LMFDB - Embedded newform 1050.2.bc.f.607.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1050.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 28x^{14} + 519x^{12} - 5404x^{10} + 40705x^{8} - 194544x^{6} + 672624x^{4} - 1306368x^{2} + 1679616 $ x^16 - 28x^14 + 519x^12 - 5404x^10 + 40705x^8 - 194544x^6 + 672624x^4 - 1306368*x^2 + 1679616
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			607.2
Root			$-3.11681 - 1.79949i$ of defining polynomial
Character	$\chi$	$=$	1050.607
Dual form			1050.2.bc.f.493.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(2.63306 - 0.258819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(2.63306 - 0.258819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-2.54487 - 4.40784i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(2.02443 + 2.02443i) q^{13} +(-2.47635 + 0.931486i) q^{14} +(0.500000 - 0.866025i) q^{16} +(6.71580 + 1.79949i) q^{17} +(0.965926 + 0.258819i) q^{18} +(-1.79751 + 3.11338i) q^{19} +(0.431486 - 2.61033i) q^{21} +(3.59899 + 3.59899i) q^{22} +(-1.79949 - 6.71580i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-2.47941 - 1.43149i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(2.15089 - 1.54067i) q^{28} -8.81568i q^{29} +(1.61338 - 0.931486i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-4.91631 + 1.31732i) q^{33} -6.95271 q^{34} -1.00000 q^{36} +(7.50959 - 2.01219i) q^{37} +(0.930461 - 3.47253i) q^{38} +(2.47941 - 1.43149i) q^{39} +4.13703i q^{41} +(0.258819 + 2.63306i) q^{42} +(-7.84163 + 7.84163i) q^{43} +(-4.40784 - 2.54487i) q^{44} +(3.47635 + 6.02122i) q^{46} +(0.482173 + 1.79949i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(6.86603 - 1.36297i) q^{49} +(3.47635 - 6.02122i) q^{51} +(2.76542 + 0.740992i) q^{52} +(0.879247 + 0.235593i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-1.67884 + 2.04487i) q^{56} +(2.54207 + 2.54207i) q^{57} +(2.28167 + 8.51530i) q^{58} +(-2.08974 - 3.61953i) q^{59} +(-5.08277 - 2.93454i) q^{61} +(-1.31732 + 1.31732i) q^{62} +(-2.40971 - 1.09239i) q^{63} -1.00000i q^{64} +(4.40784 - 2.54487i) q^{66} +(0.762637 - 2.84620i) q^{67} +(6.71580 - 1.79949i) q^{68} -6.95271 q^{69} +7.86297 q^{71} +(0.965926 - 0.258819i) q^{72} +(3.50165 - 13.0683i) q^{73} +(-6.73291 + 3.88725i) q^{74} +3.59502i q^{76} +(-7.84163 - 10.9475i) q^{77} +(-2.02443 + 2.02443i) q^{78} +(-10.4700 - 6.04487i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-1.07074 - 3.99606i) q^{82} +(-1.99099 - 1.99099i) q^{83} +(-0.931486 - 2.47635i) q^{84} +(5.54487 - 9.60399i) q^{86} +(-8.51530 - 2.28167i) q^{87} +(4.91631 + 1.31732i) q^{88} +(3.82507 - 6.62522i) q^{89} +(5.85440 + 4.80648i) q^{91} +(-4.91631 - 4.91631i) q^{92} +(-0.482173 - 1.79949i) q^{93} +(-0.931486 - 1.61338i) q^{94} +(0.866025 + 0.500000i) q^{96} +(13.4951 - 13.4951i) q^{97} +(-6.27931 + 3.09359i) 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 $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$			1.00000i			0.408248i
$7$	2.63306	−	0.258819i	0.995204	−	0.0978244i
$7$	2.63306	−	0.258819i	0.995204	−	0.0978244i
$8$	−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	$-0.445070\pi$
$12$	−0.258819	−	0.965926i	−0.0747146	−	0.278839i
$13$	2.02443	+	2.02443i	0.561475	+	0.561475i	0.929726	−	0.368251i	$-0.120043\pi$
$13$	2.02443	+	2.02443i	0.561475	+	0.561475i	−0.368251	+	0.929726i	$0.620043\pi$
$14$	−2.47635	+	0.931486i	−0.661834	+	0.248950i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	6.71580	+	1.79949i	1.62882	+	0.436441i	0.953576	−	0.301152i	$-0.0973712\pi$
$17$	6.71580	+	1.79949i	1.62882	+	0.436441i	0.675245	+	0.737593i	$0.264038\pi$
$18$	0.965926	+	0.258819i	0.227671	+	0.0610042i
$19$	−1.79751	+	3.11338i	−0.412378	+	0.714259i	−0.995149	−	0.0983771i	$-0.968635\pi$
$19$	−1.79751	+	3.11338i	−0.412378	+	0.714259i	0.582772	+	0.812636i	$0.301968\pi$
$20$		0			0
$21$	0.431486	−	2.61033i	0.0941581	−	0.569621i
$22$	3.59899	+	3.59899i	0.767307	+	0.767307i
$23$	−1.79949	−	6.71580i	−0.375220	−	1.40034i	−0.853023	−	0.521874i	$-0.825233\pi$
$23$	−1.79949	−	6.71580i	−0.375220	−	1.40034i	0.477802	−	0.878467i	$-0.341434\pi$
$24$	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
$28$	2.15089	−	1.54067i	0.406480	−	0.291160i
$29$		−	8.81568i		−	1.63703i	−0.574484	−	0.818516i	$-0.694797\pi$
$29$		−	8.81568i		−	1.63703i	0.574484	−	0.818516i	$-0.305203\pi$
$30$		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	$0.279829\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−4.91631	+	1.31732i	−0.855819	+	0.229316i
$34$	−6.95271			−1.19238
$35$		0			0
$36$	−1.00000			−0.166667
$37$	7.50959	−	2.01219i	1.23457	−	0.330802i	0.418212	−	0.908350i	$-0.362657\pi$
$37$	7.50959	−	2.01219i	1.23457	−	0.330802i	0.816357	+	0.577548i	$0.195990\pi$
$38$	0.930461	−	3.47253i	0.150941	−	0.563318i
$39$	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	$0.895293\pi$
$42$	0.258819	+	2.63306i	0.0399366	+	0.406290i
$43$	−7.84163	+	7.84163i	−1.19584	+	1.19584i	−0.220436	+	0.975402i	$0.570748\pi$
$43$	−7.84163	+	7.84163i	−1.19584	+	1.19584i	−0.975402	+	0.220436i	$0.929252\pi$
$44$	−4.40784	−	2.54487i	−0.664507	−	0.383653i
$45$		0			0
$46$	3.47635	+	6.02122i	0.512561	+	0.887781i
$47$	0.482173	+	1.79949i	0.0703321	+	0.262483i	0.992134	−	0.125177i	$-0.0399500\pi$
$47$	0.482173	+	1.79949i	0.0703321	+	0.262483i	−0.921802	+	0.387660i	$0.873283\pi$
$48$	−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
$52$	2.76542	+	0.740992i	0.383495	+	0.102757i
$53$	0.879247	+	0.235593i	0.120774	+	0.0323613i	0.318700	−	0.947856i	$-0.396754\pi$
$53$	0.879247	+	0.235593i	0.120774	+	0.0323613i	−0.197926	+	0.980217i	$0.563421\pi$
$54$	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
$58$	2.28167	+	8.51530i	0.299597	+	1.11811i
$59$	−2.08974	−	3.61953i	−0.272061	−	0.471223i	0.697329	−	0.716751i	$-0.254372\pi$
$59$	−2.08974	−	3.61953i	−0.272061	−	0.471223i	−0.969389	+	0.245529i	$0.921038\pi$
$60$		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
$63$	−2.40971	−	1.09239i	−0.303595	−	0.137628i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	4.40784	−	2.54487i	0.542568	−	0.313252i
$67$	0.762637	−	2.84620i	0.0931710	−	0.347719i	−0.903565	−	0.428451i	$-0.859059\pi$
$67$	0.762637	−	2.84620i	0.0931710	−	0.347719i	0.996736	+	0.0807326i	$0.0257260\pi$
$68$	6.71580	−	1.79949i	0.814411	−	0.218221i
$69$	−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	$0.345485\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	3.50165	−	13.0683i	0.409837	−	1.52953i	−0.385120	−	0.922867i	$-0.625840\pi$
$73$	3.50165	−	13.0683i	0.409837	−	1.52953i	0.794957	−	0.606666i	$-0.207493\pi$
$74$	−6.73291	+	3.88725i	−0.782685	+	0.451883i
$75$		0			0
$76$			3.59502i			0.412378i
$77$	−7.84163	−	10.9475i	−0.893636	−	1.24758i
$78$	−2.02443	+	2.02443i	−0.229221	+	0.229221i
$79$	−10.4700	−	6.04487i	−1.17797	−	0.680101i	−0.222425	−	0.974950i	$-0.571397\pi$
$79$	−10.4700	−	6.04487i	−1.17797	−	0.680101i	−0.955544	+	0.294849i	$0.904731\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−1.07074	−	3.99606i	−0.118244	−	0.441291i
$83$	−1.99099	−	1.99099i	−0.218539	−	0.218539i	0.589343	−	0.807883i	$-0.299387\pi$
$83$	−1.99099	−	1.99099i	−0.218539	−	0.218539i	−0.807883	+	0.589343i	$0.799387\pi$
$84$	−0.931486	−	2.47635i	−0.101634	−	0.270192i
$85$		0			0
$86$	5.54487	−	9.60399i	0.597919	−	1.03563i
$87$	−8.51530	−	2.28167i	−0.912935	−	0.244620i
$88$	4.91631	+	1.31732i	0.524080	+	0.140427i
$89$	3.82507	−	6.62522i	0.405457	−	0.702272i	−0.588918	−	0.808193i	$-0.700446\pi$
$89$	3.82507	−	6.62522i	0.405457	−	0.702272i	0.994375	+	0.105921i	$0.0337792\pi$
$90$		0			0
$91$	5.85440	+	4.80648i	0.613708	+	0.503856i
$92$	−4.91631	−	4.91631i	−0.512561	−	0.512561i
$93$	−0.482173	−	1.79949i	−0.0499990	−	0.186599i
$94$	−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	0.510101	−	0.860115i	$-0.329608\pi$
$97$	13.4951	−	13.4951i	1.37022	−	1.37022i	0.860115	−	0.510101i	$-0.170392\pi$
$98$	−6.27931	+	3.09359i	−0.634306	+	0.312500i
$99$			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	$0.311719\pi$
$102$	−1.79949	+	6.71580i	−0.178176	+	0.664963i
$103$	0.351395	−	0.0941560i	0.0346240	−	0.00927747i	−0.241465	−	0.970409i	$-0.577628\pi$
$103$	0.351395	−	0.0941560i	0.0346240	−	0.00927747i	0.276089	+	0.961132i	$0.410961\pi$
$104$	−2.86297			−0.280738
$105$		0			0
$106$	−0.910263			−0.0884126
$107$	0.205579	−	0.0550849i	0.0198741	−	0.00532525i	−0.248868	−	0.968537i	$-0.580059\pi$
$107$	0.205579	−	0.0550849i	0.0198741	−	0.00532525i	0.268742	+	0.963212i	$0.413392\pi$
$108$	−0.258819	+	0.965926i	−0.0249049	+	0.0929463i
$109$	1.35135	−	0.780202i	0.129436	−	0.0747298i	−0.433884	−	0.900969i	$-0.642857\pi$
$109$	1.35135	−	0.780202i	0.129436	−	0.0747298i	0.563320	+	0.826239i	$0.309524\pi$
$110$		0			0
$111$		−	7.77450i		−	0.737923i
$112$	1.09239	−	2.40971i	0.103221	−	0.227696i
$113$	0.0300140	−	0.0300140i	0.00282348	−	0.00282348i	−0.705694	−	0.708517i	$-0.749364\pi$
$113$	0.0300140	−	0.0300140i	0.00282348	−	0.00282348i	0.708517	+	0.705694i	$0.249364\pi$
$114$	−3.11338	−	1.79751i	−0.291595	−	0.168352i
$115$		0			0
$116$	−4.40784	−	7.63460i	−0.409258	−	0.708855i
$117$	−0.740992	−	2.76542i	−0.0685047	−	0.255663i
$118$	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
$122$	5.66909	+	1.51903i	0.513256	+	0.137526i
$123$	3.99606	+	1.07074i	0.360313	+	0.0965455i
$124$	0.931486	−	1.61338i	0.0836500	−	0.144886i
$125$		0			0
$126$	2.61033	+	0.431486i	0.232547	+	0.0384399i
$127$	−1.42723	−	1.42723i	−0.126646	−	0.126646i	0.640943	−	0.767589i	$-0.278544\pi$
$127$	−1.42723	−	1.42723i	−0.126646	−	0.126646i	−0.767589	+	0.640943i	$0.778544\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	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
$133$	−3.92716	+	8.66296i	−0.340528	+	0.751174i
$134$			2.94660i			0.254548i
$135$		0			0
$136$	−6.02122	+	3.47635i	−0.516316	+	0.298095i
$137$	−5.68916	+	21.2322i	−0.486058	+	1.81399i	0.0891925	+	0.996014i	$0.471571\pi$
$137$	−5.68916	+	21.2322i	−0.486058	+	1.81399i	−0.575250	+	0.817978i	$0.695095\pi$
$138$	6.71580	−	1.79949i	0.571687	−	0.153183i
$139$	16.5902			1.40716			0.703580	−	0.710616i	$-0.251584\pi$
$139$	16.5902			1.40716			0.703580	+	0.710616i	$0.251584\pi$
$140$		0			0
$141$	1.86297			0.156891
$142$	−7.59505	+	2.03509i	−0.637362	+	0.170781i
$143$	3.77145	−	14.0753i	0.315385	−	1.17703i
$144$	−0.866025	+	0.500000i	−0.0721688	+	0.0416667i
$145$		0			0
$146$			13.5293i			1.11970i
$147$	0.460527	−	6.98483i	0.0379837	−	0.576099i
$148$	5.49740	−	5.49740i	0.451883	−	0.451883i
$149$	−8.60723	−	4.96939i	−0.705132	−	0.407108i	0.104124	−	0.994564i	$-0.466796\pi$
$149$	−8.60723	−	4.96939i	−0.705132	−	0.407108i	−0.809256	+	0.587456i	$0.800129\pi$
$150$		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	$0.619158\pi$
$152$	−0.930461	−	3.47253i	−0.0754703	−	0.281659i
$153$	−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
$157$	15.7881	+	4.23040i	1.26003	+	0.337623i	0.826201	−	0.563375i	$-0.190497\pi$
$157$	15.7881	+	4.23040i	1.26003	+	0.337623i	0.433824	+	0.900998i	$0.357164\pi$
$158$	11.6778	+	3.12905i	0.929035	+	0.248934i
$159$	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
$163$	1.93977	+	7.23934i	0.151935	+	0.567029i	0.999348	+	0.0360951i	$0.0114919\pi$
$163$	1.93977	+	7.23934i	0.151935	+	0.567029i	−0.847413	+	0.530933i	$0.821841\pi$
$164$	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	$-0.996694\pi$
$167$	−12.7880	+	12.7880i	−0.989561	+	0.989561i	0.0103848	+	0.999946i	$0.496694\pi$
$168$	1.54067	+	2.15089i	0.118866	+	0.165945i
$169$		−	4.80339i		−	0.369491i
$170$		0			0
$171$	3.11338	−	1.79751i	0.238086	−	0.137459i
$172$	−2.87024	+	10.7119i	−0.218853	+	0.816772i
$173$	−15.6282	+	4.18756i	−1.18819	+	0.318374i	−0.798169	−	0.602433i	$-0.794198\pi$
$173$	−15.6282	+	4.18756i	−1.18819	+	0.318374i	−0.390018	+	0.920807i	$0.627531\pi$
$174$	8.81568			0.668315
$175$		0			0
$176$	−5.08974			−0.383653
$177$	−4.03706	+	1.08173i	−0.303444	+	0.0813076i
$178$	−1.98000	+	7.38947i	−0.148407	+	0.553864i
$179$	−8.60723	+	4.96939i	−0.643335	+	0.371430i	−0.785898	−	0.618356i	$-0.787799\pi$
$179$	−8.60723	+	4.96939i	−0.643335	+	0.371430i	0.142563	+	0.989786i	$0.454466\pi$
$180$		0			0
$181$			2.60285i			0.193468i	0.995310	+	0.0967342i	$0.0308397\pi$
$181$			2.60285i			0.193468i	−0.995310	+	0.0967342i	$0.969160\pi$
$182$	−6.89893	−	3.12747i	−0.511383	−	0.231824i
$183$	−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
$187$	−9.15895	−	34.1817i	−0.669769	−	2.49961i
$188$	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	$0.214489\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	12.5114	+	3.35241i	0.900587	+	0.241312i	0.679268	−	0.733890i	$-0.262297\pi$
$193$	12.5114	+	3.35241i	0.900587	+	0.241312i	0.221319	+	0.975202i	$0.428964\pi$
$194$	−9.54245	+	16.5280i	−0.685108	+	1.18664i
$195$		0			0
$196$	5.26467	−	4.61338i	0.376048	−	0.329527i
$197$	0.876148	+	0.876148i	0.0624229	+	0.0624229i	0.737629	−	0.675206i	$-0.235945\pi$
$197$	0.876148	+	0.876148i	0.0624229	+	0.0624229i	−0.675206	+	0.737629i	$0.735945\pi$
$198$	−1.31732	−	4.91631i	−0.0936179	−	0.349387i
$199$	8.63155	+	14.9503i	0.611875	+	1.05980i	0.990924	+	0.134421i	$0.0429176\pi$
$199$	8.63155	+	14.9503i	0.611875	+	1.05980i	−0.379050	+	0.925376i	$0.623749\pi$
$200$		0			0
$201$	−2.55183	−	1.47330i	−0.179993	−	0.103919i
$202$	−0.964346	+	0.964346i	−0.0678511	+	0.0678511i
$203$	−2.28167	−	23.2122i	−0.160142	−	1.62918i
$204$		−	6.95271i		−	0.486787i
$205$		0			0
$206$	−0.315052	+	0.181895i	−0.0219507	+	0.0126733i
$207$	−1.79949	+	6.71580i	−0.125073	+	0.466780i
$208$	2.76542	−	0.740992i	0.191747	−	0.0513785i
$209$	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	$0.582035\pi$
$212$	0.879247	−	0.235593i	0.0603869	−	0.0161806i
$213$	2.03509	−	7.59505i	0.139442	−	0.520404i
$214$	−0.184318	+	0.106416i	−0.0125997	+	0.00727443i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	4.00705	−	2.87024i	0.272016	−	0.194844i
$218$	−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
$222$	2.01219	+	7.50959i	0.135049	+	0.504011i
$223$	−2.69809	−	2.69809i	−0.180678	−	0.180678i	0.610973	−	0.791651i	$-0.290778\pi$
$223$	−2.69809	−	2.69809i	−0.180678	−	0.180678i	−0.791651	+	0.610973i	$0.790778\pi$
$224$	−0.431486	+	2.61033i	−0.0288299	+	0.174410i
$225$		0			0
$226$	−0.0212231	+	0.0367595i	−0.00141174	+	0.00244520i
$227$	−19.0216	−	5.09682i	−1.26251	−	0.338288i	−0.435351	−	0.900261i	$-0.643376\pi$
$227$	−19.0216	−	5.09682i	−1.26251	−	0.338288i	−0.827155	+	0.561973i	$0.810042\pi$
$228$	3.47253	+	0.930461i	0.229974	+	0.0616213i
$229$	−11.4884	+	19.8985i	−0.759173	+	1.31493i	0.184099	+	0.982908i	$0.441063\pi$
$229$	−11.4884	+	19.8985i	−0.759173	+	1.31493i	−0.943273	+	0.332019i	$0.892270\pi$
$230$		0			0
$231$	−12.6040	+	4.74102i	−0.829282	+	0.311936i
$232$	6.23363	+	6.23363i	0.409258	+	0.409258i
$233$	3.42652	+	12.7880i	0.224479	+	0.837766i	0.982613	+	0.185667i	$0.0594447\pi$
$233$	3.42652	+	12.7880i	0.224479	+	0.837766i	−0.758134	+	0.652099i	$0.773889\pi$
$234$	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
$238$	−18.3069	+	1.79949i	−1.18666	+	0.116644i
$239$			1.65014i			0.106739i	0.998575	+	0.0533694i	$0.0169961\pi$
$239$			1.65014i			0.106739i	−0.998575	+	0.0533694i	$0.983004\pi$
$240$		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	$0.466924\pi$
$242$	3.85781	−	14.3975i	0.247989	−	0.925508i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	−5.86908			−0.375729
$245$		0			0
$246$	−4.13703			−0.263767
$247$	−9.94175	+	2.66388i	−0.632578	+	0.169499i
$248$	−0.482173	+	1.79949i	−0.0306180	+	0.114268i
$249$	−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	$0.924432\pi$
$252$	−2.63306	+	0.258819i	−0.165867	+	0.0163041i
$253$	−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
$257$	4.30494	+	16.0662i	0.268535	+	1.00218i	0.960051	+	0.279824i	$0.0902762\pi$
$257$	4.30494	+	16.0662i	0.268535	+	1.00218i	−0.691517	+	0.722361i	$0.743057\pi$
$258$	−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
$262$	5.12189	+	1.37241i	0.316431	+	0.0847875i
$263$	10.6709	+	2.85925i	0.657994	+	0.176309i	0.572340	−	0.820016i	$-0.306036\pi$
$263$	10.6709	+	2.85925i	0.657994	+	0.176309i	0.0856532	+	0.996325i	$0.472702\pi$
$264$	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
$268$	−0.762637	−	2.84620i	−0.0465855	−	0.173859i
$269$	13.3014	+	23.0387i	0.811002	+	1.40470i	0.912163	+	0.409827i	$0.134411\pi$
$269$	13.3014	+	23.0387i	0.811002	+	1.40470i	−0.101161	+	0.994870i	$0.532256\pi$
$270$		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
$273$	6.15794	−	4.41091i	0.372695	−	0.266960i
$274$		−	21.9812i		−	1.32793i
$275$		0			0
$276$	−6.02122	+	3.47635i	−0.362435	+	0.209252i
$277$	−2.60623	+	9.72658i	−0.156593	+	0.584414i	0.842370	+	0.538899i	$0.181160\pi$
$277$	−2.60623	+	9.72658i	−0.156593	+	0.584414i	−0.998964	+	0.0455149i	$0.985507\pi$
$278$	−16.0249	+	4.29385i	−0.961109	+	0.257528i
$279$	−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	$0.349934\pi$
$282$	−1.79949	+	0.482173i	−0.107158	+	0.0287130i
$283$	3.83878	−	14.3265i	0.228192	−	0.851623i	−0.752909	−	0.658125i	$-0.771350\pi$
$283$	3.83878	−	14.3265i	0.228192	−	0.851623i	0.981101	−	0.193498i	$-0.0619834\pi$
$284$	6.80953	−	3.93149i	0.404072	−	0.233291i
$285$		0			0
$286$			14.5718i			0.861647i
$287$	1.07074	+	10.8930i	0.0632039	+	0.642996i
$288$	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
$292$	−3.50165	−	13.0683i	−0.204918	−	0.764766i
$293$	18.7009	+	18.7009i	1.09252	+	1.09252i	0.995259	+	0.0972583i	$0.0310073\pi$
$293$	18.7009	+	18.7009i	1.09252	+	1.09252i	0.0972583	+	0.995259i	$0.468993\pi$
$294$	1.36297	+	6.86603i	0.0794902	+	0.400435i
$295$		0			0
$296$	−3.88725	+	6.73291i	−0.225942	+	0.391343i
$297$	4.91631	+	1.31732i	0.285273	+	0.0764387i
$298$	9.60012	+	2.57234i	0.556120	+	0.149012i
$299$	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
$303$	−0.352975	−	1.31732i	−0.0202779	−	0.0756781i
$304$	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	−0.345282	+	0.938499i	$0.612217\pi$
$307$	−22.4937	+	22.4937i	−1.28378	+	1.28378i	−0.938499	+	0.345282i	$0.887783\pi$
$308$	−12.2648	−	5.55996i	−0.698851	−	0.316808i
$309$		−	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	$0.178724\pi$
$312$	−0.740992	+	2.76542i	−0.0419504	+	0.156561i
$313$	3.26105	−	0.873796i	0.184325	−	0.0493899i	−0.165476	−	0.986214i	$-0.552916\pi$
$313$	3.26105	−	0.873796i	0.184325	−	0.0493899i	0.349801	+	0.936824i	$0.386249\pi$
$314$	−16.3450			−0.922403
$315$		0			0
$316$	−12.0897			−0.680101
$317$	13.3465	−	3.57619i	0.749614	−	0.200859i	0.136267	−	0.990672i	$-0.456489\pi$
$317$	13.3465	−	3.57619i	0.749614	−	0.200859i	0.613347	+	0.789814i	$0.289823\pi$
$318$	−0.235593	+	0.879247i	−0.0132114	+	0.0493057i
$319$	−38.8581	+	22.4348i	−2.17564	+	1.25610i
$320$		0			0
$321$		−	0.212832i		−	0.0118791i
$322$	10.7119	+	14.9545i	0.596949	+	0.833382i
$323$	−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
$327$	−0.403862	−	1.50724i	−0.0223336	−	0.0833503i
$328$	−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	$0.124292\pi$
$332$	−2.71974	−	0.728752i	−0.149265	−	0.0399955i
$333$	−7.50959	−	2.01219i	−0.411523	−	0.110267i
$334$	9.04245	−	15.6620i	0.494781	−	0.856985i
$335$		0			0
$336$	−2.04487	−	1.67884i	−0.111557	−	0.0915884i
$337$	−6.52431	−	6.52431i	−0.355402	−	0.355402i	0.506713	−	0.862115i	$-0.330860\pi$
$337$	−6.52431	−	6.52431i	−0.355402	−	0.355402i	−0.862115	+	0.506713i	$0.830860\pi$
$338$	1.24321	+	4.63971i	0.0676216	+	0.252367i
$339$	−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
$343$	17.7259	−	5.36585i	0.957109	−	0.289729i
$344$		−	11.0897i		−	0.597919i
$345$		0			0
$346$	14.0118	−	8.08974i	0.753281	−	0.434907i
$347$	−8.13952	+	30.3771i	−0.436952	+	1.63073i	0.299399	+	0.954128i	$0.403214\pi$
$347$	−8.13952	+	30.3771i	−0.436952	+	1.63073i	−0.736351	+	0.676600i	$0.763453\pi$
$348$	−8.51530	+	2.28167i	−0.456468	+	0.122310i
$349$	−28.5083			−1.52601			−0.763006	−	0.646391i	$-0.776278\pi$
$349$	−28.5083			−1.52601			−0.763006	+	0.646391i	$0.776278\pi$
$350$		0			0
$351$	−2.86297			−0.152814
$352$	4.91631	−	1.31732i	0.262040	−	0.0702134i
$353$	−6.04935	+	22.5765i	−0.321974	+	1.20162i	0.595345	+	0.803471i	$0.297016\pi$
$353$	−6.04935	+	22.5765i	−0.321974	+	1.20162i	−0.917319	+	0.398154i	$0.869651\pi$
$354$	3.61953	−	2.08974i	0.192376	−	0.111068i
$355$		0			0
$356$		−	7.65014i		−	0.405457i
$357$	7.59505	−	16.7540i	0.401973	−	0.886716i
$358$	7.02778	−	7.02778i	0.371430	−	0.371430i
$359$	−14.5889	−	8.42292i	−0.769974	−	0.444545i	0.0628915	−	0.998020i	$-0.479968\pi$
$359$	−14.5889	−	8.42292i	−0.769974	−	0.444545i	−0.832865	+	0.553476i	$0.813301\pi$
$360$		0			0
$361$	3.03790	+	5.26180i	0.159890	+	0.276937i
$362$	−0.673667	−	2.51416i	−0.0354072	−	0.132141i
$363$	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
$367$	26.0453	+	6.97882i	1.35955	+	0.364291i	0.863653	−	0.504088i	$-0.168171\pi$
$367$	26.0453	+	6.97882i	1.35955	+	0.364291i	0.495901	+	0.868379i	$0.334838\pi$
$368$	−6.71580	−	1.79949i	−0.350085	−	0.0938051i
$369$	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
$373$	2.66388	+	9.94175i	0.137931	+	0.514764i	0.999969	+	0.00792053i	$0.00252121\pi$
$373$	2.66388	+	9.94175i	0.137931	+	0.514764i	−0.862038	+	0.506844i	$0.830812\pi$
$374$	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
$378$	1.09239	−	2.40971i	0.0561863	−	0.123942i
$379$		−	24.4633i		−	1.25659i	−0.777974	−	0.628297i	$-0.783752\pi$
$379$		−	24.4633i		−	1.25659i	0.777974	−	0.628297i	$-0.216248\pi$
$380$		0			0
$381$	−1.74799	+	1.00920i	−0.0895521	+	0.0517029i
$382$	1.07074	−	3.99606i	0.0547839	−	0.204456i
$383$	−5.96013	+	1.59701i	−0.304549	+	0.0816036i	−0.407857	−	0.913046i	$-0.633724\pi$
$383$	−5.96013	+	1.59701i	−0.304549	+	0.0816036i	0.103308	+	0.994649i	$0.467057\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−12.9527			−0.659276
$387$	10.7119	−	2.87024i	0.544515	−	0.145902i
$388$	4.93953	−	18.4346i	0.250767	−	0.935875i
$389$	11.9344	−	6.89034i	0.605099	−	0.349354i	−0.165946	−	0.986135i	$-0.553068\pi$
$389$	11.9344	−	6.89034i	0.605099	−	0.349354i	0.771045	+	0.636781i	$0.219734\pi$
$390$		0			0
$391$		−	48.3402i		−	2.44467i
$392$	−3.89125	+	5.81878i	−0.196538	+	0.293893i
$393$	−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
$397$	−0.298482	−	1.11395i	−0.0149804	−	0.0559075i	0.958031	−	0.286664i	$-0.0925465\pi$
$397$	−0.298482	−	1.11395i	−0.0149804	−	0.0559075i	−0.973011	+	0.230757i	$0.925880\pi$
$398$	−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	$0.232904\pi$
$402$	2.84620	+	0.762637i	0.141956	+	0.0380369i
$403$	5.15190	+	1.38045i	0.256634	+	0.0687650i
$404$	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
$408$	1.79949	+	6.71580i	0.0890882	+	0.332482i
$409$	−18.2355	−	31.5849i	−0.901690	−	1.56177i	−0.825300	−	0.564694i	$-0.808994\pi$
$409$	−18.2355	−	31.5849i	−0.901690	−	1.56177i	−0.0763896	−	0.997078i	$-0.524339\pi$
$410$		0			0
$411$	19.0363	+	10.9906i	0.938991	+	0.542127i
$412$	0.257239	−	0.257239i	0.0126733	−	0.0126733i
$413$	−6.43921	−	8.98958i	−0.316853	−	0.442348i
$414$		−	6.95271i		−	0.341707i
$415$		0			0
$416$	−2.47941	+	1.43149i	−0.121563	+	0.0701844i
$417$	4.29385	−	16.0249i	0.210271	−	0.784742i
$418$	−17.6742	+	4.73580i	−0.864476	+	0.231636i
$419$	−9.05638			−0.442433			−0.221217	−	0.975225i	$-0.571003\pi$
$419$	−9.05638			−0.442433			−0.221217	+	0.975225i	$0.571003\pi$
$420$		0			0
$421$	10.3149			0.502716			0.251358	−	0.967894i	$-0.419123\pi$
$421$	10.3149			0.502716			0.251358	+	0.967894i	$0.419123\pi$
$422$	7.15230	−	1.91645i	0.348168	−	0.0932914i
$423$	0.482173	−	1.79949i	0.0234440	−	0.0874944i
$424$	−0.788311	+	0.455132i	−0.0382838	+	0.0221031i
$425$		0			0
$426$			7.86297i			0.380962i
$427$	−14.1428	−	6.41130i	−0.684416	−	0.310265i
$428$	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	$0.647486\pi$
$432$	0.258819	+	0.965926i	0.0124524	+	0.0464731i
$433$	17.2780	+	17.2780i	0.830327	+	0.830327i	0.987561	−	0.157235i	$-0.0502579\pi$
$433$	17.2780	+	17.2780i	0.830327	+	0.830327i	−0.157235	+	0.987561i	$0.550258\pi$
$434$	−3.12764	+	3.80953i	−0.150131	+	0.182863i
$435$		0			0
$436$	0.780202	−	1.35135i	0.0373649	−	0.0647179i
$437$	24.1435	+	6.46922i	1.15494	+	0.309465i
$438$	13.0683	+	3.50165i	0.624429	+	0.167315i
$439$	−2.48269	+	4.30015i	−0.118492	+	0.205235i	−0.919170	−	0.393860i	$-0.871139\pi$
$439$	−2.48269	+	4.30015i	−0.118492	+	0.205235i	0.800678	+	0.599095i	$0.204473\pi$
$440$		0			0
$441$	−6.62764	−	2.25264i	−0.315602	−	0.107269i
$442$	−14.0753	−	14.0753i	−0.669492	−	0.669492i
$443$	−3.36339	−	12.5524i	−0.159800	−	0.596380i	−0.998646	−	0.0520128i	$-0.983436\pi$
$443$	−3.36339	−	12.5524i	−0.159800	−	0.596380i	0.838847	−	0.544368i	$-0.183230\pi$
$444$	−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
$448$	−0.258819	−	2.63306i	−0.0122281	−	0.124400i
$449$		−	15.0710i		−	0.711243i	−0.934630	−	0.355621i	$-0.884269\pi$
$449$		−	15.0710i		−	0.711243i	0.934630	−	0.355621i	$-0.115731\pi$
$450$		0			0
$451$	18.2354	−	10.5282i	0.858669	−	0.495753i
$452$	0.0109859	−	0.0409999i	0.000516733	−	0.00192847i
$453$	14.7946	−	3.96420i	0.695111	−	0.186254i
$454$	19.6926			0.924219
$455$		0			0
$456$	−3.59502			−0.168352
$457$	−25.0167	+	6.70321i	−1.17023	+	0.313563i	−0.791046	−	0.611757i	$-0.790463\pi$
$457$	−25.0167	+	6.70321i	−1.17023	+	0.313563i	−0.379187	+	0.925320i	$0.623796\pi$
$458$	5.94682	−	22.1938i	0.277877	−	1.03705i
$459$	−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	$-0.153422\pi$
$462$	10.9475	−	7.84163i	0.509322	−	0.364826i
$463$	29.0870	−	29.0870i	1.35179	−	1.35179i	0.468121	−	0.883664i	$-0.344931\pi$
$463$	29.0870	−	29.0870i	1.35179	−	1.35179i	0.883664	−	0.468121i	$-0.155069\pi$
$464$	−7.63460	−	4.40784i	−0.354428	−	0.204629i
$465$		0			0
$466$	−6.61953	−	11.4654i	−0.306644	−	0.531123i
$467$	7.37127	+	27.5100i	0.341102	+	1.27301i	0.897101	+	0.441826i	$0.145669\pi$
$467$	7.37127	+	27.5100i	0.341102	+	1.27301i	−0.555999	+	0.831183i	$0.687664\pi$
$468$	−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
$472$	4.03706	+	1.08173i	0.185821	+	0.0497905i
$473$	54.5206	+	14.6087i	2.50686	+	0.671711i
$474$	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
$478$	−0.427088	−	1.59391i	−0.0195346	−	0.0729039i
$479$	4.79770	+	8.30986i	0.219212	+	0.379687i	0.954567	−	0.297995i	$-0.0963179\pi$
$479$	4.79770	+	8.30986i	0.219212	+	0.379687i	−0.735355	+	0.677682i	$0.762985\pi$
$480$		0			0
$481$	19.2761	+	11.1291i	0.878917	+	0.507443i
$482$	8.94589	−	8.94589i	0.407474	−	0.407474i
$483$	−18.3069	+	1.79949i	−0.832993	+	0.0818798i
$484$			14.9054i			0.677519i
$485$		0			0
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	3.22698	−	12.0433i	0.146229	−	0.545733i	−0.853469	−	0.521144i	$-0.825506\pi$
$487$	3.22698	−	12.0433i	0.146229	−	0.545733i	0.999698	−	0.0245890i	$-0.00782772\pi$
$488$	5.66909	−	1.51903i	0.256628	−	0.0687632i
$489$	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	$0.194114\pi$
$492$	3.99606	−	1.07074i	0.180156	−	0.0482728i
$493$	15.8638	−	59.2044i	0.714468	−	2.66643i
$494$	8.91353	−	5.14623i	0.401039	−	0.231540i
$495$		0			0
$496$		−	1.86297i		−	0.0836500i
$497$	20.7037	−	2.03509i	0.928687	−	0.0912861i
$498$	1.99099	−	1.99099i	0.0892183	−	0.0892183i
$499$	−2.42441	−	1.39973i	−0.108531	−	0.0626606i	0.444752	−	0.895654i	$-0.353292\pi$
$499$	−2.42441	−	1.39973i	−0.108531	−	0.0626606i	−0.553283	+	0.832993i	$0.686625\pi$
$500$		0			0
$501$	9.04245	+	15.6620i	0.403987	+	0.699725i
$502$	−1.92869	−	7.19797i	−0.0860817	−	0.321261i
$503$	12.1725	+	12.1725i	0.542743	+	0.542743i	0.924332	−	0.381589i	$-0.124623\pi$
$503$	12.1725	+	12.1725i	0.542743	+	0.542743i	−0.381589	+	0.924332i	$0.624623\pi$
$504$	2.47635	−	0.931486i	0.110306	−	0.0414917i
$505$		0			0
$506$	17.6937	−	30.6464i	0.786582	−	1.36240i
$507$	−4.63971	−	1.24321i	−0.206057	−	0.0552128i
$508$	−1.94963	−	0.522401i	−0.0865007	−	0.0231778i
$509$	−10.4503	+	18.1004i	−0.463201	+	0.802287i	−0.999118	−	0.0419830i	$-0.986632\pi$
$509$	−10.4503	+	18.1004i	−0.463201	+	0.802287i	0.535917	+	0.844270i	$0.319966\pi$
$510$		0			0
$511$	5.83772	−	35.3160i	0.258246	−	1.56229i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−0.930461	−	3.47253i	−0.0410808	−	0.153316i
$514$	−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
$518$	−16.7221	+	11.9780i	−0.734726	+	0.526282i
$519$			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	$0.515384\pi$
$522$	2.28167	−	8.51530i	0.0998658	−	0.372704i
$523$	−29.0889	+	7.79435i	−1.27197	+	0.340823i	−0.830785	−	0.556594i	$-0.812108\pi$
$523$	−29.0889	+	7.79435i	−1.27197	+	0.340823i	−0.441184	+	0.897417i	$0.645441\pi$
$524$	−5.30257			−0.231644
$525$		0			0
$526$	−11.0473			−0.481685
$527$	12.5114	−	3.35241i	0.545003	−	0.146033i
$528$	−1.31732	+	4.91631i	−0.0573290	+	0.213955i
$529$	−21.9452	+	12.6701i	−0.954140	+	0.550873i
$530$		0			0
$531$			4.17947i			0.181374i
$532$	0.930461	+	9.46592i	0.0403406	+	0.410400i
$533$	−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
$537$	2.57234	+	9.60012i	0.111005	+	0.414276i
$538$	−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	$0.835853\pi$
$542$	19.6242	+	5.25830i	0.842933	+	0.225863i
$543$	2.51416	+	0.673667i	0.107893	+	0.0289098i
$544$	−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	0.989516	+	0.144420i	$0.0461317\pi$
$547$	26.5205	+	26.5205i	1.13394	+	1.13394i	0.144420	+	0.989516i	$0.453868\pi$
$548$	5.68916	+	21.2322i	0.243029	+	0.906996i
$549$	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
$553$	−29.1327	−	13.2067i	−1.23885	−	0.561605i
$554$		−	10.0697i		−	0.427821i
$555$		0			0
$556$	14.3675	−	8.29509i	0.609318	−	0.351790i
$557$	−1.34960	+	5.03679i	−0.0571845	+	0.213416i	−0.988606	−	0.150527i	$-0.951903\pi$
$557$	−1.34960	+	5.03679i	−0.0571845	+	0.213416i	0.931421	+	0.363943i	$0.118570\pi$
$558$	1.79949	−	0.482173i	0.0761786	−	0.0204120i
$559$	−31.7496			−1.34287
$560$		0			0
$561$	−35.3875			−1.49406
$562$	−14.7079	+	3.94098i	−0.620416	+	0.166240i
$563$	4.01426	−	14.9814i	0.169181	−	0.631392i	−0.828289	−	0.560301i	$-0.810685\pi$
$563$	4.01426	−	14.9814i	0.169181	−	0.631392i	0.997470	−	0.0710904i	$-0.0226479\pi$
$564$	1.61338	−	0.931486i	0.0679356	−	0.0392227i
$565$		0			0
$566$			14.8319i			0.623431i
$567$	1.54067	+	2.15089i	0.0647023	+	0.0903288i
$568$	−5.55996	+	5.55996i	−0.233291	+	0.233291i
$569$	−23.8369	−	13.7622i	−0.999295	−	0.576943i	−0.0912554	−	0.995828i	$-0.529088\pi$
$569$	−23.8369	−	13.7622i	−0.999295	−	0.576943i	−0.908040	+	0.418884i	$0.862421\pi$
$570$		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	$0.852822\pi$
$572$	−3.77145	−	14.0753i	−0.157692	−	0.588516i
$573$	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
$577$	−3.36119	−	0.900627i	−0.139928	−	0.0374936i	0.188175	−	0.982135i	$-0.439743\pi$
$577$	−3.36119	−	0.900627i	−0.139928	−	0.0374936i	−0.328103	+	0.944642i	$0.606409\pi$
$578$	−30.2723	−	8.11143i	−1.25916	−	0.337391i
$579$	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
$583$	−1.19911	−	4.47514i	−0.0496620	−	0.185341i
$584$	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	0.237407	−	0.971410i	$-0.423702\pi$
$587$	29.2873	−	29.2873i	1.20882	−	1.20882i	0.971410	−	0.237407i	$-0.0762975\pi$
$588$	−3.09359	−	6.27931i	−0.127577	−	0.258954i
$589$			6.69743i			0.275963i
$590$		0			0
$591$	1.07306	−	0.619530i	0.0441397	−	0.0254841i
$592$	2.01219	−	7.50959i	0.0827004	−	0.308642i
$593$	12.1553	−	3.25700i	0.499158	−	0.133749i	−0.000451399	−	1.00000i	$-0.500144\pi$
$593$	12.1553	−	3.25700i	0.499158	−	0.133749i	0.499609	+	0.866251i	$0.333477\pi$
$594$	−5.08974			−0.208834
$595$		0			0
$596$	−9.93878			−0.407108
$597$	16.6749	−	4.46802i	0.682457	−	0.182864i
$598$	−5.15190	+	19.2272i	−0.210677	+	0.786257i
$599$	−41.1024	+	23.7305i	−1.67940	+	0.969602i	−0.717355	+	0.696708i	$0.754647\pi$
$599$	−41.1024	+	23.7305i	−1.67940	+	0.969602i	−0.962044	+	0.272894i	$0.912019\pi$
$600$		0			0
$601$		−	39.1953i		−	1.59881i	−0.600792	−	0.799405i	$-0.705148\pi$
$601$		−	39.1953i		−	1.59881i	0.600792	−	0.799405i	$-0.294852\pi$
$602$	12.1143	−	26.7230i	0.493741	−	1.08915i
$603$	−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
$607$	3.46559	+	12.9338i	0.140664	+	0.524965i	0.999910	+	0.0134030i	$0.00426642\pi$
$607$	3.46559	+	12.9338i	0.140664	+	0.524965i	−0.859246	+	0.511562i	$0.829067\pi$
$608$	−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
$612$	−6.71580	−	1.79949i	−0.271470	−	0.0727402i
$613$	−19.9559	−	5.34717i	−0.806012	−	0.215970i	−0.167790	−	0.985823i	$-0.553663\pi$
$613$	−19.9559	−	5.34717i	−0.806012	−	0.215970i	−0.638222	+	0.769853i	$0.720330\pi$
$614$	15.9054	−	27.5490i	0.641890	−	1.11179i
$615$		0			0
$616$	13.2859	+	2.19615i	0.535304	+	0.0884855i
$617$	−3.22631	−	3.22631i	−0.129886	−	0.129886i	0.639175	−	0.769061i	$-0.279276\pi$
$617$	−3.22631	−	3.22631i	−0.129886	−	0.129886i	−0.769061	+	0.639175i	$0.779276\pi$
$618$	0.0941560	+	0.351395i	0.00378751	+	0.0141352i
$619$	−2.10527	−	3.64644i	−0.0846181	−	0.146563i	0.820610	−	0.571488i	$-0.193634\pi$
$619$	−2.10527	−	3.64644i	−0.0846181	−	0.146563i	−0.905228	+	0.424925i	$0.860300\pi$
$620$		0			0
$621$	6.02122	+	3.47635i	0.241623	+	0.139501i
$622$	−11.6431	+	11.6431i	−0.466846	+	0.466846i
$623$	8.35691	−	18.4346i	0.334813	−	0.738567i
$624$		−	2.86297i		−	0.114611i
$625$		0			0
$626$	−2.92378	+	1.68804i	−0.116858	+	0.0674678i
$627$	4.73580	−	17.6742i	0.189130	−	0.705841i
$628$	15.7881	−	4.23040i	0.630013	−	0.168811i
$629$	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	$0.253135\pi$
$632$	11.6778	−	3.12905i	0.464517	−	0.124467i
$633$	−1.91645	+	7.15230i	−0.0761721	+	0.284278i
$634$	−11.9661	+	6.90866i	−0.475236	+	0.274378i
$635$		0			0
$636$		−	0.910263i		−	0.0360943i
$637$	16.6590	+	11.1405i	0.660054	+	0.441404i
$638$	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	$0.903889\pi$
$642$	0.0550849	+	0.205579i	0.00217403	+	0.00811358i
$643$	20.3659	+	20.3659i	0.803153	+	0.803153i	0.983587	−	0.180434i	$-0.0577502\pi$
$643$	20.3659	+	20.3659i	0.803153	+	0.803153i	−0.180434	+	0.983587i	$0.557750\pi$
$644$	−14.2174	−	11.6725i	−0.560243	−	0.459961i
$645$		0			0
$646$	12.4976	−	21.6464i	0.491711	−	0.851668i
$647$	−11.0379	−	2.95760i	−0.433946	−	0.116275i	0.0352321	−	0.999379i	$-0.488783\pi$
$647$	−11.0379	−	2.95760i	−0.433946	−	0.116275i	−0.469178	+	0.883104i	$0.655450\pi$
$648$	−0.965926	−	0.258819i	−0.0379452	−	0.0101674i
$649$	−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
$653$	3.66128	+	13.6641i	0.143277	+	0.534717i	0.999826	+	0.0186516i	$0.00593735\pi$
$653$	3.66128	+	13.6641i	0.143277	+	0.534717i	−0.856549	+	0.516066i	$0.827396\pi$
$654$	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
$658$	−2.87024	−	4.00705i	−0.111893	−	0.156211i
$659$		−	11.7840i		−	0.459038i	−0.973304	−	0.229519i	$-0.926285\pi$
$659$		−	11.7840i		−	0.459038i	0.973304	−	0.229519i	$-0.0737153\pi$
$660$		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	$-0.0450145\pi$
$662$	−1.25000	+	4.66505i	−0.0485825	+	0.181312i
$663$	19.2272	−	5.15190i	0.746721	−	0.200083i
$664$	2.81568			0.109270
$665$		0			0
$666$	7.77450			0.301256
$667$	−59.2044	+	15.8638i	−2.29240	+	0.614247i
$668$	−4.68071	+	17.4687i	−0.181102	+	0.675883i
$669$	−3.30448	+	1.90784i	−0.127758	+	0.0737614i
$670$		0			0
$671$			29.8721i			1.15320i
$672$	2.40971	+	1.09239i	0.0929565	+	0.0421397i
$673$	−23.3048	+	23.3048i	−0.898334	+	0.898334i	−0.995289	−	0.0969544i	$-0.969090\pi$
$673$	−23.3048	+	23.3048i	−0.898334	+	0.898334i	0.0969544	+	0.995289i	$0.469090\pi$
$674$	7.99061	+	4.61338i	0.307787	+	0.177701i
$675$		0			0
$676$	−2.40169	−	4.15985i	−0.0923728	−	0.159994i
$677$	−1.58293	−	5.90757i	−0.0608369	−	0.227046i	0.928813	−	0.370548i	$-0.120830\pi$
$677$	−1.58293	−	5.90757i	−0.0608369	−	0.227046i	−0.989650	+	0.143502i	$0.954164\pi$
$678$	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
$682$	9.15895	+	2.45413i	0.350714	+	0.0939736i
$683$	−27.6574	−	7.41077i	−1.05828	−	0.283565i	−0.312610	−	0.949882i	$-0.601203\pi$
$683$	−27.6574	−	7.41077i	−1.05828	−	0.283565i	−0.745669	+	0.666316i	$0.767870\pi$
$684$	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
$688$	2.87024	+	10.7119i	0.109427	+	0.408386i
$689$	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
$693$	1.31732	+	13.4016i	0.0500409	+	0.509084i
$694$		−	31.4487i		−	1.19378i
$695$		0			0
$696$	7.63460	−	4.40784i	0.289389	−	0.167079i
$697$	−7.44455	+	27.7835i	−0.281983	+	1.05237i
$698$	27.5369	−	7.37848i	1.04229	−	0.279280i
$699$	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	$0.639542\pi$
$702$	2.76542	−	0.740992i	0.104374	−	0.0279669i
$703$	−7.23386	+	26.9971i	−0.272830	+	1.01822i
$704$	−4.40784	+	2.54487i	−0.166127	+	0.0959133i
$705$		0			0
$706$		−	23.3729i		−	0.879650i
$707$	2.93336	−	2.10116i	0.110320	−	0.0790222i
$708$	−2.95533	+	2.95533i	−0.111068	+	0.111068i
$709$	−6.12307	−	3.53516i	−0.229957	−	0.132766i	0.380595	−	0.924742i	$-0.375719\pi$
$709$	−6.12307	−	3.53516i	−0.229957	−	0.132766i	−0.610552	+	0.791976i	$0.709052\pi$
$710$		0			0
$711$	6.04487	+	10.4700i	0.226700	+	0.392656i
$712$	1.98000	+	7.38947i	0.0742037	+	0.276932i
$713$	−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
$717$	1.59391	+	0.427088i	0.0595258	+	0.0159499i
$718$	16.2718	+	4.36002i	0.607259	+	0.162715i
$719$	18.1121	−	31.3711i	0.675467	−	1.16994i	−0.300865	−	0.953667i	$-0.597275\pi$
$719$	18.1121	−	31.3711i	0.675467	−	1.16994i	0.976332	−	0.216277i	$-0.0693914\pi$
$720$		0			0
$721$	0.900875	−	0.338866i	0.0335503	−	0.0126200i
$722$	−4.29624	−	4.29624i	−0.159890	−	0.159890i
$723$	3.27442	+	12.2203i	0.121777	+	0.454478i
$724$	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	$-0.678767\pi$
$727$	8.46215	−	8.46215i	0.313844	−	0.313844i	0.846397	+	0.532553i	$0.178767\pi$
$728$	−7.53838	+	0.740992i	−0.279391	+	0.0274630i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−66.7738	+	38.5519i	−2.46972	+	1.42589i
$732$	−1.51903	+	5.66909i	−0.0561449	+	0.209536i
$733$	−4.51455	+	1.20967i	−0.166749	+	0.0446802i	−0.341228	−	0.939981i	$-0.610843\pi$
$733$	−4.51455	+	1.20967i	−0.166749	+	0.0446802i	0.174479	+	0.984661i	$0.444176\pi$
$734$	−26.9641			−0.995262
$735$		0			0
$736$	6.95271			0.256280
$737$	−14.4864	+	3.88162i	−0.533614	+	0.142981i
$738$	−1.07074	+	3.99606i	−0.0394145	+	0.147097i
$739$	22.4673	−	12.9715i	0.826474	−	0.477165i	−0.0261702	−	0.999658i	$-0.508331\pi$
$739$	22.4673	−	12.9715i	0.826474	−	0.477165i	0.852644	+	0.522493i	$0.174998\pi$
$740$		0			0
$741$			10.2925i			0.378103i
$742$	−2.39678	+	0.235593i	−0.0879885	+	0.00864891i
$743$	33.8328	−	33.8328i	1.24121	−	1.24121i	0.281704	−	0.959501i	$-0.409101\pi$
$743$	33.8328	−	33.8328i	1.24121	−	1.24121i	0.959501	−	0.281704i	$-0.0908995\pi$
$744$	1.61338	+	0.931486i	0.0591494	+	0.0341500i
$745$		0			0
$746$	−5.14623	−	8.91353i	−0.188417	−	0.326347i
$747$	0.728752	+	2.71974i	0.0266637	+	0.0995101i
$748$	−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	$0.225166\pi$
$752$	1.79949	+	0.482173i	0.0656208	+	0.0175830i
$753$	7.19797	+	1.92869i	0.262309	+	0.0702854i
$754$	−12.6195	+	21.8577i	−0.459576	+	0.796009i
$755$		0			0
$756$	−0.431486	+	2.61033i	−0.0156930	+	0.0949368i
$757$	2.56404	+	2.56404i	0.0931915	+	0.0931915i	0.752166	−	0.658974i	$-0.229009\pi$
$757$	2.56404	+	2.56404i	0.0931915	+	0.0931915i	−0.658974	+	0.752166i	$0.729009\pi$
$758$	6.33156	+	23.6297i	0.229973	+	0.858269i
$759$	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
$763$	3.35626	−	2.40408i	0.121505	−	0.0870334i
$764$			4.13703i			0.149672i
$765$		0			0
$766$	5.34371	−	3.08519i	0.193076	−	0.111473i
$767$	3.09696	−	11.5580i	0.111825	−	0.417335i
$768$	−0.965926	+	0.258819i	−0.0348548	+	0.00933933i
$769$	8.35895			0.301431			0.150716	−	0.988577i	$-0.451842\pi$
$769$	8.35895			0.301431			0.150716	+	0.988577i	$0.451842\pi$
$770$		0			0
$771$	16.6330			0.599023
$772$	12.5114	−	3.35241i	0.450294	−	0.120656i
$773$	−2.81515	+	10.5063i	−0.101254	+	0.377885i	−0.997893	−	0.0648769i	$-0.979335\pi$
$773$	−2.81515	+	10.5063i	−0.101254	+	0.377885i	0.896639	+	0.442762i	$0.146001\pi$
$774$	−9.60399	+	5.54487i	−0.345208	+	0.199306i
$775$		0			0
$776$			19.0849i			0.685108i
$777$	−2.01219	−	20.4707i	−0.0721868	−	0.734383i
$778$	−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
$782$	12.5114	+	46.6930i	0.447405	+	1.66974i
$783$	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
$787$	−20.0907	−	5.38330i	−0.716158	−	0.191894i	−0.117701	−	0.993049i	$-0.537552\pi$
$787$	−20.0907	−	5.38330i	−0.716158	−	0.191894i	−0.598457	+	0.801155i	$0.704219\pi$
$788$	1.19684	+	0.320692i	0.0426357	+	0.0114242i
$789$	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
$793$	−4.34894	−	16.2305i	−0.154435	−	0.576361i
$794$	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	$-0.819169\pi$
$797$	−8.60761	+	8.60761i	−0.304897	+	0.304897i	0.538029	+	0.842926i	$0.319169\pi$
$798$	−8.66296	−	3.92716i	−0.306665	−	0.139020i
$799$			12.9527i			0.458234i
$800$		0			0
$801$	−6.62522	+	3.82507i	−0.234091	+	0.135152i
$802$	2.14148	−	7.99212i	0.0756184	−	0.282212i
$803$	−66.5144	+	17.8225i	−2.34724	+	0.628941i
$804$	−2.94660			−0.103919
$805$		0			0
$806$	−5.33364			−0.187869
$807$	25.6964	−	6.88532i	0.904555	−	0.242375i
$808$	−0.352975	+	1.31732i	−0.0124176	+	0.0463432i
$809$	−13.8034	+	7.96939i	−0.485301	+	0.280189i	−0.722623	−	0.691242i	$-0.757064\pi$
$809$	−13.8034	+	7.96939i	−0.485301	+	0.280189i	0.237322	+	0.971431i	$0.423730\pi$
$810$		0			0
$811$		−	23.3056i		−	0.818369i	−0.912452	−	0.409184i	$-0.865813\pi$
$811$		−	23.3056i		−	0.818369i	0.912452	−	0.409184i	$-0.134187\pi$
$812$	−13.5821	−	18.9616i	−0.476638	−	0.665420i
$813$	−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
$817$	−10.3186	−	38.5094i	−0.361001	−	1.34727i
$818$	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	$0.120721\pi$
$822$	−21.2322	−	5.68916i	−0.740559	−	0.198432i
$823$	−31.3528	−	8.40095i	−1.09289	−	0.292839i	−0.333023	−	0.942919i	$-0.608069\pi$
$823$	−31.3528	−	8.40095i	−1.09289	−	0.292839i	−0.759866	+	0.650080i	$0.774736\pi$
$824$	−0.181895	+	0.315052i	−0.00633663	+	0.0109754i
$825$		0			0
$826$	8.54647	+	7.01668i	0.297370	+	0.244141i
$827$	−7.75116	−	7.75116i	−0.269534	−	0.269534i	0.559378	−	0.828913i	$-0.311040\pi$
$827$	−7.75116	−	7.75116i	−0.269534	−	0.269534i	−0.828913	+	0.559378i	$0.811040\pi$
$828$	1.79949	+	6.71580i	0.0625367	+	0.233390i
$829$	2.65278	+	4.59474i	0.0921347	+	0.159582i	0.908409	−	0.418082i	$-0.137298\pi$
$829$	2.65278	+	4.59474i	0.0921347	+	0.159582i	−0.816274	+	0.577664i	$0.803964\pi$
$830$		0			0
$831$	8.72062	+	5.03485i	0.302515	+	0.174657i
$832$	2.02443	−	2.02443i	0.0701844	−	0.0701844i
$833$	48.5635	+	3.20191i	1.68263	+	0.110940i
$834$			16.5902i			0.574471i
$835$		0			0
$836$	15.8463	−	9.14886i	0.548056	−	0.316420i
$837$	−0.482173	+	1.79949i	−0.0166663	+	0.0621996i
$838$	8.74779	−	2.34396i	0.302187	−	0.0809709i
$839$	−2.31971			−0.0800852			−0.0400426	−	0.999198i	$-0.512749\pi$
$839$	−2.31971			−0.0800852			−0.0400426	+	0.999198i	$0.512749\pi$
$840$		0			0
$841$	−48.7163			−1.67987
$842$	−9.96339	+	2.66968i	−0.343361	+	0.0920034i
$843$	3.94098	−	14.7079i	0.135734	−	0.506568i
$844$	−6.41257	+	3.70230i	−0.220730	+	0.127438i
$845$		0			0
$846$			1.86297i			0.0640503i
$847$	−16.2825	+	35.9177i	−0.559473	+	1.23415i
$848$	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
$852$	−2.03509	−	7.59505i	−0.0697209	−	0.260202i
$853$	−25.8556	−	25.8556i	−0.885278	−	0.885278i	0.108787	−	0.994065i	$-0.465303\pi$
$853$	−25.8556	−	25.8556i	−0.885278	−	0.885278i	−0.994065	+	0.108787i	$0.965303\pi$
$854$	15.3202	+	2.53243i	0.524247	+	0.0866579i
$855$		0			0
$856$	−0.106416	+	0.184318i	−0.00363722	+	0.00629984i
$857$	37.0519	+	9.92803i	1.26567	+	0.339135i	0.828370	−	0.560181i	$-0.189269\pi$
$857$	37.0519	+	9.92803i	1.26567	+	0.339135i	0.437299	+	0.899316i	$0.355935\pi$
$858$	14.0753	+	3.77145i	0.480521	+	0.128755i
$859$	−10.5922	+	18.3462i	−0.361400	+	0.625963i	−0.988191	−	0.153224i	$-0.951034\pi$
$859$	−10.5922	+	18.3462i	−0.361400	+	0.625963i	0.626792	+	0.779187i	$0.284368\pi$
$860$		0			0
$861$	10.7990	+	1.78507i	0.368029	+	0.0608351i
$862$	−16.1845	−	16.1845i	−0.551245	−	0.551245i
$863$	−6.19036	−	23.1027i	−0.210722	−	0.786426i	−0.987629	−	0.156810i	$-0.949879\pi$
$863$	−6.19036	−	23.1027i	−0.210722	−	0.786426i	0.776906	−	0.629616i	$-0.216788\pi$
$864$	−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
$868$	2.03509	−	4.48922i	0.0690754	−	0.152374i
$869$			61.5336i			2.08738i
$870$		0			0
$871$	7.30583	−	4.21802i	0.247549	−	0.142922i
$872$	−0.403862	+	1.50724i	−0.0136765	+	0.0510414i
$873$	−18.4346	+	4.93953i	−0.623916	+	0.167178i
$874$	−24.9952			−0.845474
$875$		0			0
$876$	−13.5293			−0.457114
$877$	−50.9006	+	13.6388i	−1.71879	+	0.460549i	−0.977553	−	0.210691i	$-0.932429\pi$
$877$	−50.9006	+	13.6388i	−1.71879	+	0.460549i	−0.741240	+	0.671240i	$0.765762\pi$
$878$	1.28514	−	4.79619i	0.0433712	−	0.161864i
$879$	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	$-0.0422860\pi$
$882$	6.98483	+	0.460527i	0.235192	+	0.0155068i
$883$	−16.6993	+	16.6993i	−0.561977	+	0.561977i	−0.929869	−	0.367892i	$-0.880080\pi$
$883$	−16.6993	+	16.6993i	−0.561977	+	0.561977i	0.367892	+	0.929869i	$0.380080\pi$
$884$	17.2386	+	9.95271i	0.579797	+	0.334746i
$885$		0			0
$886$	6.49758	+	11.2541i	0.218290	+	0.378090i
$887$	10.8924	+	40.6509i	0.365730	+	1.36492i	0.866428	+	0.499301i	$0.166410\pi$
$887$	10.8924	+	40.6509i	0.365730	+	1.36492i	−0.500698	+	0.865622i	$0.666923\pi$
$888$	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
$892$	−3.68567	−	0.987571i	−0.123405	−	0.0330663i
$893$	−6.46922	−	1.73342i	−0.216484	−	0.0580068i
$894$	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
$898$	3.90065	+	14.5574i	0.130166	+	0.485788i
$899$	−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
$903$	17.0857	+	23.8528i	0.568576	+	0.793771i
$904$			0.0424462i			0.00141174i
$905$		0			0
$906$	−13.2645	+	7.65825i	−0.440683	+	0.254428i
$907$	11.6250	−	43.3851i	0.386002	−	1.44058i	−0.450580	−	0.892736i	$-0.648783\pi$
$907$	11.6250	−	43.3851i	0.386002	−	1.44058i	0.836582	−	0.547842i	$-0.184550\pi$
$908$	−19.0216	+	5.09682i	−0.631253	+	0.169144i
$909$	−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	$0.594580\pi$
$912$	3.47253	−	0.930461i	0.114987	−	0.0308106i
$913$	−3.70916	+	13.8428i	−0.122755	+	0.458129i
$914$	22.4294	−	12.9496i	0.741898	−	0.428335i
$915$		0			0
$916$			22.9768i			0.759173i
$917$	−12.7776	−	5.79246i	−0.421955	−	0.191284i
$918$	4.91631	−	4.91631i	0.162262	−	0.162262i
$919$	49.9117	+	28.8165i	1.64643	+	0.950569i	0.978473	+	0.206373i	$0.0661662\pi$
$919$	49.9117	+	28.8165i	1.64643	+	0.950569i	0.667961	+	0.744196i	$0.267167\pi$
$920$		0			0
$921$	15.9054	+	27.5490i	0.524101	+	0.907770i
$922$	5.15190	+	19.2272i	0.169669	+	0.633213i
$923$	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
$927$	−0.351395	−	0.0941560i	−0.0115413	−	0.00309249i
$928$	8.51530	+	2.28167i	0.279528	+	0.0748994i
$929$	22.7211	−	39.3541i	0.745455	−	1.29117i	−0.204527	−	0.978861i	$-0.565566\pi$
$929$	22.7211	−	39.3541i	0.745455	−	1.29117i	0.949982	−	0.312305i	$-0.101101\pi$
$930$		0			0
$931$	−8.09831	+	23.8265i	−0.265411	+	0.780883i
$932$	9.36143	+	9.36143i	0.306644	+	0.306644i
$933$	−4.26167	−	15.9048i	−0.139521	−	0.520699i
$934$	−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	$-0.768102\pi$
$937$	−2.46056	+	2.46056i	−0.0803830	+	0.0803830i	0.665772	+	0.746155i	$0.268102\pi$
$938$	0.762637	+	7.75859i	0.0249010	+	0.253327i
$939$		−	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	$0.250348\pi$
$942$	−4.23040	+	15.7881i	−0.137834	+	0.514403i
$943$	27.7835	−	7.44455i	0.904754	−	0.242428i
$944$	−4.17947			−0.136030
$945$		0			0
$946$	−56.4438			−1.83515
$947$	5.56306	−	1.49062i	0.180775	−	0.0484386i	−0.167296	−	0.985907i	$-0.553503\pi$
$947$	5.56306	−	1.49062i	0.180775	−	0.0484386i	0.348071	+	0.937468i	$0.386837\pi$
$948$	−3.12905	+	11.6778i	−0.101627	+	0.379277i
$949$	33.5447	−	19.3671i	1.08891	−	0.628681i
$950$		0			0
$951$		−	13.8173i		−	0.448057i
$952$	−14.9545	+	10.7119i	−0.484678	+	0.347173i
$953$	−33.0749	+	33.0749i	−1.07140	+	1.07140i	−0.0741531	+	0.997247i	$0.523625\pi$
$953$	−33.0749	+	33.0749i	−1.07140	+	1.07140i	−0.997247	+	0.0741531i	$0.976375\pi$
$954$	0.788311	+	0.455132i	0.0255225	+	0.0147354i
$955$		0			0
$956$	0.825071	+	1.42906i	0.0266847	+	0.0462192i
$957$	11.6131	+	43.3406i	0.375398	+	1.40100i
$958$	−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
$962$	−21.4997	−	5.76084i	−0.693180	−	0.185737i
$963$	−0.205579	−	0.0550849i	−0.00662471	−	0.00177508i
$964$	−6.32570	+	10.9564i	−0.203737	+	0.352883i
$965$		0			0
$966$	17.2174	−	6.47635i	0.553960	−	0.208373i
$967$	12.8181	+	12.8181i	0.412203	+	0.412203i	0.882505	−	0.470302i	$-0.155855\pi$
$967$	12.8181	+	12.8181i	0.412203	+	0.412203i	−0.470302	+	0.882505i	$0.655855\pi$
$968$	−3.85781	−	14.3975i	−0.123995	−	0.462754i
$969$	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
$973$	43.6830	−	4.29385i	1.40041	−	0.137655i
$974$			12.4681i			0.399504i
$975$		0			0
$976$	−5.08277	+	2.93454i	−0.162696	+	0.0939323i
$977$	4.38709	−	16.3729i	0.140356	−	0.523814i	−0.859563	−	0.511030i	$-0.829264\pi$
$977$	4.38709	−	16.3729i	0.140356	−	0.523814i	0.999918	−	0.0127838i	$-0.00406931\pi$
$978$	−7.23934	+	1.93977i	−0.231488	+	0.0620271i
$979$	−38.9372			−1.24444
$980$		0			0
$981$	−1.56040			−0.0498199
$982$	−35.0909	+	9.40258i	−1.11980	+	0.300049i
$983$	−1.27255	+	4.74921i	−0.0405879	+	0.151476i	−0.983246	−	0.182284i	$-0.941651\pi$
$983$	−1.27255	+	4.74921i	−0.0405879	+	0.151476i	0.942658	+	0.333760i	$0.108318\pi$
$984$	−3.58277	+	2.06851i	−0.114215	+	0.0659418i
$985$		0			0
$986$			61.2929i			1.95196i
$987$	4.90532	−	0.482173i	0.156138	−	0.0153477i
$988$	−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	$0.846739\pi$
$992$	0.482173	+	1.79949i	0.0153090	+	0.0571340i
$993$	−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
$997$	13.6569	+	3.65936i	0.432518	+	0.115893i	0.468508	−	0.883459i	$-0.344792\pi$
$997$	13.6569	+	3.65936i	0.432518	+	0.115893i	−0.0359897	+	0.999352i	$0.511458\pi$
$998$	2.70408	+	0.724555i	0.0855960	+	0.0229354i
$999$	−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.f.607.2	yes	16
5.2	odd	4		1050.2.bc.e.943.2	yes	16
5.3	odd	4		1050.2.bc.e.943.3	yes	16
5.4	even	2	inner	1050.2.bc.f.607.3	yes	16
7.3	odd	6		1050.2.bc.e.157.4	yes	16
35.3	even	12	inner	1050.2.bc.f.493.2	yes	16
35.17	even	12	inner	1050.2.bc.f.493.3	yes	16
35.24	odd	6		1050.2.bc.e.157.1	✓	16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

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