LMFDB - Embedded newform 575.2.p.a.324.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(49,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 16]))

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

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

chi := DirichletCharacter("575.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.p (of order $22$, degree $10$, not 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:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{22})$
Coefficient field:	$\Q(\zeta_{44})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 115)
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			324.2
Root			$0.281733 + 0.959493i$ of defining polynomial
Character	$\chi$	$=$	575.324
Dual form			575.2.p.a.449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.835939 - 1.30075i) q^{2} +(0.989821 - 0.142315i) q^{3} +(-0.162317 - 0.355426i) q^{4} +(0.642315 - 1.40647i) q^{6} +(1.81219 + 1.57028i) q^{7} +(2.46292 + 0.354114i) q^{8} +(-1.91899 + 0.563465i) q^{9} +O(q^{10})$	\(q+(0.835939 - 1.30075i) q^{2} +(0.989821 - 0.142315i) q^{3} +(-0.162317 - 0.355426i) q^{4} +(0.642315 - 1.40647i) q^{6} +(1.81219 + 1.57028i) q^{7} +(2.46292 + 0.354114i) q^{8} +(-1.91899 + 0.563465i) q^{9} +(3.19505 - 2.05334i) q^{11} +(-0.211248 - 0.328708i) q^{12} +(-1.23516 + 1.07028i) q^{13} +(3.55742 - 1.04455i) q^{14} +(3.03122 - 3.49821i) q^{16} +(-2.60635 - 1.19028i) q^{17} +(-0.871230 + 2.96714i) q^{18} +(0.754359 + 1.65182i) q^{19} +(2.01722 + 1.29639i) q^{21} -5.87242i q^{22} +(3.27173 + 3.50654i) q^{23} +2.48825 q^{24} +(0.359636 + 2.50132i) q^{26} +(-4.54816 + 2.07708i) q^{27} +(0.263965 - 0.898983i) q^{28} +(3.57631 - 7.83103i) q^{29} +(0.185062 - 1.28713i) q^{31} +(-0.614334 - 2.09223i) q^{32} +(2.87031 - 2.48714i) q^{33} +(-3.72700 + 2.39520i) q^{34} +(0.511755 + 0.590596i) q^{36} +(-1.93221 - 6.58052i) q^{37} +(2.77919 + 0.399587i) q^{38} +(-1.07028 + 1.23516i) q^{39} +(-6.01710 - 1.76678i) q^{41} +(3.37255 - 1.54019i) q^{42} +(-11.9687 + 1.72084i) q^{43} +(-1.24842 - 0.802311i) q^{44} +(7.29608 - 1.32443i) q^{46} +4.66817i q^{47} +(2.50252 - 3.89399i) q^{48} +(-0.177920 - 1.23746i) q^{49} +(-2.74921 - 0.807241i) q^{51} +(0.580892 + 0.265284i) q^{52} +(-3.86681 - 3.35061i) q^{53} +(-1.10024 + 7.65231i) q^{54} +(3.90723 + 4.50919i) q^{56} +(0.981759 + 1.52765i) q^{57} +(-7.19661 - 11.1981i) q^{58} +(4.75399 + 5.48639i) q^{59} +(-1.23344 + 8.57875i) q^{61} +(-1.51953 - 1.31668i) q^{62} +(-4.36237 - 1.99223i) q^{63} +(5.64759 + 1.65828i) q^{64} +(-0.835732 - 5.81264i) q^{66} +(-2.80554 + 4.36550i) q^{67} +1.11956i q^{68} +(3.73746 + 3.00523i) q^{69} +(-2.38202 - 1.53083i) q^{71} +(-4.92584 + 0.708228i) q^{72} +(-1.90991 + 0.872226i) q^{73} +(-10.1748 - 2.98759i) q^{74} +(0.464652 - 0.536237i) q^{76} +(9.01436 + 1.29607i) q^{77} +(0.711950 + 2.42468i) q^{78} +(-8.09638 - 9.34373i) q^{79} +(0.841254 - 0.540641i) q^{81} +(-7.32806 + 6.34980i) q^{82} +(3.84719 + 13.1023i) q^{83} +(0.133340 - 0.927399i) q^{84} +(-7.76672 + 17.0068i) q^{86} +(2.42544 - 8.26028i) q^{87} +(8.59627 - 3.92579i) q^{88} +(-1.65356 - 11.5007i) q^{89} -3.91899 q^{91} +(0.715255 - 1.73203i) q^{92} -1.30037i q^{93} +(6.07211 + 3.90231i) q^{94} +(-0.905836 - 1.98350i) q^{96} +(-1.74792 + 5.95288i) q^{97} +(-1.75835 - 0.803012i) q^{98} +(-4.97428 + 5.74062i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{4} + 12 q^{6} - 4 q^{9}+O(q^{10}) $ 20 * q + 2 * q^4 + 12 * q^6 - 4 * q^9	$ 20 q + 2 q^{4} + 12 q^{6} - 4 q^{9} + 16 q^{11} + 6 q^{14} + 10 q^{16} + 26 q^{19} + 12 q^{21} + 12 q^{24} + 22 q^{26} - 4 q^{29} - 40 q^{31} - 32 q^{34} + 48 q^{36} - 10 q^{41} - 38 q^{44} - 32 q^{46} - 8 q^{49} - 20 q^{51} + 60 q^{54} + 6 q^{56} - 10 q^{59} - 6 q^{61} + 68 q^{64} - 8 q^{66} + 2 q^{69} - 44 q^{71} - 2 q^{74} - 4 q^{76} - 102 q^{79} - 2 q^{81} - 12 q^{84} - 18 q^{86} - 114 q^{89} - 44 q^{91} + 162 q^{94} - 14 q^{96} - 12 q^{99}+O(q^{100}) $ 20 * q + 2 * q^4 + 12 * q^6 - 4 * q^9 + 16 * q^11 + 6 * q^14 + 10 * q^16 + 26 * q^19 + 12 * q^21 + 12 * q^24 + 22 * q^26 - 4 * q^29 - 40 * q^31 - 32 * q^34 + 48 * q^36 - 10 * q^41 - 38 * q^44 - 32 * q^46 - 8 * q^49 - 20 * q^51 + 60 * q^54 + 6 * q^56 - 10 * q^59 - 6 * q^61 + 68 * q^64 - 8 * q^66 + 2 * q^69 - 44 * q^71 - 2 * q^74 - 4 * q^76 - 102 * q^79 - 2 * q^81 - 12 * q^84 - 18 * q^86 - 114 * q^89 - 44 * q^91 + 162 * q^94 - 14 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/575\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$e\left(\frac{1}{11}\right)$	$-1$

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 $

$2$	0.835939	−	1.30075i	0.591098	−	0.919767i	−0.408876	−	0.912590i	$-0.634079\pi$
$2$	0.835939	−	1.30075i	0.591098	−	0.919767i	0.999974	−	0.00717677i	$-0.00228446\pi$
$3$	0.989821	−	0.142315i	0.571474	−	0.0821655i	0.149481	−	0.988765i	$-0.452240\pi$
$3$	0.989821	−	0.142315i	0.571474	−	0.0821655i	0.421993	+	0.906599i	$0.361331\pi$
$4$	−0.162317	−	0.355426i	−0.0811587	−	0.177713i
$5$		0			0
$5$		0			0
$6$	0.642315	−	1.40647i	0.262224	−	0.574190i
$7$	1.81219	+	1.57028i	0.684945	+	0.593508i	0.926236	−	0.376944i	$-0.123025\pi$
$7$	1.81219	+	1.57028i	0.684945	+	0.593508i	−0.241291	+	0.970453i	$0.577571\pi$
$8$	2.46292	+	0.354114i	0.870773	+	0.125198i
$9$	−1.91899	+	0.563465i	−0.639662	+	0.187822i
$10$		0			0
$11$	3.19505	−	2.05334i	0.963345	−	0.619104i	0.0384230	−	0.999262i	$-0.487767\pi$
$11$	3.19505	−	2.05334i	0.963345	−	0.619104i	0.924922	+	0.380158i	$0.124130\pi$
$12$	−0.211248	−	0.328708i	−0.0609819	−	0.0948897i
$13$	−1.23516	+	1.07028i	−0.342573	+	0.296841i	−0.809106	−	0.587663i	$-0.800048\pi$
$13$	−1.23516	+	1.07028i	−0.342573	+	0.296841i	0.466533	+	0.884504i	$0.345503\pi$
$14$	3.55742	−	1.04455i	0.950759	−	0.279168i
$15$		0			0
$16$	3.03122	−	3.49821i	0.757804	−	0.874553i
$17$	−2.60635	−	1.19028i	−0.632132	−	0.288685i	0.0734657	−	0.997298i	$-0.476594\pi$
$17$	−2.60635	−	1.19028i	−0.632132	−	0.288685i	−0.705598	+	0.708613i	$0.749321\pi$
$18$	−0.871230	+	2.96714i	−0.205351	+	0.699361i
$19$	0.754359	+	1.65182i	0.173062	+	0.378953i	0.976210	−	0.216827i	$-0.0695706\pi$
$19$	0.754359	+	1.65182i	0.173062	+	0.378953i	−0.803148	+	0.595779i	$0.796843\pi$
$20$		0			0
$21$	2.01722	+	1.29639i	0.440194	+	0.282896i
$22$		−	5.87242i		−	1.25200i
$23$	3.27173	+	3.50654i	0.682202	+	0.731164i
$23$	3.27173	+	3.50654i	0.682202	+	0.731164i
$24$	2.48825			0.507911
$25$		0			0
$26$	0.359636	+	2.50132i	0.0705303	+	0.490549i
$27$	−4.54816	+	2.07708i	−0.875294	+	0.399733i
$28$	0.263965	−	0.898983i	0.0498848	−	0.169892i
$29$	3.57631	−	7.83103i	0.664104	−	1.45419i	−0.214543	−	0.976715i	$-0.568826\pi$
$29$	3.57631	−	7.83103i	0.664104	−	1.45419i	0.878647	−	0.477471i	$-0.158447\pi$
$30$		0			0
$31$	0.185062	−	1.28713i	0.0332380	−	0.231176i	−0.966430	−	0.256929i	$-0.917289\pi$
$31$	0.185062	−	1.28713i	0.0332380	−	0.231176i	0.999668	+	0.0257533i	$0.00819844\pi$
$32$	−0.614334	−	2.09223i	−0.108600	−	0.369857i
$33$	2.87031	−	2.48714i	0.499657	−	0.432955i
$34$	−3.72700	+	2.39520i	−0.639175	+	0.410773i
$35$		0			0
$36$	0.511755	+	0.590596i	0.0852924	+	0.0984327i
$37$	−1.93221	−	6.58052i	−0.317654	−	1.08183i	−0.951315	−	0.308220i	$-0.900267\pi$
$37$	−1.93221	−	6.58052i	−0.317654	−	1.08183i	0.633661	−	0.773611i	$-0.281551\pi$
$38$	2.77919	+	0.399587i	0.450844	+	0.0648216i
$39$	−1.07028	+	1.23516i	−0.171381	+	0.197785i
$40$		0			0
$41$	−6.01710	−	1.76678i	−0.939712	−	0.275924i	−0.224215	−	0.974540i	$-0.571982\pi$
$41$	−6.01710	−	1.76678i	−0.939712	−	0.275924i	−0.715498	+	0.698615i	$0.753800\pi$
$42$	3.37255	−	1.54019i	0.520396	−	0.237657i
$43$	−11.9687	+	1.72084i	−1.82521	+	0.262425i	−0.967711	−	0.252062i	$-0.918891\pi$
$43$	−11.9687	+	1.72084i	−1.82521	+	0.262425i	−0.857498	+	0.514488i	$0.827982\pi$
$44$	−1.24842	−	0.802311i	−0.188206	−	0.120953i
$45$		0			0
$46$	7.29608	−	1.32443i	1.07575	−	0.195277i
$47$			4.66817i			0.680923i	0.940258	+	0.340461i	$0.110583\pi$
$47$			4.66817i			0.680923i	−0.940258	+	0.340461i	$0.889417\pi$
$48$	2.50252	−	3.89399i	0.361207	−	0.562049i
$49$	−0.177920	−	1.23746i	−0.0254171	−	0.176780i
$50$		0			0
$51$	−2.74921	−	0.807241i	−0.384967	−	0.113036i
$52$	0.580892	+	0.265284i	0.0805552	+	0.0367883i
$53$	−3.86681	−	3.35061i	−0.531147	−	0.460241i	0.347523	−	0.937671i	$-0.387023\pi$
$53$	−3.86681	−	3.35061i	−0.531147	−	0.460241i	−0.878670	+	0.477430i	$0.841568\pi$
$54$	−1.10024	+	7.65231i	−0.149723	+	1.04135i
$55$		0			0
$56$	3.90723	+	4.50919i	0.522126	+	0.602565i
$57$	0.981759	+	1.52765i	0.130037	+	0.202342i
$58$	−7.19661	−	11.1981i	−0.944961	−	1.47039i
$59$	4.75399	+	5.48639i	0.618916	+	0.714267i	0.975501	−	0.219996i	$-0.0706043\pi$
$59$	4.75399	+	5.48639i	0.618916	+	0.714267i	−0.356585	+	0.934263i	$0.616059\pi$
$60$		0			0
$61$	−1.23344	+	8.57875i	−0.157926	+	1.09840i	0.744523	+	0.667597i	$0.232677\pi$
$61$	−1.23344	+	8.57875i	−0.157926	+	1.09840i	−0.902448	+	0.430799i	$0.858232\pi$
$62$	−1.51953	−	1.31668i	−0.192981	−	0.167219i
$63$	−4.36237	−	1.99223i	−0.549607	−	0.250997i
$64$	5.64759	+	1.65828i	0.705949	+	0.207285i
$65$		0			0
$66$	−0.835732	−	5.81264i	−0.102872	−	0.715487i
$67$	−2.80554	+	4.36550i	−0.342751	+	0.533331i	−0.969246	−	0.246095i	$-0.920853\pi$
$67$	−2.80554	+	4.36550i	−0.342751	+	0.533331i	0.626495	+	0.779426i	$0.284489\pi$
$68$			1.11956i			0.135767i
$69$	3.73746	+	3.00523i	0.449937	+	0.361787i
$70$		0			0
$71$	−2.38202	−	1.53083i	−0.282694	−	0.181676i	0.391608	−	0.920132i	$-0.371919\pi$
$71$	−2.38202	−	1.53083i	−0.282694	−	0.181676i	−0.674302	+	0.738456i	$0.735555\pi$
$72$	−4.92584	+	0.708228i	−0.580515	+	0.0834655i
$73$	−1.90991	+	0.872226i	−0.223538	+	0.102086i	−0.524036	−	0.851696i	$-0.675574\pi$
$73$	−1.90991	+	0.872226i	−0.223538	+	0.102086i	0.300498	+	0.953782i	$0.402847\pi$
$74$	−10.1748	−	2.98759i	−1.18280	−	0.347300i
$75$		0			0
$76$	0.464652	−	0.536237i	0.0532992	−	0.0615106i
$77$	9.01436	+	1.29607i	1.02728	+	0.147701i
$78$	0.711950	+	2.42468i	0.0806125	+	0.274541i
$79$	−8.09638	−	9.34373i	−0.910914	−	1.05125i	−0.998481	−	0.0550926i	$-0.982455\pi$
$79$	−8.09638	−	9.34373i	−0.910914	−	1.05125i	0.0875669	−	0.996159i	$-0.472091\pi$
$80$		0			0
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$	−7.32806	+	6.34980i	−0.809248	+	0.701218i
$83$	3.84719	+	13.1023i	0.422284	+	1.43817i	0.846394	+	0.532557i	$0.178769\pi$
$83$	3.84719	+	13.1023i	0.422284	+	1.43817i	−0.424110	+	0.905611i	$0.639413\pi$
$84$	0.133340	−	0.927399i	0.0145486	−	0.101188i
$85$		0			0
$86$	−7.76672	+	17.0068i	−0.837507	+	1.83389i
$87$	2.42544	−	8.26028i	0.260034	−	0.885595i
$88$	8.59627	−	3.92579i	0.916366	−	0.418490i
$89$	−1.65356	−	11.5007i	−0.175276	−	1.21907i	−0.867517	−	0.497408i	$-0.834285\pi$
$89$	−1.65356	−	11.5007i	−0.175276	−	1.21907i	0.692240	−	0.721667i	$-0.256624\pi$
$90$		0			0
$91$	−3.91899			−0.410821
$92$	0.715255	−	1.73203i	0.0745705	−	0.180576i
$93$		−	1.30037i		−	0.134842i
$94$	6.07211	+	3.90231i	0.626290	+	0.402492i
$95$		0			0
$96$	−0.905836	−	1.98350i	−0.0924515	−	0.202441i
$97$	−1.74792	+	5.95288i	−0.177475	+	0.604423i	0.821919	+	0.569605i	$0.192904\pi$
$97$	−1.74792	+	5.95288i	−0.177475	+	0.604423i	−0.999394	+	0.0348189i	$0.988915\pi$
$98$	−1.75835	−	0.803012i	−0.177620	−	0.0811164i
$99$	−4.97428	+	5.74062i	−0.499934	+	0.576954i
$100$		0			0
$101$	−12.2111	+	3.58550i	−1.21505	+	0.356771i	−0.825589	−	0.564273i	$-0.809157\pi$
$101$	−12.2111	+	3.58550i	−1.21505	+	0.356771i	−0.389460	+	0.921043i	$0.627339\pi$
$102$	−3.34819	+	2.90122i	−0.331520	+	0.287264i
$103$	−0.273808	−	0.426053i	−0.0269791	−	0.0419803i	0.827502	−	0.561463i	$-0.189761\pi$
$103$	−0.273808	−	0.426053i	−0.0269791	−	0.0419803i	−0.854481	+	0.519482i	$0.826125\pi$
$104$	−3.42111	+	2.19861i	−0.335467	+	0.215592i
$105$		0			0
$106$	−7.59071	+	2.22883i	−0.737275	+	0.216483i
$107$	9.42415	+	1.35499i	0.911067	+	0.130992i	0.581881	−	0.813274i	$-0.302317\pi$
$107$	9.42415	+	1.35499i	0.911067	+	0.130992i	0.329185	+	0.944265i	$0.393226\pi$
$108$	1.47649	+	1.27939i	0.142075	+	0.123109i
$109$	3.35462	−	7.34559i	0.321314	−	0.703580i	−0.678196	−	0.734881i	$-0.737238\pi$
$109$	3.35462	−	7.34559i	0.321314	−	0.703580i	0.999510	+	0.0313010i	$0.00996506\pi$
$110$		0			0
$111$	−2.84905	−	6.23856i	−0.270420	−	0.592137i
$112$	10.9863	−	1.57959i	1.03811	−	0.149258i
$113$	−1.91257	+	2.97601i	−0.179919	+	0.279960i	−0.919485	−	0.393124i	$-0.871394\pi$
$113$	−1.91257	+	2.97601i	−0.179919	+	0.279960i	0.739566	+	0.673084i	$0.235031\pi$
$114$	2.80777			0.262972
$115$		0			0
$116$	−3.36385			−0.312325
$117$	1.76720	−	2.74982i	0.163378	−	0.254221i
$118$	11.1104	−	1.59744i	1.02280	−	0.147056i
$119$	−2.85414	−	6.24970i	−0.261639	−	0.572909i
$120$		0			0
$121$	1.42261	−	3.11508i	0.129328	−	0.283189i
$122$	10.1277	+	8.77570i	0.916919	+	0.794514i
$123$	−6.20729	−	0.892473i	−0.559692	−	0.0804716i
$124$	−0.487518	+	0.143148i	−0.0437804	+	0.0128551i
$125$		0			0
$126$	−6.23806	+	4.00896i	−0.555731	+	0.357146i
$127$	0.164888	+	0.256571i	0.0146315	+	0.0227670i	0.848492	−	0.529208i	$-0.177511\pi$
$127$	0.164888	+	0.256571i	0.0146315	+	0.0227670i	−0.833861	+	0.551975i	$0.813874\pi$
$128$	10.1740	−	8.81578i	0.899259	−	0.779213i
$129$	−11.6020	+	3.40665i	−1.02150	+	0.299938i
$130$		0			0
$131$	14.5546	−	16.7968i	1.27164	−	1.46755i	0.454894	−	0.890545i	$-0.349677\pi$
$131$	14.5546	−	16.7968i	1.27164	−	1.46755i	0.816743	−	0.577002i	$-0.195778\pi$
$132$	−1.34989	−	0.616476i	−0.117493	−	0.0536574i
$133$	−1.22676	+	4.17796i	−0.106374	+	0.362275i
$134$	3.33315	+	7.29859i	0.287940	+	0.630502i
$135$		0			0
$136$	−5.99772	−	3.85450i	−0.514301	−	0.330521i
$137$			13.2706i			1.13379i	0.823791	+	0.566893i	$0.191855\pi$
$137$			13.2706i			1.13379i	−0.823791	+	0.566893i	$0.808145\pi$
$138$	7.03333	−	2.34929i	0.598717	−	0.199985i
$139$	22.1390			1.87781			0.938905	−	0.344177i	$-0.111842\pi$
$139$	22.1390			1.87781			0.938905	+	0.344177i	$0.111842\pi$
$140$		0			0
$141$	0.664350	+	4.62066i	0.0559484	+	0.389130i
$142$	−3.98245	+	1.81872i	−0.334200	+	0.152624i
$143$	−1.74878	+	5.95579i	−0.146240	+	0.498049i
$144$	−3.84574	+	8.42100i	−0.320479	+	0.701750i
$145$		0			0
$146$	−0.462022	+	3.21343i	−0.0382372	+	0.265946i
$147$	−0.352218	−	1.19954i	−0.0290504	−	0.0989366i
$148$	−2.02525	+	1.75489i	−0.166475	+	0.144251i
$149$	−19.0366	+	12.2341i	−1.55954	+	1.00225i	−0.576877	+	0.816831i	$0.695729\pi$
$149$	−19.0366	+	12.2341i	−1.55954	+	1.00225i	−0.982659	+	0.185421i	$0.940635\pi$
$150$		0			0
$151$	−1.31207	−	1.51421i	−0.106775	−	0.123224i	0.699847	−	0.714293i	$-0.253252\pi$
$151$	−1.31207	−	1.51421i	−0.106775	−	0.123224i	−0.806621	+	0.591069i	$0.798706\pi$
$152$	1.27299	+	4.33542i	0.103253	+	0.351649i
$153$	5.67222	+	0.815542i	0.458572	+	0.0659327i
$154$	9.22131	−	10.6420i	0.743075	−	0.857554i
$155$		0			0
$156$	0.612733	+	0.179915i	0.0490579	+	0.0144047i
$157$	−5.83287	+	2.66378i	−0.465514	+	0.212593i	−0.634342	−	0.773052i	$-0.718729\pi$
$157$	−5.83287	+	2.66378i	−0.465514	+	0.212593i	0.168828	+	0.985645i	$0.446002\pi$
$158$	−18.9219	+	2.72056i	−1.50535	+	0.216436i
$159$	−4.30429	−	2.76620i	−0.341352	−	0.219374i
$160$		0			0
$161$	0.422774	+	11.4920i	0.0333193	+	0.905700i
$162$		−	1.54620i		−	0.121481i
$163$	3.60160	−	5.60419i	0.282099	−	0.438954i	−0.671070	−	0.741394i	$-0.734165\pi$
$163$	3.60160	−	5.60419i	0.282099	−	0.438954i	0.953168	+	0.302440i	$0.0978012\pi$
$164$	0.348721	+	2.42541i	0.0272305	+	0.189393i
$165$		0			0
$166$	20.2588	+	5.94853i	1.57239	+	0.461695i
$167$	−3.79953	−	1.73519i	−0.294016	−	0.134273i	0.262946	−	0.964811i	$-0.415306\pi$
$167$	−3.79953	−	1.73519i	−0.294016	−	0.134273i	−0.556962	+	0.830538i	$0.688033\pi$
$168$	4.50919	+	3.90723i	0.347891	+	0.301449i
$169$	−1.46995	+	10.2237i	−0.113073	+	0.786442i
$170$		0			0
$171$	−2.37835	−	2.74476i	−0.181877	−	0.209897i
$172$	2.55436	+	3.97466i	0.194768	+	0.303065i
$173$	13.3730	+	20.8088i	1.01673	+	1.58207i	0.794678	+	0.607031i	$0.207640\pi$
$173$	13.3730	+	20.8088i	1.01673	+	1.58207i	0.222053	+	0.975034i	$0.428724\pi$
$174$	−8.71702	−	10.0600i	−0.660835	−	0.762645i
$175$		0			0
$176$	2.50190	−	17.4011i	0.188588	−	1.31166i
$177$	5.48639	+	4.75399i	0.412383	+	0.357331i
$178$	−16.3418	−	7.46305i	−1.22487	−	0.559379i
$179$	−4.59863	−	1.35028i	−0.343718	−	0.100925i	0.105318	−	0.994439i	$-0.466414\pi$
$179$	−4.59863	−	1.35028i	−0.343718	−	0.100925i	−0.449035	+	0.893514i	$0.648232\pi$
$180$		0			0
$181$	0.395108	+	2.74804i	0.0293681	+	0.204260i	0.999223	−	0.0394253i	$-0.0125527\pi$
$181$	0.395108	+	2.74804i	0.0293681	+	0.204260i	−0.969854	+	0.243685i	$0.921644\pi$
$182$	−3.27603	+	5.09761i	−0.242836	+	0.377860i
$183$			8.66696i			0.640680i
$184$	6.81628	+	9.79488i	0.502503	+	0.722088i
$185$		0			0
$186$	−1.69145	−	1.08703i	−0.124023	−	0.0797048i
$187$	−10.7715	+	1.54870i	−0.787687	+	0.113252i
$188$	1.65919	−	0.757726i	0.121009	−	0.0552628i
$189$	−11.5037	−	3.37780i	−0.836773	−	0.245699i
$190$		0			0
$191$	−0.0274926	+	0.0317282i	−0.00198930	+	0.00229577i	−0.756743	−	0.653712i	$-0.773211\pi$
$191$	−0.0274926	+	0.0317282i	−0.00198930	+	0.00229577i	0.754754	+	0.656008i	$0.227756\pi$
$192$	5.82611	+	0.837667i	0.420463	+	0.0604534i
$193$	−4.61879	−	15.7302i	−0.332468	−	1.13228i	−0.940902	−	0.338678i	$-0.890020\pi$
$193$	−4.61879	−	15.7302i	−0.332468	−	1.13228i	0.608434	−	0.793604i	$-0.291798\pi$
$194$	6.28203	+	7.24985i	0.451024	+	0.520509i
$195$		0			0
$196$	−0.410945	+	0.264098i	−0.0293532	+	0.0188642i
$197$	17.6768	−	15.3171i	1.25942	−	1.09130i	0.267618	−	0.963525i	$-0.413763\pi$
$197$	17.6768	−	15.3171i	1.25942	−	1.09130i	0.991804	−	0.127770i	$-0.0407821\pi$
$198$	3.30890	+	11.2691i	0.235153	+	0.800859i
$199$	−0.0188178	+	0.130881i	−0.00133396	+	0.00927789i	−0.990478	−	0.137674i	$-0.956037\pi$
$199$	−0.0188178	+	0.130881i	−0.00133396	+	0.00927789i	0.989144	+	0.146952i	$0.0469464\pi$
$200$		0			0
$201$	−2.15571	+	4.72034i	−0.152052	+	0.332947i
$202$	−5.54390	+	18.8808i	−0.390068	+	1.32845i
$203$	18.7779	−	8.57556i	1.31795	−	0.601886i
$204$	0.159331	+	1.10817i	0.0111554	+	0.0775874i
$205$		0			0
$206$	−0.783074			−0.0545594
$207$	−8.25421	−	4.88549i	−0.573707	−	0.339565i
$208$			7.56510i			0.524546i
$209$	5.80195	+	3.72869i	0.401329	+	0.257919i
$210$		0			0
$211$	−10.3073	−	22.5698i	−0.709582	−	1.55377i	−0.827952	−	0.560799i	$-0.810494\pi$
$211$	−10.3073	−	22.5698i	−0.709582	−	1.55377i	0.118370	−	0.992970i	$-0.462233\pi$
$212$	−0.563241	+	1.91822i	−0.0386836	+	0.131744i
$213$	−2.57564	−	1.17625i	−0.176480	−	0.0805956i
$214$	9.64051	−	11.1257i	0.659012	−	0.760540i
$215$		0			0
$216$	−11.9373	+	3.50510i	−0.812228	+	0.238492i
$217$	2.35652	−	2.04194i	0.159971	−	0.138616i
$218$	−6.75050	−	10.5040i	−0.457201	−	0.711419i
$219$	−1.76634	+	1.13516i	−0.119358	+	0.0767067i
$220$		0			0
$221$	4.49319	−	1.31932i	0.302245	−	0.0887471i
$222$	−10.4964	−	1.50916i	−0.704473	−	0.101288i
$223$	−15.2807	−	13.2408i	−1.02327	−	0.886669i	−0.0296631	−	0.999560i	$-0.509443\pi$
$223$	−15.2807	−	13.2408i	−1.02327	−	0.886669i	−0.993607	+	0.112891i	$0.963989\pi$
$224$	2.17208	−	4.75620i	0.145128	−	0.317787i
$225$		0			0
$226$	2.27225	+	4.97553i	0.151148	+	0.330968i
$227$	−12.4953	+	1.79655i	−0.829339	+	0.119241i	−0.543894	−	0.839154i	$-0.683051\pi$
$227$	−12.4953	+	1.79655i	−0.829339	+	0.119241i	−0.285445	+	0.958395i	$0.592141\pi$
$228$	0.383608	−	0.596906i	0.0254051	−	0.0395310i
$229$	−17.5666			−1.16084			−0.580418	−	0.814319i	$-0.697111\pi$
$229$	−17.5666			−1.16084			−0.580418	+	0.814319i	$0.697111\pi$
$230$		0			0
$231$	9.10706			0.599200
$232$	11.5812	−	18.0208i	0.760346	−	1.18312i
$233$	−6.78424	+	0.975427i	−0.444451	+	0.0639023i	−0.360907	−	0.932602i	$-0.617533\pi$
$233$	−6.78424	+	0.975427i	−0.444451	+	0.0639023i	−0.0835435	+	0.996504i	$0.526624\pi$
$234$	−2.09954	−	4.59736i	−0.137251	−	0.300539i
$235$		0			0
$236$	1.17835	−	2.58023i	0.0767040	−	0.167958i
$237$	−9.34373	−	8.09638i	−0.606940	−	0.525917i
$238$	−10.5152	−	1.51185i	−0.681597	−	0.0979988i
$239$	8.41649	−	2.47130i	0.544418	−	0.159855i	0.00205178	−	0.999998i	$-0.499347\pi$
$239$	8.41649	−	2.47130i	0.544418	−	0.159855i	0.542366	+	0.840142i	$0.317529\pi$
$240$		0			0
$241$	−8.54608	+	5.49223i	−0.550501	+	0.353786i	−0.786134	−	0.618057i	$-0.787920\pi$
$241$	−8.54608	+	5.49223i	−0.550501	+	0.353786i	0.235632	+	0.971842i	$0.424284\pi$
$242$	−2.86272	−	4.45447i	−0.184022	−	0.286344i
$243$	12.0920	−	10.4778i	0.775702	−	0.672149i
$244$	3.24931	−	0.954085i	0.208016	−	0.0610790i
$245$		0			0
$246$	−6.34980	+	7.32806i	−0.404848	+	0.467220i
$247$	−2.69966	−	1.23289i	−0.171775	−	0.0784470i
$248$	0.911583	−	3.10457i	0.0578856	−	0.197140i
$249$	5.67269	+	12.4215i	0.359492	+	0.787178i
$250$		0			0
$251$	10.5748	+	6.79599i	0.667473	+	0.428959i	0.830014	−	0.557743i	$-0.188332\pi$
$251$	10.5748	+	6.79599i	0.667473	+	0.428959i	−0.162541	+	0.986702i	$0.551969\pi$
$252$			1.87387i			0.118043i
$253$	17.6534	+	4.48562i	1.10986	+	0.282009i
$254$	0.471570			0.0295890
$255$		0			0
$256$	−1.28696	−	8.95099i	−0.0804348	−	0.559437i
$257$	28.8599	−	13.1799i	1.80023	−	0.822137i	0.840178	−	0.542311i	$-0.182450\pi$
$257$	28.8599	−	13.1799i	1.80023	−	0.822137i	0.960051	−	0.279826i	$-0.0902769\pi$
$258$	−5.26736	+	17.9390i	−0.327931	+	1.11683i
$259$	6.83168	−	14.9593i	0.424500	−	0.929525i
$260$		0			0
$261$	−2.45038	+	17.0428i	−0.151675	+	1.05492i
$262$	−9.68172	−	32.9729i	−0.598139	−	2.03707i
$263$	−11.4914	+	9.95732i	−0.708587	+	0.613994i	−0.932736	−	0.360561i	$-0.882585\pi$
$263$	−11.4914	+	9.95732i	−0.708587	+	0.613994i	0.224148	+	0.974555i	$0.428040\pi$
$264$	7.95008	−	5.10920i	0.489293	−	0.314450i
$265$		0			0
$266$	4.40897	+	5.08823i	0.270332	+	0.311979i
$267$	−3.27345	−	11.1483i	−0.200332	−	0.682267i
$268$	2.00700	+	0.288563i	0.122597	+	0.0176268i
$269$	14.8927	−	17.1870i	0.908022	−	1.04791i	−0.0906241	−	0.995885i	$-0.528886\pi$
$269$	14.8927	−	17.1870i	0.908022	−	1.04791i	0.998646	−	0.0520276i	$-0.0165684\pi$
$270$		0			0
$271$	21.6374	+	6.35333i	1.31438	+	0.385937i	0.862462	−	0.506122i	$-0.168921\pi$
$271$	21.6374	+	6.35333i	1.31438	+	0.385937i	0.451919	+	0.892059i	$0.350740\pi$
$272$	−12.0642	+	5.50956i	−0.731502	+	0.334066i
$273$	−3.87910	+	0.557730i	−0.234774	+	0.0337553i
$274$	17.2617	+	11.0934i	1.04282	+	0.670179i
$275$		0			0
$276$	0.461482	−	1.81619i	0.0277779	−	0.109322i
$277$		−	2.56712i		−	0.154244i	−0.997022	−	0.0771218i	$-0.975427\pi$
$277$		−	2.56712i		−	0.154244i	0.997022	−	0.0771218i	$-0.0245730\pi$
$278$	18.5069	−	28.7973i	1.10997	−	1.72715i
$279$	0.370123	+	2.57426i	0.0221587	+	0.154117i
$280$		0			0
$281$	25.8504	+	7.59036i	1.54211	+	0.452803i	0.938730	−	0.344654i	$-0.112004\pi$
$281$	25.8504	+	7.59036i	1.54211	+	0.452803i	0.603376	+	0.797457i	$0.293822\pi$
$282$	6.56566	+	2.99844i	0.390979	+	0.178554i
$283$	−1.89295	−	1.64025i	−0.112524	−	0.0975028i	0.596781	−	0.802404i	$-0.296446\pi$
$283$	−1.89295	−	1.64025i	−0.112524	−	0.0975028i	−0.709306	+	0.704901i	$0.750991\pi$
$284$	−0.157453	+	1.09511i	−0.00934314	+	0.0649830i
$285$		0			0
$286$	6.28511	+	7.25340i	0.371646	+	0.428902i
$287$	−8.12982	−	12.6502i	−0.479888	−	0.746720i
$288$	2.35780	+	3.66880i	0.138934	+	0.216186i
$289$	−5.75635	−	6.64319i	−0.338609	−	0.390776i
$290$		0			0
$291$	−0.882949	+	6.14104i	−0.0517594	+	0.359994i
$292$	0.620023	+	0.537253i	0.0362841	+	0.0314403i
$293$	−17.8819	−	8.16641i	−1.04467	−	0.477087i	−0.182239	−	0.983254i	$-0.558335\pi$
$293$	−17.8819	−	8.16641i	−1.04467	−	0.477087i	−0.862435	+	0.506167i	$0.831062\pi$
$294$	−1.85473	−	0.544599i	−0.108170	−	0.0317617i
$295$		0			0
$296$	−2.42863	−	16.8915i	−0.141161	−	0.981799i
$297$	−10.2667	+	15.9753i	−0.595733	+	0.926979i
$298$			34.9887i			2.02684i
$299$	−7.79408	−	0.829500i	−0.450743	−	0.0479712i
$300$		0			0
$301$	−24.3918	−	15.6757i	−1.40592	−	0.903530i
$302$	−3.06641	+	0.440883i	−0.176452	+	0.0253700i
$303$	−11.5765	+	5.28682i	−0.665054	+	0.303720i
$304$	8.06503	+	2.36811i	0.462561	+	0.135820i
$305$		0			0
$306$	5.80245	−	6.69638i	0.331704	−	0.382807i
$307$	−6.24845	−	0.898392i	−0.356618	−	0.0512739i	−0.0383224	−	0.999265i	$-0.512201\pi$
$307$	−6.24845	−	0.898392i	−0.356618	−	0.0512739i	−0.318296	+	0.947991i	$0.603110\pi$
$308$	−1.00253	−	3.41431i	−0.0571245	−	0.194548i
$309$	−0.331655	−	0.382750i	−0.0188672	−	0.0217739i
$310$		0			0
$311$	−19.8840	+	12.7787i	−1.12752	+	0.724612i	−0.965041	−	0.262100i	$-0.915585\pi$
$311$	−19.8840	+	12.7787i	−1.12752	+	0.724612i	−0.162478	+	0.986712i	$0.551949\pi$
$312$	−3.07339	+	2.66311i	−0.173997	+	0.150769i
$313$	−8.82958	−	30.0708i	−0.499078	−	1.69970i	−0.694937	−	0.719070i	$-0.744568\pi$
$313$	−8.82958	−	30.0708i	−0.499078	−	1.69970i	0.195860	−	0.980632i	$-0.437250\pi$
$314$	−1.41102	+	9.81384i	−0.0796283	+	0.553827i
$315$		0			0
$316$	−2.00681	+	4.39431i	−0.112892	+	0.247199i
$317$	1.96036	−	6.67638i	0.110105	−	0.374983i	−0.885944	−	0.463793i	$-0.846488\pi$
$317$	1.96036	−	6.67638i	0.110105	−	0.374983i	0.996049	+	0.0888101i	$0.0283064\pi$
$318$	−7.19625	+	3.28642i	−0.403546	+	0.184293i
$319$	−4.65323	−	32.3639i	−0.260531	−	1.81203i
$320$		0			0
$321$	9.52106			0.531414
$322$	15.3016	+	9.05672i	0.852727	+	0.504712i
$323$		−	5.20310i		−	0.289508i
$324$	−0.328708	−	0.211248i	−0.0182615	−	0.0117360i
$325$		0			0
$326$	−4.27892	−	9.36953i	−0.236987	−	0.518930i
$327$	2.27509	−	7.74824i	0.125813	−	0.428479i
$328$	−14.1940	−	6.48217i	−0.783731	−	0.357918i
$329$	−7.33032	+	8.45964i	−0.404134	+	0.466395i
$330$		0			0
$331$	20.4435	−	6.00275i	1.12368	−	0.329941i	0.333457	−	0.942765i	$-0.391785\pi$
$331$	20.4435	−	6.00275i	1.12368	−	0.329941i	0.790219	+	0.612825i	$0.209967\pi$
$332$	4.03244	−	3.49413i	0.221309	−	0.191765i
$333$	7.41578	+	11.5392i	0.406383	+	0.632344i
$334$	−5.43321	+	3.49171i	−0.297292	+	0.191058i
$335$		0			0
$336$	10.6497	−	3.12703i	0.580988	−	0.170594i
$337$	18.9936	+	2.73086i	1.03465	+	0.148760i	0.638653	−	0.769494i	$-0.279492\pi$
$337$	18.9936	+	2.73086i	1.03465	+	0.148760i	0.395992	+	0.918254i	$0.370401\pi$
$338$	12.0697	+	10.4585i	0.656506	+	0.568865i
$339$	−1.46957	+	3.21791i	−0.0798161	+	0.174773i
$340$		0			0
$341$	−2.05163	−	4.49245i	−0.111102	−	0.243280i
$342$	−5.55838	+	0.799175i	−0.300563	+	0.0432144i
$343$	10.6955	−	16.6425i	0.577501	−	0.898608i
$344$	−30.0873			−1.62220
$345$		0			0
$346$	38.2460			2.05612
$347$	−7.92583	+	12.3328i	−0.425481	+	0.662061i	−0.986127	−	0.165995i	$-0.946916\pi$
$347$	−7.92583	+	12.3328i	−0.425481	+	0.662061i	0.560646	+	0.828056i	$0.310553\pi$
$348$	−3.32961	+	0.478725i	−0.178486	+	0.0256624i
$349$	4.91073	+	10.7530i	0.262865	+	0.575595i	0.994337	−	0.106278i	$-0.0338932\pi$
$349$	4.91073	+	10.7530i	0.262865	+	0.575595i	−0.731471	+	0.681872i	$0.761166\pi$
$350$		0			0
$351$	3.39468	−	7.43331i	0.181195	−	0.396761i
$352$	−6.25888	−	5.42335i	−0.333599	−	0.289065i
$353$	−9.63498	−	1.38530i	−0.512818	−	0.0737321i	−0.118952	−	0.992900i	$-0.537954\pi$
$353$	−9.63498	−	1.38530i	−0.512818	−	0.0737321i	−0.393866	+	0.919168i	$0.628863\pi$
$354$	10.7700	−	3.16236i	0.572420	−	0.168078i
$355$		0			0
$356$	−3.81925	+	2.45448i	−0.202420	+	0.130087i
$357$	−3.71452	−	5.77990i	−0.196593	−	0.305905i
$358$	−5.60054	+	4.85290i	−0.295998	+	0.256484i
$359$	−20.2194	+	5.93694i	−1.06714	+	0.313340i	−0.767722	−	0.640783i	$-0.778610\pi$
$359$	−20.2194	+	5.93694i	−1.06714	+	0.313340i	−0.299416	+	0.954123i	$0.596792\pi$
$360$		0			0
$361$	10.2829	−	11.8671i	0.541206	−	0.624585i
$362$	3.90479	+	1.78326i	0.205231	+	0.0937258i
$363$	0.964808	−	3.28583i	0.0506393	−	0.172462i
$364$	0.636120	+	1.39291i	0.0333417	+	0.0730082i
$365$		0			0
$366$	11.2735	+	7.24505i	0.589277	+	0.378705i
$367$		−	2.10006i		−	0.109622i	−0.998497	−	0.0548112i	$-0.982544\pi$
$367$		−	2.10006i		−	0.109622i	0.998497	−	0.0548112i	$-0.0174557\pi$
$368$	22.1839	−	0.816112i	1.15642	−	0.0425428i
$369$	12.5422			0.652923
$370$		0			0
$371$	−1.74603	−	12.1439i	−0.0906494	−	0.630480i
$372$	−0.462184	+	0.211072i	−0.0239631	+	0.0109436i
$373$	−5.89462	+	20.0752i	−0.305212	+	1.03946i	0.653935	+	0.756550i	$0.273117\pi$
$373$	−5.89462	+	20.0752i	−0.305212	+	1.03946i	−0.959148	+	0.282906i	$0.908701\pi$
$374$	−6.98981	+	15.3056i	−0.361435	+	0.791431i
$375$		0			0
$376$	−1.65307	+	11.4973i	−0.0852504	+	0.592929i
$377$	3.96403	+	13.5002i	0.204158	+	0.695298i
$378$	−14.0101	+	12.1398i	−0.720601	+	0.624404i
$379$	3.16651	−	2.03499i	0.162652	−	0.104530i	−0.456782	−	0.889578i	$-0.650998\pi$
$379$	3.16651	−	2.03499i	0.162652	−	0.104530i	0.619435	+	0.785048i	$0.287362\pi$
$380$		0			0
$381$	0.199724	+	0.230493i	0.0102322	+	0.0118085i
$382$	0.0182882	+	0.0622838i	0.000935704	+	0.00318672i
$383$	20.4566	+	2.94122i	1.04528	+	0.150289i	0.643501	−	0.765446i	$-0.277481\pi$
$383$	20.4566	+	2.94122i	1.04528	+	0.150289i	0.401783	+	0.915735i	$0.368390\pi$
$384$	8.81578	−	10.1740i	0.449879	−	0.519188i
$385$		0			0
$386$	−24.3220	−	7.14158i	−1.23796	−	0.363497i
$387$	21.9981	−	10.0462i	1.11823	−	0.510677i
$388$	2.39952	−	0.344999i	0.121817	−	0.0175147i
$389$	31.6110	+	20.3152i	1.60274	+	1.03002i	0.965862	+	0.259059i	$0.0834124\pi$
$389$	31.6110	+	20.3152i	1.60274	+	1.03002i	0.636882	+	0.770962i	$0.280224\pi$
$390$		0			0
$391$	−4.35350	−	13.0335i	−0.220166	−	0.659133i
$392$		−	3.11076i		−	0.157117i
$393$	12.0160	−	18.6972i	0.606125	−	0.943149i
$394$	−5.14686	−	35.7972i	−0.259295	−	1.80344i
$395$		0			0
$396$	2.84778	+	0.836183i	0.143106	+	0.0420198i
$397$	2.90158	+	1.32511i	0.145626	+	0.0665052i	0.486895	−	0.873460i	$-0.338129\pi$
$397$	2.90158	+	1.32511i	0.145626	+	0.0665052i	−0.341269	+	0.939966i	$0.610857\pi$
$398$	0.154512	+	0.133886i	0.00774499	+	0.00671107i
$399$	−0.619688	+	4.31002i	−0.0310232	+	0.215771i
$400$		0			0
$401$	−4.53998	−	5.23942i	−0.226716	−	0.261644i	0.630983	−	0.775797i	$-0.282652\pi$
$401$	−4.53998	−	5.23942i	−0.226716	−	0.261644i	−0.857699	+	0.514153i	$0.828106\pi$
$402$	4.33792	+	6.74994i	0.216356	+	0.336656i
$403$	1.14900	+	1.78789i	0.0572360	+	0.0890609i
$404$	3.25645	+	3.75814i	0.162014	+	0.186975i
$405$		0			0
$406$	4.54251	−	31.5939i	0.225441	−	1.56798i
$407$	−19.6855	−	17.0576i	−0.975776	−	0.845515i
$408$	−6.48523	−	2.96170i	−0.321067	−	0.146626i
$409$	10.6400	+	3.12417i	0.526112	+	0.154480i	0.533994	−	0.845488i	$-0.320691\pi$
$409$	10.6400	+	3.12417i	0.526112	+	0.154480i	−0.00788151	+	0.999969i	$0.502509\pi$
$410$		0			0
$411$	1.88861	+	13.1356i	0.0931582	+	0.647929i
$412$	−0.106986	+	0.166474i	−0.00527084	+	0.00820159i
$413$			17.4075i			0.856566i
$414$	−13.2548	+	6.65266i	−0.651438	+	0.326960i
$415$		0			0
$416$	2.99806	+	1.92674i	0.146992	+	0.0944662i
$417$	21.9137	−	3.15071i	1.07312	−	0.154291i
$418$	9.70015	−	4.42991i	0.474450	−	0.216674i
$419$	16.8802	+	4.95649i	0.824654	+	0.242140i	0.666719	−	0.745309i	$-0.267698\pi$
$419$	16.8802	+	4.95649i	0.824654	+	0.242140i	0.157935	+	0.987450i	$0.449516\pi$
$420$		0			0
$421$	−10.4546	+	12.0652i	−0.509526	+	0.588024i	−0.950977	−	0.309261i	$-0.899918\pi$
$421$	−10.4546	+	12.0652i	−0.509526	+	0.588024i	0.441451	+	0.897285i	$0.354464\pi$
$422$	−37.9738	−	5.45981i	−1.84854	−	0.265779i
$423$	−2.63035	−	8.95816i	−0.127892	−	0.435561i
$424$	−8.33713	−	9.62156i	−0.404887	−	0.467264i
$425$		0			0
$426$	−3.68308	+	2.36697i	−0.178446	+	0.114680i
$427$	−15.7062	+	13.6095i	−0.760078	+	0.658611i
$428$	−1.04811	−	3.56952i	−0.0506621	−	0.172539i
$429$	−0.883381	+	6.14405i	−0.0426500	+	0.296638i
$430$		0			0
$431$	1.62218	−	3.55209i	0.0781379	−	0.171098i	−0.866531	−	0.499123i	$-0.833656\pi$
$431$	1.62218	−	3.55209i	0.0781379	−	0.171098i	0.944669	+	0.328025i	$0.106383\pi$
$432$	−6.52041	+	22.2065i	−0.313714	+	1.06841i
$433$	36.2631	−	16.5608i	1.74269	−	0.795861i	0.752094	−	0.659055i	$-0.229044\pi$
$433$	36.2631	−	16.5608i	1.74269	−	0.795861i	0.990598	−	0.136805i	$-0.0436835\pi$
$434$	−0.686134	−	4.77217i	−0.0329355	−	0.229071i
$435$		0			0
$436$	−3.15533			−0.151113
$437$	−3.32410	+	8.04948i	−0.159013	+	0.385059i
$438$			3.24648i			0.155123i
$439$	23.3284	+	14.9922i	1.11340	+	0.715541i	0.962032	−	0.272936i	$-0.0879948\pi$
$439$	23.3284	+	14.9922i	1.11340	+	0.715541i	0.151371	+	0.988477i	$0.451631\pi$
$440$		0			0
$441$	1.03869	+	2.27441i	0.0494614	+	0.108305i
$442$	2.03993	−	6.94737i	0.0970297	−	0.330453i
$443$	26.9613	+	12.3128i	1.28097	+	0.585000i	0.935466	−	0.353417i	$-0.114980\pi$
$443$	26.9613	+	12.3128i	1.28097	+	0.585000i	0.345505	+	0.938417i	$0.387708\pi$
$444$	−1.75489	+	2.02525i	−0.0832834	+	0.0961142i
$445$		0			0
$446$	−29.9966	+	8.80781i	−1.42038	+	0.417062i
$447$	−17.1017	+	14.8187i	−0.808883	+	0.700901i
$448$	7.63057	+	11.8734i	0.360511	+	0.560966i
$449$	−13.0579	+	8.39181i	−0.616241	+	0.396034i	−0.811193	−	0.584779i	$-0.801181\pi$
$449$	−13.0579	+	8.39181i	−0.616241	+	0.396034i	0.194952	+	0.980813i	$0.437545\pi$
$450$		0			0
$451$	−22.8527	+	6.71017i	−1.07609	+	0.315969i
$452$	1.36819	+	0.196717i	0.0643545	+	0.00925277i
$453$	−1.51421	−	1.31207i	−0.0711436	−	0.0616463i
$454$	−8.10842	+	17.7550i	−0.380547	+	0.833281i
$455$		0			0
$456$	1.87703	+	4.11012i	0.0879000	+	0.192474i
$457$	0.662795	−	0.0952955i	0.0310042	−	0.00445774i	−0.126795	−	0.991929i	$-0.540469\pi$
$457$	0.662795	−	0.0952955i	0.0310042	−	0.00445774i	0.157800	+	0.987471i	$0.449560\pi$
$458$	−14.6846	+	22.8497i	−0.686168	+	1.06770i
$459$	14.3264			0.668698
$460$		0			0
$461$	18.1826			0.846846			0.423423	−	0.905932i	$-0.360828\pi$
$461$	18.1826			0.846846			0.423423	+	0.905932i	$0.360828\pi$
$462$	7.61295	−	11.8460i	0.354186	−	0.551125i
$463$	13.9773	−	2.00963i	0.649580	−	0.0933955i	0.190355	−	0.981715i	$-0.439036\pi$
$463$	13.9773	−	2.00963i	0.649580	−	0.0933955i	0.459225	+	0.888320i	$0.348127\pi$
$464$	−16.5540	−	36.2482i	−0.768501	−	1.68278i
$465$		0			0
$466$	−4.40243	+	9.63998i	−0.203939	+	0.446563i
$467$	−6.21568	−	5.38591i	−0.287627	−	0.249230i	0.499081	−	0.866555i	$-0.333671\pi$
$467$	−6.21568	−	5.38591i	−0.287627	−	0.249230i	−0.786708	+	0.617325i	$0.788216\pi$
$468$	−1.26420	−	0.181765i	−0.0584378	−	0.00840208i
$469$	−11.9392	+	3.50567i	−0.551302	+	0.161877i
$470$		0			0
$471$	−5.39440	+	3.46677i	−0.248561	+	0.159740i
$472$	9.76587	+	15.1960i	0.449511	+	0.699452i
$473$	−34.7072	+	30.0739i	−1.59584	+	1.38280i
$474$	−18.3421	+	5.38573i	−0.842482	+	0.247375i
$475$		0			0
$476$	−1.75803	+	2.02887i	−0.0805790	+	0.0929931i
$477$	9.30830	+	4.25096i	0.426198	+	0.194638i
$478$	3.82113	−	13.0136i	0.174775	−	0.595227i
$479$	0.394315	+	0.863430i	0.0180167	+	0.0394511i	0.918426	−	0.395592i	$-0.129460\pi$
$479$	0.394315	+	0.863430i	0.0180167	+	0.0394511i	−0.900410	+	0.435043i	$0.856733\pi$
$480$		0			0
$481$	9.42957	+	6.06002i	0.429951	+	0.276313i
$482$			15.7075i			0.715455i
$483$	2.05396	+	11.3149i	0.0934584	+	0.514846i
$484$	−1.33809			−0.0608225
$485$		0			0
$486$	−3.52076	−	24.4874i	−0.159705	−	1.11077i
$487$	11.3832	−	5.19851i	0.515820	−	0.235567i	−0.140458	−	0.990087i	$-0.544857\pi$
$487$	11.3832	−	5.19851i	0.515820	−	0.235567i	0.656277	+	0.754520i	$0.272130\pi$
$488$	−6.07571	+	20.6920i	−0.275035	+	0.936682i
$489$	2.76738	−	6.05971i	0.125145	−	0.274030i
$490$		0			0
$491$	−4.19660	+	29.1880i	−0.189390	+	1.31724i	0.644202	+	0.764855i	$0.277190\pi$
$491$	−4.19660	+	29.1880i	−0.189390	+	1.31724i	−0.833592	+	0.552381i	$0.813720\pi$
$492$	0.690343	+	2.35109i	0.0311231	+	0.105995i
$493$	−18.6422	+	16.1536i	−0.839603	+	0.727520i
$494$	−3.86043	+	2.48095i	−0.173689	+	0.111623i
$495$		0			0
$496$	−3.94170	−	4.54896i	−0.176987	−	0.204254i
$497$	−1.91286	−	6.51460i	−0.0858034	−	0.292220i
$498$	20.8992	+	3.00485i	0.936515	+	0.134650i
$499$	−8.18657	+	9.44781i	−0.366481	+	0.422942i	−0.908801	−	0.417230i	$-0.863001\pi$
$499$	−8.18657	+	9.44781i	−0.366481	+	0.422942i	0.542319	+	0.840172i	$0.317546\pi$
$500$		0			0
$501$	−4.00780	−	1.17680i	−0.179055	−	0.0525754i
$502$	17.6797	−	8.07405i	0.789084	−	0.360363i
$503$	1.90074	−	0.273285i	0.0847497	−	0.0121852i	−0.0998095	−	0.995007i	$-0.531823\pi$
$503$	1.90074	−	0.273285i	0.0847497	−	0.0121852i	0.184559	+	0.982821i	$0.440914\pi$
$504$	−10.0387	−	6.45147i	−0.447159	−	0.287372i
$505$		0			0
$506$	20.5919	−	19.2129i	0.915420	−	0.854119i
$507$			10.3289i			0.458722i
$508$	0.0644277	−	0.100251i	0.00285852	−	0.00444794i
$509$	5.15255	+	35.8368i	0.228383	+	1.58844i	0.704923	+	0.709284i	$0.250982\pi$
$509$	5.15255	+	35.8368i	0.228383	+	1.58844i	−0.476540	+	0.879153i	$0.658109\pi$
$510$		0			0
$511$	−4.83076	−	1.41844i	−0.213700	−	0.0627481i
$512$	11.7723	+	5.37622i	0.520266	+	0.237598i
$513$	−6.86189	−	5.94586i	−0.302960	−	0.262516i
$514$	6.98143	−	48.5569i	0.307938	−	2.14175i
$515$		0			0
$516$	3.09401	+	3.57068i	0.136206	+	0.157190i
$517$	9.58533	+	14.9151i	0.421562	+	0.655963i
$518$	−13.7474	−	21.3913i	−0.604025	−	0.939881i
$519$	16.1983	+	18.6938i	0.711027	+	0.820568i
$520$		0			0
$521$	1.23847	−	8.61372i	0.0542582	−	0.377374i	−0.944542	−	0.328392i	$-0.893493\pi$
$521$	1.23847	−	8.61372i	0.0542582	−	0.377374i	0.998800	−	0.0489818i	$-0.0155976\pi$
$522$	20.1199	+	17.4340i	0.880626	+	0.763067i
$523$	−10.2483	−	4.68026i	−0.448129	−	0.204654i	0.178551	−	0.983931i	$-0.442859\pi$
$523$	−10.2483	−	4.68026i	−0.448129	−	0.204654i	−0.626680	+	0.779277i	$0.715586\pi$
$524$	−8.33249	−	2.44664i	−0.364006	−	0.106882i
$525$		0			0
$526$	3.34587	+	23.2711i	0.145887	+	1.01467i
$527$	−2.01438	+	3.13444i	−0.0877478	+	0.136538i
$528$		−	17.5800i		−	0.765072i
$529$	−1.59161	+	22.9449i	−0.0692006	+	0.997603i
$530$		0			0
$531$	−12.2142	−	7.84960i	−0.530052	−	0.340644i
$532$	1.68408	−	0.242134i	0.0730141	−	0.0104978i
$533$	9.32304	−	4.25769i	0.403826	−	0.184421i
$534$	−17.2376	−	5.06141i	−0.745943	−	0.219029i
$535$		0			0
$536$	−8.45570	+	9.75839i	−0.365230	+	0.421498i
$537$	−4.74399	−	0.682082i	−0.204718	−	0.0294340i
$538$	−9.90663	−	33.7389i	−0.427105	−	1.45459i
$539$	−3.10938	−	3.58842i	−0.133931	−	0.154564i
$540$		0			0
$541$	−15.6463	+	10.0553i	−0.672688	+	0.432311i	−0.831894	−	0.554935i	$-0.812743\pi$
$541$	−15.6463	+	10.0553i	−0.672688	+	0.432311i	0.159205	+	0.987245i	$0.449107\pi$
$542$	26.3517	−	22.8338i	1.13190	−	0.980797i
$543$	0.782173	+	2.66384i	0.0335662	+	0.114316i
$544$	−0.889168	+	6.18430i	−0.0381228	+	0.265150i
$545$		0			0
$546$	−2.51722	+	5.51195i	−0.107727	+	0.235890i
$547$	−2.82308	+	9.61453i	−0.120706	+	0.411088i	−0.997572	−	0.0696483i	$-0.977812\pi$
$547$	−2.82308	+	9.61453i	−0.120706	+	0.411088i	0.876865	+	0.480736i	$0.159630\pi$
$548$	4.71672	−	2.15406i	0.201488	−	0.0920167i
$549$	−2.46688	−	17.1575i	−0.105284	−	0.732264i
$550$		0			0
$551$	15.6332			0.665999
$552$	8.14086	+	8.72513i	0.346498	+	0.371366i
$553$		−	29.6462i		−	1.26068i
$554$	−3.33918	−	2.14596i	−0.141868	−	0.0911731i
$555$		0			0
$556$	−3.59355	−	7.86878i	−0.152401	−	0.333711i
$557$	−4.63697	+	15.7921i	−0.196475	+	0.669131i	0.801036	+	0.598616i	$0.204283\pi$
$557$	−4.63697	+	15.7921i	−0.196475	+	0.669131i	−0.997511	+	0.0705153i	$0.977536\pi$
$558$	3.65786	+	1.67049i	0.154850	+	0.0707175i
$559$	12.9415	−	14.9353i	0.547368	−	0.631697i
$560$		0			0
$561$	−10.4414	+	3.06588i	−0.440837	+	0.129441i
$562$	31.4825	−	27.2797i	1.32801	−	1.15073i
$563$	−3.61456	−	5.62436i	−0.152335	−	0.237039i	0.756695	−	0.653768i	$-0.226813\pi$
$563$	−3.61456	−	5.62436i	−0.152335	−	0.237039i	−0.909031	+	0.416729i	$0.863176\pi$
$564$	1.53446	−	0.986140i	0.0646126	−	0.0415240i
$565$		0			0
$566$	−3.71594	+	1.09110i	−0.156193	+	0.0458623i
$567$	2.37347	+	0.341254i	0.0996764	+	0.0143313i
$568$	−5.32464	−	4.61382i	−0.223417	−	0.193592i
$569$	9.29438	−	20.3518i	0.389641	−	0.853194i	−0.608576	−	0.793496i	$-0.708259\pi$
$569$	9.29438	−	20.3518i	0.389641	−	0.853194i	0.998216	−	0.0596982i	$-0.0190138\pi$
$570$		0			0
$571$	−16.5325	−	36.2012i	−0.691864	−	1.51497i	−0.849565	−	0.527484i	$-0.823135\pi$
$571$	−16.5325	−	36.2012i	−0.691864	−	1.51497i	0.157701	−	0.987487i	$-0.449592\pi$
$572$	2.40070	−	0.345168i	0.100378	−	0.0144322i
$573$	−0.0226974	+	0.0353179i	−0.000948198	+	0.00147542i
$574$	−23.2508			−0.970469
$575$		0			0
$576$	−11.7720			−0.490501
$577$	−20.1412	+	31.3403i	−0.838490	+	1.30472i	0.111920	+	0.993717i	$0.464300\pi$
$577$	−20.1412	+	31.3403i	−0.838490	+	1.30472i	−0.950410	+	0.310999i	$0.899337\pi$
$578$	−13.4531	+	1.93426i	−0.559574	+	0.0804545i
$579$	−6.81042	−	14.9127i	−0.283031	−	0.619752i
$580$		0			0
$581$	−13.6024	+	29.7851i	−0.564323	+	1.23570i
$582$	7.24985	+	6.28203i	0.300516	+	0.260399i
$583$	−19.2346	−	2.76551i	−0.796615	−	0.114536i
$584$	−5.01282	+	1.47190i	−0.207432	+	0.0609075i
$585$		0			0
$586$	−25.5706	+	16.4333i	−1.05631	+	0.678852i
$587$	−11.8579	−	18.4513i	−0.489429	−	0.761566i	0.505427	−	0.862869i	$-0.331335\pi$
$587$	−11.8579	−	18.4513i	−0.489429	−	0.761566i	−0.994856	+	0.101304i	$0.967699\pi$
$588$	−0.369177	+	0.319894i	−0.0152246	+	0.0131922i
$589$	2.26571	−	0.665272i	0.0933569	−	0.0274120i
$590$		0			0
$591$	15.3171	−	17.6768i	0.630060	−	0.727128i
$592$	−28.8770	−	13.1877i	−1.18684	−	0.542011i
$593$	0.584486	−	1.99058i	0.0240020	−	0.0817431i	−0.946621	−	0.322348i	$-0.895528\pi$
$593$	0.584486	−	1.99058i	0.0240020	−	0.0817431i	0.970623	+	0.240605i	$0.0773459\pi$
$594$	12.1975	+	26.7087i	0.500468	+	1.09587i
$595$		0			0
$596$	7.43826	+	4.78028i	0.304683	+	0.195808i
$597$			0.132227i			0.00541168i
$598$	−7.59435	+	9.44471i	−0.310556	+	0.386223i
$599$	−9.26542			−0.378575			−0.189287	−	0.981922i	$-0.560618\pi$
$599$	−9.26542			−0.378575			−0.189287	+	0.981922i	$0.560618\pi$
$600$		0			0
$601$	4.28647	+	29.8130i	0.174849	+	1.21610i	0.868463	+	0.495753i	$0.165108\pi$
$601$	4.28647	+	29.8130i	0.174849	+	1.21610i	−0.693615	+	0.720346i	$0.743983\pi$
$602$	−40.7801	+	18.6237i	−1.66207	+	0.759043i
$603$	2.92398	−	9.95816i	0.119074	−	0.405528i
$604$	−0.325216	+	0.712124i	−0.0132329	+	0.0289759i
$605$		0			0
$606$	−2.80046	+	19.4776i	−0.113761	+	0.791223i
$607$	8.17906	+	27.8553i	0.331978	+	1.13061i	0.941267	+	0.337664i	$0.109637\pi$
$607$	8.17906	+	27.8553i	0.331978	+	1.13061i	−0.609289	+	0.792949i	$0.708545\pi$
$608$	2.99255	−	2.59306i	0.121364	−	0.105162i
$609$	17.3663	−	11.1606i	0.703718	−	0.452252i
$610$		0			0
$611$	−4.99623	−	5.76596i	−0.202126	−	0.233266i
$612$	−0.630836	−	2.14843i	−0.0255000	−	0.0868451i
$613$	28.3226	+	4.07218i	1.14394	+	0.164474i	0.688119	−	0.725597i	$-0.258437\pi$
$613$	28.3226	+	4.07218i	1.14394	+	0.164474i	0.455821	+	0.890071i	$0.349346\pi$
$614$	−6.39191	+	7.37665i	−0.257956	+	0.297697i
$615$		0			0
$616$	21.7427	+	6.38423i	0.876038	+	0.257228i
$617$	−7.37096	+	3.36621i	−0.296744	+	0.135518i	−0.558223	−	0.829691i	$-0.688517\pi$
$617$	−7.37096	+	3.36621i	−0.296744	+	0.135518i	0.261480	+	0.965209i	$0.415790\pi$
$618$	−0.775104	+	0.111443i	−0.0311792	+	0.00448290i
$619$	−25.1807	−	16.1826i	−1.01210	−	0.650435i	−0.0741618	−	0.997246i	$-0.523628\pi$
$619$	−25.1807	−	16.1826i	−1.01210	−	0.650435i	−0.937935	+	0.346811i	$0.887264\pi$
$620$		0			0
$621$	−22.1637	−	9.15267i	−0.889398	−	0.367284i
$622$			36.5462i			1.46537i
$623$	15.0628	−	23.4381i	0.603476	−	0.939028i
$624$	1.07663	+	7.48810i	0.0430996	+	0.299764i
$625$		0			0
$626$	−46.4955	−	13.6523i	−1.85833	−	0.545656i
$627$	6.27354	+	2.86503i	0.250541	+	0.114418i
$628$	1.89355	+	1.64077i	0.0755610	+	0.0654740i
$629$	−2.79663	+	19.4510i	−0.111509	+	0.775562i
$630$		0			0
$631$	−5.37867	−	6.20731i	−0.214121	−	0.247109i	0.638521	−	0.769605i	$-0.279547\pi$
$631$	−5.37867	−	6.20731i	−0.214121	−	0.247109i	−0.852642	+	0.522495i	$0.825001\pi$
$632$	−16.6320	−	25.8799i	−0.661585	−	1.02945i
$633$	−13.4144	−	20.8732i	−0.533174	−	0.829634i
$634$	−7.04553	−	8.13098i	−0.279814	−	0.322922i
$635$		0			0
$636$	−0.284517	+	1.97886i	−0.0112818	+	0.0784668i
$637$	1.54418	+	1.33804i	0.0611827	+	0.0530151i
$638$	−45.9871	−	21.0016i	−1.82065	−	0.831461i
$639$	5.43364	+	1.59546i	0.214951	+	0.0631154i
$640$		0			0
$641$	−1.44375	−	10.0415i	−0.0570248	−	0.396616i	−0.998265	−	0.0588787i	$-0.981247\pi$
$641$	−1.44375	−	10.0415i	−0.0570248	−	0.396616i	0.941240	−	0.337737i	$-0.109662\pi$
$642$	7.95902	−	12.3845i	0.314118	−	0.488777i
$643$			39.0668i			1.54065i	0.637654	+	0.770323i	$0.279905\pi$
$643$			39.0668i			1.54065i	−0.637654	+	0.770323i	$0.720095\pi$
$644$	4.01594	−	2.01562i	0.158250	−	0.0794267i
$645$		0			0
$646$	−6.76792	−	4.34948i	−0.266280	−	0.171128i
$647$	4.02479	−	0.578678i	0.158231	−	0.0227502i	−0.0627440	−	0.998030i	$-0.519985\pi$
$647$	4.02479	−	0.578678i	0.158231	−	0.0227502i	0.220975	+	0.975279i	$0.429076\pi$
$648$	2.26339	−	1.03365i	0.0889143	−	0.0406058i
$649$	26.4546	+	7.76778i	1.03844	+	0.304912i
$650$		0			0
$651$	2.04194	−	2.35652i	0.0800298	−	0.0923593i
$652$	−2.57647	−	0.370441i	−0.100903	−	0.0145076i
$653$	−8.39708	−	28.5978i	−0.328603	−	1.11912i	−0.943737	−	0.330697i	$-0.892716\pi$
$653$	−8.39708	−	28.5978i	−0.328603	−	1.11912i	0.615134	−	0.788423i	$-0.289102\pi$
$654$	−8.17666	−	9.43637i	−0.319733	−	0.368991i
$655$		0			0
$656$	−24.4197	+	15.6936i	−0.953429	+	0.612731i
$657$	3.17362	−	2.74996i	0.123815	−	0.107286i
$658$	4.87615	+	16.6066i	0.190092	+	0.647394i
$659$	−1.11615	+	7.76299i	−0.0434790	+	0.302403i	0.956465	+	0.291846i	$0.0942695\pi$
$659$	−1.11615	+	7.76299i	−0.0434790	+	0.302403i	−0.999944	+	0.0105569i	$0.996640\pi$
$660$		0			0
$661$	−17.9335	+	39.2688i	−0.697531	+	1.52738i	0.145408	+	0.989372i	$0.453551\pi$
$661$	−17.9335	+	39.2688i	−0.697531	+	1.52738i	−0.842939	+	0.538009i	$0.819177\pi$
$662$	9.28145	−	31.6097i	0.360734	−	1.22855i
$663$	4.25970	−	1.94534i	0.165433	−	0.0755507i
$664$	4.83560	+	33.6323i	0.187658	+	1.30519i
$665$		0			0
$666$	21.2087			0.821820
$667$	39.1605	−	13.0805i	1.51630	−	0.506480i
$668$			1.63210i			0.0631479i
$669$	−17.0095	−	10.9314i	−0.657626	−	0.422630i
$670$		0			0
$671$	13.6742	+	29.9422i	0.527885	+	1.15591i
$672$	1.47310	−	5.01691i	0.0568260	−	0.193531i
$673$	−4.65636	−	2.12649i	−0.179489	−	0.0819701i	0.323644	−	0.946179i	$-0.395092\pi$
$673$	−4.65636	−	2.12649i	−0.179489	−	0.0819701i	−0.503133	+	0.864209i	$0.667819\pi$
$674$	19.4296	−	22.4230i	0.748401	−	0.863701i
$675$		0			0
$676$	3.87238	−	1.13703i	0.148938	−	0.0437320i
$677$	−21.1275	+	18.3071i	−0.811995	+	0.703598i	−0.958338	−	0.285636i	$-0.907795\pi$
$677$	−21.1275	+	18.3071i	−0.811995	+	0.703598i	0.146343	+	0.989234i	$0.453250\pi$
$678$	2.95721	+	4.60151i	0.113571	+	0.176720i
$679$	−12.5152	+	8.04306i	−0.480291	+	0.308664i
$680$		0			0
$681$	−12.1124	+	3.55652i	−0.464148	+	0.136286i
$682$	−7.55858	−	1.08676i	−0.289433	−	0.0416142i
$683$	11.4924	+	9.95826i	0.439746	+	0.381042i	0.846407	−	0.532537i	$-0.178761\pi$
$683$	11.4924	+	9.95826i	0.439746	+	0.381042i	−0.406660	+	0.913579i	$0.633307\pi$
$684$	−0.589510	+	1.29085i	−0.0225405	+	0.0493567i
$685$		0			0
$686$	−12.7069	−	27.8242i	−0.485151	−	1.06233i
$687$	−17.3878	+	2.49999i	−0.663387	+	0.0953807i
$688$	−30.2599	+	47.0853i	−1.15365	+	1.79511i
$689$	8.36221			0.318575
$690$		0			0
$691$	11.0471			0.420251			0.210126	−	0.977674i	$-0.432613\pi$
$691$	11.0471			0.420251			0.210126	+	0.977674i	$0.432613\pi$
$692$	5.22531	−	8.13075i	0.198637	−	0.309085i
$693$	−18.0287	+	2.59214i	−0.684855	+	0.0984672i
$694$	9.41637	+	20.6190i	0.357441	+	0.782686i
$695$		0			0
$696$	8.89874	−	19.4855i	0.337306	−	0.738597i
$697$	13.5797	+	11.7669i	0.514367	+	0.445701i
$698$	18.0920	+	2.60124i	0.684792	+	0.0984583i
$699$	−6.57637	+	1.93100i	−0.248741	+	0.0730370i
$700$		0			0
$701$	31.4181	−	20.1912i	1.18664	−	0.762610i	0.210048	−	0.977691i	$-0.432638\pi$
$701$	31.4181	−	20.1912i	1.18664	−	0.762610i	0.976596	+	0.215082i	$0.0690018\pi$
$702$	−6.83111	−	10.6294i	−0.257824	−	0.401181i
$703$	9.41222	−	8.15574i	0.354989	−	0.307599i
$704$	21.4494	−	6.29810i	0.808403	−	0.237369i
$705$		0			0
$706$	−9.85618	+	11.3746i	−0.370942	+	0.428090i
$707$	−27.7591	−	12.6772i	−1.04399	−	0.476774i
$708$	0.799151	−	2.72166i	0.0300339	−	0.102286i
$709$	−8.09489	−	17.7253i	−0.304010	−	0.665689i	0.694544	−	0.719450i	$-0.255606\pi$
$709$	−8.09489	−	17.7253i	−0.304010	−	0.665689i	−0.998554	+	0.0537614i	$0.982879\pi$
$710$		0			0
$711$	20.8017	+	13.3684i	0.780125	+	0.501356i
$712$		−	28.9109i		−	1.08348i
$713$	5.11885	−	3.56222i	0.191702	−	0.133406i
$714$	−10.6233			−0.397567
$715$		0			0
$716$	0.266514	+	1.85364i	0.00996009	+	0.0692739i
$717$	7.97912	−	3.64394i	0.297986	−	0.136086i
$718$	−9.17971	+	31.2632i	−0.342584	+	1.16673i
$719$	−0.529568	+	1.15959i	−0.0197496	+	0.0432455i	−0.919250	−	0.393675i	$-0.871204\pi$
$719$	−0.529568	+	1.15959i	−0.0197496	+	0.0432455i	0.899500	+	0.436920i	$0.143931\pi$
$720$		0			0
$721$	0.172828	−	1.20205i	0.00643645	−	0.0447665i
$722$	−6.84022	−	23.2957i	−0.254567	−	0.866974i
$723$	−7.67747	+	6.65256i	−0.285528	+	0.247412i
$724$	0.912589	−	0.586486i	0.0339161	−	0.0217966i
$725$		0			0
$726$	−3.46752	−	4.00173i	−0.128692	−	0.148518i
$727$	8.07821	+	27.5119i	0.299604	+	1.02036i	0.962418	+	0.271574i	$0.0875441\pi$
$727$	8.07821	+	27.5119i	0.299604	+	1.02036i	−0.662813	+	0.748785i	$0.730638\pi$
$728$	−9.65214	−	1.38777i	−0.357732	−	0.0514341i
$729$	8.51319	−	9.82474i	0.315303	−	0.363879i
$730$		0			0
$731$	33.2428	+	9.76098i	1.22953	+	0.361023i
$732$	3.08046	−	1.40680i	0.113857	−	0.0519968i
$733$	7.73438	−	1.11204i	0.285676	−	0.0410740i	0.00201276	−	0.999998i	$-0.499359\pi$
$733$	7.73438	−	1.11204i	0.285676	−	0.0410740i	0.283663	+	0.958924i	$0.408450\pi$
$734$	−2.73165	−	1.75552i	−0.100827	−	0.0647976i
$735$		0			0
$736$	5.32655	−	8.99938i	0.196339	−	0.331722i
$737$			19.7087i			0.725980i
$738$	10.4845	−	16.3143i	0.385942	−	0.600537i
$739$	1.47513	+	10.2597i	0.0542634	+	0.377410i	0.998799	+	0.0490005i	$0.0156036\pi$
$739$	1.47513	+	10.2597i	0.0542634	+	0.377410i	−0.944535	+	0.328410i	$0.893487\pi$
$740$		0			0
$741$	−2.84764	−	0.836141i	−0.104611	−	0.0307164i
$742$	−17.2557	−	7.88042i	−0.633477	−	0.289299i
$743$	−7.38071	−	6.39542i	−0.270772	−	0.234625i	0.508881	−	0.860837i	$-0.330059\pi$
$743$	−7.38071	−	6.39542i	−0.270772	−	0.234625i	−0.779653	+	0.626211i	$0.784605\pi$
$744$	0.460479	−	3.20270i	0.0168820	−	0.117417i
$745$		0			0
$746$	21.1853	+	24.4491i	0.775647	+	0.895145i
$747$	−14.7654	−	22.9754i	−0.540238	−	0.840627i
$748$	2.29884	+	3.57707i	0.0840540	+	0.130791i
$749$	14.9507	+	17.2540i	0.546286	+	0.630448i
$750$		0			0
$751$	1.23883	−	8.61624i	0.0452055	−	0.314411i	−0.954655	−	0.297714i	$-0.903776\pi$
$751$	1.23883	−	8.61624i	0.0452055	−	0.314411i	0.999861	−	0.0166971i	$-0.00531510\pi$
$752$	16.3303	+	14.1502i	0.595503	+	0.516006i
$753$	11.4343	+	5.22187i	0.416689	+	0.190295i
$754$	20.8741	+	6.12918i	0.760189	+	0.223212i
$755$		0			0
$756$	0.666699	+	4.63700i	0.0242476	+	0.168646i
$757$	2.67564	−	4.16337i	0.0972476	−	0.151320i	−0.789220	−	0.614110i	$-0.789515\pi$
$757$	2.67564	−	4.16337i	0.0972476	−	0.151320i	0.886468	+	0.462790i	$0.153151\pi$
$758$		−	5.81995i		−	0.211390i
$759$	18.1121	+	1.92762i	0.657428	+	0.0699681i
$760$		0			0
$761$	24.5583	+	15.7826i	0.890236	+	0.572120i	0.903880	−	0.427787i	$-0.140707\pi$
$761$	24.5583	+	15.7826i	0.890236	+	0.572120i	−0.0136435	+	0.999907i	$0.504343\pi$
$762$	0.466770	−	0.0671115i	0.0169093	−	0.00243119i
$763$	17.6138	−	8.04397i	0.637664	−	0.291211i
$764$	0.0157395	+	0.00462155i	0.000569437	+	0.000167202i
$765$		0			0
$766$	20.9263	−	24.1502i	0.756096	−	0.872582i
$767$	−11.7439	−	1.68852i	−0.424048	−	0.0609689i
$768$	−2.54772	−	8.67672i	−0.0919328	−	0.313094i
$769$	14.2646	+	16.4622i	0.514395	+	0.593644i	0.952219	−	0.305417i	$-0.0987959\pi$
$769$	14.2646	+	16.4622i	0.514395	+	0.593644i	−0.437823	+	0.899061i	$0.644250\pi$
$770$		0			0
$771$	26.6904	−	17.1529i	0.961232	−	0.617746i
$772$	−4.84119	+	4.19492i	−0.174238	+	0.150978i
$773$	3.18094	+	10.8333i	0.114411	+	0.389647i	0.996711	−	0.0810404i	$-0.0258243\pi$
$773$	3.18094	+	10.8333i	0.114411	+	0.389647i	−0.882300	+	0.470687i	$0.844006\pi$
$774$	5.32152	−	37.0120i	0.191278	−	1.33037i
$775$		0			0
$776$	−6.41299	+	14.0425i	−0.230213	+	0.504096i
$777$	4.63321	−	15.7793i	0.166216	−	0.566078i
$778$	52.8498	−	24.1357i	1.89476	−	0.865307i
$779$	−1.62066	−	11.2719i	−0.0580661	−	0.403858i
$780$		0			0
$781$	−10.7540			−0.384808
$782$	−20.5926	−	5.23243i	−0.736388	−	0.187111i
$783$			43.0450i			1.53830i
$784$	−4.86821	−	3.12861i	−0.173865	−	0.111736i
$785$		0			0
$786$	−14.2757	−	31.2595i	−0.509198	−	1.11499i
$787$	4.54099	−	15.4652i	0.161869	−	0.551275i	−0.838114	−	0.545494i	$-0.816342\pi$
$787$	4.54099	−	15.4652i	0.161869	−	0.551275i	0.999983	−	0.00578022i	$-0.00183991\pi$
$788$	−8.31333	−	3.79657i	−0.296150	−	0.135247i
$789$	−9.95732	+	11.4914i	−0.354490	+	0.409103i
$790$		0			0
$791$	−8.13911	+	2.38986i	−0.289393	+	0.0849736i
$792$	−14.2841	+	12.3772i	−0.507563	+	0.439806i
$793$	−7.65813	−	11.9163i	−0.271948	−	0.423159i
$794$	4.14917	−	2.66651i	0.147249	−	0.0946309i
$795$		0			0
$796$	0.0495728	−	0.0145559i	0.00175706	−	0.000515920i
$797$	19.2411	+	2.76646i	0.681556	+	0.0979929i	0.474393	−	0.880313i	$-0.342668\pi$
$797$	19.2411	+	2.76646i	0.681556	+	0.0979929i	0.207163	+	0.978306i	$0.433577\pi$
$798$	5.08823	+	4.40897i	0.180121	+	0.156076i
$799$	5.55643	−	12.1669i	0.196572	−	0.430433i
$800$		0			0
$801$	9.65341	+	21.1380i	0.341086	+	0.746875i
$802$	−10.6103	+	1.52553i	−0.374663	+	0.0538684i
$803$	−4.31128	+	6.70849i	−0.152142	+	0.236737i
$804$	2.02764			0.0715092
$805$		0			0
$806$	3.28608			0.115747
$807$	12.2951	−	19.1316i	0.432808	−	0.673463i
$808$	−31.3446	+	4.50667i	−1.10270	+	0.158544i
$809$	5.60048	+	12.2633i	0.196902	+	0.431156i	0.982169	−	0.188002i	$-0.0602012\pi$
$809$	5.60048	+	12.2633i	0.196902	+	0.431156i	−0.785266	+	0.619158i	$0.787474\pi$
$810$		0			0
$811$	20.5360	−	44.9675i	0.721115	−	1.57902i	−0.0912201	−	0.995831i	$-0.529077\pi$
$811$	20.5360	−	44.9675i	0.721115	−	1.57902i	0.812335	−	0.583191i	$-0.198196\pi$
$812$	−6.09594	−	5.28217i	−0.213926	−	0.185368i
$813$	22.3214	+	3.20933i	0.782845	+	0.112556i
$814$	−38.6436	+	11.3468i	−1.35446	+	0.397704i
$815$		0			0
$816$	−11.1574	+	7.17040i	−0.390586	+	0.251014i
$817$	−11.8712	−	18.4719i	−0.415321	−	0.646252i
$818$	12.9581	−	11.2283i	0.453070	−	0.392587i
$819$	7.52048	−	2.20821i	0.262787	−	0.0771612i
$820$		0			0
$821$	12.1749	−	14.0506i	0.424907	−	0.490369i	−0.502419	−	0.864624i	$-0.667556\pi$
$821$	12.1749	−	14.0506i	0.424907	−	0.490369i	0.927325	+	0.374256i	$0.122102\pi$
$822$	18.6648	+	8.52393i	0.651010	+	0.297306i
$823$	−7.60129	+	25.8876i	−0.264964	+	0.902386i	0.714307	+	0.699833i	$0.246742\pi$
$823$	−7.60129	+	25.8876i	−0.264964	+	0.902386i	−0.979271	+	0.202553i	$0.935076\pi$
$824$	−0.523495	−	1.14629i	−0.0182368	−	0.0399330i
$825$		0			0
$826$	22.6427	+	14.5516i	0.787841	+	0.506315i
$827$			18.8339i			0.654919i	0.944865	+	0.327460i	$0.106193\pi$
$827$			18.8339i			0.654919i	−0.944865	+	0.327460i	$0.893807\pi$
$828$	−0.396627	+	3.72676i	−0.0137838	+	0.129514i
$829$	−37.2107			−1.29238			−0.646191	−	0.763176i	$-0.723639\pi$
$829$	−37.2107			−1.29238			−0.646191	+	0.763176i	$0.723639\pi$
$830$		0			0
$831$	−0.365340	−	2.54099i	−0.0126735	−	0.0881461i
$832$	−8.75052	+	3.99623i	−0.303370	+	0.138544i
$833$	−1.00920	+	3.43702i	−0.0349667	+	0.119086i
$834$	14.2202	−	31.1380i	0.492407	−	1.07822i
$835$		0			0
$836$	0.383513	−	2.66739i	0.0132641	−	0.0922537i
$837$	1.83178	+	6.23847i	0.0633156	+	0.215633i
$838$	20.5580	−	17.8136i	0.710164	−	0.615361i
$839$	15.7729	−	10.1366i	0.544541	−	0.349955i	−0.239272	−	0.970953i	$-0.576909\pi$
$839$	15.7729	−	10.1366i	0.544541	−	0.349955i	0.783812	+	0.620998i	$0.213272\pi$
$840$		0			0
$841$	−29.5441	−	34.0957i	−1.01876	−	1.17571i
$842$	6.95442	+	23.6846i	0.239665	+	0.816225i
$843$	26.6675	+	3.83421i	0.918477	+	0.132057i
$844$	−6.34883	+	7.32694i	−0.218536	+	0.252204i
$845$		0			0
$846$	−13.8511	−	4.06705i	−0.476211	−	0.139828i
$847$	7.46958	−	3.41124i	0.256658	−	0.117212i
$848$	−23.4423	+	3.37049i	−0.805011	+	0.115743i
$849$	−2.10711	−	1.35416i	−0.0723160	−	0.0464747i
$850$		0			0
$851$	16.7532	−	28.3050i	0.574291	−	0.970284i
$852$			1.10637i			0.0379037i
$853$	−10.9129	+	16.9808i	−0.373650	+	0.581411i	−0.976254	−	0.216630i	$-0.930494\pi$
$853$	−10.9129	+	16.9808i	−0.373650	+	0.581411i	0.602604	+	0.798041i	$0.294130\pi$
$854$	4.57309	+	31.8066i	0.156488	+	1.08840i
$855$		0			0
$856$	22.7311	+	6.67445i	0.776933	+	0.228128i
$857$	−4.37889	−	1.99977i	−0.149580	−	0.0683110i	0.339218	−	0.940708i	$-0.389837\pi$
$857$	−4.37889	−	1.99977i	−0.149580	−	0.0683110i	−0.488799	+	0.872397i	$0.662565\pi$
$858$	7.25340	+	6.28511i	0.247627	+	0.214570i
$859$	−1.88417	+	13.1047i	−0.0642871	+	0.447126i	0.932100	+	0.362200i	$0.117974\pi$
$859$	−1.88417	+	13.1047i	−0.0642871	+	0.447126i	−0.996387	+	0.0849258i	$0.972935\pi$
$860$		0			0
$861$	−9.84739	−	11.3645i	−0.335598	−	0.387301i
$862$	−3.26432	−	5.07938i	−0.111183	−	0.173004i
$863$	−3.71222	−	5.77633i	−0.126366	−	0.196629i	0.772306	−	0.635250i	$-0.219103\pi$
$863$	−3.71222	−	5.77633i	−0.126366	−	0.196629i	−0.898672	+	0.438622i	$0.855467\pi$
$864$	7.13980	+	8.23977i	0.242901	+	0.280323i
$865$		0			0
$866$	8.77233	−	61.0129i	0.298096	−	2.07330i
$867$	−6.64319	−	5.75635i	−0.225614	−	0.195496i
$868$	−1.10826	−	0.506125i	−0.0376168	−	0.0171790i
$869$	−45.0542	−	13.2291i	−1.52836	−	0.448767i
$870$		0			0
$871$	−1.20699	−	8.39481i	−0.0408973	−	0.284447i
$872$	10.8633	−	16.9037i	0.367879	−	0.572431i
$873$		−	12.4084i		−	0.419960i
$874$	7.69159	+	11.0527i	0.260172	+	0.373863i
$875$		0			0
$876$	0.690171	+	0.443546i	0.0233187	+	0.0149860i
$877$	−2.37876	+	0.342014i	−0.0803251	+	0.0115490i	−0.182360	−	0.983232i	$-0.558374\pi$
$877$	−2.37876	+	0.342014i	−0.0803251	+	0.0115490i	0.102035	+	0.994781i	$0.467465\pi$
$878$	39.0022	−	17.8117i	1.31626	−	0.601116i
$879$	−18.8621	−	5.53842i	−0.636204	−	0.186806i
$880$		0			0
$881$	2.23506	−	2.57940i	0.0753012	−	0.0869022i	−0.716849	−	0.697229i	$-0.754416\pi$
$881$	2.23506	−	2.57940i	0.0753012	−	0.0869022i	0.792150	+	0.610326i	$0.208962\pi$
$882$	3.82672	+	0.550199i	0.128852	+	0.0185262i
$883$	−0.816661	−	2.78129i	−0.0274828	−	0.0935979i	0.944610	−	0.328196i	$-0.106441\pi$
$883$	−0.816661	−	2.78129i	−0.0274828	−	0.0935979i	−0.972092	+	0.234598i	$0.924623\pi$
$884$	−1.19824	−	1.38285i	−0.0403013	−	0.0465102i
$885$		0			0
$886$	38.5539	−	24.7771i	1.29524	−	0.832402i
$887$	−3.08825	+	2.67598i	−0.103693	+	0.0898506i	−0.705164	−	0.709044i	$-0.749127\pi$
$887$	−3.08825	+	2.67598i	−0.103693	+	0.0898506i	0.601471	+	0.798894i	$0.294581\pi$
$888$	−4.80782	−	16.3739i	−0.161340	−	0.549474i
$889$	−0.104078	+	0.723877i	−0.00349066	+	0.0242780i
$890$		0			0
$891$	1.57773	−	3.45475i	0.0528560	−	0.115739i
$892$	−2.22579	+	7.58036i	−0.0745251	+	0.253809i
$893$	−7.71096	+	3.52148i	−0.258037	+	0.117842i
$894$	4.97941	+	34.6325i	0.166536	+	1.15828i
$895$		0			0
$896$	32.2804			1.07841
$897$	−7.83280	+	0.288156i	−0.261530	+	0.00962126i
$898$			24.0001i			0.800893i
$899$	−9.41773	−	6.05241i	−0.314099	−	0.201859i
$900$		0			0
$901$	6.09008	+	13.3354i	0.202890	+	0.444267i
$902$	−10.3753	+	35.3349i	−0.345458	+	1.17652i
$903$	−26.3744	−	12.0448i	−0.877685	−	0.400825i
$904$	−5.76435	+	6.65241i	−0.191719	+	0.221256i
$905$		0			0
$906$	−2.97245	+	0.872790i	−0.0987531	+	0.0289965i
$907$	−0.865391	+	0.749866i	−0.0287348	+	0.0248989i	−0.669110	−	0.743164i	$-0.733324\pi$
$907$	−0.865391	+	0.749866i	−0.0287348	+	0.0248989i	0.640375	+	0.768062i	$0.278779\pi$
$908$	2.66674	+	4.14952i	0.0884987	+	0.137707i
$909$	21.4126	−	13.7610i	0.710211	−	0.456425i
$910$		0			0
$911$	11.6713	−	3.42700i	0.386687	−	0.113542i	−0.0826098	−	0.996582i	$-0.526326\pi$
$911$	11.6713	−	3.42700i	0.386687	−	0.113542i	0.469297	+	0.883040i	$0.344507\pi$
$912$	8.31995	+	1.19623i	0.275501	+	0.0396111i
$913$	39.1955	+	33.9631i	1.29718	+	1.12401i
$914$	0.430101	−	0.941790i	0.0142265	−	0.0311516i
$915$		0			0
$916$	2.85137	+	6.24363i	0.0942119	+	0.206295i
$917$	52.7514	−	7.58450i	1.74200	−	0.250462i
$918$	11.9760	−	18.6350i	0.395266	−	0.615046i
$919$	44.9964			1.48429			0.742147	−	0.670237i	$-0.233808\pi$
$919$	44.9964			1.48429			0.742147	+	0.670237i	$0.233808\pi$
$920$		0			0
$921$	−6.31271			−0.208011
$922$	15.1995	−	23.6509i	0.500569	−	0.778901i
$923$	4.58060	−	0.658591i	0.150772	−	0.0216778i
$924$	−1.47823	−	3.23688i	−0.0486303	−	0.106486i
$925$		0			0
$926$	9.07015	−	19.8608i	0.298063	−	0.652668i
$927$	0.765500	+	0.663309i	0.0251423	+	0.0217859i
$928$	−18.5814	−	2.67160i	−0.609963	−	0.0876994i
$929$	48.6600	−	14.2879i	1.59648	−	0.468770i	0.641918	−	0.766773i	$-0.278139\pi$
$929$	48.6600	−	14.2879i	1.59648	−	0.468770i	0.954565	+	0.298003i	$0.0963206\pi$
$930$		0			0
$931$	1.90984	−	1.22738i	0.0625924	−	0.0402257i
$932$	1.44789	+	2.25296i	0.0474273	+	0.0737983i
$933$	−17.8630	+	15.4784i	−0.584809	+	0.506740i
$934$	−12.2016	+	3.58272i	−0.399250	+	0.117230i
$935$		0			0
$936$	5.32622	−	6.14678i	0.174093	−	0.200914i
$937$	−28.2200	−	12.8876i	−0.921906	−	0.421020i	−0.102826	−	0.994699i	$-0.532788\pi$
$937$	−28.2200	−	12.8876i	−0.921906	−	0.421020i	−0.819080	+	0.573679i	$0.805516\pi$
$938$	−5.42047	+	18.4604i	−0.176985	+	0.602754i
$939$	−13.0192	−	28.5081i	−0.424867	−	0.930328i
$940$		0			0
$941$	−3.61091	−	2.32059i	−0.117712	−	0.0756491i	0.480460	−	0.877017i	$-0.340470\pi$
$941$	−3.61091	−	2.32059i	−0.117712	−	0.0756491i	−0.598172	+	0.801368i	$0.704106\pi$
$942$			9.91476i			0.323040i
$943$	−13.4910	−	26.8796i	−0.439328	−	0.875320i
$944$	33.6029			1.09368
$945$		0			0
$946$	10.1055	+	70.2852i	0.328558	+	2.28517i
$947$	37.3974	−	17.0788i	1.21525	−	0.554988i	0.298488	−	0.954413i	$-0.403518\pi$
$947$	37.3974	−	17.0788i	1.21525	−	0.554988i	0.916765	+	0.399426i	$0.130791\pi$
$948$	−1.36101	+	4.63518i	−0.0442036	+	0.150544i
$949$	1.42553	−	3.12147i	0.0462746	−	0.101327i
$950$		0			0
$951$	0.990260	−	6.88741i	0.0321114	−	0.223340i
$952$	−4.81641	−	16.4032i	−0.156101	−	0.531631i
$953$	6.42075	−	5.56361i	0.207989	−	0.180223i	−0.544637	−	0.838672i	$-0.683333\pi$
$953$	6.42075	−	5.56361i	0.207989	−	0.180223i	0.752626	+	0.658449i	$0.228787\pi$
$954$	13.3106	−	8.55420i	0.430946	−	0.276952i
$955$		0			0
$956$	−2.24451	−	2.59030i	−0.0725926	−	0.0837763i
$957$	−9.21173	−	31.3723i	−0.297773	−	1.01412i
$958$	1.45273	+	0.208871i	0.0469355	+	0.00674830i
$959$	−20.8386	+	24.0490i	−0.672912	+	0.776582i
$960$		0			0
$961$	28.1218	+	8.25731i	0.907156	+	0.266365i
$962$	15.7651	−	7.19968i	0.508287	−	0.232127i
$963$	−18.8483	+	2.70998i	−0.607378	+	0.0873277i
$964$	3.33926	+	2.14601i	0.107550	+	0.0691183i
$965$		0			0
$966$	16.4348	+	6.78689i	0.528781	+	0.218365i
$967$		−	56.7552i		−	1.82513i	−0.408937	−	0.912563i	$-0.634100\pi$
$967$		−	56.7552i		−	1.82513i	0.408937	−	0.912563i	$-0.365900\pi$
$968$	4.60687	−	7.16843i	0.148070	−	0.230402i
$969$	−0.740479	−	5.15014i	−0.0237876	−	0.165446i
$970$		0			0
$971$	1.07211	+	0.314801i	0.0344057	+	0.0101024i	0.298890	−	0.954288i	$-0.403384\pi$
$971$	1.07211	+	0.314801i	0.0344057	+	0.0101024i	−0.264484	+	0.964390i	$0.585202\pi$
$972$	−5.68681	−	2.59708i	−0.182404	−	0.0833013i
$973$	40.1203	+	34.7644i	1.28620	+	1.11450i
$974$	2.75368	−	19.1522i	0.0882335	−	0.613677i
$975$		0			0
$976$	26.2715	+	30.3189i	0.840929	+	0.970483i
$977$	1.20962	+	1.88221i	0.0386992	+	0.0602172i	0.860064	−	0.510186i	$-0.170423\pi$
$977$	1.20962	+	1.88221i	0.0386992	+	0.0602172i	−0.821365	+	0.570403i	$0.806787\pi$
$978$	−5.56879	−	8.66520i	−0.178070	−	0.277083i
$979$	−28.8981	−	33.3501i	−0.923586	−	1.06587i
$980$		0			0
$981$	−2.29848	+	15.9863i	−0.0733849	+	0.510403i
$982$	34.4581	+	29.8581i	1.09960	+	0.952810i
$983$	−16.3325	−	7.45879i	−0.520925	−	0.237898i	0.137559	−	0.990494i	$-0.456074\pi$
$983$	−16.3325	−	7.45879i	−0.520925	−	0.237898i	−0.658483	+	0.752595i	$0.728802\pi$
$984$	−14.9720	−	4.39618i	−0.477290	−	0.140145i
$985$		0			0
$986$	5.42795	+	37.7522i	0.172861	+	1.20227i
$987$	−6.05177	+	9.41674i	−0.192630	+	0.299738i
$988$			1.15965i			0.0368933i
$989$	−45.1925	−	36.3386i	−1.43704	−	1.15550i
$990$		0			0
$991$	−46.3210	−	29.7687i	−1.47144	−	0.945635i	−0.997894	−	0.0648634i	$-0.979339\pi$
$991$	−46.3210	−	29.7687i	−1.47144	−	0.945635i	−0.473542	−	0.880771i	$-0.657025\pi$
$992$	−2.80666	+	0.403537i	−0.0891117	+	0.0128123i
$993$	19.3811	−	8.85106i	0.615041	−	0.280880i
$994$	−10.0729	−	2.95766i	−0.319492	−	0.0938114i
$995$		0			0
$996$	3.49413	−	4.03244i	0.110716	−	0.127773i
$997$	−55.2693	−	7.94653i	−1.75040	−	0.251669i	−0.808721	−	0.588192i	$-0.799840\pi$
$997$	−55.2693	−	7.94653i	−1.75040	−	0.251669i	−0.941675	+	0.336523i	$0.890749\pi$
$998$	5.44573	+	18.5465i	0.172382	+	0.587078i
$999$	22.4563	+	25.9159i	0.710484	+	0.819943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.p.a.324.2		20
5.2	odd	4		575.2.k.a.301.1		10
5.3	odd	4		115.2.g.a.71.1	✓	10
5.4	even	2	inner	575.2.p.a.324.1		20
23.12	even	11	inner	575.2.p.a.449.1		20
115.12	odd	44		575.2.k.a.426.1		10
115.58	odd	44		115.2.g.a.81.1	yes	10
115.78	odd	44		2645.2.a.n.1.2		5
115.83	even	44		2645.2.a.o.1.2		5
115.104	even	22	inner	575.2.p.a.449.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.a.71.1	✓	10	5.3	odd	4
115.2.g.a.81.1	yes	10	115.58	odd	44
575.2.k.a.301.1		10	5.2	odd	4
575.2.k.a.426.1		10	115.12	odd	44
575.2.p.a.324.1		20	5.4	even	2	inner
575.2.p.a.324.2		20	1.1	even	1	trivial
575.2.p.a.449.1		20	23.12	even	11	inner
575.2.p.a.449.2		20	115.104	even	22	inner
2645.2.a.n.1.2		5	115.78	odd	44
2645.2.a.o.1.2		5	115.83	even	44

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:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.p (of order \(22\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.835939 - 1.30075i) q^{2} +(0.989821 - 0.142315i) q^{3} +(-0.162317 - 0.355426i) q^{4} +(0.642315 - 1.40647i) q^{6} +(1.81219 + 1.57028i) q^{7} +(2.46292 + 0.354114i) q^{8} +(-1.91899 + 0.563465i) q^{9} +O(q^{10})\)	\(q+(0.835939 - 1.30075i) q^{2} +(0.989821 - 0.142315i) q^{3} +(-0.162317 - 0.355426i) q^{4} +(0.642315 - 1.40647i) q^{6} +(1.81219 + 1.57028i) q^{7} +(2.46292 + 0.354114i) q^{8} +(-1.91899 + 0.563465i) q^{9} +(3.19505 - 2.05334i) q^{11} +(-0.211248 - 0.328708i) q^{12} +(-1.23516 + 1.07028i) q^{13} +(3.55742 - 1.04455i) q^{14} +(3.03122 - 3.49821i) q^{16} +(-2.60635 - 1.19028i) q^{17} +(-0.871230 + 2.96714i) q^{18} +(0.754359 + 1.65182i) q^{19} +(2.01722 + 1.29639i) q^{21} -5.87242i q^{22} +(3.27173 + 3.50654i) q^{23} +2.48825 q^{24} +(0.359636 + 2.50132i) q^{26} +(-4.54816 + 2.07708i) q^{27} +(0.263965 - 0.898983i) q^{28} +(3.57631 - 7.83103i) q^{29} +(0.185062 - 1.28713i) q^{31} +(-0.614334 - 2.09223i) q^{32} +(2.87031 - 2.48714i) q^{33} +(-3.72700 + 2.39520i) q^{34} +(0.511755 + 0.590596i) q^{36} +(-1.93221 - 6.58052i) q^{37} +(2.77919 + 0.399587i) q^{38} +(-1.07028 + 1.23516i) q^{39} +(-6.01710 - 1.76678i) q^{41} +(3.37255 - 1.54019i) q^{42} +(-11.9687 + 1.72084i) q^{43} +(-1.24842 - 0.802311i) q^{44} +(7.29608 - 1.32443i) q^{46} +4.66817i q^{47} +(2.50252 - 3.89399i) q^{48} +(-0.177920 - 1.23746i) q^{49} +(-2.74921 - 0.807241i) q^{51} +(0.580892 + 0.265284i) q^{52} +(-3.86681 - 3.35061i) q^{53} +(-1.10024 + 7.65231i) q^{54} +(3.90723 + 4.50919i) q^{56} +(0.981759 + 1.52765i) q^{57} +(-7.19661 - 11.1981i) q^{58} +(4.75399 + 5.48639i) q^{59} +(-1.23344 + 8.57875i) q^{61} +(-1.51953 - 1.31668i) q^{62} +(-4.36237 - 1.99223i) q^{63} +(5.64759 + 1.65828i) q^{64} +(-0.835732 - 5.81264i) q^{66} +(-2.80554 + 4.36550i) q^{67} +1.11956i q^{68} +(3.73746 + 3.00523i) q^{69} +(-2.38202 - 1.53083i) q^{71} +(-4.92584 + 0.708228i) q^{72} +(-1.90991 + 0.872226i) q^{73} +(-10.1748 - 2.98759i) q^{74} +(0.464652 - 0.536237i) q^{76} +(9.01436 + 1.29607i) q^{77} +(0.711950 + 2.42468i) q^{78} +(-8.09638 - 9.34373i) q^{79} +(0.841254 - 0.540641i) q^{81} +(-7.32806 + 6.34980i) q^{82} +(3.84719 + 13.1023i) q^{83} +(0.133340 - 0.927399i) q^{84} +(-7.76672 + 17.0068i) q^{86} +(2.42544 - 8.26028i) q^{87} +(8.59627 - 3.92579i) q^{88} +(-1.65356 - 11.5007i) q^{89} -3.91899 q^{91} +(0.715255 - 1.73203i) q^{92} -1.30037i q^{93} +(6.07211 + 3.90231i) q^{94} +(-0.905836 - 1.98350i) q^{96} +(-1.74792 + 5.95288i) q^{97} +(-1.75835 - 0.803012i) q^{98} +(-4.97428 + 5.74062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{4} + 12 q^{6} - 4 q^{9}+O(q^{10}) \) 20 * q + 2 * q^4 + 12 * q^6 - 4 * q^9	\( 20 q + 2 q^{4} + 12 q^{6} - 4 q^{9} + 16 q^{11} + 6 q^{14} + 10 q^{16} + 26 q^{19} + 12 q^{21} + 12 q^{24} + 22 q^{26} - 4 q^{29} - 40 q^{31} - 32 q^{34} + 48 q^{36} - 10 q^{41} - 38 q^{44} - 32 q^{46} - 8 q^{49} - 20 q^{51} + 60 q^{54} + 6 q^{56} - 10 q^{59} - 6 q^{61} + 68 q^{64} - 8 q^{66} + 2 q^{69} - 44 q^{71} - 2 q^{74} - 4 q^{76} - 102 q^{79} - 2 q^{81} - 12 q^{84} - 18 q^{86} - 114 q^{89} - 44 q^{91} + 162 q^{94} - 14 q^{96} - 12 q^{99}+O(q^{100}) \) 20 * q + 2 * q^4 + 12 * q^6 - 4 * q^9 + 16 * q^11 + 6 * q^14 + 10 * q^16 + 26 * q^19 + 12 * q^21 + 12 * q^24 + 22 * q^26 - 4 * q^29 - 40 * q^31 - 32 * q^34 + 48 * q^36 - 10 * q^41 - 38 * q^44 - 32 * q^46 - 8 * q^49 - 20 * q^51 + 60 * q^54 + 6 * q^56 - 10 * q^59 - 6 * q^61 + 68 * q^64 - 8 * q^66 + 2 * q^69 - 44 * q^71 - 2 * q^74 - 4 * q^76 - 102 * q^79 - 2 * q^81 - 12 * q^84 - 18 * q^86 - 114 * q^89 - 44 * q^91 + 162 * q^94 - 14 * q^96 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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