LMFDB - Embedded newform 1050.2.bc.h.943.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(157,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1050.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.bc (of order $12$, degree $4$, 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			943.1
Root			$-0.424637 + 3.22544i$ of defining polynomial
Character	$\chi$	$=$	1050.943
Dual form			1050.2.bc.h.157.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(-2.22701 + 1.42843i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(-2.22701 + 1.42843i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-0.230557 - 0.399337i) q^{11} +(0.965926 - 0.258819i) q^{12} +(4.00275 - 4.00275i) q^{13} +(1.95615 + 1.78142i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.424416 + 1.58394i) q^{17} +(0.258819 - 0.965926i) q^{18} +(-2.91323 + 5.04586i) q^{19} +(2.52083 - 0.803365i) q^{21} +(-0.326057 + 0.326057i) q^{22} +(4.26196 - 1.14199i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-4.90235 - 2.83037i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.21443 - 2.35056i) q^{28} -5.53773i q^{29} +(0.0280956 - 0.0162210i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(0.119345 + 0.445403i) q^{33} +1.63982 q^{34} -1.00000 q^{36} +(-2.08723 - 7.78966i) q^{37} +(5.62793 + 1.50800i) q^{38} +(-4.90235 + 2.83037i) q^{39} -10.9453i q^{41} +(-1.42843 - 2.22701i) q^{42} +(-4.75146 - 4.75146i) q^{43} +(0.399337 + 0.230557i) q^{44} +(-2.20615 - 3.82117i) q^{46} +(8.73220 - 2.33979i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(2.91917 - 6.36227i) q^{49} +(0.819909 - 1.42012i) q^{51} +(-1.46511 + 5.46786i) q^{52} +(-0.710873 + 2.65301i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.58479 - 0.564683i) q^{56} +(4.11993 - 4.11993i) q^{57} +(-5.34903 + 1.43327i) q^{58} +(0.958791 + 1.66067i) q^{59} +(-11.7393 - 6.77768i) q^{61} +(-0.0229400 - 0.0229400i) q^{62} +(-2.64286 + 0.123551i) q^{63} +1.00000i q^{64} +(0.399337 - 0.230557i) q^{66} +(-3.68040 - 0.986161i) q^{67} +(-0.424416 - 1.58394i) q^{68} -4.41231 q^{69} +8.85877 q^{71} +(0.258819 + 0.965926i) q^{72} +(3.91904 + 1.05010i) q^{73} +(-6.98401 + 4.03222i) q^{74} -5.82646i q^{76} +(1.08388 + 0.559993i) q^{77} +(4.00275 + 4.00275i) q^{78} +(-4.38319 - 2.53064i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-10.5723 + 2.83285i) q^{82} +(-1.08813 + 1.08813i) q^{83} +(-1.78142 + 1.95615i) q^{84} +(-3.35979 + 5.81932i) q^{86} +(-1.43327 + 5.34903i) q^{87} +(0.119345 - 0.445403i) q^{88} +(-5.71423 + 9.89734i) q^{89} +(-3.19652 + 14.6318i) q^{91} +(-3.11997 + 3.11997i) q^{92} +(-0.0313366 + 0.00839662i) q^{93} +(-4.52012 - 7.82908i) q^{94} +(0.866025 + 0.500000i) q^{96} +(-2.51799 - 2.51799i) q^{97} +(-6.90101 - 1.17303i) q^{98} -0.461115i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} + 4 q^{11} + 16 q^{13} + 16 q^{14} + 8 q^{16} + 12 q^{17} - 8 q^{19} + 8 q^{21} - 4 q^{22} - 32 q^{23} - 8 q^{24} - 12 q^{26} + 8 q^{28} - 24 q^{31} - 8 q^{33} + 16 q^{34} - 16 q^{36} + 8 q^{37} + 28 q^{38} - 12 q^{39} + 4 q^{42} + 24 q^{43} - 4 q^{46} + 24 q^{47} + 52 q^{49} + 8 q^{51} + 8 q^{52} - 44 q^{53} - 8 q^{54} + 8 q^{56} + 8 q^{57} - 48 q^{58} + 8 q^{59} + 24 q^{61} - 8 q^{62} - 4 q^{63} - 36 q^{67} + 12 q^{68} - 8 q^{69} - 32 q^{71} + 40 q^{73} - 24 q^{74} + 44 q^{77} + 16 q^{78} + 12 q^{79} + 8 q^{81} - 12 q^{82} + 16 q^{83} + 4 q^{84} - 8 q^{86} - 12 q^{87} - 8 q^{88} - 16 q^{89} + 8 q^{91} - 8 q^{92} - 40 q^{93} + 8 q^{94} - 44 q^{97} + 8 q^{98}+O(q^{100}) $ 16 * q + 8 * q^7 + 4 * q^11 + 16 * q^13 + 16 * q^14 + 8 * q^16 + 12 * q^17 - 8 * q^19 + 8 * q^21 - 4 * q^22 - 32 * q^23 - 8 * q^24 - 12 * q^26 + 8 * q^28 - 24 * q^31 - 8 * q^33 + 16 * q^34 - 16 * q^36 + 8 * q^37 + 28 * q^38 - 12 * q^39 + 4 * q^42 + 24 * q^43 - 4 * q^46 + 24 * q^47 + 52 * q^49 + 8 * q^51 + 8 * q^52 - 44 * q^53 - 8 * q^54 + 8 * q^56 + 8 * q^57 - 48 * q^58 + 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 - 36 * q^67 + 12 * q^68 - 8 * q^69 - 32 * q^71 + 40 * q^73 - 24 * q^74 + 44 * q^77 + 16 * q^78 + 12 * q^79 + 8 * q^81 - 12 * q^82 + 16 * q^83 + 4 * q^84 - 8 * q^86 - 12 * q^87 - 8 * q^88 - 16 * q^89 + 8 * q^91 - 8 * q^92 - 40 * q^93 + 8 * q^94 - 44 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$			1.00000i			0.408248i
$7$	−2.22701	+	1.42843i	−0.841732	+	0.539896i
$7$	−2.22701	+	1.42843i	−0.841732	+	0.539896i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$		0			0
$11$	−0.230557	−	0.399337i	−0.0695156	−	0.120405i	0.829173	−	0.558993i	$-0.188812\pi$
$11$	−0.230557	−	0.399337i	−0.0695156	−	0.120405i	−0.898688	+	0.438588i	$0.855479\pi$
$12$	0.965926	−	0.258819i	0.278839	−	0.0747146i
$13$	4.00275	−	4.00275i	1.11016	−	1.11016i	0.117035	−	0.993128i	$-0.462661\pi$
$13$	4.00275	−	4.00275i	1.11016	−	1.11016i	0.993128	−	0.117035i	$-0.0373389\pi$
$14$	1.95615	+	1.78142i	0.522803	+	0.476106i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.424416	+	1.58394i	−0.102936	+	0.384162i	−0.998103	−	0.0615689i	$-0.980390\pi$
$17$	−0.424416	+	1.58394i	−0.102936	+	0.384162i	0.895167	+	0.445731i	$0.147056\pi$
$18$	0.258819	−	0.965926i	0.0610042	−	0.227671i
$19$	−2.91323	+	5.04586i	−0.668341	+	1.15760i	0.310027	+	0.950728i	$0.399662\pi$
$19$	−2.91323	+	5.04586i	−0.668341	+	1.15760i	−0.978368	+	0.206872i	$0.933672\pi$
$20$		0			0
$21$	2.52083	−	0.803365i	0.550091	−	0.175309i
$22$	−0.326057	+	0.326057i	−0.0695156	+	0.0695156i
$23$	4.26196	−	1.14199i	0.888680	−	0.238121i	0.214532	−	0.976717i	$-0.431177\pi$
$23$	4.26196	−	1.14199i	0.888680	−	0.238121i	0.674149	+	0.738596i	$0.264511\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$		0			0
$26$	−4.90235	−	2.83037i	−0.961429	−	0.555081i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	1.21443	−	2.35056i	0.229507	−	0.444215i
$29$		−	5.53773i		−	1.02833i	−0.857691	−	0.514165i	$-0.828102\pi$
$29$		−	5.53773i		−	1.02833i	0.857691	−	0.514165i	$-0.171898\pi$
$30$		0			0
$31$	0.0280956	−	0.0162210i	0.00504612	−	0.00291338i	−0.497475	−	0.867478i	$-0.665739\pi$
$31$	0.0280956	−	0.0162210i	0.00504612	−	0.00291338i	0.502521	+	0.864565i	$0.332406\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	0.119345	+	0.445403i	0.0207753	+	0.0775346i
$34$	1.63982			0.281226
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−2.08723	−	7.78966i	−0.343139	−	1.28061i	−0.894772	−	0.446524i	$-0.852662\pi$
$37$	−2.08723	−	7.78966i	−0.343139	−	1.28061i	0.551633	−	0.834087i	$-0.314005\pi$
$38$	5.62793	+	1.50800i	0.912970	+	0.244630i
$39$	−4.90235	+	2.83037i	−0.785003	+	0.453222i
$40$		0			0
$41$		−	10.9453i		−	1.70937i	−0.519149	−	0.854684i	$-0.673751\pi$
$41$		−	10.9453i		−	1.70937i	0.519149	−	0.854684i	$-0.326249\pi$
$42$	−1.42843	−	2.22701i	−0.220412	−	0.343636i
$43$	−4.75146	−	4.75146i	−0.724591	−	0.724591i	0.244946	−	0.969537i	$-0.421230\pi$
$43$	−4.75146	−	4.75146i	−0.724591	−	0.724591i	−0.969537	+	0.244946i	$0.921230\pi$
$44$	0.399337	+	0.230557i	0.0602023	+	0.0347578i
$45$		0			0
$46$	−2.20615	−	3.82117i	−0.325280	−	0.563401i
$47$	8.73220	−	2.33979i	1.27372	−	0.341293i	0.442266	−	0.896884i	$-0.354175\pi$
$47$	8.73220	−	2.33979i	1.27372	−	0.341293i	0.831456	+	0.555591i	$0.187508\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$	2.91917	−	6.36227i	0.417025	−	0.908895i
$50$		0			0
$51$	0.819909	−	1.42012i	0.114810	−	0.198857i
$52$	−1.46511	+	5.46786i	−0.203174	+	0.758255i
$53$	−0.710873	+	2.65301i	−0.0976459	+	0.364419i	−0.997407	−	0.0719627i	$-0.977074\pi$
$53$	−0.710873	+	2.65301i	−0.0976459	+	0.364419i	0.899761	+	0.436382i	$0.143740\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$		0			0
$56$	−2.58479	−	0.564683i	−0.345407	−	0.0754589i
$57$	4.11993	−	4.11993i	0.545698	−	0.545698i
$58$	−5.34903	+	1.43327i	−0.702362	+	0.188197i
$59$	0.958791	+	1.66067i	0.124824	+	0.216201i	0.921664	−	0.387989i	$-0.126830\pi$
$59$	0.958791	+	1.66067i	0.124824	+	0.216201i	−0.796840	+	0.604190i	$0.793497\pi$
$60$		0			0
$61$	−11.7393	−	6.77768i	−1.50306	−	0.867793i	−0.999994	−	0.00354661i	$-0.998871\pi$
$61$	−11.7393	−	6.77768i	−1.50306	−	0.867793i	−0.503068	−	0.864247i	$-0.667796\pi$
$62$	−0.0229400	−	0.0229400i	−0.00291338	−	0.00291338i
$63$	−2.64286	+	0.123551i	−0.332970	+	0.0155659i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	0.399337	−	0.230557i	0.0491550	−	0.0283796i
$67$	−3.68040	−	0.986161i	−0.449633	−	0.120479i	0.0268948	−	0.999638i	$-0.491438\pi$
$67$	−3.68040	−	0.986161i	−0.449633	−	0.120479i	−0.476528	+	0.879160i	$0.658105\pi$
$68$	−0.424416	−	1.58394i	−0.0514680	−	0.192081i
$69$	−4.41231			−0.531179
$70$		0			0
$71$	8.85877			1.05134			0.525671	−	0.850688i	$-0.323814\pi$
$71$	8.85877			1.05134			0.525671	+	0.850688i	$0.323814\pi$
$72$	0.258819	+	0.965926i	0.0305021	+	0.113835i
$73$	3.91904	+	1.05010i	0.458689	+	0.122905i	0.480762	−	0.876851i	$-0.340360\pi$
$73$	3.91904	+	1.05010i	0.458689	+	0.122905i	−0.0220733	+	0.999756i	$0.507027\pi$
$74$	−6.98401	+	4.03222i	−0.811875	+	0.468736i
$75$		0			0
$76$		−	5.82646i		−	0.668341i
$77$	1.08388	+	0.559993i	0.123519	+	0.0638172i
$78$	4.00275	+	4.00275i	0.453222	+	0.453222i
$79$	−4.38319	−	2.53064i	−0.493148	−	0.284719i	0.232732	−	0.972541i	$-0.425234\pi$
$79$	−4.38319	−	2.53064i	−0.493148	−	0.284719i	−0.725879	+	0.687822i	$0.758567\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−10.5723	+	2.83285i	−1.16752	+	0.312836i
$83$	−1.08813	+	1.08813i	−0.119438	+	0.119438i	−0.764299	−	0.644861i	$-0.776915\pi$
$83$	−1.08813	+	1.08813i	−0.119438	+	0.119438i	0.644861	+	0.764299i	$0.276915\pi$
$84$	−1.78142	+	1.95615i	−0.194369	+	0.213434i
$85$		0			0
$86$	−3.35979	+	5.81932i	−0.362295	+	0.627514i
$87$	−1.43327	+	5.34903i	−0.153663	+	0.573476i
$88$	0.119345	−	0.445403i	0.0127222	−	0.0474801i
$89$	−5.71423	+	9.89734i	−0.605708	+	1.04912i	0.386232	+	0.922402i	$0.373777\pi$
$89$	−5.71423	+	9.89734i	−0.605708	+	1.04912i	−0.991939	+	0.126714i	$0.959557\pi$
$90$		0			0
$91$	−3.19652	+	14.6318i	−0.335087	+	1.53383i
$92$	−3.11997	+	3.11997i	−0.325280	+	0.325280i
$93$	−0.0313366	+	0.00839662i	−0.00324945	+	0.000870688i
$94$	−4.52012	−	7.82908i	−0.466215	−	0.807508i
$95$		0			0
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	−2.51799	−	2.51799i	−0.255663	−	0.255663i	0.567624	−	0.823288i	$-0.307863\pi$
$97$	−2.51799	−	2.51799i	−0.255663	−	0.255663i	−0.823288	+	0.567624i	$0.807863\pi$
$98$	−6.90101	−	1.17303i	−0.697108	−	0.118494i
$99$		−	0.461115i		−	0.0463438i
$100$		0			0
$101$	3.90734	−	2.25590i	0.388795	−	0.224471i	−0.292843	−	0.956161i	$-0.594601\pi$
$101$	3.90734	−	2.25590i	0.388795	−	0.224471i	0.681638	+	0.731690i	$0.261268\pi$
$102$	−1.58394	−	0.424416i	−0.156834	−	0.0420234i
$103$	−3.82414	−	14.2719i	−0.376804	−	1.40625i	−0.850692	−	0.525665i	$-0.823817\pi$
$103$	−3.82414	−	14.2719i	−0.376804	−	1.40625i	0.473888	−	0.880585i	$-0.342850\pi$
$104$	5.66074			0.555081
$105$		0			0
$106$	2.74660			0.266773
$107$	−1.52683	−	5.69821i	−0.147604	−	0.550867i	−0.999626	−	0.0273597i	$-0.991290\pi$
$107$	−1.52683	−	5.69821i	−0.147604	−	0.550867i	0.852021	−	0.523507i	$-0.175377\pi$
$108$	0.965926	+	0.258819i	0.0929463	+	0.0249049i
$109$	14.3923	−	8.30937i	1.37853	−	0.795893i	0.386546	−	0.922270i	$-0.373668\pi$
$109$	14.3923	−	8.30937i	1.37853	−	0.795893i	0.991982	+	0.126377i	$0.0403349\pi$
$110$		0			0
$111$			8.06444i			0.765443i
$112$	0.123551	+	2.64286i	0.0116744	+	0.249727i
$113$	−6.35390	−	6.35390i	−0.597724	−	0.597724i	0.341982	−	0.939706i	$-0.388902\pi$
$113$	−6.35390	−	6.35390i	−0.597724	−	0.597724i	−0.939706	+	0.341982i	$0.888902\pi$
$114$	−5.04586	−	2.91323i	−0.472588	−	0.272849i
$115$		0			0
$116$	2.76886	+	4.79581i	0.257082	+	0.445280i
$117$	5.46786	−	1.46511i	0.505503	−	0.135449i
$118$	1.35593	−	1.35593i	0.124824	−	0.124824i
$119$	−1.31737	−	4.13371i	−0.120763	−	0.378936i
$120$		0			0
$121$	5.39369	−	9.34214i	0.490335	−	0.849285i
$122$	−3.50839	+	13.0935i	−0.317634	+	1.18543i
$123$	−2.83285	+	10.5723i	−0.255430	+	0.953276i
$124$	−0.0162210	+	0.0280956i	−0.00145669	+	0.00252306i
$125$		0			0
$126$	0.803365	+	2.52083i	0.0715694	+	0.224574i
$127$	11.7757	−	11.7757i	1.04493	−	1.04493i	0.0459856	−	0.998942i	$-0.485357\pi$
$127$	11.7757	−	11.7757i	1.04493	−	1.04493i	0.998942	−	0.0459856i	$-0.0146428\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	3.35979	+	5.81932i	0.295813	+	0.512363i
$130$		0			0
$131$	16.4341	+	9.48825i	1.43586	+	0.828992i	0.997558	−	0.0698379i	$-0.0222482\pi$
$131$	16.4341	+	9.48825i	1.43586	+	0.828992i	0.438298	+	0.898830i	$0.355582\pi$
$132$	−0.326057	−	0.326057i	−0.0283796	−	0.0283796i
$133$	−0.719863	−	15.3985i	−0.0624200	−	1.33522i
$134$			3.81023i			0.329154i
$135$		0			0
$136$	−1.42012	+	0.819909i	−0.121775	+	0.0703066i
$137$	−4.27811	−	1.14632i	−0.365503	−	0.0979364i	0.0713928	−	0.997448i	$-0.477256\pi$
$137$	−4.27811	−	1.14632i	−0.365503	−	0.0979364i	−0.436896	+	0.899512i	$0.643922\pi$
$138$	1.14199	+	4.26196i	0.0972126	+	0.362802i
$139$	−4.35020			−0.368979			−0.184489	−	0.982835i	$-0.559063\pi$
$139$	−4.35020			−0.368979			−0.184489	+	0.982835i	$0.559063\pi$
$140$		0			0
$141$	−9.04024			−0.761325
$142$	−2.29282	−	8.55692i	−0.192409	−	0.718080i
$143$	−2.52131	−	0.675582i	−0.210842	−	0.0564950i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$		0			0
$146$		−	4.05729i		−	0.335784i
$147$	−4.46638	+	5.38994i	−0.368381	+	0.444555i
$148$	5.70242	+	5.70242i	0.468736	+	0.468736i
$149$	3.75900	+	2.17026i	0.307949	+	0.177794i	0.646008	−	0.763330i	$-0.276437\pi$
$149$	3.75900	+	2.17026i	0.307949	+	0.177794i	−0.338059	+	0.941125i	$0.609770\pi$
$150$		0			0
$151$	−4.09257	−	7.08854i	−0.333049	−	0.576857i	0.650059	−	0.759884i	$-0.274744\pi$
$151$	−4.09257	−	7.08854i	−0.333049	−	0.576857i	−0.983108	+	0.183026i	$0.941411\pi$
$152$	−5.62793	+	1.50800i	−0.456485	+	0.122315i
$153$	−1.15953	+	1.15953i	−0.0937421	+	0.0937421i
$154$	0.260384	−	1.19188i	0.0209823	−	0.0960447i
$155$		0			0
$156$	2.83037	−	4.90235i	0.226611	−	0.392502i
$157$	−5.63586	+	21.0333i	−0.449790	+	1.67864i	0.253178	+	0.967420i	$0.418524\pi$
$157$	−5.63586	+	21.0333i	−0.449790	+	1.67864i	−0.702969	+	0.711221i	$0.748143\pi$
$158$	−1.30995	+	4.88882i	−0.104214	+	0.388933i
$159$	1.37330	−	2.37863i	0.108910	−	0.188637i
$160$		0			0
$161$	−7.86019	+	8.63114i	−0.619470	+	0.680229i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−11.2769	+	3.02164i	−0.883275	+	0.236673i	−0.671820	−	0.740715i	$-0.734487\pi$
$163$	−11.2769	+	3.02164i	−0.883275	+	0.236673i	−0.211456	+	0.977388i	$0.567820\pi$
$164$	5.47265	+	9.47890i	0.427342	+	0.740178i
$165$		0			0
$166$	1.33268	+	0.769426i	0.103436	+	0.0597190i
$167$	15.5061	+	15.5061i	1.19990	+	1.19990i	0.974196	+	0.225703i	$0.0724679\pi$
$167$	15.5061	+	15.5061i	1.19990	+	1.19990i	0.225703	+	0.974196i	$0.427532\pi$
$168$	2.35056	+	1.21443i	0.181350	+	0.0936957i
$169$		−	19.0440i		−	1.46492i
$170$		0			0
$171$	−5.04586	+	2.91323i	−0.385867	+	0.222780i
$172$	6.49061	+	1.73915i	0.494905	+	0.132609i
$173$	2.52204	+	9.41238i	0.191747	+	0.715610i	0.993085	+	0.117398i	$0.0374553\pi$
$173$	2.52204	+	9.41238i	0.191747	+	0.715610i	−0.801338	+	0.598212i	$0.795878\pi$
$174$	5.53773			0.419814
$175$		0			0
$176$	−0.461115			−0.0347578
$177$	−0.496307	−	1.85224i	−0.0373047	−	0.139223i
$178$	11.0391	+	2.95790i	0.827412	+	0.221704i
$179$	1.39876	−	0.807576i	0.104548	−	0.0603611i	−0.446814	−	0.894627i	$-0.647441\pi$
$179$	1.39876	−	0.807576i	0.104548	−	0.0603611i	0.551363	+	0.834266i	$0.314108\pi$
$180$		0			0
$181$			12.8519i			0.955277i	0.878556	+	0.477639i	$0.158507\pi$
$181$			12.8519i			0.955277i	−0.878556	+	0.477639i	$0.841493\pi$
$182$	14.9606	−	0.699388i	1.10895	−	0.0518421i
$183$	9.58509	+	9.58509i	0.708550	+	0.708550i
$184$	3.82117	+	2.20615i	0.281700	+	0.162640i
$185$		0			0
$186$	0.0162210	+	0.0280956i	0.00118938	+	0.00206007i
$187$	0.730379	−	0.195704i	0.0534106	−	0.0143113i
$188$	−6.39241	+	6.39241i	−0.466215	+	0.466215i
$189$	2.58479	+	0.564683i	0.188016	+	0.0410746i
$190$		0			0
$191$	5.30033	−	9.18043i	0.383518	−	0.664273i	−0.608044	−	0.793903i	$-0.708046\pi$
$191$	5.30033	−	9.18043i	0.383518	−	0.664273i	0.991562	+	0.129630i	$0.0413790\pi$
$192$	0.258819	−	0.965926i	0.0186787	−	0.0697097i
$193$	−1.86766	+	6.97019i	−0.134437	+	0.501726i	0.865563	+	0.500801i	$0.166961\pi$
$193$	−1.86766	+	6.97019i	−0.134437	+	0.501726i	−1.00000		0.000924826i	$0.999706\pi$
$194$	−1.78049	+	3.08389i	−0.127832	+	0.221411i
$195$		0			0
$196$	0.653056	+	6.96947i	0.0466468	+	0.497819i
$197$	9.72803	−	9.72803i	0.693093	−	0.693093i	−0.269818	−	0.962911i	$-0.586964\pi$
$197$	9.72803	−	9.72803i	0.693093	−	0.693093i	0.962911	+	0.269818i	$0.0869635\pi$
$198$	−0.445403	+	0.119345i	−0.0316534	+	0.00848150i
$199$	4.82648	+	8.35971i	0.342140	+	0.592604i	0.984830	−	0.173522i	$-0.0555149\pi$
$199$	4.82648	+	8.35971i	0.342140	+	0.592604i	−0.642690	+	0.766127i	$0.722182\pi$
$200$		0			0
$201$	3.29976	+	1.90512i	0.232747	+	0.134377i
$202$	−3.19033	−	3.19033i	−0.224471	−	0.224471i
$203$	7.91026	+	12.3326i	0.555191	+	0.865578i
$204$			1.63982i			0.114810i
$205$		0			0
$206$	−12.7958	+	7.38767i	−0.891527	+	0.514723i
$207$	4.26196	+	1.14199i	0.296227	+	0.0793737i
$208$	−1.46511	−	5.46786i	−0.101587	−	0.379128i
$209$	2.68667			0.185841
$210$		0			0
$211$	1.33273			0.0917487			0.0458744	−	0.998947i	$-0.485393\pi$
$211$	1.33273			0.0917487			0.0458744	+	0.998947i	$0.485393\pi$
$212$	−0.710873	−	2.65301i	−0.0488229	−	0.182210i
$213$	−8.55692	−	2.29282i	−0.586310	−	0.157101i
$214$	−5.10888	+	2.94961i	−0.349236	+	0.201631i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−0.0393987	+	0.0762571i	−0.00267456	+	0.00517667i
$218$	−11.7512	−	11.7512i	−0.795893	−	0.795893i
$219$	−3.51371	−	2.02864i	−0.237435	−	0.137083i
$220$		0			0
$221$	4.64129	+	8.03895i	0.312207	+	0.540758i
$222$	7.78966	−	2.08723i	0.522807	−	0.140086i
$223$	−8.25284	+	8.25284i	−0.552651	+	0.552651i	−0.927205	−	0.374554i	$-0.877796\pi$
$223$	−8.25284	+	8.25284i	−0.552651	+	0.552651i	0.374554	+	0.927205i	$0.377796\pi$
$224$	2.52083	−	0.803365i	0.168430	−	0.0536771i
$225$		0			0
$226$	−4.49288	+	7.78190i	−0.298862	+	0.517645i
$227$	5.78787	−	21.6006i	0.384154	−	1.43368i	−0.455341	−	0.890317i	$-0.650483\pi$
$227$	5.78787	−	21.6006i	0.384154	−	1.43368i	0.839496	−	0.543367i	$-0.182851\pi$
$228$	−1.50800	+	5.62793i	−0.0998696	+	0.372719i
$229$	2.48311	−	4.30087i	0.164088	−	0.284209i	−0.772243	−	0.635328i	$-0.780865\pi$
$229$	2.48311	−	4.30087i	0.164088	−	0.284209i	0.936331	+	0.351118i	$0.114198\pi$
$230$		0			0
$231$	−0.902010	−	0.821441i	−0.0593479	−	0.0540468i
$232$	3.91576	−	3.91576i	0.257082	−	0.257082i
$233$	27.6582	−	7.41098i	1.81195	−	0.485509i	0.816210	−	0.577756i	$-0.196071\pi$
$233$	27.6582	−	7.41098i	1.81195	−	0.485509i	0.995736	+	0.0922466i	$0.0294048\pi$
$234$	−2.83037	−	4.90235i	−0.185027	−	0.320476i
$235$		0			0
$236$	−1.66067	−	0.958791i	−0.108101	−	0.0624120i
$237$	3.57886	+	3.57886i	0.232472	+	0.232472i
$238$	−3.65189	+	2.34237i	−0.236717	+	0.151833i
$239$		−	13.9230i		−	0.900603i	−0.892877	−	0.450302i	$-0.851316\pi$
$239$		−	13.9230i		−	0.900603i	0.892877	−	0.450302i	$-0.148684\pi$
$240$		0			0
$241$	0.915881	−	0.528784i	0.0589971	−	0.0340620i	−0.470211	−	0.882554i	$-0.655822\pi$
$241$	0.915881	−	0.528784i	0.0589971	−	0.0340620i	0.529208	+	0.848492i	$0.322489\pi$
$242$	−10.4198	−	2.79198i	−0.669810	−	0.179475i
$243$	−0.258819	−	0.965926i	−0.0166032	−	0.0619642i
$244$	13.5554			0.867793
$245$		0			0
$246$	10.9453			0.697847
$247$	8.53639	+	31.8582i	0.543157	+	2.02709i
$248$	0.0313366	+	0.00839662i	0.00198988	+	0.000533186i
$249$	1.33268	−	0.769426i	0.0844554	−	0.0487604i
$250$		0			0
$251$			6.36260i			0.401604i	0.979632	+	0.200802i	$0.0643548\pi$
$251$			6.36260i			0.401604i	−0.979632	+	0.200802i	$0.935645\pi$
$252$	2.22701	−	1.42843i	0.140289	−	0.0899827i
$253$	−1.43866	−	1.43866i	−0.0904481	−	0.0904481i
$254$	−14.4223	−	8.32670i	−0.904934	−	0.522464i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.0273	+	2.68681i	−0.625488	+	0.167599i	−0.557621	−	0.830096i	$-0.688286\pi$
$257$	−10.0273	+	2.68681i	−0.625488	+	0.167599i	−0.0678664	+	0.997694i	$0.521619\pi$
$258$	4.75146	−	4.75146i	0.295813	−	0.295813i
$259$	15.7753	+	14.3662i	0.980228	+	0.892672i
$260$		0			0
$261$	2.76886	−	4.79581i	0.171388	−	0.296853i
$262$	4.91148	−	18.3299i	0.303432	−	1.13242i
$263$	−6.15005	+	22.9523i	−0.379228	+	1.41530i	0.467839	+	0.883814i	$0.345033\pi$
$263$	−6.15005	+	22.9523i	−0.379228	+	1.41530i	−0.847067	+	0.531486i	$0.821634\pi$
$264$	−0.230557	+	0.399337i	−0.0141898	+	0.0245775i
$265$		0			0
$266$	−14.6875	+	4.68077i	−0.900551	+	0.286996i
$267$	8.08115	−	8.08115i	0.494558	−	0.494558i
$268$	3.68040	−	0.986161i	0.224816	−	0.0602394i
$269$	−0.710036	−	1.22982i	−0.0432917	−	0.0749834i	0.843568	−	0.537023i	$-0.180451\pi$
$269$	−0.710036	−	1.22982i	−0.0432917	−	0.0749834i	−0.886859	+	0.462040i	$0.847118\pi$
$270$		0			0
$271$	−0.306228	−	0.176801i	−0.0186020	−	0.0107399i	0.490670	−	0.871345i	$-0.336752\pi$
$271$	−0.306228	−	0.176801i	−0.0186020	−	0.0107399i	−0.509272	+	0.860606i	$0.670085\pi$
$272$	1.15953	+	1.15953i	0.0703066	+	0.0703066i
$273$	6.87460	−	13.3059i	0.416070	−	0.805312i
$274$			4.42902i			0.267567i
$275$		0			0
$276$	3.82117	−	2.20615i	0.230007	−	0.132795i
$277$	−22.7009	−	6.08269i	−1.36397	−	0.365474i	−0.498695	−	0.866778i	$-0.666187\pi$
$277$	−22.7009	−	6.08269i	−1.36397	−	0.365474i	−0.865271	+	0.501304i	$0.832854\pi$
$278$	1.12591	+	4.20197i	0.0675278	+	0.252017i
$279$	0.0324420			0.00194225
$280$		0			0
$281$	28.4747			1.69866			0.849330	−	0.527862i	$-0.177006\pi$
$281$	28.4747			1.69866			0.849330	+	0.527862i	$0.177006\pi$
$282$	2.33979	+	8.73220i	0.139332	+	0.519995i
$283$	3.62984	+	0.972612i	0.215771	+	0.0578158i	0.365085	−	0.930974i	$-0.381040\pi$
$283$	3.62984	+	0.972612i	0.215771	+	0.0578158i	−0.149314	+	0.988790i	$0.547706\pi$
$284$	−7.67192	+	4.42939i	−0.455245	+	0.262836i
$285$		0			0
$286$			2.61025i			0.154347i
$287$	15.6346	+	24.3753i	0.922881	+	1.43883i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$	12.3937	+	7.15550i	0.729041	+	0.420912i
$290$		0			0
$291$	1.78049	+	3.08389i	0.104374	+	0.180781i
$292$	−3.91904	+	1.05010i	−0.229344	+	0.0614527i
$293$	−4.18500	+	4.18500i	−0.244490	+	0.244490i	−0.818705	−	0.574215i	$-0.805308\pi$
$293$	−4.18500	+	4.18500i	−0.244490	+	0.244490i	0.574215	+	0.818705i	$0.305308\pi$
$294$	6.36227	+	2.91917i	0.371055	+	0.170250i
$295$		0			0
$296$	4.03222	−	6.98401i	0.234368	−	0.405938i
$297$	−0.119345	+	0.445403i	−0.00692511	+	0.0258449i
$298$	1.12341	−	4.19262i	0.0650773	−	0.242872i
$299$	12.4885	−	21.6307i	0.722226	−	1.25093i
$300$		0			0
$301$	17.3687	+	3.79443i	1.00111	+	0.218707i
$302$	−5.78777	+	5.78777i	−0.333049	+	0.333049i
$303$	−4.35807	+	1.16774i	−0.250365	+	0.0670850i
$304$	2.91323	+	5.04586i	0.167085	+	0.289400i
$305$		0			0
$306$	1.42012	+	0.819909i	0.0811831	+	0.0468711i
$307$	−18.0884	−	18.0884i	−1.03236	−	1.03236i	−0.999459	−	0.0329031i	$-0.989525\pi$
$307$	−18.0884	−	18.0884i	−1.03236	−	1.03236i	−0.0329031	−	0.999459i	$-0.510475\pi$
$308$	−1.21866	+	0.0569710i	−0.0694398	+	0.00324623i
$309$			14.7753i			0.840540i
$310$		0			0
$311$	−29.1137	+	16.8088i	−1.65089	+	0.953139i	−0.674177	+	0.738569i	$0.735502\pi$
$311$	−29.1137	+	16.8088i	−1.65089	+	0.953139i	−0.976709	+	0.214570i	$0.931165\pi$
$312$	−5.46786	−	1.46511i	−0.309556	−	0.0829454i
$313$	−5.94363	−	22.1819i	−0.335954	−	1.25380i	−0.902831	−	0.429995i	$-0.858515\pi$
$313$	−5.94363	−	22.1819i	−0.335954	−	1.25380i	0.566877	−	0.823802i	$-0.308151\pi$
$314$	21.7753			1.22885
$315$		0			0
$316$	5.06128			0.284719
$317$	−6.63663	−	24.7683i	−0.372751	−	1.39112i	−0.856604	−	0.515975i	$-0.827430\pi$
$317$	−6.63663	−	24.7683i	−0.372751	−	1.39112i	0.483853	−	0.875149i	$-0.339237\pi$
$318$	−2.65301	−	0.710873i	−0.148774	−	0.0398638i
$319$	−2.21142	+	1.27676i	−0.123816	+	0.0714850i
$320$		0			0
$321$			5.89922i			0.329262i
$322$	10.3714	+	5.35846i	0.577976	+	0.298615i
$323$	−6.75593	−	6.75593i	−0.375910	−	0.375910i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$		0			0
$326$	5.83736	+	10.1106i	0.323301	+	0.559974i
$327$	−16.0525	+	4.30125i	−0.887704	+	0.237860i
$328$	7.73949	−	7.73949i	0.427342	−	0.427342i
$329$	−16.1045	+	17.6841i	−0.887870	+	0.974955i
$330$		0			0
$331$	5.93242	−	10.2753i	0.326076	−	0.564779i	−0.655654	−	0.755062i	$-0.727607\pi$
$331$	5.93242	−	10.2753i	0.326076	−	0.564779i	0.981729	+	0.190282i	$0.0609403\pi$
$332$	0.398284	−	1.48642i	0.0218587	−	0.0815777i
$333$	2.08723	−	7.78966i	0.114380	−	0.426870i
$334$	10.9645	−	18.9910i	0.599950	−	1.03914i
$335$		0			0
$336$	0.564683	−	2.58479i	0.0308060	−	0.141012i
$337$	3.18746	−	3.18746i	0.173632	−	0.173632i	−0.614941	−	0.788573i	$-0.710820\pi$
$337$	3.18746	−	3.18746i	0.173632	−	0.173632i	0.788573	+	0.614941i	$0.210820\pi$
$338$	−18.3951	+	4.92895i	−1.00056	+	0.268099i
$339$	4.49288	+	7.78190i	0.244020	+	0.422655i
$340$		0			0
$341$	−0.0129553	−	0.00747975i	−0.000701569	−	0.000405051i
$342$	4.11993	+	4.11993i	0.222780	+	0.222780i
$343$	2.58702	+	18.3387i	0.139686	+	0.990196i
$344$		−	6.71958i		−	0.362295i
$345$		0			0
$346$	8.43891	−	4.87221i	0.453679	−	0.261931i
$347$	−20.6922	−	5.54445i	−1.11081	−	0.297642i	−0.343653	−	0.939097i	$-0.611664\pi$
$347$	−20.6922	−	5.54445i	−1.11081	−	0.297642i	−0.767161	+	0.641455i	$0.778331\pi$
$348$	−1.43327	−	5.34903i	−0.0768313	−	0.286738i
$349$	−16.0682			−0.860113			−0.430056	−	0.902802i	$-0.641506\pi$
$349$	−16.0682			−0.860113			−0.430056	+	0.902802i	$0.641506\pi$
$350$		0			0
$351$	−5.66074			−0.302148
$352$	0.119345	+	0.445403i	0.00636112	+	0.0237400i
$353$	28.3943	+	7.60823i	1.51128	+	0.404945i	0.916859	−	0.399211i	$-0.130716\pi$
$353$	28.3943	+	7.60823i	1.51128	+	0.404945i	0.594418	+	0.804156i	$0.297383\pi$
$354$	−1.66067	+	0.958791i	−0.0882638	+	0.0509592i
$355$		0			0
$356$		−	11.4285i		−	0.605708i
$357$	0.202601	+	4.33382i	0.0107228	+	0.229370i
$358$	−1.14209	−	1.14209i	−0.0603611	−	0.0603611i
$359$	−11.8017	−	6.81369i	−0.622868	−	0.359613i	0.155117	−	0.987896i	$-0.450425\pi$
$359$	−11.8017	−	6.81369i	−0.622868	−	0.359613i	−0.777985	+	0.628283i	$0.783758\pi$
$360$		0			0
$361$	−7.47381	−	12.9450i	−0.393359	−	0.681317i
$362$	12.4140	−	3.32633i	0.652466	−	0.174828i
$363$	−7.62782	+	7.62782i	−0.400357	+	0.400357i
$364$	−4.54764	−	14.2698i	−0.238361	−	0.747940i
$365$		0			0
$366$	6.77768	−	11.7393i	0.354275	−	0.613622i
$367$	−3.30230	+	12.3244i	−0.172379	+	0.643326i	0.824605	+	0.565709i	$0.191398\pi$
$367$	−3.30230	+	12.3244i	−0.172379	+	0.643326i	−0.996983	+	0.0776164i	$0.975269\pi$
$368$	1.14199	−	4.26196i	0.0595303	−	0.222170i
$369$	5.47265	−	9.47890i	0.284895	−	0.493452i
$370$		0			0
$371$	−2.20652	−	6.92373i	−0.114557	−	0.359462i
$372$	0.0229400	−	0.0229400i	0.00118938	−	0.00118938i
$373$	3.86501	−	1.03563i	0.200123	−	0.0536227i	−0.157365	−	0.987540i	$-0.550300\pi$
$373$	3.86501	−	1.03563i	0.200123	−	0.0536227i	0.357488	+	0.933918i	$0.383633\pi$
$374$	−0.378072	−	0.654840i	−0.0195496	−	0.0338610i
$375$		0			0
$376$	7.82908	+	4.52012i	0.403754	+	0.233107i
$377$	−22.1661	−	22.1661i	−1.14161	−	1.14161i
$378$	−0.123551	−	2.64286i	−0.00635476	−	0.135934i
$379$		−	1.00281i		−	0.0515109i	−0.999668	−	0.0257555i	$-0.991801\pi$
$379$		−	1.00281i		−	0.0515109i	0.999668	−	0.0257555i	$-0.00819912\pi$
$380$		0			0
$381$	−14.4223	+	8.32670i	−0.738875	+	0.426590i
$382$	−10.2394	−	2.74365i	−0.523895	−	0.140377i
$383$	4.60780	+	17.1965i	0.235447	+	0.878702i	0.977947	+	0.208855i	$0.0669737\pi$
$383$	4.60780	+	17.1965i	0.235447	+	0.878702i	−0.742499	+	0.669847i	$0.766360\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	7.21608			0.367289
$387$	−1.73915	−	6.49061i	−0.0884062	−	0.329936i
$388$	3.43964	+	0.921648i	0.174621	+	0.0467896i
$389$	−9.75032	+	5.62935i	−0.494361	+	0.285419i	−0.726382	−	0.687291i	$-0.758800\pi$
$389$	−9.75032	+	5.62935i	−0.494361	+	0.285419i	0.232021	+	0.972711i	$0.425466\pi$
$390$		0			0
$391$			7.23538i			0.365909i
$392$	6.56297	−	2.43463i	0.331480	−	0.122968i
$393$	−13.4184	−	13.4184i	−0.676869	−	0.676869i
$394$	−11.9144	−	6.87875i	−0.600236	−	0.346547i
$395$		0			0
$396$	0.230557	+	0.399337i	0.0115859	+	0.0200674i
$397$	3.70224	−	0.992011i	0.185810	−	0.0497876i	−0.164714	−	0.986341i	$-0.552670\pi$
$397$	3.70224	−	0.992011i	0.185810	−	0.0497876i	0.350524	+	0.936554i	$0.386003\pi$
$398$	6.82567	−	6.82567i	0.342140	−	0.342140i
$399$	−3.29010	+	15.0602i	−0.164711	+	0.753951i
$400$		0			0
$401$	−0.450022	+	0.779461i	−0.0224730	+	0.0389244i	−0.877043	−	0.480412i	$-0.840487\pi$
$401$	−0.450022	+	0.779461i	−0.0224730	+	0.0389244i	0.854570	+	0.519336i	$0.173821\pi$
$402$	0.986161	−	3.68040i	0.0491852	−	0.183562i
$403$	0.0475311	−	0.177388i	0.00236769	−	0.00883634i
$404$	−2.25590	+	3.90734i	−0.112235	+	0.194397i
$405$		0			0
$406$	9.86504	−	10.8326i	0.489594	−	0.537614i
$407$	−2.62947	+	2.62947i	−0.130338	+	0.130338i
$408$	1.58394	−	0.424416i	0.0784168	−	0.0210117i
$409$	6.44633	+	11.1654i	0.318751	+	0.552092i	0.980228	−	0.197873i	$-0.0634034\pi$
$409$	6.44633	+	11.1654i	0.318751	+	0.552092i	−0.661477	+	0.749965i	$0.730070\pi$
$410$		0			0
$411$	3.83565	+	2.21451i	0.189199	+	0.109234i
$412$	10.4477	+	10.4477i	0.514723	+	0.514723i
$413$	−4.50740	−	2.32878i	−0.221795	−	0.114592i
$414$		−	4.41231i		−	0.216853i
$415$		0			0
$416$	−4.90235	+	2.83037i	−0.240357	+	0.138770i
$417$	4.20197	+	1.12591i	0.205771	+	0.0551362i
$418$	−0.695360	−	2.59512i	−0.0340112	−	0.126931i
$419$	−19.8918			−0.971777			−0.485888	−	0.874021i	$-0.661504\pi$
$419$	−19.8918			−0.971777			−0.485888	+	0.874021i	$0.661504\pi$
$420$		0			0
$421$	−12.6339			−0.615740			−0.307870	−	0.951428i	$-0.599616\pi$
$421$	−12.6339			−0.615740			−0.307870	+	0.951428i	$0.599616\pi$
$422$	−0.344935	−	1.28732i	−0.0167912	−	0.0626655i
$423$	8.73220	+	2.33979i	0.424574	+	0.113764i
$424$	−2.37863	+	1.37330i	−0.115516	+	0.0666934i
$425$		0			0
$426$			8.85877i			0.429209i
$427$	35.8250	−	1.67477i	1.73369	−	0.0810480i
$428$	4.17138	+	4.17138i	0.201631	+	0.201631i
$429$	2.26054	+	1.30513i	0.109140	+	0.0630120i
$430$		0			0
$431$	−15.3851	−	26.6477i	−0.741073	−	1.28358i	−0.952007	−	0.306075i	$-0.900984\pi$
$431$	−15.3851	−	26.6477i	−0.741073	−	1.28358i	0.210935	−	0.977500i	$-0.432349\pi$
$432$	−0.965926	+	0.258819i	−0.0464731	+	0.0124524i
$433$	−3.04743	+	3.04743i	−0.146450	+	0.146450i	−0.776530	−	0.630080i	$-0.783022\pi$
$433$	−3.04743	+	3.04743i	−0.146450	+	0.146450i	0.630080	+	0.776530i	$0.283022\pi$
$434$	0.0838558	+	0.0183195i	0.00402521	+	0.000879362i
$435$		0			0
$436$	−8.30937	+	14.3923i	−0.397947	+	0.689264i
$437$	−6.65375	+	24.8321i	−0.318292	+	1.18788i
$438$	−1.05010	+	3.91904i	−0.0501759	+	0.187259i
$439$	−18.4993	+	32.0418i	−0.882926	+	1.52927i	−0.0348530	+	0.999392i	$0.511096\pi$
$439$	−18.4993	+	32.0418i	−0.882926	+	1.52927i	−0.848073	+	0.529880i	$0.822237\pi$
$440$		0			0
$441$	5.70921	−	4.05030i	0.271867	−	0.192871i
$442$	6.56378	−	6.56378i	0.312207	−	0.312207i
$443$	−17.1911	+	4.60633i	−0.816773	+	0.218854i	−0.642935	−	0.765921i	$-0.722283\pi$
$443$	−17.1911	+	4.60633i	−0.816773	+	0.218854i	−0.173838	+	0.984774i	$0.555617\pi$
$444$	−4.03222	−	6.98401i	−0.191361	−	0.331447i
$445$		0			0
$446$	10.1076	+	5.83564i	0.478610	+	0.276326i
$447$	−3.06921	−	3.06921i	−0.145169	−	0.145169i
$448$	−1.42843	−	2.22701i	−0.0674870	−	0.105216i
$449$		−	2.41945i		−	0.114181i	−0.998369	−	0.0570904i	$-0.981818\pi$
$449$		−	2.41945i		−	0.114181i	0.998369	−	0.0570904i	$-0.0181823\pi$
$450$		0			0
$451$	−4.37086	+	2.52352i	−0.205816	+	0.118828i
$452$	8.67959	+	2.32569i	0.408253	+	0.109391i
$453$	2.11847	+	7.90624i	0.0995345	+	0.371468i
$454$	−22.3626			−1.04953
$455$		0			0
$456$	5.82646			0.272849
$457$	7.13275	+	26.6198i	0.333656	+	1.24522i	0.905319	+	0.424732i	$0.139632\pi$
$457$	7.13275	+	26.6198i	0.333656	+	1.24522i	−0.571663	+	0.820488i	$0.693702\pi$
$458$	−4.79700	−	1.28535i	−0.224149	−	0.0600605i
$459$	1.42012	−	0.819909i	0.0662857	−	0.0382701i
$460$		0			0
$461$		−	1.02712i		−	0.0478378i	−0.999714	−	0.0239189i	$-0.992386\pi$
$461$		−	1.02712i		−	0.0478378i	0.999714	−	0.0239189i	$-0.00761434\pi$
$462$	−0.559993	+	1.08388i	−0.0260533	+	0.0504266i
$463$	8.26507	+	8.26507i	0.384111	+	0.384111i	0.872581	−	0.488470i	$-0.162445\pi$
$463$	8.26507	+	8.26507i	0.384111	+	0.384111i	−0.488470	+	0.872581i	$0.662445\pi$
$464$	−4.79581	−	2.76886i	−0.222640	−	0.128541i
$465$		0			0
$466$	−14.3169	−	24.7976i	−0.663218	−	1.14873i
$467$	17.9129	−	4.79974i	0.828910	−	0.222106i	0.180672	−	0.983543i	$-0.442173\pi$
$467$	17.9129	−	4.79974i	0.828910	−	0.222106i	0.648238	+	0.761438i	$0.275506\pi$
$468$	−4.00275	+	4.00275i	−0.185027	+	0.185027i
$469$	9.60497	−	3.06101i	0.443516	−	0.141344i
$470$		0			0
$471$	10.8876	−	18.8579i	0.501676	−	0.868928i
$472$	−0.496307	+	1.85224i	−0.0228444	+	0.0852563i
$473$	−0.801949	+	2.99292i	−0.0368737	+	0.137614i
$474$	2.53064	−	4.38319i	0.116236	−	0.201327i
$475$		0			0
$476$	3.20773	+	2.92121i	0.147026	+	0.133893i
$477$	−1.94214	+	1.94214i	−0.0889245	+	0.0889245i
$478$	−13.4486	+	3.60353i	−0.615123	+	0.164822i
$479$	4.23872	+	7.34168i	0.193672	+	0.335450i	0.946464	−	0.322808i	$-0.104627\pi$
$479$	4.23872	+	7.34168i	0.193672	+	0.335450i	−0.752792	+	0.658258i	$0.771294\pi$
$480$		0			0
$481$	−39.5347	−	22.8254i	−1.80263	−	1.04075i
$482$	−0.747813	−	0.747813i	−0.0340620	−	0.0340620i
$483$	9.82626	−	6.30267i	0.447110	−	0.286782i
$484$			10.7874i			0.490335i
$485$		0			0
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	−4.69084	−	1.25691i	−0.212562	−	0.0569558i	0.150967	−	0.988539i	$-0.451761\pi$
$487$	−4.69084	−	1.25691i	−0.212562	−	0.0569558i	−0.363529	+	0.931583i	$0.618428\pi$
$488$	−3.50839	−	13.0935i	−0.158817	−	0.592714i
$489$	11.6747			0.527949
$490$		0			0
$491$	−37.8594			−1.70857			−0.854286	−	0.519803i	$-0.826005\pi$
$491$	−37.8594			−1.70857			−0.854286	+	0.519803i	$0.826005\pi$
$492$	−2.83285	−	10.5723i	−0.127715	−	0.476638i
$493$	8.77144	+	2.35030i	0.395046	+	0.105852i
$494$	28.5633	−	16.4910i	1.28512	−	0.741967i
$495$		0			0
$496$		−	0.0324420i		−	0.00145669i
$497$	−19.7286	+	12.6541i	−0.884949	+	0.567616i
$498$	−1.08813	−	1.08813i	−0.0487604	−	0.0487604i
$499$	−0.443575	−	0.256098i	−0.0198571	−	0.0114645i	0.490039	−	0.871701i	$-0.336983\pi$
$499$	−0.443575	−	0.256098i	−0.0198571	−	0.0114645i	−0.509896	+	0.860236i	$0.670316\pi$
$500$		0			0
$501$	−10.9645	−	18.9910i	−0.489857	−	0.848457i
$502$	6.14580	−	1.64676i	0.274301	−	0.0734986i
$503$	8.58209	−	8.58209i	0.382657	−	0.382657i	−0.489402	−	0.872058i	$-0.662785\pi$
$503$	8.58209	−	8.58209i	0.382657	−	0.382657i	0.872058	+	0.489402i	$0.162785\pi$
$504$	−1.95615	−	1.78142i	−0.0871339	−	0.0793509i
$505$		0			0
$506$	−1.01729	+	1.76200i	−0.0452240	+	0.0783303i
$507$	−4.92895	+	18.3951i	−0.218902	+	0.816954i
$508$	−4.31022	+	16.0860i	−0.191235	+	0.713699i
$509$	5.69382	−	9.86199i	0.252374	−	0.437125i	−0.711805	−	0.702377i	$-0.752122\pi$
$509$	5.69382	−	9.86199i	0.252374	−	0.437125i	0.964179	+	0.265252i	$0.0854553\pi$
$510$		0			0
$511$	−10.2278	+	3.25948i	−0.452449	+	0.144191i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	5.62793	−	1.50800i	0.248479	−	0.0665798i
$514$	5.19053	+	8.99026i	0.228944	+	0.396543i
$515$		0			0
$516$	−5.81932	−	3.35979i	−0.256181	−	0.147906i
$517$	−2.94764	−	2.94764i	−0.129637	−	0.129637i
$518$	9.79374	−	18.9560i	0.430312	−	0.832878i
$519$		−	9.74441i		−	0.427732i
$520$		0			0
$521$	16.8886	−	9.75063i	0.739902	−	0.427183i	−0.0821316	−	0.996621i	$-0.526173\pi$
$521$	16.8886	−	9.75063i	0.739902	−	0.427183i	0.822034	+	0.569439i	$0.192839\pi$
$522$	−5.34903	−	1.43327i	−0.234121	−	0.0627325i
$523$	3.85439	+	14.3848i	0.168541	+	0.629003i	0.997562	+	0.0697859i	$0.0222316\pi$
$523$	3.85439	+	14.3848i	0.168541	+	0.629003i	−0.829021	+	0.559217i	$0.811102\pi$
$524$	−18.9765			−0.828992
$525$		0			0
$526$	23.7620			1.03607
$527$	0.0137689	+	0.0513863i	0.000599783	+	0.00223842i
$528$	0.445403	+	0.119345i	0.0193837	+	0.00519383i
$529$	−3.05841	+	1.76577i	−0.132974	+	0.0767728i
$530$		0			0
$531$			1.91758i			0.0832159i
$532$	8.32269	+	12.9756i	0.360834	+	0.562564i
$533$	−43.8113	−	43.8113i	−1.89768	−	1.89768i
$534$	−9.89734	−	5.71423i	−0.428300	−	0.247279i
$535$		0			0
$536$	−1.90512	−	3.29976i	−0.0822885	−	0.142528i
$537$	−1.56012	+	0.418032i	−0.0673241	+	0.0180394i
$538$	−1.00414	+	1.00414i	−0.0432917	+	0.0432917i
$539$	−3.21372	+	0.301133i	−0.138425	+	0.0129707i
$540$		0			0
$541$	−21.9060	+	37.9422i	−0.941810	+	1.63126i	−0.179796	+	0.983704i	$0.557544\pi$
$541$	−21.9060	+	37.9422i	−0.941810	+	1.63126i	−0.762015	+	0.647559i	$0.775790\pi$
$542$	−0.0915187	+	0.341553i	−0.00393107	+	0.0146709i
$543$	3.32633	−	12.4140i	0.142746	−	0.532737i
$544$	0.819909	−	1.42012i	0.0351533	−	0.0608873i
$545$		0			0
$546$	−14.6318	−	3.19652i	−0.626184	−	0.136799i
$547$	−8.59346	+	8.59346i	−0.367430	+	0.367430i	−0.866539	−	0.499109i	$-0.833661\pi$
$547$	−8.59346	+	8.59346i	−0.367430	+	0.367430i	0.499109	+	0.866539i	$0.333661\pi$
$548$	4.27811	−	1.14632i	0.182752	−	0.0489682i
$549$	−6.77768	−	11.7393i	−0.289264	−	0.501021i
$550$		0			0
$551$	27.9426	+	16.1327i	1.19039	+	0.687275i
$552$	−3.11997	−	3.11997i	−0.132795	−	0.132795i
$553$	13.3763	−	0.625324i	0.568817	−	0.0265915i
$554$			23.5017i			0.998492i
$555$		0			0
$556$	3.76738	−	2.17510i	0.159772	−	0.0922447i
$557$	8.24166	+	2.20835i	0.349210	+	0.0935706i	0.429160	−	0.903228i	$-0.358809\pi$
$557$	8.24166	+	2.20835i	0.349210	+	0.0935706i	−0.0799502	+	0.996799i	$0.525476\pi$
$558$	−0.00839662	−	0.0313366i	−0.000355457	−	0.00132658i
$559$	−38.0378			−1.60883
$560$		0			0
$561$	−0.756144			−0.0319244
$562$	−7.36980	−	27.5045i	−0.310876	−	1.16021i
$563$	0.136431	+	0.0365566i	0.00574988	+	0.00154068i	0.261693	−	0.965151i	$-0.415719\pi$
$563$	0.136431	+	0.0365566i	0.00574988	+	0.00154068i	−0.255943	+	0.966692i	$0.582386\pi$
$564$	7.82908	−	4.52012i	0.329664	−	0.190331i
$565$		0			0
$566$		−	3.75788i		−	0.157956i
$567$	−2.35056	−	1.21443i	−0.0987144	−	0.0510015i
$568$	6.26410	+	6.26410i	0.262836	+	0.262836i
$569$	3.62902	+	2.09521i	0.152136	+	0.0878359i	0.574136	−	0.818760i	$-0.305338\pi$
$569$	3.62902	+	2.09521i	0.152136	+	0.0878359i	−0.421999	+	0.906596i	$0.638672\pi$
$570$		0			0
$571$	4.89756	+	8.48282i	0.204957	+	0.354995i	0.950119	−	0.311888i	$-0.100961\pi$
$571$	4.89756	+	8.48282i	0.204957	+	0.354995i	−0.745162	+	0.666883i	$0.767628\pi$
$572$	2.52131	−	0.675582i	0.105421	−	0.0282475i
$573$	−7.49579	+	7.49579i	−0.313141	+	0.313141i
$574$	19.4982	−	21.4107i	0.813840	−	0.893663i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−2.10542	+	7.85753i	−0.0876498	+	0.327113i	−0.995803	−	0.0915250i	$-0.970826\pi$
$577$	−2.10542	+	7.85753i	−0.0876498	+	0.327113i	0.908153	+	0.418638i	$0.137493\pi$
$578$	3.70396	−	13.8234i	0.154064	−	0.574976i
$579$	3.60804	−	6.24930i	0.149945	−	0.259712i
$580$		0			0
$581$	0.868963	−	3.97761i	0.0360507	−	0.165019i
$582$	2.51799	−	2.51799i	0.104374	−	0.104374i
$583$	1.22334	−	0.327794i	0.0506657	−	0.0135758i
$584$	2.02864	+	3.51371i	0.0839459	+	0.145399i
$585$		0			0
$586$	5.12556	+	2.95924i	0.211735	+	0.122245i
$587$	−20.3618	−	20.3618i	−0.840423	−	0.840423i	0.148491	−	0.988914i	$-0.452558\pi$
$587$	−20.3618	−	20.3618i	−0.840423	−	0.840423i	−0.988914	+	0.148491i	$0.952558\pi$
$588$	1.17303	−	6.90101i	0.0483749	−	0.284593i
$589$			0.189022i			0.00778852i
$590$		0			0
$591$	−11.9144	+	6.87875i	−0.490091	+	0.282954i
$592$	−7.78966	−	2.08723i	−0.320153	−	0.0857847i
$593$	−4.85990	−	18.1374i	−0.199572	−	0.744814i	−0.991036	−	0.133597i	$-0.957347\pi$
$593$	−4.85990	−	18.1374i	−0.199572	−	0.744814i	0.791463	−	0.611217i	$-0.209320\pi$
$594$	0.461115			0.0189198
$595$		0			0
$596$	−4.34052			−0.177794
$597$	−2.49837	−	9.32405i	−0.102251	−	0.381608i
$598$	−24.1259	−	6.46450i	−0.986580	−	0.264353i
$599$	−21.0442	+	12.1499i	−0.859844	+	0.496431i	−0.863960	−	0.503561i	$-0.832023\pi$
$599$	−21.0442	+	12.1499i	−0.859844	+	0.496431i	0.00411624	+	0.999992i	$0.498690\pi$
$600$		0			0
$601$		−	21.1930i		−	0.864481i	−0.901758	−	0.432241i	$-0.857723\pi$
$601$		−	21.1930i		−	0.864481i	0.901758	−	0.432241i	$-0.142277\pi$
$602$	−0.830208	−	17.7589i	−0.0338368	−	0.723800i
$603$	−2.69424	−	2.69424i	−0.109718	−	0.109718i
$604$	7.08854	+	4.09257i	0.288429	+	0.166524i
$605$		0			0
$606$	2.25590	+	3.90734i	0.0916398	+	0.158725i
$607$	−9.20949	+	2.46768i	−0.373802	+	0.100160i	−0.440829	−	0.897591i	$-0.645315\pi$
$607$	−9.20949	+	2.46768i	−0.373802	+	0.100160i	0.0670268	+	0.997751i	$0.478649\pi$
$608$	4.11993	−	4.11993i	0.167085	−	0.167085i
$609$	−4.44881	−	13.9597i	−0.180275	−	0.565675i
$610$		0			0
$611$	25.5872	−	44.3184i	1.03515	−	1.79293i
$612$	0.424416	−	1.58394i	0.0171560	−	0.0640271i
$613$	5.77664	−	21.5587i	0.233316	−	0.870748i	−0.745585	−	0.666411i	$-0.767830\pi$
$613$	5.77664	−	21.5587i	0.233316	−	0.870748i	0.978901	−	0.204337i	$-0.0655037\pi$
$614$	−12.7905	+	22.1537i	−0.516181	+	0.894051i
$615$		0			0
$616$	0.370443	+	1.16239i	0.0149256	+	0.0468342i
$617$	−15.4571	+	15.4571i	−0.622278	+	0.622278i	−0.946113	−	0.323836i	$-0.895027\pi$
$617$	−15.4571	+	15.4571i	−0.622278	+	0.622278i	0.323836	+	0.946113i	$0.395027\pi$
$618$	14.2719	−	3.82414i	0.574099	−	0.153829i
$619$	−12.3595	−	21.4073i	−0.496772	−	0.860434i	0.503221	−	0.864158i	$-0.332148\pi$
$619$	−12.3595	−	21.4073i	−0.496772	−	0.860434i	−0.999993	+	0.00372371i	$0.998815\pi$
$620$		0			0
$621$	−3.82117	−	2.20615i	−0.153338	−	0.0885299i
$622$	23.7712	+	23.7712i	0.953139	+	0.953139i
$623$	−1.41200	−	30.2039i	−0.0565704	−	1.21009i
$624$			5.66074i			0.226611i
$625$		0			0
$626$	−19.8878	+	11.4822i	−0.794876	+	0.458922i
$627$	−2.59512	−	0.695360i	−0.103639	−	0.0277700i
$628$	−5.63586	−	21.0333i	−0.224895	−	0.839320i
$629$	13.2242			0.527284
$630$		0			0
$631$	34.7305			1.38260			0.691299	−	0.722569i	$-0.257039\pi$
$631$	34.7305			1.38260			0.691299	+	0.722569i	$0.257039\pi$
$632$	−1.30995	−	4.88882i	−0.0521072	−	0.194467i
$633$	−1.28732	−	0.344935i	−0.0511662	−	0.0137099i
$634$	−22.2066	+	12.8210i	−0.881937	+	0.509187i
$635$		0			0
$636$			2.74660i			0.108910i
$637$	−13.7818	−	37.1513i	−0.546056	−	1.47199i
$638$	1.80562	+	1.80562i	0.0714850	+	0.0714850i
$639$	7.67192	+	4.42939i	0.303497	+	0.175224i
$640$		0			0
$641$	−5.82603	−	10.0910i	−0.230115	−	0.398570i	0.727727	−	0.685867i	$-0.240577\pi$
$641$	−5.82603	−	10.0910i	−0.230115	−	0.398570i	−0.957842	+	0.287297i	$0.907243\pi$
$642$	5.69821	−	1.52683i	0.224890	−	0.0602592i
$643$	−21.8198	+	21.8198i	−0.860489	+	0.860489i	−0.991395	−	0.130906i	$-0.958211\pi$
$643$	−21.8198	+	21.8198i	−0.860489	+	0.860489i	0.130906	+	0.991395i	$0.458211\pi$
$644$	2.49155	−	11.4049i	0.0981810	−	0.449415i
$645$		0			0
$646$	−4.77716	+	8.27429i	−0.187955	+	0.325548i
$647$	−9.61474	+	35.8827i	−0.377994	+	1.41069i	0.470926	+	0.882173i	$0.343920\pi$
$647$	−9.61474	+	35.8827i	−0.377994	+	1.41069i	−0.848920	+	0.528521i	$0.822747\pi$
$648$	−0.258819	+	0.965926i	−0.0101674	+	0.0379452i
$649$	0.442112	−	0.765761i	0.0173544	−	0.0300588i
$650$		0			0
$651$	0.0577930	−	0.0634615i	0.00226509	−	0.00248725i
$652$	8.25527	−	8.25527i	0.323301	−	0.323301i
$653$	30.5404	−	8.18328i	1.19514	−	0.320237i	0.394224	−	0.919014i	$-0.371013\pi$
$653$	30.5404	−	8.18328i	1.19514	−	0.320237i	0.800915	+	0.598778i	$0.204347\pi$
$654$	8.30937	+	14.3923i	0.324922	+	0.562782i
$655$		0			0
$656$	−9.47890	−	5.47265i	−0.370089	−	0.213671i
$657$	2.86894	+	2.86894i	0.111928	+	0.111928i
$658$	21.2497	+	10.9788i	0.828398	+	0.427997i
$659$		−	38.7284i		−	1.50864i	−0.656504	−	0.754322i	$-0.727966\pi$
$659$		−	38.7284i		−	1.50864i	0.656504	−	0.754322i	$-0.272034\pi$
$660$		0			0
$661$	29.3286	−	16.9329i	1.14075	−	0.658613i	0.194135	−	0.980975i	$-0.437810\pi$
$661$	29.3286	−	16.9329i	1.14075	−	0.658613i	0.946617	+	0.322361i	$0.104477\pi$
$662$	−11.4606	−	3.07085i	−0.445427	−	0.119352i
$663$	−2.40251	−	8.96628i	−0.0933057	−	0.348222i
$664$	−1.53885			−0.0597190
$665$		0			0
$666$	−8.06444			−0.312491
$667$	−6.32402	−	23.6016i	−0.244867	−	0.913856i
$668$	−21.1817	−	5.67563i	−0.819546	−	0.219597i
$669$	10.1076	−	5.83564i	0.390784	−	0.225619i
$670$		0			0
$671$			6.25058i			0.241301i
$672$	−2.64286	+	0.123551i	−0.101951	+	0.00476607i
$673$	24.7046	+	24.7046i	0.952294	+	0.952294i	0.998913	−	0.0466190i	$-0.0148447\pi$
$673$	24.7046	+	24.7046i	0.952294	+	0.952294i	−0.0466190	+	0.998913i	$0.514845\pi$
$674$	−3.90382	−	2.25387i	−0.150370	−	0.0868159i
$675$		0			0
$676$	9.52199	+	16.4926i	0.366230	+	0.634330i
$677$	17.0046	−	4.55637i	0.653540	−	0.175116i	0.0832112	−	0.996532i	$-0.473482\pi$
$677$	17.0046	−	4.55637i	0.653540	−	0.175116i	0.570329	+	0.821416i	$0.306816\pi$
$678$	6.35390	−	6.35390i	0.244020	−	0.244020i
$679$	9.20437	+	2.01082i	0.353231	+	0.0771683i
$680$		0			0
$681$	−11.1813	+	19.3666i	−0.428469	+	0.742129i
$682$	−0.00387180	+	0.0144498i	−0.000148259	+	0.000553310i
$683$	6.25658	−	23.3499i	0.239401	−	0.893458i	−0.736714	−	0.676205i	$-0.763623\pi$
$683$	6.25658	−	23.3499i	0.239401	−	0.893458i	0.976115	−	0.217254i	$-0.0697099\pi$
$684$	2.91323	−	5.04586i	0.111390	−	0.192933i
$685$		0			0
$686$	17.0442	−	7.24527i	0.650752	−	0.276626i
$687$	−3.51165	+	3.51165i	−0.133978	+	0.133978i
$688$	−6.49061	+	1.73915i	−0.247452	+	0.0663046i
$689$	7.77390	+	13.4648i	0.296162	+	0.512968i
$690$		0			0
$691$	−2.56844	−	1.48289i	−0.0977081	−	0.0564118i	0.450350	−	0.892852i	$-0.351299\pi$
$691$	−2.56844	−	1.48289i	−0.0977081	−	0.0564118i	−0.548058	+	0.836440i	$0.684633\pi$
$692$	−6.89034	−	6.89034i	−0.261931	−	0.261931i
$693$	0.658670	+	1.02691i	0.0250208	+	0.0390090i
$694$			21.4221i			0.813172i
$695$		0			0
$696$	−4.79581	+	2.76886i	−0.181785	+	0.104953i
$697$	17.3367	+	4.64536i	0.656675	+	0.175955i
$698$	4.15876	+	15.5207i	0.157412	+	0.587468i
$699$	−28.6338			−1.08303
$700$		0			0
$701$	−18.6815			−0.705591			−0.352795	−	0.935701i	$-0.614769\pi$
$701$	−18.6815			−0.705591			−0.352795	+	0.935701i	$0.614769\pi$
$702$	1.46511	+	5.46786i	0.0552969	+	0.206371i
$703$	45.3861	+	12.1612i	1.71177	+	0.458667i
$704$	0.399337	−	0.230557i	0.0150506	−	0.00868946i
$705$		0			0
$706$		−	29.3960i		−	1.10633i
$707$	−5.47930	+	10.6053i	−0.206070	+	0.398853i
$708$	1.35593	+	1.35593i	0.0509592	+	0.0509592i
$709$	18.3186	+	10.5763i	0.687971	+	0.397200i	0.802851	−	0.596179i	$-0.203315\pi$
$709$	18.3186	+	10.5763i	0.687971	+	0.397200i	−0.114880	+	0.993379i	$0.536649\pi$
$710$		0			0
$711$	−2.53064	−	4.38319i	−0.0949063	−	0.164383i
$712$	−11.0391	+	2.95790i	−0.413706	+	0.110852i
$713$	0.101218	−	0.101218i	0.00379065	−	0.00379065i
$714$	4.13371	−	1.31737i	0.154700	−	0.0493014i
$715$		0			0
$716$	−0.807576	+	1.39876i	−0.0301805	+	0.0522742i
$717$	−3.60353	+	13.4486i	−0.134576	+	0.502246i
$718$	−3.52703	+	13.1630i	−0.131628	+	0.491241i
$719$	4.30625	−	7.45864i	0.160596	−	0.278160i	−0.774487	−	0.632590i	$-0.781992\pi$
$719$	4.30625	−	7.45864i	0.160596	−	0.278160i	0.935083	+	0.354430i	$0.115325\pi$
$720$		0			0
$721$	28.9028	+	26.3211i	1.07640	+	0.980251i
$722$	−10.5696	+	10.5696i	−0.393359	+	0.393359i
$723$	−1.02153	+	0.273719i	−0.0379912	+	0.0101797i
$724$	−6.42597	−	11.1301i	−0.238819	−	0.413647i
$725$		0			0
$726$	9.34214	+	5.39369i	0.346719	+	0.200178i
$727$	−12.8013	−	12.8013i	−0.474774	−	0.474774i	0.428682	−	0.903455i	$-0.358978\pi$
$727$	−12.8013	−	12.8013i	−0.474774	−	0.474774i	−0.903455	+	0.428682i	$0.858978\pi$
$728$	−12.6065	+	8.08597i	−0.467230	+	0.299686i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	9.54263	−	5.50944i	0.352947	−	0.203774i
$732$	−13.0935	−	3.50839i	−0.483949	−	0.129674i
$733$	8.56107	+	31.9503i	0.316210	+	1.18011i	0.922857	+	0.385142i	$0.125847\pi$
$733$	8.56107	+	31.9503i	0.316210	+	1.18011i	−0.606647	+	0.794971i	$0.707486\pi$
$734$	12.7591			0.470947
$735$		0			0
$736$	−4.41231			−0.162640
$737$	0.454733	+	1.69709i	0.0167503	+	0.0625130i
$738$	−10.5723	−	2.83285i	−0.389173	−	0.104279i
$739$	−40.9779	+	23.6586i	−1.50740	+	0.870296i	−0.507434	+	0.861690i	$0.669406\pi$
$739$	−40.9779	+	23.6586i	−1.50740	+	0.870296i	−0.999963	+	0.00860599i	$0.997261\pi$
$740$		0			0
$741$		−	32.9821i		−	1.21163i
$742$	−6.11672	+	3.92333i	−0.224552	+	0.144030i
$743$	21.5587	+	21.5587i	0.790914	+	0.790914i	0.981643	−	0.190729i	$-0.0610852\pi$
$743$	21.5587	+	21.5587i	0.790914	+	0.790914i	−0.190729	+	0.981643i	$0.561085\pi$
$744$	−0.0280956	−	0.0162210i	−0.00103004	−	0.000594691i
$745$		0			0
$746$	−2.00068	−	3.46527i	−0.0732500	−	0.126873i
$747$	−1.48642	+	0.398284i	−0.0543851	+	0.0145724i
$748$	−0.534674	+	0.534674i	−0.0195496	+	0.0195496i
$749$	11.5398	+	10.5090i	0.421654	+	0.383991i
$750$		0			0
$751$	−15.5069	+	26.8587i	−0.565854	+	0.980088i	0.431116	+	0.902297i	$0.358120\pi$
$751$	−15.5069	+	26.8587i	−0.565854	+	0.980088i	−0.996970	+	0.0777911i	$0.975213\pi$
$752$	2.33979	−	8.73220i	0.0853232	−	0.318431i
$753$	1.64676	−	6.14580i	0.0600114	−	0.223965i
$754$	−15.6738	+	27.1478i	−0.570807	+	0.988666i
$755$		0			0
$756$	−2.52083	+	0.803365i	−0.0916819	+	0.0292181i
$757$	16.7486	−	16.7486i	0.608738	−	0.608738i	−0.333879	−	0.942616i	$-0.608358\pi$
$757$	16.7486	−	16.7486i	0.608738	−	0.608738i	0.942616	+	0.333879i	$0.108358\pi$
$758$	−0.968641	+	0.259546i	−0.0351826	+	0.00942715i
$759$	1.01729	+	1.76200i	0.0369253	+	0.0639564i
$760$		0			0
$761$	−14.7359	−	8.50777i	−0.534175	−	0.308406i	0.208540	−	0.978014i	$-0.433129\pi$
$761$	−14.7359	−	8.50777i	−0.534175	−	0.308406i	−0.742715	+	0.669608i	$0.766462\pi$
$762$	11.7757	+	11.7757i	0.426590	+	0.426590i
$763$	−20.1824	+	39.0634i	−0.730651	+	1.41419i
$764$			10.6007i			0.383518i
$765$		0			0
$766$	15.4180	−	8.90158i	0.557075	−	0.321627i
$767$	10.4851	+	2.80946i	0.378593	+	0.101444i
$768$	0.258819	+	0.965926i	0.00933933	+	0.0348548i
$769$	7.70275			0.277768			0.138884	−	0.990309i	$-0.455648\pi$
$769$	7.70275			0.277768			0.138884	+	0.990309i	$0.455648\pi$
$770$		0			0
$771$	10.3811			0.373865
$772$	−1.86766	−	6.97019i	−0.0672185	−	0.250863i
$773$	−2.92305	−	0.783229i	−0.105135	−	0.0281708i	0.205868	−	0.978580i	$-0.433998\pi$
$773$	−2.92305	−	0.783229i	−0.105135	−	0.0281708i	−0.311003	+	0.950409i	$0.600665\pi$
$774$	−5.81932	+	3.35979i	−0.209171	+	0.120765i
$775$		0			0
$776$		−	3.56097i		−	0.127832i
$777$	−11.5195	−	17.9596i	−0.413260	−	0.644298i
$778$	7.96110	+	7.96110i	0.285419	+	0.285419i
$779$	55.2284	+	31.8862i	1.97876	+	1.14244i
$780$		0			0
$781$	−2.04245	−	3.53763i	−0.0730848	−	0.126587i
$782$	6.98884	−	1.87265i	0.249920	−	0.0669660i
$783$	−3.91576	+	3.91576i	−0.139938	+	0.139938i
$784$	−4.05030	−	5.70921i	−0.144654	−	0.203900i
$785$		0			0
$786$	−9.48825	+	16.4341i	−0.338435	+	0.586186i
$787$	5.80155	−	21.6517i	0.206803	−	0.771799i	−0.782089	−	0.623166i	$-0.785846\pi$
$787$	5.80155	−	21.6517i	0.206803	−	0.771799i	0.988892	−	0.148633i	$-0.0474873\pi$
$788$	−3.56071	+	13.2887i	−0.126845	+	0.473392i
$789$	11.8810	−	20.5785i	0.422974	−	0.732613i
$790$		0			0
$791$	23.2263	+	5.07411i	0.825833	+	0.180415i
$792$	0.326057	−	0.326057i	0.0115859	−	0.0115859i
$793$	−74.1188	+	19.8601i	−2.63203	+	0.705252i
$794$	−1.91642	−	3.31933i	−0.0680112	−	0.117799i
$795$		0			0
$796$	−8.35971	−	4.82648i	−0.296302	−	0.171070i
$797$	21.8939	+	21.8939i	0.775520	+	0.775520i	0.979066	−	0.203545i	$-0.0652464\pi$
$797$	21.8939	+	21.8939i	0.775520	+	0.775520i	−0.203545	+	0.979066i	$0.565246\pi$
$798$	15.3985	−	0.719863i	0.545103	−	0.0254829i
$799$			14.8243i			0.524447i
$800$		0			0
$801$	−9.89734	+	5.71423i	−0.349705	+	0.201903i
$802$	0.869376	+	0.232949i	0.0306987	+	0.00822570i
$803$	−0.484218	−	1.80713i	−0.0170877	−	0.0637721i
$804$	−3.81023			−0.134377
$805$		0			0
$806$	−0.183646			−0.00646865
$807$	0.367542	+	1.37168i	0.0129381	+	0.0482856i
$808$	4.35807	+	1.16774i	0.153316	+	0.0410810i
$809$	−0.938781	+	0.542005i	−0.0330058	+	0.0190559i	−0.516412	−	0.856340i	$-0.672733\pi$
$809$	−0.938781	+	0.542005i	−0.0330058	+	0.0190559i	0.483406	+	0.875396i	$0.339399\pi$
$810$		0			0
$811$		−	33.8754i		−	1.18953i	−0.803901	−	0.594763i	$-0.797246\pi$
$811$		−	33.8754i		−	1.18953i	0.803901	−	0.594763i	$-0.202754\pi$
$812$	−13.0168	−	6.72520i	−0.456799	−	0.236008i
$813$	0.250034	+	0.250034i	0.00876907	+	0.00876907i
$814$	3.22043	+	1.85932i	0.112876	+	0.0651690i
$815$		0			0
$816$	−0.819909	−	1.42012i	−0.0287025	−	0.0497143i
$817$	37.8173	−	10.1331i	1.32306	−	0.354513i
$818$	9.11649	−	9.11649i	0.318751	−	0.318751i
$819$	−10.0842	+	11.0733i	−0.352370	+	0.386931i
$820$		0			0
$821$	−2.43319	+	4.21441i	−0.0849190	+	0.147084i	−0.905357	−	0.424652i	$-0.860396\pi$
$821$	−2.43319	+	4.21441i	−0.0849190	+	0.147084i	0.820438	+	0.571736i	$0.193730\pi$
$822$	1.14632	−	4.27811i	0.0399823	−	0.149216i
$823$	8.98921	−	33.5482i	0.313344	−	1.16942i	−0.612177	−	0.790720i	$-0.709706\pi$
$823$	8.98921	−	33.5482i	0.313344	−	1.16942i	0.925521	−	0.378695i	$-0.123627\pi$
$824$	7.38767	−	12.7958i	0.257362	−	0.445763i
$825$		0			0
$826$	−1.08283	+	4.95654i	−0.0376763	+	0.172460i
$827$	38.4936	−	38.4936i	1.33855	−	1.33855i	0.441093	−	0.897461i	$-0.354591\pi$
$827$	38.4936	−	38.4936i	1.33855	−	1.33855i	0.897461	−	0.441093i	$-0.145409\pi$
$828$	−4.26196	+	1.14199i	−0.148113	+	0.0396869i
$829$	−20.0652	−	34.7540i	−0.696895	−	1.20706i	−0.969538	−	0.244942i	$-0.921231\pi$
$829$	−20.0652	−	34.7540i	−0.696895	−	1.20706i	0.272643	−	0.962115i	$-0.412102\pi$
$830$		0			0
$831$	20.3531	+	11.7509i	0.706041	+	0.407633i
$832$	4.00275	+	4.00275i	0.138770	+	0.138770i
$833$	8.83852	+	7.32405i	0.306236	+	0.253763i
$834$		−	4.35020i		−	0.150635i
$835$		0			0
$836$	−2.32672	+	1.34333i	−0.0804713	+	0.0464601i
$837$	−0.0313366	−	0.00839662i	−0.00108315	−	0.000290229i
$838$	5.14837	+	19.2140i	0.177848	+	0.663736i
$839$	27.8082			0.960044			0.480022	−	0.877256i	$-0.340629\pi$
$839$	27.8082			0.960044			0.480022	+	0.877256i	$0.340629\pi$
$840$		0			0
$841$	−1.66640			−0.0574621
$842$	3.26990	+	12.2034i	0.112688	+	0.420558i
$843$	−27.5045	−	7.36980i	−0.947305	−	0.253830i
$844$	−1.15418	+	0.666364i	−0.0397284	+	0.0229372i
$845$		0			0
$846$		−	9.04024i		−	0.310810i
$847$	1.33279	+	28.5096i	0.0457951	+	0.979600i
$848$	1.94214	+	1.94214i	0.0666934	+	0.0666934i
$849$	−3.25442	−	1.87894i	−0.111691	−	0.0644851i
$850$		0			0
$851$	−17.7914	−	30.8156i	−0.609881	−	1.05635i
$852$	8.55692	−	2.29282i	0.293155	−	0.0785507i
$853$	19.0929	−	19.0929i	0.653729	−	0.653729i	−0.300160	−	0.953889i	$-0.597040\pi$
$853$	19.0929	−	19.0929i	0.653729	−	0.653729i	0.953889	+	0.300160i	$0.0970400\pi$
$854$	−10.8899	−	34.1708i	−0.372645	−	1.16930i
$855$		0			0
$856$	2.94961	−	5.10888i	0.100816	−	0.174618i
$857$	5.27688	−	19.6936i	0.180255	−	0.672720i	−0.815342	−	0.578980i	$-0.803451\pi$
$857$	5.27688	−	19.6936i	0.180255	−	0.672720i	0.995597	−	0.0937404i	$-0.0298824\pi$
$858$	0.675582	−	2.52131i	0.0230640	−	0.0860760i
$859$	2.24170	−	3.88275i	0.0764860	−	0.132478i	−0.825246	−	0.564774i	$-0.808963\pi$
$859$	2.24170	−	3.88275i	0.0764860	−	0.132478i	0.901732	+	0.432297i	$0.142297\pi$
$860$		0			0
$861$	−8.79306	−	27.5913i	−0.299667	−	0.940308i
$862$	−21.7578	+	21.7578i	−0.741073	+	0.741073i
$863$	−18.9773	+	5.08496i	−0.645996	+	0.173094i	−0.566918	−	0.823774i	$-0.691864\pi$
$863$	−18.9773	+	5.08496i	−0.645996	+	0.173094i	−0.0790782	+	0.996868i	$0.525198\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$		0			0
$866$	3.73232	+	2.15486i	0.126829	+	0.0732250i
$867$	−10.1194	−	10.1194i	−0.343673	−	0.343673i
$868$	−0.00400824	−	0.0857399i	−0.000136048	−	0.00291020i
$869$			2.33383i			0.0791697i
$870$		0			0
$871$	−18.6791	+	10.7844i	−0.632916	+	0.365414i
$872$	16.0525	+	4.30125i	0.543605	+	0.145659i
$873$	−0.921648	−	3.43964i	−0.0311931	−	0.116414i
$874$	25.7081			0.869590
$875$		0			0
$876$	4.05729			0.137083
$877$	−3.48618	−	13.0106i	−0.117720	−	0.439337i	0.881756	−	0.471706i	$-0.156362\pi$
$877$	−3.48618	−	13.0106i	−0.117720	−	0.439337i	−0.999476	+	0.0323688i	$0.989695\pi$
$878$	35.7380	+	9.57597i	1.20610	+	0.323173i
$879$	5.12556	−	2.95924i	0.172881	−	0.0998127i
$880$		0			0
$881$			55.0357i			1.85420i	0.374813	+	0.927100i	$0.377707\pi$
$881$			55.0357i			1.85420i	−0.374813	+	0.927100i	$0.622293\pi$
$882$	−5.38994	−	4.46638i	−0.181489	−	0.150391i
$883$	−3.82147	−	3.82147i	−0.128603	−	0.128603i	0.639876	−	0.768478i	$-0.278986\pi$
$883$	−3.82147	−	3.82147i	−0.128603	−	0.128603i	−0.768478	+	0.639876i	$0.778986\pi$
$884$	−8.03895	−	4.64129i	−0.270379	−	0.156103i
$885$		0			0
$886$	8.89875	+	15.4131i	0.298960	+	0.517813i
$887$	22.1111	−	5.92466i	0.742419	−	0.198931i	0.132266	−	0.991214i	$-0.457775\pi$
$887$	22.1111	−	5.92466i	0.742419	−	0.198931i	0.610153	+	0.792284i	$0.291108\pi$
$888$	−5.70242	+	5.70242i	−0.191361	+	0.191361i
$889$	−9.40390	+	43.0455i	−0.315397	+	1.44370i
$890$		0			0
$891$	0.230557	−	0.399337i	0.00772396	−	0.0133783i
$892$	3.02075	−	11.2736i	0.101142	−	0.377468i
$893$	−13.6327	+	50.8778i	−0.456200	+	1.70256i
$894$	−2.17026	+	3.75900i	−0.0725843	+	0.125720i
$895$		0			0
$896$	−1.78142	+	1.95615i	−0.0595132	+	0.0653504i
$897$	−17.6614	+	17.6614i	−0.589695	+	0.589695i
$898$	−2.33701	+	0.626200i	−0.0779870	+	0.0208966i
$899$	−0.0898275	−	0.155586i	−0.00299592	−	0.00518908i
$900$		0			0
$901$	−3.90051	−	2.25196i	−0.129945	−	0.0750237i
$902$	3.56879	+	3.56879i	0.118828	+	0.118828i
$903$	−15.7948	−	8.16049i	−0.525618	−	0.271564i
$904$		−	8.98577i		−	0.298862i
$905$		0			0
$906$	7.08854	−	4.09257i	0.235501	−	0.135967i
$907$	26.4300	+	7.08190i	0.877595	+	0.235151i	0.669369	−	0.742930i	$-0.266565\pi$
$907$	26.4300	+	7.08190i	0.877595	+	0.235151i	0.208226	+	0.978081i	$0.433231\pi$
$908$	5.78787	+	21.6006i	0.192077	+	0.716842i
$909$	4.51181			0.149647
$910$		0			0
$911$	−55.5763			−1.84132			−0.920662	−	0.390360i	$-0.872350\pi$
$911$	−55.5763			−1.84132			−0.920662	+	0.390360i	$0.872350\pi$
$912$	−1.50800	−	5.62793i	−0.0499348	−	0.186359i
$913$	0.685408	+	0.183655i	0.0226837	+	0.00607808i
$914$	23.8666	−	13.7794i	0.789438	−	0.455782i
$915$		0			0
$916$			4.96622i			0.164088i
$917$	−50.1523	+	2.34456i	−1.65618	+	0.0774242i
$918$	−1.15953	−	1.15953i	−0.0382701	−	0.0382701i
$919$	17.4296	+	10.0630i	0.574948	+	0.331947i	0.759123	−	0.650947i	$-0.225628\pi$
$919$	17.4296	+	10.0630i	0.574948	+	0.331947i	−0.184175	+	0.982893i	$0.558961\pi$
$920$		0			0
$921$	12.7905	+	22.1537i	0.421460	+	0.729990i
$922$	−0.992122	+	0.265838i	−0.0326738	+	0.00875492i
$923$	35.4594	−	35.4594i	1.16716	−	1.16716i
$924$	1.19188	+	0.260384i	0.0392101	+	0.00856599i
$925$		0			0
$926$	5.84429	−	10.1226i	0.192055	−	0.332650i
$927$	3.82414	−	14.2719i	0.125601	−	0.468750i
$928$	−1.43327	+	5.34903i	−0.0470494	+	0.175591i
$929$	13.0112	−	22.5360i	0.426883	−	0.739383i	−0.569711	−	0.821845i	$-0.692945\pi$
$929$	13.0112	−	22.5360i	0.426883	−	0.739383i	0.996594	+	0.0824618i	$0.0262782\pi$
$930$		0			0
$931$	23.5989	+	33.2645i	0.773423	+	1.09020i
$932$	−20.2472	+	20.2472i	−0.663218	+	0.663218i
$933$	32.4721	−	8.70087i	1.06309	−	0.284854i
$934$	−9.27239	−	16.0603i	−0.303402	−	0.525508i
$935$		0			0
$936$	4.90235	+	2.83037i	0.160238	+	0.0925135i
$937$	17.1515	+	17.1515i	0.560314	+	0.560314i	0.929397	−	0.369082i	$-0.120328\pi$
$937$	17.1515	+	17.1515i	0.560314	+	0.560314i	−0.369082	+	0.929397i	$0.620328\pi$
$938$	−5.44265	−	8.48544i	−0.177709	−	0.277059i
$939$			22.9644i			0.749416i
$940$		0			0
$941$	14.4025	−	8.31531i	0.469509	−	0.271071i	−0.246525	−	0.969136i	$-0.579289\pi$
$941$	14.4025	−	8.31531i	0.469509	−	0.271071i	0.716034	+	0.698065i	$0.245955\pi$
$942$	−21.0333	−	5.63586i	−0.685302	−	0.183626i
$943$	−12.4994	−	46.6484i	−0.407037	−	1.51908i
$944$	1.91758			0.0624120
$945$		0			0
$946$	3.09849			0.100741
$947$	7.68510	+	28.6812i	0.249732	+	0.932013i	0.970946	+	0.239300i	$0.0769181\pi$
$947$	7.68510	+	28.6812i	0.249732	+	0.932013i	−0.721213	+	0.692713i	$0.756415\pi$
$948$	−4.88882	−	1.30995i	−0.158781	−	0.0425453i
$949$	19.8902	−	11.4836i	0.645664	−	0.372774i
$950$		0			0
$951$			25.6420i			0.831498i
$952$	1.99145	−	3.85450i	0.0645433	−	0.124925i
$953$	30.9752	+	30.9752i	1.00339	+	1.00339i	0.999994	+	0.00339090i	$0.00107936\pi$
$953$	30.9752	+	30.9752i	1.00339	+	1.00339i	0.00339090	+	0.999994i	$0.498921\pi$
$954$	2.37863	+	1.37330i	0.0770109	+	0.0444622i
$955$		0			0
$956$	6.96149	+	12.0577i	0.225151	+	0.389973i
$957$	2.46652	−	0.660901i	0.0797312	−	0.0213639i
$958$	5.99446	−	5.99446i	0.193672	−	0.193672i
$959$	11.1648	−	3.55812i	0.360531	−	0.114898i
$960$		0			0
$961$	−15.4995	+	26.8459i	−0.499983	+	0.865996i
$962$	−11.8153	+	44.0952i	−0.380940	+	1.42169i
$963$	1.52683	−	5.69821i	0.0492014	−	0.183622i
$964$	−0.528784	+	0.915881i	−0.0170310	+	0.0294985i
$965$		0			0
$966$	−8.63114	−	7.86019i	−0.277702	−	0.252897i
$967$	9.23140	−	9.23140i	0.296862	−	0.296862i	−0.542922	−	0.839783i	$-0.682682\pi$
$967$	9.23140	−	9.23140i	0.296862	−	0.296862i	0.839783	+	0.542922i	$0.182682\pi$
$968$	10.4198	−	2.79198i	0.334905	−	0.0897376i
$969$	4.77716	+	8.27429i	0.153465	+	0.265809i
$970$		0			0
$971$	21.1712	+	12.2232i	0.679416	+	0.392261i	0.799635	−	0.600486i	$-0.205026\pi$
$971$	21.1712	+	12.2232i	0.679416	+	0.392261i	−0.120219	+	0.992747i	$0.538360\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	9.68794	−	6.21395i	0.310581	−	0.199210i
$974$			4.85631i			0.155606i
$975$		0			0
$976$	−11.7393	+	6.77768i	−0.375766	+	0.216948i
$977$	−27.0527	−	7.24876i	−0.865493	−	0.231908i	−0.201355	−	0.979518i	$-0.564535\pi$
$977$	−27.0527	−	7.24876i	−0.865493	−	0.231908i	−0.664138	+	0.747610i	$0.731201\pi$
$978$	−3.02164	−	11.2769i	−0.0966213	−	0.360596i
$979$	5.26983			0.168425
$980$		0			0
$981$	16.6187			0.530596
$982$	9.79874	+	36.5694i	0.312690	+	1.16698i
$983$	−39.8535	−	10.6787i	−1.27113	−	0.340598i	−0.440666	−	0.897671i	$-0.645258\pi$
$983$	−39.8535	−	10.6787i	−1.27113	−	0.340598i	−0.830463	+	0.557073i	$0.811924\pi$
$984$	−9.47890	+	5.47265i	−0.302176	+	0.174462i
$985$		0			0
$986$		−	9.08086i		−	0.289193i
$987$	20.1327	−	12.9134i	0.640832	−	0.411037i
$988$	−23.3218	−	23.3218i	−0.741967	−	0.741967i
$989$	−25.6766	−	14.8244i	−0.816470	−	0.471389i
$990$		0			0
$991$	18.1824	+	31.4928i	0.577582	+	1.00040i	0.995756	+	0.0920347i	$0.0293371\pi$
$991$	18.1824	+	31.4928i	0.577582	+	1.00040i	−0.418173	+	0.908367i	$0.637330\pi$
$992$	−0.0313366	+	0.00839662i	−0.000994938	+	0.000266593i
$993$	−8.38971	+	8.38971i	−0.266240	+	0.266240i
$994$	17.3291	+	15.7812i	0.549646	+	0.500550i
$995$		0			0
$996$	−0.769426	+	1.33268i	−0.0243802	+	0.0422277i
$997$	4.64972	−	17.3530i	0.147258	−	0.549575i	−0.852386	−	0.522912i	$-0.824845\pi$
$997$	4.64972	−	17.3530i	0.147258	−	0.549575i	0.999644	−	0.0266623i	$-0.00848788\pi$
$998$	−0.132566	+	0.494743i	−0.00419631	+	0.0156608i
$999$	−4.03222	+	6.98401i	−0.127574	+	0.220964i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.bc.h.943.1		16
5.2	odd	4		1050.2.bc.g.607.3		16
5.3	odd	4		210.2.u.b.187.1	yes	16
5.4	even	2		210.2.u.a.103.4	✓	16
7.3	odd	6		1050.2.bc.g.493.3		16
15.8	even	4		630.2.bv.b.397.4		16
15.14	odd	2		630.2.bv.a.523.1		16
35.3	even	12		210.2.u.a.157.4	yes	16
35.9	even	6		1470.2.m.d.1273.5		16
35.17	even	12	inner	1050.2.bc.h.157.1		16
35.19	odd	6		1470.2.m.e.1273.8		16
35.23	odd	12		1470.2.m.e.97.8		16
35.24	odd	6		210.2.u.b.73.1	yes	16
35.33	even	12		1470.2.m.d.97.5		16
105.38	odd	12		630.2.bv.a.577.1		16
105.59	even	6		630.2.bv.b.73.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.103.4	✓	16	5.4	even	2
210.2.u.a.157.4	yes	16	35.3	even	12
210.2.u.b.73.1	yes	16	35.24	odd	6
210.2.u.b.187.1	yes	16	5.3	odd	4
630.2.bv.a.523.1		16	15.14	odd	2
630.2.bv.a.577.1		16	105.38	odd	12
630.2.bv.b.73.4		16	105.59	even	6
630.2.bv.b.397.4		16	15.8	even	4
1050.2.bc.g.493.3		16	7.3	odd	6
1050.2.bc.g.607.3		16	5.2	odd	4
1050.2.bc.h.157.1		16	35.17	even	12	inner
1050.2.bc.h.943.1		16	1.1	even	1	trivial
1470.2.m.d.97.5		16	35.33	even	12
1470.2.m.d.1273.5		16	35.9	even	6
1470.2.m.e.97.8		16	35.23	odd	12
1470.2.m.e.1273.8		16	35.19	odd	6

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(-2.22701 + 1.42843i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(-2.22701 + 1.42843i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-0.230557 - 0.399337i) q^{11} +(0.965926 - 0.258819i) q^{12} +(4.00275 - 4.00275i) q^{13} +(1.95615 + 1.78142i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.424416 + 1.58394i) q^{17} +(0.258819 - 0.965926i) q^{18} +(-2.91323 + 5.04586i) q^{19} +(2.52083 - 0.803365i) q^{21} +(-0.326057 + 0.326057i) q^{22} +(4.26196 - 1.14199i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-4.90235 - 2.83037i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.21443 - 2.35056i) q^{28} -5.53773i q^{29} +(0.0280956 - 0.0162210i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(0.119345 + 0.445403i) q^{33} +1.63982 q^{34} -1.00000 q^{36} +(-2.08723 - 7.78966i) q^{37} +(5.62793 + 1.50800i) q^{38} +(-4.90235 + 2.83037i) q^{39} -10.9453i q^{41} +(-1.42843 - 2.22701i) q^{42} +(-4.75146 - 4.75146i) q^{43} +(0.399337 + 0.230557i) q^{44} +(-2.20615 - 3.82117i) q^{46} +(8.73220 - 2.33979i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(2.91917 - 6.36227i) q^{49} +(0.819909 - 1.42012i) q^{51} +(-1.46511 + 5.46786i) q^{52} +(-0.710873 + 2.65301i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.58479 - 0.564683i) q^{56} +(4.11993 - 4.11993i) q^{57} +(-5.34903 + 1.43327i) q^{58} +(0.958791 + 1.66067i) q^{59} +(-11.7393 - 6.77768i) q^{61} +(-0.0229400 - 0.0229400i) q^{62} +(-2.64286 + 0.123551i) q^{63} +1.00000i q^{64} +(0.399337 - 0.230557i) q^{66} +(-3.68040 - 0.986161i) q^{67} +(-0.424416 - 1.58394i) q^{68} -4.41231 q^{69} +8.85877 q^{71} +(0.258819 + 0.965926i) q^{72} +(3.91904 + 1.05010i) q^{73} +(-6.98401 + 4.03222i) q^{74} -5.82646i q^{76} +(1.08388 + 0.559993i) q^{77} +(4.00275 + 4.00275i) q^{78} +(-4.38319 - 2.53064i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-10.5723 + 2.83285i) q^{82} +(-1.08813 + 1.08813i) q^{83} +(-1.78142 + 1.95615i) q^{84} +(-3.35979 + 5.81932i) q^{86} +(-1.43327 + 5.34903i) q^{87} +(0.119345 - 0.445403i) q^{88} +(-5.71423 + 9.89734i) q^{89} +(-3.19652 + 14.6318i) q^{91} +(-3.11997 + 3.11997i) q^{92} +(-0.0313366 + 0.00839662i) q^{93} +(-4.52012 - 7.82908i) q^{94} +(0.866025 + 0.500000i) q^{96} +(-2.51799 - 2.51799i) q^{97} +(-6.90101 - 1.17303i) q^{98} -0.461115i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} + 4 q^{11} + 16 q^{13} + 16 q^{14} + 8 q^{16} + 12 q^{17} - 8 q^{19} + 8 q^{21} - 4 q^{22} - 32 q^{23} - 8 q^{24} - 12 q^{26} + 8 q^{28} - 24 q^{31} - 8 q^{33} + 16 q^{34} - 16 q^{36} + 8 q^{37} + 28 q^{38} - 12 q^{39} + 4 q^{42} + 24 q^{43} - 4 q^{46} + 24 q^{47} + 52 q^{49} + 8 q^{51} + 8 q^{52} - 44 q^{53} - 8 q^{54} + 8 q^{56} + 8 q^{57} - 48 q^{58} + 8 q^{59} + 24 q^{61} - 8 q^{62} - 4 q^{63} - 36 q^{67} + 12 q^{68} - 8 q^{69} - 32 q^{71} + 40 q^{73} - 24 q^{74} + 44 q^{77} + 16 q^{78} + 12 q^{79} + 8 q^{81} - 12 q^{82} + 16 q^{83} + 4 q^{84} - 8 q^{86} - 12 q^{87} - 8 q^{88} - 16 q^{89} + 8 q^{91} - 8 q^{92} - 40 q^{93} + 8 q^{94} - 44 q^{97} + 8 q^{98}+O(q^{100}) \) 16 * q + 8 * q^7 + 4 * q^11 + 16 * q^13 + 16 * q^14 + 8 * q^16 + 12 * q^17 - 8 * q^19 + 8 * q^21 - 4 * q^22 - 32 * q^23 - 8 * q^24 - 12 * q^26 + 8 * q^28 - 24 * q^31 - 8 * q^33 + 16 * q^34 - 16 * q^36 + 8 * q^37 + 28 * q^38 - 12 * q^39 + 4 * q^42 + 24 * q^43 - 4 * q^46 + 24 * q^47 + 52 * q^49 + 8 * q^51 + 8 * q^52 - 44 * q^53 - 8 * q^54 + 8 * q^56 + 8 * q^57 - 48 * q^58 + 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 - 36 * q^67 + 12 * q^68 - 8 * q^69 - 32 * q^71 + 40 * q^73 - 24 * q^74 + 44 * q^77 + 16 * q^78 + 12 * q^79 + 8 * q^81 - 12 * q^82 + 16 * q^83 + 4 * q^84 - 8 * q^86 - 12 * q^87 - 8 * q^88 - 16 * q^89 + 8 * q^91 - 8 * q^92 - 40 * q^93 + 8 * q^94 - 44 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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