LMFDB - Embedded newform 4025.2.a.t.1.6

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			1.6
Root			$-1.17189$ 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)

$f(q)$	$=$	$q+1.17189 q^{2} +1.97939 q^{3} -0.626674 q^{4} +2.31962 q^{6} -1.00000 q^{7} -3.07817 q^{8} +0.917966 q^{9} +O(q^{10})$	\(q+1.17189 q^{2} +1.97939 q^{3} -0.626674 q^{4} +2.31962 q^{6} -1.00000 q^{7} -3.07817 q^{8} +0.917966 q^{9} -1.40826 q^{11} -1.24043 q^{12} +2.49151 q^{13} -1.17189 q^{14} -2.35393 q^{16} +0.453763 q^{17} +1.07576 q^{18} +1.11228 q^{19} -1.97939 q^{21} -1.65032 q^{22} -1.00000 q^{23} -6.09289 q^{24} +2.91978 q^{26} -4.12115 q^{27} +0.626674 q^{28} -9.35311 q^{29} -5.55485 q^{31} +3.39779 q^{32} -2.78748 q^{33} +0.531760 q^{34} -0.575265 q^{36} -8.19098 q^{37} +1.30347 q^{38} +4.93166 q^{39} -0.274718 q^{41} -2.31962 q^{42} +0.390696 q^{43} +0.882517 q^{44} -1.17189 q^{46} -12.9765 q^{47} -4.65934 q^{48} +1.00000 q^{49} +0.898171 q^{51} -1.56136 q^{52} -4.53708 q^{53} -4.82953 q^{54} +3.07817 q^{56} +2.20164 q^{57} -10.9608 q^{58} +8.97628 q^{59} +13.9503 q^{61} -6.50967 q^{62} -0.917966 q^{63} +8.68971 q^{64} -3.26662 q^{66} -14.0713 q^{67} -0.284361 q^{68} -1.97939 q^{69} +13.9393 q^{71} -2.82566 q^{72} +11.7557 q^{73} -9.59893 q^{74} -0.697039 q^{76} +1.40826 q^{77} +5.77937 q^{78} -15.7133 q^{79} -10.9112 q^{81} -0.321939 q^{82} -4.50677 q^{83} +1.24043 q^{84} +0.457853 q^{86} -18.5134 q^{87} +4.33486 q^{88} +12.5797 q^{89} -2.49151 q^{91} +0.626674 q^{92} -10.9952 q^{93} -15.2071 q^{94} +6.72554 q^{96} -7.20324 q^{97} +1.17189 q^{98} -1.29273 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.17189	0.828651	0.414326	−	0.910129i	$-0.364017\pi$
$2$	1.17189	0.828651	0.414326	+	0.910129i	$0.364017\pi$
$3$	1.97939	1.14280	0.571399	−	0.820672i	$-0.306401\pi$
$3$	1.97939	1.14280	0.571399	+	0.820672i	$0.306401\pi$
$4$	−0.626674	−0.313337
$5$	0	0
$5$	0	0
$6$	2.31962	0.946982
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.07817	−1.08830
$9$	0.917966	0.305989
$10$	0	0
$11$	−1.40826	−0.424605	−0.212303	−	0.977204i	$-0.568096\pi$
$11$	−1.40826	−0.424605	−0.212303	+	0.977204i	$0.568096\pi$
$12$	−1.24043	−0.358081
$13$	2.49151	0.691021	0.345511	−	0.938415i	$-0.387706\pi$
$13$	2.49151	0.691021	0.345511	+	0.938415i	$0.387706\pi$
$14$	−1.17189	−0.313201
$15$	0	0
$16$	−2.35393	−0.588483
$17$	0.453763	0.110054	0.0550268	−	0.998485i	$-0.482476\pi$
$17$	0.453763	0.110054	0.0550268	+	0.998485i	$0.482476\pi$
$18$	1.07576	0.253558
$19$	1.11228	0.255175	0.127588	−	0.991827i	$-0.459277\pi$
$19$	1.11228	0.255175	0.127588	+	0.991827i	$0.459277\pi$
$20$	0	0
$21$	−1.97939	−0.431937
$22$	−1.65032	−0.351850
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−6.09289	−1.24371
$25$	0	0
$26$	2.91978	0.572616
$27$	−4.12115	−0.793115
$28$	0.626674	0.118430
$29$	−9.35311	−1.73683	−0.868414	−	0.495840i	$-0.834860\pi$
$29$	−9.35311	−1.73683	−0.868414	+	0.495840i	$0.834860\pi$
$30$	0	0
$31$	−5.55485	−0.997681	−0.498840	−	0.866694i	$-0.666241\pi$
$31$	−5.55485	−0.997681	−0.498840	+	0.866694i	$0.666241\pi$
$32$	3.39779	0.600651
$33$	−2.78748	−0.485238
$34$	0.531760	0.0911961
$35$	0	0
$36$	−0.575265	−0.0958775
$37$	−8.19098	−1.34659	−0.673294	−	0.739375i	$-0.735121\pi$
$37$	−8.19098	−1.34659	−0.673294	+	0.739375i	$0.735121\pi$
$38$	1.30347	0.211451
$39$	4.93166	0.789698
$40$	0	0
$41$	−0.274718	−0.0429037	−0.0214519	−	0.999770i	$-0.506829\pi$
$41$	−0.274718	−0.0429037	−0.0214519	+	0.999770i	$0.506829\pi$
$42$	−2.31962	−0.357925
$43$	0.390696	0.0595806	0.0297903	−	0.999556i	$-0.490516\pi$
$43$	0.390696	0.0595806	0.0297903	+	0.999556i	$0.490516\pi$
$44$	0.882517	0.133044
$45$	0	0
$46$	−1.17189	−0.172786
$47$	−12.9765	−1.89282	−0.946411	−	0.322965i	$-0.895320\pi$
$47$	−12.9765	−1.89282	−0.946411	+	0.322965i	$0.895320\pi$
$48$	−4.65934	−0.672518
$49$	1.00000	0.142857
$50$	0	0
$51$	0.898171	0.125769
$52$	−1.56136	−0.216522
$53$	−4.53708	−0.623215	−0.311608	−	0.950211i	$-0.600867\pi$
$53$	−4.53708	−0.623215	−0.311608	+	0.950211i	$0.600867\pi$
$54$	−4.82953	−0.657216
$55$	0	0
$56$	3.07817	0.411338
$57$	2.20164	0.291614
$58$	−10.9608	−1.43923
$59$	8.97628	1.16861	0.584306	−	0.811533i	$-0.301367\pi$
$59$	8.97628	1.16861	0.584306	+	0.811533i	$0.301367\pi$
$60$	0	0
$61$	13.9503	1.78616	0.893080	−	0.449899i	$-0.148540\pi$
$61$	13.9503	1.78616	0.893080	+	0.449899i	$0.148540\pi$
$62$	−6.50967	−0.826730
$63$	−0.917966	−0.115653
$64$	8.68971	1.08621
$65$	0	0
$66$	−3.26662	−0.402094
$67$	−14.0713	−1.71909	−0.859544	−	0.511062i	$-0.829252\pi$
$67$	−14.0713	−1.71909	−0.859544	+	0.511062i	$0.829252\pi$
$68$	−0.284361	−0.0344839
$69$	−1.97939	−0.238290
$70$	0	0
$71$	13.9393	1.65430	0.827148	−	0.561984i	$-0.189962\pi$
$71$	13.9393	1.65430	0.827148	+	0.561984i	$0.189962\pi$
$72$	−2.82566	−0.333007
$73$	11.7557	1.37590	0.687951	−	0.725757i	$-0.258510\pi$
$73$	11.7557	1.37590	0.687951	+	0.725757i	$0.258510\pi$
$74$	−9.59893	−1.11585
$75$	0	0
$76$	−0.697039	−0.0799558
$77$	1.40826	0.160486
$78$	5.77937	0.654384
$79$	−15.7133	−1.76789	−0.883944	−	0.467593i	$-0.845121\pi$
$79$	−15.7133	−1.76789	−0.883944	+	0.467593i	$0.845121\pi$
$80$	0	0
$81$	−10.9112	−1.21236
$82$	−0.321939	−0.0355523
$83$	−4.50677	−0.494682	−0.247341	−	0.968928i	$-0.579557\pi$
$83$	−4.50677	−0.494682	−0.247341	+	0.968928i	$0.579557\pi$
$84$	1.24043	0.135342
$85$	0	0
$86$	0.457853	0.0493715
$87$	−18.5134	−1.98484
$88$	4.33486	0.462097
$89$	12.5797	1.33344	0.666722	−	0.745306i	$-0.267697\pi$
$89$	12.5797	1.33344	0.666722	+	0.745306i	$0.267697\pi$
$90$	0	0
$91$	−2.49151	−0.261181
$92$	0.626674	0.0653352
$93$	−10.9952	−1.14015
$94$	−15.2071	−1.56849
$95$	0	0
$96$	6.72554	0.686423
$97$	−7.20324	−0.731378	−0.365689	−	0.930737i	$-0.619167\pi$
$97$	−7.20324	−0.731378	−0.365689	+	0.930737i	$0.619167\pi$
$98$	1.17189	0.118379
$99$	−1.29273	−0.129924
$100$	0	0
$101$	−11.2981	−1.12420	−0.562100	−	0.827070i	$-0.690006\pi$
$101$	−11.2981	−1.12420	−0.562100	+	0.827070i	$0.690006\pi$
$102$	1.05256	0.104219
$103$	2.08129	0.205075	0.102538	−	0.994729i	$-0.467304\pi$
$103$	2.08129	0.205075	0.102538	+	0.994729i	$0.467304\pi$
$104$	−7.66930	−0.752037
$105$	0	0
$106$	−5.31696	−0.516428
$107$	−2.30583	−0.222913	−0.111457	−	0.993769i	$-0.535552\pi$
$107$	−2.30583	−0.222913	−0.111457	+	0.993769i	$0.535552\pi$
$108$	2.58261	0.248512
$109$	−4.98308	−0.477293	−0.238646	−	0.971107i	$-0.576704\pi$
$109$	−4.98308	−0.477293	−0.238646	+	0.971107i	$0.576704\pi$
$110$	0	0
$111$	−16.2131	−1.53888
$112$	2.35393	0.222426
$113$	−7.87482	−0.740801	−0.370401	−	0.928872i	$-0.620780\pi$
$113$	−7.87482	−0.740801	−0.370401	+	0.928872i	$0.620780\pi$
$114$	2.58008	0.241646
$115$	0	0
$116$	5.86134	0.544212
$117$	2.28712	0.211445
$118$	10.5192	0.968372
$119$	−0.453763	−0.0415964
$120$	0	0
$121$	−9.01681	−0.819710
$122$	16.3483	1.48010
$123$	−0.543773	−0.0490303
$124$	3.48108	0.312610
$125$	0	0
$126$	−1.07576	−0.0958359
$127$	−3.68719	−0.327186	−0.163593	−	0.986528i	$-0.552308\pi$
$127$	−3.68719	−0.327186	−0.163593	+	0.986528i	$0.552308\pi$
$128$	3.38779	0.299441
$129$	0.773338	0.0680886
$130$	0	0
$131$	15.8477	1.38462	0.692311	−	0.721599i	$-0.256592\pi$
$131$	15.8477	1.38462	0.692311	+	0.721599i	$0.256592\pi$
$132$	1.74684	0.152043
$133$	−1.11228	−0.0964472
$134$	−16.4901	−1.42452
$135$	0	0
$136$	−1.39676	−0.119771
$137$	0.555437	0.0474541	0.0237271	−	0.999718i	$-0.492447\pi$
$137$	0.555437	0.0474541	0.0237271	+	0.999718i	$0.492447\pi$
$138$	−2.31962	−0.197459
$139$	3.84633	0.326241	0.163121	−	0.986606i	$-0.447844\pi$
$139$	3.84633	0.326241	0.163121	+	0.986606i	$0.447844\pi$
$140$	0	0
$141$	−25.6856	−2.16311
$142$	16.3354	1.37083
$143$	−3.50869	−0.293411
$144$	−2.16083	−0.180069
$145$	0	0
$146$	13.7764	1.14014
$147$	1.97939	0.163257
$148$	5.13307	0.421936
$149$	−10.3233	−0.845719	−0.422860	−	0.906195i	$-0.638974\pi$
$149$	−10.3233	−0.845719	−0.422860	+	0.906195i	$0.638974\pi$
$150$	0	0
$151$	−14.4360	−1.17478	−0.587391	−	0.809304i	$-0.699845\pi$
$151$	−14.4360	−1.17478	−0.587391	+	0.809304i	$0.699845\pi$
$152$	−3.42380	−0.277707
$153$	0.416539	0.0336752
$154$	1.65032	0.132987
$155$	0	0
$156$	−3.09054	−0.247441
$157$	3.69978	0.295274	0.147637	−	0.989042i	$-0.452833\pi$
$157$	3.69978	0.295274	0.147637	+	0.989042i	$0.452833\pi$
$158$	−18.4143	−1.46496
$159$	−8.98062	−0.712210
$160$	0	0
$161$	1.00000	0.0788110
$162$	−12.7868	−1.00462
$163$	−16.7103	−1.30885	−0.654425	−	0.756127i	$-0.727089\pi$
$163$	−16.7103	−1.30885	−0.654425	+	0.756127i	$0.727089\pi$
$164$	0.172159	0.0134433
$165$	0	0
$166$	−5.28144	−0.409919
$167$	−14.8551	−1.14952	−0.574759	−	0.818323i	$-0.694904\pi$
$167$	−14.8551	−1.14952	−0.574759	+	0.818323i	$0.694904\pi$
$168$	6.09289	0.470077
$169$	−6.79237	−0.522490
$170$	0	0
$171$	1.02104	0.0780807
$172$	−0.244839	−0.0186688
$173$	−5.46314	−0.415355	−0.207677	−	0.978197i	$-0.566590\pi$
$173$	−5.46314	−0.415355	−0.207677	+	0.978197i	$0.566590\pi$
$174$	−21.6957	−1.64474
$175$	0	0
$176$	3.31494	0.249873
$177$	17.7675	1.33549
$178$	14.7420	1.10496
$179$	21.7442	1.62524	0.812618	−	0.582797i	$-0.198042\pi$
$179$	21.7442	1.62524	0.812618	+	0.582797i	$0.198042\pi$
$180$	0	0
$181$	−2.36633	−0.175888	−0.0879439	−	0.996125i	$-0.528030\pi$
$181$	−2.36633	−0.175888	−0.0879439	+	0.996125i	$0.528030\pi$
$182$	−2.91978	−0.216428
$183$	27.6131	2.04122
$184$	3.07817	0.226926
$185$	0	0
$186$	−12.8852	−0.944785
$187$	−0.639014	−0.0467294
$188$	8.13205	0.593091
$189$	4.12115	0.299769
$190$	0	0
$191$	15.5117	1.12239	0.561193	−	0.827685i	$-0.310342\pi$
$191$	15.5117	1.12239	0.561193	+	0.827685i	$0.310342\pi$
$192$	17.2003	1.24132
$193$	−4.72158	−0.339867	−0.169933	−	0.985456i	$-0.554355\pi$
$193$	−4.72158	−0.339867	−0.169933	+	0.985456i	$0.554355\pi$
$194$	−8.44140	−0.606058
$195$	0	0
$196$	−0.626674	−0.0447624
$197$	−4.85459	−0.345875	−0.172938	−	0.984933i	$-0.555326\pi$
$197$	−4.85459	−0.345875	−0.172938	+	0.984933i	$0.555326\pi$
$198$	−1.51494	−0.107662
$199$	13.4722	0.955018	0.477509	−	0.878627i	$-0.341540\pi$
$199$	13.4722	0.955018	0.477509	+	0.878627i	$0.341540\pi$
$200$	0	0
$201$	−27.8526	−1.96457
$202$	−13.2401	−0.931569
$203$	9.35311	0.656459
$204$	−0.562860	−0.0394081
$205$	0	0
$206$	2.43904	0.169936
$207$	−0.917966	−0.0638030
$208$	−5.86485	−0.406654
$209$	−1.56638	−0.108349
$210$	0	0
$211$	−11.8024	−0.812512	−0.406256	−	0.913759i	$-0.633166\pi$
$211$	−11.8024	−0.812512	−0.406256	+	0.913759i	$0.633166\pi$
$212$	2.84327	0.195276
$213$	27.5913	1.89053
$214$	−2.70218	−0.184717
$215$	0	0
$216$	12.6856	0.863146
$217$	5.55485	0.377088
$218$	−5.83962	−0.395509
$219$	23.2691	1.57238
$220$	0	0
$221$	1.13056	0.0760494
$222$	−19.0000	−1.27519
$223$	12.0660	0.808001	0.404001	−	0.914759i	$-0.367619\pi$
$223$	12.0660	0.808001	0.404001	+	0.914759i	$0.367619\pi$
$224$	−3.39779	−0.227025
$225$	0	0
$226$	−9.22843	−0.613866
$227$	−12.5858	−0.835352	−0.417676	−	0.908596i	$-0.637155\pi$
$227$	−12.5858	−0.835352	−0.417676	+	0.908596i	$0.637155\pi$
$228$	−1.37971	−0.0913734
$229$	15.2362	1.00684	0.503420	−	0.864042i	$-0.332075\pi$
$229$	15.2362	1.00684	0.503420	+	0.864042i	$0.332075\pi$
$230$	0	0
$231$	2.78748	0.183403
$232$	28.7905	1.89019
$233$	20.3623	1.33398	0.666989	−	0.745068i	$-0.267583\pi$
$233$	20.3623	1.33398	0.666989	+	0.745068i	$0.267583\pi$
$234$	2.68026	0.175214
$235$	0	0
$236$	−5.62520	−0.366169
$237$	−31.1027	−2.02034
$238$	−0.531760	−0.0344689
$239$	−16.2731	−1.05262	−0.526309	−	0.850293i	$-0.676425\pi$
$239$	−16.2731	−1.05262	−0.526309	+	0.850293i	$0.676425\pi$
$240$	0	0
$241$	26.3769	1.69909	0.849544	−	0.527517i	$-0.176877\pi$
$241$	26.3769	1.69909	0.849544	+	0.527517i	$0.176877\pi$
$242$	−10.5667	−0.679254
$243$	−9.23410	−0.592368
$244$	−8.74232	−0.559669
$245$	0	0
$246$	−0.637242	−0.0406291
$247$	2.77127	0.176331
$248$	17.0988	1.08577
$249$	−8.92063	−0.565322
$250$	0	0
$251$	21.0479	1.32853	0.664267	−	0.747495i	$-0.268744\pi$
$251$	21.0479	1.32853	0.664267	+	0.747495i	$0.268744\pi$
$252$	0.575265	0.0362383
$253$	1.40826	0.0885363
$254$	−4.32099	−0.271123
$255$	0	0
$256$	−13.4093	−0.838081
$257$	3.22353	0.201078	0.100539	−	0.994933i	$-0.467943\pi$
$257$	3.22353	0.201078	0.100539	+	0.994933i	$0.467943\pi$
$258$	0.906267	0.0564217
$259$	8.19098	0.508963
$260$	0	0
$261$	−8.58583	−0.531450
$262$	18.5718	1.14737
$263$	13.3963	0.826052	0.413026	−	0.910719i	$-0.364472\pi$
$263$	13.3963	0.826052	0.413026	+	0.910719i	$0.364472\pi$
$264$	8.58035	0.528084
$265$	0	0
$266$	−1.30347	−0.0799211
$267$	24.9000	1.52386
$268$	8.81814	0.538654
$269$	19.8488	1.21021	0.605103	−	0.796148i	$-0.293132\pi$
$269$	19.8488	1.21021	0.605103	+	0.796148i	$0.293132\pi$
$270$	0	0
$271$	−11.8751	−0.721363	−0.360682	−	0.932689i	$-0.617456\pi$
$271$	−11.8751	−0.721363	−0.360682	+	0.932689i	$0.617456\pi$
$272$	−1.06813	−0.0647647
$273$	−4.93166	−0.298478
$274$	0.650911	0.0393229
$275$	0	0
$276$	1.24043	0.0746650
$277$	6.98939	0.419952	0.209976	−	0.977707i	$-0.432661\pi$
$277$	6.98939	0.419952	0.209976	+	0.977707i	$0.432661\pi$
$278$	4.50747	0.270340
$279$	−5.09916	−0.305279
$280$	0	0
$281$	16.1219	0.961754	0.480877	−	0.876788i	$-0.340318\pi$
$281$	16.1219	0.961754	0.480877	+	0.876788i	$0.340318\pi$
$282$	−30.1006	−1.79247
$283$	−7.44313	−0.442448	−0.221224	−	0.975223i	$-0.571005\pi$
$283$	−7.44313	−0.442448	−0.221224	+	0.975223i	$0.571005\pi$
$284$	−8.73542	−0.518352
$285$	0	0
$286$	−4.11180	−0.243136
$287$	0.274718	0.0162161
$288$	3.11906	0.183792
$289$	−16.7941	−0.987888
$290$	0	0
$291$	−14.2580	−0.835818
$292$	−7.36700	−0.431121
$293$	3.76080	0.219708	0.109854	−	0.993948i	$-0.464962\pi$
$293$	3.76080	0.219708	0.109854	+	0.993948i	$0.464962\pi$
$294$	2.31962	0.135283
$295$	0	0
$296$	25.2132	1.46549
$297$	5.80363	0.336761
$298$	−12.0978	−0.700807
$299$	−2.49151	−0.144088
$300$	0	0
$301$	−0.390696	−0.0225193
$302$	−16.9174	−0.973484
$303$	−22.3632	−1.28473
$304$	−2.61824	−0.150166
$305$	0	0
$306$	0.488138	0.0279050
$307$	4.25817	0.243027	0.121513	−	0.992590i	$-0.461225\pi$
$307$	4.25817	0.243027	0.121513	+	0.992590i	$0.461225\pi$
$308$	−0.882517	−0.0502861
$309$	4.11967	0.234360
$310$	0	0
$311$	3.73760	0.211940	0.105970	−	0.994369i	$-0.466205\pi$
$311$	3.73760	0.211940	0.105970	+	0.994369i	$0.466205\pi$
$312$	−15.1805	−0.859427
$313$	9.90859	0.560067	0.280033	−	0.959990i	$-0.409655\pi$
$313$	9.90859	0.560067	0.280033	+	0.959990i	$0.409655\pi$
$314$	4.33573	0.244679
$315$	0	0
$316$	9.84713	0.553944
$317$	0.215525	0.0121051	0.00605256	−	0.999982i	$-0.498073\pi$
$317$	0.215525	0.0121051	0.00605256	+	0.999982i	$0.498073\pi$
$318$	−10.5243	−0.590174
$319$	13.1716	0.737467
$320$	0	0
$321$	−4.56413	−0.254745
$322$	1.17189	0.0653069
$323$	0.504713	0.0280830
$324$	6.83778	0.379877
$325$	0	0
$326$	−19.5826	−1.08458
$327$	−9.86344	−0.545449
$328$	0.845630	0.0466921
$329$	12.9765	0.715419
$330$	0	0
$331$	−31.2198	−1.71599	−0.857997	−	0.513654i	$-0.828291\pi$
$331$	−31.2198	−1.71599	−0.857997	+	0.513654i	$0.828291\pi$
$332$	2.82427	0.155002
$333$	−7.51904	−0.412041
$334$	−17.4085	−0.952550
$335$	0	0
$336$	4.65934	0.254188
$337$	19.7203	1.07423	0.537116	−	0.843508i	$-0.319514\pi$
$337$	19.7203	1.07423	0.537116	+	0.843508i	$0.319514\pi$
$338$	−7.95991	−0.432962
$339$	−15.5873	−0.846587
$340$	0	0
$341$	7.82266	0.423621
$342$	1.19654	0.0647017
$343$	−1.00000	−0.0539949
$344$	−1.20263	−0.0648415
$345$	0	0
$346$	−6.40220	−0.344184
$347$	7.42006	0.398329	0.199165	−	0.979966i	$-0.436177\pi$
$347$	7.42006	0.398329	0.199165	+	0.979966i	$0.436177\pi$
$348$	11.6019	0.621925
$349$	7.86853	0.421193	0.210596	−	0.977573i	$-0.432459\pi$
$349$	7.86853	0.421193	0.210596	+	0.977573i	$0.432459\pi$
$350$	0	0
$351$	−10.2679	−0.548059
$352$	−4.78497	−0.255040
$353$	8.64422	0.460085	0.230043	−	0.973181i	$-0.426113\pi$
$353$	8.64422	0.460085	0.230043	+	0.973181i	$0.426113\pi$
$354$	20.8216	1.10665
$355$	0	0
$356$	−7.88336	−0.417817
$357$	−0.898171	−0.0475363
$358$	25.4818	1.34675
$359$	23.4047	1.23525	0.617627	−	0.786471i	$-0.288094\pi$
$359$	23.4047	1.23525	0.617627	+	0.786471i	$0.288094\pi$
$360$	0	0
$361$	−17.7628	−0.934886
$362$	−2.77308	−0.145750
$363$	−17.8477	−0.936764
$364$	1.56136	0.0818378
$365$	0	0
$366$	32.3595	1.69146
$367$	−17.6936	−0.923596	−0.461798	−	0.886985i	$-0.652795\pi$
$367$	−17.6936	−0.923596	−0.461798	+	0.886985i	$0.652795\pi$
$368$	2.35393	0.122707
$369$	−0.252182	−0.0131281
$370$	0	0
$371$	4.53708	0.235553
$372$	6.89040	0.357250
$373$	5.81809	0.301249	0.150625	−	0.988591i	$-0.451872\pi$
$373$	5.81809	0.301249	0.150625	+	0.988591i	$0.451872\pi$
$374$	−0.748855	−0.0387224
$375$	0	0
$376$	39.9440	2.05995
$377$	−23.3034	−1.20018
$378$	4.82953	0.248404
$379$	4.47429	0.229829	0.114914	−	0.993375i	$-0.463341\pi$
$379$	4.47429	0.229829	0.114914	+	0.993375i	$0.463341\pi$
$380$	0	0
$381$	−7.29838	−0.373907
$382$	18.1780	0.930067
$383$	−24.8964	−1.27215	−0.636073	−	0.771629i	$-0.719442\pi$
$383$	−24.8964	−1.27215	−0.636073	+	0.771629i	$0.719442\pi$
$384$	6.70575	0.342201
$385$	0	0
$386$	−5.53317	−0.281631
$387$	0.358646	0.0182310
$388$	4.51408	0.229168
$389$	−18.1606	−0.920777	−0.460388	−	0.887718i	$-0.652290\pi$
$389$	−18.1606	−0.920777	−0.460388	+	0.887718i	$0.652290\pi$
$390$	0	0
$391$	−0.453763	−0.0229478
$392$	−3.07817	−0.155471
$393$	31.3688	1.58235
$394$	−5.68905	−0.286610
$395$	0	0
$396$	0.810121	0.0407101
$397$	9.09015	0.456222	0.228111	−	0.973635i	$-0.426745\pi$
$397$	9.09015	0.456222	0.228111	+	0.973635i	$0.426745\pi$
$398$	15.7879	0.791377
$399$	−2.20164	−0.110220
$400$	0	0
$401$	6.91076	0.345107	0.172554	−	0.985000i	$-0.444798\pi$
$401$	6.91076	0.345107	0.172554	+	0.985000i	$0.444798\pi$
$402$	−32.6402	−1.62794
$403$	−13.8400	−0.689418
$404$	7.08020	0.352253
$405$	0	0
$406$	10.9608	0.543976
$407$	11.5350	0.571769
$408$	−2.76473	−0.136874
$409$	−19.1526	−0.947036	−0.473518	−	0.880784i	$-0.657016\pi$
$409$	−19.1526	−0.947036	−0.473518	+	0.880784i	$0.657016\pi$
$410$	0	0
$411$	1.09942	0.0542305
$412$	−1.30429	−0.0642577
$413$	−8.97628	−0.441694
$414$	−1.07576	−0.0528705
$415$	0	0
$416$	8.46565	0.415062
$417$	7.61336	0.372828
$418$	−1.83563	−0.0897834
$419$	−12.9878	−0.634493	−0.317247	−	0.948343i	$-0.602758\pi$
$419$	−12.9878	−0.634493	−0.317247	+	0.948343i	$0.602758\pi$
$420$	0	0
$421$	33.5966	1.63740	0.818698	−	0.574224i	$-0.194696\pi$
$421$	33.5966	1.63740	0.818698	+	0.574224i	$0.194696\pi$
$422$	−13.8311	−0.673289
$423$	−11.9120	−0.579182
$424$	13.9659	0.678244
$425$	0	0
$426$	32.3340	1.56659
$427$	−13.9503	−0.675105
$428$	1.44500	0.0698469
$429$	−6.94505	−0.335310
$430$	0	0
$431$	13.7434	0.661996	0.330998	−	0.943632i	$-0.392615\pi$
$431$	13.7434	0.661996	0.330998	+	0.943632i	$0.392615\pi$
$432$	9.70091	0.466735
$433$	−3.10332	−0.149136	−0.0745681	−	0.997216i	$-0.523758\pi$
$433$	−3.10332	−0.149136	−0.0745681	+	0.997216i	$0.523758\pi$
$434$	6.50967	0.312474
$435$	0	0
$436$	3.12276	0.149553
$437$	−1.11228	−0.0532077
$438$	27.2688	1.30295
$439$	−18.9248	−0.903230	−0.451615	−	0.892213i	$-0.649152\pi$
$439$	−18.9248	−0.903230	−0.451615	+	0.892213i	$0.649152\pi$
$440$	0	0
$441$	0.917966	0.0437127
$442$	1.32489	0.0630184
$443$	29.4493	1.39918	0.699589	−	0.714545i	$-0.253366\pi$
$443$	29.4493	1.39918	0.699589	+	0.714545i	$0.253366\pi$
$444$	10.1603	0.482188
$445$	0	0
$446$	14.1401	0.669551
$447$	−20.4338	−0.966487
$448$	−8.68971	−0.410550
$449$	−16.9050	−0.797797	−0.398898	−	0.916995i	$-0.630607\pi$
$449$	−16.9050	−0.797797	−0.398898	+	0.916995i	$0.630607\pi$
$450$	0	0
$451$	0.386873	0.0182172
$452$	4.93494	0.232120
$453$	−28.5743	−1.34254
$454$	−14.7492	−0.692216
$455$	0	0
$456$	−6.77702	−0.317363
$457$	10.3402	0.483696	0.241848	−	0.970314i	$-0.422246\pi$
$457$	10.3402	0.483696	0.241848	+	0.970314i	$0.422246\pi$
$458$	17.8552	0.834319
$459$	−1.87002	−0.0872852
$460$	0	0
$461$	28.4907	1.32694	0.663471	−	0.748202i	$-0.269083\pi$
$461$	28.4907	1.32694	0.663471	+	0.748202i	$0.269083\pi$
$462$	3.26662	0.151977
$463$	−18.8108	−0.874213	−0.437107	−	0.899410i	$-0.643997\pi$
$463$	−18.8108	−0.874213	−0.437107	+	0.899410i	$0.643997\pi$
$464$	22.0166	1.02209
$465$	0	0
$466$	23.8624	1.10540
$467$	31.6039	1.46245	0.731227	−	0.682134i	$-0.238948\pi$
$467$	31.6039	1.46245	0.731227	+	0.682134i	$0.238948\pi$
$468$	−1.43328	−0.0662534
$469$	14.0713	0.649754
$470$	0	0
$471$	7.32328	0.337439
$472$	−27.6305	−1.27180
$473$	−0.550200	−0.0252982
$474$	−36.4490	−1.67416
$475$	0	0
$476$	0.284361	0.0130337
$477$	−4.16488	−0.190697
$478$	−19.0703	−0.872254
$479$	−3.33165	−0.152227	−0.0761136	−	0.997099i	$-0.524251\pi$
$479$	−3.33165	−0.152227	−0.0761136	+	0.997099i	$0.524251\pi$
$480$	0	0
$481$	−20.4079	−0.930521
$482$	30.9109	1.40795
$483$	1.97939	0.0900651
$484$	5.65060	0.256845
$485$	0	0
$486$	−10.8213	−0.490866
$487$	13.8840	0.629145	0.314572	−	0.949233i	$-0.398139\pi$
$487$	13.8840	0.629145	0.314572	+	0.949233i	$0.398139\pi$
$488$	−42.9416	−1.94387
$489$	−33.0761	−1.49575
$490$	0	0
$491$	−19.4306	−0.876891	−0.438446	−	0.898758i	$-0.644471\pi$
$491$	−19.4306	−0.876891	−0.438446	+	0.898758i	$0.644471\pi$
$492$	0.340768	0.0153630
$493$	−4.24409	−0.191144
$494$	3.24762	0.146117
$495$	0	0
$496$	13.0757	0.587118
$497$	−13.9393	−0.625265
$498$	−10.4540	−0.468455
$499$	33.6619	1.50691	0.753457	−	0.657497i	$-0.228385\pi$
$499$	33.6619	1.50691	0.753457	+	0.657497i	$0.228385\pi$
$500$	0	0
$501$	−29.4039	−1.31367
$502$	24.6659	1.10089
$503$	−34.8845	−1.55543	−0.777713	−	0.628620i	$-0.783620\pi$
$503$	−34.8845	−1.55543	−0.777713	+	0.628620i	$0.783620\pi$
$504$	2.82566	0.125865
$505$	0	0
$506$	1.65032	0.0733658
$507$	−13.4447	−0.597101
$508$	2.31067	0.102519
$509$	−5.86875	−0.260128	−0.130064	−	0.991506i	$-0.541518\pi$
$509$	−5.86875	−0.260128	−0.130064	+	0.991506i	$0.541518\pi$
$510$	0	0
$511$	−11.7557	−0.520042
$512$	−22.4898	−0.993918
$513$	−4.58388	−0.202383
$514$	3.77763	0.166624
$515$	0	0
$516$	−0.484631	−0.0213347
$517$	18.2743	0.803702
$518$	9.59893	0.421753
$519$	−10.8137	−0.474667
$520$	0	0
$521$	34.1165	1.49467	0.747336	−	0.664446i	$-0.231332\pi$
$521$	34.1165	1.49467	0.747336	+	0.664446i	$0.231332\pi$
$522$	−10.0617	−0.440387
$523$	15.8573	0.693389	0.346695	−	0.937978i	$-0.387304\pi$
$523$	15.8573	0.693389	0.346695	+	0.937978i	$0.387304\pi$
$524$	−9.93136	−0.433853
$525$	0	0
$526$	15.6990	0.684509
$527$	−2.52058	−0.109798
$528$	6.56155	0.285555
$529$	1.00000	0.0434783
$530$	0	0
$531$	8.23992	0.357582
$532$	0.697039	0.0302205
$533$	−0.684463	−0.0296474
$534$	29.1801	1.26275
$535$	0	0
$536$	43.3140	1.87088
$537$	43.0401	1.85732
$538$	23.2607	1.00284
$539$	−1.40826	−0.0606579
$540$	0	0
$541$	9.80713	0.421641	0.210821	−	0.977525i	$-0.432386\pi$
$541$	9.80713	0.421641	0.210821	+	0.977525i	$0.432386\pi$
$542$	−13.9164	−0.597759
$543$	−4.68388	−0.201004
$544$	1.54179	0.0661038
$545$	0	0
$546$	−5.77937	−0.247334
$547$	−28.4160	−1.21498	−0.607490	−	0.794327i	$-0.707824\pi$
$547$	−28.4160	−1.21498	−0.607490	+	0.794327i	$0.707824\pi$
$548$	−0.348077	−0.0148691
$549$	12.8059	0.546544
$550$	0	0
$551$	−10.4033	−0.443196
$552$	6.09289	0.259331
$553$	15.7133	0.668199
$554$	8.19079	0.347993
$555$	0	0
$556$	−2.41039	−0.102223
$557$	−1.59722	−0.0676765	−0.0338383	−	0.999427i	$-0.510773\pi$
$557$	−1.59722	−0.0676765	−0.0338383	+	0.999427i	$0.510773\pi$
$558$	−5.97566	−0.252970
$559$	0.973424	0.0411714
$560$	0	0
$561$	−1.26486	−0.0534023
$562$	18.8931	0.796959
$563$	23.0829	0.972830	0.486415	−	0.873728i	$-0.338304\pi$
$563$	23.0829	0.972830	0.486415	+	0.873728i	$0.338304\pi$
$564$	16.0965	0.677783
$565$	0	0
$566$	−8.72253	−0.366635
$567$	10.9112	0.458229
$568$	−42.9077	−1.80037
$569$	−15.3550	−0.643716	−0.321858	−	0.946788i	$-0.604307\pi$
$569$	−15.3550	−0.643716	−0.321858	+	0.946788i	$0.604307\pi$
$570$	0	0
$571$	−32.6909	−1.36807	−0.684036	−	0.729448i	$-0.739777\pi$
$571$	−32.6909	−1.36807	−0.684036	+	0.729448i	$0.739777\pi$
$572$	2.19880	0.0919365
$573$	30.7036	1.28266
$574$	0.321939	0.0134375
$575$	0	0
$576$	7.97686	0.332369
$577$	44.2351	1.84153	0.920766	−	0.390116i	$-0.127565\pi$
$577$	44.2351	1.84153	0.920766	+	0.390116i	$0.127565\pi$
$578$	−19.6808	−0.818615
$579$	−9.34582	−0.388399
$580$	0	0
$581$	4.50677	0.186972
$582$	−16.7088	−0.692602
$583$	6.38937	0.264621
$584$	−36.1861	−1.49739
$585$	0	0
$586$	4.40725	0.182062
$587$	−33.5564	−1.38502	−0.692511	−	0.721408i	$-0.743496\pi$
$587$	−33.5564	−1.38502	−0.692511	+	0.721408i	$0.743496\pi$
$588$	−1.24043	−0.0511544
$589$	−6.17857	−0.254583
$590$	0	0
$591$	−9.60911	−0.395266
$592$	19.2810	0.792445
$593$	−44.9090	−1.84419	−0.922096	−	0.386961i	$-0.873525\pi$
$593$	−44.9090	−1.84419	−0.922096	+	0.386961i	$0.873525\pi$
$594$	6.80122	0.279057
$595$	0	0
$596$	6.46935	0.264995
$597$	26.6667	1.09139
$598$	−2.91978	−0.119399
$599$	−28.7264	−1.17373	−0.586864	−	0.809685i	$-0.699638\pi$
$599$	−28.7264	−1.17373	−0.586864	+	0.809685i	$0.699638\pi$
$600$	0	0
$601$	−27.3525	−1.11573	−0.557866	−	0.829931i	$-0.688380\pi$
$601$	−27.3525	−1.11573	−0.557866	+	0.829931i	$0.688380\pi$
$602$	−0.457853	−0.0186607
$603$	−12.9170	−0.526021
$604$	9.04663	0.368102
$605$	0	0
$606$	−26.2072	−1.06460
$607$	29.9978	1.21757	0.608787	−	0.793334i	$-0.291656\pi$
$607$	29.9978	1.21757	0.608787	+	0.793334i	$0.291656\pi$
$608$	3.77931	0.153271
$609$	18.5134	0.750201
$610$	0	0
$611$	−32.3312	−1.30798
$612$	−0.261034	−0.0105517
$613$	2.86648	0.115776	0.0578881	−	0.998323i	$-0.481563\pi$
$613$	2.86648	0.115776	0.0578881	+	0.998323i	$0.481563\pi$
$614$	4.99011	0.201384
$615$	0	0
$616$	−4.33486	−0.174656
$617$	14.5704	0.586583	0.293291	−	0.956023i	$-0.405249\pi$
$617$	14.5704	0.586583	0.293291	+	0.956023i	$0.405249\pi$
$618$	4.82780	0.194203
$619$	34.0005	1.36659	0.683297	−	0.730141i	$-0.260546\pi$
$619$	34.0005	1.36659	0.683297	+	0.730141i	$0.260546\pi$
$620$	0	0
$621$	4.12115	0.165376
$622$	4.38005	0.175624
$623$	−12.5797	−0.503994
$624$	−11.6088	−0.464724
$625$	0	0
$626$	11.6118	0.464100
$627$	−3.10047	−0.123821
$628$	−2.31855	−0.0925203
$629$	−3.71676	−0.148197
$630$	0	0
$631$	43.3841	1.72710	0.863548	−	0.504267i	$-0.168237\pi$
$631$	43.3841	1.72710	0.863548	+	0.504267i	$0.168237\pi$
$632$	48.3683	1.92399
$633$	−23.3615	−0.928537
$634$	0.252572	0.0100309
$635$	0	0
$636$	5.62792	0.223162
$637$	2.49151	0.0987173
$638$	15.4356	0.611103
$639$	12.7958	0.506196
$640$	0	0
$641$	−7.41206	−0.292759	−0.146379	−	0.989229i	$-0.546762\pi$
$641$	−7.41206	−0.292759	−0.146379	+	0.989229i	$0.546762\pi$
$642$	−5.34865	−0.211095
$643$	2.96886	0.117080	0.0585401	−	0.998285i	$-0.481355\pi$
$643$	2.96886	0.117080	0.0585401	+	0.998285i	$0.481355\pi$
$644$	−0.626674	−0.0246944
$645$	0	0
$646$	0.591468	0.0232710
$647$	40.4234	1.58921	0.794605	−	0.607127i	$-0.207678\pi$
$647$	40.4234	1.58921	0.794605	+	0.607127i	$0.207678\pi$
$648$	33.5867	1.31941
$649$	−12.6409	−0.496199
$650$	0	0
$651$	10.9952	0.430935
$652$	10.4719	0.410111
$653$	−19.1597	−0.749776	−0.374888	−	0.927070i	$-0.622319\pi$
$653$	−19.1597	−0.749776	−0.374888	+	0.927070i	$0.622319\pi$
$654$	−11.5589	−0.451987
$655$	0	0
$656$	0.646668	0.0252481
$657$	10.7913	0.421011
$658$	15.2071	0.592833
$659$	24.3535	0.948677	0.474339	−	0.880342i	$-0.342687\pi$
$659$	24.3535	0.948677	0.474339	+	0.880342i	$0.342687\pi$
$660$	0	0
$661$	0.384137	0.0149412	0.00747060	−	0.999972i	$-0.497622\pi$
$661$	0.384137	0.0149412	0.00747060	+	0.999972i	$0.497622\pi$
$662$	−36.5862	−1.42196
$663$	2.23780	0.0869091
$664$	13.8726	0.538362
$665$	0	0
$666$	−8.81149	−0.341438
$667$	9.35311	0.362154
$668$	9.30927	0.360186
$669$	23.8833	0.923383
$670$	0	0
$671$	−19.6457	−0.758413
$672$	−6.72554	−0.259444
$673$	−50.1688	−1.93386	−0.966932	−	0.255035i	$-0.917913\pi$
$673$	−50.1688	−1.93386	−0.966932	+	0.255035i	$0.917913\pi$
$674$	23.1100	0.890164
$675$	0	0
$676$	4.25660	0.163715
$677$	40.8428	1.56972	0.784859	−	0.619675i	$-0.212735\pi$
$677$	40.8428	1.56972	0.784859	+	0.619675i	$0.212735\pi$
$678$	−18.2666	−0.701525
$679$	7.20324	0.276435
$680$	0	0
$681$	−24.9122	−0.954639
$682$	9.16729	0.351034
$683$	−21.9801	−0.841045	−0.420522	−	0.907282i	$-0.638153\pi$
$683$	−21.9801	−0.841045	−0.420522	+	0.907282i	$0.638153\pi$
$684$	−0.639858	−0.0244656
$685$	0	0
$686$	−1.17189	−0.0447430
$687$	30.1584	1.15061
$688$	−0.919672	−0.0350622
$689$	−11.3042	−0.430655
$690$	0	0
$691$	−17.9183	−0.681643	−0.340821	−	0.940128i	$-0.610705\pi$
$691$	−17.9183	−0.681643	−0.340821	+	0.940128i	$0.610705\pi$
$692$	3.42361	0.130146
$693$	1.29273	0.0491068
$694$	8.69549	0.330076
$695$	0	0
$696$	56.9874	2.16010
$697$	−0.124657	−0.00472171
$698$	9.22105	0.349022
$699$	40.3048	1.52447
$700$	0	0
$701$	−25.9817	−0.981316	−0.490658	−	0.871352i	$-0.663244\pi$
$701$	−25.9817	−0.981316	−0.490658	+	0.871352i	$0.663244\pi$
$702$	−12.0328	−0.454150
$703$	−9.11069	−0.343616
$704$	−12.2373	−0.461212
$705$	0	0
$706$	10.1301	0.381250
$707$	11.2981	0.424907
$708$	−11.1344	−0.418458
$709$	−17.2748	−0.648768	−0.324384	−	0.945926i	$-0.605157\pi$
$709$	−17.2748	−0.648768	−0.324384	+	0.945926i	$0.605157\pi$
$710$	0	0
$711$	−14.4243	−0.540954
$712$	−38.7224	−1.45119
$713$	5.55485	0.208031
$714$	−1.05256	−0.0393910
$715$	0	0
$716$	−13.6265	−0.509246
$717$	−32.2107	−1.20293
$718$	27.4278	1.02359
$719$	−39.2849	−1.46508	−0.732539	−	0.680725i	$-0.761665\pi$
$719$	−39.2849	−1.46508	−0.732539	+	0.680725i	$0.761665\pi$
$720$	0	0
$721$	−2.08129	−0.0775112
$722$	−20.8161	−0.774694
$723$	52.2101	1.94172
$724$	1.48292	0.0551121
$725$	0	0
$726$	−20.9156	−0.776251
$727$	−20.1104	−0.745852	−0.372926	−	0.927861i	$-0.621646\pi$
$727$	−20.1104	−0.745852	−0.372926	+	0.927861i	$0.621646\pi$
$728$	7.66930	0.284243
$729$	14.4559	0.535403
$730$	0	0
$731$	0.177283	0.00655706
$732$	−17.3044	−0.639589
$733$	−47.9033	−1.76935	−0.884674	−	0.466211i	$-0.845619\pi$
$733$	−47.9033	−1.76935	−0.884674	+	0.466211i	$0.845619\pi$
$734$	−20.7349	−0.765339
$735$	0	0
$736$	−3.39779	−0.125244
$737$	19.8161	0.729934
$738$	−0.295529	−0.0108786
$739$	−40.1448	−1.47675	−0.738374	−	0.674391i	$-0.764406\pi$
$739$	−40.1448	−1.47675	−0.738374	+	0.674391i	$0.764406\pi$
$740$	0	0
$741$	5.48541	0.201511
$742$	5.31696	0.195192
$743$	14.7495	0.541108	0.270554	−	0.962705i	$-0.412793\pi$
$743$	14.7495	0.541108	0.270554	+	0.962705i	$0.412793\pi$
$744$	33.8451	1.24082
$745$	0	0
$746$	6.81816	0.249631
$747$	−4.13706	−0.151367
$748$	0.400453	0.0146420
$749$	2.30583	0.0842532
$750$	0	0
$751$	0.666612	0.0243250	0.0121625	−	0.999926i	$-0.496128\pi$
$751$	0.666612	0.0243250	0.0121625	+	0.999926i	$0.496128\pi$
$752$	30.5459	1.11389
$753$	41.6620	1.51825
$754$	−27.3090	−0.994535
$755$	0	0
$756$	−2.58261	−0.0939288
$757$	19.5444	0.710352	0.355176	−	0.934800i	$-0.384421\pi$
$757$	19.5444	0.710352	0.355176	+	0.934800i	$0.384421\pi$
$758$	5.24337	0.190448
$759$	2.78748	0.101179
$760$	0	0
$761$	−12.6982	−0.460310	−0.230155	−	0.973154i	$-0.573923\pi$
$761$	−12.6982	−0.460310	−0.230155	+	0.973154i	$0.573923\pi$
$762$	−8.55289	−0.309839
$763$	4.98308	0.180400
$764$	−9.72077	−0.351685
$765$	0	0
$766$	−29.1758	−1.05417
$767$	22.3645	0.807536
$768$	−26.5422	−0.957758
$769$	5.74236	0.207075	0.103537	−	0.994626i	$-0.466984\pi$
$769$	5.74236	0.207075	0.103537	+	0.994626i	$0.466984\pi$
$770$	0	0
$771$	6.38061	0.229792
$772$	2.95889	0.106493
$773$	−40.5172	−1.45730	−0.728651	−	0.684885i	$-0.759853\pi$
$773$	−40.5172	−1.45730	−0.728651	+	0.684885i	$0.759853\pi$
$774$	0.420293	0.0151071
$775$	0	0
$776$	22.1728	0.795958
$777$	16.2131	0.581642
$778$	−21.2822	−0.763003
$779$	−0.305564	−0.0109480
$780$	0	0
$781$	−19.6302	−0.702423
$782$	−0.531760	−0.0190157
$783$	38.5455	1.37750
$784$	−2.35393	−0.0840690
$785$	0	0
$786$	36.7608	1.31121
$787$	−42.9465	−1.53088	−0.765438	−	0.643509i	$-0.777478\pi$
$787$	−42.9465	−1.53088	−0.765438	+	0.643509i	$0.777478\pi$
$788$	3.04224	0.108375
$789$	26.5165	0.944011
$790$	0	0
$791$	7.87482	0.279997
$792$	3.97925	0.141397
$793$	34.7575	1.23427
$794$	10.6527	0.378049
$795$	0	0
$796$	−8.44267	−0.299242
$797$	−44.2308	−1.56674	−0.783368	−	0.621558i	$-0.786500\pi$
$797$	−44.2308	−1.56674	−0.783368	+	0.621558i	$0.786500\pi$
$798$	−2.58008	−0.0913337
$799$	−5.88827	−0.208312
$800$	0	0
$801$	11.5477	0.408019
$802$	8.09866	0.285973
$803$	−16.5551	−0.584216
$804$	17.4545	0.615572
$805$	0	0
$806$	−16.2189	−0.571288
$807$	39.2885	1.38302
$808$	34.7774	1.22346
$809$	−12.3640	−0.434694	−0.217347	−	0.976094i	$-0.569740\pi$
$809$	−12.3640	−0.434694	−0.217347	+	0.976094i	$0.569740\pi$
$810$	0	0
$811$	2.51945	0.0884699	0.0442350	−	0.999021i	$-0.485915\pi$
$811$	2.51945	0.0884699	0.0442350	+	0.999021i	$0.485915\pi$
$812$	−5.86134	−0.205693
$813$	−23.5055	−0.824373
$814$	13.5178	0.473797
$815$	0	0
$816$	−2.11424	−0.0740130
$817$	0.434565	0.0152035
$818$	−22.4448	−0.784763
$819$	−2.28712	−0.0799186
$820$	0	0
$821$	−29.6931	−1.03630	−0.518148	−	0.855291i	$-0.673378\pi$
$821$	−29.6931	−1.03630	−0.518148	+	0.855291i	$0.673378\pi$
$822$	1.28840	0.0449382
$823$	26.1447	0.911347	0.455674	−	0.890147i	$-0.349398\pi$
$823$	26.1447	0.911347	0.455674	+	0.890147i	$0.349398\pi$
$824$	−6.40656	−0.223183
$825$	0	0
$826$	−10.5192	−0.366010
$827$	38.6776	1.34495	0.672475	−	0.740120i	$-0.265231\pi$
$827$	38.6776	1.34495	0.672475	+	0.740120i	$0.265231\pi$
$828$	0.575265	0.0199918
$829$	−20.2961	−0.704911	−0.352456	−	0.935828i	$-0.614653\pi$
$829$	−20.2961	−0.704911	−0.352456	+	0.935828i	$0.614653\pi$
$830$	0	0
$831$	13.8347	0.479920
$832$	21.6505	0.750596
$833$	0.453763	0.0157219
$834$	8.92202	0.308944
$835$	0	0
$836$	0.981609	0.0339497
$837$	22.8924	0.791276
$838$	−15.2202	−0.525774
$839$	−7.72024	−0.266532	−0.133266	−	0.991080i	$-0.542546\pi$
$839$	−7.72024	−0.266532	−0.133266	+	0.991080i	$0.542546\pi$
$840$	0	0
$841$	58.4806	2.01657
$842$	39.3715	1.35683
$843$	31.9115	1.09909
$844$	7.39626	0.254590
$845$	0	0
$846$	−13.9596	−0.479940
$847$	9.01681	0.309821
$848$	10.6800	0.366752
$849$	−14.7328	−0.505629
$850$	0	0
$851$	8.19098	0.280783
$852$	−17.2908	−0.592372
$853$	−29.5591	−1.01208	−0.506042	−	0.862509i	$-0.668892\pi$
$853$	−29.5591	−1.01208	−0.506042	+	0.862509i	$0.668892\pi$
$854$	−16.3483	−0.559427
$855$	0	0
$856$	7.09774	0.242596
$857$	19.2666	0.658134	0.329067	−	0.944307i	$-0.393266\pi$
$857$	19.2666	0.658134	0.329067	+	0.944307i	$0.393266\pi$
$858$	−8.13883	−0.277855
$859$	−17.8510	−0.609068	−0.304534	−	0.952501i	$-0.598501\pi$
$859$	−17.8510	−0.609068	−0.304534	+	0.952501i	$0.598501\pi$
$860$	0	0
$861$	0.543773	0.0185317
$862$	16.1057	0.548564
$863$	−10.9780	−0.373694	−0.186847	−	0.982389i	$-0.559827\pi$
$863$	−10.9780	−0.373694	−0.186847	+	0.982389i	$0.559827\pi$
$864$	−14.0028	−0.476385
$865$	0	0
$866$	−3.63675	−0.123582
$867$	−33.2420	−1.12896
$868$	−3.48108	−0.118155
$869$	22.1284	0.750655
$870$	0	0
$871$	−35.0589	−1.18793
$872$	15.3388	0.519437
$873$	−6.61233	−0.223793
$874$	−1.30347	−0.0440907
$875$	0	0
$876$	−14.5821	−0.492684
$877$	−15.4543	−0.521856	−0.260928	−	0.965358i	$-0.584029\pi$
$877$	−15.4543	−0.521856	−0.260928	+	0.965358i	$0.584029\pi$
$878$	−22.1778	−0.748463
$879$	7.44407	0.251082
$880$	0	0
$881$	−5.64690	−0.190249	−0.0951244	−	0.995465i	$-0.530325\pi$
$881$	−5.64690	−0.190249	−0.0951244	+	0.995465i	$0.530325\pi$
$882$	1.07576	0.0362226
$883$	−24.1179	−0.811630	−0.405815	−	0.913955i	$-0.633012\pi$
$883$	−24.1179	−0.811630	−0.405815	+	0.913955i	$0.633012\pi$
$884$	−0.708489	−0.0238291
$885$	0	0
$886$	34.5114	1.15943
$887$	−16.4184	−0.551277	−0.275638	−	0.961261i	$-0.588889\pi$
$887$	−16.4184	−0.551277	−0.275638	+	0.961261i	$0.588889\pi$
$888$	49.9067	1.67476
$889$	3.68719	0.123664
$890$	0	0
$891$	15.3658	0.514774
$892$	−7.56146	−0.253177
$893$	−14.4336	−0.483001
$894$	−23.9462	−0.800881
$895$	0	0
$896$	−3.38779	−0.113178
$897$	−4.93166	−0.164663
$898$	−19.8108	−0.661095
$899$	51.9551	1.73280
$900$	0	0
$901$	−2.05876	−0.0685871
$902$	0.453373	0.0150957
$903$	−0.773338	−0.0257351
$904$	24.2401	0.806213
$905$	0	0
$906$	−33.4860	−1.11250
$907$	39.0857	1.29782	0.648910	−	0.760866i	$-0.275225\pi$
$907$	39.0857	1.29782	0.648910	+	0.760866i	$0.275225\pi$
$908$	7.88722	0.261746
$909$	−10.3712	−0.343992
$910$	0	0
$911$	−45.8776	−1.51999	−0.759996	−	0.649927i	$-0.774799\pi$
$911$	−45.8776	−1.51999	−0.759996	+	0.649927i	$0.774799\pi$
$912$	−5.18251	−0.171610
$913$	6.34669	0.210045
$914$	12.1176	0.400815
$915$	0	0
$916$	−9.54815	−0.315480
$917$	−15.8477	−0.523338
$918$	−2.19146	−0.0723290
$919$	10.4959	0.346228	0.173114	−	0.984902i	$-0.444617\pi$
$919$	10.4959	0.346228	0.173114	+	0.984902i	$0.444617\pi$
$920$	0	0
$921$	8.42856	0.277730
$922$	33.3879	1.09957
$923$	34.7300	1.14315
$924$	−1.74684	−0.0574669
$925$	0	0
$926$	−22.0442	−0.724418
$927$	1.91055	0.0627507
$928$	−31.7799	−1.04323
$929$	−1.35600	−0.0444890	−0.0222445	−	0.999753i	$-0.507081\pi$
$929$	−1.35600	−0.0444890	−0.0222445	+	0.999753i	$0.507081\pi$
$930$	0	0
$931$	1.11228	0.0364536
$932$	−12.7605	−0.417984
$933$	7.39815	0.242204
$934$	37.0363	1.21186
$935$	0	0
$936$	−7.04016	−0.230115
$937$	−36.5588	−1.19432	−0.597162	−	0.802120i	$-0.703705\pi$
$937$	−36.5588	−1.19432	−0.597162	+	0.802120i	$0.703705\pi$
$938$	16.4901	0.538420
$939$	19.6129	0.640043
$940$	0	0
$941$	20.5246	0.669084	0.334542	−	0.942381i	$-0.391418\pi$
$941$	20.5246	0.669084	0.334542	+	0.942381i	$0.391418\pi$
$942$	8.58208	0.279619
$943$	0.274718	0.00894605
$944$	−21.1296	−0.687709
$945$	0	0
$946$	−0.644774	−0.0209634
$947$	−45.4591	−1.47722	−0.738611	−	0.674132i	$-0.764518\pi$
$947$	−45.4591	−1.47722	−0.738611	+	0.674132i	$0.764518\pi$
$948$	19.4913	0.633047
$949$	29.2895	0.950778
$950$	0	0
$951$	0.426608	0.0138337
$952$	1.39676	0.0452693
$953$	−55.2694	−1.79035	−0.895175	−	0.445714i	$-0.852950\pi$
$953$	−55.2694	−1.79035	−0.895175	+	0.445714i	$0.852950\pi$
$954$	−4.88078	−0.158021
$955$	0	0
$956$	10.1979	0.329824
$957$	26.0716	0.842776
$958$	−3.90433	−0.126143
$959$	−0.555437	−0.0179360
$960$	0	0
$961$	−0.143631	−0.00463327
$962$	−23.9158	−0.771078
$963$	−2.11667	−0.0682089
$964$	−16.5297	−0.532387
$965$	0	0
$966$	2.31962	0.0746326
$967$	−37.5564	−1.20773	−0.603866	−	0.797086i	$-0.706374\pi$
$967$	−37.5564	−1.20773	−0.603866	+	0.797086i	$0.706374\pi$
$968$	27.7553	0.892089
$969$	0.999021	0.0320932
$970$	0	0
$971$	56.6993	1.81957	0.909784	−	0.415082i	$-0.136247\pi$
$971$	56.6993	1.81957	0.909784	+	0.415082i	$0.136247\pi$
$972$	5.78677	0.185611
$973$	−3.84633	−0.123308
$974$	16.2705	0.521342
$975$	0	0
$976$	−32.8382	−1.05112
$977$	−30.5600	−0.977700	−0.488850	−	0.872368i	$-0.662584\pi$
$977$	−30.5600	−0.977700	−0.488850	+	0.872368i	$0.662584\pi$
$978$	−38.7616	−1.23946
$979$	−17.7154	−0.566188
$980$	0	0
$981$	−4.57430	−0.146046
$982$	−22.7705	−0.726637
$983$	2.30405	0.0734878	0.0367439	−	0.999325i	$-0.488301\pi$
$983$	2.30405	0.0734878	0.0367439	+	0.999325i	$0.488301\pi$
$984$	1.67383	0.0533596
$985$	0	0
$986$	−4.97361	−0.158392
$987$	25.6856	0.817580
$988$	−1.73668	−0.0552511
$989$	−0.390696	−0.0124234
$990$	0	0
$991$	5.41768	0.172098	0.0860491	−	0.996291i	$-0.472576\pi$
$991$	5.41768	0.172098	0.0860491	+	0.996291i	$0.472576\pi$
$992$	−18.8742	−0.599258
$993$	−61.7960	−1.96104
$994$	−16.3354	−0.518127
$995$	0	0
$996$	5.59032	0.177136
$997$	19.4355	0.615527	0.307764	−	0.951463i	$-0.400419\pi$
$997$	19.4355	0.615527	0.307764	+	0.951463i	$0.400419\pi$
$998$	39.4481	1.24871
$999$	33.7562	1.06800

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.t.1.6		8
5.4	even	2		805.2.a.m.1.3	✓	8
15.14	odd	2		7245.2.a.bp.1.6		8
35.34	odd	2		5635.2.a.bb.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.m.1.3	✓	8	5.4	even	2
4025.2.a.t.1.6		8	1.1	even	1	trivial
5635.2.a.bb.1.3		8	35.34	odd	2
7245.2.a.bp.1.6		8	15.14	odd	2

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

\(f(q)\)	\(=\)	\(q+1.17189 q^{2} +1.97939 q^{3} -0.626674 q^{4} +2.31962 q^{6} -1.00000 q^{7} -3.07817 q^{8} +0.917966 q^{9} +O(q^{10})\)	\(q+1.17189 q^{2} +1.97939 q^{3} -0.626674 q^{4} +2.31962 q^{6} -1.00000 q^{7} -3.07817 q^{8} +0.917966 q^{9} -1.40826 q^{11} -1.24043 q^{12} +2.49151 q^{13} -1.17189 q^{14} -2.35393 q^{16} +0.453763 q^{17} +1.07576 q^{18} +1.11228 q^{19} -1.97939 q^{21} -1.65032 q^{22} -1.00000 q^{23} -6.09289 q^{24} +2.91978 q^{26} -4.12115 q^{27} +0.626674 q^{28} -9.35311 q^{29} -5.55485 q^{31} +3.39779 q^{32} -2.78748 q^{33} +0.531760 q^{34} -0.575265 q^{36} -8.19098 q^{37} +1.30347 q^{38} +4.93166 q^{39} -0.274718 q^{41} -2.31962 q^{42} +0.390696 q^{43} +0.882517 q^{44} -1.17189 q^{46} -12.9765 q^{47} -4.65934 q^{48} +1.00000 q^{49} +0.898171 q^{51} -1.56136 q^{52} -4.53708 q^{53} -4.82953 q^{54} +3.07817 q^{56} +2.20164 q^{57} -10.9608 q^{58} +8.97628 q^{59} +13.9503 q^{61} -6.50967 q^{62} -0.917966 q^{63} +8.68971 q^{64} -3.26662 q^{66} -14.0713 q^{67} -0.284361 q^{68} -1.97939 q^{69} +13.9393 q^{71} -2.82566 q^{72} +11.7557 q^{73} -9.59893 q^{74} -0.697039 q^{76} +1.40826 q^{77} +5.77937 q^{78} -15.7133 q^{79} -10.9112 q^{81} -0.321939 q^{82} -4.50677 q^{83} +1.24043 q^{84} +0.457853 q^{86} -18.5134 q^{87} +4.33486 q^{88} +12.5797 q^{89} -2.49151 q^{91} +0.626674 q^{92} -10.9952 q^{93} -15.2071 q^{94} +6.72554 q^{96} -7.20324 q^{97} +1.17189 q^{98} -1.29273 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 7 q^{3} + 7 q^{4} + q^{6} - 8 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) \) 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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