$	−28.0657	−1.75069	−0.875345	−	0.483500i	$-0.839365\pi$
$257$	−28.0657	−1.75069	−0.875345	+	0.483500i	$0.839365\pi$
$258$	0.854495	0.0531985
$259$	−16.1204	−1.00167
$260$	0	0
$261$	15.2272	0.942543
$262$	−1.71170	−0.105749
$263$	10.9878	0.677537	0.338768	−	0.940870i	$-0.389990\pi$
$263$	10.9878	0.677537	0.338768	+	0.940870i	$0.389990\pi$
$264$	−2.18923	−0.134738
$265$	0	0
$266$	2.51297	0.154080
$267$	38.8012	2.37460
$268$	−26.4336	−1.61469
$269$	−14.6293	−0.891965	−0.445983	−	0.895042i	$-0.647146\pi$
$269$	−14.6293	−0.891965	−0.445983	+	0.895042i	$0.647146\pi$
$270$	0	0
$271$	−31.9043	−1.93805	−0.969025	−	0.246964i	$-0.920567\pi$
$271$	−31.9043	−1.93805	−0.969025	+	0.246964i	$0.920567\pi$
$272$	−6.29915	−0.381942
$273$	−15.3809	−0.930896
$274$	0.785384	0.0474468
$275$	0	0
$276$	−1.61121	−0.0969832
$277$	−14.7225	−0.884588	−0.442294	−	0.896870i	$-0.645835\pi$
$277$	−14.7225	−0.884588	−0.442294	+	0.896870i	$0.645835\pi$
$278$	−2.17687	−0.130560
$279$	−42.7510	−2.55943
$280$	0	0
$281$	27.3492	1.63152	0.815758	−	0.578394i	$-0.196320\pi$
$281$	27.3492	1.63152	0.815758	+	0.578394i	$0.196320\pi$
$282$	1.32580	0.0789502
$283$	−26.2831	−1.56237	−0.781183	−	0.624302i	$-0.785384\pi$
$283$	−26.2831	−1.56237	−0.781183	+	0.624302i	$0.785384\pi$
$284$	−17.2724	−1.02493
$285$	0	0
$286$	0.214216	0.0126668
$287$	−31.5774	−1.86395
$288$	−16.9244	−0.997279
$289$	−14.2503	−0.838253
$290$	0	0
$291$	2.83617	0.166259
$292$	−28.2280	−1.65192
$293$	−16.2252	−0.947884	−0.473942	−	0.880556i	$-0.657169\pi$
$293$	−16.2252	−0.947884	−0.473942	+	0.880556i	$0.657169\pi$
$294$	−3.83063	−0.223407
$295$	0	0
$296$	3.21642	0.186951
$297$	−14.5896	−0.846575
$298$	3.90879	0.226430
$299$	0.318017	0.0183914
$300$	0	0
$301$	5.15567	0.297168
$302$	−0.183668	−0.0105689
$303$	−25.4667	−1.46302
$304$	14.2355	0.816460
$305$	0	0
$306$	2.39227	0.136757
$307$	−0.0943867	−0.00538693	−0.00269347	−	0.999996i	$-0.500857\pi$
$307$	−0.0943867	−0.00538693	−0.00269347	+	0.999996i	$0.500857\pi$
$308$	−6.54828	−0.373123
$309$	−6.50806	−0.370231
$310$	0	0
$311$	−13.8783	−0.786968	−0.393484	−	0.919332i	$-0.628730\pi$
$311$	−13.8783	−0.786968	−0.393484	+	0.919332i	$0.628730\pi$
$312$	3.06887	0.173741
$313$	13.4879	0.762379	0.381190	−	0.924497i	$-0.375514\pi$
$313$	13.4879	0.762379	0.381190	+	0.924497i	$0.375514\pi$
$314$	−2.90485	−0.163930
$315$	0	0
$316$	19.9811	1.12403
$317$	2.90664	0.163253	0.0816267	−	0.996663i	$-0.473988\pi$
$317$	2.90664	0.163253	0.0816267	+	0.996663i	$0.473988\pi$
$318$	−6.32313	−0.354583
$319$	−1.76829	−0.0990050
$320$	0	0
$321$	1.05297	0.0587709
$322$	0.166784	0.00929449
$323$	−6.21406	−0.345760
$324$	−57.2835	−3.18241
$325$	0	0
$326$	−2.40995	−0.133475
$327$	41.6019	2.30059
$328$	6.30046	0.347885
$329$	7.99931	0.441016
$330$	0	0
$331$	−11.1032	−0.610288	−0.305144	−	0.952306i	$-0.598705\pi$
$331$	−11.1032	−0.610288	−0.305144	+	0.952306i	$0.598705\pi$
$332$	13.8833	0.761945
$333$	34.6809	1.90050
$334$	3.70808	0.202897
$335$	0	0
$336$	−45.6951	−2.49287
$337$	0.880266	0.0479512	0.0239756	−	0.999713i	$-0.492368\pi$
$337$	0.880266	0.0479512	0.0239756	+	0.999713i	$0.492368\pi$
$338$	2.08740	0.113540
$339$	43.4270	2.35863
$340$	0	0
$341$	4.96452	0.268844
$342$	−5.40631	−0.292340
$343$	2.44508	0.132022
$344$	−1.02868	−0.0554628
$345$	0	0
$346$	0.123430	0.00663565
$347$	−34.5128	−1.85275	−0.926373	−	0.376608i	$-0.877090\pi$
$347$	−34.5128	−1.85275	−0.926373	+	0.376608i	$0.877090\pi$
$348$	−12.5586	−0.673210
$349$	−28.8423	−1.54389	−0.771947	−	0.635687i	$-0.780717\pi$
$349$	−28.8423	−1.54389	−0.771947	+	0.635687i	$0.780717\pi$
$350$	0	0
$351$	20.4518	1.09164
$352$	1.96537	0.104755
$353$	−23.9585	−1.27518	−0.637591	−	0.770375i	$-0.720069\pi$
$353$	−23.9585	−1.27518	−0.637591	+	0.770375i	$0.720069\pi$
$354$	0.521785	0.0277326
$355$	0	0
$356$	−23.1567	−1.22730
$357$	19.9468	1.05570
$358$	0.380797	0.0201258
$359$	−1.51542	−0.0799807	−0.0399904	−	0.999200i	$-0.512733\pi$
$359$	−1.51542	−0.0799807	−0.0399904	+	0.999200i	$0.512733\pi$
$360$	0	0
$361$	−4.95681	−0.260885
$362$	−0.511463	−0.0268819
$363$	−33.5000	−1.75830
$364$	9.17940	0.481131
$365$	0	0
$366$	1.50213	0.0785178
$367$	7.67846	0.400812	0.200406	−	0.979713i	$-0.435774\pi$
$367$	7.67846	0.400812	0.200406	+	0.979713i	$0.435774\pi$
$368$	0.944794	0.0492508
$369$	67.9343	3.53652
$370$	0	0
$371$	−38.1511	−1.98071
$372$	35.2586	1.82807
$373$	−23.5390	−1.21880	−0.609402	−	0.792861i	$-0.708591\pi$
$373$	−23.5390	−1.21880	−0.609402	+	0.792861i	$0.708591\pi$
$374$	−0.277806	−0.0143650
$375$	0	0
$376$	−1.59606	−0.0823105
$377$	2.47879	0.127664
$378$	10.7259	0.551681
$379$	−23.0030	−1.18159	−0.590793	−	0.806823i	$-0.701185\pi$
$379$	−23.0030	−1.18159	−0.590793	+	0.806823i	$0.701185\pi$
$380$	0	0
$381$	−2.73629	−0.140184
$382$	−2.32749	−0.119085
$383$	−20.8953	−1.06770	−0.533851	−	0.845579i	$-0.679256\pi$
$383$	−20.8953	−1.06770	−0.533851	+	0.845579i	$0.679256\pi$
$384$	18.5557	0.946917
$385$	0	0
$386$	−1.14048	−0.0580487
$387$	−11.0917	−0.563823
$388$	−1.69264	−0.0859306
$389$	15.5215	0.786971	0.393486	−	0.919331i	$-0.371269\pi$
$389$	15.5215	0.786971	0.393486	+	0.919331i	$0.371269\pi$
$390$	0	0
$391$	−0.412422	−0.0208571
$392$	4.61149	0.232916
$393$	30.7045	1.54884
$394$	−2.72757	−0.137413
$395$	0	0
$396$	14.0877	0.707934
$397$	32.1277	1.61244	0.806222	−	0.591614i	$-0.201509\pi$
$397$	32.1277	1.61244	0.806222	+	0.591614i	$0.201509\pi$
$398$	−2.76552	−0.138623
$399$	−45.0779	−2.25672
$400$	0	0
$401$	1.10536	0.0551989	0.0275994	−	0.999619i	$-0.491214\pi$
$401$	1.10536	0.0551989	0.0275994	+	0.999619i	$0.491214\pi$
$402$	−8.13502	−0.405738
$403$	−6.95928	−0.346667
$404$	15.1986	0.756161
$405$	0	0
$406$	1.30000	0.0645178
$407$	−4.02736	−0.199629
$408$	−3.97988	−0.197033
$409$	30.4605	1.50617	0.753086	−	0.657922i	$-0.228564\pi$
$409$	30.4605	1.50617	0.753086	+	0.657922i	$0.228564\pi$
$410$	0	0
$411$	−14.0883	−0.694924
$412$	3.88404	0.191353
$413$	3.14823	0.154914
$414$	−0.358812	−0.0176346
$415$	0	0
$416$	−2.75506	−0.135078
$417$	39.0489	1.91223
$418$	0.627816	0.0307075
$419$	12.4139	0.606459	0.303230	−	0.952917i	$-0.401935\pi$
$419$	12.4139	0.606459	0.303230	+	0.952917i	$0.401935\pi$
$420$	0	0
$421$	14.3449	0.699126	0.349563	−	0.936913i	$-0.386330\pi$
$421$	14.3449	0.699126	0.349563	+	0.936913i	$0.386330\pi$
$422$	2.59580	0.126362
$423$	−17.2094	−0.836750
$424$	7.61208	0.369675
$425$	0	0
$426$	−5.31564	−0.257543
$427$	9.06324	0.438601
$428$	−0.628415	−0.0303756
$429$	−3.84262	−0.185523
$430$	0	0
$431$	−40.0541	−1.92934	−0.964668	−	0.263468i	$-0.915134\pi$
$431$	−40.0541	−1.92934	−0.964668	+	0.263468i	$0.915134\pi$
$432$	60.7600	2.92332
$433$	−30.1463	−1.44874	−0.724369	−	0.689412i	$-0.757869\pi$
$433$	−30.1463	−1.44874	−0.724369	+	0.689412i	$0.757869\pi$
$434$	−3.64978	−0.175195
$435$	0	0
$436$	−24.8282	−1.18905
$437$	0.932033	0.0445852
$438$	−8.68727	−0.415094
$439$	18.4456	0.880359	0.440179	−	0.897910i	$-0.354915\pi$
$439$	18.4456	0.880359	0.440179	+	0.897910i	$0.354915\pi$
$440$	0	0
$441$	49.7231	2.36777
$442$	0.389430	0.0185233
$443$	−4.84442	−0.230165	−0.115083	−	0.993356i	$-0.536713\pi$
$443$	−4.84442	−0.230165	−0.115083	+	0.993356i	$0.536713\pi$
$444$	−28.6028	−1.35743
$445$	0	0
$446$	−1.71046	−0.0809928
$447$	−70.1161	−3.31638
$448$	26.2940	1.24227
$449$	−21.8751	−1.03235	−0.516174	−	0.856484i	$-0.672644\pi$
$449$	−21.8751	−1.03235	−0.516174	+	0.856484i	$0.672644\pi$
$450$	0	0
$451$	−7.88897	−0.371477
$452$	−25.9174	−1.21905
$453$	3.29466	0.154797
$454$	0.0891800	0.00418542
$455$	0	0
$456$	8.99414	0.421189
$457$	−0.383056	−0.0179186	−0.00895930	−	0.999960i	$-0.502852\pi$
$457$	−0.383056	−0.0179186	−0.00895930	+	0.999960i	$0.502852\pi$
$458$	−2.82768	−0.132129
$459$	−26.5230	−1.23799
$460$	0	0
$461$	34.9368	1.62717	0.813585	−	0.581447i	$-0.197513\pi$
$461$	34.9368	1.62717	0.813585	+	0.581447i	$0.197513\pi$
$462$	−2.01525	−0.0937581
$463$	−13.6404	−0.633925	−0.316963	−	0.948438i	$-0.602663\pi$
$463$	−13.6404	−0.633925	−0.316963	+	0.948438i	$0.602663\pi$
$464$	7.36422	0.341875
$465$	0	0
$466$	−3.77448	−0.174849
$467$	30.3922	1.40638	0.703192	−	0.711000i	$-0.251757\pi$
$467$	30.3922	1.40638	0.703192	+	0.711000i	$0.251757\pi$
$468$	−19.7482	−0.912862
$469$	−49.0833	−2.26646
$470$	0	0
$471$	52.1073	2.40098
$472$	−0.628149	−0.0289129
$473$	1.28804	0.0592241
$474$	6.14925	0.282444
$475$	0	0
$476$	−11.9043	−0.545634
$477$	82.0768	3.75804
$478$	0.523545	0.0239464
$479$	−23.2203	−1.06096	−0.530482	−	0.847696i	$-0.677989\pi$
$479$	−23.2203	−1.06096	−0.530482	+	0.847696i	$0.677989\pi$
$480$	0	0
$481$	5.64558	0.257416
$482$	−2.02644	−0.0923019
$483$	−2.99178	−0.136130
$484$	19.9930	0.908771
$485$	0	0
$486$	−8.81594	−0.399899
$487$	−23.9343	−1.08457	−0.542284	−	0.840195i	$-0.682440\pi$
$487$	−23.9343	−1.08457	−0.542284	+	0.840195i	$0.682440\pi$
$488$	−1.80834	−0.0818597
$489$	43.2298	1.95492
$490$	0	0
$491$	14.5262	0.655557	0.327778	−	0.944755i	$-0.393700\pi$
$491$	14.5262	0.655557	0.327778	+	0.944755i	$0.393700\pi$
$492$	−56.0284	−2.52596
$493$	−3.21463	−0.144780
$494$	−0.880075	−0.0395964
$495$	0	0
$496$	−20.6753	−0.928347
$497$	−32.0723	−1.43864
$498$	4.27263	0.191461
$499$	19.6649	0.880322	0.440161	−	0.897919i	$-0.354921\pi$
$499$	19.6649	0.880322	0.440161	+	0.897919i	$0.354921\pi$
$500$	0	0
$501$	−66.5157	−2.97170
$502$	2.65520	0.118508
$503$	−7.56135	−0.337144	−0.168572	−	0.985689i	$-0.553916\pi$
$503$	−7.56135	−0.337144	−0.168572	+	0.985689i	$0.553916\pi$
$504$	−20.8915	−0.930582
$505$	0	0
$506$	0.0416675	0.00185235
$507$	−37.4440	−1.66294
$508$	1.63303	0.0724540
$509$	−4.07748	−0.180731	−0.0903656	−	0.995909i	$-0.528804\pi$
$509$	−4.07748	−0.180731	−0.0903656	+	0.995909i	$0.528804\pi$
$510$	0	0
$511$	−52.4154	−2.31872
$512$	−13.7196	−0.606326
$513$	59.9393	2.64639
$514$	5.15478	0.227368
$515$	0	0
$516$	9.14781	0.402710
$517$	1.99847	0.0878925
$518$	2.96081	0.130091
$519$	−2.21410	−0.0971883
$520$	0	0
$521$	−33.7144	−1.47706	−0.738528	−	0.674223i	$-0.764479\pi$
$521$	−33.7144	−1.47706	−0.738528	+	0.674223i	$0.764479\pi$
$522$	−2.79677	−0.122411
$523$	36.7350	1.60631	0.803154	−	0.595772i	$-0.203154\pi$
$523$	36.7350	1.60631	0.803154	+	0.595772i	$0.203154\pi$
$524$	−18.3246	−0.800513
$525$	0	0
$526$	−2.01811	−0.0879939
$527$	9.02517	0.393142
$528$	−11.4160	−0.496817
$529$	−22.9381	−0.997311
$530$	0	0
$531$	−6.77298	−0.293922
$532$	26.9027	1.16638
$533$	11.0588	0.479010
$534$	−7.12656	−0.308396
$535$	0	0
$536$	9.79333	0.423007
$537$	−6.83077	−0.294769
$538$	2.68694	0.115842
$539$	−5.77417	−0.248711
$540$	0	0
$541$	17.3851	0.747442	0.373721	−	0.927541i	$-0.378082\pi$
$541$	17.3851	0.747442	0.373721	+	0.927541i	$0.378082\pi$
$542$	5.85982	0.251701
$543$	9.17465	0.393722
$544$	3.57291	0.153187
$545$	0	0
$546$	2.82499	0.120898
$547$	−27.2857	−1.16665	−0.583326	−	0.812238i	$-0.698249\pi$
$547$	−27.2857	−1.16665	−0.583326	+	0.812238i	$0.698249\pi$
$548$	8.40795	0.359170
$549$	−19.4983	−0.832168
$550$	0	0
$551$	7.26475	0.309489
$552$	0.596933	0.0254071
$553$	37.1020	1.57774
$554$	2.70406	0.114884
$555$	0	0
$556$	−23.3045	−0.988333
$557$	−22.0118	−0.932669	−0.466335	−	0.884608i	$-0.654426\pi$
$557$	−22.0118	−0.932669	−0.466335	+	0.884608i	$0.654426\pi$
$558$	7.85200	0.332402
$559$	−1.80558	−0.0763679
$560$	0	0
$561$	4.98331	0.210395
$562$	−5.02318	−0.211890
$563$	34.7867	1.46609	0.733043	−	0.680183i	$-0.238100\pi$
$563$	34.7867	1.46609	0.733043	+	0.680183i	$0.238100\pi$
$564$	14.1934	0.597648
$565$	0	0
$566$	4.82737	0.202910
$567$	−106.367	−4.46700
$568$	6.39922	0.268505
$569$	4.70112	0.197081	0.0985407	−	0.995133i	$-0.468583\pi$
$569$	4.70112	0.197081	0.0985407	+	0.995133i	$0.468583\pi$
$570$	0	0
$571$	−10.1822	−0.426112	−0.213056	−	0.977040i	$-0.568342\pi$
$571$	−10.1822	−0.426112	−0.213056	+	0.977040i	$0.568342\pi$
$572$	2.29329	0.0958873
$573$	41.7506	1.74416
$574$	5.79977	0.242078
$575$	0	0
$576$	−56.5679	−2.35700
$577$	−20.5479	−0.855422	−0.427711	−	0.903916i	$-0.640680\pi$
$577$	−20.5479	−0.855422	−0.427711	+	0.903916i	$0.640680\pi$
$578$	2.61733	0.108867
$579$	20.4579	0.850203
$580$	0	0
$581$	25.7793	1.06950
$582$	−0.520914	−0.0215926
$583$	−9.53129	−0.394746
$584$	10.4582	0.432761
$585$	0	0
$586$	2.98005	0.123105
$587$	−8.40929	−0.347088	−0.173544	−	0.984826i	$-0.555522\pi$
$587$	−8.40929	−0.347088	−0.173544	+	0.984826i	$0.555522\pi$
$588$	−41.0089	−1.69118
$589$	−20.3960	−0.840403
$590$	0	0
$591$	48.9273	2.01260
$592$	16.7724	0.689341
$593$	7.48556	0.307395	0.153697	−	0.988118i	$-0.450882\pi$
$593$	7.48556	0.307395	0.153697	+	0.988118i	$0.450882\pi$
$594$	2.67965	0.109947
$595$	0	0
$596$	41.8456	1.71406
$597$	49.6080	2.03032
$598$	−0.0584097	−0.00238855
$599$	4.69324	0.191760	0.0958802	−	0.995393i	$-0.469433\pi$
$599$	4.69324	0.191760	0.0958802	+	0.995393i	$0.469433\pi$
$600$	0	0
$601$	−1.89605	−0.0773416	−0.0386708	−	0.999252i	$-0.512312\pi$
$601$	−1.89605	−0.0773416	−0.0386708	+	0.999252i	$0.512312\pi$
$602$	−0.946933	−0.0385941
$603$	105.596	4.30020
$604$	−1.96627	−0.0800062
$605$	0	0
$606$	4.67743	0.190008
$607$	19.6483	0.797501	0.398751	−	0.917059i	$-0.369444\pi$
$607$	19.6483	0.797501	0.398751	+	0.917059i	$0.369444\pi$
$608$	−8.07444	−0.327462
$609$	−23.3195	−0.944952
$610$	0	0
$611$	−2.80146	−0.113335
$612$	25.6105	1.03524
$613$	17.3399	0.700352	0.350176	−	0.936684i	$-0.386122\pi$
$613$	17.3399	0.700352	0.350176	+	0.936684i	$0.386122\pi$
$614$	0.0173359	0.000699619 0
$615$	0	0
$616$	2.42606	0.0977487
$617$	−6.60055	−0.265728	−0.132864	−	0.991134i	$-0.542417\pi$
$617$	−6.60055	−0.265728	−0.132864	+	0.991134i	$0.542417\pi$
$618$	1.19533	0.0480830
$619$	−6.67297	−0.268209	−0.134105	−	0.990967i	$-0.542816\pi$
$619$	−6.67297	−0.268209	−0.134105	+	0.990967i	$0.542816\pi$
$620$	0	0
$621$	3.97812	0.159636
$622$	2.54901	0.102206
$623$	−42.9987	−1.72271
$624$	16.0030	0.640632
$625$	0	0
$626$	−2.47730	−0.0990127
$627$	−11.2618	−0.449753
$628$	−31.0979	−1.24094
$629$	−7.32149	−0.291927
$630$	0	0
$631$	16.7963	0.668651	0.334325	−	0.942458i	$-0.391492\pi$
$631$	16.7963	0.668651	0.334325	+	0.942458i	$0.391492\pi$
$632$	−7.40276	−0.294466
$633$	−46.5637	−1.85074
$634$	−0.533859	−0.0212022
$635$	0	0
$636$	−67.6924	−2.68418
$637$	8.09426	0.320706
$638$	0.324778	0.0128581
$639$	68.9992	2.72956
$640$	0	0
$641$	20.5409	0.811316	0.405658	−	0.914025i	$-0.367042\pi$
$641$	20.5409	0.811316	0.405658	+	0.914025i	$0.367042\pi$
$642$	−0.193397	−0.00763277
$643$	−1.06457	−0.0419825	−0.0209913	−	0.999780i	$-0.506682\pi$
$643$	−1.06457	−0.0419825	−0.0209913	+	0.999780i	$0.506682\pi$
$644$	1.78550	0.0703587
$645$	0	0
$646$	1.14133	0.0449049
$647$	−29.6687	−1.16640	−0.583198	−	0.812330i	$-0.698199\pi$
$647$	−29.6687	−1.16640	−0.583198	+	0.812330i	$0.698199\pi$
$648$	21.2228	0.833712
$649$	0.786522	0.0308737
$650$	0	0
$651$	65.4701	2.56597
$652$	−25.7998	−1.01040
$653$	20.1399	0.788137	0.394069	−	0.919081i	$-0.371067\pi$
$653$	20.1399	0.788137	0.394069	+	0.919081i	$0.371067\pi$
$654$	−7.64095	−0.298785
$655$	0	0
$656$	32.8545	1.28275
$657$	112.764	4.39936
$658$	−1.46922	−0.0572762
$659$	36.5416	1.42346	0.711730	−	0.702453i	$-0.247912\pi$
$659$	36.5416	1.42346	0.711730	+	0.702453i	$0.247912\pi$
$660$	0	0
$661$	22.1043	0.859758	0.429879	−	0.902886i	$-0.358556\pi$
$661$	22.1043	0.859758	0.429879	+	0.902886i	$0.358556\pi$
$662$	2.03931	0.0792600
$663$	−6.98563	−0.271299
$664$	−5.14360	−0.199610
$665$	0	0
$666$	−6.36978	−0.246824
$667$	0.482155	0.0186691
$668$	39.6969	1.53592
$669$	30.6824	1.18625
$670$	0	0
$671$	2.26427	0.0874111
$672$	25.9185	0.999828
$673$	−30.5471	−1.17750	−0.588751	−	0.808314i	$-0.700380\pi$
$673$	−30.5471	−1.17750	−0.588751	+	0.808314i	$0.700380\pi$
$674$	−0.161677	−0.00622757
$675$	0	0
$676$	22.3467	0.859489
$677$	−24.5063	−0.941854	−0.470927	−	0.882172i	$-0.656080\pi$
$677$	−24.5063	−0.941854	−0.470927	+	0.882172i	$0.656080\pi$
$678$	−7.97617	−0.306323
$679$	−3.14298	−0.120616
$680$	0	0
$681$	−1.59972	−0.0613013
$682$	−0.911825	−0.0349156
$683$	36.8637	1.41055	0.705275	−	0.708933i	$-0.250823\pi$
$683$	36.8637	1.41055	0.705275	+	0.708933i	$0.250823\pi$
$684$	−57.8774	−2.21300
$685$	0	0
$686$	−0.449085	−0.0171461
$687$	50.7232	1.93521
$688$	−5.36418	−0.204507
$689$	13.3610	0.509014
$690$	0	0
$691$	−12.4203	−0.472492	−0.236246	−	0.971693i	$-0.575917\pi$
$691$	−12.4203	−0.472492	−0.236246	+	0.971693i	$0.575917\pi$
$692$	1.32139	0.0502315
$693$	26.1588	0.993692
$694$	6.33892	0.240622
$695$	0	0
$696$	4.65280	0.176364
$697$	−14.3416	−0.543228
$698$	5.29743	0.200511
$699$	67.7069	2.56091
$700$	0	0
$701$	28.1266	1.06233	0.531164	−	0.847269i	$-0.321755\pi$
$701$	28.1266	1.06233	0.531164	+	0.847269i	$0.321755\pi$
$702$	−3.75635	−0.141774
$703$	16.5459	0.624039
$704$	6.56903	0.247579
$705$	0	0
$706$	4.40042	0.165612
$707$	28.2217	1.06138
$708$	5.58598	0.209934
$709$	1.43051	0.0537241	0.0268620	−	0.999639i	$-0.491449\pi$
$709$	1.43051	0.0537241	0.0268620	+	0.999639i	$0.491449\pi$
$710$	0	0
$711$	−79.8198	−2.99348
$712$	8.57929	0.321523
$713$	−1.35366	−0.0506951
$714$	−3.66360	−0.137107
$715$	0	0
$716$	4.07663	0.152351
$717$	−9.39139	−0.350728
$718$	0.278335	0.0103874
$719$	16.8995	0.630244	0.315122	−	0.949051i	$-0.397955\pi$
$719$	16.8995	0.630244	0.315122	+	0.949051i	$0.397955\pi$
$720$	0	0
$721$	7.21209	0.268592
$722$	0.910409	0.0338819
$723$	36.3504	1.35189
$724$	−5.47547	−0.203494
$725$	0	0
$726$	6.15290	0.228356
$727$	−26.9422	−0.999233	−0.499616	−	0.866247i	$-0.666526\pi$
$727$	−26.9422	−0.999233	−0.499616	+	0.866247i	$0.666526\pi$
$728$	−3.40086	−0.126044
$729$	70.7417	2.62006
$730$	0	0
$731$	2.34157	0.0866062
$732$	16.0811	0.594375
$733$	9.89979	0.365657	0.182829	−	0.983145i	$-0.441475\pi$
$733$	9.89979	0.365657	0.182829	+	0.983145i	$0.441475\pi$
$734$	−1.41029	−0.0520548
$735$	0	0
$736$	−0.535893	−0.0197533
$737$	−12.2625	−0.451694
$738$	−12.4774	−0.459299
$739$	36.7085	1.35034	0.675171	−	0.737661i	$-0.264070\pi$
$739$	36.7085	1.35034	0.675171	+	0.737661i	$0.264070\pi$
$740$	0	0
$741$	15.7868	0.579944
$742$	7.00716	0.257241
$743$	40.2612	1.47704	0.738521	−	0.674231i	$-0.235525\pi$
$743$	40.2612	1.47704	0.738521	+	0.674231i	$0.235525\pi$
$744$	−13.0629	−0.478909
$745$	0	0
$746$	4.32338	0.158290
$747$	−55.4605	−2.02919
$748$	−2.97406	−0.108742
$749$	−1.16688	−0.0426367
$750$	0	0
$751$	20.0555	0.731836	0.365918	−	0.930647i	$-0.380755\pi$
$751$	20.0555	0.731836	0.365918	+	0.930647i	$0.380755\pi$
$752$	−8.32284	−0.303503
$753$	−47.6292	−1.73571
$754$	−0.455276	−0.0165802
$755$	0	0
$756$	114.826	4.17619
$757$	−38.8419	−1.41173	−0.705867	−	0.708345i	$-0.749442\pi$
$757$	−38.8419	−1.41173	−0.705867	+	0.708345i	$0.749442\pi$
$758$	4.22493	0.153456
$759$	−0.747435	−0.0271302
$760$	0	0
$761$	9.26836	0.335978	0.167989	−	0.985789i	$-0.446273\pi$
$761$	9.26836	0.335978	0.167989	+	0.985789i	$0.446273\pi$
$762$	0.502570	0.0182062
$763$	−46.1023	−1.66901
$764$	−24.9170	−0.901464
$765$	0	0
$766$	3.83781	0.138666
$767$	−1.10255	−0.0398108
$768$	44.0463	1.58939
$769$	−8.24686	−0.297389	−0.148695	−	0.988883i	$-0.547507\pi$
$769$	−8.24686	−0.297389	−0.148695	+	0.988883i	$0.547507\pi$
$770$	0	0
$771$	−92.4668	−3.33011
$772$	−12.2094	−0.439425
$773$	17.9148	0.644352	0.322176	−	0.946680i	$-0.395586\pi$
$773$	17.9148	0.644352	0.322176	+	0.946680i	$0.395586\pi$
$774$	2.03720	0.0732255
$775$	0	0
$776$	0.627102	0.0225116
$777$	−53.1113	−1.90536
$778$	−2.85081	−0.102206
$779$	32.4107	1.16123
$780$	0	0
$781$	−8.01263	−0.286714
$782$	0.0757488	0.00270877
$783$	31.0075	1.10812
$784$	24.0472	0.858827
$785$	0	0
$786$	−5.63945	−0.201153
$787$	−37.4489	−1.33491	−0.667454	−	0.744651i	$-0.732616\pi$
$787$	−37.4489	−1.33491	−0.667454	+	0.744651i	$0.732616\pi$
$788$	−29.2000	−1.04021
$789$	36.2010	1.28879
$790$	0	0
$791$	−48.1249	−1.71112
$792$	−5.21933	−0.185461
$793$	−3.17406	−0.112714
$794$	−5.90085	−0.209413
$795$	0	0
$796$	−29.6063	−1.04937
$797$	6.56429	0.232519	0.116259	−	0.993219i	$-0.462910\pi$
$797$	6.56429	0.232519	0.116259	+	0.993219i	$0.462910\pi$
$798$	8.27938	0.293087
$799$	3.63308	0.128529
$800$	0	0
$801$	92.5057	3.26853
$802$	−0.203019	−0.00716886
$803$	−13.0949	−0.462110
$804$	−87.0896	−3.07141
$805$	0	0
$806$	1.27820	0.0450227
$807$	−48.1986	−1.69667
$808$	−5.63091	−0.198095
$809$	12.8394	0.451409	0.225704	−	0.974196i	$-0.427532\pi$
$809$	12.8394	0.451409	0.225704	+	0.974196i	$0.427532\pi$
$810$	0	0
$811$	−1.31098	−0.0460347	−0.0230174	−	0.999735i	$-0.507327\pi$
$811$	−1.31098	−0.0460347	−0.0230174	+	0.999735i	$0.507327\pi$
$812$	13.9171	0.488396
$813$	−105.114	−3.68650
$814$	0.739700	0.0259265
$815$	0	0
$816$	−20.7535	−0.726519
$817$	−5.29173	−0.185134
$818$	−5.59463	−0.195612
$819$	−36.6696	−1.28134
$820$	0	0
$821$	−46.1086	−1.60920	−0.804600	−	0.593817i	$-0.797620\pi$
$821$	−46.1086	−1.60920	−0.804600	+	0.593817i	$0.797620\pi$
$822$	2.58757	0.0902520
$823$	−6.36527	−0.221879	−0.110940	−	0.993827i	$-0.535386\pi$
$823$	−6.36527	−0.221879	−0.110940	+	0.993827i	$0.535386\pi$
$824$	−1.43899	−0.0501296
$825$	0	0
$826$	−0.578231	−0.0201192
$827$	−18.4051	−0.640009	−0.320004	−	0.947416i	$-0.603684\pi$
$827$	−18.4051	−0.640009	−0.320004	+	0.947416i	$0.603684\pi$
$828$	−3.84127	−0.133493
$829$	0.214845	0.00746186	0.00373093	−	0.999993i	$-0.498812\pi$
$829$	0.214845	0.00746186	0.00373093	+	0.999993i	$0.498812\pi$
$830$	0	0
$831$	−48.5055	−1.68264
$832$	−9.20849	−0.319247
$833$	−10.4971	−0.363702
$834$	−7.17205	−0.248348
$835$	0	0
$836$	6.72109	0.232454
$837$	−87.0545	−3.00905
$838$	−2.28004	−0.0787628
$839$	8.66817	0.299259	0.149629	−	0.988742i	$-0.452192\pi$
$839$	8.66817	0.299259	0.149629	+	0.988742i	$0.452192\pi$
$840$	0	0
$841$	−25.2418	−0.870408
$842$	−2.63470	−0.0907977
$843$	90.1062	3.10342
$844$	27.7894	0.956550
$845$	0	0
$846$	3.16083	0.108671
$847$	37.1240	1.27560
$848$	39.6941	1.36310
$849$	−86.5938	−2.97189
$850$	0	0
$851$	1.09813	0.0376435
$852$	−56.9066	−1.94959
$853$	22.5241	0.771211	0.385605	−	0.922664i	$-0.373993\pi$
$853$	22.5241	0.771211	0.385605	+	0.922664i	$0.373993\pi$
$854$	−1.66463	−0.0569625
$855$	0	0
$856$	0.232820	0.00795764
$857$	45.0950	1.54041	0.770207	−	0.637794i	$-0.220153\pi$
$857$	45.0950	1.54041	0.770207	+	0.637794i	$0.220153\pi$
$858$	0.705768	0.0240945
$859$	−21.0436	−0.718000	−0.359000	−	0.933338i	$-0.616882\pi$
$859$	−21.0436	−0.718000	−0.359000	+	0.933338i	$0.616882\pi$
$860$	0	0
$861$	−104.037	−3.54556
$862$	7.35667	0.250569
$863$	2.01110	0.0684587	0.0342293	−	0.999414i	$-0.489102\pi$
$863$	2.01110	0.0684587	0.0342293	+	0.999414i	$0.489102\pi$
$864$	−34.4634	−1.17247
$865$	0	0
$866$	5.53693	0.188152
$867$	−46.9499	−1.59450
$868$	−39.0728	−1.32622
$869$	9.26919	0.314436
$870$	0	0
$871$	17.1896	0.582448
$872$	9.19854	0.311502
$873$	6.76168	0.228848
$874$	−0.171185	−0.00579042
$875$	0	0
$876$	−93.0018	−3.14224
$877$	−0.542916	−0.0183330	−0.00916648	−	0.999958i	$-0.502918\pi$
$877$	−0.542916	−0.0183330	−0.00916648	+	0.999958i	$0.502918\pi$
$878$	−3.38787	−0.114335
$879$	−53.4563	−1.80304
$880$	0	0
$881$	−8.69333	−0.292886	−0.146443	−	0.989219i	$-0.546782\pi$
$881$	−8.69333	−0.292886	−0.146443	+	0.989219i	$0.546782\pi$
$882$	−9.13257	−0.307510
$883$	−35.6778	−1.20065	−0.600327	−	0.799755i	$-0.704963\pi$
$883$	−35.6778	−1.20065	−0.600327	+	0.799755i	$0.704963\pi$
$884$	4.16905	0.140220
$885$	0	0
$886$	0.889767	0.0298923
$887$	−13.8237	−0.464154	−0.232077	−	0.972697i	$-0.574552\pi$
$887$	−13.8237	−0.464154	−0.232077	+	0.972697i	$0.574552\pi$
$888$	10.5970	0.355612
$889$	3.03230	0.101700
$890$	0	0
$891$	−26.5737	−0.890251
$892$	−18.3114	−0.613111
$893$	−8.21042	−0.274751
$894$	12.8781	0.430708
$895$	0	0
$896$	−20.5630	−0.686963
$897$	1.04776	0.0349836
$898$	4.01776	0.134074
$899$	−10.5512	−0.351901
$900$	0	0
$901$	−17.3273	−0.577255
$902$	1.44896	0.0482449
$903$	16.9862	0.565264
$904$	9.60209	0.319361
$905$	0	0
$906$	−0.605125	−0.0201039
$907$	−3.22925	−0.107225	−0.0536127	−	0.998562i	$-0.517074\pi$
$907$	−3.22925	−0.107225	−0.0536127	+	0.998562i	$0.517074\pi$
$908$	0.954717	0.0316834
$909$	−60.7150	−2.01379
$910$	0	0
$911$	−36.7510	−1.21761	−0.608807	−	0.793318i	$-0.708352\pi$
$911$	−36.7510	−1.21761	−0.608807	+	0.793318i	$0.708352\pi$
$912$	46.9010	1.55305
$913$	6.44043	0.213147
$914$	0.0703553	0.00232715
$915$	0	0
$916$	−30.2718	−1.00021
$917$	−34.0261	−1.12364
$918$	4.87143	0.160781
$919$	−50.3548	−1.66105	−0.830526	−	0.556980i	$-0.811960\pi$
$919$	−50.3548	−1.66105	−0.830526	+	0.556980i	$0.811960\pi$
$920$	0	0
$921$	−0.310972	−0.0102469
$922$	−6.41679	−0.211326
$923$	11.2321	0.369710
$924$	−21.5743	−0.709743
$925$	0	0
$926$	2.50532	0.0823299
$927$	−15.5158	−0.509606
$928$	−4.17703	−0.137118
$929$	49.9006	1.63719	0.818593	−	0.574374i	$-0.194755\pi$
$929$	49.9006	1.63719	0.818593	+	0.574374i	$0.194755\pi$
$930$	0	0
$931$	23.7224	0.777469
$932$	−40.4078	−1.32360
$933$	−45.7243	−1.49695
$934$	−5.58209	−0.182652
$935$	0	0
$936$	7.31648	0.239147
$937$	39.6375	1.29490	0.647451	−	0.762107i	$-0.275835\pi$
$937$	39.6375	1.29490	0.647451	+	0.762107i	$0.275835\pi$
$938$	9.01506	0.294352
$939$	44.4379	1.45018
$940$	0	0
$941$	25.3577	0.826637	0.413318	−	0.910587i	$-0.364370\pi$
$941$	25.3577	0.826637	0.413318	+	0.910587i	$0.364370\pi$
$942$	−9.57048	−0.311823
$943$	2.15107	0.0700484
$944$	−3.27556	−0.106610
$945$	0	0
$946$	−0.236572	−0.00769163
$947$	−5.89253	−0.191481	−0.0957407	−	0.995406i	$-0.530522\pi$
$947$	−5.89253	−0.191481	−0.0957407	+	0.995406i	$0.530522\pi$
$948$	65.8309	2.13809
$949$	18.3565	0.595878
$950$	0	0
$951$	9.57639	0.310536
$952$	4.41041	0.142942
$953$	−10.0351	−0.325070	−0.162535	−	0.986703i	$-0.551967\pi$
$953$	−10.0351	−0.325070	−0.162535	+	0.986703i	$0.551967\pi$
$954$	−15.0749	−0.488069
$955$	0	0
$956$	5.60482	0.181273
$957$	−5.82590	−0.188325
$958$	4.26484	0.137791
$959$	15.6123	0.504149
$960$	0	0
$961$	−1.37730	−0.0444291
$962$	−1.03691	−0.0334315
$963$	2.51037	0.0808956
$964$	−21.6941	−0.698720
$965$	0	0
$966$	0.549495	0.0176797
$967$	45.6262	1.46724	0.733620	−	0.679560i	$-0.237829\pi$
$967$	45.6262	1.46724	0.733620	+	0.679560i	$0.237829\pi$
$968$	−7.40716	−0.238075
$969$	−20.4732	−0.657695
$970$	0	0
$971$	50.0563	1.60638	0.803191	−	0.595721i	$-0.203134\pi$
$971$	50.0563	1.60638	0.803191	+	0.595721i	$0.203134\pi$
$972$	−94.3792	−3.02722
$973$	−43.2731	−1.38727
$974$	4.39598	0.140856
$975$	0	0
$976$	−9.42980	−0.301840
$977$	−16.8418	−0.538817	−0.269409	−	0.963026i	$-0.586828\pi$
$977$	−16.8418	−0.538817	−0.269409	+	0.963026i	$0.586828\pi$
$978$	−7.93996	−0.253892
$979$	−10.7424	−0.343327
$980$	0	0
$981$	99.1827	3.16666
$982$	−2.66800	−0.0851393
$983$	54.2760	1.73114	0.865568	−	0.500792i	$-0.166958\pi$
$983$	54.2760	1.73114	0.865568	+	0.500792i	$0.166958\pi$
$984$	20.7579	0.661736
$985$	0	0
$986$	0.590426	0.0188030
$987$	26.3550	0.838889
$988$	−9.42166	−0.299743
$989$	−0.351207	−0.0111677
$990$	0	0
$991$	−5.73279	−0.182108	−0.0910540	−	0.995846i	$-0.529024\pi$
$991$	−5.73279	−0.182108	−0.0910540	+	0.995846i	$0.529024\pi$
$992$	11.7271	0.372337
$993$	−36.5813	−1.16087
$994$	5.89067	0.186841
$995$	0	0
$996$	45.7407	1.44935
$997$	−19.9095	−0.630541	−0.315270	−	0.949002i	$-0.602095\pi$
$997$	−19.9095	−0.630541	−0.315270	+	0.949002i	$0.602095\pi$
$998$	−3.61182	−0.114330
$999$	70.6213	2.23436

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3775.2.a.p.1.3		6
5.4	even	2		151.2.a.c.1.4	✓	6
15.14	odd	2		1359.2.a.i.1.3		6
20.19	odd	2		2416.2.a.o.1.6		6
35.34	odd	2		7399.2.a.e.1.4		6
40.19	odd	2		9664.2.a.bc.1.1		6
40.29	even	2		9664.2.a.bh.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.a.c.1.4	✓	6	5.4	even	2
1359.2.a.i.1.3		6	15.14	odd	2
2416.2.a.o.1.6		6	20.19	odd	2
3775.2.a.p.1.3		6	1.1	even	1	trivial
7399.2.a.e.1.4		6	35.34	odd	2
9664.2.a.bc.1.1		6	40.19	odd	2
9664.2.a.bh.1.6		6	40.29	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3775 = 5^{2} \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3775.a (trivial)

\(f(q)\)	\(=\)	\(q-0.183668 q^{2} +3.29466 q^{3} -1.96627 q^{4} -0.605125 q^{6} -3.65107 q^{7} +0.728478 q^{8} +7.85477 q^{9} +O(q^{10})\)	\(q-0.183668 q^{2} +3.29466 q^{3} -1.96627 q^{4} -0.605125 q^{6} -3.65107 q^{7} +0.728478 q^{8} +7.85477 q^{9} -0.912147 q^{11} -6.47817 q^{12} +1.27865 q^{13} +0.670586 q^{14} +3.79873 q^{16} -1.65822 q^{17} -1.44267 q^{18} +3.74742 q^{19} -12.0290 q^{21} +0.167533 q^{22} +0.248713 q^{23} +2.40009 q^{24} -0.234848 q^{26} +15.9948 q^{27} +7.17897 q^{28} +1.93860 q^{29} -5.44267 q^{31} -2.15466 q^{32} -3.00521 q^{33} +0.304563 q^{34} -15.4446 q^{36} +4.41526 q^{37} -0.688284 q^{38} +4.21272 q^{39} +8.64880 q^{41} +2.20935 q^{42} -1.41210 q^{43} +1.79352 q^{44} -0.0456807 q^{46} -2.19095 q^{47} +12.5155 q^{48} +6.33031 q^{49} -5.46328 q^{51} -2.51417 q^{52} +10.4493 q^{53} -2.93774 q^{54} -2.65972 q^{56} +12.3465 q^{57} -0.356059 q^{58} -0.862276 q^{59} -2.48235 q^{61} +0.999648 q^{62} -28.6783 q^{63} -7.20172 q^{64} +0.551962 q^{66} +13.4435 q^{67} +3.26051 q^{68} +0.819424 q^{69} +8.78436 q^{71} +5.72203 q^{72} +14.3562 q^{73} -0.810944 q^{74} -7.36843 q^{76} +3.33031 q^{77} -0.773744 q^{78} -10.1620 q^{79} +29.1331 q^{81} -1.58851 q^{82} -7.06074 q^{83} +23.6523 q^{84} +0.259358 q^{86} +6.38702 q^{87} -0.664479 q^{88} +11.7770 q^{89} -4.66844 q^{91} -0.489036 q^{92} -17.9317 q^{93} +0.402409 q^{94} -7.09888 q^{96} +0.860838 q^{97} -1.16268 q^{98} -7.16470 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} + 5 q^{3} + 3 q^{4} - 2 q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) \) 6 * q - q^2 + 5 * q^3 + 3 * q^4 - 2 * q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9	\( 6 q - q^{2} + 5 q^{3} + 3 q^{4} - 2 q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9} + 8 q^{11} + 11 q^{12} + q^{13} + 6 q^{14} - 3 q^{16} - 9 q^{17} + 16 q^{18} - 6 q^{19} + 13 q^{21} + 12 q^{22} + 4 q^{23} + q^{24} - 7 q^{26} + 2 q^{27} + 24 q^{28} - 2 q^{29} - 8 q^{31} + 11 q^{32} - 3 q^{33} - 9 q^{34} - 25 q^{36} + 12 q^{37} + 3 q^{38} - 22 q^{39} + 41 q^{41} + 24 q^{42} - q^{43} - 17 q^{46} - 28 q^{47} - 9 q^{48} + 33 q^{49} - 31 q^{51} - 15 q^{52} - 14 q^{53} + 27 q^{54} - 9 q^{56} + 28 q^{57} - q^{58} + 12 q^{59} + 5 q^{61} + 9 q^{62} - 4 q^{63} - 27 q^{64} + 8 q^{66} + 15 q^{67} - 11 q^{68} + 33 q^{69} - 2 q^{71} - q^{72} + 7 q^{73} + 53 q^{74} - 3 q^{76} + 15 q^{77} - 16 q^{78} - 9 q^{79} + 66 q^{81} - 10 q^{82} + 11 q^{83} + 49 q^{84} - 26 q^{86} + 26 q^{87} - 24 q^{88} + 36 q^{89} - 35 q^{91} + 38 q^{92} + q^{93} + 42 q^{94} - 34 q^{96} - 11 q^{97} - 15 q^{98} + 17 q^{99}+O(q^{100}) \) 6 * q - q^2 + 5 * q^3 + 3 * q^4 - 2 * q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9 + 8 * q^11 + 11 * q^12 + q^13 + 6 * q^14 - 3 * q^16 - 9 * q^17 + 16 * q^18 - 6 * q^19 + 13 * q^21 + 12 * q^22 + 4 * q^23 + q^24 - 7 * q^26 + 2 * q^27 + 24 * q^28 - 2 * q^29 - 8 * q^31 + 11 * q^32 - 3 * q^33 - 9 * q^34 - 25 * q^36 + 12 * q^37 + 3 * q^38 - 22 * q^39 + 41 * q^41 + 24 * q^42 - q^43 - 17 * q^46 - 28 * q^47 - 9 * q^48 + 33 * q^49 - 31 * q^51 - 15 * q^52 - 14 * q^53 + 27 * q^54 - 9 * q^56 + 28 * q^57 - q^58 + 12 * q^59 + 5 * q^61 + 9 * q^62 - 4 * q^63 - 27 * q^64 + 8 * q^66 + 15 * q^67 - 11 * q^68 + 33 * q^69 - 2 * q^71 - q^72 + 7 * q^73 + 53 * q^74 - 3 * q^76 + 15 * q^77 - 16 * q^78 - 9 * q^79 + 66 * q^81 - 10 * q^82 + 11 * q^83 + 49 * q^84 - 26 * q^86 + 26 * q^87 - 24 * q^88 + 36 * q^89 - 35 * q^91 + 38 * q^92 + q^93 + 42 * q^94 - 34 * q^96 - 11 * q^97 - 15 * q^98 + 17 * q^99

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