LMFDB - Embedded newform 196.2.d.b.195.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,2,Mod(195,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("196.195");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.d (of order $2$, degree $1$, 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:	$1.56506787962$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			195.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	196.195
Dual form			196.2.d.b.195.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} -1.73205 q^{3} -2.00000i q^{4} -1.73205i q^{5} +(-1.73205 + 1.73205i) q^{6} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} -1.73205 q^{3} -2.00000i q^{4} -1.73205i q^{5} +(-1.73205 + 1.73205i) q^{6} +(-2.00000 - 2.00000i) q^{8} +(-1.73205 - 1.73205i) q^{10} -1.00000i q^{11} +3.46410i q^{12} -3.46410i q^{13} +3.00000i q^{15} -4.00000 q^{16} +1.73205i q^{17} +5.19615 q^{19} -3.46410 q^{20} +(-1.00000 - 1.00000i) q^{22} +1.00000i q^{23} +(3.46410 + 3.46410i) q^{24} +2.00000 q^{25} +(-3.46410 - 3.46410i) q^{26} +5.19615 q^{27} +4.00000 q^{29} +(3.00000 + 3.00000i) q^{30} +1.73205 q^{31} +(-4.00000 + 4.00000i) q^{32} +1.73205i q^{33} +(1.73205 + 1.73205i) q^{34} +3.00000 q^{37} +(5.19615 - 5.19615i) q^{38} +6.00000i q^{39} +(-3.46410 + 3.46410i) q^{40} +3.46410i q^{41} +2.00000i q^{43} -2.00000 q^{44} +(1.00000 + 1.00000i) q^{46} -8.66025 q^{47} +6.92820 q^{48} +(2.00000 - 2.00000i) q^{50} -3.00000i q^{51} -6.92820 q^{52} -1.00000 q^{53} +(5.19615 - 5.19615i) q^{54} -1.73205 q^{55} -9.00000 q^{57} +(4.00000 - 4.00000i) q^{58} +5.19615 q^{59} +6.00000 q^{60} -5.19615i q^{61} +(1.73205 - 1.73205i) q^{62} +8.00000i q^{64} -6.00000 q^{65} +(1.73205 + 1.73205i) q^{66} -3.00000i q^{67} +3.46410 q^{68} -1.73205i q^{69} -14.0000i q^{71} -8.66025i q^{73} +(3.00000 - 3.00000i) q^{74} -3.46410 q^{75} -10.3923i q^{76} +(6.00000 + 6.00000i) q^{78} +9.00000i q^{79} +6.92820i q^{80} -9.00000 q^{81} +(3.46410 + 3.46410i) q^{82} -13.8564 q^{83} +3.00000 q^{85} +(2.00000 + 2.00000i) q^{86} -6.92820 q^{87} +(-2.00000 + 2.00000i) q^{88} +15.5885i q^{89} +2.00000 q^{92} -3.00000 q^{93} +(-8.66025 + 8.66025i) q^{94} -9.00000i q^{95} +(6.92820 - 6.92820i) q^{96} +17.3205i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 8 * q^8	$ 4 q + 4 q^{2} - 8 q^{8} - 16 q^{16} - 4 q^{22} + 8 q^{25} + 16 q^{29} + 12 q^{30} - 16 q^{32} + 12 q^{37} - 8 q^{44} + 4 q^{46} + 8 q^{50} - 4 q^{53} - 36 q^{57} + 16 q^{58} + 24 q^{60} - 24 q^{65} + 12 q^{74} + 24 q^{78} - 36 q^{81} + 12 q^{85} + 8 q^{86} - 8 q^{88} + 8 q^{92} - 12 q^{93}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^8 - 16 * q^16 - 4 * q^22 + 8 * q^25 + 16 * q^29 + 12 * q^30 - 16 * q^32 + 12 * q^37 - 8 * q^44 + 4 * q^46 + 8 * q^50 - 4 * q^53 - 36 * q^57 + 16 * q^58 + 24 * q^60 - 24 * q^65 + 12 * q^74 + 24 * q^78 - 36 * q^81 + 12 * q^85 + 8 * q^86 - 8 * q^88 + 8 * q^92 - 12 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.00000	−	1.00000i	0.707107	−	0.707107i
$2$	1.00000	−	1.00000i	0.707107	−	0.707107i
$3$	−1.73205			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$3$	−1.73205			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$4$		−	2.00000i		−	1.00000i
$5$		−	1.73205i		−	0.774597i	−0.921954	−	0.387298i	$-0.873408\pi$
$5$		−	1.73205i		−	0.774597i	0.921954	−	0.387298i	$-0.126592\pi$
$6$	−1.73205	+	1.73205i	−0.707107	+	0.707107i
$7$		0			0
$7$		0			0
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$		0			0
$10$	−1.73205	−	1.73205i	−0.547723	−	0.547723i
$11$		−	1.00000i		−	0.301511i	−0.988571	−	0.150756i	$-0.951829\pi$
$11$		−	1.00000i		−	0.301511i	0.988571	−	0.150756i	$-0.0481707\pi$
$12$			3.46410i			1.00000i
$13$		−	3.46410i		−	0.960769i	−0.877058	−	0.480384i	$-0.840497\pi$
$13$		−	3.46410i		−	0.960769i	0.877058	−	0.480384i	$-0.159503\pi$
$14$		0			0
$15$			3.00000i			0.774597i
$16$	−4.00000			−1.00000
$17$			1.73205i			0.420084i	0.977692	+	0.210042i	$0.0673601\pi$
$17$			1.73205i			0.420084i	−0.977692	+	0.210042i	$0.932640\pi$
$18$		0			0
$19$	5.19615			1.19208			0.596040	−	0.802955i	$-0.296740\pi$
$19$	5.19615			1.19208			0.596040	+	0.802955i	$0.296740\pi$
$20$	−3.46410			−0.774597
$21$		0			0
$22$	−1.00000	−	1.00000i	−0.213201	−	0.213201i
$23$			1.00000i			0.208514i	0.994550	+	0.104257i	$0.0332465\pi$
$23$			1.00000i			0.208514i	−0.994550	+	0.104257i	$0.966753\pi$
$24$	3.46410	+	3.46410i	0.707107	+	0.707107i
$25$	2.00000			0.400000
$26$	−3.46410	−	3.46410i	−0.679366	−	0.679366i
$27$	5.19615			1.00000
$28$		0			0
$29$	4.00000			0.742781			0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000			0.742781			0.371391	+	0.928477i	$0.378881\pi$
$30$	3.00000	+	3.00000i	0.547723	+	0.547723i
$31$	1.73205			0.311086			0.155543	−	0.987829i	$-0.450287\pi$
$31$	1.73205			0.311086			0.155543	+	0.987829i	$0.450287\pi$
$32$	−4.00000	+	4.00000i	−0.707107	+	0.707107i
$33$			1.73205i			0.301511i
$34$	1.73205	+	1.73205i	0.297044	+	0.297044i
$35$		0			0
$36$		0			0
$37$	3.00000			0.493197			0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000			0.493197			0.246598	+	0.969118i	$0.420687\pi$
$38$	5.19615	−	5.19615i	0.842927	−	0.842927i
$39$			6.00000i			0.960769i
$40$	−3.46410	+	3.46410i	−0.547723	+	0.547723i
$41$			3.46410i			0.541002i	0.962720	+	0.270501i	$0.0871893\pi$
$41$			3.46410i			0.541002i	−0.962720	+	0.270501i	$0.912811\pi$
$42$		0			0
$43$			2.00000i			0.304997i	0.988304	+	0.152499i	$0.0487319\pi$
$43$			2.00000i			0.304997i	−0.988304	+	0.152499i	$0.951268\pi$
$44$	−2.00000			−0.301511
$45$		0			0
$46$	1.00000	+	1.00000i	0.147442	+	0.147442i
$47$	−8.66025			−1.26323			−0.631614	−	0.775283i	$-0.717607\pi$
$47$	−8.66025			−1.26323			−0.631614	+	0.775283i	$0.717607\pi$
$48$	6.92820			1.00000
$49$		0			0
$50$	2.00000	−	2.00000i	0.282843	−	0.282843i
$51$		−	3.00000i		−	0.420084i
$52$	−6.92820			−0.960769
$53$	−1.00000			−0.137361			−0.0686803	−	0.997639i	$-0.521879\pi$
$53$	−1.00000			−0.137361			−0.0686803	+	0.997639i	$0.521879\pi$
$54$	5.19615	−	5.19615i	0.707107	−	0.707107i
$55$	−1.73205			−0.233550
$56$		0			0
$57$	−9.00000			−1.19208
$58$	4.00000	−	4.00000i	0.525226	−	0.525226i
$59$	5.19615			0.676481			0.338241	−	0.941060i	$-0.390168\pi$
$59$	5.19615			0.676481			0.338241	+	0.941060i	$0.390168\pi$
$60$	6.00000			0.774597
$61$		−	5.19615i		−	0.665299i	−0.943051	−	0.332650i	$-0.892057\pi$
$61$		−	5.19615i		−	0.665299i	0.943051	−	0.332650i	$-0.107943\pi$
$62$	1.73205	−	1.73205i	0.219971	−	0.219971i
$63$		0			0
$64$			8.00000i			1.00000i
$65$	−6.00000			−0.744208
$66$	1.73205	+	1.73205i	0.213201	+	0.213201i
$67$		−	3.00000i		−	0.366508i	−0.983066	−	0.183254i	$-0.941337\pi$
$67$		−	3.00000i		−	0.366508i	0.983066	−	0.183254i	$-0.0586631\pi$
$68$	3.46410			0.420084
$69$		−	1.73205i		−	0.208514i
$70$		0			0
$71$		−	14.0000i		−	1.66149i	−0.556650	−	0.830747i	$-0.687914\pi$
$71$		−	14.0000i		−	1.66149i	0.556650	−	0.830747i	$-0.312086\pi$
$72$		0			0
$73$		−	8.66025i		−	1.01361i	−0.862062	−	0.506803i	$-0.830827\pi$
$73$		−	8.66025i		−	1.01361i	0.862062	−	0.506803i	$-0.169173\pi$
$74$	3.00000	−	3.00000i	0.348743	−	0.348743i
$75$	−3.46410			−0.400000
$76$		−	10.3923i		−	1.19208i
$77$		0			0
$78$	6.00000	+	6.00000i	0.679366	+	0.679366i
$79$			9.00000i			1.01258i	0.862364	+	0.506290i	$0.168983\pi$
$79$			9.00000i			1.01258i	−0.862364	+	0.506290i	$0.831017\pi$
$80$			6.92820i			0.774597i
$81$	−9.00000			−1.00000
$82$	3.46410	+	3.46410i	0.382546	+	0.382546i
$83$	−13.8564			−1.52094			−0.760469	−	0.649374i	$-0.775031\pi$
$83$	−13.8564			−1.52094			−0.760469	+	0.649374i	$0.775031\pi$
$84$		0			0
$85$	3.00000			0.325396
$86$	2.00000	+	2.00000i	0.215666	+	0.215666i
$87$	−6.92820			−0.742781
$88$	−2.00000	+	2.00000i	−0.213201	+	0.213201i
$89$			15.5885i			1.65237i	0.563397	+	0.826187i	$0.309494\pi$
$89$			15.5885i			1.65237i	−0.563397	+	0.826187i	$0.690506\pi$
$90$		0			0
$91$		0			0
$92$	2.00000			0.208514
$93$	−3.00000			−0.311086
$94$	−8.66025	+	8.66025i	−0.893237	+	0.893237i
$95$		−	9.00000i		−	0.923381i
$96$	6.92820	−	6.92820i	0.707107	−	0.707107i
$97$			17.3205i			1.75863i	0.476240	+	0.879316i	$0.342000\pi$
$97$			17.3205i			1.75863i	−0.476240	+	0.879316i	$0.658000\pi$
$98$		0			0
$99$		0			0
$100$		−	4.00000i		−	0.400000i
$101$			8.66025i			0.861727i	0.902417	+	0.430864i	$0.141791\pi$
$101$			8.66025i			0.861727i	−0.902417	+	0.430864i	$0.858209\pi$
$102$	−3.00000	−	3.00000i	−0.297044	−	0.297044i
$103$	8.66025			0.853320			0.426660	−	0.904412i	$-0.359690\pi$
$103$	8.66025			0.853320			0.426660	+	0.904412i	$0.359690\pi$
$104$	−6.92820	+	6.92820i	−0.679366	+	0.679366i
$105$		0			0
$106$	−1.00000	+	1.00000i	−0.0971286	+	0.0971286i
$107$		−	13.0000i		−	1.25676i	−0.777908	−	0.628379i	$-0.783719\pi$
$107$		−	13.0000i		−	1.25676i	0.777908	−	0.628379i	$-0.216281\pi$
$108$		−	10.3923i		−	1.00000i
$109$	9.00000			0.862044			0.431022	−	0.902342i	$-0.358153\pi$
$109$	9.00000			0.862044			0.431022	+	0.902342i	$0.358153\pi$
$110$	−1.73205	+	1.73205i	−0.165145	+	0.165145i
$111$	−5.19615			−0.493197
$112$		0			0
$113$	−16.0000			−1.50515			−0.752577	−	0.658505i	$-0.771189\pi$
$113$	−16.0000			−1.50515			−0.752577	+	0.658505i	$0.771189\pi$
$114$	−9.00000	+	9.00000i	−0.842927	+	0.842927i
$115$	1.73205			0.161515
$116$		−	8.00000i		−	0.742781i
$117$		0			0
$118$	5.19615	−	5.19615i	0.478345	−	0.478345i
$119$		0			0
$120$	6.00000	−	6.00000i	0.547723	−	0.547723i
$121$	10.0000			0.909091
$122$	−5.19615	−	5.19615i	−0.470438	−	0.470438i
$123$		−	6.00000i		−	0.541002i
$124$		−	3.46410i		−	0.311086i
$125$		−	12.1244i		−	1.08444i
$126$		0			0
$127$			6.00000i			0.532414i	0.963916	+	0.266207i	$0.0857705\pi$
$127$			6.00000i			0.532414i	−0.963916	+	0.266207i	$0.914230\pi$
$128$	8.00000	+	8.00000i	0.707107	+	0.707107i
$129$		−	3.46410i		−	0.304997i
$130$	−6.00000	+	6.00000i	−0.526235	+	0.526235i
$131$	−5.19615			−0.453990			−0.226995	−	0.973896i	$-0.572890\pi$
$131$	−5.19615			−0.453990			−0.226995	+	0.973896i	$0.572890\pi$
$132$	3.46410			0.301511
$133$		0			0
$134$	−3.00000	−	3.00000i	−0.259161	−	0.259161i
$135$		−	9.00000i		−	0.774597i
$136$	3.46410	−	3.46410i	0.297044	−	0.297044i
$137$	1.00000			0.0854358			0.0427179	−	0.999087i	$-0.486398\pi$
$137$	1.00000			0.0854358			0.0427179	+	0.999087i	$0.486398\pi$
$138$	−1.73205	−	1.73205i	−0.147442	−	0.147442i
$139$	6.92820			0.587643			0.293821	−	0.955860i	$-0.405073\pi$
$139$	6.92820			0.587643			0.293821	+	0.955860i	$0.405073\pi$
$140$		0			0
$141$	15.0000			1.26323
$142$	−14.0000	−	14.0000i	−1.17485	−	1.17485i
$143$	−3.46410			−0.289683
$144$		0			0
$145$		−	6.92820i		−	0.575356i
$146$	−8.66025	−	8.66025i	−0.716728	−	0.716728i
$147$		0			0
$148$		−	6.00000i		−	0.493197i
$149$	1.00000			0.0819232			0.0409616	−	0.999161i	$-0.486958\pi$
$149$	1.00000			0.0819232			0.0409616	+	0.999161i	$0.486958\pi$
$150$	−3.46410	+	3.46410i	−0.282843	+	0.282843i
$151$			7.00000i			0.569652i	0.958579	+	0.284826i	$0.0919358\pi$
$151$			7.00000i			0.569652i	−0.958579	+	0.284826i	$0.908064\pi$
$152$	−10.3923	−	10.3923i	−0.842927	−	0.842927i
$153$		0			0
$154$		0			0
$155$		−	3.00000i		−	0.240966i
$156$	12.0000			0.960769
$157$		−	1.73205i		−	0.138233i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$		−	1.73205i		−	0.138233i	0.997609	−	0.0691164i	$-0.0220180\pi$
$158$	9.00000	+	9.00000i	0.716002	+	0.716002i
$159$	1.73205			0.137361
$160$	6.92820	+	6.92820i	0.547723	+	0.547723i
$161$		0			0
$162$	−9.00000	+	9.00000i	−0.707107	+	0.707107i
$163$			21.0000i			1.64485i	0.568876	+	0.822423i	$0.307379\pi$
$163$			21.0000i			1.64485i	−0.568876	+	0.822423i	$0.692621\pi$
$164$	6.92820			0.541002
$165$	3.00000			0.233550
$166$	−13.8564	+	13.8564i	−1.07547	+	1.07547i
$167$	17.3205			1.34030			0.670151	−	0.742225i	$-0.266230\pi$
$167$	17.3205			1.34030			0.670151	+	0.742225i	$0.266230\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	3.00000	−	3.00000i	0.230089	−	0.230089i
$171$		0			0
$172$	4.00000			0.304997
$173$		−	12.1244i		−	0.921798i	−0.887453	−	0.460899i	$-0.847527\pi$
$173$		−	12.1244i		−	0.921798i	0.887453	−	0.460899i	$-0.152473\pi$
$174$	−6.92820	+	6.92820i	−0.525226	+	0.525226i
$175$		0			0
$176$			4.00000i			0.301511i
$177$	−9.00000			−0.676481
$178$	15.5885	+	15.5885i	1.16840	+	1.16840i
$179$			19.0000i			1.42013i	0.704138	+	0.710063i	$0.251334\pi$
$179$			19.0000i			1.42013i	−0.704138	+	0.710063i	$0.748666\pi$
$180$		0			0
$181$		−	6.92820i		−	0.514969i	−0.966282	−	0.257485i	$-0.917106\pi$
$181$		−	6.92820i		−	0.514969i	0.966282	−	0.257485i	$-0.0828937\pi$
$182$		0			0
$183$			9.00000i			0.665299i
$184$	2.00000	−	2.00000i	0.147442	−	0.147442i
$185$		−	5.19615i		−	0.382029i
$186$	−3.00000	+	3.00000i	−0.219971	+	0.219971i
$187$	1.73205			0.126660
$188$			17.3205i			1.26323i
$189$		0			0
$190$	−9.00000	−	9.00000i	−0.652929	−	0.652929i
$191$		−	1.00000i		−	0.0723575i	−0.999345	−	0.0361787i	$-0.988481\pi$
$191$		−	1.00000i		−	0.0723575i	0.999345	−	0.0361787i	$-0.0115186\pi$
$192$		−	13.8564i		−	1.00000i
$193$	−15.0000			−1.07972			−0.539862	−	0.841754i	$-0.681524\pi$
$193$	−15.0000			−1.07972			−0.539862	+	0.841754i	$0.681524\pi$
$194$	17.3205	+	17.3205i	1.24354	+	1.24354i
$195$	10.3923			0.744208
$196$		0			0
$197$	16.0000			1.13995			0.569976	−	0.821661i	$-0.306952\pi$
$197$	16.0000			1.13995			0.569976	+	0.821661i	$0.306952\pi$
$198$		0			0
$199$	22.5167			1.59616			0.798082	−	0.602549i	$-0.205848\pi$
$199$	22.5167			1.59616			0.798082	+	0.602549i	$0.205848\pi$
$200$	−4.00000	−	4.00000i	−0.282843	−	0.282843i
$201$			5.19615i			0.366508i
$202$	8.66025	+	8.66025i	0.609333	+	0.609333i
$203$		0			0
$204$	−6.00000			−0.420084
$205$	6.00000			0.419058
$206$	8.66025	−	8.66025i	0.603388	−	0.603388i
$207$		0			0
$208$			13.8564i			0.960769i
$209$		−	5.19615i		−	0.359425i
$210$		0			0
$211$			10.0000i			0.688428i	0.938891	+	0.344214i	$0.111855\pi$
$211$			10.0000i			0.688428i	−0.938891	+	0.344214i	$0.888145\pi$
$212$			2.00000i			0.137361i
$213$			24.2487i			1.66149i
$214$	−13.0000	−	13.0000i	−0.888662	−	0.888662i
$215$	3.46410			0.236250
$216$	−10.3923	−	10.3923i	−0.707107	−	0.707107i
$217$		0			0
$218$	9.00000	−	9.00000i	0.609557	−	0.609557i
$219$			15.0000i			1.01361i
$220$			3.46410i			0.233550i
$221$	6.00000			0.403604
$222$	−5.19615	+	5.19615i	−0.348743	+	0.348743i
$223$	−6.92820			−0.463947			−0.231973	−	0.972722i	$-0.574518\pi$
$223$	−6.92820			−0.463947			−0.231973	+	0.972722i	$0.574518\pi$
$224$		0			0
$225$		0			0
$226$	−16.0000	+	16.0000i	−1.06430	+	1.06430i
$227$	−19.0526			−1.26456			−0.632281	−	0.774739i	$-0.717881\pi$
$227$	−19.0526			−1.26456			−0.632281	+	0.774739i	$0.717881\pi$
$228$			18.0000i			1.19208i
$229$		−	15.5885i		−	1.03011i	−0.857156	−	0.515057i	$-0.827771\pi$
$229$		−	15.5885i		−	1.03011i	0.857156	−	0.515057i	$-0.172229\pi$
$230$	1.73205	−	1.73205i	0.114208	−	0.114208i
$231$		0			0
$232$	−8.00000	−	8.00000i	−0.525226	−	0.525226i
$233$	−7.00000			−0.458585			−0.229293	−	0.973358i	$-0.573641\pi$
$233$	−7.00000			−0.458585			−0.229293	+	0.973358i	$0.573641\pi$
$234$		0			0
$235$			15.0000i			0.978492i
$236$		−	10.3923i		−	0.676481i
$237$		−	15.5885i		−	1.01258i
$238$		0			0
$239$			20.0000i			1.29369i	0.762620	+	0.646846i	$0.223912\pi$
$239$			20.0000i			1.29369i	−0.762620	+	0.646846i	$0.776088\pi$
$240$		−	12.0000i		−	0.774597i
$241$			5.19615i			0.334714i	0.985896	+	0.167357i	$0.0535232\pi$
$241$			5.19615i			0.334714i	−0.985896	+	0.167357i	$0.946477\pi$
$242$	10.0000	−	10.0000i	0.642824	−	0.642824i
$243$		0			0
$244$	−10.3923			−0.665299
$245$		0			0
$246$	−6.00000	−	6.00000i	−0.382546	−	0.382546i
$247$		−	18.0000i		−	1.14531i
$248$	−3.46410	−	3.46410i	−0.219971	−	0.219971i
$249$	24.0000			1.52094
$250$	−12.1244	−	12.1244i	−0.766812	−	0.766812i
$251$	3.46410			0.218652			0.109326	−	0.994006i	$-0.465131\pi$
$251$	3.46410			0.218652			0.109326	+	0.994006i	$0.465131\pi$
$252$		0			0
$253$	1.00000			0.0628695
$254$	6.00000	+	6.00000i	0.376473	+	0.376473i
$255$	−5.19615			−0.325396
$256$	16.0000			1.00000
$257$			5.19615i			0.324127i	0.986780	+	0.162064i	$0.0518150\pi$
$257$			5.19615i			0.324127i	−0.986780	+	0.162064i	$0.948185\pi$
$258$	−3.46410	−	3.46410i	−0.215666	−	0.215666i
$259$		0			0
$260$			12.0000i			0.744208i
$261$		0			0
$262$	−5.19615	+	5.19615i	−0.321019	+	0.321019i
$263$		−	23.0000i		−	1.41824i	−0.705087	−	0.709120i	$-0.749092\pi$
$263$		−	23.0000i		−	1.41824i	0.705087	−	0.709120i	$-0.250908\pi$
$264$	3.46410	−	3.46410i	0.213201	−	0.213201i
$265$			1.73205i			0.106399i
$266$		0			0
$267$		−	27.0000i		−	1.65237i
$268$	−6.00000			−0.366508
$269$		−	22.5167i		−	1.37287i	−0.727194	−	0.686433i	$-0.759176\pi$
$269$		−	22.5167i		−	1.37287i	0.727194	−	0.686433i	$-0.240824\pi$
$270$	−9.00000	−	9.00000i	−0.547723	−	0.547723i
$271$	15.5885			0.946931			0.473466	−	0.880812i	$-0.343003\pi$
$271$	15.5885			0.946931			0.473466	+	0.880812i	$0.343003\pi$
$272$		−	6.92820i		−	0.420084i
$273$		0			0
$274$	1.00000	−	1.00000i	0.0604122	−	0.0604122i
$275$		−	2.00000i		−	0.120605i
$276$	−3.46410			−0.208514
$277$	−13.0000			−0.781094			−0.390547	−	0.920583i	$-0.627714\pi$
$277$	−13.0000			−0.781094			−0.390547	+	0.920583i	$0.627714\pi$
$278$	6.92820	−	6.92820i	0.415526	−	0.415526i
$279$		0			0
$280$		0			0
$281$	−4.00000			−0.238620			−0.119310	−	0.992857i	$-0.538068\pi$
$281$	−4.00000			−0.238620			−0.119310	+	0.992857i	$0.538068\pi$
$282$	15.0000	−	15.0000i	0.893237	−	0.893237i
$283$	−12.1244			−0.720718			−0.360359	−	0.932814i	$-0.617346\pi$
$283$	−12.1244			−0.720718			−0.360359	+	0.932814i	$0.617346\pi$
$284$	−28.0000			−1.66149
$285$			15.5885i			0.923381i
$286$	−3.46410	+	3.46410i	−0.204837	+	0.204837i
$287$		0			0
$288$		0			0
$289$	14.0000			0.823529
$290$	−6.92820	−	6.92820i	−0.406838	−	0.406838i
$291$		−	30.0000i		−	1.75863i
$292$	−17.3205			−1.01361
$293$			20.7846i			1.21425i	0.794606	+	0.607125i	$0.207677\pi$
$293$			20.7846i			1.21425i	−0.794606	+	0.607125i	$0.792323\pi$
$294$		0			0
$295$		−	9.00000i		−	0.524000i
$296$	−6.00000	−	6.00000i	−0.348743	−	0.348743i
$297$		−	5.19615i		−	0.301511i
$298$	1.00000	−	1.00000i	0.0579284	−	0.0579284i
$299$	3.46410			0.200334
$300$			6.92820i			0.400000i
$301$		0			0
$302$	7.00000	+	7.00000i	0.402805	+	0.402805i
$303$		−	15.0000i		−	0.861727i
$304$	−20.7846			−1.19208
$305$	−9.00000			−0.515339
$306$		0			0
$307$	−20.7846			−1.18624			−0.593120	−	0.805114i	$-0.702104\pi$
$307$	−20.7846			−1.18624			−0.593120	+	0.805114i	$0.702104\pi$
$308$		0			0
$309$	−15.0000			−0.853320
$310$	−3.00000	−	3.00000i	−0.170389	−	0.170389i
$311$	−8.66025			−0.491078			−0.245539	−	0.969387i	$-0.578965\pi$
$311$	−8.66025			−0.491078			−0.245539	+	0.969387i	$0.578965\pi$
$312$	12.0000	−	12.0000i	0.679366	−	0.679366i
$313$			1.73205i			0.0979013i	0.998801	+	0.0489506i	$0.0155877\pi$
$313$			1.73205i			0.0979013i	−0.998801	+	0.0489506i	$0.984412\pi$
$314$	−1.73205	−	1.73205i	−0.0977453	−	0.0977453i
$315$		0			0
$316$	18.0000			1.01258
$317$	11.0000			0.617822			0.308911	−	0.951091i	$-0.400036\pi$
$317$	11.0000			0.617822			0.308911	+	0.951091i	$0.400036\pi$
$318$	1.73205	−	1.73205i	0.0971286	−	0.0971286i
$319$		−	4.00000i		−	0.223957i
$320$	13.8564			0.774597
$321$			22.5167i			1.25676i
$322$		0			0
$323$			9.00000i			0.500773i
$324$			18.0000i			1.00000i
$325$		−	6.92820i		−	0.384308i
$326$	21.0000	+	21.0000i	1.16308	+	1.16308i
$327$	−15.5885			−0.862044
$328$	6.92820	−	6.92820i	0.382546	−	0.382546i
$329$		0			0
$330$	3.00000	−	3.00000i	0.165145	−	0.165145i
$331$		−	7.00000i		−	0.384755i	−0.981321	−	0.192377i	$-0.938380\pi$
$331$		−	7.00000i		−	0.384755i	0.981321	−	0.192377i	$-0.0616198\pi$
$332$			27.7128i			1.52094i
$333$		0			0
$334$	17.3205	−	17.3205i	0.947736	−	0.947736i
$335$	−5.19615			−0.283896
$336$		0			0
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	1.00000	−	1.00000i	0.0543928	−	0.0543928i
$339$	27.7128			1.50515
$340$		−	6.00000i		−	0.325396i
$341$		−	1.73205i		−	0.0937958i
$342$		0			0
$343$		0			0
$344$	4.00000	−	4.00000i	0.215666	−	0.215666i
$345$	−3.00000			−0.161515
$346$	−12.1244	−	12.1244i	−0.651809	−	0.651809i
$347$			13.0000i			0.697877i	0.937146	+	0.348938i	$0.113458\pi$
$347$			13.0000i			0.697877i	−0.937146	+	0.348938i	$0.886542\pi$
$348$			13.8564i			0.742781i
$349$		−	10.3923i		−	0.556287i	−0.960539	−	0.278144i	$-0.910281\pi$
$349$		−	10.3923i		−	0.556287i	0.960539	−	0.278144i	$-0.0897191\pi$
$350$		0			0
$351$		−	18.0000i		−	0.960769i
$352$	4.00000	+	4.00000i	0.213201	+	0.213201i
$353$			29.4449i			1.56719i	0.621271	+	0.783596i	$0.286617\pi$
$353$			29.4449i			1.56719i	−0.621271	+	0.783596i	$0.713383\pi$
$354$	−9.00000	+	9.00000i	−0.478345	+	0.478345i
$355$	−24.2487			−1.28699
$356$	31.1769			1.65237
$357$		0			0
$358$	19.0000	+	19.0000i	1.00418	+	1.00418i
$359$			23.0000i			1.21389i	0.794742	+	0.606947i	$0.207606\pi$
$359$			23.0000i			1.21389i	−0.794742	+	0.606947i	$0.792394\pi$
$360$		0			0
$361$	8.00000			0.421053
$362$	−6.92820	−	6.92820i	−0.364138	−	0.364138i
$363$	−17.3205			−0.909091
$364$		0			0
$365$	−15.0000			−0.785136
$366$	9.00000	+	9.00000i	0.470438	+	0.470438i
$367$	−1.73205			−0.0904123			−0.0452062	−	0.998978i	$-0.514394\pi$
$367$	−1.73205			−0.0904123			−0.0452062	+	0.998978i	$0.514394\pi$
$368$		−	4.00000i		−	0.208514i
$369$		0			0
$370$	−5.19615	−	5.19615i	−0.270135	−	0.270135i
$371$		0			0
$372$			6.00000i			0.311086i
$373$	−29.0000			−1.50156			−0.750782	−	0.660551i	$-0.770323\pi$
$373$	−29.0000			−1.50156			−0.750782	+	0.660551i	$0.770323\pi$
$374$	1.73205	−	1.73205i	0.0895622	−	0.0895622i
$375$			21.0000i			1.08444i
$376$	17.3205	+	17.3205i	0.893237	+	0.893237i
$377$		−	13.8564i		−	0.713641i
$378$		0			0
$379$		−	8.00000i		−	0.410932i	−0.978664	−	0.205466i	$-0.934129\pi$
$379$		−	8.00000i		−	0.410932i	0.978664	−	0.205466i	$-0.0658711\pi$
$380$	−18.0000			−0.923381
$381$		−	10.3923i		−	0.532414i
$382$	−1.00000	−	1.00000i	−0.0511645	−	0.0511645i
$383$	5.19615			0.265511			0.132755	−	0.991149i	$-0.457617\pi$
$383$	5.19615			0.265511			0.132755	+	0.991149i	$0.457617\pi$
$384$	−13.8564	−	13.8564i	−0.707107	−	0.707107i
$385$		0			0
$386$	−15.0000	+	15.0000i	−0.763480	+	0.763480i
$387$		0			0
$388$	34.6410			1.75863
$389$	−19.0000			−0.963338			−0.481669	−	0.876353i	$-0.659969\pi$
$389$	−19.0000			−0.963338			−0.481669	+	0.876353i	$0.659969\pi$
$390$	10.3923	−	10.3923i	0.526235	−	0.526235i
$391$	−1.73205			−0.0875936
$392$		0			0
$393$	9.00000			0.453990
$394$	16.0000	−	16.0000i	0.806068	−	0.806068i
$395$	15.5885			0.784340
$396$		0			0
$397$			19.0526i			0.956221i	0.878300	+	0.478110i	$0.158678\pi$
$397$			19.0526i			0.956221i	−0.878300	+	0.478110i	$0.841322\pi$
$398$	22.5167	−	22.5167i	1.12866	−	1.12866i
$399$		0			0
$400$	−8.00000			−0.400000
$401$	−23.0000			−1.14857			−0.574283	−	0.818657i	$-0.694719\pi$
$401$	−23.0000			−1.14857			−0.574283	+	0.818657i	$0.694719\pi$
$402$	5.19615	+	5.19615i	0.259161	+	0.259161i
$403$		−	6.00000i		−	0.298881i
$404$	17.3205			0.861727
$405$			15.5885i			0.774597i
$406$		0			0
$407$		−	3.00000i		−	0.148704i
$408$	−6.00000	+	6.00000i	−0.297044	+	0.297044i
$409$		−	25.9808i		−	1.28467i	−0.766426	−	0.642333i	$-0.777967\pi$
$409$		−	25.9808i		−	1.28467i	0.766426	−	0.642333i	$-0.222033\pi$
$410$	6.00000	−	6.00000i	0.296319	−	0.296319i
$411$	−1.73205			−0.0854358
$412$		−	17.3205i		−	0.853320i
$413$		0			0
$414$		0			0
$415$			24.0000i			1.17811i
$416$	13.8564	+	13.8564i	0.679366	+	0.679366i
$417$	−12.0000			−0.587643
$418$	−5.19615	−	5.19615i	−0.254152	−	0.254152i
$419$	20.7846			1.01539			0.507697	−	0.861536i	$-0.330497\pi$
$419$	20.7846			1.01539			0.507697	+	0.861536i	$0.330497\pi$
$420$		0			0
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$	10.0000	+	10.0000i	0.486792	+	0.486792i
$423$		0			0
$424$	2.00000	+	2.00000i	0.0971286	+	0.0971286i
$425$			3.46410i			0.168034i
$426$	24.2487	+	24.2487i	1.17485	+	1.17485i
$427$		0			0
$428$	−26.0000			−1.25676
$429$	6.00000			0.289683
$430$	3.46410	−	3.46410i	0.167054	−	0.167054i
$431$			23.0000i			1.10787i	0.832560	+	0.553936i	$0.186875\pi$
$431$			23.0000i			1.10787i	−0.832560	+	0.553936i	$0.813125\pi$
$432$	−20.7846			−1.00000
$433$			10.3923i			0.499422i	0.968320	+	0.249711i	$0.0803357\pi$
$433$			10.3923i			0.499422i	−0.968320	+	0.249711i	$0.919664\pi$
$434$		0			0
$435$			12.0000i			0.575356i
$436$		−	18.0000i		−	0.862044i
$437$			5.19615i			0.248566i
$438$	15.0000	+	15.0000i	0.716728	+	0.716728i
$439$	−22.5167			−1.07466			−0.537331	−	0.843372i	$-0.680567\pi$
$439$	−22.5167			−1.07466			−0.537331	+	0.843372i	$0.680567\pi$
$440$	3.46410	+	3.46410i	0.165145	+	0.165145i
$441$		0			0
$442$	6.00000	−	6.00000i	0.285391	−	0.285391i
$443$		−	17.0000i		−	0.807694i	−0.914826	−	0.403847i	$-0.867673\pi$
$443$		−	17.0000i		−	0.807694i	0.914826	−	0.403847i	$-0.132327\pi$
$444$			10.3923i			0.493197i
$445$	27.0000			1.27992
$446$	−6.92820	+	6.92820i	−0.328060	+	0.328060i
$447$	−1.73205			−0.0819232
$448$		0			0
$449$	8.00000			0.377543			0.188772	−	0.982021i	$-0.439549\pi$
$449$	8.00000			0.377543			0.188772	+	0.982021i	$0.439549\pi$
$450$		0			0
$451$	3.46410			0.163118
$452$			32.0000i			1.50515i
$453$		−	12.1244i		−	0.569652i
$454$	−19.0526	+	19.0526i	−0.894181	+	0.894181i
$455$		0			0
$456$	18.0000	+	18.0000i	0.842927	+	0.842927i
$457$	15.0000			0.701670			0.350835	−	0.936437i	$-0.385898\pi$
$457$	15.0000			0.701670			0.350835	+	0.936437i	$0.385898\pi$
$458$	−15.5885	−	15.5885i	−0.728401	−	0.728401i
$459$			9.00000i			0.420084i
$460$		−	3.46410i		−	0.161515i
$461$			17.3205i			0.806696i	0.915047	+	0.403348i	$0.132154\pi$
$461$			17.3205i			0.806696i	−0.915047	+	0.403348i	$0.867846\pi$
$462$		0			0
$463$		−	30.0000i		−	1.39422i	−0.716965	−	0.697109i	$-0.754469\pi$
$463$		−	30.0000i		−	1.39422i	0.716965	−	0.697109i	$-0.245531\pi$
$464$	−16.0000			−0.742781
$465$			5.19615i			0.240966i
$466$	−7.00000	+	7.00000i	−0.324269	+	0.324269i
$467$	8.66025			0.400749			0.200374	−	0.979719i	$-0.435784\pi$
$467$	8.66025			0.400749			0.200374	+	0.979719i	$0.435784\pi$
$468$		0			0
$469$		0			0
$470$	15.0000	+	15.0000i	0.691898	+	0.691898i
$471$			3.00000i			0.138233i
$472$	−10.3923	−	10.3923i	−0.478345	−	0.478345i
$473$	2.00000			0.0919601
$474$	−15.5885	−	15.5885i	−0.716002	−	0.716002i
$475$	10.3923			0.476832
$476$		0			0
$477$		0			0
$478$	20.0000	+	20.0000i	0.914779	+	0.914779i
$479$	12.1244			0.553976			0.276988	−	0.960873i	$-0.410664\pi$
$479$	12.1244			0.553976			0.276988	+	0.960873i	$0.410664\pi$
$480$	−12.0000	−	12.0000i	−0.547723	−	0.547723i
$481$		−	10.3923i		−	0.473848i
$482$	5.19615	+	5.19615i	0.236678	+	0.236678i
$483$		0			0
$484$		−	20.0000i		−	0.909091i
$485$	30.0000			1.36223
$486$		0			0
$487$		−	31.0000i		−	1.40474i	−0.711810	−	0.702372i	$-0.752124\pi$
$487$		−	31.0000i		−	1.40474i	0.711810	−	0.702372i	$-0.247876\pi$
$488$	−10.3923	+	10.3923i	−0.470438	+	0.470438i
$489$		−	36.3731i		−	1.64485i
$490$		0			0
$491$			32.0000i			1.44414i	0.691820	+	0.722070i	$0.256809\pi$
$491$			32.0000i			1.44414i	−0.691820	+	0.722070i	$0.743191\pi$
$492$	−12.0000			−0.541002
$493$			6.92820i			0.312031i
$494$	−18.0000	−	18.0000i	−0.809858	−	0.809858i
$495$		0			0
$496$	−6.92820			−0.311086
$497$		0			0
$498$	24.0000	−	24.0000i	1.07547	−	1.07547i
$499$		−	35.0000i		−	1.56682i	−0.621508	−	0.783408i	$-0.713480\pi$
$499$		−	35.0000i		−	1.56682i	0.621508	−	0.783408i	$-0.286520\pi$
$500$	−24.2487			−1.08444
$501$	−30.0000			−1.34030
$502$	3.46410	−	3.46410i	0.154610	−	0.154610i
$503$	6.92820			0.308913			0.154457	−	0.988000i	$-0.450637\pi$
$503$	6.92820			0.308913			0.154457	+	0.988000i	$0.450637\pi$
$504$		0			0
$505$	15.0000			0.667491
$506$	1.00000	−	1.00000i	0.0444554	−	0.0444554i
$507$	−1.73205			−0.0769231
$508$	12.0000			0.532414
$509$			12.1244i			0.537403i	0.963224	+	0.268701i	$0.0865945\pi$
$509$			12.1244i			0.537403i	−0.963224	+	0.268701i	$0.913406\pi$
$510$	−5.19615	+	5.19615i	−0.230089	+	0.230089i
$511$		0			0
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$	27.0000			1.19208
$514$	5.19615	+	5.19615i	0.229192	+	0.229192i
$515$		−	15.0000i		−	0.660979i
$516$	−6.92820			−0.304997
$517$			8.66025i			0.380878i
$518$		0			0
$519$			21.0000i			0.921798i
$520$	12.0000	+	12.0000i	0.526235	+	0.526235i
$521$		−	1.73205i		−	0.0758825i	−0.999280	−	0.0379413i	$-0.987920\pi$
$521$		−	1.73205i		−	0.0758825i	0.999280	−	0.0379413i	$-0.0120800\pi$
$522$		0			0
$523$	25.9808			1.13606			0.568030	−	0.823008i	$-0.307706\pi$
$523$	25.9808			1.13606			0.568030	+	0.823008i	$0.307706\pi$
$524$			10.3923i			0.453990i
$525$		0			0
$526$	−23.0000	−	23.0000i	−1.00285	−	1.00285i
$527$			3.00000i			0.130682i
$528$		−	6.92820i		−	0.301511i
$529$	22.0000			0.956522
$530$	1.73205	+	1.73205i	0.0752355	+	0.0752355i
$531$		0			0
$532$		0			0
$533$	12.0000			0.519778
$534$	−27.0000	−	27.0000i	−1.16840	−	1.16840i
$535$	−22.5167			−0.973480
$536$	−6.00000	+	6.00000i	−0.259161	+	0.259161i
$537$		−	32.9090i		−	1.42013i
$538$	−22.5167	−	22.5167i	−0.970762	−	0.970762i
$539$		0			0
$540$	−18.0000			−0.774597
$541$	−19.0000			−0.816874			−0.408437	−	0.912787i	$-0.633926\pi$
$541$	−19.0000			−0.816874			−0.408437	+	0.912787i	$0.633926\pi$
$542$	15.5885	−	15.5885i	0.669582	−	0.669582i
$543$			12.0000i			0.514969i
$544$	−6.92820	−	6.92820i	−0.297044	−	0.297044i
$545$		−	15.5885i		−	0.667736i
$546$		0			0
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$		−	2.00000i		−	0.0854358i
$549$		0			0
$550$	−2.00000	−	2.00000i	−0.0852803	−	0.0852803i
$551$	20.7846			0.885454
$552$	−3.46410	+	3.46410i	−0.147442	+	0.147442i
$553$		0			0
$554$	−13.0000	+	13.0000i	−0.552317	+	0.552317i
$555$			9.00000i			0.382029i
$556$		−	13.8564i		−	0.587643i
$557$	37.0000			1.56774			0.783870	−	0.620925i	$-0.213243\pi$
$557$	37.0000			1.56774			0.783870	+	0.620925i	$0.213243\pi$
$558$		0			0
$559$	6.92820			0.293032
$560$		0			0
$561$	−3.00000			−0.126660
$562$	−4.00000	+	4.00000i	−0.168730	+	0.168730i
$563$	−22.5167			−0.948964			−0.474482	−	0.880265i	$-0.657365\pi$
$563$	−22.5167			−0.948964			−0.474482	+	0.880265i	$0.657365\pi$
$564$		−	30.0000i		−	1.26323i
$565$			27.7128i			1.16589i
$566$	−12.1244	+	12.1244i	−0.509625	+	0.509625i
$567$		0			0
$568$	−28.0000	+	28.0000i	−1.17485	+	1.17485i
$569$	−13.0000			−0.544988			−0.272494	−	0.962157i	$-0.587849\pi$
$569$	−13.0000			−0.544988			−0.272494	+	0.962157i	$0.587849\pi$
$570$	15.5885	+	15.5885i	0.652929	+	0.652929i
$571$		−	21.0000i		−	0.878823i	−0.898286	−	0.439411i	$-0.855187\pi$
$571$		−	21.0000i		−	0.878823i	0.898286	−	0.439411i	$-0.144813\pi$
$572$			6.92820i			0.289683i
$573$			1.73205i			0.0723575i
$574$		0			0
$575$			2.00000i			0.0834058i
$576$		0			0
$577$			32.9090i			1.37002i	0.728535	+	0.685009i	$0.240202\pi$
$577$			32.9090i			1.37002i	−0.728535	+	0.685009i	$0.759798\pi$
$578$	14.0000	−	14.0000i	0.582323	−	0.582323i
$579$	25.9808			1.07972
$580$	−13.8564			−0.575356
$581$		0			0
$582$	−30.0000	−	30.0000i	−1.24354	−	1.24354i
$583$			1.00000i			0.0414158i
$584$	−17.3205	+	17.3205i	−0.716728	+	0.716728i
$585$		0			0
$586$	20.7846	+	20.7846i	0.858604	+	0.858604i
$587$	−6.92820			−0.285958			−0.142979	−	0.989726i	$-0.545668\pi$
$587$	−6.92820			−0.285958			−0.142979	+	0.989726i	$0.545668\pi$
$588$		0			0
$589$	9.00000			0.370839
$590$	−9.00000	−	9.00000i	−0.370524	−	0.370524i
$591$	−27.7128			−1.13995
$592$	−12.0000			−0.493197
$593$		−	15.5885i		−	0.640141i	−0.947394	−	0.320071i	$-0.896293\pi$
$593$		−	15.5885i		−	0.640141i	0.947394	−	0.320071i	$-0.103707\pi$
$594$	−5.19615	−	5.19615i	−0.213201	−	0.213201i
$595$		0			0
$596$		−	2.00000i		−	0.0819232i
$597$	−39.0000			−1.59616
$598$	3.46410	−	3.46410i	0.141658	−	0.141658i
$599$			17.0000i			0.694601i	0.937754	+	0.347301i	$0.112902\pi$
$599$			17.0000i			0.694601i	−0.937754	+	0.347301i	$0.887098\pi$
$600$	6.92820	+	6.92820i	0.282843	+	0.282843i
$601$		−	38.1051i		−	1.55434i	−0.629291	−	0.777170i	$-0.716654\pi$
$601$		−	38.1051i		−	1.55434i	0.629291	−	0.777170i	$-0.283346\pi$
$602$		0			0
$603$		0			0
$604$	14.0000			0.569652
$605$		−	17.3205i		−	0.704179i
$606$	−15.0000	−	15.0000i	−0.609333	−	0.609333i
$607$	−15.5885			−0.632716			−0.316358	−	0.948640i	$-0.602460\pi$
$607$	−15.5885			−0.632716			−0.316358	+	0.948640i	$0.602460\pi$
$608$	−20.7846	+	20.7846i	−0.842927	+	0.842927i
$609$		0			0
$610$	−9.00000	+	9.00000i	−0.364399	+	0.364399i
$611$			30.0000i			1.21367i
$612$		0			0
$613$	−31.0000			−1.25208			−0.626039	−	0.779792i	$-0.715325\pi$
$613$	−31.0000			−1.25208			−0.626039	+	0.779792i	$0.715325\pi$
$614$	−20.7846	+	20.7846i	−0.838799	+	0.838799i
$615$	−10.3923			−0.419058
$616$		0			0
$617$	20.0000			0.805170			0.402585	−	0.915383i	$-0.368112\pi$
$617$	20.0000			0.805170			0.402585	+	0.915383i	$0.368112\pi$
$618$	−15.0000	+	15.0000i	−0.603388	+	0.603388i
$619$	−15.5885			−0.626553			−0.313276	−	0.949662i	$-0.601427\pi$
$619$	−15.5885			−0.626553			−0.313276	+	0.949662i	$0.601427\pi$
$620$	−6.00000			−0.240966
$621$			5.19615i			0.208514i
$622$	−8.66025	+	8.66025i	−0.347245	+	0.347245i
$623$		0			0
$624$		−	24.0000i		−	0.960769i
$625$	−11.0000			−0.440000
$626$	1.73205	+	1.73205i	0.0692267	+	0.0692267i
$627$			9.00000i			0.359425i
$628$	−3.46410			−0.138233
$629$			5.19615i			0.207184i
$630$		0			0
$631$			30.0000i			1.19428i	0.802137	+	0.597141i	$0.203697\pi$
$631$			30.0000i			1.19428i	−0.802137	+	0.597141i	$0.796303\pi$
$632$	18.0000	−	18.0000i	0.716002	−	0.716002i
$633$		−	17.3205i		−	0.688428i
$634$	11.0000	−	11.0000i	0.436866	−	0.436866i
$635$	10.3923			0.412406
$636$		−	3.46410i		−	0.137361i
$637$		0			0
$638$	−4.00000	−	4.00000i	−0.158362	−	0.158362i
$639$		0			0
$640$	13.8564	−	13.8564i	0.547723	−	0.547723i
$641$	−13.0000			−0.513469			−0.256735	−	0.966482i	$-0.582647\pi$
$641$	−13.0000			−0.513469			−0.256735	+	0.966482i	$0.582647\pi$
$642$	22.5167	+	22.5167i	0.888662	+	0.888662i
$643$	13.8564			0.546443			0.273222	−	0.961951i	$-0.411911\pi$
$643$	13.8564			0.546443			0.273222	+	0.961951i	$0.411911\pi$
$644$		0			0
$645$	−6.00000			−0.236250
$646$	9.00000	+	9.00000i	0.354100	+	0.354100i
$647$	32.9090			1.29378			0.646892	−	0.762581i	$-0.276068\pi$
$647$	32.9090			1.29378			0.646892	+	0.762581i	$0.276068\pi$
$648$	18.0000	+	18.0000i	0.707107	+	0.707107i
$649$		−	5.19615i		−	0.203967i
$650$	−6.92820	−	6.92820i	−0.271746	−	0.271746i
$651$		0			0
$652$	42.0000			1.64485
$653$	31.0000			1.21312			0.606562	−	0.795036i	$-0.292548\pi$
$653$	31.0000			1.21312			0.606562	+	0.795036i	$0.292548\pi$
$654$	−15.5885	+	15.5885i	−0.609557	+	0.609557i
$655$			9.00000i			0.351659i
$656$		−	13.8564i		−	0.541002i
$657$		0			0
$658$		0			0
$659$		−	38.0000i		−	1.48027i	−0.672458	−	0.740135i	$-0.734762\pi$
$659$		−	38.0000i		−	1.48027i	0.672458	−	0.740135i	$-0.265238\pi$
$660$		−	6.00000i		−	0.233550i
$661$			39.8372i			1.54949i	0.632276	+	0.774743i	$0.282121\pi$
$661$			39.8372i			1.54949i	−0.632276	+	0.774743i	$0.717879\pi$
$662$	−7.00000	−	7.00000i	−0.272063	−	0.272063i
$663$	−10.3923			−0.403604
$664$	27.7128	+	27.7128i	1.07547	+	1.07547i
$665$		0			0
$666$		0			0
$667$			4.00000i			0.154881i
$668$		−	34.6410i		−	1.34030i
$669$	12.0000			0.463947
$670$	−5.19615	+	5.19615i	−0.200745	+	0.200745i
$671$	−5.19615			−0.200595
$672$		0			0
$673$	24.0000			0.925132			0.462566	−	0.886585i	$-0.346929\pi$
$673$	24.0000			0.925132			0.462566	+	0.886585i	$0.346929\pi$
$674$		0			0
$675$	10.3923			0.400000
$676$		−	2.00000i		−	0.0769231i
$677$		−	43.3013i		−	1.66420i	−0.554623	−	0.832102i	$-0.687138\pi$
$677$		−	43.3013i		−	1.66420i	0.554623	−	0.832102i	$-0.312862\pi$
$678$	27.7128	−	27.7128i	1.06430	−	1.06430i
$679$		0			0
$680$	−6.00000	−	6.00000i	−0.230089	−	0.230089i
$681$	33.0000			1.26456
$682$	−1.73205	−	1.73205i	−0.0663237	−	0.0663237i
$683$		−	25.0000i		−	0.956598i	−0.878197	−	0.478299i	$-0.841253\pi$
$683$		−	25.0000i		−	0.956598i	0.878197	−	0.478299i	$-0.158747\pi$
$684$		0			0
$685$		−	1.73205i		−	0.0661783i
$686$		0			0
$687$			27.0000i			1.03011i
$688$		−	8.00000i		−	0.304997i
$689$			3.46410i			0.131972i
$690$	−3.00000	+	3.00000i	−0.114208	+	0.114208i
$691$	−12.1244			−0.461232			−0.230616	−	0.973045i	$-0.574074\pi$
$691$	−12.1244			−0.461232			−0.230616	+	0.973045i	$0.574074\pi$
$692$	−24.2487			−0.921798
$693$		0			0
$694$	13.0000	+	13.0000i	0.493473	+	0.493473i
$695$		−	12.0000i		−	0.455186i
$696$	13.8564	+	13.8564i	0.525226	+	0.525226i
$697$	−6.00000			−0.227266
$698$	−10.3923	−	10.3923i	−0.393355	−	0.393355i
$699$	12.1244			0.458585
$700$		0			0
$701$	−26.0000			−0.982006			−0.491003	−	0.871158i	$-0.663370\pi$
$701$	−26.0000			−0.982006			−0.491003	+	0.871158i	$0.663370\pi$
$702$	−18.0000	−	18.0000i	−0.679366	−	0.679366i
$703$	15.5885			0.587930
$704$	8.00000			0.301511
$705$		−	25.9808i		−	0.978492i
$706$	29.4449	+	29.4449i	1.10817	+	1.10817i
$707$		0			0
$708$			18.0000i			0.676481i
$709$	−9.00000			−0.338002			−0.169001	−	0.985616i	$-0.554054\pi$
$709$	−9.00000			−0.338002			−0.169001	+	0.985616i	$0.554054\pi$
$710$	−24.2487	+	24.2487i	−0.910038	+	0.910038i
$711$		0			0
$712$	31.1769	−	31.1769i	1.16840	−	1.16840i
$713$			1.73205i			0.0648658i
$714$		0			0
$715$			6.00000i			0.224387i
$716$	38.0000			1.42013
$717$		−	34.6410i		−	1.29369i
$718$	23.0000	+	23.0000i	0.858352	+	0.858352i
$719$	−25.9808			−0.968919			−0.484459	−	0.874814i	$-0.660984\pi$
$719$	−25.9808			−0.968919			−0.484459	+	0.874814i	$0.660984\pi$
$720$		0			0
$721$		0			0
$722$	8.00000	−	8.00000i	0.297729	−	0.297729i
$723$		−	9.00000i		−	0.334714i
$724$	−13.8564			−0.514969
$725$	8.00000			0.297113
$726$	−17.3205	+	17.3205i	−0.642824	+	0.642824i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$	−15.0000	+	15.0000i	−0.555175	+	0.555175i
$731$	−3.46410			−0.128124
$732$	18.0000			0.665299
$733$			43.3013i			1.59937i	0.600420	+	0.799684i	$0.295000\pi$
$733$			43.3013i			1.59937i	−0.600420	+	0.799684i	$0.705000\pi$
$734$	−1.73205	+	1.73205i	−0.0639312	+	0.0639312i
$735$		0			0
$736$	−4.00000	−	4.00000i	−0.147442	−	0.147442i
$737$	−3.00000			−0.110506
$738$		0			0
$739$			51.0000i			1.87607i	0.346547	+	0.938033i	$0.387354\pi$
$739$			51.0000i			1.87607i	−0.346547	+	0.938033i	$0.612646\pi$
$740$	−10.3923			−0.382029
$741$			31.1769i			1.14531i
$742$		0			0
$743$		−	34.0000i		−	1.24734i	−0.781688	−	0.623670i	$-0.785641\pi$
$743$		−	34.0000i		−	1.24734i	0.781688	−	0.623670i	$-0.214359\pi$
$744$	6.00000	+	6.00000i	0.219971	+	0.219971i
$745$		−	1.73205i		−	0.0634574i
$746$	−29.0000	+	29.0000i	−1.06177	+	1.06177i
$747$		0			0
$748$		−	3.46410i		−	0.126660i
$749$		0			0
$750$	21.0000	+	21.0000i	0.766812	+	0.766812i
$751$		−	25.0000i		−	0.912263i	−0.889912	−	0.456131i	$-0.849235\pi$
$751$		−	25.0000i		−	0.912263i	0.889912	−	0.456131i	$-0.150765\pi$
$752$	34.6410			1.26323
$753$	−6.00000			−0.218652
$754$	−13.8564	−	13.8564i	−0.504621	−	0.504621i
$755$	12.1244			0.441250
$756$		0			0
$757$	−48.0000			−1.74459			−0.872295	−	0.488980i	$-0.837369\pi$
$757$	−48.0000			−1.74459			−0.872295	+	0.488980i	$0.837369\pi$
$758$	−8.00000	−	8.00000i	−0.290573	−	0.290573i
$759$	−1.73205			−0.0628695
$760$	−18.0000	+	18.0000i	−0.652929	+	0.652929i
$761$			19.0526i			0.690655i	0.938482	+	0.345327i	$0.112232\pi$
$761$			19.0526i			0.690655i	−0.938482	+	0.345327i	$0.887768\pi$
$762$	−10.3923	−	10.3923i	−0.376473	−	0.376473i
$763$		0			0
$764$	−2.00000			−0.0723575
$765$		0			0
$766$	5.19615	−	5.19615i	0.187745	−	0.187745i
$767$		−	18.0000i		−	0.649942i
$768$	−27.7128			−1.00000
$769$			3.46410i			0.124919i	0.998048	+	0.0624593i	$0.0198944\pi$
$769$			3.46410i			0.124919i	−0.998048	+	0.0624593i	$0.980106\pi$
$770$		0			0
$771$		−	9.00000i		−	0.324127i
$772$			30.0000i			1.07972i
$773$		−	25.9808i		−	0.934463i	−0.884135	−	0.467232i	$-0.845251\pi$
$773$		−	25.9808i		−	0.934463i	0.884135	−	0.467232i	$-0.154749\pi$
$774$		0			0
$775$	3.46410			0.124434
$776$	34.6410	−	34.6410i	1.24354	−	1.24354i
$777$		0			0
$778$	−19.0000	+	19.0000i	−0.681183	+	0.681183i
$779$			18.0000i			0.644917i
$780$		−	20.7846i		−	0.744208i
$781$	−14.0000			−0.500959
$782$	−1.73205	+	1.73205i	−0.0619380	+	0.0619380i
$783$	20.7846			0.742781
$784$		0			0
$785$	−3.00000			−0.107075
$786$	9.00000	−	9.00000i	0.321019	−	0.321019i
$787$	5.19615			0.185223			0.0926114	−	0.995702i	$-0.470479\pi$
$787$	5.19615			0.185223			0.0926114	+	0.995702i	$0.470479\pi$
$788$		−	32.0000i		−	1.13995i
$789$			39.8372i			1.41824i
$790$	15.5885	−	15.5885i	0.554612	−	0.554612i
$791$		0			0
$792$		0			0
$793$	−18.0000			−0.639199
$794$	19.0526	+	19.0526i	0.676150	+	0.676150i
$795$		−	3.00000i		−	0.106399i
$796$		−	45.0333i		−	1.59616i
$797$			10.3923i			0.368114i	0.982916	+	0.184057i	$0.0589232\pi$
$797$			10.3923i			0.368114i	−0.982916	+	0.184057i	$0.941077\pi$
$798$		0			0
$799$		−	15.0000i		−	0.530662i
$800$	−8.00000	+	8.00000i	−0.282843	+	0.282843i
$801$		0			0
$802$	−23.0000	+	23.0000i	−0.812158	+	0.812158i
$803$	−8.66025			−0.305614
$804$	10.3923			0.366508
$805$		0			0
$806$	−6.00000	−	6.00000i	−0.211341	−	0.211341i
$807$			39.0000i			1.37287i
$808$	17.3205	−	17.3205i	0.609333	−	0.609333i
$809$	43.0000			1.51180			0.755900	−	0.654687i	$-0.227200\pi$
$809$	43.0000			1.51180			0.755900	+	0.654687i	$0.227200\pi$
$810$	15.5885	+	15.5885i	0.547723	+	0.547723i
$811$	−13.8564			−0.486564			−0.243282	−	0.969956i	$-0.578224\pi$
$811$	−13.8564			−0.486564			−0.243282	+	0.969956i	$0.578224\pi$
$812$		0			0
$813$	−27.0000			−0.946931
$814$	−3.00000	−	3.00000i	−0.105150	−	0.105150i
$815$	36.3731			1.27409
$816$			12.0000i			0.420084i
$817$			10.3923i			0.363581i
$818$	−25.9808	−	25.9808i	−0.908396	−	0.908396i
$819$		0			0
$820$		−	12.0000i		−	0.419058i
$821$	−11.0000			−0.383903			−0.191951	−	0.981404i	$-0.561482\pi$
$821$	−11.0000			−0.383903			−0.191951	+	0.981404i	$0.561482\pi$
$822$	−1.73205	+	1.73205i	−0.0604122	+	0.0604122i
$823$			9.00000i			0.313720i	0.987621	+	0.156860i	$0.0501372\pi$
$823$			9.00000i			0.313720i	−0.987621	+	0.156860i	$0.949863\pi$
$824$	−17.3205	−	17.3205i	−0.603388	−	0.603388i
$825$			3.46410i			0.120605i
$826$		0			0
$827$			22.0000i			0.765015i	0.923952	+	0.382507i	$0.124939\pi$
$827$			22.0000i			0.765015i	−0.923952	+	0.382507i	$0.875061\pi$
$828$		0			0
$829$			8.66025i			0.300783i	0.988627	+	0.150392i	$0.0480534\pi$
$829$			8.66025i			0.300783i	−0.988627	+	0.150392i	$0.951947\pi$
$830$	24.0000	+	24.0000i	0.833052	+	0.833052i
$831$	22.5167			0.781094
$832$	27.7128			0.960769
$833$		0			0
$834$	−12.0000	+	12.0000i	−0.415526	+	0.415526i
$835$		−	30.0000i		−	1.03819i
$836$	−10.3923			−0.359425
$837$	9.00000			0.311086
$838$	20.7846	−	20.7846i	0.717992	−	0.717992i
$839$	−48.4974			−1.67432			−0.837158	−	0.546960i	$-0.815785\pi$
$839$	−48.4974			−1.67432			−0.837158	+	0.546960i	$0.815785\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	−20.0000	+	20.0000i	−0.689246	+	0.689246i
$843$	6.92820			0.238620
$844$	20.0000			0.688428
$845$		−	1.73205i		−	0.0595844i
$846$		0			0
$847$		0			0
$848$	4.00000			0.137361
$849$	21.0000			0.720718
$850$	3.46410	+	3.46410i	0.118818	+	0.118818i
$851$			3.00000i			0.102839i
$852$	48.4974			1.66149
$853$			24.2487i			0.830260i	0.909762	+	0.415130i	$0.136264\pi$
$853$			24.2487i			0.830260i	−0.909762	+	0.415130i	$0.863736\pi$
$854$		0			0
$855$		0			0
$856$	−26.0000	+	26.0000i	−0.888662	+	0.888662i
$857$			25.9808i			0.887486i	0.896154	+	0.443743i	$0.146350\pi$
$857$			25.9808i			0.887486i	−0.896154	+	0.443743i	$0.853650\pi$
$858$	6.00000	−	6.00000i	0.204837	−	0.204837i
$859$	−50.2295			−1.71381			−0.856904	−	0.515476i	$-0.827615\pi$
$859$	−50.2295			−1.71381			−0.856904	+	0.515476i	$0.827615\pi$
$860$		−	6.92820i		−	0.236250i
$861$		0			0
$862$	23.0000	+	23.0000i	0.783383	+	0.783383i
$863$		−	35.0000i		−	1.19141i	−0.803202	−	0.595707i	$-0.796872\pi$
$863$		−	35.0000i		−	1.19141i	0.803202	−	0.595707i	$-0.203128\pi$
$864$	−20.7846	+	20.7846i	−0.707107	+	0.707107i
$865$	−21.0000			−0.714021
$866$	10.3923	+	10.3923i	0.353145	+	0.353145i
$867$	−24.2487			−0.823529
$868$		0			0
$869$	9.00000			0.305304
$870$	12.0000	+	12.0000i	0.406838	+	0.406838i
$871$	−10.3923			−0.352130
$872$	−18.0000	−	18.0000i	−0.609557	−	0.609557i
$873$		0			0
$874$	5.19615	+	5.19615i	0.175762	+	0.175762i
$875$		0			0
$876$	30.0000			1.01361
$877$	1.00000			0.0337676			0.0168838	−	0.999857i	$-0.494625\pi$
$877$	1.00000			0.0337676			0.0168838	+	0.999857i	$0.494625\pi$
$878$	−22.5167	+	22.5167i	−0.759900	+	0.759900i
$879$		−	36.0000i		−	1.21425i
$880$	6.92820			0.233550
$881$		−	13.8564i		−	0.466834i	−0.972377	−	0.233417i	$-0.925009\pi$
$881$		−	13.8564i		−	0.466834i	0.972377	−	0.233417i	$-0.0749907\pi$
$882$		0			0
$883$		−	10.0000i		−	0.336527i	−0.985742	−	0.168263i	$-0.946184\pi$
$883$		−	10.0000i		−	0.336527i	0.985742	−	0.168263i	$-0.0538159\pi$
$884$		−	12.0000i		−	0.403604i
$885$			15.5885i			0.524000i
$886$	−17.0000	−	17.0000i	−0.571126	−	0.571126i
$887$	25.9808			0.872349			0.436174	−	0.899862i	$-0.356333\pi$
$887$	25.9808			0.872349			0.436174	+	0.899862i	$0.356333\pi$
$888$	10.3923	+	10.3923i	0.348743	+	0.348743i
$889$		0			0
$890$	27.0000	−	27.0000i	0.905042	−	0.905042i
$891$			9.00000i			0.301511i
$892$			13.8564i			0.463947i
$893$	−45.0000			−1.50587
$894$	−1.73205	+	1.73205i	−0.0579284	+	0.0579284i
$895$	32.9090			1.10003
$896$		0			0
$897$	−6.00000			−0.200334
$898$	8.00000	−	8.00000i	0.266963	−	0.266963i
$899$	6.92820			0.231069
$900$		0			0
$901$		−	1.73205i		−	0.0577030i
$902$	3.46410	−	3.46410i	0.115342	−	0.115342i
$903$		0			0
$904$	32.0000	+	32.0000i	1.06430	+	1.06430i
$905$	−12.0000			−0.398893
$906$	−12.1244	−	12.1244i	−0.402805	−	0.402805i
$907$		−	7.00000i		−	0.232431i	−0.993224	−	0.116216i	$-0.962924\pi$
$907$		−	7.00000i		−	0.232431i	0.993224	−	0.116216i	$-0.0370764\pi$
$908$			38.1051i			1.26456i
$909$		0			0
$910$		0			0
$911$		−	26.0000i		−	0.861418i	−0.902491	−	0.430709i	$-0.858263\pi$
$911$		−	26.0000i		−	0.861418i	0.902491	−	0.430709i	$-0.141737\pi$
$912$	36.0000			1.19208
$913$			13.8564i			0.458580i
$914$	15.0000	−	15.0000i	0.496156	−	0.496156i
$915$	15.5885			0.515339
$916$	−31.1769			−1.03011
$917$		0			0
$918$	9.00000	+	9.00000i	0.297044	+	0.297044i
$919$		−	1.00000i		−	0.0329870i	−0.999864	−	0.0164935i	$-0.994750\pi$
$919$		−	1.00000i		−	0.0329870i	0.999864	−	0.0164935i	$-0.00525028\pi$
$920$	−3.46410	−	3.46410i	−0.114208	−	0.114208i
$921$	36.0000			1.18624
$922$	17.3205	+	17.3205i	0.570421	+	0.570421i
$923$	−48.4974			−1.59631
$924$		0			0
$925$	6.00000			0.197279
$926$	−30.0000	−	30.0000i	−0.985861	−	0.985861i
$927$		0			0
$928$	−16.0000	+	16.0000i	−0.525226	+	0.525226i
$929$			8.66025i			0.284134i	0.989857	+	0.142067i	$0.0453748\pi$
$929$			8.66025i			0.284134i	−0.989857	+	0.142067i	$0.954625\pi$
$930$	5.19615	+	5.19615i	0.170389	+	0.170389i
$931$		0			0
$932$			14.0000i			0.458585i
$933$	15.0000			0.491078
$934$	8.66025	−	8.66025i	0.283372	−	0.283372i
$935$		−	3.00000i		−	0.0981105i
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		−	3.00000i		−	0.0979013i
$940$	30.0000			0.978492
$941$		−	57.1577i		−	1.86329i	−0.363374	−	0.931644i	$-0.618375\pi$
$941$		−	57.1577i		−	1.86329i	0.363374	−	0.931644i	$-0.381625\pi$
$942$	3.00000	+	3.00000i	0.0977453	+	0.0977453i
$943$	−3.46410			−0.112807
$944$	−20.7846			−0.676481
$945$		0			0
$946$	2.00000	−	2.00000i	0.0650256	−	0.0650256i
$947$			29.0000i			0.942373i	0.882034	+	0.471187i	$0.156174\pi$
$947$			29.0000i			0.942373i	−0.882034	+	0.471187i	$0.843826\pi$
$948$	−31.1769			−1.01258
$949$	−30.0000			−0.973841
$950$	10.3923	−	10.3923i	0.337171	−	0.337171i
$951$	−19.0526			−0.617822
$952$		0			0
$953$	−8.00000			−0.259145			−0.129573	−	0.991570i	$-0.541361\pi$
$953$	−8.00000			−0.259145			−0.129573	+	0.991570i	$0.541361\pi$
$954$		0			0
$955$	−1.73205			−0.0560478
$956$	40.0000			1.29369
$957$			6.92820i			0.223957i
$958$	12.1244	−	12.1244i	0.391720	−	0.391720i
$959$		0			0
$960$	−24.0000			−0.774597
$961$	−28.0000			−0.903226
$962$	−10.3923	−	10.3923i	−0.335061	−	0.335061i
$963$		0			0
$964$	10.3923			0.334714
$965$			25.9808i			0.836350i
$966$		0			0
$967$		−	6.00000i		−	0.192947i	−0.995336	−	0.0964735i	$-0.969244\pi$
$967$		−	6.00000i		−	0.192947i	0.995336	−	0.0964735i	$-0.0307563\pi$
$968$	−20.0000	−	20.0000i	−0.642824	−	0.642824i
$969$		−	15.5885i		−	0.500773i
$970$	30.0000	−	30.0000i	0.963242	−	0.963242i
$971$	−60.6218			−1.94545			−0.972723	−	0.231971i	$-0.925483\pi$
$971$	−60.6218			−1.94545			−0.972723	+	0.231971i	$0.925483\pi$
$972$		0			0
$973$		0			0
$974$	−31.0000	−	31.0000i	−0.993304	−	0.993304i
$975$			12.0000i			0.384308i
$976$			20.7846i			0.665299i
$977$	−31.0000			−0.991778			−0.495889	−	0.868386i	$-0.665158\pi$
$977$	−31.0000			−0.991778			−0.495889	+	0.868386i	$0.665158\pi$
$978$	−36.3731	−	36.3731i	−1.16308	−	1.16308i
$979$	15.5885			0.498209
$980$		0			0
$981$		0			0
$982$	32.0000	+	32.0000i	1.02116	+	1.02116i
$983$	−60.6218			−1.93353			−0.966767	−	0.255658i	$-0.917708\pi$
$983$	−60.6218			−1.93353			−0.966767	+	0.255658i	$0.917708\pi$
$984$	−12.0000	+	12.0000i	−0.382546	+	0.382546i
$985$		−	27.7128i		−	0.883004i
$986$	6.92820	+	6.92820i	0.220639	+	0.220639i
$987$		0			0
$988$	−36.0000			−1.14531
$989$	−2.00000			−0.0635963
$990$		0			0
$991$		−	23.0000i		−	0.730619i	−0.930886	−	0.365310i	$-0.880963\pi$
$991$		−	23.0000i		−	0.730619i	0.930886	−	0.365310i	$-0.119037\pi$
$992$	−6.92820	+	6.92820i	−0.219971	+	0.219971i
$993$			12.1244i			0.384755i
$994$		0			0
$995$		−	39.0000i		−	1.23638i
$996$		−	48.0000i		−	1.52094i
$997$		−	22.5167i		−	0.713110i	−0.934274	−	0.356555i	$-0.883951\pi$
$997$		−	22.5167i		−	0.713110i	0.934274	−	0.356555i	$-0.116049\pi$
$998$	−35.0000	−	35.0000i	−1.10791	−	1.10791i
$999$	15.5885			0.493197

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.2.d.b.195.1		4
3.2	odd	2		1764.2.b.a.1567.4		4
4.3	odd	2	inner	196.2.d.b.195.4		4
7.2	even	3		28.2.f.a.3.1	✓	4
7.3	odd	6		28.2.f.a.19.2	yes	4
7.4	even	3		196.2.f.a.19.2		4
7.5	odd	6		196.2.f.a.31.1		4
7.6	odd	2	inner	196.2.d.b.195.2		4
8.3	odd	2		3136.2.f.e.3135.2		4
8.5	even	2		3136.2.f.e.3135.4		4
12.11	even	2		1764.2.b.a.1567.2		4
21.2	odd	6		252.2.bf.e.199.2		4
21.17	even	6		252.2.bf.e.19.1		4
21.20	even	2		1764.2.b.a.1567.3		4
28.3	even	6		28.2.f.a.19.1	yes	4
28.11	odd	6		196.2.f.a.19.1		4
28.19	even	6		196.2.f.a.31.2		4
28.23	odd	6		28.2.f.a.3.2	yes	4
28.27	even	2	inner	196.2.d.b.195.3		4
35.2	odd	12		700.2.t.a.199.2		4
35.3	even	12		700.2.t.b.299.2		4
35.9	even	6		700.2.p.a.451.2		4
35.17	even	12		700.2.t.a.299.1		4
35.23	odd	12		700.2.t.b.199.1		4
35.24	odd	6		700.2.p.a.551.1		4
56.3	even	6		448.2.p.d.383.1		4
56.13	odd	2		3136.2.f.e.3135.1		4
56.27	even	2		3136.2.f.e.3135.3		4
56.37	even	6		448.2.p.d.255.1		4
56.45	odd	6		448.2.p.d.383.2		4
56.51	odd	6		448.2.p.d.255.2		4
84.23	even	6		252.2.bf.e.199.1		4
84.59	odd	6		252.2.bf.e.19.2		4
84.83	odd	2		1764.2.b.a.1567.1		4
140.3	odd	12		700.2.t.a.299.2		4
140.23	even	12		700.2.t.a.199.1		4
140.59	even	6		700.2.p.a.551.2		4
140.79	odd	6		700.2.p.a.451.1		4
140.87	odd	12		700.2.t.b.299.1		4
140.107	even	12		700.2.t.b.199.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.2.f.a.3.1	✓	4	7.2	even	3
28.2.f.a.3.2	yes	4	28.23	odd	6
28.2.f.a.19.1	yes	4	28.3	even	6
28.2.f.a.19.2	yes	4	7.3	odd	6
196.2.d.b.195.1		4	1.1	even	1	trivial
196.2.d.b.195.2		4	7.6	odd	2	inner
196.2.d.b.195.3		4	28.27	even	2	inner
196.2.d.b.195.4		4	4.3	odd	2	inner
196.2.f.a.19.1		4	28.11	odd	6
196.2.f.a.19.2		4	7.4	even	3
196.2.f.a.31.1		4	7.5	odd	6
196.2.f.a.31.2		4	28.19	even	6
252.2.bf.e.19.1		4	21.17	even	6
252.2.bf.e.19.2		4	84.59	odd	6
252.2.bf.e.199.1		4	84.23	even	6
252.2.bf.e.199.2		4	21.2	odd	6
448.2.p.d.255.1		4	56.37	even	6
448.2.p.d.255.2		4	56.51	odd	6
448.2.p.d.383.1		4	56.3	even	6
448.2.p.d.383.2		4	56.45	odd	6
700.2.p.a.451.1		4	140.79	odd	6
700.2.p.a.451.2		4	35.9	even	6
700.2.p.a.551.1		4	35.24	odd	6
700.2.p.a.551.2		4	140.59	even	6
700.2.t.a.199.1		4	140.23	even	12
700.2.t.a.199.2		4	35.2	odd	12
700.2.t.a.299.1		4	35.17	even	12
700.2.t.a.299.2		4	140.3	odd	12
700.2.t.b.199.1		4	35.23	odd	12
700.2.t.b.199.2		4	140.107	even	12
700.2.t.b.299.1		4	140.87	odd	12
700.2.t.b.299.2		4	35.3	even	12
1764.2.b.a.1567.1		4	84.83	odd	2
1764.2.b.a.1567.2		4	12.11	even	2
1764.2.b.a.1567.3		4	21.20	even	2
1764.2.b.a.1567.4		4	3.2	odd	2
3136.2.f.e.3135.1		4	56.13	odd	2
3136.2.f.e.3135.2		4	8.3	odd	2
3136.2.f.e.3135.3		4	56.27	even	2
3136.2.f.e.3135.4		4	8.5	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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} -1.73205 q^{3} -2.00000i q^{4} -1.73205i q^{5} +(-1.73205 + 1.73205i) q^{6} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} -1.73205 q^{3} -2.00000i q^{4} -1.73205i q^{5} +(-1.73205 + 1.73205i) q^{6} +(-2.00000 - 2.00000i) q^{8} +(-1.73205 - 1.73205i) q^{10} -1.00000i q^{11} +3.46410i q^{12} -3.46410i q^{13} +3.00000i q^{15} -4.00000 q^{16} +1.73205i q^{17} +5.19615 q^{19} -3.46410 q^{20} +(-1.00000 - 1.00000i) q^{22} +1.00000i q^{23} +(3.46410 + 3.46410i) q^{24} +2.00000 q^{25} +(-3.46410 - 3.46410i) q^{26} +5.19615 q^{27} +4.00000 q^{29} +(3.00000 + 3.00000i) q^{30} +1.73205 q^{31} +(-4.00000 + 4.00000i) q^{32} +1.73205i q^{33} +(1.73205 + 1.73205i) q^{34} +3.00000 q^{37} +(5.19615 - 5.19615i) q^{38} +6.00000i q^{39} +(-3.46410 + 3.46410i) q^{40} +3.46410i q^{41} +2.00000i q^{43} -2.00000 q^{44} +(1.00000 + 1.00000i) q^{46} -8.66025 q^{47} +6.92820 q^{48} +(2.00000 - 2.00000i) q^{50} -3.00000i q^{51} -6.92820 q^{52} -1.00000 q^{53} +(5.19615 - 5.19615i) q^{54} -1.73205 q^{55} -9.00000 q^{57} +(4.00000 - 4.00000i) q^{58} +5.19615 q^{59} +6.00000 q^{60} -5.19615i q^{61} +(1.73205 - 1.73205i) q^{62} +8.00000i q^{64} -6.00000 q^{65} +(1.73205 + 1.73205i) q^{66} -3.00000i q^{67} +3.46410 q^{68} -1.73205i q^{69} -14.0000i q^{71} -8.66025i q^{73} +(3.00000 - 3.00000i) q^{74} -3.46410 q^{75} -10.3923i q^{76} +(6.00000 + 6.00000i) q^{78} +9.00000i q^{79} +6.92820i q^{80} -9.00000 q^{81} +(3.46410 + 3.46410i) q^{82} -13.8564 q^{83} +3.00000 q^{85} +(2.00000 + 2.00000i) q^{86} -6.92820 q^{87} +(-2.00000 + 2.00000i) q^{88} +15.5885i q^{89} +2.00000 q^{92} -3.00000 q^{93} +(-8.66025 + 8.66025i) q^{94} -9.00000i q^{95} +(6.92820 - 6.92820i) q^{96} +17.3205i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 8 * q^8	\( 4 q + 4 q^{2} - 8 q^{8} - 16 q^{16} - 4 q^{22} + 8 q^{25} + 16 q^{29} + 12 q^{30} - 16 q^{32} + 12 q^{37} - 8 q^{44} + 4 q^{46} + 8 q^{50} - 4 q^{53} - 36 q^{57} + 16 q^{58} + 24 q^{60} - 24 q^{65} + 12 q^{74} + 24 q^{78} - 36 q^{81} + 12 q^{85} + 8 q^{86} - 8 q^{88} + 8 q^{92} - 12 q^{93}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^8 - 16 * q^16 - 4 * q^22 + 8 * q^25 + 16 * q^29 + 12 * q^30 - 16 * q^32 + 12 * q^37 - 8 * q^44 + 4 * q^46 + 8 * q^50 - 4 * q^53 - 36 * q^57 + 16 * q^58 + 24 * q^60 - 24 * q^65 + 12 * q^74 + 24 * q^78 - 36 * q^81 + 12 * q^85 + 8 * q^86 - 8 * q^88 + 8 * q^92 - 12 * q^93

Introduction

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