LMFDB - Embedded newform 1050.2.bc.a.157.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1050.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.1
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1050.157
Dual form			1050.2.bc.a.943.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(-0.189469 - 2.63896i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(-0.189469 - 2.63896i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-0.500000 + 0.866025i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(1.60368 + 1.60368i) q^{13} +(2.59808 + 0.500000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.138701 - 0.517638i) q^{17} +(0.258819 + 0.965926i) q^{18} +(-2.86603 - 4.96410i) q^{19} +(-0.866025 - 2.50000i) q^{21} +(-0.707107 - 0.707107i) q^{22} +(7.65806 + 2.05197i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-1.96410 + 1.13397i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.15539 + 2.38014i) q^{28} -6.92820i q^{29} +(-0.464102 - 0.267949i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-0.258819 + 0.965926i) q^{33} +0.535898 q^{34} -1.00000 q^{36} +(2.56961 - 9.58991i) q^{37} +(5.53674 - 1.48356i) q^{38} +(1.96410 + 1.13397i) q^{39} -5.73205i q^{41} +(2.63896 - 0.189469i) q^{42} +(3.48477 - 3.48477i) q^{43} +(0.866025 - 0.500000i) q^{44} +(-3.96410 + 6.86603i) q^{46} +(8.88280 + 2.38014i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-6.92820 + 1.00000i) q^{49} +(-0.267949 - 0.464102i) q^{51} +(-0.586988 - 2.19067i) q^{52} +(-0.258819 - 0.965926i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.00000 - 1.73205i) q^{56} +(-4.05317 - 4.05317i) q^{57} +(6.69213 + 1.79315i) q^{58} +(-2.26795 + 3.92820i) q^{59} +(3.92820 - 2.26795i) q^{61} +(0.378937 - 0.378937i) q^{62} +(-1.48356 - 2.19067i) q^{63} -1.00000i q^{64} +(-0.866025 - 0.500000i) q^{66} +(-1.93185 + 0.517638i) q^{67} +(-0.138701 + 0.517638i) q^{68} +7.92820 q^{69} +4.92820 q^{71} +(0.258819 - 0.965926i) q^{72} +(3.86370 - 1.03528i) q^{73} +(8.59808 + 4.96410i) q^{74} +5.73205i q^{76} +(2.38014 + 1.15539i) q^{77} +(-1.60368 + 1.60368i) q^{78} +(-14.6603 + 8.46410i) q^{79} +(0.500000 - 0.866025i) q^{81} +(5.53674 + 1.48356i) q^{82} +(7.34847 + 7.34847i) q^{83} +(-0.500000 + 2.59808i) q^{84} +(2.46410 + 4.26795i) q^{86} +(-1.79315 - 6.69213i) q^{87} +(0.258819 + 0.965926i) q^{88} +(3.46410 + 6.00000i) q^{89} +(3.92820 - 4.53590i) q^{91} +(-5.60609 - 5.60609i) q^{92} +(-0.517638 - 0.138701i) q^{93} +(-4.59808 + 7.96410i) q^{94} +(-0.866025 + 0.500000i) q^{96} +(-7.72741 + 7.72741i) q^{97} +(0.827225 - 6.95095i) q^{98} +1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 4 q^{11} + 4 q^{16} - 16 q^{19} + 4 q^{24} + 12 q^{26} + 24 q^{31} + 32 q^{34} - 8 q^{36} - 12 q^{39} - 4 q^{46} - 16 q^{51} + 4 q^{54} - 16 q^{56} - 32 q^{59} - 24 q^{61} + 8 q^{69} - 16 q^{71} + 48 q^{74} - 48 q^{79} + 4 q^{81} - 4 q^{84} - 8 q^{86} - 24 q^{91} - 16 q^{94}+O(q^{100}) $ 8 * q - 4 * q^11 + 4 * q^16 - 16 * q^19 + 4 * q^24 + 12 * q^26 + 24 * q^31 + 32 * q^34 - 8 * q^36 - 12 * q^39 - 4 * q^46 - 16 * q^51 + 4 * q^54 - 16 * q^56 - 32 * q^59 - 24 * q^61 + 8 * q^69 - 16 * q^71 + 48 * q^74 - 48 * q^79 + 4 * q^81 - 4 * q^84 - 8 * q^86 - 24 * q^91 - 16 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

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
$7$	−0.189469	−	2.63896i	−0.0716124	−	0.997433i
$7$	−0.189469	−	2.63896i	−0.0716124	−	0.997433i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	−0.931505	−	0.363727i	$-0.881504\pi$
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	0.780750	+	0.624844i	$0.214837\pi$
$12$	−0.965926	−	0.258819i	−0.278839	−	0.0747146i
$13$	1.60368	+	1.60368i	0.444781	+	0.444781i	0.893615	−	0.448834i	$-0.148160\pi$
$13$	1.60368	+	1.60368i	0.444781	+	0.444781i	−0.448834	+	0.893615i	$0.648160\pi$
$14$	2.59808	+	0.500000i	0.694365	+	0.133631i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.138701	−	0.517638i	−0.0336399	−	0.125546i	0.947064	−	0.321045i	$-0.104034\pi$
$17$	−0.138701	−	0.517638i	−0.0336399	−	0.125546i	−0.980704	+	0.195499i	$0.937367\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	−2.86603	−	4.96410i	−0.657511	−	1.13884i	−0.981258	−	0.192699i	$-0.938276\pi$
$19$	−2.86603	−	4.96410i	−0.657511	−	1.13884i	0.323747	−	0.946144i	$-0.395057\pi$
$20$		0			0
$21$	−0.866025	−	2.50000i	−0.188982	−	0.545545i
$22$	−0.707107	−	0.707107i	−0.150756	−	0.150756i
$23$	7.65806	+	2.05197i	1.59682	+	0.427865i	0.944079	−	0.329720i	$-0.106954\pi$
$23$	7.65806	+	2.05197i	1.59682	+	0.427865i	0.652736	+	0.757585i	$0.273621\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$		0			0
$26$	−1.96410	+	1.13397i	−0.385192	+	0.222391i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−1.15539	+	2.38014i	−0.218349	+	0.449804i
$29$		−	6.92820i		−	1.28654i	−0.765641	−	0.643268i	$-0.777578\pi$
$29$		−	6.92820i		−	1.28654i	0.765641	−	0.643268i	$-0.222422\pi$
$30$		0			0
$31$	−0.464102	−	0.267949i	−0.0833551	−	0.0481251i	0.457743	−	0.889085i	$-0.348658\pi$
$31$	−0.464102	−	0.267949i	−0.0833551	−	0.0481251i	−0.541098	+	0.840959i	$0.681991\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−0.258819	+	0.965926i	−0.0450546	+	0.168146i
$34$	0.535898			0.0919058
$35$		0			0
$36$	−1.00000			−0.166667
$37$	2.56961	−	9.58991i	0.422441	−	1.57657i	−0.347008	−	0.937862i	$-0.612802\pi$
$37$	2.56961	−	9.58991i	0.422441	−	1.57657i	0.769449	−	0.638709i	$-0.220531\pi$
$38$	5.53674	−	1.48356i	0.898177	−	0.240666i
$39$	1.96410	+	1.13397i	0.314508	+	0.181581i
$40$		0			0
$41$		−	5.73205i		−	0.895196i	−0.894235	−	0.447598i	$-0.852280\pi$
$41$		−	5.73205i		−	0.895196i	0.894235	−	0.447598i	$-0.147720\pi$
$42$	2.63896	−	0.189469i	0.407200	−	0.0292357i
$43$	3.48477	−	3.48477i	0.531422	−	0.531422i	−0.389574	−	0.920995i	$-0.627378\pi$
$43$	3.48477	−	3.48477i	0.531422	−	0.531422i	0.920995	+	0.389574i	$0.127378\pi$
$44$	0.866025	−	0.500000i	0.130558	−	0.0753778i
$45$		0			0
$46$	−3.96410	+	6.86603i	−0.584475	+	1.01234i
$47$	8.88280	+	2.38014i	1.29569	+	0.347179i	0.839819	−	0.542867i	$-0.182661\pi$
$47$	8.88280	+	2.38014i	1.29569	+	0.347179i	0.455871	+	0.890046i	$0.349328\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$	−6.92820	+	1.00000i	−0.989743	+	0.142857i
$50$		0			0
$51$	−0.267949	−	0.464102i	−0.0375204	−	0.0649872i
$52$	−0.586988	−	2.19067i	−0.0814007	−	0.303791i
$53$	−0.258819	−	0.965926i	−0.0355515	−	0.132680i	0.945869	−	0.324548i	$-0.105212\pi$
$53$	−0.258819	−	0.965926i	−0.0355515	−	0.132680i	−0.981421	+	0.191868i	$0.938546\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	−2.00000	−	1.73205i	−0.267261	−	0.231455i
$57$	−4.05317	−	4.05317i	−0.536856	−	0.536856i
$58$	6.69213	+	1.79315i	0.878720	+	0.235452i
$59$	−2.26795	+	3.92820i	−0.295262	+	0.511409i	−0.975046	−	0.222004i	$-0.928740\pi$
$59$	−2.26795	+	3.92820i	−0.295262	+	0.511409i	0.679784	+	0.733412i	$0.262074\pi$
$60$		0			0
$61$	3.92820	−	2.26795i	0.502955	−	0.290381i	−0.226978	−	0.973900i	$-0.572885\pi$
$61$	3.92820	−	2.26795i	0.502955	−	0.290381i	0.729933	+	0.683519i	$0.239551\pi$
$62$	0.378937	−	0.378937i	0.0481251	−	0.0481251i
$63$	−1.48356	−	2.19067i	−0.186911	−	0.275999i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−0.866025	−	0.500000i	−0.106600	−	0.0615457i
$67$	−1.93185	+	0.517638i	−0.236013	+	0.0632396i	−0.374887	−	0.927071i	$-0.622318\pi$
$67$	−1.93185	+	0.517638i	−0.236013	+	0.0632396i	0.138874	+	0.990310i	$0.455652\pi$
$68$	−0.138701	+	0.517638i	−0.0168199	+	0.0627728i
$69$	7.92820			0.954444
$70$		0			0
$71$	4.92820			0.584870			0.292435	−	0.956285i	$-0.405534\pi$
$71$	4.92820			0.584870			0.292435	+	0.956285i	$0.405534\pi$
$72$	0.258819	−	0.965926i	0.0305021	−	0.113835i
$73$	3.86370	−	1.03528i	0.452212	−	0.121170i	−0.0255221	−	0.999674i	$-0.508125\pi$
$73$	3.86370	−	1.03528i	0.452212	−	0.121170i	0.477734	+	0.878504i	$0.341458\pi$
$74$	8.59808	+	4.96410i	0.999506	+	0.577065i
$75$		0			0
$76$			5.73205i			0.657511i
$77$	2.38014	+	1.15539i	0.271242	+	0.131669i
$78$	−1.60368	+	1.60368i	−0.181581	+	0.181581i
$79$	−14.6603	+	8.46410i	−1.64941	+	0.952286i	−0.672100	+	0.740460i	$0.734607\pi$
$79$	−14.6603	+	8.46410i	−1.64941	+	0.952286i	−0.977308	+	0.211825i	$0.932059\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	5.53674	+	1.48356i	0.611430	+	0.163832i
$83$	7.34847	+	7.34847i	0.806599	+	0.806599i	0.984118	−	0.177518i	$-0.0568069\pi$
$83$	7.34847	+	7.34847i	0.806599	+	0.806599i	−0.177518	+	0.984118i	$0.556807\pi$
$84$	−0.500000	+	2.59808i	−0.0545545	+	0.283473i
$85$		0			0
$86$	2.46410	+	4.26795i	0.265711	+	0.460225i
$87$	−1.79315	−	6.69213i	−0.192246	−	0.717472i
$88$	0.258819	+	0.965926i	0.0275902	+	0.102968i
$89$	3.46410	+	6.00000i	0.367194	+	0.635999i	0.989126	−	0.147073i	$-0.0469852\pi$
$89$	3.46410	+	6.00000i	0.367194	+	0.635999i	−0.621932	+	0.783072i	$0.713652\pi$
$90$		0			0
$91$	3.92820	−	4.53590i	0.411788	−	0.475491i
$92$	−5.60609	−	5.60609i	−0.584475	−	0.584475i
$93$	−0.517638	−	0.138701i	−0.0536766	−	0.0143826i
$94$	−4.59808	+	7.96410i	−0.474255	+	0.821434i
$95$		0			0
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−7.72741	+	7.72741i	−0.784599	+	0.784599i	−0.980603	−	0.196004i	$-0.937203\pi$
$97$	−7.72741	+	7.72741i	−0.784599	+	0.784599i	0.196004	+	0.980603i	$0.437203\pi$
$98$	0.827225	−	6.95095i	0.0835624	−	0.702152i
$99$			1.00000i			0.100504i
$100$		0			0
$101$	−12.9282	−	7.46410i	−1.28640	−	0.742706i	−0.308393	−	0.951259i	$-0.599791\pi$
$101$	−12.9282	−	7.46410i	−1.28640	−	0.742706i	−0.978011	+	0.208553i	$0.933125\pi$
$102$	0.517638	−	0.138701i	0.0512538	−	0.0137334i
$103$	0.619174	−	2.31079i	0.0610090	−	0.227689i	−0.928689	−	0.370860i	$-0.879063\pi$
$103$	0.619174	−	2.31079i	0.0610090	−	0.227689i	0.989698	+	0.143171i	$0.0457298\pi$
$104$	2.26795			0.222391
$105$		0			0
$106$	1.00000			0.0971286
$107$	−0.277401	+	1.03528i	−0.0268174	+	0.100084i	−0.978037	−	0.208430i	$-0.933165\pi$
$107$	−0.277401	+	1.03528i	−0.0268174	+	0.100084i	0.951220	+	0.308513i	$0.0998315\pi$
$108$	−0.965926	+	0.258819i	−0.0929463	+	0.0249049i
$109$	−2.66025	−	1.53590i	−0.254806	−	0.147112i	0.367157	−	0.930159i	$-0.380331\pi$
$109$	−2.66025	−	1.53590i	−0.254806	−	0.147112i	−0.621963	+	0.783047i	$0.713665\pi$
$110$		0			0
$111$		−	9.92820i		−	0.942343i
$112$	2.19067	−	1.48356i	0.206999	−	0.140184i
$113$	0.656339	−	0.656339i	0.0617432	−	0.0617432i	−0.675561	−	0.737304i	$-0.736098\pi$
$113$	0.656339	−	0.656339i	0.0617432	−	0.0617432i	0.737304	+	0.675561i	$0.236098\pi$
$114$	4.96410	−	2.86603i	0.464931	−	0.268428i
$115$		0			0
$116$	−3.46410	+	6.00000i	−0.321634	+	0.557086i
$117$	2.19067	+	0.586988i	0.202528	+	0.0542671i
$118$	−3.20736	−	3.20736i	−0.295262	−	0.295262i
$119$	−1.33975	+	0.464102i	−0.122814	+	0.0425441i
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$	1.17398	+	4.38134i	0.106287	+	0.396668i
$123$	−1.48356	−	5.53674i	−0.133768	−	0.499231i
$124$	0.267949	+	0.464102i	0.0240625	+	0.0416776i
$125$		0			0
$126$	2.50000	−	0.866025i	0.222718	−	0.0771517i
$127$	−3.53553	−	3.53553i	−0.313728	−	0.313728i	0.532624	−	0.846352i	$-0.321206\pi$
$127$	−3.53553	−	3.53553i	−0.313728	−	0.313728i	−0.846352	+	0.532624i	$0.821206\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	2.46410	−	4.26795i	0.216952	−	0.375772i
$130$		0			0
$131$	17.4282	−	10.0622i	1.52271	−	0.879137i	0.523070	−	0.852290i	$-0.324787\pi$
$131$	17.4282	−	10.0622i	1.52271	−	0.879137i	0.999640	−	0.0268466i	$-0.00854657\pi$
$132$	0.707107	−	0.707107i	0.0615457	−	0.0615457i
$133$	−12.5570	+	8.50386i	−1.08883	+	0.737379i
$134$		−	2.00000i		−	0.172774i
$135$		0			0
$136$	−0.464102	−	0.267949i	−0.0397964	−	0.0229765i
$137$	4.89898	−	1.31268i	0.418548	−	0.112150i	−0.0433975	−	0.999058i	$-0.513818\pi$
$137$	4.89898	−	1.31268i	0.418548	−	0.112150i	0.461946	+	0.886908i	$0.347152\pi$
$138$	−2.05197	+	7.65806i	−0.174675	+	0.651897i
$139$	−10.3923			−0.881464			−0.440732	−	0.897639i	$-0.645281\pi$
$139$	−10.3923			−0.881464			−0.440732	+	0.897639i	$0.645281\pi$
$140$		0			0
$141$	9.19615			0.774456
$142$	−1.27551	+	4.76028i	−0.107039	+	0.399474i
$143$	−2.19067	+	0.586988i	−0.183193	+	0.0490864i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$		0			0
$146$			4.00000i			0.331042i
$147$	−6.43331	+	2.75908i	−0.530611	+	0.227565i
$148$	−7.02030	+	7.02030i	−0.577065	+	0.577065i
$149$	11.1962	−	6.46410i	0.917225	−	0.529560i	0.0344760	−	0.999406i	$-0.489024\pi$
$149$	11.1962	−	6.46410i	0.917225	−	0.529560i	0.882749	+	0.469846i	$0.155690\pi$
$150$		0			0
$151$	−11.9282	+	20.6603i	−0.970703	+	1.68131i	−0.277262	+	0.960794i	$0.589427\pi$
$151$	−11.9282	+	20.6603i	−0.970703	+	1.68131i	−0.693441	+	0.720513i	$0.743906\pi$
$152$	−5.53674	−	1.48356i	−0.449089	−	0.120333i
$153$	−0.378937	−	0.378937i	−0.0306353	−	0.0306353i
$154$	−1.73205	+	2.00000i	−0.139573	+	0.161165i
$155$		0			0
$156$	−1.13397	−	1.96410i	−0.0907906	−	0.157254i
$157$	3.27671	+	12.2289i	0.261510	+	0.975970i	0.964352	+	0.264623i	$0.0852476\pi$
$157$	3.27671	+	12.2289i	0.261510	+	0.975970i	−0.702842	+	0.711346i	$0.748086\pi$
$158$	−4.38134	−	16.3514i	−0.348561	−	1.30085i
$159$	−0.500000	−	0.866025i	−0.0396526	−	0.0686803i
$160$		0			0
$161$	3.96410	−	20.5981i	0.312415	−	1.62336i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	11.5911	+	3.10583i	0.907886	+	0.243267i	0.682400	−	0.730979i	$-0.260936\pi$
$163$	11.5911	+	3.10583i	0.907886	+	0.243267i	0.225486	+	0.974246i	$0.427603\pi$
$164$	−2.86603	+	4.96410i	−0.223799	+	0.387631i
$165$		0			0
$166$	−9.00000	+	5.19615i	−0.698535	+	0.403300i
$167$	−12.1595	+	12.1595i	−0.940932	+	0.940932i	−0.998350	−	0.0574186i	$-0.981713\pi$
$167$	−12.1595	+	12.1595i	−0.940932	+	0.940932i	0.0574186	+	0.998350i	$0.481713\pi$
$168$	−2.38014	−	1.15539i	−0.183632	−	0.0891406i
$169$		−	7.85641i		−	0.604339i
$170$		0			0
$171$	−4.96410	−	2.86603i	−0.379614	−	0.219170i
$172$	−4.76028	+	1.27551i	−0.362968	+	0.0972569i
$173$	−6.10514	+	22.7847i	−0.464165	+	1.73229i	0.195476	+	0.980708i	$0.437375\pi$
$173$	−6.10514	+	22.7847i	−0.464165	+	1.73229i	−0.659642	+	0.751580i	$0.729292\pi$
$174$	6.92820			0.525226
$175$		0			0
$176$	−1.00000			−0.0753778
$177$	−1.17398	+	4.38134i	−0.0882415	+	0.329322i
$178$	−6.69213	+	1.79315i	−0.501596	+	0.134402i
$179$	7.79423	+	4.50000i	0.582568	+	0.336346i	0.762153	−	0.647397i	$-0.224142\pi$
$179$	7.79423	+	4.50000i	0.582568	+	0.336346i	−0.179585	+	0.983742i	$0.557476\pi$
$180$		0			0
$181$			6.39230i			0.475136i	0.971371	+	0.237568i	$0.0763503\pi$
$181$			6.39230i			0.475136i	−0.971371	+	0.237568i	$0.923650\pi$
$182$	3.36465	+	4.96833i	0.249404	+	0.368277i
$183$	3.20736	−	3.20736i	0.237095	−	0.237095i
$184$	6.86603	−	3.96410i	0.506170	−	0.292237i
$185$		0			0
$186$	0.267949	−	0.464102i	0.0196470	−	0.0340296i
$187$	0.517638	+	0.138701i	0.0378534	+	0.0101428i
$188$	−6.50266	−	6.50266i	−0.474255	−	0.474255i
$189$	−2.00000	−	1.73205i	−0.145479	−	0.125988i
$190$		0			0
$191$	5.46410	+	9.46410i	0.395369	+	0.684798i	0.993148	−	0.116862i	$-0.0372836\pi$
$191$	5.46410	+	9.46410i	0.395369	+	0.684798i	−0.597780	+	0.801660i	$0.703950\pi$
$192$	−0.258819	−	0.965926i	−0.0186787	−	0.0697097i
$193$	−4.86181	−	18.1445i	−0.349961	−	1.30607i	−0.886708	−	0.462329i	$-0.847014\pi$
$193$	−4.86181	−	18.1445i	−0.349961	−	1.30607i	0.536747	−	0.843743i	$-0.319653\pi$
$194$	−5.46410	−	9.46410i	−0.392300	−	0.679483i
$195$		0			0
$196$	6.50000	+	2.59808i	0.464286	+	0.185577i
$197$	7.67664	+	7.67664i	0.546938	+	0.546938i	0.925554	−	0.378616i	$-0.123600\pi$
$197$	7.67664	+	7.67664i	0.546938	+	0.546938i	−0.378616	+	0.925554i	$0.623600\pi$
$198$	−0.965926	−	0.258819i	−0.0686454	−	0.0183935i
$199$	−9.73205	+	16.8564i	−0.689887	+	1.19492i	0.281987	+	0.959418i	$0.409006\pi$
$199$	−9.73205	+	16.8564i	−0.689887	+	1.19492i	−0.971874	+	0.235501i	$0.924327\pi$
$200$		0			0
$201$	−1.73205	+	1.00000i	−0.122169	+	0.0705346i
$202$	10.5558	−	10.5558i	0.742706	−	0.742706i
$203$	−18.2832	+	1.31268i	−1.28323	+	0.0921319i
$204$			0.535898i			0.0375204i
$205$		0			0
$206$	2.07180	+	1.19615i	0.144349	+	0.0833399i
$207$	7.65806	−	2.05197i	0.532272	−	0.142622i
$208$	−0.586988	+	2.19067i	−0.0407003	+	0.151896i
$209$	5.73205			0.396494
$210$		0			0
$211$	21.7846			1.49971			0.749857	−	0.661600i	$-0.230122\pi$
$211$	21.7846			1.49971			0.749857	+	0.661600i	$0.230122\pi$
$212$	−0.258819	+	0.965926i	−0.0177758	+	0.0663401i
$213$	4.76028	−	1.27551i	0.326169	−	0.0873967i
$214$	−0.928203	−	0.535898i	−0.0634507	−	0.0366333i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−0.619174	+	1.27551i	−0.0420323	+	0.0865875i
$218$	2.17209	−	2.17209i	0.147112	−	0.147112i
$219$	3.46410	−	2.00000i	0.234082	−	0.135147i
$220$		0			0
$221$	0.607695	−	1.05256i	0.0408780	−	0.0708028i
$222$	9.58991	+	2.56961i	0.643632	+	0.172461i
$223$	−17.9043	−	17.9043i	−1.19896	−	1.19896i	−0.974478	−	0.224483i	$-0.927931\pi$
$223$	−17.9043	−	17.9043i	−1.19896	−	1.19896i	−0.224483	−	0.974478i	$-0.572069\pi$
$224$	0.866025	+	2.50000i	0.0578638	+	0.167038i
$225$		0			0
$226$	0.464102	+	0.803848i	0.0308716	+	0.0534711i
$227$	−0.896575	−	3.34607i	−0.0595078	−	0.222086i	0.929768	−	0.368146i	$-0.120007\pi$
$227$	−0.896575	−	3.34607i	−0.0595078	−	0.222086i	−0.989276	+	0.146060i	$0.953341\pi$
$228$	1.48356	+	5.53674i	0.0982514	+	0.366679i
$229$	−5.46410	−	9.46410i	−0.361078	−	0.625405i	0.627061	−	0.778971i	$-0.284258\pi$
$229$	−5.46410	−	9.46410i	−0.361078	−	0.625405i	−0.988139	+	0.153565i	$0.950925\pi$
$230$		0			0
$231$	2.59808	+	0.500000i	0.170941	+	0.0328976i
$232$	−4.89898	−	4.89898i	−0.321634	−	0.321634i
$233$	−24.9754	−	6.69213i	−1.63619	−	0.438416i	−0.680490	−	0.732757i	$-0.738233\pi$
$233$	−24.9754	−	6.69213i	−1.63619	−	0.438416i	−0.955700	+	0.294341i	$0.904900\pi$
$234$	−1.13397	+	1.96410i	−0.0741302	+	0.128397i
$235$		0			0
$236$	3.92820	−	2.26795i	0.255704	−	0.147631i
$237$	−11.9700	+	11.9700i	−0.777538	+	0.777538i
$238$	−0.101536	−	1.41421i	−0.00658160	−	0.0916698i
$239$		−	24.0000i		−	1.55243i	−0.630468	−	0.776215i	$-0.717137\pi$
$239$		−	24.0000i		−	1.55243i	0.630468	−	0.776215i	$-0.282863\pi$
$240$		0			0
$241$	−22.2846	−	12.8660i	−1.43548	−	0.828774i	−0.437947	−	0.899001i	$-0.644294\pi$
$241$	−22.2846	−	12.8660i	−1.43548	−	0.828774i	−0.997531	+	0.0702273i	$0.977628\pi$
$242$	−9.65926	+	2.58819i	−0.620921	+	0.166375i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	−4.53590			−0.290381
$245$		0			0
$246$	5.73205			0.365462
$247$	3.36465	−	12.5570i	0.214087	−	0.798985i
$248$	−0.517638	+	0.138701i	−0.0328701	+	0.00880750i
$249$	9.00000	+	5.19615i	0.570352	+	0.329293i
$250$		0			0
$251$			24.6603i			1.55654i	0.627929	+	0.778271i	$0.283903\pi$
$251$			24.6603i			1.55654i	−0.627929	+	0.778271i	$0.716097\pi$
$252$	0.189469	+	2.63896i	0.0119354	+	0.166239i
$253$	−5.60609	+	5.60609i	−0.352452	+	0.352452i
$254$	4.33013	−	2.50000i	0.271696	−	0.156864i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	17.7656	+	4.76028i	1.10819	+	0.296938i	0.766094	−	0.642728i	$-0.222197\pi$
$257$	17.7656	+	4.76028i	1.10819	+	0.296938i	0.342093	+	0.939666i	$0.388864\pi$
$258$	3.48477	+	3.48477i	0.216952	+	0.216952i
$259$	−25.7942	−	4.96410i	−1.60278	−	0.308454i
$260$		0			0
$261$	−3.46410	−	6.00000i	−0.214423	−	0.371391i
$262$	5.20857	+	19.4386i	0.321786	+	1.20092i
$263$	0.554803	+	2.07055i	0.0342106	+	0.127676i	0.980919	−	0.194415i	$-0.0622809\pi$
$263$	0.554803	+	2.07055i	0.0342106	+	0.127676i	−0.946709	+	0.322091i	$0.895614\pi$
$264$	0.500000	+	0.866025i	0.0307729	+	0.0533002i
$265$		0			0
$266$	−4.96410	−	14.3301i	−0.304369	−	0.878636i
$267$	4.89898	+	4.89898i	0.299813	+	0.299813i
$268$	1.93185	+	0.517638i	0.118007	+	0.0316198i
$269$	−4.66025	+	8.07180i	−0.284141	+	0.492146i	−0.972400	−	0.233318i	$-0.925042\pi$
$269$	−4.66025	+	8.07180i	−0.284141	+	0.492146i	0.688260	+	0.725464i	$0.258375\pi$
$270$		0			0
$271$	−6.92820	+	4.00000i	−0.420858	+	0.242983i	−0.695444	−	0.718580i	$-0.744792\pi$
$271$	−6.92820	+	4.00000i	−0.420858	+	0.242983i	0.274586	+	0.961563i	$0.411459\pi$
$272$	0.378937	−	0.378937i	0.0229765	−	0.0229765i
$273$	2.62038	−	5.39804i	0.158592	−	0.326704i
$274$			5.07180i			0.306398i
$275$		0			0
$276$	−6.86603	−	3.96410i	−0.413286	−	0.238611i
$277$	−21.2504	+	5.69402i	−1.27681	+	0.342120i	−0.832636	−	0.553820i	$-0.813170\pi$
$277$	−21.2504	+	5.69402i	−1.27681	+	0.342120i	−0.444174	+	0.895940i	$0.646503\pi$
$278$	2.68973	−	10.0382i	0.161319	−	0.602051i
$279$	−0.535898			−0.0320834
$280$		0			0
$281$	−14.0718			−0.839453			−0.419727	−	0.907651i	$-0.637874\pi$
$281$	−14.0718			−0.839453			−0.419727	+	0.907651i	$0.637874\pi$
$282$	−2.38014	+	8.88280i	−0.141735	+	0.528963i
$283$	−18.8009	+	5.03768i	−1.11760	+	0.299459i	−0.769910	−	0.638152i	$-0.779699\pi$
$283$	−18.8009	+	5.03768i	−1.11760	+	0.299459i	−0.347686	+	0.937611i	$0.613032\pi$
$284$	−4.26795	−	2.46410i	−0.253256	−	0.146218i
$285$		0			0
$286$		−	2.26795i		−	0.134107i
$287$	−15.1266	+	1.08604i	−0.892898	+	0.0641072i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$	14.4737	−	8.35641i	0.851395	−	0.491553i
$290$		0			0
$291$	−5.46410	+	9.46410i	−0.320311	+	0.554795i
$292$	−3.86370	−	1.03528i	−0.226106	−	0.0605850i
$293$	1.22474	+	1.22474i	0.0715504	+	0.0715504i	0.741976	−	0.670426i	$-0.233889\pi$
$293$	1.22474	+	1.22474i	0.0715504	+	0.0715504i	−0.670426	+	0.741976i	$0.733889\pi$
$294$	−1.00000	−	6.92820i	−0.0583212	−	0.404061i
$295$		0			0
$296$	−4.96410	−	8.59808i	−0.288533	−	0.499753i
$297$	0.258819	+	0.965926i	0.0150182	+	0.0560487i
$298$	3.34607	+	12.4877i	0.193832	+	0.723392i
$299$	8.99038	+	15.5718i	0.519927	+	0.900540i
$300$		0			0
$301$	−9.85641	−	8.53590i	−0.568114	−	0.492001i
$302$	−16.8690	−	16.8690i	−0.970703	−	0.970703i
$303$	−14.4195	−	3.86370i	−0.828381	−	0.221964i
$304$	2.86603	−	4.96410i	0.164378	−	0.284711i
$305$		0			0
$306$	0.464102	−	0.267949i	0.0265309	−	0.0153176i
$307$	−1.13681	+	1.13681i	−0.0648813	+	0.0648813i	−0.738803	−	0.673922i	$-0.764609\pi$
$307$	−1.13681	+	1.13681i	−0.0648813	+	0.0648813i	0.673922	+	0.738803i	$0.264609\pi$
$308$	−1.48356	−	2.19067i	−0.0845339	−	0.124825i
$309$		−	2.39230i		−	0.136093i
$310$		0			0
$311$	−23.7846	−	13.7321i	−1.34870	−	0.778673i	−0.360636	−	0.932707i	$-0.617440\pi$
$311$	−23.7846	−	13.7321i	−1.34870	−	0.778673i	−0.988066	+	0.154034i	$0.950774\pi$
$312$	2.19067	−	0.586988i	0.124022	−	0.0332317i
$313$	8.06918	−	30.1146i	0.456097	−	1.70218i	−0.228746	−	0.973486i	$-0.573462\pi$
$313$	8.06918	−	30.1146i	0.456097	−	1.70218i	0.684843	−	0.728691i	$-0.259871\pi$
$314$	−12.6603			−0.714459
$315$		0			0
$316$	16.9282			0.952286
$317$	3.62347	−	13.5230i	0.203514	−	0.759525i	−0.786383	−	0.617739i	$-0.788049\pi$
$317$	3.62347	−	13.5230i	0.203514	−	0.759525i	0.989897	−	0.141786i	$-0.0452845\pi$
$318$	0.965926	−	0.258819i	0.0541664	−	0.0145139i
$319$	6.00000	+	3.46410i	0.335936	+	0.193952i
$320$		0			0
$321$			1.07180i			0.0598219i
$322$	18.8702	+	9.16020i	1.05160	+	0.510478i
$323$	−2.17209	+	2.17209i	−0.120858	+	0.120858i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$		0			0
$326$	−6.00000	+	10.3923i	−0.332309	+	0.575577i
$327$	−2.96713	−	0.795040i	−0.164083	−	0.0439658i
$328$	−4.05317	−	4.05317i	−0.223799	−	0.223799i
$329$	4.59808	−	23.8923i	0.253500	−	1.31723i
$330$		0			0
$331$	7.89230	+	13.6699i	0.433800	+	0.751364i	0.997197	−	0.0748224i	$-0.0238390\pi$
$331$	7.89230	+	13.6699i	0.433800	+	0.751364i	−0.563397	+	0.826187i	$0.690506\pi$
$332$	−2.68973	−	10.0382i	−0.147618	−	0.550918i
$333$	−2.56961	−	9.58991i	−0.140814	−	0.525524i
$334$	−8.59808	−	14.8923i	−0.470466	−	0.814871i
$335$		0			0
$336$	1.73205	−	2.00000i	0.0944911	−	0.109109i
$337$	17.6269	+	17.6269i	0.960199	+	0.960199i	0.999238	−	0.0390392i	$-0.0124297\pi$
$337$	17.6269	+	17.6269i	0.960199	+	0.960199i	−0.0390392	+	0.999238i	$0.512430\pi$
$338$	7.58871	+	2.03339i	0.412771	+	0.110602i
$339$	0.464102	−	0.803848i	0.0252065	−	0.0436590i
$340$		0			0
$341$	0.464102	−	0.267949i	0.0251325	−	0.0145103i
$342$	4.05317	−	4.05317i	0.219170	−	0.219170i
$343$	3.95164	+	18.0938i	0.213368	+	0.976972i
$344$		−	4.92820i		−	0.265711i
$345$		0			0
$346$	−20.4282	−	11.7942i	−1.09823	−	0.634062i
$347$	10.5558	−	2.82843i	0.566667	−	0.151838i	0.0358994	−	0.999355i	$-0.488570\pi$
$347$	10.5558	−	2.82843i	0.566667	−	0.151838i	0.530767	+	0.847517i	$0.321904\pi$
$348$	−1.79315	+	6.69213i	−0.0961230	+	0.358736i
$349$	25.8564			1.38406			0.692031	−	0.721868i	$-0.256716\pi$
$349$	25.8564			1.38406			0.692031	+	0.721868i	$0.256716\pi$
$350$		0			0
$351$	2.26795			0.121054
$352$	0.258819	−	0.965926i	0.0137951	−	0.0514840i
$353$	−6.69213	+	1.79315i	−0.356186	+	0.0954398i	−0.432475	−	0.901646i	$-0.642360\pi$
$353$	−6.69213	+	1.79315i	−0.356186	+	0.0954398i	0.0762887	+	0.997086i	$0.475693\pi$
$354$	−3.92820	−	2.26795i	−0.208782	−	0.120540i
$355$		0			0
$356$		−	6.92820i		−	0.367194i
$357$	−1.17398	+	0.795040i	−0.0621334	+	0.0420780i
$358$	−6.36396	+	6.36396i	−0.336346	+	0.336346i
$359$	−16.3923	+	9.46410i	−0.865153	+	0.499496i	−0.865734	−	0.500504i	$-0.833148\pi$
$359$	−16.3923	+	9.46410i	−0.865153	+	0.499496i	0.000581665		1.00000i	$0.499815\pi$
$360$		0			0
$361$	−6.92820	+	12.0000i	−0.364642	+	0.631579i
$362$	−6.17449	−	1.65445i	−0.324524	−	0.0869560i
$363$	7.07107	+	7.07107i	0.371135	+	0.371135i
$364$	−5.66987	+	1.96410i	−0.297182	+	0.102947i
$365$		0			0
$366$	2.26795	+	3.92820i	0.118548	+	0.205330i
$367$	3.75719	+	14.0220i	0.196124	+	0.731943i	0.991973	+	0.126449i	$0.0403580\pi$
$367$	3.75719	+	14.0220i	0.196124	+	0.731943i	−0.795849	+	0.605494i	$0.792975\pi$
$368$	2.05197	+	7.65806i	0.106966	+	0.399204i
$369$	−2.86603	−	4.96410i	−0.149199	−	0.258421i
$370$		0			0
$371$	−2.50000	+	0.866025i	−0.129794	+	0.0449618i
$372$	0.378937	+	0.378937i	0.0196470	+	0.0196470i
$373$	25.1141	+	6.72930i	1.30036	+	0.348430i	0.841585	−	0.540124i	$-0.181623\pi$
$373$	25.1141	+	6.72930i	1.30036	+	0.348430i	0.458772	+	0.888554i	$0.348289\pi$
$374$	−0.267949	+	0.464102i	−0.0138553	+	0.0239981i
$375$		0			0
$376$	7.96410	−	4.59808i	0.410717	−	0.237128i
$377$	11.1106	−	11.1106i	0.572227	−	0.572227i
$378$	2.19067	−	1.48356i	0.112676	−	0.0763063i
$379$			9.92820i			0.509978i	0.966944	+	0.254989i	$0.0820718\pi$
$379$			9.92820i			0.509978i	−0.966944	+	0.254989i	$0.917928\pi$
$380$		0			0
$381$	−4.33013	−	2.50000i	−0.221839	−	0.128079i
$382$	−10.5558	+	2.82843i	−0.540083	+	0.144715i
$383$	−7.75959	+	28.9592i	−0.396497	+	1.47975i	0.422719	+	0.906261i	$0.361076\pi$
$383$	−7.75959	+	28.9592i	−0.396497	+	1.47975i	−0.819216	+	0.573485i	$0.805591\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	18.7846			0.956111
$387$	1.27551	−	4.76028i	0.0648380	−	0.241979i
$388$	10.5558	−	2.82843i	0.535891	−	0.143592i
$389$	28.2679	+	16.3205i	1.43324	+	0.827483i	0.997367	−	0.0725245i	$-0.0231055\pi$
$389$	28.2679	+	16.3205i	1.43324	+	0.827483i	0.435875	+	0.900007i	$0.356439\pi$
$390$		0			0
$391$		−	4.24871i		−	0.214867i
$392$	−4.19187	+	5.60609i	−0.211722	+	0.283150i
$393$	14.2301	−	14.2301i	0.717812	−	0.717812i
$394$	−9.40192	+	5.42820i	−0.473662	+	0.273469i
$395$		0			0
$396$	0.500000	−	0.866025i	0.0251259	−	0.0435194i
$397$	−12.3490	−	3.30890i	−0.619778	−	0.166069i	−0.0647510	−	0.997901i	$-0.520625\pi$
$397$	−12.3490	−	3.30890i	−0.619778	−	0.166069i	−0.555027	+	0.831832i	$0.687292\pi$
$398$	−13.7632	−	13.7632i	−0.689887	−	0.689887i
$399$	−9.92820	+	11.4641i	−0.497032	+	0.573923i
$400$		0			0
$401$	5.96410	+	10.3301i	0.297833	+	0.515862i	0.975640	−	0.219378i	$-0.0704028\pi$
$401$	5.96410	+	10.3301i	0.297833	+	0.515862i	−0.677807	+	0.735240i	$0.737069\pi$
$402$	−0.517638	−	1.93185i	−0.0258174	−	0.0963520i
$403$	−0.314566	−	1.17398i	−0.0156697	−	0.0584800i
$404$	7.46410	+	12.9282i	0.371353	+	0.643202i
$405$		0			0
$406$	3.46410	−	18.0000i	0.171920	−	0.893325i
$407$	7.02030	+	7.02030i	0.347983	+	0.347983i
$408$	−0.517638	−	0.138701i	−0.0256269	−	0.00686671i
$409$	6.39230	−	11.0718i	0.316079	−	0.547465i	−0.663587	−	0.748099i	$-0.730967\pi$
$409$	6.39230	−	11.0718i	0.316079	−	0.547465i	0.979666	+	0.200634i	$0.0643002\pi$
$410$		0			0
$411$	4.39230	−	2.53590i	0.216656	−	0.125087i
$412$	−1.69161	+	1.69161i	−0.0833399	+	0.0833399i
$413$	10.7961	+	5.24075i	0.531240	+	0.257881i
$414$			7.92820i			0.389650i
$415$		0			0
$416$	−1.96410	−	1.13397i	−0.0962980	−	0.0555977i
$417$	−10.0382	+	2.68973i	−0.491573	+	0.131716i
$418$	−1.48356	+	5.53674i	−0.0725635	+	0.270811i
$419$	−27.0526			−1.32160			−0.660802	−	0.750560i	$-0.729784\pi$
$419$	−27.0526			−1.32160			−0.660802	+	0.750560i	$0.729784\pi$
$420$		0			0
$421$	13.8564			0.675320			0.337660	−	0.941268i	$-0.390365\pi$
$421$	13.8564			0.675320			0.337660	+	0.941268i	$0.390365\pi$
$422$	−5.63827	+	21.0423i	−0.274467	+	1.02432i
$423$	8.88280	−	2.38014i	0.431897	−	0.115726i
$424$	−0.866025	−	0.500000i	−0.0420579	−	0.0242821i
$425$		0			0
$426$			4.92820i			0.238772i
$427$	−6.72930	−	9.93666i	−0.325653	−	0.480869i
$428$	0.757875	−	0.757875i	0.0366333	−	0.0366333i
$429$	−1.96410	+	1.13397i	−0.0948277	+	0.0547488i
$430$		0			0
$431$	−10.8564	+	18.8038i	−0.522935	+	0.905749i	0.476709	+	0.879061i	$0.341830\pi$
$431$	−10.8564	+	18.8038i	−0.522935	+	0.905749i	−0.999644	+	0.0266884i	$0.991504\pi$
$432$	0.965926	+	0.258819i	0.0464731	+	0.0124524i
$433$	11.3137	+	11.3137i	0.543702	+	0.543702i	0.924612	−	0.380910i	$-0.124389\pi$
$433$	11.3137	+	11.3137i	0.543702	+	0.543702i	−0.380910	+	0.924612i	$0.624389\pi$
$434$	−1.07180	−	0.928203i	−0.0514479	−	0.0445552i
$435$		0			0
$436$	1.53590	+	2.66025i	0.0735562	+	0.127403i
$437$	−11.7620	−	43.8964i	−0.562653	−	2.09985i
$438$	1.03528	+	3.86370i	0.0494674	+	0.184615i
$439$	10.0000	+	17.3205i	0.477274	+	0.826663i	0.999661	−	0.0260459i	$-0.00829161\pi$
$439$	10.0000	+	17.3205i	0.477274	+	0.826663i	−0.522387	+	0.852709i	$0.674958\pi$
$440$		0			0
$441$	−5.50000	+	4.33013i	−0.261905	+	0.206197i
$442$	0.859411	+	0.859411i	0.0408780	+	0.0408780i
$443$	−0.138701	−	0.0371647i	−0.00658987	−	0.00176575i	0.255523	−	0.966803i	$-0.417752\pi$
$443$	−0.138701	−	0.0371647i	−0.00658987	−	0.00176575i	−0.262112	+	0.965037i	$0.584419\pi$
$444$	−4.96410	+	8.59808i	−0.235586	+	0.408047i
$445$		0			0
$446$	21.9282	−	12.6603i	1.03833	−	0.599480i
$447$	9.14162	−	9.14162i	0.432384	−	0.432384i
$448$	−2.63896	+	0.189469i	−0.124679	+	0.00895155i
$449$		−	0.0717968i		−	0.00338830i	−0.999999	−	0.00169415i	$-0.999461\pi$
$449$		−	0.0717968i		−	0.00338830i	0.999999	−	0.00169415i	$-0.000539265\pi$
$450$		0			0
$451$	4.96410	+	2.86603i	0.233750	+	0.134956i
$452$	−0.896575	+	0.240237i	−0.0421714	+	0.0112998i
$453$	−6.17449	+	23.0435i	−0.290103	+	1.08268i
$454$	3.46410			0.162578
$455$		0			0
$456$	−5.73205			−0.268428
$457$	3.06866	−	11.4524i	0.143546	−	0.535721i	−0.856270	−	0.516529i	$-0.827224\pi$
$457$	3.06866	−	11.4524i	0.143546	−	0.535721i	0.999816	−	0.0191922i	$-0.00610945\pi$
$458$	10.5558	−	2.82843i	0.493242	−	0.132164i
$459$	−0.464102	−	0.267949i	−0.0216624	−	0.0125068i
$460$		0			0
$461$			30.6410i			1.42709i	0.700607	+	0.713547i	$0.252913\pi$
$461$			30.6410i			1.42709i	−0.700607	+	0.713547i	$0.747087\pi$
$462$	−1.15539	+	2.38014i	−0.0537538	+	0.110734i
$463$	23.1315	−	23.1315i	1.07501	−	1.07501i	0.0780612	−	0.996949i	$-0.475127\pi$
$463$	23.1315	−	23.1315i	1.07501	−	1.07501i	0.996949	−	0.0780612i	$-0.0248729\pi$
$464$	6.00000	−	3.46410i	0.278543	−	0.160817i
$465$		0			0
$466$	12.9282	−	22.3923i	0.598887	−	1.03730i
$467$	−13.9019	−	3.72500i	−0.643303	−	0.172373i	−0.0776040	−	0.996984i	$-0.524727\pi$
$467$	−13.9019	−	3.72500i	−0.643303	−	0.172373i	−0.565699	+	0.824612i	$0.691394\pi$
$468$	−1.60368	−	1.60368i	−0.0741302	−	0.0741302i
$469$	1.73205	+	5.00000i	0.0799787	+	0.230879i
$470$		0			0
$471$	6.33013	+	10.9641i	0.291677	+	0.505199i
$472$	1.17398	+	4.38134i	0.0540367	+	0.201668i
$473$	1.27551	+	4.76028i	0.0586481	+	0.218878i
$474$	−8.46410	−	14.6603i	−0.388769	−	0.673368i
$475$		0			0
$476$	1.39230	+	0.267949i	0.0638162	+	0.0122814i
$477$	−0.707107	−	0.707107i	−0.0323762	−	0.0323762i
$478$	23.1822	+	6.21166i	1.06033	+	0.284115i
$479$	−21.4641	+	37.1769i	−0.980720	+	1.69866i	−0.321122	+	0.947038i	$0.604060\pi$
$479$	−21.4641	+	37.1769i	−0.980720	+	1.69866i	−0.659598	+	0.751619i	$0.729273\pi$
$480$		0			0
$481$	19.5000	−	11.2583i	0.889123	−	0.513336i
$482$	18.1953	−	18.1953i	0.828774	−	0.828774i
$483$	−1.50215	−	20.9222i	−0.0683500	−	0.951993i
$484$		−	10.0000i		−	0.454545i
$485$		0			0
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	21.1117	−	5.65685i	0.956661	−	0.256337i	0.253475	−	0.967342i	$-0.418427\pi$
$487$	21.1117	−	5.65685i	0.956661	−	0.256337i	0.703186	+	0.711006i	$0.251760\pi$
$488$	1.17398	−	4.38134i	0.0531434	−	0.198334i
$489$	12.0000			0.542659
$490$		0			0
$491$	43.7128			1.97273			0.986366	−	0.164568i	$-0.0526229\pi$
$491$	43.7128			1.97273			0.986366	+	0.164568i	$0.0526229\pi$
$492$	−1.48356	+	5.53674i	−0.0668842	+	0.249615i
$493$	−3.58630	+	0.960947i	−0.161519	+	0.0432789i
$494$	11.2583	+	6.50000i	0.506536	+	0.292449i
$495$		0			0
$496$		−	0.535898i		−	0.0240625i
$497$	−0.933740	−	13.0053i	−0.0418840	−	0.583368i
$498$	−7.34847	+	7.34847i	−0.329293	+	0.329293i
$499$	24.2487	−	14.0000i	1.08552	−	0.626726i	0.153141	−	0.988204i	$-0.451061\pi$
$499$	24.2487	−	14.0000i	1.08552	−	0.626726i	0.932381	+	0.361478i	$0.117728\pi$
$500$		0			0
$501$	−8.59808	+	14.8923i	−0.384134	+	0.665339i
$502$	−23.8200	−	6.38254i	−1.06314	−	0.284867i
$503$	24.3190	+	24.3190i	1.08433	+	1.08433i	0.996100	+	0.0882321i	$0.0281217\pi$
$503$	24.3190	+	24.3190i	1.08433	+	1.08433i	0.0882321	+	0.996100i	$0.471878\pi$
$504$	−2.59808	−	0.500000i	−0.115728	−	0.0222718i
$505$		0			0
$506$	−3.96410	−	6.86603i	−0.176226	−	0.305232i
$507$	−2.03339	−	7.58871i	−0.0903059	−	0.337026i
$508$	1.29410	+	4.82963i	0.0574162	+	0.214280i
$509$	−5.19615	−	9.00000i	−0.230315	−	0.398918i	0.727586	−	0.686017i	$-0.240642\pi$
$509$	−5.19615	−	9.00000i	−0.230315	−	0.398918i	−0.957901	+	0.287099i	$0.907309\pi$
$510$		0			0
$511$	−3.46410	−	10.0000i	−0.153243	−	0.442374i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−5.53674	−	1.48356i	−0.244453	−	0.0655009i
$514$	−9.19615	+	15.9282i	−0.405625	+	0.702563i
$515$		0			0
$516$	−4.26795	+	2.46410i	−0.187886	+	0.108476i
$517$	−6.50266	+	6.50266i	−0.285987	+	0.285987i
$518$	11.4710	−	23.6305i	0.504006	−	1.03826i
$519$			23.5885i			1.03542i
$520$		0			0
$521$	−6.82051	−	3.93782i	−0.298812	−	0.172519i	0.343097	−	0.939300i	$-0.388524\pi$
$521$	−6.82051	−	3.93782i	−0.298812	−	0.172519i	−0.641909	+	0.766781i	$0.721857\pi$
$522$	6.69213	−	1.79315i	0.292907	−	0.0784841i
$523$	8.76268	−	32.7028i	0.383165	−	1.42999i	−0.457873	−	0.889017i	$-0.651389\pi$
$523$	8.76268	−	32.7028i	0.383165	−	1.42999i	0.841039	−	0.540975i	$-0.181945\pi$
$524$	−20.1244			−0.879137
$525$		0			0
$526$	−2.14359			−0.0934651
$527$	−0.0743295	+	0.277401i	−0.00323784	+	0.0120838i
$528$	−0.965926	+	0.258819i	−0.0420365	+	0.0112637i
$529$	34.5167	+	19.9282i	1.50072	+	0.866444i
$530$		0			0
$531$			4.53590i			0.196841i
$532$	15.1266	−	1.08604i	0.655823	−	0.0470860i
$533$	9.19239	−	9.19239i	0.398167	−	0.398167i
$534$	−6.00000	+	3.46410i	−0.259645	+	0.149906i
$535$		0			0
$536$	−1.00000	+	1.73205i	−0.0431934	+	0.0748132i
$537$	8.69333	+	2.32937i	0.375145	+	0.100520i
$538$	−6.59059	−	6.59059i	−0.284141	−	0.284141i
$539$	2.59808	−	6.50000i	0.111907	−	0.279975i
$540$		0			0
$541$	−8.53590	−	14.7846i	−0.366987	−	0.635640i	0.622106	−	0.782933i	$-0.286277\pi$
$541$	−8.53590	−	14.7846i	−0.366987	−	0.635640i	−0.989093	+	0.147293i	$0.952944\pi$
$542$	−2.07055	−	7.72741i	−0.0889378	−	0.331921i
$543$	1.65445	+	6.17449i	0.0709993	+	0.264973i
$544$	0.267949	+	0.464102i	0.0114882	+	0.0198982i
$545$		0			0
$546$	4.53590	+	3.92820i	0.194119	+	0.168112i
$547$	21.0101	+	21.0101i	0.898328	+	0.898328i	0.995288	−	0.0969599i	$-0.0309119\pi$
$547$	21.0101	+	21.0101i	0.898328	+	0.898328i	−0.0969599	+	0.995288i	$0.530912\pi$
$548$	−4.89898	−	1.31268i	−0.209274	−	0.0560748i
$549$	2.26795	−	3.92820i	0.0967937	−	0.167652i
$550$		0			0
$551$	−34.3923	+	19.8564i	−1.46516	+	0.845911i
$552$	5.60609	−	5.60609i	0.238611	−	0.238611i
$553$	25.1141	+	37.0841i	1.06796	+	1.57698i
$554$		−	22.0000i		−	0.934690i
$555$		0			0
$556$	9.00000	+	5.19615i	0.381685	+	0.220366i
$557$	22.0776	−	5.91567i	0.935458	−	0.250655i	0.241277	−	0.970456i	$-0.422434\pi$
$557$	22.0776	−	5.91567i	0.935458	−	0.250655i	0.694180	+	0.719801i	$0.255767\pi$
$558$	0.138701	−	0.517638i	0.00587167	−	0.0219134i
$559$	11.1769			0.472733
$560$		0			0
$561$	0.535898			0.0226256
$562$	3.64205	−	13.5923i	0.153631	−	0.573357i
$563$	17.7656	−	4.76028i	0.748731	−	0.200622i	0.135776	−	0.990740i	$-0.456647\pi$
$563$	17.7656	−	4.76028i	0.748731	−	0.200622i	0.612955	+	0.790118i	$0.289981\pi$
$564$	−7.96410	−	4.59808i	−0.335349	−	0.193614i
$565$		0			0
$566$		−	19.4641i		−	0.818137i
$567$	−2.38014	−	1.15539i	−0.0999565	−	0.0485220i
$568$	3.48477	−	3.48477i	0.146218	−	0.146218i
$569$	8.47372	−	4.89230i	0.355237	−	0.205096i	−0.311752	−	0.950163i	$-0.600916\pi$
$569$	8.47372	−	4.89230i	0.355237	−	0.205096i	0.666989	+	0.745067i	$0.267583\pi$
$570$		0			0
$571$	−6.92820	+	12.0000i	−0.289936	+	0.502184i	−0.973794	−	0.227431i	$-0.926967\pi$
$571$	−6.92820	+	12.0000i	−0.289936	+	0.502184i	0.683858	+	0.729615i	$0.260301\pi$
$572$	2.19067	+	0.586988i	0.0915965	+	0.0245432i
$573$	7.72741	+	7.72741i	0.322817	+	0.322817i
$574$	2.86603	−	14.8923i	0.119626	−	0.621593i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−9.04008	−	33.7381i	−0.376344	−	1.40453i	−0.851372	−	0.524563i	$-0.824229\pi$
$577$	−9.04008	−	33.7381i	−0.376344	−	1.40453i	0.475028	−	0.879971i	$-0.342438\pi$
$578$	4.32559	+	16.1433i	0.179921	+	0.671474i
$579$	−9.39230	−	16.2679i	−0.390331	−	0.676073i
$580$		0			0
$581$	18.0000	−	20.7846i	0.746766	−	0.862291i
$582$	−7.72741	−	7.72741i	−0.320311	−	0.320311i
$583$	0.965926	+	0.258819i	0.0400046	+	0.0107192i
$584$	2.00000	−	3.46410i	0.0827606	−	0.143346i
$585$		0			0
$586$	−1.50000	+	0.866025i	−0.0619644	+	0.0357752i
$587$	−9.41902	+	9.41902i	−0.388765	+	0.388765i	−0.874247	−	0.485482i	$-0.838644\pi$
$587$	−9.41902	+	9.41902i	−0.388765	+	0.388765i	0.485482	+	0.874247i	$0.338644\pi$
$588$	6.95095	+	0.827225i	0.286652	+	0.0341142i
$589$			3.07180i			0.126571i
$590$		0			0
$591$	9.40192	+	5.42820i	0.386743	+	0.223286i
$592$	9.58991	−	2.56961i	0.394143	−	0.105610i
$593$	5.59248	−	20.8714i	0.229656	−	0.857087i	−0.750830	−	0.660496i	$-0.770346\pi$
$593$	5.59248	−	20.8714i	0.229656	−	0.857087i	0.980486	−	0.196591i	$-0.0629872\pi$
$594$	−1.00000			−0.0410305
$595$		0			0
$596$	−12.9282			−0.529560
$597$	−5.03768	+	18.8009i	−0.206179	+	0.769469i
$598$	−17.3681	+	4.65376i	−0.710234	+	0.190307i
$599$	−12.2487	−	7.07180i	−0.500469	−	0.288946i	0.228438	−	0.973558i	$-0.426638\pi$
$599$	−12.2487	−	7.07180i	−0.500469	−	0.288946i	−0.728907	+	0.684613i	$0.759971\pi$
$600$		0			0
$601$		−	12.7846i		−	0.521495i	−0.965407	−	0.260748i	$-0.916031\pi$
$601$		−	12.7846i		−	0.521495i	0.965407	−	0.260748i	$-0.0839690\pi$
$602$	10.7961	−	7.31130i	0.440015	−	0.297987i
$603$	−1.41421	+	1.41421i	−0.0575912	+	0.0575912i
$604$	20.6603	−	11.9282i	0.840654	−	0.485352i
$605$		0			0
$606$	7.46410	−	12.9282i	0.303208	−	0.525172i
$607$	−18.4034	−	4.93117i	−0.746969	−	0.200150i	−0.134796	−	0.990873i	$-0.543038\pi$
$607$	−18.4034	−	4.93117i	−0.746969	−	0.200150i	−0.612173	+	0.790724i	$0.709705\pi$
$608$	4.05317	+	4.05317i	0.164378	+	0.164378i
$609$	−17.3205	+	6.00000i	−0.701862	+	0.243132i
$610$		0			0
$611$	10.4282	+	18.0622i	0.421880	+	0.730718i
$612$	0.138701	+	0.517638i	0.00560664	+	0.0209243i
$613$	1.05386	+	3.93305i	0.0425649	+	0.158855i	0.983937	−	0.178515i	$-0.0571294\pi$
$613$	1.05386	+	3.93305i	0.0425649	+	0.158855i	−0.941372	+	0.337370i	$0.890463\pi$
$614$	−0.803848	−	1.39230i	−0.0324406	−	0.0561889i
$615$		0			0
$616$	2.50000	−	0.866025i	0.100728	−	0.0348932i
$617$	11.9700	+	11.9700i	0.481896	+	0.481896i	0.905737	−	0.423841i	$-0.139318\pi$
$617$	11.9700	+	11.9700i	0.481896	+	0.481896i	−0.423841	+	0.905737i	$0.639318\pi$
$618$	2.31079	+	0.619174i	0.0929536	+	0.0249068i
$619$	9.79423	−	16.9641i	0.393663	−	0.681845i	−0.599266	−	0.800550i	$-0.704541\pi$
$619$	9.79423	−	16.9641i	0.393663	−	0.681845i	0.992930	+	0.118705i	$0.0378743\pi$
$620$		0			0
$621$	6.86603	−	3.96410i	0.275524	−	0.159074i
$622$	19.4201	−	19.4201i	0.778673	−	0.778673i
$623$	15.1774	−	10.2784i	0.608070	−	0.411797i
$624$			2.26795i			0.0907906i
$625$		0			0
$626$	27.0000	+	15.5885i	1.07914	+	0.623040i
$627$	5.53674	−	1.48356i	0.221116	−	0.0592478i
$628$	3.27671	−	12.2289i	0.130755	−	0.487985i
$629$	−5.32051			−0.212143
$630$		0			0
$631$	1.21539			0.0483839			0.0241920	−	0.999707i	$-0.492299\pi$
$631$	1.21539			0.0483839			0.0241920	+	0.999707i	$0.492299\pi$
$632$	−4.38134	+	16.3514i	−0.174280	+	0.650423i
$633$	21.0423	−	5.63827i	0.836357	−	0.224101i
$634$	12.1244	+	7.00000i	0.481520	+	0.278006i
$635$		0			0
$636$			1.00000i			0.0396526i
$637$	−12.7143	−	9.50695i	−0.503760	−	0.376679i
$638$	−4.89898	+	4.89898i	−0.193952	+	0.193952i
$639$	4.26795	−	2.46410i	0.168837	−	0.0974784i
$640$		0			0
$641$	−9.03590	+	15.6506i	−0.356897	+	0.618163i	−0.987441	−	0.157991i	$-0.949498\pi$
$641$	−9.03590	+	15.6506i	−0.356897	+	0.618163i	0.630544	+	0.776153i	$0.282832\pi$
$642$	−1.03528	−	0.277401i	−0.0408591	−	0.0109482i
$643$	4.72311	+	4.72311i	0.186261	+	0.186261i	0.794078	−	0.607816i	$-0.207954\pi$
$643$	4.72311	+	4.72311i	0.186261	+	0.186261i	−0.607816	+	0.794078i	$0.707954\pi$
$644$	−13.7321	+	15.8564i	−0.541119	+	0.624830i
$645$		0			0
$646$	−1.53590	−	2.66025i	−0.0604291	−	0.104666i
$647$	9.21097	+	34.3758i	0.362121	+	1.35145i	0.871283	+	0.490782i	$0.163289\pi$
$647$	9.21097	+	34.3758i	0.362121	+	1.35145i	−0.509162	+	0.860671i	$0.670045\pi$
$648$	−0.258819	−	0.965926i	−0.0101674	−	0.0379452i
$649$	−2.26795	−	3.92820i	−0.0890248	−	0.154195i
$650$		0			0
$651$	−0.267949	+	1.39230i	−0.0105018	+	0.0545687i
$652$	−8.48528	−	8.48528i	−0.332309	−	0.332309i
$653$	−29.6663	−	7.94906i	−1.16093	−	0.311071i	−0.373594	−	0.927592i	$-0.621875\pi$
$653$	−29.6663	−	7.94906i	−1.16093	−	0.311071i	−0.787338	+	0.616522i	$0.788541\pi$
$654$	1.53590	−	2.66025i	0.0600584	−	0.104024i
$655$		0			0
$656$	4.96410	−	2.86603i	0.193816	−	0.111899i
$657$	2.82843	−	2.82843i	0.110347	−	0.110347i
$658$	21.8881	+	10.6252i	0.853288	+	0.414213i
$659$		−	15.7128i		−	0.612084i	−0.952018	−	0.306042i	$-0.900995\pi$
$659$		−	15.7128i		−	0.612084i	0.952018	−	0.306042i	$-0.0990048\pi$
$660$		0			0
$661$	−19.8564	−	11.4641i	−0.772325	−	0.445902i	0.0613786	−	0.998115i	$-0.480450\pi$
$661$	−19.8564	−	11.4641i	−0.772325	−	0.445902i	−0.833703	+	0.552213i	$0.813784\pi$
$662$	−15.2468	+	4.08536i	−0.592582	+	0.158782i
$663$	0.314566	−	1.17398i	0.0122167	−	0.0455935i
$664$	10.3923			0.403300
$665$		0			0
$666$	9.92820			0.384710
$667$	14.2165	−	53.0566i	0.550464	−	2.05436i
$668$	16.6102	−	4.45069i	0.642668	−	0.172202i
$669$	−21.9282	−	12.6603i	−0.847793	−	0.489474i
$670$		0			0
$671$			4.53590i			0.175106i
$672$	1.48356	+	2.19067i	0.0572297	+	0.0845070i
$673$	−11.8685	+	11.8685i	−0.457497	+	0.457497i	−0.897833	−	0.440336i	$-0.854859\pi$
$673$	−11.8685	+	11.8685i	−0.457497	+	0.457497i	0.440336	+	0.897833i	$0.354859\pi$
$674$	−21.5885	+	12.4641i	−0.831556	+	0.480099i
$675$		0			0
$676$	−3.92820	+	6.80385i	−0.151085	+	0.261686i
$677$	1.91327	+	0.512659i	0.0735329	+	0.0197031i	0.295398	−	0.955374i	$-0.404548\pi$
$677$	1.91327	+	0.512659i	0.0735329	+	0.0197031i	−0.221865	+	0.975077i	$0.571214\pi$
$678$	0.656339	+	0.656339i	0.0252065	+	0.0252065i
$679$	21.8564	+	18.9282i	0.838772	+	0.726398i
$680$		0			0
$681$	−1.73205	−	3.00000i	−0.0663723	−	0.114960i
$682$	0.138701	+	0.517638i	0.00531112	+	0.0198214i
$683$	10.8332	+	40.4302i	0.414522	+	1.54702i	0.785791	+	0.618492i	$0.212256\pi$
$683$	10.8332	+	40.4302i	0.414522	+	1.54702i	−0.371269	+	0.928526i	$0.621077\pi$
$684$	2.86603	+	4.96410i	0.109585	+	0.189807i
$685$		0			0
$686$	−18.5000	−	0.866025i	−0.706333	−	0.0330650i
$687$	−7.72741	−	7.72741i	−0.294819	−	0.294819i
$688$	4.76028	+	1.27551i	0.181484	+	0.0486285i
$689$	1.13397	−	1.96410i	0.0432010	−	0.0748263i
$690$		0			0
$691$	−7.14359	+	4.12436i	−0.271755	+	0.156898i	−0.629685	−	0.776851i	$-0.716816\pi$
$691$	−7.14359	+	4.12436i	−0.271755	+	0.156898i	0.357930	+	0.933748i	$0.383483\pi$
$692$	16.6796	−	16.6796i	0.634062	−	0.634062i
$693$	2.63896	−	0.189469i	0.100246	−	0.00719732i
$694$			10.9282i			0.414829i
$695$		0			0
$696$	−6.00000	−	3.46410i	−0.227429	−	0.131306i
$697$	−2.96713	+	0.795040i	−0.112388	+	0.0301143i
$698$	−6.69213	+	24.9754i	−0.253301	+	0.945332i
$699$	−25.8564			−0.977979
$700$		0			0
$701$	−31.8564			−1.20320			−0.601600	−	0.798798i	$-0.705470\pi$
$701$	−31.8564			−1.20320			−0.601600	+	0.798798i	$0.705470\pi$
$702$	−0.586988	+	2.19067i	−0.0221545	+	0.0826815i
$703$	−54.9698	+	14.7291i	−2.07323	+	0.555519i
$704$	0.866025	+	0.500000i	0.0326396	+	0.0188445i
$705$		0			0
$706$		−	6.92820i		−	0.260746i
$707$	−17.2480	+	35.5312i	−0.648676	+	1.33629i
$708$	3.20736	−	3.20736i	0.120540	−	0.120540i
$709$	11.3205	−	6.53590i	0.425151	−	0.245461i	−0.272128	−	0.962261i	$-0.587727\pi$
$709$	11.3205	−	6.53590i	0.425151	−	0.245461i	0.697279	+	0.716800i	$0.254394\pi$
$710$		0			0
$711$	−8.46410	+	14.6603i	−0.317429	+	0.549802i
$712$	6.69213	+	1.79315i	0.250798	+	0.0672012i
$713$	−3.00429	−	3.00429i	−0.112512	−	0.112512i
$714$	−0.464102	−	1.33975i	−0.0173686	−	0.0501387i
$715$		0			0
$716$	−4.50000	−	7.79423i	−0.168173	−	0.291284i
$717$	−6.21166	−	23.1822i	−0.231979	−	0.865756i
$718$	−4.89898	−	18.2832i	−0.182828	−	0.682324i
$719$	7.19615	+	12.4641i	0.268371	+	0.464833i	0.968441	−	0.249242i	$-0.0801813\pi$
$719$	7.19615	+	12.4641i	0.268371	+	0.464833i	−0.700070	+	0.714074i	$0.746848\pi$
$720$		0			0
$721$	−6.21539	−	1.19615i	−0.231473	−	0.0445470i
$722$	−9.79796	−	9.79796i	−0.364642	−	0.364642i
$723$	−24.8553	−	6.65994i	−0.924377	−	0.247686i
$724$	3.19615	−	5.53590i	0.118784	−	0.205740i
$725$		0			0
$726$	−8.66025	+	5.00000i	−0.321412	+	0.185567i
$727$	−23.0943	+	23.0943i	−0.856520	+	0.856520i	−0.990926	−	0.134407i	$-0.957087\pi$
$727$	−23.0943	+	23.0943i	−0.856520	+	0.856520i	0.134407	+	0.990926i	$0.457087\pi$
$728$	−0.429705	−	5.98502i	−0.0159259	−	0.221820i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−2.28719	−	1.32051i	−0.0845947	−	0.0488408i
$732$	−4.38134	+	1.17398i	−0.161939	+	0.0433914i
$733$	5.96644	−	22.2671i	0.220376	−	0.822453i	−0.763829	−	0.645418i	$-0.776683\pi$
$733$	5.96644	−	22.2671i	0.220376	−	0.822453i	0.984205	−	0.177034i	$-0.0566503\pi$
$734$	−14.5167			−0.535820
$735$		0			0
$736$	−7.92820			−0.292237
$737$	0.517638	−	1.93185i	0.0190674	−	0.0711607i
$738$	5.53674	−	1.48356i	0.203810	−	0.0546107i
$739$	5.25833	+	3.03590i	0.193431	+	0.111677i	0.593588	−	0.804769i	$-0.297711\pi$
$739$	5.25833	+	3.03590i	0.193431	+	0.111677i	−0.400157	+	0.916447i	$0.631044\pi$
$740$		0			0
$741$		−	13.0000i		−	0.477567i
$742$	−0.189469	−	2.63896i	−0.00695561	−	0.0968792i
$743$	23.8893	−	23.8893i	0.876414	−	0.876414i	−0.116747	−	0.993162i	$-0.537247\pi$
$743$	23.8893	−	23.8893i	0.876414	−	0.876414i	0.993162	+	0.116747i	$0.0372467\pi$
$744$	−0.464102	+	0.267949i	−0.0170148	+	0.00982349i
$745$		0			0
$746$	−13.0000	+	22.5167i	−0.475964	+	0.824394i
$747$	10.0382	+	2.68973i	0.367278	+	0.0984119i
$748$	−0.378937	−	0.378937i	−0.0138553	−	0.0138553i
$749$	2.78461	+	0.535898i	0.101747	+	0.0195813i
$750$		0			0
$751$	−6.92820	−	12.0000i	−0.252814	−	0.437886i	0.711486	−	0.702701i	$-0.248023\pi$
$751$	−6.92820	−	12.0000i	−0.252814	−	0.437886i	−0.964299	+	0.264814i	$0.914689\pi$
$752$	2.38014	+	8.88280i	0.0867948	+	0.323922i
$753$	6.38254	+	23.8200i	0.232593	+	0.868048i
$754$	7.85641	+	13.6077i	0.286113	+	0.495563i
$755$		0			0
$756$	0.866025	+	2.50000i	0.0314970	+	0.0909241i
$757$	12.5249	+	12.5249i	0.455223	+	0.455223i	0.897084	−	0.441860i	$-0.145681\pi$
$757$	12.5249	+	12.5249i	0.455223	+	0.455223i	−0.441860	+	0.897084i	$0.645681\pi$
$758$	−9.58991	−	2.56961i	−0.348321	−	0.0933324i
$759$	−3.96410	+	6.86603i	−0.143888	+	0.249221i
$760$		0			0
$761$	21.1077	−	12.1865i	0.765153	−	0.441761i	−0.0659896	−	0.997820i	$-0.521020\pi$
$761$	21.1077	−	12.1865i	0.765153	−	0.441761i	0.831143	+	0.556059i	$0.187687\pi$
$762$	3.53553	−	3.53553i	0.128079	−	0.128079i
$763$	−3.54914	+	7.31130i	−0.128487	+	0.264687i
$764$		−	10.9282i		−	0.395369i
$765$		0			0
$766$	−25.9641	−	14.9904i	−0.938121	−	0.541624i
$767$	−9.93666	+	2.66252i	−0.358792	+	0.0961380i
$768$	−0.258819	+	0.965926i	−0.00933933	+	0.0348548i
$769$	21.1962			0.764353			0.382176	−	0.924089i	$-0.375175\pi$
$769$	21.1962			0.764353			0.382176	+	0.924089i	$0.375175\pi$
$770$		0			0
$771$	18.3923			0.662383
$772$	−4.86181	+	18.1445i	−0.174981	+	0.653036i
$773$	35.1337	−	9.41404i	1.26367	−	0.338600i	0.436068	−	0.899914i	$-0.356371\pi$
$773$	35.1337	−	9.41404i	1.26367	−	0.338600i	0.827603	+	0.561314i	$0.189704\pi$
$774$	4.26795	+	2.46410i	0.153408	+	0.0885703i
$775$		0			0
$776$			10.9282i			0.392300i
$777$	−26.2001	+	1.88108i	−0.939924	+	0.0674835i
$778$	−23.0807	+	23.0807i	−0.827483	+	0.827483i
$779$	−28.4545	+	16.4282i	−1.01949	+	0.588601i
$780$		0			0
$781$	−2.46410	+	4.26795i	−0.0881725	+	0.152719i
$782$	4.10394	+	1.09965i	0.146757	+	0.0393233i
$783$	−4.89898	−	4.89898i	−0.175075	−	0.175075i
$784$	−4.33013	−	5.50000i	−0.154647	−	0.196429i
$785$		0			0
$786$	10.0622	+	17.4282i	0.358906	+	0.621643i
$787$	4.76028	+	17.7656i	0.169686	+	0.633275i	0.997396	+	0.0721198i	$0.0229764\pi$
$787$	4.76028	+	17.7656i	0.169686	+	0.633275i	−0.827710	+	0.561156i	$0.810357\pi$
$788$	−2.80984	−	10.4865i	−0.100097	−	0.373566i
$789$	1.07180	+	1.85641i	0.0381570	+	0.0660898i
$790$		0			0
$791$	−1.85641	−	1.60770i	−0.0660062	−	0.0571631i
$792$	0.707107	+	0.707107i	0.0251259	+	0.0251259i
$793$	9.93666	+	2.66252i	0.352861	+	0.0945489i
$794$	6.39230	−	11.0718i	0.226854	−	0.392923i
$795$		0			0
$796$	16.8564	−	9.73205i	0.597459	−	0.344943i
$797$	−1.51575	+	1.51575i	−0.0536906	+	0.0536906i	−0.733442	−	0.679752i	$-0.762088\pi$
$797$	−1.51575	+	1.51575i	−0.0536906	+	0.0536906i	0.679752	+	0.733442i	$0.262088\pi$
$798$	−8.50386	−	12.5570i	−0.301034	−	0.444514i
$799$		−	4.92820i		−	0.174347i
$800$		0			0
$801$	6.00000	+	3.46410i	0.212000	+	0.122398i
$802$	−11.5218	+	3.08725i	−0.406847	+	0.109014i
$803$	−1.03528	+	3.86370i	−0.0365341	+	0.136347i
$804$	2.00000			0.0705346
$805$		0			0
$806$	1.21539			0.0428103
$807$	−2.41233	+	9.00292i	−0.0849179	+	0.316918i
$808$	−14.4195	+	3.86370i	−0.507278	+	0.135925i
$809$	−37.7942	−	21.8205i	−1.32877	−	0.767168i	−0.343664	−	0.939093i	$-0.611668\pi$
$809$	−37.7942	−	21.8205i	−1.32877	−	0.767168i	−0.985110	+	0.171924i	$0.945002\pi$
$810$		0			0
$811$		−	42.5167i		−	1.49296i	−0.665407	−	0.746481i	$-0.731742\pi$
$811$		−	42.5167i		−	1.49296i	0.665407	−	0.746481i	$-0.268258\pi$
$812$	16.4901	+	8.00481i	0.578689	+	0.280914i
$813$	−5.65685	+	5.65685i	−0.198395	+	0.198395i
$814$	−8.59808	+	4.96410i	−0.301362	+	0.173992i
$815$		0			0
$816$	0.267949	−	0.464102i	0.00938010	−	0.0162468i
$817$	−27.2862	−	7.31130i	−0.954622	−	0.255790i
$818$	9.04008	+	9.04008i	0.316079	+	0.316079i
$819$	1.13397	−	5.89230i	0.0396243	−	0.205894i
$820$		0			0
$821$	−1.92820	−	3.33975i	−0.0672948	−	0.116558i	0.830415	−	0.557146i	$-0.188103\pi$
$821$	−1.92820	−	3.33975i	−0.0672948	−	0.116558i	−0.897710	+	0.440588i	$0.854770\pi$
$822$	1.31268	+	4.89898i	0.0457849	+	0.170872i
$823$	5.10205	+	19.0411i	0.177846	+	0.663732i	0.996049	+	0.0888021i	$0.0283039\pi$
$823$	5.10205	+	19.0411i	0.177846	+	0.663732i	−0.818203	+	0.574929i	$0.805029\pi$
$824$	−1.19615	−	2.07180i	−0.0416699	−	0.0721745i
$825$		0			0
$826$	−7.85641	+	9.07180i	−0.273359	+	0.315648i
$827$	11.4152	+	11.4152i	0.396947	+	0.396947i	0.877155	−	0.480208i	$-0.159439\pi$
$827$	11.4152	+	11.4152i	0.396947	+	0.396947i	−0.480208	+	0.877155i	$0.659439\pi$
$828$	−7.65806	−	2.05197i	−0.266136	−	0.0713109i
$829$	11.7321	−	20.3205i	0.407471	−	0.705760i	−0.587135	−	0.809489i	$-0.699744\pi$
$829$	11.7321	−	20.3205i	0.407471	−	0.705760i	0.994606	+	0.103729i	$0.0330774\pi$
$830$		0			0
$831$	−19.0526	+	11.0000i	−0.660926	+	0.381586i
$832$	1.60368	−	1.60368i	0.0555977	−	0.0555977i
$833$	1.47858	+	3.44760i	0.0512299	+	0.119452i
$834$		−	10.3923i		−	0.359856i
$835$		0			0
$836$	−4.96410	−	2.86603i	−0.171687	−	0.0991236i
$837$	−0.517638	+	0.138701i	−0.0178922	+	0.00479420i
$838$	7.00172	−	26.1308i	0.241870	−	0.902672i
$839$	15.4641			0.533880			0.266940	−	0.963713i	$-0.413987\pi$
$839$	15.4641			0.533880			0.266940	+	0.963713i	$0.413987\pi$
$840$		0			0
$841$	−19.0000			−0.655172
$842$	−3.58630	+	13.3843i	−0.123592	+	0.461252i
$843$	−13.5923	+	3.64205i	−0.468144	+	0.125439i
$844$	−18.8660	−	10.8923i	−0.649395	−	0.374929i
$845$		0			0
$846$			9.19615i			0.316170i
$847$	21.9067	−	14.8356i	0.752723	−	0.509759i
$848$	0.707107	−	0.707107i	0.0242821	−	0.0242821i
$849$	−16.8564	+	9.73205i	−0.578510	+	0.334003i
$850$		0			0
$851$	39.3564	−	68.1673i	1.34912	−	2.33674i
$852$	−4.76028	−	1.27551i	−0.163084	−	0.0436984i
$853$	−22.7153	−	22.7153i	−0.777759	−	0.777759i	0.201691	−	0.979449i	$-0.435356\pi$
$853$	−22.7153	−	22.7153i	−0.777759	−	0.777759i	−0.979449	+	0.201691i	$0.935356\pi$
$854$	11.3397	−	3.92820i	0.388038	−	0.134420i
$855$		0			0
$856$	0.535898	+	0.928203i	0.0183166	+	0.0317253i
$857$	4.14110	+	15.4548i	0.141457	+	0.527926i	0.999888	+	0.0149958i	$0.00477350\pi$
$857$	4.14110	+	15.4548i	0.141457	+	0.527926i	−0.858430	+	0.512931i	$0.828560\pi$
$858$	−0.586988	−	2.19067i	−0.0200395	−	0.0747883i
$859$	−17.1962	−	29.7846i	−0.586725	−	1.01624i	−0.994658	−	0.103226i	$-0.967084\pi$
$859$	−17.1962	−	29.7846i	−0.586725	−	1.01624i	0.407933	−	0.913012i	$-0.366250\pi$
$860$		0			0
$861$	−14.3301	+	4.96410i	−0.488369	+	0.169176i
$862$	−15.3533	−	15.3533i	−0.522935	−	0.522935i
$863$	−28.6310	−	7.67166i	−0.974611	−	0.261146i	−0.263838	−	0.964567i	$-0.584988\pi$
$863$	−28.6310	−	7.67166i	−0.974611	−	0.261146i	−0.710774	+	0.703421i	$0.751655\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$		0			0
$866$	−13.8564	+	8.00000i	−0.470860	+	0.271851i
$867$	11.8177	−	11.8177i	0.401352	−	0.401352i
$868$	1.17398	−	0.795040i	0.0398474	−	0.0269854i
$869$		−	16.9282i		−	0.574250i
$870$		0			0
$871$	−3.92820	−	2.26795i	−0.133102	−	0.0768465i
$872$	−2.96713	+	0.795040i	−0.100480	+	0.0269234i
$873$	−2.82843	+	10.5558i	−0.0957278	+	0.357261i
$874$	45.4449			1.53720
$875$		0			0
$876$	−4.00000			−0.135147
$877$	−2.56961	+	9.58991i	−0.0867695	+	0.323828i	−0.995643	−	0.0932428i	$-0.970277\pi$
$877$	−2.56961	+	9.58991i	−0.0867695	+	0.323828i	0.908874	+	0.417071i	$0.136943\pi$
$878$	−19.3185	+	5.17638i	−0.651968	+	0.174694i
$879$	1.50000	+	0.866025i	0.0505937	+	0.0292103i
$880$		0			0
$881$			28.9090i			0.973968i	0.873411	+	0.486984i	$0.161903\pi$
$881$			28.9090i			0.973968i	−0.873411	+	0.486984i	$0.838097\pi$
$882$	−2.75908	−	6.43331i	−0.0929029	−	0.216621i
$883$	−14.9000	+	14.9000i	−0.501425	+	0.501425i	−0.911881	−	0.410455i	$-0.865370\pi$
$883$	−14.9000	+	14.9000i	−0.501425	+	0.501425i	0.410455	+	0.911881i	$0.365370\pi$
$884$	−1.05256	+	0.607695i	−0.0354014	+	0.0204390i
$885$		0			0
$886$	0.0717968	−	0.124356i	0.00241206	−	0.00417781i
$887$	−3.34607	−	0.896575i	−0.112350	−	0.0301041i	0.202206	−	0.979343i	$-0.435189\pi$
$887$	−3.34607	−	0.896575i	−0.112350	−	0.0301041i	−0.314556	+	0.949239i	$0.601856\pi$
$888$	−7.02030	−	7.02030i	−0.235586	−	0.235586i
$889$	−8.66025	+	10.0000i	−0.290456	+	0.335389i
$890$		0			0
$891$	0.500000	+	0.866025i	0.0167506	+	0.0290129i
$892$	6.55343	+	24.4577i	0.219425	+	0.818905i
$893$	−13.6431	−	50.9167i	−0.456548	−	1.70386i
$894$	6.46410	+	11.1962i	0.216192	+	0.374455i
$895$		0			0
$896$	0.500000	−	2.59808i	0.0167038	−	0.0867956i
$897$	12.7143	+	12.7143i	0.424519	+	0.424519i
$898$	0.0693504	+	0.0185824i	0.00231425	+	0.000620102i
$899$	−1.85641	+	3.21539i	−0.0619146	+	0.107239i
$900$		0			0
$901$	−0.464102	+	0.267949i	−0.0154615	+	0.00892668i
$902$	−4.05317	+	4.05317i	−0.134956	+	0.134956i
$903$	−11.7298	−	5.69402i	−0.390344	−	0.189485i
$904$		−	0.928203i		−	0.0308716i
$905$		0			0
$906$	−20.6603	−	11.9282i	−0.686391	−	0.396288i
$907$	28.8391	−	7.72741i	0.957586	−	0.256584i	0.254008	−	0.967202i	$-0.418251\pi$
$907$	28.8391	−	7.72741i	0.957586	−	0.256584i	0.703578	+	0.710618i	$0.251585\pi$
$908$	−0.896575	+	3.34607i	−0.0297539	+	0.111043i
$909$	−14.9282			−0.495137
$910$		0			0
$911$	−57.7128			−1.91211			−0.956055	−	0.293186i	$-0.905284\pi$
$911$	−57.7128			−1.91211			−0.956055	+	0.293186i	$0.905284\pi$
$912$	1.48356	−	5.53674i	0.0491257	−	0.183340i
$913$	−10.0382	+	2.68973i	−0.332216	+	0.0890170i
$914$	10.2679	+	5.92820i	0.339634	+	0.196088i
$915$		0			0
$916$			10.9282i			0.361078i
$917$	−29.8558	−	44.0858i	−0.985924	−	1.45584i
$918$	0.378937	−	0.378937i	0.0125068	−	0.0125068i
$919$	2.78461	−	1.60770i	0.0918558	−	0.0530330i	−0.453368	−	0.891323i	$-0.649778\pi$
$919$	2.78461	−	1.60770i	0.0918558	−	0.0530330i	0.545224	+	0.838290i	$0.316444\pi$
$920$		0			0
$921$	−0.803848	+	1.39230i	−0.0264877	+	0.0458780i
$922$	−29.5969	−	7.93048i	−0.974724	−	0.261176i
$923$	7.90327	+	7.90327i	0.260139	+	0.260139i
$924$	−2.00000	−	1.73205i	−0.0657952	−	0.0569803i
$925$		0			0
$926$	16.3564	+	28.3301i	0.537505	+	0.930986i
$927$	−0.619174	−	2.31079i	−0.0203363	−	0.0758963i
$928$	1.79315	+	6.69213i	0.0588631	+	0.219680i
$929$	4.06218	+	7.03590i	0.133276	+	0.230840i	0.924937	−	0.380119i	$-0.124117\pi$
$929$	4.06218	+	7.03590i	0.133276	+	0.230840i	−0.791662	+	0.610960i	$0.790784\pi$
$930$		0			0
$931$	24.8205	+	31.5263i	0.813459	+	1.03323i
$932$	18.2832	+	18.2832i	0.598887	+	0.598887i
$933$	−26.5283	−	7.10823i	−0.868497	−	0.232713i
$934$	7.19615	−	12.4641i	0.235465	−	0.407838i
$935$		0			0
$936$	1.96410	−	1.13397i	0.0641987	−	0.0370651i
$937$	−21.4906	+	21.4906i	−0.702067	+	0.702067i	−0.964854	−	0.262787i	$-0.915359\pi$
$937$	−21.4906	+	21.4906i	−0.702067	+	0.702067i	0.262787	+	0.964854i	$0.415359\pi$
$938$	−5.27792	+	0.378937i	−0.172330	+	0.0123727i
$939$		−	31.1769i		−	1.01742i
$940$		0			0
$941$	41.3205	+	23.8564i	1.34701	+	0.777697i	0.987825	−	0.155570i	$-0.0497213\pi$
$941$	41.3205	+	23.8564i	1.34701	+	0.777697i	0.359185	+	0.933266i	$0.383055\pi$
$942$	−12.2289	+	3.27671i	−0.398438	+	0.106761i
$943$	11.7620	−	43.8964i	0.383023	−	1.42946i
$944$	−4.53590			−0.147631
$945$		0			0
$946$	−4.92820			−0.160230
$947$	−11.8685	+	44.2939i	−0.385675	+	1.43936i	0.451426	+	0.892309i	$0.350916\pi$
$947$	−11.8685	+	44.2939i	−0.385675	+	1.43936i	−0.837100	+	0.547049i	$0.815751\pi$
$948$	16.3514	−	4.38134i	0.531068	−	0.142299i
$949$	7.85641	+	4.53590i	0.255030	+	0.147241i
$950$		0			0
$951$		−	14.0000i		−	0.453981i
$952$	−0.619174	+	1.27551i	−0.0200675	+	0.0413396i
$953$	−26.5654	+	26.5654i	−0.860539	+	0.860539i	−0.991401	−	0.130861i	$-0.958226\pi$
$953$	−26.5654	+	26.5654i	−0.860539	+	0.860539i	0.130861	+	0.991401i	$0.458226\pi$
$954$	0.866025	−	0.500000i	0.0280386	−	0.0161881i
$955$		0			0
$956$	−12.0000	+	20.7846i	−0.388108	+	0.672222i
$957$	6.69213	+	1.79315i	0.216326	+	0.0579643i
$958$	−30.3548	−	30.3548i	−0.980720	−	0.980720i
$959$	−4.39230	−	12.6795i	−0.141835	−	0.409442i
$960$		0			0
$961$	−15.3564	−	26.5981i	−0.495368	−	0.858002i
$962$	5.82774	+	21.7494i	0.187894	+	0.701230i
$963$	0.277401	+	1.03528i	0.00893914	+	0.0333613i
$964$	12.8660	+	22.2846i	0.414387	+	0.717739i
$965$		0			0
$966$	20.5981	+	3.96410i	0.662732	+	0.127543i
$967$	1.51575	+	1.51575i	0.0487432	+	0.0487432i	0.731058	−	0.682315i	$-0.239027\pi$
$967$	1.51575	+	1.51575i	0.0487432	+	0.0487432i	−0.682315	+	0.731058i	$0.739027\pi$
$968$	9.65926	+	2.58819i	0.310460	+	0.0831876i
$969$	−1.53590	+	2.66025i	−0.0493402	+	0.0854597i
$970$		0			0
$971$	17.2128	−	9.93782i	0.552385	−	0.318920i	−0.197698	−	0.980263i	$-0.563347\pi$
$971$	17.2128	−	9.93782i	0.552385	−	0.318920i	0.750084	+	0.661343i	$0.230013\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	1.96902	+	27.4249i	0.0631238	+	0.879201i
$974$			21.8564i			0.700324i
$975$		0			0
$976$	3.92820	+	2.26795i	0.125739	+	0.0725953i
$977$	28.9778	−	7.76457i	0.927081	−	0.248411i	0.236472	−	0.971638i	$-0.424009\pi$
$977$	28.9778	−	7.76457i	0.927081	−	0.248411i	0.690610	+	0.723228i	$0.257342\pi$
$978$	−3.10583	+	11.5911i	−0.0993134	+	0.370643i
$979$	−6.92820			−0.221426
$980$		0			0
$981$	−3.07180			−0.0980749
$982$	−11.3137	+	42.2233i	−0.361035	+	1.34740i
$983$	−30.7895	+	8.25002i	−0.982033	+	0.263135i	−0.713900	−	0.700247i	$-0.753073\pi$
$983$	−30.7895	+	8.25002i	−0.982033	+	0.263135i	−0.268132	+	0.963382i	$0.586406\pi$
$984$	−4.96410	−	2.86603i	−0.158250	−	0.0913656i
$985$		0			0
$986$		−	3.71281i		−	0.118240i
$987$	−1.74238	−	24.2683i	−0.0554607	−	0.772467i
$988$	−9.19239	+	9.19239i	−0.292449	+	0.292449i
$989$	33.8372	−	19.5359i	1.07596	−	0.621205i
$990$		0			0
$991$	8.39230	−	14.5359i	0.266590	−	0.461748i	−0.701389	−	0.712779i	$-0.747436\pi$
$991$	8.39230	−	14.5359i	0.266590	−	0.461748i	0.967979	+	0.251031i	$0.0807696\pi$
$992$	0.517638	+	0.138701i	0.0164350	+	0.00440375i
$993$	11.1614	+	11.1614i	0.354196	+	0.354196i
$994$	12.8038	+	2.46410i	0.406113	+	0.0781566i
$995$		0			0
$996$	−5.19615	−	9.00000i	−0.164646	−	0.285176i
$997$	13.3843	+	49.9507i	0.423884	+	1.58196i	0.766348	+	0.642425i	$0.222072\pi$
$997$	13.3843	+	49.9507i	0.423884	+	1.58196i	−0.342465	+	0.939531i	$0.611262\pi$
$998$	7.24693	+	27.0459i	0.229398	+	0.856124i
$999$	−4.96410	−	8.59808i	−0.157057	−	0.272031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.bc.a.157.1	✓	8
5.2	odd	4		1050.2.bc.d.493.1	yes	8
5.3	odd	4		1050.2.bc.d.493.2	yes	8
5.4	even	2	inner	1050.2.bc.a.157.2	yes	8
7.5	odd	6		1050.2.bc.d.607.2	yes	8
35.12	even	12	inner	1050.2.bc.a.943.2	yes	8
35.19	odd	6		1050.2.bc.d.607.1	yes	8
35.33	even	12	inner	1050.2.bc.a.943.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.bc.a.157.1	✓	8	1.1	even	1	trivial
1050.2.bc.a.157.2	yes	8	5.4	even	2	inner
1050.2.bc.a.943.1	yes	8	35.33	even	12	inner
1050.2.bc.a.943.2	yes	8	35.12	even	12	inner
1050.2.bc.d.493.1	yes	8	5.2	odd	4
1050.2.bc.d.493.2	yes	8	5.3	odd	4
1050.2.bc.d.607.1	yes	8	35.19	odd	6
1050.2.bc.d.607.2	yes	8	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(-0.189469 - 2.63896i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(-0.189469 - 2.63896i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-0.500000 + 0.866025i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(1.60368 + 1.60368i) q^{13} +(2.59808 + 0.500000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.138701 - 0.517638i) q^{17} +(0.258819 + 0.965926i) q^{18} +(-2.86603 - 4.96410i) q^{19} +(-0.866025 - 2.50000i) q^{21} +(-0.707107 - 0.707107i) q^{22} +(7.65806 + 2.05197i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-1.96410 + 1.13397i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.15539 + 2.38014i) q^{28} -6.92820i q^{29} +(-0.464102 - 0.267949i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-0.258819 + 0.965926i) q^{33} +0.535898 q^{34} -1.00000 q^{36} +(2.56961 - 9.58991i) q^{37} +(5.53674 - 1.48356i) q^{38} +(1.96410 + 1.13397i) q^{39} -5.73205i q^{41} +(2.63896 - 0.189469i) q^{42} +(3.48477 - 3.48477i) q^{43} +(0.866025 - 0.500000i) q^{44} +(-3.96410 + 6.86603i) q^{46} +(8.88280 + 2.38014i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-6.92820 + 1.00000i) q^{49} +(-0.267949 - 0.464102i) q^{51} +(-0.586988 - 2.19067i) q^{52} +(-0.258819 - 0.965926i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.00000 - 1.73205i) q^{56} +(-4.05317 - 4.05317i) q^{57} +(6.69213 + 1.79315i) q^{58} +(-2.26795 + 3.92820i) q^{59} +(3.92820 - 2.26795i) q^{61} +(0.378937 - 0.378937i) q^{62} +(-1.48356 - 2.19067i) q^{63} -1.00000i q^{64} +(-0.866025 - 0.500000i) q^{66} +(-1.93185 + 0.517638i) q^{67} +(-0.138701 + 0.517638i) q^{68} +7.92820 q^{69} +4.92820 q^{71} +(0.258819 - 0.965926i) q^{72} +(3.86370 - 1.03528i) q^{73} +(8.59808 + 4.96410i) q^{74} +5.73205i q^{76} +(2.38014 + 1.15539i) q^{77} +(-1.60368 + 1.60368i) q^{78} +(-14.6603 + 8.46410i) q^{79} +(0.500000 - 0.866025i) q^{81} +(5.53674 + 1.48356i) q^{82} +(7.34847 + 7.34847i) q^{83} +(-0.500000 + 2.59808i) q^{84} +(2.46410 + 4.26795i) q^{86} +(-1.79315 - 6.69213i) q^{87} +(0.258819 + 0.965926i) q^{88} +(3.46410 + 6.00000i) q^{89} +(3.92820 - 4.53590i) q^{91} +(-5.60609 - 5.60609i) q^{92} +(-0.517638 - 0.138701i) q^{93} +(-4.59808 + 7.96410i) q^{94} +(-0.866025 + 0.500000i) q^{96} +(-7.72741 + 7.72741i) q^{97} +(0.827225 - 6.95095i) q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 4 q^{11} + 4 q^{16} - 16 q^{19} + 4 q^{24} + 12 q^{26} + 24 q^{31} + 32 q^{34} - 8 q^{36} - 12 q^{39} - 4 q^{46} - 16 q^{51} + 4 q^{54} - 16 q^{56} - 32 q^{59} - 24 q^{61} + 8 q^{69} - 16 q^{71} + 48 q^{74} - 48 q^{79} + 4 q^{81} - 4 q^{84} - 8 q^{86} - 24 q^{91} - 16 q^{94}+O(q^{100}) \) 8 * q - 4 * q^11 + 4 * q^16 - 16 * q^19 + 4 * q^24 + 12 * q^26 + 24 * q^31 + 32 * q^34 - 8 * q^36 - 12 * q^39 - 4 * q^46 - 16 * q^51 + 4 * q^54 - 16 * q^56 - 32 * q^59 - 24 * q^61 + 8 * q^69 - 16 * q^71 + 48 * q^74 - 48 * q^79 + 4 * q^81 - 4 * q^84 - 8 * q^86 - 24 * q^91 - 16 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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