LMFDB - Embedded newform 1450.2.c.e.1101.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1450,2,Mod(1101,1450)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1450.1101"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1450, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,0,0,-10,0,4,0,0,-14,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.5783082931$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 22x^{8} + 161x^{6} + 484x^{4} + 520x^{2} + 36 $ x^10 + 22x^8 + 161x^6 + 484x^4 + 520x^2 + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1101.7
Root			$-2.06121i$ of defining polynomial
Character	$\chi$	$=$	1450.1101
Dual form			1450.2.c.e.1101.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -2.06121i q^{3} -1.00000 q^{4} +2.06121 q^{6} +1.81264 q^{7} -1.00000i q^{8} -1.24857 q^{9} +3.98479i q^{11} +2.06121i q^{12} -6.04599 q^{13} +1.81264i q^{14} +1.00000 q^{16} +6.58819i q^{17} -1.24857i q^{18} +4.06121i q^{19} -3.73621i q^{21} -3.98479 q^{22} +0.790774 q^{23} -2.06121 q^{24} -6.04599i q^{26} -3.61006i q^{27} -1.81264 q^{28} +(-5.36291 + 0.489069i) q^{29} +3.24857i q^{31} +1.00000i q^{32} +8.21347 q^{33} -6.58819 q^{34} +1.24857 q^{36} -0.457797i q^{37} -4.06121 q^{38} +12.4620i q^{39} +9.91983i q^{41} +3.73621 q^{42} -3.62527i q^{43} -3.98479i q^{44} +0.790774i q^{46} -1.35952i q^{47} -2.06121i q^{48} -3.71435 q^{49} +13.5796 q^{51} +6.04599 q^{52} +6.90172 q^{53} +3.61006 q^{54} -1.81264i q^{56} +8.37098 q^{57} +(-0.489069 - 5.36291i) q^{58} +14.5451 q^{59} +0.827849i q^{61} -3.24857 q^{62} -2.26320 q^{63} -1.00000 q^{64} +8.21347i q^{66} +2.93505 q^{67} -6.58819i q^{68} -1.62995i q^{69} -12.2793 q^{71} +1.24857i q^{72} +6.29456i q^{73} +0.457797 q^{74} -4.06121i q^{76} +7.22296i q^{77} -12.4620 q^{78} +13.9810i q^{79} -11.1868 q^{81} -9.91983 q^{82} +12.9440 q^{83} +3.73621i q^{84} +3.62527 q^{86} +(1.00807 + 11.0541i) q^{87} +3.98479 q^{88} +1.82785i q^{89} -10.9592 q^{91} -0.790774 q^{92} +6.69597 q^{93} +1.35952 q^{94} +2.06121 q^{96} -17.0052i q^{97} -3.71435i q^{98} -4.97529i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{4} + 4 q^{6} - 14 q^{9} - 4 q^{13} + 10 q^{16} - 16 q^{23} - 4 q^{24} - 16 q^{29} - 36 q^{33} + 16 q^{34} + 14 q^{36} - 24 q^{38} - 4 q^{42} + 10 q^{49} - 20 q^{51} + 4 q^{52} + 40 q^{53} - 40 q^{54}+ \cdots + 4 q^{96}+O(q^{100}) $ 10 * q - 10 * q^4 + 4 * q^6 - 14 * q^9 - 4 * q^13 + 10 * q^16 - 16 * q^23 - 4 * q^24 - 16 * q^29 - 36 * q^33 + 16 * q^34 + 14 * q^36 - 24 * q^38 - 4 * q^42 + 10 * q^49 - 20 * q^51 + 4 * q^52 + 40 * q^53 - 40 * q^54 + 52 * q^57 - 2 * q^58 + 18 * q^59 - 34 * q^62 + 84 * q^63 - 10 * q^64 - 22 * q^67 - 28 * q^71 + 30 * q^74 - 8 * q^78 + 18 * q^81 - 8 * q^82 - 24 * q^83 + 16 * q^87 + 4 * q^91 + 16 * q^92 + 60 * q^93 + 10 * q^94 + 4 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1450\mathbb{Z}\right)^\times$.

$n$	$901$	$1277$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		−	2.06121i		−	1.19004i	−0.803712	−	0.595019i	$-0.797145\pi$
$3$		−	2.06121i		−	1.19004i	0.803712	−	0.595019i	$-0.202855\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	2.06121			0.841484
$7$	1.81264			0.685112			0.342556	−	0.939497i	$-0.388707\pi$
$7$	1.81264			0.685112			0.342556	+	0.939497i	$0.388707\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.24857			−0.416190
$10$		0			0
$11$			3.98479i			1.20146i	0.799453	+	0.600729i	$0.205123\pi$
$11$			3.98479i			1.20146i	−0.799453	+	0.600729i	$0.794877\pi$
$12$			2.06121i			0.595019i
$13$	−6.04599			−1.67686			−0.838428	−	0.545012i	$-0.816525\pi$
$13$	−6.04599			−1.67686			−0.838428	+	0.545012i	$0.816525\pi$
$14$			1.81264i			0.484447i
$15$		0			0
$16$	1.00000			0.250000
$17$			6.58819i			1.59787i	0.601416	+	0.798936i	$0.294603\pi$
$17$			6.58819i			1.59787i	−0.601416	+	0.798936i	$0.705397\pi$
$18$		−	1.24857i		−	0.294291i
$19$			4.06121i			0.931705i	0.884862	+	0.465852i	$0.154252\pi$
$19$			4.06121i			0.931705i	−0.884862	+	0.465852i	$0.845748\pi$
$20$		0			0
$21$		−	3.73621i		−	0.815309i
$22$	−3.98479			−0.849559
$23$	0.790774			0.164888			0.0824439	−	0.996596i	$-0.473727\pi$
$23$	0.790774			0.164888			0.0824439	+	0.996596i	$0.473727\pi$
$24$	−2.06121			−0.420742
$25$		0			0
$26$		−	6.04599i		−	1.18572i
$27$		−	3.61006i		−	0.694756i
$28$	−1.81264			−0.342556
$29$	−5.36291	+	0.489069i	−0.995868	+	0.0908179i
$29$	−5.36291	+	0.489069i	−0.995868	+	0.0908179i
$30$		0			0
$31$			3.24857i			0.583461i	0.956501	+	0.291730i	$0.0942310\pi$
$31$			3.24857i			0.583461i	−0.956501	+	0.291730i	$0.905769\pi$
$32$			1.00000i			0.176777i
$33$	8.21347			1.42978
$34$	−6.58819			−1.12987
$35$		0			0
$36$	1.24857			0.208095
$37$		−	0.457797i		−	0.0752614i	−0.999292	−	0.0376307i	$-0.988019\pi$
$37$		−	0.457797i		−	0.0752614i	0.999292	−	0.0376307i	$-0.0119811\pi$
$38$	−4.06121			−0.658815
$39$			12.4620i			1.99552i
$40$		0			0
$41$			9.91983i			1.54922i	0.632441	+	0.774609i	$0.282053\pi$
$41$			9.91983i			1.54922i	−0.632441	+	0.774609i	$0.717947\pi$
$42$	3.73621			0.576510
$43$		−	3.62527i		−	0.552849i	−0.961036	−	0.276424i	$-0.910850\pi$
$43$		−	3.62527i		−	0.552849i	0.961036	−	0.276424i	$-0.0891495\pi$
$44$		−	3.98479i		−	0.600729i
$45$		0			0
$46$			0.790774i			0.116593i
$47$		−	1.35952i		−	0.198306i	−0.995072	−	0.0991529i	$-0.968387\pi$
$47$		−	1.35952i		−	0.198306i	0.995072	−	0.0991529i	$-0.0316133\pi$
$48$		−	2.06121i		−	0.297509i
$49$	−3.71435			−0.530622
$50$		0			0
$51$	13.5796			1.90153
$52$	6.04599			0.838428
$53$	6.90172			0.948024			0.474012	−	0.880518i	$-0.342805\pi$
$53$	6.90172			0.948024			0.474012	+	0.880518i	$0.342805\pi$
$54$	3.61006			0.491266
$55$		0			0
$56$		−	1.81264i		−	0.242224i
$57$	8.37098			1.10876
$58$	−0.489069	−	5.36291i	−0.0642179	−	0.704185i
$59$	14.5451			1.89361			0.946806	−	0.321806i	$-0.104290\pi$
$59$	14.5451			1.89361			0.946806	+	0.321806i	$0.104290\pi$
$60$		0			0
$61$			0.827849i			0.105995i	0.998595	+	0.0529976i	$0.0168776\pi$
$61$			0.827849i			0.105995i	−0.998595	+	0.0529976i	$0.983122\pi$
$62$	−3.24857			−0.412569
$63$	−2.26320			−0.285137
$64$	−1.00000			−0.125000
$65$		0			0
$66$			8.21347i			1.01101i
$67$	2.93505			0.358573			0.179287	−	0.983797i	$-0.442621\pi$
$67$	2.93505			0.358573			0.179287	+	0.983797i	$0.442621\pi$
$68$		−	6.58819i		−	0.798936i
$69$		−	1.62995i		−	0.196223i
$70$		0			0
$71$	−12.2793			−1.45729			−0.728645	−	0.684891i	$-0.759850\pi$
$71$	−12.2793			−1.45729			−0.728645	+	0.684891i	$0.759850\pi$
$72$			1.24857i			0.147145i
$73$			6.29456i			0.736723i	0.929683	+	0.368361i	$0.120081\pi$
$73$			6.29456i			0.736723i	−0.929683	+	0.368361i	$0.879919\pi$
$74$	0.457797			0.0532178
$75$		0			0
$76$		−	4.06121i		−	0.465852i
$77$			7.22296i			0.823133i
$78$	−12.4620			−1.41105
$79$			13.9810i			1.57299i	0.617597	+	0.786495i	$0.288106\pi$
$79$			13.9810i			1.57299i	−0.617597	+	0.786495i	$0.711894\pi$
$80$		0			0
$81$	−11.1868			−1.24298
$82$	−9.91983			−1.09546
$83$	12.9440			1.42078			0.710392	−	0.703806i	$-0.248518\pi$
$83$	12.9440			1.42078			0.710392	+	0.703806i	$0.248518\pi$
$84$			3.73621i			0.407654i
$85$		0			0
$86$	3.62527			0.390923
$87$	1.00807	+	11.0541i	0.108077	+	1.18512i
$88$	3.98479			0.424780
$89$			1.82785i			0.193752i	0.995296	+	0.0968758i	$0.0308850\pi$
$89$			1.82785i			0.193752i	−0.995296	+	0.0968758i	$0.969115\pi$
$90$		0			0
$91$	−10.9592			−1.14883
$92$	−0.790774			−0.0824439
$93$	6.69597			0.694340
$94$	1.35952			0.140223
$95$		0			0
$96$	2.06121			0.210371
$97$		−	17.0052i		−	1.72661i	−0.504680	−	0.863307i	$-0.668389\pi$
$97$		−	17.0052i		−	1.72661i	0.504680	−	0.863307i	$-0.331611\pi$
$98$		−	3.71435i		−	0.375206i
$99$		−	4.97529i		−	0.500035i
$100$		0			0
$101$			0.441652i			0.0439460i	0.999759	+	0.0219730i	$0.00699479\pi$
$101$			0.441652i			0.0439460i	−0.999759	+	0.0219730i	$0.993005\pi$
$102$			13.5796i			1.34458i
$103$	−4.91319			−0.484111			−0.242055	−	0.970262i	$-0.577822\pi$
$103$	−4.91319			−0.484111			−0.242055	+	0.970262i	$0.577822\pi$
$104$			6.04599i			0.592858i
$105$		0			0
$106$			6.90172i			0.670354i
$107$	−12.2690			−1.18608			−0.593042	−	0.805171i	$-0.702073\pi$
$107$	−12.2690			−1.18608			−0.593042	+	0.805171i	$0.702073\pi$
$108$			3.61006i			0.347378i
$109$	7.44258			0.712870			0.356435	−	0.934320i	$-0.383992\pi$
$109$	7.44258			0.712870			0.356435	+	0.934320i	$0.383992\pi$
$110$		0			0
$111$	−0.943614			−0.0895639
$112$	1.81264			0.171278
$113$		−	5.57553i		−	0.524502i	−0.965000	−	0.262251i	$-0.915535\pi$
$113$		−	5.57553i		−	0.524502i	0.965000	−	0.262251i	$-0.0844648\pi$
$114$			8.37098i			0.784014i
$115$		0			0
$116$	5.36291	−	0.489069i	0.497934	−	0.0454089i
$117$	7.54885			0.697891
$118$			14.5451i			1.33899i
$119$			11.9420i			1.09472i
$120$		0			0
$121$	−4.87852			−0.443502
$122$	−0.827849			−0.0749500
$123$	20.4468			1.84363
$124$		−	3.24857i		−	0.291730i
$125$		0			0
$126$		−	2.26320i		−	0.201622i
$127$			19.9877i			1.77362i	0.462134	+	0.886810i	$0.347084\pi$
$127$			19.9877i			1.77362i	−0.462134	+	0.886810i	$0.652916\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−7.47243			−0.657911
$130$		0			0
$131$			7.79367i			0.680937i	0.940256	+	0.340468i	$0.110586\pi$
$131$			7.79367i			0.680937i	−0.940256	+	0.340468i	$0.889414\pi$
$132$	−8.21347			−0.714890
$133$			7.36149i			0.638322i
$134$			2.93505i			0.253549i
$135$		0			0
$136$	6.58819			0.564933
$137$			2.49621i			0.213266i	0.994298	+	0.106633i	$0.0340069\pi$
$137$			2.49621i			0.213266i	−0.994298	+	0.106633i	$0.965993\pi$
$138$	1.62995			0.138750
$139$	1.06027			0.0899314			0.0449657	−	0.998989i	$-0.485682\pi$
$139$	1.06027			0.0899314			0.0449657	+	0.998989i	$0.485682\pi$
$140$		0			0
$141$	−2.80224			−0.235991
$142$		−	12.2793i		−	1.03046i
$143$		−	24.0920i		−	2.01467i
$144$	−1.24857			−0.104048
$145$		0			0
$146$	−6.29456			−0.520942
$147$			7.65605i			0.631460i
$148$			0.457797i			0.0376307i
$149$	15.1925			1.24462			0.622310	−	0.782771i	$-0.286194\pi$
$149$	15.1925			1.24462			0.622310	+	0.782771i	$0.286194\pi$
$150$		0			0
$151$	−21.5299			−1.75208			−0.876039	−	0.482241i	$-0.839823\pi$
$151$	−21.5299			−1.75208			−0.876039	+	0.482241i	$0.839823\pi$
$152$	4.06121			0.329407
$153$		−	8.22583i		−	0.665019i
$154$	−7.22296			−0.582043
$155$		0			0
$156$		−	12.4620i		−	0.997761i
$157$			5.51645i			0.440261i	0.975470	+	0.220130i	$0.0706483\pi$
$157$			5.51645i			0.440261i	−0.975470	+	0.220130i	$0.929352\pi$
$158$	−13.9810			−1.11227
$159$		−	14.2259i		−	1.12818i
$160$		0			0
$161$	1.43338			0.112967
$162$		−	11.1868i		−	0.878917i
$163$		−	0.405508i		−	0.0317618i	−0.999874	−	0.0158809i	$-0.994945\pi$
$163$		−	0.405508i		−	0.0317618i	0.999874	−	0.0158809i	$-0.00505526\pi$
$164$		−	9.91983i		−	0.774609i
$165$		0			0
$166$			12.9440i			1.00465i
$167$	−8.32816			−0.644452			−0.322226	−	0.946663i	$-0.604431\pi$
$167$	−8.32816			−0.644452			−0.322226	+	0.946663i	$0.604431\pi$
$168$	−3.73621			−0.288255
$169$	23.5540			1.81185
$170$		0			0
$171$		−	5.07070i		−	0.387766i
$172$			3.62527i			0.276424i
$173$	0.228679			0.0173862			0.00869309	−	0.999962i	$-0.497233\pi$
$173$	0.228679			0.0173862			0.00869309	+	0.999962i	$0.497233\pi$
$174$	−11.0541	+	1.00807i	−0.838006	+	0.0764218i
$175$		0			0
$176$			3.98479i			0.300365i
$177$		−	29.9805i		−	2.25347i
$178$	−1.82785			−0.137003
$179$	3.67983			0.275043			0.137522	−	0.990499i	$-0.456086\pi$
$179$	3.67983			0.275043			0.137522	+	0.990499i	$0.456086\pi$
$180$		0			0
$181$	11.3127			0.840865			0.420432	−	0.907324i	$-0.361878\pi$
$181$	11.3127			0.840865			0.420432	+	0.907324i	$0.361878\pi$
$182$		−	10.9592i		−	0.812348i
$183$	1.70637			0.126138
$184$		−	0.790774i		−	0.0582966i
$185$		0			0
$186$			6.69597i			0.490973i
$187$	−26.2525			−1.91978
$188$			1.35952i			0.0991529i
$189$		−	6.54372i		−	0.475985i
$190$		0			0
$191$		−	12.0807i		−	0.874126i	−0.899431	−	0.437063i	$-0.856019\pi$
$191$		−	12.0807i		−	0.874126i	0.899431	−	0.437063i	$-0.143981\pi$
$192$			2.06121i			0.148755i
$193$		−	6.91412i		−	0.497689i	−0.968543	−	0.248845i	$-0.919949\pi$
$193$		−	6.91412i		−	0.497689i	0.968543	−	0.248845i	$-0.0800508\pi$
$194$	17.0052			1.22090
$195$		0			0
$196$	3.71435			0.265311
$197$	22.5655			1.60772			0.803862	−	0.594816i	$-0.202775\pi$
$197$	22.5655			1.60772			0.803862	+	0.594816i	$0.202775\pi$
$198$	4.97529			0.353578
$199$	0.913186			0.0647341			0.0323670	−	0.999476i	$-0.489695\pi$
$199$	0.913186			0.0647341			0.0323670	+	0.999476i	$0.489695\pi$
$200$		0			0
$201$		−	6.04974i		−	0.426716i
$202$	−0.441652			−0.0310745
$203$	−9.72100	+	0.886504i	−0.682281	+	0.0622204i
$204$	−13.5796			−0.950764
$205$		0			0
$206$		−	4.91319i		−	0.342318i
$207$	−0.987337			−0.0686247
$208$	−6.04599			−0.419214
$209$	−16.1830			−1.11940
$210$		0			0
$211$		−	9.29108i		−	0.639624i	−0.947481	−	0.319812i	$-0.896380\pi$
$211$		−	9.29108i		−	0.639624i	0.947481	−	0.319812i	$-0.103620\pi$
$212$	−6.90172			−0.474012
$213$			25.3103i			1.73423i
$214$		−	12.2690i		−	0.838689i
$215$		0			0
$216$	−3.61006			−0.245633
$217$			5.88847i			0.399736i
$218$			7.44258i			0.504075i
$219$	12.9744			0.876728
$220$		0			0
$221$		−	39.8322i		−	2.67940i
$222$		−	0.943614i		−	0.0633312i
$223$	−16.2448			−1.08783			−0.543917	−	0.839139i	$-0.683059\pi$
$223$	−16.2448			−1.08783			−0.543917	+	0.839139i	$0.683059\pi$
$224$			1.81264i			0.121112i
$225$		0			0
$226$	5.57553			0.370879
$227$	−10.9474			−0.726608			−0.363304	−	0.931671i	$-0.618351\pi$
$227$	−10.9474			−0.726608			−0.363304	+	0.931671i	$0.618351\pi$
$228$	−8.37098			−0.554382
$229$		−	10.4971i		−	0.693671i	−0.937926	−	0.346835i	$-0.887256\pi$
$229$		−	10.4971i		−	0.693671i	0.937926	−	0.346835i	$-0.112744\pi$
$230$		0			0
$231$	14.8880			0.979560
$232$	0.489069	+	5.36291i	0.0321090	+	0.352092i
$233$	−8.59577			−0.563128			−0.281564	−	0.959542i	$-0.590853\pi$
$233$	−8.59577			−0.563128			−0.281564	+	0.959542i	$0.590853\pi$
$234$			7.54885i			0.493484i
$235$		0			0
$236$	−14.5451			−0.946806
$237$	28.8178			1.87192
$238$	−11.9420			−0.774085
$239$	−9.88624			−0.639488			−0.319744	−	0.947504i	$-0.603597\pi$
$239$	−9.88624			−0.639488			−0.319744	+	0.947504i	$0.603597\pi$
$240$		0			0
$241$	29.4241			1.89537			0.947687	−	0.319201i	$-0.103415\pi$
$241$	29.4241			1.89537			0.947687	+	0.319201i	$0.103415\pi$
$242$		−	4.87852i		−	0.313603i
$243$			12.2281i			0.784433i
$244$		−	0.827849i		−	0.0529976i
$245$		0			0
$246$			20.4468i			1.30364i
$247$		−	24.5540i		−	1.56233i
$248$	3.24857			0.206284
$249$		−	26.6802i		−	1.69079i
$250$		0			0
$251$		−	17.4824i		−	1.10348i	−0.834016	−	0.551740i	$-0.813964\pi$
$251$		−	17.4824i		−	1.10348i	0.834016	−	0.551740i	$-0.186036\pi$
$252$	2.26320			0.142568
$253$			3.15106i			0.198106i
$254$	−19.9877			−1.25414
$255$		0			0
$256$	1.00000			0.0625000
$257$	−13.5995			−0.848315			−0.424157	−	0.905588i	$-0.639430\pi$
$257$	−13.5995			−0.848315			−0.424157	+	0.905588i	$0.639430\pi$
$258$		−	7.47243i		−	0.465213i
$259$		−	0.829819i		−	0.0515625i
$260$		0			0
$261$	6.69597	−	0.610638i	0.414470	−	0.0377975i
$262$	−7.79367			−0.481495
$263$			12.0020i			0.740073i	0.929017	+	0.370037i	$0.120655\pi$
$263$			12.0020i			0.740073i	−0.929017	+	0.370037i	$0.879345\pi$
$264$		−	8.21347i		−	0.505504i
$265$		0			0
$266$	−7.36149			−0.451362
$267$	3.76757			0.230572
$268$	−2.93505			−0.179287
$269$		−	23.8980i		−	1.45709i	−0.685001	−	0.728543i	$-0.740198\pi$
$269$		−	23.8980i		−	1.45709i	0.685001	−	0.728543i	$-0.259802\pi$
$270$		0			0
$271$			29.6755i			1.80266i	0.433135	+	0.901329i	$0.357407\pi$
$271$			29.6755i			1.80266i	−0.433135	+	0.901329i	$0.642593\pi$
$272$			6.58819i			0.399468i
$273$			22.5891i			1.36716i
$274$	−2.49621			−0.150802
$275$		0			0
$276$			1.62995i			0.0981113i
$277$	−27.9018			−1.67646			−0.838228	−	0.545319i	$-0.816408\pi$
$277$	−27.9018			−1.67646			−0.838228	+	0.545319i	$0.816408\pi$
$278$			1.06027i			0.0635911i
$279$		−	4.05607i		−	0.242831i
$280$		0			0
$281$	6.50660			0.388151			0.194076	−	0.980987i	$-0.437829\pi$
$281$	6.50660			0.388151			0.194076	+	0.980987i	$0.437829\pi$
$282$		−	2.80224i		−	0.166871i
$283$	5.35774			0.318485			0.159242	−	0.987240i	$-0.449095\pi$
$283$	5.35774			0.318485			0.159242	+	0.987240i	$0.449095\pi$
$284$	12.2793			0.728645
$285$		0			0
$286$	24.0920			1.42459
$287$			17.9810i			1.06139i
$288$		−	1.24857i		−	0.0735727i
$289$	−26.4043			−1.55319
$290$		0			0
$291$	−35.0512			−2.05474
$292$		−	6.29456i		−	0.368361i
$293$		−	23.0670i		−	1.34759i	−0.738919	−	0.673795i	$-0.764663\pi$
$293$		−	23.0670i		−	1.34759i	0.738919	−	0.673795i	$-0.235337\pi$
$294$	−7.65605			−0.446510
$295$		0			0
$296$	−0.457797			−0.0266089
$297$	14.3853			0.834720
$298$			15.1925i			0.880080i
$299$	−4.78101			−0.276493
$300$		0			0
$301$		−	6.57129i		−	0.378763i
$302$		−	21.5299i		−	1.23891i
$303$	0.910336			0.0522974
$304$			4.06121i			0.232926i
$305$		0			0
$306$	8.22583			0.470239
$307$		−	5.37487i		−	0.306760i	−0.988167	−	0.153380i	$-0.950984\pi$
$307$		−	5.37487i		−	0.306760i	0.988167	−	0.153380i	$-0.0490159\pi$
$308$		−	7.22296i		−	0.411567i
$309$			10.1271i			0.576110i
$310$		0			0
$311$		−	24.5568i		−	1.39249i	−0.717804	−	0.696245i	$-0.754853\pi$
$311$		−	24.5568i		−	1.39249i	0.717804	−	0.696245i	$-0.245147\pi$
$312$	12.4620			0.705524
$313$	5.03998			0.284876			0.142438	−	0.989804i	$-0.454506\pi$
$313$	5.03998			0.284876			0.142438	+	0.989804i	$0.454506\pi$
$314$	−5.51645			−0.311311
$315$		0			0
$316$		−	13.9810i		−	0.786495i
$317$			15.6531i			0.879168i	0.898201	+	0.439584i	$0.144874\pi$
$317$			15.6531i			0.879168i	−0.898201	+	0.439584i	$0.855126\pi$
$318$	14.2259			0.797747
$319$	−1.94884	−	21.3701i	−0.109114	−	1.19649i
$320$		0			0
$321$			25.2888i			1.41149i
$322$			1.43338i			0.0798794i
$323$	−26.7560			−1.48874
$324$	11.1868			0.621488
$325$		0			0
$326$	0.405508			0.0224590
$327$		−	15.3407i		−	0.848343i
$328$	9.91983			0.547731
$329$		−	2.46431i		−	0.135862i
$330$		0			0
$331$			24.3980i			1.34104i	0.741893	+	0.670518i	$0.233928\pi$
$331$			24.3980i			1.34104i	−0.741893	+	0.670518i	$0.766072\pi$
$332$	−12.9440			−0.710392
$333$			0.571592i			0.0313231i
$334$		−	8.32816i		−	0.455696i
$335$		0			0
$336$		−	3.73621i		−	0.203827i
$337$		−	27.8083i		−	1.51482i	−0.652942	−	0.757408i	$-0.726466\pi$
$337$		−	27.8083i		−	1.51482i	0.652942	−	0.757408i	$-0.273534\pi$
$338$			23.5540i			1.28117i
$339$	−11.4923			−0.624177
$340$		0			0
$341$	−12.9449			−0.701003
$342$	5.07070			0.274192
$343$	−19.4212			−1.04865
$344$	−3.62527			−0.195461
$345$		0			0
$346$			0.228679i			0.0122939i
$347$	18.6476			1.00106			0.500528	−	0.865720i	$-0.333139\pi$
$347$	18.6476			1.00106			0.500528	+	0.865720i	$0.333139\pi$
$348$	−1.00807	−	11.0541i	−0.0540384	−	0.592560i
$349$	0.948292			0.0507609			0.0253804	−	0.999678i	$-0.491920\pi$
$349$	0.948292			0.0507609			0.0253804	+	0.999678i	$0.491920\pi$
$350$		0			0
$351$			21.8264i			1.16501i
$352$	−3.98479			−0.212390
$353$	32.9307			1.75273			0.876363	−	0.481652i	$-0.159963\pi$
$353$	32.9307			1.75273			0.876363	+	0.481652i	$0.159963\pi$
$354$	29.9805			1.59344
$355$		0			0
$356$		−	1.82785i		−	0.0968758i
$357$	24.6149			1.30276
$358$			3.67983i			0.194485i
$359$		−	3.45249i		−	0.182215i	−0.995841	−	0.0911077i	$-0.970959\pi$
$359$		−	3.45249i		−	0.182215i	0.995841	−	0.0911077i	$-0.0290407\pi$
$360$		0			0
$361$	2.50660			0.131927
$362$			11.3127i			0.594581i
$363$			10.0556i			0.527784i
$364$	10.9592			0.574417
$365$		0			0
$366$			1.70637i			0.0891933i
$367$		−	4.04626i		−	0.211213i	−0.994408	−	0.105606i	$-0.966322\pi$
$367$		−	4.04626i		−	0.211213i	0.994408	−	0.105606i	$-0.0336784\pi$
$368$	0.790774			0.0412219
$369$		−	12.3856i		−	0.644769i
$370$		0			0
$371$	12.5103			0.649502
$372$	−6.69597			−0.347170
$373$	−16.3349			−0.845791			−0.422896	−	0.906178i	$-0.638986\pi$
$373$	−16.3349			−0.845791			−0.422896	+	0.906178i	$0.638986\pi$
$374$		−	26.2525i		−	1.35749i
$375$		0			0
$376$	−1.35952			−0.0701117
$377$	32.4241	−	2.95691i	1.66993	−	0.152289i
$378$	6.54372			0.336572
$379$			19.4342i			0.998266i	0.866525	+	0.499133i	$0.166348\pi$
$379$			19.4342i			0.998266i	−0.866525	+	0.499133i	$0.833652\pi$
$380$		0			0
$381$	41.1987			2.11068
$382$	12.0807			0.618100
$383$	17.2920			0.883581			0.441790	−	0.897118i	$-0.354344\pi$
$383$	17.2920			0.883581			0.441790	+	0.897118i	$0.354344\pi$
$384$	−2.06121			−0.105185
$385$		0			0
$386$	6.91412			0.351919
$387$			4.52641i			0.230090i
$388$			17.0052i			0.863307i
$389$			9.97849i			0.505929i	0.967476	+	0.252965i	$0.0814057\pi$
$389$			9.97849i			0.505929i	−0.967476	+	0.252965i	$0.918594\pi$
$390$		0			0
$391$			5.20977i			0.263469i
$392$			3.71435i			0.187603i
$393$	16.0644			0.810340
$394$			22.5655i			1.13683i
$395$		0			0
$396$			4.97529i			0.250018i
$397$	−24.2046			−1.21480			−0.607398	−	0.794398i	$-0.707787\pi$
$397$	−24.2046			−1.21480			−0.607398	+	0.794398i	$0.707787\pi$
$398$			0.913186i			0.0457739i
$399$	15.1735			0.759627
$400$		0			0
$401$	−32.7582			−1.63586			−0.817932	−	0.575315i	$-0.804880\pi$
$401$	−32.7582			−1.63586			−0.817932	+	0.575315i	$0.804880\pi$
$402$	6.04974			0.301734
$403$		−	19.6408i		−	0.978380i
$404$		−	0.441652i		−	0.0219730i
$405$		0			0
$406$	−0.886504	−	9.72100i	−0.0439965	−	0.482445i
$407$	1.82422			0.0904234
$408$		−	13.5796i		−	0.672292i
$409$		−	3.80251i		−	0.188022i	−0.995571	−	0.0940109i	$-0.970031\pi$
$409$		−	3.80251i		−	0.188022i	0.995571	−	0.0940109i	$-0.0299689\pi$
$410$		0			0
$411$	5.14521			0.253794
$412$	4.91319			0.242055
$413$	26.3650			1.29734
$414$		−	0.987337i		−	0.0485250i
$415$		0			0
$416$		−	6.04599i		−	0.296429i
$417$		−	2.18545i		−	0.107022i
$418$		−	16.1830i		−	0.791538i
$419$	36.1039			1.76379			0.881897	−	0.471443i	$-0.156267\pi$
$419$	36.1039			1.76379			0.881897	+	0.471443i	$0.156267\pi$
$420$		0			0
$421$		−	17.1854i		−	0.837567i	−0.908086	−	0.418784i	$-0.862457\pi$
$421$		−	17.1854i		−	0.837567i	0.908086	−	0.418784i	$-0.137543\pi$
$422$	9.29108			0.452283
$423$			1.69745i			0.0825329i
$424$		−	6.90172i		−	0.335177i
$425$		0			0
$426$	−25.3103			−1.22629
$427$			1.50059i			0.0726186i
$428$	12.2690			0.593042
$429$	−49.6585			−2.39754
$430$		0			0
$431$	17.4700			0.841501			0.420751	−	0.907176i	$-0.361767\pi$
$431$	17.4700			0.841501			0.420751	+	0.907176i	$0.361767\pi$
$432$		−	3.61006i		−	0.173689i
$433$			32.0734i			1.54135i	0.637230	+	0.770674i	$0.280080\pi$
$433$			32.0734i			1.54135i	−0.637230	+	0.770674i	$0.719920\pi$
$434$	−5.88847			−0.282656
$435$		0			0
$436$	−7.44258			−0.356435
$437$			3.21150i			0.153627i
$438$			12.9744i			0.619940i
$439$	−19.7730			−0.943714			−0.471857	−	0.881675i	$-0.656416\pi$
$439$	−19.7730			−0.943714			−0.471857	+	0.881675i	$0.656416\pi$
$440$		0			0
$441$	4.63763			0.220840
$442$	39.8322			1.89462
$443$			6.34238i			0.301336i	0.988584	+	0.150668i	$0.0481424\pi$
$443$			6.34238i			0.301336i	−0.988584	+	0.150668i	$0.951858\pi$
$444$	0.943614			0.0447820
$445$		0			0
$446$		−	16.2448i		−	0.769215i
$447$		−	31.3149i		−	1.48115i
$448$	−1.81264			−0.0856390
$449$			20.3567i			0.960690i	0.877080	+	0.480345i	$0.159489\pi$
$449$			20.3567i			0.960690i	−0.877080	+	0.480345i	$0.840511\pi$
$450$		0			0
$451$	−39.5284			−1.86132
$452$			5.57553i			0.262251i
$453$			44.3775i			2.08504i
$454$		−	10.9474i		−	0.513789i
$455$		0			0
$456$		−	8.37098i		−	0.392007i
$457$	31.7313			1.48433			0.742165	−	0.670217i	$-0.233799\pi$
$457$	31.7313			1.48433			0.742165	+	0.670217i	$0.233799\pi$
$458$	10.4971			0.490499
$459$	23.7838			1.11013
$460$		0			0
$461$		−	25.7477i		−	1.19919i	−0.800304	−	0.599595i	$-0.795329\pi$
$461$		−	25.7477i		−	1.19919i	0.800304	−	0.599595i	$-0.204671\pi$
$462$			14.8880i			0.692653i
$463$	−27.4355			−1.27504			−0.637518	−	0.770436i	$-0.720039\pi$
$463$	−27.4355			−1.27504			−0.637518	+	0.770436i	$0.720039\pi$
$464$	−5.36291	+	0.489069i	−0.248967	+	0.0227045i
$465$		0			0
$466$		−	8.59577i		−	0.398192i
$467$			17.9948i			0.832699i	0.909205	+	0.416349i	$0.136691\pi$
$467$			17.9948i			0.832699i	−0.909205	+	0.416349i	$0.863309\pi$
$468$	−7.54885			−0.348946
$469$	5.32017			0.245663
$470$		0			0
$471$	11.3705			0.523927
$472$		−	14.5451i		−	0.669493i
$473$	14.4459			0.664224
$474$			28.8178i			1.32365i
$475$		0			0
$476$		−	11.9420i		−	0.547360i
$477$	−8.61729			−0.394558
$478$		−	9.88624i		−	0.452186i
$479$		−	25.0189i		−	1.14314i	−0.820553	−	0.571571i	$-0.806334\pi$
$479$		−	25.0189i		−	1.14314i	0.820553	−	0.571571i	$-0.193666\pi$
$480$		0			0
$481$			2.76784i			0.126203i
$482$			29.4241i			1.34023i
$483$		−	2.95450i		−	0.134434i
$484$	4.87852			0.221751
$485$		0			0
$486$	−12.2281			−0.554678
$487$	−25.8793			−1.17270			−0.586351	−	0.810057i	$-0.699436\pi$
$487$	−25.8793			−1.17270			−0.586351	+	0.810057i	$0.699436\pi$
$488$	0.827849			0.0374750
$489$	−0.835835			−0.0377978
$490$		0			0
$491$		−	16.9849i		−	0.766519i	−0.923641	−	0.383260i	$-0.874801\pi$
$491$		−	16.9849i		−	0.766519i	0.923641	−	0.383260i	$-0.125199\pi$
$492$	−20.4468			−0.921814
$493$	−3.22208	−	35.3319i	−0.145115	−	1.59127i
$494$	24.5540			1.10474
$495$		0			0
$496$			3.24857i			0.145865i
$497$	−22.2580			−0.998407
$498$	26.6802			1.19557
$499$	15.2508			0.682721			0.341361	−	0.939932i	$-0.389112\pi$
$499$	15.2508			0.682721			0.341361	+	0.939932i	$0.389112\pi$
$500$		0			0
$501$			17.1660i			0.766922i
$502$	17.4824			0.780279
$503$			13.4194i			0.598341i	0.954200	+	0.299170i	$0.0967099\pi$
$503$			13.4194i			0.598341i	−0.954200	+	0.299170i	$0.903290\pi$
$504$			2.26320i			0.100811i
$505$		0			0
$506$	−3.15106			−0.140082
$507$		−	48.5497i		−	2.15617i
$508$		−	19.9877i		−	0.886810i
$509$	9.86330			0.437183			0.218592	−	0.975816i	$-0.429854\pi$
$509$	9.86330			0.437183			0.218592	+	0.975816i	$0.429854\pi$
$510$		0			0
$511$			11.4097i			0.504737i
$512$			1.00000i			0.0441942i
$513$	14.6612			0.647307
$514$		−	13.5995i		−	0.599849i
$515$		0			0
$516$	7.47243			0.328955
$517$	5.41738			0.238256
$518$	0.829819			0.0364602
$519$		−	0.471356i		−	0.0206902i
$520$		0			0
$521$	33.7809			1.47997			0.739983	−	0.672625i	$-0.234833\pi$
$521$	33.7809			1.47997			0.739983	+	0.672625i	$0.234833\pi$
$522$	0.610638	+	6.69597i	0.0267269	+	0.293075i
$523$	−3.25856			−0.142487			−0.0712435	−	0.997459i	$-0.522697\pi$
$523$	−3.25856			−0.142487			−0.0712435	+	0.997459i	$0.522697\pi$
$524$		−	7.79367i		−	0.340468i
$525$		0			0
$526$	−12.0020			−0.523311
$527$	−21.4022			−0.932295
$528$	8.21347			0.357445
$529$	−22.3747			−0.972812
$530$		0			0
$531$	−18.1606			−0.788103
$532$		−	7.36149i		−	0.319161i
$533$		−	59.9752i		−	2.59782i
$534$			3.76757i			0.163039i
$535$		0			0
$536$		−	2.93505i		−	0.126775i
$537$		−	7.58489i		−	0.327312i
$538$	23.8980			1.03031
$539$		−	14.8009i		−	0.637520i
$540$		0			0
$541$			16.1807i			0.695663i	0.937557	+	0.347832i	$0.113082\pi$
$541$			16.1807i			0.695663i	−0.937557	+	0.347832i	$0.886918\pi$
$542$	−29.6755			−1.27467
$543$		−	23.3178i		−	1.00066i
$544$	−6.58819			−0.282467
$545$		0			0
$546$	−22.5891			−0.966725
$547$	−32.4375			−1.38693			−0.693463	−	0.720492i	$-0.743916\pi$
$547$	−32.4375			−1.38693			−0.693463	+	0.720492i	$0.743916\pi$
$548$		−	2.49621i		−	0.106633i
$549$		−	1.03363i		−	0.0441142i
$550$		0			0
$551$	−1.98621	−	21.7799i	−0.0846154	−	0.927854i
$552$	−1.62995			−0.0693752
$553$			25.3425i			1.07767i
$554$		−	27.9018i		−	1.18543i
$555$		0			0
$556$	−1.06027			−0.0449657
$557$	14.0969			0.597305			0.298653	−	0.954362i	$-0.403463\pi$
$557$	14.0969			0.597305			0.298653	+	0.954362i	$0.403463\pi$
$558$	4.05607			0.171707
$559$			21.9184i			0.927048i
$560$		0			0
$561$			54.1119i			2.28461i
$562$			6.50660i			0.274465i
$563$			17.4516i			0.735499i	0.929925	+	0.367750i	$0.119872\pi$
$563$			17.4516i			0.735499i	−0.929925	+	0.367750i	$0.880128\pi$
$564$	2.80224			0.117996
$565$		0			0
$566$			5.35774i			0.225203i
$567$	−20.2776			−0.851577
$568$			12.2793i			0.515230i
$569$		−	37.3824i		−	1.56715i	−0.621297	−	0.783575i	$-0.713394\pi$
$569$		−	37.3824i		−	1.56715i	0.621297	−	0.783575i	$-0.286606\pi$
$570$		0			0
$571$	−30.3687			−1.27089			−0.635444	−	0.772147i	$-0.719183\pi$
$571$	−30.3687			−1.27089			−0.635444	+	0.772147i	$0.719183\pi$
$572$			24.0920i			1.00734i
$573$	−24.9007			−1.04024
$574$	−17.9810			−0.750514
$575$		0			0
$576$	1.24857			0.0520238
$577$			29.9814i			1.24814i	0.781368	+	0.624071i	$0.214522\pi$
$577$			29.9814i			1.24814i	−0.781368	+	0.624071i	$0.785478\pi$
$578$		−	26.4043i		−	1.09827i
$579$	−14.2514			−0.592269
$580$		0			0
$581$	23.4627			0.973396
$582$		−	35.0512i		−	1.45292i
$583$			27.5019i			1.13901i
$584$	6.29456			0.260471
$585$		0			0
$586$	23.0670			0.952889
$587$	15.1335			0.624625			0.312313	−	0.949979i	$-0.398896\pi$
$587$	15.1335			0.624625			0.312313	+	0.949979i	$0.398896\pi$
$588$		−	7.65605i		−	0.315730i
$589$	−13.1931			−0.543613
$590$		0			0
$591$		−	46.5121i		−	1.91325i
$592$		−	0.457797i		−	0.0188153i
$593$	−46.5827			−1.91292			−0.956461	−	0.291862i	$-0.905725\pi$
$593$	−46.5827			−1.91292			−0.956461	+	0.291862i	$0.905725\pi$
$594$			14.3853i			0.590236i
$595$		0			0
$596$	−15.1925			−0.622310
$597$		−	1.88227i		−	0.0770360i
$598$		−	4.78101i		−	0.195510i
$599$			22.1841i			0.906418i	0.891404	+	0.453209i	$0.149721\pi$
$599$			22.1841i			0.906418i	−0.891404	+	0.453209i	$0.850279\pi$
$600$		0			0
$601$			23.6670i			0.965396i	0.875787	+	0.482698i	$0.160343\pi$
$601$			23.6670i			0.965396i	−0.875787	+	0.482698i	$0.839657\pi$
$602$	6.57129			0.267826
$603$	−3.66462			−0.149235
$604$	21.5299			0.876039
$605$		0			0
$606$			0.910336i			0.0369799i
$607$			22.3900i			0.908782i	0.890802	+	0.454391i	$0.150143\pi$
$607$			22.3900i			0.908782i	−0.890802	+	0.454391i	$0.849857\pi$
$608$	−4.06121			−0.164704
$609$	1.82727	+	20.0370i	0.0740446	+	0.811940i
$610$		0			0
$611$			8.21962i			0.332530i
$612$			8.22583i			0.332509i
$613$	−13.2534			−0.535299			−0.267650	−	0.963516i	$-0.586247\pi$
$613$	−13.2534			−0.535299			−0.267650	+	0.963516i	$0.586247\pi$
$614$	5.37487			0.216912
$615$		0			0
$616$	7.22296			0.291021
$617$			44.5005i			1.79152i	0.444534	+	0.895762i	$0.353369\pi$
$617$			44.5005i			1.79152i	−0.444534	+	0.895762i	$0.646631\pi$
$618$	−10.1271			−0.407371
$619$			6.42113i			0.258087i	0.991639	+	0.129043i	$0.0411907\pi$
$619$			6.42113i			0.258087i	−0.991639	+	0.129043i	$0.958809\pi$
$620$		0			0
$621$		−	2.85474i		−	0.114557i
$622$	24.5568			0.984639
$623$			3.31322i			0.132742i
$624$			12.4620i			0.498881i
$625$		0			0
$626$			5.03998i			0.201438i
$627$			33.3566i			1.33213i
$628$		−	5.51645i		−	0.220130i
$629$	3.01606			0.120258
$630$		0			0
$631$	34.5259			1.37445			0.687227	−	0.726443i	$-0.258828\pi$
$631$	34.5259			1.37445			0.687227	+	0.726443i	$0.258828\pi$
$632$	13.9810			0.556136
$633$	−19.1508			−0.761177
$634$	−15.6531			−0.621666
$635$		0			0
$636$			14.2259i			0.564092i
$637$	22.4570			0.889777
$638$	21.3701	−	1.94884i	0.846048	−	0.0771552i
$639$	15.3316			0.606510
$640$		0			0
$641$			30.0242i			1.18588i	0.805245	+	0.592942i	$0.202034\pi$
$641$			30.0242i			1.18588i	−0.805245	+	0.592942i	$0.797966\pi$
$642$	−25.2888			−0.998071
$643$	49.1853			1.93968			0.969840	−	0.243744i	$-0.0783757\pi$
$643$	49.1853			1.93968			0.969840	+	0.243744i	$0.0783757\pi$
$644$	−1.43338			−0.0564833
$645$		0			0
$646$		−	26.7560i		−	1.05270i
$647$	47.2903			1.85917			0.929587	−	0.368602i	$-0.120164\pi$
$647$	47.2903			1.85917			0.929587	+	0.368602i	$0.120164\pi$
$648$			11.1868i			0.439458i
$649$			57.9591i			2.27509i
$650$		0			0
$651$	12.1374			0.475701
$652$			0.405508i			0.0158809i
$653$		−	22.2215i		−	0.869594i	−0.900529	−	0.434797i	$-0.856820\pi$
$653$		−	22.2215i		−	0.869594i	0.900529	−	0.434797i	$-0.143180\pi$
$654$	15.3407			0.599869
$655$		0			0
$656$			9.91983i			0.387304i
$657$		−	7.85921i		−	0.306617i
$658$	2.46431			0.0960686
$659$			36.6261i			1.42675i	0.700782	+	0.713375i	$0.252835\pi$
$659$			36.6261i			1.42675i	−0.700782	+	0.713375i	$0.747165\pi$
$660$		0			0
$661$	21.5507			0.838226			0.419113	−	0.907934i	$-0.362341\pi$
$661$	21.5507			0.838226			0.419113	+	0.907934i	$0.362341\pi$
$662$	−24.3980			−0.948256
$663$	−82.1023			−3.18859
$664$		−	12.9440i		−	0.502323i
$665$		0			0
$666$	−0.571592			−0.0221487
$667$	−4.24085	+	0.386743i	−0.164206	+	0.0149748i
$668$	8.32816			0.322226
$669$			33.4839i			1.29456i
$670$		0			0
$671$	−3.29880			−0.127349
$672$	3.73621			0.144128
$673$	−19.8560			−0.765391			−0.382695	−	0.923875i	$-0.625004\pi$
$673$	−19.8560			−0.765391			−0.382695	+	0.923875i	$0.625004\pi$
$674$	27.8083			1.07114
$675$		0			0
$676$	−23.5540			−0.905924
$677$			5.42633i			0.208551i	0.994548	+	0.104275i	$0.0332523\pi$
$677$			5.42633i			0.208551i	−0.994548	+	0.104275i	$0.966748\pi$
$678$		−	11.4923i		−	0.441360i
$679$		−	30.8242i		−	1.18292i
$680$		0			0
$681$			22.5649i			0.864691i
$682$		−	12.9449i		−	0.495684i
$683$	−31.2809			−1.19693			−0.598465	−	0.801149i	$-0.704223\pi$
$683$	−31.2809			−1.19693			−0.598465	+	0.801149i	$0.704223\pi$
$684$			5.07070i			0.193883i
$685$		0			0
$686$		−	19.4212i		−	0.741505i
$687$	−21.6368			−0.825494
$688$		−	3.62527i		−	0.138212i
$689$	−41.7277			−1.58970
$690$		0			0
$691$	−25.0367			−0.952440			−0.476220	−	0.879326i	$-0.657993\pi$
$691$	−25.0367			−0.952440			−0.476220	+	0.879326i	$0.657993\pi$
$692$	−0.228679			−0.00869309
$693$		−	9.01838i		−	0.342580i
$694$			18.6476i			0.707854i
$695$		0			0
$696$	11.0541	−	1.00807i	0.419003	−	0.0382109i
$697$	−65.3538			−2.47545
$698$			0.948292i			0.0358934i
$699$			17.7177i			0.670144i
$700$		0			0
$701$	−5.20003			−0.196402			−0.0982012	−	0.995167i	$-0.531309\pi$
$701$	−5.20003			−0.196402			−0.0982012	+	0.995167i	$0.531309\pi$
$702$	−21.8264			−0.823783
$703$	1.85921			0.0701214
$704$		−	3.98479i		−	0.150182i
$705$		0			0
$706$			32.9307i			1.23936i
$707$			0.800554i			0.0301079i
$708$			29.9805i			1.12673i
$709$	14.5305			0.545705			0.272853	−	0.962056i	$-0.412033\pi$
$709$	14.5305			0.545705			0.272853	+	0.962056i	$0.412033\pi$
$710$		0			0
$711$		−	17.4563i		−	0.654663i
$712$	1.82785			0.0685015
$713$			2.56888i			0.0962055i
$714$			24.6149i			0.921190i
$715$		0			0
$716$	−3.67983			−0.137522
$717$			20.3776i			0.761015i
$718$	3.45249			0.128846
$719$	0.980547			0.0365682			0.0182841	−	0.999833i	$-0.494180\pi$
$719$	0.980547			0.0365682			0.0182841	+	0.999833i	$0.494180\pi$
$720$		0			0
$721$	−8.90581			−0.331670
$722$			2.50660i			0.0932862i
$723$		−	60.6492i		−	2.25557i
$724$	−11.3127			−0.420432
$725$		0			0
$726$	−10.0556			−0.373200
$727$		−	34.7322i		−	1.28815i	−0.764964	−	0.644073i	$-0.777243\pi$
$727$		−	34.7322i		−	1.28815i	0.764964	−	0.644073i	$-0.222757\pi$
$728$			10.9592i			0.406174i
$729$	−8.35572			−0.309471
$730$		0			0
$731$	23.8840			0.883381
$732$	−1.70637			−0.0630692
$733$		−	32.4220i		−	1.19753i	−0.800923	−	0.598767i	$-0.795658\pi$
$733$		−	32.4220i		−	1.19753i	0.800923	−	0.598767i	$-0.204342\pi$
$734$	4.04626			0.149350
$735$		0			0
$736$			0.790774i			0.0291483i
$737$			11.6955i			0.430811i
$738$	12.3856			0.455921
$739$			14.0862i			0.518169i	0.965855	+	0.259084i	$0.0834207\pi$
$739$			14.0862i			0.518169i	−0.965855	+	0.259084i	$0.916579\pi$
$740$		0			0
$741$	−50.6109			−1.85924
$742$			12.5103i			0.459267i
$743$		−	1.67635i		−	0.0614992i	−0.999527	−	0.0307496i	$-0.990211\pi$
$743$		−	1.67635i		−	0.0614992i	0.999527	−	0.0307496i	$-0.00978944\pi$
$744$		−	6.69597i		−	0.245486i
$745$		0			0
$746$		−	16.3349i		−	0.598065i
$747$	−16.1615			−0.591317
$748$	26.2525			0.959888
$749$	−22.2391			−0.812601
$750$		0			0
$751$			22.4079i			0.817675i	0.912607	+	0.408837i	$0.134066\pi$
$751$			22.4079i			0.817675i	−0.912607	+	0.408837i	$0.865934\pi$
$752$		−	1.35952i		−	0.0495764i
$753$	−36.0349			−1.31318
$754$	2.95691	+	32.4241i	0.107684	+	1.18082i
$755$		0			0
$756$			6.54372i			0.237993i
$757$			24.5949i			0.893918i	0.894554	+	0.446959i	$0.147493\pi$
$757$			24.5949i			0.893918i	−0.894554	+	0.446959i	$0.852507\pi$
$758$	−19.4342			−0.705880
$759$	6.49499			0.235753
$760$		0			0
$761$	−1.78622			−0.0647503			−0.0323752	−	0.999476i	$-0.510307\pi$
$761$	−1.78622			−0.0647503			−0.0323752	+	0.999476i	$0.510307\pi$
$762$			41.1987i			1.49247i
$763$	13.4907			0.488396
$764$			12.0807i			0.437063i
$765$		0			0
$766$			17.2920i			0.624786i
$767$	−87.9396			−3.17531
$768$		−	2.06121i		−	0.0743774i
$769$			53.0836i			1.91424i	0.289684	+	0.957122i	$0.406450\pi$
$769$			53.0836i			1.91424i	−0.289684	+	0.957122i	$0.593550\pi$
$770$		0			0
$771$			28.0314i			1.00953i
$772$			6.91412i			0.248845i
$773$		−	18.4313i		−	0.662929i	−0.943468	−	0.331465i	$-0.892457\pi$
$773$		−	18.4313i		−	0.662929i	0.943468	−	0.331465i	$-0.107543\pi$
$774$	−4.52641			−0.162698
$775$		0			0
$776$	−17.0052			−0.610450
$777$	−1.71043			−0.0613613
$778$	−9.97849			−0.357746
$779$	−40.2865			−1.44341
$780$		0			0
$781$		−	48.9306i		−	1.75087i
$782$	−5.20977			−0.186301
$783$	1.76557	+	19.3604i	0.0630962	+	0.691885i
$784$	−3.71435			−0.132655
$785$		0			0
$786$			16.0644i			0.572997i
$787$	18.3836			0.655306			0.327653	−	0.944798i	$-0.393742\pi$
$787$	18.3836			0.655306			0.327653	+	0.944798i	$0.393742\pi$
$788$	−22.5655			−0.803862
$789$	24.7385			0.880715
$790$		0			0
$791$		−	10.1064i		−	0.359342i
$792$	−4.97529			−0.176789
$793$		−	5.00517i		−	0.177739i
$794$		−	24.2046i		−	0.858990i
$795$		0			0
$796$	−0.913186			−0.0323670
$797$		−	37.9592i		−	1.34458i	−0.740286	−	0.672292i	$-0.765310\pi$
$797$		−	37.9592i		−	1.34458i	0.740286	−	0.672292i	$-0.234690\pi$
$798$			15.1735i			0.537137i
$799$	8.95675			0.316867
$800$		0			0
$801$		−	2.28220i		−	0.0806376i
$802$		−	32.7582i		−	1.15673i
$803$	−25.0825			−0.885142
$804$			6.04974i			0.213358i
$805$		0			0
$806$	19.6408			0.691819
$807$	−49.2586			−1.73399
$808$	0.441652			0.0155373
$809$			14.3208i			0.503494i	0.967793	+	0.251747i	$0.0810051\pi$
$809$			14.3208i			0.503494i	−0.967793	+	0.251747i	$0.918995\pi$
$810$		0			0
$811$	16.1010			0.565384			0.282692	−	0.959211i	$-0.408773\pi$
$811$	16.1010			0.565384			0.282692	+	0.959211i	$0.408773\pi$
$812$	9.72100	−	0.886504i	0.341140	−	0.0311102i
$813$	61.1673			2.14523
$814$			1.82422i			0.0639390i
$815$		0			0
$816$	13.5796			0.475382
$817$	14.7230			0.515092
$818$	3.80251			0.132951
$819$	13.6833			0.478134
$820$		0			0
$821$	38.1172			1.33030			0.665150	−	0.746710i	$-0.268368\pi$
$821$	38.1172			1.33030			0.665150	+	0.746710i	$0.268368\pi$
$822$			5.14521i			0.179460i
$823$		−	28.6149i		−	0.997452i	−0.866760	−	0.498726i	$-0.833801\pi$
$823$		−	28.6149i		−	0.997452i	0.866760	−	0.498726i	$-0.166199\pi$
$824$			4.91319i			0.171159i
$825$		0			0
$826$			26.3650i			0.917355i
$827$		−	14.3083i		−	0.497548i	−0.968562	−	0.248774i	$-0.919972\pi$
$827$		−	14.3083i		−	0.497548i	0.968562	−	0.248774i	$-0.0800277\pi$
$828$	0.987337			0.0343123
$829$		−	6.46207i		−	0.224437i	−0.993684	−	0.112219i	$-0.964204\pi$
$829$		−	6.46207i		−	0.224437i	0.993684	−	0.112219i	$-0.0357957\pi$
$830$		0			0
$831$			57.5114i			1.99505i
$832$	6.04599			0.209607
$833$		−	24.4709i		−	0.847866i
$834$	2.18545			0.0756758
$835$		0			0
$836$	16.1830			0.559702
$837$	11.7275			0.405363
$838$			36.1039i			1.24719i
$839$		−	46.6896i		−	1.61190i	−0.591980	−	0.805952i	$-0.701654\pi$
$839$		−	46.6896i		−	1.61190i	0.591980	−	0.805952i	$-0.298346\pi$
$840$		0			0
$841$	28.5216	−	5.24567i	0.983504	−	0.180885i
$842$	17.1854			0.592250
$843$		−	13.4115i		−	0.461915i
$844$			9.29108i			0.319812i
$845$		0			0
$846$	−1.69745			−0.0583596
$847$	−8.84298			−0.303848
$848$	6.90172			0.237006
$849$		−	11.0434i		−	0.379009i
$850$		0			0
$851$		−	0.362014i		−	0.0124097i
$852$		−	25.3103i		−	0.867116i
$853$		−	34.3614i		−	1.17651i	−0.808674	−	0.588257i	$-0.799815\pi$
$853$		−	34.3614i		−	1.17651i	0.808674	−	0.588257i	$-0.200185\pi$
$854$	−1.50059			−0.0513491
$855$		0			0
$856$			12.2690i			0.419344i
$857$	42.0918			1.43783			0.718913	−	0.695100i	$-0.244640\pi$
$857$	42.0918			1.43783			0.718913	+	0.695100i	$0.244640\pi$
$858$		−	49.6585i		−	1.69531i
$859$		−	35.5332i		−	1.21238i	−0.795321	−	0.606189i	$-0.792697\pi$
$859$		−	35.5332i		−	1.21238i	0.795321	−	0.606189i	$-0.207303\pi$
$860$		0			0
$861$	37.0626			1.26309
$862$			17.4700i			0.595031i
$863$	−4.81185			−0.163797			−0.0818986	−	0.996641i	$-0.526098\pi$
$863$	−4.81185			−0.163797			−0.0818986	+	0.996641i	$0.526098\pi$
$864$	3.61006			0.122817
$865$		0			0
$866$	−32.0734			−1.08990
$867$			54.4247i			1.84836i
$868$		−	5.88847i		−	0.199868i
$869$	−55.7115			−1.88988
$870$		0			0
$871$	−17.7453			−0.601276
$872$		−	7.44258i		−	0.252038i
$873$			21.2322i			0.718600i
$874$	−3.21150			−0.108630
$875$		0			0
$876$	−12.9744			−0.438364
$877$	50.3310			1.69956			0.849779	−	0.527140i	$-0.176736\pi$
$877$	50.3310			1.69956			0.849779	+	0.527140i	$0.176736\pi$
$878$		−	19.7730i		−	0.667307i
$879$	−47.5459			−1.60368
$880$		0			0
$881$		−	28.4344i		−	0.957980i	−0.877820	−	0.478990i	$-0.841003\pi$
$881$		−	28.4344i		−	0.957980i	0.877820	−	0.478990i	$-0.158997\pi$
$882$			4.63763i			0.156157i
$883$	2.61607			0.0880378			0.0440189	−	0.999031i	$-0.485984\pi$
$883$	2.61607			0.0880378			0.0440189	+	0.999031i	$0.485984\pi$
$884$			39.8322i			1.33970i
$885$		0			0
$886$	−6.34238			−0.213076
$887$		−	33.6082i		−	1.12845i	−0.825620	−	0.564226i	$-0.809175\pi$
$887$		−	33.6082i		−	1.12845i	0.825620	−	0.564226i	$-0.190825\pi$
$888$			0.943614i			0.0316656i
$889$			36.2304i			1.21513i
$890$		0			0
$891$		−	44.5769i		−	1.49338i
$892$	16.2448			0.543917
$893$	5.52127			0.184762
$894$	31.3149			1.04733
$895$		0			0
$896$		−	1.81264i		−	0.0605559i
$897$			9.85465i			0.329037i
$898$	−20.3567			−0.679311
$899$	−1.58878	−	17.4218i	−0.0529887	−	0.581049i
$900$		0			0
$901$			45.4699i			1.51482i
$902$		−	39.5284i		−	1.31615i
$903$	−13.5448			−0.450742
$904$	−5.57553			−0.185439
$905$		0			0
$906$	−44.3775			−1.47435
$907$			2.03270i			0.0674946i	0.999430	+	0.0337473i	$0.0107441\pi$
$907$			2.03270i			0.0674946i	−0.999430	+	0.0337473i	$0.989256\pi$
$908$	10.9474			0.363304
$909$		−	0.551434i		−	0.0182899i
$910$		0			0
$911$		−	24.8680i		−	0.823915i	−0.911203	−	0.411957i	$-0.864845\pi$
$911$		−	24.8680i		−	0.823915i	0.911203	−	0.411957i	$-0.135155\pi$
$912$	8.37098			0.277191
$913$			51.5789i			1.70701i
$914$			31.7313i			1.04958i
$915$		0			0
$916$			10.4971i			0.346835i
$917$			14.1271i			0.466518i
$918$			23.7838i			0.784981i
$919$	32.1144			1.05936			0.529678	−	0.848199i	$-0.322313\pi$
$919$	32.1144			1.05936			0.529678	+	0.848199i	$0.322313\pi$
$920$		0			0
$921$	−11.0787			−0.365056
$922$	25.7477			0.847955
$923$	74.2408			2.44367
$924$	−14.8880			−0.489780
$925$		0			0
$926$		−	27.4355i		−	0.901586i
$927$	6.13446			0.201482
$928$	−0.489069	−	5.36291i	−0.0160545	−	0.176046i
$929$	31.9987			1.04984			0.524922	−	0.851150i	$-0.324094\pi$
$929$	31.9987			1.04984			0.524922	+	0.851150i	$0.324094\pi$
$930$		0			0
$931$		−	15.0848i		−	0.494383i
$932$	8.59577			0.281564
$933$	−50.6167			−1.65712
$934$	−17.9948			−0.588807
$935$		0			0
$936$		−	7.54885i		−	0.246742i
$937$	31.1937			1.01906			0.509528	−	0.860454i	$-0.329820\pi$
$937$	31.1937			1.01906			0.509528	+	0.860454i	$0.329820\pi$
$938$			5.32017i			0.173710i
$939$		−	10.3884i		−	0.339014i
$940$		0			0
$941$	−38.1626			−1.24407			−0.622033	−	0.782991i	$-0.713693\pi$
$941$	−38.1626			−1.24407			−0.622033	+	0.782991i	$0.713693\pi$
$942$			11.3705i			0.370472i
$943$			7.84434i			0.255447i
$944$	14.5451			0.473403
$945$		0			0
$946$			14.4459i			0.469678i
$947$			15.5896i			0.506595i	0.967388	+	0.253297i	$0.0815151\pi$
$947$			15.5896i			0.506595i	−0.967388	+	0.253297i	$0.918485\pi$
$948$	−28.8178			−0.935959
$949$		−	38.0569i		−	1.23538i
$950$		0			0
$951$	32.2644			1.04624
$952$	11.9420			0.387042
$953$	−12.6670			−0.410325			−0.205163	−	0.978728i	$-0.565772\pi$
$953$	−12.6670			−0.410325			−0.205163	+	0.978728i	$0.565772\pi$
$954$		−	8.61729i		−	0.278995i
$955$		0			0
$956$	9.88624			0.319744
$957$	−44.0481	+	4.01695i	−1.42387	+	0.129850i
$958$	25.0189			0.808323
$959$			4.52472i			0.146111i
$960$		0			0
$961$	20.4468			0.659574
$962$	−2.76784			−0.0892387
$963$	15.3187			0.493637
$964$	−29.4241			−0.947687
$965$		0			0
$966$	2.95450			0.0950595
$967$			21.9080i			0.704514i	0.935903	+	0.352257i	$0.114586\pi$
$967$			21.9080i			0.704514i	−0.935903	+	0.352257i	$0.885414\pi$
$968$			4.87852i			0.156802i
$969$			55.1497i			1.77166i
$970$		0			0
$971$			24.0732i			0.772547i	0.922384	+	0.386273i	$0.126238\pi$
$971$			24.0732i			0.772547i	−0.922384	+	0.386273i	$0.873762\pi$
$972$		−	12.2281i		−	0.392216i
$973$	1.92189			0.0616130
$974$		−	25.8793i		−	0.829225i
$975$		0			0
$976$			0.827849i			0.0264988i
$977$	19.2219			0.614963			0.307481	−	0.951554i	$-0.400514\pi$
$977$	19.2219			0.614963			0.307481	+	0.951554i	$0.400514\pi$
$978$		−	0.835835i		−	0.0267270i
$979$	−7.28359			−0.232784
$980$		0			0
$981$	−9.29259			−0.296690
$982$	16.9849			0.542011
$983$		−	36.1818i		−	1.15402i	−0.816737	−	0.577010i	$-0.804219\pi$
$983$		−	36.1818i		−	1.15402i	0.816737	−	0.577010i	$-0.195781\pi$
$984$		−	20.4468i		−	0.651821i
$985$		0			0
$986$	35.3319	−	3.22208i	1.12520	−	0.102612i
$987$	−5.07944			−0.161680
$988$			24.5540i			0.781167i
$989$		−	2.86677i		−	0.0911579i
$990$		0			0
$991$	5.49026			0.174404			0.0872020	−	0.996191i	$-0.472207\pi$
$991$	5.49026			0.174404			0.0872020	+	0.996191i	$0.472207\pi$
$992$	−3.24857			−0.103142
$993$	50.2893			1.59588
$994$		−	22.2580i		−	0.705980i
$995$		0			0
$996$			26.6802i			0.845394i
$997$			40.1313i			1.27097i	0.772112	+	0.635486i	$0.219200\pi$
$997$			40.1313i			1.27097i	−0.772112	+	0.635486i	$0.780800\pi$
$998$			15.2508i			0.482757i
$999$	−1.65267			−0.0522883

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.c.e.1101.7	yes	10
5.2	odd	4		1450.2.d.i.1449.4		10
5.3	odd	4		1450.2.d.j.1449.7		10
5.4	even	2		1450.2.c.f.1101.4	yes	10
29.28	even	2	inner	1450.2.c.e.1101.4	✓	10
145.28	odd	4		1450.2.d.i.1449.3		10
145.57	odd	4		1450.2.d.j.1449.8		10
145.144	even	2		1450.2.c.f.1101.7	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1450.2.c.e.1101.4	✓	10	29.28	even	2	inner
1450.2.c.e.1101.7	yes	10	1.1	even	1	trivial
1450.2.c.f.1101.4	yes	10	5.4	even	2
1450.2.c.f.1101.7	yes	10	145.144	even	2
1450.2.d.i.1449.3		10	145.28	odd	4
1450.2.d.i.1449.4		10	5.2	odd	4
1450.2.d.j.1449.7		10	5.3	odd	4
1450.2.d.j.1449.8		10	145.57	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -2.06121i q^{3} -1.00000 q^{4} +2.06121 q^{6} +1.81264 q^{7} -1.00000i q^{8} -1.24857 q^{9} +3.98479i q^{11} +2.06121i q^{12} -6.04599 q^{13} +1.81264i q^{14} +1.00000 q^{16} +6.58819i q^{17} -1.24857i q^{18} +4.06121i q^{19} -3.73621i q^{21} -3.98479 q^{22} +0.790774 q^{23} -2.06121 q^{24} -6.04599i q^{26} -3.61006i q^{27} -1.81264 q^{28} +(-5.36291 + 0.489069i) q^{29} +3.24857i q^{31} +1.00000i q^{32} +8.21347 q^{33} -6.58819 q^{34} +1.24857 q^{36} -0.457797i q^{37} -4.06121 q^{38} +12.4620i q^{39} +9.91983i q^{41} +3.73621 q^{42} -3.62527i q^{43} -3.98479i q^{44} +0.790774i q^{46} -1.35952i q^{47} -2.06121i q^{48} -3.71435 q^{49} +13.5796 q^{51} +6.04599 q^{52} +6.90172 q^{53} +3.61006 q^{54} -1.81264i q^{56} +8.37098 q^{57} +(-0.489069 - 5.36291i) q^{58} +14.5451 q^{59} +0.827849i q^{61} -3.24857 q^{62} -2.26320 q^{63} -1.00000 q^{64} +8.21347i q^{66} +2.93505 q^{67} -6.58819i q^{68} -1.62995i q^{69} -12.2793 q^{71} +1.24857i q^{72} +6.29456i q^{73} +0.457797 q^{74} -4.06121i q^{76} +7.22296i q^{77} -12.4620 q^{78} +13.9810i q^{79} -11.1868 q^{81} -9.91983 q^{82} +12.9440 q^{83} +3.73621i q^{84} +3.62527 q^{86} +(1.00807 + 11.0541i) q^{87} +3.98479 q^{88} +1.82785i q^{89} -10.9592 q^{91} -0.790774 q^{92} +6.69597 q^{93} +1.35952 q^{94} +2.06121 q^{96} -17.0052i q^{97} -3.71435i q^{98} -4.97529i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{4} + 4 q^{6} - 14 q^{9} - 4 q^{13} + 10 q^{16} - 16 q^{23} - 4 q^{24} - 16 q^{29} - 36 q^{33} + 16 q^{34} + 14 q^{36} - 24 q^{38} - 4 q^{42} + 10 q^{49} - 20 q^{51} + 4 q^{52} + 40 q^{53} - 40 q^{54}+ \cdots + 4 q^{96}+O(q^{100}) \) 10 * q - 10 * q^4 + 4 * q^6 - 14 * q^9 - 4 * q^13 + 10 * q^16 - 16 * q^23 - 4 * q^24 - 16 * q^29 - 36 * q^33 + 16 * q^34 + 14 * q^36 - 24 * q^38 - 4 * q^42 + 10 * q^49 - 20 * q^51 + 4 * q^52 + 40 * q^53 - 40 * q^54 + 52 * q^57 - 2 * q^58 + 18 * q^59 - 34 * q^62 + 84 * q^63 - 10 * q^64 - 22 * q^67 - 28 * q^71 + 30 * q^74 - 8 * q^78 + 18 * q^81 - 8 * q^82 - 24 * q^83 + 16 * q^87 + 4 * q^91 + 16 * q^92 + 60 * q^93 + 10 * q^94 + 4 * q^96

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