LMFDB - Embedded newform 456.2.j.c.419.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [456,2,Mod(419,456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(456, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("456.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.j (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.3493441689358336.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} + 10 x^{10} - 11 x^{9} + 13 x^{8} - 28 x^{7} + 50 x^{6} - 56 x^{5} + 52 x^{4} + \cdots + 64 $ x^12 - 5x^11 + 10x^10 - 11x^9 + 13x^8 - 28x^7 + 50x^6 - 56x^5 + 52x^4 - 88x^3 + 160x^2 - 160*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.10
Root			$1.33270 - 0.473200i$ of defining polynomial
Character	$\chi$	$=$	456.419
Dual form			456.2.j.c.419.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.896270 + 1.09394i) q^{2} +(-0.393401 - 1.68678i) q^{3} +(-0.393401 + 1.96093i) q^{4} -1.35361 q^{5} +(1.49264 - 1.94217i) q^{6} +3.92185i q^{7} +(-2.49773 + 1.32716i) q^{8} +(-2.69047 + 1.32716i) q^{9} +O(q^{10})$	\(q+(0.896270 + 1.09394i) q^{2} +(-0.393401 - 1.68678i) q^{3} +(-0.393401 + 1.96093i) q^{4} -1.35361 q^{5} +(1.49264 - 1.94217i) q^{6} +3.92185i q^{7} +(-2.49773 + 1.32716i) q^{8} +(-2.69047 + 1.32716i) q^{9} +(-1.21320 - 1.48076i) q^{10} -1.18569i q^{11} +(3.46242 - 0.107849i) q^{12} +2.28324i q^{13} +(-4.29027 + 3.51504i) q^{14} +(0.532511 + 2.28324i) q^{15} +(-3.69047 - 1.54286i) q^{16} +4.09280i q^{17} +(-3.86322 - 1.75371i) q^{18} -1.00000 q^{19} +(0.532511 - 2.65433i) q^{20} +(6.61532 - 1.54286i) q^{21} +(1.29707 - 1.06270i) q^{22} +3.14615 q^{23} +(3.22124 + 3.69101i) q^{24} -3.16774 q^{25} +(-2.49773 + 2.04640i) q^{26} +(3.29707 + 4.01613i) q^{27} +(-7.69047 - 1.54286i) q^{28} +0.914677 q^{29} +(-2.02045 + 2.62894i) q^{30} +9.16662i q^{31} +(-1.61986 - 5.41997i) q^{32} +(-2.00000 + 0.466451i) q^{33} +(-4.47727 + 3.66826i) q^{34} -5.30865i q^{35} +(-1.54404 - 5.79793i) q^{36} +0.802479i q^{37} +(-0.896270 - 1.09394i) q^{38} +(3.85133 - 0.898230i) q^{39} +(3.38094 - 1.79646i) q^{40} -9.93719i q^{41} +(7.61690 + 5.85393i) q^{42} +5.57360 q^{43} +(2.32505 + 0.466451i) q^{44} +(3.64184 - 1.79646i) q^{45} +(2.81980 + 3.44169i) q^{46} +3.67866 q^{47} +(-1.15064 + 6.83199i) q^{48} -8.38094 q^{49} +(-2.83915 - 3.46532i) q^{50} +(6.90367 - 1.61011i) q^{51} +(-4.47727 - 0.898230i) q^{52} -5.37762 q^{53} +(-1.43834 + 7.20633i) q^{54} +1.60496i q^{55} +(-5.20494 - 9.79572i) q^{56} +(0.393401 + 1.68678i) q^{57} +(0.819797 + 1.00060i) q^{58} +1.72142i q^{59} +(-4.68676 + 0.145985i) q^{60} -8.36415i q^{61} +(-10.0277 + 8.21577i) q^{62} +(-5.20494 - 10.5516i) q^{63} +(4.47727 - 6.62978i) q^{64} -3.09062i q^{65} +(-2.30281 - 1.76981i) q^{66} +12.9545 q^{67} +(-8.02569 - 1.61011i) q^{68} +(-1.23770 - 5.30687i) q^{69} +(5.80734 - 4.75799i) q^{70} +8.04802 q^{71} +(4.95870 - 6.88559i) q^{72} -8.23374 q^{73} +(-0.877863 + 0.719238i) q^{74} +(1.24619 + 5.34330i) q^{75} +(0.393401 - 1.96093i) q^{76} +4.65010 q^{77} +(4.43444 + 3.40807i) q^{78} -4.39540i q^{79} +(4.99545 + 2.08843i) q^{80} +(5.47727 - 7.14139i) q^{81} +(10.8707 - 8.90641i) q^{82} -12.3086i q^{83} +(0.422967 + 13.5791i) q^{84} -5.54005i q^{85} +(4.99545 + 6.09718i) q^{86} +(-0.359835 - 1.54286i) q^{87} +(1.57360 + 2.96153i) q^{88} -1.90493i q^{89} +(5.22929 + 2.37384i) q^{90} -8.95455 q^{91} +(-1.23770 + 6.16937i) q^{92} +(15.4621 - 3.60616i) q^{93} +(3.29707 + 4.02422i) q^{94} +1.35361 q^{95} +(-8.50505 + 4.86458i) q^{96} +6.00000 q^{97} +(-7.51159 - 9.16823i) q^{98} +(1.57360 + 3.19006i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} - 2 q^{4} + 3 q^{6} + 6 q^{9}+O(q^{10}) $ 12 * q - 2 * q^3 - 2 * q^4 + 3 * q^6 + 6 * q^9	$ 12 q - 2 q^{3} - 2 q^{4} + 3 q^{6} + 6 q^{9} - 20 q^{10} + 21 q^{12} - 6 q^{16} - q^{18} - 12 q^{19} - 20 q^{22} + 5 q^{24} + 44 q^{25} + 4 q^{27} - 54 q^{28} - 38 q^{30} - 24 q^{33} - 10 q^{34} - q^{36} - 36 q^{40} + 11 q^{42} + 56 q^{43} + 42 q^{46} + q^{48} - 24 q^{49} + 50 q^{51} - 10 q^{52} - 50 q^{54} + 2 q^{57} + 18 q^{58} - 10 q^{60} + 10 q^{64} + 24 q^{66} + 68 q^{67} + 4 q^{70} - 43 q^{72} - 44 q^{73} + 34 q^{75} + 2 q^{76} + 25 q^{78} + 22 q^{81} + 84 q^{82} + 9 q^{84} + 8 q^{88} - 10 q^{90} - 20 q^{91} + 4 q^{94} - 55 q^{96} + 72 q^{97} + 8 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 - 2 * q^4 + 3 * q^6 + 6 * q^9 - 20 * q^10 + 21 * q^12 - 6 * q^16 - q^18 - 12 * q^19 - 20 * q^22 + 5 * q^24 + 44 * q^25 + 4 * q^27 - 54 * q^28 - 38 * q^30 - 24 * q^33 - 10 * q^34 - q^36 - 36 * q^40 + 11 * q^42 + 56 * q^43 + 42 * q^46 + q^48 - 24 * q^49 + 50 * q^51 - 10 * q^52 - 50 * q^54 + 2 * q^57 + 18 * q^58 - 10 * q^60 + 10 * q^64 + 24 * q^66 + 68 * q^67 + 4 * q^70 - 43 * q^72 - 44 * q^73 + 34 * q^75 + 2 * q^76 + 25 * q^78 + 22 * q^81 + 84 * q^82 + 9 * q^84 + 8 * q^88 - 10 * q^90 - 20 * q^91 + 4 * q^94 - 55 * q^96 + 72 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.896270	+	1.09394i	0.633758	+	0.773531i
$2$	0.896270	+	1.09394i	0.633758	+	0.773531i
$3$	−0.393401	−	1.68678i	−0.227130	−	0.973864i
$3$	−0.393401	−	1.68678i	−0.227130	−	0.973864i
$4$	−0.393401	+	1.96093i	−0.196700	+	0.980464i
$5$	−1.35361			−0.605352			−0.302676	−	0.953094i	$-0.597880\pi$
$5$	−1.35361			−0.605352			−0.302676	+	0.953094i	$0.597880\pi$
$6$	1.49264	−	1.94217i	0.609369	−	0.792887i
$7$			3.92185i			1.48232i	0.671327	+	0.741161i	$0.265724\pi$
$7$			3.92185i			1.48232i	−0.671327	+	0.741161i	$0.734276\pi$
$8$	−2.49773	+	1.32716i	−0.883080	+	0.469223i
$9$	−2.69047	+	1.32716i	−0.896824	+	0.442388i
$10$	−1.21320	−	1.48076i	−0.383647	−	0.468259i
$11$		−	1.18569i		−	0.357499i	−0.983895	−	0.178749i	$-0.942795\pi$
$11$		−	1.18569i		−	0.357499i	0.983895	−	0.178749i	$-0.0572051\pi$
$12$	3.46242	−	0.107849i	0.999515	−	0.0311332i
$13$			2.28324i			0.633258i	0.948550	+	0.316629i	$0.102551\pi$
$13$			2.28324i			0.633258i	−0.948550	+	0.316629i	$0.897449\pi$
$14$	−4.29027	+	3.51504i	−1.14662	+	0.939434i
$15$	0.532511	+	2.28324i	0.137494	+	0.589531i
$16$	−3.69047	−	1.54286i	−0.922618	−	0.385715i
$17$			4.09280i			0.992651i	0.868137	+	0.496325i	$0.165318\pi$
$17$			4.09280i			0.992651i	−0.868137	+	0.496325i	$0.834682\pi$
$18$	−3.86322	−	1.75371i	−0.910570	−	0.413354i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	0.532511	−	2.65433i	0.119073	−	0.593526i
$21$	6.61532	−	1.54286i	1.44358	−	0.336680i
$22$	1.29707	−	1.06270i	0.276536	−	0.226568i
$23$	3.14615			0.656017			0.328009	−	0.944675i	$-0.393623\pi$
$23$	3.14615			0.656017			0.328009	+	0.944675i	$0.393623\pi$
$24$	3.22124	+	3.69101i	0.657534	+	0.753425i
$25$	−3.16774			−0.633549
$26$	−2.49773	+	2.04640i	−0.489844	+	0.401332i
$27$	3.29707	+	4.01613i	0.634522	+	0.772905i
$28$	−7.69047	−	1.54286i	−1.45336	−	0.291573i
$29$	0.914677			0.169851			0.0849256	−	0.996387i	$-0.472935\pi$
$29$	0.914677			0.169851			0.0849256	+	0.996387i	$0.472935\pi$
$30$	−2.02045	+	2.62894i	−0.368883	+	0.479976i
$31$			9.16662i			1.64637i	0.567770	+	0.823187i	$0.307806\pi$
$31$			9.16662i			1.64637i	−0.567770	+	0.823187i	$0.692194\pi$
$32$	−1.61986	−	5.41997i	−0.286354	−	0.958124i
$33$	−2.00000	+	0.466451i	−0.348155	+	0.0811987i
$34$	−4.47727	+	3.66826i	−0.767846	+	0.629101i
$35$		−	5.30865i		−	0.897326i
$36$	−1.54404	−	5.79793i	−0.257340	−	0.966321i
$37$			0.802479i			0.131927i	0.997822	+	0.0659634i	$0.0210121\pi$
$37$			0.802479i			0.131927i	−0.997822	+	0.0659634i	$0.978988\pi$
$38$	−0.896270	−	1.09394i	−0.145394	−	0.177460i
$39$	3.85133	−	0.898230i	0.616707	−	0.143832i
$40$	3.38094	−	1.79646i	0.534574	−	0.284045i
$41$		−	9.93719i		−	1.55193i	−0.630777	−	0.775964i	$-0.717264\pi$
$41$		−	9.93719i		−	1.55193i	0.630777	−	0.775964i	$-0.282736\pi$
$42$	7.61690	+	5.85393i	1.17531	+	0.903280i
$43$	5.57360			0.849967			0.424983	−	0.905201i	$-0.360280\pi$
$43$	5.57360			0.849967			0.424983	+	0.905201i	$0.360280\pi$
$44$	2.32505	+	0.466451i	0.350515	+	0.0703202i
$45$	3.64184	−	1.79646i	0.542894	−	0.267800i
$46$	2.81980	+	3.44169i	0.415756	+	0.507450i
$47$	3.67866			0.536587			0.268294	−	0.963337i	$-0.413540\pi$
$47$	3.67866			0.536587			0.268294	+	0.963337i	$0.413540\pi$
$48$	−1.15064	+	6.83199i	−0.166080	+	0.986112i
$49$	−8.38094			−1.19728
$50$	−2.83915	−	3.46532i	−0.401517	−	0.490070i
$51$	6.90367	−	1.61011i	0.966707	−	0.225461i
$52$	−4.47727	−	0.898230i	−0.620886	−	0.124562i
$53$	−5.37762			−0.738673			−0.369336	−	0.929296i	$-0.620415\pi$
$53$	−5.37762			−0.738673			−0.369336	+	0.929296i	$0.620415\pi$
$54$	−1.43834	+	7.20633i	−0.195733	+	0.980657i
$55$			1.60496i			0.216413i
$56$	−5.20494	−	9.79572i	−0.695540	−	1.30901i
$57$	0.393401	+	1.68678i	0.0521072	+	0.223420i
$58$	0.819797	+	1.00060i	0.107645	+	0.131385i
$59$			1.72142i			0.224110i	0.993702	+	0.112055i	$0.0357434\pi$
$59$			1.72142i			0.224110i	−0.993702	+	0.112055i	$0.964257\pi$
$60$	−4.68676	+	0.145985i	−0.605059	+	0.0188466i
$61$		−	8.36415i		−	1.07092i	−0.844561	−	0.535460i	$-0.820138\pi$
$61$		−	8.36415i		−	1.07092i	0.844561	−	0.535460i	$-0.179862\pi$
$62$	−10.0277	+	8.21577i	−1.27352	+	1.04340i
$63$	−5.20494	−	10.5516i	−0.655761	−	1.32938i
$64$	4.47727	−	6.62978i	0.559659	−	0.828723i
$65$		−	3.09062i		−	0.383344i
$66$	−2.30281	−	1.76981i	−0.283456	−	0.217849i
$67$	12.9545			1.58265			0.791325	−	0.611396i	$-0.209392\pi$
$67$	12.9545			1.58265			0.791325	+	0.611396i	$0.209392\pi$
$68$	−8.02569	−	1.61011i	−0.973258	−	0.195255i
$69$	−1.23770	−	5.30687i	−0.149001	−	0.638872i
$70$	5.80734	−	4.75799i	0.694110	−	0.568688i
$71$	8.04802			0.955124			0.477562	−	0.878598i	$-0.341521\pi$
$71$	8.04802			0.955124			0.477562	+	0.878598i	$0.341521\pi$
$72$	4.95870	−	6.88559i	0.584388	−	0.811474i
$73$	−8.23374			−0.963686			−0.481843	−	0.876258i	$-0.660032\pi$
$73$	−8.23374			−0.963686			−0.481843	+	0.876258i	$0.660032\pi$
$74$	−0.877863	+	0.719238i	−0.102049	+	0.0836097i
$75$	1.24619	+	5.34330i	0.143898	+	0.616991i
$76$	0.393401	−	1.96093i	0.0451262	−	0.224934i
$77$	4.65010			0.529928
$78$	4.43444	+	3.40807i	0.502102	+	0.385887i
$79$		−	4.39540i		−	0.494521i	−0.968949	−	0.247260i	$-0.920470\pi$
$79$		−	4.39540i		−	0.494521i	0.968949	−	0.247260i	$-0.0795303\pi$
$80$	4.99545	+	2.08843i	0.558509	+	0.233494i
$81$	5.47727	−	7.14139i	0.608586	−	0.793488i
$82$	10.8707	−	8.90641i	1.20047	−	0.983548i
$83$		−	12.3086i		−	1.35104i	−0.737341	−	0.675521i	$-0.763919\pi$
$83$		−	12.3086i		−	1.35104i	0.737341	−	0.675521i	$-0.236081\pi$
$84$	0.422967	+	13.5791i	0.0461495	+	1.48160i
$85$		−	5.54005i		−	0.600903i
$86$	4.99545	+	6.09718i	0.538674	+	0.657476i
$87$	−0.359835	−	1.54286i	−0.0385783	−	0.165412i
$88$	1.57360	+	2.96153i	0.167747	+	0.315700i
$89$		−	1.90493i		−	0.201922i	−0.994890	−	0.100961i	$-0.967808\pi$
$89$		−	1.90493i		−	0.201922i	0.994890	−	0.100961i	$-0.0321917\pi$
$90$	5.22929	+	2.37384i	0.551216	+	0.250225i
$91$	−8.95455			−0.938692
$92$	−1.23770	+	6.16937i	−0.129039	+	0.643201i
$93$	15.4621	−	3.60616i	1.60335	−	0.373941i
$94$	3.29707	+	4.02422i	0.340067	+	0.415067i
$95$	1.35361			0.138877
$96$	−8.50505	+	4.86458i	−0.868043	+	0.496489i
$97$	6.00000			0.609208			0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000			0.609208			0.304604	+	0.952479i	$0.401476\pi$
$98$	−7.51159	−	9.16823i	−0.758785	−	0.926131i
$99$	1.57360	+	3.19006i	0.158153	+	0.320613i
$100$	1.24619	−	6.21172i	0.124619	−	0.621172i
$101$	−12.2960			−1.22350			−0.611749	−	0.791052i	$-0.709534\pi$
$101$	−12.2960			−1.22350			−0.611749	+	0.791052i	$0.709534\pi$
$102$	7.94891	+	6.10909i	0.787060	+	0.604890i
$103$			11.6077i			1.14374i	0.820343	+	0.571871i	$0.193782\pi$
$103$			11.6077i			1.14374i	−0.820343	+	0.571871i	$0.806218\pi$
$104$	−3.03024	−	5.70292i	−0.297139	−	0.559217i
$105$	−8.95455	+	2.08843i	−0.873874	+	0.203810i
$106$	−4.81980	−	5.88278i	−0.468140	−	0.571386i
$107$			19.9584i			1.92946i	0.263250	+	0.964728i	$0.415206\pi$
$107$			19.9584i			1.92946i	−0.263250	+	0.964728i	$0.584794\pi$
$108$	−9.17242	+	4.88537i	−0.882616	+	0.470094i
$109$			13.4042i			1.28389i	0.766752	+	0.641944i	$0.221872\pi$
$109$			13.4042i			1.28389i	−0.766752	+	0.641944i	$0.778128\pi$
$110$	−1.75573	+	1.43848i	−0.167402	+	0.137153i
$111$	1.35361	−	0.315696i	0.128479	−	0.0299645i
$112$	6.05088	−	14.4735i	0.571754	−	1.36762i
$113$			7.93282i			0.746257i	0.927780	+	0.373128i	$0.121715\pi$
$113$			7.93282i			0.746257i	−0.927780	+	0.373128i	$0.878285\pi$
$114$	−1.49264	+	1.94217i	−0.139799	+	0.181901i
$115$	−4.25865			−0.397121
$116$	−0.359835	+	1.79361i	−0.0334098	+	0.166533i
$117$	−3.03024	−	6.14300i	−0.280146	−	0.567921i
$118$	−1.88313	+	1.54286i	−0.173356	+	0.142032i
$119$	−16.0514			−1.47143
$120$	−4.36030	−	4.99619i	−0.398039	−	0.456087i
$121$	9.59414			0.872195
$122$	9.14986	−	7.49653i	0.828389	−	0.678704i
$123$	−16.7619	+	3.90930i	−1.51137	+	0.352490i
$124$	−17.9751	−	3.60616i	−1.61421	−	0.323843i
$125$	11.0559			0.988872
$126$	6.87780	−	15.1510i	0.612724	−	1.34976i
$127$		−	1.00722i		−	0.0893763i	−0.999001	−	0.0446881i	$-0.985771\pi$
$127$		−	1.00722i		−	0.0893763i	0.999001	−	0.0446881i	$-0.0142294\pi$
$128$	11.2654	−	1.04421i	0.995732	−	0.0922964i
$129$	−2.19266	−	9.40146i	−0.193053	−	0.827752i
$130$	3.38094	−	2.77003i	0.296528	−	0.242947i
$131$			8.86572i			0.774602i	0.921953	+	0.387301i	$0.126593\pi$
$131$			8.86572i			0.774602i	−0.921953	+	0.387301i	$0.873407\pi$
$132$	−0.127875	−	4.10536i	−0.0111301	−	0.357325i
$133$		−	3.92185i		−	0.340068i
$134$	11.6108	+	14.1715i	1.00302	+	1.22423i
$135$	−4.46294	−	5.43627i	−0.384109	−	0.467880i
$136$	−5.43182	−	10.2227i	−0.465775	−	0.876590i
$137$			15.2157i			1.29996i	0.759950	+	0.649982i	$0.225224\pi$
$137$			15.2157i			1.29996i	−0.759950	+	0.649982i	$0.774776\pi$
$138$	4.69607	−	6.11035i	0.399756	−	0.520147i
$139$	12.9296			1.09668			0.548338	−	0.836256i	$-0.315261\pi$
$139$	12.9296			1.09668			0.548338	+	0.836256i	$0.315261\pi$
$140$	10.4099	+	2.08843i	0.879796	+	0.176505i
$141$	−1.44719	−	6.20510i	−0.121875	−	0.522563i
$142$	7.21320	+	8.80404i	0.605318	+	0.738818i
$143$	2.70722			0.226389
$144$	11.9767	−	0.746836i	0.998061	−	0.0622363i
$145$	−1.23811			−0.102820
$146$	−7.37965	−	9.00720i	−0.610744	−	0.745441i
$147$	3.29707	+	14.1368i	0.271938	+	1.16599i
$148$	−1.57360	−	0.315696i	−0.129349	−	0.0259501i
$149$	−6.69441			−0.548428			−0.274214	−	0.961669i	$-0.588418\pi$
$149$	−6.69441			−0.548428			−0.274214	+	0.961669i	$0.588418\pi$
$150$	−4.72831	+	6.15229i	−0.386065	+	0.502333i
$151$			21.7816i			1.77256i	0.463152	+	0.886279i	$0.346719\pi$
$151$			21.7816i			1.77256i	−0.463152	+	0.886279i	$0.653281\pi$
$152$	2.49773	−	1.32716i	0.202592	−	0.107647i
$153$	−5.43182	−	11.0116i	−0.439137	−	0.890233i
$154$	4.16774	+	5.08692i	0.335846	+	0.409916i
$155$		−	12.4080i		−	0.996636i
$156$	0.246245	+	7.90555i	0.0197154	+	0.632951i
$157$		−	19.1021i		−	1.52451i	−0.647276	−	0.762256i	$-0.724092\pi$
$157$		−	19.1021i		−	1.52451i	0.647276	−	0.762256i	$-0.275908\pi$
$158$	4.80829	−	3.93946i	0.382527	−	0.313407i
$159$	2.11556	+	9.07087i	0.167775	+	0.719367i
$160$	2.19266	+	7.33651i	0.173345	+	0.580002i
$161$			12.3387i			0.972428i
$162$	12.7214	−	0.408816i	0.999484	−	0.0321196i
$163$	3.40586			0.266767			0.133384	−	0.991064i	$-0.457416\pi$
$163$	3.40586			0.266767			0.133384	+	0.991064i	$0.457416\pi$
$164$	19.4861	+	3.90930i	1.52161	+	0.305265i
$165$	2.70722	−	0.631392i	0.210757	−	0.0491538i
$166$	13.4648	−	11.0318i	1.04507	−	0.856234i
$167$	−11.8203			−0.914679			−0.457340	−	0.889292i	$-0.651198\pi$
$167$	−11.8203			−0.914679			−0.457340	+	0.889292i	$0.651198\pi$
$168$	−14.4756	+	12.6333i	−1.11682	+	0.974677i
$169$	7.78680			0.598985
$170$	6.06047	−	4.96538i	0.464817	−	0.380827i
$171$	2.69047	−	1.32716i	0.205745	−	0.101491i
$172$	−2.19266	+	10.9294i	−0.167189	+	0.833361i
$173$	4.84511			0.368367			0.184183	−	0.982892i	$-0.441036\pi$
$173$	4.84511			0.368367			0.184183	+	0.982892i	$0.441036\pi$
$174$	1.36529	−	1.77646i	0.103502	−	0.134673i
$175$		−	12.4234i		−	0.939123i
$176$	−1.82935	+	4.37575i	−0.137893	+	0.329835i
$177$	2.90367	−	0.677210i	0.218253	−	0.0509022i
$178$	2.08387	−	1.70733i	0.156193	−	0.127970i
$179$		−	16.5849i		−	1.23961i	−0.784755	−	0.619806i	$-0.787211\pi$
$179$		−	16.5849i		−	1.23961i	0.784755	−	0.619806i	$-0.212789\pi$
$180$	2.09002	+	7.84812i	0.155781	+	0.584964i
$181$			18.5043i			1.37542i	0.725987	+	0.687708i	$0.241383\pi$
$181$			18.5043i			1.37542i	−0.725987	+	0.687708i	$0.758617\pi$
$182$	−8.02569	−	9.79572i	−0.594904	−	0.726107i
$183$	−14.1085	+	3.29046i	−1.04293	+	0.243238i
$184$	−7.85822	+	4.17545i	−0.579315	+	0.307818i
$185$		−	1.08624i		−	0.0798621i
$186$	17.8031	+	13.6825i	1.30539	+	1.00325i
$187$	4.85279			0.354871
$188$	−1.44719	+	7.21358i	−0.105547	+	0.526105i
$189$	−15.7507	+	12.9306i	−1.14569	+	0.940565i
$190$	1.21320	+	1.48076i	0.0880146	+	0.107426i
$191$	−23.1280			−1.67348			−0.836740	−	0.547600i	$-0.815542\pi$
$191$	−23.1280			−1.67348			−0.836740	+	0.547600i	$0.815542\pi$
$192$	−12.9444	−	4.94402i	−0.934179	−	0.356804i
$193$	25.0974			1.80655			0.903274	−	0.429064i	$-0.141156\pi$
$193$	25.0974			1.80655			0.903274	+	0.429064i	$0.141156\pi$
$194$	5.37762	+	6.56363i	0.386091	+	0.471241i
$195$	−5.21320	+	1.21585i	−0.373325	+	0.0870689i
$196$	3.29707	−	16.4344i	0.235505	−	1.17389i
$197$	−5.12585			−0.365201			−0.182601	−	0.983187i	$-0.558452\pi$
$197$	−5.12585			−0.365201			−0.182601	+	0.983187i	$0.558452\pi$
$198$	−2.07936	+	4.58058i	−0.147774	+	0.325528i
$199$			4.23755i			0.300392i	0.988656	+	0.150196i	$0.0479905\pi$
$199$			4.23755i			0.300392i	−0.988656	+	0.150196i	$0.952010\pi$
$200$	7.91216	−	4.20412i	0.559474	−	0.297276i
$201$	−5.09633	−	21.8515i	−0.359467	−	1.54129i
$202$	−11.0205	−	13.4511i	−0.775402	−	0.946414i
$203$			3.58723i			0.251774i
$204$	0.441404	+	14.1710i	0.0309044	+	0.992169i
$205$			13.4511i			0.939463i
$206$	−12.6981	+	10.4036i	−0.884720	+	0.724856i
$207$	−8.46462	+	4.17545i	−0.588332	+	0.290214i
$208$	3.52273	−	8.42624i	0.244257	−	0.584255i
$209$			1.18569i			0.0820158i
$210$	−10.3103	−	7.92392i	−0.711478	−	0.546803i
$211$	10.5282			0.724788			0.362394	−	0.932025i	$-0.381960\pi$
$211$	10.5282			0.724788			0.362394	+	0.932025i	$0.381960\pi$
$212$	2.11556	−	10.5451i	0.145297	−	0.724242i
$213$	−3.16610	−	13.5753i	−0.216938	−	0.930162i
$214$	−21.8333	+	17.8881i	−1.49249	+	1.22281i
$215$	−7.54448			−0.514529
$216$	−13.5652	−	5.65545i	−0.922998	−	0.384805i
$217$	−35.9502			−2.44046
$218$	−14.6633	+	12.0138i	−0.993127	+	0.813674i
$219$	3.23916	+	13.8885i	0.218882	+	0.938499i
$220$	−3.14721	−	0.631392i	−0.212185	−	0.0425685i
$221$	−9.34486			−0.628604
$222$	1.55855	+	1.19781i	0.104603	+	0.0803921i
$223$		−	24.0179i		−	1.60836i	−0.594387	−	0.804179i	$-0.702605\pi$
$223$		−	24.0179i		−	1.60836i	0.594387	−	0.804179i	$-0.297395\pi$
$224$	21.2563	−	6.35287i	1.42025	−	0.424469i
$225$	8.52273	−	4.20412i	0.568182	−	0.280274i
$226$	−8.67801	+	7.10995i	−0.577253	+	0.472947i
$227$		−	26.5522i		−	1.76233i	−0.472806	−	0.881167i	$-0.656759\pi$
$227$		−	26.5522i		−	1.76233i	0.472806	−	0.881167i	$-0.343241\pi$
$228$	−3.46242	+	0.107849i	−0.229305	+	0.00714246i
$229$			25.5456i			1.68810i	0.536266	+	0.844049i	$0.319835\pi$
$229$			25.5456i			1.68810i	−0.536266	+	0.844049i	$0.680165\pi$
$230$	−3.81690	−	4.65870i	−0.251679	−	0.307186i
$231$	−1.82935	−	7.84371i	−0.120363	−	0.516078i
$232$	−2.28461	+	1.21393i	−0.149992	+	0.0796981i
$233$		−	12.9887i		−	0.850917i	−0.904978	−	0.425459i	$-0.860113\pi$
$233$		−	12.9887i		−	0.850917i	0.904978	−	0.425459i	$-0.139887\pi$
$234$	4.00415	−	8.82068i	0.261760	−	0.576626i
$235$	−4.97946			−0.324824
$236$	−3.37559	−	0.677210i	−0.219732	−	0.0440826i
$237$	−7.41408	+	1.72915i	−0.481596	+	0.112321i
$238$	−14.3864	−	17.5592i	−0.932530	−	1.13819i
$239$	16.1450			1.04433			0.522165	−	0.852844i	$-0.325124\pi$
$239$	16.1450			1.04433			0.522165	+	0.852844i	$0.325124\pi$
$240$	1.55751	−	9.24783i	0.100537	−	0.596945i
$241$	−15.9091			−1.02479			−0.512397	−	0.858748i	$-0.671243\pi$
$241$	−15.9091			−1.02479			−0.512397	+	0.858748i	$0.671243\pi$
$242$	8.59894	+	10.4954i	0.552761	+	0.674670i
$243$	−14.2007	−	6.42954i	−0.910978	−	0.412455i
$244$	16.4015	+	3.29046i	1.05000	+	0.210650i
$245$	11.3445			0.724774
$246$	−19.2997	−	14.8327i	−1.23050	−	0.945697i
$247$		−	2.28324i		−	0.145279i
$248$	−12.1656	−	22.8957i	−0.772517	−	1.45388i
$249$	−20.7619	+	4.84220i	−1.31573	+	0.306862i
$250$	9.90909	+	12.0945i	0.626706	+	0.764923i
$251$		−	2.25716i		−	0.142471i	−0.997460	−	0.0712354i	$-0.977306\pi$
$251$		−	2.25716i		−	0.142471i	0.997460	−	0.0712354i	$-0.0226941\pi$
$252$	22.7386	−	6.05549i	1.43240	−	0.381460i
$253$		−	3.73035i		−	0.234525i
$254$	1.10184	−	0.902740i	0.0691353	−	0.0566430i
$255$	−9.34486	+	2.17946i	−0.585198	+	0.136483i
$256$	11.2392	+	11.3878i	0.702447	+	0.711736i
$257$			16.3321i			1.01877i	0.860539	+	0.509384i	$0.170127\pi$
$257$			16.3321i			1.01877i	−0.860539	+	0.509384i	$0.829873\pi$
$258$	8.31940	−	10.8249i	0.517943	−	0.673927i
$259$	−3.14721			−0.195558
$260$	6.06047	+	1.21585i	0.375855	+	0.0754039i
$261$	−2.46091	+	1.21393i	−0.152327	+	0.0751401i
$262$	−9.69855	+	7.94608i	−0.599178	+	0.490910i
$263$	31.0178			1.91264			0.956319	−	0.292324i	$-0.0944286\pi$
$263$	31.0178			1.91264			0.956319	+	0.292324i	$0.0944286\pi$
$264$	4.37640	−	3.81939i	0.269349	−	0.235067i
$265$	7.27919			0.447157
$266$	4.29027	−	3.51504i	0.263053	−	0.215521i
$267$	−3.21320	+	0.749400i	−0.196645	+	0.0458625i
$268$	−5.09633	+	25.4029i	−0.311308	+	1.55173i
$269$	−26.9570			−1.64359			−0.821797	−	0.569780i	$-0.807029\pi$
$269$	−26.9570			−1.64359			−0.821797	+	0.569780i	$0.807029\pi$
$270$	1.94694	−	9.75455i	0.118487	−	0.593643i
$271$			1.93389i			0.117476i	0.998273	+	0.0587378i	$0.0187076\pi$
$271$			1.93389i			0.117476i	−0.998273	+	0.0587378i	$0.981292\pi$
$272$	6.31463	−	15.1044i	0.382881	−	0.915837i
$273$	3.52273	+	15.1044i	0.213205	+	0.914158i
$274$	−16.6450	+	13.6374i	−1.00556	+	0.823863i
$275$			3.75596i			0.226493i
$276$	10.8933	−	0.339308i	0.655699	−	0.0204239i
$277$		−	16.4126i		−	0.986137i	−0.869990	−	0.493069i	$-0.835875\pi$
$277$		−	16.4126i		−	0.986137i	0.869990	−	0.493069i	$-0.164125\pi$
$278$	11.5884	+	14.1442i	0.695028	+	0.848314i
$279$	−12.1656	−	24.6625i	−0.728336	−	1.47651i
$280$	7.04545	+	13.2596i	0.421046	+	0.792411i
$281$			16.3173i			0.973410i	0.873566	+	0.486705i	$0.161801\pi$
$281$			16.3173i			0.973410i	−0.873566	+	0.486705i	$0.838199\pi$
$282$	5.49092	−	7.14457i	0.326980	−	0.425453i
$283$	−27.6915			−1.64609			−0.823045	−	0.567976i	$-0.807727\pi$
$283$	−27.6915			−1.64609			−0.823045	+	0.567976i	$0.807727\pi$
$284$	−3.16610	+	15.7816i	−0.187873	+	0.936465i
$285$	−0.532511	−	2.28324i	−0.0315432	−	0.135248i
$286$	2.42640	+	2.96153i	0.143476	+	0.175119i
$287$	38.9722			2.30046
$288$	11.5514	+	12.4324i	0.680672	+	0.732589i
$289$	0.248961			0.0146448
$290$	−1.10968	−	1.35442i	−0.0651629	−	0.0795343i
$291$	−2.36041	−	10.1207i	−0.138369	−	0.593286i
$292$	3.23916	−	16.1458i	0.189557	−	0.944859i
$293$	−19.8315			−1.15857			−0.579283	−	0.815126i	$-0.696667\pi$
$293$	−19.8315			−1.15857			−0.579283	+	0.815126i	$0.696667\pi$
$294$	−12.5098	+	16.2772i	−0.729583	+	0.949306i
$295$		−	2.33013i		−	0.135666i
$296$	−1.06502	−	2.00437i	−0.0619031	−	0.116502i
$297$	4.76189	−	3.90930i	0.276313	−	0.226841i
$298$	−6.00000	−	7.32327i	−0.347571	−	0.424226i
$299$			7.18342i			0.415428i
$300$	−10.9681	+	0.341637i	−0.633242	+	0.0197244i
$301$			21.8589i			1.25992i
$302$	−23.8277	+	19.5222i	−1.37113	+	1.12337i
$303$	4.83726	+	20.7407i	0.277893	+	1.19152i
$304$	3.69047	+	1.54286i	0.211663	+	0.0884892i
$305$			11.3218i			0.648283i
$306$	7.17760	−	15.8114i	0.410316	−	0.903878i
$307$	5.40586			0.308529			0.154264	−	0.988030i	$-0.450699\pi$
$307$	5.40586			0.308529			0.154264	+	0.988030i	$0.450699\pi$
$308$	−1.82935	+	9.11851i	−0.104237	+	0.519575i
$309$	19.5797	−	4.56649i	1.11385	−	0.259778i
$310$	13.5736	−	11.1209i	0.770929	−	0.631627i
$311$	−9.55197			−0.541643			−0.270821	−	0.962630i	$-0.587295\pi$
$311$	−9.55197			−0.541643			−0.270821	+	0.962630i	$0.587295\pi$
$312$	−8.42748	+	7.35488i	−0.477112	+	0.416388i
$313$	10.5282			0.595086			0.297543	−	0.954708i	$-0.403833\pi$
$313$	10.5282			0.595086			0.297543	+	0.954708i	$0.403833\pi$
$314$	20.8965	−	17.1206i	1.17926	−	0.966172i
$315$	7.04545	+	14.2828i	0.396966	+	0.804744i
$316$	8.61906	+	1.72915i	0.484860	+	0.0972725i
$317$	−0.841048			−0.0472380			−0.0236190	−	0.999721i	$-0.507519\pi$
$317$	−0.841048			−0.0472380			−0.0236190	+	0.999721i	$0.507519\pi$
$318$	−8.02686	+	10.4442i	−0.450124	+	0.585684i
$319$		−	1.08452i		−	0.0607216i
$320$	−6.06047	+	8.97413i	−0.338791	+	0.501669i
$321$	33.6656	−	7.85167i	1.87903	−	0.438237i
$322$	−13.4978	+	11.0588i	−0.752204	+	0.616285i
$323$		−	4.09280i		−	0.227730i
$324$	11.8490	+	13.5500i	0.658277	+	0.752776i
$325$		−	7.23273i		−	0.401200i
$326$	3.05257	+	3.72580i	0.169066	+	0.206353i
$327$	22.6099	−	5.27321i	1.25033	−	0.291609i
$328$	13.1883	+	24.8204i	0.728201	+	1.37048i
$329$			14.4272i			0.795395i
$330$	3.11710	+	2.39563i	0.171591	+	0.131875i
$331$	−11.9340			−0.655952			−0.327976	−	0.944686i	$-0.606367\pi$
$331$	−11.9340			−0.655952			−0.327976	+	0.944686i	$0.606367\pi$
$332$	24.1362	+	4.84220i	1.32465	+	0.265750i
$333$	−1.06502	−	2.15905i	−0.0583628	−	0.118315i
$334$	−10.5941	−	12.9306i	−0.579686	−	0.707533i
$335$	−17.5354			−0.958060
$336$	−26.7941	−	4.51263i	−1.46174	−	0.246184i
$337$	5.48270			0.298662			0.149331	−	0.988787i	$-0.452288\pi$
$337$	5.48270			0.298662			0.149331	+	0.988787i	$0.452288\pi$
$338$	6.97908	+	8.51828i	0.379612	+	0.463333i
$339$	13.3809	−	3.12078i	0.726753	−	0.169497i
$340$	10.8636	+	2.17946i	0.589164	+	0.118198i
$341$	10.8688			0.588577
$342$	3.86322	+	1.75371i	0.208899	+	0.0948299i
$343$		−	5.41586i		−	0.292429i
$344$	−13.9213	+	7.39708i	−0.750588	+	0.398824i
$345$	1.67536	+	7.18342i	0.0901982	+	0.386742i
$346$	4.34252	+	5.30025i	0.233456	+	0.284943i
$347$			6.99992i			0.375775i	0.982191	+	0.187888i	$0.0601641\pi$
$347$			6.99992i			0.375775i	−0.982191	+	0.187888i	$0.939836\pi$
$348$	3.16700	−	0.0986467i	0.169769	−	0.00528802i
$349$		−	4.56649i		−	0.244438i	−0.992503	−	0.122219i	$-0.960999\pi$
$349$		−	4.56649i		−	0.244438i	0.992503	−	0.122219i	$-0.0390011\pi$
$350$	13.5905	−	11.1347i	0.726441	−	0.595177i
$351$	−9.16981	+	7.52801i	−0.489448	+	0.401816i
$352$	−6.42640	+	1.92065i	−0.342528	+	0.102371i
$353$		−	3.52691i		−	0.187718i	−0.995585	−	0.0938591i	$-0.970080\pi$
$353$		−	3.52691i		−	0.187718i	0.995585	−	0.0938591i	$-0.0299203\pi$
$354$	3.34330	+	2.56947i	0.177694	+	0.136566i
$355$	−10.8939			−0.578186
$356$	3.73542	+	0.749400i	0.197977	+	0.0397181i
$357$	6.31463	+	27.0752i	0.334206	+	1.43297i
$358$	18.1428	−	14.8645i	0.958878	−	0.785615i
$359$	37.6554			1.98738			0.993689	−	0.112171i	$-0.0357805\pi$
$359$	37.6554			1.98738			0.993689	+	0.112171i	$0.0357805\pi$
$360$	−6.71213	+	9.32039i	−0.353761	+	0.491228i
$361$	1.00000			0.0526316
$362$	−20.2426	+	16.5849i	−1.06393	+	0.871682i
$363$	−3.77434	−	16.1832i	−0.198102	−	0.849399i
$364$	3.52273	−	17.5592i	0.184641	−	0.920353i
$365$	11.1453			0.583369
$366$	−16.2446	−	12.4847i	−0.849118	−	0.652585i
$367$		−	13.2463i		−	0.691453i	−0.938335	−	0.345726i	$-0.887633\pi$
$367$		−	13.2463i		−	0.691453i	0.938335	−	0.345726i	$-0.112367\pi$
$368$	−11.6108	−	4.85407i	−0.605253	−	0.253036i
$369$	13.1883	+	26.7357i	0.686555	+	1.39181i
$370$	1.18828	−	0.973566i	0.0617758	−	0.0506133i
$371$		−	21.0902i		−	1.09495i
$372$	0.988609	+	31.7387i	0.0512570	+	1.64558i
$373$		−	4.92907i		−	0.255218i	−0.991825	−	0.127609i	$-0.959270\pi$
$373$		−	4.92907i		−	0.255218i	0.991825	−	0.127609i	$-0.0407302\pi$
$374$	4.34941	+	5.30865i	0.224903	+	0.274504i
$375$	−4.34941	−	18.6489i	−0.224603	−	0.963027i
$376$	−9.18828	+	4.88218i	−0.473849	+	0.251779i
$377$			2.08843i			0.107560i
$378$	−28.2622	−	5.64095i	−1.45365	−	0.290139i
$379$	−18.6959			−0.960344			−0.480172	−	0.877174i	$-0.659426\pi$
$379$	−18.6959			−0.960344			−0.480172	+	0.877174i	$0.659426\pi$
$380$	−0.532511	+	2.65433i	−0.0273172	+	0.136164i
$381$	−1.69896	+	0.396241i	−0.0870404	+	0.0203000i
$382$	−20.7289	−	25.3006i	−1.06058	−	1.29449i
$383$	15.5189			0.792977			0.396489	−	0.918040i	$-0.370229\pi$
$383$	15.5189			0.792977			0.396489	+	0.918040i	$0.370229\pi$
$384$	−6.19319	−	18.5915i	−0.316045	−	0.948744i
$385$	−6.29441			−0.320793
$386$	22.4940	+	27.4550i	1.14492	+	1.39742i
$387$	−14.9956	+	7.39708i	−0.762270	+	0.376015i
$388$	−2.36041	+	11.7656i	−0.119831	+	0.597306i
$389$	7.06873			0.358399			0.179199	−	0.983813i	$-0.442649\pi$
$389$	7.06873			0.358399			0.179199	+	0.983813i	$0.442649\pi$
$390$	−6.00250	−	4.61319i	−0.303948	−	0.233598i
$391$			12.8766i			0.651196i
$392$	20.9333	−	11.1229i	1.05729	−	0.561790i
$393$	14.9545	−	3.48778i	0.754357	−	0.175935i
$394$	−4.59414	−	5.60736i	−0.231449	−	0.282495i
$395$			5.94965i			0.299359i
$396$	−6.87454	+	1.83075i	−0.345459	+	0.0919986i
$397$		−	11.1209i		−	0.558144i	−0.960270	−	0.279072i	$-0.909973\pi$
$397$		−	11.1209i		−	0.558144i	0.960270	−	0.279072i	$-0.0900267\pi$
$398$	−4.63562	+	3.79799i	−0.232363	+	0.190376i
$399$	−6.61532	+	1.54286i	−0.331180	+	0.0772397i
$400$	11.6905	+	4.88739i	0.584524	+	0.244370i
$401$		−	18.1831i		−	0.908022i	−0.890996	−	0.454011i	$-0.849993\pi$
$401$		−	18.1831i		−	0.908022i	0.890996	−	0.454011i	$-0.150007\pi$
$402$	19.3365	−	25.1599i	0.964417	−	1.25486i
$403$	−20.9296			−1.04258
$404$	4.83726	−	24.1116i	0.240663	−	1.19960i
$405$	−7.41408	+	9.66665i	−0.368409	+	0.480340i
$406$	−3.92421	+	3.21513i	−0.194755	+	0.159564i
$407$	0.951491			0.0471637
$408$	−15.1066	+	13.1839i	−0.747888	+	0.652701i
$409$	−3.18828			−0.157650			−0.0788252	−	0.996888i	$-0.525117\pi$
$409$	−3.18828			−0.157650			−0.0788252	+	0.996888i	$0.525117\pi$
$410$	−14.7146	+	12.0558i	−0.726704	+	0.595393i
$411$	25.6656	−	5.98586i	1.26599	−	0.295261i
$412$	−22.7619	−	4.56649i	−1.12140	−	0.224975i
$413$	−6.75118			−0.332204
$414$	−12.1543	−	5.51744i	−0.597350	−	0.271167i
$415$			16.6610i			0.817856i
$416$	12.3751	−	3.69854i	0.606739	−	0.181336i
$417$	−5.08653	−	21.8095i	−0.249088	−	1.06801i
$418$	−1.29707	+	1.06270i	−0.0634418	+	0.0519782i
$419$		−	6.06701i		−	0.296393i	−0.988958	−	0.148197i	$-0.952653\pi$
$419$		−	6.06701i		−	0.296393i	0.988958	−	0.148197i	$-0.0473468\pi$
$420$	−0.572532	−	18.3808i	−0.0279367	−	0.896891i
$421$		−	26.5395i		−	1.29346i	−0.762720	−	0.646729i	$-0.776136\pi$
$421$		−	26.5395i		−	1.29346i	0.762720	−	0.646729i	$-0.223864\pi$
$422$	9.43606	+	11.5171i	0.459340	+	0.560646i
$423$	−9.89733	+	4.88218i	−0.481224	+	0.237380i
$424$	13.4318	−	7.13698i	0.652307	−	0.346602i
$425$		−	12.9650i		−	0.628893i
$426$	12.0128	−	15.6306i	0.582023	−	0.757306i
$427$	32.8030			1.58745
$428$	−39.1371	−	7.85167i	−1.89176	−	0.379525i
$429$	−1.06502	−	4.56649i	−0.0514197	−	0.220472i
$430$	−6.76189	−	8.25319i	−0.326087	−	0.398004i
$431$	27.2655			1.31333			0.656666	−	0.754181i	$-0.271966\pi$
$431$	27.2655			1.31333			0.656666	+	0.754181i	$0.271966\pi$
$432$	−5.97141	−	19.9083i	−0.287300	−	0.957841i
$433$	34.8030			1.67252			0.836262	−	0.548330i	$-0.184736\pi$
$433$	34.8030			1.67252			0.836262	+	0.548330i	$0.184736\pi$
$434$	−32.2210	−	39.3273i	−1.54666	−	1.88777i
$435$	0.487075	+	2.08843i	0.0233535	+	0.100133i
$436$	−26.2846	−	5.27321i	−1.25880	−	0.252541i
$437$	−3.14615			−0.150501
$438$	−12.2900	+	15.9913i	−0.587240	+	0.764094i
$439$		−	10.9090i		−	0.520659i	−0.965520	−	0.260329i	$-0.916169\pi$
$439$		−	10.9090i		−	0.520659i	0.965520	−	0.260329i	$-0.0838312\pi$
$440$	−2.13004	−	4.00875i	−0.101546	−	0.191110i
$441$	22.5487	−	11.1229i	1.07375	−	0.529661i
$442$	−8.37552	−	10.2227i	−0.398383	−	0.486244i
$443$			0.986796i			0.0468841i	0.999725	+	0.0234420i	$0.00746252\pi$
$443$			0.986796i			0.0468841i	−0.999725	+	0.0234420i	$0.992537\pi$
$444$	0.0865464	+	2.77852i	0.00410731	+	0.131863i
$445$			2.57853i			0.122234i
$446$	26.2741	−	21.5265i	1.24411	−	1.01931i
$447$	2.63359	+	11.2920i	0.124564	+	0.534094i
$448$	26.0010	+	17.5592i	1.22843	+	0.829595i
$449$		−	14.0993i		−	0.665386i	−0.943035	−	0.332693i	$-0.892043\pi$
$449$		−	14.0993i		−	0.665386i	0.943035	−	0.332693i	$-0.107957\pi$
$450$	12.2377	+	5.55531i	0.576891	+	0.261880i
$451$	−11.7824			−0.554813
$452$	−15.5557	−	3.12078i	−0.731678	−	0.146789i
$453$	36.7408	−	8.56889i	1.72623	−	0.402601i
$454$	29.0465	−	23.7980i	1.36322	−	1.11689i
$455$	12.1209			0.568239
$456$	−3.22124	−	3.69101i	−0.150849	−	0.172848i
$457$	9.68067			0.452843			0.226421	−	0.974029i	$-0.427297\pi$
$457$	9.68067			0.452843			0.226421	+	0.974029i	$0.427297\pi$
$458$	−27.9453	+	22.8957i	−1.30580	+	1.06985i
$459$	−16.4372	+	13.4943i	−0.767225	+	0.629858i
$460$	1.67536	−	8.35091i	0.0781139	−	0.389363i
$461$	13.4746			0.627573			0.313786	−	0.949494i	$-0.398402\pi$
$461$	13.4746			0.627573			0.313786	+	0.949494i	$0.398402\pi$
$462$	6.94094	−	9.03128i	0.322922	−	0.420173i
$463$		−	17.4971i		−	0.813160i	−0.913615	−	0.406580i	$-0.866721\pi$
$463$		−	17.4971i		−	0.813160i	0.913615	−	0.406580i	$-0.133279\pi$
$464$	−3.37559	−	1.41122i	−0.156708	−	0.0655142i
$465$	−20.9296	+	4.88133i	−0.970588	+	0.226366i
$466$	14.2088	−	11.6414i	0.658211	−	0.539276i
$467$		−	10.5031i		−	0.486025i	−0.970023	−	0.243013i	$-0.921864\pi$
$467$		−	10.5031i		−	0.486025i	0.970023	−	0.243013i	$-0.0781356\pi$
$468$	13.2381	−	3.52541i	0.611930	−	0.162962i
$469$			50.8058i			2.34600i
$470$	−4.46294	−	5.44722i	−0.205860	−	0.251262i
$471$	−32.2210	+	7.51477i	−1.48467	+	0.346263i
$472$	−2.28461	−	4.29965i	−0.105158	−	0.197907i
$473$		−	6.60856i		−	0.303862i
$474$	−8.53661	−	6.56076i	−0.392099	−	0.301346i
$475$	3.16774			0.145346
$476$	6.31463	−	31.4756i	0.289430	−	1.44268i
$477$	14.4683	−	7.13698i	0.662459	−	0.326780i
$478$	14.4702	+	17.6616i	0.661853	+	0.807822i
$479$	−18.2061			−0.831859			−0.415930	−	0.909397i	$-0.636544\pi$
$479$	−18.2061			−0.831859			−0.415930	+	0.909397i	$0.636544\pi$
$480$	11.5125	−	6.58473i	0.525472	−	0.300551i
$481$	−1.83226			−0.0835436
$482$	−14.2588	−	17.4036i	−0.649472	−	0.792711i
$483$	20.8128	−	4.85407i	0.947013	−	0.220868i
$484$	−3.77434	+	18.8134i	−0.171561	+	0.855155i
$485$	−8.12165			−0.368785
$486$	−5.69418	−	21.2973i	−0.258293	−	0.966067i
$487$		−	10.1137i		−	0.458296i	−0.973392	−	0.229148i	$-0.926406\pi$
$487$		−	10.1137i		−	0.458296i	0.973392	−	0.229148i	$-0.0735940\pi$
$488$	11.1006	+	20.8913i	0.502500	+	0.945707i
$489$	−1.33987	−	5.74494i	−0.0605909	−	0.259795i
$490$	10.1677	+	12.4102i	0.459332	+	0.560635i
$491$			31.2501i			1.41030i	0.709060	+	0.705148i	$0.249119\pi$
$491$			31.2501i			1.41030i	−0.709060	+	0.705148i	$0.750881\pi$
$492$	−1.07171	−	34.4068i	−0.0483166	−	1.55118i
$493$			3.74359i			0.168603i
$494$	2.49773	−	2.04640i	0.112378	−	0.0920720i
$495$	−2.13004	−	4.31810i	−0.0957383	−	0.194084i
$496$	14.1428	−	33.8292i	0.635032	−	1.51897i
$497$			31.5632i			1.41580i
$498$	−23.9053	−	18.3723i	−1.07122	−	0.823282i
$499$	−10.4264			−0.466750			−0.233375	−	0.972387i	$-0.574977\pi$
$499$	−10.4264			−0.466750			−0.233375	+	0.972387i	$0.574977\pi$
$500$	−4.34941	+	21.6799i	−0.194512	+	0.969553i
$501$	4.65010	+	19.9382i	0.207751	+	0.890773i
$502$	2.46919	−	2.02302i	0.110206	−	0.0902920i
$503$	25.2580			1.12620			0.563099	−	0.826389i	$-0.309609\pi$
$503$	25.2580			1.12620			0.563099	+	0.826389i	$0.309609\pi$
$504$	27.0043	+	19.4473i	1.20287	+	0.866251i
$505$	16.6440			0.740647
$506$	4.08078	−	3.34340i	0.181413	−	0.148632i
$507$	−3.06333	−	13.1346i	−0.136047	−	0.583330i
$508$	1.97508	+	0.396241i	0.0876302	+	0.0175804i
$509$	−41.1101			−1.82217			−0.911087	−	0.412214i	$-0.864756\pi$
$509$	−41.1101			−1.82217			−0.911087	+	0.412214i	$0.864756\pi$
$510$	−10.7597	−	8.26932i	−0.476448	−	0.366172i
$511$		−	32.2915i		−	1.42849i
$512$	−2.38420	+	22.5015i	−0.105368	+	0.994433i
$513$	−3.29707	−	4.01613i	−0.145569	−	0.177317i
$514$	−17.8663	+	14.6380i	−0.788049	+	0.645653i
$515$		−	15.7123i		−	0.692367i
$516$	19.2982	−	0.601106i	0.849555	−	0.0264622i
$517$		−	4.36175i		−	0.191829i
$518$	−2.82075	−	3.44285i	−0.123936	−	0.151270i
$519$	−1.90607	−	8.17264i	−0.0836672	−	0.358739i
$520$	4.10175	+	7.71951i	0.179874	+	0.338523i
$521$			20.7078i			0.907227i	0.891198	+	0.453614i	$0.149865\pi$
$521$			20.7078i			0.907227i	−0.891198	+	0.453614i	$0.850135\pi$
$522$	−3.53360	−	1.60408i	−0.154662	−	0.0702087i
$523$	17.0865			0.747142			0.373571	−	0.927602i	$-0.378133\pi$
$523$	17.0865			0.747142			0.373571	+	0.927602i	$0.378133\pi$
$524$	−17.3850	−	3.48778i	−0.759469	−	0.152365i
$525$	−20.9556	+	4.88739i	−0.914579	+	0.213303i
$526$	27.8003	+	33.9315i	1.21215	+	1.47949i
$527$	−37.5172			−1.63427
$528$	8.10061	+	1.36430i	0.352534	+	0.0593734i
$529$	−13.1018			−0.569641
$530$	6.52412	+	7.96298i	0.283390	+	0.345890i
$531$	−2.28461	−	4.63144i	−0.0991437	−	0.200988i
$532$	7.69047	+	1.54286i	0.333424	+	0.0668915i
$533$	22.6890			0.982771
$534$	−3.69969	−	2.84338i	−0.160101	−	0.123045i
$535$		−	27.0159i		−	1.16800i
$536$	−32.3569	+	17.1928i	−1.39761	+	0.742616i
$537$	−27.9751	+	6.52451i	−1.20721	+	0.281553i
$538$	−24.1607	−	29.4892i	−1.04164	−	1.27137i
$539$			9.93719i			0.428025i
$540$	12.4159	−	6.61287i	0.534293	−	0.284573i
$541$			1.56131i			0.0671259i	0.999437	+	0.0335629i	$0.0106854\pi$
$541$			1.56131i			0.0671259i	−0.999437	+	0.0335629i	$0.989315\pi$
$542$	−2.11556	+	1.73329i	−0.0908711	+	0.0744512i
$543$	31.2128	−	7.27962i	1.33947	−	0.312399i
$544$	22.1829	−	6.62978i	0.951082	−	0.284250i
$545$		−	18.1440i		−	0.777204i
$546$	−13.3659	+	17.3912i	−0.572009	+	0.744276i
$547$	−18.5941			−0.795028			−0.397514	−	0.917596i	$-0.630127\pi$
$547$	−18.5941			−0.795028			−0.397514	+	0.917596i	$0.630127\pi$
$548$	−29.8369	−	5.98586i	−1.27457	−	0.255703i
$549$	11.1006	+	22.5035i	0.473762	+	0.960426i
$550$	−4.10879	+	3.36635i	−0.175199	+	0.143542i
$551$	−0.914677			−0.0389665
$552$	10.1345	+	11.6125i	0.431353	+	0.494260i
$553$	17.2381			0.733039
$554$	17.9544	−	14.7101i	0.762808	−	0.624973i
$555$	−1.83226	+	0.427329i	−0.0777749	+	0.0181391i
$556$	−5.08653	+	25.3541i	−0.215717	+	1.07525i
$557$	20.1569			0.854074			0.427037	−	0.904234i	$-0.359557\pi$
$557$	20.1569			0.854074			0.427037	+	0.904234i	$0.359557\pi$
$558$	16.0756	−	35.4127i	0.680535	−	1.49914i
$559$			12.7259i			0.538248i
$560$	−8.19052	+	19.5914i	−0.346113	+	0.827889i
$561$	−1.90909	−	8.18561i	−0.0806020	−	0.345597i
$562$	−17.8501	+	14.6247i	−0.752963	+	0.616907i
$563$			8.81183i			0.371374i	0.982609	+	0.185687i	$0.0594511\pi$
$563$			8.81183i			0.371374i	−0.982609	+	0.185687i	$0.940549\pi$
$564$	12.7371	−	0.396739i	0.536327	−	0.0167057i
$565$		−	10.7379i		−	0.451748i
$566$	−24.8191	−	30.2928i	−1.04322	−	1.27330i
$567$	28.0075	+	21.4811i	1.17620	+	0.902120i
$568$	−20.1018	+	10.6810i	−0.843451	+	0.448167i
$569$			2.66972i			0.111920i	0.998433	+	0.0559602i	$0.0178220\pi$
$569$			2.66972i			0.111920i	−0.998433	+	0.0559602i	$0.982178\pi$
$570$	2.02045	−	2.62894i	0.0846275	−	0.110114i
$571$	−25.5238			−1.06814			−0.534068	−	0.845441i	$-0.679337\pi$
$571$	−25.5238			−1.06814			−0.534068	+	0.845441i	$0.679337\pi$
$572$	−1.06502	+	5.30865i	−0.0445308	+	0.221966i
$573$	9.09856	+	39.0118i	0.380098	+	1.62974i
$574$	34.9296	+	42.6332i	1.45793	+	1.77948i
$575$	−9.96619			−0.415619
$576$	−3.24717	+	23.7793i	−0.135299	+	0.990805i
$577$	−1.54869			−0.0644727			−0.0322364	−	0.999480i	$-0.510263\pi$
$577$	−1.54869			−0.0644727			−0.0322364	+	0.999480i	$0.510263\pi$
$578$	0.223136	+	0.272348i	0.00928125	+	0.0113282i
$579$	−9.87333	−	42.3338i	−0.410322	−	1.75933i
$580$	0.487075	−	2.42785i	0.0202247	−	0.100811i
$581$	48.2724			2.00268
$582$	8.95585	−	11.6530i	0.371232	−	0.483033i
$583$			6.37618i			0.264075i
$584$	20.5656	−	10.9275i	0.851011	−	0.452184i
$585$	4.10175	+	8.31522i	0.169587	+	0.343792i
$586$	−17.7743	−	21.6944i	−0.734251	−	0.896187i
$587$		−	5.19444i		−	0.214397i	−0.994238	−	0.107199i	$-0.965812\pi$
$587$		−	5.19444i		−	0.214397i	0.994238	−	0.107199i	$-0.0341881\pi$
$588$	−29.0184	+	0.903874i	−1.19670	+	0.0372751i
$589$		−	9.16662i		−	0.377704i
$590$	2.54902	−	2.08843i	0.104942	−	0.0859793i
$591$	2.01651	+	8.64619i	0.0829482	+	0.355657i
$592$	1.23811	−	2.96153i	0.0508862	−	0.121718i
$593$			30.4917i			1.25214i	0.779765	+	0.626072i	$0.215338\pi$
$593$			30.4917i			1.25214i	−0.779765	+	0.626072i	$0.784662\pi$
$594$	8.54447	+	1.70542i	0.350584	+	0.0699742i
$595$	21.7273			0.890732
$596$	2.63359	−	13.1273i	0.107876	−	0.537713i
$597$	7.14783	−	1.66706i	0.292541	−	0.0682281i
$598$	−7.85822	+	6.43828i	−0.321346	+	0.263281i
$599$	−5.04012			−0.205934			−0.102967	−	0.994685i	$-0.532834\pi$
$599$	−5.04012			−0.205934			−0.102967	+	0.994685i	$0.532834\pi$
$600$	−10.2041	−	11.6922i	−0.416580	−	0.477332i
$601$	−0.811718			−0.0331107			−0.0165553	−	0.999863i	$-0.505270\pi$
$601$	−0.811718			−0.0331107			−0.0165553	+	0.999863i	$0.505270\pi$
$602$	−23.9122	+	19.5914i	−0.974590	+	0.798487i
$603$	−34.8538	+	17.1928i	−1.41936	+	0.700145i
$604$	−42.7121	−	8.56889i	−1.73793	−	0.348663i
$605$	−12.9867			−0.527985
$606$	−18.3535	+	23.8809i	−0.745561	+	0.970096i
$607$			13.4174i			0.544596i	0.962213	+	0.272298i	$0.0877837\pi$
$607$			13.4174i			0.544596i	−0.962213	+	0.272298i	$0.912216\pi$
$608$	1.61986	+	5.41997i	0.0656941	+	0.219809i
$609$	6.05088	−	1.41122i	0.245194	−	0.0571855i
$610$	−12.3853	+	10.1474i	−0.501467	+	0.410855i
$611$			8.39927i			0.339798i
$612$	23.7298	−	6.31944i	0.959219	−	0.255448i
$613$			4.42905i			0.178888i	0.995992	+	0.0894439i	$0.0285090\pi$
$613$			4.42905i			0.178888i	−0.995992	+	0.0894439i	$0.971491\pi$
$614$	4.84511	+	5.91367i	0.195533	+	0.238656i
$615$	22.6890	−	5.29166i	0.914910	−	0.213380i
$616$	−11.6147	+	6.17144i	−0.467969	+	0.248655i
$617$		−	31.5028i		−	1.26826i	−0.773228	−	0.634128i	$-0.781359\pi$
$617$		−	31.5028i		−	1.26826i	0.773228	−	0.634128i	$-0.218641\pi$
$618$	22.5441	+	17.3262i	0.906858	+	0.696961i
$619$	10.7619			0.432557			0.216278	−	0.976332i	$-0.430608\pi$
$619$	10.7619			0.432557			0.216278	+	0.976332i	$0.430608\pi$
$620$	24.3312	+	4.88133i	0.977165	+	0.196039i
$621$	10.3731	+	12.6353i	0.416257	+	0.507039i
$622$	−8.56115	−	10.4493i	−0.343271	−	0.418977i
$623$	7.47085			0.299313
$624$	−15.5991	−	2.62718i	−0.624463	−	0.105171i
$625$	0.873330			0.0349332
$626$	9.43606	+	11.5171i	0.377141	+	0.460318i
$627$	2.00000	−	0.466451i	0.0798723	−	0.0186283i
$628$	37.4578	+	7.51477i	1.49473	+	0.299872i
$629$	−3.28439			−0.130957
$630$	−9.30985	+	20.5085i	−0.370913	+	0.817079i
$631$		−	31.6469i		−	1.25984i	−0.776659	−	0.629921i	$-0.783087\pi$
$631$		−	31.6469i		−	1.25984i	0.776659	−	0.629921i	$-0.216913\pi$
$632$	5.83341	+	10.9785i	0.232041	+	0.436701i
$633$	−4.14178	−	17.7587i	−0.164621	−	0.705845i
$634$	−0.753806	−	0.920055i	−0.0299375	−	0.0365400i
$635$			1.36338i			0.0541041i
$636$	−18.6196	+	0.579969i	−0.738315	+	0.0229973i
$637$		−	19.1357i		−	0.758185i
$638$	1.18640	−	0.972025i	0.0469700	−	0.0384828i
$639$	−21.6530	+	10.6810i	−0.856578	+	0.422535i
$640$	−15.2490	+	1.41346i	−0.602768	+	0.0558718i
$641$		−	40.0767i		−	1.58293i	−0.611213	−	0.791466i	$-0.709318\pi$
$641$		−	40.0767i		−	1.58293i	0.611213	−	0.791466i	$-0.290682\pi$
$642$	38.7627	+	29.7908i	1.52984	+	1.17575i
$643$	−1.78242			−0.0702919			−0.0351460	−	0.999382i	$-0.511190\pi$
$643$	−1.78242			−0.0702919			−0.0351460	+	0.999382i	$0.511190\pi$
$644$	−24.1954	−	4.85407i	−0.953431	−	0.191277i
$645$	2.96800	+	12.7259i	0.116865	+	0.501081i
$646$	4.47727	−	3.66826i	0.176156	−	0.144326i
$647$	−34.6475			−1.36213			−0.681067	−	0.732221i	$-0.738484\pi$
$647$	−34.6475			−1.36213			−0.681067	+	0.732221i	$0.738484\pi$
$648$	−4.20293	+	25.1065i	−0.165107	+	0.986276i
$649$	2.04107			0.0801192
$650$	7.91216	−	6.48248i	0.310340	−	0.254264i
$651$	14.1428	+	60.6401i	0.554301	+	2.37667i
$652$	−1.33987	+	6.67864i	−0.0524733	+	0.261556i
$653$	17.5969			0.688620			0.344310	−	0.938856i	$-0.388113\pi$
$653$	17.5969			0.688620			0.344310	+	0.938856i	$0.388113\pi$
$654$	26.0332	+	20.0076i	1.01798	+	0.782361i
$655$		−	12.0007i		−	0.468907i
$656$	−15.3317	+	36.6729i	−0.598603	+	1.43184i
$657$	22.1526	−	10.9275i	0.864256	−	0.426323i
$658$	−15.7824	+	12.9306i	−0.615263	+	0.504088i
$659$			9.81402i			0.382300i	0.981561	+	0.191150i	$0.0612217\pi$
$659$			9.81402i			0.382300i	−0.981561	+	0.191150i	$0.938778\pi$
$660$	0.173093	+	5.55704i	0.00673763	+	0.216308i
$661$			6.84973i			0.266424i	0.991088	+	0.133212i	$0.0425290\pi$
$661$			6.84973i			0.266424i	−0.991088	+	0.133212i	$0.957471\pi$
$662$	−10.6961	−	13.0551i	−0.415715	−	0.507400i
$663$	3.67628	+	15.7628i	0.142775	+	0.612175i
$664$	16.3355	+	30.7434i	0.633940	+	1.19308i
$665$			5.30865i			0.205861i
$666$	1.40732	−	3.10016i	0.0545325	−	0.120129i
$667$	2.87771			0.111425
$668$	4.65010	−	23.1787i	0.179918	−	0.896810i
$669$	−40.5130	+	9.44867i	−1.56632	+	0.365307i
$670$	−15.7164	−	19.1826i	−0.607179	−	0.741089i
$671$	−9.91728			−0.382852
$672$	−19.0782	−	33.3556i	−0.735956	−	1.28672i
$673$	−16.7619			−0.646123			−0.323062	−	0.946378i	$-0.604712\pi$
$673$	−16.7619			−0.646123			−0.323062	+	0.946378i	$0.604712\pi$
$674$	4.91398	+	5.99773i	0.189279	+	0.231024i
$675$	−10.4443	−	12.7221i	−0.402000	−	0.489673i
$676$	−3.06333	+	15.2694i	−0.117821	+	0.587283i
$677$	−28.6281			−1.10027			−0.550134	−	0.835076i	$-0.685423\pi$
$677$	−28.6281			−1.10027			−0.550134	+	0.835076i	$0.685423\pi$
$678$	15.4069	+	11.8409i	0.591697	+	0.454746i
$679$			23.5311i			0.903042i
$680$	7.35256	+	13.8375i	0.281958	+	0.530645i
$681$	−44.7878	+	10.4457i	−1.71627	+	0.400279i
$682$	9.74135	+	11.8898i	0.373016	+	0.455282i
$683$		−	4.02352i		−	0.153956i	−0.997033	−	0.0769778i	$-0.975473\pi$
$683$		−	4.02352i		−	0.153956i	0.997033	−	0.0769778i	$-0.0245271\pi$
$684$	1.54404	+	5.79793i	0.0590377	+	0.221689i
$685$		−	20.5961i		−	0.786936i
$686$	5.92461	−	4.85407i	0.226203	−	0.185329i
$687$	43.0898	−	10.0496i	1.64398	−	0.383418i
$688$	−20.5692	−	8.59930i	−0.784194	−	0.327845i
$689$		−	12.2784i		−	0.467770i
$690$	−6.35664	+	8.27102i	−0.241993	+	0.314872i
$691$	26.7619			1.01807			0.509035	−	0.860746i	$-0.330002\pi$
$691$	26.7619			1.01807			0.509035	+	0.860746i	$0.330002\pi$
$692$	−1.90607	+	9.50090i	−0.0724579	+	0.361170i
$693$	−12.5110	+	6.17144i	−0.475252	+	0.234434i
$694$	−7.65748	+	6.27381i	−0.290674	+	0.238151i
$695$	−17.5017			−0.663876
$696$	2.94640	+	3.37609i	0.111683	+	0.127970i
$697$	40.6710			1.54052
$698$	4.99545	−	4.09280i	0.189081	−	0.154915i
$699$	−21.9091	+	5.10976i	−0.828678	+	0.193269i
$700$	24.3615	+	4.88739i	0.920776	+	0.184726i
$701$	52.8211			1.99503			0.997513	−	0.0704865i	$-0.0224552\pi$
$701$	52.8211			1.99503			0.997513	+	0.0704865i	$0.0224552\pi$
$702$	−16.4538	−	3.28407i	−0.621009	−	0.123949i
$703$		−	0.802479i		−	0.0302661i
$704$	−7.86086	−	5.30865i	−0.296267	−	0.200077i
$705$	1.95893	+	8.39927i	0.0737774	+	0.316335i
$706$	3.85822	−	3.16106i	0.145206	−	0.118968i
$707$		−	48.2231i		−	1.81362i
$708$	0.185653	+	5.96030i	0.00697729	+	0.224002i
$709$		−	34.7895i		−	1.30655i	−0.757122	−	0.653273i	$-0.773395\pi$
$709$		−	34.7895i		−	1.30655i	0.757122	−	0.653273i	$-0.226605\pi$
$710$	−9.76384	−	11.9172i	−0.366431	−	0.447245i
$711$	5.83341	+	11.8257i	0.218770	+	0.443498i
$712$	2.52815	+	4.75799i	0.0947464	+	0.178313i
$713$			28.8396i			1.08005i
$714$	−23.9590	+	31.1745i	−0.896642	+	1.16668i
$715$	−3.66451			−0.137045
$716$	32.5217	+	6.52451i	1.21539	+	0.243832i
$717$	−6.35144	−	27.2330i	−0.237199	−	1.01704i
$718$	33.7494	+	41.1927i	1.25952	+	1.53730i
$719$	−24.3065			−0.906480			−0.453240	−	0.891389i	$-0.649732\pi$
$719$	−24.3065			−0.906480			−0.453240	+	0.891389i	$0.649732\pi$
$720$	−16.2118	+	1.01092i	−0.604178	+	0.0376749i
$721$	−45.5238			−1.69539
$722$	0.896270	+	1.09394i	0.0333557	+	0.0407122i
$723$	6.25865	+	26.8352i	0.232762	+	0.998011i
$724$	−36.2857	−	7.27962i	−1.34855	−	0.270545i
$725$	−2.89746			−0.107609
$726$	14.3206	−	18.6334i	0.531488	−	0.691552i
$727$		−	1.59172i		−	0.0590336i	−0.999564	−	0.0295168i	$-0.990603\pi$
$727$		−	1.59172i		−	0.0590336i	0.999564	−	0.0295168i	$-0.00939686\pi$
$728$	22.3660	−	11.8841i	0.828939	−	0.440456i
$729$	−5.25865	+	26.4829i	−0.194765	+	0.980850i
$730$	9.98915	+	12.1922i	0.369715	+	0.451254i
$731$			22.8117i			0.843720i
$732$	−0.902062	−	28.9602i	−0.0333412	−	1.07040i
$733$			12.2055i			0.450819i	0.974264	+	0.225409i	$0.0723720\pi$
$733$			12.2055i			0.450819i	−0.974264	+	0.225409i	$0.927628\pi$
$734$	14.4907	−	11.8723i	0.534860	−	0.438214i
$735$	−4.46294	−	19.1357i	−0.164618	−	0.705832i
$736$	−5.09633	−	17.0520i	−0.187853	−	0.628546i
$737$		−	15.3601i		−	0.565795i
$738$	−17.4270	+	38.3896i	−0.641496	+	1.41314i
$739$	27.0205			0.993967			0.496983	−	0.867760i	$-0.334441\pi$
$739$	27.0205			0.993967			0.496983	+	0.867760i	$0.334441\pi$
$740$	2.13004	+	0.427329i	0.0783019	+	0.0157089i
$741$	−3.85133	+	0.898230i	−0.141482	+	0.0329973i
$742$	23.0714	−	18.9025i	0.846978	−	0.693934i
$743$	−1.25218			−0.0459380			−0.0229690	−	0.999736i	$-0.507312\pi$
$743$	−1.25218			−0.0459380			−0.0229690	+	0.999736i	$0.507312\pi$
$744$	−33.8341	+	29.5279i	−1.24042	+	1.08255i
$745$	9.06161			0.331992
$746$	5.39210	−	4.41778i	0.197419	−	0.161746i
$747$	16.3355	+	33.1159i	0.597684	+	1.21165i
$748$	−1.90909	+	9.51597i	−0.0698034	+	0.347938i
$749$	−78.2741			−2.86007
$750$	16.5025	−	21.4725i	0.602588	−	0.784064i
$751$			28.9674i			1.05704i	0.848922	+	0.528518i	$0.177252\pi$
$751$			28.9674i			1.05704i	−0.848922	+	0.528518i	$0.822748\pi$
$752$	−13.5760	−	5.67566i	−0.495065	−	0.206970i
$753$	−3.80734	+	0.887969i	−0.138747	+	0.0323594i
$754$	−2.28461	+	1.87180i	−0.0832007	+	0.0681668i
$755$		−	29.4837i		−	1.07302i
$756$	−19.1597	−	35.9729i	−0.696831	−	1.30832i
$757$		−	30.3604i		−	1.10347i	−0.834020	−	0.551735i	$-0.813966\pi$
$757$		−	30.3604i		−	1.10347i	0.834020	−	0.551735i	$-0.186034\pi$
$758$	−16.7566	−	20.4522i	−0.608626	−	0.742856i
$759$	−6.29230	+	1.46752i	−0.228396	+	0.0532678i
$760$	−3.38094	+	1.79646i	−0.122640	+	0.0651644i
$761$		−	40.0317i		−	1.45115i	−0.688144	−	0.725574i	$-0.741574\pi$
$761$		−	40.0317i		−	1.45115i	0.688144	−	0.725574i	$-0.258426\pi$
$762$	−1.95619	−	1.50342i	−0.0708653	−	0.0544631i
$763$	−52.5692			−1.90313
$764$	9.09856	−	45.3522i	0.329174	−	1.64079i
$765$	7.35256	+	14.9054i	0.265832	+	0.538904i
$766$	13.9091	+	16.9767i	0.502556	+	0.613392i
$767$	−3.93043			−0.141920
$768$	14.7872	−	23.4380i	0.533587	−	0.845745i
$769$	−50.9956			−1.83895			−0.919475	−	0.393149i	$-0.871385\pi$
$769$	−50.9956			−1.83895			−0.919475	+	0.393149i	$0.871385\pi$
$770$	−5.64149	−	6.88570i	−0.203305	−	0.248143i
$771$	27.5487	−	6.42506i	0.992142	−	0.231393i
$772$	−9.87333	+	49.2141i	−0.355349	+	1.77126i
$773$	8.19837			0.294875			0.147437	−	0.989071i	$-0.452898\pi$
$773$	8.19837			0.294875			0.147437	+	0.989071i	$0.452898\pi$
$774$	−21.5321	−	9.77450i	−0.773954	−	0.351337i
$775$		−	29.0375i		−	1.04306i
$776$	−14.9864	+	7.96298i	−0.537979	+	0.285854i
$777$	1.23811	+	5.30865i	0.0444171	+	0.190447i
$778$	6.33549	+	7.73275i	0.227138	+	0.277233i
$779$			9.93719i			0.356037i
$780$	−0.333319	−	10.7010i	−0.0119347	−	0.383158i
$781$		−	9.54245i		−	0.341456i
$782$	−14.0862	+	11.5409i	−0.503720	+	0.412701i
$783$	3.01575	+	3.67346i	0.107774	+	0.131279i
$784$	30.9296	+	12.9306i	1.10463	+	0.461808i
$785$			25.8567i			0.922866i
$786$	17.2187	+	13.2334i	0.614172	+	0.472018i
$787$	9.75751			0.347818			0.173909	−	0.984762i	$-0.444360\pi$
$787$	9.75751			0.347818			0.173909	+	0.984762i	$0.444360\pi$
$788$	2.01651	−	10.0514i	0.0718353	−	0.358067i
$789$	−12.2024	−	52.3203i	−0.434418	−	1.86265i
$790$	−6.50855	+	5.33249i	−0.231564	+	0.189721i
$791$	−31.1114			−1.10619
$792$	−8.16417	−	5.87947i	−0.290101	−	0.208918i
$793$	19.0974			0.678168
$794$	12.1656	−	9.96736i	0.431741	−	0.353728i
$795$	−2.86364	−	12.2784i	−0.101563	−	0.435470i
$796$	−8.30953	−	1.66706i	−0.294523	−	0.0590872i
$797$	24.2944			0.860552			0.430276	−	0.902697i	$-0.358416\pi$
$797$	24.2944			0.860552			0.430276	+	0.902697i	$0.358416\pi$
$798$	−7.61690	−	5.85393i	−0.269635	−	0.207227i
$799$			15.0560i			0.532644i
$800$	5.13131	+	17.1691i	0.181419	+	0.607018i
$801$	2.52815	+	5.12515i	0.0893278	+	0.181088i
$802$	19.8912	−	16.2970i	0.702383	−	0.575467i
$803$			9.76265i			0.344516i
$804$	44.8541	−	1.39713i	1.58188	−	0.0492730i
$805$		−	16.7018i		−	0.588662i
$806$	−18.7586	−	22.8957i	−0.660743	−	0.806467i
$807$	10.6049	+	45.4705i	0.373310	+	1.60064i
$808$	30.7121	−	16.3188i	1.08045	−	0.574094i
$809$			32.4416i			1.14058i	0.821442	+	0.570292i	$0.193170\pi$
$809$			32.4416i			1.14058i	−0.821442	+	0.570292i	$0.806830\pi$
$810$	−17.2197	+	0.553377i	−0.605040	+	0.0194437i
$811$	−46.6461			−1.63796			−0.818982	−	0.573819i	$-0.805461\pi$
$811$	−46.6461			−1.63796			−0.818982	+	0.573819i	$0.805461\pi$
$812$	−7.03430	−	1.41122i	−0.246855	−	0.0495241i
$813$	3.26206	−	0.760796i	0.114405	−	0.0266823i
$814$	0.852793	+	1.04087i	0.0298904	+	0.0364826i
$815$	−4.61020			−0.161488
$816$	−27.9620	−	4.70933i	−0.978865	−	0.164859i
$817$	−5.57360			−0.194996
$818$	−2.85756	−	3.48778i	−0.0999123	−	0.121947i
$819$	24.0920	−	11.8841i	0.841841	−	0.415266i
$820$	−26.3766	−	5.29166i	−0.921110	−	0.184793i
$821$	−29.2699			−1.02153			−0.510763	−	0.859721i	$-0.670637\pi$
$821$	−29.2699			−1.02153			−0.510763	+	0.859721i	$0.670637\pi$
$822$	29.5514	+	22.7116i	1.03072	+	0.792157i
$823$			31.7711i			1.10747i	0.832693	+	0.553735i	$0.186798\pi$
$823$			31.7711i			1.10747i	−0.832693	+	0.553735i	$0.813202\pi$
$824$	−15.4053	−	28.9929i	−0.536670	−	1.01002i
$825$	6.33549	−	1.47760i	0.220573	−	0.0514434i
$826$	−6.05088	−	7.38537i	−0.210537	−	0.256970i
$827$		−	29.2906i		−	1.01853i	−0.860608	−	0.509267i	$-0.829916\pi$
$827$		−	29.2906i		−	1.01853i	0.860608	−	0.509267i	$-0.170084\pi$
$828$	−4.85777	−	18.2411i	−0.168819	−	0.633923i
$829$		−	26.7206i		−	0.928046i	−0.885823	−	0.464023i	$-0.846406\pi$
$829$		−	26.7206i		−	0.928046i	0.885823	−	0.464023i	$-0.153594\pi$
$830$	−18.2261	+	14.9327i	−0.632637	+	0.518323i
$831$	−27.6845	+	6.45673i	−0.960364	+	0.223981i
$832$	15.1374	+	10.2227i	0.524795	+	0.354408i
$833$		−	34.3016i		−	1.18848i
$834$	19.2993	−	25.1115i	0.668281	−	0.869541i
$835$	16.0000			0.553703
$836$	−2.32505	−	0.466451i	−0.0804135	−	0.0161326i
$837$	−36.8144	+	30.2230i	−1.27249	+	1.04466i
$838$	6.63694	−	5.43768i	0.229269	−	0.187842i
$839$	−50.6790			−1.74963			−0.874816	−	0.484455i	$-0.839018\pi$
$839$	−50.6790			−1.74963			−0.874816	+	0.484455i	$0.839018\pi$
$840$	19.5943	−	17.1005i	0.676068	−	0.590022i
$841$	−28.1634			−0.971151
$842$	29.0326	−	23.7866i	1.00053	−	0.819740i
$843$	27.5238	−	6.41925i	0.947969	−	0.221091i
$844$	−4.14178	+	20.6449i	−0.142566	+	0.710628i
$845$	−10.5403			−0.362597
$846$	−14.2115	−	6.45131i	−0.488601	−	0.221801i
$847$			37.6268i			1.29287i
$848$	19.8459	+	8.29692i	0.681513	+	0.284917i
$849$	10.8939	+	46.7096i	0.373877	+	1.60307i
$850$	14.1829	−	11.6201i	0.486468	−	0.398566i
$851$			2.52472i			0.0865462i
$852$	27.8656	−	0.867969i	0.954661	−	0.0297361i
$853$			38.6136i			1.32211i	0.750339	+	0.661053i	$0.229890\pi$
$853$			38.6136i			1.32211i	−0.750339	+	0.661053i	$0.770110\pi$
$854$	29.4003	+	35.8844i	1.00606	+	1.22794i
$855$	−3.64184	+	1.79646i	−0.124548	+	0.0614376i
$856$	−26.4881	−	49.8507i	−0.905345	−	1.70386i
$857$			12.8892i			0.440288i	0.975467	+	0.220144i	$0.0706527\pi$
$857$			12.8892i			0.440288i	−0.975467	+	0.220144i	$0.929347\pi$
$858$	4.04091	−	5.25787i	0.137954	−	0.179501i
$859$	7.74666			0.264313			0.132156	−	0.991229i	$-0.457810\pi$
$859$	7.74666			0.264313			0.132156	+	0.991229i	$0.457810\pi$
$860$	2.96800	−	14.7942i	0.101208	−	0.504477i
$861$	−15.3317	−	65.7377i	−0.522503	−	2.24033i
$862$	24.4372	+	29.8268i	0.832336	+	1.01590i
$863$	−0.877863			−0.0298828			−0.0149414	−	0.999888i	$-0.504756\pi$
$863$	−0.877863			−0.0298828			−0.0149414	+	0.999888i	$0.504756\pi$
$864$	16.4265	−	24.3756i	0.558841	−	0.829275i
$865$	−6.55838			−0.222992
$866$	31.1928	+	38.0723i	1.05998	+	1.29375i
$867$	−0.0979415	−	0.419943i	−0.00332627	−	0.0142620i
$868$	14.1428	−	70.4957i	0.480039	−	2.39278i
$869$	−5.21158			−0.176791
$870$	−1.84806	+	2.40463i	−0.0626552	+	0.0815245i
$871$			29.5784i			1.00223i
$872$	−17.7895	−	33.4800i	−0.602430	−	1.13377i
$873$	−16.1428	+	7.96298i	−0.546352	+	0.269506i
$874$	−2.81980	−	3.44169i	−0.0953811	−	0.116417i
$875$			43.3597i			1.46583i
$876$	−28.5087	+	0.887998i	−0.963219	+	0.0300027i
$877$			22.1541i			0.748092i	0.927410	+	0.374046i	$0.122030\pi$
$877$			22.1541i			0.748092i	−0.927410	+	0.374046i	$0.877970\pi$
$878$	11.9338	−	9.77742i	0.402746	−	0.329972i
$879$	7.80172	+	33.4514i	0.263145	+	1.12829i
$880$	2.47623	−	5.92305i	0.0834736	−	0.199666i
$881$			5.87455i			0.197919i	0.995091	+	0.0989593i	$0.0315514\pi$
$881$			5.87455i			0.197919i	−0.995091	+	0.0989593i	$0.968449\pi$
$882$	32.3775	+	14.6978i	1.09021	+	0.494899i
$883$	41.6558			1.40183			0.700914	−	0.713246i	$-0.252776\pi$
$883$	41.6558			1.40183			0.700914	+	0.713246i	$0.252776\pi$
$884$	3.67628	−	18.3246i	0.123647	−	0.616323i
$885$	−3.93043	+	0.916677i	−0.132120	+	0.0308138i
$886$	−1.07949	+	0.884436i	−0.0362663	+	0.0297132i
$887$	29.3556			0.985666			0.492833	−	0.870124i	$-0.335961\pi$
$887$	29.3556			0.985666			0.492833	+	0.870124i	$0.335961\pi$
$888$	−2.96196	+	2.58498i	−0.0993970	+	0.0867463i
$889$	3.95017			0.132484
$890$	−2.82075	+	2.31105i	−0.0945516	+	0.0774667i
$891$	−8.46747	−	6.49434i	−0.283671	−	0.217569i
$892$	47.0974	+	9.44867i	1.57694	+	0.316365i
$893$	−3.67866			−0.123102
$894$	−9.99236	+	13.0017i	−0.334195	+	0.434841i
$895$			22.4494i			0.750402i
$896$	4.09526	+	44.1813i	0.136813	+	1.47599i
$897$	12.1169	−	2.82596i	0.404570	−	0.0943562i
$898$	15.4237	−	12.6368i	0.514697	−	0.421694i
$899$			8.38450i			0.279639i
$900$	4.89112	+	18.3664i	0.163037	+	0.612212i
$901$		−	22.0095i		−	0.733244i
$902$	−10.5602	−	12.8892i	−0.351617	−	0.429165i
$903$	36.8712	−	8.59930i	1.22700	−	0.286167i
$904$	−10.5282	−	19.8140i	−0.350161	−	0.659004i
$905$		−	25.0476i		−	0.832611i
$906$	42.3035	+	32.5121i	1.40544	+	1.08014i
$907$	34.9458			1.16036			0.580178	−	0.814490i	$-0.302983\pi$
$907$	34.9458			1.16036			0.580178	+	0.814490i	$0.302983\pi$
$908$	52.0670	+	10.4457i	1.72790	+	0.346652i
$909$	33.0820	−	16.3188i	1.09726	−	0.541261i
$910$	10.8636	+	13.2596i	0.360126	+	0.439550i
$911$	54.3776			1.80161			0.900805	−	0.434225i	$-0.142978\pi$
$911$	54.3776			1.80161			0.900805	+	0.434225i	$0.142978\pi$
$912$	1.15064	−	6.83199i	0.0381014	−	0.226230i
$913$	−14.5941			−0.482996
$914$	8.67649	+	10.5901i	0.286993	+	0.350288i
$915$	19.0974	−	4.45400i	0.631340	−	0.147245i
$916$	−50.0930	−	10.0496i	−1.65512	−	0.332050i
$917$	−34.7701			−1.14821
$918$	−29.4941	−	5.88683i	−0.973450	−	0.194294i
$919$		−	16.9634i		−	0.559572i	−0.960062	−	0.279786i	$-0.909736\pi$
$919$		−	16.9634i		−	0.559572i	0.960062	−	0.279786i	$-0.0902636\pi$
$920$	10.6369	−	5.65193i	0.350690	−	0.186339i
$921$	−2.12667	−	9.11851i	−0.0700762	−	0.300465i
$922$	12.0768	+	14.7403i	0.397729	+	0.485447i
$923$			18.3756i			0.604840i
$924$	16.1006	−	0.501507i	0.529671	−	0.0164984i
$925$		−	2.54205i		−	0.0835821i
$926$	19.1408	−	15.6821i	0.629004	−	0.515347i
$927$	−15.4053	−	31.2302i	−0.505978	−	1.02574i
$928$	−1.48165	−	4.95752i	−0.0486376	−	0.162739i
$929$		−	47.1459i		−	1.54681i	−0.633915	−	0.773403i	$-0.718553\pi$
$929$		−	47.1459i		−	1.54681i	0.633915	−	0.773403i	$-0.281447\pi$
$930$	−24.0985	−	18.5207i	−0.790220	−	0.607319i
$931$	8.38094			0.274674
$932$	25.4699	+	5.10976i	0.834293	+	0.167376i
$933$	3.75776	+	16.1121i	0.123023	+	0.527487i
$934$	11.4897	−	9.41360i	0.375955	−	0.308023i
$935$	−6.56878			−0.214822
$936$	15.7215	+	11.3219i	0.513872	+	0.370068i
$937$	32.6050			1.06516			0.532579	−	0.846380i	$-0.321223\pi$
$937$	32.6050			1.06516			0.532579	+	0.846380i	$0.321223\pi$
$938$	−55.5784	+	45.5357i	−1.81470	+	1.48679i
$939$	−4.14178	−	17.7587i	−0.135162	−	0.579533i
$940$	1.95893	−	9.76436i	0.0638931	−	0.318478i
$941$	11.7098			0.381729			0.190865	−	0.981616i	$-0.438871\pi$
$941$	11.7098			0.381729			0.190865	+	0.981616i	$0.438871\pi$
$942$	−37.0995	−	28.5126i	−1.20877	−	0.928990i
$943$		−	31.2639i		−	1.01809i
$944$	2.65592	−	6.35287i	0.0864428	−	0.206768i
$945$	21.3203	−	17.5030i	0.693548	−	0.569373i
$946$	7.22936	−	5.92305i	0.235047	−	0.192575i
$947$		−	41.5299i		−	1.34954i	−0.738028	−	0.674770i	$-0.764243\pi$
$947$		−	41.5299i		−	1.34954i	0.738028	−	0.674770i	$-0.235757\pi$
$948$	−0.474038	−	15.2187i	−0.0153960	−	0.494281i
$949$		−	18.7996i		−	0.610261i
$950$	2.83915	+	3.46532i	0.0921143	+	0.112430i
$951$	0.330869	+	1.41867i	0.0107292	+	0.0460034i
$952$	40.0920	−	21.3028i	1.29939	−	0.690428i
$953$			3.63531i			0.117759i	0.998265	+	0.0588797i	$0.0187528\pi$
$953$			3.63531i			0.117759i	−0.998265	+	0.0588797i	$0.981247\pi$
$954$	20.7749	+	9.43080i	0.672614	+	0.305333i
$955$	31.3062			1.01304
$956$	−6.35144	+	31.6591i	−0.205420	+	1.02393i
$957$	−1.82935	+	0.426652i	−0.0591346	+	0.0137917i
$958$	−16.3176	−	19.9164i	−0.527198	−	0.643469i
$959$	−59.6737			−1.92696
$960$	17.5216	+	6.69227i	0.565507	+	0.215992i
$961$	−53.0270			−1.71055
$962$	−1.64220	−	2.00437i	−0.0529465	−	0.0646236i
$963$	−26.4881	−	53.6976i	−0.853568	−	1.73038i
$964$	6.25865	−	31.1966i	0.201578	−	1.00477i
$965$	−33.9720			−1.09360
$966$	23.9639	+	18.4173i	0.771026	+	0.592567i
$967$		−	60.7854i		−	1.95473i	−0.211570	−	0.977363i	$-0.567858\pi$
$967$		−	60.7854i		−	1.95473i	0.211570	−	0.977363i	$-0.432142\pi$
$968$	−23.9635	+	12.7330i	−0.770217	+	0.409254i
$969$	−6.90367	+	1.61011i	−0.221778	+	0.0517243i
$970$	−7.27919	−	8.88458i	−0.233721	−	0.285267i
$971$			41.4009i			1.32862i	0.747458	+	0.664309i	$0.231274\pi$
$971$			41.4009i			1.32862i	−0.747458	+	0.664309i	$0.768726\pi$
$972$	18.1944	−	25.3172i	0.583587	−	0.812051i
$973$			50.7081i			1.62563i
$974$	11.0638	−	9.06462i	0.354506	−	0.290449i
$975$	−12.2000	+	2.84536i	−0.390714	+	0.0911245i
$976$	−12.9047	+	30.8676i	−0.413070	+	0.988049i
$977$		−	3.89453i		−	0.124597i	−0.998058	−	0.0622985i	$-0.980157\pi$
$977$		−	3.89453i		−	0.124597i	0.998058	−	0.0622985i	$-0.0198431\pi$
$978$	5.08373	−	6.61475i	0.162560	−	0.211516i
$979$	−2.25865			−0.0721868
$980$	−4.46294	+	22.2458i	−0.142563	+	0.710615i
$981$	−17.7895	−	36.0636i	−0.567976	−	1.15142i
$982$	−34.1856	+	28.0085i	−1.09091	+	0.893787i
$983$	18.9168			0.603352			0.301676	−	0.953411i	$-0.402454\pi$
$983$	18.9168			0.603352			0.301676	+	0.953411i	$0.402454\pi$
$984$	36.6783	−	32.0101i	1.16926	−	1.02045i
$985$	6.93839			0.221075
$986$	−4.09526	+	3.35527i	−0.130420	+	0.106854i
$987$	24.3355	−	5.67566i	0.774607	−	0.180658i
$988$	4.47727	+	0.898230i	0.142441	+	0.0285765i
$989$	17.5354			0.557593
$990$	2.81464	−	6.20031i	0.0894550	−	0.197059i
$991$			11.4030i			0.362227i	0.983462	+	0.181114i	$0.0579702\pi$
$991$			11.4030i			0.362227i	−0.983462	+	0.181114i	$0.942030\pi$
$992$	49.6828	−	14.8487i	1.57743	−	0.471446i
$993$	4.69485	+	20.1301i	0.148987	+	0.638809i
$994$	−34.5282	+	28.2891i	−1.09517	+	0.897276i
$995$		−	5.73598i		−	0.181843i
$996$	−1.32746	−	42.6175i	−0.0420623	−	1.35039i
$997$		−	33.4738i		−	1.06012i	−0.847959	−	0.530062i	$-0.822169\pi$
$997$		−	33.4738i		−	1.06012i	0.847959	−	0.530062i	$-0.177831\pi$
$998$	−9.34486	−	11.4058i	−0.295807	−	0.361045i
$999$	−3.22286	+	2.64583i	−0.101967	+	0.0837104i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.j.c.419.10	yes	12
3.2	odd	2	inner	456.2.j.c.419.3	✓	12
4.3	odd	2		1824.2.j.c.1103.7		12
8.3	odd	2	inner	456.2.j.c.419.4	yes	12
8.5	even	2		1824.2.j.c.1103.8		12
12.11	even	2		1824.2.j.c.1103.6		12
24.5	odd	2		1824.2.j.c.1103.5		12
24.11	even	2	inner	456.2.j.c.419.9	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.j.c.419.3	✓	12	3.2	odd	2	inner
456.2.j.c.419.4	yes	12	8.3	odd	2	inner
456.2.j.c.419.9	yes	12	24.11	even	2	inner
456.2.j.c.419.10	yes	12	1.1	even	1	trivial
1824.2.j.c.1103.5		12	24.5	odd	2
1824.2.j.c.1103.6		12	12.11	even	2
1824.2.j.c.1103.7		12	4.3	odd	2
1824.2.j.c.1103.8		12	8.5	even	2

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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.896270 + 1.09394i) q^{2} +(-0.393401 - 1.68678i) q^{3} +(-0.393401 + 1.96093i) q^{4} -1.35361 q^{5} +(1.49264 - 1.94217i) q^{6} +3.92185i q^{7} +(-2.49773 + 1.32716i) q^{8} +(-2.69047 + 1.32716i) q^{9} +O(q^{10})\)	\(q+(0.896270 + 1.09394i) q^{2} +(-0.393401 - 1.68678i) q^{3} +(-0.393401 + 1.96093i) q^{4} -1.35361 q^{5} +(1.49264 - 1.94217i) q^{6} +3.92185i q^{7} +(-2.49773 + 1.32716i) q^{8} +(-2.69047 + 1.32716i) q^{9} +(-1.21320 - 1.48076i) q^{10} -1.18569i q^{11} +(3.46242 - 0.107849i) q^{12} +2.28324i q^{13} +(-4.29027 + 3.51504i) q^{14} +(0.532511 + 2.28324i) q^{15} +(-3.69047 - 1.54286i) q^{16} +4.09280i q^{17} +(-3.86322 - 1.75371i) q^{18} -1.00000 q^{19} +(0.532511 - 2.65433i) q^{20} +(6.61532 - 1.54286i) q^{21} +(1.29707 - 1.06270i) q^{22} +3.14615 q^{23} +(3.22124 + 3.69101i) q^{24} -3.16774 q^{25} +(-2.49773 + 2.04640i) q^{26} +(3.29707 + 4.01613i) q^{27} +(-7.69047 - 1.54286i) q^{28} +0.914677 q^{29} +(-2.02045 + 2.62894i) q^{30} +9.16662i q^{31} +(-1.61986 - 5.41997i) q^{32} +(-2.00000 + 0.466451i) q^{33} +(-4.47727 + 3.66826i) q^{34} -5.30865i q^{35} +(-1.54404 - 5.79793i) q^{36} +0.802479i q^{37} +(-0.896270 - 1.09394i) q^{38} +(3.85133 - 0.898230i) q^{39} +(3.38094 - 1.79646i) q^{40} -9.93719i q^{41} +(7.61690 + 5.85393i) q^{42} +5.57360 q^{43} +(2.32505 + 0.466451i) q^{44} +(3.64184 - 1.79646i) q^{45} +(2.81980 + 3.44169i) q^{46} +3.67866 q^{47} +(-1.15064 + 6.83199i) q^{48} -8.38094 q^{49} +(-2.83915 - 3.46532i) q^{50} +(6.90367 - 1.61011i) q^{51} +(-4.47727 - 0.898230i) q^{52} -5.37762 q^{53} +(-1.43834 + 7.20633i) q^{54} +1.60496i q^{55} +(-5.20494 - 9.79572i) q^{56} +(0.393401 + 1.68678i) q^{57} +(0.819797 + 1.00060i) q^{58} +1.72142i q^{59} +(-4.68676 + 0.145985i) q^{60} -8.36415i q^{61} +(-10.0277 + 8.21577i) q^{62} +(-5.20494 - 10.5516i) q^{63} +(4.47727 - 6.62978i) q^{64} -3.09062i q^{65} +(-2.30281 - 1.76981i) q^{66} +12.9545 q^{67} +(-8.02569 - 1.61011i) q^{68} +(-1.23770 - 5.30687i) q^{69} +(5.80734 - 4.75799i) q^{70} +8.04802 q^{71} +(4.95870 - 6.88559i) q^{72} -8.23374 q^{73} +(-0.877863 + 0.719238i) q^{74} +(1.24619 + 5.34330i) q^{75} +(0.393401 - 1.96093i) q^{76} +4.65010 q^{77} +(4.43444 + 3.40807i) q^{78} -4.39540i q^{79} +(4.99545 + 2.08843i) q^{80} +(5.47727 - 7.14139i) q^{81} +(10.8707 - 8.90641i) q^{82} -12.3086i q^{83} +(0.422967 + 13.5791i) q^{84} -5.54005i q^{85} +(4.99545 + 6.09718i) q^{86} +(-0.359835 - 1.54286i) q^{87} +(1.57360 + 2.96153i) q^{88} -1.90493i q^{89} +(5.22929 + 2.37384i) q^{90} -8.95455 q^{91} +(-1.23770 + 6.16937i) q^{92} +(15.4621 - 3.60616i) q^{93} +(3.29707 + 4.02422i) q^{94} +1.35361 q^{95} +(-8.50505 + 4.86458i) q^{96} +6.00000 q^{97} +(-7.51159 - 9.16823i) q^{98} +(1.57360 + 3.19006i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} - 2 q^{4} + 3 q^{6} + 6 q^{9}+O(q^{10}) \) 12 * q - 2 * q^3 - 2 * q^4 + 3 * q^6 + 6 * q^9	\( 12 q - 2 q^{3} - 2 q^{4} + 3 q^{6} + 6 q^{9} - 20 q^{10} + 21 q^{12} - 6 q^{16} - q^{18} - 12 q^{19} - 20 q^{22} + 5 q^{24} + 44 q^{25} + 4 q^{27} - 54 q^{28} - 38 q^{30} - 24 q^{33} - 10 q^{34} - q^{36} - 36 q^{40} + 11 q^{42} + 56 q^{43} + 42 q^{46} + q^{48} - 24 q^{49} + 50 q^{51} - 10 q^{52} - 50 q^{54} + 2 q^{57} + 18 q^{58} - 10 q^{60} + 10 q^{64} + 24 q^{66} + 68 q^{67} + 4 q^{70} - 43 q^{72} - 44 q^{73} + 34 q^{75} + 2 q^{76} + 25 q^{78} + 22 q^{81} + 84 q^{82} + 9 q^{84} + 8 q^{88} - 10 q^{90} - 20 q^{91} + 4 q^{94} - 55 q^{96} + 72 q^{97} + 8 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 - 2 * q^4 + 3 * q^6 + 6 * q^9 - 20 * q^10 + 21 * q^12 - 6 * q^16 - q^18 - 12 * q^19 - 20 * q^22 + 5 * q^24 + 44 * q^25 + 4 * q^27 - 54 * q^28 - 38 * q^30 - 24 * q^33 - 10 * q^34 - q^36 - 36 * q^40 + 11 * q^42 + 56 * q^43 + 42 * q^46 + q^48 - 24 * q^49 + 50 * q^51 - 10 * q^52 - 50 * q^54 + 2 * q^57 + 18 * q^58 - 10 * q^60 + 10 * q^64 + 24 * q^66 + 68 * q^67 + 4 * q^70 - 43 * q^72 - 44 * q^73 + 34 * q^75 + 2 * q^76 + 25 * q^78 + 22 * q^81 + 84 * q^82 + 9 * q^84 + 8 * q^88 - 10 * q^90 - 20 * q^91 + 4 * q^94 - 55 * q^96 + 72 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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