LMFDB - Embedded newform 4025.2.a.t.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 11x^{6} + 9x^{5} + 36x^{4} - 23x^{3} - 30x^{2} + 17x - 2 $ x^8 - x^7 - 11x^6 + 9x^5 + 36x^4 - 23x^3 - 30x^2 + 17x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-2.28279$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.28279 q^{2} -0.445964 q^{3} +3.21111 q^{4} -1.01804 q^{6} -1.00000 q^{7} +2.76472 q^{8} -2.80112 q^{9} +O(q^{10})$	\(q+2.28279 q^{2} -0.445964 q^{3} +3.21111 q^{4} -1.01804 q^{6} -1.00000 q^{7} +2.76472 q^{8} -2.80112 q^{9} +0.882192 q^{11} -1.43204 q^{12} +0.264745 q^{13} -2.28279 q^{14} -0.110972 q^{16} -6.80853 q^{17} -6.39435 q^{18} +2.33311 q^{19} +0.445964 q^{21} +2.01386 q^{22} -1.00000 q^{23} -1.23296 q^{24} +0.604357 q^{26} +2.58709 q^{27} -3.21111 q^{28} +4.70357 q^{29} -5.57993 q^{31} -5.78276 q^{32} -0.393426 q^{33} -15.5424 q^{34} -8.99470 q^{36} +4.70000 q^{37} +5.32599 q^{38} -0.118067 q^{39} -5.47644 q^{41} +1.01804 q^{42} -6.78709 q^{43} +2.83282 q^{44} -2.28279 q^{46} -7.04416 q^{47} +0.0494895 q^{48} +1.00000 q^{49} +3.03636 q^{51} +0.850127 q^{52} -9.38516 q^{53} +5.90578 q^{54} -2.76472 q^{56} -1.04048 q^{57} +10.7372 q^{58} +7.44091 q^{59} -14.6378 q^{61} -12.7378 q^{62} +2.80112 q^{63} -12.9789 q^{64} -0.898108 q^{66} -4.23716 q^{67} -21.8630 q^{68} +0.445964 q^{69} -9.35459 q^{71} -7.74429 q^{72} -6.72564 q^{73} +10.7291 q^{74} +7.49188 q^{76} -0.882192 q^{77} -0.269522 q^{78} +14.6130 q^{79} +7.24960 q^{81} -12.5015 q^{82} +0.193588 q^{83} +1.43204 q^{84} -15.4935 q^{86} -2.09762 q^{87} +2.43901 q^{88} +16.7797 q^{89} -0.264745 q^{91} -3.21111 q^{92} +2.48845 q^{93} -16.0803 q^{94} +2.57890 q^{96} -10.0525 q^{97} +2.28279 q^{98} -2.47112 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 7 q^{3} + 7 q^{4} + q^{6} - 8 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) $ 8 * q - q^2 - 7 * q^3 + 7 * q^4 + q^6 - 8 * q^7 - 3 * q^8 + 9 * q^9	$ 8 q - q^{2} - 7 q^{3} + 7 q^{4} + q^{6} - 8 q^{7} - 3 q^{8} + 9 q^{9} + 6 q^{11} - 8 q^{12} - 8 q^{13} + q^{14} + q^{16} - 4 q^{17} + 11 q^{18} + 7 q^{21} + 8 q^{22} - 8 q^{23} - 8 q^{24} + 2 q^{26} - 28 q^{27} - 7 q^{28} - 3 q^{29} - 16 q^{31} - 12 q^{32} - 5 q^{33} - 4 q^{34} - 14 q^{36} + 7 q^{37} - 11 q^{38} + 16 q^{39} + 7 q^{41} - q^{42} + 10 q^{43} + 7 q^{44} + q^{46} - 19 q^{47} + 6 q^{48} + 8 q^{49} + 7 q^{51} - 18 q^{52} + q^{53} - 25 q^{54} + 3 q^{56} + 25 q^{57} + 9 q^{58} + 21 q^{59} - 7 q^{61} - 18 q^{62} - 9 q^{63} - 37 q^{64} - 43 q^{66} - 11 q^{67} + 17 q^{68} + 7 q^{69} + 8 q^{71} - 4 q^{72} + 3 q^{73} + 12 q^{74} + 8 q^{76} - 6 q^{77} + 50 q^{78} - 15 q^{79} + 28 q^{81} - 41 q^{82} - 25 q^{83} + 8 q^{84} - 12 q^{86} - 21 q^{87} + 29 q^{88} + q^{89} + 8 q^{91} - 7 q^{92} + 5 q^{93} - 36 q^{94} + 30 q^{96} - 10 q^{97} - q^{98} - 18 q^{99}+O(q^{100}) $ 8 * q - q^2 - 7 * q^3 + 7 * q^4 + q^6 - 8 * q^7 - 3 * q^8 + 9 * q^9 + 6 * q^11 - 8 * q^12 - 8 * q^13 + q^14 + q^16 - 4 * q^17 + 11 * q^18 + 7 * q^21 + 8 * q^22 - 8 * q^23 - 8 * q^24 + 2 * q^26 - 28 * q^27 - 7 * q^28 - 3 * q^29 - 16 * q^31 - 12 * q^32 - 5 * q^33 - 4 * q^34 - 14 * q^36 + 7 * q^37 - 11 * q^38 + 16 * q^39 + 7 * q^41 - q^42 + 10 * q^43 + 7 * q^44 + q^46 - 19 * q^47 + 6 * q^48 + 8 * q^49 + 7 * q^51 - 18 * q^52 + q^53 - 25 * q^54 + 3 * q^56 + 25 * q^57 + 9 * q^58 + 21 * q^59 - 7 * q^61 - 18 * q^62 - 9 * q^63 - 37 * q^64 - 43 * q^66 - 11 * q^67 + 17 * q^68 + 7 * q^69 + 8 * q^71 - 4 * q^72 + 3 * q^73 + 12 * q^74 + 8 * q^76 - 6 * q^77 + 50 * q^78 - 15 * q^79 + 28 * q^81 - 41 * q^82 - 25 * q^83 + 8 * q^84 - 12 * q^86 - 21 * q^87 + 29 * q^88 + q^89 + 8 * q^91 - 7 * q^92 + 5 * q^93 - 36 * q^94 + 30 * q^96 - 10 * q^97 - q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.28279	1.61417	0.807087	−	0.590433i	$-0.201043\pi$
$2$	2.28279	1.61417	0.807087	+	0.590433i	$0.201043\pi$
$3$	−0.445964	−0.257478	−0.128739	−	0.991679i	$-0.541093\pi$
$3$	−0.445964	−0.257478	−0.128739	+	0.991679i	$0.541093\pi$
$4$	3.21111	1.60556
$5$	0	0
$5$	0	0
$6$	−1.01804	−0.415614
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.76472	0.977475
$9$	−2.80112	−0.933705
$10$	0	0
$11$	0.882192	0.265991	0.132995	−	0.991117i	$-0.457540\pi$
$11$	0.882192	0.265991	0.132995	+	0.991117i	$0.457540\pi$
$12$	−1.43204	−0.413395
$13$	0.264745	0.0734271	0.0367136	−	0.999326i	$-0.488311\pi$
$13$	0.264745	0.0734271	0.0367136	+	0.999326i	$0.488311\pi$
$14$	−2.28279	−0.610100
$15$	0	0
$16$	−0.110972	−0.0277430
$17$	−6.80853	−1.65131	−0.825656	−	0.564174i	$-0.809195\pi$
$17$	−6.80853	−1.65131	−0.825656	+	0.564174i	$0.809195\pi$
$18$	−6.39435	−1.50716
$19$	2.33311	0.535252	0.267626	−	0.963523i	$-0.413761\pi$
$19$	2.33311	0.535252	0.267626	+	0.963523i	$0.413761\pi$
$20$	0	0
$21$	0.445964	0.0973174
$22$	2.01386	0.429356
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.23296	−0.251678
$25$	0	0
$26$	0.604357	0.118524
$27$	2.58709	0.497886
$28$	−3.21111	−0.606844
$29$	4.70357	0.873430	0.436715	−	0.899600i	$-0.356142\pi$
$29$	4.70357	0.873430	0.436715	+	0.899600i	$0.356142\pi$
$30$	0	0
$31$	−5.57993	−1.00218	−0.501092	−	0.865394i	$-0.667068\pi$
$31$	−5.57993	−1.00218	−0.501092	+	0.865394i	$0.667068\pi$
$32$	−5.78276	−1.02226
$33$	−0.393426	−0.0684867
$34$	−15.5424	−2.66550
$35$	0	0
$36$	−8.99470	−1.49912
$37$	4.70000	0.772675	0.386337	−	0.922358i	$-0.373740\pi$
$37$	4.70000	0.772675	0.386337	+	0.922358i	$0.373740\pi$
$38$	5.32599	0.863989
$39$	−0.118067	−0.0189058
$40$	0	0
$41$	−5.47644	−0.855276	−0.427638	−	0.903950i	$-0.640654\pi$
$41$	−5.47644	−0.855276	−0.427638	+	0.903950i	$0.640654\pi$
$42$	1.01804	0.157087
$43$	−6.78709	−1.03502	−0.517511	−	0.855677i	$-0.673141\pi$
$43$	−6.78709	−1.03502	−0.517511	+	0.855677i	$0.673141\pi$
$44$	2.83282	0.427064
$45$	0	0
$46$	−2.28279	−0.336579
$47$	−7.04416	−1.02750	−0.513748	−	0.857941i	$-0.671743\pi$
$47$	−7.04416	−1.02750	−0.513748	+	0.857941i	$0.671743\pi$
$48$	0.0494895	0.00714319
$49$	1.00000	0.142857
$50$	0	0
$51$	3.03636	0.425176
$52$	0.850127	0.117891
$53$	−9.38516	−1.28915	−0.644576	−	0.764540i	$-0.722966\pi$
$53$	−9.38516	−1.28915	−0.644576	+	0.764540i	$0.722966\pi$
$54$	5.90578	0.803674
$55$	0	0
$56$	−2.76472	−0.369451
$57$	−1.04048	−0.137815
$58$	10.7372	1.40987
$59$	7.44091	0.968724	0.484362	−	0.874868i	$-0.339052\pi$
$59$	7.44091	0.968724	0.484362	+	0.874868i	$0.339052\pi$
$60$	0	0
$61$	−14.6378	−1.87418	−0.937089	−	0.349090i	$-0.886491\pi$
$61$	−14.6378	−1.87418	−0.937089	+	0.349090i	$0.886491\pi$
$62$	−12.7378	−1.61770
$63$	2.80112	0.352907
$64$	−12.9789	−1.62236
$65$	0	0
$66$	−0.898108	−0.110549
$67$	−4.23716	−0.517651	−0.258826	−	0.965924i	$-0.583335\pi$
$67$	−4.23716	−0.517651	−0.258826	+	0.965924i	$0.583335\pi$
$68$	−21.8630	−2.65128
$69$	0.445964	0.0536878
$70$	0	0
$71$	−9.35459	−1.11019	−0.555093	−	0.831788i	$-0.687317\pi$
$71$	−9.35459	−1.11019	−0.555093	+	0.831788i	$0.687317\pi$
$72$	−7.74429	−0.912673
$73$	−6.72564	−0.787176	−0.393588	−	0.919287i	$-0.628766\pi$
$73$	−6.72564	−0.787176	−0.393588	+	0.919287i	$0.628766\pi$
$74$	10.7291	1.24723
$75$	0	0
$76$	7.49188	0.859377
$77$	−0.882192	−0.100535
$78$	−0.269522	−0.0305173
$79$	14.6130	1.64409	0.822047	−	0.569420i	$-0.192832\pi$
$79$	14.6130	1.64409	0.822047	+	0.569420i	$0.192832\pi$
$80$	0	0
$81$	7.24960	0.805511
$82$	−12.5015	−1.38056
$83$	0.193588	0.0212491	0.0106245	−	0.999944i	$-0.496618\pi$
$83$	0.193588	0.0212491	0.0106245	+	0.999944i	$0.496618\pi$
$84$	1.43204	0.156249
$85$	0	0
$86$	−15.4935	−1.67071
$87$	−2.09762	−0.224889
$88$	2.43901	0.259999
$89$	16.7797	1.77865	0.889323	−	0.457279i	$-0.151176\pi$
$89$	16.7797	1.77865	0.889323	+	0.457279i	$0.151176\pi$
$90$	0	0
$91$	−0.264745	−0.0277528
$92$	−3.21111	−0.334782
$93$	2.48845	0.258040
$94$	−16.0803	−1.65856
$95$	0	0
$96$	2.57890	0.263208
$97$	−10.0525	−1.02068	−0.510339	−	0.859973i	$-0.670480\pi$
$97$	−10.0525	−1.02068	−0.510339	+	0.859973i	$0.670480\pi$
$98$	2.28279	0.230596
$99$	−2.47112	−0.248357
$100$	0	0
$101$	−2.79904	−0.278515	−0.139257	−	0.990256i	$-0.544472\pi$
$101$	−2.79904	−0.278515	−0.139257	+	0.990256i	$0.544472\pi$
$102$	6.93137	0.686308
$103$	−3.72914	−0.367443	−0.183721	−	0.982978i	$-0.558814\pi$
$103$	−3.72914	−0.367443	−0.183721	+	0.982978i	$0.558814\pi$
$104$	0.731945	0.0717732
$105$	0	0
$106$	−21.4243	−2.08091
$107$	−5.46111	−0.527945	−0.263972	−	0.964530i	$-0.585033\pi$
$107$	−5.46111	−0.527945	−0.263972	+	0.964530i	$0.585033\pi$
$108$	8.30745	0.799384
$109$	11.0426	1.05769	0.528845	−	0.848718i	$-0.322625\pi$
$109$	11.0426	1.05769	0.528845	+	0.848718i	$0.322625\pi$
$110$	0	0
$111$	−2.09603	−0.198946
$112$	0.110972	0.0104859
$113$	−8.82162	−0.829868	−0.414934	−	0.909851i	$-0.636195\pi$
$113$	−8.82162	−0.829868	−0.414934	+	0.909851i	$0.636195\pi$
$114$	−2.37520	−0.222458
$115$	0	0
$116$	15.1037	1.40234
$117$	−0.741582	−0.0685593
$118$	16.9860	1.56369
$119$	6.80853	0.624137
$120$	0	0
$121$	−10.2217	−0.929249
$122$	−33.4150	−3.02525
$123$	2.44230	0.220215
$124$	−17.9178	−1.60907
$125$	0	0
$126$	6.39435	0.569654
$127$	9.06252	0.804168	0.402084	−	0.915603i	$-0.368286\pi$
$127$	9.06252	0.804168	0.402084	+	0.915603i	$0.368286\pi$
$128$	−18.0624	−1.59651
$129$	3.02680	0.266495
$130$	0	0
$131$	5.80502	0.507187	0.253594	−	0.967311i	$-0.418387\pi$
$131$	5.80502	0.507187	0.253594	+	0.967311i	$0.418387\pi$
$132$	−1.26334	−0.109959
$133$	−2.33311	−0.202306
$134$	−9.67253	−0.835579
$135$	0	0
$136$	−18.8237	−1.61412
$137$	8.15908	0.697077	0.348538	−	0.937294i	$-0.386678\pi$
$137$	8.15908	0.697077	0.348538	+	0.937294i	$0.386678\pi$
$138$	1.01804	0.0866614
$139$	−12.6407	−1.07217	−0.536085	−	0.844164i	$-0.680097\pi$
$139$	−12.6407	−1.07217	−0.536085	+	0.844164i	$0.680097\pi$
$140$	0	0
$141$	3.14144	0.264557
$142$	−21.3545	−1.79203
$143$	0.233556	0.0195309
$144$	0.310845	0.0259037
$145$	0	0
$146$	−15.3532	−1.27064
$147$	−0.445964	−0.0367825
$148$	15.0922	1.24057
$149$	15.3424	1.25690	0.628451	−	0.777849i	$-0.283689\pi$
$149$	15.3424	1.25690	0.628451	+	0.777849i	$0.283689\pi$
$150$	0	0
$151$	15.0386	1.22383	0.611914	−	0.790925i	$-0.290400\pi$
$151$	15.0386	1.22383	0.611914	+	0.790925i	$0.290400\pi$
$152$	6.45038	0.523195
$153$	19.0715	1.54184
$154$	−2.01386	−0.162281
$155$	0	0
$156$	−0.379126	−0.0303544
$157$	4.39042	0.350394	0.175197	−	0.984533i	$-0.443944\pi$
$157$	4.39042	0.350394	0.175197	+	0.984533i	$0.443944\pi$
$158$	33.3584	2.65385
$159$	4.18545	0.331928
$160$	0	0
$161$	1.00000	0.0788110
$162$	16.5493	1.30023
$163$	14.8954	1.16670	0.583350	−	0.812221i	$-0.301742\pi$
$163$	14.8954	1.16670	0.583350	+	0.812221i	$0.301742\pi$
$164$	−17.5855	−1.37320
$165$	0	0
$166$	0.441921	0.0342997
$167$	14.6029	1.13001	0.565003	−	0.825089i	$-0.308875\pi$
$167$	14.6029	1.13001	0.565003	+	0.825089i	$0.308875\pi$
$168$	1.23296	0.0951253
$169$	−12.9299	−0.994608
$170$	0	0
$171$	−6.53531	−0.499767
$172$	−21.7941	−1.66179
$173$	−8.40444	−0.638978	−0.319489	−	0.947590i	$-0.603511\pi$
$173$	−8.40444	−0.638978	−0.319489	+	0.947590i	$0.603511\pi$
$174$	−4.78843	−0.363010
$175$	0	0
$176$	−0.0978985	−0.00737937
$177$	−3.31838	−0.249425
$178$	38.3045	2.87105
$179$	−20.5071	−1.53277	−0.766386	−	0.642380i	$-0.777947\pi$
$179$	−20.5071	−1.53277	−0.766386	+	0.642380i	$0.777947\pi$
$180$	0	0
$181$	−0.525089	−0.0390296	−0.0195148	−	0.999810i	$-0.506212\pi$
$181$	−0.525089	−0.0390296	−0.0195148	+	0.999810i	$0.506212\pi$
$182$	−0.604357	−0.0447979
$183$	6.52794	0.482559
$184$	−2.76472	−0.203818
$185$	0	0
$186$	5.68060	0.416522
$187$	−6.00643	−0.439234
$188$	−22.6196	−1.64970
$189$	−2.58709	−0.188183
$190$	0	0
$191$	17.1744	1.24270	0.621350	−	0.783533i	$-0.286585\pi$
$191$	17.1744	1.24270	0.621350	+	0.783533i	$0.286585\pi$
$192$	5.78811	0.417721
$193$	8.54149	0.614830	0.307415	−	0.951576i	$-0.400536\pi$
$193$	8.54149	0.614830	0.307415	+	0.951576i	$0.400536\pi$
$194$	−22.9478	−1.64755
$195$	0	0
$196$	3.21111	0.229365
$197$	13.8400	0.986059	0.493029	−	0.870013i	$-0.335889\pi$
$197$	13.8400	0.986059	0.493029	+	0.870013i	$0.335889\pi$
$198$	−5.64104	−0.400892
$199$	9.76488	0.692214	0.346107	−	0.938195i	$-0.387503\pi$
$199$	9.76488	0.692214	0.346107	+	0.938195i	$0.387503\pi$
$200$	0	0
$201$	1.88962	0.133284
$202$	−6.38961	−0.449571
$203$	−4.70357	−0.330126
$204$	9.75011	0.682644
$205$	0	0
$206$	−8.51282	−0.593117
$207$	2.80112	0.194691
$208$	−0.0293793	−0.00203709
$209$	2.05825	0.142372
$210$	0	0
$211$	6.36816	0.438403	0.219201	−	0.975680i	$-0.429655\pi$
$211$	6.36816	0.438403	0.219201	+	0.975680i	$0.429655\pi$
$212$	−30.1368	−2.06981
$213$	4.17182	0.285848
$214$	−12.4665	−0.852195
$215$	0	0
$216$	7.15257	0.486671
$217$	5.57993	0.378790
$218$	25.2079	1.70730
$219$	2.99939	0.202680
$220$	0	0
$221$	−1.80253	−0.121251
$222$	−4.78479	−0.321134
$223$	−11.9209	−0.798282	−0.399141	−	0.916890i	$-0.630692\pi$
$223$	−11.9209	−0.798282	−0.399141	+	0.916890i	$0.630692\pi$
$224$	5.78276	0.386377
$225$	0	0
$226$	−20.1379	−1.33955
$227$	−13.4339	−0.891640	−0.445820	−	0.895123i	$-0.647088\pi$
$227$	−13.4339	−0.891640	−0.445820	+	0.895123i	$0.647088\pi$
$228$	−3.34111	−0.221270
$229$	−25.5676	−1.68956	−0.844779	−	0.535116i	$-0.820268\pi$
$229$	−25.5676	−1.68956	−0.844779	+	0.535116i	$0.820268\pi$
$230$	0	0
$231$	0.393426	0.0258855
$232$	13.0040	0.853756
$233$	23.0395	1.50937	0.754684	−	0.656089i	$-0.227790\pi$
$233$	23.0395	1.50937	0.754684	+	0.656089i	$0.227790\pi$
$234$	−1.69287	−0.110667
$235$	0	0
$236$	23.8936	1.55534
$237$	−6.51689	−0.423317
$238$	15.5424	1.00747
$239$	−14.3124	−0.925791	−0.462896	−	0.886413i	$-0.653190\pi$
$239$	−14.3124	−0.925791	−0.462896	+	0.886413i	$0.653190\pi$
$240$	0	0
$241$	−23.8646	−1.53725	−0.768626	−	0.639698i	$-0.779059\pi$
$241$	−23.8646	−1.53725	−0.768626	+	0.639698i	$0.779059\pi$
$242$	−23.3340	−1.49997
$243$	−10.9943	−0.705287
$244$	−47.0037	−3.00910
$245$	0	0
$246$	5.57524	0.355465
$247$	0.617679	0.0393020
$248$	−15.4269	−0.979610
$249$	−0.0863335	−0.00547116
$250$	0	0
$251$	21.1289	1.33364	0.666821	−	0.745218i	$-0.267655\pi$
$251$	21.1289	1.33364	0.666821	+	0.745218i	$0.267655\pi$
$252$	8.99470	0.566613
$253$	−0.882192	−0.0554629
$254$	20.6878	1.29807
$255$	0	0
$256$	−15.2750	−0.954687
$257$	7.09291	0.442443	0.221222	−	0.975224i	$-0.428996\pi$
$257$	7.09291	0.442443	0.221222	+	0.975224i	$0.428996\pi$
$258$	6.90954	0.430169
$259$	−4.70000	−0.292044
$260$	0	0
$261$	−13.1752	−0.815527
$262$	13.2516	0.818688
$263$	7.64291	0.471282	0.235641	−	0.971840i	$-0.424281\pi$
$263$	7.64291	0.471282	0.235641	+	0.971840i	$0.424281\pi$
$264$	−1.08771	−0.0669440
$265$	0	0
$266$	−5.32599	−0.326557
$267$	−7.48316	−0.457962
$268$	−13.6060	−0.831119
$269$	−15.4396	−0.941367	−0.470684	−	0.882302i	$-0.655993\pi$
$269$	−15.4396	−0.941367	−0.470684	+	0.882302i	$0.655993\pi$
$270$	0	0
$271$	−20.8328	−1.26550	−0.632752	−	0.774355i	$-0.718075\pi$
$271$	−20.8328	−1.26550	−0.632752	+	0.774355i	$0.718075\pi$
$272$	0.755555	0.0458123
$273$	0.118067	0.00714574
$274$	18.6254	1.12520
$275$	0	0
$276$	1.43204	0.0861988
$277$	−16.3374	−0.981618	−0.490809	−	0.871267i	$-0.663299\pi$
$277$	−16.3374	−0.981618	−0.490809	+	0.871267i	$0.663299\pi$
$278$	−28.8560	−1.73067
$279$	15.6300	0.935745
$280$	0	0
$281$	5.89511	0.351673	0.175836	−	0.984419i	$-0.443737\pi$
$281$	5.89511	0.351673	0.175836	+	0.984419i	$0.443737\pi$
$282$	7.17125	0.427042
$283$	6.07866	0.361339	0.180669	−	0.983544i	$-0.442174\pi$
$283$	6.07866	0.361339	0.180669	+	0.983544i	$0.442174\pi$
$284$	−30.0387	−1.78247
$285$	0	0
$286$	0.533159	0.0315263
$287$	5.47644	0.323264
$288$	16.1982	0.954487
$289$	29.3561	1.72683
$290$	0	0
$291$	4.48307	0.262802
$292$	−21.5968	−1.26386
$293$	−0.260282	−0.0152058	−0.00760292	−	0.999971i	$-0.502420\pi$
$293$	−0.260282	−0.0152058	−0.00760292	+	0.999971i	$0.502420\pi$
$294$	−1.01804	−0.0593734
$295$	0	0
$296$	12.9942	0.755270
$297$	2.28231	0.132433
$298$	35.0235	2.02886
$299$	−0.264745	−0.0153106
$300$	0	0
$301$	6.78709	0.391202
$302$	34.3300	1.97547
$303$	1.24827	0.0717113
$304$	−0.258909	−0.0148495
$305$	0	0
$306$	43.5361	2.48880
$307$	−18.1195	−1.03413	−0.517067	−	0.855945i	$-0.672976\pi$
$307$	−18.1195	−1.03413	−0.517067	+	0.855945i	$0.672976\pi$
$308$	−2.83282	−0.161415
$309$	1.66306	0.0946083
$310$	0	0
$311$	5.44175	0.308574	0.154287	−	0.988026i	$-0.450692\pi$
$311$	5.44175	0.308574	0.154287	+	0.988026i	$0.450692\pi$
$312$	−0.326422	−0.0184800
$313$	4.93195	0.278770	0.139385	−	0.990238i	$-0.455487\pi$
$313$	4.93195	0.278770	0.139385	+	0.990238i	$0.455487\pi$
$314$	10.0224	0.565597
$315$	0	0
$316$	46.9241	2.63969
$317$	16.0753	0.902880	0.451440	−	0.892302i	$-0.350911\pi$
$317$	16.0753	0.902880	0.451440	+	0.892302i	$0.350911\pi$
$318$	9.55449	0.535789
$319$	4.14945	0.232325
$320$	0	0
$321$	2.43546	0.135934
$322$	2.28279	0.127215
$323$	−15.8850	−0.883867
$324$	23.2793	1.29329
$325$	0	0
$326$	34.0031	1.88326
$327$	−4.92461	−0.272331
$328$	−15.1408	−0.836011
$329$	7.04416	0.388357
$330$	0	0
$331$	18.9626	1.04228	0.521138	−	0.853472i	$-0.325508\pi$
$331$	18.9626	1.04228	0.521138	+	0.853472i	$0.325508\pi$
$332$	0.621634	0.0341166
$333$	−13.1652	−0.721451
$334$	33.3353	1.82403
$335$	0	0
$336$	−0.0494895	−0.00269987
$337$	14.0390	0.764754	0.382377	−	0.924006i	$-0.375106\pi$
$337$	14.0390	0.764754	0.382377	+	0.924006i	$0.375106\pi$
$338$	−29.5162	−1.60547
$339$	3.93413	0.213673
$340$	0	0
$341$	−4.92257	−0.266572
$342$	−14.9187	−0.806711
$343$	−1.00000	−0.0539949
$344$	−18.7644	−1.01171
$345$	0	0
$346$	−19.1855	−1.03142
$347$	5.86904	0.315067	0.157533	−	0.987514i	$-0.449646\pi$
$347$	5.86904	0.315067	0.157533	+	0.987514i	$0.449646\pi$
$348$	−6.73571	−0.361072
$349$	−27.9408	−1.49564	−0.747818	−	0.663904i	$-0.768898\pi$
$349$	−27.9408	−1.49564	−0.747818	+	0.663904i	$0.768898\pi$
$350$	0	0
$351$	0.684920	0.0365583
$352$	−5.10150	−0.271911
$353$	−6.94530	−0.369661	−0.184830	−	0.982770i	$-0.559174\pi$
$353$	−6.94530	−0.369661	−0.184830	+	0.982770i	$0.559174\pi$
$354$	−7.57515	−0.402615
$355$	0	0
$356$	53.8816	2.85572
$357$	−3.03636	−0.160701
$358$	−46.8133	−2.47416
$359$	−19.8558	−1.04795	−0.523974	−	0.851734i	$-0.675551\pi$
$359$	−19.8558	−1.04795	−0.523974	+	0.851734i	$0.675551\pi$
$360$	0	0
$361$	−13.5566	−0.713506
$362$	−1.19867	−0.0630005
$363$	4.55853	0.239261
$364$	−0.850127	−0.0445588
$365$	0	0
$366$	14.9019	0.778934
$367$	−23.9055	−1.24786	−0.623928	−	0.781481i	$-0.714464\pi$
$367$	−23.9055	−1.24786	−0.623928	+	0.781481i	$0.714464\pi$
$368$	0.110972	0.00578481
$369$	15.3401	0.798576
$370$	0	0
$371$	9.38516	0.487253
$372$	7.99070	0.414298
$373$	3.02683	0.156723	0.0783617	−	0.996925i	$-0.475031\pi$
$373$	3.02683	0.156723	0.0783617	+	0.996925i	$0.475031\pi$
$374$	−13.7114	−0.709000
$375$	0	0
$376$	−19.4751	−1.00435
$377$	1.24525	0.0641335
$378$	−5.90578	−0.303760
$379$	7.30508	0.375237	0.187618	−	0.982242i	$-0.439923\pi$
$379$	7.30508	0.375237	0.187618	+	0.982242i	$0.439923\pi$
$380$	0	0
$381$	−4.04156	−0.207055
$382$	39.2056	2.00593
$383$	16.9449	0.865844	0.432922	−	0.901431i	$-0.357482\pi$
$383$	16.9449	0.865844	0.432922	+	0.901431i	$0.357482\pi$
$384$	8.05521	0.411066
$385$	0	0
$386$	19.4984	0.992442
$387$	19.0114	0.966405
$388$	−32.2798	−1.63876
$389$	−7.80496	−0.395727	−0.197864	−	0.980230i	$-0.563400\pi$
$389$	−7.80496	−0.395727	−0.197864	+	0.980230i	$0.563400\pi$
$390$	0	0
$391$	6.80853	0.344322
$392$	2.76472	0.139639
$393$	−2.58883	−0.130589
$394$	31.5938	1.59167
$395$	0	0
$396$	−7.93506	−0.398752
$397$	16.1944	0.812773	0.406386	−	0.913701i	$-0.366789\pi$
$397$	16.1944	0.812773	0.406386	+	0.913701i	$0.366789\pi$
$398$	22.2911	1.11735
$399$	1.04048	0.0520893
$400$	0	0
$401$	−20.8572	−1.04156	−0.520779	−	0.853691i	$-0.674358\pi$
$401$	−20.8572	−1.04156	−0.520779	+	0.853691i	$0.674358\pi$
$402$	4.31360	0.215143
$403$	−1.47726	−0.0735875
$404$	−8.98803	−0.447171
$405$	0	0
$406$	−10.7372	−0.532880
$407$	4.14630	0.205525
$408$	8.39468	0.415599
$409$	11.4886	0.568075	0.284038	−	0.958813i	$-0.408326\pi$
$409$	11.4886	0.568075	0.284038	+	0.958813i	$0.408326\pi$
$410$	0	0
$411$	−3.63866	−0.179482
$412$	−11.9747	−0.589950
$413$	−7.44091	−0.366143
$414$	6.39435	0.314265
$415$	0	0
$416$	−1.53096	−0.0750614
$417$	5.63730	0.276060
$418$	4.69854	0.229813
$419$	13.4385	0.656513	0.328257	−	0.944589i	$-0.393539\pi$
$419$	13.4385	0.656513	0.328257	+	0.944589i	$0.393539\pi$
$420$	0	0
$421$	14.0763	0.686039	0.343019	−	0.939328i	$-0.388550\pi$
$421$	14.0763	0.686039	0.343019	+	0.939328i	$0.388550\pi$
$422$	14.5372	0.707658
$423$	19.7315	0.959379
$424$	−25.9473	−1.26011
$425$	0	0
$426$	9.52336	0.461409
$427$	14.6378	0.708373
$428$	−17.5362	−0.847646
$429$	−0.104158	−0.00502878
$430$	0	0
$431$	−20.6543	−0.994884	−0.497442	−	0.867497i	$-0.665727\pi$
$431$	−20.6543	−0.994884	−0.497442	+	0.867497i	$0.665727\pi$
$432$	−0.287094	−0.0138128
$433$	37.2302	1.78917	0.894584	−	0.446900i	$-0.147472\pi$
$433$	37.2302	1.78917	0.894584	+	0.446900i	$0.147472\pi$
$434$	12.7378	0.611433
$435$	0	0
$436$	35.4591	1.69818
$437$	−2.33311	−0.111608
$438$	6.84697	0.327161
$439$	10.6210	0.506914	0.253457	−	0.967347i	$-0.418432\pi$
$439$	10.6210	0.506914	0.253457	+	0.967347i	$0.418432\pi$
$440$	0	0
$441$	−2.80112	−0.133386
$442$	−4.11478	−0.195720
$443$	3.29850	0.156717	0.0783583	−	0.996925i	$-0.475032\pi$
$443$	3.29850	0.156717	0.0783583	+	0.996925i	$0.475032\pi$
$444$	−6.73060	−0.319420
$445$	0	0
$446$	−27.2129	−1.28857
$447$	−6.84218	−0.323624
$448$	12.9789	0.613193
$449$	27.8179	1.31281	0.656405	−	0.754409i	$-0.272076\pi$
$449$	27.8179	1.31281	0.656405	+	0.754409i	$0.272076\pi$
$450$	0	0
$451$	−4.83127	−0.227496
$452$	−28.3272	−1.33240
$453$	−6.70670	−0.315108
$454$	−30.6667	−1.43926
$455$	0	0
$456$	−2.87664	−0.134711
$457$	31.9503	1.49457	0.747285	−	0.664503i	$-0.231357\pi$
$457$	31.9503	1.49457	0.747285	+	0.664503i	$0.231357\pi$
$458$	−58.3655	−2.72724
$459$	−17.6143	−0.822165
$460$	0	0
$461$	−27.2902	−1.27103	−0.635515	−	0.772089i	$-0.719212\pi$
$461$	−27.2902	−1.27103	−0.635515	+	0.772089i	$0.719212\pi$
$462$	0.898108	0.0417838
$463$	22.3258	1.03757	0.518784	−	0.854905i	$-0.326385\pi$
$463$	22.3258	1.03757	0.518784	+	0.854905i	$0.326385\pi$
$464$	−0.521963	−0.0242315
$465$	0	0
$466$	52.5943	2.43638
$467$	−1.52823	−0.0707180	−0.0353590	−	0.999375i	$-0.511257\pi$
$467$	−1.52823	−0.0707180	−0.0353590	+	0.999375i	$0.511257\pi$
$468$	−2.38130	−0.110076
$469$	4.23716	0.195654
$470$	0	0
$471$	−1.95797	−0.0902186
$472$	20.5720	0.946903
$473$	−5.98752	−0.275306
$474$	−14.8767	−0.683308
$475$	0	0
$476$	21.8630	1.00209
$477$	26.2889	1.20369
$478$	−32.6721	−1.49439
$479$	43.2948	1.97819	0.989094	−	0.147284i	$-0.0470533\pi$
$479$	43.2948	1.97819	0.989094	+	0.147284i	$0.0470533\pi$
$480$	0	0
$481$	1.24430	0.0567353
$482$	−54.4777	−2.48139
$483$	−0.445964	−0.0202921
$484$	−32.8232	−1.49196
$485$	0	0
$486$	−25.0977	−1.13846
$487$	−7.11107	−0.322233	−0.161117	−	0.986935i	$-0.551510\pi$
$487$	−7.11107	−0.322233	−0.161117	+	0.986935i	$0.551510\pi$
$488$	−40.4694	−1.83196
$489$	−6.64282	−0.300399
$490$	0	0
$491$	−24.2647	−1.09505	−0.547526	−	0.836789i	$-0.684430\pi$
$491$	−24.2647	−1.09505	−0.547526	+	0.836789i	$0.684430\pi$
$492$	7.84250	0.353567
$493$	−32.0244	−1.44231
$494$	1.41003	0.0634402
$495$	0	0
$496$	0.619215	0.0278036
$497$	9.35459	0.419611
$498$	−0.197081	−0.00883141
$499$	−5.46235	−0.244529	−0.122264	−	0.992498i	$-0.539016\pi$
$499$	−5.46235	−0.244529	−0.122264	+	0.992498i	$0.539016\pi$
$500$	0	0
$501$	−6.51237	−0.290951
$502$	48.2327	2.15273
$503$	−26.9673	−1.20241	−0.601206	−	0.799094i	$-0.705313\pi$
$503$	−26.9673	−1.20241	−0.601206	+	0.799094i	$0.705313\pi$
$504$	7.74429	0.344958
$505$	0	0
$506$	−2.01386	−0.0895268
$507$	5.76628	0.256089
$508$	29.1008	1.29114
$509$	−37.3594	−1.65593	−0.827964	−	0.560782i	$-0.810501\pi$
$509$	−37.3594	−1.65593	−0.827964	+	0.560782i	$0.810501\pi$
$510$	0	0
$511$	6.72564	0.297525
$512$	1.25533	0.0554785
$513$	6.03596	0.266494
$514$	16.1916	0.714181
$515$	0	0
$516$	9.71941	0.427873
$517$	−6.21430	−0.273305
$518$	−10.7291	−0.471409
$519$	3.74808	0.164522
$520$	0	0
$521$	0.810893	0.0355259	0.0177629	−	0.999842i	$-0.494346\pi$
$521$	0.810893	0.0355259	0.0177629	+	0.999842i	$0.494346\pi$
$522$	−30.0762	−1.31640
$523$	−6.06391	−0.265156	−0.132578	−	0.991173i	$-0.542326\pi$
$523$	−6.06391	−0.265156	−0.132578	+	0.991173i	$0.542326\pi$
$524$	18.6406	0.814318
$525$	0	0
$526$	17.4471	0.760731
$527$	37.9911	1.65492
$528$	0.0436592	0.00190002
$529$	1.00000	0.0434783
$530$	0	0
$531$	−20.8429	−0.904503
$532$	−7.49188	−0.324814
$533$	−1.44986	−0.0628005
$534$	−17.0824	−0.739230
$535$	0	0
$536$	−11.7145	−0.505991
$537$	9.14543	0.394654
$538$	−35.2452	−1.51953
$539$	0.882192	0.0379987
$540$	0	0
$541$	−38.4476	−1.65299	−0.826495	−	0.562944i	$-0.809669\pi$
$541$	−38.4476	−1.65299	−0.826495	+	0.562944i	$0.809669\pi$
$542$	−47.5569	−2.04274
$543$	0.234171	0.0100492
$544$	39.3721	1.68806
$545$	0	0
$546$	0.269522	0.0115345
$547$	−22.1779	−0.948257	−0.474128	−	0.880456i	$-0.657237\pi$
$547$	−22.1779	−0.948257	−0.474128	+	0.880456i	$0.657237\pi$
$548$	26.1997	1.11920
$549$	41.0022	1.74993
$550$	0	0
$551$	10.9739	0.467505
$552$	1.23296	0.0524785
$553$	−14.6130	−0.621409
$554$	−37.2947	−1.58450
$555$	0	0
$556$	−40.5907	−1.72143
$557$	41.7266	1.76801	0.884007	−	0.467473i	$-0.154836\pi$
$557$	41.7266	1.76801	0.884007	+	0.467473i	$0.154836\pi$
$558$	35.6800	1.51046
$559$	−1.79685	−0.0759987
$560$	0	0
$561$	2.67866	0.113093
$562$	13.4573	0.567661
$563$	34.9538	1.47313	0.736564	−	0.676368i	$-0.236447\pi$
$563$	34.9538	1.47313	0.736564	+	0.676368i	$0.236447\pi$
$564$	10.0875	0.424762
$565$	0	0
$566$	13.8763	0.583263
$567$	−7.24960	−0.304454
$568$	−25.8628	−1.08518
$569$	−43.3891	−1.81897	−0.909483	−	0.415742i	$-0.863522\pi$
$569$	−43.3891	−1.81897	−0.909483	+	0.415742i	$0.863522\pi$
$570$	0	0
$571$	−39.5626	−1.65564	−0.827822	−	0.560990i	$-0.810421\pi$
$571$	−39.5626	−1.65564	−0.827822	+	0.560990i	$0.810421\pi$
$572$	0.749976	0.0313581
$573$	−7.65919	−0.319967
$574$	12.5015	0.521805
$575$	0	0
$576$	36.3553	1.51480
$577$	−39.3010	−1.63612	−0.818061	−	0.575132i	$-0.804951\pi$
$577$	−39.3010	−1.63612	−0.818061	+	0.575132i	$0.804951\pi$
$578$	67.0138	2.78741
$579$	−3.80920	−0.158305
$580$	0	0
$581$	−0.193588	−0.00803140
$582$	10.2339	0.424208
$583$	−8.27952	−0.342903
$584$	−18.5945	−0.769445
$585$	0	0
$586$	−0.594169	−0.0245449
$587$	−17.0358	−0.703143	−0.351572	−	0.936161i	$-0.614353\pi$
$587$	−17.0358	−0.703143	−0.351572	+	0.936161i	$0.614353\pi$
$588$	−1.43204	−0.0590564
$589$	−13.0186	−0.536421
$590$	0	0
$591$	−6.17215	−0.253888
$592$	−0.521567	−0.0214363
$593$	−23.9734	−0.984470	−0.492235	−	0.870462i	$-0.663820\pi$
$593$	−23.9734	−0.984470	−0.492235	+	0.870462i	$0.663820\pi$
$594$	5.21003	0.213770
$595$	0	0
$596$	49.2663	2.01803
$597$	−4.35479	−0.178230
$598$	−0.604357	−0.0247140
$599$	13.8754	0.566934	0.283467	−	0.958982i	$-0.408515\pi$
$599$	13.8754	0.566934	0.283467	+	0.958982i	$0.408515\pi$
$600$	0	0
$601$	5.76901	0.235323	0.117661	−	0.993054i	$-0.462460\pi$
$601$	5.76901	0.235323	0.117661	+	0.993054i	$0.462460\pi$
$602$	15.4935	0.631467
$603$	11.8688	0.483334
$604$	48.2908	1.96492
$605$	0	0
$606$	2.84954	0.115754
$607$	5.73749	0.232878	0.116439	−	0.993198i	$-0.462852\pi$
$607$	5.73749	0.232878	0.116439	+	0.993198i	$0.462852\pi$
$608$	−13.4918	−0.547165
$609$	2.09762	0.0850000
$610$	0	0
$611$	−1.86491	−0.0754461
$612$	61.2407	2.47551
$613$	44.2651	1.78785	0.893926	−	0.448214i	$-0.147940\pi$
$613$	44.2651	1.78785	0.893926	+	0.448214i	$0.147940\pi$
$614$	−41.3629	−1.66927
$615$	0	0
$616$	−2.43901	−0.0982705
$617$	16.9073	0.680663	0.340332	−	0.940305i	$-0.389461\pi$
$617$	16.9073	0.680663	0.340332	+	0.940305i	$0.389461\pi$
$618$	3.79642	0.152714
$619$	−4.93954	−0.198537	−0.0992685	−	0.995061i	$-0.531650\pi$
$619$	−4.93954	−0.198537	−0.0992685	+	0.995061i	$0.531650\pi$
$620$	0	0
$621$	−2.58709	−0.103816
$622$	12.4224	0.498091
$623$	−16.7797	−0.672265
$624$	0.0131021	0.000524504 0
$625$	0	0
$626$	11.2586	0.449984
$627$	−0.917906	−0.0366576
$628$	14.0982	0.562578
$629$	−32.0001	−1.27593
$630$	0	0
$631$	1.96371	0.0781742	0.0390871	−	0.999236i	$-0.487555\pi$
$631$	1.96371	0.0781742	0.0390871	+	0.999236i	$0.487555\pi$
$632$	40.4009	1.60706
$633$	−2.83997	−0.112879
$634$	36.6965	1.45740
$635$	0	0
$636$	13.4400	0.532929
$637$	0.264745	0.0104896
$638$	9.47231	0.375012
$639$	26.2033	1.03659
$640$	0	0
$641$	8.55011	0.337709	0.168855	−	0.985641i	$-0.445993\pi$
$641$	8.55011	0.337709	0.168855	+	0.985641i	$0.445993\pi$
$642$	5.55963	0.219421
$643$	−17.1715	−0.677176	−0.338588	−	0.940935i	$-0.609949\pi$
$643$	−17.1715	−0.677176	−0.338588	+	0.940935i	$0.609949\pi$
$644$	3.21111	0.126536
$645$	0	0
$646$	−36.2622	−1.42672
$647$	−15.7971	−0.621050	−0.310525	−	0.950565i	$-0.600505\pi$
$647$	−15.7971	−0.621050	−0.310525	+	0.950565i	$0.600505\pi$
$648$	20.0431	0.787367
$649$	6.56431	0.257672
$650$	0	0
$651$	−2.48845	−0.0975300
$652$	47.8309	1.87320
$653$	4.99317	0.195398	0.0976988	−	0.995216i	$-0.468852\pi$
$653$	4.99317	0.195398	0.0976988	+	0.995216i	$0.468852\pi$
$654$	−11.2418	−0.439590
$655$	0	0
$656$	0.607731	0.0237279
$657$	18.8393	0.734990
$658$	16.0803	0.626876
$659$	−6.35794	−0.247670	−0.123835	−	0.992303i	$-0.539519\pi$
$659$	−6.35794	−0.247670	−0.123835	+	0.992303i	$0.539519\pi$
$660$	0	0
$661$	40.5733	1.57812	0.789059	−	0.614318i	$-0.210569\pi$
$661$	40.5733	1.57812	0.789059	+	0.614318i	$0.210569\pi$
$662$	43.2875	1.68242
$663$	0.803863	0.0312194
$664$	0.535217	0.0207704
$665$	0	0
$666$	−30.0534	−1.16455
$667$	−4.70357	−0.182123
$668$	46.8916	1.81429
$669$	5.31629	0.205540
$670$	0	0
$671$	−12.9134	−0.498515
$672$	−2.57890	−0.0994834
$673$	−13.2627	−0.511239	−0.255619	−	0.966777i	$-0.582279\pi$
$673$	−13.2627	−0.511239	−0.255619	+	0.966777i	$0.582279\pi$
$674$	32.0481	1.23445
$675$	0	0
$676$	−41.5194	−1.59690
$677$	−23.2209	−0.892450	−0.446225	−	0.894921i	$-0.647232\pi$
$677$	−23.2209	−0.892450	−0.446225	+	0.894921i	$0.647232\pi$
$678$	8.98078	0.344905
$679$	10.0525	0.385780
$680$	0	0
$681$	5.99104	0.229577
$682$	−11.2372	−0.430294
$683$	−42.1710	−1.61363	−0.806814	−	0.590805i	$-0.798810\pi$
$683$	−42.1710	−1.61363	−0.806814	+	0.590805i	$0.798810\pi$
$684$	−20.9856	−0.802405
$685$	0	0
$686$	−2.28279	−0.0871572
$687$	11.4023	0.435023
$688$	0.753176	0.0287146
$689$	−2.48468	−0.0946587
$690$	0	0
$691$	35.6905	1.35773	0.678865	−	0.734263i	$-0.262472\pi$
$691$	35.6905	1.35773	0.678865	+	0.734263i	$0.262472\pi$
$692$	−26.9876	−1.02592
$693$	2.47112	0.0938702
$694$	13.3978	0.508573
$695$	0	0
$696$	−5.79933	−0.219823
$697$	37.2865	1.41233
$698$	−63.7829	−2.41422
$699$	−10.2748	−0.388628
$700$	0	0
$701$	2.10394	0.0794646	0.0397323	−	0.999210i	$-0.487349\pi$
$701$	2.10394	0.0794646	0.0397323	+	0.999210i	$0.487349\pi$
$702$	1.56353	0.0590115
$703$	10.9656	0.413575
$704$	−11.4498	−0.431532
$705$	0	0
$706$	−15.8546	−0.596697
$707$	2.79904	0.105269
$708$	−10.6557	−0.400466
$709$	−0.895305	−0.0336239	−0.0168119	−	0.999859i	$-0.505352\pi$
$709$	−0.895305	−0.0336239	−0.0168119	+	0.999859i	$0.505352\pi$
$710$	0	0
$711$	−40.9328	−1.53510
$712$	46.3912	1.73858
$713$	5.57993	0.208970
$714$	−6.93137	−0.259400
$715$	0	0
$716$	−65.8506	−2.46095
$717$	6.38281	0.238371
$718$	−45.3265	−1.69157
$719$	−5.44754	−0.203159	−0.101579	−	0.994827i	$-0.532390\pi$
$719$	−5.44754	−0.203159	−0.101579	+	0.994827i	$0.532390\pi$
$720$	0	0
$721$	3.72914	0.138880
$722$	−30.9468	−1.15172
$723$	10.6427	0.395808
$724$	−1.68612	−0.0626642
$725$	0	0
$726$	10.4062	0.386209
$727$	−23.7030	−0.879096	−0.439548	−	0.898219i	$-0.644861\pi$
$727$	−23.7030	−0.879096	−0.439548	+	0.898219i	$0.644861\pi$
$728$	−0.731945	−0.0271277
$729$	−16.8457	−0.623915
$730$	0	0
$731$	46.2101	1.70914
$732$	20.9620	0.774776
$733$	27.9487	1.03231	0.516155	−	0.856495i	$-0.327363\pi$
$733$	27.9487	1.03231	0.516155	+	0.856495i	$0.327363\pi$
$734$	−54.5712	−2.01426
$735$	0	0
$736$	5.78276	0.213155
$737$	−3.73799	−0.137691
$738$	35.0183	1.28904
$739$	−45.9992	−1.69211	−0.846054	−	0.533098i	$-0.821028\pi$
$739$	−45.9992	−1.69211	−0.846054	+	0.533098i	$0.821028\pi$
$740$	0	0
$741$	−0.275463	−0.0101194
$742$	21.4243	0.786512
$743$	−3.58745	−0.131611	−0.0658053	−	0.997832i	$-0.520962\pi$
$743$	−3.58745	−0.131611	−0.0658053	+	0.997832i	$0.520962\pi$
$744$	6.87986	0.252228
$745$	0	0
$746$	6.90961	0.252979
$747$	−0.542263	−0.0198404
$748$	−19.2873	−0.705215
$749$	5.46111	0.199544
$750$	0	0
$751$	−28.5746	−1.04270	−0.521351	−	0.853342i	$-0.674572\pi$
$751$	−28.5746	−1.04270	−0.521351	+	0.853342i	$0.674572\pi$
$752$	0.781703	0.0285058
$753$	−9.42272	−0.343383
$754$	2.84263	0.103523
$755$	0	0
$756$	−8.30745	−0.302139
$757$	−9.49105	−0.344958	−0.172479	−	0.985013i	$-0.555178\pi$
$757$	−9.49105	−0.344958	−0.172479	+	0.985013i	$0.555178\pi$
$758$	16.6759	0.605698
$759$	0.393426	0.0142805
$760$	0	0
$761$	14.8526	0.538405	0.269202	−	0.963084i	$-0.413240\pi$
$761$	14.8526	0.538405	0.269202	+	0.963084i	$0.413240\pi$
$762$	−9.22602	−0.334223
$763$	−11.0426	−0.399769
$764$	55.1491	1.99523
$765$	0	0
$766$	38.6816	1.39762
$767$	1.96995	0.0711306
$768$	6.81210	0.245811
$769$	−9.25706	−0.333818	−0.166909	−	0.985972i	$-0.553379\pi$
$769$	−9.25706	−0.333818	−0.166909	+	0.985972i	$0.553379\pi$
$770$	0	0
$771$	−3.16318	−0.113919
$772$	27.4277	0.987144
$773$	6.93020	0.249262	0.124631	−	0.992203i	$-0.460225\pi$
$773$	6.93020	0.249262	0.124631	+	0.992203i	$0.460225\pi$
$774$	43.3990	1.55995
$775$	0	0
$776$	−27.7924	−0.997688
$777$	2.09603	0.0751947
$778$	−17.8171	−0.638773
$779$	−12.7771	−0.457788
$780$	0	0
$781$	−8.25255	−0.295299
$782$	15.5424	0.555796
$783$	12.1686	0.434869
$784$	−0.110972	−0.00396328
$785$	0	0
$786$	−5.90975	−0.210794
$787$	−35.6582	−1.27108	−0.635539	−	0.772069i	$-0.719222\pi$
$787$	−35.6582	−1.27108	−0.635539	+	0.772069i	$0.719222\pi$
$788$	44.4418	1.58317
$789$	−3.40847	−0.121345
$790$	0	0
$791$	8.82162	0.313661
$792$	−6.83195	−0.242763
$793$	−3.87529	−0.137616
$794$	36.9683	1.31196
$795$	0	0
$796$	31.3562	1.11139
$797$	−12.0573	−0.427092	−0.213546	−	0.976933i	$-0.568501\pi$
$797$	−12.0573	−0.427092	−0.213546	+	0.976933i	$0.568501\pi$
$798$	2.37520	0.0840812
$799$	47.9604	1.69672
$800$	0	0
$801$	−47.0019	−1.66073
$802$	−47.6125	−1.68126
$803$	−5.93330	−0.209382
$804$	6.06779	0.213994
$805$	0	0
$806$	−3.37227	−0.118783
$807$	6.88550	0.242381
$808$	−7.73854	−0.272241
$809$	−19.3977	−0.681988	−0.340994	−	0.940065i	$-0.610764\pi$
$809$	−19.3977	−0.681988	−0.340994	+	0.940065i	$0.610764\pi$
$810$	0	0
$811$	−35.5308	−1.24765	−0.623827	−	0.781562i	$-0.714423\pi$
$811$	−35.5308	−1.24765	−0.623827	+	0.781562i	$0.714423\pi$
$812$	−15.1037	−0.530036
$813$	9.29069	0.325839
$814$	9.46512	0.331752
$815$	0	0
$816$	−0.336951	−0.0117956
$817$	−15.8350	−0.553997
$818$	26.2260	0.916972
$819$	0.741582	0.0259130
$820$	0	0
$821$	34.0925	1.18984	0.594918	−	0.803786i	$-0.297184\pi$
$821$	34.0925	1.18984	0.594918	+	0.803786i	$0.297184\pi$
$822$	−8.30628	−0.289715
$823$	−52.9679	−1.84634	−0.923172	−	0.384386i	$-0.874413\pi$
$823$	−52.9679	−1.84634	−0.923172	+	0.384386i	$0.874413\pi$
$824$	−10.3100	−0.359166
$825$	0	0
$826$	−16.9860	−0.591019
$827$	−15.6761	−0.545110	−0.272555	−	0.962140i	$-0.587869\pi$
$827$	−15.6761	−0.545110	−0.272555	+	0.962140i	$0.587869\pi$
$828$	8.99470	0.312588
$829$	54.4072	1.88964	0.944820	−	0.327590i	$-0.106237\pi$
$829$	54.4072	1.88964	0.944820	+	0.327590i	$0.106237\pi$
$830$	0	0
$831$	7.28589	0.252745
$832$	−3.43609	−0.119125
$833$	−6.80853	−0.235902
$834$	12.8688	0.445608
$835$	0	0
$836$	6.60927	0.228587
$837$	−14.4358	−0.498974
$838$	30.6772	1.05973
$839$	−28.8881	−0.997329	−0.498664	−	0.866795i	$-0.666176\pi$
$839$	−28.8881	−0.997329	−0.498664	+	0.866795i	$0.666176\pi$
$840$	0	0
$841$	−6.87646	−0.237119
$842$	32.1333	1.10739
$843$	−2.62901	−0.0905478
$844$	20.4489	0.703880
$845$	0	0
$846$	45.0428	1.54860
$847$	10.2217	0.351223
$848$	1.04149	0.0357649
$849$	−2.71086	−0.0930366
$850$	0	0
$851$	−4.70000	−0.161114
$852$	13.3962	0.458945
$853$	−4.34440	−0.148750	−0.0743748	−	0.997230i	$-0.523696\pi$
$853$	−4.34440	−0.148750	−0.0743748	+	0.997230i	$0.523696\pi$
$854$	33.4150	1.14344
$855$	0	0
$856$	−15.0984	−0.516053
$857$	−6.66146	−0.227551	−0.113776	−	0.993506i	$-0.536295\pi$
$857$	−6.66146	−0.227551	−0.113776	+	0.993506i	$0.536295\pi$
$858$	−0.237770	−0.00811733
$859$	−5.08899	−0.173634	−0.0868171	−	0.996224i	$-0.527670\pi$
$859$	−5.08899	−0.173634	−0.0868171	+	0.996224i	$0.527670\pi$
$860$	0	0
$861$	−2.44230	−0.0832333
$862$	−47.1494	−1.60592
$863$	22.8511	0.777861	0.388931	−	0.921267i	$-0.372845\pi$
$863$	22.8511	0.777861	0.388931	+	0.921267i	$0.372845\pi$
$864$	−14.9605	−0.508967
$865$	0	0
$866$	84.9885	2.88803
$867$	−13.0918	−0.444620
$868$	17.9178	0.608169
$869$	12.8915	0.437314
$870$	0	0
$871$	−1.12177	−0.0380096
$872$	30.5297	1.03387
$873$	28.1583	0.953013
$874$	−5.32599	−0.180154
$875$	0	0
$876$	9.63140	0.325415
$877$	23.9219	0.807786	0.403893	−	0.914806i	$-0.367657\pi$
$877$	23.9219	0.807786	0.403893	+	0.914806i	$0.367657\pi$
$878$	24.2456	0.818248
$879$	0.116077	0.00391516
$880$	0	0
$881$	36.4566	1.22825	0.614127	−	0.789207i	$-0.289508\pi$
$881$	36.4566	1.22825	0.614127	+	0.789207i	$0.289508\pi$
$882$	−6.39435	−0.215309
$883$	−56.8606	−1.91351	−0.956755	−	0.290893i	$-0.906047\pi$
$883$	−56.8606	−1.91351	−0.956755	+	0.290893i	$0.906047\pi$
$884$	−5.78812	−0.194676
$885$	0	0
$886$	7.52977	0.252968
$887$	49.9258	1.67635	0.838173	−	0.545405i	$-0.183624\pi$
$887$	49.9258	1.67635	0.838173	+	0.545405i	$0.183624\pi$
$888$	−5.79493	−0.194465
$889$	−9.06252	−0.303947
$890$	0	0
$891$	6.39554	0.214259
$892$	−38.2794	−1.28169
$893$	−16.4348	−0.549969
$894$	−15.6192	−0.522386
$895$	0	0
$896$	18.0624	0.603424
$897$	0.118067	0.00394214
$898$	63.5024	2.11910
$899$	−26.2456	−0.875339
$900$	0	0
$901$	63.8992	2.12879
$902$	−11.0288	−0.367218
$903$	−3.02680	−0.100726
$904$	−24.3893	−0.811176
$905$	0	0
$906$	−15.3100	−0.508639
$907$	−29.8857	−0.992337	−0.496169	−	0.868226i	$-0.665260\pi$
$907$	−29.8857	−0.992337	−0.496169	+	0.868226i	$0.665260\pi$
$908$	−43.1378	−1.43158
$909$	7.84043	0.260051
$910$	0	0
$911$	−2.04089	−0.0676177	−0.0338089	−	0.999428i	$-0.510764\pi$
$911$	−2.04089	−0.0676177	−0.0338089	+	0.999428i	$0.510764\pi$
$912$	0.115464	0.00382340
$913$	0.170782	0.00565206
$914$	72.9356	2.41250
$915$	0	0
$916$	−82.1006	−2.71268
$917$	−5.80502	−0.191699
$918$	−40.2097	−1.32712
$919$	14.8402	0.489534	0.244767	−	0.969582i	$-0.421289\pi$
$919$	14.8402	0.489534	0.244767	+	0.969582i	$0.421289\pi$
$920$	0	0
$921$	8.08065	0.266266
$922$	−62.2976	−2.05166
$923$	−2.47658	−0.0815178
$924$	1.26334	0.0415607
$925$	0	0
$926$	50.9651	1.67482
$927$	10.4457	0.343083
$928$	−27.1996	−0.892870
$929$	31.6908	1.03974	0.519871	−	0.854245i	$-0.325980\pi$
$929$	31.6908	1.03974	0.519871	+	0.854245i	$0.325980\pi$
$930$	0	0
$931$	2.33311	0.0764645
$932$	73.9825	2.42338
$933$	−2.42683	−0.0794508
$934$	−3.48862	−0.114151
$935$	0	0
$936$	−2.05026	−0.0670150
$937$	7.19925	0.235189	0.117595	−	0.993062i	$-0.462482\pi$
$937$	7.19925	0.235189	0.117595	+	0.993062i	$0.462482\pi$
$938$	9.67253	0.315819
$939$	−2.19947	−0.0717771
$940$	0	0
$941$	40.1066	1.30744	0.653719	−	0.756737i	$-0.273208\pi$
$941$	40.1066	1.30744	0.653719	+	0.756737i	$0.273208\pi$
$942$	−4.46963	−0.145629
$943$	5.47644	0.178337
$944$	−0.825731	−0.0268753
$945$	0	0
$946$	−13.6682	−0.444392
$947$	−14.3124	−0.465092	−0.232546	−	0.972585i	$-0.574706\pi$
$947$	−14.3124	−0.465092	−0.232546	+	0.972585i	$0.574706\pi$
$948$	−20.9265	−0.679660
$949$	−1.78058	−0.0578001
$950$	0	0
$951$	−7.16902	−0.232471
$952$	18.8237	0.610078
$953$	−54.0632	−1.75128	−0.875639	−	0.482965i	$-0.839560\pi$
$953$	−54.0632	−1.75128	−0.875639	+	0.482965i	$0.839560\pi$
$954$	60.0120	1.94296
$955$	0	0
$956$	−45.9587	−1.48641
$957$	−1.85051	−0.0598184
$958$	98.8327	3.19314
$959$	−8.15908	−0.263470
$960$	0	0
$961$	0.135607	0.00437440
$962$	2.84048	0.0915806
$963$	15.2972	0.492945
$964$	−76.6319	−2.46815
$965$	0	0
$966$	−1.01804	−0.0327549
$967$	−37.5902	−1.20882	−0.604410	−	0.796673i	$-0.706591\pi$
$967$	−37.5902	−1.20882	−0.604410	+	0.796673i	$0.706591\pi$
$968$	−28.2602	−0.908317
$969$	7.08416	0.227576
$970$	0	0
$971$	−20.4833	−0.657340	−0.328670	−	0.944445i	$-0.606600\pi$
$971$	−20.4833	−0.657340	−0.328670	+	0.944445i	$0.606600\pi$
$972$	−35.3041	−1.13238
$973$	12.6407	0.405242
$974$	−16.2331	−0.520141
$975$	0	0
$976$	1.62438	0.0519953
$977$	26.8695	0.859633	0.429816	−	0.902916i	$-0.358578\pi$
$977$	26.8695	0.859633	0.429816	+	0.902916i	$0.358578\pi$
$978$	−15.1642	−0.484896
$979$	14.8029	0.473104
$980$	0	0
$981$	−30.9316	−0.987571
$982$	−55.3912	−1.76760
$983$	7.27097	0.231908	0.115954	−	0.993255i	$-0.463008\pi$
$983$	7.27097	0.231908	0.115954	+	0.993255i	$0.463008\pi$
$984$	6.75226	0.215254
$985$	0	0
$986$	−73.1048	−2.32813
$987$	−3.14144	−0.0999933
$988$	1.98344	0.0631016
$989$	6.78709	0.215817
$990$	0	0
$991$	11.2644	0.357826	0.178913	−	0.983865i	$-0.442742\pi$
$991$	11.2644	0.357826	0.178913	+	0.983865i	$0.442742\pi$
$992$	32.2674	1.02449
$993$	−8.45662	−0.268363
$994$	21.3545	0.677325
$995$	0	0
$996$	−0.277227	−0.00878427
$997$	−2.08601	−0.0660647	−0.0330323	−	0.999454i	$-0.510516\pi$
$997$	−2.08601	−0.0660647	−0.0330323	+	0.999454i	$0.510516\pi$
$998$	−12.4694	−0.394712
$999$	12.1593	0.384704

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.t.1.8		8
5.4	even	2		805.2.a.m.1.1	✓	8
15.14	odd	2		7245.2.a.bp.1.8		8
35.34	odd	2		5635.2.a.bb.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.m.1.1	✓	8	5.4	even	2
4025.2.a.t.1.8		8	1.1	even	1	trivial
5635.2.a.bb.1.1		8	35.34	odd	2
7245.2.a.bp.1.8		8	15.14	odd	2

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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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q+2.28279 q^{2} -0.445964 q^{3} +3.21111 q^{4} -1.01804 q^{6} -1.00000 q^{7} +2.76472 q^{8} -2.80112 q^{9} +O(q^{10})\)	\(q+2.28279 q^{2} -0.445964 q^{3} +3.21111 q^{4} -1.01804 q^{6} -1.00000 q^{7} +2.76472 q^{8} -2.80112 q^{9} +0.882192 q^{11} -1.43204 q^{12} +0.264745 q^{13} -2.28279 q^{14} -0.110972 q^{16} -6.80853 q^{17} -6.39435 q^{18} +2.33311 q^{19} +0.445964 q^{21} +2.01386 q^{22} -1.00000 q^{23} -1.23296 q^{24} +0.604357 q^{26} +2.58709 q^{27} -3.21111 q^{28} +4.70357 q^{29} -5.57993 q^{31} -5.78276 q^{32} -0.393426 q^{33} -15.5424 q^{34} -8.99470 q^{36} +4.70000 q^{37} +5.32599 q^{38} -0.118067 q^{39} -5.47644 q^{41} +1.01804 q^{42} -6.78709 q^{43} +2.83282 q^{44} -2.28279 q^{46} -7.04416 q^{47} +0.0494895 q^{48} +1.00000 q^{49} +3.03636 q^{51} +0.850127 q^{52} -9.38516 q^{53} +5.90578 q^{54} -2.76472 q^{56} -1.04048 q^{57} +10.7372 q^{58} +7.44091 q^{59} -14.6378 q^{61} -12.7378 q^{62} +2.80112 q^{63} -12.9789 q^{64} -0.898108 q^{66} -4.23716 q^{67} -21.8630 q^{68} +0.445964 q^{69} -9.35459 q^{71} -7.74429 q^{72} -6.72564 q^{73} +10.7291 q^{74} +7.49188 q^{76} -0.882192 q^{77} -0.269522 q^{78} +14.6130 q^{79} +7.24960 q^{81} -12.5015 q^{82} +0.193588 q^{83} +1.43204 q^{84} -15.4935 q^{86} -2.09762 q^{87} +2.43901 q^{88} +16.7797 q^{89} -0.264745 q^{91} -3.21111 q^{92} +2.48845 q^{93} -16.0803 q^{94} +2.57890 q^{96} -10.0525 q^{97} +2.28279 q^{98} -2.47112 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 7 q^{3} + 7 q^{4} + q^{6} - 8 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) \) 8 * q - q^2 - 7 * q^3 + 7 * q^4 + q^6 - 8 * q^7 - 3 * q^8 + 9 * q^9	\( 8 q - q^{2} - 7 q^{3} + 7 q^{4} + q^{6} - 8 q^{7} - 3 q^{8} + 9 q^{9} + 6 q^{11} - 8 q^{12} - 8 q^{13} + q^{14} + q^{16} - 4 q^{17} + 11 q^{18} + 7 q^{21} + 8 q^{22} - 8 q^{23} - 8 q^{24} + 2 q^{26} - 28 q^{27} - 7 q^{28} - 3 q^{29} - 16 q^{31} - 12 q^{32} - 5 q^{33} - 4 q^{34} - 14 q^{36} + 7 q^{37} - 11 q^{38} + 16 q^{39} + 7 q^{41} - q^{42} + 10 q^{43} + 7 q^{44} + q^{46} - 19 q^{47} + 6 q^{48} + 8 q^{49} + 7 q^{51} - 18 q^{52} + q^{53} - 25 q^{54} + 3 q^{56} + 25 q^{57} + 9 q^{58} + 21 q^{59} - 7 q^{61} - 18 q^{62} - 9 q^{63} - 37 q^{64} - 43 q^{66} - 11 q^{67} + 17 q^{68} + 7 q^{69} + 8 q^{71} - 4 q^{72} + 3 q^{73} + 12 q^{74} + 8 q^{76} - 6 q^{77} + 50 q^{78} - 15 q^{79} + 28 q^{81} - 41 q^{82} - 25 q^{83} + 8 q^{84} - 12 q^{86} - 21 q^{87} + 29 q^{88} + q^{89} + 8 q^{91} - 7 q^{92} + 5 q^{93} - 36 q^{94} + 30 q^{96} - 10 q^{97} - q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q - q^2 - 7 * q^3 + 7 * q^4 + q^6 - 8 * q^7 - 3 * q^8 + 9 * q^9 + 6 * q^11 - 8 * q^12 - 8 * q^13 + q^14 + q^16 - 4 * q^17 + 11 * q^18 + 7 * q^21 + 8 * q^22 - 8 * q^23 - 8 * q^24 + 2 * q^26 - 28 * q^27 - 7 * q^28 - 3 * q^29 - 16 * q^31 - 12 * q^32 - 5 * q^33 - 4 * q^34 - 14 * q^36 + 7 * q^37 - 11 * q^38 + 16 * q^39 + 7 * q^41 - q^42 + 10 * q^43 + 7 * q^44 + q^46 - 19 * q^47 + 6 * q^48 + 8 * q^49 + 7 * q^51 - 18 * q^52 + q^53 - 25 * q^54 + 3 * q^56 + 25 * q^57 + 9 * q^58 + 21 * q^59 - 7 * q^61 - 18 * q^62 - 9 * q^63 - 37 * q^64 - 43 * q^66 - 11 * q^67 + 17 * q^68 + 7 * q^69 + 8 * q^71 - 4 * q^72 + 3 * q^73 + 12 * q^74 + 8 * q^76 - 6 * q^77 + 50 * q^78 - 15 * q^79 + 28 * q^81 - 41 * q^82 - 25 * q^83 + 8 * q^84 - 12 * q^86 - 21 * q^87 + 29 * q^88 + q^89 + 8 * q^91 - 7 * q^92 + 5 * q^93 - 36 * q^94 + 30 * q^96 - 10 * q^97 - q^98 - 18 * q^99

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