LMFDB - Embedded newform 63.2.s.b.47.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,2,Mod(47,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("63.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	63.s (of order $6$, degree $2$, 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:	$0.503057532734$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.2
Root			$0.187540 - 0.324828i$ of defining polynomial
Character	$\chi$	$=$	63.47
Dual form			63.2.s.b.59.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.621951 + 0.359083i) q^{2} +(1.34572 + 1.09042i) q^{3} +(-0.742118 + 1.28539i) q^{4} -1.44755 q^{5} +(-1.22853 - 0.194963i) q^{6} +(2.19442 - 1.47801i) q^{7} -2.50226i q^{8} +(0.621951 + 2.93482i) q^{9} +O(q^{10})$	\(q+(-0.621951 + 0.359083i) q^{2} +(1.34572 + 1.09042i) q^{3} +(-0.742118 + 1.28539i) q^{4} -1.44755 q^{5} +(-1.22853 - 0.194963i) q^{6} +(2.19442 - 1.47801i) q^{7} -2.50226i q^{8} +(0.621951 + 2.93482i) q^{9} +(0.900304 - 0.519791i) q^{10} -1.80056i q^{11} +(-2.40030 + 0.920553i) q^{12} +(1.88867 - 1.09042i) q^{13} +(-0.834091 + 1.70723i) q^{14} +(-1.94800 - 1.57844i) q^{15} +(-0.585716 - 1.01449i) q^{16} +(-1.95230 - 3.38149i) q^{17} +(-1.44067 - 1.60198i) q^{18} +(-3.47456 - 2.00604i) q^{19} +(1.07425 - 1.86066i) q^{20} +(4.56475 + 0.403850i) q^{21} +(0.646552 + 1.11986i) q^{22} +5.67561i q^{23} +(2.72853 - 3.36736i) q^{24} -2.90460 q^{25} +(-0.783106 + 1.35638i) q^{26} +(-2.36323 + 4.62765i) q^{27} +(0.271298 + 3.91754i) q^{28} +(8.49418 + 4.90412i) q^{29} +(1.77835 + 0.282218i) q^{30} +(-2.45129 - 1.41525i) q^{31} +(5.06262 + 2.92290i) q^{32} +(1.96338 - 2.42306i) q^{33} +(2.42847 + 1.40208i) q^{34} +(-3.17653 + 2.13949i) q^{35} +(-4.23394 - 1.37854i) q^{36} +(-0.411767 + 0.713202i) q^{37} +2.88134 q^{38} +(3.73065 + 0.592040i) q^{39} +3.62215i q^{40} +(-5.90617 - 10.2298i) q^{41} +(-2.98406 + 1.38795i) q^{42} +(-3.76766 + 6.52578i) q^{43} +(2.31442 + 1.33623i) q^{44} +(-0.900304 - 4.24830i) q^{45} +(-2.03802 - 3.52995i) q^{46} +(1.16920 + 2.02511i) q^{47} +(0.318012 - 2.00390i) q^{48} +(2.63096 - 6.48676i) q^{49} +(1.80652 - 1.04299i) q^{50} +(1.05999 - 6.67939i) q^{51} +3.23689i q^{52} +(-0.996713 + 0.575453i) q^{53} +(-0.191903 - 3.72677i) q^{54} +2.60640i q^{55} +(-3.69838 - 5.49102i) q^{56} +(-2.48837 - 6.48831i) q^{57} -7.04395 q^{58} +(-4.89555 + 8.47934i) q^{59} +(3.47456 - 1.33255i) q^{60} +(2.03980 - 1.17768i) q^{61} +2.03277 q^{62} +(5.70252 + 5.52098i) q^{63} -1.85540 q^{64} +(-2.73394 + 1.57844i) q^{65} +(-0.351042 + 2.21204i) q^{66} +(0.156402 - 0.270897i) q^{67} +5.79536 q^{68} +(-6.18882 + 7.63781i) q^{69} +(1.20739 - 2.47130i) q^{70} -1.94933i q^{71} +(7.34369 - 1.55628i) q^{72} +(2.42847 - 1.40208i) q^{73} -0.591435i q^{74} +(-3.90880 - 3.16725i) q^{75} +(5.15706 - 2.97743i) q^{76} +(-2.66125 - 3.95119i) q^{77} +(-2.53287 + 0.971396i) q^{78} +(-6.21583 - 10.7661i) q^{79} +(0.847852 + 1.46852i) q^{80} +(-8.22635 + 3.65063i) q^{81} +(7.34669 + 4.24162i) q^{82} +(-3.60916 + 6.25124i) q^{83} +(-3.90669 + 5.56776i) q^{84} +(2.82605 + 4.89486i) q^{85} -5.41161i q^{86} +(6.08326 + 15.8619i) q^{87} -4.50548 q^{88} +(5.28999 - 9.16253i) q^{89} +(2.08544 + 2.31895i) q^{90} +(2.53287 - 5.18433i) q^{91} +(-7.29536 - 4.21198i) q^{92} +(-1.75553 - 4.57748i) q^{93} +(-1.45436 - 0.839677i) q^{94} +(5.02959 + 2.90383i) q^{95} +(3.62569 + 9.45383i) q^{96} +(13.4322 + 7.75510i) q^{97} +(0.692961 + 4.97918i) q^{98} +(5.28433 - 1.11986i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4} - 12 q^{6} + 3 q^{7}+O(q^{10}) $ 10 * q + 4 * q^4 - 12 * q^6 + 3 * q^7	$ 10 q + 4 q^{4} - 12 q^{6} + 3 q^{7} - 15 q^{10} + 6 q^{13} - 6 q^{14} - 3 q^{15} - 6 q^{16} - 12 q^{17} - 18 q^{18} + 3 q^{19} - 3 q^{20} + 18 q^{21} + 5 q^{22} + 27 q^{24} - 14 q^{25} + 3 q^{26} + 27 q^{27} + 2 q^{28} - 15 q^{29} - 9 q^{31} + 48 q^{32} - 9 q^{33} + 3 q^{34} - 15 q^{35} - 18 q^{36} + 6 q^{37} + 36 q^{38} + 12 q^{39} - 9 q^{41} - 6 q^{42} + 3 q^{43} + 24 q^{44} + 15 q^{45} - 13 q^{46} + 15 q^{47} - 15 q^{48} - 23 q^{49} + 3 q^{50} - 24 q^{51} - 9 q^{53} + 27 q^{54} - 51 q^{56} - 36 q^{57} - 16 q^{58} - 18 q^{59} - 3 q^{60} + 12 q^{61} + 12 q^{62} + 9 q^{63} + 6 q^{64} - 3 q^{65} - 33 q^{66} - 10 q^{67} - 54 q^{68} - 3 q^{69} + 9 q^{70} + 18 q^{72} + 3 q^{73} - 21 q^{75} + 9 q^{76} + 45 q^{77} + 24 q^{78} + 20 q^{79} - 30 q^{80} - 48 q^{81} + 9 q^{82} - 15 q^{83} + 60 q^{84} + 18 q^{85} + 30 q^{87} + 16 q^{88} + 24 q^{89} + 24 q^{90} - 24 q^{91} + 39 q^{92} + 6 q^{93} - 3 q^{94} + 3 q^{96} + 6 q^{97} + 45 q^{98} + 21 q^{99}+O(q^{100}) $ 10 * q + 4 * q^4 - 12 * q^6 + 3 * q^7 - 15 * q^10 + 6 * q^13 - 6 * q^14 - 3 * q^15 - 6 * q^16 - 12 * q^17 - 18 * q^18 + 3 * q^19 - 3 * q^20 + 18 * q^21 + 5 * q^22 + 27 * q^24 - 14 * q^25 + 3 * q^26 + 27 * q^27 + 2 * q^28 - 15 * q^29 - 9 * q^31 + 48 * q^32 - 9 * q^33 + 3 * q^34 - 15 * q^35 - 18 * q^36 + 6 * q^37 + 36 * q^38 + 12 * q^39 - 9 * q^41 - 6 * q^42 + 3 * q^43 + 24 * q^44 + 15 * q^45 - 13 * q^46 + 15 * q^47 - 15 * q^48 - 23 * q^49 + 3 * q^50 - 24 * q^51 - 9 * q^53 + 27 * q^54 - 51 * q^56 - 36 * q^57 - 16 * q^58 - 18 * q^59 - 3 * q^60 + 12 * q^61 + 12 * q^62 + 9 * q^63 + 6 * q^64 - 3 * q^65 - 33 * q^66 - 10 * q^67 - 54 * q^68 - 3 * q^69 + 9 * q^70 + 18 * q^72 + 3 * q^73 - 21 * q^75 + 9 * q^76 + 45 * q^77 + 24 * q^78 + 20 * q^79 - 30 * q^80 - 48 * q^81 + 9 * q^82 - 15 * q^83 + 60 * q^84 + 18 * q^85 + 30 * q^87 + 16 * q^88 + 24 * q^89 + 24 * q^90 - 24 * q^91 + 39 * q^92 + 6 * q^93 - 3 * q^94 + 3 * q^96 + 6 * q^97 + 45 * q^98 + 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.621951	+	0.359083i	−0.439785	+	0.253910i	−0.703507	−	0.710689i	$-0.748383\pi$
$2$	−0.621951	+	0.359083i	−0.439785	+	0.253910i	0.263721	+	0.964599i	$0.415050\pi$
$3$	1.34572	+	1.09042i	0.776955	+	0.629557i
$3$	1.34572	+	1.09042i	0.776955	+	0.629557i
$4$	−0.742118	+	1.28539i	−0.371059	+	0.642693i
$5$	−1.44755			−0.647363			−0.323682	−	0.946166i	$-0.604921\pi$
$5$	−1.44755			−0.647363			−0.323682	+	0.946166i	$0.604921\pi$
$6$	−1.22853	−	0.194963i	−0.501544	−	0.0795931i
$7$	2.19442	−	1.47801i	0.829413	−	0.558636i
$7$	2.19442	−	1.47801i	0.829413	−	0.558636i
$8$		−	2.50226i		−	0.884683i
$9$	0.621951	+	2.93482i	0.207317	+	0.978274i
$10$	0.900304	−	0.519791i	0.284701	−	0.164372i
$11$		−	1.80056i		−	0.542890i	−0.962454	−	0.271445i	$-0.912499\pi$
$11$		−	1.80056i		−	0.542890i	0.962454	−	0.271445i	$-0.0875015\pi$
$12$	−2.40030	+	0.920553i	−0.692908	+	0.265741i
$13$	1.88867	−	1.09042i	0.523823	−	0.302429i	−0.214675	−	0.976686i	$-0.568869\pi$
$13$	1.88867	−	1.09042i	0.523823	−	0.302429i	0.738497	+	0.674256i	$0.235536\pi$
$14$	−0.834091	+	1.70723i	−0.222920	+	0.456277i
$15$	−1.94800	−	1.57844i	−0.502972	−	0.407552i
$16$	−0.585716	−	1.01449i	−0.146429	−	0.253622i
$17$	−1.95230	−	3.38149i	−0.473503	−	0.820131i	0.526037	−	0.850462i	$-0.323677\pi$
$17$	−1.95230	−	3.38149i	−0.473503	−	0.820131i	−0.999540	+	0.0303308i	$0.990344\pi$
$18$	−1.44067	−	1.60198i	−0.339569	−	0.377591i
$19$	−3.47456	−	2.00604i	−0.797118	−	0.460216i	0.0453446	−	0.998971i	$-0.485561\pi$
$19$	−3.47456	−	2.00604i	−0.797118	−	0.460216i	−0.842462	+	0.538755i	$0.818895\pi$
$20$	1.07425	−	1.86066i	0.240210	−	0.416056i
$21$	4.56475	+	0.403850i	0.996109	+	0.0881274i
$22$	0.646552	+	1.11986i	0.137845	+	0.238755i
$23$			5.67561i			1.18345i	0.806141	+	0.591723i	$0.201552\pi$
$23$			5.67561i			1.18345i	−0.806141	+	0.591723i	$0.798448\pi$
$24$	2.72853	−	3.36736i	0.556958	−	0.687359i
$25$	−2.90460			−0.580921
$26$	−0.783106	+	1.35638i	−0.153580	+	0.266008i
$27$	−2.36323	+	4.62765i	−0.454803	+	0.890592i
$28$	0.271298	+	3.91754i	0.0512705	+	0.740345i
$29$	8.49418	+	4.90412i	1.57733	+	0.910672i	0.995230	+	0.0975551i	$0.0311022\pi$
$29$	8.49418	+	4.90412i	1.57733	+	0.910672i	0.582100	+	0.813117i	$0.302231\pi$
$30$	1.77835	+	0.282218i	0.324681	+	0.0515257i
$31$	−2.45129	−	1.41525i	−0.440264	−	0.254187i	0.263445	−	0.964674i	$-0.415141\pi$
$31$	−2.45129	−	1.41525i	−0.440264	−	0.254187i	−0.703710	+	0.710488i	$0.748474\pi$
$32$	5.06262	+	2.92290i	0.894953	+	0.516701i
$33$	1.96338	−	2.42306i	0.341780	−	0.421801i
$34$	2.42847	+	1.40208i	0.416479	+	0.240454i
$35$	−3.17653	+	2.13949i	−0.536931	+	0.361641i
$36$	−4.23394	−	1.37854i	−0.705657	−	0.229756i
$37$	−0.411767	+	0.713202i	−0.0676941	+	0.117250i	−0.897886	−	0.440228i	$-0.854898\pi$
$37$	−0.411767	+	0.713202i	−0.0676941	+	0.117250i	0.830192	+	0.557478i	$0.188231\pi$
$38$	2.88134			0.467414
$39$	3.73065	+	0.592040i	0.597383	+	0.0948023i
$40$			3.62215i			0.572712i
$41$	−5.90617	−	10.2298i	−0.922389	−	1.59762i	−0.795708	−	0.605681i	$-0.792901\pi$
$41$	−5.90617	−	10.2298i	−0.922389	−	1.59762i	−0.126681	−	0.991943i	$-0.540433\pi$
$42$	−2.98406	+	1.38795i	−0.460451	+	0.214165i
$43$	−3.76766	+	6.52578i	−0.574563	+	0.995172i	0.421526	+	0.906816i	$0.361494\pi$
$43$	−3.76766	+	6.52578i	−0.574563	+	0.995172i	−0.996089	+	0.0883555i	$0.971839\pi$
$44$	2.31442	+	1.33623i	0.348912	+	0.201444i
$45$	−0.900304	−	4.24830i	−0.134209	−	0.633299i
$46$	−2.03802	−	3.52995i	−0.300489	−	0.520463i
$47$	1.16920	+	2.02511i	0.170545	+	0.295392i	0.938610	−	0.344979i	$-0.112114\pi$
$47$	1.16920	+	2.02511i	0.170545	+	0.295392i	−0.768066	+	0.640371i	$0.778781\pi$
$48$	0.318012	−	2.00390i	0.0459010	−	0.289238i
$49$	2.63096	−	6.48676i	0.375851	−	0.926680i
$50$	1.80652	−	1.04299i	0.255480	−	0.147502i
$51$	1.05999	−	6.67939i	0.148429	−	0.935301i
$52$			3.23689i			0.448877i
$53$	−0.996713	+	0.575453i	−0.136909	+	0.0790445i	−0.566890	−	0.823793i	$-0.691854\pi$
$53$	−0.996713	+	0.575453i	−0.136909	+	0.0790445i	0.429981	+	0.902838i	$0.358520\pi$
$54$	−0.191903	−	3.72677i	−0.0261147	−	0.507149i
$55$			2.60640i			0.351447i
$56$	−3.69838	−	5.49102i	−0.494216	−	0.733768i
$57$	−2.48837	−	6.48831i	−0.329592	−	0.859398i
$58$	−7.04395			−0.924916
$59$	−4.89555	+	8.47934i	−0.637346	+	1.10392i	0.348666	+	0.937247i	$0.386635\pi$
$59$	−4.89555	+	8.47934i	−0.637346	+	1.10392i	−0.986013	+	0.166669i	$0.946699\pi$
$60$	3.47456	−	1.33255i	0.448563	−	0.172031i
$61$	2.03980	−	1.17768i	0.261170	−	0.150786i	−0.363698	−	0.931517i	$-0.618486\pi$
$61$	2.03980	−	1.17768i	0.261170	−	0.150786i	0.624868	+	0.780730i	$0.285153\pi$
$62$	2.03277			0.258163
$63$	5.70252	+	5.52098i	0.718450	+	0.695578i
$64$	−1.85540			−0.231925
$65$	−2.73394	+	1.57844i	−0.339104	+	0.195782i
$66$	−0.351042	+	2.21204i	−0.0432103	+	0.272283i
$67$	0.156402	−	0.270897i	0.0191076	−	0.0330953i	−0.856313	−	0.516456i	$-0.827251\pi$
$67$	0.156402	−	0.270897i	0.0191076	−	0.0330953i	0.875421	+	0.483361i	$0.160584\pi$
$68$	5.79536			0.702790
$69$	−6.18882	+	7.63781i	−0.745047	+	0.919484i
$70$	1.20739	−	2.47130i	0.144310	−	0.295377i
$71$		−	1.94933i		−	0.231343i	−0.993288	−	0.115671i	$-0.963098\pi$
$71$		−	1.94933i		−	0.231343i	0.993288	−	0.115671i	$-0.0369019\pi$
$72$	7.34369	−	1.55628i	0.865463	−	0.183410i
$73$	2.42847	−	1.40208i	0.284231	−	0.164101i	−0.351106	−	0.936336i	$-0.614194\pi$
$73$	2.42847	−	1.40208i	0.284231	−	0.164101i	0.635337	+	0.772235i	$0.280861\pi$
$74$		−	0.591435i		−	0.0687529i
$75$	−3.90880	−	3.16725i	−0.451349	−	0.365722i
$76$	5.15706	−	2.97743i	0.591556	−	0.341535i
$77$	−2.66125	−	3.95119i	−0.303278	−	0.450280i
$78$	−2.53287	+	0.971396i	−0.286792	+	0.109989i
$79$	−6.21583	−	10.7661i	−0.699336	−	1.21128i	−0.968697	−	0.248246i	$-0.920146\pi$
$79$	−6.21583	−	10.7661i	−0.699336	−	1.21128i	0.269361	−	0.963039i	$-0.413187\pi$
$80$	0.847852	+	1.46852i	0.0947927	+	0.164186i
$81$	−8.22635	+	3.65063i	−0.914039	+	0.405625i
$82$	7.34669	+	4.24162i	0.811306	+	0.468408i
$83$	−3.60916	+	6.25124i	−0.396157	+	0.686163i	−0.993248	−	0.116010i	$-0.962990\pi$
$83$	−3.60916	+	6.25124i	−0.396157	+	0.686163i	0.597092	+	0.802173i	$0.296323\pi$
$84$	−3.90669	+	5.56776i	−0.426254	+	0.607492i
$85$	2.82605	+	4.89486i	0.306528	+	0.530923i
$86$		−	5.41161i		−	0.583549i
$87$	6.08326	+	15.8619i	0.652194	+	1.70057i
$88$	−4.50548			−0.480286
$89$	5.28999	−	9.16253i	0.560737	−	0.971226i	−0.436695	−	0.899610i	$-0.643851\pi$
$89$	5.28999	−	9.16253i	0.560737	−	0.971226i	0.997432	−	0.0716161i	$-0.0228156\pi$
$90$	2.08544	+	2.31895i	0.219824	+	0.244438i
$91$	2.53287	−	5.18433i	0.265517	−	0.543465i
$92$	−7.29536	−	4.21198i	−0.760593	−	0.439129i
$93$	−1.75553	−	4.57748i	−0.182040	−	0.474663i
$94$	−1.45436	−	0.839677i	−0.150006	−	0.0866061i
$95$	5.02959	+	2.90383i	0.516025	+	0.297927i
$96$	3.62569	+	9.45383i	0.370045	+	0.964877i
$97$	13.4322	+	7.75510i	1.36384	+	0.787411i	0.990132	−	0.140137i	$-0.0447543\pi$
$97$	13.4322	+	7.75510i	1.36384	+	0.787411i	0.373704	+	0.927548i	$0.378088\pi$
$98$	0.692961	+	4.97918i	0.0699997	+	0.502973i
$99$	5.28433	−	1.11986i	0.531095	−	0.112550i
$100$	2.15556	−	3.73354i	0.215556	−	0.373354i
$101$	−3.94618			−0.392659			−0.196330	−	0.980538i	$-0.562902\pi$
$101$	−3.94618			−0.392659			−0.196330	+	0.980538i	$0.562902\pi$
$102$	1.73919	+	4.53487i	0.172206	+	0.449019i
$103$			4.15522i			0.409426i	0.978822	+	0.204713i	$0.0656261\pi$
$103$			4.15522i			0.409426i	−0.978822	+	0.204713i	$0.934374\pi$
$104$	−2.72853	−	4.72595i	−0.267554	−	0.463417i
$105$	−6.60769	−	0.584593i	−0.644845	−	0.0570504i
$106$	0.413271	−	0.715806i	0.0401404	−	0.0695253i
$107$	4.91092	+	2.83532i	0.474757	+	0.274101i	0.718229	−	0.695807i	$-0.244953\pi$
$107$	4.91092	+	2.83532i	0.474757	+	0.274101i	−0.243472	+	0.969908i	$0.578286\pi$
$108$	−4.19453	−	6.47192i	−0.403619	−	0.622761i
$109$	5.99916	+	10.3908i	0.574615	+	0.995262i	0.996083	+	0.0884193i	$0.0281815\pi$
$109$	5.99916	+	10.3908i	0.574615	+	0.995262i	−0.421468	+	0.906843i	$0.638485\pi$
$110$	−0.935915	−	1.62105i	−0.0892360	−	0.154561i
$111$	−1.33182	+	0.510772i	−0.126411	+	0.0484804i
$112$	−2.78473	−	1.36052i	−0.263133	−	0.128557i
$113$	6.27800	−	3.62461i	0.590585	−	0.340974i	−0.174744	−	0.984614i	$-0.555910\pi$
$113$	6.27800	−	3.62461i	0.590585	−	0.340974i	0.765329	+	0.643640i	$0.222576\pi$
$114$	3.87749	+	3.14188i	0.363160	+	0.294264i
$115$		−	8.21572i		−	0.766120i
$116$	−12.6074	+	7.27887i	−1.17057	+	0.675826i
$117$	4.37486	+	4.86472i	0.404456	+	0.449743i
$118$		−	7.03164i		−	0.647315i
$119$	−9.28205	−	4.53487i	−0.850884	−	0.415711i
$120$	−3.94968	+	4.87441i	−0.360554	+	0.444971i
$121$	7.75798			0.705271
$122$	−0.845770	+	1.46492i	−0.0765724	+	0.132627i
$123$	3.20673	−	20.2067i	0.289141	−	1.82198i
$124$	3.63829	−	2.10057i	0.326728	−	0.188637i
$125$	11.4423			1.02343
$126$	−5.52918	−	1.38610i	−0.492578	−	0.123483i
$127$	−0.881336			−0.0782059			−0.0391030	−	0.999235i	$-0.512450\pi$
$127$	−0.881336			−0.0782059			−0.0391030	+	0.999235i	$0.512450\pi$
$128$	−8.97127	+	5.17956i	−0.792956	+	0.457813i
$129$	−12.1861	+	4.67355i	−1.07293	+	0.411483i
$130$	1.13358	−	1.96343i	0.0994219	−	0.172204i
$131$	−2.97441			−0.259876			−0.129938	−	0.991522i	$-0.541478\pi$
$131$	−2.97441			−0.259876			−0.129938	+	0.991522i	$0.541478\pi$
$132$	1.65751	+	4.32189i	0.144268	+	0.376173i
$133$	−10.5896	+	0.733352i	−0.918233	+	0.0635897i
$134$			0.224646i			0.0194065i
$135$	3.42088	−	6.69875i	0.294423	−	0.576537i
$136$	−8.46137	+	4.88517i	−0.725556	+	0.418900i
$137$		−	11.8986i		−	1.01657i	−0.861190	−	0.508283i	$-0.830280\pi$
$137$		−	11.8986i		−	1.01657i	0.861190	−	0.508283i	$-0.169720\pi$
$138$	1.10653	−	6.97264i	0.0941942	−	0.593551i
$139$	−10.4143	+	6.01268i	−0.883327	+	0.509989i	−0.871754	−	0.489944i	$-0.837017\pi$
$139$	−10.4143	+	6.01268i	−0.883327	+	0.509989i	−0.0115731	+	0.999933i	$0.503684\pi$
$140$	−0.392717	−	5.67083i	−0.0331907	−	0.479272i
$141$	−0.634809	+	4.00015i	−0.0534606	+	0.336874i
$142$	0.699971	+	1.21239i	0.0587403	+	0.101741i
$143$	−1.96338	−	3.40067i	−0.164186	−	0.284378i
$144$	2.61306	−	2.34993i	0.217755	−	0.195828i
$145$	−12.2957	−	7.09895i	−1.02111	−	0.589536i
$146$	−1.00693	+	1.74405i	−0.0833338	+	0.144338i
$147$	10.6139	−	5.86053i	0.875417	−	0.483369i
$148$	−0.611160	−	1.05856i	−0.0502370	−	0.0870131i
$149$		−	7.07901i		−	0.579935i	−0.957036	−	0.289968i	$-0.906355\pi$
$149$		−	7.07901i		−	0.579935i	0.957036	−	0.289968i	$-0.0936446\pi$
$150$	3.56838	+	0.566289i	0.291357	+	0.0462373i
$151$	15.5819			1.26803			0.634017	−	0.773319i	$-0.281405\pi$
$151$	15.5819			1.26803			0.634017	+	0.773319i	$0.281405\pi$
$152$	−5.01963	+	8.69425i	−0.407146	+	0.705197i
$153$	8.70982	−	7.83277i	0.704147	−	0.633242i
$154$	3.07397	+	1.50183i	0.247708	+	0.121021i
$155$	3.54836	+	2.04865i	0.285011	+	0.164551i
$156$	−3.52959	+	4.35597i	−0.282593	+	0.348757i
$157$	1.80677	+	1.04314i	0.144196	+	0.0832517i	0.570362	−	0.821393i	$-0.306803\pi$
$157$	1.80677	+	1.04314i	0.144196	+	0.0832517i	−0.426166	+	0.904645i	$0.640136\pi$
$158$	7.73188	+	4.46400i	0.615115	+	0.355137i
$159$	−1.96879	−	0.312439i	−0.156135	−	0.0247780i
$160$	−7.32839	−	4.23105i	−0.579360	−	0.334494i
$161$	8.38862	+	12.4547i	0.661116	+	0.981566i
$162$	3.80551	−	5.22446i	0.298989	−	0.410472i
$163$	−5.58983	+	9.68188i	−0.437830	+	0.758343i	−0.997522	−	0.0703575i	$-0.977586\pi$
$163$	−5.58983	+	9.68188i	−0.437830	+	0.758343i	0.559692	+	0.828700i	$0.310919\pi$
$164$	17.5323			1.36904
$165$	−2.84208	+	3.50750i	−0.221256	+	0.273058i
$166$		−	5.18395i		−	0.402353i
$167$	0.960750	+	1.66407i	0.0743450	+	0.128769i	0.900801	−	0.434232i	$-0.142980\pi$
$167$	0.960750	+	1.66407i	0.0743450	+	0.128769i	−0.826456	+	0.563001i	$0.809647\pi$
$168$	1.01054	−	11.4222i	0.0779648	−	0.881241i
$169$	−4.12195	+	7.13943i	−0.317073	+	0.549187i
$170$	−3.51533	−	2.02958i	−0.269613	−	0.155661i
$171$	3.72635	−	11.4449i	0.284961	−	0.875210i
$172$	−5.59210	−	9.68580i	−0.426393	−	0.738535i
$173$	7.61290	+	13.1859i	0.578798	+	1.00251i	0.995618	+	0.0935182i	$0.0298113\pi$
$173$	7.61290	+	13.1859i	0.578798	+	1.00251i	−0.416820	+	0.908989i	$0.636855\pi$
$174$	−9.47922	−	7.68089i	−0.718618	−	0.582287i
$175$	−6.37392	+	4.29304i	−0.481823	+	0.324523i
$176$	−1.82665	+	1.05462i	−0.137689	+	0.0794948i
$177$	−15.8341	+	6.07263i	−1.19017	+	0.456447i
$178$			7.59818i			0.569508i
$179$	−0.299401	+	0.172859i	−0.0223783	+	0.0129201i	−0.511147	−	0.859493i	$-0.670779\pi$
$179$	−0.299401	+	0.172859i	−0.0223783	+	0.0129201i	0.488769	+	0.872413i	$0.337446\pi$
$180$	6.12884	+	1.99550i	0.456816	+	0.148736i
$181$			3.27661i			0.243548i	0.992558	+	0.121774i	$0.0388583\pi$
$181$			3.27661i			0.243548i	−0.992558	+	0.121774i	$0.961142\pi$
$182$	0.286282	+	4.13391i	0.0212207	+	0.306426i
$183$	4.02918	+	0.639415i	0.297846	+	0.0472669i
$184$	14.2019			1.04698
$185$	0.596053	−	1.03239i	0.0438227	−	0.0759031i
$186$	2.73555	+	2.21659i	0.200581	+	0.162528i
$187$	−6.08857	+	3.51524i	−0.445241	+	0.257060i
$188$	−3.47073			−0.253129
$189$	1.65382	+	13.6479i	0.120298	+	0.992738i
$190$	−4.17087			−0.302587
$191$	6.40096	−	3.69560i	0.463158	−	0.267404i	−0.250213	−	0.968191i	$-0.580501\pi$
$191$	6.40096	−	3.69560i	0.463158	−	0.267404i	0.713371	+	0.700787i	$0.247167\pi$
$192$	−2.49686	−	2.02317i	−0.180195	−	0.146010i
$193$	−6.51425	+	11.2830i	−0.468906	+	0.812169i	−0.999368	−	0.0355398i	$-0.988685\pi$
$193$	−6.51425	+	11.2830i	−0.468906	+	0.812169i	0.530462	+	0.847708i	$0.322018\pi$
$194$	−11.1389			−0.799727
$195$	−5.40030	−	0.857007i	−0.386724	−	0.0613716i
$196$	6.38551	+	8.19574i	0.456108	+	0.585410i
$197$			4.03035i			0.287151i	0.989639	+	0.143575i	$0.0458599\pi$
$197$			4.03035i			0.287151i	−0.989639	+	0.143575i	$0.954140\pi$
$198$	−2.88447	+	2.59401i	−0.204990	+	0.184348i
$199$	14.2096	−	8.20390i	1.00729	−	0.581559i	0.0968925	−	0.995295i	$-0.469110\pi$
$199$	14.2096	−	8.20390i	1.00729	−	0.581559i	0.910397	+	0.413736i	$0.135776\pi$
$200$			7.26808i			0.513931i
$201$	0.505867	−	0.194008i	0.0356811	−	0.0136843i
$202$	2.45433	−	1.41701i	0.172686	−	0.0997003i
$203$	25.8882	−	1.79281i	1.81699	−	0.125831i
$204$	7.79895	+	6.31940i	0.546036	+	0.442446i
$205$	8.54947	+	14.8081i	0.597121	+	1.03424i
$206$	−1.49207	−	2.58434i	−0.103957	−	0.180060i
$207$	−16.6569	+	3.52995i	−1.15774	+	0.245348i
$208$	−2.21245	−	1.27736i	−0.153406	−	0.0885688i
$209$	−3.61199	+	6.25615i	−0.249847	+	0.432747i
$210$	4.31957	−	2.00912i	0.298079	−	0.138643i
$211$	−6.00827	−	10.4066i	−0.413627	−	0.716422i	0.581657	−	0.813434i	$-0.302405\pi$
$211$	−6.00827	−	10.4066i	−0.413627	−	0.716422i	−0.995283	+	0.0970121i	$0.969071\pi$
$212$		−	1.70822i		−	0.117321i
$213$	2.12559	−	2.62326i	0.145643	−	0.179743i
$214$	−4.07247			−0.278388
$215$	5.45387	−	9.44638i	0.371951	−	0.644238i
$216$	11.5796	+	5.91341i	0.787892	+	0.402357i
$217$	−7.47092	+	0.517377i	−0.507159	+	0.0351219i
$218$	−7.46236	−	4.30839i	−0.505415	−	0.291801i
$219$	4.79691	+	0.761251i	0.324145	+	0.0514406i
$220$	−3.35023	−	1.93426i	−0.225873	−	0.130408i
$221$	−7.37451	−	4.25767i	−0.496063	−	0.286402i
$222$	0.644915	−	0.795909i	0.0432839	−	0.0534179i
$223$	−22.7932	−	13.1597i	−1.52635	−	0.881237i	−0.999511	−	0.0312693i	$-0.990045\pi$
$223$	−22.7932	−	13.1597i	−1.52635	−	0.881237i	−0.526836	−	0.849967i	$-0.676622\pi$
$224$	15.4296	−	1.06853i	1.03093	−	0.0713944i
$225$	−1.80652	−	8.52449i	−0.120435	−	0.568300i
$226$	−2.60307	+	4.50865i	−0.173154	+	0.299911i
$227$	10.8082			0.717366			0.358683	−	0.933459i	$-0.383226\pi$
$227$	10.8082			0.717366			0.358683	+	0.933459i	$0.383226\pi$
$228$	10.1867	+	1.61658i	0.674627	+	0.107061i
$229$		−	9.69691i		−	0.640790i	−0.947284	−	0.320395i	$-0.896184\pi$
$229$		−	9.69691i		−	0.640790i	0.947284	−	0.320395i	$-0.103816\pi$
$230$	2.95013	+	5.10977i	0.194526	+	0.336928i
$231$	0.727157	−	8.21911i	0.0478435	−	0.540777i
$232$	12.2714	−	21.2547i	0.805657	−	1.39544i
$233$	−1.92897	−	1.11369i	−0.126371	−	0.0729605i	0.435482	−	0.900198i	$-0.356578\pi$
$233$	−1.92897	−	1.11369i	−0.126371	−	0.0729605i	−0.561853	+	0.827237i	$0.689911\pi$
$234$	−4.46779	−	1.45468i	−0.292068	−	0.0950951i
$235$	−1.69247	−	2.93144i	−0.110404	−	0.191226i
$236$	−7.26616	−	12.5854i	−0.472986	−	0.819237i
$237$	3.37486	−	21.2661i	0.219220	−	1.38138i
$238$	7.40137	−	0.512561i	0.479760	−	0.0332244i
$239$	−15.9697	+	9.22008i	−1.03299	+	0.596398i	−0.917840	−	0.396950i	$-0.870068\pi$
$239$	−15.9697	+	9.22008i	−1.03299	+	0.596398i	−0.115151	+	0.993348i	$0.536735\pi$
$240$	−0.460337	+	2.90075i	−0.0297146	+	0.187242i
$241$		−	6.47181i		−	0.416886i	−0.978035	−	0.208443i	$-0.933160\pi$
$241$		−	6.47181i		−	0.416886i	0.978035	−	0.208443i	$-0.0668396\pi$
$242$	−4.82508	+	2.78576i	−0.310168	+	0.179075i
$243$	−15.0511	−	4.05748i	−0.965531	−	0.260287i
$244$			3.49591i			0.223803i
$245$	−3.80844	+	9.38990i	−0.243312	+	0.599899i
$246$	5.26147	+	13.7191i	0.335459	+	0.874695i
$247$	−8.74972			−0.556731
$248$	−3.54133	+	6.13377i	−0.224875	+	0.389495i
$249$	−11.6734	+	4.47694i	−0.739774	+	0.283715i
$250$	−7.11654	+	4.10874i	−0.450090	+	0.259859i
$251$	0.416679			0.0263005			0.0131503	−	0.999914i	$-0.495814\pi$
$251$	0.416679			0.0263005			0.0131503	+	0.999914i	$0.495814\pi$
$252$	−11.3285	+	3.23273i	−0.713631	+	0.203643i
$253$	10.2193			0.642481
$254$	0.548147	−	0.316473i	0.0343938	−	0.0198573i
$255$	−1.53439	+	9.66874i	−0.0960873	+	0.605480i
$256$	5.57519	−	9.65652i	0.348449	−	0.603532i
$257$	−21.1284			−1.31795			−0.658976	−	0.752164i	$-0.729010\pi$
$257$	−21.1284			−1.31795			−0.658976	+	0.752164i	$0.729010\pi$
$258$	5.90095	−	7.28254i	0.367377	−	0.453391i
$259$	0.150531	+	2.17366i	0.00935353	+	0.135065i
$260$		−	4.68556i		−	0.290586i
$261$	−9.10975	+	27.9790i	−0.563880	+	1.73186i
$262$	1.84994	−	1.06806i	0.114290	−	0.0659851i
$263$		−	22.2456i		−	1.37172i	−0.727732	−	0.685862i	$-0.759426\pi$
$263$		−	22.2456i		−	1.37172i	0.727732	−	0.685862i	$-0.240574\pi$
$264$	−6.06313	−	4.91288i	−0.373160	−	0.302367i
$265$	1.44279	−	0.832996i	0.0886299	−	0.0511705i
$266$	6.32286	−	4.25865i	0.387680	−	0.261115i
$267$	17.1099	−	6.56191i	1.04711	−	0.401582i
$268$	0.232138	+	0.402075i	0.0141801	+	0.0245607i
$269$	−14.5164	−	25.1432i	−0.885083	−	1.53301i	−0.845619	−	0.533788i	$-0.820768\pi$
$269$	−14.5164	−	25.1432i	−0.885083	−	1.53301i	−0.0394642	−	0.999221i	$-0.512565\pi$
$270$	0.277789	+	5.39467i	0.0169057	+	0.328309i
$271$	20.8174	+	12.0189i	1.26456	+	0.730097i	0.973954	−	0.226745i	$-0.0728084\pi$
$271$	20.8174	+	12.0189i	1.26456	+	0.730097i	0.290610	+	0.956842i	$0.406142\pi$
$272$	−2.28699	+	3.96118i	−0.138669	+	0.240182i
$273$	9.06167	−	4.21477i	0.548437	−	0.255089i
$274$	4.27259	+	7.40034i	0.258117	+	0.447071i
$275$			5.22992i			0.315376i
$276$	−5.22470	−	13.6232i	−0.314490	−	0.820020i
$277$	8.06485			0.484570			0.242285	−	0.970205i	$-0.422103\pi$
$277$	8.06485			0.484570			0.242285	+	0.970205i	$0.422103\pi$
$278$	4.31811	−	7.47918i	0.258983	−	0.448572i
$279$	2.62893	−	8.07431i	0.157390	−	0.483396i
$280$	5.35358	+	7.94851i	0.319937	+	0.475014i
$281$	−12.0876	−	6.97879i	−0.721087	−	0.416320i	0.0940658	−	0.995566i	$-0.470014\pi$
$281$	−12.0876	−	6.97879i	−0.721087	−	0.416320i	−0.815153	+	0.579246i	$0.803347\pi$
$282$	−1.04157	−	2.71585i	−0.0620245	−	0.161726i
$283$	13.4559	+	7.76876i	0.799869	+	0.461805i	0.843425	−	0.537246i	$-0.180535\pi$
$283$	13.4559	+	7.76876i	0.799869	+	0.461805i	−0.0435563	+	0.999051i	$0.513869\pi$
$284$	2.50564	+	1.44663i	0.148682	+	0.0858418i
$285$	3.60203	+	9.39215i	0.213366	+	0.556343i
$286$	2.44225	+	1.41003i	0.144413	+	0.0833769i
$287$	−28.0804	−	13.7191i	−1.65753	−	0.809810i
$288$	−5.42950	+	16.6758i	−0.319937	+	0.982630i
$289$	0.877036	−	1.51907i	0.0515904	−	0.0893571i
$290$	10.1965			0.598757
$291$	9.61973	+	25.0831i	0.563919	+	1.47039i
$292$			4.16203i			0.243564i
$293$	6.73712	+	11.6690i	0.393587	+	0.681712i	0.992920	−	0.118788i	$-0.0379008\pi$
$293$	6.73712	+	11.6690i	0.393587	+	0.681712i	−0.599333	+	0.800500i	$0.704567\pi$
$294$	−4.49688	+	7.45622i	−0.262263	+	0.434856i
$295$	7.08655	−	12.2743i	0.412595	−	0.714635i
$296$	1.78462	+	1.03035i	0.103729	+	0.0598879i
$297$	8.33237	+	4.25513i	0.483493	+	0.246908i
$298$	2.54196	+	4.40280i	0.147252	+	0.255047i
$299$	6.18882	+	10.7194i	0.357909	+	0.619916i
$300$	6.97193	−	2.67384i	0.402525	−	0.154374i
$301$	1.37735	+	19.8889i	0.0793893	+	1.14638i
$302$	−9.69114	+	5.59518i	−0.557663	+	0.321967i
$303$	−5.31047	−	4.30301i	−0.305079	−	0.247201i
$304$			4.69987i			0.269556i
$305$	−2.95271	+	1.70475i	−0.169072	+	0.0976136i
$306$	−2.60446	+	7.99915i	−0.148887	+	0.457281i
$307$		−	8.62791i		−	0.492421i	−0.969216	−	0.246210i	$-0.920815\pi$
$307$		−	8.62791i		−	0.492421i	0.969216	−	0.246210i	$-0.0791854\pi$
$308$	7.05377	−	0.488489i	0.401926	−	0.0278342i
$309$	−4.53095	+	5.59178i	−0.257757	+	0.318106i
$310$	−2.94254			−0.167125
$311$	−8.12200	+	14.0677i	−0.460556	+	0.797707i	−0.998989	−	0.0449616i	$-0.985683\pi$
$311$	−8.12200	+	14.0677i	−0.460556	+	0.797707i	0.538432	+	0.842669i	$0.319017\pi$
$312$	1.48144	−	9.33508i	0.0838701	−	0.528495i
$313$	5.86899	−	3.38846i	0.331735	−	0.191527i	−0.324876	−	0.945757i	$-0.605323\pi$
$313$	5.86899	−	3.38846i	0.331735	−	0.191527i	0.656611	+	0.754229i	$0.271989\pi$
$314$	−1.49830			−0.0845538
$315$	−8.25468	−	7.99189i	−0.465098	−	0.450292i
$316$	18.4515			1.03798
$317$	19.0245	−	10.9838i	1.06852	−	0.616911i	0.140744	−	0.990046i	$-0.455051\pi$
$317$	19.0245	−	10.9838i	1.06852	−	0.616911i	0.927777	+	0.373135i	$0.121717\pi$
$318$	1.33668	−	0.512638i	0.0749574	−	0.0287473i
$319$	8.83017	−	15.2943i	0.494395	−	0.856316i
$320$	2.68578			0.150140
$321$	3.51705	+	9.17056i	0.196302	+	0.511850i
$322$	−9.68958	−	4.73398i	−0.539979	−	0.263814i
$323$			15.6655i			0.871654i
$324$	1.41246	−	13.2832i	0.0784700	−	0.737958i
$325$	−5.48584	+	3.16725i	−0.304299	+	0.175687i
$326$		−	8.02886i		−	0.444678i
$327$	−3.25721	+	20.5248i	−0.180124	+	1.13503i
$328$	−25.5976	+	14.7788i	−1.41339	+	0.816022i
$329$	5.55884	+	2.71585i	0.306469	+	0.149730i
$330$	0.508150	−	3.20203i	0.0279728	−	0.176266i
$331$	7.30179	+	12.6471i	0.401342	+	0.695145i	0.993888	−	0.110391i	$-0.0352104\pi$
$331$	7.30179	+	12.6471i	0.401342	+	0.695145i	−0.592546	+	0.805537i	$0.701877\pi$
$332$	−5.35684	−	9.27833i	−0.293995	−	0.509214i
$333$	−2.34922	−	0.764887i	−0.128736	−	0.0419156i
$334$	−1.19508	−	0.689978i	−0.0653917	−	0.0377539i
$335$	−0.226400	+	0.392137i	−0.0123696	+	0.0214247i
$336$	−2.26394	−	4.86743i	−0.123508	−	0.265540i
$337$	−16.2629	−	28.1681i	−0.885894	−	1.53441i	−0.844685	−	0.535263i	$-0.820212\pi$
$337$	−16.2629	−	28.1681i	−0.885894	−	1.53441i	−0.0412090	−	0.999151i	$-0.513121\pi$
$338$		−	5.92049i		−	0.322032i
$339$	12.4008	+	1.96796i	0.673520	+	0.106885i
$340$	−8.38906			−0.454961
$341$	−2.54825	+	4.41370i	−0.137995	+	0.239015i
$342$	1.79205	+	8.45621i	0.0969029	+	0.457259i
$343$	−3.81408	−	18.1233i	−0.205941	−	0.978564i
$344$	16.3292	+	9.42767i	0.880412	+	0.508306i
$345$	8.95862	−	11.0561i	0.482316	−	0.595241i
$346$	−9.46969	−	5.46733i	−0.509094	−	0.293925i
$347$	2.76005	+	1.59352i	0.148167	+	0.0855444i	0.572251	−	0.820079i	$-0.306070\pi$
$347$	2.76005	+	1.59352i	0.148167	+	0.0855444i	−0.424084	+	0.905623i	$0.639404\pi$
$348$	−24.9031	−	3.95203i	−1.33495	−	0.211851i
$349$	−6.48224	−	3.74252i	−0.346986	−	0.200333i	0.316371	−	0.948636i	$-0.397536\pi$
$349$	−6.48224	−	3.74252i	−0.346986	−	0.200333i	−0.663357	+	0.748303i	$0.730869\pi$
$350$	2.42270	−	4.95883i	0.129499	−	0.265060i
$351$	0.582750	+	11.3170i	0.0311049	+	0.604058i
$352$	5.26287	−	9.11556i	0.280512	−	0.485861i
$353$	−11.3808			−0.605739			−0.302869	−	0.953032i	$-0.597945\pi$
$353$	−11.3808			−0.605739			−0.302869	+	0.953032i	$0.597945\pi$
$354$	7.66747	−	9.46266i	0.407522	−	0.502934i
$355$			2.82175i			0.149763i
$356$	7.85159	+	13.5994i	0.416134	+	0.720764i
$357$	−7.54615	−	16.2241i	−0.399384	−	0.858668i
$358$	0.124142	−	0.215020i	0.00656109	−	0.0113641i
$359$	−4.77569	−	2.75725i	−0.252051	−	0.145522i	0.368652	−	0.929568i	$-0.379819\pi$
$359$	−4.77569	−	2.75725i	−0.252051	−	0.145522i	−0.620703	+	0.784046i	$0.713153\pi$
$360$	−10.6304	+	2.25280i	−0.560269	+	0.118733i
$361$	−1.45164	−	2.51432i	−0.0764022	−	0.132332i
$362$	−1.17657	−	2.03789i	−0.0618394	−	0.107109i
$363$	10.4401	+	8.45949i	0.547963	+	0.444008i
$364$	4.78417	+	7.10311i	0.250759	+	0.372304i
$365$	−3.51533	+	2.02958i	−0.184001	+	0.106233i
$366$	−2.73555	+	1.04913i	−0.142990	+	0.0548387i
$367$			21.1025i			1.10154i	0.834657	+	0.550770i	$0.185666\pi$
$367$			21.1025i			1.10154i	−0.834657	+	0.550770i	$0.814334\pi$
$368$	5.75785	−	3.32430i	0.300149	−	0.173291i
$369$	26.3493	−	23.6960i	1.37169	−	1.23356i
$370$			0.856131i			0.0445081i
$371$	−1.33668	+	2.73594i	−0.0693970	+	0.142043i
$372$	7.18665	+	1.14049i	0.372611	+	0.0591318i
$373$	15.3700			0.795826			0.397913	−	0.917423i	$-0.369735\pi$
$373$	15.3700			0.795826			0.397913	+	0.917423i	$0.369735\pi$
$374$	2.52453	−	4.37261i	0.130540	−	0.226102i
$375$	15.3982	+	12.4770i	0.795159	+	0.644307i
$376$	5.06735	−	2.92563i	0.261328	−	0.150878i
$377$	21.3903			1.10166
$378$	−5.92932	−	7.89445i	−0.304971	−	0.406047i
$379$	−32.3630			−1.66238			−0.831188	−	0.555991i	$-0.812339\pi$
$379$	−32.3630			−1.66238			−0.831188	+	0.555991i	$0.812339\pi$
$380$	−7.46510	+	4.30998i	−0.382951	+	0.221097i
$381$	−1.18604	−	0.961030i	−0.0607625	−	0.0492351i
$382$	−2.65406	+	4.59696i	−0.135793	+	0.235201i
$383$	19.8346			1.01350			0.506750	−	0.862093i	$-0.330847\pi$
$383$	19.8346			1.01350			0.506750	+	0.862093i	$0.330847\pi$
$384$	−17.7208	−	2.81222i	−0.904310	−	0.143510i
$385$	3.85229	+	5.71954i	0.196331	+	0.291495i
$386$		−	9.35663i		−	0.476240i
$387$	−21.4953	−	6.99870i	−1.09267	−	0.355764i
$388$	−19.9366	+	11.5104i	−1.01213	+	0.584352i
$389$			5.10283i			0.258724i	0.991597	+	0.129362i	$0.0412928\pi$
$389$			5.10283i			0.258724i	−0.991597	+	0.129362i	$0.958707\pi$
$390$	3.66646	−	1.40614i	0.185658	−	0.0712028i
$391$	19.1920	−	11.0805i	0.970581	−	0.560365i
$392$	−16.2316	−	6.58335i	−0.819818	−	0.332509i
$393$	−4.00274	−	3.24337i	−0.201912	−	0.163607i
$394$	−1.44723	−	2.50668i	−0.0729105	−	0.126285i
$395$	8.99772	+	15.5845i	0.452724	+	0.784141i
$396$	−2.48214	+	7.62347i	−0.124732	+	0.383094i
$397$	−11.5288	−	6.65615i	−0.578613	−	0.334062i	0.181969	−	0.983304i	$-0.441753\pi$
$397$	−11.5288	−	6.65615i	−0.578613	−	0.334062i	−0.760582	+	0.649242i	$0.775086\pi$
$398$	−5.89177	+	10.2048i	−0.295328	+	0.511522i
$399$	−15.0503	−	10.5602i	−0.753459	−	0.528673i
$400$	1.70127	+	2.94669i	0.0850636	+	0.147334i
$401$		−	16.3678i		−	0.817371i	−0.912675	−	0.408685i	$-0.865987\pi$
$401$		−	16.3678i		−	0.817371i	0.912675	−	0.408685i	$-0.134013\pi$
$402$	−0.244959	+	0.302312i	−0.0122175	+	0.0150779i
$403$	−6.17290			−0.307494
$404$	2.92853	−	5.07237i	0.145700	−	0.252360i
$405$	11.9080	−	5.28446i	0.591716	−	0.262587i
$406$	−15.4574	+	10.4110i	−0.767137	+	0.516692i
$407$	1.28416	+	0.741412i	0.0636536	+	0.0367504i
$408$	−16.7136	−	2.65238i	−0.827445	−	0.131312i
$409$	3.75604	+	2.16855i	0.185724	+	0.107228i	0.589979	−	0.807418i	$-0.299136\pi$
$409$	3.75604	+	2.16855i	0.185724	+	0.107228i	−0.404255	+	0.914646i	$0.632469\pi$
$410$	−10.6347	−	6.13994i	−0.525210	−	0.303230i
$411$	12.9745	−	16.0122i	0.639986	−	0.789826i
$412$	−5.34107	−	3.08367i	−0.263135	−	0.151921i
$413$	1.78968	+	25.8429i	0.0880644	+	1.27165i
$414$	9.09223	−	8.17667i	0.446859	−	0.401862i
$415$	5.22443	−	9.04898i	0.256457	−	0.444197i
$416$	12.7488			0.625062
$417$	−20.5711	−	3.26456i	−1.00737	−	0.159866i
$418$		−	5.18802i		−	0.253754i
$419$	−9.41294	−	16.3037i	−0.459852	−	0.796487i	0.539100	−	0.842241i	$-0.318764\pi$
$419$	−9.41294	−	16.3037i	−0.459852	−	0.796487i	−0.998953	+	0.0457540i	$0.985431\pi$
$420$	5.65512	−	8.05960i	0.275941	−	0.393268i
$421$	0.913453	−	1.58215i	0.0445190	−	0.0771092i	−0.842907	−	0.538059i	$-0.819158\pi$
$421$	0.913453	−	1.58215i	0.0445190	−	0.0771092i	0.887426	+	0.460950i	$0.152491\pi$
$422$	7.47370	+	4.31494i	0.363814	+	0.210048i
$423$	−5.21614	+	4.69090i	−0.253618	+	0.228079i
$424$	1.43993	+	2.49404i	0.0699294	+	0.121121i
$425$	5.67066	+	9.82187i	0.275068	+	0.476431i
$426$	−0.380046	+	2.39480i	−0.0184133	+	0.116029i
$427$	2.73555	−	5.59917i	0.132383	−	0.270963i
$428$	−7.28897	+	4.20829i	−0.352326	+	0.203415i
$429$	1.06601	−	6.71727i	0.0514672	−	0.324313i
$430$			7.83357i			0.377768i
$431$	−12.4526	+	7.18954i	−0.599823	+	0.346308i	−0.768972	−	0.639283i	$-0.779231\pi$
$431$	−12.4526	+	7.18954i	−0.599823	+	0.346308i	0.169149	+	0.985590i	$0.445898\pi$
$432$	6.07888	−	0.313021i	0.292470	−	0.0150602i
$433$			2.22130i			0.106749i	0.998575	+	0.0533745i	$0.0169977\pi$
$433$			2.22130i			0.106749i	−0.998575	+	0.0533745i	$0.983002\pi$
$434$	4.46076	−	3.00446i	0.214123	−	0.144219i
$435$	−8.80582	−	22.9608i	−0.422207	−	1.10089i
$436$	−17.8083			−0.852865
$437$	11.3855	−	19.7202i	0.544641	−	0.943347i
$438$	−3.25680	+	1.24903i	−0.155616	+	0.0596810i
$439$	8.69907	−	5.02241i	0.415184	−	0.239706i	−0.277831	−	0.960630i	$-0.589615\pi$
$439$	8.69907	−	5.02241i	0.415184	−	0.239706i	0.693015	+	0.720924i	$0.256282\pi$
$440$	6.52190			0.310919
$441$	20.6738	+	3.68695i	0.984467	+	0.175569i
$442$	6.11544			0.290882
$443$	12.0321	−	6.94672i	0.571661	−	0.330049i	−0.186151	−	0.982521i	$-0.559602\pi$
$443$	12.0321	−	6.94672i	0.571661	−	0.330049i	0.757812	+	0.652472i	$0.226268\pi$
$444$	0.331826	−	2.09095i	0.0157478	−	0.0992323i
$445$	−7.65751	+	13.2632i	−0.363001	+	0.628736i
$446$	18.9017			0.895020
$447$	7.71913	−	9.52640i	0.365102	−	0.450583i
$448$	−4.07153	+	2.74231i	−0.192362	+	0.129562i
$449$			10.5630i			0.498498i	0.968439	+	0.249249i	$0.0801837\pi$
$449$			10.5630i			0.498498i	−0.968439	+	0.249249i	$0.919816\pi$
$450$	4.18457	+	4.65312i	0.197262	+	0.219350i
$451$	−18.4194	+	10.6344i	−0.867334	+	0.500755i
$452$			10.7595i			0.506086i
$453$	20.9689	+	16.9908i	0.985204	+	0.798299i
$454$	−6.72217	+	3.88105i	−0.315487	+	0.182147i
$455$	−3.66646	+	7.50456i	−0.171886	+	0.351819i
$456$	−16.2355	+	6.22655i	−0.760295	+	0.291585i
$457$	−2.55654	−	4.42805i	−0.119590	−	0.207135i	0.800015	−	0.599979i	$-0.204825\pi$
$457$	−2.55654	−	4.42805i	−0.119590	−	0.207135i	−0.919605	+	0.392844i	$0.871491\pi$
$458$	3.48200	+	6.03100i	0.162703	+	0.281810i
$459$	20.2621	−	1.04336i	0.945752	−	0.0486998i
$460$	10.5604	+	6.09704i	0.492380	+	0.284276i
$461$	−4.16691	+	7.21730i	−0.194072	+	0.336143i	−0.946596	−	0.322422i	$-0.895503\pi$
$461$	−4.16691	+	7.21730i	−0.194072	+	0.336143i	0.752524	+	0.658565i	$0.228836\pi$
$462$	2.49909	+	5.37299i	0.116268	+	0.249974i
$463$	10.0143	+	17.3452i	0.465403	+	0.806102i	0.999220	−	0.0394986i	$-0.0125761\pi$
$463$	10.0143	+	17.3452i	0.465403	+	0.806102i	−0.533817	+	0.845600i	$0.679243\pi$
$464$		−	11.4897i		−	0.533395i
$465$	2.54122	+	6.62613i	0.117846	+	0.307279i
$466$	1.59963			0.0741016
$467$	−10.3896	+	17.9953i	−0.480773	+	0.832723i	−0.999757	−	0.0220611i	$-0.992977\pi$
$467$	−10.3896	+	17.9953i	−0.480773	+	0.832723i	0.518984	+	0.854784i	$0.326310\pi$
$468$	−9.49971	+	2.01319i	−0.439124	+	0.0930597i
$469$	−0.0571765	−	0.825627i	−0.00264016	−	0.0381239i
$470$	2.10526	+	1.21547i	0.0971085	+	0.0560656i
$471$	1.29395	+	3.37393i	0.0596222	+	0.155462i
$472$	21.2175	+	12.2500i	0.976616	+	0.563850i
$473$	11.7501	+	6.78390i	0.540268	+	0.311924i
$474$	5.53733	+	14.4383i	0.254338	+	0.663175i
$475$	10.0922	+	5.82674i	0.463062	+	0.267349i
$476$	12.7174	−	8.56561i	0.582903	−	0.392604i
$477$	−2.30876	−	2.56727i	−0.105711	−	0.117547i
$478$	6.62156	−	11.4689i	0.302863	−	0.524574i
$479$	−32.0617			−1.46494			−0.732468	−	0.680802i	$-0.761632\pi$
$479$	−32.0617			−1.46494			−0.732468	+	0.680802i	$0.761632\pi$
$480$	−5.24836	−	13.6849i	−0.239554	−	0.624626i
$481$			1.79600i			0.0818907i
$482$	2.32392	+	4.02515i	0.105852	+	0.183340i
$483$	−2.29210	+	25.9077i	−0.104294	+	1.17884i
$484$	−5.75734	+	9.97200i	−0.261697	+	0.453273i
$485$	−19.4438	−	11.2259i	−0.882897	−	0.509741i
$486$	10.8180	−	2.88107i	0.490716	−	0.130688i
$487$	11.8375	+	20.5032i	0.536408	+	0.929087i	0.999094	+	0.0425641i	$0.0135527\pi$
$487$	11.8375	+	20.5032i	0.536408	+	0.929087i	−0.462685	+	0.886523i	$0.653114\pi$
$488$	−2.94686	−	5.10412i	−0.133398	−	0.231052i
$489$	−18.0797	+	6.93385i	−0.817594	+	0.313560i
$490$	−1.00310	−	7.20760i	−0.0453152	−	0.325606i
$491$	15.4664	−	8.92951i	0.697987	−	0.402983i	−0.108610	−	0.994084i	$-0.534640\pi$
$491$	15.4664	−	8.92951i	0.697987	−	0.402983i	0.806597	+	0.591101i	$0.201307\pi$
$492$	23.5937	+	19.1177i	1.06368	+	0.861890i
$493$		−	38.2973i		−	1.72482i
$494$	5.44189	−	3.14188i	0.244842	−	0.141360i
$495$	−7.64932	+	1.62105i	−0.343811	+	0.0728609i
$496$			3.31574i			0.148881i
$497$	−2.88113	−	4.27764i	−0.129236	−	0.191879i
$498$	5.65271	−	6.97617i	0.253304	−	0.312610i
$499$	−23.1204			−1.03501			−0.517506	−	0.855680i	$-0.673139\pi$
$499$	−23.1204			−1.03501			−0.517506	+	0.855680i	$0.673139\pi$
$500$	−8.49154	+	14.7078i	−0.379753	+	0.657752i
$501$	−0.521634	+	3.28700i	−0.0233049	+	0.146852i
$502$	−0.259154	+	0.149622i	−0.0115666	+	0.00667798i
$503$	−13.9995			−0.624206			−0.312103	−	0.950048i	$-0.601033\pi$
$503$	−13.9995			−0.624206			−0.312103	+	0.950048i	$0.601033\pi$
$504$	13.8149	−	14.2692i	0.615366	−	0.635601i
$505$	5.71228			0.254193
$506$	−6.35589	+	3.66958i	−0.282554	+	0.163133i
$507$	−13.3320	+	5.11303i	−0.592096	+	0.227078i
$508$	0.654056	−	1.13286i	0.0290190	−	0.0502624i
$509$	−13.5834			−0.602074			−0.301037	−	0.953612i	$-0.597333\pi$
$509$	−13.5834			−0.602074			−0.301037	+	0.953612i	$0.597333\pi$
$510$	−2.51757	−	6.56445i	−0.111480	−	0.290679i
$511$	3.25680	−	6.66606i	0.144072	−	0.294889i
$512$		−	12.7104i		−	0.561727i
$513$	17.4944	−	11.3383i	0.772396	−	0.500599i
$514$	13.1408	−	7.58684i	0.579616	−	0.334641i
$515$		−	6.01488i		−	0.265047i
$516$	3.03620	−	19.1322i	0.133661	−	0.842247i
$517$	3.64633	−	2.10521i	0.160365	−	0.0925870i
$518$	−0.874148	−	1.29786i	−0.0384079	−	0.0570246i
$519$	−4.13339	+	26.0459i	−0.181435	+	1.14329i
$520$	3.94968	+	6.84104i	0.173205	+	0.299999i
$521$	15.9477	+	27.6222i	0.698682	+	1.21015i	0.968924	+	0.247360i	$0.0795630\pi$
$521$	15.9477	+	27.6222i	0.698682	+	1.21015i	−0.270242	+	0.962792i	$0.587104\pi$
$522$	−4.38099	−	20.6727i	−0.191751	−	0.904821i
$523$	−1.20531	−	0.695886i	−0.0527046	−	0.0304290i	0.473416	−	0.880839i	$-0.343021\pi$
$523$	−1.20531	−	0.695886i	−0.0527046	−	0.0304290i	−0.526121	+	0.850410i	$0.676354\pi$
$524$	2.20737	−	3.82327i	0.0964293	−	0.167020i
$525$	−13.2588	−	1.17303i	−0.578660	−	0.0511950i
$526$	7.98803	+	13.8357i	0.348295	+	0.603264i
$527$			11.0520i			0.481433i
$528$	−3.60815	−	0.572599i	−0.157025	−	0.0249192i
$529$	−9.21257			−0.400546
$530$	−0.598230	+	1.03616i	−0.0259854	+	0.0450081i
$531$	−27.9301	−	9.09384i	−1.21207	−	0.394639i
$532$	6.91608	−	14.1559i	0.299850	−	0.613738i
$533$	−22.3096	−	12.8805i	−0.966337	−	0.557915i
$534$	−8.28524	+	10.2251i	−0.358538	+	0.442482i
$535$	−7.10880	−	4.10427i	−0.307340	−	0.177443i
$536$	−0.677855	−	0.391360i	−0.0292789	−	0.0169042i
$537$	−0.591401	−	0.0938530i	−0.0255208	−	0.00405006i
$538$	18.0570	+	10.4252i	0.778493	+	0.449463i
$539$	−11.6798	−	4.73720i	−0.503085	−	0.204046i
$540$	6.07178	+	9.36842i	0.261288	+	0.403153i
$541$	12.9736	−	22.4709i	0.557779	−	0.966101i	−0.439903	−	0.898045i	$-0.644987\pi$
$541$	12.9736	−	22.4709i	0.557779	−	0.966101i	0.997682	−	0.0680555i	$-0.0216795\pi$
$542$	−17.2632			−0.741516
$543$	−3.57289	+	4.40941i	−0.153327	+	0.189226i
$544$		−	22.8256i		−	0.978638i
$545$	−8.68407	−	15.0413i	−0.371985	−	0.644296i
$546$	−4.12246	+	5.87527i	−0.176425	+	0.251438i
$547$	−9.32438	+	16.1503i	−0.398682	+	0.690537i	−0.993564	−	0.113276i	$-0.963865\pi$
$547$	−9.32438	+	16.1503i	−0.398682	+	0.690537i	0.594882	+	0.803813i	$0.297199\pi$
$548$	15.2943	+	8.83017i	0.653340	+	0.377206i
$549$	4.72493	+	5.25399i	0.201655	+	0.224235i
$550$	−1.87798	−	3.25275i	−0.0800772	−	0.138698i
$551$	−19.6757	−	34.0793i	−0.838212	−	1.45183i
$552$	19.1118	+	15.4861i	0.813453	+	0.659131i
$553$	−29.5526	−	14.4383i	−1.25671	−	0.613981i
$554$	−5.01594	+	2.89595i	−0.213107	+	0.123037i
$555$	1.92787	−	0.739368i	0.0818336	−	0.0313844i
$556$		−	17.8485i		−	0.756944i
$557$	36.3567	−	20.9905i	1.54048	−	0.889398i	0.541674	−	0.840589i	$-0.317791\pi$
$557$	36.3567	−	20.9905i	1.54048	−	0.889398i	0.998808	−	0.0488092i	$-0.0155426\pi$
$558$	1.26428	+	5.96583i	0.0535214	+	0.252554i
$559$			16.4334i			0.695058i
$560$	4.03104	+	1.96942i	0.170342	+	0.0832232i
$561$	−12.0266	−	1.90858i	−0.507765	−	0.0805804i
$562$	10.0239			0.422831
$563$	19.3006	−	33.4295i	0.813422	−	1.40889i	−0.0970343	−	0.995281i	$-0.530936\pi$
$563$	19.3006	−	33.4295i	0.813422	−	1.40889i	0.910456	−	0.413606i	$-0.135731\pi$
$564$	−4.67064	−	3.78456i	−0.196669	−	0.159359i
$565$	−9.08771	+	5.24679i	−0.382323	+	0.220734i
$566$	−11.1585			−0.469028
$567$	−12.6564	+	20.1697i	−0.531519	+	0.847046i
$568$	−4.87773			−0.204665
$569$	−30.4460	+	17.5780i	−1.27636	+	0.736908i	−0.976178	−	0.216973i	$-0.930382\pi$
$569$	−30.4460	+	17.5780i	−1.27636	+	0.736908i	−0.300184	+	0.953881i	$0.597048\pi$
$570$	−5.61285	−	4.54802i	−0.235096	−	0.190496i
$571$	17.6766	−	30.6167i	0.739742	−	1.28127i	−0.212870	−	0.977081i	$-0.568281\pi$
$571$	17.6766	−	30.6167i	0.739742	−	1.28127i	0.952611	−	0.304190i	$-0.0983857\pi$
$572$	5.82823			0.243690
$573$	12.6437	+	2.00651i	0.528198	+	0.0838230i
$574$	22.3909	−	1.55062i	0.934578	−	0.0647216i
$575$		−	16.4854i		−	0.687489i
$576$	−1.15397	−	5.44527i	−0.0480820	−	0.226886i
$577$	23.2557	−	13.4267i	0.968147	−	0.558960i	0.0694761	−	0.997584i	$-0.477867\pi$
$577$	23.2557	−	13.4267i	0.968147	−	0.558960i	0.898671	+	0.438624i	$0.144534\pi$
$578$			1.25972i			0.0523973i
$579$	−21.0696	+	8.08053i	−0.875625	+	0.335815i
$580$	18.2498	−	10.5365i	0.757781	−	0.437505i
$581$	1.31941	+	19.0522i	0.0547383	+	0.790420i
$582$	−14.9899	−	12.1461i	−0.621352	−	0.503473i
$583$	1.03614	+	1.79464i	0.0429125	+	0.0743266i
$584$	−3.50837	−	6.07667i	−0.145177	−	0.251454i
$585$	−6.33282	−	7.04192i	−0.261830	−	0.291147i
$586$	−8.38031	−	4.83837i	−0.346187	−	0.199871i
$587$	15.6788	−	27.1565i	0.647134	−	1.12087i	−0.336671	−	0.941622i	$-0.609301\pi$
$587$	15.6788	−	27.1565i	0.647134	−	1.12087i	0.983804	−	0.179246i	$-0.0573657\pi$
$588$	−0.343692	+	17.9921i	−0.0141736	+	0.741983i
$589$	5.67809	+	9.83474i	0.233962	+	0.405234i
$590$			10.1786i			0.419048i
$591$	−4.39479	+	5.42374i	−0.180778	+	0.223103i
$592$	0.964714			0.0396495
$593$	−4.56131	+	7.90043i	−0.187311	+	0.324432i	−0.944353	−	0.328935i	$-0.893310\pi$
$593$	−4.56131	+	7.90043i	−0.187311	+	0.324432i	0.757042	+	0.653366i	$0.226644\pi$
$594$	−6.71027	+	0.345533i	−0.275326	+	0.0141774i
$595$	13.4362	+	6.56445i	0.550831	+	0.269116i
$596$	9.09927	+	5.25347i	0.372721	+	0.215190i
$597$	28.0679	+	4.45427i	1.14874	+	0.182301i
$598$	−7.69828	−	4.44461i	−0.314806	−	0.181753i
$599$	1.11316	+	0.642683i	0.0454825	+	0.0262593i	0.522569	−	0.852597i	$-0.324974\pi$
$599$	1.11316	+	0.642683i	0.0454825	+	0.0262593i	−0.477086	+	0.878856i	$0.658307\pi$
$600$	−7.92529	+	9.78084i	−0.323549	+	0.399301i
$601$	−16.7126	−	9.64903i	−0.681721	−	0.393592i	0.118782	−	0.992920i	$-0.462101\pi$
$601$	−16.7126	−	9.64903i	−0.681721	−	0.393592i	−0.800503	+	0.599328i	$0.795434\pi$
$602$	−7.99843	−	11.8754i	−0.325992	−	0.484003i
$603$	0.892309	+	0.290529i	0.0363376	+	0.0118312i
$604$	−11.5636	+	20.0287i	−0.470515	+	0.814956i
$605$	−11.2300			−0.456566
$606$	4.84799	+	0.769357i	0.196936	+	0.0312530i
$607$			38.9502i			1.58094i	0.612501	+	0.790470i	$0.290164\pi$
$607$			38.9502i			1.58094i	−0.612501	+	0.790470i	$0.709836\pi$
$608$	−11.7269	−	20.3116i	−0.475589	−	0.823744i
$609$	36.7933	+	25.8164i	1.49094	+	1.04613i
$610$	1.22429	−	2.12054i	0.0495702	−	0.0858581i
$611$	4.41645	+	2.54984i	0.178670	+	0.103155i
$612$	3.60442	+	17.0083i	0.145700	+	0.687521i
$613$	−3.65018	−	6.32229i	−0.147429	−	0.255355i	0.782847	−	0.622214i	$-0.213767\pi$
$613$	−3.65018	−	6.32229i	−0.147429	−	0.255355i	−0.930277	+	0.366859i	$0.880433\pi$
$614$	3.09814	+	5.36613i	0.125031	+	0.216560i
$615$	−4.64189	+	29.2502i	−0.187179	+	1.17948i
$616$	−9.88691	+	6.65915i	−0.398355	+	0.268305i
$617$	38.3641	−	22.1495i	1.54448	−	0.891706i	0.545932	−	0.837829i	$-0.316176\pi$
$617$	38.3641	−	22.1495i	1.54448	−	0.891706i	0.998548	−	0.0538763i	$-0.0171577\pi$
$618$	0.810113	−	5.10480i	0.0325875	−	0.205345i
$619$			0.471636i			0.0189566i	0.999955	+	0.00947832i	$0.00301709\pi$
$619$			0.471636i			0.0189566i	−0.999955	+	0.00947832i	$0.996983\pi$
$620$	−5.26660	+	3.04068i	−0.211512	+	0.122116i
$621$	−26.2648	−	13.4128i	−1.05397	−	0.538235i
$622$		−	11.6659i		−	0.467760i
$623$	−1.93387	−	27.9251i	−0.0774790	−	1.11880i
$624$	−1.58448	−	4.13148i	−0.0634302	−	0.165391i
$625$	−2.04026			−0.0816105
$626$	−2.43348	+	4.21491i	−0.0972614	+	0.168462i
$627$	−11.6826	+	4.48046i	−0.466558	+	0.178932i
$628$	−2.68168	+	1.54827i	−0.107011	+	0.0617826i
$629$	3.21558			0.128213
$630$	8.00376	+	2.00644i	0.318877	+	0.0799385i
$631$	10.2247			0.407038			0.203519	−	0.979071i	$-0.434762\pi$
$631$	10.2247			0.407038			0.203519	+	0.979071i	$0.434762\pi$
$632$	−26.9397	+	15.5536i	−1.07160	+	0.618691i
$633$	3.26216	−	20.5560i	0.129659	−	0.817029i
$634$	−7.88819	+	13.6627i	−0.313280	+	0.542617i
$635$	1.27578			0.0506277
$636$	1.86268	−	2.29879i	0.0738601	−	0.0911529i
$637$	−2.10431	−	15.1202i	−0.0833757	−	0.599085i
$638$			12.6831i			0.502127i
$639$	5.72093	−	1.21239i	0.226316	−	0.0479612i
$640$	12.9863	−	7.49767i	0.513330	−	0.296371i
$641$			50.1815i			1.98205i	0.133677	+	0.991025i	$0.457321\pi$
$641$			50.1815i			1.98205i	−0.133677	+	0.991025i	$0.542679\pi$
$642$	−5.48042	−	4.44072i	−0.216295	−	0.175261i
$643$	9.18633	−	5.30373i	0.362274	−	0.209159i	−0.307804	−	0.951450i	$-0.599594\pi$
$643$	9.18633	−	5.30373i	0.362274	−	0.209159i	0.670078	+	0.742291i	$0.266261\pi$
$644$	−22.2344	+	1.53978i	−0.876159	+	0.0606760i
$645$	17.6400	−	6.76520i	0.694573	−	0.266379i
$646$	−5.62524	−	9.74320i	−0.221322	−	0.383341i
$647$	14.9203	+	25.8427i	0.586577	+	1.01598i	0.994677	+	0.103044i	$0.0328582\pi$
$647$	14.9203	+	25.8427i	0.586577	+	1.01598i	−0.408100	+	0.912937i	$0.633809\pi$
$648$	9.13483	+	20.5845i	0.358850	+	0.808636i
$649$	15.2676	+	8.81474i	0.599305	+	0.346009i
$650$	2.27461	−	3.93975i	0.0892177	−	0.154530i
$651$	−10.6180	−	7.45022i	−0.416151	−	0.291997i
$652$	−8.29664	−	14.3702i	−0.324921	−	0.562780i
$653$			35.2561i			1.37968i	0.723962	+	0.689839i	$0.242319\pi$
$653$			35.2561i			1.37968i	−0.723962	+	0.689839i	$0.757681\pi$
$654$	−5.34430	−	13.9350i	−0.208979	−	0.544904i
$655$	4.30561			0.168234
$656$	−6.91868	+	11.9835i	−0.270129	+	0.467877i
$657$	5.62524	+	6.25510i	0.219461	+	0.244035i
$658$	−4.43254	+	0.306963i	−0.172798	+	0.0119667i
$659$	29.3751	+	16.9597i	1.14429	+	0.660656i	0.947489	−	0.319787i	$-0.103611\pi$
$659$	29.3751	+	16.9597i	1.14429	+	0.660656i	0.196801	+	0.980443i	$0.436945\pi$
$660$	−2.39933	−	6.25615i	−0.0933938	−	0.243520i
$661$	−13.6550	−	7.88371i	−0.531117	−	0.306641i	0.210354	−	0.977625i	$-0.432538\pi$
$661$	−13.6550	−	7.88371i	−0.531117	−	0.306641i	−0.741471	+	0.670985i	$0.765872\pi$
$662$	−9.08270	−	5.24390i	−0.353009	−	0.203810i
$663$	−5.28139	−	13.7710i	−0.205112	−	0.534821i
$664$	15.6423	+	9.03106i	0.607037	+	0.350473i
$665$	15.3289	−	1.06156i	0.594430	−	0.0411656i
$666$	1.73576	−	0.367843i	0.0672592	−	0.0142536i
$667$	−27.8339	+	48.2097i	−1.07773	+	1.86669i
$668$	−2.85196			−0.110346
$669$	−16.3238	−	42.5636i	−0.631114	−	1.64560i
$670$		−	0.325186i		−	0.0125630i
$671$	−2.12048	−	3.67279i	−0.0818604	−	0.141786i
$672$	21.9292	+	15.3869i	0.845935	+	0.593561i
$673$	−7.35627	+	12.7414i	−0.283563	+	0.491146i	−0.972260	−	0.233904i	$-0.924850\pi$
$673$	−7.35627	+	12.7414i	−0.283563	+	0.491146i	0.688696	+	0.725050i	$0.258183\pi$
$674$	20.2294	+	11.6794i	0.779207	+	0.449875i
$675$	6.86423	−	13.4415i	0.264204	−	0.517363i
$676$	−6.11795	−	10.5966i	−0.235306	−	0.407562i
$677$	1.99217	+	3.45054i	0.0765654	+	0.132615i	0.901766	−	0.432225i	$-0.142271\pi$
$677$	1.99217	+	3.45054i	0.0765654	+	0.132615i	−0.825201	+	0.564840i	$0.808938\pi$
$678$	−8.41936	+	3.22895i	−0.323344	+	0.124007i
$679$	40.9381	−	2.83505i	1.57106	−	0.108799i
$680$	12.2482	−	7.07152i	0.469698	−	0.271181i
$681$	14.5449	+	11.7855i	0.557361	+	0.451623i
$682$		−	3.66013i		−	0.140154i
$683$	−19.2812	+	11.1320i	−0.737774	+	0.425954i	−0.821259	−	0.570555i	$-0.806728\pi$
$683$	−19.2812	+	11.1320i	−0.737774	+	0.425954i	0.0834856	+	0.996509i	$0.473395\pi$
$684$	11.9457	+	13.2832i	0.456754	+	0.507898i
$685$			17.2238i			0.658088i
$686$	8.87993	+	9.90220i	0.339037	+	0.378068i
$687$	10.5737	−	13.0494i	0.403414	−	0.497865i
$688$	8.82711			0.336530
$689$	−1.25498	+	2.17368i	−0.0478107	+	0.0828106i
$690$	−1.60176	+	10.0932i	−0.0609779	+	0.384243i
$691$	−41.9003	+	24.1912i	−1.59396	+	0.920275i	−0.601346	+	0.798989i	$0.705369\pi$
$691$	−41.9003	+	24.1912i	−1.59396	+	0.920275i	−0.992618	+	0.121287i	$0.961298\pi$
$692$	−22.5987			−0.859073
$693$	9.94086	−	10.2677i	0.377622	−	0.390039i
$694$	−2.28882			−0.0868824
$695$	15.0752	−	8.70365i	0.571834	−	0.330148i
$696$	39.6905	−	15.2219i	1.50447	−	0.576986i
$697$	−23.0613	+	39.9433i	−0.873507	+	1.51296i
$698$	5.37551			0.203466
$699$	−1.38147	−	3.60212i	−0.0522520	−	0.136245i
$700$	−0.788014	−	11.3789i	−0.0297841	−	0.430082i
$701$		−	23.3129i		−	0.880514i	−0.897872	−	0.440257i	$-0.854887\pi$
$701$		−	23.3129i		−	0.880514i	0.897872	−	0.440257i	$-0.145113\pi$
$702$	−4.42620	−	6.82937i	−0.167056	−	0.257758i
$703$	2.86142	−	1.65204i	0.107920	−	0.0623079i
$704$			3.34076i			0.125910i
$705$	0.918917	−	5.79042i	0.0346084	−	0.218080i
$706$	7.07830	−	4.08666i	0.266395	−	0.153803i
$707$	−8.65957	+	5.83250i	−0.325677	+	0.219354i
$708$	3.94512	−	24.8596i	0.148267	−	0.934281i
$709$	−8.83884	−	15.3093i	−0.331949	−	0.574953i	0.650945	−	0.759125i	$-0.274373\pi$
$709$	−8.83884	−	15.3093i	−0.331949	−	0.574953i	−0.982894	+	0.184172i	$0.941040\pi$
$710$	−1.01324	−	1.75499i	−0.0380263	−	0.0658635i
$711$	27.7307	−	24.9384i	1.03998	−	0.935262i
$712$	−22.9270	−	13.2369i	−0.859227	−	0.496075i
$713$	8.03242	−	13.9126i	0.300817	−	0.521030i
$714$	10.5191	+	7.38087i	0.393668	+	0.276222i
$715$	2.84208	+	4.92263i	0.106288	+	0.184096i
$716$		−	0.513128i		−	0.0191765i
$717$	−31.5446	−	5.00600i	−1.17805	−	0.186952i
$718$	3.96033			0.147798
$719$	15.2102	−	26.3449i	0.567246	−	0.982498i	−0.429591	−	0.903024i	$-0.641342\pi$
$719$	15.2102	−	26.3449i	0.567246	−	0.982498i	0.996837	−	0.0794749i	$-0.0253244\pi$
$720$	−3.78253	+	3.40164i	−0.140967	+	0.126772i
$721$	6.14147	+	9.11830i	0.228720	+	0.339583i
$722$	1.80570	+	1.04252i	0.0672011	+	0.0387986i
$723$	7.05702	−	8.70928i	0.262453	−	0.323902i
$724$	−4.21171	−	2.43163i	−0.156527	−	0.0903708i
$725$	−24.6722	−	14.2445i	−0.916304	−	0.529028i
$726$	−9.53089	−	1.51252i	−0.353724	−	0.0561347i
$727$	38.5219	+	22.2406i	1.42870	+	0.824859i	0.997018	−	0.0771674i	$-0.0245876\pi$
$727$	38.5219	+	22.2406i	1.42870	+	0.824859i	0.431680	+	0.902027i	$0.357921\pi$
$728$	−12.9725	−	6.33792i	−0.480795	−	0.234899i
$729$	−15.8303	−	21.8724i	−0.586308	−	0.810088i
$730$	1.45757	−	2.52459i	0.0539472	−	0.0934393i
$731$	29.4224			1.08823
$732$	−3.81202	+	4.70453i	−0.140896	+	0.173885i
$733$		−	45.2954i		−	1.67302i	−0.547949	−	0.836512i	$-0.684591\pi$
$733$		−	45.2954i		−	1.67302i	0.547949	−	0.836512i	$-0.315409\pi$
$734$	−7.57755	−	13.1247i	−0.279692	−	0.484442i
$735$	−15.3641	+	8.48341i	−0.566713	+	0.312915i
$736$	−16.5893	+	28.7335i	−0.611489	+	1.05913i
$737$	−0.487767	−	0.281612i	−0.0179671	−	0.0103733i
$738$	−7.87910	+	24.1993i	−0.290034	+	0.890789i
$739$	−10.3086	−	17.8550i	−0.379208	−	0.656808i	0.611739	−	0.791060i	$-0.290470\pi$
$739$	−10.3086	−	17.8550i	−0.379208	−	0.656808i	−0.990947	+	0.134252i	$0.957137\pi$
$740$	0.884684	+	1.53232i	0.0325216	+	0.0563291i
$741$	−11.7747	−	9.54090i	−0.432555	−	0.350494i
$742$	−0.151081	−	2.18160i	−0.00554634	−	0.0800890i
$743$	7.69885	−	4.44493i	0.282443	−	0.163069i	−0.352086	−	0.935968i	$-0.614527\pi$
$743$	7.69885	−	4.44493i	0.282443	−	0.163069i	0.634529	+	0.772899i	$0.281194\pi$
$744$	−11.4541	+	4.39281i	−0.419926	+	0.161048i
$745$			10.2472i			0.375429i
$746$	−9.55935	+	5.51909i	−0.349993	+	0.202068i
$747$	−20.5910	−	6.70427i	−0.753385	−	0.245296i
$748$		−	10.4349i		−	0.381538i
$749$	14.9673	−	1.03652i	0.546892	−	0.0378735i
$750$	−14.0572	−	2.23082i	−0.513295	−	0.0814580i
$751$	−25.0017			−0.912324			−0.456162	−	0.889897i	$-0.650776\pi$
$751$	−25.0017			−0.912324			−0.456162	+	0.889897i	$0.650776\pi$
$752$	1.36963	−	2.37227i	0.0499454	−	0.0865079i
$753$	0.560735	+	0.454357i	0.0204343	+	0.0165577i
$754$	−13.3037	+	7.68089i	−0.484492	+	0.279722i
$755$	−22.5555			−0.820878
$756$	−18.7701	−	8.00255i	−0.682664	−	0.291050i
$757$	−27.1262			−0.985919			−0.492959	−	0.870052i	$-0.664085\pi$
$757$	−27.1262			−0.985919			−0.492959	+	0.870052i	$0.664085\pi$
$758$	20.1282	−	11.6210i	0.731089	−	0.422094i
$759$	13.7523	+	11.1434i	0.499179	+	0.404478i
$760$	7.26616	−	12.5854i	0.263571	−	0.456519i
$761$	−3.16732			−0.114815			−0.0574075	−	0.998351i	$-0.518283\pi$
$761$	−3.16732			−0.114815			−0.0574075	+	0.998351i	$0.518283\pi$
$762$	1.08275	+	0.171828i	0.0392237	+	0.00622465i
$763$	28.5225	+	13.9350i	1.03258	+	0.504483i
$764$			10.9703i			0.396891i
$765$	−12.6079	+	11.3383i	−0.455839	+	0.409938i
$766$	−12.3361	+	7.12228i	−0.445723	+	0.257338i
$767$			21.3529i			0.771009i
$768$	18.0324	−	6.91569i	0.650687	−	0.249548i
$769$	2.48873	−	1.43687i	0.0897460	−	0.0518149i	−0.454455	−	0.890770i	$-0.650166\pi$
$769$	2.48873	−	1.43687i	0.0897460	−	0.0518149i	0.544201	+	0.838955i	$0.316833\pi$
$770$	−4.44973	−	2.17398i	−0.160357	−	0.0783446i
$771$	−28.4330	−	23.0389i	−1.02399	−	0.829725i
$772$	−9.66868	−	16.7467i	−0.347984	−	0.602725i
$773$	6.15679	+	10.6639i	0.221444	+	0.383553i	0.955247	−	0.295810i	$-0.0955895\pi$
$773$	6.15679	+	10.6639i	0.221444	+	0.383553i	−0.733802	+	0.679363i	$0.762256\pi$
$774$	15.8821	−	3.36576i	0.570871	−	0.120980i
$775$	7.12002	+	4.11075i	0.255759	+	0.147662i
$776$	19.4053	−	33.6110i	0.696610	−	1.20656i
$777$	−2.16764	+	3.08929i	−0.0777636	+	0.110828i
$778$	−1.83234	−	3.17371i	−0.0656926	−	0.113783i
$779$			47.3920i			1.69799i
$780$	5.10925	−	6.30548i	0.182940	−	0.225772i
$781$	−3.50988			−0.125594
$782$	−7.95765	+	13.7831i	−0.284565	+	0.492881i
$783$	−42.7682	+	27.7186i	−1.52841	+	0.990581i
$784$	−8.12174	+	1.13032i	−0.290062	+	0.0403685i
$785$	−2.61539	−	1.51000i	−0.0933473	−	0.0538941i
$786$	3.65415	+	0.579899i	0.130339	+	0.0206843i
$787$	−3.30450	−	1.90785i	−0.117793	−	0.0680076i	0.439946	−	0.898024i	$-0.354998\pi$
$787$	−3.30450	−	1.90785i	−0.117793	−	0.0680076i	−0.557739	+	0.830017i	$0.688331\pi$
$788$	−5.18056	−	2.99100i	−0.184550	−	0.106550i
$789$	24.2572	−	29.9365i	0.863577	−	1.06577i
$790$	−11.1923	−	6.46186i	−0.398203	−	0.229903i
$791$	8.41936	−	17.2329i	0.299358	−	0.612730i
$792$	−2.80218	−	13.2228i	−0.0995713	−	0.469851i
$793$	2.56834	−	4.44849i	0.0912044	−	0.157971i
$794$	9.56045			0.339288
$795$	2.84992	+	0.452271i	0.101076	+	0.0160404i
$796$			24.3530i			0.863171i
$797$	24.5682	+	42.5535i	0.870252	+	1.50732i	0.861736	+	0.507357i	$0.169377\pi$
$797$	24.5682	+	42.5535i	0.870252	+	1.50732i	0.00851609	+	0.999964i	$0.497289\pi$
$798$	13.1526	+	1.16363i	0.465596	+	0.0411920i
$799$	4.56524	−	7.90724i	0.161507	−	0.279738i
$800$	−14.7049	−	8.48988i	−0.519897	−	0.300162i
$801$	30.1805	+	9.82653i	1.06638	+	0.347203i
$802$	5.87742	+	10.1800i	0.207539	+	0.359468i
$803$	−2.52453	−	4.37261i	−0.0890886	−	0.154306i
$804$	−0.126038	+	0.794212i	−0.00444503	+	0.0280097i
$805$	−12.1429	−	18.0287i	−0.427982	−	0.635430i
$806$	3.83924	−	2.21659i	0.135231	−	0.0780759i
$807$	7.88163	−	49.6649i	0.277446	−	1.74829i
$808$			9.87437i			0.347379i
$809$	39.4929	−	22.8012i	1.38850	−	0.801648i	0.395350	−	0.918531i	$-0.370623\pi$
$809$	39.4929	−	22.8012i	1.38850	−	0.801648i	0.993146	+	0.116882i	$0.0372900\pi$
$810$	−5.50866	+	7.56265i	−0.193554	+	0.265725i
$811$		−	39.1391i		−	1.37436i	−0.726488	−	0.687180i	$-0.758849\pi$
$811$		−	39.1391i		−	1.37436i	0.726488	−	0.687180i	$-0.241151\pi$
$812$	−16.9076	+	34.6068i	−0.593341	+	1.21446i
$813$	14.9087	+	38.8739i	0.522872	+	1.36337i
$814$	−1.06492			−0.0373253
$815$	8.09155	−	14.0150i	0.283435	−	0.490923i
$816$	−7.39702	+	2.83687i	−0.258948	+	0.0993103i
$817$	26.1819	−	15.1161i	0.915988	−	0.528846i
$818$	−3.11476			−0.108905
$819$	16.7904	+	4.20914i	0.586704	+	0.147079i
$820$	−25.3789			−0.886269
$821$	10.2976	−	5.94530i	0.359387	−	0.207492i	−0.309425	−	0.950924i	$-0.600136\pi$
$821$	10.2976	−	5.94530i	0.359387	−	0.207492i	0.668812	+	0.743432i	$0.266803\pi$
$822$	−2.31978	+	14.6178i	−0.0809117	+	0.509853i
$823$	−1.51195	+	2.61877i	−0.0527031	+	0.0912844i	−0.891173	−	0.453663i	$-0.850117\pi$
$823$	−1.51195	+	2.61877i	−0.0527031	+	0.0912844i	0.838470	+	0.544947i	$0.183450\pi$
$824$	10.3975			0.362213
$825$	−5.70283	+	7.03803i	−0.198547	+	0.245033i
$826$	−10.3929	−	15.4304i	−0.361614	−	0.536891i
$827$			15.2436i			0.530071i	0.964239	+	0.265035i	$0.0853836\pi$
$827$			15.2436i			0.530071i	−0.964239	+	0.265035i	$0.914616\pi$
$828$	7.82405	−	24.0302i	0.271904	−	0.835107i
$829$	−29.7306	+	17.1649i	−1.03259	+	0.596163i	−0.917724	−	0.397218i	$-0.869976\pi$
$829$	−29.7306	+	17.1649i	−1.03259	+	0.596163i	−0.114861	+	0.993382i	$0.536642\pi$
$830$			7.50402i			0.260468i
$831$	10.8531	+	8.79411i	0.376489	+	0.305064i
$832$	−3.50424	+	2.02317i	−0.121488	+	0.0701409i
$833$	−27.0713	+	3.76756i	−0.937965	+	0.130538i
$834$	13.9665	−	5.35635i	0.483619	−	0.185475i
$835$	−1.39073	−	2.40882i	−0.0481283	−	0.0833606i
$836$	−5.36105	−	9.28561i	−0.185416	−	0.321150i
$837$	12.3422	−	7.99915i	0.426610	−	0.276491i
$838$	11.7088	+	6.76006i	0.404473	+	0.233522i
$839$	−6.16024	+	10.6698i	−0.212675	+	0.368364i	−0.952551	−	0.304379i	$-0.901551\pi$
$839$	−6.16024	+	10.6698i	−0.212675	+	0.368364i	0.739876	+	0.672744i	$0.234884\pi$
$840$	−1.46281	+	16.5342i	−0.0504716	+	0.570483i
$841$	33.6008	+	58.1983i	1.15865	+	2.00684i
$842$			1.31202i			0.0452153i
$843$	−8.65677	−	22.5722i	−0.298155	−	0.777426i
$844$	17.8354			0.613920
$845$	5.96672	−	10.3347i	0.205262	−	0.355523i
$846$	1.55976	−	4.79054i	0.0536257	−	0.164702i
$847$	17.0243	−	11.4664i	0.584961	−	0.393990i
$848$	1.16758	+	0.674104i	0.0400949	+	0.0231488i
$849$	9.63667	+	25.1272i	0.330730	+	0.862364i
$850$	−7.05374	−	4.07248i	−0.241941	−	0.139685i
$851$	−4.04786	−	2.33703i	−0.138759	−	0.0801124i
$852$	1.79446	+	4.67898i	0.0614772	+	0.160299i
$853$	−3.92537	−	2.26631i	−0.134402	−	0.0775971i	0.431291	−	0.902213i	$-0.358058\pi$
$853$	−3.92537	−	2.26631i	−0.134402	−	0.0775971i	−0.565693	+	0.824616i	$0.691391\pi$
$854$	0.309190	+	4.46470i	0.0105803	+	0.152779i
$855$	−5.39408	+	16.5670i	−0.184474	+	0.566579i
$856$	7.09472	−	12.2884i	0.242493	−	0.420010i
$857$	−32.2614			−1.10203			−0.551014	−	0.834496i	$-0.685759\pi$
$857$	−32.2614			−1.10203			−0.551014	+	0.834496i	$0.685759\pi$
$858$	1.74906	+	4.56060i	0.0597119	+	0.155696i
$859$			17.6335i			0.601647i	0.953680	+	0.300824i	$0.0972615\pi$
$859$			17.6335i			0.601647i	−0.953680	+	0.300824i	$0.902738\pi$
$860$	8.09483	+	14.0207i	0.276032	+	0.478101i
$861$	−22.8289	−	49.0816i	−0.778006	−	1.67270i
$862$	5.16329	−	8.94307i	0.175862	−	0.304602i
$863$	−26.4091	−	15.2473i	−0.898975	−	0.519023i	−0.0221074	−	0.999756i	$-0.507038\pi$
$863$	−26.4091	−	15.2473i	−0.898975	−	0.519023i	−0.876867	+	0.480732i	$0.840371\pi$
$864$	−25.4903	+	16.5206i	−0.867197	+	0.562041i
$865$	−11.0200	−	19.0873i	−0.374693	−	0.648987i
$866$	−0.797632	−	1.38154i	−0.0271046	−	0.0469466i
$867$	2.83668	−	1.08791i	0.0963388	−	0.0369474i
$868$	4.87927	−	9.98697i	0.165613	−	0.338980i
$869$	−19.3851	+	11.1920i	−0.657594	+	0.379662i
$870$	13.7216	+	11.1185i	0.465207	+	0.376951i
$871$		−	0.682180i		−	0.0231148i
$872$	26.0006	−	15.0115i	0.880492	−	0.508352i
$873$	−14.4057	+	44.2445i	−0.487557	+	1.49745i
$874$			16.3533i			0.553160i
$875$	25.1092	−	16.9119i	0.848846	−	0.571725i
$876$	−4.53838	+	5.60095i	−0.153338	+	0.189239i
$877$	8.80725			0.297400			0.148700	−	0.988882i	$-0.452491\pi$
$877$	8.80725			0.297400			0.148700	+	0.988882i	$0.452491\pi$
$878$	−3.60693	+	6.24738i	−0.121728	+	0.210839i
$879$	−3.65788	+	23.0496i	−0.123377	+	0.777444i
$880$	2.64417	−	1.52661i	0.0891348	−	0.0514620i
$881$	−38.6776			−1.30308			−0.651540	−	0.758614i	$-0.725877\pi$
$881$	−38.6776			−1.30308			−0.651540	+	0.758614i	$0.725877\pi$
$882$	−14.1820	+	5.13052i	−0.477533	+	0.172754i
$883$	37.4489			1.26026			0.630128	−	0.776491i	$-0.283002\pi$
$883$	37.4489			1.26026			0.630128	+	0.776491i	$0.283002\pi$
$884$	10.9455	−	6.31940i	0.368137	−	0.212544i
$885$	22.9207	−	8.79043i	0.770471	−	0.295487i
$886$	−4.98890	+	8.64103i	−0.167605	+	0.290301i
$887$	27.4050			0.920171			0.460086	−	0.887875i	$-0.347819\pi$
$887$	27.4050			0.920171			0.460086	+	0.887875i	$0.347819\pi$
$888$	1.27809	+	3.33256i	0.0428898	+	0.111833i
$889$	−1.93402	+	1.30263i	−0.0648650	+	0.0436887i
$890$		−	10.9987i		−	0.368679i
$891$	6.57318	+	14.8121i	0.220210	+	0.496223i
$892$	33.8305	−	19.5321i	1.13273	−	0.653982i
$893$		−	9.38179i		−	0.313950i
$894$	−1.38014	+	8.69676i	−0.0461589	+	0.290863i
$895$	0.433397	−	0.250222i	0.0144869	−	0.00836400i
$896$	−12.0313	+	24.6258i	−0.401937	+	0.822690i
$897$	−3.36019	+	21.1737i	−0.112194	+	0.706971i
$898$	−3.79299	−	6.56965i	−0.126574	−	0.219232i
$899$	−13.8811	−	24.0428i	−0.462962	−	0.801873i
$900$	12.2979	+	4.00411i	0.409931	+	0.133470i
$901$	3.89177	+	2.24691i	0.129654	+	0.0748556i
$902$	7.63729	−	13.2282i	0.254294	−	0.440450i
$903$	−19.8338	+	28.2669i	−0.660029	+	0.940665i
$904$	−9.06971	−	15.7092i	−0.301654	−	0.522480i
$905$		−	4.74305i		−	0.157664i
$906$	−19.1427	−	3.03788i	−0.635975	−	0.100927i
$907$	−23.6433			−0.785062			−0.392531	−	0.919739i	$-0.628400\pi$
$907$	−23.6433			−0.785062			−0.392531	+	0.919739i	$0.628400\pi$
$908$	−8.02097	+	13.8927i	−0.266185	+	0.461046i
$909$	−2.45433	−	11.5813i	−0.0814049	−	0.384128i
$910$	−0.414407	−	5.98403i	−0.0137375	−	0.198369i
$911$	−3.92249	−	2.26465i	−0.129958	−	0.0750313i	0.433612	−	0.901100i	$-0.357239\pi$
$911$	−3.92249	−	2.26465i	−0.129958	−	0.0750313i	−0.563570	+	0.826069i	$0.690572\pi$
$912$	−5.12485	+	6.32473i	−0.169701	+	0.209433i
$913$	11.2557	+	6.49851i	0.372511	+	0.215069i
$914$	3.18008	+	1.83602i	0.105188	+	0.0607301i
$915$	−5.83243	−	0.925585i	−0.192814	−	0.0305989i
$916$	12.4643	+	7.19626i	0.411832	+	0.237771i
$917$	−6.52711	+	4.39622i	−0.215544	+	0.145176i
$918$	−12.2274	+	7.92469i	−0.403563	+	0.261554i
$919$	16.9149	−	29.2975i	0.557971	−	0.966434i	−0.439695	−	0.898147i	$-0.644913\pi$
$919$	16.9149	−	29.2975i	0.557971	−	0.966434i	0.997666	−	0.0682866i	$-0.0217532\pi$
$920$	−20.5579			−0.677774
$921$	9.40808	−	11.6108i	0.310007	−	0.382589i
$922$		−	5.98508i		−	0.197108i
$923$	−2.12559	−	3.68164i	−0.0699648	−	0.121183i
$924$	10.0251	+	7.03423i	0.329801	+	0.231409i
$925$	1.19602	−	2.07157i	0.0393249	−	0.0681127i
$926$	−12.4568	−	7.19192i	−0.409355	−	0.236341i
$927$	−12.1948	+	2.58434i	−0.400531	+	0.0848809i
$928$	28.6685	+	49.6554i	0.941091	+	1.63002i
$929$	16.4582	+	28.5064i	0.539976	+	0.935266i	0.998905	+	0.0467929i	$0.0149001\pi$
$929$	16.4582	+	28.5064i	0.539976	+	0.935266i	−0.458928	+	0.888473i	$0.651767\pi$
$930$	−3.95985	−	3.20861i	−0.129849	−	0.105215i
$931$	−22.1541	+	17.2608i	−0.726071	+	0.565700i
$932$	2.86305	−	1.65298i	0.0937824	−	0.0541453i
$933$	−26.2698	+	10.0749i	−0.860033	+	0.329836i
$934$		−	14.9229i		−	0.488293i
$935$	8.81350	−	5.08848i	0.288232	−	0.166411i
$936$	12.1728	−	10.9470i	0.397881	−	0.357815i
$937$			38.1057i			1.24486i	0.782676	+	0.622430i	$0.213854\pi$
$937$			38.1057i			1.24486i	−0.782676	+	0.622430i	$0.786146\pi$
$938$	0.332030	+	0.492968i	0.0108412	+	0.0160960i
$939$	11.5929	+	1.83975i	0.378320	+	0.0600379i
$940$	5.02404			0.163866
$941$	−9.93855	+	17.2141i	−0.323987	+	0.561163i	−0.981307	−	0.192449i	$-0.938357\pi$
$941$	−9.93855	+	17.2141i	−0.323987	+	0.561163i	0.657319	+	0.753612i	$0.271690\pi$
$942$	−2.01630	−	1.63378i	−0.0656945	−	0.0532314i
$943$	58.0603	−	33.5211i	1.89070	−	1.09160i
$944$	11.4696			0.373304
$945$	−2.39398	−	19.7560i	−0.0778762	−	0.642662i
$946$	−9.74394			−0.316803
$947$	17.9696	−	10.3747i	0.583933	−	0.337134i	−0.178762	−	0.983892i	$-0.557209\pi$
$947$	17.9696	−	10.3747i	0.583933	−	0.337134i	0.762695	+	0.646759i	$0.223876\pi$
$948$	24.8307	+	20.1200i	0.806463	+	0.653467i
$949$	3.05772	−	5.29613i	0.0992578	−	0.171919i
$950$	−8.36914			−0.271531
$951$	37.5787	+	5.96359i	1.21857	+	0.193383i
$952$	−11.3474	+	23.2261i	−0.367773	+	0.752763i
$953$			12.8345i			0.415751i	0.978155	+	0.207876i	$0.0666549\pi$
$953$			12.8345i			0.415751i	−0.978155	+	0.207876i	$0.933345\pi$
$954$	2.35780	+	0.767680i	0.0763365	+	0.0248546i
$955$	−9.26571	+	5.34956i	−0.299831	+	0.173108i
$956$		−	27.3696i		−	0.885195i
$957$	28.5603	−	10.9533i	0.923222	−	0.354070i
$958$	19.9408	−	11.5128i	0.644258	−	0.371962i
$959$	−17.5863	−	26.1105i	−0.567891	−	0.843153i
$960$	3.61433	+	2.92864i	0.116652	+	0.0945215i
$961$	−11.4941	−	19.9084i	−0.370778	−	0.642207i
$962$	−0.644915	−	1.11703i	−0.0207929	−	0.0360143i
$963$	−5.26682	+	16.1761i	−0.169721	+	0.521268i
$964$	8.31878	+	4.80285i	0.267930	+	0.154689i
$965$	9.42969	−	16.3327i	0.303552	−	0.525768i
$966$	−7.87746	−	16.9364i	−0.253453	−	0.544919i
$967$	−17.8941	−	30.9936i	−0.575437	−	0.996685i	−0.995994	−	0.0894195i	$-0.971499\pi$
$967$	−17.8941	−	30.9936i	−0.575437	−	0.996685i	0.420557	−	0.907266i	$-0.361835\pi$
$968$		−	19.4125i		−	0.623941i
$969$	−17.0821	+	21.0815i	−0.548756	+	0.677236i
$970$	16.1241			0.517714
$971$	14.5129	−	25.1370i	0.465740	−	0.806686i	−0.533494	−	0.845804i	$-0.679121\pi$
$971$	14.5129	−	25.1370i	0.465740	−	0.806686i	0.999235	+	0.0391177i	$0.0124547\pi$
$972$	16.3852	−	16.3354i	0.525554	−	0.523959i
$973$	−13.9665	+	28.5868i	−0.447744	+	0.916450i
$974$	−14.7247	−	8.50130i	−0.471809	−	0.272399i
$975$	−10.8361	−	1.71964i	−0.347032	−	0.0550726i
$976$	−2.38949	−	1.37957i	−0.0764856	−	0.0441590i
$977$	7.73439	+	4.46545i	0.247445	+	0.142862i	0.618594	−	0.785711i	$-0.287703\pi$
$977$	7.73439	+	4.46545i	0.247445	+	0.142862i	−0.371149	+	0.928573i	$0.621036\pi$
$978$	8.75487	−	10.8046i	0.279950	−	0.345494i
$979$	−16.4977	−	9.52495i	−0.527268	−	0.304419i
$980$	−9.24334	−	11.8637i	−0.295268	−	0.378973i
$981$	−26.7641	+	24.0690i	−0.854512	+	0.768466i
$982$	−6.41288	+	11.1074i	−0.204643	+	0.354452i
$983$	−52.2693			−1.66713			−0.833566	−	0.552420i	$-0.813704\pi$
$983$	−52.2693			−1.66713			−0.833566	+	0.552420i	$0.813704\pi$
$984$	−50.5625	−	8.02407i	−1.61187	−	0.255798i
$985$		−	5.83413i		−	0.185891i
$986$	13.7519	+	23.8190i	0.437950	+	0.758552i
$987$	4.51924	+	9.71627i	0.143849	+	0.309272i
$988$	6.49333	−	11.2468i	0.206580	−	0.357807i
$989$	−37.0378	−	21.3838i	−1.17773	−	0.679964i
$990$	4.17541	−	3.75496i	0.132703	−	0.119340i
$991$	−21.9151	−	37.9581i	−0.696158	−	1.20578i	−0.969789	−	0.243946i	$-0.921558\pi$
$991$	−21.9151	−	37.9581i	−0.696158	−	1.20578i	0.273631	−	0.961835i	$-0.411775\pi$
$992$	−8.27329	−	14.3298i	−0.262677	−	0.454970i
$993$	−3.96447	+	24.9815i	−0.125809	+	0.792764i
$994$	3.32795	+	1.62592i	0.105556	+	0.0515710i
$995$	−20.5690	+	11.8755i	−0.652082	+	0.376480i
$996$	2.90847	−	18.3273i	0.0921585	−	0.580723i
$997$			44.9975i			1.42508i	0.701630	+	0.712542i	$0.252456\pi$
$997$			44.9975i			1.42508i	−0.701630	+	0.712542i	$0.747544\pi$
$998$	14.3797	−	8.30215i	0.455183	−	0.262800i
$999$	−2.32735	−	3.59097i	−0.0736341	−	0.113613i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.2.s.b.47.2	yes	10
3.2	odd	2		189.2.s.b.89.4		10
4.3	odd	2		1008.2.df.b.929.2		10
7.2	even	3		441.2.o.c.146.4		10
7.3	odd	6		63.2.i.b.38.2	yes	10
7.4	even	3		441.2.i.b.227.2		10
7.5	odd	6		441.2.o.d.146.4		10
7.6	odd	2		441.2.s.b.362.2		10
9.2	odd	6		567.2.p.d.404.2		10
9.4	even	3		189.2.i.b.152.2		10
9.5	odd	6		63.2.i.b.5.4	✓	10
9.7	even	3		567.2.p.c.404.4		10
12.11	even	2		3024.2.df.b.1601.4		10
21.2	odd	6		1323.2.o.d.440.2		10
21.5	even	6		1323.2.o.c.440.2		10
21.11	odd	6		1323.2.i.b.521.4		10
21.17	even	6		189.2.i.b.143.4		10
21.20	even	2		1323.2.s.b.656.4		10
28.3	even	6		1008.2.ca.b.353.3		10
36.23	even	6		1008.2.ca.b.257.3		10
36.31	odd	6		3024.2.ca.b.2609.4		10
63.4	even	3		1323.2.s.b.962.4		10
63.5	even	6		441.2.o.c.293.4		10
63.13	odd	6		1323.2.i.b.1097.2		10
63.23	odd	6		441.2.o.d.293.4		10
63.31	odd	6		189.2.s.b.17.4		10
63.32	odd	6		441.2.s.b.374.2		10
63.38	even	6		567.2.p.c.80.4		10
63.40	odd	6		1323.2.o.d.881.2		10
63.41	even	6		441.2.i.b.68.4		10
63.52	odd	6		567.2.p.d.80.2		10
63.58	even	3		1323.2.o.c.881.2		10
63.59	even	6	inner	63.2.s.b.59.2	yes	10
84.59	odd	6		3024.2.ca.b.2033.4		10
252.31	even	6		3024.2.df.b.17.4		10
252.59	odd	6		1008.2.df.b.689.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.4	✓	10	9.5	odd	6
63.2.i.b.38.2	yes	10	7.3	odd	6
63.2.s.b.47.2	yes	10	1.1	even	1	trivial
63.2.s.b.59.2	yes	10	63.59	even	6	inner
189.2.i.b.143.4		10	21.17	even	6
189.2.i.b.152.2		10	9.4	even	3
189.2.s.b.17.4		10	63.31	odd	6
189.2.s.b.89.4		10	3.2	odd	2
441.2.i.b.68.4		10	63.41	even	6
441.2.i.b.227.2		10	7.4	even	3
441.2.o.c.146.4		10	7.2	even	3
441.2.o.c.293.4		10	63.5	even	6
441.2.o.d.146.4		10	7.5	odd	6
441.2.o.d.293.4		10	63.23	odd	6
441.2.s.b.362.2		10	7.6	odd	2
441.2.s.b.374.2		10	63.32	odd	6
567.2.p.c.80.4		10	63.38	even	6
567.2.p.c.404.4		10	9.7	even	3
567.2.p.d.80.2		10	63.52	odd	6
567.2.p.d.404.2		10	9.2	odd	6
1008.2.ca.b.257.3		10	36.23	even	6
1008.2.ca.b.353.3		10	28.3	even	6
1008.2.df.b.689.2		10	252.59	odd	6
1008.2.df.b.929.2		10	4.3	odd	2
1323.2.i.b.521.4		10	21.11	odd	6
1323.2.i.b.1097.2		10	63.13	odd	6
1323.2.o.c.440.2		10	21.5	even	6
1323.2.o.c.881.2		10	63.58	even	3
1323.2.o.d.440.2		10	21.2	odd	6
1323.2.o.d.881.2		10	63.40	odd	6
1323.2.s.b.656.4		10	21.20	even	2
1323.2.s.b.962.4		10	63.4	even	3
3024.2.ca.b.2033.4		10	84.59	odd	6
3024.2.ca.b.2609.4		10	36.31	odd	6
3024.2.df.b.17.4		10	252.31	even	6
3024.2.df.b.1601.4		10	12.11	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.621951 + 0.359083i) q^{2} +(1.34572 + 1.09042i) q^{3} +(-0.742118 + 1.28539i) q^{4} -1.44755 q^{5} +(-1.22853 - 0.194963i) q^{6} +(2.19442 - 1.47801i) q^{7} -2.50226i q^{8} +(0.621951 + 2.93482i) q^{9} +O(q^{10})\)	\(q+(-0.621951 + 0.359083i) q^{2} +(1.34572 + 1.09042i) q^{3} +(-0.742118 + 1.28539i) q^{4} -1.44755 q^{5} +(-1.22853 - 0.194963i) q^{6} +(2.19442 - 1.47801i) q^{7} -2.50226i q^{8} +(0.621951 + 2.93482i) q^{9} +(0.900304 - 0.519791i) q^{10} -1.80056i q^{11} +(-2.40030 + 0.920553i) q^{12} +(1.88867 - 1.09042i) q^{13} +(-0.834091 + 1.70723i) q^{14} +(-1.94800 - 1.57844i) q^{15} +(-0.585716 - 1.01449i) q^{16} +(-1.95230 - 3.38149i) q^{17} +(-1.44067 - 1.60198i) q^{18} +(-3.47456 - 2.00604i) q^{19} +(1.07425 - 1.86066i) q^{20} +(4.56475 + 0.403850i) q^{21} +(0.646552 + 1.11986i) q^{22} +5.67561i q^{23} +(2.72853 - 3.36736i) q^{24} -2.90460 q^{25} +(-0.783106 + 1.35638i) q^{26} +(-2.36323 + 4.62765i) q^{27} +(0.271298 + 3.91754i) q^{28} +(8.49418 + 4.90412i) q^{29} +(1.77835 + 0.282218i) q^{30} +(-2.45129 - 1.41525i) q^{31} +(5.06262 + 2.92290i) q^{32} +(1.96338 - 2.42306i) q^{33} +(2.42847 + 1.40208i) q^{34} +(-3.17653 + 2.13949i) q^{35} +(-4.23394 - 1.37854i) q^{36} +(-0.411767 + 0.713202i) q^{37} +2.88134 q^{38} +(3.73065 + 0.592040i) q^{39} +3.62215i q^{40} +(-5.90617 - 10.2298i) q^{41} +(-2.98406 + 1.38795i) q^{42} +(-3.76766 + 6.52578i) q^{43} +(2.31442 + 1.33623i) q^{44} +(-0.900304 - 4.24830i) q^{45} +(-2.03802 - 3.52995i) q^{46} +(1.16920 + 2.02511i) q^{47} +(0.318012 - 2.00390i) q^{48} +(2.63096 - 6.48676i) q^{49} +(1.80652 - 1.04299i) q^{50} +(1.05999 - 6.67939i) q^{51} +3.23689i q^{52} +(-0.996713 + 0.575453i) q^{53} +(-0.191903 - 3.72677i) q^{54} +2.60640i q^{55} +(-3.69838 - 5.49102i) q^{56} +(-2.48837 - 6.48831i) q^{57} -7.04395 q^{58} +(-4.89555 + 8.47934i) q^{59} +(3.47456 - 1.33255i) q^{60} +(2.03980 - 1.17768i) q^{61} +2.03277 q^{62} +(5.70252 + 5.52098i) q^{63} -1.85540 q^{64} +(-2.73394 + 1.57844i) q^{65} +(-0.351042 + 2.21204i) q^{66} +(0.156402 - 0.270897i) q^{67} +5.79536 q^{68} +(-6.18882 + 7.63781i) q^{69} +(1.20739 - 2.47130i) q^{70} -1.94933i q^{71} +(7.34369 - 1.55628i) q^{72} +(2.42847 - 1.40208i) q^{73} -0.591435i q^{74} +(-3.90880 - 3.16725i) q^{75} +(5.15706 - 2.97743i) q^{76} +(-2.66125 - 3.95119i) q^{77} +(-2.53287 + 0.971396i) q^{78} +(-6.21583 - 10.7661i) q^{79} +(0.847852 + 1.46852i) q^{80} +(-8.22635 + 3.65063i) q^{81} +(7.34669 + 4.24162i) q^{82} +(-3.60916 + 6.25124i) q^{83} +(-3.90669 + 5.56776i) q^{84} +(2.82605 + 4.89486i) q^{85} -5.41161i q^{86} +(6.08326 + 15.8619i) q^{87} -4.50548 q^{88} +(5.28999 - 9.16253i) q^{89} +(2.08544 + 2.31895i) q^{90} +(2.53287 - 5.18433i) q^{91} +(-7.29536 - 4.21198i) q^{92} +(-1.75553 - 4.57748i) q^{93} +(-1.45436 - 0.839677i) q^{94} +(5.02959 + 2.90383i) q^{95} +(3.62569 + 9.45383i) q^{96} +(13.4322 + 7.75510i) q^{97} +(0.692961 + 4.97918i) q^{98} +(5.28433 - 1.11986i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4} - 12 q^{6} + 3 q^{7}+O(q^{10}) \) 10 * q + 4 * q^4 - 12 * q^6 + 3 * q^7	\( 10 q + 4 q^{4} - 12 q^{6} + 3 q^{7} - 15 q^{10} + 6 q^{13} - 6 q^{14} - 3 q^{15} - 6 q^{16} - 12 q^{17} - 18 q^{18} + 3 q^{19} - 3 q^{20} + 18 q^{21} + 5 q^{22} + 27 q^{24} - 14 q^{25} + 3 q^{26} + 27 q^{27} + 2 q^{28} - 15 q^{29} - 9 q^{31} + 48 q^{32} - 9 q^{33} + 3 q^{34} - 15 q^{35} - 18 q^{36} + 6 q^{37} + 36 q^{38} + 12 q^{39} - 9 q^{41} - 6 q^{42} + 3 q^{43} + 24 q^{44} + 15 q^{45} - 13 q^{46} + 15 q^{47} - 15 q^{48} - 23 q^{49} + 3 q^{50} - 24 q^{51} - 9 q^{53} + 27 q^{54} - 51 q^{56} - 36 q^{57} - 16 q^{58} - 18 q^{59} - 3 q^{60} + 12 q^{61} + 12 q^{62} + 9 q^{63} + 6 q^{64} - 3 q^{65} - 33 q^{66} - 10 q^{67} - 54 q^{68} - 3 q^{69} + 9 q^{70} + 18 q^{72} + 3 q^{73} - 21 q^{75} + 9 q^{76} + 45 q^{77} + 24 q^{78} + 20 q^{79} - 30 q^{80} - 48 q^{81} + 9 q^{82} - 15 q^{83} + 60 q^{84} + 18 q^{85} + 30 q^{87} + 16 q^{88} + 24 q^{89} + 24 q^{90} - 24 q^{91} + 39 q^{92} + 6 q^{93} - 3 q^{94} + 3 q^{96} + 6 q^{97} + 45 q^{98} + 21 q^{99}+O(q^{100}) \) 10 * q + 4 * q^4 - 12 * q^6 + 3 * q^7 - 15 * q^10 + 6 * q^13 - 6 * q^14 - 3 * q^15 - 6 * q^16 - 12 * q^17 - 18 * q^18 + 3 * q^19 - 3 * q^20 + 18 * q^21 + 5 * q^22 + 27 * q^24 - 14 * q^25 + 3 * q^26 + 27 * q^27 + 2 * q^28 - 15 * q^29 - 9 * q^31 + 48 * q^32 - 9 * q^33 + 3 * q^34 - 15 * q^35 - 18 * q^36 + 6 * q^37 + 36 * q^38 + 12 * q^39 - 9 * q^41 - 6 * q^42 + 3 * q^43 + 24 * q^44 + 15 * q^45 - 13 * q^46 + 15 * q^47 - 15 * q^48 - 23 * q^49 + 3 * q^50 - 24 * q^51 - 9 * q^53 + 27 * q^54 - 51 * q^56 - 36 * q^57 - 16 * q^58 - 18 * q^59 - 3 * q^60 + 12 * q^61 + 12 * q^62 + 9 * q^63 + 6 * q^64 - 3 * q^65 - 33 * q^66 - 10 * q^67 - 54 * q^68 - 3 * q^69 + 9 * q^70 + 18 * q^72 + 3 * q^73 - 21 * q^75 + 9 * q^76 + 45 * q^77 + 24 * q^78 + 20 * q^79 - 30 * q^80 - 48 * q^81 + 9 * q^82 - 15 * q^83 + 60 * q^84 + 18 * q^85 + 30 * q^87 + 16 * q^88 + 24 * q^89 + 24 * q^90 - 24 * q^91 + 39 * q^92 + 6 * q^93 - 3 * q^94 + 3 * q^96 + 6 * q^97 + 45 * q^98 + 21 * q^99

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