LMFDB - Embedded newform 196.2.f.a.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,2,Mod(19,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("196.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.f (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.56506787962$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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:	$ 1 $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	196.31
Dual form			196.2.f.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 - 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(1.50000 - 0.866025i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(0.366025 - 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(1.50000 - 0.866025i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(-2.00000 + 2.00000i) q^{8} +(-0.633975 - 2.36603i) q^{10} +(-0.866025 - 0.500000i) q^{11} +(-3.00000 + 1.73205i) q^{12} +3.46410i q^{13} -3.00000i q^{15} +(2.00000 + 3.46410i) q^{16} +(1.50000 + 0.866025i) q^{17} +(-2.59808 - 4.50000i) q^{19} -3.46410 q^{20} +(-1.00000 + 1.00000i) q^{22} +(-0.866025 + 0.500000i) q^{23} +(1.26795 + 4.73205i) q^{24} +(-1.00000 + 1.73205i) q^{25} +(4.73205 + 1.26795i) q^{26} +5.19615 q^{27} +4.00000 q^{29} +(-4.09808 - 1.09808i) q^{30} +(-0.866025 + 1.50000i) q^{31} +(5.46410 - 1.46410i) q^{32} +(-1.50000 + 0.866025i) q^{33} +(1.73205 - 1.73205i) q^{34} +(-1.50000 - 2.59808i) q^{37} +(-7.09808 + 1.90192i) q^{38} +(5.19615 + 3.00000i) q^{39} +(-1.26795 + 4.73205i) q^{40} -3.46410i q^{41} -2.00000i q^{43} +(1.00000 + 1.73205i) q^{44} +(0.366025 + 1.36603i) q^{46} +(4.33013 + 7.50000i) q^{47} +6.92820 q^{48} +(2.00000 + 2.00000i) q^{50} +(2.59808 - 1.50000i) q^{51} +(3.46410 - 6.00000i) q^{52} +(0.500000 - 0.866025i) q^{53} +(1.90192 - 7.09808i) q^{54} -1.73205 q^{55} -9.00000 q^{57} +(1.46410 - 5.46410i) q^{58} +(-2.59808 + 4.50000i) q^{59} +(-3.00000 + 5.19615i) q^{60} +(4.50000 - 2.59808i) q^{61} +(1.73205 + 1.73205i) q^{62} -8.00000i q^{64} +(3.00000 + 5.19615i) q^{65} +(0.633975 + 2.36603i) q^{66} +(-2.59808 - 1.50000i) q^{67} +(-1.73205 - 3.00000i) q^{68} +1.73205i q^{69} +14.0000i q^{71} +(-7.50000 - 4.33013i) q^{73} +(-4.09808 + 1.09808i) q^{74} +(1.73205 + 3.00000i) q^{75} +10.3923i q^{76} +(6.00000 - 6.00000i) q^{78} +(-7.79423 + 4.50000i) q^{79} +(6.00000 + 3.46410i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-4.73205 - 1.26795i) q^{82} -13.8564 q^{83} +3.00000 q^{85} +(-2.73205 - 0.732051i) q^{86} +(3.46410 - 6.00000i) q^{87} +(2.73205 - 0.732051i) q^{88} +(-13.5000 + 7.79423i) q^{89} +2.00000 q^{92} +(1.50000 + 2.59808i) q^{93} +(11.8301 - 3.16987i) q^{94} +(-7.79423 - 4.50000i) q^{95} +(2.53590 - 9.46410i) q^{96} -17.3205i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 6 q^{5} - 8 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 + 6 * q^5 - 8 * q^8	$ 4 q - 2 q^{2} + 6 q^{5} - 8 q^{8} - 6 q^{10} - 12 q^{12} + 8 q^{16} + 6 q^{17} - 4 q^{22} + 12 q^{24} - 4 q^{25} + 12 q^{26} + 16 q^{29} - 6 q^{30} + 8 q^{32} - 6 q^{33} - 6 q^{37} - 18 q^{38} - 12 q^{40} + 4 q^{44} - 2 q^{46} + 8 q^{50} + 2 q^{53} + 18 q^{54} - 36 q^{57} - 8 q^{58} - 12 q^{60} + 18 q^{61} + 12 q^{65} + 6 q^{66} - 30 q^{73} - 6 q^{74} + 24 q^{78} + 24 q^{80} + 18 q^{81} - 12 q^{82} + 12 q^{85} - 4 q^{86} + 4 q^{88} - 54 q^{89} + 8 q^{92} + 6 q^{93} + 30 q^{94} + 24 q^{96}+O(q^{100}) $ 4 * q - 2 * q^2 + 6 * q^5 - 8 * q^8 - 6 * q^10 - 12 * q^12 + 8 * q^16 + 6 * q^17 - 4 * q^22 + 12 * q^24 - 4 * q^25 + 12 * q^26 + 16 * q^29 - 6 * q^30 + 8 * q^32 - 6 * q^33 - 6 * q^37 - 18 * q^38 - 12 * q^40 + 4 * q^44 - 2 * q^46 + 8 * q^50 + 2 * q^53 + 18 * q^54 - 36 * q^57 - 8 * q^58 - 12 * q^60 + 18 * q^61 + 12 * q^65 + 6 * q^66 - 30 * q^73 - 6 * q^74 + 24 * q^78 + 24 * q^80 + 18 * q^81 - 12 * q^82 + 12 * q^85 - 4 * q^86 + 4 * q^88 - 54 * q^89 + 8 * q^92 + 6 * q^93 + 30 * q^94 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i	1.00000			$0$
$4$	−1.73205	−	1.00000i	−0.866025	−	0.500000i
$5$	1.50000	−	0.866025i	0.670820	−	0.387298i	−0.125567	−	0.992085i	$-0.540075\pi$
$5$	1.50000	−	0.866025i	0.670820	−	0.387298i	0.796387	+	0.604787i	$0.206742\pi$
$6$	−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
$10$	−0.633975	−	2.36603i	−0.200480	−	0.748203i
$11$	−0.866025	−	0.500000i	−0.261116	−	0.150756i	0.363727	−	0.931505i	$-0.381504\pi$
$11$	−0.866025	−	0.500000i	−0.261116	−	0.150756i	−0.624844	+	0.780750i	$0.714837\pi$
$12$	−3.00000	+	1.73205i	−0.866025	+	0.500000i
$13$			3.46410i			0.960769i	0.877058	+	0.480384i	$0.159503\pi$
$13$			3.46410i			0.960769i	−0.877058	+	0.480384i	$0.840497\pi$
$14$		0			0
$15$		−	3.00000i		−	0.774597i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	1.50000	+	0.866025i	0.363803	+	0.210042i	0.670748	−	0.741685i	$-0.265973\pi$
$17$	1.50000	+	0.866025i	0.363803	+	0.210042i	−0.306944	+	0.951727i	$0.599307\pi$
$18$		0			0
$19$	−2.59808	−	4.50000i	−0.596040	−	1.03237i	−0.993399	−	0.114708i	$-0.963407\pi$
$19$	−2.59808	−	4.50000i	−0.596040	−	1.03237i	0.397360	−	0.917663i	$-0.369927\pi$
$20$	−3.46410			−0.774597
$21$		0			0
$22$	−1.00000	+	1.00000i	−0.213201	+	0.213201i
$23$	−0.866025	+	0.500000i	−0.180579	+	0.104257i	−0.587565	−	0.809177i	$-0.699913\pi$
$23$	−0.866025	+	0.500000i	−0.180579	+	0.104257i	0.406986	+	0.913434i	$0.366580\pi$
$24$	1.26795	+	4.73205i	0.258819	+	0.965926i
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$	4.73205	+	1.26795i	0.928032	+	0.248665i
$27$	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	$0.378881\pi$
$30$	−4.09808	−	1.09808i	−0.748203	−	0.200480i
$31$	−0.866025	+	1.50000i	−0.155543	+	0.269408i	−0.933257	−	0.359211i	$-0.883046\pi$
$31$	−0.866025	+	1.50000i	−0.155543	+	0.269408i	0.777714	+	0.628619i	$0.216379\pi$
$32$	5.46410	−	1.46410i	0.965926	−	0.258819i
$33$	−1.50000	+	0.866025i	−0.261116	+	0.150756i
$34$	1.73205	−	1.73205i	0.297044	−	0.297044i
$35$		0			0
$36$		0			0
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	0.715981	−	0.698119i	$-0.245980\pi$
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	−0.962580	+	0.270998i	$0.912646\pi$
$38$	−7.09808	+	1.90192i	−1.15146	+	0.308533i
$39$	5.19615	+	3.00000i	0.832050	+	0.480384i
$40$	−1.26795	+	4.73205i	−0.200480	+	0.748203i
$41$		−	3.46410i		−	0.541002i	−0.962720	−	0.270501i	$-0.912811\pi$
$41$		−	3.46410i		−	0.541002i	0.962720	−	0.270501i	$-0.0871893\pi$
$42$		0			0
$43$		−	2.00000i		−	0.304997i	−0.988304	−	0.152499i	$-0.951268\pi$
$43$		−	2.00000i		−	0.304997i	0.988304	−	0.152499i	$-0.0487319\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$		0			0
$46$	0.366025	+	1.36603i	0.0539675	+	0.201409i
$47$	4.33013	+	7.50000i	0.631614	+	1.09399i	0.987222	+	0.159352i	$0.0509405\pi$
$47$	4.33013	+	7.50000i	0.631614	+	1.09399i	−0.355608	+	0.934635i	$0.615726\pi$
$48$	6.92820			1.00000
$49$		0			0
$50$	2.00000	+	2.00000i	0.282843	+	0.282843i
$51$	2.59808	−	1.50000i	0.363803	−	0.210042i
$52$	3.46410	−	6.00000i	0.480384	−	0.832050i
$53$	0.500000	−	0.866025i	0.0686803	−	0.118958i	−0.829640	−	0.558298i	$-0.811454\pi$
$53$	0.500000	−	0.866025i	0.0686803	−	0.118958i	0.898321	+	0.439340i	$0.144788\pi$
$54$	1.90192	−	7.09808i	0.258819	−	0.965926i
$55$	−1.73205			−0.233550
$56$		0			0
$57$	−9.00000			−1.19208
$58$	1.46410	−	5.46410i	0.192246	−	0.717472i
$59$	−2.59808	+	4.50000i	−0.338241	+	0.585850i	−0.984102	−	0.177605i	$-0.943165\pi$
$59$	−2.59808	+	4.50000i	−0.338241	+	0.585850i	0.645861	+	0.763455i	$0.276498\pi$
$60$	−3.00000	+	5.19615i	−0.387298	+	0.670820i
$61$	4.50000	−	2.59808i	0.576166	−	0.332650i	−0.183442	−	0.983030i	$-0.558724\pi$
$61$	4.50000	−	2.59808i	0.576166	−	0.332650i	0.759608	+	0.650381i	$0.225391\pi$
$62$	1.73205	+	1.73205i	0.219971	+	0.219971i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	3.00000	+	5.19615i	0.372104	+	0.644503i
$66$	0.633975	+	2.36603i	0.0780369	+	0.291238i
$67$	−2.59808	−	1.50000i	−0.317406	−	0.183254i	0.332830	−	0.942987i	$-0.391996\pi$
$67$	−2.59808	−	1.50000i	−0.317406	−	0.183254i	−0.650236	+	0.759733i	$0.725330\pi$
$68$	−1.73205	−	3.00000i	−0.210042	−	0.363803i
$69$			1.73205i			0.208514i
$70$		0			0
$71$			14.0000i			1.66149i	0.556650	+	0.830747i	$0.312086\pi$
$71$			14.0000i			1.66149i	−0.556650	+	0.830747i	$0.687914\pi$
$72$		0			0
$73$	−7.50000	−	4.33013i	−0.877809	−	0.506803i	−0.00787336	−	0.999969i	$-0.502506\pi$
$73$	−7.50000	−	4.33013i	−0.877809	−	0.506803i	−0.869935	+	0.493166i	$0.835840\pi$
$74$	−4.09808	+	1.09808i	−0.476392	+	0.127649i
$75$	1.73205	+	3.00000i	0.200000	+	0.346410i
$76$			10.3923i			1.19208i
$77$		0			0
$78$	6.00000	−	6.00000i	0.679366	−	0.679366i
$79$	−7.79423	+	4.50000i	−0.876919	+	0.506290i	−0.869641	−	0.493684i	$-0.835650\pi$
$79$	−7.79423	+	4.50000i	−0.876919	+	0.506290i	−0.00727784	+	0.999974i	$0.502317\pi$
$80$	6.00000	+	3.46410i	0.670820	+	0.387298i
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$	−4.73205	−	1.26795i	−0.522568	−	0.140022i
$83$	−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
$86$	−2.73205	−	0.732051i	−0.294605	−	0.0789391i
$87$	3.46410	−	6.00000i	0.371391	−	0.643268i
$88$	2.73205	−	0.732051i	0.291238	−	0.0780369i
$89$	−13.5000	+	7.79423i	−1.43100	+	0.826187i	−0.997197	−	0.0748225i	$-0.976161\pi$
$89$	−13.5000	+	7.79423i	−1.43100	+	0.826187i	−0.433800	+	0.901009i	$0.642828\pi$
$90$		0			0
$91$		0			0
$92$	2.00000			0.208514
$93$	1.50000	+	2.59808i	0.155543	+	0.269408i
$94$	11.8301	−	3.16987i	1.22018	−	0.326947i
$95$	−7.79423	−	4.50000i	−0.799671	−	0.461690i
$96$	2.53590	−	9.46410i	0.258819	−	0.965926i
$97$		−	17.3205i		−	1.75863i	−0.476240	−	0.879316i	$-0.658000\pi$
$97$		−	17.3205i		−	1.75863i	0.476240	−	0.879316i	$-0.342000\pi$
$98$		0			0
$99$		0			0
$100$	3.46410	−	2.00000i	0.346410	−	0.200000i
$101$	7.50000	+	4.33013i	0.746278	+	0.430864i	0.824347	−	0.566084i	$-0.191542\pi$
$101$	7.50000	+	4.33013i	0.746278	+	0.430864i	−0.0780696	+	0.996948i	$0.524876\pi$
$102$	−1.09808	−	4.09808i	−0.108726	−	0.405770i
$103$	−4.33013	−	7.50000i	−0.426660	−	0.738997i	0.569914	−	0.821705i	$-0.306977\pi$
$103$	−4.33013	−	7.50000i	−0.426660	−	0.738997i	−0.996574	+	0.0827075i	$0.973643\pi$
$104$	−6.92820	−	6.92820i	−0.679366	−	0.679366i
$105$		0			0
$106$	−1.00000	−	1.00000i	−0.0971286	−	0.0971286i
$107$	11.2583	−	6.50000i	1.08838	−	0.628379i	0.155238	−	0.987877i	$-0.450386\pi$
$107$	11.2583	−	6.50000i	1.08838	−	0.628379i	0.933146	+	0.359498i	$0.117052\pi$
$108$	−9.00000	−	5.19615i	−0.866025	−	0.500000i
$109$	−4.50000	+	7.79423i	−0.431022	+	0.746552i	−0.996962	−	0.0778949i	$-0.975180\pi$
$109$	−4.50000	+	7.79423i	−0.431022	+	0.746552i	0.565940	+	0.824447i	$0.308513\pi$
$110$	−0.633975	+	2.36603i	−0.0604471	+	0.225592i
$111$	−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	$0.771189\pi$
$114$	−3.29423	+	12.2942i	−0.308533	+	1.15146i
$115$	−0.866025	+	1.50000i	−0.0807573	+	0.139876i
$116$	−6.92820	−	4.00000i	−0.643268	−	0.371391i
$117$		0			0
$118$	5.19615	+	5.19615i	0.478345	+	0.478345i
$119$		0			0
$120$	6.00000	+	6.00000i	0.547723	+	0.547723i
$121$	−5.00000	−	8.66025i	−0.454545	−	0.787296i
$122$	−1.90192	−	7.09808i	−0.172192	−	0.642630i
$123$	−5.19615	−	3.00000i	−0.468521	−	0.270501i
$124$	3.00000	−	1.73205i	0.269408	−	0.155543i
$125$			12.1244i			1.08444i
$126$		0			0
$127$		−	6.00000i		−	0.532414i	−0.963916	−	0.266207i	$-0.914230\pi$
$127$		−	6.00000i		−	0.532414i	0.963916	−	0.266207i	$-0.0857705\pi$
$128$	−10.9282	−	2.92820i	−0.965926	−	0.258819i
$129$	−3.00000	−	1.73205i	−0.264135	−	0.152499i
$130$	8.19615	−	2.19615i	0.718850	−	0.192615i
$131$	2.59808	+	4.50000i	0.226995	+	0.393167i	0.956916	−	0.290365i	$-0.0937766\pi$
$131$	2.59808	+	4.50000i	0.226995	+	0.393167i	−0.729921	+	0.683531i	$0.760443\pi$
$132$	3.46410			0.301511
$133$		0			0
$134$	−3.00000	+	3.00000i	−0.259161	+	0.259161i
$135$	7.79423	−	4.50000i	0.670820	−	0.387298i
$136$	−4.73205	+	1.26795i	−0.405770	+	0.108726i
$137$	−0.500000	+	0.866025i	−0.0427179	+	0.0739895i	−0.886594	−	0.462549i	$-0.846935\pi$
$137$	−0.500000	+	0.866025i	−0.0427179	+	0.0739895i	0.843876	+	0.536538i	$0.180268\pi$
$138$	2.36603	+	0.633975i	0.201409	+	0.0539675i
$139$	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
$142$	19.1244	+	5.12436i	1.60488	+	0.430026i
$143$	1.73205	−	3.00000i	0.144841	−	0.250873i
$144$		0			0
$145$	6.00000	−	3.46410i	0.498273	−	0.287678i
$146$	−8.66025	+	8.66025i	−0.716728	+	0.716728i
$147$		0			0
$148$			6.00000i			0.493197i
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	0.844818	−	0.535054i	$-0.179709\pi$
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	−0.885779	+	0.464107i	$0.846375\pi$
$150$	4.73205	−	1.26795i	0.386370	−	0.103528i
$151$	6.06218	+	3.50000i	0.493333	+	0.284826i	0.725956	−	0.687741i	$-0.241398\pi$
$151$	6.06218	+	3.50000i	0.493333	+	0.284826i	−0.232623	+	0.972567i	$0.574731\pi$
$152$	14.1962	+	3.80385i	1.15146	+	0.308533i
$153$		0			0
$154$		0			0
$155$			3.00000i			0.240966i
$156$	−6.00000	−	10.3923i	−0.480384	−	0.832050i
$157$	−1.50000	−	0.866025i	−0.119713	−	0.0691164i	0.438948	−	0.898513i	$-0.355351\pi$
$157$	−1.50000	−	0.866025i	−0.119713	−	0.0691164i	−0.558661	+	0.829396i	$0.688685\pi$
$158$	3.29423	+	12.2942i	0.262075	+	0.978076i
$159$	−0.866025	−	1.50000i	−0.0686803	−	0.118958i
$160$	6.92820	−	6.92820i	0.547723	−	0.547723i
$161$		0			0
$162$	−9.00000	−	9.00000i	−0.707107	−	0.707107i
$163$	−18.1865	+	10.5000i	−1.42448	+	0.822423i	−0.996678	−	0.0814491i	$-0.974045\pi$
$163$	−18.1865	+	10.5000i	−1.42448	+	0.822423i	−0.427802	+	0.903873i	$0.640712\pi$
$164$	−3.46410	+	6.00000i	−0.270501	+	0.468521i
$165$	−1.50000	+	2.59808i	−0.116775	+	0.202260i
$166$	−5.07180	+	18.9282i	−0.393648	+	1.46911i
$167$	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
$170$	1.09808	−	4.09808i	0.0842186	−	0.314308i
$171$		0			0
$172$	−2.00000	+	3.46410i	−0.152499	+	0.264135i
$173$	10.5000	−	6.06218i	0.798300	−	0.460899i	−0.0445762	−	0.999006i	$-0.514194\pi$
$173$	10.5000	−	6.06218i	0.798300	−	0.460899i	0.842876	+	0.538107i	$0.180860\pi$
$174$	−6.92820	−	6.92820i	−0.525226	−	0.525226i
$175$		0			0
$176$		−	4.00000i		−	0.301511i
$177$	4.50000	+	7.79423i	0.338241	+	0.585850i
$178$	5.70577	+	21.2942i	0.427666	+	1.59607i
$179$	16.4545	+	9.50000i	1.22987	+	0.710063i	0.967002	−	0.254770i	$-0.0819996\pi$
$179$	16.4545	+	9.50000i	1.22987	+	0.710063i	0.262864	+	0.964833i	$0.415333\pi$
$180$		0			0
$181$			6.92820i			0.514969i	0.966282	+	0.257485i	$0.0828937\pi$
$181$			6.92820i			0.514969i	−0.966282	+	0.257485i	$0.917106\pi$
$182$		0			0
$183$		−	9.00000i		−	0.665299i
$184$	0.732051	−	2.73205i	0.0539675	−	0.201409i
$185$	−4.50000	−	2.59808i	−0.330847	−	0.191014i
$186$	4.09808	−	1.09808i	0.300486	−	0.0805149i
$187$	−0.866025	−	1.50000i	−0.0633300	−	0.109691i
$188$		−	17.3205i		−	1.26323i
$189$		0			0
$190$	−9.00000	+	9.00000i	−0.652929	+	0.652929i
$191$	0.866025	−	0.500000i	0.0626634	−	0.0361787i	−0.468341	−	0.883548i	$-0.655148\pi$
$191$	0.866025	−	0.500000i	0.0626634	−	0.0361787i	0.531004	+	0.847369i	$0.321815\pi$
$192$	−12.0000	−	6.92820i	−0.866025	−	0.500000i
$193$	7.50000	−	12.9904i	0.539862	−	0.935068i	−0.459049	−	0.888411i	$-0.651810\pi$
$193$	7.50000	−	12.9904i	0.539862	−	0.935068i	0.998911	−	0.0466572i	$-0.0148568\pi$
$194$	−23.6603	−	6.33975i	−1.69871	−	0.455167i
$195$	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
$199$	−11.2583	+	19.5000i	−0.798082	+	1.38232i	0.122782	+	0.992434i	$0.460818\pi$
$199$	−11.2583	+	19.5000i	−0.798082	+	1.38232i	−0.920864	+	0.389885i	$0.872515\pi$
$200$	−1.46410	−	5.46410i	−0.103528	−	0.386370i
$201$	−4.50000	+	2.59808i	−0.317406	+	0.183254i
$202$	8.66025	−	8.66025i	0.609333	−	0.609333i
$203$		0			0
$204$	−6.00000			−0.420084
$205$	−3.00000	−	5.19615i	−0.209529	−	0.362915i
$206$	−11.8301	+	3.16987i	−0.824244	+	0.220856i
$207$		0			0
$208$	−12.0000	+	6.92820i	−0.832050	+	0.480384i
$209$			5.19615i			0.359425i
$210$		0			0
$211$		−	10.0000i		−	0.688428i	−0.938891	−	0.344214i	$-0.888145\pi$
$211$		−	10.0000i		−	0.688428i	0.938891	−	0.344214i	$-0.111855\pi$
$212$	−1.73205	+	1.00000i	−0.118958	+	0.0686803i
$213$	21.0000	+	12.1244i	1.43890	+	0.830747i
$214$	−4.75833	−	17.7583i	−0.325273	−	1.21393i
$215$	−1.73205	−	3.00000i	−0.118125	−	0.204598i
$216$	−10.3923	+	10.3923i	−0.707107	+	0.707107i
$217$		0			0
$218$	9.00000	+	9.00000i	0.609557	+	0.609557i
$219$	−12.9904	+	7.50000i	−0.877809	+	0.506803i
$220$	3.00000	+	1.73205i	0.202260	+	0.116775i
$221$	−3.00000	+	5.19615i	−0.201802	+	0.349531i
$222$	−1.90192	+	7.09808i	−0.127649	+	0.476392i
$223$	−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
$226$	−5.85641	+	21.8564i	−0.389562	+	1.45387i
$227$	9.52628	−	16.5000i	0.632281	−	1.09514i	−0.354803	−	0.934941i	$-0.615452\pi$
$227$	9.52628	−	16.5000i	0.632281	−	1.09514i	0.987084	−	0.160202i	$-0.0512147\pi$
$228$	15.5885	+	9.00000i	1.03237	+	0.596040i
$229$	13.5000	−	7.79423i	0.892105	−	0.515057i	0.0174746	−	0.999847i	$-0.494437\pi$
$229$	13.5000	−	7.79423i	0.892105	−	0.515057i	0.874630	+	0.484790i	$0.161104\pi$
$230$	1.73205	+	1.73205i	0.114208	+	0.114208i
$231$		0			0
$232$	−8.00000	+	8.00000i	−0.525226	+	0.525226i
$233$	3.50000	+	6.06218i	0.229293	+	0.397146i	0.957599	−	0.288106i	$-0.0930254\pi$
$233$	3.50000	+	6.06218i	0.229293	+	0.397146i	−0.728306	+	0.685252i	$0.759692\pi$
$234$		0			0
$235$	12.9904	+	7.50000i	0.847399	+	0.489246i
$236$	9.00000	−	5.19615i	0.585850	−	0.338241i
$237$			15.5885i			1.01258i
$238$		0			0
$239$		−	20.0000i		−	1.29369i	−0.762620	−	0.646846i	$-0.776088\pi$
$239$		−	20.0000i		−	1.29369i	0.762620	−	0.646846i	$-0.223912\pi$
$240$	10.3923	−	6.00000i	0.670820	−	0.387298i
$241$	4.50000	+	2.59808i	0.289870	+	0.167357i	0.637883	−	0.770133i	$-0.279810\pi$
$241$	4.50000	+	2.59808i	0.289870	+	0.167357i	−0.348013	+	0.937490i	$0.613143\pi$
$242$	−13.6603	+	3.66025i	−0.878114	+	0.235290i
$243$		0			0
$244$	−10.3923			−0.665299
$245$		0			0
$246$	−6.00000	+	6.00000i	−0.382546	+	0.382546i
$247$	15.5885	−	9.00000i	0.991870	−	0.572656i
$248$	−1.26795	−	4.73205i	−0.0805149	−	0.300486i
$249$	−12.0000	+	20.7846i	−0.760469	+	1.31717i
$250$	16.5622	+	4.43782i	1.04748	+	0.280673i
$251$	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
$254$	−8.19615	−	2.19615i	−0.514272	−	0.137799i
$255$	2.59808	−	4.50000i	0.162698	−	0.281801i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−4.50000	+	2.59808i	−0.280702	+	0.162064i	−0.633741	−	0.773545i	$-0.718482\pi$
$257$	−4.50000	+	2.59808i	−0.280702	+	0.162064i	0.353039	+	0.935609i	$0.385148\pi$
$258$	−3.46410	+	3.46410i	−0.215666	+	0.215666i
$259$		0			0
$260$		−	12.0000i		−	0.744208i
$261$		0			0
$262$	7.09808	−	1.90192i	0.438521	−	0.117501i
$263$	−19.9186	−	11.5000i	−1.22823	−	0.709120i	−0.261573	−	0.965184i	$-0.584241\pi$
$263$	−19.9186	−	11.5000i	−1.22823	−	0.709120i	−0.966660	+	0.256063i	$0.917574\pi$
$264$	1.26795	−	4.73205i	0.0780369	−	0.291238i
$265$		−	1.73205i		−	0.106399i
$266$		0			0
$267$			27.0000i			1.65237i
$268$	3.00000	+	5.19615i	0.183254	+	0.317406i
$269$	−19.5000	−	11.2583i	−1.18894	−	0.686433i	−0.230871	−	0.972984i	$-0.574158\pi$
$269$	−19.5000	−	11.2583i	−1.18894	−	0.686433i	−0.958065	+	0.286552i	$0.907491\pi$
$270$	−3.29423	−	12.2942i	−0.200480	−	0.748203i
$271$	−7.79423	−	13.5000i	−0.473466	−	0.820067i	0.526073	−	0.850439i	$-0.323664\pi$
$271$	−7.79423	−	13.5000i	−0.473466	−	0.820067i	−0.999539	+	0.0303728i	$0.990331\pi$
$272$			6.92820i			0.420084i
$273$		0			0
$274$	1.00000	+	1.00000i	0.0604122	+	0.0604122i
$275$	1.73205	−	1.00000i	0.104447	−	0.0603023i
$276$	1.73205	−	3.00000i	0.104257	−	0.180579i
$277$	6.50000	−	11.2583i	0.390547	−	0.676448i	−0.601975	−	0.798515i	$-0.705619\pi$
$277$	6.50000	−	11.2583i	0.390547	−	0.676448i	0.992522	+	0.122068i	$0.0389525\pi$
$278$	2.53590	−	9.46410i	0.152093	−	0.567619i
$279$		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	$0.538068\pi$
$282$	5.49038	−	20.4904i	0.326947	−	1.22018i
$283$	6.06218	−	10.5000i	0.360359	−	0.624160i	−0.627661	−	0.778487i	$-0.715988\pi$
$283$	6.06218	−	10.5000i	0.360359	−	0.624160i	0.988020	+	0.154327i	$0.0493208\pi$
$284$	14.0000	−	24.2487i	0.830747	−	1.43890i
$285$	−13.5000	+	7.79423i	−0.799671	+	0.461690i
$286$	−3.46410	−	3.46410i	−0.204837	−	0.204837i
$287$		0			0
$288$		0			0
$289$	−7.00000	−	12.1244i	−0.411765	−	0.713197i
$290$	−2.53590	−	9.46410i	−0.148913	−	0.555751i
$291$	−25.9808	−	15.0000i	−1.52302	−	0.879316i
$292$	8.66025	+	15.0000i	0.506803	+	0.877809i
$293$		−	20.7846i		−	1.21425i	−0.794606	−	0.607125i	$-0.792323\pi$
$293$		−	20.7846i		−	1.21425i	0.794606	−	0.607125i	$-0.207677\pi$
$294$		0			0
$295$			9.00000i			0.524000i
$296$	8.19615	+	2.19615i	0.476392	+	0.127649i
$297$	−4.50000	−	2.59808i	−0.261116	−	0.150756i
$298$	−1.36603	+	0.366025i	−0.0791317	+	0.0212033i
$299$	−1.73205	−	3.00000i	−0.100167	−	0.173494i
$300$		−	6.92820i		−	0.400000i
$301$		0			0
$302$	7.00000	−	7.00000i	0.402805	−	0.402805i
$303$	12.9904	−	7.50000i	0.746278	−	0.430864i
$304$	10.3923	−	18.0000i	0.596040	−	1.03237i
$305$	4.50000	−	7.79423i	0.257669	−	0.446296i
$306$		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
$310$	4.09808	+	1.09808i	0.232755	+	0.0623665i
$311$	4.33013	−	7.50000i	0.245539	−	0.425286i	−0.716744	−	0.697336i	$-0.754368\pi$
$311$	4.33013	−	7.50000i	0.245539	−	0.425286i	0.962283	+	0.272050i	$0.0877017\pi$
$312$	−16.3923	+	4.39230i	−0.928032	+	0.248665i
$313$	−1.50000	+	0.866025i	−0.0847850	+	0.0489506i	−0.541793	−	0.840512i	$-0.682254\pi$
$313$	−1.50000	+	0.866025i	−0.0847850	+	0.0489506i	0.457008	+	0.889463i	$0.348921\pi$
$314$	−1.73205	+	1.73205i	−0.0977453	+	0.0977453i
$315$		0			0
$316$	18.0000			1.01258
$317$	−5.50000	−	9.52628i	−0.308911	−	0.535049i	0.669214	−	0.743070i	$-0.266631\pi$
$317$	−5.50000	−	9.52628i	−0.308911	−	0.535049i	−0.978124	+	0.208021i	$0.933298\pi$
$318$	−2.36603	+	0.633975i	−0.132680	+	0.0355515i
$319$	−3.46410	−	2.00000i	−0.193952	−	0.111979i
$320$	−6.92820	−	12.0000i	−0.387298	−	0.670820i
$321$		−	22.5167i		−	1.25676i
$322$		0			0
$323$		−	9.00000i		−	0.500773i
$324$	−15.5885	+	9.00000i	−0.866025	+	0.500000i
$325$	−6.00000	−	3.46410i	−0.332820	−	0.192154i
$326$	7.68653	+	28.6865i	0.425718	+	1.58880i
$327$	7.79423	+	13.5000i	0.431022	+	0.746552i
$328$	6.92820	+	6.92820i	0.382546	+	0.382546i
$329$		0			0
$330$	3.00000	+	3.00000i	0.165145	+	0.165145i
$331$	6.06218	−	3.50000i	0.333207	−	0.192377i	−0.324057	−	0.946038i	$-0.605047\pi$
$331$	6.06218	−	3.50000i	0.333207	−	0.192377i	0.657264	+	0.753660i	$0.271714\pi$
$332$	24.0000	+	13.8564i	1.31717	+	0.760469i
$333$		0			0
$334$	6.33975	−	23.6603i	0.346895	−	1.29463i
$335$	−5.19615			−0.283896
$336$		0			0
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	0.366025	−	1.36603i	0.0199092	−	0.0743020i
$339$	−13.8564	+	24.0000i	−0.752577	+	1.30350i
$340$	−5.19615	−	3.00000i	−0.281801	−	0.162698i
$341$	1.50000	−	0.866025i	0.0812296	−	0.0468979i
$342$		0			0
$343$		0			0
$344$	4.00000	+	4.00000i	0.215666	+	0.215666i
$345$	1.50000	+	2.59808i	0.0807573	+	0.139876i
$346$	−4.43782	−	16.5622i	−0.238579	−	0.890388i
$347$	11.2583	+	6.50000i	0.604379	+	0.348938i	0.770762	−	0.637123i	$-0.219876\pi$
$347$	11.2583	+	6.50000i	0.604379	+	0.348938i	−0.166383	+	0.986061i	$0.553209\pi$
$348$	−12.0000	+	6.92820i	−0.643268	+	0.371391i
$349$			10.3923i			0.556287i	0.960539	+	0.278144i	$0.0897191\pi$
$349$			10.3923i			0.556287i	−0.960539	+	0.278144i	$0.910281\pi$
$350$		0			0
$351$			18.0000i			0.960769i
$352$	−5.46410	−	1.46410i	−0.291238	−	0.0780369i
$353$	25.5000	+	14.7224i	1.35723	+	0.783596i	0.989249	−	0.146238i	$-0.0467166\pi$
$353$	25.5000	+	14.7224i	1.35723	+	0.783596i	0.367979	+	0.929834i	$0.380050\pi$
$354$	12.2942	−	3.29423i	0.653431	−	0.175086i
$355$	12.1244	+	21.0000i	0.643494	+	1.11456i
$356$	31.1769			1.65237
$357$		0			0
$358$	19.0000	−	19.0000i	1.00418	−	1.00418i
$359$	−19.9186	+	11.5000i	−1.05126	+	0.606947i	−0.923003	−	0.384794i	$-0.874273\pi$
$359$	−19.9186	+	11.5000i	−1.05126	+	0.606947i	−0.128260	+	0.991741i	$0.540939\pi$
$360$		0			0
$361$	−4.00000	+	6.92820i	−0.210526	+	0.364642i
$362$	9.46410	+	2.53590i	0.497422	+	0.133284i
$363$	−17.3205			−0.909091
$364$		0			0
$365$	−15.0000			−0.785136
$366$	−12.2942	−	3.29423i	−0.642630	−	0.172192i
$367$	0.866025	−	1.50000i	0.0452062	−	0.0782994i	−0.842537	−	0.538639i	$-0.818939\pi$
$367$	0.866025	−	1.50000i	0.0452062	−	0.0782994i	0.887743	+	0.460339i	$0.152272\pi$
$368$	−3.46410	−	2.00000i	−0.180579	−	0.104257i
$369$		0			0
$370$	−5.19615	+	5.19615i	−0.270135	+	0.270135i
$371$		0			0
$372$		−	6.00000i		−	0.311086i
$373$	14.5000	+	25.1147i	0.750782	+	1.30039i	0.947444	+	0.319921i	$0.103656\pi$
$373$	14.5000	+	25.1147i	0.750782	+	1.30039i	−0.196663	+	0.980471i	$0.563010\pi$
$374$	−2.36603	+	0.633975i	−0.122344	+	0.0327820i
$375$	18.1865	+	10.5000i	0.939149	+	0.542218i
$376$	−23.6603	−	6.33975i	−1.22018	−	0.326947i
$377$			13.8564i			0.713641i
$378$		0			0
$379$			8.00000i			0.410932i	0.978664	+	0.205466i	$0.0658711\pi$
$379$			8.00000i			0.410932i	−0.978664	+	0.205466i	$0.934129\pi$
$380$	9.00000	+	15.5885i	0.461690	+	0.799671i
$381$	−9.00000	−	5.19615i	−0.461084	−	0.266207i
$382$	−0.366025	−	1.36603i	−0.0187275	−	0.0698919i
$383$	−2.59808	−	4.50000i	−0.132755	−	0.229939i	0.791982	−	0.610544i	$-0.209049\pi$
$383$	−2.59808	−	4.50000i	−0.132755	−	0.229939i	−0.924738	+	0.380605i	$0.875716\pi$
$384$	−13.8564	+	13.8564i	−0.707107	+	0.707107i
$385$		0			0
$386$	−15.0000	−	15.0000i	−0.763480	−	0.763480i
$387$		0			0
$388$	−17.3205	+	30.0000i	−0.879316	+	1.52302i
$389$	9.50000	−	16.4545i	0.481669	−	0.834275i	−0.518110	−	0.855314i	$-0.673364\pi$
$389$	9.50000	−	16.4545i	0.481669	−	0.834275i	0.999779	+	0.0210389i	$0.00669738\pi$
$390$	3.80385	−	14.1962i	0.192615	−	0.718850i
$391$	−1.73205			−0.0875936
$392$		0			0
$393$	9.00000			0.453990
$394$	5.85641	−	21.8564i	0.295041	−	1.10111i
$395$	−7.79423	+	13.5000i	−0.392170	+	0.679259i
$396$		0			0
$397$	−16.5000	+	9.52628i	−0.828111	+	0.478110i	−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−16.5000	+	9.52628i	−0.828111	+	0.478110i	0.0250943	+	0.999685i	$0.492011\pi$
$398$	22.5167	+	22.5167i	1.12866	+	1.12866i
$399$		0			0
$400$	−8.00000			−0.400000
$401$	11.5000	+	19.9186i	0.574283	+	0.994687i	0.996119	+	0.0880147i	$0.0280523\pi$
$401$	11.5000	+	19.9186i	0.574283	+	0.994687i	−0.421837	+	0.906672i	$0.638614\pi$
$402$	1.90192	+	7.09808i	0.0948593	+	0.354020i
$403$	−5.19615	−	3.00000i	−0.258839	−	0.149441i
$404$	−8.66025	−	15.0000i	−0.430864	−	0.746278i
$405$		−	15.5885i		−	0.774597i
$406$		0			0
$407$			3.00000i			0.148704i
$408$	−2.19615	+	8.19615i	−0.108726	+	0.405770i
$409$	−22.5000	−	12.9904i	−1.11255	−	0.642333i	−0.173064	−	0.984911i	$-0.555367\pi$
$409$	−22.5000	−	12.9904i	−1.11255	−	0.642333i	−0.939490	+	0.342578i	$0.888700\pi$
$410$	−8.19615	+	2.19615i	−0.404779	+	0.108460i
$411$	0.866025	+	1.50000i	0.0427179	+	0.0739895i
$412$			17.3205i			0.853320i
$413$		0			0
$414$		0			0
$415$	−20.7846	+	12.0000i	−1.02028	+	0.589057i
$416$	5.07180	+	18.9282i	0.248665	+	0.928032i
$417$	6.00000	−	10.3923i	0.293821	−	0.508913i
$418$	7.09808	+	1.90192i	0.347178	+	0.0930261i
$419$	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	$0.662044\pi$
$422$	−13.6603	−	3.66025i	−0.664971	−	0.178178i
$423$		0			0
$424$	0.732051	+	2.73205i	0.0355515	+	0.132680i
$425$	−3.00000	+	1.73205i	−0.145521	+	0.0840168i
$426$	24.2487	−	24.2487i	1.17485	−	1.17485i
$427$		0			0
$428$	−26.0000			−1.25676
$429$	−3.00000	−	5.19615i	−0.144841	−	0.250873i
$430$	−4.73205	+	1.26795i	−0.228200	+	0.0611459i
$431$	19.9186	+	11.5000i	0.959444	+	0.553936i	0.896002	−	0.444050i	$-0.146459\pi$
$431$	19.9186	+	11.5000i	0.959444	+	0.553936i	0.0634424	+	0.997985i	$0.479792\pi$
$432$	10.3923	+	18.0000i	0.500000	+	0.866025i
$433$		−	10.3923i		−	0.499422i	−0.968320	−	0.249711i	$-0.919664\pi$
$433$		−	10.3923i		−	0.499422i	0.968320	−	0.249711i	$-0.0803357\pi$
$434$		0			0
$435$		−	12.0000i		−	0.575356i
$436$	15.5885	−	9.00000i	0.746552	−	0.431022i
$437$	4.50000	+	2.59808i	0.215264	+	0.124283i
$438$	5.49038	+	20.4904i	0.262341	+	0.979068i
$439$	11.2583	+	19.5000i	0.537331	+	0.930684i	0.999047	+	0.0436563i	$0.0139007\pi$
$439$	11.2583	+	19.5000i	0.537331	+	0.930684i	−0.461716	+	0.887028i	$0.652766\pi$
$440$	3.46410	−	3.46410i	0.165145	−	0.165145i
$441$		0			0
$442$	6.00000	+	6.00000i	0.285391	+	0.285391i
$443$	14.7224	−	8.50000i	0.699484	−	0.403847i	−0.107671	−	0.994187i	$-0.534339\pi$
$443$	14.7224	−	8.50000i	0.699484	−	0.403847i	0.807155	+	0.590339i	$0.201006\pi$
$444$	9.00000	+	5.19615i	0.427121	+	0.246598i
$445$	−13.5000	+	23.3827i	−0.639961	+	1.10845i
$446$	−2.53590	+	9.46410i	−0.120078	+	0.448138i
$447$	−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
$451$	−1.73205	+	3.00000i	−0.0815591	+	0.141264i
$452$	27.7128	+	16.0000i	1.30350	+	0.752577i
$453$	10.5000	−	6.06218i	0.493333	−	0.284826i
$454$	−19.0526	−	19.0526i	−0.894181	−	0.894181i
$455$		0			0
$456$	18.0000	−	18.0000i	0.842927	−	0.842927i
$457$	−7.50000	−	12.9904i	−0.350835	−	0.607664i	0.635561	−	0.772051i	$-0.280769\pi$
$457$	−7.50000	−	12.9904i	−0.350835	−	0.607664i	−0.986396	+	0.164386i	$0.947436\pi$
$458$	−5.70577	−	21.2942i	−0.266613	−	0.995014i
$459$	7.79423	+	4.50000i	0.363803	+	0.210042i
$460$	3.00000	−	1.73205i	0.139876	−	0.0807573i
$461$		−	17.3205i		−	0.806696i	−0.915047	−	0.403348i	$-0.867846\pi$
$461$		−	17.3205i		−	0.806696i	0.915047	−	0.403348i	$-0.132154\pi$
$462$		0			0
$463$			30.0000i			1.39422i	0.716965	+	0.697109i	$0.245531\pi$
$463$			30.0000i			1.39422i	−0.716965	+	0.697109i	$0.754469\pi$
$464$	8.00000	+	13.8564i	0.371391	+	0.643268i
$465$	4.50000	+	2.59808i	0.208683	+	0.120483i
$466$	9.56218	−	2.56218i	0.442959	−	0.118691i
$467$	−4.33013	−	7.50000i	−0.200374	−	0.347059i	0.748275	−	0.663389i	$-0.230883\pi$
$467$	−4.33013	−	7.50000i	−0.200374	−	0.347059i	−0.948649	+	0.316330i	$0.897549\pi$
$468$		0			0
$469$		0			0
$470$	15.0000	−	15.0000i	0.691898	−	0.691898i
$471$	−2.59808	+	1.50000i	−0.119713	+	0.0691164i
$472$	−3.80385	−	14.1962i	−0.175086	−	0.653431i
$473$	−1.00000	+	1.73205i	−0.0459800	+	0.0796398i
$474$	21.2942	+	5.70577i	0.978076	+	0.262075i
$475$	10.3923			0.476832
$476$		0			0
$477$		0			0
$478$	−27.3205	−	7.32051i	−1.24961	−	0.334832i
$479$	−6.06218	+	10.5000i	−0.276988	+	0.479757i	−0.970635	−	0.240558i	$-0.922670\pi$
$479$	−6.06218	+	10.5000i	−0.276988	+	0.479757i	0.693647	+	0.720315i	$0.256003\pi$
$480$	−4.39230	−	16.3923i	−0.200480	−	0.748203i
$481$	9.00000	−	5.19615i	0.410365	−	0.236924i
$482$	5.19615	−	5.19615i	0.236678	−	0.236678i
$483$		0			0
$484$			20.0000i			0.909091i
$485$	−15.0000	−	25.9808i	−0.681115	−	1.17973i
$486$		0			0
$487$	−26.8468	−	15.5000i	−1.21654	−	0.702372i	−0.252367	−	0.967632i	$-0.581209\pi$
$487$	−26.8468	−	15.5000i	−1.21654	−	0.702372i	−0.964177	+	0.265260i	$0.914542\pi$
$488$	−3.80385	+	14.1962i	−0.172192	+	0.642630i
$489$			36.3731i			1.64485i
$490$		0			0
$491$		−	32.0000i		−	1.44414i	−0.691820	−	0.722070i	$-0.743191\pi$
$491$		−	32.0000i		−	1.44414i	0.691820	−	0.722070i	$-0.256809\pi$
$492$	6.00000	+	10.3923i	0.270501	+	0.468521i
$493$	6.00000	+	3.46410i	0.270226	+	0.156015i
$494$	−6.58846	−	24.5885i	−0.296429	−	1.10629i
$495$		0			0
$496$	−6.92820			−0.311086
$497$		0			0
$498$	24.0000	+	24.0000i	1.07547	+	1.07547i
$499$	30.3109	−	17.5000i	1.35690	−	0.783408i	0.367697	−	0.929946i	$-0.380146\pi$
$499$	30.3109	−	17.5000i	1.35690	−	0.783408i	0.989205	+	0.146538i	$0.0468131\pi$
$500$	12.1244	−	21.0000i	0.542218	−	0.939149i
$501$	15.0000	−	25.9808i	0.670151	−	1.16073i
$502$	1.26795	−	4.73205i	0.0565913	−	0.211202i
$503$	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
$506$	0.366025	−	1.36603i	0.0162718	−	0.0607272i
$507$	0.866025	−	1.50000i	0.0384615	−	0.0666173i
$508$	−6.00000	+	10.3923i	−0.266207	+	0.461084i
$509$	−10.5000	+	6.06218i	−0.465404	+	0.268701i	−0.714314	−	0.699825i	$-0.753261\pi$
$509$	−10.5000	+	6.06218i	−0.465404	+	0.268701i	0.248910	+	0.968527i	$0.419928\pi$
$510$	−5.19615	−	5.19615i	−0.230089	−	0.230089i
$511$		0			0
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	−13.5000	−	23.3827i	−0.596040	−	1.03237i
$514$	1.90192	+	7.09808i	0.0838903	+	0.313083i
$515$	−12.9904	−	7.50000i	−0.572425	−	0.330489i
$516$	3.46410	+	6.00000i	0.152499	+	0.264135i
$517$		−	8.66025i		−	0.380878i
$518$		0			0
$519$		−	21.0000i		−	0.921798i
$520$	−16.3923	−	4.39230i	−0.718850	−	0.192615i
$521$	−1.50000	−	0.866025i	−0.0657162	−	0.0379413i	0.466782	−	0.884372i	$-0.345413\pi$
$521$	−1.50000	−	0.866025i	−0.0657162	−	0.0379413i	−0.532498	+	0.846431i	$0.678747\pi$
$522$		0			0
$523$	−12.9904	−	22.5000i	−0.568030	−	0.983856i	−0.996761	−	0.0804241i	$-0.974373\pi$
$523$	−12.9904	−	22.5000i	−0.568030	−	0.983856i	0.428731	−	0.903432i	$-0.358961\pi$
$524$		−	10.3923i		−	0.453990i
$525$		0			0
$526$	−23.0000	+	23.0000i	−1.00285	+	1.00285i
$527$	−2.59808	+	1.50000i	−0.113174	+	0.0653410i
$528$	−6.00000	−	3.46410i	−0.261116	−	0.150756i
$529$	−11.0000	+	19.0526i	−0.478261	+	0.828372i
$530$	−2.36603	−	0.633975i	−0.102774	−	0.0275381i
$531$		0			0
$532$		0			0
$533$	12.0000			0.519778
$534$	36.8827	+	9.88269i	1.59607	+	0.427666i
$535$	11.2583	−	19.5000i	0.486740	−	0.843059i
$536$	8.19615	−	2.19615i	0.354020	−	0.0948593i
$537$	28.5000	−	16.4545i	1.22987	−	0.710063i
$538$	−22.5167	+	22.5167i	−0.970762	+	0.970762i
$539$		0			0
$540$	−18.0000			−0.774597
$541$	9.50000	+	16.4545i	0.408437	+	0.707433i	0.994715	−	0.102677i	$-0.0327407\pi$
$541$	9.50000	+	16.4545i	0.408437	+	0.707433i	−0.586278	+	0.810110i	$0.699407\pi$
$542$	−21.2942	+	5.70577i	−0.914665	+	0.245084i
$543$	10.3923	+	6.00000i	0.445976	+	0.257485i
$544$	9.46410	+	2.53590i	0.405770	+	0.108726i
$545$			15.5885i			0.667736i
$546$		0			0
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$	1.73205	−	1.00000i	0.0739895	−	0.0427179i
$549$		0			0
$550$	−0.732051	−	2.73205i	−0.0312148	−	0.116495i
$551$	−10.3923	−	18.0000i	−0.442727	−	0.766826i
$552$	−3.46410	−	3.46410i	−0.147442	−	0.147442i
$553$		0			0
$554$	−13.0000	−	13.0000i	−0.552317	−	0.552317i
$555$	−7.79423	+	4.50000i	−0.330847	+	0.191014i
$556$	−12.0000	−	6.92820i	−0.508913	−	0.293821i
$557$	−18.5000	+	32.0429i	−0.783870	+	1.35770i	0.145802	+	0.989314i	$0.453424\pi$
$557$	−18.5000	+	32.0429i	−0.783870	+	1.35770i	−0.929672	+	0.368389i	$0.879909\pi$
$558$		0			0
$559$	6.92820			0.293032
$560$		0			0
$561$	−3.00000			−0.126660
$562$	−1.46410	+	5.46410i	−0.0617594	+	0.230489i
$563$	11.2583	−	19.5000i	0.474482	−	0.821827i	−0.525091	−	0.851046i	$-0.675969\pi$
$563$	11.2583	−	19.5000i	0.474482	−	0.821827i	0.999573	+	0.0292191i	$0.00930205\pi$
$564$	−25.9808	−	15.0000i	−1.09399	−	0.631614i
$565$	−24.0000	+	13.8564i	−1.00969	+	0.582943i
$566$	−12.1244	−	12.1244i	−0.509625	−	0.509625i
$567$		0			0
$568$	−28.0000	−	28.0000i	−1.17485	−	1.17485i
$569$	6.50000	+	11.2583i	0.272494	+	0.471974i	0.969500	−	0.245092i	$-0.0788181\pi$
$569$	6.50000	+	11.2583i	0.272494	+	0.471974i	−0.697006	+	0.717066i	$0.745485\pi$
$570$	5.70577	+	21.2942i	0.238988	+	0.891917i
$571$	−18.1865	−	10.5000i	−0.761083	−	0.439411i	0.0686016	−	0.997644i	$-0.478146\pi$
$571$	−18.1865	−	10.5000i	−0.761083	−	0.439411i	−0.829684	+	0.558233i	$0.811480\pi$
$572$	−6.00000	+	3.46410i	−0.250873	+	0.144841i
$573$		−	1.73205i		−	0.0723575i
$574$		0			0
$575$		−	2.00000i		−	0.0834058i
$576$		0			0
$577$	28.5000	+	16.4545i	1.18647	+	0.685009i	0.957503	−	0.288425i	$-0.0931316\pi$
$577$	28.5000	+	16.4545i	1.18647	+	0.685009i	0.228968	+	0.973434i	$0.426465\pi$
$578$	−19.1244	+	5.12436i	−0.795468	+	0.213145i
$579$	−12.9904	−	22.5000i	−0.539862	−	0.935068i
$580$	−13.8564			−0.575356
$581$		0			0
$582$	−30.0000	+	30.0000i	−1.24354	+	1.24354i
$583$	−0.866025	+	0.500000i	−0.0358671	+	0.0207079i
$584$	23.6603	−	6.33975i	0.979068	−	0.262341i
$585$		0			0
$586$	−28.3923	−	7.60770i	−1.17288	−	0.314271i
$587$	−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
$590$	12.2942	+	3.29423i	0.506145	+	0.135621i
$591$	13.8564	−	24.0000i	0.569976	−	0.987228i
$592$	6.00000	−	10.3923i	0.246598	−	0.427121i
$593$	13.5000	−	7.79423i	0.554379	−	0.320071i	−0.196508	−	0.980502i	$-0.562960\pi$
$593$	13.5000	−	7.79423i	0.554379	−	0.320071i	0.750886	+	0.660432i	$0.229627\pi$
$594$	−5.19615	+	5.19615i	−0.213201	+	0.213201i
$595$		0			0
$596$			2.00000i			0.0819232i
$597$	19.5000	+	33.7750i	0.798082	+	1.38232i
$598$	−4.73205	+	1.26795i	−0.193508	+	0.0518503i
$599$	14.7224	+	8.50000i	0.601542	+	0.347301i	0.769648	−	0.638468i	$-0.220432\pi$
$599$	14.7224	+	8.50000i	0.601542	+	0.347301i	−0.168106	+	0.985769i	$0.553765\pi$
$600$	−9.46410	−	2.53590i	−0.386370	−	0.103528i
$601$			38.1051i			1.55434i	0.629291	+	0.777170i	$0.283346\pi$
$601$			38.1051i			1.55434i	−0.629291	+	0.777170i	$0.716654\pi$
$602$		0			0
$603$		0			0
$604$	−7.00000	−	12.1244i	−0.284826	−	0.493333i
$605$	−15.0000	−	8.66025i	−0.609837	−	0.352089i
$606$	−5.49038	−	20.4904i	−0.223031	−	0.832365i
$607$	7.79423	+	13.5000i	0.316358	+	0.547948i	0.979725	−	0.200346i	$-0.0642066\pi$
$607$	7.79423	+	13.5000i	0.316358	+	0.547948i	−0.663367	+	0.748294i	$0.730873\pi$
$608$	−20.7846	−	20.7846i	−0.842927	−	0.842927i
$609$		0			0
$610$	−9.00000	−	9.00000i	−0.364399	−	0.364399i
$611$	−25.9808	+	15.0000i	−1.05107	+	0.606835i
$612$		0			0
$613$	15.5000	−	26.8468i	0.626039	−	1.08433i	−0.362300	−	0.932062i	$-0.618008\pi$
$613$	15.5000	−	26.8468i	0.626039	−	1.08433i	0.988339	−	0.152270i	$-0.0486583\pi$
$614$	−7.60770	+	28.3923i	−0.307022	+	1.14582i
$615$	−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	$0.368112\pi$
$618$	−5.49038	+	20.4904i	−0.220856	+	0.824244i
$619$	7.79423	−	13.5000i	0.313276	−	0.542611i	−0.665793	−	0.746136i	$-0.731907\pi$
$619$	7.79423	−	13.5000i	0.313276	−	0.542611i	0.979070	+	0.203526i	$0.0652400\pi$
$620$	3.00000	−	5.19615i	0.120483	−	0.208683i
$621$	−4.50000	+	2.59808i	−0.180579	+	0.104257i
$622$	−8.66025	−	8.66025i	−0.347245	−	0.347245i
$623$		0			0
$624$			24.0000i			0.960769i
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	0.633975	+	2.36603i	0.0253387	+	0.0945654i
$627$	7.79423	+	4.50000i	0.311272	+	0.179713i
$628$	1.73205	+	3.00000i	0.0691164	+	0.119713i
$629$		−	5.19615i		−	0.207184i
$630$		0			0
$631$		−	30.0000i		−	1.19428i	−0.802137	−	0.597141i	$-0.796303\pi$
$631$		−	30.0000i		−	1.19428i	0.802137	−	0.597141i	$-0.203697\pi$
$632$	6.58846	−	24.5885i	0.262075	−	0.978076i
$633$	−15.0000	−	8.66025i	−0.596196	−	0.344214i
$634$	−15.0263	+	4.02628i	−0.596770	+	0.159904i
$635$	−5.19615	−	9.00000i	−0.206203	−	0.357154i
$636$			3.46410i			0.137361i
$637$		0			0
$638$	−4.00000	+	4.00000i	−0.158362	+	0.158362i
$639$		0			0
$640$	−18.9282	+	5.07180i	−0.748203	+	0.200480i
$641$	6.50000	−	11.2583i	0.256735	−	0.444677i	−0.708631	−	0.705580i	$-0.750687\pi$
$641$	6.50000	−	11.2583i	0.256735	−	0.444677i	0.965365	+	0.260902i	$0.0840201\pi$
$642$	−30.7583	−	8.24167i	−1.21393	−	0.325273i
$643$	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
$646$	−12.2942	−	3.29423i	−0.483710	−	0.129610i
$647$	−16.4545	+	28.5000i	−0.646892	+	1.12045i	0.336968	+	0.941516i	$0.390598\pi$
$647$	−16.4545	+	28.5000i	−0.646892	+	1.12045i	−0.983861	+	0.178935i	$0.942735\pi$
$648$	6.58846	+	24.5885i	0.258819	+	0.965926i
$649$	4.50000	−	2.59808i	0.176640	−	0.101983i
$650$	−6.92820	+	6.92820i	−0.271746	+	0.271746i
$651$		0			0
$652$	42.0000			1.64485
$653$	−15.5000	−	26.8468i	−0.606562	−	1.05060i	−0.991803	−	0.127780i	$-0.959215\pi$
$653$	−15.5000	−	26.8468i	−0.606562	−	1.05060i	0.385241	−	0.922816i	$-0.374118\pi$
$654$	21.2942	−	5.70577i	0.832670	−	0.223113i
$655$	7.79423	+	4.50000i	0.304546	+	0.175830i
$656$	12.0000	−	6.92820i	0.468521	−	0.270501i
$657$		0			0
$658$		0			0
$659$			38.0000i			1.48027i	0.672458	+	0.740135i	$0.265238\pi$
$659$			38.0000i			1.48027i	−0.672458	+	0.740135i	$0.734762\pi$
$660$	5.19615	−	3.00000i	0.202260	−	0.116775i
$661$	34.5000	+	19.9186i	1.34189	+	0.774743i	0.987085	−	0.160196i	$-0.0512125\pi$
$661$	34.5000	+	19.9186i	1.34189	+	0.774743i	0.354809	+	0.934939i	$0.384546\pi$
$662$	−2.56218	−	9.56218i	−0.0995819	−	0.371645i
$663$	5.19615	+	9.00000i	0.201802	+	0.349531i
$664$	27.7128	−	27.7128i	1.07547	−	1.07547i
$665$		0			0
$666$		0			0
$667$	−3.46410	+	2.00000i	−0.134131	+	0.0774403i
$668$	−30.0000	−	17.3205i	−1.16073	−	0.670151i
$669$	−6.00000	+	10.3923i	−0.231973	+	0.401790i
$670$	−1.90192	+	7.09808i	−0.0734777	+	0.274223i
$671$	−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
$675$	−5.19615	+	9.00000i	−0.200000	+	0.346410i
$676$	−1.73205	−	1.00000i	−0.0666173	−	0.0384615i
$677$	37.5000	−	21.6506i	1.44124	−	0.832102i	0.443309	−	0.896369i	$-0.353804\pi$
$677$	37.5000	−	21.6506i	1.44124	−	0.832102i	0.997933	+	0.0642672i	$0.0204710\pi$
$678$	27.7128	+	27.7128i	1.06430	+	1.06430i
$679$		0			0
$680$	−6.00000	+	6.00000i	−0.230089	+	0.230089i
$681$	−16.5000	−	28.5788i	−0.632281	−	1.09514i
$682$	−0.633975	−	2.36603i	−0.0242761	−	0.0905998i
$683$	−21.6506	−	12.5000i	−0.828439	−	0.478299i	0.0248792	−	0.999690i	$-0.492080\pi$
$683$	−21.6506	−	12.5000i	−0.828439	−	0.478299i	−0.853318	+	0.521391i	$0.825413\pi$
$684$		0			0
$685$			1.73205i			0.0661783i
$686$		0			0
$687$		−	27.0000i		−	1.03011i
$688$	6.92820	−	4.00000i	0.264135	−	0.152499i
$689$	3.00000	+	1.73205i	0.114291	+	0.0659859i
$690$	4.09808	−	1.09808i	0.156011	−	0.0418030i
$691$	6.06218	+	10.5000i	0.230616	+	0.399439i	0.957990	−	0.286803i	$-0.0925925\pi$
$691$	6.06218	+	10.5000i	0.230616	+	0.399439i	−0.727373	+	0.686242i	$0.759259\pi$
$692$	−24.2487			−0.921798
$693$		0			0
$694$	13.0000	−	13.0000i	0.493473	−	0.493473i
$695$	10.3923	−	6.00000i	0.394203	−	0.227593i
$696$	5.07180	+	18.9282i	0.192246	+	0.717472i
$697$	3.00000	−	5.19615i	0.113633	−	0.196818i
$698$	14.1962	+	3.80385i	0.537332	+	0.143978i
$699$	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	$0.663370\pi$
$702$	24.5885	+	6.58846i	0.928032	+	0.248665i
$703$	−7.79423	+	13.5000i	−0.293965	+	0.509162i
$704$	−4.00000	+	6.92820i	−0.150756	+	0.261116i
$705$	22.5000	−	12.9904i	0.847399	−	0.489246i
$706$	29.4449	−	29.4449i	1.10817	−	1.10817i
$707$		0			0
$708$		−	18.0000i		−	0.676481i
$709$	4.50000	+	7.79423i	0.169001	+	0.292718i	0.938069	−	0.346449i	$-0.112613\pi$
$709$	4.50000	+	7.79423i	0.169001	+	0.292718i	−0.769068	+	0.639167i	$0.779279\pi$
$710$	33.1244	−	8.87564i	1.24313	−	0.333097i
$711$		0			0
$712$	11.4115	−	42.5885i	0.427666	−	1.59607i
$713$		−	1.73205i		−	0.0648658i
$714$		0			0
$715$		−	6.00000i		−	0.224387i
$716$	−19.0000	−	32.9090i	−0.710063	−	1.22987i
$717$	−30.0000	−	17.3205i	−1.12037	−	0.646846i
$718$	8.41858	+	31.4186i	0.314179	+	1.17253i
$719$	12.9904	+	22.5000i	0.484459	+	0.839108i	0.999841	−	0.0178527i	$-0.00568298\pi$
$719$	12.9904	+	22.5000i	0.484459	+	0.839108i	−0.515381	+	0.856961i	$0.672350\pi$
$720$		0			0
$721$		0			0
$722$	8.00000	+	8.00000i	0.297729	+	0.297729i
$723$	7.79423	−	4.50000i	0.289870	−	0.167357i
$724$	6.92820	−	12.0000i	0.257485	−	0.445976i
$725$	−4.00000	+	6.92820i	−0.148556	+	0.257307i
$726$	−6.33975	+	23.6603i	−0.235290	+	0.878114i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$	−5.49038	+	20.4904i	−0.203208	+	0.758383i
$731$	1.73205	−	3.00000i	0.0640622	−	0.110959i
$732$	−9.00000	+	15.5885i	−0.332650	+	0.576166i
$733$	−37.5000	+	21.6506i	−1.38509	+	0.799684i	−0.992757	−	0.120137i	$-0.961667\pi$
$733$	−37.5000	+	21.6506i	−1.38509	+	0.799684i	−0.392337	+	0.919822i	$0.628333\pi$
$734$	−1.73205	−	1.73205i	−0.0639312	−	0.0639312i
$735$		0			0
$736$	−4.00000	+	4.00000i	−0.147442	+	0.147442i
$737$	1.50000	+	2.59808i	0.0552532	+	0.0957014i
$738$		0			0
$739$	44.1673	+	25.5000i	1.62472	+	0.938033i	0.985634	+	0.168898i	$0.0540208\pi$
$739$	44.1673	+	25.5000i	1.62472	+	0.938033i	0.639087	+	0.769135i	$0.279313\pi$
$740$	5.19615	+	9.00000i	0.191014	+	0.330847i
$741$		−	31.1769i		−	1.14531i
$742$		0			0
$743$			34.0000i			1.24734i	0.781688	+	0.623670i	$0.214359\pi$
$743$			34.0000i			1.24734i	−0.781688	+	0.623670i	$0.785641\pi$
$744$	−8.19615	−	2.19615i	−0.300486	−	0.0805149i
$745$	−1.50000	−	0.866025i	−0.0549557	−	0.0317287i
$746$	39.6147	−	10.6147i	1.45040	−	0.388633i
$747$		0			0
$748$			3.46410i			0.126660i
$749$		0			0
$750$	21.0000	−	21.0000i	0.766812	−	0.766812i
$751$	21.6506	−	12.5000i	0.790043	−	0.456131i	−0.0499348	−	0.998752i	$-0.515901\pi$
$751$	21.6506	−	12.5000i	0.790043	−	0.456131i	0.839978	+	0.542621i	$0.182568\pi$
$752$	−17.3205	+	30.0000i	−0.631614	+	1.09399i
$753$	3.00000	−	5.19615i	0.109326	−	0.189358i
$754$	18.9282	+	5.07180i	0.689325	+	0.184704i
$755$	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	$0.837369\pi$
$758$	10.9282	+	2.92820i	0.396930	+	0.106357i
$759$	0.866025	−	1.50000i	0.0314347	−	0.0544466i
$760$	24.5885	−	6.58846i	0.891917	−	0.238988i
$761$	−16.5000	+	9.52628i	−0.598125	+	0.345327i	−0.768303	−	0.640086i	$-0.778899\pi$
$761$	−16.5000	+	9.52628i	−0.598125	+	0.345327i	0.170179	+	0.985413i	$0.445565\pi$
$762$	−10.3923	+	10.3923i	−0.376473	+	0.376473i
$763$		0			0
$764$	−2.00000			−0.0723575
$765$		0			0
$766$	−7.09808	+	1.90192i	−0.256464	+	0.0687193i
$767$	−15.5885	−	9.00000i	−0.562867	−	0.324971i
$768$	13.8564	+	24.0000i	0.500000	+	0.866025i
$769$		−	3.46410i		−	0.124919i	−0.998048	−	0.0624593i	$-0.980106\pi$
$769$		−	3.46410i		−	0.124919i	0.998048	−	0.0624593i	$-0.0198944\pi$
$770$		0			0
$771$			9.00000i			0.324127i
$772$	−25.9808	+	15.0000i	−0.935068	+	0.539862i
$773$	−22.5000	−	12.9904i	−0.809269	−	0.467232i	0.0374331	−	0.999299i	$-0.488082\pi$
$773$	−22.5000	−	12.9904i	−0.809269	−	0.467232i	−0.846702	+	0.532068i	$0.821415\pi$
$774$		0			0
$775$	−1.73205	−	3.00000i	−0.0622171	−	0.107763i
$776$	34.6410	+	34.6410i	1.24354	+	1.24354i
$777$		0			0
$778$	−19.0000	−	19.0000i	−0.681183	−	0.681183i
$779$	−15.5885	+	9.00000i	−0.558514	+	0.322458i
$780$	−18.0000	−	10.3923i	−0.644503	−	0.372104i
$781$	7.00000	−	12.1244i	0.250480	−	0.433844i
$782$	−0.633975	+	2.36603i	−0.0226709	+	0.0846089i
$783$	20.7846			0.742781
$784$		0			0
$785$	−3.00000			−0.107075
$786$	3.29423	−	12.2942i	0.117501	−	0.438521i
$787$	−2.59808	+	4.50000i	−0.0926114	+	0.160408i	−0.908609	−	0.417647i	$-0.862855\pi$
$787$	−2.59808	+	4.50000i	−0.0926114	+	0.160408i	0.815998	+	0.578055i	$0.196188\pi$
$788$	−27.7128	−	16.0000i	−0.987228	−	0.569976i
$789$	−34.5000	+	19.9186i	−1.22823	+	0.709120i
$790$	15.5885	+	15.5885i	0.554612	+	0.554612i
$791$		0			0
$792$		0			0
$793$	9.00000	+	15.5885i	0.319599	+	0.553562i
$794$	6.97372	+	26.0263i	0.247488	+	0.923638i
$795$	−2.59808	−	1.50000i	−0.0921443	−	0.0531995i
$796$	39.0000	−	22.5167i	1.38232	−	0.798082i
$797$		−	10.3923i		−	0.368114i	−0.982916	−	0.184057i	$-0.941077\pi$
$797$		−	10.3923i		−	0.368114i	0.982916	−	0.184057i	$-0.0589232\pi$
$798$		0			0
$799$			15.0000i			0.530662i
$800$	−2.92820	+	10.9282i	−0.103528	+	0.386370i
$801$		0			0
$802$	31.4186	−	8.41858i	1.10943	−	0.297271i
$803$	4.33013	+	7.50000i	0.152807	+	0.264669i
$804$	10.3923			0.366508
$805$		0			0
$806$	−6.00000	+	6.00000i	−0.211341	+	0.211341i
$807$	−33.7750	+	19.5000i	−1.18894	+	0.686433i
$808$	−23.6603	+	6.33975i	−0.832365	+	0.223031i
$809$	−21.5000	+	37.2391i	−0.755900	+	1.30926i	0.189026	+	0.981972i	$0.439467\pi$
$809$	−21.5000	+	37.2391i	−0.755900	+	1.30926i	−0.944926	+	0.327285i	$0.893866\pi$
$810$	−21.2942	−	5.70577i	−0.748203	−	0.200480i
$811$	−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
$814$	4.09808	+	1.09808i	0.143637	+	0.0384876i
$815$	−18.1865	+	31.5000i	−0.637046	+	1.10340i
$816$	10.3923	+	6.00000i	0.363803	+	0.210042i
$817$	−9.00000	+	5.19615i	−0.314870	+	0.181790i
$818$	−25.9808	+	25.9808i	−0.908396	+	0.908396i
$819$		0			0
$820$			12.0000i			0.419058i
$821$	5.50000	+	9.52628i	0.191951	+	0.332469i	0.945897	−	0.324468i	$-0.105185\pi$
$821$	5.50000	+	9.52628i	0.191951	+	0.332469i	−0.753946	+	0.656937i	$0.771852\pi$
$822$	2.36603	−	0.633975i	0.0825246	−	0.0221124i
$823$	7.79423	+	4.50000i	0.271690	+	0.156860i	0.629655	−	0.776875i	$-0.283196\pi$
$823$	7.79423	+	4.50000i	0.271690	+	0.156860i	−0.357966	+	0.933735i	$0.616529\pi$
$824$	23.6603	+	6.33975i	0.824244	+	0.220856i
$825$		−	3.46410i		−	0.120605i
$826$		0			0
$827$		−	22.0000i		−	0.765015i	−0.923952	−	0.382507i	$-0.875061\pi$
$827$		−	22.0000i		−	0.765015i	0.923952	−	0.382507i	$-0.124939\pi$
$828$		0			0
$829$	7.50000	+	4.33013i	0.260486	+	0.150392i	0.624556	−	0.780980i	$-0.285280\pi$
$829$	7.50000	+	4.33013i	0.260486	+	0.150392i	−0.364070	+	0.931371i	$0.618613\pi$
$830$	8.78461	+	32.7846i	0.304918	+	1.13797i
$831$	−11.2583	−	19.5000i	−0.390547	−	0.676448i
$832$	27.7128			0.960769
$833$		0			0
$834$	−12.0000	−	12.0000i	−0.415526	−	0.415526i
$835$	25.9808	−	15.0000i	0.899101	−	0.519096i
$836$	5.19615	−	9.00000i	0.179713	−	0.311272i
$837$	−4.50000	+	7.79423i	−0.155543	+	0.269408i
$838$	7.60770	−	28.3923i	0.262803	−	0.980796i
$839$	−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
$842$	−7.32051	+	27.3205i	−0.252281	+	0.941527i
$843$	−3.46410	+	6.00000i	−0.119310	+	0.206651i
$844$	−10.0000	+	17.3205i	−0.344214	+	0.596196i
$845$	1.50000	−	0.866025i	0.0516016	−	0.0297922i
$846$		0			0
$847$		0			0
$848$	4.00000			0.137361
$849$	−10.5000	−	18.1865i	−0.360359	−	0.624160i
$850$	1.26795	+	4.73205i	0.0434903	+	0.162308i
$851$	2.59808	+	1.50000i	0.0890609	+	0.0514193i
$852$	−24.2487	−	42.0000i	−0.830747	−	1.43890i
$853$		−	24.2487i		−	0.830260i	−0.909762	−	0.415130i	$-0.863736\pi$
$853$		−	24.2487i		−	0.830260i	0.909762	−	0.415130i	$-0.136264\pi$
$854$		0			0
$855$		0			0
$856$	−9.51666	+	35.5167i	−0.325273	+	1.21393i
$857$	22.5000	+	12.9904i	0.768585	+	0.443743i	0.832370	−	0.554221i	$-0.186984\pi$
$857$	22.5000	+	12.9904i	0.768585	+	0.443743i	−0.0637844	+	0.997964i	$0.520317\pi$
$858$	−8.19615	+	2.19615i	−0.279812	+	0.0749754i
$859$	25.1147	+	43.5000i	0.856904	+	1.48420i	0.874868	+	0.484362i	$0.160948\pi$
$859$	25.1147	+	43.5000i	0.856904	+	1.48420i	−0.0179638	+	0.999839i	$0.505718\pi$
$860$			6.92820i			0.236250i
$861$		0			0
$862$	23.0000	−	23.0000i	0.783383	−	0.783383i
$863$	30.3109	−	17.5000i	1.03179	−	0.595707i	0.114296	−	0.993447i	$-0.463539\pi$
$863$	30.3109	−	17.5000i	1.03179	−	0.595707i	0.917498	+	0.397740i	$0.130205\pi$
$864$	28.3923	−	7.60770i	0.965926	−	0.258819i
$865$	10.5000	−	18.1865i	0.357011	−	0.618361i
$866$	−14.1962	−	3.80385i	−0.482405	−	0.129260i
$867$	−24.2487			−0.823529
$868$		0			0
$869$	9.00000			0.305304
$870$	−16.3923	−	4.39230i	−0.555751	−	0.148913i
$871$	5.19615	−	9.00000i	0.176065	−	0.304953i
$872$	−6.58846	−	24.5885i	−0.223113	−	0.832670i
$873$		0			0
$874$	5.19615	−	5.19615i	0.175762	−	0.175762i
$875$		0			0
$876$	30.0000			1.01361
$877$	−0.500000	−	0.866025i	−0.0168838	−	0.0292436i	0.857460	−	0.514551i	$-0.172041\pi$
$877$	−0.500000	−	0.866025i	−0.0168838	−	0.0292436i	−0.874344	+	0.485307i	$0.838708\pi$
$878$	30.7583	−	8.24167i	1.03804	−	0.278143i
$879$	−31.1769	−	18.0000i	−1.05157	−	0.607125i
$880$	−3.46410	−	6.00000i	−0.116775	−	0.202260i
$881$			13.8564i			0.466834i	0.972377	+	0.233417i	$0.0749907\pi$
$881$			13.8564i			0.466834i	−0.972377	+	0.233417i	$0.925009\pi$
$882$		0			0
$883$			10.0000i			0.336527i	0.985742	+	0.168263i	$0.0538159\pi$
$883$			10.0000i			0.336527i	−0.985742	+	0.168263i	$0.946184\pi$
$884$	10.3923	−	6.00000i	0.349531	−	0.201802i
$885$	13.5000	+	7.79423i	0.453798	+	0.262000i
$886$	−6.22243	−	23.2224i	−0.209047	−	0.780173i
$887$	−12.9904	−	22.5000i	−0.436174	−	0.755476i	0.561216	−	0.827669i	$-0.310334\pi$
$887$	−12.9904	−	22.5000i	−0.436174	−	0.755476i	−0.997391	+	0.0721931i	$0.977000\pi$
$888$	10.3923	−	10.3923i	0.348743	−	0.348743i
$889$		0			0
$890$	27.0000	+	27.0000i	0.905042	+	0.905042i
$891$	−7.79423	+	4.50000i	−0.261116	+	0.150756i
$892$	12.0000	+	6.92820i	0.401790	+	0.231973i
$893$	22.5000	−	38.9711i	0.752934	−	1.30412i
$894$	−0.633975	+	2.36603i	−0.0212033	+	0.0791317i
$895$	32.9090			1.10003
$896$		0			0
$897$	−6.00000			−0.200334
$898$	2.92820	−	10.9282i	0.0977154	−	0.364679i
$899$	−3.46410	+	6.00000i	−0.115534	+	0.200111i
$900$		0			0
$901$	1.50000	−	0.866025i	0.0499722	−	0.0288515i
$902$	3.46410	+	3.46410i	0.115342	+	0.115342i
$903$		0			0
$904$	32.0000	−	32.0000i	1.06430	−	1.06430i
$905$	6.00000	+	10.3923i	0.199447	+	0.345452i
$906$	−4.43782	−	16.5622i	−0.147437	−	0.550242i
$907$	−6.06218	−	3.50000i	−0.201291	−	0.116216i	0.395966	−	0.918265i	$-0.370410\pi$
$907$	−6.06218	−	3.50000i	−0.201291	−	0.116216i	−0.597258	+	0.802049i	$0.703743\pi$
$908$	−33.0000	+	19.0526i	−1.09514	+	0.632281i
$909$		0			0
$910$		0			0
$911$			26.0000i			0.861418i	0.902491	+	0.430709i	$0.141737\pi$
$911$			26.0000i			0.861418i	−0.902491	+	0.430709i	$0.858263\pi$
$912$	−18.0000	−	31.1769i	−0.596040	−	1.03237i
$913$	12.0000	+	6.92820i	0.397142	+	0.229290i
$914$	−20.4904	+	5.49038i	−0.677762	+	0.181606i
$915$	−7.79423	−	13.5000i	−0.257669	−	0.446296i
$916$	−31.1769			−1.03011
$917$		0			0
$918$	9.00000	−	9.00000i	0.297044	−	0.297044i
$919$	0.866025	−	0.500000i	0.0285675	−	0.0164935i	−0.485648	−	0.874154i	$-0.661416\pi$
$919$	0.866025	−	0.500000i	0.0285675	−	0.0164935i	0.514216	+	0.857661i	$0.328083\pi$
$920$	−1.26795	−	4.73205i	−0.0418030	−	0.156011i
$921$	−18.0000	+	31.1769i	−0.593120	+	1.02731i
$922$	−23.6603	−	6.33975i	−0.779209	−	0.208788i
$923$	−48.4974			−1.59631
$924$		0			0
$925$	6.00000			0.197279
$926$	40.9808	+	10.9808i	1.34671	+	0.360850i
$927$		0			0
$928$	21.8564	−	5.85641i	0.717472	−	0.192246i
$929$	−7.50000	+	4.33013i	−0.246067	+	0.142067i	−0.617962	−	0.786208i	$-0.712041\pi$
$929$	−7.50000	+	4.33013i	−0.246067	+	0.142067i	0.371895	+	0.928275i	$0.378708\pi$
$930$	5.19615	−	5.19615i	0.170389	−	0.170389i
$931$		0			0
$932$		−	14.0000i		−	0.458585i
$933$	−7.50000	−	12.9904i	−0.245539	−	0.425286i
$934$	−11.8301	+	3.16987i	−0.387094	+	0.103721i
$935$	−2.59808	−	1.50000i	−0.0849662	−	0.0490552i
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$			3.00000i			0.0979013i
$940$	−15.0000	−	25.9808i	−0.489246	−	0.847399i
$941$	−49.5000	−	28.5788i	−1.61365	−	0.931644i	−0.988514	−	0.151131i	$-0.951708\pi$
$941$	−49.5000	−	28.5788i	−1.61365	−	0.931644i	−0.625140	−	0.780513i	$-0.714958\pi$
$942$	1.09808	+	4.09808i	0.0357773	+	0.133523i
$943$	1.73205	+	3.00000i	0.0564033	+	0.0976934i
$944$	−20.7846			−0.676481
$945$		0			0
$946$	2.00000	+	2.00000i	0.0650256	+	0.0650256i
$947$	−25.1147	+	14.5000i	−0.816119	+	0.471187i	−0.849076	−	0.528270i	$-0.822841\pi$
$947$	−25.1147	+	14.5000i	−0.816119	+	0.471187i	0.0329571	+	0.999457i	$0.489508\pi$
$948$	15.5885	−	27.0000i	0.506290	−	0.876919i
$949$	15.0000	−	25.9808i	0.486921	−	0.843371i
$950$	3.80385	−	14.1962i	0.123413	−	0.460584i
$951$	−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
$955$	0.866025	−	1.50000i	0.0280239	−	0.0485389i
$956$	−20.0000	+	34.6410i	−0.646846	+	1.12037i
$957$	−6.00000	+	3.46410i	−0.193952	+	0.111979i
$958$	12.1244	+	12.1244i	0.391720	+	0.391720i
$959$		0			0
$960$	−24.0000			−0.774597
$961$	14.0000	+	24.2487i	0.451613	+	0.782216i
$962$	−3.80385	−	14.1962i	−0.122641	−	0.457702i
$963$		0			0
$964$	−5.19615	−	9.00000i	−0.167357	−	0.289870i
$965$		−	25.9808i		−	0.836350i
$966$		0			0
$967$			6.00000i			0.192947i	0.995336	+	0.0964735i	$0.0307563\pi$
$967$			6.00000i			0.192947i	−0.995336	+	0.0964735i	$0.969244\pi$
$968$	27.3205	+	7.32051i	0.878114	+	0.235290i
$969$	−13.5000	−	7.79423i	−0.433682	−	0.250387i
$970$	−40.9808	+	10.9808i	−1.31581	+	0.352571i
$971$	30.3109	+	52.5000i	0.972723	+	1.68481i	0.687254	+	0.726417i	$0.258816\pi$
$971$	30.3109	+	52.5000i	0.972723	+	1.68481i	0.285469	+	0.958388i	$0.407851\pi$
$972$		0			0
$973$		0			0
$974$	−31.0000	+	31.0000i	−0.993304	+	0.993304i
$975$	−10.3923	+	6.00000i	−0.332820	+	0.192154i
$976$	18.0000	+	10.3923i	0.576166	+	0.332650i
$977$	15.5000	−	26.8468i	0.495889	−	0.858905i	−0.504100	−	0.863645i	$-0.668176\pi$
$977$	15.5000	−	26.8468i	0.495889	−	0.858905i	0.999989	+	0.00474056i	$0.00150897\pi$
$978$	49.6865	+	13.3135i	1.58880	+	0.425718i
$979$	15.5885			0.498209
$980$		0			0
$981$		0			0
$982$	−43.7128	−	11.7128i	−1.39493	−	0.373771i
$983$	30.3109	−	52.5000i	0.966767	−	1.67449i	0.261977	−	0.965074i	$-0.415626\pi$
$983$	30.3109	−	52.5000i	0.966767	−	1.67449i	0.704790	−	0.709416i	$-0.251041\pi$
$984$	16.3923	−	4.39230i	0.522568	−	0.140022i
$985$	24.0000	−	13.8564i	0.764704	−	0.441502i
$986$	6.92820	−	6.92820i	0.220639	−	0.220639i
$987$		0			0
$988$	−36.0000			−1.14531
$989$	1.00000	+	1.73205i	0.0317982	+	0.0550760i
$990$		0			0
$991$	−19.9186	−	11.5000i	−0.632735	−	0.365310i	0.149076	−	0.988826i	$-0.452370\pi$
$991$	−19.9186	−	11.5000i	−0.632735	−	0.365310i	−0.781810	+	0.623516i	$0.785704\pi$
$992$	−2.53590	+	9.46410i	−0.0805149	+	0.300486i
$993$		−	12.1244i		−	0.384755i
$994$		0			0
$995$			39.0000i			1.23638i
$996$	41.5692	−	24.0000i	1.31717	−	0.760469i
$997$	−19.5000	−	11.2583i	−0.617571	−	0.356555i	0.158352	−	0.987383i	$-0.449382\pi$
$997$	−19.5000	−	11.2583i	−0.617571	−	0.356555i	−0.775923	+	0.630828i	$0.782715\pi$
$998$	−12.8109	−	47.8109i	−0.405522	−	1.51343i
$999$	−7.79423	−	13.5000i	−0.246598	−	0.427121i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.2.f.a.3.1	✓	4	28.27	even	2
28.2.f.a.3.2	yes	4	7.6	odd	2
28.2.f.a.19.1	yes	4	7.2	even	3
28.2.f.a.19.2	yes	4	28.23	odd	6
196.2.d.b.195.1		4	28.3	even	6
196.2.d.b.195.2		4	28.11	odd	6
196.2.d.b.195.3		4	7.4	even	3
196.2.d.b.195.4		4	7.3	odd	6
196.2.f.a.19.1		4	7.5	odd	6	inner
196.2.f.a.19.2		4	28.19	even	6	inner
196.2.f.a.31.1		4	4.3	odd	2	inner
196.2.f.a.31.2		4	1.1	even	1	trivial
252.2.bf.e.19.1		4	84.23	even	6
252.2.bf.e.19.2		4	21.2	odd	6
252.2.bf.e.199.1		4	21.20	even	2
252.2.bf.e.199.2		4	84.83	odd	2
448.2.p.d.255.1		4	56.27	even	2
448.2.p.d.255.2		4	56.13	odd	2
448.2.p.d.383.1		4	56.37	even	6
448.2.p.d.383.2		4	56.51	odd	6
700.2.p.a.451.1		4	35.34	odd	2
700.2.p.a.451.2		4	140.139	even	2
700.2.p.a.551.1		4	140.79	odd	6
700.2.p.a.551.2		4	35.9	even	6
700.2.t.a.199.1		4	35.13	even	4
700.2.t.a.199.2		4	140.27	odd	4
700.2.t.a.299.1		4	140.107	even	12
700.2.t.a.299.2		4	35.23	odd	12
700.2.t.b.199.1		4	140.83	odd	4
700.2.t.b.199.2		4	35.27	even	4
700.2.t.b.299.1		4	35.2	odd	12
700.2.t.b.299.2		4	140.23	even	12
1764.2.b.a.1567.1		4	21.11	odd	6
1764.2.b.a.1567.2		4	21.17	even	6
1764.2.b.a.1567.3		4	84.11	even	6
1764.2.b.a.1567.4		4	84.59	odd	6
3136.2.f.e.3135.1		4	56.11	odd	6
3136.2.f.e.3135.2		4	56.45	odd	6
3136.2.f.e.3135.3		4	56.53	even	6
3136.2.f.e.3135.4		4	56.3	even	6

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.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(1.50000 - 0.866025i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(0.366025 - 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(1.50000 - 0.866025i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(-2.00000 + 2.00000i) q^{8} +(-0.633975 - 2.36603i) q^{10} +(-0.866025 - 0.500000i) q^{11} +(-3.00000 + 1.73205i) q^{12} +3.46410i q^{13} -3.00000i q^{15} +(2.00000 + 3.46410i) q^{16} +(1.50000 + 0.866025i) q^{17} +(-2.59808 - 4.50000i) q^{19} -3.46410 q^{20} +(-1.00000 + 1.00000i) q^{22} +(-0.866025 + 0.500000i) q^{23} +(1.26795 + 4.73205i) q^{24} +(-1.00000 + 1.73205i) q^{25} +(4.73205 + 1.26795i) q^{26} +5.19615 q^{27} +4.00000 q^{29} +(-4.09808 - 1.09808i) q^{30} +(-0.866025 + 1.50000i) q^{31} +(5.46410 - 1.46410i) q^{32} +(-1.50000 + 0.866025i) q^{33} +(1.73205 - 1.73205i) q^{34} +(-1.50000 - 2.59808i) q^{37} +(-7.09808 + 1.90192i) q^{38} +(5.19615 + 3.00000i) q^{39} +(-1.26795 + 4.73205i) q^{40} -3.46410i q^{41} -2.00000i q^{43} +(1.00000 + 1.73205i) q^{44} +(0.366025 + 1.36603i) q^{46} +(4.33013 + 7.50000i) q^{47} +6.92820 q^{48} +(2.00000 + 2.00000i) q^{50} +(2.59808 - 1.50000i) q^{51} +(3.46410 - 6.00000i) q^{52} +(0.500000 - 0.866025i) q^{53} +(1.90192 - 7.09808i) q^{54} -1.73205 q^{55} -9.00000 q^{57} +(1.46410 - 5.46410i) q^{58} +(-2.59808 + 4.50000i) q^{59} +(-3.00000 + 5.19615i) q^{60} +(4.50000 - 2.59808i) q^{61} +(1.73205 + 1.73205i) q^{62} -8.00000i q^{64} +(3.00000 + 5.19615i) q^{65} +(0.633975 + 2.36603i) q^{66} +(-2.59808 - 1.50000i) q^{67} +(-1.73205 - 3.00000i) q^{68} +1.73205i q^{69} +14.0000i q^{71} +(-7.50000 - 4.33013i) q^{73} +(-4.09808 + 1.09808i) q^{74} +(1.73205 + 3.00000i) q^{75} +10.3923i q^{76} +(6.00000 - 6.00000i) q^{78} +(-7.79423 + 4.50000i) q^{79} +(6.00000 + 3.46410i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-4.73205 - 1.26795i) q^{82} -13.8564 q^{83} +3.00000 q^{85} +(-2.73205 - 0.732051i) q^{86} +(3.46410 - 6.00000i) q^{87} +(2.73205 - 0.732051i) q^{88} +(-13.5000 + 7.79423i) q^{89} +2.00000 q^{92} +(1.50000 + 2.59808i) q^{93} +(11.8301 - 3.16987i) q^{94} +(-7.79423 - 4.50000i) q^{95} +(2.53590 - 9.46410i) q^{96} -17.3205i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 6 q^{5} - 8 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 + 6 * q^5 - 8 * q^8	\( 4 q - 2 q^{2} + 6 q^{5} - 8 q^{8} - 6 q^{10} - 12 q^{12} + 8 q^{16} + 6 q^{17} - 4 q^{22} + 12 q^{24} - 4 q^{25} + 12 q^{26} + 16 q^{29} - 6 q^{30} + 8 q^{32} - 6 q^{33} - 6 q^{37} - 18 q^{38} - 12 q^{40} + 4 q^{44} - 2 q^{46} + 8 q^{50} + 2 q^{53} + 18 q^{54} - 36 q^{57} - 8 q^{58} - 12 q^{60} + 18 q^{61} + 12 q^{65} + 6 q^{66} - 30 q^{73} - 6 q^{74} + 24 q^{78} + 24 q^{80} + 18 q^{81} - 12 q^{82} + 12 q^{85} - 4 q^{86} + 4 q^{88} - 54 q^{89} + 8 q^{92} + 6 q^{93} + 30 q^{94} + 24 q^{96}+O(q^{100}) \) 4 * q - 2 * q^2 + 6 * q^5 - 8 * q^8 - 6 * q^10 - 12 * q^12 + 8 * q^16 + 6 * q^17 - 4 * q^22 + 12 * q^24 - 4 * q^25 + 12 * q^26 + 16 * q^29 - 6 * q^30 + 8 * q^32 - 6 * q^33 - 6 * q^37 - 18 * q^38 - 12 * q^40 + 4 * q^44 - 2 * q^46 + 8 * q^50 + 2 * q^53 + 18 * q^54 - 36 * q^57 - 8 * q^58 - 12 * q^60 + 18 * q^61 + 12 * q^65 + 6 * q^66 - 30 * q^73 - 6 * q^74 + 24 * q^78 + 24 * q^80 + 18 * q^81 - 12 * q^82 + 12 * q^85 - 4 * q^86 + 4 * q^88 - 54 * q^89 + 8 * q^92 + 6 * q^93 + 30 * q^94 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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