LMFDB - Embedded newform 1050.2.bc.e.943.2

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} - 28x^{14} + 519x^{12} - 5404x^{10} + 40705x^{8} - 194544x^{6} + 672624x^{4} - 1306368x^{2} + 1679616 $ x^16 - 28x^14 + 519x^12 - 5404x^10 + 40705x^8 - 194544x^6 + 672624x^4 - 1306368*x^2 + 1679616
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			943.2
Root			$3.11681 - 1.79949i$ of defining polynomial
Character	$\chi$	$=$	1050.943
Dual form			1050.2.bc.e.157.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(0.258819 + 2.63306i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(0.258819 + 2.63306i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-2.54487 - 4.40784i) q^{11} +(0.965926 - 0.258819i) q^{12} +(2.02443 - 2.02443i) q^{13} +(2.47635 - 0.931486i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.79949 + 6.71580i) q^{17} +(0.258819 - 0.965926i) q^{18} +(1.79751 - 3.11338i) q^{19} +(0.431486 - 2.61033i) q^{21} +(-3.59899 + 3.59899i) q^{22} +(-6.71580 + 1.79949i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-2.47941 - 1.43149i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.54067 - 2.15089i) q^{28} +8.81568i q^{29} +(1.61338 - 0.931486i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(1.31732 + 4.91631i) q^{33} +6.95271 q^{34} -1.00000 q^{36} +(2.01219 + 7.50959i) q^{37} +(-3.47253 - 0.930461i) q^{38} +(-2.47941 + 1.43149i) q^{39} +4.13703i q^{41} +(-2.63306 + 0.258819i) q^{42} +(7.84163 + 7.84163i) q^{43} +(4.40784 + 2.54487i) q^{44} +(3.47635 + 6.02122i) q^{46} +(-1.79949 + 0.482173i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(-6.86603 + 1.36297i) q^{49} +(3.47635 - 6.02122i) q^{51} +(-0.740992 + 2.76542i) q^{52} +(0.235593 - 0.879247i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.67884 + 2.04487i) q^{56} +(-2.54207 + 2.54207i) q^{57} +(8.51530 - 2.28167i) q^{58} +(2.08974 + 3.61953i) q^{59} +(-5.08277 - 2.93454i) q^{61} +(-1.31732 - 1.31732i) q^{62} +(-1.09239 + 2.40971i) q^{63} +1.00000i q^{64} +(4.40784 - 2.54487i) q^{66} +(2.84620 + 0.762637i) q^{67} +(-1.79949 - 6.71580i) q^{68} +6.95271 q^{69} +7.86297 q^{71} +(0.258819 + 0.965926i) q^{72} +(-13.0683 - 3.50165i) q^{73} +(6.73291 - 3.88725i) q^{74} +3.59502i q^{76} +(10.9475 - 7.84163i) q^{77} +(2.02443 + 2.02443i) q^{78} +(10.4700 + 6.04487i) q^{79} +(0.500000 + 0.866025i) q^{81} +(3.99606 - 1.07074i) q^{82} +(-1.99099 + 1.99099i) q^{83} +(0.931486 + 2.47635i) q^{84} +(5.54487 - 9.60399i) q^{86} +(2.28167 - 8.51530i) q^{87} +(1.31732 - 4.91631i) q^{88} +(-3.82507 + 6.62522i) q^{89} +(5.85440 + 4.80648i) q^{91} +(4.91631 - 4.91631i) q^{92} +(-1.79949 + 0.482173i) q^{93} +(0.931486 + 1.61338i) q^{94} +(0.866025 + 0.500000i) q^{96} +(13.4951 + 13.4951i) q^{97} +(3.09359 + 6.27931i) q^{98} -5.08974i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 4 q^{11} - 8 q^{14} + 8 q^{16} + 4 q^{19} - 4 q^{21} - 8 q^{24} + 16 q^{34} - 16 q^{36} + 12 q^{44} + 8 q^{46} - 96 q^{49} + 8 q^{51} - 8 q^{54} - 4 q^{56} - 40 q^{59} - 24 q^{61} + 12 q^{66} + 16 q^{69} + 104 q^{71} + 48 q^{74} + 12 q^{79} + 8 q^{81} + 4 q^{84} + 52 q^{86} - 60 q^{89} - 52 q^{91} + 4 q^{94}+O(q^{100}) $ 16 * q - 4 * q^11 - 8 * q^14 + 8 * q^16 + 4 * q^19 - 4 * q^21 - 8 * q^24 + 16 * q^34 - 16 * q^36 + 12 * q^44 + 8 * q^46 - 96 * q^49 + 8 * q^51 - 8 * q^54 - 4 * q^56 - 40 * q^59 - 24 * q^61 + 12 * q^66 + 16 * q^69 + 104 * q^71 + 48 * q^74 + 12 * q^79 + 8 * q^81 + 4 * q^84 + 52 * q^86 - 60 * q^89 - 52 * q^91 + 4 * q^94

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
$7$	0.258819	+	2.63306i	0.0978244	+	0.995204i
$7$	0.258819	+	2.63306i	0.0978244	+	0.995204i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$		0			0
$11$	−2.54487	−	4.40784i	−0.767307	−	1.32901i	−0.939018	−	0.343867i	$-0.888263\pi$
$11$	−2.54487	−	4.40784i	−0.767307	−	1.32901i	0.171712	−	0.985147i	$-0.445070\pi$
$12$	0.965926	−	0.258819i	0.278839	−	0.0747146i
$13$	2.02443	−	2.02443i	0.561475	−	0.561475i	−0.368251	−	0.929726i	$-0.620043\pi$
$13$	2.02443	−	2.02443i	0.561475	−	0.561475i	0.929726	+	0.368251i	$0.120043\pi$
$14$	2.47635	−	0.931486i	0.661834	−	0.248950i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.79949	+	6.71580i	−0.436441	+	1.62882i	0.301152	+	0.953576i	$0.402629\pi$
$17$	−1.79949	+	6.71580i	−0.436441	+	1.62882i	−0.737593	+	0.675245i	$0.764038\pi$
$18$	0.258819	−	0.965926i	0.0610042	−	0.227671i
$19$	1.79751	−	3.11338i	0.412378	−	0.714259i	−0.582772	−	0.812636i	$-0.698032\pi$
$19$	1.79751	−	3.11338i	0.412378	−	0.714259i	0.995149	+	0.0983771i	$0.0313651\pi$
$20$		0			0
$21$	0.431486	−	2.61033i	0.0941581	−	0.569621i
$22$	−3.59899	+	3.59899i	−0.767307	+	0.767307i
$23$	−6.71580	+	1.79949i	−1.40034	+	0.375220i	−0.878467	−	0.477802i	$-0.841434\pi$
$23$	−6.71580	+	1.79949i	−1.40034	+	0.375220i	−0.521874	+	0.853023i	$0.674767\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$		0			0
$26$	−2.47941	−	1.43149i	−0.486252	−	0.280738i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−1.54067	−	2.15089i	−0.291160	−	0.406480i
$29$			8.81568i			1.63703i	0.574484	+	0.818516i	$0.305203\pi$
$29$			8.81568i			1.63703i	−0.574484	+	0.818516i	$0.694797\pi$
$30$		0			0
$31$	1.61338	−	0.931486i	0.289772	−	0.167300i	−0.348067	−	0.937470i	$-0.613162\pi$
$31$	1.61338	−	0.931486i	0.289772	−	0.167300i	0.637839	+	0.770170i	$0.279829\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	1.31732	+	4.91631i	0.229316	+	0.855819i
$34$	6.95271			1.19238
$35$		0			0
$36$	−1.00000			−0.166667
$37$	2.01219	+	7.50959i	0.330802	+	1.23457i	0.908350	+	0.418212i	$0.137343\pi$
$37$	2.01219	+	7.50959i	0.330802	+	1.23457i	−0.577548	+	0.816357i	$0.695990\pi$
$38$	−3.47253	−	0.930461i	−0.563318	−	0.150941i
$39$	−2.47941	+	1.43149i	−0.397023	+	0.229221i
$40$		0			0
$41$			4.13703i			0.646095i	0.946383	+	0.323048i	$0.104707\pi$
$41$			4.13703i			0.646095i	−0.946383	+	0.323048i	$0.895293\pi$
$42$	−2.63306	+	0.258819i	−0.406290	+	0.0399366i
$43$	7.84163	+	7.84163i	1.19584	+	1.19584i	0.975402	+	0.220436i	$0.0707479\pi$
$43$	7.84163	+	7.84163i	1.19584	+	1.19584i	0.220436	+	0.975402i	$0.429252\pi$
$44$	4.40784	+	2.54487i	0.664507	+	0.383653i
$45$		0			0
$46$	3.47635	+	6.02122i	0.512561	+	0.887781i
$47$	−1.79949	+	0.482173i	−0.262483	+	0.0703321i	−0.387660	−	0.921802i	$-0.626717\pi$
$47$	−1.79949	+	0.482173i	−0.262483	+	0.0703321i	0.125177	+	0.992134i	$0.460050\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$	−6.86603	+	1.36297i	−0.980861	+	0.194710i
$50$		0			0
$51$	3.47635	−	6.02122i	0.486787	−	0.843140i
$52$	−0.740992	+	2.76542i	−0.102757	+	0.383495i
$53$	0.235593	−	0.879247i	0.0323613	−	0.120774i	−0.947856	−	0.318700i	$-0.896754\pi$
$53$	0.235593	−	0.879247i	0.0323613	−	0.120774i	0.980217	+	0.197926i	$0.0634205\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$		0			0
$56$	−1.67884	+	2.04487i	−0.224345	+	0.273257i
$57$	−2.54207	+	2.54207i	−0.336705	+	0.336705i
$58$	8.51530	−	2.28167i	1.11811	−	0.299597i
$59$	2.08974	+	3.61953i	0.272061	+	0.471223i	0.969389	−	0.245529i	$-0.0789616\pi$
$59$	2.08974	+	3.61953i	0.272061	+	0.471223i	−0.697329	+	0.716751i	$0.745628\pi$
$60$		0			0
$61$	−5.08277	−	2.93454i	−0.650782	−	0.375729i	0.137974	−	0.990436i	$-0.455941\pi$
$61$	−5.08277	−	2.93454i	−0.650782	−	0.375729i	−0.788756	+	0.614707i	$0.789274\pi$
$62$	−1.31732	−	1.31732i	−0.167300	−	0.167300i
$63$	−1.09239	+	2.40971i	−0.137628	+	0.303595i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	4.40784	−	2.54487i	0.542568	−	0.313252i
$67$	2.84620	+	0.762637i	0.347719	+	0.0931710i	0.428451	−	0.903565i	$-0.359059\pi$
$67$	2.84620	+	0.762637i	0.347719	+	0.0931710i	−0.0807326	+	0.996736i	$0.525726\pi$
$68$	−1.79949	−	6.71580i	−0.218221	−	0.814411i
$69$	6.95271			0.837008
$70$		0			0
$71$	7.86297			0.933163			0.466582	−	0.884478i	$-0.345485\pi$
$71$	7.86297			0.933163			0.466582	+	0.884478i	$0.345485\pi$
$72$	0.258819	+	0.965926i	0.0305021	+	0.113835i
$73$	−13.0683	−	3.50165i	−1.52953	−	0.409837i	−0.606666	−	0.794957i	$-0.707493\pi$
$73$	−13.0683	−	3.50165i	−1.52953	−	0.409837i	−0.922867	+	0.385120i	$0.874160\pi$
$74$	6.73291	−	3.88725i	0.782685	−	0.451883i
$75$		0			0
$76$			3.59502i			0.412378i
$77$	10.9475	−	7.84163i	1.24758	−	0.893636i
$78$	2.02443	+	2.02443i	0.229221	+	0.229221i
$79$	10.4700	+	6.04487i	1.17797	+	0.680101i	0.955544	−	0.294849i	$-0.0952693\pi$
$79$	10.4700	+	6.04487i	1.17797	+	0.680101i	0.222425	+	0.974950i	$0.428603\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	3.99606	−	1.07074i	0.441291	−	0.118244i
$83$	−1.99099	+	1.99099i	−0.218539	+	0.218539i	−0.807883	−	0.589343i	$-0.799387\pi$
$83$	−1.99099	+	1.99099i	−0.218539	+	0.218539i	0.589343	+	0.807883i	$0.299387\pi$
$84$	0.931486	+	2.47635i	0.101634	+	0.270192i
$85$		0			0
$86$	5.54487	−	9.60399i	0.597919	−	1.03563i
$87$	2.28167	−	8.51530i	0.244620	−	0.912935i
$88$	1.31732	−	4.91631i	0.140427	−	0.524080i
$89$	−3.82507	+	6.62522i	−0.405457	+	0.702272i	−0.994375	−	0.105921i	$-0.966221\pi$
$89$	−3.82507	+	6.62522i	−0.405457	+	0.702272i	0.588918	+	0.808193i	$0.299554\pi$
$90$		0			0
$91$	5.85440	+	4.80648i	0.613708	+	0.503856i
$92$	4.91631	−	4.91631i	0.512561	−	0.512561i
$93$	−1.79949	+	0.482173i	−0.186599	+	0.0499990i
$94$	0.931486	+	1.61338i	0.0960755	+	0.166408i
$95$		0			0
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	13.4951	+	13.4951i	1.37022	+	1.37022i	0.860115	+	0.510101i	$0.170392\pi$
$97$	13.4951	+	13.4951i	1.37022	+	1.37022i	0.510101	+	0.860115i	$0.329608\pi$
$98$	3.09359	+	6.27931i	0.312500	+	0.634306i
$99$		−	5.08974i		−	0.511538i
$100$		0			0
$101$	1.18108	−	0.681895i	0.117522	−	0.0678511i	−0.440087	−	0.897955i	$-0.645052\pi$
$101$	1.18108	−	0.681895i	0.117522	−	0.0678511i	0.557609	+	0.830104i	$0.311719\pi$
$102$	−6.71580	−	1.79949i	−0.664963	−	0.178176i
$103$	−0.0941560	−	0.351395i	−0.00927747	−	0.0346240i	0.961132	−	0.276089i	$-0.0890386\pi$
$103$	−0.0941560	−	0.351395i	−0.00927747	−	0.0346240i	−0.970409	+	0.241465i	$0.922372\pi$
$104$	2.86297			0.280738
$105$		0			0
$106$	−0.910263			−0.0884126
$107$	0.0550849	+	0.205579i	0.00532525	+	0.0198741i	0.968537	−	0.248868i	$-0.0800586\pi$
$107$	0.0550849	+	0.205579i	0.00532525	+	0.0198741i	−0.963212	+	0.268742i	$0.913392\pi$
$108$	0.965926	+	0.258819i	0.0929463	+	0.0249049i
$109$	−1.35135	+	0.780202i	−0.129436	+	0.0747298i	−0.563320	−	0.826239i	$-0.690476\pi$
$109$	−1.35135	+	0.780202i	−0.129436	+	0.0747298i	0.433884	+	0.900969i	$0.357143\pi$
$110$		0			0
$111$		−	7.77450i		−	0.737923i
$112$	2.40971	+	1.09239i	0.227696	+	0.103221i
$113$	−0.0300140	−	0.0300140i	−0.00282348	−	0.00282348i	0.705694	−	0.708517i	$-0.250636\pi$
$113$	−0.0300140	−	0.0300140i	−0.00282348	−	0.00282348i	−0.708517	+	0.705694i	$0.750636\pi$
$114$	3.11338	+	1.79751i	0.291595	+	0.168352i
$115$		0			0
$116$	−4.40784	−	7.63460i	−0.409258	−	0.708855i
$117$	2.76542	−	0.740992i	0.255663	−	0.0685047i
$118$	2.95533	−	2.95533i	0.272061	−	0.272061i
$119$	−18.1489	−	3.00000i	−1.66370	−	0.275010i
$120$		0			0
$121$	−7.45271	+	12.9085i	−0.677519	+	1.17350i
$122$	−1.51903	+	5.66909i	−0.137526	+	0.513256i
$123$	1.07074	−	3.99606i	0.0965455	−	0.360313i
$124$	−0.931486	+	1.61338i	−0.0836500	+	0.144886i
$125$		0			0
$126$	2.61033	+	0.431486i	0.232547	+	0.0384399i
$127$	1.42723	−	1.42723i	0.126646	−	0.126646i	−0.640943	−	0.767589i	$-0.721456\pi$
$127$	1.42723	−	1.42723i	0.126646	−	0.126646i	0.767589	+	0.640943i	$0.221456\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−5.54487	−	9.60399i	−0.488198	−	0.845584i
$130$		0			0
$131$	−4.59216	−	2.65128i	−0.401219	−	0.231644i	0.285791	−	0.958292i	$-0.407744\pi$
$131$	−4.59216	−	2.65128i	−0.401219	−	0.231644i	−0.687010	+	0.726648i	$0.741077\pi$
$132$	−3.59899	−	3.59899i	−0.313252	−	0.313252i
$133$	8.66296	+	3.92716i	0.751174	+	0.340528i
$134$		−	2.94660i		−	0.254548i
$135$		0			0
$136$	−6.02122	+	3.47635i	−0.516316	+	0.298095i
$137$	−21.2322	−	5.68916i	−1.81399	−	0.486058i	−0.817978	−	0.575250i	$-0.804905\pi$
$137$	−21.2322	−	5.68916i	−1.81399	−	0.486058i	−0.996014	+	0.0891925i	$0.971571\pi$
$138$	−1.79949	−	6.71580i	−0.153183	−	0.571687i
$139$	−16.5902			−1.40716			−0.703580	−	0.710616i	$-0.748416\pi$
$139$	−16.5902			−1.40716			−0.703580	+	0.710616i	$0.748416\pi$
$140$		0			0
$141$	1.86297			0.156891
$142$	−2.03509	−	7.59505i	−0.170781	−	0.637362i
$143$	−14.0753	−	3.77145i	−1.17703	−	0.315385i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$		0			0
$146$			13.5293i			1.11970i
$147$	6.98483	+	0.460527i	0.576099	+	0.0379837i
$148$	−5.49740	−	5.49740i	−0.451883	−	0.451883i
$149$	8.60723	+	4.96939i	0.705132	+	0.407108i	0.809256	−	0.587456i	$-0.199871\pi$
$149$	8.60723	+	4.96939i	0.705132	+	0.407108i	−0.104124	+	0.994564i	$0.533204\pi$
$150$		0			0
$151$	7.65825	+	13.2645i	0.623220	+	1.07945i	0.988882	+	0.148701i	$0.0475090\pi$
$151$	7.65825	+	13.2645i	0.623220	+	1.07945i	−0.365663	+	0.930747i	$0.619158\pi$
$152$	3.47253	−	0.930461i	0.281659	−	0.0754703i
$153$	−4.91631	+	4.91631i	−0.397460	+	0.397460i
$154$	−10.4078	−	8.54487i	−0.838688	−	0.688565i
$155$		0			0
$156$	1.43149	−	2.47941i	0.114611	−	0.198511i
$157$	−4.23040	+	15.7881i	−0.337623	+	1.26003i	0.563375	+	0.826201i	$0.309503\pi$
$157$	−4.23040	+	15.7881i	−0.337623	+	1.26003i	−0.900998	+	0.433824i	$0.857164\pi$
$158$	3.12905	−	11.6778i	0.248934	−	0.929035i
$159$	−0.455132	+	0.788311i	−0.0360943	+	0.0625171i
$160$		0			0
$161$	−6.47635	−	17.2174i	−0.510408	−	1.35692i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	7.23934	−	1.93977i	0.567029	−	0.151935i	0.0360951	−	0.999348i	$-0.488508\pi$
$163$	7.23934	−	1.93977i	0.567029	−	0.151935i	0.530933	+	0.847413i	$0.321841\pi$
$164$	−2.06851	−	3.58277i	−0.161524	−	0.279767i
$165$		0			0
$166$	2.43845	+	1.40784i	0.189261	+	0.109270i
$167$	−12.7880	−	12.7880i	−0.989561	−	0.989561i	0.0103848	−	0.999946i	$-0.496694\pi$
$167$	−12.7880	−	12.7880i	−0.989561	−	0.989561i	−0.999946	+	0.0103848i	$0.996694\pi$
$168$	2.15089	−	1.54067i	0.165945	−	0.118866i
$169$			4.80339i			0.369491i
$170$		0			0
$171$	3.11338	−	1.79751i	0.238086	−	0.137459i
$172$	−10.7119	−	2.87024i	−0.816772	−	0.218853i
$173$	4.18756	+	15.6282i	0.318374	+	1.18819i	0.920807	+	0.390018i	$0.127531\pi$
$173$	4.18756	+	15.6282i	0.318374	+	1.18819i	−0.602433	+	0.798169i	$0.705802\pi$
$174$	−8.81568			−0.668315
$175$		0			0
$176$	−5.08974			−0.383653
$177$	−1.08173	−	4.03706i	−0.0813076	−	0.303444i
$178$	7.38947	+	1.98000i	0.553864	+	0.148407i
$179$	8.60723	−	4.96939i	0.643335	−	0.371430i	−0.142563	−	0.989786i	$-0.545534\pi$
$179$	8.60723	−	4.96939i	0.643335	−	0.371430i	0.785898	+	0.618356i	$0.212201\pi$
$180$		0			0
$181$			2.60285i			0.193468i	0.995310	+	0.0967342i	$0.0308397\pi$
$181$			2.60285i			0.193468i	−0.995310	+	0.0967342i	$0.969160\pi$
$182$	3.12747	−	6.89893i	0.231824	−	0.511383i
$183$	4.15006	+	4.15006i	0.306782	+	0.306782i
$184$	−6.02122	−	3.47635i	−0.443890	−	0.256280i
$185$		0			0
$186$	0.931486	+	1.61338i	0.0682999	+	0.118299i
$187$	34.1817	−	9.15895i	2.49961	−	0.669769i
$188$	1.31732	−	1.31732i	0.0960755	−	0.0960755i
$189$	1.67884	−	2.04487i	0.122118	−	0.148742i
$190$		0			0
$191$	−2.06851	+	3.58277i	−0.149672	+	0.259240i	−0.931106	−	0.364748i	$-0.881155\pi$
$191$	−2.06851	+	3.58277i	−0.149672	+	0.259240i	0.781434	+	0.623988i	$0.214489\pi$
$192$	0.258819	−	0.965926i	0.0186787	−	0.0697097i
$193$	3.35241	−	12.5114i	0.241312	−	0.900587i	−0.733890	−	0.679268i	$-0.762297\pi$
$193$	3.35241	−	12.5114i	0.241312	−	0.900587i	0.975202	−	0.221319i	$-0.0710361\pi$
$194$	9.54245	−	16.5280i	0.685108	−	1.18664i
$195$		0			0
$196$	5.26467	−	4.61338i	0.376048	−	0.329527i
$197$	−0.876148	+	0.876148i	−0.0624229	+	0.0624229i	−0.737629	−	0.675206i	$-0.764055\pi$
$197$	−0.876148	+	0.876148i	−0.0624229	+	0.0624229i	0.675206	+	0.737629i	$0.264055\pi$
$198$	−4.91631	+	1.31732i	−0.349387	+	0.0936179i
$199$	−8.63155	−	14.9503i	−0.611875	−	1.05980i	−0.990924	−	0.134421i	$-0.957082\pi$
$199$	−8.63155	−	14.9503i	−0.611875	−	1.05980i	0.379050	−	0.925376i	$-0.376251\pi$
$200$		0			0
$201$	−2.55183	−	1.47330i	−0.179993	−	0.103919i
$202$	−0.964346	−	0.964346i	−0.0678511	−	0.0678511i
$203$	−23.2122	+	2.28167i	−1.62918	+	0.160142i
$204$			6.95271i			0.486787i
$205$		0			0
$206$	−0.315052	+	0.181895i	−0.0219507	+	0.0126733i
$207$	−6.71580	−	1.79949i	−0.466780	−	0.125073i
$208$	−0.740992	−	2.76542i	−0.0513785	−	0.191747i
$209$	−18.2977			−1.26568
$210$		0			0
$211$	−7.40460			−0.509754			−0.254877	−	0.966974i	$-0.582035\pi$
$211$	−7.40460			−0.509754			−0.254877	+	0.966974i	$0.582035\pi$
$212$	0.235593	+	0.879247i	0.0161806	+	0.0603869i
$213$	−7.59505	−	2.03509i	−0.520404	−	0.139442i
$214$	0.184318	−	0.106416i	0.0125997	−	0.00727443i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	2.87024	+	4.00705i	0.194844	+	0.272016i
$218$	1.10337	+	1.10337i	0.0747298	+	0.0747298i
$219$	11.7167	+	6.76467i	0.791744	+	0.457114i
$220$		0			0
$221$	9.95271	+	17.2386i	0.669492	+	1.15959i
$222$	−7.50959	+	2.01219i	−0.504011	+	0.135049i
$223$	−2.69809	+	2.69809i	−0.180678	+	0.180678i	−0.791651	−	0.610973i	$-0.790778\pi$
$223$	−2.69809	+	2.69809i	−0.180678	+	0.180678i	0.610973	+	0.791651i	$0.290778\pi$
$224$	0.431486	−	2.61033i	0.0288299	−	0.174410i
$225$		0			0
$226$	−0.0212231	+	0.0367595i	−0.00141174	+	0.00244520i
$227$	5.09682	−	19.0216i	0.338288	−	1.26251i	−0.561973	−	0.827155i	$-0.689958\pi$
$227$	5.09682	−	19.0216i	0.338288	−	1.26251i	0.900261	−	0.435351i	$-0.143376\pi$
$228$	0.930461	−	3.47253i	0.0616213	−	0.229974i
$229$	11.4884	−	19.8985i	0.759173	−	1.31493i	−0.184099	−	0.982908i	$-0.558937\pi$
$229$	11.4884	−	19.8985i	0.759173	−	1.31493i	0.943273	−	0.332019i	$-0.107730\pi$
$230$		0			0
$231$	−12.6040	+	4.74102i	−0.829282	+	0.311936i
$232$	−6.23363	+	6.23363i	−0.409258	+	0.409258i
$233$	12.7880	−	3.42652i	0.837766	−	0.224479i	0.185667	−	0.982613i	$-0.440555\pi$
$233$	12.7880	−	3.42652i	0.837766	−	0.224479i	0.652099	+	0.758134i	$0.273889\pi$
$234$	−1.43149	−	2.47941i	−0.0935792	−	0.162084i
$235$		0			0
$236$	−3.61953	−	2.08974i	−0.235611	−	0.136030i
$237$	−8.54873	−	8.54873i	−0.555300	−	0.555300i
$238$	1.79949	+	18.3069i	0.116644	+	1.18666i
$239$		−	1.65014i		−	0.106739i	−0.998575	−	0.0533694i	$-0.983004\pi$
$239$		−	1.65014i		−	0.106739i	0.998575	−	0.0533694i	$-0.0169961\pi$
$240$		0			0
$241$	−10.9564	+	6.32570i	−0.705766	+	0.407474i	−0.809491	−	0.587132i	$-0.800257\pi$
$241$	−10.9564	+	6.32570i	−0.705766	+	0.407474i	0.103725	+	0.994606i	$0.466924\pi$
$242$	14.3975	+	3.85781i	0.925508	+	0.247989i
$243$	−0.258819	−	0.965926i	−0.0166032	−	0.0619642i
$244$	5.86908			0.375729
$245$		0			0
$246$	−4.13703			−0.263767
$247$	−2.66388	−	9.94175i	−0.169499	−	0.632578i
$248$	1.79949	+	0.482173i	0.114268	+	0.0306180i
$249$	2.43845	−	1.40784i	0.154531	−	0.0892183i
$250$		0			0
$251$			7.45189i			0.470359i	0.971952	+	0.235180i	$0.0755678\pi$
$251$			7.45189i			0.470359i	−0.971952	+	0.235180i	$0.924432\pi$
$252$	−0.258819	−	2.63306i	−0.0163041	−	0.165867i
$253$	25.0227	+	25.0227i	1.57316	+	1.57316i
$254$	−1.74799	−	1.00920i	−0.109678	−	0.0633229i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−16.0662	+	4.30494i	−1.00218	+	0.268535i	−0.722361	−	0.691517i	$-0.756943\pi$
$257$	−16.0662	+	4.30494i	−1.00218	+	0.268535i	−0.279824	+	0.960051i	$0.590276\pi$
$258$	−7.84163	+	7.84163i	−0.488198	+	0.488198i
$259$	−19.2524	+	7.24184i	−1.19629	+	0.449986i
$260$		0			0
$261$	−4.40784	+	7.63460i	−0.272839	+	0.472570i
$262$	−1.37241	+	5.12189i	−0.0847875	+	0.316431i
$263$	2.85925	−	10.6709i	0.176309	−	0.657994i	−0.820016	−	0.572340i	$-0.806036\pi$
$263$	2.85925	−	10.6709i	0.176309	−	0.657994i	0.996325	−	0.0856532i	$-0.0272977\pi$
$264$	−2.54487	+	4.40784i	−0.156626	+	0.271284i
$265$		0			0
$266$	1.55120	−	9.38420i	0.0951104	−	0.575382i
$267$	5.40947	−	5.40947i	0.331054	−	0.331054i
$268$	−2.84620	+	0.762637i	−0.173859	+	0.0465855i
$269$	−13.3014	−	23.0387i	−0.811002	−	1.40470i	−0.912163	−	0.409827i	$-0.865589\pi$
$269$	−13.3014	−	23.0387i	−0.811002	−	1.40470i	0.101161	−	0.994870i	$-0.467744\pi$
$270$		0			0
$271$	−17.5946	−	10.1583i	−1.06880	−	0.617070i	−0.140944	−	0.990018i	$-0.545014\pi$
$271$	−17.5946	−	10.1583i	−1.06880	−	0.617070i	−0.927852	+	0.372948i	$0.878347\pi$
$272$	4.91631	+	4.91631i	0.298095	+	0.298095i
$273$	−4.41091	−	6.15794i	−0.266960	−	0.372695i
$274$			21.9812i			1.32793i
$275$		0			0
$276$	−6.02122	+	3.47635i	−0.362435	+	0.209252i
$277$	−9.72658	−	2.60623i	−0.584414	−	0.156593i	−0.0455149	−	0.998964i	$-0.514493\pi$
$277$	−9.72658	−	2.60623i	−0.584414	−	0.156593i	−0.538899	+	0.842370i	$0.681160\pi$
$278$	4.29385	+	16.0249i	0.257528	+	0.961109i
$279$	1.86297			0.111533
$280$		0			0
$281$	15.2268			0.908353			0.454176	−	0.890912i	$-0.349934\pi$
$281$	15.2268			0.908353			0.454176	+	0.890912i	$0.349934\pi$
$282$	−0.482173	−	1.79949i	−0.0287130	−	0.107158i
$283$	−14.3265	−	3.83878i	−0.851623	−	0.228192i	−0.193498	−	0.981101i	$-0.561983\pi$
$283$	−14.3265	−	3.83878i	−0.851623	−	0.228192i	−0.658125	+	0.752909i	$0.728650\pi$
$284$	−6.80953	+	3.93149i	−0.404072	+	0.233291i
$285$		0			0
$286$			14.5718i			0.861647i
$287$	−10.8930	+	1.07074i	−0.642996	+	0.0632039i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$	−27.1414	−	15.6701i	−1.59655	−	0.921770i
$290$		0			0
$291$	−9.54245	−	16.5280i	−0.559388	−	0.968889i
$292$	13.0683	−	3.50165i	0.764766	−	0.204918i
$293$	18.7009	−	18.7009i	1.09252	−	1.09252i	0.0972583	−	0.995259i	$-0.468993\pi$
$293$	18.7009	−	18.7009i	1.09252	−	1.09252i	0.995259	−	0.0972583i	$-0.0310073\pi$
$294$	−1.36297	−	6.86603i	−0.0794902	−	0.400435i
$295$		0			0
$296$	−3.88725	+	6.73291i	−0.225942	+	0.391343i
$297$	−1.31732	+	4.91631i	−0.0764387	+	0.285273i
$298$	2.57234	−	9.60012i	0.149012	−	0.556120i
$299$	−9.95271	+	17.2386i	−0.575580	+	0.996934i
$300$		0			0
$301$	−18.6179	+	22.6771i	−1.07312	+	1.30708i
$302$	10.8304	−	10.8304i	0.623220	−	0.623220i
$303$	−1.31732	+	0.352975i	−0.0756781	+	0.0202779i
$304$	−1.79751	−	3.11338i	−0.103094	−	0.178565i
$305$		0			0
$306$	6.02122	+	3.47635i	0.344210	+	0.198730i
$307$	−22.4937	−	22.4937i	−1.28378	−	1.28378i	−0.938499	−	0.345282i	$-0.887783\pi$
$307$	−22.4937	−	22.4937i	−1.28378	−	1.28378i	−0.345282	−	0.938499i	$-0.612217\pi$
$308$	−5.55996	+	12.2648i	−0.316808	+	0.698851i
$309$			0.363791i			0.0206953i
$310$		0			0
$311$	14.2598	−	8.23291i	0.808600	−	0.466846i	−0.0378693	−	0.999283i	$-0.512057\pi$
$311$	14.2598	−	8.23291i	0.808600	−	0.466846i	0.846470	+	0.532437i	$0.178724\pi$
$312$	−2.76542	−	0.740992i	−0.156561	−	0.0419504i
$313$	−0.873796	−	3.26105i	−0.0493899	−	0.184325i	0.936824	−	0.349801i	$-0.113751\pi$
$313$	−0.873796	−	3.26105i	−0.0493899	−	0.184325i	−0.986214	+	0.165476i	$0.947084\pi$
$314$	16.3450			0.922403
$315$		0			0
$316$	−12.0897			−0.680101
$317$	3.57619	+	13.3465i	0.200859	+	0.749614i	0.990672	+	0.136267i	$0.0435106\pi$
$317$	3.57619	+	13.3465i	0.200859	+	0.749614i	−0.789814	+	0.613347i	$0.789823\pi$
$318$	0.879247	+	0.235593i	0.0493057	+	0.0132114i
$319$	38.8581	−	22.4348i	2.17564	−	1.25610i
$320$		0			0
$321$		−	0.212832i		−	0.0118791i
$322$	−14.9545	+	10.7119i	−0.833382	+	0.596949i
$323$	17.6742	+	17.6742i	0.983421	+	0.983421i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$		0			0
$326$	−3.74736	−	6.49061i	−0.207547	−	0.359482i
$327$	1.50724	−	0.403862i	0.0833503	−	0.0223336i
$328$	−2.92532	+	2.92532i	−0.161524	+	0.161524i
$329$	−1.73533	−	4.61338i	−0.0956721	−	0.254344i
$330$		0			0
$331$	2.41481	−	4.18257i	0.132730	−	0.229895i	−0.791998	−	0.610524i	$-0.790959\pi$
$331$	2.41481	−	4.18257i	0.132730	−	0.229895i	0.924728	+	0.380629i	$0.124292\pi$
$332$	0.728752	−	2.71974i	0.0399955	−	0.149265i
$333$	−2.01219	+	7.50959i	−0.110267	+	0.411523i
$334$	−9.04245	+	15.6620i	−0.494781	+	0.856985i
$335$		0			0
$336$	−2.04487	−	1.67884i	−0.111557	−	0.0915884i
$337$	6.52431	−	6.52431i	0.355402	−	0.355402i	−0.506713	−	0.862115i	$-0.669140\pi$
$337$	6.52431	−	6.52431i	0.355402	−	0.355402i	0.862115	+	0.506713i	$0.169140\pi$
$338$	4.63971	−	1.24321i	0.252367	−	0.0676216i
$339$	0.0212231	+	0.0367595i	0.00115268	+	0.00199650i
$340$		0			0
$341$	−8.21169	−	4.74102i	−0.444688	−	0.256741i
$342$	−2.54207	−	2.54207i	−0.137459	−	0.137459i
$343$	−5.36585	−	17.7259i	−0.289729	−	0.957109i
$344$			11.0897i			0.597919i
$345$		0			0
$346$	14.0118	−	8.08974i	0.753281	−	0.434907i
$347$	−30.3771	−	8.13952i	−1.63073	−	0.436952i	−0.676600	−	0.736351i	$-0.736547\pi$
$347$	−30.3771	−	8.13952i	−1.63073	−	0.436952i	−0.954128	+	0.299399i	$0.903214\pi$
$348$	2.28167	+	8.51530i	0.122310	+	0.456468i
$349$	28.5083			1.52601			0.763006	−	0.646391i	$-0.223722\pi$
$349$	28.5083			1.52601			0.763006	+	0.646391i	$0.223722\pi$
$350$		0			0
$351$	−2.86297			−0.152814
$352$	1.31732	+	4.91631i	0.0702134	+	0.262040i
$353$	22.5765	+	6.04935i	1.20162	+	0.321974i	0.803471	−	0.595345i	$-0.202984\pi$
$353$	22.5765	+	6.04935i	1.20162	+	0.321974i	0.398154	+	0.917319i	$0.369651\pi$
$354$	−3.61953	+	2.08974i	−0.192376	+	0.111068i
$355$		0			0
$356$		−	7.65014i		−	0.405457i
$357$	16.7540	+	7.59505i	0.886716	+	0.401973i
$358$	−7.02778	−	7.02778i	−0.371430	−	0.371430i
$359$	14.5889	+	8.42292i	0.769974	+	0.444545i	0.832865	−	0.553476i	$-0.186699\pi$
$359$	14.5889	+	8.42292i	0.769974	+	0.444545i	−0.0628915	+	0.998020i	$0.520032\pi$
$360$		0			0
$361$	3.03790	+	5.26180i	0.159890	+	0.276937i
$362$	2.51416	−	0.673667i	0.132141	−	0.0354072i
$363$	10.5397	−	10.5397i	0.553192	−	0.553192i
$364$	−7.47330	−	1.23533i	−0.391707	−	0.0647491i
$365$		0			0
$366$	2.93454	−	5.08277i	0.153391	−	0.265681i
$367$	−6.97882	+	26.0453i	−0.364291	+	1.35955i	0.504088	+	0.863653i	$0.331829\pi$
$367$	−6.97882	+	26.0453i	−0.364291	+	1.35955i	−0.868379	+	0.495901i	$0.834838\pi$
$368$	−1.79949	+	6.71580i	−0.0938051	+	0.350085i
$369$	−2.06851	+	3.58277i	−0.107683	+	0.186512i
$370$		0			0
$371$	2.37609	+	0.392766i	0.123360	+	0.0203914i
$372$	1.31732	−	1.31732i	0.0682999	−	0.0682999i
$373$	9.94175	−	2.66388i	0.514764	−	0.137931i	0.00792053	−	0.999969i	$-0.497479\pi$
$373$	9.94175	−	2.66388i	0.514764	−	0.137931i	0.506844	+	0.862038i	$0.330812\pi$
$374$	−17.6937	−	30.6464i	−0.914921	−	1.58469i
$375$		0			0
$376$	−1.61338	−	0.931486i	−0.0832038	−	0.0480377i
$377$	17.8467	+	17.8467i	0.919152	+	0.919152i
$378$	−2.40971	−	1.09239i	−0.123942	−	0.0561863i
$379$			24.4633i			1.25659i	0.777974	+	0.628297i	$0.216248\pi$
$379$			24.4633i			1.25659i	−0.777974	+	0.628297i	$0.783752\pi$
$380$		0			0
$381$	−1.74799	+	1.00920i	−0.0895521	+	0.0517029i
$382$	3.99606	+	1.07074i	0.204456	+	0.0547839i
$383$	1.59701	+	5.96013i	0.0816036	+	0.304549i	0.994649	−	0.103308i	$-0.0329429\pi$
$383$	1.59701	+	5.96013i	0.0816036	+	0.304549i	−0.913046	+	0.407857i	$0.866276\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−12.9527			−0.659276
$387$	2.87024	+	10.7119i	0.145902	+	0.544515i
$388$	−18.4346	−	4.93953i	−0.935875	−	0.250767i
$389$	−11.9344	+	6.89034i	−0.605099	+	0.349354i	−0.771045	−	0.636781i	$-0.780266\pi$
$389$	−11.9344	+	6.89034i	−0.605099	+	0.349354i	0.165946	+	0.986135i	$0.446932\pi$
$390$		0			0
$391$		−	48.3402i		−	2.44467i
$392$	−5.81878	−	3.89125i	−0.293893	−	0.196538i
$393$	3.74948	+	3.74948i	0.189136	+	0.189136i
$394$	1.07306	+	0.619530i	0.0540599	+	0.0312115i
$395$		0			0
$396$	2.54487	+	4.40784i	0.127884	+	0.221502i
$397$	1.11395	−	0.298482i	0.0559075	−	0.0149804i	−0.230757	−	0.973011i	$-0.574120\pi$
$397$	1.11395	−	0.298482i	0.0559075	−	0.0149804i	0.286664	+	0.958031i	$0.407454\pi$
$398$	−12.2069	+	12.2069i	−0.611875	+	0.611875i
$399$	−7.35135	−	6.03548i	−0.368028	−	0.302152i
$400$		0			0
$401$	−4.13703	+	7.16554i	−0.206593	+	0.357830i	−0.950639	−	0.310298i	$-0.899571\pi$
$401$	−4.13703	+	7.16554i	−0.206593	+	0.357830i	0.744046	+	0.668128i	$0.232904\pi$
$402$	−0.762637	+	2.84620i	−0.0380369	+	0.141956i
$403$	1.38045	−	5.15190i	0.0687650	−	0.256634i
$404$	−0.681895	+	1.18108i	−0.0339256	+	0.0587608i
$405$		0			0
$406$	8.21169	+	21.8308i	0.407539	+	1.08344i
$407$	27.9803	−	27.9803i	1.38693	−	1.38693i
$408$	6.71580	−	1.79949i	0.332482	−	0.0890882i
$409$	18.2355	+	31.5849i	0.901690	+	1.56177i	0.825300	+	0.564694i	$0.191006\pi$
$409$	18.2355	+	31.5849i	0.901690	+	1.56177i	0.0763896	+	0.997078i	$0.475661\pi$
$410$		0			0
$411$	19.0363	+	10.9906i	0.938991	+	0.542127i
$412$	0.257239	+	0.257239i	0.0126733	+	0.0126733i
$413$	−8.98958	+	6.43921i	−0.442348	+	0.316853i
$414$			6.95271i			0.341707i
$415$		0			0
$416$	−2.47941	+	1.43149i	−0.121563	+	0.0701844i
$417$	16.0249	+	4.29385i	0.784742	+	0.210271i
$418$	4.73580	+	17.6742i	0.231636	+	0.864476i
$419$	9.05638			0.442433			0.221217	−	0.975225i	$-0.428997\pi$
$419$	9.05638			0.442433			0.221217	+	0.975225i	$0.428997\pi$
$420$		0			0
$421$	10.3149			0.502716			0.251358	−	0.967894i	$-0.419123\pi$
$421$	10.3149			0.502716			0.251358	+	0.967894i	$0.419123\pi$
$422$	1.91645	+	7.15230i	0.0932914	+	0.348168i
$423$	−1.79949	−	0.482173i	−0.0874944	−	0.0234440i
$424$	0.788311	−	0.455132i	0.0382838	−	0.0221031i
$425$		0			0
$426$			7.86297i			0.380962i
$427$	6.41130	−	14.1428i	0.310265	−	0.684416i
$428$	−0.150495	−	0.150495i	−0.00727443	−	0.00727443i
$429$	12.6195	+	7.28589i	0.609277	+	0.351766i
$430$		0			0
$431$	11.4441	+	19.8218i	0.551245	+	0.954784i	0.998185	+	0.0602202i	$0.0191803\pi$
$431$	11.4441	+	19.8218i	0.551245	+	0.954784i	−0.446940	+	0.894564i	$0.647486\pi$
$432$	−0.965926	+	0.258819i	−0.0464731	+	0.0124524i
$433$	17.2780	−	17.2780i	0.830327	−	0.830327i	−0.157235	−	0.987561i	$-0.550258\pi$
$433$	17.2780	−	17.2780i	0.830327	−	0.830327i	0.987561	+	0.157235i	$0.0502579\pi$
$434$	3.12764	−	3.80953i	0.150131	−	0.182863i
$435$		0			0
$436$	0.780202	−	1.35135i	0.0373649	−	0.0647179i
$437$	−6.46922	+	24.1435i	−0.309465	+	1.15494i
$438$	3.50165	−	13.0683i	0.167315	−	0.624429i
$439$	2.48269	−	4.30015i	0.118492	−	0.205235i	−0.800678	−	0.599095i	$-0.795527\pi$
$439$	2.48269	−	4.30015i	0.118492	−	0.205235i	0.919170	+	0.393860i	$0.128861\pi$
$440$		0			0
$441$	−6.62764	−	2.25264i	−0.315602	−	0.107269i
$442$	14.0753	−	14.0753i	0.669492	−	0.669492i
$443$	−12.5524	+	3.36339i	−0.596380	+	0.159800i	−0.544368	−	0.838847i	$-0.683230\pi$
$443$	−12.5524	+	3.36339i	−0.596380	+	0.159800i	−0.0520128	+	0.998646i	$0.516564\pi$
$444$	3.88725	+	6.73291i	0.184481	+	0.319530i
$445$		0			0
$446$	3.30448	+	1.90784i	0.156472	+	0.0903389i
$447$	−7.02778	−	7.02778i	−0.332402	−	0.332402i
$448$	−2.63306	+	0.258819i	−0.124400	+	0.0122281i
$449$			15.0710i			0.711243i	0.934630	+	0.355621i	$0.115731\pi$
$449$			15.0710i			0.711243i	−0.934630	+	0.355621i	$0.884269\pi$
$450$		0			0
$451$	18.2354	−	10.5282i	0.858669	−	0.495753i
$452$	0.0409999	+	0.0109859i	0.00192847	+	0.000516733i
$453$	−3.96420	−	14.7946i	−0.186254	−	0.695111i
$454$	−19.6926			−0.924219
$455$		0			0
$456$	−3.59502			−0.168352
$457$	−6.70321	−	25.0167i	−0.313563	−	1.17023i	−0.925320	−	0.379187i	$-0.876204\pi$
$457$	−6.70321	−	25.0167i	−0.313563	−	1.17023i	0.611757	−	0.791046i	$-0.290463\pi$
$458$	−22.1938	−	5.94682i	−1.03705	−	0.277877i
$459$	6.02122	−	3.47635i	0.281047	−	0.162262i
$460$		0			0
$461$		−	19.9054i		−	0.927088i	−0.886074	−	0.463544i	$-0.846578\pi$
$461$		−	19.9054i		−	0.927088i	0.886074	−	0.463544i	$-0.153422\pi$
$462$	7.84163	+	10.9475i	0.364826	+	0.509322i
$463$	−29.0870	−	29.0870i	−1.35179	−	1.35179i	−0.883664	−	0.468121i	$-0.844931\pi$
$463$	−29.0870	−	29.0870i	−1.35179	−	1.35179i	−0.468121	−	0.883664i	$-0.655069\pi$
$464$	7.63460	+	4.40784i	0.354428	+	0.204629i
$465$		0			0
$466$	−6.61953	−	11.4654i	−0.306644	−	0.531123i
$467$	−27.5100	+	7.37127i	−1.27301	+	0.341102i	−0.831183	−	0.555999i	$-0.812336\pi$
$467$	−27.5100	+	7.37127i	−1.27301	+	0.341102i	−0.441826	+	0.897101i	$0.645669\pi$
$468$	−2.02443	+	2.02443i	−0.0935792	+	0.0935792i
$469$	−1.27142	+	7.69161i	−0.0587087	+	0.355165i
$470$		0			0
$471$	8.17251	−	14.1552i	0.376569	−	0.652237i
$472$	−1.08173	+	4.03706i	−0.0497905	+	0.185821i
$473$	14.6087	−	54.5206i	0.671711	−	2.50686i
$474$	−6.04487	+	10.4700i	−0.277650	+	0.480904i
$475$		0			0
$476$	17.2174	−	6.47635i	0.789157	−	0.296843i
$477$	0.643653	−	0.643653i	0.0294709	−	0.0294709i
$478$	−1.59391	+	0.427088i	−0.0729039	+	0.0195346i
$479$	−4.79770	−	8.30986i	−0.219212	−	0.379687i	0.735355	−	0.677682i	$-0.237015\pi$
$479$	−4.79770	−	8.30986i	−0.219212	−	0.379687i	−0.954567	+	0.297995i	$0.903682\pi$
$480$		0			0
$481$	19.2761	+	11.1291i	0.878917	+	0.507443i
$482$	8.94589	+	8.94589i	0.407474	+	0.407474i
$483$	1.79949	+	18.3069i	0.0818798	+	0.832993i
$484$		−	14.9054i		−	0.677519i
$485$		0			0
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	12.0433	+	3.22698i	0.545733	+	0.146229i	0.521144	−	0.853469i	$-0.325506\pi$
$487$	12.0433	+	3.22698i	0.545733	+	0.146229i	0.0245890	+	0.999698i	$0.492172\pi$
$488$	−1.51903	−	5.66909i	−0.0687632	−	0.256628i
$489$	−7.49471			−0.338923
$490$		0			0
$491$	36.3288			1.63950			0.819748	−	0.572725i	$-0.194114\pi$
$491$	36.3288			1.63950			0.819748	+	0.572725i	$0.194114\pi$
$492$	1.07074	+	3.99606i	0.0482728	+	0.180156i
$493$	−59.2044	−	15.8638i	−2.66643	−	0.714468i
$494$	−8.91353	+	5.14623i	−0.401039	+	0.231540i
$495$		0			0
$496$		−	1.86297i		−	0.0836500i
$497$	2.03509	+	20.7037i	0.0912861	+	0.928687i
$498$	−1.99099	−	1.99099i	−0.0892183	−	0.0892183i
$499$	2.42441	+	1.39973i	0.108531	+	0.0626606i	0.553283	−	0.832993i	$-0.313375\pi$
$499$	2.42441	+	1.39973i	0.108531	+	0.0626606i	−0.444752	+	0.895654i	$0.646708\pi$
$500$		0			0
$501$	9.04245	+	15.6620i	0.403987	+	0.699725i
$502$	7.19797	−	1.92869i	0.321261	−	0.0860817i
$503$	12.1725	−	12.1725i	0.542743	−	0.542743i	−0.381589	−	0.924332i	$-0.624623\pi$
$503$	12.1725	−	12.1725i	0.542743	−	0.542743i	0.924332	+	0.381589i	$0.124623\pi$
$504$	−2.47635	+	0.931486i	−0.110306	+	0.0414917i
$505$		0			0
$506$	17.6937	−	30.6464i	0.786582	−	1.36240i
$507$	1.24321	−	4.63971i	0.0552128	−	0.206057i
$508$	−0.522401	+	1.94963i	−0.0231778	+	0.0865007i
$509$	10.4503	−	18.1004i	0.463201	−	0.802287i	−0.535917	−	0.844270i	$-0.680034\pi$
$509$	10.4503	−	18.1004i	0.463201	−	0.802287i	0.999118	+	0.0419830i	$0.0133675\pi$
$510$		0			0
$511$	5.83772	−	35.3160i	0.258246	−	1.56229i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−3.47253	+	0.930461i	−0.153316	+	0.0410808i
$514$	8.31650	+	14.4046i	0.366825	+	0.635360i
$515$		0			0
$516$	9.60399	+	5.54487i	0.422792	+	0.244099i
$517$	6.70482	+	6.70482i	0.294877	+	0.294877i
$518$	11.9780	+	16.7221i	0.526282	+	0.734726i
$519$		−	16.1795i		−	0.710200i
$520$		0			0
$521$	−21.3985	+	12.3544i	−0.937483	+	0.541256i	−0.889170	−	0.457576i	$-0.848718\pi$
$521$	−21.3985	+	12.3544i	−0.937483	+	0.541256i	−0.0483128	+	0.998832i	$0.515384\pi$
$522$	8.51530	+	2.28167i	0.372704	+	0.0998658i
$523$	7.79435	+	29.0889i	0.340823	+	1.27197i	0.897417	+	0.441184i	$0.145441\pi$
$523$	7.79435	+	29.0889i	0.340823	+	1.27197i	−0.556594	+	0.830785i	$0.687892\pi$
$524$	5.30257			0.231644
$525$		0			0
$526$	−11.0473			−0.481685
$527$	3.35241	+	12.5114i	0.146033	+	0.545003i
$528$	4.91631	+	1.31732i	0.213955	+	0.0573290i
$529$	21.9452	−	12.6701i	0.954140	−	0.550873i
$530$		0			0
$531$			4.17947i			0.181374i
$532$	−9.46592	+	0.930461i	−0.410400	+	0.0403406i
$533$	8.37511	+	8.37511i	0.362766	+	0.362766i
$534$	−6.62522	−	3.82507i	−0.286701	−	0.165527i
$535$		0			0
$536$	1.47330	+	2.55183i	0.0636370	+	0.110222i
$537$	−9.60012	+	2.57234i	−0.414276	+	0.111005i
$538$	−18.8111	+	18.8111i	−0.811002	+	0.811002i
$539$	23.4809	+	26.7958i	1.01139	+	1.15418i
$540$		0			0
$541$	−20.0506	+	34.7286i	−0.862041	+	1.49310i	0.00791517	+	0.999969i	$0.497480\pi$
$541$	−20.0506	+	34.7286i	−0.862041	+	1.49310i	−0.869956	+	0.493130i	$0.835853\pi$
$542$	−5.25830	+	19.6242i	−0.225863	+	0.842933i
$543$	0.673667	−	2.51416i	0.0289098	−	0.107893i
$544$	3.47635	−	6.02122i	0.149047	−	0.258158i
$545$		0			0
$546$	−4.80648	+	5.85440i	−0.205698	+	0.250545i
$547$	−26.5205	+	26.5205i	−1.13394	+	1.13394i	−0.144420	+	0.989516i	$0.546132\pi$
$547$	−26.5205	+	26.5205i	−1.13394	+	1.13394i	−0.989516	+	0.144420i	$0.953868\pi$
$548$	21.2322	−	5.68916i	0.906996	−	0.243029i
$549$	−2.93454	−	5.08277i	−0.125243	−	0.216927i
$550$		0			0
$551$	27.4466	+	15.8463i	1.16926	+	0.675075i
$552$	4.91631	+	4.91631i	0.209252	+	0.209252i
$553$	−13.2067	+	29.1327i	−0.561605	+	1.23885i
$554$			10.0697i			0.427821i
$555$		0			0
$556$	14.3675	−	8.29509i	0.609318	−	0.351790i
$557$	−5.03679	−	1.34960i	−0.213416	−	0.0571845i	0.150527	−	0.988606i	$-0.451903\pi$
$557$	−5.03679	−	1.34960i	−0.213416	−	0.0571845i	−0.363943	+	0.931421i	$0.618570\pi$
$558$	−0.482173	−	1.79949i	−0.0204120	−	0.0761786i
$559$	31.7496			1.34287
$560$		0			0
$561$	−35.3875			−1.49406
$562$	−3.94098	−	14.7079i	−0.166240	−	0.620416i
$563$	−14.9814	−	4.01426i	−0.631392	−	0.169181i	−0.0710904	−	0.997470i	$-0.522648\pi$
$563$	−14.9814	−	4.01426i	−0.631392	−	0.169181i	−0.560301	+	0.828289i	$0.689315\pi$
$564$	−1.61338	+	0.931486i	−0.0679356	+	0.0392227i
$565$		0			0
$566$			14.8319i			0.623431i
$567$	−2.15089	+	1.54067i	−0.0903288	+	0.0647023i
$568$	5.55996	+	5.55996i	0.233291	+	0.233291i
$569$	23.8369	+	13.7622i	0.999295	+	0.576943i	0.908040	−	0.418884i	$-0.137579\pi$
$569$	23.8369	+	13.7622i	0.999295	+	0.576943i	0.0912554	+	0.995828i	$0.470912\pi$
$570$		0			0
$571$	−1.46210	−	2.53243i	−0.0611869	−	0.105979i	0.833809	−	0.552053i	$-0.186155\pi$
$571$	−1.46210	−	2.53243i	−0.0611869	−	0.105979i	−0.894996	+	0.446074i	$0.852822\pi$
$572$	14.0753	−	3.77145i	0.588516	−	0.157692i
$573$	2.92532	−	2.92532i	0.122207	−	0.122207i
$574$	3.85358	+	10.2447i	0.160846	+	0.427607i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	0.900627	−	3.36119i	0.0374936	−	0.139928i	−0.944642	−	0.328103i	$-0.893591\pi$
$577$	0.900627	−	3.36119i	0.0374936	−	0.139928i	0.982135	+	0.188175i	$0.0602573\pi$
$578$	−8.11143	+	30.2723i	−0.337391	+	1.25916i
$579$	−6.47635	+	11.2174i	−0.269148	+	0.466178i
$580$		0			0
$581$	−5.75770	−	4.72709i	−0.238870	−	0.196113i
$582$	−13.4951	+	13.4951i	−0.559388	+	0.559388i
$583$	−4.47514	+	1.19911i	−0.185341	+	0.0496620i
$584$	−6.76467	−	11.7167i	−0.279924	−	0.484842i
$585$		0			0
$586$	−22.9038	−	13.2235i	−0.946148	−	0.546259i
$587$	29.2873	+	29.2873i	1.20882	+	1.20882i	0.971410	+	0.237407i	$0.0762975\pi$
$587$	29.2873	+	29.2873i	1.20882	+	1.20882i	0.237407	+	0.971410i	$0.423702\pi$
$588$	−6.27931	+	3.09359i	−0.258954	+	0.127577i
$589$		−	6.69743i		−	0.275963i
$590$		0			0
$591$	1.07306	−	0.619530i	0.0441397	−	0.0254841i
$592$	7.50959	+	2.01219i	0.308642	+	0.0827004i
$593$	−3.25700	−	12.1553i	−0.133749	−	0.499158i	0.866251	−	0.499609i	$-0.166523\pi$
$593$	−3.25700	−	12.1553i	−0.133749	−	0.499158i	−1.00000		0.000451399i	$0.999856\pi$
$594$	5.08974			0.208834
$595$		0			0
$596$	−9.93878			−0.407108
$597$	4.46802	+	16.6749i	0.182864	+	0.682457i
$598$	19.2272	+	5.15190i	0.786257	+	0.210677i
$599$	41.1024	−	23.7305i	1.67940	−	0.969602i	0.717355	−	0.696708i	$-0.245353\pi$
$599$	41.1024	−	23.7305i	1.67940	−	0.969602i	0.962044	−	0.272894i	$-0.0879807\pi$
$600$		0			0
$601$		−	39.1953i		−	1.59881i	−0.600792	−	0.799405i	$-0.705148\pi$
$601$		−	39.1953i		−	1.59881i	0.600792	−	0.799405i	$-0.294852\pi$
$602$	26.7230	+	12.1143i	1.08915	+	0.493741i
$603$	2.08356	+	2.08356i	0.0848493	+	0.0848493i
$604$	−13.2645	−	7.65825i	−0.539724	−	0.311610i
$605$		0			0
$606$	0.681895	+	1.18108i	0.0277001	+	0.0479780i
$607$	−12.9338	+	3.46559i	−0.524965	+	0.140664i	−0.511562	−	0.859246i	$-0.670933\pi$
$607$	−12.9338	+	3.46559i	−0.524965	+	0.140664i	−0.0134030	+	0.999910i	$0.504266\pi$
$608$	−2.54207	+	2.54207i	−0.103094	+	0.103094i
$609$	23.0118	+	3.80385i	0.932487	+	0.154140i
$610$		0			0
$611$	−2.66682	+	4.61907i	−0.107888	+	0.186868i
$612$	1.79949	−	6.71580i	0.0727402	−	0.271470i
$613$	−5.34717	+	19.9559i	−0.215970	+	0.806012i	0.769853	+	0.638222i	$0.220330\pi$
$613$	−5.34717	+	19.9559i	−0.215970	+	0.806012i	−0.985823	+	0.167790i	$0.946337\pi$
$614$	−15.9054	+	27.5490i	−0.641890	+	1.11179i
$615$		0			0
$616$	13.2859	+	2.19615i	0.535304	+	0.0884855i
$617$	3.22631	−	3.22631i	0.129886	−	0.129886i	−0.639175	−	0.769061i	$-0.720724\pi$
$617$	3.22631	−	3.22631i	0.129886	−	0.129886i	0.769061	+	0.639175i	$0.220724\pi$
$618$	0.351395	−	0.0941560i	0.0141352	−	0.00378751i
$619$	2.10527	+	3.64644i	0.0846181	+	0.146563i	0.905228	−	0.424925i	$-0.139700\pi$
$619$	2.10527	+	3.64644i	0.0846181	+	0.146563i	−0.820610	+	0.571488i	$0.806366\pi$
$620$		0			0
$621$	6.02122	+	3.47635i	0.241623	+	0.139501i
$622$	−11.6431	−	11.6431i	−0.466846	−	0.466846i
$623$	−18.4346	−	8.35691i	−0.738567	−	0.334813i
$624$			2.86297i			0.114611i
$625$		0			0
$626$	−2.92378	+	1.68804i	−0.116858	+	0.0674678i
$627$	17.6742	+	4.73580i	0.705841	+	0.189130i
$628$	−4.23040	−	15.7881i	−0.168811	−	0.630013i
$629$	−54.0538			−2.15527
$630$		0			0
$631$	35.1730			1.40021			0.700107	−	0.714038i	$-0.253135\pi$
$631$	35.1730			1.40021			0.700107	+	0.714038i	$0.253135\pi$
$632$	3.12905	+	11.6778i	0.124467	+	0.464517i
$633$	7.15230	+	1.91645i	0.284278	+	0.0761721i
$634$	11.9661	−	6.90866i	0.475236	−	0.274378i
$635$		0			0
$636$		−	0.910263i		−	0.0360943i
$637$	−11.1405	+	16.6590i	−0.441404	+	0.660054i
$638$	−31.7275	−	31.7275i	−1.25610	−	1.25610i
$639$	6.80953	+	3.93149i	0.269381	+	0.155527i
$640$		0			0
$641$	−5.56609	−	9.64075i	−0.219847	−	0.380787i	0.734914	−	0.678161i	$-0.237223\pi$
$641$	−5.56609	−	9.64075i	−0.219847	−	0.380787i	−0.954761	+	0.297374i	$0.903889\pi$
$642$	−0.205579	+	0.0550849i	−0.00811358	+	0.00217403i
$643$	20.3659	−	20.3659i	0.803153	−	0.803153i	−0.180434	−	0.983587i	$-0.557750\pi$
$643$	20.3659	−	20.3659i	0.803153	−	0.803153i	0.983587	+	0.180434i	$0.0577502\pi$
$644$	14.2174	+	11.6725i	0.560243	+	0.459961i
$645$		0			0
$646$	12.4976	−	21.6464i	0.491711	−	0.851668i
$647$	2.95760	−	11.0379i	0.116275	−	0.433946i	−0.883104	−	0.469178i	$-0.844550\pi$
$647$	2.95760	−	11.0379i	0.116275	−	0.433946i	0.999379	+	0.0352321i	$0.0112171\pi$
$648$	−0.258819	+	0.965926i	−0.0101674	+	0.0379452i
$649$	10.6362	−	18.4225i	0.417508	−	0.723145i
$650$		0			0
$651$	−1.73533	−	4.61338i	−0.0680131	−	0.180813i
$652$	−5.29956	+	5.29956i	−0.207547	+	0.207547i
$653$	13.6641	−	3.66128i	0.534717	−	0.143277i	0.0186516	−	0.999826i	$-0.494063\pi$
$653$	13.6641	−	3.66128i	0.534717	−	0.143277i	0.516066	+	0.856549i	$0.327396\pi$
$654$	−0.780202	−	1.35135i	−0.0305083	−	0.0528420i
$655$		0			0
$656$	3.58277	+	2.06851i	0.139884	+	0.0807619i
$657$	−9.56668	−	9.56668i	−0.373232	−	0.373232i
$658$	−4.00705	+	2.87024i	−0.156211	+	0.111893i
$659$			11.7840i			0.459038i	0.973304	+	0.229519i	$0.0737153\pi$
$659$			11.7840i			0.459038i	−0.973304	+	0.229519i	$0.926285\pi$
$660$		0			0
$661$	41.3181	−	23.8550i	1.60709	−	0.927853i	0.617072	−	0.786907i	$-0.288319\pi$
$661$	41.3181	−	23.8550i	1.60709	−	0.927853i	0.990017	−	0.140946i	$-0.0450145\pi$
$662$	−4.66505	−	1.25000i	−0.181312	−	0.0485825i
$663$	−5.15190	−	19.2272i	−0.200083	−	0.746721i
$664$	−2.81568			−0.109270
$665$		0			0
$666$	7.77450			0.301256
$667$	−15.8638	−	59.2044i	−0.614247	−	2.29240i
$668$	17.4687	+	4.68071i	0.675883	+	0.181102i
$669$	3.30448	−	1.90784i	0.127758	−	0.0737614i
$670$		0			0
$671$			29.8721i			1.15320i
$672$	−1.09239	+	2.40971i	−0.0421397	+	0.0929565i
$673$	23.3048	+	23.3048i	0.898334	+	0.898334i	0.995289	−	0.0969544i	$-0.0309101\pi$
$673$	23.3048	+	23.3048i	0.898334	+	0.898334i	−0.0969544	+	0.995289i	$0.530910\pi$
$674$	−7.99061	−	4.61338i	−0.307787	−	0.177701i
$675$		0			0
$676$	−2.40169	−	4.15985i	−0.0923728	−	0.159994i
$677$	5.90757	−	1.58293i	0.227046	−	0.0608369i	−0.143502	−	0.989650i	$-0.545836\pi$
$677$	5.90757	−	1.58293i	0.227046	−	0.0608369i	0.370548	+	0.928813i	$0.379170\pi$
$678$	0.0300140	−	0.0300140i	0.00115268	−	0.00115268i
$679$	−32.0405	+	39.0261i	−1.22960	+	1.49768i
$680$		0			0
$681$	−9.84629	+	17.0543i	−0.377311	+	0.653521i
$682$	−2.45413	+	9.15895i	−0.0939736	+	0.350714i
$683$	−7.41077	+	27.6574i	−0.283565	+	1.05828i	0.666316	+	0.745669i	$0.267870\pi$
$683$	−7.41077	+	27.6574i	−0.283565	+	1.05828i	−0.949882	+	0.312610i	$0.898797\pi$
$684$	−1.79751	+	3.11338i	−0.0687296	+	0.119043i
$685$		0			0
$686$	−15.7331	+	9.77081i	−0.600693	+	0.373051i
$687$	−16.2470	+	16.2470i	−0.619862	+	0.619862i
$688$	10.7119	−	2.87024i	0.408386	−	0.109427i
$689$	−1.30303	−	2.25691i	−0.0496415	−	0.0859816i
$690$		0			0
$691$	−8.56043	−	4.94237i	−0.325654	−	0.188016i	0.328256	−	0.944589i	$-0.393539\pi$
$691$	−8.56043	−	4.94237i	−0.325654	−	0.188016i	−0.653910	+	0.756572i	$0.726873\pi$
$692$	−11.4406	−	11.4406i	−0.434907	−	0.434907i
$693$	13.4016	−	1.31732i	0.509084	−	0.0500409i
$694$			31.4487i			1.19378i
$695$		0			0
$696$	7.63460	−	4.40784i	0.289389	−	0.167079i
$697$	−27.7835	−	7.44455i	−1.05237	−	0.281983i
$698$	−7.37848	−	27.5369i	−0.279280	−	1.04229i
$699$	−13.2391			−0.500747
$700$		0			0
$701$	−22.4772			−0.848952			−0.424476	−	0.905439i	$-0.639542\pi$
$701$	−22.4772			−0.848952			−0.424476	+	0.905439i	$0.639542\pi$
$702$	0.740992	+	2.76542i	0.0279669	+	0.104374i
$703$	26.9971	+	7.23386i	1.01822	+	0.272830i
$704$	4.40784	−	2.54487i	0.166127	−	0.0959133i
$705$		0			0
$706$		−	23.3729i		−	0.879650i
$707$	2.10116	+	2.93336i	0.0790222	+	0.110320i
$708$	2.95533	+	2.95533i	0.111068	+	0.111068i
$709$	6.12307	+	3.53516i	0.229957	+	0.132766i	0.610552	−	0.791976i	$-0.290948\pi$
$709$	6.12307	+	3.53516i	0.229957	+	0.132766i	−0.380595	+	0.924742i	$0.624281\pi$
$710$		0			0
$711$	6.04487	+	10.4700i	0.226700	+	0.392656i
$712$	−7.38947	+	1.98000i	−0.276932	+	0.0742037i
$713$	−9.15895	+	9.15895i	−0.343005	+	0.343005i
$714$	3.00000	−	18.1489i	0.112272	−	0.679204i
$715$		0			0
$716$	−4.96939	+	8.60723i	−0.185715	+	0.321667i
$717$	−0.427088	+	1.59391i	−0.0159499	+	0.0595258i
$718$	4.36002	−	16.2718i	0.162715	−	0.607259i
$719$	−18.1121	+	31.3711i	−0.675467	+	1.16994i	0.300865	+	0.953667i	$0.402725\pi$
$719$	−18.1121	+	31.3711i	−0.675467	+	1.16994i	−0.976332	+	0.216277i	$0.930609\pi$
$720$		0			0
$721$	0.900875	−	0.338866i	0.0335503	−	0.0126200i
$722$	4.29624	−	4.29624i	0.159890	−	0.159890i
$723$	12.2203	−	3.27442i	0.454478	−	0.121777i
$724$	−1.30143	−	2.25414i	−0.0483671	−	0.0837743i
$725$		0			0
$726$	−12.9085	−	7.45271i	−0.479078	−	0.276596i
$727$	8.46215	+	8.46215i	0.313844	+	0.313844i	0.846397	−	0.532553i	$-0.178767\pi$
$727$	8.46215	+	8.46215i	0.313844	+	0.313844i	−0.532553	+	0.846397i	$0.678767\pi$
$728$	0.740992	+	7.53838i	0.0274630	+	0.279391i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−66.7738	+	38.5519i	−2.46972	+	1.42589i
$732$	−5.66909	−	1.51903i	−0.209536	−	0.0561449i
$733$	1.20967	+	4.51455i	0.0446802	+	0.166749i	0.984661	−	0.174479i	$-0.0558240\pi$
$733$	1.20967	+	4.51455i	0.0446802	+	0.166749i	−0.939981	+	0.341228i	$0.889157\pi$
$734$	26.9641			0.995262
$735$		0			0
$736$	6.95271			0.256280
$737$	−3.88162	−	14.4864i	−0.142981	−	0.533614i
$738$	3.99606	+	1.07074i	0.147097	+	0.0394145i
$739$	−22.4673	+	12.9715i	−0.826474	+	0.477165i	−0.852644	−	0.522493i	$-0.825002\pi$
$739$	−22.4673	+	12.9715i	−0.826474	+	0.477165i	0.0261702	+	0.999658i	$0.491669\pi$
$740$		0			0
$741$			10.2925i			0.378103i
$742$	−0.235593	−	2.39678i	−0.00864891	−	0.0879885i
$743$	−33.8328	−	33.8328i	−1.24121	−	1.24121i	−0.959501	−	0.281704i	$-0.909101\pi$
$743$	−33.8328	−	33.8328i	−1.24121	−	1.24121i	−0.281704	−	0.959501i	$-0.590899\pi$
$744$	−1.61338	−	0.931486i	−0.0591494	−	0.0341500i
$745$		0			0
$746$	−5.14623	−	8.91353i	−0.188417	−	0.326347i
$747$	−2.71974	+	0.728752i	−0.0995101	+	0.0266637i
$748$	−25.0227	+	25.0227i	−0.914921	+	0.914921i
$749$	−0.527046	+	0.198250i	−0.0192579	+	0.00724389i
$750$		0			0
$751$	−5.00811	+	8.67430i	−0.182748	+	0.316530i	−0.942816	−	0.333315i	$-0.891833\pi$
$751$	−5.00811	+	8.67430i	−0.182748	+	0.316530i	0.760067	+	0.649845i	$0.225166\pi$
$752$	−0.482173	+	1.79949i	−0.0175830	+	0.0656208i
$753$	1.92869	−	7.19797i	0.0702854	−	0.262309i
$754$	12.6195	−	21.8577i	0.459576	−	0.796009i
$755$		0			0
$756$	−0.431486	+	2.61033i	−0.0156930	+	0.0949368i
$757$	−2.56404	+	2.56404i	−0.0931915	+	0.0931915i	−0.752166	−	0.658974i	$-0.770991\pi$
$757$	−2.56404	+	2.56404i	−0.0931915	+	0.0931915i	0.658974	+	0.752166i	$0.270991\pi$
$758$	23.6297	−	6.33156i	0.858269	−	0.229973i
$759$	−17.6937	−	30.6464i	−0.642242	−	1.11240i
$760$		0			0
$761$	1.98202	+	1.14432i	0.0718481	+	0.0414815i	0.535494	−	0.844539i	$-0.320126\pi$
$761$	1.98202	+	1.14432i	0.0718481	+	0.0414815i	−0.463646	+	0.886021i	$0.653459\pi$
$762$	1.42723	+	1.42723i	0.0517029	+	0.0517029i
$763$	−2.40408	−	3.35626i	−0.0870334	−	0.121505i
$764$		−	4.13703i		−	0.149672i
$765$		0			0
$766$	5.34371	−	3.08519i	0.193076	−	0.111473i
$767$	11.5580	+	3.09696i	0.417335	+	0.111825i
$768$	0.258819	+	0.965926i	0.00933933	+	0.0348548i
$769$	−8.35895			−0.301431			−0.150716	−	0.988577i	$-0.548158\pi$
$769$	−8.35895			−0.301431			−0.150716	+	0.988577i	$0.548158\pi$
$770$		0			0
$771$	16.6330			0.599023
$772$	3.35241	+	12.5114i	0.120656	+	0.450294i
$773$	10.5063	+	2.81515i	0.377885	+	0.101254i	0.442762	−	0.896639i	$-0.353999\pi$
$773$	10.5063	+	2.81515i	0.377885	+	0.101254i	−0.0648769	+	0.997893i	$0.520665\pi$
$774$	9.60399	−	5.54487i	0.345208	−	0.199306i
$775$		0			0
$776$			19.0849i			0.685108i
$777$	20.4707	−	2.01219i	0.734383	−	0.0721868i
$778$	9.74442	+	9.74442i	0.349354	+	0.349354i
$779$	12.8801	+	7.43636i	0.461479	+	0.266435i
$780$		0			0
$781$	−20.0102	−	34.6587i	−0.716022	−	1.24019i
$782$	−46.6930	+	12.5114i	−1.66974	+	0.447405i
$783$	6.23363	−	6.23363i	0.222772	−	0.222772i
$784$	−2.25264	+	6.62764i	−0.0804516	+	0.236701i
$785$		0			0
$786$	2.65128	−	4.59216i	0.0945682	−	0.163797i
$787$	5.38330	−	20.0907i	0.191894	−	0.716158i	−0.801155	−	0.598457i	$-0.795781\pi$
$787$	5.38330	−	20.0907i	0.191894	−	0.716158i	0.993049	−	0.117701i	$-0.0375524\pi$
$788$	0.320692	−	1.19684i	0.0114242	−	0.0426357i
$789$	−5.52365	+	9.56723i	−0.196647	+	0.340603i
$790$		0			0
$791$	0.0712605	−	0.0867969i	0.00253373	−	0.00308614i
$792$	3.59899	−	3.59899i	0.127884	−	0.127884i
$793$	−16.2305	+	4.34894i	−0.576361	+	0.154435i
$794$	−0.576622	−	0.998739i	−0.0204636	−	0.0354439i
$795$		0			0
$796$	14.9503	+	8.63155i	0.529899	+	0.305937i
$797$	−8.60761	−	8.60761i	−0.304897	−	0.304897i	0.538029	−	0.842926i	$-0.319169\pi$
$797$	−8.60761	−	8.60761i	−0.304897	−	0.304897i	−0.842926	+	0.538029i	$0.819169\pi$
$798$	−3.92716	+	8.66296i	−0.139020	+	0.306665i
$799$		−	12.9527i		−	0.458234i
$800$		0			0
$801$	−6.62522	+	3.82507i	−0.234091	+	0.135152i
$802$	7.99212	+	2.14148i	0.282212	+	0.0756184i
$803$	17.8225	+	66.5144i	0.628941	+	2.34724i
$804$	2.94660			0.103919
$805$		0			0
$806$	−5.33364			−0.187869
$807$	6.88532	+	25.6964i	0.242375	+	0.904555i
$808$	1.31732	+	0.352975i	0.0463432	+	0.0124176i
$809$	13.8034	−	7.96939i	0.485301	−	0.280189i	−0.237322	−	0.971431i	$-0.576270\pi$
$809$	13.8034	−	7.96939i	0.485301	−	0.280189i	0.722623	+	0.691242i	$0.242936\pi$
$810$		0			0
$811$		−	23.3056i		−	0.818369i	−0.912452	−	0.409184i	$-0.865813\pi$
$811$		−	23.3056i		−	0.818369i	0.912452	−	0.409184i	$-0.134187\pi$
$812$	18.9616	−	13.5821i	0.665420	−	0.476638i
$813$	14.3659	+	14.3659i	0.503835	+	0.503835i
$814$	−34.2687	−	19.7851i	−1.20112	−	0.693466i
$815$		0			0
$816$	−3.47635	−	6.02122i	−0.121697	−	0.210785i
$817$	38.5094	−	10.3186i	1.34727	−	0.361001i
$818$	25.7890	−	25.7890i	0.901690	−	0.901690i
$819$	2.66682	+	7.08974i	0.0931862	+	0.247735i
$820$		0			0
$821$	4.12149	−	7.13863i	0.143841	−	0.249140i	−0.785099	−	0.619370i	$-0.787388\pi$
$821$	4.12149	−	7.13863i	0.143841	−	0.249140i	0.928940	+	0.370230i	$0.120721\pi$
$822$	5.68916	−	21.2322i	0.198432	−	0.740559i
$823$	−8.40095	+	31.3528i	−0.292839	+	1.09289i	0.650080	+	0.759866i	$0.274736\pi$
$823$	−8.40095	+	31.3528i	−0.292839	+	1.09289i	−0.942919	+	0.333023i	$0.891931\pi$
$824$	0.181895	−	0.315052i	0.00633663	−	0.0109754i
$825$		0			0
$826$	8.54647	+	7.01668i	0.297370	+	0.244141i
$827$	7.75116	−	7.75116i	0.269534	−	0.269534i	−0.559378	−	0.828913i	$-0.688960\pi$
$827$	7.75116	−	7.75116i	0.269534	−	0.269534i	0.828913	+	0.559378i	$0.188960\pi$
$828$	6.71580	−	1.79949i	0.233390	−	0.0625367i
$829$	−2.65278	−	4.59474i	−0.0921347	−	0.159582i	0.816274	−	0.577664i	$-0.196036\pi$
$829$	−2.65278	−	4.59474i	−0.0921347	−	0.159582i	−0.908409	+	0.418082i	$0.862702\pi$
$830$		0			0
$831$	8.72062	+	5.03485i	0.302515	+	0.174657i
$832$	2.02443	+	2.02443i	0.0701844	+	0.0701844i
$833$	3.20191	−	48.5635i	0.110940	−	1.68263i
$834$		−	16.5902i		−	0.574471i
$835$		0			0
$836$	15.8463	−	9.14886i	0.548056	−	0.316420i
$837$	−1.79949	−	0.482173i	−0.0621996	−	0.0166663i
$838$	−2.34396	−	8.74779i	−0.0809709	−	0.302187i
$839$	2.31971			0.0800852			0.0400426	−	0.999198i	$-0.487251\pi$
$839$	2.31971			0.0800852			0.0400426	+	0.999198i	$0.487251\pi$
$840$		0			0
$841$	−48.7163			−1.67987
$842$	−2.66968	−	9.96339i	−0.0920034	−	0.343361i
$843$	−14.7079	−	3.94098i	−0.506568	−	0.135734i
$844$	6.41257	−	3.70230i	0.220730	−	0.127438i
$845$		0			0
$846$			1.86297i			0.0640503i
$847$	−35.9177	−	16.2825i	−1.23415	−	0.559473i
$848$	−0.643653	−	0.643653i	−0.0221031	−	0.0221031i
$849$	12.8448	+	7.41595i	0.440832	+	0.254515i
$850$		0			0
$851$	−27.0269	−	46.8120i	−0.926471	−	1.60469i
$852$	7.59505	−	2.03509i	0.260202	−	0.0697209i
$853$	−25.8556	+	25.8556i	−0.885278	+	0.885278i	−0.994065	−	0.108787i	$-0.965303\pi$
$853$	−25.8556	+	25.8556i	−0.885278	+	0.885278i	0.108787	+	0.994065i	$0.465303\pi$
$854$	−15.3202	−	2.53243i	−0.524247	−	0.0866579i
$855$		0			0
$856$	−0.106416	+	0.184318i	−0.00363722	+	0.00629984i
$857$	−9.92803	+	37.0519i	−0.339135	+	1.26567i	0.560181	+	0.828370i	$0.310731\pi$
$857$	−9.92803	+	37.0519i	−0.339135	+	1.26567i	−0.899316	+	0.437299i	$0.855935\pi$
$858$	3.77145	−	14.0753i	0.128755	−	0.480521i
$859$	10.5922	−	18.3462i	0.361400	−	0.625963i	−0.626792	−	0.779187i	$-0.715632\pi$
$859$	10.5922	−	18.3462i	0.361400	−	0.625963i	0.988191	+	0.153224i	$0.0489656\pi$
$860$		0			0
$861$	10.7990	+	1.78507i	0.368029	+	0.0608351i
$862$	16.1845	−	16.1845i	0.551245	−	0.551245i
$863$	−23.1027	+	6.19036i	−0.786426	+	0.210722i	−0.629616	−	0.776906i	$-0.716788\pi$
$863$	−23.1027	+	6.19036i	−0.786426	+	0.210722i	−0.156810	+	0.987629i	$0.550121\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$		0			0
$866$	−21.1611	−	12.2174i	−0.719084	−	0.415163i
$867$	22.1608	+	22.1608i	0.752622	+	0.752622i
$868$	−4.48922	−	2.03509i	−0.152374	−	0.0690754i
$869$		−	61.5336i		−	2.08738i
$870$		0			0
$871$	7.30583	−	4.21802i	0.247549	−	0.142922i
$872$	−1.50724	−	0.403862i	−0.0510414	−	0.0136765i
$873$	4.93953	+	18.4346i	0.167178	+	0.623916i
$874$	24.9952			0.845474
$875$		0			0
$876$	−13.5293			−0.457114
$877$	−13.6388	−	50.9006i	−0.460549	−	1.71879i	−0.671240	−	0.741240i	$-0.734238\pi$
$877$	−13.6388	−	50.9006i	−0.460549	−	1.71879i	0.210691	−	0.977553i	$-0.432429\pi$
$878$	−4.79619	−	1.28514i	−0.161864	−	0.0433712i
$879$	−22.9038	+	13.2235i	−0.772527	+	0.446018i
$880$		0			0
$881$		−	7.86297i		−	0.264910i	−0.991189	−	0.132455i	$-0.957714\pi$
$881$		−	7.86297i		−	0.264910i	0.991189	−	0.132455i	$-0.0422860\pi$
$882$	−0.460527	+	6.98483i	−0.0155068	+	0.235192i
$883$	16.6993	+	16.6993i	0.561977	+	0.561977i	0.929869	−	0.367892i	$-0.119920\pi$
$883$	16.6993	+	16.6993i	0.561977	+	0.561977i	−0.367892	+	0.929869i	$0.619920\pi$
$884$	−17.2386	−	9.95271i	−0.579797	−	0.334746i
$885$		0			0
$886$	6.49758	+	11.2541i	0.218290	+	0.378090i
$887$	−40.6509	+	10.8924i	−1.36492	+	0.365730i	−0.865622	−	0.500698i	$-0.833077\pi$
$887$	−40.6509	+	10.8924i	−1.36492	+	0.365730i	−0.499301	+	0.866428i	$0.666410\pi$
$888$	5.49740	−	5.49740i	0.184481	−	0.184481i
$889$	4.12736	+	3.38858i	0.138427	+	0.113649i
$890$		0			0
$891$	2.54487	−	4.40784i	0.0852563	−	0.147668i
$892$	0.987571	−	3.68567i	0.0330663	−	0.123405i
$893$	−1.73342	+	6.46922i	−0.0580068	+	0.216484i
$894$	−4.96939	+	8.60723i	−0.166201	+	0.287869i
$895$		0			0
$896$	0.931486	+	2.47635i	0.0311188	+	0.0827292i
$897$	14.0753	−	14.0753i	0.469959	−	0.469959i
$898$	14.5574	−	3.90065i	0.485788	−	0.130166i
$899$	8.21169	+	14.2231i	0.273875	+	0.474366i
$900$		0			0
$901$	5.48090	+	3.16440i	0.182595	+	0.105421i
$902$	−14.8891	−	14.8891i	−0.495753	−	0.495753i
$903$	23.8528	−	17.0857i	0.793771	−	0.568576i
$904$		−	0.0424462i		−	0.00141174i
$905$		0			0
$906$	−13.2645	+	7.65825i	−0.440683	+	0.254428i
$907$	43.3851	+	11.6250i	1.44058	+	0.386002i	0.892736	−	0.450580i	$-0.148783\pi$
$907$	43.3851	+	11.6250i	1.44058	+	0.386002i	0.547842	+	0.836582i	$0.315450\pi$
$908$	5.09682	+	19.0216i	0.169144	+	0.631253i
$909$	1.36379			0.0452341
$910$		0			0
$911$	−17.6738			−0.585559			−0.292780	−	0.956180i	$-0.594580\pi$
$911$	−17.6738			−0.585559			−0.292780	+	0.956180i	$0.594580\pi$
$912$	0.930461	+	3.47253i	0.0308106	+	0.114987i
$913$	13.8428	+	3.70916i	0.458129	+	0.122755i
$914$	−22.4294	+	12.9496i	−0.741898	+	0.428335i
$915$		0			0
$916$			22.9768i			0.759173i
$917$	5.79246	−	12.7776i	0.191284	−	0.421955i
$918$	−4.91631	−	4.91631i	−0.162262	−	0.162262i
$919$	−49.9117	−	28.8165i	−1.64643	−	0.950569i	−0.978473	−	0.206373i	$-0.933834\pi$
$919$	−49.9117	−	28.8165i	−1.64643	−	0.950569i	−0.667961	−	0.744196i	$-0.732833\pi$
$920$		0			0
$921$	15.9054	+	27.5490i	0.524101	+	0.907770i
$922$	−19.2272	+	5.15190i	−0.633213	+	0.169669i
$923$	15.9180	−	15.9180i	0.523948	−	0.523948i
$924$	8.54487	−	10.4078i	0.281106	−	0.342393i
$925$		0			0
$926$	−20.5676	+	35.6241i	−0.675893	+	1.17068i
$927$	0.0941560	−	0.351395i	0.00309249	−	0.0115413i
$928$	2.28167	−	8.51530i	0.0748994	−	0.279528i
$929$	−22.7211	+	39.3541i	−0.745455	+	1.29117i	0.204527	+	0.978861i	$0.434434\pi$
$929$	−22.7211	+	39.3541i	−0.745455	+	1.29117i	−0.949982	+	0.312305i	$0.898899\pi$
$930$		0			0
$931$	−8.09831	+	23.8265i	−0.265411	+	0.780883i
$932$	−9.36143	+	9.36143i	−0.306644	+	0.306644i
$933$	−15.9048	+	4.26167i	−0.520699	+	0.139521i
$934$	14.2402	+	24.6648i	0.465954	+	0.807055i
$935$		0			0
$936$	2.47941	+	1.43149i	0.0810420	+	0.0467896i
$937$	−2.46056	−	2.46056i	−0.0803830	−	0.0803830i	0.665772	−	0.746155i	$-0.268102\pi$
$937$	−2.46056	−	2.46056i	−0.0803830	−	0.0803830i	−0.746155	+	0.665772i	$0.768102\pi$
$938$	7.75859	−	0.762637i	0.253327	−	0.0249010i
$939$			3.37609i			0.110174i
$940$		0			0
$941$	13.6954	−	7.90702i	0.446456	−	0.257762i	−0.259876	−	0.965642i	$-0.583682\pi$
$941$	13.6954	−	7.90702i	0.446456	−	0.257762i	0.706332	+	0.707880i	$0.250348\pi$
$942$	−15.7881	−	4.23040i	−0.514403	−	0.137834i
$943$	−7.44455	−	27.7835i	−0.242428	−	0.904754i
$944$	4.17947			0.136030
$945$		0			0
$946$	−56.4438			−1.83515
$947$	1.49062	+	5.56306i	0.0484386	+	0.180775i	0.985907	−	0.167296i	$-0.0535035\pi$
$947$	1.49062	+	5.56306i	0.0484386	+	0.180775i	−0.937468	+	0.348071i	$0.886837\pi$
$948$	11.6778	+	3.12905i	0.379277	+	0.101627i
$949$	−33.5447	+	19.3671i	−1.08891	+	0.628681i
$950$		0			0
$951$		−	13.8173i		−	0.448057i
$952$	−10.7119	−	14.9545i	−0.347173	−	0.484678i
$953$	33.0749	+	33.0749i	1.07140	+	1.07140i	0.997247	+	0.0741531i	$0.0236253\pi$
$953$	33.0749	+	33.0749i	1.07140	+	1.07140i	0.0741531	+	0.997247i	$0.476375\pi$
$954$	−0.788311	−	0.455132i	−0.0255225	−	0.0147354i
$955$		0			0
$956$	0.825071	+	1.42906i	0.0266847	+	0.0462192i
$957$	−43.3406	+	11.6131i	−1.40100	+	0.375398i
$958$	−6.78497	+	6.78497i	−0.219212	+	0.219212i
$959$	9.48460	−	57.3782i	0.306274	−	1.85284i
$960$		0			0
$961$	−13.7647	+	23.8411i	−0.444021	+	0.769068i
$962$	5.76084	−	21.4997i	0.185737	−	0.693180i
$963$	−0.0550849	+	0.205579i	−0.00177508	+	0.00662471i
$964$	6.32570	−	10.9564i	0.203737	−	0.352883i
$965$		0			0
$966$	17.2174	−	6.47635i	0.553960	−	0.208373i
$967$	−12.8181	+	12.8181i	−0.412203	+	0.412203i	−0.882505	−	0.470302i	$-0.844145\pi$
$967$	−12.8181	+	12.8181i	−0.412203	+	0.412203i	0.470302	+	0.882505i	$0.344145\pi$
$968$	−14.3975	+	3.85781i	−0.462754	+	0.123995i
$969$	−12.4976	−	21.6464i	−0.401480	−	0.695384i
$970$		0			0
$971$	3.40830	+	1.96778i	0.109378	+	0.0631492i	0.553691	−	0.832722i	$-0.313219\pi$
$971$	3.40830	+	1.96778i	0.109378	+	0.0631492i	−0.444313	+	0.895872i	$0.646552\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	−4.29385	−	43.6830i	−0.137655	−	1.40041i
$974$		−	12.4681i		−	0.399504i
$975$		0			0
$976$	−5.08277	+	2.93454i	−0.162696	+	0.0939323i
$977$	16.3729	+	4.38709i	0.523814	+	0.140356i	0.511030	−	0.859563i	$-0.329264\pi$
$977$	16.3729	+	4.38709i	0.523814	+	0.140356i	0.0127838	+	0.999918i	$0.495931\pi$
$978$	1.93977	+	7.23934i	0.0620271	+	0.231488i
$979$	38.9372			1.24444
$980$		0			0
$981$	−1.56040			−0.0498199
$982$	−9.40258	−	35.0909i	−0.300049	−	1.11980i
$983$	4.74921	+	1.27255i	0.151476	+	0.0405879i	0.333760	−	0.942658i	$-0.391682\pi$
$983$	4.74921	+	1.27255i	0.151476	+	0.0405879i	−0.182284	+	0.983246i	$0.558349\pi$
$984$	3.58277	−	2.06851i	0.114215	−	0.0659418i
$985$		0			0
$986$			61.2929i			1.95196i
$987$	0.482173	+	4.90532i	0.0153477	+	0.156138i
$988$	7.27787	+	7.27787i	0.231540	+	0.231540i
$989$	−66.7738	−	38.5519i	−2.12328	−	1.22588i
$990$		0			0
$991$	−1.32540	−	2.29565i	−0.0421026	−	0.0729238i	0.844206	−	0.536019i	$-0.180072\pi$
$991$	−1.32540	−	2.29565i	−0.0421026	−	0.0729238i	−0.886309	+	0.463095i	$0.846739\pi$
$992$	−1.79949	+	0.482173i	−0.0571340	+	0.0153090i
$993$	−3.41505	+	3.41505i	−0.108373	+	0.108373i
$994$	19.4715	−	7.32425i	0.617599	−	0.232311i
$995$		0			0
$996$	−1.40784	+	2.43845i	−0.0446092	+	0.0772653i
$997$	−3.65936	+	13.6569i	−0.115893	+	0.432518i	−0.999352	−	0.0359897i	$-0.988542\pi$
$997$	−3.65936	+	13.6569i	−0.115893	+	0.432518i	0.883459	+	0.468508i	$0.155208\pi$
$998$	0.724555	−	2.70408i	0.0229354	−	0.0855960i
$999$	3.88725	−	6.73291i	0.122987	−	0.213020i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.bc.e.943.2	yes	16
5.2	odd	4		1050.2.bc.f.607.3	yes	16
5.3	odd	4		1050.2.bc.f.607.2	yes	16
5.4	even	2	inner	1050.2.bc.e.943.3	yes	16
7.3	odd	6		1050.2.bc.f.493.3	yes	16
35.3	even	12	inner	1050.2.bc.e.157.4	yes	16
35.17	even	12	inner	1050.2.bc.e.157.1	✓	16
35.24	odd	6		1050.2.bc.f.493.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.bc.e.157.1	✓	16	35.17	even	12	inner
1050.2.bc.e.157.4	yes	16	35.3	even	12	inner
1050.2.bc.e.943.2	yes	16	1.1	even	1	trivial
1050.2.bc.e.943.3	yes	16	5.4	even	2	inner
1050.2.bc.f.493.2	yes	16	35.24	odd	6
1050.2.bc.f.493.3	yes	16	7.3	odd	6
1050.2.bc.f.607.2	yes	16	5.3	odd	4
1050.2.bc.f.607.3	yes	16	5.2	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(0.258819 + 2.63306i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(0.258819 + 2.63306i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-2.54487 - 4.40784i) q^{11} +(0.965926 - 0.258819i) q^{12} +(2.02443 - 2.02443i) q^{13} +(2.47635 - 0.931486i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.79949 + 6.71580i) q^{17} +(0.258819 - 0.965926i) q^{18} +(1.79751 - 3.11338i) q^{19} +(0.431486 - 2.61033i) q^{21} +(-3.59899 + 3.59899i) q^{22} +(-6.71580 + 1.79949i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-2.47941 - 1.43149i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.54067 - 2.15089i) q^{28} +8.81568i q^{29} +(1.61338 - 0.931486i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(1.31732 + 4.91631i) q^{33} +6.95271 q^{34} -1.00000 q^{36} +(2.01219 + 7.50959i) q^{37} +(-3.47253 - 0.930461i) q^{38} +(-2.47941 + 1.43149i) q^{39} +4.13703i q^{41} +(-2.63306 + 0.258819i) q^{42} +(7.84163 + 7.84163i) q^{43} +(4.40784 + 2.54487i) q^{44} +(3.47635 + 6.02122i) q^{46} +(-1.79949 + 0.482173i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(-6.86603 + 1.36297i) q^{49} +(3.47635 - 6.02122i) q^{51} +(-0.740992 + 2.76542i) q^{52} +(0.235593 - 0.879247i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.67884 + 2.04487i) q^{56} +(-2.54207 + 2.54207i) q^{57} +(8.51530 - 2.28167i) q^{58} +(2.08974 + 3.61953i) q^{59} +(-5.08277 - 2.93454i) q^{61} +(-1.31732 - 1.31732i) q^{62} +(-1.09239 + 2.40971i) q^{63} +1.00000i q^{64} +(4.40784 - 2.54487i) q^{66} +(2.84620 + 0.762637i) q^{67} +(-1.79949 - 6.71580i) q^{68} +6.95271 q^{69} +7.86297 q^{71} +(0.258819 + 0.965926i) q^{72} +(-13.0683 - 3.50165i) q^{73} +(6.73291 - 3.88725i) q^{74} +3.59502i q^{76} +(10.9475 - 7.84163i) q^{77} +(2.02443 + 2.02443i) q^{78} +(10.4700 + 6.04487i) q^{79} +(0.500000 + 0.866025i) q^{81} +(3.99606 - 1.07074i) q^{82} +(-1.99099 + 1.99099i) q^{83} +(0.931486 + 2.47635i) q^{84} +(5.54487 - 9.60399i) q^{86} +(2.28167 - 8.51530i) q^{87} +(1.31732 - 4.91631i) q^{88} +(-3.82507 + 6.62522i) q^{89} +(5.85440 + 4.80648i) q^{91} +(4.91631 - 4.91631i) q^{92} +(-1.79949 + 0.482173i) q^{93} +(0.931486 + 1.61338i) q^{94} +(0.866025 + 0.500000i) q^{96} +(13.4951 + 13.4951i) q^{97} +(3.09359 + 6.27931i) q^{98} -5.08974i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 4 q^{11} - 8 q^{14} + 8 q^{16} + 4 q^{19} - 4 q^{21} - 8 q^{24} + 16 q^{34} - 16 q^{36} + 12 q^{44} + 8 q^{46} - 96 q^{49} + 8 q^{51} - 8 q^{54} - 4 q^{56} - 40 q^{59} - 24 q^{61} + 12 q^{66} + 16 q^{69} + 104 q^{71} + 48 q^{74} + 12 q^{79} + 8 q^{81} + 4 q^{84} + 52 q^{86} - 60 q^{89} - 52 q^{91} + 4 q^{94}+O(q^{100}) \) 16 * q - 4 * q^11 - 8 * q^14 + 8 * q^16 + 4 * q^19 - 4 * q^21 - 8 * q^24 + 16 * q^34 - 16 * q^36 + 12 * q^44 + 8 * q^46 - 96 * q^49 + 8 * q^51 - 8 * q^54 - 4 * q^56 - 40 * q^59 - 24 * q^61 + 12 * q^66 + 16 * q^69 + 104 * q^71 + 48 * q^74 + 12 * q^79 + 8 * q^81 + 4 * q^84 + 52 * q^86 - 60 * q^89 - 52 * q^91 + 4 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more