LMFDB - Embedded newform 1638.2.y.d.827.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(827,1638)]

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([2, 0, 1]))

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

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

chi := DirichletCharacter("1638.827");

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.y (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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 20 x^{14} - 12 x^{13} + 40 x^{12} + 40 x^{11} + 82 x^{10} + 104 x^{9} + 537 x^{8} + \cdots + 16 $ x^16 - 8x^15 + 20x^14 - 12x^13 + 40x^12 + 40x^11 + 82x^10 + 104x^9 + 537x^8 - 2528x^7 + 5494x^6 - 7284x^5 + 6002x^4 - 2984x^3 + 1000x^2 - 192*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			827.2
Root			$-1.90660 + 0.789738i$ of defining polynomial
Character	$\chi$	$=$	1638.827
Dual form			1638.2.y.d.1331.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.746053 + 0.746053i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.746053 + 0.746053i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.05508i q^{10} +(-3.35792 - 3.35792i) q^{11} +(-1.20860 + 3.39695i) q^{13} -1.00000i q^{14} -1.00000 q^{16} -2.02598 q^{17} +(5.03497 + 5.03497i) q^{19} +(0.746053 + 0.746053i) q^{20} +4.74881 q^{22} +2.39154 q^{23} +3.88681i q^{25} +(-1.54740 - 3.25662i) q^{26} +(0.707107 + 0.707107i) q^{28} -8.46166i q^{29} +(-5.55035 - 5.55035i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.43258 - 1.43258i) q^{34} -1.05508i q^{35} +(6.97346 - 6.97346i) q^{37} -7.12053 q^{38} -1.05508 q^{40} +(-2.39122 + 2.39122i) q^{41} -9.24408i q^{43} +(-3.35792 + 3.35792i) q^{44} +(-1.69107 + 1.69107i) q^{46} +(-3.48199 - 3.48199i) q^{47} -1.00000i q^{49} +(-2.74839 - 2.74839i) q^{50} +(3.39695 + 1.20860i) q^{52} -1.35557i q^{53} +5.01037 q^{55} -1.00000 q^{56} +(5.98330 + 5.98330i) q^{58} +(-4.49527 - 4.49527i) q^{59} -1.56297 q^{61} +7.84938 q^{62} +1.00000i q^{64} +(-1.63263 - 3.43599i) q^{65} +(-1.78711 - 1.78711i) q^{67} +2.02598i q^{68} +(0.746053 + 0.746053i) q^{70} +(-9.95954 + 9.95954i) q^{71} +(-3.90170 + 3.90170i) q^{73} +9.86196i q^{74} +(5.03497 - 5.03497i) q^{76} +4.74881 q^{77} +10.2625 q^{79} +(0.746053 - 0.746053i) q^{80} -3.38170i q^{82} +(10.2261 - 10.2261i) q^{83} +(1.51149 - 1.51149i) q^{85} +(6.53655 + 6.53655i) q^{86} -4.74881i q^{88} +(4.40919 + 4.40919i) q^{89} +(-1.54740 - 3.25662i) q^{91} -2.39154i q^{92} +4.92428 q^{94} -7.51271 q^{95} +(-11.0928 - 11.0928i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{5}+O(q^{10}) $ 16 * q + 4 * q^5	$ 16 q + 4 q^{5} - 8 q^{11} + 4 q^{13} - 16 q^{16} - 8 q^{17} + 16 q^{19} - 4 q^{20} - 8 q^{22} + 24 q^{23} + 8 q^{26} - 8 q^{31} + 4 q^{34} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 8 q^{44} + 4 q^{47} - 16 q^{50} - 16 q^{55} - 16 q^{56} + 4 q^{58} - 8 q^{59} - 40 q^{61} + 24 q^{62} + 56 q^{65} - 4 q^{67} - 4 q^{70} - 24 q^{71} - 12 q^{73} + 16 q^{76} - 8 q^{77} + 16 q^{79} - 4 q^{80} + 8 q^{85} + 24 q^{86} + 16 q^{89} + 8 q^{91} - 8 q^{94} - 40 q^{95} - 28 q^{97}+O(q^{100}) $ 16 * q + 4 * q^5 - 8 * q^11 + 4 * q^13 - 16 * q^16 - 8 * q^17 + 16 * q^19 - 4 * q^20 - 8 * q^22 + 24 * q^23 + 8 * q^26 - 8 * q^31 + 4 * q^34 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 8 * q^44 + 4 * q^47 - 16 * q^50 - 16 * q^55 - 16 * q^56 + 4 * q^58 - 8 * q^59 - 40 * q^61 + 24 * q^62 + 56 * q^65 - 4 * q^67 - 4 * q^70 - 24 * q^71 - 12 * q^73 + 16 * q^76 - 8 * q^77 + 16 * q^79 - 4 * q^80 + 8 * q^85 + 24 * q^86 + 16 * q^89 + 8 * q^91 - 8 * q^94 - 40 * q^95 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−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
$5$	−0.746053	+	0.746053i	−0.333645	+	0.333645i	−0.853969	−	0.520324i	$-0.825811\pi$
$5$	−0.746053	+	0.746053i	−0.333645	+	0.333645i	0.520324	+	0.853969i	$0.325811\pi$
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$		−	1.05508i		−	0.333645i
$11$	−3.35792	−	3.35792i	−1.01245	−	1.01245i	−0.999922	−	0.0125287i	$-0.996012\pi$
$11$	−3.35792	−	3.35792i	−1.01245	−	1.01245i	−0.0125287	−	0.999922i	$-0.503988\pi$
$12$		0			0
$13$	−1.20860	+	3.39695i	−0.335206	+	0.942145i
$13$	−1.20860	+	3.39695i	−0.335206	+	0.942145i
$14$		−	1.00000i		−	0.267261i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−2.02598			−0.491372			−0.245686	−	0.969349i	$-0.579013\pi$
$17$	−2.02598			−0.491372			−0.245686	+	0.969349i	$0.579013\pi$
$18$		0			0
$19$	5.03497	+	5.03497i	1.15510	+	1.15510i	0.985515	+	0.169586i	$0.0542432\pi$
$19$	5.03497	+	5.03497i	1.15510	+	1.15510i	0.169586	+	0.985515i	$0.445757\pi$
$20$	0.746053	+	0.746053i	0.166823	+	0.166823i
$21$		0			0
$22$	4.74881			1.01245
$23$	2.39154			0.498670			0.249335	−	0.968417i	$-0.419788\pi$
$23$	2.39154			0.498670			0.249335	+	0.968417i	$0.419788\pi$
$24$		0			0
$25$			3.88681i			0.777362i
$26$	−1.54740	−	3.25662i	−0.303470	−	0.638675i
$27$		0			0
$28$	0.707107	+	0.707107i	0.133631	+	0.133631i
$29$		−	8.46166i		−	1.57129i	−0.618677	−	0.785645i	$-0.712331\pi$
$29$		−	8.46166i		−	1.57129i	0.618677	−	0.785645i	$-0.287669\pi$
$30$		0			0
$31$	−5.55035	−	5.55035i	−0.996872	−	0.996872i	0.00312287	−	0.999995i	$-0.499006\pi$
$31$	−5.55035	−	5.55035i	−0.996872	−	0.996872i	−0.999995	+	0.00312287i	$0.999006\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	1.43258	−	1.43258i	0.245686	−	0.245686i
$35$		−	1.05508i		−	0.178341i
$36$		0			0
$37$	6.97346	−	6.97346i	1.14643	−	1.14643i	0.159180	−	0.987250i	$-0.449115\pi$
$37$	6.97346	−	6.97346i	1.14643	−	1.14643i	0.987250	−	0.159180i	$-0.0508849\pi$
$38$	−7.12053			−1.15510
$39$		0			0
$40$	−1.05508			−0.166823
$41$	−2.39122	+	2.39122i	−0.373446	+	0.373446i	−0.868731	−	0.495285i	$-0.835064\pi$
$41$	−2.39122	+	2.39122i	−0.373446	+	0.373446i	0.495285	+	0.868731i	$0.335064\pi$
$42$		0			0
$43$		−	9.24408i		−	1.40971i	−0.709352	−	0.704855i	$-0.751012\pi$
$43$		−	9.24408i		−	1.40971i	0.709352	−	0.704855i	$-0.248988\pi$
$44$	−3.35792	+	3.35792i	−0.506225	+	0.506225i
$45$		0			0
$46$	−1.69107	+	1.69107i	−0.249335	+	0.249335i
$47$	−3.48199	−	3.48199i	−0.507901	−	0.507901i	0.405981	−	0.913882i	$-0.366930\pi$
$47$	−3.48199	−	3.48199i	−0.507901	−	0.507901i	−0.913882	+	0.405981i	$0.866930\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$	−2.74839	−	2.74839i	−0.388681	−	0.388681i
$51$		0			0
$52$	3.39695	+	1.20860i	0.471072	+	0.167603i
$53$		−	1.35557i		−	0.186202i	−0.995657	−	0.0931011i	$-0.970322\pi$
$53$		−	1.35557i		−	0.186202i	0.995657	−	0.0931011i	$-0.0296780\pi$
$54$		0			0
$55$	5.01037			0.675598
$56$	−1.00000			−0.133631
$57$		0			0
$58$	5.98330	+	5.98330i	0.785645	+	0.785645i
$59$	−4.49527	−	4.49527i	−0.585235	−	0.585235i	0.351103	−	0.936337i	$-0.385807\pi$
$59$	−4.49527	−	4.49527i	−0.585235	−	0.585235i	−0.936337	+	0.351103i	$0.885807\pi$
$60$		0			0
$61$	−1.56297			−0.200118			−0.100059	−	0.994982i	$-0.531903\pi$
$61$	−1.56297			−0.200118			−0.100059	+	0.994982i	$0.531903\pi$
$62$	7.84938			0.996872
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−1.63263	−	3.43599i	−0.202502	−	0.426182i
$66$		0			0
$67$	−1.78711	−	1.78711i	−0.218331	−	0.218331i	0.589464	−	0.807795i	$-0.299339\pi$
$67$	−1.78711	−	1.78711i	−0.218331	−	0.218331i	−0.807795	+	0.589464i	$0.799339\pi$
$68$			2.02598i			0.245686i
$69$		0			0
$70$	0.746053	+	0.746053i	0.0891704	+	0.0891704i
$71$	−9.95954	+	9.95954i	−1.18198	+	1.18198i	−0.202749	+	0.979231i	$0.564987\pi$
$71$	−9.95954	+	9.95954i	−1.18198	+	1.18198i	−0.979231	+	0.202749i	$0.935013\pi$
$72$		0			0
$73$	−3.90170	+	3.90170i	−0.456659	+	0.456659i	−0.897557	−	0.440898i	$-0.854660\pi$
$73$	−3.90170	+	3.90170i	−0.456659	+	0.456659i	0.440898	+	0.897557i	$0.354660\pi$
$74$			9.86196i			1.14643i
$75$		0			0
$76$	5.03497	−	5.03497i	0.577551	−	0.577551i
$77$	4.74881			0.541177
$78$		0			0
$79$	10.2625			1.15463			0.577313	−	0.816523i	$-0.304101\pi$
$79$	10.2625			1.15463			0.577313	+	0.816523i	$0.304101\pi$
$80$	0.746053	−	0.746053i	0.0834113	−	0.0834113i
$81$		0			0
$82$		−	3.38170i		−	0.373446i
$83$	10.2261	−	10.2261i	1.12246	−	1.12246i	0.131088	−	0.991371i	$-0.458153\pi$
$83$	10.2261	−	10.2261i	1.12246	−	1.12246i	0.991371	−	0.131088i	$-0.0418469\pi$
$84$		0			0
$85$	1.51149	−	1.51149i	0.163944	−	0.163944i
$86$	6.53655	+	6.53655i	0.704855	+	0.704855i
$87$		0			0
$88$		−	4.74881i		−	0.506225i
$89$	4.40919	+	4.40919i	0.467373	+	0.467373i	0.901062	−	0.433690i	$-0.142789\pi$
$89$	4.40919	+	4.40919i	0.467373	+	0.467373i	−0.433690	+	0.901062i	$0.642789\pi$
$90$		0			0
$91$	−1.54740	−	3.25662i	−0.162211	−	0.341386i
$92$		−	2.39154i		−	0.249335i
$93$		0			0
$94$	4.92428			0.507901
$95$	−7.51271			−0.770788
$96$		0			0
$97$	−11.0928	−	11.0928i	−1.12630	−	1.12630i	−0.990773	−	0.135531i	$-0.956726\pi$
$97$	−11.0928	−	11.0928i	−1.12630	−	1.12630i	−0.135531	−	0.990773i	$-0.543274\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$		0			0
$100$	3.88681			0.388681
$101$	−4.43684			−0.441482			−0.220741	−	0.975332i	$-0.570848\pi$
$101$	−4.43684			−0.441482			−0.220741	+	0.975332i	$0.570848\pi$
$102$		0			0
$103$		−	9.93465i		−	0.978890i	−0.872034	−	0.489445i	$-0.837199\pi$
$103$		−	9.93465i		−	0.978890i	0.872034	−	0.489445i	$-0.162801\pi$
$104$	−3.25662	+	1.54740i	−0.319338	+	0.151735i
$105$		0			0
$106$	0.958534	+	0.958534i	0.0931011	+	0.0931011i
$107$		−	12.0250i		−	1.16250i	−0.813725	−	0.581250i	$-0.802564\pi$
$107$		−	12.0250i		−	1.16250i	0.813725	−	0.581250i	$-0.197436\pi$
$108$		0			0
$109$	2.47819	+	2.47819i	0.237367	+	0.237367i	0.815759	−	0.578392i	$-0.196320\pi$
$109$	2.47819	+	2.47819i	0.237367	+	0.237367i	−0.578392	+	0.815759i	$0.696320\pi$
$110$	−3.54287	+	3.54287i	−0.337799	+	0.337799i
$111$		0			0
$112$	0.707107	−	0.707107i	0.0668153	−	0.0668153i
$113$		−	19.4049i		−	1.82546i	−0.408561	−	0.912731i	$-0.633969\pi$
$113$		−	19.4049i		−	1.82546i	0.408561	−	0.912731i	$-0.366031\pi$
$114$		0			0
$115$	−1.78421	+	1.78421i	−0.166379	+	0.166379i
$116$	−8.46166			−0.785645
$117$		0			0
$118$	6.35727			0.585235
$119$	1.43258	−	1.43258i	0.131325	−	0.131325i
$120$		0			0
$121$			11.5512i			1.05011i
$122$	1.10519	−	1.10519i	0.100059	−	0.100059i
$123$		0			0
$124$	−5.55035	+	5.55035i	−0.498436	+	0.498436i
$125$	−6.63003	−	6.63003i	−0.593008	−	0.593008i
$126$		0			0
$127$		−	14.6946i		−	1.30393i	−0.758248	−	0.651966i	$-0.773944\pi$
$127$		−	14.6946i		−	1.30393i	0.758248	−	0.651966i	$-0.226056\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	3.58405	+	1.27517i	0.314342	+	0.111840i
$131$		−	2.22152i		−	0.194095i	−0.995280	−	0.0970477i	$-0.969060\pi$
$131$		−	2.22152i		−	0.194095i	0.995280	−	0.0970477i	$-0.0309399\pi$
$132$		0			0
$133$	−7.12053			−0.617428
$134$	2.52736			0.218331
$135$		0			0
$136$	−1.43258	−	1.43258i	−0.122843	−	0.122843i
$137$	−0.387266	−	0.387266i	−0.0330864	−	0.0330864i	0.690370	−	0.723456i	$-0.257448\pi$
$137$	−0.387266	−	0.387266i	−0.0330864	−	0.0330864i	−0.723456	+	0.690370i	$0.757448\pi$
$138$		0			0
$139$	−2.80074			−0.237556			−0.118778	−	0.992921i	$-0.537898\pi$
$139$	−2.80074			−0.237556			−0.118778	+	0.992921i	$0.537898\pi$
$140$	−1.05508			−0.0891704
$141$		0			0
$142$		−	14.0849i		−	1.18198i
$143$	15.4651	−	7.34830i	1.29325	−	0.614496i
$144$		0			0
$145$	6.31285	+	6.31285i	0.524253	+	0.524253i
$146$		−	5.51784i		−	0.456659i
$147$		0			0
$148$	−6.97346	−	6.97346i	−0.573215	−	0.573215i
$149$	−0.866918	+	0.866918i	−0.0710207	+	0.0710207i	−0.741725	−	0.670704i	$-0.765992\pi$
$149$	−0.866918	+	0.866918i	−0.0710207	+	0.0710207i	0.670704	+	0.741725i	$0.265992\pi$
$150$		0			0
$151$	14.7845	−	14.7845i	1.20315	−	1.20315i	0.229945	−	0.973204i	$-0.426145\pi$
$151$	14.7845	−	14.7845i	1.20315	−	1.20315i	0.973204	−	0.229945i	$-0.0738546\pi$
$152$			7.12053i			0.577551i
$153$		0			0
$154$	−3.35792	+	3.35792i	−0.270589	+	0.270589i
$155$	8.28171			0.665203
$156$		0			0
$157$	15.2471			1.21685			0.608424	−	0.793612i	$-0.291802\pi$
$157$	15.2471			1.21685			0.608424	+	0.793612i	$0.291802\pi$
$158$	−7.25671	+	7.25671i	−0.577313	+	0.577313i
$159$		0			0
$160$			1.05508i			0.0834113i
$161$	−1.69107	+	1.69107i	−0.133275	+	0.133275i
$162$		0			0
$163$	−16.2208	+	16.2208i	−1.27051	+	1.27051i	−0.324693	+	0.945819i	$0.605261\pi$
$163$	−16.2208	+	16.2208i	−1.27051	+	1.27051i	−0.945819	+	0.324693i	$0.894739\pi$
$164$	2.39122	+	2.39122i	0.186723	+	0.186723i
$165$		0			0
$166$			14.4619i			1.12246i
$167$	17.0656	+	17.0656i	1.32058	+	1.32058i	0.913308	+	0.407269i	$0.133519\pi$
$167$	17.0656	+	17.0656i	1.32058	+	1.32058i	0.407269	+	0.913308i	$0.366481\pi$
$168$		0			0
$169$	−10.0786	−	8.21112i	−0.775274	−	0.631625i
$170$			2.13757i			0.163944i
$171$		0			0
$172$	−9.24408			−0.704855
$173$	−8.52210			−0.647923			−0.323961	−	0.946070i	$-0.605015\pi$
$173$	−8.52210			−0.647923			−0.323961	+	0.946070i	$0.605015\pi$
$174$		0			0
$175$	−2.74839	−	2.74839i	−0.207759	−	0.207759i
$176$	3.35792	+	3.35792i	0.253113	+	0.253113i
$177$		0			0
$178$	−6.23553			−0.467373
$179$	3.46058			0.258656			0.129328	−	0.991602i	$-0.458718\pi$
$179$	3.46058			0.258656			0.129328	+	0.991602i	$0.458718\pi$
$180$		0			0
$181$			24.8236i			1.84513i	0.385846	+	0.922563i	$0.373910\pi$
$181$			24.8236i			1.84513i	−0.385846	+	0.922563i	$0.626090\pi$
$182$	3.39695	+	1.20860i	0.251799	+	0.0895875i
$183$		0			0
$184$	1.69107	+	1.69107i	0.124668	+	0.124668i
$185$			10.4051i			0.765001i
$186$		0			0
$187$	6.80307	+	6.80307i	0.497490	+	0.497490i
$188$	−3.48199	+	3.48199i	−0.253951	+	0.253951i
$189$		0			0
$190$	5.31229	−	5.31229i	0.385394	−	0.385394i
$191$		−	7.86219i		−	0.568888i	−0.958693	−	0.284444i	$-0.908191\pi$
$191$		−	7.86219i		−	0.568888i	0.958693	−	0.284444i	$-0.0918090\pi$
$192$		0			0
$193$	4.85067	−	4.85067i	0.349159	−	0.349159i	−0.510637	−	0.859796i	$-0.670591\pi$
$193$	4.85067	−	4.85067i	0.349159	−	0.349159i	0.859796	+	0.510637i	$0.170591\pi$
$194$	15.6876			1.12630
$195$		0			0
$196$	−1.00000			−0.0714286
$197$	−9.34718	+	9.34718i	−0.665959	+	0.665959i	−0.956778	−	0.290819i	$-0.906072\pi$
$197$	−9.34718	+	9.34718i	−0.665959	+	0.665959i	0.290819	+	0.956778i	$0.406072\pi$
$198$		0			0
$199$		−	23.0454i		−	1.63365i	−0.576887	−	0.816824i	$-0.695733\pi$
$199$		−	23.0454i		−	1.63365i	0.576887	−	0.816824i	$-0.304267\pi$
$200$	−2.74839	+	2.74839i	−0.194340	+	0.194340i
$201$		0			0
$202$	3.13732	−	3.13732i	0.220741	−	0.220741i
$203$	5.98330	+	5.98330i	0.419945	+	0.419945i
$204$		0			0
$205$		−	3.56796i		−	0.249197i
$206$	7.02486	+	7.02486i	0.489445	+	0.489445i
$207$		0			0
$208$	1.20860	−	3.39695i	0.0838014	−	0.235536i
$209$		−	33.8140i		−	2.33897i
$210$		0			0
$211$	−0.931807			−0.0641482			−0.0320741	−	0.999485i	$-0.510211\pi$
$211$	−0.931807			−0.0641482			−0.0320741	+	0.999485i	$0.510211\pi$
$212$	−1.35557			−0.0931011
$213$		0			0
$214$	8.50295	+	8.50295i	0.581250	+	0.581250i
$215$	6.89658	+	6.89658i	0.470343	+	0.470343i
$216$		0			0
$217$	7.84938			0.532851
$218$	−3.50468			−0.237367
$219$		0			0
$220$		−	5.01037i		−	0.337799i
$221$	2.44860	−	6.88216i	0.164711	−	0.462944i
$222$		0			0
$223$	−0.806330	−	0.806330i	−0.0539959	−	0.0539959i	0.679593	−	0.733589i	$-0.262156\pi$
$223$	−0.806330	−	0.806330i	−0.0539959	−	0.0539959i	−0.733589	+	0.679593i	$0.762156\pi$
$224$			1.00000i			0.0668153i
$225$		0			0
$226$	13.7214	+	13.7214i	0.912731	+	0.912731i
$227$	−2.04742	+	2.04742i	−0.135892	+	0.135892i	−0.771781	−	0.635889i	$-0.780634\pi$
$227$	−2.04742	+	2.04742i	−0.135892	+	0.135892i	0.635889	+	0.771781i	$0.280634\pi$
$228$		0			0
$229$	−12.3112	+	12.3112i	−0.813549	+	0.813549i	−0.985164	−	0.171615i	$-0.945101\pi$
$229$	−12.3112	+	12.3112i	−0.813549	+	0.813549i	0.171615	+	0.985164i	$0.445101\pi$
$230$		−	2.52326i		−	0.166379i
$231$		0			0
$232$	5.98330	−	5.98330i	0.392823	−	0.392823i
$233$	−24.7227			−1.61964			−0.809818	−	0.586682i	$-0.800434\pi$
$233$	−24.7227			−1.61964			−0.809818	+	0.586682i	$0.800434\pi$
$234$		0			0
$235$	5.19550			0.338917
$236$	−4.49527	+	4.49527i	−0.292617	+	0.292617i
$237$		0			0
$238$			2.02598i			0.131325i
$239$	1.69453	−	1.69453i	0.109610	−	0.109610i	−0.650175	−	0.759785i	$-0.725304\pi$
$239$	1.69453	−	1.69453i	0.109610	−	0.109610i	0.759785	+	0.650175i	$0.225304\pi$
$240$		0			0
$241$	4.52253	−	4.52253i	0.291322	−	0.291322i	−0.546281	−	0.837602i	$-0.683957\pi$
$241$	4.52253	−	4.52253i	0.291322	−	0.291322i	0.837602	+	0.546281i	$0.183957\pi$
$242$	−8.16794	−	8.16794i	−0.525055	−	0.525055i
$243$		0			0
$244$			1.56297i			0.100059i
$245$	0.746053	+	0.746053i	0.0476636	+	0.0476636i
$246$		0			0
$247$	−23.1888	+	11.0183i	−1.47547	+	0.701077i
$248$		−	7.84938i		−	0.498436i
$249$		0			0
$250$	9.37628			0.593008
$251$	27.3370			1.72549			0.862747	−	0.505636i	$-0.168742\pi$
$251$	27.3370			1.72549			0.862747	+	0.505636i	$0.168742\pi$
$252$		0			0
$253$	−8.03059	−	8.03059i	−0.504879	−	0.504879i
$254$	10.3906	+	10.3906i	0.651966	+	0.651966i
$255$		0			0
$256$	1.00000			0.0625000
$257$	27.6049			1.72195			0.860975	−	0.508648i	$-0.169855\pi$
$257$	27.6049			1.72195			0.860975	+	0.508648i	$0.169855\pi$
$258$		0			0
$259$			9.86196i			0.612792i
$260$	−3.43599	+	1.63263i	−0.213091	+	0.101251i
$261$		0			0
$262$	1.57085	+	1.57085i	0.0970477	+	0.0970477i
$263$			26.9692i			1.66299i	0.555529	+	0.831497i	$0.312516\pi$
$263$			26.9692i			1.66299i	−0.555529	+	0.831497i	$0.687484\pi$
$264$		0			0
$265$	1.01133	+	1.01133i	0.0621254	+	0.0621254i
$266$	5.03497	−	5.03497i	0.308714	−	0.308714i
$267$		0			0
$268$	−1.78711	+	1.78711i	−0.109165	+	0.109165i
$269$			15.1618i			0.924433i	0.886767	+	0.462217i	$0.152946\pi$
$269$			15.1618i			0.924433i	−0.886767	+	0.462217i	$0.847054\pi$
$270$		0			0
$271$	−17.8111	+	17.8111i	−1.08195	+	1.08195i	−0.0856179	+	0.996328i	$0.527286\pi$
$271$	−17.8111	+	17.8111i	−1.08195	+	1.08195i	−0.996328	+	0.0856179i	$0.972714\pi$
$272$	2.02598			0.122843
$273$		0			0
$274$	0.547677			0.0330864
$275$	13.0516	−	13.0516i	0.787040	−	0.787040i
$276$		0			0
$277$		−	3.04741i		−	0.183101i	−0.995800	−	0.0915507i	$-0.970818\pi$
$277$		−	3.04741i		−	0.183101i	0.995800	−	0.0915507i	$-0.0291823\pi$
$278$	1.98042	−	1.98042i	0.118778	−	0.118778i
$279$		0			0
$280$	0.746053	−	0.746053i	0.0445852	−	0.0445852i
$281$	−10.5654	−	10.5654i	−0.630278	−	0.630278i	0.317859	−	0.948138i	$-0.397036\pi$
$281$	−10.5654	−	10.5654i	−0.630278	−	0.630278i	−0.948138	+	0.317859i	$0.897036\pi$
$282$		0			0
$283$		−	21.8771i		−	1.30046i	−0.759738	−	0.650229i	$-0.774673\pi$
$283$		−	21.8771i		−	1.30046i	0.759738	−	0.650229i	$-0.225327\pi$
$284$	9.95954	+	9.95954i	0.590990	+	0.590990i
$285$		0			0
$286$	−5.73942	+	16.1315i	−0.339379	+	0.953875i
$287$		−	3.38170i		−	0.199615i
$288$		0			0
$289$	−12.8954			−0.758553
$290$	−8.92771			−0.524253
$291$		0			0
$292$	3.90170	+	3.90170i	0.228330	+	0.228330i
$293$	−9.78815	−	9.78815i	−0.571830	−	0.571830i	0.360809	−	0.932640i	$-0.382500\pi$
$293$	−9.78815	−	9.78815i	−0.571830	−	0.571830i	−0.932640	+	0.360809i	$0.882500\pi$
$294$		0			0
$295$	6.70742			0.390521
$296$	9.86196			0.573215
$297$		0			0
$298$		−	1.22601i		−	0.0710207i
$299$	−2.89042	+	8.12394i	−0.167157	+	0.469820i
$300$		0			0
$301$	6.53655	+	6.53655i	0.376761	+	0.376761i
$302$			20.9085i			1.20315i
$303$		0			0
$304$	−5.03497	−	5.03497i	−0.288775	−	0.288775i
$305$	1.16606	−	1.16606i	0.0667684	−	0.0667684i
$306$		0			0
$307$	−12.3093	+	12.3093i	−0.702527	+	0.702527i	−0.964952	−	0.262425i	$-0.915478\pi$
$307$	−12.3093	+	12.3093i	−0.702527	+	0.702527i	0.262425	+	0.964952i	$0.415478\pi$
$308$		−	4.74881i		−	0.270589i
$309$		0			0
$310$	−5.85605	+	5.85605i	−0.332601	+	0.332601i
$311$	2.57110			0.145794			0.0728968	−	0.997339i	$-0.476776\pi$
$311$	2.57110			0.145794			0.0728968	+	0.997339i	$0.476776\pi$
$312$		0			0
$313$	1.14291			0.0646013			0.0323006	−	0.999478i	$-0.489717\pi$
$313$	1.14291			0.0646013			0.0323006	+	0.999478i	$0.489717\pi$
$314$	−10.7813	+	10.7813i	−0.608424	+	0.608424i
$315$		0			0
$316$		−	10.2625i		−	0.577313i
$317$	−9.45116	+	9.45116i	−0.530830	+	0.530830i	−0.920819	−	0.389989i	$-0.872479\pi$
$317$	−9.45116	+	9.45116i	−0.530830	+	0.530830i	0.389989	+	0.920819i	$0.372479\pi$
$318$		0			0
$319$	−28.4136	+	28.4136i	−1.59085	+	1.59085i
$320$	−0.746053	−	0.746053i	−0.0417056	−	0.0417056i
$321$		0			0
$322$		−	2.39154i		−	0.133275i
$323$	−10.2008	−	10.2008i	−0.567585	−	0.567585i
$324$		0			0
$325$	−13.2033	−	4.69760i	−0.732388	−	0.260576i
$326$		−	22.9397i		−	1.27051i
$327$		0			0
$328$	−3.38170			−0.186723
$329$	4.92428			0.271485
$330$		0			0
$331$	8.76490	+	8.76490i	0.481763	+	0.481763i	0.905694	−	0.423932i	$-0.139350\pi$
$331$	8.76490	+	8.76490i	0.481763	+	0.481763i	−0.423932	+	0.905694i	$0.639350\pi$
$332$	−10.2261	−	10.2261i	−0.561229	−	0.561229i
$333$		0			0
$334$	−24.1344			−1.32058
$335$	2.66656			0.145690
$336$		0			0
$337$		−	31.8297i		−	1.73387i	−0.498418	−	0.866937i	$-0.666086\pi$
$337$		−	31.8297i		−	1.73387i	0.498418	−	0.866937i	$-0.333914\pi$
$338$	12.9328	−	1.32048i	0.703449	−	0.0718249i
$339$		0			0
$340$	−1.51149	−	1.51149i	−0.0819720	−	0.0819720i
$341$			37.2752i			2.01857i
$342$		0			0
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	6.53655	−	6.53655i	0.352427	−	0.352427i
$345$		0			0
$346$	6.02603	−	6.02603i	0.323961	−	0.323961i
$347$			20.0727i			1.07756i	0.842447	+	0.538780i	$0.181114\pi$
$347$			20.0727i			1.07756i	−0.842447	+	0.538780i	$0.818886\pi$
$348$		0			0
$349$	−8.88355	+	8.88355i	−0.475525	+	0.475525i	−0.903697	−	0.428172i	$-0.859158\pi$
$349$	−8.88355	+	8.88355i	−0.475525	+	0.475525i	0.428172	+	0.903697i	$0.359158\pi$
$350$	3.88681			0.207759
$351$		0			0
$352$	−4.74881			−0.253113
$353$	12.9241	−	12.9241i	0.687878	−	0.687878i	−0.273884	−	0.961763i	$-0.588309\pi$
$353$	12.9241	−	12.9241i	0.687878	−	0.687878i	0.961763	+	0.273884i	$0.0883085\pi$
$354$		0			0
$355$		−	14.8607i		−	0.788723i
$356$	4.40919	−	4.40919i	0.233686	−	0.233686i
$357$		0			0
$358$	−2.44700	+	2.44700i	−0.129328	+	0.129328i
$359$	10.7224	+	10.7224i	0.565907	+	0.565907i	0.930979	−	0.365072i	$-0.118956\pi$
$359$	10.7224	+	10.7224i	0.565907	+	0.565907i	−0.365072	+	0.930979i	$0.618956\pi$
$360$		0			0
$361$			31.7019i			1.66852i
$362$	−17.5530	−	17.5530i	−0.922563	−	0.922563i
$363$		0			0
$364$	−3.25662	+	1.54740i	−0.170693	+	0.0811057i
$365$		−	5.82175i		−	0.304724i
$366$		0			0
$367$	−14.5681			−0.760447			−0.380224	−	0.924895i	$-0.624153\pi$
$367$	−14.5681			−0.760447			−0.380224	+	0.924895i	$0.624153\pi$
$368$	−2.39154			−0.124668
$369$		0			0
$370$	−7.35754	−	7.35754i	−0.382500	−	0.382500i
$371$	0.958534	+	0.958534i	0.0497646	+	0.0497646i
$372$		0			0
$373$	−4.64322			−0.240417			−0.120208	−	0.992749i	$-0.538356\pi$
$373$	−4.64322			−0.240417			−0.120208	+	0.992749i	$0.538356\pi$
$374$	−9.62100			−0.497490
$375$		0			0
$376$		−	4.92428i		−	0.253951i
$377$	28.7438	+	10.2268i	1.48038	+	0.526705i
$378$		0			0
$379$	−6.74493	−	6.74493i	−0.346464	−	0.346464i	0.512327	−	0.858791i	$-0.328784\pi$
$379$	−6.74493	−	6.74493i	−0.346464	−	0.346464i	−0.858791	+	0.512327i	$0.828784\pi$
$380$			7.51271i			0.385394i
$381$		0			0
$382$	5.55941	+	5.55941i	0.284444	+	0.284444i
$383$	−1.32694	+	1.32694i	−0.0678037	+	0.0678037i	−0.740195	−	0.672392i	$-0.765267\pi$
$383$	−1.32694	+	1.32694i	−0.0678037	+	0.0678037i	0.672392	+	0.740195i	$0.265267\pi$
$384$		0			0
$385$	−3.54287	+	3.54287i	−0.180561	+	0.180561i
$386$			6.85988i			0.349159i
$387$		0			0
$388$	−11.0928	+	11.0928i	−0.563152	+	0.563152i
$389$	−25.9151			−1.31395			−0.656974	−	0.753913i	$-0.728164\pi$
$389$	−25.9151			−1.31395			−0.656974	+	0.753913i	$0.728164\pi$
$390$		0			0
$391$	−4.84521			−0.245033
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$		0			0
$394$		−	13.2189i		−	0.665959i
$395$	−7.65639	+	7.65639i	−0.385235	+	0.385235i
$396$		0			0
$397$	−21.1031	+	21.1031i	−1.05913	+	1.05913i	−0.0609954	+	0.998138i	$0.519427\pi$
$397$	−21.1031	+	21.1031i	−1.05913	+	1.05913i	−0.998138	+	0.0609954i	$0.980573\pi$
$398$	16.2956	+	16.2956i	0.816824	+	0.816824i
$399$		0			0
$400$		−	3.88681i		−	0.194340i
$401$	−18.9302	−	18.9302i	−0.945332	−	0.945332i	0.0532497	−	0.998581i	$-0.483042\pi$
$401$	−18.9302	−	18.9302i	−0.945332	−	0.945332i	−0.998581	+	0.0532497i	$0.983042\pi$
$402$		0			0
$403$	25.5624	−	12.1461i	1.27336	−	0.605041i
$404$			4.43684i			0.220741i
$405$		0			0
$406$	−8.46166			−0.419945
$407$	−46.8326			−2.32141
$408$		0			0
$409$	−10.4950	−	10.4950i	−0.518945	−	0.518945i	0.398307	−	0.917252i	$-0.369598\pi$
$409$	−10.4950	−	10.4950i	−0.518945	−	0.518945i	−0.917252	+	0.398307i	$0.869598\pi$
$410$	2.52293	+	2.52293i	0.124598	+	0.124598i
$411$		0			0
$412$	−9.93465			−0.489445
$413$	6.35727			0.312821
$414$		0			0
$415$			15.2584i			0.749005i
$416$	1.54740	+	3.25662i	0.0758674	+	0.159669i
$417$		0			0
$418$	23.9101	+	23.9101i	1.16948	+	1.16948i
$419$			22.9538i			1.12136i	0.828031	+	0.560682i	$0.189461\pi$
$419$			22.9538i			1.12136i	−0.828031	+	0.560682i	$0.810539\pi$
$420$		0			0
$421$	20.3182	+	20.3182i	0.990247	+	0.990247i	0.999953	−	0.00970630i	$-0.00308966\pi$
$421$	20.3182	+	20.3182i	0.990247	+	0.990247i	−0.00970630	+	0.999953i	$0.503090\pi$
$422$	0.658887	−	0.658887i	0.0320741	−	0.0320741i
$423$		0			0
$424$	0.958534	−	0.958534i	0.0465505	−	0.0465505i
$425$		−	7.87460i		−	0.381974i
$426$		0			0
$427$	1.10519	−	1.10519i	0.0534838	−	0.0534838i
$428$	−12.0250			−0.581250
$429$		0			0
$430$	−9.75323			−0.470343
$431$	0.553365	−	0.553365i	0.0266547	−	0.0266547i	−0.693654	−	0.720309i	$-0.744000\pi$
$431$	0.553365	−	0.553365i	0.0266547	−	0.0266547i	0.720309	+	0.693654i	$0.244000\pi$
$432$		0			0
$433$		−	1.38424i		−	0.0665222i	−0.999447	−	0.0332611i	$-0.989411\pi$
$433$		−	1.38424i		−	0.0665222i	0.999447	−	0.0332611i	$-0.0105893\pi$
$434$	−5.55035	+	5.55035i	−0.266425	+	0.266425i
$435$		0			0
$436$	2.47819	−	2.47819i	0.118684	−	0.118684i
$437$	12.0413	+	12.0413i	0.576015	+	0.576015i
$438$		0			0
$439$		−	14.3680i		−	0.685746i	−0.939382	−	0.342873i	$-0.888600\pi$
$439$		−	14.3680i		−	0.685746i	0.939382	−	0.342873i	$-0.111400\pi$
$440$	3.54287	+	3.54287i	0.168899	+	0.168899i
$441$		0			0
$442$	3.13500	+	6.59784i	0.149117	+	0.313827i
$443$			7.27225i			0.345515i	0.984964	+	0.172758i	$0.0552677\pi$
$443$			7.27225i			0.345515i	−0.984964	+	0.172758i	$0.944732\pi$
$444$		0			0
$445$	−6.57897			−0.311873
$446$	1.14032			0.0539959
$447$		0			0
$448$	−0.707107	−	0.707107i	−0.0334077	−	0.0334077i
$449$	11.1201	+	11.1201i	0.524789	+	0.524789i	0.919014	−	0.394225i	$-0.128987\pi$
$449$	11.1201	+	11.1201i	0.524789	+	0.524789i	−0.394225	+	0.919014i	$0.628987\pi$
$450$		0			0
$451$	16.0591			0.756191
$452$	−19.4049			−0.912731
$453$		0			0
$454$		−	2.89548i		−	0.135892i
$455$	3.58405	+	1.27517i	0.168023	+	0.0597808i
$456$		0			0
$457$	7.25037	+	7.25037i	0.339158	+	0.339158i	0.856050	−	0.516892i	$-0.172911\pi$
$457$	7.25037	+	7.25037i	0.339158	+	0.339158i	−0.516892	+	0.856050i	$0.672911\pi$
$458$		−	17.4107i		−	0.813549i
$459$		0			0
$460$	1.78421	+	1.78421i	0.0831894	+	0.0831894i
$461$	−20.4191	+	20.4191i	−0.951011	+	0.951011i	−0.998855	−	0.0478439i	$-0.984765\pi$
$461$	−20.4191	+	20.4191i	−0.951011	+	0.951011i	0.0478439	+	0.998855i	$0.484765\pi$
$462$		0			0
$463$	5.16963	−	5.16963i	0.240253	−	0.240253i	−0.576702	−	0.816955i	$-0.695661\pi$
$463$	5.16963	−	5.16963i	0.240253	−	0.240253i	0.816955	+	0.576702i	$0.195661\pi$
$464$			8.46166i			0.392823i
$465$		0			0
$466$	17.4816	−	17.4816i	0.809818	−	0.809818i
$467$	16.6030			0.768293			0.384147	−	0.923272i	$-0.374496\pi$
$467$	16.6030			0.768293			0.384147	+	0.923272i	$0.374496\pi$
$468$		0			0
$469$	2.52736			0.116703
$470$	−3.67378	+	3.67378i	−0.169459	+	0.169459i
$471$		0			0
$472$		−	6.35727i		−	0.292617i
$473$	−31.0409	+	31.0409i	−1.42726	+	1.42726i
$474$		0			0
$475$	−19.5700	+	19.5700i	−0.897932	+	0.897932i
$476$	−1.43258	−	1.43258i	−0.0656624	−	0.0656624i
$477$		0			0
$478$			2.39642i			0.109610i
$479$	−20.7447	−	20.7447i	−0.947851	−	0.947851i	0.0508550	−	0.998706i	$-0.483805\pi$
$479$	−20.7447	−	20.7447i	−0.947851	−	0.947851i	−0.998706	+	0.0508550i	$0.983805\pi$
$480$		0			0
$481$	15.2604	+	32.1166i	0.695813	+	1.46439i
$482$			6.39582i			0.291322i
$483$		0			0
$484$	11.5512			0.525055
$485$	16.5516			0.751572
$486$		0			0
$487$	−5.21573	−	5.21573i	−0.236347	−	0.236347i	0.578989	−	0.815336i	$-0.303448\pi$
$487$	−5.21573	−	5.21573i	−0.236347	−	0.236347i	−0.815336	+	0.578989i	$0.803448\pi$
$488$	−1.10519	−	1.10519i	−0.0500295	−	0.0500295i
$489$		0			0
$490$	−1.05508			−0.0476636
$491$	11.0398			0.498220			0.249110	−	0.968475i	$-0.419862\pi$
$491$	11.0398			0.498220			0.249110	+	0.968475i	$0.419862\pi$
$492$		0			0
$493$			17.1431i			0.772089i
$494$	8.60587	−	24.1881i	0.387197	−	1.08827i
$495$		0			0
$496$	5.55035	+	5.55035i	0.249218	+	0.249218i
$497$		−	14.0849i		−	0.631795i
$498$		0			0
$499$	3.56893	+	3.56893i	0.159767	+	0.159767i	0.782464	−	0.622696i	$-0.213963\pi$
$499$	3.56893	+	3.56893i	0.159767	+	0.159767i	−0.622696	+	0.782464i	$0.713963\pi$
$500$	−6.63003	+	6.63003i	−0.296504	+	0.296504i
$501$		0			0
$502$	−19.3302	+	19.3302i	−0.862747	+	0.862747i
$503$		−	36.7436i		−	1.63832i	−0.573566	−	0.819159i	$-0.694441\pi$
$503$		−	36.7436i		−	1.63832i	0.573566	−	0.819159i	$-0.305559\pi$
$504$		0			0
$505$	3.31012	−	3.31012i	0.147298	−	0.147298i
$506$	11.3570			0.504879
$507$		0			0
$508$	−14.6946			−0.651966
$509$	−8.92586	+	8.92586i	−0.395632	+	0.395632i	−0.876689	−	0.481057i	$-0.840253\pi$
$509$	−8.92586	+	8.92586i	−0.395632	+	0.395632i	0.481057	+	0.876689i	$0.340253\pi$
$510$		0			0
$511$		−	5.51784i		−	0.244095i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	−19.5196	+	19.5196i	−0.860975	+	0.860975i
$515$	7.41178	+	7.41178i	0.326602	+	0.326602i
$516$		0			0
$517$			23.3845i			1.02845i
$518$	−6.97346	−	6.97346i	−0.306396	−	0.306396i
$519$		0			0
$520$	1.27517	−	3.58405i	0.0559198	−	0.157171i
$521$		−	11.5826i		−	0.507445i	−0.967277	−	0.253722i	$-0.918345\pi$
$521$		−	11.5826i		−	0.507445i	0.967277	−	0.253722i	$-0.0816550\pi$
$522$		0			0
$523$	31.9601			1.39752			0.698758	−	0.715358i	$-0.253737\pi$
$523$	31.9601			1.39752			0.698758	+	0.715358i	$0.253737\pi$
$524$	−2.22152			−0.0970477
$525$		0			0
$526$	−19.0701	−	19.0701i	−0.831497	−	0.831497i
$527$	11.2449	+	11.2449i	0.489835	+	0.489835i
$528$		0			0
$529$	−17.2805			−0.751328
$530$	−1.43023			−0.0621254
$531$		0			0
$532$			7.12053i			0.308714i
$533$	−5.23283	−	11.0129i	−0.226659	−	0.477022i
$534$		0			0
$535$	8.97127	+	8.97127i	0.387862	+	0.387862i
$536$		−	2.52736i		−	0.109165i
$537$		0			0
$538$	−10.7210	−	10.7210i	−0.462217	−	0.462217i
$539$	−3.35792	+	3.35792i	−0.144636	+	0.144636i
$540$		0			0
$541$	3.83741	−	3.83741i	0.164983	−	0.164983i	−0.619787	−	0.784770i	$-0.712781\pi$
$541$	3.83741	−	3.83741i	0.164983	−	0.164983i	0.784770	+	0.619787i	$0.212781\pi$
$542$		−	25.1887i		−	1.08195i
$543$		0			0
$544$	−1.43258	+	1.43258i	−0.0614215	+	0.0614215i
$545$	−3.69772			−0.158393
$546$		0			0
$547$	−10.7371			−0.459087			−0.229544	−	0.973298i	$-0.573723\pi$
$547$	−10.7371			−0.459087			−0.229544	+	0.973298i	$0.573723\pi$
$548$	−0.387266	+	0.387266i	−0.0165432	+	0.0165432i
$549$		0			0
$550$			18.4577i			0.787040i
$551$	42.6042	−	42.6042i	1.81500	−	1.81500i
$552$		0			0
$553$	−7.25671	+	7.25671i	−0.308587	+	0.308587i
$554$	2.15485	+	2.15485i	0.0915507	+	0.0915507i
$555$		0			0
$556$			2.80074i			0.118778i
$557$	5.56727	+	5.56727i	0.235893	+	0.235893i	0.815147	−	0.579254i	$-0.196656\pi$
$557$	5.56727	+	5.56727i	0.235893	+	0.235893i	−0.579254	+	0.815147i	$0.696656\pi$
$558$		0			0
$559$	31.4017	+	11.1724i	1.32815	+	0.472543i
$560$			1.05508i			0.0445852i
$561$		0			0
$562$	14.9417			0.630278
$563$	35.8520			1.51098			0.755491	−	0.655159i	$-0.227399\pi$
$563$	35.8520			1.51098			0.755491	+	0.655159i	$0.227399\pi$
$564$		0			0
$565$	14.4771	+	14.4771i	0.609056	+	0.609056i
$566$	15.4694	+	15.4694i	0.650229	+	0.650229i
$567$		0			0
$568$	−14.0849			−0.590990
$569$	−11.7932			−0.494398			−0.247199	−	0.968965i	$-0.579510\pi$
$569$	−11.7932			−0.494398			−0.247199	+	0.968965i	$0.579510\pi$
$570$		0			0
$571$		−	36.8437i		−	1.54186i	−0.636920	−	0.770930i	$-0.719792\pi$
$571$		−	36.8437i		−	1.54186i	0.636920	−	0.770930i	$-0.280208\pi$
$572$	−7.34830	−	15.4651i	−0.307248	−	0.646627i
$573$		0			0
$574$	2.39122	+	2.39122i	0.0998077	+	0.0998077i
$575$			9.29545i			0.387647i
$576$		0			0
$577$	−2.65397	−	2.65397i	−0.110486	−	0.110486i	0.649702	−	0.760189i	$-0.274893\pi$
$577$	−2.65397	−	2.65397i	−0.110486	−	0.110486i	−0.760189	+	0.649702i	$0.774893\pi$
$578$	9.11843	−	9.11843i	0.379277	−	0.379277i
$579$		0			0
$580$	6.31285	−	6.31285i	0.262127	−	0.262127i
$581$			14.4619i			0.599979i
$582$		0			0
$583$	−4.55190	+	4.55190i	−0.188520	+	0.188520i
$584$	−5.51784			−0.228330
$585$		0			0
$586$	13.8425			0.571830
$587$	8.67198	−	8.67198i	0.357931	−	0.357931i	−0.505119	−	0.863050i	$-0.668551\pi$
$587$	8.67198	−	8.67198i	0.357931	−	0.357931i	0.863050	+	0.505119i	$0.168551\pi$
$588$		0			0
$589$		−	55.8917i		−	2.30298i
$590$	−4.74286	+	4.74286i	−0.195261	+	0.195261i
$591$		0			0
$592$	−6.97346	+	6.97346i	−0.286607	+	0.286607i
$593$	−23.0726	−	23.0726i	−0.947478	−	0.947478i	0.0512098	−	0.998688i	$-0.483692\pi$
$593$	−23.0726	−	23.0726i	−0.947478	−	0.947478i	−0.998688	+	0.0512098i	$0.983692\pi$
$594$		0			0
$595$			2.13757i			0.0876317i
$596$	0.866918	+	0.866918i	0.0355103	+	0.0355103i
$597$		0			0
$598$	−3.70066	−	7.78833i	−0.151331	−	0.318488i
$599$			12.1997i			0.498465i	0.968444	+	0.249232i	$0.0801783\pi$
$599$			12.1997i			0.498465i	−0.968444	+	0.249232i	$0.919822\pi$
$600$		0			0
$601$	−0.975365			−0.0397860			−0.0198930	−	0.999802i	$-0.506333\pi$
$601$	−0.975365			−0.0397860			−0.0198930	+	0.999802i	$0.506333\pi$
$602$	−9.24408			−0.376761
$603$		0			0
$604$	−14.7845	−	14.7845i	−0.601574	−	0.601574i
$605$	−8.61782	−	8.61782i	−0.350364	−	0.350364i
$606$		0			0
$607$	−21.1566			−0.858721			−0.429360	−	0.903133i	$-0.641261\pi$
$607$	−21.1566			−0.858721			−0.429360	+	0.903133i	$0.641261\pi$
$608$	7.12053			0.288775
$609$		0			0
$610$			1.64906i			0.0667684i
$611$	16.0365	−	7.61983i	0.648768	−	0.308265i
$612$		0			0
$613$	−3.67466	−	3.67466i	−0.148418	−	0.148418i	0.628993	−	0.777411i	$-0.283467\pi$
$613$	−3.67466	−	3.67466i	−0.148418	−	0.148418i	−0.777411	+	0.628993i	$0.783467\pi$
$614$		−	17.4079i		−	0.702527i
$615$		0			0
$616$	3.35792	+	3.35792i	0.135294	+	0.135294i
$617$	−28.6513	+	28.6513i	−1.15346	+	1.15346i	−0.167604	+	0.985854i	$0.553603\pi$
$617$	−28.6513	+	28.6513i	−1.15346	+	1.15346i	−0.985854	+	0.167604i	$0.946397\pi$
$618$		0			0
$619$	20.2324	−	20.2324i	0.813211	−	0.813211i	−0.171903	−	0.985114i	$-0.554992\pi$
$619$	20.2324	−	20.2324i	0.813211	−	0.813211i	0.985114	+	0.171903i	$0.0549916\pi$
$620$		−	8.28171i		−	0.332601i
$621$		0			0
$622$	−1.81804	+	1.81804i	−0.0728968	+	0.0728968i
$623$	−6.23553			−0.249821
$624$		0			0
$625$	−9.54134			−0.381654
$626$	−0.808162	+	0.808162i	−0.0323006	+	0.0323006i
$627$		0			0
$628$		−	15.2471i		−	0.608424i
$629$	−14.1281	+	14.1281i	−0.563324	+	0.563324i
$630$		0			0
$631$	15.8814	−	15.8814i	0.632228	−	0.632228i	−0.316398	−	0.948626i	$-0.602474\pi$
$631$	15.8814	−	15.8814i	0.632228	−	0.632228i	0.948626	+	0.316398i	$0.102474\pi$
$632$	7.25671	+	7.25671i	0.288656	+	0.288656i
$633$		0			0
$634$		−	13.3660i		−	0.530830i
$635$	10.9629	+	10.9629i	0.435051	+	0.435051i
$636$		0			0
$637$	3.39695	+	1.20860i	0.134592	+	0.0478865i
$638$		−	40.1828i		−	1.59085i
$639$		0			0
$640$	1.05508			0.0417056
$641$	−35.2108			−1.39074			−0.695371	−	0.718651i	$-0.744760\pi$
$641$	−35.2108			−1.39074			−0.695371	+	0.718651i	$0.744760\pi$
$642$		0			0
$643$	−19.8170	−	19.8170i	−0.781505	−	0.781505i	0.198580	−	0.980085i	$-0.436367\pi$
$643$	−19.8170	−	19.8170i	−0.781505	−	0.781505i	−0.980085	+	0.198580i	$0.936367\pi$
$644$	1.69107	+	1.69107i	0.0666376	+	0.0666376i
$645$		0			0
$646$	14.4260			0.567585
$647$	−11.6901			−0.459585			−0.229793	−	0.973240i	$-0.573805\pi$
$647$	−11.6901			−0.459585			−0.229793	+	0.973240i	$0.573805\pi$
$648$		0			0
$649$			30.1895i			1.18504i
$650$	12.6579	−	6.01444i	0.496482	−	0.235906i
$651$		0			0
$652$	16.2208	+	16.2208i	0.635256	+	0.635256i
$653$			34.8963i			1.36560i	0.730606	+	0.682800i	$0.239238\pi$
$653$			34.8963i			1.36560i	−0.730606	+	0.682800i	$0.760762\pi$
$654$		0			0
$655$	1.65737	+	1.65737i	0.0647590	+	0.0647590i
$656$	2.39122	−	2.39122i	0.0933616	−	0.0933616i
$657$		0			0
$658$	−3.48199	+	3.48199i	−0.135742	+	0.135742i
$659$		−	10.9137i		−	0.425136i	−0.977146	−	0.212568i	$-0.931817\pi$
$659$		−	10.9137i		−	0.425136i	0.977146	−	0.212568i	$-0.0681828\pi$
$660$		0			0
$661$	17.9445	−	17.9445i	0.697959	−	0.697959i	−0.266011	−	0.963970i	$-0.585706\pi$
$661$	17.9445	−	17.9445i	0.697959	−	0.697959i	0.963970	+	0.266011i	$0.0857056\pi$
$662$	−12.3954			−0.481763
$663$		0			0
$664$	14.4619			0.561229
$665$	5.31229	−	5.31229i	0.206002	−	0.206002i
$666$		0			0
$667$		−	20.2364i		−	0.783556i
$668$	17.0656	−	17.0656i	0.660289	−	0.660289i
$669$		0			0
$670$	−1.88554	+	1.88554i	−0.0728449	+	0.0728449i
$671$	5.24833	+	5.24833i	0.202610	+	0.202610i
$672$		0			0
$673$		−	44.1565i		−	1.70211i	−0.525078	−	0.851054i	$-0.675964\pi$
$673$		−	44.1565i		−	1.70211i	0.525078	−	0.851054i	$-0.324036\pi$
$674$	22.5070	+	22.5070i	0.866937	+	0.866937i
$675$		0			0
$676$	−8.21112	+	10.0786i	−0.315812	+	0.387637i
$677$			14.9679i			0.575262i	0.957741	+	0.287631i	$0.0928676\pi$
$677$			14.9679i			0.575262i	−0.957741	+	0.287631i	$0.907132\pi$
$678$		0			0
$679$	15.6876			0.602035
$680$	2.13757			0.0819720
$681$		0			0
$682$	−26.3576	−	26.3576i	−1.00928	−	1.00928i
$683$	−9.38498	−	9.38498i	−0.359106	−	0.359106i	0.504377	−	0.863483i	$-0.331722\pi$
$683$	−9.38498	−	9.38498i	−0.359106	−	0.359106i	−0.863483	+	0.504377i	$0.831722\pi$
$684$		0			0
$685$	0.577842			0.0220782
$686$	−1.00000			−0.0381802
$687$		0			0
$688$			9.24408i			0.352427i
$689$	4.60481	+	1.63835i	0.175429	+	0.0624160i
$690$		0			0
$691$	−15.2672	−	15.2672i	−0.580793	−	0.580793i	0.354328	−	0.935121i	$-0.384710\pi$
$691$	−15.2672	−	15.2672i	−0.580793	−	0.580793i	−0.935121	+	0.354328i	$0.884710\pi$
$692$			8.52210i			0.323961i
$693$		0			0
$694$	−14.1935	−	14.1935i	−0.538780	−	0.538780i
$695$	2.08950	−	2.08950i	0.0792594	−	0.0792594i
$696$		0			0
$697$	4.84457	−	4.84457i	0.183501	−	0.183501i
$698$		−	12.5632i		−	0.475525i
$699$		0			0
$700$	−2.74839	+	2.74839i	−0.103879	+	0.103879i
$701$	1.91734			0.0724168			0.0362084	−	0.999344i	$-0.488472\pi$
$701$	1.91734			0.0724168			0.0362084	+	0.999344i	$0.488472\pi$
$702$		0			0
$703$	70.2223			2.64848
$704$	3.35792	−	3.35792i	0.126556	−	0.126556i
$705$		0			0
$706$			18.2774i			0.687878i
$707$	3.13732	−	3.13732i	0.117991	−	0.117991i
$708$		0			0
$709$	−35.5754	+	35.5754i	−1.33606	+	1.33606i	−0.436222	+	0.899839i	$0.643684\pi$
$709$	−35.5754	+	35.5754i	−1.33606	+	1.33606i	−0.899839	+	0.436222i	$0.856316\pi$
$710$	10.5081	+	10.5081i	0.394362	+	0.394362i
$711$		0			0
$712$			6.23553i			0.233686i
$713$	−13.2739	−	13.2739i	−0.497110	−	0.497110i
$714$		0			0
$715$	−6.05554	+	17.0200i	−0.226464	+	0.636511i
$716$		−	3.46058i		−	0.129328i
$717$		0			0
$718$	−15.1638			−0.565907
$719$	3.52562			0.131484			0.0657418	−	0.997837i	$-0.479059\pi$
$719$	3.52562			0.131484			0.0657418	+	0.997837i	$0.479059\pi$
$720$		0			0
$721$	7.02486	+	7.02486i	0.261619	+	0.261619i
$722$	−22.4166	−	22.4166i	−0.834260	−	0.834260i
$723$		0			0
$724$	24.8236			0.922563
$725$	32.8889			1.22146
$726$		0			0
$727$		−	20.5218i		−	0.761112i	−0.924758	−	0.380556i	$-0.875733\pi$
$727$		−	20.5218i		−	0.761112i	0.924758	−	0.380556i	$-0.124267\pi$
$728$	1.20860	−	3.39695i	0.0447937	−	0.125899i
$729$		0			0
$730$	4.11660	+	4.11660i	0.152362	+	0.152362i
$731$			18.7283i			0.692692i
$732$		0			0
$733$	7.62778	+	7.62778i	0.281739	+	0.281739i	0.833802	−	0.552064i	$-0.186159\pi$
$733$	7.62778	+	7.62778i	0.281739	+	0.281739i	−0.552064	+	0.833802i	$0.686159\pi$
$734$	10.3012	−	10.3012i	0.380224	−	0.380224i
$735$		0			0
$736$	1.69107	−	1.69107i	0.0623338	−	0.0623338i
$737$			12.0020i			0.442098i
$738$		0			0
$739$	22.0350	−	22.0350i	0.810572	−	0.810572i	−0.174148	−	0.984720i	$-0.555717\pi$
$739$	22.0350	−	22.0350i	0.810572	−	0.810572i	0.984720	+	0.174148i	$0.0557170\pi$
$740$	10.4051			0.382500
$741$		0			0
$742$	−1.35557			−0.0497646
$743$	−7.44855	+	7.44855i	−0.273261	+	0.273261i	−0.830411	−	0.557151i	$-0.811895\pi$
$743$	−7.44855	+	7.44855i	−0.273261	+	0.273261i	0.557151	+	0.830411i	$0.311895\pi$
$744$		0			0
$745$		−	1.29353i		−	0.0473914i
$746$	3.28325	−	3.28325i	0.120208	−	0.120208i
$747$		0			0
$748$	6.80307	−	6.80307i	0.248745	−	0.248745i
$749$	8.50295	+	8.50295i	0.310691	+	0.310691i
$750$		0			0
$751$			9.76517i			0.356336i	0.984000	+	0.178168i	$0.0570171\pi$
$751$			9.76517i			0.356336i	−0.984000	+	0.178168i	$0.942983\pi$
$752$	3.48199	+	3.48199i	0.126975	+	0.126975i
$753$		0			0
$754$	−27.5564	+	13.0936i	−1.00354	+	0.476839i
$755$			22.0601i			0.802849i
$756$		0			0
$757$	23.6708			0.860329			0.430165	−	0.902750i	$-0.358456\pi$
$757$	23.6708			0.860329			0.430165	+	0.902750i	$0.358456\pi$
$758$	9.53877			0.346464
$759$		0			0
$760$	−5.31229	−	5.31229i	−0.192697	−	0.192697i
$761$	20.9560	+	20.9560i	0.759656	+	0.759656i	0.976260	−	0.216604i	$-0.0694980\pi$
$761$	20.9560	+	20.9560i	0.759656	+	0.759656i	−0.216604	+	0.976260i	$0.569498\pi$
$762$		0			0
$763$	−3.50468			−0.126878
$764$	−7.86219			−0.284444
$765$		0			0
$766$		−	1.87658i		−	0.0678037i
$767$	20.7032	−	9.83723i	0.747550	−	0.355202i
$768$		0			0
$769$	26.9775	+	26.9775i	0.972835	+	0.972835i	0.999641	−	0.0268055i	$-0.00853346\pi$
$769$	26.9775	+	26.9775i	0.972835	+	0.972835i	−0.0268055	+	0.999641i	$0.508533\pi$
$770$		−	5.01037i		−	0.180561i
$771$		0			0
$772$	−4.85067	−	4.85067i	−0.174579	−	0.174579i
$773$	−22.9037	+	22.9037i	−0.823788	+	0.823788i	−0.986649	−	0.162861i	$-0.947928\pi$
$773$	−22.9037	+	22.9037i	−0.823788	+	0.823788i	0.162861	+	0.986649i	$0.447928\pi$
$774$		0			0
$775$	21.5732	−	21.5732i	0.774931	−	0.774931i
$776$		−	15.6876i		−	0.563152i
$777$		0			0
$778$	18.3247	−	18.3247i	0.656974	−	0.656974i
$779$	−24.0795			−0.862737
$780$		0			0
$781$	66.8866			2.39339
$782$	3.42608	−	3.42608i	0.122516	−	0.122516i
$783$		0			0
$784$			1.00000i			0.0357143i
$785$	−11.3751	+	11.3751i	−0.405995	+	0.405995i
$786$		0			0
$787$	7.47326	−	7.47326i	0.266393	−	0.266393i	−0.561252	−	0.827645i	$-0.689680\pi$
$787$	7.47326	−	7.47326i	0.266393	−	0.266393i	0.827645	+	0.561252i	$0.189680\pi$
$788$	9.34718	+	9.34718i	0.332979	+	0.332979i
$789$		0			0
$790$		−	10.8278i		−	0.385235i
$791$	13.7214	+	13.7214i	0.487875	+	0.487875i
$792$		0			0
$793$	1.88901	−	5.30934i	0.0670807	−	0.188540i
$794$		−	29.8443i		−	1.05913i
$795$		0			0
$796$	−23.0454			−0.816824
$797$	−23.7417			−0.840973			−0.420487	−	0.907299i	$-0.638141\pi$
$797$	−23.7417			−0.840973			−0.420487	+	0.907299i	$0.638141\pi$
$798$		0			0
$799$	7.05445	+	7.05445i	0.249569	+	0.249569i
$800$	2.74839	+	2.74839i	0.0971702	+	0.0971702i
$801$		0			0
$802$	26.7714			0.945332
$803$	26.2032			0.924690
$804$		0			0
$805$		−	2.52326i		−	0.0889332i
$806$	−9.48677	+	26.6640i	−0.334157	+	0.939198i
$807$		0			0
$808$	−3.13732	−	3.13732i	−0.110371	−	0.110371i
$809$		−	28.8848i		−	1.01553i	−0.861494	−	0.507767i	$-0.830471\pi$
$809$		−	28.8848i		−	1.01553i	0.861494	−	0.507767i	$-0.169529\pi$
$810$		0			0
$811$	19.3037	+	19.3037i	0.677845	+	0.677845i	0.959512	−	0.281667i	$-0.0908873\pi$
$811$	19.3037	+	19.3037i	0.677845	+	0.677845i	−0.281667	+	0.959512i	$0.590887\pi$
$812$	5.98330	−	5.98330i	0.209973	−	0.209973i
$813$		0			0
$814$	33.1156	−	33.1156i	1.16070	−	1.16070i
$815$		−	24.2032i		−	0.847800i
$816$		0			0
$817$	46.5437	−	46.5437i	1.62836	−	1.62836i
$818$	14.8422			0.518945
$819$		0			0
$820$	−3.56796			−0.124598
$821$	31.2406	−	31.2406i	1.09030	−	1.09030i	0.0948096	−	0.995495i	$-0.469776\pi$
$821$	31.2406	−	31.2406i	1.09030	−	1.09030i	0.995495	−	0.0948096i	$-0.0302242\pi$
$822$		0			0
$823$			19.6275i			0.684173i	0.939668	+	0.342086i	$0.111134\pi$
$823$			19.6275i			0.684173i	−0.939668	+	0.342086i	$0.888866\pi$
$824$	7.02486	−	7.02486i	0.244723	−	0.244723i
$825$		0			0
$826$	−4.49527	+	4.49527i	−0.156411	+	0.156411i
$827$	−24.2147	−	24.2147i	−0.842026	−	0.842026i	0.147096	−	0.989122i	$-0.453007\pi$
$827$	−24.2147	−	24.2147i	−0.842026	−	0.842026i	−0.989122	+	0.147096i	$0.953007\pi$
$828$		0			0
$829$		−	29.0909i		−	1.01037i	−0.863012	−	0.505184i	$-0.831425\pi$
$829$		−	29.0909i		−	1.01037i	0.863012	−	0.505184i	$-0.168575\pi$
$830$	−10.7893	−	10.7893i	−0.374503	−	0.374503i
$831$		0			0
$832$	−3.39695	−	1.20860i	−0.117768	−	0.0419007i
$833$			2.02598i			0.0701960i
$834$		0			0
$835$	−25.4637			−0.881208
$836$	−33.8140			−1.16948
$837$		0			0
$838$	−16.2308	−	16.2308i	−0.560682	−	0.560682i
$839$	13.2912	+	13.2912i	0.458863	+	0.458863i	0.898282	−	0.439419i	$-0.144816\pi$
$839$	13.2912	+	13.2912i	0.458863	+	0.458863i	−0.439419	+	0.898282i	$0.644816\pi$
$840$		0			0
$841$	−42.5997			−1.46895
$842$	−28.7342			−0.990247
$843$		0			0
$844$			0.931807i			0.0320741i
$845$	13.6451	−	1.39321i	0.469405	−	0.0479280i
$846$		0			0
$847$	−8.16794	−	8.16794i	−0.280654	−	0.280654i
$848$			1.35557i			0.0465505i
$849$		0			0
$850$	5.56818	+	5.56818i	0.190987	+	0.190987i
$851$	16.6773	−	16.6773i	0.571690	−	0.571690i
$852$		0			0
$853$	−15.3079	+	15.3079i	−0.524133	+	0.524133i	−0.918817	−	0.394684i	$-0.870854\pi$
$853$	−15.3079	+	15.3079i	−0.524133	+	0.524133i	0.394684	+	0.918817i	$0.370854\pi$
$854$			1.56297i			0.0534838i
$855$		0			0
$856$	8.50295	−	8.50295i	0.290625	−	0.290625i
$857$	−37.8080			−1.29150			−0.645749	−	0.763550i	$-0.723455\pi$
$857$	−37.8080			−1.29150			−0.645749	+	0.763550i	$0.723455\pi$
$858$		0			0
$859$	22.6413			0.772512			0.386256	−	0.922392i	$-0.373768\pi$
$859$	22.6413			0.772512			0.386256	+	0.922392i	$0.373768\pi$
$860$	6.89658	−	6.89658i	0.235171	−	0.235171i
$861$		0			0
$862$			0.782576i			0.0266547i
$863$	29.0990	−	29.0990i	0.990543	−	0.990543i	−0.00941262	−	0.999956i	$-0.502996\pi$
$863$	29.0990	−	29.0990i	0.990543	−	0.990543i	0.999956	+	0.00941262i	$0.00299617\pi$
$864$		0			0
$865$	6.35793	−	6.35793i	0.216176	−	0.216176i
$866$	0.978804	+	0.978804i	0.0332611	+	0.0332611i
$867$		0			0
$868$		−	7.84938i		−	0.266425i
$869$	−34.4607	−	34.4607i	−1.16900	−	1.16900i
$870$		0			0
$871$	8.23064	−	3.91083i	0.278885	−	0.132513i
$872$			3.50468i			0.118684i
$873$		0			0
$874$	−17.0290			−0.576015
$875$	9.37628			0.316976
$876$		0			0
$877$	−19.6423	−	19.6423i	−0.663273	−	0.663273i	0.292877	−	0.956150i	$-0.405387\pi$
$877$	−19.6423	−	19.6423i	−0.663273	−	0.663273i	−0.956150	+	0.292877i	$0.905387\pi$
$878$	10.1597	+	10.1597i	0.342873	+	0.342873i
$879$		0			0
$880$	−5.01037			−0.168899
$881$	19.3210			0.650942			0.325471	−	0.945552i	$-0.394477\pi$
$881$	19.3210			0.650942			0.325471	+	0.945552i	$0.394477\pi$
$882$		0			0
$883$		−	15.1008i		−	0.508181i	−0.967180	−	0.254090i	$-0.918224\pi$
$883$		−	15.1008i		−	0.508181i	0.967180	−	0.254090i	$-0.0817761\pi$
$884$	−6.88216	−	2.44860i	−0.231472	−	0.0823554i
$885$		0			0
$886$	−5.14226	−	5.14226i	−0.172758	−	0.172758i
$887$			51.8363i			1.74049i	0.492617	+	0.870246i	$0.336040\pi$
$887$			51.8363i			1.74049i	−0.492617	+	0.870246i	$0.663960\pi$
$888$		0			0
$889$	10.3906	+	10.3906i	0.348491	+	0.348491i
$890$	4.65204	−	4.65204i	0.155937	−	0.155937i
$891$		0			0
$892$	−0.806330	+	0.806330i	−0.0269979	+	0.0269979i
$893$		−	35.0635i		−	1.17335i
$894$		0			0
$895$	−2.58178	+	2.58178i	−0.0862993	+	0.0862993i
$896$	1.00000			0.0334077
$897$		0			0
$898$	−15.7262			−0.524789
$899$	−46.9652	+	46.9652i	−1.56638	+	1.56638i
$900$		0			0
$901$			2.74636i			0.0914946i
$902$	−11.3555	+	11.3555i	−0.378096	+	0.378096i
$903$		0			0
$904$	13.7214	−	13.7214i	0.456365	−	0.456365i
$905$	−18.5197	−	18.5197i	−0.615617	−	0.615617i
$906$		0			0
$907$		−	50.0706i		−	1.66257i	−0.555848	−	0.831284i	$-0.687606\pi$
$907$		−	50.0706i		−	1.66257i	0.555848	−	0.831284i	$-0.312394\pi$
$908$	2.04742	+	2.04742i	0.0679459	+	0.0679459i
$909$		0			0
$910$	−3.43599	+	1.63263i	−0.113902	+	0.0541210i
$911$		−	4.50281i		−	0.149185i	−0.997214	−	0.0745924i	$-0.976234\pi$
$911$		−	4.50281i		−	0.149185i	0.997214	−	0.0745924i	$-0.0237656\pi$
$912$		0			0
$913$	−68.6767			−2.27287
$914$	−10.2536			−0.339158
$915$		0			0
$916$	12.3112	+	12.3112i	0.406774	+	0.406774i
$917$	1.57085	+	1.57085i	0.0518742	+	0.0518742i
$918$		0			0
$919$	−18.6075			−0.613806			−0.306903	−	0.951741i	$-0.599293\pi$
$919$	−18.6075			−0.613806			−0.306903	+	0.951741i	$0.599293\pi$
$920$	−2.52326			−0.0831894
$921$		0			0
$922$		−	28.8769i		−	0.951011i
$923$	−21.7950	−	45.8692i	−0.717390	−	1.50980i
$924$		0			0
$925$	27.1045	+	27.1045i	0.891191	+	0.891191i
$926$			7.31096i			0.240253i
$927$		0			0
$928$	−5.98330	−	5.98330i	−0.196411	−	0.196411i
$929$	−31.8475	+	31.8475i	−1.04488	+	1.04488i	−0.0459383	+	0.998944i	$0.514628\pi$
$929$	−31.8475	+	31.8475i	−1.04488	+	1.04488i	−0.998944	+	0.0459383i	$0.985372\pi$
$930$		0			0
$931$	5.03497	−	5.03497i	0.165015	−	0.165015i
$932$			24.7227i			0.809818i
$933$		0			0
$934$	−11.7401	+	11.7401i	−0.384147	+	0.384147i
$935$	−10.1509			−0.331970
$936$		0			0
$937$	20.3250			0.663987			0.331994	−	0.943282i	$-0.392279\pi$
$937$	20.3250			0.663987			0.331994	+	0.943282i	$0.392279\pi$
$938$	−1.78711	+	1.78711i	−0.0583513	+	0.0583513i
$939$		0			0
$940$		−	5.19550i		−	0.169459i
$941$	32.4919	−	32.4919i	1.05921	−	1.05921i	0.0610727	−	0.998133i	$-0.480548\pi$
$941$	32.4919	−	32.4919i	1.05921	−	1.05921i	0.998133	−	0.0610727i	$-0.0194522\pi$
$942$		0			0
$943$	−5.71870	+	5.71870i	−0.186226	+	0.186226i
$944$	4.49527	+	4.49527i	0.146309	+	0.146309i
$945$		0			0
$946$		−	43.8984i		−	1.42726i
$947$	−14.9562	−	14.9562i	−0.486013	−	0.486013i	0.421033	−	0.907045i	$-0.361668\pi$
$947$	−14.9562	−	14.9562i	−0.486013	−	0.486013i	−0.907045	+	0.421033i	$0.861668\pi$
$948$		0			0
$949$	−8.53829	−	17.9695i	−0.277165	−	0.583314i
$950$		−	27.6761i		−	0.897932i
$951$		0			0
$952$	2.02598			0.0656624
$953$	−4.44039			−0.143838			−0.0719192	−	0.997410i	$-0.522912\pi$
$953$	−4.44039			−0.143838			−0.0719192	+	0.997410i	$0.522912\pi$
$954$		0			0
$955$	5.86561	+	5.86561i	0.189807	+	0.189807i
$956$	−1.69453	−	1.69453i	−0.0548050	−	0.0548050i
$957$		0			0
$958$	29.3375			0.947851
$959$	0.547677			0.0176854
$960$		0			0
$961$			30.6128i			0.987509i
$962$	−33.5006	−	11.9192i	−1.08010	−	0.384290i
$963$		0			0
$964$	−4.52253	−	4.52253i	−0.145661	−	0.145661i
$965$			7.23771i			0.232990i
$966$		0			0
$967$	13.2096	+	13.2096i	0.424792	+	0.424792i	0.886850	−	0.462058i	$-0.152889\pi$
$967$	13.2096	+	13.2096i	0.424792	+	0.424792i	−0.462058	+	0.886850i	$0.652889\pi$
$968$	−8.16794	+	8.16794i	−0.262528	+	0.262528i
$969$		0			0
$970$	−11.7038	+	11.7038i	−0.375786	+	0.375786i
$971$			26.3005i			0.844025i	0.906590	+	0.422012i	$0.138676\pi$
$971$			26.3005i			0.844025i	−0.906590	+	0.422012i	$0.861324\pi$
$972$		0			0
$973$	1.98042	−	1.98042i	0.0634895	−	0.0634895i
$974$	7.37615			0.236347
$975$		0			0
$976$	1.56297			0.0500295
$977$	35.2572	−	35.2572i	1.12798	−	1.12798i	0.137470	−	0.990506i	$-0.456103\pi$
$977$	35.2572	−	35.2572i	1.12798	−	1.12798i	0.990506	−	0.137470i	$-0.0438972\pi$
$978$		0			0
$979$		−	29.6114i		−	0.946383i
$980$	0.746053	−	0.746053i	0.0238318	−	0.0238318i
$981$		0			0
$982$	−7.80634	+	7.80634i	−0.249110	+	0.249110i
$983$	20.2759	+	20.2759i	0.646699	+	0.646699i	0.952194	−	0.305494i	$-0.0988218\pi$
$983$	20.2759	+	20.2759i	0.646699	+	0.646699i	−0.305494	+	0.952194i	$0.598822\pi$
$984$		0			0
$985$		−	13.9470i		−	0.444388i
$986$	−12.1220	−	12.1220i	−0.386044	−	0.386044i
$987$		0			0
$988$	11.0183	+	23.1888i	0.350538	+	0.737735i
$989$		−	22.1076i		−	0.702980i
$990$		0			0
$991$	−3.24098			−0.102953			−0.0514765	−	0.998674i	$-0.516393\pi$
$991$	−3.24098			−0.102953			−0.0514765	+	0.998674i	$0.516393\pi$
$992$	−7.84938			−0.249218
$993$		0			0
$994$	9.95954	+	9.95954i	0.315897	+	0.315897i
$995$	17.1931	+	17.1931i	0.545059	+	0.545059i
$996$		0			0
$997$	19.8807			0.629629			0.314814	−	0.949153i	$-0.398058\pi$
$997$	19.8807			0.629629			0.314814	+	0.949153i	$0.398058\pi$
$998$	−5.04723			−0.159767
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.y.d.827.2	yes	16
3.2	odd	2		1638.2.y.c.827.7	✓	16
13.5	odd	4		1638.2.y.c.1331.7	yes	16
39.5	even	4	inner	1638.2.y.d.1331.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.y.c.827.7	✓	16	3.2	odd	2
1638.2.y.c.1331.7	yes	16	13.5	odd	4
1638.2.y.d.827.2	yes	16	1.1	even	1	trivial
1638.2.y.d.1331.2	yes	16	39.5	even	4	inner

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.y (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.746053 + 0.746053i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.746053 + 0.746053i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.05508i q^{10} +(-3.35792 - 3.35792i) q^{11} +(-1.20860 + 3.39695i) q^{13} -1.00000i q^{14} -1.00000 q^{16} -2.02598 q^{17} +(5.03497 + 5.03497i) q^{19} +(0.746053 + 0.746053i) q^{20} +4.74881 q^{22} +2.39154 q^{23} +3.88681i q^{25} +(-1.54740 - 3.25662i) q^{26} +(0.707107 + 0.707107i) q^{28} -8.46166i q^{29} +(-5.55035 - 5.55035i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.43258 - 1.43258i) q^{34} -1.05508i q^{35} +(6.97346 - 6.97346i) q^{37} -7.12053 q^{38} -1.05508 q^{40} +(-2.39122 + 2.39122i) q^{41} -9.24408i q^{43} +(-3.35792 + 3.35792i) q^{44} +(-1.69107 + 1.69107i) q^{46} +(-3.48199 - 3.48199i) q^{47} -1.00000i q^{49} +(-2.74839 - 2.74839i) q^{50} +(3.39695 + 1.20860i) q^{52} -1.35557i q^{53} +5.01037 q^{55} -1.00000 q^{56} +(5.98330 + 5.98330i) q^{58} +(-4.49527 - 4.49527i) q^{59} -1.56297 q^{61} +7.84938 q^{62} +1.00000i q^{64} +(-1.63263 - 3.43599i) q^{65} +(-1.78711 - 1.78711i) q^{67} +2.02598i q^{68} +(0.746053 + 0.746053i) q^{70} +(-9.95954 + 9.95954i) q^{71} +(-3.90170 + 3.90170i) q^{73} +9.86196i q^{74} +(5.03497 - 5.03497i) q^{76} +4.74881 q^{77} +10.2625 q^{79} +(0.746053 - 0.746053i) q^{80} -3.38170i q^{82} +(10.2261 - 10.2261i) q^{83} +(1.51149 - 1.51149i) q^{85} +(6.53655 + 6.53655i) q^{86} -4.74881i q^{88} +(4.40919 + 4.40919i) q^{89} +(-1.54740 - 3.25662i) q^{91} -2.39154i q^{92} +4.92428 q^{94} -7.51271 q^{95} +(-11.0928 - 11.0928i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{5}+O(q^{10}) \) 16 * q + 4 * q^5	\( 16 q + 4 q^{5} - 8 q^{11} + 4 q^{13} - 16 q^{16} - 8 q^{17} + 16 q^{19} - 4 q^{20} - 8 q^{22} + 24 q^{23} + 8 q^{26} - 8 q^{31} + 4 q^{34} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 8 q^{44} + 4 q^{47} - 16 q^{50} - 16 q^{55} - 16 q^{56} + 4 q^{58} - 8 q^{59} - 40 q^{61} + 24 q^{62} + 56 q^{65} - 4 q^{67} - 4 q^{70} - 24 q^{71} - 12 q^{73} + 16 q^{76} - 8 q^{77} + 16 q^{79} - 4 q^{80} + 8 q^{85} + 24 q^{86} + 16 q^{89} + 8 q^{91} - 8 q^{94} - 40 q^{95} - 28 q^{97}+O(q^{100}) \) 16 * q + 4 * q^5 - 8 * q^11 + 4 * q^13 - 16 * q^16 - 8 * q^17 + 16 * q^19 - 4 * q^20 - 8 * q^22 + 24 * q^23 + 8 * q^26 - 8 * q^31 + 4 * q^34 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 8 * q^44 + 4 * q^47 - 16 * q^50 - 16 * q^55 - 16 * q^56 + 4 * q^58 - 8 * q^59 - 40 * q^61 + 24 * q^62 + 56 * q^65 - 4 * q^67 - 4 * q^70 - 24 * q^71 - 12 * q^73 + 16 * q^76 - 8 * q^77 + 16 * q^79 - 4 * q^80 + 8 * q^85 + 24 * q^86 + 16 * q^89 + 8 * q^91 - 8 * q^94 - 40 * q^95 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more