LMFDB - Embedded newform 1875.2.a.o.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1875,2,Mod(1,1875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1875.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1875.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:	$14.9719503790$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.8.13366265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 12x^{6} + 10x^{5} + 41x^{4} - 20x^{3} - 48x^{2} + 8x + 16 $ x^8 - x^7 - 12x^6 + 10x^5 + 41x^4 - 20x^3 - 48x^2 + 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.770071$ of defining polynomial
Character	$\chi$	$=$	1875.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.770071 q^{2} +1.00000 q^{3} -1.40699 q^{4} -0.770071 q^{6} +3.98808 q^{7} +2.62363 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.770071 q^{2} +1.00000 q^{3} -1.40699 q^{4} -0.770071 q^{6} +3.98808 q^{7} +2.62363 q^{8} +1.00000 q^{9} -6.35014 q^{11} -1.40699 q^{12} +5.35433 q^{13} -3.07111 q^{14} +0.793602 q^{16} -3.45746 q^{17} -0.770071 q^{18} +2.32026 q^{19} +3.98808 q^{21} +4.89006 q^{22} +0.955221 q^{23} +2.62363 q^{24} -4.12322 q^{26} +1.00000 q^{27} -5.61119 q^{28} +7.26630 q^{29} +6.40484 q^{31} -5.85838 q^{32} -6.35014 q^{33} +2.66249 q^{34} -1.40699 q^{36} -2.83348 q^{37} -1.78677 q^{38} +5.35433 q^{39} -5.35164 q^{41} -3.07111 q^{42} +3.93593 q^{43} +8.93458 q^{44} -0.735588 q^{46} +2.48348 q^{47} +0.793602 q^{48} +8.90478 q^{49} -3.45746 q^{51} -7.53350 q^{52} +3.95079 q^{53} -0.770071 q^{54} +10.4632 q^{56} +2.32026 q^{57} -5.59557 q^{58} +0.0941232 q^{59} -6.61174 q^{61} -4.93218 q^{62} +3.98808 q^{63} +2.92417 q^{64} +4.89006 q^{66} -10.2811 q^{67} +4.86461 q^{68} +0.955221 q^{69} -5.81587 q^{71} +2.62363 q^{72} +3.79897 q^{73} +2.18198 q^{74} -3.26459 q^{76} -25.3249 q^{77} -4.12322 q^{78} -5.44480 q^{79} +1.00000 q^{81} +4.12114 q^{82} +9.24696 q^{83} -5.61119 q^{84} -3.03095 q^{86} +7.26630 q^{87} -16.6604 q^{88} +10.1278 q^{89} +21.3535 q^{91} -1.34399 q^{92} +6.40484 q^{93} -1.91245 q^{94} -5.85838 q^{96} +7.89936 q^{97} -6.85731 q^{98} -6.35014 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 8 q^{3} + 9 q^{4} + q^{6} + 12 q^{7} + 3 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + q^2 + 8 * q^3 + 9 * q^4 + q^6 + 12 * q^7 + 3 * q^8 + 8 * q^9	$ 8 q + q^{2} + 8 q^{3} + 9 q^{4} + q^{6} + 12 q^{7} + 3 q^{8} + 8 q^{9} + 12 q^{11} + 9 q^{12} + 14 q^{13} + 16 q^{14} + 15 q^{16} - q^{17} + q^{18} + 16 q^{19} + 12 q^{21} + 18 q^{22} - 4 q^{23} + 3 q^{24} - 34 q^{26} + 8 q^{27} - 21 q^{28} + 2 q^{29} + 13 q^{31} - 18 q^{32} + 12 q^{33} - 37 q^{34} + 9 q^{36} - 8 q^{37} - 24 q^{38} + 14 q^{39} - 12 q^{41} + 16 q^{42} + 20 q^{43} + 47 q^{44} + 33 q^{46} - 15 q^{47} + 15 q^{48} + 30 q^{49} - q^{51} - q^{52} - 4 q^{53} + q^{54} + 60 q^{56} + 16 q^{57} + 2 q^{58} + 14 q^{59} + 10 q^{61} + 4 q^{62} + 12 q^{63} + 41 q^{64} + 18 q^{66} + 19 q^{67} - 33 q^{68} - 4 q^{69} + 21 q^{71} + 3 q^{72} - 19 q^{73} - 9 q^{74} - q^{76} - 11 q^{77} - 34 q^{78} + 10 q^{79} + 8 q^{81} + 24 q^{82} - 27 q^{83} - 21 q^{84} + 42 q^{86} + 2 q^{87} + 53 q^{88} - 9 q^{89} - 12 q^{91} - 63 q^{92} + 13 q^{93} + 14 q^{94} - 18 q^{96} + 24 q^{97} - 24 q^{98} + 12 q^{99}+O(q^{100}) $ 8 * q + q^2 + 8 * q^3 + 9 * q^4 + q^6 + 12 * q^7 + 3 * q^8 + 8 * q^9 + 12 * q^11 + 9 * q^12 + 14 * q^13 + 16 * q^14 + 15 * q^16 - q^17 + q^18 + 16 * q^19 + 12 * q^21 + 18 * q^22 - 4 * q^23 + 3 * q^24 - 34 * q^26 + 8 * q^27 - 21 * q^28 + 2 * q^29 + 13 * q^31 - 18 * q^32 + 12 * q^33 - 37 * q^34 + 9 * q^36 - 8 * q^37 - 24 * q^38 + 14 * q^39 - 12 * q^41 + 16 * q^42 + 20 * q^43 + 47 * q^44 + 33 * q^46 - 15 * q^47 + 15 * q^48 + 30 * q^49 - q^51 - q^52 - 4 * q^53 + q^54 + 60 * q^56 + 16 * q^57 + 2 * q^58 + 14 * q^59 + 10 * q^61 + 4 * q^62 + 12 * q^63 + 41 * q^64 + 18 * q^66 + 19 * q^67 - 33 * q^68 - 4 * q^69 + 21 * q^71 + 3 * q^72 - 19 * q^73 - 9 * q^74 - q^76 - 11 * q^77 - 34 * q^78 + 10 * q^79 + 8 * q^81 + 24 * q^82 - 27 * q^83 - 21 * q^84 + 42 * q^86 + 2 * q^87 + 53 * q^88 - 9 * q^89 - 12 * q^91 - 63 * q^92 + 13 * q^93 + 14 * q^94 - 18 * q^96 + 24 * q^97 - 24 * q^98 + 12 * 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 $

$2$	−0.770071	−0.544523	−0.272261	−	0.962223i	$-0.587772\pi$
$2$	−0.770071	−0.544523	−0.272261	+	0.962223i	$0.587772\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.40699	−0.703495
$5$	0	0
$5$	0	0
$6$	−0.770071	−0.314380
$7$	3.98808	1.50735	0.753676	−	0.657246i	$-0.228279\pi$
$7$	3.98808	1.50735	0.753676	+	0.657246i	$0.228279\pi$
$8$	2.62363	0.927592
$9$	1.00000	0.333333
$10$	0	0
$11$	−6.35014	−1.91464	−0.957319	−	0.289033i	$-0.906666\pi$
$11$	−6.35014	−1.91464	−0.957319	+	0.289033i	$0.906666\pi$
$12$	−1.40699	−0.406163
$13$	5.35433	1.48503	0.742513	−	0.669832i	$-0.233634\pi$
$13$	5.35433	1.48503	0.742513	+	0.669832i	$0.233634\pi$
$14$	−3.07111	−0.820787
$15$	0	0
$16$	0.793602	0.198400
$17$	−3.45746	−0.838557	−0.419279	−	0.907858i	$-0.637717\pi$
$17$	−3.45746	−0.838557	−0.419279	+	0.907858i	$0.637717\pi$
$18$	−0.770071	−0.181508
$19$	2.32026	0.532305	0.266152	−	0.963931i	$-0.414248\pi$
$19$	2.32026	0.532305	0.266152	+	0.963931i	$0.414248\pi$
$20$	0	0
$21$	3.98808	0.870270
$22$	4.89006	1.04256
$23$	0.955221	0.199177	0.0995886	−	0.995029i	$-0.468247\pi$
$23$	0.955221	0.199177	0.0995886	+	0.995029i	$0.468247\pi$
$24$	2.62363	0.535545
$25$	0	0
$26$	−4.12322	−0.808630
$27$	1.00000	0.192450
$28$	−5.61119	−1.06042
$29$	7.26630	1.34932	0.674659	−	0.738129i	$-0.264291\pi$
$29$	7.26630	1.34932	0.674659	+	0.738129i	$0.264291\pi$
$30$	0	0
$31$	6.40484	1.15034	0.575172	−	0.818033i	$-0.304935\pi$
$31$	6.40484	1.15034	0.575172	+	0.818033i	$0.304935\pi$
$32$	−5.85838	−1.03563
$33$	−6.35014	−1.10542
$34$	2.66249	0.456613
$35$	0	0
$36$	−1.40699	−0.234498
$37$	−2.83348	−0.465821	−0.232911	−	0.972498i	$-0.574825\pi$
$37$	−2.83348	−0.465821	−0.232911	+	0.972498i	$0.574825\pi$
$38$	−1.78677	−0.289852
$39$	5.35433	0.857380
$40$	0	0
$41$	−5.35164	−0.835785	−0.417893	−	0.908496i	$-0.637231\pi$
$41$	−5.35164	−0.835785	−0.417893	+	0.908496i	$0.637231\pi$
$42$	−3.07111	−0.473882
$43$	3.93593	0.600224	0.300112	−	0.953904i	$-0.402976\pi$
$43$	3.93593	0.600224	0.300112	+	0.953904i	$0.402976\pi$
$44$	8.93458	1.34694
$45$	0	0
$46$	−0.735588	−0.108457
$47$	2.48348	0.362252	0.181126	−	0.983460i	$-0.442026\pi$
$47$	2.48348	0.362252	0.181126	+	0.983460i	$0.442026\pi$
$48$	0.793602	0.114547
$49$	8.90478	1.27211
$50$	0	0
$51$	−3.45746	−0.484141
$52$	−7.53350	−1.04471
$53$	3.95079	0.542682	0.271341	−	0.962483i	$-0.412533\pi$
$53$	3.95079	0.542682	0.271341	+	0.962483i	$0.412533\pi$
$54$	−0.770071	−0.104793
$55$	0	0
$56$	10.4632	1.39821
$57$	2.32026	0.307326
$58$	−5.59557	−0.734735
$59$	0.0941232	0.0122538	0.00612690	−	0.999981i	$-0.498050\pi$
$59$	0.0941232	0.0122538	0.00612690	+	0.999981i	$0.498050\pi$
$60$	0	0
$61$	−6.61174	−0.846547	−0.423273	−	0.906002i	$-0.639119\pi$
$61$	−6.61174	−0.846547	−0.423273	+	0.906002i	$0.639119\pi$
$62$	−4.93218	−0.626388
$63$	3.98808	0.502451
$64$	2.92417	0.365521
$65$	0	0
$66$	4.89006	0.601925
$67$	−10.2811	−1.25603	−0.628016	−	0.778201i	$-0.716133\pi$
$67$	−10.2811	−1.25603	−0.628016	+	0.778201i	$0.716133\pi$
$68$	4.86461	0.589921
$69$	0.955221	0.114995
$70$	0	0
$71$	−5.81587	−0.690217	−0.345109	−	0.938563i	$-0.612158\pi$
$71$	−5.81587	−0.690217	−0.345109	+	0.938563i	$0.612158\pi$
$72$	2.62363	0.309197
$73$	3.79897	0.444635	0.222318	−	0.974974i	$-0.428638\pi$
$73$	3.79897	0.444635	0.222318	+	0.974974i	$0.428638\pi$
$74$	2.18198	0.253650
$75$	0	0
$76$	−3.26459	−0.374474
$77$	−25.3249	−2.88603
$78$	−4.12322	−0.466863
$79$	−5.44480	−0.612587	−0.306294	−	0.951937i	$-0.599089\pi$
$79$	−5.44480	−0.612587	−0.306294	+	0.951937i	$0.599089\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	4.12114	0.455104
$83$	9.24696	1.01499	0.507493	−	0.861656i	$-0.330572\pi$
$83$	9.24696	1.01499	0.507493	+	0.861656i	$0.330572\pi$
$84$	−5.61119	−0.612231
$85$	0	0
$86$	−3.03095	−0.326836
$87$	7.26630	0.779030
$88$	−16.6604	−1.77600
$89$	10.1278	1.07355	0.536773	−	0.843727i	$-0.319643\pi$
$89$	10.1278	1.07355	0.536773	+	0.843727i	$0.319643\pi$
$90$	0	0
$91$	21.3535	2.23846
$92$	−1.34399	−0.140120
$93$	6.40484	0.664151
$94$	−1.91245	−0.197255
$95$	0	0
$96$	−5.85838	−0.597918
$97$	7.89936	0.802058	0.401029	−	0.916065i	$-0.368653\pi$
$97$	7.89936	0.802058	0.401029	+	0.916065i	$0.368653\pi$
$98$	−6.85731	−0.692693
$99$	−6.35014	−0.638213
$100$	0	0
$101$	8.72974	0.868641	0.434321	−	0.900758i	$-0.356989\pi$
$101$	8.72974	0.868641	0.434321	+	0.900758i	$0.356989\pi$
$102$	2.66249	0.263626
$103$	−3.82390	−0.376780	−0.188390	−	0.982094i	$-0.560327\pi$
$103$	−3.82390	−0.376780	−0.188390	+	0.982094i	$0.560327\pi$
$104$	14.0478	1.37750
$105$	0	0
$106$	−3.04239	−0.295503
$107$	14.1662	1.36950	0.684748	−	0.728780i	$-0.259912\pi$
$107$	14.1662	1.36950	0.684748	+	0.728780i	$0.259912\pi$
$108$	−1.40699	−0.135388
$109$	14.0557	1.34629	0.673145	−	0.739511i	$-0.264943\pi$
$109$	14.0557	1.34629	0.673145	+	0.739511i	$0.264943\pi$
$110$	0	0
$111$	−2.83348	−0.268942
$112$	3.16495	0.299059
$113$	9.26557	0.871632	0.435816	−	0.900036i	$-0.356460\pi$
$113$	9.26557	0.871632	0.435816	+	0.900036i	$0.356460\pi$
$114$	−1.78677	−0.167346
$115$	0	0
$116$	−10.2236	−0.949239
$117$	5.35433	0.495008
$118$	−0.0724815	−0.00667247
$119$	−13.7886	−1.26400
$120$	0	0
$121$	29.3242	2.66584
$122$	5.09151	0.460964
$123$	−5.35164	−0.482541
$124$	−9.01155	−0.809261
$125$	0	0
$126$	−3.07111	−0.273596
$127$	6.91919	0.613979	0.306989	−	0.951713i	$-0.400678\pi$
$127$	6.91919	0.613979	0.306989	+	0.951713i	$0.400678\pi$
$128$	9.46494	0.836591
$129$	3.93593	0.346540
$130$	0	0
$131$	22.0453	1.92611	0.963055	−	0.269305i	$-0.0867938\pi$
$131$	22.0453	1.92611	0.963055	+	0.269305i	$0.0867938\pi$
$132$	8.93458	0.777655
$133$	9.25339	0.802371
$134$	7.91715	0.683938
$135$	0	0
$136$	−9.07108	−0.777839
$137$	1.29992	0.111060	0.0555299	−	0.998457i	$-0.482315\pi$
$137$	1.29992	0.111060	0.0555299	+	0.998457i	$0.482315\pi$
$138$	−0.735588	−0.0626174
$139$	3.84419	0.326060	0.163030	−	0.986621i	$-0.447873\pi$
$139$	3.84419	0.326060	0.163030	+	0.986621i	$0.447873\pi$
$140$	0	0
$141$	2.48348	0.209146
$142$	4.47864	0.375839
$143$	−34.0008	−2.84329
$144$	0.793602	0.0661335
$145$	0	0
$146$	−2.92547	−0.242114
$147$	8.90478	0.734454
$148$	3.98668	0.327703
$149$	16.1035	1.31925	0.659623	−	0.751596i	$-0.270716\pi$
$149$	16.1035	1.31925	0.659623	+	0.751596i	$0.270716\pi$
$150$	0	0
$151$	−14.8215	−1.20616	−0.603079	−	0.797682i	$-0.706059\pi$
$151$	−14.8215	−1.20616	−0.603079	+	0.797682i	$0.706059\pi$
$152$	6.08750	0.493761
$153$	−3.45746	−0.279519
$154$	19.5019	1.57151
$155$	0	0
$156$	−7.53350	−0.603162
$157$	−5.29762	−0.422796	−0.211398	−	0.977400i	$-0.567802\pi$
$157$	−5.29762	−0.422796	−0.211398	+	0.977400i	$0.567802\pi$
$158$	4.19288	0.333568
$159$	3.95079	0.313318
$160$	0	0
$161$	3.80950	0.300230
$162$	−0.770071	−0.0605025
$163$	−2.86408	−0.224332	−0.112166	−	0.993689i	$-0.535779\pi$
$163$	−2.86408	−0.224332	−0.112166	+	0.993689i	$0.535779\pi$
$164$	7.52970	0.587971
$165$	0	0
$166$	−7.12082	−0.552683
$167$	−2.57868	−0.199544	−0.0997720	−	0.995010i	$-0.531811\pi$
$167$	−2.57868	−0.199544	−0.0997720	+	0.995010i	$0.531811\pi$
$168$	10.4632	0.807255
$169$	15.6689	1.20530
$170$	0	0
$171$	2.32026	0.177435
$172$	−5.53782	−0.422255
$173$	−20.2272	−1.53784	−0.768921	−	0.639343i	$-0.779206\pi$
$173$	−20.2272	−1.53784	−0.768921	+	0.639343i	$0.779206\pi$
$174$	−5.59557	−0.424199
$175$	0	0
$176$	−5.03948	−0.379865
$177$	0.0941232	0.00707473
$178$	−7.79913	−0.584570
$179$	−26.2365	−1.96101	−0.980506	−	0.196491i	$-0.937045\pi$
$179$	−26.2365	−1.96101	−0.980506	+	0.196491i	$0.937045\pi$
$180$	0	0
$181$	2.37843	0.176787	0.0883936	−	0.996086i	$-0.471827\pi$
$181$	2.37843	0.176787	0.0883936	+	0.996086i	$0.471827\pi$
$182$	−16.4437	−1.21889
$183$	−6.61174	−0.488754
$184$	2.50614	0.184755
$185$	0	0
$186$	−4.93218	−0.361645
$187$	21.9553	1.60553
$188$	−3.49423	−0.254843
$189$	3.98808	0.290090
$190$	0	0
$191$	5.71292	0.413372	0.206686	−	0.978407i	$-0.433732\pi$
$191$	5.71292	0.413372	0.206686	+	0.978407i	$0.433732\pi$
$192$	2.92417	0.211034
$193$	4.18017	0.300895	0.150448	−	0.988618i	$-0.451929\pi$
$193$	4.18017	0.300895	0.150448	+	0.988618i	$0.451929\pi$
$194$	−6.08307	−0.436739
$195$	0	0
$196$	−12.5289	−0.894924
$197$	−14.6732	−1.04542	−0.522710	−	0.852511i	$-0.675079\pi$
$197$	−14.6732	−1.04542	−0.522710	+	0.852511i	$0.675079\pi$
$198$	4.89006	0.347521
$199$	8.77623	0.622130	0.311065	−	0.950389i	$-0.399314\pi$
$199$	8.77623	0.622130	0.311065	+	0.950389i	$0.399314\pi$
$200$	0	0
$201$	−10.2811	−0.725170
$202$	−6.72252	−0.472995
$203$	28.9786	2.03390
$204$	4.86461	0.340591
$205$	0	0
$206$	2.94467	0.205165
$207$	0.955221	0.0663924
$208$	4.24921	0.294630
$209$	−14.7340	−1.01917
$210$	0	0
$211$	18.7411	1.29019	0.645095	−	0.764103i	$-0.276818\pi$
$211$	18.7411	1.29019	0.645095	+	0.764103i	$0.276818\pi$
$212$	−5.55872	−0.381774
$213$	−5.81587	−0.398497
$214$	−10.9090	−0.745722
$215$	0	0
$216$	2.62363	0.178515
$217$	25.5430	1.73397
$218$	−10.8239	−0.733085
$219$	3.79897	0.256710
$220$	0	0
$221$	−18.5124	−1.24528
$222$	2.18198	0.146445
$223$	16.5574	1.10877	0.554383	−	0.832262i	$-0.312954\pi$
$223$	16.5574	1.10877	0.554383	+	0.832262i	$0.312954\pi$
$224$	−23.3637	−1.56105
$225$	0	0
$226$	−7.13515	−0.474623
$227$	−5.07350	−0.336740	−0.168370	−	0.985724i	$-0.553850\pi$
$227$	−5.07350	−0.336740	−0.168370	+	0.985724i	$0.553850\pi$
$228$	−3.26459	−0.216203
$229$	−23.9323	−1.58149	−0.790744	−	0.612147i	$-0.790306\pi$
$229$	−23.9323	−1.58149	−0.790744	+	0.612147i	$0.790306\pi$
$230$	0	0
$231$	−25.3249	−1.66625
$232$	19.0641	1.25162
$233$	−18.5301	−1.21395	−0.606974	−	0.794722i	$-0.707617\pi$
$233$	−18.5301	−1.21395	−0.606974	+	0.794722i	$0.707617\pi$
$234$	−4.12322	−0.269543
$235$	0	0
$236$	−0.132430	−0.00862048
$237$	−5.44480	−0.353678
$238$	10.6182	0.688277
$239$	−14.5812	−0.943179	−0.471590	−	0.881818i	$-0.656320\pi$
$239$	−14.5812	−0.943179	−0.471590	+	0.881818i	$0.656320\pi$
$240$	0	0
$241$	0.0849630	0.00547295	0.00273647	−	0.999996i	$-0.499129\pi$
$241$	0.0849630	0.00547295	0.00273647	+	0.999996i	$0.499129\pi$
$242$	−22.5818	−1.45161
$243$	1.00000	0.0641500
$244$	9.30266	0.595541
$245$	0	0
$246$	4.12114	0.262754
$247$	12.4235	0.790486
$248$	16.8039	1.06705
$249$	9.24696	0.586002
$250$	0	0
$251$	20.6190	1.30146	0.650729	−	0.759310i	$-0.274463\pi$
$251$	20.6190	1.30146	0.650729	+	0.759310i	$0.274463\pi$
$252$	−5.61119	−0.353472
$253$	−6.06578	−0.381352
$254$	−5.32827	−0.334325
$255$	0	0
$256$	−13.1370	−0.821063
$257$	−12.1228	−0.756199	−0.378100	−	0.925765i	$-0.623422\pi$
$257$	−12.1228	−0.756199	−0.378100	+	0.925765i	$0.623422\pi$
$258$	−3.03095	−0.188699
$259$	−11.3001	−0.702157
$260$	0	0
$261$	7.26630	0.449773
$262$	−16.9765	−1.04881
$263$	−7.25319	−0.447251	−0.223625	−	0.974675i	$-0.571789\pi$
$263$	−7.25319	−0.447251	−0.223625	+	0.974675i	$0.571789\pi$
$264$	−16.6604	−1.02538
$265$	0	0
$266$	−7.12577	−0.436909
$267$	10.1278	0.619812
$268$	14.4654	0.883612
$269$	10.3778	0.632744	0.316372	−	0.948635i	$-0.397535\pi$
$269$	10.3778	0.632744	0.316372	+	0.948635i	$0.397535\pi$
$270$	0	0
$271$	−29.4681	−1.79006	−0.895031	−	0.446004i	$-0.852847\pi$
$271$	−29.4681	−1.79006	−0.895031	+	0.446004i	$0.852847\pi$
$272$	−2.74385	−0.166370
$273$	21.3535	1.29237
$274$	−1.00103	−0.0604745
$275$	0	0
$276$	−1.34399	−0.0808985
$277$	17.4446	1.04815	0.524073	−	0.851673i	$-0.324412\pi$
$277$	17.4446	1.04815	0.524073	+	0.851673i	$0.324412\pi$
$278$	−2.96030	−0.177547
$279$	6.40484	0.383448
$280$	0	0
$281$	8.95212	0.534039	0.267019	−	0.963691i	$-0.413961\pi$
$281$	8.95212	0.534039	0.267019	+	0.963691i	$0.413961\pi$
$282$	−1.91245	−0.113885
$283$	−26.1417	−1.55396	−0.776982	−	0.629523i	$-0.783250\pi$
$283$	−26.1417	−1.55396	−0.776982	+	0.629523i	$0.783250\pi$
$284$	8.18288	0.485564
$285$	0	0
$286$	26.1830	1.54823
$287$	−21.3428	−1.25982
$288$	−5.85838	−0.345208
$289$	−5.04597	−0.296822
$290$	0	0
$291$	7.89936	0.463069
$292$	−5.34511	−0.312799
$293$	−18.9520	−1.10719	−0.553594	−	0.832787i	$-0.686744\pi$
$293$	−18.9520	−1.10719	−0.553594	+	0.832787i	$0.686744\pi$
$294$	−6.85731	−0.399927
$295$	0	0
$296$	−7.43399	−0.432092
$297$	−6.35014	−0.368472
$298$	−12.4008	−0.718360
$299$	5.11457	0.295783
$300$	0	0
$301$	15.6968	0.904749
$302$	11.4136	0.656780
$303$	8.72974	0.501510
$304$	1.84137	0.105610
$305$	0	0
$306$	2.66249	0.152204
$307$	−6.75782	−0.385689	−0.192845	−	0.981229i	$-0.561771\pi$
$307$	−6.75782	−0.385689	−0.192845	+	0.981229i	$0.561771\pi$
$308$	35.6318	2.03031
$309$	−3.82390	−0.217534
$310$	0	0
$311$	13.0403	0.739445	0.369723	−	0.929142i	$-0.379453\pi$
$311$	13.0403	0.739445	0.369723	+	0.929142i	$0.379453\pi$
$312$	14.0478	0.795298
$313$	20.1274	1.13767	0.568833	−	0.822453i	$-0.307395\pi$
$313$	20.1274	1.13767	0.568833	+	0.822453i	$0.307395\pi$
$314$	4.07955	0.230222
$315$	0	0
$316$	7.66078	0.430952
$317$	−12.7288	−0.714921	−0.357460	−	0.933928i	$-0.616357\pi$
$317$	−12.7288	−0.714921	−0.357460	+	0.933928i	$0.616357\pi$
$318$	−3.04239	−0.170609
$319$	−46.1420	−2.58346
$320$	0	0
$321$	14.1662	0.790679
$322$	−2.93358	−0.163482
$323$	−8.02222	−0.446368
$324$	−1.40699	−0.0781661
$325$	0	0
$326$	2.20554	0.122154
$327$	14.0557	0.777281
$328$	−14.0407	−0.775267
$329$	9.90430	0.546042
$330$	0	0
$331$	−16.3131	−0.896649	−0.448324	−	0.893871i	$-0.647979\pi$
$331$	−16.3131	−0.896649	−0.448324	+	0.893871i	$0.647979\pi$
$332$	−13.0104	−0.714038
$333$	−2.83348	−0.155274
$334$	1.98576	0.108656
$335$	0	0
$336$	3.16495	0.172662
$337$	11.0359	0.601166	0.300583	−	0.953756i	$-0.402819\pi$
$337$	11.0359	0.601166	0.300583	+	0.953756i	$0.402819\pi$
$338$	−12.0662	−0.656313
$339$	9.26557	0.503237
$340$	0	0
$341$	−40.6716	−2.20249
$342$	−1.78677	−0.0966173
$343$	7.59641	0.410168
$344$	10.3264	0.556763
$345$	0	0
$346$	15.5764	0.837390
$347$	−30.3961	−1.63175	−0.815875	−	0.578229i	$-0.803744\pi$
$347$	−30.3961	−1.63175	−0.815875	+	0.578229i	$0.803744\pi$
$348$	−10.2236	−0.548044
$349$	−6.45842	−0.345711	−0.172856	−	0.984947i	$-0.555299\pi$
$349$	−6.45842	−0.345711	−0.172856	+	0.984947i	$0.555299\pi$
$350$	0	0
$351$	5.35433	0.285793
$352$	37.2015	1.98285
$353$	4.25227	0.226325	0.113163	−	0.993576i	$-0.463902\pi$
$353$	4.25227	0.226325	0.113163	+	0.993576i	$0.463902\pi$
$354$	−0.0724815	−0.00385235
$355$	0	0
$356$	−14.2497	−0.755234
$357$	−13.7886	−0.729772
$358$	20.2040	1.06782
$359$	−8.14893	−0.430084	−0.215042	−	0.976605i	$-0.568989\pi$
$359$	−8.14893	−0.430084	−0.215042	+	0.976605i	$0.568989\pi$
$360$	0	0
$361$	−13.6164	−0.716652
$362$	−1.83156	−0.0962646
$363$	29.3242	1.53912
$364$	−30.0442	−1.57474
$365$	0	0
$366$	5.09151	0.266138
$367$	7.18365	0.374984	0.187492	−	0.982266i	$-0.439964\pi$
$367$	7.18365	0.374984	0.187492	+	0.982266i	$0.439964\pi$
$368$	0.758065	0.0395169
$369$	−5.35164	−0.278595
$370$	0	0
$371$	15.7561	0.818013
$372$	−9.01155	−0.467227
$373$	−7.23599	−0.374666	−0.187333	−	0.982297i	$-0.559984\pi$
$373$	−7.23599	−0.374666	−0.187333	+	0.982297i	$0.559984\pi$
$374$	−16.9072	−0.874250
$375$	0	0
$376$	6.51571	0.336022
$377$	38.9062	2.00377
$378$	−3.07111	−0.157961
$379$	1.57210	0.0807535	0.0403767	−	0.999185i	$-0.487144\pi$
$379$	1.57210	0.0807535	0.0403767	+	0.999185i	$0.487144\pi$
$380$	0	0
$381$	6.91919	0.354481
$382$	−4.39935	−0.225090
$383$	28.4834	1.45543	0.727717	−	0.685878i	$-0.240581\pi$
$383$	28.4834	1.45543	0.727717	+	0.685878i	$0.240581\pi$
$384$	9.46494	0.483006
$385$	0	0
$386$	−3.21903	−0.163844
$387$	3.93593	0.200075
$388$	−11.1143	−0.564244
$389$	5.45707	0.276684	0.138342	−	0.990385i	$-0.455823\pi$
$389$	5.45707	0.276684	0.138342	+	0.990385i	$0.455823\pi$
$390$	0	0
$391$	−3.30264	−0.167022
$392$	23.3628	1.18000
$393$	22.0453	1.11204
$394$	11.2994	0.569255
$395$	0	0
$396$	8.93458	0.448980
$397$	−13.6918	−0.687172	−0.343586	−	0.939121i	$-0.611642\pi$
$397$	−13.6918	−0.687172	−0.343586	+	0.939121i	$0.611642\pi$
$398$	−6.75832	−0.338764
$399$	9.25339	0.463249
$400$	0	0
$401$	10.6255	0.530614	0.265307	−	0.964164i	$-0.414527\pi$
$401$	10.6255	0.530614	0.265307	+	0.964164i	$0.414527\pi$
$402$	7.91715	0.394872
$403$	34.2937	1.70829
$404$	−12.2827	−0.611085
$405$	0	0
$406$	−22.3156	−1.10750
$407$	17.9930	0.891879
$408$	−9.07108	−0.449085
$409$	−20.5777	−1.01750	−0.508750	−	0.860914i	$-0.669892\pi$
$409$	−20.5777	−1.01750	−0.508750	+	0.860914i	$0.669892\pi$
$410$	0	0
$411$	1.29992	0.0641204
$412$	5.38018	0.265063
$413$	0.375371	0.0184708
$414$	−0.735588	−0.0361522
$415$	0	0
$416$	−31.3677	−1.53793
$417$	3.84419	0.188251
$418$	11.3462	0.554962
$419$	7.44362	0.363644	0.181822	−	0.983331i	$-0.441800\pi$
$419$	7.44362	0.363644	0.181822	+	0.983331i	$0.441800\pi$
$420$	0	0
$421$	26.2168	1.27773	0.638863	−	0.769320i	$-0.279405\pi$
$421$	26.2168	1.27773	0.638863	+	0.769320i	$0.279405\pi$
$422$	−14.4320	−0.702537
$423$	2.48348	0.120751
$424$	10.3654	0.503387
$425$	0	0
$426$	4.47864	0.216991
$427$	−26.3682	−1.27604
$428$	−19.9317	−0.963434
$429$	−34.0008	−1.64157
$430$	0	0
$431$	−22.9859	−1.10719	−0.553597	−	0.832785i	$-0.686745\pi$
$431$	−22.9859	−1.10719	−0.553597	+	0.832785i	$0.686745\pi$
$432$	0.793602	0.0381822
$433$	−29.5347	−1.41934	−0.709672	−	0.704532i	$-0.751157\pi$
$433$	−29.5347	−1.41934	−0.709672	+	0.704532i	$0.751157\pi$
$434$	−19.6699	−0.944188
$435$	0	0
$436$	−19.7762	−0.947108
$437$	2.21636	0.106023
$438$	−2.92547	−0.139785
$439$	23.4898	1.12111	0.560553	−	0.828119i	$-0.310589\pi$
$439$	23.4898	1.12111	0.560553	+	0.828119i	$0.310589\pi$
$440$	0	0
$441$	8.90478	0.424037
$442$	14.2559	0.678082
$443$	19.5349	0.928130	0.464065	−	0.885801i	$-0.346390\pi$
$443$	19.5349	0.928130	0.464065	+	0.885801i	$0.346390\pi$
$444$	3.98668	0.189199
$445$	0	0
$446$	−12.7504	−0.603748
$447$	16.1035	0.761667
$448$	11.6618	0.550969
$449$	1.18687	0.0560118	0.0280059	−	0.999608i	$-0.491084\pi$
$449$	1.18687	0.0560118	0.0280059	+	0.999608i	$0.491084\pi$
$450$	0	0
$451$	33.9836	1.60023
$452$	−13.0366	−0.613189
$453$	−14.8215	−0.696375
$454$	3.90696	0.183363
$455$	0	0
$456$	6.08750	0.285073
$457$	−23.4359	−1.09629	−0.548144	−	0.836384i	$-0.684665\pi$
$457$	−23.4359	−1.09629	−0.548144	+	0.836384i	$0.684665\pi$
$458$	18.4295	0.861156
$459$	−3.45746	−0.161380
$460$	0	0
$461$	35.4249	1.64990	0.824950	−	0.565205i	$-0.191203\pi$
$461$	35.4249	1.64990	0.824950	+	0.565205i	$0.191203\pi$
$462$	19.5019	0.907312
$463$	9.44996	0.439177	0.219588	−	0.975593i	$-0.429529\pi$
$463$	9.44996	0.439177	0.219588	+	0.975593i	$0.429529\pi$
$464$	5.76655	0.267706
$465$	0	0
$466$	14.2695	0.661022
$467$	−0.0277734	−0.00128520	−0.000642599	−	1.00000i	$-0.500205\pi$
$467$	−0.0277734	−0.00128520	−0.000642599		1.00000i	$0.500205\pi$
$468$	−7.53350	−0.348236
$469$	−41.0017	−1.89328
$470$	0	0
$471$	−5.29762	−0.244102
$472$	0.246944	0.0113665
$473$	−24.9937	−1.14921
$474$	4.19288	0.192585
$475$	0	0
$476$	19.4005	0.889219
$477$	3.95079	0.180894
$478$	11.2286	0.513583
$479$	9.30016	0.424935	0.212467	−	0.977168i	$-0.431850\pi$
$479$	9.30016	0.424935	0.212467	+	0.977168i	$0.431850\pi$
$480$	0	0
$481$	−15.1714	−0.691756
$482$	−0.0654276	−0.00298014
$483$	3.80950	0.173338
$484$	−41.2589	−1.87541
$485$	0	0
$486$	−0.770071	−0.0349311
$487$	−32.5963	−1.47708	−0.738539	−	0.674211i	$-0.764484\pi$
$487$	−32.5963	−1.47708	−0.738539	+	0.674211i	$0.764484\pi$
$488$	−17.3467	−0.785250
$489$	−2.86408	−0.129518
$490$	0	0
$491$	−1.08119	−0.0487932	−0.0243966	−	0.999702i	$-0.507766\pi$
$491$	−1.08119	−0.0487932	−0.0243966	+	0.999702i	$0.507766\pi$
$492$	7.52970	0.339465
$493$	−25.1230	−1.13148
$494$	−9.56695	−0.430437
$495$	0	0
$496$	5.08290	0.228229
$497$	−23.1942	−1.04040
$498$	−7.12082	−0.319092
$499$	−43.9536	−1.96763	−0.983816	−	0.179181i	$-0.942655\pi$
$499$	−43.9536	−1.96763	−0.983816	+	0.179181i	$0.942655\pi$
$500$	0	0
$501$	−2.57868	−0.115207
$502$	−15.8781	−0.708673
$503$	−29.0142	−1.29368	−0.646841	−	0.762625i	$-0.723910\pi$
$503$	−29.0142	−1.29368	−0.646841	+	0.762625i	$0.723910\pi$
$504$	10.4632	0.466069
$505$	0	0
$506$	4.67108	0.207655
$507$	15.6689	0.695880
$508$	−9.73523	−0.431931
$509$	5.13104	0.227429	0.113715	−	0.993513i	$-0.463725\pi$
$509$	5.13104	0.227429	0.113715	+	0.993513i	$0.463725\pi$
$510$	0	0
$511$	15.1506	0.670222
$512$	−8.81345	−0.389503
$513$	2.32026	0.102442
$514$	9.33541	0.411767
$515$	0	0
$516$	−5.53782	−0.243789
$517$	−15.7704	−0.693582
$518$	8.70191	0.382340
$519$	−20.2272	−0.887874
$520$	0	0
$521$	−8.20068	−0.359278	−0.179639	−	0.983733i	$-0.557493\pi$
$521$	−8.20068	−0.359278	−0.179639	+	0.983733i	$0.557493\pi$
$522$	−5.59557	−0.244912
$523$	5.23806	0.229044	0.114522	−	0.993421i	$-0.463466\pi$
$523$	5.23806	0.229044	0.114522	+	0.993421i	$0.463466\pi$
$524$	−31.0176	−1.35501
$525$	0	0
$526$	5.58547	0.243538
$527$	−22.1445	−0.964629
$528$	−5.03948	−0.219315
$529$	−22.0876	−0.960328
$530$	0	0
$531$	0.0941232	0.00408460
$532$	−13.0194	−0.564464
$533$	−28.6545	−1.24116
$534$	−7.79913	−0.337502
$535$	0	0
$536$	−26.9737	−1.16508
$537$	−26.2365	−1.13219
$538$	−7.99163	−0.344544
$539$	−56.5466	−2.43563
$540$	0	0
$541$	13.2888	0.571329	0.285664	−	0.958330i	$-0.407786\pi$
$541$	13.2888	0.571329	0.285664	+	0.958330i	$0.407786\pi$
$542$	22.6926	0.974729
$543$	2.37843	0.102068
$544$	20.2551	0.868431
$545$	0	0
$546$	−16.4437	−0.703726
$547$	−40.1311	−1.71588	−0.857940	−	0.513750i	$-0.828256\pi$
$547$	−40.1311	−1.71588	−0.857940	+	0.513750i	$0.828256\pi$
$548$	−1.82898	−0.0781300
$549$	−6.61174	−0.282182
$550$	0	0
$551$	16.8597	0.718249
$552$	2.50614	0.106668
$553$	−21.7143	−0.923385
$554$	−13.4336	−0.570740
$555$	0	0
$556$	−5.40874	−0.229382
$557$	−45.6945	−1.93614	−0.968069	−	0.250686i	$-0.919344\pi$
$557$	−45.6945	−1.93614	−0.968069	+	0.250686i	$0.919344\pi$
$558$	−4.93218	−0.208796
$559$	21.0743	0.891348
$560$	0	0
$561$	21.9553	0.926956
$562$	−6.89377	−0.290796
$563$	0.600201	0.0252955	0.0126477	−	0.999920i	$-0.495974\pi$
$563$	0.600201	0.0252955	0.0126477	+	0.999920i	$0.495974\pi$
$564$	−3.49423	−0.147134
$565$	0	0
$566$	20.1310	0.846168
$567$	3.98808	0.167484
$568$	−15.2587	−0.640240
$569$	−11.9725	−0.501914	−0.250957	−	0.967998i	$-0.580745\pi$
$569$	−11.9725	−0.501914	−0.250957	+	0.967998i	$0.580745\pi$
$570$	0	0
$571$	−19.4133	−0.812422	−0.406211	−	0.913779i	$-0.633150\pi$
$571$	−19.4133	−0.812422	−0.406211	+	0.913779i	$0.633150\pi$
$572$	47.8387	2.00024
$573$	5.71292	0.238660
$574$	16.4354	0.686002
$575$	0	0
$576$	2.92417	0.121840
$577$	26.0641	1.08506	0.542532	−	0.840035i	$-0.317466\pi$
$577$	26.0641	1.08506	0.542532	+	0.840035i	$0.317466\pi$
$578$	3.88575	0.161626
$579$	4.18017	0.173722
$580$	0	0
$581$	36.8776	1.52994
$582$	−6.08307	−0.252151
$583$	−25.0880	−1.03904
$584$	9.96706	0.412440
$585$	0	0
$586$	14.5944	0.602888
$587$	2.53968	0.104824	0.0524120	−	0.998626i	$-0.483309\pi$
$587$	2.53968	0.104824	0.0524120	+	0.998626i	$0.483309\pi$
$588$	−12.5289	−0.516685
$589$	14.8609	0.612333
$590$	0	0
$591$	−14.6732	−0.603573
$592$	−2.24865	−0.0924191
$593$	4.27995	0.175757	0.0878783	−	0.996131i	$-0.471991\pi$
$593$	4.27995	0.175757	0.0878783	+	0.996131i	$0.471991\pi$
$594$	4.89006	0.200642
$595$	0	0
$596$	−22.6574	−0.928084
$597$	8.77623	0.359187
$598$	−3.93858	−0.161061
$599$	27.1909	1.11099	0.555495	−	0.831520i	$-0.312529\pi$
$599$	27.1909	1.11099	0.555495	+	0.831520i	$0.312529\pi$
$600$	0	0
$601$	−44.6772	−1.82242	−0.911211	−	0.411940i	$-0.864851\pi$
$601$	−44.6772	−1.82242	−0.911211	+	0.411940i	$0.864851\pi$
$602$	−12.0877	−0.492656
$603$	−10.2811	−0.418677
$604$	20.8537	0.848526
$605$	0	0
$606$	−6.72252	−0.273084
$607$	3.48433	0.141425	0.0707123	−	0.997497i	$-0.477473\pi$
$607$	3.48433	0.141425	0.0707123	+	0.997497i	$0.477473\pi$
$608$	−13.5930	−0.551268
$609$	28.9786	1.17427
$610$	0	0
$611$	13.2974	0.537954
$612$	4.86461	0.196640
$613$	−11.1118	−0.448803	−0.224402	−	0.974497i	$-0.572043\pi$
$613$	−11.1118	−0.448803	−0.224402	+	0.974497i	$0.572043\pi$
$614$	5.20400	0.210016
$615$	0	0
$616$	−66.4429	−2.67706
$617$	−33.0355	−1.32996	−0.664980	−	0.746861i	$-0.731560\pi$
$617$	−33.0355	−1.32996	−0.664980	+	0.746861i	$0.731560\pi$
$618$	2.94467	0.118452
$619$	17.0417	0.684964	0.342482	−	0.939524i	$-0.388732\pi$
$619$	17.0417	0.684964	0.342482	+	0.939524i	$0.388732\pi$
$620$	0	0
$621$	0.955221	0.0383317
$622$	−10.0419	−0.402645
$623$	40.3905	1.61821
$624$	4.24921	0.170105
$625$	0	0
$626$	−15.4995	−0.619485
$627$	−14.7340	−0.588419
$628$	7.45370	0.297435
$629$	9.79664	0.390618
$630$	0	0
$631$	7.72790	0.307643	0.153821	−	0.988099i	$-0.450842\pi$
$631$	7.72790	0.307643	0.153821	+	0.988099i	$0.450842\pi$
$632$	−14.2851	−0.568231
$633$	18.7411	0.744891
$634$	9.80208	0.389290
$635$	0	0
$636$	−5.55872	−0.220417
$637$	47.6792	1.88912
$638$	35.5327	1.40675
$639$	−5.81587	−0.230072
$640$	0	0
$641$	14.4910	0.572361	0.286181	−	0.958176i	$-0.407614\pi$
$641$	14.4910	0.572361	0.286181	+	0.958176i	$0.407614\pi$
$642$	−10.9090	−0.430543
$643$	42.5134	1.67656	0.838282	−	0.545238i	$-0.183561\pi$
$643$	42.5134	1.67656	0.838282	+	0.545238i	$0.183561\pi$
$644$	−5.35992	−0.211211
$645$	0	0
$646$	6.17768	0.243058
$647$	−26.3343	−1.03531	−0.517655	−	0.855590i	$-0.673195\pi$
$647$	−26.3343	−1.03531	−0.517655	+	0.855590i	$0.673195\pi$
$648$	2.62363	0.103066
$649$	−0.597695	−0.0234616
$650$	0	0
$651$	25.5430	1.00111
$652$	4.02973	0.157816
$653$	4.46840	0.174862	0.0874310	−	0.996171i	$-0.472134\pi$
$653$	4.46840	0.174862	0.0874310	+	0.996171i	$0.472134\pi$
$654$	−10.8239	−0.423247
$655$	0	0
$656$	−4.24707	−0.165820
$657$	3.79897	0.148212
$658$	−7.62702	−0.297332
$659$	40.2092	1.56633	0.783165	−	0.621814i	$-0.213604\pi$
$659$	40.2092	1.56633	0.783165	+	0.621814i	$0.213604\pi$
$660$	0	0
$661$	−16.0012	−0.622374	−0.311187	−	0.950349i	$-0.600727\pi$
$661$	−16.0012	−0.622374	−0.311187	+	0.950349i	$0.600727\pi$
$662$	12.5622	0.488246
$663$	−18.5124	−0.718962
$664$	24.2606	0.941492
$665$	0	0
$666$	2.18198	0.0845500
$667$	6.94092	0.268754
$668$	3.62817	0.140378
$669$	16.5574	0.640146
$670$	0	0
$671$	41.9855	1.62083
$672$	−23.3637	−0.901274
$673$	−10.6585	−0.410854	−0.205427	−	0.978672i	$-0.565858\pi$
$673$	−10.6585	−0.410854	−0.205427	+	0.978672i	$0.565858\pi$
$674$	−8.49846	−0.327349
$675$	0	0
$676$	−22.0460	−0.847922
$677$	15.9650	0.613585	0.306793	−	0.951776i	$-0.400744\pi$
$677$	15.9650	0.613585	0.306793	+	0.951776i	$0.400744\pi$
$678$	−7.13515	−0.274024
$679$	31.5033	1.20898
$680$	0	0
$681$	−5.07350	−0.194417
$682$	31.3201	1.19931
$683$	1.13294	0.0433508	0.0216754	−	0.999765i	$-0.493100\pi$
$683$	1.13294	0.0433508	0.0216754	+	0.999765i	$0.493100\pi$
$684$	−3.26459	−0.124825
$685$	0	0
$686$	−5.84978	−0.223346
$687$	−23.9323	−0.913072
$688$	3.12356	0.119085
$689$	21.1538	0.805897
$690$	0	0
$691$	−11.4786	−0.436668	−0.218334	−	0.975874i	$-0.570062\pi$
$691$	−11.4786	−0.436668	−0.218334	+	0.975874i	$0.570062\pi$
$692$	28.4594	1.08186
$693$	−25.3249	−0.962012
$694$	23.4072	0.888525
$695$	0	0
$696$	19.0641	0.722621
$697$	18.5031	0.700854
$698$	4.97344	0.188248
$699$	−18.5301	−0.700873
$700$	0	0
$701$	−27.9382	−1.05521	−0.527605	−	0.849490i	$-0.676910\pi$
$701$	−27.9382	−1.05521	−0.527605	+	0.849490i	$0.676910\pi$
$702$	−4.12322	−0.155621
$703$	−6.57442	−0.247959
$704$	−18.5689	−0.699840
$705$	0	0
$706$	−3.27455	−0.123239
$707$	34.8149	1.30935
$708$	−0.132430	−0.00497704
$709$	26.2614	0.986266	0.493133	−	0.869954i	$-0.335852\pi$
$709$	26.2614	0.986266	0.493133	+	0.869954i	$0.335852\pi$
$710$	0	0
$711$	−5.44480	−0.204196
$712$	26.5716	0.995812
$713$	6.11804	0.229122
$714$	10.6182	0.397377
$715$	0	0
$716$	36.9146	1.37956
$717$	−14.5812	−0.544545
$718$	6.27526	0.234191
$719$	−47.8778	−1.78554	−0.892771	−	0.450510i	$-0.851242\pi$
$719$	−47.8778	−1.78554	−0.892771	+	0.450510i	$0.851242\pi$
$720$	0	0
$721$	−15.2500	−0.567940
$722$	10.4856	0.390233
$723$	0.0849630	0.00315981
$724$	−3.34642	−0.124369
$725$	0	0
$726$	−22.5818	−0.838088
$727$	−6.74514	−0.250163	−0.125082	−	0.992146i	$-0.539919\pi$
$727$	−6.74514	−0.250163	−0.125082	+	0.992146i	$0.539919\pi$
$728$	56.0236	2.07637
$729$	1.00000	0.0370370
$730$	0	0
$731$	−13.6083	−0.503322
$732$	9.30266	0.343836
$733$	42.9974	1.58815	0.794073	−	0.607822i	$-0.207957\pi$
$733$	42.9974	1.58815	0.794073	+	0.607822i	$0.207957\pi$
$734$	−5.53192	−0.204187
$735$	0	0
$736$	−5.59605	−0.206273
$737$	65.2862	2.40485
$738$	4.12114	0.151701
$739$	−17.0432	−0.626943	−0.313472	−	0.949598i	$-0.601492\pi$
$739$	−17.0432	−0.626943	−0.313472	+	0.949598i	$0.601492\pi$
$740$	0	0
$741$	12.4235	0.456387
$742$	−12.1333	−0.445427
$743$	−50.4068	−1.84925	−0.924623	−	0.380884i	$-0.875620\pi$
$743$	−50.4068	−1.84925	−0.924623	+	0.380884i	$0.875620\pi$
$744$	16.8039	0.616061
$745$	0	0
$746$	5.57223	0.204014
$747$	9.24696	0.338329
$748$	−30.8910	−1.12949
$749$	56.4958	2.06431
$750$	0	0
$751$	−3.00535	−0.109667	−0.0548334	−	0.998496i	$-0.517463\pi$
$751$	−3.00535	−0.109667	−0.0548334	+	0.998496i	$0.517463\pi$
$752$	1.97089	0.0718710
$753$	20.6190	0.751397
$754$	−29.9606	−1.09110
$755$	0	0
$756$	−5.61119	−0.204077
$757$	−8.74406	−0.317808	−0.158904	−	0.987294i	$-0.550796\pi$
$757$	−8.74406	−0.317808	−0.158904	+	0.987294i	$0.550796\pi$
$758$	−1.21063	−0.0439721
$759$	−6.06578	−0.220174
$760$	0	0
$761$	−31.8086	−1.15306	−0.576530	−	0.817076i	$-0.695594\pi$
$761$	−31.8086	−1.15306	−0.576530	+	0.817076i	$0.695594\pi$
$762$	−5.32827	−0.193023
$763$	56.0551	2.02933
$764$	−8.03802	−0.290805
$765$	0	0
$766$	−21.9342	−0.792517
$767$	0.503967	0.0181972
$768$	−13.1370	−0.474041
$769$	28.7776	1.03775	0.518874	−	0.854851i	$-0.326351\pi$
$769$	28.7776	1.03775	0.518874	+	0.854851i	$0.326351\pi$
$770$	0	0
$771$	−12.1228	−0.436592
$772$	−5.88146	−0.211678
$773$	34.6320	1.24563	0.622814	−	0.782370i	$-0.285989\pi$
$773$	34.6320	1.24563	0.622814	+	0.782370i	$0.285989\pi$
$774$	−3.03095	−0.108945
$775$	0	0
$776$	20.7250	0.743983
$777$	−11.3001	−0.405390
$778$	−4.20233	−0.150661
$779$	−12.4172	−0.444893
$780$	0	0
$781$	36.9316	1.32152
$782$	2.54327	0.0909470
$783$	7.26630	0.259677
$784$	7.06685	0.252388
$785$	0	0
$786$	−16.9765	−0.605531
$787$	−52.9281	−1.88668	−0.943342	−	0.331821i	$-0.892337\pi$
$787$	−52.9281	−1.88668	−0.943342	+	0.331821i	$0.892337\pi$
$788$	20.6450	0.735448
$789$	−7.25319	−0.258220
$790$	0	0
$791$	36.9518	1.31386
$792$	−16.6604	−0.592001
$793$	−35.4015	−1.25714
$794$	10.5437	0.374181
$795$	0	0
$796$	−12.3481	−0.437666
$797$	32.9585	1.16745	0.583724	−	0.811952i	$-0.301595\pi$
$797$	32.9585	1.16745	0.583724	+	0.811952i	$0.301595\pi$
$798$	−7.12577	−0.252250
$799$	−8.58652	−0.303769
$800$	0	0
$801$	10.1278	0.357849
$802$	−8.18242	−0.288931
$803$	−24.1240	−0.851316
$804$	14.4654	0.510154
$805$	0	0
$806$	−26.4086	−0.930202
$807$	10.3778	0.365315
$808$	22.9036	0.805744
$809$	−33.7389	−1.18620	−0.593098	−	0.805130i	$-0.702095\pi$
$809$	−33.7389	−1.18620	−0.593098	+	0.805130i	$0.702095\pi$
$810$	0	0
$811$	−23.3207	−0.818902	−0.409451	−	0.912332i	$-0.634280\pi$
$811$	−23.3207	−0.818902	−0.409451	+	0.912332i	$0.634280\pi$
$812$	−40.7726	−1.43084
$813$	−29.4681	−1.03349
$814$	−13.8559	−0.485648
$815$	0	0
$816$	−2.74385	−0.0960539
$817$	9.13240	0.319502
$818$	15.8463	0.554052
$819$	21.3535	0.746152
$820$	0	0
$821$	16.9918	0.593018	0.296509	−	0.955030i	$-0.404178\pi$
$821$	16.9918	0.593018	0.296509	+	0.955030i	$0.404178\pi$
$822$	−1.00103	−0.0349150
$823$	−29.8674	−1.04111	−0.520555	−	0.853828i	$-0.674275\pi$
$823$	−29.8674	−1.04111	−0.520555	+	0.853828i	$0.674275\pi$
$824$	−10.0325	−0.349498
$825$	0	0
$826$	−0.289062	−0.0100578
$827$	−34.1803	−1.18857	−0.594283	−	0.804256i	$-0.702564\pi$
$827$	−34.1803	−1.18857	−0.594283	+	0.804256i	$0.702564\pi$
$828$	−1.34399	−0.0467067
$829$	45.5662	1.58258	0.791289	−	0.611442i	$-0.209410\pi$
$829$	45.5662	1.58258	0.791289	+	0.611442i	$0.209410\pi$
$830$	0	0
$831$	17.4446	0.605148
$832$	15.6570	0.542808
$833$	−30.7879	−1.06674
$834$	−2.96030	−0.102507
$835$	0	0
$836$	20.7306	0.716982
$837$	6.40484	0.221384
$838$	−5.73212	−0.198013
$839$	−5.10480	−0.176237	−0.0881186	−	0.996110i	$-0.528085\pi$
$839$	−5.10480	−0.176237	−0.0881186	+	0.996110i	$0.528085\pi$
$840$	0	0
$841$	23.7992	0.820661
$842$	−20.1888	−0.695751
$843$	8.95212	0.308328
$844$	−26.3685	−0.907642
$845$	0	0
$846$	−1.91245	−0.0657515
$847$	116.947	4.01836
$848$	3.13535	0.107668
$849$	−26.1417	−0.897181
$850$	0	0
$851$	−2.70660	−0.0927810
$852$	8.18288	0.280341
$853$	57.1027	1.95516	0.977580	−	0.210564i	$-0.0675301\pi$
$853$	57.1027	1.95516	0.977580	+	0.210564i	$0.0675301\pi$
$854$	20.3054	0.694835
$855$	0	0
$856$	37.1667	1.27033
$857$	46.0057	1.57153	0.785763	−	0.618528i	$-0.212271\pi$
$857$	46.0057	1.57153	0.785763	+	0.618528i	$0.212271\pi$
$858$	26.1830	0.893873
$859$	−39.1766	−1.33669	−0.668343	−	0.743853i	$-0.732996\pi$
$859$	−39.1766	−1.33669	−0.668343	+	0.743853i	$0.732996\pi$
$860$	0	0
$861$	−21.3428	−0.727359
$862$	17.7008	0.602892
$863$	−34.8513	−1.18635	−0.593175	−	0.805073i	$-0.702126\pi$
$863$	−34.8513	−1.18635	−0.593175	+	0.805073i	$0.702126\pi$
$864$	−5.85838	−0.199306
$865$	0	0
$866$	22.7438	0.772865
$867$	−5.04597	−0.171370
$868$	−35.9388	−1.21984
$869$	34.5752	1.17288
$870$	0	0
$871$	−55.0482	−1.86524
$872$	36.8768	1.24881
$873$	7.89936	0.267353
$874$	−1.70676	−0.0577319
$875$	0	0
$876$	−5.34511	−0.180594
$877$	24.0922	0.813537	0.406768	−	0.913531i	$-0.366656\pi$
$877$	24.0922	0.813537	0.406768	+	0.913531i	$0.366656\pi$
$878$	−18.0888	−0.610467
$879$	−18.9520	−0.639235
$880$	0	0
$881$	−2.41163	−0.0812499	−0.0406250	−	0.999174i	$-0.512935\pi$
$881$	−2.41163	−0.0812499	−0.0406250	+	0.999174i	$0.512935\pi$
$882$	−6.85731	−0.230898
$883$	−1.48748	−0.0500578	−0.0250289	−	0.999687i	$-0.507968\pi$
$883$	−1.48748	−0.0500578	−0.0250289	+	0.999687i	$0.507968\pi$
$884$	26.0468	0.876047
$885$	0	0
$886$	−15.0432	−0.505388
$887$	−20.1745	−0.677392	−0.338696	−	0.940896i	$-0.609986\pi$
$887$	−20.1745	−0.677392	−0.338696	+	0.940896i	$0.609986\pi$
$888$	−7.43399	−0.249468
$889$	27.5943	0.925482
$890$	0	0
$891$	−6.35014	−0.212738
$892$	−23.2961	−0.780011
$893$	5.76232	0.192829
$894$	−12.4008	−0.414745
$895$	0	0
$896$	37.7470	1.26104
$897$	5.11457	0.170771
$898$	−0.913974	−0.0304997
$899$	46.5395	1.55218
$900$	0	0
$901$	−13.6597	−0.455070
$902$	−26.1698	−0.871360
$903$	15.6968	0.522357
$904$	24.3094	0.808518
$905$	0	0
$906$	11.4136	0.379192
$907$	26.2850	0.872778	0.436389	−	0.899758i	$-0.356257\pi$
$907$	26.2850	0.872778	0.436389	+	0.899758i	$0.356257\pi$
$908$	7.13837	0.236895
$909$	8.72974	0.289547
$910$	0	0
$911$	−22.8586	−0.757340	−0.378670	−	0.925532i	$-0.623619\pi$
$911$	−22.8586	−0.757340	−0.378670	+	0.925532i	$0.623619\pi$
$912$	1.84137	0.0609737
$913$	−58.7195	−1.94333
$914$	18.0473	0.596953
$915$	0	0
$916$	33.6724	1.11257
$917$	87.9186	2.90333
$918$	2.66249	0.0878753
$919$	−15.7960	−0.521061	−0.260530	−	0.965466i	$-0.583897\pi$
$919$	−15.7960	−0.521061	−0.260530	+	0.965466i	$0.583897\pi$
$920$	0	0
$921$	−6.75782	−0.222678
$922$	−27.2797	−0.898408
$923$	−31.1401	−1.02499
$924$	35.6318	1.17220
$925$	0	0
$926$	−7.27714	−0.239142
$927$	−3.82390	−0.125593
$928$	−42.5688	−1.39739
$929$	48.5302	1.59222	0.796111	−	0.605150i	$-0.206887\pi$
$929$	48.5302	1.59222	0.796111	+	0.605150i	$0.206887\pi$
$930$	0	0
$931$	20.6614	0.677151
$932$	26.0717	0.854006
$933$	13.0403	0.426919
$934$	0.0213875	0.000699819 0
$935$	0	0
$936$	14.0478	0.459166
$937$	−51.4725	−1.68153	−0.840767	−	0.541397i	$-0.817896\pi$
$937$	−51.4725	−1.68153	−0.840767	+	0.541397i	$0.817896\pi$
$938$	31.5742	1.03094
$939$	20.1274	0.656832
$940$	0	0
$941$	−19.4724	−0.634782	−0.317391	−	0.948295i	$-0.602807\pi$
$941$	−19.4724	−0.634782	−0.317391	+	0.948295i	$0.602807\pi$
$942$	4.07955	0.132919
$943$	−5.11199	−0.166469
$944$	0.0746963	0.00243116
$945$	0	0
$946$	19.2469	0.625772
$947$	38.9572	1.26594	0.632970	−	0.774177i	$-0.281836\pi$
$947$	38.9572	1.26594	0.632970	+	0.774177i	$0.281836\pi$
$948$	7.66078	0.248810
$949$	20.3409	0.660295
$950$	0	0
$951$	−12.7288	−0.412760
$952$	−36.1762	−1.17248
$953$	0.532270	0.0172419	0.00862095	−	0.999963i	$-0.497256\pi$
$953$	0.532270	0.0172419	0.00862095	+	0.999963i	$0.497256\pi$
$954$	−3.04239	−0.0985009
$955$	0	0
$956$	20.5156	0.663522
$957$	−46.1420	−1.49156
$958$	−7.16178	−0.231387
$959$	5.18419	0.167406
$960$	0	0
$961$	10.0220	0.323290
$962$	11.6831	0.376677
$963$	14.1662	0.456499
$964$	−0.119542	−0.00385019
$965$	0	0
$966$	−2.93358	−0.0943865
$967$	−36.8517	−1.18507	−0.592536	−	0.805544i	$-0.701873\pi$
$967$	−36.8517	−1.18507	−0.592536	+	0.805544i	$0.701873\pi$
$968$	76.9358	2.47281
$969$	−8.02222	−0.257711
$970$	0	0
$971$	4.25064	0.136410	0.0682048	−	0.997671i	$-0.478273\pi$
$971$	4.25064	0.136410	0.0682048	+	0.997671i	$0.478273\pi$
$972$	−1.40699	−0.0451292
$973$	15.3310	0.491488
$974$	25.1014	0.804302
$975$	0	0
$976$	−5.24709	−0.167955
$977$	31.6086	1.01125	0.505625	−	0.862754i	$-0.331262\pi$
$977$	31.6086	1.01125	0.505625	+	0.862754i	$0.331262\pi$
$978$	2.20554	0.0705255
$979$	−64.3130	−2.05545
$980$	0	0
$981$	14.0557	0.448763
$982$	0.832590	0.0265690
$983$	−45.3330	−1.44590	−0.722949	−	0.690901i	$-0.757214\pi$
$983$	−45.3330	−1.44590	−0.722949	+	0.690901i	$0.757214\pi$
$984$	−14.0407	−0.447601
$985$	0	0
$986$	19.3465	0.616117
$987$	9.90430	0.315257
$988$	−17.4797	−0.556103
$989$	3.75968	0.119551
$990$	0	0
$991$	9.20124	0.292287	0.146143	−	0.989263i	$-0.453314\pi$
$991$	9.20124	0.292287	0.146143	+	0.989263i	$0.453314\pi$
$992$	−37.5220	−1.19132
$993$	−16.3131	−0.517680
$994$	17.8612	0.566522
$995$	0	0
$996$	−13.0104	−0.412250
$997$	−13.1014	−0.414924	−0.207462	−	0.978243i	$-0.566520\pi$
$997$	−13.1014	−0.414924	−0.207462	+	0.978243i	$0.566520\pi$
$998$	33.8474	1.07142
$999$	−2.83348	−0.0896473

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.a.o.1.4	yes	8
3.2	odd	2		5625.2.a.u.1.5		8
5.2	odd	4		1875.2.b.g.1249.7		16
5.3	odd	4		1875.2.b.g.1249.10		16
5.4	even	2		1875.2.a.n.1.5	✓	8
15.14	odd	2		5625.2.a.bc.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1875.2.a.n.1.5	✓	8	5.4	even	2
1875.2.a.o.1.4	yes	8	1.1	even	1	trivial
1875.2.b.g.1249.7		16	5.2	odd	4
1875.2.b.g.1249.10		16	5.3	odd	4
5625.2.a.u.1.5		8	3.2	odd	2
5625.2.a.bc.1.4		8	15.14	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:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1875.a (trivial)

\(f(q)\)	\(=\)	\(q-0.770071 q^{2} +1.00000 q^{3} -1.40699 q^{4} -0.770071 q^{6} +3.98808 q^{7} +2.62363 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.770071 q^{2} +1.00000 q^{3} -1.40699 q^{4} -0.770071 q^{6} +3.98808 q^{7} +2.62363 q^{8} +1.00000 q^{9} -6.35014 q^{11} -1.40699 q^{12} +5.35433 q^{13} -3.07111 q^{14} +0.793602 q^{16} -3.45746 q^{17} -0.770071 q^{18} +2.32026 q^{19} +3.98808 q^{21} +4.89006 q^{22} +0.955221 q^{23} +2.62363 q^{24} -4.12322 q^{26} +1.00000 q^{27} -5.61119 q^{28} +7.26630 q^{29} +6.40484 q^{31} -5.85838 q^{32} -6.35014 q^{33} +2.66249 q^{34} -1.40699 q^{36} -2.83348 q^{37} -1.78677 q^{38} +5.35433 q^{39} -5.35164 q^{41} -3.07111 q^{42} +3.93593 q^{43} +8.93458 q^{44} -0.735588 q^{46} +2.48348 q^{47} +0.793602 q^{48} +8.90478 q^{49} -3.45746 q^{51} -7.53350 q^{52} +3.95079 q^{53} -0.770071 q^{54} +10.4632 q^{56} +2.32026 q^{57} -5.59557 q^{58} +0.0941232 q^{59} -6.61174 q^{61} -4.93218 q^{62} +3.98808 q^{63} +2.92417 q^{64} +4.89006 q^{66} -10.2811 q^{67} +4.86461 q^{68} +0.955221 q^{69} -5.81587 q^{71} +2.62363 q^{72} +3.79897 q^{73} +2.18198 q^{74} -3.26459 q^{76} -25.3249 q^{77} -4.12322 q^{78} -5.44480 q^{79} +1.00000 q^{81} +4.12114 q^{82} +9.24696 q^{83} -5.61119 q^{84} -3.03095 q^{86} +7.26630 q^{87} -16.6604 q^{88} +10.1278 q^{89} +21.3535 q^{91} -1.34399 q^{92} +6.40484 q^{93} -1.91245 q^{94} -5.85838 q^{96} +7.89936 q^{97} -6.85731 q^{98} -6.35014 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 8 q^{3} + 9 q^{4} + q^{6} + 12 q^{7} + 3 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + q^2 + 8 * q^3 + 9 * q^4 + q^6 + 12 * q^7 + 3 * q^8 + 8 * q^9	\( 8 q + q^{2} + 8 q^{3} + 9 q^{4} + q^{6} + 12 q^{7} + 3 q^{8} + 8 q^{9} + 12 q^{11} + 9 q^{12} + 14 q^{13} + 16 q^{14} + 15 q^{16} - q^{17} + q^{18} + 16 q^{19} + 12 q^{21} + 18 q^{22} - 4 q^{23} + 3 q^{24} - 34 q^{26} + 8 q^{27} - 21 q^{28} + 2 q^{29} + 13 q^{31} - 18 q^{32} + 12 q^{33} - 37 q^{34} + 9 q^{36} - 8 q^{37} - 24 q^{38} + 14 q^{39} - 12 q^{41} + 16 q^{42} + 20 q^{43} + 47 q^{44} + 33 q^{46} - 15 q^{47} + 15 q^{48} + 30 q^{49} - q^{51} - q^{52} - 4 q^{53} + q^{54} + 60 q^{56} + 16 q^{57} + 2 q^{58} + 14 q^{59} + 10 q^{61} + 4 q^{62} + 12 q^{63} + 41 q^{64} + 18 q^{66} + 19 q^{67} - 33 q^{68} - 4 q^{69} + 21 q^{71} + 3 q^{72} - 19 q^{73} - 9 q^{74} - q^{76} - 11 q^{77} - 34 q^{78} + 10 q^{79} + 8 q^{81} + 24 q^{82} - 27 q^{83} - 21 q^{84} + 42 q^{86} + 2 q^{87} + 53 q^{88} - 9 q^{89} - 12 q^{91} - 63 q^{92} + 13 q^{93} + 14 q^{94} - 18 q^{96} + 24 q^{97} - 24 q^{98} + 12 q^{99}+O(q^{100}) \) 8 * q + q^2 + 8 * q^3 + 9 * q^4 + q^6 + 12 * q^7 + 3 * q^8 + 8 * q^9 + 12 * q^11 + 9 * q^12 + 14 * q^13 + 16 * q^14 + 15 * q^16 - q^17 + q^18 + 16 * q^19 + 12 * q^21 + 18 * q^22 - 4 * q^23 + 3 * q^24 - 34 * q^26 + 8 * q^27 - 21 * q^28 + 2 * q^29 + 13 * q^31 - 18 * q^32 + 12 * q^33 - 37 * q^34 + 9 * q^36 - 8 * q^37 - 24 * q^38 + 14 * q^39 - 12 * q^41 + 16 * q^42 + 20 * q^43 + 47 * q^44 + 33 * q^46 - 15 * q^47 + 15 * q^48 + 30 * q^49 - q^51 - q^52 - 4 * q^53 + q^54 + 60 * q^56 + 16 * q^57 + 2 * q^58 + 14 * q^59 + 10 * q^61 + 4 * q^62 + 12 * q^63 + 41 * q^64 + 18 * q^66 + 19 * q^67 - 33 * q^68 - 4 * q^69 + 21 * q^71 + 3 * q^72 - 19 * q^73 - 9 * q^74 - q^76 - 11 * q^77 - 34 * q^78 + 10 * q^79 + 8 * q^81 + 24 * q^82 - 27 * q^83 - 21 * q^84 + 42 * q^86 + 2 * q^87 + 53 * q^88 - 9 * q^89 - 12 * q^91 - 63 * q^92 + 13 * q^93 + 14 * q^94 - 18 * q^96 + 24 * q^97 - 24 * q^98 + 12 * q^99

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