LMFDB - Embedded newform 429.2.s.a.199.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(166,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("429.166");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.12
Character	$\chi$	$=$	429.199
Dual form			429.2.s.a.166.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.17798 + 1.25745i) q^{2} +(0.500000 - 0.866025i) q^{3} +(2.16238 + 3.74536i) q^{4} +2.19769i q^{5} +(2.17798 - 1.25745i) q^{6} +(-0.966057 + 0.557753i) q^{7} +5.84658i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(2.17798 + 1.25745i) q^{2} +(0.500000 - 0.866025i) q^{3} +(2.16238 + 3.74536i) q^{4} +2.19769i q^{5} +(2.17798 - 1.25745i) q^{6} +(-0.966057 + 0.557753i) q^{7} +5.84658i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.76349 + 4.78651i) q^{10} +(-0.866025 - 0.500000i) q^{11} +4.32477 q^{12} +(0.632462 - 3.54965i) q^{13} -2.80540 q^{14} +(1.90325 + 1.09884i) q^{15} +(-3.02704 + 5.24299i) q^{16} +(-0.814810 - 1.41129i) q^{17} -2.51491i q^{18} +(1.33197 - 0.769014i) q^{19} +(-8.23113 + 4.75225i) q^{20} +1.11551i q^{21} +(-1.25745 - 2.17798i) q^{22} +(-0.716364 + 1.24078i) q^{23} +(5.06329 + 2.92329i) q^{24} +0.170164 q^{25} +(5.84101 - 6.93575i) q^{26} -1.00000 q^{27} +(-4.17797 - 2.41215i) q^{28} +(1.52868 - 2.64776i) q^{29} +(2.76349 + 4.78651i) q^{30} -5.05265i q^{31} +(-3.05906 + 1.76615i) q^{32} +(-0.866025 + 0.500000i) q^{33} -4.09834i q^{34} +(-1.22577 - 2.12309i) q^{35} +(2.16238 - 3.74536i) q^{36} +(2.85446 + 1.64803i) q^{37} +3.86800 q^{38} +(-2.75785 - 2.32255i) q^{39} -12.8490 q^{40} +(3.07989 + 1.77818i) q^{41} +(-1.40270 + 2.42955i) q^{42} +(0.848380 + 1.46944i) q^{43} -4.32477i q^{44} +(1.90325 - 1.09884i) q^{45} +(-3.12044 + 1.80159i) q^{46} +4.92754i q^{47} +(3.02704 + 5.24299i) q^{48} +(-2.87782 + 4.98453i) q^{49} +(0.370614 + 0.213974i) q^{50} -1.62962 q^{51} +(14.6623 - 5.30690i) q^{52} -13.6569 q^{53} +(-2.17798 - 1.25745i) q^{54} +(1.09884 - 1.90325i) q^{55} +(-3.26095 - 5.64813i) q^{56} -1.53803i q^{57} +(6.65887 - 3.84450i) q^{58} +(-4.58684 + 2.64821i) q^{59} +9.50449i q^{60} +(-3.21066 - 5.56102i) q^{61} +(6.35347 - 11.0045i) q^{62} +(0.966057 + 0.557753i) q^{63} +3.22474 q^{64} +(7.80102 + 1.38995i) q^{65} -2.51491 q^{66} +(-6.63362 - 3.82992i) q^{67} +(3.52386 - 6.10351i) q^{68} +(0.716364 + 1.24078i) q^{69} -6.16539i q^{70} +(0.858690 - 0.495765i) q^{71} +(5.06329 - 2.92329i) q^{72} -15.4089i q^{73} +(4.14463 + 7.17872i) q^{74} +(0.0850822 - 0.147367i) q^{75} +(5.76047 + 3.32581i) q^{76} +1.11551 q^{77} +(-3.08603 - 8.52633i) q^{78} -12.4731 q^{79} +(-11.5225 - 6.65249i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.47195 + 7.74565i) q^{82} +13.3536i q^{83} +(-4.17797 + 2.41215i) q^{84} +(3.10158 - 1.79070i) q^{85} +4.26720i q^{86} +(-1.52868 - 2.64776i) q^{87} +(2.92329 - 5.06329i) q^{88} +(-3.97646 - 2.29581i) q^{89} +5.52699 q^{90} +(1.36883 + 3.78192i) q^{91} -6.19621 q^{92} +(-4.37572 - 2.52632i) q^{93} +(-6.19616 + 10.7321i) q^{94} +(1.69005 + 2.92726i) q^{95} +3.53230i q^{96} +(16.1448 - 9.32119i) q^{97} +(-12.5356 + 7.23746i) q^{98} +1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9	$ 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9} + 28 q^{12} - 4 q^{13} + 20 q^{14} - 6 q^{15} - 14 q^{16} + 10 q^{17} - 18 q^{20} + 2 q^{22} - 14 q^{23} + 4 q^{25} - 34 q^{26} - 24 q^{27} - 30 q^{28} + 4 q^{29} + 30 q^{32} + 6 q^{35} + 14 q^{36} + 12 q^{38} - 2 q^{39} + 20 q^{40} - 30 q^{41} + 10 q^{42} - 4 q^{43} - 6 q^{45} - 24 q^{46} + 14 q^{48} + 18 q^{49} - 84 q^{50} + 20 q^{51} + 40 q^{52} - 56 q^{53} - 4 q^{55} + 26 q^{56} + 48 q^{58} + 60 q^{59} - 2 q^{61} + 18 q^{62} - 6 q^{63} - 48 q^{64} - 10 q^{65} + 4 q^{66} - 42 q^{67} - 18 q^{68} + 14 q^{69} + 6 q^{71} + 2 q^{75} - 48 q^{76} + 24 q^{77} - 26 q^{78} - 20 q^{79} + 30 q^{80} - 12 q^{81} - 10 q^{82} - 30 q^{84} + 6 q^{85} - 4 q^{87} - 12 q^{88} + 12 q^{89} + 18 q^{91} + 8 q^{92} + 12 q^{93} - 22 q^{94} + 4 q^{95} + 6 q^{97} - 114 q^{98}+O(q^{100}) $ 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9 + 28 * q^12 - 4 * q^13 + 20 * q^14 - 6 * q^15 - 14 * q^16 + 10 * q^17 - 18 * q^20 + 2 * q^22 - 14 * q^23 + 4 * q^25 - 34 * q^26 - 24 * q^27 - 30 * q^28 + 4 * q^29 + 30 * q^32 + 6 * q^35 + 14 * q^36 + 12 * q^38 - 2 * q^39 + 20 * q^40 - 30 * q^41 + 10 * q^42 - 4 * q^43 - 6 * q^45 - 24 * q^46 + 14 * q^48 + 18 * q^49 - 84 * q^50 + 20 * q^51 + 40 * q^52 - 56 * q^53 - 4 * q^55 + 26 * q^56 + 48 * q^58 + 60 * q^59 - 2 * q^61 + 18 * q^62 - 6 * q^63 - 48 * q^64 - 10 * q^65 + 4 * q^66 - 42 * q^67 - 18 * q^68 + 14 * q^69 + 6 * q^71 + 2 * q^75 - 48 * q^76 + 24 * q^77 - 26 * q^78 - 20 * q^79 + 30 * q^80 - 12 * q^81 - 10 * q^82 - 30 * q^84 + 6 * q^85 - 4 * q^87 - 12 * q^88 + 12 * q^89 + 18 * q^91 + 8 * q^92 + 12 * q^93 - 22 * q^94 + 4 * q^95 + 6 * q^97 - 114 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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 $

$2$	2.17798	+	1.25745i	1.54006	+	0.889155i	0.998834	+	0.0482782i	$0.0153734\pi$
$2$	2.17798	+	1.25745i	1.54006	+	0.889155i	0.541227	+	0.840876i	$0.317960\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	2.16238	+	3.74536i	1.08119	+	1.87268i
$5$			2.19769i			0.982836i	0.870924	+	0.491418i	$0.163521\pi$
$5$			2.19769i			0.982836i	−0.870924	+	0.491418i	$0.836479\pi$
$6$	2.17798	−	1.25745i	0.889155	−	0.513354i
$7$	−0.966057	+	0.557753i	−0.365135	+	0.210811i	−0.671331	−	0.741158i	$-0.734277\pi$
$7$	−0.966057	+	0.557753i	−0.365135	+	0.210811i	0.306196	+	0.951969i	$0.400944\pi$
$8$			5.84658i			2.06708i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−2.76349	+	4.78651i	−0.873893	+	1.51363i
$11$	−0.866025	−	0.500000i	−0.261116	−	0.150756i
$11$	−0.866025	−	0.500000i	−0.261116	−	0.150756i
$12$	4.32477			1.24845
$13$	0.632462	−	3.54965i	0.175413	−	0.984495i
$13$	0.632462	−	3.54965i	0.175413	−	0.984495i
$14$	−2.80540			−0.749774
$15$	1.90325	+	1.09884i	0.491418	+	0.283720i
$16$	−3.02704	+	5.24299i	−0.756760	+	1.31075i
$17$	−0.814810	−	1.41129i	−0.197620	−	0.342288i	0.750136	−	0.661284i	$-0.229988\pi$
$17$	−0.814810	−	1.41129i	−0.197620	−	0.342288i	−0.947756	+	0.318995i	$0.896655\pi$
$18$		−	2.51491i		−	0.592770i
$19$	1.33197	−	0.769014i	0.305575	−	0.176424i	−0.339370	−	0.940653i	$-0.610214\pi$
$19$	1.33197	−	0.769014i	0.305575	−	0.176424i	0.644945	+	0.764229i	$0.276880\pi$
$20$	−8.23113	+	4.75225i	−1.84054	+	1.06263i
$21$			1.11551i			0.243424i
$22$	−1.25745	−	2.17798i	−0.268090	−	0.464346i
$23$	−0.716364	+	1.24078i	−0.149372	+	0.258720i	−0.930996	−	0.365030i	$-0.881059\pi$
$23$	−0.716364	+	1.24078i	−0.149372	+	0.258720i	0.781623	+	0.623751i	$0.214392\pi$
$24$	5.06329	+	2.92329i	1.03354	+	0.596714i
$25$	0.170164			0.0340329
$26$	5.84101	−	6.93575i	1.14552	−	1.36021i
$27$	−1.00000			−0.192450
$28$	−4.17797	−	2.41215i	−0.789563	−	0.455854i
$29$	1.52868	−	2.64776i	0.283869	−	0.491676i	−0.688465	−	0.725270i	$-0.741715\pi$
$29$	1.52868	−	2.64776i	0.283869	−	0.491676i	0.972334	+	0.233593i	$0.0750484\pi$
$30$	2.76349	+	4.78651i	0.504543	+	0.873893i
$31$		−	5.05265i		−	0.907482i	−0.891134	−	0.453741i	$-0.850089\pi$
$31$		−	5.05265i		−	0.907482i	0.891134	−	0.453741i	$-0.149911\pi$
$32$	−3.05906	+	1.76615i	−0.540771	+	0.312214i
$33$	−0.866025	+	0.500000i	−0.150756	+	0.0870388i
$34$		−	4.09834i		−	0.702860i
$35$	−1.22577	−	2.12309i	−0.207193	−	0.358868i
$36$	2.16238	−	3.74536i	0.360397	−	0.624226i
$37$	2.85446	+	1.64803i	0.469271	+	0.270934i	0.715935	−	0.698167i	$-0.246001\pi$
$37$	2.85446	+	1.64803i	0.469271	+	0.270934i	−0.246663	+	0.969101i	$0.579334\pi$
$38$	3.86800			0.627473
$39$	−2.75785	−	2.32255i	−0.441610	−	0.371906i
$40$	−12.8490			−2.03160
$41$	3.07989	+	1.77818i	0.480999	+	0.277705i	0.720833	−	0.693109i	$-0.243760\pi$
$41$	3.07989	+	1.77818i	0.480999	+	0.277705i	−0.239834	+	0.970814i	$0.577093\pi$
$42$	−1.40270	+	2.42955i	−0.216441	+	0.374887i
$43$	0.848380	+	1.46944i	0.129377	+	0.224087i	0.923435	−	0.383754i	$-0.125369\pi$
$43$	0.848380	+	1.46944i	0.129377	+	0.224087i	−0.794058	+	0.607841i	$0.792036\pi$
$44$		−	4.32477i		−	0.651983i
$45$	1.90325	−	1.09884i	0.283720	−	0.163806i
$46$	−3.12044	+	1.80159i	−0.460084	+	0.265630i
$47$			4.92754i			0.718756i	0.933192	+	0.359378i	$0.117011\pi$
$47$			4.92754i			0.718756i	−0.933192	+	0.359378i	$0.882989\pi$
$48$	3.02704	+	5.24299i	0.436916	+	0.756760i
$49$	−2.87782	+	4.98453i	−0.411117	+	0.712076i
$50$	0.370614	+	0.213974i	0.0524127	+	0.0302605i
$51$	−1.62962			−0.228192
$52$	14.6623	−	5.30690i	2.03330	−	0.735935i
$53$	−13.6569			−1.87591			−0.937957	−	0.346750i	$-0.887285\pi$
$53$	−13.6569			−1.87591			−0.937957	+	0.346750i	$0.887285\pi$
$54$	−2.17798	−	1.25745i	−0.296385	−	0.171118i
$55$	1.09884	−	1.90325i	0.148168	−	0.256635i
$56$	−3.26095	−	5.64813i	−0.435763	−	0.754763i
$57$		−	1.53803i		−	0.203717i
$58$	6.65887	−	3.84450i	0.874353	−	0.504808i
$59$	−4.58684	+	2.64821i	−0.597156	+	0.344768i	−0.767922	−	0.640544i	$-0.778709\pi$
$59$	−4.58684	+	2.64821i	−0.597156	+	0.344768i	0.170766	+	0.985312i	$0.445376\pi$
$60$			9.50449i			1.22702i
$61$	−3.21066	−	5.56102i	−0.411082	−	0.712016i	0.583926	−	0.811807i	$-0.301516\pi$
$61$	−3.21066	−	5.56102i	−0.411082	−	0.712016i	−0.995008	+	0.0997913i	$0.968182\pi$
$62$	6.35347	−	11.0045i	0.806892	−	1.39758i
$63$	0.966057	+	0.557753i	0.121712	+	0.0702703i
$64$	3.22474			0.403093
$65$	7.80102	+	1.38995i	0.967597	+	0.172403i
$66$	−2.51491			−0.309564
$67$	−6.63362	−	3.82992i	−0.810425	−	0.467899i	0.0366781	−	0.999327i	$-0.488322\pi$
$67$	−6.63362	−	3.82992i	−0.810425	−	0.467899i	−0.847104	+	0.531428i	$0.821656\pi$
$68$	3.52386	−	6.10351i	0.427331	−	0.740159i
$69$	0.716364	+	1.24078i	0.0862401	+	0.149372i
$70$		−	6.16539i		−	0.736905i
$71$	0.858690	−	0.495765i	0.101908	−	0.0588365i	−0.448180	−	0.893943i	$-0.647928\pi$
$71$	0.858690	−	0.495765i	0.101908	−	0.0588365i	0.550088	+	0.835107i	$0.314594\pi$
$72$	5.06329	−	2.92329i	0.596714	−	0.344513i
$73$		−	15.4089i		−	1.80348i	−0.432283	−	0.901738i	$-0.642292\pi$
$73$		−	15.4089i		−	1.80348i	0.432283	−	0.901738i	$-0.357708\pi$
$74$	4.14463	+	7.17872i	0.481804	+	0.834509i
$75$	0.0850822	−	0.147367i	0.00982444	−	0.0170164i
$76$	5.76047	+	3.32581i	0.660771	+	0.381496i
$77$	1.11551			0.127124
$78$	−3.08603	−	8.52633i	−0.349425	−	0.965417i
$79$	−12.4731			−1.40334			−0.701668	−	0.712504i	$-0.747561\pi$
$79$	−12.4731			−1.40334			−0.701668	+	0.712504i	$0.747561\pi$
$80$	−11.5225	−	6.65249i	−1.28825	−	0.743771i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.47195	+	7.74565i	0.493845	+	0.855364i
$83$			13.3536i			1.46575i	0.680366	+	0.732873i	$0.261821\pi$
$83$			13.3536i			1.46575i	−0.680366	+	0.732873i	$0.738179\pi$
$84$	−4.17797	+	2.41215i	−0.455854	+	0.263188i
$85$	3.10158	−	1.79070i	0.336414	−	0.194228i
$86$			4.26720i			0.460144i
$87$	−1.52868	−	2.64776i	−0.163892	−	0.283869i
$88$	2.92329	−	5.06329i	0.311624	−	0.539748i
$89$	−3.97646	−	2.29581i	−0.421504	−	0.243355i	0.274217	−	0.961668i	$-0.411581\pi$
$89$	−3.97646	−	2.29581i	−0.421504	−	0.243355i	−0.695720	+	0.718313i	$0.744915\pi$
$90$	5.52699			0.582596
$91$	1.36883	+	3.78192i	0.143493	+	0.396453i
$92$	−6.19621			−0.646000
$93$	−4.37572	−	2.52632i	−0.453741	−	0.261968i
$94$	−6.19616	+	10.7321i	−0.639085	+	1.10693i
$95$	1.69005	+	2.92726i	0.173396	+	0.300330i
$96$			3.53230i			0.360514i
$97$	16.1448	−	9.32119i	1.63925	−	0.946423i	0.658162	−	0.752876i	$-0.271334\pi$
$97$	16.1448	−	9.32119i	1.63925	−	0.946423i	0.981091	−	0.193547i	$-0.0619991\pi$
$98$	−12.5356	+	7.23746i	−1.26629	+	0.731094i
$99$			1.00000i			0.100504i
$100$	0.367961	+	0.637327i	0.0367961	+	0.0637327i
$101$	3.96992	−	6.87610i	0.395022	−	0.684198i	−0.598082	−	0.801435i	$-0.704070\pi$
$101$	3.96992	−	6.87610i	0.395022	−	0.684198i	0.993104	+	0.117237i	$0.0374037\pi$
$102$	−3.54927	−	2.04917i	−0.351430	−	0.202898i
$103$	−17.6034			−1.73451			−0.867255	−	0.497864i	$-0.834118\pi$
$103$	−17.6034			−1.73451			−0.867255	+	0.497864i	$0.834118\pi$
$104$	20.7533	+	3.69774i	2.03503	+	0.362593i
$105$	−2.45154			−0.239246
$106$	−29.7443	−	17.1729i	−2.88902	−	1.66798i
$107$	−5.55718	+	9.62533i	−0.537233	+	0.930515i	0.461818	+	0.886975i	$0.347197\pi$
$107$	−5.55718	+	9.62533i	−0.537233	+	0.930515i	−0.999052	+	0.0435408i	$0.986136\pi$
$108$	−2.16238	−	3.74536i	−0.208075	−	0.360397i
$109$			17.6748i			1.69294i	0.532437	+	0.846469i	$0.321276\pi$
$109$			17.6748i			1.69294i	−0.532437	+	0.846469i	$0.678724\pi$
$110$	4.78651	−	2.76349i	0.456376	−	0.263489i
$111$	2.85446	−	1.64803i	0.270934	−	0.156424i
$112$		−	6.75337i		−	0.638133i
$113$	5.83807	+	10.1118i	0.549199	+	0.951241i	0.998330	+	0.0577746i	$0.0184005\pi$
$113$	5.83807	+	10.1118i	0.549199	+	0.951241i	−0.449131	+	0.893466i	$0.648266\pi$
$114$	1.93400	−	3.34979i	0.181136	−	0.313736i
$115$	−2.72684	−	1.57434i	−0.254280	−	0.146808i
$116$	13.2224			1.22767
$117$	−3.39032	+	1.22710i	−0.313435	+	0.113445i
$118$	−13.3200			−1.22621
$119$	1.57431	+	0.908926i	0.144316	+	0.0833211i
$120$	−6.42448	+	11.1275i	−0.586472	+	1.01580i
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$		−	16.1490i		−	1.46206i
$123$	3.07989	−	1.77818i	0.277705	−	0.160333i
$124$	18.9240	−	10.9258i	1.69942	−	0.981162i
$125$			11.3624i			1.01629i
$126$	1.40270	+	2.42955i	0.124962	+	0.216441i
$127$	−7.71646	+	13.3653i	−0.684725	+	1.18598i	0.288798	+	0.957390i	$0.406744\pi$
$127$	−7.71646	+	13.3653i	−0.684725	+	1.18598i	−0.973523	+	0.228588i	$0.926589\pi$
$128$	13.1415	+	7.58727i	1.16156	+	0.670626i
$129$	1.69676			0.149391
$130$	15.2426	+	12.8367i	1.33687	+	1.12585i
$131$	18.2663			1.59593			0.797966	−	0.602702i	$-0.205909\pi$
$131$	18.2663			1.59593			0.797966	+	0.602702i	$0.205909\pi$
$132$	−3.74536	−	2.16238i	−0.325992	−	0.188211i
$133$	−0.857841	+	1.48582i	−0.0743842	+	0.128837i
$134$	−9.63190	−	16.6829i	−0.832070	−	1.44119i
$135$		−	2.19769i		−	0.189147i
$136$	8.25123	−	4.76385i	0.707537	−	0.408497i
$137$	6.02357	−	3.47771i	0.514629	−	0.297121i	−0.220106	−	0.975476i	$-0.570640\pi$
$137$	6.02357	−	3.47771i	0.514629	−	0.297121i	0.734734	+	0.678355i	$0.237307\pi$
$138$			3.60318i			0.306723i
$139$	−7.95054	−	13.7707i	−0.674356	−	1.16802i	−0.976657	−	0.214806i	$-0.931088\pi$
$139$	−7.95054	−	13.7707i	−0.674356	−	1.16802i	0.302301	−	0.953213i	$-0.402245\pi$
$140$	5.30116	−	9.18189i	0.448030	−	0.776011i
$141$	4.26738	+	2.46377i	0.359378	+	0.207487i
$142$	2.49361			0.209259
$143$	−2.32255	+	2.75785i	−0.194221	+	0.230623i
$144$	6.05408			0.504507
$145$	5.81895	+	3.35957i	0.483237	+	0.278997i
$146$	19.3760	−	33.5602i	1.60357	−	2.77746i
$147$	2.87782	+	4.98453i	0.237359	+	0.411117i
$148$			14.2547i			1.17173i
$149$	9.66165	−	5.57816i	0.791514	−	0.456981i	−0.0489815	−	0.998800i	$-0.515598\pi$
$149$	9.66165	−	5.57816i	0.791514	−	0.456981i	0.840495	+	0.541819i	$0.182264\pi$
$150$	0.370614	−	0.213974i	0.0302605	−	0.0174709i
$151$			6.85946i			0.558215i	0.960260	+	0.279108i	$0.0900386\pi$
$151$			6.85946i			0.558215i	−0.960260	+	0.279108i	$0.909961\pi$
$152$	4.49610	+	7.78748i	0.364682	+	0.631648i
$153$	−0.814810	+	1.41129i	−0.0658734	+	0.114096i
$154$	2.42955	+	1.40270i	0.195778	+	0.113033i
$155$	11.1041			0.891906
$156$	2.73525	−	15.3514i	0.218995	−	1.22910i
$157$	18.4829			1.47510			0.737548	−	0.675294i	$-0.235983\pi$
$157$	18.4829			1.47510			0.737548	+	0.675294i	$0.235983\pi$
$158$	−27.1662	−	15.6844i	−2.16122	−	1.24778i
$159$	−6.82843	+	11.8272i	−0.541530	+	0.937957i
$160$	−3.88145	−	6.72287i	−0.306856	−	0.531490i
$161$		−	1.59822i		−	0.125957i
$162$	−2.17798	+	1.25745i	−0.171118	+	0.0987950i
$163$	−0.995127	+	0.574537i	−0.0779443	+	0.0450012i	−0.538466	−	0.842647i	$-0.680996\pi$
$163$	−0.995127	+	0.574537i	−0.0779443	+	0.0450012i	0.460521	+	0.887649i	$0.347662\pi$
$164$			15.3804i			1.20101i
$165$	−1.09884	−	1.90325i	−0.0855449	−	0.148168i
$166$	−16.7915	+	29.0838i	−1.30327	+	2.25734i
$167$	14.6052	+	8.43231i	1.13018	+	0.652511i	0.943981	−	0.330000i	$-0.107049\pi$
$167$	14.6052	+	8.43231i	1.13018	+	0.652511i	0.186202	+	0.982511i	$0.440382\pi$
$168$	−6.52190			−0.503176
$169$	−12.2000	−	4.49003i	−0.938460	−	0.345387i
$170$	9.00688			0.690796
$171$	−1.33197	−	0.769014i	−0.101858	−	0.0588080i
$172$	−3.66905	+	6.35498i	−0.279762	+	0.484563i
$173$	2.32529	+	4.02753i	0.176789	+	0.306207i	0.940779	−	0.339021i	$-0.110096\pi$
$173$	2.32529	+	4.02753i	0.176789	+	0.306207i	−0.763990	+	0.645228i	$0.776762\pi$
$174$		−	7.68900i		−	0.582902i
$175$	−0.164389	+	0.0949098i	−0.0124266	+	0.00717450i
$176$	5.24299	−	3.02704i	0.395205	−	0.228172i
$177$			5.29643i			0.398104i
$178$	−5.77375	−	10.0004i	−0.432761	−	0.749564i
$179$	−1.99485	+	3.45517i	−0.149102	+	0.258252i	−0.930896	−	0.365285i	$-0.880972\pi$
$179$	−1.99485	+	3.45517i	−0.149102	+	0.258252i	0.781794	+	0.623537i	$0.214305\pi$
$180$	8.23113	+	4.75225i	0.613512	+	0.354212i
$181$	−23.9266			−1.77845			−0.889226	−	0.457468i	$-0.848756\pi$
$181$	−23.9266			−1.77845			−0.889226	+	0.457468i	$0.848756\pi$
$182$	−1.77431	+	9.95817i	−0.131520	+	0.738149i
$183$	−6.42131			−0.474677
$184$	−7.25431	−	4.18828i	−0.534795	−	0.308764i
$185$	−3.62185	+	6.27322i	−0.266284	+	0.461217i
$186$	−6.35347	−	11.0045i	−0.465859	−	0.806892i
$187$			1.62962i			0.119170i
$188$	−18.4554	+	10.6552i	−1.34600	+	0.777113i
$189$	0.966057	−	0.557753i	0.0702703	−	0.0405706i
$190$			8.50066i			0.616703i
$191$	−0.932170	−	1.61457i	−0.0674495	−	0.116826i	0.830328	−	0.557274i	$-0.188153\pi$
$191$	−0.932170	−	1.61457i	−0.0674495	−	0.116826i	−0.897778	+	0.440448i	$0.854819\pi$
$192$	1.61237	−	2.79271i	0.116363	−	0.201546i
$193$	6.59737	+	3.80900i	0.474889	+	0.274178i	0.718284	−	0.695750i	$-0.244928\pi$
$193$	6.59737	+	3.80900i	0.474889	+	0.274178i	−0.243395	+	0.969927i	$0.578261\pi$
$194$	46.8839			3.36607
$195$	5.10424	−	6.06090i	0.365523	−	0.434030i
$196$	−24.8918			−1.77799
$197$	−0.397202	−	0.229325i	−0.0282995	−	0.0163387i	0.485784	−	0.874079i	$-0.338534\pi$
$197$	−0.397202	−	0.229325i	−0.0282995	−	0.0163387i	−0.514083	+	0.857740i	$0.671868\pi$
$198$	−1.25745	+	2.17798i	−0.0893634	+	0.154782i
$199$	1.18392	+	2.05061i	0.0839260	+	0.145364i	0.904933	−	0.425554i	$-0.139921\pi$
$199$	1.18392	+	2.05061i	0.0839260	+	0.145364i	−0.821007	+	0.570918i	$0.806587\pi$
$200$			0.994880i			0.0703486i
$201$	−6.63362	+	3.82992i	−0.467899	+	0.270142i
$202$	17.2928	−	9.98399i	1.21672	−	0.702471i
$203$			3.41052i			0.239371i
$204$	−3.52386	−	6.10351i	−0.246720	−	0.427331i
$205$	−3.90788	+	6.76865i	−0.272938	+	0.472743i
$206$	−38.3397	−	22.1354i	−2.67125	−	1.54225i
$207$	1.43273			0.0995814
$208$	16.6963	+	14.0609i	1.15768	+	0.974949i
$209$	−1.53803			−0.106388
$210$	−5.33939	−	3.08270i	−0.368453	−	0.212726i
$211$	9.30467	−	16.1162i	0.640560	−	1.10948i	−0.344748	−	0.938695i	$-0.612036\pi$
$211$	9.30467	−	16.1162i	0.640560	−	1.10948i	0.985308	−	0.170787i	$-0.0546310\pi$
$212$	−29.5314	−	51.1499i	−2.02822	−	3.51299i
$213$		−	0.991530i		−	0.0679385i
$214$	−24.2068	+	13.9758i	−1.65474	+	0.955367i
$215$	−3.22937	+	1.86448i	−0.220241	+	0.127156i
$216$		−	5.84658i		−	0.397809i
$217$	2.81813	+	4.88115i	0.191307	+	0.331354i
$218$	−22.2253	+	38.4953i	−1.50528	+	2.60723i
$219$	−13.3445	−	7.70445i	−0.901738	−	0.520619i
$220$	9.50449			0.640793
$221$	−5.52492	+	1.99970i	−0.371646	+	0.134514i
$222$	8.28927			0.556339
$223$	−17.6163	−	10.1708i	−1.17967	−	0.681085i	−0.223734	−	0.974650i	$-0.571825\pi$
$223$	−17.6163	−	10.1708i	−1.17967	−	0.681085i	−0.955939	+	0.293565i	$0.905158\pi$
$224$	1.97015	−	3.41241i	0.131636	−	0.228001i
$225$	−0.0850822	−	0.147367i	−0.00567215	−	0.00982444i
$226$			29.3644i			1.95329i
$227$	3.53771	−	2.04250i	0.234806	−	0.135565i	−0.377981	−	0.925813i	$-0.623382\pi$
$227$	3.53771	−	2.04250i	0.234806	−	0.135565i	0.612787	+	0.790248i	$0.290048\pi$
$228$	5.76047	−	3.32581i	0.381496	−	0.220257i
$229$			1.34188i			0.0886742i	0.999017	+	0.0443371i	$0.0141176\pi$
$229$			1.34188i			0.0886742i	−0.999017	+	0.0443371i	$0.985882\pi$
$230$	−3.95933	−	6.85777i	−0.261071	−	0.452188i
$231$	0.557753	−	0.966057i	0.0366975	−	0.0635619i
$232$	15.4803	+	8.93757i	1.01633	+	0.586780i
$233$	−7.45011			−0.488073			−0.244037	−	0.969766i	$-0.578472\pi$
$233$	−7.45011			−0.488073			−0.244037	+	0.969766i	$0.578472\pi$
$234$	−8.92704	−	1.59058i	−0.583579	−	0.103980i
$235$	−10.8292			−0.706420
$236$	−19.8370	−	11.4529i	−1.29128	−	0.745521i
$237$	−6.23656	+	10.8020i	−0.405108	+	0.701668i
$238$	2.28587	+	3.95924i	0.148171	+	0.256639i
$239$			0.459687i			0.0297347i	0.999889	+	0.0148673i	$0.00473259\pi$
$239$			0.459687i			0.0297347i	−0.999889	+	0.0148673i	$0.995267\pi$
$240$	−11.5225	+	6.65249i	−0.743771	+	0.429417i
$241$	15.9823	−	9.22740i	1.02951	−	0.594389i	0.112667	−	0.993633i	$-0.464061\pi$
$241$	15.9823	−	9.22740i	1.02951	−	0.594389i	0.916845	+	0.399244i	$0.130727\pi$
$242$			2.51491i			0.161664i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	13.8853	−	24.0501i	0.888918	−	1.53965i
$245$	−10.9545	−	6.32456i	−0.699854	−	0.404061i
$246$	8.94391			0.570243
$247$	−1.88731	−	5.21440i	−0.120087	−	0.331784i
$248$	29.5407			1.87584
$249$	11.5645	+	6.67679i	0.732873	+	0.423124i
$250$	−14.2877	+	24.7471i	−0.903635	+	1.56514i
$251$	−10.3216	−	17.8776i	−0.651496	−	1.12842i	−0.982760	−	0.184886i	$-0.940809\pi$
$251$	−10.3216	−	17.8776i	−0.651496	−	1.12842i	0.331264	−	0.943538i	$-0.392525\pi$
$252$			4.82431i			0.303903i
$253$	1.24078	−	0.716364i	0.0780071	−	0.0450374i
$254$	−33.6125	+	19.4062i	−2.10904	+	1.21765i
$255$		−	3.58140i		−	0.224276i
$256$	15.8565	+	27.4643i	0.991034	+	1.71652i
$257$	−13.7931	+	23.8904i	−0.860391	+	1.49024i	0.0111613	+	0.999938i	$0.496447\pi$
$257$	−13.7931	+	23.8904i	−0.860391	+	1.49024i	−0.871552	+	0.490303i	$0.836886\pi$
$258$	3.69550	+	2.13360i	0.230072	+	0.132832i
$259$	−3.67677			−0.228463
$260$	11.6629	+	32.2232i	0.723304	+	1.99840i
$261$	−3.05737			−0.189246
$262$	39.7835	+	22.9690i	2.45783	+	1.41903i
$263$	−2.36595	+	4.09795i	−0.145891	+	0.252691i	−0.929705	−	0.368305i	$-0.879938\pi$
$263$	−2.36595	+	4.09795i	−0.145891	+	0.252691i	0.783814	+	0.620996i	$0.213272\pi$
$264$	−2.92329	−	5.06329i	−0.179916	−	0.311624i
$265$		−	30.0135i		−	1.84372i
$266$	−3.73671	+	2.15739i	−0.229112	+	0.132278i
$267$	−3.97646	+	2.29581i	−0.243355	+	0.140501i
$268$		−	33.1270i		−	2.02356i
$269$	3.46463	+	6.00092i	0.211242	+	0.365883i	0.952104	−	0.305776i	$-0.0989157\pi$
$269$	3.46463	+	6.00092i	0.211242	+	0.365883i	−0.740861	+	0.671658i	$0.765582\pi$
$270$	2.76349	−	4.78651i	0.168181	−	0.291298i
$271$	19.5392	+	11.2809i	1.18692	+	0.685268i	0.957605	−	0.288084i	$-0.0930182\pi$
$271$	19.5392	+	11.2809i	1.18692	+	0.685268i	0.229315	+	0.973352i	$0.426352\pi$
$272$	9.86584			0.598205
$273$	3.95966	+	0.705515i	0.239649	+	0.0426997i
$274$	17.4923			1.05675
$275$	−0.147367	−	0.0850822i	−0.00888654	−	0.00513065i
$276$	−3.09811	+	5.36608i	−0.186484	+	0.323000i
$277$	−1.60748	−	2.78424i	−0.0965842	−	0.167289i	0.813684	−	0.581307i	$-0.197458\pi$
$277$	−1.60748	−	2.78424i	−0.0965842	−	0.167289i	−0.910269	+	0.414018i	$0.864125\pi$
$278$		−	39.9898i		−	2.39843i
$279$	−4.37572	+	2.52632i	−0.261968	+	0.151247i
$280$	12.4128	−	7.16655i	0.741809	−	0.428283i
$281$			17.1825i			1.02502i	0.858680	+	0.512511i	$0.171285\pi$
$281$			17.1825i			1.02502i	−0.858680	+	0.512511i	$0.828715\pi$
$282$	6.19616	+	10.7321i	0.368976	+	0.639085i
$283$	2.19762	−	3.80639i	0.130635	−	0.226267i	−0.793287	−	0.608849i	$-0.791632\pi$
$283$	2.19762	−	3.80639i	0.130635	−	0.226267i	0.923922	+	0.382582i	$0.124965\pi$
$284$	3.71364	+	2.14407i	0.220364	+	0.127227i
$285$	3.38011			0.200220
$286$	−8.52633	+	3.08603i	−0.504173	+	0.182481i
$287$	−3.96714			−0.234173
$288$	3.05906	+	1.76615i	0.180257	+	0.104071i
$289$	7.17217	−	12.4226i	0.421892	−	0.730739i
$290$	8.44902	+	14.6341i	0.496143	+	0.859345i
$291$		−	18.6424i		−	1.09284i
$292$	57.7119	−	33.3200i	3.37733	−	1.94990i
$293$	21.4372	−	12.3768i	1.25238	−	0.723060i	0.280796	−	0.959767i	$-0.409402\pi$
$293$	21.4372	−	12.3768i	1.25238	−	0.723060i	0.971581	+	0.236707i	$0.0760682\pi$
$294$			14.4749i			0.844195i
$295$	−5.81995	−	10.0804i	−0.338850	−	0.586906i
$296$	−9.63531	+	16.6889i	−0.560041	+	0.970020i
$297$	0.866025	+	0.500000i	0.0502519	+	0.0290129i
$298$	28.0571			1.62531
$299$	3.95125	+	3.32758i	0.228507	+	0.192439i
$300$	0.735921			0.0424884
$301$	−1.63917	−	0.946374i	−0.0944801	−	0.0545481i
$302$	−8.62546	+	14.9397i	−0.496340	+	0.859686i
$303$	−3.96992	−	6.87610i	−0.228066	−	0.395022i
$304$			9.31135i			0.534042i
$305$	12.2214	−	7.05602i	0.699795	−	0.404027i
$306$	−3.54927	+	2.04917i	−0.202898	+	0.117143i
$307$		−	10.9037i		−	0.622307i	−0.950360	−	0.311153i	$-0.899285\pi$
$307$		−	10.9037i		−	0.622307i	0.950360	−	0.311153i	$-0.100715\pi$
$308$	2.41215	+	4.17797i	0.137445	+	0.238062i
$309$	−8.80168	+	15.2449i	−0.500710	+	0.867255i
$310$	24.1845	+	13.9630i	1.37359	+	0.793043i
$311$	−28.3721			−1.60883			−0.804416	−	0.594066i	$-0.797522\pi$
$311$	−28.3721			−1.60883			−0.804416	+	0.594066i	$0.797522\pi$
$312$	13.5790	−	16.1240i	0.768758	−	0.912842i
$313$	25.5132			1.44209			0.721046	−	0.692887i	$-0.243661\pi$
$313$	25.5132			1.44209			0.721046	+	0.692887i	$0.243661\pi$
$314$	40.2553	+	23.2414i	2.27174	+	1.31159i
$315$	−1.22577	+	2.12309i	−0.0690642	+	0.119623i
$316$	−26.9717	−	46.7163i	−1.51728	−	2.62800i
$317$			16.8944i			0.948884i	0.880287	+	0.474442i	$0.157350\pi$
$317$			16.8944i			0.948884i	−0.880287	+	0.474442i	$0.842650\pi$
$318$	−29.7443	+	17.1729i	−1.66798	+	0.963008i
$319$	−2.64776	+	1.52868i	−0.148246	+	0.0855899i
$320$			7.08698i			0.396174i
$321$	5.55718	+	9.62533i	0.310172	+	0.537233i
$322$	2.00969	−	3.48088i	0.111995	−	0.193982i
$323$	−2.17061	−	1.25320i	−0.120776	−	0.0697299i
$324$	−4.32477			−0.240265
$325$	0.107622	−	0.604023i	0.00596982	−	0.0335052i
$326$	−2.88981			−0.160052
$327$	15.3068	+	8.83740i	0.846469	+	0.488709i
$328$	−10.3963	+	18.0068i	−0.574037	+	0.994261i
$329$	−2.74836	−	4.76029i	−0.151522	−	0.262443i
$330$		−	5.52699i		−	0.304251i
$331$	0.628805	−	0.363041i	0.0345622	−	0.0199545i	−0.482619	−	0.875830i	$-0.660315\pi$
$331$	0.628805	−	0.363041i	0.0345622	−	0.0199545i	0.517182	+	0.855876i	$0.326981\pi$
$332$	−50.0139	+	28.8756i	−2.74487	+	1.58475i
$333$		−	3.29605i		−	0.180622i
$334$	21.2065	+	36.7307i	1.16037	+	2.00982i
$335$	8.41697	−	14.5786i	0.459868	−	0.796516i
$336$	−5.84859	−	3.37668i	−0.319067	−	0.184213i
$337$	9.66025			0.526227			0.263114	−	0.964765i	$-0.415251\pi$
$337$	9.66025			0.526227			0.263114	+	0.964765i	$0.415251\pi$
$338$	−20.9253	−	25.1201i	−1.13818	−	1.36635i
$339$	11.6761			0.634160
$340$	13.4136	+	7.74435i	0.727455	+	0.419996i
$341$	−2.52632	+	4.37572i	−0.136808	+	0.236959i
$342$	−1.93400	−	3.34979i	−0.104579	−	0.181136i
$343$		−	14.2290i		−	0.768294i
$344$	−8.59119	+	4.96012i	−0.463206	+	0.267432i
$345$	−2.72684	+	1.57434i	−0.146808	+	0.0847599i
$346$			11.6958i			0.628771i
$347$	−17.1860	−	29.7670i	−0.922591	−	1.59797i	−0.795390	−	0.606097i	$-0.792734\pi$
$347$	−17.1860	−	29.7670i	−0.922591	−	1.59797i	−0.127201	−	0.991877i	$-0.540599\pi$
$348$	6.61120	−	11.4509i	0.354398	−	0.613835i
$349$	7.29368	+	4.21101i	0.390421	+	0.225410i	0.682343	−	0.731032i	$-0.260961\pi$
$349$	7.29368	+	4.21101i	0.390421	+	0.225410i	−0.291921	+	0.956442i	$0.594295\pi$
$350$	−0.477379			−0.0255170
$351$	−0.632462	+	3.54965i	−0.0337583	+	0.189466i
$352$	3.53230			0.188272
$353$	4.49912	+	2.59757i	0.239464	+	0.138255i	0.614930	−	0.788581i	$-0.289184\pi$
$353$	4.49912	+	2.59757i	0.239464	+	0.138255i	−0.375466	+	0.926836i	$0.622517\pi$
$354$	−6.66002	+	11.5355i	−0.353976	+	0.613104i
$355$	1.08954	+	1.88713i	0.0578266	+	0.100159i
$356$		−	19.8577i		−	1.05245i
$357$	1.57431	−	0.908926i	0.0833211	−	0.0481055i
$358$	−8.68945	+	5.01685i	−0.459252	+	0.265149i
$359$			22.1488i			1.16897i	0.811405	+	0.584484i	$0.198703\pi$
$359$			22.1488i			1.16897i	−0.811405	+	0.584484i	$0.801297\pi$
$360$	6.42448	+	11.1275i	0.338600	+	0.586472i
$361$	−8.31723	+	14.4059i	−0.437749	+	0.758204i
$362$	−52.1116	−	30.0866i	−2.73892	−	1.58132i
$363$	1.00000			0.0524864
$364$	−11.2047	+	13.3047i	−0.587286	+	0.697358i
$365$	33.8640			1.77252
$366$	−13.9855	−	8.07451i	−0.731032	−	0.422061i
$367$	−2.34048	+	4.05382i	−0.122172	+	0.211608i	−0.920624	−	0.390451i	$-0.872319\pi$
$367$	−2.34048	+	4.05382i	−0.122172	+	0.211608i	0.798452	+	0.602058i	$0.205653\pi$
$368$	−4.33692	−	7.51177i	−0.226078	−	0.391578i
$369$		−	3.55635i		−	0.185136i
$370$	−15.7766	+	9.10862i	−0.820186	+	0.473534i
$371$	13.1933	−	7.61716i	0.684963	−	0.395464i
$372$		−	21.8515i		−	1.13295i
$373$	2.15302	+	3.72913i	0.111479	+	0.193087i	0.916367	−	0.400340i	$-0.131108\pi$
$373$	2.15302	+	3.72913i	0.111479	+	0.193087i	−0.804888	+	0.593427i	$0.797775\pi$
$374$	−2.04917	+	3.54927i	−0.105960	+	0.183528i
$375$	9.84014	+	5.68121i	0.508143	+	0.293376i
$376$	−28.8093			−1.48573
$377$	−8.43177	−	7.10089i	−0.434258	−	0.365715i
$378$	2.80540			0.144294
$379$	16.6746	+	9.62709i	0.856517	+	0.494511i	0.862845	−	0.505469i	$-0.168681\pi$
$379$	16.6746	+	9.62709i	0.856517	+	0.494511i	−0.00632705	+	0.999980i	$0.502014\pi$
$380$	−7.30909	+	12.6597i	−0.374948	+	0.649430i
$381$	7.71646	+	13.3653i	0.395326	+	0.684725i
$382$		−	4.68865i		−	0.239892i
$383$	22.5250	−	13.0048i	1.15097	−	0.664515i	0.201850	−	0.979416i	$-0.435305\pi$
$383$	22.5250	−	13.0048i	1.15097	−	0.664515i	0.949125	+	0.314901i	$0.101971\pi$
$384$	13.1415	−	7.58727i	0.670626	−	0.387186i
$385$			2.45154i			0.124942i
$386$	9.57928	+	16.5918i	0.487572	+	0.844500i
$387$	0.848380	−	1.46944i	0.0431256	−	0.0746957i
$388$	69.8224	+	40.3120i	3.54469	+	2.04653i
$389$	−15.5446			−0.788143			−0.394072	−	0.919080i	$-0.628934\pi$
$389$	−15.5446			−0.788143			−0.394072	+	0.919080i	$0.628934\pi$
$390$	18.7382	−	6.78214i	0.948847	−	0.343427i
$391$	2.33480			0.118076
$392$	−29.1425	−	16.8254i	−1.47192	−	0.849812i
$393$	9.13314	−	15.8191i	0.460706	−	0.797966i
$394$	−0.576730	−	0.998926i	−0.0290553	−	0.0503252i
$395$		−	27.4120i		−	1.37925i
$396$	−3.74536	+	2.16238i	−0.188211	+	0.108664i
$397$	2.58148	−	1.49042i	0.129561	−	0.0748021i	−0.433819	−	0.901000i	$-0.642834\pi$
$397$	2.58148	−	1.49042i	0.129561	−	0.0748021i	0.563380	+	0.826198i	$0.309501\pi$
$398$			5.95491i			0.298493i
$399$	0.857841	+	1.48582i	0.0429457	+	0.0743842i
$400$	−0.515094	+	0.892170i	−0.0257547	+	0.0446085i
$401$	−31.4787	−	18.1743i	−1.57197	−	0.907579i	−0.995927	−	0.0901615i	$-0.971262\pi$
$401$	−31.4787	−	18.1743i	−1.57197	−	0.907579i	−0.576046	−	0.817417i	$-0.695405\pi$
$402$	−19.2638			−0.960791
$403$	−17.9351	−	3.19560i	−0.893411	−	0.159184i
$404$	34.3380			1.70838
$405$	−1.90325	−	1.09884i	−0.0945735	−	0.0546020i
$406$	−4.28857	+	7.42802i	−0.212838	+	0.368646i
$407$	−1.64803	−	2.85446i	−0.0816896	−	0.141491i
$408$		−	9.52770i		−	0.471691i
$409$	16.0202	−	9.24929i	0.792150	−	0.457348i	−0.0485691	−	0.998820i	$-0.515466\pi$
$409$	16.0202	−	9.24929i	0.792150	−	0.457348i	0.840719	+	0.541472i	$0.182133\pi$
$410$	−17.0225	+	9.82796i	−0.840683	+	0.485369i
$411$		−	6.95542i		−	0.343086i
$412$	−38.0652	−	65.9309i	−1.87534	−	3.24818i
$413$	2.95410	−	5.11665i	0.145362	−	0.251774i
$414$	3.12044	+	1.80159i	0.153361	+	0.0885433i
$415$	−29.3470			−1.44059
$416$	4.33447	+	11.9756i	0.212515	+	0.587153i
$417$	−15.9011			−0.778679
$418$	−3.34979	−	1.93400i	−0.163843	−	0.0945951i
$419$	9.36228	−	16.2160i	0.457377	−	0.792201i	−0.541444	−	0.840737i	$-0.682122\pi$
$419$	9.36228	−	16.2160i	0.457377	−	0.792201i	0.998821	+	0.0485358i	$0.0154555\pi$
$420$	−5.30116	−	9.18189i	−0.258670	−	0.448030i
$421$		−	11.6278i		−	0.566704i	−0.959016	−	0.283352i	$-0.908554\pi$
$421$		−	11.6278i		−	0.566704i	0.959016	−	0.283352i	$-0.0914464\pi$
$422$	40.5307	−	23.4004i	1.97300	−	1.13911i
$423$	4.26738	−	2.46377i	0.207487	−	0.119793i
$424$		−	79.8460i		−	3.87766i
$425$	−0.138652	−	0.240152i	−0.00672559	−	0.0116491i
$426$	1.24680	−	2.15953i	0.0604079	−	0.104629i
$427$	6.20336	+	3.58151i	0.300201	+	0.173321i
$428$	−48.0671			−2.32341
$429$	1.22710	+	3.39032i	0.0592447	+	0.163686i
$430$	−9.37798			−0.452246
$431$	−14.2371	−	8.21982i	−0.685779	−	0.395935i	0.116250	−	0.993220i	$-0.462913\pi$
$431$	−14.2371	−	8.21982i	−0.685779	−	0.395935i	−0.802029	+	0.597285i	$0.796246\pi$
$432$	3.02704	−	5.24299i	0.145639	−	0.252253i
$433$	7.37466	+	12.7733i	0.354404	+	0.613845i	0.987016	−	0.160624i	$-0.0513506\pi$
$433$	7.37466	+	12.7733i	0.354404	+	0.613845i	−0.632612	+	0.774469i	$0.718017\pi$
$434$			14.1747i			0.680407i
$435$	5.81895	−	3.35957i	0.278997	−	0.161079i
$436$	−66.1985	+	38.2197i	−3.17033	+	1.83039i
$437$			2.20358i			0.105411i
$438$	−19.3760	−	33.5602i	−0.925821	−	1.60357i
$439$	5.47927	−	9.49037i	0.261511	−	0.452951i	−0.705132	−	0.709076i	$-0.749112\pi$
$439$	5.47927	−	9.49037i	0.261511	−	0.452951i	0.966644	+	0.256125i	$0.0824458\pi$
$440$	11.1275	+	6.42448i	0.530484	+	0.306275i
$441$	5.75564			0.274078
$442$	−14.5477	−	2.59204i	−0.691962	−	0.123291i
$443$	5.34741			0.254063			0.127032	−	0.991899i	$-0.459455\pi$
$443$	5.34741			0.254063			0.127032	+	0.991899i	$0.459455\pi$
$444$	12.3449	+	7.12733i	0.585863	+	0.338248i
$445$	5.04547	−	8.73902i	0.239178	−	0.414269i
$446$	−25.5785	−	44.3033i	−1.21118	−	2.09782i
$447$		−	11.1563i		−	0.527676i
$448$	−3.11528	+	1.79861i	−0.147183	+	0.0849763i
$449$	11.1725	−	6.45044i	0.527263	−	0.304415i	−0.212638	−	0.977131i	$-0.568206\pi$
$449$	11.1725	−	6.45044i	0.527263	−	0.304415i	0.739901	+	0.672716i	$0.234872\pi$
$450$		−	0.427948i		−	0.0201737i
$451$	−1.77818	−	3.07989i	−0.0837311	−	0.145027i
$452$	−25.2483	+	43.7313i	−1.18758	+	2.05695i
$453$	5.94047	+	3.42973i	0.279108	+	0.161143i
$454$	10.2734			0.482154
$455$	−8.31148	+	3.00827i	−0.389648	+	0.141030i
$456$	8.99220			0.421099
$457$	−20.5346	−	11.8557i	−0.960569	−	0.554585i	−0.0642206	−	0.997936i	$-0.520456\pi$
$457$	−20.5346	−	11.8557i	−0.960569	−	0.554585i	−0.896348	+	0.443351i	$0.853789\pi$
$458$	−1.68736	+	2.92259i	−0.0788450	+	0.136564i
$459$	0.814810	+	1.41129i	0.0380321	+	0.0658734i
$460$		−	13.6173i		−	0.634912i
$461$	27.2186	−	15.7147i	1.26770	−	0.731905i	0.293145	−	0.956068i	$-0.405298\pi$
$461$	27.2186	−	15.7147i	1.26770	−	0.731905i	0.974552	+	0.224163i	$0.0719649\pi$
$462$	2.42955	−	1.40270i	0.113033	−	0.0652595i
$463$		−	7.92403i		−	0.368261i	−0.982902	−	0.184130i	$-0.941053\pi$
$463$		−	7.92403i		−	0.368261i	0.982902	−	0.184130i	$-0.0589469\pi$
$464$	9.25478	+	16.0297i	0.429642	+	0.744162i
$465$	5.55207	−	9.61647i	0.257471	−	0.445953i
$466$	−16.2262	−	9.36818i	−0.751662	−	0.433972i
$467$	−14.0801			−0.651549			−0.325775	−	0.945447i	$-0.605625\pi$
$467$	−14.0801			−0.651549			−0.325775	+	0.945447i	$0.605625\pi$
$468$	−11.9271	−	10.0445i	−0.551329	−	0.464307i
$469$	8.54461			0.394553
$470$	−23.5857	−	13.6172i	−1.08793	−	0.628116i
$471$	9.24145	−	16.0067i	0.425824	−	0.737548i
$472$	−15.4830	−	26.8173i	−0.712662	−	1.23437i
$473$		−	1.69676i		−	0.0780171i
$474$	−27.1662	+	15.6844i	−1.24778	+	0.720408i
$475$	0.226654	−	0.130859i	0.0103996	−	0.00600421i
$476$			7.86179i			0.360344i
$477$	6.82843	+	11.8272i	0.312652	+	0.541530i
$478$	−0.578035	+	1.00119i	−0.0264387	+	0.0457932i
$479$	−5.99544	−	3.46147i	−0.273939	−	0.158159i	0.356737	−	0.934205i	$-0.383889\pi$
$479$	−5.99544	−	3.46147i	−0.273939	−	0.158159i	−0.630676	+	0.776046i	$0.717222\pi$
$480$	−7.76290			−0.354326
$481$	7.65525	−	9.09003i	0.349049	−	0.414470i
$482$	46.4121			2.11402
$483$	−1.38410	−	0.799109i	−0.0629786	−	0.0363607i
$484$	−2.16238	+	3.74536i	−0.0982902	+	0.170244i
$485$	20.4851	+	35.4812i	0.930179	+	1.61112i
$486$			2.51491i			0.114079i
$487$	−9.53493	+	5.50499i	−0.432069	+	0.249455i	−0.700228	−	0.713920i	$-0.746918\pi$
$487$	−9.53493	+	5.50499i	−0.432069	+	0.249455i	0.268159	+	0.963375i	$0.413585\pi$
$488$	32.5129	−	18.7714i	1.47179	−	0.849739i
$489$			1.14907i			0.0519629i
$490$	−15.9057	−	27.5495i	−0.718546	−	1.24456i
$491$	−3.66649	+	6.35054i	−0.165466	+	0.286596i	−0.936821	−	0.349810i	$-0.886246\pi$
$491$	−3.66649	+	6.35054i	−0.165466	+	0.286596i	0.771354	+	0.636406i	$0.219580\pi$
$492$	13.3198	+	7.69020i	0.600504	+	0.346701i
$493$	−4.98234			−0.224394
$494$	2.44636	−	13.7300i	0.110067	−	0.617744i
$495$	−2.19769			−0.0987788
$496$	26.4910	+	15.2946i	1.18948	+	0.686746i
$497$	−0.553029	+	0.957875i	−0.0248068	+	0.0429666i
$498$	16.7915	+	29.0838i	0.752446	+	1.30327i
$499$		−	4.54754i		−	0.203576i	−0.994806	−	0.101788i	$-0.967544\pi$
$499$		−	4.54754i		−	0.203576i	0.994806	−	0.101788i	$-0.0324563\pi$
$500$	−42.5563	+	24.5699i	−1.90318	+	1.09880i
$501$	14.6052	−	8.43231i	0.652511	−	0.376728i
$502$		−	51.9159i		−	2.31712i
$503$	2.45457	+	4.25143i	0.109444	+	0.189562i	0.915545	−	0.402215i	$-0.131760\pi$
$503$	2.45457	+	4.25143i	0.109444	+	0.189562i	−0.806101	+	0.591778i	$0.798426\pi$
$504$	−3.26095	+	5.64813i	−0.145254	+	0.251588i
$505$	15.1115	+	8.72465i	0.672454	+	0.388242i
$506$	3.60318			0.160181
$507$	−9.98847	+	8.32048i	−0.443604	+	0.369526i
$508$	−66.7438			−2.96128
$509$	1.00162	+	0.578287i	0.0443962	+	0.0256321i	0.522034	−	0.852925i	$-0.325173\pi$
$509$	1.00162	+	0.578287i	0.0443962	+	0.0256321i	−0.477638	+	0.878557i	$0.658507\pi$
$510$	4.50344	−	7.80019i	0.199416	−	0.345398i
$511$	8.59437	+	14.8859i	0.380193	+	0.658513i
$512$			49.4065i			2.18348i
$513$	−1.33197	+	0.769014i	−0.0588080	+	0.0339528i
$514$	−60.0821	+	34.6884i	−2.65011	+	1.53004i
$515$		−	38.6867i		−	1.70474i
$516$	3.66905	+	6.35498i	0.161521	+	0.279762i
$517$	2.46377	−	4.26738i	0.108357	−	0.187679i
$518$	−8.00791	−	4.62337i	−0.351847	−	0.203139i
$519$	4.65059			0.204138
$520$	−8.12647	+	45.6093i	−0.356369	+	2.00010i
$521$	37.4572			1.64103			0.820515	−	0.571625i	$-0.193687\pi$
$521$	37.4572			1.64103			0.820515	+	0.571625i	$0.193687\pi$
$522$	−6.65887	−	3.84450i	−0.291451	−	0.168269i
$523$	−16.1476	+	27.9685i	−0.706085	+	1.22298i	0.260213	+	0.965551i	$0.416207\pi$
$523$	−16.1476	+	27.9685i	−0.706085	+	1.22298i	−0.966299	+	0.257424i	$0.917126\pi$
$524$	39.4987	+	68.4138i	1.72551	+	2.98867i
$525$			0.189820i			0.00828440i
$526$	−10.3060	+	5.95016i	−0.449362	+	0.259439i
$527$	−7.13076	+	4.11694i	−0.310621	+	0.179337i
$528$		−	6.05408i		−	0.263470i
$529$	10.4736	+	18.1409i	0.455376	+	0.788734i
$530$	37.7407	−	65.3687i	1.63935	−	2.83944i
$531$	4.58684	+	2.64821i	0.199052	+	0.114923i
$532$	−7.41992			−0.321694
$533$	8.25982	−	9.80790i	0.357772	−	0.424828i
$534$	−11.5475			−0.499709
$535$	−21.1535	−	12.2130i	−0.914544	−	0.528012i
$536$	22.3919	−	38.7840i	0.967184	−	1.67521i
$537$	1.99485	+	3.45517i	0.0860839	+	0.149102i
$538$			17.4265i			0.751309i
$539$	4.98453	−	2.87782i	0.214699	−	0.123957i
$540$	8.23113	−	4.75225i	0.354212	−	0.204504i
$541$			6.77075i			0.291097i	0.989351	+	0.145549i	$0.0464947\pi$
$541$			6.77075i			0.291097i	−0.989351	+	0.145549i	$0.953505\pi$
$542$	28.3705	+	49.1392i	1.21862	+	2.11071i
$543$	−11.9633	+	20.7211i	−0.513395	+	0.889226i
$544$	4.98511	+	2.87815i	0.213735	+	0.123400i
$545$	−38.8437			−1.66388
$546$	7.73688	+	6.51568i	0.331108	+	0.278845i
$547$	37.7469			1.61394			0.806971	−	0.590591i	$-0.201105\pi$
$547$	37.7469			1.61394			0.806971	+	0.590591i	$0.201105\pi$
$548$	26.0506	+	15.0403i	1.11282	+	0.642489i
$549$	−3.21066	+	5.56102i	−0.137027	+	0.237339i
$550$	−0.213974	−	0.370614i	−0.00912388	−	0.0158030i
$551$		−	4.70232i		−	0.200325i
$552$	−7.25431	+	4.18828i	−0.308764	+	0.178265i
$553$	12.0498	−	6.95693i	0.512408	−	0.295839i
$554$		−	8.08534i		−	0.343513i
$555$	3.62185	+	6.27322i	0.153739	+	0.266284i
$556$	34.3842	−	59.5552i	1.45822	−	2.52570i
$557$	−35.7670	−	20.6501i	−1.51549	−	0.874971i	−0.999835	−	0.0181778i	$-0.994214\pi$
$557$	−35.7670	−	20.6501i	−1.51549	−	0.874971i	−0.515660	−	0.856793i	$-0.672453\pi$
$558$	−12.7069			−0.537928
$559$	5.75255	−	2.08209i	0.243307	−	0.0880629i
$560$	14.8418			0.627181
$561$	1.41129	+	0.814810i	0.0595848	+	0.0344013i
$562$	−21.6062	+	37.4231i	−0.911404	+	1.57860i
$563$	7.01825	+	12.1560i	0.295784	+	0.512313i	0.975167	−	0.221471i	$-0.0710858\pi$
$563$	7.01825	+	12.1560i	0.295784	+	0.512313i	−0.679383	+	0.733784i	$0.737753\pi$
$564$			21.3105i			0.897333i
$565$	−22.2226	+	12.8303i	−0.934914	+	0.539773i
$566$	9.57273	−	5.52682i	0.402372	−	0.232309i
$567$		−	1.11551i		−	0.0468469i
$568$	2.89853	+	5.02040i	0.121620	+	0.210651i
$569$	10.0731	−	17.4472i	0.422288	−	0.731425i	−0.573875	−	0.818943i	$-0.694560\pi$
$569$	10.0731	−	17.4472i	0.422288	−	0.731425i	0.996163	+	0.0875184i	$0.0278936\pi$
$570$	7.36179	+	4.25033i	0.308351	+	0.178027i
$571$	10.1569			0.425052			0.212526	−	0.977155i	$-0.431831\pi$
$571$	10.1569			0.425052			0.212526	+	0.977155i	$0.431831\pi$
$572$	−15.3514	−	2.73525i	−0.641874	−	0.114367i
$573$	−1.86434			−0.0778839
$574$	−8.64033	−	4.98850i	−0.360640	−	0.208216i
$575$	−0.121900	+	0.211136i	−0.00508356	+	0.00880499i
$576$	−1.61237	−	2.79271i	−0.0671821	−	0.116363i
$577$			27.5846i			1.14836i	0.818729	+	0.574181i	$0.194679\pi$
$577$			27.5846i			1.14836i	−0.818729	+	0.574181i	$0.805321\pi$
$578$	31.2416	−	18.0374i	1.29948	−	0.750255i
$579$	6.59737	−	3.80900i	0.274178	−	0.158296i
$580$			29.0587i			1.20660i
$581$	−7.44800	−	12.9003i	−0.308995	−	0.535196i
$582$	23.4419	−	40.6026i	0.971700	−	1.68303i
$583$	11.8272	+	6.82843i	0.489832	+	0.282805i
$584$	90.0894			3.72793
$585$	−2.69677	−	7.45086i	−0.111498	−	0.308055i
$586$	62.2530			2.57165
$587$	−30.2006	−	17.4363i	−1.24651	−	0.719675i	−0.276101	−	0.961129i	$-0.589042\pi$
$587$	−30.2006	−	17.4363i	−1.24651	−	0.719675i	−0.970412	+	0.241454i	$0.922376\pi$
$588$	−12.4459	+	21.5570i	−0.513261	+	0.888994i
$589$	−3.88556	−	6.72998i	−0.160102	−	0.277304i
$590$		−	29.2733i		−	1.20516i
$591$	−0.397202	+	0.229325i	−0.0163387	+	0.00943315i
$592$	−17.2812	+	9.97728i	−0.710251	+	0.410064i
$593$			6.08762i			0.249989i	0.992157	+	0.124994i	$0.0398913\pi$
$593$			6.08762i			0.249989i	−0.992157	+	0.124994i	$0.960109\pi$
$594$	1.25745	+	2.17798i	0.0515940	+	0.0893634i
$595$	−1.99754	+	3.45983i	−0.0818910	+	0.141839i
$596$	41.7844	+	24.1242i	1.71156	+	0.988167i
$597$	2.36784			0.0969094
$598$	4.42145	+	12.2159i	0.180806	+	0.499546i
$599$	6.56763			0.268346			0.134173	−	0.990958i	$-0.457162\pi$
$599$	6.56763			0.268346			0.134173	+	0.990958i	$0.457162\pi$
$600$	0.861591	+	0.497440i	0.0351743	+	0.0203079i
$601$	23.2972	−	40.3519i	0.950311	−	1.64599i	0.205561	−	0.978644i	$-0.434098\pi$
$601$	23.2972	−	40.3519i	0.950311	−	1.64599i	0.744750	−	0.667343i	$-0.232569\pi$
$602$	−2.38005	−	4.12236i	−0.0970034	−	0.168015i
$603$			7.65984i			0.311933i
$604$	−25.6912	+	14.8328i	−1.04536	+	0.603538i
$605$	−1.90325	+	1.09884i	−0.0773783	+	0.0446744i
$606$		−	19.9680i		−	0.811143i
$607$	9.45255	+	16.3723i	0.383667	+	0.664531i	0.991583	−	0.129470i	$-0.0413277\pi$
$607$	9.45255	+	16.3723i	0.383667	+	0.664531i	−0.607916	+	0.794001i	$0.707994\pi$
$608$	−2.71639	+	4.70493i	−0.110164	+	0.190810i
$609$	2.95359	+	1.70526i	0.119686	+	0.0691005i
$610$	35.4905			1.43697
$611$	17.4910	+	3.11648i	0.707612	+	0.126079i
$612$	−7.04772			−0.284887
$613$	11.0842	+	6.39947i	0.447687	+	0.258472i	0.706853	−	0.707361i	$-0.250114\pi$
$613$	11.0842	+	6.39947i	0.447687	+	0.258472i	−0.259166	+	0.965833i	$0.583448\pi$
$614$	13.7109	−	23.7480i	0.553327	−	0.958391i
$615$	3.90788	+	6.76865i	0.157581	+	0.272938i
$616$			6.52190i			0.262775i
$617$	−27.0776	+	15.6332i	−1.09010	+	0.629371i	−0.933604	−	0.358307i	$-0.883354\pi$
$617$	−27.0776	+	15.6332i	−1.09010	+	0.629371i	−0.156499	+	0.987678i	$0.550021\pi$
$618$	−38.3397	+	22.1354i	−1.54225	+	0.890417i
$619$		−	2.76424i		−	0.111104i	−0.998456	−	0.0555521i	$-0.982308\pi$
$619$		−	2.76424i		−	0.111104i	0.998456	−	0.0555521i	$-0.0176919\pi$
$620$	24.0114	+	41.5890i	0.964322	+	1.67025i
$621$	0.716364	−	1.24078i	0.0287467	−	0.0497907i
$622$	−61.7936	−	35.6766i	−2.47770	−	1.43050i
$623$	5.12198			0.205208
$624$	20.5252	−	7.42894i	0.821667	−	0.297395i
$625$	−24.1202			−0.964809
$626$	55.5672	+	32.0817i	2.22091	+	1.28224i
$627$	−0.769014	+	1.33197i	−0.0307115	+	0.0531938i
$628$	39.9671	+	69.2251i	1.59486	+	2.76238i
$629$		−	5.37131i		−	0.214168i
$630$	−5.33939	+	3.08270i	−0.212726	+	0.122818i
$631$	−30.7575	+	17.7578i	−1.22444	+	0.706928i	−0.965860	−	0.259063i	$-0.916586\pi$
$631$	−30.7575	+	17.7578i	−1.22444	+	0.706928i	−0.258575	+	0.965991i	$0.583253\pi$
$632$		−	72.9251i		−	2.90081i
$633$	−9.30467	−	16.1162i	−0.369827	−	0.640560i
$634$	−21.2439	+	36.7956i	−0.843705	+	1.46134i
$635$	−29.3728	−	16.9584i	−1.16562	−	0.672973i
$636$	−59.0628			−2.34199
$637$	15.8732	+	13.3678i	0.628920	+	0.529651i
$638$	−7.68900			−0.304411
$639$	−0.858690	−	0.495765i	−0.0339693	−	0.0196122i
$640$	−16.6745	+	28.8810i	−0.659116	+	1.14162i
$641$	13.3660	+	23.1506i	0.527925	+	0.914393i	0.999470	+	0.0325509i	$0.0103631\pi$
$641$	13.3660	+	23.1506i	0.527925	+	0.914393i	−0.471545	+	0.881842i	$0.656304\pi$
$642$			27.9516i			1.10316i
$643$	−3.85866	+	2.22780i	−0.152171	+	0.0878558i	−0.574152	−	0.818749i	$-0.694668\pi$
$643$	−3.85866	+	2.22780i	−0.152171	+	0.0878558i	0.421981	+	0.906605i	$0.361335\pi$
$644$	5.98590	−	3.45596i	0.235877	−	0.136184i
$645$			3.72895i			0.146827i
$646$	−3.15168	−	5.45888i	−0.124001	−	0.214777i
$647$	−17.6855	+	30.6322i	−0.695288	+	1.20427i	0.274795	+	0.961503i	$0.411390\pi$
$647$	−17.6855	+	30.6322i	−0.695288	+	1.20427i	−0.970083	+	0.242772i	$0.921943\pi$
$648$	−5.06329	−	2.92329i	−0.198905	−	0.114838i
$649$	5.29643			0.207903
$650$	0.993931	−	1.18022i	0.0389852	−	0.0462919i
$651$	5.63626			0.220903
$652$	−4.30369	−	2.48474i	−0.168546	−	0.0973098i
$653$	−5.69435	+	9.86290i	−0.222837	+	0.385965i	−0.955668	−	0.294445i	$-0.904865\pi$
$653$	−5.69435	+	9.86290i	−0.222837	+	0.385965i	0.732831	+	0.680410i	$0.238198\pi$
$654$	22.2253	+	38.4953i	0.869076	+	1.50528i
$655$			40.1436i			1.56854i
$656$	−18.6459	+	10.7652i	−0.728001	+	0.420312i
$657$	−13.3445	+	7.70445i	−0.520619	+	0.300579i
$658$		−	13.8237i		−	0.538905i
$659$	−20.2968	−	35.1550i	−0.790649	−	1.36944i	−0.925565	−	0.378588i	$-0.876410\pi$
$659$	−20.2968	−	35.1550i	−0.790649	−	1.36944i	0.134916	−	0.990857i	$-0.456923\pi$
$660$	4.75225	−	8.23113i	0.184981	−	0.320396i
$661$	−28.7483	−	16.5978i	−1.11818	−	0.645580i	−0.177243	−	0.984167i	$-0.556718\pi$
$661$	−28.7483	−	16.5978i	−1.11818	−	0.645580i	−0.940935	+	0.338587i	$0.890051\pi$
$662$	1.82603			0.0709706
$663$	−1.03067	+	5.78457i	−0.0400280	+	0.224654i
$664$	−78.0728			−3.02981
$665$	−3.26538	−	1.88527i	−0.126626	−	0.0731075i
$666$	4.14463	−	7.17872i	0.160601	−	0.278170i
$667$	2.19019	+	3.79352i	0.0848044	+	0.146886i
$668$			72.9355i			2.82196i
$669$	−17.6163	+	10.1708i	−0.681085	+	0.393224i
$670$	36.6639	−	21.1679i	1.41645	−	0.817788i
$671$			6.42131i			0.247892i
$672$	−1.97015	−	3.41241i	−0.0760003	−	0.131636i
$673$	21.2405	−	36.7896i	0.818760	−	1.41813i	−0.0878364	−	0.996135i	$-0.527995\pi$
$673$	21.2405	−	36.7896i	0.818760	−	1.41813i	0.906596	−	0.421999i	$-0.138671\pi$
$674$	21.0398	+	12.1473i	0.810422	+	0.467897i
$675$	−0.170164			−0.00654963
$676$	−9.56428	−	55.4025i	−0.367857	−	2.13086i
$677$	−22.9257			−0.881106			−0.440553	−	0.897727i	$-0.645218\pi$
$677$	−22.9257			−0.881106			−0.440553	+	0.897727i	$0.645218\pi$
$678$	25.4303	+	14.6822i	0.976646	+	0.563867i
$679$	−10.3978	+	18.0096i	−0.399033	+	0.691145i
$680$	10.4695	+	18.1336i	0.401485	+	0.695393i
$681$		−	4.08500i		−	0.156537i
$682$	−11.0045	+	6.35347i	−0.421386	+	0.243287i
$683$	22.7888	−	13.1571i	0.871989	−	0.503443i	0.00398053	−	0.999992i	$-0.498733\pi$
$683$	22.7888	−	13.1571i	0.871989	−	0.503443i	0.868009	+	0.496549i	$0.165400\pi$
$684$		−	6.65161i		−	0.254331i
$685$	7.64293	+	13.2379i	0.292021	+	0.505796i
$686$	17.8923	−	30.9904i	0.683132	−	1.18322i
$687$	1.16211	+	0.670942i	0.0443371	+	0.0255980i
$688$	−10.2723			−0.391629
$689$	−8.63744	+	48.4771i	−0.329060	+	1.84683i
$690$	−7.91867			−0.301458
$691$	−19.3664	−	11.1812i	−0.736732	−	0.425352i	0.0841481	−	0.996453i	$-0.473183\pi$
$691$	−19.3664	−	11.1812i	−0.736732	−	0.425352i	−0.820880	+	0.571101i	$0.806516\pi$
$692$	−10.0564	+	17.4181i	−0.382285	+	0.662138i
$693$	−0.557753	−	0.966057i	−0.0211873	−	0.0366975i
$694$		−	86.4423i		−	3.28130i
$695$	30.2638	−	17.4728i	1.14797	−	0.662781i
$696$	15.4803	−	8.93757i	0.586780	−	0.338778i
$697$		−	5.79550i		−	0.219520i
$698$	10.5903	+	18.3429i	0.400849	+	0.694290i
$699$	−3.72506	+	6.45199i	−0.140895	+	0.244037i
$700$	−0.710942	−	0.410463i	−0.0268711	−	0.0155140i
$701$	8.15009			0.307825			0.153912	−	0.988084i	$-0.450813\pi$
$701$	8.15009			0.307825			0.153912	+	0.988084i	$0.450813\pi$
$702$	−5.84101	+	6.93575i	−0.220455	+	0.261773i
$703$	5.06942			0.191197
$704$	−2.79271	−	1.61237i	−0.105254	−	0.0607685i
$705$	−5.41460	+	9.37837i	−0.203926	+	0.353210i
$706$	6.53265	+	11.3149i	0.245859	+	0.425841i
$707$			8.85695i			0.333100i
$708$	−19.8370	+	11.4529i	−0.745521	+	0.430427i
$709$	9.91180	−	5.72258i	0.372246	−	0.214916i	−0.302194	−	0.953247i	$-0.597719\pi$
$709$	9.91180	−	5.72258i	0.372246	−	0.214916i	0.674439	+	0.738331i	$0.264386\pi$
$710$			5.48017i			0.205667i
$711$	6.23656	+	10.8020i	0.233889	+	0.405108i
$712$	13.4226	−	23.2487i	0.503034	−	0.871281i
$713$	6.26921	+	3.61953i	0.234784	+	0.135553i
$714$	4.57173			0.171093
$715$	−6.06090	−	5.10424i	−0.226665	−	0.190888i
$716$	−17.2545			−0.644830
$717$	0.398100	+	0.229843i	0.0148673	+	0.00858366i
$718$	−27.8511	+	48.2395i	−1.03939	+	1.80028i
$719$	12.3807	+	21.4439i	0.461720	+	0.799723i	0.999047	−	0.0436512i	$-0.0138990\pi$
$719$	12.3807	+	21.4439i	0.461720	+	0.799723i	−0.537326	+	0.843374i	$0.680566\pi$
$720$			13.3050i			0.495847i
$721$	17.0058	−	9.81833i	0.633331	−	0.365654i
$722$	−36.2295	+	20.9171i	−1.34832	+	0.778453i
$723$		−	18.4548i		−	0.686341i
$724$	−51.7385	−	89.6138i	−1.92285	−	3.33047i
$725$	0.260128	−	0.450554i	0.00966089	−	0.0167332i
$726$	2.17798	+	1.25745i	0.0808322	+	0.0466685i
$727$	32.3026			1.19804			0.599018	−	0.800735i	$-0.295558\pi$
$727$	32.3026			1.19804			0.599018	+	0.800735i	$0.295558\pi$
$728$	−22.1113	+	8.00300i	−0.819499	+	0.296611i
$729$	1.00000			0.0370370
$730$	73.7549	+	42.5824i	2.72979	+	1.57605i
$731$	1.38254	−	2.39462i	0.0511350	−	0.0885684i
$732$	−13.8853	−	24.0501i	−0.513217	−	0.888918i
$733$		−	5.09305i		−	0.188116i	−0.995567	−	0.0940581i	$-0.970016\pi$
$733$		−	5.09305i		−	0.188116i	0.995567	−	0.0940581i	$-0.0299839\pi$
$734$	−10.1950	+	5.88609i	−0.376304	+	0.217259i
$735$	−10.9545	+	6.32456i	−0.404061	+	0.233285i
$736$		−	5.06083i		−	0.186545i
$737$	3.82992	+	6.63362i	0.141077	+	0.244352i
$738$	4.47195	−	7.74565i	0.164615	−	0.285121i
$739$	−9.68842	−	5.59361i	−0.356394	−	0.205764i	0.311104	−	0.950376i	$-0.399301\pi$
$739$	−9.68842	−	5.59361i	−0.356394	−	0.205764i	−0.667498	+	0.744612i	$0.732635\pi$
$740$	−31.3273			−1.15161
$741$	−5.45946	−	0.972744i	−0.200558	−	0.0357346i
$742$	38.3130			1.40651
$743$	−15.1928	−	8.77159i	−0.557371	−	0.321798i	0.194718	−	0.980859i	$-0.437621\pi$
$743$	−15.1928	−	8.77159i	−0.557371	−	0.321798i	−0.752090	+	0.659061i	$0.770954\pi$
$744$	14.7703	−	25.5830i	0.541507	−	0.937918i
$745$	12.2591	+	21.2333i	0.449137	+	0.777928i
$746$			10.8293i			0.396488i
$747$	11.5645	−	6.67679i	0.423124	−	0.244291i
$748$	−6.10351	+	3.52386i	−0.223166	+	0.128845i
$749$		−	12.3982i		−	0.453019i
$750$	14.2877	+	24.7471i	0.521714	+	0.903635i
$751$	8.90157	−	15.4180i	0.324823	−	0.562610i	−0.656653	−	0.754192i	$-0.728029\pi$
$751$	8.90157	−	15.4180i	0.324823	−	0.562610i	0.981477	+	0.191582i	$0.0613619\pi$
$752$	−25.8351	−	14.9159i	−0.942108	−	0.543926i
$753$	−20.6433			−0.752282
$754$	−9.43514	−	26.0681i	−0.343608	−	0.949346i
$755$	−15.0750			−0.548634
$756$	4.17797	+	2.41215i	0.151951	+	0.0877292i
$757$	−7.25158	+	12.5601i	−0.263563	+	0.456505i	−0.967186	−	0.254069i	$-0.918231\pi$
$757$	−7.25158	+	12.5601i	−0.263563	+	0.456505i	0.703623	+	0.710573i	$0.251564\pi$
$758$	24.2113	+	41.9351i	0.879393	+	1.52315i
$759$		−	1.43273i		−	0.0520047i
$760$	−17.1145	+	9.88103i	−0.620806	+	0.358423i
$761$	20.4965	−	11.8337i	0.742999	−	0.428970i	−0.0801599	−	0.996782i	$-0.525543\pi$
$761$	20.4965	−	11.8337i	0.742999	−	0.428970i	0.823159	+	0.567812i	$0.192210\pi$
$762$			38.8124i			1.40602i
$763$	−9.85818	−	17.0749i	−0.356890	−	0.618152i
$764$	4.03142	−	6.98262i	0.145852	−	0.252622i
$765$	−3.10158	−	1.79070i	−0.112138	−	0.0647428i
$766$	65.4119			2.36343
$767$	6.49922	+	17.9566i	0.234673	+	0.648374i
$768$	31.7131			1.14435
$769$	3.50248	+	2.02216i	0.126303	+	0.0729209i	0.561820	−	0.827259i	$-0.310101\pi$
$769$	3.50248	+	2.02216i	0.126303	+	0.0729209i	−0.435517	+	0.900180i	$0.643435\pi$
$770$	−3.08270	+	5.33939i	−0.111093	+	0.192418i
$771$	13.7931	+	23.8904i	0.496747	+	0.860391i
$772$			32.9460i			1.18575i
$773$	−11.6193	+	6.70841i	−0.417918	+	0.241285i	−0.694186	−	0.719796i	$-0.744235\pi$
$773$	−11.6193	+	6.70841i	−0.417918	+	0.241285i	0.276268	+	0.961081i	$0.410902\pi$
$774$	3.69550	−	2.13360i	0.132832	−	0.0766907i
$775$		−	0.859780i		−	0.0308842i
$776$	54.4971	+	94.3917i	1.95633	+	3.38846i
$777$	−1.83838	+	3.18417i	−0.0659517	+	0.114232i
$778$	−33.8558	−	19.5466i	−1.21379	−	0.700781i
$779$	5.46977			0.195975
$780$	33.7376	+	6.01123i	1.20800	+	0.215236i
$781$	−0.991530			−0.0354797
$782$	5.08514	+	2.93590i	0.181844	+	0.104988i
$783$	−1.52868	+	2.64776i	−0.0546307	+	0.0946232i
$784$	−17.4226	−	30.1768i	−0.622235	−	1.07774i
$785$			40.6197i			1.44978i
$786$	39.7835	−	22.9690i	1.41903	−	0.819278i
$787$	−20.2012	+	11.6632i	−0.720096	+	0.415748i	−0.814788	−	0.579759i	$-0.803147\pi$
$787$	−20.2012	+	11.6632i	−0.720096	+	0.415748i	0.0946920	+	0.995507i	$0.469813\pi$
$788$		−	1.98355i		−	0.0706611i
$789$	2.36595	+	4.09795i	0.0842302	+	0.145891i
$790$	34.4694	−	59.7028i	1.22637	−	2.12413i
$791$	−11.2798	−	6.51240i	−0.401064	−	0.231554i
$792$	−5.84658			−0.207749
$793$	−21.7703	+	7.87956i	−0.773085	+	0.279811i
$794$	7.49654			0.266042
$795$	−25.9925	−	15.0068i	−0.921859	−	0.532235i
$796$	−5.12019	+	8.86842i	−0.181480	+	0.314333i
$797$	−13.1380	−	22.7557i	−0.465373	−	0.806049i	0.533846	−	0.845582i	$-0.320746\pi$
$797$	−13.1380	−	22.7557i	−0.465373	−	0.806049i	−0.999218	+	0.0395330i	$0.987413\pi$
$798$			4.31478i			0.152742i
$799$	6.95420	−	4.01501i	0.246022	−	0.142041i
$800$	−0.520544	+	0.300536i	−0.0184040	+	0.0106256i
$801$			4.59162i			0.162237i
$802$	−45.7066	−	79.1661i	−1.61396	−	2.79545i
$803$	−7.70445	+	13.3445i	−0.271884	+	0.470917i
$804$	−28.6889	−	16.5635i	−1.01178	−	0.584150i
$805$	3.51238			0.123795
$806$	−35.0439	−	29.5125i	−1.23437	−	1.03953i
$807$	6.92927			0.243922
$808$	40.2017	+	23.2104i	1.41429	+	0.816541i
$809$	−3.68978	+	6.39089i	−0.129726	+	0.224692i	−0.923570	−	0.383429i	$-0.874743\pi$
$809$	−3.68978	+	6.39089i	−0.129726	+	0.224692i	0.793845	+	0.608121i	$0.208076\pi$
$810$	−2.76349	−	4.78651i	−0.0970993	−	0.168181i
$811$		−	43.4408i		−	1.52541i	−0.646745	−	0.762706i	$-0.723870\pi$
$811$		−	43.4408i		−	1.52541i	0.646745	−	0.762706i	$-0.276130\pi$
$812$	−12.7736	+	7.37484i	−0.448266	+	0.258806i
$813$	19.5392	−	11.2809i	0.685268	−	0.395640i
$814$		−	8.28927i		−	0.290539i
$815$	−1.26265	−	2.18698i	−0.0442288	−	0.0766065i
$816$	4.93292	−	8.54407i	0.172687	−	0.299102i
$817$	2.26004	+	1.30483i	0.0790687	+	0.0456503i
$818$	46.5222			1.62661
$819$	2.59082	−	3.07640i	0.0905307	−	0.107498i
$820$	−33.8013			−1.18039
$821$	−39.1138	−	22.5824i	−1.36508	−	0.788131i	−0.374787	−	0.927111i	$-0.622284\pi$
$821$	−39.1138	−	22.5824i	−1.36508	−	0.788131i	−0.990295	+	0.138980i	$0.955617\pi$
$822$	8.74613	−	15.1487i	0.305056	−	0.528373i
$823$	15.6611	+	27.1258i	0.545911	+	0.945545i	0.998549	+	0.0538506i	$0.0171495\pi$
$823$	15.6611	+	27.1258i	0.545911	+	0.945545i	−0.452638	+	0.891694i	$0.649517\pi$
$824$		−	102.919i		−	3.58537i
$825$	−0.147367	+	0.0850822i	−0.00513065	+	0.00296218i
$826$	12.8679	−	7.42929i	0.447732	−	0.258498i
$827$			26.9060i			0.935612i	0.883831	+	0.467806i	$0.154955\pi$
$827$			26.9060i			0.935612i	−0.883831	+	0.467806i	$0.845045\pi$
$828$	3.09811	+	5.36608i	0.107667	+	0.186484i
$829$	−4.45952	+	7.72412i	−0.154886	+	0.268270i	−0.933017	−	0.359831i	$-0.882834\pi$
$829$	−4.45952	+	7.72412i	−0.154886	+	0.268270i	0.778132	+	0.628101i	$0.216168\pi$
$830$	−63.9171	−	36.9025i	−2.21859	−	1.28091i
$831$	−3.21496			−0.111526
$832$	2.03952	−	11.4467i	0.0707078	−	0.396843i
$833$	9.37951			0.324981
$834$	−34.6321	−	19.9949i	−1.19921	−	0.692366i
$835$	−18.5316	+	32.0976i	−0.641312	+	1.11078i
$836$	−3.32581	−	5.76047i	−0.115025	−	0.199230i
$837$			5.05265i			0.174645i
$838$	40.7816	−	23.5453i	1.40878	−	0.813359i
$839$	−32.6416	+	18.8457i	−1.12691	+	0.650624i	−0.943157	−	0.332347i	$-0.892159\pi$
$839$	−32.6416	+	18.8457i	−1.12691	+	0.650624i	−0.183757	+	0.982972i	$0.558826\pi$
$840$		−	14.3331i		−	0.494539i
$841$	9.82625	+	17.0196i	0.338836	+	0.586882i
$842$	14.6214	−	25.3250i	0.503887	−	0.872758i
$843$	14.8805	+	8.59125i	0.512511	+	0.295899i
$844$	80.4811			2.77027
$845$	9.86769	−	26.8118i	0.339459	−	0.922353i
$846$	12.3923			0.426057
$847$	−0.966057	−	0.557753i	−0.0331941	−	0.0191646i
$848$	41.3399	−	71.6028i	1.41962	−	2.45885i
$849$	−2.19762	−	3.80639i	−0.0754222	−	0.130635i
$850$		−	0.697392i		−	0.0239204i
$851$	−4.08967	+	2.36117i	−0.140192	+	0.0809399i
$852$	3.71364	−	2.14407i	0.127227	−	0.0734546i
$853$			35.1545i			1.20367i	0.798621	+	0.601834i	$0.205563\pi$
$853$			35.1545i			1.20367i	−0.798621	+	0.601834i	$0.794437\pi$
$854$	9.00717	+	15.6009i	0.308219	+	0.533851i
$855$	1.69005	−	2.92726i	0.0577986	−	0.100110i
$856$	−56.2752	−	32.4905i	−1.92345	−	1.11050i
$857$	−44.5808			−1.52285			−0.761425	−	0.648253i	$-0.775500\pi$
$857$	−44.5808			−1.52285			−0.761425	+	0.648253i	$0.775500\pi$
$858$	−1.59058	+	8.92704i	−0.0543016	+	0.304764i
$859$	−39.5937			−1.35092			−0.675461	−	0.737396i	$-0.736055\pi$
$859$	−39.5937			−1.35092			−0.675461	+	0.737396i	$0.736055\pi$
$860$	−13.9663	−	8.06343i	−0.476246	−	0.274961i
$861$	−1.98357	+	3.43564i	−0.0675999	+	0.117086i
$862$	−20.6721	−	35.8051i	−0.704095	−	1.21953i
$863$			25.2675i			0.860114i	0.902802	+	0.430057i	$0.141507\pi$
$863$			25.2675i			0.860114i	−0.902802	+	0.430057i	$0.858493\pi$
$864$	3.05906	−	1.76615i	0.104071	−	0.0600857i
$865$	−8.85125	+	5.11027i	−0.300952	+	0.173755i
$866$			37.0932i			1.26048i
$867$	−7.17217	−	12.4226i	−0.243580	−	0.421892i
$868$	−12.1878	+	21.1098i	−0.413680	+	0.716514i
$869$	10.8020	+	6.23656i	0.366434	+	0.211561i
$870$	16.8980			0.572897
$871$	−17.7904	+	21.1247i	−0.602804	+	0.715784i
$872$	−103.337			−3.49944
$873$	−16.1448	−	9.32119i	−0.546418	−	0.315474i
$874$	−2.77090	+	4.79933i	−0.0937269	+	0.162340i
$875$	−6.33742	−	10.9767i	−0.214244	−	0.371082i
$876$		−	66.6399i		−	2.25155i
$877$	30.5737	−	17.6517i	1.03240	−	0.596057i	0.114730	−	0.993397i	$-0.463400\pi$
$877$	30.5737	−	17.6517i	1.03240	−	0.596057i	0.917672	+	0.397340i	$0.130066\pi$
$878$	23.8674	−	13.7799i	0.805487	−	0.465048i
$879$		−	24.7536i		−	0.834918i
$880$	6.65249	+	11.5225i	0.224255	+	0.388422i
$881$	0.595886	−	1.03210i	0.0200759	−	0.0347725i	−0.855813	−	0.517285i	$-0.826943\pi$
$881$	0.595886	−	1.03210i	0.0200759	−	0.0347725i	0.875889	+	0.482513i	$0.160276\pi$
$882$	12.5356	+	7.23746i	0.422097	+	0.243698i
$883$	−26.2438			−0.883175			−0.441587	−	0.897218i	$-0.645585\pi$
$883$	−26.2438			−0.883175			−0.441587	+	0.897218i	$0.645585\pi$
$884$	−19.4366	−	16.3687i	−0.653723	−	0.550539i
$885$	−11.6399			−0.391271
$886$	11.6465	+	6.72413i	0.391273	+	0.225901i
$887$	5.52034	−	9.56151i	0.185355	−	0.321044i	−0.758341	−	0.651858i	$-0.773990\pi$
$887$	5.52034	−	9.56151i	0.185355	−	0.321044i	0.943696	+	0.330814i	$0.107323\pi$
$888$	9.63531	+	16.6889i	0.323340	+	0.560041i
$889$		−	17.2155i		−	0.577390i
$890$	21.9778	−	12.6889i	0.736699	−	0.425333i
$891$	0.866025	−	0.500000i	0.0290129	−	0.0167506i
$892$		−	87.9724i		−	2.94553i
$893$	3.78935	+	6.56335i	0.126806	+	0.219634i
$894$	14.0286	−	24.2982i	0.469185	−	0.812653i
$895$	−7.59340	−	4.38405i	−0.253819	−	0.146543i
$896$	−16.9273			−0.565501
$897$	4.85740	−	1.75809i	0.162184	−	0.0587010i
$898$	32.4446			1.08269
$899$	−13.3782	−	7.72390i	−0.446187	−	0.257606i
$900$	0.367961	−	0.637327i	0.0122654	−	0.0212442i
$901$	11.1277	+	19.2738i	0.370719	+	0.642104i
$902$		−	8.94391i		−	0.297800i
$903$	−1.63917	+	0.946374i	−0.0545481	+	0.0314934i
$904$	−59.1196	+	34.1327i	−1.96629	+	1.13524i
$905$		−	52.5833i		−	1.74793i
$906$	8.62546	+	14.9397i	0.286562	+	0.496340i
$907$	−21.6380	+	37.4782i	−0.718479	+	1.24444i	0.243123	+	0.969995i	$0.421828\pi$
$907$	−21.6380	+	37.4782i	−0.718479	+	1.24444i	−0.961602	+	0.274447i	$0.911505\pi$
$908$	15.2998	+	8.83333i	0.507741	+	0.293144i
$909$	−7.93984			−0.263348
$910$	−21.8850	−	3.89937i	−0.725480	−	0.129263i
$911$	35.3173			1.17011			0.585057	−	0.810992i	$-0.301072\pi$
$911$	35.3173			1.17011			0.585057	+	0.810992i	$0.301072\pi$
$912$	8.06386	+	4.65567i	0.267021	+	0.154165i
$913$	6.67679	−	11.5645i	0.220969	−	0.382730i
$914$	−29.8159	−	51.6427i	−0.986223	−	1.70819i
$915$		−	14.1120i		−	0.466530i
$916$	−5.02584	+	2.90167i	−0.166058	+	0.0958738i
$917$	−17.6463	+	10.1881i	−0.582732	+	0.336440i
$918$			4.09834i			0.135265i
$919$	27.9447	+	48.4017i	0.921811	+	1.59662i	0.796612	+	0.604492i	$0.206624\pi$
$919$	27.9447	+	48.4017i	0.921811	+	1.59662i	0.125199	+	0.992132i	$0.460043\pi$
$920$	9.20453	−	15.9427i	0.303464	−	0.525616i
$921$	−9.44288	−	5.45185i	−0.311153	−	0.179645i
$922$	79.0419			2.60311
$923$	−1.21670	−	3.36160i	−0.0400482	−	0.110648i
$924$	4.82431			0.158708
$925$	0.485728	+	0.280435i	0.0159706	+	0.00922065i
$926$	9.96410	−	17.2583i	0.327441	−	0.567144i
$927$	8.80168	+	15.2449i	0.289085	+	0.500710i
$928$			10.7995i			0.354513i
$929$	11.7457	−	6.78140i	0.385365	−	0.222490i	−0.294785	−	0.955564i	$-0.595248\pi$
$929$	11.7457	−	6.78140i	0.385365	−	0.222490i	0.680150	+	0.733073i	$0.261915\pi$
$930$	24.1845	−	13.9630i	0.793043	−	0.457863i
$931$			8.85234i			0.290124i
$932$	−16.1100	−	27.9033i	−0.527701	−	0.914004i
$933$	−14.1860	+	24.5709i	−0.464430	+	0.804416i
$934$	−30.6661	−	17.7051i	−1.00343	−	0.579328i
$935$	−3.58140			−0.117124
$936$	−7.17431	−	19.8217i	−0.234500	−	0.647894i
$937$	−37.2906			−1.21823			−0.609116	−	0.793081i	$-0.708476\pi$
$937$	−37.2906			−1.21823			−0.609116	+	0.793081i	$0.708476\pi$
$938$	18.6099	+	10.7445i	0.607636	+	0.350819i
$939$	12.7566	−	22.0951i	0.416296	−	0.721046i
$940$	−23.4169	−	40.5593i	−0.763775	−	1.32290i
$941$			27.1103i			0.883769i	0.897072	+	0.441885i	$0.145690\pi$
$941$			27.1103i			0.883769i	−0.897072	+	0.441885i	$0.854310\pi$
$942$	40.2553	−	23.2414i	1.31159	−	0.757246i
$943$	−4.41265	+	2.54764i	−0.143696	+	0.0829627i
$944$		−	32.0650i		−	1.04363i
$945$	1.22577	+	2.12309i	0.0398743	+	0.0690642i
$946$	2.13360	−	3.69550i	0.0693693	−	0.120151i
$947$	20.8686	+	12.0485i	0.678137	+	0.391523i	0.799153	−	0.601128i	$-0.205282\pi$
$947$	20.8686	+	12.0485i	0.678137	+	0.391523i	−0.121016	+	0.992651i	$0.538615\pi$
$948$	−53.9434			−1.75200
$949$	−54.6962	−	9.74554i	−1.77551	−	0.316354i
$950$	0.658196			0.0213547
$951$	14.6310	+	8.44720i	0.474442	+	0.273919i
$952$	−5.31411	+	9.20430i	−0.172231	+	0.298313i
$953$	1.39027	+	2.40801i	0.0450351	+	0.0780031i	0.887664	−	0.460491i	$-0.152327\pi$
$953$	1.39027	+	2.40801i	0.0450351	+	0.0780031i	−0.842629	+	0.538494i	$0.818993\pi$
$954$			34.3458i			1.11199i
$955$	3.54831	−	2.04862i	0.114821	−	0.0662918i
$956$	−1.72169	+	0.994019i	−0.0556835	+	0.0321489i
$957$			3.05737i			0.0988307i
$958$	−8.70528	−	15.0780i	−0.281255	−	0.487148i
$959$	−3.87941	+	6.71934i	−0.125273	+	0.216979i
$960$	6.13750	+	3.54349i	0.198087	+	0.114366i
$961$	5.47076			0.176476
$962$	28.1032	−	10.1717i	0.906085	−	0.327950i
$963$	11.1144			0.358156
$964$	69.1198	+	39.9064i	2.22620	+	1.28530i
$965$	−8.37099	+	14.4990i	−0.269472	+	0.466738i
$966$	−2.00969	−	3.48088i	−0.0646606	−	0.111995i
$967$			19.6965i			0.633396i	0.948526	+	0.316698i	$0.102574\pi$
$967$			19.6965i			0.633396i	−0.948526	+	0.316698i	$0.897426\pi$
$968$	−5.06329	+	2.92329i	−0.162740	+	0.0939581i
$969$	−2.17061	+	1.25320i	−0.0697299	+	0.0402586i
$970$			103.036i			3.30829i
$971$	11.3150	+	19.5982i	0.363116	+	0.628935i	0.988472	−	0.151404i	$-0.0483796\pi$
$971$	11.3150	+	19.5982i	0.363116	+	0.628935i	−0.625356	+	0.780340i	$0.715046\pi$
$972$	−2.16238	+	3.74536i	−0.0693585	+	0.120132i
$973$	15.3614	+	8.86888i	0.492462	+	0.284323i
$974$	−27.6891			−0.887217
$975$	−0.469288	−	0.395215i	−0.0150293	−	0.0126570i
$976$	38.8751			1.24436
$977$	29.1761	+	16.8448i	0.933427	+	0.538914i	0.887894	−	0.460049i	$-0.152168\pi$
$977$	29.1761	+	16.8448i	0.933427	+	0.538914i	0.0455329	+	0.998963i	$0.485501\pi$
$978$	−1.44491	+	2.50265i	−0.0462030	+	0.0800260i
$979$	2.29581	+	3.97646i	0.0733744	+	0.127088i
$980$		−	54.7045i		−	1.74747i
$981$	15.3068	−	8.83740i	0.488709	−	0.282156i
$982$	−15.9710	+	9.22088i	−0.509656	+	0.294250i
$983$		−	53.5000i		−	1.70638i	−0.521597	−	0.853192i	$-0.674664\pi$
$983$		−	53.5000i		−	1.70638i	0.521597	−	0.853192i	$-0.325336\pi$
$984$	10.3963	+	18.0068i	0.331420	+	0.574037i
$985$	0.503984	−	0.872926i	0.0160583	−	0.0278137i
$986$	−10.8514	−	6.26507i	−0.345580	−	0.199521i
$987$	−5.49671			−0.174962
$988$	15.4487	−	18.3442i	0.491489	−	0.583606i
$989$	−2.43100			−0.0773012
$990$	−4.78651	−	2.76349i	−0.152125	−	0.0878296i
$991$	11.0522	−	19.1430i	0.351086	−	0.608098i	−0.635354	−	0.772221i	$-0.719146\pi$
$991$	11.0522	−	19.1430i	0.351086	−	0.608098i	0.986440	+	0.164122i	$0.0524792\pi$
$992$	8.92374	+	15.4564i	0.283329	+	0.490740i
$993$		−	0.726081i		−	0.0230415i
$994$	−2.40897	+	1.39082i	−0.0764078	+	0.0441141i
$995$	−4.50661	+	2.60189i	−0.142869	+	0.0824855i
$996$			57.7511i			1.82991i
$997$	−22.9078	−	39.6775i	−0.725498	−	1.25660i	−0.958769	−	0.284188i	$-0.908276\pi$
$997$	−22.9078	−	39.6775i	−0.725498	−	1.25660i	0.233270	−	0.972412i	$-0.425057\pi$
$998$	5.71832	−	9.90442i	0.181010	−	0.313519i
$999$	−2.85446	−	1.64803i	−0.0903112	−	0.0521412i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.s.a.199.12	yes	24
13.6	odd	12		5577.2.a.be.1.1		12
13.7	odd	12		5577.2.a.z.1.12		12
13.10	even	6	inner	429.2.s.a.166.12	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.s.a.166.12	✓	24	13.10	even	6	inner
429.2.s.a.199.12	yes	24	1.1	even	1	trivial
5577.2.a.z.1.12		12	13.7	odd	12
5577.2.a.be.1.1		12	13.6	odd	12

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.17798 + 1.25745i) q^{2} +(0.500000 - 0.866025i) q^{3} +(2.16238 + 3.74536i) q^{4} +2.19769i q^{5} +(2.17798 - 1.25745i) q^{6} +(-0.966057 + 0.557753i) q^{7} +5.84658i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(2.17798 + 1.25745i) q^{2} +(0.500000 - 0.866025i) q^{3} +(2.16238 + 3.74536i) q^{4} +2.19769i q^{5} +(2.17798 - 1.25745i) q^{6} +(-0.966057 + 0.557753i) q^{7} +5.84658i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.76349 + 4.78651i) q^{10} +(-0.866025 - 0.500000i) q^{11} +4.32477 q^{12} +(0.632462 - 3.54965i) q^{13} -2.80540 q^{14} +(1.90325 + 1.09884i) q^{15} +(-3.02704 + 5.24299i) q^{16} +(-0.814810 - 1.41129i) q^{17} -2.51491i q^{18} +(1.33197 - 0.769014i) q^{19} +(-8.23113 + 4.75225i) q^{20} +1.11551i q^{21} +(-1.25745 - 2.17798i) q^{22} +(-0.716364 + 1.24078i) q^{23} +(5.06329 + 2.92329i) q^{24} +0.170164 q^{25} +(5.84101 - 6.93575i) q^{26} -1.00000 q^{27} +(-4.17797 - 2.41215i) q^{28} +(1.52868 - 2.64776i) q^{29} +(2.76349 + 4.78651i) q^{30} -5.05265i q^{31} +(-3.05906 + 1.76615i) q^{32} +(-0.866025 + 0.500000i) q^{33} -4.09834i q^{34} +(-1.22577 - 2.12309i) q^{35} +(2.16238 - 3.74536i) q^{36} +(2.85446 + 1.64803i) q^{37} +3.86800 q^{38} +(-2.75785 - 2.32255i) q^{39} -12.8490 q^{40} +(3.07989 + 1.77818i) q^{41} +(-1.40270 + 2.42955i) q^{42} +(0.848380 + 1.46944i) q^{43} -4.32477i q^{44} +(1.90325 - 1.09884i) q^{45} +(-3.12044 + 1.80159i) q^{46} +4.92754i q^{47} +(3.02704 + 5.24299i) q^{48} +(-2.87782 + 4.98453i) q^{49} +(0.370614 + 0.213974i) q^{50} -1.62962 q^{51} +(14.6623 - 5.30690i) q^{52} -13.6569 q^{53} +(-2.17798 - 1.25745i) q^{54} +(1.09884 - 1.90325i) q^{55} +(-3.26095 - 5.64813i) q^{56} -1.53803i q^{57} +(6.65887 - 3.84450i) q^{58} +(-4.58684 + 2.64821i) q^{59} +9.50449i q^{60} +(-3.21066 - 5.56102i) q^{61} +(6.35347 - 11.0045i) q^{62} +(0.966057 + 0.557753i) q^{63} +3.22474 q^{64} +(7.80102 + 1.38995i) q^{65} -2.51491 q^{66} +(-6.63362 - 3.82992i) q^{67} +(3.52386 - 6.10351i) q^{68} +(0.716364 + 1.24078i) q^{69} -6.16539i q^{70} +(0.858690 - 0.495765i) q^{71} +(5.06329 - 2.92329i) q^{72} -15.4089i q^{73} +(4.14463 + 7.17872i) q^{74} +(0.0850822 - 0.147367i) q^{75} +(5.76047 + 3.32581i) q^{76} +1.11551 q^{77} +(-3.08603 - 8.52633i) q^{78} -12.4731 q^{79} +(-11.5225 - 6.65249i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.47195 + 7.74565i) q^{82} +13.3536i q^{83} +(-4.17797 + 2.41215i) q^{84} +(3.10158 - 1.79070i) q^{85} +4.26720i q^{86} +(-1.52868 - 2.64776i) q^{87} +(2.92329 - 5.06329i) q^{88} +(-3.97646 - 2.29581i) q^{89} +5.52699 q^{90} +(1.36883 + 3.78192i) q^{91} -6.19621 q^{92} +(-4.37572 - 2.52632i) q^{93} +(-6.19616 + 10.7321i) q^{94} +(1.69005 + 2.92726i) q^{95} +3.53230i q^{96} +(16.1448 - 9.32119i) q^{97} +(-12.5356 + 7.23746i) q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9	\( 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9} + 28 q^{12} - 4 q^{13} + 20 q^{14} - 6 q^{15} - 14 q^{16} + 10 q^{17} - 18 q^{20} + 2 q^{22} - 14 q^{23} + 4 q^{25} - 34 q^{26} - 24 q^{27} - 30 q^{28} + 4 q^{29} + 30 q^{32} + 6 q^{35} + 14 q^{36} + 12 q^{38} - 2 q^{39} + 20 q^{40} - 30 q^{41} + 10 q^{42} - 4 q^{43} - 6 q^{45} - 24 q^{46} + 14 q^{48} + 18 q^{49} - 84 q^{50} + 20 q^{51} + 40 q^{52} - 56 q^{53} - 4 q^{55} + 26 q^{56} + 48 q^{58} + 60 q^{59} - 2 q^{61} + 18 q^{62} - 6 q^{63} - 48 q^{64} - 10 q^{65} + 4 q^{66} - 42 q^{67} - 18 q^{68} + 14 q^{69} + 6 q^{71} + 2 q^{75} - 48 q^{76} + 24 q^{77} - 26 q^{78} - 20 q^{79} + 30 q^{80} - 12 q^{81} - 10 q^{82} - 30 q^{84} + 6 q^{85} - 4 q^{87} - 12 q^{88} + 12 q^{89} + 18 q^{91} + 8 q^{92} + 12 q^{93} - 22 q^{94} + 4 q^{95} + 6 q^{97} - 114 q^{98}+O(q^{100}) \) 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9 + 28 * q^12 - 4 * q^13 + 20 * q^14 - 6 * q^15 - 14 * q^16 + 10 * q^17 - 18 * q^20 + 2 * q^22 - 14 * q^23 + 4 * q^25 - 34 * q^26 - 24 * q^27 - 30 * q^28 + 4 * q^29 + 30 * q^32 + 6 * q^35 + 14 * q^36 + 12 * q^38 - 2 * q^39 + 20 * q^40 - 30 * q^41 + 10 * q^42 - 4 * q^43 - 6 * q^45 - 24 * q^46 + 14 * q^48 + 18 * q^49 - 84 * q^50 + 20 * q^51 + 40 * q^52 - 56 * q^53 - 4 * q^55 + 26 * q^56 + 48 * q^58 + 60 * q^59 - 2 * q^61 + 18 * q^62 - 6 * q^63 - 48 * q^64 - 10 * q^65 + 4 * q^66 - 42 * q^67 - 18 * q^68 + 14 * q^69 + 6 * q^71 + 2 * q^75 - 48 * q^76 + 24 * q^77 - 26 * q^78 - 20 * q^79 + 30 * q^80 - 12 * q^81 - 10 * q^82 - 30 * q^84 + 6 * q^85 - 4 * q^87 - 12 * q^88 + 12 * q^89 + 18 * q^91 + 8 * q^92 + 12 * q^93 - 22 * q^94 + 4 * q^95 + 6 * q^97 - 114 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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