LMFDB - Embedded newform 1764.2.w.b.509.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(509,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 5]))

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

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

chi := DirichletCharacter("1764.509");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.w (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			509.3
Root			$1.68124 - 0.416458i$ of defining polynomial
Character	$\chi$	$=$	1764.509
Dual form			1764.2.w.b.1109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06740 + 1.36406i) q^{3} +(-0.349828 - 0.605920i) q^{5} +(-0.721326 - 2.91199i) q^{9} +O(q^{10})$	\(q+(-1.06740 + 1.36406i) q^{3} +(-0.349828 - 0.605920i) q^{5} +(-0.721326 - 2.91199i) q^{9} +(0.229685 + 0.132608i) q^{11} +(-1.13823 - 0.657156i) q^{13} +(1.19992 + 0.169570i) q^{15} +(1.86392 + 3.22840i) q^{17} +(0.382449 + 0.220807i) q^{19} +(-4.29949 + 2.48231i) q^{23} +(2.25524 - 3.90619i) q^{25} +(4.74208 + 2.12432i) q^{27} +(-0.273287 + 0.157782i) q^{29} -5.60632i q^{31} +(-0.426051 + 0.171758i) q^{33} +(-0.351124 + 0.608164i) q^{37} +(2.11134 - 0.851166i) q^{39} +(5.39354 - 9.34189i) q^{41} +(3.73131 + 6.46283i) q^{43} +(-1.51209 + 1.45576i) q^{45} +7.00570 q^{47} +(-6.39328 - 0.903488i) q^{51} +(8.51919 - 4.91856i) q^{53} -0.185561i q^{55} +(-0.709419 + 0.285995i) q^{57} +13.4636 q^{59} +5.65207i q^{61} +0.919566i q^{65} -5.94120 q^{67} +(1.20324 - 8.51439i) q^{69} +13.4323i q^{71} +(6.66182 - 3.84620i) q^{73} +(2.92105 + 7.24575i) q^{75} +1.39672 q^{79} +(-7.95938 + 4.20099i) q^{81} +(3.72399 + 6.45014i) q^{83} +(1.30410 - 2.25877i) q^{85} +(0.0764809 - 0.541196i) q^{87} +(-5.59261 + 9.68668i) q^{89} +(7.64736 + 5.98417i) q^{93} -0.308978i q^{95} +(9.18225 - 5.30138i) q^{97} +(0.220477 - 0.764493i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{9}+O(q^{10}) $ 16 * q + 6 * q^9	$ 16 q + 6 q^{9} - 6 q^{11} + 3 q^{13} - 3 q^{15} - 9 q^{17} + 21 q^{23} - 8 q^{25} - 9 q^{27} + 6 q^{29} + q^{37} - 3 q^{39} + 6 q^{41} - 2 q^{43} + 30 q^{45} + 36 q^{47} - 33 q^{51} + 15 q^{57} + 30 q^{59} + 14 q^{67} - 21 q^{69} + 57 q^{75} + 2 q^{79} + 18 q^{81} + 6 q^{85} - 48 q^{87} - 21 q^{89} + 21 q^{93} + 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q + 6 * q^9 - 6 * q^11 + 3 * q^13 - 3 * q^15 - 9 * q^17 + 21 * q^23 - 8 * q^25 - 9 * q^27 + 6 * q^29 + q^37 - 3 * q^39 + 6 * q^41 - 2 * q^43 + 30 * q^45 + 36 * q^47 - 33 * q^51 + 15 * q^57 + 30 * q^59 + 14 * q^67 - 21 * q^69 + 57 * q^75 + 2 * q^79 + 18 * q^81 + 6 * q^85 - 48 * q^87 - 21 * q^89 + 21 * q^93 + 3 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.06740	+	1.36406i	−0.616262	+	0.787541i
$3$	−1.06740	+	1.36406i	−0.616262	+	0.787541i
$4$		0			0
$5$	−0.349828	−	0.605920i	−0.156448	−	0.270975i	0.777137	−	0.629331i	$-0.216671\pi$
$5$	−0.349828	−	0.605920i	−0.156448	−	0.270975i	−0.933585	+	0.358355i	$0.883338\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.721326	−	2.91199i	−0.240442	−	0.970663i
$10$		0			0
$11$	0.229685	+	0.132608i	0.0692525	+	0.0399829i	0.534226	−	0.845341i	$-0.320603\pi$
$11$	0.229685	+	0.132608i	0.0692525	+	0.0399829i	−0.464974	+	0.885324i	$0.653936\pi$
$12$		0			0
$13$	−1.13823	−	0.657156i	−0.315688	−	0.182262i	0.333781	−	0.942651i	$-0.391675\pi$
$13$	−1.13823	−	0.657156i	−0.315688	−	0.182262i	−0.649469	+	0.760388i	$0.725009\pi$
$14$		0			0
$15$	1.19992	+	0.169570i	0.309817	+	0.0437829i
$16$		0			0
$17$	1.86392	+	3.22840i	0.452067	+	0.783003i	0.998514	−	0.0544906i	$-0.0173535\pi$
$17$	1.86392	+	3.22840i	0.452067	+	0.783003i	−0.546447	+	0.837493i	$0.684020\pi$
$18$		0			0
$19$	0.382449	+	0.220807i	0.0877398	+	0.0506566i	0.543228	−	0.839585i	$-0.317202\pi$
$19$	0.382449	+	0.220807i	0.0877398	+	0.0506566i	−0.455488	+	0.890242i	$0.650535\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.29949	+	2.48231i	−0.896507	+	0.517598i	−0.876065	−	0.482193i	$-0.839840\pi$
$23$	−4.29949	+	2.48231i	−0.896507	+	0.517598i	−0.0204414	+	0.999791i	$0.506507\pi$
$24$		0			0
$25$	2.25524	−	3.90619i	0.451048	−	0.781238i
$26$		0			0
$27$	4.74208	+	2.12432i	0.912613	+	0.408825i
$28$		0			0
$29$	−0.273287	+	0.157782i	−0.0507480	+	0.0292994i	−0.525159	−	0.851004i	$-0.675994\pi$
$29$	−0.273287	+	0.157782i	−0.0507480	+	0.0292994i	0.474411	+	0.880303i	$0.342661\pi$
$30$		0			0
$31$		−	5.60632i		−	1.00692i	−0.864017	−	0.503462i	$-0.832059\pi$
$31$		−	5.60632i		−	1.00692i	0.864017	−	0.503462i	$-0.167941\pi$
$32$		0			0
$33$	−0.426051	+	0.171758i	−0.0741659	+	0.0298992i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.351124	+	0.608164i	−0.0577244	+	0.0999816i	−0.893444	−	0.449175i	$-0.851718\pi$
$37$	−0.351124	+	0.608164i	−0.0577244	+	0.0999816i	0.835719	+	0.549157i	$0.185051\pi$
$38$		0			0
$39$	2.11134	−	0.851166i	0.338085	−	0.136296i
$40$		0			0
$41$	5.39354	−	9.34189i	0.842330	−	1.45896i	−0.0455900	−	0.998960i	$-0.514517\pi$
$41$	5.39354	−	9.34189i	0.842330	−	1.45896i	0.887920	−	0.459998i	$-0.152150\pi$
$42$		0			0
$43$	3.73131	+	6.46283i	0.569020	+	0.985572i	0.996663	+	0.0816240i	$0.0260106\pi$
$43$	3.73131	+	6.46283i	0.569020	+	0.985572i	−0.427643	+	0.903948i	$0.640656\pi$
$44$		0			0
$45$	−1.51209	+	1.45576i	−0.225409	+	0.217012i
$46$		0			0
$47$	7.00570			1.02189			0.510943	−	0.859614i	$-0.329296\pi$
$47$	7.00570			1.02189			0.510943	+	0.859614i	$0.329296\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−6.39328	−	0.903488i	−0.895239	−	0.126514i
$52$		0			0
$53$	8.51919	−	4.91856i	1.17020	−	0.675616i	0.216474	−	0.976288i	$-0.430544\pi$
$53$	8.51919	−	4.91856i	1.17020	−	0.675616i	0.953727	+	0.300672i	$0.0972111\pi$
$54$		0			0
$55$		−	0.185561i		−	0.0250210i
$56$		0			0
$57$	−0.709419	+	0.285995i	−0.0939648	+	0.0378809i
$58$		0			0
$59$	13.4636			1.75282			0.876408	−	0.481570i	$-0.159933\pi$
$59$	13.4636			1.75282			0.876408	+	0.481570i	$0.159933\pi$
$60$		0			0
$61$			5.65207i			0.723674i	0.932241	+	0.361837i	$0.117850\pi$
$61$			5.65207i			0.723674i	−0.932241	+	0.361837i	$0.882150\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			0.919566i			0.114058i
$66$		0			0
$67$	−5.94120			−0.725833			−0.362916	−	0.931822i	$-0.618219\pi$
$67$	−5.94120			−0.725833			−0.362916	+	0.931822i	$0.618219\pi$
$68$		0			0
$69$	1.20324	−	8.51439i	0.144853	−	1.02501i
$70$		0			0
$71$			13.4323i			1.59412i	0.603900	+	0.797060i	$0.293613\pi$
$71$			13.4323i			1.59412i	−0.603900	+	0.797060i	$0.706387\pi$
$72$		0			0
$73$	6.66182	−	3.84620i	0.779707	−	0.450164i	−0.0566194	−	0.998396i	$-0.518032\pi$
$73$	6.66182	−	3.84620i	0.779707	−	0.450164i	0.836326	+	0.548232i	$0.184699\pi$
$74$		0			0
$75$	2.92105	+	7.24575i	0.337293	+	0.836667i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	1.39672			0.157143			0.0785716	−	0.996908i	$-0.474964\pi$
$79$	1.39672			0.157143			0.0785716	+	0.996908i	$0.474964\pi$
$80$		0			0
$81$	−7.95938	+	4.20099i	−0.884375	+	0.466777i
$82$		0			0
$83$	3.72399	+	6.45014i	0.408761	+	0.707995i	0.994751	−	0.102323i	$-0.0326276\pi$
$83$	3.72399	+	6.45014i	0.408761	+	0.707995i	−0.585990	+	0.810318i	$0.699294\pi$
$84$		0			0
$85$	1.30410	−	2.25877i	0.141450	−	0.244998i
$86$		0			0
$87$	0.0764809	−	0.541196i	0.00819961	−	0.0580223i
$88$		0			0
$89$	−5.59261	+	9.68668i	−0.592815	+	1.02679i	0.401036	+	0.916062i	$0.368650\pi$
$89$	−5.59261	+	9.68668i	−0.592815	+	1.02679i	−0.993851	+	0.110724i	$0.964683\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	7.64736	+	5.98417i	0.792995	+	0.620529i
$94$		0			0
$95$		−	0.308978i		−	0.0317004i
$96$		0			0
$97$	9.18225	−	5.30138i	0.932316	−	0.538273i	0.0447729	−	0.998997i	$-0.485744\pi$
$97$	9.18225	−	5.30138i	0.932316	−	0.538273i	0.887543	+	0.460724i	$0.152410\pi$
$98$		0			0
$99$	0.220477	−	0.764493i	0.0221588	−	0.0768345i
$100$		0			0
$101$	−8.75357	+	15.1616i	−0.871013	+	1.50864i	−0.0100634	+	0.999949i	$0.503203\pi$
$101$	−8.75357	+	15.1616i	−0.871013	+	1.50864i	−0.860950	+	0.508690i	$0.830130\pi$
$102$		0			0
$103$	−7.39775	+	4.27110i	−0.728922	+	0.420844i	−0.818028	−	0.575179i	$-0.804933\pi$
$103$	−7.39775	+	4.27110i	−0.728922	+	0.420844i	0.0891054	+	0.996022i	$0.471599\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.09489	+	5.25093i	0.879236	+	0.507627i	0.870406	−	0.492334i	$-0.163856\pi$
$107$	9.09489	+	5.25093i	0.879236	+	0.507627i	0.00882940	+	0.999961i	$0.497189\pi$
$108$		0			0
$109$	−7.12110	−	12.3341i	−0.682078	−	1.18139i	−0.974346	−	0.225057i	$-0.927743\pi$
$109$	−7.12110	−	12.3341i	−0.682078	−	1.18139i	0.292268	−	0.956337i	$-0.405590\pi$
$110$		0			0
$111$	−0.454785	−	1.12811i	−0.0431663	−	0.107075i
$112$		0			0
$113$	13.3783	+	7.72396i	1.25852	+	0.726609i	0.972788	−	0.231699i	$-0.0744284\pi$
$113$	13.3783	+	7.72396i	1.25852	+	0.726609i	0.285737	+	0.958308i	$0.407762\pi$
$114$		0			0
$115$	3.00817	+	1.73677i	0.280513	+	0.161954i
$116$		0			0
$117$	−1.09260	+	3.78853i	−0.101011	+	0.350250i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−5.46483	−	9.46536i	−0.496803	−	0.860488i
$122$		0			0
$123$	6.98586	+	17.3286i	0.629894	+	1.56247i
$124$		0			0
$125$	−6.65406			−0.595157
$126$		0			0
$127$	21.8304			1.93713			0.968566	−	0.248758i	$-0.0800225\pi$
$127$	21.8304			1.93713			0.968566	+	0.248758i	$0.0800225\pi$
$128$		0			0
$129$	−12.7985	−	1.80866i	−1.12684	−	0.159244i
$130$		0			0
$131$	−2.60461	−	4.51132i	−0.227566	−	0.394156i	0.729520	−	0.683959i	$-0.239743\pi$
$131$	−2.60461	−	4.51132i	−0.227566	−	0.394156i	−0.957086	+	0.289803i	$0.906410\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.371744	−	3.61646i	−0.0319947	−	0.311255i
$136$		0			0
$137$	−2.33589	−	1.34863i	−0.199568	−	0.115221i	0.396886	−	0.917868i	$-0.370091\pi$
$137$	−2.33589	−	1.34863i	−0.199568	−	0.115221i	−0.596454	+	0.802647i	$0.703424\pi$
$138$		0			0
$139$	10.1448	+	5.85710i	0.860470	+	0.496793i	0.864170	−	0.503200i	$-0.167844\pi$
$139$	10.1448	+	5.85710i	0.860470	+	0.496793i	−0.00369951	+	0.999993i	$0.501178\pi$
$140$		0			0
$141$	−7.47787	+	9.55621i	−0.629750	+	0.804778i
$142$		0			0
$143$	−0.174289	−	0.301877i	−0.0145748	−	0.0252442i
$144$		0			0
$145$	0.191206	+	0.110393i	0.0158788	+	0.00916765i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	16.3055	−	9.41399i	1.33580	−	0.771224i	0.349618	−	0.936892i	$-0.386311\pi$
$149$	16.3055	−	9.41399i	1.33580	−	0.771224i	0.986182	+	0.165668i	$0.0529781\pi$
$150$		0			0
$151$	−5.00143	+	8.66273i	−0.407010	+	0.704963i	−0.994553	−	0.104230i	$-0.966762\pi$
$151$	−5.00143	+	8.66273i	−0.407010	+	0.704963i	0.587543	+	0.809193i	$0.300095\pi$
$152$		0			0
$153$	8.05659	−	7.75645i	0.651336	−	0.627072i
$154$		0			0
$155$	−3.39698	+	1.96125i	−0.272852	+	0.157531i
$156$		0			0
$157$		−	0.252063i		−	0.0201168i	−0.999949	−	0.0100584i	$-0.996798\pi$
$157$		−	0.252063i		−	0.0201168i	0.999949	−	0.0100584i	$-0.00320175\pi$
$158$		0			0
$159$	−2.38415	+	16.8708i	−0.189075	+	1.33794i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	4.29780	−	7.44400i	0.336629	−	0.583059i	−0.647167	−	0.762348i	$-0.724046\pi$
$163$	4.29780	−	7.44400i	0.336629	−	0.583059i	0.983796	+	0.179289i	$0.0573797\pi$
$164$		0			0
$165$	0.253116	+	0.198067i	0.0197050	+	0.0154195i
$166$		0			0
$167$	−2.24437	+	3.88736i	−0.173674	+	0.300813i	−0.939702	−	0.341995i	$-0.888897\pi$
$167$	−2.24437	+	3.88736i	−0.173674	+	0.300813i	0.766027	+	0.642808i	$0.222231\pi$
$168$		0			0
$169$	−5.63629	−	9.76234i	−0.433561	−	0.750949i
$170$		0			0
$171$	0.367117	−	1.27296i	0.0280742	−	0.0973457i
$172$		0			0
$173$	7.12145			0.541434			0.270717	−	0.962659i	$-0.412739\pi$
$173$	7.12145			0.541434			0.270717	+	0.962659i	$0.412739\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−14.3710	+	18.3652i	−1.08019	+	1.38041i
$178$		0			0
$179$	22.1270	−	12.7750i	1.65385	−	0.954848i	0.678376	−	0.734715i	$-0.262684\pi$
$179$	22.1270	−	12.7750i	1.65385	−	0.954848i	0.975470	−	0.220134i	$-0.0706494\pi$
$180$		0			0
$181$		−	0.943175i		−	0.0701057i	−0.999385	−	0.0350528i	$-0.988840\pi$
$181$		−	0.943175i		−	0.0701057i	0.999385	−	0.0350528i	$-0.0111599\pi$
$182$		0			0
$183$	−7.70977	−	6.03301i	−0.569923	−	0.445973i
$184$		0			0
$185$	0.491332			0.0361234
$186$		0			0
$187$			0.988686i			0.0722999i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			2.97235i			0.215072i	0.994201	+	0.107536i	$0.0342960\pi$
$191$			2.97235i			0.215072i	−0.994201	+	0.107536i	$0.965704\pi$
$192$		0			0
$193$	−18.5144			−1.33270			−0.666348	−	0.745641i	$-0.732144\pi$
$193$	−18.5144			−1.33270			−0.666348	+	0.745641i	$0.732144\pi$
$194$		0			0
$195$	−1.25434	−	0.981542i	−0.0898255	−	0.0702897i
$196$		0			0
$197$			14.1774i			1.01010i	0.863091	+	0.505048i	$0.168525\pi$
$197$			14.1774i			1.01010i	−0.863091	+	0.505048i	$0.831475\pi$
$198$		0			0
$199$	20.5293	−	11.8526i	1.45529	−	0.840209i	0.456512	−	0.889717i	$-0.349099\pi$
$199$	20.5293	−	11.8526i	1.45529	−	0.840209i	0.998774	+	0.0495081i	$0.0157654\pi$
$200$		0			0
$201$	6.34162	−	8.10416i	0.447303	−	0.571623i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−7.54725			−0.527123
$206$		0			0
$207$	10.3298	+	10.7295i	0.717972	+	0.745754i
$208$		0			0
$209$	0.0585617	+	0.101432i	0.00405080	+	0.00701619i
$210$		0			0
$211$	3.04004	−	5.26550i	0.209285	−	0.362492i	−0.742205	−	0.670173i	$-0.766220\pi$
$211$	3.04004	−	5.26550i	0.209285	−	0.362492i	0.951489	+	0.307681i	$0.0995531\pi$
$212$		0			0
$213$	−18.3225	−	14.3376i	−1.25544	−	0.982396i
$214$		0			0
$215$	2.61063	−	4.52175i	0.178044	−	0.308381i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−1.86435	+	13.1926i	−0.125981	+	0.891470i
$220$		0			0
$221$		−	4.89954i		−	0.329579i
$222$		0			0
$223$	−0.796137	+	0.459650i	−0.0533133	+	0.0307804i	−0.526420	−	0.850225i	$-0.676466\pi$
$223$	−0.796137	+	0.459650i	−0.0533133	+	0.0307804i	0.473106	+	0.881005i	$0.343133\pi$
$224$		0			0
$225$	−13.0016	−	3.74960i	−0.866771	−	0.249973i
$226$		0			0
$227$	−5.00297	+	8.66540i	−0.332059	+	0.575143i	−0.982915	−	0.184058i	$-0.941077\pi$
$227$	−5.00297	+	8.66540i	−0.332059	+	0.575143i	0.650857	+	0.759201i	$0.274410\pi$
$228$		0			0
$229$	2.38179	−	1.37513i	0.157393	−	0.0908710i	−0.419235	−	0.907878i	$-0.637702\pi$
$229$	2.38179	−	1.37513i	0.157393	−	0.0908710i	0.576628	+	0.817007i	$0.304368\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.55513	−	3.20725i	−0.363928	−	0.210114i	0.306874	−	0.951750i	$-0.400717\pi$
$233$	−5.55513	−	3.20725i	−0.363928	−	0.210114i	−0.670803	+	0.741636i	$0.734050\pi$
$234$		0			0
$235$	−2.45079	−	4.24489i	−0.159872	−	0.276906i
$236$		0			0
$237$	−1.49085	+	1.90521i	−0.0968414	+	0.123757i
$238$		0			0
$239$	−11.4288	−	6.59844i	−0.739270	−	0.426818i	0.0825337	−	0.996588i	$-0.473699\pi$
$239$	−11.4288	−	6.59844i	−0.739270	−	0.426818i	−0.821804	+	0.569770i	$0.807032\pi$
$240$		0			0
$241$	2.20722	+	1.27434i	0.142180	+	0.0820874i	0.569402	−	0.822059i	$-0.307175\pi$
$241$	2.20722	+	1.27434i	0.142180	+	0.0820874i	−0.427223	+	0.904146i	$0.640508\pi$
$242$		0			0
$243$	2.76541	−	15.3412i	0.177401	−	0.984139i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.290209	−	0.502657i	−0.0184656	−	0.0319833i
$248$		0			0
$249$	−12.7734	−	1.80511i	−0.809479	−	0.114394i
$250$		0			0
$251$	−18.7893			−1.18597			−0.592986	−	0.805213i	$-0.702051\pi$
$251$	−18.7893			−1.18597			−0.592986	+	0.805213i	$0.702051\pi$
$252$		0			0
$253$	−1.31670			−0.0827804
$254$		0			0
$255$	1.68911	+	4.18988i	0.105776	+	0.262380i
$256$		0			0
$257$	−7.19727	−	12.4660i	−0.448953	−	0.777610i	0.549365	−	0.835583i	$-0.314870\pi$
$257$	−7.19727	−	12.4660i	−0.448953	−	0.777610i	−0.998318	+	0.0579725i	$0.981536\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	0.656589	+	0.681995i	0.0406418	+	0.0422145i
$262$		0			0
$263$	6.79810	+	3.92488i	0.419189	+	0.242019i	0.694730	−	0.719271i	$-0.255524\pi$
$263$	6.79810	+	3.92488i	0.419189	+	0.242019i	−0.275542	+	0.961289i	$0.588857\pi$
$264$		0			0
$265$	−5.96050	−	3.44130i	−0.366151	−	0.211397i
$266$		0			0
$267$	−7.24369	−	17.9682i	−0.443307	−	1.09964i
$268$		0			0
$269$	7.72267	+	13.3760i	0.470859	+	0.815552i	0.999444	−	0.0333281i	$-0.0106106\pi$
$269$	7.72267	+	13.3760i	0.470859	+	0.815552i	−0.528585	+	0.848880i	$0.677277\pi$
$270$		0			0
$271$	−10.9476	−	6.32057i	−0.665016	−	0.383947i	0.129169	−	0.991623i	$-0.458769\pi$
$271$	−10.9476	−	6.32057i	−0.665016	−	0.383947i	−0.794186	+	0.607675i	$0.792102\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.03599	−	0.598128i	0.0624724	−	0.0360685i
$276$		0			0
$277$	5.94531	−	10.2976i	0.357219	−	0.618722i	−0.630276	−	0.776371i	$-0.717058\pi$
$277$	5.94531	−	10.2976i	0.357219	−	0.618722i	0.987495	+	0.157649i	$0.0503915\pi$
$278$		0			0
$279$	−16.3255	+	4.04399i	−0.977385	+	0.242107i
$280$		0			0
$281$	−2.75411	+	1.59009i	−0.164297	+	0.0948568i	−0.579894	−	0.814692i	$-0.696906\pi$
$281$	−2.75411	+	1.59009i	−0.164297	+	0.0948568i	0.415597	+	0.909549i	$0.363573\pi$
$282$		0			0
$283$		−	18.4978i		−	1.09958i	−0.835303	−	0.549789i	$-0.814708\pi$
$283$		−	18.4978i		−	1.09958i	0.835303	−	0.549789i	$-0.185292\pi$
$284$		0			0
$285$	0.421464	+	0.329802i	0.0249654	+	0.0195358i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	1.55161	−	2.68746i	0.0912711	−	0.158086i
$290$		0			0
$291$	−2.56971	+	18.1838i	−0.150639	+	1.06595i
$292$		0			0
$293$	1.42975	−	2.47639i	0.0835266	−	0.144672i	−0.821236	−	0.570589i	$-0.806715\pi$
$293$	1.42975	−	2.47639i	0.0835266	−	0.144672i	0.904762	+	0.425917i	$0.140048\pi$
$294$		0			0
$295$	−4.70995	−	8.15788i	−0.274224	−	0.474970i
$296$		0			0
$297$	0.807479	+	1.11676i	0.0468547	+	0.0648011i
$298$		0			0
$299$	6.52507			0.377355
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−11.3379	−	28.1239i	−0.651343	−	1.61568i
$304$		0			0
$305$	3.42470	−	1.97725i	0.196098	−	0.113217i
$306$		0			0
$307$			21.6746i			1.23704i	0.785771	+	0.618518i	$0.212266\pi$
$307$			21.6746i			1.23704i	−0.785771	+	0.618518i	$0.787734\pi$
$308$		0			0
$309$	2.07031	−	14.6499i	0.117776	−	0.833406i
$310$		0			0
$311$	23.6925			1.34348			0.671738	−	0.740789i	$-0.265548\pi$
$311$	23.6925			1.34348			0.671738	+	0.740789i	$0.265548\pi$
$312$		0			0
$313$		−	27.2836i		−	1.54216i	−0.636737	−	0.771081i	$-0.719716\pi$
$313$		−	27.2836i		−	1.54216i	0.636737	−	0.771081i	$-0.280284\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			24.5544i			1.37911i	0.724232	+	0.689556i	$0.242194\pi$
$317$			24.5544i			1.37911i	−0.724232	+	0.689556i	$0.757806\pi$
$318$		0			0
$319$	−0.0836929			−0.00468590
$320$		0			0
$321$	−16.8705	+	6.80115i	−0.941617	+	0.379603i
$322$		0			0
$323$			1.64626i			0.0916006i
$324$		0			0
$325$	−5.13396	+	2.96409i	−0.284781	+	0.164418i
$326$		0			0
$327$	24.4255	+	3.45178i	1.35074	+	0.190884i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	16.3116			0.896566			0.448283	−	0.893892i	$-0.352036\pi$
$331$	16.3116			0.896566			0.448283	+	0.893892i	$0.352036\pi$
$332$		0			0
$333$	2.02424	+	0.583784i	0.110928	+	0.0319912i
$334$		0			0
$335$	2.07840	+	3.59989i	0.113555	+	0.196683i
$336$		0			0
$337$	13.6580	−	23.6563i	0.743998	−	1.28864i	−0.206663	−	0.978412i	$-0.566261\pi$
$337$	13.6580	−	23.6563i	0.743998	−	1.28864i	0.950661	−	0.310230i	$-0.100406\pi$
$338$		0			0
$339$	−24.8159	+	10.0043i	−1.34782	+	0.543358i
$340$		0			0
$341$	0.743445	−	1.28768i	0.0402598	−	0.0697320i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−5.57996	+	2.24950i	−0.300415	+	0.121109i
$346$		0			0
$347$		−	6.21213i		−	0.333485i	−0.986001	−	0.166742i	$-0.946675\pi$
$347$		−	6.21213i		−	0.333485i	0.986001	−	0.166742i	$-0.0533248\pi$
$348$		0			0
$349$	−24.6529	+	14.2334i	−1.31964	+	0.761896i	−0.983671	−	0.179977i	$-0.942398\pi$
$349$	−24.6529	+	14.2334i	−1.31964	+	0.761896i	−0.335971	+	0.941872i	$0.609064\pi$
$350$		0			0
$351$	−4.00155	−	5.53424i	−0.213587	−	0.295396i
$352$		0			0
$353$	−1.49346	+	2.58674i	−0.0794887	+	0.137678i	−0.903029	−	0.429579i	$-0.858662\pi$
$353$	−1.49346	+	2.58674i	−0.0794887	+	0.137678i	0.823541	+	0.567257i	$0.191995\pi$
$354$		0			0
$355$	8.13889	−	4.69899i	0.431968	−	0.249397i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−26.5977	−	15.3562i	−1.40377	−	0.810468i	−0.408994	−	0.912537i	$-0.634120\pi$
$359$	−26.5977	−	15.3562i	−1.40377	−	0.810468i	−0.994777	+	0.102070i	$0.967454\pi$
$360$		0			0
$361$	−9.40249	−	16.2856i	−0.494868	−	0.857136i
$362$		0			0
$363$	18.7445	+	2.64894i	0.983830	+	0.139033i
$364$		0			0
$365$	−4.66098	−	2.69102i	−0.243967	−	0.140854i
$366$		0			0
$367$	−16.4877	−	9.51918i	−0.860651	−	0.496897i	0.00357920	−	0.999994i	$-0.498861\pi$
$367$	−16.4877	−	9.51918i	−0.860651	−	0.496897i	−0.864230	+	0.503096i	$0.832194\pi$
$368$		0			0
$369$	−31.0940	−	8.96739i	−1.61869	−	0.466824i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−2.05869	−	3.56576i	−0.106595	−	0.184628i	0.807794	−	0.589465i	$-0.200661\pi$
$373$	−2.05869	−	3.56576i	−0.106595	−	0.184628i	−0.914389	+	0.404837i	$0.867328\pi$
$374$		0			0
$375$	7.10253	−	9.07655i	0.366773	−	0.468711i
$376$		0			0
$377$	0.414750			0.0213607
$378$		0			0
$379$	−11.2436			−0.577546			−0.288773	−	0.957398i	$-0.593247\pi$
$379$	−11.2436			−0.577546			−0.288773	+	0.957398i	$0.593247\pi$
$380$		0			0
$381$	−23.3017	+	29.7779i	−1.19378	+	1.52557i
$382$		0			0
$383$	−15.8046	−	27.3745i	−0.807580	−	1.39877i	−0.914536	−	0.404505i	$-0.867444\pi$
$383$	−15.8046	−	27.3745i	−0.807580	−	1.39877i	0.106956	−	0.994264i	$-0.465890\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	16.1282	−	15.5274i	0.819842	−	0.789300i
$388$		0			0
$389$	18.4018	+	10.6243i	0.933007	+	0.538672i	0.887761	−	0.460304i	$-0.152260\pi$
$389$	18.4018	+	10.6243i	0.933007	+	0.538672i	0.0452458	+	0.998976i	$0.485593\pi$
$390$		0			0
$391$	−16.0278	−	9.25367i	−0.810562	−	0.467978i
$392$		0			0
$393$	8.93387	+	1.26252i	0.450654	+	0.0636857i
$394$		0			0
$395$	−0.488611	−	0.846300i	−0.0245847	−	0.0425820i
$396$		0			0
$397$	−20.6927	−	11.9469i	−1.03854	−	0.599599i	−0.119118	−	0.992880i	$-0.538007\pi$
$397$	−20.6927	−	11.9469i	−1.03854	−	0.599599i	−0.919419	+	0.393281i	$0.871340\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	22.0121	−	12.7087i	1.09923	−	0.634642i	0.163213	−	0.986591i	$-0.447814\pi$
$401$	22.0121	−	12.7087i	1.09923	−	0.634642i	0.936019	+	0.351948i	$0.114481\pi$
$402$		0			0
$403$	−3.68423	+	6.38127i	−0.183524	+	0.317874i
$404$		0			0
$405$	5.32987	+	3.35312i	0.264844	+	0.166618i
$406$		0			0
$407$	−0.161295	+	0.0931240i	−0.00799512	+	0.00461598i
$408$		0			0
$409$		−	22.3817i		−	1.10670i	−0.832948	−	0.553351i	$-0.813349\pi$
$409$		−	22.3817i		−	1.10670i	0.832948	−	0.553351i	$-0.186651\pi$
$410$		0			0
$411$	4.33293	−	1.74678i	0.213728	−	0.0861621i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	2.60551	−	4.51288i	0.127900	−	0.221528i
$416$		0			0
$417$	−18.8180	+	7.58627i	−0.921520	+	0.371501i
$418$		0			0
$419$	−7.04181	+	12.1968i	−0.344015	+	0.595851i	−0.985174	−	0.171556i	$-0.945120\pi$
$419$	−7.04181	+	12.1968i	−0.344015	+	0.595851i	0.641159	+	0.767408i	$0.278454\pi$
$420$		0			0
$421$	8.07639	+	13.9887i	0.393619	+	0.681768i	0.992924	−	0.118753i	$-0.0378896\pi$
$421$	8.07639	+	13.9887i	0.393619	+	0.681768i	−0.599305	+	0.800521i	$0.704556\pi$
$422$		0			0
$423$	−5.05340	−	20.4005i	−0.245705	−	0.991908i
$424$		0			0
$425$	16.8143			0.815616
$426$		0			0
$427$		0			0
$428$		0			0
$429$	0.597815	+	0.0844822i	0.0288628	+	0.00407884i
$430$		0			0
$431$	−7.16179	+	4.13486i	−0.344971	+	0.199169i	−0.662468	−	0.749090i	$-0.730491\pi$
$431$	−7.16179	+	4.13486i	−0.344971	+	0.199169i	0.317497	+	0.948259i	$0.397158\pi$
$432$		0			0
$433$		−	4.35102i		−	0.209097i	−0.994520	−	0.104548i	$-0.966660\pi$
$433$		−	4.35102i		−	0.209097i	0.994520	−	0.104548i	$-0.0333397\pi$
$434$		0			0
$435$	−0.354676	+	0.142984i	−0.0170054	+	0.00685556i
$436$		0			0
$437$	−2.19245			−0.104879
$438$		0			0
$439$			20.8077i			0.993098i	0.868009	+	0.496549i	$0.165400\pi$
$439$			20.8077i			0.993098i	−0.868009	+	0.496549i	$0.834600\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			30.9376i			1.46989i	0.678127	+	0.734945i	$0.262792\pi$
$443$			30.9376i			1.46989i	−0.678127	+	0.734945i	$0.737208\pi$
$444$		0			0
$445$	7.82580			0.370978
$446$		0			0
$447$	−4.56320	+	32.2902i	−0.215832	+	1.52727i
$448$		0			0
$449$		−	20.9215i		−	0.987346i	−0.869648	−	0.493673i	$-0.835654\pi$
$449$		−	20.9215i		−	0.987346i	0.869648	−	0.493673i	$-0.164346\pi$
$450$		0			0
$451$	2.47763	−	1.43046i	0.116667	−	0.0673577i
$452$		0			0
$453$	−6.47798	−	16.0688i	−0.304362	−	0.754979i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	2.30115			0.107643			0.0538217	−	0.998551i	$-0.482860\pi$
$457$	2.30115			0.107643			0.0538217	+	0.998551i	$0.482860\pi$
$458$		0			0
$459$	1.98069	+	19.2689i	0.0924509	+	0.899395i
$460$		0			0
$461$	−8.92497	−	15.4585i	−0.415677	−	0.719974i	0.579822	−	0.814743i	$-0.303122\pi$
$461$	−8.92497	−	15.4585i	−0.415677	−	0.719974i	−0.995499	+	0.0947688i	$0.969789\pi$
$462$		0			0
$463$	−6.24034	+	10.8086i	−0.290013	+	0.502318i	−0.973813	−	0.227353i	$-0.926993\pi$
$463$	−6.24034	+	10.8086i	−0.290013	+	0.502318i	0.683799	+	0.729670i	$0.260326\pi$
$464$		0			0
$465$	0.950665	−	6.72712i	0.0440860	−	0.311963i
$466$		0			0
$467$	2.42799	−	4.20541i	0.112354	−	0.194603i	−0.804365	−	0.594136i	$-0.797494\pi$
$467$	2.42799	−	4.20541i	0.112354	−	0.194603i	0.916719	+	0.399533i	$0.130828\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.343830	+	0.269052i	0.0158428	+	0.0123972i
$472$		0			0
$473$			1.97921i			0.0910044i
$474$		0			0
$475$	1.72503	−	0.995945i	0.0791497	−	0.0456971i
$476$		0			0
$477$	−20.4679	−	21.2599i	−0.937161	−	0.973425i
$478$		0			0
$479$	−4.40542	+	7.63041i	−0.201289	+	0.348642i	−0.948944	−	0.315445i	$-0.897846\pi$
$479$	−4.40542	+	7.63041i	−0.201289	+	0.348642i	0.747655	+	0.664087i	$0.231180\pi$
$480$		0			0
$481$	0.799318	−	0.461486i	0.0364458	−	0.0210420i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−6.42441	−	3.70914i	−0.291718	−	0.168423i
$486$		0			0
$487$	4.66185	+	8.07456i	0.211249	+	0.365893i	0.952106	−	0.305770i	$-0.0989137\pi$
$487$	4.66185	+	8.07456i	0.211249	+	0.365893i	−0.740857	+	0.671663i	$0.765580\pi$
$488$		0			0
$489$	5.56662	+	13.8082i	0.251731	+	0.624427i
$490$		0			0
$491$	−26.9192	−	15.5418i	−1.21485	−	0.701391i	−0.251034	−	0.967978i	$-0.580771\pi$
$491$	−26.9192	−	15.5418i	−1.21485	−	0.701391i	−0.963811	+	0.266587i	$0.914104\pi$
$492$		0			0
$493$	−1.01877	−	0.588186i	−0.0458830	−	0.0264906i
$494$		0			0
$495$	−0.540350	+	0.133850i	−0.0242869	+	0.00601610i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	11.1694	+	19.3459i	0.500010	+	0.866043i	1.00000		1.16519e-5i	$3.70891e-6\pi$
$499$	11.1694	+	19.3459i	0.500010	+	0.866043i	−0.499990	+	0.866031i	$0.666663\pi$
$500$		0			0
$501$	−2.90697	−	7.21081i	−0.129874	−	0.322155i
$502$		0			0
$503$	12.2396			0.545738			0.272869	−	0.962051i	$-0.412027\pi$
$503$	12.2396			0.545738			0.272869	+	0.962051i	$0.412027\pi$
$504$		0			0
$505$	12.2490			0.545072
$506$		0			0
$507$	19.3326	+	2.73205i	0.858591	+	0.121335i
$508$		0			0
$509$	7.05496	+	12.2195i	0.312706	+	0.541622i	0.978947	−	0.204114i	$-0.0654314\pi$
$509$	7.05496	+	12.2195i	0.312706	+	0.541622i	−0.666242	+	0.745736i	$0.732098\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	1.34454	+	1.85953i	0.0593627	+	0.0821000i
$514$		0			0
$515$	5.17588	+	2.98830i	0.228077	+	0.131680i
$516$		0			0
$517$	1.60910	+	0.929015i	0.0707682	+	0.0408580i
$518$		0			0
$519$	−7.60141	+	9.71409i	−0.333665	+	0.426401i
$520$		0			0
$521$	−2.81632	−	4.87800i	−0.123385	−	0.213709i	0.797715	−	0.603034i	$-0.206042\pi$
$521$	−2.81632	−	4.87800i	−0.123385	−	0.213709i	−0.921101	+	0.389325i	$0.872708\pi$
$522$		0			0
$523$	33.2293	+	19.1849i	1.45302	+	0.838899i	0.998651	−	0.0519176i	$-0.0165333\pi$
$523$	33.2293	+	19.1849i	1.45302	+	0.838899i	0.454364	+	0.890816i	$0.349867\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	18.0995	−	10.4497i	0.788425	−	0.455197i
$528$		0			0
$529$	0.823769	−	1.42681i	0.0358161	−	0.0620352i
$530$		0			0
$531$	−9.71167	−	39.2060i	−0.421451	−	1.70139i
$532$		0			0
$533$	−12.2782	+	7.08880i	−0.531826	+	0.307050i
$534$		0			0
$535$		−	7.34769i		−	0.317668i
$536$		0			0
$537$	−6.19236	+	43.8185i	−0.267220	+	1.89091i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−3.21673	+	5.57154i	−0.138298	+	0.239539i	−0.926852	−	0.375426i	$-0.877496\pi$
$541$	−3.21673	+	5.57154i	−0.138298	+	0.239539i	0.788555	+	0.614965i	$0.210830\pi$
$542$		0			0
$543$	1.28655	+	1.00674i	0.0552111	+	0.0432035i
$544$		0			0
$545$	−4.98232	+	8.62963i	−0.213419	+	0.369653i
$546$		0			0
$547$	−6.52889	−	11.3084i	−0.279155	−	0.483511i	0.692020	−	0.721878i	$-0.256721\pi$
$547$	−6.52889	−	11.3084i	−0.279155	−	0.483511i	−0.971175	+	0.238368i	$0.923388\pi$
$548$		0			0
$549$	16.4588	−	4.07699i	0.702444	−	0.174002i
$550$		0			0
$551$	−0.139357			−0.00593683
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.524446	+	0.670206i	−0.0222615	+	0.0284487i
$556$		0			0
$557$	−25.5409	+	14.7460i	−1.08220	+	0.624809i	−0.931489	−	0.363769i	$-0.881490\pi$
$557$	−25.5409	+	14.7460i	−1.08220	+	0.624809i	−0.150712	+	0.988578i	$0.548157\pi$
$558$		0			0
$559$		−	9.80822i		−	0.414844i
$560$		0			0
$561$	−1.34863	−	1.05532i	−0.0569391	−	0.0445557i
$562$		0			0
$563$	10.5187			0.443310			0.221655	−	0.975125i	$-0.428854\pi$
$563$	10.5187			0.443310			0.221655	+	0.975125i	$0.428854\pi$
$564$		0			0
$565$		−	10.8082i		−	0.454706i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			26.3334i			1.10395i	0.833859	+	0.551977i	$0.186126\pi$
$569$			26.3334i			1.10395i	−0.833859	+	0.551977i	$0.813874\pi$
$570$		0			0
$571$	−44.0590			−1.84381			−0.921906	−	0.387413i	$-0.873369\pi$
$571$	−44.0590			−1.84381			−0.921906	+	0.387413i	$0.873369\pi$
$572$		0			0
$573$	−4.05447	−	3.17268i	−0.169378	−	0.132540i
$574$		0			0
$575$			22.3929i			0.933847i
$576$		0			0
$577$	−12.1535	+	7.01684i	−0.505957	+	0.292115i	−0.731170	−	0.682195i	$-0.761026\pi$
$577$	−12.1535	+	7.01684i	−0.505957	+	0.292115i	0.225213	+	0.974310i	$0.427692\pi$
$578$		0			0
$579$	19.7622	−	25.2548i	0.821290	−	1.04955i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	2.60897			0.108052
$584$		0			0
$585$	2.67777	−	0.663307i	0.110712	−	0.0274244i
$586$		0			0
$587$	−1.52469	−	2.64085i	−0.0629308	−	0.108999i	0.832843	−	0.553509i	$-0.186711\pi$
$587$	−1.52469	−	2.64085i	−0.0629308	−	0.108999i	−0.895774	+	0.444509i	$0.853378\pi$
$588$		0			0
$589$	1.23791	−	2.14413i	0.0510073	−	0.0883473i
$590$		0			0
$591$	−19.3388	−	15.1329i	−0.795493	−	0.622484i
$592$		0			0
$593$	−13.3041	+	23.0434i	−0.546334	+	0.946278i	0.452188	+	0.891923i	$0.350644\pi$
$593$	−13.3041	+	23.0434i	−0.546334	+	0.946278i	−0.998522	+	0.0543552i	$0.982690\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−5.74526	+	40.6547i	−0.235138	+	1.66389i
$598$		0			0
$599$		−	4.46099i		−	0.182271i	−0.995838	−	0.0911356i	$-0.970950\pi$
$599$		−	4.46099i		−	0.182271i	0.995838	−	0.0911356i	$-0.0290497\pi$
$600$		0			0
$601$	−5.25019	+	3.03120i	−0.214160	+	0.123645i	−0.603243	−	0.797557i	$-0.706125\pi$
$601$	−5.25019	+	3.03120i	−0.214160	+	0.123645i	0.389083	+	0.921203i	$0.372792\pi$
$602$		0			0
$603$	4.28554	+	17.3007i	0.174521	+	0.704539i
$604$		0			0
$605$	−3.82350	+	6.62250i	−0.155447	+	0.269243i
$606$		0			0
$607$	−39.2581	+	22.6657i	−1.59344	+	0.919971i	−0.600725	+	0.799455i	$0.705121\pi$
$607$	−39.2581	+	22.6657i	−1.59344	+	0.919971i	−0.992711	+	0.120516i	$0.961545\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−7.97409	−	4.60384i	−0.322597	−	0.186251i
$612$		0			0
$613$	16.6294	+	28.8029i	0.671654	+	1.16334i	0.977435	+	0.211237i	$0.0677492\pi$
$613$	16.6294	+	28.8029i	0.671654	+	1.16334i	−0.305781	+	0.952102i	$0.598917\pi$
$614$		0			0
$615$	8.05591	−	10.2949i	0.324846	−	0.415131i
$616$		0			0
$617$	31.3001	+	18.0711i	1.26010	+	0.727516i	0.973093	−	0.230414i	$-0.0740079\pi$
$617$	31.3001	+	18.0711i	1.26010	+	0.727516i	0.287002	+	0.957930i	$0.407341\pi$
$618$		0			0
$619$	22.9031	+	13.2231i	0.920554	+	0.531482i	0.883812	−	0.467843i	$-0.154969\pi$
$619$	22.9031	+	13.2231i	0.920554	+	0.531482i	0.0367423	+	0.999325i	$0.488302\pi$
$620$		0			0
$621$	−25.6617	+	2.63783i	−1.02977	+	0.105852i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−8.94843	−	15.4991i	−0.357937	−	0.619965i
$626$		0			0
$627$	−0.200868	−	0.0283863i	−0.00802189	−	0.00113364i
$628$		0			0
$629$	−2.61787			−0.104381
$630$		0			0
$631$	−32.0484			−1.27583			−0.637914	−	0.770107i	$-0.720203\pi$
$631$	−32.0484			−1.27583			−0.637914	+	0.770107i	$0.720203\pi$
$632$		0			0
$633$	3.93754	+	9.76717i	0.156503	+	0.388210i
$634$		0			0
$635$	−7.63687	−	13.2274i	−0.303060	−	0.524915i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	39.1147	−	9.68907i	1.54735	−	0.383294i
$640$		0			0
$641$	−21.1444	−	12.2077i	−0.835153	−	0.482176i	0.0204610	−	0.999791i	$-0.493487\pi$
$641$	−21.1444	−	12.2077i	−0.835153	−	0.482176i	−0.855614	+	0.517615i	$0.826820\pi$
$642$		0			0
$643$	31.9014	+	18.4183i	1.25807	+	0.726346i	0.972699	−	0.232071i	$-0.0745503\pi$
$643$	31.9014	+	18.4183i	1.25807	+	0.726346i	0.285370	+	0.958418i	$0.407884\pi$
$644$		0			0
$645$	3.38136	+	8.38757i	0.133141	+	0.330260i
$646$		0			0
$647$	−13.2847	−	23.0098i	−0.522276	−	0.904608i	−0.999664	−	0.0259155i	$-0.991750\pi$
$647$	−13.2847	−	23.0098i	−0.522276	−	0.904608i	0.477389	−	0.878692i	$-0.341583\pi$
$648$		0			0
$649$	3.09239	+	1.78539i	0.121387	+	0.0700827i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	26.2767	−	15.1709i	1.02829	−	0.593683i	0.111794	−	0.993731i	$-0.464340\pi$
$653$	26.2767	−	15.1709i	1.02829	−	0.593683i	0.916494	+	0.400049i	$0.131007\pi$
$654$		0			0
$655$	−1.82233	+	3.15637i	−0.0712044	+	0.123330i
$656$		0			0
$657$	−16.0055	−	16.6248i	−0.624432	−	0.648595i
$658$		0			0
$659$	40.9873	−	23.6640i	1.59664	−	0.921820i	0.604511	−	0.796597i	$-0.293369\pi$
$659$	40.9873	−	23.6640i	1.59664	−	0.921820i	0.992129	−	0.125223i	$-0.0399647\pi$
$660$		0			0
$661$			35.1245i			1.36618i	0.730332	+	0.683092i	$0.239365\pi$
$661$			35.1245i			1.36618i	−0.730332	+	0.683092i	$0.760635\pi$
$662$		0			0
$663$	6.68328	+	5.22976i	0.259557	+	0.203107i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.783329	−	1.35677i	0.0303306	−	0.0525342i
$668$		0			0
$669$	0.222804	−	1.57661i	0.00861409	−	0.0609552i
$670$		0			0
$671$	−0.749513	+	1.29819i	−0.0289346	+	0.0501162i
$672$		0			0
$673$	−2.54758	−	4.41254i	−0.0982020	−	0.170091i	0.812738	−	0.582629i	$-0.197976\pi$
$673$	−2.54758	−	4.41254i	−0.0982020	−	0.170091i	−0.910940	+	0.412538i	$0.864642\pi$
$674$		0			0
$675$	18.9925	−	13.7326i	0.731022	−	0.528568i
$676$		0			0
$677$	16.8414			0.647269			0.323635	−	0.946182i	$-0.395095\pi$
$677$	16.8414			0.647269			0.323635	+	0.946182i	$0.395095\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−6.47998	−	16.0738i	−0.248313	−	0.615949i
$682$		0			0
$683$	15.7555	−	9.09645i	0.602868	−	0.348066i	−0.167301	−	0.985906i	$-0.553505\pi$
$683$	15.7555	−	9.09645i	0.602868	−	0.348066i	0.770169	+	0.637840i	$0.220172\pi$
$684$		0			0
$685$			1.88715i			0.0721042i
$686$		0			0
$687$	−0.666559	+	4.71672i	−0.0254308	+	0.179954i
$688$		0			0
$689$	−12.9290			−0.492557
$690$		0			0
$691$			3.52652i			0.134155i	0.997748	+	0.0670775i	$0.0213675\pi$
$691$			3.52652i			0.134155i	−0.997748	+	0.0670775i	$0.978633\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	8.19591i		−	0.310888i
$696$		0			0
$697$	40.2125			1.52316
$698$		0			0
$699$	10.3044	−	4.15412i	0.389749	−	0.157123i
$700$		0			0
$701$			13.3502i			0.504229i	0.967697	+	0.252114i	$0.0811259\pi$
$701$			13.3502i			0.504229i	−0.967697	+	0.252114i	$0.918874\pi$
$702$		0			0
$703$	−0.268574	+	0.155061i	−0.0101295	+	0.00584824i
$704$		0			0
$705$	8.40626	+	1.18796i	0.316598	+	0.0447411i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−42.2894			−1.58821			−0.794107	−	0.607779i	$-0.792061\pi$
$709$	−42.2894			−1.58821			−0.794107	+	0.607779i	$0.792061\pi$
$710$		0			0
$711$	−1.00749	−	4.06723i	−0.0377838	−	0.152533i
$712$		0			0
$713$	13.9166	+	24.1043i	0.521182	+	0.902715i
$714$		0			0
$715$	−0.121942	+	0.211210i	−0.00456038	+	0.00789881i
$716$		0			0
$717$	21.1998	−	8.54648i	0.791721	−	0.319174i
$718$		0			0
$719$	−15.2035	+	26.3332i	−0.566994	+	0.982062i	0.429868	+	0.902892i	$0.358560\pi$
$719$	−15.2035	+	26.3332i	−0.566994	+	0.982062i	−0.996861	+	0.0791697i	$0.974773\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−4.09426	+	1.65056i	−0.152267	+	0.0613849i
$724$		0			0
$725$			1.42335i			0.0528617i
$726$		0			0
$727$	11.3671	−	6.56280i	0.421583	−	0.243401i	−0.274171	−	0.961681i	$-0.588404\pi$
$727$	11.3671	−	6.56280i	0.421583	−	0.243401i	0.695754	+	0.718280i	$0.255070\pi$
$728$		0			0
$729$	17.9746	+	20.1473i	0.665724	+	0.746198i
$730$		0			0
$731$	−13.9097	+	24.0924i	−0.514470	+	0.891089i
$732$		0			0
$733$	32.7001	−	18.8794i	1.20781	−	0.697327i	0.245527	−	0.969390i	$-0.421039\pi$
$733$	32.7001	−	18.8794i	1.20781	−	0.697327i	0.962280	+	0.272063i	$0.0877058\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.36460	−	0.787853i	−0.0502657	−	0.0290209i
$738$		0			0
$739$	−13.1215	−	22.7271i	−0.482683	−	0.836031i	0.517119	−	0.855913i	$-0.327004\pi$
$739$	−13.1215	−	22.7271i	−0.482683	−	0.836031i	−0.999802	+	0.0198820i	$0.993671\pi$
$740$		0			0
$741$	0.995424	+	0.140672i	0.0365678	+	0.00516770i
$742$		0			0
$743$	−8.78379	−	5.07132i	−0.322246	−	0.186049i	0.330147	−	0.943929i	$-0.392902\pi$
$743$	−8.78379	−	5.07132i	−0.322246	−	0.186049i	−0.652393	+	0.757881i	$0.726235\pi$
$744$		0			0
$745$	−11.4082	−	6.58655i	−0.417966	−	0.241313i
$746$		0			0
$747$	16.0965	−	15.4969i	0.588941	−	0.567001i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−3.95369	−	6.84798i	−0.144272	−	0.249886i	0.784829	−	0.619712i	$-0.212751\pi$
$751$	−3.95369	−	6.84798i	−0.144272	−	0.249886i	−0.929101	+	0.369826i	$0.879417\pi$
$752$		0			0
$753$	20.0557	−	25.6298i	0.730870	−	0.934002i
$754$		0			0
$755$	6.99855			0.254703
$756$		0			0
$757$	29.8903			1.08638			0.543191	−	0.839609i	$-0.317216\pi$
$757$	29.8903			1.08638			0.543191	+	0.839609i	$0.317216\pi$
$758$		0			0
$759$	1.40545	−	1.79606i	0.0510144	−	0.0651930i
$760$		0			0
$761$	3.05687	+	5.29465i	0.110811	+	0.191931i	0.916098	−	0.400955i	$-0.131322\pi$
$761$	3.05687	+	5.29465i	0.110811	+	0.191931i	−0.805286	+	0.592886i	$0.797988\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−7.51820	−	2.16822i	−0.271821	−	0.0783922i
$766$		0			0
$767$	−15.3247	−	8.84771i	−0.553342	−	0.319472i
$768$		0			0
$769$	9.79863	+	5.65724i	0.353348	+	0.204005i	0.666159	−	0.745810i	$-0.267937\pi$
$769$	9.79863	+	5.65724i	0.353348	+	0.204005i	−0.312811	+	0.949815i	$0.601271\pi$
$770$		0			0
$771$	24.6868	+	3.48870i	0.889073	+	0.125642i
$772$		0			0
$773$	−19.2106	−	33.2737i	−0.690956	−	1.19677i	−0.971525	−	0.236937i	$-0.923856\pi$
$773$	−19.2106	−	33.2737i	−0.690956	−	1.19677i	0.280569	−	0.959834i	$-0.409477\pi$
$774$		0			0
$775$	−21.8994	−	12.6436i	−0.786648	−	0.454172i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4.12551	−	2.38186i	0.147812	−	0.0853391i
$780$		0			0
$781$	−1.78124	+	3.08519i	−0.0637376	+	0.110397i
$782$		0			0
$783$	−1.63112	+	0.167667i	−0.0582916	+	0.00599193i
$784$		0			0
$785$	−0.152730	+	0.0881788i	−0.00545117	+	0.00314723i
$786$		0			0
$787$			47.6600i			1.69889i	0.527674	+	0.849447i	$0.323064\pi$
$787$			47.6600i			1.69889i	−0.527674	+	0.849447i	$0.676936\pi$
$788$		0			0
$789$	−12.6100	+	5.08361i	−0.448930	+	0.180981i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	3.71430	−	6.43335i	0.131898	−	0.228455i
$794$		0			0
$795$	11.0564	−	4.45726i	0.392129	−	0.158083i
$796$		0			0
$797$	15.1359	−	26.2161i	0.536139	−	0.928621i	−0.462968	−	0.886375i	$-0.653215\pi$
$797$	15.1359	−	26.2161i	0.536139	−	0.928621i	0.999107	−	0.0422457i	$-0.0134512\pi$
$798$		0			0
$799$	13.0581	+	22.6172i	0.461961	+	0.800140i
$800$		0			0
$801$	32.2416	+	9.29836i	1.13920	+	0.328541i
$802$		0			0
$803$	2.04016			0.0719955
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−26.4889	−	3.74337i	−0.932454	−	0.131773i
$808$		0			0
$809$	0.219373	−	0.126655i	0.00771273	−	0.00445295i	−0.496139	−	0.868243i	$-0.665249\pi$
$809$	0.219373	−	0.126655i	0.00771273	−	0.00445295i	0.503851	+	0.863790i	$0.331916\pi$
$810$		0			0
$811$		−	22.0629i		−	0.774735i	−0.921925	−	0.387367i	$-0.873385\pi$
$811$		−	22.0629i		−	0.774735i	0.921925	−	0.387367i	$-0.126615\pi$
$812$		0			0
$813$	20.3070	−	8.18657i	0.712199	−	0.287116i
$814$		0			0
$815$	−6.01395			−0.210660
$816$		0			0
$817$			3.29560i			0.115298i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	27.9976i		−	0.977124i	−0.872529	−	0.488562i	$-0.837522\pi$
$821$		−	27.9976i		−	0.977124i	0.872529	−	0.488562i	$-0.162478\pi$
$822$		0			0
$823$	48.9542			1.70643			0.853217	−	0.521556i	$-0.174648\pi$
$823$	48.9542			1.70643			0.853217	+	0.521556i	$0.174648\pi$
$824$		0			0
$825$	−0.289928	+	2.05159i	−0.0100940	+	0.0714272i
$826$		0			0
$827$		−	0.641658i		−	0.0223126i	−0.999938	−	0.0111563i	$-0.996449\pi$
$827$		−	0.641658i		−	0.0223126i	0.999938	−	0.0111563i	$-0.00355124\pi$
$828$		0			0
$829$	−9.57180	+	5.52628i	−0.332442	+	0.191936i	−0.656925	−	0.753956i	$-0.728143\pi$
$829$	−9.57180	+	5.52628i	−0.332442	+	0.191936i	0.324483	+	0.945892i	$0.394810\pi$
$830$		0			0
$831$	7.70053	+	19.1014i	0.267128	+	0.662620i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	3.14057			0.108684
$836$		0			0
$837$	11.9096	−	26.5856i	0.411656	−	0.918932i
$838$		0			0
$839$	4.62330	+	8.00780i	0.159614	+	0.276460i	0.934730	−	0.355360i	$-0.115642\pi$
$839$	4.62330	+	8.00780i	0.159614	+	0.276460i	−0.775115	+	0.631820i	$0.782308\pi$
$840$		0			0
$841$	−14.4502	+	25.0285i	−0.498283	+	0.863052i
$842$		0			0
$843$	0.770756	−	5.45404i	0.0265462	−	0.187847i
$844$		0			0
$845$	−3.94346	+	6.83028i	−0.135659	+	0.234969i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	25.2321	+	19.7445i	0.865963	+	0.677629i
$850$		0			0
$851$		−	3.48640i		−	0.119512i
$852$		0			0
$853$	34.3256	−	19.8179i	1.17529	−	0.678551i	0.220366	−	0.975417i	$-0.429275\pi$
$853$	34.3256	−	19.8179i	1.17529	−	0.678551i	0.954919	+	0.296866i	$0.0959414\pi$
$854$		0			0
$855$	−0.899740	+	0.222874i	−0.0307705	+	0.00762212i
$856$		0			0
$857$	11.9260	−	20.6565i	0.407385	−	0.705612i	−0.587211	−	0.809434i	$-0.699774\pi$
$857$	11.9260	−	20.6565i	0.407385	−	0.705612i	0.994596	+	0.103822i	$0.0331074\pi$
$858$		0			0
$859$	9.62480	−	5.55688i	0.328394	−	0.189598i	−0.326734	−	0.945116i	$-0.605948\pi$
$859$	9.62480	−	5.55688i	0.328394	−	0.189598i	0.655128	+	0.755518i	$0.272615\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−38.7780	−	22.3885i	−1.32002	−	0.762113i	−0.336287	−	0.941759i	$-0.609171\pi$
$863$	−38.7780	−	22.3885i	−1.32002	−	0.762113i	−0.983731	+	0.179646i	$0.942505\pi$
$864$		0			0
$865$	−2.49128	−	4.31503i	−0.0847061	−	0.146715i
$866$		0			0
$867$	2.00968	+	4.98508i	0.0682525	+	0.169302i
$868$		0			0
$869$	0.320805	+	0.185217i	0.0108826	+	0.00628305i
$870$		0			0
$871$	6.76244	+	3.90429i	0.229136	+	0.132292i
$872$		0			0
$873$	−22.0610	−	22.9146i	−0.746650	−	0.775542i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.84096	−	3.18863i	−0.0621647	−	0.107672i	0.833268	−	0.552869i	$-0.186467\pi$
$877$	−1.84096	−	3.18863i	−0.0621647	−	0.107672i	−0.895433	+	0.445197i	$0.853134\pi$
$878$		0			0
$879$	1.85184	+	4.59355i	0.0624611	+	0.154937i
$880$		0			0
$881$	−17.3992			−0.586194			−0.293097	−	0.956083i	$-0.594686\pi$
$881$	−17.3992			−0.586194			−0.293097	+	0.956083i	$0.594686\pi$
$882$		0			0
$883$	−2.02834			−0.0682592			−0.0341296	−	0.999417i	$-0.510866\pi$
$883$	−2.02834			−0.0682592			−0.0341296	+	0.999417i	$0.510866\pi$
$884$		0			0
$885$	16.1552	+	2.28303i	0.543052	+	0.0767433i
$886$		0			0
$887$	−23.1890	−	40.1645i	−0.778610	−	1.34859i	−0.932743	−	0.360542i	$-0.882592\pi$
$887$	−23.1890	−	40.1645i	−0.778610	−	1.34859i	0.154132	−	0.988050i	$-0.450742\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−2.38523	−	0.0905779i	−0.0799083	−	0.00303447i
$892$		0			0
$893$	2.67932	+	1.54691i	0.0896601	+	0.0517653i
$894$		0			0
$895$	−15.4812	−	8.93810i	−0.517481	−	0.298768i
$896$		0			0
$897$	−6.96484	+	8.90060i	−0.232549	+	0.297182i
$898$		0			0
$899$	0.884576	+	1.53213i	0.0295023	+	0.0510994i
$900$		0			0
$901$	31.7582	+	18.3356i	1.05802	+	0.610847i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.571488	+	0.329949i	−0.0189969	+	0.0109679i
$906$		0			0
$907$	−8.01957	+	13.8903i	−0.266285	+	0.461220i	−0.967900	−	0.251337i	$-0.919130\pi$
$907$	−8.01957	+	13.8903i	−0.266285	+	0.461220i	0.701614	+	0.712557i	$0.252463\pi$
$908$		0			0
$909$	50.4647	+	14.5538i	1.67381	+	0.482720i
$910$		0			0
$911$	17.7833	−	10.2672i	0.589187	−	0.340167i	−0.175589	−	0.984464i	$-0.556183\pi$
$911$	17.7833	−	10.2672i	0.589187	−	0.340167i	0.764776	+	0.644296i	$0.222850\pi$
$912$		0			0
$913$			1.97533i			0.0653739i
$914$		0			0
$915$	−0.958424	+	6.78202i	−0.0316845	+	0.224207i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−17.7069	+	30.6693i	−0.584097	+	1.01169i	0.410890	+	0.911685i	$0.365218\pi$
$919$	−17.7069	+	30.6693i	−0.584097	+	1.01169i	−0.994987	+	0.100001i	$0.968115\pi$
$920$		0			0
$921$	−29.5655	−	23.1354i	−0.974216	−	0.762338i
$922$		0			0
$923$	8.82712	−	15.2890i	0.290548	−	0.503244i
$924$		0			0
$925$	1.58374	+	2.74311i	0.0520730	+	0.0901930i
$926$		0			0
$927$	17.7736	+	18.4613i	0.583761	+	0.606350i
$928$		0			0
$929$	39.7251			1.30334			0.651670	−	0.758503i	$-0.274069\pi$
$929$	39.7251			1.30334			0.651670	+	0.758503i	$0.274069\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−25.2893	+	32.3180i	−0.827933	+	1.05804i
$934$		0			0
$935$	0.599064	−	0.345870i	0.0195915	−	0.0113112i
$936$		0			0
$937$		−	23.2142i		−	0.758376i	−0.925320	−	0.379188i	$-0.876203\pi$
$937$		−	23.2142i		−	0.758376i	0.925320	−	0.379188i	$-0.123797\pi$
$938$		0			0
$939$	37.2165	+	29.1225i	1.21452	+	0.950376i
$940$		0			0
$941$	35.9232			1.17106			0.585531	−	0.810650i	$-0.300886\pi$
$941$	35.9232			1.17106			0.585531	+	0.810650i	$0.300886\pi$
$942$		0			0
$943$			53.5539i			1.74395i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			30.8726i			1.00322i	0.865093	+	0.501612i	$0.167260\pi$
$947$			30.8726i			1.00322i	−0.865093	+	0.501612i	$0.832740\pi$
$948$		0			0
$949$	−10.1102			−0.328192
$950$		0			0
$951$	−33.4937	−	26.2093i	−1.08611	−	0.849894i
$952$		0			0
$953$		−	30.4640i		−	0.986826i	−0.869795	−	0.493413i	$-0.835749\pi$
$953$		−	30.4640i		−	0.986826i	0.869795	−	0.493413i	$-0.164251\pi$
$954$		0			0
$955$	1.80100	−	1.03981i	0.0582791	−	0.0336475i
$956$		0			0
$957$	0.0893336	−	0.114162i	0.00288774	−	0.00369034i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.430813			−0.0138972
$962$		0			0
$963$	8.73029	−	30.2719i	0.281330	−	0.975497i
$964$		0			0
$965$	6.47686	+	11.2182i	0.208497	+	0.361128i
$966$		0			0
$967$	−6.75865	+	11.7063i	−0.217343	+	0.376450i	−0.953995	−	0.299823i	$-0.903072\pi$
$967$	−6.75865	+	11.7063i	−0.217343	+	0.376450i	0.736652	+	0.676272i	$0.236406\pi$
$968$		0			0
$969$	−2.24561	−	1.75722i	−0.0721393	−	0.0564500i
$970$		0			0
$971$	−16.6428	+	28.8261i	−0.534092	+	0.925074i	0.465115	+	0.885250i	$0.346013\pi$
$971$	−16.6428	+	28.8261i	−0.534092	+	0.925074i	−0.999207	+	0.0398238i	$0.987320\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	1.43677	−	10.1669i	0.0460134	−	0.325601i
$976$		0			0
$977$			44.9325i			1.43752i	0.695260	+	0.718758i	$0.255289\pi$
$977$			44.9325i			1.43752i	−0.695260	+	0.718758i	$0.744711\pi$
$978$		0			0
$979$	−2.56907	+	1.48325i	−0.0821079	+	0.0474050i
$980$		0			0
$981$	−30.7802	+	29.6335i	−0.982736	+	0.946125i
$982$		0			0
$983$	13.4474	−	23.2916i	0.428907	−	0.742888i	−0.567870	−	0.823118i	$-0.692232\pi$
$983$	13.4474	−	23.2916i	0.428907	−	0.742888i	0.996776	+	0.0802305i	$0.0255656\pi$
$984$		0			0
$985$	8.59035	−	4.95964i	0.273711	−	0.158027i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−32.0855	−	18.5246i	−1.02026	−	0.589048i
$990$		0			0
$991$	17.7201	+	30.6920i	0.562896	+	0.974965i	0.997242	+	0.0742186i	$0.0236463\pi$
$991$	17.7201	+	30.6920i	0.562896	+	0.974965i	−0.434346	+	0.900746i	$0.643020\pi$
$992$		0			0
$993$	−17.4109	+	22.2500i	−0.552520	+	0.706082i
$994$		0			0
$995$	−14.3635	−	8.29275i	−0.455352	−	0.262898i
$996$		0			0
$997$	28.1418	+	16.2477i	0.891259	+	0.514568i	0.874354	−	0.485289i	$-0.161286\pi$
$997$	28.1418	+	16.2477i	0.891259	+	0.514568i	0.0169046	+	0.999857i	$0.494619\pi$
$998$		0			0
$999$	−2.95699	+	2.13806i	−0.0935550	+	0.0676453i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.w.b.509.3		16
3.2	odd	2		5292.2.w.b.1097.5		16
7.2	even	3		1764.2.x.b.293.3		16
7.3	odd	6		1764.2.bm.a.1697.1		16
7.4	even	3		252.2.bm.a.185.8	yes	16
7.5	odd	6		1764.2.x.a.293.6		16
7.6	odd	2		252.2.w.a.5.6	✓	16
9.2	odd	6		1764.2.bm.a.1685.1		16
9.7	even	3		5292.2.bm.a.4625.5		16
21.2	odd	6		5292.2.x.b.881.5		16
21.5	even	6		5292.2.x.a.881.4		16
21.11	odd	6		756.2.bm.a.17.4		16
21.17	even	6		5292.2.bm.a.2285.5		16
21.20	even	2		756.2.w.a.341.4		16
28.11	odd	6		1008.2.df.d.689.1		16
28.27	even	2		1008.2.ca.d.257.3		16
63.2	odd	6		1764.2.x.a.1469.6		16
63.4	even	3		2268.2.t.a.1781.4		16
63.11	odd	6		252.2.w.a.101.6	yes	16
63.13	odd	6		2268.2.t.b.2105.5		16
63.16	even	3		5292.2.x.a.4409.4		16
63.20	even	6		252.2.bm.a.173.8	yes	16
63.25	even	3		756.2.w.a.521.4		16
63.32	odd	6		2268.2.t.b.1781.5		16
63.34	odd	6		756.2.bm.a.89.4		16
63.38	even	6	inner	1764.2.w.b.1109.3		16
63.41	even	6		2268.2.t.a.2105.4		16
63.47	even	6		1764.2.x.b.1469.3		16
63.52	odd	6		5292.2.w.b.521.5		16
63.61	odd	6		5292.2.x.b.4409.5		16
84.11	even	6		3024.2.df.d.17.4		16
84.83	odd	2		3024.2.ca.d.2609.4		16
252.11	even	6		1008.2.ca.d.353.3		16
252.83	odd	6		1008.2.df.d.929.1		16
252.151	odd	6		3024.2.ca.d.2033.4		16
252.223	even	6		3024.2.df.d.1601.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.6	✓	16	7.6	odd	2
252.2.w.a.101.6	yes	16	63.11	odd	6
252.2.bm.a.173.8	yes	16	63.20	even	6
252.2.bm.a.185.8	yes	16	7.4	even	3
756.2.w.a.341.4		16	21.20	even	2
756.2.w.a.521.4		16	63.25	even	3
756.2.bm.a.17.4		16	21.11	odd	6
756.2.bm.a.89.4		16	63.34	odd	6
1008.2.ca.d.257.3		16	28.27	even	2
1008.2.ca.d.353.3		16	252.11	even	6
1008.2.df.d.689.1		16	28.11	odd	6
1008.2.df.d.929.1		16	252.83	odd	6
1764.2.w.b.509.3		16	1.1	even	1	trivial
1764.2.w.b.1109.3		16	63.38	even	6	inner
1764.2.x.a.293.6		16	7.5	odd	6
1764.2.x.a.1469.6		16	63.2	odd	6
1764.2.x.b.293.3		16	7.2	even	3
1764.2.x.b.1469.3		16	63.47	even	6
1764.2.bm.a.1685.1		16	9.2	odd	6
1764.2.bm.a.1697.1		16	7.3	odd	6
2268.2.t.a.1781.4		16	63.4	even	3
2268.2.t.a.2105.4		16	63.41	even	6
2268.2.t.b.1781.5		16	63.32	odd	6
2268.2.t.b.2105.5		16	63.13	odd	6
3024.2.ca.d.2033.4		16	252.151	odd	6
3024.2.ca.d.2609.4		16	84.83	odd	2
3024.2.df.d.17.4		16	84.11	even	6
3024.2.df.d.1601.4		16	252.223	even	6
5292.2.w.b.521.5		16	63.52	odd	6
5292.2.w.b.1097.5		16	3.2	odd	2
5292.2.x.a.881.4		16	21.5	even	6
5292.2.x.a.4409.4		16	63.16	even	3
5292.2.x.b.881.5		16	21.2	odd	6
5292.2.x.b.4409.5		16	63.61	odd	6
5292.2.bm.a.2285.5		16	21.17	even	6
5292.2.bm.a.4625.5		16	9.7	even	3

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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.06740 + 1.36406i) q^{3} +(-0.349828 - 0.605920i) q^{5} +(-0.721326 - 2.91199i) q^{9} +O(q^{10})\)	\(q+(-1.06740 + 1.36406i) q^{3} +(-0.349828 - 0.605920i) q^{5} +(-0.721326 - 2.91199i) q^{9} +(0.229685 + 0.132608i) q^{11} +(-1.13823 - 0.657156i) q^{13} +(1.19992 + 0.169570i) q^{15} +(1.86392 + 3.22840i) q^{17} +(0.382449 + 0.220807i) q^{19} +(-4.29949 + 2.48231i) q^{23} +(2.25524 - 3.90619i) q^{25} +(4.74208 + 2.12432i) q^{27} +(-0.273287 + 0.157782i) q^{29} -5.60632i q^{31} +(-0.426051 + 0.171758i) q^{33} +(-0.351124 + 0.608164i) q^{37} +(2.11134 - 0.851166i) q^{39} +(5.39354 - 9.34189i) q^{41} +(3.73131 + 6.46283i) q^{43} +(-1.51209 + 1.45576i) q^{45} +7.00570 q^{47} +(-6.39328 - 0.903488i) q^{51} +(8.51919 - 4.91856i) q^{53} -0.185561i q^{55} +(-0.709419 + 0.285995i) q^{57} +13.4636 q^{59} +5.65207i q^{61} +0.919566i q^{65} -5.94120 q^{67} +(1.20324 - 8.51439i) q^{69} +13.4323i q^{71} +(6.66182 - 3.84620i) q^{73} +(2.92105 + 7.24575i) q^{75} +1.39672 q^{79} +(-7.95938 + 4.20099i) q^{81} +(3.72399 + 6.45014i) q^{83} +(1.30410 - 2.25877i) q^{85} +(0.0764809 - 0.541196i) q^{87} +(-5.59261 + 9.68668i) q^{89} +(7.64736 + 5.98417i) q^{93} -0.308978i q^{95} +(9.18225 - 5.30138i) q^{97} +(0.220477 - 0.764493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{9}+O(q^{10}) \) 16 * q + 6 * q^9	\( 16 q + 6 q^{9} - 6 q^{11} + 3 q^{13} - 3 q^{15} - 9 q^{17} + 21 q^{23} - 8 q^{25} - 9 q^{27} + 6 q^{29} + q^{37} - 3 q^{39} + 6 q^{41} - 2 q^{43} + 30 q^{45} + 36 q^{47} - 33 q^{51} + 15 q^{57} + 30 q^{59} + 14 q^{67} - 21 q^{69} + 57 q^{75} + 2 q^{79} + 18 q^{81} + 6 q^{85} - 48 q^{87} - 21 q^{89} + 21 q^{93} + 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q + 6 * q^9 - 6 * q^11 + 3 * q^13 - 3 * q^15 - 9 * q^17 + 21 * q^23 - 8 * q^25 - 9 * q^27 + 6 * q^29 + q^37 - 3 * q^39 + 6 * q^41 - 2 * q^43 + 30 * q^45 + 36 * q^47 - 33 * q^51 + 15 * q^57 + 30 * q^59 + 14 * q^67 - 21 * q^69 + 57 * q^75 + 2 * q^79 + 18 * q^81 + 6 * q^85 - 48 * q^87 - 21 * q^89 + 21 * q^93 + 3 * q^97 - 9 * q^99

Introduction

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