LMFDB - Embedded newform 1050.2.bc.g.607.3

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			607.3
Root			$-0.424637 + 3.22544i$ of defining polynomial
Character	$\chi$	$=$	1050.607
Dual form			1050.2.bc.g.493.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(-1.42843 - 2.22701i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(-1.42843 - 2.22701i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.230557 - 0.399337i) q^{11} +(0.258819 + 0.965926i) q^{12} +(-4.00275 - 4.00275i) q^{13} +(-1.95615 - 1.78142i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.58394 - 0.424416i) q^{17} +(-0.965926 - 0.258819i) q^{18} +(2.91323 - 5.04586i) q^{19} +(2.52083 - 0.803365i) q^{21} +(-0.326057 - 0.326057i) q^{22} +(-1.14199 - 4.26196i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.90235 - 2.83037i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.35056 - 1.21443i) q^{28} +5.53773i q^{29} +(0.0280956 - 0.0162210i) q^{31} +(0.258819 - 0.965926i) q^{32} +(0.445403 - 0.119345i) q^{33} -1.63982 q^{34} -1.00000 q^{36} +(7.78966 - 2.08723i) q^{37} +(1.50800 - 5.62793i) q^{38} +(4.90235 - 2.83037i) q^{39} -10.9453i q^{41} +(2.22701 - 1.42843i) q^{42} +(-4.75146 + 4.75146i) q^{43} +(-0.399337 - 0.230557i) q^{44} +(-2.20615 - 3.82117i) q^{46} +(2.33979 + 8.73220i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-2.91917 + 6.36227i) q^{49} +(0.819909 - 1.42012i) q^{51} +(-5.46786 - 1.46511i) q^{52} +(2.65301 + 0.710873i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.58479 - 0.564683i) q^{56} +(4.11993 + 4.11993i) q^{57} +(1.43327 + 5.34903i) q^{58} +(-0.958791 - 1.66067i) q^{59} +(-11.7393 - 6.77768i) q^{61} +(0.0229400 - 0.0229400i) q^{62} +(0.123551 + 2.64286i) q^{63} -1.00000i q^{64} +(0.399337 - 0.230557i) q^{66} +(0.986161 - 3.68040i) q^{67} +(-1.58394 + 0.424416i) q^{68} +4.41231 q^{69} +8.85877 q^{71} +(-0.965926 + 0.258819i) q^{72} +(1.05010 - 3.91904i) q^{73} +(6.98401 - 4.03222i) q^{74} -5.82646i q^{76} +(-0.559993 + 1.08388i) q^{77} +(4.00275 - 4.00275i) q^{78} +(4.38319 + 2.53064i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-2.83285 - 10.5723i) q^{82} +(1.08813 + 1.08813i) q^{83} +(1.78142 - 1.95615i) q^{84} +(-3.35979 + 5.81932i) q^{86} +(-5.34903 - 1.43327i) q^{87} +(-0.445403 - 0.119345i) q^{88} +(5.71423 - 9.89734i) q^{89} +(-3.19652 + 14.6318i) q^{91} +(-3.11997 - 3.11997i) q^{92} +(0.00839662 + 0.0313366i) q^{93} +(4.52012 + 7.82908i) q^{94} +(0.866025 + 0.500000i) q^{96} +(2.51799 - 2.51799i) q^{97} +(-1.17303 + 6.90101i) q^{98} +0.461115i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{7}+O(q^{10}) $ 16 * q + 4 * q^7	$ 16 q + 4 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} + 40 q^{23} + 8 q^{24} - 12 q^{26} + 4 q^{28} - 24 q^{31} - 4 q^{33} - 16 q^{34} - 16 q^{36} + 8 q^{37} + 20 q^{38} + 12 q^{39} - 8 q^{42} + 24 q^{43} - 4 q^{46} - 52 q^{49} + 8 q^{51} - 8 q^{52} + 28 q^{53} + 8 q^{54} + 8 q^{56} + 8 q^{57} + 12 q^{58} - 8 q^{59} + 24 q^{61} + 8 q^{62} + 4 q^{63} + 84 q^{67} - 12 q^{68} + 8 q^{69} - 32 q^{71} - 16 q^{73} + 24 q^{74} - 44 q^{77} + 16 q^{78} - 12 q^{79} + 8 q^{81} - 36 q^{82} - 16 q^{83} - 4 q^{84} - 8 q^{86} - 48 q^{87} + 4 q^{88} + 16 q^{89} + 8 q^{91} - 8 q^{92} + 32 q^{93} - 8 q^{94} + 44 q^{97} - 24 q^{98}+O(q^{100}) $ 16 * q + 4 * 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 + 40 * q^23 + 8 * q^24 - 12 * q^26 + 4 * q^28 - 24 * q^31 - 4 * q^33 - 16 * q^34 - 16 * q^36 + 8 * q^37 + 20 * q^38 + 12 * q^39 - 8 * q^42 + 24 * q^43 - 4 * q^46 - 52 * q^49 + 8 * q^51 - 8 * q^52 + 28 * q^53 + 8 * q^54 + 8 * q^56 + 8 * q^57 + 12 * q^58 - 8 * q^59 + 24 * q^61 + 8 * q^62 + 4 * q^63 + 84 * q^67 - 12 * q^68 + 8 * q^69 - 32 * q^71 - 16 * q^73 + 24 * q^74 - 44 * q^77 + 16 * q^78 - 12 * q^79 + 8 * q^81 - 36 * q^82 - 16 * q^83 - 4 * q^84 - 8 * q^86 - 48 * q^87 + 4 * q^88 + 16 * q^89 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 8 * q^94 + 44 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$			1.00000i			0.408248i
$7$	−1.42843	−	2.22701i	−0.539896	−	0.841732i
$7$	−1.42843	−	2.22701i	−0.539896	−	0.841732i
$8$	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	$0.855479\pi$
$12$	0.258819	+	0.965926i	0.0747146	+	0.278839i
$13$	−4.00275	−	4.00275i	−1.11016	−	1.11016i	−0.993128	−	0.117035i	$-0.962661\pi$
$13$	−4.00275	−	4.00275i	−1.11016	−	1.11016i	−0.117035	−	0.993128i	$-0.537339\pi$
$14$	−1.95615	−	1.78142i	−0.522803	−	0.476106i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.58394	−	0.424416i	−0.384162	−	0.102936i	0.0615689	−	0.998103i	$-0.480390\pi$
$17$	−1.58394	−	0.424416i	−0.384162	−	0.102936i	−0.445731	+	0.895167i	$0.647056\pi$
$18$	−0.965926	−	0.258819i	−0.227671	−	0.0610042i
$19$	2.91323	−	5.04586i	0.668341	−	1.15760i	−0.310027	−	0.950728i	$-0.600338\pi$
$19$	2.91323	−	5.04586i	0.668341	−	1.15760i	0.978368	−	0.206872i	$-0.0663285\pi$
$20$		0			0
$21$	2.52083	−	0.803365i	0.550091	−	0.175309i
$22$	−0.326057	−	0.326057i	−0.0695156	−	0.0695156i
$23$	−1.14199	−	4.26196i	−0.238121	−	0.888680i	−0.976717	−	0.214532i	$-0.931177\pi$
$23$	−1.14199	−	4.26196i	−0.238121	−	0.888680i	0.738596	−	0.674149i	$-0.235489\pi$
$24$	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
$28$	−2.35056	−	1.21443i	−0.444215	−	0.229507i
$29$			5.53773i			1.02833i	0.857691	+	0.514165i	$0.171898\pi$
$29$			5.53773i			1.02833i	−0.857691	+	0.514165i	$0.828102\pi$
$30$		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	$0.332406\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	0.445403	−	0.119345i	0.0775346	−	0.0207753i
$34$	−1.63982			−0.281226
$35$		0			0
$36$	−1.00000			−0.166667
$37$	7.78966	−	2.08723i	1.28061	−	0.343139i	0.446524	−	0.894772i	$-0.352662\pi$
$37$	7.78966	−	2.08723i	1.28061	−	0.343139i	0.834087	+	0.551633i	$0.185995\pi$
$38$	1.50800	−	5.62793i	0.244630	−	0.912970i
$39$	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	$-0.326249\pi$
$42$	2.22701	−	1.42843i	0.343636	−	0.220412i
$43$	−4.75146	+	4.75146i	−0.724591	+	0.724591i	−0.969537	−	0.244946i	$-0.921230\pi$
$43$	−4.75146	+	4.75146i	−0.724591	+	0.724591i	0.244946	+	0.969537i	$0.421230\pi$
$44$	−0.399337	−	0.230557i	−0.0602023	−	0.0347578i
$45$		0			0
$46$	−2.20615	−	3.82117i	−0.325280	−	0.563401i
$47$	2.33979	+	8.73220i	0.341293	+	1.27372i	0.896884	+	0.442266i	$0.145825\pi$
$47$	2.33979	+	8.73220i	0.341293	+	1.27372i	−0.555591	+	0.831456i	$0.687508\pi$
$48$	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
$52$	−5.46786	−	1.46511i	−0.758255	−	0.203174i
$53$	2.65301	+	0.710873i	0.364419	+	0.0976459i	0.436382	−	0.899761i	$-0.356260\pi$
$53$	2.65301	+	0.710873i	0.364419	+	0.0976459i	−0.0719627	+	0.997407i	$0.522926\pi$
$54$	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
$58$	1.43327	+	5.34903i	0.188197	+	0.702362i
$59$	−0.958791	−	1.66067i	−0.124824	−	0.216201i	0.796840	−	0.604190i	$-0.206503\pi$
$59$	−0.958791	−	1.66067i	−0.124824	−	0.216201i	−0.921664	+	0.387989i	$0.873170\pi$
$60$		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
$63$	0.123551	+	2.64286i	0.0155659	+	0.332970i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	0.399337	−	0.230557i	0.0491550	−	0.0283796i
$67$	0.986161	−	3.68040i	0.120479	−	0.449633i	−0.879160	−	0.476528i	$-0.841895\pi$
$67$	0.986161	−	3.68040i	0.120479	−	0.449633i	0.999638	+	0.0268948i	$0.00856192\pi$
$68$	−1.58394	+	0.424416i	−0.192081	+	0.0514680i
$69$	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	$0.323814\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	1.05010	−	3.91904i	0.122905	−	0.458689i	−0.876851	−	0.480762i	$-0.840360\pi$
$73$	1.05010	−	3.91904i	0.122905	−	0.458689i	0.999756	+	0.0220733i	$0.00702672\pi$
$74$	6.98401	−	4.03222i	0.811875	−	0.468736i
$75$		0			0
$76$		−	5.82646i		−	0.668341i
$77$	−0.559993	+	1.08388i	−0.0638172	+	0.123519i
$78$	4.00275	−	4.00275i	0.453222	−	0.453222i
$79$	4.38319	+	2.53064i	0.493148	+	0.284719i	0.725879	−	0.687822i	$-0.241433\pi$
$79$	4.38319	+	2.53064i	0.493148	+	0.284719i	−0.232732	+	0.972541i	$0.574766\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−2.83285	−	10.5723i	−0.312836	−	1.16752i
$83$	1.08813	+	1.08813i	0.119438	+	0.119438i	0.764299	−	0.644861i	$-0.223085\pi$
$83$	1.08813	+	1.08813i	0.119438	+	0.119438i	−0.644861	+	0.764299i	$0.723085\pi$
$84$	1.78142	−	1.95615i	0.194369	−	0.213434i
$85$		0			0
$86$	−3.35979	+	5.81932i	−0.362295	+	0.627514i
$87$	−5.34903	−	1.43327i	−0.573476	−	0.153663i
$88$	−0.445403	−	0.119345i	−0.0474801	−	0.0127222i
$89$	5.71423	−	9.89734i	0.605708	−	1.04912i	−0.386232	−	0.922402i	$-0.626223\pi$
$89$	5.71423	−	9.89734i	0.605708	−	1.04912i	0.991939	−	0.126714i	$-0.0404432\pi$
$90$		0			0
$91$	−3.19652	+	14.6318i	−0.335087	+	1.53383i
$92$	−3.11997	−	3.11997i	−0.325280	−	0.325280i
$93$	0.00839662	+	0.0313366i	0.000870688	+	0.00324945i
$94$	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	$-0.692137\pi$
$97$	2.51799	−	2.51799i	0.255663	−	0.255663i	0.823288	+	0.567624i	$0.192137\pi$
$98$	−1.17303	+	6.90101i	−0.118494	+	0.697108i
$99$			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	$0.261268\pi$
$102$	0.424416	−	1.58394i	0.0420234	−	0.156834i
$103$	−14.2719	+	3.82414i	−1.40625	+	0.376804i	−0.880585	−	0.473888i	$-0.842850\pi$
$103$	−14.2719	+	3.82414i	−1.40625	+	0.376804i	−0.525665	+	0.850692i	$0.676183\pi$
$104$	−5.66074			−0.555081
$105$		0			0
$106$	2.74660			0.266773
$107$	5.69821	−	1.52683i	0.550867	−	0.147604i	0.0273597	−	0.999626i	$-0.491290\pi$
$107$	5.69821	−	1.52683i	0.550867	−	0.147604i	0.523507	+	0.852021i	$0.324623\pi$
$108$	0.258819	−	0.965926i	0.0249049	−	0.0929463i
$109$	−14.3923	+	8.30937i	−1.37853	+	0.795893i	−0.991982	−	0.126377i	$-0.959665\pi$
$109$	−14.3923	+	8.30937i	−1.37853	+	0.795893i	−0.386546	+	0.922270i	$0.626332\pi$
$110$		0			0
$111$			8.06444i			0.765443i
$112$	−2.64286	+	0.123551i	−0.249727	+	0.0116744i
$113$	−6.35390	+	6.35390i	−0.597724	+	0.597724i	−0.939706	−	0.341982i	$-0.888902\pi$
$113$	−6.35390	+	6.35390i	−0.597724	+	0.597724i	0.341982	+	0.939706i	$0.388902\pi$
$114$	5.04586	+	2.91323i	0.472588	+	0.272849i
$115$		0			0
$116$	2.76886	+	4.79581i	0.257082	+	0.445280i
$117$	1.46511	+	5.46786i	0.135449	+	0.505503i
$118$	−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
$122$	−13.0935	−	3.50839i	−1.18543	−	0.317634i
$123$	10.5723	+	2.83285i	0.953276	+	0.255430i
$124$	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	0.998942	+	0.0459856i	$0.0146428\pi$
$127$	11.7757	+	11.7757i	1.04493	+	1.04493i	0.0459856	+	0.998942i	$0.485357\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	−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
$133$	−15.3985	+	0.719863i	−1.33522	+	0.0624200i
$134$		−	3.81023i		−	0.329154i
$135$		0			0
$136$	−1.42012	+	0.819909i	−0.121775	+	0.0703066i
$137$	1.14632	−	4.27811i	0.0979364	−	0.365503i	−0.899512	−	0.436896i	$-0.856078\pi$
$137$	1.14632	−	4.27811i	0.0979364	−	0.365503i	0.997448	+	0.0713928i	$0.0227444\pi$
$138$	4.26196	−	1.14199i	0.362802	−	0.0972126i
$139$	4.35020			0.368979			0.184489	−	0.982835i	$-0.440937\pi$
$139$	4.35020			0.368979			0.184489	+	0.982835i	$0.440937\pi$
$140$		0			0
$141$	−9.04024			−0.761325
$142$	8.55692	−	2.29282i	0.718080	−	0.192409i
$143$	−0.675582	+	2.52131i	−0.0564950	+	0.210842i
$144$	−0.866025	+	0.500000i	−0.0721688	+	0.0416667i
$145$		0			0
$146$		−	4.05729i		−	0.335784i
$147$	−5.38994	−	4.46638i	−0.444555	−	0.368381i
$148$	5.70242	−	5.70242i	0.468736	−	0.468736i
$149$	−3.75900	−	2.17026i	−0.307949	−	0.177794i	0.338059	−	0.941125i	$-0.390230\pi$
$149$	−3.75900	−	2.17026i	−0.307949	−	0.177794i	−0.646008	+	0.763330i	$0.723563\pi$
$150$		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	$0.941411\pi$
$152$	−1.50800	−	5.62793i	−0.122315	−	0.456485i
$153$	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
$157$	−21.0333	−	5.63586i	−1.67864	−	0.449790i	−0.711221	−	0.702969i	$-0.751857\pi$
$157$	−21.0333	−	5.63586i	−1.67864	−	0.449790i	−0.967420	+	0.253178i	$0.918524\pi$
$158$	4.88882	+	1.30995i	0.388933	+	0.104214i
$159$	−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
$163$	3.02164	+	11.2769i	0.236673	+	0.883275i	0.977388	+	0.211456i	$0.0678204\pi$
$163$	3.02164	+	11.2769i	0.236673	+	0.883275i	−0.740715	+	0.671820i	$0.765513\pi$
$164$	−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	−0.225703	+	0.974196i	$0.572468\pi$
$167$	−15.5061	+	15.5061i	−1.19990	+	1.19990i	−0.974196	+	0.225703i	$0.927532\pi$
$168$	1.21443	−	2.35056i	0.0936957	−	0.181350i
$169$			19.0440i			1.46492i
$170$		0			0
$171$	−5.04586	+	2.91323i	−0.385867	+	0.222780i
$172$	−1.73915	+	6.49061i	−0.132609	+	0.494905i
$173$	9.41238	−	2.52204i	0.715610	−	0.191747i	0.117398	−	0.993085i	$-0.462545\pi$
$173$	9.41238	−	2.52204i	0.715610	−	0.191747i	0.598212	+	0.801338i	$0.295878\pi$
$174$	−5.53773			−0.419814
$175$		0			0
$176$	−0.461115			−0.0347578
$177$	1.85224	−	0.496307i	0.139223	−	0.0373047i
$178$	2.95790	−	11.0391i	0.221704	−	0.827412i
$179$	−1.39876	+	0.807576i	−0.104548	+	0.0603611i	−0.551363	−	0.834266i	$-0.685892\pi$
$179$	−1.39876	+	0.807576i	−0.104548	+	0.0603611i	0.446814	+	0.894627i	$0.352559\pi$
$180$		0			0
$181$			12.8519i			0.955277i	0.878556	+	0.477639i	$0.158507\pi$
$181$			12.8519i			0.955277i	−0.878556	+	0.477639i	$0.841493\pi$
$182$	0.699388	+	14.9606i	0.0518421	+	1.10895i
$183$	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
$187$	0.195704	+	0.730379i	0.0143113	+	0.0534106i
$188$	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	$0.0413790\pi$
$192$	0.965926	+	0.258819i	0.0697097	+	0.0186787i
$193$	6.97019	+	1.86766i	0.501726	+	0.134437i	0.500801	−	0.865563i	$-0.333039\pi$
$193$	6.97019	+	1.86766i	0.501726	+	0.134437i	0.000924826		1.00000i	$0.499706\pi$
$194$	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	0.962911	−	0.269818i	$-0.0869635\pi$
$197$	9.72803	+	9.72803i	0.693093	+	0.693093i	−0.269818	+	0.962911i	$0.586964\pi$
$198$	0.119345	+	0.445403i	0.00848150	+	0.0316534i
$199$	−4.82648	−	8.35971i	−0.342140	−	0.592604i	0.642690	−	0.766127i	$-0.277818\pi$
$199$	−4.82648	−	8.35971i	−0.342140	−	0.592604i	−0.984830	+	0.173522i	$0.944485\pi$
$200$		0			0
$201$	3.29976	+	1.90512i	0.232747	+	0.134377i
$202$	3.19033	−	3.19033i	0.224471	−	0.224471i
$203$	12.3326	−	7.91026i	0.865578	−	0.555191i
$204$		−	1.63982i		−	0.114810i
$205$		0			0
$206$	−12.7958	+	7.38767i	−0.891527	+	0.514723i
$207$	−1.14199	+	4.26196i	−0.0793737	+	0.296227i
$208$	−5.46786	+	1.46511i	−0.379128	+	0.101587i
$209$	−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	$0.485393\pi$
$212$	2.65301	−	0.710873i	0.182210	−	0.0488229i
$213$	−2.29282	+	8.55692i	−0.157101	+	0.586310i
$214$	5.10888	−	2.94961i	0.349236	−	0.201631i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−0.0762571	−	0.0393987i	−0.00517667	−	0.00267456i
$218$	−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
$222$	2.08723	+	7.78966i	0.140086	+	0.522807i
$223$	8.25284	+	8.25284i	0.552651	+	0.552651i	0.927205	−	0.374554i	$-0.122204\pi$
$223$	8.25284	+	8.25284i	0.552651	+	0.552651i	−0.374554	+	0.927205i	$0.622204\pi$
$224$	−2.52083	+	0.803365i	−0.168430	+	0.0536771i
$225$		0			0
$226$	−4.49288	+	7.78190i	−0.298862	+	0.517645i
$227$	21.6006	+	5.78787i	1.43368	+	0.384154i	0.890317	−	0.455341i	$-0.150483\pi$
$227$	21.6006	+	5.78787i	1.43368	+	0.384154i	0.543367	+	0.839496i	$0.317149\pi$
$228$	5.62793	+	1.50800i	0.372719	+	0.0998696i
$229$	−2.48311	+	4.30087i	−0.164088	+	0.284209i	−0.936331	−	0.351118i	$-0.885802\pi$
$229$	−2.48311	+	4.30087i	−0.164088	+	0.284209i	0.772243	+	0.635328i	$0.219135\pi$
$230$		0			0
$231$	−0.902010	−	0.821441i	−0.0593479	−	0.0540468i
$232$	3.91576	+	3.91576i	0.257082	+	0.257082i
$233$	−7.41098	−	27.6582i	−0.485509	−	1.81195i	−0.577756	−	0.816210i	$-0.696071\pi$
$233$	−7.41098	−	27.6582i	−0.485509	−	1.81195i	0.0922466	−	0.995736i	$-0.470595\pi$
$234$	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
$238$	2.34237	+	3.65189i	0.151833	+	0.236717i
$239$			13.9230i			0.900603i	0.892877	+	0.450302i	$0.148684\pi$
$239$			13.9230i			0.900603i	−0.892877	+	0.450302i	$0.851316\pi$
$240$		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	$0.322489\pi$
$242$	2.79198	−	10.4198i	0.179475	−	0.669810i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	−13.5554			−0.867793
$245$		0			0
$246$	10.9453			0.697847
$247$	−31.8582	+	8.53639i	−2.02709	+	0.543157i
$248$	0.00839662	−	0.0313366i	0.000533186	−	0.00198988i
$249$	−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	$0.935645\pi$
$252$	1.42843	+	2.22701i	0.0899827	+	0.140289i
$253$	−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
$257$	−2.68681	−	10.0273i	−0.167599	−	0.625488i	−0.997694	−	0.0678664i	$-0.978381\pi$
$257$	−2.68681	−	10.0273i	−0.167599	−	0.625488i	0.830096	−	0.557621i	$-0.188286\pi$
$258$	−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
$262$	18.3299	+	4.91148i	1.13242	+	0.303432i
$263$	22.9523	+	6.15005i	1.41530	+	0.379228i	0.883814	−	0.467839i	$-0.154967\pi$
$263$	22.9523	+	6.15005i	1.41530	+	0.379228i	0.531486	+	0.847067i	$0.321634\pi$
$264$	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
$268$	−0.986161	−	3.68040i	−0.0602394	−	0.224816i
$269$	0.710036	+	1.22982i	0.0432917	+	0.0749834i	0.886859	−	0.462040i	$-0.152882\pi$
$269$	0.710036	+	1.22982i	0.0432917	+	0.0749834i	−0.843568	+	0.537023i	$0.819549\pi$
$270$		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
$273$	−13.3059	−	6.87460i	−0.805312	−	0.416070i
$274$		−	4.42902i		−	0.267567i
$275$		0			0
$276$	3.82117	−	2.20615i	0.230007	−	0.132795i
$277$	6.08269	−	22.7009i	0.365474	−	1.36397i	−0.501304	−	0.865271i	$-0.667146\pi$
$277$	6.08269	−	22.7009i	0.365474	−	1.36397i	0.866778	−	0.498695i	$-0.166187\pi$
$278$	4.20197	−	1.12591i	0.252017	−	0.0675278i
$279$	−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	$0.177006\pi$
$282$	−8.73220	+	2.33979i	−0.519995	+	0.139332i
$283$	0.972612	−	3.62984i	0.0578158	−	0.215771i	−0.930974	−	0.365085i	$-0.881040\pi$
$283$	0.972612	−	3.62984i	0.0578158	−	0.215771i	0.988790	+	0.149314i	$0.0477065\pi$
$284$	7.67192	−	4.42939i	0.455245	−	0.262836i
$285$		0			0
$286$			2.61025i			0.154347i
$287$	−24.3753	+	15.6346i	−1.43883	+	0.922881i
$288$	−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
$292$	−1.05010	−	3.91904i	−0.0614527	−	0.229344i
$293$	4.18500	+	4.18500i	0.244490	+	0.244490i	0.818705	−	0.574215i	$-0.194692\pi$
$293$	4.18500	+	4.18500i	0.244490	+	0.244490i	−0.574215	+	0.818705i	$0.694692\pi$
$294$	−6.36227	−	2.91917i	−0.371055	−	0.170250i
$295$		0			0
$296$	4.03222	−	6.98401i	0.234368	−	0.405938i
$297$	−0.445403	−	0.119345i	−0.0258449	−	0.00692511i
$298$	−4.19262	−	1.12341i	−0.242872	−	0.0650773i
$299$	−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
$303$	1.16774	+	4.35807i	0.0670850	+	0.250365i
$304$	−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	0.0329031	−	0.999459i	$-0.489525\pi$
$307$	18.0884	−	18.0884i	1.03236	−	1.03236i	0.999459	−	0.0329031i	$-0.0104753\pi$
$308$	0.0569710	+	1.21866i	0.00324623	+	0.0694398i
$309$		−	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	$0.931165\pi$
$312$	1.46511	−	5.46786i	0.0829454	−	0.309556i
$313$	−22.1819	+	5.94363i	−1.25380	+	0.335954i	−0.823802	−	0.566877i	$-0.808151\pi$
$313$	−22.1819	+	5.94363i	−1.25380	+	0.335954i	−0.429995	+	0.902831i	$0.641485\pi$
$314$	−21.7753			−1.22885
$315$		0			0
$316$	5.06128			0.284719
$317$	24.7683	−	6.63663i	1.39112	−	0.372751i	0.515975	−	0.856604i	$-0.327430\pi$
$317$	24.7683	−	6.63663i	1.39112	−	0.372751i	0.875149	+	0.483853i	$0.160763\pi$
$318$	−0.710873	+	2.65301i	−0.0398638	+	0.148774i
$319$	2.21142	−	1.27676i	0.123816	−	0.0714850i
$320$		0			0
$321$			5.89922i			0.329262i
$322$	−5.35846	+	10.3714i	−0.298615	+	0.577976i
$323$	−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
$327$	−4.30125	−	16.0525i	−0.237860	−	0.887704i
$328$	−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	$0.0609403\pi$
$332$	1.48642	+	0.398284i	0.0815777	+	0.0218587i
$333$	−7.78966	−	2.08723i	−0.426870	−	0.114380i
$334$	−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	0.788573	−	0.614941i	$-0.210820\pi$
$337$	3.18746	+	3.18746i	0.173632	+	0.173632i	−0.614941	+	0.788573i	$0.710820\pi$
$338$	4.92895	+	18.3951i	0.268099	+	1.00056i
$339$	−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
$343$	18.3387	−	2.58702i	0.990196	−	0.139686i
$344$			6.71958i			0.362295i
$345$		0			0
$346$	8.43891	−	4.87221i	0.453679	−	0.261931i
$347$	5.54445	−	20.6922i	0.297642	−	1.11081i	−0.641455	−	0.767161i	$-0.721669\pi$
$347$	5.54445	−	20.6922i	0.297642	−	1.11081i	0.939097	−	0.343653i	$-0.111664\pi$
$348$	−5.34903	+	1.43327i	−0.286738	+	0.0768313i
$349$	16.0682			0.860113			0.430056	−	0.902802i	$-0.358494\pi$
$349$	16.0682			0.860113			0.430056	+	0.902802i	$0.358494\pi$
$350$		0			0
$351$	−5.66074			−0.302148
$352$	−0.445403	+	0.119345i	−0.0237400	+	0.00636112i
$353$	7.60823	−	28.3943i	0.404945	−	1.51128i	−0.399211	−	0.916859i	$-0.630716\pi$
$353$	7.60823	−	28.3943i	0.404945	−	1.51128i	0.804156	−	0.594418i	$-0.202617\pi$
$354$	1.66067	−	0.958791i	0.0882638	−	0.0509592i
$355$		0			0
$356$		−	11.4285i		−	0.605708i
$357$	−4.33382	+	0.202601i	−0.229370	+	0.0107228i
$358$	−1.14209	+	1.14209i	−0.0603611	+	0.0603611i
$359$	11.8017	+	6.81369i	0.622868	+	0.359613i	0.777985	−	0.628283i	$-0.216242\pi$
$359$	11.8017	+	6.81369i	0.622868	+	0.359613i	−0.155117	+	0.987896i	$0.549575\pi$
$360$		0			0
$361$	−7.47381	−	12.9450i	−0.393359	−	0.681317i
$362$	3.32633	+	12.4140i	0.174828	+	0.652466i
$363$	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
$367$	−12.3244	−	3.30230i	−0.643326	−	0.172379i	−0.0776164	−	0.996983i	$-0.524731\pi$
$367$	−12.3244	−	3.30230i	−0.643326	−	0.172379i	−0.565709	+	0.824605i	$0.691398\pi$
$368$	−4.26196	−	1.14199i	−0.222170	−	0.0595303i
$369$	−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
$373$	−1.03563	−	3.86501i	−0.0536227	−	0.200123i	0.933918	−	0.357488i	$-0.116367\pi$
$373$	−1.03563	−	3.86501i	−0.0536227	−	0.200123i	−0.987540	+	0.157365i	$0.949700\pi$
$374$	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
$378$	−2.64286	+	0.123551i	−0.135934	+	0.00635476i
$379$			1.00281i			0.0515109i	0.999668	+	0.0257555i	$0.00819912\pi$
$379$			1.00281i			0.0515109i	−0.999668	+	0.0257555i	$0.991801\pi$
$380$		0			0
$381$	−14.4223	+	8.32670i	−0.738875	+	0.426590i
$382$	2.74365	−	10.2394i	0.140377	−	0.523895i
$383$	17.1965	−	4.60780i	0.878702	−	0.235447i	0.208855	−	0.977947i	$-0.433026\pi$
$383$	17.1965	−	4.60780i	0.878702	−	0.235447i	0.669847	+	0.742499i	$0.266360\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	7.21608			0.367289
$387$	6.49061	−	1.73915i	0.329936	−	0.0884062i
$388$	0.921648	−	3.43964i	0.0467896	−	0.174621i
$389$	9.75032	−	5.62935i	0.494361	−	0.285419i	−0.232021	−	0.972711i	$-0.574534\pi$
$389$	9.75032	−	5.62935i	0.494361	−	0.285419i	0.726382	+	0.687291i	$0.241200\pi$
$390$		0			0
$391$			7.23538i			0.365909i
$392$	2.43463	+	6.56297i	0.122968	+	0.331480i
$393$	−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
$397$	0.992011	+	3.70224i	0.0497876	+	0.185810i	0.986341	−	0.164714i	$-0.0526702\pi$
$397$	0.992011	+	3.70224i	0.0497876	+	0.185810i	−0.936554	+	0.350524i	$0.886003\pi$
$398$	−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	$0.173821\pi$
$402$	3.68040	+	0.986161i	0.183562	+	0.0491852i
$403$	−0.177388	−	0.0475311i	−0.00883634	−	0.00236769i
$404$	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
$408$	−0.424416	−	1.58394i	−0.0210117	−	0.0784168i
$409$	−6.44633	−	11.1654i	−0.318751	−	0.552092i	0.661477	−	0.749965i	$-0.269930\pi$
$409$	−6.44633	−	11.1654i	−0.318751	−	0.552092i	−0.980228	+	0.197873i	$0.936597\pi$
$410$		0			0
$411$	3.83565	+	2.21451i	0.189199	+	0.109234i
$412$	−10.4477	+	10.4477i	−0.514723	+	0.514723i
$413$	−2.32878	+	4.50740i	−0.114592	+	0.221795i
$414$			4.41231i			0.216853i
$415$		0			0
$416$	−4.90235	+	2.83037i	−0.240357	+	0.138770i
$417$	−1.12591	+	4.20197i	−0.0551362	+	0.205771i
$418$	−2.59512	+	0.695360i	−0.126931	+	0.0340112i
$419$	19.8918			0.971777			0.485888	−	0.874021i	$-0.338496\pi$
$419$	19.8918			0.971777			0.485888	+	0.874021i	$0.338496\pi$
$420$		0			0
$421$	−12.6339			−0.615740			−0.307870	−	0.951428i	$-0.599616\pi$
$421$	−12.6339			−0.615740			−0.307870	+	0.951428i	$0.599616\pi$
$422$	1.28732	−	0.344935i	0.0626655	−	0.0167912i
$423$	2.33979	−	8.73220i	0.113764	−	0.424574i
$424$	2.37863	−	1.37330i	0.115516	−	0.0666934i
$425$		0			0
$426$			8.85877i			0.429209i
$427$	1.67477	+	35.8250i	0.0810480	+	1.73369i
$428$	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	$-0.432349\pi$
$432$	−0.258819	−	0.965926i	−0.0124524	−	0.0464731i
$433$	3.04743	+	3.04743i	0.146450	+	0.146450i	0.776530	−	0.630080i	$-0.216978\pi$
$433$	3.04743	+	3.04743i	0.146450	+	0.146450i	−0.630080	+	0.776530i	$0.716978\pi$
$434$	−0.0838558	−	0.0183195i	−0.00402521	−	0.000879362i
$435$		0			0
$436$	−8.30937	+	14.3923i	−0.397947	+	0.689264i
$437$	−24.8321	−	6.65375i	−1.18788	−	0.318292i
$438$	3.91904	+	1.05010i	0.187259	+	0.0501759i
$439$	18.4993	−	32.0418i	0.882926	−	1.52927i	0.0348530	−	0.999392i	$-0.488904\pi$
$439$	18.4993	−	32.0418i	0.882926	−	1.52927i	0.848073	−	0.529880i	$-0.177763\pi$
$440$		0			0
$441$	5.70921	−	4.05030i	0.271867	−	0.192871i
$442$	6.56378	+	6.56378i	0.312207	+	0.312207i
$443$	4.60633	+	17.1911i	0.218854	+	0.816773i	0.984774	+	0.173838i	$0.0556168\pi$
$443$	4.60633	+	17.1911i	0.218854	+	0.816773i	−0.765921	+	0.642935i	$0.777717\pi$
$444$	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
$448$	−2.22701	+	1.42843i	−0.105216	+	0.0674870i
$449$			2.41945i			0.114181i	0.998369	+	0.0570904i	$0.0181823\pi$
$449$			2.41945i			0.114181i	−0.998369	+	0.0570904i	$0.981818\pi$
$450$		0			0
$451$	−4.37086	+	2.52352i	−0.205816	+	0.118828i
$452$	−2.32569	+	8.67959i	−0.109391	+	0.408253i
$453$	7.90624	−	2.11847i	0.371468	−	0.0995345i
$454$	22.3626			1.04953
$455$		0			0
$456$	5.82646			0.272849
$457$	−26.6198	+	7.13275i	−1.24522	+	0.333656i	−0.820488	−	0.571663i	$-0.806298\pi$
$457$	−26.6198	+	7.13275i	−1.24522	+	0.333656i	−0.424732	+	0.905319i	$0.639632\pi$
$458$	−1.28535	+	4.79700i	−0.0600605	+	0.224149i
$459$	−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	$-0.00761434\pi$
$462$	−1.08388	−	0.559993i	−0.0504266	−	0.0260533i
$463$	8.26507	−	8.26507i	0.384111	−	0.384111i	−0.488470	−	0.872581i	$-0.662445\pi$
$463$	8.26507	−	8.26507i	0.384111	−	0.384111i	0.872581	+	0.488470i	$0.162445\pi$
$464$	4.79581	+	2.76886i	0.222640	+	0.128541i
$465$		0			0
$466$	−14.3169	−	24.7976i	−0.663218	−	1.14873i
$467$	4.79974	+	17.9129i	0.222106	+	0.828910i	0.983543	+	0.180672i	$0.0578271\pi$
$467$	4.79974	+	17.9129i	0.222106	+	0.828910i	−0.761438	+	0.648238i	$0.775506\pi$
$468$	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
$472$	−1.85224	−	0.496307i	−0.0852563	−	0.0228444i
$473$	2.99292	+	0.801949i	0.137614	+	0.0368737i
$474$	−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
$478$	3.60353	+	13.4486i	0.164822	+	0.615123i
$479$	−4.23872	−	7.34168i	−0.193672	−	0.335450i	0.752792	−	0.658258i	$-0.228706\pi$
$479$	−4.23872	−	7.34168i	−0.193672	−	0.335450i	−0.946464	+	0.322808i	$0.895373\pi$
$480$		0			0
$481$	−39.5347	−	22.8254i	−1.80263	−	1.04075i
$482$	0.747813	−	0.747813i	0.0340620	−	0.0340620i
$483$	−6.30267	−	9.82626i	−0.286782	−	0.447110i
$484$		−	10.7874i		−	0.490335i
$485$		0			0
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	1.25691	−	4.69084i	0.0569558	−	0.212562i	−0.931583	−	0.363529i	$-0.881572\pi$
$487$	1.25691	−	4.69084i	0.0569558	−	0.212562i	0.988539	+	0.150967i	$0.0482386\pi$
$488$	−13.0935	+	3.50839i	−0.592714	+	0.158817i
$489$	−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	$0.826005\pi$
$492$	10.5723	−	2.83285i	0.476638	−	0.127715i
$493$	2.35030	−	8.77144i	0.105852	−	0.395046i
$494$	−28.5633	+	16.4910i	−1.28512	+	0.741967i
$495$		0			0
$496$		−	0.0324420i		−	0.00145669i
$497$	−12.6541	−	19.7286i	−0.567616	−	0.884949i
$498$	−1.08813	+	1.08813i	−0.0487604	+	0.0487604i
$499$	0.443575	+	0.256098i	0.0198571	+	0.0114645i	0.509896	−	0.860236i	$-0.329684\pi$
$499$	0.443575	+	0.256098i	0.0198571	+	0.0114645i	−0.490039	+	0.871701i	$0.663017\pi$
$500$		0			0
$501$	−10.9645	−	18.9910i	−0.489857	−	0.848457i
$502$	1.64676	+	6.14580i	0.0734986	+	0.274301i
$503$	−8.58209	−	8.58209i	−0.382657	−	0.382657i	0.489402	−	0.872058i	$-0.337215\pi$
$503$	−8.58209	−	8.58209i	−0.382657	−	0.382657i	−0.872058	+	0.489402i	$0.837215\pi$
$504$	1.95615	+	1.78142i	0.0871339	+	0.0793509i
$505$		0			0
$506$	−1.01729	+	1.76200i	−0.0452240	+	0.0783303i
$507$	−18.3951	−	4.92895i	−0.816954	−	0.218902i
$508$	16.0860	+	4.31022i	0.713699	+	0.191235i
$509$	−5.69382	+	9.86199i	−0.252374	+	0.437125i	−0.964179	−	0.265252i	$-0.914545\pi$
$509$	−5.69382	+	9.86199i	−0.252374	+	0.437125i	0.711805	+	0.702377i	$0.247878\pi$
$510$		0			0
$511$	−10.2278	+	3.25948i	−0.452449	+	0.144191i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−1.50800	−	5.62793i	−0.0665798	−	0.248479i
$514$	−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
$518$	−18.9560	−	9.79374i	−0.832878	−	0.430312i
$519$			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	$0.192839\pi$
$522$	1.43327	−	5.34903i	0.0627325	−	0.234121i
$523$	14.3848	−	3.85439i	0.629003	−	0.168541i	0.0697859	−	0.997562i	$-0.477768\pi$
$523$	14.3848	−	3.85439i	0.629003	−	0.168541i	0.559217	+	0.829021i	$0.311102\pi$
$524$	18.9765			0.828992
$525$		0			0
$526$	23.7620			1.03607
$527$	−0.0513863	+	0.0137689i	−0.00223842	+	0.000599783i
$528$	0.119345	−	0.445403i	0.00519383	−	0.0193837i
$529$	3.05841	−	1.76577i	0.132974	−	0.0767728i
$530$		0			0
$531$			1.91758i			0.0832159i
$532$	−12.9756	+	8.32269i	−0.562564	+	0.360834i
$533$	−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
$537$	−0.418032	−	1.56012i	−0.0180394	−	0.0673241i
$538$	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	$0.775790\pi$
$542$	−0.341553	−	0.0915187i	−0.0146709	−	0.00393107i
$543$	−12.4140	−	3.32633i	−0.532737	−	0.142746i
$544$	−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	0.499109	−	0.866539i	$-0.333661\pi$
$547$	−8.59346	−	8.59346i	−0.367430	−	0.367430i	−0.866539	+	0.499109i	$0.833661\pi$
$548$	−1.14632	−	4.27811i	−0.0489682	−	0.182752i
$549$	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
$553$	−0.625324	−	13.3763i	−0.0265915	−	0.568817i
$554$		−	23.5017i		−	0.998492i
$555$		0			0
$556$	3.76738	−	2.17510i	0.159772	−	0.0922447i
$557$	−2.20835	+	8.24166i	−0.0935706	+	0.349210i	−0.996799	−	0.0799502i	$-0.974524\pi$
$557$	−2.20835	+	8.24166i	−0.0935706	+	0.349210i	0.903228	+	0.429160i	$0.141191\pi$
$558$	−0.0313366	+	0.00839662i	−0.00132658	+	0.000355457i
$559$	38.0378			1.60883
$560$		0			0
$561$	−0.756144			−0.0319244
$562$	27.5045	−	7.36980i	1.16021	−	0.310876i
$563$	0.0365566	−	0.136431i	0.00154068	−	0.00574988i	−0.965151	−	0.261693i	$-0.915719\pi$
$563$	0.0365566	−	0.136431i	0.00154068	−	0.00574988i	0.966692	+	0.255943i	$0.0823859\pi$
$564$	−7.82908	+	4.52012i	−0.329664	+	0.190331i
$565$		0			0
$566$		−	3.75788i		−	0.157956i
$567$	1.21443	−	2.35056i	0.0510015	−	0.0987144i
$568$	6.26410	−	6.26410i	0.262836	−	0.262836i
$569$	−3.62902	−	2.09521i	−0.152136	−	0.0878359i	0.421999	−	0.906596i	$-0.361328\pi$
$569$	−3.62902	−	2.09521i	−0.152136	−	0.0878359i	−0.574136	+	0.818760i	$0.694662\pi$
$570$		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	$0.767628\pi$
$572$	0.675582	+	2.52131i	0.0282475	+	0.105421i
$573$	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
$577$	−7.85753	−	2.10542i	−0.327113	−	0.0876498i	0.0915250	−	0.995803i	$-0.470826\pi$
$577$	−7.85753	−	2.10542i	−0.327113	−	0.0876498i	−0.418638	+	0.908153i	$0.637493\pi$
$578$	−13.8234	−	3.70396i	−0.574976	−	0.154064i
$579$	−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
$583$	−0.327794	−	1.22334i	−0.0135758	−	0.0506657i
$584$	−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	$-0.547442\pi$
$587$	20.3618	−	20.3618i	0.840423	−	0.840423i	0.988914	+	0.148491i	$0.0474416\pi$
$588$	−6.90101	−	1.17303i	−0.284593	−	0.0483749i
$589$		−	0.189022i		−	0.00778852i
$590$		0			0
$591$	−11.9144	+	6.87875i	−0.490091	+	0.282954i
$592$	2.08723	−	7.78966i	0.0857847	−	0.320153i
$593$	−18.1374	+	4.85990i	−0.744814	+	0.199572i	−0.611217	−	0.791463i	$-0.709320\pi$
$593$	−18.1374	+	4.85990i	−0.744814	+	0.199572i	−0.133597	+	0.991036i	$0.542653\pi$
$594$	−0.461115			−0.0189198
$595$		0			0
$596$	−4.34052			−0.177794
$597$	9.32405	−	2.49837i	0.381608	−	0.102251i
$598$	−6.46450	+	24.1259i	−0.264353	+	0.986580i
$599$	21.0442	−	12.1499i	0.859844	−	0.496431i	−0.00411624	−	0.999992i	$-0.501310\pi$
$599$	21.0442	−	12.1499i	0.859844	−	0.496431i	0.863960	+	0.503561i	$0.167977\pi$
$600$		0			0
$601$		−	21.1930i		−	0.864481i	−0.901758	−	0.432241i	$-0.857723\pi$
$601$		−	21.1930i		−	0.864481i	0.901758	−	0.432241i	$-0.142277\pi$
$602$	17.7589	−	0.830208i	0.723800	−	0.0338368i
$603$	−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
$607$	−2.46768	−	9.20949i	−0.100160	−	0.373802i	0.897591	−	0.440829i	$-0.145315\pi$
$607$	−2.46768	−	9.20949i	−0.100160	−	0.373802i	−0.997751	+	0.0670268i	$0.978649\pi$
$608$	−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
$612$	1.58394	+	0.424416i	0.0640271	+	0.0171560i
$613$	−21.5587	−	5.77664i	−0.870748	−	0.233316i	−0.204337	−	0.978901i	$-0.565504\pi$
$613$	−21.5587	−	5.77664i	−0.870748	−	0.233316i	−0.666411	+	0.745585i	$0.732170\pi$
$614$	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	0.323836	−	0.946113i	$-0.395027\pi$
$617$	−15.4571	−	15.4571i	−0.622278	−	0.622278i	−0.946113	+	0.323836i	$0.895027\pi$
$618$	−3.82414	−	14.2719i	−0.153829	−	0.574099i
$619$	12.3595	+	21.4073i	0.496772	+	0.860434i	0.999993	−	0.00372371i	$-0.00118530\pi$
$619$	12.3595	+	21.4073i	0.496772	+	0.860434i	−0.503221	+	0.864158i	$0.667852\pi$
$620$		0			0
$621$	−3.82117	−	2.20615i	−0.153338	−	0.0885299i
$622$	−23.7712	+	23.7712i	−0.953139	+	0.953139i
$623$	−30.2039	+	1.41200i	−1.21009	+	0.0565704i
$624$		−	5.66074i		−	0.226611i
$625$		0			0
$626$	−19.8878	+	11.4822i	−0.794876	+	0.458922i
$627$	0.695360	−	2.59512i	0.0277700	−	0.103639i
$628$	−21.0333	+	5.63586i	−0.839320	+	0.224895i
$629$	−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	$0.257039\pi$
$632$	4.88882	−	1.30995i	0.194467	−	0.0521072i
$633$	−0.344935	+	1.28732i	−0.0137099	+	0.0511662i
$634$	22.2066	−	12.8210i	0.881937	−	0.509187i
$635$		0			0
$636$			2.74660i			0.108910i
$637$	37.1513	−	13.7818i	1.47199	−	0.546056i
$638$	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	$0.907243\pi$
$642$	1.52683	+	5.69821i	0.0602592	+	0.224890i
$643$	21.8198	+	21.8198i	0.860489	+	0.860489i	0.991395	−	0.130906i	$-0.0417886\pi$
$643$	21.8198	+	21.8198i	0.860489	+	0.860489i	−0.130906	+	0.991395i	$0.541789\pi$
$644$	−2.49155	+	11.4049i	−0.0981810	+	0.449415i
$645$		0			0
$646$	−4.77716	+	8.27429i	−0.187955	+	0.325548i
$647$	−35.8827	−	9.61474i	−1.41069	−	0.377994i	−0.528521	−	0.848920i	$-0.677253\pi$
$647$	−35.8827	−	9.61474i	−1.41069	−	0.377994i	−0.882173	+	0.470926i	$0.843920\pi$
$648$	0.965926	+	0.258819i	0.0379452	+	0.0101674i
$649$	−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
$653$	−8.18328	−	30.5404i	−0.320237	−	1.19514i	−0.919014	−	0.394224i	$-0.871013\pi$
$653$	−8.18328	−	30.5404i	−0.320237	−	1.19514i	0.598778	−	0.800915i	$-0.295653\pi$
$654$	−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
$658$	10.9788	−	21.2497i	0.427997	−	0.828398i
$659$			38.7284i			1.50864i	0.656504	+	0.754322i	$0.272034\pi$
$659$			38.7284i			1.50864i	−0.656504	+	0.754322i	$0.727966\pi$
$660$		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	$0.104477\pi$
$662$	3.07085	−	11.4606i	0.119352	−	0.445427i
$663$	−8.96628	+	2.40251i	−0.348222	+	0.0933057i
$664$	1.53885			0.0597190
$665$		0			0
$666$	−8.06444			−0.312491
$667$	23.6016	−	6.32402i	0.913856	−	0.244867i
$668$	−5.67563	+	21.1817i	−0.219597	+	0.819546i
$669$	−10.1076	+	5.83564i	−0.390784	+	0.225619i
$670$		0			0
$671$			6.25058i			0.241301i
$672$	−0.123551	−	2.64286i	−0.00476607	−	0.101951i
$673$	24.7046	−	24.7046i	0.952294	−	0.952294i	−0.0466190	−	0.998913i	$-0.514845\pi$
$673$	24.7046	−	24.7046i	0.952294	−	0.952294i	0.998913	+	0.0466190i	$0.0148447\pi$
$674$	3.90382	+	2.25387i	0.150370	+	0.0868159i
$675$		0			0
$676$	9.52199	+	16.4926i	0.366230	+	0.634330i
$677$	4.55637	+	17.0046i	0.175116	+	0.653540i	0.996532	+	0.0832112i	$0.0265176\pi$
$677$	4.55637	+	17.0046i	0.175116	+	0.653540i	−0.821416	+	0.570329i	$0.806816\pi$
$678$	−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
$682$	−0.0144498	−	0.00387180i	−0.000553310	−	0.000148259i
$683$	−23.3499	−	6.25658i	−0.893458	−	0.239401i	−0.217254	−	0.976115i	$-0.569710\pi$
$683$	−23.3499	−	6.25658i	−0.893458	−	0.239401i	−0.676205	+	0.736714i	$0.736377\pi$
$684$	−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
$688$	1.73915	+	6.49061i	0.0663046	+	0.247452i
$689$	−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
$693$	1.02691	−	0.658670i	0.0390090	−	0.0250208i
$694$		−	21.4221i		−	0.813172i
$695$		0			0
$696$	−4.79581	+	2.76886i	−0.181785	+	0.104953i
$697$	−4.64536	+	17.3367i	−0.175955	+	0.656675i
$698$	15.5207	−	4.15876i	0.587468	−	0.157412i
$699$	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	$0.614769\pi$
$702$	−5.46786	+	1.46511i	−0.206371	+	0.0552969i
$703$	12.1612	−	45.3861i	0.458667	−	1.71177i
$704$	−0.399337	+	0.230557i	−0.0150506	+	0.00868946i
$705$		0			0
$706$		−	29.3960i		−	1.10633i
$707$	−10.6053	−	5.47930i	−0.398853	−	0.206070i
$708$	1.35593	−	1.35593i	0.0509592	−	0.0509592i
$709$	−18.3186	−	10.5763i	−0.687971	−	0.397200i	0.114880	−	0.993379i	$-0.463351\pi$
$709$	−18.3186	−	10.5763i	−0.687971	−	0.397200i	−0.802851	+	0.596179i	$0.796685\pi$
$710$		0			0
$711$	−2.53064	−	4.38319i	−0.0949063	−	0.164383i
$712$	−2.95790	−	11.0391i	−0.110852	−	0.413706i
$713$	−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
$717$	−13.4486	−	3.60353i	−0.502246	−	0.134576i
$718$	13.1630	+	3.52703i	0.491241	+	0.131628i
$719$	−4.30625	+	7.45864i	−0.160596	+	0.278160i	−0.935083	−	0.354430i	$-0.884675\pi$
$719$	−4.30625	+	7.45864i	−0.160596	+	0.278160i	0.774487	+	0.632590i	$0.218008\pi$
$720$		0			0
$721$	28.9028	+	26.3211i	1.07640	+	0.980251i
$722$	−10.5696	−	10.5696i	−0.393359	−	0.393359i
$723$	0.273719	+	1.02153i	0.0101797	+	0.0379912i
$724$	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	$-0.641022\pi$
$727$	12.8013	−	12.8013i	0.474774	−	0.474774i	0.903455	+	0.428682i	$0.141022\pi$
$728$	8.08597	+	12.6065i	0.299686	+	0.467230i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	9.54263	−	5.50944i	0.352947	−	0.203774i
$732$	3.50839	−	13.0935i	0.129674	−	0.483949i
$733$	31.9503	−	8.56107i	1.18011	−	0.316210i	0.385142	−	0.922857i	$-0.374153\pi$
$733$	31.9503	−	8.56107i	1.18011	−	0.316210i	0.794971	+	0.606647i	$0.207486\pi$
$734$	−12.7591			−0.470947
$735$		0			0
$736$	−4.41231			−0.162640
$737$	−1.69709	+	0.454733i	−0.0625130	+	0.0167503i
$738$	−2.83285	+	10.5723i	−0.104279	+	0.389173i
$739$	40.9779	−	23.6586i	1.50740	−	0.870296i	0.507434	−	0.861690i	$-0.330594\pi$
$739$	40.9779	−	23.6586i	1.50740	−	0.870296i	0.999963	−	0.00860599i	$-0.00273940\pi$
$740$		0			0
$741$		−	32.9821i		−	1.21163i
$742$	−3.92333	−	6.11672i	−0.144030	−	0.224552i
$743$	21.5587	−	21.5587i	0.790914	−	0.790914i	−0.190729	−	0.981643i	$-0.561085\pi$
$743$	21.5587	−	21.5587i	0.790914	−	0.790914i	0.981643	+	0.190729i	$0.0610852\pi$
$744$	0.0280956	+	0.0162210i	0.00103004	+	0.000594691i
$745$		0			0
$746$	−2.00068	−	3.46527i	−0.0732500	−	0.126873i
$747$	−0.398284	−	1.48642i	−0.0145724	−	0.0543851i
$748$	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	$0.975213\pi$
$752$	8.73220	+	2.33979i	0.318431	+	0.0853232i
$753$	−6.14580	−	1.64676i	−0.223965	−	0.0600114i
$754$	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	0.942616	−	0.333879i	$-0.108358\pi$
$757$	16.7486	+	16.7486i	0.608738	+	0.608738i	−0.333879	+	0.942616i	$0.608358\pi$
$758$	0.259546	+	0.968641i	0.00942715	+	0.0351826i
$759$	−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
$763$	39.0634	+	20.1824i	1.41419	+	0.730651i
$764$		−	10.6007i		−	0.383518i
$765$		0			0
$766$	15.4180	−	8.90158i	0.557075	−	0.321627i
$767$	−2.80946	+	10.4851i	−0.101444	+	0.378593i
$768$	0.965926	−	0.258819i	0.0348548	−	0.00933933i
$769$	−7.70275			−0.277768			−0.138884	−	0.990309i	$-0.544352\pi$
$769$	−7.70275			−0.277768			−0.138884	+	0.990309i	$0.544352\pi$
$770$		0			0
$771$	10.3811			0.373865
$772$	6.97019	−	1.86766i	0.250863	−	0.0672185i
$773$	−0.783229	+	2.92305i	−0.0281708	+	0.105135i	−0.978580	−	0.205868i	$-0.933998\pi$
$773$	−0.783229	+	2.92305i	−0.0281708	+	0.105135i	0.950409	+	0.311003i	$0.100665\pi$
$774$	5.81932	−	3.35979i	0.209171	−	0.120765i
$775$		0			0
$776$		−	3.56097i		−	0.127832i
$777$	17.9596	−	11.5195i	0.644298	−	0.413260i
$778$	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
$782$	1.87265	+	6.98884i	0.0669660	+	0.249920i
$783$	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
$787$	21.6517	+	5.80155i	0.771799	+	0.206803i	0.623166	−	0.782089i	$-0.285846\pi$
$787$	21.6517	+	5.80155i	0.771799	+	0.206803i	0.148633	+	0.988892i	$0.452513\pi$
$788$	13.2887	+	3.56071i	0.473392	+	0.126845i
$789$	−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
$793$	19.8601	+	74.1188i	0.705252	+	2.63203i
$794$	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	$-0.934754\pi$
$797$	−21.8939	+	21.8939i	−0.775520	+	0.775520i	0.203545	+	0.979066i	$0.434754\pi$
$798$	−0.719863	−	15.3985i	−0.0254829	−	0.545103i
$799$		−	14.8243i		−	0.524447i
$800$		0			0
$801$	−9.89734	+	5.71423i	−0.349705	+	0.201903i
$802$	−0.232949	+	0.869376i	−0.00822570	+	0.0306987i
$803$	−1.80713	+	0.484218i	−0.0637721	+	0.0170877i
$804$	3.81023			0.134377
$805$		0			0
$806$	−0.183646			−0.00646865
$807$	−1.37168	+	0.367542i	−0.0482856	+	0.0129381i
$808$	1.16774	−	4.35807i	0.0410810	−	0.153316i
$809$	0.938781	−	0.542005i	0.0330058	−	0.0190559i	−0.483406	−	0.875396i	$-0.660601\pi$
$809$	0.938781	−	0.542005i	0.0330058	−	0.0190559i	0.516412	+	0.856340i	$0.327267\pi$
$810$		0			0
$811$		−	33.8754i		−	1.18953i	−0.803901	−	0.594763i	$-0.797246\pi$
$811$		−	33.8754i		−	1.18953i	0.803901	−	0.594763i	$-0.202754\pi$
$812$	6.72520	−	13.0168i	0.236008	−	0.456799i
$813$	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
$817$	10.1331	+	37.8173i	0.354513	+	1.32306i
$818$	−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	$0.193730\pi$
$822$	4.27811	+	1.14632i	0.149216	+	0.0399823i
$823$	−33.5482	−	8.98921i	−1.16942	−	0.313344i	−0.378695	−	0.925521i	$-0.623627\pi$
$823$	−33.5482	−	8.98921i	−1.16942	−	0.313344i	−0.790720	+	0.612177i	$0.790294\pi$
$824$	−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	0.897461	+	0.441093i	$0.145409\pi$
$827$	38.4936	+	38.4936i	1.33855	+	1.33855i	0.441093	+	0.897461i	$0.354591\pi$
$828$	1.14199	+	4.26196i	0.0396869	+	0.148113i
$829$	20.0652	+	34.7540i	0.696895	+	1.20706i	0.969538	+	0.244942i	$0.0787689\pi$
$829$	20.0652	+	34.7540i	0.696895	+	1.20706i	−0.272643	+	0.962115i	$0.587898\pi$
$830$		0			0
$831$	20.3531	+	11.7509i	0.706041	+	0.407633i
$832$	−4.00275	+	4.00275i	−0.138770	+	0.138770i
$833$	7.32405	−	8.83852i	0.253763	−	0.306236i
$834$			4.35020i			0.150635i
$835$		0			0
$836$	−2.32672	+	1.34333i	−0.0804713	+	0.0464601i
$837$	0.00839662	−	0.0313366i	0.000290229	−	0.00108315i
$838$	19.2140	−	5.14837i	0.663736	−	0.177848i
$839$	−27.8082			−0.960044			−0.480022	−	0.877256i	$-0.659371\pi$
$839$	−27.8082			−0.960044			−0.480022	+	0.877256i	$0.659371\pi$
$840$		0			0
$841$	−1.66640			−0.0574621
$842$	−12.2034	+	3.26990i	−0.420558	+	0.112688i
$843$	−7.36980	+	27.5045i	−0.253830	+	0.947305i
$844$	1.15418	−	0.666364i	0.0397284	−	0.0229372i
$845$		0			0
$846$		−	9.04024i		−	0.310810i
$847$	−28.5096	+	1.33279i	−0.979600	+	0.0457951i
$848$	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
$852$	2.29282	+	8.55692i	0.0785507	+	0.293155i
$853$	−19.0929	−	19.0929i	−0.653729	−	0.653729i	0.300160	−	0.953889i	$-0.402960\pi$
$853$	−19.0929	−	19.0929i	−0.653729	−	0.653729i	−0.953889	+	0.300160i	$0.902960\pi$
$854$	10.8899	+	34.1708i	0.372645	+	1.16930i
$855$		0			0
$856$	2.94961	−	5.10888i	0.100816	−	0.174618i
$857$	19.6936	+	5.27688i	0.672720	+	0.180255i	0.578980	−	0.815342i	$-0.303451\pi$
$857$	19.6936	+	5.27688i	0.672720	+	0.180255i	0.0937404	+	0.995597i	$0.470118\pi$
$858$	−2.52131	−	0.675582i	−0.0860760	−	0.0230640i
$859$	−2.24170	+	3.88275i	−0.0764860	+	0.132478i	−0.901732	−	0.432297i	$-0.857703\pi$
$859$	−2.24170	+	3.88275i	−0.0764860	+	0.132478i	0.825246	+	0.564774i	$0.191037\pi$
$860$		0			0
$861$	−8.79306	−	27.5913i	−0.299667	−	0.940308i
$862$	−21.7578	−	21.7578i	−0.741073	−	0.741073i
$863$	5.08496	+	18.9773i	0.173094	+	0.645996i	0.996868	+	0.0790782i	$0.0251977\pi$
$863$	5.08496	+	18.9773i	0.173094	+	0.645996i	−0.823774	+	0.566918i	$0.808136\pi$
$864$	−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
$868$	−0.0857399	+	0.00400824i	−0.00291020	+	0.000136048i
$869$		−	2.33383i		−	0.0791697i
$870$		0			0
$871$	−18.6791	+	10.7844i	−0.632916	+	0.365414i
$872$	−4.30125	+	16.0525i	−0.145659	+	0.543605i
$873$	−3.43964	+	0.921648i	−0.116414	+	0.0311931i
$874$	−25.7081			−0.869590
$875$		0			0
$876$	4.05729			0.137083
$877$	13.0106	−	3.48618i	0.439337	−	0.117720i	−0.0323688	−	0.999476i	$-0.510305\pi$
$877$	13.0106	−	3.48618i	0.439337	−	0.117720i	0.471706	+	0.881756i	$0.343638\pi$
$878$	9.57597	−	35.7380i	0.323173	−	1.20610i
$879$	−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	$0.622293\pi$
$882$	4.46638	−	5.38994i	0.150391	−	0.181489i
$883$	−3.82147	+	3.82147i	−0.128603	+	0.128603i	−0.768478	−	0.639876i	$-0.778986\pi$
$883$	−3.82147	+	3.82147i	−0.128603	+	0.128603i	0.639876	+	0.768478i	$0.278986\pi$
$884$	8.03895	+	4.64129i	0.270379	+	0.156103i
$885$		0			0
$886$	8.89875	+	15.4131i	0.298960	+	0.517813i
$887$	5.92466	+	22.1111i	0.198931	+	0.742419i	0.991214	+	0.132266i	$0.0422254\pi$
$887$	5.92466	+	22.1111i	0.198931	+	0.742419i	−0.792284	+	0.610153i	$0.791108\pi$
$888$	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
$892$	11.2736	+	3.02075i	0.377468	+	0.101142i
$893$	50.8778	+	13.6327i	1.70256	+	0.456200i
$894$	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
$898$	0.626200	+	2.33701i	0.0208966	+	0.0779870i
$899$	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
$903$	−8.16049	+	15.7948i	−0.271564	+	0.525618i
$904$			8.98577i			0.298862i
$905$		0			0
$906$	7.08854	−	4.09257i	0.235501	−	0.135967i
$907$	−7.08190	+	26.4300i	−0.235151	+	0.877595i	0.742930	+	0.669369i	$0.233435\pi$
$907$	−7.08190	+	26.4300i	−0.235151	+	0.877595i	−0.978081	+	0.208226i	$0.933231\pi$
$908$	21.6006	−	5.78787i	0.716842	−	0.192077i
$909$	−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	$0.872350\pi$
$912$	5.62793	−	1.50800i	0.186359	−	0.0499348i
$913$	0.183655	−	0.685408i	0.00607808	−	0.0226837i
$914$	−23.8666	+	13.7794i	−0.789438	+	0.455782i
$915$		0			0
$916$			4.96622i			0.164088i
$917$	−2.34456	−	50.1523i	−0.0774242	−	1.65618i
$918$	−1.15953	+	1.15953i	−0.0382701	+	0.0382701i
$919$	−17.4296	−	10.0630i	−0.574948	−	0.331947i	0.184175	−	0.982893i	$-0.441039\pi$
$919$	−17.4296	−	10.0630i	−0.574948	−	0.331947i	−0.759123	+	0.650947i	$0.774372\pi$
$920$		0			0
$921$	12.7905	+	22.1537i	0.421460	+	0.729990i
$922$	−0.265838	−	0.992122i	−0.00875492	−	0.0326738i
$923$	−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
$927$	14.2719	+	3.82414i	0.468750	+	0.125601i
$928$	5.34903	+	1.43327i	0.175591	+	0.0470494i
$929$	−13.0112	+	22.5360i	−0.426883	+	0.739383i	−0.996594	−	0.0824618i	$-0.973722\pi$
$929$	−13.0112	+	22.5360i	−0.426883	+	0.739383i	0.569711	+	0.821845i	$0.307055\pi$
$930$		0			0
$931$	23.5989	+	33.2645i	0.773423	+	1.09020i
$932$	−20.2472	−	20.2472i	−0.663218	−	0.663218i
$933$	−8.70087	−	32.4721i	−0.284854	−	1.06309i
$934$	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	$-0.879672\pi$
$937$	−17.1515	+	17.1515i	−0.560314	+	0.560314i	0.369082	+	0.929397i	$0.379672\pi$
$938$	−8.48544	+	5.44265i	−0.277059	+	0.177709i
$939$		−	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	$0.245955\pi$
$942$	5.63586	−	21.0333i	0.183626	−	0.685302i
$943$	−46.6484	+	12.4994i	−1.51908	+	0.407037i
$944$	−1.91758			−0.0624120
$945$		0			0
$946$	3.09849			0.100741
$947$	−28.6812	+	7.68510i	−0.932013	+	0.249732i	−0.692713	−	0.721213i	$-0.743585\pi$
$947$	−28.6812	+	7.68510i	−0.932013	+	0.249732i	−0.239300	+	0.970946i	$0.576918\pi$
$948$	−1.30995	+	4.88882i	−0.0425453	+	0.158781i
$949$	−19.8902	+	11.4836i	−0.645664	+	0.372774i
$950$		0			0
$951$			25.6420i			0.831498i
$952$	3.85450	+	1.99145i	0.124925	+	0.0645433i
$953$	30.9752	−	30.9752i	1.00339	−	1.00339i	0.00339090	−	0.999994i	$-0.498921\pi$
$953$	30.9752	−	30.9752i	1.00339	−	1.00339i	0.999994	−	0.00339090i	$-0.00107936\pi$
$954$	−2.37863	−	1.37330i	−0.0770109	−	0.0444622i
$955$		0			0
$956$	6.96149	+	12.0577i	0.225151	+	0.389973i
$957$	0.660901	+	2.46652i	0.0213639	+	0.0797312i
$958$	−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
$962$	−44.0952	−	11.8153i	−1.42169	−	0.380940i
$963$	−5.69821	−	1.52683i	−0.183622	−	0.0492014i
$964$	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	0.839783	−	0.542922i	$-0.182682\pi$
$967$	9.23140	+	9.23140i	0.296862	+	0.296862i	−0.542922	+	0.839783i	$0.682682\pi$
$968$	−2.79198	−	10.4198i	−0.0897376	−	0.334905i
$969$	−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
$973$	−6.21395	−	9.68794i	−0.199210	−	0.310581i
$974$		−	4.85631i		−	0.155606i
$975$		0			0
$976$	−11.7393	+	6.77768i	−0.375766	+	0.216948i
$977$	7.24876	−	27.0527i	0.231908	−	0.865493i	−0.747610	−	0.664138i	$-0.768799\pi$
$977$	7.24876	−	27.0527i	0.231908	−	0.865493i	0.979518	−	0.201355i	$-0.0645346\pi$
$978$	−11.2769	+	3.02164i	−0.360596	+	0.0966213i
$979$	−5.26983			−0.168425
$980$		0			0
$981$	16.6187			0.530596
$982$	−36.5694	+	9.79874i	−1.16698	+	0.312690i
$983$	−10.6787	+	39.8535i	−0.340598	+	1.27113i	0.557073	+	0.830463i	$0.311924\pi$
$983$	−10.6787	+	39.8535i	−0.340598	+	1.27113i	−0.897671	+	0.440666i	$0.854742\pi$
$984$	9.47890	−	5.47265i	0.302176	−	0.174462i
$985$		0			0
$986$		−	9.08086i		−	0.289193i
$987$	12.9134	+	20.1327i	0.411037	+	0.640832i
$988$	−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	$0.637330\pi$
$992$	−0.00839662	−	0.0313366i	−0.000266593	−	0.000994938i
$993$	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
$997$	17.3530	+	4.64972i	0.549575	+	0.147258i	0.522912	−	0.852386i	$-0.324845\pi$
$997$	17.3530	+	4.64972i	0.549575	+	0.147258i	0.0266623	+	0.999644i	$0.491512\pi$
$998$	0.494743	+	0.132566i	0.0156608	+	0.00419631i
$999$	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.g.607.3		16
5.2	odd	4		210.2.u.a.103.4	✓	16
5.3	odd	4		1050.2.bc.h.943.1		16
5.4	even	2		210.2.u.b.187.1	yes	16
7.3	odd	6		1050.2.bc.h.157.1		16
15.2	even	4		630.2.bv.a.523.1		16
15.14	odd	2		630.2.bv.b.397.4		16
35.2	odd	12		1470.2.m.d.1273.5		16
35.3	even	12	inner	1050.2.bc.g.493.3		16
35.9	even	6		1470.2.m.e.97.8		16
35.12	even	12		1470.2.m.e.1273.8		16
35.17	even	12		210.2.u.b.73.1	yes	16
35.19	odd	6		1470.2.m.d.97.5		16
35.24	odd	6		210.2.u.a.157.4	yes	16
105.17	odd	12		630.2.bv.b.73.4		16
105.59	even	6		630.2.bv.a.577.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.103.4	✓	16	5.2	odd	4
210.2.u.a.157.4	yes	16	35.24	odd	6
210.2.u.b.73.1	yes	16	35.17	even	12
210.2.u.b.187.1	yes	16	5.4	even	2
630.2.bv.a.523.1		16	15.2	even	4
630.2.bv.a.577.1		16	105.59	even	6
630.2.bv.b.73.4		16	105.17	odd	12
630.2.bv.b.397.4		16	15.14	odd	2
1050.2.bc.g.493.3		16	35.3	even	12	inner
1050.2.bc.g.607.3		16	1.1	even	1	trivial
1050.2.bc.h.157.1		16	7.3	odd	6
1050.2.bc.h.943.1		16	5.3	odd	4
1470.2.m.d.97.5		16	35.19	odd	6
1470.2.m.d.1273.5		16	35.2	odd	12
1470.2.m.e.97.8		16	35.9	even	6
1470.2.m.e.1273.8		16	35.12	even	12

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)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(-1.42843 - 2.22701i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(-1.42843 - 2.22701i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.230557 - 0.399337i) q^{11} +(0.258819 + 0.965926i) q^{12} +(-4.00275 - 4.00275i) q^{13} +(-1.95615 - 1.78142i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.58394 - 0.424416i) q^{17} +(-0.965926 - 0.258819i) q^{18} +(2.91323 - 5.04586i) q^{19} +(2.52083 - 0.803365i) q^{21} +(-0.326057 - 0.326057i) q^{22} +(-1.14199 - 4.26196i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.90235 - 2.83037i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.35056 - 1.21443i) q^{28} +5.53773i q^{29} +(0.0280956 - 0.0162210i) q^{31} +(0.258819 - 0.965926i) q^{32} +(0.445403 - 0.119345i) q^{33} -1.63982 q^{34} -1.00000 q^{36} +(7.78966 - 2.08723i) q^{37} +(1.50800 - 5.62793i) q^{38} +(4.90235 - 2.83037i) q^{39} -10.9453i q^{41} +(2.22701 - 1.42843i) q^{42} +(-4.75146 + 4.75146i) q^{43} +(-0.399337 - 0.230557i) q^{44} +(-2.20615 - 3.82117i) q^{46} +(2.33979 + 8.73220i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-2.91917 + 6.36227i) q^{49} +(0.819909 - 1.42012i) q^{51} +(-5.46786 - 1.46511i) q^{52} +(2.65301 + 0.710873i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.58479 - 0.564683i) q^{56} +(4.11993 + 4.11993i) q^{57} +(1.43327 + 5.34903i) q^{58} +(-0.958791 - 1.66067i) q^{59} +(-11.7393 - 6.77768i) q^{61} +(0.0229400 - 0.0229400i) q^{62} +(0.123551 + 2.64286i) q^{63} -1.00000i q^{64} +(0.399337 - 0.230557i) q^{66} +(0.986161 - 3.68040i) q^{67} +(-1.58394 + 0.424416i) q^{68} +4.41231 q^{69} +8.85877 q^{71} +(-0.965926 + 0.258819i) q^{72} +(1.05010 - 3.91904i) q^{73} +(6.98401 - 4.03222i) q^{74} -5.82646i q^{76} +(-0.559993 + 1.08388i) q^{77} +(4.00275 - 4.00275i) q^{78} +(4.38319 + 2.53064i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-2.83285 - 10.5723i) q^{82} +(1.08813 + 1.08813i) q^{83} +(1.78142 - 1.95615i) q^{84} +(-3.35979 + 5.81932i) q^{86} +(-5.34903 - 1.43327i) q^{87} +(-0.445403 - 0.119345i) q^{88} +(5.71423 - 9.89734i) q^{89} +(-3.19652 + 14.6318i) q^{91} +(-3.11997 - 3.11997i) q^{92} +(0.00839662 + 0.0313366i) q^{93} +(4.52012 + 7.82908i) q^{94} +(0.866025 + 0.500000i) q^{96} +(2.51799 - 2.51799i) q^{97} +(-1.17303 + 6.90101i) q^{98} +0.461115i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{7}+O(q^{10}) \) 16 * q + 4 * q^7	\( 16 q + 4 q^{7} + 4 q^{11} - 16 q^{13} - 16 q^{14} + 8 q^{16} - 12 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{22} + 40 q^{23} + 8 q^{24} - 12 q^{26} + 4 q^{28} - 24 q^{31} - 4 q^{33} - 16 q^{34} - 16 q^{36} + 8 q^{37} + 20 q^{38} + 12 q^{39} - 8 q^{42} + 24 q^{43} - 4 q^{46} - 52 q^{49} + 8 q^{51} - 8 q^{52} + 28 q^{53} + 8 q^{54} + 8 q^{56} + 8 q^{57} + 12 q^{58} - 8 q^{59} + 24 q^{61} + 8 q^{62} + 4 q^{63} + 84 q^{67} - 12 q^{68} + 8 q^{69} - 32 q^{71} - 16 q^{73} + 24 q^{74} - 44 q^{77} + 16 q^{78} - 12 q^{79} + 8 q^{81} - 36 q^{82} - 16 q^{83} - 4 q^{84} - 8 q^{86} - 48 q^{87} + 4 q^{88} + 16 q^{89} + 8 q^{91} - 8 q^{92} + 32 q^{93} - 8 q^{94} + 44 q^{97} - 24 q^{98}+O(q^{100}) \) 16 * q + 4 * 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 + 40 * q^23 + 8 * q^24 - 12 * q^26 + 4 * q^28 - 24 * q^31 - 4 * q^33 - 16 * q^34 - 16 * q^36 + 8 * q^37 + 20 * q^38 + 12 * q^39 - 8 * q^42 + 24 * q^43 - 4 * q^46 - 52 * q^49 + 8 * q^51 - 8 * q^52 + 28 * q^53 + 8 * q^54 + 8 * q^56 + 8 * q^57 + 12 * q^58 - 8 * q^59 + 24 * q^61 + 8 * q^62 + 4 * q^63 + 84 * q^67 - 12 * q^68 + 8 * q^69 - 32 * q^71 - 16 * q^73 + 24 * q^74 - 44 * q^77 + 16 * q^78 - 12 * q^79 + 8 * q^81 - 36 * q^82 - 16 * q^83 - 4 * q^84 - 8 * q^86 - 48 * q^87 + 4 * q^88 + 16 * q^89 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 8 * q^94 + 44 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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