LMFDB - Embedded newform 74.2.c.c.47.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,2,Mod(47,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("74.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	74.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.590892974957$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.4406832.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 6x^{4} + 7x^{3} + 24x^{2} + 5x + 1 $ x^6 - x^5 + 6x^4 + 7x^3 + 24x^2 + 5x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			47.1
Root			$-0.105378 - 0.182520i$ of defining polynomial
Character	$\chi$	$=$	74.47
Dual form			74.2.c.c.63.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.26704 - 2.19457i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.97779 - 3.42563i) q^{5} +2.53407 q^{6} +(1.26704 + 2.19457i) q^{7} +1.00000 q^{8} +(-1.71076 + 2.96312i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.26704 - 2.19457i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.97779 - 3.42563i) q^{5} +2.53407 q^{6} +(1.26704 + 2.19457i) q^{7} +1.00000 q^{8} +(-1.71076 + 2.96312i) q^{9} +3.95558 q^{10} +2.42151 q^{11} +(-1.26704 + 2.19457i) q^{12} +(-1.00000 - 1.73205i) q^{13} -2.53407 q^{14} +(-5.01186 + 8.68080i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.03407 - 5.25516i) q^{17} +(-1.71076 - 2.96312i) q^{18} +(1.74483 + 3.02213i) q^{19} +(-1.97779 + 3.42563i) q^{20} +(3.21076 - 5.56119i) q^{21} +(-1.21076 + 2.09709i) q^{22} -0.955582 q^{23} +(-1.26704 - 2.19457i) q^{24} +(-5.32331 + 9.22025i) q^{25} +2.00000 q^{26} +1.06814 q^{27} +(1.26704 - 2.19457i) q^{28} +1.53407 q^{29} +(-5.01186 - 8.68080i) q^{30} +7.48965 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.06814 - 5.31418i) q^{33} +(3.03407 + 5.25516i) q^{34} +(5.01186 - 8.68080i) q^{35} +3.42151 q^{36} +(-0.0222090 - 6.08272i) q^{37} -3.48965 q^{38} +(-2.53407 + 4.38914i) q^{39} +(-1.97779 - 3.42563i) q^{40} +(4.24483 + 7.35225i) q^{41} +(3.21076 + 5.56119i) q^{42} +4.11256 q^{43} +(-1.21076 - 2.09709i) q^{44} +13.5341 q^{45} +(0.477791 - 0.827558i) q^{46} -11.4897 q^{47} +2.53407 q^{48} +(0.289244 - 0.500986i) q^{49} +(-5.32331 - 9.22025i) q^{50} -15.3771 q^{51} +(-1.00000 + 1.73205i) q^{52} +(-4.21076 + 7.29324i) q^{53} +(-0.534070 + 0.925037i) q^{54} +(-4.78924 - 8.29521i) q^{55} +(1.26704 + 2.19457i) q^{56} +(4.42151 - 7.65828i) q^{57} +(-0.767035 + 1.32854i) q^{58} +(-2.11256 + 3.65906i) q^{59} +10.0237 q^{60} +(-0.232965 - 0.403507i) q^{61} +(-3.74483 + 6.48623i) q^{62} -8.67035 q^{63} +1.00000 q^{64} +(-3.95558 + 6.85127i) q^{65} +6.13628 q^{66} +(3.21076 + 5.56119i) q^{67} -6.06814 q^{68} +(1.21076 + 2.09709i) q^{69} +(5.01186 + 8.68080i) q^{70} +(0.732965 + 1.26953i) q^{71} +(-1.71076 + 2.96312i) q^{72} -0.421512 q^{73} +(5.27890 + 3.02213i) q^{74} +26.9793 q^{75} +(1.74483 - 3.02213i) q^{76} +(3.06814 + 5.31418i) q^{77} +(-2.53407 - 4.38914i) q^{78} +(-1.32331 - 2.29205i) q^{79} +3.95558 q^{80} +(3.77890 + 6.54524i) q^{81} -8.48965 q^{82} +(1.68855 - 2.92465i) q^{83} -6.42151 q^{84} -24.0030 q^{85} +(-2.05628 + 3.56158i) q^{86} +(-1.94372 - 3.36662i) q^{87} +2.42151 q^{88} +(5.20041 - 9.00737i) q^{89} +(-6.76704 + 11.7208i) q^{90} +(2.53407 - 4.38914i) q^{91} +(0.477791 + 0.827558i) q^{92} +(-9.48965 - 16.4366i) q^{93} +(5.74483 - 9.95033i) q^{94} +(6.90180 - 11.9543i) q^{95} +(-1.26704 + 2.19457i) q^{96} +10.4897 q^{97} +(0.289244 + 0.500986i) q^{98} +(-4.14262 + 7.17522i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} - q^{5} + 6 q^{8} - 7 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 - q^5 + 6 * q^8 - 7 * q^9	$ 6 q - 3 q^{2} - 3 q^{4} - q^{5} + 6 q^{8} - 7 q^{9} + 2 q^{10} + 8 q^{11} - 6 q^{13} - 4 q^{15} - 3 q^{16} + 3 q^{17} - 7 q^{18} - 8 q^{19} - q^{20} + 16 q^{21} - 4 q^{22} + 16 q^{23} - 20 q^{25} + 12 q^{26} - 24 q^{27} - 6 q^{29} - 4 q^{30} + 8 q^{31} - 3 q^{32} + 12 q^{33} + 3 q^{34} + 4 q^{35} + 14 q^{36} - 11 q^{37} + 16 q^{38} - q^{40} + 7 q^{41} + 16 q^{42} + 16 q^{43} - 4 q^{44} + 66 q^{45} - 8 q^{46} - 32 q^{47} + 5 q^{49} - 20 q^{50} - 64 q^{51} - 6 q^{52} - 22 q^{53} + 12 q^{54} - 32 q^{55} + 20 q^{57} + 3 q^{58} - 4 q^{59} + 8 q^{60} - 9 q^{61} - 4 q^{62} + 24 q^{63} + 6 q^{64} - 2 q^{65} - 24 q^{66} + 16 q^{67} - 6 q^{68} + 4 q^{69} + 4 q^{70} + 12 q^{71} - 7 q^{72} + 4 q^{73} - 2 q^{74} + 88 q^{75} - 8 q^{76} - 12 q^{77} + 4 q^{79} + 2 q^{80} - 11 q^{81} - 14 q^{82} - 4 q^{83} - 32 q^{84} - 18 q^{85} - 8 q^{86} - 16 q^{87} + 8 q^{88} - 9 q^{89} - 33 q^{90} - 8 q^{92} - 20 q^{93} + 16 q^{94} + 36 q^{95} + 26 q^{97} + 5 q^{98} - 52 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 - q^5 + 6 * q^8 - 7 * q^9 + 2 * q^10 + 8 * q^11 - 6 * q^13 - 4 * q^15 - 3 * q^16 + 3 * q^17 - 7 * q^18 - 8 * q^19 - q^20 + 16 * q^21 - 4 * q^22 + 16 * q^23 - 20 * q^25 + 12 * q^26 - 24 * q^27 - 6 * q^29 - 4 * q^30 + 8 * q^31 - 3 * q^32 + 12 * q^33 + 3 * q^34 + 4 * q^35 + 14 * q^36 - 11 * q^37 + 16 * q^38 - q^40 + 7 * q^41 + 16 * q^42 + 16 * q^43 - 4 * q^44 + 66 * q^45 - 8 * q^46 - 32 * q^47 + 5 * q^49 - 20 * q^50 - 64 * q^51 - 6 * q^52 - 22 * q^53 + 12 * q^54 - 32 * q^55 + 20 * q^57 + 3 * q^58 - 4 * q^59 + 8 * q^60 - 9 * q^61 - 4 * q^62 + 24 * q^63 + 6 * q^64 - 2 * q^65 - 24 * q^66 + 16 * q^67 - 6 * q^68 + 4 * q^69 + 4 * q^70 + 12 * q^71 - 7 * q^72 + 4 * q^73 - 2 * q^74 + 88 * q^75 - 8 * q^76 - 12 * q^77 + 4 * q^79 + 2 * q^80 - 11 * q^81 - 14 * q^82 - 4 * q^83 - 32 * q^84 - 18 * q^85 - 8 * q^86 - 16 * q^87 + 8 * q^88 - 9 * q^89 - 33 * q^90 - 8 * q^92 - 20 * q^93 + 16 * q^94 + 36 * q^95 + 26 * q^97 + 5 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.26704	−	2.19457i	−0.731523	−	1.26704i	−0.956232	−	0.292609i	$-0.905477\pi$
$3$	−1.26704	−	2.19457i	−0.731523	−	1.26704i	0.224709	−	0.974426i	$-0.427857\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.97779	−	3.42563i	−0.884495	−	1.53199i	−0.846291	−	0.532720i	$-0.821170\pi$
$5$	−1.97779	−	3.42563i	−0.884495	−	1.53199i	−0.0382037	−	0.999270i	$-0.512164\pi$
$6$	2.53407			1.03453
$7$	1.26704	+	2.19457i	0.478894	+	0.829469i	0.999707	−	0.0242017i	$-0.00770440\pi$
$7$	1.26704	+	2.19457i	0.478894	+	0.829469i	−0.520813	+	0.853671i	$0.674371\pi$
$8$	1.00000			0.353553
$9$	−1.71076	+	2.96312i	−0.570252	+	0.987705i
$10$	3.95558			1.25086
$11$	2.42151			0.730113			0.365057	−	0.930985i	$-0.381050\pi$
$11$	2.42151			0.730113			0.365057	+	0.930985i	$0.381050\pi$
$12$	−1.26704	+	2.19457i	−0.365762	+	0.633518i
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	−2.53407			−0.677259
$15$	−5.01186	+	8.68080i	−1.29406	+	2.24137i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.03407	−	5.25516i	0.735870	−	1.27456i	−0.218470	−	0.975844i	$-0.570107\pi$
$17$	3.03407	−	5.25516i	0.735870	−	1.27456i	0.954341	−	0.298721i	$-0.0965599\pi$
$18$	−1.71076	−	2.96312i	−0.403229	−	0.698413i
$19$	1.74483	+	3.02213i	0.400291	+	0.693324i	0.993761	−	0.111532i	$-0.0355759\pi$
$19$	1.74483	+	3.02213i	0.400291	+	0.693324i	−0.593470	+	0.804856i	$0.702243\pi$
$20$	−1.97779	+	3.42563i	−0.442248	+	0.765995i
$21$	3.21076	−	5.56119i	0.700644	−	1.21355i
$22$	−1.21076	+	2.09709i	−0.258134	+	0.447101i
$23$	−0.955582			−0.199253			−0.0996263	−	0.995025i	$-0.531765\pi$
$23$	−0.955582			−0.199253			−0.0996263	+	0.995025i	$0.531765\pi$
$24$	−1.26704	−	2.19457i	−0.258632	−	0.447965i
$25$	−5.32331	+	9.22025i	−1.06466	+	1.84405i
$26$	2.00000			0.392232
$27$	1.06814			0.205564
$28$	1.26704	−	2.19457i	0.239447	−	0.414735i
$29$	1.53407			0.284870			0.142435	−	0.989804i	$-0.454507\pi$
$29$	1.53407			0.284870			0.142435	+	0.989804i	$0.454507\pi$
$30$	−5.01186	−	8.68080i	−0.915036	−	1.58489i
$31$	7.48965			1.34518			0.672591	−	0.740015i	$-0.265182\pi$
$31$	7.48965			1.34518			0.672591	+	0.740015i	$0.265182\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−3.06814	−	5.31418i	−0.534095	−	0.925079i
$34$	3.03407	+	5.25516i	0.520339	+	0.901253i
$35$	5.01186	−	8.68080i	0.847159	−	1.46732i
$36$	3.42151			0.570252
$37$	−0.0222090	−	6.08272i	−0.00365114	−	0.999993i
$37$	−0.0222090	−	6.08272i	−0.00365114	−	0.999993i
$38$	−3.48965			−0.566096
$39$	−2.53407	+	4.38914i	−0.405776	+	0.702825i
$40$	−1.97779	−	3.42563i	−0.312716	−	0.541640i
$41$	4.24483	+	7.35225i	0.662930	+	1.14823i	0.979842	+	0.199774i	$0.0640208\pi$
$41$	4.24483	+	7.35225i	0.662930	+	1.14823i	−0.316912	+	0.948455i	$0.602646\pi$
$42$	3.21076	+	5.56119i	0.495430	+	0.858111i
$43$	4.11256			0.627159			0.313580	−	0.949562i	$-0.398472\pi$
$43$	4.11256			0.627159			0.313580	+	0.949562i	$0.398472\pi$
$44$	−1.21076	−	2.09709i	−0.182528	−	0.316148i
$45$	13.5341			2.01754
$46$	0.477791	−	0.827558i	0.0704464	−	0.122017i
$47$	−11.4897			−1.67594			−0.837969	−	0.545718i	$-0.816257\pi$
$47$	−11.4897			−1.67594			−0.837969	+	0.545718i	$0.816257\pi$
$48$	2.53407			0.365762
$49$	0.289244	−	0.500986i	0.0413206	−	0.0715694i
$50$	−5.32331	−	9.22025i	−0.752830	−	1.30394i
$51$	−15.3771			−2.15322
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	−4.21076	+	7.29324i	−0.578392	+	1.00180i	0.417272	+	0.908782i	$0.362986\pi$
$53$	−4.21076	+	7.29324i	−0.578392	+	1.00180i	−0.995664	+	0.0930224i	$0.970347\pi$
$54$	−0.534070	+	0.925037i	−0.0726777	+	0.125882i
$55$	−4.78924	−	8.29521i	−0.645782	−	1.11853i
$56$	1.26704	+	2.19457i	0.169315	+	0.293262i
$57$	4.42151	−	7.65828i	0.585644	−	1.01436i
$58$	−0.767035	+	1.32854i	−0.100717	+	0.174446i
$59$	−2.11256	+	3.65906i	−0.275032	+	0.476369i	−0.970143	−	0.242533i	$-0.922022\pi$
$59$	−2.11256	+	3.65906i	−0.275032	+	0.476369i	0.695111	+	0.718902i	$0.255355\pi$
$60$	10.0237			1.29406
$61$	−0.232965	−	0.403507i	−0.0298281	−	0.0516638i	0.850726	−	0.525609i	$-0.176163\pi$
$61$	−0.232965	−	0.403507i	−0.0298281	−	0.0516638i	−0.880554	+	0.473946i	$0.842829\pi$
$62$	−3.74483	+	6.48623i	−0.475593	+	0.823752i
$63$	−8.67035			−1.09236
$64$	1.00000			0.125000
$65$	−3.95558	+	6.85127i	−0.490630	+	0.849795i
$66$	6.13628			0.755324
$67$	3.21076	+	5.56119i	0.392256	+	0.679408i	0.992747	−	0.120224i	$-0.0383613\pi$
$67$	3.21076	+	5.56119i	0.392256	+	0.679408i	−0.600491	+	0.799632i	$0.705028\pi$
$68$	−6.06814			−0.735870
$69$	1.21076	+	2.09709i	0.145758	+	0.252460i
$70$	5.01186	+	8.68080i	0.599032	+	1.03755i
$71$	0.732965	+	1.26953i	0.0869869	+	0.150666i	0.906236	−	0.422772i	$-0.138943\pi$
$71$	0.732965	+	1.26953i	0.0869869	+	0.150666i	−0.819249	+	0.573438i	$0.805609\pi$
$72$	−1.71076	+	2.96312i	−0.201615	+	0.349207i
$73$	−0.421512			−0.0493342			−0.0246671	−	0.999696i	$-0.507853\pi$
$73$	−0.421512			−0.0493342			−0.0246671	+	0.999696i	$0.507853\pi$
$74$	5.27890	+	3.02213i	0.613659	+	0.351315i
$75$	26.9793			3.11530
$76$	1.74483	−	3.02213i	0.200145	−	0.346662i
$77$	3.06814	+	5.31418i	0.349647	+	0.605606i
$78$	−2.53407	−	4.38914i	−0.286927	−	0.496972i
$79$	−1.32331	−	2.29205i	−0.148884	−	0.257876i	0.781931	−	0.623365i	$-0.214235\pi$
$79$	−1.32331	−	2.29205i	−0.148884	−	0.257876i	−0.930815	+	0.365490i	$0.880902\pi$
$80$	3.95558			0.442248
$81$	3.77890	+	6.54524i	0.419877	+	0.727249i
$82$	−8.48965			−0.937525
$83$	1.68855	−	2.92465i	0.185342	−	0.321022i	−0.758350	−	0.651848i	$-0.773994\pi$
$83$	1.68855	−	2.92465i	0.185342	−	0.321022i	0.943692	+	0.330826i	$0.107327\pi$
$84$	−6.42151			−0.700644
$85$	−24.0030			−2.60349
$86$	−2.05628	+	3.56158i	−0.221734	+	0.384055i
$87$	−1.94372	−	3.36662i	−0.208389	−	0.360940i
$88$	2.42151			0.258134
$89$	5.20041	−	9.00737i	0.551242	−	0.954779i	−0.446943	−	0.894562i	$-0.647487\pi$
$89$	5.20041	−	9.00737i	0.551242	−	0.954779i	0.998185	−	0.0602171i	$-0.0191793\pi$
$90$	−6.76704	+	11.7208i	−0.713308	+	1.23549i
$91$	2.53407	−	4.38914i	0.265643	−	0.460107i
$92$	0.477791	+	0.827558i	0.0498132	+	0.0862789i
$93$	−9.48965	−	16.4366i	−0.984031	−	1.70439i
$94$	5.74483	−	9.95033i	0.592534	−	1.02630i
$95$	6.90180	−	11.9543i	0.708110	−	1.22648i
$96$	−1.26704	+	2.19457i	−0.129316	+	0.223982i
$97$	10.4897			1.06506			0.532531	−	0.846410i	$-0.321241\pi$
$97$	10.4897			1.06506			0.532531	+	0.846410i	$0.321241\pi$
$98$	0.289244	+	0.500986i	0.0292181	+	0.0506072i
$99$	−4.14262	+	7.17522i	−0.416349	+	0.721137i
$100$	10.6466			1.06466
$101$	−5.11256			−0.508719			−0.254359	−	0.967110i	$-0.581865\pi$
$101$	−5.11256			−0.508719			−0.254359	+	0.967110i	$0.581865\pi$
$102$	7.68855	−	13.3170i	0.761280	−	1.31857i
$103$	0.397789			0.0391954			0.0195977	−	0.999808i	$-0.493761\pi$
$103$	0.397789			0.0391954			0.0195977	+	0.999808i	$0.493761\pi$
$104$	−1.00000	−	1.73205i	−0.0980581	−	0.169842i
$105$	−25.4008			−2.47887
$106$	−4.21076	−	7.29324i	−0.408985	−	0.708382i
$107$	4.05628	+	7.02568i	0.392135	+	0.679198i	0.992731	−	0.120355i	$-0.0384032\pi$
$107$	4.05628	+	7.02568i	0.392135	+	0.679198i	−0.600596	+	0.799553i	$0.705070\pi$
$108$	−0.534070	−	0.925037i	−0.0513909	−	0.0890117i
$109$	−5.72262	+	9.91186i	−0.548127	+	0.949384i	0.450276	+	0.892890i	$0.351326\pi$
$109$	−5.72262	+	9.91186i	−0.548127	+	0.949384i	−0.998403	+	0.0564947i	$0.982008\pi$
$110$	9.57849			0.913273
$111$	−13.3208	+	7.75576i	−1.26436	+	0.736144i
$112$	−2.53407			−0.239447
$113$	1.78924	−	3.09906i	0.168318	−	0.291535i	−0.769511	−	0.638634i	$-0.779500\pi$
$113$	1.78924	−	3.09906i	0.168318	−	0.291535i	0.937829	+	0.347099i	$0.112833\pi$
$114$	4.42151	+	7.65828i	0.414113	+	0.717264i
$115$	1.88994	+	3.27347i	0.176238	+	0.305253i
$116$	−0.767035	−	1.32854i	−0.0712174	−	0.123352i
$117$	6.84302			0.632638
$118$	−2.11256	−	3.65906i	−0.194477	−	0.336844i
$119$	15.3771			1.40962
$120$	−5.01186	+	8.68080i	−0.457518	+	0.792445i
$121$	−5.13628			−0.466935
$122$	0.465930			0.0421833
$123$	10.7567	−	18.6311i	0.969898	−	1.67991i
$124$	−3.74483	−	6.48623i	−0.336295	−	0.582481i
$125$	22.3357			1.99777
$126$	4.33518	−	7.50874i	0.386208	−	0.668932i
$127$	0.365233	−	0.632601i	0.0324091	−	0.0561343i	−0.849366	−	0.527804i	$-0.823015\pi$
$127$	0.365233	−	0.632601i	0.0324091	−	0.0561343i	0.881775	+	0.471670i	$0.156349\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−5.21076	−	9.02529i	−0.458781	−	0.794633i
$130$	−3.95558	−	6.85127i	−0.346927	−	0.600896i
$131$	−8.64413	+	14.9721i	−0.755241	+	1.30812i	0.190013	+	0.981782i	$0.439147\pi$
$131$	−8.64413	+	14.9721i	−0.755241	+	1.30812i	−0.945254	+	0.326334i	$0.894186\pi$
$132$	−3.06814	+	5.31418i	−0.267047	+	0.462540i
$133$	−4.42151	+	7.65828i	−0.383394	+	0.664057i
$134$	−6.42151			−0.554734
$135$	−2.11256	−	3.65906i	−0.181820	−	0.314922i
$136$	3.03407	−	5.25516i	0.260169	−	0.450627i
$137$	11.0474			0.943847			0.471923	−	0.881640i	$-0.343560\pi$
$137$	11.0474			0.943847			0.471923	+	0.881640i	$0.343560\pi$
$138$	−2.42151			−0.206133
$139$	6.11006	−	10.5829i	0.518248	−	0.897633i	−0.481527	−	0.876431i	$-0.659918\pi$
$139$	6.11006	−	10.5829i	0.518248	−	0.897633i	0.999775	−	0.0212012i	$-0.00674906\pi$
$140$	−10.0237			−0.847159
$141$	14.5578	+	25.2148i	1.22599	+	2.12347i
$142$	−1.46593			−0.123018
$143$	−2.42151	−	4.19418i	−0.202497	−	0.350735i
$144$	−1.71076	−	2.96312i	−0.142563	−	0.246926i
$145$	−3.03407	−	5.25516i	−0.251966	−	0.436418i
$146$	0.210756	−	0.365040i	0.0174423	−	0.0302109i
$147$	−1.46593			−0.120908
$148$	−5.25669	+	3.06059i	−0.432097	+	0.251579i
$149$	2.55477			0.209295			0.104647	−	0.994509i	$-0.466629\pi$
$149$	2.55477			0.209295			0.104647	+	0.994509i	$0.466629\pi$
$150$	−13.4897	+	23.3648i	−1.10143	+	1.90772i
$151$	3.43337	+	5.94678i	0.279404	+	0.483942i	0.971237	−	0.238116i	$-0.0765298\pi$
$151$	3.43337	+	5.94678i	0.279404	+	0.483942i	−0.691833	+	0.722058i	$0.743196\pi$
$152$	1.74483	+	3.02213i	0.141524	+	0.245127i
$153$	10.3811	+	17.9806i	0.839263	+	1.45365i
$154$	−6.13628			−0.494476
$155$	−14.8130	−	25.6568i	−1.18981	−	2.06080i
$156$	5.06814			0.405776
$157$	1.87959	−	3.25555i	0.150008	−	0.259821i	−0.781222	−	0.624253i	$-0.785403\pi$
$157$	1.87959	−	3.25555i	0.150008	−	0.259821i	0.931230	+	0.364432i	$0.118737\pi$
$158$	2.64663			0.210554
$159$	21.3407			1.69243
$160$	−1.97779	+	3.42563i	−0.156358	+	0.270820i
$161$	−1.21076	−	2.09709i	−0.0954209	−	0.165274i
$162$	−7.55779			−0.593796
$163$	−3.01186	+	5.21670i	−0.235907	+	0.408603i	−0.959536	−	0.281586i	$-0.909139\pi$
$163$	−3.01186	+	5.21670i	−0.235907	+	0.408603i	0.723629	+	0.690189i	$0.242473\pi$
$164$	4.24483	−	7.35225i	0.331465	−	0.574115i
$165$	−12.1363	+	21.0207i	−0.944808	+	1.63646i
$166$	1.68855	+	2.92465i	0.131057	+	0.226997i
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	0.999169	−	0.0407502i	$-0.0129748\pi$
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	−0.534875	+	0.844931i	$0.679641\pi$
$168$	3.21076	−	5.56119i	0.247715	−	0.429055i
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	12.0015	−	20.7872i	0.920474	−	1.59431i
$171$	−11.9399			−0.913066
$172$	−2.05628	−	3.56158i	−0.156790	−	0.271568i
$173$	−7.72262	+	13.3760i	−0.587140	+	1.01696i	0.407465	+	0.913221i	$0.366413\pi$
$173$	−7.72262	+	13.3760i	−0.587140	+	1.01696i	−0.994605	+	0.103735i	$0.966921\pi$
$174$	3.88744			0.294706
$175$	−26.9793			−2.03944
$176$	−1.21076	+	2.09709i	−0.0912642	+	0.158074i
$177$	10.7067			0.804768
$178$	5.20041	+	9.00737i	0.389787	+	0.675131i
$179$	−2.93186			−0.219137			−0.109569	−	0.993979i	$-0.534947\pi$
$179$	−2.93186			−0.219137			−0.109569	+	0.993979i	$0.534947\pi$
$180$	−6.76704	−	11.7208i	−0.504385	−	0.873620i
$181$	3.09035	+	5.35264i	0.229704	+	0.397859i	0.957720	−	0.287701i	$-0.0928909\pi$
$181$	3.09035	+	5.35264i	0.229704	+	0.397859i	−0.728016	+	0.685560i	$0.759558\pi$
$182$	2.53407	+	4.38914i	0.187838	+	0.325345i
$183$	−0.590349	+	1.02252i	−0.0436399	+	0.0755865i
$184$	−0.955582			−0.0704464
$185$	−20.7933	+	12.1064i	−1.52875	+	0.890083i
$186$	18.9793			1.39163
$187$	7.34704	−	12.7254i	0.537269	−	0.930576i
$188$	5.74483	+	9.95033i	0.418985	+	0.725702i
$189$	1.35337	+	2.34411i	0.0984433	+	0.170509i
$190$	6.90180	+	11.9543i	0.500709	+	0.867254i
$191$	−21.0030			−1.51973			−0.759863	−	0.650083i	$-0.774734\pi$
$191$	−21.0030			−1.51973			−0.759863	+	0.650083i	$0.774734\pi$
$192$	−1.26704	−	2.19457i	−0.0914404	−	0.158379i
$193$	−2.91116			−0.209550			−0.104775	−	0.994496i	$-0.533412\pi$
$193$	−2.91116			−0.209550			−0.104775	+	0.994496i	$0.533412\pi$
$194$	−5.24483	+	9.08431i	−0.376557	+	0.652215i
$195$	20.0474			1.43563
$196$	−0.578488			−0.0413206
$197$	3.76704	−	6.52470i	0.268390	−	0.464865i	−0.700056	−	0.714088i	$-0.746842\pi$
$197$	3.76704	−	6.52470i	0.268390	−	0.464865i	0.968446	+	0.249222i	$0.0801750\pi$
$198$	−4.14262	−	7.17522i	−0.294403	−	0.509921i
$199$	−18.3564			−1.30125			−0.650625	−	0.759399i	$-0.725493\pi$
$199$	−18.3564			−1.30125			−0.650625	+	0.759399i	$0.725493\pi$
$200$	−5.32331	+	9.22025i	−0.376415	+	0.651970i
$201$	8.13628	−	14.0925i	0.573889	−	0.994005i
$202$	2.55628	−	4.42761i	0.179859	−	0.311525i
$203$	1.94372	+	3.36662i	0.136422	+	0.236291i
$204$	7.68855	+	13.3170i	0.538306	+	0.932373i
$205$	16.7908	−	29.0824i	1.17272	−	2.03121i
$206$	−0.198895	+	0.344496i	−0.0138577	+	0.0240022i
$207$	1.63477	−	2.83150i	0.113624	−	0.196803i
$208$	2.00000			0.138675
$209$	4.22512	+	7.31812i	0.292257	+	0.506205i
$210$	12.7004	−	21.9978i	0.876411	−	1.51799i
$211$	8.33768			0.573989			0.286995	−	0.957932i	$-0.407344\pi$
$211$	8.33768			0.573989			0.286995	+	0.957932i	$0.407344\pi$
$212$	8.42151			0.578392
$213$	1.85738	−	3.21708i	0.127266	−	0.220431i
$214$	−8.11256			−0.554563
$215$	−8.13378	−	14.0881i	−0.554719	−	0.960802i
$216$	1.06814			0.0726777
$217$	9.48965	+	16.4366i	0.644200	+	1.11579i
$218$	−5.72262	−	9.91186i	−0.387585	−	0.671316i
$219$	0.534070	+	0.925037i	0.0360891	+	0.0625082i
$220$	−4.78924	+	8.29521i	−0.322891	+	0.559263i
$221$	−12.1363			−0.816375
$222$	−0.0562792	−	15.4140i	−0.00377721	−	1.03452i
$223$	−23.0919			−1.54635			−0.773173	−	0.634195i	$-0.781331\pi$
$223$	−23.0919			−1.54635			−0.773173	+	0.634195i	$0.781331\pi$
$224$	1.26704	−	2.19457i	0.0846573	−	0.146631i
$225$	−18.2138	−	31.5472i	−1.21425	−	2.10315i
$226$	1.78924	+	3.09906i	0.119019	+	0.206147i
$227$	−9.32331	−	16.1485i	−0.618810	−	1.07181i	−0.989703	−	0.143135i	$-0.954282\pi$
$227$	−9.32331	−	16.1485i	−0.618810	−	1.07181i	0.370893	−	0.928676i	$-0.379052\pi$
$228$	−8.84302			−0.585644
$229$	−10.2567	−	17.7651i	−0.677781	−	1.17395i	−0.975648	−	0.219344i	$-0.929608\pi$
$229$	−10.2567	−	17.7651i	−0.677781	−	1.17395i	0.297867	−	0.954607i	$-0.403725\pi$
$230$	−3.77988			−0.249238
$231$	7.77488	−	13.4665i	0.511550	−	0.886030i
$232$	1.53407			0.100717
$233$	18.8223			1.23309			0.616546	−	0.787319i	$-0.288531\pi$
$233$	18.8223			1.23309			0.616546	+	0.787319i	$0.288531\pi$
$234$	−3.42151	+	5.92623i	−0.223671	+	0.387410i
$235$	22.7241	+	39.3593i	1.48236	+	2.56752i
$236$	4.22512			0.275032
$237$	−3.35337	+	5.80821i	−0.217825	+	0.377284i
$238$	−7.68855	+	13.3170i	−0.498374	+	0.863210i
$239$	10.7567	−	18.6311i	0.695792	−	1.20515i	−0.274121	−	0.961695i	$-0.588387\pi$
$239$	10.7567	−	18.6311i	0.695792	−	1.20515i	0.969913	−	0.243452i	$-0.0782799\pi$
$240$	−5.01186	−	8.68080i	−0.323514	−	0.560343i
$241$	−8.85738	−	15.3414i	−0.570554	−	0.988229i	−0.996509	−	0.0834846i	$-0.973395\pi$
$241$	−8.85738	−	15.3414i	−0.570554	−	0.988229i	0.425955	−	0.904744i	$-0.359938\pi$
$242$	2.56814	−	4.44815i	0.165086	−	0.285938i
$243$	11.1782	−	19.3612i	0.717082	−	1.24202i
$244$	−0.232965	+	0.403507i	−0.0149140	+	0.0258319i
$245$	−2.28826			−0.146191
$246$	10.7567	+	18.6311i	0.685821	+	1.18788i
$247$	3.48965	−	6.04425i	0.222041	−	0.384587i
$248$	7.48965			0.475593
$249$	−8.55779			−0.542328
$250$	−11.1679	+	19.3433i	−0.706317	+	1.22338i
$251$	−5.79861			−0.366005			−0.183002	−	0.983112i	$-0.558582\pi$
$251$	−5.79861			−0.366005			−0.183002	+	0.983112i	$0.558582\pi$
$252$	4.33518	+	7.50874i	0.273090	+	0.473006i
$253$	−2.31395			−0.145477
$254$	0.365233	+	0.632601i	0.0229167	+	0.0396929i
$255$	30.4127	+	52.6763i	1.90452	+	3.29872i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−14.8470	+	25.7158i	−0.926133	+	1.60411i	−0.136403	+	0.990653i	$0.543554\pi$
$257$	−14.8470	+	25.7158i	−0.926133	+	1.60411i	−0.789729	+	0.613456i	$0.789779\pi$
$258$	10.4215			0.648815
$259$	13.3208	−	7.75576i	0.827715	−	0.481920i
$260$	7.91116			0.490630
$261$	−2.62442	+	4.54563i	−0.162447	+	0.281367i
$262$	−8.64413	−	14.9721i	−0.534036	−	0.924978i
$263$	9.37709	+	16.2416i	0.578216	+	1.00150i	0.995684	+	0.0928083i	$0.0295844\pi$
$263$	9.37709	+	16.2416i	0.578216	+	1.00150i	−0.417468	+	0.908692i	$0.637082\pi$
$264$	−3.06814	−	5.31418i	−0.188831	−	0.327065i
$265$	33.3120			2.04634
$266$	−4.42151	−	7.65828i	−0.271100	−	0.469559i
$267$	−26.3564			−1.61299
$268$	3.21076	−	5.56119i	0.196128	−	0.339704i
$269$	23.1156			1.40938			0.704691	−	0.709514i	$-0.251086\pi$
$269$	23.1156			1.40938			0.704691	+	0.709514i	$0.251086\pi$
$270$	4.22512			0.257132
$271$	−11.3470	+	19.6536i	−0.689283	+	1.19387i	0.282787	+	0.959183i	$0.408741\pi$
$271$	−11.3470	+	19.6536i	−0.689283	+	1.19387i	−0.972070	+	0.234691i	$0.924592\pi$
$272$	3.03407	+	5.25516i	0.183968	+	0.318641i
$273$	−12.8430			−0.777295
$274$	−5.52372	+	9.56737i	−0.333700	+	0.577986i
$275$	−12.8905	+	22.3269i	−0.777324	+	1.34637i
$276$	1.21076	−	2.09709i	0.0728789	−	0.126230i
$277$	−9.35488	−	16.2031i	−0.562081	−	0.973552i	−0.997315	−	0.0732348i	$-0.976668\pi$
$277$	−9.35488	−	16.2031i	−0.562081	−	0.973552i	0.435234	−	0.900317i	$-0.356666\pi$
$278$	6.11006	+	10.5829i	0.366457	+	0.634722i
$279$	−12.8130	+	22.1927i	−0.767092	+	1.32864i
$280$	5.01186	−	8.68080i	0.299516	−	0.518777i
$281$	13.5681	−	23.5007i	0.809407	−	1.40193i	−0.103868	−	0.994591i	$-0.533122\pi$
$281$	13.5681	−	23.5007i	0.809407	−	1.40193i	0.913275	−	0.407344i	$-0.133545\pi$
$282$	−29.1156			−1.73381
$283$	−0.454069	−	0.786470i	−0.0269916	−	0.0467508i	0.852214	−	0.523193i	$-0.175259\pi$
$283$	−0.454069	−	0.786470i	−0.0269916	−	0.0467508i	−0.879206	+	0.476442i	$0.841926\pi$
$284$	0.732965	−	1.26953i	0.0434935	−	0.0753329i
$285$	−34.9793			−2.07200
$286$	4.84302			0.286374
$287$	−10.7567	+	18.6311i	−0.634947	+	1.09976i
$288$	3.42151			0.201615
$289$	−9.91116	−	17.1666i	−0.583010	−	1.00980i
$290$	6.06814			0.356333
$291$	−13.2908	−	23.0203i	−0.779118	−	1.34947i
$292$	0.210756	+	0.365040i	0.0123336	+	0.0213623i
$293$	−8.23296	−	14.2599i	−0.480975	−	0.833073i	0.518787	−	0.854904i	$-0.326384\pi$
$293$	−8.23296	−	14.2599i	−0.480975	−	0.833073i	−0.999762	+	0.0218306i	$0.993051\pi$
$294$	0.732965	−	1.26953i	0.0427474	−	0.0740406i
$295$	16.7128			0.973057
$296$	−0.0222090	−	6.08272i	−0.00129087	−	0.353551i
$297$	2.58651			0.150085
$298$	−1.27738	+	2.21249i	−0.0739968	+	0.128166i
$299$	0.955582	+	1.65512i	0.0552627	+	0.0957179i
$300$	−13.4897	−	23.3648i	−0.778825	−	1.34897i
$301$	5.21076	+	9.02529i	0.300343	+	0.520209i
$302$	−6.86675			−0.395137
$303$	6.47779	+	11.2199i	0.372139	+	0.644564i
$304$	−3.48965			−0.200145
$305$	−0.921512	+	1.59611i	−0.0527656	+	0.0913927i
$306$	−20.7622			−1.18690
$307$	−3.04442			−0.173754			−0.0868771	−	0.996219i	$-0.527689\pi$
$307$	−3.04442			−0.173754			−0.0868771	+	0.996219i	$0.527689\pi$
$308$	3.06814	−	5.31418i	0.174824	−	0.302803i
$309$	−0.504013	−	0.872976i	−0.0286723	−	0.0496619i
$310$	29.6259			1.68264
$311$	−0.222617	+	0.385584i	−0.0126235	+	0.0218645i	−0.872268	−	0.489028i	$-0.837352\pi$
$311$	−0.222617	+	0.385584i	−0.0126235	+	0.0218645i	0.859645	+	0.510892i	$0.170685\pi$
$312$	−2.53407	+	4.38914i	−0.143463	+	0.248486i
$313$	−13.6663	+	23.6708i	−0.772467	+	1.33795i	0.163740	+	0.986504i	$0.447644\pi$
$313$	−13.6663	+	23.6708i	−0.772467	+	1.33795i	−0.936207	+	0.351449i	$0.885689\pi$
$314$	1.87959	+	3.25555i	0.106072	+	0.183721i
$315$	17.1481	+	29.7015i	0.966188	+	1.67349i
$316$	−1.32331	+	2.29205i	−0.0744422	+	0.128938i
$317$	−10.7370	+	18.5970i	−0.603049	+	1.04451i	0.389308	+	0.921108i	$0.372714\pi$
$317$	−10.7370	+	18.5970i	−0.603049	+	1.04451i	−0.992357	+	0.123403i	$0.960619\pi$
$318$	−10.6704	+	18.4816i	−0.598364	+	1.03640i
$319$	3.71477			0.207987
$320$	−1.97779	−	3.42563i	−0.110562	−	0.191499i
$321$	10.2789	−	17.8036i	0.573712	−	0.993698i
$322$	2.42151			0.134946
$323$	21.1757			1.17825
$324$	3.77890	−	6.54524i	0.209939	−	0.363624i
$325$	21.2933			1.18114
$326$	−3.01186	−	5.21670i	−0.166812	−	0.288926i
$327$	29.0030			1.60387
$328$	4.24483	+	7.35225i	0.234381	+	0.405960i
$329$	−14.5578	−	25.2148i	−0.802597	−	1.39014i
$330$	−12.1363	−	21.0207i	−0.668080	−	1.15715i
$331$	4.55779	−	7.89433i	0.250519	−	0.433912i	−0.713150	−	0.701012i	$-0.752732\pi$
$331$	4.55779	−	7.89433i	0.250519	−	0.433912i	0.963669	+	0.267100i	$0.0860654\pi$
$332$	−3.37709			−0.185342
$333$	18.0618	+	10.3402i	0.989781	+	0.566642i
$334$	−12.0000			−0.656611
$335$	12.7004	−	21.9978i	0.693897	−	1.20187i
$336$	3.21076	+	5.56119i	0.175161	+	0.303388i
$337$	13.2004	+	22.8638i	0.719072	+	1.24547i	0.961368	+	0.275267i	$0.0887662\pi$
$337$	13.2004	+	22.8638i	0.719072	+	1.24547i	−0.242296	+	0.970202i	$0.577900\pi$
$338$	4.50000	+	7.79423i	0.244768	+	0.423950i
$339$	−9.06814			−0.492514
$340$	12.0015	+	20.7872i	0.650873	+	1.12735i
$341$	18.1363			0.982135
$342$	5.96994	−	10.3402i	0.322818	−	0.559136i
$343$	19.2044			1.03694
$344$	4.11256			0.221734
$345$	4.78924	−	8.29521i	0.257844	−	0.446599i
$346$	−7.72262	−	13.3760i	−0.415170	−	0.719096i
$347$	−31.8748			−1.71113			−0.855564	−	0.517698i	$-0.826789\pi$
$347$	−31.8748			−1.71113			−0.855564	+	0.517698i	$0.826789\pi$
$348$	−1.94372	+	3.36662i	−0.104194	+	0.180470i
$349$	11.8208	−	20.4743i	0.632754	−	1.09596i	−0.354233	−	0.935157i	$-0.615258\pi$
$349$	11.8208	−	20.4743i	0.632754	−	1.09596i	0.986986	−	0.160804i	$-0.0514088\pi$
$350$	13.4897	−	23.3648i	0.721052	−	1.24890i
$351$	−1.06814	−	1.85007i	−0.0570131	−	0.0987496i
$352$	−1.21076	−	2.09709i	−0.0645335	−	0.111775i
$353$	−11.7789	+	20.4016i	−0.626927	+	1.08587i	0.361237	+	0.932474i	$0.382354\pi$
$353$	−11.7789	+	20.4016i	−0.626927	+	1.08587i	−0.988165	+	0.153396i	$0.950979\pi$
$354$	−5.35337	+	9.27231i	−0.284528	+	0.492818i
$355$	2.89930	−	5.02174i	0.153879	−	0.266526i
$356$	−10.4008			−0.551242
$357$	−19.4833	−	33.7461i	−1.03117	−	1.78603i
$358$	1.46593	−	2.53906i	0.0774768	−	0.134194i
$359$	−5.86372			−0.309475			−0.154738	−	0.987956i	$-0.549453\pi$
$359$	−5.86372			−0.309475			−0.154738	+	0.987956i	$0.549453\pi$
$360$	13.5341			0.713308
$361$	3.41116	−	5.90831i	0.179535	−	0.310964i
$362$	−6.18070			−0.324850
$363$	6.50785	+	11.2719i	0.341573	+	0.591623i
$364$	−5.06814			−0.265643
$365$	0.833662	+	1.44395i	0.0436359	+	0.0755795i
$366$	−0.590349	−	1.02252i	−0.0308581	−	0.0534477i
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	0.913493	−	0.406855i	$-0.133375\pi$
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	−0.809093	+	0.587680i	$0.800041\pi$
$368$	0.477791	−	0.827558i	0.0249066	−	0.0431395i
$369$	−29.0474			−1.51215
$370$	−0.0878496	−	24.0607i	−0.00456708	−	1.25086i
$371$	−21.3407			−1.10795
$372$	−9.48965	+	16.4366i	−0.492016	+	0.852196i
$373$	16.1822	+	28.0284i	0.837883	+	1.45126i	0.891661	+	0.452703i	$0.149540\pi$
$373$	16.1822	+	28.0284i	0.837883	+	1.45126i	−0.0537780	+	0.998553i	$0.517126\pi$
$374$	7.34704	+	12.7254i	0.379906	+	0.658017i
$375$	−28.3001	−	49.0172i	−1.46141	−	2.53124i
$376$	−11.4897			−0.592534
$377$	−1.53407	−	2.65709i	−0.0790086	−	0.136847i
$378$	−2.70674			−0.139220
$379$	−15.4571	+	26.7725i	−0.793978	+	1.37521i	0.129509	+	0.991578i	$0.458660\pi$
$379$	−15.4571	+	26.7725i	−0.793978	+	1.37521i	−0.923486	+	0.383631i	$0.874673\pi$
$380$	−13.8036			−0.708110
$381$	−1.85105			−0.0948322
$382$	10.5015	−	18.1892i	0.537304	−	0.930638i
$383$	−15.5997	−	27.0195i	−0.797108	−	1.38063i	−0.921492	−	0.388397i	$-0.873029\pi$
$383$	−15.5997	−	27.0195i	−0.797108	−	1.38063i	0.124384	−	0.992234i	$-0.460305\pi$
$384$	2.53407			0.129316
$385$	12.1363	−	21.0207i	0.618522	−	1.07131i
$386$	1.45558	−	2.52114i	0.0740872	−	0.128323i
$387$	−7.03558	+	12.1860i	−0.357639	+	0.619449i
$388$	−5.24483	−	9.08431i	−0.266266	−	0.461186i
$389$	−2.62442	−	4.54563i	−0.133063	−	0.230472i	0.791793	−	0.610790i	$-0.209148\pi$
$389$	−2.62442	−	4.54563i	−0.133063	−	0.230472i	−0.924856	+	0.380318i	$0.875815\pi$
$390$	−10.0237	+	17.3616i	−0.507571	+	0.879139i
$391$	−2.89930	+	5.02174i	−0.146624	+	0.253960i
$392$	0.289244	−	0.500986i	0.0146090	−	0.0253036i
$393$	43.8097			2.20990
$394$	3.76704	+	6.52470i	0.189780	+	0.328709i
$395$	−5.23448	+	9.06638i	−0.263375	+	0.456179i
$396$	8.28523			0.416349
$397$	17.4740			0.876993			0.438496	−	0.898733i	$-0.355511\pi$
$397$	17.4740			0.876993			0.438496	+	0.898733i	$0.355511\pi$
$398$	9.17820	−	15.8971i	0.460062	−	0.796850i
$399$	22.4088			1.12185
$400$	−5.32331	−	9.22025i	−0.266166	−	0.461013i
$401$	2.28523			0.114119			0.0570595	−	0.998371i	$-0.481828\pi$
$401$	2.28523			0.114119			0.0570595	+	0.998371i	$0.481828\pi$
$402$	8.13628	+	14.0925i	0.405801	+	0.702868i
$403$	−7.48965	−	12.9725i	−0.373086	−	0.646204i
$404$	2.55628	+	4.42761i	0.127180	+	0.220282i
$405$	14.9477	−	25.8902i	0.742759	−	1.28650i
$406$	−3.88744			−0.192930
$407$	−0.0537794	−	14.7294i	−0.00266575	−	0.730108i
$408$	−15.3771			−0.761280
$409$	−13.1560	+	22.7868i	−0.650522	+	1.12674i	0.332475	+	0.943112i	$0.392116\pi$
$409$	−13.1560	+	22.7868i	−0.650522	+	1.12674i	−0.982996	+	0.183625i	$0.941217\pi$
$410$	16.7908	+	29.0824i	0.829236	+	1.43628i
$411$	−13.9975	−	24.2444i	−0.690446	−	1.19589i
$412$	−0.198895	−	0.344496i	−0.00979884	−	0.0169721i
$413$	−10.7067			−0.526844
$414$	1.63477	+	2.83150i	0.0803444	+	0.139161i
$415$	−13.3584			−0.655737
$416$	−1.00000	+	1.73205i	−0.0490290	+	0.0849208i
$417$	−30.9666			−1.51644
$418$	−8.45023			−0.413314
$419$	−13.1244	+	22.7322i	−0.641170	+	1.11054i	0.344002	+	0.938969i	$0.388217\pi$
$419$	−13.1244	+	22.7322i	−0.641170	+	1.11054i	−0.985172	+	0.171570i	$0.945116\pi$
$420$	12.7004	+	21.9978i	0.619716	+	1.07338i
$421$	12.9763			0.632425			0.316213	−	0.948688i	$-0.397589\pi$
$421$	12.9763			0.632425			0.316213	+	0.948688i	$0.397589\pi$
$422$	−4.16884	+	7.22064i	−0.202936	+	0.351495i
$423$	19.6560	−	34.0452i	0.955707	−	1.65533i
$424$	−4.21076	+	7.29324i	−0.204492	+	0.354191i
$425$	32.3026	+	55.9498i	1.56691	+	2.71396i
$426$	1.85738	+	3.21708i	0.0899906	+	0.155868i
$427$	0.590349	−	1.02252i	0.0285690	−	0.0494830i
$428$	4.05628	−	7.02568i	0.196068	−	0.339599i
$429$	−6.13628	+	10.6284i	−0.296262	+	0.513142i
$430$	16.2676			0.784491
$431$	6.25517	+	10.8343i	0.301301	+	0.521869i	0.976431	−	0.215830i	$-0.0692457\pi$
$431$	6.25517	+	10.8343i	0.301301	+	0.521869i	−0.675130	+	0.737699i	$0.735912\pi$
$432$	−0.534070	+	0.925037i	−0.0256955	+	0.0445058i
$433$	2.03942			0.0980082			0.0490041	−	0.998799i	$-0.484395\pi$
$433$	2.03942			0.0980082			0.0490041	+	0.998799i	$0.484395\pi$
$434$	−18.9793			−0.911036
$435$	−7.68855	+	13.3170i	−0.368638	+	0.638499i
$436$	11.4452			0.548127
$437$	−1.66732	−	2.88789i	−0.0797589	−	0.138147i
$438$	−1.06814			−0.0510377
$439$	14.4452	+	25.0199i	0.689433	+	1.19413i	0.972021	+	0.234892i	$0.0754737\pi$
$439$	14.4452	+	25.0199i	0.689433	+	1.19413i	−0.282588	+	0.959241i	$0.591193\pi$
$440$	−4.78924	−	8.29521i	−0.228318	−	0.395459i
$441$	0.989652	+	1.71413i	0.0471263	+	0.0816251i
$442$	6.06814	−	10.5103i	0.288632	−	0.499925i
$443$	−2.52907			−0.120160			−0.0600799	−	0.998194i	$-0.519136\pi$
$443$	−2.52907			−0.120160			−0.0600799	+	0.998194i	$0.519136\pi$
$444$	13.3771	+	7.65828i	0.634849	+	0.363446i
$445$	−41.1413			−1.95028
$446$	11.5459	−	19.9981i	0.546716	−	0.946939i
$447$	−3.23698	−	5.60661i	−0.153104	−	0.265184i
$448$	1.26704	+	2.19457i	0.0598618	+	0.103684i
$449$	−2.43587	−	4.21906i	−0.114956	−	0.199110i	0.802806	−	0.596240i	$-0.203339\pi$
$449$	−2.43587	−	4.21906i	−0.114956	−	0.199110i	−0.917762	+	0.397131i	$0.870006\pi$
$450$	36.4276			1.71721
$451$	10.2789	+	17.8036i	0.484014	+	0.838337i
$452$	−3.57849			−0.168318
$453$	8.70041	−	15.0695i	0.408781	−	0.708029i
$454$	18.6466			0.875130
$455$	−20.0474			−0.939839
$456$	4.42151	−	7.65828i	0.207056	−	0.358632i
$457$	−3.52372	−	6.10327i	−0.164833	−	0.285499i	0.771763	−	0.635910i	$-0.219375\pi$
$457$	−3.52372	−	6.10327i	−0.164833	−	0.285499i	−0.936596	+	0.350411i	$0.886042\pi$
$458$	20.5134			0.958527
$459$	3.24081	−	5.61325i	0.151268	−	0.262004i
$460$	1.88994	−	3.27347i	0.0881190	−	0.152627i
$461$	0.0681404	−	0.118023i	0.00317361	−	0.00549686i	−0.864434	−	0.502746i	$-0.832323\pi$
$461$	0.0681404	−	0.118023i	0.00317361	−	0.00549686i	0.867608	+	0.497249i	$0.165656\pi$
$462$	7.77488	+	13.4665i	0.361720	+	0.626518i
$463$	−8.11006	−	14.0470i	−0.376906	−	0.652821i	0.613704	−	0.789536i	$-0.289679\pi$
$463$	−8.11006	−	14.0470i	−0.376906	−	0.652821i	−0.990610	+	0.136715i	$0.956345\pi$
$464$	−0.767035	+	1.32854i	−0.0356087	+	0.0616761i
$465$	−37.5371	+	65.0162i	−1.74074	+	3.01505i
$466$	−9.41116	+	16.3006i	−0.435964	+	0.755111i
$467$	38.1837			1.76693			0.883466	−	0.468495i	$-0.155204\pi$
$467$	38.1837			1.76693			0.883466	+	0.468495i	$0.155204\pi$
$468$	−3.42151	−	5.92623i	−0.158159	−	0.273940i
$469$	−8.13628	+	14.0925i	−0.375699	+	0.650729i
$470$	−45.4483			−2.09637
$471$	−9.52604			−0.438937
$472$	−2.11256	+	3.65906i	−0.0972384	+	0.168422i
$473$	9.95861			0.457897
$474$	−3.35337	−	5.80821i	−0.154025	−	0.266780i
$475$	−37.1530			−1.70470
$476$	−7.68855	−	13.3170i	−0.352404	−	0.610382i
$477$	−14.4072	−	24.9539i	−0.659658	−	1.14256i
$478$	10.7567	+	18.6311i	0.491999	+	0.852168i
$479$	14.2488	−	24.6797i	0.651046	−	1.12764i	−0.331823	−	0.943342i	$-0.607664\pi$
$479$	14.2488	−	24.6797i	0.651046	−	1.12764i	0.982869	−	0.184303i	$-0.0590029\pi$
$480$	10.0237			0.457518
$481$	−10.5134	+	6.12119i	−0.479369	+	0.279102i
$482$	17.7148			0.806886
$483$	−3.06814	+	5.31418i	−0.139605	+	0.241803i
$484$	2.56814	+	4.44815i	0.116734	+	0.202189i
$485$	−20.7463	−	35.9337i	−0.942043	−	1.63167i
$486$	11.1782	+	19.3612i	0.507053	+	0.878242i
$487$	28.1126			1.27390			0.636951	−	0.770904i	$-0.280195\pi$
$487$	28.1126			1.27390			0.636951	+	0.770904i	$0.280195\pi$
$488$	−0.232965	−	0.403507i	−0.0105458	−	0.0182659i
$489$	15.2645			0.690286
$490$	1.14413	−	1.98169i	0.0516865	−	0.0895236i
$491$	−2.42151			−0.109281			−0.0546406	−	0.998506i	$-0.517401\pi$
$491$	−2.42151			−0.109281			−0.0546406	+	0.998506i	$0.517401\pi$
$492$	−21.5134			−0.969898
$493$	4.65448	−	8.06179i	0.209627	−	0.363085i
$494$	3.48965	+	6.04425i	0.157007	+	0.271944i
$495$	32.7729			1.47303
$496$	−3.74483	+	6.48623i	−0.168148	+	0.291240i
$497$	−1.85738	+	3.21708i	−0.0833151	+	0.144306i
$498$	4.27890	−	7.41127i	0.191742	−	0.332107i
$499$	1.23448	+	2.13818i	0.0552628	+	0.0957180i	0.892333	−	0.451377i	$-0.149067\pi$
$499$	1.23448	+	2.13818i	0.0552628	+	0.0957180i	−0.837071	+	0.547095i	$0.815734\pi$
$500$	−11.1679	−	19.3433i	−0.499441	−	0.865058i
$501$	15.2044	−	26.3348i	0.679283	−	1.17655i
$502$	2.89930	−	5.02174i	0.129402	−	0.224131i
$503$	−18.7004	+	32.3901i	−0.833810	+	1.44420i	0.0611857	+	0.998126i	$0.480512\pi$
$503$	−18.7004	+	32.3901i	−0.833810	+	1.44420i	−0.894996	+	0.446075i	$0.852822\pi$
$504$	−8.67035			−0.386208
$505$	10.1116	+	17.5138i	0.449959	+	0.779352i
$506$	1.15698	−	2.00394i	0.0514339	−	0.0890861i
$507$	−22.8066			−1.01288
$508$	−0.730465			−0.0324091
$509$	4.97779	−	8.62179i	0.220637	−	0.382154i	−0.734365	−	0.678755i	$-0.762520\pi$
$509$	4.97779	−	8.62179i	0.220637	−	0.382154i	0.955001	+	0.296601i	$0.0958532\pi$
$510$	−60.8254			−2.69339
$511$	−0.534070	−	0.925037i	−0.0236259	−	0.0409212i
$512$	1.00000			0.0441942
$513$	1.86372	+	3.22806i	0.0822852	+	0.142522i
$514$	−14.8470	−	25.7158i	−0.654875	−	1.13428i
$515$	−0.786744	−	1.36268i	−0.0346681	−	0.0600469i
$516$	−5.21076	+	9.02529i	−0.229391	+	0.397316i
$517$	−27.8223			−1.22362
$518$	0.0562792	+	15.4140i	0.00247277	+	0.677254i
$519$	39.1393			1.71802
$520$	−3.95558	+	6.85127i	−0.173464	+	0.300448i
$521$	−5.36773	−	9.29719i	−0.235165	−	0.407317i	0.724156	−	0.689636i	$-0.242230\pi$
$521$	−5.36773	−	9.29719i	−0.235165	−	0.407317i	−0.959321	+	0.282319i	$0.908896\pi$
$522$	−2.62442	−	4.54563i	−0.114868	−	0.198957i
$523$	−9.60471	−	16.6358i	−0.419985	−	0.727435i	0.575953	−	0.817483i	$-0.304631\pi$
$523$	−9.60471	−	16.6358i	−0.419985	−	0.727435i	−0.995937	+	0.0900482i	$0.971298\pi$
$524$	17.2883			0.755241
$525$	34.1837	+	59.2079i	1.49190	+	2.58405i
$526$	−18.7542			−0.817721
$527$	22.7241	−	39.3593i	0.989879	−	1.71452i
$528$	6.13628			0.267047
$529$	−22.0869			−0.960298
$530$	−16.6560	+	28.8490i	−0.723490	+	1.25312i
$531$	−7.22814	−	12.5195i	−0.313675	−	0.543301i
$532$	8.84302			0.383394
$533$	8.48965	−	14.7045i	0.367728	−	0.636923i
$534$	13.1782	−	22.8253i	0.570276	−	0.987748i
$535$	16.0449	−	27.7907i	0.693683	−	1.20149i
$536$	3.21076	+	5.56119i	0.138684	+	0.240207i
$537$	3.71477	+	6.43417i	0.160304	+	0.277655i
$538$	−11.5578	+	20.0187i	−0.498292	+	0.863067i
$539$	0.700408	−	1.21314i	0.0301687	−	0.0522537i
$540$	−2.11256	+	3.65906i	−0.0909100	+	0.157461i
$541$	−29.6704			−1.27563			−0.637814	−	0.770190i	$-0.720161\pi$
$541$	−29.6704			−1.27563			−0.637814	+	0.770190i	$0.720161\pi$
$542$	−11.3470	−	19.6536i	−0.487397	−	0.844196i
$543$	7.83116	−	13.5640i	0.336067	−	0.582086i
$544$	−6.06814			−0.260169
$545$	45.2726			1.93926
$546$	6.42151	−	11.1224i	0.274815	−	0.475994i
$547$	−4.78291			−0.204502			−0.102251	−	0.994759i	$-0.532605\pi$
$547$	−4.78291			−0.204502			−0.102251	+	0.994759i	$0.532605\pi$
$548$	−5.52372	−	9.56737i	−0.235962	−	0.408698i
$549$	1.59418			0.0680381
$550$	−12.8905	−	22.3269i	−0.549651	−	0.952024i
$551$	2.67669	+	4.63616i	0.114031	+	0.197507i
$552$	1.21076	+	2.09709i	0.0515332	+	0.0892581i
$553$	3.35337	−	5.80821i	0.142600	−	0.246990i
$554$	18.7098			0.794902
$555$	52.9142	+	30.2930i	2.24608	+	1.28586i
$556$	−12.2201			−0.518248
$557$	10.0222	−	17.3590i	0.424655	−	0.735523i	−0.571733	−	0.820439i	$-0.693729\pi$
$557$	10.0222	−	17.3590i	0.424655	−	0.735523i	0.996388	+	0.0849160i	$0.0270622\pi$
$558$	−12.8130	−	22.1927i	−0.542416	−	0.939492i
$559$	−4.11256	−	7.12316i	−0.173943	−	0.301278i
$560$	5.01186	+	8.68080i	0.211790	+	0.366831i
$561$	−37.2358			−1.57210
$562$	13.5681	+	23.5007i	0.572337	+	0.991318i
$563$	−24.4452			−1.03024			−0.515122	−	0.857117i	$-0.672253\pi$
$563$	−24.4452			−1.03024			−0.515122	+	0.857117i	$0.672253\pi$
$564$	14.5578	−	25.2148i	0.612994	−	1.06174i
$565$	−14.1550			−0.595505
$566$	0.908137			0.0381719
$567$	−9.57599	+	16.5861i	−0.402154	+	0.696551i
$568$	0.732965	+	1.26953i	0.0307545	+	0.0532684i
$569$	6.09686			0.255594			0.127797	−	0.991800i	$-0.459209\pi$
$569$	6.09686			0.255594			0.127797	+	0.991800i	$0.459209\pi$
$570$	17.4897	−	30.2930i	0.732561	−	1.26883i
$571$	5.49215	−	9.51269i	0.229839	−	0.398094i	−0.727921	−	0.685661i	$-0.759513\pi$
$571$	5.49215	−	9.51269i	0.229839	−	0.398094i	0.957760	+	0.287568i	$0.0928466\pi$
$572$	−2.42151	+	4.19418i	−0.101248	+	0.175368i
$573$	26.6116	+	46.0926i	1.11171	+	1.92555i
$574$	−10.7567	−	18.6311i	−0.448975	−	0.777648i
$575$	5.08686	−	8.81071i	0.212137	−	0.367432i
$576$	−1.71076	+	2.96312i	−0.0712815	+	0.123463i
$577$	20.9586	−	36.3014i	0.872518	−	1.51125i	0.0131352	−	0.999914i	$-0.495819\pi$
$577$	20.9586	−	36.3014i	0.872518	−	1.51125i	0.859383	−	0.511332i	$-0.170848\pi$
$578$	19.8223			0.824500
$579$	3.68855	+	6.38875i	0.153291	+	0.265507i
$580$	−3.03407	+	5.25516i	−0.125983	+	0.218209i
$581$	8.55779			0.355037
$582$	26.5815			1.10184
$583$	−10.1964	+	17.6607i	−0.422292	+	0.731430i
$584$	−0.421512			−0.0174423
$585$	−13.5341	−	23.4417i	−0.559565	−	0.969195i
$586$	16.4659			0.680201
$587$	10.8930	+	18.8672i	0.449601	+	0.778732i	0.998360	−	0.0572490i	$-0.0182329\pi$
$587$	10.8930	+	18.8672i	0.449601	+	0.778732i	−0.548759	+	0.835981i	$0.684900\pi$
$588$	0.732965	+	1.26953i	0.0302270	+	0.0523546i
$589$	13.0681	+	22.6347i	0.538463	+	0.932646i
$590$	−8.35640	+	14.4737i	−0.344027	+	0.595873i
$591$	−19.0919			−0.785334
$592$	5.27890	+	3.02213i	0.216961	+	0.124209i
$593$	−1.73546			−0.0712670			−0.0356335	−	0.999365i	$-0.511345\pi$
$593$	−1.73546			−0.0712670			−0.0356335	+	0.999365i	$0.511345\pi$
$594$	−1.29326	+	2.23999i	−0.0530630	+	0.0919078i
$595$	−30.4127	−	52.6763i	−1.24680	−	2.15952i
$596$	−1.27738	−	2.21249i	−0.0523236	−	0.0906272i
$597$	23.2582	+	40.2844i	0.951895	+	1.64873i
$598$	−1.91116			−0.0781533
$599$	4.14262	+	7.17522i	0.169263	+	0.293172i	0.938161	−	0.346200i	$-0.112528\pi$
$599$	4.14262	+	7.17522i	0.169263	+	0.293172i	−0.768898	+	0.639371i	$0.779195\pi$
$600$	26.9793			1.10143
$601$	−18.1466	+	31.4309i	−0.740216	+	1.28209i	0.212180	+	0.977231i	$0.431944\pi$
$601$	−18.1466	+	31.4309i	−0.740216	+	1.28209i	−0.952397	+	0.304862i	$0.901390\pi$
$602$	−10.4215			−0.424749
$603$	−21.9713			−0.894740
$604$	3.43337	−	5.94678i	0.139702	−	0.241971i
$605$	10.1585	+	17.5950i	0.413001	+	0.715339i
$606$	−12.9556			−0.526285
$607$	14.0538	−	24.3419i	0.570425	−	0.988006i	−0.426097	−	0.904678i	$-0.640112\pi$
$607$	14.0538	−	24.3419i	0.570425	−	0.988006i	0.996522	−	0.0833281i	$-0.0265549\pi$
$608$	1.74483	−	3.02213i	0.0707620	−	0.122563i
$609$	4.92552	−	8.53126i	0.199592	−	0.345704i
$610$	−0.921512	−	1.59611i	−0.0373109	−	0.0646244i
$611$	11.4897	+	19.9007i	0.464822	+	0.805095i
$612$	10.3811	−	17.9806i	0.419631	−	0.726823i
$613$	3.73698	−	6.47264i	0.150935	−	0.261427i	−0.780636	−	0.624985i	$-0.785105\pi$
$613$	3.73698	−	6.47264i	0.150935	−	0.261427i	0.931571	+	0.363558i	$0.118438\pi$
$614$	1.52221	−	2.63654i	0.0614314	−	0.106402i
$615$	−85.0979			−3.43148
$616$	3.06814	+	5.31418i	0.123619	+	0.214114i
$617$	−10.3470	+	17.9216i	−0.416556	+	0.721496i	−0.995590	−	0.0938069i	$-0.970096\pi$
$617$	−10.3470	+	17.9216i	−0.416556	+	0.721496i	0.579034	+	0.815303i	$0.303430\pi$
$618$	1.00803			0.0405488
$619$	−5.63093			−0.226326			−0.113163	−	0.993576i	$-0.536098\pi$
$619$	−5.63093			−0.226326			−0.113163	+	0.993576i	$0.536098\pi$
$620$	−14.8130	+	25.6568i	−0.594903	+	1.03040i
$621$	−1.02070			−0.0409591
$622$	−0.222617	−	0.385584i	−0.00892613	−	0.0154605i
$623$	26.3564			1.05595
$624$	−2.53407	−	4.38914i	−0.101444	−	0.175706i
$625$	−17.5588	−	30.4127i	−0.702351	−	1.21651i
$626$	−13.6663	−	23.6708i	−0.546217	−	0.946075i
$627$	10.7067	−	18.5446i	0.427586	−	0.740601i
$628$	−3.75919			−0.150008
$629$	−32.0331	−	18.3387i	−1.27724	−	0.731212i
$630$	−34.2963			−1.36640
$631$	−7.99117	+	13.8411i	−0.318123	+	0.551006i	−0.980096	−	0.198522i	$-0.936386\pi$
$631$	−7.99117	+	13.8411i	−0.318123	+	0.551006i	0.661973	+	0.749528i	$0.269719\pi$
$632$	−1.32331	−	2.29205i	−0.0526386	−	0.0911728i
$633$	−10.5641	−	18.2976i	−0.419886	−	0.727265i
$634$	−10.7370	−	18.5970i	−0.426420	−	0.738581i
$635$	−2.88941			−0.114663
$636$	−10.6704	−	18.4816i	−0.423107	−	0.732843i
$637$	−1.15698			−0.0458411
$638$	−1.85738	+	3.21708i	−0.0735346	+	0.127366i
$639$	−5.01570			−0.198418
$640$	3.95558			0.156358
$641$	−1.89145	+	3.27610i	−0.0747080	+	0.129398i	−0.900959	−	0.433904i	$-0.857136\pi$
$641$	−1.89145	+	3.27610i	−0.0747080	+	0.129398i	0.826251	+	0.563302i	$0.190469\pi$
$642$	10.2789	+	17.8036i	0.405676	+	0.702651i
$643$	15.6673			0.617859			0.308929	−	0.951085i	$-0.400029\pi$
$643$	15.6673			0.617859			0.308929	+	0.951085i	$0.400029\pi$
$644$	−1.21076	+	2.09709i	−0.0477105	+	0.0826370i
$645$	−20.6116	+	35.7003i	−0.811580	+	1.40570i
$646$	−10.5878	+	18.3387i	−0.416573	+	0.721526i
$647$	4.82180	+	8.35160i	0.189565	+	0.328335i	0.945105	−	0.326766i	$-0.105959\pi$
$647$	4.82180	+	8.35160i	0.189565	+	0.328335i	−0.755541	+	0.655102i	$0.772626\pi$
$648$	3.77890	+	6.54524i	0.148449	+	0.257121i
$649$	−5.11559	+	8.86045i	−0.200804	+	0.347803i
$650$	−10.6466	+	18.4405i	−0.417595	+	0.723296i
$651$	24.0474	−	41.6514i	0.942494	−	1.63245i
$652$	6.02372			0.235907
$653$	4.97779	+	8.62179i	0.194796	+	0.337397i	0.946834	−	0.321724i	$-0.104262\pi$
$653$	4.97779	+	8.62179i	0.194796	+	0.337397i	−0.752038	+	0.659120i	$0.770929\pi$
$654$	−14.5015	+	25.1174i	−0.567054	+	0.982166i
$655$	68.3851			2.67203
$656$	−8.48965			−0.331465
$657$	0.721104	−	1.24899i	0.0281329	−	0.0487277i
$658$	29.1156			1.13504
$659$	18.8905	+	32.7193i	0.735868	+	1.27456i	0.954341	+	0.298718i	$0.0965590\pi$
$659$	18.8905	+	32.7193i	0.735868	+	1.27456i	−0.218473	+	0.975843i	$0.570108\pi$
$660$	24.2726			0.944808
$661$	15.3993	+	26.6724i	0.598963	+	1.03744i	0.992974	+	0.118329i	$0.0377539\pi$
$661$	15.3993	+	26.6724i	0.598963	+	1.03744i	−0.394011	+	0.919106i	$0.628913\pi$
$662$	4.55779	+	7.89433i	0.177144	+	0.306822i
$663$	15.3771	+	26.6339i	0.597197	+	1.03438i
$664$	1.68855	−	2.92465i	0.0655283	−	0.113498i
$665$	34.9793			1.35644
$666$	−17.9858	+	10.4719i	−0.696936	+	0.405776i
$667$	−1.46593			−0.0567610
$668$	6.00000	−	10.3923i	0.232147	−	0.402090i
$669$	29.2582	+	50.6767i	1.13119	+	1.95927i
$670$	12.7004	+	21.9978i	0.490660	+	0.849847i
$671$	−0.564127	−	0.977097i	−0.0217779	−	0.0377204i
$672$	−6.42151			−0.247715
$673$	−21.7479	−	37.6684i	−0.838318	−	1.45201i	−0.891300	−	0.453414i	$-0.850206\pi$
$673$	−21.7479	−	37.6684i	−0.838318	−	1.45201i	0.0529819	−	0.998595i	$-0.483127\pi$
$674$	−26.4008			−1.01692
$675$	−5.68605	+	9.84852i	−0.218856	+	0.379070i
$676$	−9.00000			−0.346154
$677$	−11.7592			−0.451942			−0.225971	−	0.974134i	$-0.572556\pi$
$677$	−11.7592			−0.451942			−0.225971	+	0.974134i	$0.572556\pi$
$678$	4.53407	−	7.85324i	0.174130	−	0.301602i
$679$	13.2908	+	23.0203i	0.510052	+	0.883437i
$680$	−24.0030			−0.920474
$681$	−23.6259	+	40.9213i	−0.905348	+	1.56811i
$682$	−9.06814	+	15.7065i	−0.347237	+	0.601432i
$683$	−10.9467	+	18.9603i	−0.418866	+	0.725497i	−0.995826	−	0.0912758i	$-0.970906\pi$
$683$	−10.9467	+	18.9603i	−0.418866	+	0.725497i	0.576960	+	0.816772i	$0.304239\pi$
$684$	5.96994	+	10.3402i	0.228266	+	0.395369i
$685$	−21.8495	−	37.8445i	−0.834828	−	1.44596i
$686$	−9.60221	+	16.6315i	−0.366614	+	0.634994i
$687$	−25.9912	+	45.0180i	−0.991625	+	1.71754i
$688$	−2.05628	+	3.56158i	−0.0783949	+	0.135784i
$689$	16.8430			0.641668
$690$	4.78924	+	8.29521i	0.182323	+	0.315793i
$691$	10.8130	−	18.7286i	0.411345	−	0.712470i	−0.583692	−	0.811975i	$-0.698393\pi$
$691$	10.8130	−	18.7286i	0.411345	−	0.712470i	0.995037	+	0.0995050i	$0.0317259\pi$
$692$	15.4452			0.587140
$693$	−20.9954			−0.797548
$694$	15.9374	−	27.6044i	0.604975	−	1.04785i
$695$	−48.3377			−1.83355
$696$	−1.94372	−	3.36662i	−0.0736765	−	0.127612i
$697$	51.5164			1.95132
$698$	11.8208	+	20.4743i	0.447424	+	0.774962i
$699$	−23.8485	−	41.3069i	−0.902035	−	1.56237i
$700$	13.4897	+	23.3648i	0.509861	+	0.883105i
$701$	7.46896	−	12.9366i	0.282099	−	0.488609i	−0.689803	−	0.723997i	$-0.742303\pi$
$701$	7.46896	−	12.9366i	0.282099	−	0.488609i	0.971901	+	0.235388i	$0.0756361\pi$
$702$	2.13628			0.0806287
$703$	18.3440	−	10.6804i	0.691857	−	0.402819i
$704$	2.42151			0.0912642
$705$	57.5845	−	99.7394i	2.16876	−	3.75640i
$706$	−11.7789	−	20.4016i	−0.443305	−	0.767826i
$707$	−6.47779	−	11.2199i	−0.243622	−	0.421966i
$708$	−5.35337	−	9.27231i	−0.201192	−	0.348475i
$709$	−21.2519			−0.798131			−0.399065	−	0.916923i	$-0.630665\pi$
$709$	−21.2519			−0.798131			−0.399065	+	0.916923i	$0.630665\pi$
$710$	2.89930	+	5.02174i	0.108809	+	0.188463i
$711$	9.05547			0.339607
$712$	5.20041	−	9.00737i	0.194894	−	0.337565i
$713$	−7.15698			−0.268031
$714$	38.9666			1.45829
$715$	−9.57849	+	16.5904i	−0.358215	+	0.620447i
$716$	1.46593	+	2.53906i	0.0547844	+	0.0948893i
$717$	−54.5164			−2.03595
$718$	2.93186	−	5.07813i	0.109416	−	0.189514i
$719$	21.9912	−	38.0898i	0.820132	−	1.42051i	−0.0854514	−	0.996342i	$-0.527233\pi$
$719$	21.9912	−	38.0898i	0.820132	−	1.42051i	0.905583	−	0.424168i	$-0.139433\pi$
$720$	−6.76704	+	11.7208i	−0.252193	+	0.436810i
$721$	0.504013	+	0.872976i	0.0187704	+	0.0325113i
$722$	3.41116	+	5.90831i	0.126950	+	0.219885i
$723$	−22.4452	+	38.8763i	−0.834747	+	1.44582i
$724$	3.09035	−	5.35264i	0.114852	−	0.198929i
$725$	−8.16634	+	14.1445i	−0.303290	+	0.525314i
$726$	−13.0157			−0.483058
$727$	−26.1313	−	45.2607i	−0.969156	−	1.67863i	−0.698010	−	0.716088i	$-0.745931\pi$
$727$	−26.1313	−	45.2607i	−0.969156	−	1.67863i	−0.271146	−	0.962538i	$-0.587403\pi$
$728$	2.53407	−	4.38914i	0.0939189	−	0.162672i
$729$	−33.9793			−1.25849
$730$	−1.66732			−0.0617104
$731$	12.4778	−	21.6122i	0.461508	−	0.799355i
$732$	1.18070			0.0436399
$733$	−5.33268	−	9.23647i	−0.196967	−	0.341157i	0.750577	−	0.660783i	$-0.229776\pi$
$733$	−5.33268	−	9.23647i	−0.196967	−	0.341157i	−0.947544	+	0.319627i	$0.896442\pi$
$734$	−4.00000			−0.147643
$735$	2.89930	+	5.02174i	0.106942	+	0.185230i
$736$	0.477791	+	0.827558i	0.0176116	+	0.0305042i
$737$	7.77488	+	13.4665i	0.286392	+	0.496045i
$738$	14.5237	−	25.1558i	0.534626	−	0.925999i
$739$	−36.4927			−1.34240			−0.671202	−	0.741274i	$-0.734222\pi$
$739$	−36.4927			−1.34240			−0.671202	+	0.741274i	$0.734222\pi$
$740$	20.8811	+	11.9543i	0.767605	+	0.439448i
$741$	−17.6860			−0.649713
$742$	10.6704	−	18.4816i	0.391721	−	0.678481i
$743$	−10.0775	−	17.4547i	−0.369708	−	0.640352i	0.619812	−	0.784750i	$-0.287209\pi$
$743$	−10.0775	−	17.4547i	−0.369708	−	0.640352i	−0.989520	+	0.144398i	$0.953876\pi$
$744$	−9.48965	−	16.4366i	−0.347908	−	0.602594i
$745$	−5.05279	−	8.75169i	−0.185120	−	0.320637i
$746$	−32.3644			−1.18495
$747$	5.77738	+	10.0067i	0.211383	+	0.366127i
$748$	−14.6941			−0.537269
$749$	−10.2789	+	17.8036i	−0.375583	+	0.650528i
$750$	56.6002			2.06675
$751$	51.4720			1.87824			0.939120	−	0.343590i	$-0.111643\pi$
$751$	51.4720			1.87824			0.939120	+	0.343590i	$0.111643\pi$
$752$	5.74483	−	9.95033i	0.209492	−	0.362851i
$753$	7.34704	+	12.7254i	0.267741	+	0.463741i
$754$	3.06814			0.111735
$755$	13.5810	−	23.5230i	0.494263	−	0.856088i
$756$	1.35337	−	2.34411i	0.0492216	−	0.0852544i
$757$	−1.38994	+	2.40745i	−0.0505183	+	0.0875002i	−0.890179	−	0.455611i	$-0.849421\pi$
$757$	−1.38994	+	2.40745i	−0.0505183	+	0.0875002i	0.839660	+	0.543112i	$0.182754\pi$
$758$	−15.4571	−	26.7725i	−0.561427	−	0.972420i
$759$	2.93186	+	5.07813i	0.106420	+	0.184324i
$760$	6.90180	−	11.9543i	0.250355	−	0.433627i
$761$	22.5712	−	39.0944i	0.818204	−	1.41717i	−0.0888000	−	0.996049i	$-0.528303\pi$
$761$	22.5712	−	39.0944i	0.818204	−	1.41717i	0.907004	−	0.421122i	$-0.138363\pi$
$762$	0.925525	−	1.60306i	0.0335282	−	0.0580726i
$763$	−29.0030			−1.04998
$764$	10.5015	+	18.1892i	0.379931	+	0.658061i
$765$	41.0633	−	71.1238i	1.48465	−	2.57148i
$766$	31.1994			1.12728
$767$	8.45023			0.305120
$768$	−1.26704	+	2.19457i	−0.0457202	+	0.0791897i
$769$	−27.2231			−0.981692			−0.490846	−	0.871246i	$-0.663312\pi$
$769$	−27.2231			−0.981692			−0.490846	+	0.871246i	$0.663312\pi$
$770$	12.1363	+	21.0207i	0.437361	+	0.757532i
$771$	75.2469			2.70995
$772$	1.45558	+	2.52114i	0.0523875	+	0.0907379i
$773$	18.7701	+	32.5107i	0.675112	+	1.16933i	0.976436	+	0.215807i	$0.0692381\pi$
$773$	18.7701	+	32.5107i	0.675112	+	1.16933i	−0.301324	+	0.953522i	$0.597429\pi$
$774$	−7.03558	−	12.1860i	−0.252889	−	0.438016i
$775$	−39.8698	+	69.0565i	−1.43216	+	2.48058i
$776$	10.4897			0.376557
$777$	−33.8985	−	19.4066i	−1.21610	−	0.696209i
$778$	5.24884			0.188180
$779$	−14.8130	+	25.6568i	−0.530730	+	0.919251i
$780$	−10.0237	−	17.3616i	−0.358907	−	0.621645i
$781$	1.77488	+	3.07419i	0.0635103	+	0.110003i
$782$	−2.89930	−	5.02174i	−0.103679	−	0.179577i
$783$	1.63860			0.0585589
$784$	0.289244	+	0.500986i	0.0103301	+	0.0178923i
$785$	−14.8698			−0.530725
$786$	−21.9048	+	37.9403i	−0.781319	+	1.35328i
$787$	9.50837			0.338937			0.169468	−	0.985536i	$-0.445795\pi$
$787$	9.50837			0.338937			0.169468	+	0.985536i	$0.445795\pi$
$788$	−7.53407			−0.268390
$789$	23.7622	−	41.1574i	0.845957	−	1.46524i
$790$	−5.23448	−	9.06638i	−0.186234	−	0.322567i
$791$	9.06814			0.322426
$792$	−4.14262	+	7.17522i	−0.147201	+	0.254960i
$793$	−0.465930	+	0.807014i	−0.0165457	+	0.0286579i
$794$	−8.73698	+	15.1329i	−0.310064	+	0.537046i
$795$	−42.2074	−	73.1054i	−1.49694	−	2.59278i
$796$	9.17820	+	15.8971i	0.325313	+	0.563458i
$797$	−3.61791	+	6.26640i	−0.128153	+	0.221967i	−0.922961	−	0.384894i	$-0.874238\pi$
$797$	−3.61791	+	6.26640i	−0.128153	+	0.221967i	0.794808	+	0.606861i	$0.207571\pi$
$798$	−11.2044	+	19.4066i	−0.396632	+	0.686987i
$799$	−34.8604	+	60.3800i	−1.23327	+	2.13609i
$800$	10.6466			0.376415
$801$	17.7933	+	30.8188i	0.628694	+	1.08893i
$802$	−1.14262	+	1.97907i	−0.0403472	+	0.0698833i
$803$	−1.02070			−0.0360196
$804$	−16.2726			−0.573889
$805$	−4.78924	+	8.29521i	−0.168799	+	0.292368i
$806$	14.9793			0.527623
$807$	−29.2883	−	50.7288i	−1.03100	−	1.78574i
$808$	−5.11256			−0.179859
$809$	−15.1901	−	26.3100i	−0.534054	−	0.925009i	−0.999208	−	0.0397792i	$-0.987335\pi$
$809$	−15.1901	−	26.3100i	−0.534054	−	0.925009i	0.465154	−	0.885230i	$-0.345999\pi$
$810$	14.9477	+	25.8902i	0.525210	+	0.909690i
$811$	−19.2044	−	33.2630i	−0.674358	−	1.16802i	−0.976656	−	0.214809i	$-0.931087\pi$
$811$	−19.2044	−	33.2630i	−0.674358	−	1.16802i	0.302298	−	0.953214i	$-0.402246\pi$
$812$	1.94372	−	3.36662i	0.0682112	−	0.118145i
$813$	57.5084			2.01691
$814$	12.7829	+	7.31812i	0.448041	+	0.256500i
$815$	23.8273			0.834635
$816$	7.68855	−	13.3170i	0.269153	−	0.466187i
$817$	7.17570	+	12.4287i	0.251046	+	0.434824i
$818$	−13.1560	−	22.7868i	−0.459988	−	0.796723i
$819$	8.67035	+	15.0175i	0.302967	+	0.524754i
$820$	−33.5815			−1.17272
$821$	5.55779	+	9.62638i	0.193968	+	0.335963i	0.946562	−	0.322522i	$-0.104531\pi$
$821$	5.55779	+	9.62638i	0.193968	+	0.335963i	−0.752594	+	0.658485i	$0.771197\pi$
$822$	27.9950			0.976438
$823$	−17.2320	+	29.8467i	−0.600669	+	1.04039i	0.392051	+	0.919944i	$0.371766\pi$
$823$	−17.2320	+	29.8467i	−0.600669	+	1.04039i	−0.992720	+	0.120446i	$0.961568\pi$
$824$	0.397789			0.0138577
$825$	65.3307			2.27452
$826$	5.35337	−	9.27231i	0.186268	−	0.322625i
$827$	13.5371	+	23.4469i	0.470731	+	0.815330i	0.999440	−	0.0334734i	$-0.0106569\pi$
$827$	13.5371	+	23.4469i	0.470731	+	0.815330i	−0.528709	+	0.848803i	$0.677324\pi$
$828$	−3.26953			−0.113624
$829$	−10.6860	+	18.5088i	−0.371142	+	0.642836i	−0.989741	−	0.142870i	$-0.954367\pi$
$829$	−10.6860	+	18.5088i	−0.371142	+	0.642836i	0.618600	+	0.785706i	$0.287700\pi$
$830$	6.67919	−	11.5687i	0.231838	−	0.401555i
$831$	−23.7059	+	41.0599i	−0.822350	+	1.42435i
$832$	−1.00000	−	1.73205i	−0.0346688	−	0.0600481i
$833$	−1.75517	−	3.04005i	−0.0608132	−	0.105332i
$834$	15.4833	−	26.8179i	0.536143	−	0.928628i
$835$	23.7335	−	41.1076i	0.821331	−	1.42259i
$836$	4.22512	−	7.31812i	0.146129	−	0.253102i
$837$	8.00000			0.276520
$838$	−13.1244	−	22.7322i	−0.453376	−	0.785269i
$839$	26.9705	−	46.7142i	0.931124	−	1.61275i	0.149720	−	0.988728i	$-0.452163\pi$
$839$	26.9705	−	46.7142i	0.931124	−	1.61275i	0.781404	−	0.624026i	$-0.214504\pi$
$840$	−25.4008			−0.876411
$841$	−26.6466			−0.918849
$842$	−6.48814	+	11.2378i	−0.223596	+	0.387280i
$843$	−68.7652			−2.36840
$844$	−4.16884	−	7.22064i	−0.143497	−	0.248545i
$845$	−35.6002			−1.22469
$846$	19.6560	+	34.0452i	0.675787	+	1.17050i
$847$	−6.50785	−	11.2719i	−0.223612	−	0.387308i
$848$	−4.21076	−	7.29324i	−0.144598	−	0.250451i
$849$	−1.15064	+	1.99297i	−0.0394899	+	0.0683986i
$850$	−64.6052			−2.21594
$851$	0.0212225	+	5.81254i	0.000727499	+	0.199251i
$852$	−3.71477			−0.127266
$853$	−20.4818	+	35.4755i	−0.701284	+	1.21466i	0.266732	+	0.963771i	$0.414056\pi$
$853$	−20.4818	+	35.4755i	−0.701284	+	1.21466i	−0.968016	+	0.250888i	$0.919277\pi$
$854$	0.590349	+	1.02252i	0.0202013	+	0.0349897i
$855$	23.6146	+	40.9017i	0.807602	+	1.39881i
$856$	4.05628	+	7.02568i	0.138641	+	0.240133i
$857$	−1.33268			−0.0455233			−0.0227617	−	0.999741i	$-0.507246\pi$
$857$	−1.33268			−0.0455233			−0.0227617	+	0.999741i	$0.507246\pi$
$858$	−6.13628	−	10.6284i	−0.209489	−	0.362846i
$859$	0.160003			0.00545924			0.00272962	−	0.999996i	$-0.499131\pi$
$859$	0.160003			0.00545924			0.00272962	+	0.999996i	$0.499131\pi$
$860$	−8.13378	+	14.0881i	−0.277360	+	0.480401i
$861$	54.5164			1.85791
$862$	−12.5103			−0.426104
$863$	−2.86675	+	4.96535i	−0.0975852	+	0.169022i	−0.910685	−	0.413102i	$-0.864445\pi$
$863$	−2.86675	+	4.96535i	−0.0975852	+	0.169022i	0.813099	+	0.582125i	$0.197779\pi$
$864$	−0.534070	−	0.925037i	−0.0181694	−	0.0314704i
$865$	61.0949			2.07729
$866$	−1.01971	+	1.76619i	−0.0346511	+	0.0600175i
$867$	−25.1156	+	43.5015i	−0.852970	+	1.47739i
$868$	9.48965	−	16.4366i	0.322100	−	0.557893i
$869$	−3.20442	−	5.55022i	−0.108703	−	0.188278i
$870$	−7.68855	−	13.3170i	−0.260666	−	0.451487i
$871$	6.42151	−	11.1224i	0.217585	−	0.376868i
$872$	−5.72262	+	9.91186i	−0.193792	+	0.335658i
$873$	−17.9452	+	31.0821i	−0.607354	+	1.05197i
$874$	3.33465			0.112796
$875$	28.3001	+	49.0172i	0.956719	+	1.65709i
$876$	0.534070	−	0.925037i	0.0180446	−	0.0312541i
$877$	12.6309			0.426516			0.213258	−	0.976996i	$-0.431592\pi$
$877$	12.6309			0.426516			0.213258	+	0.976996i	$0.431592\pi$
$878$	−28.8905			−0.975006
$879$	−20.8629	+	36.1356i	−0.703689	+	1.21882i
$880$	9.57849			0.322891
$881$	1.56814	+	2.71610i	0.0528320	+	0.0915077i	0.891232	−	0.453548i	$-0.149842\pi$
$881$	1.56814	+	2.71610i	0.0528320	+	0.0915077i	−0.838400	+	0.545056i	$0.816509\pi$
$882$	−1.97930			−0.0666466
$883$	−26.0449	−	45.1112i	−0.876482	−	1.51811i	−0.855175	−	0.518339i	$-0.826551\pi$
$883$	−26.0449	−	45.1112i	−0.876482	−	1.51811i	−0.0213068	−	0.999773i	$-0.506783\pi$
$884$	6.06814	+	10.5103i	0.204094	+	0.353501i
$885$	−21.1757	−	36.6774i	−0.711813	−	1.23290i
$886$	1.26454	−	2.19024i	0.0424829	−	0.0735825i
$887$	29.0505			0.975419			0.487710	−	0.873006i	$-0.337832\pi$
$887$	29.0505			0.975419			0.487710	+	0.873006i	$0.337832\pi$
$888$	−13.3208	+	7.75576i	−0.447017	+	0.260266i
$889$	1.85105			0.0620822
$890$	20.5706	−	35.6294i	0.689529	−	1.19430i
$891$	9.15064	+	15.8494i	0.306558	+	0.530974i
$892$	11.5459	+	19.9981i	0.386586	+	0.669587i
$893$	−20.0474	−	34.7232i	−0.670862	−	1.16197i
$894$	6.47396			0.216521
$895$	5.79861	+	10.0435i	0.193826	+	0.335716i
$896$	−2.53407			−0.0846573
$897$	2.42151	−	4.19418i	0.0808519	−	0.140040i
$898$	4.87175			0.162572
$899$	11.4897			0.383201
$900$	−18.2138	+	31.5472i	−0.607126	+	1.05157i
$901$	25.5515	+	44.2564i	0.851242	+	1.47440i
$902$	−20.5578			−0.684500
$903$	13.2044	−	22.8707i	0.439416	−	0.761090i
$904$	1.78924	−	3.09906i	0.0595094	−	0.103073i
$905$	12.2241	−	21.1728i	0.406344	−	0.703808i
$906$	8.70041	+	15.0695i	0.289052	+	0.500652i
$907$	11.1219	+	19.2637i	0.369297	+	0.639642i	0.989456	−	0.144835i	$-0.0462651\pi$
$907$	11.1219	+	19.2637i	0.369297	+	0.639642i	−0.620159	+	0.784476i	$0.712932\pi$
$908$	−9.32331	+	16.1485i	−0.309405	+	0.535905i
$909$	8.74634	−	15.1491i	0.290098	−	0.502464i
$910$	10.0237	−	17.3616i	0.332283	−	0.575531i
$911$	−14.6516			−0.485430			−0.242715	−	0.970098i	$-0.578038\pi$
$911$	−14.6516			−0.485430			−0.242715	+	0.970098i	$0.578038\pi$
$912$	4.42151	+	7.65828i	0.146411	+	0.253591i
$913$	4.08884	−	7.08207i	0.135321	−	0.234382i
$914$	7.04744			0.233109
$915$	4.67035			0.154397
$916$	−10.2567	+	17.7651i	−0.338890	+	0.586976i
$917$	−43.8097			−1.44672
$918$	3.24081	+	5.61325i	0.106963	+	0.185265i
$919$	−26.6991			−0.880721			−0.440361	−	0.897821i	$-0.645149\pi$
$919$	−26.6991			−0.880721			−0.440361	+	0.897821i	$0.645149\pi$
$920$	1.88994	+	3.27347i	0.0623095	+	0.107923i
$921$	3.85738	+	6.68119i	0.127105	+	0.220153i
$922$	0.0681404	+	0.118023i	0.00224408	+	0.00388687i
$923$	1.46593	−	2.53906i	0.0482517	−	0.0835743i
$924$	−15.5498			−0.511550
$925$	56.2024	+	32.1755i	1.84793	+	1.05792i
$926$	16.2201			0.533026
$927$	−0.680521	+	1.17870i	−0.0223512	+	0.0387135i
$928$	−0.767035	−	1.32854i	−0.0251792	−	0.0436116i
$929$	−29.7138	−	51.4658i	−0.974878	−	1.68854i	−0.680338	−	0.732898i	$-0.738167\pi$
$929$	−29.7138	−	51.4658i	−0.974878	−	1.68854i	−0.294539	−	0.955639i	$-0.595166\pi$
$930$	−37.5371	−	65.0162i	−1.23089	−	2.13196i
$931$	2.01872			0.0661610
$932$	−9.41116	−	16.3006i	−0.308273	−	0.533944i
$933$	1.12825			0.0369374
$934$	−19.0919	+	33.0681i	−0.624705	+	1.08202i
$935$	−58.1236			−1.90085
$936$	6.84302			0.223671
$937$	−26.6219	+	46.1105i	−0.869700	+	1.50636i	−0.00739700	+	0.999973i	$0.502355\pi$
$937$	−26.6219	+	46.1105i	−0.869700	+	1.50636i	−0.862303	+	0.506392i	$0.830979\pi$
$938$	−8.13628	−	14.0925i	−0.265659	−	0.460135i
$939$	69.2629			2.26031
$940$	22.7241	−	39.3593i	0.741179	−	1.28376i
$941$	−13.1047	+	22.6980i	−0.427201	+	0.739934i	−0.996623	−	0.0821110i	$-0.973834\pi$
$941$	−13.1047	+	22.6980i	−0.427201	+	0.739934i	0.569422	+	0.822045i	$0.307167\pi$
$942$	4.76302	−	8.24980i	0.155188	−	0.268793i
$943$	−4.05628	−	7.02568i	−0.132091	−	0.228788i
$944$	−2.11256	−	3.65906i	−0.0687579	−	0.119092i
$945$	5.35337	−	9.27231i	0.174145	−	0.301628i
$946$	−4.97930	+	8.62441i	−0.161891	+	0.280404i
$947$	5.04442	−	8.73719i	0.163922	−	0.283920i	−0.772350	−	0.635197i	$-0.780919\pi$
$947$	5.04442	−	8.73719i	0.163922	−	0.283920i	0.936272	+	0.351276i	$0.114252\pi$
$948$	6.70674			0.217825
$949$	0.421512	+	0.730080i	0.0136829	+	0.0236994i
$950$	18.5765	−	32.1755i	0.602702	−	1.04391i
$951$	54.4165			1.76458
$952$	15.3771			0.498374
$953$	9.70041	−	16.8016i	0.314227	−	0.544257i	−0.665046	−	0.746803i	$-0.731588\pi$
$953$	9.70041	−	16.8016i	0.314227	−	0.544257i	0.979273	+	0.202545i	$0.0649213\pi$
$954$	28.8143			0.932897
$955$	41.5396	+	71.9487i	1.34419	+	2.32820i
$956$	−21.5134			−0.695792
$957$	−4.70674	−	8.15232i	−0.152147	−	0.263527i
$958$	14.2488	+	24.6797i	0.460359	+	0.797365i
$959$	13.9975	+	24.2444i	0.452003	+	0.782892i
$960$	−5.01186	+	8.68080i	−0.161757	+	0.280172i
$961$	25.0949			0.809513
$962$	−0.0444180	−	12.1654i	−0.00143210	−	0.392230i
$963$	−27.7572			−0.894464
$964$	−8.85738	+	15.3414i	−0.285277	+	0.494115i
$965$	5.75767	+	9.97258i	0.185346	+	0.321029i
$966$	−3.06814	−	5.31418i	−0.0987158	−	0.170981i
$967$	17.5134	+	30.3341i	0.563192	+	0.975477i	0.997215	+	0.0745757i	$0.0237603\pi$
$967$	17.5134	+	30.3341i	0.563192	+	0.975477i	−0.434023	+	0.900902i	$0.642906\pi$
$968$	−5.13628			−0.165086
$969$	−26.8304	−	46.4715i	−0.861915	−	1.49288i
$970$	41.4927			1.33225
$971$	−0.732965	+	1.26953i	−0.0235220	+	0.0407412i	−0.877547	−	0.479491i	$-0.840821\pi$
$971$	−0.732965	+	1.26953i	−0.0235220	+	0.0407412i	0.854025	+	0.520232i	$0.174155\pi$
$972$	−22.3564			−0.717082
$973$	30.9666			0.992745
$974$	−14.0563	+	24.3462i	−0.450392	+	0.780102i
$975$	−26.9793	−	46.7295i	−0.864029	−	1.49654i
$976$	0.465930			0.0149140
$977$	−21.7004	+	37.5862i	−0.694258	+	1.20249i	0.276173	+	0.961108i	$0.410934\pi$
$977$	−21.7004	+	37.5862i	−0.694258	+	1.20249i	−0.970430	+	0.241381i	$0.922400\pi$
$978$	−7.63227	+	13.2195i	−0.244053	+	0.422712i
$979$	12.5928	−	21.8115i	0.402469	−	0.697097i
$980$	1.14413	+	1.98169i	0.0365479	+	0.0633027i
$981$	−19.5800	−	33.9136i	−0.625141	−	1.08278i
$982$	1.21076	−	2.09709i	0.0386368	−	0.0669209i
$983$	16.4803	−	28.5447i	0.525640	−	0.910435i	−0.473914	−	0.880571i	$-0.657159\pi$
$983$	16.4803	−	28.5447i	0.525640	−	0.910435i	0.999554	−	0.0298636i	$-0.00950730\pi$
$984$	10.7567	−	18.6311i	0.342911	−	0.593939i
$985$	−29.8016			−0.949559
$986$	4.65448	+	8.06179i	0.148229	+	0.256740i
$987$	−36.8905	+	63.8962i	−1.17424	+	2.03384i
$988$	−6.97930			−0.222041
$989$	−3.92989			−0.124963
$990$	−16.3865	+	28.3822i	−0.520796	+	0.902045i
$991$	35.2469			1.11965			0.559827	−	0.828610i	$-0.310868\pi$
$991$	35.2469			1.11965			0.559827	+	0.828610i	$0.310868\pi$
$992$	−3.74483	−	6.48623i	−0.118898	−	0.205938i
$993$	−23.0995			−0.733042
$994$	−1.85738	−	3.21708i	−0.0589127	−	0.102040i
$995$	36.3051	+	62.8823i	1.15095	+	1.99350i
$996$	4.27890	+	7.41127i	0.135582	+	0.234835i
$997$	25.1837	−	43.6195i	0.797577	−	1.38144i	−0.123614	−	0.992330i	$-0.539448\pi$
$997$	25.1837	−	43.6195i	0.797577	−	1.38144i	0.921190	−	0.389113i	$-0.127218\pi$
$998$	−2.46896			−0.0781535
$999$	−0.0237224	−	6.49720i	−0.000750542	−	0.205562i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.2.c.c.47.1	✓	6
3.2	odd	2		666.2.f.j.343.3		6
4.3	odd	2		592.2.i.e.417.3		6
37.10	even	3		2738.2.a.o.1.3		3
37.26	even	3	inner	74.2.c.c.63.1	yes	6
37.27	even	6		2738.2.a.n.1.3		3
111.26	odd	6		666.2.f.j.433.3		6
148.63	odd	6		592.2.i.e.433.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.c.c.47.1	✓	6	1.1	even	1	trivial
74.2.c.c.63.1	yes	6	37.26	even	3	inner
592.2.i.e.417.3		6	4.3	odd	2
592.2.i.e.433.3		6	148.63	odd	6
666.2.f.j.343.3		6	3.2	odd	2
666.2.f.j.433.3		6	111.26	odd	6
2738.2.a.n.1.3		3	37.27	even	6
2738.2.a.o.1.3		3	37.10	even	3

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.26704 - 2.19457i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.97779 - 3.42563i) q^{5} +2.53407 q^{6} +(1.26704 + 2.19457i) q^{7} +1.00000 q^{8} +(-1.71076 + 2.96312i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.26704 - 2.19457i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.97779 - 3.42563i) q^{5} +2.53407 q^{6} +(1.26704 + 2.19457i) q^{7} +1.00000 q^{8} +(-1.71076 + 2.96312i) q^{9} +3.95558 q^{10} +2.42151 q^{11} +(-1.26704 + 2.19457i) q^{12} +(-1.00000 - 1.73205i) q^{13} -2.53407 q^{14} +(-5.01186 + 8.68080i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.03407 - 5.25516i) q^{17} +(-1.71076 - 2.96312i) q^{18} +(1.74483 + 3.02213i) q^{19} +(-1.97779 + 3.42563i) q^{20} +(3.21076 - 5.56119i) q^{21} +(-1.21076 + 2.09709i) q^{22} -0.955582 q^{23} +(-1.26704 - 2.19457i) q^{24} +(-5.32331 + 9.22025i) q^{25} +2.00000 q^{26} +1.06814 q^{27} +(1.26704 - 2.19457i) q^{28} +1.53407 q^{29} +(-5.01186 - 8.68080i) q^{30} +7.48965 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.06814 - 5.31418i) q^{33} +(3.03407 + 5.25516i) q^{34} +(5.01186 - 8.68080i) q^{35} +3.42151 q^{36} +(-0.0222090 - 6.08272i) q^{37} -3.48965 q^{38} +(-2.53407 + 4.38914i) q^{39} +(-1.97779 - 3.42563i) q^{40} +(4.24483 + 7.35225i) q^{41} +(3.21076 + 5.56119i) q^{42} +4.11256 q^{43} +(-1.21076 - 2.09709i) q^{44} +13.5341 q^{45} +(0.477791 - 0.827558i) q^{46} -11.4897 q^{47} +2.53407 q^{48} +(0.289244 - 0.500986i) q^{49} +(-5.32331 - 9.22025i) q^{50} -15.3771 q^{51} +(-1.00000 + 1.73205i) q^{52} +(-4.21076 + 7.29324i) q^{53} +(-0.534070 + 0.925037i) q^{54} +(-4.78924 - 8.29521i) q^{55} +(1.26704 + 2.19457i) q^{56} +(4.42151 - 7.65828i) q^{57} +(-0.767035 + 1.32854i) q^{58} +(-2.11256 + 3.65906i) q^{59} +10.0237 q^{60} +(-0.232965 - 0.403507i) q^{61} +(-3.74483 + 6.48623i) q^{62} -8.67035 q^{63} +1.00000 q^{64} +(-3.95558 + 6.85127i) q^{65} +6.13628 q^{66} +(3.21076 + 5.56119i) q^{67} -6.06814 q^{68} +(1.21076 + 2.09709i) q^{69} +(5.01186 + 8.68080i) q^{70} +(0.732965 + 1.26953i) q^{71} +(-1.71076 + 2.96312i) q^{72} -0.421512 q^{73} +(5.27890 + 3.02213i) q^{74} +26.9793 q^{75} +(1.74483 - 3.02213i) q^{76} +(3.06814 + 5.31418i) q^{77} +(-2.53407 - 4.38914i) q^{78} +(-1.32331 - 2.29205i) q^{79} +3.95558 q^{80} +(3.77890 + 6.54524i) q^{81} -8.48965 q^{82} +(1.68855 - 2.92465i) q^{83} -6.42151 q^{84} -24.0030 q^{85} +(-2.05628 + 3.56158i) q^{86} +(-1.94372 - 3.36662i) q^{87} +2.42151 q^{88} +(5.20041 - 9.00737i) q^{89} +(-6.76704 + 11.7208i) q^{90} +(2.53407 - 4.38914i) q^{91} +(0.477791 + 0.827558i) q^{92} +(-9.48965 - 16.4366i) q^{93} +(5.74483 - 9.95033i) q^{94} +(6.90180 - 11.9543i) q^{95} +(-1.26704 + 2.19457i) q^{96} +10.4897 q^{97} +(0.289244 + 0.500986i) q^{98} +(-4.14262 + 7.17522i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} - q^{5} + 6 q^{8} - 7 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 - q^5 + 6 * q^8 - 7 * q^9	\( 6 q - 3 q^{2} - 3 q^{4} - q^{5} + 6 q^{8} - 7 q^{9} + 2 q^{10} + 8 q^{11} - 6 q^{13} - 4 q^{15} - 3 q^{16} + 3 q^{17} - 7 q^{18} - 8 q^{19} - q^{20} + 16 q^{21} - 4 q^{22} + 16 q^{23} - 20 q^{25} + 12 q^{26} - 24 q^{27} - 6 q^{29} - 4 q^{30} + 8 q^{31} - 3 q^{32} + 12 q^{33} + 3 q^{34} + 4 q^{35} + 14 q^{36} - 11 q^{37} + 16 q^{38} - q^{40} + 7 q^{41} + 16 q^{42} + 16 q^{43} - 4 q^{44} + 66 q^{45} - 8 q^{46} - 32 q^{47} + 5 q^{49} - 20 q^{50} - 64 q^{51} - 6 q^{52} - 22 q^{53} + 12 q^{54} - 32 q^{55} + 20 q^{57} + 3 q^{58} - 4 q^{59} + 8 q^{60} - 9 q^{61} - 4 q^{62} + 24 q^{63} + 6 q^{64} - 2 q^{65} - 24 q^{66} + 16 q^{67} - 6 q^{68} + 4 q^{69} + 4 q^{70} + 12 q^{71} - 7 q^{72} + 4 q^{73} - 2 q^{74} + 88 q^{75} - 8 q^{76} - 12 q^{77} + 4 q^{79} + 2 q^{80} - 11 q^{81} - 14 q^{82} - 4 q^{83} - 32 q^{84} - 18 q^{85} - 8 q^{86} - 16 q^{87} + 8 q^{88} - 9 q^{89} - 33 q^{90} - 8 q^{92} - 20 q^{93} + 16 q^{94} + 36 q^{95} + 26 q^{97} + 5 q^{98} - 52 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 - q^5 + 6 * q^8 - 7 * q^9 + 2 * q^10 + 8 * q^11 - 6 * q^13 - 4 * q^15 - 3 * q^16 + 3 * q^17 - 7 * q^18 - 8 * q^19 - q^20 + 16 * q^21 - 4 * q^22 + 16 * q^23 - 20 * q^25 + 12 * q^26 - 24 * q^27 - 6 * q^29 - 4 * q^30 + 8 * q^31 - 3 * q^32 + 12 * q^33 + 3 * q^34 + 4 * q^35 + 14 * q^36 - 11 * q^37 + 16 * q^38 - q^40 + 7 * q^41 + 16 * q^42 + 16 * q^43 - 4 * q^44 + 66 * q^45 - 8 * q^46 - 32 * q^47 + 5 * q^49 - 20 * q^50 - 64 * q^51 - 6 * q^52 - 22 * q^53 + 12 * q^54 - 32 * q^55 + 20 * q^57 + 3 * q^58 - 4 * q^59 + 8 * q^60 - 9 * q^61 - 4 * q^62 + 24 * q^63 + 6 * q^64 - 2 * q^65 - 24 * q^66 + 16 * q^67 - 6 * q^68 + 4 * q^69 + 4 * q^70 + 12 * q^71 - 7 * q^72 + 4 * q^73 - 2 * q^74 + 88 * q^75 - 8 * q^76 - 12 * q^77 + 4 * q^79 + 2 * q^80 - 11 * q^81 - 14 * q^82 - 4 * q^83 - 32 * q^84 - 18 * q^85 - 8 * q^86 - 16 * q^87 + 8 * q^88 - 9 * q^89 - 33 * q^90 - 8 * q^92 - 20 * q^93 + 16 * q^94 + 36 * q^95 + 26 * q^97 + 5 * q^98 - 52 * q^99

Introduction

L-functions

Modular forms

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