LMFDB - Embedded newform 465.2.k.b.32.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [465,2,Mod(32,465)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(465, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("465.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			32.4
Character	$\chi$	$=$	465.32
Dual form			465.2.k.b.218.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.67772 + 1.67772i) q^{2} +(-0.586503 - 1.62973i) q^{3} -3.62946i q^{4} +(1.63852 + 1.52159i) q^{5} +(3.71821 + 1.75024i) q^{6} +(-2.99940 - 2.99940i) q^{7} +(2.73377 + 2.73377i) q^{8} +(-2.31203 + 1.91168i) q^{9} +O(q^{10})$	\(q+(-1.67772 + 1.67772i) q^{2} +(-0.586503 - 1.62973i) q^{3} -3.62946i q^{4} +(1.63852 + 1.52159i) q^{5} +(3.71821 + 1.75024i) q^{6} +(-2.99940 - 2.99940i) q^{7} +(2.73377 + 2.73377i) q^{8} +(-2.31203 + 1.91168i) q^{9} +(-5.30178 + 0.196172i) q^{10} -2.13202i q^{11} +(-5.91503 + 2.12869i) q^{12} +(1.06389 - 1.06389i) q^{13} +10.0643 q^{14} +(1.51879 - 3.56276i) q^{15} -1.91406 q^{16} +(-4.06676 + 4.06676i) q^{17} +(0.671673 - 7.08618i) q^{18} +7.95813i q^{19} +(5.52256 - 5.94695i) q^{20} +(-3.12905 + 6.64736i) q^{21} +(3.57692 + 3.57692i) q^{22} +(-1.54880 - 1.54880i) q^{23} +(2.85194 - 6.05867i) q^{24} +(0.369506 + 4.98633i) q^{25} +3.56982i q^{26} +(4.47153 + 2.64678i) q^{27} +(-10.8862 + 10.8862i) q^{28} -5.69509 q^{29} +(3.42921 + 8.52540i) q^{30} -1.00000 q^{31} +(-2.25629 + 2.25629i) q^{32} +(-3.47461 + 1.25043i) q^{33} -13.6457i q^{34} +(-0.350714 - 9.47845i) q^{35} +(6.93837 + 8.39142i) q^{36} +(-4.40694 - 4.40694i) q^{37} +(-13.3515 - 13.3515i) q^{38} +(-2.35783 - 1.10988i) q^{39} +(0.319655 + 8.63903i) q^{40} +2.72235i q^{41} +(-5.90273 - 16.4020i) q^{42} +(-1.63010 + 1.63010i) q^{43} -7.73807 q^{44} +(-6.69711 - 0.385640i) q^{45} +5.19688 q^{46} +(-2.99168 + 2.99168i) q^{47} +(1.12260 + 3.11940i) q^{48} +10.9928i q^{49} +(-8.98557 - 7.74571i) q^{50} +(9.01288 + 4.24255i) q^{51} +(-3.86136 - 3.86136i) q^{52} +(-0.906752 - 0.906752i) q^{53} +(-11.9425 + 3.06142i) q^{54} +(3.24406 - 3.49336i) q^{55} -16.3994i q^{56} +(12.9696 - 4.66746i) q^{57} +(9.55474 - 9.55474i) q^{58} +5.63531 q^{59} +(-12.9309 - 5.51238i) q^{60} -9.56665 q^{61} +(1.67772 - 1.67772i) q^{62} +(12.6686 + 1.20081i) q^{63} -11.3990i q^{64} +(3.36203 - 0.124399i) q^{65} +(3.73154 - 7.92728i) q^{66} +(-6.08897 - 6.08897i) q^{67} +(14.7601 + 14.7601i) q^{68} +(-1.61575 + 3.43249i) q^{69} +(16.4905 + 15.3137i) q^{70} -12.1228i q^{71} +(-11.5467 - 1.09446i) q^{72} +(-10.6352 + 10.6352i) q^{73} +14.7872 q^{74} +(7.90964 - 3.52669i) q^{75} +28.8837 q^{76} +(-6.39478 + 6.39478i) q^{77} +(5.81784 - 2.09371i) q^{78} +9.68971i q^{79} +(-3.13623 - 2.91243i) q^{80} +(1.69096 - 8.83972i) q^{81} +(-4.56732 - 4.56732i) q^{82} +(1.44379 + 1.44379i) q^{83} +(24.1263 + 11.3568i) q^{84} +(-12.8514 + 0.475519i) q^{85} -5.46970i q^{86} +(3.34018 + 9.28144i) q^{87} +(5.82845 - 5.82845i) q^{88} -6.55718 q^{89} +(11.8828 - 10.5889i) q^{90} -6.38209 q^{91} +(-5.62130 + 5.62130i) q^{92} +(0.586503 + 1.62973i) q^{93} -10.0384i q^{94} +(-12.1090 + 13.0396i) q^{95} +(5.00046 + 2.35382i) q^{96} +(3.25891 + 3.25891i) q^{97} +(-18.4428 - 18.4428i) q^{98} +(4.07574 + 4.92929i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 4 q^{6}+O(q^{10}) $ 60 * q - 4 * q^6	$ 60 q - 4 q^{6} + 16 q^{10} - 12 q^{13} - 8 q^{15} - 60 q^{16} + 34 q^{18} - 4 q^{21} + 8 q^{22} + 8 q^{25} - 6 q^{27} - 80 q^{28} - 54 q^{30} - 60 q^{31} + 10 q^{33} + 28 q^{36} - 12 q^{37} + 60 q^{40} - 12 q^{42} - 24 q^{43} - 58 q^{45} + 8 q^{46} + 80 q^{48} + 32 q^{51} + 52 q^{52} + 64 q^{55} - 14 q^{57} - 48 q^{58} - 108 q^{60} - 56 q^{61} + 62 q^{63} + 40 q^{66} + 104 q^{67} + 108 q^{70} - 76 q^{72} - 108 q^{73} - 38 q^{75} - 120 q^{76} + 112 q^{78} + 60 q^{81} + 20 q^{82} + 48 q^{85} - 110 q^{87} - 28 q^{88} - 82 q^{90} - 32 q^{91} + 120 q^{96} + 56 q^{97}+O(q^{100}) $ 60 * q - 4 * q^6 + 16 * q^10 - 12 * q^13 - 8 * q^15 - 60 * q^16 + 34 * q^18 - 4 * q^21 + 8 * q^22 + 8 * q^25 - 6 * q^27 - 80 * q^28 - 54 * q^30 - 60 * q^31 + 10 * q^33 + 28 * q^36 - 12 * q^37 + 60 * q^40 - 12 * q^42 - 24 * q^43 - 58 * q^45 + 8 * q^46 + 80 * q^48 + 32 * q^51 + 52 * q^52 + 64 * q^55 - 14 * q^57 - 48 * q^58 - 108 * q^60 - 56 * q^61 + 62 * q^63 + 40 * q^66 + 104 * q^67 + 108 * q^70 - 76 * q^72 - 108 * q^73 - 38 * q^75 - 120 * q^76 + 112 * q^78 + 60 * q^81 + 20 * q^82 + 48 * q^85 - 110 * q^87 - 28 * q^88 - 82 * q^90 - 32 * q^91 + 120 * q^96 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.67772	+	1.67772i	−1.18632	+	1.18632i	−0.208248	+	0.978076i	$0.566776\pi$
$2$	−1.67772	+	1.67772i	−1.18632	+	1.18632i	−0.978076	+	0.208248i	$0.933224\pi$
$3$	−0.586503	−	1.62973i	−0.338617	−	0.940924i
$3$	−0.586503	−	1.62973i	−0.338617	−	0.940924i
$4$		−	3.62946i		−	1.81473i
$5$	1.63852	+	1.52159i	0.732769	+	0.680477i
$5$	1.63852	+	1.52159i	0.732769	+	0.680477i
$6$	3.71821	+	1.75024i	1.51795	+	0.714531i
$7$	−2.99940	−	2.99940i	−1.13367	−	1.13367i	−0.989562	−	0.144104i	$-0.953970\pi$
$7$	−2.99940	−	2.99940i	−1.13367	−	1.13367i	−0.144104	−	0.989562i	$-0.546030\pi$
$8$	2.73377	+	2.73377i	0.966534	+	0.966534i
$9$	−2.31203	+	1.91168i	−0.770677	+	0.637227i
$10$	−5.30178	+	0.196172i	−1.67657	+	0.0620351i
$11$		−	2.13202i		−	0.642828i	−0.946939	−	0.321414i	$-0.895842\pi$
$11$		−	2.13202i		−	0.642828i	0.946939	−	0.321414i	$-0.104158\pi$
$12$	−5.91503	+	2.12869i	−1.70752	+	0.614499i
$13$	1.06389	−	1.06389i	0.295071	−	0.295071i	−0.544009	−	0.839080i	$-0.683094\pi$
$13$	1.06389	−	1.06389i	0.295071	−	0.295071i	0.839080	+	0.544009i	$0.183094\pi$
$14$	10.0643			2.68979
$15$	1.51879	−	3.56276i	0.392149	−	0.919902i
$16$	−1.91406			−0.478516
$17$	−4.06676	+	4.06676i	−0.986334	+	0.986334i	−0.999908	−	0.0135736i	$-0.995679\pi$
$17$	−4.06676	+	4.06676i	−0.986334	+	0.986334i	0.0135736	+	0.999908i	$0.495679\pi$
$18$	0.671673	−	7.08618i	0.158315	−	1.67023i
$19$			7.95813i			1.82572i	0.408273	+	0.912860i	$0.366131\pi$
$19$			7.95813i			1.82572i	−0.408273	+	0.912860i	$0.633869\pi$
$20$	5.52256	−	5.94695i	1.23488	−	1.32978i
$21$	−3.12905	+	6.64736i	−0.682815	+	1.45057i
$22$	3.57692	+	3.57692i	0.762602	+	0.762602i
$23$	−1.54880	−	1.54880i	−0.322947	−	0.322947i	0.526950	−	0.849896i	$-0.323336\pi$
$23$	−1.54880	−	1.54880i	−0.322947	−	0.322947i	−0.849896	+	0.526950i	$0.823336\pi$
$24$	2.85194	−	6.05867i	0.582150	−	1.23672i
$25$	0.369506	+	4.98633i	0.0739013	+	0.997266i
$26$			3.56982i			0.700100i
$27$	4.47153	+	2.64678i	0.860546	+	0.509372i
$28$	−10.8862	+	10.8862i	−2.05730	+	2.05730i
$29$	−5.69509			−1.05755			−0.528776	−	0.848762i	$-0.677349\pi$
$29$	−5.69509			−1.05755			−0.528776	+	0.848762i	$0.677349\pi$
$30$	3.42921	+	8.52540i	0.626086	+	1.55652i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	−2.25629	+	2.25629i	−0.398860	+	0.398860i
$33$	−3.47461	+	1.25043i	−0.604852	+	0.217673i
$34$		−	13.6457i		−	2.34022i
$35$	−0.350714	−	9.47845i	−0.0592815	−	1.60215i
$36$	6.93837	+	8.39142i	1.15639	+	1.39857i
$37$	−4.40694	−	4.40694i	−0.724496	−	0.724496i	0.245021	−	0.969518i	$-0.421205\pi$
$37$	−4.40694	−	4.40694i	−0.724496	−	0.724496i	−0.969518	+	0.245021i	$0.921205\pi$
$38$	−13.3515	−	13.3515i	−2.16590	−	2.16590i
$39$	−2.35783	−	1.10988i	−0.377556	−	0.177723i
$40$	0.319655	+	8.63903i	0.0505419	+	1.36595i
$41$			2.72235i			0.425159i	0.977144	+	0.212579i	$0.0681864\pi$
$41$			2.72235i			0.425159i	−0.977144	+	0.212579i	$0.931814\pi$
$42$	−5.90273	−	16.4020i	−0.910811	−	2.53089i
$43$	−1.63010	+	1.63010i	−0.248589	+	0.248589i	−0.820391	−	0.571803i	$-0.806244\pi$
$43$	−1.63010	+	1.63010i	−0.248589	+	0.248589i	0.571803	+	0.820391i	$0.306244\pi$
$44$	−7.73807			−1.16656
$45$	−6.69711	−	0.385640i	−0.998346	−	0.0574879i
$46$	5.19688			0.766239
$47$	−2.99168	+	2.99168i	−0.436382	+	0.436382i	−0.890792	−	0.454411i	$-0.849850\pi$
$47$	−2.99168	+	2.99168i	−0.436382	+	0.436382i	0.454411	+	0.890792i	$0.349850\pi$
$48$	1.12260	+	3.11940i	0.162034	+	0.450247i
$49$			10.9928i			1.57040i
$50$	−8.98557	−	7.74571i	−1.27075	−	1.09541i
$51$	9.01288	+	4.24255i	1.26206	+	0.594076i
$52$	−3.86136	−	3.86136i	−0.535474	−	0.535474i
$53$	−0.906752	−	0.906752i	−0.124552	−	0.124552i	0.642083	−	0.766635i	$-0.278070\pi$
$53$	−0.906752	−	0.906752i	−0.124552	−	0.124552i	−0.766635	+	0.642083i	$0.778070\pi$
$54$	−11.9425	+	3.06142i	−1.62517	+	0.416607i
$55$	3.24406	−	3.49336i	0.437430	−	0.471044i
$56$		−	16.3994i		−	2.19146i
$57$	12.9696	−	4.66746i	1.71786	−	0.618221i
$58$	9.55474	−	9.55474i	1.25460	−	1.25460i
$59$	5.63531			0.733656			0.366828	−	0.930289i	$-0.380444\pi$
$59$	5.63531			0.733656			0.366828	+	0.930289i	$0.380444\pi$
$60$	−12.9309	−	5.51238i	−1.66937	−	0.711645i
$61$	−9.56665			−1.22488			−0.612442	−	0.790515i	$-0.709813\pi$
$61$	−9.56665			−1.22488			−0.612442	+	0.790515i	$0.709813\pi$
$62$	1.67772	−	1.67772i	0.213070	−	0.213070i
$63$	12.6686	+	1.20081i	1.59609	+	0.151288i
$64$		−	11.3990i		−	1.42487i
$65$	3.36203	−	0.124399i	0.417008	−	0.0154298i
$66$	3.73154	−	7.92728i	0.459320	−	0.975781i
$67$	−6.08897	−	6.08897i	−0.743886	−	0.743886i	0.229438	−	0.973323i	$-0.426311\pi$
$67$	−6.08897	−	6.08897i	−0.743886	−	0.743886i	−0.973323	+	0.229438i	$0.926311\pi$
$68$	14.7601	+	14.7601i	1.78993	+	1.78993i
$69$	−1.61575	+	3.43249i	−0.194513	+	0.413224i
$70$	16.4905	+	15.3137i	1.97100	+	1.83034i
$71$		−	12.1228i		−	1.43871i	−0.694644	−	0.719354i	$-0.744438\pi$
$71$		−	12.1228i		−	1.43871i	0.694644	−	0.719354i	$-0.255562\pi$
$72$	−11.5467	−	1.09446i	−1.36079	−	0.128984i
$73$	−10.6352	+	10.6352i	−1.24476	+	1.24476i	−0.286757	+	0.958003i	$0.592577\pi$
$73$	−10.6352	+	10.6352i	−1.24476	+	1.24476i	−0.958003	+	0.286757i	$0.907423\pi$
$74$	14.7872			1.71897
$75$	7.90964	−	3.52669i	0.913327	−	0.407227i
$76$	28.8837			3.31319
$77$	−6.39478	+	6.39478i	−0.728752	+	0.728752i
$78$	5.81784	−	2.09371i	0.658741	−	0.237066i
$79$			9.68971i			1.09018i	0.838378	+	0.545089i	$0.183504\pi$
$79$			9.68971i			1.09018i	−0.838378	+	0.545089i	$0.816496\pi$
$80$	−3.13623	−	2.91243i	−0.350642	−	0.325619i
$81$	1.69096	−	8.83972i	0.187885	−	0.982191i
$82$	−4.56732	−	4.56732i	−0.504376	−	0.504376i
$83$	1.44379	+	1.44379i	0.158477	+	0.158477i	0.781891	−	0.623415i	$-0.214255\pi$
$83$	1.44379	+	1.44379i	0.158477	+	0.158477i	−0.623415	+	0.781891i	$0.714255\pi$
$84$	24.1263	+	11.3568i	2.63240	+	1.23913i
$85$	−12.8514	+	0.475519i	−1.39393	+	0.0515772i
$86$		−	5.46970i		−	0.589813i
$87$	3.34018	+	9.28144i	0.358105	+	0.995075i
$88$	5.82845	−	5.82845i	0.621315	−	0.621315i
$89$	−6.55718			−0.695060			−0.347530	−	0.937669i	$-0.612979\pi$
$89$	−6.55718			−0.695060			−0.347530	+	0.937669i	$0.612979\pi$
$90$	11.8828	−	10.5889i	1.25256	−	1.11616i
$91$	−6.38209			−0.669024
$92$	−5.62130	+	5.62130i	−0.586061	+	0.586061i
$93$	0.586503	+	1.62973i	0.0608175	+	0.168995i
$94$		−	10.0384i		−	1.03538i
$95$	−12.1090	+	13.0396i	−1.24236	+	1.33783i
$96$	5.00046	+	2.35382i	0.510357	+	0.240236i
$97$	3.25891	+	3.25891i	0.330892	+	0.330892i	0.852925	−	0.522033i	$-0.174826\pi$
$97$	3.25891	+	3.25891i	0.330892	+	0.330892i	−0.522033	+	0.852925i	$0.674826\pi$
$98$	−18.4428	−	18.4428i	−1.86301	−	1.86301i
$99$	4.07574	+	4.92929i	0.409627	+	0.495412i
$100$	18.0977	−	1.34111i	1.80977	−	0.134111i
$101$			2.09306i			0.208267i	0.994563	+	0.104133i	$0.0332069\pi$
$101$			2.09306i			0.208267i	−0.994563	+	0.104133i	$0.966793\pi$
$102$	−22.2388	+	8.00326i	−2.20197	+	0.792441i
$103$	−2.90407	+	2.90407i	−0.286146	+	0.286146i	−0.835554	−	0.549408i	$-0.814853\pi$
$103$	−2.90407	+	2.90407i	−0.286146	+	0.286146i	0.549408	+	0.835554i	$0.314853\pi$
$104$	5.81688			0.570392
$105$	−15.2416	+	6.13071i	−1.48743	+	0.598296i
$106$	3.04255			0.295518
$107$	9.91555	−	9.91555i	0.958572	−	0.958572i	−0.0406034	−	0.999175i	$-0.512928\pi$
$107$	9.91555	−	9.91555i	0.958572	−	0.958572i	0.999175	+	0.0406034i	$0.0129280\pi$
$108$	9.60637	−	16.2292i	0.924373	−	1.56166i
$109$		−	5.78545i		−	0.554145i	−0.960849	−	0.277073i	$-0.910636\pi$
$109$		−	5.78545i		−	0.554145i	0.960849	−	0.277073i	$-0.0893643\pi$
$110$	0.418243	+	11.3035i	0.0398779	+	1.07774i
$111$	−4.59743	+	9.76679i	−0.436369	+	0.927023i
$112$	5.74104	+	5.74104i	0.542477	+	0.542477i
$113$	5.15961	+	5.15961i	0.485375	+	0.485375i	0.906843	−	0.421468i	$-0.138485\pi$
$113$	5.15961	+	5.15961i	0.485375	+	0.485375i	−0.421468	+	0.906843i	$0.638485\pi$
$114$	−13.9286	+	29.5900i	−1.30453	+	2.77135i
$115$	−0.181098	−	4.89438i	−0.0168875	−	0.456403i
$116$			20.6701i			1.91917i
$117$	−0.425929	+	4.49358i	−0.0393772	+	0.415431i
$118$	−9.45446	+	9.45446i	−0.870353	+	0.870353i
$119$	24.3957			2.23635
$120$	13.8918	−	5.58777i	1.26814	−	0.510091i
$121$	6.45450			0.586773
$122$	16.0501	−	16.0501i	1.45311	−	1.45311i
$123$	4.43668	−	1.59666i	0.400042	−	0.143966i
$124$			3.62946i			0.325935i
$125$	−6.98172	+	8.73244i	−0.624464	+	0.781054i
$126$	−23.2689	+	19.2397i	−2.07296	+	1.71401i
$127$	4.00562	+	4.00562i	0.355441	+	0.355441i	0.862129	−	0.506688i	$-0.169131\pi$
$127$	4.00562	+	4.00562i	0.355441	+	0.355441i	−0.506688	+	0.862129i	$0.669131\pi$
$128$	14.6116	+	14.6116i	1.29150	+	1.29150i
$129$	3.61269	+	1.70057i	0.318079	+	0.149727i
$130$	−5.43182	+	5.84923i	−0.476402	+	0.513011i
$131$			6.83158i			0.596878i	0.954429	+	0.298439i	$0.0964660\pi$
$131$			6.83158i			0.596878i	−0.954429	+	0.298439i	$0.903534\pi$
$132$	4.53840	+	12.6110i	0.395017	+	1.09764i
$133$	23.8696	−	23.8696i	2.06976	−	2.06976i
$134$	20.4311			1.76498
$135$	3.29938	+	11.1406i	0.283966	+	0.958834i
$136$	−22.2352			−1.90665
$137$	−4.60209	+	4.60209i	−0.393183	+	0.393183i	−0.875820	−	0.482637i	$-0.839679\pi$
$137$	−4.60209	+	4.60209i	−0.393183	+	0.393183i	0.482637	+	0.875820i	$0.339679\pi$
$138$	−3.04799	−	8.46951i	−0.259462	−	0.720973i
$139$		−	22.8577i		−	1.93877i	−0.245553	−	0.969383i	$-0.578970\pi$
$139$		−	22.8577i		−	1.93877i	0.245553	−	0.969383i	$-0.421030\pi$
$140$	−34.4017	+	1.27290i	−2.90747	+	0.107580i
$141$	6.63026	+	3.12100i	0.558368	+	0.262836i
$142$	20.3386	+	20.3386i	1.70677	+	1.70677i
$143$	−2.26824	−	2.26824i	−0.189680	−	0.189680i
$144$	4.42537	−	3.65907i	0.368781	−	0.304923i
$145$	−9.33152	−	8.66561i	−0.774941	−	0.719639i
$146$		−	35.6858i		−	2.95338i
$147$	17.9153	−	6.44731i	1.47763	−	0.531765i
$148$	−15.9948	+	15.9948i	−1.31477	+	1.31477i
$149$	7.22028			0.591508			0.295754	−	0.955264i	$-0.404429\pi$
$149$	7.22028			0.591508			0.295754	+	0.955264i	$0.404429\pi$
$150$	−7.35335	+	19.1869i	−0.600399	+	1.56661i
$151$	5.01348			0.407992			0.203996	−	0.978972i	$-0.434607\pi$
$151$	5.01348			0.407992			0.203996	+	0.978972i	$0.434607\pi$
$152$	−21.7557	+	21.7557i	−1.76462	+	1.76462i
$153$	1.62813	−	17.1768i	0.131626	−	1.38866i
$154$		−	21.4572i		−	1.72907i
$155$	−1.63852	−	1.52159i	−0.131609	−	0.122217i
$156$	−4.02827	+	8.55766i	−0.322520	+	0.685161i
$157$	12.4223	+	12.4223i	0.991405	+	0.991405i	0.999963	−	0.00855833i	$-0.00272423\pi$
$157$	12.4223	+	12.4223i	0.991405	+	0.991405i	−0.00855833	+	0.999963i	$0.502724\pi$
$158$	−16.2566	−	16.2566i	−1.29330	−	1.29330i
$159$	−0.945948	+	2.00957i	−0.0750185	+	0.159369i
$160$	−7.13014	+	0.263824i	−0.563687	+	0.0208571i
$161$			9.29093i			0.732228i
$162$	11.9936	+	17.6675i	0.942305	+	1.38809i
$163$	−1.17654	+	1.17654i	−0.0921540	+	0.0921540i	−0.751681	−	0.659527i	$-0.770757\pi$
$163$	−1.17654	+	1.17654i	−0.0921540	+	0.0921540i	0.659527	+	0.751681i	$0.270757\pi$
$164$	9.88065			0.771549
$165$	−7.59588	−	3.23808i	−0.591338	−	0.252084i
$166$	−4.84455			−0.376010
$167$	−8.33562	+	8.33562i	−0.645030	+	0.645030i	−0.951788	−	0.306758i	$-0.900756\pi$
$167$	−8.33562	+	8.33562i	−0.645030	+	0.645030i	0.306758	+	0.951788i	$0.400756\pi$
$168$	−26.7265	+	9.61826i	−2.06199	+	0.742065i
$169$			10.7363i			0.825866i
$170$	20.7633	−	22.3588i	1.59247	−	1.71484i
$171$	−15.2134	−	18.3994i	−1.16340	−	1.40704i
$172$	5.91640	+	5.91640i	0.451121	+	0.451121i
$173$	0.794338	+	0.794338i	0.0603924	+	0.0603924i	0.736658	−	0.676266i	$-0.236403\pi$
$173$	0.794338	+	0.794338i	0.0603924	+	0.0603924i	−0.676266	+	0.736658i	$0.736403\pi$
$174$	−21.1755	−	9.96775i	−1.60531	−	0.755653i
$175$	13.8477	−	16.0643i	1.04679	−	1.21435i
$176$			4.08082i			0.307603i
$177$	−3.30513	−	9.18403i	−0.248429	−	0.690314i
$178$	11.0011	−	11.0011i	0.824566	−	0.824566i
$179$	−18.5774			−1.38854			−0.694270	−	0.719715i	$-0.744272\pi$
$179$	−18.5774			−1.38854			−0.694270	+	0.719715i	$0.744272\pi$
$180$	−1.39967	+	24.3069i	−0.104325	+	1.81173i
$181$	−14.9009			−1.10757			−0.553786	−	0.832659i	$-0.686818\pi$
$181$	−14.9009			−1.10757			−0.553786	+	0.832659i	$0.686818\pi$
$182$	10.7073	−	10.7073i	0.793680	−	0.793680i
$183$	5.61086	+	15.5910i	0.414767	+	1.15252i
$184$		−	8.46812i		−	0.624278i
$185$	−0.515295	−	13.9264i	−0.0378852	−	1.02389i
$186$	−3.71821	−	1.75024i	−0.272632	−	0.128334i
$187$	8.67041	+	8.67041i	0.634043	+	0.634043i
$188$	10.8582	+	10.8582i	0.791915	+	0.791915i
$189$	−5.47317	−	21.3506i	−0.398115	−	1.55303i
$190$	−1.56116	−	42.1922i	−0.113259	−	3.06094i
$191$		−	22.8963i		−	1.65672i	−0.560198	−	0.828359i	$-0.689275\pi$
$191$		−	22.8963i		−	1.65672i	0.560198	−	0.828359i	$-0.310725\pi$
$192$	−18.5772	+	6.68551i	−1.34069	+	0.482485i
$193$	16.9406	−	16.9406i	1.21941	−	1.21941i	0.251571	−	0.967839i	$-0.419053\pi$
$193$	16.9406	−	16.9406i	1.21941	−	1.21941i	0.967839	−	0.251571i	$-0.0809471\pi$
$194$	−10.9350			−0.785090
$195$	−2.17457	−	5.40623i	−0.155724	−	0.387148i
$196$	39.8980			2.84985
$197$	14.0361	−	14.0361i	1.00003	−	1.00003i	2.89839e−5	−	1.00000i	$-0.499991\pi$
$197$	14.0361	−	14.0361i	1.00003	−	1.00003i	1.00000		2.89839e-5i	$-9.22587e-6\pi$
$198$	−15.1079	−	1.43202i	−1.07367	−	0.101769i
$199$		−	20.7498i		−	1.47091i	−0.677572	−	0.735457i	$-0.736968\pi$
$199$		−	20.7498i		−	1.47091i	0.677572	−	0.735457i	$-0.263032\pi$
$200$	−12.6213	+	14.6416i	−0.892463	+	1.03532i
$201$	−6.35217	+	13.4946i	−0.448047	+	0.951833i
$202$	−3.51155	−	3.51155i	−0.247072	−	0.247072i
$203$	17.0818	+	17.0818i	1.19891	+	1.19891i
$204$	15.3982	−	32.7119i	1.07809	−	2.29029i
$205$	−4.14230	+	4.46062i	−0.289311	+	0.311543i
$206$		−	9.74440i		−	0.678925i
$207$	6.54167	+	0.620061i	0.454678	+	0.0430972i
$208$	−2.03636	+	2.03636i	−0.141196	+	0.141196i
$209$	16.9669			1.17362
$210$	15.2855	−	35.8567i	1.05480	−	2.47435i
$211$	−21.1539			−1.45629			−0.728146	−	0.685422i	$-0.759618\pi$
$211$	−21.1539			−1.45629			−0.728146	+	0.685422i	$0.759618\pi$
$212$	−3.29102	+	3.29102i	−0.226028	+	0.226028i
$213$	−19.7568	+	7.11003i	−1.35371	+	0.487171i
$214$			33.2709i			2.27435i
$215$	−5.15132	+	0.190605i	−0.351317	+	0.0129992i
$216$	4.98846	+	19.4598i	0.339422	+	1.32407i
$217$	2.99940	+	2.99940i	0.203613	+	0.203613i
$218$	9.70634	+	9.70634i	0.657396	+	0.657396i
$219$	23.5701	+	11.0950i	1.59272	+	0.749728i
$220$	−12.6790	−	11.7742i	−0.854818	−	0.793817i
$221$			8.65320i			0.582077i
$222$	−8.67272	−	24.0991i	−0.582075	−	1.61742i
$223$	−8.85852	+	8.85852i	−0.593210	+	0.593210i	−0.938497	−	0.345287i	$-0.887782\pi$
$223$	−8.85852	+	8.85852i	−0.593210	+	0.593210i	0.345287	+	0.938497i	$0.387782\pi$
$224$	13.5350			0.904348
$225$	−10.3866	−	10.8222i	−0.692438	−	0.721477i
$226$	−17.3127			−1.15163
$227$	−7.86041	+	7.86041i	−0.521714	+	0.521714i	−0.918089	−	0.396375i	$-0.870268\pi$
$227$	−7.86041	+	7.86041i	−0.521714	+	0.521714i	0.396375	+	0.918089i	$0.370268\pi$
$228$	−16.9404	−	47.0726i	−1.12190	−	3.11746i
$229$		−	13.7960i		−	0.911663i	−0.890066	−	0.455832i	$-0.849342\pi$
$229$		−	13.7960i		−	0.911663i	0.890066	−	0.455832i	$-0.150658\pi$
$230$	8.51521	+	7.90755i	0.561476	+	0.521408i
$231$	14.1723	+	6.67120i	0.932469	+	0.438932i
$232$	−15.5691	−	15.5691i	−1.02216	−	1.02216i
$233$	−7.56402	−	7.56402i	−0.495535	−	0.495535i	0.414510	−	0.910045i	$-0.363953\pi$
$233$	−7.56402	−	7.56402i	−0.495535	−	0.495535i	−0.910045	+	0.414510i	$0.863953\pi$
$234$	−6.82436	−	8.25353i	−0.446122	−	0.539550i
$235$	−9.45406	+	0.349812i	−0.616715	+	0.0228192i
$236$		−	20.4532i		−	1.33139i
$237$	15.7916	−	5.68304i	1.02577	−	0.369153i
$238$	−40.9290	+	40.9290i	−2.65303	+	2.65303i
$239$	1.96069			0.126827			0.0634133	−	0.997987i	$-0.479801\pi$
$239$	1.96069			0.126827			0.0634133	+	0.997987i	$0.479801\pi$
$240$	−2.90705	+	6.81935i	−0.187649	+	0.440187i
$241$	−10.4844			−0.675360			−0.337680	−	0.941261i	$-0.609642\pi$
$241$	−10.4844			−0.675360			−0.337680	+	0.941261i	$0.609642\pi$
$242$	−10.8288	+	10.8288i	−0.696103	+	0.696103i
$243$	−15.3981	+	2.42871i	−0.987788	+	0.155802i
$244$			34.7218i			2.22283i
$245$	−16.7266	+	18.0120i	−1.06862	+	1.15074i
$246$	−4.76475	+	10.1222i	−0.303789	+	0.645371i
$247$	8.46660	+	8.46660i	0.538717	+	0.538717i
$248$	−2.73377	−	2.73377i	−0.173595	−	0.173595i
$249$	1.50620	−	3.19978i	0.0954517	−	0.202778i
$250$	−2.93722	−	26.3639i	−0.185766	−	1.66740i
$251$		−	5.61954i		−	0.354702i	−0.984148	−	0.177351i	$-0.943247\pi$
$251$		−	5.61954i		−	0.354702i	0.984148	−	0.177351i	$-0.0567528\pi$
$252$	4.35829	−	45.9802i	0.274546	−	2.89648i
$253$	−3.30206	+	3.30206i	−0.207599	+	0.207599i
$254$	−13.4406			−0.843336
$255$	8.31236	+	20.6654i	0.520540	+	1.29412i
$256$	−26.2304			−1.63940
$257$	1.10613	−	1.10613i	0.0689985	−	0.0689985i	−0.671765	−	0.740764i	$-0.734464\pi$
$257$	1.10613	−	1.10613i	0.0689985	−	0.0689985i	0.740764	+	0.671765i	$0.234464\pi$
$258$	−8.91413	+	3.20800i	−0.554970	+	0.199721i
$259$			26.4363i			1.64267i
$260$	−0.451502	−	12.2023i	−0.0280009	−	0.756757i
$261$	13.1672	−	10.8872i	0.815030	−	0.673900i
$262$	−11.4615	−	11.4615i	−0.708091	−	0.708091i
$263$	−13.3968	−	13.3968i	−0.826082	−	0.826082i	0.160890	−	0.986972i	$-0.448564\pi$
$263$	−13.3968	−	13.3968i	−0.826082	−	0.826082i	−0.986972	+	0.160890i	$0.948564\pi$
$264$	−12.9172	−	6.08039i	−0.794998	−	0.374222i
$265$	−0.106025	−	2.86544i	−0.00651306	−	0.176023i
$266$			80.0929i			4.91081i
$267$	3.84580	+	10.6864i	0.235359	+	0.653999i
$268$	−22.0997	+	22.0997i	−1.34995	+	1.34995i
$269$	−3.93393			−0.239856			−0.119928	−	0.992783i	$-0.538266\pi$
$269$	−3.93393			−0.239856			−0.119928	+	0.992783i	$0.538266\pi$
$270$	−24.2263	−	13.1554i	−1.47436	−	0.800613i
$271$	−14.6277			−0.888571			−0.444286	−	0.895885i	$-0.646542\pi$
$271$	−14.6277			−0.888571			−0.444286	+	0.895885i	$0.646542\pi$
$272$	7.78403	−	7.78403i	0.471976	−	0.471976i
$273$	3.74311	+	10.4011i	0.226543	+	0.629501i
$274$		−	15.4420i		−	0.932886i
$275$	10.6309	−	0.787794i	0.641070	−	0.0475058i
$276$	12.4581	+	5.86429i	0.749889	+	0.352989i
$277$	−9.66204	−	9.66204i	−0.580535	−	0.580535i	0.354515	−	0.935050i	$-0.384646\pi$
$277$	−9.66204	−	9.66204i	−0.580535	−	0.580535i	−0.935050	+	0.354515i	$0.884646\pi$
$278$	38.3488	+	38.3488i	2.30001	+	2.30001i
$279$	2.31203	−	1.91168i	0.138418	−	0.114449i
$280$	24.9531	−	26.8707i	1.49124	−	1.60583i
$281$			20.7964i			1.24061i	0.784360	+	0.620306i	$0.212992\pi$
$281$			20.7964i			1.24061i	−0.784360	+	0.620306i	$0.787008\pi$
$282$	−16.3598	+	5.88754i	−0.974214	+	0.350598i
$283$	9.98593	−	9.98593i	0.593602	−	0.593602i	−0.345001	−	0.938602i	$-0.612121\pi$
$283$	9.98593	−	9.98593i	0.593602	−	0.593602i	0.938602	+	0.345001i	$0.112121\pi$
$284$	−43.9991			−2.61087
$285$	28.3529	+	12.0867i	1.67948	+	0.715955i
$286$	7.61092			0.450043
$287$	8.16541	−	8.16541i	0.481989	−	0.481989i
$288$	0.903305	−	9.52991i	0.0532278	−	0.561556i
$289$		−	16.0771i		−	0.945710i
$290$	30.1941	−	1.11722i	1.77306	−	0.0656053i
$291$	3.39978	−	7.22249i	0.199298	−	0.423390i
$292$	38.6002	+	38.6002i	2.25890	+	2.25890i
$293$	14.2559	+	14.2559i	0.832841	+	0.832841i	0.987905	−	0.155063i	$-0.0495582\pi$
$293$	14.2559	+	14.2559i	0.832841	+	0.832841i	−0.155063	+	0.987905i	$0.549558\pi$
$294$	−19.2400	+	40.8735i	−1.12210	+	2.38379i
$295$	9.23359	+	8.57466i	0.537600	+	0.499236i
$296$		−	24.0951i		−	1.40050i
$297$	5.64297	−	9.53338i	0.327438	−	0.553183i
$298$	−12.1136	+	12.1136i	−0.701721	+	0.701721i
$299$	−3.29551			−0.190584
$300$	−12.8000	−	28.7077i	−0.739007	−	1.65744i
$301$	9.77867			0.563633
$302$	−8.41120	+	8.41120i	−0.484010	+	0.484010i
$303$	3.41111	−	1.22758i	0.195963	−	0.0705228i
$304$		−	15.2324i		−	0.873636i
$305$	−15.6752	−	14.5566i	−0.897557	−	0.833506i
$306$	26.0863	+	31.5493i	1.49125	+	1.80356i
$307$	−2.93815	−	2.93815i	−0.167689	−	0.167689i	0.618274	−	0.785963i	$-0.287832\pi$
$307$	−2.93815	−	2.93815i	−0.167689	−	0.167689i	−0.785963	+	0.618274i	$0.787832\pi$
$308$	23.2096	+	23.2096i	1.32249	+	1.32249i
$309$	6.43608	+	3.02960i	0.366136	+	0.172348i
$310$	5.30178	−	0.196172i	0.301121	−	0.0111418i
$311$		−	9.38795i		−	0.532342i	−0.963926	−	0.266171i	$-0.914241\pi$
$311$		−	9.38795i		−	0.532342i	0.963926	−	0.266171i	$-0.0857586\pi$
$312$	−3.41162	−	9.47994i	−0.193145	−	0.536696i
$313$	−7.23887	+	7.23887i	−0.409165	+	0.409165i	−0.881447	−	0.472282i	$-0.843430\pi$
$313$	−7.23887	+	7.23887i	−0.409165	+	0.409165i	0.472282	+	0.881447i	$0.343430\pi$
$314$	−41.6821			−2.35226
$315$	18.9306	+	21.2440i	1.06662	+	1.19696i
$316$	35.1684			1.97838
$317$	1.79834	−	1.79834i	0.101005	−	0.101005i	−0.654799	−	0.755803i	$-0.727247\pi$
$317$	1.79834	−	1.79834i	0.101005	−	0.101005i	0.755803	+	0.654799i	$0.227247\pi$
$318$	−1.78446	−	4.95852i	−0.100068	−	0.278060i
$319$			12.1420i			0.679823i
$320$	17.3446	−	18.6774i	0.969591	−	1.04410i
$321$	−21.9751	−	10.3442i	−1.22653	−	0.577354i
$322$	−15.5875	−	15.5875i	−0.868660	−	0.868660i
$323$	−32.3638	−	32.3638i	−1.80077	−	1.80077i
$324$	−32.0834	−	6.13728i	−1.78241	−	0.340960i
$325$	5.69804	+	4.91181i	0.316070	+	0.272458i
$326$		−	3.94781i		−	0.218649i
$327$	−9.42871	+	3.39318i	−0.521409	+	0.187643i
$328$	−7.44227	+	7.44227i	−0.410931	+	0.410931i
$329$	17.9465			0.989423
$330$	18.1763	−	7.31114i	1.00057	−	0.402465i
$331$	12.2508			0.673363			0.336681	−	0.941619i	$-0.390695\pi$
$331$	12.2508			0.673363			0.336681	+	0.941619i	$0.390695\pi$
$332$	5.24019	−	5.24019i	0.287593	−	0.287593i
$333$	18.6136	+	1.76432i	1.02002	+	0.0966840i
$334$		−	27.9696i		−	1.53043i
$335$	−0.711972	−	19.2418i	−0.0388992	−	1.05129i
$336$	5.98920	−	12.7235i	0.326738	−	0.694122i
$337$	5.83427	+	5.83427i	0.317813	+	0.317813i	0.847927	−	0.530114i	$-0.177851\pi$
$337$	5.83427	+	5.83427i	0.317813	+	0.317813i	−0.530114	+	0.847927i	$0.677851\pi$
$338$	−18.0124	−	18.0124i	−0.979745	−	0.979745i
$339$	5.38264	−	11.4349i	0.292345	−	0.621058i
$340$	1.72588	+	46.6438i	0.0935988	+	2.52961i
$341$			2.13202i			0.115455i
$342$	56.3928	+	5.34526i	3.04937	+	0.289039i
$343$	11.9760	−	11.9760i	0.646645	−	0.646645i
$344$	−8.91267			−0.480539
$345$	−7.87029	+	3.16571i	−0.423722	+	0.170436i
$346$	−2.66535			−0.143290
$347$	−21.4765	+	21.4765i	−1.15292	+	1.15292i	−0.166954	+	0.985965i	$0.553393\pi$
$347$	−21.4765	+	21.4765i	−1.15292	+	1.15292i	−0.985965	+	0.166954i	$0.946607\pi$
$348$	33.6866	−	12.1231i	1.80579	−	0.649864i
$349$		−	0.785065i		−	0.0420235i	−0.999779	−	0.0210118i	$-0.993311\pi$
$349$		−	0.785065i		−	0.0420235i	0.999779	−	0.0210118i	$-0.00668875\pi$
$350$	3.71882	+	50.1838i	0.198779	+	2.68244i
$351$	7.57312	−	1.94134i	0.404223	−	0.103621i
$352$	4.81045	+	4.81045i	0.256398	+	0.256398i
$353$	12.5982	+	12.5982i	0.670532	+	0.670532i	0.957839	−	0.287306i	$-0.0927598\pi$
$353$	12.5982	+	12.5982i	0.670532	+	0.670532i	−0.287306	+	0.957839i	$0.592760\pi$
$354$	20.9533	+	9.86313i	1.11365	+	0.524220i
$355$	18.4459	−	19.8634i	0.979008	−	1.05424i
$356$			23.7990i			1.26135i
$357$	−14.3081	−	39.7583i	−0.757267	−	2.10423i
$358$	31.1676	−	31.1676i	1.64726	−	1.64726i
$359$	−21.9008			−1.15588			−0.577941	−	0.816079i	$-0.696143\pi$
$359$	−21.9008			−1.15588			−0.577941	+	0.816079i	$0.696143\pi$
$360$	−17.2541	−	19.3626i	−0.909372	−	1.02050i
$361$	−44.3318			−2.33325
$362$	24.9994	−	24.9994i	1.31394	−	1.31394i
$363$	−3.78558	−	10.5191i	−0.198691	−	0.552109i
$364$			23.1635i			1.21410i
$365$	−33.6086	+	1.24356i	−1.75915	+	0.0650908i
$366$	−35.5708	−	16.7439i	−1.85931	−	0.875218i
$367$	−17.4130	−	17.4130i	−0.908949	−	0.908949i	0.0872383	−	0.996187i	$-0.472196\pi$
$367$	−17.4130	−	17.4130i	−0.908949	−	0.908949i	−0.996187	+	0.0872383i	$0.972196\pi$
$368$	2.96450	+	2.96450i	0.154535	+	0.154535i
$369$	−5.20425	−	6.29414i	−0.270923	−	0.327660i
$370$	24.2291	+	22.5001i	1.25961	+	1.16972i
$371$			5.43943i			0.282401i
$372$	5.91503	−	2.12869i	0.306680	−	0.110367i
$373$	12.1020	−	12.1020i	0.626618	−	0.626618i	−0.320597	−	0.947216i	$-0.603884\pi$
$373$	12.1020	−	12.1020i	0.626618	−	0.626618i	0.947216	+	0.320597i	$0.103884\pi$
$374$	−29.0930			−1.50436
$375$	18.3263	+	6.25671i	0.946367	+	0.323095i
$376$	−16.3571			−0.843556
$377$	−6.05897	+	6.05897i	−0.312053	+	0.312053i
$378$	45.0027	+	26.6379i	2.31469	+	1.37011i
$379$			24.2201i			1.24411i	0.782975	+	0.622053i	$0.213701\pi$
$379$			24.2201i			1.24411i	−0.782975	+	0.622053i	$0.786299\pi$
$380$	47.3266	+	43.9493i	2.42780	+	2.25455i
$381$	4.17876	−	8.87737i	0.214084	−	0.454801i
$382$	38.4135	+	38.4135i	1.96540	+	1.96540i
$383$	11.4091	+	11.4091i	0.582977	+	0.582977i	0.935720	−	0.352744i	$-0.114751\pi$
$383$	11.4091	+	11.4091i	0.582977	+	0.582977i	−0.352744	+	0.935720i	$0.614751\pi$
$384$	15.2432	−	32.3827i	0.777877	−	1.65252i
$385$	−20.2082	+	0.747729i	−1.02991	+	0.0381078i
$386$			56.8430i			2.89323i
$387$	0.652612	−	6.88509i	0.0331741	−	0.349989i
$388$	11.8281	−	11.8281i	0.600479	−	0.600479i
$389$	35.7730			1.81376			0.906881	−	0.421386i	$-0.138456\pi$
$389$	35.7730			1.81376			0.906881	+	0.421386i	$0.138456\pi$
$390$	12.7184	+	5.42180i	0.644023	+	0.274543i
$391$	12.5972			0.637067
$392$	−30.0518	+	30.0518i	−1.51785	+	1.51785i
$393$	11.1336	−	4.00674i	0.561617	−	0.202113i
$394$			47.0971i			2.37272i
$395$	−14.7438	+	15.8768i	−0.741841	+	0.798849i
$396$	17.8907	−	14.7927i	0.899039	−	0.743362i
$397$	0.850877	+	0.850877i	0.0427043	+	0.0427043i	0.728136	−	0.685432i	$-0.240387\pi$
$397$	0.850877	+	0.850877i	0.0427043	+	0.0427043i	−0.685432	+	0.728136i	$0.740387\pi$
$398$	34.8122	+	34.8122i	1.74498	+	1.74498i
$399$	−52.9006	−	24.9014i	−2.64834	−	1.24663i
$400$	−0.707258	−	9.54414i	−0.0353629	−	0.477207i
$401$		−	24.9667i		−	1.24678i	−0.781912	−	0.623389i	$-0.785755\pi$
$401$		−	24.9667i		−	1.24678i	0.781912	−	0.623389i	$-0.214245\pi$
$402$	−11.9829	−	33.2972i	−0.597653	−	1.66071i
$403$	−1.06389	+	1.06389i	−0.0529963	+	0.0529963i
$404$	7.59667			0.377948
$405$	16.2211	−	11.9111i	0.806035	−	0.591868i
$406$	−57.3170			−2.84459
$407$	−9.39567	+	9.39567i	−0.465726	+	0.465726i
$408$	13.0410	+	36.2373i	0.645625	+	1.79401i
$409$			0.475032i			0.0234888i	0.999931	+	0.0117444i	$0.00373845\pi$
$409$			0.475032i			0.0234888i	−0.999931	+	0.0117444i	$0.996262\pi$
$410$	−0.534049	−	14.4333i	−0.0263748	−	0.712808i
$411$	10.1993	+	4.80102i	0.503095	+	0.236817i
$412$	10.5402	+	10.5402i	0.519278	+	0.519278i
$413$	−16.9026	−	16.9026i	−0.831721	−	0.831721i
$414$	−12.0154	+	9.93478i	−0.590522	+	0.488268i
$415$	0.168820	+	4.56255i	0.00828705	+	0.223967i
$416$			4.80090i			0.235384i
$417$	−37.2519	+	13.4061i	−1.82423	+	0.656500i
$418$	−28.4656	+	28.4656i	−1.39230	+	1.39230i
$419$	12.4369			0.607584			0.303792	−	0.952738i	$-0.401747\pi$
$419$	12.4369			0.607584			0.303792	+	0.952738i	$0.401747\pi$
$420$	22.2512	+	55.3188i	1.08575	+	2.69928i
$421$	−24.8858			−1.21286			−0.606429	−	0.795137i	$-0.707399\pi$
$421$	−24.8858			−1.21286			−0.606429	+	0.795137i	$0.707399\pi$
$422$	35.4902	−	35.4902i	1.72764	−	1.72764i
$423$	1.19772	−	12.6360i	0.0582351	−	0.614383i
$424$		−	4.95771i		−	0.240768i
$425$	−21.7809	−	18.7755i	−1.05653	−	0.910746i
$426$	21.2177	−	45.0749i	1.02800	−	2.18389i
$427$	28.6942	+	28.6942i	1.38861	+	1.38861i
$428$	−35.9881	−	35.9881i	−1.73955	−	1.73955i
$429$	−2.36629	+	5.02694i	−0.114245	+	0.242703i
$430$	8.32267	−	8.96223i	0.401355	−	0.432197i
$431$		−	7.25914i		−	0.349660i	−0.984599	−	0.174830i	$-0.944062\pi$
$431$		−	7.25914i		−	0.349660i	0.984599	−	0.174830i	$-0.0559376\pi$
$432$	−8.55879	−	5.06609i	−0.411785	−	0.243743i
$433$	18.1531	−	18.1531i	0.872384	−	0.872384i	−0.120348	−	0.992732i	$-0.538401\pi$
$433$	18.1531	−	18.1531i	0.872384	−	0.872384i	0.992732	+	0.120348i	$0.0384009\pi$
$434$	−10.0643			−0.483101
$435$	−8.64962	+	20.2902i	−0.414718	+	0.972843i
$436$	−20.9981			−1.00562
$437$	12.3255	−	12.3255i	0.589610	−	0.589610i
$438$	−58.1582	+	20.9298i	−2.77891	+	1.00007i
$439$			1.87434i			0.0894574i	0.998999	+	0.0447287i	$0.0142423\pi$
$439$			1.87434i			0.0894574i	−0.998999	+	0.0447287i	$0.985758\pi$
$440$	18.4186	−	0.681510i	0.878071	−	0.0324897i
$441$	−21.0147	−	25.4157i	−1.00070	−	1.21027i
$442$	−14.5176	−	14.5176i	−0.690532	−	0.690532i
$443$	−23.4694	−	23.4694i	−1.11506	−	1.11506i	−0.992455	−	0.122609i	$-0.960874\pi$
$443$	−23.4694	−	23.4694i	−1.11506	−	1.11506i	−0.122609	−	0.992455i	$-0.539126\pi$
$444$	35.4482	+	16.6862i	1.68230	+	0.791892i
$445$	−10.7441	−	9.97736i	−0.509318	−	0.472972i
$446$		−	29.7242i		−	1.40748i
$447$	−4.23471	−	11.7671i	−0.200295	−	0.556565i
$448$	−34.1900	+	34.1900i	−1.61533	+	1.61533i
$449$	14.1151			0.666135			0.333067	−	0.942903i	$-0.391916\pi$
$449$	14.1151			0.666135			0.333067	+	0.942903i	$0.391916\pi$
$450$	35.5822	+	0.730792i	1.67736	+	0.0344499i
$451$	5.80409			0.273304
$452$	18.7266	−	18.7266i	0.880825	−	0.880825i
$453$	−2.94042	−	8.17062i	−0.138153	−	0.383889i
$454$		−	26.3751i		−	1.23784i
$455$	−10.4572	−	9.71094i	−0.490240	−	0.455256i
$456$	48.2157	+	22.6961i	2.25791	+	1.06284i
$457$	11.9309	+	11.9309i	0.558104	+	0.558104i	0.928767	−	0.370663i	$-0.120870\pi$
$457$	11.9309	+	11.9309i	0.558104	+	0.558104i	−0.370663	+	0.928767i	$0.620870\pi$
$458$	23.1457	+	23.1457i	1.08153	+	1.08153i
$459$	−28.9484	+	7.42084i	−1.35120	+	0.346375i
$460$	−17.7640	+	0.657288i	−0.828249	+	0.0306462i
$461$			32.6705i			1.52162i	0.648975	+	0.760810i	$0.275198\pi$
$461$			32.6705i			1.52162i	−0.648975	+	0.760810i	$0.724802\pi$
$462$	−34.9695	+	12.5847i	−1.62693	+	0.585494i
$463$	1.27508	−	1.27508i	0.0592582	−	0.0592582i	−0.676857	−	0.736115i	$-0.736658\pi$
$463$	1.27508	−	1.27508i	0.0592582	−	0.0592582i	0.736115	+	0.676857i	$0.236658\pi$
$464$	10.9008			0.506055
$465$	−1.51879	+	3.56276i	−0.0704321	+	0.165219i
$466$	25.3805			1.17573
$467$	8.83646	−	8.83646i	0.408903	−	0.408903i	−0.472453	−	0.881356i	$-0.656631\pi$
$467$	8.83646	−	8.83646i	0.408903	−	0.408903i	0.881356	+	0.472453i	$0.156631\pi$
$468$	16.3093	+	1.54589i	0.753896	+	0.0714590i
$469$			36.5265i			1.68664i
$470$	15.2743	−	16.4481i	0.704553	−	0.758695i
$471$	12.9592	−	27.5306i	0.597130	−	1.26854i
$472$	15.4057	+	15.4057i	0.709103	+	0.709103i
$473$	3.47541	+	3.47541i	0.159800	+	0.159800i
$474$	−16.9593	+	36.0283i	−0.778966	+	1.65484i
$475$	−39.6818	+	2.94058i	−1.82073	+	0.134923i
$476$		−	88.5432i		−	4.05837i
$477$	3.82986	+	0.363018i	0.175357	+	0.0166215i
$478$	−3.28948	+	3.28948i	−0.150457	+	0.150457i
$479$	6.30145			0.287921			0.143960	−	0.989583i	$-0.454016\pi$
$479$	6.30145			0.287921			0.143960	+	0.989583i	$0.454016\pi$
$480$	4.61180	+	11.4655i	0.210499	+	0.523324i
$481$	−9.37702			−0.427556
$482$	17.5898	−	17.5898i	0.801196	−	0.801196i
$483$	15.1417	−	5.44915i	0.688971	−	0.247945i
$484$		−	23.4264i		−	1.06483i
$485$	0.381058	+	10.2985i	0.0173029	+	0.467632i
$486$	21.7589	−	29.9083i	0.987006	−	1.35667i
$487$	6.41498	+	6.41498i	0.290691	+	0.290691i	0.837353	−	0.546662i	$-0.184102\pi$
$487$	6.41498	+	6.41498i	0.290691	+	0.290691i	−0.546662	+	0.837353i	$0.684102\pi$
$488$	−26.1530	−	26.1530i	−1.18389	−	1.18389i
$489$	2.60749	+	1.22740i	0.117915	+	0.0555050i
$490$	−2.15648	−	58.2814i	−0.0974200	−	2.63289i
$491$		−	10.7314i		−	0.484302i	−0.970239	−	0.242151i	$-0.922147\pi$
$491$		−	10.7314i		−	0.484302i	0.970239	−	0.242151i	$-0.0778529\pi$
$492$	−5.79502	−	16.1028i	−0.261260	−	0.725969i
$493$	23.1606	−	23.1606i	1.04310	−	1.04310i
$494$	−28.4091			−1.27819
$495$	−0.822192	+	14.2784i	−0.0369548	+	0.641764i
$496$	1.91406			0.0859439
$497$	−36.3610	+	36.3610i	−1.63101	+	1.63101i
$498$	2.84134	+	7.89530i	0.127323	+	0.353797i
$499$			22.5880i			1.01118i	0.862774	+	0.505589i	$0.168725\pi$
$499$			22.5880i			1.01118i	−0.862774	+	0.505589i	$0.831275\pi$
$500$	31.6941	+	25.3399i	1.41740	+	1.13323i
$501$	18.4737	+	8.69594i	0.825342	+	0.388506i
$502$	9.42799	+	9.42799i	0.420792	+	0.420792i
$503$	14.4991	+	14.4991i	0.646484	+	0.646484i	0.952142	−	0.305658i	$-0.0988763\pi$
$503$	14.4991	+	14.4991i	0.646484	+	0.646484i	−0.305658	+	0.952142i	$0.598876\pi$
$504$	31.3503	+	37.9158i	1.39645	+	1.68890i
$505$	−3.18478	+	3.42952i	−0.141721	+	0.152612i
$506$		−	11.0799i		−	0.492559i
$507$	17.4972	−	6.29684i	0.777078	−	0.279653i
$508$	14.5382	−	14.5382i	0.645029	−	0.645029i
$509$	11.7022			0.518690			0.259345	−	0.965785i	$-0.416493\pi$
$509$	11.7022			0.518690			0.259345	+	0.965785i	$0.416493\pi$
$510$	−48.6165	−	20.7250i	−2.15278	−	0.917717i
$511$	63.7987			2.82229
$512$	14.7839	−	14.7839i	0.653362	−	0.653362i
$513$	−21.0634	+	35.5850i	−0.929971	+	1.57112i
$514$			3.71155i			0.163709i
$515$	−9.17719	+	0.339567i	−0.404395	+	0.0149631i
$516$	6.17214	−	13.1121i	0.271713	−	0.577228i
$517$	6.37832	+	6.37832i	0.280518	+	0.280518i
$518$	−44.3527	−	44.3527i	−1.94874	−	1.94874i
$519$	0.828674	−	1.76044i	0.0363748	−	0.0772746i
$520$	9.53109	+	8.85093i	0.417966	+	0.388139i
$521$			20.0069i			0.876520i	0.898848	+	0.438260i	$0.144405\pi$
$521$			20.0069i			0.876520i	−0.898848	+	0.438260i	$0.855595\pi$
$522$	−3.82524	+	40.3564i	−0.167426	+	1.76635i
$523$	−2.83267	+	2.83267i	−0.123864	+	0.123864i	−0.766321	−	0.642457i	$-0.777915\pi$
$523$	−2.83267	+	2.83267i	−0.123864	+	0.123864i	0.642457	+	0.766321i	$0.277915\pi$
$524$	24.7950			1.08317
$525$	−34.3021	−	13.1462i	−1.49707	−	0.573749i
$526$	44.9521			1.96000
$527$	4.06676	−	4.06676i	0.177151	−	0.177151i
$528$	6.65062	−	2.39341i	0.289431	−	0.104160i
$529$		−	18.2025i		−	0.791411i
$530$	4.98528	+	4.62952i	0.216547	+	0.201093i
$531$	−13.0290	+	10.7729i	−0.565411	+	0.467505i
$532$	−86.6338	−	86.6338i	−3.75605	−	3.75605i
$533$	2.89629	+	2.89629i	0.125452	+	0.125452i
$534$	−24.3809	−	11.4766i	−1.05507	−	0.496642i
$535$	31.3343	−	1.15941i	1.35470	−	0.0501255i
$536$		−	33.2917i		−	1.43798i
$537$	10.8957	+	30.2761i	0.470184	+	1.30651i
$538$	6.60001	−	6.60001i	0.284547	−	0.284547i
$539$	23.4369			1.00950
$540$	40.4345	−	11.9750i	1.74003	−	0.515321i
$541$	8.80625			0.378610			0.189305	−	0.981918i	$-0.439376\pi$
$541$	8.80625			0.378610			0.189305	+	0.981918i	$0.439376\pi$
$542$	24.5412	−	24.5412i	1.05413	−	1.05413i
$543$	8.73940	+	24.2844i	0.375043	+	1.04214i
$544$		−	18.3516i		−	0.786818i
$545$	8.80310	−	9.47958i	0.377083	−	0.406061i
$546$	−23.7299	−	11.1702i	−1.01555	−	0.478039i
$547$	0.0518238	+	0.0518238i	0.00221583	+	0.00221583i	0.708214	−	0.705998i	$-0.249501\pi$
$547$	0.0518238	+	0.0518238i	0.00221583	+	0.00221583i	−0.705998	+	0.708214i	$0.749501\pi$
$548$	16.7031	+	16.7031i	0.713522	+	0.713522i
$549$	22.1184	−	18.2884i	0.943989	−	0.780529i
$550$	−16.5140	+	19.1574i	−0.704159	+	0.816874i
$551$		−	45.3222i		−	1.93079i
$552$	−13.8007	+	4.96657i	−0.587398	+	0.211391i
$553$	29.0633	−	29.0633i	1.23590	−	1.23590i
$554$	32.4203			1.37741
$555$	−22.3941	+	9.00768i	−0.950576	+	0.382355i
$556$	−82.9612			−3.51834
$557$	−3.16460	+	3.16460i	−0.134088	+	0.134088i	−0.770965	−	0.636877i	$-0.780226\pi$
$557$	−3.16460	+	3.16460i	−0.134088	+	0.134088i	0.636877	+	0.770965i	$0.280226\pi$
$558$	−0.671673	+	7.08618i	−0.0284342	+	0.299982i
$559$			3.46851i			0.146703i
$560$	0.671289	+	18.1423i	0.0283671	+	0.766654i
$561$	9.04519	−	19.2156i	0.381888	−	0.811284i
$562$	−34.8905	−	34.8905i	−1.47177	−	1.47177i
$563$	11.2255	+	11.2255i	0.473100	+	0.473100i	0.902916	−	0.429817i	$-0.141422\pi$
$563$	11.2255	+	11.2255i	0.473100	+	0.473100i	−0.429817	+	0.902916i	$0.641422\pi$
$564$	11.3275	−	24.0643i	0.476976	−	1.01329i
$565$	0.603304	+	16.3050i	0.0253812	+	0.685955i
$566$			33.5071i			1.40841i
$567$	−31.5857	+	21.4420i	−1.32648	+	0.900479i
$568$	33.1409	−	33.1409i	1.39056	−	1.39056i
$569$	−29.5687			−1.23959			−0.619793	−	0.784766i	$-0.712783\pi$
$569$	−29.5687			−1.23959			−0.619793	+	0.784766i	$0.712783\pi$
$570$	−67.8462	+	27.2901i	−2.84177	+	1.14306i
$571$	3.15522			0.132042			0.0660209	−	0.997818i	$-0.478970\pi$
$571$	3.15522			0.132042			0.0660209	+	0.997818i	$0.478970\pi$
$572$	−8.23249	+	8.23249i	−0.344218	+	0.344218i
$573$	−37.3147	+	13.4287i	−1.55885	+	0.560994i
$574$			27.3985i			1.14359i
$575$	7.15052	−	8.29510i	0.298197	−	0.345930i
$576$	21.7911	+	26.3547i	0.907964	+	1.09811i
$577$	−8.16210	−	8.16210i	−0.339793	−	0.339793i	0.516497	−	0.856289i	$-0.327236\pi$
$577$	−8.16210	−	8.16210i	−0.339793	−	0.339793i	−0.856289	+	0.516497i	$0.827236\pi$
$578$	26.9728	+	26.9728i	1.12192	+	1.12192i
$579$	−37.5442	−	17.6729i	−1.56029	−	0.734459i
$580$	−31.4515	+	33.8684i	−1.30595	+	1.40631i
$581$		−	8.66103i		−	0.359320i
$582$	6.41343	+	17.8211i	0.265845	+	0.738710i
$583$	−1.93321	+	1.93321i	−0.0800655	+	0.0800655i
$584$	−58.1486			−2.40621
$585$	−7.53529	+	6.71473i	−0.311546	+	0.277620i
$586$	−47.8348			−1.97604
$587$	−7.81339	+	7.81339i	−0.322493	+	0.322493i	−0.849723	−	0.527230i	$-0.823231\pi$
$587$	−7.81339	+	7.81339i	−0.322493	+	0.322493i	0.527230	+	0.849723i	$0.323231\pi$
$588$	−23.4003	−	65.0228i	−0.965010	−	2.68150i
$589$		−	7.95813i		−	0.327909i
$590$	−29.8772	+	1.10549i	−1.23002	+	0.0455124i
$591$	−31.1072	−	14.6428i	−1.27958	−	0.602324i
$592$	8.43516	+	8.43516i	0.346683	+	0.346683i
$593$	−30.1675	−	30.1675i	−1.23883	−	1.23883i	−0.960480	−	0.278350i	$-0.910212\pi$
$593$	−30.1675	−	30.1675i	−1.23883	−	1.23883i	−0.278350	−	0.960480i	$-0.589788\pi$
$594$	6.52700	+	25.4616i	0.267806	+	1.04470i
$595$	39.9729	+	37.1203i	1.63873	+	1.52178i
$596$		−	26.2057i		−	1.07343i
$597$	−33.8165	+	12.1698i	−1.38402	+	0.498077i
$598$	5.52893	−	5.52893i	0.226095	−	0.226095i
$599$	−0.925378			−0.0378099			−0.0189050	−	0.999821i	$-0.506018\pi$
$599$	−0.925378			−0.0378099			−0.0189050	+	0.999821i	$0.506018\pi$
$600$	31.2643	+	11.9820i	1.27636	+	0.489163i
$601$	−10.7491			−0.438466			−0.219233	−	0.975672i	$-0.570356\pi$
$601$	−10.7491			−0.438466			−0.219233	+	0.975672i	$0.570356\pi$
$602$	−16.4058	+	16.4058i	−0.668652	+	0.668652i
$603$	25.7180	+	2.43772i	1.04732	+	0.0992715i
$604$		−	18.1962i		−	0.740395i
$605$	10.5758	+	9.82112i	0.429969	+	0.399286i
$606$	−3.66334	+	7.78241i	−0.148813	+	0.316139i
$607$	3.69050	+	3.69050i	0.149793	+	0.149793i	0.778025	−	0.628233i	$-0.216221\pi$
$607$	3.69050	+	3.69050i	0.149793	+	0.149793i	−0.628233	+	0.778025i	$0.716221\pi$
$608$	−17.9559	−	17.9559i	−0.728206	−	0.728206i
$609$	17.8202	−	37.8573i	0.722112	−	1.53406i
$610$	50.7202	−	1.87671i	2.05360	−	0.0759858i
$611$			6.36566i			0.257527i
$612$	−62.3426	−	5.90922i	−2.52005	−	0.238866i
$613$	−21.7192	+	21.7192i	−0.877230	+	0.877230i	−0.993247	−	0.116017i	$-0.962987\pi$
$613$	−21.7192	+	21.7192i	−0.877230	+	0.877230i	0.116017	+	0.993247i	$0.462987\pi$
$614$	9.85875			0.397867
$615$	9.69907	+	4.13466i	0.391104	+	0.166726i
$616$	−34.9637			−1.40873
$617$	−21.9327	+	21.9327i	−0.882979	+	0.882979i	−0.993836	−	0.110858i	$-0.964640\pi$
$617$	−21.9327	+	21.9327i	−0.882979	+	0.882979i	0.110858	+	0.993836i	$0.464640\pi$
$618$	−15.8807	+	5.71512i	−0.638816	+	0.229896i
$619$		−	15.9173i		−	0.639772i	−0.947456	−	0.319886i	$-0.896355\pi$
$619$		−	15.9173i		−	0.639772i	0.947456	−	0.319886i	$-0.103645\pi$
$620$	−5.52256	+	5.94695i	−0.221791	+	0.238835i
$621$	−2.82618	−	11.0248i	−0.113411	−	0.442411i
$622$	15.7503	+	15.7503i	0.631530	+	0.631530i
$623$	19.6676	+	19.6676i	0.787966	+	0.787966i
$624$	4.51304	+	2.12438i	0.180666	+	0.0850433i
$625$	−24.7269	+	3.68496i	−0.989077	+	0.147398i
$626$		−	24.2895i		−	0.970805i
$627$	−9.95112	−	27.6514i	−0.397409	−	1.10429i
$628$	45.0861	−	45.0861i	1.79913	−	1.79913i
$629$	35.8439			1.42919
$630$	−67.4016	−	3.88119i	−2.68534	−	0.154630i
$631$	17.6427			0.702346			0.351173	−	0.936311i	$-0.385783\pi$
$631$	17.6427			0.702346			0.351173	+	0.936311i	$0.385783\pi$
$632$	−26.4895	+	26.4895i	−1.05369	+	1.05369i
$633$	12.4068	+	34.4751i	0.493126	+	1.37026i
$634$			6.03420i			0.239649i
$635$	0.468369	+	12.6582i	0.0185867	+	0.502326i
$636$	7.29367	+	3.43328i	0.289213	+	0.136138i
$637$	11.6952	+	11.6952i	0.463380	+	0.463380i
$638$	−20.3709	−	20.3709i	−0.806490	−	0.806490i
$639$	23.1748	+	28.0282i	0.916783	+	1.10878i
$640$	1.70851	+	46.1744i	0.0675348	+	1.82520i
$641$			9.89547i			0.390847i	0.980719	+	0.195424i	$0.0626082\pi$
$641$			9.89547i			0.390847i	−0.980719	+	0.195424i	$0.937392\pi$
$642$	54.2226	−	19.5135i	2.13999	−	0.770136i
$643$	−22.3509	+	22.3509i	−0.881435	+	0.881435i	−0.993680	−	0.112246i	$-0.964196\pi$
$643$	−22.3509	+	22.3509i	−0.881435	+	0.881435i	0.112246	+	0.993680i	$0.464196\pi$
$644$	33.7211			1.32880
$645$	3.33190	+	8.28346i	0.131193	+	0.326161i
$646$	108.595			4.27259
$647$	20.3426	−	20.3426i	0.799748	−	0.799748i	−0.183307	−	0.983056i	$-0.558680\pi$
$647$	20.3426	−	20.3426i	0.799748	−	0.799748i	0.983056	+	0.183307i	$0.0586804\pi$
$648$	28.7885	−	19.5431i	1.13092	−	0.767724i
$649$		−	12.0146i		−	0.471614i
$650$	−17.8003	+	1.31907i	−0.698185	+	0.0517383i
$651$	3.12905	−	6.64736i	0.122637	−	0.260531i
$652$	4.27022	+	4.27022i	0.167235	+	0.167235i
$653$	−11.0916	−	11.0916i	−0.434046	−	0.434046i	0.455956	−	0.890002i	$-0.349297\pi$
$653$	−11.0916	−	11.0916i	−0.434046	−	0.434046i	−0.890002	+	0.455956i	$0.849297\pi$
$654$	10.1259	−	21.5115i	0.395954	−	0.841166i
$655$	−10.3949	+	11.1937i	−0.406162	+	0.437374i
$656$		−	5.21074i		−	0.203445i
$657$	4.25782	−	44.9202i	0.166113	−	1.75250i
$658$	−30.1091	+	30.1091i	−1.17378	+	1.17378i
$659$	−44.3623			−1.72811			−0.864055	−	0.503398i	$-0.832083\pi$
$659$	−44.3623			−1.72811			−0.864055	+	0.503398i	$0.832083\pi$
$660$	−11.7525	+	27.5689i	−0.457465	+	1.07312i
$661$	31.2294			1.21468			0.607342	−	0.794440i	$-0.292236\pi$
$661$	31.2294			1.21468			0.607342	+	0.794440i	$0.292236\pi$
$662$	−20.5533	+	20.5533i	−0.798826	+	0.798826i
$663$	14.1024	−	5.07512i	0.547690	−	0.197101i
$664$			7.89400i			0.306347i
$665$	75.4307	−	2.79103i	2.92508	−	0.108232i
$666$	−34.1884	+	28.2684i	−1.32477	+	1.09538i
$667$	8.82054	+	8.82054i	0.341533	+	0.341533i
$668$	30.2538	+	30.2538i	1.17056	+	1.17056i
$669$	19.6325	+	9.24144i	0.759037	+	0.357295i
$670$	33.4768	+	31.0878i	1.29332	+	1.20103i
$671$			20.3963i			0.787389i
$672$	−7.93833	−	22.0584i	−0.306228	−	0.850923i
$673$	25.7960	−	25.7960i	0.994362	−	0.994362i	−0.00562265	−	0.999984i	$-0.501790\pi$
$673$	25.7960	−	25.7960i	0.994362	−	0.994362i	0.999984	+	0.00562265i	$0.00178975\pi$
$674$	−19.5765			−0.754058
$675$	−11.5454	+	23.2745i	−0.444384	+	0.895837i
$676$	38.9668			1.49872
$677$	−14.3491	+	14.3491i	−0.551482	+	0.551482i	−0.926868	−	0.375387i	$-0.877510\pi$
$677$	−14.3491	+	14.3491i	−0.551482	+	0.551482i	0.375387	+	0.926868i	$0.377510\pi$
$678$	10.1540	+	28.2150i	0.389960	+	1.08359i
$679$		−	19.5495i		−	0.750242i
$680$	−36.4328	−	33.8329i	−1.39714	−	1.29743i
$681$	17.4205	+	8.20018i	0.667554	+	0.314232i
$682$	−3.57692	−	3.57692i	−0.136967	−	0.136967i
$683$	32.4348	+	32.4348i	1.24108	+	1.24108i	0.959552	+	0.281531i	$0.0908423\pi$
$683$	32.4348	+	32.4348i	1.24108	+	1.24108i	0.281531	+	0.959552i	$0.409158\pi$
$684$	−66.7800	+	55.2164i	−2.55340	+	2.11125i
$685$	−14.5431	+	0.538114i	−0.555665	+	0.0205603i
$686$			40.1848i			1.53426i
$687$	−22.4837	+	8.09137i	−0.857806	+	0.308705i
$688$	3.12012	−	3.12012i	0.118954	−	0.118954i
$689$	−1.92938			−0.0735034
$690$	7.89296	−	18.5153i	0.300480	−	0.704864i
$691$	−5.87568			−0.223521			−0.111761	−	0.993735i	$-0.535649\pi$
$691$	−5.87568			−0.223521			−0.111761	+	0.993735i	$0.535649\pi$
$692$	2.88302	−	2.88302i	0.109596	−	0.109596i
$693$	2.56015	−	27.0097i	0.0972519	−	1.02601i
$694$		−	72.0629i		−	2.73547i
$695$	34.7802	−	37.4529i	1.31929	−	1.42067i
$696$	−16.2421	+	34.5046i	−0.615653	+	1.30790i
$697$	−11.0711	−	11.0711i	−0.419349	−	0.419349i
$698$	1.31712	+	1.31712i	0.0498535	+	0.0498535i
$699$	−7.89098	+	16.7636i	−0.298464	+	0.634058i
$700$	−58.3047	−	50.2597i	−2.20371	−	1.89964i
$701$			49.9435i			1.88634i	0.332312	+	0.943170i	$0.392171\pi$
$701$			49.9435i			1.88634i	−0.332312	+	0.943170i	$0.607829\pi$
$702$	−9.44851	+	15.9626i	−0.356611	+	0.602468i
$703$	35.0710	−	35.0710i	1.32273	−	1.32273i
$704$	−24.3028			−0.915945
$705$	6.11493	+	15.2024i	0.230302	+	0.572555i
$706$	−42.2723			−1.59094
$707$	6.27792	−	6.27792i	0.236105	−	0.236105i
$708$	−33.3331	+	11.9958i	−1.25273	+	0.450831i
$709$			10.3180i			0.387501i	0.981051	+	0.193751i	$0.0620653\pi$
$709$			10.3180i			0.387501i	−0.981051	+	0.193751i	$0.937935\pi$
$710$	2.37815	+	64.2722i	0.0892503	+	2.41209i
$711$	−18.5236	−	22.4029i	−0.694690	−	0.840174i
$712$	−17.9258	−	17.9258i	−0.671799	−	0.671799i
$713$	1.54880	+	1.54880i	0.0580029	+	0.0580029i
$714$	90.7082	+	42.6982i	3.39467	+	1.59794i
$715$	−0.265221	−	7.16790i	−0.00991871	−	0.268064i
$716$			67.4259i			2.51982i
$717$	−1.14995	−	3.19539i	−0.0429457	−	0.119334i
$718$	36.7434	−	36.7434i	1.37125	−	1.37125i
$719$	−40.0181			−1.49242			−0.746211	−	0.665710i	$-0.768129\pi$
$719$	−40.0181			−1.49242			−0.746211	+	0.665710i	$0.768129\pi$
$720$	12.8187	+	0.738140i	0.477724	+	0.0275088i
$721$	17.4209			0.648789
$722$	74.3762	−	74.3762i	2.76800	−	2.76800i
$723$	6.14913	+	17.0867i	0.228689	+	0.635462i
$724$			54.0821i			2.00995i
$725$	−2.10437	−	28.3976i	−0.0781544	−	1.05466i
$726$	23.9992	+	11.2969i	0.890692	+	0.419267i
$727$	−16.5015	−	16.5015i	−0.612007	−	0.612007i	0.331462	−	0.943469i	$-0.392458\pi$
$727$	−16.5015	−	16.5015i	−0.612007	−	0.612007i	−0.943469	+	0.331462i	$0.892458\pi$
$728$	−17.4472	−	17.4472i	−0.646635	−	0.646635i
$729$	12.9892	+	23.6703i	0.481080	+	0.876677i
$730$	54.2993	−	58.4720i	2.00971	−	2.16415i
$731$		−	13.2585i		−	0.490383i
$732$	56.5871	−	20.3644i	2.09152	−	0.752690i
$733$	−28.3344	+	28.3344i	−1.04655	+	1.04655i	−0.0476910	+	0.998862i	$0.515186\pi$
$733$	−28.3344	+	28.3344i	−1.04655	+	1.04655i	−0.998862	+	0.0476910i	$0.984814\pi$
$734$	58.4280			2.15662
$735$	39.1648	+	16.6957i	1.44461	+	0.615832i
$736$	6.98907			0.257621
$737$	−12.9818	+	12.9818i	−0.478190	+	0.478190i
$738$	19.2910	+	1.82853i	0.710113	+	0.0673090i
$739$			20.7055i			0.761666i	0.924644	+	0.380833i	$0.124363\pi$
$739$			20.7055i			0.761666i	−0.924644	+	0.380833i	$0.875637\pi$
$740$	−50.5454	+	1.87024i	−1.85809	+	0.0687515i
$741$	8.83258	−	18.7639i	0.324473	−	0.689311i
$742$	−9.12581	−	9.12581i	−0.335019	−	0.335019i
$743$	−2.02605	−	2.02605i	−0.0743286	−	0.0743286i	0.668965	−	0.743294i	$-0.266738\pi$
$743$	−2.02605	−	2.02605i	−0.0743286	−	0.0743286i	−0.743294	+	0.668965i	$0.766738\pi$
$744$	−2.85194	+	6.05867i	−0.104557	+	0.222122i
$745$	11.8306	+	10.9863i	0.433439	+	0.402508i
$746$			40.6075i			1.48674i
$747$	−6.09816	−	0.578022i	−0.223120	−	0.0211487i
$748$	31.4689	−	31.4689i	1.15062	−	1.15062i
$749$	−59.4814			−2.17340
$750$	−41.2433	+	20.2494i	−1.50599	+	0.739402i
$751$	8.22429			0.300108			0.150054	−	0.988678i	$-0.452055\pi$
$751$	8.22429			0.300108			0.150054	+	0.988678i	$0.452055\pi$
$752$	5.72627	−	5.72627i	0.208815	−	0.208815i
$753$	−9.15832	+	3.29587i	−0.333748	+	0.120108i
$754$		−	20.3304i		−	0.740391i
$755$	8.21470	+	7.62848i	0.298964	+	0.277629i
$756$	−77.4913	+	19.8647i	−2.81833	+	0.722471i
$757$	−18.0136	−	18.0136i	−0.654717	−	0.654717i	0.299408	−	0.954125i	$-0.403211\pi$
$757$	−18.0136	−	18.0136i	−0.654717	−	0.654717i	−0.954125	+	0.299408i	$0.903211\pi$
$758$	−40.6345	−	40.6345i	−1.47591	−	1.47591i
$759$	7.31814	+	3.44480i	0.265632	+	0.125038i
$760$	−68.7505	+	2.54385i	−2.49384	+	0.0922753i
$761$		−	24.7594i		−	0.897529i	−0.893650	−	0.448764i	$-0.851864\pi$
$761$		−	24.7594i		−	0.897529i	0.893650	−	0.448764i	$-0.148136\pi$
$762$	7.88293	+	21.9045i	0.285568	+	0.793515i
$763$	−17.3529	+	17.3529i	−0.628216	+	0.628216i
$764$	−83.1012			−3.00650
$765$	28.8038	−	25.6672i	1.04141	−	0.928001i
$766$	−38.2824			−1.38320
$767$	5.99537	−	5.99537i	0.216480	−	0.216480i
$768$	15.3842	+	42.7484i	0.555129	+	1.54255i
$769$			0.511883i			0.0184590i	0.999957	+	0.00922948i	$0.00293788\pi$
$769$			0.511883i			0.0184590i	−0.999957	+	0.00922948i	$0.997062\pi$
$770$	32.6492	−	35.1581i	1.17660	−	1.26701i
$771$	−2.45144	−	1.15394i	−0.0882865	−	0.0415583i
$772$	−61.4852	−	61.4852i	−2.21290	−	2.21290i
$773$	2.35138	+	2.35138i	0.0845731	+	0.0845731i	0.748128	−	0.663555i	$-0.230953\pi$
$773$	2.35138	+	2.35138i	0.0845731	+	0.0845731i	−0.663555	+	0.748128i	$0.730953\pi$
$774$	10.4563	+	12.6461i	0.375845	+	0.454555i
$775$	−0.369506	−	4.98633i	−0.0132731	−	0.179114i
$776$			17.8182i			0.639636i
$777$	43.0841	−	15.5050i	1.54563	−	0.556238i
$778$	−60.0169	+	60.0169i	−2.15171	+	2.15171i
$779$	−21.6648			−0.776221
$780$	−19.6217	+	7.89253i	−0.702569	+	0.282598i
$781$	−25.8459			−0.924841
$782$	−21.1345	+	21.1345i	−0.755768	+	0.755768i
$783$	−25.4658	−	15.0736i	−0.910072	−	0.538687i
$784$		−	21.0409i		−	0.751462i
$785$	1.45251	+	39.2558i	0.0518424	+	1.40110i
$786$	−11.9569	+	25.4012i	−0.426488	+	0.906032i
$787$	9.76926	+	9.76926i	0.348237	+	0.348237i	0.859452	−	0.511216i	$-0.170805\pi$
$787$	9.76926	+	9.76926i	0.348237	+	0.348237i	−0.511216	+	0.859452i	$0.670805\pi$
$788$	−50.9434	−	50.9434i	−1.81478	−	1.81478i
$789$	−13.9759	+	29.6904i	−0.497555	+	1.05701i
$790$	−1.90085	−	51.3727i	−0.0676293	−	1.82776i
$791$		−	30.9515i		−	1.10051i
$792$	−2.33342	+	24.6177i	−0.0829144	+	0.874751i
$793$	−10.1779	+	10.1779i	−0.361428	+	0.361428i
$794$	−2.85506			−0.101322
$795$	−4.60771	+	1.85338i	−0.163419	+	0.0657326i
$796$	−75.3105			−2.66931
$797$	−0.129192	+	0.129192i	−0.00457621	+	0.00457621i	−0.709391	−	0.704815i	$-0.751030\pi$
$797$	−0.129192	+	0.129192i	−0.00457621	+	0.00457621i	0.704815	+	0.709391i	$0.251030\pi$
$798$	130.530	−	46.9747i	4.62070	−	1.66289i
$799$		−	24.3329i		−	0.860836i
$800$	−12.0843	−	10.4169i	−0.427245	−	0.368293i
$801$	15.1604	−	12.5352i	0.535666	−	0.442911i
$802$	41.8870	+	41.8870i	1.47908	+	1.47908i
$803$	22.6745	+	22.6745i	0.800166	+	0.800166i
$804$	48.9780	+	23.0549i	1.72732	+	0.813085i
$805$	−14.1370	+	15.2234i	−0.498264	+	0.536554i
$806$		−	3.56982i		−	0.125742i
$807$	2.30726	+	6.41123i	0.0812193	+	0.225686i
$808$	−5.72194	+	5.72194i	−0.201297	+	0.201297i
$809$	18.6649			0.656223			0.328111	−	0.944639i	$-0.393588\pi$
$809$	18.6649			0.656223			0.328111	+	0.944639i	$0.393588\pi$
$810$	−7.23099	+	47.1979i	−0.254071	+	1.65837i
$811$	37.8587			1.32940			0.664699	−	0.747112i	$-0.268560\pi$
$811$	37.8587			1.32940			0.664699	+	0.747112i	$0.268560\pi$
$812$	61.9979	−	61.9979i	2.17570	−	2.17570i
$813$	8.57920	+	23.8392i	0.300886	+	0.836078i
$814$		−	31.5265i		−	1.10500i
$815$	−3.71801	+	0.137571i	−0.130236	+	0.00481890i
$816$	−17.2512	−	8.12051i	−0.603913	−	0.284275i
$817$	−12.9726	−	12.9726i	−0.453853	−	0.453853i
$818$	−0.796968	−	0.796968i	−0.0278653	−	0.0278653i
$819$	14.7556	−	12.2005i	0.515601	−	0.426320i
$820$	16.1897	+	15.0343i	0.565367	+	0.525021i
$821$			41.2270i			1.43883i	0.694580	+	0.719415i	$0.255590\pi$
$821$			41.2270i			1.43883i	−0.694580	+	0.719415i	$0.744410\pi$
$822$	−25.1663	+	9.05678i	−0.877775	+	0.315892i
$823$	−8.84297	+	8.84297i	−0.308246	+	0.308246i	−0.844229	−	0.535983i	$-0.819941\pi$
$823$	−8.84297	+	8.84297i	−0.308246	+	0.308246i	0.535983	+	0.844229i	$0.319941\pi$
$824$	−15.8781			−0.553140
$825$	−7.51896	−	16.8635i	−0.261777	−	0.587112i
$826$	56.7154			1.97338
$827$	14.5480	−	14.5480i	0.505885	−	0.505885i	−0.407376	−	0.913261i	$-0.633556\pi$
$827$	14.5480	−	14.5480i	0.505885	−	0.505885i	0.913261	+	0.407376i	$0.133556\pi$
$828$	2.25049	−	23.7427i	0.0782098	−	0.825117i
$829$		−	26.8076i		−	0.931067i	−0.885030	−	0.465533i	$-0.845863\pi$
$829$		−	26.8076i		−	0.931067i	0.885030	−	0.465533i	$-0.154137\pi$
$830$	−7.93790	−	7.37143i	−0.275528	−	0.255866i
$831$	−10.0797	+	21.4133i	−0.349660	+	0.742819i
$832$	−12.1273	−	12.1273i	−0.420437	−	0.420437i
$833$	−44.7051	−	44.7051i	−1.54894	−	1.54894i
$834$	40.0064	−	84.9897i	1.38531	−	2.94295i
$835$	−26.3415	+	0.974669i	−0.911586	+	0.0337298i
$836$		−	61.5806i		−	2.12981i
$837$	−4.47153	−	2.64678i	−0.154559	−	0.0914859i
$838$	−20.8656	+	20.8656i	−0.720791	+	0.720791i
$839$	1.56631			0.0540750			0.0270375	−	0.999634i	$-0.491393\pi$
$839$	1.56631			0.0540750			0.0270375	+	0.999634i	$0.491393\pi$
$840$	−58.4270	−	24.9071i	−2.01592	−	0.859377i
$841$	3.43401			0.118414
$842$	41.7513	−	41.7513i	1.43884	−	1.43884i
$843$	33.8926	−	12.1972i	1.16732	−	0.420093i
$844$			76.7771i			2.64278i
$845$	−16.3362	+	17.5916i	−0.561983	+	0.605169i
$846$	19.1902	+	23.2090i	0.659772	+	0.797943i
$847$	−19.3596	−	19.3596i	−0.665205	−	0.665205i
$848$	1.73558	+	1.73558i	0.0596001	+	0.0596001i
$849$	−22.1311	−	10.4176i	−0.759538	−	0.357530i
$850$	68.0421	−	5.04219i	2.33383	−	0.172946i
$851$			13.6509i			0.467947i
$852$	25.8056	+	71.7066i	0.884085	+	2.45663i
$853$	14.6674	−	14.6674i	0.502203	−	0.502203i	−0.409919	−	0.912122i	$-0.634443\pi$
$853$	14.6674	−	14.6674i	0.502203	−	0.502203i	0.912122	+	0.409919i	$0.134443\pi$
$854$	−96.2815			−3.29468
$855$	3.06898	−	53.2965i	0.104957	−	1.82270i
$856$	54.2137			1.85299
$857$	0.583031	−	0.583031i	0.0199159	−	0.0199159i	−0.697079	−	0.716995i	$-0.745517\pi$
$857$	0.583031	−	0.583031i	0.0199159	−	0.0199159i	0.716995	+	0.697079i	$0.245517\pi$
$858$	−4.46383	−	12.4037i	−0.152393	−	0.423457i
$859$		−	4.01133i		−	0.136865i	−0.997656	−	0.0684324i	$-0.978200\pi$
$859$		−	4.01133i		−	0.136865i	0.997656	−	0.0684324i	$-0.0217998\pi$
$860$	0.691794	+	18.6965i	0.0235900	+	0.637545i
$861$	−18.0964	−	8.51836i	−0.616725	−	0.290305i
$862$	12.1788	+	12.1788i	0.414810	+	0.414810i
$863$	6.75504	+	6.75504i	0.229944	+	0.229944i	0.812669	−	0.582725i	$-0.198014\pi$
$863$	6.75504	+	6.75504i	0.229944	+	0.229944i	−0.582725	+	0.812669i	$0.698014\pi$
$864$	−16.0610	+	4.11718i	−0.546405	+	0.140069i
$865$	0.0928805	+	2.51020i	0.00315803	+	0.0853494i
$866$			60.9116i			2.06986i
$867$	−26.2013	+	9.42925i	−0.889842	+	0.320234i
$868$	10.8862	−	10.8862i	0.369502	−	0.369502i
$869$	20.6586			0.700796
$870$	−19.5297	−	48.5529i	−0.662117	−	1.64610i
$871$	−12.9560			−0.438998
$872$	15.8161	−	15.8161i	0.535601	−	0.535601i
$873$	−13.7647	−	1.30470i	−0.465864	−	0.0441575i
$874$			41.3575i			1.39894i
$875$	47.1331	−	5.25113i	1.59339	−	0.177520i
$876$	40.2687	−	85.5469i	1.36055	−	2.89036i
$877$	−16.2066	−	16.2066i	−0.547257	−	0.547257i	0.378389	−	0.925646i	$-0.376478\pi$
$877$	−16.2066	−	16.2066i	−0.547257	−	0.547257i	−0.925646	+	0.378389i	$0.876478\pi$
$878$	−3.14461	−	3.14461i	−0.106125	−	0.106125i
$879$	14.8722	−	31.5945i	0.501626	−	1.06565i
$880$	−6.20934	+	6.68650i	−0.209317	+	0.225402i
$881$		−	22.3971i		−	0.754577i	−0.926096	−	0.377289i	$-0.876856\pi$
$881$		−	22.3971i		−	0.754577i	0.926096	−	0.377289i	$-0.123144\pi$
$882$	77.8971	+	7.38357i	2.62293	+	0.248618i
$883$	−35.9634	+	35.9634i	−1.21027	+	1.21027i	−0.239326	+	0.970939i	$0.576926\pi$
$883$	−35.9634	+	35.9634i	−1.21027	+	1.21027i	−0.970939	+	0.239326i	$0.923074\pi$
$884$	31.4064			1.05631
$885$	8.55884	−	20.0773i	0.287702	−	0.674891i
$886$	78.7499			2.64566
$887$	−20.3059	+	20.3059i	−0.681806	+	0.681806i	−0.960407	−	0.278601i	$-0.910129\pi$
$887$	−20.3059	+	20.3059i	−0.681806	+	0.681806i	0.278601	+	0.960407i	$0.410129\pi$
$888$	−39.2685	+	14.1319i	−1.31776	+	0.474234i
$889$		−	24.0289i		−	0.805903i
$890$	34.7647	−	1.28634i	1.16532	−	0.0431181i
$891$	−18.8464	−	3.60516i	−0.631380	−	0.120777i
$892$	32.1516	+	32.1516i	1.07652	+	1.07652i
$893$	−23.8082	−	23.8082i	−0.796711	−	0.796711i
$894$	26.8465	+	12.6372i	0.897881	+	0.422651i
$895$	−30.4395	−	28.2672i	−1.01748	−	0.944870i
$896$		−	87.6522i		−	2.92826i
$897$	1.93283	+	5.37079i	0.0645352	+	0.179325i
$898$	−23.6812	+	23.6812i	−0.790252	+	0.790252i
$899$	5.69509			0.189942
$900$	−39.2786	+	37.6977i	−1.30929	+	1.25659i
$901$	7.37509			0.245700
$902$	−9.73761	+	9.73761i	−0.324227	+	0.324227i
$903$	−5.73522	−	15.9366i	−0.190856	−	0.530336i
$904$			28.2104i			0.938264i
$905$	−24.4154	−	22.6731i	−0.811595	−	0.753678i
$906$	18.6412	+	8.77478i	0.619311	+	0.291523i
$907$	−23.0428	−	23.0428i	−0.765125	−	0.765125i	0.212119	−	0.977244i	$-0.431964\pi$
$907$	−23.0428	−	23.0428i	−0.765125	−	0.765125i	−0.977244	+	0.212119i	$0.931964\pi$
$908$	28.5290	+	28.5290i	0.946770	+	0.946770i
$909$	−4.00125	−	4.83921i	−0.132713	−	0.160506i
$910$	33.8364	−	1.25199i	1.12167	−	0.0415030i
$911$		−	25.6275i		−	0.849077i	−0.905410	−	0.424539i	$-0.860436\pi$
$911$		−	25.6275i		−	0.849077i	0.905410	−	0.424539i	$-0.139564\pi$
$912$	−24.8246	+	8.93382i	−0.822025	+	0.295828i
$913$	3.07819	−	3.07819i	0.101873	−	0.101873i
$914$	−40.0333			−1.32419
$915$	−14.5297	+	34.0837i	−0.480337	+	1.12677i
$916$	−50.0719			−1.65442
$917$	20.4907	−	20.4907i	0.676661	−	0.676661i
$918$	36.1172	−	61.0173i	1.19205	−	2.01387i
$919$			52.0237i			1.71610i	0.513562	+	0.858052i	$0.328326\pi$
$919$			52.0237i			1.71610i	−0.513562	+	0.858052i	$0.671674\pi$
$920$	12.8850	−	13.8752i	0.424807	−	0.457452i
$921$	−3.06515	+	6.51161i	−0.101000	+	0.214565i
$922$	−54.8119	−	54.8119i	−1.80513	−	1.80513i
$923$	−12.8973	−	12.8973i	−0.424521	−	0.424521i
$924$	24.2128	−	51.4378i	0.796544	−	1.69218i
$925$	20.3460	−	23.6028i	0.668974	−	0.776056i
$926$			4.27846i			0.140599i
$927$	1.16264	−	12.2659i	0.0381862	−	0.402866i
$928$	12.8498	−	12.8498i	0.421814	−	0.421814i
$929$	28.0126			0.919065			0.459532	−	0.888161i	$-0.348017\pi$
$929$	28.0126			0.919065			0.459532	+	0.888161i	$0.348017\pi$
$930$	−3.42921	−	8.52540i	−0.112448	−	0.279559i
$931$	−87.4822			−2.86711
$932$	−27.4533	+	27.4533i	−0.899263	+	0.899263i
$933$	−15.2998	+	5.50606i	−0.500894	+	0.180260i
$934$			29.6501i			0.970182i
$935$	1.01381	+	27.3995i	0.0331553	+	0.896059i
$936$	−13.4488	+	11.1200i	−0.439588	+	0.363469i
$937$	28.8082	+	28.8082i	0.941123	+	0.941123i	0.998361	−	0.0572374i	$-0.0182292\pi$
$937$	28.8082	+	28.8082i	0.941123	+	0.941123i	−0.0572374	+	0.998361i	$0.518229\pi$
$938$	−61.2811	−	61.2811i	−2.00090	−	2.00090i
$939$	16.0430	+	7.55178i	0.523544	+	0.246443i
$940$	1.26963	+	34.3131i	0.0414107	+	1.11917i
$941$		−	32.7271i		−	1.06687i	−0.845840	−	0.533437i	$-0.820900\pi$
$941$		−	32.7271i		−	1.06687i	0.845840	−	0.533437i	$-0.179100\pi$
$942$	24.4466	+	67.9305i	0.796515	+	2.21329i
$943$	4.21636	−	4.21636i	0.137304	−	0.137304i
$944$	−10.7863			−0.351066
$945$	23.5191	−	43.3114i	0.765076	−	1.40892i
$946$	−11.6615			−0.379148
$947$	39.0589	−	39.0589i	1.26924	−	1.26924i	0.322763	−	0.946480i	$-0.395388\pi$
$947$	39.0589	−	39.0589i	1.26924	−	1.26924i	0.946480	−	0.322763i	$-0.104612\pi$
$948$	−20.6264	−	57.3150i	−0.669913	−	1.86150i
$949$			22.6295i			0.734585i
$950$	61.6414	−	71.5083i	1.99991	−	2.32004i
$951$	−3.98553	−	1.87607i	−0.129240	−	0.0608358i
$952$	66.6922	+	66.6922i	2.16151	+	2.16151i
$953$	−15.5786	−	15.5786i	−0.504639	−	0.504639i	0.408237	−	0.912876i	$-0.366144\pi$
$953$	−15.5786	−	15.5786i	−0.504639	−	0.504639i	−0.912876	+	0.408237i	$0.866144\pi$
$954$	−7.03446	+	5.81637i	−0.227749	+	0.188312i
$955$	34.8389	−	37.5161i	1.12736	−	1.21399i
$956$		−	7.11625i		−	0.230156i
$957$	19.7882	−	7.12133i	0.639662	−	0.230200i
$958$	−10.5720	+	10.5720i	−0.341567	+	0.341567i
$959$	27.6071			0.891478
$960$	−40.6118	−	17.3126i	−1.31074	−	0.558761i
$961$	1.00000			0.0322581
$962$	15.7320	−	15.7320i	0.507219	−	0.507219i
$963$	−3.96969	+	41.8804i	−0.127921	+	1.34958i
$964$			38.0527i			1.22560i
$965$	53.5342	−	1.98083i	1.72333	−	0.0637652i
$966$	−16.2613	+	34.5456i	−0.523200	+	1.11149i
$967$	0.214357	+	0.214357i	0.00689327	+	0.00689327i	0.710545	−	0.703652i	$-0.248448\pi$
$967$	0.214357	+	0.214357i	0.00689327	+	0.00689327i	−0.703652	+	0.710545i	$0.748448\pi$
$968$	17.6451	+	17.6451i	0.567136	+	0.567136i
$969$	−33.7628	+	71.7257i	−1.08462	+	2.30416i
$970$	−17.9173	−	16.6387i	−0.575290	−	0.534236i
$971$			40.0100i			1.28398i	0.766712	+	0.641991i	$0.221891\pi$
$971$			40.0100i			1.28398i	−0.766712	+	0.641991i	$0.778109\pi$
$972$	8.81491	+	55.8868i	0.282738	+	1.79257i
$973$	−68.5595	+	68.5595i	−2.19792	+	2.19792i
$974$	−21.5250			−0.689707
$975$	4.66300	−	12.1670i	0.149335	−	0.389657i
$976$	18.3112			0.586126
$977$	−40.7077	+	40.7077i	−1.30236	+	1.30236i	−0.375557	+	0.926799i	$0.622548\pi$
$977$	−40.7077	+	40.7077i	−1.30236	+	1.30236i	−0.926799	+	0.375557i	$0.877452\pi$
$978$	−6.43386	+	2.31540i	−0.205732	+	0.0740384i
$979$			13.9800i			0.446804i
$980$	65.3737	+	60.7085i	2.08829	+	1.93926i
$981$	11.0599	+	13.3761i	0.353116	+	0.427067i
$982$	18.0042	+	18.0042i	0.574539	+	0.574539i
$983$	41.6073	+	41.6073i	1.32707	+	1.32707i	0.907917	+	0.419150i	$0.137672\pi$
$983$	41.6073	+	41.6073i	1.32707	+	1.32707i	0.419150	+	0.907917i	$0.362328\pi$
$984$	16.4938	+	7.76397i	0.525803	+	0.247506i
$985$	44.3556	−	1.64121i	1.41329	−	0.0522934i
$986$			77.7136i			2.47491i
$987$	−10.5257	−	29.2479i	−0.335036	−	0.930972i
$988$	30.7292	−	30.7292i	0.977626	−	0.977626i
$989$	5.04940			0.160562
$990$	−22.5756	−	25.3344i	−0.717500	−	0.805181i
$991$	25.4132			0.807275			0.403638	−	0.914919i	$-0.367746\pi$
$991$	25.4132			0.807275			0.403638	+	0.914919i	$0.367746\pi$
$992$	2.25629	−	2.25629i	0.0716373	−	0.0716373i
$993$	−7.18510	−	19.9654i	−0.228012	−	0.633583i
$994$		−	122.007i		−	3.86982i
$995$	31.5727	−	33.9990i	1.00092	−	1.07784i
$996$	−11.6135	−	5.46670i	−0.367987	−	0.173219i
$997$	24.4178	+	24.4178i	0.773320	+	0.773320i	0.978685	−	0.205365i	$-0.0658383\pi$
$997$	24.4178	+	24.4178i	0.773320	+	0.773320i	−0.205365	+	0.978685i	$0.565838\pi$
$998$	−37.8963	−	37.8963i	−1.19959	−	1.19959i
$999$	−8.04158	−	31.3699i	−0.254424	−	0.992501i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.k.b.32.4	✓	60
3.2	odd	2	inner	465.2.k.b.32.27	yes	60
5.3	odd	4	inner	465.2.k.b.218.27	yes	60
15.8	even	4	inner	465.2.k.b.218.4	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.k.b.32.4	✓	60	1.1	even	1	trivial
465.2.k.b.32.27	yes	60	3.2	odd	2	inner
465.2.k.b.218.4	yes	60	15.8	even	4	inner
465.2.k.b.218.27	yes	60	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.67772 + 1.67772i) q^{2} +(-0.586503 - 1.62973i) q^{3} -3.62946i q^{4} +(1.63852 + 1.52159i) q^{5} +(3.71821 + 1.75024i) q^{6} +(-2.99940 - 2.99940i) q^{7} +(2.73377 + 2.73377i) q^{8} +(-2.31203 + 1.91168i) q^{9} +O(q^{10})\)	\(q+(-1.67772 + 1.67772i) q^{2} +(-0.586503 - 1.62973i) q^{3} -3.62946i q^{4} +(1.63852 + 1.52159i) q^{5} +(3.71821 + 1.75024i) q^{6} +(-2.99940 - 2.99940i) q^{7} +(2.73377 + 2.73377i) q^{8} +(-2.31203 + 1.91168i) q^{9} +(-5.30178 + 0.196172i) q^{10} -2.13202i q^{11} +(-5.91503 + 2.12869i) q^{12} +(1.06389 - 1.06389i) q^{13} +10.0643 q^{14} +(1.51879 - 3.56276i) q^{15} -1.91406 q^{16} +(-4.06676 + 4.06676i) q^{17} +(0.671673 - 7.08618i) q^{18} +7.95813i q^{19} +(5.52256 - 5.94695i) q^{20} +(-3.12905 + 6.64736i) q^{21} +(3.57692 + 3.57692i) q^{22} +(-1.54880 - 1.54880i) q^{23} +(2.85194 - 6.05867i) q^{24} +(0.369506 + 4.98633i) q^{25} +3.56982i q^{26} +(4.47153 + 2.64678i) q^{27} +(-10.8862 + 10.8862i) q^{28} -5.69509 q^{29} +(3.42921 + 8.52540i) q^{30} -1.00000 q^{31} +(-2.25629 + 2.25629i) q^{32} +(-3.47461 + 1.25043i) q^{33} -13.6457i q^{34} +(-0.350714 - 9.47845i) q^{35} +(6.93837 + 8.39142i) q^{36} +(-4.40694 - 4.40694i) q^{37} +(-13.3515 - 13.3515i) q^{38} +(-2.35783 - 1.10988i) q^{39} +(0.319655 + 8.63903i) q^{40} +2.72235i q^{41} +(-5.90273 - 16.4020i) q^{42} +(-1.63010 + 1.63010i) q^{43} -7.73807 q^{44} +(-6.69711 - 0.385640i) q^{45} +5.19688 q^{46} +(-2.99168 + 2.99168i) q^{47} +(1.12260 + 3.11940i) q^{48} +10.9928i q^{49} +(-8.98557 - 7.74571i) q^{50} +(9.01288 + 4.24255i) q^{51} +(-3.86136 - 3.86136i) q^{52} +(-0.906752 - 0.906752i) q^{53} +(-11.9425 + 3.06142i) q^{54} +(3.24406 - 3.49336i) q^{55} -16.3994i q^{56} +(12.9696 - 4.66746i) q^{57} +(9.55474 - 9.55474i) q^{58} +5.63531 q^{59} +(-12.9309 - 5.51238i) q^{60} -9.56665 q^{61} +(1.67772 - 1.67772i) q^{62} +(12.6686 + 1.20081i) q^{63} -11.3990i q^{64} +(3.36203 - 0.124399i) q^{65} +(3.73154 - 7.92728i) q^{66} +(-6.08897 - 6.08897i) q^{67} +(14.7601 + 14.7601i) q^{68} +(-1.61575 + 3.43249i) q^{69} +(16.4905 + 15.3137i) q^{70} -12.1228i q^{71} +(-11.5467 - 1.09446i) q^{72} +(-10.6352 + 10.6352i) q^{73} +14.7872 q^{74} +(7.90964 - 3.52669i) q^{75} +28.8837 q^{76} +(-6.39478 + 6.39478i) q^{77} +(5.81784 - 2.09371i) q^{78} +9.68971i q^{79} +(-3.13623 - 2.91243i) q^{80} +(1.69096 - 8.83972i) q^{81} +(-4.56732 - 4.56732i) q^{82} +(1.44379 + 1.44379i) q^{83} +(24.1263 + 11.3568i) q^{84} +(-12.8514 + 0.475519i) q^{85} -5.46970i q^{86} +(3.34018 + 9.28144i) q^{87} +(5.82845 - 5.82845i) q^{88} -6.55718 q^{89} +(11.8828 - 10.5889i) q^{90} -6.38209 q^{91} +(-5.62130 + 5.62130i) q^{92} +(0.586503 + 1.62973i) q^{93} -10.0384i q^{94} +(-12.1090 + 13.0396i) q^{95} +(5.00046 + 2.35382i) q^{96} +(3.25891 + 3.25891i) q^{97} +(-18.4428 - 18.4428i) q^{98} +(4.07574 + 4.92929i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{6}+O(q^{10}) \) 60 * q - 4 * q^6	\( 60 q - 4 q^{6} + 16 q^{10} - 12 q^{13} - 8 q^{15} - 60 q^{16} + 34 q^{18} - 4 q^{21} + 8 q^{22} + 8 q^{25} - 6 q^{27} - 80 q^{28} - 54 q^{30} - 60 q^{31} + 10 q^{33} + 28 q^{36} - 12 q^{37} + 60 q^{40} - 12 q^{42} - 24 q^{43} - 58 q^{45} + 8 q^{46} + 80 q^{48} + 32 q^{51} + 52 q^{52} + 64 q^{55} - 14 q^{57} - 48 q^{58} - 108 q^{60} - 56 q^{61} + 62 q^{63} + 40 q^{66} + 104 q^{67} + 108 q^{70} - 76 q^{72} - 108 q^{73} - 38 q^{75} - 120 q^{76} + 112 q^{78} + 60 q^{81} + 20 q^{82} + 48 q^{85} - 110 q^{87} - 28 q^{88} - 82 q^{90} - 32 q^{91} + 120 q^{96} + 56 q^{97}+O(q^{100}) \) 60 * q - 4 * q^6 + 16 * q^10 - 12 * q^13 - 8 * q^15 - 60 * q^16 + 34 * q^18 - 4 * q^21 + 8 * q^22 + 8 * q^25 - 6 * q^27 - 80 * q^28 - 54 * q^30 - 60 * q^31 + 10 * q^33 + 28 * q^36 - 12 * q^37 + 60 * q^40 - 12 * q^42 - 24 * q^43 - 58 * q^45 + 8 * q^46 + 80 * q^48 + 32 * q^51 + 52 * q^52 + 64 * q^55 - 14 * q^57 - 48 * q^58 - 108 * q^60 - 56 * q^61 + 62 * q^63 + 40 * q^66 + 104 * q^67 + 108 * q^70 - 76 * q^72 - 108 * q^73 - 38 * q^75 - 120 * q^76 + 112 * q^78 + 60 * q^81 + 20 * q^82 + 48 * q^85 - 110 * q^87 - 28 * q^88 - 82 * q^90 - 32 * q^91 + 120 * q^96 + 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more