LMFDB - Embedded newform 322.2.e.d.93.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(93,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("322.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.e (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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.6498455769.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} + 3x^{5} + 25x^{4} - 3x^{3} + 6x^{2} + x + 1 $ x^8 - x^7 + 6x^6 + 3x^5 + 25x^4 - 3x^3 + 6*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			93.3
Root			$-0.186817 - 0.323577i$ of defining polynomial
Character	$\chi$	$=$	322.93
Dual form			322.2.e.d.277.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.186817 + 0.323577i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.58159 + 2.73939i) q^{5} +0.373635 q^{6} +(2.36323 + 1.18960i) q^{7} -1.00000 q^{8} +(1.43020 - 2.47718i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.186817 + 0.323577i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.58159 + 2.73939i) q^{5} +0.373635 q^{6} +(2.36323 + 1.18960i) q^{7} -1.00000 q^{8} +(1.43020 - 2.47718i) q^{9} +(1.58159 + 2.73939i) q^{10} +(1.05939 + 1.83493i) q^{11} +(0.186817 - 0.323577i) q^{12} +2.92914 q^{13} +(2.21184 - 1.45181i) q^{14} -1.18187 q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.08159 + 5.33746i) q^{17} +(-1.43020 - 2.47718i) q^{18} +(-0.0948241 + 0.164240i) q^{19} +3.16317 q^{20} +(0.0565638 + 0.986925i) q^{21} +2.11879 q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.186817 - 0.323577i) q^{24} +(-2.50283 - 4.33503i) q^{25} +(1.46457 - 2.53671i) q^{26} +2.18965 q^{27} +(-0.151388 - 2.64142i) q^{28} -7.27630 q^{29} +(-0.590936 + 1.02353i) q^{30} +(-2.91979 - 5.05723i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.395827 + 0.685592i) q^{33} +6.16317 q^{34} +(-6.99643 + 4.59234i) q^{35} -2.86040 q^{36} +(3.69754 - 6.40434i) q^{37} +(0.0948241 + 0.164240i) q^{38} +(0.547214 + 0.947803i) q^{39} +(1.58159 - 2.73939i) q^{40} -10.6613 q^{41} +(0.882984 + 0.444477i) q^{42} -5.86606 q^{43} +(1.05939 - 1.83493i) q^{44} +(4.52396 + 7.83574i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(4.45133 - 7.70993i) q^{47} -0.373635 q^{48} +(4.16969 + 5.62260i) q^{49} -5.00566 q^{50} +(-1.15139 + 1.99426i) q^{51} +(-1.46457 - 2.53671i) q^{52} +(-3.56045 - 6.16688i) q^{53} +(1.09482 - 1.89629i) q^{54} -6.70210 q^{55} +(-2.36323 - 1.18960i) q^{56} -0.0708591 q^{57} +(-3.63815 + 6.30146i) q^{58} +(5.61702 + 9.72896i) q^{59} +(0.590936 + 1.02353i) q^{60} +(-2.45522 + 4.25257i) q^{61} -5.83958 q^{62} +(6.32674 - 4.15276i) q^{63} +1.00000 q^{64} +(-4.63269 + 8.02405i) q^{65} +(0.395827 + 0.685592i) q^{66} +(-0.573690 - 0.993660i) q^{67} +(3.08159 - 5.33746i) q^{68} +0.373635 q^{69} +(0.478866 + 8.35526i) q^{70} +11.8610 q^{71} +(-1.43020 + 2.47718i) q^{72} +(-2.66706 - 4.61949i) q^{73} +(-3.69754 - 6.40434i) q^{74} +(0.935145 - 1.61972i) q^{75} +0.189648 q^{76} +(0.320759 + 5.59660i) q^{77} +1.09443 q^{78} +(3.19471 - 5.53341i) q^{79} +(-1.58159 - 2.73939i) q^{80} +(-3.88153 - 6.72301i) q^{81} +(-5.33063 + 9.23292i) q^{82} +5.05005 q^{83} +(0.826420 - 0.542448i) q^{84} -19.4952 q^{85} +(-2.93303 + 5.08016i) q^{86} +(-1.35934 - 2.35444i) q^{87} +(-1.05939 - 1.83493i) q^{88} +(3.90518 - 6.76396i) q^{89} +9.04793 q^{90} +(6.92223 + 3.48451i) q^{91} -1.00000 q^{92} +(1.09094 - 1.88956i) q^{93} +(-4.45133 - 7.70993i) q^{94} +(-0.299945 - 0.519520i) q^{95} +(-0.186817 + 0.323577i) q^{96} -14.7401 q^{97} +(6.95416 - 0.799757i) q^{98} +6.06058 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - q^{3} - 4 q^{4} + 5 q^{5} - 2 q^{6} - 3 q^{7} - 8 q^{8} + q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 - q^3 - 4 * q^4 + 5 * q^5 - 2 * q^6 - 3 * q^7 - 8 * q^8 + q^9	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} + 5 q^{5} - 2 q^{6} - 3 q^{7} - 8 q^{8} + q^{9} - 5 q^{10} + 2 q^{11} - q^{12} + 14 q^{13} + 3 q^{14} - 10 q^{15} - 4 q^{16} + 7 q^{17} - q^{18} + q^{19} - 10 q^{20} - 5 q^{21} + 4 q^{22} + 4 q^{23} + q^{24} - 19 q^{25} + 7 q^{26} + 14 q^{27} + 6 q^{28} - 12 q^{29} - 5 q^{30} + 4 q^{31} + 4 q^{32} + 13 q^{33} + 14 q^{34} - 14 q^{35} - 2 q^{36} - q^{38} - 19 q^{39} - 5 q^{40} - 30 q^{41} + 20 q^{42} - 24 q^{43} + 2 q^{44} + 25 q^{45} - 4 q^{46} + 15 q^{47} + 2 q^{48} + 17 q^{49} - 38 q^{50} - 2 q^{51} - 7 q^{52} - 21 q^{53} + 7 q^{54} + 24 q^{55} + 3 q^{56} - 10 q^{57} - 6 q^{58} + 32 q^{59} + 5 q^{60} + 3 q^{61} + 8 q^{62} + 25 q^{63} + 8 q^{64} + 6 q^{65} - 13 q^{66} - 13 q^{67} + 7 q^{68} - 2 q^{69} + 14 q^{70} - 14 q^{71} - q^{72} + 16 q^{73} - 6 q^{75} - 2 q^{76} + 23 q^{77} - 38 q^{78} - 3 q^{79} + 5 q^{80} - 15 q^{82} + 16 q^{83} + 25 q^{84} - 48 q^{85} - 12 q^{86} + 9 q^{87} - 2 q^{88} + 33 q^{89} + 50 q^{90} - 18 q^{91} - 8 q^{92} + 9 q^{93} - 15 q^{94} + 11 q^{95} + q^{96} - 24 q^{97} + 34 q^{98} - 70 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 + 5 * q^5 - 2 * q^6 - 3 * q^7 - 8 * q^8 + q^9 - 5 * q^10 + 2 * q^11 - q^12 + 14 * q^13 + 3 * q^14 - 10 * q^15 - 4 * q^16 + 7 * q^17 - q^18 + q^19 - 10 * q^20 - 5 * q^21 + 4 * q^22 + 4 * q^23 + q^24 - 19 * q^25 + 7 * q^26 + 14 * q^27 + 6 * q^28 - 12 * q^29 - 5 * q^30 + 4 * q^31 + 4 * q^32 + 13 * q^33 + 14 * q^34 - 14 * q^35 - 2 * q^36 - q^38 - 19 * q^39 - 5 * q^40 - 30 * q^41 + 20 * q^42 - 24 * q^43 + 2 * q^44 + 25 * q^45 - 4 * q^46 + 15 * q^47 + 2 * q^48 + 17 * q^49 - 38 * q^50 - 2 * q^51 - 7 * q^52 - 21 * q^53 + 7 * q^54 + 24 * q^55 + 3 * q^56 - 10 * q^57 - 6 * q^58 + 32 * q^59 + 5 * q^60 + 3 * q^61 + 8 * q^62 + 25 * q^63 + 8 * q^64 + 6 * q^65 - 13 * q^66 - 13 * q^67 + 7 * q^68 - 2 * q^69 + 14 * q^70 - 14 * q^71 - q^72 + 16 * q^73 - 6 * q^75 - 2 * q^76 + 23 * q^77 - 38 * q^78 - 3 * q^79 + 5 * q^80 - 15 * q^82 + 16 * q^83 + 25 * q^84 - 48 * q^85 - 12 * q^86 + 9 * q^87 - 2 * q^88 + 33 * q^89 + 50 * q^90 - 18 * q^91 - 8 * q^92 + 9 * q^93 - 15 * q^94 + 11 * q^95 + q^96 - 24 * q^97 + 34 * q^98 - 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.186817	+	0.323577i	0.107859	+	0.186817i	0.914903	−	0.403674i	$-0.132267\pi$
$3$	0.186817	+	0.323577i	0.107859	+	0.186817i	−0.807044	+	0.590492i	$0.798934\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.58159	+	2.73939i	−0.707307	+	1.22509i	0.258546	+	0.965999i	$0.416757\pi$
$5$	−1.58159	+	2.73939i	−0.707307	+	1.22509i	−0.965853	+	0.259092i	$0.916577\pi$
$6$	0.373635			0.152536
$7$	2.36323	+	1.18960i	0.893216	+	0.449628i
$7$	2.36323	+	1.18960i	0.893216	+	0.449628i
$8$	−1.00000			−0.353553
$9$	1.43020	−	2.47718i	0.476733	−	0.825726i
$10$	1.58159	+	2.73939i	0.500142	+	0.866271i
$11$	1.05939	+	1.83493i	0.319419	+	0.553251i	0.980367	−	0.197181i	$-0.0631788\pi$
$11$	1.05939	+	1.83493i	0.319419	+	0.553251i	−0.660948	+	0.750432i	$0.729845\pi$
$12$	0.186817	−	0.323577i	0.0539295	−	0.0934087i
$13$	2.92914			0.812398			0.406199	−	0.913785i	$-0.366854\pi$
$13$	2.92914			0.812398			0.406199	+	0.913785i	$0.366854\pi$
$14$	2.21184	−	1.45181i	0.591139	−	0.388014i
$15$	−1.18187			−0.305158
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.08159	+	5.33746i	0.747394	+	1.29453i	0.949068	+	0.315072i	$0.102029\pi$
$17$	3.08159	+	5.33746i	0.747394	+	1.29453i	−0.201673	+	0.979453i	$0.564638\pi$
$18$	−1.43020	−	2.47718i	−0.337101	−	0.583876i
$19$	−0.0948241	+	0.164240i	−0.0217541	+	0.0376793i	−0.876698	−	0.481042i	$-0.840258\pi$
$19$	−0.0948241	+	0.164240i	−0.0217541	+	0.0376793i	0.854943	+	0.518721i	$0.173592\pi$
$20$	3.16317			0.707307
$21$	0.0565638	+	0.986925i	0.0123432	+	0.215365i
$22$	2.11879			0.451727
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$	−0.186817	−	0.323577i	−0.0381339	−	0.0660499i
$25$	−2.50283	−	4.33503i	−0.500566	−	0.867006i
$26$	1.46457	−	2.53671i	0.287226	−	0.497490i
$27$	2.18965			0.421398
$28$	−0.151388	−	2.64142i	−0.0286096	−	0.499181i
$29$	−7.27630			−1.35118			−0.675588	−	0.737280i	$-0.736110\pi$
$29$	−7.27630			−1.35118			−0.675588	+	0.737280i	$0.736110\pi$
$30$	−0.590936	+	1.02353i	−0.107890	+	0.186870i
$31$	−2.91979	−	5.05723i	−0.524410	−	0.908305i	−0.999596	−	0.0284195i	$-0.990953\pi$
$31$	−2.91979	−	5.05723i	−0.524410	−	0.908305i	0.475186	−	0.879885i	$-0.342381\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.395827	+	0.685592i	−0.0689046	+	0.119346i
$34$	6.16317			1.05698
$35$	−6.99643	+	4.59234i	−1.18261	+	0.776247i
$36$	−2.86040			−0.476733
$37$	3.69754	−	6.40434i	0.607873	−	1.05287i	−0.383718	−	0.923450i	$-0.625356\pi$
$37$	3.69754	−	6.40434i	0.607873	−	1.05287i	0.991590	−	0.129416i	$-0.0413102\pi$
$38$	0.0948241	+	0.164240i	0.0153825	+	0.0266433i
$39$	0.547214	+	0.947803i	0.0876244	+	0.151770i
$40$	1.58159	−	2.73939i	0.250071	−	0.433135i
$41$	−10.6613			−1.66501			−0.832504	−	0.554018i	$-0.813094\pi$
$41$	−10.6613			−1.66501			−0.832504	+	0.554018i	$0.813094\pi$
$42$	0.882984	+	0.444477i	0.136247	+	0.0685843i
$43$	−5.86606			−0.894566			−0.447283	−	0.894393i	$-0.647608\pi$
$43$	−5.86606			−0.894566			−0.447283	+	0.894393i	$0.647608\pi$
$44$	1.05939	−	1.83493i	0.159710	−	0.276625i
$45$	4.52396	+	7.83574i	0.674393	+	1.16808i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	4.45133	−	7.70993i	0.649294	−	1.12461i	−0.333998	−	0.942574i	$-0.608398\pi$
$47$	4.45133	−	7.70993i	0.649294	−	1.12461i	0.983292	−	0.182036i	$-0.0582687\pi$
$48$	−0.373635			−0.0539295
$49$	4.16969	+	5.62260i	0.595670	+	0.803229i
$50$	−5.00566			−0.707907
$51$	−1.15139	+	1.99426i	−0.161227	+	0.279253i
$52$	−1.46457	−	2.53671i	−0.203099	−	0.351778i
$53$	−3.56045	−	6.16688i	−0.489066	−	0.847087i	0.510855	−	0.859667i	$-0.329329\pi$
$53$	−3.56045	−	6.16688i	−0.489066	−	0.847087i	−0.999921	+	0.0125801i	$0.995996\pi$
$54$	1.09482	−	1.89629i	0.148987	−	0.258053i
$55$	−6.70210			−0.903710
$56$	−2.36323	−	1.18960i	−0.315800	−	0.158967i
$57$	−0.0708591			−0.00938552
$58$	−3.63815	+	6.30146i	−0.477713	+	0.827422i
$59$	5.61702	+	9.72896i	0.731273	+	1.26660i	0.956339	+	0.292259i	$0.0944069\pi$
$59$	5.61702	+	9.72896i	0.731273	+	1.26660i	−0.225066	+	0.974344i	$0.572260\pi$
$60$	0.590936	+	1.02353i	0.0762895	+	0.132137i
$61$	−2.45522	+	4.25257i	−0.314359	+	0.544486i	−0.979301	−	0.202409i	$-0.935123\pi$
$61$	−2.45522	+	4.25257i	−0.314359	+	0.544486i	0.664942	+	0.746895i	$0.268456\pi$
$62$	−5.83958			−0.741628
$63$	6.32674	−	4.15276i	0.797094	−	0.523199i
$64$	1.00000			0.125000
$65$	−4.63269	+	8.02405i	−0.574614	+	0.995261i
$66$	0.395827	+	0.685592i	0.0487229	+	0.0843905i
$67$	−0.573690	−	0.993660i	−0.0700874	−	0.121395i	0.828852	−	0.559468i	$-0.188994\pi$
$67$	−0.573690	−	0.993660i	−0.0700874	−	0.121395i	−0.898939	+	0.438073i	$0.855661\pi$
$68$	3.08159	−	5.33746i	0.373697	−	0.647263i
$69$	0.373635			0.0449803
$70$	0.478866	+	8.35526i	0.0572354	+	0.998644i
$71$	11.8610			1.40765			0.703823	−	0.710375i	$-0.251475\pi$
$71$	11.8610			1.40765			0.703823	+	0.710375i	$0.251475\pi$
$72$	−1.43020	+	2.47718i	−0.168551	+	0.291938i
$73$	−2.66706	−	4.61949i	−0.312156	−	0.540670i	0.666673	−	0.745350i	$-0.267718\pi$
$73$	−2.66706	−	4.61949i	−0.312156	−	0.540670i	−0.978829	+	0.204681i	$0.934384\pi$
$74$	−3.69754	−	6.40434i	−0.429831	−	0.744489i
$75$	0.935145	−	1.61972i	0.107981	−	0.187029i
$76$	0.189648			0.0217541
$77$	0.320759	+	5.59660i	0.0365539	+	0.637792i
$78$	1.09443			0.123920
$79$	3.19471	−	5.53341i	0.359433	−	0.622557i	−0.628433	−	0.777864i	$-0.716303\pi$
$79$	3.19471	−	5.53341i	0.359433	−	0.622557i	0.987866	+	0.155307i	$0.0496367\pi$
$80$	−1.58159	−	2.73939i	−0.176827	−	0.306273i
$81$	−3.88153	−	6.72301i	−0.431281	−	0.747001i
$82$	−5.33063	+	9.23292i	−0.588669	+	1.01961i
$83$	5.05005			0.554314			0.277157	−	0.960825i	$-0.410608\pi$
$83$	5.05005			0.554314			0.277157	+	0.960825i	$0.410608\pi$
$84$	0.826420	−	0.542448i	0.0901699	−	0.0591860i
$85$	−19.4952			−2.11455
$86$	−2.93303	+	5.08016i	−0.316277	+	0.547807i
$87$	−1.35934	−	2.35444i	−0.145736	−	0.252423i
$88$	−1.05939	−	1.83493i	−0.112932	−	0.195604i
$89$	3.90518	−	6.76396i	0.413948	−	0.716979i	−0.581370	−	0.813640i	$-0.697483\pi$
$89$	3.90518	−	6.76396i	0.413948	−	0.716979i	0.995317	+	0.0966610i	$0.0308163\pi$
$90$	9.04793			0.953736
$91$	6.92223	+	3.48451i	0.725647	+	0.365276i
$92$	−1.00000			−0.104257
$93$	1.09094	−	1.88956i	0.113125	−	0.195938i
$94$	−4.45133	−	7.70993i	−0.459120	−	0.795219i
$95$	−0.299945	−	0.519520i	−0.0307737	−	0.0533016i
$96$	−0.186817	+	0.323577i	−0.0190670	+	0.0330250i
$97$	−14.7401			−1.49663			−0.748317	−	0.663341i	$-0.769138\pi$
$97$	−14.7401			−1.49663			−0.748317	+	0.663341i	$0.769138\pi$
$98$	6.95416	−	0.799757i	0.702477	−	0.0807876i
$99$	6.06058			0.609111
$100$	−2.50283	+	4.33503i	−0.250283	+	0.433503i
$101$	−3.09514	−	5.36095i	−0.307978	−	0.533434i	0.669942	−	0.742414i	$-0.266319\pi$
$101$	−3.09514	−	5.36095i	−0.307978	−	0.533434i	−0.977920	+	0.208980i	$0.932986\pi$
$102$	1.15139	+	1.99426i	0.114004	+	0.197461i
$103$	4.79909	−	8.31226i	0.472868	−	0.819032i	−0.526650	−	0.850082i	$-0.676552\pi$
$103$	4.79909	−	8.31226i	0.472868	−	0.819032i	0.999518	+	0.0310507i	$0.00988535\pi$
$104$	−2.92914			−0.287226
$105$	−2.79303	−	1.40596i	−0.272572	−	0.137207i
$106$	−7.12090			−0.691643
$107$	−9.59652	+	16.6217i	−0.927731	+	1.60688i	−0.140621	+	0.990063i	$0.544910\pi$
$107$	−9.59652	+	16.6217i	−0.927731	+	1.60688i	−0.787109	+	0.616813i	$0.788423\pi$
$108$	−1.09482	−	1.89629i	−0.105349	−	0.182471i
$109$	1.50566	+	2.60788i	0.144216	+	0.249790i	0.929080	−	0.369878i	$-0.120601\pi$
$109$	1.50566	+	2.60788i	0.144216	+	0.249790i	−0.784864	+	0.619668i	$0.787267\pi$
$110$	−3.35105	+	5.80418i	−0.319510	+	0.553407i
$111$	2.76306			0.262258
$112$	−2.21184	+	1.45181i	−0.208999	+	0.137184i
$113$	−7.53681			−0.709003			−0.354502	−	0.935055i	$-0.615349\pi$
$113$	−7.53681			−0.709003			−0.354502	+	0.935055i	$0.615349\pi$
$114$	−0.0354296	+	0.0613658i	−0.00331828	+	0.00574743i
$115$	1.58159	+	2.73939i	0.147484	+	0.255449i
$116$	3.63815	+	6.30146i	0.337794	+	0.585076i
$117$	4.18925	−	7.25600i	0.387297	−	0.670817i
$118$	11.2340			1.03418
$119$	0.933029	+	16.2795i	0.0855307	+	1.49234i
$120$	1.18187			0.107890
$121$	3.25537	−	5.63846i	0.295942	−	0.512587i
$122$	2.45522	+	4.25257i	0.222285	+	0.385009i
$123$	−1.99171	−	3.44974i	−0.179586	−	0.311053i
$124$	−2.91979	+	5.05723i	−0.262205	+	0.454152i
$125$	0.0179083			0.00160176
$126$	−0.433029	−	7.55550i	−0.0385773	−	0.673097i
$127$	13.1237			1.16454			0.582268	−	0.812997i	$-0.302165\pi$
$127$	13.1237			1.16454			0.582268	+	0.812997i	$0.302165\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−1.09588	−	1.89812i	−0.0964870	−	0.167120i
$130$	4.63269	+	8.02405i	0.406314	+	0.703756i
$131$	−0.123735	+	0.214315i	−0.0108108	+	0.0187248i	−0.871380	−	0.490608i	$-0.836775\pi$
$131$	−0.123735	+	0.214315i	−0.0108108	+	0.0187248i	0.860569	+	0.509333i	$0.170108\pi$
$132$	0.791653			0.0689046
$133$	−0.419471	+	0.275334i	−0.0363728	+	0.0238745i
$134$	−1.14738			−0.0991185
$135$	−3.46312	+	5.99830i	−0.298058	+	0.516251i
$136$	−3.08159	−	5.33746i	−0.264244	−	0.457684i
$137$	−2.98570	−	5.17139i	−0.255086	−	0.441822i	0.709833	−	0.704370i	$-0.248770\pi$
$137$	−2.98570	−	5.17139i	−0.255086	−	0.441822i	−0.964919	+	0.262548i	$0.915437\pi$
$138$	0.186817	−	0.323577i	0.0159030	−	0.0275447i
$139$	1.20309			0.102044			0.0510222	−	0.998698i	$-0.483752\pi$
$139$	1.20309			0.102044			0.0510222	+	0.998698i	$0.483752\pi$
$140$	7.47530	+	3.76292i	0.631778	+	0.318025i
$141$	3.32635			0.280129
$142$	5.93052	−	10.2720i	0.497678	−	0.862004i
$143$	3.10312	+	5.37475i	0.259496	+	0.449460i
$144$	1.43020	+	2.47718i	0.119183	+	0.206431i
$145$	11.5081	−	19.9326i	0.955695	−	1.65531i
$146$	−5.33412			−0.441455
$147$	−1.04038	+	2.39962i	−0.0858087	+	0.197917i
$148$	−7.39509			−0.607873
$149$	1.81813	−	3.14909i	0.148947	−	0.257984i	−0.781892	−	0.623414i	$-0.785745\pi$
$149$	1.81813	−	3.14909i	0.148947	−	0.257984i	0.930839	+	0.365431i	$0.119078\pi$
$150$	−0.935145	−	1.61972i	−0.0763542	−	0.132249i
$151$	−9.15560	−	15.8580i	−0.745072	−	1.29050i	−0.950161	−	0.311759i	$-0.899082\pi$
$151$	−9.15560	−	15.8580i	−0.745072	−	1.29050i	0.205089	−	0.978743i	$-0.434252\pi$
$152$	0.0948241	−	0.164240i	0.00769125	−	0.0133216i
$153$	17.6291			1.42523
$154$	5.00718	+	2.52052i	0.403490	+	0.203109i
$155$	18.4716			1.48368
$156$	0.547214	−	0.947803i	0.0438122	−	0.0758850i
$157$	5.58948	+	9.68127i	0.446089	+	0.772649i	0.998127	−	0.0611696i	$-0.0194830\pi$
$157$	5.58948	+	9.68127i	0.446089	+	0.772649i	−0.552038	+	0.833819i	$0.686150\pi$
$158$	−3.19471	−	5.53341i	−0.254158	−	0.440214i
$159$	1.33031	−	2.30416i	0.105500	−	0.182732i
$160$	−3.16317			−0.250071
$161$	2.21184	−	1.45181i	0.174317	−	0.114419i
$162$	−7.76306			−0.609924
$163$	0.880354	−	1.52482i	0.0689546	−	0.119433i	−0.829487	−	0.558526i	$-0.811367\pi$
$163$	0.880354	−	1.52482i	0.0689546	−	0.119433i	0.898441	+	0.439093i	$0.144700\pi$
$164$	5.33063	+	9.23292i	0.416252	+	0.720970i
$165$	−1.25207	−	2.16865i	−0.0974734	−	0.168829i
$166$	2.52502	−	4.37347i	0.195980	−	0.339447i
$167$	10.7014			0.828100			0.414050	−	0.910254i	$-0.364114\pi$
$167$	10.7014			0.828100			0.414050	+	0.910254i	$0.364114\pi$
$168$	−0.0565638	−	0.986925i	−0.00436399	−	0.0761429i
$169$	−4.42013			−0.340010
$170$	−9.74759	+	16.8833i	−0.747606	+	1.29489i
$171$	0.271234	+	0.469792i	0.0207418	+	0.0359259i
$172$	2.93303	+	5.08016i	0.223641	+	0.387358i
$173$	5.34610	−	9.25972i	0.406457	−	0.704003i	−0.588033	−	0.808837i	$-0.700098\pi$
$173$	5.34610	−	9.25972i	0.406457	−	0.704003i	0.994490	+	0.104833i	$0.0334309\pi$
$174$	−2.71868			−0.206103
$175$	−0.757796	−	13.2220i	−0.0572840	−	0.999492i
$176$	−2.11879			−0.159710
$177$	−2.09871	+	3.63508i	−0.157749	+	0.273229i
$178$	−3.90518	−	6.76396i	−0.292705	−	0.506980i
$179$	6.95943	+	12.0541i	0.520172	+	0.900965i	0.999725	+	0.0234516i	$0.00746557\pi$
$179$	6.95943	+	12.0541i	0.520172	+	0.900965i	−0.479553	+	0.877513i	$0.659201\pi$
$180$	4.52396	−	7.83574i	0.337196	−	0.584041i
$181$	−0.296474			−0.0220367			−0.0110184	−	0.999939i	$-0.503507\pi$
$181$	−0.296474			−0.0220367			−0.0110184	+	0.999939i	$0.503507\pi$
$182$	6.47879	−	4.25257i	0.480240	−	0.315221i
$183$	−1.83471			−0.135626
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	11.6960	+	20.2580i	0.859905	+	1.48940i
$186$	−1.09094	−	1.88956i	−0.0799913	−	0.138549i
$187$	−6.52923	+	11.3090i	−0.477465	+	0.826993i
$188$	−8.90267			−0.649294
$189$	5.17464	+	2.60481i	0.376399	+	0.189472i
$190$	−0.599890			−0.0435206
$191$	10.6462	−	18.4398i	0.770335	−	1.33426i	−0.167044	−	0.985949i	$-0.553422\pi$
$191$	10.6462	−	18.4398i	0.770335	−	1.33426i	0.937379	−	0.348311i	$-0.113245\pi$
$192$	0.186817	+	0.323577i	0.0134824	+	0.0233522i
$193$	0.294679	+	0.510398i	0.0212114	+	0.0367393i	0.876436	−	0.481518i	$-0.159914\pi$
$193$	0.294679	+	0.510398i	0.0212114	+	0.0367393i	−0.855225	+	0.518257i	$0.826581\pi$
$194$	−7.37007	+	12.7653i	−0.529140	+	0.916497i
$195$	−3.46187			−0.247909
$196$	2.78447	−	6.42236i	0.198891	−	0.458740i
$197$	−26.1300			−1.86168			−0.930841	−	0.365424i	$-0.880924\pi$
$197$	−26.1300			−1.86168			−0.930841	+	0.365424i	$0.880924\pi$
$198$	3.03029	−	5.24861i	0.215353	−	0.373003i
$199$	−0.696167	−	1.20580i	−0.0493499	−	0.0854766i	0.840295	−	0.542129i	$-0.182382\pi$
$199$	−0.696167	−	1.20580i	−0.0493499	−	0.0854766i	−0.889645	+	0.456652i	$0.849048\pi$
$200$	2.50283	+	4.33503i	0.176977	+	0.306533i
$201$	0.214350	−	0.371266i	0.0151191	−	0.0261871i
$202$	−6.19029			−0.435547
$203$	−17.1956	−	8.65591i	−1.20689	−	0.607525i
$204$	2.30278			0.161227
$205$	16.8617	−	29.2053i	1.17767	−	2.03979i
$206$	−4.79909	−	8.31226i	−0.334368	−	0.579143i
$207$	−1.43020	−	2.47718i	−0.0994057	−	0.172176i
$208$	−1.46457	+	2.53671i	−0.101550	+	0.175889i
$209$	−0.401824			−0.0277948
$210$	−2.61411	+	1.71586i	−0.180391	+	0.118405i
$211$	21.1402			1.45535			0.727677	−	0.685920i	$-0.240600\pi$
$211$	21.1402			1.45535			0.727677	+	0.685920i	$0.240600\pi$
$212$	−3.56045	+	6.16688i	−0.244533	+	0.423543i
$213$	2.21585	+	3.83796i	0.151827	+	0.262973i
$214$	9.59652	+	16.6217i	0.656005	+	1.13623i
$215$	9.27768	−	16.0694i	0.632732	−	1.09592i
$216$	−2.18965			−0.148987
$217$	−0.884042	−	15.4248i	−0.0600127	−	1.04710i
$218$	3.01132			0.203953
$219$	0.996507	−	1.72600i	0.0673377	−	0.116632i
$220$	3.35105	+	5.80418i	0.225928	+	0.391318i
$221$	9.02640	+	15.6342i	0.607181	+	1.05167i
$222$	1.38153	−	2.39288i	0.0927223	−	0.160600i
$223$	−18.6510			−1.24896			−0.624481	−	0.781040i	$-0.714689\pi$
$223$	−18.6510			−1.24896			−0.624481	+	0.781040i	$0.714689\pi$
$224$	0.151388	+	2.64142i	0.0101150	+	0.176487i
$225$	−14.3182			−0.954545
$226$	−3.76840	+	6.52707i	−0.250670	+	0.434174i
$227$	4.86534	+	8.42702i	0.322924	+	0.559321i	0.981090	−	0.193552i	$-0.0620008\pi$
$227$	4.86534	+	8.42702i	0.322924	+	0.559321i	−0.658166	+	0.752873i	$0.728667\pi$
$228$	0.0354296	+	0.0613658i	0.00234638	+	0.00406405i
$229$	−3.67146	+	6.35916i	−0.242617	+	0.420225i	−0.961459	−	0.274948i	$-0.911339\pi$
$229$	−3.67146	+	6.35916i	−0.242617	+	0.420225i	0.718842	+	0.695174i	$0.244673\pi$
$230$	3.16317			0.208573
$231$	−1.75101	+	1.14933i	−0.115208	+	0.0756206i
$232$	7.27630			0.477713
$233$	−13.8159	+	23.9299i	−0.905112	+	1.56770i	−0.0843457	+	0.996437i	$0.526880\pi$
$233$	−13.8159	+	23.9299i	−0.905112	+	1.56770i	−0.820767	+	0.571264i	$0.806453\pi$
$234$	−4.18925	−	7.25600i	−0.273860	−	0.474339i
$235$	14.0803	+	24.3879i	0.918500	+	1.59089i
$236$	5.61702	−	9.72896i	0.365637	−	0.633301i
$237$	2.38731			0.155073
$238$	14.5650	+	7.33173i	0.944107	+	0.475245i
$239$	0.225615			0.0145938			0.00729690	−	0.999973i	$-0.497677\pi$
$239$	0.225615			0.0145938			0.00729690	+	0.999973i	$0.497677\pi$
$240$	0.590936	−	1.02353i	0.0381447	−	0.0660686i
$241$	9.16495	+	15.8742i	0.590366	+	1.02254i	0.994183	+	0.107704i	$0.0343499\pi$
$241$	9.16495	+	15.8742i	0.590366	+	1.02254i	−0.403817	+	0.914840i	$0.632317\pi$
$242$	−3.25537	−	5.63846i	−0.209263	−	0.362454i
$243$	4.73475	−	8.20082i	0.303734	−	0.526083i
$244$	4.91044			0.314359
$245$	−21.9972	+	2.52977i	−1.40535	+	0.161621i
$246$	−3.98342			−0.253973
$247$	−0.277753	+	0.481082i	−0.0176730	+	0.0306105i
$248$	2.91979	+	5.05723i	0.185407	+	0.321134i
$249$	0.943436	+	1.63408i	0.0597878	+	0.103556i
$250$	0.00895413	−	0.0155090i	0.000566309	−	0.000980876i
$251$	−22.3552			−1.41105			−0.705523	−	0.708687i	$-0.749288\pi$
$251$	−22.3552			−1.41105			−0.705523	+	0.708687i	$0.749288\pi$
$252$	−6.75977	−	3.40274i	−0.425825	−	0.214352i
$253$	2.11879			0.133207
$254$	6.56183	−	11.3654i	0.411726	−	0.713130i
$255$	−3.64204	−	6.30820i	−0.228073	−	0.395035i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−11.5059	+	19.9288i	−0.717719	+	1.24313i	0.244183	+	0.969729i	$0.421480\pi$
$257$	−11.5059	+	19.9288i	−0.717719	+	1.24313i	−0.961902	+	0.273396i	$0.911853\pi$
$258$	−2.19176			−0.136453
$259$	16.3568	−	10.7363i	1.01636	−	0.667121i
$260$	9.26538			0.574614
$261$	−10.4066	+	18.0247i	−0.644150	+	1.11570i
$262$	0.123735	+	0.214315i	0.00764438	+	0.0132405i
$263$	−0.00849223	−	0.0147090i	−0.000523653	−	0.000906994i	0.865763	−	0.500453i	$-0.166833\pi$
$263$	−0.00849223	−	0.0147090i	−0.000523653	−	0.000906994i	−0.866287	+	0.499546i	$0.833500\pi$
$264$	0.395827	−	0.685592i	0.0243614	−	0.0421953i
$265$	22.5247			1.38368
$266$	0.0287104	+	0.500940i	0.00176035	+	0.0307146i
$267$	2.91822			0.178592
$268$	−0.573690	+	0.993660i	−0.0350437	+	0.0606974i
$269$	11.2379	+	19.4646i	0.685188	+	1.18678i	0.973378	+	0.229207i	$0.0736133\pi$
$269$	11.2379	+	19.4646i	0.685188	+	1.18678i	−0.288190	+	0.957573i	$0.593053\pi$
$270$	3.46312	+	5.99830i	0.210759	+	0.365045i
$271$	−12.3091	+	21.3200i	−0.747725	+	1.29510i	0.201186	+	0.979553i	$0.435520\pi$
$271$	−12.3091	+	21.3200i	−0.747725	+	1.29510i	−0.948911	+	0.315544i	$0.897813\pi$
$272$	−6.16317			−0.373697
$273$	0.165683	+	2.89084i	0.0100276	+	0.174962i
$274$	−5.97141			−0.360746
$275$	5.30297	−	9.18501i	0.319781	−	0.553877i
$276$	−0.186817	−	0.323577i	−0.0112451	−	0.0194771i
$277$	1.72013	+	2.97936i	0.103353	+	0.179012i	0.913064	−	0.407816i	$-0.133710\pi$
$277$	1.72013	+	2.97936i	0.103353	+	0.179012i	−0.809711	+	0.586828i	$0.800376\pi$
$278$	0.601543	−	1.04190i	0.0360782	−	0.0624892i
$279$	−16.7035			−1.00001
$280$	6.99643	−	4.59234i	0.418117	−	0.274445i
$281$	−0.178726			−0.0106619			−0.00533096	−	0.999986i	$-0.501697\pi$
$281$	−0.178726			−0.0106619			−0.00533096	+	0.999986i	$0.501697\pi$
$282$	1.66317	−	2.88070i	0.0990405	−	0.171543i
$283$	−7.29586	−	12.6368i	−0.433694	−	0.751180i	0.563494	−	0.826120i	$-0.309457\pi$
$283$	−7.29586	−	12.6368i	−0.433694	−	0.751180i	−0.997188	+	0.0749401i	$0.976123\pi$
$284$	−5.93052	−	10.2720i	−0.351912	−	0.609529i
$285$	0.112070	−	0.194111i	0.00663844	−	0.0114981i
$286$	6.20623			0.366982
$287$	−25.1950	−	12.6827i	−1.48721	−	0.748634i
$288$	2.86040			0.168551
$289$	−10.4923	+	18.1733i	−0.617197	+	1.06902i
$290$	−11.5081	−	19.9326i	−0.675779	−	1.17048i
$291$	−2.75371	−	4.76957i	−0.161426	−	0.279597i
$292$	−2.66706	+	4.61949i	−0.156078	+	0.270335i
$293$	−21.6062			−1.26225			−0.631124	−	0.775682i	$-0.717406\pi$
$293$	−21.6062			−1.26225			−0.631124	+	0.775682i	$0.717406\pi$
$294$	1.55794	+	2.10080i	0.0908610	+	0.122521i
$295$	−35.5352			−2.06894
$296$	−3.69754	+	6.40434i	−0.214915	+	0.372244i
$297$	2.31970	+	4.01784i	0.134603	+	0.233139i
$298$	−1.81813	−	3.14909i	−0.105321	−	0.182422i
$299$	1.46457	−	2.53671i	0.0846983	−	0.146702i
$300$	−1.87029			−0.107981
$301$	−13.8628	−	6.97828i	−0.799040	−	0.402221i
$302$	−18.3112			−1.05369
$303$	1.15645	−	2.00304i	0.0664365	−	0.115071i
$304$	−0.0948241	−	0.164240i	−0.00543853	−	0.00941982i
$305$	−7.76629	−	13.4516i	−0.444696	−	0.770237i
$306$	8.81456	−	15.2673i	0.503895	−	0.872772i
$307$	−2.18817			−0.124886			−0.0624428	−	0.998049i	$-0.519889\pi$
$307$	−2.18817			−0.124886			−0.0624428	+	0.998049i	$0.519889\pi$
$308$	4.68642	−	3.07609i	0.267034	−	0.175276i
$309$	3.58621			0.204012
$310$	9.23580	−	15.9969i	0.524558	−	0.908562i
$311$	1.76168	+	3.05133i	0.0998960	+	0.173025i	0.911641	−	0.410986i	$-0.134816\pi$
$311$	1.76168	+	3.05133i	0.0998960	+	0.173025i	−0.811745	+	0.584011i	$0.801482\pi$
$312$	−0.547214	−	0.947803i	−0.0309799	−	0.0536588i
$313$	5.76260	−	9.98112i	0.325721	−	0.564166i	−0.655937	−	0.754816i	$-0.727726\pi$
$313$	5.76260	−	9.98112i	0.325721	−	0.564166i	0.981658	+	0.190650i	$0.0610595\pi$
$314$	11.1790			0.630866
$315$	1.36975	+	23.8994i	0.0771765	+	1.34658i
$316$	−6.38943			−0.359433
$317$	14.0537	−	24.3416i	0.789332	−	1.36716i	−0.137045	−	0.990565i	$-0.543760\pi$
$317$	14.0537	−	24.3416i	0.789332	−	1.36716i	0.926377	−	0.376598i	$-0.122906\pi$
$318$	−1.33031	−	2.30416i	−0.0746000	−	0.129211i
$319$	−7.70847	−	13.3515i	−0.431592	−	0.747539i
$320$	−1.58159	+	2.73939i	−0.0884134	+	0.153136i
$321$	−7.17119			−0.400257
$322$	−0.151388	−	2.64142i	−0.00843651	−	0.147200i
$323$	−1.16883			−0.0650357
$324$	−3.88153	+	6.72301i	−0.215641	+	0.373501i
$325$	−7.33114	−	12.6979i	−0.406659	−	0.704354i
$326$	−0.880354	−	1.52482i	−0.0487583	−	0.0844518i
$327$	−0.562567	+	0.974395i	−0.0311101	+	0.0538842i
$328$	10.6613			0.588669
$329$	19.6913	−	12.9250i	1.08561	−	0.712579i
$330$	−2.50414			−0.137848
$331$	9.85420	−	17.0680i	0.541636	−	0.938141i	−0.457175	−	0.889377i	$-0.651139\pi$
$331$	9.85420	−	17.0680i	0.541636	−	0.938141i	0.998810	−	0.0487637i	$-0.0155281\pi$
$332$	−2.52502	−	4.37347i	−0.138579	−	0.240025i
$333$	−10.5764	−	18.3189i	−0.579586	−	1.00387i
$334$	5.35071	−	9.26769i	0.292778	−	0.507106i
$335$	3.62936			0.198293
$336$	−0.882984	−	0.444477i	−0.0481707	−	0.0242482i
$337$	28.7051			1.56367			0.781833	−	0.623488i	$-0.214285\pi$
$337$	28.7051			1.56367			0.781833	+	0.623488i	$0.214285\pi$
$338$	−2.21007	+	3.82795i	−0.120212	+	0.208213i
$339$	−1.40801	−	2.43874i	−0.0764724	−	0.132454i
$340$	9.74759	+	16.8833i	0.528637	+	0.915627i
$341$	6.18642	−	10.7152i	0.335014	−	0.580260i
$342$	0.542469			0.0293334
$343$	3.16527	+	18.2478i	0.170908	+	0.985287i
$344$	5.86606			0.316277
$345$	−0.590936	+	1.02353i	−0.0318149	+	0.0551050i
$346$	−5.34610	−	9.25972i	−0.287408	−	0.497806i
$347$	−6.65099	−	11.5199i	−0.357044	−	0.618418i	0.630422	−	0.776253i	$-0.282882\pi$
$347$	−6.65099	−	11.5199i	−0.357044	−	0.618418i	−0.987466	+	0.157835i	$0.949549\pi$
$348$	−1.35934	+	2.35444i	−0.0728682	+	0.126211i
$349$	−25.5902			−1.36981			−0.684907	−	0.728630i	$-0.740157\pi$
$349$	−25.5902			−1.36981			−0.684907	+	0.728630i	$0.740157\pi$
$350$	−11.8295	−	5.95475i	−0.632314	−	0.318295i
$351$	6.41379			0.342343
$352$	−1.05939	+	1.83493i	−0.0564659	+	0.0978018i
$353$	−16.5056	−	28.5885i	−0.878504	−	1.52161i	−0.852983	−	0.521939i	$-0.825209\pi$
$353$	−16.5056	−	28.5885i	−0.878504	−	1.52161i	−0.0255208	−	0.999674i	$-0.508124\pi$
$354$	2.09871	+	3.63508i	0.111545	+	0.193202i
$355$	−18.7593	+	32.4920i	−0.995638	+	1.72450i
$356$	−7.81035			−0.413948
$357$	−5.09337	+	3.34320i	−0.269570	+	0.176941i
$358$	13.9189			0.735635
$359$	−2.60924	+	4.51933i	−0.137710	+	0.238521i	−0.926630	−	0.375976i	$-0.877308\pi$
$359$	−2.60924	+	4.51933i	−0.137710	+	0.238521i	0.788919	+	0.614497i	$0.210641\pi$
$360$	−4.52396	−	7.83574i	−0.238434	−	0.412980i
$361$	9.48202	+	16.4233i	0.499054	+	0.864386i
$362$	−0.148237	+	0.256754i	−0.00779116	+	0.0134947i
$363$	2.43264			0.127680
$364$	−0.443436	−	7.73708i	−0.0232424	−	0.405533i
$365$	16.8727			0.883160
$366$	−0.917356	+	1.58891i	−0.0479510	+	0.0830535i
$367$	−1.22225	−	2.11699i	−0.0638008	−	0.110506i	0.832361	−	0.554234i	$-0.186989\pi$
$367$	−1.22225	−	2.11699i	−0.0638008	−	0.110506i	−0.896161	+	0.443728i	$0.853656\pi$
$368$	0.500000	+	0.866025i	0.0260643	+	0.0451447i
$369$	−15.2477	+	26.4098i	−0.793764	+	1.37484i
$370$	23.3919			1.21609
$371$	−1.07802	−	18.8093i	−0.0559679	−	0.976529i
$372$	−2.18187			−0.113125
$373$	1.45891	−	2.52690i	0.0755394	−	0.130838i	−0.825781	−	0.563990i	$-0.809265\pi$
$373$	1.45891	−	2.52690i	0.0755394	−	0.130838i	0.901321	+	0.433152i	$0.142599\pi$
$374$	6.52923	+	11.3090i	0.337619	+	0.584772i
$375$	0.00334557	+	0.00579471i	0.000172765	+	0.000299237i
$376$	−4.45133	+	7.70993i	−0.229560	+	0.397610i
$377$	−21.3133			−1.09769
$378$	4.84315	−	3.17896i	0.249105	−	0.163508i
$379$	35.4866			1.82282			0.911412	−	0.411494i	$-0.134993\pi$
$379$	35.4866			1.82282			0.911412	+	0.411494i	$0.134993\pi$
$380$	−0.299945	+	0.519520i	−0.0153868	+	0.0266508i
$381$	2.45173	+	4.24652i	0.125606	+	0.217556i
$382$	−10.6462	−	18.4398i	−0.544709	−	0.943464i
$383$	−17.7315	+	30.7119i	−0.906038	+	1.56930i	−0.0865212	+	0.996250i	$0.527575\pi$
$383$	−17.7315	+	30.7119i	−0.906038	+	1.56930i	−0.819517	+	0.573055i	$0.805758\pi$
$384$	0.373635			0.0190670
$385$	−15.8386	−	7.97283i	−0.807209	−	0.406333i
$386$	0.589357			0.0299975
$387$	−8.38963	+	14.5313i	−0.426469	+	0.738666i
$388$	7.37007	+	12.7653i	0.374158	+	0.648061i
$389$	12.1545	+	21.0521i	0.616256	+	1.06739i	0.990163	+	0.139920i	$0.0446846\pi$
$389$	12.1545	+	21.0521i	0.616256	+	1.06739i	−0.373907	+	0.927466i	$0.621982\pi$
$390$	−1.73093	+	2.99807i	−0.0876492	+	0.151813i
$391$	6.16317			0.311685
$392$	−4.16969	−	5.62260i	−0.210601	−	0.283984i
$393$	−0.0924634			−0.00466416
$394$	−13.0650	+	22.6292i	−0.658204	+	1.14004i
$395$	10.1054	+	17.5031i	0.508459	+	0.880678i
$396$	−3.03029	−	5.24861i	−0.152278	−	0.263753i
$397$	−4.17114	+	7.22463i	−0.209344	+	0.362594i	−0.951508	−	0.307624i	$-0.900466\pi$
$397$	−4.17114	+	7.22463i	−0.209344	+	0.362594i	0.742164	+	0.670218i	$0.233799\pi$
$398$	−1.39233			−0.0697914
$399$	−0.167456	−	0.0842942i	−0.00838330	−	0.00421999i
$400$	5.00566			0.250283
$401$	−6.70301	+	11.6099i	−0.334732	+	0.579773i	−0.983433	−	0.181270i	$-0.941979\pi$
$401$	−6.70301	+	11.6099i	−0.334732	+	0.579773i	0.648701	+	0.761043i	$0.275312\pi$
$402$	−0.214350	−	0.371266i	−0.0106908	−	0.0185171i
$403$	−8.55248	−	14.8133i	−0.426029	−	0.737905i
$404$	−3.09514	+	5.36095i	−0.153989	+	0.266717i
$405$	24.5559			1.22019
$406$	−16.0940	+	10.5638i	−0.798732	+	0.524274i
$407$	15.6686			0.776665
$408$	1.15139	−	1.99426i	0.0570022	−	0.0987307i
$409$	3.37100	+	5.83875i	0.166685	+	0.288708i	0.937253	−	0.348651i	$-0.113360\pi$
$409$	3.37100	+	5.83875i	0.166685	+	0.288708i	−0.770567	+	0.637359i	$0.780027\pi$
$410$	−16.8617	−	29.2053i	−0.832740	−	1.44235i
$411$	1.11556	−	1.93221i	0.0550267	−	0.0953090i
$412$	−9.59818			−0.472868
$413$	1.70070	+	29.6738i	0.0836858	+	1.46015i
$414$	−2.86040			−0.140581
$415$	−7.98708	+	13.8340i	−0.392070	+	0.679086i
$416$	1.46457	+	2.53671i	0.0718065	+	0.124372i
$417$	0.224757	+	0.389291i	0.0110064	+	0.0190637i
$418$	−0.200912	+	0.347990i	−0.00982694	+	0.0170208i
$419$	15.8546			0.774547			0.387274	−	0.921965i	$-0.373417\pi$
$419$	15.8546			0.774547			0.387274	+	0.921965i	$0.373417\pi$
$420$	0.178921	+	3.12181i	0.00873045	+	0.152329i
$421$	12.7296			0.620403			0.310202	−	0.950671i	$-0.399603\pi$
$421$	12.7296			0.620403			0.310202	+	0.950671i	$0.399603\pi$
$422$	10.5701	−	18.3080i	0.514545	−	0.891219i
$423$	−12.7326	−	22.0535i	−0.619079	−	1.07228i
$424$	3.56045	+	6.16688i	0.172911	+	0.299490i
$425$	15.4254	−	26.7175i	0.748241	−	1.29599i
$426$	4.43170			0.214716
$427$	−10.8611	+	7.12905i	−0.525606	+	0.344999i
$428$	19.1930			0.927731
$429$	−1.15943	+	2.00820i	−0.0559779	+	0.0969566i
$430$	−9.27768	−	16.0694i	−0.447409	−	0.774936i
$431$	−2.75042	−	4.76387i	−0.132483	−	0.229467i	0.792150	−	0.610326i	$-0.208962\pi$
$431$	−2.75042	−	4.76387i	−0.132483	−	0.229467i	−0.924633	+	0.380859i	$0.875628\pi$
$432$	−1.09482	+	1.89629i	−0.0526747	+	0.0912353i
$433$	12.2604			0.589195			0.294598	−	0.955621i	$-0.404814\pi$
$433$	12.2604			0.589195			0.294598	+	0.955621i	$0.404814\pi$
$434$	−13.8003	−	6.94678i	−0.662434	−	0.333456i
$435$	8.59965			0.412322
$436$	1.50566	−	2.60788i	0.0721081	−	0.124895i
$437$	0.0948241	+	0.164240i	0.00453605	+	0.00785667i
$438$	−0.996507	−	1.72600i	−0.0476149	−	0.0824715i
$439$	1.06867	−	1.85099i	0.0510048	−	0.0883429i	−0.839396	−	0.543521i	$-0.817091\pi$
$439$	1.06867	−	1.85099i	0.0510048	−	0.0883429i	0.890401	+	0.455178i	$0.150424\pi$
$440$	6.70210			0.319510
$441$	19.8917	−	2.28762i	0.947222	−	0.108934i
$442$	18.0528			0.858684
$443$	20.0360	−	34.7034i	0.951939	−	1.64881i	0.210716	−	0.977547i	$-0.432420\pi$
$443$	20.0360	−	34.7034i	0.951939	−	1.64881i	0.741223	−	0.671259i	$-0.234246\pi$
$444$	−1.38153	−	2.39288i	−0.0655646	−	0.113561i
$445$	12.3527	+	21.3956i	0.585576	+	1.01425i
$446$	−9.32549	+	16.1522i	−0.441575	+	0.764830i
$447$	1.35863			0.0642611
$448$	2.36323	+	1.18960i	0.111652	+	0.0562034i
$449$	18.2393			0.860766			0.430383	−	0.902646i	$-0.358379\pi$
$449$	18.2393			0.860766			0.430383	+	0.902646i	$0.358379\pi$
$450$	−7.15909	+	12.3999i	−0.337483	+	0.584537i
$451$	−11.2945	−	19.5626i	−0.531836	−	0.921167i
$452$	3.76840	+	6.52707i	0.177251	+	0.307007i
$453$	3.42085	−	5.92508i	0.160726	−	0.278385i
$454$	9.73069			0.456684
$455$	−20.4935	+	13.4516i	−0.960752	+	0.630621i
$456$	0.0708591			0.00331828
$457$	3.90577	−	6.76500i	0.182704	−	0.316453i	−0.760096	−	0.649811i	$-0.774848\pi$
$457$	3.90577	−	6.76500i	0.182704	−	0.316453i	0.942801	+	0.333357i	$0.108182\pi$
$458$	3.67146	+	6.35916i	0.171556	+	0.297144i
$459$	6.74759	+	11.6872i	0.314951	+	0.545510i
$460$	1.58159	−	2.73939i	0.0737418	−	0.127725i
$461$	−11.9196			−0.555153			−0.277577	−	0.960703i	$-0.589531\pi$
$461$	−11.9196			−0.555153			−0.277577	+	0.960703i	$0.589531\pi$
$462$	0.119847	+	2.09109i	0.00557577	+	0.0972861i
$463$	−13.4649			−0.625768			−0.312884	−	0.949791i	$-0.601295\pi$
$463$	−13.4649			−0.625768			−0.312884	+	0.949791i	$0.601295\pi$
$464$	3.63815	−	6.30146i	0.168897	−	0.292538i
$465$	3.45082	+	5.97699i	0.160028	+	0.277176i
$466$	13.8159	+	23.9299i	0.640011	+	1.10853i
$467$	−5.75740	+	9.97211i	−0.266421	+	0.461454i	−0.967935	−	0.251201i	$-0.919174\pi$
$467$	−5.75740	+	9.97211i	−0.266421	+	0.461454i	0.701514	+	0.712656i	$0.252508\pi$
$468$	−8.37851			−0.387297
$469$	−0.173699	−	3.03071i	−0.00802069	−	0.139945i
$470$	28.1607			1.29895
$471$	−2.08843	+	3.61726i	−0.0962296	+	0.166674i
$472$	−5.61702	−	9.72896i	−0.258544	−	0.447812i
$473$	−6.21447	−	10.7638i	−0.285742	−	0.494919i
$474$	1.19366	−	2.06747i	0.0548264	−	0.0949622i
$475$	0.949314			0.0435575
$476$	13.6320	−	8.94778i	0.624819	−	0.410121i
$477$	−20.3686			−0.932615
$478$	0.112807	−	0.195388i	0.00515968	−	0.00893684i
$479$	6.87784	+	11.9128i	0.314257	+	0.544309i	0.979279	−	0.202515i	$-0.0649114\pi$
$479$	6.87784	+	11.9128i	0.314257	+	0.544309i	−0.665023	+	0.746823i	$0.731578\pi$
$480$	−0.590936	−	1.02353i	−0.0269724	−	0.0467176i
$481$	10.8306	−	18.7592i	0.493834	−	0.855346i
$482$	18.3299			0.834904
$483$	0.882984	+	0.444477i	0.0401772	+	0.0202244i
$484$	−6.51073			−0.295942
$485$	23.3128	−	40.3789i	1.05858	−	1.83351i
$486$	−4.73475	−	8.20082i	−0.214772	−	0.371997i
$487$	17.2811	+	29.9318i	0.783082	+	1.35634i	0.930138	+	0.367209i	$0.119687\pi$
$487$	17.2811	+	29.9318i	0.783082	+	1.35634i	−0.147057	+	0.989128i	$0.546980\pi$
$488$	2.45522	−	4.25257i	0.111143	−	0.192505i
$489$	0.657862			0.0297495
$490$	−8.80777	+	20.3150i	−0.397894	+	0.917740i
$491$	−5.54339			−0.250170			−0.125085	−	0.992146i	$-0.539920\pi$
$491$	−5.54339			−0.250170			−0.125085	+	0.992146i	$0.539920\pi$
$492$	−1.99171	+	3.44974i	−0.0897931	+	0.155526i
$493$	−22.4225	−	38.8370i	−1.00986	−	1.74913i
$494$	0.277753	+	0.481082i	0.0124967	+	0.0216449i
$495$	−9.58533	+	16.6023i	−0.430828	+	0.746217i
$496$	5.83958			0.262205
$497$	28.0303	+	14.1099i	1.25733	+	0.632916i
$498$	1.88687			0.0845528
$499$	−13.7982	+	23.8992i	−0.617694	+	1.06988i	0.372212	+	0.928148i	$0.378599\pi$
$499$	−13.7982	+	23.8992i	−0.617694	+	1.06988i	−0.989905	+	0.141729i	$0.954734\pi$
$500$	−0.00895413	−	0.0155090i	−0.000400441	−	0.000693584i
$501$	1.99921	+	3.46273i	0.0893181	+	0.154703i
$502$	−11.1776	+	19.3601i	−0.498880	+	0.864086i
$503$	11.2311			0.500771			0.250386	−	0.968146i	$-0.419443\pi$
$503$	11.2311			0.500771			0.250386	+	0.968146i	$0.419443\pi$
$504$	−6.32674	+	4.15276i	−0.281815	+	0.184979i
$505$	19.5810			0.871341
$506$	1.05939	−	1.83493i	0.0470958	−	0.0815724i
$507$	−0.825758	−	1.43025i	−0.0366732	−	0.0635198i
$508$	−6.56183	−	11.3654i	−0.291134	−	0.504259i
$509$	15.2687	−	26.4462i	0.676774	−	1.17221i	−0.299173	−	0.954199i	$-0.596711\pi$
$509$	15.2687	−	26.4462i	0.676774	−	1.17221i	0.975947	−	0.218008i	$-0.0699560\pi$
$510$	−7.28408			−0.322544
$511$	−0.807521	−	14.0896i	−0.0357226	−	0.623289i
$512$	−1.00000			−0.0441942
$513$	−0.207631	+	0.359628i	−0.00916715	+	0.0158780i
$514$	11.5059	+	19.9288i	0.507504	+	0.879022i
$515$	15.1803	+	26.2931i	0.668926	+	1.15861i
$516$	−1.09588	+	1.89812i	−0.0482435	+	0.0835602i
$517$	18.8629			0.829588
$518$	−1.11953	−	19.5335i	−0.0491892	−	0.858253i
$519$	3.99498			0.175360
$520$	4.63269	−	8.02405i	0.203157	−	0.351878i
$521$	5.16790	+	8.95106i	0.226410	+	0.392153i	0.956741	−	0.290940i	$-0.0939679\pi$
$521$	5.16790	+	8.95106i	0.226410	+	0.392153i	−0.730332	+	0.683093i	$0.760635\pi$
$522$	10.4066	+	18.0247i	0.455482	+	0.788919i
$523$	−17.6891	+	30.6384i	−0.773491	+	1.33973i	0.162148	+	0.986766i	$0.448158\pi$
$523$	−17.6891	+	30.6384i	−0.773491	+	1.33973i	−0.935639	+	0.352959i	$0.885176\pi$
$524$	0.247470			0.0108108
$525$	4.13678	−	2.71531i	0.180544	−	0.118506i
$526$	−0.0169845			−0.000740558
$527$	17.9952	−	31.1686i	0.783882	−	1.35772i
$528$	−0.395827	−	0.685592i	−0.0172261	−	0.0298366i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	11.2623	−	19.5069i	0.489204	−	0.847326i
$531$	32.1338			1.39449
$532$	0.448182	+	0.225606i	0.0194311	+	0.00978126i
$533$	−31.2283			−1.35265
$534$	1.45911	−	2.52725i	0.0631418	−	0.109365i
$535$	−30.3555	−	52.5772i	−1.31238	−	2.27311i
$536$	0.573690	+	0.993660i	0.0247796	+	0.0429196i
$537$	−2.60028	+	4.50383i	−0.112211	+	0.194354i
$538$	22.4758			0.969002
$539$	−5.89971	+	13.6076i	−0.254118	+	0.586122i
$540$	6.92624			0.298058
$541$	−16.7045	+	28.9331i	−0.718183	+	1.24393i	0.243536	+	0.969892i	$0.421693\pi$
$541$	−16.7045	+	28.9331i	−0.718183	+	1.24393i	−0.961719	+	0.274037i	$0.911641\pi$
$542$	12.3091	+	21.3200i	0.528721	+	0.915772i
$543$	−0.0553864	−	0.0959321i	−0.00237686	−	0.00411684i
$544$	−3.08159	+	5.33746i	−0.132122	+	0.228842i
$545$	−9.52533			−0.408021
$546$	2.58638	+	1.30194i	0.110687	+	0.0557177i
$547$	3.23654			0.138384			0.0691922	−	0.997603i	$-0.477958\pi$
$547$	3.23654			0.138384			0.0691922	+	0.997603i	$0.477958\pi$
$548$	−2.98570	+	5.17139i	−0.127543	+	0.220911i
$549$	7.02291	+	12.1640i	0.299730	+	0.519148i
$550$	−5.30297	−	9.18501i	−0.226119	−	0.391650i
$551$	0.689968	−	1.19506i	0.0293936	−	0.0509113i
$552$	−0.373635			−0.0159030
$553$	14.1324	−	9.27626i	0.600970	−	0.394467i
$554$	3.44026			0.146163
$555$	−4.37002	+	7.56910i	−0.185497	+	0.321290i
$556$	−0.601543	−	1.04190i	−0.0255111	−	0.0441865i
$557$	−3.48295	−	6.03264i	−0.147577	−	0.255611i	0.782754	−	0.622331i	$-0.213814\pi$
$557$	−3.48295	−	6.03264i	−0.147577	−	0.255611i	−0.930332	+	0.366720i	$0.880481\pi$
$558$	−8.35176	+	14.4657i	−0.353558	+	0.612381i
$559$	−17.1825			−0.726743
$560$	−0.478866	−	8.35526i	−0.0202358	−	0.353074i
$561$	−4.87910			−0.205996
$562$	−0.0893632	+	0.154782i	−0.00376956	+	0.00652907i
$563$	−5.41756	−	9.38348i	−0.228323	−	0.395467i	0.728988	−	0.684526i	$-0.239991\pi$
$563$	−5.41756	−	9.38348i	−0.228323	−	0.395467i	−0.957311	+	0.289059i	$0.906657\pi$
$564$	−1.66317	−	2.88070i	−0.0700322	−	0.121299i
$565$	11.9201	−	20.6462i	0.501483	−	0.868594i
$566$	−14.5917			−0.613336
$567$	−1.17523	−	20.5055i	−0.0493552	−	0.861149i
$568$	−11.8610			−0.497678
$569$	4.62248	−	8.00636i	0.193784	−	0.335644i	−0.752717	−	0.658344i	$-0.771257\pi$
$569$	4.62248	−	8.00636i	0.193784	−	0.335644i	0.946501	+	0.322700i	$0.104590\pi$
$570$	−0.112070	−	0.194111i	−0.00469409	−	0.00813040i
$571$	15.8854	+	27.5144i	0.664784	+	1.15144i	0.979344	+	0.202202i	$0.0648098\pi$
$571$	15.8854	+	27.5144i	0.664784	+	1.15144i	−0.314560	+	0.949238i	$0.601857\pi$
$572$	3.10312	−	5.37475i	0.129748	−	0.224730i
$573$	7.95562			0.332351
$574$	−23.5810	+	15.4782i	−0.984252	+	0.646046i
$575$	−5.00566			−0.208751
$576$	1.43020	−	2.47718i	0.0595916	−	0.103216i
$577$	−9.94942	−	17.2329i	−0.414200	−	0.717415i	0.581144	−	0.813800i	$-0.302605\pi$
$577$	−9.94942	−	17.2329i	−0.414200	−	0.717415i	−0.995344	+	0.0963856i	$0.969272\pi$
$578$	10.4923	+	18.1733i	0.436424	+	0.755909i
$579$	−0.110102	+	0.190703i	−0.00457569	+	0.00792533i
$580$	−23.0162			−0.955695
$581$	11.9344	+	6.00755i	0.495123	+	0.249235i
$582$	−5.50743			−0.228290
$583$	7.54385	−	13.0663i	0.312434	−	0.541152i
$584$	2.66706	+	4.61949i	0.110364	+	0.191156i
$585$	13.2513	+	22.9520i	0.547875	+	0.948947i
$586$	−10.8031	+	18.7115i	−0.446272	+	0.772965i
$587$	13.1985			0.544759			0.272380	−	0.962190i	$-0.412189\pi$
$587$	13.1985			0.544759			0.272380	+	0.962190i	$0.412189\pi$
$588$	2.59832	−	0.298817i	0.107153	−	0.0123230i
$589$	1.10747			0.0456323
$590$	−17.7676	+	30.7744i	−0.731480	+	1.26696i
$591$	−4.88153	−	8.45506i	−0.200799	−	0.347795i
$592$	3.69754	+	6.40434i	0.151968	+	0.263217i
$593$	−19.9566	+	34.5658i	−0.819519	+	1.41945i	0.0865176	+	0.996250i	$0.472426\pi$
$593$	−19.9566	+	34.5658i	−0.819519	+	1.41945i	−0.906037	+	0.423199i	$0.860907\pi$
$594$	4.63940			0.190357
$595$	−46.0716	−	23.1915i	−1.88875	−	0.950759i
$596$	−3.63626			−0.148947
$597$	0.260112	−	0.450527i	0.0106457	−	0.0184389i
$598$	−1.46457	−	2.53671i	−0.0598907	−	0.103734i
$599$	−14.2740	−	24.7233i	−0.583219	−	1.01017i	−0.995095	−	0.0989255i	$-0.968459\pi$
$599$	−14.2740	−	24.7233i	−0.583219	−	1.01017i	0.411875	−	0.911240i	$-0.364874\pi$
$600$	−0.935145	+	1.61972i	−0.0381771	+	0.0661247i
$601$	−1.82802			−0.0745665			−0.0372833	−	0.999305i	$-0.511870\pi$
$601$	−1.82802			−0.0745665			−0.0372833	+	0.999305i	$0.511870\pi$
$602$	−12.9748	+	8.51643i	−0.528813	+	0.347104i
$603$	−3.28196			−0.133652
$604$	−9.15560	+	15.8580i	−0.372536	+	0.645251i
$605$	10.2973	+	17.8354i	0.418644	+	0.725113i
$606$	−1.15645	−	2.00304i	−0.0469777	−	0.0813678i
$607$	−1.67589	+	2.90273i	−0.0680223	+	0.117818i	−0.898031	−	0.439933i	$-0.855002\pi$
$607$	−1.67589	+	2.90273i	−0.0680223	+	0.117818i	0.830008	+	0.557751i	$0.188336\pi$
$608$	−0.189648			−0.00769125
$609$	−0.411575	−	7.18116i	−0.0166779	−	0.290995i
$610$	−15.5326			−0.628896
$611$	13.0386	−	22.5835i	0.527485	−	0.913630i
$612$	−8.81456	−	15.2673i	−0.356307	−	0.617143i
$613$	−23.3194	−	40.3904i	−0.941862	−	1.63135i	−0.761915	−	0.647677i	$-0.775741\pi$
$613$	−23.3194	−	40.3904i	−0.941862	−	1.63135i	−0.179947	−	0.983676i	$-0.557593\pi$
$614$	−1.09409	+	1.89501i	−0.0441537	+	0.0764765i
$615$	12.6002			0.508091
$616$	−0.320759	−	5.59660i	−0.0129237	−	0.225494i
$617$	37.7330			1.51907			0.759537	−	0.650464i	$-0.225426\pi$
$617$	37.7330			1.51907			0.759537	+	0.650464i	$0.225426\pi$
$618$	1.79311	−	3.10575i	0.0721293	−	0.124932i
$619$	6.12888	+	10.6155i	0.246340	+	0.426674i	0.962508	−	0.271255i	$-0.0874386\pi$
$619$	6.12888	+	10.6155i	0.246340	+	0.426674i	−0.716167	+	0.697929i	$0.754105\pi$
$620$	−9.23580	−	15.9969i	−0.370919	−	0.642450i
$621$	1.09482	−	1.89629i	0.0439338	−	0.0760955i
$622$	3.52337			0.141274
$623$	17.2752	−	11.3392i	0.692118	−	0.454295i
$624$	−1.09443			−0.0438122
$625$	12.4858	−	21.6261i	0.499433	−	0.865044i
$626$	−5.76260	−	9.98112i	−0.230320	−	0.398926i
$627$	−0.0750678	−	0.130021i	−0.00299792	−	0.00519255i
$628$	5.58948	−	9.68127i	0.223045	−	0.386325i
$629$	45.5772			1.81728
$630$	21.3823	+	10.7634i	0.851892	+	0.428826i
$631$	4.74623			0.188944			0.0944722	−	0.995528i	$-0.469884\pi$
$631$	4.74623			0.188944			0.0944722	+	0.995528i	$0.469884\pi$
$632$	−3.19471	+	5.53341i	−0.127079	+	0.220107i
$633$	3.94937	+	6.84050i	0.156973	+	0.271886i
$634$	−14.0537	−	24.3416i	−0.558142	−	0.966730i
$635$	−20.7562	+	35.9508i	−0.823685	+	1.42666i
$636$	−2.66062			−0.105500
$637$	12.2136	+	16.4694i	0.483921	+	0.652541i
$638$	−15.4169			−0.610363
$639$	16.9636	−	29.3819i	0.671071	−	1.16233i
$640$	1.58159	+	2.73939i	0.0625177	+	0.108284i
$641$	−6.03410	−	10.4514i	−0.238332	−	0.412804i	0.721903	−	0.691994i	$-0.243267\pi$
$641$	−6.03410	−	10.4514i	−0.238332	−	0.412804i	−0.960236	+	0.279190i	$0.909934\pi$
$642$	−3.58559	+	6.21043i	−0.141512	+	0.245106i
$643$	−22.2950			−0.879229			−0.439615	−	0.898186i	$-0.644885\pi$
$643$	−22.2950			−0.879229			−0.439615	+	0.898186i	$0.644885\pi$
$644$	−2.36323	−	1.18960i	−0.0931242	−	0.0468769i
$645$	6.93293			0.272984
$646$	−0.584417	+	1.01224i	−0.0229936	+	0.0398261i
$647$	6.89014	+	11.9341i	0.270879	+	0.469177i	0.969087	−	0.246718i	$-0.0793522\pi$
$647$	6.89014	+	11.9341i	0.270879	+	0.469177i	−0.698208	+	0.715895i	$0.746019\pi$
$648$	3.88153	+	6.72301i	0.152481	+	0.264105i
$649$	−11.9013	+	20.6136i	−0.467166	+	0.809155i
$650$	−14.6623			−0.575102
$651$	4.82595	−	3.16767i	0.189144	−	0.124151i
$652$	−1.76071			−0.0689546
$653$	−5.94944	+	10.3047i	−0.232820	+	0.403255i	−0.958637	−	0.284632i	$-0.908128\pi$
$653$	−5.94944	+	10.3047i	−0.232820	+	0.403255i	0.725817	+	0.687888i	$0.241462\pi$
$654$	0.562567	+	0.974395i	0.0219981	+	0.0381019i
$655$	−0.391395	−	0.677917i	−0.0152931	−	0.0264884i
$656$	5.33063	−	9.23292i	0.208126	−	0.360485i
$657$	−15.2577			−0.595260
$658$	−1.34776	−	23.5156i	−0.0525410	−	0.916735i
$659$	−44.1271			−1.71895			−0.859473	−	0.511181i	$-0.829208\pi$
$659$	−44.1271			−1.71895			−0.859473	+	0.511181i	$0.829208\pi$
$660$	−1.25207	+	2.16865i	−0.0487367	+	0.0844144i
$661$	12.3421	+	21.3772i	0.480054	+	0.831477i	0.999738	−	0.0228810i	$-0.00728389\pi$
$661$	12.3421	+	21.3772i	0.480054	+	0.831477i	−0.519685	+	0.854358i	$0.673951\pi$
$662$	−9.85420	−	17.0680i	−0.382994	−	0.663366i
$663$	−3.37258	+	5.84147i	−0.130980	+	0.226864i
$664$	−5.05005			−0.195980
$665$	−0.0908160	−	1.58456i	−0.00352169	−	0.0614466i
$666$	−21.1529			−0.819658
$667$	−3.63815	+	6.30146i	−0.140870	+	0.243994i
$668$	−5.35071	−	9.26769i	−0.207025	−	0.358578i
$669$	−3.48433	−	6.03503i	−0.134712	−	0.233328i
$670$	1.81468	−	3.14312i	0.0701072	−	0.121429i
$671$	−10.4042			−0.401649
$672$	−0.826420	+	0.542448i	−0.0318799	+	0.0209254i
$673$	−17.3000			−0.666867			−0.333433	−	0.942774i	$-0.608207\pi$
$673$	−17.3000			−0.666867			−0.333433	+	0.942774i	$0.608207\pi$
$674$	14.3525	−	24.8593i	0.552839	−	0.957546i
$675$	−5.48032	−	9.49219i	−0.210938	−	0.365355i
$676$	2.21007	+	3.82795i	0.0850026	+	0.147229i
$677$	7.04373	−	12.2001i	0.270712	−	0.468888i	−0.698332	−	0.715774i	$-0.746074\pi$
$677$	7.04373	−	12.2001i	0.270712	−	0.468888i	0.969044	+	0.246886i	$0.0794074\pi$
$678$	−2.81601			−0.108148
$679$	−34.8343	−	17.5349i	−1.33682	−	0.672928i
$680$	19.4952			0.747606
$681$	−1.81786	+	3.14863i	−0.0696606	+	0.120656i
$682$	−6.18642	−	10.7152i	−0.236890	−	0.410306i
$683$	−17.3797	−	30.1026i	−0.665017	−	1.15184i	−0.979281	−	0.202508i	$-0.935091\pi$
$683$	−17.3797	−	30.1026i	−0.665017	−	1.15184i	0.314264	−	0.949336i	$-0.398242\pi$
$684$	0.271234	−	0.469792i	0.0103709	−	0.0179629i
$685$	18.8886			0.721696
$686$	17.3857	+	6.38268i	0.663788	+	0.243692i
$687$	−2.74357			−0.104674
$688$	2.93303	−	5.08016i	0.111821	−	0.193679i
$689$	−10.4291	−	18.0637i	−0.397316	−	0.688171i
$690$	0.590936	+	1.02353i	0.0224965	+	0.0389651i
$691$	−12.6485	+	21.9078i	−0.481171	+	0.833413i	−0.999767	−	0.0216071i	$-0.993122\pi$
$691$	−12.6485	+	21.9078i	−0.481171	+	0.833413i	0.518596	+	0.855020i	$0.326455\pi$
$692$	−10.6922			−0.406457
$693$	14.3225	+	7.20968i	0.544068	+	0.273873i
$694$	−13.3020			−0.504936
$695$	−1.90279	+	3.29572i	−0.0721768	+	0.125014i
$696$	1.35934	+	2.35444i	0.0515256	+	0.0892450i
$697$	−32.8536	−	56.9041i	−1.24442	−	2.15540i
$698$	−12.7951	+	22.1618i	−0.484303	+	0.838837i
$699$	−10.3242			−0.390498
$700$	−11.0717	+	7.26729i	−0.418472	+	0.274678i
$701$	22.7818			0.860455			0.430228	−	0.902720i	$-0.358433\pi$
$701$	22.7818			0.860455			0.430228	+	0.902720i	$0.358433\pi$
$702$	3.20689	−	5.55450i	0.121036	−	0.209641i
$703$	0.701232	+	1.21457i	0.0264475	+	0.0458084i
$704$	1.05939	+	1.83493i	0.0399274	+	0.0691563i
$705$	−5.26090	+	9.11215i	−0.198137	+	0.343183i
$706$	−33.0112			−1.24239
$707$	−0.937134	−	16.3511i	−0.0352446	−	0.614948i
$708$	4.19742			0.157749
$709$	−17.8646	+	30.9424i	−0.670919	+	1.16207i	0.306724	+	0.951798i	$0.400767\pi$
$709$	−17.8646	+	30.9424i	−0.670919	+	1.16207i	−0.977644	+	0.210268i	$0.932566\pi$
$710$	18.7593	+	32.4920i	0.704022	+	1.21940i
$711$	−9.13815	−	15.8277i	−0.342707	−	0.593587i
$712$	−3.90518	+	6.76396i	−0.146353	+	0.253490i
$713$	−5.83958			−0.218694
$714$	0.348612	+	6.08259i	0.0130465	+	0.227635i
$715$	−19.6314			−0.734172
$716$	6.95943	−	12.0541i	0.260086	−	0.450482i
$717$	0.0421487	+	0.0730037i	0.00157407	+	0.00272637i
$718$	2.60924	+	4.51933i	0.0973759	+	0.168660i
$719$	8.44467	−	14.6266i	0.314933	−	0.545480i	−0.664490	−	0.747297i	$-0.731351\pi$
$719$	8.44467	−	14.6266i	0.314933	−	0.545480i	0.979423	+	0.201817i	$0.0646846\pi$
$720$	−9.04793			−0.337196
$721$	21.2296	−	13.9348i	0.790633	−	0.518958i
$722$	18.9640			0.705768
$723$	−3.42434	+	5.93114i	−0.127353	+	0.220581i
$724$	0.148237	+	0.256754i	0.00550918	+	0.00954218i
$725$	18.2113	+	31.5430i	0.676352	+	1.17148i
$726$	1.21632	−	2.10672i	0.0451418	−	0.0781879i
$727$	42.8443			1.58901			0.794504	−	0.607259i	$-0.207731\pi$
$727$	42.8443			1.58901			0.794504	+	0.607259i	$0.207731\pi$
$728$	−6.92223	−	3.48451i	−0.256555	−	0.129145i
$729$	−19.7511			−0.731521
$730$	8.43637	−	14.6122i	0.312244	−	0.540823i
$731$	−18.0768	−	31.3099i	−0.668593	−	1.15804i
$732$	0.917356	+	1.58891i	0.0339065	+	0.0587277i
$733$	10.6938	−	18.5222i	0.394984	−	0.684132i	−0.598115	−	0.801410i	$-0.704084\pi$
$733$	10.6938	−	18.5222i	0.394984	−	0.684132i	0.993099	+	0.117278i	$0.0374169\pi$
$734$	−2.44449			−0.0902279
$735$	−4.92804	−	6.64519i	−0.181773	−	0.245112i
$736$	1.00000			0.0368605
$737$	1.21553	−	2.10536i	0.0447745	−	0.0775518i
$738$	15.2477	+	26.4098i	0.561276	+	0.972159i
$739$	2.47571	+	4.28806i	0.0910706	+	0.157739i	0.907962	−	0.419053i	$-0.137638\pi$
$739$	2.47571	+	4.28806i	0.0910706	+	0.157739i	−0.816891	+	0.576792i	$0.804304\pi$
$740$	11.6960	−	20.2580i	0.429952	−	0.744700i
$741$	−0.207556			−0.00762477
$742$	−16.8283	−	8.47105i	−0.617787	−	0.310982i
$743$	−38.6224			−1.41692			−0.708459	−	0.705752i	$-0.750609\pi$
$743$	−38.6224			−1.41692			−0.708459	+	0.705752i	$0.750609\pi$
$744$	−1.09094	+	1.88956i	−0.0399956	+	0.0692745i
$745$	5.75106	+	9.96112i	0.210702	+	0.364947i
$746$	−1.45891	−	2.52690i	−0.0534145	−	0.0925165i
$747$	7.22257	−	12.5099i	0.264260	−	0.457712i
$748$	13.0585			0.477465
$749$	−42.4519	+	27.8647i	−1.55116	+	1.01816i
$750$	0.00669115			0.000244326
$751$	−3.23160	+	5.59729i	−0.117923	+	0.204248i	−0.918944	−	0.394387i	$-0.870957\pi$
$751$	−3.23160	+	5.59729i	−0.117923	+	0.204248i	0.801022	+	0.598635i	$0.204290\pi$
$752$	4.45133	+	7.70993i	0.162323	+	0.281152i
$753$	−4.17634	−	7.23363i	−0.152194	−	0.263608i
$754$	−10.6567	+	18.4579i	−0.388092	+	0.672196i
$755$	57.9215			2.10798
$756$	−0.331486	−	5.78377i	−0.0120560	−	0.210354i
$757$	−0.825265			−0.0299948			−0.0149974	−	0.999888i	$-0.504774\pi$
$757$	−0.825265			−0.0299948			−0.0149974	+	0.999888i	$0.504774\pi$
$758$	17.7433	−	30.7323i	0.644466	−	1.11625i
$759$	0.395827	+	0.685592i	0.0143676	+	0.0248854i
$760$	0.299945	+	0.519520i	0.0108801	+	0.0188450i
$761$	−2.68285	+	4.64684i	−0.0972534	+	0.168448i	−0.910547	−	0.413406i	$-0.864339\pi$
$761$	−2.68285	+	4.64684i	−0.0972534	+	0.168448i	0.813293	+	0.581854i	$0.197672\pi$
$762$	4.90346			0.177633
$763$	0.455878	+	7.95416i	0.0165039	+	0.287960i
$764$	−21.2925			−0.770335
$765$	−27.8820	+	48.2930i	−1.00808	+	1.74604i
$766$	17.7315	+	30.7119i	0.640666	+	1.10967i
$767$	16.4530	+	28.4975i	0.594085	+	1.02898i
$768$	0.186817	−	0.323577i	0.00674119	−	0.0116761i
$769$	−13.1192			−0.473090			−0.236545	−	0.971621i	$-0.576015\pi$
$769$	−13.1192			−0.473090			−0.236545	+	0.971621i	$0.576015\pi$
$770$	−14.8240	+	9.73020i	−0.534219	+	0.350652i
$771$	−8.59801			−0.309650
$772$	0.294679	−	0.510398i	0.0106057	−	0.0183696i
$773$	−7.19589	−	12.4636i	−0.258818	−	0.448286i	0.707107	−	0.707106i	$-0.250000\pi$
$773$	−7.19589	−	12.4636i	−0.258818	−	0.448286i	−0.965926	+	0.258820i	$0.916666\pi$
$774$	8.38963	+	14.5313i	0.301559	+	0.522315i
$775$	−14.6155	+	25.3148i	−0.525004	+	0.909333i
$776$	14.7401			0.529140
$777$	6.52975	+	3.28695i	0.234253	+	0.117919i
$778$	24.3089			0.871517
$779$	1.01094	−	1.75101i	0.0362208	−	0.0627363i
$780$	1.73093	+	2.99807i	0.0619774	+	0.107348i
$781$	12.5655	+	21.7641i	0.449630	+	0.778781i
$782$	3.08159	−	5.33746i	0.110197	−	0.190867i
$783$	−15.9325			−0.569382
$784$	−6.95416	+	0.799757i	−0.248363	+	0.0285627i
$785$	−35.3610			−1.26209
$786$	−0.0462317	+	0.0800757i	−0.00164903	+	0.00285621i
$787$	1.12248	+	1.94420i	0.0400122	+	0.0693031i	0.885338	−	0.464948i	$-0.153927\pi$
$787$	1.12248	+	1.94420i	0.0400122	+	0.0693031i	−0.845326	+	0.534251i	$0.820594\pi$
$788$	13.0650	+	22.6292i	0.465421	+	0.806132i
$789$	0.00317299	−	0.00549578i	0.000112962	−	0.000195655i
$790$	20.2109			0.719070
$791$	−17.8112	−	8.96581i	−0.633293	−	0.318787i
$792$	−6.06058			−0.215353
$793$	−7.19169	+	12.4564i	−0.255384	+	0.442339i
$794$	4.17114	+	7.22463i	0.148028	+	0.256393i
$795$	4.20800	+	7.28846i	0.149242	+	0.258495i
$796$	−0.696167	+	1.20580i	−0.0246750	+	0.0427383i
$797$	17.8533			0.632396			0.316198	−	0.948693i	$-0.397594\pi$
$797$	17.8533			0.632396			0.316198	+	0.948693i	$0.397594\pi$
$798$	−0.156729	+	0.102874i	−0.00554815	+	0.00364171i
$799$	54.8687			1.94111
$800$	2.50283	−	4.33503i	0.0884884	−	0.153266i
$801$	−11.1704	−	19.3476i	−0.394685	−	0.683615i
$802$	6.70301	+	11.6099i	0.236691	+	0.409961i
$803$	5.65094	−	9.78771i	0.199417	−	0.345401i
$804$	−0.428701			−0.0151191
$805$	0.478866	+	8.35526i	0.0168778	+	0.294484i
$806$	−17.1050			−0.602497
$807$	−4.19888	+	7.27267i	−0.147807	+	0.256010i
$808$	3.09514	+	5.36095i	0.108887	+	0.188597i
$809$	11.1677	+	19.3430i	0.392635	+	0.680065i	0.992796	−	0.119815i	$-0.0382301\pi$
$809$	11.1677	+	19.3430i	0.392635	+	0.680065i	−0.600161	+	0.799879i	$0.704897\pi$
$810$	12.2780	−	21.2660i	0.431403	−	0.747212i
$811$	−3.64611			−0.128032			−0.0640160	−	0.997949i	$-0.520391\pi$
$811$	−3.64611			−0.128032			−0.0640160	+	0.997949i	$0.520391\pi$
$812$	1.10154	+	19.2197i	0.0386566	+	0.674481i
$813$	−9.19822			−0.322595
$814$	7.83432	−	13.5694i	0.274593	−	0.475608i
$815$	2.78471	+	4.82326i	0.0975442	+	0.168951i
$816$	−1.15139	−	1.99426i	−0.0403066	−	0.0698131i
$817$	0.556244	−	0.963442i	0.0194605	−	0.0337066i
$818$	6.74201			0.235729
$819$	18.5319	−	12.1640i	0.647557	−	0.425046i
$820$	−33.7234			−1.17767
$821$	20.9756	−	36.3308i	0.732054	−	1.26796i	−0.223949	−	0.974601i	$-0.571895\pi$
$821$	20.9756	−	36.3308i	0.732054	−	1.26796i	0.956004	−	0.293355i	$-0.0947716\pi$
$822$	−1.11556	−	1.93221i	−0.0389097	−	0.0673936i
$823$	−0.274922	−	0.476179i	−0.00958319	−	0.0165986i	0.861194	−	0.508276i	$-0.169717\pi$
$823$	−0.274922	−	0.476179i	−0.00958319	−	0.0165986i	−0.870777	+	0.491678i	$0.836384\pi$
$824$	−4.79909	+	8.31226i	−0.167184	+	0.289571i
$825$	3.96275			0.137965
$826$	26.5486	+	13.3640i	0.923743	+	0.464994i
$827$	55.0697			1.91496			0.957480	−	0.288499i	$-0.0931562\pi$
$827$	55.0697			1.91496			0.957480	+	0.288499i	$0.0931562\pi$
$828$	−1.43020	+	2.47718i	−0.0497028	+	0.0860878i
$829$	14.8578	+	25.7344i	0.516032	+	0.893793i	0.999827	+	0.0186117i	$0.00592462\pi$
$829$	14.8578	+	25.7344i	0.516032	+	0.893793i	−0.483795	+	0.875181i	$0.660742\pi$
$830$	7.98708	+	13.8340i	0.277236	+	0.480186i
$831$	−0.642701	+	1.11319i	−0.0222951	+	0.0386162i
$832$	2.92914			0.101550
$833$	−17.1612	+	39.5821i	−0.594600	+	1.37144i
$834$	0.449515			0.0155654
$835$	−16.9252	+	29.3153i	−0.585721	+	1.01450i
$836$	0.200912	+	0.347990i	0.00694869	+	0.0120355i
$837$	−6.39332	−	11.0735i	−0.220985	−	0.382758i
$838$	7.92729	−	13.7305i	0.273844	−	0.474311i
$839$	−34.7078			−1.19824			−0.599122	−	0.800657i	$-0.704484\pi$
$839$	−34.7078			−1.19824			−0.599122	+	0.800657i	$0.704484\pi$
$840$	2.79303	+	1.40596i	0.0963687	+	0.0485101i
$841$	23.9445			0.825674
$842$	6.36481	−	11.0242i	0.219346	−	0.379918i
$843$	−0.0333892	−	0.0578318i	−0.00114998	−	0.00199183i
$844$	−10.5701	−	18.3080i	−0.363839	−	0.630187i
$845$	6.99082	−	12.1085i	0.240492	−	0.416544i
$846$	−25.4652			−0.875510
$847$	14.4007	−	9.45237i	0.494814	−	0.324787i
$848$	7.12090			0.244533
$849$	2.72599	−	4.72155i	0.0935557	−	0.162043i
$850$	−15.4254	−	26.7175i	−0.529086	−	0.916404i
$851$	−3.69754	−	6.40434i	−0.126750	−	0.219538i
$852$	2.21585	−	3.83796i	0.0759137	−	0.131486i
$853$	20.0595			0.686824			0.343412	−	0.939185i	$-0.388417\pi$
$853$	20.0595			0.686824			0.343412	+	0.939185i	$0.388417\pi$
$854$	0.743381	+	12.9705i	0.0254380	+	0.443842i
$855$	−1.71592			−0.0586833
$856$	9.59652	−	16.6217i	0.328002	−	0.568117i
$857$	−25.1710	−	43.5974i	−0.859825	−	1.48926i	−0.872096	−	0.489335i	$-0.837239\pi$
$857$	−25.1710	−	43.5974i	−0.859825	−	1.48926i	0.0122708	−	0.999925i	$-0.496094\pi$
$858$	1.15943	+	2.00820i	0.0395824	+	0.0685586i
$859$	−3.28388	+	5.68784i	−0.112044	+	0.194067i	−0.916594	−	0.399818i	$-0.869073\pi$
$859$	−3.28388	+	5.68784i	−0.112044	+	0.194067i	0.804550	+	0.593885i	$0.202407\pi$
$860$	−18.5554			−0.632732
$861$	−0.603041	−	10.5219i	−0.0205516	−	0.358584i
$862$	−5.50084			−0.187359
$863$	12.7309	−	22.0505i	0.433364	−	0.750609i	−0.563796	−	0.825914i	$-0.690660\pi$
$863$	12.7309	−	22.0505i	0.433364	−	0.750609i	0.997161	+	0.0753050i	$0.0239930\pi$
$864$	1.09482	+	1.89629i	0.0372467	+	0.0645131i
$865$	16.9106	+	29.2901i	0.574979	+	0.995893i
$866$	6.13018	−	10.6178i	0.208312	−	0.360807i
$867$	−7.84061			−0.266281
$868$	−12.9162	+	8.47799i	−0.438405	+	0.287762i
$869$	13.5378			0.459240
$870$	4.29983	−	7.44752i	0.145778	−	0.252494i
$871$	−1.68042	−	2.91057i	−0.0569388	−	0.0986209i
$872$	−1.50566	−	2.60788i	−0.0509881	−	0.0883140i
$873$	−21.0813	+	36.5139i	−0.713494	+	1.23581i
$874$	0.189648			0.00641494
$875$	0.0423213	+	0.0213037i	0.00143072	+	0.000720197i
$876$	−1.99301			−0.0673377
$877$	−21.1890	+	36.7004i	−0.715501	+	1.23928i	0.247265	+	0.968948i	$0.420468\pi$
$877$	−21.1890	+	36.7004i	−0.715501	+	1.23928i	−0.962766	+	0.270336i	$0.912865\pi$
$878$	−1.06867	−	1.85099i	−0.0360658	−	0.0624678i
$879$	−4.03641	−	6.99127i	−0.136145	−	0.235810i
$880$	3.35105	−	5.80418i	0.112964	−	0.195659i
$881$	−29.4616			−0.992587			−0.496293	−	0.868155i	$-0.665306\pi$
$881$	−29.4616			−0.992587			−0.496293	+	0.868155i	$0.665306\pi$
$882$	7.96470	−	18.3705i	0.268185	−	0.618567i
$883$	−0.878455			−0.0295624			−0.0147812	−	0.999891i	$-0.504705\pi$
$883$	−0.878455			−0.0295624			−0.0147812	+	0.999891i	$0.504705\pi$
$884$	9.02640	−	15.6342i	0.303591	−	0.525835i
$885$	−6.63859	−	11.4984i	−0.223154	−	0.386514i
$886$	−20.0360	−	34.7034i	−0.673122	−	1.16588i
$887$	23.7480	−	41.1327i	0.797379	−	1.38110i	−0.123938	−	0.992290i	$-0.539553\pi$
$887$	23.7480	−	41.1327i	0.797379	−	1.38110i	0.921318	−	0.388811i	$-0.127114\pi$
$888$	−2.76306			−0.0927223
$889$	31.0142	+	15.6119i	1.04018	+	0.523608i
$890$	24.7055			0.828130
$891$	8.22415	−	14.2446i	0.275519	−	0.477213i
$892$	9.32549	+	16.1522i	0.312240	+	0.540816i
$893$	0.844187	+	1.46217i	0.0282496	+	0.0489298i
$894$	0.679316	−	1.17661i	0.0227197	−	0.0393517i
$895$	−44.0278			−1.47169
$896$	2.21184	−	1.45181i	0.0738924	−	0.0485017i
$897$	1.09443			0.0365419
$898$	9.11965	−	15.7957i	0.304327	−	0.527109i
$899$	21.2453	+	36.7979i	0.708570	+	1.22728i
$900$	7.15909	+	12.3999i	0.238636	+	0.413330i
$901$	21.9437	−	38.0076i	0.731050	−	1.26622i
$902$	−22.5890			−0.752130
$903$	−0.331806	−	5.78936i	−0.0110418	−	0.192658i
$904$	7.53681			0.250670
$905$	0.468899	−	0.812156i	0.0155867	−	0.0269970i
$906$	−3.42085	−	5.92508i	−0.113650	−	0.196848i
$907$	6.87819	+	11.9134i	0.228386	+	0.395577i	0.957330	−	0.288997i	$-0.0933217\pi$
$907$	6.87819	+	11.9134i	0.228386	+	0.395577i	−0.728944	+	0.684574i	$0.759988\pi$
$908$	4.86534	−	8.42702i	0.161462	−	0.279661i
$909$	−17.7067			−0.587294
$910$	1.40267	+	24.4737i	0.0464979	+	0.811296i
$911$	−24.6605			−0.817038			−0.408519	−	0.912750i	$-0.633955\pi$
$911$	−24.6605			−0.817038			−0.408519	+	0.912750i	$0.633955\pi$
$912$	0.0354296	−	0.0613658i	0.00117319	−	0.00203203i
$913$	5.34999	+	9.26645i	0.177059	+	0.306675i
$914$	−3.90577	−	6.76500i	−0.129191	−	0.223766i
$915$	2.90176	−	5.02599i	0.0959291	−	0.166154i
$916$	7.34293			0.242617
$917$	−0.547364	+	0.359281i	−0.0180756	+	0.0118645i
$918$	13.4952			0.445407
$919$	−14.7259	+	25.5060i	−0.485763	+	0.841367i	−0.999866	−	0.0163619i	$-0.994792\pi$
$919$	−14.7259	+	25.5060i	−0.485763	+	0.841367i	0.514103	+	0.857729i	$0.328125\pi$
$920$	−1.58159	−	2.73939i	−0.0521434	−	0.0903149i
$921$	−0.408789	−	0.708043i	−0.0134700	−	0.0233308i
$922$	−5.95982	+	10.3227i	−0.196276	+	0.339961i
$923$	34.7426			1.14357
$924$	1.87086	+	0.941753i	0.0615467	+	0.0309814i
$925$	−37.0173			−1.21712
$926$	−6.73246	+	11.6610i	−0.221242	+	0.383203i
$927$	−13.7273	−	23.7764i	−0.450864	−	0.780919i
$928$	−3.63815	−	6.30146i	−0.119428	−	0.206856i
$929$	23.6867	−	41.0266i	0.777137	−	1.34604i	−0.156449	−	0.987686i	$-0.550005\pi$
$929$	23.6867	−	41.0266i	0.777137	−	1.34604i	0.933586	−	0.358354i	$-0.116662\pi$
$930$	6.90164			0.226314
$931$	−1.31884	+	0.151672i	−0.0432234	+	0.00497086i
$932$	27.6319			0.905112
$933$	−0.658227	+	1.14008i	−0.0215494	+	0.0373246i
$934$	5.75740	+	9.97211i	0.188388	+	0.326297i
$935$	−20.6531	−	35.7722i	−0.675428	−	1.16988i
$936$	−4.18925	+	7.25600i	−0.136930	+	0.237170i
$937$	−35.9048			−1.17296			−0.586479	−	0.809964i	$-0.699486\pi$
$937$	−35.9048			−1.17296			−0.586479	+	0.809964i	$0.699486\pi$
$938$	−2.71152	−	1.36493i	−0.0885343	−	0.0445664i
$939$	4.30622			0.140528
$940$	14.0803	−	24.3879i	0.459250	−	0.795444i
$941$	14.3636	+	24.8784i	0.468239	+	0.811014i	0.999341	−	0.0362941i	$-0.0115553\pi$
$941$	14.3636	+	24.8784i	0.468239	+	0.811014i	−0.531102	+	0.847308i	$0.678222\pi$
$942$	2.08843	+	3.61726i	0.0680446	+	0.117857i
$943$	−5.33063	+	9.23292i	−0.173589	+	0.300665i
$944$	−11.2340			−0.365637
$945$	−15.3197	+	10.0556i	−0.498351	+	0.327109i
$946$	−12.4289			−0.404100
$947$	−18.9069	+	32.7476i	−0.614390	+	1.06415i	0.376101	+	0.926579i	$0.377265\pi$
$947$	−18.9069	+	32.7476i	−0.614390	+	1.06415i	−0.990491	+	0.137576i	$0.956069\pi$
$948$	−1.19366	−	2.06747i	−0.0387682	−	0.0671484i
$949$	−7.81220	−	13.5311i	−0.253595	−	0.439239i
$950$	0.474657	−	0.822130i	0.0153999	−	0.0266734i
$951$	10.5019			0.340546
$952$	−0.933029	−	16.2795i	−0.0302397	−	0.527622i
$953$	36.2519			1.17431			0.587157	−	0.809473i	$-0.300247\pi$
$953$	36.2519			1.17431			0.587157	+	0.809473i	$0.300247\pi$
$954$	−10.1843	+	17.6397i	−0.329729	+	0.571108i
$955$	33.6759	+	58.3284i	1.08973	+	1.88746i
$956$	−0.112807	−	0.195388i	−0.00364845	−	0.00631930i
$957$	2.88015	−	4.98857i	0.0931021	−	0.161258i
$958$	13.7557			0.444426
$959$	−0.903999	−	15.7730i	−0.0291916	−	0.509336i
$960$	−1.18187			−0.0381447
$961$	−1.55037	+	2.68531i	−0.0500118	+	0.0866230i
$962$	−10.8306	−	18.7592i	−0.349193	−	0.604821i
$963$	27.4499	+	47.5446i	0.884559	+	1.53210i
$964$	9.16495	−	15.8742i	0.295183	−	0.511272i
$965$	−1.86424			−0.0600120
$966$	0.826420	−	0.542448i	0.0265896	−	0.0174530i
$967$	14.6319			0.470529			0.235265	−	0.971931i	$-0.424404\pi$
$967$	14.6319			0.470529			0.235265	+	0.971931i	$0.424404\pi$
$968$	−3.25537	+	5.63846i	−0.104631	+	0.181227i
$969$	−0.218359	−	0.378208i	−0.00701469	−	0.0121498i
$970$	−23.3128	−	40.3789i	−0.748529	−	1.29649i
$971$	17.3529	−	30.0562i	0.556883	−	0.964549i	−0.440872	−	0.897570i	$-0.645331\pi$
$971$	17.3529	−	30.0562i	0.556883	−	0.964549i	0.997754	−	0.0669788i	$-0.0213360\pi$
$972$	−9.46949			−0.303734
$973$	2.84317	+	1.43119i	0.0911478	+	0.0458820i
$974$	34.5622			1.10744
$975$	2.73917	−	4.74438i	0.0877237	−	0.151942i
$976$	−2.45522	−	4.25257i	−0.0785897	−	0.136121i
$977$	6.43863	+	11.1520i	0.205990	+	0.356785i	0.950448	−	0.310884i	$-0.100625\pi$
$977$	6.43863	+	11.1520i	0.205990	+	0.356785i	−0.744458	+	0.667670i	$0.767292\pi$
$978$	0.328931	−	0.569725i	0.0105180	−	0.0182178i
$979$	16.5485			0.528892
$980$	13.1895	+	17.7853i	0.421322	+	0.568130i
$981$	8.61358			0.275010
$982$	−2.77170	+	4.80072i	−0.0884484	+	0.153197i
$983$	−1.32160	−	2.28908i	−0.0421525	−	0.0730103i	0.844179	−	0.536061i	$-0.180088\pi$
$983$	−1.32160	−	2.28908i	−0.0421525	−	0.0730103i	−0.886332	+	0.463050i	$0.846755\pi$
$984$	1.99171	+	3.44974i	0.0634933	+	0.109974i
$985$	41.3268	−	71.5801i	1.31678	−	2.28073i
$986$	−44.8451			−1.42816
$987$	7.86091	+	3.95703i	0.250216	+	0.125954i
$988$	0.555506			0.0176730
$989$	−2.93303	+	5.08016i	−0.0932649	+	0.161540i
$990$	9.58533	+	16.6023i	0.304642	+	0.527655i
$991$	31.2338	+	54.0986i	0.992175	+	1.71850i	0.604216	+	0.796820i	$0.293486\pi$
$991$	31.2338	+	54.0986i	0.992175	+	1.71850i	0.387959	+	0.921677i	$0.373180\pi$
$992$	2.91979	−	5.05723i	0.0927035	−	0.160567i
$993$	7.36374			0.233681
$994$	26.2347	−	17.2200i	0.832115	−	0.546186i
$995$	4.40419			0.139622
$996$	0.943436	−	1.63408i	0.0298939	−	0.0517778i
$997$	−11.6779	−	20.2268i	−0.369844	−	0.640588i	0.619697	−	0.784841i	$-0.287255\pi$
$997$	−11.6779	−	20.2268i	−0.369844	−	0.640588i	−0.989541	+	0.144253i	$0.953922\pi$
$998$	13.7982	+	23.8992i	0.436775	+	0.756517i
$999$	8.09632	−	14.0232i	0.256156	−	0.443676i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.e.d.93.3	✓	8
7.2	even	3		2254.2.a.u.1.2		4
7.4	even	3	inner	322.2.e.d.277.3	yes	8
7.5	odd	6		2254.2.a.r.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.e.d.93.3	✓	8	1.1	even	1	trivial
322.2.e.d.277.3	yes	8	7.4	even	3	inner
2254.2.a.r.1.3		4	7.5	odd	6
2254.2.a.u.1.2		4	7.2	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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.186817 + 0.323577i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.58159 + 2.73939i) q^{5} +0.373635 q^{6} +(2.36323 + 1.18960i) q^{7} -1.00000 q^{8} +(1.43020 - 2.47718i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.186817 + 0.323577i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.58159 + 2.73939i) q^{5} +0.373635 q^{6} +(2.36323 + 1.18960i) q^{7} -1.00000 q^{8} +(1.43020 - 2.47718i) q^{9} +(1.58159 + 2.73939i) q^{10} +(1.05939 + 1.83493i) q^{11} +(0.186817 - 0.323577i) q^{12} +2.92914 q^{13} +(2.21184 - 1.45181i) q^{14} -1.18187 q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.08159 + 5.33746i) q^{17} +(-1.43020 - 2.47718i) q^{18} +(-0.0948241 + 0.164240i) q^{19} +3.16317 q^{20} +(0.0565638 + 0.986925i) q^{21} +2.11879 q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.186817 - 0.323577i) q^{24} +(-2.50283 - 4.33503i) q^{25} +(1.46457 - 2.53671i) q^{26} +2.18965 q^{27} +(-0.151388 - 2.64142i) q^{28} -7.27630 q^{29} +(-0.590936 + 1.02353i) q^{30} +(-2.91979 - 5.05723i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.395827 + 0.685592i) q^{33} +6.16317 q^{34} +(-6.99643 + 4.59234i) q^{35} -2.86040 q^{36} +(3.69754 - 6.40434i) q^{37} +(0.0948241 + 0.164240i) q^{38} +(0.547214 + 0.947803i) q^{39} +(1.58159 - 2.73939i) q^{40} -10.6613 q^{41} +(0.882984 + 0.444477i) q^{42} -5.86606 q^{43} +(1.05939 - 1.83493i) q^{44} +(4.52396 + 7.83574i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(4.45133 - 7.70993i) q^{47} -0.373635 q^{48} +(4.16969 + 5.62260i) q^{49} -5.00566 q^{50} +(-1.15139 + 1.99426i) q^{51} +(-1.46457 - 2.53671i) q^{52} +(-3.56045 - 6.16688i) q^{53} +(1.09482 - 1.89629i) q^{54} -6.70210 q^{55} +(-2.36323 - 1.18960i) q^{56} -0.0708591 q^{57} +(-3.63815 + 6.30146i) q^{58} +(5.61702 + 9.72896i) q^{59} +(0.590936 + 1.02353i) q^{60} +(-2.45522 + 4.25257i) q^{61} -5.83958 q^{62} +(6.32674 - 4.15276i) q^{63} +1.00000 q^{64} +(-4.63269 + 8.02405i) q^{65} +(0.395827 + 0.685592i) q^{66} +(-0.573690 - 0.993660i) q^{67} +(3.08159 - 5.33746i) q^{68} +0.373635 q^{69} +(0.478866 + 8.35526i) q^{70} +11.8610 q^{71} +(-1.43020 + 2.47718i) q^{72} +(-2.66706 - 4.61949i) q^{73} +(-3.69754 - 6.40434i) q^{74} +(0.935145 - 1.61972i) q^{75} +0.189648 q^{76} +(0.320759 + 5.59660i) q^{77} +1.09443 q^{78} +(3.19471 - 5.53341i) q^{79} +(-1.58159 - 2.73939i) q^{80} +(-3.88153 - 6.72301i) q^{81} +(-5.33063 + 9.23292i) q^{82} +5.05005 q^{83} +(0.826420 - 0.542448i) q^{84} -19.4952 q^{85} +(-2.93303 + 5.08016i) q^{86} +(-1.35934 - 2.35444i) q^{87} +(-1.05939 - 1.83493i) q^{88} +(3.90518 - 6.76396i) q^{89} +9.04793 q^{90} +(6.92223 + 3.48451i) q^{91} -1.00000 q^{92} +(1.09094 - 1.88956i) q^{93} +(-4.45133 - 7.70993i) q^{94} +(-0.299945 - 0.519520i) q^{95} +(-0.186817 + 0.323577i) q^{96} -14.7401 q^{97} +(6.95416 - 0.799757i) q^{98} +6.06058 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} + 5 q^{5} - 2 q^{6} - 3 q^{7} - 8 q^{8} + q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 + 5 * q^5 - 2 * q^6 - 3 * q^7 - 8 * q^8 + q^9	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} + 5 q^{5} - 2 q^{6} - 3 q^{7} - 8 q^{8} + q^{9} - 5 q^{10} + 2 q^{11} - q^{12} + 14 q^{13} + 3 q^{14} - 10 q^{15} - 4 q^{16} + 7 q^{17} - q^{18} + q^{19} - 10 q^{20} - 5 q^{21} + 4 q^{22} + 4 q^{23} + q^{24} - 19 q^{25} + 7 q^{26} + 14 q^{27} + 6 q^{28} - 12 q^{29} - 5 q^{30} + 4 q^{31} + 4 q^{32} + 13 q^{33} + 14 q^{34} - 14 q^{35} - 2 q^{36} - q^{38} - 19 q^{39} - 5 q^{40} - 30 q^{41} + 20 q^{42} - 24 q^{43} + 2 q^{44} + 25 q^{45} - 4 q^{46} + 15 q^{47} + 2 q^{48} + 17 q^{49} - 38 q^{50} - 2 q^{51} - 7 q^{52} - 21 q^{53} + 7 q^{54} + 24 q^{55} + 3 q^{56} - 10 q^{57} - 6 q^{58} + 32 q^{59} + 5 q^{60} + 3 q^{61} + 8 q^{62} + 25 q^{63} + 8 q^{64} + 6 q^{65} - 13 q^{66} - 13 q^{67} + 7 q^{68} - 2 q^{69} + 14 q^{70} - 14 q^{71} - q^{72} + 16 q^{73} - 6 q^{75} - 2 q^{76} + 23 q^{77} - 38 q^{78} - 3 q^{79} + 5 q^{80} - 15 q^{82} + 16 q^{83} + 25 q^{84} - 48 q^{85} - 12 q^{86} + 9 q^{87} - 2 q^{88} + 33 q^{89} + 50 q^{90} - 18 q^{91} - 8 q^{92} + 9 q^{93} - 15 q^{94} + 11 q^{95} + q^{96} - 24 q^{97} + 34 q^{98} - 70 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 + 5 * q^5 - 2 * q^6 - 3 * q^7 - 8 * q^8 + q^9 - 5 * q^10 + 2 * q^11 - q^12 + 14 * q^13 + 3 * q^14 - 10 * q^15 - 4 * q^16 + 7 * q^17 - q^18 + q^19 - 10 * q^20 - 5 * q^21 + 4 * q^22 + 4 * q^23 + q^24 - 19 * q^25 + 7 * q^26 + 14 * q^27 + 6 * q^28 - 12 * q^29 - 5 * q^30 + 4 * q^31 + 4 * q^32 + 13 * q^33 + 14 * q^34 - 14 * q^35 - 2 * q^36 - q^38 - 19 * q^39 - 5 * q^40 - 30 * q^41 + 20 * q^42 - 24 * q^43 + 2 * q^44 + 25 * q^45 - 4 * q^46 + 15 * q^47 + 2 * q^48 + 17 * q^49 - 38 * q^50 - 2 * q^51 - 7 * q^52 - 21 * q^53 + 7 * q^54 + 24 * q^55 + 3 * q^56 - 10 * q^57 - 6 * q^58 + 32 * q^59 + 5 * q^60 + 3 * q^61 + 8 * q^62 + 25 * q^63 + 8 * q^64 + 6 * q^65 - 13 * q^66 - 13 * q^67 + 7 * q^68 - 2 * q^69 + 14 * q^70 - 14 * q^71 - q^72 + 16 * q^73 - 6 * q^75 - 2 * q^76 + 23 * q^77 - 38 * q^78 - 3 * q^79 + 5 * q^80 - 15 * q^82 + 16 * q^83 + 25 * q^84 - 48 * q^85 - 12 * q^86 + 9 * q^87 - 2 * q^88 + 33 * q^89 + 50 * q^90 - 18 * q^91 - 8 * q^92 + 9 * q^93 - 15 * q^94 + 11 * q^95 + q^96 - 24 * q^97 + 34 * q^98 - 70 * q^99

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