LMFDB - Embedded newform 975.2.k.d.307.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(307,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("975.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.k (of order $4$, degree $2$, 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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.4
Character	$\chi$	$=$	975.307
Dual form			975.2.k.d.343.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.58074i q^{2} +(-0.707107 + 0.707107i) q^{3} -0.498726 q^{4} +(1.11775 + 1.11775i) q^{6} -0.974287 q^{7} -2.37312i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.58074i q^{2} +(-0.707107 + 0.707107i) q^{3} -0.498726 q^{4} +(1.11775 + 1.11775i) q^{6} -0.974287 q^{7} -2.37312i q^{8} -1.00000i q^{9} +(-0.601309 + 0.601309i) q^{11} +(0.352653 - 0.352653i) q^{12} +(-3.34435 - 1.34733i) q^{13} +1.54009i q^{14} -4.74872 q^{16} +(-1.16444 + 1.16444i) q^{17} -1.58074 q^{18} +(0.691537 - 0.691537i) q^{19} +(0.688925 - 0.688925i) q^{21} +(0.950511 + 0.950511i) q^{22} +(1.66029 + 1.66029i) q^{23} +(1.67805 + 1.67805i) q^{24} +(-2.12977 + 5.28654i) q^{26} +(0.707107 + 0.707107i) q^{27} +0.485902 q^{28} -6.37081i q^{29} +(-7.57606 - 7.57606i) q^{31} +2.76024i q^{32} -0.850380i q^{33} +(1.84067 + 1.84067i) q^{34} +0.498726i q^{36} -7.22558 q^{37} +(-1.09314 - 1.09314i) q^{38} +(3.31752 - 1.41211i) q^{39} +(3.65114 + 3.65114i) q^{41} +(-1.08901 - 1.08901i) q^{42} +(-2.71746 - 2.71746i) q^{43} +(0.299889 - 0.299889i) q^{44} +(2.62449 - 2.62449i) q^{46} -3.25740 q^{47} +(3.35786 - 3.35786i) q^{48} -6.05077 q^{49} -1.64677i q^{51} +(1.66792 + 0.671949i) q^{52} +(-5.65843 + 5.65843i) q^{53} +(1.11775 - 1.11775i) q^{54} +2.31210i q^{56} +0.977981i q^{57} -10.0706 q^{58} +(-5.91615 - 5.91615i) q^{59} +2.69124 q^{61} +(-11.9757 + 11.9757i) q^{62} +0.974287i q^{63} -5.13423 q^{64} -1.34423 q^{66} +6.40792i q^{67} +(0.580737 - 0.580737i) q^{68} -2.34801 q^{69} +(7.17864 + 7.17864i) q^{71} -2.37312 q^{72} -10.2299i q^{73} +11.4217i q^{74} +(-0.344887 + 0.344887i) q^{76} +(0.585848 - 0.585848i) q^{77} +(-2.23217 - 5.24413i) q^{78} +7.43682i q^{79} -1.00000 q^{81} +(5.77149 - 5.77149i) q^{82} +14.2841 q^{83} +(-0.343585 + 0.343585i) q^{84} +(-4.29559 + 4.29559i) q^{86} +(4.50484 + 4.50484i) q^{87} +(1.42698 + 1.42698i) q^{88} +(-10.6606 - 10.6606i) q^{89} +(3.25836 + 1.31269i) q^{91} +(-0.828032 - 0.828032i) q^{92} +10.7142 q^{93} +5.14908i q^{94} +(-1.95179 - 1.95179i) q^{96} -14.4866i q^{97} +9.56466i q^{98} +(0.601309 + 0.601309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4}+O(q^{10}) $ 28 * q - 28 * q^4	$ 28 q - 28 q^{4} - 8 q^{11} - 8 q^{12} + 12 q^{13} + 28 q^{16} + 28 q^{17} + 4 q^{18} + 8 q^{21} + 32 q^{22} - 8 q^{23} - 16 q^{31} + 28 q^{34} - 32 q^{37} + 8 q^{39} + 4 q^{41} + 40 q^{44} - 16 q^{46} + 24 q^{47} + 16 q^{48} - 28 q^{49} - 52 q^{52} - 20 q^{53} + 8 q^{58} + 32 q^{59} + 8 q^{61} - 72 q^{62} - 28 q^{64} + 16 q^{66} - 60 q^{68} + 8 q^{69} + 40 q^{71} - 12 q^{72} - 40 q^{76} + 48 q^{77} - 8 q^{78} - 28 q^{81} - 4 q^{82} + 104 q^{83} - 32 q^{84} + 16 q^{86} + 24 q^{87} - 72 q^{88} - 36 q^{89} - 56 q^{91} + 32 q^{92} + 8 q^{99}+O(q^{100}) $ 28 * q - 28 * q^4 - 8 * q^11 - 8 * q^12 + 12 * q^13 + 28 * q^16 + 28 * q^17 + 4 * q^18 + 8 * q^21 + 32 * q^22 - 8 * q^23 - 16 * q^31 + 28 * q^34 - 32 * q^37 + 8 * q^39 + 4 * q^41 + 40 * q^44 - 16 * q^46 + 24 * q^47 + 16 * q^48 - 28 * q^49 - 52 * q^52 - 20 * q^53 + 8 * q^58 + 32 * q^59 + 8 * q^61 - 72 * q^62 - 28 * q^64 + 16 * q^66 - 60 * q^68 + 8 * q^69 + 40 * q^71 - 12 * q^72 - 40 * q^76 + 48 * q^77 - 8 * q^78 - 28 * q^81 - 4 * q^82 + 104 * q^83 - 32 * q^84 + 16 * q^86 + 24 * q^87 - 72 * q^88 - 36 * q^89 - 56 * q^91 + 32 * q^92 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$		−	1.58074i		−	1.11775i	−0.829252	−	0.558875i	$-0.811233\pi$
$2$		−	1.58074i		−	1.11775i	0.829252	−	0.558875i	$-0.188767\pi$
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−0.498726			−0.249363
$5$		0			0
$5$		0			0
$6$	1.11775	+	1.11775i	0.456319	+	0.456319i
$7$	−0.974287			−0.368246			−0.184123	−	0.982903i	$-0.558944\pi$
$7$	−0.974287			−0.368246			−0.184123	+	0.982903i	$0.558944\pi$
$8$		−	2.37312i		−	0.839024i
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−0.601309	+	0.601309i	−0.181302	+	0.181302i	−0.791923	−	0.610621i	$-0.790920\pi$
$11$	−0.601309	+	0.601309i	−0.181302	+	0.181302i	0.610621	+	0.791923i	$0.290920\pi$
$12$	0.352653	−	0.352653i	0.101802	−	0.101802i
$13$	−3.34435	−	1.34733i	−0.927557	−	0.373682i
$13$	−3.34435	−	1.34733i	−0.927557	−	0.373682i
$14$			1.54009i			0.411606i
$15$		0			0
$16$	−4.74872			−1.18718
$17$	−1.16444	+	1.16444i	−0.282419	+	0.282419i	−0.834073	−	0.551654i	$-0.813997\pi$
$17$	−1.16444	+	1.16444i	−0.282419	+	0.282419i	0.551654	+	0.834073i	$0.313997\pi$
$18$	−1.58074			−0.372583
$19$	0.691537	−	0.691537i	0.158649	−	0.158649i	−0.623319	−	0.781968i	$-0.714216\pi$
$19$	0.691537	−	0.691537i	0.158649	−	0.158649i	0.781968	+	0.623319i	$0.214216\pi$
$20$		0			0
$21$	0.688925	−	0.688925i	0.150336	−	0.150336i
$22$	0.950511	+	0.950511i	0.202650	+	0.202650i
$23$	1.66029	+	1.66029i	0.346195	+	0.346195i	0.858690	−	0.512495i	$-0.171279\pi$
$23$	1.66029	+	1.66029i	0.346195	+	0.346195i	−0.512495	+	0.858690i	$0.671279\pi$
$24$	1.67805	+	1.67805i	0.342530	+	0.342530i
$25$		0			0
$26$	−2.12977	+	5.28654i	−0.417683	+	1.03678i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	0.485902			0.0918269
$29$		−	6.37081i		−	1.18303i	−0.806294	−	0.591515i	$-0.798530\pi$
$29$		−	6.37081i		−	1.18303i	0.806294	−	0.591515i	$-0.201470\pi$
$30$		0			0
$31$	−7.57606	−	7.57606i	−1.36070	−	1.36070i	−0.873026	−	0.487674i	$-0.837845\pi$
$31$	−7.57606	−	7.57606i	−1.36070	−	1.36070i	−0.487674	−	0.873026i	$-0.662155\pi$
$32$			2.76024i			0.487947i
$33$		−	0.850380i		−	0.148032i
$34$	1.84067	+	1.84067i	0.315673	+	0.315673i
$35$		0			0
$36$			0.498726i			0.0831210i
$37$	−7.22558			−1.18788			−0.593939	−	0.804510i	$-0.702428\pi$
$37$	−7.22558			−1.18788			−0.593939	+	0.804510i	$0.702428\pi$
$38$	−1.09314	−	1.09314i	−0.177330	−	0.177330i
$39$	3.31752	−	1.41211i	0.531229	−	0.226118i
$40$		0			0
$41$	3.65114	+	3.65114i	0.570212	+	0.570212i	0.932188	−	0.361975i	$-0.117898\pi$
$41$	3.65114	+	3.65114i	0.570212	+	0.570212i	−0.361975	+	0.932188i	$0.617898\pi$
$42$	−1.08901	−	1.08901i	−0.168038	−	0.168038i
$43$	−2.71746	−	2.71746i	−0.414409	−	0.414409i	0.468862	−	0.883271i	$-0.344664\pi$
$43$	−2.71746	−	2.71746i	−0.414409	−	0.414409i	−0.883271	+	0.468862i	$0.844664\pi$
$44$	0.299889	−	0.299889i	0.0452099	−	0.0452099i
$45$		0			0
$46$	2.62449	−	2.62449i	0.386959	−	0.386959i
$47$	−3.25740			−0.475140			−0.237570	−	0.971370i	$-0.576351\pi$
$47$	−3.25740			−0.475140			−0.237570	+	0.971370i	$0.576351\pi$
$48$	3.35786	−	3.35786i	0.484665	−	0.484665i
$49$	−6.05077			−0.864395
$50$		0			0
$51$		−	1.64677i		−	0.230594i
$52$	1.66792	+	0.671949i	0.231298	+	0.0931826i
$53$	−5.65843	+	5.65843i	−0.777245	+	0.777245i	−0.979361	−	0.202117i	$-0.935218\pi$
$53$	−5.65843	+	5.65843i	−0.777245	+	0.777245i	0.202117	+	0.979361i	$0.435218\pi$
$54$	1.11775	−	1.11775i	0.152106	−	0.152106i
$55$		0			0
$56$			2.31210i			0.308967i
$57$			0.977981i			0.129537i
$58$	−10.0706			−1.32233
$59$	−5.91615	−	5.91615i	−0.770218	−	0.770218i	0.207927	−	0.978144i	$-0.433328\pi$
$59$	−5.91615	−	5.91615i	−0.770218	−	0.770218i	−0.978144	+	0.207927i	$0.933328\pi$
$60$		0			0
$61$	2.69124			0.344578			0.172289	−	0.985046i	$-0.444884\pi$
$61$	2.69124			0.344578			0.172289	+	0.985046i	$0.444884\pi$
$62$	−11.9757	+	11.9757i	−1.52092	+	1.52092i
$63$			0.974287i			0.122749i
$64$	−5.13423			−0.641779
$65$		0			0
$66$	−1.34423			−0.165463
$67$			6.40792i			0.782851i	0.920210	+	0.391426i	$0.128018\pi$
$67$			6.40792i			0.782851i	−0.920210	+	0.391426i	$0.871982\pi$
$68$	0.580737	−	0.580737i	0.0704247	−	0.0704247i
$69$	−2.34801			−0.282667
$70$		0			0
$71$	7.17864	+	7.17864i	0.851948	+	0.851948i	0.990373	−	0.138425i	$-0.0442040\pi$
$71$	7.17864	+	7.17864i	0.851948	+	0.851948i	−0.138425	+	0.990373i	$0.544204\pi$
$72$	−2.37312			−0.279675
$73$		−	10.2299i		−	1.19732i	−0.801004	−	0.598659i	$-0.795701\pi$
$73$		−	10.2299i		−	1.19732i	0.801004	−	0.598659i	$-0.204299\pi$
$74$			11.4217i			1.32775i
$75$		0			0
$76$	−0.344887	+	0.344887i	−0.0395613	+	0.0395613i
$77$	0.585848	−	0.585848i	0.0667635	−	0.0667635i
$78$	−2.23217	−	5.24413i	−0.252744	−	0.593780i
$79$			7.43682i			0.836708i	0.908284	+	0.418354i	$0.137393\pi$
$79$			7.43682i			0.836708i	−0.908284	+	0.418354i	$0.862607\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	5.77149	−	5.77149i	0.637354	−	0.637354i
$83$	14.2841			1.56788			0.783940	−	0.620837i	$-0.213207\pi$
$83$	14.2841			1.56788			0.783940	+	0.620837i	$0.213207\pi$
$84$	−0.343585	+	0.343585i	−0.0374882	+	0.0374882i
$85$		0			0
$86$	−4.29559	+	4.29559i	−0.463205	+	0.463205i
$87$	4.50484	+	4.50484i	0.482970	+	0.482970i
$88$	1.42698	+	1.42698i	0.152116	+	0.152116i
$89$	−10.6606	−	10.6606i	−1.13002	−	1.13002i	−0.990173	−	0.139846i	$-0.955339\pi$
$89$	−10.6606	−	10.6606i	−1.13002	−	1.13002i	−0.139846	−	0.990173i	$-0.544661\pi$
$90$		0			0
$91$	3.25836	+	1.31269i	0.341569	+	0.137607i
$92$	−0.828032	−	0.828032i	−0.0863283	−	0.0863283i
$93$	10.7142			1.11101
$94$			5.14908i			0.531087i
$95$		0			0
$96$	−1.95179	−	1.95179i	−0.199203	−	0.199203i
$97$		−	14.4866i		−	1.47089i	−0.677583	−	0.735446i	$-0.736973\pi$
$97$		−	14.4866i		−	1.47089i	0.677583	−	0.735446i	$-0.263027\pi$
$98$			9.56466i			0.966177i
$99$	0.601309	+	0.601309i	0.0604339	+	0.0604339i
$100$		0			0
$101$			5.61850i			0.559062i	0.960137	+	0.279531i	$0.0901789\pi$
$101$			5.61850i			0.559062i	−0.960137	+	0.279531i	$0.909821\pi$
$102$	−2.60311			−0.257746
$103$	0.00240087	+	0.00240087i	0.000236565	+	0.000236565i	0.707225	−	0.706988i	$-0.249947\pi$
$103$	0.00240087	+	0.00240087i	0.000236565	+	0.000236565i	−0.706988	+	0.707225i	$0.749947\pi$
$104$	−3.19737	+	7.93654i	−0.313528	+	0.778242i
$105$		0			0
$106$	8.94448	+	8.94448i	0.868765	+	0.868765i
$107$	5.70114	+	5.70114i	0.551150	+	0.551150i	0.926773	−	0.375623i	$-0.122571\pi$
$107$	5.70114	+	5.70114i	0.551150	+	0.551150i	−0.375623	+	0.926773i	$0.622571\pi$
$108$	−0.352653	−	0.352653i	−0.0339340	−	0.0339340i
$109$	−2.16428	+	2.16428i	−0.207300	+	0.207300i	−0.803119	−	0.595819i	$-0.796828\pi$
$109$	−2.16428	+	2.16428i	−0.207300	+	0.207300i	0.595819	+	0.803119i	$0.296828\pi$
$110$		0			0
$111$	5.10926	−	5.10926i	0.484949	−	0.484949i
$112$	4.62662			0.437174
$113$	11.5213	−	11.5213i	1.08383	−	1.08383i	0.0876801	−	0.996149i	$-0.472055\pi$
$113$	11.5213	−	11.5213i	1.08383	−	1.08383i	0.996149	−	0.0876801i	$-0.0279453\pi$
$114$	1.54593			0.144790
$115$		0			0
$116$			3.17729i			0.295004i
$117$	−1.34733	+	3.34435i	−0.124561	+	0.309186i
$118$	−9.35188	+	9.35188i	−0.860910	+	0.860910i
$119$	1.13450	−	1.13450i	0.103999	−	0.103999i
$120$		0			0
$121$			10.2769i			0.934259i
$122$		−	4.25414i		−	0.385151i
$123$	−5.16349			−0.465576
$124$	3.77838	+	3.77838i	0.339308	+	0.339308i
$125$		0			0
$126$	1.54009			0.137202
$127$	−4.66491	+	4.66491i	−0.413943	+	0.413943i	−0.883110	−	0.469166i	$-0.844554\pi$
$127$	−4.66491	+	4.66491i	−0.413943	+	0.413943i	0.469166	+	0.883110i	$0.344554\pi$
$128$			13.6364i			1.20529i
$129$	3.84307			0.338363
$130$		0			0
$131$	1.57885			0.137945			0.0689725	−	0.997619i	$-0.478028\pi$
$131$	1.57885			0.137945			0.0689725	+	0.997619i	$0.478028\pi$
$132$			0.424107i			0.0369137i
$133$	−0.673755	+	0.673755i	−0.0584220	+	0.0584220i
$134$	10.1292			0.875031
$135$		0			0
$136$	2.76336	+	2.76336i	0.236956	+	0.236956i
$137$	−3.52318			−0.301006			−0.150503	−	0.988610i	$-0.548089\pi$
$137$	−3.52318			−0.301006			−0.150503	+	0.988610i	$0.548089\pi$
$138$			3.71159i			0.315951i
$139$		−	18.8913i		−	1.60234i	−0.598439	−	0.801168i	$-0.704212\pi$
$139$		−	18.8913i		−	1.60234i	0.598439	−	0.801168i	$-0.295788\pi$
$140$		0			0
$141$	2.30333	−	2.30333i	0.193975	−	0.193975i
$142$	11.3475	−	11.3475i	0.952264	−	0.952264i
$143$	2.82115	−	1.20083i	0.235917	−	0.100418i
$144$			4.74872i			0.395727i
$145$		0			0
$146$	−16.1707			−1.33830
$147$	4.27854	−	4.27854i	0.352888	−	0.352888i
$148$	3.60359			0.296213
$149$	−9.84579	+	9.84579i	−0.806599	+	0.806599i	−0.984117	−	0.177519i	$-0.943193\pi$
$149$	−9.84579	+	9.84579i	−0.806599	+	0.806599i	0.177519	+	0.984117i	$0.443193\pi$
$150$		0			0
$151$	11.8809	−	11.8809i	0.966858	−	0.966858i	−0.0326102	−	0.999468i	$-0.510382\pi$
$151$	11.8809	−	11.8809i	0.966858	−	0.966858i	0.999468	+	0.0326102i	$0.0103820\pi$
$152$	−1.64110	−	1.64110i	−0.133111	−	0.133111i
$153$	1.16444	+	1.16444i	0.0941395	+	0.0941395i
$154$	−0.926070	−	0.926070i	−0.0746249	−	0.0746249i
$155$		0			0
$156$	−1.65453	+	0.704255i	−0.132469	+	0.0563855i
$157$	−4.93383	−	4.93383i	−0.393763	−	0.393763i	0.482264	−	0.876026i	$-0.339815\pi$
$157$	−4.93383	−	4.93383i	−0.393763	−	0.393763i	−0.876026	+	0.482264i	$0.839815\pi$
$158$	11.7556			0.935229
$159$		−	8.00223i		−	0.634618i
$160$		0			0
$161$	−1.61760	−	1.61760i	−0.127485	−	0.127485i
$162$			1.58074i			0.124194i
$163$		−	17.8032i		−	1.39445i	−0.716851	−	0.697226i	$-0.754417\pi$
$163$		−	17.8032i		−	1.39445i	0.716851	−	0.697226i	$-0.245583\pi$
$164$	−1.82092	−	1.82092i	−0.142190	−	0.142190i
$165$		0			0
$166$		−	22.5793i		−	1.75250i
$167$	8.68228			0.671855			0.335928	−	0.941888i	$-0.390950\pi$
$167$	8.68228			0.671855			0.335928	+	0.941888i	$0.390950\pi$
$168$	−1.63490	−	1.63490i	−0.126135	−	0.126135i
$169$	9.36940	+	9.01190i	0.720723	+	0.693223i
$170$		0			0
$171$	−0.691537	−	0.691537i	−0.0528831	−	0.0528831i
$172$	1.35527	+	1.35527i	0.103338	+	0.103338i
$173$	7.68305	+	7.68305i	0.584131	+	0.584131i	0.936036	−	0.351905i	$-0.114466\pi$
$173$	7.68305	+	7.68305i	0.584131	+	0.584131i	−0.351905	+	0.936036i	$0.614466\pi$
$174$	7.12097	−	7.12097i	0.539839	−	0.539839i
$175$		0			0
$176$	2.85545	−	2.85545i	0.215238	−	0.215238i
$177$	8.36670			0.628880
$178$	−16.8516	+	16.8516i	−1.26308	+	1.26308i
$179$	23.0188			1.72051			0.860253	−	0.509867i	$-0.170305\pi$
$179$	23.0188			1.72051			0.860253	+	0.509867i	$0.170305\pi$
$180$		0			0
$181$			4.94015i			0.367199i	0.983001	+	0.183599i	$0.0587749\pi$
$181$			4.94015i			0.367199i	−0.983001	+	0.183599i	$0.941225\pi$
$182$	2.07501	−	5.15060i	0.153810	−	0.381788i
$183$	−1.90299	+	1.90299i	−0.140673	+	0.140673i
$184$	3.94007	−	3.94007i	0.290466	−	0.290466i
$185$		0			0
$186$		−	16.9363i		−	1.24183i
$187$		−	1.40038i		−	0.102406i
$188$	1.62455			0.118482
$189$	−0.688925	−	0.688925i	−0.0501119	−	0.0501119i
$190$		0			0
$191$	−6.77759			−0.490409			−0.245205	−	0.969471i	$-0.578855\pi$
$191$	−6.77759			−0.490409			−0.245205	+	0.969471i	$0.578855\pi$
$192$	3.63045	−	3.63045i	0.262005	−	0.262005i
$193$		−	8.23243i		−	0.592583i	−0.955098	−	0.296292i	$-0.904250\pi$
$193$		−	8.23243i		−	0.592583i	0.955098	−	0.296292i	$-0.0957500\pi$
$194$	−22.8995			−1.64409
$195$		0			0
$196$	3.01767			0.215548
$197$			23.1914i			1.65232i	0.563434	+	0.826161i	$0.309480\pi$
$197$			23.1914i			1.65232i	−0.563434	+	0.826161i	$0.690520\pi$
$198$	0.950511	−	0.950511i	0.0675499	−	0.0675499i
$199$	19.1896			1.36031			0.680156	−	0.733068i	$-0.261912\pi$
$199$	19.1896			1.36031			0.680156	+	0.733068i	$0.261912\pi$
$200$		0			0
$201$	−4.53108	−	4.53108i	−0.319598	−	0.319598i
$202$	8.88137			0.624891
$203$			6.20700i			0.435646i
$204$			0.821287i			0.0575016i
$205$		0			0
$206$	0.00379514	−	0.00379514i	0.000264420	−	0.000264420i
$207$	1.66029	−	1.66029i	0.115398	−	0.115398i
$208$	15.8814	+	6.39810i	1.10118	+	0.443629i
$209$			0.831655i			0.0575268i
$210$		0			0
$211$	−22.9847			−1.58233			−0.791165	−	0.611602i	$-0.790525\pi$
$211$	−22.9847			−1.58233			−0.791165	+	0.611602i	$0.790525\pi$
$212$	2.82201	−	2.82201i	0.193816	−	0.193816i
$213$	−10.1521			−0.695613
$214$	9.01200	−	9.01200i	0.616048	−	0.616048i
$215$		0			0
$216$	1.67805	−	1.67805i	0.114177	−	0.114177i
$217$	7.38125	+	7.38125i	0.501072	+	0.501072i
$218$	3.42115	+	3.42115i	0.231709	+	0.231709i
$219$	7.23362	+	7.23362i	0.488803	+	0.488803i
$220$		0			0
$221$	5.46319	−	2.32542i	0.367494	−	0.156424i
$222$	−8.07639	−	8.07639i	−0.542052	−	0.542052i
$223$	23.3874			1.56614			0.783069	−	0.621935i	$-0.213653\pi$
$223$	23.3874			1.56614			0.783069	+	0.621935i	$0.213653\pi$
$224$		−	2.68927i		−	0.179684i
$225$		0			0
$226$	−18.2121	−	18.2121i	−1.21145	−	1.21145i
$227$		−	17.4176i		−	1.15605i	−0.816020	−	0.578024i	$-0.803824\pi$
$227$		−	17.4176i		−	1.15605i	0.816020	−	0.578024i	$-0.196176\pi$
$228$		−	0.487745i		−	0.0323017i
$229$	−8.50725	−	8.50725i	−0.562175	−	0.562175i	0.367750	−	0.929925i	$-0.380128\pi$
$229$	−8.50725	−	8.50725i	−0.562175	−	0.562175i	−0.929925	+	0.367750i	$0.880128\pi$
$230$		0			0
$231$			0.828514i			0.0545122i
$232$	−15.1187			−0.992590
$233$	−19.9157	−	19.9157i	−1.30472	−	1.30472i	−0.925169	−	0.379555i	$-0.876077\pi$
$233$	−19.9157	−	19.9157i	−1.30472	−	1.30472i	−0.379555	−	0.925169i	$-0.623923\pi$
$234$	5.28654	+	2.12977i	0.345592	+	0.139228i
$235$		0			0
$236$	2.95054	+	2.95054i	0.192064	+	0.192064i
$237$	−5.25863	−	5.25863i	−0.341584	−	0.341584i
$238$	−1.79334	−	1.79334i	−0.116245	−	0.116245i
$239$	7.69506	−	7.69506i	0.497752	−	0.497752i	−0.412985	−	0.910738i	$-0.635514\pi$
$239$	7.69506	−	7.69506i	0.497752	−	0.497752i	0.910738	+	0.412985i	$0.135514\pi$
$240$		0			0
$241$	−2.69323	+	2.69323i	−0.173486	+	0.173486i	−0.788509	−	0.615023i	$-0.789147\pi$
$241$	−2.69323	+	2.69323i	−0.173486	+	0.173486i	0.615023	+	0.788509i	$0.289147\pi$
$242$	16.2450			1.04427
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−1.34219			−0.0859249
$245$		0			0
$246$			8.16212i			0.520398i
$247$	−3.24447	+	1.38101i	−0.206441	+	0.0878719i
$248$	−17.9789	+	17.9789i	−1.14166	+	1.14166i
$249$	−10.1004	+	10.1004i	−0.640084	+	0.640084i
$250$		0			0
$251$		−	11.1070i		−	0.701070i	−0.936550	−	0.350535i	$-0.886000\pi$
$251$		−	11.1070i		−	0.701070i	0.936550	−	0.350535i	$-0.114000\pi$
$252$		−	0.485902i		−	0.0306090i
$253$	−1.99670			−0.125532
$254$	7.37398	+	7.37398i	0.462685	+	0.462685i
$255$		0			0
$256$	11.2870			0.705438
$257$	6.59109	−	6.59109i	0.411141	−	0.411141i	−0.470995	−	0.882136i	$-0.656105\pi$
$257$	6.59109	−	6.59109i	0.411141	−	0.411141i	0.882136	+	0.470995i	$0.156105\pi$
$258$		−	6.07488i		−	0.378205i
$259$	7.03979			0.437431
$260$		0			0
$261$	−6.37081			−0.394343
$262$		−	2.49575i		−	0.154188i
$263$	−9.97308	+	9.97308i	−0.614966	+	0.614966i	−0.944236	−	0.329270i	$-0.893198\pi$
$263$	−9.97308	+	9.97308i	−0.614966	+	0.614966i	0.329270	+	0.944236i	$0.393198\pi$
$264$	−2.01805			−0.124202
$265$		0			0
$266$	1.06503	+	1.06503i	0.0653011	+	0.0653011i
$267$	15.0763			0.922657
$268$		−	3.19579i		−	0.195214i
$269$		−	6.04616i		−	0.368641i	−0.982866	−	0.184320i	$-0.940992\pi$
$269$		−	6.04616i		−	0.368641i	0.982866	−	0.184320i	$-0.0590084\pi$
$270$		0			0
$271$	2.75407	−	2.75407i	0.167298	−	0.167298i	−0.618493	−	0.785791i	$-0.712256\pi$
$271$	2.75407	−	2.75407i	0.167298	−	0.167298i	0.785791	+	0.618493i	$0.212256\pi$
$272$	5.52961	−	5.52961i	0.335282	−	0.335282i
$273$	−3.23222	+	1.37580i	−0.195623	+	0.0832671i
$274$			5.56922i			0.336449i
$275$		0			0
$276$	1.17101			0.0704868
$277$	3.74616	−	3.74616i	0.225085	−	0.225085i	−0.585551	−	0.810636i	$-0.699122\pi$
$277$	3.74616	−	3.74616i	0.225085	−	0.225085i	0.810636	+	0.585551i	$0.199122\pi$
$278$	−29.8621			−1.79101
$279$	−7.57606	+	7.57606i	−0.453567	+	0.453567i
$280$		0			0
$281$	23.0861	−	23.0861i	1.37720	−	1.37720i	0.527883	−	0.849317i	$-0.322986\pi$
$281$	23.0861	−	23.0861i	1.37720	−	1.37720i	0.849317	−	0.527883i	$-0.177014\pi$
$282$	−3.64095	−	3.64095i	−0.216815	−	0.216815i
$283$	10.9905	+	10.9905i	0.653319	+	0.653319i	0.953791	−	0.300472i	$-0.0971441\pi$
$283$	10.9905	+	10.9905i	0.653319	+	0.653319i	−0.300472	+	0.953791i	$0.597144\pi$
$284$	−3.58018	−	3.58018i	−0.212444	−	0.212444i
$285$		0			0
$286$	−1.89819	−	4.45950i	−0.112242	−	0.263696i
$287$	−3.55726	−	3.55726i	−0.209978	−	0.209978i
$288$	2.76024			0.162649
$289$			14.2882i			0.840480i
$290$		0			0
$291$	10.2436	+	10.2436i	0.600489	+	0.600489i
$292$			5.10191i			0.298567i
$293$		−	1.95323i		−	0.114109i	−0.998371	−	0.0570544i	$-0.981829\pi$
$293$		−	1.95323i		−	0.114109i	0.998371	−	0.0570544i	$-0.0181708\pi$
$294$	−6.76324	−	6.76324i	−0.394440	−	0.394440i
$295$		0			0
$296$			17.1472i			0.996658i
$297$	−0.850380			−0.0493440
$298$	15.5636	+	15.5636i	0.901575	+	0.901575i
$299$	−3.31565	−	7.78958i	−0.191749	−	0.450483i
$300$		0			0
$301$	2.64758	+	2.64758i	0.152604	+	0.152604i
$302$	−18.7806	−	18.7806i	−1.08070	−	1.08070i
$303$	−3.97288	−	3.97288i	−0.228236	−	0.228236i
$304$	−3.28392	+	3.28392i	−0.188346	+	0.188346i
$305$		0			0
$306$	1.84067	−	1.84067i	0.105224	−	0.105224i
$307$	23.6877			1.35193			0.675965	−	0.736933i	$-0.263727\pi$
$307$	23.6877			1.35193			0.675965	+	0.736933i	$0.263727\pi$
$308$	−0.292177	+	0.292177i	−0.0166484	+	0.0166484i
$309$	−0.00339534			−0.000193154
$310$		0			0
$311$		−	0.782006i		−	0.0443435i	−0.999754	−	0.0221717i	$-0.992942\pi$
$311$		−	0.782006i		−	0.0443435i	0.999754	−	0.0221717i	$-0.00705806\pi$
$312$	−3.35110	−	7.87287i	−0.189719	−	0.445713i
$313$	−1.09467	+	1.09467i	−0.0618743	+	0.0618743i	−0.737367	−	0.675493i	$-0.763931\pi$
$313$	−1.09467	+	1.09467i	−0.0618743	+	0.0618743i	0.675493	+	0.737367i	$0.263931\pi$
$314$	−7.79909	+	7.79909i	−0.440128	+	0.440128i
$315$		0			0
$316$		−	3.70894i		−	0.208644i
$317$		−	21.0388i		−	1.18166i	−0.806797	−	0.590828i	$-0.798801\pi$
$317$		−	21.0388i		−	1.18166i	0.806797	−	0.590828i	$-0.201199\pi$
$318$	−12.6494			−0.709343
$319$	3.83083	+	3.83083i	0.214485	+	0.214485i
$320$		0			0
$321$	−8.06263			−0.450012
$322$	−2.55700	+	2.55700i	−0.142496	+	0.142496i
$323$			1.61051i			0.0896111i
$324$	0.498726			0.0277070
$325$		0			0
$326$	−28.1421			−1.55865
$327$		−	3.06075i		−	0.169260i
$328$	8.66458	−	8.66458i	0.478422	−	0.478422i
$329$	3.17364			0.174968
$330$		0			0
$331$	−10.0574	−	10.0574i	−0.552804	−	0.552804i	0.374445	−	0.927249i	$-0.377833\pi$
$331$	−10.0574	−	10.0574i	−0.552804	−	0.552804i	−0.927249	+	0.374445i	$0.877833\pi$
$332$	−7.12384			−0.390971
$333$			7.22558i			0.395959i
$334$		−	13.7244i		−	0.750965i
$335$		0			0
$336$	−3.27151	+	3.27151i	−0.178476	+	0.178476i
$337$	−19.9405	+	19.9405i	−1.08623	+	1.08623i	−0.0903167	+	0.995913i	$0.528788\pi$
$337$	−19.9405	+	19.9405i	−1.08623	+	1.08623i	−0.995913	+	0.0903167i	$0.971212\pi$
$338$	14.2454	−	14.8105i	0.774849	−	0.805588i
$339$			16.2935i			0.884943i
$340$		0			0
$341$	9.11111			0.493394
$342$	−1.09314	+	1.09314i	−0.0591101	+	0.0591101i
$343$	12.7152			0.686555
$344$	−6.44885	+	6.44885i	−0.347699	+	0.347699i
$345$		0			0
$346$	12.1449	−	12.1449i	0.652912	−	0.652912i
$347$	−11.4590	−	11.4590i	−0.615150	−	0.615150i	0.329133	−	0.944283i	$-0.393243\pi$
$347$	−11.4590	−	11.4590i	−0.615150	−	0.615150i	−0.944283	+	0.329133i	$0.893243\pi$
$348$	−2.24668	−	2.24668i	−0.120435	−	0.120435i
$349$	−19.4188	−	19.4188i	−1.03946	−	1.03946i	−0.999189	−	0.0402751i	$-0.987177\pi$
$349$	−19.4188	−	19.4188i	−1.03946	−	1.03946i	−0.0402751	−	0.999189i	$-0.512823\pi$
$350$		0			0
$351$	−1.41211	−	3.31752i	−0.0753728	−	0.177076i
$352$	−1.65976	−	1.65976i	−0.0884655	−	0.0884655i
$353$	19.1849			1.02111			0.510556	−	0.859845i	$-0.329440\pi$
$353$	19.1849			1.02111			0.510556	+	0.859845i	$0.329440\pi$
$354$		−	13.2255i		−	0.702930i
$355$		0			0
$356$	5.31671	+	5.31671i	0.281785	+	0.281785i
$357$			1.60442i			0.0849152i
$358$		−	36.3867i		−	1.92309i
$359$	−7.19553	−	7.19553i	−0.379766	−	0.379766i	0.491252	−	0.871018i	$-0.336539\pi$
$359$	−7.19553	−	7.19553i	−0.379766	−	0.379766i	−0.871018	+	0.491252i	$0.836539\pi$
$360$		0			0
$361$			18.0436i			0.949661i
$362$	7.80908			0.410436
$363$	−7.26683	−	7.26683i	−0.381410	−	0.381410i
$364$	−1.62503	−	0.654671i	−0.0851746	−	0.0343141i
$365$		0			0
$366$	3.00813	+	3.00813i	0.157237	+	0.157237i
$367$	25.6674	+	25.6674i	1.33983	+	1.33983i	0.896224	+	0.443602i	$0.146300\pi$
$367$	25.6674	+	25.6674i	1.33983	+	1.33983i	0.443602	+	0.896224i	$0.353700\pi$
$368$	−7.88428	−	7.88428i	−0.410997	−	0.410997i
$369$	3.65114	−	3.65114i	0.190071	−	0.190071i
$370$		0			0
$371$	5.51293	−	5.51293i	0.286217	−	0.286217i
$372$	−5.34343			−0.277044
$373$	−10.6993	+	10.6993i	−0.553988	+	0.553988i	−0.927589	−	0.373602i	$-0.878123\pi$
$373$	−10.6993	+	10.6993i	−0.553988	+	0.553988i	0.373602	+	0.927589i	$0.378123\pi$
$374$	−2.21363			−0.114464
$375$		0			0
$376$			7.73018i			0.398654i
$377$	−8.58359	+	21.3062i	−0.442077	+	1.09733i
$378$	−1.08901	+	1.08901i	−0.0560125	+	0.0560125i
$379$	4.27043	−	4.27043i	0.219357	−	0.219357i	−0.588870	−	0.808228i	$-0.700427\pi$
$379$	4.27043	−	4.27043i	0.219357	−	0.219357i	0.808228	+	0.588870i	$0.200427\pi$
$380$		0			0
$381$		−	6.59717i		−	0.337983i
$382$			10.7136i			0.548155i
$383$	8.57646			0.438237			0.219118	−	0.975698i	$-0.429682\pi$
$383$	8.57646			0.438237			0.219118	+	0.975698i	$0.429682\pi$
$384$	−9.64236	−	9.64236i	−0.492060	−	0.492060i
$385$		0			0
$386$	−13.0133			−0.662359
$387$	−2.71746	+	2.71746i	−0.138136	+	0.138136i
$388$			7.22485i			0.366786i
$389$	1.83143			0.0928571			0.0464286	−	0.998922i	$-0.485216\pi$
$389$	1.83143			0.0928571			0.0464286	+	0.998922i	$0.485216\pi$
$390$		0			0
$391$	−3.86663			−0.195544
$392$			14.3592i			0.725248i
$393$	−1.11642	+	1.11642i	−0.0563158	+	0.0563158i
$394$	36.6596			1.84688
$395$		0			0
$396$	−0.299889	−	0.299889i	−0.0150700	−	0.0150700i
$397$	−22.1034			−1.10934			−0.554668	−	0.832071i	$-0.687155\pi$
$397$	−22.1034			−1.10934			−0.554668	+	0.832071i	$0.687155\pi$
$398$		−	30.3336i		−	1.52049i
$399$		−	0.952834i		−	0.0477013i
$400$		0			0
$401$	−22.6339	+	22.6339i	−1.13028	+	1.13028i	−0.140155	+	0.990130i	$0.544760\pi$
$401$	−22.6339	+	22.6339i	−1.13028	+	1.13028i	−0.990130	+	0.140155i	$0.955240\pi$
$402$	−7.16244	+	7.16244i	−0.357230	+	0.357230i
$403$	15.1296	+	35.5445i	0.753657	+	1.77060i
$404$		−	2.80209i		−	0.139409i
$405$		0			0
$406$	9.81162			0.486943
$407$	4.34481	−	4.34481i	0.215364	−	0.215364i
$408$	−3.90798			−0.193474
$409$	−1.79506	+	1.79506i	−0.0887598	+	0.0887598i	−0.750093	−	0.661333i	$-0.769991\pi$
$409$	−1.79506	+	1.79506i	−0.0887598	+	0.0887598i	0.661333	+	0.750093i	$0.269991\pi$
$410$		0			0
$411$	2.49127	−	2.49127i	0.122885	−	0.122885i
$412$	−0.00119738	−	0.00119738i	−5.89905e−5	−	5.89905e-5i
$413$	5.76403	+	5.76403i	0.283629	+	0.283629i
$414$	−2.62449	−	2.62449i	−0.128986	−	0.128986i
$415$		0			0
$416$	3.71896	−	9.23123i	0.182337	−	0.452598i
$417$	13.3581	+	13.3581i	0.654151	+	0.654151i
$418$	1.31463			0.0643005
$419$			9.83778i			0.480607i	0.970698	+	0.240304i	$0.0772470\pi$
$419$			9.83778i			0.480607i	−0.970698	+	0.240304i	$0.922753\pi$
$420$		0			0
$421$	11.1987	+	11.1987i	0.545789	+	0.545789i	0.925220	−	0.379431i	$-0.123880\pi$
$421$	11.1987	+	11.1987i	0.545789	+	0.545789i	−0.379431	+	0.925220i	$0.623880\pi$
$422$			36.3327i			1.76865i
$423$			3.25740i			0.158380i
$424$	13.4281	+	13.4281i	0.652127	+	0.652127i
$425$		0			0
$426$			16.0478i			0.777520i
$427$	−2.62204			−0.126889
$428$	−2.84331	−	2.84331i	−0.137436	−	0.137436i
$429$	−1.14574	+	2.84397i	−0.0553170	+	0.137308i
$430$		0			0
$431$	21.8983	+	21.8983i	1.05480	+	1.05480i	0.998409	+	0.0563955i	$0.0179608\pi$
$431$	21.8983	+	21.8983i	1.05480	+	1.05480i	0.0563955	+	0.998409i	$0.482039\pi$
$432$	−3.35786	−	3.35786i	−0.161555	−	0.161555i
$433$	−7.01215	−	7.01215i	−0.336982	−	0.336982i	0.518248	−	0.855230i	$-0.326584\pi$
$433$	−7.01215	−	7.01215i	−0.336982	−	0.336982i	−0.855230	+	0.518248i	$0.826584\pi$
$434$	11.6678	−	11.6678i	0.560073	−	0.560073i
$435$		0			0
$436$	1.07938	−	1.07938i	0.0516930	−	0.0516930i
$437$	2.29631			0.109847
$438$	11.4344	−	11.4344i	0.546359	−	0.546359i
$439$	−15.7738			−0.752841			−0.376420	−	0.926449i	$-0.622845\pi$
$439$	−15.7738			−0.752841			−0.376420	+	0.926449i	$0.622845\pi$
$440$		0			0
$441$			6.05077i			0.288132i
$442$	−3.67587	−	8.63586i	−0.174843	−	0.410766i
$443$	−0.477834	+	0.477834i	−0.0227026	+	0.0227026i	−0.718367	−	0.695664i	$-0.755110\pi$
$443$	−0.477834	+	0.477834i	−0.0227026	+	0.0227026i	0.695664	+	0.718367i	$0.255110\pi$
$444$	−2.54812	+	2.54812i	−0.120928	+	0.120928i
$445$		0			0
$446$		−	36.9694i		−	1.75055i
$447$		−	13.9241i		−	0.658585i
$448$	5.00221			0.236332
$449$	10.9559	+	10.9559i	0.517039	+	0.517039i	0.916674	−	0.399635i	$-0.130863\pi$
$449$	10.9559	+	10.9559i	0.517039	+	0.517039i	−0.399635	+	0.916674i	$0.630863\pi$
$450$		0			0
$451$	−4.39093			−0.206761
$452$	−5.74595	+	5.74595i	−0.270267	+	0.270267i
$453$			16.8022i			0.789436i
$454$	−27.5327			−1.29217
$455$		0			0
$456$	2.32086			0.108684
$457$			22.0567i			1.03177i	0.856659	+	0.515884i	$0.172536\pi$
$457$			22.0567i			1.03177i	−0.856659	+	0.515884i	$0.827464\pi$
$458$	−13.4477	+	13.4477i	−0.628371	+	0.628371i
$459$	−1.64677			−0.0768646
$460$		0			0
$461$	−5.75708	−	5.75708i	−0.268134	−	0.268134i	0.560214	−	0.828348i	$-0.310719\pi$
$461$	−5.75708	−	5.75708i	−0.268134	−	0.268134i	−0.828348	+	0.560214i	$0.810719\pi$
$462$	1.30966			0.0609310
$463$		−	26.2127i		−	1.21821i	−0.793091	−	0.609103i	$-0.791530\pi$
$463$		−	26.2127i		−	1.21821i	0.793091	−	0.609103i	$-0.208470\pi$
$464$			30.2532i			1.40447i
$465$		0			0
$466$	−31.4815	+	31.4815i	−1.45835	+	1.45835i
$467$	0.905259	−	0.905259i	0.0418904	−	0.0418904i	−0.685851	−	0.727742i	$-0.740570\pi$
$467$	0.905259	−	0.905259i	0.0418904	−	0.0418904i	0.727742	+	0.685851i	$0.240570\pi$
$468$	0.671949	−	1.66792i	0.0310609	−	0.0770995i
$469$		−	6.24315i		−	0.288282i
$470$		0			0
$471$	6.97749			0.321506
$472$	−14.0397	+	14.0397i	−0.646231	+	0.646231i
$473$	3.26807			0.150266
$474$	−8.31250	+	8.31250i	−0.381806	+	0.381806i
$475$		0			0
$476$	−0.565805	+	0.565805i	−0.0259336	+	0.0259336i
$477$	5.65843	+	5.65843i	0.259082	+	0.259082i
$478$	−12.1639	−	12.1639i	−0.556362	−	0.556362i
$479$	−1.36271	−	1.36271i	−0.0622640	−	0.0622640i	0.675289	−	0.737553i	$-0.264019\pi$
$479$	−1.36271	−	1.36271i	−0.0622640	−	0.0622640i	−0.737553	+	0.675289i	$0.764019\pi$
$480$		0			0
$481$	24.1649	+	9.73525i	1.10182	+	0.443889i
$482$	4.25728	+	4.25728i	0.193914	+	0.193914i
$483$	2.28764			0.104091
$484$		−	5.12534i		−	0.232970i
$485$		0			0
$486$	−1.11775	−	1.11775i	−0.0507021	−	0.0507021i
$487$		−	15.2289i		−	0.690086i	−0.938587	−	0.345043i	$-0.887864\pi$
$487$		−	15.2289i		−	0.690086i	0.938587	−	0.345043i	$-0.112136\pi$
$488$		−	6.38662i		−	0.289109i
$489$	12.5887	+	12.5887i	0.569283	+	0.569283i
$490$		0			0
$491$			12.1779i			0.549581i	0.961504	+	0.274791i	$0.0886085\pi$
$491$			12.1779i			0.549581i	−0.961504	+	0.274791i	$0.911391\pi$
$492$	2.57517			0.116098
$493$	7.41844	+	7.41844i	0.334110	+	0.334110i
$494$	2.18302	+	5.12865i	0.0982187	+	0.230749i
$495$		0			0
$496$	35.9766	+	35.9766i	1.61540	+	1.61540i
$497$	−6.99405	−	6.99405i	−0.313726	−	0.313726i
$498$	15.9660	+	15.9660i	0.715454	+	0.715454i
$499$	−23.1658	+	23.1658i	−1.03704	+	1.03704i	−0.0377562	+	0.999287i	$0.512021\pi$
$499$	−23.1658	+	23.1658i	−1.03704	+	1.03704i	−0.999287	+	0.0377562i	$0.987979\pi$
$500$		0			0
$501$	−6.13930	+	6.13930i	−0.274284	+	0.274284i
$502$	−17.5573			−0.783620
$503$	−15.0692	+	15.0692i	−0.671901	+	0.671901i	−0.958154	−	0.286253i	$-0.907590\pi$
$503$	−15.0692	+	15.0692i	−0.671901	+	0.671901i	0.286253	+	0.958154i	$0.407590\pi$
$504$	2.31210			0.102989
$505$		0			0
$506$			3.15626i			0.140313i
$507$	−12.9975	+	0.252790i	−0.577241	+	0.0112268i
$508$	2.32651	−	2.32651i	0.103222	−	0.103222i
$509$	−1.14746	+	1.14746i	−0.0508604	+	0.0508604i	−0.732080	−	0.681219i	$-0.761450\pi$
$509$	−1.14746	+	1.14746i	−0.0508604	+	0.0508604i	0.681219	+	0.732080i	$0.261450\pi$
$510$		0			0
$511$			9.96684i			0.440907i
$512$			9.43092i			0.416792i
$513$	0.977981			0.0431789
$514$	−10.4188	−	10.4188i	−0.459552	−	0.459552i
$515$		0			0
$516$	−1.91664			−0.0843753
$517$	1.95870	−	1.95870i	0.0861436	−	0.0861436i
$518$		−	11.1280i		−	0.488938i
$519$	−10.8655			−0.476941
$520$		0			0
$521$	−0.617681			−0.0270611			−0.0135306	−	0.999908i	$-0.504307\pi$
$521$	−0.617681			−0.0270611			−0.0135306	+	0.999908i	$0.504307\pi$
$522$			10.0706i			0.440777i
$523$	−30.8113	+	30.8113i	−1.34728	+	1.34728i	−0.458684	+	0.888600i	$0.651679\pi$
$523$	−30.8113	+	30.8113i	−1.34728	+	1.34728i	−0.888600	+	0.458684i	$0.848321\pi$
$524$	−0.787415			−0.0343984
$525$		0			0
$526$	15.7648	+	15.7648i	0.687378	+	0.687378i
$527$	17.6437			0.768574
$528$			4.03822i			0.175741i
$529$		−	17.4868i		−	0.760298i
$530$		0			0
$531$	−5.91615	+	5.91615i	−0.256739	+	0.256739i
$532$	0.336019	−	0.336019i	0.0145683	−	0.0145683i
$533$	−7.29141	−	17.1300i	−0.315826	−	0.741982i
$534$		−	23.8317i		−	1.03130i
$535$		0			0
$536$	15.2067			0.656831
$537$	−16.2768	+	16.2768i	−0.702394	+	0.702394i
$538$	−9.55738			−0.412048
$539$	3.63838	−	3.63838i	0.156716	−	0.156716i
$540$		0			0
$541$	−18.1597	+	18.1597i	−0.780745	+	0.780745i	−0.979956	−	0.199212i	$-0.936162\pi$
$541$	−18.1597	+	18.1597i	−0.780745	+	0.780745i	0.199212	+	0.979956i	$0.436162\pi$
$542$	−4.35346	−	4.35346i	−0.186997	−	0.186997i
$543$	−3.49322	−	3.49322i	−0.149908	−	0.149908i
$544$	−3.21414	−	3.21414i	−0.137805	−	0.137805i
$545$		0			0
$546$	2.17477	+	5.10928i	0.0930717	+	0.218657i
$547$	−5.87516	−	5.87516i	−0.251204	−	0.251204i	0.570260	−	0.821464i	$-0.306842\pi$
$547$	−5.87516	−	5.87516i	−0.251204	−	0.251204i	−0.821464	+	0.570260i	$0.806842\pi$
$548$	1.75710			0.0750597
$549$		−	2.69124i		−	0.114859i
$550$		0			0
$551$	−4.40565	−	4.40565i	−0.187687	−	0.187687i
$552$			5.57211i			0.237165i
$553$		−	7.24559i		−	0.308114i
$554$	−5.92169	−	5.92169i	−0.251588	−	0.251588i
$555$		0			0
$556$			9.42157i			0.399564i
$557$	−6.73062			−0.285185			−0.142593	−	0.989781i	$-0.545544\pi$
$557$	−6.73062			−0.285185			−0.142593	+	0.989781i	$0.545544\pi$
$558$	11.9757	+	11.9757i	0.506974	+	0.506974i
$559$	5.42683	+	12.7495i	0.229530	+	0.539245i
$560$		0			0
$561$	0.990217	+	0.990217i	0.0418070	+	0.0418070i
$562$	−36.4930	−	36.4930i	−1.53936	−	1.53936i
$563$	−11.5415	−	11.5415i	−0.486415	−	0.486415i	0.420758	−	0.907173i	$-0.361764\pi$
$563$	−11.5415	−	11.5415i	−0.486415	−	0.486415i	−0.907173	+	0.420758i	$0.861764\pi$
$564$	−1.14873	+	1.14873i	−0.0483702	+	0.0483702i
$565$		0			0
$566$	17.3731	−	17.3731i	0.730247	−	0.730247i
$567$	0.974287			0.0409162
$568$	17.0358	−	17.0358i	0.714805	−	0.714805i
$569$	20.2098			0.847240			0.423620	−	0.905840i	$-0.360759\pi$
$569$	20.2098			0.847240			0.423620	+	0.905840i	$0.360759\pi$
$570$		0			0
$571$			0.257974i			0.0107959i	0.999985	+	0.00539793i	$0.00171822\pi$
$571$			0.257974i			0.0107959i	−0.999985	+	0.00539793i	$0.998282\pi$
$572$	−1.40698	+	0.598884i	−0.0588289	+	0.0250406i
$573$	4.79248	−	4.79248i	0.200209	−	0.200209i
$574$	−5.62308	+	5.62308i	−0.234703	+	0.234703i
$575$		0			0
$576$			5.13423i			0.213926i
$577$		−	4.50480i		−	0.187537i	−0.995594	−	0.0937687i	$-0.970109\pi$
$577$		−	4.50480i		−	0.187537i	0.995594	−	0.0937687i	$-0.0298914\pi$
$578$	22.5858			0.939445
$579$	5.82121	+	5.82121i	0.241921	+	0.241921i
$580$		0			0
$581$	−13.9168			−0.577365
$582$	16.1924	−	16.1924i	0.671196	−	0.671196i
$583$		−	6.80493i		−	0.281831i
$584$	−24.2767			−1.00458
$585$		0			0
$586$	−3.08754			−0.127545
$587$		−	27.5111i		−	1.13550i	−0.823200	−	0.567752i	$-0.807813\pi$
$587$		−	27.5111i		−	1.13550i	0.823200	−	0.567752i	$-0.192187\pi$
$588$	−2.13382	+	2.13382i	−0.0879972	+	0.0879972i
$589$	−10.4782			−0.431749
$590$		0			0
$591$	−16.3988	−	16.3988i	−0.674558	−	0.674558i
$592$	34.3123			1.41023
$593$		−	46.1002i		−	1.89311i	−0.322548	−	0.946553i	$-0.604539\pi$
$593$		−	46.1002i		−	1.89311i	0.322548	−	0.946553i	$-0.395461\pi$
$594$			1.34423i			0.0551543i
$595$		0			0
$596$	4.91035	−	4.91035i	0.201136	−	0.201136i
$597$	−13.5691	+	13.5691i	−0.555345	+	0.555345i
$598$	−12.3133	+	5.24116i	−0.503527	+	0.214327i
$599$			22.5207i			0.920169i	0.887875	+	0.460084i	$0.152181\pi$
$599$			22.5207i			0.920169i	−0.887875	+	0.460084i	$0.847819\pi$
$600$		0			0
$601$	−35.0110			−1.42813			−0.714064	−	0.700081i	$-0.753147\pi$
$601$	−35.0110			−1.42813			−0.714064	+	0.700081i	$0.753147\pi$
$602$	4.18513	−	4.18513i	0.170573	−	0.170573i
$603$	6.40792			0.260950
$604$	−5.92534	+	5.92534i	−0.241099	+	0.241099i
$605$		0			0
$606$	−6.28008	+	6.28008i	−0.255111	+	0.255111i
$607$	−19.4448	−	19.4448i	−0.789241	−	0.789241i	0.192129	−	0.981370i	$-0.438461\pi$
$607$	−19.4448	−	19.4448i	−0.789241	−	0.789241i	−0.981370	+	0.192129i	$0.938461\pi$
$608$	1.90881	+	1.90881i	0.0774125	+	0.0774125i
$609$	−4.38901	−	4.38901i	−0.177852	−	0.177852i
$610$		0			0
$611$	10.8939	+	4.38879i	0.440719	+	0.177551i
$612$	−0.580737	−	0.580737i	−0.0234749	−	0.0234749i
$613$	−20.6580			−0.834367			−0.417184	−	0.908822i	$-0.636983\pi$
$613$	−20.6580			−0.834367			−0.417184	+	0.908822i	$0.636983\pi$
$614$		−	37.4441i		−	1.51112i
$615$		0			0
$616$	−1.39029	−	1.39029i	−0.0560162	−	0.0560162i
$617$			37.6970i			1.51762i	0.651309	+	0.758812i	$0.274220\pi$
$617$			37.6970i			1.51762i	−0.651309	+	0.758812i	$0.725780\pi$
$618$			0.00536714i			0.000215898i
$619$	14.7879	+	14.7879i	0.594375	+	0.594375i	0.938810	−	0.344435i	$-0.111930\pi$
$619$	14.7879	+	14.7879i	0.594375	+	0.594375i	−0.344435	+	0.938810i	$0.611930\pi$
$620$		0			0
$621$			2.34801i			0.0942224i
$622$	−1.23614			−0.0495649
$623$	10.3865	+	10.3865i	0.416125	+	0.416125i
$624$	−15.7540	+	6.70571i	−0.630665	+	0.268443i
$625$		0			0
$626$	1.73038	+	1.73038i	0.0691600	+	0.0691600i
$627$	−0.588069	−	0.588069i	−0.0234852	−	0.0234852i
$628$	2.46063	+	2.46063i	0.0981899	+	0.0981899i
$629$	8.41376	−	8.41376i	0.335479	−	0.335479i
$630$		0			0
$631$	1.91402	−	1.91402i	0.0761958	−	0.0761958i	−0.667982	−	0.744178i	$-0.732842\pi$
$631$	1.91402	−	1.91402i	0.0761958	−	0.0761958i	0.744178	+	0.667982i	$0.232842\pi$
$632$	17.6485			0.702018
$633$	16.2526	−	16.2526i	0.645984	−	0.645984i
$634$	−33.2568			−1.32080
$635$		0			0
$636$			3.99092i			0.158250i
$637$	20.2359	+	8.15238i	0.801776	+	0.323009i
$638$	6.05553	−	6.05553i	0.239741	−	0.239741i
$639$	7.17864	−	7.17864i	0.283983	−	0.283983i
$640$		0			0
$641$		−	40.1627i		−	1.58633i	−0.609005	−	0.793166i	$-0.708431\pi$
$641$		−	40.1627i		−	1.58633i	0.609005	−	0.793166i	$-0.291569\pi$
$642$			12.7449i			0.503001i
$643$	−11.9456			−0.471088			−0.235544	−	0.971864i	$-0.575687\pi$
$643$	−11.9456			−0.471088			−0.235544	+	0.971864i	$0.575687\pi$
$644$	0.806741	+	0.806741i	0.0317900	+	0.0317900i
$645$		0			0
$646$	2.54579			0.100163
$647$	14.4871	−	14.4871i	0.569546	−	0.569546i	−0.362455	−	0.932001i	$-0.618061\pi$
$647$	14.4871	−	14.4871i	0.569546	−	0.569546i	0.932001	+	0.362455i	$0.118061\pi$
$648$			2.37312i			0.0932249i
$649$	7.11488			0.279283
$650$		0			0
$651$	−10.4387			−0.409124
$652$			8.87891i			0.347725i
$653$	−31.1908	+	31.1908i	−1.22059	+	1.22059i	−0.253168	+	0.967422i	$0.581472\pi$
$653$	−31.1908	+	31.1908i	−1.22059	+	1.22059i	−0.967422	+	0.253168i	$0.918528\pi$
$654$	−4.83823			−0.189190
$655$		0			0
$656$	−17.3383	−	17.3383i	−0.676945	−	0.676945i
$657$	−10.2299			−0.399106
$658$		−	5.01668i		−	0.195571i
$659$		−	29.4886i		−	1.14871i	−0.818606	−	0.574356i	$-0.805252\pi$
$659$		−	29.4886i		−	1.14871i	0.818606	−	0.574356i	$-0.194748\pi$
$660$		0			0
$661$	3.86425	−	3.86425i	0.150302	−	0.150302i	−0.627951	−	0.778253i	$-0.716106\pi$
$661$	3.86425	−	3.86425i	0.150302	−	0.150302i	0.778253	+	0.627951i	$0.216106\pi$
$662$	−15.8981	+	15.8981i	−0.617897	+	0.617897i
$663$	−2.21874	+	5.50738i	−0.0861688	+	0.213889i
$664$		−	33.8978i		−	1.31549i
$665$		0			0
$666$	11.4217			0.442583
$667$	10.5774	−	10.5774i	0.409560	−	0.409560i
$668$	−4.33008			−0.167536
$669$	−16.5374	+	16.5374i	−0.639373	+	0.639373i
$670$		0			0
$671$	−1.61827	+	1.61827i	−0.0624725	+	0.0624725i
$672$	1.90160	+	1.90160i	0.0733558	+	0.0733558i
$673$	−10.2250	−	10.2250i	−0.394143	−	0.394143i	0.482018	−	0.876161i	$-0.339904\pi$
$673$	−10.2250	−	10.2250i	−0.394143	−	0.394143i	−0.876161	+	0.482018i	$0.839904\pi$
$674$	31.5207	+	31.5207i	1.21413	+	1.21413i
$675$		0			0
$676$	−4.67276	−	4.49447i	−0.179722	−	0.172864i
$677$	−28.6819	−	28.6819i	−1.10234	−	1.10234i	−0.994128	−	0.108207i	$-0.965489\pi$
$677$	−28.6819	−	28.6819i	−1.10234	−	1.10234i	−0.108207	−	0.994128i	$-0.534511\pi$
$678$	25.7558			0.989144
$679$			14.1141i			0.541650i
$680$		0			0
$681$	12.3161	+	12.3161i	0.471955	+	0.471955i
$682$		−	14.4023i		−	0.551491i
$683$			2.15178i			0.0823357i	0.999152	+	0.0411679i	$0.0131078\pi$
$683$			2.15178i			0.0823357i	−0.999152	+	0.0411679i	$0.986892\pi$
$684$	0.344887	+	0.344887i	0.0131871	+	0.0131871i
$685$		0			0
$686$		−	20.0994i		−	0.767397i
$687$	12.0311			0.459014
$688$	12.9045	+	12.9045i	0.491978	+	0.491978i
$689$	26.5476	−	11.3000i	1.01138	−	0.430496i
$690$		0			0
$691$	−2.15129	−	2.15129i	−0.0818390	−	0.0818390i	0.665002	−	0.746841i	$-0.268431\pi$
$691$	−2.15129	−	2.15129i	−0.0818390	−	0.0818390i	−0.746841	+	0.665002i	$0.768431\pi$
$692$	−3.83174	−	3.83174i	−0.145661	−	0.145661i
$693$	−0.585848	−	0.585848i	−0.0222545	−	0.0222545i
$694$	−18.1136	+	18.1136i	−0.687583	+	0.687583i
$695$		0			0
$696$	10.6905	−	10.6905i	0.405223	−	0.405223i
$697$	−8.50308			−0.322077
$698$	−30.6960	+	30.6960i	−1.16186	+	1.16186i
$699$	28.1651			1.06530
$700$		0			0
$701$		−	26.1324i		−	0.987007i	−0.869744	−	0.493503i	$-0.835716\pi$
$701$		−	26.1324i		−	0.987007i	0.869744	−	0.493503i	$-0.164284\pi$
$702$	−5.24413	+	2.23217i	−0.197927	+	0.0842478i
$703$	−4.99676	+	4.99676i	−0.188456	+	0.188456i
$704$	3.08726	−	3.08726i	0.116356	−	0.116356i
$705$		0			0
$706$		−	30.3263i		−	1.14135i
$707$		−	5.47403i		−	0.205872i
$708$	−4.17269			−0.156819
$709$	19.5616	+	19.5616i	0.734651	+	0.734651i	0.971537	−	0.236886i	$-0.0761268\pi$
$709$	19.5616	+	19.5616i	0.734651	+	0.734651i	−0.236886	+	0.971537i	$0.576127\pi$
$710$		0			0
$711$	7.43682			0.278903
$712$	−25.2988	+	25.2988i	−0.948113	+	0.948113i
$713$		−	25.1570i		−	0.942136i
$714$	2.53617			0.0949138
$715$		0			0
$716$	−11.4801			−0.429031
$717$			10.8825i			0.406413i
$718$	−11.3742	+	11.3742i	−0.424483	+	0.424483i
$719$	−31.4983			−1.17469			−0.587345	−	0.809337i	$-0.699827\pi$
$719$	−31.4983			−1.17469			−0.587345	+	0.809337i	$0.699827\pi$
$720$		0			0
$721$	−0.00233914	−	0.00233914i	−8.71140e−5	−	8.71140e-5i
$722$	28.5221			1.06148
$723$		−	3.80880i		−	0.141651i
$724$		−	2.46378i		−	0.0915658i
$725$		0			0
$726$	−11.4869	+	11.4869i	−0.426320	+	0.426320i
$727$	15.0417	−	15.0417i	0.557864	−	0.557864i	−0.370835	−	0.928699i	$-0.620928\pi$
$727$	15.0417	−	15.0417i	0.557864	−	0.557864i	0.928699	+	0.370835i	$0.120928\pi$
$728$	3.11516	−	7.73247i	0.115455	−	0.286584i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	6.32864			0.234073
$732$	0.949072	−	0.949072i	0.0350787	−	0.0350787i
$733$	−24.6952			−0.912139			−0.456070	−	0.889944i	$-0.650743\pi$
$733$	−24.6952			−0.912139			−0.456070	+	0.889944i	$0.650743\pi$
$734$	40.5733	−	40.5733i	1.49759	−	1.49759i
$735$		0			0
$736$	−4.58282	+	4.58282i	−0.168925	+	0.168925i
$737$	−3.85314	−	3.85314i	−0.141932	−	0.141932i
$738$	−5.77149	−	5.77149i	−0.212451	−	0.212451i
$739$	−27.5591	−	27.5591i	−1.01378	−	1.01378i	−0.999904	−	0.0138749i	$-0.995583\pi$
$739$	−27.5591	−	27.5591i	−1.01378	−	1.01378i	−0.0138749	−	0.999904i	$-0.504417\pi$
$740$		0			0
$741$	1.31766	−	3.27071i	0.0484056	−	0.120153i
$742$	−8.71449	−	8.71449i	−0.319919	−	0.319919i
$743$	15.3445			0.562934			0.281467	−	0.959571i	$-0.409179\pi$
$743$	15.3445			0.562934			0.281467	+	0.959571i	$0.409179\pi$
$744$		−	25.4260i		−	0.932161i
$745$		0			0
$746$	16.9127	+	16.9127i	0.619219	+	0.619219i
$747$		−	14.2841i		−	0.522627i
$748$			0.698406i			0.0255362i
$749$	−5.55455	−	5.55455i	−0.202959	−	0.202959i
$750$		0			0
$751$		−	40.8827i		−	1.49183i	−0.666041	−	0.745915i	$-0.732012\pi$
$751$		−	40.8827i		−	1.49183i	0.666041	−	0.745915i	$-0.267988\pi$
$752$	15.4685			0.564077
$753$	7.85386	+	7.85386i	0.286210	+	0.286210i
$754$	33.6796	+	13.5684i	1.22654	+	0.494132i
$755$		0			0
$756$	0.343585	+	0.343585i	0.0124961	+	0.0124961i
$757$	3.88542	+	3.88542i	0.141218	+	0.141218i	0.774182	−	0.632964i	$-0.218162\pi$
$757$	3.88542	+	3.88542i	0.141218	+	0.141218i	−0.632964	+	0.774182i	$0.718162\pi$
$758$	−6.75042	−	6.75042i	−0.245186	−	0.245186i
$759$	1.41188	−	1.41188i	0.0512480	−	0.0512480i
$760$		0			0
$761$	−6.29974	+	6.29974i	−0.228366	+	0.228366i	−0.812010	−	0.583644i	$-0.801626\pi$
$761$	−6.29974	+	6.29974i	−0.228366	+	0.228366i	0.583644	+	0.812010i	$0.301626\pi$
$762$	−10.4284			−0.377781
$763$	2.10862	−	2.10862i	0.0763373	−	0.0763373i
$764$	3.38016			0.122290
$765$		0			0
$766$		−	13.5571i		−	0.489839i
$767$	11.8147	+	27.7567i	0.426604	+	1.00224i
$768$	−7.98112	+	7.98112i	−0.287994	+	0.287994i
$769$	−8.18663	+	8.18663i	−0.295217	+	0.295217i	−0.839137	−	0.543920i	$-0.816940\pi$
$769$	−8.18663	+	8.18663i	−0.295217	+	0.295217i	0.543920	+	0.839137i	$0.316940\pi$
$770$		0			0
$771$			9.32121i			0.335695i
$772$			4.10573i			0.147768i
$773$	−17.5543			−0.631385			−0.315692	−	0.948862i	$-0.602237\pi$
$773$	−17.5543			−0.631385			−0.315692	+	0.948862i	$0.602237\pi$
$774$	4.29559	+	4.29559i	0.154402	+	0.154402i
$775$		0			0
$776$	−34.3784			−1.23411
$777$	−4.97788	+	4.97788i	−0.178580	+	0.178580i
$778$		−	2.89501i		−	0.103791i
$779$	5.04980			0.180928
$780$		0			0
$781$	−8.63317			−0.308919
$782$			6.11212i			0.218569i
$783$	4.50484	−	4.50484i	0.160990	−	0.160990i
$784$	28.7334			1.02619
$785$		0			0
$786$	1.76476	+	1.76476i	0.0629469	+	0.0629469i
$787$	−8.38195			−0.298784			−0.149392	−	0.988778i	$-0.547732\pi$
$787$	−8.38195			−0.298784			−0.149392	+	0.988778i	$0.547732\pi$
$788$		−	11.5662i		−	0.412028i
$789$		−	14.1041i		−	0.502118i
$790$		0			0
$791$	−11.2250	+	11.2250i	−0.399115	+	0.399115i
$792$	1.42698	−	1.42698i	0.0507054	−	0.0507054i
$793$	−9.00045	−	3.62599i	−0.319615	−	0.128763i
$794$			34.9396i			1.23996i
$795$		0			0
$796$	−9.57033			−0.339211
$797$	−21.7988	+	21.7988i	−0.772152	+	0.772152i	−0.978482	−	0.206331i	$-0.933848\pi$
$797$	−21.7988	+	21.7988i	−0.772152	+	0.772152i	0.206331	+	0.978482i	$0.433848\pi$
$798$	−1.50618			−0.0533181
$799$	3.79305	−	3.79305i	0.134188	−	0.134188i
$800$		0			0
$801$	−10.6606	+	10.6606i	−0.376673	+	0.376673i
$802$	35.7783	+	35.7783i	1.26337	+	1.26337i
$803$	6.15132	+	6.15132i	0.217076	+	0.217076i
$804$	2.25977	+	2.25977i	0.0796959	+	0.0796959i
$805$		0			0
$806$	56.1864	−	23.9158i	1.97908	−	0.842399i
$807$	4.27528	+	4.27528i	0.150497	+	0.150497i
$808$	13.3334			0.469066
$809$		−	20.0206i		−	0.703887i	−0.936021	−	0.351943i	$-0.885521\pi$
$809$		−	20.0206i		−	0.703887i	0.936021	−	0.351943i	$-0.114479\pi$
$810$		0			0
$811$	−34.6145	−	34.6145i	−1.21548	−	1.21548i	−0.969199	−	0.246279i	$-0.920792\pi$
$811$	−34.6145	−	34.6145i	−1.21548	−	1.21548i	−0.246279	−	0.969199i	$-0.579208\pi$
$812$		−	3.09559i		−	0.108634i
$813$			3.89484i			0.136598i
$814$	−6.86800	−	6.86800i	−0.240723	−	0.240723i
$815$		0			0
$816$			7.82005i			0.273757i
$817$	−3.75845			−0.131491
$818$	2.83751	+	2.83751i	0.0992112	+	0.0992112i
$819$	1.31269	−	3.25836i	0.0458690	−	0.113856i
$820$		0			0
$821$	−15.8296	−	15.8296i	−0.552457	−	0.552457i	0.374692	−	0.927149i	$-0.377748\pi$
$821$	−15.8296	−	15.8296i	−0.552457	−	0.552457i	−0.927149	+	0.374692i	$0.877748\pi$
$822$	−3.93803	−	3.93803i	−0.137355	−	0.137355i
$823$	−13.5057	−	13.5057i	−0.470780	−	0.470780i	0.431387	−	0.902167i	$-0.358024\pi$
$823$	−13.5057	−	13.5057i	−0.470780	−	0.470780i	−0.902167	+	0.431387i	$0.858024\pi$
$824$	0.00569755	−	0.00569755i	0.000198483	−	0.000198483i
$825$		0			0
$826$	9.11141	−	9.11141i	0.317026	−	0.317026i
$827$	6.62864			0.230500			0.115250	−	0.993337i	$-0.463233\pi$
$827$	6.62864			0.230500			0.115250	+	0.993337i	$0.463233\pi$
$828$	−0.828032	+	0.828032i	−0.0287761	+	0.0287761i
$829$	−22.1289			−0.768570			−0.384285	−	0.923215i	$-0.625552\pi$
$829$	−22.1289			−0.768570			−0.384285	+	0.923215i	$0.625552\pi$
$830$		0			0
$831$			5.29787i			0.183781i
$832$	17.1707	+	6.91751i	0.595286	+	0.239821i
$833$	7.04576	−	7.04576i	0.244121	−	0.244121i
$834$	21.1157	−	21.1157i	0.731177	−	0.731177i
$835$		0			0
$836$		−	0.414768i		−	0.0143451i
$837$		−	10.7142i		−	0.370336i
$838$	15.5509			0.537198
$839$	31.6130	+	31.6130i	1.09140	+	1.09140i	0.995379	+	0.0960213i	$0.0306117\pi$
$839$	31.6130	+	31.6130i	1.09140	+	1.09140i	0.0960213	+	0.995379i	$0.469388\pi$
$840$		0			0
$841$	−11.5873			−0.399561
$842$	17.7021	−	17.7021i	0.610056	−	0.610056i
$843$			32.6487i			1.12448i
$844$	11.4631			0.394575
$845$		0			0
$846$	5.14908			0.177029
$847$		−	10.0126i		−	0.344037i
$848$	26.8703	−	26.8703i	0.922730	−	0.922730i
$849$	−15.5430			−0.533433
$850$		0			0
$851$	−11.9966	−	11.9966i	−0.411238	−	0.411238i
$852$	5.06313			0.173460
$853$			51.1679i			1.75196i	0.482352	+	0.875978i	$0.339783\pi$
$853$			51.1679i			1.75196i	−0.482352	+	0.875978i	$0.660217\pi$
$854$			4.14475i			0.141830i
$855$		0			0
$856$	13.5295	−	13.5295i	0.462428	−	0.462428i
$857$	34.0042	−	34.0042i	1.16156	−	1.16156i	0.177426	−	0.984134i	$-0.443223\pi$
$857$	34.0042	−	34.0042i	1.16156	−	1.16156i	0.984134	−	0.177426i	$-0.0567770\pi$
$858$	4.49557	+	1.81112i	0.153476	+	0.0618305i
$859$		−	27.1852i		−	0.927546i	−0.885954	−	0.463773i	$-0.846495\pi$
$859$		−	27.1852i		−	0.927546i	0.885954	−	0.463773i	$-0.153505\pi$
$860$		0			0
$861$	5.03072			0.171446
$862$	34.6154	−	34.6154i	1.17901	−	1.17901i
$863$	24.8172			0.844786			0.422393	−	0.906413i	$-0.361190\pi$
$863$	24.8172			0.844786			0.422393	+	0.906413i	$0.361190\pi$
$864$	−1.95179	+	1.95179i	−0.0664012	+	0.0664012i
$865$		0			0
$866$	−11.0843	+	11.0843i	−0.376662	+	0.376662i
$867$	−10.1032	−	10.1032i	−0.343124	−	0.343124i
$868$	−3.68122	−	3.68122i	−0.124949	−	0.124949i
$869$	−4.47183	−	4.47183i	−0.151696	−	0.151696i
$870$		0			0
$871$	8.63358	−	21.4303i	0.292538	−	0.726139i
$872$	5.13608	+	5.13608i	0.173930	+	0.173930i
$873$	−14.4866			−0.490297
$874$		−	3.62986i		−	0.122782i
$875$		0			0
$876$	−3.60760	−	3.60760i	−0.121889	−	0.121889i
$877$		−	8.63720i		−	0.291657i	−0.989310	−	0.145829i	$-0.953415\pi$
$877$		−	8.63720i		−	0.291657i	0.989310	−	0.145829i	$-0.0465848\pi$
$878$			24.9342i			0.841487i
$879$	1.38114	+	1.38114i	0.0465847	+	0.0465847i
$880$		0			0
$881$			15.5330i			0.523320i	0.965160	+	0.261660i	$0.0842700\pi$
$881$			15.5330i			0.523320i	−0.965160	+	0.261660i	$0.915730\pi$
$882$	9.56466			0.322059
$883$	20.1472	+	20.1472i	0.678006	+	0.678006i	0.959549	−	0.281542i	$-0.0908460\pi$
$883$	20.1472	+	20.1472i	0.678006	+	0.678006i	−0.281542	+	0.959549i	$0.590846\pi$
$884$	−2.72464	+	1.15975i	−0.0916394	+	0.0390065i
$885$		0			0
$886$	0.755329	+	0.755329i	0.0253758	+	0.0253758i
$887$	−25.0749	−	25.0749i	−0.841933	−	0.841933i	0.147177	−	0.989110i	$-0.452981\pi$
$887$	−25.0749	−	25.0749i	−0.841933	−	0.841933i	−0.989110	+	0.147177i	$0.952981\pi$
$888$	−12.1249	−	12.1249i	−0.406884	−	0.406884i
$889$	4.54495	−	4.54495i	0.152433	−	0.152433i
$890$		0			0
$891$	0.601309	−	0.601309i	0.0201446	−	0.0201446i
$892$	−11.6639			−0.390537
$893$	−2.25261	+	2.25261i	−0.0753807	+	0.0753807i
$894$	−22.0103			−0.736133
$895$		0			0
$896$		−	13.2857i		−	0.443845i
$897$	7.85258	+	3.16355i	0.262190	+	0.105628i
$898$	17.3183	−	17.3183i	0.577920	−	0.577920i
$899$	−48.2656	+	48.2656i	−1.60975	+	1.60975i
$900$		0			0
$901$		−	13.1778i		−	0.439017i
$902$			6.94090i			0.231107i
$903$	−3.74425			−0.124601
$904$	−27.3413	−	27.3413i	−0.909358	−	0.909358i
$905$		0			0
$906$	26.5598			0.882392
$907$	15.8243	−	15.8243i	0.525439	−	0.525439i	−0.393770	−	0.919209i	$-0.628829\pi$
$907$	15.8243	−	15.8243i	0.525439	−	0.525439i	0.919209	+	0.393770i	$0.128829\pi$
$908$			8.68663i			0.288276i
$909$	5.61850			0.186354
$910$		0			0
$911$	21.9928			0.728655			0.364327	−	0.931271i	$-0.381299\pi$
$911$	21.9928			0.728655			0.364327	+	0.931271i	$0.381299\pi$
$912$		−	4.64416i		−	0.153784i
$913$	−8.58914	+	8.58914i	−0.284259	+	0.284259i
$914$	34.8658			1.15326
$915$		0			0
$916$	4.24279	+	4.24279i	0.140186	+	0.140186i
$917$	−1.53825			−0.0507976
$918$			2.60311i			0.0859153i
$919$			53.4478i			1.76308i	0.472108	+	0.881541i	$0.343493\pi$
$919$			53.4478i			1.76308i	−0.472108	+	0.881541i	$0.656507\pi$
$920$		0			0
$921$	−16.7498	+	16.7498i	−0.551923	+	0.551923i
$922$	−9.10043	+	9.10043i	−0.299707	+	0.299707i
$923$	−14.3359	−	33.6799i	−0.471872	−	1.10859i
$924$		−	0.413201i		−	0.0135933i
$925$		0			0
$926$	−41.4353			−1.36165
$927$	0.00240087	−	0.00240087i	7.88549e−5	−	7.88549e-5i
$928$	17.5850			0.577256
$929$	7.45064	−	7.45064i	0.244448	−	0.244448i	−0.574240	−	0.818687i	$-0.694702\pi$
$929$	7.45064	−	7.45064i	0.244448	−	0.244448i	0.818687	+	0.574240i	$0.194702\pi$
$930$		0			0
$931$	−4.18433	+	4.18433i	−0.137136	+	0.137136i
$932$	9.93250	+	9.93250i	0.325350	+	0.325350i
$933$	0.552962	+	0.552962i	0.0181031	+	0.0181031i
$934$	−1.43098	−	1.43098i	−0.0468230	−	0.0468230i
$935$		0			0
$936$	7.93654	+	3.19737i	0.259414	+	0.104509i
$937$	13.8571	+	13.8571i	0.452693	+	0.452693i	0.896247	−	0.443555i	$-0.146283\pi$
$937$	13.8571	+	13.8571i	0.452693	+	0.452693i	−0.443555	+	0.896247i	$0.646283\pi$
$938$	−9.86876			−0.322227
$939$		−	1.54810i		−	0.0505202i
$940$		0			0
$941$	3.55621	+	3.55621i	0.115929	+	0.115929i	0.762692	−	0.646762i	$-0.223877\pi$
$941$	3.55621	+	3.55621i	0.115929	+	0.115929i	−0.646762	+	0.762692i	$0.723877\pi$
$942$		−	11.0296i		−	0.359363i
$943$			12.1239i			0.394810i
$944$	28.0942	+	28.0942i	0.914388	+	0.914388i
$945$		0			0
$946$		−	5.16595i		−	0.167960i
$947$	−28.4349			−0.924010			−0.462005	−	0.886877i	$-0.652870\pi$
$947$	−28.4349			−0.924010			−0.462005	+	0.886877i	$0.652870\pi$
$948$	2.62261	+	2.62261i	0.0851785	+	0.0851785i
$949$	−13.7830	+	34.2123i	−0.447416	+	1.11058i
$950$		0			0
$951$	14.8767	+	14.8767i	0.482409	+	0.482409i
$952$	−2.69230	−	2.69230i	−0.0872580	−	0.0872580i
$953$	−1.81293	−	1.81293i	−0.0587266	−	0.0587266i	0.677134	−	0.735860i	$-0.263222\pi$
$953$	−1.81293	−	1.81293i	−0.0587266	−	0.0587266i	−0.735860	+	0.677134i	$0.763222\pi$
$954$	8.94448	−	8.94448i	0.289588	−	0.289588i
$955$		0			0
$956$	−3.83773	+	3.83773i	−0.124121	+	0.124121i
$957$	−5.41761			−0.175126
$958$	−2.15409	+	2.15409i	−0.0695956	+	0.0695956i
$959$	3.43259			0.110844
$960$		0			0
$961$			83.7933i			2.70301i
$962$	15.3889	−	38.1983i	0.496157	−	1.23156i
$963$	5.70114	−	5.70114i	0.183717	−	0.183717i
$964$	1.34318	−	1.34318i	0.0432610	−	0.0432610i
$965$		0			0
$966$		−	3.61615i		−	0.116348i
$967$			7.13250i			0.229366i	0.993402	+	0.114683i	$0.0365852\pi$
$967$			7.13250i			0.229366i	−0.993402	+	0.114683i	$0.963415\pi$
$968$	24.3882			0.783866
$969$	−1.13880	−	1.13880i	−0.0365836	−	0.0365836i
$970$		0			0
$971$	50.6017			1.62389			0.811943	−	0.583737i	$-0.198410\pi$
$971$	50.6017			1.62389			0.811943	+	0.583737i	$0.198410\pi$
$972$	−0.352653	+	0.352653i	−0.0113113	+	0.0113113i
$973$			18.4055i			0.590054i
$974$	−24.0728			−0.771343
$975$		0			0
$976$	−12.7799			−0.409076
$977$		−	34.3015i		−	1.09740i	−0.836019	−	0.548701i	$-0.815123\pi$
$977$		−	34.3015i		−	1.09740i	0.836019	−	0.548701i	$-0.184877\pi$
$978$	19.8995	−	19.8995i	0.636315	−	0.636315i
$979$	12.8206			0.409749
$980$		0			0
$981$	2.16428	+	2.16428i	0.0691000	+	0.0691000i
$982$	19.2501			0.614294
$983$			47.7005i			1.52141i	0.649097	+	0.760705i	$0.275147\pi$
$983$			47.7005i			1.52141i	−0.649097	+	0.760705i	$0.724853\pi$
$984$			12.2536i			0.390630i
$985$		0			0
$986$	11.7266	−	11.7266i	0.373451	−	0.373451i
$987$	−2.24410	+	2.24410i	−0.0714305	+	0.0714305i
$988$	1.61810	−	0.688748i	0.0514787	−	0.0219120i
$989$		−	9.02357i		−	0.286933i
$990$		0			0
$991$	−13.9606			−0.443474			−0.221737	−	0.975107i	$-0.571173\pi$
$991$	−13.9606			−0.443474			−0.221737	+	0.975107i	$0.571173\pi$
$992$	20.9118	−	20.9118i	0.663949	−	0.663949i
$993$	14.2233			0.451363
$994$	−11.0558	+	11.0558i	−0.350667	+	0.350667i
$995$		0			0
$996$	5.03731	−	5.03731i	0.159613	−	0.159613i
$997$	−30.9797	−	30.9797i	−0.981136	−	0.981136i	0.0186893	−	0.999825i	$-0.494051\pi$
$997$	−30.9797	−	30.9797i	−0.981136	−	0.981136i	−0.999825	+	0.0186893i	$0.994051\pi$
$998$	36.6190	+	36.6190i	1.15915	+	1.15915i
$999$	−5.10926	−	5.10926i	−0.161650	−	0.161650i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.k.d.307.4		28
5.2	odd	4		195.2.t.a.73.11	yes	28
5.3	odd	4		975.2.t.d.268.4		28
5.4	even	2		195.2.k.a.112.11	✓	28
13.5	odd	4		975.2.t.d.382.4		28
15.2	even	4		585.2.w.g.73.4		28
15.14	odd	2		585.2.n.g.307.4		28
65.18	even	4	inner	975.2.k.d.343.11		28
65.44	odd	4		195.2.t.a.187.11	yes	28
65.57	even	4		195.2.k.a.148.4	yes	28
195.44	even	4		585.2.w.g.577.4		28
195.122	odd	4		585.2.n.g.343.11		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.k.a.112.11	✓	28	5.4	even	2
195.2.k.a.148.4	yes	28	65.57	even	4
195.2.t.a.73.11	yes	28	5.2	odd	4
195.2.t.a.187.11	yes	28	65.44	odd	4
585.2.n.g.307.4		28	15.14	odd	2
585.2.n.g.343.11		28	195.122	odd	4
585.2.w.g.73.4		28	15.2	even	4
585.2.w.g.577.4		28	195.44	even	4
975.2.k.d.307.4		28	1.1	even	1	trivial
975.2.k.d.343.11		28	65.18	even	4	inner
975.2.t.d.268.4		28	5.3	odd	4
975.2.t.d.382.4		28	13.5	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.58074i q^{2} +(-0.707107 + 0.707107i) q^{3} -0.498726 q^{4} +(1.11775 + 1.11775i) q^{6} -0.974287 q^{7} -2.37312i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.58074i q^{2} +(-0.707107 + 0.707107i) q^{3} -0.498726 q^{4} +(1.11775 + 1.11775i) q^{6} -0.974287 q^{7} -2.37312i q^{8} -1.00000i q^{9} +(-0.601309 + 0.601309i) q^{11} +(0.352653 - 0.352653i) q^{12} +(-3.34435 - 1.34733i) q^{13} +1.54009i q^{14} -4.74872 q^{16} +(-1.16444 + 1.16444i) q^{17} -1.58074 q^{18} +(0.691537 - 0.691537i) q^{19} +(0.688925 - 0.688925i) q^{21} +(0.950511 + 0.950511i) q^{22} +(1.66029 + 1.66029i) q^{23} +(1.67805 + 1.67805i) q^{24} +(-2.12977 + 5.28654i) q^{26} +(0.707107 + 0.707107i) q^{27} +0.485902 q^{28} -6.37081i q^{29} +(-7.57606 - 7.57606i) q^{31} +2.76024i q^{32} -0.850380i q^{33} +(1.84067 + 1.84067i) q^{34} +0.498726i q^{36} -7.22558 q^{37} +(-1.09314 - 1.09314i) q^{38} +(3.31752 - 1.41211i) q^{39} +(3.65114 + 3.65114i) q^{41} +(-1.08901 - 1.08901i) q^{42} +(-2.71746 - 2.71746i) q^{43} +(0.299889 - 0.299889i) q^{44} +(2.62449 - 2.62449i) q^{46} -3.25740 q^{47} +(3.35786 - 3.35786i) q^{48} -6.05077 q^{49} -1.64677i q^{51} +(1.66792 + 0.671949i) q^{52} +(-5.65843 + 5.65843i) q^{53} +(1.11775 - 1.11775i) q^{54} +2.31210i q^{56} +0.977981i q^{57} -10.0706 q^{58} +(-5.91615 - 5.91615i) q^{59} +2.69124 q^{61} +(-11.9757 + 11.9757i) q^{62} +0.974287i q^{63} -5.13423 q^{64} -1.34423 q^{66} +6.40792i q^{67} +(0.580737 - 0.580737i) q^{68} -2.34801 q^{69} +(7.17864 + 7.17864i) q^{71} -2.37312 q^{72} -10.2299i q^{73} +11.4217i q^{74} +(-0.344887 + 0.344887i) q^{76} +(0.585848 - 0.585848i) q^{77} +(-2.23217 - 5.24413i) q^{78} +7.43682i q^{79} -1.00000 q^{81} +(5.77149 - 5.77149i) q^{82} +14.2841 q^{83} +(-0.343585 + 0.343585i) q^{84} +(-4.29559 + 4.29559i) q^{86} +(4.50484 + 4.50484i) q^{87} +(1.42698 + 1.42698i) q^{88} +(-10.6606 - 10.6606i) q^{89} +(3.25836 + 1.31269i) q^{91} +(-0.828032 - 0.828032i) q^{92} +10.7142 q^{93} +5.14908i q^{94} +(-1.95179 - 1.95179i) q^{96} -14.4866i q^{97} +9.56466i q^{98} +(0.601309 + 0.601309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4}+O(q^{10}) \) 28 * q - 28 * q^4	\( 28 q - 28 q^{4} - 8 q^{11} - 8 q^{12} + 12 q^{13} + 28 q^{16} + 28 q^{17} + 4 q^{18} + 8 q^{21} + 32 q^{22} - 8 q^{23} - 16 q^{31} + 28 q^{34} - 32 q^{37} + 8 q^{39} + 4 q^{41} + 40 q^{44} - 16 q^{46} + 24 q^{47} + 16 q^{48} - 28 q^{49} - 52 q^{52} - 20 q^{53} + 8 q^{58} + 32 q^{59} + 8 q^{61} - 72 q^{62} - 28 q^{64} + 16 q^{66} - 60 q^{68} + 8 q^{69} + 40 q^{71} - 12 q^{72} - 40 q^{76} + 48 q^{77} - 8 q^{78} - 28 q^{81} - 4 q^{82} + 104 q^{83} - 32 q^{84} + 16 q^{86} + 24 q^{87} - 72 q^{88} - 36 q^{89} - 56 q^{91} + 32 q^{92} + 8 q^{99}+O(q^{100}) \) 28 * q - 28 * q^4 - 8 * q^11 - 8 * q^12 + 12 * q^13 + 28 * q^16 + 28 * q^17 + 4 * q^18 + 8 * q^21 + 32 * q^22 - 8 * q^23 - 16 * q^31 + 28 * q^34 - 32 * q^37 + 8 * q^39 + 4 * q^41 + 40 * q^44 - 16 * q^46 + 24 * q^47 + 16 * q^48 - 28 * q^49 - 52 * q^52 - 20 * q^53 + 8 * q^58 + 32 * q^59 + 8 * q^61 - 72 * q^62 - 28 * q^64 + 16 * q^66 - 60 * q^68 + 8 * q^69 + 40 * q^71 - 12 * q^72 - 40 * q^76 + 48 * q^77 - 8 * q^78 - 28 * q^81 - 4 * q^82 + 104 * q^83 - 32 * q^84 + 16 * q^86 + 24 * q^87 - 72 * q^88 - 36 * q^89 - 56 * q^91 + 32 * q^92 + 8 * q^99

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