LMFDB - Embedded newform 1925.2.a.be.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1925,2,Mod(1,1925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1925, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1925.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1925 = 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1925.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:	$15.3712023891$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 7x^{6} + 30x^{5} + 24x^{4} - 66x^{3} - 42x^{2} + 34x + 14 $ x^8 - 4x^7 - 7x^6 + 30x^5 + 24x^4 - 66x^3 - 42x^2 + 34*x + 14
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.79793$ of defining polynomial
Character	$\chi$	$=$	1925.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.797933 q^{2} -3.35029 q^{3} -1.36330 q^{4} -2.67331 q^{6} -1.00000 q^{7} -2.68369 q^{8} +8.22444 q^{9} +O(q^{10})$	\(q+0.797933 q^{2} -3.35029 q^{3} -1.36330 q^{4} -2.67331 q^{6} -1.00000 q^{7} -2.68369 q^{8} +8.22444 q^{9} +1.00000 q^{11} +4.56746 q^{12} -4.12953 q^{13} -0.797933 q^{14} +0.585197 q^{16} +2.39850 q^{17} +6.56256 q^{18} +3.81613 q^{19} +3.35029 q^{21} +0.797933 q^{22} +5.37188 q^{23} +8.99115 q^{24} -3.29509 q^{26} -17.5034 q^{27} +1.36330 q^{28} -4.69490 q^{29} +0.178755 q^{31} +5.83433 q^{32} -3.35029 q^{33} +1.91385 q^{34} -11.2124 q^{36} +1.61850 q^{37} +3.04502 q^{38} +13.8351 q^{39} +9.62697 q^{41} +2.67331 q^{42} +6.65747 q^{43} -1.36330 q^{44} +4.28641 q^{46} -6.41257 q^{47} -1.96058 q^{48} +1.00000 q^{49} -8.03569 q^{51} +5.62980 q^{52} +3.38729 q^{53} -13.9666 q^{54} +2.68369 q^{56} -12.7851 q^{57} -3.74622 q^{58} -13.8654 q^{59} -4.92577 q^{61} +0.142635 q^{62} -8.22444 q^{63} +3.48501 q^{64} -2.67331 q^{66} -9.36925 q^{67} -3.26989 q^{68} -17.9974 q^{69} -12.5513 q^{71} -22.0719 q^{72} -7.66695 q^{73} +1.29145 q^{74} -5.20253 q^{76} -1.00000 q^{77} +11.0395 q^{78} +5.01475 q^{79} +33.9682 q^{81} +7.68168 q^{82} -10.9588 q^{83} -4.56746 q^{84} +5.31222 q^{86} +15.7293 q^{87} -2.68369 q^{88} -1.59622 q^{89} +4.12953 q^{91} -7.32350 q^{92} -0.598883 q^{93} -5.11681 q^{94} -19.5467 q^{96} -2.88399 q^{97} +0.797933 q^{98} +8.22444 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 6 q^{3} + 14 q^{4} - 6 q^{6} - 8 q^{7} - 12 q^{8} + 10 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 6 * q^3 + 14 * q^4 - 6 * q^6 - 8 * q^7 - 12 * q^8 + 10 * q^9	$ 8 q - 4 q^{2} - 6 q^{3} + 14 q^{4} - 6 q^{6} - 8 q^{7} - 12 q^{8} + 10 q^{9} + 8 q^{11} - 12 q^{12} - 6 q^{13} + 4 q^{14} + 18 q^{16} - 6 q^{17} - 6 q^{18} - 6 q^{19} + 6 q^{21} - 4 q^{22} - 4 q^{23} + 6 q^{24} - 4 q^{26} - 24 q^{27} - 14 q^{28} + 4 q^{29} - 14 q^{31} - 18 q^{32} - 6 q^{33} - 6 q^{34} + 18 q^{36} - 10 q^{37} + 30 q^{38} + 16 q^{39} - 4 q^{41} + 6 q^{42} - 34 q^{43} + 14 q^{44} - 24 q^{46} + 8 q^{47} - 12 q^{48} + 8 q^{49} + 16 q^{51} - 46 q^{52} - 18 q^{53} + 6 q^{54} + 12 q^{56} - 6 q^{57} + 6 q^{58} - 40 q^{59} - 26 q^{62} - 10 q^{63} + 10 q^{64} - 6 q^{66} - 42 q^{67} - 16 q^{68} - 50 q^{69} + 6 q^{71} - 28 q^{72} - 40 q^{73} - 44 q^{76} - 8 q^{77} + 76 q^{78} + 12 q^{79} + 40 q^{81} - 42 q^{82} - 2 q^{83} + 12 q^{84} + 44 q^{86} - 2 q^{87} - 12 q^{88} + 22 q^{89} + 6 q^{91} - 6 q^{92} + 32 q^{93} - 50 q^{94} - 16 q^{96} + 6 q^{97} - 4 q^{98} + 10 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 - 6 * q^3 + 14 * q^4 - 6 * q^6 - 8 * q^7 - 12 * q^8 + 10 * q^9 + 8 * q^11 - 12 * q^12 - 6 * q^13 + 4 * q^14 + 18 * q^16 - 6 * q^17 - 6 * q^18 - 6 * q^19 + 6 * q^21 - 4 * q^22 - 4 * q^23 + 6 * q^24 - 4 * q^26 - 24 * q^27 - 14 * q^28 + 4 * q^29 - 14 * q^31 - 18 * q^32 - 6 * q^33 - 6 * q^34 + 18 * q^36 - 10 * q^37 + 30 * q^38 + 16 * q^39 - 4 * q^41 + 6 * q^42 - 34 * q^43 + 14 * q^44 - 24 * q^46 + 8 * q^47 - 12 * q^48 + 8 * q^49 + 16 * q^51 - 46 * q^52 - 18 * q^53 + 6 * q^54 + 12 * q^56 - 6 * q^57 + 6 * q^58 - 40 * q^59 - 26 * q^62 - 10 * q^63 + 10 * q^64 - 6 * q^66 - 42 * q^67 - 16 * q^68 - 50 * q^69 + 6 * q^71 - 28 * q^72 - 40 * q^73 - 44 * q^76 - 8 * q^77 + 76 * q^78 + 12 * q^79 + 40 * q^81 - 42 * q^82 - 2 * q^83 + 12 * q^84 + 44 * q^86 - 2 * q^87 - 12 * q^88 + 22 * q^89 + 6 * q^91 - 6 * q^92 + 32 * q^93 - 50 * q^94 - 16 * q^96 + 6 * q^97 - 4 * q^98 + 10 * 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 $

$2$	0.797933	0.564224	0.282112	−	0.959381i	$-0.408965\pi$
$2$	0.797933	0.564224	0.282112	+	0.959381i	$0.408965\pi$
$3$	−3.35029	−1.93429	−0.967145	−	0.254224i	$-0.918180\pi$
$3$	−3.35029	−1.93429	−0.967145	+	0.254224i	$0.918180\pi$
$4$	−1.36330	−0.681651
$5$	0	0
$5$	0	0
$6$	−2.67331	−1.09137
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.68369	−0.948828
$9$	8.22444	2.74148
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	4.56746	1.31851
$13$	−4.12953	−1.14533	−0.572663	−	0.819791i	$-0.694090\pi$
$13$	−4.12953	−1.14533	−0.572663	+	0.819791i	$0.694090\pi$
$14$	−0.797933	−0.213257
$15$	0	0
$16$	0.585197	0.146299
$17$	2.39850	0.581723	0.290861	−	0.956765i	$-0.406058\pi$
$17$	2.39850	0.581723	0.290861	+	0.956765i	$0.406058\pi$
$18$	6.56256	1.54681
$19$	3.81613	0.875480	0.437740	−	0.899102i	$-0.355779\pi$
$19$	3.81613	0.875480	0.437740	+	0.899102i	$0.355779\pi$
$20$	0	0
$21$	3.35029	0.731093
$22$	0.797933	0.170120
$23$	5.37188	1.12012	0.560058	−	0.828454i	$-0.310779\pi$
$23$	5.37188	1.12012	0.560058	+	0.828454i	$0.310779\pi$
$24$	8.99115	1.83531
$25$	0	0
$26$	−3.29509	−0.646221
$27$	−17.5034	−3.36853
$28$	1.36330	0.257640
$29$	−4.69490	−0.871821	−0.435911	−	0.899990i	$-0.643574\pi$
$29$	−4.69490	−0.871821	−0.435911	+	0.899990i	$0.643574\pi$
$30$	0	0
$31$	0.178755	0.0321054	0.0160527	−	0.999871i	$-0.494890\pi$
$31$	0.178755	0.0321054	0.0160527	+	0.999871i	$0.494890\pi$
$32$	5.83433	1.03137
$33$	−3.35029	−0.583211
$34$	1.91385	0.328222
$35$	0	0
$36$	−11.2124	−1.86873
$37$	1.61850	0.266079	0.133040	−	0.991111i	$-0.457526\pi$
$37$	1.61850	0.266079	0.133040	+	0.991111i	$0.457526\pi$
$38$	3.04502	0.493967
$39$	13.8351	2.21539
$40$	0	0
$41$	9.62697	1.50348	0.751740	−	0.659459i	$-0.229215\pi$
$41$	9.62697	1.50348	0.751740	+	0.659459i	$0.229215\pi$
$42$	2.67331	0.412500
$43$	6.65747	1.01525	0.507627	−	0.861577i	$-0.330523\pi$
$43$	6.65747	1.01525	0.507627	+	0.861577i	$0.330523\pi$
$44$	−1.36330	−0.205526
$45$	0	0
$46$	4.28641	0.631996
$47$	−6.41257	−0.935370	−0.467685	−	0.883895i	$-0.654912\pi$
$47$	−6.41257	−0.935370	−0.467685	+	0.883895i	$0.654912\pi$
$48$	−1.96058	−0.282985
$49$	1.00000	0.142857
$50$	0	0
$51$	−8.03569	−1.12522
$52$	5.62980	0.780713
$53$	3.38729	0.465279	0.232640	−	0.972563i	$-0.425264\pi$
$53$	3.38729	0.465279	0.232640	+	0.972563i	$0.425264\pi$
$54$	−13.9666	−1.90061
$55$	0	0
$56$	2.68369	0.358623
$57$	−12.7851	−1.69343
$58$	−3.74622	−0.491903
$59$	−13.8654	−1.80512	−0.902561	−	0.430563i	$-0.858315\pi$
$59$	−13.8654	−1.80512	−0.902561	+	0.430563i	$0.858315\pi$
$60$	0	0
$61$	−4.92577	−0.630680	−0.315340	−	0.948979i	$-0.602119\pi$
$61$	−4.92577	−0.630680	−0.315340	+	0.948979i	$0.602119\pi$
$62$	0.142635	0.0181147
$63$	−8.22444	−1.03618
$64$	3.48501	0.435627
$65$	0	0
$66$	−2.67331	−0.329062
$67$	−9.36925	−1.14464	−0.572318	−	0.820032i	$-0.693956\pi$
$67$	−9.36925	−1.14464	−0.572318	+	0.820032i	$0.693956\pi$
$68$	−3.26989	−0.396532
$69$	−17.9974	−2.16663
$70$	0	0
$71$	−12.5513	−1.48956	−0.744780	−	0.667310i	$-0.767446\pi$
$71$	−12.5513	−1.48956	−0.744780	+	0.667310i	$0.767446\pi$
$72$	−22.0719	−2.60119
$73$	−7.66695	−0.897349	−0.448674	−	0.893695i	$-0.648104\pi$
$73$	−7.66695	−0.897349	−0.448674	+	0.893695i	$0.648104\pi$
$74$	1.29145	0.150128
$75$	0	0
$76$	−5.20253	−0.596772
$77$	−1.00000	−0.113961
$78$	11.0395	1.24998
$79$	5.01475	0.564204	0.282102	−	0.959384i	$-0.408968\pi$
$79$	5.01475	0.564204	0.282102	+	0.959384i	$0.408968\pi$
$80$	0	0
$81$	33.9682	3.77424
$82$	7.68168	0.848300
$83$	−10.9588	−1.20288	−0.601442	−	0.798916i	$-0.705407\pi$
$83$	−10.9588	−1.20288	−0.601442	+	0.798916i	$0.705407\pi$
$84$	−4.56746	−0.498351
$85$	0	0
$86$	5.31222	0.572831
$87$	15.7293	1.68636
$88$	−2.68369	−0.286082
$89$	−1.59622	−0.169199	−0.0845997	−	0.996415i	$-0.526961\pi$
$89$	−1.59622	−0.169199	−0.0845997	+	0.996415i	$0.526961\pi$
$90$	0	0
$91$	4.12953	0.432893
$92$	−7.32350	−0.763528
$93$	−0.598883	−0.0621012
$94$	−5.11681	−0.527758
$95$	0	0
$96$	−19.5467	−1.99498
$97$	−2.88399	−0.292824	−0.146412	−	0.989224i	$-0.546773\pi$
$97$	−2.88399	−0.292824	−0.146412	+	0.989224i	$0.546773\pi$
$98$	0.797933	0.0806035
$99$	8.22444	0.826588
$100$	0	0
$101$	5.35986	0.533326	0.266663	−	0.963790i	$-0.414079\pi$
$101$	5.35986	0.533326	0.266663	+	0.963790i	$0.414079\pi$
$102$	−6.41194	−0.634877
$103$	−9.74871	−0.960569	−0.480285	−	0.877113i	$-0.659467\pi$
$103$	−9.74871	−0.960569	−0.480285	+	0.877113i	$0.659467\pi$
$104$	11.0824	1.08672
$105$	0	0
$106$	2.70283	0.262522
$107$	−18.8790	−1.82511	−0.912553	−	0.408958i	$-0.865892\pi$
$107$	−18.8790	−1.82511	−0.912553	+	0.408958i	$0.865892\pi$
$108$	23.8624	2.29616
$109$	6.19025	0.592918	0.296459	−	0.955046i	$-0.404194\pi$
$109$	6.19025	0.592918	0.296459	+	0.955046i	$0.404194\pi$
$110$	0	0
$111$	−5.42244	−0.514675
$112$	−0.585197	−0.0552959
$113$	7.02428	0.660789	0.330394	−	0.943843i	$-0.392818\pi$
$113$	7.02428	0.660789	0.330394	+	0.943843i	$0.392818\pi$
$114$	−10.2017	−0.955475
$115$	0	0
$116$	6.40057	0.594278
$117$	−33.9631	−3.13989
$118$	−11.0637	−1.01849
$119$	−2.39850	−0.219871
$120$	0	0
$121$	1.00000	0.0909091
$122$	−3.93044	−0.355845
$123$	−32.2532	−2.90817
$124$	−0.243698	−0.0218847
$125$	0	0
$126$	−6.56256	−0.584639
$127$	9.89186	0.877761	0.438880	−	0.898545i	$-0.355375\pi$
$127$	9.89186	0.877761	0.438880	+	0.898545i	$0.355375\pi$
$128$	−8.88785	−0.785583
$129$	−22.3045	−1.96380
$130$	0	0
$131$	2.56418	0.224033	0.112017	−	0.993706i	$-0.464269\pi$
$131$	2.56418	0.224033	0.112017	+	0.993706i	$0.464269\pi$
$132$	4.56746	0.397546
$133$	−3.81613	−0.330900
$134$	−7.47604	−0.645831
$135$	0	0
$136$	−6.43685	−0.551955
$137$	15.4418	1.31928	0.659640	−	0.751582i	$-0.270709\pi$
$137$	15.4418	1.31928	0.659640	+	0.751582i	$0.270709\pi$
$138$	−14.3607	−1.22246
$139$	6.26603	0.531478	0.265739	−	0.964045i	$-0.414384\pi$
$139$	6.26603	0.531478	0.265739	+	0.964045i	$0.414384\pi$
$140$	0	0
$141$	21.4840	1.80928
$142$	−10.0151	−0.840446
$143$	−4.12953	−0.345329
$144$	4.81292	0.401077
$145$	0	0
$146$	−6.11772	−0.506306
$147$	−3.35029	−0.276327
$148$	−2.20650	−0.181373
$149$	0.0104027	0.000852226 0	0.000426113	−	1.00000i	$-0.499864\pi$
$149$	0.0104027	0.000852226 0	0.000426113		1.00000i	$0.499864\pi$
$150$	0	0
$151$	−22.7287	−1.84963	−0.924817	−	0.380411i	$-0.875782\pi$
$151$	−22.7287	−1.84963	−0.924817	+	0.380411i	$0.875782\pi$
$152$	−10.2413	−0.830680
$153$	19.7264	1.59478
$154$	−0.797933	−0.0642993
$155$	0	0
$156$	−18.8615	−1.51013
$157$	10.3659	0.827286	0.413643	−	0.910439i	$-0.364256\pi$
$157$	10.3659	0.827286	0.413643	+	0.910439i	$0.364256\pi$
$158$	4.00144	0.318337
$159$	−11.3484	−0.899986
$160$	0	0
$161$	−5.37188	−0.423364
$162$	27.1043	2.12952
$163$	10.9201	0.855331	0.427666	−	0.903937i	$-0.359336\pi$
$163$	10.9201	0.855331	0.427666	+	0.903937i	$0.359336\pi$
$164$	−13.1245	−1.02485
$165$	0	0
$166$	−8.74439	−0.678696
$167$	−1.33048	−0.102956	−0.0514780	−	0.998674i	$-0.516393\pi$
$167$	−1.33048	−0.102956	−0.0514780	+	0.998674i	$0.516393\pi$
$168$	−8.99115	−0.693682
$169$	4.05305	0.311773
$170$	0	0
$171$	31.3855	2.40011
$172$	−9.07614	−0.692050
$173$	2.18567	0.166173	0.0830866	−	0.996542i	$-0.473522\pi$
$173$	2.18567	0.166173	0.0830866	+	0.996542i	$0.473522\pi$
$174$	12.5509	0.951483
$175$	0	0
$176$	0.585197	0.0441109
$177$	46.4531	3.49163
$178$	−1.27368	−0.0954664
$179$	−11.6122	−0.867938	−0.433969	−	0.900928i	$-0.642887\pi$
$179$	−11.6122	−0.867938	−0.433969	+	0.900928i	$0.642887\pi$
$180$	0	0
$181$	−13.3547	−0.992650	−0.496325	−	0.868137i	$-0.665318\pi$
$181$	−13.3547	−0.992650	−0.496325	+	0.868137i	$0.665318\pi$
$182$	3.29509	0.244249
$183$	16.5028	1.21992
$184$	−14.4165	−1.06280
$185$	0	0
$186$	−0.477869	−0.0350390
$187$	2.39850	0.175396
$188$	8.74228	0.637596
$189$	17.5034	1.27319
$190$	0	0
$191$	7.46670	0.540271	0.270136	−	0.962822i	$-0.412931\pi$
$191$	7.46670	0.540271	0.270136	+	0.962822i	$0.412931\pi$
$192$	−11.6758	−0.842629
$193$	11.2724	0.811406	0.405703	−	0.914005i	$-0.367027\pi$
$193$	11.2724	0.811406	0.405703	+	0.914005i	$0.367027\pi$
$194$	−2.30123	−0.165219
$195$	0	0
$196$	−1.36330	−0.0973787
$197$	−3.35956	−0.239359	−0.119680	−	0.992813i	$-0.538187\pi$
$197$	−3.35956	−0.239359	−0.119680	+	0.992813i	$0.538187\pi$
$198$	6.56256	0.466381
$199$	3.66974	0.260141	0.130070	−	0.991505i	$-0.458480\pi$
$199$	3.66974	0.260141	0.130070	+	0.991505i	$0.458480\pi$
$200$	0	0
$201$	31.3897	2.21406
$202$	4.27681	0.300915
$203$	4.69490	0.329518
$204$	10.9551	0.767008
$205$	0	0
$206$	−7.77882	−0.541976
$207$	44.1808	3.07077
$208$	−2.41659	−0.167560
$209$	3.81613	0.263967
$210$	0	0
$211$	−10.9960	−0.756994	−0.378497	−	0.925603i	$-0.623559\pi$
$211$	−10.9960	−0.756994	−0.378497	+	0.925603i	$0.623559\pi$
$212$	−4.61789	−0.317158
$213$	42.0504	2.88124
$214$	−15.0642	−1.02977
$215$	0	0
$216$	46.9737	3.19616
$217$	−0.178755	−0.0121347
$218$	4.93941	0.334539
$219$	25.6865	1.73573
$220$	0	0
$221$	−9.90471	−0.666263
$222$	−4.32674	−0.290392
$223$	−13.4635	−0.901583	−0.450791	−	0.892629i	$-0.648858\pi$
$223$	−13.4635	−0.901583	−0.450791	+	0.892629i	$0.648858\pi$
$224$	−5.83433	−0.389823
$225$	0	0
$226$	5.60491	0.372833
$227$	−23.3143	−1.54743	−0.773714	−	0.633536i	$-0.781603\pi$
$227$	−23.3143	−1.54743	−0.773714	+	0.633536i	$0.781603\pi$
$228$	17.4300	1.15433
$229$	7.17549	0.474169	0.237085	−	0.971489i	$-0.423808\pi$
$229$	7.17549	0.474169	0.237085	+	0.971489i	$0.423808\pi$
$230$	0	0
$231$	3.35029	0.220433
$232$	12.5997	0.827209
$233$	−13.1921	−0.864242	−0.432121	−	0.901816i	$-0.642235\pi$
$233$	−13.1921	−0.864242	−0.432121	+	0.901816i	$0.642235\pi$
$234$	−27.1003	−1.77160
$235$	0	0
$236$	18.9027	1.23046
$237$	−16.8009	−1.09133
$238$	−1.91385	−0.124056
$239$	−1.63196	−0.105563	−0.0527814	−	0.998606i	$-0.516809\pi$
$239$	−1.63196	−0.105563	−0.0527814	+	0.998606i	$0.516809\pi$
$240$	0	0
$241$	−22.7470	−1.46526	−0.732630	−	0.680627i	$-0.761707\pi$
$241$	−22.7470	−1.46526	−0.732630	+	0.680627i	$0.761707\pi$
$242$	0.797933	0.0512931
$243$	−61.2930	−3.93195
$244$	6.71531	0.429904
$245$	0	0
$246$	−25.7359	−1.64086
$247$	−15.7588	−1.00271
$248$	−0.479725	−0.0304625
$249$	36.7151	2.32673
$250$	0	0
$251$	−28.4769	−1.79745	−0.898724	−	0.438514i	$-0.855505\pi$
$251$	−28.4769	−1.79745	−0.898724	+	0.438514i	$0.855505\pi$
$252$	11.2124	0.706315
$253$	5.37188	0.337727
$254$	7.89305	0.495254
$255$	0	0
$256$	−14.0619	−0.878871
$257$	17.1130	1.06748	0.533741	−	0.845648i	$-0.320786\pi$
$257$	17.1130	1.06748	0.533741	+	0.845648i	$0.320786\pi$
$258$	−17.7975	−1.10802
$259$	−1.61850	−0.100569
$260$	0	0
$261$	−38.6130	−2.39008
$262$	2.04604	0.126405
$263$	7.87948	0.485870	0.242935	−	0.970043i	$-0.421890\pi$
$263$	7.87948	0.485870	0.242935	+	0.970043i	$0.421890\pi$
$264$	8.99115	0.553367
$265$	0	0
$266$	−3.04502	−0.186702
$267$	5.34781	0.327281
$268$	12.7731	0.780242
$269$	1.76219	0.107442	0.0537212	−	0.998556i	$-0.482892\pi$
$269$	1.76219	0.107442	0.0537212	+	0.998556i	$0.482892\pi$
$270$	0	0
$271$	18.3889	1.11704	0.558522	−	0.829490i	$-0.311369\pi$
$271$	18.3889	1.11704	0.558522	+	0.829490i	$0.311369\pi$
$272$	1.40360	0.0851056
$273$	−13.8351	−0.837340
$274$	12.3215	0.744369
$275$	0	0
$276$	24.5359	1.47688
$277$	7.40712	0.445050	0.222525	−	0.974927i	$-0.428570\pi$
$277$	7.40712	0.445050	0.222525	+	0.974927i	$0.428570\pi$
$278$	4.99988	0.299873
$279$	1.47016	0.0880164
$280$	0	0
$281$	3.10235	0.185070	0.0925352	−	0.995709i	$-0.470503\pi$
$281$	3.10235	0.185070	0.0925352	+	0.995709i	$0.470503\pi$
$282$	17.1428	1.02084
$283$	−1.35054	−0.0802813	−0.0401406	−	0.999194i	$-0.512781\pi$
$283$	−1.35054	−0.0802813	−0.0401406	+	0.999194i	$0.512781\pi$
$284$	17.1112	1.01536
$285$	0	0
$286$	−3.29509	−0.194843
$287$	−9.62697	−0.568262
$288$	47.9841	2.82749
$289$	−11.2472	−0.661599
$290$	0	0
$291$	9.66219	0.566408
$292$	10.4524	0.611679
$293$	8.90303	0.520121	0.260060	−	0.965592i	$-0.416258\pi$
$293$	8.90303	0.520121	0.260060	+	0.965592i	$0.416258\pi$
$294$	−2.67331	−0.155911
$295$	0	0
$296$	−4.34355	−0.252464
$297$	−17.5034	−1.01565
$298$	0.00830070	0.000480847 0
$299$	−22.1834	−1.28290
$300$	0	0
$301$	−6.65747	−0.383730
$302$	−18.1360	−1.04361
$303$	−17.9571	−1.03161
$304$	2.23319	0.128082
$305$	0	0
$306$	15.7403	0.899815
$307$	−23.0892	−1.31777	−0.658884	−	0.752244i	$-0.728971\pi$
$307$	−23.0892	−1.31777	−0.658884	+	0.752244i	$0.728971\pi$
$308$	1.36330	0.0776814
$309$	32.6610	1.85802
$310$	0	0
$311$	−22.2458	−1.26145	−0.630723	−	0.776008i	$-0.717241\pi$
$311$	−22.2458	−1.26145	−0.630723	+	0.776008i	$0.717241\pi$
$312$	−37.1292	−2.10203
$313$	−6.82412	−0.385722	−0.192861	−	0.981226i	$-0.561777\pi$
$313$	−6.82412	−0.385722	−0.192861	+	0.981226i	$0.561777\pi$
$314$	8.27127	0.466775
$315$	0	0
$316$	−6.83662	−0.384590
$317$	0.616108	0.0346041	0.0173020	−	0.999850i	$-0.494492\pi$
$317$	0.616108	0.0346041	0.0173020	+	0.999850i	$0.494492\pi$
$318$	−9.05526	−0.507794
$319$	−4.69490	−0.262864
$320$	0	0
$321$	63.2503	3.53029
$322$	−4.28641	−0.238872
$323$	9.15300	0.509286
$324$	−46.3089	−2.57271
$325$	0	0
$326$	8.71355	0.482599
$327$	−20.7391	−1.14688
$328$	−25.8358	−1.42654
$329$	6.41257	0.353537
$330$	0	0
$331$	13.3327	0.732829	0.366414	−	0.930452i	$-0.380585\pi$
$331$	13.3327	0.732829	0.366414	+	0.930452i	$0.380585\pi$
$332$	14.9402	0.819947
$333$	13.3112	0.729452
$334$	−1.06164	−0.0580903
$335$	0	0
$336$	1.96058	0.106958
$337$	−7.73334	−0.421262	−0.210631	−	0.977566i	$-0.567552\pi$
$337$	−7.73334	−0.421262	−0.210631	+	0.977566i	$0.567552\pi$
$338$	3.23406	0.175910
$339$	−23.5334	−1.27816
$340$	0	0
$341$	0.178755	0.00968015
$342$	25.0436	1.35420
$343$	−1.00000	−0.0539949
$344$	−17.8666	−0.963302
$345$	0	0
$346$	1.74402	0.0937590
$347$	23.1016	1.24016	0.620080	−	0.784538i	$-0.287100\pi$
$347$	23.1016	1.24016	0.620080	+	0.784538i	$0.287100\pi$
$348$	−21.4438	−1.14951
$349$	28.4526	1.52303	0.761516	−	0.648146i	$-0.224455\pi$
$349$	28.4526	1.52303	0.761516	+	0.648146i	$0.224455\pi$
$350$	0	0
$351$	72.2809	3.85807
$352$	5.83433	0.310971
$353$	6.51762	0.346898	0.173449	−	0.984843i	$-0.444509\pi$
$353$	6.51762	0.346898	0.173449	+	0.984843i	$0.444509\pi$
$354$	37.0665	1.97006
$355$	0	0
$356$	2.17613	0.115335
$357$	8.03569	0.425294
$358$	−9.26578	−0.489712
$359$	−17.4936	−0.923277	−0.461639	−	0.887068i	$-0.652738\pi$
$359$	−17.4936	−0.923277	−0.461639	+	0.887068i	$0.652738\pi$
$360$	0	0
$361$	−4.43717	−0.233536
$362$	−10.6562	−0.560077
$363$	−3.35029	−0.175845
$364$	−5.62980	−0.295082
$365$	0	0
$366$	13.1681	0.688308
$367$	8.28566	0.432508	0.216254	−	0.976337i	$-0.430616\pi$
$367$	8.28566	0.432508	0.216254	+	0.976337i	$0.430616\pi$
$368$	3.14361	0.163872
$369$	79.1765	4.12176
$370$	0	0
$371$	−3.38729	−0.175859
$372$	0.816458	0.0423314
$373$	−17.9518	−0.929510	−0.464755	−	0.885439i	$-0.653858\pi$
$373$	−17.9518	−0.929510	−0.464755	+	0.885439i	$0.653858\pi$
$374$	1.91385	0.0989627
$375$	0	0
$376$	17.2094	0.887506
$377$	19.3878	0.998520
$378$	13.9666	0.718362
$379$	−15.2670	−0.784213	−0.392107	−	0.919920i	$-0.628254\pi$
$379$	−15.2670	−0.784213	−0.392107	+	0.919920i	$0.628254\pi$
$380$	0	0
$381$	−33.1406	−1.69784
$382$	5.95793	0.304834
$383$	23.8895	1.22070	0.610348	−	0.792133i	$-0.291030\pi$
$383$	23.8895	1.22070	0.610348	+	0.792133i	$0.291030\pi$
$384$	29.7769	1.51955
$385$	0	0
$386$	8.99463	0.457815
$387$	54.7540	2.78330
$388$	3.93174	0.199604
$389$	−30.6608	−1.55456	−0.777282	−	0.629153i	$-0.783402\pi$
$389$	−30.6608	−1.55456	−0.777282	+	0.629153i	$0.783402\pi$
$390$	0	0
$391$	12.8845	0.651597
$392$	−2.68369	−0.135547
$393$	−8.59073	−0.433345
$394$	−2.68071	−0.135052
$395$	0	0
$396$	−11.2124	−0.563444
$397$	−12.1375	−0.609164	−0.304582	−	0.952486i	$-0.598517\pi$
$397$	−12.1375	−0.609164	−0.304582	+	0.952486i	$0.598517\pi$
$398$	2.92820	0.146778
$399$	12.7851	0.640057
$400$	0	0
$401$	−25.3914	−1.26798	−0.633992	−	0.773339i	$-0.718585\pi$
$401$	−25.3914	−1.26798	−0.633992	+	0.773339i	$0.718585\pi$
$402$	25.0469	1.24923
$403$	−0.738177	−0.0367712
$404$	−7.30711	−0.363542
$405$	0	0
$406$	3.74622	0.185922
$407$	1.61850	0.0802260
$408$	21.5653	1.06764
$409$	−15.1784	−0.750523	−0.375262	−	0.926919i	$-0.622447\pi$
$409$	−15.1784	−0.750523	−0.375262	+	0.926919i	$0.622447\pi$
$410$	0	0
$411$	−51.7344	−2.55187
$412$	13.2904	0.654773
$413$	13.8654	0.682272
$414$	35.2533	1.73261
$415$	0	0
$416$	−24.0931	−1.18126
$417$	−20.9930	−1.02803
$418$	3.04502	0.148937
$419$	2.28908	0.111829	0.0559144	−	0.998436i	$-0.482193\pi$
$419$	2.28908	0.111829	0.0559144	+	0.998436i	$0.482193\pi$
$420$	0	0
$421$	33.8765	1.65104	0.825520	−	0.564373i	$-0.190882\pi$
$421$	33.8765	1.65104	0.825520	+	0.564373i	$0.190882\pi$
$422$	−8.77406	−0.427114
$423$	−52.7399	−2.56430
$424$	−9.09043	−0.441470
$425$	0	0
$426$	33.5534	1.62567
$427$	4.92577	0.238375
$428$	25.7378	1.24409
$429$	13.8351	0.667967
$430$	0	0
$431$	−0.862418	−0.0415412	−0.0207706	−	0.999784i	$-0.506612\pi$
$431$	−0.862418	−0.0415412	−0.0207706	+	0.999784i	$0.506612\pi$
$432$	−10.2429	−0.492814
$433$	−21.6310	−1.03952	−0.519759	−	0.854313i	$-0.673978\pi$
$433$	−21.6310	−1.03952	−0.519759	+	0.854313i	$0.673978\pi$
$434$	−0.142635	−0.00684670
$435$	0	0
$436$	−8.43918	−0.404163
$437$	20.4998	0.980638
$438$	20.4961	0.979343
$439$	−15.7035	−0.749489	−0.374745	−	0.927128i	$-0.622270\pi$
$439$	−15.7035	−0.749489	−0.374745	+	0.927128i	$0.622270\pi$
$440$	0	0
$441$	8.22444	0.391640
$442$	−7.90330	−0.375921
$443$	6.25590	0.297227	0.148613	−	0.988895i	$-0.452519\pi$
$443$	6.25590	0.297227	0.148613	+	0.988895i	$0.452519\pi$
$444$	7.39242	0.350829
$445$	0	0
$446$	−10.7430	−0.508695
$447$	−0.0348522	−0.00164845
$448$	−3.48501	−0.164651
$449$	7.23339	0.341365	0.170682	−	0.985326i	$-0.445403\pi$
$449$	7.23339	0.341365	0.170682	+	0.985326i	$0.445403\pi$
$450$	0	0
$451$	9.62697	0.453316
$452$	−9.57622	−0.450427
$453$	76.1477	3.57773
$454$	−18.6033	−0.873096
$455$	0	0
$456$	34.3114	1.60678
$457$	−32.9201	−1.53994	−0.769970	−	0.638081i	$-0.779729\pi$
$457$	−32.9201	−1.53994	−0.769970	+	0.638081i	$0.779729\pi$
$458$	5.72556	0.267538
$459$	−41.9820	−1.95955
$460$	0	0
$461$	−39.2101	−1.82619	−0.913097	−	0.407742i	$-0.866316\pi$
$461$	−39.2101	−1.82619	−0.913097	+	0.407742i	$0.866316\pi$
$462$	2.67331	0.124374
$463$	−2.58305	−0.120045	−0.0600223	−	0.998197i	$-0.519117\pi$
$463$	−2.58305	−0.120045	−0.0600223	+	0.998197i	$0.519117\pi$
$464$	−2.74744	−0.127547
$465$	0	0
$466$	−10.5264	−0.487626
$467$	−4.07631	−0.188629	−0.0943145	−	0.995542i	$-0.530066\pi$
$467$	−4.07631	−0.188629	−0.0943145	+	0.995542i	$0.530066\pi$
$468$	46.3020	2.14031
$469$	9.36925	0.432632
$470$	0	0
$471$	−34.7287	−1.60021
$472$	37.2105	1.71275
$473$	6.65747	0.306111
$474$	−13.4060	−0.615757
$475$	0	0
$476$	3.26989	0.149875
$477$	27.8585	1.27555
$478$	−1.30220	−0.0595611
$479$	36.1232	1.65051	0.825255	−	0.564761i	$-0.191032\pi$
$479$	36.1232	1.65051	0.825255	+	0.564761i	$0.191032\pi$
$480$	0	0
$481$	−6.68364	−0.304748
$482$	−18.1506	−0.826735
$483$	17.9974	0.818909
$484$	−1.36330	−0.0619683
$485$	0	0
$486$	−48.9077	−2.21850
$487$	28.1074	1.27367	0.636835	−	0.771000i	$-0.280243\pi$
$487$	28.1074	1.27367	0.636835	+	0.771000i	$0.280243\pi$
$488$	13.2192	0.598407
$489$	−36.5856	−1.65446
$490$	0	0
$491$	−34.3079	−1.54829	−0.774146	−	0.633006i	$-0.781821\pi$
$491$	−34.3079	−1.54829	−0.774146	+	0.633006i	$0.781821\pi$
$492$	43.9708	1.98236
$493$	−11.2607	−0.507158
$494$	−12.5745	−0.565753
$495$	0	0
$496$	0.104607	0.00469700
$497$	12.5513	0.563001
$498$	29.2962	1.31280
$499$	−17.0567	−0.763563	−0.381781	−	0.924253i	$-0.624689\pi$
$499$	−17.0567	−0.763563	−0.381781	+	0.924253i	$0.624689\pi$
$500$	0	0
$501$	4.45751	0.199147
$502$	−22.7227	−1.01416
$503$	−5.82900	−0.259902	−0.129951	−	0.991520i	$-0.541482\pi$
$503$	−5.82900	−0.259902	−0.129951	+	0.991520i	$0.541482\pi$
$504$	22.0719	0.983159
$505$	0	0
$506$	4.28641	0.190554
$507$	−13.5789	−0.603059
$508$	−13.4856	−0.598327
$509$	−11.2700	−0.499533	−0.249766	−	0.968306i	$-0.580354\pi$
$509$	−11.2700	−0.499533	−0.249766	+	0.968306i	$0.580354\pi$
$510$	0	0
$511$	7.66695	0.339166
$512$	6.55521	0.289702
$513$	−66.7952	−2.94908
$514$	13.6551	0.602299
$515$	0	0
$516$	30.4077	1.33863
$517$	−6.41257	−0.282025
$518$	−1.29145	−0.0567432
$519$	−7.32262	−0.321427
$520$	0	0
$521$	20.8291	0.912538	0.456269	−	0.889842i	$-0.349185\pi$
$521$	20.8291	0.912538	0.456269	+	0.889842i	$0.349185\pi$
$522$	−30.8106	−1.34854
$523$	−18.3128	−0.800761	−0.400380	−	0.916349i	$-0.631122\pi$
$523$	−18.3128	−0.800761	−0.400380	+	0.916349i	$0.631122\pi$
$524$	−3.49575	−0.152712
$525$	0	0
$526$	6.28730	0.274139
$527$	0.428746	0.0186765
$528$	−1.96058	−0.0853233
$529$	5.85713	0.254658
$530$	0	0
$531$	−114.035	−4.94871
$532$	5.20253	0.225558
$533$	−39.7549	−1.72198
$534$	4.26720	0.184660
$535$	0	0
$536$	25.1442	1.08606
$537$	38.9043	1.67884
$538$	1.40611	0.0606216
$539$	1.00000	0.0430730
$540$	0	0
$541$	−4.62874	−0.199005	−0.0995024	−	0.995037i	$-0.531725\pi$
$541$	−4.62874	−0.199005	−0.0995024	+	0.995037i	$0.531725\pi$
$542$	14.6731	0.630263
$543$	44.7423	1.92007
$544$	13.9937	0.599974
$545$	0	0
$546$	−11.0395	−0.472448
$547$	5.29280	0.226304	0.113152	−	0.993578i	$-0.463905\pi$
$547$	5.29280	0.226304	0.113152	+	0.993578i	$0.463905\pi$
$548$	−21.0518	−0.899288
$549$	−40.5117	−1.72900
$550$	0	0
$551$	−17.9163	−0.763262
$552$	48.2994	2.05576
$553$	−5.01475	−0.213249
$554$	5.91039	0.251108
$555$	0	0
$556$	−8.54249	−0.362282
$557$	30.8724	1.30810	0.654052	−	0.756449i	$-0.273068\pi$
$557$	30.8724	1.30810	0.654052	+	0.756449i	$0.273068\pi$
$558$	1.17309	0.0496610
$559$	−27.4922	−1.16280
$560$	0	0
$561$	−8.03569	−0.339267
$562$	2.47547	0.104421
$563$	−8.93668	−0.376636	−0.188318	−	0.982108i	$-0.560304\pi$
$563$	−8.93668	−0.376636	−0.188318	+	0.982108i	$0.560304\pi$
$564$	−29.2892	−1.23330
$565$	0	0
$566$	−1.07764	−0.0452966
$567$	−33.9682	−1.42653
$568$	33.6837	1.41334
$569$	−22.6323	−0.948795	−0.474397	−	0.880311i	$-0.657334\pi$
$569$	−22.6323	−0.948795	−0.474397	+	0.880311i	$0.657334\pi$
$570$	0	0
$571$	−35.1276	−1.47004	−0.735021	−	0.678044i	$-0.762828\pi$
$571$	−35.1276	−1.47004	−0.735021	+	0.678044i	$0.762828\pi$
$572$	5.62980	0.235394
$573$	−25.0156	−1.04504
$574$	−7.68168	−0.320627
$575$	0	0
$576$	28.6623	1.19426
$577$	−23.4725	−0.977172	−0.488586	−	0.872516i	$-0.662487\pi$
$577$	−23.4725	−0.977172	−0.488586	+	0.872516i	$0.662487\pi$
$578$	−8.97450	−0.373290
$579$	−37.7658	−1.56949
$580$	0	0
$581$	10.9588	0.454647
$582$	7.70978	0.319581
$583$	3.38729	0.140287
$584$	20.5757	0.851430
$585$	0	0
$586$	7.10403	0.293465
$587$	42.3602	1.74839	0.874196	−	0.485573i	$-0.161389\pi$
$587$	42.3602	1.74839	0.874196	+	0.485573i	$0.161389\pi$
$588$	4.56746	0.188359
$589$	0.682154	0.0281076
$590$	0	0
$591$	11.2555	0.462990
$592$	0.947140	0.0389272
$593$	−29.5279	−1.21257	−0.606283	−	0.795249i	$-0.707340\pi$
$593$	−29.5279	−1.21257	−0.606283	+	0.795249i	$0.707340\pi$
$594$	−13.9666	−0.573055
$595$	0	0
$596$	−0.0141821	−0.000580921 0
$597$	−12.2947	−0.503188
$598$	−17.7009	−0.723842
$599$	24.1777	0.987872	0.493936	−	0.869498i	$-0.335558\pi$
$599$	24.1777	0.987872	0.493936	+	0.869498i	$0.335558\pi$
$600$	0	0
$601$	45.7960	1.86806	0.934029	−	0.357196i	$-0.116267\pi$
$601$	45.7960	1.86806	0.934029	+	0.357196i	$0.116267\pi$
$602$	−5.31222	−0.216510
$603$	−77.0569	−3.13800
$604$	30.9861	1.26081
$605$	0	0
$606$	−14.3286	−0.582058
$607$	3.04518	0.123600	0.0618001	−	0.998089i	$-0.480316\pi$
$607$	3.04518	0.123600	0.0618001	+	0.998089i	$0.480316\pi$
$608$	22.2645	0.902947
$609$	−15.7293	−0.637383
$610$	0	0
$611$	26.4809	1.07130
$612$	−26.8930	−1.08709
$613$	21.6734	0.875379	0.437689	−	0.899126i	$-0.355797\pi$
$613$	21.6734	0.875379	0.437689	+	0.899126i	$0.355797\pi$
$614$	−18.4236	−0.743517
$615$	0	0
$616$	2.68369	0.108129
$617$	−30.0380	−1.20929	−0.604643	−	0.796497i	$-0.706684\pi$
$617$	−30.0380	−1.20929	−0.604643	+	0.796497i	$0.706684\pi$
$618$	26.0613	1.04834
$619$	−4.89723	−0.196836	−0.0984182	−	0.995145i	$-0.531378\pi$
$619$	−4.89723	−0.196836	−0.0984182	+	0.995145i	$0.531378\pi$
$620$	0	0
$621$	−94.0263	−3.77314
$622$	−17.7507	−0.711738
$623$	1.59622	0.0639513
$624$	8.09628	0.324111
$625$	0	0
$626$	−5.44519	−0.217634
$627$	−12.7851	−0.510589
$628$	−14.1318	−0.563921
$629$	3.88197	0.154784
$630$	0	0
$631$	−33.9402	−1.35114	−0.675570	−	0.737296i	$-0.736102\pi$
$631$	−33.9402	−1.35114	−0.675570	+	0.737296i	$0.736102\pi$
$632$	−13.4580	−0.535332
$633$	36.8397	1.46425
$634$	0.491613	0.0195244
$635$	0	0
$636$	15.4713	0.613476
$637$	−4.12953	−0.163618
$638$	−3.74622	−0.148314
$639$	−103.227	−4.08360
$640$	0	0
$641$	13.9464	0.550849	0.275425	−	0.961323i	$-0.411182\pi$
$641$	13.9464	0.550849	0.275425	+	0.961323i	$0.411182\pi$
$642$	50.4695	1.99187
$643$	−11.0863	−0.437200	−0.218600	−	0.975815i	$-0.570149\pi$
$643$	−11.0863	−0.437200	−0.218600	+	0.975815i	$0.570149\pi$
$644$	7.32350	0.288586
$645$	0	0
$646$	7.30348	0.287352
$647$	2.08904	0.0821285	0.0410643	−	0.999157i	$-0.486925\pi$
$647$	2.08904	0.0821285	0.0410643	+	0.999157i	$0.486925\pi$
$648$	−91.1600	−3.58110
$649$	−13.8654	−0.544265
$650$	0	0
$651$	0.598883	0.0234721
$652$	−14.8875	−0.583038
$653$	−20.8643	−0.816483	−0.408242	−	0.912874i	$-0.633858\pi$
$653$	−20.8643	−0.816483	−0.408242	+	0.912874i	$0.633858\pi$
$654$	−16.5484	−0.647095
$655$	0	0
$656$	5.63368	0.219958
$657$	−63.0564	−2.46006
$658$	5.11681	0.199474
$659$	−26.8555	−1.04614	−0.523071	−	0.852289i	$-0.675214\pi$
$659$	−26.8555	−1.04614	−0.523071	+	0.852289i	$0.675214\pi$
$660$	0	0
$661$	−21.5994	−0.840117	−0.420059	−	0.907497i	$-0.637991\pi$
$661$	−21.5994	−0.840117	−0.420059	+	0.907497i	$0.637991\pi$
$662$	10.6386	0.413480
$663$	33.1836	1.28875
$664$	29.4100	1.14133
$665$	0	0
$666$	10.6215	0.411574
$667$	−25.2205	−0.976540
$668$	1.81385	0.0701801
$669$	45.1066	1.74392
$670$	0	0
$671$	−4.92577	−0.190157
$672$	19.5467	0.754030
$673$	−36.2361	−1.39680	−0.698400	−	0.715708i	$-0.746104\pi$
$673$	−36.2361	−1.39680	−0.698400	+	0.715708i	$0.746104\pi$
$674$	−6.17069	−0.237686
$675$	0	0
$676$	−5.52553	−0.212520
$677$	29.1547	1.12051	0.560254	−	0.828321i	$-0.310704\pi$
$677$	29.1547	1.12051	0.560254	+	0.828321i	$0.310704\pi$
$678$	−18.7781	−0.721167
$679$	2.88399	0.110677
$680$	0	0
$681$	78.1098	2.99317
$682$	0.142635	0.00546178
$683$	−21.6906	−0.829969	−0.414984	−	0.909828i	$-0.636213\pi$
$683$	−21.6906	−0.829969	−0.414984	+	0.909828i	$0.636213\pi$
$684$	−42.7880	−1.63604
$685$	0	0
$686$	−0.797933	−0.0304652
$687$	−24.0400	−0.917182
$688$	3.89593	0.148531
$689$	−13.9879	−0.532897
$690$	0	0
$691$	3.31880	0.126253	0.0631265	−	0.998006i	$-0.479893\pi$
$691$	3.31880	0.126253	0.0631265	+	0.998006i	$0.479893\pi$
$692$	−2.97973	−0.113272
$693$	−8.22444	−0.312421
$694$	18.4336	0.699729
$695$	0	0
$696$	−42.2125	−1.60006
$697$	23.0903	0.874609
$698$	22.7033	0.859332
$699$	44.1973	1.67169
$700$	0	0
$701$	−13.0884	−0.494341	−0.247170	−	0.968972i	$-0.579501\pi$
$701$	−13.0884	−0.494341	−0.247170	+	0.968972i	$0.579501\pi$
$702$	57.6753	2.17682
$703$	6.17639	0.232947
$704$	3.48501	0.131346
$705$	0	0
$706$	5.20063	0.195728
$707$	−5.35986	−0.201578
$708$	−63.3296	−2.38007
$709$	12.0877	0.453965	0.226982	−	0.973899i	$-0.427114\pi$
$709$	12.0877	0.453965	0.226982	+	0.973899i	$0.427114\pi$
$710$	0	0
$711$	41.2435	1.54675
$712$	4.28377	0.160541
$713$	0.960254	0.0359618
$714$	6.41194	0.239961
$715$	0	0
$716$	15.8310	0.591631
$717$	5.46754	0.204189
$718$	−13.9587	−0.520935
$719$	−14.3804	−0.536298	−0.268149	−	0.963378i	$-0.586412\pi$
$719$	−14.3804	−0.536298	−0.268149	+	0.963378i	$0.586412\pi$
$720$	0	0
$721$	9.74871	0.363061
$722$	−3.54057	−0.131766
$723$	76.2089	2.83424
$724$	18.2065	0.676641
$725$	0	0
$726$	−2.67331	−0.0992158
$727$	−10.9328	−0.405475	−0.202738	−	0.979233i	$-0.564984\pi$
$727$	−10.9328	−0.405475	−0.202738	+	0.979233i	$0.564984\pi$
$728$	−11.0824	−0.410741
$729$	103.445	3.83129
$730$	0	0
$731$	15.9680	0.590597
$732$	−22.4982	−0.831559
$733$	23.3456	0.862288	0.431144	−	0.902283i	$-0.358110\pi$
$733$	23.3456	0.862288	0.431144	+	0.902283i	$0.358110\pi$
$734$	6.61140	0.244031
$735$	0	0
$736$	31.3413	1.15526
$737$	−9.36925	−0.345121
$738$	63.1776	2.32560
$739$	32.2528	1.18644	0.593220	−	0.805040i	$-0.297856\pi$
$739$	32.2528	1.18644	0.593220	+	0.805040i	$0.297856\pi$
$740$	0	0
$741$	52.7966	1.93953
$742$	−2.70283	−0.0992239
$743$	20.9235	0.767608	0.383804	−	0.923415i	$-0.374614\pi$
$743$	20.9235	0.767608	0.383804	+	0.923415i	$0.374614\pi$
$744$	1.60722	0.0589234
$745$	0	0
$746$	−14.3244	−0.524452
$747$	−90.1300	−3.29768
$748$	−3.26989	−0.119559
$749$	18.8790	0.689825
$750$	0	0
$751$	46.1159	1.68279	0.841396	−	0.540419i	$-0.181734\pi$
$751$	46.1159	1.68279	0.841396	+	0.540419i	$0.181734\pi$
$752$	−3.75262	−0.136844
$753$	95.4060	3.47679
$754$	15.4701	0.563389
$755$	0	0
$756$	−23.8624	−0.867868
$757$	−20.0773	−0.729723	−0.364862	−	0.931062i	$-0.618884\pi$
$757$	−20.0773	−0.729723	−0.364862	+	0.931062i	$0.618884\pi$
$758$	−12.1821	−0.442472
$759$	−17.9974	−0.653263
$760$	0	0
$761$	−17.4218	−0.631538	−0.315769	−	0.948836i	$-0.602262\pi$
$761$	−17.4218	−0.631538	−0.315769	+	0.948836i	$0.602262\pi$
$762$	−26.4440	−0.957965
$763$	−6.19025	−0.224102
$764$	−10.1794	−0.368277
$765$	0	0
$766$	19.0622	0.688746
$767$	57.2576	2.06745
$768$	47.1116	1.69999
$769$	−49.9302	−1.80053	−0.900264	−	0.435345i	$-0.856626\pi$
$769$	−49.9302	−1.80053	−0.900264	+	0.435345i	$0.856626\pi$
$770$	0	0
$771$	−57.3336	−2.06482
$772$	−15.3677	−0.553096
$773$	10.6184	0.381917	0.190958	−	0.981598i	$-0.438840\pi$
$773$	10.6184	0.381917	0.190958	+	0.981598i	$0.438840\pi$
$774$	43.6901	1.57041
$775$	0	0
$776$	7.73973	0.277840
$777$	5.42244	0.194529
$778$	−24.4653	−0.877122
$779$	36.7377	1.31627
$780$	0	0
$781$	−12.5513	−0.449120
$782$	10.2810	0.367647
$783$	82.1768	2.93676
$784$	0.585197	0.0208999
$785$	0	0
$786$	−6.85483	−0.244504
$787$	−31.6350	−1.12767	−0.563833	−	0.825889i	$-0.690674\pi$
$787$	−31.6350	−1.12767	−0.563833	+	0.825889i	$0.690674\pi$
$788$	4.58010	0.163159
$789$	−26.3986	−0.939813
$790$	0	0
$791$	−7.02428	−0.249755
$792$	−22.0719	−0.784290
$793$	20.3411	0.722335
$794$	−9.68492	−0.343705
$795$	0	0
$796$	−5.00296	−0.177325
$797$	−3.58709	−0.127061	−0.0635306	−	0.997980i	$-0.520236\pi$
$797$	−3.58709	−0.127061	−0.0635306	+	0.997980i	$0.520236\pi$
$798$	10.2017	0.361136
$799$	−15.3806	−0.544126
$800$	0	0
$801$	−13.1281	−0.463857
$802$	−20.2606	−0.715428
$803$	−7.66695	−0.270561
$804$	−42.7936	−1.50922
$805$	0	0
$806$	−0.589016	−0.0207472
$807$	−5.90383	−0.207825
$808$	−14.3842	−0.506035
$809$	−5.40377	−0.189986	−0.0949932	−	0.995478i	$-0.530283\pi$
$809$	−5.40377	−0.189986	−0.0949932	+	0.995478i	$0.530283\pi$
$810$	0	0
$811$	−29.4659	−1.03469	−0.517344	−	0.855778i	$-0.673079\pi$
$811$	−29.4659	−1.03469	−0.517344	+	0.855778i	$0.673079\pi$
$812$	−6.40057	−0.224616
$813$	−61.6080	−2.16069
$814$	1.29145	0.0452654
$815$	0	0
$816$	−4.70246	−0.164619
$817$	25.4058	0.888835
$818$	−12.1113	−0.423463
$819$	33.9631	1.18677
$820$	0	0
$821$	−38.7200	−1.35134	−0.675668	−	0.737206i	$-0.736145\pi$
$821$	−38.7200	−1.35134	−0.675668	+	0.737206i	$0.736145\pi$
$822$	−41.2806	−1.43983
$823$	21.5724	0.751966	0.375983	−	0.926627i	$-0.377305\pi$
$823$	21.5724	0.751966	0.375983	+	0.926627i	$0.377305\pi$
$824$	26.1625	0.911415
$825$	0	0
$826$	11.0637	0.384954
$827$	19.2791	0.670398	0.335199	−	0.942147i	$-0.391196\pi$
$827$	19.2791	0.670398	0.335199	+	0.942147i	$0.391196\pi$
$828$	−60.2317	−2.09320
$829$	−46.9956	−1.63223	−0.816113	−	0.577893i	$-0.803875\pi$
$829$	−46.9956	−1.63223	−0.816113	+	0.577893i	$0.803875\pi$
$830$	0	0
$831$	−24.8160	−0.860857
$832$	−14.3915	−0.498935
$833$	2.39850	0.0831033
$834$	−16.7510	−0.580041
$835$	0	0
$836$	−5.20253	−0.179933
$837$	−3.12883	−0.108148
$838$	1.82653	0.0630965
$839$	26.4241	0.912261	0.456130	−	0.889913i	$-0.349235\pi$
$839$	26.4241	0.912261	0.456130	+	0.889913i	$0.349235\pi$
$840$	0	0
$841$	−6.95789	−0.239927
$842$	27.0312	0.931556
$843$	−10.3938	−0.357980
$844$	14.9908	0.516006
$845$	0	0
$846$	−42.0829	−1.44684
$847$	−1.00000	−0.0343604
$848$	1.98223	0.0680700
$849$	4.52470	0.155287
$850$	0	0
$851$	8.69438	0.298040
$852$	−57.3274	−1.96400
$853$	37.4410	1.28195	0.640977	−	0.767560i	$-0.278529\pi$
$853$	37.4410	1.28195	0.640977	+	0.767560i	$0.278529\pi$
$854$	3.93044	0.134497
$855$	0	0
$856$	50.6655	1.73171
$857$	−39.5752	−1.35186	−0.675932	−	0.736964i	$-0.736259\pi$
$857$	−39.5752	−1.35186	−0.675932	+	0.736964i	$0.736259\pi$
$858$	11.0395	0.376883
$859$	50.6777	1.72910	0.864550	−	0.502547i	$-0.167604\pi$
$859$	50.6777	1.72910	0.864550	+	0.502547i	$0.167604\pi$
$860$	0	0
$861$	32.2532	1.09918
$862$	−0.688152	−0.0234386
$863$	31.8393	1.08382	0.541912	−	0.840435i	$-0.317701\pi$
$863$	31.8393	1.08382	0.541912	+	0.840435i	$0.317701\pi$
$864$	−102.121	−3.47422
$865$	0	0
$866$	−17.2601	−0.586521
$867$	37.6813	1.27972
$868$	0.243698	0.00827164
$869$	5.01475	0.170114
$870$	0	0
$871$	38.6906	1.31098
$872$	−16.6127	−0.562578
$873$	−23.7192	−0.802773
$874$	16.3575	0.553300
$875$	0	0
$876$	−35.0185	−1.18316
$877$	1.91150	0.0645466	0.0322733	−	0.999479i	$-0.489725\pi$
$877$	1.91150	0.0645466	0.0322733	+	0.999479i	$0.489725\pi$
$878$	−12.5304	−0.422880
$879$	−29.8277	−1.00606
$880$	0	0
$881$	13.0876	0.440933	0.220467	−	0.975395i	$-0.429242\pi$
$881$	13.0876	0.440933	0.220467	+	0.975395i	$0.429242\pi$
$882$	6.56256	0.220973
$883$	−48.9907	−1.64867	−0.824334	−	0.566103i	$-0.808450\pi$
$883$	−48.9907	−1.64867	−0.824334	+	0.566103i	$0.808450\pi$
$884$	13.5031	0.454159
$885$	0	0
$886$	4.99179	0.167703
$887$	51.8353	1.74046	0.870230	−	0.492645i	$-0.163970\pi$
$887$	51.8353	1.74046	0.870230	+	0.492645i	$0.163970\pi$
$888$	14.5521	0.488338
$889$	−9.89186	−0.331762
$890$	0	0
$891$	33.9682	1.13798
$892$	18.3548	0.614565
$893$	−24.4712	−0.818897
$894$	−0.0278098	−0.000930097 0
$895$	0	0
$896$	8.88785	0.296922
$897$	74.3207	2.48150
$898$	5.77176	0.192606
$899$	−0.839239	−0.0279902
$900$	0	0
$901$	8.12442	0.270664
$902$	7.68168	0.255772
$903$	22.3045	0.742246
$904$	−18.8510	−0.626975
$905$	0	0
$906$	60.7608	2.01864
$907$	−25.5876	−0.849624	−0.424812	−	0.905282i	$-0.639660\pi$
$907$	−25.5876	−0.849624	−0.424812	+	0.905282i	$0.639660\pi$
$908$	31.7845	1.05481
$909$	44.0819	1.46210
$910$	0	0
$911$	7.77170	0.257488	0.128744	−	0.991678i	$-0.458905\pi$
$911$	7.77170	0.257488	0.128744	+	0.991678i	$0.458905\pi$
$912$	−7.48182	−0.247748
$913$	−10.9588	−0.362683
$914$	−26.2681	−0.868871
$915$	0	0
$916$	−9.78236	−0.323218
$917$	−2.56418	−0.0846765
$918$	−33.4988	−1.10563
$919$	−59.7859	−1.97215	−0.986077	−	0.166288i	$-0.946822\pi$
$919$	−59.7859	−1.97215	−0.986077	+	0.166288i	$0.946822\pi$
$920$	0	0
$921$	77.3554	2.54895
$922$	−31.2870	−1.03038
$923$	51.8309	1.70603
$924$	−4.56746	−0.150258
$925$	0	0
$926$	−2.06110	−0.0677320
$927$	−80.1777	−2.63338
$928$	−27.3916	−0.899174
$929$	4.00274	0.131325	0.0656627	−	0.997842i	$-0.479084\pi$
$929$	4.00274	0.131325	0.0656627	+	0.997842i	$0.479084\pi$
$930$	0	0
$931$	3.81613	0.125069
$932$	17.9848	0.589111
$933$	74.5300	2.44000
$934$	−3.25262	−0.106429
$935$	0	0
$936$	91.1465	2.97922
$937$	−35.7269	−1.16715	−0.583574	−	0.812060i	$-0.698346\pi$
$937$	−35.7269	−1.16715	−0.583574	+	0.812060i	$0.698346\pi$
$938$	7.47604	0.244101
$939$	22.8628	0.746099
$940$	0	0
$941$	18.3331	0.597641	0.298821	−	0.954309i	$-0.403407\pi$
$941$	18.3331	0.597641	0.298821	+	0.954309i	$0.403407\pi$
$942$	−27.7112	−0.902879
$943$	51.7150	1.68407
$944$	−8.11399	−0.264088
$945$	0	0
$946$	5.31222	0.172715
$947$	−44.2770	−1.43881	−0.719405	−	0.694591i	$-0.755585\pi$
$947$	−44.2770	−1.43881	−0.719405	+	0.694591i	$0.755585\pi$
$948$	22.9047	0.743909
$949$	31.6609	1.02776
$950$	0	0
$951$	−2.06414	−0.0669343
$952$	6.43685	0.208619
$953$	−37.3141	−1.20872	−0.604362	−	0.796710i	$-0.706572\pi$
$953$	−37.3141	−1.20872	−0.604362	+	0.796710i	$0.706572\pi$
$954$	22.2293	0.719699
$955$	0	0
$956$	2.22486	0.0719570
$957$	15.7293	0.508456
$958$	28.8239	0.931257
$959$	−15.4418	−0.498641
$960$	0	0
$961$	−30.9680	−0.998969
$962$	−5.33310	−0.171946
$963$	−155.270	−5.00350
$964$	31.0110	0.998796
$965$	0	0
$966$	14.3607	0.462048
$967$	10.4524	0.336126	0.168063	−	0.985776i	$-0.446249\pi$
$967$	10.4524	0.336126	0.168063	+	0.985776i	$0.446249\pi$
$968$	−2.68369	−0.0862571
$969$	−30.6652	−0.985108
$970$	0	0
$971$	39.1967	1.25788	0.628940	−	0.777454i	$-0.283489\pi$
$971$	39.1967	1.25788	0.628940	+	0.777454i	$0.283489\pi$
$972$	83.5608	2.68021
$973$	−6.26603	−0.200880
$974$	22.4279	0.718635
$975$	0	0
$976$	−2.88255	−0.0922680
$977$	41.1607	1.31685	0.658424	−	0.752648i	$-0.271224\pi$
$977$	41.1607	1.31685	0.658424	+	0.752648i	$0.271224\pi$
$978$	−29.1929	−0.933486
$979$	−1.59622	−0.0510155
$980$	0	0
$981$	50.9114	1.62547
$982$	−27.3754	−0.873584
$983$	42.4686	1.35454	0.677270	−	0.735735i	$-0.263163\pi$
$983$	42.4686	1.35454	0.677270	+	0.735735i	$0.263163\pi$
$984$	86.5575	2.75935
$985$	0	0
$986$	−8.98533	−0.286151
$987$	−21.4840	−0.683843
$988$	21.4840	0.683498
$989$	35.7632	1.13720
$990$	0	0
$991$	51.7970	1.64539	0.822693	−	0.568486i	$-0.192471\pi$
$991$	51.7970	1.64539	0.822693	+	0.568486i	$0.192471\pi$
$992$	1.04292	0.0331127
$993$	−44.6683	−1.41750
$994$	10.0151	0.317659
$995$	0	0
$996$	−50.0538	−1.58602
$997$	40.2050	1.27331	0.636653	−	0.771150i	$-0.280318\pi$
$997$	40.2050	1.27331	0.636653	+	0.771150i	$0.280318\pi$
$998$	−13.6101	−0.430821
$999$	−28.3292	−0.896297

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1925.2.a.be.1.6		8
5.2	odd	4		385.2.b.d.309.10	yes	16
5.3	odd	4		385.2.b.d.309.7	✓	16
5.4	even	2		1925.2.a.bf.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.b.d.309.7	✓	16	5.3	odd	4
385.2.b.d.309.10	yes	16	5.2	odd	4
1925.2.a.be.1.6		8	1.1	even	1	trivial
1925.2.a.bf.1.3		8	5.4	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:	\( N \)	\(=\)	\( 1925 = 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1925.a (trivial)

\(f(q)\)	\(=\)	\(q+0.797933 q^{2} -3.35029 q^{3} -1.36330 q^{4} -2.67331 q^{6} -1.00000 q^{7} -2.68369 q^{8} +8.22444 q^{9} +O(q^{10})\)	\(q+0.797933 q^{2} -3.35029 q^{3} -1.36330 q^{4} -2.67331 q^{6} -1.00000 q^{7} -2.68369 q^{8} +8.22444 q^{9} +1.00000 q^{11} +4.56746 q^{12} -4.12953 q^{13} -0.797933 q^{14} +0.585197 q^{16} +2.39850 q^{17} +6.56256 q^{18} +3.81613 q^{19} +3.35029 q^{21} +0.797933 q^{22} +5.37188 q^{23} +8.99115 q^{24} -3.29509 q^{26} -17.5034 q^{27} +1.36330 q^{28} -4.69490 q^{29} +0.178755 q^{31} +5.83433 q^{32} -3.35029 q^{33} +1.91385 q^{34} -11.2124 q^{36} +1.61850 q^{37} +3.04502 q^{38} +13.8351 q^{39} +9.62697 q^{41} +2.67331 q^{42} +6.65747 q^{43} -1.36330 q^{44} +4.28641 q^{46} -6.41257 q^{47} -1.96058 q^{48} +1.00000 q^{49} -8.03569 q^{51} +5.62980 q^{52} +3.38729 q^{53} -13.9666 q^{54} +2.68369 q^{56} -12.7851 q^{57} -3.74622 q^{58} -13.8654 q^{59} -4.92577 q^{61} +0.142635 q^{62} -8.22444 q^{63} +3.48501 q^{64} -2.67331 q^{66} -9.36925 q^{67} -3.26989 q^{68} -17.9974 q^{69} -12.5513 q^{71} -22.0719 q^{72} -7.66695 q^{73} +1.29145 q^{74} -5.20253 q^{76} -1.00000 q^{77} +11.0395 q^{78} +5.01475 q^{79} +33.9682 q^{81} +7.68168 q^{82} -10.9588 q^{83} -4.56746 q^{84} +5.31222 q^{86} +15.7293 q^{87} -2.68369 q^{88} -1.59622 q^{89} +4.12953 q^{91} -7.32350 q^{92} -0.598883 q^{93} -5.11681 q^{94} -19.5467 q^{96} -2.88399 q^{97} +0.797933 q^{98} +8.22444 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 6 q^{3} + 14 q^{4} - 6 q^{6} - 8 q^{7} - 12 q^{8} + 10 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 6 * q^3 + 14 * q^4 - 6 * q^6 - 8 * q^7 - 12 * q^8 + 10 * q^9	\( 8 q - 4 q^{2} - 6 q^{3} + 14 q^{4} - 6 q^{6} - 8 q^{7} - 12 q^{8} + 10 q^{9} + 8 q^{11} - 12 q^{12} - 6 q^{13} + 4 q^{14} + 18 q^{16} - 6 q^{17} - 6 q^{18} - 6 q^{19} + 6 q^{21} - 4 q^{22} - 4 q^{23} + 6 q^{24} - 4 q^{26} - 24 q^{27} - 14 q^{28} + 4 q^{29} - 14 q^{31} - 18 q^{32} - 6 q^{33} - 6 q^{34} + 18 q^{36} - 10 q^{37} + 30 q^{38} + 16 q^{39} - 4 q^{41} + 6 q^{42} - 34 q^{43} + 14 q^{44} - 24 q^{46} + 8 q^{47} - 12 q^{48} + 8 q^{49} + 16 q^{51} - 46 q^{52} - 18 q^{53} + 6 q^{54} + 12 q^{56} - 6 q^{57} + 6 q^{58} - 40 q^{59} - 26 q^{62} - 10 q^{63} + 10 q^{64} - 6 q^{66} - 42 q^{67} - 16 q^{68} - 50 q^{69} + 6 q^{71} - 28 q^{72} - 40 q^{73} - 44 q^{76} - 8 q^{77} + 76 q^{78} + 12 q^{79} + 40 q^{81} - 42 q^{82} - 2 q^{83} + 12 q^{84} + 44 q^{86} - 2 q^{87} - 12 q^{88} + 22 q^{89} + 6 q^{91} - 6 q^{92} + 32 q^{93} - 50 q^{94} - 16 q^{96} + 6 q^{97} - 4 q^{98} + 10 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 6 * q^3 + 14 * q^4 - 6 * q^6 - 8 * q^7 - 12 * q^8 + 10 * q^9 + 8 * q^11 - 12 * q^12 - 6 * q^13 + 4 * q^14 + 18 * q^16 - 6 * q^17 - 6 * q^18 - 6 * q^19 + 6 * q^21 - 4 * q^22 - 4 * q^23 + 6 * q^24 - 4 * q^26 - 24 * q^27 - 14 * q^28 + 4 * q^29 - 14 * q^31 - 18 * q^32 - 6 * q^33 - 6 * q^34 + 18 * q^36 - 10 * q^37 + 30 * q^38 + 16 * q^39 - 4 * q^41 + 6 * q^42 - 34 * q^43 + 14 * q^44 - 24 * q^46 + 8 * q^47 - 12 * q^48 + 8 * q^49 + 16 * q^51 - 46 * q^52 - 18 * q^53 + 6 * q^54 + 12 * q^56 - 6 * q^57 + 6 * q^58 - 40 * q^59 - 26 * q^62 - 10 * q^63 + 10 * q^64 - 6 * q^66 - 42 * q^67 - 16 * q^68 - 50 * q^69 + 6 * q^71 - 28 * q^72 - 40 * q^73 - 44 * q^76 - 8 * q^77 + 76 * q^78 + 12 * q^79 + 40 * q^81 - 42 * q^82 - 2 * q^83 + 12 * q^84 + 44 * q^86 - 2 * q^87 - 12 * q^88 + 22 * q^89 + 6 * q^91 - 6 * q^92 + 32 * q^93 - 50 * q^94 - 16 * q^96 + 6 * q^97 - 4 * q^98 + 10 * q^99

Introduction

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