LMFDB - Embedded newform 760.2.f.b.381.28

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [760,2,Mod(381,760)] 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("760.381"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(760, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 760 = 2^{3} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	760.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [44] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.06863055362$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			381.28
Character	$\chi$	$=$	760.381
Dual form			760.2.f.b.381.27

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.561724 + 1.29787i) q^{2} +0.777674i q^{3} +(-1.36893 + 1.45809i) q^{4} +1.00000i q^{5} +(-1.00932 + 0.436838i) q^{6} +2.42638 q^{7} +(-2.66137 - 0.957654i) q^{8} +2.39522 q^{9} +(-1.29787 + 0.561724i) q^{10} +2.16463i q^{11} +(-1.13392 - 1.06458i) q^{12} +3.60762i q^{13} +(1.36296 + 3.14913i) q^{14} -0.777674 q^{15} +(-0.252044 - 3.99205i) q^{16} -3.85504 q^{17} +(1.34545 + 3.10869i) q^{18} +1.00000i q^{19} +(-1.45809 - 1.36893i) q^{20} +1.88693i q^{21} +(-2.80941 + 1.21592i) q^{22} +5.10533 q^{23} +(0.744743 - 2.06968i) q^{24} -1.00000 q^{25} +(-4.68222 + 2.02648i) q^{26} +4.19572i q^{27} +(-3.32155 + 3.53788i) q^{28} +0.0158030i q^{29} +(-0.436838 - 1.00932i) q^{30} -9.21232 q^{31} +(5.03958 - 2.56955i) q^{32} -1.68338 q^{33} +(-2.16547 - 5.00334i) q^{34} +2.42638i q^{35} +(-3.27890 + 3.49245i) q^{36} -11.4598i q^{37} +(-1.29787 + 0.561724i) q^{38} -2.80555 q^{39} +(0.957654 - 2.66137i) q^{40} +11.4676 q^{41} +(-2.44899 + 1.05994i) q^{42} +5.75007i q^{43} +(-3.15622 - 2.96323i) q^{44} +2.39522i q^{45} +(2.86779 + 6.62606i) q^{46} -12.1163 q^{47} +(3.10451 - 0.196008i) q^{48} -1.11267 q^{49} +(-0.561724 - 1.29787i) q^{50} -2.99796i q^{51} +(-5.26022 - 4.93858i) q^{52} -2.84802i q^{53} +(-5.44550 + 2.35684i) q^{54} -2.16463 q^{55} +(-6.45750 - 2.32364i) q^{56} -0.777674 q^{57} +(-0.0205102 + 0.00887690i) q^{58} -5.56877i q^{59} +(1.06458 - 1.13392i) q^{60} +1.31105i q^{61} +(-5.17478 - 11.9564i) q^{62} +5.81173 q^{63} +(6.16580 + 5.09735i) q^{64} -3.60762 q^{65} +(-0.945592 - 2.18480i) q^{66} -4.07518i q^{67} +(5.27729 - 5.62099i) q^{68} +3.97028i q^{69} +(-3.14913 + 1.36296i) q^{70} +15.3553 q^{71} +(-6.37458 - 2.29380i) q^{72} -7.41737 q^{73} +(14.8733 - 6.43722i) q^{74} -0.777674i q^{75} +(-1.45809 - 1.36893i) q^{76} +5.25222i q^{77} +(-1.57594 - 3.64124i) q^{78} +2.07712 q^{79} +(3.99205 - 0.252044i) q^{80} +3.92277 q^{81} +(6.44162 + 14.8835i) q^{82} +16.3734i q^{83} +(-2.75132 - 2.58309i) q^{84} -3.85504i q^{85} +(-7.46285 + 3.22995i) q^{86} -0.0122896 q^{87} +(2.07297 - 5.76089i) q^{88} +14.8972 q^{89} +(-3.10869 + 1.34545i) q^{90} +8.75345i q^{91} +(-6.98886 + 7.44403i) q^{92} -7.16418i q^{93} +(-6.80604 - 15.7254i) q^{94} -1.00000 q^{95} +(1.99827 + 3.91915i) q^{96} +14.3523 q^{97} +(-0.625014 - 1.44410i) q^{98} +5.18477i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{2} - 2 q^{4} - 6 q^{6} + 4 q^{7} + 8 q^{8} - 60 q^{9} + 4 q^{12} + 4 q^{14} - 6 q^{16} + 24 q^{17} - 14 q^{18} - 4 q^{20} - 4 q^{22} + 4 q^{23} + 2 q^{24} - 44 q^{25} + 18 q^{26} - 14 q^{28}+ \cdots + 78 q^{98}+O(q^{100}) $ 44 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 + 4 * q^7 + 8 * q^8 - 60 * q^9 + 4 * q^12 + 4 * q^14 - 6 * q^16 + 24 * q^17 - 14 * q^18 - 4 * q^20 - 4 * q^22 + 4 * q^23 + 2 * q^24 - 44 * q^25 + 18 * q^26 - 14 * q^28 + 12 * q^32 + 40 * q^33 + 32 * q^34 - 28 * q^36 - 24 * q^39 + 6 * q^40 - 32 * q^41 + 46 * q^42 - 36 * q^44 - 16 * q^46 - 20 * q^47 + 64 * q^48 + 108 * q^49 - 2 * q^50 - 24 * q^52 - 26 * q^54 + 8 * q^55 + 60 * q^56 + 2 * q^58 - 14 * q^60 - 72 * q^62 + 20 * q^63 + 22 * q^64 + 12 * q^65 + 88 * q^66 - 62 * q^68 - 18 * q^70 - 8 * q^71 + 48 * q^72 - 88 * q^73 + 84 * q^74 - 4 * q^76 - 116 * q^78 + 40 * q^79 + 8 * q^80 + 116 * q^81 + 44 * q^82 - 108 * q^84 - 88 * q^86 + 48 * q^87 + 76 * q^88 - 64 * q^89 + 30 * q^90 - 62 * q^92 - 24 * q^94 - 44 * q^95 + 118 * q^96 + 116 * q^97 + 78 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/760\mathbb{Z}\right)^\times$.

$n$	$191$	$381$	$401$	$457$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$	0.561724	+	1.29787i	0.397199	+	0.917733i
$2$	0.561724	+	1.29787i	0.397199	+	0.917733i
$3$			0.777674i			0.448990i	0.974475	+	0.224495i	$0.0720733\pi$
$3$			0.777674i			0.448990i	−0.974475	+	0.224495i	$0.927927\pi$
$4$	−1.36893	+	1.45809i	−0.684467	+	0.729044i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−1.00932	+	0.436838i	−0.412053	+	0.178338i
$7$	2.42638			0.917086			0.458543	−	0.888672i	$-0.348371\pi$
$7$	2.42638			0.917086			0.458543	+	0.888672i	$0.348371\pi$
$8$	−2.66137	−	0.957654i	−0.940937	−	0.338582i
$9$	2.39522			0.798408
$10$	−1.29787	+	0.561724i	−0.410423	+	0.177633i
$11$			2.16463i			0.652661i	0.945256	+	0.326330i	$0.105812\pi$
$11$			2.16463i			0.652661i	−0.945256	+	0.326330i	$0.894188\pi$
$12$	−1.13392	−	1.06458i	−0.327334	−	0.307319i
$13$			3.60762i			1.00057i	0.865860	+	0.500286i	$0.166772\pi$
$13$			3.60762i			1.00057i	−0.865860	+	0.500286i	$0.833228\pi$
$14$	1.36296	+	3.14913i	0.364265	+	0.841640i
$15$	−0.777674			−0.200795
$16$	−0.252044	−	3.99205i	−0.0630111	−	0.998013i
$17$	−3.85504			−0.934984			−0.467492	−	0.883997i	$-0.654842\pi$
$17$	−3.85504			−0.934984			−0.467492	+	0.883997i	$0.654842\pi$
$18$	1.34545	+	3.10869i	0.317126	+	0.732725i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	−1.45809	−	1.36893i	−0.326039	−	0.306103i
$21$			1.88693i			0.411763i
$22$	−2.80941	+	1.21592i	−0.598968	+	0.259236i
$23$	5.10533			1.06454			0.532268	−	0.846576i	$-0.321340\pi$
$23$	5.10533			1.06454			0.532268	+	0.846576i	$0.321340\pi$
$24$	0.744743	−	2.06968i	0.152020	−	0.422471i
$25$	−1.00000			−0.200000
$26$	−4.68222	+	2.02648i	−0.918258	+	0.397426i
$27$			4.19572i			0.807467i
$28$	−3.32155	+	3.53788i	−0.627715	+	0.668596i
$29$			0.0158030i			0.00293454i	0.999999	+	0.00146727i	$0.000467046\pi$
$29$			0.0158030i			0.00293454i	−0.999999	+	0.00146727i	$0.999533\pi$
$30$	−0.436838	−	1.00932i	−0.0797553	−	0.184276i
$31$	−9.21232			−1.65458			−0.827291	−	0.561774i	$-0.810119\pi$
$31$	−9.21232			−1.65458			−0.827291	+	0.561774i	$0.810119\pi$
$32$	5.03958	−	2.56955i	0.890881	−	0.454237i
$33$	−1.68338			−0.293038
$34$	−2.16547	−	5.00334i	−0.371374	−	0.858065i
$35$			2.42638i			0.410133i
$36$	−3.27890	+	3.49245i	−0.546483	+	0.582075i
$37$		−	11.4598i		−	1.88397i	−0.335650	−	0.941987i	$-0.608956\pi$
$37$		−	11.4598i		−	1.88397i	0.335650	−	0.941987i	$-0.391044\pi$
$38$	−1.29787	+	0.561724i	−0.210542	+	0.0911236i
$39$	−2.80555			−0.449247
$40$	0.957654	−	2.66137i	0.151418	−	0.420800i
$41$	11.4676			1.79094			0.895469	−	0.445124i	$-0.146840\pi$
$41$	11.4676			1.79094			0.895469	+	0.445124i	$0.146840\pi$
$42$	−2.44899	+	1.05994i	−0.377888	+	0.163552i
$43$			5.75007i			0.876878i	0.898761	+	0.438439i	$0.144468\pi$
$43$			5.75007i			0.876878i	−0.898761	+	0.438439i	$0.855532\pi$
$44$	−3.15622	−	2.96323i	−0.475818	−	0.446724i
$45$			2.39522i			0.357059i
$46$	2.86779	+	6.62606i	0.422832	+	0.976959i
$47$	−12.1163			−1.76735			−0.883675	−	0.468101i	$-0.844938\pi$
$47$	−12.1163			−1.76735			−0.883675	+	0.468101i	$0.844938\pi$
$48$	3.10451	−	0.196008i	0.448098	−	0.0282913i
$49$	−1.11267			−0.158953
$50$	−0.561724	−	1.29787i	−0.0794397	−	0.183547i
$51$		−	2.99796i		−	0.419799i
$52$	−5.26022	−	4.93858i	−0.729462	−	0.684858i
$53$		−	2.84802i		−	0.391206i	−0.980683	−	0.195603i	$-0.937334\pi$
$53$		−	2.84802i		−	0.391206i	0.980683	−	0.195603i	$-0.0626664\pi$
$54$	−5.44550	+	2.35684i	−0.741039	+	0.320725i
$55$	−2.16463			−0.291879
$56$	−6.45750	−	2.32364i	−0.862920	−	0.310509i
$57$	−0.777674			−0.103005
$58$	−0.0205102	+	0.00887690i	−0.00269312	+	0.00116559i
$59$		−	5.56877i		−	0.724992i	−0.931985	−	0.362496i	$-0.881925\pi$
$59$		−	5.56877i		−	0.724992i	0.931985	−	0.362496i	$-0.118075\pi$
$60$	1.06458	−	1.13392i	0.137437	−	0.146388i
$61$			1.31105i			0.167863i	0.996472	+	0.0839313i	$0.0267476\pi$
$61$			1.31105i			0.167863i	−0.996472	+	0.0839313i	$0.973252\pi$
$62$	−5.17478	−	11.9564i	−0.657197	−	1.51846i
$63$	5.81173			0.732209
$64$	6.16580	+	5.09735i	0.770724	+	0.637169i
$65$	−3.60762			−0.447470
$66$	−0.945592	−	2.18480i	−0.116394	−	0.268931i
$67$		−	4.07518i		−	0.497863i	−0.968521	−	0.248931i	$-0.919921\pi$
$67$		−	4.07518i		−	0.497863i	0.968521	−	0.248931i	$-0.0800794\pi$
$68$	5.27729	−	5.62099i	0.639965	−	0.681645i
$69$			3.97028i			0.477966i
$70$	−3.14913	+	1.36296i	−0.376393	+	0.162904i
$71$	15.3553			1.82234			0.911172	−	0.412026i	$-0.135179\pi$
$71$	15.3553			1.82234			0.911172	+	0.412026i	$0.135179\pi$
$72$	−6.37458	−	2.29380i	−0.751251	−	0.270326i
$73$	−7.41737			−0.868137			−0.434069	−	0.900880i	$-0.642922\pi$
$73$	−7.41737			−0.868137			−0.434069	+	0.900880i	$0.642922\pi$
$74$	14.8733	−	6.43722i	1.72898	−	0.748312i
$75$		−	0.777674i		−	0.0897980i
$76$	−1.45809	−	1.36893i	−0.167254	−	0.157027i
$77$			5.25222i			0.598546i
$78$	−1.57594	−	3.64124i	−0.178440	−	0.412289i
$79$	2.07712			0.233694			0.116847	−	0.993150i	$-0.462721\pi$
$79$	2.07712			0.233694			0.116847	+	0.993150i	$0.462721\pi$
$80$	3.99205	−	0.252044i	0.446325	−	0.0281794i
$81$	3.92277			0.435863
$82$	6.44162	+	14.8835i	0.711358	+	1.64360i
$83$			16.3734i			1.79721i	0.438754	+	0.898607i	$0.355420\pi$
$83$			16.3734i			1.79721i	−0.438754	+	0.898607i	$0.644580\pi$
$84$	−2.75132	−	2.58309i	−0.300193	−	0.281838i
$85$		−	3.85504i		−	0.418138i
$86$	−7.46285	+	3.22995i	−0.804739	+	0.348295i
$87$	−0.0122896			−0.00131758
$88$	2.07297	−	5.76089i	0.220979	−	0.614112i
$89$	14.8972			1.57910			0.789552	−	0.613684i	$-0.210313\pi$
$89$	14.8972			1.57910			0.789552	+	0.613684i	$0.210313\pi$
$90$	−3.10869	+	1.34545i	−0.327685	+	0.141823i
$91$			8.75345i			0.917611i
$92$	−6.98886	+	7.44403i	−0.728639	+	0.776094i
$93$		−	7.16418i		−	0.742891i
$94$	−6.80604	−	15.7254i	−0.701989	−	1.62195i
$95$	−1.00000			−0.102598
$96$	1.99827	+	3.91915i	0.203948	+	0.399997i
$97$	14.3523			1.45726			0.728628	−	0.684909i	$-0.240158\pi$
$97$	14.3523			1.45726			0.728628	+	0.684909i	$0.240158\pi$
$98$	−0.625014	−	1.44410i	−0.0631359	−	0.145876i
$99$			5.18477i			0.521089i
$100$	1.36893	−	1.45809i	0.136893	−	0.145809i
$101$			12.4726i			1.24107i	0.784177	+	0.620537i	$0.213086\pi$
$101$			12.4726i			1.24107i	−0.784177	+	0.620537i	$0.786914\pi$
$102$	3.89097	−	1.68403i	0.385263	−	0.166743i
$103$	−3.30285			−0.325440			−0.162720	−	0.986672i	$-0.552027\pi$
$103$	−3.30285			−0.325440			−0.162720	+	0.986672i	$0.552027\pi$
$104$	3.45485	−	9.60121i	0.338776	−	0.941476i
$105$	−1.88693			−0.184146
$106$	3.69636	−	1.59980i	0.359022	−	0.155386i
$107$			12.0211i			1.16213i	0.813859	+	0.581063i	$0.197363\pi$
$107$			12.0211i			1.16213i	−0.813859	+	0.581063i	$0.802637\pi$
$108$	−6.11774	−	5.74367i	−0.588680	−	0.552684i
$109$		−	20.0940i		−	1.92466i	−0.271884	−	0.962330i	$-0.587647\pi$
$109$		−	20.0940i		−	1.92466i	0.271884	−	0.962330i	$-0.412353\pi$
$110$	−1.21592	−	2.80941i	−0.115934	−	0.267867i
$111$	8.91196			0.845886
$112$	−0.611556	−	9.68624i	−0.0577866	−	0.915264i
$113$	9.76712			0.918813			0.459407	−	0.888226i	$-0.348062\pi$
$113$	9.76712			0.918813			0.459407	+	0.888226i	$0.348062\pi$
$114$	−0.436838	−	1.00932i	−0.0409136	−	0.0945314i
$115$			5.10533i			0.476075i
$116$	−0.0230421	−	0.0216332i	−0.00213941	−	0.00200859i
$117$			8.64105i			0.798865i
$118$	7.22754	−	3.12811i	0.665349	−	0.287966i
$119$	−9.35379			−0.857461
$120$	2.06968	+	0.744743i	0.188935	+	0.0679854i
$121$	6.31438			0.574034
$122$	−1.70157	+	0.736447i	−0.154053	+	0.0666748i
$123$			8.91805i			0.804114i
$124$	12.6110	−	13.4324i	1.13251	−	1.20626i
$125$		−	1.00000i		−	0.0894427i
$126$	3.26458	+	7.54287i	0.290832	+	0.671972i
$127$	3.02645			0.268554			0.134277	−	0.990944i	$-0.457129\pi$
$127$	3.02645			0.268554			0.134277	+	0.990944i	$0.457129\pi$
$128$	−3.15222	+	10.8657i	−0.278620	+	0.960401i
$129$	−4.47168			−0.393710
$130$	−2.02648	−	4.68222i	−0.177734	−	0.410658i
$131$		−	5.81087i		−	0.507698i	−0.967244	−	0.253849i	$-0.918303\pi$
$131$		−	5.81087i		−	0.507698i	0.967244	−	0.253849i	$-0.0816967\pi$
$132$	2.30443	−	2.45451i	0.200575	−	0.213638i
$133$			2.42638i			0.210394i
$134$	5.28906	−	2.28913i	0.456905	−	0.197750i
$135$	−4.19572			−0.361110
$136$	10.2597	+	3.69179i	0.879761	+	0.316569i
$137$	−3.25503			−0.278096			−0.139048	−	0.990286i	$-0.544404\pi$
$137$	−3.25503			−0.278096			−0.139048	+	0.990286i	$0.544404\pi$
$138$	−5.15291	+	2.23020i	−0.438645	+	0.189847i
$139$		−	4.64148i		−	0.393685i	−0.980435	−	0.196843i	$-0.936931\pi$
$139$		−	4.64148i		−	0.393685i	0.980435	−	0.196843i	$-0.0630688\pi$
$140$	−3.53788	−	3.32155i	−0.299005	−	0.280723i
$141$		−	9.42256i		−	0.793523i
$142$	8.62546	+	19.9292i	0.723832	+	1.67242i
$143$	−7.80915			−0.653034
$144$	−0.603702	−	9.56185i	−0.0503085	−	0.796821i
$145$	−0.0158030			−0.00131236
$146$	−4.16651	−	9.62678i	−0.344823	−	0.796718i
$147$		−	0.865295i		−	0.0713683i
$148$	16.7093	+	15.6876i	1.37350	+	1.28952i
$149$		−	18.3885i		−	1.50645i	−0.657765	−	0.753223i	$-0.728498\pi$
$149$		−	18.3885i		−	1.50645i	0.657765	−	0.753223i	$-0.271502\pi$
$150$	1.00932	−	0.436838i	0.0824106	−	0.0356677i
$151$	−11.7559			−0.956685			−0.478342	−	0.878173i	$-0.658762\pi$
$151$	−11.7559			−0.956685			−0.478342	+	0.878173i	$0.658762\pi$
$152$	0.957654	−	2.66137i	0.0776760	−	0.215866i
$153$	−9.23368			−0.746499
$154$	−6.81670	+	2.95030i	−0.549305	+	0.237742i
$155$		−	9.21232i		−	0.739951i
$156$	3.84061	−	4.09074i	0.307495	−	0.327521i
$157$		−	14.8964i		−	1.18887i	−0.804145	−	0.594433i	$-0.797377\pi$
$157$		−	14.8964i		−	1.18887i	0.804145	−	0.594433i	$-0.202623\pi$
$158$	1.16677	+	2.69583i	0.0928230	+	0.214469i
$159$	2.21483			0.175648
$160$	2.56955	+	5.03958i	0.203141	+	0.398414i
$161$	12.3875			0.976271
$162$	2.20351	+	5.09124i	0.173124	+	0.400006i
$163$			7.57618i			0.593412i	0.954969	+	0.296706i	$0.0958882\pi$
$163$			7.57618i			0.593412i	−0.954969	+	0.296706i	$0.904112\pi$
$164$	−15.6984	+	16.7208i	−1.22584	+	1.30567i
$165$		−	1.68338i		−	0.131051i
$166$	−21.2506	+	9.19733i	−1.64936	+	0.713851i
$167$	15.0342			1.16338			0.581692	−	0.813409i	$-0.302391\pi$
$167$	15.0342			1.16338			0.581692	+	0.813409i	$0.302391\pi$
$168$	1.80703	−	5.02183i	0.139415	−	0.387443i
$169$	−0.0148907			−0.00114544
$170$	5.00334	−	2.16547i	0.383739	−	0.166084i
$171$			2.39522i			0.183167i
$172$	−8.38411	−	7.87146i	−0.639283	−	0.600194i
$173$			6.59767i			0.501612i	0.968037	+	0.250806i	$0.0806956\pi$
$173$			6.59767i			0.501612i	−0.968037	+	0.250806i	$0.919304\pi$
$174$	−0.00690333	−	0.0159502i	−0.000523340	−	0.00120918i
$175$	−2.42638			−0.183417
$176$	8.64132	−	0.545583i	0.651364	−	0.0411248i
$177$	4.33069			0.325514
$178$	8.36813	+	19.3347i	0.627218	+	1.44920i
$179$			23.0731i			1.72456i	0.506430	+	0.862281i	$0.330965\pi$
$179$			23.0731i			1.72456i	−0.506430	+	0.862281i	$0.669035\pi$
$180$	−3.49245	−	3.27890i	−0.260312	−	0.244395i
$181$		−	11.6959i		−	0.869346i	−0.900588	−	0.434673i	$-0.856864\pi$
$181$		−	11.6959i		−	0.869346i	0.900588	−	0.434673i	$-0.143136\pi$
$182$	−11.3608	+	4.91702i	−0.842122	+	0.364474i
$183$	−1.01957			−0.0753687
$184$	−13.5872	−	4.88915i	−1.00166	−	0.360433i
$185$	11.4598			0.842539
$186$	9.29817	−	4.02429i	0.681775	−	0.295075i
$187$		−	8.34473i		−	0.610227i
$188$	16.5865	−	17.6667i	1.20969	−	1.28848i
$189$			10.1804i			0.740517i
$190$	−0.561724	−	1.29787i	−0.0407517	−	0.0941574i
$191$	−11.5764			−0.837639			−0.418819	−	0.908070i	$-0.637556\pi$
$191$	−11.5764			−0.837639			−0.418819	+	0.908070i	$0.637556\pi$
$192$	−3.96407	+	4.79498i	−0.286082	+	0.346048i
$193$	0.560028			0.0403117			0.0201559	−	0.999797i	$-0.493584\pi$
$193$	0.560028			0.0403117			0.0201559	+	0.999797i	$0.493584\pi$
$194$	8.06203	+	18.6274i	0.578820	+	1.33737i
$195$		−	2.80555i		−	0.200909i
$196$	1.52317	−	1.62237i	0.108798	−	0.115884i
$197$			1.15117i			0.0820172i	0.999159	+	0.0410086i	$0.0130571\pi$
$197$			1.15117i			0.0820172i	−0.999159	+	0.0410086i	$0.986943\pi$
$198$	−6.72916	+	2.91241i	−0.478221	+	0.206976i
$199$	22.4183			1.58919			0.794596	−	0.607139i	$-0.207683\pi$
$199$	22.4183			1.58919			0.794596	+	0.607139i	$0.207683\pi$
$200$	2.66137	+	0.957654i	0.188187	+	0.0677164i
$201$	3.16916			0.223535
$202$	−16.1879	+	7.00618i	−1.13898	+	0.492953i
$203$			0.0383440i			0.00269122i
$204$	4.37129	+	4.10401i	0.306052	+	0.287338i
$205$			11.4676i			0.800932i
$206$	−1.85529	−	4.28667i	−0.129264	−	0.298667i
$207$	12.2284			0.849934
$208$	14.4018	−	0.909279i	0.998584	−	0.0630471i
$209$	−2.16463			−0.149731
$210$	−1.05994	−	2.44899i	−0.0731425	−	0.168997i
$211$		−	4.33221i		−	0.298242i	−0.988819	−	0.149121i	$-0.952356\pi$
$211$		−	4.33221i		−	0.298242i	0.988819	−	0.149121i	$-0.0476443\pi$
$212$	4.15267	+	3.89875i	0.285206	+	0.267767i
$213$			11.9414i			0.818215i
$214$	−15.6019	+	6.75255i	−1.06652	+	0.461595i
$215$	−5.75007			−0.392152
$216$	4.01805	−	11.1664i	0.273394	−	0.759776i
$217$	−22.3526			−1.51739
$218$	26.0795	−	11.2873i	1.76632	−	0.764472i
$219$		−	5.76829i		−	0.389785i
$220$	2.96323	−	3.15622i	0.199781	−	0.212792i
$221$		−	13.9075i		−	0.935519i
$222$	5.00606	+	11.5666i	0.335985	+	0.776297i
$223$	−5.66321			−0.379237			−0.189618	−	0.981858i	$-0.560725\pi$
$223$	−5.66321			−0.379237			−0.189618	+	0.981858i	$0.560725\pi$
$224$	12.2280	−	6.23471i	0.817015	−	0.416574i
$225$	−2.39522			−0.159682
$226$	5.48642	+	12.6764i	0.364951	+	0.843225i
$227$		−	6.61434i		−	0.439009i	−0.975611	−	0.219505i	$-0.929556\pi$
$227$		−	6.61434i		−	0.439009i	0.975611	−	0.219505i	$-0.0704441\pi$
$228$	1.06458	−	1.13392i	0.0705038	−	0.0750955i
$229$		−	23.4253i		−	1.54799i	−0.633194	−	0.773993i	$-0.718257\pi$
$229$		−	23.4253i		−	1.54799i	0.633194	−	0.773993i	$-0.281743\pi$
$230$	−6.62606	+	2.86779i	−0.436909	+	0.189096i
$231$	−4.08451			−0.268741
$232$	0.0151338	−	0.0420576i	0.000993581	−	0.00276121i
$233$	−1.62715			−0.106598			−0.0532992	−	0.998579i	$-0.516974\pi$
$233$	−1.62715			−0.106598			−0.0532992	+	0.998579i	$0.516974\pi$
$234$	−11.2150	+	4.85388i	−0.733144	+	0.317308i
$235$		−	12.1163i		−	0.790383i
$236$	8.11976	+	7.62327i	0.528551	+	0.496233i
$237$			1.61532i			0.104926i
$238$	−5.25425	−	12.1400i	−0.340582	−	0.786920i
$239$	−3.05674			−0.197724			−0.0988619	−	0.995101i	$-0.531520\pi$
$239$	−3.05674			−0.197724			−0.0988619	+	0.995101i	$0.531520\pi$
$240$	0.196008	+	3.10451i	0.0126523	+	0.200396i
$241$	19.1609			1.23426			0.617130	−	0.786861i	$-0.288295\pi$
$241$	19.1609			1.23426			0.617130	+	0.786861i	$0.288295\pi$
$242$	3.54693	+	8.19524i	0.228006	+	0.526810i
$243$			15.6378i			1.00317i
$244$	−1.91163	−	1.79474i	−0.122379	−	0.114896i
$245$		−	1.11267i		−	0.0710859i
$246$	−11.5745	+	5.00948i	−0.737961	+	0.319393i
$247$	−3.60762			−0.229547
$248$	24.5174	+	8.82222i	1.55686	+	0.560211i
$249$	−12.7332			−0.806932
$250$	1.29787	−	0.561724i	0.0820845	−	0.0355265i
$251$		−	7.40799i		−	0.467588i	−0.972286	−	0.233794i	$-0.924886\pi$
$251$		−	7.40799i		−	0.467588i	0.972286	−	0.233794i	$-0.0751141\pi$
$252$	−7.95587	+	8.47401i	−0.501172	+	0.533813i
$253$			11.0512i			0.694781i
$254$	1.70003	+	3.92795i	0.106669	+	0.246461i
$255$	2.99796			0.187740
$256$	−15.8729	+	2.01235i	−0.992059	+	0.125772i
$257$	−22.5334			−1.40560			−0.702799	−	0.711389i	$-0.748067\pi$
$257$	−22.5334			−1.40560			−0.702799	+	0.711389i	$0.748067\pi$
$258$	−2.51185	−	5.80366i	−0.156381	−	0.361320i
$259$		−	27.8058i		−	1.72777i
$260$	4.93858	−	5.26022i	0.306278	−	0.326225i
$261$			0.0378516i			0.00234296i
$262$	7.54176	−	3.26411i	0.465931	−	0.201657i
$263$	−1.10540			−0.0681620			−0.0340810	−	0.999419i	$-0.510850\pi$
$263$	−1.10540			−0.0681620			−0.0340810	+	0.999419i	$0.510850\pi$
$264$	4.48009	+	1.61209i	0.275730	+	0.0992175i
$265$	2.84802			0.174953
$266$	−3.14913	+	1.36296i	−0.193085	+	0.0835682i
$267$			11.5852i			0.709002i
$268$	5.94198	+	5.57865i	0.362964	+	0.340770i
$269$		−	19.9527i		−	1.21654i	−0.793732	−	0.608268i	$-0.791865\pi$
$269$		−	19.9527i		−	1.21654i	0.793732	−	0.608268i	$-0.208135\pi$
$270$	−2.35684	−	5.44550i	−0.143433	−	0.331403i
$271$	1.05787			0.0642609			0.0321304	−	0.999484i	$-0.489771\pi$
$271$	1.05787			0.0642609			0.0321304	+	0.999484i	$0.489771\pi$
$272$	0.971640	+	15.3895i	0.0589143	+	0.933126i
$273$	−6.80733			−0.411998
$274$	−1.82843	−	4.22460i	−0.110459	−	0.255217i
$275$		−	2.16463i		−	0.130532i
$276$	−5.78903	−	5.43505i	−0.348458	−	0.327152i
$277$		−	1.69939i		−	0.102107i	−0.998696	−	0.0510534i	$-0.983742\pi$
$277$		−	1.69939i		−	0.102107i	0.998696	−	0.0510534i	$-0.0162579\pi$
$278$	6.02404	−	2.60723i	0.361298	−	0.156371i
$279$	−22.0656			−1.32103
$280$	2.32364	−	6.45750i	0.138864	−	0.385910i
$281$	20.8335			1.24282			0.621411	−	0.783485i	$-0.286560\pi$
$281$	20.8335			1.24282			0.621411	+	0.783485i	$0.286560\pi$
$282$	12.2293	−	5.29288i	0.728242	−	0.315186i
$283$			13.2328i			0.786607i	0.919409	+	0.393303i	$0.128668\pi$
$283$			13.2328i			0.786607i	−0.919409	+	0.393303i	$0.871332\pi$
$284$	−21.0204	+	22.3894i	−1.24733	+	1.32857i
$285$		−	0.777674i		−	0.0460654i
$286$	−4.38659	−	10.1353i	−0.259384	−	0.599311i
$287$	27.8248			1.64244
$288$	12.0709	−	6.15465i	0.711286	−	0.362666i
$289$	−2.13868			−0.125805
$290$	−0.00887690	−	0.0205102i	−0.000521269	−	0.00120440i
$291$			11.1614i			0.654294i
$292$	10.1539	−	10.8152i	0.594211	−	0.632910i
$293$			27.0040i			1.57759i	0.614658	+	0.788794i	$0.289294\pi$
$293$			27.0040i			1.57759i	−0.614658	+	0.788794i	$0.710706\pi$
$294$	1.12304	−	0.486057i	0.0654971	−	0.0283474i
$295$	5.56877			0.324226
$296$	−10.9745	+	30.4987i	−0.637879	+	1.77270i
$297$	−9.08219			−0.527002
$298$	23.8659	−	10.3293i	1.38251	−	0.598358i
$299$			18.4181i			1.06515i
$300$	1.13392	+	1.06458i	0.0654667	+	0.0614638i
$301$			13.9519i			0.804172i
$302$	−6.60359	−	15.2577i	−0.379994	−	0.877981i
$303$	−9.69965			−0.557231
$304$	3.99205	−	0.252044i	0.228960	−	0.0144557i
$305$	−1.31105			−0.0750705
$306$	−5.18677	−	11.9841i	−0.296508	−	0.685086i
$307$		−	16.1303i		−	0.920604i	−0.887762	−	0.460302i	$-0.847741\pi$
$307$		−	16.1303i		−	0.920604i	0.887762	−	0.460302i	$-0.152259\pi$
$308$	−7.65820	−	7.18994i	−0.436367	−	0.409685i
$309$		−	2.56854i		−	0.146119i
$310$	11.9564	−	5.17478i	0.679078	−	0.293908i
$311$	5.05986			0.286918			0.143459	−	0.989656i	$-0.454177\pi$
$311$	5.05986			0.286918			0.143459	+	0.989656i	$0.454177\pi$
$312$	7.46661	+	2.68675i	0.422713	+	0.152107i
$313$	−25.9367			−1.46603			−0.733015	−	0.680212i	$-0.761888\pi$
$313$	−25.9367			−1.46603			−0.733015	+	0.680212i	$0.761888\pi$
$314$	19.3337	−	8.36769i	1.09106	−	0.472216i
$315$			5.81173i			0.327454i
$316$	−2.84344	+	3.02862i	−0.159956	+	0.170373i
$317$		−	12.6961i		−	0.713082i	−0.934280	−	0.356541i	$-0.883956\pi$
$317$		−	12.6961i		−	0.713082i	0.934280	−	0.356541i	$-0.116044\pi$
$318$	1.24412	+	2.87456i	0.0697670	+	0.161198i
$319$	−0.0342076			−0.00191526
$320$	−5.09735	+	6.16580i	−0.284950	+	0.344678i
$321$	−9.34851			−0.521783
$322$	6.95835	+	16.0774i	0.387773	+	0.895956i
$323$		−	3.85504i		−	0.214500i
$324$	−5.37000	+	5.71974i	−0.298334	+	0.317763i
$325$		−	3.60762i		−	0.200115i
$326$	−9.83290	+	4.25572i	−0.544594	+	0.235703i
$327$	15.6266			0.864154
$328$	−30.5195	−	10.9820i	−1.68516	−	0.606379i
$329$	−29.3989			−1.62081
$330$	2.18480	−	0.945592i	0.120269	−	0.0520531i
$331$		−	25.6782i		−	1.41140i	−0.708509	−	0.705701i	$-0.750632\pi$
$331$		−	25.6782i		−	1.41140i	0.708509	−	0.705701i	$-0.249368\pi$
$332$	−23.8739	−	22.4141i	−1.31025	−	1.23013i
$333$		−	27.4487i		−	1.50418i
$334$	8.44508	+	19.5125i	0.462094	+	1.06768i
$335$	4.07518			0.222651
$336$	7.53274	−	0.475591i	0.410944	−	0.0259456i
$337$	−3.39684			−0.185038			−0.0925189	−	0.995711i	$-0.529492\pi$
$337$	−3.39684			−0.185038			−0.0925189	+	0.995711i	$0.529492\pi$
$338$	−0.00836448	−	0.0193263i	−0.000454968	−	0.00105121i
$339$			7.59563i			0.412538i
$340$	5.62099	+	5.27729i	0.304841	+	0.286201i
$341$		−	19.9413i		−	1.07988i
$342$	−3.10869	+	1.34545i	−0.168099	+	0.0727538i
$343$	−19.6844			−1.06286
$344$	5.50658	−	15.3031i	0.296895	−	0.825087i
$345$	−3.97028			−0.213753
$346$	−8.56292	+	3.70607i	−0.460345	+	0.199239i
$347$		−	25.1646i		−	1.35091i	−0.737402	−	0.675454i	$-0.763948\pi$
$347$		−	25.1646i		−	1.35091i	0.737402	−	0.675454i	$-0.236052\pi$
$348$	0.0168236	−	0.0179193i	0.000901838	−	0.000960573i
$349$			1.81121i			0.0969521i	0.998824	+	0.0484760i	$0.0154365\pi$
$349$			1.81121i			0.0969521i	−0.998824	+	0.0484760i	$0.984564\pi$
$350$	−1.36296	−	3.14913i	−0.0728531	−	0.168328i
$351$	−15.1366			−0.807930
$352$	5.56213	+	10.9088i	0.296462	+	0.581443i
$353$	21.4490			1.14161			0.570806	−	0.821085i	$-0.306631\pi$
$353$	21.4490			1.14161			0.570806	+	0.821085i	$0.306631\pi$
$354$	2.43265	+	5.62067i	0.129294	+	0.298735i
$355$			15.3553i			0.814977i
$356$	−20.3933	+	21.7215i	−1.08084	+	1.15124i
$357$		−	7.27420i		−	0.384992i
$358$	−29.9458	+	12.9607i	−1.58269	+	0.684994i
$359$	15.2626			0.805527			0.402763	−	0.915304i	$-0.368050\pi$
$359$	15.2626			0.805527			0.402763	+	0.915304i	$0.368050\pi$
$360$	2.29380	−	6.37458i	0.120894	−	0.335970i
$361$	−1.00000			−0.0526316
$362$	15.1797	−	6.56984i	0.797827	−	0.345303i
$363$			4.91052i			0.257736i
$364$	−12.7633	−	11.9829i	−0.668979	−	0.628074i
$365$		−	7.41737i		−	0.388243i
$366$	−0.572716	−	1.32327i	−0.0299363	−	0.0691683i
$367$	−35.0414			−1.82915			−0.914573	−	0.404420i	$-0.867473\pi$
$367$	−35.0414			−1.82915			−0.914573	+	0.404420i	$0.867473\pi$
$368$	−1.28677	−	20.3808i	−0.0670775	−	1.06242i
$369$	27.4675			1.42990
$370$	6.43722	+	14.8733i	0.334655	+	0.773225i
$371$		−	6.91039i		−	0.358770i
$372$	10.4460	+	9.80728i	0.541600	+	0.508484i
$373$			2.83276i			0.146675i	0.997307	+	0.0733375i	$0.0233650\pi$
$373$			2.83276i			0.146675i	−0.997307	+	0.0733375i	$0.976635\pi$
$374$	10.8304	−	4.68743i	0.560026	−	0.242381i
$375$	0.777674			0.0401589
$376$	32.2461	+	11.6033i	1.66296	+	0.598393i
$377$	−0.0570110			−0.00293622
$378$	−13.2129	+	5.71859i	−0.679597	+	0.294132i
$379$		−	17.8185i		−	0.915274i	−0.889139	−	0.457637i	$-0.848696\pi$
$379$		−	17.8185i		−	0.915274i	0.889139	−	0.457637i	$-0.151304\pi$
$380$	1.36893	−	1.45809i	0.0702248	−	0.0747984i
$381$			2.35359i			0.120578i
$382$	−6.50274	−	15.0247i	−0.332709	−	0.768728i
$383$	12.8717			0.657714			0.328857	−	0.944380i	$-0.393337\pi$
$383$	12.8717			0.657714			0.328857	+	0.944380i	$0.393337\pi$
$384$	−8.44997	−	2.45140i	−0.431211	−	0.125098i
$385$	−5.25222			−0.267678
$386$	0.314581	+	0.726844i	0.0160118	+	0.0369954i
$387$			13.7727i			0.700106i
$388$	−19.6474	+	20.9269i	−0.997444	+	1.06240i
$389$			18.9373i			0.960157i	0.877225	+	0.480079i	$0.159392\pi$
$389$			18.9373i			0.960157i	−0.877225	+	0.480079i	$0.840608\pi$
$390$	3.64124	−	1.57594i	0.184381	−	0.0798010i
$391$	−19.6813			−0.995324
$392$	2.96123	+	1.06555i	0.149565	+	0.0538186i
$393$	4.51896			0.227952
$394$	−1.49406	+	0.646637i	−0.0752699	+	0.0325771i
$395$			2.07712i			0.104511i
$396$	−7.55986	−	7.09761i	−0.379897	−	0.356668i
$397$			19.5608i			0.981728i	0.871236	+	0.490864i	$0.163319\pi$
$397$			19.5608i			0.981728i	−0.871236	+	0.490864i	$0.836681\pi$
$398$	12.5929	+	29.0960i	0.631224	+	1.45845i
$399$	−1.88693			−0.0944648
$400$	0.252044	+	3.99205i	0.0126022	+	0.199603i
$401$	−23.5167			−1.17437			−0.587185	−	0.809453i	$-0.699764\pi$
$401$	−23.5167			−1.17437			−0.587185	+	0.809453i	$0.699764\pi$
$402$	1.78019	+	4.11316i	0.0887880	+	0.205146i
$403$		−	33.2345i		−	1.65553i
$404$	−18.1862	−	17.0742i	−0.904799	−	0.849474i
$405$			3.92277i			0.194924i
$406$	−0.0497656	+	0.0215387i	−0.00246982	+	0.00106895i
$407$	24.8062			1.22960
$408$	−2.87101	+	7.97869i	−0.142136	+	0.395004i
$409$	−34.4938			−1.70561			−0.852803	−	0.522233i	$-0.825099\pi$
$409$	−34.4938			−1.70561			−0.852803	+	0.522233i	$0.825099\pi$
$410$	−14.8835	+	6.44162i	−0.735041	+	0.318129i
$411$		−	2.53135i		−	0.124862i
$412$	4.52138	−	4.81585i	0.222752	−	0.237260i
$413$		−	13.5120i		−	0.664880i
$414$	6.86899	+	15.8709i	0.337592	+	0.780012i
$415$	−16.3734			−0.803739
$416$	9.26995	+	18.1809i	0.454497	+	0.891391i
$417$	3.60956			0.176761
$418$	−1.21592	−	2.80941i	−0.0594728	−	0.137413i
$419$			1.02786i			0.0502144i	0.999685	+	0.0251072i	$0.00799272\pi$
$419$			1.02786i			0.0502144i	−0.999685	+	0.0251072i	$0.992007\pi$
$420$	2.58309	−	2.75132i	0.126042	−	0.134250i
$421$			0.713127i			0.0347557i	0.999849	+	0.0173778i	$0.00553182\pi$
$421$			0.713127i			0.0347557i	−0.999849	+	0.0173778i	$0.994468\pi$
$422$	5.62265	−	2.43350i	0.273706	−	0.118461i
$423$	−29.0213			−1.41107
$424$	−2.72742	+	7.57964i	−0.132455	+	0.368100i
$425$	3.85504			0.186997
$426$	−15.4984	+	6.70779i	−0.750902	+	0.324994i
$427$			3.18111i			0.153944i
$428$	−17.5279	−	16.4561i	−0.847241	−	0.795436i
$429$		−	6.07298i		−	0.293206i
$430$	−3.22995	−	7.46285i	−0.155762	−	0.359890i
$431$	−10.1758			−0.490150			−0.245075	−	0.969504i	$-0.578813\pi$
$431$	−10.1758			−0.490150			−0.245075	+	0.969504i	$0.578813\pi$
$432$	16.7495	−	1.05751i	0.805863	−	0.0508794i
$433$	−4.69815			−0.225779			−0.112889	−	0.993608i	$-0.536011\pi$
$433$	−4.69815			−0.225779			−0.112889	+	0.993608i	$0.536011\pi$
$434$	−12.5560	−	29.0108i	−0.602707	−	1.39256i
$435$		−	0.0122896i		−	0.000589239i
$436$	29.2989	+	27.5074i	1.40316	+	1.31737i
$437$			5.10533i			0.244221i
$438$	7.48649	−	3.24019i	0.357719	−	0.154822i
$439$	−2.53473			−0.120976			−0.0604879	−	0.998169i	$-0.519266\pi$
$439$	−2.53473			−0.120976			−0.0604879	+	0.998169i	$0.519266\pi$
$440$	5.76089	+	2.07297i	0.274639	+	0.0988249i
$441$	−2.66510			−0.126909
$442$	18.0501	−	7.81217i	0.858557	−	0.371587i
$443$		−	8.91941i		−	0.423774i	−0.977294	−	0.211887i	$-0.932039\pi$
$443$		−	8.91941i		−	0.423774i	0.977294	−	0.211887i	$-0.0679609\pi$
$444$	−12.1999	+	12.9944i	−0.578980	+	0.616688i
$445$			14.8972i			0.706197i
$446$	−3.18116	−	7.35011i	−0.150632	−	0.348038i
$447$	14.3003			0.676379
$448$	14.9606	+	12.3681i	0.706821	+	0.584338i
$449$	−4.64897			−0.219398			−0.109699	−	0.993965i	$-0.534989\pi$
$449$	−4.64897			−0.219398			−0.109699	+	0.993965i	$0.534989\pi$
$450$	−1.34545	−	3.10869i	−0.0634253	−	0.146545i
$451$			24.8231i			1.16887i
$452$	−13.3705	+	14.2413i	−0.628897	+	0.669855i
$453$		−	9.14228i		−	0.429542i
$454$	8.58455	−	3.71543i	0.402893	−	0.174374i
$455$	−8.75345			−0.410368
$456$	2.06968	+	0.744743i	0.0969216	+	0.0348758i
$457$	−15.0176			−0.702495			−0.351248	−	0.936283i	$-0.614242\pi$
$457$	−15.0176			−0.702495			−0.351248	+	0.936283i	$0.614242\pi$
$458$	30.4030	−	13.1585i	1.42064	−	0.614858i
$459$		−	16.1747i		−	0.754969i
$460$	−7.44403	−	6.98886i	−0.347080	−	0.325857i
$461$		−	5.80968i		−	0.270584i	−0.990806	−	0.135292i	$-0.956803\pi$
$461$		−	5.80968i		−	0.270584i	0.990806	−	0.135292i	$-0.0431972\pi$
$462$	−2.29437	−	5.30117i	−0.106744	−	0.246633i
$463$	−40.5335			−1.88375			−0.941875	−	0.335964i	$-0.890938\pi$
$463$	−40.5335			−1.88375			−0.941875	+	0.335964i	$0.890938\pi$
$464$	0.0630862	−	0.00398305i	0.00292871	−	0.000184908i
$465$	7.16418			0.332231
$466$	−0.914010	−	2.11183i	−0.0423407	−	0.0978288i
$467$		−	11.4858i		−	0.531501i	−0.964042	−	0.265751i	$-0.914380\pi$
$467$		−	11.4858i		−	0.531501i	0.964042	−	0.265751i	$-0.0856198\pi$
$468$	−12.5994	−	11.8290i	−0.582408	−	0.546796i
$469$		−	9.88795i		−	0.456583i
$470$	15.7254	−	6.80604i	0.725360	−	0.313939i
$471$	11.5846			0.533789
$472$	−5.33296	+	14.8206i	−0.245469	+	0.682172i
$473$	−12.4468			−0.572304
$474$	−2.09648	+	0.907364i	−0.0962944	+	0.0416766i
$475$		−	1.00000i		−	0.0458831i
$476$	12.8047	−	13.6387i	0.586903	−	0.625127i
$477$		−	6.82165i		−	0.312342i
$478$	−1.71704	−	3.96725i	−0.0785357	−	0.181458i
$479$	12.0504			0.550595			0.275298	−	0.961359i	$-0.411224\pi$
$479$	12.0504			0.550595			0.275298	+	0.961359i	$0.411224\pi$
$480$	−3.91915	+	1.99827i	−0.178884	+	0.0912082i
$481$	41.3424			1.88505
$482$	10.7631	+	24.8683i	0.490247	+	1.13272i
$483$			9.63343i			0.438336i
$484$	−8.64396	+	9.20692i	−0.392907	+	0.418496i
$485$			14.3523i			0.651705i
$486$	−20.2958	+	8.78412i	−0.920638	+	0.398456i
$487$	1.48578			0.0673269			0.0336635	−	0.999433i	$-0.489283\pi$
$487$	1.48578			0.0673269			0.0336635	+	0.999433i	$0.489283\pi$
$488$	1.25553	−	3.48919i	0.0568353	−	0.157948i
$489$	−5.89180			−0.266436
$490$	1.44410	−	0.625014i	0.0652379	−	0.0282352i
$491$		−	29.6936i		−	1.34005i	−0.742337	−	0.670027i	$-0.766283\pi$
$491$		−	29.6936i		−	1.34005i	0.742337	−	0.670027i	$-0.233717\pi$
$492$	−13.0033	−	12.2082i	−0.586234	−	0.550389i
$493$		−	0.0609210i		−	0.00274375i
$494$	−2.02648	−	4.68222i	−0.0911758	−	0.210663i
$495$	−5.18477			−0.233038
$496$	2.32191	+	36.7761i	0.104257	+	1.65129i
$497$	37.2579			1.67125
$498$	−7.15252	−	16.5260i	−0.320512	−	0.740548i
$499$			31.4369i			1.40731i	0.710542	+	0.703654i	$0.248450\pi$
$499$			31.4369i			1.40731i	−0.710542	+	0.703654i	$0.751550\pi$
$500$	1.45809	+	1.36893i	0.0652077	+	0.0612206i
$501$			11.6917i			0.522348i
$502$	9.61460	−	4.16124i	0.429121	−	0.185725i
$503$	−1.94409			−0.0866828			−0.0433414	−	0.999060i	$-0.513800\pi$
$503$	−1.94409			−0.0866828			−0.0433414	+	0.999060i	$0.513800\pi$
$504$	−15.4672	−	5.56563i	−0.688962	−	0.247913i
$505$	−12.4726			−0.555026
$506$	−14.3430	+	6.20770i	−0.637623	+	0.275966i
$507$		−	0.0115801i		−	0.000514292i
$508$	−4.14301	+	4.41284i	−0.183817	+	0.195788i
$509$			24.4620i			1.08426i	0.840296	+	0.542129i	$0.182381\pi$
$509$			24.4620i			1.08426i	−0.840296	+	0.542129i	$0.817619\pi$
$510$	1.68403	+	3.89097i	0.0745699	+	0.172295i
$511$	−17.9974			−0.796157
$512$	−11.5280	−	19.4706i	−0.509469	−	0.860489i
$513$	−4.19572			−0.185246
$514$	−12.6576	−	29.2455i	−0.558301	−	1.28996i
$515$		−	3.30285i		−	0.145541i
$516$	6.12143	−	6.52011i	0.269481	−	0.287032i
$517$		−	26.2274i		−	1.15348i
$518$	36.0883	−	15.6192i	1.58563	−	0.686266i
$519$	−5.13084			−0.225219
$520$	9.60121	+	3.45485i	0.421041	+	0.151505i
$521$	2.91231			0.127591			0.0637954	−	0.997963i	$-0.479679\pi$
$521$	2.91231			0.127591			0.0637954	+	0.997963i	$0.479679\pi$
$522$	−0.0491265	+	0.0212622i	−0.00215021	+	0.000930619i
$523$			17.9564i			0.785178i	0.919714	+	0.392589i	$0.128420\pi$
$523$			17.9564i			0.785178i	−0.919714	+	0.392589i	$0.871580\pi$
$524$	8.47277	+	7.95470i	0.370135	+	0.347503i
$525$		−	1.88693i		−	0.0823525i
$526$	−0.620930	−	1.43467i	−0.0270738	−	0.0625545i
$527$	35.5138			1.54701
$528$	0.424285	+	6.72013i	0.0184646	+	0.292456i
$529$	3.06444			0.133236
$530$	1.59980	+	3.69636i	0.0694909	+	0.160560i
$531$		−	13.3384i		−	0.578839i
$532$	−3.53788	−	3.32155i	−0.153387	−	0.144008i
$533$			41.3707i			1.79196i
$534$	−15.0361	+	6.50768i	−0.650675	+	0.281615i
$535$	−12.0211			−0.519718
$536$	−3.90262	+	10.8456i	−0.168567	+	0.468457i
$537$	−17.9433			−0.774312
$538$	25.8960	−	11.2079i	1.11645	−	0.483206i
$539$		−	2.40852i		−	0.103742i
$540$	5.74367	−	6.11774i	0.247168	−	0.263265i
$541$		−	4.16184i		−	0.178931i	−0.995990	−	0.0894656i	$-0.971484\pi$
$541$		−	4.16184i		−	0.178931i	0.995990	−	0.0894656i	$-0.0285159\pi$
$542$	0.594229	+	1.37297i	0.0255243	+	0.0589743i
$543$	9.09556			0.390328
$544$	−19.4278	+	9.90571i	−0.832960	+	0.424704i
$545$	20.0940			0.860734
$546$	−3.82384	−	8.83503i	−0.163645	−	0.378104i
$547$			28.8705i			1.23442i	0.786800	+	0.617208i	$0.211736\pi$
$547$			28.8705i			1.23442i	−0.786800	+	0.617208i	$0.788264\pi$
$548$	4.45591	−	4.74612i	0.190347	−	0.202744i
$549$			3.14026i			0.134023i
$550$	2.80941	−	1.21592i	0.119794	−	0.0518472i
$551$	−0.0158030			−0.000673229
$552$	3.80216	−	10.5664i	0.161831	−	0.449736i
$553$	5.03988			0.214318
$554$	2.20559	−	0.954590i	0.0937067	−	0.0405566i
$555$			8.91196i			0.378292i
$556$	6.76769	+	6.35388i	0.287014	+	0.269464i
$557$			29.9532i			1.26916i	0.772858	+	0.634579i	$0.218826\pi$
$557$			29.9532i			1.26916i	−0.772858	+	0.634579i	$0.781174\pi$
$558$	−12.3947	−	28.6382i	−0.524712	−	1.21235i
$559$	−20.7441			−0.877380
$560$	9.68624	−	0.611556i	0.409318	−	0.0258429i
$561$	6.48948			0.273986
$562$	11.7027	+	27.0392i	0.493647	+	1.14058i
$563$		−	15.3052i		−	0.645037i	−0.946563	−	0.322518i	$-0.895471\pi$
$563$		−	15.3052i		−	0.645037i	0.946563	−	0.322518i	$-0.104529\pi$
$564$	13.7389	+	12.8989i	0.578513	+	0.543140i
$565$			9.76712i			0.410906i
$566$	−17.1744	+	7.43316i	−0.721895	+	0.312439i
$567$	9.51813			0.399724
$568$	−40.8663	−	14.7051i	−1.71471	−	0.617013i
$569$	−26.2404			−1.10005			−0.550027	−	0.835147i	$-0.685383\pi$
$569$	−26.2404			−1.10005			−0.550027	+	0.835147i	$0.685383\pi$
$570$	1.00932	−	0.436838i	0.0422757	−	0.0182971i
$571$		−	19.6428i		−	0.822024i	−0.911630	−	0.411012i	$-0.865175\pi$
$571$		−	19.6428i		−	0.822024i	0.911630	−	0.411012i	$-0.134825\pi$
$572$	10.6902	−	11.3864i	0.446980	−	0.476091i
$573$		−	9.00266i		−	0.376092i
$574$	15.6298	+	36.1129i	0.652377	+	1.50732i
$575$	−5.10533			−0.212907
$576$	14.7685	+	12.2093i	0.615352	+	0.508720i
$577$	26.8816			1.11910			0.559548	−	0.828798i	$-0.310975\pi$
$577$	26.8816			1.11910			0.559548	+	0.828798i	$0.310975\pi$
$578$	−1.20135	−	2.77573i	−0.0499695	−	0.115455i
$579$			0.435519i			0.0180996i
$580$	0.0216332	−	0.0230421i	0.000898270	−	0.000956772i
$581$			39.7281i			1.64820i
$582$	−14.4861	+	6.26963i	−0.600467	+	0.259885i
$583$	6.16491			0.255325
$584$	19.7404	+	7.10328i	0.816862	+	0.293936i
$585$	−8.64105			−0.357263
$586$	−35.0476	+	15.1688i	−1.44780	+	0.626616i
$587$			4.35767i			0.179860i	0.995948	+	0.0899302i	$0.0286644\pi$
$587$			4.35767i			0.179860i	−0.995948	+	0.0899302i	$0.971336\pi$
$588$	1.26168	+	1.18453i	0.0520307	+	0.0488492i
$589$		−	9.21232i		−	0.379587i
$590$	3.12811	+	7.22754i	0.128782	+	0.297553i
$591$	−0.895232			−0.0368249
$592$	−45.7480	+	2.88837i	−1.88023	+	0.118711i
$593$	−3.80956			−0.156440			−0.0782200	−	0.996936i	$-0.524924\pi$
$593$	−3.80956			−0.156440			−0.0782200	+	0.996936i	$0.524924\pi$
$594$	−5.10168	−	11.7875i	−0.209325	−	0.483647i
$595$		−	9.35379i		−	0.383468i
$596$	26.8121	+	25.1726i	1.09827	+	1.03111i
$597$			17.4341i			0.713531i
$598$	−23.9043	+	10.3459i	−0.977519	+	0.423074i
$599$	5.33523			0.217992			0.108996	−	0.994042i	$-0.465236\pi$
$599$	5.33523			0.217992			0.108996	+	0.994042i	$0.465236\pi$
$600$	−0.744743	+	2.06968i	−0.0304040	+	0.0844943i
$601$	9.94251			0.405563			0.202782	−	0.979224i	$-0.435002\pi$
$601$	9.94251			0.405563			0.202782	+	0.979224i	$0.435002\pi$
$602$	−18.1077	+	7.83710i	−0.738015	+	0.319416i
$603$		−	9.76097i		−	0.397497i
$604$	16.0931	−	17.1412i	0.654819	−	0.697465i
$605$			6.31438i			0.256716i
$606$	−5.44852	−	12.5889i	−0.221331	−	0.511389i
$607$	28.5500			1.15881			0.579405	−	0.815040i	$-0.303285\pi$
$607$	28.5500			1.15881			0.579405	+	0.815040i	$0.303285\pi$
$608$	2.56955	+	5.03958i	0.104209	+	0.204382i
$609$	−0.0298191			−0.00120833
$610$	−0.736447	−	1.70157i	−0.0298179	−	0.0688946i
$611$		−	43.7111i		−	1.76836i
$612$	12.6403	−	13.4635i	0.510953	−	0.544230i
$613$			31.2407i			1.26180i	0.775864	+	0.630900i	$0.217314\pi$
$613$			31.2407i			1.26180i	−0.775864	+	0.630900i	$0.782686\pi$
$614$	20.9350	−	9.06076i	0.844869	−	0.365663i
$615$	−8.91805			−0.359611
$616$	5.02981	−	13.9781i	0.202657	−	0.563194i
$617$	16.1416			0.649837			0.324918	−	0.945742i	$-0.394663\pi$
$617$	16.1416			0.649837			0.324918	+	0.945742i	$0.394663\pi$
$618$	3.33363	−	1.44281i	0.134098	−	0.0580383i
$619$			9.62836i			0.386997i	0.981101	+	0.193498i	$0.0619834\pi$
$619$			9.62836i			0.386997i	−0.981101	+	0.193498i	$0.938017\pi$
$620$	13.4324	+	12.6110i	0.539457	+	0.506472i
$621$			21.4206i			0.859578i
$622$	2.84224	+	6.56704i	0.113964	+	0.263314i
$623$	36.1464			1.44817
$624$	0.707122	+	11.1999i	0.0283075	+	0.448355i
$625$	1.00000			0.0400000
$626$	−14.5693	−	33.6625i	−0.582305	−	1.34542i
$627$		−	1.68338i		−	0.0672276i
$628$	21.7203	+	20.3922i	0.866736	+	0.813739i
$629$			44.1778i			1.76149i
$630$	−7.54287	+	3.26458i	−0.300515	+	0.130064i
$631$	11.8631			0.472261			0.236131	−	0.971721i	$-0.424121\pi$
$631$	11.8631			0.472261			0.236131	+	0.971721i	$0.424121\pi$
$632$	−5.52799	−	1.98916i	−0.219891	−	0.0791246i
$633$	3.36905			0.133908
$634$	16.4778	−	7.13168i	0.654419	−	0.283235i
$635$			3.02645i			0.120101i
$636$	−3.03196	+	3.22942i	−0.120225	+	0.128055i
$637$		−	4.01409i		−	0.159044i
$638$	−0.0192152	−	0.0443970i	−0.000760737	−	0.00175769i
$639$	36.7795			1.45497
$640$	−10.8657	−	3.15222i	−0.429505	−	0.124603i
$641$	11.6662			0.460788			0.230394	−	0.973097i	$-0.425998\pi$
$641$	11.6662			0.460788			0.230394	+	0.973097i	$0.425998\pi$
$642$	−5.25128	−	12.1332i	−0.207251	−	0.478857i
$643$		−	9.82447i		−	0.387439i	−0.981057	−	0.193720i	$-0.937945\pi$
$643$		−	9.82447i		−	0.387439i	0.981057	−	0.193720i	$-0.0620552\pi$
$644$	−16.9576	+	18.0621i	−0.668225	+	0.711745i
$645$		−	4.47168i		−	0.176072i
$646$	5.00334	−	2.16547i	0.196854	−	0.0851991i
$647$	−18.3731			−0.722319			−0.361160	−	0.932504i	$-0.617619\pi$
$647$	−18.3731			−0.722319			−0.361160	+	0.932504i	$0.617619\pi$
$648$	−10.4399	−	3.75665i	−0.410119	−	0.147575i
$649$	12.0543			0.473174
$650$	4.68222	−	2.02648i	0.183652	−	0.0794852i
$651$		−	17.3830i		−	0.681295i
$652$	−11.0467	−	10.3713i	−0.432624	−	0.406171i
$653$			2.23290i			0.0873803i	0.999045	+	0.0436901i	$0.0139114\pi$
$653$			2.23290i			0.0873803i	−0.999045	+	0.0436901i	$0.986089\pi$
$654$	8.77784	+	20.2813i	0.343241	+	0.793062i
$655$	5.81087			0.227050
$656$	−2.89034	−	45.7792i	−0.112849	−	1.78738i
$657$	−17.7663			−0.693128
$658$	−16.5140	−	38.1559i	−0.643784	−	1.48747i
$659$		−	40.7083i		−	1.58577i	−0.609370	−	0.792886i	$-0.708578\pi$
$659$		−	40.7083i		−	1.58577i	0.609370	−	0.792886i	$-0.291422\pi$
$660$	2.45451	+	2.30443i	0.0955417	+	0.0896998i
$661$		−	29.6681i		−	1.15395i	−0.816760	−	0.576977i	$-0.804232\pi$
$661$		−	29.6681i		−	1.15395i	0.816760	−	0.576977i	$-0.195768\pi$
$662$	33.3270	−	14.4241i	1.29529	−	0.560607i
$663$	10.8155			0.420039
$664$	15.6801	−	43.5757i	0.608505	−	1.69107i
$665$	−2.42638			−0.0940911
$666$	35.6248	−	15.4186i	1.38043	−	0.597458i
$667$			0.0806794i			0.00312392i
$668$	−20.5809	+	21.9212i	−0.796297	+	0.848158i
$669$		−	4.40413i		−	0.170274i
$670$	2.28913	+	5.28906i	0.0884366	+	0.204334i
$671$	−2.83794			−0.109557
$672$	4.84857	+	9.50936i	0.187038	+	0.366832i
$673$	−0.592899			−0.0228546			−0.0114273	−	0.999935i	$-0.503637\pi$
$673$	−0.592899			−0.0228546			−0.0114273	+	0.999935i	$0.503637\pi$
$674$	−1.90809	−	4.40866i	−0.0734968	−	0.169815i
$675$		−	4.19572i		−	0.161493i
$676$	0.0203844	−	0.0217120i	0.000784017	−	0.000835078i
$677$		−	36.2140i		−	1.39182i	−0.718131	−	0.695908i	$-0.755002\pi$
$677$		−	36.2140i		−	1.39182i	0.718131	−	0.695908i	$-0.244998\pi$
$678$	−9.85814	+	4.26665i	−0.378600	+	0.163860i
$679$	34.8242			1.33643
$680$	−3.69179	+	10.2597i	−0.141574	+	0.393441i
$681$	5.14380			0.197111
$682$	25.8812	−	11.2015i	0.991041	−	0.428927i
$683$		−	10.4184i		−	0.398649i	−0.979934	−	0.199324i	$-0.936125\pi$
$683$		−	10.4184i		−	0.398649i	0.979934	−	0.199324i	$-0.0638748\pi$
$684$	−3.49245	−	3.27890i	−0.133537	−	0.125372i
$685$		−	3.25503i		−	0.124368i
$686$	−11.0572	−	25.5478i	−0.422166	−	0.975421i
$687$	18.2172			0.695030
$688$	22.9546	−	1.44927i	0.875135	−	0.0552530i
$689$	10.2746			0.391430
$690$	−2.23020	−	5.15291i	−0.0849024	−	0.196168i
$691$			27.3353i			1.03988i	0.854201	+	0.519942i	$0.174047\pi$
$691$			27.3353i			1.03988i	−0.854201	+	0.519942i	$0.825953\pi$
$692$	−9.61999	−	9.03177i	−0.365697	−	0.343336i
$693$			12.5802i			0.477884i
$694$	32.6604	−	14.1356i	1.23977	−	0.536579i
$695$	4.64148			0.176061
$696$	0.0327071	+	0.0117691i	0.00123976	+	0.000446108i
$697$	−44.2080			−1.67450
$698$	−2.35072	+	1.01740i	−0.0889761	+	0.0385092i
$699$		−	1.26539i		−	0.0478616i
$700$	3.32155	−	3.53788i	0.125543	−	0.133719i
$701$			9.48933i			0.358407i	0.983812	+	0.179203i	$0.0573520\pi$
$701$			9.48933i			0.358407i	−0.983812	+	0.179203i	$0.942648\pi$
$702$	−8.50256	−	19.6453i	−0.320909	−	0.741464i
$703$	11.4598			0.432213
$704$	−11.0339	+	13.3467i	−0.415855	+	0.503022i
$705$	9.42256			0.354874
$706$	12.0484	+	27.8380i	0.453447	+	1.04770i
$707$			30.2634i			1.13817i
$708$	−5.92842	+	6.31452i	−0.222804	+	0.237314i
$709$			39.4572i			1.48185i	0.671590	+	0.740923i	$0.265612\pi$
$709$			39.4572i			1.48185i	−0.671590	+	0.740923i	$0.734388\pi$
$710$	−19.9292	+	8.62546i	−0.747931	+	0.323708i
$711$	4.97516			0.186583
$712$	−39.6471	−	14.2664i	−1.48584	−	0.534656i
$713$	−47.0320			−1.76136
$714$	9.44097	−	4.08609i	0.353319	−	0.152918i
$715$		−	7.80915i		−	0.292046i
$716$	−33.6426	−	31.5855i	−1.25728	−	1.18041i
$717$		−	2.37714i		−	0.0887761i
$718$	8.57334	+	19.8088i	0.319954	+	0.739258i
$719$	30.5190			1.13817			0.569084	−	0.822279i	$-0.307298\pi$
$719$	30.5190			1.13817			0.569084	+	0.822279i	$0.307298\pi$
$720$	9.56185	−	0.603702i	0.356349	−	0.0224987i
$721$	−8.01398			−0.298456
$722$	−0.561724	−	1.29787i	−0.0209052	−	0.0483017i
$723$			14.9009i			0.554171i
$724$	17.0536	+	16.0108i	0.633792	+	0.595038i
$725$		−	0.0158030i		−	0.000586907i
$726$	−6.37322	+	2.75836i	−0.236532	+	0.102372i
$727$	−21.2523			−0.788204			−0.394102	−	0.919067i	$-0.628944\pi$
$727$	−21.2523			−0.788204			−0.394102	+	0.919067i	$0.628944\pi$
$728$	8.38278	−	23.2962i	0.310687	−	0.863414i
$729$	−0.392816			−0.0145487
$730$	9.62678	−	4.16651i	0.356303	−	0.154209i
$731$		−	22.1667i		−	0.819867i
$732$	1.39572	−	1.48662i	0.0515873	−	0.0549471i
$733$		−	19.8239i		−	0.732212i	−0.930573	−	0.366106i	$-0.880691\pi$
$733$		−	19.8239i		−	0.732212i	0.930573	−	0.366106i	$-0.119309\pi$
$734$	−19.6836	−	45.4792i	−0.726534	−	1.67867i
$735$	0.865295			0.0319169
$736$	25.7288	−	13.1184i	0.948375	−	0.483551i
$737$	8.82126			0.324935
$738$	15.4291	+	35.6492i	0.567954	+	1.31226i
$739$			31.8107i			1.17018i	0.810969	+	0.585089i	$0.198940\pi$
$739$			31.8107i			1.17018i	−0.810969	+	0.585089i	$0.801060\pi$
$740$	−15.6876	+	16.7093i	−0.576689	+	0.614248i
$741$		−	2.80555i		−	0.103064i
$742$	8.96879	−	3.88173i	0.329255	−	0.142503i
$743$	18.4884			0.678273			0.339137	−	0.940737i	$-0.389865\pi$
$743$	18.4884			0.678273			0.339137	+	0.940737i	$0.389865\pi$
$744$	−6.86081	+	19.0665i	−0.251529	+	0.699013i
$745$	18.3885			0.673703
$746$	−3.67656	+	1.59123i	−0.134608	+	0.0582591i
$747$			39.2180i			1.43491i
$748$	12.1674	+	11.4234i	0.444883	+	0.417680i
$749$			29.1678i			1.06577i
$750$	0.436838	+	1.00932i	0.0159511	+	0.0368551i
$751$	−32.2524			−1.17691			−0.588454	−	0.808531i	$-0.700263\pi$
$751$	−32.2524			−1.17691			−0.588454	+	0.808531i	$0.700263\pi$
$752$	3.05385	+	48.3691i	0.111363	+	1.76384i
$753$	5.76100			0.209942
$754$	−0.0320244	−	0.0739929i	−0.00116626	−	0.00269466i
$755$		−	11.7559i		−	0.427842i
$756$	−14.8440	−	13.9363i	−0.539870	−	0.506859i
$757$		−	28.0963i		−	1.02118i	−0.859825	−	0.510588i	$-0.829428\pi$
$757$		−	28.0963i		−	1.02118i	0.859825	−	0.510588i	$-0.170572\pi$
$758$	23.1261	−	10.0091i	0.839977	−	0.363545i
$759$	−8.59420			−0.311950
$760$	2.66137	+	0.957654i	0.0965381	+	0.0347378i
$761$	−5.52851			−0.200408			−0.100204	−	0.994967i	$-0.531950\pi$
$761$	−5.52851			−0.200408			−0.100204	+	0.994967i	$0.531950\pi$
$762$	−3.05466	+	1.32207i	−0.110659	+	0.0478935i
$763$		−	48.7558i		−	1.76508i
$764$	15.8473	−	16.8794i	0.573336	−	0.610676i
$765$		−	9.23368i		−	0.333844i
$766$	7.23035	+	16.7058i	0.261243	+	0.603606i
$767$	20.0900			0.725407
$768$	−1.56495	−	12.3440i	−0.0564703	−	0.445425i
$769$	29.7719			1.07360			0.536800	−	0.843709i	$-0.319633\pi$
$769$	29.7719			1.07360			0.536800	+	0.843709i	$0.319633\pi$
$770$	−2.95030	−	6.81670i	−0.106321	−	0.245657i
$771$		−	17.5237i		−	0.631099i
$772$	−0.766641	+	0.816571i	−0.0275920	+	0.0293890i
$773$			15.9477i			0.573600i	0.957991	+	0.286800i	$0.0925915\pi$
$773$			15.9477i			0.573600i	−0.957991	+	0.286800i	$0.907409\pi$
$774$	−17.8752	+	7.73646i	−0.642510	+	0.278081i
$775$	9.21232			0.330916
$776$	−38.1968	−	13.7446i	−1.37119	−	0.493401i
$777$	21.6238			0.775750
$778$	−24.5781	+	10.6375i	−0.881168	+	0.381373i
$779$			11.4676i			0.410869i
$780$	4.09074	+	3.84061i	0.146472	+	0.137516i
$781$			33.2386i			1.18937i
$782$	−11.0554	−	25.5437i	−0.395341	−	0.913441i
$783$	−0.0663049			−0.00236954
$784$	0.280442	+	4.44184i	0.0100158	+	0.158637i
$785$	14.8964			0.531677
$786$	2.53841	+	5.86503i	0.0905421	+	0.209199i
$787$		−	11.1170i		−	0.396277i	−0.980174	−	0.198138i	$-0.936510\pi$
$787$		−	11.1170i		−	0.396277i	0.980174	−	0.198138i	$-0.0634896\pi$
$788$	−1.67850	−	1.57587i	−0.0597942	−	0.0561380i
$789$		−	0.859642i		−	0.0306041i
$790$	−2.69583	+	1.16677i	−0.0959134	+	0.0415117i
$791$	23.6988			0.842631
$792$	4.96522	−	13.7986i	0.176431	−	0.490312i
$793$	−4.72976			−0.167959
$794$	−25.3874	+	10.9878i	−0.900964	+	0.389941i
$795$			2.21483i			0.0785520i
$796$	−30.6892	+	32.6879i	−1.08775	+	1.15859i
$797$			37.8295i			1.33999i	0.742366	+	0.669995i	$0.233704\pi$
$797$			37.8295i			1.33999i	−0.742366	+	0.669995i	$0.766296\pi$
$798$	−1.05994	−	2.44899i	−0.0375213	−	0.0866935i
$799$	46.7090			1.65244
$800$	−5.03958	+	2.56955i	−0.178176	+	0.0908473i
$801$	35.6822			1.26077
$802$	−13.2099	−	30.5217i	−0.466458	−	1.07776i
$803$		−	16.0559i		−	0.566599i
$804$	−4.33837	+	4.62092i	−0.153003	+	0.162967i
$805$			12.3875i			0.436602i
$806$	43.1341	−	18.6686i	1.51933	−	0.657574i
$807$	15.5167			0.546213
$808$	11.9445	−	33.1944i	0.420206	−	1.16777i
$809$	9.28290			0.326369			0.163185	−	0.986596i	$-0.447823\pi$
$809$	9.28290			0.326369			0.163185	+	0.986596i	$0.447823\pi$
$810$	−5.09124	+	2.20351i	−0.178888	+	0.0774234i
$811$			17.0390i			0.598321i	0.954203	+	0.299160i	$0.0967066\pi$
$811$			17.0390i			0.598321i	−0.954203	+	0.299160i	$0.903293\pi$
$812$	−0.0559090	−	0.0524904i	−0.00196202	−	0.00184205i
$813$			0.822676i			0.0288525i
$814$	13.9342	+	32.1952i	0.488393	+	1.12844i
$815$	−7.57618			−0.265382
$816$	−11.9680	+	0.755619i	−0.418964	+	0.0264520i
$817$	−5.75007			−0.201170
$818$	−19.3760	−	44.7684i	−0.677464	−	1.56529i
$819$			20.9665i			0.732628i
$820$	−16.7208	−	15.6984i	−0.583915	−	0.548211i
$821$		−	27.6848i		−	0.966206i	−0.875564	−	0.483103i	$-0.839510\pi$
$821$		−	27.6848i		−	0.966206i	0.875564	−	0.483103i	$-0.160490\pi$
$822$	3.28536	−	1.42192i	0.114590	−	0.0495951i
$823$	−34.9120			−1.21696			−0.608478	−	0.793570i	$-0.708220\pi$
$823$	−34.9120			−1.21696			−0.608478	+	0.793570i	$0.708220\pi$
$824$	8.79011	+	3.16299i	0.306218	+	0.110188i
$825$	1.68338			0.0586076
$826$	17.5368	−	7.58999i	0.610182	−	0.264089i
$827$		−	32.2541i		−	1.12158i	−0.827957	−	0.560792i	$-0.810497\pi$
$827$		−	32.2541i		−	1.12158i	0.827957	−	0.560792i	$-0.189503\pi$
$828$	−16.7399	+	17.8301i	−0.581751	+	0.619639i
$829$		−	5.17638i		−	0.179783i	−0.995952	−	0.0898916i	$-0.971348\pi$
$829$		−	5.17638i		−	0.179783i	0.995952	−	0.0898916i	$-0.0286521\pi$
$830$	−9.19733	−	21.2506i	−0.319244	−	0.737617i
$831$	1.32157			0.0458449
$832$	−18.3893	+	22.2438i	−0.637533	+	0.771166i
$833$	4.28939			0.148619
$834$	2.02757	+	4.68474i	0.0702092	+	0.162219i
$835$			15.0342i			0.520281i
$836$	2.96323	−	3.15622i	0.102486	−	0.109160i
$837$		−	38.6524i		−	1.33602i
$838$	−1.33403	+	0.577376i	−0.0460834	+	0.0199451i
$839$	−33.6197			−1.16068			−0.580341	−	0.814374i	$-0.697081\pi$
$839$	−33.6197			−1.16068			−0.580341	+	0.814374i	$0.697081\pi$
$840$	5.02183	+	1.80703i	0.173270	+	0.0623485i
$841$	28.9998			0.999991
$842$	−0.925546	+	0.400580i	−0.0318964	+	0.0138049i
$843$			16.2017i			0.558015i
$844$	6.31675	+	5.93051i	0.217431	+	0.204136i
$845$		−	0.0148907i		−	0.000512257i
$846$	−16.3020	−	37.6659i	−0.560473	−	1.29498i
$847$	15.3211			0.526439
$848$	−11.3694	+	0.717827i	−0.390429	+	0.0246503i
$849$	−10.2908			−0.353179
$850$	2.16547	+	5.00334i	0.0742749	+	0.171613i
$851$		−	58.5059i		−	2.00556i
$852$	−17.4117	−	16.3470i	−0.596515	−	0.560040i
$853$		−	25.5027i		−	0.873198i	−0.899656	−	0.436599i	$-0.856183\pi$
$853$		−	25.5027i		−	0.873198i	0.899656	−	0.436599i	$-0.143817\pi$
$854$	−4.12866	+	1.78690i	−0.141280	+	0.0611465i
$855$	−2.39522			−0.0819149
$856$	11.5121	−	31.9927i	0.393475	−	1.09349i
$857$	−50.1701			−1.71378			−0.856890	−	0.515500i	$-0.827606\pi$
$857$	−50.1701			−1.71378			−0.856890	+	0.515500i	$0.827606\pi$
$858$	7.88193	−	3.41133i	0.269085	−	0.116461i
$859$			11.1713i			0.381161i	0.981672	+	0.190581i	$0.0610371\pi$
$859$			11.1713i			0.381161i	−0.981672	+	0.190581i	$0.938963\pi$
$860$	7.87146	−	8.38411i	0.268415	−	0.285896i
$861$			21.6386i			0.737441i
$862$	−5.71597	−	13.2068i	−0.194687	−	0.449827i
$863$	5.42074			0.184524			0.0922621	−	0.995735i	$-0.470590\pi$
$863$	5.42074			0.184524			0.0922621	+	0.995735i	$0.470590\pi$
$864$	10.7811	+	21.1447i	0.366781	+	0.719358i
$865$	−6.59767			−0.224328
$866$	−2.63906	−	6.09758i	−0.0896789	−	0.207204i
$867$		−	1.66320i		−	0.0564851i
$868$	30.5992	−	32.5921i	1.03861	−	1.10625i
$869$			4.49620i			0.152523i
$870$	0.0159502	−	0.00690333i	0.000540764	−	0.000234045i
$871$	14.7017			0.498148
$872$	−19.2431	+	53.4777i	−0.651655	+	1.81098i
$873$	34.3770			1.16349
$874$	−6.62606	+	2.86779i	−0.224130	+	0.0970043i
$875$		−	2.42638i		−	0.0820267i
$876$	8.41068	+	7.89641i	0.284171	+	0.266795i
$877$			0.298036i			0.0100640i	0.999987	+	0.00503198i	$0.00160173\pi$
$877$			0.298036i			0.0100640i	−0.999987	+	0.00503198i	$0.998398\pi$
$878$	−1.42382	−	3.28974i	−0.0480514	−	0.111024i
$879$	−21.0003			−0.708322
$880$	0.545583	+	8.64132i	0.0183916	+	0.291299i
$881$	−43.7048			−1.47245			−0.736227	−	0.676735i	$-0.763394\pi$
$881$	−43.7048			−1.47245			−0.736227	+	0.676735i	$0.763394\pi$
$882$	−1.49705	−	3.45895i	−0.0504082	−	0.116469i
$883$		−	39.0064i		−	1.31267i	−0.754470	−	0.656334i	$-0.772106\pi$
$883$		−	39.0064i		−	1.31267i	0.754470	−	0.656334i	$-0.227894\pi$
$884$	20.2784	+	19.0384i	0.682035	+	0.640332i
$885$			4.33069i			0.145574i
$886$	11.5762	−	5.01024i	0.388911	−	0.168322i
$887$	−21.7960			−0.731837			−0.365918	−	0.930647i	$-0.619245\pi$
$887$	−21.7960			−0.731837			−0.365918	+	0.930647i	$0.619245\pi$
$888$	−23.7180	−	8.53458i	−0.795925	−	0.286402i
$889$	7.34334			0.246288
$890$	−19.3347	+	8.36813i	−0.648100	+	0.280500i
$891$			8.49134i			0.284470i
$892$	7.75256	−	8.25747i	0.259575	−	0.276480i
$893$		−	12.1163i		−	0.405458i
$894$	8.03280	+	18.5599i	0.268657	+	0.620735i
$895$	−23.0731			−0.771248
$896$	−7.64850	+	26.3643i	−0.255518	+	0.880771i
$897$	−14.3233			−0.478240
$898$	−2.61144	−	6.03376i	−0.0871448	−	0.201349i
$899$		−	0.145582i		−	0.00485543i
$900$	3.27890	−	3.49245i	0.109297	−	0.116415i
$901$			10.9792i			0.365771i
$902$	−32.2172	+	13.9437i	−1.07271	+	0.464275i
$903$	−10.8500			−0.361066
$904$	−25.9939	−	9.35352i	−0.864545	−	0.311094i
$905$	11.6959			0.388783
$906$	11.8655	−	5.13544i	0.394205	−	0.170613i
$907$		−	56.7570i		−	1.88458i	−0.334792	−	0.942292i	$-0.608666\pi$
$907$		−	56.7570i		−	1.88458i	0.334792	−	0.942292i	$-0.391334\pi$
$908$	9.64429	+	9.05459i	0.320057	+	0.300487i
$909$			29.8748i			0.990884i
$910$	−4.91702	−	11.3608i	−0.162998	−	0.376608i
$911$	2.93914			0.0973781			0.0486891	−	0.998814i	$-0.484496\pi$
$911$	2.93914			0.0973781			0.0486891	+	0.998814i	$0.484496\pi$
$912$	0.196008	+	3.10451i	0.00649048	+	0.102801i
$913$	−35.4424			−1.17297
$914$	−8.43576	−	19.4909i	−0.279030	−	0.644703i
$915$		−	1.01957i		−	0.0337059i
$916$	34.1561	+	32.0676i	1.12855	+	1.05954i
$917$		−	14.0994i		−	0.465603i
$918$	20.9926	−	9.08570i	0.692860	−	0.299873i
$919$	25.0484			0.826270			0.413135	−	0.910670i	$-0.364434\pi$
$919$	25.0484			0.826270			0.413135	+	0.910670i	$0.364434\pi$
$920$	4.88915	−	13.5872i	0.161190	−	0.447956i
$921$	12.5441			0.413342
$922$	7.54021	−	3.26344i	0.248324	−	0.107476i
$923$			55.3962i			1.82339i
$924$	5.59143	−	5.95558i	0.183944	−	0.195924i
$925$			11.4598i			0.376795i
$926$	−22.7686	−	52.6072i	−0.748223	−	1.72878i
$927$	−7.91107			−0.259833
$928$	0.0406065	+	0.0796404i	0.00133297	+	0.00261432i
$929$	45.5879			1.49569			0.747845	−	0.663873i	$-0.231089\pi$
$929$	45.5879			1.49569			0.747845	+	0.663873i	$0.231089\pi$
$930$	4.02429	+	9.29817i	0.131962	+	0.304899i
$931$		−	1.11267i		−	0.0364663i
$932$	2.22746	−	2.37253i	0.0729630	−	0.0777149i
$933$			3.93492i			0.128824i
$934$	14.9071	−	6.45187i	0.487776	−	0.211112i
$935$	8.34473			0.272902
$936$	8.27514	−	22.9970i	0.270481	−	0.751681i
$937$	−14.1297			−0.461596			−0.230798	−	0.973002i	$-0.574134\pi$
$937$	−14.1297			−0.461596			−0.230798	+	0.973002i	$0.574134\pi$
$938$	12.8333	−	5.55429i	0.419021	−	0.181354i
$939$		−	20.1703i		−	0.658233i
$940$	17.6667	+	16.5865i	0.576224	+	0.540991i
$941$			47.1678i			1.53763i	0.639473	+	0.768814i	$0.279153\pi$
$941$			47.1678i			1.53763i	−0.639473	+	0.768814i	$0.720847\pi$
$942$	6.50733	+	15.0353i	0.212020	+	0.489876i
$943$	58.5459			1.90652
$944$	−22.2308	+	1.40358i	−0.723551	+	0.0456825i
$945$	−10.1804			−0.331169
$946$	−6.99165	−	16.1543i	−0.227318	−	0.525222i
$947$			31.5579i			1.02549i	0.858540	+	0.512747i	$0.171372\pi$
$947$			31.5579i			1.02549i	−0.858540	+	0.512747i	$0.828628\pi$
$948$	−2.35528	−	2.21127i	−0.0764960	−	0.0718186i
$949$		−	26.7590i		−	0.868634i
$950$	1.29787	−	0.561724i	0.0421085	−	0.0182247i
$951$	9.87340			0.320167
$952$	24.8939	+	8.95770i	0.806817	+	0.290321i
$953$	7.84917			0.254260			0.127130	−	0.991886i	$-0.459424\pi$
$953$	7.84917			0.254260			0.127130	+	0.991886i	$0.459424\pi$
$954$	8.85361	−	3.83188i	0.286646	−	0.124062i
$955$		−	11.5764i		−	0.374603i
$956$	4.18447	−	4.45699i	0.135335	−	0.144149i
$957$		−	0.0266023i		−	0.000859931i
$958$	6.76898	+	15.6398i	0.218696	+	0.505299i
$959$	−7.89794			−0.255038
$960$	−4.79498	−	3.96407i	−0.154757	−	0.127940i
$961$	53.8668			1.73764
$962$	23.2230	+	53.6571i	0.748740	+	1.72997i
$963$			28.7933i			0.927850i
$964$	−26.2300	+	27.9383i	−0.844810	+	0.899831i
$965$			0.560028i			0.0180279i
$966$	−12.5029	+	5.41132i	−0.402275	+	0.174106i
$967$	25.1503			0.808779			0.404390	−	0.914587i	$-0.367484\pi$
$967$	25.1503			0.808779			0.404390	+	0.914587i	$0.367484\pi$
$968$	−16.8049	−	6.04699i	−0.540130	−	0.194358i
$969$	2.99796			0.0963084
$970$	−18.6274	+	8.06203i	−0.598091	+	0.258856i
$971$			41.9225i			1.34536i	0.739935	+	0.672679i	$0.234856\pi$
$971$			41.9225i			1.34536i	−0.739935	+	0.672679i	$0.765144\pi$
$972$	−22.8013	−	21.4071i	−0.731352	−	0.686633i
$973$		−	11.2620i		−	0.361043i
$974$	0.834596	+	1.92834i	0.0267422	+	0.0617881i
$975$	2.80555			0.0898495
$976$	5.23378	−	0.330442i	0.167529	−	0.0105772i
$977$	−15.0371			−0.481079			−0.240540	−	0.970639i	$-0.577324\pi$
$977$	−15.0371			−0.481079			−0.240540	+	0.970639i	$0.577324\pi$
$978$	−3.30956	−	7.64679i	−0.105828	−	0.244517i
$979$			32.2470i			1.03062i
$980$	1.62237	+	1.52317i	0.0518248	+	0.0486559i
$981$		−	48.1297i		−	1.53666i
$982$	38.5384	−	16.6796i	1.22981	−	0.532267i
$983$	−10.7761			−0.343703			−0.171852	−	0.985123i	$-0.554975\pi$
$983$	−10.7761			−0.343703			−0.171852	+	0.985123i	$0.554975\pi$
$984$	8.54041	−	23.7342i	0.272258	−	0.756620i
$985$	−1.15117			−0.0366792
$986$	0.0790676	−	0.0342208i	0.00251802	−	0.00108981i
$987$		−	22.8627i		−	0.727729i
$988$	4.93858	−	5.26022i	0.157117	−	0.167350i
$989$			29.3560i			0.933468i
$990$	−2.91241	−	6.72916i	−0.0925625	−	0.213867i
$991$	24.6508			0.783060			0.391530	−	0.920165i	$-0.371946\pi$
$991$	24.6508			0.783060			0.391530	+	0.920165i	$0.371946\pi$
$992$	−46.4263	+	23.6715i	−1.47404	+	0.751571i
$993$	19.9693			0.633706
$994$	20.9287	+	48.3559i	0.663817	+	1.53376i
$995$			22.4183i			0.710708i
$996$	17.4309	−	18.5661i	0.552318	−	0.588289i
$997$		−	15.6869i		−	0.496809i	−0.968656	−	0.248404i	$-0.920094\pi$
$997$		−	15.6869i		−	0.496809i	0.968656	−	0.248404i	$-0.0799062\pi$
$998$	−40.8010	+	17.6588i	−1.29153	+	0.558981i
$999$	48.0820			1.52125

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	760.2.f.b.381.28	yes	44
4.3	odd	2		3040.2.f.b.1521.19		44
8.3	odd	2		3040.2.f.b.1521.26		44
8.5	even	2	inner	760.2.f.b.381.27	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.f.b.381.27	✓	44	8.5	even	2	inner
760.2.f.b.381.28	yes	44	1.1	even	1	trivial
3040.2.f.b.1521.19		44	4.3	odd	2
3040.2.f.b.1521.26		44	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.561724 + 1.29787i) q^{2} +0.777674i q^{3} +(-1.36893 + 1.45809i) q^{4} +1.00000i q^{5} +(-1.00932 + 0.436838i) q^{6} +2.42638 q^{7} +(-2.66137 - 0.957654i) q^{8} +2.39522 q^{9} +(-1.29787 + 0.561724i) q^{10} +2.16463i q^{11} +(-1.13392 - 1.06458i) q^{12} +3.60762i q^{13} +(1.36296 + 3.14913i) q^{14} -0.777674 q^{15} +(-0.252044 - 3.99205i) q^{16} -3.85504 q^{17} +(1.34545 + 3.10869i) q^{18} +1.00000i q^{19} +(-1.45809 - 1.36893i) q^{20} +1.88693i q^{21} +(-2.80941 + 1.21592i) q^{22} +5.10533 q^{23} +(0.744743 - 2.06968i) q^{24} -1.00000 q^{25} +(-4.68222 + 2.02648i) q^{26} +4.19572i q^{27} +(-3.32155 + 3.53788i) q^{28} +0.0158030i q^{29} +(-0.436838 - 1.00932i) q^{30} -9.21232 q^{31} +(5.03958 - 2.56955i) q^{32} -1.68338 q^{33} +(-2.16547 - 5.00334i) q^{34} +2.42638i q^{35} +(-3.27890 + 3.49245i) q^{36} -11.4598i q^{37} +(-1.29787 + 0.561724i) q^{38} -2.80555 q^{39} +(0.957654 - 2.66137i) q^{40} +11.4676 q^{41} +(-2.44899 + 1.05994i) q^{42} +5.75007i q^{43} +(-3.15622 - 2.96323i) q^{44} +2.39522i q^{45} +(2.86779 + 6.62606i) q^{46} -12.1163 q^{47} +(3.10451 - 0.196008i) q^{48} -1.11267 q^{49} +(-0.561724 - 1.29787i) q^{50} -2.99796i q^{51} +(-5.26022 - 4.93858i) q^{52} -2.84802i q^{53} +(-5.44550 + 2.35684i) q^{54} -2.16463 q^{55} +(-6.45750 - 2.32364i) q^{56} -0.777674 q^{57} +(-0.0205102 + 0.00887690i) q^{58} -5.56877i q^{59} +(1.06458 - 1.13392i) q^{60} +1.31105i q^{61} +(-5.17478 - 11.9564i) q^{62} +5.81173 q^{63} +(6.16580 + 5.09735i) q^{64} -3.60762 q^{65} +(-0.945592 - 2.18480i) q^{66} -4.07518i q^{67} +(5.27729 - 5.62099i) q^{68} +3.97028i q^{69} +(-3.14913 + 1.36296i) q^{70} +15.3553 q^{71} +(-6.37458 - 2.29380i) q^{72} -7.41737 q^{73} +(14.8733 - 6.43722i) q^{74} -0.777674i q^{75} +(-1.45809 - 1.36893i) q^{76} +5.25222i q^{77} +(-1.57594 - 3.64124i) q^{78} +2.07712 q^{79} +(3.99205 - 0.252044i) q^{80} +3.92277 q^{81} +(6.44162 + 14.8835i) q^{82} +16.3734i q^{83} +(-2.75132 - 2.58309i) q^{84} -3.85504i q^{85} +(-7.46285 + 3.22995i) q^{86} -0.0122896 q^{87} +(2.07297 - 5.76089i) q^{88} +14.8972 q^{89} +(-3.10869 + 1.34545i) q^{90} +8.75345i q^{91} +(-6.98886 + 7.44403i) q^{92} -7.16418i q^{93} +(-6.80604 - 15.7254i) q^{94} -1.00000 q^{95} +(1.99827 + 3.91915i) q^{96} +14.3523 q^{97} +(-0.625014 - 1.44410i) q^{98} +5.18477i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} - 2 q^{4} - 6 q^{6} + 4 q^{7} + 8 q^{8} - 60 q^{9} + 4 q^{12} + 4 q^{14} - 6 q^{16} + 24 q^{17} - 14 q^{18} - 4 q^{20} - 4 q^{22} + 4 q^{23} + 2 q^{24} - 44 q^{25} + 18 q^{26} - 14 q^{28}+ \cdots + 78 q^{98}+O(q^{100}) \) 44 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 + 4 * q^7 + 8 * q^8 - 60 * q^9 + 4 * q^12 + 4 * q^14 - 6 * q^16 + 24 * q^17 - 14 * q^18 - 4 * q^20 - 4 * q^22 + 4 * q^23 + 2 * q^24 - 44 * q^25 + 18 * q^26 - 14 * q^28 + 12 * q^32 + 40 * q^33 + 32 * q^34 - 28 * q^36 - 24 * q^39 + 6 * q^40 - 32 * q^41 + 46 * q^42 - 36 * q^44 - 16 * q^46 - 20 * q^47 + 64 * q^48 + 108 * q^49 - 2 * q^50 - 24 * q^52 - 26 * q^54 + 8 * q^55 + 60 * q^56 + 2 * q^58 - 14 * q^60 - 72 * q^62 + 20 * q^63 + 22 * q^64 + 12 * q^65 + 88 * q^66 - 62 * q^68 - 18 * q^70 - 8 * q^71 + 48 * q^72 - 88 * q^73 + 84 * q^74 - 4 * q^76 - 116 * q^78 + 40 * q^79 + 8 * q^80 + 116 * q^81 + 44 * q^82 - 108 * q^84 - 88 * q^86 + 48 * q^87 + 76 * q^88 - 64 * q^89 + 30 * q^90 - 62 * q^92 - 24 * q^94 - 44 * q^95 + 118 * q^96 + 116 * q^97 + 78 * q^98

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