LMFDB - Embedded newform 6825.2.a.bd.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6825,2,Mod(1,6825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6825, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6825.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6825 = 3 \cdot 5^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6825.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:	$54.4978993795$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.470683$ of defining polynomial
Character	$\chi$	$=$	6825.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.529317 q^{2} +1.00000 q^{3} -1.71982 q^{4} +0.529317 q^{6} +1.00000 q^{7} -1.96896 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.529317 q^{2} +1.00000 q^{3} -1.71982 q^{4} +0.529317 q^{6} +1.00000 q^{7} -1.96896 q^{8} +1.00000 q^{9} -6.49828 q^{11} -1.71982 q^{12} +1.00000 q^{13} +0.529317 q^{14} +2.39744 q^{16} +2.94137 q^{17} +0.529317 q^{18} -4.83709 q^{19} +1.00000 q^{21} -3.43965 q^{22} +5.77846 q^{23} -1.96896 q^{24} +0.529317 q^{26} +1.00000 q^{27} -1.71982 q^{28} -2.83709 q^{29} +6.27674 q^{31} +5.20693 q^{32} -6.49828 q^{33} +1.55691 q^{34} -1.71982 q^{36} -9.55691 q^{37} -2.56035 q^{38} +1.00000 q^{39} -3.05863 q^{41} +0.529317 q^{42} -2.71982 q^{43} +11.1759 q^{44} +3.05863 q^{46} +8.71982 q^{47} +2.39744 q^{48} +1.00000 q^{49} +2.94137 q^{51} -1.71982 q^{52} -6.39400 q^{53} +0.529317 q^{54} -1.96896 q^{56} -4.83709 q^{57} -1.50172 q^{58} +1.55691 q^{59} +3.88273 q^{61} +3.32238 q^{62} +1.00000 q^{63} -2.03877 q^{64} -3.43965 q^{66} -5.67418 q^{67} -5.05863 q^{68} +5.77846 q^{69} +10.0552 q^{71} -1.96896 q^{72} +15.8337 q^{73} -5.05863 q^{74} +8.31894 q^{76} -6.49828 q^{77} +0.529317 q^{78} -1.28018 q^{79} +1.00000 q^{81} -1.61899 q^{82} +2.83709 q^{83} -1.71982 q^{84} -1.43965 q^{86} -2.83709 q^{87} +12.7949 q^{88} -7.66119 q^{89} +1.00000 q^{91} -9.93793 q^{92} +6.27674 q^{93} +4.61555 q^{94} +5.20693 q^{96} +17.7164 q^{97} +0.529317 q^{98} -6.49828 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} + 3 q^{3} + 4 q^{4} + 2 q^{6} + 3 q^{7} + 12 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 + 3 * q^3 + 4 * q^4 + 2 * q^6 + 3 * q^7 + 12 * q^8 + 3 * q^9	$ 3 q + 2 q^{2} + 3 q^{3} + 4 q^{4} + 2 q^{6} + 3 q^{7} + 12 q^{8} + 3 q^{9} - 2 q^{11} + 4 q^{12} + 3 q^{13} + 2 q^{14} + 18 q^{16} + 8 q^{17} + 2 q^{18} - 7 q^{19} + 3 q^{21} + 8 q^{22} + 9 q^{23} + 12 q^{24} + 2 q^{26} + 3 q^{27} + 4 q^{28} - q^{29} - 7 q^{31} + 36 q^{32} - 2 q^{33} - 12 q^{34} + 4 q^{36} - 12 q^{37} - 26 q^{38} + 3 q^{39} - 10 q^{41} + 2 q^{42} + q^{43} + 36 q^{44} + 10 q^{46} + 17 q^{47} + 18 q^{48} + 3 q^{49} + 8 q^{51} + 4 q^{52} + 5 q^{53} + 2 q^{54} + 12 q^{56} - 7 q^{57} - 22 q^{58} - 12 q^{59} + 10 q^{61} - 10 q^{62} + 3 q^{63} + 58 q^{64} + 8 q^{66} - 2 q^{67} - 16 q^{68} + 9 q^{69} - 4 q^{71} + 12 q^{72} + 5 q^{73} - 16 q^{74} - 30 q^{76} - 2 q^{77} + 2 q^{78} - 13 q^{79} + 3 q^{81} - 24 q^{82} + q^{83} + 4 q^{84} + 14 q^{86} - q^{87} + 60 q^{88} - 13 q^{89} + 3 q^{91} + 6 q^{92} - 7 q^{93} - 2 q^{94} + 36 q^{96} + 9 q^{97} + 2 q^{98} - 2 q^{99}+O(q^{100}) $ 3 * q + 2 * q^2 + 3 * q^3 + 4 * q^4 + 2 * q^6 + 3 * q^7 + 12 * q^8 + 3 * q^9 - 2 * q^11 + 4 * q^12 + 3 * q^13 + 2 * q^14 + 18 * q^16 + 8 * q^17 + 2 * q^18 - 7 * q^19 + 3 * q^21 + 8 * q^22 + 9 * q^23 + 12 * q^24 + 2 * q^26 + 3 * q^27 + 4 * q^28 - q^29 - 7 * q^31 + 36 * q^32 - 2 * q^33 - 12 * q^34 + 4 * q^36 - 12 * q^37 - 26 * q^38 + 3 * q^39 - 10 * q^41 + 2 * q^42 + q^43 + 36 * q^44 + 10 * q^46 + 17 * q^47 + 18 * q^48 + 3 * q^49 + 8 * q^51 + 4 * q^52 + 5 * q^53 + 2 * q^54 + 12 * q^56 - 7 * q^57 - 22 * q^58 - 12 * q^59 + 10 * q^61 - 10 * q^62 + 3 * q^63 + 58 * q^64 + 8 * q^66 - 2 * q^67 - 16 * q^68 + 9 * q^69 - 4 * q^71 + 12 * q^72 + 5 * q^73 - 16 * q^74 - 30 * q^76 - 2 * q^77 + 2 * q^78 - 13 * q^79 + 3 * q^81 - 24 * q^82 + q^83 + 4 * q^84 + 14 * q^86 - q^87 + 60 * q^88 - 13 * q^89 + 3 * q^91 + 6 * q^92 - 7 * q^93 - 2 * q^94 + 36 * q^96 + 9 * q^97 + 2 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.529317	0.374283	0.187142	−	0.982333i	$-0.440078\pi$
$2$	0.529317	0.374283	0.187142	+	0.982333i	$0.440078\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.71982	−0.859912
$5$	0	0
$5$	0	0
$6$	0.529317	0.216093
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.96896	−0.696134
$9$	1.00000	0.333333
$10$	0	0
$11$	−6.49828	−1.95931	−0.979653	−	0.200700i	$-0.935678\pi$
$11$	−6.49828	−1.95931	−0.979653	+	0.200700i	$0.935678\pi$
$12$	−1.71982	−0.496470
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.529317	0.141466
$15$	0	0
$16$	2.39744	0.599361
$17$	2.94137	0.713386	0.356693	−	0.934222i	$-0.383904\pi$
$17$	2.94137	0.713386	0.356693	+	0.934222i	$0.383904\pi$
$18$	0.529317	0.124761
$19$	−4.83709	−1.10970	−0.554852	−	0.831949i	$-0.687225\pi$
$19$	−4.83709	−1.10970	−0.554852	+	0.831949i	$0.687225\pi$
$20$	0	0
$21$	1.00000	0.218218
$22$	−3.43965	−0.733335
$23$	5.77846	1.20489	0.602446	−	0.798160i	$-0.294193\pi$
$23$	5.77846	1.20489	0.602446	+	0.798160i	$0.294193\pi$
$24$	−1.96896	−0.401913
$25$	0	0
$26$	0.529317	0.103808
$27$	1.00000	0.192450
$28$	−1.71982	−0.325016
$29$	−2.83709	−0.526834	−0.263417	−	0.964682i	$-0.584850\pi$
$29$	−2.83709	−0.526834	−0.263417	+	0.964682i	$0.584850\pi$
$30$	0	0
$31$	6.27674	1.12734	0.563668	−	0.826002i	$-0.309390\pi$
$31$	6.27674	1.12734	0.563668	+	0.826002i	$0.309390\pi$
$32$	5.20693	0.920465
$33$	−6.49828	−1.13121
$34$	1.55691	0.267009
$35$	0	0
$36$	−1.71982	−0.286637
$37$	−9.55691	−1.57115	−0.785574	−	0.618768i	$-0.787632\pi$
$37$	−9.55691	−1.57115	−0.785574	+	0.618768i	$0.787632\pi$
$38$	−2.56035	−0.415344
$39$	1.00000	0.160128
$40$	0	0
$41$	−3.05863	−0.477678	−0.238839	−	0.971059i	$-0.576767\pi$
$41$	−3.05863	−0.477678	−0.238839	+	0.971059i	$0.576767\pi$
$42$	0.529317	0.0816753
$43$	−2.71982	−0.414769	−0.207385	−	0.978259i	$-0.566495\pi$
$43$	−2.71982	−0.414769	−0.207385	+	0.978259i	$0.566495\pi$
$44$	11.1759	1.68483
$45$	0	0
$46$	3.05863	0.450971
$47$	8.71982	1.27192	0.635959	−	0.771723i	$-0.280605\pi$
$47$	8.71982	1.27192	0.635959	+	0.771723i	$0.280605\pi$
$48$	2.39744	0.346041
$49$	1.00000	0.142857
$50$	0	0
$51$	2.94137	0.411874
$52$	−1.71982	−0.238497
$53$	−6.39400	−0.878284	−0.439142	−	0.898418i	$-0.644718\pi$
$53$	−6.39400	−0.878284	−0.439142	+	0.898418i	$0.644718\pi$
$54$	0.529317	0.0720309
$55$	0	0
$56$	−1.96896	−0.263114
$57$	−4.83709	−0.640688
$58$	−1.50172	−0.197185
$59$	1.55691	0.202693	0.101346	−	0.994851i	$-0.467685\pi$
$59$	1.55691	0.202693	0.101346	+	0.994851i	$0.467685\pi$
$60$	0	0
$61$	3.88273	0.497133	0.248567	−	0.968615i	$-0.420041\pi$
$61$	3.88273	0.497133	0.248567	+	0.968615i	$0.420041\pi$
$62$	3.32238	0.421943
$63$	1.00000	0.125988
$64$	−2.03877	−0.254846
$65$	0	0
$66$	−3.43965	−0.423391
$67$	−5.67418	−0.693211	−0.346606	−	0.938011i	$-0.612666\pi$
$67$	−5.67418	−0.693211	−0.346606	+	0.938011i	$0.612666\pi$
$68$	−5.05863	−0.613449
$69$	5.77846	0.695644
$70$	0	0
$71$	10.0552	1.19333	0.596666	−	0.802490i	$-0.296492\pi$
$71$	10.0552	1.19333	0.596666	+	0.802490i	$0.296492\pi$
$72$	−1.96896	−0.232045
$73$	15.8337	1.85319	0.926594	−	0.376062i	$-0.122722\pi$
$73$	15.8337	1.85319	0.926594	+	0.376062i	$0.122722\pi$
$74$	−5.05863	−0.588054
$75$	0	0
$76$	8.31894	0.954248
$77$	−6.49828	−0.740548
$78$	0.529317	0.0599333
$79$	−1.28018	−0.144031	−0.0720155	−	0.997404i	$-0.522943\pi$
$79$	−1.28018	−0.144031	−0.0720155	+	0.997404i	$0.522943\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−1.61899	−0.178787
$83$	2.83709	0.311411	0.155706	−	0.987804i	$-0.450235\pi$
$83$	2.83709	0.311411	0.155706	+	0.987804i	$0.450235\pi$
$84$	−1.71982	−0.187648
$85$	0	0
$86$	−1.43965	−0.155241
$87$	−2.83709	−0.304168
$88$	12.7949	1.36394
$89$	−7.66119	−0.812085	−0.406042	−	0.913854i	$-0.633091\pi$
$89$	−7.66119	−0.812085	−0.406042	+	0.913854i	$0.633091\pi$
$90$	0	0
$91$	1.00000	0.104828
$92$	−9.93793	−1.03610
$93$	6.27674	0.650867
$94$	4.61555	0.476057
$95$	0	0
$96$	5.20693	0.531431
$97$	17.7164	1.79883	0.899413	−	0.437099i	$-0.143994\pi$
$97$	17.7164	1.79883	0.899413	+	0.437099i	$0.143994\pi$
$98$	0.529317	0.0534690
$99$	−6.49828	−0.653102
$100$	0	0
$101$	6.73281	0.669940	0.334970	−	0.942229i	$-0.391274\pi$
$101$	6.73281	0.669940	0.334970	+	0.942229i	$0.391274\pi$
$102$	1.55691	0.154157
$103$	−10.8793	−1.07197	−0.535984	−	0.844228i	$-0.680059\pi$
$103$	−10.8793	−1.07197	−0.535984	+	0.844228i	$0.680059\pi$
$104$	−1.96896	−0.193073
$105$	0	0
$106$	−3.38445	−0.328727
$107$	8.49828	0.821560	0.410780	−	0.911735i	$-0.365256\pi$
$107$	8.49828	0.821560	0.410780	+	0.911735i	$0.365256\pi$
$108$	−1.71982	−0.165490
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	0	0
$111$	−9.55691	−0.907102
$112$	2.39744	0.226537
$113$	−14.6026	−1.37369	−0.686847	−	0.726802i	$-0.741006\pi$
$113$	−14.6026	−1.37369	−0.686847	+	0.726802i	$0.741006\pi$
$114$	−2.56035	−0.239799
$115$	0	0
$116$	4.87930	0.453031
$117$	1.00000	0.0924500
$118$	0.824101	0.0758646
$119$	2.94137	0.269635
$120$	0	0
$121$	31.2277	2.83888
$122$	2.05520	0.186069
$123$	−3.05863	−0.275788
$124$	−10.7949	−0.969409
$125$	0	0
$126$	0.529317	0.0471553
$127$	9.88273	0.876951	0.438475	−	0.898743i	$-0.355519\pi$
$127$	9.88273	0.876951	0.438475	+	0.898743i	$0.355519\pi$
$128$	−11.4930	−1.01585
$129$	−2.71982	−0.239467
$130$	0	0
$131$	3.76547	0.328990	0.164495	−	0.986378i	$-0.447400\pi$
$131$	3.76547	0.328990	0.164495	+	0.986378i	$0.447400\pi$
$132$	11.1759	0.972737
$133$	−4.83709	−0.419429
$134$	−3.00344	−0.259458
$135$	0	0
$136$	−5.79145	−0.496612
$137$	16.9966	1.45211	0.726057	−	0.687634i	$-0.241351\pi$
$137$	16.9966	1.45211	0.726057	+	0.687634i	$0.241351\pi$
$138$	3.05863	0.260368
$139$	−8.55348	−0.725496	−0.362748	−	0.931887i	$-0.618161\pi$
$139$	−8.55348	−0.725496	−0.362748	+	0.931887i	$0.618161\pi$
$140$	0	0
$141$	8.71982	0.734342
$142$	5.32238	0.446644
$143$	−6.49828	−0.543414
$144$	2.39744	0.199787
$145$	0	0
$146$	8.38101	0.693618
$147$	1.00000	0.0824786
$148$	16.4362	1.35105
$149$	−15.5569	−1.27447	−0.637236	−	0.770669i	$-0.719922\pi$
$149$	−15.5569	−1.27447	−0.637236	+	0.770669i	$0.719922\pi$
$150$	0	0
$151$	4.99656	0.406614	0.203307	−	0.979115i	$-0.434831\pi$
$151$	4.99656	0.406614	0.203307	+	0.979115i	$0.434831\pi$
$152$	9.52406	0.772503
$153$	2.94137	0.237795
$154$	−3.43965	−0.277175
$155$	0	0
$156$	−1.71982	−0.137696
$157$	18.7880	1.49945	0.749723	−	0.661752i	$-0.230187\pi$
$157$	18.7880	1.49945	0.749723	+	0.661752i	$0.230187\pi$
$158$	−0.677618	−0.0539084
$159$	−6.39400	−0.507078
$160$	0	0
$161$	5.77846	0.455406
$162$	0.529317	0.0415870
$163$	9.88273	0.774075	0.387038	−	0.922064i	$-0.373498\pi$
$163$	9.88273	0.774075	0.387038	+	0.922064i	$0.373498\pi$
$164$	5.26031	0.410761
$165$	0	0
$166$	1.50172	0.116556
$167$	7.04564	0.545208	0.272604	−	0.962126i	$-0.412115\pi$
$167$	7.04564	0.545208	0.272604	+	0.962126i	$0.412115\pi$
$168$	−1.96896	−0.151909
$169$	1.00000	0.0769231
$170$	0	0
$171$	−4.83709	−0.369902
$172$	4.67762	0.356665
$173$	14.2897	1.08643	0.543214	−	0.839594i	$-0.317207\pi$
$173$	14.2897	1.08643	0.543214	+	0.839594i	$0.317207\pi$
$174$	−1.50172	−0.113845
$175$	0	0
$176$	−15.5793	−1.17433
$177$	1.55691	0.117025
$178$	−4.05520	−0.303950
$179$	−8.65775	−0.647111	−0.323555	−	0.946209i	$-0.604878\pi$
$179$	−8.65775	−0.647111	−0.323555	+	0.946209i	$0.604878\pi$
$180$	0	0
$181$	26.3449	1.95820	0.979101	−	0.203373i	$-0.0651904\pi$
$181$	26.3449	1.95820	0.979101	+	0.203373i	$0.0651904\pi$
$182$	0.529317	0.0392356
$183$	3.88273	0.287020
$184$	−11.3776	−0.838766
$185$	0	0
$186$	3.32238	0.243609
$187$	−19.1138	−1.39774
$188$	−14.9966	−1.09374
$189$	1.00000	0.0727393
$190$	0	0
$191$	6.61555	0.478684	0.239342	−	0.970935i	$-0.423068\pi$
$191$	6.61555	0.478684	0.239342	+	0.970935i	$0.423068\pi$
$192$	−2.03877	−0.147135
$193$	−11.8827	−0.855338	−0.427669	−	0.903935i	$-0.640665\pi$
$193$	−11.8827	−0.855338	−0.427669	+	0.903935i	$0.640665\pi$
$194$	9.37758	0.673271
$195$	0	0
$196$	−1.71982	−0.122845
$197$	−11.5569	−0.823396	−0.411698	−	0.911320i	$-0.635064\pi$
$197$	−11.5569	−0.823396	−0.411698	+	0.911320i	$0.635064\pi$
$198$	−3.43965	−0.244445
$199$	0.996562	0.0706444	0.0353222	−	0.999376i	$-0.488754\pi$
$199$	0.996562	0.0706444	0.0353222	+	0.999376i	$0.488754\pi$
$200$	0	0
$201$	−5.67418	−0.400226
$202$	3.56379	0.250747
$203$	−2.83709	−0.199125
$204$	−5.05863	−0.354175
$205$	0	0
$206$	−5.75859	−0.401220
$207$	5.77846	0.401631
$208$	2.39744	0.166233
$209$	31.4328	2.17425
$210$	0	0
$211$	26.8302	1.84707	0.923534	−	0.383516i	$-0.125287\pi$
$211$	26.8302	1.84707	0.923534	+	0.383516i	$0.125287\pi$
$212$	10.9966	0.755247
$213$	10.0552	0.688971
$214$	4.49828	0.307496
$215$	0	0
$216$	−1.96896	−0.133971
$217$	6.27674	0.426093
$218$	5.29317	0.358498
$219$	15.8337	1.06994
$220$	0	0
$221$	2.94137	0.197858
$222$	−5.05863	−0.339513
$223$	2.92838	0.196099	0.0980493	−	0.995182i	$-0.468740\pi$
$223$	2.92838	0.196099	0.0980493	+	0.995182i	$0.468740\pi$
$224$	5.20693	0.347903
$225$	0	0
$226$	−7.72938	−0.514150
$227$	9.79145	0.649881	0.324941	−	0.945734i	$-0.394656\pi$
$227$	9.79145	0.649881	0.324941	+	0.945734i	$0.394656\pi$
$228$	8.31894	0.550936
$229$	3.88273	0.256578	0.128289	−	0.991737i	$-0.459051\pi$
$229$	3.88273	0.256578	0.128289	+	0.991737i	$0.459051\pi$
$230$	0	0
$231$	−6.49828	−0.427556
$232$	5.58613	0.366747
$233$	15.8337	1.03730	0.518649	−	0.854988i	$-0.326435\pi$
$233$	15.8337	1.03730	0.518649	+	0.854988i	$0.326435\pi$
$234$	0.529317	0.0346025
$235$	0	0
$236$	−2.67762	−0.174298
$237$	−1.28018	−0.0831564
$238$	1.55691	0.100920
$239$	−6.94137	−0.449000	−0.224500	−	0.974474i	$-0.572075\pi$
$239$	−6.94137	−0.449000	−0.224500	+	0.974474i	$0.572075\pi$
$240$	0	0
$241$	7.28018	0.468957	0.234479	−	0.972121i	$-0.424662\pi$
$241$	7.28018	0.468957	0.234479	+	0.972121i	$0.424662\pi$
$242$	16.5293	1.06254
$243$	1.00000	0.0641500
$244$	−6.67762	−0.427491
$245$	0	0
$246$	−1.61899	−0.103223
$247$	−4.83709	−0.307777
$248$	−12.3587	−0.784777
$249$	2.83709	0.179793
$250$	0	0
$251$	23.3224	1.47210	0.736048	−	0.676930i	$-0.236690\pi$
$251$	23.3224	1.47210	0.736048	+	0.676930i	$0.236690\pi$
$252$	−1.71982	−0.108339
$253$	−37.5500	−2.36075
$254$	5.23109	0.328228
$255$	0	0
$256$	−2.00591	−0.125370
$257$	−15.4948	−0.966542	−0.483271	−	0.875471i	$-0.660551\pi$
$257$	−15.4948	−0.966542	−0.483271	+	0.875471i	$0.660551\pi$
$258$	−1.43965	−0.0896286
$259$	−9.55691	−0.593838
$260$	0	0
$261$	−2.83709	−0.175611
$262$	1.99312	0.123136
$263$	−3.42666	−0.211297	−0.105648	−	0.994404i	$-0.533692\pi$
$263$	−3.42666	−0.211297	−0.105648	+	0.994404i	$0.533692\pi$
$264$	12.7949	0.787471
$265$	0	0
$266$	−2.56035	−0.156985
$267$	−7.66119	−0.468857
$268$	9.75859	0.596101
$269$	−0.172462	−0.0105152	−0.00525759	−	0.999986i	$-0.501674\pi$
$269$	−0.172462	−0.0105152	−0.00525759	+	0.999986i	$0.501674\pi$
$270$	0	0
$271$	−25.9931	−1.57897	−0.789485	−	0.613770i	$-0.789652\pi$
$271$	−25.9931	−1.57897	−0.789485	+	0.613770i	$0.789652\pi$
$272$	7.05176	0.427576
$273$	1.00000	0.0605228
$274$	8.99656	0.543502
$275$	0	0
$276$	−9.93793	−0.598193
$277$	−3.72326	−0.223709	−0.111855	−	0.993725i	$-0.535679\pi$
$277$	−3.72326	−0.223709	−0.111855	+	0.993725i	$0.535679\pi$
$278$	−4.52750	−0.271541
$279$	6.27674	0.375778
$280$	0	0
$281$	−21.5500	−1.28557	−0.642784	−	0.766048i	$-0.722221\pi$
$281$	−21.5500	−1.28557	−0.642784	+	0.766048i	$0.722221\pi$
$282$	4.61555	0.274852
$283$	31.8759	1.89482	0.947412	−	0.320018i	$-0.103689\pi$
$283$	31.8759	1.89482	0.947412	+	0.320018i	$0.103689\pi$
$284$	−17.2932	−1.02616
$285$	0	0
$286$	−3.43965	−0.203391
$287$	−3.05863	−0.180545
$288$	5.20693	0.306822
$289$	−8.34836	−0.491080
$290$	0	0
$291$	17.7164	1.03855
$292$	−27.2311	−1.59358
$293$	−3.42666	−0.200188	−0.100094	−	0.994978i	$-0.531914\pi$
$293$	−3.42666	−0.200188	−0.100094	+	0.994978i	$0.531914\pi$
$294$	0.529317	0.0308704
$295$	0	0
$296$	18.8172	1.09373
$297$	−6.49828	−0.377069
$298$	−8.23453	−0.477014
$299$	5.77846	0.334177
$300$	0	0
$301$	−2.71982	−0.156768
$302$	2.64476	0.152189
$303$	6.73281	0.386790
$304$	−11.5966	−0.665113
$305$	0	0
$306$	1.55691	0.0890029
$307$	3.39744	0.193902	0.0969511	−	0.995289i	$-0.469091\pi$
$307$	3.39744	0.193902	0.0969511	+	0.995289i	$0.469091\pi$
$308$	11.1759	0.636806
$309$	−10.8793	−0.618902
$310$	0	0
$311$	−0.443086	−0.0251251	−0.0125625	−	0.999921i	$-0.503999\pi$
$311$	−0.443086	−0.0251251	−0.0125625	+	0.999921i	$0.503999\pi$
$312$	−1.96896	−0.111471
$313$	19.8827	1.12384	0.561919	−	0.827192i	$-0.310063\pi$
$313$	19.8827	1.12384	0.561919	+	0.827192i	$0.310063\pi$
$314$	9.94480	0.561218
$315$	0	0
$316$	2.20168	0.123854
$317$	−9.46563	−0.531643	−0.265821	−	0.964022i	$-0.585643\pi$
$317$	−9.46563	−0.531643	−0.265821	+	0.964022i	$0.585643\pi$
$318$	−3.38445	−0.189791
$319$	18.4362	1.03223
$320$	0	0
$321$	8.49828	0.474328
$322$	3.05863	0.170451
$323$	−14.2277	−0.791648
$324$	−1.71982	−0.0955458
$325$	0	0
$326$	5.23109	0.289724
$327$	10.0000	0.553001
$328$	6.02234	0.332528
$329$	8.71982	0.480739
$330$	0	0
$331$	−27.4328	−1.50784	−0.753921	−	0.656965i	$-0.771840\pi$
$331$	−27.4328	−1.50784	−0.753921	+	0.656965i	$0.771840\pi$
$332$	−4.87930	−0.267786
$333$	−9.55691	−0.523716
$334$	3.72938	0.204062
$335$	0	0
$336$	2.39744	0.130791
$337$	20.2767	1.10454	0.552272	−	0.833664i	$-0.313761\pi$
$337$	20.2767	1.10454	0.552272	+	0.833664i	$0.313761\pi$
$338$	0.529317	0.0287910
$339$	−14.6026	−0.793102
$340$	0	0
$341$	−40.7880	−2.20879
$342$	−2.56035	−0.138448
$343$	1.00000	0.0539949
$344$	5.35524	0.288735
$345$	0	0
$346$	7.56379	0.406632
$347$	−16.7328	−0.898265	−0.449132	−	0.893465i	$-0.648267\pi$
$347$	−16.7328	−0.898265	−0.449132	+	0.893465i	$0.648267\pi$
$348$	4.87930	0.261558
$349$	22.3940	1.19872	0.599362	−	0.800478i	$-0.295421\pi$
$349$	22.3940	1.19872	0.599362	+	0.800478i	$0.295421\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	−33.8361	−1.80347
$353$	27.1690	1.44606	0.723031	−	0.690816i	$-0.242749\pi$
$353$	27.1690	1.44606	0.723031	+	0.690816i	$0.242749\pi$
$354$	0.824101	0.0438004
$355$	0	0
$356$	13.1759	0.698321
$357$	2.94137	0.155674
$358$	−4.58269	−0.242203
$359$	−29.0586	−1.53366	−0.766828	−	0.641853i	$-0.778166\pi$
$359$	−29.0586	−1.53366	−0.766828	+	0.641853i	$0.778166\pi$
$360$	0	0
$361$	4.39744	0.231444
$362$	13.9448	0.732923
$363$	31.2277	1.63903
$364$	−1.71982	−0.0901433
$365$	0	0
$366$	2.05520	0.107427
$367$	4.44309	0.231927	0.115964	−	0.993253i	$-0.463004\pi$
$367$	4.44309	0.231927	0.115964	+	0.993253i	$0.463004\pi$
$368$	13.8535	0.722165
$369$	−3.05863	−0.159226
$370$	0	0
$371$	−6.39400	−0.331960
$372$	−10.7949	−0.559689
$373$	−31.3415	−1.62280	−0.811400	−	0.584491i	$-0.801294\pi$
$373$	−31.3415	−1.62280	−0.811400	+	0.584491i	$0.801294\pi$
$374$	−10.1173	−0.523151
$375$	0	0
$376$	−17.1690	−0.885425
$377$	−2.83709	−0.146118
$378$	0.529317	0.0272251
$379$	−11.5569	−0.593639	−0.296819	−	0.954934i	$-0.595926\pi$
$379$	−11.5569	−0.593639	−0.296819	+	0.954934i	$0.595926\pi$
$380$	0	0
$381$	9.88273	0.506308
$382$	3.50172	0.179164
$383$	25.6673	1.31154	0.655769	−	0.754962i	$-0.272345\pi$
$383$	25.6673	1.31154	0.655769	+	0.754962i	$0.272345\pi$
$384$	−11.4930	−0.586501
$385$	0	0
$386$	−6.28973	−0.320139
$387$	−2.71982	−0.138256
$388$	−30.4691	−1.54683
$389$	−24.2277	−1.22839	−0.614195	−	0.789154i	$-0.710519\pi$
$389$	−24.2277	−1.22839	−0.614195	+	0.789154i	$0.710519\pi$
$390$	0	0
$391$	16.9966	0.859553
$392$	−1.96896	−0.0994477
$393$	3.76547	0.189943
$394$	−6.11727	−0.308183
$395$	0	0
$396$	11.1759	0.561610
$397$	14.3680	0.721111	0.360555	−	0.932738i	$-0.382587\pi$
$397$	14.3680	0.721111	0.360555	+	0.932738i	$0.382587\pi$
$398$	0.527497	0.0264410
$399$	−4.83709	−0.242157
$400$	0	0
$401$	−21.8827	−1.09277	−0.546386	−	0.837534i	$-0.683997\pi$
$401$	−21.8827	−1.09277	−0.546386	+	0.837534i	$0.683997\pi$
$402$	−3.00344	−0.149798
$403$	6.27674	0.312667
$404$	−11.5793	−0.576089
$405$	0	0
$406$	−1.50172	−0.0745291
$407$	62.1035	3.07836
$408$	−5.79145	−0.286719
$409$	7.39057	0.365440	0.182720	−	0.983165i	$-0.441510\pi$
$409$	7.39057	0.365440	0.182720	+	0.983165i	$0.441510\pi$
$410$	0	0
$411$	16.9966	0.838379
$412$	18.7105	0.921799
$413$	1.55691	0.0766107
$414$	3.05863	0.150324
$415$	0	0
$416$	5.20693	0.255291
$417$	−8.55348	−0.418866
$418$	16.6379	0.813786
$419$	33.7846	1.65048	0.825242	−	0.564779i	$-0.191039\pi$
$419$	33.7846	1.65048	0.825242	+	0.564779i	$0.191039\pi$
$420$	0	0
$421$	−35.5500	−1.73260	−0.866301	−	0.499522i	$-0.833509\pi$
$421$	−35.5500	−1.73260	−0.866301	+	0.499522i	$0.833509\pi$
$422$	14.2017	0.691327
$423$	8.71982	0.423972
$424$	12.5896	0.611403
$425$	0	0
$426$	5.32238	0.257870
$427$	3.88273	0.187899
$428$	−14.6155	−0.706469
$429$	−6.49828	−0.313740
$430$	0	0
$431$	23.7294	1.14300	0.571502	−	0.820601i	$-0.306361\pi$
$431$	23.7294	1.14300	0.571502	+	0.820601i	$0.306361\pi$
$432$	2.39744	0.115347
$433$	5.55691	0.267048	0.133524	−	0.991046i	$-0.457371\pi$
$433$	5.55691	0.267048	0.133524	+	0.991046i	$0.457371\pi$
$434$	3.32238	0.159479
$435$	0	0
$436$	−17.1982	−0.823646
$437$	−27.9509	−1.33707
$438$	8.38101	0.400460
$439$	5.32926	0.254352	0.127176	−	0.991880i	$-0.459409\pi$
$439$	5.32926	0.254352	0.127176	+	0.991880i	$0.459409\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	1.55691	0.0740549
$443$	−5.33537	−0.253491	−0.126746	−	0.991935i	$-0.540453\pi$
$443$	−5.33537	−0.253491	−0.126746	+	0.991935i	$0.540453\pi$
$444$	16.4362	0.780028
$445$	0	0
$446$	1.55004	0.0733965
$447$	−15.5569	−0.735817
$448$	−2.03877	−0.0963227
$449$	26.2277	1.23776	0.618880	−	0.785486i	$-0.287587\pi$
$449$	26.2277	1.23776	0.618880	+	0.785486i	$0.287587\pi$
$450$	0	0
$451$	19.8759	0.935918
$452$	25.1138	1.18126
$453$	4.99656	0.234759
$454$	5.18278	0.243240
$455$	0	0
$456$	9.52406	0.446005
$457$	−11.4396	−0.535124	−0.267562	−	0.963541i	$-0.586218\pi$
$457$	−11.4396	−0.535124	−0.267562	+	0.963541i	$0.586218\pi$
$458$	2.05520	0.0960330
$459$	2.94137	0.137291
$460$	0	0
$461$	−28.0552	−1.30666	−0.653330	−	0.757073i	$-0.726629\pi$
$461$	−28.0552	−1.30666	−0.653330	+	0.757073i	$0.726629\pi$
$462$	−3.43965	−0.160027
$463$	10.5604	0.490781	0.245391	−	0.969424i	$-0.421084\pi$
$463$	10.5604	0.490781	0.245391	+	0.969424i	$0.421084\pi$
$464$	−6.80176	−0.315764
$465$	0	0
$466$	8.38101	0.388243
$467$	−16.6776	−0.771748	−0.385874	−	0.922551i	$-0.626100\pi$
$467$	−16.6776	−0.771748	−0.385874	+	0.922551i	$0.626100\pi$
$468$	−1.71982	−0.0794989
$469$	−5.67418	−0.262009
$470$	0	0
$471$	18.7880	0.865706
$472$	−3.06551	−0.141101
$473$	17.6742	0.812660
$474$	−0.677618	−0.0311240
$475$	0	0
$476$	−5.05863	−0.231862
$477$	−6.39400	−0.292761
$478$	−3.67418	−0.168053
$479$	4.06819	0.185880	0.0929401	−	0.995672i	$-0.470374\pi$
$479$	4.06819	0.185880	0.0929401	+	0.995672i	$0.470374\pi$
$480$	0	0
$481$	−9.55691	−0.435758
$482$	3.85352	0.175523
$483$	5.77846	0.262929
$484$	−53.7061	−2.44119
$485$	0	0
$486$	0.529317	0.0240103
$487$	0.443086	0.0200781	0.0100391	−	0.999950i	$-0.496804\pi$
$487$	0.443086	0.0200781	0.0100391	+	0.999950i	$0.496804\pi$
$488$	−7.64496	−0.346071
$489$	9.88273	0.446913
$490$	0	0
$491$	20.7328	0.935659	0.467829	−	0.883819i	$-0.345036\pi$
$491$	20.7328	0.935659	0.467829	+	0.883819i	$0.345036\pi$
$492$	5.26031	0.237153
$493$	−8.34492	−0.375836
$494$	−2.56035	−0.115196
$495$	0	0
$496$	15.0481	0.675680
$497$	10.0552	0.451037
$498$	1.50172	0.0672936
$499$	−13.9931	−0.626418	−0.313209	−	0.949684i	$-0.601404\pi$
$499$	−13.9931	−0.626418	−0.313209	+	0.949684i	$0.601404\pi$
$500$	0	0
$501$	7.04564	0.314776
$502$	12.3449	0.550981
$503$	−5.67418	−0.252999	−0.126500	−	0.991967i	$-0.540374\pi$
$503$	−5.67418	−0.252999	−0.126500	+	0.991967i	$0.540374\pi$
$504$	−1.96896	−0.0877046
$505$	0	0
$506$	−19.8759	−0.883590
$507$	1.00000	0.0444116
$508$	−16.9966	−0.754101
$509$	−6.22154	−0.275765	−0.137883	−	0.990449i	$-0.544030\pi$
$509$	−6.22154	−0.275765	−0.137883	+	0.990449i	$0.544030\pi$
$510$	0	0
$511$	15.8337	0.700440
$512$	21.9243	0.968926
$513$	−4.83709	−0.213563
$514$	−8.20168	−0.361760
$515$	0	0
$516$	4.67762	0.205921
$517$	−56.6639	−2.49207
$518$	−5.05863	−0.222264
$519$	14.2897	0.627249
$520$	0	0
$521$	−10.2897	−0.450801	−0.225401	−	0.974266i	$-0.572369\pi$
$521$	−10.2897	−0.450801	−0.225401	+	0.974266i	$0.572369\pi$
$522$	−1.50172	−0.0657285
$523$	2.32582	0.101701	0.0508505	−	0.998706i	$-0.483807\pi$
$523$	2.32582	0.101701	0.0508505	+	0.998706i	$0.483807\pi$
$524$	−6.47594	−0.282903
$525$	0	0
$526$	−1.81379	−0.0790849
$527$	18.4622	0.804226
$528$	−15.5793	−0.678000
$529$	10.3906	0.451764
$530$	0	0
$531$	1.55691	0.0675643
$532$	8.31894	0.360672
$533$	−3.05863	−0.132484
$534$	−4.05520	−0.175485
$535$	0	0
$536$	11.1723	0.482568
$537$	−8.65775	−0.373610
$538$	−0.0912868	−0.00393565
$539$	−6.49828	−0.279901
$540$	0	0
$541$	5.55691	0.238910	0.119455	−	0.992840i	$-0.461885\pi$
$541$	5.55691	0.238910	0.119455	+	0.992840i	$0.461885\pi$
$542$	−13.7586	−0.590982
$543$	26.3449	1.13057
$544$	15.3155	0.656647
$545$	0	0
$546$	0.529317	0.0226527
$547$	5.48873	0.234681	0.117341	−	0.993092i	$-0.462563\pi$
$547$	5.48873	0.234681	0.117341	+	0.993092i	$0.462563\pi$
$548$	−29.2311	−1.24869
$549$	3.88273	0.165711
$550$	0	0
$551$	13.7233	0.584631
$552$	−11.3776	−0.484262
$553$	−1.28018	−0.0544386
$554$	−1.97078	−0.0837306
$555$	0	0
$556$	14.7105	0.623863
$557$	22.9897	0.974104	0.487052	−	0.873373i	$-0.338072\pi$
$557$	22.9897	0.974104	0.487052	+	0.873373i	$0.338072\pi$
$558$	3.32238	0.140648
$559$	−2.71982	−0.115036
$560$	0	0
$561$	−19.1138	−0.806986
$562$	−11.4068	−0.481167
$563$	32.7620	1.38075	0.690377	−	0.723449i	$-0.257444\pi$
$563$	32.7620	1.38075	0.690377	+	0.723449i	$0.257444\pi$
$564$	−14.9966	−0.631469
$565$	0	0
$566$	16.8724	0.709201
$567$	1.00000	0.0419961
$568$	−19.7983	−0.830719
$569$	36.1526	1.51560	0.757798	−	0.652489i	$-0.226275\pi$
$569$	36.1526	1.51560	0.757798	+	0.652489i	$0.226275\pi$
$570$	0	0
$571$	6.48529	0.271401	0.135700	−	0.990750i	$-0.456672\pi$
$571$	6.48529	0.271401	0.135700	+	0.990750i	$0.456672\pi$
$572$	11.1759	0.467288
$573$	6.61555	0.276368
$574$	−1.61899	−0.0675751
$575$	0	0
$576$	−2.03877	−0.0849487
$577$	−3.99312	−0.166236	−0.0831180	−	0.996540i	$-0.526488\pi$
$577$	−3.99312	−0.166236	−0.0831180	+	0.996540i	$0.526488\pi$
$578$	−4.41893	−0.183803
$579$	−11.8827	−0.493830
$580$	0	0
$581$	2.83709	0.117702
$582$	9.37758	0.388713
$583$	41.5500	1.72083
$584$	−31.1759	−1.29007
$585$	0	0
$586$	−1.81379	−0.0749268
$587$	−4.16635	−0.171964	−0.0859818	−	0.996297i	$-0.527403\pi$
$587$	−4.16635	−0.171964	−0.0859818	+	0.996297i	$0.527403\pi$
$588$	−1.71982	−0.0709243
$589$	−30.3611	−1.25101
$590$	0	0
$591$	−11.5569	−0.475388
$592$	−22.9122	−0.941684
$593$	−16.1303	−0.662390	−0.331195	−	0.943562i	$-0.607452\pi$
$593$	−16.1303	−0.662390	−0.331195	+	0.943562i	$0.607452\pi$
$594$	−3.43965	−0.141130
$595$	0	0
$596$	26.7552	1.09593
$597$	0.996562	0.0407866
$598$	3.05863	0.125077
$599$	−33.2372	−1.35804	−0.679018	−	0.734122i	$-0.737594\pi$
$599$	−33.2372	−1.35804	−0.679018	+	0.734122i	$0.737594\pi$
$600$	0	0
$601$	−28.9897	−1.18251	−0.591257	−	0.806483i	$-0.701368\pi$
$601$	−28.9897	−1.18251	−0.591257	+	0.806483i	$0.701368\pi$
$602$	−1.43965	−0.0586757
$603$	−5.67418	−0.231070
$604$	−8.59321	−0.349653
$605$	0	0
$606$	3.56379	0.144769
$607$	25.7846	1.04656	0.523282	−	0.852160i	$-0.324708\pi$
$607$	25.7846	1.04656	0.523282	+	0.852160i	$0.324708\pi$
$608$	−25.1864	−1.02144
$609$	−2.83709	−0.114965
$610$	0	0
$611$	8.71982	0.352766
$612$	−5.05863	−0.204483
$613$	7.43965	0.300485	0.150242	−	0.988649i	$-0.451995\pi$
$613$	7.43965	0.300485	0.150242	+	0.988649i	$0.451995\pi$
$614$	1.79832	0.0725744
$615$	0	0
$616$	12.7949	0.515521
$617$	2.67074	0.107520	0.0537600	−	0.998554i	$-0.482879\pi$
$617$	2.67074	0.107520	0.0537600	+	0.998554i	$0.482879\pi$
$618$	−5.75859	−0.231645
$619$	−4.46907	−0.179627	−0.0898134	−	0.995959i	$-0.528627\pi$
$619$	−4.46907	−0.179627	−0.0898134	+	0.995959i	$0.528627\pi$
$620$	0	0
$621$	5.77846	0.231881
$622$	−0.234533	−0.00940390
$623$	−7.66119	−0.306939
$624$	2.39744	0.0959745
$625$	0	0
$626$	10.5243	0.420634
$627$	31.4328	1.25530
$628$	−32.3121	−1.28939
$629$	−28.1104	−1.12083
$630$	0	0
$631$	23.0878	0.919113	0.459556	−	0.888149i	$-0.348008\pi$
$631$	23.0878	0.919113	0.459556	+	0.888149i	$0.348008\pi$
$632$	2.52062	0.100265
$633$	26.8302	1.06641
$634$	−5.01031	−0.198985
$635$	0	0
$636$	10.9966	0.436042
$637$	1.00000	0.0396214
$638$	9.75859	0.386346
$639$	10.0552	0.397777
$640$	0	0
$641$	41.8268	1.65206	0.826029	−	0.563627i	$-0.190595\pi$
$641$	41.8268	1.65206	0.826029	+	0.563627i	$0.190595\pi$
$642$	4.49828	0.177533
$643$	−3.11383	−0.122797	−0.0613987	−	0.998113i	$-0.519556\pi$
$643$	−3.11383	−0.122797	−0.0613987	+	0.998113i	$0.519556\pi$
$644$	−9.93793	−0.391609
$645$	0	0
$646$	−7.53093	−0.296301
$647$	−30.4362	−1.19657	−0.598285	−	0.801283i	$-0.704151\pi$
$647$	−30.4362	−1.19657	−0.598285	+	0.801283i	$0.704151\pi$
$648$	−1.96896	−0.0773482
$649$	−10.1173	−0.397137
$650$	0	0
$651$	6.27674	0.246005
$652$	−16.9966	−0.665637
$653$	−3.99312	−0.156263	−0.0781315	−	0.996943i	$-0.524895\pi$
$653$	−3.99312	−0.156263	−0.0781315	+	0.996943i	$0.524895\pi$
$654$	5.29317	0.206979
$655$	0	0
$656$	−7.33290	−0.286302
$657$	15.8337	0.617730
$658$	4.61555	0.179933
$659$	32.6578	1.27217	0.636083	−	0.771621i	$-0.280554\pi$
$659$	32.6578	1.27217	0.636083	+	0.771621i	$0.280554\pi$
$660$	0	0
$661$	43.7355	1.70111	0.850557	−	0.525883i	$-0.176265\pi$
$661$	43.7355	1.70111	0.850557	+	0.525883i	$0.176265\pi$
$662$	−14.5206	−0.564360
$663$	2.94137	0.114233
$664$	−5.58613	−0.216784
$665$	0	0
$666$	−5.05863	−0.196018
$667$	−16.3940	−0.634778
$668$	−12.1173	−0.468831
$669$	2.92838	0.113218
$670$	0	0
$671$	−25.2311	−0.974036
$672$	5.20693	0.200862
$673$	9.63198	0.371285	0.185643	−	0.982617i	$-0.440563\pi$
$673$	9.63198	0.371285	0.185643	+	0.982617i	$0.440563\pi$
$674$	10.7328	0.413413
$675$	0	0
$676$	−1.71982	−0.0661471
$677$	−16.4914	−0.633816	−0.316908	−	0.948456i	$-0.602645\pi$
$677$	−16.4914	−0.633816	−0.316908	+	0.948456i	$0.602645\pi$
$678$	−7.72938	−0.296845
$679$	17.7164	0.679892
$680$	0	0
$681$	9.79145	0.375209
$682$	−21.5898	−0.826715
$683$	−41.9311	−1.60445	−0.802224	−	0.597024i	$-0.796350\pi$
$683$	−41.9311	−1.60445	−0.802224	+	0.597024i	$0.796350\pi$
$684$	8.31894	0.318083
$685$	0	0
$686$	0.529317	0.0202094
$687$	3.88273	0.148136
$688$	−6.52062	−0.248596
$689$	−6.39400	−0.243592
$690$	0	0
$691$	38.1786	1.45238	0.726191	−	0.687493i	$-0.241289\pi$
$691$	38.1786	1.45238	0.726191	+	0.687493i	$0.241289\pi$
$692$	−24.5758	−0.934232
$693$	−6.49828	−0.246849
$694$	−8.85696	−0.336205
$695$	0	0
$696$	5.58613	0.211742
$697$	−8.99656	−0.340769
$698$	11.8535	0.448662
$699$	15.8337	0.598884
$700$	0	0
$701$	16.5957	0.626810	0.313405	−	0.949620i	$-0.398530\pi$
$701$	16.5957	0.626810	0.313405	+	0.949620i	$0.398530\pi$
$702$	0.529317	0.0199778
$703$	46.2277	1.74351
$704$	13.2485	0.499321
$705$	0	0
$706$	14.3810	0.541237
$707$	6.73281	0.253214
$708$	−2.67762	−0.100631
$709$	21.7655	0.817419	0.408710	−	0.912664i	$-0.365979\pi$
$709$	21.7655	0.817419	0.408710	+	0.912664i	$0.365979\pi$
$710$	0	0
$711$	−1.28018	−0.0480104
$712$	15.0846	0.565320
$713$	36.2699	1.35832
$714$	1.55691	0.0582661
$715$	0	0
$716$	14.8898	0.556458
$717$	−6.94137	−0.259230
$718$	−15.3812	−0.574022
$719$	36.7880	1.37196	0.685981	−	0.727620i	$-0.259373\pi$
$719$	36.7880	1.37196	0.685981	+	0.727620i	$0.259373\pi$
$720$	0	0
$721$	−10.8793	−0.405166
$722$	2.32764	0.0866258
$723$	7.28018	0.270753
$724$	−45.3086	−1.68388
$725$	0	0
$726$	16.5293	0.613460
$727$	32.3189	1.19864	0.599322	−	0.800508i	$-0.295437\pi$
$727$	32.3189	1.19864	0.599322	+	0.800508i	$0.295437\pi$
$728$	−1.96896	−0.0729747
$729$	1.00000	0.0370370
$730$	0	0
$731$	−8.00000	−0.295891
$732$	−6.67762	−0.246812
$733$	12.7198	0.469817	0.234909	−	0.972017i	$-0.424521\pi$
$733$	12.7198	0.469817	0.234909	+	0.972017i	$0.424521\pi$
$734$	2.35180	0.0868065
$735$	0	0
$736$	30.0881	1.10906
$737$	36.8724	1.35821
$738$	−1.61899	−0.0595957
$739$	23.1982	0.853361	0.426681	−	0.904402i	$-0.359683\pi$
$739$	23.1982	0.853361	0.426681	+	0.904402i	$0.359683\pi$
$740$	0	0
$741$	−4.83709	−0.177695
$742$	−3.38445	−0.124247
$743$	−31.8138	−1.16713	−0.583567	−	0.812065i	$-0.698344\pi$
$743$	−31.8138	−1.16713	−0.583567	+	0.812065i	$0.698344\pi$
$744$	−12.3587	−0.453091
$745$	0	0
$746$	−16.5896	−0.607387
$747$	2.83709	0.103804
$748$	32.8724	1.20193
$749$	8.49828	0.310520
$750$	0	0
$751$	−0.863070	−0.0314939	−0.0157469	−	0.999876i	$-0.505013\pi$
$751$	−0.863070	−0.0314939	−0.0157469	+	0.999876i	$0.505013\pi$
$752$	20.9053	0.762337
$753$	23.3224	0.849915
$754$	−1.50172	−0.0546894
$755$	0	0
$756$	−1.71982	−0.0625494
$757$	13.3974	0.486938	0.243469	−	0.969909i	$-0.421715\pi$
$757$	13.3974	0.486938	0.243469	+	0.969909i	$0.421715\pi$
$758$	−6.11727	−0.222189
$759$	−37.5500	−1.36298
$760$	0	0
$761$	−35.5630	−1.28916	−0.644579	−	0.764537i	$-0.722967\pi$
$761$	−35.5630	−1.28916	−0.644579	+	0.764537i	$0.722967\pi$
$762$	5.23109	0.189503
$763$	10.0000	0.362024
$764$	−11.3776	−0.411626
$765$	0	0
$766$	13.5861	0.490887
$767$	1.55691	0.0562169
$768$	−2.00591	−0.0723821
$769$	−48.3871	−1.74488	−0.872442	−	0.488717i	$-0.837465\pi$
$769$	−48.3871	−1.74488	−0.872442	+	0.488717i	$0.837465\pi$
$770$	0	0
$771$	−15.4948	−0.558033
$772$	20.4362	0.735515
$773$	−17.9379	−0.645182	−0.322591	−	0.946538i	$-0.604554\pi$
$773$	−17.9379	−0.645182	−0.322591	+	0.946538i	$0.604554\pi$
$774$	−1.43965	−0.0517471
$775$	0	0
$776$	−34.8829	−1.25222
$777$	−9.55691	−0.342852
$778$	−12.8241	−0.459766
$779$	14.7949	0.530082
$780$	0	0
$781$	−65.3415	−2.33810
$782$	8.99656	0.321716
$783$	−2.83709	−0.101389
$784$	2.39744	0.0856229
$785$	0	0
$786$	1.99312	0.0710924
$787$	3.71639	0.132475	0.0662374	−	0.997804i	$-0.478901\pi$
$787$	3.71639	0.132475	0.0662374	+	0.997804i	$0.478901\pi$
$788$	19.8759	0.708048
$789$	−3.42666	−0.121992
$790$	0	0
$791$	−14.6026	−0.519207
$792$	12.7949	0.454646
$793$	3.88273	0.137880
$794$	7.60523	0.269900
$795$	0	0
$796$	−1.71391	−0.0607480
$797$	−14.9673	−0.530171	−0.265085	−	0.964225i	$-0.585400\pi$
$797$	−14.9673	−0.530171	−0.265085	+	0.964225i	$0.585400\pi$
$798$	−2.56035	−0.0906355
$799$	25.6482	0.907368
$800$	0	0
$801$	−7.66119	−0.270695
$802$	−11.5829	−0.409006
$803$	−102.892	−3.63096
$804$	9.75859	0.344159
$805$	0	0
$806$	3.32238	0.117026
$807$	−0.172462	−0.00607094
$808$	−13.2567	−0.466368
$809$	11.7233	0.412168	0.206084	−	0.978534i	$-0.433928\pi$
$809$	11.7233	0.412168	0.206084	+	0.978534i	$0.433928\pi$
$810$	0	0
$811$	−0.886172	−0.0311177	−0.0155588	−	0.999879i	$-0.504953\pi$
$811$	−0.886172	−0.0311177	−0.0155588	+	0.999879i	$0.504953\pi$
$812$	4.87930	0.171230
$813$	−25.9931	−0.911619
$814$	32.8724	1.15218
$815$	0	0
$816$	7.05176	0.246861
$817$	13.1560	0.460271
$818$	3.91195	0.136778
$819$	1.00000	0.0349428
$820$	0	0
$821$	−53.7846	−1.87709	−0.938547	−	0.345151i	$-0.887828\pi$
$821$	−53.7846	−1.87709	−0.938547	+	0.345151i	$0.887828\pi$
$822$	8.99656	0.313791
$823$	35.7655	1.24671	0.623353	−	0.781941i	$-0.285770\pi$
$823$	35.7655	1.24671	0.623353	+	0.781941i	$0.285770\pi$
$824$	21.4209	0.746234
$825$	0	0
$826$	0.824101	0.0286741
$827$	−7.41043	−0.257686	−0.128843	−	0.991665i	$-0.541126\pi$
$827$	−7.41043	−0.257686	−0.128843	+	0.991665i	$0.541126\pi$
$828$	−9.93793	−0.345367
$829$	−31.9931	−1.11117	−0.555584	−	0.831461i	$-0.687505\pi$
$829$	−31.9931	−1.11117	−0.555584	+	0.831461i	$0.687505\pi$
$830$	0	0
$831$	−3.72326	−0.129159
$832$	−2.03877	−0.0706816
$833$	2.94137	0.101912
$834$	−4.52750	−0.156774
$835$	0	0
$836$	−54.0588	−1.86966
$837$	6.27674	0.216956
$838$	17.8827	0.617749
$839$	−1.55691	−0.0537506	−0.0268753	−	0.999639i	$-0.508556\pi$
$839$	−1.55691	−0.0537506	−0.0268753	+	0.999639i	$0.508556\pi$
$840$	0	0
$841$	−20.9509	−0.722445
$842$	−18.8172	−0.648484
$843$	−21.5500	−0.742223
$844$	−46.1432	−1.58832
$845$	0	0
$846$	4.61555	0.158686
$847$	31.2277	1.07299
$848$	−15.3293	−0.526409
$849$	31.8759	1.09398
$850$	0	0
$851$	−55.2242	−1.89306
$852$	−17.2932	−0.592454
$853$	−35.4750	−1.21464	−0.607320	−	0.794457i	$-0.707755\pi$
$853$	−35.4750	−1.21464	−0.607320	+	0.794457i	$0.707755\pi$
$854$	2.05520	0.0703273
$855$	0	0
$856$	−16.7328	−0.571916
$857$	2.49828	0.0853397	0.0426698	−	0.999089i	$-0.486414\pi$
$857$	2.49828	0.0853397	0.0426698	+	0.999089i	$0.486414\pi$
$858$	−3.43965	−0.117428
$859$	52.0122	1.77463	0.887317	−	0.461160i	$-0.152566\pi$
$859$	52.0122	1.77463	0.887317	+	0.461160i	$0.152566\pi$
$860$	0	0
$861$	−3.05863	−0.104238
$862$	12.5604	0.427807
$863$	−34.8172	−1.18519	−0.592596	−	0.805500i	$-0.701897\pi$
$863$	−34.8172	−1.18519	−0.592596	+	0.805500i	$0.701897\pi$
$864$	5.20693	0.177144
$865$	0	0
$866$	2.94137	0.0999517
$867$	−8.34836	−0.283525
$868$	−10.7949	−0.366402
$869$	8.31894	0.282201
$870$	0	0
$871$	−5.67418	−0.192262
$872$	−19.6896	−0.666776
$873$	17.7164	0.599609
$874$	−14.7949	−0.500444
$875$	0	0
$876$	−27.2311	−0.920053
$877$	11.2571	0.380124	0.190062	−	0.981772i	$-0.439131\pi$
$877$	11.2571	0.380124	0.190062	+	0.981772i	$0.439131\pi$
$878$	2.82086	0.0951996
$879$	−3.42666	−0.115578
$880$	0	0
$881$	−9.50172	−0.320121	−0.160061	−	0.987107i	$-0.551169\pi$
$881$	−9.50172	−0.320121	−0.160061	+	0.987107i	$0.551169\pi$
$882$	0.529317	0.0178230
$883$	−23.7655	−0.799772	−0.399886	−	0.916565i	$-0.630950\pi$
$883$	−23.7655	−0.799772	−0.399886	+	0.916565i	$0.630950\pi$
$884$	−5.05863	−0.170140
$885$	0	0
$886$	−2.82410	−0.0948775
$887$	−18.3518	−0.616193	−0.308097	−	0.951355i	$-0.599692\pi$
$887$	−18.3518	−0.616193	−0.308097	+	0.951355i	$0.599692\pi$
$888$	18.8172	0.631465
$889$	9.88273	0.331456
$890$	0	0
$891$	−6.49828	−0.217701
$892$	−5.03629	−0.168628
$893$	−42.1786	−1.41145
$894$	−8.23453	−0.275404
$895$	0	0
$896$	−11.4930	−0.383955
$897$	5.77846	0.192937
$898$	13.8827	0.463273
$899$	−17.8077	−0.593919
$900$	0	0
$901$	−18.8071	−0.626556
$902$	10.5206	0.350298
$903$	−2.71982	−0.0905101
$904$	28.7519	0.956275
$905$	0	0
$906$	2.64476	0.0878664
$907$	−35.7164	−1.18594	−0.592972	−	0.805223i	$-0.702045\pi$
$907$	−35.7164	−1.18594	−0.592972	+	0.805223i	$0.702045\pi$
$908$	−16.8396	−0.558841
$909$	6.73281	0.223313
$910$	0	0
$911$	−16.2147	−0.537216	−0.268608	−	0.963250i	$-0.586564\pi$
$911$	−16.2147	−0.537216	−0.268608	+	0.963250i	$0.586564\pi$
$912$	−11.5966	−0.384003
$913$	−18.4362	−0.610149
$914$	−6.05520	−0.200288
$915$	0	0
$916$	−6.67762	−0.220635
$917$	3.76547	0.124347
$918$	1.55691	0.0513858
$919$	−34.4622	−1.13680	−0.568401	−	0.822751i	$-0.692438\pi$
$919$	−34.4622	−1.13680	−0.568401	+	0.822751i	$0.692438\pi$
$920$	0	0
$921$	3.39744	0.111950
$922$	−14.8501	−0.489061
$923$	10.0552	0.330971
$924$	11.1759	0.367660
$925$	0	0
$926$	5.58977	0.183691
$927$	−10.8793	−0.357323
$928$	−14.7725	−0.484933
$929$	−28.4492	−0.933388	−0.466694	−	0.884419i	$-0.654555\pi$
$929$	−28.4492	−0.933388	−0.466694	+	0.884419i	$0.654555\pi$
$930$	0	0
$931$	−4.83709	−0.158529
$932$	−27.2311	−0.891984
$933$	−0.443086	−0.0145060
$934$	−8.82774	−0.288852
$935$	0	0
$936$	−1.96896	−0.0643576
$937$	−2.91215	−0.0951358	−0.0475679	−	0.998868i	$-0.515147\pi$
$937$	−2.91215	−0.0951358	−0.0475679	+	0.998868i	$0.515147\pi$
$938$	−3.00344	−0.0980657
$939$	19.8827	0.648848
$940$	0	0
$941$	−59.0096	−1.92366	−0.961828	−	0.273654i	$-0.911768\pi$
$941$	−59.0096	−1.92366	−0.961828	+	0.273654i	$0.911768\pi$
$942$	9.94480	0.324019
$943$	−17.6742	−0.575551
$944$	3.73261	0.121486
$945$	0	0
$946$	9.35524	0.304165
$947$	−34.8432	−1.13225	−0.566126	−	0.824319i	$-0.691558\pi$
$947$	−34.8432	−1.13225	−0.566126	+	0.824319i	$0.691558\pi$
$948$	2.20168	0.0715072
$949$	15.8337	0.513982
$950$	0	0
$951$	−9.46563	−0.306944
$952$	−5.79145	−0.187702
$953$	−23.9578	−0.776069	−0.388035	−	0.921645i	$-0.626846\pi$
$953$	−23.9578	−0.776069	−0.388035	+	0.921645i	$0.626846\pi$
$954$	−3.38445	−0.109576
$955$	0	0
$956$	11.9379	0.386100
$957$	18.4362	0.595958
$958$	2.15336	0.0695718
$959$	16.9966	0.548848
$960$	0	0
$961$	8.39744	0.270885
$962$	−5.05863	−0.163097
$963$	8.49828	0.273853
$964$	−12.5206	−0.403262
$965$	0	0
$966$	3.05863	0.0984099
$967$	37.3155	1.19999	0.599993	−	0.800005i	$-0.295170\pi$
$967$	37.3155	1.19999	0.599993	+	0.800005i	$0.295170\pi$
$968$	−61.4861	−1.97624
$969$	−14.2277	−0.457058
$970$	0	0
$971$	20.7880	0.667119	0.333559	−	0.942729i	$-0.391750\pi$
$971$	20.7880	0.667119	0.333559	+	0.942729i	$0.391750\pi$
$972$	−1.71982	−0.0551634
$973$	−8.55348	−0.274212
$974$	0.234533	0.00751491
$975$	0	0
$976$	9.30863	0.297962
$977$	−49.0810	−1.57024	−0.785120	−	0.619344i	$-0.787399\pi$
$977$	−49.0810	−1.57024	−0.785120	+	0.619344i	$0.787399\pi$
$978$	5.23109	0.167272
$979$	49.7846	1.59112
$980$	0	0
$981$	10.0000	0.319275
$982$	10.9742	0.350201
$983$	−10.1855	−0.324865	−0.162433	−	0.986720i	$-0.551934\pi$
$983$	−10.1855	−0.324865	−0.162433	+	0.986720i	$0.551934\pi$
$984$	6.02234	0.191985
$985$	0	0
$986$	−4.41711	−0.140669
$987$	8.71982	0.277555
$988$	8.31894	0.264661
$989$	−15.7164	−0.499752
$990$	0	0
$991$	4.34492	0.138021	0.0690105	−	0.997616i	$-0.478016\pi$
$991$	4.34492	0.138021	0.0690105	+	0.997616i	$0.478016\pi$
$992$	32.6826	1.03767
$993$	−27.4328	−0.870553
$994$	5.32238	0.168816
$995$	0	0
$996$	−4.87930	−0.154606
$997$	−44.9637	−1.42401	−0.712007	−	0.702172i	$-0.752214\pi$
$997$	−44.9637	−1.42401	−0.712007	+	0.702172i	$0.752214\pi$
$998$	−7.40679	−0.234458
$999$	−9.55691	−0.302367

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6825.2.a.bd.1.2		3
5.4	even	2		273.2.a.d.1.2	✓	3
15.14	odd	2		819.2.a.j.1.2		3
20.19	odd	2		4368.2.a.bq.1.3		3
35.34	odd	2		1911.2.a.n.1.2		3
65.64	even	2		3549.2.a.t.1.2		3
105.104	even	2		5733.2.a.bc.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.a.d.1.2	✓	3	5.4	even	2
819.2.a.j.1.2		3	15.14	odd	2
1911.2.a.n.1.2		3	35.34	odd	2
3549.2.a.t.1.2		3	65.64	even	2
4368.2.a.bq.1.3		3	20.19	odd	2
5733.2.a.bc.1.2		3	105.104	even	2
6825.2.a.bd.1.2		3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6825 = 3 \cdot 5^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6825.a (trivial)

\(f(q)\)	\(=\)	\(q+0.529317 q^{2} +1.00000 q^{3} -1.71982 q^{4} +0.529317 q^{6} +1.00000 q^{7} -1.96896 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.529317 q^{2} +1.00000 q^{3} -1.71982 q^{4} +0.529317 q^{6} +1.00000 q^{7} -1.96896 q^{8} +1.00000 q^{9} -6.49828 q^{11} -1.71982 q^{12} +1.00000 q^{13} +0.529317 q^{14} +2.39744 q^{16} +2.94137 q^{17} +0.529317 q^{18} -4.83709 q^{19} +1.00000 q^{21} -3.43965 q^{22} +5.77846 q^{23} -1.96896 q^{24} +0.529317 q^{26} +1.00000 q^{27} -1.71982 q^{28} -2.83709 q^{29} +6.27674 q^{31} +5.20693 q^{32} -6.49828 q^{33} +1.55691 q^{34} -1.71982 q^{36} -9.55691 q^{37} -2.56035 q^{38} +1.00000 q^{39} -3.05863 q^{41} +0.529317 q^{42} -2.71982 q^{43} +11.1759 q^{44} +3.05863 q^{46} +8.71982 q^{47} +2.39744 q^{48} +1.00000 q^{49} +2.94137 q^{51} -1.71982 q^{52} -6.39400 q^{53} +0.529317 q^{54} -1.96896 q^{56} -4.83709 q^{57} -1.50172 q^{58} +1.55691 q^{59} +3.88273 q^{61} +3.32238 q^{62} +1.00000 q^{63} -2.03877 q^{64} -3.43965 q^{66} -5.67418 q^{67} -5.05863 q^{68} +5.77846 q^{69} +10.0552 q^{71} -1.96896 q^{72} +15.8337 q^{73} -5.05863 q^{74} +8.31894 q^{76} -6.49828 q^{77} +0.529317 q^{78} -1.28018 q^{79} +1.00000 q^{81} -1.61899 q^{82} +2.83709 q^{83} -1.71982 q^{84} -1.43965 q^{86} -2.83709 q^{87} +12.7949 q^{88} -7.66119 q^{89} +1.00000 q^{91} -9.93793 q^{92} +6.27674 q^{93} +4.61555 q^{94} +5.20693 q^{96} +17.7164 q^{97} +0.529317 q^{98} -6.49828 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} + 3 q^{3} + 4 q^{4} + 2 q^{6} + 3 q^{7} + 12 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 + 3 * q^3 + 4 * q^4 + 2 * q^6 + 3 * q^7 + 12 * q^8 + 3 * q^9	\( 3 q + 2 q^{2} + 3 q^{3} + 4 q^{4} + 2 q^{6} + 3 q^{7} + 12 q^{8} + 3 q^{9} - 2 q^{11} + 4 q^{12} + 3 q^{13} + 2 q^{14} + 18 q^{16} + 8 q^{17} + 2 q^{18} - 7 q^{19} + 3 q^{21} + 8 q^{22} + 9 q^{23} + 12 q^{24} + 2 q^{26} + 3 q^{27} + 4 q^{28} - q^{29} - 7 q^{31} + 36 q^{32} - 2 q^{33} - 12 q^{34} + 4 q^{36} - 12 q^{37} - 26 q^{38} + 3 q^{39} - 10 q^{41} + 2 q^{42} + q^{43} + 36 q^{44} + 10 q^{46} + 17 q^{47} + 18 q^{48} + 3 q^{49} + 8 q^{51} + 4 q^{52} + 5 q^{53} + 2 q^{54} + 12 q^{56} - 7 q^{57} - 22 q^{58} - 12 q^{59} + 10 q^{61} - 10 q^{62} + 3 q^{63} + 58 q^{64} + 8 q^{66} - 2 q^{67} - 16 q^{68} + 9 q^{69} - 4 q^{71} + 12 q^{72} + 5 q^{73} - 16 q^{74} - 30 q^{76} - 2 q^{77} + 2 q^{78} - 13 q^{79} + 3 q^{81} - 24 q^{82} + q^{83} + 4 q^{84} + 14 q^{86} - q^{87} + 60 q^{88} - 13 q^{89} + 3 q^{91} + 6 q^{92} - 7 q^{93} - 2 q^{94} + 36 q^{96} + 9 q^{97} + 2 q^{98} - 2 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 + 3 * q^3 + 4 * q^4 + 2 * q^6 + 3 * q^7 + 12 * q^8 + 3 * q^9 - 2 * q^11 + 4 * q^12 + 3 * q^13 + 2 * q^14 + 18 * q^16 + 8 * q^17 + 2 * q^18 - 7 * q^19 + 3 * q^21 + 8 * q^22 + 9 * q^23 + 12 * q^24 + 2 * q^26 + 3 * q^27 + 4 * q^28 - q^29 - 7 * q^31 + 36 * q^32 - 2 * q^33 - 12 * q^34 + 4 * q^36 - 12 * q^37 - 26 * q^38 + 3 * q^39 - 10 * q^41 + 2 * q^42 + q^43 + 36 * q^44 + 10 * q^46 + 17 * q^47 + 18 * q^48 + 3 * q^49 + 8 * q^51 + 4 * q^52 + 5 * q^53 + 2 * q^54 + 12 * q^56 - 7 * q^57 - 22 * q^58 - 12 * q^59 + 10 * q^61 - 10 * q^62 + 3 * q^63 + 58 * q^64 + 8 * q^66 - 2 * q^67 - 16 * q^68 + 9 * q^69 - 4 * q^71 + 12 * q^72 + 5 * q^73 - 16 * q^74 - 30 * q^76 - 2 * q^77 + 2 * q^78 - 13 * q^79 + 3 * q^81 - 24 * q^82 + q^83 + 4 * q^84 + 14 * q^86 - q^87 + 60 * q^88 - 13 * q^89 + 3 * q^91 + 6 * q^92 - 7 * q^93 - 2 * q^94 + 36 * q^96 + 9 * q^97 + 2 * q^98 - 2 * q^99

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