LMFDB - Embedded newform 1638.2.y.c.827.3

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			827.3
Root			$0.743579 - 1.79516i$ of defining polynomial
Character	$\chi$	$=$	1638.827
Dual form			1638.2.y.c.1331.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.162918 - 0.162918i) q^{5} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.162918 - 0.162918i) q^{5} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +0.230401i q^{10} +(4.08255 + 4.08255i) q^{11} +(-2.63937 + 2.45637i) q^{13} +1.00000i q^{14} -1.00000 q^{16} +5.67098 q^{17} +(-0.614788 - 0.614788i) q^{19} +(-0.162918 - 0.162918i) q^{20} -5.77360 q^{22} -3.92055 q^{23} +4.94692i q^{25} +(0.129398 - 3.60323i) q^{26} +(-0.707107 - 0.707107i) q^{28} -6.30144i q^{29} +(-3.79597 - 3.79597i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-4.00999 + 4.00999i) q^{34} -0.230401i q^{35} +(-1.73845 + 1.73845i) q^{37} +0.869442 q^{38} +0.230401 q^{40} +(1.60775 - 1.60775i) q^{41} +1.74723i q^{43} +(4.08255 - 4.08255i) q^{44} +(2.77225 - 2.77225i) q^{46} +(8.71241 + 8.71241i) q^{47} -1.00000i q^{49} +(-3.49800 - 3.49800i) q^{50} +(2.45637 + 2.63937i) q^{52} +9.16630i q^{53} +1.33024 q^{55} +1.00000 q^{56} +(4.45579 + 4.45579i) q^{58} +(4.02637 + 4.02637i) q^{59} -1.44376 q^{61} +5.36831 q^{62} +1.00000i q^{64} +(-0.0298134 + 0.830188i) q^{65} +(1.99258 + 1.99258i) q^{67} -5.67098i q^{68} +(0.162918 + 0.162918i) q^{70} +(-5.82911 + 5.82911i) q^{71} +(0.662193 - 0.662193i) q^{73} -2.45854i q^{74} +(-0.614788 + 0.614788i) q^{76} +5.77360 q^{77} +2.96905 q^{79} +(-0.162918 + 0.162918i) q^{80} +2.27370i q^{82} +(7.73430 - 7.73430i) q^{83} +(0.923907 - 0.923907i) q^{85} +(-1.23548 - 1.23548i) q^{86} +5.77360i q^{88} +(9.62508 + 9.62508i) q^{89} +(-0.129398 + 3.60323i) q^{91} +3.92055i q^{92} -12.3212 q^{94} -0.200320 q^{95} +(5.78171 + 5.78171i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.162918	−	0.162918i	0.0728593	−	0.0728593i	−0.669738	−	0.742597i	$-0.733594\pi$
$5$	0.162918	−	0.162918i	0.0728593	−	0.0728593i	0.742597	+	0.669738i	$0.233594\pi$
$6$		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
$10$			0.230401i			0.0728593i
$11$	4.08255	+	4.08255i	1.23094	+	1.23094i	0.963605	+	0.267330i	$0.0861415\pi$
$11$	4.08255	+	4.08255i	1.23094	+	1.23094i	0.267330	+	0.963605i	$0.413859\pi$
$12$		0			0
$13$	−2.63937	+	2.45637i	−0.732028	+	0.681274i
$13$	−2.63937	+	2.45637i	−0.732028	+	0.681274i
$14$			1.00000i			0.267261i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	5.67098			1.37542			0.687708	−	0.725988i	$-0.258617\pi$
$17$	5.67098			1.37542			0.687708	+	0.725988i	$0.258617\pi$
$18$		0			0
$19$	−0.614788	−	0.614788i	−0.141042	−	0.141042i	0.633060	−	0.774102i	$-0.281798\pi$
$19$	−0.614788	−	0.614788i	−0.141042	−	0.141042i	−0.774102	+	0.633060i	$0.781798\pi$
$20$	−0.162918	−	0.162918i	−0.0364296	−	0.0364296i
$21$		0			0
$22$	−5.77360			−1.23094
$23$	−3.92055			−0.817491			−0.408745	−	0.912649i	$-0.634034\pi$
$23$	−3.92055			−0.817491			−0.408745	+	0.912649i	$0.634034\pi$
$24$		0			0
$25$			4.94692i			0.989383i
$26$	0.129398	−	3.60323i	0.0253770	−	0.706651i
$27$		0			0
$28$	−0.707107	−	0.707107i	−0.133631	−	0.133631i
$29$		−	6.30144i		−	1.17015i	−0.810980	−	0.585074i	$-0.801065\pi$
$29$		−	6.30144i		−	1.17015i	0.810980	−	0.585074i	$-0.198935\pi$
$30$		0			0
$31$	−3.79597	−	3.79597i	−0.681776	−	0.681776i	0.278624	−	0.960400i	$-0.410122\pi$
$31$	−3.79597	−	3.79597i	−0.681776	−	0.681776i	−0.960400	+	0.278624i	$0.910122\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	−4.00999	+	4.00999i	−0.687708	+	0.687708i
$35$		−	0.230401i		−	0.0389449i
$36$		0			0
$37$	−1.73845	+	1.73845i	−0.285800	+	0.285800i	−0.835417	−	0.549617i	$-0.814774\pi$
$37$	−1.73845	+	1.73845i	−0.285800	+	0.285800i	0.549617	+	0.835417i	$0.314774\pi$
$38$	0.869442			0.141042
$39$		0			0
$40$	0.230401			0.0364296
$41$	1.60775	−	1.60775i	0.251088	−	0.251088i	−0.570329	−	0.821417i	$-0.693184\pi$
$41$	1.60775	−	1.60775i	0.251088	−	0.251088i	0.821417	+	0.570329i	$0.193184\pi$
$42$		0			0
$43$			1.74723i			0.266450i	0.991086	+	0.133225i	$0.0425333\pi$
$43$			1.74723i			0.266450i	−0.991086	+	0.133225i	$0.957467\pi$
$44$	4.08255	−	4.08255i	0.615468	−	0.615468i
$45$		0			0
$46$	2.77225	−	2.77225i	0.408745	−	0.408745i
$47$	8.71241	+	8.71241i	1.27084	+	1.27084i	0.945651	+	0.325184i	$0.105426\pi$
$47$	8.71241	+	8.71241i	1.27084	+	1.27084i	0.325184	+	0.945651i	$0.394574\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$	−3.49800	−	3.49800i	−0.494692	−	0.494692i
$51$		0			0
$52$	2.45637	+	2.63937i	0.340637	+	0.366014i
$53$			9.16630i			1.25909i	0.776965	+	0.629544i	$0.216758\pi$
$53$			9.16630i			1.25909i	−0.776965	+	0.629544i	$0.783242\pi$
$54$		0			0
$55$	1.33024			0.179370
$56$	1.00000			0.133631
$57$		0			0
$58$	4.45579	+	4.45579i	0.585074	+	0.585074i
$59$	4.02637	+	4.02637i	0.524189	+	0.524189i	0.918834	−	0.394645i	$-0.129132\pi$
$59$	4.02637	+	4.02637i	0.524189	+	0.524189i	−0.394645	+	0.918834i	$0.629132\pi$
$60$		0			0
$61$	−1.44376			−0.184855			−0.0924274	−	0.995719i	$-0.529463\pi$
$61$	−1.44376			−0.184855			−0.0924274	+	0.995719i	$0.529463\pi$
$62$	5.36831			0.681776
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−0.0298134	+	0.830188i	−0.00369790	+	0.102972i
$66$		0			0
$67$	1.99258	+	1.99258i	0.243432	+	0.243432i	0.818268	−	0.574836i	$-0.194934\pi$
$67$	1.99258	+	1.99258i	0.243432	+	0.243432i	−0.574836	+	0.818268i	$0.694934\pi$
$68$		−	5.67098i		−	0.687708i
$69$		0			0
$70$	0.162918	+	0.162918i	0.0194725	+	0.0194725i
$71$	−5.82911	+	5.82911i	−0.691788	+	0.691788i	−0.962625	−	0.270837i	$-0.912700\pi$
$71$	−5.82911	+	5.82911i	−0.691788	+	0.691788i	0.270837	+	0.962625i	$0.412700\pi$
$72$		0			0
$73$	0.662193	−	0.662193i	0.0775039	−	0.0775039i	−0.667292	−	0.744796i	$-0.732547\pi$
$73$	0.662193	−	0.662193i	0.0775039	−	0.0775039i	0.744796	+	0.667292i	$0.232547\pi$
$74$		−	2.45854i		−	0.285800i
$75$		0			0
$76$	−0.614788	+	0.614788i	−0.0705210	+	0.0705210i
$77$	5.77360			0.657963
$78$		0			0
$79$	2.96905			0.334044			0.167022	−	0.985953i	$-0.446585\pi$
$79$	2.96905			0.334044			0.167022	+	0.985953i	$0.446585\pi$
$80$	−0.162918	+	0.162918i	−0.0182148	+	0.0182148i
$81$		0			0
$82$			2.27370i			0.251088i
$83$	7.73430	−	7.73430i	0.848950	−	0.848950i	−0.141052	−	0.990002i	$-0.545049\pi$
$83$	7.73430	−	7.73430i	0.848950	−	0.848950i	0.990002	+	0.141052i	$0.0450486\pi$
$84$		0			0
$85$	0.923907	−	0.923907i	0.100212	−	0.100212i
$86$	−1.23548	−	1.23548i	−0.133225	−	0.133225i
$87$		0			0
$88$			5.77360i			0.615468i
$89$	9.62508	+	9.62508i	1.02026	+	1.02026i	0.999791	+	0.0204657i	$0.00651489\pi$
$89$	9.62508	+	9.62508i	1.02026	+	1.02026i	0.0204657	+	0.999791i	$0.493485\pi$
$90$		0			0
$91$	−0.129398	+	3.60323i	−0.0135646	+	0.377721i
$92$			3.92055i			0.408745i
$93$		0			0
$94$	−12.3212			−1.27084
$95$	−0.200320			−0.0205524
$96$		0			0
$97$	5.78171	+	5.78171i	0.587043	+	0.587043i	0.936830	−	0.349786i	$-0.113746\pi$
$97$	5.78171	+	5.78171i	0.587043	+	0.587043i	−0.349786	+	0.936830i	$0.613746\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$		0			0
$100$	4.94692			0.494692
$101$	1.43008			0.142299			0.0711493	−	0.997466i	$-0.477333\pi$
$101$	1.43008			0.142299			0.0711493	+	0.997466i	$0.477333\pi$
$102$		0			0
$103$			10.9910i			1.08297i	0.840710	+	0.541486i	$0.182138\pi$
$103$			10.9910i			1.08297i	−0.840710	+	0.541486i	$0.817862\pi$
$104$	−3.60323	−	0.129398i	−0.353326	−	0.0126885i
$105$		0			0
$106$	−6.48155	−	6.48155i	−0.629544	−	0.629544i
$107$		−	8.72927i		−	0.843890i	−0.906621	−	0.421945i	$-0.861347\pi$
$107$		−	8.72927i		−	0.843890i	0.906621	−	0.421945i	$-0.138653\pi$
$108$		0			0
$109$	−5.76482	−	5.76482i	−0.552170	−	0.552170i	0.374897	−	0.927067i	$-0.377678\pi$
$109$	−5.76482	−	5.76482i	−0.552170	−	0.552170i	−0.927067	+	0.374897i	$0.877678\pi$
$110$	−0.940625	+	0.940625i	−0.0896850	+	0.0896850i
$111$		0			0
$112$	−0.707107	+	0.707107i	−0.0668153	+	0.0668153i
$113$			6.65802i			0.626334i	0.949698	+	0.313167i	$0.101390\pi$
$113$			6.65802i			0.626334i	−0.949698	+	0.313167i	$0.898610\pi$
$114$		0			0
$115$	−0.638729	+	0.638729i	−0.0595618	+	0.0595618i
$116$	−6.30144			−0.585074
$117$		0			0
$118$	−5.69414			−0.524189
$119$	4.00999	−	4.00999i	0.367595	−	0.367595i
$120$		0			0
$121$			22.3344i			2.03040i
$122$	1.02089	−	1.02089i	0.0924274	−	0.0924274i
$123$		0			0
$124$	−3.79597	+	3.79597i	−0.340888	+	0.340888i
$125$	1.62053	+	1.62053i	0.144945	+	0.144945i
$126$		0			0
$127$		−	10.4452i		−	0.926860i	−0.886133	−	0.463430i	$-0.846618\pi$
$127$		−	10.4452i		−	0.926860i	0.886133	−	0.463430i	$-0.153382\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−0.565950	−	0.608113i	−0.0496371	−	0.0533350i
$131$			8.30185i			0.725336i	0.931918	+	0.362668i	$0.118134\pi$
$131$			8.30185i			0.725336i	−0.931918	+	0.362668i	$0.881866\pi$
$132$		0			0
$133$	−0.869442			−0.0753901
$134$	−2.81793			−0.243432
$135$		0			0
$136$	4.00999	+	4.00999i	0.343854	+	0.343854i
$137$	3.24150	+	3.24150i	0.276940	+	0.276940i	0.831886	−	0.554946i	$-0.187261\pi$
$137$	3.24150	+	3.24150i	0.276940	+	0.276940i	−0.554946	+	0.831886i	$0.687261\pi$
$138$		0			0
$139$	16.6634			1.41337			0.706687	−	0.707526i	$-0.250189\pi$
$139$	16.6634			1.41337			0.706687	+	0.707526i	$0.250189\pi$
$140$	−0.230401			−0.0194725
$141$		0			0
$142$		−	8.24361i		−	0.691788i
$143$	−20.8036	−	0.747091i	−1.73968	−	0.0624749i
$144$		0			0
$145$	−1.02662	−	1.02662i	−0.0852561	−	0.0852561i
$146$			0.936483i			0.0775039i
$147$		0			0
$148$	1.73845	+	1.73845i	0.142900	+	0.142900i
$149$	0.735226	−	0.735226i	0.0602320	−	0.0602320i	−0.676349	−	0.736581i	$-0.736439\pi$
$149$	0.735226	−	0.735226i	0.0602320	−	0.0602320i	0.736581	+	0.676349i	$0.236439\pi$
$150$		0			0
$151$	−13.8878	+	13.8878i	−1.13017	+	1.13017i	−0.140024	+	0.990148i	$0.544718\pi$
$151$	−13.8878	+	13.8878i	−1.13017	+	1.13017i	−0.990148	+	0.140024i	$0.955282\pi$
$152$		−	0.869442i		−	0.0705210i
$153$		0			0
$154$	−4.08255	+	4.08255i	−0.328981	+	0.328981i
$155$	−1.23686			−0.0993474
$156$		0			0
$157$	−13.6370			−1.08835			−0.544176	−	0.838971i	$-0.683157\pi$
$157$	−13.6370			−1.08835			−0.544176	+	0.838971i	$0.683157\pi$
$158$	−2.09943	+	2.09943i	−0.167022	+	0.167022i
$159$		0			0
$160$		−	0.230401i		−	0.0182148i
$161$	−2.77225	+	2.77225i	−0.218484	+	0.218484i
$162$		0			0
$163$	5.57284	−	5.57284i	0.436499	−	0.436499i	−0.454333	−	0.890832i	$-0.650122\pi$
$163$	5.57284	−	5.57284i	0.436499	−	0.436499i	0.890832	+	0.454333i	$0.150122\pi$
$164$	−1.60775	−	1.60775i	−0.125544	−	0.125544i
$165$		0			0
$166$			10.9380i			0.848950i
$167$	2.62135	+	2.62135i	0.202846	+	0.202846i	0.801218	−	0.598372i	$-0.204186\pi$
$167$	2.62135	+	2.62135i	0.202846	+	0.202846i	−0.598372	+	0.801218i	$0.704186\pi$
$168$		0			0
$169$	0.932499	−	12.9665i	0.0717307	−	0.997424i
$170$			1.30660i			0.100212i
$171$		0			0
$172$	1.74723			0.133225
$173$	−1.62409			−0.123477			−0.0617385	−	0.998092i	$-0.519664\pi$
$173$	−1.62409			−0.123477			−0.0617385	+	0.998092i	$0.519664\pi$
$174$		0			0
$175$	3.49800	+	3.49800i	0.264424	+	0.264424i
$176$	−4.08255	−	4.08255i	−0.307734	−	0.307734i
$177$		0			0
$178$	−13.6119			−1.02026
$179$	−15.7480			−1.17706			−0.588532	−	0.808474i	$-0.700294\pi$
$179$	−15.7480			−1.17706			−0.588532	+	0.808474i	$0.700294\pi$
$180$		0			0
$181$			2.91439i			0.216625i	0.994117	+	0.108312i	$0.0345447\pi$
$181$			2.91439i			0.216625i	−0.994117	+	0.108312i	$0.965455\pi$
$182$	−2.45637	−	2.63937i	−0.182078	−	0.195643i
$183$		0			0
$184$	−2.77225	−	2.77225i	−0.204373	−	0.204373i
$185$			0.566451i			0.0416463i
$186$		0			0
$187$	23.1521	+	23.1521i	1.69305	+	1.69305i
$188$	8.71241	−	8.71241i	0.635418	−	0.635418i
$189$		0			0
$190$	0.141648	−	0.141648i	0.0102762	−	0.0102762i
$191$			12.8576i			0.930343i	0.885221	+	0.465172i	$0.154007\pi$
$191$			12.8576i			0.930343i	−0.885221	+	0.465172i	$0.845993\pi$
$192$		0			0
$193$	17.1851	−	17.1851i	1.23701	−	1.23701i	0.275792	−	0.961217i	$-0.411060\pi$
$193$	17.1851	−	17.1851i	1.23701	−	1.23701i	0.961217	−	0.275792i	$-0.0889401\pi$
$194$	−8.17657			−0.587043
$195$		0			0
$196$	−1.00000			−0.0714286
$197$	7.46747	−	7.46747i	0.532035	−	0.532035i	−0.389143	−	0.921178i	$-0.627229\pi$
$197$	7.46747	−	7.46747i	0.532035	−	0.532035i	0.921178	+	0.389143i	$0.127229\pi$
$198$		0			0
$199$		−	10.3453i		−	0.733357i	−0.930348	−	0.366678i	$-0.880495\pi$
$199$		−	10.3453i		−	0.733357i	0.930348	−	0.366678i	$-0.119505\pi$
$200$	−3.49800	+	3.49800i	−0.247346	+	0.247346i
$201$		0			0
$202$	−1.01122	+	1.01122i	−0.0711493	+	0.0711493i
$203$	−4.45579	−	4.45579i	−0.312735	−	0.312735i
$204$		0			0
$205$		−	0.523863i		−	0.0365882i
$206$	−7.77178	−	7.77178i	−0.541486	−	0.541486i
$207$		0			0
$208$	2.63937	−	2.45637i	0.183007	−	0.170319i
$209$		−	5.01981i		−	0.347227i
$210$		0			0
$211$	−3.26222			−0.224580			−0.112290	−	0.993675i	$-0.535819\pi$
$211$	−3.26222			−0.224580			−0.112290	+	0.993675i	$0.535819\pi$
$212$	9.16630			0.629544
$213$		0			0
$214$	6.17252	+	6.17252i	0.421945	+	0.421945i
$215$	0.284656	+	0.284656i	0.0194134	+	0.0194134i
$216$		0			0
$217$	−5.36831			−0.364425
$218$	8.15269			0.552170
$219$		0			0
$220$		−	1.33024i		−	0.0896850i
$221$	−14.9678	+	13.9300i	−1.00684	+	0.937035i
$222$		0			0
$223$	−10.8917	−	10.8917i	−0.729360	−	0.729360i	0.241133	−	0.970492i	$-0.422481\pi$
$223$	−10.8917	−	10.8917i	−0.729360	−	0.729360i	−0.970492	+	0.241133i	$0.922481\pi$
$224$		−	1.00000i		−	0.0668153i
$225$		0			0
$226$	−4.70793	−	4.70793i	−0.313167	−	0.313167i
$227$	6.39849	−	6.39849i	0.424682	−	0.424682i	−0.462130	−	0.886812i	$-0.652915\pi$
$227$	6.39849	−	6.39849i	0.424682	−	0.424682i	0.886812	+	0.462130i	$0.152915\pi$
$228$		0			0
$229$	16.8871	−	16.8871i	1.11593	−	1.11593i	0.123600	−	0.992332i	$-0.460556\pi$
$229$	16.8871	−	16.8871i	1.11593	−	1.11593i	0.992332	−	0.123600i	$-0.0394440\pi$
$230$		−	0.903299i		−	0.0595618i
$231$		0			0
$232$	4.45579	−	4.45579i	0.292537	−	0.292537i
$233$	28.9998			1.89984			0.949920	−	0.312494i	$-0.101165\pi$
$233$	28.9998			1.89984			0.949920	+	0.312494i	$0.101165\pi$
$234$		0			0
$235$	2.83882			0.185184
$236$	4.02637	−	4.02637i	0.262094	−	0.262094i
$237$		0			0
$238$			5.67098i			0.367595i
$239$	−20.6898	+	20.6898i	−1.33831	+	1.33831i	−0.440617	+	0.897695i	$0.645240\pi$
$239$	−20.6898	+	20.6898i	−1.33831	+	1.33831i	−0.897695	+	0.440617i	$0.854760\pi$
$240$		0			0
$241$	18.8181	−	18.8181i	1.21218	−	1.21218i	0.241871	−	0.970308i	$-0.422239\pi$
$241$	18.8181	−	18.8181i	1.21218	−	1.21218i	0.970308	−	0.241871i	$-0.0777610\pi$
$242$	−15.7928	−	15.7928i	−1.01520	−	1.01520i
$243$		0			0
$244$			1.44376i			0.0924274i
$245$	−0.162918	−	0.162918i	−0.0104085	−	0.0104085i
$246$		0			0
$247$	3.13280	+	0.112504i	0.199335	+	0.00715844i
$248$		−	5.36831i		−	0.340888i
$249$		0			0
$250$	−2.29178			−0.144945
$251$	−3.19220			−0.201490			−0.100745	−	0.994912i	$-0.532123\pi$
$251$	−3.19220			−0.201490			−0.100745	+	0.994912i	$0.532123\pi$
$252$		0			0
$253$	−16.0058	−	16.0058i	−1.00628	−	1.00628i
$254$	7.38586	+	7.38586i	0.463430	+	0.463430i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−16.2982			−1.01665			−0.508326	−	0.861165i	$-0.669736\pi$
$257$	−16.2982			−1.01665			−0.508326	+	0.861165i	$0.669736\pi$
$258$		0			0
$259$			2.45854i			0.152766i
$260$	0.830188	+	0.0298134i	0.0514861	+	0.00184895i
$261$		0			0
$262$	−5.87029	−	5.87029i	−0.362668	−	0.362668i
$263$			30.8839i			1.90439i	0.305497	+	0.952193i	$0.401177\pi$
$263$			30.8839i			1.90439i	−0.305497	+	0.952193i	$0.598823\pi$
$264$		0			0
$265$	1.49336	+	1.49336i	0.0917362	+	0.0917362i
$266$	0.614788	−	0.614788i	0.0376951	−	0.0376951i
$267$		0			0
$268$	1.99258	−	1.99258i	0.121716	−	0.121716i
$269$		−	1.28265i		−	0.0782046i	−0.999235	−	0.0391023i	$-0.987550\pi$
$269$		−	1.28265i		−	0.0782046i	0.999235	−	0.0391023i	$-0.0124498\pi$
$270$		0			0
$271$	−17.9233	+	17.9233i	−1.08877	+	1.08877i	−0.0931095	+	0.995656i	$0.529681\pi$
$271$	−17.9233	+	17.9233i	−1.08877	+	1.08877i	−0.995656	+	0.0931095i	$0.970319\pi$
$272$	−5.67098			−0.343854
$273$		0			0
$274$	−4.58418			−0.276940
$275$	−20.1960	+	20.1960i	−1.21787	+	1.21787i
$276$		0			0
$277$			10.3482i			0.621762i	0.950449	+	0.310881i	$0.100624\pi$
$277$			10.3482i			0.621762i	−0.950449	+	0.310881i	$0.899376\pi$
$278$	−11.7828	+	11.7828i	−0.706687	+	0.706687i
$279$		0			0
$280$	0.162918	−	0.162918i	0.00973623	−	0.00973623i
$281$	−6.19562	−	6.19562i	−0.369600	−	0.369600i	0.497731	−	0.867331i	$-0.334167\pi$
$281$	−6.19562	−	6.19562i	−0.369600	−	0.369600i	−0.867331	+	0.497731i	$0.834167\pi$
$282$		0			0
$283$			10.9087i			0.648454i	0.945979	+	0.324227i	$0.105104\pi$
$283$			10.9087i			0.648454i	−0.945979	+	0.324227i	$0.894896\pi$
$284$	5.82911	+	5.82911i	0.345894	+	0.345894i
$285$		0			0
$286$	15.2386	−	14.1821i	0.901079	−	0.838605i
$287$		−	2.27370i		−	0.134212i
$288$		0			0
$289$	15.1601			0.891768
$290$	1.45186			0.0852561
$291$		0			0
$292$	−0.662193	−	0.662193i	−0.0387519	−	0.0387519i
$293$	−12.8749	−	12.8749i	−0.752160	−	0.752160i	0.222722	−	0.974882i	$-0.428506\pi$
$293$	−12.8749	−	12.8749i	−0.752160	−	0.752160i	−0.974882	+	0.222722i	$0.928506\pi$
$294$		0			0
$295$	1.31194			0.0763840
$296$	−2.45854			−0.142900
$297$		0			0
$298$			1.03977i			0.0602320i
$299$	10.3478	−	9.63031i	0.598426	−	0.556935i
$300$		0			0
$301$	1.23548	+	1.23548i	0.0712118	+	0.0712118i
$302$		−	19.6403i		−	1.13017i
$303$		0			0
$304$	0.614788	+	0.614788i	0.0352605	+	0.0352605i
$305$	−0.235215	+	0.235215i	−0.0134684	+	0.0134684i
$306$		0			0
$307$	−16.2891	+	16.2891i	−0.929671	+	0.929671i	−0.997684	−	0.0680138i	$-0.978334\pi$
$307$	−16.2891	+	16.2891i	−0.929671	+	0.929671i	0.0680138	+	0.997684i	$0.478334\pi$
$308$		−	5.77360i		−	0.328981i
$309$		0			0
$310$	0.874595	−	0.874595i	0.0496737	−	0.0496737i
$311$	4.53135			0.256949			0.128475	−	0.991713i	$-0.458992\pi$
$311$	4.53135			0.256949			0.128475	+	0.991713i	$0.458992\pi$
$312$		0			0
$313$	−13.1287			−0.742081			−0.371040	−	0.928617i	$-0.620999\pi$
$313$	−13.1287			−0.742081			−0.371040	+	0.928617i	$0.620999\pi$
$314$	9.64282	−	9.64282i	0.544176	−	0.544176i
$315$		0			0
$316$		−	2.96905i		−	0.167022i
$317$	12.6336	−	12.6336i	0.709575	−	0.709575i	−0.256871	−	0.966446i	$-0.582691\pi$
$317$	12.6336	−	12.6336i	0.709575	−	0.709575i	0.966446	+	0.256871i	$0.0826914\pi$
$318$		0			0
$319$	25.7260	−	25.7260i	1.44038	−	1.44038i
$320$	0.162918	+	0.162918i	0.00910741	+	0.00910741i
$321$		0			0
$322$		−	3.92055i		−	0.218484i
$323$	−3.48645	−	3.48645i	−0.193991	−	0.193991i
$324$		0			0
$325$	−12.1515	−	13.0567i	−0.674041	−	0.724256i
$326$			7.88119i			0.436499i
$327$		0			0
$328$	2.27370			0.125544
$329$	12.3212			0.679290
$330$		0			0
$331$	3.22572	+	3.22572i	0.177302	+	0.177302i	0.790178	−	0.612877i	$-0.209988\pi$
$331$	3.22572	+	3.22572i	0.177302	+	0.177302i	−0.612877	+	0.790178i	$0.709988\pi$
$332$	−7.73430	−	7.73430i	−0.424475	−	0.424475i
$333$		0			0
$334$	−3.70715			−0.202846
$335$	0.649254			0.0354725
$336$		0			0
$337$		−	18.5406i		−	1.00997i	−0.863129	−	0.504984i	$-0.831498\pi$
$337$		−	18.5406i		−	1.00997i	0.863129	−	0.504984i	$-0.168502\pi$
$338$	8.50933	+	9.82809i	0.462847	+	0.534577i
$339$		0			0
$340$	−0.923907	−	0.923907i	−0.0501059	−	0.0501059i
$341$		−	30.9945i		−	1.67844i
$342$		0			0
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−1.23548	+	1.23548i	−0.0666125	+	0.0666125i
$345$		0			0
$346$	1.14840	−	1.14840i	0.0617385	−	0.0617385i
$347$		−	20.3037i		−	1.08996i	−0.838448	−	0.544981i	$-0.816537\pi$
$347$		−	20.3037i		−	1.08996i	0.838448	−	0.544981i	$-0.183463\pi$
$348$		0			0
$349$	10.5695	−	10.5695i	0.565772	−	0.565772i	−0.365169	−	0.930941i	$-0.618989\pi$
$349$	10.5695	−	10.5695i	0.565772	−	0.565772i	0.930941	+	0.365169i	$0.118989\pi$
$350$	−4.94692			−0.264424
$351$		0			0
$352$	5.77360			0.307734
$353$	−0.737031	+	0.737031i	−0.0392282	+	0.0392282i	−0.726449	−	0.687221i	$-0.758831\pi$
$353$	−0.737031	+	0.737031i	−0.0392282	+	0.0392282i	0.687221	+	0.726449i	$0.258831\pi$
$354$		0			0
$355$			1.89934i			0.100806i
$356$	9.62508	−	9.62508i	0.510128	−	0.510128i
$357$		0			0
$358$	11.1355	−	11.1355i	0.588532	−	0.588532i
$359$	−20.6265	−	20.6265i	−1.08863	−	1.08863i	−0.995670	−	0.0929548i	$-0.970369\pi$
$359$	−20.6265	−	20.6265i	−1.08863	−	1.08863i	−0.0929548	−	0.995670i	$-0.529631\pi$
$360$		0			0
$361$		−	18.2441i		−	0.960214i
$362$	−2.06078	−	2.06078i	−0.108312	−	0.108312i
$363$		0			0
$364$	3.60323	+	0.129398i	0.188860	+	0.00678229i
$365$		−	0.215767i		−	0.0112937i
$366$		0			0
$367$	12.3551			0.644929			0.322464	−	0.946582i	$-0.395489\pi$
$367$	12.3551			0.644929			0.322464	+	0.946582i	$0.395489\pi$
$368$	3.92055			0.204373
$369$		0			0
$370$	−0.400542	−	0.400542i	−0.0208232	−	0.0208232i
$371$	6.48155	+	6.48155i	0.336506	+	0.336506i
$372$		0			0
$373$	9.82127			0.508526			0.254263	−	0.967135i	$-0.418167\pi$
$373$	9.82127			0.508526			0.254263	+	0.967135i	$0.418167\pi$
$374$	−32.7420			−1.69305
$375$		0			0
$376$			12.3212i			0.635418i
$377$	15.4787	+	16.6318i	0.797192	+	0.856582i
$378$		0			0
$379$	−21.0592	−	21.0592i	−1.08174	−	1.08174i	−0.996348	−	0.0853908i	$-0.972786\pi$
$379$	−21.0592	−	21.0592i	−1.08174	−	1.08174i	−0.0853908	−	0.996348i	$-0.527214\pi$
$380$			0.200320i			0.0102762i
$381$		0			0
$382$	−9.09169	−	9.09169i	−0.465172	−	0.465172i
$383$	15.1870	−	15.1870i	0.776017	−	0.776017i	−0.203134	−	0.979151i	$-0.565113\pi$
$383$	15.1870	−	15.1870i	0.776017	−	0.776017i	0.979151	+	0.203134i	$0.0651126\pi$
$384$		0			0
$385$	0.940625	−	0.940625i	0.0479387	−	0.0479387i
$386$			24.3034i			1.23701i
$387$		0			0
$388$	5.78171	−	5.78171i	0.293522	−	0.293522i
$389$	18.7919			0.952786			0.476393	−	0.879232i	$-0.341944\pi$
$389$	18.7919			0.952786			0.476393	+	0.879232i	$0.341944\pi$
$390$		0			0
$391$	−22.2334			−1.12439
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$		0			0
$394$			10.5606i			0.532035i
$395$	0.483712	−	0.483712i	0.0243382	−	0.0243382i
$396$		0			0
$397$	26.4052	−	26.4052i	1.32524	−	1.32524i	0.415769	−	0.909470i	$-0.363512\pi$
$397$	26.4052	−	26.4052i	1.32524	−	1.32524i	0.909470	−	0.415769i	$-0.136488\pi$
$398$	7.31521	+	7.31521i	0.366678	+	0.366678i
$399$		0			0
$400$		−	4.94692i		−	0.247346i
$401$	−21.4650	−	21.4650i	−1.07191	−	1.07191i	−0.997206	−	0.0747068i	$-0.976198\pi$
$401$	−21.4650	−	21.4650i	−1.07191	−	1.07191i	−0.0747068	−	0.997206i	$-0.523802\pi$
$402$		0			0
$403$	19.3432	+	0.694647i	0.963556	+	0.0346028i
$404$		−	1.43008i		−	0.0711493i
$405$		0			0
$406$	6.30144			0.312735
$407$	−14.1946			−0.703602
$408$		0			0
$409$	−15.3763	−	15.3763i	−0.760307	−	0.760307i	0.216071	−	0.976378i	$-0.430676\pi$
$409$	−15.3763	−	15.3763i	−0.760307	−	0.760307i	−0.976378	+	0.216071i	$0.930676\pi$
$410$	0.370427	+	0.370427i	0.0182941	+	0.0182941i
$411$		0			0
$412$	10.9910			0.541486
$413$	5.69414			0.280191
$414$		0			0
$415$		−	2.52012i		−	0.123708i
$416$	−0.129398	+	3.60323i	−0.00634425	+	0.176663i
$417$		0			0
$418$	3.54954	+	3.54954i	0.173614	+	0.173614i
$419$		−	27.3101i		−	1.33419i	−0.744974	−	0.667093i	$-0.767538\pi$
$419$		−	27.3101i		−	1.33419i	0.744974	−	0.667093i	$-0.232462\pi$
$420$		0			0
$421$	−19.7493	−	19.7493i	−0.962520	−	0.962520i	0.0368023	−	0.999323i	$-0.488283\pi$
$421$	−19.7493	−	19.7493i	−0.962520	−	0.962520i	−0.999323	+	0.0368023i	$0.988283\pi$
$422$	2.30674	−	2.30674i	0.112290	−	0.112290i
$423$		0			0
$424$	−6.48155	+	6.48155i	−0.314772	+	0.314772i
$425$			28.0539i			1.36081i
$426$		0			0
$427$	−1.02089	+	1.02089i	−0.0494045	+	0.0494045i
$428$	−8.72927			−0.421945
$429$		0			0
$430$	−0.402564			−0.0194134
$431$	−7.26876	+	7.26876i	−0.350124	+	0.350124i	−0.860156	−	0.510032i	$-0.829634\pi$
$431$	−7.26876	+	7.26876i	−0.350124	+	0.350124i	0.510032	+	0.860156i	$0.329634\pi$
$432$		0			0
$433$			13.5738i			0.652314i	0.945316	+	0.326157i	$0.105754\pi$
$433$			13.5738i			0.652314i	−0.945316	+	0.326157i	$0.894246\pi$
$434$	3.79597	−	3.79597i	0.182212	−	0.182212i
$435$		0			0
$436$	−5.76482	+	5.76482i	−0.276085	+	0.276085i
$437$	2.41031	+	2.41031i	0.115301	+	0.115301i
$438$		0			0
$439$			30.8182i			1.47087i	0.677594	+	0.735436i	$0.263023\pi$
$439$			30.8182i			1.47087i	−0.677594	+	0.735436i	$0.736977\pi$
$440$	0.940625	+	0.940625i	0.0448425	+	0.0448425i
$441$		0			0
$442$	0.733812	−	20.4338i	0.0349039	−	0.971939i
$443$			10.0491i			0.477448i	0.971087	+	0.238724i	$0.0767291\pi$
$443$			10.0491i			0.477448i	−0.971087	+	0.238724i	$0.923271\pi$
$444$		0			0
$445$	3.13620			0.148670
$446$	15.4031			0.729360
$447$		0			0
$448$	0.707107	+	0.707107i	0.0334077	+	0.0334077i
$449$	−14.2791	−	14.2791i	−0.673874	−	0.673874i	0.284733	−	0.958607i	$-0.408095\pi$
$449$	−14.2791	−	14.2791i	−0.673874	−	0.673874i	−0.958607	+	0.284733i	$0.908095\pi$
$450$		0			0
$451$	13.1274			0.618146
$452$	6.65802			0.313167
$453$		0			0
$454$			9.04883i			0.424682i
$455$	0.565950	+	0.608113i	0.0265322	+	0.0285088i
$456$		0			0
$457$	20.8985	+	20.8985i	0.977588	+	0.977588i	0.999754	−	0.0221658i	$-0.00705618\pi$
$457$	20.8985	+	20.8985i	0.977588	+	0.977588i	−0.0221658	+	0.999754i	$0.507056\pi$
$458$			23.8820i			1.11593i
$459$		0			0
$460$	0.638729	+	0.638729i	0.0297809	+	0.0297809i
$461$	26.0725	−	26.0725i	1.21432	−	1.21432i	0.244723	−	0.969593i	$-0.421303\pi$
$461$	26.0725	−	26.0725i	1.21432	−	1.21432i	0.969593	−	0.244723i	$-0.0786971\pi$
$462$		0			0
$463$	18.8204	−	18.8204i	0.874660	−	0.874660i	−0.118316	−	0.992976i	$-0.537750\pi$
$463$	18.8204	−	18.8204i	0.874660	−	0.874660i	0.992976	+	0.118316i	$0.0377495\pi$
$464$			6.30144i			0.292537i
$465$		0			0
$466$	−20.5059	+	20.5059i	−0.949920	+	0.949920i
$467$	−1.70225			−0.0787708			−0.0393854	−	0.999224i	$-0.512540\pi$
$467$	−1.70225			−0.0787708			−0.0393854	+	0.999224i	$0.512540\pi$
$468$		0			0
$469$	2.81793			0.130120
$470$	−2.00735	+	2.00735i	−0.0925921	+	0.0925921i
$471$		0			0
$472$			5.69414i			0.262094i
$473$	−7.13315	+	7.13315i	−0.327983	+	0.327983i
$474$		0			0
$475$	3.04130	−	3.04130i	0.139545	−	0.139545i
$476$	−4.00999	−	4.00999i	−0.183798	−	0.183798i
$477$		0			0
$478$		−	29.2598i		−	1.33831i
$479$	17.8661	+	17.8661i	0.816321	+	0.816321i	0.985573	−	0.169252i	$-0.0541351\pi$
$479$	17.8661	+	17.8661i	0.816321	+	0.816321i	−0.169252	+	0.985573i	$0.554135\pi$
$480$		0			0
$481$	0.318130	−	8.85869i	0.0145055	−	0.403922i
$482$			26.6128i			1.21218i
$483$		0			0
$484$	22.3344			1.01520
$485$	1.88389			0.0855431
$486$		0			0
$487$	9.93432	+	9.93432i	0.450167	+	0.450167i	0.895410	−	0.445243i	$-0.146883\pi$
$487$	9.93432	+	9.93432i	0.450167	+	0.450167i	−0.445243	+	0.895410i	$0.646883\pi$
$488$	−1.02089	−	1.02089i	−0.0462137	−	0.0462137i
$489$		0			0
$490$	0.230401			0.0104085
$491$	−44.1094			−1.99063			−0.995315	−	0.0966839i	$-0.969176\pi$
$491$	−44.1094			−1.99063			−0.995315	+	0.0966839i	$0.969176\pi$
$492$		0			0
$493$		−	35.7354i		−	1.60944i
$494$	−2.29477	+	2.13567i	−0.103247	+	0.0960883i
$495$		0			0
$496$	3.79597	+	3.79597i	0.170444	+	0.170444i
$497$			8.24361i			0.369776i
$498$		0			0
$499$	−15.3738	−	15.3738i	−0.688225	−	0.688225i	0.273615	−	0.961839i	$-0.411781\pi$
$499$	−15.3738	−	15.3738i	−0.688225	−	0.688225i	−0.961839	+	0.273615i	$0.911781\pi$
$500$	1.62053	−	1.62053i	0.0724725	−	0.0724725i
$501$		0			0
$502$	2.25723	−	2.25723i	0.100745	−	0.100745i
$503$		−	5.26611i		−	0.234804i	−0.993084	−	0.117402i	$-0.962543\pi$
$503$		−	5.26611i		−	0.234804i	0.993084	−	0.117402i	$-0.0374566\pi$
$504$		0			0
$505$	0.232987	−	0.232987i	0.0103678	−	0.0103678i
$506$	22.6357			1.00628
$507$		0			0
$508$	−10.4452			−0.463430
$509$	28.6945	−	28.6945i	1.27186	−	1.27186i	0.326751	−	0.945110i	$-0.394046\pi$
$509$	28.6945	−	28.6945i	1.27186	−	1.27186i	0.945110	−	0.326751i	$-0.105954\pi$
$510$		0			0
$511$		−	0.936483i		−	0.0414276i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	11.5246	−	11.5246i	0.508326	−	0.508326i
$515$	1.79063	+	1.79063i	0.0789045	+	0.0789045i
$516$		0			0
$517$			71.1377i			3.12863i
$518$	−1.73845	−	1.73845i	−0.0763832	−	0.0763832i
$519$		0			0
$520$	−0.608113	+	0.565950i	−0.0266675	+	0.0248186i
$521$			6.39907i			0.280348i	0.990127	+	0.140174i	$0.0447662\pi$
$521$			6.39907i			0.280348i	−0.990127	+	0.140174i	$0.955234\pi$
$522$		0			0
$523$	21.6045			0.944700			0.472350	−	0.881411i	$-0.343406\pi$
$523$	21.6045			0.944700			0.472350	+	0.881411i	$0.343406\pi$
$524$	8.30185			0.362668
$525$		0			0
$526$	−21.8382	−	21.8382i	−0.952193	−	0.952193i
$527$	−21.5269	−	21.5269i	−0.937725	−	0.937725i
$528$		0			0
$529$	−7.62931			−0.331709
$530$	−2.11193			−0.0917362
$531$		0			0
$532$			0.869442i			0.0376951i
$533$	−0.294211	+	8.19265i	−0.0127437	+	0.354863i
$534$		0			0
$535$	−1.42216	−	1.42216i	−0.0614852	−	0.0614852i
$536$			2.81793i			0.121716i
$537$		0			0
$538$	0.906971	+	0.906971i	0.0391023	+	0.0391023i
$539$	4.08255	−	4.08255i	0.175848	−	0.175848i
$540$		0			0
$541$	−24.9816	+	24.9816i	−1.07404	+	1.07404i	−0.0770131	+	0.997030i	$0.524538\pi$
$541$	−24.9816	+	24.9816i	−1.07404	+	1.07404i	−0.997030	+	0.0770131i	$0.975462\pi$
$542$		−	25.3474i		−	1.08877i
$543$		0			0
$544$	4.00999	−	4.00999i	0.171927	−	0.171927i
$545$	−1.87839			−0.0804614
$546$		0			0
$547$	−29.4595			−1.25960			−0.629798	−	0.776759i	$-0.716862\pi$
$547$	−29.4595			−1.25960			−0.629798	+	0.776759i	$0.716862\pi$
$548$	3.24150	−	3.24150i	0.138470	−	0.138470i
$549$		0			0
$550$		−	28.5615i		−	1.21787i
$551$	−3.87405	+	3.87405i	−0.165040	+	0.165040i
$552$		0			0
$553$	2.09943	−	2.09943i	0.0892770	−	0.0892770i
$554$	−7.31727	−	7.31727i	−0.310881	−	0.310881i
$555$		0			0
$556$		−	16.6634i		−	0.706687i
$557$	−26.4935	−	26.4935i	−1.12257	−	1.12257i	−0.991354	−	0.131212i	$-0.958113\pi$
$557$	−26.4935	−	26.4935i	−1.12257	−	1.12257i	−0.131212	−	0.991354i	$-0.541887\pi$
$558$		0			0
$559$	−4.29184	−	4.61158i	−0.181526	−	0.195049i
$560$			0.230401i			0.00973623i
$561$		0			0
$562$	8.76193			0.369600
$563$	17.3153			0.729751			0.364875	−	0.931056i	$-0.381112\pi$
$563$	17.3153			0.729751			0.364875	+	0.931056i	$0.381112\pi$
$564$		0			0
$565$	1.08471	+	1.08471i	0.0456342	+	0.0456342i
$566$	−7.71360	−	7.71360i	−0.324227	−	0.324227i
$567$		0			0
$568$	−8.24361			−0.345894
$569$	0.495097			0.0207556			0.0103778	−	0.999946i	$-0.496697\pi$
$569$	0.495097			0.0207556			0.0103778	+	0.999946i	$0.496697\pi$
$570$		0			0
$571$		−	28.2719i		−	1.18314i	−0.806253	−	0.591571i	$-0.798508\pi$
$571$		−	28.2719i		−	1.18314i	0.806253	−	0.591571i	$-0.201492\pi$
$572$	−0.747091	+	20.8036i	−0.0312374	+	0.869842i
$573$		0			0
$574$	1.60775	+	1.60775i	0.0671061	+	0.0671061i
$575$		−	19.3946i		−	0.808811i
$576$		0			0
$577$	−29.9186	−	29.9186i	−1.24553	−	1.24553i	−0.957675	−	0.287852i	$-0.907059\pi$
$577$	−29.9186	−	29.9186i	−1.24553	−	1.24553i	−0.287852	−	0.957675i	$-0.592941\pi$
$578$	−10.7198	+	10.7198i	−0.445884	+	0.445884i
$579$		0			0
$580$	−1.02662	+	1.02662i	−0.0426281	+	0.0426281i
$581$		−	10.9380i		−	0.453783i
$582$		0			0
$583$	−37.4219	+	37.4219i	−1.54986	+	1.54986i
$584$	0.936483			0.0387519
$585$		0			0
$586$	18.2079			0.752160
$587$	−14.1632	+	14.1632i	−0.584577	+	0.584577i	−0.936157	−	0.351581i	$-0.885644\pi$
$587$	−14.1632	+	14.1632i	−0.584577	+	0.584577i	0.351581	+	0.936157i	$0.385644\pi$
$588$		0			0
$589$			4.66743i			0.192318i
$590$	−0.927680	+	0.927680i	−0.0381920	+	0.0381920i
$591$		0			0
$592$	1.73845	−	1.73845i	0.0714500	−	0.0714500i
$593$	31.4482	+	31.4482i	1.29142	+	1.29142i	0.933907	+	0.357515i	$0.116376\pi$
$593$	31.4482	+	31.4482i	1.29142	+	1.29142i	0.357515	+	0.933907i	$0.383624\pi$
$594$		0			0
$595$		−	1.30660i		−	0.0535654i
$596$	−0.735226	−	0.735226i	−0.0301160	−	0.0301160i
$597$		0			0
$598$	−0.507310	+	14.1266i	−0.0207454	+	0.577681i
$599$		−	4.82442i		−	0.197120i	−0.995131	−	0.0985602i	$-0.968576\pi$
$599$		−	4.82442i		−	0.197120i	0.995131	−	0.0985602i	$-0.0314237\pi$
$600$		0			0
$601$	−33.6504			−1.37263			−0.686313	−	0.727306i	$-0.740772\pi$
$601$	−33.6504			−1.37263			−0.686313	+	0.727306i	$0.740772\pi$
$602$	−1.74723			−0.0712118
$603$		0			0
$604$	13.8878	+	13.8878i	0.565086	+	0.565086i
$605$	3.63869	+	3.63869i	0.147934	+	0.147934i
$606$		0			0
$607$	32.0700			1.30168			0.650841	−	0.759214i	$-0.274417\pi$
$607$	32.0700			1.30168			0.650841	+	0.759214i	$0.274417\pi$
$608$	−0.869442			−0.0352605
$609$		0			0
$610$		−	0.332645i		−	0.0134684i
$611$	−44.3961	−	1.59434i	−1.79607	−	0.0644999i
$612$		0			0
$613$	−5.65697	−	5.65697i	−0.228483	−	0.228483i	0.583576	−	0.812059i	$-0.301653\pi$
$613$	−5.65697	−	5.65697i	−0.228483	−	0.228483i	−0.812059	+	0.583576i	$0.801653\pi$
$614$		−	23.0363i		−	0.929671i
$615$		0			0
$616$	4.08255	+	4.08255i	0.164491	+	0.164491i
$617$	18.9706	−	18.9706i	0.763728	−	0.763728i	−0.213266	−	0.976994i	$-0.568410\pi$
$617$	18.9706	−	18.9706i	0.763728	−	0.763728i	0.976994	+	0.213266i	$0.0684100\pi$
$618$		0			0
$619$	2.98592	−	2.98592i	0.120014	−	0.120014i	−0.644549	−	0.764563i	$-0.722955\pi$
$619$	2.98592	−	2.98592i	0.120014	−	0.120014i	0.764563	+	0.644549i	$0.222955\pi$
$620$			1.23686i			0.0496737i
$621$		0			0
$622$	−3.20415	+	3.20415i	−0.128475	+	0.128475i
$623$	13.6119			0.545350
$624$		0			0
$625$	−24.2065			−0.968262
$626$	9.28342	−	9.28342i	0.371040	−	0.371040i
$627$		0			0
$628$			13.6370i			0.544176i
$629$	−9.85874	+	9.85874i	−0.393094	+	0.393094i
$630$		0			0
$631$	7.67190	−	7.67190i	0.305413	−	0.305413i	−0.537714	−	0.843127i	$-0.680712\pi$
$631$	7.67190	−	7.67190i	0.305413	−	0.305413i	0.843127	+	0.537714i	$0.180712\pi$
$632$	2.09943	+	2.09943i	0.0835110	+	0.0835110i
$633$		0			0
$634$			17.8666i			0.709575i
$635$	−1.70171	−	1.70171i	−0.0675304	−	0.0675304i
$636$		0			0
$637$	2.45637	+	2.63937i	0.0973249	+	0.104575i
$638$			36.3820i			1.44038i
$639$		0			0
$640$	−0.230401			−0.00910741
$641$	31.4231			1.24114			0.620570	−	0.784151i	$-0.286901\pi$
$641$	31.4231			1.24114			0.620570	+	0.784151i	$0.286901\pi$
$642$		0			0
$643$	18.6582	+	18.6582i	0.735808	+	0.735808i	0.971764	−	0.235956i	$-0.0758220\pi$
$643$	18.6582	+	18.6582i	0.735808	+	0.735808i	−0.235956	+	0.971764i	$0.575822\pi$
$644$	2.77225	+	2.77225i	0.109242	+	0.109242i
$645$		0			0
$646$	4.93059			0.193991
$647$	−22.8331			−0.897663			−0.448831	−	0.893616i	$-0.648160\pi$
$647$	−22.8331			−0.897663			−0.448831	+	0.893616i	$0.648160\pi$
$648$		0			0
$649$			32.8757i			1.29048i
$650$	17.8249	+	0.640120i	0.699149	+	0.0251076i
$651$		0			0
$652$	−5.57284	−	5.57284i	−0.218249	−	0.218249i
$653$			7.22188i			0.282614i	0.989966	+	0.141307i	$0.0451305\pi$
$653$			7.22188i			0.282614i	−0.989966	+	0.141307i	$0.954870\pi$
$654$		0			0
$655$	1.35252	+	1.35252i	0.0528474	+	0.0528474i
$656$	−1.60775	+	1.60775i	−0.0627720	+	0.0627720i
$657$		0			0
$658$	−8.71241	+	8.71241i	−0.339645	+	0.339645i
$659$			28.9240i			1.12672i	0.826212	+	0.563360i	$0.190492\pi$
$659$			28.9240i			1.12672i	−0.826212	+	0.563360i	$0.809508\pi$
$660$		0			0
$661$	−5.67813	+	5.67813i	−0.220854	+	0.220854i	−0.808858	−	0.588004i	$-0.799914\pi$
$661$	−5.67813	+	5.67813i	−0.220854	+	0.220854i	0.588004	+	0.808858i	$0.299914\pi$
$662$	−4.56186			−0.177302
$663$		0			0
$664$	10.9380			0.424475
$665$	−0.141648	+	0.141648i	−0.00549287	+	0.00549287i
$666$		0			0
$667$			24.7051i			0.956585i
$668$	2.62135	−	2.62135i	0.101423	−	0.101423i
$669$		0			0
$670$	−0.459092	+	0.459092i	−0.0177363	+	0.0177363i
$671$	−5.89423	−	5.89423i	−0.227544	−	0.227544i
$672$		0			0
$673$		−	5.95763i		−	0.229650i	−0.993386	−	0.114825i	$-0.963369\pi$
$673$		−	5.95763i		−	0.229650i	0.993386	−	0.114825i	$-0.0366307\pi$
$674$	13.1101	+	13.1101i	0.504984	+	0.504984i
$675$		0			0
$676$	−12.9665	−	0.932499i	−0.498712	−	0.0358654i
$677$			22.9056i			0.880333i	0.897916	+	0.440167i	$0.145081\pi$
$677$			22.9056i			0.880333i	−0.897916	+	0.440167i	$0.854919\pi$
$678$		0			0
$679$	8.17657			0.313788
$680$	1.30660			0.0501059
$681$		0			0
$682$	21.9164	+	21.9164i	0.839222	+	0.839222i
$683$	−5.19462	−	5.19462i	−0.198767	−	0.198767i	0.600705	−	0.799471i	$-0.294887\pi$
$683$	−5.19462	−	5.19462i	−0.198767	−	0.198767i	−0.799471	+	0.600705i	$0.794887\pi$
$684$		0			0
$685$	1.05620			0.0403553
$686$	1.00000			0.0381802
$687$		0			0
$688$		−	1.74723i		−	0.0666125i
$689$	−22.5158	−	24.1932i	−0.857785	−	0.921688i
$690$		0			0
$691$	−35.4663	−	35.4663i	−1.34920	−	1.34920i	−0.886529	−	0.462673i	$-0.846890\pi$
$691$	−35.4663	−	35.4663i	−1.34920	−	1.34920i	−0.462673	−	0.886529i	$-0.653110\pi$
$692$			1.62409i			0.0617385i
$693$		0			0
$694$	14.3569	+	14.3569i	0.544981	+	0.544981i
$695$	2.71478	−	2.71478i	0.102977	−	0.102977i
$696$		0			0
$697$	9.11751	−	9.11751i	0.345350	−	0.345350i
$698$			14.9475i			0.565772i
$699$		0			0
$700$	3.49800	−	3.49800i	0.132212	−	0.132212i
$701$	−7.05109			−0.266316			−0.133158	−	0.991095i	$-0.542512\pi$
$701$	−7.05109			−0.266316			−0.133158	+	0.991095i	$0.542512\pi$
$702$		0			0
$703$	2.13756			0.0806196
$704$	−4.08255	+	4.08255i	−0.153867	+	0.153867i
$705$		0			0
$706$		−	1.04232i		−	0.0392282i
$707$	1.01122	−	1.01122i	0.0380309	−	0.0380309i
$708$		0			0
$709$	−22.1606	+	22.1606i	−0.832260	+	0.832260i	−0.987826	−	0.155565i	$-0.950280\pi$
$709$	−22.1606	+	22.1606i	−0.832260	+	0.832260i	0.155565	+	0.987826i	$0.450280\pi$
$710$	−1.34303	−	1.34303i	−0.0504032	−	0.0504032i
$711$		0			0
$712$			13.6119i			0.510128i
$713$	14.8823	+	14.8823i	0.557345	+	0.557345i
$714$		0			0
$715$	−3.51100	+	3.26757i	−0.131304	+	0.122200i
$716$			15.7480i			0.588532i
$717$		0			0
$718$	29.1703			1.08863
$719$	9.76571			0.364199			0.182100	−	0.983280i	$-0.441711\pi$
$719$	9.76571			0.364199			0.182100	+	0.983280i	$0.441711\pi$
$720$		0			0
$721$	7.77178	+	7.77178i	0.289436	+	0.289436i
$722$	12.9005	+	12.9005i	0.480107	+	0.480107i
$723$		0			0
$724$	2.91439			0.108312
$725$	31.1727			1.15772
$726$		0			0
$727$			14.9625i			0.554929i	0.960736	+	0.277464i	$0.0894941\pi$
$727$			14.9625i			0.554929i	−0.960736	+	0.277464i	$0.910506\pi$
$728$	−2.63937	+	2.45637i	−0.0978214	+	0.0910391i
$729$		0			0
$730$	0.152570	+	0.152570i	0.00564687	+	0.00564687i
$731$			9.90851i			0.366479i
$732$		0			0
$733$	15.1963	+	15.1963i	0.561290	+	0.561290i	0.929674	−	0.368384i	$-0.120089\pi$
$733$	15.1963	+	15.1963i	0.561290	+	0.561290i	−0.368384	+	0.929674i	$0.620089\pi$
$734$	−8.73635	+	8.73635i	−0.322464	+	0.322464i
$735$		0			0
$736$	−2.77225	+	2.77225i	−0.102186	+	0.102186i
$737$			16.2696i			0.599298i
$738$		0			0
$739$	1.90889	−	1.90889i	0.0702197	−	0.0702197i	−0.671125	−	0.741344i	$-0.734189\pi$
$739$	1.90889	−	1.90889i	0.0702197	−	0.0702197i	0.741344	+	0.671125i	$0.234189\pi$
$740$	0.566451			0.0208232
$741$		0			0
$742$	−9.16630			−0.336506
$743$	−25.8983	+	25.8983i	−0.950118	+	0.950118i	−0.998814	−	0.0486957i	$-0.984494\pi$
$743$	−25.8983	+	25.8983i	−0.950118	+	0.950118i	0.0486957	+	0.998814i	$0.484494\pi$
$744$		0			0
$745$		−	0.239563i		−	0.00877692i
$746$	−6.94469	+	6.94469i	−0.254263	+	0.254263i
$747$		0			0
$748$	23.1521	−	23.1521i	0.846524	−	0.846524i
$749$	−6.17252	−	6.17252i	−0.225539	−	0.225539i
$750$		0			0
$751$			24.0441i			0.877382i	0.898638	+	0.438691i	$0.144558\pi$
$751$			24.0441i			0.877382i	−0.898638	+	0.438691i	$0.855442\pi$
$752$	−8.71241	−	8.71241i	−0.317709	−	0.317709i
$753$		0			0
$754$	−22.7055	−	0.815392i	−0.826887	−	0.0296948i
$755$			4.52515i			0.164687i
$756$		0			0
$757$	−50.7047			−1.84289			−0.921446	−	0.388505i	$-0.872991\pi$
$757$	−50.7047			−1.84289			−0.921446	+	0.388505i	$0.872991\pi$
$758$	29.7822			1.08174
$759$		0			0
$760$	−0.141648	−	0.141648i	−0.00513811	−	0.00513811i
$761$	5.46292	+	5.46292i	0.198031	+	0.198031i	0.799155	−	0.601125i	$-0.205281\pi$
$761$	5.46292	+	5.46292i	0.198031	+	0.198031i	−0.601125	+	0.799155i	$0.705281\pi$
$762$		0			0
$763$	−8.15269			−0.295147
$764$	12.8576			0.465172
$765$		0			0
$766$			21.4776i			0.776017i
$767$	−20.5173	−	0.736810i	−0.740837	−	0.0266047i
$768$		0			0
$769$	−5.02811	−	5.02811i	−0.181318	−	0.181318i	0.610612	−	0.791930i	$-0.290924\pi$
$769$	−5.02811	−	5.02811i	−0.181318	−	0.181318i	−0.791930	+	0.610612i	$0.790924\pi$
$770$			1.33024i			0.0479387i
$771$		0			0
$772$	−17.1851	−	17.1851i	−0.618505	−	0.618505i
$773$	−4.00188	+	4.00188i	−0.143938	+	0.143938i	−0.775404	−	0.631466i	$-0.782454\pi$
$773$	−4.00188	+	4.00188i	−0.143938	+	0.143938i	0.631466	+	0.775404i	$0.282454\pi$
$774$		0			0
$775$	18.7783	−	18.7783i	0.674537	−	0.674537i
$776$			8.17657i			0.293522i
$777$		0			0
$778$	−13.2879	+	13.2879i	−0.476393	+	0.476393i
$779$	−1.97685			−0.0708279
$780$		0			0
$781$	−47.5953			−1.70309
$782$	15.7214	−	15.7214i	0.562195	−	0.562195i
$783$		0			0
$784$			1.00000i			0.0357143i
$785$	−2.22172	+	2.22172i	−0.0792965	+	0.0792965i
$786$		0			0
$787$	−3.67205	+	3.67205i	−0.130895	+	0.130895i	−0.769519	−	0.638624i	$-0.779504\pi$
$787$	−3.67205	+	3.67205i	−0.130895	+	0.130895i	0.638624	+	0.769519i	$0.279504\pi$
$788$	−7.46747	−	7.46747i	−0.266018	−	0.266018i
$789$		0			0
$790$			0.684072i			0.0243382i
$791$	4.70793	+	4.70793i	0.167395	+	0.167395i
$792$		0			0
$793$	3.81062	−	3.54641i	0.135319	−	0.125937i
$794$			37.3426i			1.32524i
$795$		0			0
$796$	−10.3453			−0.366678
$797$	−21.6686			−0.767543			−0.383771	−	0.923428i	$-0.625375\pi$
$797$	−21.6686			−0.767543			−0.383771	+	0.923428i	$0.625375\pi$
$798$		0			0
$799$	49.4079	+	49.4079i	1.74793	+	1.74793i
$800$	3.49800	+	3.49800i	0.123673	+	0.123673i
$801$		0			0
$802$	30.3561			1.07191
$803$	5.40687			0.190804
$804$		0			0
$805$			0.903299i			0.0318371i
$806$	−14.1689	+	13.1865i	−0.499079	+	0.464476i
$807$		0			0
$808$	1.01122	+	1.01122i	0.0355747	+	0.0355747i
$809$		−	27.1541i		−	0.954687i	−0.878717	−	0.477343i	$-0.841600\pi$
$809$		−	27.1541i		−	0.954687i	0.878717	−	0.477343i	$-0.158400\pi$
$810$		0			0
$811$	−9.72923	−	9.72923i	−0.341639	−	0.341639i	0.515344	−	0.856983i	$-0.327664\pi$
$811$	−9.72923	−	9.72923i	−0.341639	−	0.341639i	−0.856983	+	0.515344i	$0.827664\pi$
$812$	−4.45579	+	4.45579i	−0.156368	+	0.156368i
$813$		0			0
$814$	10.0371	−	10.0371i	0.351801	−	0.351801i
$815$		−	1.81584i		−	0.0636059i
$816$		0			0
$817$	1.07418	−	1.07418i	0.0375807	−	0.0375807i
$818$	21.7453			0.760307
$819$		0			0
$820$	−0.523863			−0.0182941
$821$	27.4869	−	27.4869i	0.959298	−	0.959298i	−0.0399056	−	0.999203i	$-0.512706\pi$
$821$	27.4869	−	27.4869i	0.959298	−	0.959298i	0.999203	+	0.0399056i	$0.0127057\pi$
$822$		0			0
$823$			41.7829i			1.45646i	0.685333	+	0.728229i	$0.259656\pi$
$823$			41.7829i			1.45646i	−0.685333	+	0.728229i	$0.740344\pi$
$824$	−7.77178	+	7.77178i	−0.270743	+	0.270743i
$825$		0			0
$826$	−4.02637	+	4.02637i	−0.140095	+	0.140095i
$827$	−12.5495	−	12.5495i	−0.436387	−	0.436387i	0.454407	−	0.890794i	$-0.349851\pi$
$827$	−12.5495	−	12.5495i	−0.436387	−	0.436387i	−0.890794	+	0.454407i	$0.849851\pi$
$828$		0			0
$829$			47.9505i			1.66539i	0.553733	+	0.832694i	$0.313203\pi$
$829$			47.9505i			1.66539i	−0.553733	+	0.832694i	$0.686797\pi$
$830$	1.78199	+	1.78199i	0.0618539	+	0.0618539i
$831$		0			0
$832$	−2.45637	−	2.63937i	−0.0851593	−	0.0915035i
$833$		−	5.67098i		−	0.196488i
$834$		0			0
$835$	0.854132			0.0295585
$836$	−5.01981			−0.173614
$837$		0			0
$838$	19.3112	+	19.3112i	0.667093	+	0.667093i
$839$	−4.12541	−	4.12541i	−0.142425	−	0.142425i	0.632299	−	0.774724i	$-0.282111\pi$
$839$	−4.12541	−	4.12541i	−0.142425	−	0.142425i	−0.774724	+	0.632299i	$0.782111\pi$
$840$		0			0
$841$	−10.7082			−0.369247
$842$	27.9297			0.962520
$843$		0			0
$844$			3.26222i			0.112290i
$845$	−1.96056	−	2.26440i	−0.0674453	−	0.0778978i
$846$		0			0
$847$	15.7928	+	15.7928i	0.542648	+	0.542648i
$848$		−	9.16630i		−	0.314772i
$849$		0			0
$850$	−19.8371	−	19.8371i	−0.680406	−	0.680406i
$851$	6.81569	−	6.81569i	0.233639	−	0.233639i
$852$		0			0
$853$	5.89653	−	5.89653i	0.201893	−	0.201893i	−0.598917	−	0.800811i	$-0.704402\pi$
$853$	5.89653	−	5.89653i	0.201893	−	0.201893i	0.800811	+	0.598917i	$0.204402\pi$
$854$		−	1.44376i		−	0.0494045i
$855$		0			0
$856$	6.17252	−	6.17252i	0.210973	−	0.210973i
$857$	−7.16082			−0.244609			−0.122305	−	0.992493i	$-0.539028\pi$
$857$	−7.16082			−0.244609			−0.122305	+	0.992493i	$0.539028\pi$
$858$		0			0
$859$	−45.4887			−1.55205			−0.776027	−	0.630700i	$-0.782768\pi$
$859$	−45.4887			−1.55205			−0.776027	+	0.630700i	$0.782768\pi$
$860$	0.284656	−	0.284656i	0.00970668	−	0.00970668i
$861$		0			0
$862$		−	10.2796i		−	0.350124i
$863$	24.5063	−	24.5063i	0.834206	−	0.834206i	−0.153883	−	0.988089i	$-0.549178\pi$
$863$	24.5063	−	24.5063i	0.834206	−	0.834206i	0.988089	+	0.153883i	$0.0491780\pi$
$864$		0			0
$865$	−0.264593	+	0.264593i	−0.00899644	+	0.00899644i
$866$	−9.59811	−	9.59811i	−0.326157	−	0.326157i
$867$		0			0
$868$			5.36831i			0.182212i
$869$	12.1213	+	12.1213i	0.411187	+	0.411187i
$870$		0			0
$871$	−10.1536	−	0.364634i	−0.344043	−	0.0123551i
$872$		−	8.15269i		−	0.276085i
$873$		0			0
$874$	−3.40869			−0.115301
$875$	2.29178			0.0774763
$876$		0			0
$877$	5.13378	+	5.13378i	0.173355	+	0.173355i	0.788452	−	0.615096i	$-0.210883\pi$
$877$	5.13378	+	5.13378i	0.173355	+	0.173355i	−0.615096	+	0.788452i	$0.710883\pi$
$878$	−21.7918	−	21.7918i	−0.735436	−	0.735436i
$879$		0			0
$880$	−1.33024			−0.0448425
$881$	30.0679			1.01301			0.506506	−	0.862236i	$-0.330937\pi$
$881$	30.0679			1.01301			0.506506	+	0.862236i	$0.330937\pi$
$882$		0			0
$883$			36.5069i			1.22855i	0.789090	+	0.614277i	$0.210552\pi$
$883$			36.5069i			1.22855i	−0.789090	+	0.614277i	$0.789448\pi$
$884$	13.9300	+	14.9678i	0.468518	+	0.503421i
$885$		0			0
$886$	−7.10580	−	7.10580i	−0.238724	−	0.238724i
$887$		−	51.4020i		−	1.72591i	−0.505281	−	0.862955i	$-0.668611\pi$
$887$		−	51.4020i		−	1.72591i	0.505281	−	0.862955i	$-0.331389\pi$
$888$		0			0
$889$	−7.38586	−	7.38586i	−0.247714	−	0.247714i
$890$	−2.21763	+	2.21763i	−0.0743351	+	0.0743351i
$891$		0			0
$892$	−10.8917	+	10.8917i	−0.364680	+	0.364680i
$893$		−	10.7126i		−	0.358482i
$894$		0			0
$895$	−2.56564	+	2.56564i	−0.0857600	+	0.0857600i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	20.1937			0.673874
$899$	−23.9201	+	23.9201i	−0.797779	+	0.797779i
$900$		0			0
$901$			51.9819i			1.73177i
$902$	−9.28249	+	9.28249i	−0.309073	+	0.309073i
$903$		0			0
$904$	−4.70793	+	4.70793i	−0.156583	+	0.156583i
$905$	0.474807	+	0.474807i	0.0157831	+	0.0157831i
$906$		0			0
$907$		−	0.0195937i		−	0.000650599i	−1.00000		0.000325300i	$-0.999896\pi$
$907$		−	0.0195937i		−	0.000650599i	1.00000		0.000325300i	$-0.000103546\pi$
$908$	−6.39849	−	6.39849i	−0.212341	−	0.212341i
$909$		0			0
$910$	−0.830188	−	0.0298134i	−0.0275205	−	0.000988305i
$911$		−	3.57159i		−	0.118332i	−0.998248	−	0.0591660i	$-0.981156\pi$
$911$		−	3.57159i		−	0.118332i	0.998248	−	0.0591660i	$-0.0188441\pi$
$912$		0			0
$913$	63.1513			2.09000
$914$	−29.5549			−0.977588
$915$		0			0
$916$	−16.8871	−	16.8871i	−0.557966	−	0.557966i
$917$	5.87029	+	5.87029i	0.193854	+	0.193854i
$918$		0			0
$919$	−12.3306			−0.406750			−0.203375	−	0.979101i	$-0.565191\pi$
$919$	−12.3306			−0.406750			−0.203375	+	0.979101i	$0.565191\pi$
$920$	−0.903299			−0.0297809
$921$		0			0
$922$			36.8720i			1.21432i
$923$	1.06670	−	29.7036i	0.0351110	−	0.977706i
$924$		0			0
$925$	−8.59998	−	8.59998i	−0.282766	−	0.282766i
$926$			26.6161i			0.874660i
$927$		0			0
$928$	−4.45579	−	4.45579i	−0.146269	−	0.146269i
$929$	30.5081	−	30.5081i	1.00094	−	1.00094i	0.000939371	−	1.00000i	$-0.499701\pi$
$929$	30.5081	−	30.5081i	1.00094	−	1.00094i	1.00000		0.000939371i	$-0.000299011\pi$
$930$		0			0
$931$	−0.614788	+	0.614788i	−0.0201489	+	0.0201489i
$932$		−	28.9998i		−	0.949920i
$933$		0			0
$934$	1.20367	−	1.20367i	0.0393854	−	0.0393854i
$935$	7.54379			0.246708
$936$		0			0
$937$	53.3798			1.74384			0.871920	−	0.489647i	$-0.162875\pi$
$937$	53.3798			1.74384			0.871920	+	0.489647i	$0.162875\pi$
$938$	−1.99258	+	1.99258i	−0.0650599	+	0.0650599i
$939$		0			0
$940$		−	2.83882i		−	0.0925921i
$941$	17.5192	−	17.5192i	0.571111	−	0.571111i	−0.361328	−	0.932439i	$-0.617677\pi$
$941$	17.5192	−	17.5192i	0.571111	−	0.571111i	0.932439	+	0.361328i	$0.117677\pi$
$942$		0			0
$943$	−6.30325	+	6.30325i	−0.205262	+	0.205262i
$944$	−4.02637	−	4.02637i	−0.131047	−	0.131047i
$945$		0			0
$946$		−	10.0878i		−	0.327983i
$947$	32.4908	+	32.4908i	1.05581	+	1.05581i	0.998348	+	0.0574601i	$0.0183002\pi$
$947$	32.4908	+	32.4908i	1.05581	+	1.05581i	0.0574601	+	0.998348i	$0.481700\pi$
$948$		0			0
$949$	−0.121179	+	3.37436i	−0.00393363	+	0.109536i
$950$			4.30105i			0.139545i
$951$		0			0
$952$	5.67098			0.183798
$953$	−18.5436			−0.600685			−0.300342	−	0.953831i	$-0.597101\pi$
$953$	−18.5436			−0.600685			−0.300342	+	0.953831i	$0.597101\pi$
$954$		0			0
$955$	2.09474	+	2.09474i	0.0677841	+	0.0677841i
$956$	20.6898	+	20.6898i	0.669156	+	0.669156i
$957$		0			0
$958$	−25.2664			−0.816321
$959$	4.58418			0.148031
$960$		0			0
$961$		−	2.18126i		−	0.0703634i
$962$	6.03909	+	6.48900i	0.194708	+	0.209214i
$963$		0			0
$964$	−18.8181	−	18.8181i	−0.606090	−	0.606090i
$965$		−	5.59953i		−	0.180255i
$966$		0			0
$967$	−14.4865	−	14.4865i	−0.465855	−	0.465855i	0.434714	−	0.900569i	$-0.356850\pi$
$967$	−14.4865	−	14.4865i	−0.465855	−	0.465855i	−0.900569	+	0.434714i	$0.856850\pi$
$968$	−15.7928	+	15.7928i	−0.507601	+	0.507601i
$969$		0			0
$970$	−1.33211	+	1.33211i	−0.0427715	+	0.0427715i
$971$			32.9835i			1.05849i	0.848469	+	0.529245i	$0.177525\pi$
$971$			32.9835i			1.05849i	−0.848469	+	0.529245i	$0.822475\pi$
$972$		0			0
$973$	11.7828	−	11.7828i	0.377740	−	0.377740i
$974$	−14.0492			−0.450167
$975$		0			0
$976$	1.44376			0.0462137
$977$	−14.0353	+	14.0353i	−0.449030	+	0.449030i	−0.895032	−	0.446002i	$-0.852848\pi$
$977$	−14.0353	+	14.0353i	−0.449030	+	0.449030i	0.446002	+	0.895032i	$0.352848\pi$
$978$		0			0
$979$			78.5897i			2.51174i
$980$	−0.162918	+	0.162918i	−0.00520423	+	0.00520423i
$981$		0			0
$982$	31.1901	−	31.1901i	0.995315	−	0.995315i
$983$	−12.8674	−	12.8674i	−0.410408	−	0.410408i	0.471473	−	0.881881i	$-0.343723\pi$
$983$	−12.8674	−	12.8674i	−0.410408	−	0.410408i	−0.881881	+	0.471473i	$0.843723\pi$
$984$		0			0
$985$		−	2.43317i		−	0.0775274i
$986$	25.2687	+	25.2687i	0.804720	+	0.804720i
$987$		0			0
$988$	0.112504	−	3.13280i	0.00357922	−	0.0996675i
$989$		−	6.85010i		−	0.217820i
$990$		0			0
$991$	−56.4959			−1.79465			−0.897325	−	0.441370i	$-0.854492\pi$
$991$	−56.4959			−1.79465			−0.897325	+	0.441370i	$0.854492\pi$
$992$	−5.36831			−0.170444
$993$		0			0
$994$	−5.82911	−	5.82911i	−0.184888	−	0.184888i
$995$	−1.68543	−	1.68543i	−0.0534318	−	0.0534318i
$996$		0			0
$997$	−7.94077			−0.251487			−0.125743	−	0.992063i	$-0.540132\pi$
$997$	−7.94077			−0.251487			−0.125743	+	0.992063i	$0.540132\pi$
$998$	21.7418			0.688225
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.y.c.827.3	✓	16
3.2	odd	2		1638.2.y.d.827.6	yes	16
13.5	odd	4		1638.2.y.d.1331.6	yes	16
39.5	even	4	inner	1638.2.y.c.1331.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.y.c.827.3	✓	16	1.1	even	1	trivial
1638.2.y.c.1331.3	yes	16	39.5	even	4	inner
1638.2.y.d.827.6	yes	16	3.2	odd	2
1638.2.y.d.1331.6	yes	16	13.5	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.162918 - 0.162918i) q^{5} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.162918 - 0.162918i) q^{5} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +0.230401i q^{10} +(4.08255 + 4.08255i) q^{11} +(-2.63937 + 2.45637i) q^{13} +1.00000i q^{14} -1.00000 q^{16} +5.67098 q^{17} +(-0.614788 - 0.614788i) q^{19} +(-0.162918 - 0.162918i) q^{20} -5.77360 q^{22} -3.92055 q^{23} +4.94692i q^{25} +(0.129398 - 3.60323i) q^{26} +(-0.707107 - 0.707107i) q^{28} -6.30144i q^{29} +(-3.79597 - 3.79597i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-4.00999 + 4.00999i) q^{34} -0.230401i q^{35} +(-1.73845 + 1.73845i) q^{37} +0.869442 q^{38} +0.230401 q^{40} +(1.60775 - 1.60775i) q^{41} +1.74723i q^{43} +(4.08255 - 4.08255i) q^{44} +(2.77225 - 2.77225i) q^{46} +(8.71241 + 8.71241i) q^{47} -1.00000i q^{49} +(-3.49800 - 3.49800i) q^{50} +(2.45637 + 2.63937i) q^{52} +9.16630i q^{53} +1.33024 q^{55} +1.00000 q^{56} +(4.45579 + 4.45579i) q^{58} +(4.02637 + 4.02637i) q^{59} -1.44376 q^{61} +5.36831 q^{62} +1.00000i q^{64} +(-0.0298134 + 0.830188i) q^{65} +(1.99258 + 1.99258i) q^{67} -5.67098i q^{68} +(0.162918 + 0.162918i) q^{70} +(-5.82911 + 5.82911i) q^{71} +(0.662193 - 0.662193i) q^{73} -2.45854i q^{74} +(-0.614788 + 0.614788i) q^{76} +5.77360 q^{77} +2.96905 q^{79} +(-0.162918 + 0.162918i) q^{80} +2.27370i q^{82} +(7.73430 - 7.73430i) q^{83} +(0.923907 - 0.923907i) q^{85} +(-1.23548 - 1.23548i) q^{86} +5.77360i q^{88} +(9.62508 + 9.62508i) q^{89} +(-0.129398 + 3.60323i) q^{91} +3.92055i q^{92} -12.3212 q^{94} -0.200320 q^{95} +(5.78171 + 5.78171i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{5}+O(q^{10}) \) 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

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