LMFDB - Embedded newform 1764.2.x.a.293.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(293,1764)]

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, 3]))

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

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

chi := DirichletCharacter("1764.293");

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.x (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.0856109166$
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			293.6
Root			$1.68124 - 0.416458i$ of defining polynomial
Character	$\chi$	$=$	1764.293
Dual form			1764.2.x.a.1469.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.647613 + 1.60642i) q^{3} +(0.349828 - 0.605920i) q^{5} +(-2.16119 + 2.08068i) q^{9} +O(q^{10})$	\(q+(0.647613 + 1.60642i) q^{3} +(0.349828 - 0.605920i) q^{5} +(-2.16119 + 2.08068i) q^{9} +(-0.229685 + 0.132608i) q^{11} +(1.13823 + 0.657156i) q^{13} +(1.19992 + 0.169570i) q^{15} +3.72784 q^{17} +0.441614i q^{19} +(4.29949 + 2.48231i) q^{23} +(2.25524 + 3.90619i) q^{25} +(-4.74208 - 2.12432i) q^{27} +(-0.273287 + 0.157782i) q^{29} +(-4.85521 - 2.80316i) q^{31} +(-0.361772 - 0.283092i) q^{33} +0.702248 q^{37} +(-0.318540 + 2.25406i) q^{39} +(-5.39354 + 9.34189i) q^{41} +(3.73131 + 6.46283i) q^{43} +(0.504680 + 2.03739i) q^{45} +(3.50285 + 6.06712i) q^{47} +(2.41420 + 5.98849i) q^{51} +9.83712i q^{53} +0.185561i q^{55} +(-0.709419 + 0.285995i) q^{57} +(6.73182 - 11.6598i) q^{59} +(-4.89484 + 2.82604i) q^{61} +(0.796368 - 0.459783i) q^{65} +(2.97060 - 5.14523i) q^{67} +(-1.20324 + 8.51439i) q^{69} +13.4323i q^{71} -7.69241i q^{73} +(-4.81448 + 6.15257i) q^{75} +(-0.698360 - 1.20959i) q^{79} +(0.341524 - 8.99352i) q^{81} +(-3.72399 - 6.45014i) q^{83} +(1.30410 - 2.25877i) q^{85} +(-0.430449 - 0.336832i) q^{87} -11.1852 q^{89} +(1.35876 - 9.61489i) q^{93} +(0.267582 + 0.154489i) q^{95} +(-9.18225 + 5.30138i) q^{97} +(0.220477 - 0.764493i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 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} - 18 q^{17} - 21 q^{23} - 8 q^{25} + 9 q^{27} + 6 q^{29} + 6 q^{31} - 27 q^{33} - 2 q^{37} + 6 q^{39} - 6 q^{41} - 2 q^{43} + 15 q^{45} + 18 q^{47} + 18 q^{51} + 15 q^{57} + 15 q^{59} + 3 q^{61} + 39 q^{65} - 7 q^{67} + 21 q^{69} + 42 q^{75} - q^{79} - 18 q^{81} + 6 q^{85} - 51 q^{87} - 42 q^{89} + 48 q^{93} - 6 q^{95} - 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q - 6 * q^9 + 6 * q^11 - 3 * q^13 - 3 * q^15 - 18 * q^17 - 21 * q^23 - 8 * q^25 + 9 * q^27 + 6 * q^29 + 6 * q^31 - 27 * q^33 - 2 * q^37 + 6 * q^39 - 6 * q^41 - 2 * q^43 + 15 * q^45 + 18 * q^47 + 18 * q^51 + 15 * q^57 + 15 * q^59 + 3 * q^61 + 39 * q^65 - 7 * q^67 + 21 * q^69 + 42 * q^75 - q^79 - 18 * q^81 + 6 * q^85 - 51 * q^87 - 42 * q^89 + 48 * 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 $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.647613	+	1.60642i	0.373900	+	0.927469i
$3$	0.647613	+	1.60642i	0.373900	+	0.927469i
$4$		0			0
$5$	0.349828	−	0.605920i	0.156448	−	0.270975i	−0.777137	−	0.629331i	$-0.783329\pi$
$5$	0.349828	−	0.605920i	0.156448	−	0.270975i	0.933585	+	0.358355i	$0.116662\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2.16119	+	2.08068i	−0.720398	+	0.693561i
$10$		0			0
$11$	−0.229685	+	0.132608i	−0.0692525	+	0.0399829i	−0.534226	−	0.845341i	$-0.679397\pi$
$11$	−0.229685	+	0.132608i	−0.0692525	+	0.0399829i	0.464974	+	0.885324i	$0.346064\pi$
$12$		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
$17$	3.72784			0.904134			0.452067	−	0.891984i	$-0.350687\pi$
$17$	3.72784			0.904134			0.452067	+	0.891984i	$0.350687\pi$
$18$		0			0
$19$			0.441614i			0.101313i	0.998716	+	0.0506566i	$0.0161314\pi$
$19$			0.441614i			0.101313i	−0.998716	+	0.0506566i	$0.983869\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.29949	+	2.48231i	0.896507	+	0.517598i	0.876065	−	0.482193i	$-0.160160\pi$
$23$	4.29949	+	2.48231i	0.896507	+	0.517598i	0.0204414	+	0.999791i	$0.493493\pi$
$24$		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
$31$	−4.85521	−	2.80316i	−0.872022	−	0.503462i	−0.00400255	−	0.999992i	$-0.501274\pi$
$31$	−4.85521	−	2.80316i	−0.872022	−	0.503462i	−0.868020	+	0.496530i	$0.834607\pi$
$32$		0			0
$33$	−0.361772	−	0.283092i	−0.0629764	−	0.0492799i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.702248			0.115449			0.0577244	−	0.998333i	$-0.481616\pi$
$37$	0.702248			0.115449			0.0577244	+	0.998333i	$0.481616\pi$
$38$		0			0
$39$	−0.318540	+	2.25406i	−0.0510072	+	0.360938i
$40$		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
$45$	0.504680	+	2.03739i	0.0752333	+	0.303716i
$46$		0			0
$47$	3.50285	+	6.06712i	0.510943	+	0.884980i	0.999920	+	0.0126827i	$0.00403713\pi$
$47$	3.50285	+	6.06712i	0.510943	+	0.884980i	−0.488976	+	0.872297i	$0.662630\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	2.41420	+	5.98849i	0.338055	+	0.838556i
$52$		0			0
$53$			9.83712i			1.35123i	0.737254	+	0.675616i	$0.236122\pi$
$53$			9.83712i			1.35123i	−0.737254	+	0.675616i	$0.763878\pi$
$54$		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	0.0211522	−	0.999776i	$-0.493267\pi$
$59$	6.73182	−	11.6598i	0.876408	−	1.51798i	0.855256	−	0.518206i	$-0.173400\pi$
$60$		0			0
$61$	−4.89484	+	2.82604i	−0.626720	+	0.361837i	−0.779481	−	0.626426i	$-0.784517\pi$
$61$	−4.89484	+	2.82604i	−0.626720	+	0.361837i	0.152761	+	0.988263i	$0.451184\pi$
$62$		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	−0.625523	−	0.780206i	$-0.715114\pi$
$67$	2.97060	−	5.14523i	0.362916	−	0.628590i	0.988439	+	0.151616i	$0.0484477\pi$
$68$		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
$73$		−	7.69241i		−	0.900328i	−0.892946	−	0.450164i	$-0.851366\pi$
$73$		−	7.69241i		−	0.900328i	0.892946	−	0.450164i	$-0.148634\pi$
$74$		0			0
$75$	−4.81448	+	6.15257i	−0.555928	+	0.710438i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.698360	−	1.20959i	−0.0785716	−	0.136090i	0.824062	−	0.566499i	$-0.191703\pi$
$79$	−0.698360	−	1.20959i	−0.0785716	−	0.136090i	−0.902634	+	0.430409i	$0.858369\pi$
$80$		0			0
$81$	0.341524	−	8.99352i	0.0379471	−	0.999280i
$82$		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
$87$	−0.430449	−	0.336832i	−0.0461490	−	0.0361122i
$88$		0			0
$89$	−11.1852			−1.18563			−0.592815	−	0.805339i	$-0.701984\pi$
$89$	−11.1852			−1.18563			−0.592815	+	0.805339i	$0.701984\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.35876	−	9.61489i	0.140897	−	0.997018i
$94$		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
$101$	8.75357	+	15.1616i	0.871013	+	1.50864i	0.860950	+	0.508690i	$0.169870\pi$
$101$	8.75357	+	15.1616i	0.871013	+	1.50864i	0.0100634	+	0.999949i	$0.496797\pi$
$102$		0			0
$103$	−7.39775	−	4.27110i	−0.728922	−	0.420844i	0.0891054	−	0.996022i	$-0.471599\pi$
$103$	−7.39775	−	4.27110i	−0.728922	−	0.420844i	−0.818028	+	0.575179i	$0.804933\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	10.5019i		−	1.01525i	−0.861577	−	0.507627i	$-0.830523\pi$
$107$		−	10.5019i		−	1.01525i	0.861577	−	0.507627i	$-0.169477\pi$
$108$		0			0
$109$	14.2422			1.36416			0.682078	−	0.731279i	$-0.261076\pi$
$109$	14.2422			1.36416			0.682078	+	0.731279i	$0.261076\pi$
$110$		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
$117$	−3.82727	+	0.948048i	−0.353831	+	0.0876471i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−5.46483	+	9.46536i	−0.496803	+	0.860488i
$122$		0			0
$123$	−18.5000	−	2.61439i	−1.66809	−	0.235731i
$124$		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
$129$	−7.96559	+	10.1795i	−0.701331	+	0.896253i
$130$		0			0
$131$	2.60461	−	4.51132i	0.227566	−	0.394156i	−0.729520	−	0.683959i	$-0.760257\pi$
$131$	2.60461	−	4.51132i	0.227566	−	0.394156i	0.957086	+	0.289803i	$0.0935899\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−2.94608	+	2.13017i	−0.253558	+	0.183336i
$136$		0			0
$137$	2.33589	−	1.34863i	0.199568	−	0.115221i	−0.396886	−	0.917868i	$-0.629909\pi$
$137$	2.33589	−	1.34863i	0.199568	−	0.115221i	0.596454	+	0.802647i	$0.296576\pi$
$138$		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
$143$	−0.348578			−0.0291495
$144$		0			0
$145$			0.220786i			0.0183353i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−16.3055	−	9.41399i	−1.33580	−	0.771224i	−0.349618	−	0.936892i	$-0.613689\pi$
$149$	−16.3055	−	9.41399i	−1.33580	−	0.771224i	−0.986182	+	0.165668i	$0.947022\pi$
$150$		0			0
$151$	−5.00143	−	8.66273i	−0.407010	−	0.704963i	0.587543	−	0.809193i	$-0.300095\pi$
$151$	−5.00143	−	8.66273i	−0.407010	−	0.704963i	−0.994553	+	0.104230i	$0.966762\pi$
$152$		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	$-0.336535\pi$
$157$	−0.218293	−	0.126032i	−0.0174217	−	0.0100584i	−0.508686	+	0.860952i	$0.669868\pi$
$158$		0			0
$159$	−15.8026	+	6.37065i	−1.25323	+	0.505225i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−8.59559			−0.673259			−0.336629	−	0.941637i	$-0.609287\pi$
$163$	−8.59559			−0.673259			−0.336629	+	0.941637i	$0.609287\pi$
$164$		0			0
$165$	−0.298089	+	0.120171i	−0.0232062	+	0.00935533i
$166$		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
$171$	−0.918858	−	0.954413i	−0.0702668	−	0.0729858i
$172$		0			0
$173$	3.56072	+	6.16736i	0.270717	+	0.468895i	0.969046	−	0.246882i	$-0.0794060\pi$
$173$	3.56072	+	6.16736i	0.270717	+	0.468895i	−0.698329	+	0.715777i	$0.746073\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	23.0903	+	3.26308i	1.73557	+	0.245268i
$178$		0			0
$179$			25.5500i			1.90970i	0.297093	+	0.954848i	$0.403983\pi$
$179$			25.5500i			1.90970i	−0.297093	+	0.954848i	$0.596017\pi$
$180$		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	$-0.632371\pi$
$191$	2.57413	−	1.48617i	0.186258	−	0.107536i	0.590229	+	0.807236i	$0.299037\pi$
$192$		0			0
$193$	9.25721	−	16.0340i	0.666348	−	1.15415i	−0.312570	−	0.949895i	$-0.601190\pi$
$193$	9.25721	−	16.0340i	0.666348	−	1.15415i	0.978918	−	0.204254i	$-0.0654769\pi$
$194$		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
$199$		−	23.7052i		−	1.68042i	−0.542262	−	0.840209i	$-0.682432\pi$
$199$		−	23.7052i		−	1.68042i	0.542262	−	0.840209i	$-0.317568\pi$
$200$		0			0
$201$	10.1892	+	1.43992i	0.718692	+	0.101564i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	3.77362	+	6.53611i	0.263561	+	0.456502i
$206$		0			0
$207$	−14.4570	+	3.58112i	−1.00483	+	0.248905i
$208$		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
$213$	−21.5780	+	8.69893i	−1.47850	+	0.596041i
$214$		0			0
$215$	5.22127			0.356088
$216$		0			0
$217$		0			0
$218$		0			0
$219$	12.3573	−	4.98170i	0.835027	−	0.336632i
$220$		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
$227$	5.00297	+	8.66540i	0.332059	+	0.575143i	0.982915	−	0.184058i	$-0.0589234\pi$
$227$	5.00297	+	8.66540i	0.332059	+	0.575143i	−0.650857	+	0.759201i	$0.725590\pi$
$228$		0			0
$229$	2.38179	+	1.37513i	0.157393	+	0.0908710i	0.576628	−	0.817007i	$-0.304368\pi$
$229$	2.38179	+	1.37513i	0.157393	+	0.0908710i	−0.419235	+	0.907878i	$0.637702\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			6.41451i			0.420228i	0.977677	+	0.210114i	$0.0673836\pi$
$233$			6.41451i			0.420228i	−0.977677	+	0.210114i	$0.932616\pi$
$234$		0			0
$235$	4.90158			0.319744
$236$		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	−0.427223	−	0.904146i	$-0.640508\pi$
$241$	2.20722	−	1.27434i	0.142180	−	0.0820874i	0.569402	+	0.822059i	$0.307175\pi$
$242$		0			0
$243$	14.6686	−	5.27569i	0.940990	−	0.338436i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.290209	+	0.502657i	−0.0184656	+	0.0319833i
$248$		0			0
$249$	7.94995	−	10.1595i	0.503808	−	0.643832i
$250$		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
$255$	4.47310	+	0.632131i	0.280116	+	0.0395856i
$256$		0			0
$257$	7.19727	−	12.4660i	0.448953	−	0.777610i	−0.549365	−	0.835583i	$-0.685130\pi$
$257$	7.19727	−	12.4660i	0.448953	−	0.777610i	0.998318	+	0.0579725i	$0.0184636\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	0.262331	−	0.909620i	0.0162379	−	0.0563041i
$262$		0			0
$263$	−6.79810	+	3.92488i	−0.419189	+	0.242019i	−0.694730	−	0.719271i	$-0.744476\pi$
$263$	−6.79810	+	3.92488i	−0.419189	+	0.242019i	0.275542	+	0.961289i	$0.411143\pi$
$264$		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
$269$	15.4453			0.941719			0.470859	−	0.882208i	$-0.343944\pi$
$269$	15.4453			0.941719			0.470859	+	0.882208i	$0.343944\pi$
$270$		0			0
$271$		−	12.6411i		−	0.767895i	−0.923355	−	0.383947i	$-0.874564\pi$
$271$		−	12.6411i		−	0.767895i	0.923355	−	0.383947i	$-0.125436\pi$
$272$		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	0.987495	−	0.157649i	$-0.0503915\pi$
$277$	5.94531	+	10.2976i	0.357219	+	0.618722i	−0.630276	+	0.776371i	$0.717058\pi$
$278$		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	$-0.518625\pi$
$283$	−16.0195	−	9.24889i	−0.952263	−	0.549789i	−0.893783	+	0.448499i	$0.851959\pi$
$284$		0			0
$285$	−0.0748846	+	0.529900i	−0.00443578	+	0.0313886i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−3.10322			−0.182542
$290$		0			0
$291$	−14.4628	−	11.3173i	−0.847824	−	0.663435i
$292$		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
$297$	1.37088	−	0.140916i	0.0795467	−	0.00817679i
$298$		0			0
$299$	3.26254	+	5.65088i	0.188677	+	0.326799i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−18.6871	+	23.8808i	−1.07354	+	1.37192i
$304$		0			0
$305$			3.95451i			0.226434i
$306$		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	−0.305673	−	0.952136i	$-0.598881\pi$
$311$	11.8462	−	20.5183i	0.671738	−	1.16348i	0.977411	−	0.211348i	$-0.0677852\pi$
$312$		0			0
$313$	23.6283	−	13.6418i	1.33555	−	0.771081i	0.349407	−	0.936971i	$-0.386383\pi$
$313$	23.6283	−	13.6418i	1.33555	−	0.771081i	0.986144	+	0.165890i	$0.0530496\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	21.2647	−	12.2772i	1.19435	−	0.689556i	0.235057	−	0.971982i	$-0.424472\pi$
$317$	21.2647	−	12.2772i	1.19435	−	0.689556i	0.959289	+	0.282426i	$0.0911391\pi$
$318$		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
$325$			5.92818i			0.328836i
$326$		0			0
$327$	9.22344	+	22.8790i	0.510057	+	1.26521i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−8.15579	−	14.1262i	−0.448283	−	0.776449i	0.549991	−	0.835170i	$-0.314631\pi$
$331$	−8.15579	−	14.1262i	−0.448283	−	0.776449i	−0.998274	+	0.0587215i	$0.981298\pi$
$332$		0			0
$333$	−1.51769	+	1.46115i	−0.0831691	+	0.0800708i
$334$		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
$339$	−3.74400	+	26.4934i	−0.203346	+	1.43892i
$340$		0			0
$341$	1.48689			0.0805196
$342$		0			0
$343$		0			0
$344$		0			0
$345$	4.73811	+	3.70764i	0.255091	+	0.199612i
$346$		0			0
$347$	5.37986	+	3.10606i	0.288806	+	0.166742i	0.637403	−	0.770530i	$-0.280009\pi$
$347$	5.37986	+	3.10606i	0.288806	+	0.166742i	−0.348597	+	0.937273i	$0.613342\pi$
$348$		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
$353$	1.49346	+	2.58674i	0.0794887	+	0.137678i	0.903029	−	0.429579i	$-0.141338\pi$
$353$	1.49346	+	2.58674i	0.0794887	+	0.137678i	−0.823541	+	0.567257i	$0.808005\pi$
$354$		0			0
$355$	8.13889	+	4.69899i	0.431968	+	0.249397i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			30.7123i			1.62094i	0.585784	+	0.810468i	$0.300787\pi$
$359$			30.7123i			1.62094i	−0.585784	+	0.810468i	$0.699213\pi$
$360$		0			0
$361$	18.8050			0.989736
$362$		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	−0.864230	−	0.503096i	$-0.832194\pi$
$367$	−16.4877	+	9.51918i	−0.860651	+	0.496897i	0.00357920	+	0.999994i	$0.498861\pi$
$368$		0			0
$369$	−7.78101	−	31.4119i	−0.405063	−	1.63524i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−2.05869	+	3.56576i	−0.106595	+	0.184628i	−0.914389	−	0.404837i	$-0.867328\pi$
$373$	−2.05869	+	3.56576i	−0.106595	+	0.184628i	0.807794	+	0.589465i	$0.200661\pi$
$374$		0			0
$375$	4.30926	+	10.6892i	0.222529	+	0.551990i
$376$		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
$381$	14.1376	+	35.0688i	0.724293	+	1.79663i
$382$		0			0
$383$	15.8046	−	27.3745i	0.807580	−	1.39877i	−0.106956	−	0.994264i	$-0.534110\pi$
$383$	15.8046	−	27.3745i	0.807580	−	1.39877i	0.914536	−	0.404505i	$-0.132556\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−21.5112	−	6.20374i	−1.09347	−	0.315354i
$388$		0			0
$389$	−18.4018	+	10.6243i	−0.933007	+	0.538672i	−0.887761	−	0.460304i	$-0.847740\pi$
$389$	−18.4018	+	10.6243i	−0.933007	+	0.538672i	−0.0452458	+	0.998976i	$0.514407\pi$
$390$		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
$395$	−0.977223			−0.0491694
$396$		0			0
$397$		−	23.8939i		−	1.19920i	−0.800300	−	0.599599i	$-0.795327\pi$
$397$		−	23.8939i		−	1.19920i	0.800300	−	0.599599i	$-0.204673\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−22.0121	−	12.7087i	−1.09923	−	0.634642i	−0.163213	−	0.986591i	$-0.552186\pi$
$401$	−22.0121	−	12.7087i	−1.09923	−	0.634642i	−0.936019	+	0.351948i	$0.885519\pi$
$402$		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
$409$	−19.3831	−	11.1908i	−0.958433	−	0.553351i	−0.0627424	−	0.998030i	$-0.519985\pi$
$409$	−19.3831	−	11.1908i	−0.958433	−	0.553351i	−0.895690	+	0.444678i	$0.853318\pi$
$410$		0			0
$411$	3.67922	+	2.87904i	0.181482	+	0.142013i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−5.21102			−0.255799
$416$		0			0
$417$	2.83908	−	20.0900i	0.139030	−	0.983810i
$418$		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
$423$	−20.1941	−	5.82390i	−0.981870	−	0.283168i
$424$		0			0
$425$	8.40717	+	14.5617i	0.407808	+	0.706344i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.225744	−	0.559964i	−0.0108990	−	0.0270353i
$430$		0			0
$431$		−	8.26972i		−	0.398338i	−0.979965	−	0.199169i	$-0.936176\pi$
$431$		−	8.26972i		−	0.398338i	0.979965	−	0.199169i	$-0.0638243\pi$
$432$		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	$-0.832066\pi$
$439$	−18.0200	+	10.4039i	−0.860048	+	0.496549i	0.00398054	+	0.999992i	$0.498733\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	26.7927	−	15.4688i	1.27296	−	0.734945i	0.297417	−	0.954748i	$-0.403875\pi$
$443$	26.7927	−	15.4688i	1.27296	−	0.734945i	0.975544	+	0.219803i	$0.0705414\pi$
$444$		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
$451$		−	2.86092i		−	0.134715i
$452$		0			0
$453$	10.6770	−	13.6445i	0.501650	−	0.641075i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.15058	−	1.99286i	−0.0538217	−	0.0932218i	0.837859	−	0.545886i	$-0.183807\pi$
$457$	−1.15058	−	1.99286i	−0.0538217	−	0.0932218i	−0.891681	+	0.452664i	$0.850474\pi$
$458$		0			0
$459$	−17.6777	−	7.91911i	−0.825124	−	0.369633i
$460$		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
$465$	−5.35052	−	4.18686i	−0.248124	−	0.194161i
$466$		0			0
$467$	4.85599			0.224708			0.112354	−	0.993668i	$-0.464161\pi$
$467$	4.85599			0.224708			0.112354	+	0.993668i	$0.464161\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.0610907	−	0.432291i	0.00281491	−	0.0199189i
$472$		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
$479$	4.40542	+	7.63041i	0.201289	+	0.348642i	0.948944	−	0.315445i	$-0.102154\pi$
$479$	4.40542	+	7.63041i	0.201289	+	0.348642i	−0.747655	+	0.664087i	$0.768820\pi$
$480$		0			0
$481$	0.799318	+	0.461486i	0.0364458	+	0.0210420i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			7.41827i			0.336847i
$486$		0			0
$487$	−9.32370			−0.422497			−0.211249	−	0.977432i	$-0.567753\pi$
$487$	−9.32370			−0.422497			−0.211249	+	0.977432i	$0.567753\pi$
$488$		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
$495$	−0.386092	−	0.401032i	−0.0173536	−	0.0180251i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	11.1694	−	19.3459i	0.500010	−	0.866043i	−0.499990	−	0.866031i	$-0.666663\pi$
$499$	11.1694	−	19.3459i	0.500010	−	0.866043i	1.00000		1.16519e-5i	$-3.70891e-6\pi$
$500$		0			0
$501$	7.69823	+	1.08790i	0.343932	+	0.0486039i
$502$		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
$507$	12.0323	−	15.3765i	0.534374	−	0.682894i
$508$		0			0
$509$	−7.05496	+	12.2195i	−0.312706	+	0.541622i	−0.978947	−	0.204114i	$-0.934569\pi$
$509$	−7.05496	+	12.2195i	−0.312706	+	0.541622i	0.666242	+	0.745736i	$0.267902\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	0.938128	−	2.09417i	0.0414193	−	0.0924597i
$514$		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
$521$	−5.63263			−0.246770			−0.123385	−	0.992359i	$-0.539375\pi$
$521$	−5.63263			−0.246770			−0.123385	+	0.992359i	$0.539375\pi$
$522$		0			0
$523$			38.3699i			1.67780i	0.544288	+	0.838899i	$0.316800\pi$
$523$			38.3699i			1.67780i	−0.544288	+	0.838899i	$0.683200\pi$
$524$		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
$535$	−6.36329	−	3.67385i	−0.275109	−	0.158834i
$536$		0			0
$537$	−41.0441	+	16.5465i	−1.77118	+	0.714035i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	6.43346			0.276596			0.138298	−	0.990391i	$-0.455837\pi$
$541$	6.43346			0.276596			0.138298	+	0.990391i	$0.455837\pi$
$542$		0			0
$543$	−1.51514	+	0.610813i	−0.0650208	+	0.0262125i
$544$		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
$549$	4.69862	−	16.2922i	0.200532	−	0.695335i
$550$		0			0
$551$	−0.0696787	−	0.120687i	−0.00296841	−	0.00514144i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	0.842639	+	0.119080i	0.0357680	+	0.00505468i
$556$		0			0
$557$		−	29.4920i		−	1.24962i	−0.780778	−	0.624809i	$-0.785177\pi$
$557$		−	29.4920i		−	1.24962i	0.780778	−	0.624809i	$-0.214823\pi$
$558$		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	−0.733656	−	0.679521i	$-0.762188\pi$
$563$	5.25934	−	9.10944i	0.221655	−	0.383917i	0.955311	+	0.295604i	$0.0955209\pi$
$564$		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	$-0.480540\pi$
$569$	22.8054	−	13.1667i	0.956053	−	0.551977i	0.894956	+	0.446155i	$0.147207\pi$
$570$		0			0
$571$	22.0295	−	38.1562i	0.921906	−	1.59679i	0.125444	−	0.992101i	$-0.459965\pi$
$571$	22.0295	−	38.1562i	0.921906	−	1.59679i	0.796463	−	0.604688i	$-0.206702\pi$
$572$		0			0
$573$	4.05447	+	3.17268i	0.169378	+	0.132540i
$574$		0			0
$575$			22.3929i			0.933847i
$576$		0			0
$577$			14.0337i			0.584229i	0.956383	+	0.292115i	$0.0943589\pi$
$577$			14.0337i			0.584229i	−0.956383	+	0.292115i	$0.905641\pi$
$578$		0			0
$579$	31.7524	+	4.48720i	1.31959	+	0.186482i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−1.30448	−	2.25943i	−0.0540262	−	0.0935762i
$584$		0			0
$585$	−0.764443	+	2.65067i	−0.0316058	+	0.109592i
$586$		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
$591$	−22.7749	+	9.18146i	−0.936834	+	0.377675i
$592$		0			0
$593$	−26.6082			−1.09267			−0.546334	−	0.837568i	$-0.683977\pi$
$593$	−26.6082			−1.09267			−0.546334	+	0.837568i	$0.683977\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	38.0806	−	15.3518i	1.55854	−	0.628308i
$598$		0			0
$599$	3.86333	+	2.23050i	0.157852	+	0.0911356i	0.576845	−	0.816854i	$-0.304284\pi$
$599$	3.86333	+	2.23050i	0.157852	+	0.0911356i	−0.418993	+	0.907989i	$0.637617\pi$
$600$		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
$605$	3.82350	+	6.62250i	0.155447	+	0.269243i
$606$		0			0
$607$	−39.2581	−	22.6657i	−1.59344	−	0.919971i	−0.992711	−	0.120516i	$-0.961545\pi$
$607$	−39.2581	−	22.6657i	−1.59344	−	0.919971i	−0.600725	−	0.799455i	$-0.705121\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			9.20768i			0.372503i
$612$		0			0
$613$	−33.2588			−1.34331			−0.671654	−	0.740865i	$-0.734416\pi$
$613$	−33.2588			−1.34331			−0.671654	+	0.740865i	$0.734416\pi$
$614$		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	0.0367423	−	0.999325i	$-0.488302\pi$
$619$	22.9031	−	13.2231i	0.920554	−	0.531482i	0.883812	+	0.467843i	$0.154969\pi$
$620$		0			0
$621$	−15.1153	−	20.9048i	−0.606556	−	0.838881i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−8.94843	+	15.4991i	−0.357937	+	0.619965i
$626$		0			0
$627$	0.125017	−	0.159764i	0.00499271	−	0.00638034i
$628$		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
$633$	10.4274	+	1.47358i	0.414451	+	0.0585696i
$634$		0			0
$635$	7.63687	−	13.2274i	0.303060	−	0.524915i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−27.9483	−	29.0298i	−1.10562	−	1.14840i
$640$		0			0
$641$	21.1444	−	12.2077i	0.835153	−	0.482176i	−0.0204610	−	0.999791i	$-0.506513\pi$
$641$	21.1444	−	12.2077i	0.835153	−	0.482176i	0.855614	+	0.517615i	$0.173180\pi$
$642$		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
$647$	−26.5694			−1.04455			−0.522276	−	0.852777i	$-0.674917\pi$
$647$	−26.5694			−1.04455			−0.522276	+	0.852777i	$0.674917\pi$
$648$		0			0
$649$			3.57078i			0.140165i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−26.2767	−	15.1709i	−1.02829	−	0.593683i	−0.111794	−	0.993731i	$-0.535660\pi$
$653$	−26.2767	−	15.1709i	−1.02829	−	0.593683i	−0.916494	+	0.400049i	$0.868993\pi$
$654$		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
$661$	30.4187	+	17.5623i	1.18315	+	0.683092i	0.956741	−	0.290940i	$-0.0939679\pi$
$661$	30.4187	+	17.5623i	1.18315	+	0.683092i	0.226409	+	0.974032i	$0.427301\pi$
$662$		0			0
$663$	−1.18747	+	8.40277i	−0.0461174	+	0.326337i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1.56666			−0.0606613
$668$		0			0
$669$	1.25398	+	0.981258i	0.0484817	+	0.0379376i
$670$		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
$675$	−2.39653	−	23.3143i	−0.0922425	−	0.897368i
$676$		0			0
$677$	8.42072	+	14.5851i	0.323635	+	0.560551i	0.981235	−	0.192815i	$-0.0617618\pi$
$677$	8.42072	+	14.5851i	0.323635	+	0.560551i	−0.657601	+	0.753367i	$0.728429\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−10.6803	+	13.6487i	−0.409271	+	0.523020i
$682$		0			0
$683$			18.1929i			0.696132i	0.937470	+	0.348066i	$0.113162\pi$
$683$			18.1929i			0.696132i	−0.937470	+	0.348066i	$0.886838\pi$
$684$		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	$-0.688034\pi$
$691$	−3.05405	+	1.76326i	−0.116182	+	0.0670775i	0.440783	+	0.897614i	$0.354701\pi$
$692$		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
$703$			0.310122i			0.0116965i
$704$		0			0
$705$	3.17433	+	7.87401i	0.119552	+	0.296552i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	21.1447	+	36.6237i	0.794107	+	1.37543i	0.923405	+	0.383827i	$0.125394\pi$
$709$	21.1447	+	36.6237i	0.794107	+	1.37543i	−0.129298	+	0.991606i	$0.541273\pi$
$710$		0			0
$711$	4.02607	+	1.16110i	0.150990	+	0.0435448i
$712$		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
$717$	3.19843	−	22.6328i	0.119448	−	0.845237i
$718$		0			0
$719$	−30.4069			−1.13399			−0.566994	−	0.823722i	$-0.691894\pi$
$719$	−30.4069			−1.13399			−0.566994	+	0.823722i	$0.691894\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	3.47655	+	2.72045i	0.129294	+	0.101175i
$724$		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
$731$	13.9097	+	24.0924i	0.514470	+	0.891089i
$732$		0			0
$733$	32.7001	+	18.8794i	1.20781	+	0.697327i	0.962280	−	0.272063i	$-0.0877058\pi$
$733$	32.7001	+	18.8794i	1.20781	+	0.697327i	0.245527	+	0.969390i	$0.421039\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			1.57571i			0.0580419i
$738$		0			0
$739$	26.2430			0.965366			0.482683	−	0.875795i	$-0.339662\pi$
$739$	26.2430			0.965366			0.482683	+	0.875795i	$0.339662\pi$
$740$		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
$747$	21.4690	+	6.19157i	0.785508	+	0.226538i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−3.95369	+	6.84798i	−0.144272	+	0.249886i	−0.929101	−	0.369826i	$-0.879417\pi$
$751$	−3.95369	+	6.84798i	−0.144272	+	0.249886i	0.784829	+	0.619712i	$0.212751\pi$
$752$		0			0
$753$	12.1682	+	30.1836i	0.443435	+	1.09995i
$754$		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
$759$	−0.852714	−	2.11518i	−0.0309516	−	0.0767763i
$760$		0			0
$761$	−3.05687	+	5.29465i	−0.110811	+	0.191931i	−0.916098	−	0.400955i	$-0.868678\pi$
$761$	−3.05687	+	5.29465i	−0.110811	+	0.191931i	0.805286	+	0.592886i	$0.202012\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1.88137	+	7.59506i	0.0680209	+	0.274600i
$766$		0			0
$767$	15.3247	−	8.84771i	0.553342	−	0.319472i
$768$		0			0
$769$	−9.79863	−	5.65724i	−0.353348	−	0.204005i	0.312811	−	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
$773$	−38.4211			−1.38191			−0.690956	−	0.722896i	$-0.742810\pi$
$773$	−38.4211			−1.38191			−0.690956	+	0.722896i	$0.742810\pi$
$774$		0			0
$775$		−	25.2872i		−	0.908343i
$776$		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
$787$	41.2747	+	23.8300i	1.47129	+	0.849447i	0.999480	−	0.0322557i	$-0.0102691\pi$
$787$	41.2747	+	23.8300i	1.47129	+	0.849447i	0.471806	+	0.881703i	$0.343602\pi$
$788$		0			0
$789$	−10.7076	−	8.37882i	−0.381199	−	0.298294i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−7.42859			−0.263797
$794$		0			0
$795$	−1.66808	+	11.8037i	−0.0591608	+	0.418635i
$796$		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
$801$	24.1734	−	23.2729i	0.854126	−	0.822307i
$802$		0			0
$803$	1.02008	+	1.76683i	0.0359978	+	0.0623500i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	10.0026	+	24.8117i	0.352108	+	0.873415i
$808$		0			0
$809$			0.253310i			0.00890590i	0.999990	+	0.00445295i	$0.00141742\pi$
$809$			0.253310i			0.00890590i	−0.999990	+	0.00445295i	$0.998583\pi$
$810$		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	$-0.829145\pi$
$821$	−24.2467	+	13.9988i	−0.846214	+	0.488562i	0.0131576	+	0.999913i	$0.495812\pi$
$822$		0			0
$823$	−24.4771	+	42.3955i	−0.853217	+	1.47782i	0.0250719	+	0.999686i	$0.492019\pi$
$823$	−24.4771	+	42.3955i	−0.853217	+	1.47782i	−0.878289	+	0.478130i	$0.841315\pi$
$824$		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
$829$			11.0526i			0.383871i	0.981408	+	0.191936i	$0.0614765\pi$
$829$			11.0526i			0.383871i	−0.981408	+	0.191936i	$0.938523\pi$
$830$		0			0
$831$	−12.6920	+	16.2195i	−0.440281	+	0.562650i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.57029	−	2.71981i	−0.0543420	−	0.0941230i
$836$		0			0
$837$	17.0690	+	23.6068i	0.589991	+	0.815971i
$838$		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
$843$	−4.33796	−	3.39451i	−0.149407	−	0.116913i
$844$		0			0
$845$	−7.88693			−0.271319
$846$		0			0
$847$		0			0
$848$		0			0
$849$	4.48317	−	31.7239i	0.153862	−	1.08876i
$850$		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
$857$	−11.9260	−	20.6565i	−0.407385	−	0.705612i	0.587211	−	0.809434i	$-0.300226\pi$
$857$	−11.9260	−	20.6565i	−0.407385	−	0.705612i	−0.994596	+	0.103822i	$0.966893\pi$
$858$		0			0
$859$	9.62480	+	5.55688i	0.328394	+	0.189598i	0.655128	−	0.755518i	$-0.272615\pi$
$859$	9.62480	+	5.55688i	0.328394	+	0.189598i	−0.326734	+	0.945116i	$0.605948\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			44.7770i			1.52423i	0.647444	+	0.762113i	$0.275838\pi$
$863$			44.7770i			1.52423i	−0.647444	+	0.762113i	$0.724162\pi$
$864$		0			0
$865$	4.98256			0.169412
$866$		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
$873$	8.81415	−	30.5626i	0.298314	−	1.03439i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.84096	+	3.18863i	−0.0621647	+	0.107672i	−0.895433	−	0.445197i	$-0.853134\pi$
$877$	−1.84096	+	3.18863i	−0.0621647	+	0.107672i	0.833268	+	0.552869i	$0.186467\pi$
$878$		0			0
$879$	−4.90406	−	0.693033i	−0.165410	−	0.0233754i
$880$		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
$885$	10.0548	−	12.8493i	0.337988	−	0.431925i
$886$		0			0
$887$	23.1890	−	40.1645i	0.778610	−	1.34859i	−0.154132	−	0.988050i	$-0.549258\pi$
$887$	23.1890	−	40.1645i	0.778610	−	1.34859i	0.932743	−	0.360542i	$-0.117408\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.11417	+	2.11096i	0.0373262	+	0.0707199i
$892$		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
$899$	1.76915			0.0590046
$900$		0			0
$901$			36.6712i			1.22169i
$902$		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	0.701614	−	0.712557i	$-0.252463\pi$
$907$	−8.01957	−	13.8903i	−0.266285	−	0.461220i	−0.967900	+	0.251337i	$0.919130\pi$
$908$		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
$915$	−6.35261	+	2.56099i	−0.210011	+	0.0846637i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	35.4138			1.16819			0.584097	−	0.811684i	$-0.301449\pi$
$919$	35.4138			1.16819			0.584097	+	0.811684i	$0.301449\pi$
$920$		0			0
$921$	34.8186	−	14.0368i	1.14731	−	0.462527i
$922$		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
$927$	24.8748	−	6.16171i	0.816995	−	0.202377i
$928$		0			0
$929$	19.8626	+	34.4030i	0.651670	+	1.12873i	0.982718	+	0.185111i	$0.0592646\pi$
$929$	19.8626	+	34.4030i	0.651670	+	1.12873i	−0.331048	+	0.943614i	$0.607402\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	40.6328	+	5.74216i	1.33026	+	0.187990i
$934$		0			0
$935$			0.691740i			0.0226223i
$936$		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	−0.409278	−	0.912410i	$-0.634219\pi$
$941$	17.9616	−	31.1104i	0.585531	−	1.01417i	0.994809	−	0.101760i	$-0.0324474\pi$
$942$		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	$-0.499407\pi$
$947$	26.7365	−	15.4363i	0.868818	−	0.501612i	0.866955	+	0.498386i	$0.166074\pi$
$948$		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
$955$		−	2.07962i		−	0.0672950i
$956$		0			0
$957$	0.143534	+	0.0202840i	0.00463980	+	0.000655689i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.215406	+	0.373095i	0.00694859	+	0.0120353i
$962$		0			0
$963$	21.8511	+	22.6966i	0.704140	+	0.731387i
$964$		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
$969$	−2.64460	+	1.06614i	−0.0849568	+	0.0342494i
$970$		0			0
$971$	−33.2855			−1.06818			−0.534092	−	0.845427i	$-0.679346\pi$
$971$	−33.2855			−1.06818			−0.534092	+	0.845427i	$0.679346\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−9.52317	+	3.83917i	−0.304986	+	0.122952i
$976$		0			0
$977$	−38.9127	−	22.4662i	−1.24493	−	0.718758i	−0.274833	−	0.961492i	$-0.588623\pi$
$977$	−38.9127	−	22.4662i	−1.24493	−	0.718758i	−0.970093	+	0.242734i	$0.921956\pi$
$978$		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	$-0.307768\pi$
$983$	−13.4474	−	23.2916i	−0.428907	−	0.742888i	−0.996776	+	0.0802305i	$0.974434\pi$
$984$		0			0
$985$	8.59035	+	4.95964i	0.273711	+	0.158027i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			37.0492i			1.17810i
$990$		0			0
$991$	−35.4401			−1.12579			−0.562896	−	0.826528i	$-0.690313\pi$
$991$	−35.4401			−1.12579			−0.562896	+	0.826528i	$0.690313\pi$
$992$		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	0.0169046	−	0.999857i	$-0.494619\pi$
$997$	28.1418	−	16.2477i	0.891259	−	0.514568i	0.874354	+	0.485289i	$0.161286\pi$
$998$		0			0
$999$	−3.33011	−	1.49180i	−0.105360	−	0.0471984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.x.a.293.6		16
3.2	odd	2		5292.2.x.a.881.4		16
7.2	even	3		1764.2.bm.a.1697.1		16
7.3	odd	6		1764.2.w.b.509.3		16
7.4	even	3		252.2.w.a.5.6	✓	16
7.5	odd	6		252.2.bm.a.185.8	yes	16
7.6	odd	2		1764.2.x.b.293.3		16
9.2	odd	6		1764.2.x.b.1469.3		16
9.7	even	3		5292.2.x.b.4409.5		16
21.2	odd	6		5292.2.bm.a.2285.5		16
21.5	even	6		756.2.bm.a.17.4		16
21.11	odd	6		756.2.w.a.341.4		16
21.17	even	6		5292.2.w.b.1097.5		16
21.20	even	2		5292.2.x.b.881.5		16
28.11	odd	6		1008.2.ca.d.257.3		16
28.19	even	6		1008.2.df.d.689.1		16
63.2	odd	6		1764.2.w.b.1109.3		16
63.4	even	3		2268.2.t.b.2105.5		16
63.5	even	6		2268.2.t.b.1781.5		16
63.11	odd	6		252.2.bm.a.173.8	yes	16
63.16	even	3		5292.2.w.b.521.5		16
63.20	even	6	inner	1764.2.x.a.1469.6		16
63.25	even	3		756.2.bm.a.89.4		16
63.32	odd	6		2268.2.t.a.2105.4		16
63.34	odd	6		5292.2.x.a.4409.4		16
63.38	even	6		1764.2.bm.a.1685.1		16
63.40	odd	6		2268.2.t.a.1781.4		16
63.47	even	6		252.2.w.a.101.6	yes	16
63.52	odd	6		5292.2.bm.a.4625.5		16
63.61	odd	6		756.2.w.a.521.4		16
84.11	even	6		3024.2.ca.d.2609.4		16
84.47	odd	6		3024.2.df.d.17.4		16
252.11	even	6		1008.2.df.d.929.1		16
252.47	odd	6		1008.2.ca.d.353.3		16
252.151	odd	6		3024.2.df.d.1601.4		16
252.187	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	7.4	even	3
252.2.w.a.101.6	yes	16	63.47	even	6
252.2.bm.a.173.8	yes	16	63.11	odd	6
252.2.bm.a.185.8	yes	16	7.5	odd	6
756.2.w.a.341.4		16	21.11	odd	6
756.2.w.a.521.4		16	63.61	odd	6
756.2.bm.a.17.4		16	21.5	even	6
756.2.bm.a.89.4		16	63.25	even	3
1008.2.ca.d.257.3		16	28.11	odd	6
1008.2.ca.d.353.3		16	252.47	odd	6
1008.2.df.d.689.1		16	28.19	even	6
1008.2.df.d.929.1		16	252.11	even	6
1764.2.w.b.509.3		16	7.3	odd	6
1764.2.w.b.1109.3		16	63.2	odd	6
1764.2.x.a.293.6		16	1.1	even	1	trivial
1764.2.x.a.1469.6		16	63.20	even	6	inner
1764.2.x.b.293.3		16	7.6	odd	2
1764.2.x.b.1469.3		16	9.2	odd	6
1764.2.bm.a.1685.1		16	63.38	even	6
1764.2.bm.a.1697.1		16	7.2	even	3
2268.2.t.a.1781.4		16	63.40	odd	6
2268.2.t.a.2105.4		16	63.32	odd	6
2268.2.t.b.1781.5		16	63.5	even	6
2268.2.t.b.2105.5		16	63.4	even	3
3024.2.ca.d.2033.4		16	252.187	even	6
3024.2.ca.d.2609.4		16	84.11	even	6
3024.2.df.d.17.4		16	84.47	odd	6
3024.2.df.d.1601.4		16	252.151	odd	6
5292.2.w.b.521.5		16	63.16	even	3
5292.2.w.b.1097.5		16	21.17	even	6
5292.2.x.a.881.4		16	3.2	odd	2
5292.2.x.a.4409.4		16	63.34	odd	6
5292.2.x.b.881.5		16	21.20	even	2
5292.2.x.b.4409.5		16	9.7	even	3
5292.2.bm.a.2285.5		16	21.2	odd	6
5292.2.bm.a.4625.5		16	63.52	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.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.647613 + 1.60642i) q^{3} +(0.349828 - 0.605920i) q^{5} +(-2.16119 + 2.08068i) q^{9} +O(q^{10})\)	\(q+(0.647613 + 1.60642i) q^{3} +(0.349828 - 0.605920i) q^{5} +(-2.16119 + 2.08068i) q^{9} +(-0.229685 + 0.132608i) q^{11} +(1.13823 + 0.657156i) q^{13} +(1.19992 + 0.169570i) q^{15} +3.72784 q^{17} +0.441614i q^{19} +(4.29949 + 2.48231i) q^{23} +(2.25524 + 3.90619i) q^{25} +(-4.74208 - 2.12432i) q^{27} +(-0.273287 + 0.157782i) q^{29} +(-4.85521 - 2.80316i) q^{31} +(-0.361772 - 0.283092i) q^{33} +0.702248 q^{37} +(-0.318540 + 2.25406i) q^{39} +(-5.39354 + 9.34189i) q^{41} +(3.73131 + 6.46283i) q^{43} +(0.504680 + 2.03739i) q^{45} +(3.50285 + 6.06712i) q^{47} +(2.41420 + 5.98849i) q^{51} +9.83712i q^{53} +0.185561i q^{55} +(-0.709419 + 0.285995i) q^{57} +(6.73182 - 11.6598i) q^{59} +(-4.89484 + 2.82604i) q^{61} +(0.796368 - 0.459783i) q^{65} +(2.97060 - 5.14523i) q^{67} +(-1.20324 + 8.51439i) q^{69} +13.4323i q^{71} -7.69241i q^{73} +(-4.81448 + 6.15257i) q^{75} +(-0.698360 - 1.20959i) q^{79} +(0.341524 - 8.99352i) q^{81} +(-3.72399 - 6.45014i) q^{83} +(1.30410 - 2.25877i) q^{85} +(-0.430449 - 0.336832i) q^{87} -11.1852 q^{89} +(1.35876 - 9.61489i) q^{93} +(0.267582 + 0.154489i) q^{95} +(-9.18225 + 5.30138i) q^{97} +(0.220477 - 0.764493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{9}+O(q^{10}) \) 16 * q - 6 * q^9	\( 16 q - 6 q^{9} + 6 q^{11} - 3 q^{13} - 3 q^{15} - 18 q^{17} - 21 q^{23} - 8 q^{25} + 9 q^{27} + 6 q^{29} + 6 q^{31} - 27 q^{33} - 2 q^{37} + 6 q^{39} - 6 q^{41} - 2 q^{43} + 15 q^{45} + 18 q^{47} + 18 q^{51} + 15 q^{57} + 15 q^{59} + 3 q^{61} + 39 q^{65} - 7 q^{67} + 21 q^{69} + 42 q^{75} - q^{79} - 18 q^{81} + 6 q^{85} - 51 q^{87} - 42 q^{89} + 48 q^{93} - 6 q^{95} - 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q - 6 * q^9 + 6 * q^11 - 3 * q^13 - 3 * q^15 - 18 * q^17 - 21 * q^23 - 8 * q^25 + 9 * q^27 + 6 * q^29 + 6 * q^31 - 27 * q^33 - 2 * q^37 + 6 * q^39 - 6 * q^41 - 2 * q^43 + 15 * q^45 + 18 * q^47 + 18 * q^51 + 15 * q^57 + 15 * q^59 + 3 * q^61 + 39 * q^65 - 7 * q^67 + 21 * q^69 + 42 * q^75 - q^79 - 18 * q^81 + 6 * q^85 - 51 * q^87 - 42 * q^89 + 48 * q^93 - 6 * q^95 - 3 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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