LMFDB - Embedded newform 1638.2.x.c.811.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(307,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("1638.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.x (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.836829184.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 14x^{6} + 61x^{4} + 84x^{2} + 4 $ x^8 + 14x^6 + 61x^4 + 84*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			811.2
Root			$-2.63640i$ of defining polynomial
Character	$\chi$	$=$	1638.811
Dual form			1638.2.x.c.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(1.15711 + 1.15711i) q^{5} +(2.02133 - 1.70711i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(1.15711 + 1.15711i) q^{5} +(2.02133 - 1.70711i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.63640 q^{10} +(-1.37930 - 1.37930i) q^{11} +(-1.50062 - 3.27843i) q^{13} +(-0.222191 + 2.63640i) q^{14} -1.00000 q^{16} +1.50625 q^{17} +(-0.934922 - 0.934922i) q^{19} +(1.15711 - 1.15711i) q^{20} +1.95063 q^{22} -4.19327i q^{23} -2.32218i q^{25} +(3.37930 + 1.25710i) q^{26} +(-1.70711 - 2.02133i) q^{28} +0.406261 q^{29} +(-2.31423 - 2.31423i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.06508 + 1.06508i) q^{34} +(4.31423 + 0.363595i) q^{35} +(0.257101 + 0.257101i) q^{37} +1.32218 q^{38} +1.63640i q^{40} +(-3.60624 - 3.60624i) q^{41} -2.46483i q^{43} +(-1.37930 + 1.37930i) q^{44} +(2.96509 + 2.96509i) q^{46} +(1.41421 - 1.41421i) q^{47} +(1.17157 - 6.90126i) q^{49} +(1.64203 + 1.64203i) q^{50} +(-3.27843 + 1.50062i) q^{52} -13.4456 q^{53} -3.19202i q^{55} +(2.63640 + 0.222191i) q^{56} +(-0.287270 + 0.287270i) q^{58} +(-8.75986 + 8.75986i) q^{59} +11.7394i q^{61} +3.27281 q^{62} +1.00000i q^{64} +(2.05713 - 5.52991i) q^{65} +(11.1012 - 11.1012i) q^{67} -1.50625i q^{68} +(-3.30772 + 2.79352i) q^{70} +(5.18078 - 5.18078i) q^{71} +(-2.56008 + 2.56008i) q^{73} -0.363595 q^{74} +(-0.934922 + 0.934922i) q^{76} +(-5.14265 - 0.433413i) q^{77} +1.42546 q^{79} +(-1.15711 - 1.15711i) q^{80} +5.09999 q^{82} +(-4.90797 - 4.90797i) q^{83} +(1.74290 + 1.74290i) q^{85} +(1.74290 + 1.74290i) q^{86} -1.95063i q^{88} +(-2.03017 + 2.03017i) q^{89} +(-8.62990 - 4.06508i) q^{91} -4.19327 q^{92} +2.00000i q^{94} -2.16362i q^{95} +(10.2741 + 10.2741i) q^{97} +(4.05150 + 5.70836i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{5}+O(q^{10}) $ 8 * q + 4 * q^5	$ 8 q + 4 q^{5} + 4 q^{10} + 16 q^{13} + 4 q^{14} - 8 q^{16} - 4 q^{17} - 8 q^{19} + 4 q^{20} - 12 q^{22} + 16 q^{26} - 8 q^{28} - 12 q^{29} - 8 q^{31} - 8 q^{34} + 24 q^{35} - 4 q^{37} + 4 q^{38} - 12 q^{41} + 24 q^{46} + 32 q^{49} + 8 q^{50} - 4 q^{52} - 40 q^{53} + 4 q^{56} + 4 q^{58} + 8 q^{59} - 8 q^{62} + 12 q^{65} + 32 q^{67} + 8 q^{70} + 12 q^{71} + 20 q^{73} - 20 q^{74} - 8 q^{76} - 8 q^{77} + 24 q^{79} - 4 q^{80} + 40 q^{82} - 44 q^{83} + 20 q^{85} + 20 q^{86} - 16 q^{89} - 28 q^{91} + 28 q^{92} - 8 q^{97} + 16 q^{98}+O(q^{100}) $ 8 * q + 4 * q^5 + 4 * q^10 + 16 * q^13 + 4 * q^14 - 8 * q^16 - 4 * q^17 - 8 * q^19 + 4 * q^20 - 12 * q^22 + 16 * q^26 - 8 * q^28 - 12 * q^29 - 8 * q^31 - 8 * q^34 + 24 * q^35 - 4 * q^37 + 4 * q^38 - 12 * q^41 + 24 * q^46 + 32 * q^49 + 8 * q^50 - 4 * q^52 - 40 * q^53 + 4 * q^56 + 4 * q^58 + 8 * q^59 - 8 * q^62 + 12 * q^65 + 32 * q^67 + 8 * q^70 + 12 * q^71 + 20 * q^73 - 20 * q^74 - 8 * q^76 - 8 * q^77 + 24 * q^79 - 4 * q^80 + 40 * q^82 - 44 * q^83 + 20 * q^85 + 20 * q^86 - 16 * q^89 - 28 * q^91 + 28 * q^92 - 8 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	1.15711	+	1.15711i	0.517477	+	0.517477i	0.916807	−	0.399330i	$-0.130757\pi$
$5$	1.15711	+	1.15711i	0.517477	+	0.517477i	−0.399330	+	0.916807i	$0.630757\pi$
$6$		0			0
$7$	2.02133	−	1.70711i	0.763992	−	0.645226i
$7$	2.02133	−	1.70711i	0.763992	−	0.645226i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	−1.63640			−0.517477
$11$	−1.37930	−	1.37930i	−0.415876	−	0.415876i	0.467904	−	0.883780i	$-0.345009\pi$
$11$	−1.37930	−	1.37930i	−0.415876	−	0.415876i	−0.883780	+	0.467904i	$0.845009\pi$
$12$		0			0
$13$	−1.50062	−	3.27843i	−0.416198	−	0.909274i
$13$	−1.50062	−	3.27843i	−0.416198	−	0.909274i
$14$	−0.222191	+	2.63640i	−0.0593831	+	0.704609i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.50625			0.365319			0.182659	−	0.983176i	$-0.441529\pi$
$17$	1.50625			0.365319			0.182659	+	0.983176i	$0.441529\pi$
$18$		0			0
$19$	−0.934922	−	0.934922i	−0.214486	−	0.214486i	0.591684	−	0.806170i	$-0.298463\pi$
$19$	−0.934922	−	0.934922i	−0.214486	−	0.214486i	−0.806170	+	0.591684i	$0.798463\pi$
$20$	1.15711	−	1.15711i	0.258738	−	0.258738i
$21$		0			0
$22$	1.95063			0.415876
$23$		−	4.19327i		−	0.874358i	−0.899375	−	0.437179i	$-0.855978\pi$
$23$		−	4.19327i		−	0.874358i	0.899375	−	0.437179i	$-0.144022\pi$
$24$		0			0
$25$		−	2.32218i		−	0.464436i
$26$	3.37930	+	1.25710i	0.662736	+	0.246538i
$27$		0			0
$28$	−1.70711	−	2.02133i	−0.322613	−	0.381996i
$29$	0.406261			0.0754407			0.0377204	−	0.999288i	$-0.487990\pi$
$29$	0.406261			0.0754407			0.0377204	+	0.999288i	$0.487990\pi$
$30$		0			0
$31$	−2.31423	−	2.31423i	−0.415647	−	0.415647i	0.468053	−	0.883700i	$-0.344956\pi$
$31$	−2.31423	−	2.31423i	−0.415647	−	0.415647i	−0.883700	+	0.468053i	$0.844956\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	−1.06508	+	1.06508i	−0.182659	+	0.182659i
$35$	4.31423	+	0.363595i	0.729237	+	0.0614588i
$36$		0			0
$37$	0.257101	+	0.257101i	0.0422671	+	0.0422671i	0.727924	−	0.685657i	$-0.240485\pi$
$37$	0.257101	+	0.257101i	0.0422671	+	0.0422671i	−0.685657	+	0.727924i	$0.740485\pi$
$38$	1.32218			0.214486
$39$		0			0
$40$			1.63640i			0.258738i
$41$	−3.60624	−	3.60624i	−0.563199	−	0.563199i	0.367015	−	0.930215i	$-0.380380\pi$
$41$	−3.60624	−	3.60624i	−0.563199	−	0.563199i	−0.930215	+	0.367015i	$0.880380\pi$
$42$		0			0
$43$		−	2.46483i		−	0.375883i	−0.982180	−	0.187942i	$-0.939818\pi$
$43$		−	2.46483i		−	0.375883i	0.982180	−	0.187942i	$-0.0601816\pi$
$44$	−1.37930	+	1.37930i	−0.207938	+	0.207938i
$45$		0			0
$46$	2.96509	+	2.96509i	0.437179	+	0.437179i
$47$	1.41421	−	1.41421i	0.206284	−	0.206284i	−0.596402	−	0.802686i	$-0.703403\pi$
$47$	1.41421	−	1.41421i	0.206284	−	0.206284i	0.802686	+	0.596402i	$0.203403\pi$
$48$		0			0
$49$	1.17157	−	6.90126i	0.167368	−	0.985895i
$50$	1.64203	+	1.64203i	0.232218	+	0.232218i
$51$		0			0
$52$	−3.27843	+	1.50062i	−0.454637	+	0.208099i
$53$	−13.4456			−1.84690			−0.923450	−	0.383719i	$-0.874643\pi$
$53$	−13.4456			−1.84690			−0.923450	+	0.383719i	$0.874643\pi$
$54$		0			0
$55$		−	3.19202i		−	0.430412i
$56$	2.63640	+	0.222191i	0.352304	+	0.0296916i
$57$		0			0
$58$	−0.287270	+	0.287270i	−0.0377204	+	0.0377204i
$59$	−8.75986	+	8.75986i	−1.14044	+	1.14044i	−0.152066	+	0.988370i	$0.548593\pi$
$59$	−8.75986	+	8.75986i	−1.14044	+	1.14044i	−0.988370	+	0.152066i	$0.951407\pi$
$60$		0			0
$61$			11.7394i			1.50308i	0.659689	+	0.751539i	$0.270688\pi$
$61$			11.7394i			1.50308i	−0.659689	+	0.751539i	$0.729312\pi$
$62$	3.27281			0.415647
$63$		0			0
$64$			1.00000i			0.125000i
$65$	2.05713	−	5.52991i	0.255155	−	0.685901i
$66$		0			0
$67$	11.1012	−	11.1012i	1.35623	−	1.35623i	0.477720	−	0.878512i	$-0.341464\pi$
$67$	11.1012	−	11.1012i	1.35623	−	1.35623i	0.878512	−	0.477720i	$-0.158536\pi$
$68$		−	1.50625i		−	0.182659i
$69$		0			0
$70$	−3.30772	+	2.79352i	−0.395348	+	0.333889i
$71$	5.18078	−	5.18078i	0.614845	−	0.614845i	−0.329360	−	0.944205i	$-0.606833\pi$
$71$	5.18078	−	5.18078i	0.614845	−	0.614845i	0.944205	+	0.329360i	$0.106833\pi$
$72$		0			0
$73$	−2.56008	+	2.56008i	−0.299635	+	0.299635i	−0.840871	−	0.541236i	$-0.817957\pi$
$73$	−2.56008	+	2.56008i	−0.299635	+	0.299635i	0.541236	+	0.840871i	$0.317957\pi$
$74$	−0.363595			−0.0422671
$75$		0			0
$76$	−0.934922	+	0.934922i	−0.107243	+	0.107243i
$77$	−5.14265	−	0.433413i	−0.586060	−	0.0493920i
$78$		0			0
$79$	1.42546			0.160377			0.0801884	−	0.996780i	$-0.474448\pi$
$79$	1.42546			0.160377			0.0801884	+	0.996780i	$0.474448\pi$
$80$	−1.15711	−	1.15711i	−0.129369	−	0.129369i
$81$		0			0
$82$	5.09999			0.563199
$83$	−4.90797	−	4.90797i	−0.538719	−	0.538719i	0.384434	−	0.923153i	$-0.374397\pi$
$83$	−4.90797	−	4.90797i	−0.538719	−	0.538719i	−0.923153	+	0.384434i	$0.874397\pi$
$84$		0			0
$85$	1.74290	+	1.74290i	0.189044	+	0.189044i
$86$	1.74290	+	1.74290i	0.187942	+	0.187942i
$87$		0			0
$88$		−	1.95063i		−	0.207938i
$89$	−2.03017	+	2.03017i	−0.215198	+	0.215198i	−0.806471	−	0.591274i	$-0.798625\pi$
$89$	−2.03017	+	2.03017i	−0.215198	+	0.215198i	0.591274	+	0.806471i	$0.298625\pi$
$90$		0			0
$91$	−8.62990	−	4.06508i	−0.904659	−	0.426136i
$92$	−4.19327			−0.437179
$93$		0			0
$94$			2.00000i			0.206284i
$95$		−	2.16362i		−	0.221983i
$96$		0			0
$97$	10.2741	+	10.2741i	1.04317	+	1.04317i	0.999025	+	0.0441477i	$0.0140572\pi$
$97$	10.2741	+	10.2741i	1.04317	+	1.04317i	0.0441477	+	0.999025i	$0.485943\pi$
$98$	4.05150	+	5.70836i	0.409264	+	0.576631i
$99$		0			0
$100$	−2.32218			−0.232218
$101$	1.93018			0.192060			0.0960301	−	0.995378i	$-0.469385\pi$
$101$	1.93018			0.192060			0.0960301	+	0.995378i	$0.469385\pi$
$102$		0			0
$103$	7.94886			0.783225			0.391612	−	0.920130i	$-0.371917\pi$
$103$	7.94886			0.783225			0.391612	+	0.920130i	$0.371917\pi$
$104$	1.25710	−	3.37930i	0.123269	−	0.331368i
$105$		0			0
$106$	9.50750	−	9.50750i	0.923450	−	0.923450i
$107$	3.33315			0.322228			0.161114	−	0.986936i	$-0.448491\pi$
$107$	3.33315			0.322228			0.161114	+	0.986936i	$0.448491\pi$
$108$		0			0
$109$	9.58382	−	9.58382i	0.917964	−	0.917964i	−0.0789174	−	0.996881i	$-0.525146\pi$
$109$	9.58382	−	9.58382i	0.917964	−	0.917964i	0.996881	+	0.0789174i	$0.0251463\pi$
$110$	2.25710	+	2.25710i	0.215206	+	0.215206i
$111$		0			0
$112$	−2.02133	+	1.70711i	−0.190998	+	0.161306i
$113$	10.3865			0.977084			0.488542	−	0.872540i	$-0.337529\pi$
$113$	10.3865			0.977084			0.488542	+	0.872540i	$0.337529\pi$
$114$		0			0
$115$	4.85209	−	4.85209i	0.452460	−	0.452460i
$116$		−	0.406261i		−	0.0377204i
$117$		0			0
$118$		−	12.3883i		−	1.14044i
$119$	3.04463	−	2.57133i	0.279101	−	0.235713i
$120$		0			0
$121$		−	7.19504i		−	0.654094i
$122$	−8.30102	−	8.30102i	−0.751539	−	0.751539i
$123$		0			0
$124$	−2.31423	+	2.31423i	−0.207824	+	0.207824i
$125$	8.47259	−	8.47259i	0.757811	−	0.757811i
$126$		0			0
$127$		−	9.12016i		−	0.809283i	−0.914475	−	0.404642i	$-0.867396\pi$
$127$		−	9.12016i		−	0.809283i	0.914475	−	0.404642i	$-0.132604\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	2.45563	+	5.36484i	0.215373	+	0.470528i
$131$			3.98205i			0.347913i	0.984753	+	0.173957i	$0.0556553\pi$
$131$			3.98205i			0.347913i	−0.984753	+	0.173957i	$0.944345\pi$
$132$		0			0
$133$	−3.48580	−	0.293777i	−0.302257	−	0.0254737i
$134$			15.6995i			1.35623i
$135$		0			0
$136$	1.06508	+	1.06508i	0.0913297	+	0.0913297i
$137$	−13.8868	−	13.8868i	−1.18643	−	1.18643i	−0.978047	−	0.208382i	$-0.933180\pi$
$137$	−13.8868	−	13.8868i	−1.18643	−	1.18643i	−0.208382	−	0.978047i	$-0.566820\pi$
$138$		0			0
$139$		−	7.37155i		−	0.625247i	−0.949877	−	0.312623i	$-0.898792\pi$
$139$		−	7.37155i		−	0.625247i	0.949877	−	0.312623i	$-0.101208\pi$
$140$	0.363595	−	4.31423i	0.0307294	−	0.364619i
$141$		0			0
$142$			7.32672i			0.614845i
$143$	−2.45214	+	6.59178i	−0.205058	+	0.551232i
$144$		0			0
$145$	0.470090	+	0.470090i	0.0390388	+	0.0390388i
$146$		−	3.62050i		−	0.299635i
$147$		0			0
$148$	0.257101	−	0.257101i	0.0211335	−	0.0211335i
$149$	11.7376	−	11.7376i	0.961585	−	0.961585i	−0.0377039	−	0.999289i	$-0.512004\pi$
$149$	11.7376	−	11.7376i	0.961585	−	0.961585i	0.999289	+	0.0377039i	$0.0120044\pi$
$150$		0			0
$151$	2.79529	+	2.79529i	0.227477	+	0.227477i	0.811638	−	0.584161i	$-0.198576\pi$
$151$	2.79529	+	2.79529i	0.227477	+	0.227477i	−0.584161	+	0.811638i	$0.698576\pi$
$152$		−	1.32218i		−	0.107243i
$153$		0			0
$154$	3.94287	−	3.32994i	0.317726	−	0.268334i
$155$		−	5.35564i		−	0.430176i
$156$		0			0
$157$			10.4472i			0.833774i	0.908958	+	0.416887i	$0.136879\pi$
$157$			10.4472i			0.833774i	−0.908958	+	0.416887i	$0.863121\pi$
$158$	−1.00795	+	1.00795i	−0.0801884	+	0.0801884i
$159$		0			0
$160$	1.63640			0.129369
$161$	−7.15836	−	8.47600i	−0.564158	−	0.668002i
$162$		0			0
$163$	9.07232	+	9.07232i	0.710599	+	0.710599i	0.966660	−	0.256062i	$-0.0824250\pi$
$163$	9.07232	+	9.07232i	0.710599	+	0.710599i	−0.256062	+	0.966660i	$0.582425\pi$
$164$	−3.60624	+	3.60624i	−0.281600	+	0.281600i
$165$		0			0
$166$	6.94091			0.538719
$167$	9.04741	−	9.04741i	0.700109	−	0.700109i	−0.264325	−	0.964434i	$-0.585149\pi$
$167$	9.04741	−	9.04741i	0.700109	−	0.700109i	0.964434	+	0.264325i	$0.0851490\pi$
$168$		0			0
$169$	−8.49625	+	9.83940i	−0.653558	+	0.756877i
$170$	−2.46483			−0.189044
$171$		0			0
$172$	−2.46483			−0.187942
$173$	0.0159057			0.00120928			0.000604642	−	1.00000i	$-0.499808\pi$
$173$	0.0159057			0.00120928			0.000604642		1.00000i	$0.499808\pi$
$174$		0			0
$175$	−3.96421	−	4.69390i	−0.299666	−	0.354825i
$176$	1.37930	+	1.37930i	0.103969	+	0.103969i
$177$		0			0
$178$		−	2.87109i		−	0.215198i
$179$			10.3710i			0.775167i	0.921835	+	0.387584i	$0.126690\pi$
$179$			10.3710i			0.775167i	−0.921835	+	0.387584i	$0.873310\pi$
$180$		0			0
$181$	1.42973			0.106271			0.0531354	−	0.998587i	$-0.483079\pi$
$181$	1.42973			0.106271			0.0531354	+	0.998587i	$0.483079\pi$
$182$	8.97670	−	3.22781i	0.665398	−	0.239262i
$183$		0			0
$184$	2.96509	−	2.96509i	0.218589	−	0.218589i
$185$			0.594989i			0.0437444i
$186$		0			0
$187$	−2.07757	−	2.07757i	−0.151927	−	0.151927i
$188$	−1.41421	−	1.41421i	−0.103142	−	0.103142i
$189$		0			0
$190$	1.52991	+	1.52991i	0.110991	+	0.110991i
$191$	23.1833			1.67748			0.838741	−	0.544530i	$-0.183292\pi$
$191$	23.1833			1.67748			0.838741	+	0.544530i	$0.183292\pi$
$192$		0			0
$193$	13.6264	+	13.6264i	0.980850	+	0.980850i	0.999820	−	0.0189698i	$-0.00603863\pi$
$193$	13.6264	+	13.6264i	0.980850	+	0.980850i	−0.0189698	+	0.999820i	$0.506039\pi$
$194$	−14.5297			−1.04317
$195$		0			0
$196$	−6.90126	−	1.17157i	−0.492947	−	0.0836838i
$197$	−10.1950	+	10.1950i	−0.726366	+	0.726366i	−0.969894	−	0.243528i	$-0.921695\pi$
$197$	−10.1950	+	10.1950i	−0.726366	+	0.726366i	0.243528	+	0.969894i	$0.421695\pi$
$198$		0			0
$199$	−1.42518			−0.101029			−0.0505143	−	0.998723i	$-0.516086\pi$
$199$	−1.42518			−0.101029			−0.0505143	+	0.998723i	$0.516086\pi$
$200$	1.64203	−	1.64203i	0.116109	−	0.116109i
$201$		0			0
$202$	−1.36484	+	1.36484i	−0.0960301	+	0.0960301i
$203$	0.821188	−	0.693530i	0.0576361	−	0.0486763i
$204$		0			0
$205$		−	8.34564i		−	0.582885i
$206$	−5.62070	+	5.62070i	−0.391612	+	0.391612i
$207$		0			0
$208$	1.50062	+	3.27843i	0.104050	+	0.227318i
$209$			2.57908i			0.178399i
$210$		0			0
$211$	5.45234			0.375354			0.187677	−	0.982231i	$-0.439904\pi$
$211$	5.45234			0.375354			0.187677	+	0.982231i	$0.439904\pi$
$212$			13.4456i			0.923450i
$213$		0			0
$214$	−2.35689	+	2.35689i	−0.161114	+	0.161114i
$215$	2.85209	−	2.85209i	0.194511	−	0.194511i
$216$		0			0
$217$	−8.62845	−	0.727190i	−0.585737	−	0.0493649i
$218$			13.5536i			0.917964i
$219$		0			0
$220$	−3.19202			−0.215206
$221$	−2.26031	−	4.93813i	−0.152045	−	0.332175i
$222$		0			0
$223$	−18.3548	−	18.3548i	−1.22913	−	1.22913i	−0.964293	−	0.264839i	$-0.914681\pi$
$223$	−18.3548	−	18.3548i	−1.22913	−	1.22913i	−0.264839	−	0.964293i	$-0.585319\pi$
$224$	0.222191	−	2.63640i	0.0148458	−	0.176152i
$225$		0			0
$226$	−7.34440	+	7.34440i	−0.488542	+	0.488542i
$227$	6.91251	+	6.91251i	0.458799	+	0.458799i	0.898261	−	0.439462i	$-0.144831\pi$
$227$	6.91251	+	6.91251i	0.458799	+	0.458799i	−0.439462	+	0.898261i	$0.644831\pi$
$228$		0			0
$229$	−2.96035	+	2.96035i	−0.195625	+	0.195625i	−0.798122	−	0.602496i	$-0.794173\pi$
$229$	−2.96035	+	2.96035i	−0.195625	+	0.195625i	0.602496	+	0.798122i	$0.294173\pi$
$230$			6.86189i			0.452460i
$231$		0			0
$232$	0.287270	+	0.287270i	0.0188602	+	0.0188602i
$233$			6.59953i			0.432350i	0.976355	+	0.216175i	$0.0693581\pi$
$233$			6.59953i			0.432350i	−0.976355	+	0.216175i	$0.930642\pi$
$234$		0			0
$235$	3.27281			0.213495
$236$	8.75986	+	8.75986i	0.570218	+	0.570218i
$237$		0			0
$238$	−0.334675	+	3.97108i	−0.0216938	+	0.257407i
$239$	10.9611	−	10.9611i	0.709014	−	0.709014i	−0.257314	−	0.966328i	$-0.582838\pi$
$239$	10.9611	−	10.9611i	0.709014	−	0.709014i	0.966328	+	0.257314i	$0.0828376\pi$
$240$		0			0
$241$	−20.1598	+	20.1598i	−1.29861	+	1.29861i	−0.369295	+	0.929312i	$0.620401\pi$
$241$	−20.1598	+	20.1598i	−1.29861	+	1.29861i	−0.929312	+	0.369295i	$0.879599\pi$
$242$	5.08766	+	5.08766i	0.327047	+	0.327047i
$243$		0			0
$244$	11.7394			0.751539
$245$	9.34118	−	6.62990i	0.596786	−	0.423569i
$246$		0			0
$247$	−1.66211	+	4.46804i	−0.105758	+	0.284295i
$248$		−	3.27281i		−	0.207824i
$249$		0			0
$250$			11.9820i			0.757811i
$251$	6.62641			0.418255			0.209128	−	0.977888i	$-0.432938\pi$
$251$	6.62641			0.418255			0.209128	+	0.977888i	$0.432938\pi$
$252$		0			0
$253$	−5.78380	+	5.78380i	−0.363624	+	0.363624i
$254$	6.44893	+	6.44893i	0.404642	+	0.404642i
$255$		0			0
$256$	1.00000			0.0625000
$257$	10.5297			0.656826			0.328413	−	0.944534i	$-0.393486\pi$
$257$	10.5297			0.656826			0.328413	+	0.944534i	$0.393486\pi$
$258$		0			0
$259$	0.958584	+	0.0807877i	0.0595635	+	0.00501990i
$260$	−5.52991	−	2.05713i	−0.342950	−	0.127578i
$261$		0			0
$262$	−2.81573	−	2.81573i	−0.173957	−	0.173957i
$263$	−11.3310			−0.698699			−0.349349	−	0.936993i	$-0.613597\pi$
$263$	−11.3310			−0.698699			−0.349349	+	0.936993i	$0.613597\pi$
$264$		0			0
$265$	−15.5581	−	15.5581i	−0.955727	−	0.955727i
$266$	2.67256	−	2.25710i	0.163865	−	0.138392i
$267$		0			0
$268$	−11.1012	−	11.1012i	−0.678116	−	0.678116i
$269$			11.6504i			0.710339i	0.934802	+	0.355170i	$0.115577\pi$
$269$			11.6504i			0.710339i	−0.934802	+	0.355170i	$0.884423\pi$
$270$		0			0
$271$	−9.41876	+	9.41876i	−0.572149	+	0.572149i	−0.932728	−	0.360580i	$-0.882579\pi$
$271$	−9.41876	+	9.41876i	−0.572149	+	0.572149i	0.360580	+	0.932728i	$0.382579\pi$
$272$	−1.50625			−0.0913297
$273$		0			0
$274$	19.6389			1.18643
$275$	−3.20299	+	3.20299i	−0.193148	+	0.193148i
$276$		0			0
$277$			5.99357i			0.360119i	0.983656	+	0.180059i	$0.0576290\pi$
$277$			5.99357i			0.360119i	−0.983656	+	0.180059i	$0.942371\pi$
$278$	5.21247	+	5.21247i	0.312623	+	0.312623i
$279$		0			0
$280$	2.79352	+	3.30772i	0.166945	+	0.197674i
$281$	−12.4581	−	12.4581i	−0.743190	−	0.743190i	0.230001	−	0.973190i	$-0.426127\pi$
$281$	−12.4581	−	12.4581i	−0.743190	−	0.743190i	−0.973190	+	0.230001i	$0.926127\pi$
$282$		0			0
$283$	12.9995			0.772739			0.386370	−	0.922344i	$-0.373729\pi$
$283$	12.9995			0.772739			0.386370	+	0.922344i	$0.373729\pi$
$284$	−5.18078	−	5.18078i	−0.307422	−	0.307422i
$285$		0			0
$286$	−2.92717	−	6.39501i	−0.173087	−	0.378145i
$287$	−13.4456	−	1.13317i	−0.793671	−	0.0668891i
$288$		0			0
$289$	−14.7312			−0.866542
$290$	−0.664807			−0.0390388
$291$		0			0
$292$	2.56008	+	2.56008i	0.149817	+	0.149817i
$293$	1.51545	−	1.51545i	0.0885336	−	0.0885336i	−0.661453	−	0.749987i	$-0.730060\pi$
$293$	1.51545	−	1.51545i	0.0885336	−	0.0885336i	0.749987	+	0.661453i	$0.230060\pi$
$294$		0			0
$295$	−20.2723			−1.18030
$296$			0.363595i			0.0211335i
$297$		0			0
$298$			16.5995i			0.961585i
$299$	−13.7474	+	6.29253i	−0.795030	+	0.363906i
$300$		0			0
$301$	−4.20773	−	4.98225i	−0.242530	−	0.287172i
$302$	−3.95313			−0.227477
$303$		0			0
$304$	0.934922	+	0.934922i	0.0536214	+	0.0536214i
$305$	−13.5838	+	13.5838i	−0.777807	+	0.777807i
$306$		0			0
$307$	4.87286	−	4.87286i	0.278109	−	0.278109i	−0.554245	−	0.832354i	$-0.686993\pi$
$307$	4.87286	−	4.87286i	0.278109	−	0.278109i	0.832354	+	0.554245i	$0.186993\pi$
$308$	−0.433413	+	5.14265i	−0.0246960	+	0.293030i
$309$		0			0
$310$	3.78701	+	3.78701i	0.215088	+	0.215088i
$311$	26.8179			1.52070			0.760352	−	0.649511i	$-0.225026\pi$
$311$	26.8179			1.52070			0.760352	+	0.649511i	$0.225026\pi$
$312$		0			0
$313$			1.96858i			0.111271i	0.998451	+	0.0556354i	$0.0177184\pi$
$313$			1.96858i			0.111271i	−0.998451	+	0.0556354i	$0.982282\pi$
$314$	−7.38726	−	7.38726i	−0.416887	−	0.416887i
$315$		0			0
$316$		−	1.42546i		−	0.0801884i
$317$	−9.47705	+	9.47705i	−0.532284	+	0.532284i	−0.921252	−	0.388967i	$-0.872832\pi$
$317$	−9.47705	+	9.47705i	−0.532284	+	0.532284i	0.388967	+	0.921252i	$0.372832\pi$
$318$		0			0
$319$	−0.560357	−	0.560357i	−0.0313740	−	0.0313740i
$320$	−1.15711	+	1.15711i	−0.0646846	+	0.0646846i
$321$		0			0
$322$	11.0552	+	0.931709i	0.616080	+	0.0519221i
$323$	−1.40822	−	1.40822i	−0.0783557	−	0.0783557i
$324$		0			0
$325$	−7.61311	+	3.48472i	−0.422299	+	0.193297i
$326$	−12.8302			−0.710599
$327$		0			0
$328$		−	5.09999i		−	0.281600i
$329$	0.444383	−	5.27281i	0.0244996	−	0.290699i
$330$		0			0
$331$	−13.2853	+	13.2853i	−0.730226	+	0.730226i	−0.970664	−	0.240438i	$-0.922709\pi$
$331$	−13.2853	+	13.2853i	−0.730226	+	0.730226i	0.240438	+	0.970664i	$0.422709\pi$
$332$	−4.90797	+	4.90797i	−0.269360	+	0.269360i
$333$		0			0
$334$			12.7950i			0.700109i
$335$	25.6908			1.40364
$336$		0			0
$337$			10.6200i			0.578507i	0.957252	+	0.289254i	$0.0934071\pi$
$337$			10.6200i			0.578507i	−0.957252	+	0.289254i	$0.906593\pi$
$338$	−0.949747	−	12.9653i	−0.0516595	−	0.705217i
$339$		0			0
$340$	1.74290	−	1.74290i	0.0945220	−	0.0945220i
$341$			6.38404i			0.345715i
$342$		0			0
$343$	−9.41305	−	15.9497i	−0.508257	−	0.861205i
$344$	1.74290	−	1.74290i	0.0939708	−	0.0939708i
$345$		0			0
$346$	−0.0112470	+	0.0112470i	−0.000604642	+	0.000604642i
$347$	33.6050			1.80401			0.902007	−	0.431722i	$-0.142094\pi$
$347$	33.6050			1.80401			0.902007	+	0.431722i	$0.142094\pi$
$348$		0			0
$349$	22.5833	−	22.5833i	1.20886	−	1.20886i	0.237462	−	0.971397i	$-0.423684\pi$
$349$	22.5833	−	22.5833i	1.20886	−	1.20886i	0.971397	−	0.237462i	$-0.0763156\pi$
$350$	6.12220	+	0.515968i	0.327246	+	0.0275797i
$351$		0			0
$352$	−1.95063			−0.103969
$353$	−10.4681	−	10.4681i	−0.557162	−	0.557162i	0.371336	−	0.928498i	$-0.378900\pi$
$353$	−10.4681	−	10.4681i	−0.557162	−	0.557162i	−0.928498	+	0.371336i	$0.878900\pi$
$354$		0			0
$355$	11.9895			0.636336
$356$	2.03017	+	2.03017i	0.107599	+	0.107599i
$357$		0			0
$358$	−7.33343	−	7.33343i	−0.387584	−	0.387584i
$359$	2.68248	+	2.68248i	0.141576	+	0.141576i	0.774343	−	0.632767i	$-0.218081\pi$
$359$	2.68248	+	2.68248i	0.141576	+	0.141576i	−0.632767	+	0.774343i	$0.718081\pi$
$360$		0			0
$361$		−	17.2518i		−	0.907992i
$362$	−1.01097	+	1.01097i	−0.0531354	+	0.0531354i
$363$		0			0
$364$	−4.06508	+	8.62990i	−0.213068	+	0.452330i
$365$	−5.92460			−0.310108
$366$		0			0
$367$			8.08749i			0.422164i	0.977468	+	0.211082i	$0.0676986\pi$
$367$			8.08749i			0.422164i	−0.977468	+	0.211082i	$0.932301\pi$
$368$			4.19327i			0.218589i
$369$		0			0
$370$	−0.420721	−	0.420721i	−0.0218722	−	0.0218722i
$371$	−27.1781	+	22.9531i	−1.41102	+	1.19167i
$372$		0			0
$373$	−27.5920			−1.42866			−0.714331	−	0.699808i	$-0.753269\pi$
$373$	−27.5920			−1.42866			−0.714331	+	0.699808i	$0.753269\pi$
$374$	2.93813			0.151927
$375$		0			0
$376$	2.00000			0.103142
$377$	−0.609645	−	1.33190i	−0.0313983	−	0.0685963i
$378$		0			0
$379$	−7.79457	+	7.79457i	−0.400380	+	0.400380i	−0.878367	−	0.477987i	$-0.841367\pi$
$379$	−7.79457	+	7.79457i	−0.400380	+	0.400380i	0.477987	+	0.878367i	$0.341367\pi$
$380$	−2.16362			−0.110991
$381$		0			0
$382$	−16.3931	+	16.3931i	−0.838741	+	0.838741i
$383$	11.3366	+	11.3366i	0.579275	+	0.579275i	0.934704	−	0.355428i	$-0.115665\pi$
$383$	11.3366	+	11.3366i	0.579275	+	0.579275i	−0.355428	+	0.934704i	$0.615665\pi$
$384$		0			0
$385$	−5.44912	−	6.45214i	−0.277713	−	0.328831i
$386$	−19.2707			−0.980850
$387$		0			0
$388$	10.2741	−	10.2741i	0.521586	−	0.521586i
$389$			17.5669i			0.890675i	0.895363	+	0.445338i	$0.146916\pi$
$389$			17.5669i			0.890675i	−0.895363	+	0.445338i	$0.853084\pi$
$390$		0			0
$391$		−	6.31611i		−	0.319419i
$392$	5.70836	−	4.05150i	0.288316	−	0.204632i
$393$		0			0
$394$		−	14.4180i		−	0.726366i
$395$	1.64942	+	1.64942i	0.0829913	+	0.0829913i
$396$		0			0
$397$	−24.6394	+	24.6394i	−1.23662	+	1.23662i	−0.275242	+	0.961375i	$0.588758\pi$
$397$	−24.6394	+	24.6394i	−1.23662	+	1.23662i	−0.961375	+	0.275242i	$0.911242\pi$
$398$	1.00776	−	1.00776i	0.0505143	−	0.0505143i
$399$		0			0
$400$			2.32218i			0.116109i
$401$	−20.8486	−	20.8486i	−1.04113	−	1.04113i	−0.999117	−	0.0420122i	$-0.986623\pi$
$401$	−20.8486	−	20.8486i	−1.04113	−	1.04113i	−0.0420122	−	0.999117i	$-0.513377\pi$
$402$		0			0
$403$	−4.11425	+	11.0598i	−0.204945	+	0.550929i
$404$		−	1.93018i		−	0.0960301i
$405$		0			0
$406$	−0.0902676	+	1.07107i	−0.00447991	+	0.0531562i
$407$		−	0.709240i		−	0.0351557i
$408$		0			0
$409$	13.8170	+	13.8170i	0.683206	+	0.683206i	0.960721	−	0.277515i	$-0.0895109\pi$
$409$	13.8170	+	13.8170i	0.683206	+	0.683206i	−0.277515	+	0.960721i	$0.589511\pi$
$410$	5.90126	+	5.90126i	0.291443	+	0.291443i
$411$		0			0
$412$		−	7.94886i		−	0.391612i
$413$	−2.75258	+	32.6606i	−0.135445	+	1.60712i
$414$		0			0
$415$		−	11.3581i		−	0.557549i
$416$	−3.37930	−	1.25710i	−0.165684	−	0.0616344i
$417$		0			0
$418$	−1.82369	−	1.82369i	−0.0891995	−	0.0891995i
$419$			16.3845i			0.800435i	0.916420	+	0.400218i	$0.131065\pi$
$419$			16.3845i			0.800435i	−0.916420	+	0.400218i	$0.868935\pi$
$420$		0			0
$421$	−17.2214	+	17.2214i	−0.839319	+	0.839319i	−0.988769	−	0.149450i	$-0.952250\pi$
$421$	−17.2214	+	17.2214i	−0.839319	+	0.839319i	0.149450	+	0.988769i	$0.452250\pi$
$422$	−3.85538	+	3.85538i	−0.187677	+	0.187677i
$423$		0			0
$424$	−9.50750	−	9.50750i	−0.461725	−	0.461725i
$425$		−	3.49778i		−	0.169667i
$426$		0			0
$427$	20.0404	+	23.7293i	0.969824	+	1.14834i
$428$		−	3.33315i		−	0.161114i
$429$		0			0
$430$			4.03346i			0.194511i
$431$	−22.5749	+	22.5749i	−1.08739	+	1.08739i	−0.0915975	+	0.995796i	$0.529197\pi$
$431$	−22.5749	+	22.5749i	−1.08739	+	1.08739i	−0.995796	+	0.0915975i	$0.970803\pi$
$432$		0			0
$433$	35.8075			1.72080			0.860400	−	0.509620i	$-0.170214\pi$
$433$	35.8075			1.72080			0.860400	+	0.509620i	$0.170214\pi$
$434$	6.61544	−	5.58704i	0.317551	−	0.268186i
$435$		0			0
$436$	−9.58382	−	9.58382i	−0.458982	−	0.458982i
$437$	−3.92038	+	3.92038i	−0.187537	+	0.187537i
$438$		0			0
$439$	9.78979			0.467241			0.233621	−	0.972328i	$-0.424943\pi$
$439$	9.78979			0.467241			0.233621	+	0.972328i	$0.424943\pi$
$440$	2.25710	−	2.25710i	0.107603	−	0.107603i
$441$		0			0
$442$	5.09007	+	1.89351i	0.242110	+	0.0900649i
$443$	2.71378			0.128936			0.0644679	−	0.997920i	$-0.479465\pi$
$443$	2.71378			0.128936			0.0644679	+	0.997920i	$0.479465\pi$
$444$		0			0
$445$	−4.69827			−0.222719
$446$	25.9577			1.22913
$447$		0			0
$448$	1.70711	+	2.02133i	0.0806532	+	0.0954990i
$449$	−14.7825	−	14.7825i	−0.697632	−	0.697632i	0.266268	−	0.963899i	$-0.414210\pi$
$449$	−14.7825	−	14.7825i	−0.697632	−	0.697632i	−0.963899	+	0.266268i	$0.914210\pi$
$450$		0			0
$451$			9.94819i			0.468442i
$452$		−	10.3865i		−	0.488542i
$453$		0			0
$454$	−9.77576			−0.458799
$455$	−5.28201	−	14.6895i	−0.247625	−	0.688655i
$456$		0			0
$457$	−17.9920	+	17.9920i	−0.841632	+	0.841632i	−0.989071	−	0.147439i	$-0.952897\pi$
$457$	−17.9920	+	17.9920i	−0.841632	+	0.841632i	0.147439	+	0.989071i	$0.452897\pi$
$458$		−	4.18657i		−	0.195625i
$459$		0			0
$460$	−4.85209	−	4.85209i	−0.226230	−	0.226230i
$461$	−23.4424	−	23.4424i	−1.09182	−	1.09182i	−0.995334	−	0.0964882i	$-0.969239\pi$
$461$	−23.4424	−	23.4424i	−1.09182	−	1.09182i	−0.0964882	−	0.995334i	$-0.530761\pi$
$462$		0			0
$463$	12.4486	+	12.4486i	0.578536	+	0.578536i	0.934500	−	0.355964i	$-0.115847\pi$
$463$	12.4486	+	12.4486i	0.578536	+	0.578536i	−0.355964	+	0.934500i	$0.615847\pi$
$464$	−0.406261			−0.0188602
$465$		0			0
$466$	−4.66657	−	4.66657i	−0.216175	−	0.216175i
$467$	−27.6932			−1.28149			−0.640744	−	0.767754i	$-0.721374\pi$
$467$	−27.6932			−1.28149			−0.640744	+	0.767754i	$0.721374\pi$
$468$		0			0
$469$	3.48830	−	41.3903i	0.161075	−	1.91123i
$470$	−2.31423	+	2.31423i	−0.106747	+	0.106747i
$471$		0			0
$472$	−12.3883			−0.570218
$473$	−3.39975	+	3.39975i	−0.156321	+	0.156321i
$474$		0			0
$475$	−2.17106	+	2.17106i	−0.0996148	+	0.0996148i
$476$	−2.57133	−	3.04463i	−0.117857	−	0.139550i
$477$		0			0
$478$			15.5013i			0.709014i
$479$	−7.69426	+	7.69426i	−0.351560	+	0.351560i	−0.860690	−	0.509130i	$-0.829967\pi$
$479$	−7.69426	+	7.69426i	−0.351560	+	0.351560i	0.509130	+	0.860690i	$0.329967\pi$
$480$		0			0
$481$	0.457076	−	1.22870i	0.0208409	−	0.0560238i
$482$		−	28.5103i		−	1.29861i
$483$		0			0
$484$	−7.19504			−0.327047
$485$			23.7765i			1.07964i
$486$		0			0
$487$	−3.65436	+	3.65436i	−0.165595	+	0.165595i	−0.785040	−	0.619445i	$-0.787358\pi$
$487$	−3.65436	+	3.65436i	−0.165595	+	0.165595i	0.619445	+	0.785040i	$0.287358\pi$
$488$	−8.30102	+	8.30102i	−0.375769	+	0.375769i
$489$		0			0
$490$	−1.91717	+	11.2933i	−0.0866088	+	0.510177i
$491$		−	12.9652i		−	0.585110i	−0.956249	−	0.292555i	$-0.905495\pi$
$491$		−	12.9652i		−	0.585110i	0.956249	−	0.292555i	$-0.0945055\pi$
$492$		0			0
$493$	0.611930			0.0275599
$494$	−1.98409	−	4.33468i	−0.0892686	−	0.195026i
$495$		0			0
$496$	2.31423	+	2.31423i	0.103912	+	0.103912i
$497$	1.62793	−	19.3162i	0.0730228	−	0.866450i
$498$		0			0
$499$	15.8982	−	15.8982i	0.711703	−	0.711703i	−0.255188	−	0.966891i	$-0.582137\pi$
$499$	15.8982	−	15.8982i	0.711703	−	0.711703i	0.966891	+	0.255188i	$0.0821374\pi$
$500$	−8.47259	−	8.47259i	−0.378906	−	0.378906i
$501$		0			0
$502$	−4.68558	+	4.68558i	−0.209128	+	0.209128i
$503$		−	7.72073i		−	0.344250i	−0.985075	−	0.172125i	$-0.944937\pi$
$503$		−	7.72073i		−	0.344250i	0.985075	−	0.172125i	$-0.0550633\pi$
$504$		0			0
$505$	2.23344	+	2.23344i	0.0993867	+	0.0993867i
$506$		−	8.17953i		−	0.363624i
$507$		0			0
$508$	−9.12016			−0.404642
$509$	−23.7432	−	23.7432i	−1.05240	−	1.05240i	−0.998549	−	0.0538516i	$-0.982850\pi$
$509$	−23.7432	−	23.7432i	−1.05240	−	1.05240i	−0.0538516	−	0.998549i	$-0.517150\pi$
$510$		0			0
$511$	−0.804444	+	9.54510i	−0.0355865	+	0.422250i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	−7.44563	+	7.44563i	−0.328413	+	0.328413i
$515$	9.19773	+	9.19773i	0.405301	+	0.405301i
$516$		0			0
$517$	−3.90126			−0.171577
$518$	−0.734947	+	0.620696i	−0.0322917	+	0.0272718i
$519$		0			0
$520$	5.36484	−	2.45563i	0.235264	−	0.107686i
$521$			11.2520i			0.492958i	0.969148	+	0.246479i	$0.0792736\pi$
$521$			11.2520i			0.492958i	−0.969148	+	0.246479i	$0.920726\pi$
$522$		0			0
$523$			39.7356i			1.73752i	0.495237	+	0.868758i	$0.335081\pi$
$523$			39.7356i			1.73752i	−0.495237	+	0.868758i	$0.664919\pi$
$524$	3.98205			0.173957
$525$		0			0
$526$	8.01222	−	8.01222i	0.349349	−	0.349349i
$527$	−3.48580	−	3.48580i	−0.151844	−	0.151844i
$528$		0			0
$529$	5.41647			0.235499
$530$	22.0025			0.955727
$531$		0			0
$532$	−0.293777	+	3.48580i	−0.0127368	+	0.151129i
$533$	−6.41120	+	17.2344i	−0.277700	+	0.746505i
$534$		0			0
$535$	3.85683	+	3.85683i	0.166745	+	0.166745i
$536$	15.6995			0.678116
$537$		0			0
$538$	−8.23810	−	8.23810i	−0.355170	−	0.355170i
$539$	−11.1349	+	7.90299i	−0.479614	+	0.340406i
$540$		0			0
$541$	−10.4751	−	10.4751i	−0.450359	−	0.450359i	0.445114	−	0.895474i	$-0.353163\pi$
$541$	−10.4751	−	10.4751i	−0.450359	−	0.450359i	−0.895474	+	0.445114i	$0.853163\pi$
$542$		−	13.3201i		−	0.572149i
$543$		0			0
$544$	1.06508	−	1.06508i	0.0456649	−	0.0456649i
$545$	22.1791			0.950050
$546$		0			0
$547$	17.4124			0.744502			0.372251	−	0.928132i	$-0.378586\pi$
$547$	17.4124			0.744502			0.372251	+	0.928132i	$0.378586\pi$
$548$	−13.8868	+	13.8868i	−0.593215	+	0.593215i
$549$		0			0
$550$		−	4.52971i		−	0.193148i
$551$	−0.379822	−	0.379822i	−0.0161810	−	0.0161810i
$552$		0			0
$553$	2.88133	−	2.43341i	0.122527	−	0.103479i
$554$	−4.23810	−	4.23810i	−0.180059	−	0.180059i
$555$		0			0
$556$	−7.37155			−0.312623
$557$	−6.23417	−	6.23417i	−0.264150	−	0.264150i	0.562587	−	0.826738i	$-0.309806\pi$
$557$	−6.23417	−	6.23417i	−0.264150	−	0.264150i	−0.826738	+	0.562587i	$0.809806\pi$
$558$		0			0
$559$	−8.08079	+	3.69879i	−0.341781	+	0.156442i
$560$	−4.31423	−	0.363595i	−0.182309	−	0.0153647i
$561$		0			0
$562$	17.6185			0.743190
$563$	−32.2131			−1.35762			−0.678809	−	0.734315i	$-0.737504\pi$
$563$	−32.2131			−1.35762			−0.678809	+	0.734315i	$0.737504\pi$
$564$		0			0
$565$	12.0184	+	12.0184i	0.505618	+	0.505618i
$566$	−9.19202	+	9.19202i	−0.386370	+	0.386370i
$567$		0			0
$568$	7.32672			0.307422
$569$			25.5422i			1.07079i	0.844603	+	0.535393i	$0.179836\pi$
$569$			25.5422i			1.07079i	−0.844603	+	0.535393i	$0.820164\pi$
$570$		0			0
$571$		−	34.8620i		−	1.45893i	−0.684020	−	0.729464i	$-0.739770\pi$
$571$		−	34.8620i		−	1.45893i	0.684020	−	0.729464i	$-0.260230\pi$
$572$	6.59178	+	2.45214i	0.275616	+	0.102529i
$573$		0			0
$574$	10.3088	−	8.70622i	0.430280	−	0.363391i
$575$	−9.73753			−0.406083
$576$		0			0
$577$	11.7404	+	11.7404i	0.488760	+	0.488760i	0.907915	−	0.419155i	$-0.137674\pi$
$577$	11.7404	+	11.7404i	0.488760	+	0.488760i	−0.419155	+	0.907915i	$0.637674\pi$
$578$	10.4165	−	10.4165i	0.433271	−	0.433271i
$579$		0			0
$580$	0.470090	−	0.470090i	0.0195194	−	0.0195194i
$581$	−18.2991	−	1.54221i	−0.759173	−	0.0639817i
$582$		0			0
$583$	18.5456	+	18.5456i	0.768081	+	0.768081i
$584$	−3.62050			−0.149817
$585$		0			0
$586$			2.14317i			0.0885336i
$587$	−25.6920	−	25.6920i	−1.06042	−	1.06042i	−0.998053	−	0.0623701i	$-0.980134\pi$
$587$	−25.6920	−	25.6920i	−1.06042	−	1.06042i	−0.0623701	−	0.998053i	$-0.519866\pi$
$588$		0			0
$589$			4.32724i			0.178301i
$590$	14.3347	−	14.3347i	0.590149	−	0.590149i
$591$		0			0
$592$	−0.257101	−	0.257101i	−0.0105668	−	0.0105668i
$593$	−6.06857	+	6.06857i	−0.249206	+	0.249206i	−0.820645	−	0.571439i	$-0.806386\pi$
$593$	−6.06857	+	6.06857i	−0.249206	+	0.249206i	0.571439	+	0.820645i	$0.306386\pi$
$594$		0			0
$595$	6.49830	+	0.547664i	0.266404	+	0.0224521i
$596$	−11.7376	−	11.7376i	−0.480793	−	0.480793i
$597$		0			0
$598$	5.27136	−	14.1703i	0.215562	−	0.579468i
$599$	42.6492			1.74260			0.871300	−	0.490750i	$-0.163277\pi$
$599$	42.6492			1.74260			0.871300	+	0.490750i	$0.163277\pi$
$600$		0			0
$601$		−	4.02249i		−	0.164081i	−0.996629	−	0.0820405i	$-0.973856\pi$
$601$		−	4.02249i		−	0.164081i	0.996629	−	0.0820405i	$-0.0261437\pi$
$602$	6.49830	+	0.547664i	0.264851	+	0.0223211i
$603$		0			0
$604$	2.79529	−	2.79529i	0.113739	−	0.113739i
$605$	8.32547	−	8.32547i	0.338479	−	0.338479i
$606$		0			0
$607$			39.1674i			1.58975i	0.606770	+	0.794877i	$0.292465\pi$
$607$			39.1674i			1.58975i	−0.606770	+	0.794877i	$0.707535\pi$
$608$	−1.32218			−0.0536214
$609$		0			0
$610$		−	19.2104i		−	0.777807i
$611$	−6.75861	−	2.51420i	−0.273424	−	0.101714i
$612$		0			0
$613$	−15.7609	+	15.7609i	−0.636577	+	0.636577i	−0.949710	−	0.313132i	$-0.898622\pi$
$613$	−15.7609	+	15.7609i	−0.636577	+	0.636577i	0.313132	+	0.949710i	$0.398622\pi$
$614$			6.89126i			0.278109i
$615$		0			0
$616$	−3.32994	−	3.94287i	−0.134167	−	0.158863i
$617$	19.4135	−	19.4135i	0.781558	−	0.781558i	−0.198536	−	0.980094i	$-0.563619\pi$
$617$	19.4135	−	19.4135i	0.781558	−	0.781558i	0.980094	+	0.198536i	$0.0636185\pi$
$618$		0			0
$619$	28.9913	−	28.9913i	1.16526	−	1.16526i	0.181953	−	0.983307i	$-0.441758\pi$
$619$	28.9913	−	28.9913i	1.16526	−	1.16526i	0.983307	−	0.181953i	$-0.0582418\pi$
$620$	−5.35564			−0.215088
$621$		0			0
$622$	−18.9631	+	18.9631i	−0.760352	+	0.760352i
$623$	−0.637932	+	7.56936i	−0.0255582	+	0.303260i
$624$		0			0
$625$	7.99659			0.319864
$626$	−1.39200	−	1.39200i	−0.0556354	−	0.0556354i
$627$		0			0
$628$	10.4472			0.416887
$629$	0.387257	+	0.387257i	0.0154410	+	0.0154410i
$630$		0			0
$631$	−14.3025	−	14.3025i	−0.569375	−	0.569375i	0.362578	−	0.931953i	$-0.381897\pi$
$631$	−14.3025	−	14.3025i	−0.569375	−	0.569375i	−0.931953	+	0.362578i	$0.881897\pi$
$632$	1.00795	+	1.00795i	0.0400942	+	0.0400942i
$633$		0			0
$634$		−	13.4026i		−	0.532284i
$635$	10.5531	−	10.5531i	0.418785	−	0.418785i
$636$		0			0
$637$	−24.3834	+	6.51528i	−0.966106	+	0.258145i
$638$	0.792465			0.0313740
$639$		0			0
$640$		−	1.63640i		−	0.0646846i
$641$		−	41.5501i		−	1.64113i	−0.571553	−	0.820565i	$-0.693659\pi$
$641$		−	41.5501i		−	1.64113i	0.571553	−	0.820565i	$-0.306341\pi$
$642$		0			0
$643$	23.7094	+	23.7094i	0.935009	+	0.935009i	0.998013	−	0.0630044i	$-0.0200682\pi$
$643$	23.7094	+	23.7094i	0.935009	+	0.935009i	−0.0630044	+	0.998013i	$0.520068\pi$
$644$	−8.47600	+	7.15836i	−0.334001	+	0.282079i
$645$		0			0
$646$	1.99153			0.0783557
$647$	26.3735			1.03685			0.518425	−	0.855123i	$-0.326518\pi$
$647$	26.3735			1.03685			0.518425	+	0.855123i	$0.326518\pi$
$648$		0			0
$649$	24.1650			0.948560
$650$	2.91921	−	7.84735i	0.114501	−	0.307798i
$651$		0			0
$652$	9.07232	−	9.07232i	0.355299	−	0.355299i
$653$	12.3520			0.483369			0.241685	−	0.970355i	$-0.422300\pi$
$653$	12.3520			0.483369			0.241685	+	0.970355i	$0.422300\pi$
$654$		0			0
$655$	−4.60768	+	4.60768i	−0.180037	+	0.180037i
$656$	3.60624	+	3.60624i	0.140800	+	0.140800i
$657$		0			0
$658$	3.41421	+	4.04267i	0.133100	+	0.157600i
$659$	40.1732			1.56492			0.782462	−	0.622698i	$-0.213964\pi$
$659$	40.1732			1.56492			0.782462	+	0.622698i	$0.213964\pi$
$660$		0			0
$661$	26.5576	−	26.5576i	1.03297	−	1.03297i	0.0335333	−	0.999438i	$-0.489324\pi$
$661$	26.5576	−	26.5576i	1.03297	−	1.03297i	0.999438	−	0.0335333i	$-0.0106760\pi$
$662$		−	18.7883i		−	0.730226i
$663$		0			0
$664$		−	6.94091i		−	0.269360i
$665$	−3.69353	−	4.37340i	−0.143229	−	0.169593i
$666$		0			0
$667$		−	1.70356i		−	0.0659622i
$668$	−9.04741	−	9.04741i	−0.350055	−	0.350055i
$669$		0			0
$670$	−18.1661	+	18.1661i	−0.701818	+	0.701818i
$671$	16.1922	−	16.1922i	0.625094	−	0.625094i
$672$		0			0
$673$		−	3.49388i		−	0.134679i	−0.997730	−	0.0673395i	$-0.978549\pi$
$673$		−	3.49388i		−	0.134679i	0.997730	−	0.0673395i	$-0.0214511\pi$
$674$	−7.50946	−	7.50946i	−0.289254	−	0.289254i
$675$		0			0
$676$	9.83940	+	8.49625i	0.378438	+	0.326779i
$677$			25.1586i			0.966922i	0.875366	+	0.483461i	$0.160620\pi$
$677$			25.1586i			0.966922i	−0.875366	+	0.483461i	$0.839380\pi$
$678$		0			0
$679$	38.3062	+	3.22838i	1.47006	+	0.123894i
$680$			2.46483i			0.0945220i
$681$		0			0
$682$	−4.51420	−	4.51420i	−0.172858	−	0.172858i
$683$	26.5689	+	26.5689i	1.01663	+	1.01663i	0.999859	+	0.0167709i	$0.00533861\pi$
$683$	26.5689	+	26.5689i	1.01663	+	1.01663i	0.0167709	+	0.999859i	$0.494661\pi$
$684$		0			0
$685$		−	32.1372i		−	1.22790i
$686$	17.9342	+	4.62214i	0.684731	+	0.176474i
$687$		0			0
$688$			2.46483i			0.0939708i
$689$	20.1768	+	44.0806i	0.768677	+	1.67934i
$690$		0			0
$691$	−1.14265	−	1.14265i	−0.0434686	−	0.0434686i	0.685038	−	0.728507i	$-0.259785\pi$
$691$	−1.14265	−	1.14265i	−0.0434686	−	0.0434686i	−0.728507	+	0.685038i	$0.759785\pi$
$692$		−	0.0159057i		−	0.000604642i
$693$		0			0
$694$	−23.7624	+	23.7624i	−0.902007	+	0.902007i
$695$	8.52971	−	8.52971i	0.323550	−	0.323550i
$696$		0			0
$697$	−5.43189	−	5.43189i	−0.205747	−	0.205747i
$698$			31.9377i			1.20886i
$699$		0			0
$700$	−4.69390	+	3.96421i	−0.177413	+	0.149833i
$701$			21.5853i			0.815264i	0.913146	+	0.407632i	$0.133645\pi$
$701$			21.5853i			0.815264i	−0.913146	+	0.407632i	$0.866355\pi$
$702$		0			0
$703$		−	0.480738i		−	0.0181314i
$704$	1.37930	−	1.37930i	0.0519845	−	0.0519845i
$705$		0			0
$706$	14.8042			0.557162
$707$	3.90154	−	3.29503i	0.146732	−	0.123922i
$708$		0			0
$709$	29.2210	+	29.2210i	1.09742	+	1.09742i	0.994712	+	0.102706i	$0.0327501\pi$
$709$	29.2210	+	29.2210i	1.09742	+	1.09742i	0.102706	+	0.994712i	$0.467250\pi$
$710$	−8.47785	+	8.47785i	−0.318168	+	0.318168i
$711$		0			0
$712$	−2.87109			−0.107599
$713$	−9.70418	+	9.70418i	−0.363424	+	0.363424i
$714$		0			0
$715$	−10.4648	+	4.79003i	−0.391363	+	0.179137i
$716$	10.3710			0.387584
$717$		0			0
$718$	−3.79360			−0.141576
$719$	13.2373			0.493668			0.246834	−	0.969058i	$-0.420610\pi$
$719$	13.2373			0.493668			0.246834	+	0.969058i	$0.420610\pi$
$720$		0			0
$721$	16.0673	−	13.5696i	0.598378	−	0.505357i
$722$	12.1989	+	12.1989i	0.453996	+	0.453996i
$723$		0			0
$724$		−	1.42973i		−	0.0531354i
$725$		−	0.943410i		−	0.0350374i
$726$		0			0
$727$	−17.2911			−0.641291			−0.320646	−	0.947199i	$-0.603900\pi$
$727$	−17.2911			−0.641291			−0.320646	+	0.947199i	$0.603900\pi$
$728$	−3.22781	−	8.97670i	−0.119631	−	0.332699i
$729$		0			0
$730$	4.18933	−	4.18933i	0.155054	−	0.155054i
$731$		−	3.71265i		−	0.137317i
$732$		0			0
$733$	−14.5279	−	14.5279i	−0.536602	−	0.536602i	0.385927	−	0.922529i	$-0.373882\pi$
$733$	−14.5279	−	14.5279i	−0.536602	−	0.536602i	−0.922529	+	0.385927i	$0.873882\pi$
$734$	−5.71872	−	5.71872i	−0.211082	−	0.211082i
$735$		0			0
$736$	−2.96509	−	2.96509i	−0.109295	−	0.109295i
$737$	−30.6240			−1.12805
$738$		0			0
$739$	−12.3646	−	12.3646i	−0.454838	−	0.454838i	0.442119	−	0.896957i	$-0.354227\pi$
$739$	−12.3646	−	12.3646i	−0.454838	−	0.454838i	−0.896957	+	0.442119i	$0.854227\pi$
$740$	0.594989			0.0218722
$741$		0			0
$742$	2.98750	−	35.4481i	0.109675	−	1.30134i
$743$	12.6873	−	12.6873i	0.465452	−	0.465452i	−0.434986	−	0.900437i	$-0.643247\pi$
$743$	12.6873	−	12.6873i	0.465452	−	0.465452i	0.900437	+	0.434986i	$0.143247\pi$
$744$		0			0
$745$	27.1636			0.995196
$746$	19.5105	−	19.5105i	0.714331	−	0.714331i
$747$		0			0
$748$	−2.07757	+	2.07757i	−0.0759637	+	0.0759637i
$749$	6.73740	−	5.69004i	0.246179	−	0.207910i
$750$		0			0
$751$		−	15.8031i		−	0.576663i	−0.957531	−	0.288331i	$-0.906900\pi$
$751$		−	15.8031i		−	0.576663i	0.957531	−	0.288331i	$-0.0931004\pi$
$752$	−1.41421	+	1.41421i	−0.0515711	+	0.0515711i
$753$		0			0
$754$	1.37288	+	0.510711i	0.0499973	+	0.0185990i
$755$			6.46892i			0.235428i
$756$		0			0
$757$	36.8200			1.33825			0.669123	−	0.743152i	$-0.266670\pi$
$757$	36.8200			1.33825			0.669123	+	0.743152i	$0.266670\pi$
$758$		−	11.0232i		−	0.400380i
$759$		0			0
$760$	1.52991	−	1.52991i	0.0554957	−	0.0554957i
$761$	−29.9773	+	29.9773i	−1.08668	+	1.08668i	−0.0908090	+	0.995868i	$0.528945\pi$
$761$	−29.9773	+	29.9773i	−1.08668	+	1.08668i	−0.995868	+	0.0908090i	$0.971055\pi$
$762$		0			0
$763$	3.01149	−	35.7327i	0.109023	−	1.29361i
$764$		−	23.1833i		−	0.838741i
$765$		0			0
$766$	−16.0324			−0.579275
$767$	41.8639	+	15.5734i	1.51162	+	0.562321i
$768$		0			0
$769$	−28.6613	−	28.6613i	−1.03355	−	1.03355i	−0.999417	−	0.0341363i	$-0.989132\pi$
$769$	−28.6613	−	28.6613i	−1.03355	−	1.03355i	−0.0341363	−	0.999417i	$-0.510868\pi$
$770$	8.41546	+	0.709240i	0.303272	+	0.0255592i
$771$		0			0
$772$	13.6264	−	13.6264i	0.490425	−	0.490425i
$773$	31.7211	+	31.7211i	1.14093	+	1.14093i	0.988280	+	0.152650i	$0.0487806\pi$
$773$	31.7211	+	31.7211i	1.14093	+	1.14093i	0.152650	+	0.988280i	$0.451219\pi$
$774$		0			0
$775$	−5.37405	+	5.37405i	−0.193041	+	0.193041i
$776$			14.5297i			0.521586i
$777$		0			0
$778$	−12.4216	−	12.4216i	−0.445338	−	0.445338i
$779$			6.74310i			0.241596i
$780$		0			0
$781$	−14.2917			−0.511398
$782$	4.46616	+	4.46616i	0.159710	+	0.159710i
$783$		0			0
$784$	−1.17157	+	6.90126i	−0.0418419	+	0.246474i
$785$	−12.0885	+	12.0885i	−0.431459	+	0.431459i
$786$		0			0
$787$	−33.6855	+	33.6855i	−1.20076	+	1.20076i	−0.226823	+	0.973936i	$0.572834\pi$
$787$	−33.6855	+	33.6855i	−1.20076	+	1.20076i	−0.973936	+	0.226823i	$0.927166\pi$
$788$	10.1950	+	10.1950i	0.363183	+	0.363183i
$789$		0			0
$790$	−2.33263			−0.0829913
$791$	20.9947	−	17.7309i	0.746484	−	0.630440i
$792$		0			0
$793$	38.4869	−	17.6164i	1.36671	−	0.625578i
$794$		−	34.8454i		−	1.23662i
$795$		0			0
$796$			1.42518i			0.0505143i
$797$	36.5386			1.29426			0.647132	−	0.762378i	$-0.275968\pi$
$797$	36.5386			1.29426			0.647132	+	0.762378i	$0.275968\pi$
$798$		0			0
$799$	2.13016	−	2.13016i	0.0753595	−	0.0753595i
$800$	−1.64203	−	1.64203i	−0.0580545	−	0.0580545i
$801$		0			0
$802$	29.4844			1.04113
$803$	7.06226			0.249222
$804$		0			0
$805$	1.52465	−	18.0907i	0.0537370	−	0.637614i
$806$	−4.91126	−	10.7297i	−0.172992	−	0.377937i
$807$		0			0
$808$	1.36484	+	1.36484i	0.0480151	+	0.0480151i
$809$	−19.7133			−0.693082			−0.346541	−	0.938035i	$-0.612644\pi$
$809$	−19.7133			−0.693082			−0.346541	+	0.938035i	$0.612644\pi$
$810$		0			0
$811$	−0.988834	−	0.988834i	−0.0347227	−	0.0347227i	0.689532	−	0.724255i	$-0.257816\pi$
$811$	−0.988834	−	0.988834i	−0.0347227	−	0.0347227i	−0.724255	+	0.689532i	$0.757816\pi$
$812$	−0.693530	−	0.821188i	−0.0243381	−	0.0288181i
$813$		0			0
$814$	0.501508	+	0.501508i	0.0175779	+	0.0175779i
$815$			20.9954i			0.735437i
$816$		0			0
$817$	−2.30442	+	2.30442i	−0.0806216	+	0.0806216i
$818$	−19.5402			−0.683206
$819$		0			0
$820$	−8.34564			−0.291443
$821$	7.22975	−	7.22975i	0.252320	−	0.252320i	−0.569601	−	0.821921i	$-0.692902\pi$
$821$	7.22975	−	7.22975i	0.252320	−	0.252320i	0.821921	+	0.569601i	$0.192902\pi$
$822$		0			0
$823$		−	1.41848i		−	0.0494451i	−0.999694	−	0.0247225i	$-0.992130\pi$
$823$		−	1.41848i		−	0.0494451i	0.999694	−	0.0247225i	$-0.00787023\pi$
$824$	5.62070	+	5.62070i	0.195806	+	0.195806i
$825$		0			0
$826$	−21.1482	−	25.0409i	−0.735839	−	0.871284i
$827$	18.4680	+	18.4680i	0.642197	+	0.642197i	0.951095	−	0.308898i	$-0.0999603\pi$
$827$	18.4680	+	18.4680i	0.642197	+	0.642197i	−0.308898	+	0.951095i	$0.599960\pi$
$828$		0			0
$829$	2.23560			0.0776455			0.0388228	−	0.999246i	$-0.487639\pi$
$829$	2.23560			0.0776455			0.0388228	+	0.999246i	$0.487639\pi$
$830$	8.03142	+	8.03142i	0.278775	+	0.278775i
$831$		0			0
$832$	3.27843	−	1.50062i	0.113659	−	0.0520248i
$833$	1.76468	−	10.3950i	0.0611425	−	0.360166i
$834$		0			0
$835$	20.9377			0.724580
$836$	2.57908			0.0891995
$837$		0			0
$838$	−11.5856	−	11.5856i	−0.400218	−	0.400218i
$839$	−18.5594	+	18.5594i	−0.640740	+	0.640740i	−0.950738	−	0.309997i	$-0.899672\pi$
$839$	−18.5594	+	18.5594i	−0.640740	+	0.640740i	0.309997	+	0.950738i	$0.399672\pi$
$840$		0			0
$841$	−28.8350			−0.994309
$842$		−	24.3547i		−	0.839319i
$843$		0			0
$844$		−	5.45234i		−	0.187677i
$845$	−21.2164	+	1.55417i	−0.729867	+	0.0534651i
$846$		0			0
$847$	−12.2827	−	14.5436i	−0.422039	−	0.499723i
$848$	13.4456			0.461725
$849$		0			0
$850$	2.47330	+	2.47330i	0.0848336	+	0.0848336i
$851$	1.07809	−	1.07809i	0.0369565	−	0.0369565i
$852$		0			0
$853$	−14.9138	+	14.9138i	−0.510637	+	0.510637i	−0.914722	−	0.404084i	$-0.867590\pi$
$853$	−14.9138	+	14.9138i	−0.510637	+	0.510637i	0.404084	+	0.914722i	$0.367590\pi$
$854$	−30.9498	−	2.60840i	−1.05908	−	0.0892575i
$855$		0			0
$856$	2.35689	+	2.35689i	0.0805569	+	0.0805569i
$857$	54.4574			1.86023			0.930115	−	0.367268i	$-0.119707\pi$
$857$	54.4574			1.86023			0.930115	+	0.367268i	$0.119707\pi$
$858$		0			0
$859$		−	39.4294i		−	1.34531i	−0.739954	−	0.672657i	$-0.765153\pi$
$859$		−	39.4294i		−	1.34531i	0.739954	−	0.672657i	$-0.234847\pi$
$860$	−2.85209	−	2.85209i	−0.0972554	−	0.0972554i
$861$		0			0
$862$		−	31.9257i		−	1.08739i
$863$	−18.5773	+	18.5773i	−0.632379	+	0.632379i	−0.948664	−	0.316285i	$-0.897564\pi$
$863$	−18.5773	+	18.5773i	−0.632379	+	0.632379i	0.316285	+	0.948664i	$0.397564\pi$
$864$		0			0
$865$	0.0184046	+	0.0184046i	0.000625776	+	0.000625776i
$866$	−25.3197	+	25.3197i	−0.860400	+	0.860400i
$867$		0			0
$868$	−0.727190	+	8.62845i	−0.0246824	+	0.292869i
$869$	−1.96614	−	1.96614i	−0.0666969	−	0.0666969i
$870$		0			0
$871$	−53.0535	−	19.7359i	−1.79765	−	0.668725i
$872$	13.5536			0.458982
$873$		0			0
$874$		−	5.54426i		−	0.187537i
$875$	2.66231	−	31.5895i	0.0900024	−	1.06792i
$876$		0			0
$877$	5.10175	−	5.10175i	0.172274	−	0.172274i	−0.615704	−	0.787978i	$-0.711128\pi$
$877$	5.10175	−	5.10175i	0.172274	−	0.172274i	0.787978	+	0.615704i	$0.211128\pi$
$878$	−6.92243	+	6.92243i	−0.233621	+	0.233621i
$879$		0			0
$880$			3.19202i			0.107603i
$881$	−3.68123			−0.124024			−0.0620119	−	0.998075i	$-0.519752\pi$
$881$	−3.68123			−0.124024			−0.0620119	+	0.998075i	$0.519752\pi$
$882$		0			0
$883$		−	51.2530i		−	1.72480i	−0.506226	−	0.862401i	$-0.668960\pi$
$883$		−	51.2530i		−	1.72480i	0.506226	−	0.862401i	$-0.331040\pi$
$884$	−4.93813	+	2.26031i	−0.166087	+	0.0760226i
$885$		0			0
$886$	−1.91893	+	1.91893i	−0.0644679	+	0.0644679i
$887$		−	35.1063i		−	1.17875i	−0.807858	−	0.589377i	$-0.799373\pi$
$887$		−	35.1063i		−	1.17875i	0.807858	−	0.589377i	$-0.200627\pi$
$888$		0			0
$889$	−15.5691	−	18.4349i	−0.522170	−	0.618286i
$890$	3.32218	−	3.32218i	0.111360	−	0.111360i
$891$		0			0
$892$	−18.3548	+	18.3548i	−0.614566	+	0.614566i
$893$	−2.64436			−0.0884901
$894$		0			0
$895$	−12.0005	+	12.0005i	−0.401131	+	0.401131i
$896$	−2.63640	−	0.222191i	−0.0880761	−	0.00742289i
$897$		0			0
$898$	20.9057			0.697632
$899$	−0.940179	−	0.940179i	−0.0313567	−	0.0313567i
$900$		0			0
$901$	−20.2525			−0.674707
$902$	−7.03444	−	7.03444i	−0.234221	−	0.234221i
$903$		0			0
$904$	7.34440	+	7.34440i	0.244271	+	0.244271i
$905$	1.65436	+	1.65436i	0.0549926	+	0.0549926i
$906$		0			0
$907$			39.1741i			1.30075i	0.759612	+	0.650377i	$0.225389\pi$
$907$			39.1741i			1.30075i	−0.759612	+	0.650377i	$0.774611\pi$
$908$	6.91251	−	6.91251i	0.229400	−	0.229400i
$909$		0			0
$910$	14.1220	+	6.65211i	0.468140	+	0.220515i
$911$	36.7864			1.21879			0.609394	−	0.792868i	$-0.291413\pi$
$911$	36.7864			1.21879			0.609394	+	0.792868i	$0.291413\pi$
$912$		0			0
$913$			13.5392i			0.448081i
$914$		−	25.4446i		−	0.841632i
$915$		0			0
$916$	2.96035	+	2.96035i	0.0978127	+	0.0978127i
$917$	6.79778	+	8.04905i	0.224483	+	0.265803i
$918$		0			0
$919$	38.3072			1.26364			0.631820	−	0.775115i	$-0.282308\pi$
$919$	38.3072			1.26364			0.631820	+	0.775115i	$0.282308\pi$
$920$	6.86189			0.226230
$921$		0			0
$922$	33.1526			1.09182
$923$	−24.7592	−	9.21043i	−0.814960	−	0.303165i
$924$		0			0
$925$	0.597033	−	0.597033i	0.0196303	−	0.0196303i
$926$	−17.6050			−0.578536
$927$		0			0
$928$	0.287270	−	0.287270i	0.00943009	−	0.00943009i
$929$	30.8995	+	30.8995i	1.01378	+	1.01378i	0.999904	+	0.0138758i	$0.00441695\pi$
$929$	30.8995	+	30.8995i	1.01378	+	1.01378i	0.0138758	+	0.999904i	$0.495583\pi$
$930$		0			0
$931$	−7.54747	+	5.35681i	−0.247358	+	0.175562i
$932$	6.59953			0.216175
$933$		0			0
$934$	19.5821	−	19.5821i	0.640744	−	0.640744i
$935$		−	4.80798i		−	0.157238i
$936$		0			0
$937$		−	23.1904i		−	0.757596i	−0.925479	−	0.378798i	$-0.876337\pi$
$937$		−	23.1904i		−	0.757596i	0.925479	−	0.378798i	$-0.123663\pi$
$938$	26.8008	+	31.7340i	0.875076	+	1.03615i
$939$		0			0
$940$		−	3.27281i		−	0.106747i
$941$	−21.8417	−	21.8417i	−0.712018	−	0.712018i	0.254939	−	0.966957i	$-0.417944\pi$
$941$	−21.8417	−	21.8417i	−0.712018	−	0.712018i	−0.966957	+	0.254939i	$0.917944\pi$
$942$		0			0
$943$	−15.1219	+	15.1219i	−0.492438	+	0.492438i
$944$	8.75986	−	8.75986i	0.285109	−	0.285109i
$945$		0			0
$946$		−	4.80798i		−	0.156321i
$947$	−18.1943	−	18.1943i	−0.591236	−	0.591236i	0.346729	−	0.937965i	$-0.387292\pi$
$947$	−18.1943	−	18.1943i	−0.591236	−	0.591236i	−0.937965	+	0.346729i	$0.887292\pi$
$948$		0			0
$949$	12.2348	+	4.55133i	0.397157	+	0.147742i
$950$		−	3.07034i		−	0.0996148i
$951$		0			0
$952$	3.97108	+	0.334675i	0.128703	+	0.0108469i
$953$			10.2539i			0.332156i	0.986113	+	0.166078i	$0.0531104\pi$
$953$			10.2539i			0.332156i	−0.986113	+	0.166078i	$0.946890\pi$
$954$		0			0
$955$	26.8257	+	26.8257i	0.868058	+	0.868058i
$956$	−10.9611	−	10.9611i	−0.354507	−	0.354507i
$957$		0			0
$958$		−	10.8813i		−	0.351560i
$959$	−51.7761	−	4.36360i	−1.67194	−	0.140908i
$960$		0			0
$961$		−	20.2887i		−	0.654475i
$962$	0.545620	+	1.19202i	0.0175915	+	0.0384323i
$963$		0			0
$964$	20.1598	+	20.1598i	0.649304	+	0.649304i
$965$			31.5346i			1.01513i
$966$		0			0
$967$	21.4696	−	21.4696i	0.690417	−	0.690417i	−0.271907	−	0.962324i	$-0.587654\pi$
$967$	21.4696	−	21.4696i	0.690417	−	0.690417i	0.962324	+	0.271907i	$0.0876542\pi$
$968$	5.08766	−	5.08766i	0.163524	−	0.163524i
$969$		0			0
$970$	−16.8125	−	16.8125i	−0.539818	−	0.539818i
$971$		−	43.1357i		−	1.38429i	−0.721759	−	0.692145i	$-0.756666\pi$
$971$		−	43.1357i		−	1.38429i	0.721759	−	0.692145i	$-0.243334\pi$
$972$		0			0
$973$	−12.5840	−	14.9004i	−0.403425	−	0.477683i
$974$		−	5.16804i		−	0.165595i
$975$		0			0
$976$		−	11.7394i		−	0.375769i
$977$	17.7281	−	17.7281i	0.567173	−	0.567173i	−0.364163	−	0.931335i	$-0.618645\pi$
$977$	17.7281	−	17.7281i	0.567173	−	0.567173i	0.931335	+	0.364163i	$0.118645\pi$
$978$		0			0
$979$	5.60044			0.178991
$980$	−6.62990	−	9.34118i	−0.211784	−	0.298393i
$981$		0			0
$982$	9.16776	+	9.16776i	0.292555	+	0.292555i
$983$	30.2120	−	30.2120i	0.963613	−	0.963613i	−0.0357478	−	0.999361i	$-0.511381\pi$
$983$	30.2120	−	30.2120i	0.963613	−	0.963613i	0.999361	+	0.0357478i	$0.0113813\pi$
$984$		0			0
$985$	−23.5936			−0.751755
$986$	−0.432700	+	0.432700i	−0.0137800	+	0.0137800i
$987$		0			0
$988$	4.46804	+	1.66211i	0.142147	+	0.0528788i
$989$	−10.3357			−0.328656
$990$		0			0
$991$	−45.3635			−1.44102			−0.720510	−	0.693445i	$-0.756092\pi$
$991$	−45.3635			−1.44102			−0.720510	+	0.693445i	$0.756092\pi$
$992$	−3.27281			−0.103912
$993$		0			0
$994$	12.5075	+	14.8097i	0.396714	+	0.469737i
$995$	−1.64910	−	1.64910i	−0.0522799	−	0.0522799i
$996$		0			0
$997$		−	29.1744i		−	0.923963i	−0.886890	−	0.461981i	$-0.847139\pi$
$997$		−	29.1744i		−	0.923963i	0.886890	−	0.461981i	$-0.152861\pi$
$998$			22.4835i			0.711703i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.x.c.811.2		8
3.2	odd	2		546.2.o.b.265.3	✓	8
7.6	odd	2		1638.2.x.a.811.1		8
13.8	odd	4		1638.2.x.a.307.1		8
21.20	even	2		546.2.o.c.265.4	yes	8
39.8	even	4		546.2.o.c.307.4	yes	8
91.34	even	4	inner	1638.2.x.c.307.2		8
273.125	odd	4		546.2.o.b.307.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.o.b.265.3	✓	8	3.2	odd	2
546.2.o.b.307.3	yes	8	273.125	odd	4
546.2.o.c.265.4	yes	8	21.20	even	2
546.2.o.c.307.4	yes	8	39.8	even	4
1638.2.x.a.307.1		8	13.8	odd	4
1638.2.x.a.811.1		8	7.6	odd	2
1638.2.x.c.307.2		8	91.34	even	4	inner
1638.2.x.c.811.2		8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(1.15711 + 1.15711i) q^{5} +(2.02133 - 1.70711i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(1.15711 + 1.15711i) q^{5} +(2.02133 - 1.70711i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.63640 q^{10} +(-1.37930 - 1.37930i) q^{11} +(-1.50062 - 3.27843i) q^{13} +(-0.222191 + 2.63640i) q^{14} -1.00000 q^{16} +1.50625 q^{17} +(-0.934922 - 0.934922i) q^{19} +(1.15711 - 1.15711i) q^{20} +1.95063 q^{22} -4.19327i q^{23} -2.32218i q^{25} +(3.37930 + 1.25710i) q^{26} +(-1.70711 - 2.02133i) q^{28} +0.406261 q^{29} +(-2.31423 - 2.31423i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.06508 + 1.06508i) q^{34} +(4.31423 + 0.363595i) q^{35} +(0.257101 + 0.257101i) q^{37} +1.32218 q^{38} +1.63640i q^{40} +(-3.60624 - 3.60624i) q^{41} -2.46483i q^{43} +(-1.37930 + 1.37930i) q^{44} +(2.96509 + 2.96509i) q^{46} +(1.41421 - 1.41421i) q^{47} +(1.17157 - 6.90126i) q^{49} +(1.64203 + 1.64203i) q^{50} +(-3.27843 + 1.50062i) q^{52} -13.4456 q^{53} -3.19202i q^{55} +(2.63640 + 0.222191i) q^{56} +(-0.287270 + 0.287270i) q^{58} +(-8.75986 + 8.75986i) q^{59} +11.7394i q^{61} +3.27281 q^{62} +1.00000i q^{64} +(2.05713 - 5.52991i) q^{65} +(11.1012 - 11.1012i) q^{67} -1.50625i q^{68} +(-3.30772 + 2.79352i) q^{70} +(5.18078 - 5.18078i) q^{71} +(-2.56008 + 2.56008i) q^{73} -0.363595 q^{74} +(-0.934922 + 0.934922i) q^{76} +(-5.14265 - 0.433413i) q^{77} +1.42546 q^{79} +(-1.15711 - 1.15711i) q^{80} +5.09999 q^{82} +(-4.90797 - 4.90797i) q^{83} +(1.74290 + 1.74290i) q^{85} +(1.74290 + 1.74290i) q^{86} -1.95063i q^{88} +(-2.03017 + 2.03017i) q^{89} +(-8.62990 - 4.06508i) q^{91} -4.19327 q^{92} +2.00000i q^{94} -2.16362i q^{95} +(10.2741 + 10.2741i) q^{97} +(4.05150 + 5.70836i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{5}+O(q^{10}) \) 8 * q + 4 * q^5	\( 8 q + 4 q^{5} + 4 q^{10} + 16 q^{13} + 4 q^{14} - 8 q^{16} - 4 q^{17} - 8 q^{19} + 4 q^{20} - 12 q^{22} + 16 q^{26} - 8 q^{28} - 12 q^{29} - 8 q^{31} - 8 q^{34} + 24 q^{35} - 4 q^{37} + 4 q^{38} - 12 q^{41} + 24 q^{46} + 32 q^{49} + 8 q^{50} - 4 q^{52} - 40 q^{53} + 4 q^{56} + 4 q^{58} + 8 q^{59} - 8 q^{62} + 12 q^{65} + 32 q^{67} + 8 q^{70} + 12 q^{71} + 20 q^{73} - 20 q^{74} - 8 q^{76} - 8 q^{77} + 24 q^{79} - 4 q^{80} + 40 q^{82} - 44 q^{83} + 20 q^{85} + 20 q^{86} - 16 q^{89} - 28 q^{91} + 28 q^{92} - 8 q^{97} + 16 q^{98}+O(q^{100}) \) 8 * q + 4 * q^5 + 4 * q^10 + 16 * q^13 + 4 * q^14 - 8 * q^16 - 4 * q^17 - 8 * q^19 + 4 * q^20 - 12 * q^22 + 16 * q^26 - 8 * q^28 - 12 * q^29 - 8 * q^31 - 8 * q^34 + 24 * q^35 - 4 * q^37 + 4 * q^38 - 12 * q^41 + 24 * q^46 + 32 * q^49 + 8 * q^50 - 4 * q^52 - 40 * q^53 + 4 * q^56 + 4 * q^58 + 8 * q^59 - 8 * q^62 + 12 * q^65 + 32 * q^67 + 8 * q^70 + 12 * q^71 + 20 * q^73 - 20 * q^74 - 8 * q^76 - 8 * q^77 + 24 * q^79 - 4 * q^80 + 40 * q^82 - 44 * q^83 + 20 * q^85 + 20 * q^86 - 16 * q^89 - 28 * q^91 + 28 * q^92 - 8 * q^97 + 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more