LMFDB - Embedded newform 475.2.l.f.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(101,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("475.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (of order $9$, degree $6$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			101.2
Character	$\chi$	$=$	475.101
Dual form			475.2.l.f.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36714 + 1.14717i) q^{2} +(2.24001 + 0.815296i) q^{3} +(0.205786 - 1.16707i) q^{4} +(-3.99769 + 1.45504i) q^{6} +(2.11955 - 3.67118i) q^{7} +(-0.727188 - 1.25953i) q^{8} +(2.05480 + 1.72418i) q^{9} +O(q^{10})$	\(q+(-1.36714 + 1.14717i) q^{2} +(2.24001 + 0.815296i) q^{3} +(0.205786 - 1.16707i) q^{4} +(-3.99769 + 1.45504i) q^{6} +(2.11955 - 3.67118i) q^{7} +(-0.727188 - 1.25953i) q^{8} +(2.05480 + 1.72418i) q^{9} +(0.245445 + 0.425123i) q^{11} +(1.41247 - 2.44648i) q^{12} +(3.91099 - 1.42349i) q^{13} +(1.31373 + 7.45051i) q^{14} +(4.66628 + 1.69839i) q^{16} +(1.55982 - 1.30884i) q^{17} -4.78713 q^{18} +(1.86816 + 3.93827i) q^{19} +(7.74092 - 6.49540i) q^{21} +(-0.823245 - 0.299637i) q^{22} +(-0.763227 + 4.32847i) q^{23} +(-0.602020 - 3.41422i) q^{24} +(-3.71391 + 6.43268i) q^{26} +(-0.378606 - 0.655764i) q^{27} +(-3.84835 - 3.22915i) q^{28} +(-2.49937 - 2.09722i) q^{29} +(-2.04416 + 3.54059i) q^{31} +(-5.59447 + 2.03622i) q^{32} +(0.203197 + 1.15239i) q^{33} +(-0.631029 + 3.57874i) q^{34} +(2.43509 - 2.04328i) q^{36} +2.14440 q^{37} +(-7.07191 - 3.24108i) q^{38} +9.92123 q^{39} +(-4.10271 - 1.49327i) q^{41} +(-3.13162 + 17.7603i) q^{42} +(-1.84485 - 10.4627i) q^{43} +(0.546658 - 0.198967i) q^{44} +(-3.92205 - 6.79319i) q^{46} +(-2.00812 - 1.68502i) q^{47} +(9.06781 + 7.60880i) q^{48} +(-5.48502 - 9.50033i) q^{49} +(4.56109 - 1.66010i) q^{51} +(-0.856482 - 4.85735i) q^{52} +(-1.98551 + 11.2604i) q^{53} +(1.26988 + 0.462199i) q^{54} -6.16526 q^{56} +(0.973843 + 10.3449i) q^{57} +5.82287 q^{58} +(-0.415431 + 0.348588i) q^{59} +(-2.36895 + 13.4350i) q^{61} +(-1.26700 - 7.18550i) q^{62} +(10.6850 - 3.88903i) q^{63} +(0.346803 - 0.600680i) q^{64} +(-1.59978 - 1.34238i) q^{66} +(5.48257 + 4.60042i) q^{67} +(-1.20652 - 2.08976i) q^{68} +(-5.23862 + 9.07356i) q^{69} +(1.04859 + 5.94684i) q^{71} +(0.677426 - 3.84187i) q^{72} +(1.93031 + 0.702575i) q^{73} +(-2.93170 + 2.45999i) q^{74} +(4.98069 - 1.36984i) q^{76} +2.08093 q^{77} +(-13.5637 + 11.3813i) q^{78} +(-5.01823 - 1.82649i) q^{79} +(-1.71079 - 9.70238i) q^{81} +(7.32202 - 2.66500i) q^{82} +(4.05789 - 7.02847i) q^{83} +(-5.98763 - 10.3709i) q^{84} +(14.5246 + 12.1876i) q^{86} +(-3.88876 - 6.73553i) q^{87} +(0.356969 - 0.618288i) q^{88} +(4.07920 - 1.48471i) q^{89} +(3.06370 - 17.3751i) q^{91} +(4.89458 + 1.78148i) q^{92} +(-7.46558 + 6.26436i) q^{93} +4.67839 q^{94} -14.1918 q^{96} +(-4.32562 + 3.62962i) q^{97} +(18.3973 + 6.69607i) q^{98} +(-0.228649 + 1.29673i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9}+O(q^{10}) $ 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9	$ 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 42 q^{16} - 12 q^{19} - 54 q^{21} - 24 q^{24} + 12 q^{26} - 42 q^{31} + 36 q^{34} + 18 q^{36} + 48 q^{39} + 6 q^{41} + 6 q^{44} - 6 q^{46} - 12 q^{49} + 108 q^{51} - 24 q^{54} + 36 q^{56} + 36 q^{59} + 48 q^{61} + 180 q^{66} - 66 q^{69} - 24 q^{71} - 84 q^{74} + 66 q^{76} - 48 q^{79} - 78 q^{81} + 54 q^{84} - 42 q^{86} + 12 q^{89} - 30 q^{91} + 72 q^{94} - 240 q^{96} + 36 q^{99}+O(q^{100}) $ 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 42 * q^16 - 12 * q^19 - 54 * q^21 - 24 * q^24 + 12 * q^26 - 42 * q^31 + 36 * q^34 + 18 * q^36 + 48 * q^39 + 6 * q^41 + 6 * q^44 - 6 * q^46 - 12 * q^49 + 108 * q^51 - 24 * q^54 + 36 * q^56 + 36 * q^59 + 48 * q^61 + 180 * q^66 - 66 * q^69 - 24 * q^71 - 84 * q^74 + 66 * q^76 - 48 * q^79 - 78 * q^81 + 54 * q^84 - 42 * q^86 + 12 * q^89 - 30 * q^91 + 72 * q^94 - 240 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−1.36714	+	1.14717i	−0.966716	+	0.811171i	−0.982033	−	0.188712i	$-0.939569\pi$
$2$	−1.36714	+	1.14717i	−0.966716	+	0.811171i	0.0153165	+	0.999883i	$0.495124\pi$
$3$	2.24001	+	0.815296i	1.29327	+	0.470712i	0.894799	−	0.446469i	$-0.147319\pi$
$3$	2.24001	+	0.815296i	1.29327	+	0.470712i	0.398471	+	0.917181i	$0.369541\pi$
$4$	0.205786	−	1.16707i	0.102893	−	0.583536i
$5$		0			0
$5$		0			0
$6$	−3.99769	+	1.45504i	−1.63205	+	0.594018i
$7$	2.11955	−	3.67118i	0.801116	−	1.38757i	−0.117766	−	0.993041i	$-0.537573\pi$
$7$	2.11955	−	3.67118i	0.801116	−	1.38757i	0.918882	−	0.394532i	$-0.129093\pi$
$8$	−0.727188	−	1.25953i	−0.257100	−	0.445310i
$9$	2.05480	+	1.72418i	0.684932	+	0.574726i
$10$		0			0
$11$	0.245445	+	0.425123i	0.0740043	+	0.128179i	0.900653	−	0.434539i	$-0.143089\pi$
$11$	0.245445	+	0.425123i	0.0740043	+	0.128179i	−0.826649	+	0.562719i	$0.809755\pi$
$12$	1.41247	−	2.44648i	0.407746	−	0.706237i
$13$	3.91099	−	1.42349i	1.08471	−	0.394804i	0.263054	−	0.964781i	$-0.415270\pi$
$13$	3.91099	−	1.42349i	1.08471	−	0.394804i	0.821661	+	0.569977i	$0.193048\pi$
$14$	1.31373	+	7.45051i	0.351108	+	1.99123i
$15$		0			0
$16$	4.66628	+	1.69839i	1.16657	+	0.424596i
$17$	1.55982	−	1.30884i	0.378311	−	0.317440i	−0.433728	−	0.901044i	$-0.642802\pi$
$17$	1.55982	−	1.30884i	0.378311	−	0.317440i	0.812039	+	0.583603i	$0.198358\pi$
$18$	−4.78713			−1.12834
$19$	1.86816	+	3.93827i	0.428586	+	0.903501i
$19$	1.86816	+	3.93827i	0.428586	+	0.903501i
$20$		0			0
$21$	7.74092	−	6.49540i	1.68921	−	1.41741i
$22$	−0.823245	−	0.299637i	−0.175517	−	0.0638828i
$23$	−0.763227	+	4.32847i	−0.159144	+	0.902549i	0.795755	+	0.605618i	$0.207074\pi$
$23$	−0.763227	+	4.32847i	−0.159144	+	0.902549i	−0.954899	+	0.296931i	$0.904037\pi$
$24$	−0.602020	−	3.41422i	−0.122887	−	0.696925i
$25$		0			0
$26$	−3.71391	+	6.43268i	−0.728358	+	1.26155i
$27$	−0.378606	−	0.655764i	−0.0728627	−	0.126202i
$28$	−3.84835	−	3.22915i	−0.727270	−	0.610252i
$29$	−2.49937	−	2.09722i	−0.464122	−	0.389445i	0.380523	−	0.924772i	$-0.375744\pi$
$29$	−2.49937	−	2.09722i	−0.464122	−	0.389445i	−0.844645	+	0.535327i	$0.820188\pi$
$30$		0			0
$31$	−2.04416	+	3.54059i	−0.367143	+	0.635909i	−0.989118	−	0.147128i	$-0.952997\pi$
$31$	−2.04416	+	3.54059i	−0.367143	+	0.635909i	0.621975	+	0.783037i	$0.286331\pi$
$32$	−5.59447	+	2.03622i	−0.988972	+	0.359956i
$33$	0.203197	+	1.15239i	0.0353721	+	0.200605i
$34$	−0.631029	+	3.57874i	−0.108221	+	0.613750i
$35$		0			0
$36$	2.43509	−	2.04328i	0.405849	−	0.340547i
$37$	2.14440			0.352538			0.176269	−	0.984342i	$-0.443597\pi$
$37$	2.14440			0.352538			0.176269	+	0.984342i	$0.443597\pi$
$38$	−7.07191	−	3.24108i	−1.14721	−	0.525772i
$39$	9.92123			1.58867
$40$		0			0
$41$	−4.10271	−	1.49327i	−0.640736	−	0.233209i	0.00116142	−	0.999999i	$-0.499630\pi$
$41$	−4.10271	−	1.49327i	−0.640736	−	0.233209i	−0.641897	+	0.766790i	$0.721853\pi$
$42$	−3.13162	+	17.7603i	−0.483219	+	2.74047i
$43$	−1.84485	−	10.4627i	−0.281337	−	1.59554i	−0.718085	−	0.695956i	$-0.754981\pi$
$43$	−1.84485	−	10.4627i	−0.281337	−	1.59554i	0.436748	−	0.899584i	$-0.356130\pi$
$44$	0.546658	−	0.198967i	0.0824118	−	0.0299955i
$45$		0			0
$46$	−3.92205	−	6.79319i	−0.578275	−	1.00160i
$47$	−2.00812	−	1.68502i	−0.292915	−	0.245785i	0.484473	−	0.874806i	$-0.339011\pi$
$47$	−2.00812	−	1.68502i	−0.292915	−	0.245785i	−0.777388	+	0.629021i	$0.783456\pi$
$48$	9.06781	+	7.60880i	1.30883	+	1.09824i
$49$	−5.48502	−	9.50033i	−0.783574	−	1.35719i
$50$		0			0
$51$	4.56109	−	1.66010i	0.638681	−	0.232461i
$52$	−0.856482	−	4.85735i	−0.118773	−	0.673593i
$53$	−1.98551	+	11.2604i	−0.272730	+	1.54673i	0.473350	+	0.880874i	$0.343045\pi$
$53$	−1.98551	+	11.2604i	−0.272730	+	1.54673i	−0.746080	+	0.665856i	$0.768066\pi$
$54$	1.26988	+	0.462199i	0.172809	+	0.0628973i
$55$		0			0
$56$	−6.16526			−0.823867
$57$	0.973843	+	10.3449i	0.128989	+	1.37021i
$58$	5.82287			0.764581
$59$	−0.415431	+	0.348588i	−0.0540845	+	0.0453823i	−0.669429	−	0.742876i	$-0.733461\pi$
$59$	−0.415431	+	0.348588i	−0.0540845	+	0.0453823i	0.615345	+	0.788258i	$0.289017\pi$
$60$		0			0
$61$	−2.36895	+	13.4350i	−0.303313	+	1.72018i	0.328026	+	0.944669i	$0.393617\pi$
$61$	−2.36895	+	13.4350i	−0.303313	+	1.72018i	−0.631339	+	0.775507i	$0.717494\pi$
$62$	−1.26700	−	7.18550i	−0.160909	−	0.912559i
$63$	10.6850	−	3.88903i	1.34619	−	0.489972i
$64$	0.346803	−	0.600680i	0.0433503	−	0.0750850i
$65$		0			0
$66$	−1.59978	−	1.34238i	−0.196920	−	0.165235i
$67$	5.48257	+	4.60042i	0.669802	+	0.562031i	0.913007	−	0.407944i	$-0.133754\pi$
$67$	5.48257	+	4.60042i	0.669802	+	0.562031i	−0.243205	+	0.969975i	$0.578199\pi$
$68$	−1.20652	−	2.08976i	−0.146312	−	0.253421i
$69$	−5.23862	+	9.07356i	−0.630656	+	1.09233i
$70$		0			0
$71$	1.04859	+	5.94684i	0.124444	+	0.705760i	0.981636	+	0.190762i	$0.0610960\pi$
$71$	1.04859	+	5.94684i	0.124444	+	0.705760i	−0.857192	+	0.514997i	$0.827793\pi$
$72$	0.677426	−	3.84187i	0.0798354	−	0.452769i
$73$	1.93031	+	0.702575i	0.225925	+	0.0822302i	0.452503	−	0.891763i	$-0.350531\pi$
$73$	1.93031	+	0.702575i	0.225925	+	0.0822302i	−0.226577	+	0.973993i	$0.572754\pi$
$74$	−2.93170	+	2.45999i	−0.340804	+	0.285968i
$75$		0			0
$76$	4.98069	−	1.36984i	0.571324	−	0.157131i
$77$	2.08093			0.237144
$78$	−13.5637	+	11.3813i	−1.53579	+	1.28868i
$79$	−5.01823	−	1.82649i	−0.564595	−	0.205496i	0.0439240	−	0.999035i	$-0.486014\pi$
$79$	−5.01823	−	1.82649i	−0.564595	−	0.205496i	−0.608519	+	0.793539i	$0.708236\pi$
$80$		0			0
$81$	−1.71079	−	9.70238i	−0.190088	−	1.07804i
$82$	7.32202	−	2.66500i	0.808582	−	0.294300i
$83$	4.05789	−	7.02847i	0.445411	−	0.771475i	−0.552669	−	0.833401i	$-0.686391\pi$
$83$	4.05789	−	7.02847i	0.445411	−	0.771475i	0.998081	+	0.0619255i	$0.0197241\pi$
$84$	−5.98763	−	10.3709i	−0.653304	−	1.13156i
$85$		0			0
$86$	14.5246	+	12.1876i	1.56623	+	1.31422i
$87$	−3.88876	−	6.73553i	−0.416919	−	0.722125i
$88$	0.356969	−	0.618288i	0.0380530	−	0.0659097i
$89$	4.07920	−	1.48471i	0.432394	−	0.157379i	−0.116648	−	0.993173i	$-0.537215\pi$
$89$	4.07920	−	1.48471i	0.432394	−	0.157379i	0.549042	+	0.835795i	$0.314993\pi$
$90$		0			0
$91$	3.06370	−	17.3751i	0.321163	−	1.82141i
$92$	4.89458	+	1.78148i	0.510296	+	0.185732i
$93$	−7.46558	+	6.26436i	−0.774144	+	0.649584i
$94$	4.67839			0.482539
$95$		0			0
$96$	−14.1918			−1.44844
$97$	−4.32562	+	3.62962i	−0.439200	+	0.368533i	−0.835410	−	0.549627i	$-0.814770\pi$
$97$	−4.32562	+	3.62962i	−0.439200	+	0.368533i	0.396210	+	0.918160i	$0.370325\pi$
$98$	18.3973	+	6.69607i	1.85841	+	0.676405i
$99$	−0.228649	+	1.29673i	−0.0229801	+	0.130326i
$100$		0			0
$101$	3.10176	−	1.12895i	0.308637	−	0.112335i	−0.183058	−	0.983102i	$-0.558600\pi$
$101$	3.10176	−	1.12895i	0.308637	−	0.112335i	0.491695	+	0.870767i	$0.336378\pi$
$102$	−4.33125	+	7.50194i	−0.428858	+	0.742803i
$103$	−1.70783	−	2.95805i	−0.168278	−	0.291466i	0.769537	−	0.638603i	$-0.220487\pi$
$103$	−1.70783	−	2.95805i	−0.168278	−	0.291466i	−0.937814	+	0.347137i	$0.887154\pi$
$104$	−4.63695	−	3.89086i	−0.454690	−	0.381530i
$105$		0			0
$106$	−10.2031	−	17.6722i	−0.991010	−	1.71648i
$107$	−0.876258	+	1.51772i	−0.0847110	+	0.146724i	−0.905268	−	0.424841i	$-0.860330\pi$
$107$	−0.876258	+	1.51772i	−0.0847110	+	0.146724i	0.820557	+	0.571565i	$0.193663\pi$
$108$	−0.843237	+	0.306913i	−0.0811405	+	0.0295327i
$109$	−0.611108	−	3.46576i	−0.0585335	−	0.331960i	0.941453	−	0.337144i	$-0.109461\pi$
$109$	−0.611108	−	3.46576i	−0.0585335	−	0.331960i	−0.999987	+	0.00518405i	$0.998350\pi$
$110$		0			0
$111$	4.80348	+	1.74832i	0.455926	+	0.165944i
$112$	16.1255	−	13.5309i	1.52372	−	1.27855i
$113$	−13.2583			−1.24723			−0.623616	−	0.781731i	$-0.714337\pi$
$113$	−13.2583			−1.24723			−0.623616	+	0.781731i	$0.714337\pi$
$114$	−13.1987	−	13.0257i	−1.23617	−	1.21997i
$115$		0			0
$116$	−2.96195	+	2.48537i	−0.275010	+	0.230761i
$117$	10.4906	+	3.81828i	0.969860	+	0.353000i
$118$	0.168064	−	0.953138i	0.0154715	−	0.0877435i
$119$	−1.49887	−	8.50051i	−0.137401	−	0.779241i
$120$		0			0
$121$	5.37951	−	9.31759i	0.489047	−	0.847054i
$122$	−12.1735	−	21.0852i	−1.10214	−	1.90896i
$123$	−7.97266	−	6.68985i	−0.718870	−	0.603204i
$124$	3.71147	+	3.11429i	0.333300	+	0.279672i
$125$		0			0
$126$	−10.1466	+	17.5744i	−0.903929	+	1.56565i
$127$	−18.6136	+	6.77480i	−1.65169	+	0.601166i	−0.989025	−	0.147749i	$-0.952797\pi$
$127$	−18.6136	+	6.77480i	−1.65169	+	0.601166i	−0.662666	+	0.748915i	$0.730575\pi$
$128$	−1.85268	−	10.5071i	−0.163755	−	0.928702i
$129$	4.39769	−	24.9405i	0.387195	−	2.19589i
$130$		0			0
$131$	−2.62756	+	2.20479i	−0.229571	+	0.192633i	−0.750316	−	0.661079i	$-0.770099\pi$
$131$	−2.62756	+	2.20479i	−0.229571	+	0.192633i	0.520745	+	0.853712i	$0.325654\pi$
$132$	1.38674			0.120700
$133$	18.4178	+	1.48902i	1.59702	+	0.129115i
$134$	−12.7729			−1.10341
$135$		0			0
$136$	−2.78280	−	1.01286i	−0.238623	−	0.0868517i
$137$	−0.105629	+	0.599055i	−0.00902454	+	0.0511807i	−0.988987	−	0.147999i	$-0.952717\pi$
$137$	−0.105629	+	0.599055i	−0.00902454	+	0.0511807i	0.979963	+	0.199180i	$0.0638278\pi$
$138$	−3.24696	−	18.4144i	−0.276400	−	1.56754i
$139$	7.94791	−	2.89280i	0.674133	−	0.245364i	0.0178066	−	0.999841i	$-0.494332\pi$
$139$	7.94791	−	2.89280i	0.674133	−	0.245364i	0.656326	+	0.754477i	$0.272109\pi$
$140$		0			0
$141$	−3.12443	−	5.41167i	−0.263124	−	0.455744i
$142$	−8.25560	−	6.92727i	−0.692794	−	0.581324i
$143$	1.56509	+	1.31327i	0.130879	+	0.109821i
$144$	6.65993	+	11.5353i	0.554994	+	0.961278i
$145$		0			0
$146$	−3.44498	+	1.25387i	−0.285109	+	0.103771i
$147$	−4.54090	−	25.7527i	−0.374527	−	2.12405i
$148$	0.441289	−	2.50267i	0.0362737	−	0.205719i
$149$	4.35768	+	1.58607i	0.356995	+	0.129936i	0.514291	−	0.857616i	$-0.328055\pi$
$149$	4.35768	+	1.58607i	0.356995	+	0.129936i	−0.157295	+	0.987552i	$0.550277\pi$
$150$		0			0
$151$	14.2109			1.15646			0.578232	−	0.815872i	$-0.303743\pi$
$151$	14.2109			1.15646			0.578232	+	0.815872i	$0.303743\pi$
$152$	3.60185	−	5.21686i	0.292149	−	0.423143i
$153$	5.46178			0.441559
$154$	−2.84493	+	2.38718i	−0.229251	+	0.192365i
$155$		0			0
$156$	2.04165	−	11.5788i	0.163463	−	0.927045i
$157$	−1.86291	−	10.5651i	−0.148676	−	0.843186i	−0.964341	−	0.264662i	$-0.914740\pi$
$157$	−1.86291	−	10.5651i	−0.148676	−	0.843186i	0.815665	−	0.578525i	$-0.196371\pi$
$158$	8.95593	−	3.25969i	0.712496	−	0.259327i
$159$	−13.6281	+	23.6045i	−1.08078	+	1.87196i
$160$		0			0
$161$	14.2729	+	11.9764i	1.12486	+	0.943870i
$162$	13.4692	+	11.3020i	1.05824	+	0.887967i
$163$	−8.46831	−	14.6675i	−0.663289	−	1.14885i	−0.979746	−	0.200244i	$-0.935827\pi$
$163$	−8.46831	−	14.6675i	−0.663289	−	1.14885i	0.316457	−	0.948607i	$-0.397507\pi$
$164$	−2.58703	+	4.48087i	−0.202013	+	0.349897i
$165$		0			0
$166$	2.51513	+	14.2640i	0.195212	+	1.10710i
$167$	−2.82295	+	16.0097i	−0.218446	+	1.23887i	0.656379	+	0.754432i	$0.272087\pi$
$167$	−2.82295	+	16.0097i	−0.218446	+	1.23887i	−0.874825	+	0.484439i	$0.839024\pi$
$168$	−13.8102	−	5.02651i	−1.06548	−	0.387804i
$169$	3.31099	−	2.77825i	0.254692	−	0.213712i
$170$		0			0
$171$	−2.95159	+	11.3134i	−0.225714	+	0.865157i
$172$	−12.5903			−0.960003
$173$	−6.58118	+	5.52227i	−0.500358	+	0.419850i	−0.857721	−	0.514115i	$-0.828120\pi$
$173$	−6.58118	+	5.52227i	−0.500358	+	0.419850i	0.357363	+	0.933966i	$0.383676\pi$
$174$	13.0433	+	4.74737i	0.988809	+	0.359897i
$175$		0			0
$176$	0.423290	+	2.40060i	0.0319067	+	0.180952i
$177$	−1.21477	+	0.442140i	−0.0913077	+	0.0332333i
$178$	−3.87364	+	6.70934i	−0.290342	+	0.502886i
$179$	11.7638	+	20.3755i	0.879267	+	1.52293i	0.852147	+	0.523302i	$0.175300\pi$
$179$	11.7638	+	20.3755i	0.879267	+	1.52293i	0.0271196	+	0.999632i	$0.491367\pi$
$180$		0			0
$181$	−12.7266	−	10.6789i	−0.945964	−	0.793758i	0.0326493	−	0.999467i	$-0.489606\pi$
$181$	−12.7266	−	10.6789i	−0.945964	−	0.793758i	−0.978613	+	0.205709i	$0.934050\pi$
$182$	15.7437	+	27.2688i	1.16700	+	2.02130i
$183$	−16.2600	+	28.1631i	−1.20197	+	2.08188i
$184$	6.00684	−	2.18631i	0.442830	−	0.161177i
$185$		0			0
$186$	3.02023	−	17.1286i	0.221454	−	1.25593i
$187$	0.939266	+	0.341865i	0.0686859	+	0.0249996i
$188$	−2.37978	+	1.99687i	−0.173563	+	0.145637i
$189$	−3.20990			−0.233486
$190$		0			0
$191$	−12.8109			−0.926965			−0.463482	−	0.886106i	$-0.653400\pi$
$191$	−12.8109			−0.926965			−0.463482	+	0.886106i	$0.653400\pi$
$192$	1.26657	−	1.06278i	0.0914071	−	0.0766996i
$193$	9.05848	+	3.29702i	0.652043	+	0.237324i	0.646797	−	0.762662i	$-0.276108\pi$
$193$	9.05848	+	3.29702i	0.652043	+	0.237324i	0.00524597	+	0.999986i	$0.498330\pi$
$194$	1.74994	−	9.92443i	0.125639	−	0.712533i
$195$		0			0
$196$	−12.2163	+	4.44638i	−0.872594	+	0.317598i
$197$	1.55121	−	2.68677i	0.110519	−	0.191424i	−0.805461	−	0.592649i	$-0.798082\pi$
$197$	1.55121	−	2.68677i	0.110519	−	0.191424i	0.915980	+	0.401225i	$0.131415\pi$
$198$	−1.17497	−	2.03512i	−0.0835018	−	0.144629i
$199$	0.401629	+	0.337007i	0.0284708	+	0.0238898i	0.656912	−	0.753967i	$-0.271862\pi$
$199$	0.401629	+	0.337007i	0.0284708	+	0.0238898i	−0.628441	+	0.777857i	$0.716307\pi$
$200$		0			0
$201$	8.53029	+	14.7749i	0.601681	+	1.04214i
$202$	−2.94545	+	5.10168i	−0.207241	+	0.358953i
$203$	−12.9968	+	4.73046i	−0.912199	+	0.332013i
$204$	−0.998849	−	5.66475i	−0.0699334	−	0.396612i
$205$		0			0
$206$	5.72824	+	2.08491i	0.399105	+	0.145262i
$207$	−9.03134	+	7.57819i	−0.627722	+	0.526721i
$208$	20.6674			1.43303
$209$	−1.21572	+	1.76083i	−0.0840929	+	0.121799i
$210$		0			0
$211$	−14.6037	+	12.2539i	−1.00536	+	0.843596i	−0.987718	−	0.156249i	$-0.950060\pi$
$211$	−14.6037	+	12.2539i	−1.00536	+	0.843596i	−0.0176404	+	0.999844i	$0.505615\pi$
$212$	12.7331	+	4.63446i	0.874512	+	0.318296i
$213$	−2.49959	+	14.1759i	−0.171269	+	0.971315i
$214$	−0.543115	−	3.08016i	−0.0371266	−	0.210555i
$215$		0			0
$216$	−0.550635	+	0.953728i	−0.0374660	+	0.0648929i
$217$	8.66543	+	15.0090i	0.588248	+	1.01887i
$218$	4.81129	+	4.03715i	0.325862	+	0.273430i
$219$	3.75110	+	3.14755i	0.253476	+	0.212692i
$220$		0			0
$221$	4.23731	−	7.33924i	0.285033	−	0.493691i
$222$	−8.57267	+	3.12020i	−0.575360	+	0.209414i
$223$	0.549220	+	3.11478i	0.0367785	+	0.208581i	0.997659	−	0.0683812i	$-0.0217834\pi$
$223$	0.549220	+	3.11478i	0.0367785	+	0.208581i	−0.960881	+	0.276962i	$0.910672\pi$
$224$	−4.38246	+	24.8542i	−0.292815	+	1.66064i
$225$		0			0
$226$	18.1259	−	15.2095i	1.20572	−	1.01172i
$227$	9.04654			0.600440			0.300220	−	0.953870i	$-0.402940\pi$
$227$	9.04654			0.600440			0.300220	+	0.953870i	$0.402940\pi$
$228$	12.2736	+	0.992287i	0.812840	+	0.0657158i
$229$	−17.8920			−1.18234			−0.591168	−	0.806549i	$-0.701333\pi$
$229$	−17.8920			−1.18234			−0.591168	+	0.806549i	$0.701333\pi$
$230$		0			0
$231$	4.66131	+	1.69658i	0.306692	+	0.111627i
$232$	−0.823994	+	4.67310i	−0.0540979	+	0.306804i
$233$	−1.11887	−	6.34541i	−0.0732994	−	0.415701i	−0.999273	−	0.0381142i	$-0.987865\pi$
$233$	−1.11887	−	6.34541i	−0.0732994	−	0.415701i	0.925974	−	0.377587i	$-0.123246\pi$
$234$	−18.7224	+	6.81441i	−1.22392	+	0.445472i
$235$		0			0
$236$	0.321337	+	0.556572i	0.0209173	+	0.0362298i
$237$	−9.75176	−	8.18270i	−0.633445	−	0.531523i
$238$	11.8007	+	9.90196i	0.764926	+	0.641849i
$239$	6.73708	+	11.6690i	0.435785	+	0.754802i	0.997359	−	0.0726241i	$-0.0231374\pi$
$239$	6.73708	+	11.6690i	0.435785	+	0.754802i	−0.561574	+	0.827426i	$0.689804\pi$
$240$		0			0
$241$	16.5716	−	6.03157i	1.06747	−	0.388528i	0.252241	−	0.967664i	$-0.418832\pi$
$241$	16.5716	−	6.03157i	1.06747	−	0.388528i	0.815231	+	0.579137i	$0.196610\pi$
$242$	3.33429	+	18.9097i	0.214336	+	1.21556i
$243$	3.68366	−	20.8911i	0.236307	−	1.34016i
$244$	15.1921	+	5.52948i	0.972576	+	0.353989i
$245$		0			0
$246$	18.5742			1.18424
$247$	12.9124	+	12.7433i	0.821599	+	0.810834i
$248$	5.94596			0.377569
$249$	14.8200	−	12.4355i	0.939179	−	0.788065i
$250$		0			0
$251$	3.07923	−	17.4632i	0.194360	−	1.10227i	−0.718968	−	0.695043i	$-0.755385\pi$
$251$	3.07923	−	17.4632i	0.194360	−	1.10227i	0.913328	−	0.407225i	$-0.133504\pi$
$252$	−2.33995	−	13.2705i	−0.147403	−	0.835963i
$253$	−2.02746	+	0.737936i	−0.127465	+	0.0463936i
$254$	17.6756	−	30.6151i	1.10907	−	1.92096i
$255$		0			0
$256$	15.6489	+	13.1310i	0.978058	+	0.820688i
$257$	−21.2558	−	17.8358i	−1.32590	−	1.11256i	−0.985017	−	0.172459i	$-0.944829\pi$
$257$	−21.2558	−	17.8358i	−1.32590	−	1.11256i	−0.340885	−	0.940105i	$-0.610727\pi$
$258$	22.5987	+	39.1422i	1.40694	+	2.43688i
$259$	4.54518	−	7.87248i	0.282424	−	0.489172i
$260$		0			0
$261$	−1.51972	−	8.61874i	−0.0940681	−	0.533487i
$262$	1.06299	−	6.02852i	0.0656718	−	0.372443i
$263$	−5.22499	−	1.90174i	−0.322187	−	0.117266i	0.175864	−	0.984415i	$-0.443728\pi$
$263$	−5.22499	−	1.90174i	−0.322187	−	0.117266i	−0.498050	+	0.867148i	$0.665950\pi$
$264$	1.30370	−	1.09394i	0.0802373	−	0.0673271i
$265$		0			0
$266$	−26.8879	+	19.0926i	−1.64860	+	1.17064i
$267$	10.3479			0.633282
$268$	6.49727	−	5.45185i	0.396884	−	0.333025i
$269$	4.34856	+	1.58275i	0.265137	+	0.0965019i	0.471168	−	0.882044i	$-0.343833\pi$
$269$	4.34856	+	1.58275i	0.265137	+	0.0965019i	−0.206031	+	0.978545i	$0.566055\pi$
$270$		0			0
$271$	−1.32118	−	7.49279i	−0.0802561	−	0.455155i	−0.998280	−	0.0586294i	$-0.981327\pi$
$271$	−1.32118	−	7.49279i	−0.0802561	−	0.455155i	0.918024	−	0.396525i	$-0.129784\pi$
$272$	9.50144	−	3.45824i	0.576110	−	0.209687i
$273$	21.0286	−	36.4226i	1.27271	−	2.20439i
$274$	−0.542806	−	0.940168i	−0.0327921	−	0.0567976i
$275$		0			0
$276$	9.51147	+	7.98107i	0.572523	+	0.480404i
$277$	−3.76772	−	6.52588i	−0.226380	−	0.392102i	0.730352	−	0.683071i	$-0.239356\pi$
$277$	−3.76772	−	6.52588i	−0.226380	−	0.392102i	−0.956733	+	0.290968i	$0.906023\pi$
$278$	−7.54740	+	13.0725i	−0.452663	+	0.784035i
$279$	−10.3050	+	3.75070i	−0.616942	+	0.224548i
$280$		0			0
$281$	−3.16993	+	17.9776i	−0.189102	+	1.07245i	0.731468	+	0.681876i	$0.238836\pi$
$281$	−3.16993	+	17.9776i	−0.189102	+	1.07245i	−0.920570	+	0.390577i	$0.872276\pi$
$282$	10.4796	+	3.81427i	0.624053	+	0.227137i
$283$	−23.6963	+	19.8836i	−1.40860	+	1.18196i	−0.451474	+	0.892284i	$0.649102\pi$
$283$	−23.6963	+	19.8836i	−1.40860	+	1.18196i	−0.957126	+	0.289671i	$0.906454\pi$
$284$	7.15618			0.424641
$285$		0			0
$286$	−3.64624			−0.215607
$287$	−14.1780	+	11.8967i	−0.836898	+	0.702241i
$288$	−15.0063	−	5.46185i	−0.884255	−	0.321842i
$289$	−2.23206	+	12.6586i	−0.131298	+	0.744625i
$290$		0			0
$291$	−12.6486	+	4.60373i	−0.741476	+	0.269875i
$292$	1.21719	−	2.10823i	0.0712305	−	0.123375i
$293$	−10.9496	−	18.9653i	−0.639683	−	1.10796i	−0.985502	−	0.169662i	$-0.945732\pi$
$293$	−10.9496	−	18.9653i	−0.639683	−	1.10796i	0.345820	−	0.938301i	$-0.387601\pi$
$294$	35.7508	+	29.9985i	2.08503	+	1.74955i
$295$		0			0
$296$	−1.55938	−	2.70093i	−0.0906373	−	0.156988i
$297$	0.185853	−	0.321908i	0.0107843	−	0.0186790i
$298$	−7.77706	+	2.83062i	−0.450513	+	0.163973i
$299$	3.17654	+	18.0151i	0.183704	+	1.04184i
$300$		0			0
$301$	−42.3205	−	15.4034i	−2.43931	−	0.887837i
$302$	−19.4283	+	16.3023i	−1.11797	+	0.938090i
$303$	7.86840			0.452028
$304$	2.02866	+	21.5499i	0.116352	+	1.23597i
$305$		0			0
$306$	−7.46703	+	6.26559i	−0.426862	+	0.358180i
$307$	5.12643	+	1.86587i	0.292581	+	0.106491i	0.484141	−	0.874990i	$-0.339132\pi$
$307$	5.12643	+	1.86587i	0.292581	+	0.106491i	−0.191560	+	0.981481i	$0.561355\pi$
$308$	0.428228	−	2.42860i	0.0244005	−	0.138382i
$309$	−1.41387	−	8.01845i	−0.0804322	−	0.456154i
$310$		0			0
$311$	−3.34861	+	5.79996i	−0.189882	+	0.328885i	−0.945211	−	0.326461i	$-0.894144\pi$
$311$	−3.34861	+	5.79996i	−0.189882	+	0.328885i	0.755329	+	0.655346i	$0.227477\pi$
$312$	−7.21459	−	12.4960i	−0.408446	−	0.707449i
$313$	3.51062	+	2.94576i	0.198432	+	0.166504i	0.736590	−	0.676340i	$-0.236435\pi$
$313$	3.51062	+	2.94576i	0.198432	+	0.166504i	−0.538157	+	0.842844i	$0.680879\pi$
$314$	14.6668	+	12.3069i	0.827696	+	0.694520i
$315$		0			0
$316$	−3.16433	+	5.48078i	−0.178007	+	0.308318i
$317$	26.0101	−	9.46690i	1.46087	−	0.531714i	0.515267	−	0.857030i	$-0.327693\pi$
$317$	26.0101	−	9.46690i	1.46087	−	0.531714i	0.945605	+	0.325316i	$0.105471\pi$
$318$	−8.44686	−	47.9045i	−0.473676	−	2.68635i
$319$	0.278119	−	1.57729i	0.0155717	−	0.0883115i
$320$		0			0
$321$	−3.20022	+	2.68530i	−0.178619	+	0.149879i
$322$	−33.2520			−1.85306
$323$	8.06856	+	3.69785i	0.448946	+	0.205754i
$324$	−11.6754			−0.648636
$325$		0			0
$326$	28.4035	+	10.3380i	1.57313	+	0.572571i
$327$	1.45674	−	8.26158i	0.0805579	−	0.456866i
$328$	1.10264	+	6.25336i	0.0608829	+	0.345284i
$329$	−10.4423	+	3.80069i	−0.575703	+	0.209539i
$330$		0			0
$331$	7.06509	+	12.2371i	0.388332	+	0.672611i	0.992225	−	0.124454i	$-0.0397179\pi$
$331$	7.06509	+	12.2371i	0.388332	+	0.672611i	−0.603893	+	0.797065i	$0.706385\pi$
$332$	−7.36768	−	6.18222i	−0.404354	−	0.339293i
$333$	4.40631	+	3.69733i	0.241464	+	0.202613i
$334$	−14.5065	−	25.1260i	−0.793761	−	1.37483i
$335$		0			0
$336$	47.1529	−	17.1623i	2.57240	−	0.936278i
$337$	2.60428	+	14.7696i	0.141864	+	0.804550i	0.969832	+	0.243775i	$0.0783858\pi$
$337$	2.60428	+	14.7696i	0.141864	+	0.804550i	−0.827968	+	0.560775i	$0.810503\pi$
$338$	−1.33947	+	7.59654i	−0.0728578	+	0.413197i
$339$	−29.6986	−	10.8094i	−1.61301	−	0.587087i
$340$		0			0
$341$	−2.00692			−0.108681
$342$	−8.94313	−	18.8530i	−0.483589	−	1.01945i
$343$	−16.8294			−0.908703
$344$	−11.8364	+	9.93195i	−0.638178	+	0.535495i
$345$		0			0
$346$	2.66244	−	15.0995i	0.143134	−	0.811752i
$347$	−3.63155	−	20.5956i	−0.194952	−	1.10563i	−0.912487	−	0.409106i	$-0.865841\pi$
$347$	−3.63155	−	20.5956i	−0.194952	−	1.10563i	0.717535	−	0.696522i	$-0.245270\pi$
$348$	−8.66111	+	3.15239i	−0.464284	+	0.168986i
$349$	1.56527	−	2.71113i	0.0837872	−	0.145124i	−0.821087	−	0.570804i	$-0.806632\pi$
$349$	1.56527	−	2.71113i	0.0837872	−	0.145124i	0.904874	+	0.425680i	$0.139965\pi$
$350$		0			0
$351$	−2.41420	−	2.02575i	−0.128860	−	0.108127i
$352$	−2.23878	−	1.87856i	−0.119327	−	0.100127i
$353$	−4.02269	−	6.96750i	−0.214106	−	0.370843i	0.738890	−	0.673827i	$-0.235350\pi$
$353$	−4.02269	−	6.96750i	−0.214106	−	0.370843i	−0.952996	+	0.302984i	$0.902017\pi$
$354$	1.15356	−	1.99802i	0.0613108	−	0.106193i
$355$		0			0
$356$	−0.893318	−	5.06626i	−0.0473457	−	0.268511i
$357$	3.57296	−	20.2632i	0.189101	−	1.07244i
$358$	−39.4569	−	14.3611i	−2.08536	−	0.759010i
$359$	23.4289	−	19.6592i	1.23653	−	1.03757i	0.238742	−	0.971083i	$-0.423265\pi$
$359$	23.4289	−	19.6592i	1.23653	−	1.03757i	0.997787	−	0.0664886i	$-0.0211796\pi$
$360$		0			0
$361$	−12.0199	+	14.7147i	−0.632628	+	0.774456i
$362$	29.6497			1.55835
$363$	19.6468	−	16.4856i	1.03119	−	0.865269i
$364$	−19.6475	−	7.15112i	−1.02981	−	0.374821i
$365$		0			0
$366$	−10.0781	−	57.1560i	−0.526793	−	2.98759i
$367$	9.35159	−	3.40370i	0.488149	−	0.177672i	−0.0862072	−	0.996277i	$-0.527475\pi$
$367$	9.35159	−	3.40370i	0.488149	−	0.177672i	0.574356	+	0.818606i	$0.305252\pi$
$368$	−10.9128	+	18.9016i	−0.568871	+	0.985314i
$369$	−5.85558	−	10.1422i	−0.304830	−	0.527980i
$370$		0			0
$371$	37.1304	+	31.1561i	1.92771	+	1.61754i
$372$	5.77465	+	10.0020i	0.299402	+	0.518579i
$373$	4.63806	−	8.03335i	0.240149	−	0.415951i	−0.720607	−	0.693343i	$-0.756137\pi$
$373$	4.63806	−	8.03335i	0.240149	−	0.415951i	0.960757	+	0.277392i	$0.0894702\pi$
$374$	−1.67629	+	0.610119i	−0.0866788	+	0.0315485i
$375$		0			0
$376$	−0.662039	+	3.75461i	−0.0341420	+	0.193629i
$377$	−12.7604	−	4.64441i	−0.657195	−	0.239199i
$378$	4.38839	−	3.68230i	0.225715	−	0.189397i
$379$	−21.1472			−1.08626			−0.543129	−	0.839649i	$-0.682761\pi$
$379$	−21.1472			−1.08626			−0.543129	+	0.839649i	$0.682761\pi$
$380$		0			0
$381$	−47.2181			−2.41906
$382$	17.5143	−	14.6963i	0.896112	−	0.751927i
$383$	14.2365	+	5.18165i	0.727450	+	0.264770i	0.679085	−	0.734060i	$-0.262377\pi$
$383$	14.2365	+	5.18165i	0.727450	+	0.264770i	0.0483649	+	0.998830i	$0.484599\pi$
$384$	4.41636	−	25.0464i	0.225371	−	1.27814i
$385$		0			0
$386$	−16.1665	+	5.88411i	−0.822851	+	0.299493i
$387$	14.2487	−	24.6795i	0.724302	−	1.25453i
$388$	3.34588	+	5.79524i	0.169861	+	0.294209i
$389$	−24.0908	−	20.2146i	−1.22145	−	1.02492i	−0.998747	−	0.0500353i	$-0.984067\pi$
$389$	−24.0908	−	20.2146i	−1.22145	−	1.02492i	−0.222706	−	0.974886i	$-0.571489\pi$
$390$		0			0
$391$	4.47479	+	7.75056i	0.226300	+	0.391963i
$392$	−7.97728	+	13.8171i	−0.402913	+	0.697866i
$393$	−7.68332	+	2.79650i	−0.387572	+	0.141065i
$394$	0.961457	+	5.45269i	0.0484375	+	0.274703i
$395$		0			0
$396$	1.46633	+	0.533699i	0.0736857	+	0.0268194i
$397$	−7.18978	+	6.03294i	−0.360844	+	0.302784i	−0.805127	−	0.593102i	$-0.797903\pi$
$397$	−7.18978	+	6.03294i	−0.360844	+	0.302784i	0.444283	+	0.895887i	$0.353459\pi$
$398$	−0.935689			−0.0469019
$399$	40.0419	+	18.3514i	2.00460	+	0.918717i
$400$		0			0
$401$	4.71921	−	3.95989i	0.235666	−	0.197747i	−0.517305	−	0.855801i	$-0.673065\pi$
$401$	4.71921	−	3.95989i	0.235666	−	0.197747i	0.752971	+	0.658054i	$0.228620\pi$
$402$	−28.6114	−	10.4137i	−1.42701	−	0.519389i
$403$	−2.95473	+	16.7571i	−0.147185	+	0.834730i
$404$	−0.679265	−	3.85230i	−0.0337947	−	0.191659i
$405$		0			0
$406$	12.3419	−	21.3768i	0.612518	−	1.06091i
$407$	0.526332	+	0.911634i	0.0260893	+	0.0451880i
$408$	−5.40771	−	4.53761i	−0.267722	−	0.224645i
$409$	1.75027	+	1.46865i	0.0865454	+	0.0726202i	0.685034	−	0.728511i	$-0.259787\pi$
$409$	1.75027	+	1.46865i	0.0865454	+	0.0726202i	−0.598489	+	0.801131i	$0.704232\pi$
$410$		0			0
$411$	−0.725018	+	1.25577i	−0.0357625	+	0.0619425i
$412$	−3.80371	+	1.38444i	−0.187395	+	0.0682064i
$413$	0.399199	+	2.26397i	0.0196433	+	0.111403i
$414$	3.65366	−	20.7210i	0.179568	−	1.01838i
$415$		0			0
$416$	−18.9814	+	15.9273i	−0.930640	+	0.780900i
$417$	20.1619			0.987332
$418$	−0.357906	−	3.80193i	−0.0175057	−	0.185959i
$419$	−22.6494			−1.10649			−0.553247	−	0.833017i	$-0.686611\pi$
$419$	−22.6494			−1.10649			−0.553247	+	0.833017i	$0.686611\pi$
$420$		0			0
$421$	21.6100	+	7.86540i	1.05321	+	0.383336i	0.809872	−	0.586606i	$-0.199536\pi$
$421$	21.6100	+	7.86540i	1.05321	+	0.383336i	0.243335	+	0.969942i	$0.421759\pi$
$422$	5.90797	−	33.5058i	0.287595	−	1.63103i
$423$	−1.22102	−	6.92473i	−0.0593679	−	0.336692i
$424$	15.6266	−	5.68761i	0.758893	−	0.276215i
$425$		0			0
$426$	−12.8448	−	22.2479i	−0.622334	−	1.07791i
$427$	44.3011	+	37.1730i	2.14388	+	1.79893i
$428$	1.59097	+	1.33498i	0.0769025	+	0.0645289i
$429$	2.43511	+	4.21774i	0.117568	+	0.203634i
$430$		0			0
$431$	−24.0861	+	8.76663i	−1.16019	+	0.422274i	−0.849164	−	0.528129i	$-0.822894\pi$
$431$	−24.0861	+	8.76663i	−1.16019	+	0.422274i	−0.311023	+	0.950402i	$0.600672\pi$
$432$	−0.652938	−	3.70299i	−0.0314145	−	0.178160i
$433$	−0.410383	+	2.32740i	−0.0197217	+	0.111847i	−0.993079	−	0.117444i	$-0.962530\pi$
$433$	−0.410383	+	2.32740i	−0.0197217	+	0.111847i	0.973358	+	0.229292i	$0.0736410\pi$
$434$	−29.0647	−	10.5787i	−1.39515	−	0.507793i
$435$		0			0
$436$	−4.17056			−0.199734
$437$	−18.4725	+	5.08050i	−0.883661	+	0.243033i
$438$	−8.73906			−0.417568
$439$	−4.83879	+	4.06022i	−0.230943	+	0.193784i	−0.750914	−	0.660400i	$-0.770387\pi$
$439$	−4.83879	+	4.06022i	−0.230943	+	0.193784i	0.519972	+	0.854183i	$0.325942\pi$
$440$		0			0
$441$	5.10967	−	28.9784i	0.243318	−	1.37992i
$442$	2.62634	+	14.8947i	0.124922	+	0.708469i
$443$	29.6234	−	10.7821i	1.40745	−	0.512271i	0.477071	−	0.878865i	$-0.341698\pi$
$443$	29.6234	−	10.7821i	1.40745	−	0.512271i	0.930381	+	0.366594i	$0.119476\pi$
$444$	3.02891	−	5.24623i	0.143746	−	0.248975i
$445$		0			0
$446$	−4.32404	−	3.62830i	−0.204749	−	0.171805i
$447$	8.46813	+	7.10561i	0.400529	+	0.336084i
$448$	−1.47013	−	2.54635i	−0.0694573	−	0.120304i
$449$	7.54142	−	13.0621i	0.355902	−	0.616440i	−0.631370	−	0.775482i	$-0.717507\pi$
$449$	7.54142	−	13.0621i	0.355902	−	0.616440i	0.987272	+	0.159042i	$0.0508405\pi$
$450$		0			0
$451$	−0.372168	−	2.11067i	−0.0175247	−	0.0993876i
$452$	−2.72837	+	15.4734i	−0.128332	+	0.727805i
$453$	31.8325	+	11.5861i	1.49562	+	0.544361i
$454$	−12.3679	+	10.3779i	−0.580455	+	0.487059i
$455$		0			0
$456$	12.3215	−	8.74924i	0.577005	−	0.409721i
$457$	−20.1347			−0.941861			−0.470930	−	0.882170i	$-0.656082\pi$
$457$	−20.1347			−0.941861			−0.470930	+	0.882170i	$0.656082\pi$
$458$	24.4609	−	20.5251i	1.14298	−	0.959076i
$459$	−1.44885	−	0.527337i	−0.0676263	−	0.0246140i
$460$		0			0
$461$	−1.29974	−	7.37118i	−0.0605348	−	0.343310i	−1.00000		0.000665051i	$-0.999788\pi$
$461$	−1.29974	−	7.37118i	−0.0605348	−	0.343310i	0.939465	−	0.342645i	$-0.111323\pi$
$462$	−8.31893	+	3.02784i	−0.387032	+	0.140868i
$463$	−10.7986	+	18.7038i	−0.501855	+	0.869239i	0.498142	+	0.867095i	$0.334016\pi$
$463$	−10.7986	+	18.7038i	−0.501855	+	0.869239i	−0.999998	+	0.00214362i	$0.999318\pi$
$464$	−8.10087	−	14.0311i	−0.376074	−	0.651379i
$465$		0			0
$466$	8.80891	+	7.39155i	0.408065	+	0.342407i
$467$	−13.5252	−	23.4263i	−0.625870	−	1.08404i	−0.988372	−	0.152056i	$-0.951411\pi$
$467$	−13.5252	−	23.4263i	−0.625870	−	1.08404i	0.362501	−	0.931983i	$-0.381923\pi$
$468$	6.61505	−	11.4576i	0.305781	−	0.529628i
$469$	28.5096	−	10.3766i	1.31645	−	0.479148i
$470$		0			0
$471$	4.44075	−	25.1847i	0.204619	−	1.16045i
$472$	0.741151	+	0.269757i	0.0341143	+	0.0124166i
$473$	3.99510	−	3.35229i	0.183695	−	0.154138i
$474$	22.7190			1.04352
$475$		0			0
$476$	−10.2292			−0.468853
$477$	−23.4947	+	19.7144i	−1.07575	+	0.902660i
$478$	−22.5968	−	8.22457i	−1.03355	−	0.376183i
$479$	−6.60791	+	37.4753i	−0.301923	+	1.71229i	0.335723	+	0.941961i	$0.391019\pi$
$479$	−6.60791	+	37.4753i	−0.301923	+	1.71229i	−0.637646	+	0.770329i	$0.720092\pi$
$480$		0			0
$481$	8.38675	−	3.05253i	0.382403	−	0.139183i
$482$	−15.7365	+	27.2565i	−0.716779	+	1.24150i
$483$	22.2071	+	38.4638i	1.01046	+	1.75016i
$484$	−9.76728	−	8.19572i	−0.443967	−	0.372533i
$485$		0			0
$486$	18.9295	+	32.7869i	0.858661	+	1.48724i
$487$	−9.16764	+	15.8788i	−0.415426	+	0.719538i	−0.995473	−	0.0950445i	$-0.969701\pi$
$487$	−9.16764	+	15.8788i	−0.415426	+	0.719538i	0.580047	+	0.814583i	$0.303034\pi$
$488$	18.6444	−	6.78601i	0.843993	−	0.307188i
$489$	−7.01069	−	39.7596i	−0.317034	−	1.79799i
$490$		0			0
$491$	14.1588	+	5.15338i	0.638978	+	0.232569i	0.641134	−	0.767429i	$-0.278464\pi$
$491$	14.1588	+	5.15338i	0.638978	+	0.232569i	−0.00215650	+	0.999998i	$0.500686\pi$
$492$	−9.44821	+	7.92799i	−0.425958	+	0.357421i
$493$	−6.64350			−0.299208
$494$	−32.2718	−	2.60909i	−1.45198	−	0.117388i
$495$		0			0
$496$	−15.5519	+	13.0496i	−0.698302	+	0.585945i
$497$	24.0544	+	8.75509i	1.07899	+	0.392720i
$498$	−5.99549	+	34.0021i	−0.268664	+	1.52367i
$499$	5.99606	+	34.0053i	0.268420	+	1.52229i	0.759115	+	0.650956i	$0.225632\pi$
$499$	5.99606	+	34.0053i	0.268420	+	1.52229i	−0.490695	+	0.871332i	$0.663257\pi$
$500$		0			0
$501$	−19.3761	+	33.5604i	−0.865661	+	1.49937i
$502$	15.8235	+	27.4071i	0.706237	+	1.22324i
$503$	23.6481	+	19.8431i	1.05442	+	0.884760i	0.993551	−	0.113386i	$-0.0361697\pi$
$503$	23.6481	+	19.8431i	1.05442	+	0.884760i	0.0608649	+	0.998146i	$0.480614\pi$
$504$	−12.6683	−	10.6300i	−0.564293	−	0.473498i
$505$		0			0
$506$	1.92529	−	3.33471i	0.0855897	−	0.148246i
$507$	9.68175	−	3.52387i	0.429982	−	0.156501i
$508$	4.07626	+	23.1176i	0.180855	+	1.02568i
$509$	1.76734	−	10.0231i	0.0783358	−	0.444264i	−0.920261	−	0.391305i	$-0.872024\pi$
$509$	1.76734	−	10.0231i	0.0783358	−	0.444264i	0.998597	−	0.0529589i	$-0.0168652\pi$
$510$		0			0
$511$	6.67067	−	5.59735i	0.295093	−	0.247612i
$512$	−15.1195			−0.668194
$513$	1.87528	−	2.71613i	0.0827956	−	0.119920i
$514$	49.5204			2.18425
$515$		0			0
$516$	−28.2024	−	10.2648i	−1.24154	−	0.451885i
$517$	0.223455	−	1.26728i	0.00982754	−	0.0557348i
$518$	2.81716	+	15.9769i	0.123779	+	0.701984i
$519$	−19.2442	+	7.00431i	−0.844726	+	0.307455i
$520$		0			0
$521$	−8.27116	−	14.3261i	−0.362366	−	0.627636i	0.625984	−	0.779836i	$-0.284698\pi$
$521$	−8.27116	−	14.3261i	−0.362366	−	0.627636i	−0.988350	+	0.152200i	$0.951364\pi$
$522$	11.9648	+	10.0397i	0.523686	+	0.439425i
$523$	6.12683	+	5.14102i	0.267908	+	0.224801i	0.766838	−	0.641841i	$-0.221829\pi$
$523$	6.12683	+	5.14102i	0.267908	+	0.224801i	−0.498930	+	0.866642i	$0.666274\pi$
$524$	2.03243	+	3.52027i	0.0887871	+	0.153784i
$525$		0			0
$526$	9.32492	−	3.39399i	0.406586	−	0.147985i
$527$	1.44556	+	8.19816i	0.0629694	+	0.357117i
$528$	−1.00903	+	5.72247i	−0.0439122	+	0.249039i
$529$	3.45976	+	1.25925i	0.150424	+	0.0547500i
$530$		0			0
$531$	−1.45465			−0.0631266
$532$	5.52792	−	21.1884i	0.239666	−	0.918635i
$533$	−18.1713			−0.787088
$534$	−14.1471	+	11.8708i	−0.612204	+	0.513700i
$535$		0			0
$536$	1.80749	−	10.2508i	0.0780719	−	0.442768i
$537$	9.73893	+	55.2322i	0.420266	+	2.38345i
$538$	−7.76079	+	2.82470i	−0.334591	+	0.121781i
$539$	2.69254	−	4.66361i	0.115976	−	0.200876i
$540$		0			0
$541$	3.98380	+	3.34280i	0.171277	+	0.143718i	0.724397	−	0.689383i	$-0.242118\pi$
$541$	3.98380	+	3.34280i	0.171277	+	0.143718i	−0.553120	+	0.833102i	$0.686563\pi$
$542$	10.4017	+	8.72810i	0.446793	+	0.374904i
$543$	−19.8013	−	34.2969i	−0.849755	−	1.47182i
$544$	−6.06125	+	10.4984i	−0.259874	+	0.450115i
$545$		0			0
$546$	13.0338	+	73.9182i	0.557794	+	3.16341i
$547$	−1.91602	+	10.8663i	−0.0819233	+	0.464610i	0.916055	+	0.401053i	$0.131356\pi$
$547$	−1.91602	+	10.8663i	−0.0819233	+	0.464610i	−0.997978	+	0.0635572i	$0.979755\pi$
$548$	0.677403	+	0.246555i	0.0289372	+	0.0105323i
$549$	−28.0321	+	23.5217i	−1.19638	+	1.00388i
$550$		0			0
$551$	3.59020	−	13.7612i	0.152948	−	0.586245i
$552$	15.2379			0.648566
$553$	−17.3418	+	14.5515i	−0.737447	+	0.618792i
$554$	12.6373	+	4.59960i	0.536907	+	0.195418i
$555$		0			0
$556$	−1.74054	−	9.87109i	−0.0738153	−	0.418628i
$557$	−19.9983	+	7.27877i	−0.847353	+	0.308411i	−0.728961	−	0.684555i	$-0.759996\pi$
$557$	−19.9983	+	7.27877i	−0.847353	+	0.308411i	−0.118393	+	0.992967i	$0.537774\pi$
$558$	9.78567	−	16.9493i	0.414260	−	0.717520i
$559$	−22.1086	−	38.2933i	−0.935095	−	1.61963i
$560$		0			0
$561$	1.82524	+	1.53156i	0.0770618	+	0.0646625i
$562$	−16.2896	−	28.2144i	−0.687134	−	1.19015i
$563$	7.35358	−	12.7368i	0.309917	−	0.536791i	−0.668427	−	0.743778i	$-0.733032\pi$
$563$	7.35358	−	12.7368i	0.309917	−	0.536791i	0.978344	+	0.206986i	$0.0663655\pi$
$564$	−6.95877	+	2.53279i	−0.293017	+	0.106650i
$565$		0			0
$566$	9.58644	−	54.3674i	0.402948	−	2.28523i
$567$	−39.2453	−	14.2841i	−1.64815	−	0.599876i
$568$	6.72768	−	5.64519i	0.282287	−	0.236867i
$569$	40.6551			1.70435			0.852174	−	0.523258i	$-0.175284\pi$
$569$	40.6551			1.70435			0.852174	+	0.523258i	$0.175284\pi$
$570$		0			0
$571$	−24.3240			−1.01793			−0.508964	−	0.860788i	$-0.669972\pi$
$571$	−24.3240			−1.01793			−0.508964	+	0.860788i	$0.669972\pi$
$572$	1.85475	−	1.55632i	0.0775510	−	0.0650730i
$573$	−28.6966	−	10.4447i	−1.19882	−	0.436333i
$574$	5.73575	−	32.5290i	0.239405	−	1.35774i
$575$		0			0
$576$	1.74829	−	0.636325i	0.0728454	−	0.0265136i
$577$	16.8438	−	29.1743i	0.701216	−	1.21454i	−0.266824	−	0.963745i	$-0.585974\pi$
$577$	16.8438	−	29.1743i	0.701216	−	1.21454i	0.968040	−	0.250796i	$-0.0806925\pi$
$578$	−11.4700	−	19.8667i	−0.477091	−	0.826346i
$579$	17.6030	+	14.7707i	0.731557	+	0.613849i
$580$		0			0
$581$	−17.2018	−	29.7945i	−0.713652	−	1.23608i
$582$	12.0112	−	20.8041i	0.497882	−	0.862357i
$583$	−5.27437	+	1.91971i	−0.218442	+	0.0795064i
$584$	−0.518785	−	2.94218i	−0.0214675	−	0.121748i
$585$		0			0
$586$	36.7261	+	13.3672i	1.51714	+	0.552194i
$587$	1.72343	−	1.44613i	0.0711334	−	0.0596880i	−0.606528	−	0.795062i	$-0.707438\pi$
$587$	1.72343	−	1.44613i	0.0711334	−	0.0596880i	0.677661	+	0.735374i	$0.262994\pi$
$588$	−30.9898			−1.27800
$589$	−17.7626	−	1.43606i	−0.731897	−	0.0591718i
$590$		0			0
$591$	5.66523	−	4.75369i	0.233036	−	0.195541i
$592$	10.0064	+	3.64202i	0.411259	+	0.149686i
$593$	5.45032	−	30.9103i	0.223818	−	1.26933i	−0.641115	−	0.767445i	$-0.721528\pi$
$593$	5.45032	−	30.9103i	0.223818	−	1.26933i	0.864932	−	0.501888i	$-0.167361\pi$
$594$	0.115194	+	0.653299i	0.00472648	+	0.0268052i
$595$		0			0
$596$	2.74781	−	4.75934i	0.112555	−	0.194950i
$597$	0.624893	+	1.08235i	0.0255752	+	0.0442975i
$598$	−25.0091	−	20.9852i	−1.02270	−	0.858147i
$599$	7.97210	+	6.68939i	0.325731	+	0.273321i	0.790958	−	0.611871i	$-0.209583\pi$
$599$	7.97210	+	6.68939i	0.325731	+	0.273321i	−0.465227	+	0.885192i	$0.654027\pi$
$600$		0			0
$601$	0.647959	−	1.12230i	0.0264308	−	0.0457795i	−0.852507	−	0.522715i	$-0.824919\pi$
$601$	0.647959	−	1.12230i	0.0264308	−	0.0457795i	0.878938	+	0.476936i	$0.158253\pi$
$602$	75.5285	−	27.4901i	3.07831	−	1.12041i
$603$	3.33361	+	18.9059i	0.135755	+	0.769906i
$604$	2.92440	−	16.5851i	0.118992	−	0.674839i
$605$		0			0
$606$	−10.7572	+	9.02638i	−0.436982	+	0.366672i
$607$	−5.50902			−0.223604			−0.111802	−	0.993730i	$-0.535662\pi$
$607$	−5.50902			−0.223604			−0.111802	+	0.993730i	$0.535662\pi$
$608$	−18.4706	−	18.2285i	−0.749080	−	0.739265i
$609$	−32.9698			−1.33600
$610$		0			0
$611$	−10.2524	−	3.73155i	−0.414766	−	0.150962i
$612$	1.12396	−	6.37430i	0.0454334	−	0.257666i
$613$	7.06273	+	40.0547i	0.285261	+	1.61780i	0.704351	+	0.709851i	$0.251238\pi$
$613$	7.06273	+	40.0547i	0.285261	+	1.61780i	−0.419090	+	0.907945i	$0.637651\pi$
$614$	−9.14903	+	3.32997i	−0.369225	+	0.134387i
$615$		0			0
$616$	−1.51323	−	2.62099i	−0.0609697	−	0.105603i
$617$	−23.3684	−	19.6085i	−0.940778	−	0.789407i	0.0369423	−	0.999317i	$-0.488238\pi$
$617$	−23.3684	−	19.6085i	−0.940778	−	0.789407i	−0.977721	+	0.209911i	$0.932683\pi$
$618$	11.1315	+	9.34043i	0.447774	+	0.375727i
$619$	−2.90205	−	5.02651i	−0.116643	−	0.202032i	0.801792	−	0.597603i	$-0.203880\pi$
$619$	−2.90205	−	5.02651i	−0.116643	−	0.202032i	−0.918436	+	0.395571i	$0.870547\pi$
$620$		0			0
$621$	3.12742	−	1.13829i	0.125499	−	0.0456779i
$622$	−2.07551	−	11.7708i	−0.0832203	−	0.471966i
$623$	3.19546	−	18.1224i	0.128024	−	0.726058i
$624$	46.2952	+	16.8501i	1.85329	+	0.674542i
$625$		0			0
$626$	−8.17881			−0.326891
$627$	−4.15881	+	2.95309i	−0.166087	+	0.117935i
$628$	−12.7136			−0.507328
$629$	3.34487	−	2.80668i	0.133369	−	0.111910i
$630$		0			0
$631$	−4.05716	+	23.0093i	−0.161513	+	0.915985i	0.791074	+	0.611720i	$0.209522\pi$
$631$	−4.05716	+	23.0093i	−0.161513	+	0.915985i	−0.952587	+	0.304265i	$0.901589\pi$
$632$	1.34869	+	7.64880i	0.0536480	+	0.304253i
$633$	−42.7029	+	15.5426i	−1.69729	+	0.617763i
$634$	−24.6994	+	42.7806i	−0.980937	+	1.69903i
$635$		0			0
$636$	24.7437	+	20.7625i	0.981153	+	0.823285i
$637$	−34.9755	−	29.3479i	−1.38578	−	1.16281i
$638$	1.42919	+	2.47544i	0.0565823	+	0.0980034i
$639$	−8.09878	+	14.0275i	−0.320383	+	0.554919i
$640$		0			0
$641$	3.18574	+	18.0672i	0.125829	+	0.713612i	0.980812	+	0.194956i	$0.0624564\pi$
$641$	3.18574	+	18.0672i	0.125829	+	0.713612i	−0.854983	+	0.518656i	$0.826432\pi$
$642$	1.29466	−	7.34238i	0.0510962	−	0.289781i
$643$	14.8124	+	5.39128i	0.584144	+	0.212611i	0.617152	−	0.786844i	$-0.288286\pi$
$643$	14.8124	+	5.39128i	0.584144	+	0.212611i	−0.0330077	+	0.999455i	$0.510509\pi$
$644$	16.9145	−	14.1929i	0.666523	−	0.559279i
$645$		0			0
$646$	−15.2729	+	4.20051i	−0.600905	+	0.165267i
$647$	25.0443			0.984592			0.492296	−	0.870428i	$-0.336158\pi$
$647$	25.0443			0.984592			0.492296	+	0.870428i	$0.336158\pi$
$648$	−10.9763	+	9.21024i	−0.431191	+	0.361812i
$649$	−0.250158	−	0.0910500i	−0.00981955	−	0.00357402i
$650$		0			0
$651$	7.17388	+	40.6851i	0.281167	+	1.59457i
$652$	−18.8608	+	6.86475i	−0.738644	+	0.268844i
$653$	1.49426	−	2.58813i	0.0584749	−	0.101282i	−0.835306	−	0.549785i	$-0.814710\pi$
$653$	1.49426	−	2.58813i	0.0584749	−	0.101282i	0.893781	+	0.448504i	$0.148043\pi$
$654$	7.48586	+	12.9659i	0.292720	+	0.507006i
$655$		0			0
$656$	−16.6082	−	13.9360i	−0.648443	−	0.544108i
$657$	2.75503	+	4.77185i	0.107484	+	0.186167i
$658$	9.91610	−	17.1752i	0.386570	−	0.669559i
$659$	33.6123	−	12.2339i	1.30935	−	0.476564i	0.409320	−	0.912391i	$-0.365766\pi$
$659$	33.6123	−	12.2339i	1.30935	−	0.476564i	0.900031	+	0.435827i	$0.143544\pi$
$660$		0			0
$661$	0.559402	−	3.17253i	0.0217582	−	0.123397i	−0.971994	−	0.235006i	$-0.924489\pi$
$661$	0.559402	−	3.17253i	0.0217582	−	0.123397i	0.993752	+	0.111609i	$0.0356003\pi$
$662$	−23.6970	−	8.62500i	−0.921010	−	0.335220i
$663$	15.4753	−	12.9853i	0.601010	−	0.504307i
$664$	−11.8034			−0.458061
$665$		0			0
$666$	−10.2655			−0.397781
$667$	10.9854	−	9.21782i	0.425355	−	0.356915i
$668$	18.1036	+	6.58918i	0.700450	+	0.254943i
$669$	−1.30921	+	7.42491i	−0.0506170	+	0.287064i
$670$		0			0
$671$	−6.29297	+	2.29045i	−0.242937	+	0.0884220i
$672$	−30.0802	+	52.1005i	−1.16037	+	2.00982i
$673$	−0.319853	−	0.554001i	−0.0123294	−	0.0213552i	0.859795	−	0.510640i	$-0.170591\pi$
$673$	−0.319853	−	0.554001i	−0.0123294	−	0.0213552i	−0.872124	+	0.489284i	$0.837258\pi$
$674$	−20.5036	−	17.2046i	−0.789770	−	0.662696i
$675$		0			0
$676$	−2.56107	−	4.43590i	−0.0985025	−	0.170611i
$677$	12.9002	−	22.3439i	0.495796	−	0.858744i	−0.504192	−	0.863592i	$-0.668210\pi$
$677$	12.9002	−	22.3439i	0.495796	−	0.858744i	0.999988	+	0.00484733i	$0.00154296\pi$
$678$	53.0025	−	19.2913i	2.03555	−	0.740879i
$679$	4.15661	+	23.5733i	0.159516	+	0.904660i
$680$		0			0
$681$	20.2643	+	7.37561i	0.776530	+	0.282634i
$682$	2.74374	−	2.30227i	0.105063	−	0.0881585i
$683$	−5.33696			−0.204213			−0.102107	−	0.994773i	$-0.532558\pi$
$683$	−5.33696			−0.204213			−0.102107	+	0.994773i	$0.532558\pi$
$684$	12.5962	+	5.77286i	0.481626	+	0.220731i
$685$		0			0
$686$	23.0082	−	19.3062i	0.878458	−	0.737114i
$687$	−40.0782	−	14.5873i	−1.52908	−	0.556539i
$688$	9.16105	−	51.9549i	0.349262	−	1.98076i
$689$	8.26367	+	46.8656i	0.314821	+	1.78544i
$690$		0			0
$691$	−6.62534	+	11.4754i	−0.252040	+	0.436545i	−0.964087	−	0.265586i	$-0.914435\pi$
$691$	−6.62534	+	11.4754i	−0.252040	+	0.436545i	0.712048	+	0.702131i	$0.247768\pi$
$692$	5.09057	+	8.81712i	0.193514	+	0.335177i
$693$	4.27589	+	3.58790i	0.162428	+	0.136293i
$694$	28.5915	+	23.9911i	1.08532	+	0.910689i
$695$		0			0
$696$	−5.65572	+	9.79599i	−0.214379	+	0.371316i
$697$	−8.35392	+	3.04058i	−0.316427	+	0.115170i
$698$	0.970176	+	5.50214i	0.0367217	+	0.208259i
$699$	2.66712	−	15.1260i	0.100880	−	0.572117i
$700$		0			0
$701$	31.3081	−	26.2706i	1.18249	−	0.992228i	0.182533	−	0.983200i	$-0.441571\pi$
$701$	31.3081	−	26.2706i	1.18249	−	0.992228i	0.999959	−	0.00902862i	$-0.00287394\pi$
$702$	5.62443			0.212280
$703$	4.00609	+	8.44523i	0.151093	+	0.318518i
$704$	0.340484			0.0128325
$705$		0			0
$706$	13.4925	+	4.91087i	0.507797	+	0.184823i
$707$	2.42978	−	13.7800i	0.0913813	−	0.518249i
$708$	0.266027	+	1.50871i	0.00999789	+	0.0567009i
$709$	−6.91375	+	2.51640i	−0.259651	+	0.0945053i	−0.468566	−	0.883429i	$-0.655229\pi$
$709$	−6.91375	+	2.51640i	−0.259651	+	0.0945053i	0.208915	+	0.977934i	$0.433007\pi$
$710$		0			0
$711$	−7.16226	−	12.4054i	−0.268606	−	0.465239i
$712$	−4.83637	−	4.05820i	−0.181251	−	0.152087i
$713$	−13.7652	−	11.5504i	−0.515511	−	0.432565i
$714$	18.3606	+	31.8015i	0.687129	+	1.19014i
$715$		0			0
$716$	26.2005	−	9.53620i	0.979158	−	0.356384i
$717$	5.57745	+	31.6313i	0.208294	+	1.18129i
$718$	−9.47825	+	53.7538i	−0.353725	+	2.00607i
$719$	30.0323	+	10.9309i	1.12002	+	0.407653i	0.834658	−	0.550768i	$-0.185665\pi$
$719$	30.0323	+	10.9309i	1.12002	+	0.407653i	0.285358	+	0.958421i	$0.407887\pi$
$720$		0			0
$721$	−14.4794			−0.539240
$722$	−0.447227	−	33.9059i	−0.0166441	−	1.26185i
$723$	42.0381			1.56341
$724$	−15.0820	+	12.6553i	−0.560520	+	0.470332i
$725$		0			0
$726$	−7.94817	+	45.0763i	−0.294984	+	1.67294i
$727$	5.10323	+	28.9418i	0.189268	+	1.07339i	0.920348	+	0.391101i	$0.127906\pi$
$727$	5.10323	+	28.9418i	0.189268	+	1.07339i	−0.731079	+	0.682292i	$0.760983\pi$
$728$	−24.1123	+	8.77615i	−0.893661	+	0.325266i
$729$	10.5058	−	18.1966i	0.389103	−	0.673947i
$730$		0			0
$731$	−16.5716	−	13.9052i	−0.612922	−	0.514302i
$732$	29.5223	+	24.7722i	1.09118	+	0.915606i
$733$	−25.4142	−	44.0187i	−0.938696	−	1.62587i	−0.767906	−	0.640562i	$-0.778701\pi$
$733$	−25.4142	−	44.0187i	−0.938696	−	1.62587i	−0.170790	−	0.985307i	$-0.554632\pi$
$734$	−8.88034	+	15.3812i	−0.327779	+	0.567730i
$735$		0			0
$736$	−4.54388	−	25.7696i	−0.167490	−	0.949880i
$737$	−0.610076	+	3.45991i	−0.0224724	+	0.127448i
$738$	19.6402	+	7.14845i	0.722966	+	0.263138i
$739$	11.2796	−	9.46473i	0.414928	−	0.348166i	−0.411302	−	0.911499i	$-0.634926\pi$
$739$	11.2796	−	9.46473i	0.414928	−	0.348166i	0.826230	+	0.563334i	$0.190481\pi$
$740$		0			0
$741$	18.5345	+	39.0725i	0.680880	+	1.43536i
$742$	−86.5039			−3.17566
$743$	−26.5487	+	22.2770i	−0.973976	+	0.817263i	−0.983170	−	0.182695i	$-0.941518\pi$
$743$	−26.5487	+	22.2770i	−0.973976	+	0.817263i	0.00919385	+	0.999958i	$0.497073\pi$
$744$	13.3190	+	4.84772i	0.488298	+	0.177726i
$745$		0			0
$746$	2.87472	+	16.3034i	0.105251	+	0.596909i
$747$	20.4565	−	7.44555i	0.748464	−	0.272418i
$748$	0.592270	−	1.02584i	0.0216555	−	0.0375085i
$749$	3.71455	+	6.43379i	0.135727	+	0.235086i
$750$		0			0
$751$	−6.40060	−	5.37074i	−0.233561	−	0.195981i	0.518494	−	0.855081i	$-0.326493\pi$
$751$	−6.40060	−	5.37074i	−0.233561	−	0.195981i	−0.752055	+	0.659100i	$0.770937\pi$
$752$	−6.50865	−	11.2733i	−0.237346	−	0.411095i
$753$	21.1352	−	36.6072i	0.770210	−	1.33404i
$754$	22.7732	−	8.28878i	0.829352	−	0.301859i
$755$		0			0
$756$	−0.660554	+	3.74619i	−0.0240241	+	0.136248i
$757$	13.0344	+	4.74412i	0.473742	+	0.172428i	0.567847	−	0.823134i	$-0.307777\pi$
$757$	13.0344	+	4.74412i	0.473742	+	0.172428i	−0.0941046	+	0.995562i	$0.529999\pi$
$758$	28.9112	−	24.2594i	1.05010	−	0.881142i
$759$	−5.14317			−0.186685
$760$		0			0
$761$	44.3970			1.60939			0.804696	−	0.593687i	$-0.202328\pi$
$761$	44.3970			1.60939			0.804696	+	0.593687i	$0.202328\pi$
$762$	64.5539	−	54.1672i	2.33854	−	1.96227i
$763$	−14.0187	−	5.10239i	−0.507511	−	0.184719i
$764$	−2.63631	+	14.9513i	−0.0953784	+	0.540918i
$765$		0			0
$766$	−25.4075	+	9.24758i	−0.918011	+	0.334129i
$767$	−1.12854	+	1.95468i	−0.0407491	+	0.0705796i
$768$	24.3481	+	42.1721i	0.878585	+	1.52175i
$769$	14.5549	+	12.2130i	0.524863	+	0.440412i	0.866323	−	0.499484i	$-0.166477\pi$
$769$	14.5549	+	12.2130i	0.524863	+	0.440412i	−0.341460	+	0.939896i	$0.610921\pi$
$770$		0			0
$771$	−33.0718	−	57.2820i	−1.19105	−	2.06296i
$772$	5.71197	−	9.89342i	0.205578	−	0.356072i
$773$	−1.75476	+	0.638682i	−0.0631144	+	0.0229718i	−0.373384	−	0.927677i	$-0.621803\pi$
$773$	−1.75476	+	0.638682i	−0.0631144	+	0.0229718i	0.310270	+	0.950648i	$0.399581\pi$
$774$	8.83152	+	50.0860i	0.317442	+	1.80031i
$775$		0			0
$776$	7.71714	+	2.80881i	0.277029	+	0.100830i
$777$	16.5996	−	13.9287i	0.595509	−	0.499691i
$778$	56.1252			2.01218
$779$	−1.78365	−	18.9473i	−0.0639060	−	0.678856i
$780$		0			0
$781$	−2.27077	+	1.90540i	−0.0812544	+	0.0681805i
$782$	−15.0089	−	5.46279i	−0.536717	−	0.195349i
$783$	−0.429007	+	2.43302i	−0.0153315	+	0.0869491i
$784$	−9.45938	−	53.6468i	−0.337835	−	1.91596i
$785$		0			0
$786$	7.29614	−	12.6373i	0.260245	−	0.450757i
$787$	6.48445	+	11.2314i	0.231146	+	0.400356i	0.958146	−	0.286282i	$-0.0924193\pi$
$787$	6.48445	+	11.2314i	0.231146	+	0.400356i	−0.727000	+	0.686638i	$0.759086\pi$
$788$	−2.81644	−	2.36327i	−0.100331	−	0.0841881i
$789$	−10.1535	−	8.51983i	−0.361475	−	0.303314i
$790$		0			0
$791$	−28.1016	+	48.6734i	−0.999178	+	1.73063i
$792$	1.79954	−	0.654978i	0.0639438	−	0.0232736i
$793$	9.85957	+	55.9164i	0.350124	+	1.98565i
$794$	2.90865	−	16.4958i	0.103224	−	0.585413i
$795$		0			0
$796$	0.475962	−	0.399379i	0.0168700	−	0.0141556i
$797$	29.9226			1.05991			0.529956	−	0.848025i	$-0.322209\pi$
$797$	29.9226			1.05991			0.529956	+	0.848025i	$0.322209\pi$
$798$	−75.7951	+	20.8459i	−2.68312	+	0.737938i
$799$	−5.33772			−0.188835
$800$		0			0
$801$	10.9418	+	3.98250i	0.386611	+	0.140715i
$802$	−1.90918	+	10.8275i	−0.0674153	+	0.382331i
$803$	0.175103	+	0.993061i	0.00617927	+	0.0350444i
$804$	18.9988	−	6.91500i	0.670036	−	0.243873i
$805$		0			0
$806$	−15.1837	−	26.2989i	−0.534822	−	0.926339i
$807$	8.45041	+	7.09074i	0.297469	+	0.249606i
$808$	−3.67750	−	3.08579i	−0.129374	−	0.108558i
$809$	−21.2289	−	36.7696i	−0.746369	−	1.29275i	−0.949552	−	0.313608i	$-0.898462\pi$
$809$	−21.2289	−	36.7696i	−0.746369	−	1.29275i	0.203183	−	0.979141i	$-0.434871\pi$
$810$		0			0
$811$	29.2727	−	10.6544i	1.02790	−	0.374126i	0.227621	−	0.973750i	$-0.426905\pi$
$811$	29.2727	−	10.6544i	1.02790	−	0.374126i	0.800282	+	0.599623i	$0.204683\pi$
$812$	2.84622	+	16.1417i	0.0998828	+	0.566463i
$813$	3.14939	−	17.8611i	0.110454	−	0.626415i
$814$	−1.76537	−	0.642542i	−0.0618762	−	0.0225211i
$815$		0			0
$816$	24.1028			0.843767
$817$	37.7583	−	26.8114i	1.32099	−	0.938014i
$818$	−4.07767			−0.142572
$819$	36.2531	−	30.4199i	1.26678	−	1.06296i
$820$		0			0
$821$	−1.07790	+	6.11310i	−0.0376191	+	0.213349i	−0.997823	−	0.0659521i	$-0.978992\pi$
$821$	−1.07790	+	6.11310i	−0.0376191	+	0.213349i	0.960204	+	0.279301i	$0.0901026\pi$
$822$	−0.449375	−	2.54853i	−0.0156738	−	0.0888903i
$823$	33.8009	−	12.3025i	1.17823	−	0.428839i	0.322651	−	0.946518i	$-0.395426\pi$
$823$	33.8009	−	12.3025i	1.17823	−	0.428839i	0.855575	+	0.517679i	$0.173204\pi$
$824$	−2.48383	+	4.30212i	−0.0865283	+	0.149871i
$825$		0			0
$826$	−3.14292	−	2.63722i	−0.109356	−	0.0917606i
$827$	11.7846	+	9.88848i	0.409792	+	0.343856i	0.824264	−	0.566206i	$-0.191589\pi$
$827$	11.7846	+	9.88848i	0.409792	+	0.343856i	−0.414472	+	0.910062i	$0.636034\pi$
$828$	6.98578	+	12.0997i	0.242773	+	0.420494i
$829$	12.0970	−	20.9527i	0.420148	−	0.727717i	−0.575806	−	0.817586i	$-0.695312\pi$
$829$	12.0970	−	20.9527i	0.420148	−	0.727717i	0.995954	+	0.0898693i	$0.0286449\pi$
$830$		0			0
$831$	−3.11920	−	17.6898i	−0.108204	−	0.613654i
$832$	0.501284	−	2.84293i	0.0173789	−	0.0985607i
$833$	−20.9900	−	7.63975i	−0.727262	−	0.264702i
$834$	−27.5642	+	23.1291i	−0.954469	+	0.800895i
$835$		0			0
$836$	1.80483	+	1.78118i	0.0624215	+	0.0616035i
$837$	3.09573			0.107004
$838$	30.9649	−	25.9827i	1.06967	−	0.897556i
$839$	−11.6771	−	4.25013i	−0.403139	−	0.146731i	0.132489	−	0.991184i	$-0.457703\pi$
$839$	−11.6771	−	4.25013i	−0.403139	−	0.146731i	−0.535628	+	0.844454i	$0.679925\pi$
$840$		0			0
$841$	−3.18727	−	18.0759i	−0.109906	−	0.623308i
$842$	−38.5669	+	14.0372i	−1.32910	+	0.483754i
$843$	−21.7577	+	37.6855i	−0.749376	+	1.29796i
$844$	11.2960	+	19.5652i	0.388824	+	0.673463i
$845$		0			0
$846$	9.61314	+	8.06638i	0.330507	+	0.277328i
$847$	−22.8043	−	39.4983i	−0.783566	−	1.35718i
$848$	−28.3894	+	49.1718i	−0.974895	+	1.68857i
$849$	−69.2910	+	25.2199i	−2.37806	+	0.865543i
$850$		0			0
$851$	−1.63667	+	9.28199i	−0.0561042	+	0.318182i
$852$	16.0299	+	5.83441i	0.549175	+	0.199883i
$853$	17.7360	−	14.8823i	0.607270	−	0.509560i	−0.286503	−	0.958079i	$-0.592493\pi$
$853$	17.7360	−	14.8823i	0.607270	−	0.509560i	0.893773	+	0.448519i	$0.148049\pi$
$854$	−103.210			−3.53176
$855$		0			0
$856$	2.54882			0.0871167
$857$	−2.17765	+	1.82726i	−0.0743870	+	0.0624181i	−0.679223	−	0.733932i	$-0.737683\pi$
$857$	−2.17765	+	1.82726i	−0.0743870	+	0.0624181i	0.604836	+	0.796350i	$0.293239\pi$
$858$	−8.16760	−	2.97276i	−0.278837	−	0.101489i
$859$	−4.49254	+	25.4785i	−0.153284	+	0.869314i	0.807055	+	0.590477i	$0.201060\pi$
$859$	−4.49254	+	25.4785i	−0.153284	+	0.869314i	−0.960338	+	0.278838i	$0.910051\pi$
$860$		0			0
$861$	−41.4581	+	15.0895i	−1.41289	+	0.514249i
$862$	22.8724	−	39.6161i	0.779036	−	1.34933i
$863$	19.0016	+	32.9118i	0.646823	+	1.12033i	0.983877	+	0.178844i	$0.0572359\pi$
$863$	19.0016	+	32.9118i	0.646823	+	1.12033i	−0.337055	+	0.941485i	$0.609431\pi$
$864$	3.45338	+	2.89773i	0.117486	+	0.0985827i
$865$		0			0
$866$	−2.10886	−	3.65266i	−0.0716621	−	0.124122i
$867$	−15.3204	+	26.5357i	−0.520307	+	0.901198i
$868$	19.2998	−	7.02455i	0.655077	−	0.238429i
$869$	−0.455217	−	2.58167i	−0.0154422	−	0.0875770i
$870$		0			0
$871$	27.9909	+	10.1879i	0.948437	+	0.345203i
$872$	−3.92083	+	3.28997i	−0.132776	+	0.111412i
$873$	−15.1464			−0.512628
$874$	19.4264	−	28.1369i	0.657108	−	0.951744i
$875$		0			0
$876$	4.44534	−	3.73008i	0.150194	−	0.126028i
$877$	−46.1335	−	16.7912i	−1.55782	−	0.567000i	−0.587583	−	0.809164i	$-0.699921\pi$
$877$	−46.1335	−	16.7912i	−1.55782	−	0.567000i	−0.970235	+	0.242164i	$0.922143\pi$
$878$	1.95755	−	11.1018i	0.0660641	−	0.374668i
$879$	−9.06489	−	51.4095i	−0.305751	−	1.73400i
$880$		0			0
$881$	27.8747	−	48.2804i	0.939123	−	1.62661i	0.172011	−	0.985095i	$-0.444973\pi$
$881$	27.8747	−	48.2804i	0.939123	−	1.62661i	0.767112	−	0.641514i	$-0.221693\pi$
$882$	26.2575	+	45.4793i	0.884135	+	1.53137i
$883$	−12.7435	−	10.6931i	−0.428853	−	0.359851i	0.402666	−	0.915347i	$-0.368084\pi$
$883$	−12.7435	−	10.6931i	−0.428853	−	0.359851i	−0.831519	+	0.555496i	$0.812528\pi$
$884$	−7.69345	−	6.45557i	−0.258759	−	0.217124i
$885$		0			0
$886$	−28.1307	+	48.7237i	−0.945068	+	1.63691i
$887$	−40.7717	+	14.8397i	−1.36898	+	0.498267i	−0.918818	−	0.394680i	$-0.870855\pi$
$887$	−40.7717	+	14.8397i	−1.36898	+	0.498267i	−0.450160	+	0.892948i	$0.648633\pi$
$888$	−1.29097	−	7.32147i	−0.0433222	−	0.245692i
$889$	−14.5811	+	82.6934i	−0.489034	+	2.77345i
$890$		0			0
$891$	3.70480	−	3.10869i	0.124115	−	0.104145i
$892$	3.74820			0.125499
$893$	2.88455	−	11.0564i	0.0965276	−	0.369989i
$894$	−19.7285			−0.659819
$895$		0			0
$896$	−42.5001	−	15.4688i	−1.41983	−	0.516776i
$897$	−7.57214	+	42.9438i	−0.252827	+	1.43385i
$898$	4.67426	+	26.5091i	0.155982	+	0.884619i
$899$	12.5345	−	4.56220i	0.418051	−	0.152158i
$900$		0			0
$901$	11.6410	+	20.1628i	0.387818	+	0.671721i
$902$	2.93010	+	2.45865i	0.0975617	+	0.0818640i
$903$	−82.2399	−	69.0075i	−2.73677	−	2.29643i
$904$	9.64125	+	16.6991i	0.320663	+	0.555405i
$905$		0			0
$906$	−56.8107	+	20.6774i	−1.88741	+	0.686961i
$907$	3.44455	+	19.5350i	0.114374	+	0.648649i	0.987058	+	0.160363i	$0.0512666\pi$
$907$	3.44455	+	19.5350i	0.114374	+	0.648649i	−0.872684	+	0.488286i	$0.837622\pi$
$908$	1.86165	−	10.5580i	0.0617812	−	0.350378i
$909$	8.32000	+	3.02823i	0.275957	+	0.100440i
$910$		0			0
$911$	15.4076			0.510478			0.255239	−	0.966878i	$-0.417846\pi$
$911$	15.4076			0.510478			0.255239	+	0.966878i	$0.417846\pi$
$912$	−13.0253	+	49.9259i	−0.431312	+	1.65321i
$913$	3.98395			0.131849
$914$	27.5270	−	23.0979i	0.910512	−	0.764010i
$915$		0			0
$916$	−3.68193	+	20.8812i	−0.121654	+	0.689936i
$917$	2.52490	+	14.3194i	0.0833795	+	0.472869i
$918$	2.58572	−	0.941127i	0.0853416	−	0.0310618i
$919$	6.62805	−	11.4801i	0.218639	−	0.378694i	−0.735753	−	0.677250i	$-0.763172\pi$
$919$	6.62805	−	11.4801i	0.218639	−	0.378694i	0.954392	+	0.298556i	$0.0965049\pi$
$920$		0			0
$921$	9.96201	+	8.35912i	0.328259	+	0.275442i
$922$	10.2329	+	8.58644i	0.337003	+	0.282779i
$923$	12.5663	+	21.7654i	0.413624	+	0.716417i
$924$	2.93926	−	5.09095i	0.0966947	−	0.167480i
$925$		0			0
$926$	−6.69313	−	37.9586i	−0.219950	−	1.24740i
$927$	1.59096	−	9.02281i	0.0522541	−	0.296348i
$928$	18.2531	+	6.64358i	0.599187	+	0.218086i
$929$	23.9018	−	20.0560i	0.784193	−	0.658016i	−0.160108	−	0.987100i	$-0.551184\pi$
$929$	23.9018	−	20.0560i	0.784193	−	0.658016i	0.944301	+	0.329083i	$0.106740\pi$
$930$		0			0
$931$	27.1680	−	39.3496i	0.890394	−	1.28963i
$932$	−7.63580			−0.250119
$933$	−12.2296	+	10.2618i	−0.400379	+	0.335958i
$934$	45.3648	+	16.5114i	1.48438	+	0.540270i
$935$		0			0
$936$	−2.81944	−	15.9899i	−0.0921564	−	0.522645i
$937$	15.2405	−	5.54711i	0.497887	−	0.181216i	−0.0808564	−	0.996726i	$-0.525766\pi$
$937$	15.2405	−	5.54711i	0.497887	−	0.181216i	0.578743	+	0.815510i	$0.303543\pi$
$938$	−27.0729	+	46.8916i	−0.883961	+	1.53107i
$939$	5.46216	+	9.46074i	0.178251	+	0.308739i
$940$		0			0
$941$	26.9454	+	22.6099i	0.878396	+	0.737062i	0.965849	−	0.259107i	$-0.0834281\pi$
$941$	26.9454	+	22.6099i	0.878396	+	0.737062i	−0.0874525	+	0.996169i	$0.527873\pi$
$942$	22.8200	+	39.5254i	0.743516	+	1.28781i
$943$	9.59486	−	16.6188i	0.312452	−	0.541182i
$944$	−2.53055	+	0.921045i	−0.0823624	+	0.0299775i
$945$		0			0
$946$	−1.61623	+	9.16612i	−0.0525483	+	0.298016i
$947$	20.9348	+	7.61965i	0.680290	+	0.247605i	0.658972	−	0.752167i	$-0.270991\pi$
$947$	20.9348	+	7.61965i	0.680290	+	0.247605i	0.0213182	+	0.999773i	$0.493214\pi$
$948$	−11.5566	+	9.69713i	−0.375340	+	0.314948i
$949$	8.54953			0.277530
$950$		0			0
$951$	65.9811			2.13958
$952$	−9.61666	+	8.06934i	−0.311678	+	0.261529i
$953$	4.00305	+	1.45699i	0.129672	+	0.0471966i	0.406041	−	0.913855i	$-0.366909\pi$
$953$	4.00305	+	1.45699i	0.129672	+	0.0471966i	−0.276369	+	0.961052i	$0.589131\pi$
$954$	9.50487	−	53.9048i	0.307732	−	1.74523i
$955$		0			0
$956$	15.0049	−	5.46135i	0.485294	−	0.176633i
$957$	1.90895	−	3.30640i	0.0617076	−	0.106881i
$958$	−33.9566	−	58.8145i	−1.09709	−	1.90021i
$959$	1.97535	+	1.65751i	0.0637873	+	0.0535239i
$960$		0			0
$961$	7.14280	+	12.3717i	0.230413	+	0.399087i
$962$	−7.96412	+	13.7943i	−0.256773	+	0.444745i
$963$	−4.41736	+	1.60779i	−0.142347	+	0.0518102i
$964$	−3.62907	−	20.5815i	−0.116885	−	0.662885i
$965$		0			0
$966$	−74.4848	−	27.1102i	−2.39651	−	0.872258i
$967$	−0.933854	+	0.783596i	−0.0300307	+	0.0251988i	−0.657679	−	0.753298i	$-0.728462\pi$
$967$	−0.933854	+	0.783596i	−0.0300307	+	0.0251988i	0.627649	+	0.778497i	$0.284017\pi$
$968$	−15.6477			−0.502935
$969$	15.0588	+	14.8615i	0.483758	+	0.477419i
$970$		0			0
$971$	−3.32466	+	2.78972i	−0.106693	+	0.0895264i	−0.694574	−	0.719421i	$-0.744407\pi$
$971$	−3.32466	+	2.78972i	−0.106693	+	0.0895264i	0.587880	+	0.808948i	$0.299963\pi$
$972$	−23.6234	−	8.59821i	−0.757720	−	0.275788i
$973$	6.22604	−	35.3096i	0.199598	−	1.13197i
$974$	−5.68222	−	32.2255i	−0.182070	−	1.03257i
$975$		0			0
$976$	−33.8720	+	58.6680i	−1.08422	+	1.87792i
$977$	−10.7635	−	18.6429i	−0.344355	−	0.596440i	0.640882	−	0.767640i	$-0.278569\pi$
$977$	−10.7635	−	18.6429i	−0.344355	−	0.596440i	−0.985236	+	0.171200i	$0.945236\pi$
$978$	55.1956	+	46.3146i	1.76496	+	1.48098i
$979$	1.63240	+	1.36975i	0.0521718	+	0.0437773i
$980$		0			0
$981$	4.71990	−	8.17510i	0.150695	−	0.261011i
$982$	−25.2689	+	9.19713i	−0.806363	+	0.293492i
$983$	2.53522	+	14.3780i	0.0808611	+	0.458586i	0.998173	+	0.0604172i	$0.0192431\pi$
$983$	2.53522	+	14.3780i	0.0808611	+	0.458586i	−0.917312	+	0.398169i	$0.869646\pi$
$984$	−2.62843	+	14.9066i	−0.0837912	+	0.475204i
$985$		0			0
$986$	9.08261	−	7.62121i	0.289249	−	0.242709i
$987$	−26.4896			−0.843172
$988$	17.5295	−	12.4474i	0.557688	−	0.396004i
$989$	46.6954			1.48483
$990$		0			0
$991$	−30.0031	−	10.9202i	−0.953080	−	0.346893i	−0.181762	−	0.983343i	$-0.558180\pi$
$991$	−30.0031	−	10.9202i	−0.953080	−	0.346893i	−0.771318	+	0.636450i	$0.780402\pi$
$992$	4.22658	−	23.9701i	0.134194	−	0.761052i
$993$	5.84900	+	33.1713i	0.185612	+	1.05266i
$994$	−42.9294	+	15.6250i	−1.36164	+	0.495596i
$995$		0			0
$996$	−11.4633	−	19.8551i	−0.363229	−	0.629132i
$997$	42.2712	+	35.4698i	1.33874	+	1.12334i	0.981947	+	0.189157i	$0.0605756\pi$
$997$	42.2712	+	35.4698i	1.33874	+	1.12334i	0.356797	+	0.934182i	$0.383869\pi$
$998$	−47.2073	−	39.6117i	−1.49432	−	1.25389i
$999$	−0.811883	−	1.40622i	−0.0256868	−	0.0444909i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.l.f.101.2		48
5.2	odd	4		95.2.p.a.44.2	✓	48
5.3	odd	4		95.2.p.a.44.7	yes	48
5.4	even	2	inner	475.2.l.f.101.7		48
15.2	even	4		855.2.da.b.424.7		48
15.8	even	4		855.2.da.b.424.2		48
19.4	even	9		9025.2.a.cu.1.5		24
19.15	odd	18		9025.2.a.ct.1.20		24
19.16	even	9	inner	475.2.l.f.301.2		48
95.4	even	18		9025.2.a.cu.1.20		24
95.23	odd	36		1805.2.b.k.1084.20		24
95.34	odd	18		9025.2.a.ct.1.5		24
95.42	odd	36		1805.2.b.k.1084.5		24
95.53	even	36		1805.2.b.l.1084.5		24
95.54	even	18	inner	475.2.l.f.301.7		48
95.72	even	36		1805.2.b.l.1084.20		24
95.73	odd	36		95.2.p.a.54.2	yes	48
95.92	odd	36		95.2.p.a.54.7	yes	48
285.92	even	36		855.2.da.b.244.2		48
285.263	even	36		855.2.da.b.244.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.44.2	✓	48	5.2	odd	4
95.2.p.a.44.7	yes	48	5.3	odd	4
95.2.p.a.54.2	yes	48	95.73	odd	36
95.2.p.a.54.7	yes	48	95.92	odd	36
475.2.l.f.101.2		48	1.1	even	1	trivial
475.2.l.f.101.7		48	5.4	even	2	inner
475.2.l.f.301.2		48	19.16	even	9	inner
475.2.l.f.301.7		48	95.54	even	18	inner
855.2.da.b.244.2		48	285.92	even	36
855.2.da.b.244.7		48	285.263	even	36
855.2.da.b.424.2		48	15.8	even	4
855.2.da.b.424.7		48	15.2	even	4
1805.2.b.k.1084.5		24	95.42	odd	36
1805.2.b.k.1084.20		24	95.23	odd	36
1805.2.b.l.1084.5		24	95.53	even	36
1805.2.b.l.1084.20		24	95.72	even	36
9025.2.a.ct.1.5		24	95.34	odd	18
9025.2.a.ct.1.20		24	19.15	odd	18
9025.2.a.cu.1.5		24	19.4	even	9
9025.2.a.cu.1.20		24	95.4	even	18

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36714 + 1.14717i) q^{2} +(2.24001 + 0.815296i) q^{3} +(0.205786 - 1.16707i) q^{4} +(-3.99769 + 1.45504i) q^{6} +(2.11955 - 3.67118i) q^{7} +(-0.727188 - 1.25953i) q^{8} +(2.05480 + 1.72418i) q^{9} +O(q^{10})\)	\(q+(-1.36714 + 1.14717i) q^{2} +(2.24001 + 0.815296i) q^{3} +(0.205786 - 1.16707i) q^{4} +(-3.99769 + 1.45504i) q^{6} +(2.11955 - 3.67118i) q^{7} +(-0.727188 - 1.25953i) q^{8} +(2.05480 + 1.72418i) q^{9} +(0.245445 + 0.425123i) q^{11} +(1.41247 - 2.44648i) q^{12} +(3.91099 - 1.42349i) q^{13} +(1.31373 + 7.45051i) q^{14} +(4.66628 + 1.69839i) q^{16} +(1.55982 - 1.30884i) q^{17} -4.78713 q^{18} +(1.86816 + 3.93827i) q^{19} +(7.74092 - 6.49540i) q^{21} +(-0.823245 - 0.299637i) q^{22} +(-0.763227 + 4.32847i) q^{23} +(-0.602020 - 3.41422i) q^{24} +(-3.71391 + 6.43268i) q^{26} +(-0.378606 - 0.655764i) q^{27} +(-3.84835 - 3.22915i) q^{28} +(-2.49937 - 2.09722i) q^{29} +(-2.04416 + 3.54059i) q^{31} +(-5.59447 + 2.03622i) q^{32} +(0.203197 + 1.15239i) q^{33} +(-0.631029 + 3.57874i) q^{34} +(2.43509 - 2.04328i) q^{36} +2.14440 q^{37} +(-7.07191 - 3.24108i) q^{38} +9.92123 q^{39} +(-4.10271 - 1.49327i) q^{41} +(-3.13162 + 17.7603i) q^{42} +(-1.84485 - 10.4627i) q^{43} +(0.546658 - 0.198967i) q^{44} +(-3.92205 - 6.79319i) q^{46} +(-2.00812 - 1.68502i) q^{47} +(9.06781 + 7.60880i) q^{48} +(-5.48502 - 9.50033i) q^{49} +(4.56109 - 1.66010i) q^{51} +(-0.856482 - 4.85735i) q^{52} +(-1.98551 + 11.2604i) q^{53} +(1.26988 + 0.462199i) q^{54} -6.16526 q^{56} +(0.973843 + 10.3449i) q^{57} +5.82287 q^{58} +(-0.415431 + 0.348588i) q^{59} +(-2.36895 + 13.4350i) q^{61} +(-1.26700 - 7.18550i) q^{62} +(10.6850 - 3.88903i) q^{63} +(0.346803 - 0.600680i) q^{64} +(-1.59978 - 1.34238i) q^{66} +(5.48257 + 4.60042i) q^{67} +(-1.20652 - 2.08976i) q^{68} +(-5.23862 + 9.07356i) q^{69} +(1.04859 + 5.94684i) q^{71} +(0.677426 - 3.84187i) q^{72} +(1.93031 + 0.702575i) q^{73} +(-2.93170 + 2.45999i) q^{74} +(4.98069 - 1.36984i) q^{76} +2.08093 q^{77} +(-13.5637 + 11.3813i) q^{78} +(-5.01823 - 1.82649i) q^{79} +(-1.71079 - 9.70238i) q^{81} +(7.32202 - 2.66500i) q^{82} +(4.05789 - 7.02847i) q^{83} +(-5.98763 - 10.3709i) q^{84} +(14.5246 + 12.1876i) q^{86} +(-3.88876 - 6.73553i) q^{87} +(0.356969 - 0.618288i) q^{88} +(4.07920 - 1.48471i) q^{89} +(3.06370 - 17.3751i) q^{91} +(4.89458 + 1.78148i) q^{92} +(-7.46558 + 6.26436i) q^{93} +4.67839 q^{94} -14.1918 q^{96} +(-4.32562 + 3.62962i) q^{97} +(18.3973 + 6.69607i) q^{98} +(-0.228649 + 1.29673i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9}+O(q^{10}) \) 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9	\( 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 42 q^{16} - 12 q^{19} - 54 q^{21} - 24 q^{24} + 12 q^{26} - 42 q^{31} + 36 q^{34} + 18 q^{36} + 48 q^{39} + 6 q^{41} + 6 q^{44} - 6 q^{46} - 12 q^{49} + 108 q^{51} - 24 q^{54} + 36 q^{56} + 36 q^{59} + 48 q^{61} + 180 q^{66} - 66 q^{69} - 24 q^{71} - 84 q^{74} + 66 q^{76} - 48 q^{79} - 78 q^{81} + 54 q^{84} - 42 q^{86} + 12 q^{89} - 30 q^{91} + 72 q^{94} - 240 q^{96} + 36 q^{99}+O(q^{100}) \) 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 42 * q^16 - 12 * q^19 - 54 * q^21 - 24 * q^24 + 12 * q^26 - 42 * q^31 + 36 * q^34 + 18 * q^36 + 48 * q^39 + 6 * q^41 + 6 * q^44 - 6 * q^46 - 12 * q^49 + 108 * q^51 - 24 * q^54 + 36 * q^56 + 36 * q^59 + 48 * q^61 + 180 * q^66 - 66 * q^69 - 24 * q^71 - 84 * q^74 + 66 * q^76 - 48 * q^79 - 78 * q^81 + 54 * q^84 - 42 * q^86 + 12 * q^89 - 30 * q^91 + 72 * q^94 - 240 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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