LMFDB - Embedded newform 1575.2.m.a.1457.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1575,2,Mod(1268,1575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1575, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1575.1268");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1575 = 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1575.m (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:	$12.5764383184$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1457.1
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1575.1457
Dual form			1575.2.m.a.1268.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 + 1.36603i) q^{2} -1.73205i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.366025 - 0.366025i) q^{8} +O(q^{10})$	\(q+(-1.36603 + 1.36603i) q^{2} -1.73205i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.366025 - 0.366025i) q^{8} +2.44949i q^{11} +(1.03528 - 1.03528i) q^{13} +1.93185 q^{14} +4.46410 q^{16} +(-2.00000 + 2.00000i) q^{17} -2.00000i q^{19} +(-3.34607 - 3.34607i) q^{22} +(-0.464102 - 0.464102i) q^{23} +2.82843i q^{26} +(-1.22474 + 1.22474i) q^{28} +3.48477 q^{29} +8.92820 q^{31} +(-5.36603 + 5.36603i) q^{32} -5.46410i q^{34} +(-5.27792 - 5.27792i) q^{37} +(2.73205 + 2.73205i) q^{38} +7.72741i q^{41} +(-2.82843 + 2.82843i) q^{43} +4.24264 q^{44} +1.26795 q^{46} +(-0.535898 + 0.535898i) q^{47} +1.00000i q^{49} +(-1.79315 - 1.79315i) q^{52} +(5.73205 + 5.73205i) q^{53} +0.517638i q^{56} +(-4.76028 + 4.76028i) q^{58} -6.96953 q^{59} +4.92820 q^{61} +(-12.1962 + 12.1962i) q^{62} -5.73205i q^{64} +(3.48477 + 3.48477i) q^{67} +(3.46410 + 3.46410i) q^{68} +10.1769i q^{71} +(-3.86370 + 3.86370i) q^{73} +14.4195 q^{74} -3.46410 q^{76} +(1.73205 - 1.73205i) q^{77} +4.00000i q^{79} +(-10.5558 - 10.5558i) q^{82} +(11.4641 + 11.4641i) q^{83} -7.72741i q^{86} +(0.896575 - 0.896575i) q^{88} -14.1421 q^{89} -1.46410 q^{91} +(-0.803848 + 0.803848i) q^{92} -1.46410i q^{94} +(13.6617 + 13.6617i) q^{97} +(-1.36603 - 1.36603i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 4 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 + 4 * q^8	$ 8 q - 4 q^{2} + 4 q^{8} + 8 q^{16} - 16 q^{17} + 24 q^{23} + 16 q^{31} - 36 q^{32} + 8 q^{38} + 24 q^{46} - 32 q^{47} + 32 q^{53} - 16 q^{61} - 56 q^{62} + 64 q^{83} + 16 q^{91} - 48 q^{92} - 4 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 4 * q^8 + 8 * q^16 - 16 * q^17 + 24 * q^23 + 16 * q^31 - 36 * q^32 + 8 * q^38 + 24 * q^46 - 32 * q^47 + 32 * q^53 - 16 * q^61 - 56 * q^62 + 64 * q^83 + 16 * q^91 - 48 * q^92 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$1226$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	−1.36603	+	1.36603i	−0.965926	+	0.965926i	−0.999438	−	0.0335125i	$-0.989331\pi$
$2$	−1.36603	+	1.36603i	−0.965926	+	0.965926i	0.0335125	+	0.999438i	$0.489331\pi$
$3$		0			0
$3$		0			0
$4$		−	1.73205i		−	0.866025i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	−0.366025	−	0.366025i	−0.129410	−	0.129410i
$9$		0			0
$10$		0			0
$11$			2.44949i			0.738549i	0.929320	+	0.369274i	$0.120394\pi$
$11$			2.44949i			0.738549i	−0.929320	+	0.369274i	$0.879606\pi$
$12$		0			0
$13$	1.03528	−	1.03528i	0.287134	−	0.287134i	−0.548812	−	0.835946i	$-0.684920\pi$
$13$	1.03528	−	1.03528i	0.287134	−	0.287134i	0.835946	+	0.548812i	$0.184920\pi$
$14$	1.93185			0.516309
$15$		0			0
$16$	4.46410			1.11603
$17$	−2.00000	+	2.00000i	−0.485071	+	0.485071i	−0.906747	−	0.421676i	$-0.861442\pi$
$17$	−2.00000	+	2.00000i	−0.485071	+	0.485071i	0.421676	+	0.906747i	$0.361442\pi$
$18$		0			0
$19$		−	2.00000i		−	0.458831i	−0.973329	−	0.229416i	$-0.926318\pi$
$19$		−	2.00000i		−	0.458831i	0.973329	−	0.229416i	$-0.0736815\pi$
$20$		0			0
$21$		0			0
$22$	−3.34607	−	3.34607i	−0.713384	−	0.713384i
$23$	−0.464102	−	0.464102i	−0.0967719	−	0.0967719i	0.657063	−	0.753835i	$-0.271798\pi$
$23$	−0.464102	−	0.464102i	−0.0967719	−	0.0967719i	−0.753835	+	0.657063i	$0.771798\pi$
$24$		0			0
$25$		0			0
$26$			2.82843i			0.554700i
$27$		0			0
$28$	−1.22474	+	1.22474i	−0.231455	+	0.231455i
$29$	3.48477			0.647105			0.323552	−	0.946210i	$-0.395123\pi$
$29$	3.48477			0.647105			0.323552	+	0.946210i	$0.395123\pi$
$30$		0			0
$31$	8.92820			1.60355			0.801776	−	0.597624i	$-0.203889\pi$
$31$	8.92820			1.60355			0.801776	+	0.597624i	$0.203889\pi$
$32$	−5.36603	+	5.36603i	−0.948588	+	0.948588i
$33$		0			0
$34$		−	5.46410i		−	0.937086i
$35$		0			0
$36$		0			0
$37$	−5.27792	−	5.27792i	−0.867684	−	0.867684i	0.124531	−	0.992216i	$-0.460257\pi$
$37$	−5.27792	−	5.27792i	−0.867684	−	0.867684i	−0.992216	+	0.124531i	$0.960257\pi$
$38$	2.73205	+	2.73205i	0.443197	+	0.443197i
$39$		0			0
$40$		0			0
$41$			7.72741i			1.20682i	0.797432	+	0.603409i	$0.206191\pi$
$41$			7.72741i			1.20682i	−0.797432	+	0.603409i	$0.793809\pi$
$42$		0			0
$43$	−2.82843	+	2.82843i	−0.431331	+	0.431331i	−0.889081	−	0.457750i	$-0.848656\pi$
$43$	−2.82843	+	2.82843i	−0.431331	+	0.431331i	0.457750	+	0.889081i	$0.348656\pi$
$44$	4.24264			0.639602
$45$		0			0
$46$	1.26795			0.186949
$47$	−0.535898	+	0.535898i	−0.0781688	+	0.0781688i	−0.745110	−	0.666941i	$-0.767603\pi$
$47$	−0.535898	+	0.535898i	−0.0781688	+	0.0781688i	0.666941	+	0.745110i	$0.267603\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$		0			0
$52$	−1.79315	−	1.79315i	−0.248665	−	0.248665i
$53$	5.73205	+	5.73205i	0.787358	+	0.787358i	0.981060	−	0.193703i	$-0.0620497\pi$
$53$	5.73205	+	5.73205i	0.787358	+	0.787358i	−0.193703	+	0.981060i	$0.562050\pi$
$54$		0			0
$55$		0			0
$56$			0.517638i			0.0691723i
$57$		0			0
$58$	−4.76028	+	4.76028i	−0.625055	+	0.625055i
$59$	−6.96953			−0.907356			−0.453678	−	0.891166i	$-0.649888\pi$
$59$	−6.96953			−0.907356			−0.453678	+	0.891166i	$0.649888\pi$
$60$		0			0
$61$	4.92820			0.630992			0.315496	−	0.948927i	$-0.397829\pi$
$61$	4.92820			0.630992			0.315496	+	0.948927i	$0.397829\pi$
$62$	−12.1962	+	12.1962i	−1.54891	+	1.54891i
$63$		0			0
$64$		−	5.73205i		−	0.716506i
$65$		0			0
$66$		0			0
$67$	3.48477	+	3.48477i	0.425732	+	0.425732i	0.887172	−	0.461440i	$-0.152667\pi$
$67$	3.48477	+	3.48477i	0.425732	+	0.425732i	−0.461440	+	0.887172i	$0.652667\pi$
$68$	3.46410	+	3.46410i	0.420084	+	0.420084i
$69$		0			0
$70$		0			0
$71$			10.1769i			1.20778i	0.797069	+	0.603888i	$0.206382\pi$
$71$			10.1769i			1.20778i	−0.797069	+	0.603888i	$0.793618\pi$
$72$		0			0
$73$	−3.86370	+	3.86370i	−0.452212	+	0.452212i	−0.896088	−	0.443876i	$-0.853603\pi$
$73$	−3.86370	+	3.86370i	−0.452212	+	0.452212i	0.443876	+	0.896088i	$0.353603\pi$
$74$	14.4195			1.67624
$75$		0			0
$76$	−3.46410			−0.397360
$77$	1.73205	−	1.73205i	0.197386	−	0.197386i
$78$		0			0
$79$			4.00000i			0.450035i	0.974355	+	0.225018i	$0.0722440\pi$
$79$			4.00000i			0.450035i	−0.974355	+	0.225018i	$0.927756\pi$
$80$		0			0
$81$		0			0
$82$	−10.5558	−	10.5558i	−1.16570	−	1.16570i
$83$	11.4641	+	11.4641i	1.25835	+	1.25835i	0.951881	+	0.306468i	$0.0991471\pi$
$83$	11.4641	+	11.4641i	1.25835	+	1.25835i	0.306468	+	0.951881i	$0.400853\pi$
$84$		0			0
$85$		0			0
$86$		−	7.72741i		−	0.833268i
$87$		0			0
$88$	0.896575	−	0.896575i	0.0955753	−	0.0955753i
$89$	−14.1421			−1.49906			−0.749532	−	0.661968i	$-0.769721\pi$
$89$	−14.1421			−1.49906			−0.749532	+	0.661968i	$0.769721\pi$
$90$		0			0
$91$	−1.46410			−0.153480
$92$	−0.803848	+	0.803848i	−0.0838069	+	0.0838069i
$93$		0			0
$94$		−	1.46410i		−	0.151011i
$95$		0			0
$96$		0			0
$97$	13.6617	+	13.6617i	1.38713	+	1.38713i	0.831285	+	0.555847i	$0.187606\pi$
$97$	13.6617	+	13.6617i	1.38713	+	1.38713i	0.555847	+	0.831285i	$0.312394\pi$
$98$	−1.36603	−	1.36603i	−0.137989	−	0.137989i
$99$		0			0
$100$		0			0
$101$		−	17.5254i		−	1.74384i	−0.489649	−	0.871920i	$-0.662875\pi$
$101$		−	17.5254i		−	1.74384i	0.489649	−	0.871920i	$-0.337125\pi$
$102$		0			0
$103$	−8.48528	+	8.48528i	−0.836080	+	0.836080i	−0.988340	−	0.152261i	$-0.951345\pi$
$103$	−8.48528	+	8.48528i	−0.836080	+	0.836080i	0.152261	+	0.988340i	$0.451345\pi$
$104$	−0.757875			−0.0743157
$105$		0			0
$106$	−15.6603			−1.52106
$107$	5.92820	−	5.92820i	0.573101	−	0.573101i	−0.359893	−	0.932994i	$-0.617187\pi$
$107$	5.92820	−	5.92820i	0.573101	−	0.573101i	0.932994	+	0.359893i	$0.117187\pi$
$108$		0			0
$109$			14.9282i			1.42986i	0.699195	+	0.714931i	$0.253542\pi$
$109$			14.9282i			1.42986i	−0.699195	+	0.714931i	$0.746458\pi$
$110$		0			0
$111$		0			0
$112$	−3.15660	−	3.15660i	−0.298270	−	0.298270i
$113$	3.73205	+	3.73205i	0.351082	+	0.351082i	0.860512	−	0.509430i	$-0.170144\pi$
$113$	3.73205	+	3.73205i	0.351082	+	0.351082i	−0.509430	+	0.860512i	$0.670144\pi$
$114$		0			0
$115$		0			0
$116$		−	6.03579i		−	0.560409i
$117$		0			0
$118$	9.52056	−	9.52056i	0.876438	−	0.876438i
$119$	2.82843			0.259281
$120$		0			0
$121$	5.00000			0.454545
$122$	−6.73205	+	6.73205i	−0.609491	+	0.609491i
$123$		0			0
$124$		−	15.4641i		−	1.38872i
$125$		0			0
$126$		0			0
$127$	−14.0406	−	14.0406i	−1.24590	−	1.24590i	−0.957514	−	0.288388i	$-0.906881\pi$
$127$	−14.0406	−	14.0406i	−1.24590	−	1.24590i	−0.288388	−	0.957514i	$-0.593119\pi$
$128$	−2.90192	−	2.90192i	−0.256496	−	0.256496i
$129$		0			0
$130$		0			0
$131$			3.58630i			0.313337i	0.987651	+	0.156668i	$0.0500754\pi$
$131$			3.58630i			0.313337i	−0.987651	+	0.156668i	$0.949925\pi$
$132$		0			0
$133$	−1.41421	+	1.41421i	−0.122628	+	0.122628i
$134$	−9.52056			−0.822451
$135$		0			0
$136$	1.46410			0.125546
$137$	−3.19615	+	3.19615i	−0.273066	+	0.273066i	−0.830333	−	0.557267i	$-0.811850\pi$
$137$	−3.19615	+	3.19615i	−0.273066	+	0.273066i	0.557267	+	0.830333i	$0.311850\pi$
$138$		0			0
$139$			15.8564i			1.34492i	0.740132	+	0.672461i	$0.234763\pi$
$139$			15.8564i			1.34492i	−0.740132	+	0.672461i	$0.765237\pi$
$140$		0			0
$141$		0			0
$142$	−13.9019	−	13.9019i	−1.16662	−	1.16662i
$143$	2.53590	+	2.53590i	0.212062	+	0.212062i
$144$		0			0
$145$		0			0
$146$		−	10.5558i		−	0.873607i
$147$		0			0
$148$	−9.14162	+	9.14162i	−0.751437	+	0.751437i
$149$	−10.4543			−0.856449			−0.428225	−	0.903672i	$-0.640861\pi$
$149$	−10.4543			−0.856449			−0.428225	+	0.903672i	$0.640861\pi$
$150$		0			0
$151$	−10.3923			−0.845714			−0.422857	−	0.906196i	$-0.638973\pi$
$151$	−10.3923			−0.845714			−0.422857	+	0.906196i	$0.638973\pi$
$152$	−0.732051	+	0.732051i	−0.0593772	+	0.0593772i
$153$		0			0
$154$			4.73205i			0.381320i
$155$		0			0
$156$		0			0
$157$	12.3490	+	12.3490i	0.985556	+	0.985556i	0.999897	−	0.0143409i	$-0.00456500\pi$
$157$	12.3490	+	12.3490i	0.985556	+	0.985556i	−0.0143409	+	0.999897i	$0.504565\pi$
$158$	−5.46410	−	5.46410i	−0.434701	−	0.434701i
$159$		0			0
$160$		0			0
$161$			0.656339i			0.0517267i
$162$		0			0
$163$	−11.2122	+	11.2122i	−0.878205	+	0.878205i	−0.993349	−	0.115144i	$-0.963267\pi$
$163$	−11.2122	+	11.2122i	−0.878205	+	0.878205i	0.115144	+	0.993349i	$0.463267\pi$
$164$	13.3843			1.04514
$165$		0			0
$166$	−31.3205			−2.43094
$167$	−10.9282	+	10.9282i	−0.845650	+	0.845650i	−0.989587	−	0.143937i	$-0.954024\pi$
$167$	−10.9282	+	10.9282i	−0.845650	+	0.845650i	0.143937	+	0.989587i	$0.454024\pi$
$168$		0			0
$169$			10.8564i			0.835108i
$170$		0			0
$171$		0			0
$172$	4.89898	+	4.89898i	0.373544	+	0.373544i
$173$	−6.39230	−	6.39230i	−0.485998	−	0.485998i	0.421043	−	0.907041i	$-0.361664\pi$
$173$	−6.39230	−	6.39230i	−0.485998	−	0.485998i	−0.907041	+	0.421043i	$0.861664\pi$
$174$		0			0
$175$		0			0
$176$			10.9348i			0.824239i
$177$		0			0
$178$	19.3185	−	19.3185i	1.44798	−	1.44798i
$179$	3.96524			0.296376			0.148188	−	0.988959i	$-0.452656\pi$
$179$	3.96524			0.296376			0.148188	+	0.988959i	$0.452656\pi$
$180$		0			0
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$	2.00000	−	2.00000i	0.148250	−	0.148250i
$183$		0			0
$184$			0.339746i			0.0250464i
$185$		0			0
$186$		0			0
$187$	−4.89898	−	4.89898i	−0.358249	−	0.358249i
$188$	0.928203	+	0.928203i	0.0676962	+	0.0676962i
$189$		0			0
$190$		0			0
$191$		−	21.4906i		−	1.55501i	−0.628879	−	0.777503i	$-0.716486\pi$
$191$		−	21.4906i		−	1.55501i	0.628879	−	0.777503i	$-0.283514\pi$
$192$		0			0
$193$	6.59059	−	6.59059i	0.474401	−	0.474401i	−0.428934	−	0.903336i	$-0.641111\pi$
$193$	6.59059	−	6.59059i	0.474401	−	0.474401i	0.903336	+	0.428934i	$0.141111\pi$
$194$	−37.3244			−2.67973
$195$		0			0
$196$	1.73205			0.123718
$197$	13.7321	−	13.7321i	0.978368	−	0.978368i	−0.0214028	−	0.999771i	$-0.506813\pi$
$197$	13.7321	−	13.7321i	0.978368	−	0.978368i	0.999771	+	0.0214028i	$0.00681325\pi$
$198$		0			0
$199$			7.07180i			0.501306i	0.968077	+	0.250653i	$0.0806454\pi$
$199$			7.07180i			0.501306i	−0.968077	+	0.250653i	$0.919355\pi$
$200$		0			0
$201$		0			0
$202$	23.9401	+	23.9401i	1.68442	+	1.68442i
$203$	−2.46410	−	2.46410i	−0.172946	−	0.172946i
$204$		0			0
$205$		0			0
$206$		−	23.1822i		−	1.61518i
$207$		0			0
$208$	4.62158	−	4.62158i	0.320449	−	0.320449i
$209$	4.89898			0.338869
$210$		0			0
$211$	−7.46410			−0.513850			−0.256925	−	0.966431i	$-0.582709\pi$
$211$	−7.46410			−0.513850			−0.256925	+	0.966431i	$0.582709\pi$
$212$	9.92820	−	9.92820i	0.681872	−	0.681872i
$213$		0			0
$214$			16.1962i			1.10715i
$215$		0			0
$216$		0			0
$217$	−6.31319	−	6.31319i	−0.428567	−	0.428567i
$218$	−20.3923	−	20.3923i	−1.38114	−	1.38114i
$219$		0			0
$220$		0			0
$221$			4.14110i			0.278561i
$222$		0			0
$223$	17.5254	−	17.5254i	1.17359	−	1.17359i	0.192237	−	0.981349i	$-0.438426\pi$
$223$	17.5254	−	17.5254i	1.17359	−	1.17359i	0.981349	−	0.192237i	$-0.0615741\pi$
$224$	7.58871			0.507042
$225$		0			0
$226$	−10.1962			−0.678238
$227$	−4.39230	+	4.39230i	−0.291528	+	0.291528i	−0.837683	−	0.546156i	$-0.816091\pi$
$227$	−4.39230	+	4.39230i	−0.291528	+	0.291528i	0.546156	+	0.837683i	$0.316091\pi$
$228$		0			0
$229$		−	11.0718i		−	0.731645i	−0.930685	−	0.365822i	$-0.880788\pi$
$229$		−	11.0718i		−	0.731645i	0.930685	−	0.365822i	$-0.119212\pi$
$230$		0			0
$231$		0			0
$232$	−1.27551	−	1.27551i	−0.0837415	−	0.0837415i
$233$	−3.73205	−	3.73205i	−0.244495	−	0.244495i	0.574212	−	0.818707i	$-0.305309\pi$
$233$	−3.73205	−	3.73205i	−0.244495	−	0.244495i	−0.818707	+	0.574212i	$0.805309\pi$
$234$		0			0
$235$		0			0
$236$			12.0716i			0.785793i
$237$		0			0
$238$	−3.86370	+	3.86370i	−0.250447	+	0.250447i
$239$	−22.2485			−1.43913			−0.719567	−	0.694423i	$-0.755660\pi$
$239$	−22.2485			−1.43913			−0.719567	+	0.694423i	$0.755660\pi$
$240$		0			0
$241$	−0.928203			−0.0597908			−0.0298954	−	0.999553i	$-0.509517\pi$
$241$	−0.928203			−0.0597908			−0.0298954	+	0.999553i	$0.509517\pi$
$242$	−6.83013	+	6.83013i	−0.439057	+	0.439057i
$243$		0			0
$244$		−	8.53590i		−	0.546455i
$245$		0			0
$246$		0			0
$247$	−2.07055	−	2.07055i	−0.131746	−	0.131746i
$248$	−3.26795	−	3.26795i	−0.207515	−	0.207515i
$249$		0			0
$250$		0			0
$251$			14.1421i			0.892644i	0.894873	+	0.446322i	$0.147266\pi$
$251$			14.1421i			0.892644i	−0.894873	+	0.446322i	$0.852734\pi$
$252$		0			0
$253$	1.13681	−	1.13681i	0.0714708	−	0.0714708i
$254$	38.3596			2.40690
$255$		0			0
$256$	19.3923			1.21202
$257$	21.4641	−	21.4641i	1.33889	−	1.33889i	0.441761	−	0.897133i	$-0.354354\pi$
$257$	21.4641	−	21.4641i	1.33889	−	1.33889i	0.897133	−	0.441761i	$-0.145646\pi$
$258$		0			0
$259$			7.46410i			0.463797i
$260$		0			0
$261$		0			0
$262$	−4.89898	−	4.89898i	−0.302660	−	0.302660i
$263$	13.3923	+	13.3923i	0.825805	+	0.825805i	0.986933	−	0.161129i	$-0.0515134\pi$
$263$	13.3923	+	13.3923i	0.825805	+	0.825805i	−0.161129	+	0.986933i	$0.551513\pi$
$264$		0			0
$265$		0			0
$266$		−	3.86370i		−	0.236899i
$267$		0			0
$268$	6.03579	−	6.03579i	0.368695	−	0.368695i
$269$	0.757875			0.0462084			0.0231042	−	0.999733i	$-0.492645\pi$
$269$	0.757875			0.0462084			0.0231042	+	0.999733i	$0.492645\pi$
$270$		0			0
$271$	3.85641			0.234260			0.117130	−	0.993117i	$-0.462631\pi$
$271$	3.85641			0.234260			0.117130	+	0.993117i	$0.462631\pi$
$272$	−8.92820	+	8.92820i	−0.541352	+	0.541352i
$273$		0			0
$274$		−	8.73205i		−	0.527522i
$275$		0			0
$276$		0			0
$277$	12.0716	+	12.0716i	0.725311	+	0.725311i	0.969682	−	0.244371i	$-0.0785814\pi$
$277$	12.0716	+	12.0716i	0.725311	+	0.725311i	−0.244371	+	0.969682i	$0.578581\pi$
$278$	−21.6603	−	21.6603i	−1.29910	−	1.29910i
$279$		0			0
$280$		0			0
$281$		−	1.41421i		−	0.0843649i	−0.999110	−	0.0421825i	$-0.986569\pi$
$281$		−	1.41421i		−	0.0843649i	0.999110	−	0.0421825i	$-0.0134311\pi$
$282$		0			0
$283$	−19.0411	+	19.0411i	−1.13188	+	1.13188i	−0.142012	+	0.989865i	$0.545357\pi$
$283$	−19.0411	+	19.0411i	−1.13188	+	1.13188i	−0.989865	+	0.142012i	$0.954643\pi$
$284$	17.6269			1.04596
$285$		0			0
$286$	−6.92820			−0.409673
$287$	5.46410	−	5.46410i	0.322536	−	0.322536i
$288$		0			0
$289$			9.00000i			0.529412i
$290$		0			0
$291$		0			0
$292$	6.69213	+	6.69213i	0.391627	+	0.391627i
$293$	12.3923	+	12.3923i	0.723966	+	0.723966i	0.969411	−	0.245444i	$-0.0789339\pi$
$293$	12.3923	+	12.3923i	0.723966	+	0.723966i	−0.245444	+	0.969411i	$0.578934\pi$
$294$		0			0
$295$		0			0
$296$			3.86370i			0.224573i
$297$		0			0
$298$	14.2808	−	14.2808i	0.827267	−	0.827267i
$299$	−0.960947			−0.0555730
$300$		0			0
$301$	4.00000			0.230556
$302$	14.1962	−	14.1962i	0.816897	−	0.816897i
$303$		0			0
$304$		−	8.92820i		−	0.512068i
$305$		0			0
$306$		0			0
$307$	18.2832	+	18.2832i	1.04348	+	1.04348i	0.999011	+	0.0444689i	$0.0141596\pi$
$307$	18.2832	+	18.2832i	1.04348	+	1.04348i	0.0444689	+	0.999011i	$0.485840\pi$
$308$	−3.00000	−	3.00000i	−0.170941	−	0.170941i
$309$		0			0
$310$		0			0
$311$			11.8685i			0.673002i	0.941683	+	0.336501i	$0.109243\pi$
$311$			11.8685i			0.673002i	−0.941683	+	0.336501i	$0.890757\pi$
$312$		0			0
$313$	−5.17638	+	5.17638i	−0.292586	+	0.292586i	−0.838101	−	0.545515i	$-0.816334\pi$
$313$	−5.17638	+	5.17638i	−0.292586	+	0.292586i	0.545515	+	0.838101i	$0.316334\pi$
$314$	−33.7381			−1.90395
$315$		0			0
$316$	6.92820			0.389742
$317$	17.7321	−	17.7321i	0.995931	−	0.995931i	−0.00406056	−	0.999992i	$-0.501293\pi$
$317$	17.7321	−	17.7321i	0.995931	−	0.995931i	0.999992	+	0.00406056i	$0.00129252\pi$
$318$		0			0
$319$			8.53590i			0.477919i
$320$		0			0
$321$		0			0
$322$	−0.896575	−	0.896575i	−0.0499642	−	0.0499642i
$323$	4.00000	+	4.00000i	0.222566	+	0.222566i
$324$		0			0
$325$		0			0
$326$		−	30.6322i		−	1.69656i
$327$		0			0
$328$	2.82843	−	2.82843i	0.156174	−	0.156174i
$329$	0.757875			0.0417830
$330$		0			0
$331$	23.4641			1.28970			0.644852	−	0.764308i	$-0.276919\pi$
$331$	23.4641			1.28970			0.644852	+	0.764308i	$0.276919\pi$
$332$	19.8564	−	19.8564i	1.08976	−	1.08976i
$333$		0			0
$334$		−	29.8564i		−	1.63367i
$335$		0			0
$336$		0			0
$337$	−0.933740	−	0.933740i	−0.0508641	−	0.0508641i	0.681217	−	0.732081i	$-0.261451\pi$
$337$	−0.933740	−	0.933740i	−0.0508641	−	0.0508641i	−0.732081	+	0.681217i	$0.761451\pi$
$338$	−14.8301	−	14.8301i	−0.806653	−	0.806653i
$339$		0			0
$340$		0			0
$341$			21.8695i			1.18430i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	2.07055			0.111637
$345$		0			0
$346$	17.4641			0.938876
$347$	1.00000	−	1.00000i	0.0536828	−	0.0536828i	−0.679756	−	0.733439i	$-0.737914\pi$
$347$	1.00000	−	1.00000i	0.0536828	−	0.0536828i	0.733439	+	0.679756i	$0.237914\pi$
$348$		0			0
$349$		−	25.7128i		−	1.37638i	−0.725533	−	0.688188i	$-0.758407\pi$
$349$		−	25.7128i		−	1.37638i	0.725533	−	0.688188i	$-0.241593\pi$
$350$		0			0
$351$		0			0
$352$	−13.1440	−	13.1440i	−0.700579	−	0.700579i
$353$	−5.07180	−	5.07180i	−0.269945	−	0.269945i	0.559133	−	0.829078i	$-0.311134\pi$
$353$	−5.07180	−	5.07180i	−0.269945	−	0.269945i	−0.829078	+	0.559133i	$0.811134\pi$
$354$		0			0
$355$		0			0
$356$			24.4949i			1.29823i
$357$		0			0
$358$	−5.41662	+	5.41662i	−0.286277	+	0.286277i
$359$	16.5916			0.875672			0.437836	−	0.899055i	$-0.355745\pi$
$359$	16.5916			0.875672			0.437836	+	0.899055i	$0.355745\pi$
$360$		0			0
$361$	15.0000			0.789474
$362$	8.19615	−	8.19615i	0.430780	−	0.430780i
$363$		0			0
$364$			2.53590i			0.132917i
$365$		0			0
$366$		0			0
$367$	14.6969	+	14.6969i	0.767174	+	0.767174i	0.977608	−	0.210434i	$-0.0674877\pi$
$367$	14.6969	+	14.6969i	0.767174	+	0.767174i	−0.210434	+	0.977608i	$0.567488\pi$
$368$	−2.07180	−	2.07180i	−0.108000	−	0.108000i
$369$		0			0
$370$		0			0
$371$		−	8.10634i		−	0.420860i
$372$		0			0
$373$	−19.7990	+	19.7990i	−1.02515	+	1.02515i	−0.0254774	+	0.999675i	$0.508111\pi$
$373$	−19.7990	+	19.7990i	−1.02515	+	1.02515i	−0.999675	+	0.0254774i	$0.991889\pi$
$374$	13.3843			0.692084
$375$		0			0
$376$	0.392305			0.0202316
$377$	3.60770	−	3.60770i	0.185806	−	0.185806i
$378$		0			0
$379$		−	34.3923i		−	1.76661i	−0.468795	−	0.883307i	$-0.655312\pi$
$379$		−	34.3923i		−	1.76661i	0.468795	−	0.883307i	$-0.344688\pi$
$380$		0			0
$381$		0			0
$382$	29.3567	+	29.3567i	1.50202	+	1.50202i
$383$	19.8564	+	19.8564i	1.01461	+	1.01461i	0.999892	+	0.0147234i	$0.00468676\pi$
$383$	19.8564	+	19.8564i	1.01461	+	1.01461i	0.0147234	+	0.999892i	$0.495313\pi$
$384$		0			0
$385$		0			0
$386$			18.0058i			0.916473i
$387$		0			0
$388$	23.6627	−	23.6627i	1.20129	−	1.20129i
$389$	24.7995			1.25738			0.628692	−	0.777654i	$-0.283590\pi$
$389$	24.7995			1.25738			0.628692	+	0.777654i	$0.283590\pi$
$390$		0			0
$391$	1.85641			0.0938825
$392$	0.366025	−	0.366025i	0.0184871	−	0.0184871i
$393$		0			0
$394$			37.5167i			1.89006i
$395$		0			0
$396$		0			0
$397$	3.86370	+	3.86370i	0.193914	+	0.193914i	0.797385	−	0.603471i	$-0.206216\pi$
$397$	3.86370	+	3.86370i	0.193914	+	0.193914i	−0.603471	+	0.797385i	$0.706216\pi$
$398$	−9.66025	−	9.66025i	−0.484225	−	0.484225i
$399$		0			0
$400$		0			0
$401$		−	2.92996i		−	0.146315i	−0.997320	−	0.0731577i	$-0.976692\pi$
$401$		−	2.92996i		−	0.146315i	0.997320	−	0.0731577i	$-0.0233076\pi$
$402$		0			0
$403$	9.24316	−	9.24316i	0.460434	−	0.460434i
$404$	−30.3548			−1.51021
$405$		0			0
$406$	6.73205			0.334106
$407$	12.9282	−	12.9282i	0.640827	−	0.640827i
$408$		0			0
$409$			4.92820i			0.243684i	0.992550	+	0.121842i	$0.0388801\pi$
$409$			4.92820i			0.243684i	−0.992550	+	0.121842i	$0.961120\pi$
$410$		0			0
$411$		0			0
$412$	14.6969	+	14.6969i	0.724066	+	0.724066i
$413$	4.92820	+	4.92820i	0.242501	+	0.242501i
$414$		0			0
$415$		0			0
$416$			11.1106i			0.544744i
$417$		0			0
$418$	−6.69213	+	6.69213i	−0.327323	+	0.327323i
$419$	−5.65685			−0.276355			−0.138178	−	0.990407i	$-0.544125\pi$
$419$	−5.65685			−0.276355			−0.138178	+	0.990407i	$0.544125\pi$
$420$		0			0
$421$	25.7128			1.25317			0.626583	−	0.779355i	$-0.284453\pi$
$421$	25.7128			1.25317			0.626583	+	0.779355i	$0.284453\pi$
$422$	10.1962	−	10.1962i	0.496341	−	0.496341i
$423$		0			0
$424$		−	4.19615i		−	0.203783i
$425$		0			0
$426$		0			0
$427$	−3.48477	−	3.48477i	−0.168640	−	0.168640i
$428$	−10.2679	−	10.2679i	−0.496320	−	0.496320i
$429$		0			0
$430$		0			0
$431$			0.378937i			0.0182528i	0.999958	+	0.00912639i	$0.00290506\pi$
$431$			0.378937i			0.0182528i	−0.999958	+	0.00912639i	$0.997095\pi$
$432$		0			0
$433$	15.1774	−	15.1774i	0.729380	−	0.729380i	−0.241116	−	0.970496i	$-0.577514\pi$
$433$	15.1774	−	15.1774i	0.729380	−	0.729380i	0.970496	+	0.241116i	$0.0775135\pi$
$434$	17.2480			0.827929
$435$		0			0
$436$	25.8564			1.23830
$437$	−0.928203	+	0.928203i	−0.0444020	+	0.0444020i
$438$		0			0
$439$		−	12.1436i		−	0.579582i	−0.957090	−	0.289791i	$-0.906414\pi$
$439$		−	12.1436i		−	0.579582i	0.957090	−	0.289791i	$-0.0935858\pi$
$440$		0			0
$441$		0			0
$442$	−5.65685	−	5.65685i	−0.269069	−	0.269069i
$443$	−1.92820	−	1.92820i	−0.0916117	−	0.0916117i	0.659816	−	0.751427i	$-0.270634\pi$
$443$	−1.92820	−	1.92820i	−0.0916117	−	0.0916117i	−0.751427	+	0.659816i	$0.770634\pi$
$444$		0			0
$445$		0			0
$446$			47.8802i			2.26719i
$447$		0			0
$448$	−4.05317	+	4.05317i	−0.191494	+	0.191494i
$449$	−2.92996			−0.138274			−0.0691368	−	0.997607i	$-0.522024\pi$
$449$	−2.92996			−0.138274			−0.0691368	+	0.997607i	$0.522024\pi$
$450$		0			0
$451$	−18.9282			−0.891294
$452$	6.46410	−	6.46410i	0.304046	−	0.304046i
$453$		0			0
$454$		−	12.0000i		−	0.563188i
$455$		0			0
$456$		0			0
$457$	6.79367	+	6.79367i	0.317794	+	0.317794i	0.847919	−	0.530125i	$-0.177855\pi$
$457$	6.79367	+	6.79367i	0.317794	+	0.317794i	−0.530125	+	0.847919i	$0.677855\pi$
$458$	15.1244	+	15.1244i	0.706715	+	0.706715i
$459$		0			0
$460$		0			0
$461$			0.203072i			0.00945800i	0.999989	+	0.00472900i	$0.00150529\pi$
$461$			0.203072i			0.00945800i	−0.999989	+	0.00472900i	$0.998495\pi$
$462$		0			0
$463$	−5.75839	+	5.75839i	−0.267615	+	0.267615i	−0.828139	−	0.560523i	$-0.810600\pi$
$463$	−5.75839	+	5.75839i	−0.267615	+	0.267615i	0.560523	+	0.828139i	$0.310600\pi$
$464$	15.5563			0.722185
$465$		0			0
$466$	10.1962			0.472328
$467$	−13.4641	+	13.4641i	−0.623044	+	0.623044i	−0.946309	−	0.323264i	$-0.895220\pi$
$467$	−13.4641	+	13.4641i	−0.623044	+	0.623044i	0.323264	+	0.946309i	$0.395220\pi$
$468$		0			0
$469$		−	4.92820i		−	0.227563i
$470$		0			0
$471$		0			0
$472$	2.55103	+	2.55103i	0.117420	+	0.117420i
$473$	−6.92820	−	6.92820i	−0.318559	−	0.318559i
$474$		0			0
$475$		0			0
$476$		−	4.89898i		−	0.224544i
$477$		0			0
$478$	30.3920	−	30.3920i	1.39010	−	1.39010i
$479$	40.1528			1.83463			0.917314	−	0.398165i	$-0.130353\pi$
$479$	40.1528			1.83463			0.917314	+	0.398165i	$0.130353\pi$
$480$		0			0
$481$	−10.9282			−0.498283
$482$	1.26795	−	1.26795i	0.0577535	−	0.0577535i
$483$		0			0
$484$		−	8.66025i		−	0.393648i
$485$		0			0
$486$		0			0
$487$	−9.24316	−	9.24316i	−0.418847	−	0.418847i	0.465959	−	0.884806i	$-0.345709\pi$
$487$	−9.24316	−	9.24316i	−0.418847	−	0.418847i	−0.884806	+	0.465959i	$0.845709\pi$
$488$	−1.80385	−	1.80385i	−0.0816563	−	0.0816563i
$489$		0			0
$490$		0			0
$491$		−	21.2875i		−	0.960693i	−0.877079	−	0.480346i	$-0.840511\pi$
$491$		−	21.2875i		−	0.960693i	0.877079	−	0.480346i	$-0.159489\pi$
$492$		0			0
$493$	−6.96953	+	6.96953i	−0.313892	+	0.313892i
$494$	5.65685			0.254514
$495$		0			0
$496$	39.8564			1.78961
$497$	7.19615	−	7.19615i	0.322792	−	0.322792i
$498$		0			0
$499$		−	17.3205i		−	0.775372i	−0.921791	−	0.387686i	$-0.873274\pi$
$499$		−	17.3205i		−	0.775372i	0.921791	−	0.387686i	$-0.126726\pi$
$500$		0			0
$501$		0			0
$502$	−19.3185	−	19.3185i	−0.862228	−	0.862228i
$503$	−0.928203	−	0.928203i	−0.0413865	−	0.0413865i	0.686111	−	0.727497i	$-0.259317\pi$
$503$	−0.928203	−	0.928203i	−0.0413865	−	0.0413865i	−0.727497	+	0.686111i	$0.759317\pi$
$504$		0			0
$505$		0			0
$506$			3.10583i			0.138071i
$507$		0			0
$508$	−24.3190	+	24.3190i	−1.07898	+	1.07898i
$509$	−29.0421			−1.28727			−0.643635	−	0.765332i	$-0.722575\pi$
$509$	−29.0421			−1.28727			−0.643635	+	0.765332i	$0.722575\pi$
$510$		0			0
$511$	5.46410			0.241718
$512$	−20.6865	+	20.6865i	−0.914224	+	0.914224i
$513$		0			0
$514$			58.6410i			2.58654i
$515$		0			0
$516$		0			0
$517$	−1.31268	−	1.31268i	−0.0577315	−	0.0577315i
$518$	−10.1962	−	10.1962i	−0.447993	−	0.447993i
$519$		0			0
$520$		0			0
$521$			39.9497i			1.75023i	0.483916	+	0.875114i	$0.339214\pi$
$521$			39.9497i			1.75023i	−0.483916	+	0.875114i	$0.660786\pi$
$522$		0			0
$523$	−2.82843	+	2.82843i	−0.123678	+	0.123678i	−0.766237	−	0.642558i	$-0.777873\pi$
$523$	−2.82843	+	2.82843i	−0.123678	+	0.123678i	0.642558	+	0.766237i	$0.277873\pi$
$524$	6.21166			0.271357
$525$		0			0
$526$	−36.5885			−1.59533
$527$	−17.8564	+	17.8564i	−0.777837	+	0.777837i
$528$		0			0
$529$		−	22.5692i		−	0.981270i
$530$		0			0
$531$		0			0
$532$	2.44949	+	2.44949i	0.106199	+	0.106199i
$533$	8.00000	+	8.00000i	0.346518	+	0.346518i
$534$		0			0
$535$		0			0
$536$		−	2.55103i		−	0.110188i
$537$		0			0
$538$	−1.03528	+	1.03528i	−0.0446339	+	0.0446339i
$539$	−2.44949			−0.105507
$540$		0			0
$541$	−15.8564			−0.681720			−0.340860	−	0.940114i	$-0.610718\pi$
$541$	−15.8564			−0.681720			−0.340860	+	0.940114i	$0.610718\pi$
$542$	−5.26795	+	5.26795i	−0.226278	+	0.226278i
$543$		0			0
$544$		−	21.4641i		−	0.920266i
$545$		0			0
$546$		0			0
$547$	−14.7985	−	14.7985i	−0.632737	−	0.632737i	0.316017	−	0.948754i	$-0.397654\pi$
$547$	−14.7985	−	14.7985i	−0.632737	−	0.632737i	−0.948754	+	0.316017i	$0.897654\pi$
$548$	5.53590	+	5.53590i	0.236482	+	0.236482i
$549$		0			0
$550$		0			0
$551$		−	6.96953i		−	0.296912i
$552$		0			0
$553$	2.82843	−	2.82843i	0.120277	−	0.120277i
$554$	−32.9802			−1.40119
$555$		0			0
$556$	27.4641			1.16474
$557$	17.7321	−	17.7321i	0.751331	−	0.751331i	−0.223397	−	0.974728i	$-0.571714\pi$
$557$	17.7321	−	17.7321i	0.751331	−	0.751331i	0.974728	+	0.223397i	$0.0717145\pi$
$558$		0			0
$559$			5.85641i			0.247700i
$560$		0			0
$561$		0			0
$562$	1.93185	+	1.93185i	0.0814902	+	0.0814902i
$563$	−18.7846	−	18.7846i	−0.791677	−	0.791677i	0.190090	−	0.981767i	$-0.439122\pi$
$563$	−18.7846	−	18.7846i	−0.791677	−	0.791677i	−0.981767	+	0.190090i	$0.939122\pi$
$564$		0			0
$565$		0			0
$566$		−	52.0213i		−	2.18662i
$567$		0			0
$568$	3.72500	−	3.72500i	0.156298	−	0.156298i
$569$	9.89949			0.415008			0.207504	−	0.978234i	$-0.433466\pi$
$569$	9.89949			0.415008			0.207504	+	0.978234i	$0.433466\pi$
$570$		0			0
$571$	9.85641			0.412478			0.206239	−	0.978502i	$-0.433878\pi$
$571$	9.85641			0.412478			0.206239	+	0.978502i	$0.433878\pi$
$572$	4.39230	−	4.39230i	0.183651	−	0.183651i
$573$		0			0
$574$			14.9282i			0.623091i
$575$		0			0
$576$		0			0
$577$	13.6617	+	13.6617i	0.568742	+	0.568742i	0.931776	−	0.363034i	$-0.118259\pi$
$577$	13.6617	+	13.6617i	0.568742	+	0.568742i	−0.363034	+	0.931776i	$0.618259\pi$
$578$	−12.2942	−	12.2942i	−0.511372	−	0.511372i
$579$		0			0
$580$		0			0
$581$		−	16.2127i		−	0.672616i
$582$		0			0
$583$	−14.0406	+	14.0406i	−0.581502	+	0.581502i
$584$	2.82843			0.117041
$585$		0			0
$586$	−33.8564			−1.39860
$587$	−14.0000	+	14.0000i	−0.577842	+	0.577842i	−0.934308	−	0.356466i	$-0.883981\pi$
$587$	−14.0000	+	14.0000i	−0.577842	+	0.577842i	0.356466	+	0.934308i	$0.383981\pi$
$588$		0			0
$589$		−	17.8564i		−	0.735760i
$590$		0			0
$591$		0			0
$592$	−23.5612	−	23.5612i	−0.968358	−	0.968358i
$593$	−21.8564	−	21.8564i	−0.897535	−	0.897535i	0.0976826	−	0.995218i	$-0.468857\pi$
$593$	−21.8564	−	21.8564i	−0.897535	−	0.897535i	−0.995218	+	0.0976826i	$0.968857\pi$
$594$		0			0
$595$		0			0
$596$			18.1074i			0.741707i
$597$		0			0
$598$	1.31268	−	1.31268i	0.0536794	−	0.0536794i
$599$	7.55154			0.308548			0.154274	−	0.988028i	$-0.450696\pi$
$599$	7.55154			0.308548			0.154274	+	0.988028i	$0.450696\pi$
$600$		0			0
$601$	−46.7846			−1.90838			−0.954192	−	0.299195i	$-0.903282\pi$
$601$	−46.7846			−1.90838			−0.954192	+	0.299195i	$0.903282\pi$
$602$	−5.46410	+	5.46410i	−0.222700	+	0.222700i
$603$		0			0
$604$			18.0000i			0.732410i
$605$		0			0
$606$		0			0
$607$	2.82843	+	2.82843i	0.114802	+	0.114802i	0.762174	−	0.647372i	$-0.224132\pi$
$607$	2.82843	+	2.82843i	0.114802	+	0.114802i	−0.647372	+	0.762174i	$0.724132\pi$
$608$	10.7321	+	10.7321i	0.435242	+	0.435242i
$609$		0			0
$610$		0			0
$611$			1.10961i			0.0448898i
$612$		0			0
$613$	20.3538	−	20.3538i	0.822082	−	0.822082i	−0.164324	−	0.986406i	$-0.552544\pi$
$613$	20.3538	−	20.3538i	0.822082	−	0.822082i	0.986406	+	0.164324i	$0.0525444\pi$
$614$	−49.9507			−2.01585
$615$		0			0
$616$	−1.26795			−0.0510871
$617$	9.05256	−	9.05256i	0.364442	−	0.364442i	−0.501003	−	0.865445i	$-0.667036\pi$
$617$	9.05256	−	9.05256i	0.364442	−	0.364442i	0.865445	+	0.501003i	$0.167036\pi$
$618$		0			0
$619$			12.9282i			0.519628i	0.965659	+	0.259814i	$0.0836613\pi$
$619$			12.9282i			0.519628i	−0.965659	+	0.259814i	$0.916339\pi$
$620$		0			0
$621$		0			0
$622$	−16.2127	−	16.2127i	−0.650070	−	0.650070i
$623$	10.0000	+	10.0000i	0.400642	+	0.400642i
$624$		0			0
$625$		0			0
$626$		−	14.1421i		−	0.565233i
$627$		0			0
$628$	21.3891	−	21.3891i	0.853517	−	0.853517i
$629$	21.1117			0.841777
$630$		0			0
$631$	−1.85641			−0.0739024			−0.0369512	−	0.999317i	$-0.511765\pi$
$631$	−1.85641			−0.0739024			−0.0369512	+	0.999317i	$0.511765\pi$
$632$	1.46410	−	1.46410i	0.0582388	−	0.0582388i
$633$		0			0
$634$			48.4449i			1.92399i
$635$		0			0
$636$		0			0
$637$	1.03528	+	1.03528i	0.0410191	+	0.0410191i
$638$	−11.6603	−	11.6603i	−0.461634	−	0.461634i
$639$		0			0
$640$		0			0
$641$		−	44.9502i		−	1.77543i	−0.460396	−	0.887714i	$-0.652293\pi$
$641$		−	44.9502i		−	1.77543i	0.460396	−	0.887714i	$-0.347707\pi$
$642$		0			0
$643$	−17.7284	+	17.7284i	−0.699141	+	0.699141i	−0.964225	−	0.265084i	$-0.914600\pi$
$643$	−17.7284	+	17.7284i	−0.699141	+	0.699141i	0.265084	+	0.964225i	$0.414600\pi$
$644$	1.13681			0.0447967
$645$		0			0
$646$	−10.9282			−0.429964
$647$	−20.0000	+	20.0000i	−0.786281	+	0.786281i	−0.980882	−	0.194601i	$-0.937659\pi$
$647$	−20.0000	+	20.0000i	−0.786281	+	0.786281i	0.194601	+	0.980882i	$0.437659\pi$
$648$		0			0
$649$		−	17.0718i		−	0.670127i
$650$		0			0
$651$		0			0
$652$	19.4201	+	19.4201i	0.760548	+	0.760548i
$653$	−20.6603	−	20.6603i	−0.808498	−	0.808498i	0.175908	−	0.984407i	$-0.443714\pi$
$653$	−20.6603	−	20.6603i	−0.808498	−	0.808498i	−0.984407	+	0.175908i	$0.943714\pi$
$654$		0			0
$655$		0			0
$656$			34.4959i			1.34684i
$657$		0			0
$658$	−1.03528	+	1.03528i	−0.0403593	+	0.0403593i
$659$	−20.1779			−0.786020			−0.393010	−	0.919534i	$-0.628566\pi$
$659$	−20.1779			−0.786020			−0.393010	+	0.919534i	$0.628566\pi$
$660$		0			0
$661$	−22.7846			−0.886219			−0.443109	−	0.896468i	$-0.646125\pi$
$661$	−22.7846			−0.886219			−0.443109	+	0.896468i	$0.646125\pi$
$662$	−32.0526	+	32.0526i	−1.24576	+	1.24576i
$663$		0			0
$664$		−	8.39230i		−	0.325685i
$665$		0			0
$666$		0			0
$667$	−1.61729	−	1.61729i	−0.0626215	−	0.0626215i
$668$	18.9282	+	18.9282i	0.732354	+	0.732354i
$669$		0			0
$670$		0			0
$671$			12.0716i			0.466018i
$672$		0			0
$673$	26.3896	−	26.3896i	1.01724	−	1.01724i	0.0173950	−	0.999849i	$-0.494463\pi$
$673$	26.3896	−	26.3896i	1.01724	−	1.01724i	0.999849	−	0.0173950i	$-0.00553729\pi$
$674$	2.55103			0.0982618
$675$		0			0
$676$	18.8038			0.723225
$677$	−7.32051	+	7.32051i	−0.281350	+	0.281350i	−0.833647	−	0.552297i	$-0.813751\pi$
$677$	−7.32051	+	7.32051i	−0.281350	+	0.281350i	0.552297	+	0.833647i	$0.313751\pi$
$678$		0			0
$679$		−	19.3205i		−	0.741453i
$680$		0			0
$681$		0			0
$682$	−29.8744	−	29.8744i	−1.14395	−	1.14395i
$683$	32.8564	+	32.8564i	1.25722	+	1.25722i	0.952417	+	0.304799i	$0.0985892\pi$
$683$	32.8564	+	32.8564i	1.25722	+	1.25722i	0.304799	+	0.952417i	$0.401411\pi$
$684$		0			0
$685$		0			0
$686$			1.93185i			0.0737584i
$687$		0			0
$688$	−12.6264	+	12.6264i	−0.481376	+	0.481376i
$689$	11.8685			0.452154
$690$		0			0
$691$	−30.7846			−1.17110			−0.585551	−	0.810636i	$-0.699122\pi$
$691$	−30.7846			−1.17110			−0.585551	+	0.810636i	$0.699122\pi$
$692$	−11.0718	+	11.0718i	−0.420887	+	0.420887i
$693$		0			0
$694$			2.73205i			0.103707i
$695$		0			0
$696$		0			0
$697$	−15.4548	−	15.4548i	−0.585393	−	0.585393i
$698$	35.1244	+	35.1244i	1.32948	+	1.32948i
$699$		0			0
$700$		0			0
$701$		−	27.4249i		−	1.03582i	−0.855434	−	0.517911i	$-0.826710\pi$
$701$		−	27.4249i		−	1.03582i	0.855434	−	0.517911i	$-0.173290\pi$
$702$		0			0
$703$	−10.5558	+	10.5558i	−0.398121	+	0.398121i
$704$	14.0406			0.529175
$705$		0			0
$706$	13.8564			0.521493
$707$	−12.3923	+	12.3923i	−0.466061	+	0.466061i
$708$		0			0
$709$			16.7846i			0.630359i	0.949032	+	0.315180i	$0.102065\pi$
$709$			16.7846i			0.630359i	−0.949032	+	0.315180i	$0.897935\pi$
$710$		0			0
$711$		0			0
$712$	5.17638	+	5.17638i	0.193993	+	0.193993i
$713$	−4.14359	−	4.14359i	−0.155179	−	0.155179i
$714$		0			0
$715$		0			0
$716$		−	6.86800i		−	0.256669i
$717$		0			0
$718$	−22.6646	+	22.6646i	−0.845835	+	0.845835i
$719$	−10.0010			−0.372976			−0.186488	−	0.982457i	$-0.559710\pi$
$719$	−10.0010			−0.372976			−0.186488	+	0.982457i	$0.559710\pi$
$720$		0			0
$721$	12.0000			0.446903
$722$	−20.4904	+	20.4904i	−0.762573	+	0.762573i
$723$		0			0
$724$			10.3923i			0.386227i
$725$		0			0
$726$		0			0
$727$	−30.9096	−	30.9096i	−1.14637	−	1.14637i	−0.987260	−	0.159114i	$-0.949136\pi$
$727$	−30.9096	−	30.9096i	−1.14637	−	1.14637i	−0.159114	−	0.987260i	$-0.550864\pi$
$728$	0.535898	+	0.535898i	0.0198617	+	0.0198617i
$729$		0			0
$730$		0			0
$731$		−	11.3137i		−	0.418453i
$732$		0			0
$733$	−13.8647	+	13.8647i	−0.512106	+	0.512106i	−0.915171	−	0.403065i	$-0.867945\pi$
$733$	−13.8647	+	13.8647i	−0.512106	+	0.512106i	0.403065	+	0.915171i	$0.367945\pi$
$734$	−40.1528			−1.48207
$735$		0			0
$736$	4.98076			0.183593
$737$	−8.53590	+	8.53590i	−0.314424	+	0.314424i
$738$		0			0
$739$			17.8564i			0.656859i	0.944529	+	0.328429i	$0.106519\pi$
$739$			17.8564i			0.656859i	−0.944529	+	0.328429i	$0.893481\pi$
$740$		0			0
$741$		0			0
$742$	11.0735	+	11.0735i	0.406520	+	0.406520i
$743$	29.3923	+	29.3923i	1.07830	+	1.07830i	0.996662	+	0.0816370i	$0.0260148\pi$
$743$	29.3923	+	29.3923i	1.07830	+	1.07830i	0.0816370	+	0.996662i	$0.473985\pi$
$744$		0			0
$745$		0			0
$746$		−	54.0918i		−	1.98044i
$747$		0			0
$748$	−8.48528	+	8.48528i	−0.310253	+	0.310253i
$749$	−8.38375			−0.306335
$750$		0			0
$751$	−26.1051			−0.952589			−0.476295	−	0.879286i	$-0.658020\pi$
$751$	−26.1051			−0.952589			−0.476295	+	0.879286i	$0.658020\pi$
$752$	−2.39230	+	2.39230i	−0.0872384	+	0.0872384i
$753$		0			0
$754$			9.85641i			0.358949i
$755$		0			0
$756$		0			0
$757$	16.3886	+	16.3886i	0.595652	+	0.595652i	0.939153	−	0.343500i	$-0.111613\pi$
$757$	16.3886	+	16.3886i	0.595652	+	0.595652i	−0.343500	+	0.939153i	$0.611613\pi$
$758$	46.9808	+	46.9808i	1.70642	+	1.70642i
$759$		0			0
$760$		0			0
$761$		−	32.2223i		−	1.16806i	−0.811733	−	0.584029i	$-0.801476\pi$
$761$		−	32.2223i		−	1.16806i	0.811733	−	0.584029i	$-0.198524\pi$
$762$		0			0
$763$	10.5558	−	10.5558i	0.382147	−	0.382147i
$764$	−37.2228			−1.34667
$765$		0			0
$766$	−54.2487			−1.96009
$767$	−7.21539	+	7.21539i	−0.260533	+	0.260533i
$768$		0			0
$769$			30.7846i			1.11012i	0.831810	+	0.555061i	$0.187305\pi$
$769$			30.7846i			1.11012i	−0.831810	+	0.555061i	$0.812695\pi$
$770$		0			0
$771$		0			0
$772$	−11.4152	−	11.4152i	−0.410844	−	0.410844i
$773$	−13.3205	−	13.3205i	−0.479105	−	0.479105i	0.425740	−	0.904845i	$-0.360014\pi$
$773$	−13.3205	−	13.3205i	−0.479105	−	0.479105i	−0.904845	+	0.425740i	$0.860014\pi$
$774$		0			0
$775$		0			0
$776$		−	10.0010i		−	0.359016i
$777$		0			0
$778$	−33.8768	+	33.8768i	−1.21454	+	1.21454i
$779$	15.4548			0.553726
$780$		0			0
$781$	−24.9282			−0.892001
$782$	−2.53590	+	2.53590i	−0.0906835	+	0.0906835i
$783$		0			0
$784$			4.46410i			0.159432i
$785$		0			0
$786$		0			0
$787$	−16.2127	−	16.2127i	−0.577920	−	0.577920i	0.356410	−	0.934330i	$-0.384001\pi$
$787$	−16.2127	−	16.2127i	−0.577920	−	0.577920i	−0.934330	+	0.356410i	$0.884001\pi$
$788$	−23.7846	−	23.7846i	−0.847292	−	0.847292i
$789$		0			0
$790$		0			0
$791$		−	5.27792i		−	0.187661i
$792$		0			0
$793$	5.10205	−	5.10205i	0.181179	−	0.181179i
$794$	−10.5558			−0.374613
$795$		0			0
$796$	12.2487			0.434144
$797$	35.1769	−	35.1769i	1.24603	−	1.24603i	0.288572	−	0.957458i	$-0.406820\pi$
$797$	35.1769	−	35.1769i	1.24603	−	1.24603i	0.957458	−	0.288572i	$-0.0931805\pi$
$798$		0			0
$799$		−	2.14359i		−	0.0758349i
$800$		0			0
$801$		0			0
$802$	4.00240	+	4.00240i	0.141330	+	0.141330i
$803$	−9.46410	−	9.46410i	−0.333981	−	0.333981i
$804$		0			0
$805$		0			0
$806$			25.2528i			0.889491i
$807$		0			0
$808$	−6.41473	+	6.41473i	−0.225669	+	0.225669i
$809$	24.0416			0.845259			0.422629	−	0.906303i	$-0.361107\pi$
$809$	24.0416			0.845259			0.422629	+	0.906303i	$0.361107\pi$
$810$		0			0
$811$	−11.0718			−0.388783			−0.194392	−	0.980924i	$-0.562273\pi$
$811$	−11.0718			−0.388783			−0.194392	+	0.980924i	$0.562273\pi$
$812$	−4.26795	+	4.26795i	−0.149776	+	0.149776i
$813$		0			0
$814$			35.3205i			1.23798i
$815$		0			0
$816$		0			0
$817$	5.65685	+	5.65685i	0.197908	+	0.197908i
$818$	−6.73205	−	6.73205i	−0.235381	−	0.235381i
$819$		0			0
$820$		0			0
$821$		−	2.17209i		−	0.0758064i	−0.999281	−	0.0379032i	$-0.987932\pi$
$821$		−	2.17209i		−	0.0758064i	0.999281	−	0.0379032i	$-0.0120679\pi$
$822$		0			0
$823$	−15.5563	+	15.5563i	−0.542260	+	0.542260i	−0.924191	−	0.381931i	$-0.875259\pi$
$823$	−15.5563	+	15.5563i	−0.542260	+	0.542260i	0.381931	+	0.924191i	$0.375259\pi$
$824$	6.21166			0.216393
$825$		0			0
$826$	−13.4641			−0.468476
$827$	−21.0000	+	21.0000i	−0.730242	+	0.730242i	−0.970667	−	0.240426i	$-0.922713\pi$
$827$	−21.0000	+	21.0000i	−0.730242	+	0.730242i	0.240426	+	0.970667i	$0.422713\pi$
$828$		0			0
$829$		−	10.7846i		−	0.374565i	−0.982306	−	0.187282i	$-0.940032\pi$
$829$		−	10.7846i		−	0.374565i	0.982306	−	0.187282i	$-0.0599680\pi$
$830$		0			0
$831$		0			0
$832$	−5.93426	−	5.93426i	−0.205733	−	0.205733i
$833$	−2.00000	−	2.00000i	−0.0692959	−	0.0692959i
$834$		0			0
$835$		0			0
$836$		−	8.48528i		−	0.293470i
$837$		0			0
$838$	7.72741	−	7.72741i	0.266939	−	0.266939i
$839$	−13.1812			−0.455065			−0.227533	−	0.973770i	$-0.573066\pi$
$839$	−13.1812			−0.455065			−0.227533	+	0.973770i	$0.573066\pi$
$840$		0			0
$841$	−16.8564			−0.581255
$842$	−35.1244	+	35.1244i	−1.21047	+	1.21047i
$843$		0			0
$844$			12.9282i			0.445007i
$845$		0			0
$846$		0			0
$847$	−3.53553	−	3.53553i	−0.121482	−	0.121482i
$848$	25.5885	+	25.5885i	0.878711	+	0.878711i
$849$		0			0
$850$		0			0
$851$			4.89898i			0.167935i
$852$		0			0
$853$	−7.24693	+	7.24693i	−0.248130	+	0.248130i	−0.820203	−	0.572073i	$-0.806140\pi$
$853$	−7.24693	+	7.24693i	−0.248130	+	0.248130i	0.572073	+	0.820203i	$0.306140\pi$
$854$	9.52056			0.325787
$855$		0			0
$856$	−4.33975			−0.148329
$857$	10.3923	−	10.3923i	0.354994	−	0.354994i	−0.506970	−	0.861964i	$-0.669234\pi$
$857$	10.3923	−	10.3923i	0.354994	−	0.354994i	0.861964	+	0.506970i	$0.169234\pi$
$858$		0			0
$859$		−	22.7846i		−	0.777401i	−0.921364	−	0.388700i	$-0.872924\pi$
$859$		−	22.7846i		−	0.777401i	0.921364	−	0.388700i	$-0.127076\pi$
$860$		0			0
$861$		0			0
$862$	−0.517638	−	0.517638i	−0.0176308	−	0.0176308i
$863$	25.2487	+	25.2487i	0.859476	+	0.859476i	0.991276	−	0.131800i	$-0.0420757\pi$
$863$	25.2487	+	25.2487i	0.859476	+	0.859476i	−0.131800	+	0.991276i	$0.542076\pi$
$864$		0			0
$865$		0			0
$866$			41.4655i			1.40905i
$867$		0			0
$868$	−10.9348	+	10.9348i	−0.371150	+	0.371150i
$869$	−9.79796			−0.332373
$870$		0			0
$871$	7.21539			0.244484
$872$	5.46410	−	5.46410i	0.185038	−	0.185038i
$873$		0			0
$874$		−	2.53590i		−	0.0857780i
$875$		0			0
$876$		0			0
$877$	31.6675	+	31.6675i	1.06934	+	1.06934i	0.997410	+	0.0719255i	$0.0229144\pi$
$877$	31.6675	+	31.6675i	1.06934	+	1.06934i	0.0719255	+	0.997410i	$0.477086\pi$
$878$	16.5885	+	16.5885i	0.559833	+	0.559833i
$879$		0			0
$880$		0			0
$881$			33.9411i			1.14351i	0.820426	+	0.571753i	$0.193736\pi$
$881$			33.9411i			1.14351i	−0.820426	+	0.571753i	$0.806264\pi$
$882$		0			0
$883$	24.4949	−	24.4949i	0.824319	−	0.824319i	−0.162405	−	0.986724i	$-0.551925\pi$
$883$	24.4949	−	24.4949i	0.824319	−	0.824319i	0.986724	+	0.162405i	$0.0519252\pi$
$884$	7.17260			0.241241
$885$		0			0
$886$	5.26795			0.176980
$887$	−6.67949	+	6.67949i	−0.224275	+	0.224275i	−0.810296	−	0.586021i	$-0.800694\pi$
$887$	−6.67949	+	6.67949i	−0.224275	+	0.224275i	0.586021	+	0.810296i	$0.300694\pi$
$888$		0			0
$889$			19.8564i			0.665962i
$890$		0			0
$891$		0			0
$892$	−30.3548	−	30.3548i	−1.01635	−	1.01635i
$893$	1.07180	+	1.07180i	0.0358663	+	0.0358663i
$894$		0			0
$895$		0			0
$896$			4.10394i			0.137103i
$897$		0			0
$898$	4.00240	−	4.00240i	0.133562	−	0.133562i
$899$	31.1127			1.03767
$900$		0			0
$901$	−22.9282			−0.763849
$902$	25.8564	−	25.8564i	0.860924	−	0.860924i
$903$		0			0
$904$		−	2.73205i		−	0.0908667i
$905$		0			0
$906$		0			0
$907$	−21.8695	−	21.8695i	−0.726166	−	0.726166i	0.243688	−	0.969854i	$-0.421643\pi$
$907$	−21.8695	−	21.8695i	−0.726166	−	0.726166i	−0.969854	+	0.243688i	$0.921643\pi$
$908$	7.60770	+	7.60770i	0.252470	+	0.252470i
$909$		0			0
$910$		0			0
$911$		−	32.0464i		−	1.06175i	−0.847451	−	0.530873i	$-0.821864\pi$
$911$		−	32.0464i		−	1.06175i	0.847451	−	0.530873i	$-0.178136\pi$
$912$		0			0
$913$	−28.0812	+	28.0812i	−0.929352	+	0.929352i
$914$	−18.5606			−0.613931
$915$		0			0
$916$	−19.1769			−0.633623
$917$	2.53590	−	2.53590i	0.0837427	−	0.0837427i
$918$		0			0
$919$		−	11.1769i		−	0.368692i	−0.982861	−	0.184346i	$-0.940983\pi$
$919$		−	11.1769i		−	0.368692i	0.982861	−	0.184346i	$-0.0590168\pi$
$920$		0			0
$921$		0			0
$922$	−0.277401	−	0.277401i	−0.00913573	−	0.00913573i
$923$	10.5359	+	10.5359i	0.346793	+	0.346793i
$924$		0			0
$925$		0			0
$926$		−	15.7322i		−	0.516993i
$927$		0			0
$928$	−18.6993	+	18.6993i	−0.613836	+	0.613836i
$929$	−4.34418			−0.142528			−0.0712639	−	0.997457i	$-0.522703\pi$
$929$	−4.34418			−0.142528			−0.0712639	+	0.997457i	$0.522703\pi$
$930$		0			0
$931$	2.00000			0.0655474
$932$	−6.46410	+	6.46410i	−0.211739	+	0.211739i
$933$		0			0
$934$		−	36.7846i		−	1.20363i
$935$		0			0
$936$		0			0
$937$	−37.0470	−	37.0470i	−1.21027	−	1.21027i	−0.970937	−	0.239334i	$-0.923071\pi$
$937$	−37.0470	−	37.0470i	−1.21027	−	1.21027i	−0.239334	−	0.970937i	$-0.576929\pi$
$938$	6.73205	+	6.73205i	0.219809	+	0.219809i
$939$		0			0
$940$		0			0
$941$			1.51575i			0.0494120i	0.999695	+	0.0247060i	$0.00786497\pi$
$941$			1.51575i			0.0494120i	−0.999695	+	0.0247060i	$0.992135\pi$
$942$		0			0
$943$	3.58630	−	3.58630i	0.116786	−	0.116786i
$944$	−31.1127			−1.01263
$945$		0			0
$946$	18.9282			0.615409
$947$	−31.0000	+	31.0000i	−1.00736	+	1.00736i	−0.00739197	+	0.999973i	$0.502353\pi$
$947$	−31.0000	+	31.0000i	−1.00736	+	1.00736i	−0.999973	+	0.00739197i	$0.997647\pi$
$948$		0			0
$949$			8.00000i			0.259691i
$950$		0			0
$951$		0			0
$952$	−1.03528	−	1.03528i	−0.0335535	−	0.0335535i
$953$	−21.3397	−	21.3397i	−0.691262	−	0.691262i	0.271247	−	0.962510i	$-0.412564\pi$
$953$	−21.3397	−	21.3397i	−0.691262	−	0.691262i	−0.962510	+	0.271247i	$0.912564\pi$
$954$		0			0
$955$		0			0
$956$			38.5355i			1.24633i
$957$		0			0
$958$	−54.8497	+	54.8497i	−1.77211	+	1.77211i
$959$	4.52004			0.145960
$960$		0			0
$961$	48.7128			1.57138
$962$	14.9282	−	14.9282i	0.481305	−	0.481305i
$963$		0			0
$964$			1.60770i			0.0517804i
$965$		0			0
$966$		0			0
$967$	−9.34469	−	9.34469i	−0.300505	−	0.300505i	0.540706	−	0.841211i	$-0.318157\pi$
$967$	−9.34469	−	9.34469i	−0.300505	−	0.300505i	−0.841211	+	0.540706i	$0.818157\pi$
$968$	−1.83013	−	1.83013i	−0.0588225	−	0.0588225i
$969$		0			0
$970$		0			0
$971$			0.757875i			0.0243214i	0.999926	+	0.0121607i	$0.00387096\pi$
$971$			0.757875i			0.0243214i	−0.999926	+	0.0121607i	$0.996129\pi$
$972$		0			0
$973$	11.2122	−	11.2122i	0.359446	−	0.359446i
$974$	25.2528			0.809151
$975$		0			0
$976$	22.0000			0.704203
$977$	12.2679	−	12.2679i	0.392486	−	0.392486i	−0.483086	−	0.875573i	$-0.660484\pi$
$977$	12.2679	−	12.2679i	0.392486	−	0.392486i	0.875573	+	0.483086i	$0.160484\pi$
$978$		0			0
$979$		−	34.6410i		−	1.10713i
$980$		0			0
$981$		0			0
$982$	29.0793	+	29.0793i	0.927958	+	0.927958i
$983$	−11.3205	−	11.3205i	−0.361068	−	0.361068i	0.503138	−	0.864206i	$-0.332179\pi$
$983$	−11.3205	−	11.3205i	−0.361068	−	0.361068i	−0.864206	+	0.503138i	$0.832179\pi$
$984$		0			0
$985$		0			0
$986$		−	19.0411i		−	0.606393i
$987$		0			0
$988$	−3.58630	+	3.58630i	−0.114095	+	0.114095i
$989$	2.62536			0.0834814
$990$		0			0
$991$	21.3205			0.677268			0.338634	−	0.940918i	$-0.390035\pi$
$991$	21.3205			0.677268			0.338634	+	0.940918i	$0.390035\pi$
$992$	−47.9090	+	47.9090i	−1.52111	+	1.52111i
$993$		0			0
$994$			19.6603i			0.623585i
$995$		0			0
$996$		0			0
$997$	28.5617	+	28.5617i	0.904557	+	0.904557i	0.995826	−	0.0912690i	$-0.0290923\pi$
$997$	28.5617	+	28.5617i	0.904557	+	0.904557i	−0.0912690	+	0.995826i	$0.529092\pi$
$998$	23.6603	+	23.6603i	0.748952	+	0.748952i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1575.2.m.a.1457.1	yes	8
3.2	odd	2		1575.2.m.b.1457.3	yes	8
5.2	odd	4	inner	1575.2.m.a.1268.2	yes	8
5.3	odd	4		1575.2.m.b.1268.3	yes	8
5.4	even	2		1575.2.m.b.1457.4	yes	8
15.2	even	4		1575.2.m.b.1268.4	yes	8
15.8	even	4	inner	1575.2.m.a.1268.1	✓	8
15.14	odd	2	inner	1575.2.m.a.1457.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1575.2.m.a.1268.1	✓	8	15.8	even	4	inner
1575.2.m.a.1268.2	yes	8	5.2	odd	4	inner
1575.2.m.a.1457.1	yes	8	1.1	even	1	trivial
1575.2.m.a.1457.2	yes	8	15.14	odd	2	inner
1575.2.m.b.1268.3	yes	8	5.3	odd	4
1575.2.m.b.1268.4	yes	8	15.2	even	4
1575.2.m.b.1457.3	yes	8	3.2	odd	2
1575.2.m.b.1457.4	yes	8	5.4	even	2

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:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1575.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 + 1.36603i) q^{2} -1.73205i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.366025 - 0.366025i) q^{8} +O(q^{10})\)	\(q+(-1.36603 + 1.36603i) q^{2} -1.73205i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.366025 - 0.366025i) q^{8} +2.44949i q^{11} +(1.03528 - 1.03528i) q^{13} +1.93185 q^{14} +4.46410 q^{16} +(-2.00000 + 2.00000i) q^{17} -2.00000i q^{19} +(-3.34607 - 3.34607i) q^{22} +(-0.464102 - 0.464102i) q^{23} +2.82843i q^{26} +(-1.22474 + 1.22474i) q^{28} +3.48477 q^{29} +8.92820 q^{31} +(-5.36603 + 5.36603i) q^{32} -5.46410i q^{34} +(-5.27792 - 5.27792i) q^{37} +(2.73205 + 2.73205i) q^{38} +7.72741i q^{41} +(-2.82843 + 2.82843i) q^{43} +4.24264 q^{44} +1.26795 q^{46} +(-0.535898 + 0.535898i) q^{47} +1.00000i q^{49} +(-1.79315 - 1.79315i) q^{52} +(5.73205 + 5.73205i) q^{53} +0.517638i q^{56} +(-4.76028 + 4.76028i) q^{58} -6.96953 q^{59} +4.92820 q^{61} +(-12.1962 + 12.1962i) q^{62} -5.73205i q^{64} +(3.48477 + 3.48477i) q^{67} +(3.46410 + 3.46410i) q^{68} +10.1769i q^{71} +(-3.86370 + 3.86370i) q^{73} +14.4195 q^{74} -3.46410 q^{76} +(1.73205 - 1.73205i) q^{77} +4.00000i q^{79} +(-10.5558 - 10.5558i) q^{82} +(11.4641 + 11.4641i) q^{83} -7.72741i q^{86} +(0.896575 - 0.896575i) q^{88} -14.1421 q^{89} -1.46410 q^{91} +(-0.803848 + 0.803848i) q^{92} -1.46410i q^{94} +(13.6617 + 13.6617i) q^{97} +(-1.36603 - 1.36603i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 4 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 + 4 * q^8	\( 8 q - 4 q^{2} + 4 q^{8} + 8 q^{16} - 16 q^{17} + 24 q^{23} + 16 q^{31} - 36 q^{32} + 8 q^{38} + 24 q^{46} - 32 q^{47} + 32 q^{53} - 16 q^{61} - 56 q^{62} + 64 q^{83} + 16 q^{91} - 48 q^{92} - 4 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 4 * q^8 + 8 * q^16 - 16 * q^17 + 24 * q^23 + 16 * q^31 - 36 * q^32 + 8 * q^38 + 24 * q^46 - 32 * q^47 + 32 * q^53 - 16 * q^61 - 56 * q^62 + 64 * q^83 + 16 * q^91 - 48 * q^92 - 4 * q^98

Introduction

L-functions

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