LMFDB - Embedded newform 1075.2.a.q.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,2,Mod(1,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, 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("1075.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1075.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:	$8.58391821729$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.282109865.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 11x^{4} + 8x^{3} + 34x^{2} - 12x - 27 $ x^6 - x^5 - 11x^4 + 8x^3 + 34x^2 - 12x - 27
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.920974$ of defining polynomial
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.920974 q^{2} -3.18563 q^{3} -1.15181 q^{4} -2.93388 q^{6} -2.23083 q^{7} -2.90273 q^{8} +7.14823 q^{9} +O(q^{10})$	\(q+0.920974 q^{2} -3.18563 q^{3} -1.15181 q^{4} -2.93388 q^{6} -2.23083 q^{7} -2.90273 q^{8} +7.14823 q^{9} -6.02758 q^{11} +3.66923 q^{12} -0.827279 q^{13} -2.05454 q^{14} -0.369730 q^{16} -3.19701 q^{17} +6.58334 q^{18} +1.19701 q^{19} +7.10660 q^{21} -5.55124 q^{22} -5.21678 q^{23} +9.24703 q^{24} -0.761903 q^{26} -13.2147 q^{27} +2.56949 q^{28} +9.80965 q^{29} -6.20030 q^{31} +5.46495 q^{32} +19.2016 q^{33} -2.94436 q^{34} -8.23338 q^{36} +2.53033 q^{37} +1.10241 q^{38} +2.63540 q^{39} +8.55689 q^{41} +6.54500 q^{42} +1.00000 q^{43} +6.94260 q^{44} -4.80452 q^{46} +11.7549 q^{47} +1.17782 q^{48} -2.02339 q^{49} +10.1845 q^{51} +0.952865 q^{52} -8.72019 q^{53} -12.1704 q^{54} +6.47551 q^{56} -3.81323 q^{57} +9.03444 q^{58} +3.63808 q^{59} +4.61943 q^{61} -5.71032 q^{62} -15.9465 q^{63} +5.77254 q^{64} +17.6842 q^{66} +7.63693 q^{67} +3.68233 q^{68} +16.6187 q^{69} +0.418505 q^{71} -20.7494 q^{72} -9.88154 q^{73} +2.33037 q^{74} -1.37872 q^{76} +13.4465 q^{77} +2.42714 q^{78} -10.3498 q^{79} +20.6525 q^{81} +7.88067 q^{82} +7.74888 q^{83} -8.18543 q^{84} +0.920974 q^{86} -31.2499 q^{87} +17.4964 q^{88} -7.86050 q^{89} +1.84552 q^{91} +6.00872 q^{92} +19.7519 q^{93} +10.8260 q^{94} -17.4093 q^{96} -5.93400 q^{97} -1.86349 q^{98} -43.0865 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 2 q^{3} + 11 q^{4} + 11 q^{6} - 2 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 6 * q - q^2 - 2 * q^3 + 11 * q^4 + 11 * q^6 - 2 * q^7 - 6 * q^8 + 12 * q^9	$ 6 q - q^{2} - 2 q^{3} + 11 q^{4} + 11 q^{6} - 2 q^{7} - 6 q^{8} + 12 q^{9} - 6 q^{11} + 4 q^{12} + 17 q^{14} + 5 q^{16} - 7 q^{17} + 15 q^{18} - 5 q^{19} + 19 q^{21} - 34 q^{22} + 3 q^{23} + 9 q^{24} + 14 q^{26} - 5 q^{27} + 21 q^{28} + 18 q^{29} - 12 q^{31} - 3 q^{32} + 10 q^{33} + q^{34} - 10 q^{36} - 7 q^{37} + q^{38} - 3 q^{39} + 9 q^{42} + 6 q^{43} + 9 q^{44} - 14 q^{46} + 6 q^{47} - 2 q^{48} - q^{51} - 3 q^{52} + 8 q^{53} + 12 q^{54} + 20 q^{56} + 5 q^{57} + 24 q^{58} + 21 q^{59} - 8 q^{61} - 47 q^{62} - 19 q^{63} + 6 q^{64} + q^{66} + 35 q^{68} + 37 q^{69} + 14 q^{71} - 44 q^{72} + q^{73} + 2 q^{74} - 57 q^{76} - 13 q^{77} + 49 q^{78} - 31 q^{79} + 62 q^{81} - 32 q^{82} + 13 q^{83} + 21 q^{84} - q^{86} - 22 q^{87} - 39 q^{88} + 40 q^{89} + 11 q^{91} + 32 q^{92} + 15 q^{93} + 35 q^{94} - 50 q^{96} - 11 q^{97} + 44 q^{98} - 53 q^{99}+O(q^{100}) $ 6 * q - q^2 - 2 * q^3 + 11 * q^4 + 11 * q^6 - 2 * q^7 - 6 * q^8 + 12 * q^9 - 6 * q^11 + 4 * q^12 + 17 * q^14 + 5 * q^16 - 7 * q^17 + 15 * q^18 - 5 * q^19 + 19 * q^21 - 34 * q^22 + 3 * q^23 + 9 * q^24 + 14 * q^26 - 5 * q^27 + 21 * q^28 + 18 * q^29 - 12 * q^31 - 3 * q^32 + 10 * q^33 + q^34 - 10 * q^36 - 7 * q^37 + q^38 - 3 * q^39 + 9 * q^42 + 6 * q^43 + 9 * q^44 - 14 * q^46 + 6 * q^47 - 2 * q^48 - q^51 - 3 * q^52 + 8 * q^53 + 12 * q^54 + 20 * q^56 + 5 * q^57 + 24 * q^58 + 21 * q^59 - 8 * q^61 - 47 * q^62 - 19 * q^63 + 6 * q^64 + q^66 + 35 * q^68 + 37 * q^69 + 14 * q^71 - 44 * q^72 + q^73 + 2 * q^74 - 57 * q^76 - 13 * q^77 + 49 * q^78 - 31 * q^79 + 62 * q^81 - 32 * q^82 + 13 * q^83 + 21 * q^84 - q^86 - 22 * q^87 - 39 * q^88 + 40 * q^89 + 11 * q^91 + 32 * q^92 + 15 * q^93 + 35 * q^94 - 50 * q^96 - 11 * q^97 + 44 * q^98 - 53 * 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 $

$2$	0.920974	0.651227	0.325614	−	0.945503i	$-0.394429\pi$
$2$	0.920974	0.651227	0.325614	+	0.945503i	$0.394429\pi$
$3$	−3.18563	−1.83922	−0.919612	−	0.392828i	$-0.871497\pi$
$3$	−3.18563	−1.83922	−0.919612	+	0.392828i	$0.871497\pi$
$4$	−1.15181	−0.575903
$5$	0	0
$5$	0	0
$6$	−2.93388	−1.19775
$7$	−2.23083	−0.843175	−0.421588	−	0.906788i	$-0.638527\pi$
$7$	−2.23083	−0.843175	−0.421588	+	0.906788i	$0.638527\pi$
$8$	−2.90273	−1.02627
$9$	7.14823	2.38274
$10$	0	0
$11$	−6.02758	−1.81738	−0.908692	−	0.417468i	$-0.862918\pi$
$11$	−6.02758	−1.81738	−0.908692	+	0.417468i	$0.862918\pi$
$12$	3.66923	1.05921
$13$	−0.827279	−0.229446	−0.114723	−	0.993398i	$-0.536598\pi$
$13$	−0.827279	−0.229446	−0.114723	+	0.993398i	$0.536598\pi$
$14$	−2.05454	−0.549099
$15$	0	0
$16$	−0.369730	−0.0924324
$17$	−3.19701	−0.775389	−0.387694	−	0.921788i	$-0.626728\pi$
$17$	−3.19701	−0.775389	−0.387694	+	0.921788i	$0.626728\pi$
$18$	6.58334	1.55171
$19$	1.19701	0.274613	0.137306	−	0.990529i	$-0.456156\pi$
$19$	1.19701	0.274613	0.137306	+	0.990529i	$0.456156\pi$
$20$	0	0
$21$	7.10660	1.55079
$22$	−5.55124	−1.18353
$23$	−5.21678	−1.08777	−0.543887	−	0.839159i	$-0.683048\pi$
$23$	−5.21678	−1.08777	−0.543887	+	0.839159i	$0.683048\pi$
$24$	9.24703	1.88754
$25$	0	0
$26$	−0.761903	−0.149421
$27$	−13.2147	−2.54318
$28$	2.56949	0.485587
$29$	9.80965	1.82161	0.910804	−	0.412840i	$-0.135463\pi$
$29$	9.80965	1.82161	0.910804	+	0.412840i	$0.135463\pi$
$30$	0	0
$31$	−6.20030	−1.11361	−0.556803	−	0.830644i	$-0.687972\pi$
$31$	−6.20030	−1.11361	−0.556803	+	0.830644i	$0.687972\pi$
$32$	5.46495	0.966076
$33$	19.2016	3.34257
$34$	−2.94436	−0.504954
$35$	0	0
$36$	−8.23338	−1.37223
$37$	2.53033	0.415984	0.207992	−	0.978131i	$-0.433307\pi$
$37$	2.53033	0.415984	0.207992	+	0.978131i	$0.433307\pi$
$38$	1.10241	0.178835
$39$	2.63540	0.422003
$40$	0	0
$41$	8.55689	1.33636	0.668181	−	0.743999i	$-0.267073\pi$
$41$	8.55689	1.33636	0.668181	+	0.743999i	$0.267073\pi$
$42$	6.54500	1.00992
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	6.94260	1.04664
$45$	0	0
$46$	−4.80452	−0.708388
$47$	11.7549	1.71463	0.857315	−	0.514791i	$-0.172131\pi$
$47$	11.7549	1.71463	0.857315	+	0.514791i	$0.172131\pi$
$48$	1.17782	0.170004
$49$	−2.02339	−0.289056
$50$	0	0
$51$	10.1845	1.42611
$52$	0.952865	0.132139
$53$	−8.72019	−1.19781	−0.598905	−	0.800820i	$-0.704397\pi$
$53$	−8.72019	−1.19781	−0.598905	+	0.800820i	$0.704397\pi$
$54$	−12.1704	−1.65619
$55$	0	0
$56$	6.47551	0.865326
$57$	−3.81323	−0.505074
$58$	9.03444	1.18628
$59$	3.63808	0.473637	0.236819	−	0.971554i	$-0.423895\pi$
$59$	3.63808	0.473637	0.236819	+	0.971554i	$0.423895\pi$
$60$	0	0
$61$	4.61943	0.591458	0.295729	−	0.955272i	$-0.404438\pi$
$61$	4.61943	0.591458	0.295729	+	0.955272i	$0.404438\pi$
$62$	−5.71032	−0.725211
$63$	−15.9465	−2.00907
$64$	5.77254	0.721568
$65$	0	0
$66$	17.6842	2.17678
$67$	7.63693	0.933000	0.466500	−	0.884521i	$-0.345515\pi$
$67$	7.63693	0.933000	0.466500	+	0.884521i	$0.345515\pi$
$68$	3.68233	0.446549
$69$	16.6187	2.00066
$70$	0	0
$71$	0.418505	0.0496674	0.0248337	−	0.999692i	$-0.492094\pi$
$71$	0.418505	0.0496674	0.0248337	+	0.999692i	$0.492094\pi$
$72$	−20.7494	−2.44534
$73$	−9.88154	−1.15655	−0.578273	−	0.815843i	$-0.696273\pi$
$73$	−9.88154	−1.15655	−0.578273	+	0.815843i	$0.696273\pi$
$74$	2.33037	0.270900
$75$	0	0
$76$	−1.37872	−0.158150
$77$	13.4465	1.53237
$78$	2.42714	0.274820
$79$	−10.3498	−1.16445	−0.582224	−	0.813029i	$-0.697817\pi$
$79$	−10.3498	−1.16445	−0.582224	+	0.813029i	$0.697817\pi$
$80$	0	0
$81$	20.6525	2.29473
$82$	7.88067	0.870275
$83$	7.74888	0.850550	0.425275	−	0.905064i	$-0.360177\pi$
$83$	7.74888	0.850550	0.425275	+	0.905064i	$0.360177\pi$
$84$	−8.18543	−0.893104
$85$	0	0
$86$	0.920974	0.0993112
$87$	−31.2499	−3.35034
$88$	17.4964	1.86513
$89$	−7.86050	−0.833211	−0.416606	−	0.909087i	$-0.636780\pi$
$89$	−7.86050	−0.833211	−0.416606	+	0.909087i	$0.636780\pi$
$90$	0	0
$91$	1.84552	0.193463
$92$	6.00872	0.626452
$93$	19.7519	2.04817
$94$	10.8260	1.11661
$95$	0	0
$96$	−17.4093	−1.77683
$97$	−5.93400	−0.602507	−0.301253	−	0.953544i	$-0.597405\pi$
$97$	−5.93400	−0.602507	−0.301253	+	0.953544i	$0.597405\pi$
$98$	−1.86349	−0.188241
$99$	−43.0865	−4.33036
$100$	0	0
$101$	4.16338	0.414272	0.207136	−	0.978312i	$-0.433586\pi$
$101$	4.16338	0.414272	0.207136	+	0.978312i	$0.433586\pi$
$102$	9.37965	0.928724
$103$	6.70757	0.660916	0.330458	−	0.943821i	$-0.392797\pi$
$103$	6.70757	0.660916	0.330458	+	0.943821i	$0.392797\pi$
$104$	2.40137	0.235474
$105$	0	0
$106$	−8.03108	−0.780047
$107$	−2.42160	−0.234105	−0.117052	−	0.993126i	$-0.537344\pi$
$107$	−2.42160	−0.234105	−0.117052	+	0.993126i	$0.537344\pi$
$108$	15.2208	1.46462
$109$	−5.23781	−0.501692	−0.250846	−	0.968027i	$-0.580709\pi$
$109$	−5.23781	−0.501692	−0.250846	+	0.968027i	$0.580709\pi$
$110$	0	0
$111$	−8.06069	−0.765087
$112$	0.824805	0.0779367
$113$	−16.9968	−1.59893	−0.799464	−	0.600713i	$-0.794883\pi$
$113$	−16.9968	−1.59893	−0.799464	+	0.600713i	$0.794883\pi$
$114$	−3.51188	−0.328918
$115$	0	0
$116$	−11.2988	−1.04907
$117$	−5.91359	−0.546711
$118$	3.35058	0.308446
$119$	7.13199	0.653788
$120$	0	0
$121$	25.3317	2.30288
$122$	4.25438	0.385173
$123$	−27.2591	−2.45787
$124$	7.14154	0.641330
$125$	0	0
$126$	−14.6863	−1.30836
$127$	5.00267	0.443915	0.221958	−	0.975056i	$-0.428755\pi$
$127$	5.00267	0.443915	0.221958	+	0.975056i	$0.428755\pi$
$128$	−5.61354	−0.496172
$129$	−3.18563	−0.280479
$130$	0	0
$131$	−3.58651	−0.313355	−0.156677	−	0.987650i	$-0.550078\pi$
$131$	−3.58651	−0.313355	−0.156677	+	0.987650i	$0.550078\pi$
$132$	−22.1166	−1.92500
$133$	−2.67033	−0.231547
$134$	7.03342	0.607595
$135$	0	0
$136$	9.28006	0.795759
$137$	5.88193	0.502527	0.251264	−	0.967919i	$-0.419154\pi$
$137$	5.88193	0.502527	0.251264	+	0.967919i	$0.419154\pi$
$138$	15.3054	1.30288
$139$	3.84348	0.326000	0.163000	−	0.986626i	$-0.447883\pi$
$139$	3.84348	0.326000	0.163000	+	0.986626i	$0.447883\pi$
$140$	0	0
$141$	−37.4468	−3.15359
$142$	0.385432	0.0323447
$143$	4.98649	0.416991
$144$	−2.64291	−0.220243
$145$	0	0
$146$	−9.10064	−0.753174
$147$	6.44577	0.531638
$148$	−2.91445	−0.239566
$149$	−17.7268	−1.45224	−0.726119	−	0.687569i	$-0.758678\pi$
$149$	−17.7268	−1.45224	−0.726119	+	0.687569i	$0.758678\pi$
$150$	0	0
$151$	0.490789	0.0399398	0.0199699	−	0.999801i	$-0.493643\pi$
$151$	0.490789	0.0399398	0.0199699	+	0.999801i	$0.493643\pi$
$152$	−3.47460	−0.281827
$153$	−22.8530	−1.84755
$154$	12.3839	0.997923
$155$	0	0
$156$	−3.03548	−0.243033
$157$	2.49569	0.199177	0.0995887	−	0.995029i	$-0.468247\pi$
$157$	2.49569	0.199177	0.0995887	+	0.995029i	$0.468247\pi$
$158$	−9.53193	−0.758320
$159$	27.7793	2.20304
$160$	0	0
$161$	11.6378	0.917184
$162$	19.0205	1.49439
$163$	22.1544	1.73527	0.867634	−	0.497204i	$-0.165640\pi$
$163$	22.1544	1.73527	0.867634	+	0.497204i	$0.165640\pi$
$164$	−9.85588	−0.769615
$165$	0	0
$166$	7.13652	0.553902
$167$	13.6238	1.05424	0.527120	−	0.849791i	$-0.323272\pi$
$167$	13.6238	1.05424	0.527120	+	0.849791i	$0.323272\pi$
$168$	−20.6286	−1.59153
$169$	−12.3156	−0.947355
$170$	0	0
$171$	8.55650	0.654332
$172$	−1.15181	−0.0878244
$173$	9.58487	0.728724	0.364362	−	0.931257i	$-0.381287\pi$
$173$	9.58487	0.728724	0.364362	+	0.931257i	$0.381287\pi$
$174$	−28.7804	−2.18183
$175$	0	0
$176$	2.22857	0.167985
$177$	−11.5896	−0.871125
$178$	−7.23932	−0.542610
$179$	22.7649	1.70153	0.850764	−	0.525549i	$-0.176140\pi$
$179$	22.7649	1.70153	0.850764	+	0.525549i	$0.176140\pi$
$180$	0	0
$181$	1.04780	0.0778822	0.0389411	−	0.999242i	$-0.487602\pi$
$181$	1.04780	0.0778822	0.0389411	+	0.999242i	$0.487602\pi$
$182$	1.69968	0.125988
$183$	−14.7158	−1.08782
$184$	15.1429	1.11635
$185$	0	0
$186$	18.1910	1.33383
$187$	19.2702	1.40918
$188$	−13.5394	−0.987461
$189$	29.4799	2.14434
$190$	0	0
$191$	−4.76445	−0.344744	−0.172372	−	0.985032i	$-0.555143\pi$
$191$	−4.76445	−0.344744	−0.172372	+	0.985032i	$0.555143\pi$
$192$	−18.3892	−1.32712
$193$	8.50247	0.612021	0.306011	−	0.952028i	$-0.401006\pi$
$193$	8.50247	0.612021	0.306011	+	0.952028i	$0.401006\pi$
$194$	−5.46507	−0.392369
$195$	0	0
$196$	2.33055	0.166468
$197$	−19.2227	−1.36956	−0.684779	−	0.728751i	$-0.740101\pi$
$197$	−19.2227	−1.36956	−0.684779	+	0.728751i	$0.740101\pi$
$198$	−39.6816	−2.82005
$199$	−16.6617	−1.18112	−0.590559	−	0.806995i	$-0.701093\pi$
$199$	−16.6617	−1.18112	−0.590559	+	0.806995i	$0.701093\pi$
$200$	0	0
$201$	−24.3284	−1.71600
$202$	3.83437	0.269785
$203$	−21.8837	−1.53593
$204$	−11.7306	−0.821303
$205$	0	0
$206$	6.17750	0.430407
$207$	−37.2908	−2.59189
$208$	0.305870	0.0212082
$209$	−7.21506	−0.499076
$210$	0	0
$211$	−19.7154	−1.35726	−0.678631	−	0.734479i	$-0.737426\pi$
$211$	−19.7154	−1.35726	−0.678631	+	0.734479i	$0.737426\pi$
$212$	10.0440	0.689823
$213$	−1.33320	−0.0913494
$214$	−2.23023	−0.152455
$215$	0	0
$216$	38.3588	2.60999
$217$	13.8318	0.938965
$218$	−4.82389	−0.326715
$219$	31.4789	2.12715
$220$	0	0
$221$	2.64482	0.177910
$222$	−7.42369	−0.498246
$223$	−23.6343	−1.58267	−0.791334	−	0.611385i	$-0.790613\pi$
$223$	−23.6343	−1.58267	−0.791334	+	0.611385i	$0.790613\pi$
$224$	−12.1914	−0.814572
$225$	0	0
$226$	−15.6537	−1.04127
$227$	5.33292	0.353958	0.176979	−	0.984215i	$-0.443367\pi$
$227$	5.33292	0.353958	0.176979	+	0.984215i	$0.443367\pi$
$228$	4.39210	0.290874
$229$	8.01915	0.529921	0.264960	−	0.964259i	$-0.414641\pi$
$229$	8.01915	0.529921	0.264960	+	0.964259i	$0.414641\pi$
$230$	0	0
$231$	−42.8356	−2.81838
$232$	−28.4748	−1.86946
$233$	23.6181	1.54727	0.773637	−	0.633629i	$-0.218435\pi$
$233$	23.6181	1.54727	0.773637	+	0.633629i	$0.218435\pi$
$234$	−5.44626	−0.356033
$235$	0	0
$236$	−4.19036	−0.272769
$237$	32.9707	2.14168
$238$	6.56838	0.425765
$239$	8.41088	0.544055	0.272027	−	0.962290i	$-0.412306\pi$
$239$	8.41088	0.544055	0.272027	+	0.962290i	$0.412306\pi$
$240$	0	0
$241$	−25.2640	−1.62740	−0.813698	−	0.581288i	$-0.802549\pi$
$241$	−25.2640	−1.62740	−0.813698	+	0.581288i	$0.802549\pi$
$242$	23.3298	1.49970
$243$	−26.1472	−1.67734
$244$	−5.32069	−0.340622
$245$	0	0
$246$	−25.1049	−1.60063
$247$	−0.990261	−0.0630088
$248$	17.9978	1.14286
$249$	−24.6851	−1.56435
$250$	0	0
$251$	−4.07895	−0.257461	−0.128730	−	0.991680i	$-0.541090\pi$
$251$	−4.07895	−0.257461	−0.128730	+	0.991680i	$0.541090\pi$
$252$	18.3673	1.15703
$253$	31.4445	1.97690
$254$	4.60733	0.289090
$255$	0	0
$256$	−16.7150	−1.04469
$257$	17.7131	1.10491	0.552455	−	0.833543i	$-0.313691\pi$
$257$	17.7131	1.10491	0.552455	+	0.833543i	$0.313691\pi$
$258$	−2.93388	−0.182656
$259$	−5.64474	−0.350747
$260$	0	0
$261$	70.1217	4.34042
$262$	−3.30308	−0.204065
$263$	−7.12925	−0.439608	−0.219804	−	0.975544i	$-0.570542\pi$
$263$	−7.12925	−0.439608	−0.219804	+	0.975544i	$0.570542\pi$
$264$	−55.7372	−3.43039
$265$	0	0
$266$	−2.45930	−0.150789
$267$	25.0406	1.53246
$268$	−8.79627	−0.537318
$269$	28.4501	1.73463	0.867317	−	0.497756i	$-0.165842\pi$
$269$	28.4501	1.73463	0.867317	+	0.497756i	$0.165842\pi$
$270$	0	0
$271$	5.50403	0.334346	0.167173	−	0.985928i	$-0.446536\pi$
$271$	5.50403	0.334346	0.167173	+	0.985928i	$0.446536\pi$
$272$	1.18203	0.0716711
$273$	−5.87915	−0.355822
$274$	5.41711	0.327259
$275$	0	0
$276$	−19.1416	−1.15219
$277$	2.58762	0.155475	0.0777374	−	0.996974i	$-0.475230\pi$
$277$	2.58762	0.155475	0.0777374	+	0.996974i	$0.475230\pi$
$278$	3.53974	0.212300
$279$	−44.3212	−2.65344
$280$	0	0
$281$	−20.6194	−1.23005	−0.615026	−	0.788506i	$-0.710855\pi$
$281$	−20.6194	−1.23005	−0.615026	+	0.788506i	$0.710855\pi$
$282$	−34.4875	−2.05370
$283$	10.3853	0.617342	0.308671	−	0.951169i	$-0.400116\pi$
$283$	10.3853	0.617342	0.308671	+	0.951169i	$0.400116\pi$
$284$	−0.482036	−0.0286036
$285$	0	0
$286$	4.59243	0.271556
$287$	−19.0890	−1.12679
$288$	39.0648	2.30191
$289$	−6.77913	−0.398773
$290$	0	0
$291$	18.9035	1.10814
$292$	11.3816	0.666059
$293$	15.2912	0.893322	0.446661	−	0.894703i	$-0.352613\pi$
$293$	15.2912	0.893322	0.446661	+	0.894703i	$0.352613\pi$
$294$	5.93639	0.346217
$295$	0	0
$296$	−7.34487	−0.426912
$297$	79.6529	4.62193
$298$	−16.3260	−0.945737
$299$	4.31573	0.249585
$300$	0	0
$301$	−2.23083	−0.128583
$302$	0.452004	0.0260099
$303$	−13.2630	−0.761939
$304$	−0.442570	−0.0253831
$305$	0	0
$306$	−21.0470	−1.20318
$307$	21.6017	1.23287	0.616437	−	0.787404i	$-0.288576\pi$
$307$	21.6017	1.23287	0.616437	+	0.787404i	$0.288576\pi$
$308$	−15.4878	−0.882498
$309$	−21.3678	−1.21557
$310$	0	0
$311$	29.3890	1.66650	0.833249	−	0.552898i	$-0.186478\pi$
$311$	29.3890	1.66650	0.833249	+	0.552898i	$0.186478\pi$
$312$	−7.64988	−0.433089
$313$	7.88896	0.445911	0.222955	−	0.974829i	$-0.428430\pi$
$313$	7.88896	0.445911	0.222955	+	0.974829i	$0.428430\pi$
$314$	2.29846	0.129710
$315$	0	0
$316$	11.9210	0.670609
$317$	−1.10994	−0.0623404	−0.0311702	−	0.999514i	$-0.509923\pi$
$317$	−1.10994	−0.0623404	−0.0311702	+	0.999514i	$0.509923\pi$
$318$	25.5840	1.43468
$319$	−59.1285	−3.31056
$320$	0	0
$321$	7.71431	0.430571
$322$	10.7181	0.597295
$323$	−3.82685	−0.212932
$324$	−23.7877	−1.32154
$325$	0	0
$326$	20.4036	1.13005
$327$	16.6857	0.922723
$328$	−24.8384	−1.37147
$329$	−26.2232	−1.44573
$330$	0	0
$331$	−10.9028	−0.599270	−0.299635	−	0.954054i	$-0.596865\pi$
$331$	−10.9028	−0.599270	−0.299635	+	0.954054i	$0.596865\pi$
$332$	−8.92521	−0.489835
$333$	18.0874	0.991183
$334$	12.5472	0.686550
$335$	0	0
$336$	−2.62752	−0.143343
$337$	32.6494	1.77853	0.889263	−	0.457397i	$-0.151218\pi$
$337$	32.6494	1.77853	0.889263	+	0.457397i	$0.151218\pi$
$338$	−11.3424	−0.616943
$339$	54.1457	2.94079
$340$	0	0
$341$	37.3728	2.02385
$342$	7.88032	0.426119
$343$	20.1297	1.08690
$344$	−2.90273	−0.156505
$345$	0	0
$346$	8.82742	0.474565
$347$	6.75915	0.362850	0.181425	−	0.983405i	$-0.441929\pi$
$347$	6.75915	0.362850	0.181425	+	0.983405i	$0.441929\pi$
$348$	35.9939	1.92947
$349$	33.5638	1.79663	0.898313	−	0.439355i	$-0.144793\pi$
$349$	33.5638	1.79663	0.898313	+	0.439355i	$0.144793\pi$
$350$	0	0
$351$	10.9323	0.583522
$352$	−32.9404	−1.75573
$353$	33.8726	1.80286	0.901429	−	0.432928i	$-0.142519\pi$
$353$	33.8726	1.80286	0.901429	+	0.432928i	$0.142519\pi$
$354$	−10.6737	−0.567300
$355$	0	0
$356$	9.05377	0.479849
$357$	−22.7199	−1.20246
$358$	20.9659	1.10808
$359$	25.6258	1.35248	0.676238	−	0.736683i	$-0.263609\pi$
$359$	25.6258	1.35248	0.676238	+	0.736683i	$0.263609\pi$
$360$	0	0
$361$	−17.5672	−0.924588
$362$	0.964995	0.0507190
$363$	−80.6974	−4.23551
$364$	−2.12568	−0.111416
$365$	0	0
$366$	−13.5529	−0.708420
$367$	−3.64783	−0.190415	−0.0952077	−	0.995457i	$-0.530352\pi$
$367$	−3.64783	−0.190415	−0.0952077	+	0.995457i	$0.530352\pi$
$368$	1.92880	0.100546
$369$	61.1666	3.18421
$370$	0	0
$371$	19.4533	1.00996
$372$	−22.7503	−1.17955
$373$	17.3176	0.896669	0.448335	−	0.893866i	$-0.352017\pi$
$373$	17.3176	0.896669	0.448335	+	0.893866i	$0.352017\pi$
$374$	17.7474	0.917695
$375$	0	0
$376$	−34.1214	−1.75968
$377$	−8.11532	−0.417960
$378$	27.1502	1.39646
$379$	35.4068	1.81873	0.909363	−	0.416003i	$-0.136569\pi$
$379$	35.4068	1.81873	0.909363	+	0.416003i	$0.136569\pi$
$380$	0	0
$381$	−15.9367	−0.816460
$382$	−4.38794	−0.224506
$383$	−15.7587	−0.805234	−0.402617	−	0.915369i	$-0.631899\pi$
$383$	−15.7587	−0.805234	−0.402617	+	0.915369i	$0.631899\pi$
$384$	17.8827	0.912571
$385$	0	0
$386$	7.83056	0.398565
$387$	7.14823	0.363365
$388$	6.83482	0.346986
$389$	−28.3444	−1.43712	−0.718559	−	0.695466i	$-0.755198\pi$
$389$	−28.3444	−1.43712	−0.718559	+	0.695466i	$0.755198\pi$
$390$	0	0
$391$	16.6781	0.843447
$392$	5.87336	0.296649
$393$	11.4253	0.576330
$394$	−17.7036	−0.891894
$395$	0	0
$396$	49.6273	2.49387
$397$	−22.3142	−1.11992	−0.559959	−	0.828521i	$-0.689183\pi$
$397$	−22.3142	−1.11992	−0.559959	+	0.828521i	$0.689183\pi$
$398$	−15.3450	−0.769176
$399$	8.50667	0.425866
$400$	0	0
$401$	21.2383	1.06059	0.530295	−	0.847813i	$-0.322081\pi$
$401$	21.2383	1.06059	0.530295	+	0.847813i	$0.322081\pi$
$402$	−22.4059	−1.11750
$403$	5.12938	0.255513
$404$	−4.79541	−0.238581
$405$	0	0
$406$	−20.1543	−1.00024
$407$	−15.2518	−0.756002
$408$	−29.5628	−1.46358
$409$	−1.54546	−0.0764180	−0.0382090	−	0.999270i	$-0.512165\pi$
$409$	−1.54546	−0.0764180	−0.0382090	+	0.999270i	$0.512165\pi$
$410$	0	0
$411$	−18.7376	−0.924260
$412$	−7.72582	−0.380624
$413$	−8.11594	−0.399359
$414$	−34.3438	−1.68791
$415$	0	0
$416$	−4.52104	−0.221662
$417$	−12.2439	−0.599586
$418$	−6.64489	−0.325012
$419$	−9.37059	−0.457783	−0.228892	−	0.973452i	$-0.573510\pi$
$419$	−9.37059	−0.457783	−0.228892	+	0.973452i	$0.573510\pi$
$420$	0	0
$421$	−9.15495	−0.446185	−0.223092	−	0.974797i	$-0.571615\pi$
$421$	−9.15495	−0.446185	−0.223092	+	0.974797i	$0.571615\pi$
$422$	−18.1573	−0.883886
$423$	84.0269	4.08553
$424$	25.3124	1.22928
$425$	0	0
$426$	−1.22784	−0.0594892
$427$	−10.3052	−0.498703
$428$	2.78921	0.134822
$429$	−15.8851	−0.766940
$430$	0	0
$431$	3.00769	0.144875	0.0724376	−	0.997373i	$-0.476922\pi$
$431$	3.00769	0.144875	0.0724376	+	0.997373i	$0.476922\pi$
$432$	4.88588	0.235072
$433$	0.799530	0.0384230	0.0192115	−	0.999815i	$-0.493884\pi$
$433$	0.799530	0.0384230	0.0192115	+	0.999815i	$0.493884\pi$
$434$	12.7388	0.611480
$435$	0	0
$436$	6.03295	0.288926
$437$	−6.24453	−0.298716
$438$	28.9913	1.38526
$439$	−36.1043	−1.72317	−0.861583	−	0.507617i	$-0.830527\pi$
$439$	−36.1043	−1.72317	−0.861583	+	0.507617i	$0.830527\pi$
$440$	0	0
$441$	−14.4637	−0.688746
$442$	2.43581	0.115860
$443$	−9.06007	−0.430457	−0.215228	−	0.976564i	$-0.569050\pi$
$443$	−9.06007	−0.430457	−0.215228	+	0.976564i	$0.569050\pi$
$444$	9.28436	0.440616
$445$	0	0
$446$	−21.7665	−1.03068
$447$	56.4711	2.67099
$448$	−12.8776	−0.608408
$449$	−6.21426	−0.293269	−0.146635	−	0.989191i	$-0.546844\pi$
$449$	−6.21426	−0.293269	−0.146635	+	0.989191i	$0.546844\pi$
$450$	0	0
$451$	−51.5773	−2.42868
$452$	19.5771	0.920828
$453$	−1.56347	−0.0734583
$454$	4.91148	0.230507
$455$	0	0
$456$	11.0688	0.518343
$457$	−12.8856	−0.602763	−0.301381	−	0.953504i	$-0.597448\pi$
$457$	−12.8856	−0.602763	−0.301381	+	0.953504i	$0.597448\pi$
$458$	7.38543	0.345099
$459$	42.2476	1.97195
$460$	0	0
$461$	31.2002	1.45314	0.726568	−	0.687095i	$-0.241114\pi$
$461$	31.2002	1.45314	0.726568	+	0.687095i	$0.241114\pi$
$462$	−39.4505	−1.83540
$463$	−12.7993	−0.594832	−0.297416	−	0.954748i	$-0.596125\pi$
$463$	−12.7993	−0.594832	−0.297416	+	0.954748i	$0.596125\pi$
$464$	−3.62692	−0.168376
$465$	0	0
$466$	21.7517	1.00763
$467$	16.9429	0.784024	0.392012	−	0.919960i	$-0.371779\pi$
$467$	16.9429	0.784024	0.392012	+	0.919960i	$0.371779\pi$
$468$	6.81130	0.314853
$469$	−17.0367	−0.786682
$470$	0	0
$471$	−7.95033	−0.366332
$472$	−10.5604	−0.486080
$473$	−6.02758	−0.277148
$474$	30.3652	1.39472
$475$	0	0
$476$	−8.21467	−0.376519
$477$	−62.3340	−2.85408
$478$	7.74620	0.354303
$479$	16.8246	0.768735	0.384368	−	0.923180i	$-0.374420\pi$
$479$	16.8246	0.768735	0.384368	+	0.923180i	$0.374420\pi$
$480$	0	0
$481$	−2.09329	−0.0954458
$482$	−23.2675	−1.05980
$483$	−37.0736	−1.68691
$484$	−29.1772	−1.32624
$485$	0	0
$486$	−24.0809	−1.09233
$487$	−20.9673	−0.950119	−0.475060	−	0.879954i	$-0.657573\pi$
$487$	−20.9673	−0.950119	−0.475060	+	0.879954i	$0.657573\pi$
$488$	−13.4090	−0.606996
$489$	−70.5758	−3.19155
$490$	0	0
$491$	−1.84207	−0.0831316	−0.0415658	−	0.999136i	$-0.513235\pi$
$491$	−1.84207	−0.0831316	−0.0415658	+	0.999136i	$0.513235\pi$
$492$	31.3972	1.41549
$493$	−31.3616	−1.41245
$494$	−0.912005	−0.0410330
$495$	0	0
$496$	2.29243	0.102933
$497$	−0.933613	−0.0418783
$498$	−22.7343	−1.01875
$499$	−20.2655	−0.907207	−0.453604	−	0.891204i	$-0.649862\pi$
$499$	−20.2655	−0.907207	−0.453604	+	0.891204i	$0.649862\pi$
$500$	0	0
$501$	−43.4003	−1.93898
$502$	−3.75661	−0.167666
$503$	−0.0128212	−0.000571667 0	−0.000285834	−	1.00000i	$-0.500091\pi$
$503$	−0.0128212	−0.000571667 0	−0.000285834		1.00000i	$0.500091\pi$
$504$	46.2885	2.06185
$505$	0	0
$506$	28.9596	1.28741
$507$	39.2330	1.74240
$508$	−5.76211	−0.255652
$509$	34.4372	1.52640	0.763201	−	0.646162i	$-0.223627\pi$
$509$	34.4372	1.52640	0.763201	+	0.646162i	$0.223627\pi$
$510$	0	0
$511$	22.0440	0.975171
$512$	−4.16701	−0.184158
$513$	−15.8182	−0.698389
$514$	16.3133	0.719547
$515$	0	0
$516$	3.66923	0.161529
$517$	−70.8537	−3.11614
$518$	−5.19866	−0.228416
$519$	−30.5338	−1.34029
$520$	0	0
$521$	11.5077	0.504159	0.252080	−	0.967706i	$-0.418886\pi$
$521$	11.5077	0.504159	0.252080	+	0.967706i	$0.418886\pi$
$522$	64.5803	2.82660
$523$	−2.17138	−0.0949477	−0.0474739	−	0.998872i	$-0.515117\pi$
$523$	−2.17138	−0.0949477	−0.0474739	+	0.998872i	$0.515117\pi$
$524$	4.13096	0.180462
$525$	0	0
$526$	−6.56586	−0.286285
$527$	19.8224	0.863478
$528$	−7.09941	−0.308962
$529$	4.21479	0.183252
$530$	0	0
$531$	26.0058	1.12856
$532$	3.07570	0.133348
$533$	−7.07894	−0.306623
$534$	23.0618	0.997981
$535$	0	0
$536$	−22.1680	−0.957511
$537$	−72.5205	−3.12949
$538$	26.2018	1.12964
$539$	12.1961	0.525325
$540$	0	0
$541$	20.3867	0.876493	0.438246	−	0.898855i	$-0.355600\pi$
$541$	20.3867	0.876493	0.438246	+	0.898855i	$0.355600\pi$
$542$	5.06907	0.217735
$543$	−3.33790	−0.143243
$544$	−17.4715	−0.749085
$545$	0	0
$546$	−5.41454	−0.231721
$547$	−8.61617	−0.368401	−0.184200	−	0.982889i	$-0.558970\pi$
$547$	−8.61617	−0.368401	−0.184200	+	0.982889i	$0.558970\pi$
$548$	−6.77484	−0.289407
$549$	33.0208	1.40929
$550$	0	0
$551$	11.7422	0.500236
$552$	−48.2397	−2.05322
$553$	23.0887	0.981833
$554$	2.38313	0.101249
$555$	0	0
$556$	−4.42694	−0.187744
$557$	−0.175038	−0.00741659	−0.00370829	−	0.999993i	$-0.501180\pi$
$557$	−0.175038	−0.00741659	−0.00370829	+	0.999993i	$0.501180\pi$
$558$	−40.8187	−1.72799
$559$	−0.827279	−0.0349902
$560$	0	0
$561$	−61.3878	−2.59179
$562$	−18.9900	−0.801044
$563$	−27.6675	−1.16605	−0.583024	−	0.812455i	$-0.698131\pi$
$563$	−27.6675	−1.16605	−0.583024	+	0.812455i	$0.698131\pi$
$564$	43.1315	1.81616
$565$	0	0
$566$	9.56460	0.402030
$567$	−46.0724	−1.93486
$568$	−1.21481	−0.0509722
$569$	−25.5683	−1.07188	−0.535939	−	0.844257i	$-0.680042\pi$
$569$	−25.5683	−1.07188	−0.535939	+	0.844257i	$0.680042\pi$
$570$	0	0
$571$	21.9812	0.919883	0.459941	−	0.887949i	$-0.347870\pi$
$571$	21.9812	0.919883	0.459941	+	0.887949i	$0.347870\pi$
$572$	−5.74347	−0.240147
$573$	15.1778	0.634061
$574$	−17.5805	−0.733794
$575$	0	0
$576$	41.2635	1.71931
$577$	17.0335	0.709112	0.354556	−	0.935035i	$-0.384632\pi$
$577$	17.0335	0.709112	0.354556	+	0.935035i	$0.384632\pi$
$578$	−6.24341	−0.259692
$579$	−27.0857	−1.12564
$580$	0	0
$581$	−17.2865	−0.717163
$582$	17.4097	0.721654
$583$	52.5617	2.17688
$584$	28.6835	1.18693
$585$	0	0
$586$	14.0828	0.581756
$587$	37.8869	1.56376	0.781879	−	0.623430i	$-0.214261\pi$
$587$	37.8869	1.56376	0.781879	+	0.623430i	$0.214261\pi$
$588$	−7.42427	−0.306172
$589$	−7.42181	−0.305810
$590$	0	0
$591$	61.2363	2.51892
$592$	−0.935538	−0.0384504
$593$	−16.8345	−0.691310	−0.345655	−	0.938362i	$-0.612343\pi$
$593$	−16.8345	−0.691310	−0.345655	+	0.938362i	$0.612343\pi$
$594$	73.3582	3.00992
$595$	0	0
$596$	20.4179	0.836348
$597$	53.0781	2.17234
$598$	3.97468	0.162537
$599$	13.2862	0.542860	0.271430	−	0.962458i	$-0.412503\pi$
$599$	13.2862	0.542860	0.271430	+	0.962458i	$0.412503\pi$
$600$	0	0
$601$	19.0981	0.779028	0.389514	−	0.921021i	$-0.372643\pi$
$601$	19.0981	0.779028	0.389514	+	0.921021i	$0.372643\pi$
$602$	−2.05454	−0.0837368
$603$	54.5906	2.22310
$604$	−0.565294	−0.0230015
$605$	0	0
$606$	−12.2149	−0.496196
$607$	12.6302	0.512643	0.256322	−	0.966592i	$-0.417489\pi$
$607$	12.6302	0.512643	0.256322	+	0.966592i	$0.417489\pi$
$608$	6.54160	0.265297
$609$	69.7133	2.82493
$610$	0	0
$611$	−9.72460	−0.393415
$612$	26.3222	1.06401
$613$	0.918115	0.0370823	0.0185412	−	0.999828i	$-0.494098\pi$
$613$	0.918115	0.0370823	0.0185412	+	0.999828i	$0.494098\pi$
$614$	19.8946	0.802881
$615$	0	0
$616$	−39.0316	−1.57263
$617$	−10.2963	−0.414513	−0.207256	−	0.978287i	$-0.566453\pi$
$617$	−10.2963	−0.414513	−0.207256	+	0.978287i	$0.566453\pi$
$618$	−19.6792	−0.791614
$619$	19.5465	0.785641	0.392820	−	0.919615i	$-0.371499\pi$
$619$	19.5465	0.785641	0.392820	+	0.919615i	$0.371499\pi$
$620$	0	0
$621$	68.9384	2.76640
$622$	27.0665	1.08527
$623$	17.5355	0.702543
$624$	−0.974388	−0.0390067
$625$	0	0
$626$	7.26553	0.290389
$627$	22.9845	0.917913
$628$	−2.87455	−0.114707
$629$	−8.08949	−0.322549
$630$	0	0
$631$	−4.32943	−0.172352	−0.0861759	−	0.996280i	$-0.527465\pi$
$631$	−4.32943	−0.172352	−0.0861759	+	0.996280i	$0.527465\pi$
$632$	30.0428	1.19504
$633$	62.8059	2.49631
$634$	−1.02223	−0.0405978
$635$	0	0
$636$	−31.9964	−1.26874
$637$	1.67391	0.0663226
$638$	−54.4558	−2.15593
$639$	2.99157	0.118345
$640$	0	0
$641$	−32.5697	−1.28642	−0.643212	−	0.765688i	$-0.722399\pi$
$641$	−32.5697	−1.28642	−0.643212	+	0.765688i	$0.722399\pi$
$642$	7.10468	0.280399
$643$	−42.9291	−1.69296	−0.846479	−	0.532421i	$-0.821282\pi$
$643$	−42.9291	−1.69296	−0.846479	+	0.532421i	$0.821282\pi$
$644$	−13.4044	−0.528209
$645$	0	0
$646$	−3.52443	−0.138667
$647$	−1.74432	−0.0685765	−0.0342882	−	0.999412i	$-0.510916\pi$
$647$	−1.74432	−0.0685765	−0.0342882	+	0.999412i	$0.510916\pi$
$648$	−59.9488	−2.35501
$649$	−21.9288	−0.860781
$650$	0	0
$651$	−44.0631	−1.72697
$652$	−25.5176	−0.999346
$653$	−5.07029	−0.198416	−0.0992078	−	0.995067i	$-0.531631\pi$
$653$	−5.07029	−0.198416	−0.0992078	+	0.995067i	$0.531631\pi$
$654$	15.3671	0.600903
$655$	0	0
$656$	−3.16374	−0.123523
$657$	−70.6355	−2.75575
$658$	−24.1509	−0.941501
$659$	−15.7173	−0.612260	−0.306130	−	0.951990i	$-0.599034\pi$
$659$	−15.7173	−0.612260	−0.306130	+	0.951990i	$0.599034\pi$
$660$	0	0
$661$	26.5033	1.03086	0.515430	−	0.856932i	$-0.327632\pi$
$661$	26.5033	1.03086	0.515430	+	0.856932i	$0.327632\pi$
$662$	−10.0412	−0.390261
$663$	−8.42541	−0.327216
$664$	−22.4929	−0.872895
$665$	0	0
$666$	16.6580	0.645485
$667$	−51.1748	−1.98150
$668$	−15.6920	−0.607140
$669$	75.2900	2.91088
$670$	0	0
$671$	−27.8440	−1.07491
$672$	38.8373	1.49818
$673$	−34.4298	−1.32717	−0.663586	−	0.748100i	$-0.730966\pi$
$673$	−34.4298	−1.32717	−0.663586	+	0.748100i	$0.730966\pi$
$674$	30.0692	1.15822
$675$	0	0
$676$	14.1852	0.545584
$677$	−25.5650	−0.982542	−0.491271	−	0.871007i	$-0.663468\pi$
$677$	−25.5650	−0.982542	−0.491271	+	0.871007i	$0.663468\pi$
$678$	49.8668	1.91512
$679$	13.2378	0.508019
$680$	0	0
$681$	−16.9887	−0.651008
$682$	34.4194	1.31799
$683$	−1.47320	−0.0563705	−0.0281852	−	0.999603i	$-0.508973\pi$
$683$	−1.47320	−0.0563705	−0.0281852	+	0.999603i	$0.508973\pi$
$684$	−9.85543	−0.376832
$685$	0	0
$686$	18.5389	0.707819
$687$	−25.5461	−0.974643
$688$	−0.369730	−0.0140958
$689$	7.21404	0.274833
$690$	0	0
$691$	−20.1606	−0.766945	−0.383472	−	0.923552i	$-0.625272\pi$
$691$	−20.1606	−0.766945	−0.383472	+	0.923552i	$0.625272\pi$
$692$	−11.0399	−0.419674
$693$	96.1188	3.65125
$694$	6.22500	0.236298
$695$	0	0
$696$	90.7102	3.43836
$697$	−27.3564	−1.03620
$698$	30.9114	1.17001
$699$	−75.2386	−2.84578
$700$	0	0
$701$	50.6488	1.91298	0.956489	−	0.291767i	$-0.0942433\pi$
$701$	50.6488	1.91298	0.956489	+	0.291767i	$0.0942433\pi$
$702$	10.0683	0.380005
$703$	3.02883	0.114234
$704$	−34.7944	−1.31136
$705$	0	0
$706$	31.1958	1.17407
$707$	−9.28781	−0.349304
$708$	13.3489	0.501684
$709$	−1.50121	−0.0563793	−0.0281896	−	0.999603i	$-0.508974\pi$
$709$	−1.50121	−0.0563793	−0.0281896	+	0.999603i	$0.508974\pi$
$710$	0	0
$711$	−73.9830	−2.77458
$712$	22.8169	0.855101
$713$	32.3456	1.21135
$714$	−20.9244	−0.783077
$715$	0	0
$716$	−26.2207	−0.979915
$717$	−26.7939	−1.00064
$718$	23.6007	0.880770
$719$	10.0122	0.373393	0.186696	−	0.982418i	$-0.440222\pi$
$719$	10.0122	0.373393	0.186696	+	0.982418i	$0.440222\pi$
$720$	0	0
$721$	−14.9635	−0.557268
$722$	−16.1789	−0.602117
$723$	80.4817	2.99315
$724$	−1.20686	−0.0448526
$725$	0	0
$726$	−74.3202	−2.75828
$727$	8.61092	0.319361	0.159681	−	0.987169i	$-0.448954\pi$
$727$	8.61092	0.319361	0.159681	+	0.987169i	$0.448954\pi$
$728$	−5.35705	−0.198546
$729$	21.3375	0.790278
$730$	0	0
$731$	−3.19701	−0.118246
$732$	16.9498	0.626481
$733$	−2.35205	−0.0868749	−0.0434375	−	0.999056i	$-0.513831\pi$
$733$	−2.35205	−0.0868749	−0.0434375	+	0.999056i	$0.513831\pi$
$734$	−3.35956	−0.124004
$735$	0	0
$736$	−28.5095	−1.05087
$737$	−46.0322	−1.69562
$738$	56.3329	2.07364
$739$	19.5242	0.718208	0.359104	−	0.933297i	$-0.383082\pi$
$739$	19.5242	0.718208	0.359104	+	0.933297i	$0.383082\pi$
$740$	0	0
$741$	3.15460	0.115887
$742$	17.9160	0.657716
$743$	−10.4332	−0.382758	−0.191379	−	0.981516i	$-0.561296\pi$
$743$	−10.4332	−0.382758	−0.191379	+	0.981516i	$0.561296\pi$
$744$	−57.3344	−2.10198
$745$	0	0
$746$	15.9490	0.583936
$747$	55.3908	2.02664
$748$	−22.1956	−0.811550
$749$	5.40217	0.197391
$750$	0	0
$751$	24.3185	0.887395	0.443698	−	0.896177i	$-0.353666\pi$
$751$	24.3185	0.887395	0.443698	+	0.896177i	$0.353666\pi$
$752$	−4.34614	−0.158488
$753$	12.9940	0.473528
$754$	−7.47400	−0.272187
$755$	0	0
$756$	−33.9551	−1.23493
$757$	−21.2779	−0.773360	−0.386680	−	0.922214i	$-0.626378\pi$
$757$	−21.2779	−0.773360	−0.386680	+	0.922214i	$0.626378\pi$
$758$	32.6088	1.18440
$759$	−100.171	−3.63596
$760$	0	0
$761$	34.5183	1.25129	0.625644	−	0.780109i	$-0.284836\pi$
$761$	34.5183	1.25129	0.625644	+	0.780109i	$0.284836\pi$
$762$	−14.6773	−0.531701
$763$	11.6847	0.423014
$764$	5.48773	0.198539
$765$	0	0
$766$	−14.5134	−0.524390
$767$	−3.00971	−0.108674
$768$	53.2478	1.92142
$769$	−14.9892	−0.540524	−0.270262	−	0.962787i	$-0.587110\pi$
$769$	−14.9892	−0.540524	−0.270262	+	0.962787i	$0.587110\pi$
$770$	0	0
$771$	−56.4272	−2.03218
$772$	−9.79320	−0.352465
$773$	−37.7719	−1.35856	−0.679281	−	0.733878i	$-0.737708\pi$
$773$	−37.7719	−1.35856	−0.679281	+	0.733878i	$0.737708\pi$
$774$	6.58334	0.236633
$775$	0	0
$776$	17.2248	0.618335
$777$	17.9821	0.645103
$778$	−26.1045	−0.935891
$779$	10.2427	0.366982
$780$	0	0
$781$	−2.52257	−0.0902646
$782$	15.3601	0.549276
$783$	−129.632	−4.63267
$784$	0.748107	0.0267181
$785$	0	0
$786$	10.5224	0.375321
$787$	27.7105	0.987771	0.493886	−	0.869527i	$-0.335576\pi$
$787$	27.7105	0.987771	0.493886	+	0.869527i	$0.335576\pi$
$788$	22.1408	0.788733
$789$	22.7112	0.808538
$790$	0	0
$791$	37.9171	1.34818
$792$	125.069	4.44412
$793$	−3.82156	−0.135708
$794$	−20.5508	−0.729321
$795$	0	0
$796$	19.1911	0.680209
$797$	43.2267	1.53117	0.765584	−	0.643336i	$-0.222450\pi$
$797$	43.2267	1.53117	0.765584	+	0.643336i	$0.222450\pi$
$798$	7.83442	0.277336
$799$	−37.5806	−1.32951
$800$	0	0
$801$	−56.1887	−1.98533
$802$	19.5599	0.690685
$803$	59.5617	2.10189
$804$	28.0216	0.988247
$805$	0	0
$806$	4.72403	0.166397
$807$	−90.6315	−3.19038
$808$	−12.0852	−0.425156
$809$	4.09860	0.144099	0.0720496	−	0.997401i	$-0.477046\pi$
$809$	4.09860	0.144099	0.0720496	+	0.997401i	$0.477046\pi$
$810$	0	0
$811$	40.7497	1.43092	0.715459	−	0.698655i	$-0.246218\pi$
$811$	40.7497	1.43092	0.715459	+	0.698655i	$0.246218\pi$
$812$	25.2058	0.884549
$813$	−17.5338	−0.614937
$814$	−14.0465	−0.492329
$815$	0	0
$816$	−3.76551	−0.131819
$817$	1.19701	0.0418780
$818$	−1.42333	−0.0497655
$819$	13.1922	0.460973
$820$	0	0
$821$	−16.7905	−0.585994	−0.292997	−	0.956113i	$-0.594653\pi$
$821$	−16.7905	−0.585994	−0.292997	+	0.956113i	$0.594653\pi$
$822$	−17.2569	−0.601903
$823$	−15.8303	−0.551810	−0.275905	−	0.961185i	$-0.588978\pi$
$823$	−15.8303	−0.551810	−0.275905	+	0.961185i	$0.588978\pi$
$824$	−19.4703	−0.678279
$825$	0	0
$826$	−7.47457	−0.260074
$827$	−13.5789	−0.472185	−0.236092	−	0.971731i	$-0.575867\pi$
$827$	−13.5789	−0.472185	−0.236092	+	0.971731i	$0.575867\pi$
$828$	42.9517	1.49268
$829$	−7.01805	−0.243747	−0.121874	−	0.992546i	$-0.538890\pi$
$829$	−7.01805	−0.243747	−0.121874	+	0.992546i	$0.538890\pi$
$830$	0	0
$831$	−8.24319	−0.285953
$832$	−4.77550	−0.165561
$833$	6.46879	0.224130
$834$	−11.2763	−0.390467
$835$	0	0
$836$	8.31036	0.287420
$837$	81.9353	2.83210
$838$	−8.63007	−0.298121
$839$	−17.2572	−0.595786	−0.297893	−	0.954599i	$-0.596284\pi$
$839$	−17.2572	−0.595786	−0.297893	+	0.954599i	$0.596284\pi$
$840$	0	0
$841$	67.2293	2.31825
$842$	−8.43147	−0.290568
$843$	65.6859	2.26234
$844$	22.7083	0.781651
$845$	0	0
$846$	77.3866	2.66061
$847$	−56.5108	−1.94173
$848$	3.22412	0.110717
$849$	−33.0837	−1.13543
$850$	0	0
$851$	−13.2002	−0.452496
$852$	1.53559	0.0526084
$853$	23.9573	0.820283	0.410142	−	0.912022i	$-0.365479\pi$
$853$	23.9573	0.820283	0.410142	+	0.912022i	$0.365479\pi$
$854$	−9.49080	−0.324769
$855$	0	0
$856$	7.02925	0.240255
$857$	24.8654	0.849387	0.424694	−	0.905337i	$-0.360382\pi$
$857$	24.8654	0.849387	0.424694	+	0.905337i	$0.360382\pi$
$858$	−14.6298	−0.499452
$859$	36.9039	1.25914	0.629572	−	0.776942i	$-0.283230\pi$
$859$	36.9039	1.25914	0.629572	+	0.776942i	$0.283230\pi$
$860$	0	0
$861$	60.8104	2.07241
$862$	2.77000	0.0943466
$863$	21.3201	0.725743	0.362872	−	0.931839i	$-0.381796\pi$
$863$	21.3201	0.725743	0.362872	+	0.931839i	$0.381796\pi$
$864$	−72.2179	−2.45690
$865$	0	0
$866$	0.736347	0.0250221
$867$	21.5958	0.733432
$868$	−15.9316	−0.540753
$869$	62.3844	2.11625
$870$	0	0
$871$	−6.31788	−0.214073
$872$	15.2040	0.514872
$873$	−42.4176	−1.43562
$874$	−5.75105	−0.194532
$875$	0	0
$876$	−36.2576	−1.22503
$877$	−30.8431	−1.04150	−0.520749	−	0.853710i	$-0.674347\pi$
$877$	−30.8431	−1.04150	−0.520749	+	0.853710i	$0.674347\pi$
$878$	−33.2512	−1.12217
$879$	−48.7121	−1.64302
$880$	0	0
$881$	26.5915	0.895889	0.447944	−	0.894061i	$-0.352156\pi$
$881$	26.5915	0.895889	0.447944	+	0.894061i	$0.352156\pi$
$882$	−13.3207	−0.448530
$883$	−5.13923	−0.172949	−0.0864745	−	0.996254i	$-0.527560\pi$
$883$	−5.13923	−0.172949	−0.0864745	+	0.996254i	$0.527560\pi$
$884$	−3.04632	−0.102459
$885$	0	0
$886$	−8.34409	−0.280325
$887$	20.4753	0.687494	0.343747	−	0.939062i	$-0.388304\pi$
$887$	20.4753	0.687494	0.343747	+	0.939062i	$0.388304\pi$
$888$	23.3980	0.785187
$889$	−11.1601	−0.374298
$890$	0	0
$891$	−124.485	−4.17040
$892$	27.2221	0.911463
$893$	14.0707	0.470859
$894$	52.0084	1.73942
$895$	0	0
$896$	12.5229	0.418360
$897$	−13.7483	−0.459043
$898$	−5.72318	−0.190985
$899$	−60.8228	−2.02855
$900$	0	0
$901$	27.8785	0.928769
$902$	−47.5014	−1.58162
$903$	7.10660	0.236493
$904$	49.3373	1.64093
$905$	0	0
$906$	−1.43992	−0.0478381
$907$	−13.2349	−0.439457	−0.219728	−	0.975561i	$-0.570517\pi$
$907$	−13.2349	−0.439457	−0.219728	+	0.975561i	$0.570517\pi$
$908$	−6.14249	−0.203846
$909$	29.7608	0.987105
$910$	0	0
$911$	47.3412	1.56848	0.784242	−	0.620455i	$-0.213052\pi$
$911$	47.3412	1.56848	0.784242	+	0.620455i	$0.213052\pi$
$912$	1.40986	0.0466852
$913$	−46.7070	−1.54578
$914$	−11.8673	−0.392535
$915$	0	0
$916$	−9.23651	−0.305183
$917$	8.00090	0.264213
$918$	38.9090	1.28419
$919$	−30.3350	−1.00066	−0.500330	−	0.865835i	$-0.666788\pi$
$919$	−30.3350	−1.00066	−0.500330	+	0.865835i	$0.666788\pi$
$920$	0	0
$921$	−68.8150	−2.26753
$922$	28.7345	0.946322
$923$	−0.346220	−0.0113960
$924$	49.3383	1.62311
$925$	0	0
$926$	−11.7878	−0.387371
$927$	47.9473	1.57479
$928$	53.6093	1.75981
$929$	−25.2857	−0.829598	−0.414799	−	0.909913i	$-0.636148\pi$
$929$	−25.2857	−0.829598	−0.414799	+	0.909913i	$0.636148\pi$
$930$	0	0
$931$	−2.42201	−0.0793783
$932$	−27.2035	−0.891080
$933$	−93.6225	−3.06506
$934$	15.6040	0.510578
$935$	0	0
$936$	17.1656	0.561074
$937$	44.6718	1.45936	0.729681	−	0.683787i	$-0.239668\pi$
$937$	44.6718	1.45936	0.729681	+	0.683787i	$0.239668\pi$
$938$	−15.6904	−0.512309
$939$	−25.1313	−0.820129
$940$	0	0
$941$	−39.2393	−1.27917	−0.639583	−	0.768722i	$-0.720893\pi$
$941$	−39.2393	−1.27917	−0.639583	+	0.768722i	$0.720893\pi$
$942$	−7.32205	−0.238565
$943$	−44.6394	−1.45366
$944$	−1.34511	−0.0437795
$945$	0	0
$946$	−5.55124	−0.180487
$947$	−33.4001	−1.08536	−0.542678	−	0.839941i	$-0.682590\pi$
$947$	−33.4001	−1.08536	−0.542678	+	0.839941i	$0.682590\pi$
$948$	−37.9759	−1.23340
$949$	8.17479	0.265365
$950$	0	0
$951$	3.53586	0.114658
$952$	−20.7023	−0.670964
$953$	−3.27030	−0.105936	−0.0529678	−	0.998596i	$-0.516868\pi$
$953$	−3.27030	−0.105936	−0.0529678	+	0.998596i	$0.516868\pi$
$954$	−57.4080	−1.85865
$955$	0	0
$956$	−9.68770	−0.313323
$957$	188.361	6.08886
$958$	15.4950	0.500621
$959$	−13.1216	−0.423718
$960$	0	0
$961$	7.44371	0.240120
$962$	−1.92787	−0.0621569
$963$	−17.3101	−0.557811
$964$	29.0992	0.937222
$965$	0	0
$966$	−34.1438	−1.09856
$967$	10.8952	0.350366	0.175183	−	0.984536i	$-0.443948\pi$
$967$	10.8952	0.350366	0.175183	+	0.984536i	$0.443948\pi$
$968$	−73.5311	−2.36338
$969$	12.1909	0.391629
$970$	0	0
$971$	22.8205	0.732346	0.366173	−	0.930547i	$-0.380668\pi$
$971$	22.8205	0.732346	0.366173	+	0.930547i	$0.380668\pi$
$972$	30.1165	0.965986
$973$	−8.57415	−0.274875
$974$	−19.3103	−0.618743
$975$	0	0
$976$	−1.70794	−0.0546699
$977$	14.0590	0.449787	0.224894	−	0.974383i	$-0.427797\pi$
$977$	14.0590	0.449787	0.224894	+	0.974383i	$0.427797\pi$
$978$	−64.9985	−2.07842
$979$	47.3798	1.51426
$980$	0	0
$981$	−37.4411	−1.19540
$982$	−1.69650	−0.0541376
$983$	−18.9691	−0.605021	−0.302511	−	0.953146i	$-0.597825\pi$
$983$	−18.9691	−0.605021	−0.302511	+	0.953146i	$0.597825\pi$
$984$	79.1258	2.52244
$985$	0	0
$986$	−28.8832	−0.919828
$987$	83.5375	2.65903
$988$	1.14059	0.0362869
$989$	−5.21678	−0.165884
$990$	0	0
$991$	1.99010	0.0632177	0.0316088	−	0.999500i	$-0.489937\pi$
$991$	1.99010	0.0632177	0.0316088	+	0.999500i	$0.489937\pi$
$992$	−33.8843	−1.07583
$993$	34.7322	1.10219
$994$	−0.859834	−0.0272723
$995$	0	0
$996$	28.4324	0.900916
$997$	33.2899	1.05430	0.527151	−	0.849772i	$-0.323260\pi$
$997$	33.2899	1.05430	0.527151	+	0.849772i	$0.323260\pi$
$998$	−18.6640	−0.590798
$999$	−33.4376	−1.05792

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.2.a.q.1.4	✓	6
3.2	odd	2		9675.2.a.ck.1.3		6
5.2	odd	4		1075.2.b.j.474.7		12
5.3	odd	4		1075.2.b.j.474.6		12
5.4	even	2		1075.2.a.r.1.3	yes	6
15.14	odd	2		9675.2.a.cj.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1075.2.a.q.1.4	✓	6	1.1	even	1	trivial
1075.2.a.r.1.3	yes	6	5.4	even	2
1075.2.b.j.474.6		12	5.3	odd	4
1075.2.b.j.474.7		12	5.2	odd	4
9675.2.a.cj.1.4		6	15.14	odd	2
9675.2.a.ck.1.3		6	3.2	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:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q+0.920974 q^{2} -3.18563 q^{3} -1.15181 q^{4} -2.93388 q^{6} -2.23083 q^{7} -2.90273 q^{8} +7.14823 q^{9} +O(q^{10})\)	\(q+0.920974 q^{2} -3.18563 q^{3} -1.15181 q^{4} -2.93388 q^{6} -2.23083 q^{7} -2.90273 q^{8} +7.14823 q^{9} -6.02758 q^{11} +3.66923 q^{12} -0.827279 q^{13} -2.05454 q^{14} -0.369730 q^{16} -3.19701 q^{17} +6.58334 q^{18} +1.19701 q^{19} +7.10660 q^{21} -5.55124 q^{22} -5.21678 q^{23} +9.24703 q^{24} -0.761903 q^{26} -13.2147 q^{27} +2.56949 q^{28} +9.80965 q^{29} -6.20030 q^{31} +5.46495 q^{32} +19.2016 q^{33} -2.94436 q^{34} -8.23338 q^{36} +2.53033 q^{37} +1.10241 q^{38} +2.63540 q^{39} +8.55689 q^{41} +6.54500 q^{42} +1.00000 q^{43} +6.94260 q^{44} -4.80452 q^{46} +11.7549 q^{47} +1.17782 q^{48} -2.02339 q^{49} +10.1845 q^{51} +0.952865 q^{52} -8.72019 q^{53} -12.1704 q^{54} +6.47551 q^{56} -3.81323 q^{57} +9.03444 q^{58} +3.63808 q^{59} +4.61943 q^{61} -5.71032 q^{62} -15.9465 q^{63} +5.77254 q^{64} +17.6842 q^{66} +7.63693 q^{67} +3.68233 q^{68} +16.6187 q^{69} +0.418505 q^{71} -20.7494 q^{72} -9.88154 q^{73} +2.33037 q^{74} -1.37872 q^{76} +13.4465 q^{77} +2.42714 q^{78} -10.3498 q^{79} +20.6525 q^{81} +7.88067 q^{82} +7.74888 q^{83} -8.18543 q^{84} +0.920974 q^{86} -31.2499 q^{87} +17.4964 q^{88} -7.86050 q^{89} +1.84552 q^{91} +6.00872 q^{92} +19.7519 q^{93} +10.8260 q^{94} -17.4093 q^{96} -5.93400 q^{97} -1.86349 q^{98} -43.0865 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 2 q^{3} + 11 q^{4} + 11 q^{6} - 2 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 6 * q - q^2 - 2 * q^3 + 11 * q^4 + 11 * q^6 - 2 * q^7 - 6 * q^8 + 12 * q^9	\( 6 q - q^{2} - 2 q^{3} + 11 q^{4} + 11 q^{6} - 2 q^{7} - 6 q^{8} + 12 q^{9} - 6 q^{11} + 4 q^{12} + 17 q^{14} + 5 q^{16} - 7 q^{17} + 15 q^{18} - 5 q^{19} + 19 q^{21} - 34 q^{22} + 3 q^{23} + 9 q^{24} + 14 q^{26} - 5 q^{27} + 21 q^{28} + 18 q^{29} - 12 q^{31} - 3 q^{32} + 10 q^{33} + q^{34} - 10 q^{36} - 7 q^{37} + q^{38} - 3 q^{39} + 9 q^{42} + 6 q^{43} + 9 q^{44} - 14 q^{46} + 6 q^{47} - 2 q^{48} - q^{51} - 3 q^{52} + 8 q^{53} + 12 q^{54} + 20 q^{56} + 5 q^{57} + 24 q^{58} + 21 q^{59} - 8 q^{61} - 47 q^{62} - 19 q^{63} + 6 q^{64} + q^{66} + 35 q^{68} + 37 q^{69} + 14 q^{71} - 44 q^{72} + q^{73} + 2 q^{74} - 57 q^{76} - 13 q^{77} + 49 q^{78} - 31 q^{79} + 62 q^{81} - 32 q^{82} + 13 q^{83} + 21 q^{84} - q^{86} - 22 q^{87} - 39 q^{88} + 40 q^{89} + 11 q^{91} + 32 q^{92} + 15 q^{93} + 35 q^{94} - 50 q^{96} - 11 q^{97} + 44 q^{98} - 53 q^{99}+O(q^{100}) \) 6 * q - q^2 - 2 * q^3 + 11 * q^4 + 11 * q^6 - 2 * q^7 - 6 * q^8 + 12 * q^9 - 6 * q^11 + 4 * q^12 + 17 * q^14 + 5 * q^16 - 7 * q^17 + 15 * q^18 - 5 * q^19 + 19 * q^21 - 34 * q^22 + 3 * q^23 + 9 * q^24 + 14 * q^26 - 5 * q^27 + 21 * q^28 + 18 * q^29 - 12 * q^31 - 3 * q^32 + 10 * q^33 + q^34 - 10 * q^36 - 7 * q^37 + q^38 - 3 * q^39 + 9 * q^42 + 6 * q^43 + 9 * q^44 - 14 * q^46 + 6 * q^47 - 2 * q^48 - q^51 - 3 * q^52 + 8 * q^53 + 12 * q^54 + 20 * q^56 + 5 * q^57 + 24 * q^58 + 21 * q^59 - 8 * q^61 - 47 * q^62 - 19 * q^63 + 6 * q^64 + q^66 + 35 * q^68 + 37 * q^69 + 14 * q^71 - 44 * q^72 + q^73 + 2 * q^74 - 57 * q^76 - 13 * q^77 + 49 * q^78 - 31 * q^79 + 62 * q^81 - 32 * q^82 + 13 * q^83 + 21 * q^84 - q^86 - 22 * q^87 - 39 * q^88 + 40 * q^89 + 11 * q^91 + 32 * q^92 + 15 * q^93 + 35 * q^94 - 50 * q^96 - 11 * q^97 + 44 * q^98 - 53 * q^99

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