LMFDB - Embedded newform 444.2.c.c.371.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [444,2,Mod(371,444)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(444, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("444.371");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 444 = 2^{2} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	444.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.54535784974$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} + 3x^{16} - 7x^{14} + 12x^{12} - 40x^{10} + 48x^{8} - 112x^{6} + 192x^{4} - 256x^{2} + 1024 $ x^20 - x^18 + 3x^16 - 7x^14 + 12x^12 - 40x^10 + 48x^8 - 112x^6 + 192x^4 - 256x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			371.15
Root			$1.03439 - 0.964383i$ of defining polynomial
Character	$\chi$	$=$	444.371
Dual form			444.2.c.c.371.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.03439 - 0.964383i) q^{2} +(-0.504486 - 1.65695i) q^{3} +(0.139930 - 1.99510i) q^{4} -4.11408i q^{5} +(-2.11977 - 1.22742i) q^{6} +2.35617i q^{7} +(-1.77930 - 2.19866i) q^{8} +(-2.49099 + 1.67182i) q^{9} +O(q^{10})$	\(q+(1.03439 - 0.964383i) q^{2} +(-0.504486 - 1.65695i) q^{3} +(0.139930 - 1.99510i) q^{4} -4.11408i q^{5} +(-2.11977 - 1.22742i) q^{6} +2.35617i q^{7} +(-1.77930 - 2.19866i) q^{8} +(-2.49099 + 1.67182i) q^{9} +(-3.96755 - 4.25557i) q^{10} +6.51405 q^{11} +(-3.37638 + 0.774643i) q^{12} -0.0134242 q^{13} +(2.27225 + 2.43720i) q^{14} +(-6.81684 + 2.07550i) q^{15} +(-3.96084 - 0.558348i) q^{16} +4.36699i q^{17} +(-0.964379 + 4.13158i) q^{18} +1.88516i q^{19} +(-8.20800 - 0.575683i) q^{20} +(3.90406 - 1.18866i) q^{21} +(6.73808 - 6.28204i) q^{22} +3.70036 q^{23} +(-2.74544 + 4.05741i) q^{24} -11.9257 q^{25} +(-0.0138859 + 0.0129461i) q^{26} +(4.02680 + 3.28404i) q^{27} +(4.70079 + 0.329699i) q^{28} -6.11880i q^{29} +(-5.04970 + 8.72092i) q^{30} +0.859683i q^{31} +(-4.63552 + 3.24222i) q^{32} +(-3.28625 - 10.7935i) q^{33} +(4.21145 + 4.51717i) q^{34} +9.69348 q^{35} +(2.98688 + 5.20370i) q^{36} +1.00000 q^{37} +(1.81802 + 1.95000i) q^{38} +(0.00677235 + 0.0222433i) q^{39} +(-9.04546 + 7.32018i) q^{40} -1.33893i q^{41} +(2.89201 - 4.99455i) q^{42} +3.41012i q^{43} +(0.911510 - 12.9962i) q^{44} +(6.87801 + 10.2481i) q^{45} +(3.82762 - 3.56857i) q^{46} -5.35745 q^{47} +(1.07303 + 6.84460i) q^{48} +1.44846 q^{49} +(-12.3358 + 11.5009i) q^{50} +(7.23589 - 2.20309i) q^{51} +(-0.00187845 + 0.0267827i) q^{52} -9.92263i q^{53} +(7.33235 - 0.486396i) q^{54} -26.7993i q^{55} +(5.18042 - 4.19233i) q^{56} +(3.12363 - 0.951040i) q^{57} +(-5.90087 - 6.32923i) q^{58} -9.22850 q^{59} +(3.18694 + 13.8907i) q^{60} -1.41144 q^{61} +(0.829064 + 0.889249i) q^{62} +(-3.93909 - 5.86919i) q^{63} +(-1.66820 + 7.82414i) q^{64} +0.0552284i q^{65} +(-13.8083 - 7.99547i) q^{66} -2.48483i q^{67} +(8.71257 + 0.611072i) q^{68} +(-1.86678 - 6.13133i) q^{69} +(10.0268 - 9.34823i) q^{70} +10.9848 q^{71} +(8.10797 + 2.50216i) q^{72} +5.93027 q^{73} +(1.03439 - 0.964383i) q^{74} +(6.01634 + 19.7603i) q^{75} +(3.76109 + 0.263791i) q^{76} +15.3482i q^{77} +(0.0284564 + 0.0164772i) q^{78} +10.1452i q^{79} +(-2.29709 + 16.2952i) q^{80} +(3.41003 - 8.32897i) q^{81} +(-1.29124 - 1.38497i) q^{82} -4.54450 q^{83} +(-1.82519 - 7.95532i) q^{84} +17.9661 q^{85} +(3.28866 + 3.52740i) q^{86} +(-10.1386 + 3.08685i) q^{87} +(-11.5904 - 14.3222i) q^{88} +4.03296i q^{89} +(16.9977 + 3.96753i) q^{90} -0.0316298i q^{91} +(0.517791 - 7.38259i) q^{92} +(1.42445 - 0.433698i) q^{93} +(-5.54169 + 5.16663i) q^{94} +7.75572 q^{95} +(7.71076 + 6.04518i) q^{96} -10.3574 q^{97} +(1.49827 - 1.39687i) q^{98} +(-16.2264 + 10.8903i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{4} - q^{6} - 6 q^{9}+O(q^{10}) $ 20 * q + 2 * q^4 - q^6 - 6 * q^9	$ 20 q + 2 q^{4} - q^{6} - 6 q^{9} + 6 q^{10} + 9 q^{12} + 32 q^{13} - 10 q^{16} - 5 q^{18} + 48 q^{21} + 16 q^{22} + 37 q^{24} - 48 q^{25} - 10 q^{28} - 44 q^{30} - 60 q^{33} + 30 q^{34} + 25 q^{36} + 20 q^{37} - 38 q^{40} - 18 q^{42} + 18 q^{45} - 8 q^{46} - 15 q^{48} - 96 q^{49} - 84 q^{52} + 59 q^{54} - 20 q^{57} + 14 q^{58} + 20 q^{60} - 36 q^{61} + 26 q^{64} - 52 q^{66} - 22 q^{69} + 136 q^{70} - 19 q^{72} + 48 q^{73} + 22 q^{76} - 99 q^{78} + 58 q^{81} + 2 q^{82} + 40 q^{84} + 48 q^{85} - 100 q^{88} + 11 q^{90} + 16 q^{93} - 20 q^{94} + 45 q^{96} + 48 q^{97}+O(q^{100}) $ 20 * q + 2 * q^4 - q^6 - 6 * q^9 + 6 * q^10 + 9 * q^12 + 32 * q^13 - 10 * q^16 - 5 * q^18 + 48 * q^21 + 16 * q^22 + 37 * q^24 - 48 * q^25 - 10 * q^28 - 44 * q^30 - 60 * q^33 + 30 * q^34 + 25 * q^36 + 20 * q^37 - 38 * q^40 - 18 * q^42 + 18 * q^45 - 8 * q^46 - 15 * q^48 - 96 * q^49 - 84 * q^52 + 59 * q^54 - 20 * q^57 + 14 * q^58 + 20 * q^60 - 36 * q^61 + 26 * q^64 - 52 * q^66 - 22 * q^69 + 136 * q^70 - 19 * q^72 + 48 * q^73 + 22 * q^76 - 99 * q^78 + 58 * q^81 + 2 * q^82 + 40 * q^84 + 48 * q^85 - 100 * q^88 + 11 * q^90 + 16 * q^93 - 20 * q^94 + 45 * q^96 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/444\mathbb{Z}\right)^\times$.

$n$	$149$	$223$	$409$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.03439	−	0.964383i	0.731425	−	0.681922i
$2$	1.03439	−	0.964383i	0.731425	−	0.681922i
$3$	−0.504486	−	1.65695i	−0.291265	−	0.956642i
$3$	−0.504486	−	1.65695i	−0.291265	−	0.956642i
$4$	0.139930	−	1.99510i	0.0699649	−	0.997549i
$5$		−	4.11408i		−	1.83987i	−0.392067	−	0.919937i	$-0.628240\pi$
$5$		−	4.11408i		−	1.83987i	0.392067	−	0.919937i	$-0.371760\pi$
$6$	−2.11977	−	1.22742i	−0.865394	−	0.501092i
$7$			2.35617i			0.890549i	0.895394	+	0.445274i	$0.146894\pi$
$7$			2.35617i			0.890549i	−0.895394	+	0.445274i	$0.853106\pi$
$8$	−1.77930	−	2.19866i	−0.629077	−	0.777343i
$9$	−2.49099	+	1.67182i	−0.830329	+	0.557274i
$10$	−3.96755	−	4.25557i	−1.25465	−	1.34573i
$11$	6.51405			1.96406			0.982030	−	0.188724i	$-0.0604353\pi$
$11$	6.51405			1.96406			0.982030	+	0.188724i	$0.0604353\pi$
$12$	−3.37638	+	0.774643i	−0.974676	+	0.223620i
$13$	−0.0134242			−0.00372321			−0.00186161	−	0.999998i	$-0.500593\pi$
$13$	−0.0134242			−0.00372321			−0.00186161	+	0.999998i	$0.500593\pi$
$14$	2.27225	+	2.43720i	0.607285	+	0.651370i
$15$	−6.81684	+	2.07550i	−1.76010	+	0.535891i
$16$	−3.96084	−	0.558348i	−0.990210	−	0.139587i
$17$			4.36699i			1.05915i	0.848263	+	0.529575i	$0.177649\pi$
$17$			4.36699i			1.05915i	−0.848263	+	0.529575i	$0.822351\pi$
$18$	−0.964379	+	4.13158i	−0.227306	+	0.973823i
$19$			1.88516i			0.432486i	0.976340	+	0.216243i	$0.0693804\pi$
$19$			1.88516i			0.432486i	−0.976340	+	0.216243i	$0.930620\pi$
$20$	−8.20800	−	0.575683i	−1.83536	−	0.128727i
$21$	3.90406	−	1.18866i	0.851937	−	0.259386i
$22$	6.73808	−	6.28204i	1.43656	−	1.33934i
$23$	3.70036			0.771579			0.385789	−	0.922587i	$-0.373929\pi$
$23$	3.70036			0.771579			0.385789	+	0.922587i	$0.373929\pi$
$24$	−2.74544	+	4.05741i	−0.560411	+	0.828215i
$25$	−11.9257			−2.38513
$26$	−0.0138859	+	0.0129461i	−0.00272325	+	0.00253894i
$27$	4.02680	+	3.28404i	0.774957	+	0.632013i
$28$	4.70079	+	0.329699i	0.888367	+	0.0623072i
$29$		−	6.11880i		−	1.13623i	−0.822948	−	0.568116i	$-0.807672\pi$
$29$		−	6.11880i		−	1.13623i	0.822948	−	0.568116i	$-0.192328\pi$
$30$	−5.04970	+	8.72092i	−0.921945	+	1.59222i
$31$			0.859683i			0.154404i	0.997015	+	0.0772018i	$0.0245986\pi$
$31$			0.859683i			0.154404i	−0.997015	+	0.0772018i	$0.975401\pi$
$32$	−4.63552	+	3.24222i	−0.819452	+	0.573148i
$33$	−3.28625	−	10.7935i	−0.572063	−	1.87890i
$34$	4.21145	+	4.51717i	0.722258	+	0.774689i
$35$	9.69348			1.63850
$36$	2.98688	+	5.20370i	0.497814	+	0.867284i
$37$	1.00000			0.164399
$37$	1.00000			0.164399
$38$	1.81802	+	1.95000i	0.294922	+	0.316331i
$39$	0.00677235	+	0.0222433i	0.00108444	+	0.00356178i
$40$	−9.04546	+	7.32018i	−1.43021	+	1.15742i
$41$		−	1.33893i		−	0.209105i	−0.994519	−	0.104552i	$-0.966659\pi$
$41$		−	1.33893i		−	0.209105i	0.994519	−	0.104552i	$-0.0333410\pi$
$42$	2.89201	−	4.99455i	0.446247	−	0.770676i
$43$			3.41012i			0.520038i	0.965603	+	0.260019i	$0.0837289\pi$
$43$			3.41012i			0.520038i	−0.965603	+	0.260019i	$0.916271\pi$
$44$	0.911510	−	12.9962i	0.137415	−	1.95925i
$45$	6.87801	+	10.2481i	1.02531	+	1.52770i
$46$	3.82762	−	3.56857i	0.564352	−	0.526157i
$47$	−5.35745			−0.781464			−0.390732	−	0.920505i	$-0.627778\pi$
$47$	−5.35745			−0.781464			−0.390732	+	0.920505i	$0.627778\pi$
$48$	1.07303	+	6.84460i	0.154879	+	0.987933i
$49$	1.44846			0.206923
$50$	−12.3358	+	11.5009i	−1.74455	+	1.62647i
$51$	7.23589	−	2.20309i	1.01323	−	0.308494i
$52$	−0.00187845	+	0.0267827i	−0.000260494	+	0.00371409i
$53$		−	9.92263i		−	1.36298i	−0.731828	−	0.681489i	$-0.761333\pi$
$53$		−	9.92263i		−	1.36298i	0.731828	−	0.681489i	$-0.238667\pi$
$54$	7.33235	−	0.486396i	0.997807	−	0.0661901i
$55$		−	26.7993i		−	3.61362i
$56$	5.18042	−	4.19233i	0.692262	−	0.560224i
$57$	3.12363	−	0.951040i	0.413735	−	0.125968i
$58$	−5.90087	−	6.32923i	−0.774822	−	0.831069i
$59$	−9.22850			−1.20145			−0.600724	−	0.799456i	$-0.705121\pi$
$59$	−9.22850			−1.20145			−0.600724	+	0.799456i	$0.705121\pi$
$60$	3.18694	+	13.8907i	0.411433	+	1.79328i
$61$	−1.41144			−0.180716			−0.0903579	−	0.995909i	$-0.528801\pi$
$61$	−1.41144			−0.180716			−0.0903579	+	0.995909i	$0.528801\pi$
$62$	0.829064	+	0.889249i	0.105291	+	0.112935i
$63$	−3.93909	−	5.86919i	−0.496279	−	0.739449i
$64$	−1.66820	+	7.82414i	−0.208525	+	0.978017i
$65$			0.0552284i			0.00685024i
$66$	−13.8083	−	7.99547i	−1.69969	−	0.984175i
$67$		−	2.48483i		−	0.303570i	−0.988414	−	0.151785i	$-0.951498\pi$
$67$		−	2.48483i		−	0.303570i	0.988414	−	0.151785i	$-0.0485021\pi$
$68$	8.71257	+	0.611072i	1.05655	+	0.0741034i
$69$	−1.86678	−	6.13133i	−0.224734	−	0.738125i
$70$	10.0268	−	9.34823i	1.19844	−	1.11733i
$71$	10.9848			1.30366			0.651829	−	0.758366i	$-0.274002\pi$
$71$	10.9848			1.30366			0.651829	+	0.758366i	$0.274002\pi$
$72$	8.10797	+	2.50216i	0.955533	+	0.294883i
$73$	5.93027			0.694085			0.347043	−	0.937849i	$-0.387186\pi$
$73$	5.93027			0.694085			0.347043	+	0.937849i	$0.387186\pi$
$74$	1.03439	−	0.964383i	0.120246	−	0.112107i
$75$	6.01634	+	19.7603i	0.694707	+	2.28172i
$76$	3.76109	+	0.263791i	0.431427	+	0.0302589i
$77$			15.3482i			1.74909i
$78$	0.0284564	+	0.0164772i	0.00322205	+	0.00186567i
$79$			10.1452i			1.14142i	0.821152	+	0.570710i	$0.193332\pi$
$79$			10.1452i			1.14142i	−0.821152	+	0.570710i	$0.806668\pi$
$80$	−2.29709	+	16.2952i	−0.256822	+	1.82186i
$81$	3.41003	−	8.32897i	0.378892	−	0.925441i
$82$	−1.29124	−	1.38497i	−0.142593	−	0.152945i
$83$	−4.54450			−0.498824			−0.249412	−	0.968397i	$-0.580237\pi$
$83$	−4.54450			−0.498824			−0.249412	+	0.968397i	$0.580237\pi$
$84$	−1.82519	−	7.95532i	−0.199145	−	0.867997i
$85$	17.9661			1.94870
$86$	3.28866	+	3.52740i	0.354626	+	0.380369i
$87$	−10.1386	+	3.08685i	−1.08697	+	0.330945i
$88$	−11.5904	−	14.3222i	−1.23554	−	1.52675i
$89$			4.03296i			0.427493i	0.976889	+	0.213747i	$0.0685667\pi$
$89$			4.03296i			0.427493i	−0.976889	+	0.213747i	$0.931433\pi$
$90$	16.9977	+	3.96753i	1.79171	+	0.418215i
$91$		−	0.0316298i		−	0.00331570i
$92$	0.517791	−	7.38259i	0.0539835	−	0.769688i
$93$	1.42445	−	0.433698i	0.147709	−	0.0449724i
$94$	−5.54169	+	5.16663i	−0.571582	+	0.532897i
$95$	7.75572			0.795720
$96$	7.71076	+	6.04518i	0.786976	+	0.616984i
$97$	−10.3574			−1.05163			−0.525815	−	0.850599i	$-0.676240\pi$
$97$	−10.3574			−1.05163			−0.525815	+	0.850599i	$0.676240\pi$
$98$	1.49827	−	1.39687i	0.151348	−	0.141105i
$99$	−16.2264	+	10.8903i	−1.63082	+	1.09452i
$100$	−1.66876	+	23.7929i	−0.166876	+	2.37929i
$101$			3.73912i			0.372057i	0.982544	+	0.186028i	$0.0595616\pi$
$101$			3.73912i			0.372057i	−0.982544	+	0.186028i	$0.940438\pi$
$102$	5.36012	−	9.25703i	0.530731	−	0.916582i
$103$			8.48855i			0.836401i	0.908355	+	0.418201i	$0.137339\pi$
$103$			8.48855i			0.836401i	−0.908355	+	0.418201i	$0.862661\pi$
$104$	0.0238857	+	0.0295153i	0.00234219	+	0.00289422i
$105$	−4.89023	−	16.0616i	−0.477237	−	1.56746i
$106$	−9.56922	−	10.2639i	−0.929445	−	0.996916i
$107$	6.39303			0.618037			0.309019	−	0.951056i	$-0.399999\pi$
$107$	6.39303			0.618037			0.309019	+	0.951056i	$0.399999\pi$
$108$	7.11545	−	7.57432i	0.684684	−	0.728840i
$109$	14.6244			1.40077			0.700383	−	0.713767i	$-0.253012\pi$
$109$	14.6244			1.40077			0.700383	+	0.713767i	$0.253012\pi$
$110$	−25.8448	−	27.7210i	−2.46421	−	2.64309i
$111$	−0.504486	−	1.65695i	−0.0478837	−	0.157271i
$112$	1.31556	−	9.33241i	0.124309	−	0.881830i
$113$			12.5192i			1.17771i	0.808240	+	0.588854i	$0.200421\pi$
$113$			12.5192i			1.17771i	−0.808240	+	0.588854i	$0.799579\pi$
$114$	2.31389	−	3.99612i	0.216715	−	0.374271i
$115$		−	15.2236i		−	1.41961i
$116$	−12.2076	−	0.856203i	−1.13345	−	0.0794964i
$117$	0.0334396	−	0.0224429i	0.00309149	−	0.00207485i
$118$	−9.54588	+	8.89982i	−0.878770	+	0.819294i
$119$	−10.2894			−0.943225
$120$	16.6925	+	11.2950i	1.52381	+	1.03109i
$121$	31.4329			2.85753
$122$	−1.45998	+	1.36116i	−0.132180	+	0.123234i
$123$	−2.21854	+	0.675470i	−0.200039	+	0.0609050i
$124$	1.71515	+	0.120295i	0.154025	+	0.0108028i
$125$			28.4928i			2.54847i
$126$	−9.73471	−	2.27224i	−0.867237	−	0.202427i
$127$			1.31126i			0.116355i	0.998306	+	0.0581777i	$0.0185290\pi$
$127$			1.31126i			0.116355i	−0.998306	+	0.0581777i	$0.981471\pi$
$128$	5.81990	+	9.70200i	0.514411	+	0.857544i
$129$	5.65041	−	1.72036i	0.497491	−	0.151469i
$130$	0.0532614	+	0.0571278i	0.00467133	+	0.00501044i
$131$	−1.15185			−0.100637			−0.0503186	−	0.998733i	$-0.516024\pi$
$131$	−1.15185			−0.100637			−0.0503186	+	0.998733i	$0.516024\pi$
$132$	−21.9939	+	5.04606i	−1.91432	+	0.439203i
$133$	−4.44177			−0.385150
$134$	−2.39632	−	2.57028i	−0.207011	−	0.222038i
$135$	13.5108	−	16.5666i	1.16282	−	1.42582i
$136$	9.60151	−	7.77017i	0.823323	−	0.666287i
$137$		−	14.1515i		−	1.20904i	−0.796589	−	0.604521i	$-0.793364\pi$
$137$		−	14.1515i		−	1.20904i	0.796589	−	0.604521i	$-0.206636\pi$
$138$	−7.84393	−	4.54190i	−0.667720	−	0.386632i
$139$		−	4.79331i		−	0.406563i	−0.979120	−	0.203281i	$-0.934839\pi$
$139$		−	4.79331i		−	0.406563i	0.979120	−	0.203281i	$-0.0651606\pi$
$140$	1.35641	−	19.3394i	0.114637	−	1.63448i
$141$	2.70276	+	8.87704i	0.227613	+	0.747581i
$142$	11.3626	−	10.5936i	0.953528	−	0.888993i
$143$	−0.0874462			−0.00731262
$144$	10.7999	−	5.23097i	0.899988	−	0.435915i
$145$	−25.1732			−2.09052
$146$	6.13422	−	5.71905i	0.507671	−	0.473312i
$147$	−0.730728	−	2.40003i	−0.0602694	−	0.197951i
$148$	0.139930	−	1.99510i	0.0115022	−	0.163996i
$149$		−	10.5003i		−	0.860219i	−0.902777	−	0.430110i	$-0.858475\pi$
$149$		−	10.5003i		−	0.860219i	0.902777	−	0.430110i	$-0.141525\pi$
$150$	25.2797	+	14.6378i	2.06408	+	1.19517i
$151$		−	5.42078i		−	0.441137i	−0.975372	−	0.220568i	$-0.929209\pi$
$151$		−	5.42078i		−	0.441137i	0.975372	−	0.220568i	$-0.0707912\pi$
$152$	4.14483	−	3.35427i	0.336190	−	0.272067i
$153$	−7.30082	−	10.8781i	−0.590236	−	0.879443i
$154$	14.8016	+	15.8761i	1.19274	+	1.27933i
$155$	3.53681			0.284083
$156$	0.0453253	−	0.0103990i	0.00362893	−	0.000832586i
$157$	−16.4801			−1.31526			−0.657629	−	0.753342i	$-0.728441\pi$
$157$	−16.4801			−1.31526			−0.657629	+	0.753342i	$0.728441\pi$
$158$	9.78383	+	10.4941i	0.778360	+	0.834863i
$159$	−16.4413	+	5.00583i	−1.30388	+	0.396988i
$160$	13.3387	+	19.0709i	1.05452	+	1.50769i
$161$			8.71868i			0.687129i
$162$	−4.50501	−	11.9040i	−0.353947	−	0.935266i
$163$			20.8077i			1.62978i	0.579614	+	0.814891i	$0.303203\pi$
$163$			20.8077i			1.62978i	−0.579614	+	0.814891i	$0.696797\pi$
$164$	−2.67129	−	0.187356i	−0.208593	−	0.0146300i
$165$	−44.4052	+	13.5199i	−3.45694	+	1.05252i
$166$	−4.70079	+	4.38264i	−0.364852	+	0.340159i
$167$	7.98684			0.618040			0.309020	−	0.951056i	$-0.399999\pi$
$167$	7.98684			0.618040			0.309020	+	0.951056i	$0.399999\pi$
$168$	−9.55994	−	6.46873i	−0.737566	−	0.499073i
$169$	−12.9998			−0.999986
$170$	18.5840	−	17.3262i	1.42533	−	1.32886i
$171$	−3.15166	−	4.69592i	−0.241013	−	0.359106i
$172$	6.80353	+	0.477178i	0.518764	+	0.0363845i
$173$			7.99435i			0.607799i	0.952704	+	0.303900i	$0.0982887\pi$
$173$			7.99435i			0.607799i	−0.952704	+	0.303900i	$0.901711\pi$
$174$	−7.51033	+	12.9705i	−0.569357	+	0.983289i
$175$		−	28.0989i		−	2.12408i
$176$	−25.8011	−	3.63711i	−1.94483	−	0.274157i
$177$	4.65566	+	15.2912i	0.349940	+	1.14936i
$178$	3.88932	+	4.17166i	0.291517	+	0.312679i
$179$	−14.5009			−1.08385			−0.541924	−	0.840428i	$-0.682304\pi$
$179$	−14.5009			−1.08385			−0.541924	+	0.840428i	$0.682304\pi$
$180$	21.4085	−	12.2883i	1.59569	−	0.915915i
$181$	7.76460			0.577138			0.288569	−	0.957459i	$-0.406820\pi$
$181$	7.76460			0.577138			0.288569	+	0.957459i	$0.406820\pi$
$182$	−0.0305033	−	0.0327176i	−0.00226105	−	0.00242519i
$183$	0.712050	+	2.33868i	0.0526362	+	0.172880i
$184$	−6.58405	−	8.13583i	−0.485382	−	0.599782i
$185$		−	4.11408i		−	0.302473i
$186$	1.05519	−	1.82233i	0.0773704	−	0.133620i
$187$			28.4468i			2.08023i
$188$	−0.749667	+	10.6886i	−0.0546751	+	0.779549i
$189$	−7.73775	+	9.48782i	−0.562839	+	0.690138i
$190$	8.02245	−	7.47949i	0.582010	−	0.542619i
$191$	−10.0532			−0.727427			−0.363713	−	0.931511i	$-0.618491\pi$
$191$	−10.0532			−0.727427			−0.363713	+	0.931511i	$0.618491\pi$
$192$	13.8058	−	1.18304i	0.996349	−	0.0853787i
$193$	0.367849			0.0264783			0.0132392	−	0.999912i	$-0.495786\pi$
$193$	0.367849			0.0264783			0.0132392	+	0.999912i	$0.495786\pi$
$194$	−10.7136	+	9.98846i	−0.769189	+	0.717130i
$195$	0.0915109	−	0.0278620i	0.00655323	−	0.00199524i
$196$	0.202683	−	2.88982i	0.0144773	−	0.206416i
$197$			2.78729i			0.198586i	0.995058	+	0.0992930i	$0.0316581\pi$
$197$			2.78729i			0.198586i	−0.995058	+	0.0992930i	$0.968342\pi$
$198$	−6.28201	+	26.9133i	−0.446443	+	1.91265i
$199$		−	8.12246i		−	0.575786i	−0.957663	−	0.287893i	$-0.907045\pi$
$199$		−	8.12246i		−	0.575786i	0.957663	−	0.287893i	$-0.0929548\pi$
$200$	21.2193	+	26.2205i	1.50043	+	1.85407i
$201$	−4.11724	+	1.25356i	−0.290408	+	0.0884193i
$202$	3.60595	+	3.86771i	0.253714	+	0.272131i
$203$	14.4169			1.01187
$204$	−3.38286	−	14.7446i	−0.236847	−	1.03233i
$205$	−5.50845			−0.384727
$206$	8.18621	+	8.78048i	0.570360	+	0.611765i
$207$	−9.21755	+	6.18634i	−0.640664	+	0.429980i
$208$	0.0531713	+	0.00749540i	0.00368676	+	0.000519712i
$209$			12.2801i			0.849429i
$210$	−20.5480	−	11.8980i	−1.41795	−	0.821037i
$211$		−	18.7935i		−	1.29380i	−0.762576	−	0.646898i	$-0.776066\pi$
$211$		−	18.7935i		−	1.29380i	0.762576	−	0.646898i	$-0.223934\pi$
$212$	−19.7966	−	1.38847i	−1.35964	−	0.0953607i
$213$	−5.54169	−	18.2013i	−0.379711	−	1.24713i
$214$	6.61289	−	6.16533i	0.452048	−	0.421453i
$215$	14.0295			0.956805
$216$	0.0556069	−	14.6968i	0.00378357	−	0.999993i
$217$	−2.02556			−0.137504
$218$	15.1274	−	14.1036i	1.02456	−	0.955214i
$219$	−2.99174	−	9.82618i	−0.202163	−	0.663992i
$220$	−53.4673	−	3.75003i	−3.60477	−	0.252827i
$221$		−	0.0586235i		−	0.00394344i
$222$	−2.11977	−	1.22742i	−0.142270	−	0.0823790i
$223$			9.60554i			0.643234i	0.946870	+	0.321617i	$0.104226\pi$
$223$			9.60554i			0.643234i	−0.946870	+	0.321617i	$0.895774\pi$
$224$	−7.63922	−	10.9221i	−0.510417	−	0.729762i
$225$	29.7067	−	19.9376i	1.98045	−	1.32917i
$226$	12.0733	+	12.9497i	0.803104	+	0.861405i
$227$	2.57972			0.171222			0.0856109	−	0.996329i	$-0.472716\pi$
$227$	2.57972			0.171222			0.0856109	+	0.996329i	$0.472716\pi$
$228$	−1.46033	−	6.36503i	−0.0967127	−	0.421534i
$229$	6.90741			0.456454			0.228227	−	0.973608i	$-0.426707\pi$
$229$	6.90741			0.456454			0.228227	+	0.973608i	$0.426707\pi$
$230$	−14.6814	−	15.7471i	−0.968061	−	1.03834i
$231$	25.4313	−	7.74297i	1.67326	−	0.509450i
$232$	−13.4531	+	10.8872i	−0.883242	+	0.714777i
$233$			27.2502i			1.78522i	0.450833	+	0.892609i	$0.351127\pi$
$233$			27.2502i			1.78522i	−0.450833	+	0.892609i	$0.648873\pi$
$234$	0.0129461	−	0.0554634i	0.000846310	−	0.00362575i
$235$			22.0410i			1.43779i
$236$	−1.29134	+	18.4118i	−0.0840593	+	1.19850i
$237$	16.8101	−	5.11810i	1.09193	−	0.332456i
$238$	−10.6432	+	9.92289i	−0.689898	+	0.643206i
$239$	9.90671			0.640812			0.320406	−	0.947280i	$-0.396181\pi$
$239$	9.90671			0.640812			0.320406	+	0.947280i	$0.396181\pi$
$240$	28.1593	−	4.41455i	1.81767	−	0.284958i
$241$	−9.71310			−0.625676			−0.312838	−	0.949807i	$-0.601280\pi$
$241$	−9.71310			−0.625676			−0.312838	+	0.949807i	$0.601280\pi$
$242$	32.5139	−	30.3133i	2.09007	−	1.94861i
$243$	−15.5210	−	1.44841i	−0.995674	−	0.0929158i
$244$	−0.197502	+	2.81595i	−0.0126438	+	0.180273i
$245$		−	5.95908i		−	0.380712i
$246$	−1.64342	+	2.83822i	−0.104781	+	0.180958i
$247$		−	0.0253069i		−	0.00161024i
$248$	1.89015	−	1.52963i	0.120025	−	0.0971318i
$249$	2.29264	+	7.53003i	0.145290	+	0.477196i
$250$	27.4779	+	29.4727i	1.73786	+	1.86401i
$251$	−17.6211			−1.11224			−0.556118	−	0.831104i	$-0.687710\pi$
$251$	−17.6211			−1.11224			−0.556118	+	0.831104i	$0.687710\pi$
$252$	−12.2608	+	7.03761i	−0.772359	+	0.443328i
$253$	24.1043			1.51543
$254$	1.26456	+	1.35635i	0.0793453	+	0.0851052i
$255$	−9.06367	−	29.7691i	−0.567589	−	1.86421i
$256$	15.3765	+	4.42305i	0.961031	+	0.276441i
$257$			14.6296i			0.912567i	0.889834	+	0.456283i	$0.150820\pi$
$257$			14.6296i			0.912567i	−0.889834	+	0.456283i	$0.849180\pi$
$258$	4.18565	−	7.22868i	0.260587	−	0.450038i
$259$			2.35617i			0.146405i
$260$	0.110186	+	0.00772811i	0.00683346	+	0.000479277i
$261$	10.2295	+	15.2418i	0.633192	+	0.943447i
$262$	−1.19146	+	1.11082i	−0.0736086	+	0.0686267i
$263$	18.0074			1.11039			0.555193	−	0.831722i	$-0.312644\pi$
$263$	18.0074			1.11039			0.555193	+	0.831722i	$0.312644\pi$
$264$	−17.8840	+	26.4301i	−1.10068	+	1.62666i
$265$	−40.8225			−2.50771
$266$	−4.59453	+	4.28357i	−0.281709	+	0.262642i
$267$	6.68243	−	2.03457i	0.408958	−	0.124514i
$268$	−4.95747	−	0.347701i	−0.302826	−	0.0212392i
$269$		−	31.4982i		−	1.92048i	−0.279179	−	0.960239i	$-0.590062\pi$
$269$		−	31.4982i		−	1.92048i	0.279179	−	0.960239i	$-0.409938\pi$
$270$	−2.00107	−	30.1659i	−0.121781	−	1.83584i
$271$		−	1.16439i		−	0.0707314i	−0.999374	−	0.0353657i	$-0.988740\pi$
$271$		−	1.16439i		−	0.0707314i	0.999374	−	0.0353657i	$-0.0112596\pi$
$272$	2.43830	−	17.2969i	0.147844	−	1.04878i
$273$	−0.0524091	+	0.0159568i	−0.00317194	+	0.000965750i
$274$	−13.6474	−	14.6382i	−0.824473	−	0.884324i
$275$	−77.6844			−4.68455
$276$	−12.4938	+	2.86646i	−0.752040	+	0.172541i
$277$	−21.3098			−1.28038			−0.640192	−	0.768215i	$-0.721145\pi$
$277$	−21.3098			−1.28038			−0.640192	+	0.768215i	$0.721145\pi$
$278$	−4.62258	−	4.95815i	−0.277244	−	0.297370i
$279$	−1.43724	−	2.14146i	−0.0860451	−	0.128206i
$280$	−17.2476	−	21.3127i	−1.03074	−	1.27367i
$281$		−	9.12502i		−	0.544353i	−0.962247	−	0.272176i	$-0.912257\pi$
$281$		−	9.12502i		−	0.544353i	0.962247	−	0.272176i	$-0.0877434\pi$
$282$	11.3566	+	6.57583i	0.676274	+	0.391585i
$283$			11.2786i			0.670442i	0.942140	+	0.335221i	$0.108811\pi$
$283$			11.2786i			0.670442i	−0.942140	+	0.335221i	$0.891189\pi$
$284$	1.53711	−	21.9158i	0.0912104	−	1.30046i
$285$	−3.91266	−	12.8509i	−0.231766	−	0.761219i
$286$	−0.0904536	+	0.0843316i	−0.00534863	+	0.00498663i
$287$	3.15474			0.186218
$288$	6.12661	−	15.8261i	0.361014	−	0.932560i
$289$	−2.07058			−0.121799
$290$	−26.0390	+	24.2766i	−1.52906	+	1.42557i
$291$	5.22515	+	17.1617i	0.306303	+	1.00603i
$292$	0.829822	−	11.8315i	0.0485617	−	0.692385i
$293$		−	13.3189i		−	0.778096i	−0.921218	−	0.389048i	$-0.872804\pi$
$293$		−	13.3189i		−	0.778096i	0.921218	−	0.389048i	$-0.127196\pi$
$294$	−3.07041	−	1.77787i	−0.179070	−	0.103687i
$295$			37.9668i			2.21051i
$296$	−1.77930	−	2.19866i	−0.103420	−	0.127794i
$297$	26.2308	+	21.3924i	1.52206	+	1.24131i
$298$	−10.1263	−	10.8614i	−0.586603	−	0.629186i
$299$	−0.0496745			−0.00287275
$300$	40.2656	−	9.23813i	2.32473	−	0.533364i
$301$	−8.03483			−0.463120
$302$	−5.22771	−	5.60720i	−0.300821	−	0.322658i
$303$	6.19555	−	1.88634i	0.355925	−	0.108367i
$304$	1.05258	−	7.46683i	0.0603695	−	0.428252i
$305$			5.80676i			0.332494i
$306$	−18.0426	−	4.21143i	−1.03142	−	0.240751i
$307$			9.08791i			0.518674i	0.965787	+	0.259337i	$0.0835041\pi$
$307$			9.08791i			0.518674i	−0.965787	+	0.259337i	$0.916496\pi$
$308$	30.6212	+	2.14767i	1.74481	+	0.122375i
$309$	14.0651	−	4.28236i	0.800137	−	0.243615i
$310$	3.65844	−	3.41084i	0.207786	−	0.193723i
$311$	13.9573			0.791446			0.395723	−	0.918370i	$-0.370494\pi$
$311$	13.9573			0.791446			0.395723	+	0.918370i	$0.370494\pi$
$312$	0.0368555	−	0.0544676i	0.00208653	−	0.00308362i
$313$	−1.29244			−0.0730530			−0.0365265	−	0.999333i	$-0.511629\pi$
$313$	−1.29244			−0.0730530			−0.0365265	+	0.999333i	$0.511629\pi$
$314$	−17.0469	+	15.8932i	−0.962013	+	0.896904i
$315$	−24.1463	+	16.2058i	−1.36049	+	0.913091i
$316$	20.2406	+	1.41961i	1.13862	+	0.0798594i
$317$		−	19.4468i		−	1.09224i	−0.837706	−	0.546122i	$-0.816104\pi$
$317$		−	19.4468i		−	1.09224i	0.837706	−	0.546122i	$-0.183896\pi$
$318$	−12.1792	+	21.0337i	−0.682977	+	1.17951i
$319$		−	39.8582i		−	2.23163i
$320$	32.1891	+	6.86311i	1.79943	+	0.383659i
$321$	−3.22520	−	10.5929i	−0.180013	−	0.591241i
$322$	8.40815	+	9.01853i	0.468568	+	0.502583i
$323$	−8.23249			−0.458068
$324$	−16.1399	−	7.96882i	−0.896664	−	0.442712i
$325$	0.160093			0.00888036
$326$	20.0666	+	21.5233i	1.11138	+	1.19206i
$327$	−7.37783	−	24.2320i	−0.407995	−	1.34003i
$328$	−2.94384	+	2.38235i	−0.162546	+	0.131543i
$329$		−	12.6231i		−	0.695932i
$330$	−32.8940	+	56.8085i	−1.81076	+	3.12721i
$331$			34.7111i			1.90790i	0.299973	+	0.953948i	$0.403022\pi$
$331$			34.7111i			1.90790i	−0.299973	+	0.953948i	$0.596978\pi$
$332$	−0.635912	+	9.06673i	−0.0349002	+	0.497602i
$333$	−2.49099	+	1.67182i	−0.136505	+	0.0916152i
$334$	8.26151	−	7.70237i	0.452050	−	0.421455i
$335$	−10.2228			−0.558530
$336$	−16.1271	+	2.52825i	−0.879803	+	0.137927i
$337$	2.97013			0.161793			0.0808966	−	0.996722i	$-0.474222\pi$
$337$	2.97013			0.161793			0.0808966	+	0.996722i	$0.474222\pi$
$338$	−13.4469	+	12.5368i	−0.731415	+	0.681912i
$339$	20.7437	−	6.31577i	1.12664	−	0.343025i
$340$	2.51400	−	35.8442i	0.136341	−	1.94393i
$341$			5.60002i			0.303258i
$342$	−7.78871	−	1.81801i	−0.421165	−	0.0983069i
$343$			19.9060i			1.07482i
$344$	7.49769	−	6.06762i	0.404248	−	0.327144i
$345$	−25.2248	+	7.68009i	−1.35806	+	0.413482i
$346$	7.70962	+	8.26928i	0.414472	+	0.444559i
$347$	12.4481			0.668248			0.334124	−	0.942529i	$-0.391560\pi$
$347$	12.4481			0.668248			0.334124	+	0.942529i	$0.391560\pi$
$348$	4.73988	+	20.6594i	0.254084	+	1.10746i
$349$	15.3219			0.820162			0.410081	−	0.912049i	$-0.365501\pi$
$349$	15.3219			0.820162			0.410081	+	0.912049i	$0.365501\pi$
$350$	−27.0981	−	29.0653i	−1.44846	−	1.55360i
$351$	−0.0540567	−	0.0440857i	−0.00288533	−	0.00235312i
$352$	−30.1960	+	21.1200i	−1.60945	+	1.12570i
$353$			18.6947i			0.995019i	0.867459	+	0.497509i	$0.165752\pi$
$353$			18.6947i			0.995019i	−0.867459	+	0.497509i	$0.834248\pi$
$354$	19.5623	+	11.3272i	1.03973	+	0.602036i
$355$		−	45.1925i		−	2.39857i
$356$	8.04616	+	0.564332i	0.426445	+	0.0299095i
$357$	5.19085	+	17.0490i	0.274729	+	0.902329i
$358$	−14.9996	+	13.9844i	−0.792753	+	0.739099i
$359$	−13.2976			−0.701819			−0.350910	−	0.936409i	$-0.614128\pi$
$359$	−13.2976			−0.701819			−0.350910	+	0.936409i	$0.614128\pi$
$360$	10.2941	−	33.3569i	0.542547	−	1.75806i
$361$	15.4462			0.812956
$362$	8.03164	−	7.48805i	0.422133	−	0.393563i
$363$	−15.8574	−	52.0828i	−0.832300	−	2.73364i
$364$	−0.0631046	−	0.00442595i	−0.00330758	−	0.000231983i
$365$		−	24.3976i		−	1.27703i
$366$	2.99192	+	1.73242i	0.156390	+	0.0905552i
$367$			2.51601i			0.131335i	0.997842	+	0.0656673i	$0.0209176\pi$
$367$			2.51601i			0.131335i	−0.997842	+	0.0656673i	$0.979082\pi$
$368$	−14.6565	−	2.06609i	−0.764025	−	0.107702i
$369$	2.23844	+	3.33525i	0.116529	+	0.173626i
$370$	−3.96755	−	4.25557i	−0.206263	−	0.221237i
$371$	23.3794			1.21380
$372$	−0.665948	−	2.90262i	−0.0345278	−	0.150494i
$373$	−32.5250			−1.68408			−0.842041	−	0.539413i	$-0.818646\pi$
$373$	−32.5250			−1.68408			−0.842041	+	0.539413i	$0.818646\pi$
$374$	27.4336	+	29.4251i	1.41856	+	1.52154i
$375$	47.2112	−	14.3742i	2.43797	−	0.742281i
$376$	9.53249	+	11.7792i	0.491601	+	0.607465i
$377$			0.0821402i			0.00423044i
$378$	1.14603	+	17.2763i	0.0589456	+	0.888596i
$379$			13.4283i			0.689765i	0.938646	+	0.344883i	$0.112081\pi$
$379$			13.4283i			0.689765i	−0.938646	+	0.344883i	$0.887919\pi$
$380$	1.08526	−	15.4734i	0.0556725	−	0.793770i
$381$	2.17269	−	0.661512i	0.111310	−	0.0338903i
$382$	−10.3990	+	9.69517i	−0.532058	+	0.496048i
$383$	−11.1763			−0.571080			−0.285540	−	0.958367i	$-0.592173\pi$
$383$	−11.1763			−0.571080			−0.285540	+	0.958367i	$0.592173\pi$
$384$	13.1397	−	14.5378i	0.670533	−	0.741880i
$385$	63.1438			3.21811
$386$	0.380499	−	0.354747i	0.0193669	−	0.0180561i
$387$	−5.70111	−	8.49457i	−0.289804	−	0.431803i
$388$	−1.44930	+	20.6640i	−0.0735773	+	1.04905i
$389$			3.87382i			0.196410i	0.995166	+	0.0982051i	$0.0313101\pi$
$389$			3.87382i			0.196410i	−0.995166	+	0.0982051i	$0.968690\pi$
$390$	0.0677884	−	0.117072i	0.00343260	−	0.00592816i
$391$			16.1594i			0.817218i
$392$	−2.57724	−	3.18467i	−0.130170	−	0.160850i
$393$	0.581090	+	1.90855i	0.0293121	+	0.0962738i
$394$	2.68801	+	2.88315i	0.135420	+	0.145251i
$395$	41.7380			2.10007
$396$	19.4567	+	33.8972i	0.977737	+	1.70340i
$397$	26.8211			1.34611			0.673057	−	0.739590i	$-0.264981\pi$
$397$	26.8211			1.34611			0.673057	+	0.739590i	$0.264981\pi$
$398$	−7.83317	−	8.40180i	−0.392641	−	0.421144i
$399$	2.24081	+	7.35980i	0.112181	+	0.368451i
$400$	47.2357	+	6.65867i	2.36178	+	0.332934i
$401$		−	16.0690i		−	0.802448i	−0.915980	−	0.401224i	$-0.868585\pi$
$401$		−	16.0690i		−	0.802448i	0.915980	−	0.401224i	$-0.131415\pi$
$402$	−3.04992	+	5.26727i	−0.152116	+	0.262707i
$403$		−	0.0115406i		−	0.000574878i
$404$	7.45992	+	0.523215i	0.371145	+	0.0260309i
$405$	−34.2660	−	14.0292i	−1.70269	−	0.697114i
$406$	14.9127	−	13.9034i	0.740107	−	0.690017i
$407$	6.51405			0.322890
$408$	−17.7186	−	11.9893i	−0.877203	−	0.593559i
$409$	32.1898			1.59168			0.795842	−	0.605504i	$-0.207029\pi$
$409$	32.1898			1.59168			0.795842	+	0.605504i	$0.207029\pi$
$410$	−5.69789	+	5.31225i	−0.281399	+	0.262354i
$411$	−23.4483	+	7.13923i	−1.15662	+	0.352152i
$412$	16.9355	+	1.18780i	0.834352	+	0.0585188i
$413$		−	21.7439i		−	1.06995i
$414$	−3.56855	+	15.2884i	−0.175385	+	0.751381i
$415$			18.6965i			0.917773i
$416$	0.0622283	−	0.0435243i	0.00305099	−	0.00213395i
$417$	−7.94228	+	2.41816i	−0.388935	+	0.118418i
$418$	11.8427	+	12.7024i	0.579244	+	0.621294i
$419$	13.4633			0.657725			0.328862	−	0.944378i	$-0.393335\pi$
$419$	13.4633			0.657725			0.328862	+	0.944378i	$0.393335\pi$
$420$	−32.7288	+	7.50899i	−1.59700	+	0.366401i
$421$	−4.47237			−0.217970			−0.108985	−	0.994043i	$-0.534760\pi$
$421$	−4.47237			−0.217970			−0.108985	+	0.994043i	$0.534760\pi$
$422$	−18.1241	−	19.4398i	−0.882268	−	0.946315i
$423$	13.3453	−	8.95669i	0.648872	−	0.435489i
$424$	−21.8165	+	17.6553i	−1.05950	+	0.857418i
$425$		−	52.0792i		−	2.52621i
$426$	−23.2853	−	13.4830i	−1.12818	−	0.653253i
$427$		−	3.32558i		−	0.160936i
$428$	0.894576	−	12.7547i	0.0432409	−	0.616523i
$429$	0.0441154	+	0.144894i	0.00212991	+	0.00699556i
$430$	14.5120	−	13.5298i	0.699831	−	0.652466i
$431$	39.7047			1.91251			0.956253	−	0.292541i	$-0.0945009\pi$
$431$	39.7047			1.91251			0.956253	+	0.292541i	$0.0945009\pi$
$432$	−14.1159	−	15.2559i	−0.679150	−	0.734000i
$433$	−38.9784			−1.87318			−0.936592	−	0.350423i	$-0.886038\pi$
$433$	−38.9784			−1.87318			−0.936592	+	0.350423i	$0.886038\pi$
$434$	−2.09522	+	1.95342i	−0.100574	+	0.0937670i
$435$	12.6996	+	41.7109i	0.608897	+	1.99988i
$436$	2.04640	−	29.1772i	0.0980046	−	1.39733i
$437$			6.97579i			0.333697i
$438$	−12.5708	−	7.27893i	−0.600658	−	0.347801i
$439$		−	35.9709i		−	1.71680i	−0.512981	−	0.858400i	$-0.671459\pi$
$439$		−	35.9709i		−	1.71680i	0.512981	−	0.858400i	$-0.328541\pi$
$440$	−58.9226	+	47.6840i	−2.80902	+	2.27325i
$441$	−3.60809	+	2.42156i	−0.171814	+	0.115313i
$442$	−0.0565355	−	0.0606396i	−0.00268912	−	0.00288433i
$443$	8.28646			0.393702			0.196851	−	0.980433i	$-0.436929\pi$
$443$	8.28646			0.393702			0.196851	+	0.980433i	$0.436929\pi$
$444$	−3.37638	+	0.774643i	−0.160236	+	0.0367629i
$445$	16.5919			0.786533
$446$	9.26342	+	9.93588i	0.438636	+	0.470478i
$447$	−17.3985	+	5.29727i	−0.822922	+	0.250552i
$448$	−18.4350	−	3.93056i	−0.870972	−	0.185702i
$449$			17.5535i			0.828401i	0.910186	+	0.414201i	$0.135939\pi$
$449$			17.5535i			0.828401i	−0.910186	+	0.414201i	$0.864061\pi$
$450$	11.5009	−	49.2719i	0.542156	−	2.32270i
$451$		−	8.72183i		−	0.410695i
$452$	24.9770	+	1.75181i	1.17482	+	0.0823982i
$453$	−8.98197	+	2.73471i	−0.422010	+	0.128488i
$454$	2.66844	−	2.48783i	0.125236	−	0.116760i
$455$	−0.130128			−0.00610048
$456$	−7.64888	−	5.17561i	−0.358192	−	0.242370i
$457$	−4.19316			−0.196148			−0.0980738	−	0.995179i	$-0.531268\pi$
$457$	−4.19316			−0.196148			−0.0980738	+	0.995179i	$0.531268\pi$
$458$	7.14496	−	6.66139i	0.333862	−	0.311266i
$459$	−14.3414	+	17.5850i	−0.669397	+	0.820796i
$460$	−30.3726	−	2.13024i	−1.41613	−	0.0993227i
$461$		−	13.3781i		−	0.623081i	−0.950233	−	0.311540i	$-0.899155\pi$
$461$		−	13.3781i		−	0.623081i	0.950233	−	0.311540i	$-0.100845\pi$
$462$	18.8387	−	32.5348i	0.876456	−	1.51365i
$463$		−	1.01063i		−	0.0469682i	−0.999724	−	0.0234841i	$-0.992524\pi$
$463$		−	1.01063i		−	0.0469682i	0.999724	−	0.0234841i	$-0.00747590\pi$
$464$	−3.41642	+	24.2356i	−0.158603	+	1.12511i
$465$	−1.78427	−	5.86032i	−0.0827436	−	0.271766i
$466$	26.2796	+	28.1873i	1.21738	+	1.30575i
$467$	11.9661			0.553724			0.276862	−	0.960910i	$-0.410705\pi$
$467$	11.9661			0.553724			0.276862	+	0.960910i	$0.410705\pi$
$468$	−0.0400966	−	0.0698558i	−0.00185347	−	0.00322908i
$469$	5.85467			0.270344
$470$	21.2559	+	22.7990i	0.980463	+	1.05164i
$471$	8.31401	+	27.3068i	0.383089	+	1.25823i
$472$	16.4203	+	20.2903i	0.755804	+	0.933938i
$473$			22.2137i			1.02139i
$474$	12.4524	−	21.5055i	0.571956	−	0.987778i
$475$		−	22.4818i		−	1.03154i
$476$	−1.43979	+	20.5283i	−0.0659927	+	0.940913i
$477$	16.5889	+	24.7171i	0.759552	+	1.13172i
$478$	10.2474	−	9.55386i	0.468706	−	0.436984i
$479$	−21.9963			−1.00504			−0.502518	−	0.864566i	$-0.667593\pi$
$479$	−21.9963			−1.00504			−0.502518	+	0.864566i	$0.667593\pi$
$480$	24.8704	−	31.7227i	1.13517	−	1.44794i
$481$	−0.0134242			−0.000612093
$482$	−10.0471	+	9.36715i	−0.457635	+	0.426662i
$483$	14.4465	−	4.39846i	0.657336	−	0.200137i
$484$	4.39840	−	62.7117i	0.199927	−	2.85053i
$485$			42.6110i			1.93487i
$486$	−17.4516	+	13.4700i	−0.791622	+	0.611011i
$487$		−	6.55268i		−	0.296930i	−0.988918	−	0.148465i	$-0.952567\pi$
$487$		−	6.55268i		−	0.296930i	0.988918	−	0.148465i	$-0.0474333\pi$
$488$	2.51136	+	3.10326i	0.113684	+	0.140478i
$489$	34.4773	−	10.4972i	1.55912	−	0.474699i
$490$	−5.74684	−	6.16402i	−0.259616	−	0.278462i
$491$	−16.8248			−0.759294			−0.379647	−	0.925131i	$-0.623955\pi$
$491$	−16.8248			−0.759294			−0.379647	+	0.925131i	$0.623955\pi$
$492$	1.03719	+	4.52072i	0.0467601	+	0.203810i
$493$	26.7207			1.20344
$494$	−0.0244055	−	0.0261772i	−0.00109806	−	0.00117777i
$495$	44.8037	+	66.7568i	2.01378	+	3.00049i
$496$	0.480002	−	3.40507i	0.0215527	−	0.152892i
$497$			25.8821i			1.16097i
$498$	9.63332	+	5.57801i	0.431679	+	0.249957i
$499$			0.899541i			0.0402690i	0.999797	+	0.0201345i	$0.00640944\pi$
$499$			0.899541i			0.0402690i	−0.999797	+	0.0201345i	$0.993591\pi$
$500$	56.8459	+	3.98699i	2.54222	+	0.178304i
$501$	−4.02925	−	13.2338i	−0.180014	−	0.591243i
$502$	−18.2271	+	16.9935i	−0.813517	+	0.758458i
$503$	−30.5864			−1.36378			−0.681891	−	0.731454i	$-0.738842\pi$
$503$	−30.5864			−1.36378			−0.681891	+	0.731454i	$0.738842\pi$
$504$	−5.89552	+	19.1038i	−0.262608	+	0.850949i
$505$	15.3831			0.684537
$506$	24.9333	−	23.2458i	1.10842	−	1.03340i
$507$	6.55823	+	21.5401i	0.291261	+	0.956629i
$508$	2.61609	+	0.183484i	0.116070	+	0.00814079i
$509$			34.2213i			1.51683i	0.651770	+	0.758416i	$0.274027\pi$
$509$			34.2213i			1.51683i	−0.651770	+	0.758416i	$0.725973\pi$
$510$	−38.0842	−	22.0520i	−1.68639	−	0.976478i
$511$			13.9727i			0.618117i
$512$	20.1708	−	10.2537i	0.891433	−	0.453152i
$513$	−6.19095	+	7.59117i	−0.273337	+	0.335159i
$514$	14.1085	+	15.1327i	0.622299	+	0.667474i
$515$	34.9226			1.53887
$516$	−2.64163	−	11.5139i	−0.116291	−	0.506869i
$517$	−34.8987			−1.53484
$518$	2.27225	+	2.43720i	0.0998370	+	0.107085i
$519$	13.2463	−	4.03304i	0.581446	−	0.177031i
$520$	0.121428	−	0.0982678i	0.00532499	−	0.00430933i
$521$		−	34.6900i		−	1.51980i	−0.650042	−	0.759898i	$-0.725249\pi$
$521$		−	34.6900i		−	1.51980i	0.650042	−	0.759898i	$-0.274751\pi$
$522$	25.2803	+	5.90084i	1.10649	+	0.258273i
$523$			11.6361i			0.508810i	0.967098	+	0.254405i	$0.0818796\pi$
$523$			11.6361i			0.508810i	−0.967098	+	0.254405i	$0.918120\pi$
$524$	−0.161178	+	2.29805i	−0.00704108	+	0.100391i
$525$	−46.5586	+	14.1755i	−2.03198	+	0.618670i
$526$	18.6267	−	17.3661i	0.812164	−	0.757196i
$527$	−3.75423			−0.163537
$528$	6.98979	+	44.5861i	0.304192	+	1.94036i
$529$	−9.30732			−0.404666
$530$	−42.2264	+	39.3685i	−1.83420	+	1.71006i
$531$	22.9881	−	15.4284i	0.997598	−	0.669536i
$532$	−0.621536	+	8.86177i	−0.0269470	+	0.384206i
$533$			0.0179741i			0.000778543i
$534$	4.95013	−	8.54897i	0.214213	−	0.369950i
$535$		−	26.3014i		−	1.13711i
$536$	−5.46328	+	4.42124i	−0.235978	+	0.190969i
$537$	7.31550	+	24.0273i	0.315687	+	1.03685i
$538$	−30.3763	−	32.5814i	−1.30962	−	1.40469i
$539$	9.43534			0.406409
$540$	−31.1614	−	29.2735i	−1.34097	−	1.25973i
$541$	−1.64329			−0.0706504			−0.0353252	−	0.999376i	$-0.511247\pi$
$541$	−1.64329			−0.0706504			−0.0353252	+	0.999376i	$0.511247\pi$
$542$	−1.12291	−	1.20443i	−0.0482333	−	0.0517347i
$543$	−3.91714	−	12.8656i	−0.168100	−	0.552115i
$544$	−14.1587	−	20.2432i	−0.607050	−	0.867922i
$545$		−	60.1661i		−	2.57723i
$546$	−0.0388230	+	0.0670480i	−0.00166147	+	0.00286939i
$547$			3.28427i			0.140425i	0.997532	+	0.0702125i	$0.0223677\pi$
$547$			3.28427i			0.140425i	−0.997532	+	0.0702125i	$0.977632\pi$
$548$	−28.2336	−	1.98021i	−1.20608	−	0.0845906i
$549$	3.51587	−	2.35967i	0.150054	−	0.100708i
$550$	−80.3561	+	74.9175i	−3.42639	+	3.19449i
$551$	11.5349			0.491405
$552$	−10.1591	+	15.0139i	−0.432401	+	0.639033i
$553$	−23.9037			−1.01649
$554$	−22.0427	+	20.5509i	−0.936505	+	0.873122i
$555$	−6.81684	+	2.07550i	−0.289359	+	0.0881000i
$556$	−9.56312	−	0.670727i	−0.405567	−	0.0284452i
$557$			28.3215i			1.20002i	0.799992	+	0.600011i	$0.204837\pi$
$557$			28.3215i			1.20002i	−0.799992	+	0.600011i	$0.795163\pi$
$558$	−3.55185	−	0.829061i	−0.150362	−	0.0350969i
$559$		−	0.0457783i		−	0.00193621i
$560$	−38.3943	−	5.41233i	−1.62246	−	0.228713i
$561$	47.1350	−	14.3510i	1.99004	−	0.605900i
$562$	−8.80001	−	9.43884i	−0.371206	−	0.398153i
$563$	−28.3040			−1.19287			−0.596437	−	0.802660i	$-0.703417\pi$
$563$	−28.3040			−1.19287			−0.596437	+	0.802660i	$0.703417\pi$
$564$	18.0888	−	4.15011i	0.761674	−	0.174751i
$565$	51.5050			2.16683
$566$	10.8769	+	11.6665i	0.457189	+	0.490378i
$567$	19.6245	+	8.03462i	0.824150	+	0.337422i
$568$	−19.5453	−	24.1519i	−0.820101	−	1.01339i
$569$		−	24.0390i		−	1.00777i	−0.863772	−	0.503884i	$-0.831904\pi$
$569$		−	24.0390i		−	1.00777i	0.863772	−	0.503884i	$-0.168096\pi$
$570$	−16.4404	−	9.51952i	−0.688611	−	0.398729i
$571$			17.4737i			0.731252i	0.930762	+	0.365626i	$0.119145\pi$
$571$			17.4737i			0.731252i	−0.930762	+	0.365626i	$0.880855\pi$
$572$	−0.0122363	+	0.174464i	−0.000511627	+	0.00729470i
$573$	5.07172	+	16.6577i	0.211874	+	0.695887i
$574$	3.26323	−	3.04238i	0.136205	−	0.126986i
$575$	−44.1293			−1.84032
$576$	−8.92509	−	22.2788i	−0.371879	−	0.928281i
$577$	22.7332			0.946395			0.473197	−	0.880956i	$-0.343100\pi$
$577$	22.7332			0.946395			0.473197	+	0.880956i	$0.343100\pi$
$578$	−2.14179	+	1.99683i	−0.0890865	+	0.0830571i
$579$	−0.185575	−	0.609508i	−0.00771222	−	0.0253303i
$580$	−3.52249	+	50.2231i	−0.146263	+	2.08540i
$581$		−	10.7076i		−	0.444227i
$582$	21.9553	+	12.7128i	0.910075	+	0.526963i
$583$		−	64.6365i		−	2.67697i
$584$	−10.5517	−	13.0386i	−0.436633	−	0.539543i
$585$	−0.0923320	−	0.137573i	−0.00381746	−	0.00568795i
$586$	−12.8445	−	13.7769i	−0.530600	−	0.569119i
$587$	−20.6908			−0.854000			−0.427000	−	0.904252i	$-0.640430\pi$
$587$	−20.6908			−0.854000			−0.427000	+	0.904252i	$0.640430\pi$
$588$	−4.89054	+	1.12204i	−0.201683	+	0.0462721i
$589$	−1.62064			−0.0667775
$590$	36.6146	+	39.2725i	1.50740	+	1.61682i
$591$	4.61840	−	1.40615i	0.189976	−	0.0578412i
$592$	−3.96084	−	0.558348i	−0.162789	−	0.0229480i
$593$			12.0673i			0.495543i	0.968818	+	0.247772i	$0.0796983\pi$
$593$			12.0673i			0.495543i	−0.968818	+	0.247772i	$0.920302\pi$
$594$	47.7633	−	3.16841i	1.95975	−	0.130001i
$595$			42.3313i			1.73541i
$596$	−20.9492	−	1.46931i	−0.858111	−	0.0601852i
$597$	−13.4585	+	4.09767i	−0.550821	+	0.167707i
$598$	−0.0513829	+	0.0479053i	−0.00210120	+	0.00195899i
$599$	−26.4232			−1.07962			−0.539811	−	0.841786i	$-0.681504\pi$
$599$	−26.4232			−1.07962			−0.539811	+	0.841786i	$0.681504\pi$
$600$	32.7412	−	48.3873i	1.33666	−	1.97540i
$601$	−26.5160			−1.08161			−0.540805	−	0.841148i	$-0.681880\pi$
$601$	−26.5160			−1.08161			−0.540805	+	0.841148i	$0.681880\pi$
$602$	−8.31115	+	7.74865i	−0.338737	+	0.315811i
$603$	4.15418	+	6.18967i	0.169171	+	0.252063i
$604$	−10.8150	−	0.758529i	−0.440056	−	0.0308641i
$605$		−	129.317i		−	5.25750i
$606$	4.58947	−	7.92609i	0.186435	−	0.321976i
$607$		−	39.3500i		−	1.59717i	−0.601884	−	0.798584i	$-0.705583\pi$
$607$		−	39.3500i		−	1.59717i	0.601884	−	0.798584i	$-0.294417\pi$
$608$	−6.11211	−	8.73871i	−0.247879	−	0.354402i
$609$	−7.27315	−	23.8882i	−0.294723	−	0.967998i
$610$	5.59994	+	6.00646i	0.226735	+	0.243194i
$611$	0.0719196			0.00290956
$612$	−22.7245	+	13.0437i	−0.918584	+	0.527260i
$613$	−28.1158			−1.13559			−0.567793	−	0.823172i	$-0.692202\pi$
$613$	−28.1158			−1.13559			−0.567793	+	0.823172i	$0.692202\pi$
$614$	8.76423	+	9.40045i	0.353695	+	0.379371i
$615$	2.77894	+	9.12724i	0.112058	+	0.368046i
$616$	33.7455	−	27.3090i	1.35964	−	1.10031i
$617$			20.7667i			0.836036i	0.908439	+	0.418018i	$0.137275\pi$
$617$			20.7667i			0.836036i	−0.908439	+	0.418018i	$0.862725\pi$
$618$	10.4190	−	17.9938i	0.419114	−	0.723817i
$619$			30.8664i			1.24062i	0.784355	+	0.620312i	$0.212994\pi$
$619$			30.8664i			1.24062i	−0.784355	+	0.620312i	$0.787006\pi$
$620$	0.494905	−	7.05628i	0.0198759	−	0.283387i
$621$	14.9006	+	12.1521i	0.597941	+	0.487648i
$622$	14.4373	−	13.4602i	0.578884	−	0.539705i
$623$	−9.50234			−0.380703
$624$	−0.0144047	−	0.0918836i	−0.000576648	−	0.00367829i
$625$	57.5932			2.30373
$626$	−1.33689	+	1.24641i	−0.0534328	+	0.0498164i
$627$	20.3475	−	6.19512i	0.812600	−	0.247409i
$628$	−2.30606	+	32.8795i	−0.0920220	+	1.31204i
$629$			4.36699i			0.174123i
$630$	−9.34819	+	40.0494i	−0.372441	+	1.59561i
$631$		−	25.5657i		−	1.01775i	−0.860839	−	0.508877i	$-0.830061\pi$
$631$		−	25.5657i		−	1.01775i	0.860839	−	0.508877i	$-0.169939\pi$
$632$	22.3058	−	18.0513i	0.887275	−	0.718041i
$633$	−31.1399	+	9.48106i	−1.23770	+	0.376838i
$634$	−18.7542	−	20.1156i	−0.744825	−	0.798894i
$635$	5.39462			0.214079
$636$	7.68650	+	33.5026i	0.304789	+	1.32846i
$637$	−0.0194445			−0.000770418
$638$	−38.4385	−	41.2289i	−1.52180	−	1.63227i
$639$	−27.3631	+	18.3647i	−1.08247	+	0.726494i
$640$	39.9148	−	23.9435i	1.57777	−	0.946451i
$641$		−	9.64406i		−	0.380917i	−0.981695	−	0.190459i	$-0.939002\pi$
$641$		−	9.64406i		−	0.380917i	0.981695	−	0.190459i	$-0.0609975\pi$
$642$	−13.5518	−	7.84693i	−0.534846	−	0.309693i
$643$			5.86317i			0.231221i	0.993295	+	0.115610i	$0.0368824\pi$
$643$			5.86317i			0.231221i	−0.993295	+	0.115610i	$0.963118\pi$
$644$	17.3946	+	1.22000i	0.685445	+	0.0480749i
$645$	−7.07770	−	23.2462i	−0.278684	−	0.915320i
$646$	−8.51561	+	7.93927i	−0.335042	+	0.312367i
$647$	−37.4487			−1.47226			−0.736130	−	0.676840i	$-0.763349\pi$
$647$	−37.4487			−1.47226			−0.736130	+	0.676840i	$0.763349\pi$
$648$	−24.3800	+	7.32221i	−0.957737	+	0.287644i
$649$	−60.1149			−2.35972
$650$	0.165599	−	0.154391i	0.00649532	−	0.00605571i
$651$	1.02187	+	3.35626i	0.0400502	+	0.131542i
$652$	41.5133	+	2.91161i	1.62579	+	0.114028i
$653$			3.51598i			0.137591i	0.997631	+	0.0687954i	$0.0219156\pi$
$653$			3.51598i			0.137591i	−0.997631	+	0.0687954i	$0.978084\pi$
$654$	−31.0005	−	17.9503i	−1.21222	−	0.701913i
$655$			4.73879i			0.185160i
$656$	−0.747586	+	5.30327i	−0.0291883	+	0.207058i
$657$	−14.7722	+	9.91435i	−0.576319	+	0.386795i
$658$	−12.1735	−	13.0572i	−0.474571	−	0.509022i
$659$	−28.1494			−1.09655			−0.548273	−	0.836299i	$-0.684715\pi$
$659$	−28.1494			−1.09655			−0.548273	+	0.836299i	$0.684715\pi$
$660$	20.7599	+	90.4847i	0.808079	+	3.52211i
$661$	36.0021			1.40032			0.700160	−	0.713986i	$-0.253112\pi$
$661$	36.0021			1.40032			0.700160	+	0.713986i	$0.253112\pi$
$662$	33.4748	+	35.9049i	1.30104	+	1.39548i
$663$	−0.0971364	+	0.0295747i	−0.00377246	+	0.00114859i
$664$	8.08602	+	9.99181i	0.313799	+	0.387757i
$665$			18.2738i			0.708628i
$666$	−0.964379	+	4.13158i	−0.0373689	+	0.160096i
$667$		−	22.6418i		−	0.876693i
$668$	1.11760	−	15.9345i	0.0432411	−	0.616525i
$669$	15.9159	−	4.84586i	0.615345	−	0.187352i
$670$	−10.5743	+	9.85867i	−0.408523	+	0.380874i
$671$	−9.19416			−0.354937
$672$	−14.2435	+	18.1679i	−0.549454	+	0.700840i
$673$	−16.9715			−0.654204			−0.327102	−	0.944989i	$-0.606072\pi$
$673$	−16.9715			−0.654204			−0.327102	+	0.944989i	$0.606072\pi$
$674$	3.07228	−	2.86434i	0.118340	−	0.110330i
$675$	−48.0222	−	39.1643i	−1.84838	−	1.50744i
$676$	−1.81906	+	25.9359i	−0.0699640	+	0.997536i
$677$		−	26.3238i		−	1.01170i	−0.862620	−	0.505852i	$-0.831178\pi$
$677$		−	26.3238i		−	1.01170i	0.862620	−	0.505852i	$-0.168822\pi$
$678$	15.3663	−	26.5379i	0.590140	−	1.01918i
$679$		−	24.4037i		−	0.936528i
$680$	−31.9671	−	39.5014i	−1.22588	−	1.51481i
$681$	−1.30143	−	4.27447i	−0.0498710	−	0.163798i
$682$	5.40057	+	5.79261i	0.206798	+	0.221811i
$683$	10.8022			0.413335			0.206667	−	0.978411i	$-0.433738\pi$
$683$	10.8022			0.413335			0.206667	+	0.978411i	$0.433738\pi$
$684$	−9.80984	+	5.63077i	−0.375088	+	0.215298i
$685$	−58.2203			−2.22448
$686$	19.1970	+	20.5906i	0.732946	+	0.786153i
$687$	−3.48469	−	11.4453i	−0.132949	−	0.436664i
$688$	1.90403	−	13.5069i	0.0725906	−	0.514947i
$689$			0.133204i			0.00507466i
$690$	−18.6857	+	32.2706i	−0.711354	+	1.22852i
$691$			32.7717i			1.24670i	0.781945	+	0.623348i	$0.214228\pi$
$691$			32.7717i			1.24670i	−0.781945	+	0.623348i	$0.785772\pi$
$692$	15.9495	+	1.11865i	0.606310	+	0.0425246i
$693$	−25.6595	−	38.2322i	−0.974722	−	1.45232i
$694$	12.8762	−	12.0047i	0.488774	−	0.455693i
$695$	−19.7201			−0.748024
$696$	24.8264	+	16.7988i	0.941044	+	0.636757i
$697$	5.84707			0.221474
$698$	15.8488	−	14.7762i	0.599887	−	0.559286i
$699$	45.1522	−	13.7473i	1.70781	−	0.519972i
$700$	−56.0601	−	3.93188i	−2.11887	−	0.148611i
$701$			20.4189i			0.771210i	0.922664	+	0.385605i	$0.126007\pi$
$701$			20.4189i			0.771210i	−0.922664	+	0.385605i	$0.873993\pi$
$702$	−0.0984313	+	0.00652950i	−0.00371505	+	0.000246440i
$703$			1.88516i			0.0711003i
$704$	−10.8667	+	50.9668i	−0.409555	+	1.92088i
$705$	36.5208	−	11.1194i	1.37545	−	0.418780i
$706$	18.0289	+	19.3376i	0.678525	+	0.727782i
$707$	−8.81001			−0.331335
$708$	31.1589	−	7.14880i	1.17102	−	0.268668i
$709$	−18.7313			−0.703467			−0.351733	−	0.936100i	$-0.614408\pi$
$709$	−18.7313			−0.703467			−0.351733	+	0.936100i	$0.614408\pi$
$710$	−43.5828	−	46.7467i	−1.63564	−	1.75437i
$711$	−16.9609	−	25.2715i	−0.636083	−	0.947754i
$712$	8.86710	−	7.17584i	0.332309	−	0.268926i
$713$			3.18114i			0.119135i
$714$	21.8111	+	12.6294i	0.816261	+	0.472642i
$715$			0.359761i			0.0134543i
$716$	−2.02911	+	28.9307i	−0.0758313	+	1.08119i
$717$	−4.99780	−	16.4150i	−0.186646	−	0.613028i
$718$	−13.7549	+	12.8240i	−0.513328	+	0.478586i
$719$	35.7292			1.33248			0.666238	−	0.745740i	$-0.267904\pi$
$719$	35.7292			1.33248			0.666238	+	0.745740i	$0.267904\pi$
$720$	−21.5207	−	44.4315i	−0.802028	−	1.65586i
$721$	−20.0005			−0.744856
$722$	15.9774	−	14.8960i	0.594616	−	0.554372i
$723$	4.90013	+	16.0941i	0.182238	+	0.598548i
$724$	1.08650	−	15.4912i	0.0403795	−	0.575724i
$725$			72.9707i			2.71007i
$726$	−66.6306	−	38.5813i	−2.47289	−	1.43189i
$727$			11.4503i			0.424666i	0.977197	+	0.212333i	$0.0681062\pi$
$727$			11.4503i			0.424666i	−0.977197	+	0.212333i	$0.931894\pi$
$728$	−0.0695431	+	0.0562788i	−0.00257744	+	0.00208583i
$729$	5.43019	+	26.4483i	0.201118	+	0.979567i
$730$	−23.5286	−	25.2367i	−0.870834	−	0.934051i
$731$	−14.8920			−0.550799
$732$	4.76554	−	1.09336i	0.176139	−	0.0404117i
$733$	−39.5473			−1.46071			−0.730356	−	0.683067i	$-0.760646\pi$
$733$	−39.5473			−1.46071			−0.730356	+	0.683067i	$0.760646\pi$
$734$	2.42640	+	2.60254i	0.0895599	+	0.0960613i
$735$	−9.87391	+	3.00627i	−0.364205	+	0.110888i
$736$	−17.1531	+	11.9974i	−0.632271	+	0.442229i
$737$		−	16.1863i		−	0.596229i
$738$	5.53188	+	1.29123i	0.203631	+	0.0475309i
$739$		−	45.8734i		−	1.68748i	−0.536752	−	0.843740i	$-0.680349\pi$
$739$		−	45.8734i		−	1.68748i	0.536752	−	0.843740i	$-0.319651\pi$
$740$	−8.20800	−	0.575683i	−0.301732	−	0.0211625i
$741$	−0.0419323	+	0.0127670i	−0.00154042	+	0.000469007i
$742$	24.1835	−	22.5467i	0.887803	−	0.827716i
$743$	12.4263			0.455876			0.227938	−	0.973676i	$-0.426802\pi$
$743$	12.4263			0.455876			0.227938	+	0.973676i	$0.426802\pi$
$744$	−3.48808	−	2.36021i	−0.127879	−	0.0865295i
$745$	−43.1992			−1.58269
$746$	−33.6436	+	31.3666i	−1.23178	+	1.14841i
$747$	11.3203	−	7.59759i	0.414188	−	0.277981i
$748$	56.7541	+	3.98055i	2.07514	+	0.145543i
$749$			15.0631i			0.550392i
$750$	34.9726	−	60.3982i	1.27702	−	2.20543i
$751$			12.5652i			0.458509i	0.973367	+	0.229254i	$0.0736288\pi$
$751$			12.5652i			0.458509i	−0.973367	+	0.229254i	$0.926371\pi$
$752$	21.2200	+	2.99132i	0.773813	+	0.109082i
$753$	8.88962	+	29.1974i	0.323956	+	1.06401i
$754$	0.0792146	+	0.0849651i	0.00288483	+	0.00309425i
$755$	−22.3015			−0.811635
$756$	17.8464	+	16.7652i	0.649067	+	0.609745i
$757$	24.7686			0.900230			0.450115	−	0.892971i	$-0.351383\pi$
$757$	24.7686			0.900230			0.450115	+	0.892971i	$0.351383\pi$
$758$	12.9500	+	13.8901i	0.470366	+	0.504511i
$759$	−12.1603	−	39.9398i	−0.441391	−	1.44972i
$760$	−13.7997	−	17.0522i	−0.500569	−	0.618548i
$761$		−	31.0441i		−	1.12535i	−0.826679	−	0.562674i	$-0.809773\pi$
$761$		−	31.0441i		−	1.12535i	0.826679	−	0.562674i	$-0.190227\pi$
$762$	1.60946	−	2.77957i	0.0583047	−	0.100693i
$763$			34.4577i			1.24745i
$764$	−1.40675	+	20.0572i	−0.0508944	+	0.725644i
$765$	−44.7534	+	30.0362i	−1.61806	+	1.08596i
$766$	−11.5606	+	10.7782i	−0.417702	+	0.389432i
$767$	0.123886			0.00447325
$768$	−0.428441	−	27.7095i	−0.0154600	−	0.999880i
$769$	−48.6952			−1.75599			−0.877997	−	0.478665i	$-0.841121\pi$
$769$	−48.6952			−1.75599			−0.877997	+	0.478665i	$0.841121\pi$
$770$	65.3154	−	60.8948i	2.35380	−	2.19450i
$771$	24.2405	−	7.38041i	0.873000	−	0.265799i
$772$	0.0514730	−	0.733894i	0.00185255	−	0.0264134i
$773$		−	25.3478i		−	0.911696i	−0.890058	−	0.455848i	$-0.849336\pi$
$773$		−	25.3478i		−	0.911696i	0.890058	−	0.455848i	$-0.150664\pi$
$774$	−14.0892	−	3.28865i	−0.506426	−	0.118208i
$775$		−	10.2523i		−	0.368273i
$776$	18.4288	+	22.7723i	0.661556	+	0.817478i
$777$	3.90406	−	1.18866i	0.140058	−	0.0426428i
$778$	3.73584	+	4.00704i	0.133936	+	0.143659i
$779$	2.52409			0.0904351
$780$	−0.0427823	−	0.186472i	−0.00153185	−	0.00667677i
$781$	71.5557			2.56046
$782$	15.5839	+	16.7152i	0.557279	+	0.597733i
$783$	20.0944	−	24.6392i	0.718114	−	0.880532i
$784$	−5.73711	−	0.808744i	−0.204897	−	0.0288837i
$785$			67.8006i			2.41991i
$786$	2.44165	+	1.41380i	0.0870909	+	0.0504285i
$787$		−	38.0716i		−	1.35711i	−0.734551	−	0.678553i	$-0.762607\pi$
$787$		−	38.0716i		−	1.35711i	0.734551	−	0.678553i	$-0.237393\pi$
$788$	5.56091	+	0.390025i	0.198099	+	0.0138941i
$789$	−9.08450	−	29.8375i	−0.323417	−	1.06224i
$790$	43.1735	−	40.2515i	1.53604	−	1.43208i
$791$	−29.4974			−1.04881
$792$	52.8157	+	16.2992i	1.87673	+	0.579168i
$793$	0.0189474			0.000672844
$794$	27.7435	−	25.8659i	0.984582	−	0.917945i
$795$	20.5944	+	67.6410i	0.730408	+	2.39898i
$796$	−16.2051	−	1.13658i	−0.574375	−	0.0402848i
$797$		−	8.75185i		−	0.310006i	−0.987914	−	0.155003i	$-0.950461\pi$
$797$		−	8.75185i		−	0.310006i	0.987914	−	0.155003i	$-0.0495388\pi$
$798$	9.41555	+	5.45191i	0.333307	+	0.192996i
$799$		−	23.3959i		−	0.827687i
$800$	55.2816	−	38.6656i	1.95450	−	1.36704i
$801$	−6.74239	−	10.0461i	−0.238231	−	0.354960i
$802$	−15.4967	−	16.6216i	−0.547207	−	0.586930i
$803$	38.6301			1.36323
$804$	1.92485	+	8.38971i	0.0678843	+	0.295882i
$805$	35.8694			1.26423
$806$	−0.0111296	−	0.0119375i	−0.000392022	−	0.000420480i
$807$	−52.1910	+	15.8904i	−1.83721	+	0.559369i
$808$	8.22105	−	6.65301i	0.289216	−	0.234052i
$809$		−	35.0870i		−	1.23359i	−0.787122	−	0.616797i	$-0.788430\pi$
$809$		−	35.0870i		−	1.23359i	0.787122	−	0.616797i	$-0.211570\pi$
$810$	−48.9740	+	18.5340i	−1.72077	+	0.651217i
$811$		−	1.92502i		−	0.0675967i	−0.999429	−	0.0337983i	$-0.989240\pi$
$811$		−	1.92502i		−	0.0675967i	0.999429	−	0.0337983i	$-0.0107604\pi$
$812$	2.01736	−	28.7632i	0.0707954	−	1.00939i
$813$	−1.92933	+	0.587417i	−0.0676647	+	0.0206016i
$814$	6.73808	−	6.28204i	0.236169	−	0.220185i
$815$	85.6044			2.99859
$816$	−29.8903	+	4.68592i	−1.04637	+	0.164040i
$817$	−6.42864			−0.224910
$818$	33.2969	−	31.0433i	1.16420	−	1.08540i
$819$	0.0528794	+	0.0787894i	0.00184775	+	0.00275313i
$820$	−0.770796	+	10.9899i	−0.0269174	+	0.383784i
$821$			49.1712i			1.71609i	0.513577	+	0.858044i	$0.328320\pi$
$821$			49.1712i			1.71609i	−0.513577	+	0.858044i	$0.671680\pi$
$822$	−17.3698	+	29.9979i	−0.605841	+	1.04630i
$823$		−	2.10253i		−	0.0732896i	−0.999328	−	0.0366448i	$-0.988333\pi$
$823$		−	2.10253i		−	0.0732896i	0.999328	−	0.0366448i	$-0.0116670\pi$
$824$	18.6634	−	15.1036i	0.650171	−	0.526161i
$825$	39.1907	+	128.719i	1.36445	+	4.48143i
$826$	−20.9695	−	22.4917i	−0.729622	−	0.782587i
$827$	34.8692			1.21252			0.606260	−	0.795266i	$-0.292669\pi$
$827$	34.8692			1.21252			0.606260	+	0.795266i	$0.292669\pi$
$828$	11.0526	+	19.2556i	0.384103	+	0.669178i
$829$	−8.25630			−0.286753			−0.143377	−	0.989668i	$-0.545796\pi$
$829$	−8.25630			−0.286753			−0.143377	+	0.989668i	$0.545796\pi$
$830$	18.0306	+	19.3394i	0.625850	+	0.671282i
$831$	10.7505	+	35.3094i	0.372932	+	1.22487i
$832$	0.0223943	−	0.105033i	0.000776383	−	0.00364137i
$833$			6.32540i			0.219162i
$834$	−5.88340	+	10.1607i	−0.203725	+	0.351837i
$835$		−	32.8585i		−	1.13712i
$836$	24.4999	+	1.71835i	0.847348	+	0.0594303i
$837$	−2.82323	+	3.46177i	−0.0975852	+	0.119656i
$838$	13.9263	−	12.9838i	0.481076	−	0.448517i
$839$	−18.0970			−0.624779			−0.312389	−	0.949954i	$-0.601129\pi$
$839$	−18.0970			−0.624779			−0.312389	+	0.949954i	$0.601129\pi$
$840$	−26.6129	+	39.3304i	−0.918232	+	1.35703i
$841$	−8.43968			−0.291024
$842$	−4.62618	+	4.31308i	−0.159429	+	0.148639i
$843$	−15.1197	+	4.60345i	−0.520751	+	0.158551i
$844$	−37.4949	−	2.62977i	−1.29063	−	0.0905204i
$845$			53.4823i			1.83985i
$846$	5.16661	−	22.1347i	0.177632	−	0.761008i
$847$			74.0612i			2.54477i
$848$	−5.54028	+	39.3019i	−0.190254	+	1.34963i
$849$	18.6881	−	5.68989i	0.641373	−	0.195277i
$850$	−50.2243	−	53.8703i	−1.72268	−	1.84774i
$851$	3.70036			0.126847
$852$	−37.0889	+	8.50932i	−1.27065	+	0.291524i
$853$	0.799242			0.0273655			0.0136828	−	0.999906i	$-0.495645\pi$
$853$	0.799242			0.0273655			0.0136828	+	0.999906i	$0.495645\pi$
$854$	−3.20714	−	3.43995i	−0.109746	−	0.117713i
$855$	−19.3194	+	12.9662i	−0.660709	+	0.443434i
$856$	−11.3751	−	14.0561i	−0.388793	−	0.480427i
$857$			46.0168i			1.57191i	0.618287	+	0.785953i	$0.287827\pi$
$857$			46.0168i			1.57191i	−0.618287	+	0.785953i	$0.712173\pi$
$858$	0.185366	+	0.107333i	0.00632830	+	0.00366429i
$859$			31.6388i			1.07950i	0.841825	+	0.539750i	$0.181481\pi$
$859$			31.6388i			1.07950i	−0.841825	+	0.539750i	$0.818519\pi$
$860$	1.96315	−	27.9903i	0.0669428	−	0.954460i
$861$	−1.59152	−	5.22725i	−0.0542389	−	0.178144i
$862$	41.0701	−	38.2905i	1.39885	−	1.30418i
$863$	−9.26390			−0.315347			−0.157673	−	0.987491i	$-0.550399\pi$
$863$	−9.26390			−0.315347			−0.157673	+	0.987491i	$0.550399\pi$
$864$	−29.3139	−	2.16747i	−0.997278	−	0.0737387i
$865$	32.8894			1.11827
$866$	−40.3189	+	37.5901i	−1.37009	+	1.27736i
$867$	1.04458	+	3.43085i	0.0354757	+	0.116518i
$868$	−0.283436	+	4.04119i	−0.00962046	+	0.137167i
$869$			66.0861i			2.24182i
$870$	53.3616	+	30.8981i	1.80913	+	1.04754i
$871$			0.0333569i			0.00113026i
$872$	−26.0212	−	32.1541i	−0.881190	−	1.08888i
$873$	25.8000	−	17.3156i	0.873199	−	0.586046i
$874$	6.72734	+	7.21570i	0.227556	+	0.244075i
$875$	−67.1338			−2.26954
$876$	−20.0228	+	4.59384i	−0.676509	+	0.155212i
$877$	−12.8467			−0.433802			−0.216901	−	0.976194i	$-0.569595\pi$
$877$	−12.8467			−0.433802			−0.216901	+	0.976194i	$0.569595\pi$
$878$	−34.6898	−	37.2080i	−1.17072	−	1.25571i
$879$	−22.0687	+	6.71918i	−0.744359	+	0.226632i
$880$	−14.9634	+	106.148i	−0.504415	+	3.57824i
$881$		−	41.4697i		−	1.39715i	−0.715537	−	0.698574i	$-0.753818\pi$
$881$		−	41.4697i		−	1.39715i	0.715537	−	0.698574i	$-0.246182\pi$
$882$	−1.39686	+	5.98443i	−0.0470348	+	0.201506i
$883$			3.62346i			0.121939i	0.998140	+	0.0609695i	$0.0194192\pi$
$883$			3.62346i			0.121939i	−0.998140	+	0.0609695i	$0.980581\pi$
$884$	−0.116960	−	0.00820318i	−0.00393378	−	0.000275903i
$885$	62.9092	−	19.1537i	2.11467	−	0.643846i
$886$	8.57144	−	7.99132i	0.287963	−	0.268474i
$887$	−52.1940			−1.75250			−0.876251	−	0.481855i	$-0.839963\pi$
$887$	−52.1940			−1.75250			−0.876251	+	0.481855i	$0.839963\pi$
$888$	−2.74544	+	4.05741i	−0.0921310	+	0.136158i
$889$	−3.08955			−0.103620
$890$	17.1625	−	16.0010i	0.575290	−	0.536354i
$891$	22.2131	−	54.2553i	0.744168	−	1.81762i
$892$	19.1640	+	1.34410i	0.641658	+	0.0450039i
$893$		−	10.0997i		−	0.337972i
$894$	−12.8883	+	22.2583i	−0.431049	+	0.744429i
$895$			59.6578i			1.99414i
$896$	−22.8596	+	13.7127i	−0.763685	+	0.458108i
$897$	0.0250601	+	0.0823084i	0.000836733	+	0.00274820i
$898$	16.9283	+	18.1572i	0.564905	+	0.605913i
$899$	5.26023			0.175438
$900$	−35.6206	−	62.0576i	−1.18735	−	2.06859i
$901$	43.3320			1.44360
$902$	−8.41118	−	9.02178i	−0.280062	−	0.300392i
$903$	4.05346	+	13.3133i	0.134891	+	0.443040i
$904$	27.5254	−	22.2754i	0.915483	−	0.740868i
$905$		−	31.9442i		−	1.06186i
$906$	−6.65357	+	11.4908i	−0.221050	+	0.381757i
$907$		−	43.9723i		−	1.46008i	−0.683406	−	0.730039i	$-0.739502\pi$
$907$		−	43.9723i		−	1.46008i	0.683406	−	0.730039i	$-0.260498\pi$
$908$	0.360979	−	5.14679i	0.0119795	−	0.170802i
$909$	−6.25114	−	9.31410i	−0.207337	−	0.308929i
$910$	−0.134603	+	0.125493i	−0.00446204	+	0.00416005i
$911$	−55.0296			−1.82321			−0.911605	−	0.411066i	$-0.865156\pi$
$911$	−55.0296			−1.82321			−0.911605	+	0.411066i	$0.865156\pi$
$912$	−12.9032	+	2.02284i	−0.427268	+	0.0669831i
$913$	−29.6031			−0.979720
$914$	−4.33737	+	4.04381i	−0.143467	+	0.133757i
$915$	9.62153	−	2.92943i	0.318078	−	0.0968440i
$916$	0.966553	−	13.7810i	0.0319358	−	0.455336i
$917$		−	2.71395i		−	0.0896224i
$918$	2.12409	+	32.0203i	0.0701053	+	1.05683i
$919$			10.1422i			0.334559i	0.985910	+	0.167279i	$0.0534982\pi$
$919$			10.1422i			0.334559i	−0.985910	+	0.167279i	$0.946502\pi$
$920$	−33.4715	+	27.0873i	−1.10352	+	0.893042i
$921$	15.0582	−	4.58473i	0.496186	−	0.151072i
$922$	−12.9016	−	13.8382i	−0.424892	−	0.455737i
$923$	−0.147463			−0.00485380
$924$	−11.8894	−	51.8214i	−0.391132	−	1.70480i
$925$	−11.9257			−0.392114
$926$	−0.974639	−	1.04539i	−0.0320286	−	0.0343537i
$927$	−14.1913	−	21.1449i	−0.466104	−	0.694488i
$928$	19.8385	+	28.3638i	0.651230	+	0.931087i
$929$			32.6924i			1.07260i	0.844027	+	0.536301i	$0.180179\pi$
$929$			32.6924i			1.07260i	−0.844027	+	0.536301i	$0.819821\pi$
$930$	−7.49723	−	4.34115i	−0.245844	−	0.142352i
$931$			2.73058i			0.0894912i
$932$	54.3668	+	3.81311i	1.78084	+	0.124903i
$933$	−7.04127	−	23.1266i	−0.230521	−	0.757131i
$934$	12.3776	−	11.5399i	0.405008	−	0.377597i
$935$	117.032			3.82737
$936$	−0.108843	−	0.0335896i	−0.00355766	−	0.00109791i
$937$	−16.3721			−0.534854			−0.267427	−	0.963578i	$-0.586173\pi$
$937$	−16.3721			−0.534854			−0.267427	+	0.963578i	$0.586173\pi$
$938$	6.05602	−	5.64615i	0.197736	−	0.184353i
$939$	0.652018	+	2.14151i	0.0212778	+	0.0698856i
$940$	43.9739	+	3.08419i	1.43427	+	0.100595i
$941$		−	30.7163i		−	1.00132i	−0.865643	−	0.500662i	$-0.833090\pi$
$941$		−	30.7163i		−	1.00132i	0.865643	−	0.500662i	$-0.166910\pi$
$942$	34.9342	+	20.2280i	1.13822	+	0.659065i
$943$		−	4.95451i		−	0.161341i
$944$	36.5526	+	5.15272i	1.18969	+	0.167707i
$945$	39.0337	+	31.8338i	1.26977	+	1.03555i
$946$	21.4225	+	22.9777i	0.696506	+	0.747068i
$947$	−40.5453			−1.31754			−0.658772	−	0.752343i	$-0.728924\pi$
$947$	−40.5453			−1.31754			−0.658772	+	0.752343i	$0.728924\pi$
$948$	−7.85888	−	34.2539i	−0.255245	−	1.11252i
$949$	−0.0796094			−0.00258423
$950$	−21.6811	−	23.2550i	−0.703428	−	0.754492i
$951$	−32.2225	+	9.81067i	−1.04489	+	0.318133i
$952$	18.3078	+	22.6228i	0.593361	+	0.733209i
$953$		−	0.907656i		−	0.0294019i	−0.999892	−	0.0147009i	$-0.995320\pi$
$953$		−	0.907656i		−	0.0294019i	0.999892	−	0.0147009i	$-0.00467962\pi$
$954$	40.9962	+	9.56918i	1.32730	+	0.309814i
$955$			41.3598i			1.33837i
$956$	1.38624	−	19.7649i	0.0448344	−	0.639241i
$957$	−66.0431	+	20.1079i	−2.13487	+	0.649996i
$958$	−22.7528	+	21.2129i	−0.735109	+	0.685357i
$959$	33.3433			1.07671
$960$	−4.86713	−	56.7982i	−0.157086	−	1.83316i
$961$	30.2609			0.976160
$962$	−0.0138859	+	0.0129461i	−0.000447700	+	0.000417399i
$963$	−15.9249	+	10.6880i	−0.513174	+	0.344416i
$964$	−1.35915	+	19.3786i	−0.0437754	+	0.624142i
$965$		−	1.51336i		−	0.0487168i
$966$	10.7015	−	18.4816i	0.344315	−	0.594637i
$967$			46.2854i			1.48844i	0.667936	+	0.744218i	$0.267178\pi$
$967$			46.2854i			1.48844i	−0.667936	+	0.744218i	$0.732822\pi$
$968$	−55.9284	−	69.1101i	−1.79761	−	2.22128i
$969$	4.15318	+	13.6408i	0.133419	+	0.438207i
$970$	41.0933	+	44.0765i	1.31943	+	1.41521i
$971$	26.7435			0.858239			0.429119	−	0.903248i	$-0.358824\pi$
$971$	26.7435			0.858239			0.429119	+	0.903248i	$0.358824\pi$
$972$	−5.06158	+	30.7633i	−0.162350	+	0.986733i
$973$	11.2938			0.362064
$974$	−6.31930	−	6.77804i	−0.202483	−	0.217182i
$975$	−0.0807648	−	0.265267i	−0.00258654	−	0.00849533i
$976$	5.59047	+	0.788072i	0.178947	+	0.0252256i
$977$		−	18.9020i		−	0.604729i	−0.953192	−	0.302365i	$-0.902224\pi$
$977$		−	18.9020i		−	0.604729i	0.953192	−	0.302365i	$-0.0977760\pi$
$978$	25.5397	−	44.1075i	0.816670	−	1.41040i
$979$			26.2709i			0.839622i
$980$	−11.8890	−	0.833853i	−0.379779	−	0.0266365i
$981$	−36.4293	+	24.4494i	−1.16310	+	0.780610i
$982$	−17.4035	+	16.2256i	−0.555367	+	0.517780i
$983$	27.7333			0.884556			0.442278	−	0.896878i	$-0.354170\pi$
$983$	27.7333			0.884556			0.442278	+	0.896878i	$0.354170\pi$
$984$	5.43256	+	3.67594i	0.173184	+	0.117185i
$985$	11.4671			0.365373
$986$	27.6397	−	25.7690i	0.880226	−	0.820652i
$987$	−20.9158	+	6.36816i	−0.665758	+	0.202701i
$988$	−0.0504898	−	0.00354119i	−0.00160629	−	0.000112660i
$989$			12.6187i			0.401251i
$990$	110.724	+	25.8447i	3.51903	+	0.821399i
$991$		−	29.7647i		−	0.945507i	−0.881195	−	0.472754i	$-0.843260\pi$
$991$		−	29.7647i		−	0.945507i	0.881195	−	0.472754i	$-0.156740\pi$
$992$	−2.78728	−	3.98508i	−0.0884962	−	0.126526i
$993$	57.5147	−	17.5113i	1.82517	−	0.555704i
$994$	24.9603	+	26.7722i	0.791692	+	0.849164i
$995$	−33.4165			−1.05937
$996$	15.3440	−	3.52037i	0.486192	−	0.111547i
$997$	−33.3325			−1.05565			−0.527825	−	0.849353i	$-0.676992\pi$
$997$	−33.3325			−1.05565			−0.527825	+	0.849353i	$0.676992\pi$
$998$	0.867502	+	0.930477i	0.0274603	+	0.0294537i
$999$	4.02680	+	3.28404i	0.127402	+	0.103902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	444.2.c.c.371.15	yes	20
3.2	odd	2	inner	444.2.c.c.371.6	yes	20
4.3	odd	2	inner	444.2.c.c.371.5	✓	20
12.11	even	2	inner	444.2.c.c.371.16	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
444.2.c.c.371.5	✓	20	4.3	odd	2	inner
444.2.c.c.371.6	yes	20	3.2	odd	2	inner
444.2.c.c.371.15	yes	20	1.1	even	1	trivial
444.2.c.c.371.16	yes	20	12.11	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 444 = 2^{2} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	444.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.03439 - 0.964383i) q^{2} +(-0.504486 - 1.65695i) q^{3} +(0.139930 - 1.99510i) q^{4} -4.11408i q^{5} +(-2.11977 - 1.22742i) q^{6} +2.35617i q^{7} +(-1.77930 - 2.19866i) q^{8} +(-2.49099 + 1.67182i) q^{9} +O(q^{10})\)	\(q+(1.03439 - 0.964383i) q^{2} +(-0.504486 - 1.65695i) q^{3} +(0.139930 - 1.99510i) q^{4} -4.11408i q^{5} +(-2.11977 - 1.22742i) q^{6} +2.35617i q^{7} +(-1.77930 - 2.19866i) q^{8} +(-2.49099 + 1.67182i) q^{9} +(-3.96755 - 4.25557i) q^{10} +6.51405 q^{11} +(-3.37638 + 0.774643i) q^{12} -0.0134242 q^{13} +(2.27225 + 2.43720i) q^{14} +(-6.81684 + 2.07550i) q^{15} +(-3.96084 - 0.558348i) q^{16} +4.36699i q^{17} +(-0.964379 + 4.13158i) q^{18} +1.88516i q^{19} +(-8.20800 - 0.575683i) q^{20} +(3.90406 - 1.18866i) q^{21} +(6.73808 - 6.28204i) q^{22} +3.70036 q^{23} +(-2.74544 + 4.05741i) q^{24} -11.9257 q^{25} +(-0.0138859 + 0.0129461i) q^{26} +(4.02680 + 3.28404i) q^{27} +(4.70079 + 0.329699i) q^{28} -6.11880i q^{29} +(-5.04970 + 8.72092i) q^{30} +0.859683i q^{31} +(-4.63552 + 3.24222i) q^{32} +(-3.28625 - 10.7935i) q^{33} +(4.21145 + 4.51717i) q^{34} +9.69348 q^{35} +(2.98688 + 5.20370i) q^{36} +1.00000 q^{37} +(1.81802 + 1.95000i) q^{38} +(0.00677235 + 0.0222433i) q^{39} +(-9.04546 + 7.32018i) q^{40} -1.33893i q^{41} +(2.89201 - 4.99455i) q^{42} +3.41012i q^{43} +(0.911510 - 12.9962i) q^{44} +(6.87801 + 10.2481i) q^{45} +(3.82762 - 3.56857i) q^{46} -5.35745 q^{47} +(1.07303 + 6.84460i) q^{48} +1.44846 q^{49} +(-12.3358 + 11.5009i) q^{50} +(7.23589 - 2.20309i) q^{51} +(-0.00187845 + 0.0267827i) q^{52} -9.92263i q^{53} +(7.33235 - 0.486396i) q^{54} -26.7993i q^{55} +(5.18042 - 4.19233i) q^{56} +(3.12363 - 0.951040i) q^{57} +(-5.90087 - 6.32923i) q^{58} -9.22850 q^{59} +(3.18694 + 13.8907i) q^{60} -1.41144 q^{61} +(0.829064 + 0.889249i) q^{62} +(-3.93909 - 5.86919i) q^{63} +(-1.66820 + 7.82414i) q^{64} +0.0552284i q^{65} +(-13.8083 - 7.99547i) q^{66} -2.48483i q^{67} +(8.71257 + 0.611072i) q^{68} +(-1.86678 - 6.13133i) q^{69} +(10.0268 - 9.34823i) q^{70} +10.9848 q^{71} +(8.10797 + 2.50216i) q^{72} +5.93027 q^{73} +(1.03439 - 0.964383i) q^{74} +(6.01634 + 19.7603i) q^{75} +(3.76109 + 0.263791i) q^{76} +15.3482i q^{77} +(0.0284564 + 0.0164772i) q^{78} +10.1452i q^{79} +(-2.29709 + 16.2952i) q^{80} +(3.41003 - 8.32897i) q^{81} +(-1.29124 - 1.38497i) q^{82} -4.54450 q^{83} +(-1.82519 - 7.95532i) q^{84} +17.9661 q^{85} +(3.28866 + 3.52740i) q^{86} +(-10.1386 + 3.08685i) q^{87} +(-11.5904 - 14.3222i) q^{88} +4.03296i q^{89} +(16.9977 + 3.96753i) q^{90} -0.0316298i q^{91} +(0.517791 - 7.38259i) q^{92} +(1.42445 - 0.433698i) q^{93} +(-5.54169 + 5.16663i) q^{94} +7.75572 q^{95} +(7.71076 + 6.04518i) q^{96} -10.3574 q^{97} +(1.49827 - 1.39687i) q^{98} +(-16.2264 + 10.8903i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{4} - q^{6} - 6 q^{9}+O(q^{10}) \) 20 * q + 2 * q^4 - q^6 - 6 * q^9	\( 20 q + 2 q^{4} - q^{6} - 6 q^{9} + 6 q^{10} + 9 q^{12} + 32 q^{13} - 10 q^{16} - 5 q^{18} + 48 q^{21} + 16 q^{22} + 37 q^{24} - 48 q^{25} - 10 q^{28} - 44 q^{30} - 60 q^{33} + 30 q^{34} + 25 q^{36} + 20 q^{37} - 38 q^{40} - 18 q^{42} + 18 q^{45} - 8 q^{46} - 15 q^{48} - 96 q^{49} - 84 q^{52} + 59 q^{54} - 20 q^{57} + 14 q^{58} + 20 q^{60} - 36 q^{61} + 26 q^{64} - 52 q^{66} - 22 q^{69} + 136 q^{70} - 19 q^{72} + 48 q^{73} + 22 q^{76} - 99 q^{78} + 58 q^{81} + 2 q^{82} + 40 q^{84} + 48 q^{85} - 100 q^{88} + 11 q^{90} + 16 q^{93} - 20 q^{94} + 45 q^{96} + 48 q^{97}+O(q^{100}) \) 20 * q + 2 * q^4 - q^6 - 6 * q^9 + 6 * q^10 + 9 * q^12 + 32 * q^13 - 10 * q^16 - 5 * q^18 + 48 * q^21 + 16 * q^22 + 37 * q^24 - 48 * q^25 - 10 * q^28 - 44 * q^30 - 60 * q^33 + 30 * q^34 + 25 * q^36 + 20 * q^37 - 38 * q^40 - 18 * q^42 + 18 * q^45 - 8 * q^46 - 15 * q^48 - 96 * q^49 - 84 * q^52 + 59 * q^54 - 20 * q^57 + 14 * q^58 + 20 * q^60 - 36 * q^61 + 26 * q^64 - 52 * q^66 - 22 * q^69 + 136 * q^70 - 19 * q^72 + 48 * q^73 + 22 * q^76 - 99 * q^78 + 58 * q^81 + 2 * q^82 + 40 * q^84 + 48 * q^85 - 100 * q^88 + 11 * q^90 + 16 * q^93 - 20 * q^94 + 45 * q^96 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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