LMFDB - Embedded newform 546.2.g.d.209.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(209,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("546.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 4x^{10} - 8x^{8} + 26x^{7} - 50x^{6} + 78x^{5} - 72x^{4} + 324x^{2} - 486x + 729 $ x^12 - 2x^11 + 4x^10 - 8x^8 + 26x^7 - 50x^6 + 78x^5 - 72x^4 + 324x^2 - 486*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			209.5
Root			$0.684481 + 1.59106i$ of defining polynomial
Character	$\chi$	$=$	546.209
Dual form			546.2.g.d.209.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.59106 + 0.684481i) q^{3} -1.00000 q^{4} +4.42062 q^{5} +(0.684481 - 1.59106i) q^{6} +(-2.43879 - 1.02583i) q^{7} +1.00000i q^{8} +(2.06297 + 2.17811i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.59106 + 0.684481i) q^{3} -1.00000 q^{4} +4.42062 q^{5} +(0.684481 - 1.59106i) q^{6} +(-2.43879 - 1.02583i) q^{7} +1.00000i q^{8} +(2.06297 + 2.17811i) q^{9} -4.42062i q^{10} -5.78958i q^{11} +(-1.59106 - 0.684481i) q^{12} +1.00000i q^{13} +(-1.02583 + 2.43879i) q^{14} +(7.03349 + 3.02583i) q^{15} +1.00000 q^{16} -2.97358 q^{17} +(2.17811 - 2.06297i) q^{18} -2.66098i q^{19} -4.42062 q^{20} +(-3.17811 - 3.30146i) q^{21} -5.78958 q^{22} +6.57281i q^{23} +(-0.684481 + 1.59106i) q^{24} +14.5419 q^{25} +1.00000 q^{26} +(1.79145 + 4.87757i) q^{27} +(2.43879 + 1.02583i) q^{28} +3.44234i q^{29} +(3.02583 - 7.03349i) q^{30} +3.06154i q^{31} -1.00000i q^{32} +(3.96286 - 9.21159i) q^{33} +2.97358i q^{34} +(-10.7809 - 4.53479i) q^{35} +(-2.06297 - 2.17811i) q^{36} -4.71246 q^{37} -2.66098 q^{38} +(-0.684481 + 1.59106i) q^{39} +4.42062i q^{40} +2.07429 q^{41} +(-3.30146 + 3.17811i) q^{42} -5.24653 q^{43} +5.78958i q^{44} +(9.11961 + 9.62857i) q^{45} +6.57281 q^{46} -4.28287 q^{47} +(1.59106 + 0.684481i) q^{48} +(4.89535 + 5.00355i) q^{49} -14.5419i q^{50} +(-4.73115 - 2.03536i) q^{51} -1.00000i q^{52} +5.36539i q^{53} +(4.87757 - 1.79145i) q^{54} -25.5935i q^{55} +(1.02583 - 2.43879i) q^{56} +(1.82139 - 4.23378i) q^{57} +3.44234 q^{58} +2.04344 q^{59} +(-7.03349 - 3.02583i) q^{60} -7.83301i q^{61} +3.06154 q^{62} +(-2.79679 - 7.42819i) q^{63} -1.00000 q^{64} +4.42062i q^{65} +(-9.21159 - 3.96286i) q^{66} -2.80059 q^{67} +2.97358 q^{68} +(-4.49896 + 10.4578i) q^{69} +(-4.53479 + 10.7809i) q^{70} -4.46876i q^{71} +(-2.17811 + 2.06297i) q^{72} -4.11227i q^{73} +4.71246i q^{74} +(23.1370 + 9.95362i) q^{75} +2.66098i q^{76} +(-5.93911 + 14.1195i) q^{77} +(1.59106 + 0.684481i) q^{78} +1.88228 q^{79} +4.42062 q^{80} +(-0.488293 + 8.98674i) q^{81} -2.07429i q^{82} -13.7296 q^{83} +(3.17811 + 3.30146i) q^{84} -13.1451 q^{85} +5.24653i q^{86} +(-2.35621 + 5.47698i) q^{87} +5.78958 q^{88} -14.5365 q^{89} +(9.62857 - 9.11961i) q^{90} +(1.02583 - 2.43879i) q^{91} -6.57281i q^{92} +(-2.09556 + 4.87111i) q^{93} +4.28287i q^{94} -11.7632i q^{95} +(0.684481 - 1.59106i) q^{96} -5.79946i q^{97} +(5.00355 - 4.89535i) q^{98} +(12.6103 - 11.9437i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} - 12 q^{4} - 4 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9}+O(q^{10}) $ 12 * q + 2 * q^3 - 12 * q^4 - 4 * q^5 + 2 * q^6 - 8 * q^7 + 4 * q^9	$ 12 q + 2 q^{3} - 12 q^{4} - 4 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9} - 2 q^{12} + 10 q^{14} + 4 q^{15} + 12 q^{16} + 12 q^{17} + 8 q^{18} + 4 q^{20} - 20 q^{21} - 2 q^{24} + 20 q^{25} + 12 q^{26} + 8 q^{27} + 8 q^{28} + 14 q^{30} + 46 q^{33} - 22 q^{35} - 4 q^{36} + 16 q^{37} - 8 q^{38} - 2 q^{39} + 28 q^{41} + 4 q^{42} - 8 q^{43} + 24 q^{46} - 68 q^{47} + 2 q^{48} + 26 q^{49} - 50 q^{51} + 16 q^{54} - 10 q^{56} - 28 q^{57} - 24 q^{58} + 8 q^{59} - 4 q^{60} + 16 q^{62} - 2 q^{63} - 12 q^{64} - 12 q^{66} + 8 q^{67} - 12 q^{68} - 24 q^{69} - 28 q^{70} - 8 q^{72} + 92 q^{75} - 8 q^{77} + 2 q^{78} + 36 q^{79} - 4 q^{80} + 16 q^{81} - 32 q^{83} + 20 q^{84} + 8 q^{87} - 48 q^{89} + 2 q^{90} - 10 q^{91} + 8 q^{93} + 2 q^{96} + 16 q^{98}+O(q^{100}) $ 12 * q + 2 * q^3 - 12 * q^4 - 4 * q^5 + 2 * q^6 - 8 * q^7 + 4 * q^9 - 2 * q^12 + 10 * q^14 + 4 * q^15 + 12 * q^16 + 12 * q^17 + 8 * q^18 + 4 * q^20 - 20 * q^21 - 2 * q^24 + 20 * q^25 + 12 * q^26 + 8 * q^27 + 8 * q^28 + 14 * q^30 + 46 * q^33 - 22 * q^35 - 4 * q^36 + 16 * q^37 - 8 * q^38 - 2 * q^39 + 28 * q^41 + 4 * q^42 - 8 * q^43 + 24 * q^46 - 68 * q^47 + 2 * q^48 + 26 * q^49 - 50 * q^51 + 16 * q^54 - 10 * q^56 - 28 * q^57 - 24 * q^58 + 8 * q^59 - 4 * q^60 + 16 * q^62 - 2 * q^63 - 12 * q^64 - 12 * q^66 + 8 * q^67 - 12 * q^68 - 24 * q^69 - 28 * q^70 - 8 * q^72 + 92 * q^75 - 8 * q^77 + 2 * q^78 + 36 * q^79 - 4 * q^80 + 16 * q^81 - 32 * q^83 + 20 * q^84 + 8 * q^87 - 48 * q^89 + 2 * q^90 - 10 * q^91 + 8 * q^93 + 2 * q^96 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.59106	+	0.684481i	0.918601	+	0.395185i
$3$	1.59106	+	0.684481i	0.918601	+	0.395185i
$4$	−1.00000			−0.500000
$5$	4.42062			1.97696			0.988480	−	0.151351i	$-0.0483624\pi$
$5$	4.42062			1.97696			0.988480	+	0.151351i	$0.0483624\pi$
$6$	0.684481	−	1.59106i	0.279438	−	0.649549i
$7$	−2.43879	−	1.02583i	−0.921774	−	0.387726i
$7$	−2.43879	−	1.02583i	−0.921774	−	0.387726i
$8$			1.00000i			0.353553i
$9$	2.06297	+	2.17811i	0.687657	+	0.726035i
$10$		−	4.42062i		−	1.39792i
$11$		−	5.78958i		−	1.74562i	−0.488057	−	0.872812i	$-0.662294\pi$
$11$		−	5.78958i		−	1.74562i	0.488057	−	0.872812i	$-0.337706\pi$
$12$	−1.59106	−	0.684481i	−0.459301	−	0.197593i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−1.02583	+	2.43879i	−0.274164	+	0.651793i
$15$	7.03349	+	3.02583i	1.81604	+	0.781265i
$16$	1.00000			0.250000
$17$	−2.97358			−0.721199			−0.360599	−	0.932721i	$-0.617428\pi$
$17$	−2.97358			−0.721199			−0.360599	+	0.932721i	$0.617428\pi$
$18$	2.17811	−	2.06297i	0.513385	−	0.486247i
$19$		−	2.66098i		−	0.610470i	−0.952277	−	0.305235i	$-0.901265\pi$
$19$		−	2.66098i		−	0.610470i	0.952277	−	0.305235i	$-0.0987350\pi$
$20$	−4.42062			−0.988480
$21$	−3.17811	−	3.30146i	−0.693520	−	0.720438i
$22$	−5.78958			−1.23434
$23$			6.57281i			1.37053i	0.728296	+	0.685263i	$0.240313\pi$
$23$			6.57281i			1.37053i	−0.728296	+	0.685263i	$0.759687\pi$
$24$	−0.684481	+	1.59106i	−0.139719	+	0.324775i
$25$	14.5419			2.90837
$26$	1.00000			0.196116
$27$	1.79145	+	4.87757i	0.344765	+	0.938689i
$28$	2.43879	+	1.02583i	0.460887	+	0.193863i
$29$			3.44234i			0.639226i	0.947548	+	0.319613i	$0.103553\pi$
$29$			3.44234i			0.639226i	−0.947548	+	0.319613i	$0.896447\pi$
$30$	3.02583	−	7.03349i	0.552438	−	1.28413i
$31$			3.06154i			0.549869i	0.961463	+	0.274934i	$0.0886561\pi$
$31$			3.06154i			0.549869i	−0.961463	+	0.274934i	$0.911344\pi$
$32$		−	1.00000i		−	0.176777i
$33$	3.96286	−	9.21159i	0.689845	−	1.60353i
$34$			2.97358i			0.509964i
$35$	−10.7809	−	4.53479i	−1.82231	−	0.766520i
$36$	−2.06297	−	2.17811i	−0.343829	−	0.363018i
$37$	−4.71246			−0.774723			−0.387362	−	0.921928i	$-0.626613\pi$
$37$	−4.71246			−0.774723			−0.387362	+	0.921928i	$0.626613\pi$
$38$	−2.66098			−0.431667
$39$	−0.684481	+	1.59106i	−0.109605	+	0.254774i
$40$			4.42062i			0.698961i
$41$	2.07429			0.323949			0.161975	−	0.986795i	$-0.448214\pi$
$41$	2.07429			0.323949			0.161975	+	0.986795i	$0.448214\pi$
$42$	−3.30146	+	3.17811i	−0.509426	+	0.490392i
$43$	−5.24653			−0.800089			−0.400044	−	0.916496i	$-0.631005\pi$
$43$	−5.24653			−0.800089			−0.400044	+	0.916496i	$0.631005\pi$
$44$			5.78958i			0.872812i
$45$	9.11961	+	9.62857i	1.35947	+	1.43534i
$46$	6.57281			0.969108
$47$	−4.28287			−0.624721			−0.312360	−	0.949964i	$-0.601120\pi$
$47$	−4.28287			−0.624721			−0.312360	+	0.949964i	$0.601120\pi$
$48$	1.59106	+	0.684481i	0.229650	+	0.0987963i
$49$	4.89535	+	5.00355i	0.699336	+	0.714793i
$50$		−	14.5419i		−	2.05653i
$51$	−4.73115	−	2.03536i	−0.662494	−	0.285007i
$52$		−	1.00000i		−	0.138675i
$53$			5.36539i			0.736993i	0.929629	+	0.368496i	$0.120127\pi$
$53$			5.36539i			0.736993i	−0.929629	+	0.368496i	$0.879873\pi$
$54$	4.87757	−	1.79145i	0.663753	−	0.243785i
$55$		−	25.5935i		−	3.45103i
$56$	1.02583	−	2.43879i	0.137082	−	0.325896i
$57$	1.82139	−	4.23378i	0.241249	−	0.560778i
$58$	3.44234			0.452001
$59$	2.04344			0.266033			0.133016	−	0.991114i	$-0.457534\pi$
$59$	2.04344			0.266033			0.133016	+	0.991114i	$0.457534\pi$
$60$	−7.03349	−	3.02583i	−0.908019	−	0.390633i
$61$		−	7.83301i		−	1.00291i	−0.865182	−	0.501457i	$-0.832797\pi$
$61$		−	7.83301i		−	1.00291i	0.865182	−	0.501457i	$-0.167203\pi$
$62$	3.06154			0.388816
$63$	−2.79679	−	7.42819i	−0.352362	−	0.935864i
$64$	−1.00000			−0.125000
$65$			4.42062i			0.548310i
$66$	−9.21159	−	3.96286i	−1.13387	−	0.487794i
$67$	−2.80059			−0.342147			−0.171073	−	0.985258i	$-0.554724\pi$
$67$	−2.80059			−0.342147			−0.171073	+	0.985258i	$0.554724\pi$
$68$	2.97358			0.360599
$69$	−4.49896	+	10.4578i	−0.541611	+	1.25897i
$70$	−4.53479	+	10.7809i	−0.542011	+	1.28857i
$71$		−	4.46876i		−	0.530344i	−0.964201	−	0.265172i	$-0.914571\pi$
$71$		−	4.46876i		−	0.530344i	0.964201	−	0.265172i	$-0.0854287\pi$
$72$	−2.17811	+	2.06297i	−0.256692	+	0.243124i
$73$		−	4.11227i		−	0.481305i	−0.970611	−	0.240652i	$-0.922639\pi$
$73$		−	4.11227i		−	0.481305i	0.970611	−	0.240652i	$-0.0773614\pi$
$74$			4.71246i			0.547812i
$75$	23.1370	+	9.95362i	2.67163	+	1.14935i
$76$			2.66098i			0.305235i
$77$	−5.93911	+	14.1195i	−0.676825	+	1.60907i
$78$	1.59106	+	0.684481i	0.180153	+	0.0775022i
$79$	1.88228			0.211773			0.105886	−	0.994378i	$-0.466232\pi$
$79$	1.88228			0.211773			0.105886	+	0.994378i	$0.466232\pi$
$80$	4.42062			0.494240
$81$	−0.488293	+	8.98674i	−0.0542548	+	0.998527i
$82$		−	2.07429i		−	0.229067i
$83$	−13.7296			−1.50702			−0.753512	−	0.657434i	$-0.771642\pi$
$83$	−13.7296			−1.50702			−0.753512	+	0.657434i	$0.771642\pi$
$84$	3.17811	+	3.30146i	0.346760	+	0.360219i
$85$	−13.1451			−1.42578
$86$			5.24653i			0.565748i
$87$	−2.35621	+	5.47698i	−0.252612	+	0.587194i
$88$	5.78958			0.617171
$89$	−14.5365			−1.54087			−0.770433	−	0.637521i	$-0.779960\pi$
$89$	−14.5365			−1.54087			−0.770433	+	0.637521i	$0.779960\pi$
$90$	9.62857	−	9.11961i	1.01494	−	0.961291i
$91$	1.02583	−	2.43879i	0.107536	−	0.255654i
$92$		−	6.57281i		−	0.685263i
$93$	−2.09556	+	4.87111i	−0.217300	+	0.505110i
$94$			4.28287i			0.441744i
$95$		−	11.7632i		−	1.20687i
$96$	0.684481	−	1.59106i	0.0698595	−	0.162387i
$97$		−	5.79946i		−	0.588846i	−0.955675	−	0.294423i	$-0.904873\pi$
$97$		−	5.79946i		−	0.588846i	0.955675	−	0.294423i	$-0.0951275\pi$
$98$	5.00355	−	4.89535i	0.505435	−	0.494505i
$99$	12.6103	−	11.9437i	1.26738	−	1.20039i
$100$	−14.5419			−1.45419
$101$	−1.71982			−0.171128			−0.0855642	−	0.996333i	$-0.527269\pi$
$101$	−1.71982			−0.171128			−0.0855642	+	0.996333i	$0.527269\pi$
$102$	−2.03536	+	4.73115i	−0.201530	+	0.468454i
$103$			1.49961i			0.147761i	0.997267	+	0.0738805i	$0.0235383\pi$
$103$			1.49961i			0.147761i	−0.997267	+	0.0738805i	$0.976462\pi$
$104$	−1.00000			−0.0980581
$105$	−14.0492	−	14.5945i	−1.37106	−	1.42428i
$106$	5.36539			0.521133
$107$			1.90372i			0.184040i	0.995757	+	0.0920198i	$0.0293323\pi$
$107$			1.90372i			0.184040i	−0.995757	+	0.0920198i	$0.970668\pi$
$108$	−1.79145	−	4.87757i	−0.172382	−	0.469345i
$109$	10.9889			1.05255			0.526273	−	0.850316i	$-0.323589\pi$
$109$	10.9889			1.05255			0.526273	+	0.850316i	$0.323589\pi$
$110$	−25.5935			−2.44025
$111$	−7.49782	−	3.22559i	−0.711662	−	0.306159i
$112$	−2.43879	−	1.02583i	−0.230444	−	0.0969316i
$113$			12.3835i			1.16494i	0.812852	+	0.582470i	$0.197914\pi$
$113$			12.3835i			1.16494i	−0.812852	+	0.582470i	$0.802086\pi$
$114$	−4.23378	−	1.82139i	−0.396530	−	0.170589i
$115$			29.0559i			2.70947i
$116$		−	3.44234i		−	0.319613i
$117$	−2.17811	+	2.06297i	−0.201366	+	0.190722i
$118$		−	2.04344i		−	0.188113i
$119$	7.25192	+	3.05038i	0.664783	+	0.279628i
$120$	−3.02583	+	7.03349i	−0.276219	+	0.642067i
$121$	−22.5192			−2.04720
$122$	−7.83301			−0.709168
$123$	3.30033	+	1.41981i	0.297580	+	0.128020i
$124$		−	3.06154i		−	0.274934i
$125$	42.1809			3.77277
$126$	−7.42819	+	2.79679i	−0.661756	+	0.249157i
$127$	−4.22104			−0.374556			−0.187278	−	0.982307i	$-0.559967\pi$
$127$	−4.22104			−0.374556			−0.187278	+	0.982307i	$0.559967\pi$
$128$			1.00000i			0.0883883i
$129$	−8.34757	−	3.59115i	−0.734963	−	0.316183i
$130$	4.42062			0.387714
$131$	−0.0690766			−0.00603525			−0.00301763	−	0.999995i	$-0.500961\pi$
$131$	−0.0690766			−0.00603525			−0.00301763	+	0.999995i	$0.500961\pi$
$132$	−3.96286	+	9.21159i	−0.344922	+	0.801766i
$133$	−2.72970	+	6.48955i	−0.236695	+	0.562715i
$134$			2.80059i			0.241934i
$135$	7.91931	+	21.5619i	0.681586	+	1.85575i
$136$		−	2.97358i		−	0.254982i
$137$			9.16032i			0.782619i	0.920259	+	0.391310i	$0.127978\pi$
$137$			9.16032i			0.782619i	−0.920259	+	0.391310i	$0.872022\pi$
$138$	10.4578	+	4.49896i	0.890224	+	0.382977i
$139$			5.91082i			0.501349i	0.968071	+	0.250675i	$0.0806524\pi$
$139$			5.91082i			0.501349i	−0.968071	+	0.250675i	$0.919348\pi$
$140$	10.7809	+	4.53479i	0.911156	+	0.383260i
$141$	−6.81432	−	2.93154i	−0.573870	−	0.246880i
$142$	−4.46876			−0.375010
$143$	5.78958			0.484149
$144$	2.06297	+	2.17811i	0.171914	+	0.181509i
$145$			15.2172i			1.26372i
$146$	−4.11227			−0.340334
$147$	4.36399	+	11.3117i	0.359936	+	0.932977i
$148$	4.71246			0.387362
$149$			16.3060i			1.33584i	0.744233	+	0.667920i	$0.232815\pi$
$149$			16.3060i			1.33584i	−0.744233	+	0.667920i	$0.767185\pi$
$150$	9.95362	−	23.1370i	0.812710	−	1.88913i
$151$	13.8392			1.12622			0.563109	−	0.826383i	$-0.309605\pi$
$151$	13.8392			1.12622			0.563109	+	0.826383i	$0.309605\pi$
$152$	2.66098			0.215834
$153$	−6.13441	−	6.47677i	−0.495938	−	0.523616i
$154$	14.1195	+	5.93911i	1.13779	+	0.478587i
$155$			13.5339i			1.08707i
$156$	0.684481	−	1.59106i	0.0548023	−	0.127387i
$157$		−	17.4503i		−	1.39268i	−0.717710	−	0.696342i	$-0.754810\pi$
$157$		−	17.4503i		−	1.39268i	0.717710	−	0.696342i	$-0.245190\pi$
$158$		−	1.88228i		−	0.149746i
$159$	−3.67251	+	8.53668i	−0.291249	+	0.677003i
$160$		−	4.42062i		−	0.349480i
$161$	6.74257	−	16.0297i	0.531389	−	1.26332i
$162$	8.98674	+	0.488293i	0.706065	+	0.0383639i
$163$	1.52302			0.119292			0.0596462	−	0.998220i	$-0.481003\pi$
$163$	1.52302			0.119292			0.0596462	+	0.998220i	$0.481003\pi$
$164$	−2.07429			−0.161975
$165$	17.5183	−	40.7209i	1.36380	−	3.17012i
$166$			13.7296i			1.06563i
$167$	10.0997			0.781541			0.390770	−	0.920488i	$-0.372209\pi$
$167$	10.0997			0.781541			0.390770	+	0.920488i	$0.372209\pi$
$168$	3.30146	−	3.17811i	0.254713	−	0.245196i
$169$	−1.00000			−0.0769231
$170$			13.1451i			1.00818i
$171$	5.79589	−	5.48952i	0.443223	−	0.419794i
$172$	5.24653			0.400044
$173$	−9.12994			−0.694136			−0.347068	−	0.937840i	$-0.612823\pi$
$173$	−9.12994			−0.694136			−0.347068	+	0.937840i	$0.612823\pi$
$174$	5.47698	+	2.35621i	0.415209	+	0.178624i
$175$	−35.4645	−	14.9174i	−2.68086	−	1.12765i
$176$		−	5.78958i		−	0.436406i
$177$	3.25124	+	1.39869i	0.244378	+	0.105132i
$178$			14.5365i			1.08956i
$179$		−	23.1002i		−	1.72659i	−0.504698	−	0.863296i	$-0.668396\pi$
$179$		−	23.1002i		−	1.72659i	0.504698	−	0.863296i	$-0.331604\pi$
$180$	−9.11961	−	9.62857i	−0.679736	−	0.717672i
$181$			14.1049i			1.04841i	0.851592	+	0.524205i	$0.175638\pi$
$181$			14.1049i			1.04841i	−0.851592	+	0.524205i	$0.824362\pi$
$182$	−2.43879	−	1.02583i	−0.180775	−	0.0760394i
$183$	5.36155	−	12.4628i	0.396337	−	0.921279i
$184$	−6.57281			−0.484554
$185$	−20.8320			−1.53160
$186$	4.87111	+	2.09556i	0.357167	+	0.153654i
$187$			17.2158i			1.25894i
$188$	4.28287			0.312360
$189$	0.634587	−	13.7331i	0.0461594	−	0.998934i
$190$	−11.7632			−0.853389
$191$		−	2.89642i		−	0.209578i	−0.994494	−	0.104789i	$-0.966583\pi$
$191$		−	2.89642i		−	0.209578i	0.994494	−	0.104789i	$-0.0334167\pi$
$192$	−1.59106	−	0.684481i	−0.114825	−	0.0493981i
$193$	−3.12768			−0.225135			−0.112568	−	0.993644i	$-0.535908\pi$
$193$	−3.12768			−0.225135			−0.112568	+	0.993644i	$0.535908\pi$
$194$	−5.79946			−0.416377
$195$	−3.02583	+	7.03349i	−0.216684	+	0.503678i
$196$	−4.89535	−	5.00355i	−0.349668	−	0.357396i
$197$			13.2555i			0.944413i	0.881488	+	0.472207i	$0.156542\pi$
$197$			13.2555i			0.944413i	−0.881488	+	0.472207i	$0.843458\pi$
$198$	−11.9437	−	12.6103i	−0.848805	−	0.896176i
$199$		−	14.0635i		−	0.996932i	−0.866909	−	0.498466i	$-0.833897\pi$
$199$		−	14.0635i		−	0.996932i	0.866909	−	0.498466i	$-0.166103\pi$
$200$			14.5419i			1.02826i
$201$	−4.45592	−	1.91695i	−0.314297	−	0.135211i
$202$			1.71982i			0.121006i
$203$	3.53124	−	8.39512i	0.247845	−	0.589222i
$204$	4.73115	+	2.03536i	0.331247	+	0.142504i
$205$	9.16963			0.640435
$206$	1.49961			0.104483
$207$	−14.3163	+	13.5595i	−0.995050	+	0.942452i
$208$			1.00000i			0.0693375i
$209$	−15.4059			−1.06565
$210$	−14.5945	+	14.0492i	−1.00712	+	0.969486i
$211$	−0.508960			−0.0350382			−0.0175191	−	0.999847i	$-0.505577\pi$
$211$	−0.508960			−0.0350382			−0.0175191	+	0.999847i	$0.505577\pi$
$212$		−	5.36539i		−	0.368496i
$213$	3.05878	−	7.11008i	0.209584	−	0.487175i
$214$	1.90372			0.130136
$215$	−23.1929			−1.58174
$216$	−4.87757	+	1.79145i	−0.331877	+	0.121893i
$217$	3.14061	−	7.46644i	0.213199	−	0.506855i
$218$		−	10.9889i		−	0.744262i
$219$	2.81477	−	6.54289i	0.190205	−	0.442127i
$220$			25.5935i			1.72551i
$221$		−	2.97358i		−	0.200025i
$222$	−3.22559	+	7.49782i	−0.216487	+	0.503221i
$223$		−	12.0398i		−	0.806245i	−0.915146	−	0.403122i	$-0.867925\pi$
$223$		−	12.0398i		−	0.806245i	0.915146	−	0.403122i	$-0.132075\pi$
$224$	−1.02583	+	2.43879i	−0.0685410	+	0.162948i
$225$	29.9994	+	31.6737i	1.99996	+	2.11158i
$226$	12.3835			0.823738
$227$	10.9044			0.723753			0.361876	−	0.932226i	$-0.382136\pi$
$227$	10.9044			0.723753			0.361876	+	0.932226i	$0.382136\pi$
$228$	−1.82139	+	4.23378i	−0.120624	+	0.280389i
$229$		−	12.4163i		−	0.820490i	−0.911975	−	0.410245i	$-0.865443\pi$
$229$		−	12.4163i		−	0.820490i	0.911975	−	0.410245i	$-0.134557\pi$
$230$	29.0559			1.91589
$231$	−19.1141	+	18.3999i	−1.25761	+	1.21062i
$232$	−3.44234			−0.226000
$233$		−	21.7343i		−	1.42386i	−0.702250	−	0.711931i	$-0.747821\pi$
$233$		−	21.7343i		−	1.42386i	0.702250	−	0.711931i	$-0.252179\pi$
$234$	2.06297	+	2.17811i	0.134861	+	0.142387i
$235$	−18.9329			−1.23505
$236$	−2.04344			−0.133016
$237$	2.99482	+	1.28838i	0.194535	+	0.0836894i
$238$	3.05038	−	7.25192i	0.197727	−	0.470072i
$239$		−	15.1287i		−	0.978593i	−0.872117	−	0.489297i	$-0.837254\pi$
$239$		−	15.1287i		−	0.978593i	0.872117	−	0.489297i	$-0.162746\pi$
$240$	7.03349	+	3.02583i	0.454010	+	0.195316i
$241$		−	7.84569i		−	0.505385i	−0.967547	−	0.252693i	$-0.918684\pi$
$241$		−	7.84569i		−	0.505385i	0.967547	−	0.252693i	$-0.0813162\pi$
$242$			22.5192i			1.44759i
$243$	−6.92816	+	13.9643i	−0.444442	+	0.895808i
$244$			7.83301i			0.501457i
$245$	21.6405	+	22.1188i	1.38256	+	1.41312i
$246$	1.41981	−	3.30033i	0.0905238	−	0.210421i
$247$	2.66098			0.169314
$248$	−3.06154			−0.194408
$249$	−21.8448	−	9.39768i	−1.38435	−	0.595554i
$250$		−	42.1809i		−	2.66775i
$251$	−17.6842			−1.11622			−0.558109	−	0.829768i	$-0.688473\pi$
$251$	−17.6842			−1.11622			−0.558109	+	0.829768i	$0.688473\pi$
$252$	2.79679	+	7.42819i	0.176181	+	0.467932i
$253$	38.0538			2.39242
$254$			4.22104i			0.264851i
$255$	−20.9146	−	8.99754i	−1.30972	−	0.563448i
$256$	1.00000			0.0625000
$257$	20.1239			1.25529			0.627647	−	0.778498i	$-0.284018\pi$
$257$	20.1239			1.25529			0.627647	+	0.778498i	$0.284018\pi$
$258$	−3.59115	+	8.34757i	−0.223575	+	0.519697i
$259$	11.4927	+	4.83417i	0.714120	+	0.300381i
$260$		−	4.42062i		−	0.274155i
$261$	−7.49777	+	7.10144i	−0.464100	+	0.439568i
$262$			0.0690766i			0.00426757i
$263$		−	9.05875i		−	0.558586i	−0.960206	−	0.279293i	$-0.909900\pi$
$263$		−	9.05875i		−	0.558586i	0.960206	−	0.279293i	$-0.0901001\pi$
$264$	9.21159	+	3.96286i	0.566934	+	0.243897i
$265$			23.7183i			1.45701i
$266$	6.48955	+	2.72970i	0.397900	+	0.167369i
$267$	−23.1285	−	9.94996i	−1.41544	−	0.608928i
$268$	2.80059			0.171073
$269$	−13.5820			−0.828106			−0.414053	−	0.910253i	$-0.635887\pi$
$269$	−13.5820			−0.828106			−0.414053	+	0.910253i	$0.635887\pi$
$270$	21.5619	−	7.91931i	1.31221	−	0.481954i
$271$			12.7197i			0.772667i	0.922359	+	0.386333i	$0.126259\pi$
$271$			12.7197i			0.772667i	−0.922359	+	0.386333i	$0.873741\pi$
$272$	−2.97358			−0.180300
$273$	3.30146	−	3.17811i	0.199813	−	0.192348i
$274$	9.16032			0.553395
$275$		−	84.1912i		−	5.07692i
$276$	4.49896	−	10.4578i	0.270806	−	0.629483i
$277$	10.8847			0.653996			0.326998	−	0.945025i	$-0.393963\pi$
$277$	10.8847			0.653996			0.326998	+	0.945025i	$0.393963\pi$
$278$	5.91082			0.354507
$279$	−6.66836	+	6.31587i	−0.399224	+	0.378121i
$280$	4.53479	−	10.7809i	0.271006	−	0.644284i
$281$			8.55633i			0.510428i	0.966885	+	0.255214i	$0.0821459\pi$
$281$			8.55633i			0.510428i	−0.966885	+	0.255214i	$0.917854\pi$
$282$	−2.93154	+	6.81432i	−0.174571	+	0.405787i
$283$		−	5.57380i		−	0.331328i	−0.986182	−	0.165664i	$-0.947023\pi$
$283$		−	5.57380i		−	0.331328i	0.986182	−	0.165664i	$-0.0529768\pi$
$284$			4.46876i			0.265172i
$285$	8.05166	−	18.7159i	0.476939	−	1.10864i
$286$		−	5.78958i		−	0.342345i
$287$	−5.05875	−	2.12786i	−0.298608	−	0.125604i
$288$	2.17811	−	2.06297i	0.128346	−	0.121562i
$289$	−8.15783			−0.479873
$290$	15.2172			0.893587
$291$	3.96962	−	9.22732i	0.232703	−	0.540915i
$292$			4.11227i			0.240652i
$293$	0.217641			0.0127147			0.00635737	−	0.999980i	$-0.497976\pi$
$293$	0.217641			0.0127147			0.00635737	+	0.999980i	$0.497976\pi$
$294$	11.3117	−	4.36399i	0.659714	−	0.254513i
$295$	9.03325			0.525936
$296$		−	4.71246i		−	0.273906i
$297$	28.2391	−	10.3717i	1.63860	−	0.601829i
$298$	16.3060			0.944581
$299$	−6.57281			−0.380115
$300$	−23.1370	−	9.95362i	−1.33582	−	0.574673i
$301$	12.7952	+	5.38204i	0.737502	+	0.310216i
$302$		−	13.8392i		−	0.796356i
$303$	−2.73634	−	1.17718i	−0.157199	−	0.0676274i
$304$		−	2.66098i		−	0.152617i
$305$		−	34.6268i		−	1.98272i
$306$	−6.47677	+	6.13441i	−0.370252	+	0.350681i
$307$		−	23.2744i		−	1.32834i	−0.747581	−	0.664171i	$-0.768785\pi$
$307$		−	23.2744i		−	1.32834i	0.747581	−	0.664171i	$-0.231215\pi$
$308$	5.93911	−	14.1195i	0.338412	−	0.804536i
$309$	−1.02645	+	2.38598i	−0.0583929	+	0.135733i
$310$	13.5339			0.768673
$311$	28.7412			1.62976			0.814882	−	0.579626i	$-0.196801\pi$
$311$	28.7412			1.62976			0.814882	+	0.579626i	$0.196801\pi$
$312$	−1.59106	−	0.684481i	−0.0900763	−	0.0387511i
$313$		−	28.6034i		−	1.61676i	−0.588661	−	0.808380i	$-0.700345\pi$
$313$		−	28.6034i		−	1.61676i	0.588661	−	0.808380i	$-0.299655\pi$
$314$	−17.4503			−0.984777
$315$	−12.3635	−	32.8372i	−0.696605	−	1.85017i
$316$	−1.88228			−0.105886
$317$			14.8542i			0.834293i	0.908839	+	0.417147i	$0.136970\pi$
$317$			14.8542i			0.834293i	−0.908839	+	0.417147i	$0.863030\pi$
$318$	8.53668	+	3.67251i	0.478713	+	0.205944i
$319$	19.9297			1.11585
$320$	−4.42062			−0.247120
$321$	−1.30306	+	3.02894i	−0.0727297	+	0.169059i
$322$	−16.0297	−	6.74257i	−0.893299	−	0.375749i
$323$			7.91262i			0.440270i
$324$	0.488293	−	8.98674i	0.0271274	−	0.499264i
$325$			14.5419i			0.806637i
$326$		−	1.52302i		−	0.0843524i
$327$	17.4840	+	7.52169i	0.966870	+	0.415950i
$328$			2.07429i			0.114533i
$329$	10.4450	+	4.39349i	0.575852	+	0.242221i
$330$	−40.7209	−	17.5183i	−2.24161	−	0.964349i
$331$	−11.8754			−0.652733			−0.326366	−	0.945243i	$-0.605824\pi$
$331$	−11.8754			−0.652733			−0.326366	+	0.945243i	$0.605824\pi$
$332$	13.7296			0.753512
$333$	−9.72167	−	10.2642i	−0.532744	−	0.562476i
$334$		−	10.0997i		−	0.552633i
$335$	−12.3803			−0.676411
$336$	−3.17811	−	3.30146i	−0.173380	−	0.180109i
$337$	6.42342			0.349906			0.174953	−	0.984577i	$-0.444023\pi$
$337$	6.42342			0.349906			0.174953	+	0.984577i	$0.444023\pi$
$338$			1.00000i			0.0543928i
$339$	−8.47626	+	19.7029i	−0.460367	+	1.07012i
$340$	13.1451			0.712890
$341$	17.7250			0.959864
$342$	−5.48952	−	5.79589i	−0.296839	−	0.313406i
$343$	−6.80594	−	17.2244i	−0.367486	−	0.930029i
$344$		−	5.24653i		−	0.282874i
$345$	−19.8882	+	46.2298i	−1.07074	+	2.48893i
$346$			9.12994i			0.490829i
$347$			32.2119i			1.72922i	0.502440	+	0.864612i	$0.332436\pi$
$347$			32.2119i			1.72922i	−0.502440	+	0.864612i	$0.667564\pi$
$348$	2.35621	−	5.47698i	0.126306	−	0.293597i
$349$			15.5401i			0.831844i	0.909400	+	0.415922i	$0.136541\pi$
$349$			15.5401i			0.831844i	−0.909400	+	0.415922i	$0.863459\pi$
$350$	−14.9174	+	35.4645i	−0.797371	+	1.89566i
$351$	−4.87757	+	1.79145i	−0.260346	+	0.0956205i
$352$	−5.78958			−0.308586
$353$	−0.507480			−0.0270104			−0.0135052	−	0.999909i	$-0.504299\pi$
$353$	−0.507480			−0.0270104			−0.0135052	+	0.999909i	$0.504299\pi$
$354$	1.39869	−	3.25124i	0.0743397	−	0.172801i
$355$		−	19.7547i		−	1.04847i
$356$	14.5365			0.770433
$357$	9.45035	+	9.81715i	0.500165	+	0.519579i
$358$	−23.1002			−1.22088
$359$			34.8558i			1.83962i	0.392363	+	0.919811i	$0.371658\pi$
$359$			34.8558i			1.83962i	−0.392363	+	0.919811i	$0.628342\pi$
$360$	−9.62857	+	9.11961i	−0.507470	+	0.480646i
$361$	11.9192			0.627327
$362$	14.1049			0.741338
$363$	−35.8295	−	15.4140i	−1.88056	−	0.809024i
$364$	−1.02583	+	2.43879i	−0.0537680	+	0.127827i
$365$		−	18.1788i		−	0.951521i
$366$	−12.4628	−	5.36155i	−0.651443	−	0.280253i
$367$		−	10.7760i		−	0.562505i	−0.959634	−	0.281252i	$-0.909250\pi$
$367$		−	10.7760i		−	0.562505i	0.959634	−	0.281252i	$-0.0907498\pi$
$368$			6.57281i			0.342631i
$369$	4.27920	+	4.51802i	0.222766	+	0.235199i
$370$			20.8320i			1.08300i
$371$	5.50396	−	13.0850i	0.285752	−	0.679341i
$372$	2.09556	−	4.87111i	0.108650	−	0.252555i
$373$	27.5173			1.42479			0.712395	−	0.701779i	$-0.247611\pi$
$373$	27.5173			1.42479			0.712395	+	0.701779i	$0.247611\pi$
$374$	17.2158			0.890206
$375$	67.1125	+	28.8720i	3.46568	+	1.49094i
$376$		−	4.28287i		−	0.220872i
$377$	−3.44234			−0.177289
$378$	−13.7331	−	0.634587i	−0.706353	−	0.0326397i
$379$	30.5492			1.56921			0.784604	−	0.619998i	$-0.212867\pi$
$379$	30.5492			1.56921			0.784604	+	0.619998i	$0.212867\pi$
$380$			11.7632i			0.603437i
$381$	−6.71594	−	2.88922i	−0.344068	−	0.148019i
$382$	−2.89642			−0.148194
$383$	22.7708			1.16353			0.581767	−	0.813355i	$-0.302362\pi$
$383$	22.7708			1.16353			0.581767	+	0.813355i	$0.302362\pi$
$384$	−0.684481	+	1.59106i	−0.0349298	+	0.0811937i
$385$	−26.2545	+	62.4171i	−1.33806	+	3.18107i
$386$			3.12768i			0.159195i
$387$	−10.8235	−	11.4275i	−0.550187	−	0.580893i
$388$			5.79946i			0.294423i
$389$		−	26.7682i		−	1.35720i	−0.734507	−	0.678601i	$-0.762587\pi$
$389$		−	26.7682i		−	1.35720i	0.734507	−	0.678601i	$-0.237413\pi$
$390$	7.03349	+	3.02583i	0.356154	+	0.153219i
$391$		−	19.5448i		−	0.988421i
$392$	−5.00355	+	4.89535i	−0.252717	+	0.247253i
$393$	−0.109905	−	0.0472816i	−0.00554399	−	0.00238504i
$394$	13.2555			0.667801
$395$	8.32082			0.418666
$396$	−12.6103	+	11.9437i	−0.633692	+	0.600195i
$397$			9.36879i			0.470206i	0.971970	+	0.235103i	$0.0755428\pi$
$397$			9.36879i			0.470206i	−0.971970	+	0.235103i	$0.924457\pi$
$398$	−14.0635			−0.704937
$399$	−8.78511	+	8.45686i	−0.439805	+	0.423373i
$400$	14.5419			0.727093
$401$			3.54852i			0.177205i	0.996067	+	0.0886024i	$0.0282400\pi$
$401$			3.54852i			0.177205i	−0.996067	+	0.0886024i	$0.971760\pi$
$402$	−1.91695	+	4.45592i	−0.0956089	+	0.222241i
$403$	−3.06154			−0.152506
$404$	1.71982			0.0855642
$405$	−2.15856	+	39.7270i	−0.107260	+	1.97405i
$406$	−8.39512	−	3.53124i	−0.416643	−	0.175253i
$407$			27.2831i			1.35238i
$408$	2.03536	−	4.73115i	0.100765	−	0.234227i
$409$		−	31.5942i		−	1.56223i	−0.624385	−	0.781116i	$-0.714651\pi$
$409$		−	31.5942i		−	1.56223i	0.624385	−	0.781116i	$-0.285349\pi$
$410$		−	9.16963i		−	0.452856i
$411$	−6.27006	+	14.5747i	−0.309279	+	0.718915i
$412$		−	1.49961i		−	0.0738805i
$413$	−4.98350	−	2.09621i	−0.245222	−	0.103148i
$414$	13.5595	+	14.3163i	0.666414	+	0.703607i
$415$	−60.6935			−2.97933
$416$	1.00000			0.0490290
$417$	−4.04584	+	9.40449i	−0.198126	+	0.460540i
$418$			15.4059i			0.753529i
$419$	−2.06628			−0.100945			−0.0504723	−	0.998725i	$-0.516073\pi$
$419$	−2.06628			−0.100945			−0.0504723	+	0.998725i	$0.516073\pi$
$420$	14.0492	+	14.5945i	0.685530	+	0.712138i
$421$	−5.52392			−0.269219			−0.134610	−	0.990899i	$-0.542978\pi$
$421$	−5.52392			−0.269219			−0.134610	+	0.990899i	$0.542978\pi$
$422$			0.508960i			0.0247758i
$423$	−8.83544	−	9.32855i	−0.429594	−	0.453570i
$424$	−5.36539			−0.260566
$425$	−43.2413			−2.09751
$426$	−7.11008	−	3.05878i	−0.344485	−	0.148198i
$427$	−8.03532	+	19.1030i	−0.388857	+	0.924461i
$428$		−	1.90372i		−	0.0920198i
$429$	9.21159	+	3.96286i	0.444740	+	0.191328i
$430$			23.1929i			1.11846i
$431$		−	0.0573873i		−	0.00276425i	−0.999999	−	0.00138212i	$-0.999560\pi$
$431$		−	0.0573873i		−	0.00276425i	0.999999	−	0.00138212i	$-0.000439944\pi$
$432$	1.79145	+	4.87757i	0.0861911	+	0.234672i
$433$		−	11.7659i		−	0.565434i	−0.959203	−	0.282717i	$-0.908764\pi$
$433$		−	11.7659i		−	0.565434i	0.959203	−	0.282717i	$-0.0912357\pi$
$434$	−7.46644	−	3.14061i	−0.358401	−	0.150754i
$435$	−10.4159	+	24.2116i	−0.499405	+	1.16086i
$436$	−10.9889			−0.526273
$437$	17.4901			0.836664
$438$	−6.54289	−	2.81477i	−0.312631	−	0.134495i
$439$			8.88441i			0.424030i	0.977266	+	0.212015i	$0.0680026\pi$
$439$			8.88441i			0.424030i	−0.977266	+	0.212015i	$0.931997\pi$
$440$	25.5935			1.22012
$441$	−0.799282	+	20.9848i	−0.0380610	+	0.999275i
$442$	−2.97358			−0.141439
$443$			32.7864i			1.55773i	0.627191	+	0.778865i	$0.284204\pi$
$443$			32.7864i			1.55773i	−0.627191	+	0.778865i	$0.715796\pi$
$444$	7.49782	+	3.22559i	0.355831	+	0.153080i
$445$	−64.2603			−3.04623
$446$	−12.0398			−0.570101
$447$	−11.1611	+	25.9439i	−0.527904	+	1.22710i
$448$	2.43879	+	1.02583i	0.115222	+	0.0484658i
$449$		−	23.4377i		−	1.10609i	−0.833150	−	0.553047i	$-0.813465\pi$
$449$		−	23.4377i		−	1.10609i	0.833150	−	0.553047i	$-0.186535\pi$
$450$	31.6737	−	29.9994i	1.49311	−	1.41419i
$451$		−	12.0093i		−	0.565494i
$452$		−	12.3835i		−	0.582470i
$453$	22.0190	+	9.47266i	1.03454	+	0.445064i
$454$		−	10.9044i		−	0.511771i
$455$	4.53479	−	10.7809i	0.212594	−	0.505418i
$456$	4.23378	+	1.82139i	0.198265	+	0.0852943i
$457$	8.00329			0.374378			0.187189	−	0.982324i	$-0.440062\pi$
$457$	8.00329			0.374378			0.187189	+	0.982324i	$0.440062\pi$
$458$	−12.4163			−0.580174
$459$	−5.32701	−	14.5038i	−0.248644	−	0.676981i
$460$		−	29.0559i		−	1.35474i
$461$	18.9716			0.883594			0.441797	−	0.897115i	$-0.354341\pi$
$461$	18.9716			0.883594			0.441797	+	0.897115i	$0.354341\pi$
$462$	18.3999	+	19.1141i	0.856041	+	0.889267i
$463$	9.48421			0.440769			0.220384	−	0.975413i	$-0.429269\pi$
$463$	9.48421			0.440769			0.220384	+	0.975413i	$0.429269\pi$
$464$			3.44234i			0.159806i
$465$	−9.26369	+	21.5333i	−0.429593	+	0.998583i
$466$	−21.7343			−1.00682
$467$	−38.4973			−1.78144			−0.890722	−	0.454548i	$-0.849801\pi$
$467$	−38.4973			−1.78144			−0.890722	+	0.454548i	$0.849801\pi$
$468$	2.17811	−	2.06297i	0.100683	−	0.0953609i
$469$	6.83005	+	2.87293i	0.315382	+	0.132659i
$470$			18.9329i			0.873311i
$471$	11.9444	−	27.7645i	0.550368	−	1.27932i
$472$			2.04344i			0.0940567i
$473$			30.3752i			1.39665i
$474$	1.28838	−	2.99482i	0.0591773	−	0.137557i
$475$		−	38.6955i		−	1.77547i
$476$	−7.25192	−	3.05038i	−0.332391	−	0.139814i
$477$	−11.6864	+	11.0686i	−0.535083	+	0.506798i
$478$	−15.1287			−0.691970
$479$	−31.3595			−1.43285			−0.716426	−	0.697663i	$-0.754223\pi$
$479$	−31.3595			−1.43285			−0.716426	+	0.697663i	$0.754223\pi$
$480$	3.02583	−	7.03349i	0.138110	−	0.321033i
$481$		−	4.71246i		−	0.214870i
$482$	−7.84569			−0.357361
$483$	21.6999	−	20.8891i	0.987378	−	0.950486i
$484$	22.5192			1.02360
$485$		−	25.6372i		−	1.16413i
$486$	13.9643	+	6.92816i	0.633432	+	0.314268i
$487$	−13.6604			−0.619010			−0.309505	−	0.950898i	$-0.600163\pi$
$487$	−13.6604			−0.619010			−0.309505	+	0.950898i	$0.600163\pi$
$488$	7.83301			0.354584
$489$	2.42323	+	1.04248i	0.109582	+	0.0471426i
$490$	22.1188	−	21.6405i	0.999224	−	0.977618i
$491$			28.3534i			1.27957i	0.768553	+	0.639786i	$0.220977\pi$
$491$			28.3534i			1.27957i	−0.768553	+	0.639786i	$0.779023\pi$
$492$	−3.30033	−	1.41981i	−0.148790	−	0.0640100i
$493$		−	10.2361i		−	0.461009i
$494$		−	2.66098i		−	0.119723i
$495$	55.7454	−	52.7987i	2.50557	−	2.37313i
$496$			3.06154i			0.137467i
$497$	−4.58418	+	10.8983i	−0.205628	+	0.488857i
$498$	−9.39768	+	21.8448i	−0.421120	+	0.978887i
$499$	−1.59987			−0.0716201			−0.0358101	−	0.999359i	$-0.511401\pi$
$499$	−1.59987			−0.0716201			−0.0358101	+	0.999359i	$0.511401\pi$
$500$	−42.1809			−1.88639
$501$	16.0693	+	6.91307i	0.717924	+	0.308853i
$502$			17.6842i			0.789285i
$503$	33.6551			1.50061			0.750304	−	0.661093i	$-0.229907\pi$
$503$	33.6551			1.50061			0.750304	+	0.661093i	$0.229907\pi$
$504$	7.42819	−	2.79679i	0.330878	−	0.124579i
$505$	−7.60267			−0.338314
$506$		−	38.0538i		−	1.69170i
$507$	−1.59106	−	0.684481i	−0.0706617	−	0.0303989i
$508$	4.22104			0.187278
$509$	7.66428			0.339713			0.169857	−	0.985469i	$-0.445670\pi$
$509$	7.66428			0.339713			0.169857	+	0.985469i	$0.445670\pi$
$510$	−8.99754	+	20.9146i	−0.398418	+	0.926115i
$511$	−4.21848	+	10.0290i	−0.186615	+	0.443655i
$512$		−	1.00000i		−	0.0441942i
$513$	12.9791	−	4.76700i	0.573041	−	0.210468i
$514$		−	20.1239i		−	0.887626i
$515$			6.62920i			0.292117i
$516$	8.34757	+	3.59115i	0.367481	+	0.158092i
$517$			24.7960i			1.09053i
$518$	4.83417	−	11.4927i	0.212401	−	0.504959i
$519$	−14.5263	−	6.24927i	−0.637635	−	0.274312i
$520$	−4.42062			−0.193857
$521$	45.1199			1.97674			0.988369	−	0.152076i	$-0.0485958\pi$
$521$	45.1199			1.97674			0.988369	+	0.152076i	$0.0485958\pi$
$522$	7.10144	+	7.49777i	0.310822	+	0.328169i
$523$			11.3166i			0.494840i	0.968908	+	0.247420i	$0.0795828\pi$
$523$			11.3166i			0.494840i	−0.968908	+	0.247420i	$0.920417\pi$
$524$	0.0690766			0.00301763
$525$	−46.2156	−	48.0094i	−2.01701	−	2.09530i
$526$	−9.05875			−0.394980
$527$		−	9.10373i		−	0.396565i
$528$	3.96286	−	9.21159i	0.172461	−	0.400883i
$529$	−20.2018			−0.878340
$530$	23.7183			1.03026
$531$	4.21555	+	4.45082i	0.182939	+	0.193149i
$532$	2.72970	−	6.48955i	0.118348	−	0.281358i
$533$			2.07429i			0.0898474i
$534$	−9.94996	+	23.1285i	−0.430577	+	1.00087i
$535$			8.41562i			0.363839i
$536$		−	2.80059i		−	0.120967i
$537$	15.8117	−	36.7539i	0.682323	−	1.58605i
$538$			13.5820i			0.585560i
$539$	28.9684	−	28.3420i	1.24776	−	1.22078i
$540$	−7.91931	−	21.5619i	−0.340793	−	0.927876i
$541$	−31.5579			−1.35678			−0.678389	−	0.734703i	$-0.737322\pi$
$541$	−31.5579			−1.35678			−0.678389	+	0.734703i	$0.737322\pi$
$542$	12.7197			0.546358
$543$	−9.65455	+	22.4418i	−0.414316	+	0.963072i
$544$			2.97358i			0.127491i
$545$	48.5777			2.08084
$546$	−3.17811	−	3.30146i	−0.136010	−	0.141289i
$547$	−25.0069			−1.06922			−0.534609	−	0.845099i	$-0.679541\pi$
$547$	−25.0069			−1.06922			−0.534609	+	0.845099i	$0.679541\pi$
$548$		−	9.16032i		−	0.391310i
$549$	17.0611	−	16.1593i	0.728152	−	0.689662i
$550$	−84.1912			−3.58993
$551$	9.15997			0.390228
$552$	−10.4578	−	4.49896i	−0.445112	−	0.191489i
$553$	−4.59047	−	1.93089i	−0.195207	−	0.0821098i
$554$		−	10.8847i		−	0.462445i
$555$	−33.1450	−	14.2591i	−1.40693	−	0.605264i
$556$		−	5.91082i		−	0.250675i
$557$		−	13.1413i		−	0.556816i	−0.960463	−	0.278408i	$-0.910193\pi$
$557$		−	13.1413i		−	0.556816i	0.960463	−	0.278408i	$-0.0898068\pi$
$558$	6.31587	+	6.66836i	0.267372	+	0.282294i
$559$		−	5.24653i		−	0.221905i
$560$	−10.7809	−	4.53479i	−0.455578	−	0.191630i
$561$	−11.7839	+	27.3914i	−0.497515	+	1.15647i
$562$	8.55633			0.360927
$563$	−6.02277			−0.253829			−0.126915	−	0.991914i	$-0.540507\pi$
$563$	−6.02277			−0.253829			−0.126915	+	0.991914i	$0.540507\pi$
$564$	6.81432	+	2.93154i	0.286935	+	0.123440i
$565$			54.7427i			2.30304i
$566$	−5.57380			−0.234284
$567$	10.4097	−	21.4158i	0.437166	−	0.899381i
$568$	4.46876			0.187505
$569$			9.62158i			0.403358i	0.979452	+	0.201679i	$0.0646397\pi$
$569$			9.62158i			0.403358i	−0.979452	+	0.201679i	$0.935360\pi$
$570$	−18.7159	−	8.05166i	−0.783924	−	0.337247i
$571$	20.9873			0.878289			0.439145	−	0.898416i	$-0.355282\pi$
$571$	20.9873			0.878289			0.439145	+	0.898416i	$0.355282\pi$
$572$	−5.78958			−0.242074
$573$	1.98255	−	4.60840i	0.0828221	−	0.192519i
$574$	−2.12786	+	5.05875i	−0.0888153	+	0.211148i
$575$			95.5808i			3.98600i
$576$	−2.06297	−	2.17811i	−0.0859572	−	0.0907544i
$577$			35.9071i			1.49483i	0.664356	+	0.747416i	$0.268706\pi$
$577$			35.9071i			1.49483i	−0.664356	+	0.747416i	$0.731294\pi$
$578$			8.15783i			0.339321i
$579$	−4.97634	−	2.14084i	−0.206810	−	0.0889701i
$580$		−	15.2172i		−	0.631862i
$581$	33.4837	+	14.0843i	1.38914	+	0.584313i
$582$	−9.22732	−	3.96962i	−0.382485	−	0.164546i
$583$	31.0633			1.28651
$584$	4.11227			0.170167
$585$	−9.62857	+	9.11961i	−0.398093	+	0.377049i
$586$		−	0.217641i		−	0.00899068i
$587$	18.8573			0.778322			0.389161	−	0.921170i	$-0.372765\pi$
$587$	18.8573			0.778322			0.389161	+	0.921170i	$0.372765\pi$
$588$	−4.36399	−	11.3117i	−0.179968	−	0.466489i
$589$	8.14668			0.335678
$590$		−	9.03325i		−	0.371893i
$591$	−9.07312	+	21.0903i	−0.373218	+	0.867539i
$592$	−4.71246			−0.193681
$593$	7.04969			0.289496			0.144748	−	0.989469i	$-0.453763\pi$
$593$	7.04969			0.289496			0.144748	+	0.989469i	$0.453763\pi$
$594$	−10.3717	−	28.2391i	−0.425558	−	1.15866i
$595$	32.0580	+	13.4846i	1.31425	+	0.552813i
$596$		−	16.3060i		−	0.667920i
$597$	9.62617	−	22.3759i	0.393973	−	0.915783i
$598$			6.57281i			0.268782i
$599$		−	10.2108i		−	0.417202i	−0.978001	−	0.208601i	$-0.933109\pi$
$599$		−	10.2108i		−	0.417202i	0.978001	−	0.208601i	$-0.0668911\pi$
$600$	−9.95362	+	23.1370i	−0.406355	+	0.944565i
$601$		−	30.2260i		−	1.23294i	−0.787377	−	0.616472i	$-0.788561\pi$
$601$		−	30.2260i		−	1.23294i	0.787377	−	0.616472i	$-0.211439\pi$
$602$	5.38204	−	12.7952i	0.219356	−	0.521492i
$603$	−5.77754	−	6.09999i	−0.235280	−	0.248411i
$604$	−13.8392			−0.563109
$605$	−99.5489			−4.04724
$606$	−1.17718	+	2.73634i	−0.0478198	+	0.111156i
$607$			28.0418i			1.13818i	0.822275	+	0.569090i	$0.192705\pi$
$607$			28.0418i			1.13818i	−0.822275	+	0.569090i	$0.807295\pi$
$608$	−2.66098			−0.107917
$609$	11.3647	−	10.9401i	0.460522	−	0.443315i
$610$	−34.6268			−1.40200
$611$		−	4.28287i		−	0.173266i
$612$	6.13441	+	6.47677i	0.247969	+	0.261808i
$613$	−16.6450			−0.672284			−0.336142	−	0.941811i	$-0.609122\pi$
$613$	−16.6450			−0.672284			−0.336142	+	0.941811i	$0.609122\pi$
$614$	−23.2744			−0.939279
$615$	14.5895	+	6.27644i	0.588305	+	0.253090i
$616$	−14.1195	−	5.93911i	−0.568893	−	0.239294i
$617$		−	26.2320i		−	1.05606i	−0.849225	−	0.528031i	$-0.822931\pi$
$617$		−	26.2320i		−	1.05606i	0.849225	−	0.528031i	$-0.177069\pi$
$618$	2.38598	+	1.02645i	0.0959780	+	0.0412900i
$619$		−	22.7636i		−	0.914946i	−0.889224	−	0.457473i	$-0.848755\pi$
$619$		−	22.7636i		−	0.914946i	0.889224	−	0.457473i	$-0.151245\pi$
$620$		−	13.5339i		−	0.543534i
$621$	−32.0593	+	11.7749i	−1.28650	+	0.472509i
$622$		−	28.7412i		−	1.15242i
$623$	35.4514	+	14.9119i	1.42033	+	0.597435i
$624$	−0.684481	+	1.59106i	−0.0274012	+	0.0636936i
$625$	113.756			4.55025
$626$	−28.6034			−1.14322
$627$	−24.5118	−	10.5451i	−0.978908	−	0.421129i
$628$			17.4503i			0.696342i
$629$	14.0129			0.558729
$630$	−32.8372	+	12.3635i	−1.30826	+	0.492574i
$631$	−0.162308			−0.00646136			−0.00323068	−	0.999995i	$-0.501028\pi$
$631$	−0.162308			−0.00646136			−0.00323068	+	0.999995i	$0.501028\pi$
$632$			1.88228i			0.0748729i
$633$	−0.809788	−	0.348373i	−0.0321862	−	0.0138466i
$634$	14.8542			0.589934
$635$	−18.6596			−0.740483
$636$	3.67251	−	8.53668i	0.145624	−	0.338501i
$637$	−5.00355	+	4.89535i	−0.198248	+	0.193961i
$638$		−	19.9297i		−	0.789023i
$639$	9.73343	−	9.21892i	0.385048	−	0.364695i
$640$			4.42062i			0.174740i
$641$		−	48.6132i		−	1.92011i	−0.279816	−	0.960054i	$-0.590273\pi$
$641$		−	48.6132i		−	1.92011i	0.279816	−	0.960054i	$-0.409727\pi$
$642$	3.02894	+	1.30306i	0.119543	+	0.0514277i
$643$			37.0866i			1.46255i	0.682082	+	0.731276i	$0.261075\pi$
$643$			37.0866i			1.46255i	−0.682082	+	0.731276i	$0.738925\pi$
$644$	−6.74257	+	16.0297i	−0.265694	+	0.631658i
$645$	−36.9014	−	15.8751i	−1.45299	−	0.625082i
$646$	7.91262			0.311318
$647$	−2.76336			−0.108639			−0.0543194	−	0.998524i	$-0.517299\pi$
$647$	−2.76336			−0.108639			−0.0543194	+	0.998524i	$0.517299\pi$
$648$	−8.98674	−	0.488293i	−0.353033	−	0.0191820i
$649$		−	11.8306i		−	0.464393i
$650$	14.5419			0.570379
$651$	10.1076	−	9.72990i	0.396146	−	0.381345i
$652$	−1.52302			−0.0596462
$653$		−	3.35505i		−	0.131293i	−0.997843	−	0.0656466i	$-0.979089\pi$
$653$		−	3.35505i		−	0.131293i	0.997843	−	0.0656466i	$-0.0209110\pi$
$654$	7.52169	−	17.4840i	0.294121	−	0.683680i
$655$	−0.305361			−0.0119315
$656$	2.07429			0.0809874
$657$	8.95696	−	8.48350i	0.349444	−	0.330973i
$658$	4.39349	−	10.4450i	0.171276	−	0.407189i
$659$			31.9684i			1.24531i	0.782495	+	0.622657i	$0.213947\pi$
$659$			31.9684i			1.24531i	−0.782495	+	0.622657i	$0.786053\pi$
$660$	−17.5183	+	40.7209i	−0.681898	+	1.58506i
$661$		−	19.9277i		−	0.775097i	−0.921849	−	0.387548i	$-0.873322\pi$
$661$		−	19.9277i		−	0.775097i	0.921849	−	0.387548i	$-0.126678\pi$
$662$			11.8754i			0.461552i
$663$	2.03536	−	4.73115i	0.0790467	−	0.183743i
$664$		−	13.7296i		−	0.532814i
$665$	−12.0670	+	28.6878i	−0.467937	+	1.11247i
$666$	−10.2642	+	9.72167i	−0.397731	+	0.376707i
$667$	−22.6258			−0.876075
$668$	−10.0997			−0.390770
$669$	8.24101	−	19.1561i	0.318616	−	0.740618i
$670$			12.3803i			0.478295i
$671$	−45.3499			−1.75071
$672$	−3.30146	+	3.17811i	−0.127357	+	0.122598i
$673$	16.8513			0.649570			0.324785	−	0.945788i	$-0.394708\pi$
$673$	16.8513			0.649570			0.324785	+	0.945788i	$0.394708\pi$
$674$		−	6.42342i		−	0.247421i
$675$	26.0510	+	70.9290i	1.00270	+	2.73006i
$676$	1.00000			0.0384615
$677$	−37.5910			−1.44474			−0.722369	−	0.691508i	$-0.756947\pi$
$677$	−37.5910			−1.44474			−0.722369	+	0.691508i	$0.756947\pi$
$678$	19.7029	+	8.47626i	0.756687	+	0.325529i
$679$	−5.94925	+	14.1436i	−0.228311	+	0.542783i
$680$		−	13.1451i		−	0.504090i
$681$	17.3497	+	7.46388i	0.664840	+	0.286016i
$682$		−	17.7250i		−	0.678726i
$683$			24.2136i			0.926509i	0.886225	+	0.463255i	$0.153319\pi$
$683$			24.2136i			0.926509i	−0.886225	+	0.463255i	$0.846681\pi$
$684$	−5.79589	+	5.48952i	−0.221611	+	0.209897i
$685$			40.4943i			1.54721i
$686$	−17.2244	+	6.80594i	−0.657630	+	0.259852i
$687$	8.49869	−	19.7551i	0.324245	−	0.753703i
$688$	−5.24653			−0.200022
$689$	−5.36539			−0.204405
$690$	46.2298	+	19.8882i	1.75994	+	0.757130i
$691$		−	36.7542i		−	1.39820i	−0.715026	−	0.699098i	$-0.753585\pi$
$691$		−	36.7542i		−	1.39820i	0.715026	−	0.699098i	$-0.246415\pi$
$692$	9.12994			0.347068
$693$	−43.0061	+	16.1922i	−1.63367	+	0.615091i
$694$	32.2119			1.22275
$695$			26.1295i			0.991147i
$696$	−5.47698	−	2.35621i	−0.207604	−	0.0893120i
$697$	−6.16806			−0.233632
$698$	15.5401			0.588202
$699$	14.8767	−	34.5807i	0.562689	−	1.30796i
$700$	35.4645	+	14.9174i	1.34043	+	0.563826i
$701$		−	18.2532i		−	0.689413i	−0.938710	−	0.344707i	$-0.887978\pi$
$701$		−	18.2532i		−	0.689413i	0.938710	−	0.344707i	$-0.112022\pi$
$702$	1.79145	+	4.87757i	0.0676139	+	0.184092i
$703$			12.5397i			0.472945i
$704$			5.78958i			0.218203i
$705$	−30.1235	−	12.9592i	−1.13452	−	0.488073i
$706$			0.507480i			0.0190993i
$707$	4.19427	+	1.76424i	0.157742	+	0.0663510i
$708$	−3.25124	−	1.39869i	−0.122189	−	0.0525661i
$709$	34.7784			1.30613			0.653066	−	0.757301i	$-0.273482\pi$
$709$	34.7784			1.30613			0.653066	+	0.757301i	$0.273482\pi$
$710$	−19.7547			−0.741379
$711$	3.88308	+	4.09980i	0.145627	+	0.153754i
$712$		−	14.5365i		−	0.544778i
$713$	−20.1229			−0.753609
$714$	9.81715	−	9.45035i	0.367398	−	0.353670i
$715$	25.5935			0.957143
$716$			23.1002i			0.863296i
$717$	10.3553	−	24.0707i	0.386726	−	0.898937i
$718$	34.8558			1.30081
$719$	−26.7270			−0.996748			−0.498374	−	0.866962i	$-0.666069\pi$
$719$	−26.7270			−0.996748			−0.498374	+	0.866962i	$0.666069\pi$
$720$	9.11961	+	9.62857i	0.339868	+	0.358836i
$721$	1.53834	−	3.65723i	0.0572908	−	0.136202i
$722$		−	11.9192i		−	0.443587i
$723$	5.37023	−	12.4830i	0.199721	−	0.464248i
$724$		−	14.1049i		−	0.524205i
$725$			50.0579i			1.85911i
$726$	−15.4140	+	35.8295i	−0.572066	+	1.32976i
$727$			19.0095i			0.705025i	0.935807	+	0.352513i	$0.114673\pi$
$727$			19.0095i			0.705025i	−0.935807	+	0.352513i	$0.885327\pi$
$728$	2.43879	+	1.02583i	0.0903874	+	0.0380197i
$729$	−20.5814	+	17.4758i	−0.762275	+	0.647254i
$730$	−18.1788			−0.672827
$731$	15.6010			0.577023
$732$	−5.36155	+	12.4628i	−0.198169	+	0.460639i
$733$		−	41.4833i		−	1.53222i	−0.642710	−	0.766110i	$-0.722190\pi$
$733$		−	41.4833i		−	1.53222i	0.642710	−	0.766110i	$-0.277810\pi$
$734$	−10.7760			−0.397751
$735$	19.2915	+	50.0049i	0.711579	+	1.84446i
$736$	6.57281			0.242277
$737$			16.2143i			0.597260i
$738$	4.51802	−	4.27920i	0.166311	−	0.157519i
$739$	−31.3268			−1.15237			−0.576187	−	0.817318i	$-0.695460\pi$
$739$	−31.3268			−1.15237			−0.576187	+	0.817318i	$0.695460\pi$
$740$	20.8320			0.765798
$741$	4.23378	+	1.82139i	0.155532	+	0.0669103i
$742$	−13.0850	−	5.50396i	−0.480367	−	0.202057i
$743$			6.91989i			0.253866i	0.991911	+	0.126933i	$0.0405133\pi$
$743$			6.91989i			0.253866i	−0.991911	+	0.126933i	$0.959487\pi$
$744$	−4.87111	−	2.09556i	−0.178583	−	0.0768271i
$745$			72.0826i			2.64090i
$746$		−	27.5173i		−	1.00748i
$747$	−28.3239	−	29.9046i	−1.03632	−	1.09415i
$748$		−	17.2158i		−	0.629471i
$749$	1.95289	−	4.64277i	0.0713570	−	0.169643i
$750$	28.8720	−	67.1125i	1.05426	−	2.45060i
$751$	36.2605			1.32317			0.661583	−	0.749872i	$-0.269885\pi$
$751$	36.2605			1.32317			0.661583	+	0.749872i	$0.269885\pi$
$752$	−4.28287			−0.156180
$753$	−28.1367	−	12.1045i	−1.02536	−	0.441113i
$754$			3.44234i			0.125362i
$755$	61.1778			2.22649
$756$	−0.634587	+	13.7331i	−0.0230797	+	0.499467i
$757$	17.6516			0.641558			0.320779	−	0.947154i	$-0.396055\pi$
$757$	17.6516			0.641558			0.320779	+	0.947154i	$0.396055\pi$
$758$		−	30.5492i		−	1.10960i
$759$	60.5460	+	26.0471i	2.19768	+	0.945450i
$760$	11.7632			0.426695
$761$	−16.3531			−0.592798			−0.296399	−	0.955064i	$-0.595786\pi$
$761$	−16.3531			−0.592798			−0.296399	+	0.955064i	$0.595786\pi$
$762$	−2.88922	+	6.71594i	−0.104665	+	0.243293i
$763$	−26.7996	−	11.2727i	−0.970209	−	0.408100i
$764$			2.89642i			0.104789i
$765$	−27.1179	−	28.6313i	−0.980449	−	1.03517i
$766$		−	22.7708i		−	0.822743i
$767$			2.04344i			0.0737842i
$768$	1.59106	+	0.684481i	0.0574126	+	0.0246991i
$769$		−	14.5077i		−	0.523161i	−0.965182	−	0.261581i	$-0.915756\pi$
$769$		−	14.5077i		−	0.523161i	0.965182	−	0.261581i	$-0.0842438\pi$
$770$	62.4171	+	26.2545i	2.24936	+	0.946148i
$771$	32.0184	+	13.7744i	1.15311	+	0.496073i
$772$	3.12768			0.112568
$773$	−42.8584			−1.54151			−0.770755	−	0.637132i	$-0.780121\pi$
$773$	−42.8584			−1.54151			−0.770755	+	0.637132i	$0.780121\pi$
$774$	−11.4275	+	10.8235i	−0.410753	+	0.389041i
$775$			44.5205i			1.59922i
$776$	5.79946			0.208189
$777$	14.9767	+	15.5580i	0.537286	+	0.558140i
$778$	−26.7682			−0.959687
$779$		−	5.51963i		−	0.197761i
$780$	3.02583	−	7.03349i	0.108342	−	0.251839i
$781$	−25.8722			−0.925781
$782$	−19.5448			−0.698919
$783$	−16.7902	+	6.16677i	−0.600034	+	0.220382i
$784$	4.89535	+	5.00355i	0.174834	+	0.178698i
$785$		−	77.1411i		−	2.75328i
$786$	−0.0472816	+	0.109905i	−0.00168648	+	0.00392020i
$787$		−	20.6512i		−	0.736136i	−0.929799	−	0.368068i	$-0.880019\pi$
$787$		−	20.6512i		−	0.736136i	0.929799	−	0.368068i	$-0.119981\pi$
$788$		−	13.2555i		−	0.472207i
$789$	6.20054	−	14.4130i	0.220745	−	0.513118i
$790$		−	8.32082i		−	0.296042i
$791$	12.7033	−	30.2007i	0.451678	−	1.07381i
$792$	11.9437	+	12.6103i	0.424402	+	0.448088i
$793$	7.83301			0.278159
$794$	9.36879			0.332486
$795$	−16.2347	+	37.7374i	−0.575787	+	1.33841i
$796$			14.0635i			0.498466i
$797$	−3.37172			−0.119432			−0.0597162	−	0.998215i	$-0.519020\pi$
$797$	−3.37172			−0.119432			−0.0597162	+	0.998215i	$0.519020\pi$
$798$	8.45686	+	8.78511i	0.299370	+	0.310989i
$799$	12.7355			0.450548
$800$		−	14.5419i		−	0.514132i
$801$	−29.9884	−	31.6620i	−1.05959	−	1.11872i
$802$	3.54852			0.125303
$803$	−23.8083			−0.840177
$804$	4.45592	+	1.91695i	0.157148	+	0.0676057i
$805$	29.8063	−	70.8611i	1.05053	−	2.49752i
$806$			3.06154i			0.107838i
$807$	−21.6098	−	9.29659i	−0.760700	−	0.327255i
$808$		−	1.71982i		−	0.0605031i
$809$			7.99680i			0.281153i	0.990070	+	0.140576i	$0.0448955\pi$
$809$			7.99680i			0.281153i	−0.990070	+	0.140576i	$0.955104\pi$
$810$	39.7270	+	2.15856i	1.39586	+	0.0758440i
$811$		−	17.6134i		−	0.618488i	−0.950983	−	0.309244i	$-0.899924\pi$
$811$		−	17.6134i		−	0.618488i	0.950983	−	0.309244i	$-0.100076\pi$
$812$	−3.53124	+	8.39512i	−0.123922	+	0.294611i
$813$	−8.70639	+	20.2379i	−0.305346	+	0.709773i
$814$	27.2831			0.956274
$815$	6.73270			0.235836
$816$	−4.73115	−	2.03536i	−0.165624	−	0.0712518i
$817$			13.9609i			0.488430i
$818$	−31.5942			−1.10467
$819$	7.42819	−	2.79679i	0.259562	−	0.0977276i
$820$	−9.16963			−0.320218
$821$			1.03397i			0.0360858i	0.999837	+	0.0180429i	$0.00574354\pi$
$821$			1.03397i			0.0360858i	−0.999837	+	0.0180429i	$0.994256\pi$
$822$	14.5747	+	6.27006i	0.508350	+	0.218694i
$823$	54.2317			1.89040			0.945199	−	0.326494i	$-0.105867\pi$
$823$	54.2317			1.89040			0.945199	+	0.326494i	$0.105867\pi$
$824$	−1.49961			−0.0522414
$825$	57.6273	−	133.954i	2.00632	−	4.66367i
$826$	−2.09621	+	4.98350i	−0.0729366	+	0.173398i
$827$		−	44.5320i		−	1.54853i	−0.632862	−	0.774264i	$-0.718120\pi$
$827$		−	44.5320i		−	1.54853i	0.632862	−	0.774264i	$-0.281880\pi$
$828$	14.3163	−	13.5595i	0.497525	−	0.471226i
$829$		−	47.8410i		−	1.66159i	−0.556582	−	0.830793i	$-0.687888\pi$
$829$		−	47.8410i		−	1.66159i	0.556582	−	0.830793i	$-0.312112\pi$
$830$			60.6935i			2.10670i
$831$	17.3182	+	7.45035i	0.600762	+	0.258450i
$832$		−	1.00000i		−	0.0346688i
$833$	−14.5567	−	14.8784i	−0.504360	−	0.515508i
$834$	9.40449	+	4.04584i	0.325651	+	0.140096i
$835$	44.6470			1.54507
$836$	15.4059			0.532825
$837$	−14.9329	+	5.48459i	−0.516156	+	0.189575i
$838$			2.06628i			0.0713786i
$839$	32.5702			1.12445			0.562225	−	0.826985i	$-0.309946\pi$
$839$	32.5702			1.12445			0.562225	+	0.826985i	$0.309946\pi$
$840$	14.5945	−	14.0492i	0.503558	−	0.484743i
$841$	17.1503			0.591391
$842$			5.52392i			0.190367i
$843$	−5.85665	+	13.6137i	−0.201714	+	0.468880i
$844$	0.508960			0.0175191
$845$	−4.42062			−0.152074
$846$	−9.32855	+	8.83544i	−0.320722	+	0.303769i
$847$	54.9196	+	23.1008i	1.88706	+	0.793754i
$848$			5.36539i			0.184248i
$849$	3.81516	−	8.86828i	0.130936	−	0.304359i
$850$			43.2413i			1.48317i
$851$		−	30.9741i		−	1.06178i
$852$	−3.05878	+	7.11008i	−0.104792	+	0.243587i
$853$			18.9585i			0.649128i	0.945864	+	0.324564i	$0.105218\pi$
$853$			18.9585i			0.649128i	−0.945864	+	0.324564i	$0.894782\pi$
$854$	19.1030	+	8.03532i	0.653693	+	0.274963i
$855$	25.6214	−	24.2671i	0.876234	−	0.829916i
$856$	−1.90372			−0.0650678
$857$	−21.5956			−0.737691			−0.368846	−	0.929491i	$-0.620247\pi$
$857$	−21.5956			−0.737691			−0.368846	+	0.929491i	$0.620247\pi$
$858$	3.96286	−	9.21159i	0.135290	−	0.314479i
$859$		−	16.6740i		−	0.568908i	−0.958690	−	0.284454i	$-0.908188\pi$
$859$		−	16.6740i		−	0.568908i	0.958690	−	0.284454i	$-0.0918123\pi$
$860$	23.1929			0.790872
$861$	−6.59231	−	6.84818i	−0.224665	−	0.233385i
$862$	−0.0573873			−0.00195462
$863$			24.3612i			0.829264i	0.909989	+	0.414632i	$0.136090\pi$
$863$			24.3612i			0.829264i	−0.909989	+	0.414632i	$0.863910\pi$
$864$	4.87757	−	1.79145i	0.165938	−	0.0609463i
$865$	−40.3600			−1.37228
$866$	−11.7659			−0.399822
$867$	−12.9796	−	5.58388i	−0.440812	−	0.189639i
$868$	−3.14061	+	7.46644i	−0.106599	+	0.253427i
$869$		−	10.8976i		−	0.369675i
$870$	24.2116	+	10.4159i	0.820851	+	0.353133i
$871$		−	2.80059i		−	0.0948945i
$872$			10.9889i			0.372131i
$873$	12.6318	−	11.9641i	0.427523	−	0.404924i
$874$		−	17.4901i		−	0.591611i
$875$	−102.870	−	43.2703i	−3.47765	−	1.46280i
$876$	−2.81477	+	6.54289i	−0.0951023	+	0.221064i
$877$	−47.1505			−1.59216			−0.796080	−	0.605192i	$-0.793096\pi$
$877$	−47.1505			−1.59216			−0.796080	+	0.605192i	$0.793096\pi$
$878$	8.88441			0.299834
$879$	0.346281	+	0.148971i	0.0116798	+	0.00502468i
$880$		−	25.5935i		−	0.862757i
$881$	−37.6634			−1.26891			−0.634456	−	0.772959i	$-0.718776\pi$
$881$	−37.6634			−1.26891			−0.634456	+	0.772959i	$0.718776\pi$
$882$	20.9848	+	0.799282i	0.706594	+	0.0269132i
$883$	−26.8290			−0.902868			−0.451434	−	0.892304i	$-0.649087\pi$
$883$	−26.8290			−0.902868			−0.451434	+	0.892304i	$0.649087\pi$
$884$			2.97358i			0.100012i
$885$	14.3725	+	6.18308i	0.483126	+	0.207842i
$886$	32.7864			1.10148
$887$	28.2189			0.947498			0.473749	−	0.880660i	$-0.342900\pi$
$887$	28.2189			0.947498			0.473749	+	0.880660i	$0.342900\pi$
$888$	3.22559	−	7.49782i	0.108244	−	0.251610i
$889$	10.2942	+	4.33006i	0.345256	+	0.145225i
$890$			64.2603i			2.15401i
$891$	52.0295	+	2.82701i	1.74305	+	0.0947085i
$892$			12.0398i			0.403122i
$893$			11.3966i			0.381373i
$894$	25.9439	+	11.1611i	0.867693	+	0.373284i
$895$		−	102.117i		−	3.41340i
$896$	1.02583	−	2.43879i	0.0342705	−	0.0814741i
$897$	−10.4578	−	4.49896i	−0.349174	−	0.150216i
$898$	−23.4377			−0.782126
$899$	−10.5388			−0.351490
$900$	−29.9994	−	31.6737i	−0.999981	−	1.05579i
$901$		−	15.9544i		−	0.531518i
$902$	−12.0093			−0.399864
$903$	16.6740	+	17.3212i	0.554877	+	0.576414i
$904$	−12.3835			−0.411869
$905$			62.3525i			2.07267i
$906$	9.47266	−	22.0190i	0.314708	−	0.731534i
$907$	−54.2379			−1.80094			−0.900470	−	0.434918i	$-0.856777\pi$
$907$	−54.2379			−1.80094			−0.900470	+	0.434918i	$0.856777\pi$
$908$	−10.9044			−0.361876
$909$	−3.54794	−	3.74595i	−0.117678	−	0.124245i
$910$	−10.7809	−	4.53479i	−0.357385	−	0.150327i
$911$			34.2520i			1.13482i	0.823436	+	0.567410i	$0.192054\pi$
$911$			34.2520i			1.13482i	−0.823436	+	0.567410i	$0.807946\pi$
$912$	1.82139	−	4.23378i	0.0603122	−	0.140195i
$913$			79.4889i			2.63070i
$914$		−	8.00329i		−	0.264725i
$915$	23.7014	−	55.0934i	0.783543	−	1.82133i
$916$			12.4163i			0.410245i
$917$	0.168463	+	0.0708607i	0.00556314	+	0.00234003i
$918$	−14.5038	+	5.32701i	−0.478698	+	0.175818i
$919$	26.8897			0.887009			0.443504	−	0.896272i	$-0.353735\pi$
$919$	26.8897			0.887009			0.443504	+	0.896272i	$0.353735\pi$
$920$	−29.0559			−0.957944
$921$	15.9309	−	37.0311i	0.524941	−	1.22022i
$922$		−	18.9716i		−	0.624795i
$923$	4.46876			0.147091
$924$	19.1141	−	18.3999i	0.628807	−	0.605312i
$925$	−68.5279			−2.25318
$926$		−	9.48421i		−	0.311670i
$927$	−3.26631	+	3.09365i	−0.107280	+	0.101609i
$928$	3.44234			0.113000
$929$	−35.9690			−1.18011			−0.590053	−	0.807365i	$-0.700893\pi$
$929$	−35.9690			−1.18011			−0.590053	+	0.807365i	$0.700893\pi$
$930$	21.5333	+	9.26369i	0.706105	+	0.303768i
$931$	13.3143	−	13.0264i	0.436359	−	0.426924i
$932$			21.7343i			0.711931i
$933$	45.7291	+	19.6728i	1.49710	+	0.644059i
$934$			38.4973i			1.25967i
$935$			76.1043i			2.48888i
$936$	−2.06297	−	2.17811i	−0.0674303	−	0.0711936i
$937$			34.5420i			1.12844i	0.825626	+	0.564218i	$0.190822\pi$
$937$			34.5420i			1.12844i	−0.825626	+	0.564218i	$0.809178\pi$
$938$	2.87293	−	6.83005i	0.0938044	−	0.223009i
$939$	19.5785	−	45.5099i	0.638920	−	1.48516i
$940$	18.9329			0.617524
$941$	45.7047			1.48993			0.744965	−	0.667103i	$-0.232466\pi$
$941$	45.7047			1.48993			0.744965	+	0.667103i	$0.232466\pi$
$942$	−27.7645	−	11.9444i	−0.904617	−	0.389169i
$943$			13.6339i			0.443981i
$944$	2.04344			0.0665082
$945$	2.80527	−	60.7087i	0.0912554	−	1.97485i
$946$	30.3752			0.987584
$947$		−	5.46612i		−	0.177625i	−0.996048	−	0.0888125i	$-0.971693\pi$
$947$		−	5.46612i		−	0.177625i	0.996048	−	0.0888125i	$-0.0283072\pi$
$948$	−2.99482	−	1.28838i	−0.0972673	−	0.0418447i
$949$	4.11227			0.133490
$950$	−38.6955			−1.25545
$951$	−10.1674	+	23.6339i	−0.329700	+	0.766383i
$952$	−3.05038	+	7.25192i	−0.0988634	+	0.235036i
$953$		−	29.8057i		−	0.965501i	−0.875758	−	0.482750i	$-0.839638\pi$
$953$		−	29.8057i		−	0.965501i	0.875758	−	0.482750i	$-0.160362\pi$
$954$	11.0686	+	11.6864i	0.358361	+	0.378361i
$955$		−	12.8040i		−	0.414327i
$956$			15.1287i			0.489297i
$957$	31.7094	+	13.6415i	1.02502	+	0.440966i
$958$			31.3595i			1.01318i
$959$	9.39691	−	22.3401i	0.303442	−	0.721398i
$960$	−7.03349	−	3.02583i	−0.227005	−	0.0976582i
$961$	21.6270			0.697644
$962$	−4.71246			−0.151936
$963$	−4.14651	+	3.92732i	−0.133619	+	0.126556i
$964$			7.84569i			0.252693i
$965$	−13.8263			−0.445084
$966$	−20.8891	−	21.6999i	−0.672095	−	0.698182i
$967$	−50.2137			−1.61476			−0.807382	−	0.590029i	$-0.799116\pi$
$967$	−50.2137			−1.61476			−0.807382	+	0.590029i	$0.799116\pi$
$968$		−	22.5192i		−	0.723795i
$969$	−5.41604	+	12.5895i	−0.173988	+	0.404433i
$970$	−25.6372			−0.823161
$971$	1.20083			0.0385364			0.0192682	−	0.999814i	$-0.493866\pi$
$971$	1.20083			0.0385364			0.0192682	+	0.999814i	$0.493866\pi$
$972$	6.92816	−	13.9643i	0.222221	−	0.447904i
$973$	6.06348	−	14.4152i	0.194386	−	0.462131i
$974$			13.6604i			0.437706i
$975$	−9.95362	+	23.1370i	−0.318771	+	0.740978i
$976$		−	7.83301i		−	0.250729i
$977$		−	12.0398i		−	0.385186i	−0.981279	−	0.192593i	$-0.938310\pi$
$977$		−	12.0398i		−	0.385186i	0.981279	−	0.192593i	$-0.0616898\pi$
$978$	1.04248	−	2.42323i	0.0333348	−	0.0774863i
$979$			84.1602i			2.68977i
$980$	−21.6405	−	22.1188i	−0.691280	−	0.706558i
$981$	22.6698	+	23.9350i	0.723791	+	0.764185i
$982$	28.3534			0.904794
$983$	29.4887			0.940543			0.470271	−	0.882522i	$-0.344156\pi$
$983$	29.4887			0.940543			0.470271	+	0.882522i	$0.344156\pi$
$984$	−1.41981	+	3.30033i	−0.0452619	+	0.105211i
$985$			58.5974i			1.86707i
$986$	−10.2361			−0.325982
$987$	13.6114	+	14.1397i	0.433256	+	0.450073i
$988$	−2.66098			−0.0846569
$989$		−	34.4845i		−	1.09654i
$990$	−52.7987	−	55.7454i	−1.67805	−	1.77170i
$991$	36.8517			1.17063			0.585317	−	0.810805i	$-0.300970\pi$
$991$	36.8517			1.17063			0.585317	+	0.810805i	$0.300970\pi$
$992$	3.06154			0.0972040
$993$	−18.8946	−	8.12850i	−0.599601	−	0.257950i
$994$	10.8983	+	4.58418i	0.345674	+	0.145401i
$995$		−	62.1692i		−	1.97090i
$996$	21.8448	+	9.39768i	0.692177	+	0.297777i
$997$			10.5650i			0.334596i	0.985906	+	0.167298i	$0.0535042\pi$
$997$			10.5650i			0.334596i	−0.985906	+	0.167298i	$0.946496\pi$
$998$			1.59987i			0.0506431i
$999$	−8.44213	−	22.9853i	−0.267097	−	0.727224i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.g.d.209.5	yes	12
3.2	odd	2		546.2.g.c.209.8	yes	12
7.6	odd	2		546.2.g.c.209.2	✓	12
21.20	even	2	inner	546.2.g.d.209.11	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.g.c.209.2	✓	12	7.6	odd	2
546.2.g.c.209.8	yes	12	3.2	odd	2
546.2.g.d.209.5	yes	12	1.1	even	1	trivial
546.2.g.d.209.11	yes	12	21.20	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.59106 + 0.684481i) q^{3} -1.00000 q^{4} +4.42062 q^{5} +(0.684481 - 1.59106i) q^{6} +(-2.43879 - 1.02583i) q^{7} +1.00000i q^{8} +(2.06297 + 2.17811i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.59106 + 0.684481i) q^{3} -1.00000 q^{4} +4.42062 q^{5} +(0.684481 - 1.59106i) q^{6} +(-2.43879 - 1.02583i) q^{7} +1.00000i q^{8} +(2.06297 + 2.17811i) q^{9} -4.42062i q^{10} -5.78958i q^{11} +(-1.59106 - 0.684481i) q^{12} +1.00000i q^{13} +(-1.02583 + 2.43879i) q^{14} +(7.03349 + 3.02583i) q^{15} +1.00000 q^{16} -2.97358 q^{17} +(2.17811 - 2.06297i) q^{18} -2.66098i q^{19} -4.42062 q^{20} +(-3.17811 - 3.30146i) q^{21} -5.78958 q^{22} +6.57281i q^{23} +(-0.684481 + 1.59106i) q^{24} +14.5419 q^{25} +1.00000 q^{26} +(1.79145 + 4.87757i) q^{27} +(2.43879 + 1.02583i) q^{28} +3.44234i q^{29} +(3.02583 - 7.03349i) q^{30} +3.06154i q^{31} -1.00000i q^{32} +(3.96286 - 9.21159i) q^{33} +2.97358i q^{34} +(-10.7809 - 4.53479i) q^{35} +(-2.06297 - 2.17811i) q^{36} -4.71246 q^{37} -2.66098 q^{38} +(-0.684481 + 1.59106i) q^{39} +4.42062i q^{40} +2.07429 q^{41} +(-3.30146 + 3.17811i) q^{42} -5.24653 q^{43} +5.78958i q^{44} +(9.11961 + 9.62857i) q^{45} +6.57281 q^{46} -4.28287 q^{47} +(1.59106 + 0.684481i) q^{48} +(4.89535 + 5.00355i) q^{49} -14.5419i q^{50} +(-4.73115 - 2.03536i) q^{51} -1.00000i q^{52} +5.36539i q^{53} +(4.87757 - 1.79145i) q^{54} -25.5935i q^{55} +(1.02583 - 2.43879i) q^{56} +(1.82139 - 4.23378i) q^{57} +3.44234 q^{58} +2.04344 q^{59} +(-7.03349 - 3.02583i) q^{60} -7.83301i q^{61} +3.06154 q^{62} +(-2.79679 - 7.42819i) q^{63} -1.00000 q^{64} +4.42062i q^{65} +(-9.21159 - 3.96286i) q^{66} -2.80059 q^{67} +2.97358 q^{68} +(-4.49896 + 10.4578i) q^{69} +(-4.53479 + 10.7809i) q^{70} -4.46876i q^{71} +(-2.17811 + 2.06297i) q^{72} -4.11227i q^{73} +4.71246i q^{74} +(23.1370 + 9.95362i) q^{75} +2.66098i q^{76} +(-5.93911 + 14.1195i) q^{77} +(1.59106 + 0.684481i) q^{78} +1.88228 q^{79} +4.42062 q^{80} +(-0.488293 + 8.98674i) q^{81} -2.07429i q^{82} -13.7296 q^{83} +(3.17811 + 3.30146i) q^{84} -13.1451 q^{85} +5.24653i q^{86} +(-2.35621 + 5.47698i) q^{87} +5.78958 q^{88} -14.5365 q^{89} +(9.62857 - 9.11961i) q^{90} +(1.02583 - 2.43879i) q^{91} -6.57281i q^{92} +(-2.09556 + 4.87111i) q^{93} +4.28287i q^{94} -11.7632i q^{95} +(0.684481 - 1.59106i) q^{96} -5.79946i q^{97} +(5.00355 - 4.89535i) q^{98} +(12.6103 - 11.9437i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} - 12 q^{4} - 4 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9}+O(q^{10}) \) 12 * q + 2 * q^3 - 12 * q^4 - 4 * q^5 + 2 * q^6 - 8 * q^7 + 4 * q^9	\( 12 q + 2 q^{3} - 12 q^{4} - 4 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9} - 2 q^{12} + 10 q^{14} + 4 q^{15} + 12 q^{16} + 12 q^{17} + 8 q^{18} + 4 q^{20} - 20 q^{21} - 2 q^{24} + 20 q^{25} + 12 q^{26} + 8 q^{27} + 8 q^{28} + 14 q^{30} + 46 q^{33} - 22 q^{35} - 4 q^{36} + 16 q^{37} - 8 q^{38} - 2 q^{39} + 28 q^{41} + 4 q^{42} - 8 q^{43} + 24 q^{46} - 68 q^{47} + 2 q^{48} + 26 q^{49} - 50 q^{51} + 16 q^{54} - 10 q^{56} - 28 q^{57} - 24 q^{58} + 8 q^{59} - 4 q^{60} + 16 q^{62} - 2 q^{63} - 12 q^{64} - 12 q^{66} + 8 q^{67} - 12 q^{68} - 24 q^{69} - 28 q^{70} - 8 q^{72} + 92 q^{75} - 8 q^{77} + 2 q^{78} + 36 q^{79} - 4 q^{80} + 16 q^{81} - 32 q^{83} + 20 q^{84} + 8 q^{87} - 48 q^{89} + 2 q^{90} - 10 q^{91} + 8 q^{93} + 2 q^{96} + 16 q^{98}+O(q^{100}) \) 12 * q + 2 * q^3 - 12 * q^4 - 4 * q^5 + 2 * q^6 - 8 * q^7 + 4 * q^9 - 2 * q^12 + 10 * q^14 + 4 * q^15 + 12 * q^16 + 12 * q^17 + 8 * q^18 + 4 * q^20 - 20 * q^21 - 2 * q^24 + 20 * q^25 + 12 * q^26 + 8 * q^27 + 8 * q^28 + 14 * q^30 + 46 * q^33 - 22 * q^35 - 4 * q^36 + 16 * q^37 - 8 * q^38 - 2 * q^39 + 28 * q^41 + 4 * q^42 - 8 * q^43 + 24 * q^46 - 68 * q^47 + 2 * q^48 + 26 * q^49 - 50 * q^51 + 16 * q^54 - 10 * q^56 - 28 * q^57 - 24 * q^58 + 8 * q^59 - 4 * q^60 + 16 * q^62 - 2 * q^63 - 12 * q^64 - 12 * q^66 + 8 * q^67 - 12 * q^68 - 24 * q^69 - 28 * q^70 - 8 * q^72 + 92 * q^75 - 8 * q^77 + 2 * q^78 + 36 * q^79 - 4 * q^80 + 16 * q^81 - 32 * q^83 + 20 * q^84 + 8 * q^87 - 48 * q^89 + 2 * q^90 - 10 * q^91 + 8 * q^93 + 2 * q^96 + 16 * q^98

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