LMFDB - Embedded newform 975.2.a.o.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(1,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, 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("975.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 195)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.34292$ of defining polynomial
Character	$\chi$	$=$	975.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.48929 q^{2} +1.00000 q^{3} +4.19656 q^{4} +2.48929 q^{6} +1.19656 q^{7} +5.46787 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.48929 q^{2} +1.00000 q^{3} +4.19656 q^{4} +2.48929 q^{6} +1.19656 q^{7} +5.46787 q^{8} +1.00000 q^{9} -1.19656 q^{11} +4.19656 q^{12} -1.00000 q^{13} +2.97858 q^{14} +5.21798 q^{16} -6.17513 q^{17} +2.48929 q^{18} +6.97858 q^{19} +1.19656 q^{21} -2.97858 q^{22} -4.17513 q^{23} +5.46787 q^{24} -2.48929 q^{26} +1.00000 q^{27} +5.02142 q^{28} +6.00000 q^{29} -2.97858 q^{31} +2.05333 q^{32} -1.19656 q^{33} -15.3717 q^{34} +4.19656 q^{36} -7.78202 q^{37} +17.3717 q^{38} -1.00000 q^{39} -6.17513 q^{41} +2.97858 q^{42} +9.95715 q^{43} -5.02142 q^{44} -10.3931 q^{46} +1.02142 q^{47} +5.21798 q^{48} -5.56825 q^{49} -6.17513 q^{51} -4.19656 q^{52} -10.1751 q^{53} +2.48929 q^{54} +6.54262 q^{56} +6.97858 q^{57} +14.9357 q^{58} +5.37169 q^{59} +12.5682 q^{61} -7.41454 q^{62} +1.19656 q^{63} -5.32464 q^{64} -2.97858 q^{66} -9.37169 q^{67} -25.9143 q^{68} -4.17513 q^{69} -5.19656 q^{71} +5.46787 q^{72} +11.9572 q^{73} -19.3717 q^{74} +29.2860 q^{76} -1.43175 q^{77} -2.48929 q^{78} -1.78202 q^{79} +1.00000 q^{81} -15.3717 q^{82} +5.37169 q^{83} +5.02142 q^{84} +24.7862 q^{86} +6.00000 q^{87} -6.54262 q^{88} +10.1751 q^{89} -1.19656 q^{91} -17.5212 q^{92} -2.97858 q^{93} +2.54262 q^{94} +2.05333 q^{96} +1.82487 q^{97} -13.8610 q^{98} -1.19656 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{3} + 8 q^{4} - q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^3 + 8 * q^4 - q^7 - 6 * q^8 + 3 * q^9	$ 3 q + 3 q^{3} + 8 q^{4} - q^{7} - 6 q^{8} + 3 q^{9} + q^{11} + 8 q^{12} - 3 q^{13} - 6 q^{14} + 26 q^{16} + q^{17} + 6 q^{19} - q^{21} + 6 q^{22} + 7 q^{23} - 6 q^{24} + 3 q^{27} + 30 q^{28} + 18 q^{29} + 6 q^{31} - 22 q^{32} + q^{33} - 22 q^{34} + 8 q^{36} - 13 q^{37} + 28 q^{38} - 3 q^{39} + q^{41} - 6 q^{42} - 30 q^{44} - 22 q^{46} + 18 q^{47} + 26 q^{48} + 12 q^{49} + q^{51} - 8 q^{52} - 11 q^{53} - 16 q^{56} + 6 q^{57} - 8 q^{59} + 9 q^{61} - 28 q^{62} - q^{63} + 30 q^{64} + 6 q^{66} - 4 q^{67} - 18 q^{68} + 7 q^{69} - 11 q^{71} - 6 q^{72} + 6 q^{73} - 34 q^{74} + 4 q^{76} - 33 q^{77} + 5 q^{79} + 3 q^{81} - 22 q^{82} - 8 q^{83} + 30 q^{84} + 56 q^{86} + 18 q^{87} + 16 q^{88} + 11 q^{89} + q^{91} - 2 q^{92} + 6 q^{93} - 28 q^{94} - 22 q^{96} + 25 q^{97} - 10 q^{98} + q^{99}+O(q^{100}) $ 3 * q + 3 * q^3 + 8 * q^4 - q^7 - 6 * q^8 + 3 * q^9 + q^11 + 8 * q^12 - 3 * q^13 - 6 * q^14 + 26 * q^16 + q^17 + 6 * q^19 - q^21 + 6 * q^22 + 7 * q^23 - 6 * q^24 + 3 * q^27 + 30 * q^28 + 18 * q^29 + 6 * q^31 - 22 * q^32 + q^33 - 22 * q^34 + 8 * q^36 - 13 * q^37 + 28 * q^38 - 3 * q^39 + q^41 - 6 * q^42 - 30 * q^44 - 22 * q^46 + 18 * q^47 + 26 * q^48 + 12 * q^49 + q^51 - 8 * q^52 - 11 * q^53 - 16 * q^56 + 6 * q^57 - 8 * q^59 + 9 * q^61 - 28 * q^62 - q^63 + 30 * q^64 + 6 * q^66 - 4 * q^67 - 18 * q^68 + 7 * q^69 - 11 * q^71 - 6 * q^72 + 6 * q^73 - 34 * q^74 + 4 * q^76 - 33 * q^77 + 5 * q^79 + 3 * q^81 - 22 * q^82 - 8 * q^83 + 30 * q^84 + 56 * q^86 + 18 * q^87 + 16 * q^88 + 11 * q^89 + q^91 - 2 * q^92 + 6 * q^93 - 28 * q^94 - 22 * q^96 + 25 * q^97 - 10 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.48929	1.76019	0.880096	−	0.474795i	$-0.157478\pi$
$2$	2.48929	1.76019	0.880096	+	0.474795i	$0.157478\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.19656	2.09828
$5$	0	0
$5$	0	0
$6$	2.48929	1.01625
$7$	1.19656	0.452256	0.226128	−	0.974098i	$-0.427393\pi$
$7$	1.19656	0.452256	0.226128	+	0.974098i	$0.427393\pi$
$8$	5.46787	1.93318
$9$	1.00000	0.333333
$10$	0	0
$11$	−1.19656	−0.360776	−0.180388	−	0.983596i	$-0.557735\pi$
$11$	−1.19656	−0.360776	−0.180388	+	0.983596i	$0.557735\pi$
$12$	4.19656	1.21144
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.97858	0.796058
$15$	0	0
$16$	5.21798	1.30450
$17$	−6.17513	−1.49769	−0.748845	−	0.662745i	$-0.769391\pi$
$17$	−6.17513	−1.49769	−0.748845	+	0.662745i	$0.769391\pi$
$18$	2.48929	0.586731
$19$	6.97858	1.60100	0.800498	−	0.599336i	$-0.204569\pi$
$19$	6.97858	1.60100	0.800498	+	0.599336i	$0.204569\pi$
$20$	0	0
$21$	1.19656	0.261110
$22$	−2.97858	−0.635035
$23$	−4.17513	−0.870576	−0.435288	−	0.900291i	$-0.643353\pi$
$23$	−4.17513	−0.870576	−0.435288	+	0.900291i	$0.643353\pi$
$24$	5.46787	1.11612
$25$	0	0
$26$	−2.48929	−0.488190
$27$	1.00000	0.192450
$28$	5.02142	0.948960
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	0	0
$31$	−2.97858	−0.534968	−0.267484	−	0.963562i	$-0.586192\pi$
$31$	−2.97858	−0.534968	−0.267484	+	0.963562i	$0.586192\pi$
$32$	2.05333	0.362980
$33$	−1.19656	−0.208294
$34$	−15.3717	−2.63622
$35$	0	0
$36$	4.19656	0.699426
$37$	−7.78202	−1.27936	−0.639678	−	0.768643i	$-0.720932\pi$
$37$	−7.78202	−1.27936	−0.639678	+	0.768643i	$0.720932\pi$
$38$	17.3717	2.81806
$39$	−1.00000	−0.160128
$40$	0	0
$41$	−6.17513	−0.964394	−0.482197	−	0.876063i	$-0.660161\pi$
$41$	−6.17513	−0.964394	−0.482197	+	0.876063i	$0.660161\pi$
$42$	2.97858	0.459604
$43$	9.95715	1.51845	0.759226	−	0.650827i	$-0.225578\pi$
$43$	9.95715	1.51845	0.759226	+	0.650827i	$0.225578\pi$
$44$	−5.02142	−0.757008
$45$	0	0
$46$	−10.3931	−1.53238
$47$	1.02142	0.148990	0.0744949	−	0.997221i	$-0.476266\pi$
$47$	1.02142	0.148990	0.0744949	+	0.997221i	$0.476266\pi$
$48$	5.21798	0.753151
$49$	−5.56825	−0.795464
$50$	0	0
$51$	−6.17513	−0.864692
$52$	−4.19656	−0.581958
$53$	−10.1751	−1.39766	−0.698831	−	0.715287i	$-0.746296\pi$
$53$	−10.1751	−1.39766	−0.698831	+	0.715287i	$0.746296\pi$
$54$	2.48929	0.338749
$55$	0	0
$56$	6.54262	0.874294
$57$	6.97858	0.924335
$58$	14.9357	1.96116
$59$	5.37169	0.699335	0.349667	−	0.936874i	$-0.386295\pi$
$59$	5.37169	0.699335	0.349667	+	0.936874i	$0.386295\pi$
$60$	0	0
$61$	12.5682	1.60920	0.804600	−	0.593818i	$-0.202380\pi$
$61$	12.5682	1.60920	0.804600	+	0.593818i	$0.202380\pi$
$62$	−7.41454	−0.941647
$63$	1.19656	0.150752
$64$	−5.32464	−0.665579
$65$	0	0
$66$	−2.97858	−0.366638
$67$	−9.37169	−1.14493	−0.572467	−	0.819928i	$-0.694014\pi$
$67$	−9.37169	−1.14493	−0.572467	+	0.819928i	$0.694014\pi$
$68$	−25.9143	−3.14257
$69$	−4.17513	−0.502627
$70$	0	0
$71$	−5.19656	−0.616718	−0.308359	−	0.951270i	$-0.599780\pi$
$71$	−5.19656	−0.616718	−0.308359	+	0.951270i	$0.599780\pi$
$72$	5.46787	0.644394
$73$	11.9572	1.39948	0.699740	−	0.714398i	$-0.253299\pi$
$73$	11.9572	1.39948	0.699740	+	0.714398i	$0.253299\pi$
$74$	−19.3717	−2.25191
$75$	0	0
$76$	29.2860	3.35933
$77$	−1.43175	−0.163163
$78$	−2.48929	−0.281856
$79$	−1.78202	−0.200493	−0.100246	−	0.994963i	$-0.531963\pi$
$79$	−1.78202	−0.200493	−0.100246	+	0.994963i	$0.531963\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−15.3717	−1.69752
$83$	5.37169	0.589620	0.294810	−	0.955556i	$-0.404744\pi$
$83$	5.37169	0.589620	0.294810	+	0.955556i	$0.404744\pi$
$84$	5.02142	0.547882
$85$	0	0
$86$	24.7862	2.67277
$87$	6.00000	0.643268
$88$	−6.54262	−0.697445
$89$	10.1751	1.07856	0.539281	−	0.842126i	$-0.318696\pi$
$89$	10.1751	1.07856	0.539281	+	0.842126i	$0.318696\pi$
$90$	0	0
$91$	−1.19656	−0.125433
$92$	−17.5212	−1.82671
$93$	−2.97858	−0.308864
$94$	2.54262	0.262251
$95$	0	0
$96$	2.05333	0.209567
$97$	1.82487	0.185287	0.0926435	−	0.995699i	$-0.470468\pi$
$97$	1.82487	0.185287	0.0926435	+	0.995699i	$0.470468\pi$
$98$	−13.8610	−1.40017
$99$	−1.19656	−0.120259
$100$	0	0
$101$	−10.3503	−1.02989	−0.514945	−	0.857223i	$-0.672188\pi$
$101$	−10.3503	−1.02989	−0.514945	+	0.857223i	$0.672188\pi$
$102$	−15.3717	−1.52202
$103$	−18.7434	−1.84684	−0.923420	−	0.383790i	$-0.874619\pi$
$103$	−18.7434	−1.84684	−0.923420	+	0.383790i	$0.874619\pi$
$104$	−5.46787	−0.536168
$105$	0	0
$106$	−25.3288	−2.46016
$107$	18.5682	1.79506	0.897530	−	0.440953i	$-0.145359\pi$
$107$	18.5682	1.79506	0.897530	+	0.440953i	$0.145359\pi$
$108$	4.19656	0.403814
$109$	8.39312	0.803915	0.401957	−	0.915658i	$-0.368330\pi$
$109$	8.39312	0.803915	0.401957	+	0.915658i	$0.368330\pi$
$110$	0	0
$111$	−7.78202	−0.738637
$112$	6.24361	0.589966
$113$	−7.95715	−0.748546	−0.374273	−	0.927319i	$-0.622108\pi$
$113$	−7.95715	−0.748546	−0.374273	+	0.927319i	$0.622108\pi$
$114$	17.3717	1.62701
$115$	0	0
$116$	25.1793	2.33784
$117$	−1.00000	−0.0924500
$118$	13.3717	1.23096
$119$	−7.38890	−0.677340
$120$	0	0
$121$	−9.56825	−0.869841
$122$	31.2860	2.83250
$123$	−6.17513	−0.556793
$124$	−12.4998	−1.12251
$125$	0	0
$126$	2.97858	0.265353
$127$	10.3931	0.922240	0.461120	−	0.887338i	$-0.347448\pi$
$127$	10.3931	0.922240	0.461120	+	0.887338i	$0.347448\pi$
$128$	−17.3612	−1.53453
$129$	9.95715	0.876679
$130$	0	0
$131$	−6.39312	−0.558569	−0.279285	−	0.960208i	$-0.590097\pi$
$131$	−6.39312	−0.558569	−0.279285	+	0.960208i	$0.590097\pi$
$132$	−5.02142	−0.437059
$133$	8.35027	0.724060
$134$	−23.3288	−2.01531
$135$	0	0
$136$	−33.7648	−2.89531
$137$	−16.7434	−1.43048	−0.715242	−	0.698877i	$-0.753684\pi$
$137$	−16.7434	−1.43048	−0.715242	+	0.698877i	$0.753684\pi$
$138$	−10.3931	−0.884721
$139$	5.78202	0.490424	0.245212	−	0.969469i	$-0.421142\pi$
$139$	5.78202	0.490424	0.245212	+	0.969469i	$0.421142\pi$
$140$	0	0
$141$	1.02142	0.0860193
$142$	−12.9357	−1.08554
$143$	1.19656	0.100061
$144$	5.21798	0.434832
$145$	0	0
$146$	29.7648	2.46335
$147$	−5.56825	−0.459262
$148$	−32.6577	−2.68445
$149$	15.3461	1.25720	0.628599	−	0.777730i	$-0.283629\pi$
$149$	15.3461	1.25720	0.628599	+	0.777730i	$0.283629\pi$
$150$	0	0
$151$	−8.58546	−0.698675	−0.349337	−	0.936997i	$-0.613593\pi$
$151$	−8.58546	−0.698675	−0.349337	+	0.936997i	$0.613593\pi$
$152$	38.1579	3.09502
$153$	−6.17513	−0.499230
$154$	−3.56404	−0.287198
$155$	0	0
$156$	−4.19656	−0.335994
$157$	−2.78623	−0.222365	−0.111183	−	0.993800i	$-0.535464\pi$
$157$	−2.78623	−0.222365	−0.111183	+	0.993800i	$0.535464\pi$
$158$	−4.43596	−0.352906
$159$	−10.1751	−0.806941
$160$	0	0
$161$	−4.99579	−0.393723
$162$	2.48929	0.195577
$163$	−8.76060	−0.686183	−0.343091	−	0.939302i	$-0.611474\pi$
$163$	−8.76060	−0.686183	−0.343091	+	0.939302i	$0.611474\pi$
$164$	−25.9143	−2.02357
$165$	0	0
$166$	13.3717	1.03784
$167$	17.3717	1.34426	0.672131	−	0.740432i	$-0.265379\pi$
$167$	17.3717	1.34426	0.672131	+	0.740432i	$0.265379\pi$
$168$	6.54262	0.504774
$169$	1.00000	0.0769231
$170$	0	0
$171$	6.97858	0.533665
$172$	41.7858	3.18614
$173$	7.95715	0.604971	0.302486	−	0.953154i	$-0.402184\pi$
$173$	7.95715	0.604971	0.302486	+	0.953154i	$0.402184\pi$
$174$	14.9357	1.13227
$175$	0	0
$176$	−6.24361	−0.470630
$177$	5.37169	0.403761
$178$	25.3288	1.89848
$179$	−15.5640	−1.16331	−0.581655	−	0.813435i	$-0.697595\pi$
$179$	−15.5640	−1.16331	−0.581655	+	0.813435i	$0.697595\pi$
$180$	0	0
$181$	15.7820	1.17307	0.586534	−	0.809925i	$-0.300492\pi$
$181$	15.7820	1.17307	0.586534	+	0.809925i	$0.300492\pi$
$182$	−2.97858	−0.220787
$183$	12.5682	0.929072
$184$	−22.8291	−1.68298
$185$	0	0
$186$	−7.41454	−0.543660
$187$	7.38890	0.540330
$188$	4.28646	0.312622
$189$	1.19656	0.0870368
$190$	0	0
$191$	10.7434	0.777364	0.388682	−	0.921372i	$-0.372930\pi$
$191$	10.7434	0.777364	0.388682	+	0.921372i	$0.372930\pi$
$192$	−5.32464	−0.384272
$193$	−9.73917	−0.701041	−0.350521	−	0.936555i	$-0.613995\pi$
$193$	−9.73917	−0.701041	−0.350521	+	0.936555i	$0.613995\pi$
$194$	4.54262	0.326141
$195$	0	0
$196$	−23.3675	−1.66911
$197$	9.56404	0.681410	0.340705	−	0.940170i	$-0.389334\pi$
$197$	9.56404	0.681410	0.340705	+	0.940170i	$0.389334\pi$
$198$	−2.97858	−0.211678
$199$	5.95715	0.422291	0.211146	−	0.977455i	$-0.432281\pi$
$199$	5.95715	0.422291	0.211146	+	0.977455i	$0.432281\pi$
$200$	0	0
$201$	−9.37169	−0.661028
$202$	−25.7648	−1.81281
$203$	7.17935	0.503891
$204$	−25.9143	−1.81436
$205$	0	0
$206$	−46.6577	−3.25080
$207$	−4.17513	−0.290192
$208$	−5.21798	−0.361802
$209$	−8.35027	−0.577600
$210$	0	0
$211$	23.9143	1.64633	0.823164	−	0.567803i	$-0.192206\pi$
$211$	23.9143	1.64633	0.823164	+	0.567803i	$0.192206\pi$
$212$	−42.7005	−2.93269
$213$	−5.19656	−0.356062
$214$	46.2217	3.15965
$215$	0	0
$216$	5.46787	0.372041
$217$	−3.56404	−0.241943
$218$	20.8929	1.41504
$219$	11.9572	0.807990
$220$	0	0
$221$	6.17513	0.415385
$222$	−19.3717	−1.30014
$223$	−2.62831	−0.176004	−0.0880022	−	0.996120i	$-0.528048\pi$
$223$	−2.62831	−0.176004	−0.0880022	+	0.996120i	$0.528048\pi$
$224$	2.45692	0.164160
$225$	0	0
$226$	−19.8077	−1.31759
$227$	−15.7648	−1.04635	−0.523174	−	0.852226i	$-0.675252\pi$
$227$	−15.7648	−1.04635	−0.523174	+	0.852226i	$0.675252\pi$
$228$	29.2860	1.93951
$229$	8.74338	0.577779	0.288890	−	0.957362i	$-0.406714\pi$
$229$	8.74338	0.577779	0.288890	+	0.957362i	$0.406714\pi$
$230$	0	0
$231$	−1.43175	−0.0942022
$232$	32.8072	2.15390
$233$	2.17513	0.142498	0.0712489	−	0.997459i	$-0.477302\pi$
$233$	2.17513	0.142498	0.0712489	+	0.997459i	$0.477302\pi$
$234$	−2.48929	−0.162730
$235$	0	0
$236$	22.5426	1.46740
$237$	−1.78202	−0.115755
$238$	−18.3931	−1.19225
$239$	2.80344	0.181340	0.0906698	−	0.995881i	$-0.471099\pi$
$239$	2.80344	0.181340	0.0906698	+	0.995881i	$0.471099\pi$
$240$	0	0
$241$	−6.00000	−0.386494	−0.193247	−	0.981150i	$-0.561902\pi$
$241$	−6.00000	−0.386494	−0.193247	+	0.981150i	$0.561902\pi$
$242$	−23.8181	−1.53109
$243$	1.00000	0.0641500
$244$	52.7434	3.37655
$245$	0	0
$246$	−15.3717	−0.980063
$247$	−6.97858	−0.444036
$248$	−16.2865	−1.03419
$249$	5.37169	0.340417
$250$	0	0
$251$	−23.9143	−1.50946	−0.754729	−	0.656037i	$-0.772232\pi$
$251$	−23.9143	−1.50946	−0.754729	+	0.656037i	$0.772232\pi$
$252$	5.02142	0.316320
$253$	4.99579	0.314083
$254$	25.8715	1.62332
$255$	0	0
$256$	−32.5678	−2.03549
$257$	19.9572	1.24489	0.622447	−	0.782662i	$-0.286139\pi$
$257$	19.9572	1.24489	0.622447	+	0.782662i	$0.286139\pi$
$258$	24.7862	1.54312
$259$	−9.31163	−0.578597
$260$	0	0
$261$	6.00000	0.371391
$262$	−15.9143	−0.983189
$263$	−8.00000	−0.493301	−0.246651	−	0.969104i	$-0.579330\pi$
$263$	−8.00000	−0.493301	−0.246651	+	0.969104i	$0.579330\pi$
$264$	−6.54262	−0.402670
$265$	0	0
$266$	20.7862	1.27449
$267$	10.1751	0.622708
$268$	−39.3288	−2.40239
$269$	−2.35027	−0.143298	−0.0716492	−	0.997430i	$-0.522826\pi$
$269$	−2.35027	−0.143298	−0.0716492	+	0.997430i	$0.522826\pi$
$270$	0	0
$271$	10.9786	0.666901	0.333451	−	0.942768i	$-0.391787\pi$
$271$	10.9786	0.666901	0.333451	+	0.942768i	$0.391787\pi$
$272$	−32.2217	−1.95373
$273$	−1.19656	−0.0724190
$274$	−41.6791	−2.51793
$275$	0	0
$276$	−17.5212	−1.05465
$277$	−1.21377	−0.0729283	−0.0364642	−	0.999335i	$-0.511609\pi$
$277$	−1.21377	−0.0729283	−0.0364642	+	0.999335i	$0.511609\pi$
$278$	14.3931	0.863242
$279$	−2.97858	−0.178323
$280$	0	0
$281$	11.9572	0.713304	0.356652	−	0.934237i	$-0.383918\pi$
$281$	11.9572	0.713304	0.356652	+	0.934237i	$0.383918\pi$
$282$	2.54262	0.151411
$283$	29.8715	1.77567	0.887837	−	0.460158i	$-0.152207\pi$
$283$	29.8715	1.77567	0.887837	+	0.460158i	$0.152207\pi$
$284$	−21.8077	−1.29405
$285$	0	0
$286$	2.97858	0.176127
$287$	−7.38890	−0.436153
$288$	2.05333	0.120993
$289$	21.1323	1.24308
$290$	0	0
$291$	1.82487	0.106975
$292$	50.1789	2.93650
$293$	−0.777809	−0.0454401	−0.0227200	−	0.999742i	$-0.507233\pi$
$293$	−0.777809	−0.0454401	−0.0227200	+	0.999742i	$0.507233\pi$
$294$	−13.8610	−0.808389
$295$	0	0
$296$	−42.5510	−2.47323
$297$	−1.19656	−0.0694313
$298$	38.2008	2.21291
$299$	4.17513	0.241454
$300$	0	0
$301$	11.9143	0.686729
$302$	−21.3717	−1.22980
$303$	−10.3503	−0.594607
$304$	36.4141	2.08849
$305$	0	0
$306$	−15.3717	−0.878741
$307$	−0.760597	−0.0434095	−0.0217048	−	0.999764i	$-0.506909\pi$
$307$	−0.760597	−0.0434095	−0.0217048	+	0.999764i	$0.506909\pi$
$308$	−6.00842	−0.342362
$309$	−18.7434	−1.06627
$310$	0	0
$311$	−23.1281	−1.31147	−0.655736	−	0.754990i	$-0.727642\pi$
$311$	−23.1281	−1.31147	−0.655736	+	0.754990i	$0.727642\pi$
$312$	−5.46787	−0.309557
$313$	33.9143	1.91695	0.958475	−	0.285176i	$-0.0920522\pi$
$313$	33.9143	1.91695	0.958475	+	0.285176i	$0.0920522\pi$
$314$	−6.93573	−0.391406
$315$	0	0
$316$	−7.47835	−0.420690
$317$	−9.64973	−0.541983	−0.270991	−	0.962582i	$-0.587352\pi$
$317$	−9.64973	−0.541983	−0.270991	+	0.962582i	$0.587352\pi$
$318$	−25.3288	−1.42037
$319$	−7.17935	−0.401966
$320$	0	0
$321$	18.5682	1.03638
$322$	−12.4360	−0.693029
$323$	−43.0937	−2.39780
$324$	4.19656	0.233142
$325$	0	0
$326$	−21.8077	−1.20781
$327$	8.39312	0.464140
$328$	−33.7648	−1.86435
$329$	1.22219	0.0673816
$330$	0	0
$331$	15.3288	0.842550	0.421275	−	0.906933i	$-0.361583\pi$
$331$	15.3288	0.842550	0.421275	+	0.906933i	$0.361583\pi$
$332$	22.5426	1.23719
$333$	−7.78202	−0.426452
$334$	43.2432	2.36616
$335$	0	0
$336$	6.24361	0.340617
$337$	22.3503	1.21750	0.608748	−	0.793363i	$-0.291672\pi$
$337$	22.3503	1.21750	0.608748	+	0.793363i	$0.291672\pi$
$338$	2.48929	0.135399
$339$	−7.95715	−0.432173
$340$	0	0
$341$	3.56404	0.193004
$342$	17.3717	0.939354
$343$	−15.0386	−0.812010
$344$	54.4444	2.93544
$345$	0	0
$346$	19.8077	1.06487
$347$	5.78202	0.310395	0.155198	−	0.987883i	$-0.450399\pi$
$347$	5.78202	0.310395	0.155198	+	0.987883i	$0.450399\pi$
$348$	25.1793	1.34975
$349$	−27.5212	−1.47318	−0.736588	−	0.676342i	$-0.763564\pi$
$349$	−27.5212	−1.47318	−0.736588	+	0.676342i	$0.763564\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	−2.45692	−0.130955
$353$	28.7434	1.52986	0.764928	−	0.644116i	$-0.222775\pi$
$353$	28.7434	1.52986	0.764928	+	0.644116i	$0.222775\pi$
$354$	13.3717	0.710697
$355$	0	0
$356$	42.7005	2.26312
$357$	−7.38890	−0.391062
$358$	−38.7434	−2.04765
$359$	−12.5855	−0.664235	−0.332118	−	0.943238i	$-0.607763\pi$
$359$	−12.5855	−0.664235	−0.332118	+	0.943238i	$0.607763\pi$
$360$	0	0
$361$	29.7005	1.56319
$362$	39.2860	2.06483
$363$	−9.56825	−0.502203
$364$	−5.02142	−0.263194
$365$	0	0
$366$	31.2860	1.63535
$367$	27.9143	1.45712	0.728558	−	0.684985i	$-0.240191\pi$
$367$	27.9143	1.45712	0.728558	+	0.684985i	$0.240191\pi$
$368$	−21.7858	−1.13566
$369$	−6.17513	−0.321465
$370$	0	0
$371$	−12.1751	−0.632102
$372$	−12.4998	−0.648083
$373$	2.35027	0.121692	0.0608462	−	0.998147i	$-0.480620\pi$
$373$	2.35027	0.121692	0.0608462	+	0.998147i	$0.480620\pi$
$374$	18.3931	0.951085
$375$	0	0
$376$	5.58500	0.288025
$377$	−6.00000	−0.309016
$378$	2.97858	0.153201
$379$	24.5510	1.26110	0.630551	−	0.776148i	$-0.282829\pi$
$379$	24.5510	1.26110	0.630551	+	0.776148i	$0.282829\pi$
$380$	0	0
$381$	10.3931	0.532455
$382$	26.7434	1.36831
$383$	−5.80765	−0.296757	−0.148379	−	0.988931i	$-0.547405\pi$
$383$	−5.80765	−0.296757	−0.148379	+	0.988931i	$0.547405\pi$
$384$	−17.3612	−0.885961
$385$	0	0
$386$	−24.2436	−1.23397
$387$	9.95715	0.506151
$388$	7.65815	0.388784
$389$	13.6497	0.692069	0.346034	−	0.938222i	$-0.387528\pi$
$389$	13.6497	0.692069	0.346034	+	0.938222i	$0.387528\pi$
$390$	0	0
$391$	25.7820	1.30385
$392$	−30.4464	−1.53778
$393$	−6.39312	−0.322490
$394$	23.8077	1.19941
$395$	0	0
$396$	−5.02142	−0.252336
$397$	12.1323	0.608902	0.304451	−	0.952528i	$-0.401527\pi$
$397$	12.1323	0.608902	0.304451	+	0.952528i	$0.401527\pi$
$398$	14.8291	0.743314
$399$	8.35027	0.418036
$400$	0	0
$401$	−37.4439	−1.86986	−0.934930	−	0.354832i	$-0.884538\pi$
$401$	−37.4439	−1.86986	−0.934930	+	0.354832i	$0.884538\pi$
$402$	−23.3288	−1.16354
$403$	2.97858	0.148373
$404$	−43.4355	−2.16100
$405$	0	0
$406$	17.8715	0.886946
$407$	9.31163	0.461561
$408$	−33.7648	−1.67161
$409$	−14.0000	−0.692255	−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000	−0.692255	−0.346128	+	0.938187i	$0.612504\pi$
$410$	0	0
$411$	−16.7434	−0.825890
$412$	−78.6577	−3.87519
$413$	6.42754	0.316279
$414$	−10.3931	−0.510794
$415$	0	0
$416$	−2.05333	−0.100673
$417$	5.78202	0.283147
$418$	−20.7862	−1.01669
$419$	3.17935	0.155321	0.0776606	−	0.996980i	$-0.475255\pi$
$419$	3.17935	0.155321	0.0776606	+	0.996980i	$0.475255\pi$
$420$	0	0
$421$	−16.3074	−0.794775	−0.397388	−	0.917651i	$-0.630083\pi$
$421$	−16.3074	−0.794775	−0.397388	+	0.917651i	$0.630083\pi$
$422$	59.5296	2.89786
$423$	1.02142	0.0496633
$424$	−55.6363	−2.70194
$425$	0	0
$426$	−12.9357	−0.626738
$427$	15.0386	0.727771
$428$	77.9227	3.76654
$429$	1.19656	0.0577703
$430$	0	0
$431$	4.58546	0.220874	0.110437	−	0.993883i	$-0.464775\pi$
$431$	4.58546	0.220874	0.110437	+	0.993883i	$0.464775\pi$
$432$	5.21798	0.251050
$433$	38.3503	1.84300	0.921498	−	0.388383i	$-0.126966\pi$
$433$	38.3503	1.84300	0.921498	+	0.388383i	$0.126966\pi$
$434$	−8.87192	−0.425866
$435$	0	0
$436$	35.2222	1.68684
$437$	−29.1365	−1.39379
$438$	29.7648	1.42222
$439$	7.73917	0.369371	0.184685	−	0.982798i	$-0.440873\pi$
$439$	7.73917	0.369371	0.184685	+	0.982798i	$0.440873\pi$
$440$	0	0
$441$	−5.56825	−0.265155
$442$	15.3717	0.731157
$443$	−34.9185	−1.65903	−0.829514	−	0.558485i	$-0.811383\pi$
$443$	−34.9185	−1.65903	−0.829514	+	0.558485i	$0.811383\pi$
$444$	−32.6577	−1.54987
$445$	0	0
$446$	−6.54262	−0.309802
$447$	15.3461	0.725844
$448$	−6.37123	−0.301012
$449$	−6.17513	−0.291423	−0.145711	−	0.989327i	$-0.546547\pi$
$449$	−6.17513	−0.291423	−0.145711	+	0.989327i	$0.546547\pi$
$450$	0	0
$451$	7.38890	0.347930
$452$	−33.3927	−1.57066
$453$	−8.58546	−0.403380
$454$	−39.2432	−1.84177
$455$	0	0
$456$	38.1579	1.78691
$457$	−1.38890	−0.0649702	−0.0324851	−	0.999472i	$-0.510342\pi$
$457$	−1.38890	−0.0649702	−0.0324851	+	0.999472i	$0.510342\pi$
$458$	21.7648	1.01700
$459$	−6.17513	−0.288231
$460$	0	0
$461$	28.4826	1.32657	0.663283	−	0.748369i	$-0.269163\pi$
$461$	28.4826	1.32657	0.663283	+	0.748369i	$0.269163\pi$
$462$	−3.56404	−0.165814
$463$	−16.3759	−0.761053	−0.380526	−	0.924770i	$-0.624257\pi$
$463$	−16.3759	−0.761053	−0.380526	+	0.924770i	$0.624257\pi$
$464$	31.3079	1.45343
$465$	0	0
$466$	5.41454	0.250824
$467$	−25.7476	−1.19146	−0.595728	−	0.803186i	$-0.703136\pi$
$467$	−25.7476	−1.19146	−0.595728	+	0.803186i	$0.703136\pi$
$468$	−4.19656	−0.193986
$469$	−11.2138	−0.517804
$470$	0	0
$471$	−2.78623	−0.128383
$472$	29.3717	1.35194
$473$	−11.9143	−0.547820
$474$	−4.43596	−0.203750
$475$	0	0
$476$	−31.0080	−1.42125
$477$	−10.1751	−0.465887
$478$	6.97858	0.319193
$479$	−7.58967	−0.346781	−0.173391	−	0.984853i	$-0.555472\pi$
$479$	−7.58967	−0.346781	−0.173391	+	0.984853i	$0.555472\pi$
$480$	0	0
$481$	7.78202	0.354830
$482$	−14.9357	−0.680304
$483$	−4.99579	−0.227316
$484$	−40.1537	−1.82517
$485$	0	0
$486$	2.48929	0.112916
$487$	−4.41033	−0.199851	−0.0999255	−	0.994995i	$-0.531860\pi$
$487$	−4.41033	−0.199851	−0.0999255	+	0.994995i	$0.531860\pi$
$488$	68.7215	3.11088
$489$	−8.76060	−0.396168
$490$	0	0
$491$	−0.0856914	−0.00386720	−0.00193360	−	0.999998i	$-0.500615\pi$
$491$	−0.0856914	−0.00386720	−0.00193360	+	0.999998i	$0.500615\pi$
$492$	−25.9143	−1.16831
$493$	−37.0508	−1.66868
$494$	−17.3717	−0.781589
$495$	0	0
$496$	−15.5422	−0.697863
$497$	−6.21798	−0.278915
$498$	13.3717	0.599200
$499$	−17.7220	−0.793344	−0.396672	−	0.917960i	$-0.629835\pi$
$499$	−17.7220	−0.793344	−0.396672	+	0.917960i	$0.629835\pi$
$500$	0	0
$501$	17.3717	0.776110
$502$	−59.5296	−2.65694
$503$	8.70054	0.387938	0.193969	−	0.981008i	$-0.437864\pi$
$503$	8.70054	0.387938	0.193969	+	0.981008i	$0.437864\pi$
$504$	6.54262	0.291431
$505$	0	0
$506$	12.4360	0.552846
$507$	1.00000	0.0444116
$508$	43.6153	1.93512
$509$	−33.3545	−1.47841	−0.739206	−	0.673480i	$-0.764799\pi$
$509$	−33.3545	−1.47841	−0.739206	+	0.673480i	$0.764799\pi$
$510$	0	0
$511$	14.3074	0.632923
$512$	−46.3482	−2.04832
$513$	6.97858	0.308112
$514$	49.6791	2.19125
$515$	0	0
$516$	41.7858	1.83952
$517$	−1.22219	−0.0537519
$518$	−23.1793	−1.01844
$519$	7.95715	0.349280
$520$	0	0
$521$	18.7005	0.819285	0.409643	−	0.912246i	$-0.365653\pi$
$521$	18.7005	0.819285	0.409643	+	0.912246i	$0.365653\pi$
$522$	14.9357	0.653719
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	−26.8291	−1.17203
$525$	0	0
$526$	−19.9143	−0.868305
$527$	18.3931	0.801217
$528$	−6.24361	−0.271718
$529$	−5.56825	−0.242098
$530$	0	0
$531$	5.37169	0.233112
$532$	35.0424	1.51928
$533$	6.17513	0.267475
$534$	25.3288	1.09609
$535$	0	0
$536$	−51.2432	−2.21337
$537$	−15.5640	−0.671638
$538$	−5.85050	−0.252233
$539$	6.66273	0.286984
$540$	0	0
$541$	−41.5296	−1.78550	−0.892749	−	0.450555i	$-0.851226\pi$
$541$	−41.5296	−1.78550	−0.892749	+	0.450555i	$0.851226\pi$
$542$	27.3288	1.17387
$543$	15.7820	0.677271
$544$	−12.6796	−0.543632
$545$	0	0
$546$	−2.97858	−0.127471
$547$	7.91431	0.338391	0.169196	−	0.985582i	$-0.445883\pi$
$547$	7.91431	0.338391	0.169196	+	0.985582i	$0.445883\pi$
$548$	−70.2646	−3.00155
$549$	12.5682	0.536400
$550$	0	0
$551$	41.8715	1.78378
$552$	−22.8291	−0.971670
$553$	−2.13229	−0.0906742
$554$	−3.02142	−0.128368
$555$	0	0
$556$	24.2646	1.02905
$557$	−42.7005	−1.80928	−0.904640	−	0.426177i	$-0.859860\pi$
$557$	−42.7005	−1.80928	−0.904640	+	0.426177i	$0.859860\pi$
$558$	−7.41454	−0.313882
$559$	−9.95715	−0.421143
$560$	0	0
$561$	7.38890	0.311960
$562$	29.7648	1.25555
$563$	−1.04706	−0.0441282	−0.0220641	−	0.999757i	$-0.507024\pi$
$563$	−1.04706	−0.0441282	−0.0220641	+	0.999757i	$0.507024\pi$
$564$	4.28646	0.180493
$565$	0	0
$566$	74.3587	3.12553
$567$	1.19656	0.0502507
$568$	−28.4141	−1.19223
$569$	16.7778	0.703362	0.351681	−	0.936120i	$-0.385610\pi$
$569$	16.7778	0.703362	0.351681	+	0.936120i	$0.385610\pi$
$570$	0	0
$571$	−20.6111	−0.862548	−0.431274	−	0.902221i	$-0.641936\pi$
$571$	−20.6111	−0.862548	−0.431274	+	0.902221i	$0.641936\pi$
$572$	5.02142	0.209956
$573$	10.7434	0.448811
$574$	−18.3931	−0.767714
$575$	0	0
$576$	−5.32464	−0.221860
$577$	−1.38890	−0.0578208	−0.0289104	−	0.999582i	$-0.509204\pi$
$577$	−1.38890	−0.0578208	−0.0289104	+	0.999582i	$0.509204\pi$
$578$	52.6044	2.18805
$579$	−9.73917	−0.404746
$580$	0	0
$581$	6.42754	0.266659
$582$	4.54262	0.188298
$583$	12.1751	0.504243
$584$	65.3801	2.70545
$585$	0	0
$586$	−1.93619	−0.0799833
$587$	0.935731	0.0386218	0.0193109	−	0.999814i	$-0.493853\pi$
$587$	0.935731	0.0386218	0.0193109	+	0.999814i	$0.493853\pi$
$588$	−23.3675	−0.963659
$589$	−20.7862	−0.856482
$590$	0	0
$591$	9.56404	0.393412
$592$	−40.6064	−1.66891
$593$	0.478807	0.0196622	0.00983112	−	0.999952i	$-0.496871\pi$
$593$	0.478807	0.0196622	0.00983112	+	0.999952i	$0.496871\pi$
$594$	−2.97858	−0.122213
$595$	0	0
$596$	64.4006	2.63795
$597$	5.95715	0.243810
$598$	10.3931	0.425006
$599$	29.0852	1.18839	0.594195	−	0.804321i	$-0.297471\pi$
$599$	29.0852	1.18839	0.594195	+	0.804321i	$0.297471\pi$
$600$	0	0
$601$	11.4318	0.466311	0.233155	−	0.972439i	$-0.425095\pi$
$601$	11.4318	0.466311	0.233155	+	0.972439i	$0.425095\pi$
$602$	29.6582	1.20878
$603$	−9.37169	−0.381645
$604$	−36.0294	−1.46601
$605$	0	0
$606$	−25.7648	−1.04662
$607$	−27.9143	−1.13301	−0.566503	−	0.824059i	$-0.691704\pi$
$607$	−27.9143	−1.13301	−0.566503	+	0.824059i	$0.691704\pi$
$608$	14.3293	0.581130
$609$	7.17935	0.290922
$610$	0	0
$611$	−1.02142	−0.0413223
$612$	−25.9143	−1.04752
$613$	4.65394	0.187971	0.0939855	−	0.995574i	$-0.470039\pi$
$613$	4.65394	0.187971	0.0939855	+	0.995574i	$0.470039\pi$
$614$	−1.89334	−0.0764092
$615$	0	0
$616$	−7.82862	−0.315424
$617$	15.9572	0.642411	0.321205	−	0.947010i	$-0.395912\pi$
$617$	15.9572	0.642411	0.321205	+	0.947010i	$0.395912\pi$
$618$	−46.6577	−1.87685
$619$	1.02142	0.0410545	0.0205272	−	0.999789i	$-0.493466\pi$
$619$	1.02142	0.0410545	0.0205272	+	0.999789i	$0.493466\pi$
$620$	0	0
$621$	−4.17513	−0.167542
$622$	−57.5725	−2.30845
$623$	12.1751	0.487786
$624$	−5.21798	−0.208886
$625$	0	0
$626$	84.4225	3.37420
$627$	−8.35027	−0.333478
$628$	−11.6926	−0.466585
$629$	48.0550	1.91608
$630$	0	0
$631$	−20.4998	−0.816083	−0.408041	−	0.912963i	$-0.633788\pi$
$631$	−20.4998	−0.816083	−0.408041	+	0.912963i	$0.633788\pi$
$632$	−9.74384	−0.387589
$633$	23.9143	0.950508
$634$	−24.0210	−0.953994
$635$	0	0
$636$	−42.7005	−1.69319
$637$	5.56825	0.220622
$638$	−17.8715	−0.707538
$639$	−5.19656	−0.205573
$640$	0	0
$641$	38.2646	1.51136	0.755680	−	0.654941i	$-0.227307\pi$
$641$	38.2646	1.51136	0.755680	+	0.654941i	$0.227307\pi$
$642$	46.2217	1.82423
$643$	33.1109	1.30577	0.652883	−	0.757459i	$-0.273560\pi$
$643$	33.1109	1.30577	0.652883	+	0.757459i	$0.273560\pi$
$644$	−20.9651	−0.826141
$645$	0	0
$646$	−107.273	−4.22058
$647$	16.9614	0.666820	0.333410	−	0.942782i	$-0.391801\pi$
$647$	16.9614	0.666820	0.333410	+	0.942782i	$0.391801\pi$
$648$	5.46787	0.214798
$649$	−6.42754	−0.252303
$650$	0	0
$651$	−3.56404	−0.139686
$652$	−36.7643	−1.43980
$653$	19.1709	0.750216	0.375108	−	0.926981i	$-0.377606\pi$
$653$	19.1709	0.750216	0.375108	+	0.926981i	$0.377606\pi$
$654$	20.8929	0.816976
$655$	0	0
$656$	−32.2217	−1.25805
$657$	11.9572	0.466493
$658$	3.04239	0.118605
$659$	37.8715	1.47526	0.737631	−	0.675204i	$-0.235944\pi$
$659$	37.8715	1.47526	0.737631	+	0.675204i	$0.235944\pi$
$660$	0	0
$661$	24.3931	0.948782	0.474391	−	0.880314i	$-0.342668\pi$
$661$	24.3931	0.948782	0.474391	+	0.880314i	$0.342668\pi$
$662$	38.1579	1.48305
$663$	6.17513	0.239822
$664$	29.3717	1.13984
$665$	0	0
$666$	−19.3717	−0.750638
$667$	−25.0508	−0.969971
$668$	72.9013	2.82064
$669$	−2.62831	−0.101616
$670$	0	0
$671$	−15.0386	−0.580560
$672$	2.45692	0.0947779
$673$	21.1281	0.814428	0.407214	−	0.913333i	$-0.366500\pi$
$673$	21.1281	0.814428	0.407214	+	0.913333i	$0.366500\pi$
$674$	55.6363	2.14303
$675$	0	0
$676$	4.19656	0.161406
$677$	15.3973	0.591767	0.295884	−	0.955224i	$-0.404386\pi$
$677$	15.3973	0.591767	0.295884	+	0.955224i	$0.404386\pi$
$678$	−19.8077	−0.760708
$679$	2.18356	0.0837972
$680$	0	0
$681$	−15.7648	−0.604109
$682$	8.87192	0.339723
$683$	−30.0722	−1.15068	−0.575341	−	0.817914i	$-0.695131\pi$
$683$	−30.0722	−1.15068	−0.575341	+	0.817914i	$0.695131\pi$
$684$	29.2860	1.11978
$685$	0	0
$686$	−37.4355	−1.42929
$687$	8.74338	0.333581
$688$	51.9562	1.98081
$689$	10.1751	0.387642
$690$	0	0
$691$	−8.14950	−0.310022	−0.155011	−	0.987913i	$-0.549541\pi$
$691$	−8.14950	−0.310022	−0.155011	+	0.987913i	$0.549541\pi$
$692$	33.3927	1.26940
$693$	−1.43175	−0.0543877
$694$	14.3931	0.546355
$695$	0	0
$696$	32.8072	1.24355
$697$	38.1323	1.44436
$698$	−68.5082	−2.59307
$699$	2.17513	0.0822712
$700$	0	0
$701$	−28.6921	−1.08369	−0.541843	−	0.840480i	$-0.682273\pi$
$701$	−28.6921	−1.08369	−0.541843	+	0.840480i	$0.682273\pi$
$702$	−2.48929	−0.0939521
$703$	−54.3074	−2.04824
$704$	6.37123	0.240125
$705$	0	0
$706$	71.5506	2.69284
$707$	−12.3847	−0.465774
$708$	22.5426	0.847203
$709$	12.3074	0.462215	0.231108	−	0.972928i	$-0.425765\pi$
$709$	12.3074	0.462215	0.231108	+	0.972928i	$0.425765\pi$
$710$	0	0
$711$	−1.78202	−0.0668310
$712$	55.6363	2.08506
$713$	12.4360	0.465730
$714$	−18.3931	−0.688345
$715$	0	0
$716$	−65.3154	−2.44095
$717$	2.80344	0.104696
$718$	−31.3288	−1.16918
$719$	−28.7862	−1.07355	−0.536773	−	0.843727i	$-0.680357\pi$
$719$	−28.7862	−1.07355	−0.536773	+	0.843727i	$0.680357\pi$
$720$	0	0
$721$	−22.4275	−0.835245
$722$	73.9332	2.75151
$723$	−6.00000	−0.223142
$724$	66.2302	2.46142
$725$	0	0
$726$	−23.8181	−0.883974
$727$	−34.3931	−1.27557	−0.637785	−	0.770214i	$-0.720149\pi$
$727$	−34.3931	−1.27557	−0.637785	+	0.770214i	$0.720149\pi$
$728$	−6.54262	−0.242485
$729$	1.00000	0.0370370
$730$	0	0
$731$	−61.4868	−2.27417
$732$	52.7434	1.94945
$733$	29.0042	1.07129	0.535647	−	0.844442i	$-0.320068\pi$
$733$	29.0042	1.07129	0.535647	+	0.844442i	$0.320068\pi$
$734$	69.4868	2.56480
$735$	0	0
$736$	−8.57292	−0.316002
$737$	11.2138	0.413065
$738$	−15.3717	−0.565840
$739$	−6.27804	−0.230941	−0.115471	−	0.993311i	$-0.536838\pi$
$739$	−6.27804	−0.230941	−0.115471	+	0.993311i	$0.536838\pi$
$740$	0	0
$741$	−6.97858	−0.256364
$742$	−30.3074	−1.11262
$743$	−12.2352	−0.448866	−0.224433	−	0.974490i	$-0.572053\pi$
$743$	−12.2352	−0.448866	−0.224433	+	0.974490i	$0.572053\pi$
$744$	−16.2865	−0.597091
$745$	0	0
$746$	5.85050	0.214202
$747$	5.37169	0.196540
$748$	31.0080	1.13376
$749$	22.2180	0.811827
$750$	0	0
$751$	−28.8757	−1.05369	−0.526844	−	0.849962i	$-0.676625\pi$
$751$	−28.8757	−1.05369	−0.526844	+	0.849962i	$0.676625\pi$
$752$	5.32976	0.194357
$753$	−23.9143	−0.871486
$754$	−14.9357	−0.543927
$755$	0	0
$756$	5.02142	0.182627
$757$	−30.3503	−1.10310	−0.551550	−	0.834142i	$-0.685963\pi$
$757$	−30.3503	−1.10310	−0.551550	+	0.834142i	$0.685963\pi$
$758$	61.1146	2.21978
$759$	4.99579	0.181336
$760$	0	0
$761$	−27.1709	−0.984945	−0.492473	−	0.870328i	$-0.663907\pi$
$761$	−27.1709	−0.984945	−0.492473	+	0.870328i	$0.663907\pi$
$762$	25.8715	0.937224
$763$	10.0428	0.363575
$764$	45.0852	1.63113
$765$	0	0
$766$	−14.4569	−0.522350
$767$	−5.37169	−0.193961
$768$	−32.5678	−1.17519
$769$	−38.3503	−1.38295	−0.691473	−	0.722402i	$-0.743038\pi$
$769$	−38.3503	−1.38295	−0.691473	+	0.722402i	$0.743038\pi$
$770$	0	0
$771$	19.9572	0.718739
$772$	−40.8710	−1.47098
$773$	50.2646	1.80789	0.903946	−	0.427647i	$-0.140658\pi$
$773$	50.2646	1.80789	0.903946	+	0.427647i	$0.140658\pi$
$774$	24.7862	0.890923
$775$	0	0
$776$	9.97812	0.358194
$777$	−9.31163	−0.334053
$778$	33.9781	1.21817
$779$	−43.0937	−1.54399
$780$	0	0
$781$	6.21798	0.222497
$782$	64.1789	2.29503
$783$	6.00000	0.214423
$784$	−29.0550	−1.03768
$785$	0	0
$786$	−15.9143	−0.567645
$787$	13.2860	0.473595	0.236797	−	0.971559i	$-0.423902\pi$
$787$	13.2860	0.473595	0.236797	+	0.971559i	$0.423902\pi$
$788$	40.1360	1.42979
$789$	−8.00000	−0.284808
$790$	0	0
$791$	−9.52119	−0.338535
$792$	−6.54262	−0.232482
$793$	−12.5682	−0.446312
$794$	30.2008	1.07179
$795$	0	0
$796$	24.9995	0.886085
$797$	−9.82487	−0.348015	−0.174007	−	0.984744i	$-0.555672\pi$
$797$	−9.82487	−0.348015	−0.174007	+	0.984744i	$0.555672\pi$
$798$	20.7862	0.735825
$799$	−6.30742	−0.223141
$800$	0	0
$801$	10.1751	0.359521
$802$	−93.2087	−3.29131
$803$	−14.3074	−0.504898
$804$	−39.3288	−1.38702
$805$	0	0
$806$	7.41454	0.261166
$807$	−2.35027	−0.0827334
$808$	−56.5939	−1.99097
$809$	−9.91431	−0.348569	−0.174284	−	0.984695i	$-0.555761\pi$
$809$	−9.91431	−0.348569	−0.174284	+	0.984695i	$0.555761\pi$
$810$	0	0
$811$	−36.5855	−1.28469	−0.642345	−	0.766416i	$-0.722038\pi$
$811$	−36.5855	−1.28469	−0.642345	+	0.766416i	$0.722038\pi$
$812$	30.1285	1.05730
$813$	10.9786	0.385036
$814$	23.1793	0.812436
$815$	0	0
$816$	−32.2217	−1.12799
$817$	69.4868	2.43103
$818$	−34.8500	−1.21850
$819$	−1.19656	−0.0418111
$820$	0	0
$821$	−34.4741	−1.20316	−0.601578	−	0.798814i	$-0.705461\pi$
$821$	−34.4741	−1.20316	−0.601578	+	0.798814i	$0.705461\pi$
$822$	−41.6791	−1.45373
$823$	−13.2566	−0.462097	−0.231048	−	0.972942i	$-0.574216\pi$
$823$	−13.2566	−0.462097	−0.231048	+	0.972942i	$0.574216\pi$
$824$	−102.486	−3.57028
$825$	0	0
$826$	16.0000	0.556711
$827$	−28.1495	−0.978854	−0.489427	−	0.872044i	$-0.662794\pi$
$827$	−28.1495	−0.978854	−0.489427	+	0.872044i	$0.662794\pi$
$828$	−17.5212	−0.608904
$829$	16.3418	0.567576	0.283788	−	0.958887i	$-0.408409\pi$
$829$	16.3418	0.567576	0.283788	+	0.958887i	$0.408409\pi$
$830$	0	0
$831$	−1.21377	−0.0421052
$832$	5.32464	0.184599
$833$	34.3847	1.19136
$834$	14.3931	0.498393
$835$	0	0
$836$	−35.0424	−1.21197
$837$	−2.97858	−0.102955
$838$	7.91431	0.273395
$839$	−30.3675	−1.04840	−0.524201	−	0.851595i	$-0.675636\pi$
$839$	−30.3675	−1.04840	−0.524201	+	0.851595i	$0.675636\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−40.5939	−1.39896
$843$	11.9572	0.411826
$844$	100.358	3.45446
$845$	0	0
$846$	2.54262	0.0874169
$847$	−11.4490	−0.393391
$848$	−53.0937	−1.82324
$849$	29.8715	1.02519
$850$	0	0
$851$	32.4910	1.11378
$852$	−21.8077	−0.747118
$853$	42.1407	1.44287	0.721435	−	0.692482i	$-0.243483\pi$
$853$	42.1407	1.44287	0.721435	+	0.692482i	$0.243483\pi$
$854$	37.4355	1.28102
$855$	0	0
$856$	101.529	3.47018
$857$	2.17513	0.0743012	0.0371506	−	0.999310i	$-0.488172\pi$
$857$	2.17513	0.0743012	0.0371506	+	0.999310i	$0.488172\pi$
$858$	2.97858	0.101687
$859$	18.5682	0.633541	0.316770	−	0.948502i	$-0.397402\pi$
$859$	18.5682	0.633541	0.316770	+	0.948502i	$0.397402\pi$
$860$	0	0
$861$	−7.38890	−0.251813
$862$	11.4145	0.388781
$863$	−33.7220	−1.14791	−0.573954	−	0.818887i	$-0.694591\pi$
$863$	−33.7220	−1.14791	−0.573954	+	0.818887i	$0.694591\pi$
$864$	2.05333	0.0698556
$865$	0	0
$866$	95.4649	3.24403
$867$	21.1323	0.717690
$868$	−14.9567	−0.507663
$869$	2.13229	0.0723330
$870$	0	0
$871$	9.37169	0.317548
$872$	45.8924	1.55411
$873$	1.82487	0.0617623
$874$	−72.5292	−2.45334
$875$	0	0
$876$	50.1789	1.69539
$877$	−43.4868	−1.46844	−0.734222	−	0.678910i	$-0.762453\pi$
$877$	−43.4868	−1.46844	−0.734222	+	0.678910i	$0.762453\pi$
$878$	19.2650	0.650164
$879$	−0.777809	−0.0262348
$880$	0	0
$881$	26.7005	0.899564	0.449782	−	0.893138i	$-0.351502\pi$
$881$	26.7005	0.899564	0.449782	+	0.893138i	$0.351502\pi$
$882$	−13.8610	−0.466724
$883$	−20.2990	−0.683116	−0.341558	−	0.939861i	$-0.610955\pi$
$883$	−20.2990	−0.683116	−0.341558	+	0.939861i	$0.610955\pi$
$884$	25.9143	0.871593
$885$	0	0
$886$	−86.9223	−2.92021
$887$	−36.0550	−1.21061	−0.605305	−	0.795994i	$-0.706949\pi$
$887$	−36.0550	−1.21061	−0.605305	+	0.795994i	$0.706949\pi$
$888$	−42.5510	−1.42792
$889$	12.4360	0.417089
$890$	0	0
$891$	−1.19656	−0.0400862
$892$	−11.0298	−0.369307
$893$	7.12808	0.238532
$894$	38.2008	1.27762
$895$	0	0
$896$	−20.7737	−0.694000
$897$	4.17513	0.139404
$898$	−15.3717	−0.512960
$899$	−17.8715	−0.596047
$900$	0	0
$901$	62.8328	2.09326
$902$	18.3931	0.612424
$903$	11.9143	0.396483
$904$	−43.5087	−1.44708
$905$	0	0
$906$	−21.3717	−0.710027
$907$	7.26504	0.241232	0.120616	−	0.992699i	$-0.461513\pi$
$907$	7.26504	0.241232	0.120616	+	0.992699i	$0.461513\pi$
$908$	−66.1579	−2.19553
$909$	−10.3503	−0.343297
$910$	0	0
$911$	−6.65769	−0.220579	−0.110290	−	0.993899i	$-0.535178\pi$
$911$	−6.65769	−0.220579	−0.110290	+	0.993899i	$0.535178\pi$
$912$	36.4141	1.20579
$913$	−6.42754	−0.212721
$914$	−3.45738	−0.114360
$915$	0	0
$916$	36.6921	1.21234
$917$	−7.64973	−0.252616
$918$	−15.3717	−0.507341
$919$	−27.1831	−0.896688	−0.448344	−	0.893861i	$-0.647986\pi$
$919$	−27.1831	−0.896688	−0.448344	+	0.893861i	$0.647986\pi$
$920$	0	0
$921$	−0.760597	−0.0250625
$922$	70.9013	2.33501
$923$	5.19656	0.171047
$924$	−6.00842	−0.197663
$925$	0	0
$926$	−40.7643	−1.33960
$927$	−18.7434	−0.615614
$928$	12.3200	0.404423
$929$	−15.3973	−0.505170	−0.252585	−	0.967575i	$-0.581281\pi$
$929$	−15.3973	−0.505170	−0.252585	+	0.967575i	$0.581281\pi$
$930$	0	0
$931$	−38.8585	−1.27353
$932$	9.12808	0.299000
$933$	−23.1281	−0.757179
$934$	−64.0932	−2.09719
$935$	0	0
$936$	−5.46787	−0.178723
$937$	−1.12808	−0.0368527	−0.0184264	−	0.999830i	$-0.505866\pi$
$937$	−1.12808	−0.0368527	−0.0184264	+	0.999830i	$0.505866\pi$
$938$	−27.9143	−0.911434
$939$	33.9143	1.10675
$940$	0	0
$941$	−30.1407	−0.982559	−0.491280	−	0.871002i	$-0.663471\pi$
$941$	−30.1407	−0.982559	−0.491280	+	0.871002i	$0.663471\pi$
$942$	−6.93573	−0.225978
$943$	25.7820	0.839578
$944$	28.0294	0.912279
$945$	0	0
$946$	−29.6582	−0.964270
$947$	20.0294	0.650868	0.325434	−	0.945565i	$-0.394490\pi$
$947$	20.0294	0.650868	0.325434	+	0.945565i	$0.394490\pi$
$948$	−7.47835	−0.242885
$949$	−11.9572	−0.388146
$950$	0	0
$951$	−9.64973	−0.312914
$952$	−40.4015	−1.30942
$953$	43.2259	1.40023	0.700113	−	0.714032i	$-0.253133\pi$
$953$	43.2259	1.40023	0.700113	+	0.714032i	$0.253133\pi$
$954$	−25.3288	−0.820052
$955$	0	0
$956$	11.7648	0.380501
$957$	−7.17935	−0.232075
$958$	−18.8929	−0.610401
$959$	−20.0344	−0.646945
$960$	0	0
$961$	−22.1281	−0.713809
$962$	19.3717	0.624568
$963$	18.5682	0.598353
$964$	−25.1793	−0.810972
$965$	0	0
$966$	−12.4360	−0.400120
$967$	−57.6875	−1.85511	−0.927553	−	0.373691i	$-0.878092\pi$
$967$	−57.6875	−1.85511	−0.927553	+	0.373691i	$0.878092\pi$
$968$	−52.3179	−1.68156
$969$	−43.0937	−1.38437
$970$	0	0
$971$	−19.5296	−0.626735	−0.313368	−	0.949632i	$-0.601457\pi$
$971$	−19.5296	−0.626735	−0.313368	+	0.949632i	$0.601457\pi$
$972$	4.19656	0.134605
$973$	6.91852	0.221798
$974$	−10.9786	−0.351776
$975$	0	0
$976$	65.5809	2.09919
$977$	40.3074	1.28955	0.644774	−	0.764373i	$-0.276951\pi$
$977$	40.3074	1.28955	0.644774	+	0.764373i	$0.276951\pi$
$978$	−21.8077	−0.697332
$979$	−12.1751	−0.389119
$980$	0	0
$981$	8.39312	0.267972
$982$	−0.213311	−0.00680702
$983$	−32.2008	−1.02705	−0.513523	−	0.858076i	$-0.671660\pi$
$983$	−32.2008	−1.02705	−0.513523	+	0.858076i	$0.671660\pi$
$984$	−33.7648	−1.07638
$985$	0	0
$986$	−92.2302	−2.93721
$987$	1.22219	0.0389028
$988$	−29.2860	−0.931712
$989$	−41.5725	−1.32193
$990$	0	0
$991$	26.4826	0.841246	0.420623	−	0.907235i	$-0.361811\pi$
$991$	26.4826	0.841246	0.420623	+	0.907235i	$0.361811\pi$
$992$	−6.11599	−0.194183
$993$	15.3288	0.486446
$994$	−15.4783	−0.490943
$995$	0	0
$996$	22.5426	0.714290
$997$	−35.1365	−1.11278	−0.556392	−	0.830920i	$-0.687815\pi$
$997$	−35.1365	−1.11278	−0.556392	+	0.830920i	$0.687815\pi$
$998$	−44.1151	−1.39644
$999$	−7.78202	−0.246212

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.a.o.1.3		3
3.2	odd	2		2925.2.a.bh.1.1		3
5.2	odd	4		975.2.c.i.274.5		6
5.3	odd	4		975.2.c.i.274.2		6
5.4	even	2		195.2.a.e.1.1	✓	3
15.2	even	4		2925.2.c.w.2224.2		6
15.8	even	4		2925.2.c.w.2224.5		6
15.14	odd	2		585.2.a.n.1.3		3
20.19	odd	2		3120.2.a.bj.1.2		3
35.34	odd	2		9555.2.a.bq.1.1		3
60.59	even	2		9360.2.a.dd.1.2		3
65.64	even	2		2535.2.a.bc.1.3		3
195.194	odd	2		7605.2.a.bx.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.a.e.1.1	✓	3	5.4	even	2
585.2.a.n.1.3		3	15.14	odd	2
975.2.a.o.1.3		3	1.1	even	1	trivial
975.2.c.i.274.2		6	5.3	odd	4
975.2.c.i.274.5		6	5.2	odd	4
2535.2.a.bc.1.3		3	65.64	even	2
2925.2.a.bh.1.1		3	3.2	odd	2
2925.2.c.w.2224.2		6	15.2	even	4
2925.2.c.w.2224.5		6	15.8	even	4
3120.2.a.bj.1.2		3	20.19	odd	2
7605.2.a.bx.1.1		3	195.194	odd	2
9360.2.a.dd.1.2		3	60.59	even	2
9555.2.a.bq.1.1		3	35.34	odd	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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.a (trivial)

\(f(q)\)	\(=\)	\(q+2.48929 q^{2} +1.00000 q^{3} +4.19656 q^{4} +2.48929 q^{6} +1.19656 q^{7} +5.46787 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.48929 q^{2} +1.00000 q^{3} +4.19656 q^{4} +2.48929 q^{6} +1.19656 q^{7} +5.46787 q^{8} +1.00000 q^{9} -1.19656 q^{11} +4.19656 q^{12} -1.00000 q^{13} +2.97858 q^{14} +5.21798 q^{16} -6.17513 q^{17} +2.48929 q^{18} +6.97858 q^{19} +1.19656 q^{21} -2.97858 q^{22} -4.17513 q^{23} +5.46787 q^{24} -2.48929 q^{26} +1.00000 q^{27} +5.02142 q^{28} +6.00000 q^{29} -2.97858 q^{31} +2.05333 q^{32} -1.19656 q^{33} -15.3717 q^{34} +4.19656 q^{36} -7.78202 q^{37} +17.3717 q^{38} -1.00000 q^{39} -6.17513 q^{41} +2.97858 q^{42} +9.95715 q^{43} -5.02142 q^{44} -10.3931 q^{46} +1.02142 q^{47} +5.21798 q^{48} -5.56825 q^{49} -6.17513 q^{51} -4.19656 q^{52} -10.1751 q^{53} +2.48929 q^{54} +6.54262 q^{56} +6.97858 q^{57} +14.9357 q^{58} +5.37169 q^{59} +12.5682 q^{61} -7.41454 q^{62} +1.19656 q^{63} -5.32464 q^{64} -2.97858 q^{66} -9.37169 q^{67} -25.9143 q^{68} -4.17513 q^{69} -5.19656 q^{71} +5.46787 q^{72} +11.9572 q^{73} -19.3717 q^{74} +29.2860 q^{76} -1.43175 q^{77} -2.48929 q^{78} -1.78202 q^{79} +1.00000 q^{81} -15.3717 q^{82} +5.37169 q^{83} +5.02142 q^{84} +24.7862 q^{86} +6.00000 q^{87} -6.54262 q^{88} +10.1751 q^{89} -1.19656 q^{91} -17.5212 q^{92} -2.97858 q^{93} +2.54262 q^{94} +2.05333 q^{96} +1.82487 q^{97} -13.8610 q^{98} -1.19656 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{3} + 8 q^{4} - q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^3 + 8 * q^4 - q^7 - 6 * q^8 + 3 * q^9	\( 3 q + 3 q^{3} + 8 q^{4} - q^{7} - 6 q^{8} + 3 q^{9} + q^{11} + 8 q^{12} - 3 q^{13} - 6 q^{14} + 26 q^{16} + q^{17} + 6 q^{19} - q^{21} + 6 q^{22} + 7 q^{23} - 6 q^{24} + 3 q^{27} + 30 q^{28} + 18 q^{29} + 6 q^{31} - 22 q^{32} + q^{33} - 22 q^{34} + 8 q^{36} - 13 q^{37} + 28 q^{38} - 3 q^{39} + q^{41} - 6 q^{42} - 30 q^{44} - 22 q^{46} + 18 q^{47} + 26 q^{48} + 12 q^{49} + q^{51} - 8 q^{52} - 11 q^{53} - 16 q^{56} + 6 q^{57} - 8 q^{59} + 9 q^{61} - 28 q^{62} - q^{63} + 30 q^{64} + 6 q^{66} - 4 q^{67} - 18 q^{68} + 7 q^{69} - 11 q^{71} - 6 q^{72} + 6 q^{73} - 34 q^{74} + 4 q^{76} - 33 q^{77} + 5 q^{79} + 3 q^{81} - 22 q^{82} - 8 q^{83} + 30 q^{84} + 56 q^{86} + 18 q^{87} + 16 q^{88} + 11 q^{89} + q^{91} - 2 q^{92} + 6 q^{93} - 28 q^{94} - 22 q^{96} + 25 q^{97} - 10 q^{98} + q^{99}+O(q^{100}) \) 3 * q + 3 * q^3 + 8 * q^4 - q^7 - 6 * q^8 + 3 * q^9 + q^11 + 8 * q^12 - 3 * q^13 - 6 * q^14 + 26 * q^16 + q^17 + 6 * q^19 - q^21 + 6 * q^22 + 7 * q^23 - 6 * q^24 + 3 * q^27 + 30 * q^28 + 18 * q^29 + 6 * q^31 - 22 * q^32 + q^33 - 22 * q^34 + 8 * q^36 - 13 * q^37 + 28 * q^38 - 3 * q^39 + q^41 - 6 * q^42 - 30 * q^44 - 22 * q^46 + 18 * q^47 + 26 * q^48 + 12 * q^49 + q^51 - 8 * q^52 - 11 * q^53 - 16 * q^56 + 6 * q^57 - 8 * q^59 + 9 * q^61 - 28 * q^62 - q^63 + 30 * q^64 + 6 * q^66 - 4 * q^67 - 18 * q^68 + 7 * q^69 - 11 * q^71 - 6 * q^72 + 6 * q^73 - 34 * q^74 + 4 * q^76 - 33 * q^77 + 5 * q^79 + 3 * q^81 - 22 * q^82 - 8 * q^83 + 30 * q^84 + 56 * q^86 + 18 * q^87 + 16 * q^88 + 11 * q^89 + q^91 - 2 * q^92 + 6 * q^93 - 28 * q^94 - 22 * q^96 + 25 * q^97 - 10 * q^98 + q^99

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