LMFDB - Embedded newform 74.2.c.c.63.3

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			63.3
Root			$-0.827721 + 1.43366i$ of defining polynomial
Character	$\chi$	$=$	74.63
Dual form			74.2.c.c.47.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.52569 - 2.64257i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.629755 + 1.09077i) q^{5} -3.05137 q^{6} +(-1.52569 + 2.64257i) q^{7} +1.00000 q^{8} +(-3.15544 - 5.46539i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.52569 - 2.64257i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.629755 + 1.09077i) q^{5} -3.05137 q^{6} +(-1.52569 + 2.64257i) q^{7} +1.00000 q^{8} +(-3.15544 - 5.46539i) q^{9} +1.25951 q^{10} +5.31088 q^{11} +(1.52569 + 2.64257i) q^{12} +(-1.00000 + 1.73205i) q^{13} +3.05137 q^{14} +(1.92162 + 3.32834i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.55137 - 4.41911i) q^{17} +(-3.15544 + 5.46539i) q^{18} +(-2.39593 + 4.14988i) q^{19} +(-0.629755 - 1.09077i) q^{20} +(4.65544 + 8.06346i) q^{21} +(-2.65544 - 4.59936i) q^{22} +1.74049 q^{23} +(1.52569 - 2.64257i) q^{24} +(1.70682 + 2.95629i) q^{25} +2.00000 q^{26} -10.1027 q^{27} +(-1.52569 - 2.64257i) q^{28} -4.05137 q^{29} +(1.92162 - 3.32834i) q^{30} -0.791864 q^{31} +(-0.500000 + 0.866025i) q^{32} +(8.10275 - 14.0344i) q^{33} +(-2.55137 + 4.41911i) q^{34} +(-1.92162 - 3.32834i) q^{35} +6.31088 q^{36} +(-1.37024 - 5.92642i) q^{37} +4.79186 q^{38} +(3.05137 + 5.28514i) q^{39} +(-0.629755 + 1.09077i) q^{40} +(0.104068 - 0.180251i) q^{41} +(4.65544 - 8.06346i) q^{42} -4.36226 q^{43} +(-2.65544 + 4.59936i) q^{44} +7.94863 q^{45} +(-0.870245 - 1.50731i) q^{46} -3.20814 q^{47} -3.05137 q^{48} +(-1.15544 - 2.00128i) q^{49} +(1.70682 - 2.95629i) q^{50} -15.5704 q^{51} +(-1.00000 - 1.73205i) q^{52} +(-5.65544 - 9.79551i) q^{53} +(5.05137 + 8.74924i) q^{54} +(-3.34456 + 5.79294i) q^{55} +(-1.52569 + 2.64257i) q^{56} +(7.31088 + 12.6628i) q^{57} +(2.02569 + 3.50859i) q^{58} +(6.36226 + 11.0198i) q^{59} -3.84324 q^{60} +(-3.02569 + 5.24064i) q^{61} +(0.395932 + 0.685774i) q^{62} +19.2569 q^{63} +1.00000 q^{64} +(-1.25951 - 2.18154i) q^{65} -16.2055 q^{66} +(4.65544 - 8.06346i) q^{67} +5.10275 q^{68} +(2.65544 - 4.59936i) q^{69} +(-1.92162 + 3.32834i) q^{70} +(3.52569 - 6.10667i) q^{71} +(-3.15544 - 5.46539i) q^{72} -3.31088 q^{73} +(-4.44731 + 4.14988i) q^{74} +10.4163 q^{75} +(-2.39593 - 4.14988i) q^{76} +(-8.10275 + 14.0344i) q^{77} +(3.05137 - 5.28514i) q^{78} +(5.70682 - 9.88450i) q^{79} +1.25951 q^{80} +(-5.94731 + 10.3010i) q^{81} -0.208136 q^{82} +(1.78520 + 3.09205i) q^{83} -9.31088 q^{84} +6.42697 q^{85} +(2.18113 + 3.77783i) q^{86} +(-6.18113 + 10.7060i) q^{87} +5.31088 q^{88} +(-1.63642 - 2.83436i) q^{89} +(-3.97431 - 6.88371i) q^{90} +(-3.05137 - 5.28514i) q^{91} +(-0.870245 + 1.50731i) q^{92} +(-1.20814 + 2.09255i) q^{93} +(1.60407 + 2.77833i) q^{94} +(-3.01770 - 5.22681i) q^{95} +(1.52569 + 2.64257i) q^{96} +2.20814 q^{97} +(-1.15544 + 2.00128i) q^{98} +(-16.7582 - 29.0260i) 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 $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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
$3$	1.52569	−	2.64257i	0.880856	−	1.52569i	0.0304649	−	0.999536i	$-0.490301\pi$
$3$	1.52569	−	2.64257i	0.880856	−	1.52569i	0.850391	−	0.526151i	$-0.176365\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.629755	+	1.09077i	−0.281635	+	0.487806i	−0.971788	−	0.235858i	$-0.924210\pi$
$5$	−0.629755	+	1.09077i	−0.281635	+	0.487806i	0.690153	+	0.723664i	$0.257543\pi$
$6$	−3.05137			−1.24572
$7$	−1.52569	+	2.64257i	−0.576656	+	0.998797i	0.419204	+	0.907892i	$0.362309\pi$
$7$	−1.52569	+	2.64257i	−0.576656	+	0.998797i	−0.995860	+	0.0909046i	$0.971024\pi$
$8$	1.00000			0.353553
$9$	−3.15544	−	5.46539i	−1.05181	−	1.82180i
$10$	1.25951			0.398292
$11$	5.31088			1.60129			0.800646	−	0.599138i	$-0.204490\pi$
$11$	5.31088			1.60129			0.800646	+	0.599138i	$0.204490\pi$
$12$	1.52569	+	2.64257i	0.440428	+	0.762844i
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	3.05137			0.815514
$15$	1.92162	+	3.32834i	0.496160	+	0.859374i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.55137	−	4.41911i	−0.618799	−	1.07179i	−0.989705	−	0.143121i	$-0.954286\pi$
$17$	−2.55137	−	4.41911i	−0.618799	−	1.07179i	0.370906	−	0.928670i	$-0.379047\pi$
$18$	−3.15544	+	5.46539i	−0.743745	+	1.28820i
$19$	−2.39593	+	4.14988i	−0.549664	+	0.952047i	0.448633	+	0.893716i	$0.351911\pi$
$19$	−2.39593	+	4.14988i	−0.549664	+	0.952047i	−0.998297	+	0.0583306i	$0.981422\pi$
$20$	−0.629755	−	1.09077i	−0.140818	−	0.243903i
$21$	4.65544	+	8.06346i	1.01590	+	1.75959i
$22$	−2.65544	−	4.59936i	−0.566142	−	0.980587i
$23$	1.74049			0.362917			0.181459	−	0.983399i	$-0.441918\pi$
$23$	1.74049			0.362917			0.181459	+	0.983399i	$0.441918\pi$
$24$	1.52569	−	2.64257i	0.311430	−	0.539412i
$25$	1.70682	+	2.95629i	0.341363	+	0.591259i
$26$	2.00000			0.392232
$27$	−10.1027			−1.94427
$28$	−1.52569	−	2.64257i	−0.288328	−	0.499398i
$29$	−4.05137			−0.752321			−0.376161	−	0.926554i	$-0.622756\pi$
$29$	−4.05137			−0.752321			−0.376161	+	0.926554i	$0.622756\pi$
$30$	1.92162	−	3.32834i	0.350838	−	0.607669i
$31$	−0.791864			−0.142223			−0.0711115	−	0.997468i	$-0.522655\pi$
$31$	−0.791864			−0.142223			−0.0711115	+	0.997468i	$0.522655\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	8.10275	−	14.0344i	1.41051	−	2.44307i
$34$	−2.55137	+	4.41911i	−0.437557	+	0.757871i
$35$	−1.92162	−	3.32834i	−0.324813	−	0.562592i
$36$	6.31088			1.05181
$37$	−1.37024	−	5.92642i	−0.225267	−	0.974297i
$37$	−1.37024	−	5.92642i	−0.225267	−	0.974297i
$38$	4.79186			0.777343
$39$	3.05137	+	5.28514i	0.488611	+	0.846299i
$40$	−0.629755	+	1.09077i	−0.0995730	+	0.172466i
$41$	0.104068	−	0.180251i	0.0162527	−	0.0281505i	−0.857785	−	0.514009i	$-0.828160\pi$
$41$	0.104068	−	0.180251i	0.0162527	−	0.0281505i	0.874037	+	0.485859i	$0.161493\pi$
$42$	4.65544	−	8.06346i	0.718350	−	1.24422i
$43$	−4.36226			−0.665238			−0.332619	−	0.943061i	$-0.607932\pi$
$43$	−4.36226			−0.665238			−0.332619	+	0.943061i	$0.607932\pi$
$44$	−2.65544	+	4.59936i	−0.400323	+	0.693380i
$45$	7.94863			1.18491
$46$	−0.870245	−	1.50731i	−0.128311	−	0.222240i
$47$	−3.20814			−0.467955			−0.233977	−	0.972242i	$-0.575174\pi$
$47$	−3.20814			−0.467955			−0.233977	+	0.972242i	$0.575174\pi$
$48$	−3.05137			−0.440428
$49$	−1.15544	−	2.00128i	−0.165063	−	0.285898i
$50$	1.70682	−	2.95629i	0.241380	−	0.418083i
$51$	−15.5704			−2.18029
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	−5.65544	−	9.79551i	−0.776835	−	1.34552i	−0.933757	−	0.357906i	$-0.883491\pi$
$53$	−5.65544	−	9.79551i	−0.776835	−	1.34552i	0.156923	−	0.987611i	$-0.449843\pi$
$54$	5.05137	+	8.74924i	0.687405	+	1.19062i
$55$	−3.34456	+	5.79294i	−0.450980	+	0.781120i
$56$	−1.52569	+	2.64257i	−0.203879	+	0.353128i
$57$	7.31088	+	12.6628i	0.968350	+	1.67723i
$58$	2.02569	+	3.50859i	0.265986	+	0.460701i
$59$	6.36226	+	11.0198i	0.828296	+	1.43465i	0.899374	+	0.437179i	$0.144022\pi$
$59$	6.36226	+	11.0198i	0.828296	+	1.43465i	−0.0710788	+	0.997471i	$0.522644\pi$
$60$	−3.84324			−0.496160
$61$	−3.02569	+	5.24064i	−0.387400	+	0.670996i	−0.992099	−	0.125458i	$-0.959960\pi$
$61$	−3.02569	+	5.24064i	−0.387400	+	0.670996i	0.604699	+	0.796454i	$0.293293\pi$
$62$	0.395932	+	0.685774i	0.0502834	+	0.0870934i
$63$	19.2569			2.42614
$64$	1.00000			0.125000
$65$	−1.25951	−	2.18154i	−0.156223	−	0.270586i
$66$	−16.2055			−1.99476
$67$	4.65544	−	8.06346i	0.568753	−	0.985109i	−0.427937	−	0.903809i	$-0.640759\pi$
$67$	4.65544	−	8.06346i	0.568753	−	0.985109i	0.996690	−	0.0813001i	$-0.0259072\pi$
$68$	5.10275			0.618799
$69$	2.65544	−	4.59936i	0.319678	−	0.553698i
$70$	−1.92162	+	3.32834i	−0.229677	+	0.397813i
$71$	3.52569	−	6.10667i	0.418422	−	0.724728i	−0.577359	−	0.816491i	$-0.695917\pi$
$71$	3.52569	−	6.10667i	0.418422	−	0.724728i	0.995781	+	0.0917622i	$0.0292500\pi$
$72$	−3.15544	−	5.46539i	−0.371872	−	0.644102i
$73$	−3.31088			−0.387510			−0.193755	−	0.981050i	$-0.562067\pi$
$73$	−3.31088			−0.387510			−0.193755	+	0.981050i	$0.562067\pi$
$74$	−4.44731	+	4.14988i	−0.516989	+	0.482413i
$75$	10.4163			1.20277
$76$	−2.39593	−	4.14988i	−0.274832	−	0.476023i
$77$	−8.10275	+	14.0344i	−0.923394	+	1.59937i
$78$	3.05137	−	5.28514i	0.345500	−	0.598424i
$79$	5.70682	−	9.88450i	0.642067	−	1.11209i	−0.342904	−	0.939371i	$-0.611410\pi$
$79$	5.70682	−	9.88450i	0.642067	−	1.11209i	0.984971	−	0.172722i	$-0.0552563\pi$
$80$	1.25951			0.140818
$81$	−5.94731	+	10.3010i	−0.660812	+	1.14456i
$82$	−0.208136			−0.0229848
$83$	1.78520	+	3.09205i	0.195951	+	0.339397i	0.947212	−	0.320608i	$-0.103887\pi$
$83$	1.78520	+	3.09205i	0.195951	+	0.339397i	−0.751261	+	0.660005i	$0.770554\pi$
$84$	−9.31088			−1.01590
$85$	6.42697			0.697102
$86$	2.18113	+	3.77783i	0.235197	+	0.407374i
$87$	−6.18113	+	10.7060i	−0.662687	+	1.14781i
$88$	5.31088			0.566142
$89$	−1.63642	−	2.83436i	−0.173460	−	0.300442i	0.766167	−	0.642641i	$-0.222162\pi$
$89$	−1.63642	−	2.83436i	−0.173460	−	0.300442i	−0.939627	+	0.342199i	$0.888828\pi$
$90$	−3.97431	−	6.88371i	−0.418929	−	0.725607i
$91$	−3.05137	−	5.28514i	−0.319871	−	0.554033i
$92$	−0.870245	+	1.50731i	−0.0907293	+	0.157148i
$93$	−1.20814	+	2.09255i	−0.125278	+	0.216988i
$94$	1.60407	+	2.77833i	0.165447	+	0.286563i
$95$	−3.01770	−	5.22681i	−0.309610	−	0.536260i
$96$	1.52569	+	2.64257i	0.155715	+	0.269706i
$97$	2.20814			0.224202			0.112101	−	0.993697i	$-0.464242\pi$
$97$	2.20814			0.224202			0.112101	+	0.993697i	$0.464242\pi$
$98$	−1.15544	+	2.00128i	−0.116717	+	0.202160i
$99$	−16.7582	−	29.0260i	−1.68426	−	2.91723i
$100$	−3.41363			−0.341363
$101$	3.36226			0.334557			0.167279	−	0.985910i	$-0.446502\pi$
$101$	3.36226			0.334557			0.167279	+	0.985910i	$0.446502\pi$
$102$	7.78520	+	13.4844i	0.770849	+	1.33515i
$103$	17.1541			1.69025			0.845123	−	0.534572i	$-0.179527\pi$
$103$	17.1541			1.69025			0.845123	+	0.534572i	$0.179527\pi$
$104$	−1.00000	+	1.73205i	−0.0980581	+	0.169842i
$105$	−11.7272			−1.14445
$106$	−5.65544	+	9.79551i	−0.549305	+	0.951424i
$107$	−0.181130	+	0.313726i	−0.0175104	+	0.0303290i	−0.874648	−	0.484759i	$-0.838907\pi$
$107$	−0.181130	+	0.313726i	−0.0175104	+	0.0303290i	0.857137	+	0.515088i	$0.172241\pi$
$108$	5.05137	−	8.74924i	0.486069	−	0.841896i
$109$	−0.233823	−	0.404994i	−0.0223962	−	0.0387914i	0.854610	−	0.519270i	$-0.173796\pi$
$109$	−0.233823	−	0.404994i	−0.0223962	−	0.0387914i	−0.877006	+	0.480479i	$0.840463\pi$
$110$	6.68912			0.637782
$111$	−17.7515	−	5.42090i	−1.68490	−	0.514529i
$112$	3.05137			0.288328
$113$	0.344558	+	0.596791i	0.0324133	+	0.0561414i	0.881777	−	0.471667i	$-0.156347\pi$
$113$	0.344558	+	0.596791i	0.0324133	+	0.0561414i	−0.849364	+	0.527808i	$0.823014\pi$
$114$	7.31088	−	12.6628i	0.684727	−	1.18598i
$115$	−1.09608	+	1.89847i	−0.102210	+	0.177033i
$116$	2.02569	−	3.50859i	0.188080	−	0.325765i
$117$	12.6218			1.16688
$118$	6.36226	−	11.0198i	0.585693	−	1.01445i
$119$	15.5704			1.42734
$120$	1.92162	+	3.32834i	0.175419	+	0.303835i
$121$	17.2055			1.56414
$122$	6.05137			0.547866
$123$	−0.317551	−	0.550014i	−0.0286326	−	0.0495931i
$124$	0.395932	−	0.685774i	0.0355557	−	0.0615843i
$125$	−10.5971			−0.947830
$126$	−9.62844	−	16.6769i	−0.857769	−	1.48570i
$127$	7.49201	+	12.9765i	0.664809	+	1.15148i	0.979337	+	0.202234i	$0.0648203\pi$
$127$	7.49201	+	12.9765i	0.664809	+	1.15148i	−0.314528	+	0.949248i	$0.601846\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−6.65544	+	11.5276i	−0.585979	+	1.01495i
$130$	−1.25951	+	2.18154i	−0.110466	+	0.191333i
$131$	−6.04471	−	10.4697i	−0.528129	−	0.914746i	−0.999462	−	0.0327906i	$-0.989561\pi$
$131$	−6.04471	−	10.4697i	−0.528129	−	0.914746i	0.471334	−	0.881955i	$-0.343773\pi$
$132$	8.10275	+	14.0344i	0.705254	+	1.22154i
$133$	−7.31088	−	12.6628i	−0.633934	−	1.09801i
$134$	−9.31088			−0.804338
$135$	6.36226	−	11.0198i	0.547576	−	0.948430i
$136$	−2.55137	−	4.41911i	−0.218779	−	0.378936i
$137$	−16.6865			−1.42562			−0.712811	−	0.701356i	$-0.752578\pi$
$137$	−16.6865			−1.42562			−0.712811	+	0.701356i	$0.752578\pi$
$138$	−5.31088			−0.452093
$139$	9.09608	+	15.7549i	0.771520	+	1.33631i	0.936730	+	0.350053i	$0.113836\pi$
$139$	9.09608	+	15.7549i	0.771520	+	1.33631i	−0.165210	+	0.986258i	$0.552830\pi$
$140$	3.84324			0.324813
$141$	−4.89461	+	8.47772i	−0.412201	+	0.713953i
$142$	−7.05137			−0.591738
$143$	−5.31088	+	9.19872i	−0.444118	+	0.769236i
$144$	−3.15544	+	5.46539i	−0.262954	+	0.455449i
$145$	2.55137	−	4.41911i	0.211880	−	0.366987i
$146$	1.65544	+	2.86731i	0.137005	+	0.237300i
$147$	−7.05137			−0.581588
$148$	5.81755	+	1.77654i	0.478200	+	0.146031i
$149$	13.5324			1.10861			0.554307	−	0.832312i	$-0.312983\pi$
$149$	13.5324			1.10861			0.554307	+	0.832312i	$0.312983\pi$
$150$	−5.20814	−	9.02076i	−0.425243	−	0.736542i
$151$	−0.610734	+	1.05782i	−0.0497008	+	0.0860844i	−0.889806	−	0.456340i	$-0.849160\pi$
$151$	−0.610734	+	1.05782i	−0.0497008	+	0.0860844i	0.840105	+	0.542424i	$0.182493\pi$
$152$	−2.39593	+	4.14988i	−0.194336	+	0.336599i
$153$	−16.1014	+	27.8885i	−1.30172	+	2.25465i
$154$	16.2055			1.30588
$155$	0.498680	−	0.863740i	0.0400550	−	0.0693772i
$156$	−6.10275			−0.488611
$157$	−9.38795	−	16.2604i	−0.749240	−	1.29772i	−0.948188	−	0.317711i	$-0.897086\pi$
$157$	−9.38795	−	16.2604i	−0.749240	−	1.29772i	0.198948	−	0.980010i	$-0.436248\pi$
$158$	−11.4136			−0.908020
$159$	−34.5137			−2.73712
$160$	−0.629755	−	1.09077i	−0.0497865	−	0.0862328i
$161$	−2.65544	+	4.59936i	−0.209278	+	0.362480i
$162$	11.8946			0.934529
$163$	3.92162	+	6.79244i	0.307165	+	0.532025i	0.977741	−	0.209816i	$-0.0672863\pi$
$163$	3.92162	+	6.79244i	0.307165	+	0.532025i	−0.670576	+	0.741841i	$0.733953\pi$
$164$	0.104068	+	0.180251i	0.00812636	+	0.0140753i
$165$	10.2055	+	17.6764i	0.794497	+	1.37611i
$166$	1.78520	−	3.09205i	0.138558	−	0.239990i
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	−0.534875	−	0.844931i	$-0.679641\pi$
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	0.999169	+	0.0407502i	$0.0129748\pi$
$168$	4.65544	+	8.06346i	0.359175	+	0.622110i
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	−3.21348	−	5.56592i	−0.246463	−	0.426886i
$171$	30.2409			2.31258
$172$	2.18113	−	3.77783i	0.166310	−	0.288057i
$173$	−2.23382	−	3.86910i	−0.169834	−	0.294162i	0.768527	−	0.639817i	$-0.220990\pi$
$173$	−2.23382	−	3.86910i	−0.169834	−	0.294162i	−0.938362	+	0.345655i	$0.887657\pi$
$174$	12.3623			0.937180
$175$	−10.4163			−0.787396
$176$	−2.65544	−	4.59936i	−0.200162	−	0.346690i
$177$	38.8273			2.91844
$178$	−1.63642	+	2.83436i	−0.122655	+	0.212445i
$179$	−14.1027			−1.05409			−0.527044	−	0.849838i	$-0.676700\pi$
$179$	−14.1027			−1.05409			−0.527044	+	0.849838i	$0.676700\pi$
$180$	−3.97431	+	6.88371i	−0.296228	+	0.513082i
$181$	−6.73250	+	11.6610i	−0.500423	+	0.866758i	0.499577	+	0.866270i	$0.333489\pi$
$181$	−6.73250	+	11.6610i	−0.500423	+	0.866758i	−1.00000		0.000488579i	$0.999844\pi$
$182$	−3.05137	+	5.28514i	−0.226183	+	0.391760i
$183$	9.23250	+	15.9912i	0.682486	+	1.18210i
$184$	1.74049			0.128311
$185$	7.32727	+	2.23757i	0.538711	+	0.164510i
$186$	2.41627			0.177170
$187$	−13.5501	−	23.4694i	−0.990878	−	1.71625i
$188$	1.60407	−	2.77833i	0.116989	−	0.202630i
$189$	15.4136	−	26.6972i	1.12118	−	1.94194i
$190$	−3.01770	+	5.22681i	−0.218927	+	0.379193i
$191$	9.42697			0.682111			0.341056	−	0.940043i	$-0.389216\pi$
$191$	9.42697			0.682111			0.341056	+	0.940043i	$0.389216\pi$
$192$	1.52569	−	2.64257i	0.110107	−	0.190711i
$193$	2.48098			0.178585			0.0892924	−	0.996005i	$-0.471539\pi$
$193$	2.48098			0.178585			0.0892924	+	0.996005i	$0.471539\pi$
$194$	−1.10407	−	1.91230i	−0.0792675	−	0.137295i
$195$	−7.68648			−0.550440
$196$	2.31088			0.165063
$197$	0.974313	+	1.68756i	0.0694169	+	0.120234i	0.898645	−	0.438677i	$-0.144553\pi$
$197$	0.974313	+	1.68756i	0.0694169	+	0.120234i	−0.829228	+	0.558911i	$0.811219\pi$
$198$	−16.7582	+	29.0260i	−1.19095	+	2.06279i
$199$	−1.98667			−0.140831			−0.0704156	−	0.997518i	$-0.522433\pi$
$199$	−1.98667			−0.140831			−0.0704156	+	0.997518i	$0.522433\pi$
$200$	1.70682	+	2.95629i	0.120690	+	0.209041i
$201$	−14.2055	−	24.6046i	−1.00198	−	1.73548i
$202$	−1.68113	−	2.91180i	−0.118284	−	0.204874i
$203$	6.18113	−	10.7060i	0.433830	−	0.751416i
$204$	7.78520	−	13.4844i	0.545073	−	0.944094i
$205$	0.131075	+	0.227028i	0.00915467	+	0.0158564i
$206$	−8.57706	−	14.8559i	−0.597592	−	1.03506i
$207$	−5.49201	−	9.51245i	−0.381721	−	0.661161i
$208$	2.00000			0.138675
$209$	−12.7245	+	22.0395i	−0.880173	+	1.52450i
$210$	5.86358	+	10.1560i	0.404625	+	0.700832i
$211$	−17.0868			−1.17630			−0.588151	−	0.808751i	$-0.700144\pi$
$211$	−17.0868			−1.17630			−0.588151	+	0.808751i	$0.700144\pi$
$212$	11.3109			0.776835
$213$	−10.7582	−	18.6337i	−0.737139	−	1.27676i
$214$	0.362259			0.0247635
$215$	2.74716	−	4.75821i	0.187354	−	0.324507i
$216$	−10.1027			−0.687405
$217$	1.20814	−	2.09255i	0.0820136	−	0.142052i
$218$	−0.233823	+	0.404994i	−0.0158365	+	0.0274297i
$219$	−5.05137	+	8.74924i	−0.341340	+	0.591219i
$220$	−3.34456	−	5.79294i	−0.225490	−	0.390560i
$221$	10.2055			0.686496
$222$	4.18113	+	18.0837i	0.280619	+	1.21370i
$223$	1.94599			0.130313			0.0651564	−	0.997875i	$-0.479245\pi$
$223$	1.94599			0.130313			0.0651564	+	0.997875i	$0.479245\pi$
$224$	−1.52569	−	2.64257i	−0.101939	−	0.176564i
$225$	10.7715	−	18.6568i	0.718102	−	1.24379i
$226$	0.344558	−	0.596791i	0.0229196	−	0.0396980i
$227$	−2.29318	+	3.97191i	−0.152204	+	0.263625i	−0.932037	−	0.362362i	$-0.881970\pi$
$227$	−2.29318	+	3.97191i	−0.152204	+	0.263625i	0.779833	+	0.625987i	$0.215304\pi$
$228$	−14.6218			−0.968350
$229$	0.817551	−	1.41604i	0.0540253	−	0.0935745i	−0.837748	−	0.546057i	$-0.816128\pi$
$229$	0.817551	−	1.41604i	0.0540253	−	0.0935745i	0.891773	+	0.452483i	$0.149462\pi$
$230$	2.19216			0.144547
$231$	24.7245	+	42.8241i	1.62675	+	2.81762i
$232$	−4.05137			−0.265986
$233$	8.03804			0.526590			0.263295	−	0.964715i	$-0.415191\pi$
$233$	8.03804			0.526590			0.263295	+	0.964715i	$0.415191\pi$
$234$	−6.31088	−	10.9308i	−0.412555	−	0.714567i
$235$	2.02034	−	3.49933i	0.131792	−	0.228271i
$236$	−12.7245			−0.828296
$237$	−17.4136	−	30.1613i	−1.13114	−	1.95919i
$238$	−7.78520	−	13.4844i	−0.504639	−	0.874061i
$239$	−0.317551	−	0.550014i	−0.0205407	−	0.0355775i	0.855572	−	0.517683i	$-0.173205\pi$
$239$	−0.317551	−	0.550014i	−0.0205407	−	0.0355775i	−0.876113	+	0.482106i	$0.839872\pi$
$240$	1.92162	−	3.32834i	0.124040	−	0.214844i
$241$	3.75819	−	6.50938i	0.242086	−	0.419306i	−0.719222	−	0.694780i	$-0.755502\pi$
$241$	3.75819	−	6.50938i	0.242086	−	0.419306i	0.961308	+	0.275474i	$0.0888349\pi$
$242$	−8.60275	−	14.9004i	−0.553006	−	0.957834i
$243$	2.99333	+	5.18461i	0.192022	+	0.332593i
$244$	−3.02569	−	5.24064i	−0.193700	−	0.335498i
$245$	2.91058			0.185950
$246$	−0.317551	+	0.550014i	−0.0202463	+	0.0350676i
$247$	−4.79186	−	8.29975i	−0.304899	−	0.528101i
$248$	−0.791864			−0.0502834
$249$	10.8946			0.690418
$250$	5.29853	+	9.17732i	0.335108	+	0.580425i
$251$	−8.88128			−0.560581			−0.280291	−	0.959915i	$-0.590431\pi$
$251$	−8.88128			−0.560581			−0.280291	+	0.959915i	$0.590431\pi$
$252$	−9.62844	+	16.6769i	−0.606534	+	1.05055i
$253$	9.24354			0.581136
$254$	7.49201	−	12.9765i	0.470091	−	0.814221i
$255$	9.80554	−	16.9837i	0.614047	−	1.06356i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.05005	+	10.4790i	0.377392	+	0.653662i	0.990682	−	0.136196i	$-0.0434876\pi$
$257$	6.05005	+	10.4790i	0.377392	+	0.653662i	−0.613290	+	0.789858i	$0.710154\pi$
$258$	13.3109			0.828699
$259$	17.7515	+	5.42090i	1.10303	+	0.336838i
$260$	2.51902			0.156223
$261$	12.7839	+	22.1423i	0.791302	+	1.37058i
$262$	−6.04471	+	10.4697i	−0.373443	+	0.646823i
$263$	9.57040	−	16.5764i	0.590136	−	1.02215i	−0.404078	−	0.914725i	$-0.632408\pi$
$263$	9.57040	−	16.5764i	0.590136	−	1.02215i	0.994214	−	0.107421i	$-0.0342592\pi$
$264$	8.10275	−	14.0344i	0.498690	−	0.863756i
$265$	14.2462			0.875136
$266$	−7.31088	+	12.6628i	−0.448259	+	0.776408i
$267$	−9.98667			−0.611174
$268$	4.65544	+	8.06346i	0.284376	+	0.492554i
$269$	−15.7892			−0.962686			−0.481343	−	0.876532i	$-0.659851\pi$
$269$	−15.7892			−0.962686			−0.481343	+	0.876532i	$0.659851\pi$
$270$	−12.7245			−0.774390
$271$	9.55005	+	16.5412i	0.580125	+	1.00481i	0.995464	+	0.0951386i	$0.0303294\pi$
$271$	9.55005	+	16.5412i	0.580125	+	1.00481i	−0.415340	+	0.909666i	$0.636337\pi$
$272$	−2.55137	+	4.41911i	−0.154700	+	0.267948i
$273$	−18.6218			−1.12704
$274$	8.34324	+	14.4509i	0.504033	+	0.873012i
$275$	9.06471	+	15.7005i	0.546622	+	0.946778i
$276$	2.65544	+	4.59936i	0.159839	+	0.276849i
$277$	−8.20015	+	14.2031i	−0.492699	+	0.853380i	−0.999965	−	0.00840971i	$-0.997323\pi$
$277$	−8.20015	+	14.2031i	−0.492699	+	0.853380i	0.507265	+	0.861790i	$0.330656\pi$
$278$	9.09608	−	15.7549i	0.545547	−	0.944915i
$279$	2.49868	+	4.32784i	0.149592	+	0.259101i
$280$	−1.92162	−	3.32834i	−0.114839	−	0.198906i
$281$	2.39725	+	4.15216i	0.143008	+	0.247697i	0.928628	−	0.371012i	$-0.120989\pi$
$281$	2.39725	+	4.15216i	0.143008	+	0.247697i	−0.785620	+	0.618709i	$0.787656\pi$
$282$	9.78922			0.582940
$283$	−12.9730	+	22.4699i	−0.771164	+	1.33570i	0.165761	+	0.986166i	$0.446992\pi$
$283$	−12.9730	+	22.4699i	−0.771164	+	1.33570i	−0.936925	+	0.349530i	$0.886341\pi$
$284$	3.52569	+	6.10667i	0.209211	+	0.362364i
$285$	−18.4163			−1.09089
$286$	10.6218			0.628078
$287$	0.317551	+	0.550014i	0.0187444	+	0.0324663i
$288$	6.31088			0.371872
$289$	−4.51902	+	7.82717i	−0.265825	+	0.460422i
$290$	−5.10275			−0.299644
$291$	3.36893	−	5.83515i	0.197490	−	0.342063i
$292$	1.65544	−	2.86731i	0.0968774	−	0.167797i
$293$	−11.0257	+	19.0971i	−0.644128	+	1.11566i	0.340375	+	0.940290i	$0.389446\pi$
$293$	−11.0257	+	19.0971i	−0.644128	+	1.11566i	−0.984502	+	0.175372i	$0.943887\pi$
$294$	3.52569	+	6.10667i	0.205622	+	0.356148i
$295$	−16.0267			−0.933108
$296$	−1.37024	−	5.92642i	−0.0796439	−	0.344466i
$297$	−53.6545			−3.11335
$298$	−6.76618	−	11.7194i	−0.391954	−	0.678884i
$299$	−1.74049	+	3.01462i	−0.100655	+	0.174340i
$300$	−5.20814	+	9.02076i	−0.300692	+	0.520814i
$301$	6.65544	−	11.5276i	0.383613	−	0.664438i
$302$	1.22147			0.0702876
$303$	5.12976	−	8.88500i	0.294697	−	0.510430i
$304$	4.79186			0.274832
$305$	−3.81088	−	6.60065i	−0.218211	−	0.377952i
$306$	32.2029			1.84091
$307$	−5.74049			−0.327627			−0.163814	−	0.986491i	$-0.552380\pi$
$307$	−5.74049			−0.327627			−0.163814	+	0.986491i	$0.552380\pi$
$308$	−8.10275	−	14.0344i	−0.461697	−	0.799683i
$309$	26.1718	−	45.3309i	1.48886	−	2.57879i
$310$	−0.997361			−0.0566463
$311$	5.26618	+	9.12129i	0.298617	+	0.517221i	0.975820	−	0.218576i	$-0.0701412\pi$
$311$	5.26618	+	9.12129i	0.298617	+	0.517221i	−0.677202	+	0.735797i	$0.736808\pi$
$312$	3.05137	+	5.28514i	0.172750	+	0.299212i
$313$	−12.4150	−	21.5033i	−0.701735	−	1.21544i	−0.967857	−	0.251501i	$-0.919076\pi$
$313$	−12.4150	−	21.5033i	−0.701735	−	1.21544i	0.266122	−	0.963939i	$-0.414257\pi$
$314$	−9.38795	+	16.2604i	−0.529792	+	0.917627i
$315$	−12.1271	+	21.0048i	−0.683286	+	1.18349i
$316$	5.70682	+	9.88450i	0.321034	+	0.556046i
$317$	13.1461	+	22.7698i	0.738361	+	1.27888i	0.953233	+	0.302236i	$0.0977331\pi$
$317$	13.1461	+	22.7698i	0.738361	+	1.27888i	−0.214873	+	0.976642i	$0.568934\pi$
$318$	17.2569	+	29.8898i	0.967717	+	1.67614i
$319$	−21.5164			−1.20469
$320$	−0.629755	+	1.09077i	−0.0352044	+	0.0609758i
$321$	0.552694	+	0.957294i	0.0308484	+	0.0534309i
$322$	5.31088			0.295964
$323$	24.4517			1.36053
$324$	−5.94731	−	10.3010i	−0.330406	−	0.572280i
$325$	−6.82727			−0.378709
$326$	3.92162	−	6.79244i	0.217198	−	0.376199i
$327$	−1.42697			−0.0789114
$328$	0.104068	−	0.180251i	0.00574620	−	0.00995271i
$329$	4.89461	−	8.47772i	0.269849	−	0.467392i
$330$	10.2055	−	17.6764i	0.561794	−	0.973056i
$331$	−14.8946	−	25.7982i	−0.818682	−	1.41800i	−0.906654	−	0.421876i	$-0.861372\pi$
$331$	−14.8946	−	25.7982i	−0.818682	−	1.41800i	0.0879717	−	0.996123i	$-0.471961\pi$
$332$	−3.57040			−0.195951
$333$	−28.0664	+	26.1894i	−1.53803	+	1.43517i
$334$	−12.0000			−0.656611
$335$	5.86358	+	10.1560i	0.320362	+	0.554882i
$336$	4.65544	−	8.06346i	0.253975	−	0.439898i
$337$	6.36358	−	11.0220i	0.346646	−	0.600409i	−0.639005	−	0.769202i	$-0.720654\pi$
$337$	6.36358	−	11.0220i	0.346646	−	0.600409i	0.985651	+	0.168794i	$0.0539871\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$	2.10275			0.114206
$340$	−3.21348	+	5.56592i	−0.174276	+	0.301854i
$341$	−4.20550			−0.227740
$342$	−15.1204	−	26.1894i	−0.817620	−	1.41616i
$343$	−14.3082			−0.772573
$344$	−4.36226			−0.235197
$345$	3.34456	+	5.79294i	0.180065	+	0.311882i
$346$	−2.23382	+	3.86910i	−0.120091	+	0.208004i
$347$	29.5651			1.58714			0.793569	−	0.608480i	$-0.208220\pi$
$347$	29.5651			1.58714			0.793569	+	0.608480i	$0.208220\pi$
$348$	−6.18113	−	10.7060i	−0.331343	−	0.573903i
$349$	16.2515	+	28.1485i	0.869924	+	1.50675i	0.862073	+	0.506784i	$0.169166\pi$
$349$	16.2515	+	28.1485i	0.869924	+	1.50675i	0.00785093	+	0.999969i	$0.497501\pi$
$350$	5.20814	+	9.02076i	0.278387	+	0.482180i
$351$	10.1027	−	17.4985i	0.539245	−	0.933999i
$352$	−2.65544	+	4.59936i	−0.141536	+	0.245147i
$353$	−2.05269	−	3.55537i	−0.109254	−	0.189233i	0.806214	−	0.591624i	$-0.201513\pi$
$353$	−2.05269	−	3.55537i	−0.109254	−	0.189233i	−0.915468	+	0.402390i	$0.868179\pi$
$354$	−19.4136	−	33.6254i	−1.03182	−	1.78717i
$355$	4.44064	+	7.69141i	0.235685	+	0.408218i
$356$	3.27284			0.173460
$357$	23.7556	−	41.1458i	1.25728	−	2.17767i
$358$	7.05137	+	12.2133i	0.372677	+	0.645495i
$359$	−28.2055			−1.48863			−0.744315	−	0.667829i	$-0.767224\pi$
$359$	−28.2055			−1.48863			−0.744315	+	0.667829i	$0.767224\pi$
$360$	7.94863			0.418929
$361$	−1.98098	−	3.43116i	−0.104262	−	0.180587i
$362$	13.4650			0.707705
$363$	26.2502	−	45.4667i	1.37778	−	2.38638i
$364$	6.10275			0.319871
$365$	2.08505	−	3.61141i	0.109136	−	0.189030i
$366$	9.23250	−	15.9912i	0.482591	−	0.835872i
$367$	2.00000	−	3.46410i	0.104399	−	0.180825i	−0.809093	−	0.587680i	$-0.800041\pi$
$367$	2.00000	−	3.46410i	0.104399	−	0.180825i	0.913493	+	0.406855i	$0.133375\pi$
$368$	−0.870245	−	1.50731i	−0.0453646	−	0.0785739i
$369$	−1.31352			−0.0683793
$370$	−1.72584	−	7.46439i	−0.0897220	−	0.388055i
$371$	34.5137			1.79186
$372$	−1.20814	−	2.09255i	−0.0626389	−	0.108494i
$373$	−18.6785	+	32.3521i	−0.967136	+	1.67513i	−0.263371	+	0.964695i	$0.584834\pi$
$373$	−18.6785	+	32.3521i	−0.967136	+	1.67513i	−0.703765	+	0.710433i	$0.748499\pi$
$374$	−13.5501	+	23.4694i	−0.700657	+	1.21357i
$375$	−16.1678	+	28.0034i	−0.834901	+	1.44609i
$376$	−3.20814			−0.165447
$377$	4.05137	−	7.01719i	0.208656	−	0.361403i
$378$	−30.8273			−1.58558
$379$	2.45397	+	4.25040i	0.126052	+	0.218329i	0.922144	−	0.386848i	$-0.126436\pi$
$379$	2.45397	+	4.25040i	0.126052	+	0.218329i	−0.796092	+	0.605176i	$0.793103\pi$
$380$	6.03540			0.309610
$381$	45.7219			2.34240
$382$	−4.71348	−	8.16399i	−0.241163	−	0.417706i
$383$	−10.3042	+	17.8474i	−0.526521	+	0.911961i	0.473002	+	0.881062i	$0.343171\pi$
$383$	−10.3042	+	17.8474i	−0.526521	+	0.911961i	−0.999522	+	0.0308995i	$0.990163\pi$
$384$	−3.05137			−0.155715
$385$	−10.2055	−	17.6764i	−0.520120	−	0.900875i
$386$	−1.24049	−	2.14859i	−0.0631393	−	0.109360i
$387$	13.7649	+	23.8414i	0.699707	+	1.21193i
$388$	−1.10407	+	1.91230i	−0.0560506	+	0.0970824i
$389$	12.7839	−	22.1423i	0.648168	−	1.12266i	−0.335392	−	0.942079i	$-0.608869\pi$
$389$	12.7839	−	22.1423i	0.648168	−	1.12266i	0.983560	−	0.180582i	$-0.0577980\pi$
$390$	3.84324	+	6.65668i	0.194610	+	0.337074i
$391$	−4.44064	−	7.69141i	−0.224573	−	0.388972i
$392$	−1.15544	−	2.00128i	−0.0583587	−	0.101080i
$393$	−36.8893			−1.86082
$394$	0.974313	−	1.68756i	0.0490852	−	0.0850180i
$395$	7.18780	+	12.4496i	0.361657	+	0.626409i
$396$	33.5164			1.68426
$397$	−30.2923			−1.52033			−0.760163	−	0.649733i	$-0.774881\pi$
$397$	−30.2923			−1.52033			−0.760163	+	0.649733i	$0.774881\pi$
$398$	0.993334	+	1.72050i	0.0497913	+	0.0862411i
$399$	−44.6165			−2.23362
$400$	1.70682	−	2.95629i	0.0853408	−	0.147815i
$401$	27.5164			1.37410			0.687051	−	0.726609i	$-0.258905\pi$
$401$	27.5164			1.37410			0.687051	+	0.726609i	$0.258905\pi$
$402$	−14.2055	+	24.6046i	−0.708506	+	1.22717i
$403$	0.791864	−	1.37155i	0.0394455	−	0.0683217i
$404$	−1.68113	+	2.91180i	−0.0836393	+	0.144868i
$405$	−7.49069	−	12.9743i	−0.372216	−	0.644696i
$406$	−12.3623			−0.613529
$407$	−7.27721	−	31.4745i	−0.360718	−	1.56013i
$408$	−15.5704			−0.770849
$409$	−3.62309	−	6.27537i	−0.179150	−	0.310297i	0.762439	−	0.647060i	$-0.224001\pi$
$409$	−3.62309	−	6.27537i	−0.179150	−	0.310297i	−0.941590	+	0.336762i	$0.890668\pi$
$410$	0.131075	−	0.227028i	0.00647333	−	0.0112121i
$411$	−25.4583	+	44.0951i	−1.25577	+	2.17505i
$412$	−8.57706	+	14.8559i	−0.422561	+	0.731898i
$413$	−38.8273			−1.91056
$414$	−5.49201	+	9.51245i	−0.269918	+	0.467511i
$415$	−4.49695			−0.220747
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$	55.5111			2.71839
$418$	25.4490			1.24475
$419$	2.28388	+	3.95579i	0.111575	+	0.193253i	0.916405	−	0.400251i	$-0.131077\pi$
$419$	2.28388	+	3.95579i	0.111575	+	0.193253i	−0.804831	+	0.593505i	$0.797744\pi$
$420$	5.86358	−	10.1560i	0.286113	−	0.495563i
$421$	26.8432			1.30826			0.654130	−	0.756382i	$-0.273035\pi$
$421$	26.8432			1.30826			0.654130	+	0.756382i	$0.273035\pi$
$422$	8.54339	+	14.7976i	0.415886	+	0.720335i
$423$	10.1231	+	17.5337i	0.492201	+	0.852518i
$424$	−5.65544	−	9.79551i	−0.274653	−	0.475712i
$425$	8.70946	−	15.0852i	0.422471	−	0.731741i
$426$	−10.7582	+	18.6337i	−0.521236	+	0.902807i
$427$	−9.23250	−	15.9912i	−0.446792	−	0.773867i
$428$	−0.181130	−	0.313726i	−0.00875522	−	0.0151645i
$429$	16.2055	+	28.0687i	0.782409	+	1.35517i
$430$	−5.49431			−0.264959
$431$	10.3959	−	18.0063i	0.500754	−	0.867332i	−0.499245	−	0.866461i	$-0.666389\pi$
$431$	10.3959	−	18.0063i	0.500754	−	0.867332i	1.00000		0.000871345i	$-0.000277358\pi$
$432$	5.05137	+	8.74924i	0.243034	+	0.420948i
$433$	27.6572			1.32912			0.664559	−	0.747235i	$-0.268619\pi$
$433$	27.6572			1.32912			0.664559	+	0.747235i	$0.268619\pi$
$434$	−2.41627			−0.115985
$435$	−7.78520	−	13.4844i	−0.373272	−	0.646525i
$436$	0.467647			0.0223962
$437$	−4.17009	+	7.22282i	−0.199483	+	0.345514i
$438$	10.1027			0.482728
$439$	3.46765	−	6.00614i	0.165502	−	0.286657i	−0.771332	−	0.636433i	$-0.780409\pi$
$439$	3.46765	−	6.00614i	0.165502	−	0.286657i	0.936833	+	0.349776i	$0.113742\pi$
$440$	−3.34456	+	5.79294i	−0.159446	+	0.276168i
$441$	−7.29186	+	12.6299i	−0.347232	+	0.601423i
$442$	−5.10275	−	8.83822i	−0.242713	−	0.420391i
$443$	−19.8653			−0.943829			−0.471915	−	0.881644i	$-0.656437\pi$
$443$	−19.8653			−0.943829			−0.471915	+	0.881644i	$0.656437\pi$
$444$	13.5704	−	12.6628i	0.644022	−	0.600951i
$445$	4.12218			0.195410
$446$	−0.972993	−	1.68527i	−0.0460726	−	0.0798000i
$447$	20.6461	−	35.7602i	0.976529	−	1.69140i
$448$	−1.52569	+	2.64257i	−0.0720819	+	0.124850i
$449$	13.0691	−	22.6363i	0.616768	−	1.06827i	−0.373304	−	0.927709i	$-0.621775\pi$
$449$	13.0691	−	22.6363i	0.616768	−	1.06827i	0.990072	−	0.140564i	$-0.0448916\pi$
$450$	−21.5430			−1.01555
$451$	0.552694	−	0.957294i	0.0260253	−	0.0450772i
$452$	−0.689115			−0.0324133
$453$	1.86358	+	3.22781i	0.0875586	+	0.151656i
$454$	4.58637			0.215249
$455$	7.68648			0.360348
$456$	7.31088	+	12.6628i	0.342364	+	0.592991i
$457$	10.3432	−	17.9150i	0.483836	−	0.838029i	−0.515991	−	0.856594i	$-0.672576\pi$
$457$	10.3432	−	17.9150i	0.483836	−	0.838029i	0.999828	+	0.0185648i	$0.00590969\pi$
$458$	−1.63510			−0.0764033
$459$	25.7759	+	44.6452i	1.20312	+	2.08386i
$460$	−1.09608	−	1.89847i	−0.0511051	−	0.0885166i
$461$	−11.1027	−	19.2305i	−0.517107	−	0.895655i	−0.999803	−	0.0198669i	$-0.993676\pi$
$461$	−11.1027	−	19.2305i	−0.517107	−	0.895655i	0.482696	−	0.875788i	$-0.339658\pi$
$462$	24.7245	−	42.8241i	1.15029	−	1.99236i
$463$	−11.0961	+	19.2190i	−0.515679	+	0.893182i	0.484156	+	0.874982i	$0.339127\pi$
$463$	−11.0961	+	19.2190i	−0.515679	+	0.893182i	−0.999834	+	0.0181998i	$0.994207\pi$
$464$	2.02569	+	3.50859i	0.0940402	+	0.162882i
$465$	−1.52166	−	2.63559i	−0.0705653	−	0.122223i
$466$	−4.01902	−	6.96115i	−0.186178	−	0.322469i
$467$	−11.8920			−0.550295			−0.275147	−	0.961402i	$-0.588727\pi$
$467$	−11.8920			−0.550295			−0.275147	+	0.961402i	$0.588727\pi$
$468$	−6.31088	+	10.9308i	−0.291721	+	0.505275i
$469$	14.2055	+	24.6046i	0.655949	+	1.13614i
$470$	−4.04068			−0.186383
$471$	−57.2923			−2.63989
$472$	6.36226	+	11.0198i	0.292847	+	0.507225i
$473$	−23.1675			−1.06524
$474$	−17.4136	+	30.1613i	−0.799835	+	1.38535i
$475$	−16.3577			−0.750541
$476$	−7.78520	+	13.4844i	−0.356834	+	0.618055i
$477$	−35.6908	+	61.8184i	−1.63417	+	2.83047i
$478$	−0.317551	+	0.550014i	−0.0145244	+	0.0251571i
$479$	−16.5678	−	28.6962i	−0.757000	−	1.31116i	−0.944374	−	0.328874i	$-0.893331\pi$
$479$	−16.5678	−	28.6962i	−0.757000	−	1.31116i	0.187374	−	0.982289i	$-0.440002\pi$
$480$	−3.84324			−0.175419
$481$	11.6351	+	3.55308i	0.530515	+	0.162007i
$482$	−7.51638			−0.342362
$483$	8.10275	+	14.0344i	0.368688	+	0.638586i
$484$	−8.60275	+	14.9004i	−0.391034	+	0.677291i
$485$	−1.39059	+	2.40856i	−0.0631432	+	0.109367i
$486$	2.99333	−	5.18461i	0.135780	−	0.235179i
$487$	19.6377			0.889871			0.444935	−	0.895563i	$-0.353227\pi$
$487$	19.6377			0.889871			0.444935	+	0.895563i	$0.353227\pi$
$488$	−3.02569	+	5.24064i	−0.136966	+	0.237233i
$489$	23.9327			1.08227
$490$	−1.45529	−	2.52064i	−0.0657434	−	0.113871i
$491$	−5.31088			−0.239677			−0.119838	−	0.992793i	$-0.538238\pi$
$491$	−5.31088			−0.239677			−0.119838	+	0.992793i	$0.538238\pi$
$492$	0.635102			0.0286326
$493$	10.3366	+	17.9035i	0.465536	+	0.806332i
$494$	−4.79186	+	8.29975i	−0.215596	+	0.373423i
$495$	42.2142			1.89739
$496$	0.395932	+	0.685774i	0.0177779	+	0.0307922i
$497$	10.7582	+	18.6337i	0.482571	+	0.835837i
$498$	−5.44731	−	9.43501i	−0.244100	−	0.422793i
$499$	−11.1878	+	19.3778i	−0.500835	+	0.867471i	0.499165	+	0.866507i	$0.333640\pi$
$499$	−11.1878	+	19.3778i	−0.500835	+	0.867471i	−1.00000		0.000963882i	$0.999693\pi$
$500$	5.29853	−	9.17732i	0.236957	−	0.410422i
$501$	−18.3082	−	31.7108i	−0.817952	−	1.41673i
$502$	4.44064	+	7.69141i	0.198195	+	0.343285i
$503$	−11.8636	−	20.5483i	−0.528971	−	0.916204i	−0.999429	−	0.0337822i	$-0.989245\pi$
$503$	−11.8636	−	20.5483i	−0.528971	−	0.916204i	0.470458	−	0.882422i	$-0.344089\pi$
$504$	19.2569			0.857769
$505$	−2.11740	+	3.66744i	−0.0942231	+	0.163199i
$506$	−4.62177	−	8.00514i	−0.205463	−	0.355872i
$507$	27.4624			1.21965
$508$	−14.9840			−0.664809
$509$	3.62976	+	6.28692i	0.160886	+	0.278663i	0.935187	−	0.354155i	$-0.115231\pi$
$509$	3.62976	+	6.28692i	0.160886	+	0.278663i	−0.774301	+	0.632818i	$0.781898\pi$
$510$	−19.6111			−0.868393
$511$	5.05137	−	8.74924i	0.223460	−	0.387043i
$512$	1.00000			0.0441942
$513$	24.2055	−	41.9252i	1.06870	−	1.85104i
$514$	6.05005	−	10.4790i	0.266856	−	0.462209i
$515$	−10.8029	+	18.7112i	−0.476033	+	0.824513i
$516$	−6.65544	−	11.5276i	−0.292990	−	0.507473i
$517$	−17.0380			−0.749332
$518$	−4.18113	−	18.0837i	−0.183708	−	0.794553i
$519$	−13.6325			−0.598399
$520$	−1.25951	−	2.18154i	−0.0552332	−	0.0956667i
$521$	−1.03367	+	1.79037i	−0.0452860	+	0.0784377i	−0.887780	−	0.460268i	$-0.847753\pi$
$521$	−1.03367	+	1.79037i	−0.0452860	+	0.0784377i	0.842494	+	0.538706i	$0.181087\pi$
$522$	12.7839	−	22.1423i	0.559535	−	0.969143i
$523$	18.6125	−	32.2377i	0.813866	−	1.40966i	−0.0962729	−	0.995355i	$-0.530692\pi$
$523$	18.6125	−	32.2377i	0.813866	−	1.40966i	0.910139	−	0.414303i	$-0.135975\pi$
$524$	12.0894			0.528129
$525$	−15.8920	+	27.5257i	−0.693583	+	1.20132i
$526$	−19.1408			−0.834578
$527$	2.02034	+	3.49933i	0.0880074	+	0.152433i
$528$	−16.2055			−0.705254
$529$	−19.9707			−0.868291
$530$	−7.12309	−	12.3376i	−0.309407	−	0.535909i
$531$	40.1515	−	69.5444i	1.74243	−	3.01797i
$532$	14.6218			0.633934
$533$	0.208136	+	0.360503i	0.00901538	+	0.0156151i
$534$	4.99333	+	8.64871i	0.216083	+	0.374266i
$535$	−0.228135	−	0.395141i	−0.00986312	−	0.0170834i
$536$	4.65544	−	8.06346i	0.201084	−	0.348289i
$537$	−21.5164	+	37.2675i	−0.928500	+	1.60821i
$538$	7.89461	+	13.6739i	0.340361	+	0.589522i
$539$	−6.13642	−	10.6286i	−0.264314	−	0.457806i
$540$	6.36226	+	11.0198i	0.273788	+	0.474215i
$541$	−1.74313			−0.0749430			−0.0374715	−	0.999298i	$-0.511930\pi$
$541$	−1.74313			−0.0749430			−0.0374715	+	0.999298i	$0.511930\pi$
$542$	9.55005	−	16.5412i	0.410210	−	0.710505i
$543$	20.5434	+	35.5822i	0.881601	+	1.52698i
$544$	5.10275			0.218779
$545$	0.589006			0.0252302
$546$	9.31088	+	16.1269i	0.398469	+	0.690169i
$547$	31.6191			1.35194			0.675968	−	0.736931i	$-0.263726\pi$
$547$	31.6191			1.35194			0.675968	+	0.736931i	$0.263726\pi$
$548$	8.34324	−	14.4509i	0.356405	−	0.617312i
$549$	38.1895			1.62989
$550$	9.06471	−	15.7005i	0.386520	−	0.669473i
$551$	9.70682	−	16.8127i	0.413524	−	0.716245i
$552$	2.65544	−	4.59936i	0.113023	−	0.195762i
$553$	17.4136	+	30.1613i	0.740503	+	1.28259i
$554$	16.4003			0.696782
$555$	17.0921	−	15.9490i	0.725517	−	0.676996i
$556$	−18.1922			−0.771520
$557$	11.3702	+	19.6938i	0.481773	+	0.834455i	0.999781	−	0.0209207i	$-0.00665974\pi$
$557$	11.3702	+	19.6938i	0.481773	+	0.834455i	−0.518008	+	0.855376i	$0.673326\pi$
$558$	2.49868	−	4.32784i	0.105778	−	0.183212i
$559$	4.36226	−	7.55565i	0.184504	−	0.319570i
$560$	−1.92162	+	3.32834i	−0.0812032	+	0.140648i
$561$	−82.6926			−3.49128
$562$	2.39725	−	4.15216i	0.101122	−	0.175148i
$563$	−13.4676			−0.567594			−0.283797	−	0.958884i	$-0.591594\pi$
$563$	−13.4676			−0.567594			−0.283797	+	0.958884i	$0.591594\pi$
$564$	−4.89461	−	8.47772i	−0.206100	−	0.356976i
$565$	−0.867948			−0.0365148
$566$	25.9460			1.09059
$567$	−18.1475	−	31.4323i	−0.762122	−	1.32003i
$568$	3.52569	−	6.10667i	0.147935	−	0.256230i
$569$	−41.8627			−1.75497			−0.877487	−	0.479600i	$-0.840782\pi$
$569$	−41.8627			−1.75497			−0.877487	+	0.479600i	$0.840782\pi$
$570$	9.20814	+	15.9490i	0.385686	+	0.668028i
$571$	−14.2502	−	24.6821i	−0.596353	−	1.03291i	−0.993354	−	0.115095i	$-0.963283\pi$
$571$	−14.2502	−	24.6821i	−0.596353	−	1.03291i	0.397002	−	0.917818i	$-0.370051\pi$
$572$	−5.31088	−	9.19872i	−0.222059	−	0.384618i
$573$	14.3826	−	24.9114i	0.600842	−	1.04069i
$574$	0.317551	−	0.550014i	0.0132543	−	0.0229571i
$575$	2.97070	+	5.14540i	0.123887	+	0.214578i
$576$	−3.15544	−	5.46539i	−0.131477	−	0.227724i
$577$	−12.1675	−	21.0747i	−0.506538	−	0.877349i	−0.999971	−	0.00756570i	$-0.997592\pi$
$577$	−12.1675	−	21.0747i	−0.506538	−	0.877349i	0.493434	−	0.869783i	$-0.335742\pi$
$578$	9.03804			0.375933
$579$	3.78520	−	6.55615i	0.157307	−	0.272464i
$580$	2.55137	+	4.41911i	0.105940	+	0.183494i
$581$	−10.8946			−0.451985
$582$	−6.73785			−0.279293
$583$	−30.0354	−	52.0228i	−1.24394	−	2.15457i
$584$	−3.31088			−0.137005
$585$	−7.94863	+	13.7674i	−0.328635	+	0.569213i
$586$	22.0514			0.910934
$587$	−22.5230	+	39.0111i	−0.929626	+	1.61016i	−0.145678	+	0.989332i	$0.546536\pi$
$587$	−22.5230	+	39.0111i	−0.929626	+	1.61016i	−0.783948	+	0.620827i	$0.786797\pi$
$588$	3.52569	−	6.10667i	0.145397	−	0.251835i
$589$	1.89725	−	3.28614i	0.0781749	−	0.135403i
$590$	8.01333	+	13.8795i	0.329904	+	0.571410i
$591$	5.94599			0.244585
$592$	−4.44731	+	4.14988i	−0.182783	+	0.170559i
$593$	6.93265			0.284690			0.142345	−	0.989817i	$-0.454536\pi$
$593$	6.93265			0.284690			0.142345	+	0.989817i	$0.454536\pi$
$594$	26.8273	+	46.4662i	1.10074	+	1.90653i
$595$	−9.80554	+	16.9837i	−0.401988	+	0.696263i
$596$	−6.76618	+	11.7194i	−0.277153	+	0.480044i
$597$	−3.03103	+	5.24990i	−0.124052	+	0.214864i
$598$	3.48098			0.142348
$599$	16.7582	−	29.0260i	0.684721	−	1.18597i	−0.288803	−	0.957388i	$-0.593257\pi$
$599$	16.7582	−	29.0260i	0.684721	−	1.18597i	0.973524	−	0.228583i	$-0.0734093\pi$
$600$	10.4163			0.425243
$601$	−4.08637	−	7.07779i	−0.166686	−	0.288709i	0.770566	−	0.637360i	$-0.219973\pi$
$601$	−4.08637	−	7.07779i	−0.166686	−	0.288709i	−0.937253	+	0.348650i	$0.886640\pi$
$602$	−13.3109			−0.542511
$603$	−58.7599			−2.39289
$604$	−0.610734	−	1.05782i	−0.0248504	−	0.0430422i
$605$	−10.8353	+	18.7672i	−0.440516	+	0.762995i
$606$	−10.2595			−0.416764
$607$	21.2772	+	36.8532i	0.863615	+	1.49583i	0.868415	+	0.495837i	$0.165139\pi$
$607$	21.2772	+	36.8532i	0.863615	+	1.49583i	−0.00480007	+	0.999988i	$0.501528\pi$
$608$	−2.39593	−	4.14988i	−0.0971679	−	0.168300i
$609$	−18.8609	−	32.6681i	−0.764284	−	1.32378i
$610$	−3.81088	+	6.60065i	−0.154298	+	0.267252i
$611$	3.20814	−	5.55666i	0.129787	−	0.224798i
$612$	−16.1014	−	27.8885i	−0.650862	−	1.12733i
$613$	−20.1461	−	34.8941i	−0.813695	−	1.40936i	−0.910261	−	0.414034i	$-0.864119\pi$
$613$	−20.1461	−	34.8941i	−0.813695	−	1.40936i	0.0965665	−	0.995327i	$-0.469214\pi$
$614$	2.87024	+	4.97141i	0.115834	+	0.200630i
$615$	0.799917			0.0322558
$616$	−8.10275	+	14.0344i	−0.326469	+	0.565461i
$617$	10.5501	+	18.2732i	0.424729	+	0.735653i	0.996395	−	0.0848339i	$-0.0270360\pi$
$617$	10.5501	+	18.2732i	0.424729	+	0.735653i	−0.571666	+	0.820487i	$0.693703\pi$
$618$	−52.3436			−2.10557
$619$	47.9140			1.92583			0.962914	−	0.269808i	$-0.0869604\pi$
$619$	47.9140			1.92583			0.962914	+	0.269808i	$0.0869604\pi$
$620$	0.498680	+	0.863740i	0.0200275	+	0.0346886i
$621$	−17.5837			−0.705611
$622$	5.26618	−	9.12129i	0.211154	−	0.365730i
$623$	9.98667			0.400107
$624$	3.05137	−	5.28514i	0.122153	−	0.211575i
$625$	−1.86053	+	3.22253i	−0.0744212	+	0.128901i
$626$	−12.4150	+	21.5033i	−0.496201	+	0.859446i
$627$	38.8273	+	67.2508i	1.55061	+	2.68574i
$628$	18.7759			0.749240
$629$	−22.6935	+	21.1758i	−0.904848	+	0.844333i
$630$	24.2542			0.966312
$631$	15.5053	+	26.8560i	0.617258	+	1.06912i	0.989984	+	0.141181i	$0.0450899\pi$
$631$	15.5053	+	26.8560i	0.617258	+	1.06912i	−0.372726	+	0.927942i	$0.621577\pi$
$632$	5.70682	−	9.88450i	0.227005	−	0.393184i
$633$	−26.0691	+	45.1530i	−1.03615	+	1.79467i
$634$	13.1461	−	22.7698i	0.522100	−	0.904303i
$635$	−18.8725			−0.748934
$636$	17.2569	−	29.8898i	0.684279	−	1.18521i
$637$	4.62177			0.183121
$638$	10.7582	+	18.6337i	0.425921	+	0.737717i
$639$	−44.5004			−1.76041
$640$	1.25951			0.0497865
$641$	16.3096	+	28.2490i	0.644189	+	1.11577i	0.984488	+	0.175451i	$0.0561384\pi$
$641$	16.3096	+	28.2490i	0.644189	+	1.11577i	−0.340299	+	0.940317i	$0.610528\pi$
$642$	0.552694	−	0.957294i	0.0218131	−	0.0377814i
$643$	18.1701			0.716559			0.358279	−	0.933614i	$-0.383364\pi$
$643$	18.1701			0.716559			0.358279	+	0.933614i	$0.383364\pi$
$644$	−2.65544	−	4.59936i	−0.104639	−	0.181240i
$645$	−8.38260	−	14.5191i	−0.330065	−	0.571689i
$646$	−12.2258	−	21.1758i	−0.481019	−	0.833150i
$647$	13.0067	−	22.5282i	0.511345	−	0.885675i	−0.488569	−	0.872525i	$-0.662481\pi$
$647$	13.0067	−	22.5282i	0.511345	−	0.885675i	0.999914	−	0.0131498i	$-0.00418582\pi$
$648$	−5.94731	+	10.3010i	−0.233632	+	0.404663i
$649$	33.7892	+	58.5247i	1.32634	+	2.29729i
$650$	3.41363	+	5.91259i	0.133894	+	0.231911i
$651$	−3.68648	−	6.38516i	−0.144484	−	0.250254i
$652$	−7.84324			−0.307165
$653$	3.62976	−	6.28692i	0.142043	−	0.246026i	−0.786223	−	0.617943i	$-0.787966\pi$
$653$	3.62976	−	6.28692i	0.142043	−	0.246026i	0.928266	+	0.371917i	$0.121299\pi$
$654$	0.713483	+	1.23579i	0.0278994	+	0.0483231i
$655$	15.2267			0.594958
$656$	−0.208136			−0.00812636
$657$	10.4473	+	18.0953i	0.407588	+	0.705964i
$658$	−9.78922			−0.381624
$659$	−3.06471	+	5.30823i	−0.119384	+	0.206779i	−0.919524	−	0.393034i	$-0.871425\pi$
$659$	−3.06471	+	5.30823i	−0.119384	+	0.206779i	0.800140	+	0.599814i	$0.204759\pi$
$660$	−20.4110			−0.794497
$661$	16.9406	−	29.3420i	0.658915	−	1.14127i	−0.321982	−	0.946746i	$-0.604349\pi$
$661$	16.9406	−	29.3420i	0.658915	−	1.14127i	0.980897	−	0.194528i	$-0.0623175\pi$
$662$	−14.8946	+	25.7982i	−0.578896	+	1.00268i
$663$	15.5704	−	26.9687i	0.604704	−	1.04738i
$664$	1.78520	+	3.09205i	0.0692791	+	0.119995i
$665$	18.4163			0.714152
$666$	36.7139	+	11.2116i	1.42263	+	0.434439i
$667$	−7.05137			−0.273030
$668$	6.00000	+	10.3923i	0.232147	+	0.402090i
$669$	2.96897	−	5.14240i	0.114787	−	0.198817i
$670$	5.86358	−	10.1560i	0.226530	−	0.392361i
$671$	−16.0691	+	27.8325i	−0.620340	+	1.07446i
$672$	−9.31088			−0.359175
$673$	12.8229	−	22.2099i	0.494286	−	0.856129i	−0.505692	−	0.862714i	$-0.668763\pi$
$673$	12.8229	−	22.2099i	0.494286	−	0.856129i	0.999978	+	0.00658502i	$0.00209609\pi$
$674$	−12.7272			−0.490232
$675$	−17.2435	−	29.8667i	−0.663704	−	1.14957i
$676$	−9.00000			−0.346154
$677$	10.7759			0.414151			0.207076	−	0.978325i	$-0.433605\pi$
$677$	10.7759			0.414151			0.207076	+	0.978325i	$0.433605\pi$
$678$	−1.05137	−	1.82103i	−0.0403778	−	0.0699364i
$679$	−3.36893	+	5.83515i	−0.129287	+	0.223932i
$680$	6.42697			0.246463
$681$	6.99736	+	12.1198i	0.268139	+	0.464431i
$682$	2.10275	+	3.64207i	0.0805184	+	0.139462i
$683$	15.2458	+	26.4066i	0.583366	+	1.01042i	0.995077	+	0.0991047i	$0.0315979\pi$
$683$	15.2458	+	26.4066i	0.583366	+	1.01042i	−0.411711	+	0.911314i	$0.635069\pi$
$684$	−15.1204	+	26.1894i	−0.578145	+	1.00138i
$685$	10.5084	−	18.2011i	0.401505	−	0.695427i
$686$	7.15412	+	12.3913i	0.273146	+	0.473102i
$687$	−2.49465	−	4.32087i	−0.0951770	−	0.164851i
$688$	2.18113	+	3.77783i	0.0831548	+	0.144028i
$689$	22.6218			0.861821
$690$	3.34456	−	5.79294i	0.127325	−	0.220534i
$691$	−4.49868	−	7.79194i	−0.171138	−	0.296419i	0.767680	−	0.640833i	$-0.221411\pi$
$691$	−4.49868	−	7.79194i	−0.171138	−	0.296419i	−0.938818	+	0.344414i	$0.888078\pi$
$692$	4.46765			0.169834
$693$	102.271			3.88495
$694$	−14.7826	−	25.6041i	−0.561138	−	0.971920i
$695$	−22.9132			−0.869148
$696$	−6.18113	+	10.7060i	−0.234295	+	0.405811i
$697$	−1.06207			−0.0402287
$698$	16.2515	−	28.1485i	0.615129	−	1.06544i
$699$	12.2635	−	21.2411i	0.463850	−	0.803411i
$700$	5.20814	−	9.02076i	0.196849	−	0.340953i
$701$	−17.3756	−	30.0954i	−0.656267	−	1.13669i	−0.981575	−	0.191080i	$-0.938801\pi$
$701$	−17.3756	−	30.0954i	−0.656267	−	1.13669i	0.325308	−	0.945608i	$-0.394532\pi$
$702$	−20.2055			−0.762607
$703$	27.8769	+	8.51295i	1.05140	+	0.321072i
$704$	5.31088			0.200162
$705$	−6.16482	−	10.6778i	−0.232180	−	0.402148i
$706$	−2.05269	+	3.55537i	−0.0772542	+	0.133808i
$707$	−5.12976	+	8.88500i	−0.192924	+	0.334155i
$708$	−19.4136	+	33.6254i	−0.729609	+	1.26372i
$709$	39.9947			1.50203			0.751017	−	0.660283i	$-0.229564\pi$
$709$	39.9947			1.50203			0.751017	+	0.660283i	$0.229564\pi$
$710$	4.44064	−	7.69141i	0.166654	−	0.288654i
$711$	−72.0301			−2.70134
$712$	−1.63642	−	2.83436i	−0.0613275	−	0.106222i
$713$	−1.37823			−0.0516151
$714$	−47.5111			−1.77806
$715$	−6.68912	−	11.5859i	−0.250159	−	0.433288i
$716$	7.05137	−	12.2133i	0.263522	−	0.456434i
$717$	−1.93793			−0.0723734
$718$	14.1027	+	24.4267i	0.526310	+	0.911595i
$719$	−1.50535	−	2.60734i	−0.0561399	−	0.0972372i	0.836590	−	0.547830i	$-0.184546\pi$
$719$	−1.50535	−	2.60734i	−0.0561399	−	0.0972372i	−0.892730	+	0.450593i	$0.851213\pi$
$720$	−3.97431	−	6.88371i	−0.148114	−	0.256541i
$721$	−26.1718	+	45.3309i	−0.974690	+	1.68821i
$722$	−1.98098	+	3.43116i	−0.0737244	+	0.127694i
$723$	−11.4676	−	19.8625i	−0.426486	−	0.738696i
$724$	−6.73250	−	11.6610i	−0.250212	−	0.433379i
$725$	−6.91495	−	11.9770i	−0.256815	−	0.444816i
$726$	−52.5004			−1.94847
$727$	−26.7112	+	46.2651i	−0.990663	+	1.71588i	−0.377264	+	0.926106i	$0.623135\pi$
$727$	−26.7112	+	46.2651i	−0.990663	+	1.71588i	−0.613399	+	0.789773i	$0.710198\pi$
$728$	−3.05137	−	5.28514i	−0.113091	−	0.195880i
$729$	−17.4163			−0.645047
$730$	−4.17009			−0.154342
$731$	11.1298	+	19.2773i	0.411649	+	0.712997i
$732$	−18.4650			−0.682486
$733$	−2.82991	+	4.90154i	−0.104525	+	0.181043i	−0.913544	−	0.406740i	$-0.866666\pi$
$733$	−2.82991	+	4.90154i	−0.104525	+	0.181043i	0.809019	+	0.587782i	$0.199999\pi$
$734$	−4.00000			−0.147643
$735$	4.44064	−	7.69141i	0.163795	−	0.283702i
$736$	−0.870245	+	1.50731i	−0.0320776	+	0.0555601i
$737$	24.7245	−	42.8241i	0.910739	−	1.57745i
$738$	0.656762	+	1.13755i	0.0241757	+	0.0418736i
$739$	2.21883			0.0816209			0.0408105	−	0.999167i	$-0.487006\pi$
$739$	2.21883			0.0816209			0.0408105	+	0.999167i	$0.487006\pi$
$740$	−5.60143	+	5.22681i	−0.205913	+	0.192141i
$741$	−29.2435			−1.07429
$742$	−17.2569	−	29.8898i	−0.633520	−	1.09729i
$743$	−3.43397	+	5.94782i	−0.125980	+	0.218204i	−0.922116	−	0.386914i	$-0.873541\pi$
$743$	−3.43397	+	5.94782i	−0.125980	+	0.218204i	0.796135	+	0.605119i	$0.206874\pi$
$744$	−1.20814	+	2.09255i	−0.0442924	+	0.0767167i
$745$	−8.52207	+	14.7607i	−0.312225	+	0.540789i
$746$	37.3570			1.36774
$747$	11.2662	−	19.5136i	0.412208	−	0.713965i
$748$	27.1001			0.990878
$749$	−0.552694	−	0.957294i	−0.0201950	−	0.0349788i
$750$	32.3356			1.18073
$751$	−3.80256			−0.138757			−0.0693786	−	0.997590i	$-0.522102\pi$
$751$	−3.80256			−0.138757			−0.0693786	+	0.997590i	$0.522102\pi$
$752$	1.60407	+	2.77833i	0.0584943	+	0.101315i
$753$	−13.5501	+	23.4694i	−0.493791	+	0.855272i
$754$	−8.10275			−0.295085
$755$	−0.769226	−	1.33234i	−0.0279950	−	0.0484888i
$756$	15.4136	+	26.6972i	0.560588	+	0.970968i
$757$	1.59608	+	2.76450i	0.0580106	+	0.100477i	0.893572	−	0.448919i	$-0.148191\pi$
$757$	1.59608	+	2.76450i	0.0580106	+	0.100477i	−0.835562	+	0.549397i	$0.814858\pi$
$758$	2.45397	−	4.25040i	0.0891323	−	0.154382i
$759$	14.1027	−	24.4267i	0.511897	−	0.886632i
$760$	−3.01770	−	5.22681i	−0.109464	−	0.189596i
$761$	−19.0297	−	32.9604i	−0.689827	−	1.19481i	−0.971894	−	0.235420i	$-0.924353\pi$
$761$	−19.0297	−	32.9604i	−0.689827	−	1.19481i	0.282067	−	0.959395i	$-0.408980\pi$
$762$	−22.8609	−	39.5963i	−0.828164	−	1.43442i
$763$	1.42697			0.0516596
$764$	−4.71348	+	8.16399i	−0.170528	+	0.295363i
$765$	−20.2799	−	35.1259i	−0.733222	−	1.26998i
$766$	20.6084			0.744613
$767$	−25.4490			−0.918911
$768$	1.52569	+	2.64257i	0.0550535	+	0.0953554i
$769$	−2.76520			−0.0997156			−0.0498578	−	0.998756i	$-0.515877\pi$
$769$	−2.76520			−0.0997156			−0.0498578	+	0.998756i	$0.515877\pi$
$770$	−10.2055	+	17.6764i	−0.367781	+	0.637015i
$771$	36.9220			1.32971
$772$	−1.24049	+	2.14859i	−0.0446462	+	0.0773295i
$773$	−14.4527	+	25.0327i	−0.519826	+	0.900365i	0.479909	+	0.877318i	$0.340670\pi$
$773$	−14.4527	+	25.0327i	−0.519826	+	0.900365i	−0.999734	+	0.0230462i	$0.992664\pi$
$774$	13.7649	−	23.8414i	0.494768	−	0.856963i
$775$	−1.35157	−	2.34098i	−0.0485497	−	0.0840905i
$776$	2.20814			0.0792675
$777$	41.4084	−	38.6390i	1.48552	−	1.38617i
$778$	−25.5678			−0.916648
$779$	0.498680	+	0.863740i	0.0178671	+	0.0309467i
$780$	3.84324	−	6.65668i	0.137610	−	0.238348i
$781$	18.7245	−	32.4318i	0.670016	−	1.16050i
$782$	−4.44064	+	7.69141i	−0.158797	+	0.275044i
$783$	40.9300			1.46272
$784$	−1.15544	+	2.00128i	−0.0412658	+	0.0714745i
$785$	23.6484			0.844049
$786$	18.4447	+	31.9471i	0.657899	+	1.13952i
$787$	10.2816			0.366499			0.183249	−	0.983066i	$-0.441338\pi$
$787$	10.2816			0.366499			0.183249	+	0.983066i	$0.441338\pi$
$788$	−1.94863			−0.0694169
$789$	−29.2029	−	50.5808i	−1.03965	−	1.80073i
$790$	7.18780	−	12.4496i	0.255730	−	0.442938i
$791$	−2.10275			−0.0747651
$792$	−16.7582	−	29.0260i	−0.595476	−	1.03140i
$793$	−6.05137	−	10.4813i	−0.214891	−	0.372201i
$794$	15.1461	+	26.2339i	0.537516	+	0.931006i
$795$	21.7352	−	37.6465i	0.770868	−	1.33518i
$796$	0.993334	−	1.72050i	0.0352078	−	0.0609817i
$797$	−26.3463	−	45.6331i	−0.933233	−	1.61641i	−0.777754	−	0.628568i	$-0.783641\pi$
$797$	−26.3463	−	45.6331i	−0.933233	−	1.61641i	−0.155479	−	0.987839i	$-0.549692\pi$
$798$	22.3082	+	38.6390i	0.789703	+	1.36781i
$799$	8.18516	+	14.1771i	0.289570	+	0.501550i
$800$	−3.41363			−0.120690
$801$	−10.3273	+	17.8874i	−0.364896	+	0.632018i
$802$	−13.7582	−	23.8299i	−0.485819	−	0.841463i
$803$	−17.5837			−0.620516
$804$	28.4110			1.00198
$805$	−3.34456	−	5.79294i	−0.117880	−	0.204174i
$806$	−1.58373			−0.0557844
$807$	−24.0894	+	41.7241i	−0.847988	+	1.46876i
$808$	3.36226			0.118284
$809$	−0.0717149	+	0.124214i	−0.00252136	+	0.00436713i	−0.867283	−	0.497815i	$-0.834136\pi$
$809$	−0.0717149	+	0.124214i	−0.00252136	+	0.00436713i	0.864762	+	0.502182i	$0.167469\pi$
$810$	−7.49069	+	12.9743i	−0.263196	+	0.455869i
$811$	14.3082	−	24.7826i	0.502430	−	0.870235i	−0.497566	−	0.867426i	$-0.665773\pi$
$811$	14.3082	−	24.7826i	0.502430	−	0.870235i	0.999996	−	0.00280872i	$-0.000894045\pi$
$812$	6.18113	+	10.7060i	0.216915	+	0.375708i
$813$	58.2816			2.04402
$814$	−23.6191	+	22.0395i	−0.827850	+	0.772484i
$815$	−9.87864			−0.346034
$816$	7.78520	+	13.4844i	0.272536	+	0.472047i
$817$	10.4517	−	18.1028i	0.365658	−	0.633338i
$818$	−3.62309	+	6.27537i	−0.126678	+	0.219413i
$819$	−19.2569	+	33.3539i	−0.672890	+	1.16548i
$820$	−0.262150			−0.00915467
$821$	−13.8946	+	24.0662i	−0.484925	+	0.839915i	−0.999850	−	0.0173201i	$-0.994487\pi$
$821$	−13.8946	+	24.0662i	−0.484925	+	0.839915i	0.514925	+	0.857235i	$0.327820\pi$
$822$	50.9167			1.77592
$823$	−16.2705	−	28.1814i	−0.567156	−	0.982342i	−0.996846	−	0.0793658i	$-0.974710\pi$
$823$	−16.2705	−	28.1814i	−0.567156	−	0.982342i	0.429690	−	0.902976i	$-0.358623\pi$
$824$	17.1541			0.597592
$825$	55.3196			1.92598
$826$	19.4136	+	33.6254i	0.675487	+	1.16998i
$827$	−22.4783	+	38.9336i	−0.781648	+	1.35385i	0.149332	+	0.988787i	$0.452288\pi$
$827$	−22.4783	+	38.9336i	−0.781648	+	1.35385i	−0.930981	+	0.365068i	$0.881046\pi$
$828$	10.9840			0.381721
$829$	−22.2435	−	38.5269i	−0.772550	−	1.33810i	−0.936161	−	0.351571i	$-0.885648\pi$
$829$	−22.2435	−	38.5269i	−0.772550	−	1.33810i	0.163611	−	0.986525i	$-0.447686\pi$
$830$	2.24848	+	3.89447i	0.0780457	+	0.135179i
$831$	25.0217	+	43.3389i	0.867994	+	1.50341i
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$	−5.89593	+	10.2121i	−0.204282	+	0.353827i
$834$	−27.7556	−	48.0740i	−0.961096	−	1.66467i
$835$	7.55706	+	13.0892i	0.261523	+	0.452971i
$836$	−12.7245	−	22.0395i	−0.440087	−	0.762252i
$837$	8.00000			0.276520
$838$	2.28388	−	3.95579i	0.0788953	−	0.136651i
$839$	−13.0891	−	22.6709i	−0.451885	−	0.782688i	0.546618	−	0.837382i	$-0.315915\pi$
$839$	−13.0891	−	22.6709i	−0.451885	−	0.782688i	−0.998503	+	0.0546942i	$0.982582\pi$
$840$	−11.7272			−0.404625
$841$	−12.5864			−0.434013
$842$	−13.4216	−	23.2469i	−0.462540	−	0.801142i
$843$	14.6298			0.503878
$844$	8.54339	−	14.7976i	0.294076	−	0.509354i
$845$	−11.3356			−0.389956
$846$	10.1231	−	17.5337i	0.348039	−	0.602821i
$847$	−26.2502	+	45.4667i	−0.901968	+	1.56225i
$848$	−5.65544	+	9.79551i	−0.194209	+	0.336379i
$849$	39.5855	+	68.5640i	1.35857	+	2.35311i
$850$	−17.4189			−0.597464
$851$	−2.38490	−	10.3149i	−0.0817532	−	0.353589i
$852$	21.5164			0.737139
$853$	7.54207	+	13.0632i	0.258236	+	0.447277i	0.965769	−	0.259402i	$-0.0835256\pi$
$853$	7.54207	+	13.0632i	0.258236	+	0.447277i	−0.707534	+	0.706680i	$0.750192\pi$
$854$	−9.23250	+	15.9912i	−0.315930	+	0.547206i
$855$	−19.0444	+	32.9858i	−0.651304	+	1.12809i
$856$	−0.181130	+	0.313726i	−0.00619088	+	0.0107229i
$857$	1.17009			0.0399697			0.0199848	−	0.999800i	$-0.493638\pi$
$857$	1.17009			0.0399697			0.0199848	+	0.999800i	$0.493638\pi$
$858$	16.2055	−	28.0687i	0.553247	−	0.958251i
$859$	−36.0487			−1.22997			−0.614983	−	0.788540i	$-0.710837\pi$
$859$	−36.0487			−1.22997			−0.614983	+	0.788540i	$0.710837\pi$
$860$	2.74716	+	4.75821i	0.0936772	+	0.162254i
$861$	1.93793			0.0660446
$862$	−20.7919			−0.708174
$863$	5.22147	+	9.04385i	0.177741	+	0.307856i	0.941106	−	0.338111i	$-0.109788\pi$
$863$	5.22147	+	9.04385i	0.177741	+	0.307856i	−0.763366	+	0.645967i	$0.776454\pi$
$864$	5.05137	−	8.74924i	0.171851	−	0.297655i
$865$	5.62705			0.191325
$866$	−13.8286	−	23.9518i	−0.469914	−	0.813916i
$867$	13.7892	+	23.8836i	0.468307	+	0.811131i
$868$	1.20814	+	2.09255i	0.0410068	+	0.0710259i
$869$	30.3082	−	52.4954i	1.02814	−	1.78079i
$870$	−7.78520	+	13.4844i	−0.263943	+	0.457163i
$871$	9.31088	+	16.1269i	0.315487	+	0.546440i
$872$	−0.233823	−	0.404994i	−0.00791826	−	0.0137148i
$873$	−6.96765	−	12.0683i	−0.235819	−	0.408451i
$874$	8.34019			0.282111
$875$	16.1678	−	28.0034i	0.546571	−	0.946689i
$876$	−5.05137	−	8.74924i	−0.170670	−	0.295609i
$877$	−40.9140			−1.38157			−0.690785	−	0.723061i	$-0.742735\pi$
$877$	−40.9140			−1.38157			−0.690785	+	0.723061i	$0.742735\pi$
$878$	−6.93529			−0.234055
$879$	33.6435	+	58.2722i	1.13477	+	1.96547i
$880$	6.68912			0.225490
$881$	−9.60275	+	16.6324i	−0.323525	+	0.560361i	−0.981213	−	0.192929i	$-0.938201\pi$
$881$	−9.60275	+	16.6324i	−0.323525	+	0.560361i	0.657688	+	0.753291i	$0.271535\pi$
$882$	14.5837			0.491060
$883$	−9.77187	+	16.9254i	−0.328849	+	0.569584i	−0.982284	−	0.187399i	$-0.939994\pi$
$883$	−9.77187	+	16.9254i	−0.328849	+	0.569584i	0.653434	+	0.756983i	$0.273328\pi$
$884$	−5.10275	+	8.83822i	−0.171624	+	0.297261i
$885$	−24.4517	+	42.3515i	−0.821934	+	1.42363i
$886$	9.93265	+	17.2039i	0.333694	+	0.577975i
$887$	−29.1134			−0.977534			−0.488767	−	0.872414i	$-0.662553\pi$
$887$	−29.1134			−0.977534			−0.488767	+	0.872414i	$0.662553\pi$
$888$	−17.7515	−	5.42090i	−0.595702	−	0.181913i
$889$	−45.7219			−1.53346
$890$	−2.06109	−	3.56991i	−0.0690879	−	0.119664i
$891$	−31.5855	+	54.7076i	−1.05815	+	1.83277i
$892$	−0.972993	+	1.68527i	−0.0325782	+	0.0564271i
$893$	7.68648	−	13.3134i	0.257218	−	0.445515i
$894$	−41.2923			−1.38102
$895$	8.88128	−	15.3828i	0.296868	−	0.514191i
$896$	3.05137			0.101939
$897$	5.31088	+	9.19872i	0.177325	+	0.307136i
$898$	−26.1382			−0.872241
$899$	3.20814			0.106997
$900$	10.7715	+	18.6568i	0.359051	+	0.621894i
$901$	−28.8583	+	49.9840i	−0.961409	+	1.66521i
$902$	−1.10539			−0.0368054
$903$	−20.3082	−	35.1749i	−0.675816	−	1.17055i
$904$	0.344558	+	0.596791i	0.0114598	+	0.0198490i
$905$	−8.47966	−	14.6872i	−0.281873	−	0.488219i
$906$	1.86358	−	3.22781i	0.0619133	−	0.107237i
$907$	7.17446	−	12.4265i	0.238224	−	0.412616i	−0.721981	−	0.691913i	$-0.756768\pi$
$907$	7.17446	−	12.4265i	0.238224	−	0.412616i	0.960205	+	0.279297i	$0.0901014\pi$
$908$	−2.29318	−	3.97191i	−0.0761020	−	0.131812i
$909$	−10.6094	−	18.3760i	−0.351892	−	0.609495i
$910$	−3.84324	−	6.65668i	−0.127402	−	0.220667i
$911$	22.3303			0.739836			0.369918	−	0.929064i	$-0.379386\pi$
$911$	22.3303			0.739836			0.369918	+	0.929064i	$0.379386\pi$
$912$	7.31088	−	12.6628i	0.242088	−	0.419308i
$913$	9.48098	+	16.4215i	0.313775	+	0.543474i
$914$	−20.6865			−0.684248
$915$	−23.2569			−0.768848
$916$	0.817551	+	1.41604i	0.0270126	+	0.0467873i
$917$	36.8893			1.21819
$918$	25.7759	−	44.6452i	0.850731	−	1.47351i
$919$	38.0168			1.25406			0.627029	−	0.778996i	$-0.284271\pi$
$919$	38.0168			1.25406			0.627029	+	0.778996i	$0.284271\pi$
$920$	−1.09608	+	1.89847i	−0.0361368	+	0.0625907i
$921$	−8.75819	+	15.1696i	−0.288592	+	0.499856i
$922$	−11.1027	+	19.2305i	−0.365650	+	0.633324i
$923$	7.05137	+	12.2133i	0.232099	+	0.402007i
$924$	−49.4490			−1.62675
$925$	15.1815	−	14.1662i	0.499164	−	0.465780i
$926$	22.1922			0.729280
$927$	−54.1288	−	93.7539i	−1.77782	−	3.07928i
$928$	2.02569	−	3.50859i	0.0664964	−	0.115175i
$929$	−0.728477	+	1.26176i	−0.0239006	+	0.0413970i	−0.877728	−	0.479159i	$-0.840942\pi$
$929$	−0.728477	+	1.26176i	−0.0239006	+	0.0413970i	0.853828	+	0.520556i	$0.174275\pi$
$930$	−1.52166	+	2.63559i	−0.0498972	+	0.0864245i
$931$	11.0734			0.362917
$932$	−4.01902	+	6.96115i	−0.131647	+	0.228020i
$933$	32.1382			1.05216
$934$	5.94599	+	10.2988i	0.194559	+	0.336985i
$935$	34.1329			1.11626
$936$	12.6218			0.412555
$937$	−22.6745	−	39.2733i	−0.740742	−	1.28300i	−0.952158	−	0.305607i	$-0.901141\pi$
$937$	−22.6745	−	39.2733i	−0.740742	−	1.28300i	0.211415	−	0.977396i	$-0.432193\pi$
$938$	14.2055	−	24.6046i	0.463826	−	0.803370i
$939$	−75.7653			−2.47251
$940$	2.02034	+	3.49933i	0.0658962	+	0.114136i
$941$	15.1125	+	26.1756i	0.492652	+	0.853299i	0.999964	−	0.00846377i	$-0.00269413\pi$
$941$	15.1125	+	26.1756i	0.492652	+	0.853299i	−0.507312	+	0.861762i	$0.669361\pi$
$942$	28.6461	+	49.6166i	0.933342	+	1.61660i
$943$	0.181130	−	0.313726i	0.00589839	−	0.0102163i
$944$	6.36226	−	11.0198i	0.207074	−	0.358663i
$945$	19.4136	+	33.6254i	0.631526	+	1.09383i
$946$	11.5837	+	20.0636i	0.376619	+	0.652324i
$947$	7.74049	+	13.4069i	0.251532	+	0.435666i	0.963948	−	0.266091i	$-0.0857323\pi$
$947$	7.74049	+	13.4069i	0.251532	+	0.435666i	−0.712416	+	0.701758i	$0.752399\pi$
$948$	34.8273			1.13114
$949$	3.31088	−	5.73462i	0.107476	−	0.186154i
$950$	8.17883	+	14.1662i	0.265356	+	0.459611i
$951$	80.2276			2.60156
$952$	15.5704			0.504639
$953$	2.86358	+	4.95986i	0.0927604	+	0.160666i	0.908672	−	0.417511i	$-0.137098\pi$
$953$	2.86358	+	4.95986i	0.0927604	+	0.160666i	−0.815911	+	0.578177i	$0.803764\pi$
$954$	71.3817			2.31107
$955$	−5.93668	+	10.2826i	−0.192106	+	0.332738i
$956$	0.635102			0.0205407
$957$	−32.8273	+	56.8585i	−1.06115	+	1.83797i
$958$	−16.5678	+	28.6962i	−0.535280	+	0.927132i
$959$	25.4583	−	44.0951i	0.822093	−	1.42391i
$960$	1.92162	+	3.32834i	0.0620200	+	0.107422i
$961$	−30.3730			−0.979773
$962$	−2.74049	−	11.8528i	−0.0883569	−	0.382151i
$963$	2.28617			0.0736710
$964$	3.75819	+	6.50938i	0.121043	+	0.209653i
$965$	−1.56241	+	2.70617i	−0.0502957	+	0.0871148i
$966$	8.10275	−	14.0344i	0.260702	−	0.451549i
$967$	−4.63510	+	8.02823i	−0.149055	+	0.258171i	−0.930878	−	0.365329i	$-0.880956\pi$
$967$	−4.63510	+	8.02823i	−0.149055	+	0.258171i	0.781824	+	0.623500i	$0.214290\pi$
$968$	17.2055			0.553006
$969$	37.3056	−	64.6152i	1.19843	−	2.07574i
$970$	2.78117			0.0892980
$971$	−3.52569	−	6.10667i	−0.113145	−	0.195972i	0.803892	−	0.594775i	$-0.202759\pi$
$971$	−3.52569	−	6.10667i	−0.113145	−	0.195972i	−0.917037	+	0.398803i	$0.869426\pi$
$972$	−5.98667			−0.192022
$973$	−55.5111			−1.77960
$974$	−9.81887	−	17.0068i	−0.314617	−	0.544932i
$975$	−10.4163	+	18.0415i	−0.333588	+	0.577791i
$976$	6.05137			0.193700
$977$	−14.8636	−	25.7445i	−0.475528	−	0.823639i	0.524079	−	0.851670i	$-0.324410\pi$
$977$	−14.8636	−	25.7445i	−0.475528	−	0.823639i	−0.999607	+	0.0280310i	$0.991076\pi$
$978$	−11.9663	−	20.7263i	−0.382641	−	0.662754i
$979$	−8.69085	−	15.0530i	−0.277761	−	0.481095i
$980$	−1.45529	+	2.52064i	−0.0464876	+	0.0805189i
$981$	−1.47563	+	2.55587i	−0.0471133	+	0.0816027i
$982$	2.65544	+	4.59936i	0.0847386	+	0.146772i
$983$	3.67141	+	6.35908i	0.117100	+	0.202823i	0.918617	−	0.395149i	$-0.129307\pi$
$983$	3.67141	+	6.35908i	0.117100	+	0.202823i	−0.801517	+	0.597972i	$0.795974\pi$
$984$	−0.317551	−	0.550014i	−0.0101232	−	0.0175338i
$985$	−2.45431			−0.0782010
$986$	10.3366	−	17.9035i	0.329184	−	0.570163i
$987$	−14.9353	−	25.8687i	−0.475396	−	0.823409i
$988$	9.58373			0.304899
$989$	−7.59247			−0.241426
$990$	−21.1071	−	36.5586i	−0.670828	−	1.16191i
$991$	−3.07804			−0.0977771			−0.0488886	−	0.998804i	$-0.515568\pi$
$991$	−3.07804			−0.0977771			−0.0488886	+	0.998804i	$0.515568\pi$
$992$	0.395932	−	0.685774i	0.0125708	−	0.0217733i
$993$	−90.8981			−2.88456
$994$	10.7582	−	18.6337i	0.341229	−	0.591026i
$995$	1.25111	−	2.16699i	0.0396630	−	0.0686983i
$996$	−5.44731	+	9.43501i	−0.172604	+	0.298960i
$997$	−24.8920	−	43.1142i	−0.788337	−	1.36544i	−0.926985	−	0.375098i	$-0.877609\pi$
$997$	−24.8920	−	43.1142i	−0.788337	−	1.36544i	0.138649	−	0.990342i	$-0.455724\pi$
$998$	22.3756			0.708287
$999$	13.8432	+	59.8731i	0.437981	+	1.89430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.2.c.c.63.3	yes	6
3.2	odd	2		666.2.f.j.433.2		6
4.3	odd	2		592.2.i.e.433.1		6
37.10	even	3	inner	74.2.c.c.47.3	✓	6
37.11	even	6		2738.2.a.n.1.1		3
37.26	even	3		2738.2.a.o.1.1		3
111.47	odd	6		666.2.f.j.343.2		6
148.47	odd	6		592.2.i.e.417.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.c.c.47.3	✓	6	37.10	even	3	inner
74.2.c.c.63.3	yes	6	1.1	even	1	trivial
592.2.i.e.417.1		6	148.47	odd	6
592.2.i.e.433.1		6	4.3	odd	2
666.2.f.j.343.2		6	111.47	odd	6
666.2.f.j.433.2		6	3.2	odd	2
2738.2.a.n.1.1		3	37.11	even	6
2738.2.a.o.1.1		3	37.26	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.52569 - 2.64257i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.629755 + 1.09077i) q^{5} -3.05137 q^{6} +(-1.52569 + 2.64257i) q^{7} +1.00000 q^{8} +(-3.15544 - 5.46539i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.52569 - 2.64257i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.629755 + 1.09077i) q^{5} -3.05137 q^{6} +(-1.52569 + 2.64257i) q^{7} +1.00000 q^{8} +(-3.15544 - 5.46539i) q^{9} +1.25951 q^{10} +5.31088 q^{11} +(1.52569 + 2.64257i) q^{12} +(-1.00000 + 1.73205i) q^{13} +3.05137 q^{14} +(1.92162 + 3.32834i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.55137 - 4.41911i) q^{17} +(-3.15544 + 5.46539i) q^{18} +(-2.39593 + 4.14988i) q^{19} +(-0.629755 - 1.09077i) q^{20} +(4.65544 + 8.06346i) q^{21} +(-2.65544 - 4.59936i) q^{22} +1.74049 q^{23} +(1.52569 - 2.64257i) q^{24} +(1.70682 + 2.95629i) q^{25} +2.00000 q^{26} -10.1027 q^{27} +(-1.52569 - 2.64257i) q^{28} -4.05137 q^{29} +(1.92162 - 3.32834i) q^{30} -0.791864 q^{31} +(-0.500000 + 0.866025i) q^{32} +(8.10275 - 14.0344i) q^{33} +(-2.55137 + 4.41911i) q^{34} +(-1.92162 - 3.32834i) q^{35} +6.31088 q^{36} +(-1.37024 - 5.92642i) q^{37} +4.79186 q^{38} +(3.05137 + 5.28514i) q^{39} +(-0.629755 + 1.09077i) q^{40} +(0.104068 - 0.180251i) q^{41} +(4.65544 - 8.06346i) q^{42} -4.36226 q^{43} +(-2.65544 + 4.59936i) q^{44} +7.94863 q^{45} +(-0.870245 - 1.50731i) q^{46} -3.20814 q^{47} -3.05137 q^{48} +(-1.15544 - 2.00128i) q^{49} +(1.70682 - 2.95629i) q^{50} -15.5704 q^{51} +(-1.00000 - 1.73205i) q^{52} +(-5.65544 - 9.79551i) q^{53} +(5.05137 + 8.74924i) q^{54} +(-3.34456 + 5.79294i) q^{55} +(-1.52569 + 2.64257i) q^{56} +(7.31088 + 12.6628i) q^{57} +(2.02569 + 3.50859i) q^{58} +(6.36226 + 11.0198i) q^{59} -3.84324 q^{60} +(-3.02569 + 5.24064i) q^{61} +(0.395932 + 0.685774i) q^{62} +19.2569 q^{63} +1.00000 q^{64} +(-1.25951 - 2.18154i) q^{65} -16.2055 q^{66} +(4.65544 - 8.06346i) q^{67} +5.10275 q^{68} +(2.65544 - 4.59936i) q^{69} +(-1.92162 + 3.32834i) q^{70} +(3.52569 - 6.10667i) q^{71} +(-3.15544 - 5.46539i) q^{72} -3.31088 q^{73} +(-4.44731 + 4.14988i) q^{74} +10.4163 q^{75} +(-2.39593 - 4.14988i) q^{76} +(-8.10275 + 14.0344i) q^{77} +(3.05137 - 5.28514i) q^{78} +(5.70682 - 9.88450i) q^{79} +1.25951 q^{80} +(-5.94731 + 10.3010i) q^{81} -0.208136 q^{82} +(1.78520 + 3.09205i) q^{83} -9.31088 q^{84} +6.42697 q^{85} +(2.18113 + 3.77783i) q^{86} +(-6.18113 + 10.7060i) q^{87} +5.31088 q^{88} +(-1.63642 - 2.83436i) q^{89} +(-3.97431 - 6.88371i) q^{90} +(-3.05137 - 5.28514i) q^{91} +(-0.870245 + 1.50731i) q^{92} +(-1.20814 + 2.09255i) q^{93} +(1.60407 + 2.77833i) q^{94} +(-3.01770 - 5.22681i) q^{95} +(1.52569 + 2.64257i) q^{96} +2.20814 q^{97} +(-1.15544 + 2.00128i) q^{98} +(-16.7582 - 29.0260i) 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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