LMFDB - Embedded newform 1764.2.bm.a.1697.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1685,1764)]

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, 1, 5]))

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

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

chi := DirichletCharacter("1764.1685");

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.bm (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			1697.1
Root			$1.68124 + 0.416458i$ of defining polynomial
Character	$\chi$	$=$	1764.1697
Dual form			1764.2.bm.a.1685.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71501 - 0.242362i) q^{3} -0.699656 q^{5} +(2.88252 + 0.831308i) q^{9} +O(q^{10})$	\(q+(-1.71501 - 0.242362i) q^{3} -0.699656 q^{5} +(2.88252 + 0.831308i) q^{9} -0.265217i q^{11} +(1.13823 + 0.657156i) q^{13} +(1.19992 + 0.169570i) q^{15} +(-1.86392 + 3.22840i) q^{17} +(0.382449 - 0.220807i) q^{19} -4.96463i q^{23} -4.51048 q^{25} +(-4.74208 - 2.12432i) q^{27} +(-0.273287 + 0.157782i) q^{29} +(4.85521 - 2.80316i) q^{31} +(-0.0642786 + 0.454850i) q^{33} +(-0.351124 - 0.608164i) q^{37} +(-1.79280 - 1.40289i) q^{39} +(-5.39354 + 9.34189i) q^{41} +(3.73131 + 6.46283i) q^{43} +(-2.01677 - 0.581630i) q^{45} +(3.50285 - 6.06712i) q^{47} +(3.97908 - 5.08500i) q^{51} +(-8.51919 - 4.91856i) q^{53} +0.185561i q^{55} +(-0.709419 + 0.285995i) q^{57} +(6.73182 + 11.6598i) q^{59} +(4.89484 + 2.82604i) q^{61} +(-0.796368 - 0.459783i) q^{65} +(2.97060 + 5.14523i) q^{67} +(-1.20324 + 8.51439i) q^{69} +13.4323i q^{71} +(6.66182 + 3.84620i) q^{73} +(7.73552 + 1.09317i) q^{75} +(-0.698360 + 1.20959i) q^{79} +(7.61785 + 4.79253i) q^{81} +(-3.72399 - 6.45014i) q^{83} +(1.30410 - 2.25877i) q^{85} +(0.506930 - 0.204363i) q^{87} +(5.59261 + 9.68668i) q^{89} +(-9.00612 + 3.63073i) q^{93} +(-0.267582 + 0.154489i) q^{95} +(-9.18225 + 5.30138i) q^{97} +(0.220477 - 0.764493i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 3 q^{13} - 3 q^{15} + 9 q^{17} + 16 q^{25} + 9 q^{27} + 6 q^{29} - 6 q^{31} + 27 q^{33} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{51} + 15 q^{57} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} + 21 q^{69} + 15 q^{75} - q^{79} + 6 q^{85} + 3 q^{87} + 21 q^{89} - 69 q^{93} + 6 q^{95} - 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q - 3 * q^13 - 3 * q^15 + 9 * q^17 + 16 * q^25 + 9 * q^27 + 6 * q^29 - 6 * q^31 + 27 * q^33 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^51 + 15 * q^57 + 15 * q^59 - 3 * q^61 - 39 * q^65 - 7 * q^67 + 21 * q^69 + 15 * q^75 - q^79 + 6 * q^85 + 3 * q^87 + 21 * q^89 - 69 * q^93 + 6 * q^95 - 3 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.71501	−	0.242362i	−0.990162	−	0.139928i
$3$	−1.71501	−	0.242362i	−0.990162	−	0.139928i
$4$		0			0
$5$	−0.699656			−0.312896			−0.156448	−	0.987686i	$-0.550004\pi$
$5$	−0.699656			−0.312896			−0.156448	+	0.987686i	$0.550004\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	2.88252	+	0.831308i	0.960840	+	0.277103i
$10$		0			0
$11$		−	0.265217i		−	0.0799659i	−0.999200	−	0.0399829i	$-0.987270\pi$
$11$		−	0.265217i		−	0.0799659i	0.999200	−	0.0399829i	$-0.0127304\pi$
$12$		0			0
$13$	1.13823	+	0.657156i	0.315688	+	0.182262i	0.649469	−	0.760388i	$-0.274991\pi$
$13$	1.13823	+	0.657156i	0.315688	+	0.182262i	−0.333781	+	0.942651i	$0.608325\pi$
$14$		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	$-0.982646\pi$
$17$	−1.86392	+	3.22840i	−0.452067	+	0.783003i	0.546447	+	0.837493i	$0.315980\pi$
$18$		0			0
$19$	0.382449	−	0.220807i	0.0877398	−	0.0506566i	−0.455488	−	0.890242i	$-0.650535\pi$
$19$	0.382449	−	0.220807i	0.0877398	−	0.0506566i	0.543228	+	0.839585i	$0.317202\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	4.96463i		−	1.03520i	−0.855624	−	0.517598i	$-0.826826\pi$
$23$		−	4.96463i		−	1.03520i	0.855624	−	0.517598i	$-0.173174\pi$
$24$		0			0
$25$	−4.51048			−0.902096
$26$		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
$31$	4.85521	−	2.80316i	0.872022	−	0.503462i	0.00400255	−	0.999992i	$-0.498726\pi$
$31$	4.85521	−	2.80316i	0.872022	−	0.503462i	0.868020	+	0.496530i	$0.165393\pi$
$32$		0			0
$33$	−0.0642786	+	0.454850i	−0.0111895	+	0.0791792i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.351124	−	0.608164i	−0.0577244	−	0.0999816i	0.835719	−	0.549157i	$-0.185051\pi$
$37$	−0.351124	−	0.608164i	−0.0577244	−	0.0999816i	−0.893444	+	0.449175i	$0.851718\pi$
$38$		0			0
$39$	−1.79280	−	1.40289i	−0.287078	−	0.224643i
$40$		0			0
$41$	−5.39354	+	9.34189i	−0.842330	+	1.45896i	0.0455900	+	0.998960i	$0.485483\pi$
$41$	−5.39354	+	9.34189i	−0.842330	+	1.45896i	−0.887920	+	0.459998i	$0.847850\pi$
$42$		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
$45$	−2.01677	−	0.581630i	−0.300643	−	0.0867042i
$46$		0			0
$47$	3.50285	−	6.06712i	0.510943	−	0.884980i	−0.488976	−	0.872297i	$-0.662630\pi$
$47$	3.50285	−	6.06712i	0.510943	−	0.884980i	0.999920	−	0.0126827i	$-0.00403713\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	3.97908	−	5.08500i	0.557183	−	0.712043i
$52$		0			0
$53$	−8.51919	−	4.91856i	−1.17020	−	0.675616i	−0.216474	−	0.976288i	$-0.569456\pi$
$53$	−8.51919	−	4.91856i	−1.17020	−	0.675616i	−0.953727	+	0.300672i	$0.902789\pi$
$54$		0			0
$55$			0.185561i			0.0250210i
$56$		0			0
$57$	−0.709419	+	0.285995i	−0.0939648	+	0.0378809i
$58$		0			0
$59$	6.73182	+	11.6598i	0.876408	+	1.51798i	0.855256	+	0.518206i	$0.173400\pi$
$59$	6.73182	+	11.6598i	0.876408	+	1.51798i	0.0211522	+	0.999776i	$0.493267\pi$
$60$		0			0
$61$	4.89484	+	2.82604i	0.626720	+	0.361837i	0.779481	−	0.626426i	$-0.215483\pi$
$61$	4.89484	+	2.82604i	0.626720	+	0.361837i	−0.152761	+	0.988263i	$0.548816\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.796368	−	0.459783i	−0.0987773	−	0.0570291i
$66$		0			0
$67$	2.97060	+	5.14523i	0.362916	+	0.628590i	0.988439	−	0.151616i	$-0.0484477\pi$
$67$	2.97060	+	5.14523i	0.362916	+	0.628590i	−0.625523	+	0.780206i	$0.715114\pi$
$68$		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	0.836326	−	0.548232i	$-0.184699\pi$
$73$	6.66182	+	3.84620i	0.779707	+	0.450164i	−0.0566194	+	0.998396i	$0.518032\pi$
$74$		0			0
$75$	7.73552	+	1.09317i	0.893221	+	0.126229i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.698360	+	1.20959i	−0.0785716	+	0.136090i	−0.902634	−	0.430409i	$-0.858369\pi$
$79$	−0.698360	+	1.20959i	−0.0785716	+	0.136090i	0.824062	+	0.566499i	$0.191703\pi$
$80$		0			0
$81$	7.61785	+	4.79253i	0.846428	+	0.532503i
$82$		0			0
$83$	−3.72399	−	6.45014i	−0.408761	−	0.707995i	0.585990	−	0.810318i	$-0.300706\pi$
$83$	−3.72399	−	6.45014i	−0.408761	−	0.707995i	−0.994751	+	0.102323i	$0.967372\pi$
$84$		0			0
$85$	1.30410	−	2.25877i	0.141450	−	0.244998i
$86$		0			0
$87$	0.506930	−	0.204363i	0.0543486	−	0.0219101i
$88$		0			0
$89$	5.59261	+	9.68668i	0.592815	+	1.02679i	0.993851	+	0.110724i	$0.0353168\pi$
$89$	5.59261	+	9.68668i	0.592815	+	1.02679i	−0.401036	+	0.916062i	$0.631350\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−9.00612	+	3.63073i	−0.933892	+	0.376489i
$94$		0			0
$95$	−0.267582	+	0.154489i	−0.0274534	+	0.0158502i
$96$		0			0
$97$	−9.18225	+	5.30138i	−0.932316	+	0.538273i	−0.887543	−	0.460724i	$-0.847590\pi$
$97$	−9.18225	+	5.30138i	−0.932316	+	0.538273i	−0.0447729	+	0.998997i	$0.514256\pi$
$98$		0			0
$99$	0.220477	−	0.764493i	0.0221588	−	0.0768345i
$100$		0			0
$101$	−17.5071			−1.74203			−0.871013	−	0.491260i	$-0.836537\pi$
$101$	−17.5071			−1.74203			−0.871013	+	0.491260i	$0.836537\pi$
$102$		0			0
$103$			8.54219i			0.841687i	0.907133	+	0.420844i	$0.138266\pi$
$103$			8.54219i			0.841687i	−0.907133	+	0.420844i	$0.861734\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.09489	+	5.25093i	−0.879236	+	0.507627i	−0.870406	−	0.492334i	$-0.836144\pi$
$107$	−9.09489	+	5.25093i	−0.879236	+	0.507627i	−0.00882940	+	0.999961i	$0.502811\pi$
$108$		0			0
$109$	−7.12110	+	12.3341i	−0.682078	+	1.18139i	0.292268	+	0.956337i	$0.405590\pi$
$109$	−7.12110	+	12.3341i	−0.682078	+	1.18139i	−0.974346	+	0.225057i	$0.927743\pi$
$110$		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
$115$			3.47353i			0.323908i
$116$		0			0
$117$	2.73467	+	2.84048i	0.252820	+	0.262603i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	10.9297			0.993605
$122$		0			0
$123$	11.5141	−	14.7142i	1.03819	−	1.32674i
$124$		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
$129$	−4.83290	−	11.9881i	−0.425513	−	1.05550i
$130$		0			0
$131$	−5.20922			−0.455132			−0.227566	−	0.973763i	$-0.573077\pi$
$131$	−5.20922			−0.455132			−0.227566	+	0.973763i	$0.573077\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	3.31782	+	1.48629i	0.285552	+	0.127920i
$136$		0			0
$137$			2.69725i			0.230442i	0.993340	+	0.115221i	$0.0367576\pi$
$137$			2.69725i			0.230442i	−0.993340	+	0.115221i	$0.963242\pi$
$138$		0			0
$139$	−10.1448	−	5.85710i	−0.860470	−	0.496793i	0.00369951	−	0.999993i	$-0.498822\pi$
$139$	−10.1448	−	5.85710i	−0.860470	−	0.496793i	−0.864170	+	0.503200i	$0.832156\pi$
$140$		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
$149$			18.8280i			1.54245i	0.636564	+	0.771224i	$0.280355\pi$
$149$			18.8280i			1.54245i	−0.636564	+	0.771224i	$0.719645\pi$
$150$		0			0
$151$	10.0029			0.814021			0.407010	−	0.913424i	$-0.366571\pi$
$151$	10.0029			0.814021			0.407010	+	0.913424i	$0.366571\pi$
$152$		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
$157$	0.218293	−	0.126032i	0.0174217	−	0.0100584i	−0.491264	−	0.871011i	$-0.663465\pi$
$157$	0.218293	−	0.126032i	0.0174217	−	0.0100584i	0.508686	+	0.860952i	$0.330132\pi$
$158$		0			0
$159$	13.4184	+	10.5001i	1.06415	+	0.832713i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	4.29780	+	7.44400i	0.336629	+	0.583059i	0.983796	−	0.179289i	$-0.0573797\pi$
$163$	4.29780	+	7.44400i	0.336629	+	0.583059i	−0.647167	+	0.762348i	$0.724046\pi$
$164$		0			0
$165$	0.0449729	−	0.318238i	0.00350114	−	0.0247748i
$166$		0			0
$167$	2.24437	−	3.88736i	0.173674	−	0.300813i	−0.766027	−	0.642808i	$-0.777769\pi$
$167$	2.24437	−	3.88736i	0.173674	−	0.300813i	0.939702	+	0.341995i	$0.111103\pi$
$168$		0			0
$169$	−5.63629	−	9.76234i	−0.433561	−	0.750949i
$170$		0			0
$171$	1.28598	−	0.318548i	0.0983410	−	0.0243599i
$172$		0			0
$173$	3.56072	−	6.16736i	0.270717	−	0.468895i	−0.698329	−	0.715777i	$-0.746073\pi$
$173$	3.56072	−	6.16736i	0.270717	−	0.468895i	0.969046	+	0.246882i	$0.0794060\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−8.71922	−	21.6283i	−0.655377	−	1.62568i
$178$		0			0
$179$	−22.1270	−	12.7750i	−1.65385	−	0.954848i	−0.975470	−	0.220134i	$-0.929351\pi$
$179$	−22.1270	−	12.7750i	−1.65385	−	0.954848i	−0.678376	−	0.734715i	$-0.737316\pi$
$180$		0			0
$181$			0.943175i			0.0701057i	0.999385	+	0.0350528i	$0.0111599\pi$
$181$			0.943175i			0.0701057i	−0.999385	+	0.0350528i	$0.988840\pi$
$182$		0			0
$183$	−7.70977	−	6.03301i	−0.569923	−	0.445973i
$184$		0			0
$185$	0.245666	+	0.425506i	0.0180617	+	0.0312838i
$186$		0			0
$187$	0.856227	+	0.494343i	0.0626135	+	0.0361499i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.57413	−	1.48617i	−0.186258	−	0.107536i	0.403972	−	0.914771i	$-0.367629\pi$
$191$	−2.57413	−	1.48617i	−0.186258	−	0.107536i	−0.590229	+	0.807236i	$0.700963\pi$
$192$		0			0
$193$	9.25721	+	16.0340i	0.666348	+	1.15415i	0.978918	+	0.204254i	$0.0654769\pi$
$193$	9.25721	+	16.0340i	0.666348	+	1.15415i	−0.312570	+	0.949895i	$0.601190\pi$
$194$		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	0.998774	−	0.0495081i	$-0.0157654\pi$
$199$	20.5293	+	11.8526i	1.45529	+	0.840209i	0.456512	+	0.889717i	$0.349099\pi$
$200$		0			0
$201$	−3.84760	−	9.54408i	−0.271389	−	0.673187i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	3.77362	−	6.53611i	0.263561	−	0.456502i
$206$		0			0
$207$	4.12714	−	14.3106i	0.286856	−	0.994659i
$208$		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
$213$	3.25549	−	23.0365i	0.223062	−	1.57844i
$214$		0			0
$215$	−2.61063	−	4.52175i	−0.178044	−	0.308381i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−10.4929	−	8.21085i	−0.709045	−	0.554838i
$220$		0			0
$221$	−4.24313	+	2.44977i	−0.285424	+	0.164790i
$222$		0			0
$223$	0.796137	−	0.459650i	0.0533133	−	0.0307804i	−0.473106	−	0.881005i	$-0.656867\pi$
$223$	0.796137	−	0.459650i	0.0533133	−	0.0307804i	0.526420	+	0.850225i	$0.323534\pi$
$224$		0			0
$225$	−13.0016	−	3.74960i	−0.866771	−	0.249973i
$226$		0			0
$227$	−10.0059			−0.664118			−0.332059	−	0.943259i	$-0.607743\pi$
$227$	−10.0059			−0.664118			−0.332059	+	0.943259i	$0.607743\pi$
$228$		0			0
$229$		−	2.75025i		−	0.181742i	−0.995863	−	0.0908710i	$-0.971035\pi$
$229$		−	2.75025i		−	0.181742i	0.995863	−	0.0908710i	$-0.0289651\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.55513	−	3.20725i	0.363928	−	0.210114i	−0.306874	−	0.951750i	$-0.599283\pi$
$233$	5.55513	−	3.20725i	0.363928	−	0.210114i	0.670803	+	0.741636i	$0.265950\pi$
$234$		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
$241$			2.54868i			0.164175i	0.996625	+	0.0820874i	$0.0261587\pi$
$241$			2.54868i			0.164175i	−0.996625	+	0.0820874i	$0.973841\pi$
$242$		0			0
$243$	−11.9032	−	10.0655i	−0.763589	−	0.645703i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.580418			0.0369311
$248$		0			0
$249$	4.82341	+	11.9646i	0.305671	+	0.758227i
$250$		0			0
$251$	18.7893			1.18597			0.592986	−	0.805213i	$-0.297949\pi$
$251$	18.7893			1.18597			0.592986	+	0.805213i	$0.297949\pi$
$252$		0			0
$253$	−1.31670			−0.0827804
$254$		0			0
$255$	−2.78399	+	3.55775i	−0.174340	+	0.222795i
$256$		0			0
$257$	−14.3945			−0.897907			−0.448953	−	0.893555i	$-0.648203\pi$
$257$	−14.3945			−0.897907			−0.448953	+	0.893555i	$0.648203\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.918920	+	0.227625i	−0.0568797	+	0.0140896i
$262$		0			0
$263$		−	7.84976i		−	0.484037i	−0.970272	−	0.242019i	$-0.922190\pi$
$263$		−	7.84976i		−	0.484037i	0.970272	−	0.242019i	$-0.0778095\pi$
$264$		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	$-0.989389\pi$
$269$	−7.72267	+	13.3760i	−0.470859	+	0.815552i	0.528585	+	0.848880i	$0.322723\pi$
$270$		0			0
$271$	−10.9476	+	6.32057i	−0.665016	+	0.383947i	−0.794186	−	0.607675i	$-0.792102\pi$
$271$	−10.9476	+	6.32057i	−0.665016	+	0.383947i	0.129169	+	0.991623i	$0.458769\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			1.19626i			0.0721369i
$276$		0			0
$277$	−11.8906			−0.714439			−0.357219	−	0.934021i	$-0.616275\pi$
$277$	−11.8906			−0.714439			−0.357219	+	0.934021i	$0.616275\pi$
$278$		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
$283$	16.0195	−	9.24889i	0.952263	−	0.549789i	0.0584799	−	0.998289i	$-0.481375\pi$
$283$	16.0195	−	9.24889i	0.952263	−	0.549789i	0.893783	+	0.448499i	$0.148041\pi$
$284$		0			0
$285$	0.496349	−	0.200098i	0.0294012	−	0.0118528i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	1.55161	+	2.68746i	0.0912711	+	0.158086i
$290$		0			0
$291$	17.0325	−	6.86648i	0.998463	−	0.402520i
$292$		0			0
$293$	−1.42975	+	2.47639i	−0.0835266	+	0.144672i	−0.904762	−	0.425917i	$-0.859952\pi$
$293$	−1.42975	+	2.47639i	−0.0835266	+	0.144672i	0.821236	+	0.570589i	$0.193285\pi$
$294$		0			0
$295$	−4.70995	−	8.15788i	−0.274224	−	0.474970i
$296$		0			0
$297$	−0.563405	+	1.25768i	−0.0326921	+	0.0729779i
$298$		0			0
$299$	3.26254	−	5.65088i	0.188677	−	0.326799i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	30.0249	+	4.24308i	1.72489	+	0.243758i
$304$		0			0
$305$	−3.42470	−	1.97725i	−0.196098	−	0.113217i
$306$		0			0
$307$		−	21.6746i		−	1.23704i	−0.785771	−	0.618518i	$-0.787734\pi$
$307$		−	21.6746i		−	1.23704i	0.785771	−	0.618518i	$-0.212266\pi$
$308$		0			0
$309$	2.07031	−	14.6499i	0.117776	−	0.833406i
$310$		0			0
$311$	11.8462	+	20.5183i	0.671738	+	1.16348i	0.977411	+	0.211348i	$0.0677852\pi$
$311$	11.8462	+	20.5183i	0.671738	+	1.16348i	−0.305673	+	0.952136i	$0.598881\pi$
$312$		0			0
$313$	−23.6283	−	13.6418i	−1.33555	−	0.771081i	−0.349407	−	0.936971i	$-0.613617\pi$
$313$	−23.6283	−	13.6418i	−1.33555	−	0.771081i	−0.986144	+	0.165890i	$0.946950\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−21.2647	−	12.2772i	−1.19435	−	0.689556i	−0.235057	−	0.971982i	$-0.575528\pi$
$317$	−21.2647	−	12.2772i	−1.19435	−	0.689556i	−0.959289	+	0.282426i	$0.908861\pi$
$318$		0			0
$319$	0.0418465	+	0.0724802i	0.00234295	+	0.00405811i
$320$		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
$327$	15.2021	−	19.4272i	0.840678	−	1.07433i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−8.15579	+	14.1262i	−0.448283	+	0.776449i	−0.998274	−	0.0587215i	$-0.981298\pi$
$331$	−8.15579	+	14.1262i	−0.448283	+	0.776449i	0.549991	+	0.835170i	$0.314631\pi$
$332$		0			0
$333$	−0.506550	−	2.04494i	−0.0277588	−	0.112062i
$334$		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
$339$	−21.0719	−	16.4891i	−1.14447	−	0.895564i
$340$		0			0
$341$	−0.743445	−	1.28768i	−0.0402598	−	0.0697320i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	0.841854	−	5.95714i	0.0453239	−	0.320722i
$346$		0			0
$347$	−5.37986	+	3.10606i	−0.288806	+	0.166742i	−0.637403	−	0.770530i	$-0.719991\pi$
$347$	−5.37986	+	3.10606i	−0.288806	+	0.166742i	0.348597	+	0.937273i	$0.386658\pi$
$348$		0			0
$349$	24.6529	−	14.2334i	1.31964	−	0.761896i	0.335971	−	0.941872i	$-0.390936\pi$
$349$	24.6529	−	14.2334i	1.31964	−	0.761896i	0.983671	+	0.179977i	$0.0576023\pi$
$350$		0			0
$351$	−4.00155	−	5.53424i	−0.213587	−	0.295396i
$352$		0			0
$353$	−2.98691			−0.158977			−0.0794887	−	0.996836i	$-0.525329\pi$
$353$	−2.98691			−0.158977			−0.0794887	+	0.996836i	$0.525329\pi$
$354$		0			0
$355$		−	9.39798i		−	0.498793i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	26.5977	−	15.3562i	1.40377	−	0.810468i	0.408994	−	0.912537i	$-0.365880\pi$
$359$	26.5977	−	15.3562i	1.40377	−	0.810468i	0.994777	+	0.102070i	$0.0325465\pi$
$360$		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
$367$		−	19.0384i		−	0.993794i	−0.867809	−	0.496897i	$-0.834473\pi$
$367$		−	19.0384i		−	0.993794i	0.867809	−	0.496897i	$-0.165527\pi$
$368$		0			0
$369$	−23.3130	+	22.4445i	−1.21363	+	1.16841i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	4.11738			0.213190			0.106595	−	0.994303i	$-0.466005\pi$
$373$	4.11738			0.213190			0.106595	+	0.994303i	$0.466005\pi$
$374$		0			0
$375$	−11.4118	−	1.61270i	−0.589302	−	0.0832792i
$376$		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
$381$	−37.4393	−	5.29086i	−1.91807	−	0.271059i
$382$		0			0
$383$	−31.6093			−1.61516			−0.807580	−	0.589758i	$-0.799223\pi$
$383$	−31.6093			−1.61516			−0.807580	+	0.589758i	$0.799223\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	5.38299	+	21.7311i	0.273633	+	1.10465i
$388$		0			0
$389$		−	21.2485i		−	1.07734i	−0.842516	−	0.538672i	$-0.818926\pi$
$389$		−	21.2485i		−	1.07734i	0.842516	−	0.538672i	$-0.181074\pi$
$390$		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	−0.919419	−	0.393281i	$-0.871340\pi$
$397$	−20.6927	+	11.9469i	−1.03854	+	0.599599i	−0.119118	+	0.992880i	$0.538007\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			25.4174i			1.26928i	0.772806	+	0.634642i	$0.218853\pi$
$401$			25.4174i			1.26928i	−0.772806	+	0.634642i	$0.781147\pi$
$402$		0			0
$403$	7.36845			0.367049
$404$		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
$409$	19.3831	−	11.1908i	0.958433	−	0.553351i	0.0627424	−	0.998030i	$-0.480015\pi$
$409$	19.3831	−	11.1908i	0.958433	−	0.553351i	0.895690	+	0.444678i	$0.146682\pi$
$410$		0			0
$411$	0.653713	−	4.62582i	0.0322453	−	0.228175i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	2.60551	+	4.51288i	0.127900	+	0.221528i
$416$		0			0
$417$	15.9789	+	12.5037i	0.782489	+	0.612309i
$418$		0			0
$419$	7.04181	−	12.1968i	0.344015	−	0.595851i	−0.641159	−	0.767408i	$-0.721546\pi$
$419$	7.04181	−	12.1968i	0.344015	−	0.595851i	0.985174	+	0.171556i	$0.0548796\pi$
$420$		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
$423$	15.1407	−	14.5766i	0.736165	−	0.708740i
$424$		0			0
$425$	8.40717	−	14.5617i	0.407808	−	0.706344i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.372071	+	0.475482i	−0.0179638	+	0.0229565i
$430$		0			0
$431$	7.16179	+	4.13486i	0.344971	+	0.199169i	0.662468	−	0.749090i	$-0.269509\pi$
$431$	7.16179	+	4.13486i	0.344971	+	0.199169i	−0.317497	+	0.948259i	$0.602842\pi$
$432$		0			0
$433$			4.35102i			0.209097i	0.994520	+	0.104548i	$0.0333397\pi$
$433$			4.35102i			0.209097i	−0.994520	+	0.104548i	$0.966660\pi$
$434$		0			0
$435$	−0.354676	+	0.142984i	−0.0170054	+	0.00685556i
$436$		0			0
$437$	−1.09622	−	1.89872i	−0.0524395	−	0.0908279i
$438$		0			0
$439$	18.0200	+	10.4039i	0.860048	+	0.496549i	0.864028	−	0.503443i	$-0.167934\pi$
$439$	18.0200	+	10.4039i	0.860048	+	0.496549i	−0.00398054	+	0.999992i	$0.501267\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−26.7927	−	15.4688i	−1.27296	−	0.734945i	−0.297417	−	0.954748i	$-0.596125\pi$
$443$	−26.7927	−	15.4688i	−1.27296	−	0.734945i	−0.975544	+	0.219803i	$0.929459\pi$
$444$		0			0
$445$	−3.91290	−	6.77734i	−0.185489	−	0.321277i
$446$		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
$453$	−17.1550	−	2.42432i	−0.806012	−	0.113904i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.15058	+	1.99286i	−0.0538217	+	0.0932218i	−0.891681	−	0.452664i	$-0.850474\pi$
$457$	−1.15058	+	1.99286i	−0.0538217	+	0.0932218i	0.837859	+	0.545886i	$0.183807\pi$
$458$		0			0
$459$	15.6970	−	11.3498i	0.732673	−	0.529762i
$460$		0			0
$461$	8.92497	+	15.4585i	0.415677	+	0.719974i	0.995499	−	0.0947688i	$-0.0302112\pi$
$461$	8.92497	+	15.4585i	0.415677	+	0.719974i	−0.579822	+	0.814743i	$0.696878\pi$
$462$		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
$465$	6.30119	−	2.54026i	0.292211	−	0.117802i
$466$		0			0
$467$	−2.42799	−	4.20541i	−0.112354	−	0.194603i	0.804365	−	0.594136i	$-0.202506\pi$
$467$	−2.42799	−	4.20541i	−0.112354	−	0.194603i	−0.916719	+	0.399533i	$0.869172\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−0.404920	+	0.163239i	−0.0186577	+	0.00752168i
$472$		0			0
$473$	1.71405	−	0.989607i	0.0788121	−	0.0455022i
$474$		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
$479$	−8.81084			−0.402577			−0.201289	−	0.979532i	$-0.564513\pi$
$479$	−8.81084			−0.402577			−0.201289	+	0.979532i	$0.564513\pi$
$480$		0			0
$481$		−	0.922973i		−	0.0420839i
$482$		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	−0.740857	−	0.671663i	$-0.765580\pi$
$487$	4.66185	−	8.07456i	0.211249	−	0.365893i	0.952106	+	0.305770i	$0.0989137\pi$
$488$		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
$493$		−	1.17637i		−	0.0529811i
$494$		0			0
$495$	−0.154258	+	0.534882i	−0.00693338	+	0.0240412i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−22.3388			−1.00002			−0.500010	−	0.866020i	$-0.666670\pi$
$499$	−22.3388			−1.00002			−0.500010	+	0.866020i	$0.666670\pi$
$500$		0			0
$501$	−4.79127	+	6.12291i	−0.214058	+	0.273552i
$502$		0			0
$503$	−12.2396			−0.545738			−0.272869	−	0.962051i	$-0.587973\pi$
$503$	−12.2396			−0.545738			−0.272869	+	0.962051i	$0.587973\pi$
$504$		0			0
$505$	12.2490			0.545072
$506$		0			0
$507$	7.30027	+	18.1085i	0.324216	+	0.804229i
$508$		0			0
$509$	14.1099			0.625411			0.312706	−	0.949850i	$-0.398765\pi$
$509$	14.1099			0.625411			0.312706	+	0.949850i	$0.398765\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−2.28266	+	0.234640i	−0.100782	+	0.0103596i
$514$		0			0
$515$		−	5.97659i		−	0.263360i
$516$		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	$-0.793958\pi$
$521$	2.81632	−	4.87800i	0.123385	−	0.213709i	0.921101	+	0.389325i	$0.127292\pi$
$522$		0			0
$523$	33.2293	−	19.1849i	1.45302	−	0.838899i	0.454364	−	0.890816i	$-0.349867\pi$
$523$	33.2293	−	19.1849i	1.45302	−	0.838899i	0.998651	+	0.0519176i	$0.0165333\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			20.8995i			0.910395i
$528$		0			0
$529$	−1.64754			−0.0716321
$530$		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
$535$	6.36329	−	3.67385i	0.275109	−	0.158834i
$536$		0			0
$537$	34.8518	+	27.2720i	1.50396	+	1.17687i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−3.21673	−	5.57154i	−0.138298	−	0.239539i	0.788555	−	0.614965i	$-0.210830\pi$
$541$	−3.21673	−	5.57154i	−0.138298	−	0.239539i	−0.926852	+	0.375426i	$0.877496\pi$
$542$		0			0
$543$	0.228590	−	1.61756i	0.00980975	−	0.0694159i
$544$		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
$549$	11.7602	+	12.2152i	0.501912	+	0.521333i
$550$		0			0
$551$	−0.0696787	+	0.120687i	−0.00296841	+	0.00514144i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.318193	−	0.789287i	−0.0135065	−	0.0335034i
$556$		0			0
$557$	25.5409	+	14.7460i	1.08220	+	0.624809i	0.931489	−	0.363769i	$-0.118510\pi$
$557$	25.5409	+	14.7460i	1.08220	+	0.624809i	0.150712	+	0.988578i	$0.451843\pi$
$558$		0			0
$559$			9.80822i			0.414844i
$560$		0			0
$561$	−1.34863	−	1.05532i	−0.0569391	−	0.0445557i
$562$		0			0
$563$	5.25934	+	9.10944i	0.221655	+	0.383917i	0.955311	−	0.295604i	$-0.0955209\pi$
$563$	5.25934	+	9.10944i	0.221655	+	0.383917i	−0.733656	+	0.679521i	$0.762188\pi$
$564$		0			0
$565$	−9.36020	−	5.40411i	−0.393787	−	0.227353i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−22.8054	−	13.1667i	−0.956053	−	0.551977i	−0.0610967	−	0.998132i	$-0.519460\pi$
$569$	−22.8054	−	13.1667i	−0.956053	−	0.551977i	−0.894956	+	0.446155i	$0.852793\pi$
$570$		0			0
$571$	22.0295	+	38.1562i	0.921906	+	1.59679i	0.796463	+	0.604688i	$0.206702\pi$
$571$	22.0295	+	38.1562i	0.921906	+	1.59679i	0.125444	+	0.992101i	$0.459965\pi$
$572$		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	0.225213	−	0.974310i	$-0.427692\pi$
$577$	−12.1535	−	7.01684i	−0.505957	−	0.292115i	−0.731170	+	0.682195i	$0.761026\pi$
$578$		0			0
$579$	−11.9902	−	29.7420i	−0.498295	−	1.23604i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−1.30448	+	2.25943i	−0.0540262	+	0.0935762i
$584$		0			0
$585$	−1.91332	−	1.98736i	−0.0791062	−	0.0821673i
$586$		0			0
$587$	1.52469	+	2.64085i	0.0629308	+	0.108999i	0.895774	−	0.444509i	$-0.146622\pi$
$587$	1.52469	+	2.64085i	0.0629308	+	0.108999i	−0.832843	+	0.553509i	$0.813289\pi$
$588$		0			0
$589$	1.23791	−	2.14413i	0.0510073	−	0.0883473i
$590$		0			0
$591$	3.43607	−	24.3144i	0.141341	−	1.00016i
$592$		0			0
$593$	13.3041	+	23.0434i	0.546334	+	0.946278i	0.998522	+	0.0543552i	$0.0173103\pi$
$593$	13.3041	+	23.0434i	0.546334	+	0.946278i	−0.452188	+	0.891923i	$0.649356\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−32.3354	−	25.3029i	−1.32340	−	1.03558i
$598$		0			0
$599$	−3.86333	+	2.23050i	−0.157852	+	0.0911356i	−0.576845	−	0.816854i	$-0.695716\pi$
$599$	−3.86333	+	2.23050i	−0.157852	+	0.0911356i	0.418993	+	0.907989i	$0.362383\pi$
$600$		0			0
$601$	5.25019	−	3.03120i	0.214160	−	0.123645i	−0.389083	−	0.921203i	$-0.627208\pi$
$601$	5.25019	−	3.03120i	0.214160	−	0.123645i	0.603243	+	0.797557i	$0.293875\pi$
$602$		0			0
$603$	4.28554	+	17.3007i	0.174521	+	0.704539i
$604$		0			0
$605$	−7.64700			−0.310895
$606$		0			0
$607$			45.3313i			1.83994i	0.391986	+	0.919971i	$0.371788\pi$
$607$			45.3313i			1.83994i	−0.391986	+	0.919971i	$0.628212\pi$
$608$		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	−0.305781	−	0.952102i	$-0.598917\pi$
$613$	16.6294	−	28.8029i	0.671654	−	1.16334i	0.977435	−	0.211237i	$-0.0677492\pi$
$614$		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
$619$			26.4462i			1.06296i	0.847069	+	0.531482i	$0.178365\pi$
$619$			26.4462i			1.06296i	−0.847069	+	0.531482i	$0.821635\pi$
$620$		0			0
$621$	−10.5464	+	23.5426i	−0.423214	+	0.944734i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	17.8969			0.715874
$626$		0			0
$627$	0.0758507	+	0.188150i	0.00302918	+	0.00751398i
$628$		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
$633$	−6.48985	+	8.29359i	−0.257949	+	0.329641i
$634$		0			0
$635$	−15.2737			−0.606120
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−11.1664	+	38.7189i	−0.441735	+	1.53170i
$640$		0			0
$641$			24.4154i			0.964351i	0.876075	+	0.482176i	$0.160153\pi$
$641$			24.4154i			0.964351i	−0.876075	+	0.482176i	$0.839847\pi$
$642$		0			0
$643$	−31.9014	−	18.4183i	−1.25807	−	0.726346i	−0.285370	−	0.958418i	$-0.592116\pi$
$643$	−31.9014	−	18.4183i	−1.25807	−	0.726346i	−0.972699	+	0.232071i	$0.925450\pi$
$644$		0			0
$645$	3.38136	+	8.38757i	0.133141	+	0.330260i
$646$		0			0
$647$	13.2847	−	23.0098i	0.522276	−	0.904608i	−0.477389	−	0.878692i	$-0.658417\pi$
$647$	13.2847	−	23.0098i	0.522276	−	0.904608i	0.999664	−	0.0259155i	$-0.00825009\pi$
$648$		0			0
$649$	3.09239	−	1.78539i	0.121387	−	0.0700827i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			30.3418i			1.18737i	0.804699	+	0.593683i	$0.202327\pi$
$653$			30.3418i			1.18737i	−0.804699	+	0.593683i	$0.797673\pi$
$654$		0			0
$655$	3.64466			0.142409
$656$		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
$661$	−30.4187	+	17.5623i	−1.18315	+	0.683092i	−0.956741	−	0.290940i	$-0.906032\pi$
$661$	−30.4187	+	17.5623i	−1.18315	+	0.683092i	−0.226409	+	0.974032i	$0.572699\pi$
$662$		0			0
$663$	7.87075	−	3.17301i	0.305674	−	0.123229i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.783329	+	1.35677i	0.0303306	+	0.0525342i
$668$		0			0
$669$	−1.47679	+	0.595351i	−0.0570958	+	0.0230176i
$670$		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
$675$	21.3890	+	9.58169i	0.823265	+	0.368800i
$676$		0			0
$677$	8.42072	−	14.5851i	0.323635	−	0.560551i	−0.657601	−	0.753367i	$-0.728429\pi$
$677$	8.42072	−	14.5851i	0.323635	−	0.560551i	0.981235	+	0.192815i	$0.0617618\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	17.1603	+	2.42506i	0.657584	+	0.0929287i
$682$		0			0
$683$	−15.7555	−	9.09645i	−0.602868	−	0.348066i	0.167301	−	0.985906i	$-0.446495\pi$
$683$	−15.7555	−	9.09645i	−0.602868	−	0.348066i	−0.770169	+	0.637840i	$0.779828\pi$
$684$		0			0
$685$		−	1.88715i		−	0.0721042i
$686$		0			0
$687$	−0.666559	+	4.71672i	−0.0254308	+	0.179954i
$688$		0			0
$689$	−6.46452	−	11.1969i	−0.246279	−	0.426567i
$690$		0			0
$691$	3.05405	+	1.76326i	0.116182	+	0.0670775i	0.556965	−	0.830536i	$-0.311966\pi$
$691$	3.05405	+	1.76326i	0.116182	+	0.0670775i	−0.440783	+	0.897614i	$0.645299\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	7.09786	+	4.09795i	0.269237	+	0.155444i
$696$		0			0
$697$	−20.1063	−	34.8251i	−0.761579	−	1.31909i
$698$		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
$705$	5.23193	−	6.68605i	0.197046	−	0.251811i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	21.1447	−	36.6237i	0.794107	−	1.37543i	−0.129298	−	0.991606i	$-0.541273\pi$
$709$	21.1447	−	36.6237i	0.794107	−	1.37543i	0.923405	−	0.383827i	$-0.125394\pi$
$710$		0			0
$711$	−3.01858	+	2.90613i	−0.113206	+	0.108988i
$712$		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
$717$	18.0014	+	14.0863i	0.672273	+	0.526063i
$718$		0			0
$719$	15.2035	+	26.3332i	0.566994	+	0.982062i	0.996861	+	0.0791697i	$0.0252269\pi$
$719$	15.2035	+	26.3332i	0.566994	+	0.982062i	−0.429868	+	0.902892i	$0.641440\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	0.617704	−	4.37101i	0.0229727	−	0.162560i
$724$		0			0
$725$	1.23265	−	0.711673i	0.0457796	−	0.0264309i
$726$		0			0
$727$	−11.3671	+	6.56280i	−0.421583	+	0.243401i	−0.695754	−	0.718280i	$-0.744930\pi$
$727$	−11.3671	+	6.56280i	−0.421583	+	0.243401i	0.274171	+	0.961681i	$0.411596\pi$
$728$		0			0
$729$	17.9746	+	20.1473i	0.665724	+	0.746198i
$730$		0			0
$731$	−27.8195			−1.02894
$732$		0			0
$733$		−	37.7588i		−	1.39465i	−0.716753	−	0.697327i	$-0.754372\pi$
$733$		−	37.7588i		−	1.39465i	0.716753	−	0.697327i	$-0.245628\pi$
$734$		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	−0.999802	−	0.0198820i	$-0.993671\pi$
$739$	−13.1215	+	22.7271i	−0.482683	+	0.836031i	0.517119	+	0.855913i	$0.327004\pi$
$740$		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
$745$		−	13.1731i		−	0.482625i
$746$		0			0
$747$	−5.37242	−	21.6884i	−0.196567	−	0.793539i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	7.90737			0.288544			0.144272	−	0.989538i	$-0.453916\pi$
$751$	7.90737			0.288544			0.144272	+	0.989538i	$0.453916\pi$
$752$		0			0
$753$	−32.2239	−	4.55383i	−1.17430	−	0.165951i
$754$		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
$759$	2.25816	+	0.319119i	0.0819660	+	0.0115833i
$760$		0			0
$761$	6.11374			0.221623			0.110811	−	0.993841i	$-0.464655\pi$
$761$	6.11374			0.221623			0.110811	+	0.993841i	$0.464655\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	5.63684	−	5.42684i	0.203800	−	0.196208i
$766$		0			0
$767$			17.6954i			0.638944i
$768$		0			0
$769$	−9.79863	−	5.65724i	−0.353348	−	0.204005i	0.312811	−	0.949815i	$-0.398729\pi$
$769$	−9.79863	−	5.65724i	−0.353348	−	0.204005i	−0.666159	+	0.745810i	$0.732063\pi$
$770$		0			0
$771$	24.6868	+	3.48870i	0.889073	+	0.125642i
$772$		0			0
$773$	19.2106	−	33.2737i	0.690956	−	1.19677i	−0.280569	−	0.959834i	$-0.590523\pi$
$773$	19.2106	−	33.2737i	0.690956	−	1.19677i	0.971525	−	0.236937i	$-0.0761437\pi$
$774$		0			0
$775$	−21.8994	+	12.6436i	−0.786648	+	0.454172i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			4.76373i			0.170678i
$780$		0			0
$781$	3.56247			0.127475
$782$		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
$787$	−41.2747	+	23.8300i	−1.47129	+	0.849447i	−0.999480	−	0.0322557i	$-0.989731\pi$
$787$	−41.2747	+	23.8300i	−1.47129	+	0.849447i	−0.471806	+	0.881703i	$0.656398\pi$
$788$		0			0
$789$	−1.90249	+	13.4624i	−0.0677304	+	0.479275i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	3.71430	+	6.43335i	0.131898	+	0.228455i
$794$		0			0
$795$	−9.38828	−	7.34646i	−0.332968	−	0.260552i
$796$		0			0
$797$	−15.1359	+	26.2161i	−0.536139	+	0.928621i	0.462968	+	0.886375i	$0.346785\pi$
$797$	−15.1359	+	26.2161i	−0.536139	+	0.928621i	−0.999107	+	0.0422457i	$0.986549\pi$
$798$		0			0
$799$	13.0581	+	22.6172i	0.461961	+	0.800140i
$800$		0			0
$801$	8.06819	+	32.5712i	0.285075	+	1.15085i
$802$		0			0
$803$	1.02008	−	1.76683i	0.0359978	−	0.0623500i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	16.4863	−	21.0684i	0.580345	−	0.741642i
$808$		0			0
$809$	−0.219373	−	0.126655i	−0.00771273	−	0.00445295i	0.496139	−	0.868243i	$-0.334751\pi$
$809$	−0.219373	−	0.126655i	−0.00771273	−	0.00445295i	−0.503851	+	0.863790i	$0.668084\pi$
$810$		0			0
$811$			22.0629i			0.774735i	0.921925	+	0.387367i	$0.126615\pi$
$811$			22.0629i			0.774735i	−0.921925	+	0.387367i	$0.873385\pi$
$812$		0			0
$813$	20.3070	−	8.18657i	0.712199	−	0.287116i
$814$		0			0
$815$	−3.00698	−	5.20824i	−0.105330	−	0.182437i
$816$		0			0
$817$	2.85407	+	1.64780i	0.0998514	+	0.0576492i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	24.2467	+	13.9988i	0.846214	+	0.488562i	0.859372	−	0.511352i	$-0.170855\pi$
$821$	24.2467	+	13.9988i	0.846214	+	0.488562i	−0.0131576	+	0.999913i	$0.504188\pi$
$822$		0			0
$823$	−24.4771	−	42.3955i	−0.853217	−	1.47782i	−0.878289	−	0.478130i	$-0.841315\pi$
$823$	−24.4771	−	42.3955i	−0.853217	−	1.47782i	0.0250719	−	0.999686i	$-0.492019\pi$
$824$		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	0.324483	−	0.945892i	$-0.394810\pi$
$829$	−9.57180	−	5.52628i	−0.332442	−	0.191936i	−0.656925	+	0.753956i	$0.728143\pi$
$830$		0			0
$831$	20.3926	+	2.88184i	0.707410	+	0.0999700i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.57029	+	2.71981i	−0.0543420	+	0.0941230i
$836$		0			0
$837$	−28.9786	+	2.97878i	−1.00165	+	0.102962i
$838$		0			0
$839$	−4.62330	−	8.00780i	−0.159614	−	0.276460i	0.775115	−	0.631820i	$-0.217692\pi$
$839$	−4.62330	−	8.00780i	−0.159614	−	0.276460i	−0.934730	+	0.355360i	$0.884358\pi$
$840$		0			0
$841$	−14.4502	+	25.0285i	−0.498283	+	0.863052i
$842$		0			0
$843$	5.10871	−	2.05952i	0.175953	−	0.0709338i
$844$		0			0
$845$	3.94346	+	6.83028i	0.135659	+	0.234969i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−29.7153	+	11.9794i	−1.01983	+	0.411132i
$850$		0			0
$851$	−3.01931	+	1.74320i	−0.103501	+	0.0597561i
$852$		0			0
$853$	−34.3256	+	19.8179i	−1.17529	+	0.678551i	−0.954919	−	0.296866i	$-0.904059\pi$
$853$	−34.3256	+	19.8179i	−1.17529	+	0.678551i	−0.220366	+	0.975417i	$0.570725\pi$
$854$		0			0
$855$	−0.899740	+	0.222874i	−0.0307705	+	0.00762212i
$856$		0			0
$857$	23.8520			0.814770			0.407385	−	0.913256i	$-0.366441\pi$
$857$	23.8520			0.814770			0.407385	+	0.913256i	$0.366441\pi$
$858$		0			0
$859$		−	11.1138i		−	0.379197i	−0.981862	−	0.189598i	$-0.939281\pi$
$859$		−	11.1138i		−	0.379197i	0.981862	−	0.189598i	$-0.0607186\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	38.7780	−	22.3885i	1.32002	−	0.762113i	0.336287	−	0.941759i	$-0.390829\pi$
$863$	38.7780	−	22.3885i	1.32002	−	0.762113i	0.983731	+	0.179646i	$0.0574954\pi$
$864$		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
$871$			7.80859i			0.264584i
$872$		0			0
$873$	−30.8751	+	7.64804i	−1.04496	+	0.258847i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	3.68191			0.124329			0.0621647	−	0.998066i	$-0.480200\pi$
$877$	3.68191			0.124329			0.0621647	+	0.998066i	$0.480200\pi$
$878$		0			0
$879$	3.05221	−	3.90052i	0.102949	−	0.131561i
$880$		0			0
$881$	17.3992			0.586194			0.293097	−	0.956083i	$-0.405314\pi$
$881$	17.3992			0.586194			0.293097	+	0.956083i	$0.405314\pi$
$882$		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
$885$	6.10045	+	15.1324i	0.205065	+	0.508669i
$886$		0			0
$887$	−46.3780			−1.55722			−0.778610	−	0.627508i	$-0.784075\pi$
$887$	−46.3780			−1.55722			−0.778610	+	0.627508i	$0.784075\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.27106	−	2.02038i	0.0425821	−	0.0676854i
$892$		0			0
$893$		−	3.09381i		−	0.103531i
$894$		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
$905$		−	0.659898i		−	0.0219357i
$906$		0			0
$907$	16.0391			0.532571			0.266285	−	0.963894i	$-0.414204\pi$
$907$	16.0391			0.532571			0.266285	+	0.963894i	$0.414204\pi$
$908$		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
$913$	−1.71069	+	0.987665i	−0.0566154	+	0.0326869i
$914$		0			0
$915$	5.39419	+	4.22103i	0.178326	+	0.139543i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−17.7069	−	30.6693i	−0.584097	−	1.01169i	−0.994987	−	0.100001i	$-0.968115\pi$
$919$	−17.7069	−	30.6693i	−0.584097	−	1.01169i	0.410890	−	0.911685i	$-0.365218\pi$
$920$		0			0
$921$	−5.25311	+	37.1722i	−0.173096	+	1.22486i
$922$		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
$927$	−7.10119	+	24.6230i	−0.233234	+	0.808727i
$928$		0			0
$929$	19.8626	−	34.4030i	0.651670	−	1.12873i	−0.331048	−	0.943614i	$-0.607402\pi$
$929$	19.8626	−	34.4030i	0.651670	−	1.12873i	0.982718	−	0.185111i	$-0.0592646\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−15.3435	−	38.0601i	−0.502325	−	1.24603i
$934$		0			0
$935$	−0.599064	−	0.345870i	−0.0195915	−	0.0113112i
$936$		0			0
$937$			23.2142i			0.758376i	0.925320	+	0.379188i	$0.123797\pi$
$937$			23.2142i			0.758376i	−0.925320	+	0.379188i	$0.876203\pi$
$938$		0			0
$939$	37.2165	+	29.1225i	1.21452	+	0.950376i
$940$		0			0
$941$	17.9616	+	31.1104i	0.585531	+	1.01417i	0.994809	+	0.101760i	$0.0324474\pi$
$941$	17.9616	+	31.1104i	0.585531	+	1.01417i	−0.409278	+	0.912410i	$0.634219\pi$
$942$		0			0
$943$	46.3790	+	26.7769i	1.51031	+	0.871977i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−26.7365	−	15.4363i	−0.868818	−	0.501612i	−0.00186277	−	0.999998i	$-0.500593\pi$
$947$	−26.7365	−	15.4363i	−0.868818	−	0.501612i	−0.866955	+	0.498386i	$0.833926\pi$
$948$		0			0
$949$	5.05511	+	8.75571i	0.164096	+	0.284222i
$950$		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
$957$	−0.0542006	−	0.134446i	−0.00175206	−	0.00434603i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.215406	−	0.373095i	0.00694859	−	0.0120353i
$962$		0			0
$963$	−30.5813	+	7.57527i	−0.985470	+	0.244110i
$964$		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
$969$	0.398993	−	2.82336i	0.0128175	−	0.0906994i
$970$		0			0
$971$	16.6428	+	28.8261i	0.534092	+	0.925074i	0.999207	+	0.0398238i	$0.0126797\pi$
$971$	16.6428	+	28.8261i	0.534092	+	0.925074i	−0.465115	+	0.885250i	$0.653987\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	8.08640	+	6.32773i	0.258972	+	0.202649i
$976$		0			0
$977$	38.9127	−	22.4662i	1.24493	−	0.718758i	0.274833	−	0.961492i	$-0.411377\pi$
$977$	38.9127	−	22.4662i	1.24493	−	0.718758i	0.970093	+	0.242734i	$0.0780441\pi$
$978$		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
$983$	26.8949			0.857813			0.428907	−	0.903349i	$-0.358899\pi$
$983$	26.8949			0.857813			0.428907	+	0.903349i	$0.358899\pi$
$984$		0			0
$985$		−	9.91929i		−	0.316055i
$986$		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	−0.434346	−	0.900746i	$-0.643020\pi$
$991$	17.7201	−	30.6920i	0.562896	−	0.974965i	0.997242	−	0.0742186i	$-0.0236463\pi$
$992$		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
$997$			32.4953i			1.02914i	0.857449	+	0.514568i	$0.172048\pi$
$997$			32.4953i			1.02914i	−0.857449	+	0.514568i	$0.827952\pi$
$998$		0			0
$999$	0.373122	+	3.62986i	0.0118050	+	0.114844i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.6	✓	16	7.2	even	3
252.2.w.a.101.6	yes	16	63.20	even	6
252.2.bm.a.173.8	yes	16	63.2	odd	6
252.2.bm.a.185.8	yes	16	7.6	odd	2
756.2.w.a.341.4		16	21.2	odd	6
756.2.w.a.521.4		16	63.34	odd	6
756.2.bm.a.17.4		16	21.20	even	2
756.2.bm.a.89.4		16	63.16	even	3
1008.2.ca.d.257.3		16	28.23	odd	6
1008.2.ca.d.353.3		16	252.83	odd	6
1008.2.df.d.689.1		16	28.27	even	2
1008.2.df.d.929.1		16	252.191	even	6
1764.2.w.b.509.3		16	7.5	odd	6
1764.2.w.b.1109.3		16	9.2	odd	6
1764.2.x.a.293.6		16	7.4	even	3
1764.2.x.a.1469.6		16	63.38	even	6
1764.2.x.b.293.3		16	7.3	odd	6
1764.2.x.b.1469.3		16	63.11	odd	6
1764.2.bm.a.1685.1		16	63.47	even	6	inner
1764.2.bm.a.1697.1		16	1.1	even	1	trivial
2268.2.t.a.1781.4		16	63.13	odd	6
2268.2.t.a.2105.4		16	63.23	odd	6
2268.2.t.b.1781.5		16	63.41	even	6
2268.2.t.b.2105.5		16	63.58	even	3
3024.2.ca.d.2033.4		16	252.223	even	6
3024.2.ca.d.2609.4		16	84.23	even	6
3024.2.df.d.17.4		16	84.83	odd	2
3024.2.df.d.1601.4		16	252.79	odd	6
5292.2.w.b.521.5		16	9.7	even	3
5292.2.w.b.1097.5		16	21.5	even	6
5292.2.x.a.881.4		16	21.11	odd	6
5292.2.x.a.4409.4		16	63.52	odd	6
5292.2.x.b.881.5		16	21.17	even	6
5292.2.x.b.4409.5		16	63.25	even	3
5292.2.bm.a.2285.5		16	3.2	odd	2
5292.2.bm.a.4625.5		16	63.61	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.71501 - 0.242362i) q^{3} -0.699656 q^{5} +(2.88252 + 0.831308i) q^{9} +O(q^{10})\)	\(q+(-1.71501 - 0.242362i) q^{3} -0.699656 q^{5} +(2.88252 + 0.831308i) q^{9} -0.265217i q^{11} +(1.13823 + 0.657156i) q^{13} +(1.19992 + 0.169570i) q^{15} +(-1.86392 + 3.22840i) q^{17} +(0.382449 - 0.220807i) q^{19} -4.96463i q^{23} -4.51048 q^{25} +(-4.74208 - 2.12432i) q^{27} +(-0.273287 + 0.157782i) q^{29} +(4.85521 - 2.80316i) q^{31} +(-0.0642786 + 0.454850i) q^{33} +(-0.351124 - 0.608164i) q^{37} +(-1.79280 - 1.40289i) q^{39} +(-5.39354 + 9.34189i) q^{41} +(3.73131 + 6.46283i) q^{43} +(-2.01677 - 0.581630i) q^{45} +(3.50285 - 6.06712i) q^{47} +(3.97908 - 5.08500i) q^{51} +(-8.51919 - 4.91856i) q^{53} +0.185561i q^{55} +(-0.709419 + 0.285995i) q^{57} +(6.73182 + 11.6598i) q^{59} +(4.89484 + 2.82604i) q^{61} +(-0.796368 - 0.459783i) q^{65} +(2.97060 + 5.14523i) q^{67} +(-1.20324 + 8.51439i) q^{69} +13.4323i q^{71} +(6.66182 + 3.84620i) q^{73} +(7.73552 + 1.09317i) q^{75} +(-0.698360 + 1.20959i) q^{79} +(7.61785 + 4.79253i) q^{81} +(-3.72399 - 6.45014i) q^{83} +(1.30410 - 2.25877i) q^{85} +(0.506930 - 0.204363i) q^{87} +(5.59261 + 9.68668i) q^{89} +(-9.00612 + 3.63073i) q^{93} +(-0.267582 + 0.154489i) q^{95} +(-9.18225 + 5.30138i) q^{97} +(0.220477 - 0.764493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 3 q^{13} - 3 q^{15} + 9 q^{17} + 16 q^{25} + 9 q^{27} + 6 q^{29} - 6 q^{31} + 27 q^{33} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{51} + 15 q^{57} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} + 21 q^{69} + 15 q^{75} - q^{79} + 6 q^{85} + 3 q^{87} + 21 q^{89} - 69 q^{93} + 6 q^{95} - 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q - 3 * q^13 - 3 * q^15 + 9 * q^17 + 16 * q^25 + 9 * q^27 + 6 * q^29 - 6 * q^31 + 27 * q^33 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^51 + 15 * q^57 + 15 * q^59 - 3 * q^61 - 39 * q^65 - 7 * q^67 + 21 * q^69 + 15 * q^75 - q^79 + 6 * q^85 + 3 * q^87 + 21 * q^89 - 69 * q^93 + 6 * q^95 - 3 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more