LMFDB - Embedded newform 429.2.s.a.166.1

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			166.1
Character	$\chi$	$=$	429.166
Dual form			429.2.s.a.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.37717 + 1.37246i) q^{2} +(0.500000 + 0.866025i) q^{3} +(2.76728 - 4.79308i) q^{4} +0.261284i q^{5} +(-2.37717 - 1.37246i) q^{6} +(-3.66637 - 2.11678i) q^{7} +9.70209i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.37717 + 1.37246i) q^{2} +(0.500000 + 0.866025i) q^{3} +(2.76728 - 4.79308i) q^{4} +0.261284i q^{5} +(-2.37717 - 1.37246i) q^{6} +(-3.66637 - 2.11678i) q^{7} +9.70209i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.358601 - 0.621115i) q^{10} +(-0.866025 + 0.500000i) q^{11} +5.53457 q^{12} +(2.85325 + 2.20430i) q^{13} +11.6208 q^{14} +(-0.226278 + 0.130642i) q^{15} +(-7.78115 - 13.4773i) q^{16} +(1.36188 - 2.35885i) q^{17} -2.74492i q^{18} +(-5.81884 - 3.35951i) q^{19} +(1.25235 + 0.723046i) q^{20} -4.23356i q^{21} +(1.37246 - 2.37717i) q^{22} +(-0.874963 - 1.51548i) q^{23} +(-8.40226 + 4.85105i) q^{24} +4.93173 q^{25} +(-9.80797 - 1.32402i) q^{26} -1.00000 q^{27} +(-20.2918 + 11.7155i) q^{28} +(-3.86964 - 6.70241i) q^{29} +(0.358601 - 0.621115i) q^{30} -10.7765i q^{31} +(20.1897 + 11.6565i) q^{32} +(-0.866025 - 0.500000i) q^{33} +7.47650i q^{34} +(0.553080 - 0.957962i) q^{35} +(2.76728 + 4.79308i) q^{36} +(6.26674 - 3.61811i) q^{37} +18.4431 q^{38} +(-0.482352 + 3.57314i) q^{39} -2.53500 q^{40} +(2.89252 - 1.67000i) q^{41} +(5.81038 + 10.0639i) q^{42} +(-0.416235 + 0.720940i) q^{43} +5.53457i q^{44} +(-0.226278 - 0.130642i) q^{45} +(4.15987 + 2.40170i) q^{46} -1.56588i q^{47} +(7.78115 - 13.4773i) q^{48} +(5.46151 + 9.45961i) q^{49} +(-11.7236 + 6.76859i) q^{50} +2.72376 q^{51} +(18.4611 - 7.57594i) q^{52} -9.11606 q^{53} +(2.37717 - 1.37246i) q^{54} +(-0.130642 - 0.226278i) q^{55} +(20.5372 - 35.5714i) q^{56} -6.71902i q^{57} +(18.3976 + 10.6218i) q^{58} +(0.210488 + 0.121525i) q^{59} +1.44609i q^{60} +(1.08961 - 1.88726i) q^{61} +(14.7903 + 25.6176i) q^{62} +(3.66637 - 2.11678i) q^{63} -32.8677 q^{64} +(-0.575947 + 0.745509i) q^{65} +2.74492 q^{66} +(0.440958 - 0.254587i) q^{67} +(-7.53742 - 13.0552i) q^{68} +(0.874963 - 1.51548i) q^{69} +3.03632i q^{70} +(-1.85791 - 1.07267i) q^{71} +(-8.40226 - 4.85105i) q^{72} -0.229657i q^{73} +(-9.93140 + 17.2017i) q^{74} +(2.46587 + 4.27100i) q^{75} +(-32.2048 + 18.5934i) q^{76} +4.23356 q^{77} +(-3.75735 - 9.15596i) q^{78} -0.717632 q^{79} +(3.52141 - 2.03309i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.58400 + 7.93973i) q^{82} +10.2885i q^{83} +(-20.2918 - 11.7155i) q^{84} +(0.616328 + 0.355837i) q^{85} -2.28506i q^{86} +(3.86964 - 6.70241i) q^{87} +(-4.85105 - 8.40226i) q^{88} +(-5.53187 + 3.19383i) q^{89} +0.717202 q^{90} +(-5.79507 - 14.1215i) q^{91} -9.68508 q^{92} +(9.33273 - 5.38825i) q^{93} +(2.14911 + 3.72237i) q^{94} +(0.877784 - 1.52037i) q^{95} +23.3130i q^{96} +(-4.99134 - 2.88175i) q^{97} +(-25.9658 - 14.9914i) 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 $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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 $

$2$	−2.37717	+	1.37246i	−1.68091	+	0.970475i	−0.719854	+	0.694126i	$0.755791\pi$
$2$	−2.37717	+	1.37246i	−1.68091	+	0.970475i	−0.961057	+	0.276349i	$0.910875\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	2.76728	−	4.79308i	1.38364	−	2.39654i
$5$			0.261284i			0.116850i	0.998292	+	0.0584248i	$0.0186078\pi$
$5$			0.261284i			0.116850i	−0.998292	+	0.0584248i	$0.981392\pi$
$6$	−2.37717	−	1.37246i	−0.970475	−	0.560304i
$7$	−3.66637	−	2.11678i	−1.38576	−	0.800067i	−0.392923	−	0.919571i	$-0.628536\pi$
$7$	−3.66637	−	2.11678i	−1.38576	−	0.800067i	−0.992834	+	0.119504i	$0.961870\pi$
$8$			9.70209i			3.43021i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.358601	−	0.621115i	−0.113400	−	0.196414i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$	5.53457			1.59769
$13$	2.85325	+	2.20430i	0.791350	+	0.611363i
$13$	2.85325	+	2.20430i	0.791350	+	0.611363i
$14$	11.6208			3.10578
$15$	−0.226278	+	0.130642i	−0.0584248	+	0.0337316i
$16$	−7.78115	−	13.4773i	−1.94529	−	3.36934i
$17$	1.36188	−	2.35885i	0.330305	−	0.572104i	−0.652267	−	0.757989i	$-0.726182\pi$
$17$	1.36188	−	2.35885i	0.330305	−	0.572104i	0.982571	+	0.185885i	$0.0595152\pi$
$18$		−	2.74492i		−	0.646983i
$19$	−5.81884	−	3.35951i	−1.33493	−	0.770724i	−0.348882	−	0.937167i	$-0.613439\pi$
$19$	−5.81884	−	3.35951i	−1.33493	−	0.770724i	−0.986051	+	0.166443i	$0.946772\pi$
$20$	1.25235	+	0.723046i	0.280034	+	0.161678i
$21$		−	4.23356i		−	0.923838i
$22$	1.37246	−	2.37717i	0.292609	−	0.506814i
$23$	−0.874963	−	1.51548i	−0.182442	−	0.315999i	0.760269	−	0.649608i	$-0.225067\pi$
$23$	−0.874963	−	1.51548i	−0.182442	−	0.315999i	−0.942712	+	0.333609i	$0.891734\pi$
$24$	−8.40226	+	4.85105i	−1.71510	+	0.990216i
$25$	4.93173			0.986346
$26$	−9.80797	−	1.32402i	−1.92350	−	0.259661i
$27$	−1.00000			−0.192450
$28$	−20.2918	+	11.7155i	−3.83478	+	2.21401i
$29$	−3.86964	−	6.70241i	−0.718574	−	1.24461i	−0.961565	−	0.274578i	$-0.911462\pi$
$29$	−3.86964	−	6.70241i	−0.718574	−	1.24461i	0.242991	−	0.970028i	$-0.421871\pi$
$30$	0.358601	−	0.621115i	0.0654713	−	0.113400i
$31$		−	10.7765i		−	1.93552i	−0.251878	−	0.967759i	$-0.581048\pi$
$31$		−	10.7765i		−	1.93552i	0.251878	−	0.967759i	$-0.418952\pi$
$32$	20.1897	+	11.6565i	3.56906	+	2.06060i
$33$	−0.866025	−	0.500000i	−0.150756	−	0.0870388i
$34$			7.47650i			1.28221i
$35$	0.553080	−	0.957962i	0.0934875	−	0.161925i
$36$	2.76728	+	4.79308i	0.461214	+	0.798846i
$37$	6.26674	−	3.61811i	1.03025	−	0.594813i	0.113191	−	0.993573i	$-0.463893\pi$
$37$	6.26674	−	3.61811i	1.03025	−	0.594813i	0.917055	+	0.398760i	$0.130559\pi$
$38$	18.4431			2.99187
$39$	−0.482352	+	3.57314i	−0.0772382	+	0.572160i
$40$	−2.53500			−0.400818
$41$	2.89252	−	1.67000i	0.451736	−	0.260810i	−0.256827	−	0.966457i	$-0.582677\pi$
$41$	2.89252	−	1.67000i	0.451736	−	0.260810i	0.708563	+	0.705648i	$0.249344\pi$
$42$	5.81038	+	10.0639i	0.896561	+	1.55289i
$43$	−0.416235	+	0.720940i	−0.0634752	+	0.109942i	−0.896017	−	0.444021i	$-0.853552\pi$
$43$	−0.416235	+	0.720940i	−0.0634752	+	0.109942i	0.832541	+	0.553963i	$0.186885\pi$
$44$			5.53457i			0.834367i
$45$	−0.226278	−	0.130642i	−0.0337316	−	0.0194749i
$46$	4.15987	+	2.40170i	0.613339	+	0.354111i
$47$		−	1.56588i		−	0.228408i	−0.993457	−	0.114204i	$-0.963568\pi$
$47$		−	1.56588i		−	0.228408i	0.993457	−	0.114204i	$-0.0364317\pi$
$48$	7.78115	−	13.4773i	1.12311	−	1.94529i
$49$	5.46151	+	9.45961i	0.780215	+	1.35137i
$50$	−11.7236	+	6.76859i	−1.65796	+	0.957224i
$51$	2.72376			0.381403
$52$	18.4611	−	7.57594i	2.56010	−	1.05059i
$53$	−9.11606			−1.25219			−0.626094	−	0.779748i	$-0.715347\pi$
$53$	−9.11606			−1.25219			−0.626094	+	0.779748i	$0.715347\pi$
$54$	2.37717	−	1.37246i	0.323492	−	0.186768i
$55$	−0.130642	−	0.226278i	−0.0176157	−	0.0305114i
$56$	20.5372	−	35.5714i	2.74440	−	4.75343i
$57$		−	6.71902i		−	0.889955i
$58$	18.3976	+	10.6218i	2.41572	+	1.39471i
$59$	0.210488	+	0.121525i	0.0274032	+	0.0158213i	0.513639	−	0.858006i	$-0.328297\pi$
$59$	0.210488	+	0.121525i	0.0274032	+	0.0158213i	−0.486236	+	0.873828i	$0.661630\pi$
$60$			1.44609i			0.186690i
$61$	1.08961	−	1.88726i	0.139511	−	0.241639i	−0.787801	−	0.615930i	$-0.788780\pi$
$61$	1.08961	−	1.88726i	0.139511	−	0.241639i	0.927311	+	0.374291i	$0.122114\pi$
$62$	14.7903	+	25.6176i	1.87837	+	3.25343i
$63$	3.66637	−	2.11678i	0.461919	−	0.266689i
$64$	−32.8677			−4.10846
$65$	−0.575947	+	0.745509i	−0.0714375	+	0.0924690i
$66$	2.74492			0.337876
$67$	0.440958	−	0.254587i	0.0538715	−	0.0311028i	−0.472822	−	0.881158i	$-0.656765\pi$
$67$	0.440958	−	0.254587i	0.0538715	−	0.0311028i	0.526694	+	0.850055i	$0.323431\pi$
$68$	−7.53742	−	13.0552i	−0.914046	−	1.58317i
$69$	0.874963	−	1.51548i	0.105333	−	0.182442i
$70$			3.03632i			0.362909i
$71$	−1.85791	−	1.07267i	−0.220494	−	0.127302i	0.385685	−	0.922630i	$-0.373965\pi$
$71$	−1.85791	−	1.07267i	−0.220494	−	0.127302i	−0.606179	+	0.795328i	$0.707298\pi$
$72$	−8.40226	−	4.85105i	−0.990216	−	0.571701i
$73$		−	0.229657i		−	0.0268793i	−0.999910	−	0.0134396i	$-0.995722\pi$
$73$		−	0.229657i		−	0.0268793i	0.999910	−	0.0134396i	$-0.00427810\pi$
$74$	−9.93140	+	17.2017i	−1.15450	+	1.99966i
$75$	2.46587	+	4.27100i	0.284734	+	0.493173i
$76$	−32.2048	+	18.5934i	−3.69414	+	2.13281i
$77$	4.23356			0.482459
$78$	−3.75735	−	9.15596i	−0.425437	−	1.03671i
$79$	−0.717632			−0.0807399			−0.0403699	−	0.999185i	$-0.512854\pi$
$79$	−0.717632			−0.0807399			−0.0403699	+	0.999185i	$0.512854\pi$
$80$	3.52141	−	2.03309i	0.393706	−	0.227306i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.58400	+	7.93973i	−0.506218	+	0.876796i
$83$			10.2885i			1.12931i	0.825326	+	0.564657i	$0.190991\pi$
$83$			10.2885i			1.12931i	−0.825326	+	0.564657i	$0.809009\pi$
$84$	−20.2918	−	11.7155i	−2.21401	−	1.27826i
$85$	0.616328	+	0.355837i	0.0668501	+	0.0385959i
$86$		−	2.28506i		−	0.246404i
$87$	3.86964	−	6.70241i	0.414869	−	0.718574i
$88$	−4.85105	−	8.40226i	−0.517123	−	0.895684i
$89$	−5.53187	+	3.19383i	−0.586377	+	0.338545i	−0.763664	−	0.645614i	$-0.776601\pi$
$89$	−5.53187	+	3.19383i	−0.586377	+	0.338545i	0.177287	+	0.984159i	$0.443268\pi$
$90$	0.717202			0.0755997
$91$	−5.79507	−	14.1215i	−0.607488	−	1.48033i
$92$	−9.68508			−1.00974
$93$	9.33273	−	5.38825i	0.967759	−	0.558736i
$94$	2.14911	+	3.72237i	0.221664	+	0.383933i
$95$	0.877784	−	1.52037i	0.0900588	−	0.155986i
$96$			23.3130i			2.37938i
$97$	−4.99134	−	2.88175i	−0.506794	−	0.292598i	0.224721	−	0.974423i	$-0.427853\pi$
$97$	−4.99134	−	2.88175i	−0.506794	−	0.292598i	−0.731515	+	0.681826i	$0.761186\pi$
$98$	−25.9658	−	14.9914i	−2.62295	−	1.51436i
$99$		−	1.00000i		−	0.100504i
$100$	13.6475	−	23.6382i	1.36475	−	2.36382i
$101$	−4.80590	−	8.32406i	−0.478205	−	0.828275i	0.521483	−	0.853262i	$-0.325379\pi$
$101$	−4.80590	−	8.32406i	−0.478205	−	0.828275i	−0.999688	+	0.0249869i	$0.992046\pi$
$102$	−6.47484	+	3.73825i	−0.641104	+	0.370142i
$103$	0.646999			0.0637507			0.0318753	−	0.999492i	$-0.489852\pi$
$103$	0.646999			0.0637507			0.0318753	+	0.999492i	$0.489852\pi$
$104$	−21.3863	+	27.6825i	−2.09710	+	2.71450i
$105$	1.10616			0.107950
$106$	21.6704	−	12.5114i	2.10482	−	1.21522i
$107$	−8.69154	−	15.0542i	−0.840243	−	1.45534i	−0.889689	−	0.456566i	$-0.849079\pi$
$107$	−8.69154	−	15.0542i	−0.840243	−	1.45534i	0.0494467	−	0.998777i	$-0.484254\pi$
$108$	−2.76728	+	4.79308i	−0.266282	+	0.461214i
$109$			1.96329i			0.188049i	0.995570	+	0.0940247i	$0.0299733\pi$
$109$			1.96329i			0.188049i	−0.995570	+	0.0940247i	$0.970027\pi$
$110$	0.621115	+	0.358601i	0.0592210	+	0.0341913i
$111$	6.26674	+	3.61811i	0.594813	+	0.343415i
$112$			65.8839i			6.22544i
$113$	−3.59150	+	6.22066i	−0.337860	+	0.585191i	−0.984030	−	0.178003i	$-0.943036\pi$
$113$	−3.59150	+	6.22066i	−0.337860	+	0.585191i	0.646170	+	0.763194i	$0.276370\pi$
$114$	9.22157	+	15.9722i	0.863679	+	1.49594i
$115$	0.395970	−	0.228613i	0.0369244	−	0.0213183i
$116$	−42.8335			−3.97699
$117$	−3.33561	+	1.36884i	−0.308377	+	0.126549i
$118$	−0.667154			−0.0614165
$119$	−9.98631	+	5.76560i	−0.915444	+	0.528532i
$120$	−1.26750	−	2.19537i	−0.115706	−	0.200409i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$			5.98179i			0.541566i
$123$	2.89252	+	1.67000i	0.260810	+	0.150579i
$124$	−51.6526	−	29.8217i	−4.63854	−	2.67806i
$125$			2.59500i			0.232104i
$126$	−5.81038	+	10.0639i	−0.517630	+	0.896561i
$127$	6.74343	+	11.6800i	0.598383	+	1.03643i	0.993060	+	0.117610i	$0.0375232\pi$
$127$	6.74343	+	11.6800i	0.598383	+	1.03643i	−0.394677	+	0.918820i	$0.629143\pi$
$128$	37.7527	−	21.7965i	3.33690	−	1.92656i
$129$	−0.832470			−0.0732949
$130$	0.345944	−	2.56266i	0.0303413	−	0.224760i
$131$	2.82627			0.246932			0.123466	−	0.992349i	$-0.460599\pi$
$131$	2.82627			0.246932			0.123466	+	0.992349i	$0.460599\pi$
$132$	−4.79308	+	2.76728i	−0.417184	+	0.240861i
$133$	14.2227	+	24.6344i	1.23326	+	2.13607i
$134$	−0.698820	+	1.21039i	−0.0603689	+	0.104562i
$135$		−	0.261284i		−	0.0224877i
$136$	22.8857	+	13.2131i	1.96244	+	1.13301i
$137$	4.84408	+	2.79673i	0.413858	+	0.238941i	0.692446	−	0.721470i	$-0.256533\pi$
$137$	4.84408	+	2.79673i	0.413858	+	0.238941i	−0.278588	+	0.960411i	$0.589866\pi$
$138$			4.80340i			0.408892i
$139$	8.93246	−	15.4715i	0.757642	−	1.31227i	−0.186409	−	0.982472i	$-0.559685\pi$
$139$	8.93246	−	15.4715i	0.757642	−	1.31227i	0.944050	−	0.329801i	$-0.106982\pi$
$140$	−3.06106	−	5.30191i	−0.258707	−	0.448093i
$141$	1.35610	−	0.782942i	0.114204	−	0.0659356i
$142$	5.88876			0.494173
$143$	−3.57314	−	0.482352i	−0.298801	−	0.0403363i
$144$	15.5623			1.29686
$145$	1.75123	−	1.01107i	0.145432	−	0.0839650i
$146$	0.315194	+	0.545933i	0.0260857	+	0.0451817i
$147$	−5.46151	+	9.45961i	−0.450458	+	0.780215i
$148$		−	40.0493i		−	3.29203i
$149$	−6.59373	−	3.80689i	−0.540180	−	0.311873i	0.204972	−	0.978768i	$-0.434290\pi$
$149$	−6.59373	−	3.80689i	−0.540180	−	0.311873i	−0.745152	+	0.666895i	$0.767623\pi$
$150$	−11.7236	−	6.76859i	−0.957224	−	0.552653i
$151$			16.2349i			1.32117i	0.750749	+	0.660587i	$0.229693\pi$
$151$			16.2349i			1.32117i	−0.750749	+	0.660587i	$0.770307\pi$
$152$	32.5943	−	56.4549i	2.64374	−	4.57910i
$153$	1.36188	+	2.35885i	0.110102	+	0.190701i
$154$	−10.0639	+	5.81038i	−0.810970	+	0.468214i
$155$	2.81573			0.226165
$156$	15.7915	+	12.1998i	1.26433	+	0.976769i
$157$	−7.83092			−0.624975			−0.312488	−	0.949922i	$-0.601162\pi$
$157$	−7.83092			−0.624975			−0.312488	+	0.949922i	$0.601162\pi$
$158$	1.70593	−	0.984919i	0.135717	−	0.0783560i
$159$	−4.55803	−	7.89474i	−0.361475	−	0.626094i
$160$	−3.04566	+	5.27523i	−0.240780	+	0.417044i
$161$			7.40841i			0.583864i
$162$	2.37717	+	1.37246i	0.186768	+	0.107831i
$163$	−0.143362	−	0.0827702i	−0.0112290	−	0.00648306i	0.494375	−	0.869249i	$-0.335397\pi$
$163$	−0.143362	−	0.0827702i	−0.0112290	−	0.00648306i	−0.505604	+	0.862766i	$0.668730\pi$
$164$		−	18.4854i		−	1.44347i
$165$	0.130642	−	0.226278i	0.0101705	−	0.0176157i
$166$	−14.1206	−	24.4576i	−1.09597	−	1.89828i
$167$	15.4311	−	8.90914i	1.19409	−	0.689410i	0.234860	−	0.972029i	$-0.424537\pi$
$167$	15.4311	−	8.90914i	1.19409	−	0.689410i	0.959232	+	0.282619i	$0.0912033\pi$
$168$	41.0744			3.16896
$169$	3.28212	+	12.5789i	0.252471	+	0.967604i
$170$	−1.95349			−0.149826
$171$	5.81884	−	3.35951i	0.444978	−	0.256908i
$172$	2.30368	+	3.99009i	0.175654	+	0.304242i
$173$	0.722438	−	1.25130i	0.0549259	−	0.0951345i	−0.837255	−	0.546812i	$-0.815841\pi$
$173$	0.722438	−	1.25130i	0.0549259	−	0.0951345i	0.892181	+	0.451678i	$0.149174\pi$
$174$			21.2437i			1.61048i
$175$	−18.0815	−	10.4394i	−1.36684	−	0.789143i
$176$	13.4773	+	7.78115i	1.01589	+	0.586526i
$177$			0.243051i			0.0182688i
$178$	8.76678	−	15.1845i	0.657098	−	1.13813i
$179$	−8.92421	−	15.4572i	−0.667027	−	1.15532i	−0.978732	−	0.205145i	$-0.934233\pi$
$179$	−8.92421	−	15.4572i	−0.667027	−	1.15532i	0.311705	−	0.950179i	$-0.399100\pi$
$180$	−1.25235	+	0.723046i	−0.0933448	+	0.0538927i
$181$	−17.9879			−1.33703			−0.668516	−	0.743697i	$-0.733070\pi$
$181$	−17.9879			−1.33703			−0.668516	+	0.743697i	$0.733070\pi$
$182$	33.1570	+	25.6156i	2.45776	+	1.89876i
$183$	2.17923			0.161093
$184$	14.7033	−	8.48897i	1.08394	−	0.625815i
$185$	0.945352	+	1.63740i	0.0695037	+	0.120384i
$186$	−14.7903	+	25.6176i	−1.08448	+	1.87837i
$187$			2.72376i			0.199181i
$188$	−7.50540	−	4.33325i	−0.547388	−	0.316035i
$189$	3.66637	+	2.11678i	0.266689	+	0.153973i
$190$			4.81889i			0.349599i
$191$	−4.41214	+	7.64205i	−0.319251	+	0.552960i	−0.980332	−	0.197355i	$-0.936765\pi$
$191$	−4.41214	+	7.64205i	−0.319251	+	0.552960i	0.661081	+	0.750315i	$0.270098\pi$
$192$	−16.4339	−	28.4643i	−1.18601	−	2.05423i
$193$	−5.56525	+	3.21310i	−0.400595	+	0.231284i	−0.686741	−	0.726902i	$-0.740959\pi$
$193$	−5.56525	+	3.21310i	−0.400595	+	0.231284i	0.286145	+	0.958186i	$0.407626\pi$
$194$	15.8203			1.13583
$195$	−0.933603	−	0.126031i	−0.0668567	−	0.00902525i
$196$	60.4542			4.31815
$197$	15.6228	−	9.01980i	1.11308	−	0.642634i	0.173451	−	0.984842i	$-0.444508\pi$
$197$	15.6228	−	9.01980i	1.11308	−	0.642634i	0.939624	+	0.342208i	$0.111175\pi$
$198$	1.37246	+	2.37717i	0.0975364	+	0.168938i
$199$	−7.54076	+	13.0610i	−0.534550	+	0.925868i	0.464635	+	0.885502i	$0.346186\pi$
$199$	−7.54076	+	13.0610i	−0.534550	+	0.925868i	−0.999185	+	0.0403654i	$0.987148\pi$
$200$			47.8481i			3.38337i
$201$	0.440958	+	0.254587i	0.0311028	+	0.0179572i
$202$	22.8488	+	13.1918i	1.60764	+	0.928171i
$203$			32.7647i			2.29963i
$204$	7.53742	−	13.0552i	0.527725	−	0.914046i
$205$	0.436343	+	0.755768i	0.0304755	+	0.0527851i
$206$	−1.53802	+	0.887978i	−0.107159	+	0.0618684i
$207$	1.74993			0.121628
$208$	7.50651	−	55.6063i	0.520483	−	3.85560i
$209$	6.71902			0.464764
$210$	−2.62953	+	1.51816i	−0.181455	+	0.104763i
$211$	−0.171756	−	0.297490i	−0.0118242	−	0.0204801i	0.860053	−	0.510205i	$-0.170431\pi$
$211$	−0.171756	−	0.297490i	−0.0118242	−	0.0204801i	−0.871877	+	0.489725i	$0.837097\pi$
$212$	−25.2267	+	43.6940i	−1.73258	+	3.00091i
$213$		−	2.14533i		−	0.146996i
$214$	41.3225	+	23.8575i	2.82475	+	1.63087i
$215$	−0.188370	−	0.108755i	−0.0128467	−	0.00741705i
$216$		−	9.70209i		−	0.660144i
$217$	−22.8115	+	39.5107i	−1.54854	+	2.68216i
$218$	−2.69454	−	4.66708i	−0.182497	−	0.316094i
$219$	0.198889	−	0.114828i	0.0134396	−	0.00775938i
$220$	−1.44609			−0.0974955
$221$	9.08540	−	3.72840i	0.611150	−	0.250799i
$222$	−19.8628			−1.33310
$223$	−6.23498	+	3.59977i	−0.417525	+	0.241058i	−0.694018	−	0.719958i	$-0.744161\pi$
$223$	−6.23498	+	3.59977i	−0.417525	+	0.241058i	0.276493	+	0.961016i	$0.410828\pi$
$224$	−49.3485	−	85.4742i	−3.29724	−	5.71098i
$225$	−2.46587	+	4.27100i	−0.164391	+	0.284734i
$226$		−	19.7167i		−	1.31154i
$227$	−21.9290	−	12.6607i	−1.45548	−	0.840322i	−0.456696	−	0.889623i	$-0.650967\pi$
$227$	−21.9290	−	12.6607i	−1.45548	−	0.840322i	−0.998784	+	0.0493009i	$0.984301\pi$
$228$	−32.2048	−	18.5934i	−2.13281	−	1.23138i
$229$		−	15.4332i		−	1.01986i	−0.860217	−	0.509929i	$-0.829672\pi$
$229$		−	15.4332i		−	1.01986i	0.860217	−	0.509929i	$-0.170328\pi$
$230$	−0.627525	+	1.08690i	−0.0413778	+	0.0716684i
$231$	2.11678	+	3.66637i	0.139274	+	0.241229i
$232$	65.0274	−	37.5436i	4.26926	−	2.46486i
$233$	−8.83197			−0.578602			−0.289301	−	0.957238i	$-0.593423\pi$
$233$	−8.83197			−0.578602			−0.289301	+	0.957238i	$0.593423\pi$
$234$	6.05062	−	7.83195i	0.395541	−	0.511990i
$235$	0.409140			0.0266894
$236$	1.16496	−	0.672591i	0.0758325	−	0.0437819i
$237$	−0.358816	−	0.621487i	−0.0233076	−	0.0403699i
$238$	15.8261	−	27.4116i	1.02585	−	1.77683i
$239$		−	14.9029i		−	0.963986i	−0.876175	−	0.481993i	$-0.839913\pi$
$239$		−	14.9029i		−	0.963986i	0.876175	−	0.481993i	$-0.160087\pi$
$240$	3.52141	+	2.03309i	0.227306	+	0.131235i
$241$	12.2160	+	7.05291i	0.786902	+	0.454318i	0.838871	−	0.544331i	$-0.183216\pi$
$241$	12.2160	+	7.05291i	0.786902	+	0.454318i	−0.0519689	+	0.998649i	$0.516550\pi$
$242$			2.74492i			0.176450i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−6.03053	−	10.4452i	−0.386065	−	0.668685i
$245$	−2.47164	+	1.42700i	−0.157907	+	0.0911678i
$246$	−9.16801			−0.584531
$247$	−9.19727	−	22.4120i	−0.585208	−	1.42604i
$248$	104.555			6.63923
$249$	−8.91013	+	5.14427i	−0.564657	+	0.326005i
$250$	−3.56153	−	6.16875i	−0.225251	−	0.390146i
$251$	3.09488	−	5.36049i	0.195347	−	0.338351i	−0.751667	−	0.659543i	$-0.770750\pi$
$251$	3.09488	−	5.36049i	0.195347	−	0.338351i	0.947014	+	0.321192i	$0.104083\pi$
$252$		−	23.4309i		−	1.47601i
$253$	1.51548	+	0.874963i	0.0952774	+	0.0550084i
$254$	−32.0605	−	18.5102i	−2.01166	−	1.16143i
$255$			0.711674i			0.0445668i
$256$	−26.9620	+	46.6995i	−1.68512	+	2.91872i
$257$	7.58741	+	13.1418i	0.473290	+	0.819762i	0.999533	−	0.0305727i	$-0.00973310\pi$
$257$	7.58741	+	13.1418i	0.473290	+	0.819762i	−0.526243	+	0.850334i	$0.676400\pi$
$258$	1.97892	−	1.14253i	0.123202	−	0.0711308i
$259$	−30.6349			−1.90356
$260$	1.97947	+	4.82359i	0.122762	+	0.299147i
$261$	7.73927			0.479049
$262$	−6.71852	+	3.87894i	−0.415072	+	0.239642i
$263$	14.1379	+	24.4876i	0.871783	+	1.50997i	0.860151	+	0.510039i	$0.170369\pi$
$263$	14.1379	+	24.4876i	0.871783	+	1.50997i	0.0116316	+	0.999932i	$0.496297\pi$
$264$	4.85105	−	8.40226i	0.298561	−	0.517123i
$265$		−	2.38188i		−	0.146318i
$266$	−67.6194	−	39.0401i	−4.14601	−	2.39370i
$267$	−5.53187	−	3.19383i	−0.338545	−	0.195459i
$268$		−	2.81806i		−	0.172140i
$269$	−3.34219	+	5.78885i	−0.203777	+	0.352952i	−0.949742	−	0.313033i	$-0.898655\pi$
$269$	−3.34219	+	5.78885i	−0.203777	+	0.352952i	0.745965	+	0.665985i	$0.231988\pi$
$270$	0.358601	+	0.621115i	0.0218238	+	0.0377999i
$271$	12.9324	−	7.46654i	0.785589	−	0.453560i	−0.0528182	−	0.998604i	$-0.516820\pi$
$271$	12.9324	−	7.46654i	0.785589	−	0.453560i	0.838407	+	0.545044i	$0.183487\pi$
$272$	−42.3880			−2.57015
$273$	9.33203	−	12.0794i	0.564800	−	0.731080i
$274$	−15.3536			−0.927544
$275$	−4.27100	+	2.46587i	−0.257551	+	0.148697i
$276$	−4.84254	−	8.38752i	−0.291487	−	0.504870i
$277$	1.82409	−	3.15942i	0.109599	−	0.189831i	−0.806009	−	0.591904i	$-0.798377\pi$
$277$	1.82409	−	3.15942i	0.109599	−	0.189831i	0.915608	+	0.402072i	$0.131710\pi$
$278$			49.0377i			2.94109i
$279$	9.33273	+	5.38825i	0.558736	+	0.322586i
$280$	9.29424	+	5.36603i	0.555437	+	0.320682i
$281$			3.81830i			0.227780i	0.993493	+	0.113890i	$0.0363312\pi$
$281$			3.81830i			0.227780i	−0.993493	+	0.113890i	$0.963669\pi$
$282$	−2.14911	+	3.72237i	−0.127978	+	0.221664i
$283$	4.62926	+	8.01812i	0.275181	+	0.476628i	0.970181	−	0.242382i	$-0.0779288\pi$
$283$	4.62926	+	8.01812i	0.275181	+	0.476628i	−0.695000	+	0.719010i	$0.744595\pi$
$284$	−10.2827	+	5.93674i	−0.610168	+	0.352281i
$285$	1.75557			0.103991
$286$	9.15596	−	3.75735i	0.541403	−	0.222177i
$287$	−14.1401			−0.834661
$288$	−20.1897	+	11.6565i	−1.18969	+	0.686867i
$289$	4.79056	+	8.29750i	0.281798	+	0.488088i
$290$	−2.77531	+	4.80698i	−0.162972	+	0.282276i
$291$		−	5.76350i		−	0.337863i
$292$	−1.10076	−	0.635525i	−0.0644172	−	0.0371913i
$293$	8.38292	+	4.83988i	0.489735	+	0.282749i	0.724465	−	0.689312i	$-0.242087\pi$
$293$	8.38292	+	4.83988i	0.489735	+	0.282749i	−0.234729	+	0.972061i	$0.575420\pi$
$294$		−	29.9828i		−	1.74863i
$295$	−0.0317526	+	0.0549971i	−0.00184871	+	0.00320206i
$296$	35.1032	+	60.8005i	2.04033	+	3.53396i
$297$	0.866025	−	0.500000i	0.0502519	−	0.0290129i
$298$	20.8992			1.21066
$299$	0.844080	−	6.25273i	0.0488144	−	0.361605i
$300$	27.2950			1.57588
$301$	3.05214	−	1.76215i	0.175923	−	0.101569i
$302$	−22.2817	−	38.5930i	−1.28217	−	2.22078i
$303$	4.80590	−	8.32406i	0.276092	−	0.478205i
$304$			104.563i			5.99712i
$305$	0.493111	+	0.284698i	0.0282355	+	0.0163018i
$306$	−6.47484	−	3.73825i	−0.370142	−	0.213701i
$307$			24.8554i			1.41857i	0.704920	+	0.709287i	$0.250983\pi$
$307$			24.8554i			1.41857i	−0.704920	+	0.709287i	$0.749017\pi$
$308$	11.7155	−	20.2918i	0.667550	−	1.15623i
$309$	0.323499	+	0.560317i	0.0184032	+	0.0318753i
$310$	−6.69345	+	3.86447i	−0.380162	+	0.219487i
$311$	22.1302			1.25489			0.627444	−	0.778662i	$-0.284101\pi$
$311$	22.1302			1.25489			0.627444	+	0.778662i	$0.284101\pi$
$312$	−34.6669	−	4.67983i	−1.96263	−	0.264943i
$313$	−9.33248			−0.527503			−0.263751	−	0.964591i	$-0.584960\pi$
$313$	−9.33248			−0.527503			−0.263751	+	0.964591i	$0.584960\pi$
$314$	18.6154	−	10.7476i	1.05053	−	0.606523i
$315$	0.553080	+	0.957962i	0.0311625	+	0.0539751i
$316$	−1.98589	+	3.43966i	−0.111715	+	0.193496i
$317$		−	22.7618i		−	1.27843i	−0.769028	−	0.639215i	$-0.779259\pi$
$317$		−	22.7618i		−	1.27843i	0.769028	−	0.639215i	$-0.220741\pi$
$318$	21.6704	+	12.5114i	1.21522	+	0.701605i
$319$	6.70241	+	3.86964i	0.375263	+	0.216658i
$320$		−	8.58780i		−	0.480072i
$321$	8.69154	−	15.0542i	0.485114	−	0.840243i
$322$	−10.1677	−	17.6110i	−0.566626	−	0.981424i
$323$	−15.8491	+	9.15050i	−0.881869	+	0.509147i
$324$	−5.53457			−0.307476
$325$	14.0715	+	10.8710i	0.780546	+	0.603015i
$326$	0.454395			0.0251666
$327$	−1.70026	+	0.981646i	−0.0940247	+	0.0542852i
$328$	16.2025	+	28.0635i	0.894631	+	1.54955i
$329$	−3.31463	+	5.74111i	−0.182742	+	0.316518i
$330$			0.717202i			0.0394807i
$331$	1.68158	+	0.970859i	0.0924278	+	0.0533632i	0.545501	−	0.838110i	$-0.316339\pi$
$331$	1.68158	+	0.970859i	0.0924278	+	0.0533632i	−0.453074	+	0.891473i	$0.649673\pi$
$332$	49.3137	+	28.4713i	2.70644	+	1.56256i
$333$			7.23621i			0.396542i
$334$	−24.4548	+	42.3570i	−1.33811	+	2.31767i
$335$	0.0665194	+	0.115215i	0.00363434	+	0.00629487i
$336$	−57.0571	+	32.9419i	−3.11272	+	1.79713i
$337$	−22.2194			−1.21037			−0.605185	−	0.796085i	$-0.706901\pi$
$337$	−22.2194			−1.21037			−0.605185	+	0.796085i	$0.706901\pi$
$338$	−25.0661	−	25.3975i	−1.36342	−	1.38144i
$339$	−7.18300			−0.390127
$340$	3.41111	−	1.96940i	0.184993	−	0.106806i
$341$	5.38825	+	9.33273i	0.291790	+	0.505396i
$342$	−9.22157	+	15.9722i	−0.498645	+	0.863679i
$343$		−	16.6083i		−	0.896764i
$344$	−6.99463	−	4.03835i	−0.377125	−	0.217733i
$345$	0.395970	+	0.228613i	0.0213183	+	0.0123081i
$346$			3.96606i			0.213217i
$347$	−3.32281	+	5.75528i	−0.178378	+	0.308960i	−0.941325	−	0.337501i	$-0.890418\pi$
$347$	−3.32281	+	5.75528i	−0.178378	+	0.308960i	0.762947	+	0.646461i	$0.223752\pi$
$348$	−21.4168	−	37.0949i	−1.14806	−	1.98850i
$349$	10.9837	−	6.34144i	0.587944	−	0.339450i	−0.176340	−	0.984329i	$-0.556426\pi$
$349$	10.9837	−	6.34144i	0.587944	−	0.339450i	0.764284	+	0.644880i	$0.223093\pi$
$350$	57.3105			3.06337
$351$	−2.85325	−	2.20430i	−0.152295	−	0.117657i
$352$	−23.3130			−1.24259
$353$	−12.9885	+	7.49893i	−0.691309	+	0.399128i	−0.804102	−	0.594491i	$-0.797354\pi$
$353$	−12.9885	+	7.49893i	−0.691309	+	0.399128i	0.112793	+	0.993619i	$0.464020\pi$
$354$	−0.333577	−	0.577773i	−0.0177294	−	0.0307083i
$355$	0.280270	−	0.485442i	0.0148752	−	0.0257646i
$356$			35.3529i			1.87370i
$357$	−9.98631	−	5.76560i	−0.528532	−	0.305148i
$358$	42.4287	+	24.4962i	2.24243	+	1.29467i
$359$			5.96498i			0.314819i	0.987533	+	0.157410i	$0.0503143\pi$
$359$			5.96498i			0.314819i	−0.987533	+	0.157410i	$0.949686\pi$
$360$	1.26750	−	2.19537i	0.0668031	−	0.115706i
$361$	13.0726	+	22.6424i	0.688031	+	1.19170i
$362$	42.7603	−	24.6877i	2.24743	−	1.29756i
$363$	1.00000			0.0524864
$364$	−83.7219	−	11.3020i	−4.38822	−	0.592383i
$365$	0.0600056			0.00314083
$366$	−5.18038	+	2.99090i	−0.270783	+	0.156337i
$367$	−1.98413	−	3.43662i	−0.103571	−	0.179390i	0.809583	−	0.587006i	$-0.199694\pi$
$367$	−1.98413	−	3.43662i	−0.103571	−	0.179390i	−0.913153	+	0.407616i	$0.866360\pi$
$368$	−13.6164	+	23.5843i	−0.709805	+	1.22942i
$369$			3.33999i			0.173873i
$370$	−4.49452	−	2.59491i	−0.233659	−	0.134903i
$371$	33.4228	+	19.2967i	1.73523	+	1.00183i
$372$		−	59.6433i		−	3.09236i
$373$	17.0922	−	29.6045i	0.885000	−	1.53286i	0.0392859	−	0.999228i	$-0.487492\pi$
$373$	17.0922	−	29.6045i	0.885000	−	1.53286i	0.845714	−	0.533637i	$-0.179175\pi$
$374$	−3.73825	−	6.47484i	−0.193300	−	0.334806i
$375$	−2.24733	+	1.29750i	−0.116052	+	0.0670026i
$376$	15.1924			0.783486
$377$	3.73306	−	27.6535i	0.192262	−	1.42423i
$378$	−11.6208			−0.597708
$379$	−13.2240	+	7.63485i	−0.679269	+	0.392176i	−0.799580	−	0.600560i	$-0.794944\pi$
$379$	−13.2240	+	7.63485i	−0.679269	+	0.392176i	0.120311	+	0.992736i	$0.461611\pi$
$380$	−4.85816	−	8.41457i	−0.249218	−	0.431659i
$381$	−6.74343	+	11.6800i	−0.345477	+	0.598383i
$382$		−	24.2219i		−	1.23930i
$383$	−27.7955	−	16.0477i	−1.42028	−	0.820002i	−0.423961	−	0.905680i	$-0.639361\pi$
$383$	−27.7955	−	16.0477i	−1.42028	−	0.820002i	−0.996323	+	0.0856787i	$0.972694\pi$
$384$	37.7527	+	21.7965i	1.92656	+	1.11230i
$385$			1.10616i			0.0563751i
$386$	8.81969	−	15.2761i	0.448910	−	0.777535i
$387$	−0.416235	−	0.720940i	−0.0211584	−	0.0366474i
$388$	−27.6249	+	15.9493i	−1.40244	+	0.809701i
$389$	17.8146			0.903235			0.451617	−	0.892212i	$-0.350847\pi$
$389$	17.8146			0.903235			0.451617	+	0.892212i	$0.350847\pi$
$390$	2.39230	−	0.981735i	0.121139	−	0.0497121i
$391$	−4.76638			−0.241046
$392$	−91.7780	+	52.9880i	−4.63549	+	2.67630i
$393$	1.41314	+	2.44762i	0.0712833	+	0.123466i
$394$	−24.7586	+	42.8832i	−1.24732	+	2.16042i
$395$		−	0.187505i		−	0.00943442i
$396$	−4.79308	−	2.76728i	−0.240861	−	0.139061i
$397$	−2.39388	−	1.38211i	−0.120145	−	0.0693659i	0.438723	−	0.898622i	$-0.355431\pi$
$397$	−2.39388	−	1.38211i	−0.120145	−	0.0693659i	−0.558868	+	0.829256i	$0.688764\pi$
$398$		−	41.3975i		−	2.07507i
$399$	−14.2227	+	24.6344i	−0.712024	+	1.23326i
$400$	−38.3745	−	66.4666i	−1.91873	−	3.32333i
$401$	20.5425	−	11.8602i	1.02584	−	0.592271i	0.110052	−	0.993926i	$-0.464898\pi$
$401$	20.5425	−	11.8602i	1.02584	−	0.592271i	0.915791	+	0.401655i	$0.131565\pi$
$402$	−1.39764			−0.0697080
$403$	23.7547	−	30.7481i	1.18330	−	1.53167i
$404$	−53.1971			−2.64666
$405$	0.226278	−	0.130642i	0.0112439	−	0.00649164i
$406$	−44.9681	−	77.8871i	−2.23173	−	3.86547i
$407$	−3.61811	+	6.26674i	−0.179343	+	0.310631i
$408$			26.4262i			1.30829i
$409$	10.8007	+	6.23581i	0.534062	+	0.308341i	0.742669	−	0.669659i	$-0.233560\pi$
$409$	10.8007	+	6.23581i	0.534062	+	0.308341i	−0.208607	+	0.978000i	$0.566893\pi$
$410$	−2.07452	−	1.19772i	−0.102453	−	0.0591514i
$411$			5.59346i			0.275905i
$412$	1.79043	−	3.10111i	0.0882081	−	0.152781i
$413$	−0.514485	−	0.891114i	−0.0253161	−	0.0438489i
$414$	−4.15987	+	2.40170i	−0.204446	+	0.118037i
$415$	−2.68823			−0.131960
$416$	31.9118	+	77.7631i	1.56461	+	3.81265i
$417$	17.8649			0.874849
$418$	−15.9722	+	9.22157i	−0.781227	+	0.451042i
$419$	17.3519	+	30.0544i	0.847695	+	1.46825i	0.883260	+	0.468884i	$0.155344\pi$
$419$	17.3519	+	30.0544i	0.847695	+	1.46825i	−0.0355644	+	0.999367i	$0.511323\pi$
$420$	3.06106	−	5.30191i	0.149364	−	0.258707i
$421$		−	32.2528i		−	1.57191i	−0.618286	−	0.785954i	$-0.712172\pi$
$421$		−	32.2528i		−	1.57191i	0.618286	−	0.785954i	$-0.287828\pi$
$422$	0.816586	+	0.471456i	0.0397508	+	0.0229501i
$423$	1.35610	+	0.782942i	0.0659356	+	0.0380680i
$424$		−	88.4448i		−	4.29526i
$425$	6.71643	−	11.6332i	0.325795	−	0.564293i
$426$	2.94438	+	5.09981i	0.142656	+	0.247087i
$427$	−7.98984	+	4.61294i	−0.386656	+	0.223236i
$428$	−96.2078			−4.65038
$429$	−1.36884	−	3.33561i	−0.0660883	−	0.161045i
$430$	0.597049			0.0287922
$431$	23.3561	−	13.4847i	1.12502	−	0.649533i	0.182346	−	0.983234i	$-0.441631\pi$
$431$	23.3561	−	13.4847i	1.12502	−	0.649533i	0.942679	+	0.333701i	$0.108298\pi$
$432$	7.78115	+	13.4773i	0.374371	+	0.648429i
$433$	−2.26399	+	3.92134i	−0.108800	+	0.188447i	−0.915284	−	0.402808i	$-0.868034\pi$
$433$	−2.26399	+	3.92134i	−0.108800	+	0.188447i	0.806484	+	0.591256i	$0.201368\pi$
$434$		−	125.231i		−	6.01129i
$435$	1.75123	+	1.01107i	0.0839650	+	0.0484772i
$436$	9.41021	+	5.43299i	0.450667	+	0.260193i
$437$			11.7578i			0.562451i
$438$	−0.315194	+	0.545933i	−0.0150606	+	0.0260857i
$439$	−14.1836	−	24.5667i	−0.676946	−	1.17251i	−0.975896	−	0.218237i	$-0.929970\pi$
$439$	−14.1836	−	24.5667i	−0.676946	−	1.17251i	0.298950	−	0.954269i	$-0.403364\pi$
$440$	2.19537	−	1.26750i	0.104660	−	0.0604256i
$441$	−10.9230			−0.520144
$442$	−16.4804	+	21.3323i	−0.783895	+	1.01468i
$443$	−37.9484			−1.80298			−0.901491	−	0.432798i	$-0.857526\pi$
$443$	−37.9484			−1.80298			−0.901491	+	0.432798i	$0.857526\pi$
$444$	34.6837	−	20.0247i	1.64602	−	0.950328i
$445$	−0.834494	−	1.44539i	−0.0395588	−	0.0685179i
$446$	9.88107	−	17.1145i	0.467882	−	0.810396i
$447$		−	7.61379i		−	0.360120i
$448$	120.505	+	69.5737i	5.69333	+	3.28705i
$449$	30.4613	+	17.5868i	1.43756	+	0.829974i	0.997680	−	0.0680836i	$-0.0216885\pi$
$449$	30.4613	+	17.5868i	1.43756	+	0.829974i	0.439878	+	0.898058i	$0.355022\pi$
$450$		−	13.5372i		−	0.638149i
$451$	−1.67000	+	2.89252i	−0.0786371	+	0.136203i
$452$	19.8774	+	34.4287i	0.934955	+	1.61939i
$453$	−14.0598	+	8.11743i	−0.660587	+	0.381390i
$454$	69.5053			3.26204
$455$	3.68971	−	1.51416i	0.172976	−	0.0709848i
$456$	65.1885			3.05273
$457$	3.54305	−	2.04558i	0.165737	−	0.0956882i	−0.414837	−	0.909896i	$-0.636161\pi$
$457$	3.54305	−	2.04558i	0.165737	−	0.0956882i	0.580574	+	0.814207i	$0.302828\pi$
$458$	21.1815	+	36.6874i	0.989746	+	1.71429i
$459$	−1.36188	+	2.35885i	−0.0635671	+	0.110102i
$460$		−	2.53055i		−	0.117988i
$461$	0.204968	+	0.118338i	0.00954631	+	0.00551157i	0.504766	−	0.863256i	$-0.331579\pi$
$461$	0.204968	+	0.118338i	0.00954631	+	0.00551157i	−0.495219	+	0.868768i	$0.664912\pi$
$462$	−10.0639	−	5.81038i	−0.468214	−	0.270323i
$463$		−	19.0621i		−	0.885891i	−0.896549	−	0.442946i	$-0.853933\pi$
$463$		−	19.0621i		−	0.885891i	0.896549	−	0.442946i	$-0.146067\pi$
$464$	−60.2204	+	104.305i	−2.79566	+	4.84223i
$465$	1.40786	+	2.43849i	0.0652881	+	0.113082i
$466$	20.9951	−	12.1215i	0.972578	−	0.561518i
$467$	4.08576			0.189066			0.0945332	−	0.995522i	$-0.469864\pi$
$467$	4.08576			0.189066			0.0945332	+	0.995522i	$0.469864\pi$
$468$	−2.66961	+	19.7758i	−0.123403	+	0.914136i
$469$	−2.15562			−0.0995372
$470$	−0.972594	+	0.561528i	−0.0448624	+	0.0259013i
$471$	−3.91546	−	6.78177i	−0.180415	−	0.312488i
$472$	−1.17905	+	2.04218i	−0.0542702	+	0.0939988i
$473$		−	0.832470i		−	0.0382770i
$474$	1.70593	+	0.984919i	0.0783560	+	0.0452388i
$475$	−28.6969	−	16.5682i	−1.31671	−	0.760201i
$476$			63.8202i			2.92519i
$477$	4.55803	−	7.89474i	0.208698	−	0.361475i
$478$	20.4536	+	35.4266i	0.935524	+	1.62038i
$479$	21.7701	−	12.5690i	0.994701	−	0.574291i	0.0880250	−	0.996118i	$-0.471944\pi$
$479$	21.7701	−	12.5690i	0.994701	−	0.574291i	0.906676	+	0.421827i	$0.138611\pi$
$480$	−6.09131			−0.278029
$481$	25.8560	+	3.49040i	1.17893	+	0.159149i
$482$	−38.7193			−1.76362
$483$	−6.41587	+	3.70420i	−0.291932	+	0.168547i
$484$	−2.76728	−	4.79308i	−0.125786	−	0.217867i
$485$	0.752955	−	1.30416i	0.0341899	−	0.0592187i
$486$			2.74492i			0.124512i
$487$	−16.6679	−	9.62324i	−0.755296	−	0.436070i	0.0723082	−	0.997382i	$-0.476963\pi$
$487$	−16.6679	−	9.62324i	−0.755296	−	0.436070i	−0.827604	+	0.561312i	$0.810297\pi$
$488$	18.3104	+	10.5715i	0.828874	+	0.478550i
$489$		−	0.165540i		−	0.00748600i
$490$	3.91700	−	6.78445i	0.176952	−	0.306490i
$491$	−19.4615	−	33.7083i	−0.878284	−	1.52123i	−0.853222	−	0.521547i	$-0.825355\pi$
$491$	−19.4615	−	33.7083i	−0.878284	−	1.52123i	−0.0250619	−	0.999686i	$-0.507978\pi$
$492$	16.0088	−	9.24271i	0.721734	−	0.416694i
$493$	−21.0799			−0.949392
$494$	52.6230	+	40.6542i	2.36762	+	1.82912i
$495$	0.261284			0.0117438
$496$	−145.239	+	83.8536i	−6.52141	+	3.76514i
$497$	4.54119	+	7.86558i	0.203700	+	0.352819i
$498$	14.1206	−	24.4576i	0.632758	−	1.09597i
$499$			15.9751i			0.715142i	0.933886	+	0.357571i	$0.116395\pi$
$499$			15.9751i			0.715142i	−0.933886	+	0.357571i	$0.883605\pi$
$500$	12.4380	+	7.18110i	0.556245	+	0.321148i
$501$	15.4311	+	8.90914i	0.689410	+	0.398031i
$502$			16.9904i			0.758317i
$503$	14.2547	−	24.6898i	0.635584	−	1.10086i	−0.350807	−	0.936448i	$-0.614093\pi$
$503$	14.2547	−	24.6898i	0.635584	−	1.10086i	0.986391	−	0.164416i	$-0.0525740\pi$
$504$	20.5372	+	35.5714i	0.914799	+	1.58448i
$505$	2.17494	−	1.25570i	0.0967836	−	0.0558780i
$506$	−4.80340			−0.213537
$507$	−9.25255	+	9.13183i	−0.410920	+	0.405559i
$508$	74.6440			3.31179
$509$	37.7414	−	21.7900i	1.67286	−	0.965825i	0.706831	−	0.707382i	$-0.250124\pi$
$509$	37.7414	−	21.7900i	1.67286	−	0.965825i	0.966027	−	0.258443i	$-0.0832093\pi$
$510$	−0.976743	−	1.69177i	−0.0432509	−	0.0749128i
$511$	−0.486133	+	0.842006i	−0.0215052	+	0.0372482i
$512$		−	60.8306i		−	2.68836i
$513$	5.81884	+	3.35951i	0.256908	+	0.148326i
$514$	−36.0731	−	20.8268i	−1.59112	−	0.918631i
$515$			0.169050i			0.00744924i
$516$	−2.30368	+	3.99009i	−0.101414	+	0.175654i
$517$	0.782942	+	1.35610i	0.0344338	+	0.0596410i
$518$	72.8244	−	42.0452i	3.19972	−	1.84736i
$519$	1.44488			0.0634230
$520$	−7.23299	−	5.58789i	−0.317188	−	0.245045i
$521$	−16.2569			−0.712227			−0.356114	−	0.934443i	$-0.615898\pi$
$521$	−16.2569			−0.712227			−0.356114	+	0.934443i	$0.615898\pi$
$522$	−18.3976	+	10.6218i	−0.805239	+	0.464905i
$523$	10.7413	+	18.6044i	0.469682	+	0.813513i	0.999399	−	0.0346612i	$-0.0110352\pi$
$523$	10.7413	+	18.6044i	0.469682	+	0.813513i	−0.529717	+	0.848174i	$0.677702\pi$
$524$	7.82109	−	13.5465i	0.341666	−	0.591783i
$525$		−	20.8788i		−	0.911224i
$526$	−67.2165	−	38.8075i	−2.93078	−	1.69209i
$527$	−25.4201	−	14.6763i	−1.10732	−	0.639310i
$528$			15.5623i			0.677262i
$529$	9.96888	−	17.2666i	0.433430	−	0.750722i
$530$	3.26903	+	5.66212i	0.141997	+	0.245947i
$531$	−0.210488	+	0.121525i	−0.00913441	+	0.00527375i
$532$	157.433			6.82557
$533$	11.9343	+	1.61105i	0.516931	+	0.0697825i
$534$	17.5336			0.758752
$535$	3.93341	−	2.27096i	0.170056	−	0.0981820i
$536$	2.47003	+	4.27821i	0.106689	+	0.184791i
$537$	8.92421	−	15.4572i	0.385108	−	0.667027i
$538$		−	18.3481i		−	0.791042i
$539$	−9.45961	−	5.46151i	−0.407454	−	0.235244i
$540$	−1.25235	−	0.723046i	−0.0538927	−	0.0311149i
$541$			5.37085i			0.230911i	0.993313	+	0.115455i	$0.0368327\pi$
$541$			5.37085i			0.230911i	−0.993313	+	0.115455i	$0.963167\pi$
$542$	−20.4950	+	35.4984i	−0.880337	+	1.52479i
$543$	−8.99397	−	15.5780i	−0.385968	−	0.668516i
$544$	54.9918	−	31.7496i	2.35776	−	1.36125i
$545$	−0.512976			−0.0219735
$546$	−5.60530	+	41.5226i	−0.239885	+	1.77700i
$547$	21.8159			0.932781			0.466390	−	0.884579i	$-0.345554\pi$
$547$	21.8159			0.932781			0.466390	+	0.884579i	$0.345554\pi$
$548$	26.8099	−	15.4787i	1.14526	−	0.661217i
$549$	1.08961	+	1.88726i	0.0465035	+	0.0805465i
$550$	6.76859	−	11.7236i	0.288614	−	0.499894i
$551$			52.0003i			2.21529i
$552$	14.7033	+	8.48897i	0.625815	+	0.361314i
$553$	2.63110	+	1.51907i	0.111886	+	0.0645973i
$554$			10.0140i			0.425453i
$555$	−0.945352	+	1.63740i	−0.0401280	+	0.0695037i
$556$	−49.4373	−	85.6279i	−2.09661	−	3.63143i
$557$	−3.43978	+	1.98596i	−0.145748	+	0.0841477i	−0.571101	−	0.820880i	$-0.693483\pi$
$557$	−3.43978	+	1.98596i	−0.145748	+	0.0841477i	0.425353	+	0.905028i	$0.360150\pi$
$558$	−29.5806			−1.25225
$559$	−2.77679	+	1.13952i	−0.117446	+	0.0481965i
$560$	−17.2144			−0.727440
$561$	−2.35885	+	1.36188i	−0.0995906	+	0.0574986i
$562$	−5.24045	−	9.07673i	−0.221055	−	0.382879i
$563$	−9.78508	+	16.9483i	−0.412392	+	0.714284i	−0.995151	−	0.0983613i	$-0.968640\pi$
$563$	−9.78508	+	16.9483i	−0.412392	+	0.714284i	0.582759	+	0.812645i	$0.301973\pi$
$564$		−	8.66649i		−	0.364925i
$565$	−1.62536	−	0.938401i	−0.0683793	−	0.0394788i
$566$	−22.0091	−	12.7069i	−0.925110	−	0.534113i
$567$			4.23356i			0.177793i
$568$	10.4071	−	18.0256i	0.436672	−	0.756339i
$569$	14.0447	+	24.3261i	0.588784	+	1.01980i	0.994392	+	0.105757i	$0.0337266\pi$
$569$	14.0447	+	24.3261i	0.588784	+	1.01980i	−0.405608	+	0.914047i	$0.632940\pi$
$570$	−4.17328	+	2.40945i	−0.174800	+	0.100921i
$571$	−36.1552			−1.51305			−0.756524	−	0.653966i	$-0.773104\pi$
$571$	−36.1552			−1.51305			−0.756524	+	0.653966i	$0.773104\pi$
$572$	−12.1998	+	15.7915i	−0.510101	+	0.660277i
$573$	−8.82428			−0.368640
$574$	33.6133	−	19.4066i	1.40299	−	0.810018i
$575$	−4.31508	−	7.47394i	−0.179951	−	0.311685i
$576$	16.4339	−	28.4643i	0.684744	−	1.18601i
$577$			28.0661i			1.16841i	0.811608	+	0.584203i	$0.198593\pi$
$577$			28.0661i			1.16841i	−0.811608	+	0.584203i	$0.801407\pi$
$578$	−22.7759	−	13.1497i	−0.947354	−	0.546955i
$579$	−5.56525	−	3.21310i	−0.231284	−	0.133532i
$580$		−	11.1917i		−	0.464710i
$581$	21.7786	−	37.7216i	0.903527	−	1.56495i
$582$	7.91017	+	13.7008i	0.327887	+	0.567917i
$583$	7.89474	−	4.55803i	0.326967	−	0.188774i
$584$	2.22815			0.0922016
$585$	−0.357656	−	0.871539i	−0.0147872	−	0.0360337i
$586$	−26.5701			−1.09760
$587$	3.49332	−	2.01687i	0.144185	−	0.0832450i	−0.426172	−	0.904642i	$-0.640138\pi$
$587$	3.49332	−	2.01687i	0.144185	−	0.0832450i	0.570357	+	0.821397i	$0.306805\pi$
$588$	30.2271	+	52.3548i	1.24654	+	2.15908i
$589$	−36.2038	+	62.7068i	−1.49175	+	2.58379i
$590$		−	0.174316i		−	0.00717650i
$591$	15.6228	+	9.01980i	0.642634	+	0.371025i
$592$	−97.5249	−	56.3061i	−4.00825	−	2.31416i
$593$		−	29.4434i		−	1.20909i	−0.796569	−	0.604547i	$-0.793354\pi$
$593$		−	29.4434i		−	1.20909i	0.796569	−	0.604547i	$-0.206646\pi$
$594$	−1.37246	+	2.37717i	−0.0563126	+	0.0975364i
$595$	−1.50646	−	2.60926i	−0.0617587	−	0.106969i
$596$	−36.4934	+	21.0695i	−1.49483	+	0.863040i
$597$	−15.0815			−0.617245
$598$	6.57509	+	16.0222i	0.268875	+	0.655199i
$599$	15.6238			0.638372			0.319186	−	0.947692i	$-0.396591\pi$
$599$	15.6238			0.638372			0.319186	+	0.947692i	$0.396591\pi$
$600$	−41.4377	+	23.9241i	−1.69169	+	0.976695i
$601$	4.98763	+	8.63883i	0.203450	+	0.352385i	0.949638	−	0.313350i	$-0.101451\pi$
$601$	4.98763	+	8.63883i	0.203450	+	0.352385i	−0.746188	+	0.665735i	$0.768118\pi$
$602$	−4.83697	+	8.37787i	−0.197140	+	0.341457i
$603$			0.509174i			0.0207352i
$604$	77.8149	+	44.9265i	3.16625	+	1.82803i
$605$	0.226278	+	0.130642i	0.00919952	+	0.00531134i
$606$			26.3836i			1.07176i
$607$	2.48136	−	4.29785i	0.100715	−	0.174444i	−0.811264	−	0.584680i	$-0.801220\pi$
$607$	2.48136	−	4.29785i	0.100715	−	0.174444i	0.911980	+	0.410236i	$0.134554\pi$
$608$	−78.3203	−	135.655i	−3.17631	−	5.50153i
$609$	−28.3750	+	16.3823i	−1.14981	+	0.663846i
$610$	−1.56294			−0.0632818
$611$	3.45168	−	4.46787i	0.139640	−	0.180751i
$612$	15.0748			0.609364
$613$	−2.65280	+	1.53160i	−0.107146	+	0.0618606i	−0.552615	−	0.833437i	$-0.686370\pi$
$613$	−2.65280	+	1.53160i	−0.107146	+	0.0618606i	0.445470	+	0.895297i	$0.353037\pi$
$614$	−34.1130	−	59.0855i	−1.37669	−	2.38450i
$615$	−0.436343	+	0.755768i	−0.0175950	+	0.0304755i
$616$			41.0744i			1.65493i
$617$	15.1015	+	8.71888i	0.607965	+	0.351009i	0.772169	−	0.635418i	$-0.219172\pi$
$617$	15.1015	+	8.71888i	0.607965	+	0.351009i	−0.164203	+	0.986426i	$0.552505\pi$
$618$	−1.53802	−	0.887978i	−0.0618684	−	0.0357197i
$619$			32.0178i			1.28690i	0.765487	+	0.643452i	$0.222498\pi$
$619$			32.0178i			1.28690i	−0.765487	+	0.643452i	$0.777502\pi$
$620$	7.79191	−	13.4960i	0.312931	−	0.542012i
$621$	0.874963	+	1.51548i	0.0351110	+	0.0608141i
$622$	−52.6072	+	30.3728i	−2.10936	+	1.21784i
$623$	27.0425			1.08343
$624$	51.9097	−	21.3023i	2.07805	−	0.852775i
$625$	23.9806			0.959225
$626$	22.1849	−	12.8084i	0.886685	−	0.511928i
$627$	3.35951	+	5.81884i	0.134166	+	0.232382i
$628$	−21.6704	+	37.5342i	−0.864742	+	1.49778i
$629$		−	19.7097i		−	0.785878i
$630$	−2.62953	−	1.51816i	−0.104763	−	0.0604848i
$631$	−26.0951	−	15.0660i	−1.03883	−	0.599768i	−0.119327	−	0.992855i	$-0.538074\pi$
$631$	−26.0951	−	15.0660i	−1.03883	−	0.599768i	−0.919501	+	0.393087i	$0.871407\pi$
$632$		−	6.96253i		−	0.276954i
$633$	0.171756	−	0.297490i	0.00682669	−	0.0118242i
$634$	31.2396	+	54.1086i	1.24068	+	2.14893i
$635$	−3.05179	+	1.76195i	−0.121106	+	0.0699208i
$636$	−50.4534			−2.00061
$637$	−5.26874	+	39.0295i	−0.208755	+	1.54640i
$638$	−21.2437			−0.841045
$639$	1.85791	−	1.07267i	0.0734978	−	0.0424340i
$640$	5.69508	+	9.86417i	0.225118	+	0.389915i
$641$	12.7832	−	22.1411i	0.504905	−	0.874522i	−0.495079	−	0.868848i	$-0.664861\pi$
$641$	12.7832	−	22.1411i	0.504905	−	0.874522i	0.999984	−	0.00567343i	$-0.00180592\pi$
$642$			47.7151i			1.88316i
$643$	36.8728	+	21.2885i	1.45412	+	0.839536i	0.998712	−	0.0507465i	$-0.0161601\pi$
$643$	36.8728	+	21.2885i	1.45412	+	0.839536i	0.455408	+	0.890283i	$0.349493\pi$
$644$	35.5091	+	20.5012i	1.39925	+	0.807859i
$645$		−	0.217511i		−	0.00856448i
$646$	25.1173	−	43.5045i	0.988229	−	1.71166i
$647$	11.3847	+	19.7190i	0.447580	+	0.775232i	0.998228	−	0.0595058i	$-0.0189525\pi$
$647$	11.3847	+	19.7190i	0.447580	+	0.775232i	−0.550647	+	0.834738i	$0.685619\pi$
$648$	8.40226	−	4.85105i	0.330072	−	0.190567i
$649$	−0.243051			−0.00954058
$650$	−48.3703	−	6.52969i	−1.89724	−	0.256116i
$651$	−45.6230			−1.78811
$652$	−0.793448	+	0.458097i	−0.0310738	+	0.0179405i
$653$	13.1770	+	22.8232i	0.515654	+	0.893139i	0.999835	+	0.0181710i	$0.00578434\pi$
$653$	13.1770	+	22.8232i	0.515654	+	0.893139i	−0.484181	+	0.874968i	$0.660882\pi$
$654$	2.69454	−	4.66708i	0.105365	−	0.182497i
$655$			0.738458i			0.0288540i
$656$	−45.0143	−	25.9890i	−1.75751	−	1.01470i
$657$	0.198889	+	0.114828i	0.00775938	+	0.00447988i
$658$		−	18.1968i		−	0.709384i
$659$	3.87244	−	6.70726i	0.150849	−	0.261278i	−0.780691	−	0.624917i	$-0.785133\pi$
$659$	3.87244	−	6.70726i	0.150849	−	0.261278i	0.931540	+	0.363639i	$0.118466\pi$
$660$	−0.723046	−	1.25235i	−0.0281445	−	0.0487477i
$661$	8.85905	−	5.11478i	0.344577	−	0.198942i	−0.317717	−	0.948186i	$-0.602916\pi$
$661$	8.85905	−	5.11478i	0.344577	−	0.198942i	0.662294	+	0.749244i	$0.269583\pi$
$662$	−5.32985			−0.207151
$663$	7.77158	+	6.00399i	0.301823	+	0.233175i
$664$	−99.8203			−3.87378
$665$	−6.43656	+	3.71615i	−0.249599	+	0.144106i
$666$	−9.93140	−	17.2017i	−0.384834	−	0.666552i
$667$	−6.77158	+	11.7287i	−0.262196	+	0.454138i
$668$		−	98.6164i		−	3.81558i
$669$	−6.23498	−	3.59977i	−0.241058	−	0.139175i
$670$	−0.316256	−	0.182590i	−0.0122180	−	0.00705408i
$671$			2.17923i			0.0841281i
$672$	49.3485	−	85.4742i	1.90366	−	3.29724i
$673$	−18.6143	−	32.2409i	−0.717529	−	1.24280i	−0.961976	−	0.273134i	$-0.911940\pi$
$673$	−18.6143	−	32.2409i	−0.717529	−	1.24280i	0.244447	−	0.969663i	$-0.421394\pi$
$674$	52.8193	−	30.4953i	2.03452	−	1.17463i
$675$	−4.93173			−0.189822
$676$	69.3740	+	19.0778i	2.66823	+	0.733761i
$677$	−29.1348			−1.11974			−0.559871	−	0.828579i	$-0.689149\pi$
$677$	−29.1348			−1.11974			−0.559871	+	0.828579i	$0.689149\pi$
$678$	17.0752	−	9.85837i	0.655769	−	0.378609i
$679$	12.2001	+	21.1311i	0.468196	+	0.810938i
$680$	−3.45236	+	5.97967i	−0.132392	+	0.229310i
$681$		−	25.3215i		−	0.970320i
$682$	−25.6176	−	14.7903i	−0.980947	−	0.566350i
$683$	−38.8443	−	22.4268i	−1.48634	−	0.858137i	−0.486457	−	0.873704i	$-0.661711\pi$
$683$	−38.8443	−	22.4268i	−1.48634	−	0.858137i	−0.999879	+	0.0155678i	$0.995044\pi$
$684$		−	37.1868i		−	1.42187i
$685$	−0.730740	+	1.26568i	−0.0279201	+	0.0483591i
$686$	22.7942	+	39.4807i	0.870287	+	1.50738i
$687$	13.3656	−	7.71662i	0.509929	−	0.294407i
$688$	12.9551			0.493910
$689$	−26.0104	−	20.0945i	−0.990919	−	0.765541i
$690$	−1.25505			−0.0477789
$691$	−12.9587	+	7.48172i	−0.492973	+	0.284618i	−0.725807	−	0.687899i	$-0.758533\pi$
$691$	−12.9587	+	7.48172i	−0.492973	+	0.284618i	0.232834	+	0.972516i	$0.425200\pi$
$692$	−3.99838	−	6.92540i	−0.151996	−	0.263264i
$693$	−2.11678	+	3.66637i	−0.0804098	+	0.139274i
$694$		−	18.2417i		−	0.692445i
$695$	4.04244	+	2.33391i	0.153339	+	0.0885301i
$696$	65.0274	+	37.5436i	2.46486	+	1.42309i
$697$		−	9.09735i		−	0.344587i
$698$	−17.4067	+	30.1493i	−0.658854	+	1.14117i
$699$	−4.41599	−	7.64871i	−0.167028	−	0.289301i
$700$	−100.074	+	57.7775i	−3.78242	+	2.18378i
$701$	41.5151			1.56800			0.784001	−	0.620759i	$-0.213175\pi$
$701$	41.5151			1.56800			0.784001	+	0.620759i	$0.213175\pi$
$702$	9.80797	+	1.32402i	0.370178	+	0.0499718i
$703$	−48.6202			−1.83375
$704$	28.4643	−	16.4339i	1.07279	−	0.619374i
$705$	0.204570	+	0.354326i	0.00770455	+	0.0133447i
$706$	20.5839	−	35.6524i	0.774686	−	1.34180i
$707$			40.6921i			1.53038i
$708$	1.16496	+	0.672591i	0.0437819	+	0.0252775i
$709$	−1.83299	−	1.05828i	−0.0688392	−	0.0397444i	0.465185	−	0.885213i	$-0.345988\pi$
$709$	−1.83299	−	1.05828i	−0.0688392	−	0.0397444i	−0.534025	+	0.845469i	$0.679321\pi$
$710$			1.53864i			0.0577440i
$711$	0.358816	−	0.621487i	0.0134566	−	0.0233076i
$712$	−30.9868	−	53.6707i	−1.16128	−	2.01139i
$713$	−16.3316	+	9.42904i	−0.611622	+	0.353120i
$714$	31.6522			1.18455
$715$	0.126031	−	0.933603i	0.00471328	−	0.0349148i
$716$	−98.7833			−3.69170
$717$	12.9063	−	7.45143i	0.481993	−	0.278279i
$718$	−8.18668	−	14.1797i	−0.305524	−	0.529184i
$719$	8.43502	−	14.6099i	0.314573	−	0.544857i	−0.664773	−	0.747045i	$-0.731472\pi$
$719$	8.43502	−	14.6099i	0.314573	−	0.544857i	0.979347	+	0.202188i	$0.0648052\pi$
$720$			4.06617i			0.151537i
$721$	−2.37214	−	1.36955i	−0.0883429	−	0.0510048i
$722$	−62.1515	−	35.8832i	−2.31304	−	1.33543i
$723$			14.1058i			0.524601i
$724$	−49.7777	+	86.2175i	−1.84997	+	3.20425i
$725$	−19.0840	−	33.0545i	−0.708762	−	1.22761i
$726$	−2.37717	+	1.37246i	−0.0882250	+	0.0509367i
$727$	49.8000			1.84698			0.923490	−	0.383623i	$-0.125324\pi$
$727$	49.8000			1.84698			0.923490	+	0.383623i	$0.125324\pi$
$728$	137.008	−	56.2243i	5.07785	−	2.08381i
$729$	1.00000			0.0370370
$730$	−0.142643	+	0.0823551i	−0.00527946	+	0.00304810i
$731$	1.13372	+	1.96367i	0.0419323	+	0.0726289i
$732$	6.03053	−	10.4452i	0.222895	−	0.386065i
$733$			27.3911i			1.01171i	0.862618	+	0.505856i	$0.168823\pi$
$733$			27.3911i			1.01171i	−0.862618	+	0.505856i	$0.831177\pi$
$734$	9.43324	+	5.44628i	0.348187	+	0.201026i
$735$	−2.47164	−	1.42700i	−0.0911678	−	0.0526358i
$736$		−	40.7961i		−	1.50376i
$737$	−0.254587	+	0.440958i	−0.00937783	+	0.0162429i
$738$	−4.58400	−	7.93973i	−0.168739	−	0.292265i
$739$	−10.1912	+	5.88390i	−0.374890	+	0.216443i	−0.675593	−	0.737275i	$-0.736112\pi$
$739$	−10.1912	+	5.88390i	−0.374890	+	0.216443i	0.300703	+	0.953718i	$0.402779\pi$
$740$	10.4642			0.384673
$741$	14.8107	−	19.1711i	0.544086	−	0.704267i
$742$	−105.936			−3.88902
$743$	18.6089	−	10.7438i	0.682694	−	0.394153i	−0.118175	−	0.992993i	$-0.537705\pi$
$743$	18.6089	−	10.7438i	0.682694	−	0.394153i	0.800869	+	0.598839i	$0.204371\pi$
$744$	52.2773	+	90.5470i	1.91658	+	3.31961i
$745$	0.994679	−	1.72283i	0.0364422	−	0.0631198i
$746$			93.8332i			3.43548i
$747$	−8.91013	−	5.14427i	−0.326005	−	0.188219i
$748$	13.0552	+	7.53742i	0.477345	+	0.275595i
$749$			73.5923i			2.68900i
$750$	3.56153	−	6.16875i	0.130049	−	0.225251i
$751$	12.2614	+	21.2374i	0.447426	+	0.774965i	0.998218	−	0.0596777i	$-0.0190073\pi$
$751$	12.2614	+	21.2374i	0.447426	+	0.774965i	−0.550791	+	0.834643i	$0.685674\pi$
$752$	−21.1040	+	12.1844i	−0.769583	+	0.444319i
$753$	6.18976			0.225567
$754$	29.0792	+	70.8605i	1.05900	+	2.58059i
$755$	−4.24190			−0.154379
$756$	20.2918	−	11.7155i	0.738004	−	0.426087i
$757$	−13.6627	−	23.6644i	−0.496578	−	0.860099i	0.503414	−	0.864045i	$-0.332077\pi$
$757$	−13.6627	−	23.6644i	−0.496578	−	0.860099i	−0.999992	+	0.00394665i	$0.998744\pi$
$758$	20.9570	−	36.2986i	0.761194	−	1.31843i
$759$			1.74993i			0.0635183i
$760$	14.7507	+	8.51635i	0.535066	+	0.308920i
$761$	−31.7790	−	18.3476i	−1.15199	−	0.665100i	−0.202617	−	0.979258i	$-0.564945\pi$
$761$	−31.7790	−	18.3476i	−1.15199	−	0.665100i	−0.949371	+	0.314158i	$0.898278\pi$
$762$		−	37.0203i		−	1.34111i
$763$	4.15586	−	7.19816i	0.150452	−	0.260591i
$764$	24.4193	+	42.2955i	0.883459	+	1.53020i
$765$	−0.616328	+	0.355837i	−0.0222834	+	0.0128653i
$766$	88.0994			3.18316
$767$	0.332698	+	0.810722i	0.0120130	+	0.0292735i
$768$	−53.9240			−1.94581
$769$	34.8378	−	20.1136i	1.25628	−	0.725316i	0.283934	−	0.958844i	$-0.408360\pi$
$769$	34.8378	−	20.1136i	1.25628	−	0.725316i	0.972350	+	0.233528i	$0.0750271\pi$
$770$	−1.51816	−	2.62953i	−0.0547106	−	0.0947615i
$771$	−7.58741	+	13.1418i	−0.273254	+	0.473290i
$772$			35.5662i			1.28006i
$773$	3.41235	+	1.97012i	0.122734	+	0.0708602i	0.560110	−	0.828418i	$-0.310759\pi$
$773$	3.41235	+	1.97012i	0.122734	+	0.0708602i	−0.437376	+	0.899279i	$0.644092\pi$
$774$	1.97892	+	1.14253i	0.0711308	+	0.0410674i
$775$		−	53.1468i		−	1.90909i
$776$	27.9590	−	48.4265i	1.00367	−	1.73841i
$777$	−15.3175	−	26.5306i	−0.549511	−	0.951781i
$778$	−42.3482	+	24.4498i	−1.51826	+	0.876567i
$779$	−22.4415			−0.804049
$780$	−3.18762	+	4.12607i	−0.114135	+	0.147737i
$781$	2.14533			0.0767660
$782$	11.3305	−	6.54165i	0.405177	−	0.233929i
$783$	3.86964	+	6.70241i	0.138290	+	0.239525i
$784$	84.9936	−	147.213i	3.03549	−	5.25762i
$785$		−	2.04609i		−	0.0730281i
$786$	−6.71852	−	3.87894i	−0.239642	−	0.138357i
$787$	−5.26138	−	3.03766i	−0.187548	−	0.108281i	0.403286	−	0.915074i	$-0.367868\pi$
$787$	−5.26138	−	3.03766i	−0.187548	−	0.108281i	−0.590834	+	0.806793i	$0.701201\pi$
$788$		−	99.8414i		−	3.55670i
$789$	−14.1379	+	24.4876i	−0.503324	+	0.871783i
$790$	0.257343	+	0.445732i	0.00915586	+	0.0158584i
$791$	26.3355	−	15.2048i	0.936384	−	0.540622i
$792$	9.70209			0.344749
$793$	7.26904	−	2.98301i	0.258131	−	0.105930i
$794$	7.58753			0.269271
$795$	2.06277	−	1.19094i	0.0731588	−	0.0422382i
$796$	41.7348	+	72.2868i	1.47925	+	2.56214i
$797$	−20.2778	+	35.1222i	−0.718277	+	1.24409i	0.243404	+	0.969925i	$0.421736\pi$
$797$	−20.2778	+	35.1222i	−0.718277	+	1.24409i	−0.961682	+	0.274168i	$0.911598\pi$
$798$		−	78.0801i		−	2.76401i
$799$	−3.69368	−	2.13255i	−0.130673	−	0.0754441i
$800$	99.5700	+	57.4868i	3.52033	+	2.03246i
$801$		−	6.38765i		−	0.225697i
$802$	−32.5553	+	56.3875i	−1.14957	+	1.99111i
$803$	0.114828	+	0.198889i	0.00405221	+	0.00701863i
$804$	2.44051	−	1.40903i	0.0860701	−	0.0496926i
$805$	−1.93570			−0.0682243
$806$	−14.2683	+	105.696i	−0.502579	+	3.72297i
$807$	−6.68439			−0.235302
$808$	80.7608	−	46.6273i	2.84115	−	1.64034i
$809$	4.60910	+	7.98320i	0.162047	+	0.280674i	0.935603	−	0.353054i	$-0.114857\pi$
$809$	4.60910	+	7.98320i	0.162047	+	0.280674i	−0.773555	+	0.633729i	$0.781524\pi$
$810$	−0.358601	+	0.621115i	−0.0126000	+	0.0218238i
$811$		−	27.5990i		−	0.969133i	−0.874754	−	0.484566i	$-0.838977\pi$
$811$		−	27.5990i		−	0.969133i	0.874754	−	0.484566i	$-0.161023\pi$
$812$	157.044	+	90.6691i	5.51115	+	3.18186i
$813$	12.9324	+	7.46654i	0.453560	+	0.261863i
$814$		−	19.8628i		−	0.696191i
$815$	0.0216265	−	0.0374582i	0.000757543	−	0.00131210i
$816$	−21.1940	−	36.7091i	−0.741938	−	1.28507i
$817$	4.84401	−	2.79669i	0.169470	−	0.0978438i
$818$	−34.2336			−1.19695
$819$	15.1271	+	2.04207i	0.528584	+	0.0713556i
$820$	4.82994			0.168669
$821$	−46.2732	+	26.7159i	−1.61495	+	0.932390i	−0.626747	+	0.779223i	$0.715614\pi$
$821$	−46.2732	+	26.7159i	−1.61495	+	0.932390i	−0.988200	+	0.153167i	$0.951053\pi$
$822$	−7.67679	−	13.2966i	−0.267759	−	0.463772i
$823$	17.8133	−	30.8536i	0.620933	−	1.07549i	−0.368379	−	0.929676i	$-0.620087\pi$
$823$	17.8133	−	30.8536i	0.620933	−	1.07549i	0.989312	−	0.145812i	$-0.0465796\pi$
$824$			6.27724i			0.218678i
$825$	−4.27100	−	2.46587i	−0.148697	−	0.0858504i
$826$	2.44603	+	1.41222i	0.0851084	+	0.0491374i
$827$			37.4132i			1.30098i	0.759513	+	0.650492i	$0.225437\pi$
$827$			37.4132i			1.30098i	−0.759513	+	0.650492i	$0.774563\pi$
$828$	4.84254	−	8.38752i	0.168290	−	0.291487i
$829$	10.0682	+	17.4386i	0.349681	+	0.605666i	0.986193	−	0.165601i	$-0.0529565\pi$
$829$	10.0682	+	17.4386i	0.349681	+	0.605666i	−0.636511	+	0.771267i	$0.719623\pi$
$830$	6.39036	−	3.68948i	0.221813	−	0.128064i
$831$	3.64819			0.126554
$832$	−93.7800	−	72.4503i	−3.25124	−	2.51176i
$833$	29.7517			1.03083
$834$	−42.4679	+	24.5189i	−1.47054	+	0.849019i
$835$	2.32781	+	4.03189i	0.0805572	+	0.139529i
$836$	18.5934	−	32.2048i	0.643067	−	1.11382i
$837$			10.7765i			0.372491i
$838$	−82.4967	−	47.6295i	−2.84980	−	1.64533i
$839$	4.68773	+	2.70646i	0.161838	+	0.0934374i	0.578732	−	0.815518i	$-0.303548\pi$
$839$	4.68773	+	2.70646i	0.161838	+	0.0934374i	−0.416893	+	0.908955i	$0.636881\pi$
$840$			10.7321i			0.370291i
$841$	−15.4482	+	26.7570i	−0.532696	+	0.922657i
$842$	44.2657	+	76.6704i	1.52550	+	2.64224i
$843$	−3.30674	+	1.90915i	−0.113890	+	0.0657545i
$844$	−1.90119			−0.0654417
$845$	−3.28665	+	0.857565i	−0.113064	+	0.0295011i
$846$	−4.29822			−0.147776
$847$	−3.66637	+	2.11678i	−0.125978	+	0.0727334i
$848$	70.9334	+	122.860i	2.43586	+	4.21904i
$849$	−4.62926	+	8.01812i	−0.158876	+	0.275181i
$850$			36.8721i			1.26470i
$851$	−10.9663	−	6.33142i	−0.375921	−	0.217038i
$852$	−10.2827	−	5.93674i	−0.352281	−	0.203389i
$853$			17.5763i			0.601802i	0.953655	+	0.300901i	$0.0972873\pi$
$853$			17.5763i			0.601802i	−0.953655	+	0.300901i	$0.902713\pi$
$854$	12.6621	−	21.9315i	0.433289	−	0.750479i
$855$	0.877784	+	1.52037i	0.0300196	+	0.0519955i
$856$	146.057	−	84.3261i	4.99213	−	2.88221i
$857$	−1.78252			−0.0608896			−0.0304448	−	0.999536i	$-0.509692\pi$
$857$	−1.78252			−0.0608896			−0.0304448	+	0.999536i	$0.509692\pi$
$858$	7.83195	+	6.05062i	0.267378	+	0.206565i
$859$	43.0487			1.46880			0.734401	−	0.678716i	$-0.237463\pi$
$859$	43.0487			1.46880			0.734401	+	0.678716i	$0.237463\pi$
$860$	−1.04255	+	0.601914i	−0.0355505	+	0.0205251i
$861$	−7.07003	−	12.2457i	−0.240946	−	0.417331i
$862$	−37.0143	+	64.1106i	−1.26071	+	2.18362i
$863$		−	18.1069i		−	0.616367i	−0.951327	−	0.308184i	$-0.900279\pi$
$863$		−	18.1069i		−	0.616367i	0.951327	−	0.308184i	$-0.0997211\pi$
$864$	−20.1897	−	11.6565i	−0.686867	−	0.396563i
$865$	0.326944	+	0.188761i	0.0111164	+	0.00641807i
$866$		−	12.4289i		−	0.422351i
$867$	−4.79056	+	8.29750i	−0.162696	+	0.281798i
$868$	126.252	+	218.674i	4.28526	+	7.42229i
$869$	0.621487	−	0.358816i	0.0210825	−	0.0121720i
$870$	−5.55062			−0.188184
$871$	1.81935	+	0.245601i	0.0616463	+	0.00832188i
$872$	−19.0480			−0.645048
$873$	4.99134	−	2.88175i	0.168931	−	0.0975325i
$874$	−16.1371	−	27.9502i	−0.545844	−	0.945430i
$875$	5.49304	−	9.51422i	0.185699	−	0.321639i
$876$		−	1.27105i		−	0.0429448i
$877$	−43.1331	−	24.9029i	−1.45650	−	0.840911i	−0.457664	−	0.889125i	$-0.651314\pi$
$877$	−43.1331	−	24.9029i	−1.45650	−	0.840911i	−0.998837	+	0.0482139i	$0.984647\pi$
$878$	67.4336	+	38.9328i	2.27577	+	1.31392i
$879$			9.67976i			0.326490i
$880$	−2.03309	+	3.52141i	−0.0685353	+	0.118707i
$881$	−0.586205	−	1.01534i	−0.0197497	−	0.0342076i	0.855982	−	0.517006i	$-0.172954\pi$
$881$	−0.586205	−	1.01534i	−0.0197497	−	0.0342076i	−0.875731	+	0.482799i	$0.839620\pi$
$882$	25.9658	−	14.9914i	0.874315	−	0.504786i
$883$	39.2895			1.32220			0.661099	−	0.750298i	$-0.270090\pi$
$883$	39.2895			1.32220			0.661099	+	0.750298i	$0.270090\pi$
$884$	7.27138	−	53.8645i	0.244563	−	1.81166i
$885$	−0.0635052			−0.00213470
$886$	90.2097	−	52.0826i	3.03065	−	1.74975i
$887$	−7.12644	−	12.3434i	−0.239283	−	0.414450i	0.721226	−	0.692700i	$-0.243579\pi$
$887$	−7.12644	−	12.3434i	−0.239283	−	0.414450i	−0.960509	+	0.278250i	$0.910246\pi$
$888$	−35.1032	+	60.8005i	−1.17799	+	2.04033i
$889$		−	57.0974i		−	1.91499i
$890$	3.96746	+	2.29062i	0.132990	+	0.0767817i
$891$	0.866025	+	0.500000i	0.0290129	+	0.0167506i
$892$			39.8463i			1.33415i
$893$	−5.26060	+	9.11163i	−0.176039	+	0.304909i
$894$	10.4496	+	18.0992i	0.349487	+	0.605329i
$895$	4.03871	−	2.33175i	0.134999	−	0.0779418i
$896$	−184.554			−6.16551
$897$	5.83706	−	2.39537i	0.194894	−	0.0799791i
$898$	−96.5488			−3.22187
$899$	−72.2286	+	41.7012i	−2.40896	+	1.39081i
$900$	13.6475	+	23.6382i	0.454917	+	0.787939i
$901$	−12.4150	+	21.5034i	−0.413603	+	0.716381i
$902$		−	9.16801i		−	0.305261i
$903$	3.05214	+	1.76215i	0.101569	+	0.0586408i
$904$	−60.3534	−	34.8451i	−2.00733	−	1.15893i
$905$		−	4.69995i		−	0.156232i
$906$	22.2817	−	38.5930i	0.740259	−	1.28217i
$907$	−7.44539	−	12.8958i	−0.247220	−	0.428198i	0.715533	−	0.698579i	$-0.246184\pi$
$907$	−7.44539	−	12.8958i	−0.247220	−	0.428198i	−0.962753	+	0.270381i	$0.912850\pi$
$908$	−121.368	+	70.0716i	−4.02773	+	2.32541i
$909$	9.61179			0.318803
$910$	−6.69295	+	8.66338i	−0.221869	+	0.287188i
$911$	−9.19490			−0.304641			−0.152320	−	0.988331i	$-0.548675\pi$
$911$	−9.19490			−0.304641			−0.152320	+	0.988331i	$0.548675\pi$
$912$	−90.5545	+	52.2817i	−2.99856	+	1.73122i
$913$	−5.14427	−	8.91013i	−0.170250	−	0.294882i
$914$	−5.61495	+	9.72538i	−0.185726	+	0.321687i
$915$			0.569396i			0.0188236i
$916$	−73.9727	−	42.7082i	−2.44413	−	1.41112i
$917$	−10.3622	−	5.98259i	−0.342188	−	0.197563i
$918$		−	7.47650i		−	0.246761i
$919$	−13.9726	+	24.2013i	−0.460914	+	0.798327i	−0.999007	−	0.0445591i	$-0.985812\pi$
$919$	−13.9726	+	24.2013i	−0.460914	+	0.798327i	0.538093	+	0.842886i	$0.319145\pi$
$920$	2.21803	+	3.84174i	0.0731262	+	0.126658i
$921$	−21.5254	+	12.4277i	−0.709287	+	0.409507i
$922$	−0.649658			−0.0213953
$923$	−2.93662	−	7.15598i	−0.0966600	−	0.235542i
$924$	23.4309			0.770820
$925$	30.9059	−	17.8435i	1.01618	−	0.586692i
$926$	26.1619	+	45.3138i	0.859735	+	1.48910i
$927$	−0.323499	+	0.560317i	−0.0106251	+	0.0184032i
$928$		−	180.426i		−	5.92277i
$929$	−28.8220	−	16.6404i	−0.945619	−	0.545953i	−0.0539017	−	0.998546i	$-0.517166\pi$
$929$	−28.8220	−	16.6404i	−0.945619	−	0.545953i	−0.891717	+	0.452593i	$0.850499\pi$
$930$	−6.69345	−	3.86447i	−0.219487	−	0.126721i
$931$		−	73.3919i		−	2.40532i
$932$	−24.4406	+	42.3323i	−0.800578	+	1.38664i
$933$	11.0651	+	19.1653i	0.362255	+	0.627444i
$934$	−9.71253	+	5.60753i	−0.317804	+	0.183484i
$935$	−0.711674			−0.0232742
$936$	−13.2806	−	32.3624i	−0.434091	−	1.05780i
$937$	28.2184			0.921855			0.460928	−	0.887438i	$-0.347517\pi$
$937$	28.2184			0.921855			0.460928	+	0.887438i	$0.347517\pi$
$938$	5.12426	−	2.95850i	0.167313	−	0.0965983i
$939$	−4.66624	−	8.08216i	−0.152277	−	0.263751i
$940$	1.13221	−	1.96104i	0.0369285	−	0.0639620i
$941$		−	31.7917i		−	1.03638i	−0.855266	−	0.518189i	$-0.826606\pi$
$941$		−	31.7917i		−	1.03638i	0.855266	−	0.518189i	$-0.173394\pi$
$942$	18.6154	+	10.7476i	0.606523	+	0.350176i
$943$	−5.06169	−	2.92237i	−0.164831	−	0.0951655i
$944$		−	3.78243i		−	0.123108i
$945$	−0.553080	+	0.957962i	−0.0179917	+	0.0311625i
$946$	1.14253	+	1.97892i	0.0371469	+	0.0643402i
$947$	40.4870	−	23.3752i	1.31565	−	0.759590i	0.332624	−	0.943060i	$-0.392066\pi$
$947$	40.4870	−	23.3752i	1.31565	−	0.759590i	0.983025	+	0.183469i	$0.0587328\pi$
$948$	−3.97178			−0.128997
$949$	0.506232	−	0.655269i	0.0164330	−	0.0212709i
$950$	90.9566			2.95102
$951$	19.7123	−	11.3809i	0.639215	−	0.369051i
$952$	−55.9384	−	96.8881i	−1.81297	−	3.14016i
$953$	−3.18202	+	5.51142i	−0.103076	+	0.178532i	−0.912950	−	0.408071i	$-0.866202\pi$
$953$	−3.18202	+	5.51142i	−0.103076	+	0.178532i	0.809875	+	0.586603i	$0.199535\pi$
$954$			25.0228i			0.810144i
$955$	−1.99674	−	1.15282i	−0.0646131	−	0.0373044i
$956$	−71.4306	−	41.2405i	−2.31023	−	1.33381i
$957$			7.73927i			0.250175i
$958$	−34.5008	+	59.7571i	−1.11467	+	1.93066i
$959$	−11.8401	−	20.5077i	−0.382337	−	0.662228i
$960$	7.43725	−	4.29390i	0.240036	−	0.138585i
$961$	−85.1332			−2.74623
$962$	−66.2545	+	27.1890i	−2.13613	+	0.876609i
$963$	17.3831			0.560162
$964$	67.6103	−	39.0348i	2.17758	−	1.25723i
$965$	−0.839530	−	1.45411i	−0.0270254	−	0.0468094i
$966$	10.1677	−	17.6110i	0.327141	−	0.566626i
$967$		−	19.1487i		−	0.615782i	−0.951422	−	0.307891i	$-0.900377\pi$
$967$		−	19.1487i		−	0.615782i	0.951422	−	0.307891i	$-0.0996233\pi$
$968$	8.40226	+	4.85105i	0.270059	+	0.155919i
$969$	−15.8491	−	9.15050i	−0.509147	−	0.293956i
$970$			4.13360i			0.132722i
$971$	14.7961	−	25.6276i	0.474829	−	0.822427i	−0.524756	−	0.851253i	$-0.675843\pi$
$971$	14.7961	−	25.6276i	0.474829	−	0.822427i	0.999584	+	0.0288255i	$0.00917670\pi$
$972$	−2.76728	−	4.79308i	−0.0887607	−	0.153738i
$973$	−65.4994	+	37.8161i	−2.09981	+	1.21233i
$974$	52.8300			1.69278
$975$	−2.37883	+	17.6218i	−0.0761836	+	0.564348i
$976$	−33.9138			−1.08555
$977$	−34.7495	+	20.0626i	−1.11174	+	0.641861i	−0.939278	−	0.343156i	$-0.888504\pi$
$977$	−34.7495	+	20.0626i	−1.11174	+	0.641861i	−0.172457	+	0.985017i	$0.555171\pi$
$978$	0.227197	+	0.393517i	0.00726497	+	0.0125833i
$979$	3.19383	−	5.53187i	0.102075	−	0.176799i
$980$			15.7957i			0.504575i
$981$	−1.70026	−	0.981646i	−0.0542852	−	0.0313416i
$982$	92.5264	+	53.4201i	2.95264	+	1.70471i
$983$			22.5116i			0.718008i	0.933336	+	0.359004i	$0.116883\pi$
$983$			22.5116i			0.718008i	−0.933336	+	0.359004i	$0.883117\pi$
$984$	−16.2025	+	28.0635i	−0.516516	+	0.894631i
$985$	2.35673	+	4.08197i	0.0750916	+	0.130062i
$986$	50.1105	−	28.9313i	1.59584	−	0.921361i
$987$	−6.62926			−0.211012
$988$	−132.874	−	17.9372i	−4.22728	−	0.570657i
$989$	1.45676			0.0463223
$990$	−0.621115	+	0.358601i	−0.0197403	+	0.0113971i
$991$	5.70179	+	9.87578i	0.181123	+	0.313715i	0.942263	−	0.334873i	$-0.108693\pi$
$991$	5.70179	+	9.87578i	0.181123	+	0.313715i	−0.761140	+	0.648587i	$0.775360\pi$
$992$	125.617	−	217.574i	3.98833	−	6.90799i
$993$			1.94172i			0.0616185i
$994$	−21.5904	−	12.4652i	−0.684804	−	0.395372i
$995$	−3.41262	−	1.97028i	−0.108187	−	0.0624619i
$996$			56.9426i			1.80429i
$997$	22.8420	−	39.5634i	0.723412	−	1.25299i	−0.236212	−	0.971701i	$-0.575906\pi$
$997$	22.8420	−	39.5634i	0.723412	−	1.25299i	0.959624	−	0.281285i	$-0.0907606\pi$
$998$	−21.9251	−	37.9754i	−0.694027	−	1.20209i
$999$	−6.26674	+	3.61811i	−0.198271	+	0.114472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.s.a.166.1	✓	24
13.2	odd	12		5577.2.a.z.1.1		12
13.4	even	6	inner	429.2.s.a.199.1	yes	24
13.11	odd	12		5577.2.a.be.1.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.s.a.166.1	✓	24	1.1	even	1	trivial
429.2.s.a.199.1	yes	24	13.4	even	6	inner
5577.2.a.z.1.1		12	13.2	odd	12
5577.2.a.be.1.12		12	13.11	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)

\(f(q)\)	\(=\)	\(q+(-2.37717 + 1.37246i) q^{2} +(0.500000 + 0.866025i) q^{3} +(2.76728 - 4.79308i) q^{4} +0.261284i q^{5} +(-2.37717 - 1.37246i) q^{6} +(-3.66637 - 2.11678i) q^{7} +9.70209i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.37717 + 1.37246i) q^{2} +(0.500000 + 0.866025i) q^{3} +(2.76728 - 4.79308i) q^{4} +0.261284i q^{5} +(-2.37717 - 1.37246i) q^{6} +(-3.66637 - 2.11678i) q^{7} +9.70209i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.358601 - 0.621115i) q^{10} +(-0.866025 + 0.500000i) q^{11} +5.53457 q^{12} +(2.85325 + 2.20430i) q^{13} +11.6208 q^{14} +(-0.226278 + 0.130642i) q^{15} +(-7.78115 - 13.4773i) q^{16} +(1.36188 - 2.35885i) q^{17} -2.74492i q^{18} +(-5.81884 - 3.35951i) q^{19} +(1.25235 + 0.723046i) q^{20} -4.23356i q^{21} +(1.37246 - 2.37717i) q^{22} +(-0.874963 - 1.51548i) q^{23} +(-8.40226 + 4.85105i) q^{24} +4.93173 q^{25} +(-9.80797 - 1.32402i) q^{26} -1.00000 q^{27} +(-20.2918 + 11.7155i) q^{28} +(-3.86964 - 6.70241i) q^{29} +(0.358601 - 0.621115i) q^{30} -10.7765i q^{31} +(20.1897 + 11.6565i) q^{32} +(-0.866025 - 0.500000i) q^{33} +7.47650i q^{34} +(0.553080 - 0.957962i) q^{35} +(2.76728 + 4.79308i) q^{36} +(6.26674 - 3.61811i) q^{37} +18.4431 q^{38} +(-0.482352 + 3.57314i) q^{39} -2.53500 q^{40} +(2.89252 - 1.67000i) q^{41} +(5.81038 + 10.0639i) q^{42} +(-0.416235 + 0.720940i) q^{43} +5.53457i q^{44} +(-0.226278 - 0.130642i) q^{45} +(4.15987 + 2.40170i) q^{46} -1.56588i q^{47} +(7.78115 - 13.4773i) q^{48} +(5.46151 + 9.45961i) q^{49} +(-11.7236 + 6.76859i) q^{50} +2.72376 q^{51} +(18.4611 - 7.57594i) q^{52} -9.11606 q^{53} +(2.37717 - 1.37246i) q^{54} +(-0.130642 - 0.226278i) q^{55} +(20.5372 - 35.5714i) q^{56} -6.71902i q^{57} +(18.3976 + 10.6218i) q^{58} +(0.210488 + 0.121525i) q^{59} +1.44609i q^{60} +(1.08961 - 1.88726i) q^{61} +(14.7903 + 25.6176i) q^{62} +(3.66637 - 2.11678i) q^{63} -32.8677 q^{64} +(-0.575947 + 0.745509i) q^{65} +2.74492 q^{66} +(0.440958 - 0.254587i) q^{67} +(-7.53742 - 13.0552i) q^{68} +(0.874963 - 1.51548i) q^{69} +3.03632i q^{70} +(-1.85791 - 1.07267i) q^{71} +(-8.40226 - 4.85105i) q^{72} -0.229657i q^{73} +(-9.93140 + 17.2017i) q^{74} +(2.46587 + 4.27100i) q^{75} +(-32.2048 + 18.5934i) q^{76} +4.23356 q^{77} +(-3.75735 - 9.15596i) q^{78} -0.717632 q^{79} +(3.52141 - 2.03309i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.58400 + 7.93973i) q^{82} +10.2885i q^{83} +(-20.2918 - 11.7155i) q^{84} +(0.616328 + 0.355837i) q^{85} -2.28506i q^{86} +(3.86964 - 6.70241i) q^{87} +(-4.85105 - 8.40226i) q^{88} +(-5.53187 + 3.19383i) q^{89} +0.717202 q^{90} +(-5.79507 - 14.1215i) q^{91} -9.68508 q^{92} +(9.33273 - 5.38825i) q^{93} +(2.14911 + 3.72237i) q^{94} +(0.877784 - 1.52037i) q^{95} +23.3130i q^{96} +(-4.99134 - 2.88175i) q^{97} +(-25.9658 - 14.9914i) 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

Related objects

Downloads

Learn more