LMFDB - Embedded newform 1175.2.a.j.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1175,2,Mod(1,1175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1175, 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("1175.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1175 = 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1175.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:	$9.38242223750$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4x^{10} - 8x^{9} + 44x^{8} + 8x^{7} - 156x^{6} + 48x^{5} + 208x^{4} - 96x^{3} - 86x^{2} + 41x + 4 $ x^11 - 4x^10 - 8x^9 + 44x^8 + 8x^7 - 156x^6 + 48x^5 + 208x^4 - 96x^3 - 86x^2 + 41x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 235)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.798376$ of defining polynomial
Character	$\chi$	$=$	1175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.798376 q^{2} -2.73702 q^{3} -1.36260 q^{4} +2.18517 q^{6} +5.15058 q^{7} +2.68462 q^{8} +4.49128 q^{9} +O(q^{10})$	\(q-0.798376 q^{2} -2.73702 q^{3} -1.36260 q^{4} +2.18517 q^{6} +5.15058 q^{7} +2.68462 q^{8} +4.49128 q^{9} -2.53954 q^{11} +3.72945 q^{12} +3.48491 q^{13} -4.11210 q^{14} +0.581859 q^{16} +2.87606 q^{17} -3.58573 q^{18} -5.84224 q^{19} -14.0972 q^{21} +2.02751 q^{22} -4.20609 q^{23} -7.34785 q^{24} -2.78227 q^{26} -4.08166 q^{27} -7.01816 q^{28} -1.35608 q^{29} +7.06707 q^{31} -5.83377 q^{32} +6.95078 q^{33} -2.29617 q^{34} -6.11980 q^{36} -3.58047 q^{37} +4.66431 q^{38} -9.53826 q^{39} +4.00521 q^{41} +11.2549 q^{42} +2.98594 q^{43} +3.46037 q^{44} +3.35804 q^{46} -1.00000 q^{47} -1.59256 q^{48} +19.5285 q^{49} -7.87183 q^{51} -4.74852 q^{52} +5.74891 q^{53} +3.25870 q^{54} +13.8273 q^{56} +15.9903 q^{57} +1.08266 q^{58} -8.29343 q^{59} -5.13388 q^{61} -5.64218 q^{62} +23.1327 q^{63} +3.49383 q^{64} -5.54933 q^{66} +0.105743 q^{67} -3.91890 q^{68} +11.5121 q^{69} -3.47265 q^{71} +12.0574 q^{72} +7.62797 q^{73} +2.85856 q^{74} +7.96062 q^{76} -13.0801 q^{77} +7.61512 q^{78} +16.4418 q^{79} -2.30225 q^{81} -3.19766 q^{82} +0.282291 q^{83} +19.2089 q^{84} -2.38390 q^{86} +3.71163 q^{87} -6.81770 q^{88} -12.4705 q^{89} +17.9493 q^{91} +5.73120 q^{92} -19.3427 q^{93} +0.798376 q^{94} +15.9672 q^{96} +12.5682 q^{97} -15.5911 q^{98} -11.4058 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 4 q^{2} + 4 q^{3} + 10 q^{4} - 2 q^{6} + 12 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) $ 11 * q + 4 * q^2 + 4 * q^3 + 10 * q^4 - 2 * q^6 + 12 * q^7 + 12 * q^8 + 9 * q^9	$ 11 q + 4 q^{2} + 4 q^{3} + 10 q^{4} - 2 q^{6} + 12 q^{7} + 12 q^{8} + 9 q^{9} + 12 q^{12} + 19 q^{13} + 12 q^{16} + 16 q^{17} - 10 q^{18} - 6 q^{21} + 22 q^{22} + 3 q^{23} - 12 q^{24} + 6 q^{26} + 16 q^{27} + 18 q^{28} + 4 q^{29} + 2 q^{31} + 28 q^{32} + 18 q^{33} - 16 q^{34} - 8 q^{36} + 40 q^{37} - 14 q^{38} - 10 q^{39} + 4 q^{41} + 16 q^{42} + 23 q^{43} + 24 q^{44} - 16 q^{46} - 11 q^{47} - 18 q^{48} + 5 q^{49} + 12 q^{51} + 46 q^{52} + 16 q^{53} + 26 q^{56} + 42 q^{57} + 16 q^{58} + 7 q^{59} - 7 q^{61} + 14 q^{63} + 24 q^{64} + 12 q^{66} + 32 q^{67} - 58 q^{68} - 2 q^{69} - 17 q^{71} + 57 q^{73} - 16 q^{74} - 10 q^{76} + 8 q^{77} - 22 q^{78} - 13 q^{79} - 25 q^{81} + 12 q^{82} + 8 q^{83} - 4 q^{84} - 6 q^{86} - 10 q^{87} + 26 q^{88} - 37 q^{89} + 32 q^{91} + 4 q^{92} - 10 q^{93} - 4 q^{94} - 6 q^{96} + 32 q^{97} - 20 q^{98} - 8 q^{99}+O(q^{100}) $ 11 * q + 4 * q^2 + 4 * q^3 + 10 * q^4 - 2 * q^6 + 12 * q^7 + 12 * q^8 + 9 * q^9 + 12 * q^12 + 19 * q^13 + 12 * q^16 + 16 * q^17 - 10 * q^18 - 6 * q^21 + 22 * q^22 + 3 * q^23 - 12 * q^24 + 6 * q^26 + 16 * q^27 + 18 * q^28 + 4 * q^29 + 2 * q^31 + 28 * q^32 + 18 * q^33 - 16 * q^34 - 8 * q^36 + 40 * q^37 - 14 * q^38 - 10 * q^39 + 4 * q^41 + 16 * q^42 + 23 * q^43 + 24 * q^44 - 16 * q^46 - 11 * q^47 - 18 * q^48 + 5 * q^49 + 12 * q^51 + 46 * q^52 + 16 * q^53 + 26 * q^56 + 42 * q^57 + 16 * q^58 + 7 * q^59 - 7 * q^61 + 14 * q^63 + 24 * q^64 + 12 * q^66 + 32 * q^67 - 58 * q^68 - 2 * q^69 - 17 * q^71 + 57 * q^73 - 16 * q^74 - 10 * q^76 + 8 * q^77 - 22 * q^78 - 13 * q^79 - 25 * q^81 + 12 * q^82 + 8 * q^83 - 4 * q^84 - 6 * q^86 - 10 * q^87 + 26 * q^88 - 37 * q^89 + 32 * q^91 + 4 * q^92 - 10 * q^93 - 4 * q^94 - 6 * q^96 + 32 * q^97 - 20 * q^98 - 8 * 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 $

$2$	−0.798376	−0.564537	−0.282269	−	0.959335i	$-0.591087\pi$
$2$	−0.798376	−0.564537	−0.282269	+	0.959335i	$0.591087\pi$
$3$	−2.73702	−1.58022	−0.790110	−	0.612966i	$-0.789976\pi$
$3$	−2.73702	−1.58022	−0.790110	+	0.612966i	$0.789976\pi$
$4$	−1.36260	−0.681298
$5$	0	0
$5$	0	0
$6$	2.18517	0.892092
$7$	5.15058	1.94674	0.973369	−	0.229245i	$-0.0736257\pi$
$7$	5.15058	1.94674	0.973369	+	0.229245i	$0.0736257\pi$
$8$	2.68462	0.949155
$9$	4.49128	1.49709
$10$	0	0
$11$	−2.53954	−0.765701	−0.382850	−	0.923810i	$-0.625058\pi$
$11$	−2.53954	−0.765701	−0.382850	+	0.923810i	$0.625058\pi$
$12$	3.72945	1.07660
$13$	3.48491	0.966540	0.483270	−	0.875471i	$-0.339449\pi$
$13$	3.48491	0.966540	0.483270	+	0.875471i	$0.339449\pi$
$14$	−4.11210	−1.09901
$15$	0	0
$16$	0.581859	0.145465
$17$	2.87606	0.697546	0.348773	−	0.937207i	$-0.386598\pi$
$17$	2.87606	0.697546	0.348773	+	0.937207i	$0.386598\pi$
$18$	−3.58573	−0.845164
$19$	−5.84224	−1.34030	−0.670151	−	0.742224i	$-0.733771\pi$
$19$	−5.84224	−1.34030	−0.670151	+	0.742224i	$0.733771\pi$
$20$	0	0
$21$	−14.0972	−3.07627
$22$	2.02751	0.432266
$23$	−4.20609	−0.877030	−0.438515	−	0.898724i	$-0.644495\pi$
$23$	−4.20609	−0.877030	−0.438515	+	0.898724i	$0.644495\pi$
$24$	−7.34785	−1.49987
$25$	0	0
$26$	−2.78227	−0.545647
$27$	−4.08166	−0.785516
$28$	−7.01816	−1.32631
$29$	−1.35608	−0.251818	−0.125909	−	0.992042i	$-0.540185\pi$
$29$	−1.35608	−0.251818	−0.125909	+	0.992042i	$0.540185\pi$
$30$	0	0
$31$	7.06707	1.26928	0.634642	−	0.772806i	$-0.281148\pi$
$31$	7.06707	1.26928	0.634642	+	0.772806i	$0.281148\pi$
$32$	−5.83377	−1.03128
$33$	6.95078	1.20998
$34$	−2.29617	−0.393791
$35$	0	0
$36$	−6.11980	−1.01997
$37$	−3.58047	−0.588626	−0.294313	−	0.955709i	$-0.595091\pi$
$37$	−3.58047	−0.588626	−0.294313	+	0.955709i	$0.595091\pi$
$38$	4.66431	0.756651
$39$	−9.53826	−1.52734
$40$	0	0
$41$	4.00521	0.625509	0.312754	−	0.949834i	$-0.398748\pi$
$41$	4.00521	0.625509	0.312754	+	0.949834i	$0.398748\pi$
$42$	11.2549	1.73667
$43$	2.98594	0.455352	0.227676	−	0.973737i	$-0.426887\pi$
$43$	2.98594	0.455352	0.227676	+	0.973737i	$0.426887\pi$
$44$	3.46037	0.521670
$45$	0	0
$46$	3.35804	0.495116
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	−1.59256	−0.229866
$49$	19.5285	2.78979
$50$	0	0
$51$	−7.87183	−1.10228
$52$	−4.74852	−0.658501
$53$	5.74891	0.789674	0.394837	−	0.918751i	$-0.370801\pi$
$53$	5.74891	0.789674	0.394837	+	0.918751i	$0.370801\pi$
$54$	3.25870	0.443453
$55$	0	0
$56$	13.8273	1.84776
$57$	15.9903	2.11797
$58$	1.08266	0.142161
$59$	−8.29343	−1.07971	−0.539856	−	0.841757i	$-0.681521\pi$
$59$	−8.29343	−1.07971	−0.539856	+	0.841757i	$0.681521\pi$
$60$	0	0
$61$	−5.13388	−0.657326	−0.328663	−	0.944447i	$-0.606598\pi$
$61$	−5.13388	−0.657326	−0.328663	+	0.944447i	$0.606598\pi$
$62$	−5.64218	−0.716558
$63$	23.1327	2.91445
$64$	3.49383	0.436728
$65$	0	0
$66$	−5.54933	−0.683076
$67$	0.105743	0.0129186	0.00645929	−	0.999979i	$-0.497944\pi$
$67$	0.105743	0.0129186	0.00645929	+	0.999979i	$0.497944\pi$
$68$	−3.91890	−0.475237
$69$	11.5121	1.38590
$70$	0	0
$71$	−3.47265	−0.412128	−0.206064	−	0.978539i	$-0.566065\pi$
$71$	−3.47265	−0.412128	−0.206064	+	0.978539i	$0.566065\pi$
$72$	12.0574	1.42097
$73$	7.62797	0.892786	0.446393	−	0.894837i	$-0.352708\pi$
$73$	7.62797	0.892786	0.446393	+	0.894837i	$0.352708\pi$
$74$	2.85856	0.332301
$75$	0	0
$76$	7.96062	0.913146
$77$	−13.0801	−1.49062
$78$	7.61512	0.862243
$79$	16.4418	1.84985	0.924923	−	0.380155i	$-0.124129\pi$
$79$	16.4418	1.84985	0.924923	+	0.380155i	$0.124129\pi$
$80$	0	0
$81$	−2.30225	−0.255806
$82$	−3.19766	−0.353123
$83$	0.282291	0.0309855	0.0154927	−	0.999880i	$-0.495068\pi$
$83$	0.282291	0.0309855	0.0154927	+	0.999880i	$0.495068\pi$
$84$	19.2089	2.09586
$85$	0	0
$86$	−2.38390	−0.257063
$87$	3.71163	0.397928
$88$	−6.81770	−0.726769
$89$	−12.4705	−1.32187	−0.660936	−	0.750442i	$-0.729841\pi$
$89$	−12.4705	−1.32187	−0.660936	+	0.750442i	$0.729841\pi$
$90$	0	0
$91$	17.9493	1.88160
$92$	5.73120	0.597519
$93$	−19.3427	−2.00575
$94$	0.798376	0.0823462
$95$	0	0
$96$	15.9672	1.62964
$97$	12.5682	1.27611	0.638053	−	0.769992i	$-0.279740\pi$
$97$	12.5682	1.27611	0.638053	+	0.769992i	$0.279740\pi$
$98$	−15.5911	−1.57494
$99$	−11.4058	−1.14633
$100$	0	0
$101$	12.2572	1.21964	0.609818	−	0.792542i	$-0.291243\pi$
$101$	12.2572	1.21964	0.609818	+	0.792542i	$0.291243\pi$
$102$	6.28468	0.622276
$103$	−0.0774875	−0.00763507	−0.00381754	−	0.999993i	$-0.501215\pi$
$103$	−0.0774875	−0.00763507	−0.00381754	+	0.999993i	$0.501215\pi$
$104$	9.35564	0.917396
$105$	0	0
$106$	−4.58979	−0.445800
$107$	8.16071	0.788925	0.394463	−	0.918912i	$-0.370931\pi$
$107$	8.16071	0.788925	0.394463	+	0.918912i	$0.370931\pi$
$108$	5.56165	0.535170
$109$	−8.41021	−0.805552	−0.402776	−	0.915299i	$-0.631955\pi$
$109$	−8.41021	−0.805552	−0.402776	+	0.915299i	$0.631955\pi$
$110$	0	0
$111$	9.79982	0.930158
$112$	2.99691	0.283182
$113$	12.0130	1.13009	0.565043	−	0.825061i	$-0.308859\pi$
$113$	12.0130	1.13009	0.565043	+	0.825061i	$0.308859\pi$
$114$	−12.7663	−1.19567
$115$	0	0
$116$	1.84779	0.171563
$117$	15.6517	1.44700
$118$	6.62127	0.609538
$119$	14.8134	1.35794
$120$	0	0
$121$	−4.55072	−0.413702
$122$	4.09877	0.371085
$123$	−10.9623	−0.988441
$124$	−9.62956	−0.864760
$125$	0	0
$126$	−18.4686	−1.64531
$127$	−8.13474	−0.721842	−0.360921	−	0.932596i	$-0.617538\pi$
$127$	−8.13474	−0.721842	−0.360921	+	0.932596i	$0.617538\pi$
$128$	8.87816	0.784726
$129$	−8.17258	−0.719556
$130$	0	0
$131$	6.33039	0.553089	0.276544	−	0.961001i	$-0.410811\pi$
$131$	6.33039	0.553089	0.276544	+	0.961001i	$0.410811\pi$
$132$	−9.47110	−0.824354
$133$	−30.0910	−2.60922
$134$	−0.0844227	−0.00729301
$135$	0	0
$136$	7.72111	0.662080
$137$	14.0910	1.20388	0.601939	−	0.798542i	$-0.294395\pi$
$137$	14.0910	1.20388	0.601939	+	0.798542i	$0.294395\pi$
$138$	−9.19102	−0.782392
$139$	7.50817	0.636835	0.318417	−	0.947951i	$-0.396849\pi$
$139$	7.50817	0.636835	0.318417	+	0.947951i	$0.396849\pi$
$140$	0	0
$141$	2.73702	0.230499
$142$	2.77248	0.232661
$143$	−8.85007	−0.740080
$144$	2.61329	0.217774
$145$	0	0
$146$	−6.08998	−0.504011
$147$	−53.4499	−4.40847
$148$	4.87874	0.401030
$149$	3.42343	0.280458	0.140229	−	0.990119i	$-0.455216\pi$
$149$	3.42343	0.280458	0.140229	+	0.990119i	$0.455216\pi$
$150$	0	0
$151$	−12.0865	−0.983585	−0.491793	−	0.870712i	$-0.663658\pi$
$151$	−12.0865	−0.983585	−0.491793	+	0.870712i	$0.663658\pi$
$152$	−15.6842	−1.27216
$153$	12.9172	1.04429
$154$	10.4429	0.841509
$155$	0	0
$156$	12.9968	1.04058
$157$	0.567595	0.0452990	0.0226495	−	0.999743i	$-0.492790\pi$
$157$	0.567595	0.0452990	0.0226495	+	0.999743i	$0.492790\pi$
$158$	−13.1267	−1.04431
$159$	−15.7349	−1.24786
$160$	0	0
$161$	−21.6638	−1.70735
$162$	1.83806	0.144412
$163$	2.51421	0.196928	0.0984642	−	0.995141i	$-0.468607\pi$
$163$	2.51421	0.196928	0.0984642	+	0.995141i	$0.468607\pi$
$164$	−5.45748	−0.426158
$165$	0	0
$166$	−0.225374	−0.0174924
$167$	−4.87434	−0.377188	−0.188594	−	0.982055i	$-0.560393\pi$
$167$	−4.87434	−0.377188	−0.188594	+	0.982055i	$0.560393\pi$
$168$	−37.8457	−2.91986
$169$	−0.855414	−0.0658011
$170$	0	0
$171$	−26.2391	−2.00656
$172$	−4.06863	−0.310230
$173$	4.70622	0.357807	0.178903	−	0.983867i	$-0.442745\pi$
$173$	4.70622	0.357807	0.178903	+	0.983867i	$0.442745\pi$
$174$	−2.96327	−0.224645
$175$	0	0
$176$	−1.47766	−0.111383
$177$	22.6993	1.70618
$178$	9.95616	0.746246
$179$	1.77675	0.132801	0.0664004	−	0.997793i	$-0.478849\pi$
$179$	1.77675	0.132801	0.0664004	+	0.997793i	$0.478849\pi$
$180$	0	0
$181$	6.19746	0.460654	0.230327	−	0.973113i	$-0.426020\pi$
$181$	6.19746	0.460654	0.230327	+	0.973113i	$0.426020\pi$
$182$	−14.3303	−1.06223
$183$	14.0515	1.03872
$184$	−11.2917	−0.832437
$185$	0	0
$186$	15.4428	1.13232
$187$	−7.30387	−0.534112
$188$	1.36260	0.0993775
$189$	−21.0229	−1.52919
$190$	0	0
$191$	−14.2418	−1.03050	−0.515251	−	0.857039i	$-0.672301\pi$
$191$	−14.2418	−1.03050	−0.515251	+	0.857039i	$0.672301\pi$
$192$	−9.56267	−0.690126
$193$	23.1004	1.66280	0.831401	−	0.555673i	$-0.187539\pi$
$193$	23.1004	1.66280	0.831401	+	0.555673i	$0.187539\pi$
$194$	−10.0341	−0.720409
$195$	0	0
$196$	−26.6095	−1.90068
$197$	15.7669	1.12334	0.561672	−	0.827360i	$-0.310158\pi$
$197$	15.7669	1.12334	0.561672	+	0.827360i	$0.310158\pi$
$198$	9.10611	0.647143
$199$	16.2886	1.15467	0.577335	−	0.816508i	$-0.304093\pi$
$199$	16.2886	1.15467	0.577335	+	0.816508i	$0.304093\pi$
$200$	0	0
$201$	−0.289421	−0.0204142
$202$	−9.78584	−0.688529
$203$	−6.98462	−0.490224
$204$	10.7261	0.750978
$205$	0	0
$206$	0.0618642	0.00431028
$207$	−18.8907	−1.31300
$208$	2.02773	0.140597
$209$	14.8366	1.02627
$210$	0	0
$211$	13.3335	0.917915	0.458958	−	0.888458i	$-0.348223\pi$
$211$	13.3335	0.917915	0.458958	+	0.888458i	$0.348223\pi$
$212$	−7.83344	−0.538003
$213$	9.50471	0.651252
$214$	−6.51531	−0.445378
$215$	0	0
$216$	−10.9577	−0.745576
$217$	36.3995	2.47096
$218$	6.71451	0.454764
$219$	−20.8779	−1.41080
$220$	0	0
$221$	10.0228	0.674206
$222$	−7.82394	−0.525109
$223$	7.06205	0.472910	0.236455	−	0.971642i	$-0.424014\pi$
$223$	7.06205	0.472910	0.236455	+	0.971642i	$0.424014\pi$
$224$	−30.0473	−2.00762
$225$	0	0
$226$	−9.59088	−0.637976
$227$	2.01427	0.133692	0.0668459	−	0.997763i	$-0.478706\pi$
$227$	2.01427	0.133692	0.0668459	+	0.997763i	$0.478706\pi$
$228$	−21.7884	−1.44297
$229$	22.0923	1.45990	0.729950	−	0.683501i	$-0.239543\pi$
$229$	22.0923	1.45990	0.729950	+	0.683501i	$0.239543\pi$
$230$	0	0
$231$	35.8006	2.35550
$232$	−3.64056	−0.239015
$233$	3.09200	0.202564	0.101282	−	0.994858i	$-0.467706\pi$
$233$	3.09200	0.202564	0.101282	+	0.994858i	$0.467706\pi$
$234$	−12.4959	−0.816885
$235$	0	0
$236$	11.3006	0.735606
$237$	−45.0015	−2.92316
$238$	−11.8266	−0.766607
$239$	−12.4023	−0.802240	−0.401120	−	0.916026i	$-0.631379\pi$
$239$	−12.4023	−0.802240	−0.401120	+	0.916026i	$0.631379\pi$
$240$	0	0
$241$	0.259261	0.0167005	0.00835023	−	0.999965i	$-0.497342\pi$
$241$	0.259261	0.0167005	0.00835023	+	0.999965i	$0.497342\pi$
$242$	3.63319	0.233550
$243$	18.5463	1.18974
$244$	6.99541	0.447835
$245$	0	0
$246$	8.75207	0.558012
$247$	−20.3597	−1.29546
$248$	18.9724	1.20475
$249$	−0.772636	−0.0489638
$250$	0	0
$251$	3.66765	0.231500	0.115750	−	0.993278i	$-0.463073\pi$
$251$	3.66765	0.231500	0.115750	+	0.993278i	$0.463073\pi$
$252$	−31.5205	−1.98561
$253$	10.6815	0.671542
$254$	6.49458	0.407506
$255$	0	0
$256$	−14.0758	−0.879735
$257$	−7.18947	−0.448467	−0.224233	−	0.974535i	$-0.571988\pi$
$257$	−7.18947	−0.448467	−0.224233	+	0.974535i	$0.571988\pi$
$258$	6.52479	0.406216
$259$	−18.4415	−1.14590
$260$	0	0
$261$	−6.09054	−0.376995
$262$	−5.05403	−0.312239
$263$	−5.33787	−0.329147	−0.164574	−	0.986365i	$-0.552625\pi$
$263$	−5.33787	−0.329147	−0.164574	+	0.986365i	$0.552625\pi$
$264$	18.6602	1.14845
$265$	0	0
$266$	24.0239	1.47300
$267$	34.1321	2.08885
$268$	−0.144085	−0.00880140
$269$	4.42888	0.270034	0.135017	−	0.990843i	$-0.456891\pi$
$269$	4.42888	0.270034	0.135017	+	0.990843i	$0.456891\pi$
$270$	0	0
$271$	20.2578	1.23057	0.615287	−	0.788303i	$-0.289040\pi$
$271$	20.2578	1.23057	0.615287	+	0.788303i	$0.289040\pi$
$272$	1.67346	0.101468
$273$	−49.1276	−2.97334
$274$	−11.2499	−0.679634
$275$	0	0
$276$	−15.6864	−0.944210
$277$	8.12662	0.488282	0.244141	−	0.969740i	$-0.421494\pi$
$277$	8.12662	0.488282	0.244141	+	0.969740i	$0.421494\pi$
$278$	−5.99434	−0.359517
$279$	31.7402	1.90024
$280$	0	0
$281$	23.3322	1.39188	0.695942	−	0.718098i	$-0.254987\pi$
$281$	23.3322	1.39188	0.695942	+	0.718098i	$0.254987\pi$
$282$	−2.18517	−0.130125
$283$	−4.92382	−0.292691	−0.146345	−	0.989234i	$-0.546751\pi$
$283$	−4.92382	−0.292691	−0.146345	+	0.989234i	$0.546751\pi$
$284$	4.73182	0.280782
$285$	0	0
$286$	7.06568	0.417803
$287$	20.6292	1.21770
$288$	−26.2011	−1.54391
$289$	−8.72830	−0.513429
$290$	0	0
$291$	−34.3994	−2.01653
$292$	−10.3938	−0.608253
$293$	25.8821	1.51205	0.756024	−	0.654544i	$-0.227139\pi$
$293$	25.8821	1.51205	0.756024	+	0.654544i	$0.227139\pi$
$294$	42.6731	2.48875
$295$	0	0
$296$	−9.61219	−0.558697
$297$	10.3655	0.601470
$298$	−2.73319	−0.158329
$299$	−14.6578	−0.847684
$300$	0	0
$301$	15.3793	0.886450
$302$	9.64957	0.555270
$303$	−33.5482	−1.92729
$304$	−3.39936	−0.194967
$305$	0	0
$306$	−10.3128	−0.589541
$307$	1.02022	0.0582270	0.0291135	−	0.999576i	$-0.490732\pi$
$307$	1.02022	0.0582270	0.0291135	+	0.999576i	$0.490732\pi$
$308$	17.8229	1.01556
$309$	0.212085	0.0120651
$310$	0	0
$311$	−29.8174	−1.69079	−0.845394	−	0.534143i	$-0.820634\pi$
$311$	−29.8174	−1.69079	−0.845394	+	0.534143i	$0.820634\pi$
$312$	−25.6066	−1.44969
$313$	−12.9499	−0.731971	−0.365986	−	0.930620i	$-0.619268\pi$
$313$	−12.9499	−0.731971	−0.365986	+	0.930620i	$0.619268\pi$
$314$	−0.453154	−0.0255730
$315$	0	0
$316$	−22.4035	−1.26030
$317$	−27.8286	−1.56301	−0.781506	−	0.623898i	$-0.785548\pi$
$317$	−27.8286	−1.56301	−0.781506	+	0.623898i	$0.785548\pi$
$318$	12.5624	0.704462
$319$	3.44383	0.192817
$320$	0	0
$321$	−22.3360	−1.24667
$322$	17.2959	0.963861
$323$	−16.8026	−0.934923
$324$	3.13704	0.174280
$325$	0	0
$326$	−2.00729	−0.111173
$327$	23.0189	1.27295
$328$	10.7525	0.593705
$329$	−5.15058	−0.283961
$330$	0	0
$331$	21.9735	1.20777	0.603887	−	0.797070i	$-0.293618\pi$
$331$	21.9735	1.20777	0.603887	+	0.797070i	$0.293618\pi$
$332$	−0.384648	−0.0211103
$333$	−16.0809	−0.881228
$334$	3.89156	0.212936
$335$	0	0
$336$	−8.20261	−0.447489
$337$	16.4372	0.895394	0.447697	−	0.894185i	$-0.352244\pi$
$337$	16.4372	0.895394	0.447697	+	0.894185i	$0.352244\pi$
$338$	0.682942	0.0371471
$339$	−32.8798	−1.78578
$340$	0	0
$341$	−17.9471	−0.971892
$342$	20.9487	1.13278
$343$	64.5291	3.48424
$344$	8.01611	0.432199
$345$	0	0
$346$	−3.75733	−0.201995
$347$	−29.6860	−1.59363	−0.796815	−	0.604223i	$-0.793483\pi$
$347$	−29.6860	−1.59363	−0.796815	+	0.604223i	$0.793483\pi$
$348$	−5.05745	−0.271108
$349$	4.63250	0.247972	0.123986	−	0.992284i	$-0.460432\pi$
$349$	4.63250	0.247972	0.123986	+	0.992284i	$0.460432\pi$
$350$	0	0
$351$	−14.2242	−0.759232
$352$	14.8151	0.789648
$353$	−36.9985	−1.96923	−0.984617	−	0.174729i	$-0.944095\pi$
$353$	−36.9985	−1.96923	−0.984617	+	0.174729i	$0.944095\pi$
$354$	−18.1226	−0.963203
$355$	0	0
$356$	16.9923	0.900589
$357$	−40.5445	−2.14584
$358$	−1.41852	−0.0749710
$359$	20.5667	1.08547	0.542735	−	0.839904i	$-0.317389\pi$
$359$	20.5667	1.08547	0.542735	+	0.839904i	$0.317389\pi$
$360$	0	0
$361$	15.1318	0.796412
$362$	−4.94790	−0.260056
$363$	12.4554	0.653740
$364$	−24.4577	−1.28193
$365$	0	0
$366$	−11.2184	−0.586396
$367$	−10.0243	−0.523264	−0.261632	−	0.965168i	$-0.584261\pi$
$367$	−10.0243	−0.523264	−0.261632	+	0.965168i	$0.584261\pi$
$368$	−2.44735	−0.127577
$369$	17.9885	0.936445
$370$	0	0
$371$	29.6103	1.53729
$372$	26.3563	1.36651
$373$	33.8655	1.75349	0.876744	−	0.480956i	$-0.159710\pi$
$373$	33.8655	1.75349	0.876744	+	0.480956i	$0.159710\pi$
$374$	5.83123	0.301526
$375$	0	0
$376$	−2.68462	−0.138448
$377$	−4.72582	−0.243392
$378$	16.7842	0.863286
$379$	−5.15844	−0.264971	−0.132486	−	0.991185i	$-0.542296\pi$
$379$	−5.15844	−0.264971	−0.132486	+	0.991185i	$0.542296\pi$
$380$	0	0
$381$	22.2650	1.14067
$382$	11.3703	0.581756
$383$	−2.11007	−0.107820	−0.0539098	−	0.998546i	$-0.517168\pi$
$383$	−2.11007	−0.107820	−0.0539098	+	0.998546i	$0.517168\pi$
$384$	−24.2997	−1.24004
$385$	0	0
$386$	−18.4428	−0.938713
$387$	13.4107	0.681704
$388$	−17.1254	−0.869409
$389$	30.3859	1.54063	0.770313	−	0.637666i	$-0.220100\pi$
$389$	30.3859	1.54063	0.770313	+	0.637666i	$0.220100\pi$
$390$	0	0
$391$	−12.0969	−0.611769
$392$	52.4265	2.64794
$393$	−17.3264	−0.874001
$394$	−12.5879	−0.634170
$395$	0	0
$396$	15.5415	0.780989
$397$	−19.3060	−0.968938	−0.484469	−	0.874808i	$-0.660987\pi$
$397$	−19.3060	−0.968938	−0.484469	+	0.874808i	$0.660987\pi$
$398$	−13.0044	−0.651854
$399$	82.3596	4.12314
$400$	0	0
$401$	−6.50071	−0.324630	−0.162315	−	0.986739i	$-0.551896\pi$
$401$	−6.50071	−0.324630	−0.162315	+	0.986739i	$0.551896\pi$
$402$	0.231067	0.0115246
$403$	24.6281	1.22681
$404$	−16.7016	−0.830935
$405$	0	0
$406$	5.57635	0.276750
$407$	9.09276	0.450711
$408$	−21.1328	−1.04623
$409$	−18.7576	−0.927506	−0.463753	−	0.885965i	$-0.653497\pi$
$409$	−18.7576	−0.927506	−0.463753	+	0.885965i	$0.653497\pi$
$410$	0	0
$411$	−38.5675	−1.90239
$412$	0.105584	0.00520176
$413$	−42.7160	−2.10192
$414$	15.0819	0.741234
$415$	0	0
$416$	−20.3302	−0.996768
$417$	−20.5500	−1.00634
$418$	−11.8452	−0.579368
$419$	−6.57030	−0.320980	−0.160490	−	0.987037i	$-0.551307\pi$
$419$	−6.57030	−0.320980	−0.160490	+	0.987037i	$0.551307\pi$
$420$	0	0
$421$	8.33285	0.406118	0.203059	−	0.979166i	$-0.434912\pi$
$421$	8.33285	0.406118	0.203059	+	0.979166i	$0.434912\pi$
$422$	−10.6451	−0.518197
$423$	−4.49128	−0.218373
$424$	15.4336	0.749523
$425$	0	0
$426$	−7.58833	−0.367656
$427$	−26.4425	−1.27964
$428$	−11.1197	−0.537493
$429$	24.2228	1.16949
$430$	0	0
$431$	−10.2418	−0.493332	−0.246666	−	0.969101i	$-0.579335\pi$
$431$	−10.2418	−0.493332	−0.246666	+	0.969101i	$0.579335\pi$
$432$	−2.37495	−0.114265
$433$	7.33852	0.352667	0.176333	−	0.984331i	$-0.443576\pi$
$433$	7.33852	0.352667	0.176333	+	0.984331i	$0.443576\pi$
$434$	−29.0605	−1.39495
$435$	0	0
$436$	11.4597	0.548821
$437$	24.5730	1.17549
$438$	16.6684	0.796447
$439$	−18.8730	−0.900759	−0.450379	−	0.892837i	$-0.648711\pi$
$439$	−18.8730	−0.900759	−0.450379	+	0.892837i	$0.648711\pi$
$440$	0	0
$441$	87.7080	4.17657
$442$	−8.00196	−0.380614
$443$	−32.0543	−1.52295	−0.761473	−	0.648196i	$-0.775524\pi$
$443$	−32.0543	−1.52295	−0.761473	+	0.648196i	$0.775524\pi$
$444$	−13.3532	−0.633715
$445$	0	0
$446$	−5.63817	−0.266975
$447$	−9.37000	−0.443186
$448$	17.9952	0.850195
$449$	40.4830	1.91051	0.955255	−	0.295785i	$-0.0955812\pi$
$449$	40.4830	1.91051	0.955255	+	0.295785i	$0.0955812\pi$
$450$	0	0
$451$	−10.1714	−0.478953
$452$	−16.3688	−0.769926
$453$	33.0810	1.55428
$454$	−1.60814	−0.0754740
$455$	0	0
$456$	42.9279	2.01028
$457$	8.11311	0.379515	0.189758	−	0.981831i	$-0.439230\pi$
$457$	8.11311	0.379515	0.189758	+	0.981831i	$0.439230\pi$
$458$	−17.6380	−0.824167
$459$	−11.7391	−0.547934
$460$	0	0
$461$	27.0956	1.26197	0.630983	−	0.775797i	$-0.282652\pi$
$461$	27.0956	1.26197	0.630983	+	0.775797i	$0.282652\pi$
$462$	−28.5823	−1.32977
$463$	18.0058	0.836799	0.418400	−	0.908263i	$-0.362591\pi$
$463$	18.0058	0.836799	0.418400	+	0.908263i	$0.362591\pi$
$464$	−0.789049	−0.0366307
$465$	0	0
$466$	−2.46858	−0.114355
$467$	7.63665	0.353382	0.176691	−	0.984266i	$-0.443461\pi$
$467$	7.63665	0.353382	0.176691	+	0.984266i	$0.443461\pi$
$468$	−21.3269	−0.985838
$469$	0.544639	0.0251491
$470$	0	0
$471$	−1.55352	−0.0715824
$472$	−22.2647	−1.02481
$473$	−7.58292	−0.348663
$474$	35.9281	1.65023
$475$	0	0
$476$	−20.1846	−0.925161
$477$	25.8200	1.18222
$478$	9.90172	0.452894
$479$	−39.1055	−1.78678	−0.893389	−	0.449284i	$-0.851679\pi$
$479$	−39.1055	−1.78678	−0.893389	+	0.449284i	$0.851679\pi$
$480$	0	0
$481$	−12.4776	−0.568930
$482$	−0.206988	−0.00942802
$483$	59.2943	2.69798
$484$	6.20080	0.281854
$485$	0	0
$486$	−14.8069	−0.671655
$487$	7.48717	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$487$	7.48717	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$488$	−13.7825	−0.623904
$489$	−6.88146	−0.311190
$490$	0	0
$491$	25.3123	1.14233	0.571164	−	0.820836i	$-0.306492\pi$
$491$	25.3123	1.14233	0.571164	+	0.820836i	$0.306492\pi$
$492$	14.9372	0.673423
$493$	−3.90017	−0.175655
$494$	16.2547	0.731333
$495$	0	0
$496$	4.11204	0.184636
$497$	−17.8862	−0.802304
$498$	0.616854	0.0276419
$499$	12.5024	0.559682	0.279841	−	0.960046i	$-0.409718\pi$
$499$	12.5024	0.559682	0.279841	+	0.960046i	$0.409718\pi$
$500$	0	0
$501$	13.3412	0.596039
$502$	−2.92817	−0.130690
$503$	6.25604	0.278943	0.139472	−	0.990226i	$-0.455460\pi$
$503$	6.25604	0.278943	0.139472	+	0.990226i	$0.455460\pi$
$504$	62.1024	2.76626
$505$	0	0
$506$	−8.52788	−0.379111
$507$	2.34128	0.103980
$508$	11.0844	0.491789
$509$	14.8641	0.658838	0.329419	−	0.944184i	$-0.393147\pi$
$509$	14.8641	0.658838	0.329419	+	0.944184i	$0.393147\pi$
$510$	0	0
$511$	39.2885	1.73802
$512$	−6.51857	−0.288083
$513$	23.8461	1.05283
$514$	5.73990	0.253176
$515$	0	0
$516$	11.1359	0.490232
$517$	2.53954	0.111689
$518$	14.7233	0.646903
$519$	−12.8810	−0.565413
$520$	0	0
$521$	−28.6238	−1.25403	−0.627017	−	0.779006i	$-0.715724\pi$
$521$	−28.6238	−1.25403	−0.627017	+	0.779006i	$0.715724\pi$
$522$	4.86254	0.212828
$523$	−43.7423	−1.91272	−0.956358	−	0.292199i	$-0.905613\pi$
$523$	−43.7423	−1.91272	−0.956358	+	0.292199i	$0.905613\pi$
$524$	−8.62576	−0.376818
$525$	0	0
$526$	4.26163	0.185816
$527$	20.3253	0.885384
$528$	4.04437	0.176009
$529$	−5.30883	−0.230819
$530$	0	0
$531$	−37.2481	−1.61643
$532$	41.0018	1.77765
$533$	13.9578	0.604579
$534$	−27.2502	−1.17923
$535$	0	0
$536$	0.283880	0.0122617
$537$	−4.86301	−0.209854
$538$	−3.53591	−0.152444
$539$	−49.5935	−2.13614
$540$	0	0
$541$	−13.8321	−0.594687	−0.297343	−	0.954771i	$-0.596101\pi$
$541$	−13.8321	−0.594687	−0.297343	+	0.954771i	$0.596101\pi$
$542$	−16.1734	−0.694705
$543$	−16.9626	−0.727934
$544$	−16.7783	−0.719362
$545$	0	0
$546$	39.2223	1.67856
$547$	25.0432	1.07077	0.535386	−	0.844608i	$-0.320166\pi$
$547$	25.0432	1.07077	0.535386	+	0.844608i	$0.320166\pi$
$548$	−19.2004	−0.820200
$549$	−23.0577	−0.984078
$550$	0	0
$551$	7.92257	0.337513
$552$	30.9057	1.31543
$553$	84.6848	3.60116
$554$	−6.48810	−0.275653
$555$	0	0
$556$	−10.2306	−0.433874
$557$	−11.6840	−0.495065	−0.247532	−	0.968880i	$-0.579620\pi$
$557$	−11.6840	−0.495065	−0.247532	+	0.968880i	$0.579620\pi$
$558$	−25.3406	−1.07275
$559$	10.4057	0.440116
$560$	0	0
$561$	19.9908	0.844014
$562$	−18.6279	−0.785770
$563$	−36.4846	−1.53764	−0.768822	−	0.639463i	$-0.779157\pi$
$563$	−36.4846	−1.53764	−0.768822	+	0.639463i	$0.779157\pi$
$564$	−3.72945	−0.157038
$565$	0	0
$566$	3.93106	0.165235
$567$	−11.8579	−0.497987
$568$	−9.32273	−0.391173
$569$	−27.0196	−1.13272	−0.566360	−	0.824158i	$-0.691649\pi$
$569$	−27.0196	−1.13272	−0.566360	+	0.824158i	$0.691649\pi$
$570$	0	0
$571$	−16.9914	−0.711069	−0.355534	−	0.934663i	$-0.615701\pi$
$571$	−16.9914	−0.711069	−0.355534	+	0.934663i	$0.615701\pi$
$572$	12.0591	0.504215
$573$	38.9801	1.62842
$574$	−16.4698	−0.687438
$575$	0	0
$576$	15.6917	0.653823
$577$	45.5669	1.89698	0.948488	−	0.316813i	$-0.102613\pi$
$577$	45.5669	1.89698	0.948488	+	0.316813i	$0.102613\pi$
$578$	6.96846	0.289850
$579$	−63.2262	−2.62759
$580$	0	0
$581$	1.45396	0.0603205
$582$	27.4636	1.13840
$583$	−14.5996	−0.604654
$584$	20.4782	0.847392
$585$	0	0
$586$	−20.6636	−0.853607
$587$	−23.8728	−0.985335	−0.492667	−	0.870218i	$-0.663978\pi$
$587$	−23.8728	−0.985335	−0.492667	+	0.870218i	$0.663978\pi$
$588$	72.8306	3.00348
$589$	−41.2876	−1.70122
$590$	0	0
$591$	−43.1543	−1.77513
$592$	−2.08333	−0.0856243
$593$	−3.74886	−0.153947	−0.0769735	−	0.997033i	$-0.524526\pi$
$593$	−3.74886	−0.153947	−0.0769735	+	0.997033i	$0.524526\pi$
$594$	−8.27560	−0.339552
$595$	0	0
$596$	−4.66475	−0.191076
$597$	−44.5823	−1.82463
$598$	11.7025	0.478549
$599$	22.0058	0.899131	0.449566	−	0.893247i	$-0.351579\pi$
$599$	22.0058	0.899131	0.449566	+	0.893247i	$0.351579\pi$
$600$	0	0
$601$	−41.2496	−1.68261	−0.841303	−	0.540564i	$-0.818211\pi$
$601$	−41.2496	−1.68261	−0.841303	+	0.540564i	$0.818211\pi$
$602$	−12.2785	−0.500434
$603$	0.474922	0.0193403
$604$	16.4690	0.670114
$605$	0	0
$606$	26.7840	1.08803
$607$	25.9778	1.05441	0.527204	−	0.849739i	$-0.323240\pi$
$607$	25.9778	1.05441	0.527204	+	0.849739i	$0.323240\pi$
$608$	34.0823	1.38222
$609$	19.1170	0.774661
$610$	0	0
$611$	−3.48491	−0.140984
$612$	−17.6009	−0.711474
$613$	−14.3295	−0.578764	−0.289382	−	0.957214i	$-0.593450\pi$
$613$	−14.3295	−0.578764	−0.289382	+	0.957214i	$0.593450\pi$
$614$	−0.814519	−0.0328713
$615$	0	0
$616$	−35.1151	−1.41483
$617$	−5.16279	−0.207846	−0.103923	−	0.994585i	$-0.533140\pi$
$617$	−5.16279	−0.207846	−0.103923	+	0.994585i	$0.533140\pi$
$618$	−0.169324	−0.00681119
$619$	−28.8849	−1.16098	−0.580492	−	0.814266i	$-0.697140\pi$
$619$	−28.8849	−1.16098	−0.580492	+	0.814266i	$0.697140\pi$
$620$	0	0
$621$	17.1678	0.688921
$622$	23.8055	0.954513
$623$	−64.2305	−2.57334
$624$	−5.54993	−0.222175
$625$	0	0
$626$	10.3389	0.413225
$627$	−40.6081	−1.62173
$628$	−0.773403	−0.0308621
$629$	−10.2976	−0.410594
$630$	0	0
$631$	23.0297	0.916797	0.458399	−	0.888747i	$-0.348423\pi$
$631$	23.0297	0.916797	0.458399	+	0.888747i	$0.348423\pi$
$632$	44.1399	1.75579
$633$	−36.4940	−1.45051
$634$	22.2177	0.882378
$635$	0	0
$636$	21.4403	0.850163
$637$	68.0551	2.69644
$638$	−2.74947	−0.108853
$639$	−15.5966	−0.616993
$640$	0	0
$641$	11.0755	0.437455	0.218728	−	0.975786i	$-0.429809\pi$
$641$	11.0755	0.437455	0.218728	+	0.975786i	$0.429809\pi$
$642$	17.8325	0.703794
$643$	35.9558	1.41796	0.708979	−	0.705229i	$-0.249156\pi$
$643$	35.9558	1.41796	0.708979	+	0.705229i	$0.249156\pi$
$644$	29.5190	1.16321
$645$	0	0
$646$	13.4148	0.527799
$647$	34.2942	1.34825	0.674123	−	0.738619i	$-0.264522\pi$
$647$	34.2942	1.34825	0.674123	+	0.738619i	$0.264522\pi$
$648$	−6.18066	−0.242799
$649$	21.0615	0.826737
$650$	0	0
$651$	−99.6263	−3.90466
$652$	−3.42586	−0.134167
$653$	30.1798	1.18103	0.590513	−	0.807028i	$-0.298925\pi$
$653$	30.1798	1.18103	0.590513	+	0.807028i	$0.298925\pi$
$654$	−18.3777	−0.718626
$655$	0	0
$656$	2.33047	0.0909895
$657$	34.2593	1.33658
$658$	4.11210	0.160306
$659$	−42.0475	−1.63794	−0.818969	−	0.573838i	$-0.805454\pi$
$659$	−42.0475	−1.63794	−0.818969	+	0.573838i	$0.805454\pi$
$660$	0	0
$661$	−39.7509	−1.54613	−0.773065	−	0.634327i	$-0.781277\pi$
$661$	−39.7509	−1.54613	−0.773065	+	0.634327i	$0.781277\pi$
$662$	−17.5431	−0.681833
$663$	−27.4326	−1.06539
$664$	0.757843	0.0294100
$665$	0	0
$666$	12.8386	0.497486
$667$	5.70380	0.220852
$668$	6.64176	0.256977
$669$	−19.3290	−0.747302
$670$	0	0
$671$	13.0377	0.503315
$672$	82.2402	3.17248
$673$	25.9498	1.00029	0.500146	−	0.865941i	$-0.333279\pi$
$673$	25.9498	1.00029	0.500146	+	0.865941i	$0.333279\pi$
$674$	−13.1231	−0.505483
$675$	0	0
$676$	1.16558	0.0448301
$677$	12.9757	0.498695	0.249348	−	0.968414i	$-0.419784\pi$
$677$	12.9757	0.498695	0.249348	+	0.968414i	$0.419784\pi$
$678$	26.2504	1.00814
$679$	64.7335	2.48424
$680$	0	0
$681$	−5.51310	−0.211262
$682$	14.3286	0.548669
$683$	50.9981	1.95139	0.975694	−	0.219136i	$-0.0703239\pi$
$683$	50.9981	1.95139	0.975694	+	0.219136i	$0.0703239\pi$
$684$	35.7534	1.36706
$685$	0	0
$686$	−51.5185	−1.96699
$687$	−60.4670	−2.30696
$688$	1.73740	0.0662377
$689$	20.0344	0.763251
$690$	0	0
$691$	−30.9847	−1.17871	−0.589357	−	0.807873i	$-0.700619\pi$
$691$	−30.9847	−1.17871	−0.589357	+	0.807873i	$0.700619\pi$
$692$	−6.41267	−0.243773
$693$	−58.7465	−2.23159
$694$	23.7006	0.899663
$695$	0	0
$696$	9.96429	0.377695
$697$	11.5192	0.436321
$698$	−3.69848	−0.139990
$699$	−8.46287	−0.320095
$700$	0	0
$701$	−36.5844	−1.38178	−0.690888	−	0.722962i	$-0.742780\pi$
$701$	−36.5844	−1.38178	−0.690888	+	0.722962i	$0.742780\pi$
$702$	11.3563	0.428615
$703$	20.9180	0.788937
$704$	−8.87272	−0.334403
$705$	0	0
$706$	29.5387	1.11171
$707$	63.1316	2.37431
$708$	−30.9299	−1.16242
$709$	19.2975	0.724733	0.362367	−	0.932036i	$-0.381969\pi$
$709$	19.2975	0.724733	0.362367	+	0.932036i	$0.381969\pi$
$710$	0	0
$711$	73.8446	2.76939
$712$	−33.4786	−1.25466
$713$	−29.7247	−1.11320
$714$	32.3697	1.21141
$715$	0	0
$716$	−2.42100	−0.0904769
$717$	33.9454	1.26771
$718$	−16.4200	−0.612788
$719$	−12.5284	−0.467230	−0.233615	−	0.972329i	$-0.575056\pi$
$719$	−12.5284	−0.467230	−0.233615	+	0.972329i	$0.575056\pi$
$720$	0	0
$721$	−0.399106	−0.0148635
$722$	−12.0809	−0.449604
$723$	−0.709602	−0.0263904
$724$	−8.44463	−0.313842
$725$	0	0
$726$	−9.94411	−0.369061
$727$	−20.9357	−0.776461	−0.388231	−	0.921562i	$-0.626914\pi$
$727$	−20.9357	−0.776461	−0.388231	+	0.921562i	$0.626914\pi$
$728$	48.1870	1.78593
$729$	−43.8548	−1.62425
$730$	0	0
$731$	8.58774	0.317629
$732$	−19.1466	−0.707677
$733$	12.3131	0.454796	0.227398	−	0.973802i	$-0.426978\pi$
$733$	12.3131	0.454796	0.227398	+	0.973802i	$0.426978\pi$
$734$	8.00316	0.295402
$735$	0	0
$736$	24.5374	0.904459
$737$	−0.268539	−0.00989176
$738$	−14.3616	−0.528658
$739$	20.4345	0.751695	0.375847	−	0.926682i	$-0.377352\pi$
$739$	20.4345	0.751695	0.375847	+	0.926682i	$0.377352\pi$
$740$	0	0
$741$	55.7249	2.04710
$742$	−23.6401	−0.867856
$743$	−19.9709	−0.732662	−0.366331	−	0.930485i	$-0.619386\pi$
$743$	−19.9709	−0.732662	−0.366331	+	0.930485i	$0.619386\pi$
$744$	−51.9278	−1.90376
$745$	0	0
$746$	−27.0374	−0.989909
$747$	1.26785	0.0463881
$748$	9.95222	0.363889
$749$	42.0324	1.53583
$750$	0	0
$751$	32.9091	1.20087	0.600435	−	0.799673i	$-0.294994\pi$
$751$	32.9091	1.20087	0.600435	+	0.799673i	$0.294994\pi$
$752$	−0.581859	−0.0212182
$753$	−10.0384	−0.365821
$754$	3.77298	0.137404
$755$	0	0
$756$	28.6458	1.04184
$757$	−25.6161	−0.931034	−0.465517	−	0.885039i	$-0.654132\pi$
$757$	−25.6161	−0.931034	−0.465517	+	0.885039i	$0.654132\pi$
$758$	4.11837	0.149586
$759$	−29.2356	−1.06118
$760$	0	0
$761$	−8.80755	−0.319273	−0.159637	−	0.987176i	$-0.551032\pi$
$761$	−8.80755	−0.319273	−0.159637	+	0.987176i	$0.551032\pi$
$762$	−17.7758	−0.643950
$763$	−43.3175	−1.56820
$764$	19.4058	0.702079
$765$	0	0
$766$	1.68463	0.0608682
$767$	−28.9018	−1.04358
$768$	38.5256	1.39017
$769$	−18.9224	−0.682361	−0.341180	−	0.939998i	$-0.610827\pi$
$769$	−18.9224	−0.682361	−0.341180	+	0.939998i	$0.610827\pi$
$770$	0	0
$771$	19.6777	0.708676
$772$	−31.4765	−1.13286
$773$	31.2759	1.12492	0.562458	−	0.826826i	$-0.309856\pi$
$773$	31.2759	1.12492	0.562458	+	0.826826i	$0.309856\pi$
$774$	−10.7068	−0.384847
$775$	0	0
$776$	33.7408	1.21122
$777$	50.4748	1.81077
$778$	−24.2594	−0.869740
$779$	−23.3994	−0.838371
$780$	0	0
$781$	8.81894	0.315566
$782$	9.65791	0.345366
$783$	5.53507	0.197807
$784$	11.3628	0.405816
$785$	0	0
$786$	13.8330	0.493406
$787$	−20.8564	−0.743452	−0.371726	−	0.928343i	$-0.621234\pi$
$787$	−20.8564	−0.743452	−0.371726	+	0.928343i	$0.621234\pi$
$788$	−21.4839	−0.765332
$789$	14.6099	0.520125
$790$	0	0
$791$	61.8739	2.19998
$792$	−30.6202	−1.08804
$793$	−17.8911	−0.635332
$794$	15.4134	0.547001
$795$	0	0
$796$	−22.1948	−0.786674
$797$	3.92253	0.138943	0.0694716	−	0.997584i	$-0.477869\pi$
$797$	3.92253	0.138943	0.0694716	+	0.997584i	$0.477869\pi$
$798$	−65.7539	−2.32766
$799$	−2.87606	−0.101748
$800$	0	0
$801$	−56.0086	−1.97897
$802$	5.19001	0.183266
$803$	−19.3715	−0.683607
$804$	0.394364	0.0139081
$805$	0	0
$806$	−19.6625	−0.692581
$807$	−12.1219	−0.426712
$808$	32.9058	1.15762
$809$	31.7626	1.11671	0.558356	−	0.829601i	$-0.311432\pi$
$809$	31.7626	1.11671	0.558356	+	0.829601i	$0.311432\pi$
$810$	0	0
$811$	−23.1717	−0.813670	−0.406835	−	0.913502i	$-0.633368\pi$
$811$	−23.1717	−0.813670	−0.406835	+	0.913502i	$0.633368\pi$
$812$	9.51721	0.333989
$813$	−55.4460	−1.94458
$814$	−7.25944	−0.254443
$815$	0	0
$816$	−4.58029	−0.160342
$817$	−17.4446	−0.610309
$818$	14.9757	0.523611
$819$	80.6154	2.81693
$820$	0	0
$821$	−13.7977	−0.481544	−0.240772	−	0.970582i	$-0.577401\pi$
$821$	−13.7977	−0.481544	−0.240772	+	0.970582i	$0.577401\pi$
$822$	30.7913	1.07397
$823$	17.2763	0.602213	0.301106	−	0.953591i	$-0.402644\pi$
$823$	17.2763	0.602213	0.301106	+	0.953591i	$0.402644\pi$
$824$	−0.208024	−0.00724687
$825$	0	0
$826$	34.1034	1.18661
$827$	−30.8446	−1.07257	−0.536285	−	0.844037i	$-0.680173\pi$
$827$	−30.8446	−1.07257	−0.536285	+	0.844037i	$0.680173\pi$
$828$	25.7404	0.894541
$829$	38.7881	1.34717	0.673584	−	0.739111i	$-0.264754\pi$
$829$	38.7881	1.34717	0.673584	+	0.739111i	$0.264754\pi$
$830$	0	0
$831$	−22.2427	−0.771592
$832$	12.1757	0.422115
$833$	56.1651	1.94601
$834$	16.4066	0.568115
$835$	0	0
$836$	−20.2163	−0.699196
$837$	−28.8454	−0.997042
$838$	5.24557	0.181205
$839$	0.673570	0.0232542	0.0116271	−	0.999932i	$-0.496299\pi$
$839$	0.673570	0.0232542	0.0116271	+	0.999932i	$0.496299\pi$
$840$	0	0
$841$	−27.1610	−0.936588
$842$	−6.65275	−0.229269
$843$	−63.8608	−2.19948
$844$	−18.1682	−0.625374
$845$	0	0
$846$	3.58573	0.123280
$847$	−23.4389	−0.805370
$848$	3.34506	0.114870
$849$	13.4766	0.462515
$850$	0	0
$851$	15.0598	0.516242
$852$	−12.9511	−0.443697
$853$	−39.1921	−1.34191	−0.670956	−	0.741497i	$-0.734116\pi$
$853$	−39.1921	−1.34191	−0.670956	+	0.741497i	$0.734116\pi$
$854$	21.1110	0.722405
$855$	0	0
$856$	21.9084	0.748812
$857$	−25.4385	−0.868962	−0.434481	−	0.900681i	$-0.643068\pi$
$857$	−25.4385	−0.868962	−0.434481	+	0.900681i	$0.643068\pi$
$858$	−19.3389	−0.660220
$859$	16.7981	0.573145	0.286573	−	0.958059i	$-0.407484\pi$
$859$	16.7981	0.573145	0.286573	+	0.958059i	$0.407484\pi$
$860$	0	0
$861$	−56.4624	−1.92424
$862$	8.17684	0.278504
$863$	−2.44234	−0.0831381	−0.0415691	−	0.999136i	$-0.513236\pi$
$863$	−2.44234	−0.0831381	−0.0415691	+	0.999136i	$0.513236\pi$
$864$	23.8115	0.810083
$865$	0	0
$866$	−5.85889	−0.199093
$867$	23.8895	0.811331
$868$	−49.5979	−1.68346
$869$	−41.7546	−1.41643
$870$	0	0
$871$	0.368505	0.0124863
$872$	−22.5782	−0.764593
$873$	56.4472	1.91045
$874$	−19.6185	−0.663605
$875$	0	0
$876$	28.4481	0.961173
$877$	32.0699	1.08292	0.541462	−	0.840725i	$-0.317871\pi$
$877$	32.0699	1.08292	0.541462	+	0.840725i	$0.317871\pi$
$878$	15.0677	0.508512
$879$	−70.8398	−2.38937
$880$	0	0
$881$	22.4441	0.756162	0.378081	−	0.925773i	$-0.376584\pi$
$881$	22.4441	0.756162	0.378081	+	0.925773i	$0.376584\pi$
$882$	−70.0239	−2.35783
$883$	4.27524	0.143873	0.0719366	−	0.997409i	$-0.477082\pi$
$883$	4.27524	0.143873	0.0719366	+	0.997409i	$0.477082\pi$
$884$	−13.6570	−0.459335
$885$	0	0
$886$	25.5914	0.859760
$887$	0.990067	0.0332432	0.0166216	−	0.999862i	$-0.494709\pi$
$887$	0.990067	0.0332432	0.0166216	+	0.999862i	$0.494709\pi$
$888$	26.3088	0.882864
$889$	−41.8987	−1.40524
$890$	0	0
$891$	5.84667	0.195871
$892$	−9.62272	−0.322193
$893$	5.84224	0.195503
$894$	7.48078	0.250195
$895$	0	0
$896$	45.7277	1.52766
$897$	40.1188	1.33953
$898$	−32.3206	−1.07855
$899$	−9.58353	−0.319629
$900$	0	0
$901$	16.5342	0.550834
$902$	8.12060	0.270386
$903$	−42.0936	−1.40079
$904$	32.2502	1.07263
$905$	0	0
$906$	−26.4111	−0.877449
$907$	−4.99673	−0.165914	−0.0829568	−	0.996553i	$-0.526436\pi$
$907$	−4.99673	−0.165914	−0.0829568	+	0.996553i	$0.526436\pi$
$908$	−2.74464	−0.0910839
$909$	55.0504	1.82591
$910$	0	0
$911$	−33.9990	−1.12644	−0.563219	−	0.826308i	$-0.690437\pi$
$911$	−33.9990	−1.12644	−0.563219	+	0.826308i	$0.690437\pi$
$912$	9.30413	0.308090
$913$	−0.716890	−0.0237256
$914$	−6.47732	−0.214251
$915$	0	0
$916$	−30.1029	−0.994626
$917$	32.6052	1.07672
$918$	9.37220	0.309329
$919$	−38.5035	−1.27011	−0.635056	−	0.772466i	$-0.719023\pi$
$919$	−38.5035	−1.27011	−0.635056	+	0.772466i	$0.719023\pi$
$920$	0	0
$921$	−2.79236	−0.0920115
$922$	−21.6324	−0.712427
$923$	−12.1019	−0.398338
$924$	−48.7817	−1.60480
$925$	0	0
$926$	−14.3754	−0.472404
$927$	−0.348018	−0.0114304
$928$	7.91108	0.259694
$929$	35.8053	1.17473	0.587367	−	0.809321i	$-0.300165\pi$
$929$	35.8053	1.17473	0.587367	+	0.809321i	$0.300165\pi$
$930$	0	0
$931$	−114.090	−3.73916
$932$	−4.21315	−0.138006
$933$	81.6108	2.67182
$934$	−6.09692	−0.199497
$935$	0	0
$936$	42.0188	1.37343
$937$	3.45895	0.112999	0.0564995	−	0.998403i	$-0.482006\pi$
$937$	3.45895	0.112999	0.0564995	+	0.998403i	$0.482006\pi$
$938$	−0.434826	−0.0141976
$939$	35.4441	1.15668
$940$	0	0
$941$	−2.16806	−0.0706768	−0.0353384	−	0.999375i	$-0.511251\pi$
$941$	−2.16806	−0.0706768	−0.0353384	+	0.999375i	$0.511251\pi$
$942$	1.24029	0.0404109
$943$	−16.8463	−0.548590
$944$	−4.82561	−0.157060
$945$	0	0
$946$	6.05402	0.196833
$947$	−15.5310	−0.504689	−0.252344	−	0.967637i	$-0.581202\pi$
$947$	−15.5310	−0.504689	−0.252344	+	0.967637i	$0.581202\pi$
$948$	61.3189	1.99154
$949$	26.5828	0.862913
$950$	0	0
$951$	76.1676	2.46990
$952$	39.7682	1.28890
$953$	26.2782	0.851233	0.425617	−	0.904904i	$-0.360057\pi$
$953$	26.2782	0.851233	0.425617	+	0.904904i	$0.360057\pi$
$954$	−20.6140	−0.667404
$955$	0	0
$956$	16.8994	0.546564
$957$	−9.42583	−0.304694
$958$	31.2209	1.00870
$959$	72.5771	2.34364
$960$	0	0
$961$	18.9435	0.611081
$962$	9.96183	0.321182
$963$	36.6520	1.18109
$964$	−0.353268	−0.0113780
$965$	0	0
$966$	−47.3391	−1.52311
$967$	7.97304	0.256396	0.128198	−	0.991749i	$-0.459081\pi$
$967$	7.97304	0.256396	0.128198	+	0.991749i	$0.459081\pi$
$968$	−12.2169	−0.392668
$969$	45.9891	1.47738
$970$	0	0
$971$	−20.0634	−0.643866	−0.321933	−	0.946762i	$-0.604333\pi$
$971$	−20.0634	−0.643866	−0.321933	+	0.946762i	$0.604333\pi$
$972$	−25.2711	−0.810571
$973$	38.6714	1.23975
$974$	−5.97758	−0.191534
$975$	0	0
$976$	−2.98720	−0.0956178
$977$	−0.496284	−0.0158775	−0.00793877	−	0.999968i	$-0.502527\pi$
$977$	−0.496284	−0.0158775	−0.00793877	+	0.999968i	$0.502527\pi$
$978$	5.49399	0.175678
$979$	31.6694	1.01216
$980$	0	0
$981$	−37.7726	−1.20599
$982$	−20.2087	−0.644887
$983$	−3.71990	−0.118646	−0.0593232	−	0.998239i	$-0.518894\pi$
$983$	−3.71990	−0.118646	−0.0593232	+	0.998239i	$0.518894\pi$
$984$	−29.4297	−0.938184
$985$	0	0
$986$	3.11380	0.0991637
$987$	14.0972	0.448720
$988$	27.7420	0.882591
$989$	−12.5591	−0.399357
$990$	0	0
$991$	−10.2849	−0.326711	−0.163355	−	0.986567i	$-0.552232\pi$
$991$	−10.2849	−0.326711	−0.163355	+	0.986567i	$0.552232\pi$
$992$	−41.2277	−1.30898
$993$	−60.1419	−1.90855
$994$	14.2799	0.452930
$995$	0	0
$996$	1.05279	0.0333589
$997$	−47.0347	−1.48960	−0.744802	−	0.667285i	$-0.767456\pi$
$997$	−47.0347	−1.48960	−0.744802	+	0.667285i	$0.767456\pi$
$998$	−9.98158	−0.315961
$999$	14.6143	0.462375

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1175.2.a.j.1.4		11
5.2	odd	4		235.2.c.a.189.8	✓	22
5.3	odd	4		235.2.c.a.189.15	yes	22
5.4	even	2		1175.2.a.i.1.8		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
235.2.c.a.189.8	✓	22	5.2	odd	4
235.2.c.a.189.15	yes	22	5.3	odd	4
1175.2.a.i.1.8		11	5.4	even	2
1175.2.a.j.1.4		11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1175 = 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1175.a (trivial)

\(f(q)\)	\(=\)	\(q-0.798376 q^{2} -2.73702 q^{3} -1.36260 q^{4} +2.18517 q^{6} +5.15058 q^{7} +2.68462 q^{8} +4.49128 q^{9} +O(q^{10})\)	\(q-0.798376 q^{2} -2.73702 q^{3} -1.36260 q^{4} +2.18517 q^{6} +5.15058 q^{7} +2.68462 q^{8} +4.49128 q^{9} -2.53954 q^{11} +3.72945 q^{12} +3.48491 q^{13} -4.11210 q^{14} +0.581859 q^{16} +2.87606 q^{17} -3.58573 q^{18} -5.84224 q^{19} -14.0972 q^{21} +2.02751 q^{22} -4.20609 q^{23} -7.34785 q^{24} -2.78227 q^{26} -4.08166 q^{27} -7.01816 q^{28} -1.35608 q^{29} +7.06707 q^{31} -5.83377 q^{32} +6.95078 q^{33} -2.29617 q^{34} -6.11980 q^{36} -3.58047 q^{37} +4.66431 q^{38} -9.53826 q^{39} +4.00521 q^{41} +11.2549 q^{42} +2.98594 q^{43} +3.46037 q^{44} +3.35804 q^{46} -1.00000 q^{47} -1.59256 q^{48} +19.5285 q^{49} -7.87183 q^{51} -4.74852 q^{52} +5.74891 q^{53} +3.25870 q^{54} +13.8273 q^{56} +15.9903 q^{57} +1.08266 q^{58} -8.29343 q^{59} -5.13388 q^{61} -5.64218 q^{62} +23.1327 q^{63} +3.49383 q^{64} -5.54933 q^{66} +0.105743 q^{67} -3.91890 q^{68} +11.5121 q^{69} -3.47265 q^{71} +12.0574 q^{72} +7.62797 q^{73} +2.85856 q^{74} +7.96062 q^{76} -13.0801 q^{77} +7.61512 q^{78} +16.4418 q^{79} -2.30225 q^{81} -3.19766 q^{82} +0.282291 q^{83} +19.2089 q^{84} -2.38390 q^{86} +3.71163 q^{87} -6.81770 q^{88} -12.4705 q^{89} +17.9493 q^{91} +5.73120 q^{92} -19.3427 q^{93} +0.798376 q^{94} +15.9672 q^{96} +12.5682 q^{97} -15.5911 q^{98} -11.4058 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 4 q^{2} + 4 q^{3} + 10 q^{4} - 2 q^{6} + 12 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 11 * q + 4 * q^2 + 4 * q^3 + 10 * q^4 - 2 * q^6 + 12 * q^7 + 12 * q^8 + 9 * q^9	\( 11 q + 4 q^{2} + 4 q^{3} + 10 q^{4} - 2 q^{6} + 12 q^{7} + 12 q^{8} + 9 q^{9} + 12 q^{12} + 19 q^{13} + 12 q^{16} + 16 q^{17} - 10 q^{18} - 6 q^{21} + 22 q^{22} + 3 q^{23} - 12 q^{24} + 6 q^{26} + 16 q^{27} + 18 q^{28} + 4 q^{29} + 2 q^{31} + 28 q^{32} + 18 q^{33} - 16 q^{34} - 8 q^{36} + 40 q^{37} - 14 q^{38} - 10 q^{39} + 4 q^{41} + 16 q^{42} + 23 q^{43} + 24 q^{44} - 16 q^{46} - 11 q^{47} - 18 q^{48} + 5 q^{49} + 12 q^{51} + 46 q^{52} + 16 q^{53} + 26 q^{56} + 42 q^{57} + 16 q^{58} + 7 q^{59} - 7 q^{61} + 14 q^{63} + 24 q^{64} + 12 q^{66} + 32 q^{67} - 58 q^{68} - 2 q^{69} - 17 q^{71} + 57 q^{73} - 16 q^{74} - 10 q^{76} + 8 q^{77} - 22 q^{78} - 13 q^{79} - 25 q^{81} + 12 q^{82} + 8 q^{83} - 4 q^{84} - 6 q^{86} - 10 q^{87} + 26 q^{88} - 37 q^{89} + 32 q^{91} + 4 q^{92} - 10 q^{93} - 4 q^{94} - 6 q^{96} + 32 q^{97} - 20 q^{98} - 8 q^{99}+O(q^{100}) \) 11 * q + 4 * q^2 + 4 * q^3 + 10 * q^4 - 2 * q^6 + 12 * q^7 + 12 * q^8 + 9 * q^9 + 12 * q^12 + 19 * q^13 + 12 * q^16 + 16 * q^17 - 10 * q^18 - 6 * q^21 + 22 * q^22 + 3 * q^23 - 12 * q^24 + 6 * q^26 + 16 * q^27 + 18 * q^28 + 4 * q^29 + 2 * q^31 + 28 * q^32 + 18 * q^33 - 16 * q^34 - 8 * q^36 + 40 * q^37 - 14 * q^38 - 10 * q^39 + 4 * q^41 + 16 * q^42 + 23 * q^43 + 24 * q^44 - 16 * q^46 - 11 * q^47 - 18 * q^48 + 5 * q^49 + 12 * q^51 + 46 * q^52 + 16 * q^53 + 26 * q^56 + 42 * q^57 + 16 * q^58 + 7 * q^59 - 7 * q^61 + 14 * q^63 + 24 * q^64 + 12 * q^66 + 32 * q^67 - 58 * q^68 - 2 * q^69 - 17 * q^71 + 57 * q^73 - 16 * q^74 - 10 * q^76 + 8 * q^77 - 22 * q^78 - 13 * q^79 - 25 * q^81 + 12 * q^82 + 8 * q^83 - 4 * q^84 - 6 * q^86 - 10 * q^87 + 26 * q^88 - 37 * q^89 + 32 * q^91 + 4 * q^92 - 10 * q^93 - 4 * q^94 - 6 * q^96 + 32 * q^97 - 20 * q^98 - 8 * q^99

Introduction

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