LMFDB - Embedded newform 1050.2.bc.e.943.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1050.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 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			943.3
Root			$-3.11681 + 1.79949i$ of defining polynomial
Character	$\chi$	$=$	1050.943
Dual form			1050.2.bc.e.157.4

$q$-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	−0.929726	−	0.368251i	$-0.879957\pi$
$13$	−2.02443	+	2.02443i	−0.561475	+	0.561475i	0.368251	+	0.929726i	$0.379957\pi$
$14$	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	$-0.597371\pi$
$17$	1.79949	−	6.71580i	0.436441	−	1.62882i	0.737593	−	0.675245i	$-0.235962\pi$
$18$	−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	0.521874	−	0.853023i	$-0.325233\pi$
$23$	6.71580	−	1.79949i	1.40034	−	0.375220i	0.878467	+	0.477802i	$0.158566\pi$
$24$	−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	$-0.862657\pi$
$37$	−2.01219	−	7.50959i	−0.330802	−	1.23457i	0.577548	−	0.816357i	$-0.304010\pi$
$38$	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	$-0.929252\pi$
$43$	−7.84163	−	7.84163i	−1.19584	−	1.19584i	−0.220436	−	0.975402i	$-0.570748\pi$
$44$	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	−0.125177	−	0.992134i	$-0.539950\pi$
$47$	1.79949	−	0.482173i	0.262483	−	0.0703321i	0.387660	+	0.921802i	$0.373283\pi$
$48$	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	−0.980217	−	0.197926i	$-0.936579\pi$
$53$	−0.235593	+	0.879247i	−0.0323613	+	0.120774i	0.947856	+	0.318700i	$0.103246\pi$
$54$	−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	0.0807326	−	0.996736i	$-0.474274\pi$
$67$	−2.84620	−	0.762637i	−0.347719	−	0.0931710i	−0.428451	+	0.903565i	$0.640941\pi$
$68$	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	0.922867	−	0.385120i	$-0.125840\pi$
$73$	13.0683	+	3.50165i	1.52953	+	0.409837i	0.606666	+	0.794957i	$0.292507\pi$
$74$	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	−0.589343	−	0.807883i	$-0.700613\pi$
$83$	1.99099	−	1.99099i	0.218539	−	0.218539i	0.807883	+	0.589343i	$0.200613\pi$
$84$	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	$-0.829608\pi$
$97$	−13.4951	−	13.4951i	−1.37022	−	1.37022i	−0.510101	−	0.860115i	$-0.670392\pi$
$98$	−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	0.970409	−	0.241465i	$-0.0776281\pi$
$103$	0.0941560	+	0.351395i	0.00927747	+	0.0346240i	−0.961132	+	0.276089i	$0.910961\pi$
$104$	2.86297			0.280738
$105$		0			0
$106$	−0.910263			−0.0884126
$107$	−0.0550849	−	0.205579i	−0.00532525	−	0.0198741i	0.963212	−	0.268742i	$-0.0866080\pi$
$107$	−0.0550849	−	0.205579i	−0.00532525	−	0.0198741i	−0.968537	+	0.248868i	$0.919941\pi$
$108$	−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	0.708517	−	0.705694i	$-0.249364\pi$
$113$	0.0300140	+	0.0300140i	0.00282348	+	0.00282348i	−0.705694	+	0.708517i	$0.749364\pi$
$114$	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	−0.767589	−	0.640943i	$-0.778544\pi$
$127$	−1.42723	+	1.42723i	−0.126646	+	0.126646i	0.640943	+	0.767589i	$0.278544\pi$
$128$	−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	0.996014	−	0.0891925i	$-0.0284286\pi$
$137$	21.2322	+	5.68916i	1.81399	+	0.486058i	0.817978	+	0.575250i	$0.195095\pi$
$138$	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	$-0.690497\pi$
$157$	4.23040	−	15.7881i	0.337623	−	1.26003i	0.900998	−	0.433824i	$-0.142836\pi$
$158$	−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	−0.530933	−	0.847413i	$-0.678159\pi$
$163$	−7.23934	+	1.93977i	−0.567029	+	0.151935i	−0.0360951	+	0.999348i	$0.511492\pi$
$164$	−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	0.999946	−	0.0103848i	$-0.00330564\pi$
$167$	12.7880	+	12.7880i	0.989561	+	0.989561i	−0.0103848	+	0.999946i	$0.503306\pi$
$168$	−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	$-0.872469\pi$
$173$	−4.18756	−	15.6282i	−0.318374	−	1.18819i	0.602433	−	0.798169i	$-0.294198\pi$
$174$	−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	$0.237703\pi$
$193$	−3.35241	+	12.5114i	−0.241312	+	0.900587i	−0.975202	+	0.221319i	$0.928964\pi$
$194$	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	−0.675206	−	0.737629i	$-0.735945\pi$
$197$	0.876148	−	0.876148i	0.0624229	−	0.0624229i	0.737629	+	0.675206i	$0.235945\pi$
$198$	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	−0.610973	−	0.791651i	$-0.709222\pi$
$223$	2.69809	−	2.69809i	0.180678	−	0.180678i	0.791651	+	0.610973i	$0.209222\pi$
$224$	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	$0.310042\pi$
$227$	−5.09682	+	19.0216i	−0.338288	+	1.26251i	−0.900261	+	0.435351i	$0.856624\pi$
$228$	−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	−0.652099	−	0.758134i	$-0.726111\pi$
$233$	−12.7880	+	3.42652i	−0.837766	+	0.224479i	−0.185667	+	0.982613i	$0.559445\pi$
$234$	−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	0.279824	−	0.960051i	$-0.409724\pi$
$257$	16.0662	−	4.30494i	1.00218	−	0.268535i	0.722361	+	0.691517i	$0.243057\pi$
$258$	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	$0.193964\pi$
$263$	−2.85925	+	10.6709i	−0.176309	+	0.657994i	−0.996325	+	0.0856532i	$0.972702\pi$
$264$	−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	0.538899	−	0.842370i	$-0.318840\pi$
$277$	9.72658	+	2.60623i	0.584414	+	0.156593i	0.0455149	+	0.998964i	$0.485507\pi$
$278$	−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	0.658125	−	0.752909i	$-0.271350\pi$
$283$	14.3265	+	3.83878i	0.851623	+	0.228192i	0.193498	+	0.981101i	$0.438017\pi$
$284$	−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	$0.531007\pi$
$293$	−18.7009	+	18.7009i	−1.09252	+	1.09252i	−0.995259	+	0.0972583i	$0.968993\pi$
$294$	−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	$0.112217\pi$
$307$	22.4937	+	22.4937i	1.28378	+	1.28378i	0.345282	+	0.938499i	$0.387783\pi$
$308$	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	0.986214	−	0.165476i	$-0.0529159\pi$
$313$	0.873796	+	3.26105i	0.0493899	+	0.184325i	−0.936824	+	0.349801i	$0.886249\pi$
$314$	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	$-0.956489\pi$
$317$	−3.57619	−	13.3465i	−0.200859	−	0.749614i	0.789814	−	0.613347i	$-0.210177\pi$
$318$	−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	−0.862115	−	0.506713i	$-0.830860\pi$
$337$	−6.52431	+	6.52431i	−0.355402	+	0.355402i	0.506713	+	0.862115i	$0.330860\pi$
$338$	−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	0.954128	−	0.299399i	$-0.0967861\pi$
$347$	30.3771	+	8.13952i	1.63073	+	0.436952i	0.676600	+	0.736351i	$0.263453\pi$
$348$	−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	−0.398154	−	0.917319i	$-0.630349\pi$
$353$	−22.5765	−	6.04935i	−1.20162	−	0.321974i	−0.803471	+	0.595345i	$0.797016\pi$
$354$	−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	$-0.668171\pi$
$367$	6.97882	−	26.0453i	0.364291	−	1.35955i	0.868379	−	0.495901i	$-0.165162\pi$
$368$	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	−0.506844	−	0.862038i	$-0.669188\pi$
$373$	−9.94175	+	2.66388i	−0.514764	+	0.137931i	−0.00792053	+	0.999969i	$0.502521\pi$
$374$	−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	0.913046	−	0.407857i	$-0.133724\pi$
$383$	−1.59701	−	5.96013i	−0.0816036	−	0.304549i	−0.994649	+	0.103308i	$0.967057\pi$
$384$	−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	−0.286664	−	0.958031i	$-0.592546\pi$
$397$	−1.11395	+	0.298482i	−0.0559075	+	0.0149804i	0.230757	+	0.973011i	$0.425880\pi$
$398$	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	−0.987561	−	0.157235i	$-0.949742\pi$
$433$	−17.2780	+	17.2780i	−0.830327	+	0.830327i	0.157235	+	0.987561i	$0.449742\pi$
$434$	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	0.0520128	−	0.998646i	$-0.483436\pi$
$443$	12.5524	−	3.36339i	0.596380	−	0.159800i	0.544368	+	0.838847i	$0.316770\pi$
$444$	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	$0.123796\pi$
$457$	6.70321	+	25.0167i	0.313563	+	1.17023i	−0.611757	+	0.791046i	$0.709537\pi$
$458$	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	$0.155069\pi$
$463$	29.0870	+	29.0870i	1.35179	+	1.35179i	0.468121	+	0.883664i	$0.344931\pi$
$464$	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	0.441826	−	0.897101i	$-0.354331\pi$
$467$	27.5100	−	7.37127i	1.27301	−	0.341102i	0.831183	+	0.555999i	$0.187664\pi$
$468$	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	−0.0245890	−	0.999698i	$-0.507828\pi$
$487$	−12.0433	−	3.22698i	−0.545733	−	0.146229i	−0.521144	+	0.853469i	$0.674494\pi$
$488$	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	−0.924332	−	0.381589i	$-0.875377\pi$
$503$	−12.1725	+	12.1725i	−0.542743	+	0.542743i	0.381589	+	0.924332i	$0.375377\pi$
$504$	−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	$-0.854559\pi$
$523$	−7.79435	−	29.0889i	−0.340823	−	1.27197i	0.556594	−	0.830785i	$-0.312108\pi$
$524$	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	$-0.453868\pi$
$547$	26.5205	−	26.5205i	1.13394	−	1.13394i	0.989516	−	0.144420i	$-0.0461317\pi$
$548$	−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	0.363943	−	0.931421i	$-0.381430\pi$
$557$	5.03679	+	1.34960i	0.213416	+	0.0571845i	−0.150527	+	0.988606i	$0.548097\pi$
$558$	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	0.560301	−	0.828289i	$-0.310685\pi$
$563$	14.9814	+	4.01426i	0.631392	+	0.169181i	0.0710904	+	0.997470i	$0.477352\pi$
$564$	−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	−0.982135	−	0.188175i	$-0.939743\pi$
$577$	−0.900627	+	3.36119i	−0.0374936	+	0.139928i	0.944642	+	0.328103i	$0.106409\pi$
$578$	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	$-0.923702\pi$
$587$	−29.2873	−	29.2873i	−1.20882	−	1.20882i	−0.237407	−	0.971410i	$-0.576298\pi$
$588$	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	1.00000		0.000451399i	$-0.000143685\pi$
$593$	3.25700	+	12.1553i	0.133749	+	0.499158i	−0.866251	+	0.499609i	$0.833477\pi$
$594$	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	0.0134030	−	0.999910i	$-0.495734\pi$
$607$	12.9338	−	3.46559i	0.524965	−	0.140664i	0.511562	+	0.859246i	$0.329067\pi$
$608$	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	$-0.779670\pi$
$613$	5.34717	−	19.9559i	0.215970	−	0.806012i	0.985823	−	0.167790i	$-0.0536630\pi$
$614$	−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	−0.769061	−	0.639175i	$-0.779276\pi$
$617$	−3.22631	+	3.22631i	−0.129886	+	0.129886i	0.639175	+	0.769061i	$0.279276\pi$
$618$	−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	−0.983587	−	0.180434i	$-0.942250\pi$
$643$	−20.3659	+	20.3659i	−0.803153	+	0.803153i	0.180434	+	0.983587i	$0.442250\pi$
$644$	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	−0.999379	−	0.0352321i	$-0.988783\pi$
$647$	−2.95760	+	11.0379i	−0.116275	+	0.433946i	0.883104	+	0.469178i	$0.155450\pi$
$648$	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	−0.516066	−	0.856549i	$-0.672604\pi$
$653$	−13.6641	+	3.66128i	−0.534717	+	0.143277i	−0.0186516	+	0.999826i	$0.505937\pi$
$654$	−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	0.0969544	−	0.995289i	$-0.469090\pi$
$673$	−23.3048	−	23.3048i	−0.898334	−	0.898334i	−0.995289	+	0.0969544i	$0.969090\pi$
$674$	−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	−0.370548	−	0.928813i	$-0.620830\pi$
$677$	−5.90757	+	1.58293i	−0.227046	+	0.0608369i	0.143502	+	0.989650i	$0.454164\pi$
$678$	−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	$-0.732130\pi$
$683$	7.41077	−	27.6574i	0.283565	−	1.05828i	0.949882	−	0.312610i	$-0.101203\pi$
$684$	−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	0.532553	−	0.846397i	$-0.321233\pi$
$727$	−8.46215	−	8.46215i	−0.313844	−	0.313844i	−0.846397	+	0.532553i	$0.821233\pi$
$728$	−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	0.939981	−	0.341228i	$-0.110843\pi$
$733$	−1.20967	−	4.51455i	−0.0446802	−	0.166749i	−0.984661	+	0.174479i	$0.944176\pi$
$734$	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	$0.0908995\pi$
$743$	33.8328	+	33.8328i	1.24121	+	1.24121i	0.281704	+	0.959501i	$0.409101\pi$
$744$	−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	−0.658974	−	0.752166i	$-0.729009\pi$
$757$	2.56404	−	2.56404i	0.0931915	−	0.0931915i	0.752166	+	0.658974i	$0.229009\pi$
$758$	−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	0.0648769	−	0.997893i	$-0.479335\pi$
$773$	−10.5063	−	2.81515i	−0.377885	−	0.101254i	−0.442762	+	0.896639i	$0.646001\pi$
$774$	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	$0.204219\pi$
$787$	−5.38330	+	20.0907i	−0.191894	+	0.716158i	−0.993049	+	0.117701i	$0.962448\pi$
$788$	−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	0.842926	−	0.538029i	$-0.180831\pi$
$797$	8.60761	+	8.60761i	0.304897	+	0.304897i	−0.538029	+	0.842926i	$0.680831\pi$
$798$	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	$-0.725264\pi$
$823$	8.40095	−	31.3528i	0.292839	−	1.09289i	0.942919	−	0.333023i	$-0.108069\pi$
$824$	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	−0.828913	−	0.559378i	$-0.811040\pi$
$827$	−7.75116	+	7.75116i	−0.269534	+	0.269534i	0.559378	+	0.828913i	$0.311040\pi$
$828$	−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	−0.108787	−	0.994065i	$-0.534697\pi$
$853$	25.8556	−	25.8556i	0.885278	−	0.885278i	0.994065	+	0.108787i	$0.0346967\pi$
$854$	−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	$-0.689269\pi$
$857$	9.92803	−	37.0519i	0.339135	−	1.26567i	0.899316	−	0.437299i	$-0.144065\pi$
$858$	−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	0.156810	−	0.987629i	$-0.449879\pi$
$863$	23.1027	−	6.19036i	0.786426	−	0.210722i	0.629616	+	0.776906i	$0.283212\pi$
$864$	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	$0.265762\pi$
$877$	13.6388	+	50.9006i	0.460549	+	1.71879i	−0.210691	+	0.977553i	$0.567571\pi$
$878$	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	0.367892	−	0.929869i	$-0.380080\pi$
$883$	−16.6993	−	16.6993i	−0.561977	−	0.561977i	−0.929869	+	0.367892i	$0.880080\pi$
$884$	−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	0.499301	−	0.866428i	$-0.333590\pi$
$887$	40.6509	−	10.8924i	1.36492	−	0.365730i	0.865622	+	0.500698i	$0.166923\pi$
$888$	−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	−0.547842	−	0.836582i	$-0.684550\pi$
$907$	−43.3851	−	11.6250i	−1.44058	−	0.386002i	−0.892736	+	0.450580i	$0.851217\pi$
$908$	−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	0.746155	−	0.665772i	$-0.231898\pi$
$937$	2.46056	+	2.46056i	0.0803830	+	0.0803830i	−0.665772	+	0.746155i	$0.731898\pi$
$938$	−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	0.937468	−	0.348071i	$-0.113163\pi$
$947$	−1.49062	−	5.56306i	−0.0484386	−	0.180775i	−0.985907	+	0.167296i	$0.946497\pi$
$948$	−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	$-0.976375\pi$
$953$	−33.0749	−	33.0749i	−1.07140	−	1.07140i	−0.0741531	−	0.997247i	$-0.523625\pi$
$954$	−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	−0.470302	−	0.882505i	$-0.655855\pi$
$967$	12.8181	−	12.8181i	0.412203	−	0.412203i	0.882505	+	0.470302i	$0.155855\pi$
$968$	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	−0.0127838	−	0.999918i	$-0.504069\pi$
$977$	−16.3729	−	4.38709i	−0.523814	−	0.140356i	−0.511030	+	0.859563i	$0.670736\pi$
$978$	−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	0.182284	−	0.983246i	$-0.441651\pi$
$983$	−4.74921	−	1.27255i	−0.151476	−	0.0405879i	−0.333760	+	0.942658i	$0.608318\pi$
$984$	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	−0.883459	−	0.468508i	$-0.844792\pi$
$997$	3.65936	−	13.6569i	0.115893	−	0.432518i	0.999352	+	0.0359897i	$0.0114584\pi$
$998$	−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.943.3	yes	16
5.2	odd	4		1050.2.bc.f.607.2	yes	16
5.3	odd	4		1050.2.bc.f.607.3	yes	16
5.4	even	2	inner	1050.2.bc.e.943.2	yes	16
7.3	odd	6		1050.2.bc.f.493.2	yes	16
35.3	even	12	inner	1050.2.bc.e.157.1	✓	16
35.17	even	12	inner	1050.2.bc.e.157.4	yes	16
35.24	odd	6		1050.2.bc.f.493.3	yes	16

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

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Representations

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Database

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