LMFDB - Embedded newform 729.2.i.a.10.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(10,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(162))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("729.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.i (of order $81$, degree $54$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			10.8
Character	$\chi$	$=$	729.10
Dual form			729.2.i.a.73.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35949 - 0.212621i) q^{2} +(-0.101477 - 0.0325373i) q^{4} +(3.22186 + 1.46451i) q^{5} +(0.584445 + 4.27889i) q^{7} +(2.59035 + 1.30092i) q^{8} +O(q^{10})$	\(q+(-1.35949 - 0.212621i) q^{2} +(-0.101477 - 0.0325373i) q^{4} +(3.22186 + 1.46451i) q^{5} +(0.584445 + 4.27889i) q^{7} +(2.59035 + 1.30092i) q^{8} +(-4.06871 - 2.67603i) q^{10} +(5.43439 - 0.422394i) q^{11} +(-0.0701422 - 0.204998i) q^{13} +(0.115233 - 5.94140i) q^{14} +(-3.07158 - 2.19543i) q^{16} +(-0.981582 + 2.27556i) q^{17} +(-1.97195 + 2.64879i) q^{19} +(-0.279293 - 0.253445i) q^{20} +(-7.47784 - 0.581224i) q^{22} +(-3.96219 - 3.07093i) q^{23} +(4.94795 + 5.66972i) q^{25} +(0.0517710 + 0.293608i) q^{26} +(0.0799158 - 0.453225i) q^{28} +(-4.49735 + 2.71417i) q^{29} +(-6.71823 + 0.260698i) q^{31} +(-0.429909 - 0.421652i) q^{32} +(1.81829 - 2.88491i) q^{34} +(-4.38350 + 14.6419i) q^{35} +(4.90612 - 5.20018i) q^{37} +(3.24404 - 3.18174i) q^{38} +(6.44053 + 7.98500i) q^{40} +(2.40381 - 6.22602i) q^{41} +(-0.0486951 - 0.189046i) q^{43} +(-0.565210 - 0.133957i) q^{44} +(4.73364 + 5.01736i) q^{46} +(9.52815 + 0.369736i) q^{47} +(-11.2237 + 3.12434i) q^{49} +(-5.52121 - 8.75999i) q^{50} +(0.000447730 + 0.0230849i) q^{52} +(8.82337 - 3.21144i) q^{53} +(18.1274 + 6.59785i) q^{55} +(-4.05260 + 11.8442i) q^{56} +(6.69122 - 2.73366i) q^{58} +(0.139348 + 0.291422i) q^{59} +(-2.94866 + 0.945449i) q^{61} +(9.18884 + 1.07402i) q^{62} +(5.00397 + 6.72149i) q^{64} +(0.0742347 - 0.763199i) q^{65} +(-4.98615 - 3.00916i) q^{67} +(0.173649 - 0.198979i) q^{68} +(9.07252 - 18.9736i) q^{70} +(-0.0548875 + 0.942381i) q^{71} +(-2.84459 + 1.87092i) q^{73} +(-7.77552 + 6.02648i) q^{74} +(0.286292 - 0.204629i) q^{76} +(4.98348 + 23.0063i) q^{77} +(-4.53689 + 5.62486i) q^{79} +(-6.68094 - 11.5717i) q^{80} +(-4.59175 + 7.95315i) q^{82} +(2.11065 + 5.46672i) q^{83} +(-6.49511 + 5.89400i) q^{85} +(0.0260056 + 0.267361i) q^{86} +(14.6265 + 5.97559i) q^{88} +(-0.0688294 - 1.18176i) q^{89} +(0.836172 - 0.419941i) q^{91} +(0.302152 + 0.440548i) q^{92} +(-12.8749 - 2.52854i) q^{94} +(-10.2325 + 5.64607i) q^{95} +(1.17303 - 0.533206i) q^{97} +(15.9229 - 1.86112i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{81}\right)$

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 $

$2$	−1.35949	−	0.212621i	−0.961308	−	0.150346i	−0.345654	−	0.938362i	$-0.612343\pi$
$2$	−1.35949	−	0.212621i	−0.961308	−	0.150346i	−0.615654	+	0.788016i	$0.711108\pi$
$3$		0			0
$3$		0			0
$4$	−0.101477	−	0.0325373i	−0.0507385	−	0.0162686i
$5$	3.22186	+	1.46451i	1.44086	+	0.654950i	0.973410	−	0.229071i	$-0.0735687\pi$
$5$	3.22186	+	1.46451i	1.44086	+	0.654950i	0.467448	+	0.884021i	$0.345174\pi$
$6$		0			0
$7$	0.584445	+	4.27889i	0.220899	+	1.61727i	0.682984	+	0.730433i	$0.260682\pi$
$7$	0.584445	+	4.27889i	0.220899	+	1.61727i	−0.462085	+	0.886836i	$0.652898\pi$
$8$	2.59035	+	1.30092i	0.915829	+	0.459946i
$9$		0			0
$10$	−4.06871	−	2.67603i	−1.28664	−	0.846236i
$11$	5.43439	−	0.422394i	1.63853	−	0.127357i	0.775105	−	0.631832i	$-0.217697\pi$
$11$	5.43439	−	0.422394i	1.63853	−	0.127357i	0.863426	+	0.504475i	$0.168314\pi$
$12$		0			0
$13$	−0.0701422	−	0.204998i	−0.0194540	−	0.0568563i	0.935994	−	0.352016i	$-0.114504\pi$
$13$	−0.0701422	−	0.204998i	−0.0194540	−	0.0568563i	−0.955448	+	0.295160i	$0.904627\pi$
$14$	0.115233	−	5.94140i	0.0307974	−	1.58790i
$15$		0			0
$16$	−3.07158	−	2.19543i	−0.767894	−	0.548858i
$17$	−0.981582	+	2.27556i	−0.238069	+	0.551905i	−0.994803	−	0.101817i	$-0.967534\pi$
$17$	−0.981582	+	2.27556i	−0.238069	+	0.551905i	0.756734	+	0.653722i	$0.226794\pi$
$18$		0			0
$19$	−1.97195	+	2.64879i	−0.452396	+	0.607674i	−0.968549	−	0.248823i	$-0.919956\pi$
$19$	−1.97195	+	2.64879i	−0.452396	+	0.607674i	0.516153	+	0.856497i	$0.327364\pi$
$20$	−0.279293	−	0.253445i	−0.0624518	−	0.0566720i
$21$		0			0
$22$	−7.47784	−	0.581224i	−1.59428	−	0.123917i
$23$	−3.96219	−	3.07093i	−0.826174	−	0.640333i	0.109189	−	0.994021i	$-0.465175\pi$
$23$	−3.96219	−	3.07093i	−0.826174	−	0.640333i	−0.935364	+	0.353688i	$0.884928\pi$
$24$		0			0
$25$	4.94795	+	5.66972i	0.989589	+	1.13394i
$26$	0.0517710	+	0.293608i	0.0101531	+	0.0575813i
$27$		0			0
$28$	0.0799158	−	0.453225i	0.0151027	−	0.0856515i
$29$	−4.49735	+	2.71417i	−0.835138	+	0.504008i	−0.868648	−	0.495430i	$-0.835010\pi$
$29$	−4.49735	+	2.71417i	−0.835138	+	0.504008i	0.0335102	+	0.999438i	$0.489331\pi$
$30$		0			0
$31$	−6.71823	+	0.260698i	−1.20663	+	0.0468228i	−0.634225	−	0.773148i	$-0.718681\pi$
$31$	−6.71823	+	0.260698i	−1.20663	+	0.0468228i	−0.572405	+	0.819971i	$0.693990\pi$
$32$	−0.429909	−	0.421652i	−0.0759980	−	0.0745383i
$33$		0			0
$34$	1.81829	−	2.88491i	0.311834	−	0.494758i
$35$	−4.38350	+	14.6419i	−0.740946	+	2.47493i
$36$		0			0
$37$	4.90612	−	5.20018i	0.806561	−	0.854905i	−0.185240	−	0.982693i	$-0.559306\pi$
$37$	4.90612	−	5.20018i	0.806561	−	0.854905i	0.991801	+	0.127788i	$0.0407878\pi$
$38$	3.24404	−	3.18174i	0.526253	−	0.516146i
$39$		0			0
$40$	6.44053	+	7.98500i	1.01834	+	1.26254i
$41$	2.40381	−	6.22602i	0.375412	−	0.972342i	−0.608479	−	0.793570i	$-0.708220\pi$
$41$	2.40381	−	6.22602i	0.375412	−	0.972342i	0.983891	−	0.178771i	$-0.0572123\pi$
$42$		0			0
$43$	−0.0486951	−	0.189046i	−0.00742593	−	0.0288292i	0.964570	−	0.263828i	$-0.0849852\pi$
$43$	−0.0486951	−	0.189046i	−0.00742593	−	0.0288292i	−0.971996	+	0.234999i	$0.924491\pi$
$44$	−0.565210	−	0.133957i	−0.0852085	−	0.0201948i
$45$		0			0
$46$	4.73364	+	5.01736i	0.697937	+	0.739770i
$47$	9.52815	+	0.369736i	1.38982	+	0.0539315i	0.722775	−	0.691083i	$-0.242866\pi$
$47$	9.52815	+	0.369736i	1.38982	+	0.0539315i	0.667048	+	0.745015i	$0.267558\pi$
$48$		0			0
$49$	−11.2237	+	3.12434i	−1.60339	+	0.446334i
$50$	−5.52121	−	8.75999i	−0.780816	−	1.23885i
$51$		0			0
$52$	0.000447730		0.0230849i	6.20890e−5		0.00320129i
$53$	8.82337	−	3.21144i	1.21198	−	0.441126i	0.344592	−	0.938753i	$-0.388017\pi$
$53$	8.82337	−	3.21144i	1.21198	−	0.441126i	0.867391	+	0.497627i	$0.165795\pi$
$54$		0			0
$55$	18.1274	+	6.59785i	2.44430	+	0.889653i
$56$	−4.05260	+	11.8442i	−0.541551	+	1.58274i
$57$		0			0
$58$	6.69122	−	2.73366i	0.878600	−	0.358948i
$59$	0.139348	+	0.291422i	0.0181416	+	0.0379398i	0.911039	−	0.412321i	$-0.135282\pi$
$59$	0.139348	+	0.291422i	0.0181416	+	0.0379398i	−0.892897	+	0.450261i	$0.851331\pi$
$60$		0			0
$61$	−2.94866	+	0.945449i	−0.377537	+	0.121052i	−0.488035	−	0.872824i	$-0.662286\pi$
$61$	−2.94866	+	0.945449i	−0.377537	+	0.121052i	0.110498	+	0.993876i	$0.464755\pi$
$62$	9.18884	+	1.07402i	1.16698	+	0.136401i
$63$		0			0
$64$	5.00397	+	6.72149i	0.625496	+	0.840187i
$65$	0.0742347	−	0.763199i	0.00920768	−	0.0946632i
$66$		0			0
$67$	−4.98615	−	3.00916i	−0.609155	−	0.367627i	0.178321	−	0.983972i	$-0.442934\pi$
$67$	−4.98615	−	3.00916i	−0.609155	−	0.367627i	−0.787476	+	0.616345i	$0.788613\pi$
$68$	0.173649	−	0.198979i	0.0210580	−	0.0241298i
$69$		0			0
$70$	9.07252	−	18.9736i	1.08437	−	2.26777i
$71$	−0.0548875	+	0.942381i	−0.00651394	+	0.111840i	−0.999998	−	0.00213349i	$-0.999321\pi$
$71$	−0.0548875	+	0.942381i	−0.00651394	+	0.111840i	0.993484	+	0.113974i	$0.0363579\pi$
$72$		0			0
$73$	−2.84459	+	1.87092i	−0.332934	+	0.218974i	−0.704958	−	0.709249i	$-0.749034\pi$
$73$	−2.84459	+	1.87092i	−0.332934	+	0.218974i	0.372024	+	0.928223i	$0.378664\pi$
$74$	−7.77552	+	6.02648i	−0.903885	+	0.700564i
$75$		0			0
$76$	0.286292	−	0.204629i	0.0328399	−	0.0234726i
$77$	4.98348	+	23.0063i	0.567920	+	2.62181i
$78$		0			0
$79$	−4.53689	+	5.62486i	−0.510439	+	0.632846i	−0.966366	−	0.257172i	$-0.917209\pi$
$79$	−4.53689	+	5.62486i	−0.510439	+	0.632846i	0.455926	+	0.890018i	$0.349308\pi$
$80$	−6.68094	−	11.5717i	−0.746951	−	1.29376i
$81$		0			0
$82$	−4.59175	+	7.95315i	−0.507074	+	0.878278i
$83$	2.11065	+	5.46672i	0.231674	+	0.600051i	0.999158	−	0.0410169i	$-0.0130597\pi$
$83$	2.11065	+	5.46672i	0.231674	+	0.600051i	−0.767484	+	0.641068i	$0.778492\pi$
$84$		0			0
$85$	−6.49511	+	5.89400i	−0.704493	+	0.639294i
$86$	0.0260056	+	0.267361i	0.00280425	+	0.0288302i
$87$		0			0
$88$	14.6265	+	5.97559i	1.55919	+	0.637000i
$89$	−0.0688294	−	1.18176i	−0.00729590	−	0.125266i	−0.999989	−	0.00460261i	$-0.998535\pi$
$89$	−0.0688294	−	1.18176i	−0.00729590	−	0.125266i	0.992694	−	0.120663i	$-0.0385021\pi$
$90$		0			0
$91$	0.836172	−	0.419941i	0.0876546	−	0.0440218i
$92$	0.302152	+	0.440548i	0.0315015	+	0.0459303i
$93$		0			0
$94$	−12.8749	−	2.52854i	−1.32794	−	0.260799i
$95$	−10.2325	+	5.64607i	−1.04983	+	0.579274i
$96$		0			0
$97$	1.17303	−	0.533206i	0.119103	−	0.0541389i	−0.353373	−	0.935483i	$-0.614965\pi$
$97$	1.17303	−	0.533206i	0.119103	−	0.0541389i	0.472476	+	0.881344i	$0.343360\pi$
$98$	15.9229	−	1.86112i	1.60846	−	0.188002i
$99$		0			0
$100$	−0.317625	−	0.736339i	−0.0317625	−	0.0736339i
$101$	0.377975	−	1.74493i	0.0376099	−	0.173627i	−0.954666	−	0.297680i	$-0.903787\pi$
$101$	0.377975	−	1.74493i	0.0376099	−	0.173627i	0.992276	+	0.124054i	$0.0395895\pi$
$102$		0			0
$103$	6.00085	−	8.74946i	0.591281	−	0.862109i	−0.407410	−	0.913245i	$-0.633568\pi$
$103$	6.00085	−	8.74946i	0.591281	−	0.862109i	0.998692	+	0.0511358i	$0.0162841\pi$
$104$	0.0849943	−	0.622268i	0.00833438	−	0.0610184i
$105$		0			0
$106$	−12.6781	+	2.48991i	−1.23141	+	0.241841i
$107$	−11.9969	+	10.0666i	−1.15979	+	0.973178i	−0.999903	−	0.0139578i	$-0.995557\pi$
$107$	−11.9969	+	10.0666i	−1.15979	+	0.973178i	−0.159886	+	0.987136i	$0.551113\pi$
$108$		0			0
$109$	1.60923	+	1.35031i	0.154136	+	0.129336i	0.716595	−	0.697490i	$-0.245700\pi$
$109$	1.60923	+	1.35031i	0.154136	+	0.129336i	−0.562458	+	0.826826i	$0.690144\pi$
$110$	−23.2413	−	12.8240i	−2.21597	−	1.22272i
$111$		0			0
$112$	7.59884	−	14.4260i	0.718023	−	1.36313i
$113$	2.17447	−	8.44183i	0.204557	−	0.794140i	−0.780962	−	0.624578i	$-0.785271\pi$
$113$	2.17447	−	8.44183i	0.204557	−	0.794140i	0.985520	−	0.169562i	$-0.0542353\pi$
$114$		0			0
$115$	−8.26819	−	15.6968i	−0.771013	−	1.46373i
$116$	0.544690	−	0.129094i	0.0505732	−	0.0119861i
$117$		0			0
$118$	−0.127480	−	0.425814i	−0.0117355	−	0.0391994i
$119$	−10.3106	−	2.87014i	−0.945168	−	0.263106i
$120$		0			0
$121$	18.4863	−	2.89121i	1.68058	−	0.262837i
$122$	4.20971	−	0.658386i	0.381129	−	0.0596075i
$123$		0			0
$124$	0.690229	+	0.192138i	0.0619844	+	0.0172545i
$125$	2.56308	+	8.56129i	0.229249	+	0.765745i
$126$		0			0
$127$	2.26631	−	0.537124i	0.201102	−	0.0476621i	−0.128830	−	0.991667i	$-0.541122\pi$
$127$	2.26631	−	0.537124i	0.201102	−	0.0476621i	0.329932	+	0.944005i	$0.392974\pi$
$128$	−4.81246	−	9.13623i	−0.425365	−	0.807536i
$129$		0			0
$130$	−0.263194	+	1.02178i	−0.0230836	+	0.0896162i
$131$	7.52718	−	14.2900i	0.657653	−	1.24852i	−0.298152	−	0.954519i	$-0.596370\pi$
$131$	7.52718	−	14.2900i	0.657653	−	1.24852i	0.955804	−	0.294004i	$-0.0949879\pi$
$132$		0			0
$133$	−12.4864	−	6.88969i	−1.08271	−	0.597412i
$134$	6.13883	+	5.15109i	0.530314	+	0.444987i
$135$		0			0
$136$	−5.50298	+	4.61755i	−0.471877	+	0.395952i
$137$	15.6616	−	3.07584i	1.33806	−	0.262787i	0.528056	−	0.849209i	$-0.322921\pi$
$137$	15.6616	−	3.07584i	1.33806	−	0.262787i	0.810005	+	0.586423i	$0.199464\pi$
$138$		0			0
$139$	−0.855711	+	6.26491i	−0.0725805	+	0.531383i	0.918222	+	0.396066i	$0.129625\pi$
$139$	−0.855711	+	6.26491i	−0.0725805	+	0.531383i	−0.990802	+	0.135317i	$0.956795\pi$
$140$	0.921232	−	1.34319i	0.0778583	−	0.113520i
$141$		0			0
$142$	0.274989	−	1.26949i	0.0230766	−	0.106533i
$143$	−0.467771	−	1.08441i	−0.0391169	−	0.0906833i
$144$		0			0
$145$	−18.4648	+	2.15822i	−1.53341	+	0.179230i
$146$	4.26501	−	1.93868i	0.352975	−	0.160447i
$147$		0			0
$148$	−0.667058	+	0.368067i	−0.0548319	+	0.0302549i
$149$	−8.60546	−	1.69006i	−0.704986	−	0.138455i	−0.172644	−	0.984984i	$-0.555231\pi$
$149$	−8.60546	−	1.69006i	−0.704986	−	0.138455i	−0.532342	+	0.846529i	$0.678688\pi$
$150$		0			0
$151$	5.52496	+	8.05558i	0.449615	+	0.655554i	0.981544	−	0.191234i	$-0.0612490\pi$
$151$	5.52496	+	8.05558i	0.449615	+	0.655554i	−0.531930	+	0.846788i	$0.678533\pi$
$152$	−8.55392	+	4.29594i	−0.693815	+	0.348447i
$153$		0			0
$154$	−1.88339	−	32.3366i	−0.151768	−	2.60575i
$155$	−22.0270	−	8.99901i	−1.76925	−	0.722818i
$156$		0			0
$157$	−0.616656	−	6.33977i	−0.0492145	−	0.505969i	−0.987222	−	0.159353i	$-0.949059\pi$
$157$	−0.616656	−	6.33977i	−0.0492145	−	0.505969i	0.938007	−	0.346616i	$-0.112669\pi$
$158$	7.36384	−	6.68232i	0.585835	−	0.531617i
$159$		0			0
$160$	−0.767591	−	1.98811i	−0.0606834	−	0.157174i
$161$	10.8245	−	18.7486i	0.853090	−	1.47760i
$162$		0			0
$163$	10.1758	+	17.6250i	0.797030	+	1.38050i	0.921542	+	0.388279i	$0.126930\pi$
$163$	10.1758	+	17.6250i	0.797030	+	1.38050i	−0.124512	+	0.992218i	$0.539736\pi$
$164$	−0.446509	+	0.553585i	−0.0348665	+	0.0432277i
$165$		0			0
$166$	−1.70708	−	7.88075i	−0.132495	−	0.611665i
$167$	−3.22619	+	2.30594i	−0.249650	+	0.178439i	−0.699432	−	0.714699i	$-0.746564\pi$
$167$	−3.22619	+	2.30594i	−0.249650	+	0.178439i	0.449782	+	0.893139i	$0.351502\pi$
$168$		0			0
$169$	10.2380	−	7.93505i	0.787538	−	0.610388i
$170$	10.0833	−	6.63186i	0.773350	−	0.508641i
$171$		0			0
$172$	−0.00120961	+	0.0207682i	−9.22320e−5	+	0.00158356i
$173$	8.01974	−	16.7719i	0.609730	−	1.27514i	−0.333422	−	0.942778i	$-0.608203\pi$
$173$	8.01974	−	16.7719i	0.609730	−	1.27514i	0.943151	−	0.332364i	$-0.107846\pi$
$174$		0			0
$175$	−21.3683	+	24.4854i	−1.61529	+	1.85092i
$176$	−17.6195	−	10.6334i	−1.32812	−	0.801524i
$177$		0			0
$178$	−0.157693	+	1.62122i	−0.0118196	+	0.121516i
$179$	5.00316	+	6.72041i	0.373954	+	0.502307i	0.948767	−	0.315978i	$-0.102333\pi$
$179$	5.00316	+	6.72041i	0.373954	+	0.502307i	−0.574813	+	0.818285i	$0.694925\pi$
$180$		0			0
$181$	−17.2271	−	2.01355i	−1.28048	−	0.149666i	−0.551483	−	0.834186i	$-0.685938\pi$
$181$	−17.2271	−	2.01355i	−1.28048	−	0.149666i	−0.728994	+	0.684520i	$0.760012\pi$
$182$	−1.22606	+	0.393120i	−0.0908816	+	0.0291400i
$183$		0			0
$184$	−6.26843	−	13.1093i	−0.462115	−	0.966431i
$185$	23.4225	−	9.56916i	1.72206	−	0.703539i
$186$		0			0
$187$	−4.37312	+	12.7809i	−0.319794	+	0.934634i
$188$	−0.954858	−	0.347540i	−0.0696402	−	0.0253469i
$189$		0			0
$190$	15.1115	−	5.50015i	1.09631	−	0.399023i
$191$	0.424340	+	21.8789i	0.0307042	+	1.58310i	0.626150	+	0.779703i	$0.284630\pi$
$191$	0.424340	+	21.8789i	0.0307042	+	1.58310i	−0.595446	+	0.803396i	$0.703025\pi$
$192$		0			0
$193$	−3.71483	−	5.89397i	−0.267399	−	0.424257i	0.685260	−	0.728299i	$-0.259689\pi$
$193$	−3.71483	−	5.89397i	−0.267399	−	0.424257i	−0.952659	+	0.304041i	$0.901664\pi$
$194$	−1.70810	+	0.475481i	−0.122634	+	0.0341375i
$195$		0			0
$196$	1.24061	+	0.0481413i	0.0886149	+	0.00343866i
$197$	−3.33296	−	3.53273i	−0.237464	−	0.251697i	0.597672	−	0.801741i	$-0.296092\pi$
$197$	−3.33296	−	3.53273i	−0.237464	−	0.251697i	−0.835136	+	0.550044i	$0.814611\pi$
$198$		0			0
$199$	5.88341	+	1.39439i	0.417064	+	0.0988459i	0.433790	−	0.901014i	$-0.357176\pi$
$199$	5.88341	+	1.39439i	0.417064	+	0.0988459i	−0.0167260	+	0.999860i	$0.505324\pi$
$200$	5.44106	+	21.1235i	0.384741	+	1.49366i
$201$		0			0
$202$	−0.884863	+	2.29185i	−0.0622588	+	0.161254i
$203$	−14.2421	−	17.6574i	−0.999598	−	1.23931i
$204$		0			0
$205$	16.8628	−	16.5389i	1.17775	−	1.15513i
$206$	−10.0184	+	10.6189i	−0.698018	+	0.739856i
$207$		0			0
$208$	−0.234613	+	0.783661i	−0.0162675	+	0.0543371i
$209$	−9.59752	+	15.2275i	−0.663874	+	1.05331i
$210$		0			0
$211$	1.26981	+	1.24542i	0.0874176	+	0.0857385i	0.742613	−	0.669721i	$-0.233586\pi$
$211$	1.26981	+	1.24542i	0.0874176	+	0.0857385i	−0.655195	+	0.755460i	$0.727414\pi$
$212$	−0.999861	+	0.0387992i	−0.0686707	+	0.00266474i
$213$		0			0
$214$	18.4502	−	11.1347i	1.26123	−	0.761154i
$215$	0.119972	−	0.680393i	0.00818200	−	0.0464024i
$216$		0			0
$217$	−5.04193	−	28.5942i	−0.342269	−	1.94110i
$218$	−1.90064	−	2.17789i	−0.128727	−	0.147505i
$219$		0			0
$220$	−1.62484	−	1.25935i	−0.109547	−	0.0849052i
$221$	0.535337	+	0.0416097i	0.0360107	+	0.00279897i
$222$		0			0
$223$	−16.0878	−	14.5989i	−1.07732	−	0.977617i	−0.0775092	−	0.996992i	$-0.524697\pi$
$223$	−16.0878	−	14.5989i	−1.07732	−	0.977617i	−0.999812	+	0.0193745i	$0.993833\pi$
$224$	1.55295	−	2.08597i	0.103761	−	0.139375i
$225$		0			0
$226$	−4.75110	+	11.0143i	−0.316038	+	0.732659i
$227$	4.87097	+	3.48156i	0.323298	+	0.231079i	0.731547	−	0.681791i	$-0.238799\pi$
$227$	4.87097	+	3.48156i	0.323298	+	0.231079i	−0.408249	+	0.912871i	$0.633860\pi$
$228$		0			0
$229$	−0.190532	+	9.82381i	−0.0125907	+	0.649175i	0.939361	+	0.342929i	$0.111419\pi$
$229$	−0.190532	+	9.82381i	−0.0125907	+	0.649175i	−0.951952	+	0.306247i	$0.900927\pi$
$230$	7.90310	+	23.0977i	0.521115	+	1.52302i
$231$		0			0
$232$	−15.1807	+	1.17993i	−0.996659	+	0.0774665i
$233$	−17.6812	−	11.6291i	−1.15833	−	0.761846i	−0.183113	−	0.983092i	$-0.558617\pi$
$233$	−17.6812	−	11.6291i	−1.15833	−	0.761846i	−0.975218	+	0.221246i	$0.928988\pi$
$234$		0			0
$235$	30.1568	+	15.1453i	1.96721	+	0.987973i
$236$	−0.00465855	−	0.0341066i	−0.000303245	−	0.00222015i
$237$		0			0
$238$	13.4069	+	6.09419i	0.869041	+	0.395028i
$239$	−6.55571	−	2.10201i	−0.424054	−	0.135967i	0.0856342	−	0.996327i	$-0.472708\pi$
$239$	−6.55571	−	2.10201i	−0.424054	−	0.135967i	−0.509688	+	0.860359i	$0.670239\pi$
$240$		0			0
$241$	5.50833	+	0.861486i	0.354822	+	0.0554932i	0.329418	−	0.944184i	$-0.393147\pi$
$241$	5.50833	+	0.861486i	0.354822	+	0.0554932i	0.0254040	+	0.999677i	$0.491913\pi$
$242$	−25.7468			−1.65507
$243$		0			0
$244$	0.329983			0.0211250
$245$	−40.7369	−	6.37113i	−2.60258	−	0.407037i
$246$		0			0
$247$	0.681314	+	0.218455i	0.0433510	+	0.0138999i
$248$	−17.7418	−	8.06462i	−1.12660	−	0.512104i
$249$		0			0
$250$	−1.66419	−	12.1840i	−0.105252	−	0.770583i
$251$	−10.0009	−	5.02262i	−0.631249	−	0.317025i	0.104250	−	0.994551i	$-0.466756\pi$
$251$	−10.0009	−	5.02262i	−0.631249	−	0.317025i	−0.735499	+	0.677526i	$0.763052\pi$
$252$		0			0
$253$	−22.8293	−	15.0150i	−1.43526	−	0.943987i
$254$	−3.19524	+	0.248353i	−0.200487	+	0.0155831i
$255$		0			0
$256$	−0.825582	−	2.41286i	−0.0515989	−	0.150803i
$257$	0.285049	−	14.6970i	0.0177808	−	0.916776i	−0.879650	−	0.475621i	$-0.842223\pi$
$257$	0.285049	−	14.6970i	0.0177808	−	0.916776i	0.897431	−	0.441155i	$-0.145431\pi$
$258$		0			0
$259$	25.1184	+	17.9535i	1.56078	+	1.11558i
$260$	−0.0323656	+	0.0750318i	−0.00200723	+	0.00465327i
$261$		0			0
$262$	−13.2715	+	17.8267i	−0.819917	+	1.10134i
$263$	18.7681	+	17.0311i	1.15729	+	1.05018i	0.998017	+	0.0629488i	$0.0200505\pi$
$263$	18.7681	+	17.0311i	1.15729	+	1.05018i	0.159272	+	0.987235i	$0.449085\pi$
$264$		0			0
$265$	33.1308	+	2.57513i	2.03521	+	0.158189i
$266$	15.5103	+	12.0214i	0.950995	+	0.737077i
$267$		0			0
$268$	0.408070	+	0.467596i	0.0249268	+	0.0285630i
$269$	−2.45403	−	13.9175i	−0.149625	−	0.848565i	−0.963537	−	0.267577i	$-0.913777\pi$
$269$	−2.45403	−	13.9175i	−0.149625	−	0.848565i	0.813912	−	0.580989i	$-0.197334\pi$
$270$		0			0
$271$	4.76077	−	26.9997i	0.289196	−	1.64011i	−0.400703	−	0.916208i	$-0.631234\pi$
$271$	4.76077	−	26.9997i	0.289196	−	1.64011i	0.689899	−	0.723905i	$-0.257655\pi$
$272$	8.01085	−	4.83457i	0.485729	−	0.293139i
$273$		0			0
$274$	−21.9459	+	0.851599i	−1.32580	+	0.0514470i
$275$	29.2839	+	28.7215i	1.76589	+	1.73197i
$276$		0			0
$277$	−1.34792	+	2.13862i	−0.0809887	+	0.128497i	−0.884038	−	0.467416i	$-0.845185\pi$
$277$	−1.34792	+	2.13862i	−0.0809887	+	0.128497i	0.803049	+	0.595913i	$0.203210\pi$
$278$	2.49539	−	8.33518i	0.149663	−	0.499911i
$279$		0			0
$280$	−30.4028	+	32.2251i	−1.81692	+	1.92582i
$281$	1.65401	−	1.62224i	0.0986701	−	0.0967750i	−0.649208	−	0.760611i	$-0.724900\pi$
$281$	1.65401	−	1.62224i	0.0986701	−	0.0967750i	0.747879	+	0.663836i	$0.231073\pi$
$282$		0			0
$283$	17.9478	+	22.2518i	1.06689	+	1.32273i	0.943867	+	0.330326i	$0.107159\pi$
$283$	17.9478	+	22.2518i	1.06689	+	1.32273i	0.123019	+	0.992404i	$0.460742\pi$
$284$	0.0362324	−	0.0938441i	0.00214999	−	0.00556863i
$285$		0			0
$286$	0.405362	+	1.57371i	0.0239696	+	0.0930556i
$287$	28.0454	+	6.64688i	1.65547	+	0.392353i
$288$		0			0
$289$	7.45142	+	7.89805i	0.438319	+	0.464591i
$290$	25.5616	+	0.991907i	1.50103	+	0.0582468i
$291$		0			0
$292$	0.349535	−	0.0972998i	0.0204550	−	0.00569404i
$293$	10.6057	+	16.8270i	0.619589	+	0.983046i	0.998343	+	0.0575479i	$0.0183282\pi$
$293$	10.6057	+	16.8270i	0.619589	+	0.983046i	−0.378753	+	0.925498i	$0.623647\pi$
$294$		0			0
$295$	0.0221684	+	1.14299i	0.00129069	+	0.0665477i
$296$	19.4736	−	7.08783i	1.13188	−	0.411971i
$297$		0			0
$298$	11.3397	+	4.12733i	0.656893	+	0.239090i
$299$	−0.351619	+	1.02765i	−0.0203346	+	0.0594303i
$300$		0			0
$301$	0.780447	−	0.318848i	0.0449842	−	0.0183781i
$302$	−5.79836	−	12.1262i	−0.333658	−	0.697787i
$303$		0			0
$304$	11.8722	−	3.80668i	0.680919	−	0.218328i
$305$	−10.8848	−	1.27225i	−0.623260	−	0.0728487i
$306$		0			0
$307$	−1.62137	−	2.17788i	−0.0925364	−	0.124298i	0.753444	−	0.657512i	$-0.228391\pi$
$307$	−1.62137	−	2.17788i	−0.0925364	−	0.124298i	−0.845980	+	0.533214i	$0.820984\pi$
$308$	0.242854	−	2.49676i	0.0138379	−	0.142266i
$309$		0			0
$310$	28.0322	+	16.9175i	1.59212	+	0.960850i
$311$	10.0022	−	11.4612i	0.567171	−	0.649905i	−0.396173	−	0.918176i	$-0.629662\pi$
$311$	10.0022	−	11.4612i	0.567171	−	0.649905i	0.963344	+	0.268270i	$0.0864521\pi$
$312$		0			0
$313$	11.6750	−	24.4161i	0.659907	−	1.38008i	−0.251210	−	0.967933i	$-0.580828\pi$
$313$	11.6750	−	24.4161i	0.659907	−	1.38008i	0.911117	−	0.412147i	$-0.135221\pi$
$314$	−0.509630	+	8.75001i	−0.0287601	+	0.493791i
$315$		0			0
$316$	0.643407	−	0.423175i	0.0361945	−	0.0238055i
$317$	11.7235	−	9.08644i	0.658460	−	0.510345i	−0.227696	−	0.973732i	$-0.573119\pi$
$317$	11.7235	−	9.08644i	0.658460	−	0.510345i	0.886156	+	0.463387i	$0.153366\pi$
$318$		0			0
$319$	−23.2939	+	16.6495i	−1.30421	+	0.932193i
$320$	6.27834	+	28.9841i	0.350970	+	1.62026i
$321$		0			0
$322$	−18.7022	+	23.1871i	−1.04223	+	1.29217i
$323$	−4.09186	−	7.08730i	−0.227677	−	0.394348i
$324$		0			0
$325$	0.815223	−	1.41201i	0.0452204	−	0.0783241i
$326$	−10.0865	−	26.1247i	−0.558640	−	1.44691i
$327$		0			0
$328$	14.3263	−	13.0004i	0.791038	−	0.717829i
$329$	3.98662	+	40.9860i	0.219789	+	2.25963i
$330$		0			0
$331$	−32.7652	−	13.3861i	−1.80094	−	0.735764i	−0.988207	−	0.153124i	$-0.951067\pi$
$331$	−32.7652	−	13.3861i	−1.80094	−	0.735764i	−0.812730	−	0.582640i	$-0.802020\pi$
$332$	−0.0363102	−	0.623421i	−0.00199278	−	0.0342147i
$333$		0			0
$334$	4.87628	−	2.44896i	0.266818	−	0.134001i
$335$	−11.6577	−	16.9973i	−0.636928	−	0.928664i
$336$		0			0
$337$	2.20838	+	0.433712i	0.120298	+	0.0236258i	0.252499	−	0.967597i	$-0.418748\pi$
$337$	2.20838	+	0.433712i	0.120298	+	0.0236258i	−0.132201	+	0.991223i	$0.542204\pi$
$338$	−15.6057	+	8.61084i	−0.848836	+	0.468368i
$339$		0			0
$340$	0.850879	−	0.386772i	0.0461454	−	0.0209757i
$341$	−36.3994	+	4.25448i	−1.97114	+	0.230393i
$342$		0			0
$343$	−7.95474	−	18.4412i	−0.429515	−	0.995729i
$344$	0.119797	−	0.553045i	0.00645902	−	0.0298182i
$345$		0			0
$346$	−14.4689	+	21.0961i	−0.777850	+	1.13413i
$347$	−1.15741	+	8.47377i	−0.0621332	+	0.454896i	0.933274	+	0.359165i	$0.116938\pi$
$347$	−1.15741	+	8.47377i	−0.0621332	+	0.454896i	−0.995407	+	0.0957306i	$0.969481\pi$
$348$		0			0
$349$	−18.2791	+	3.58989i	−0.978457	+	0.192163i	−0.656280	−	0.754517i	$-0.727871\pi$
$349$	−18.2791	+	3.58989i	−0.978457	+	0.192163i	−0.322176	+	0.946680i	$0.604414\pi$
$350$	34.2562	−	28.7444i	1.83107	−	1.53645i
$351$		0			0
$352$	−2.51440	−	2.10983i	−0.134018	−	0.112454i
$353$	19.4254	+	10.7185i	1.03391	+	0.570488i	0.906870	−	0.421410i	$-0.138465\pi$
$353$	19.4254	+	10.7185i	1.03391	+	0.570488i	0.127040	+	0.991898i	$0.459452\pi$
$354$		0			0
$355$	−1.55697	+	2.95583i	−0.0826353	+	0.156879i
$356$	−0.0314665	+	0.122160i	−0.00166772	+	0.00647449i
$357$		0			0
$358$	−5.37287	−	10.2001i	−0.283965	−	0.539094i
$359$	8.91427	−	2.11272i	0.470477	−	0.111505i	0.0114633	−	0.999934i	$-0.496351\pi$
$359$	8.91427	−	2.11272i	0.470477	−	0.111505i	0.459014	+	0.888429i	$0.348203\pi$
$360$		0			0
$361$	2.32177	+	7.75524i	0.122198	+	0.408171i
$362$	22.9920	+	6.40025i	1.20843	+	0.336390i
$363$		0			0
$364$	−0.0985159	+	0.0154076i	−0.00516364	+	0.000807578i
$365$	−11.9049	+	1.86188i	−0.623128	+	0.0974555i
$366$		0			0
$367$	−6.59405	−	1.83558i	−0.344207	−	0.0958165i	0.0917552	−	0.995782i	$-0.470752\pi$
$367$	−6.59405	−	1.83558i	−0.344207	−	0.0958165i	−0.435962	+	0.899965i	$0.643592\pi$
$368$	5.42816	+	18.1313i	0.282962	+	0.945160i
$369$		0			0
$370$	−33.8774	+	8.02910i	−1.76120	+	0.417413i
$371$	18.8982	+	35.8773i	0.981145	+	1.86266i
$372$		0			0
$373$	3.15814	−	12.2607i	0.163523	−	0.634833i	−0.833130	−	0.553077i	$-0.813453\pi$
$373$	3.15814	−	12.2607i	0.163523	−	0.634833i	0.996652	−	0.0817560i	$-0.0260528\pi$
$374$	8.66273	−	16.4458i	0.447939	−	0.850391i
$375$		0			0
$376$	24.2003	+	13.3532i	1.24803	+	0.688636i
$377$	0.871854	+	0.731573i	0.0449028	+	0.0376779i
$378$		0			0
$379$	−18.7184	+	15.7066i	−0.961498	+	0.806792i	−0.981196	−	0.193014i	$-0.938174\pi$
$379$	−18.7184	+	15.7066i	−0.961498	+	0.806792i	0.0196983	+	0.999806i	$0.493729\pi$
$380$	1.22207	−	0.240007i	0.0626910	−	0.0123121i
$381$		0			0
$382$	4.07502	−	29.8344i	0.208496	−	1.52646i
$383$	4.04874	−	5.90320i	0.206881	−	0.301640i	−0.707326	−	0.706887i	$-0.750099\pi$
$383$	4.04874	−	5.90320i	0.206881	−	0.301640i	0.914207	+	0.405248i	$0.132815\pi$
$384$		0			0
$385$	−17.6370	+	81.4214i	−0.898864	+	4.14962i
$386$	3.79710	+	8.80268i	0.193267	+	0.448044i
$387$		0			0
$388$	−0.136384	+	0.0159411i	−0.00692387	+	0.000809284i
$389$	10.6962	−	4.86200i	0.542316	−	0.246513i	−0.123870	−	0.992298i	$-0.539531\pi$
$389$	10.6962	−	4.86200i	0.542316	−	0.246513i	0.666186	+	0.745785i	$0.267926\pi$
$390$		0			0
$391$	10.8773	−	6.00185i	0.550090	−	0.303527i
$392$	−33.1380	−	6.50809i	−1.67372	−	0.328708i
$393$		0			0
$394$	3.78001	+	5.51139i	0.190434	+	0.277660i
$395$	−22.8549	+	11.4781i	−1.14995	+	0.577528i
$396$		0			0
$397$	−1.12205	−	19.2649i	−0.0563142	−	0.966877i	−0.901602	−	0.432566i	$-0.857608\pi$
$397$	−1.12205	−	19.2649i	−0.0563142	−	0.966877i	0.845288	−	0.534311i	$-0.179429\pi$
$398$	−7.70198	−	3.14661i	−0.386066	−	0.157725i
$399$		0			0
$400$	−2.75052	−	28.2778i	−0.137526	−	1.41389i
$401$	−8.41156	+	7.63309i	−0.420053	+	0.381178i	−0.854441	−	0.519548i	$-0.826100\pi$
$401$	−8.41156	+	7.63309i	−0.420053	+	0.381178i	0.434388	+	0.900726i	$0.356965\pi$
$402$		0			0
$403$	0.524675	+	1.35894i	0.0261359	+	0.0676937i
$404$	−0.0951309	+	0.164772i	−0.00473294	+	0.00819770i
$405$		0			0
$406$	15.6077	+	27.0333i	0.774597	+	1.34164i
$407$	24.4653	−	30.3322i	1.21270	−	1.50351i
$408$		0			0
$409$	5.74310	+	26.5131i	0.283978	+	1.31099i	0.866909	+	0.498466i	$0.166103\pi$
$409$	5.74310	+	26.5131i	0.283978	+	1.31099i	−0.582931	+	0.812521i	$0.698094\pi$
$410$	−26.4414	+	18.8992i	−1.30585	+	0.933366i
$411$		0			0
$412$	−0.893632	+	0.692617i	−0.0440261	+	0.0341228i
$413$	−1.16552	+	0.766574i	−0.0573515	+	0.0377207i
$414$		0			0
$415$	−1.20587	+	20.7041i	−0.0591940	+	1.01632i
$416$	−0.0562832	+	0.117706i	−0.00275951	+	0.00577103i
$417$		0			0
$418$	16.2855	−	18.6611i	0.796548	−	0.912743i
$419$	32.3716	+	19.5364i	1.58146	+	0.954414i	0.988849	+	0.148924i	$0.0475810\pi$
$419$	32.3716	+	19.5364i	1.58146	+	0.954414i	0.592609	+	0.805490i	$0.298098\pi$
$420$		0			0
$421$	−1.44067	+	14.8114i	−0.0702141	+	0.721864i	0.892447	+	0.451153i	$0.148987\pi$
$421$	−1.44067	+	14.8114i	−0.0702141	+	0.721864i	−0.962661	+	0.270711i	$0.912741\pi$
$422$	−1.46150	−	1.96314i	−0.0711448	−	0.0955640i
$423$		0			0
$424$	27.0335	+	3.15976i	1.31286	+	0.153452i
$425$	−17.7586	+	5.69407i	−0.861420	+	0.276203i
$426$		0			0
$427$	−5.76880	−	12.0644i	−0.279172	−	0.583838i
$428$	1.54495	−	0.631183i	0.0746782	−	0.0305094i
$429$		0			0
$430$	−0.307767	+	0.899483i	−0.0148418	+	0.0433769i
$431$	5.86902	+	2.13615i	0.282701	+	0.102895i	0.479479	−	0.877553i	$-0.340826\pi$
$431$	5.86902	+	2.13615i	0.282701	+	0.102895i	−0.196778	+	0.980448i	$0.563048\pi$
$432$		0			0
$433$	32.7182	−	11.9085i	1.57234	−	0.572284i	0.598817	−	0.800886i	$-0.295638\pi$
$433$	32.7182	−	11.9085i	1.57234	−	0.572284i	0.973520	+	0.228602i	$0.0734153\pi$
$434$	0.774747	+	39.9457i	0.0371890	+	1.91746i
$435$		0			0
$436$	−0.119365	−	0.189385i	−0.00571653	−	0.00906989i
$437$	15.9475	−	4.43929i	0.762872	−	0.212360i
$438$		0			0
$439$	−7.44524	−	0.288909i	−0.355342	−	0.0137889i	−0.139513	−	0.990220i	$-0.544554\pi$
$439$	−7.44524	−	0.288909i	−0.355342	−	0.0137889i	−0.215828	+	0.976431i	$0.569245\pi$
$440$	38.3732	+	40.6732i	1.82937	+	1.93902i
$441$		0			0
$442$	−0.718941	−	0.170392i	−0.0341965	−	0.00810473i
$443$	−4.55382	−	17.6790i	−0.216359	−	0.839956i	−0.980760	−	0.195216i	$-0.937459\pi$
$443$	−4.55382	−	17.6790i	−0.216359	−	0.839956i	0.764402	−	0.644740i	$-0.223035\pi$
$444$		0			0
$445$	1.50894	−	3.90825i	0.0715305	−	0.185269i
$446$	18.7673	+	23.2678i	0.888657	+	1.10176i
$447$		0			0
$448$	−25.8360	+	25.3398i	−1.22064	+	1.19719i
$449$	13.6548	−	14.4732i	0.644410	−	0.683034i	−0.320009	−	0.947415i	$-0.603686\pi$
$449$	13.6548	−	14.4732i	0.644410	−	0.683034i	0.964419	+	0.264380i	$0.0851673\pi$
$450$		0			0
$451$	10.4334	−	34.8500i	0.491290	−	1.64102i
$452$	−0.495333	+	0.785900i	−0.0232985	+	0.0369656i
$453$		0			0
$454$	−5.88181	−	5.76884i	−0.276047	−	0.270745i
$455$	3.30903	−	0.128406i	0.155130	−	0.00601974i
$456$		0			0
$457$	8.19122	−	4.94343i	0.383169	−	0.231244i	−0.312012	−	0.950078i	$-0.601003\pi$
$457$	8.19122	−	4.94343i	0.383169	−	0.231244i	0.695182	+	0.718834i	$0.255324\pi$
$458$	2.34778	−	13.3149i	0.109704	−	0.622165i
$459$		0			0
$460$	0.328301	+	1.86189i	0.0153071	+	0.0868109i
$461$	−20.1957	−	23.1417i	−0.940608	−	1.07782i	−0.996843	−	0.0794000i	$-0.974700\pi$
$461$	−20.1957	−	23.1417i	−0.940608	−	1.07782i	0.0562345	−	0.998418i	$-0.482091\pi$
$462$		0			0
$463$	−15.9529	−	12.3644i	−0.741393	−	0.574623i	0.170350	−	0.985384i	$-0.445510\pi$
$463$	−15.9529	−	12.3644i	−0.741393	−	0.574623i	−0.911743	+	0.410761i	$0.865263\pi$
$464$	19.7727	+	1.53686i	0.917926	+	0.0713468i
$465$		0			0
$466$	21.5648	+	19.5691i	0.998972	+	0.906519i
$467$	−13.1496	+	17.6629i	−0.608490	+	0.817344i	−0.994454	−	0.105170i	$-0.966461\pi$
$467$	−13.1496	+	17.6629i	−0.608490	+	0.817344i	0.385964	+	0.922514i	$0.373869\pi$
$468$		0			0
$469$	9.96172	−	23.0939i	0.459990	−	1.06638i
$470$	−37.7778	−	27.0020i	−1.74256	−	1.24551i
$471$		0			0
$472$	−0.0181569	+	0.936166i	−0.000835740	+	0.0430905i
$473$	−0.344480	−	1.00678i	−0.0158392	−	0.0462919i
$474$		0			0
$475$	−24.7750	+	1.92566i	−1.13675	+	0.0883555i
$476$	0.952899	+	0.626732i	0.0436761	+	0.0287262i
$477$		0			0
$478$	8.46553	+	4.25155i	0.387204	+	0.194461i
$479$	1.48901	+	10.9014i	0.0680344	+	0.498100i	0.993006	+	0.118064i	$0.0376687\pi$
$479$	1.48901	+	10.9014i	0.0680344	+	0.498100i	−0.924972	+	0.380036i	$0.875912\pi$
$480$		0			0
$481$	−1.41016	−	0.640994i	−0.0642976	−	0.0292268i
$482$	−7.30537	−	2.34237i	−0.332751	−	0.106692i
$483$		0			0
$484$	−1.97001	−	0.308104i	−0.0895459	−	0.0140047i
$485$	4.56021			0.207069
$486$		0			0
$487$	−29.2145			−1.32384			−0.661919	−	0.749576i	$-0.730258\pi$
$487$	−29.2145			−1.32384			−0.661919	+	0.749576i	$0.730258\pi$
$488$	−8.86803	−	1.38693i	−0.401437	−	0.0627836i
$489$		0			0
$490$	54.0270	+	17.3230i	2.44069	+	0.782576i
$491$	−0.252614	−	0.114827i	−0.0114003	−	0.00518209i	0.408102	−	0.912936i	$-0.366191\pi$
$491$	−0.252614	−	0.114827i	−0.0114003	−	0.00518209i	−0.419503	+	0.907754i	$0.637796\pi$
$492$		0			0
$493$	−1.76174	−	12.8982i	−0.0793446	−	0.580905i
$494$	−0.879795	−	0.441850i	−0.0395839	−	0.0198798i
$495$		0			0
$496$	21.2079	+	13.9487i	0.952263	+	0.626313i
$497$	−4.06443	+	0.315912i	−0.182314	+	0.0141706i
$498$		0			0
$499$	8.99129	+	26.2780i	0.402506	+	1.17637i	0.942358	+	0.334607i	$0.108604\pi$
$499$	8.99129	+	26.2780i	0.402506	+	1.17637i	−0.539852	+	0.841760i	$0.681520\pi$
$500$	0.0184673	−	0.952170i	0.000825883	−	0.0425823i
$501$		0			0
$502$	12.5282	+	8.95463i	0.559161	+	0.399665i
$503$	4.23467	−	9.81706i	0.188815	−	0.437721i	−0.797344	−	0.603525i	$-0.793762\pi$
$503$	4.23467	−	9.81706i	0.188815	−	0.437721i	0.986159	+	0.165803i	$0.0530217\pi$
$504$		0			0
$505$	3.77325	−	5.06835i	0.167907	−	0.225539i
$506$	27.8437	+	25.2669i	1.23781	+	1.12325i
$507$		0			0
$508$	−0.247455	−	0.0192337i	−0.0109790	−	0.000853357i
$509$	−20.9477	−	16.2357i	−0.928490	−	0.719634i	0.0315486	−	0.999502i	$-0.489956\pi$
$509$	−20.9477	−	16.2357i	−0.928490	−	0.719634i	−0.960038	+	0.279868i	$0.909709\pi$
$510$		0			0
$511$	−9.66796	−	11.0783i	−0.427686	−	0.490073i
$512$	4.19560	+	23.7944i	0.185421	+	1.05158i
$513$		0			0
$514$	−3.51242	+	19.9199i	−0.154926	+	0.878631i
$515$	32.1476	−	19.4012i	1.41659	−	0.854917i
$516$		0			0
$517$	51.9359	−	2.01535i	2.28414	−	0.0886349i
$518$	−30.3310	−	29.7484i	−1.33267	−	1.30707i
$519$		0			0
$520$	1.18516	−	1.88038i	0.0519727	−	0.0824602i
$521$	3.19272	−	10.6644i	0.139876	−	0.467217i	−0.859132	−	0.511754i	$-0.828996\pi$
$521$	3.19272	−	10.6644i	0.139876	−	0.467217i	0.999008	+	0.0445367i	$0.0141812\pi$
$522$		0			0
$523$	28.8731	−	30.6037i	1.26253	−	1.33821i	0.346006	−	0.938232i	$-0.387538\pi$
$523$	28.8731	−	30.6037i	1.26253	−	1.33821i	0.916526	−	0.399974i	$-0.130981\pi$
$524$	−1.22879	+	1.20519i	−0.0536801	+	0.0526490i
$525$		0			0
$526$	−21.8939	−	27.1442i	−0.954620	−	1.18354i
$527$	6.00127	−	15.5437i	0.261419	−	0.677093i
$528$		0			0
$529$	0.531207	+	2.06227i	0.0230959	+	0.0896639i
$530$	−44.4937	−	10.5452i	−1.93268	−	0.458054i
$531$		0			0
$532$	1.04291	+	1.10542i	0.0452158	+	0.0479259i
$533$	−1.44493	−	0.0560700i	−0.0625870	−	0.00242866i
$534$		0			0
$535$	−53.3951	+	14.8635i	−2.30847	+	0.642607i
$536$	−9.00121	−	14.2814i	−0.388793	−	0.616862i
$537$		0			0
$538$	0.377088	+	19.4426i	0.0162574	+	0.838228i
$539$	−59.6745	+	21.7197i	−2.57036	+	0.935535i
$540$		0			0
$541$	−23.3009	−	8.48084i	−1.00178	−	0.364620i	−0.211512	−	0.977375i	$-0.567839\pi$
$541$	−23.3009	−	8.48084i	−1.00178	−	0.364620i	−0.790272	+	0.612756i	$0.790061\pi$
$542$	−12.2129	+	35.6937i	−0.524591	+	1.53317i
$543$		0			0
$544$	1.38149	−	0.564400i	0.0592308	−	0.0241984i
$545$	3.20717	+	6.70723i	0.137380	+	0.287306i
$546$		0			0
$547$	−24.3132	+	7.79572i	−1.03956	+	0.333321i	−0.775608	−	0.631215i	$-0.782557\pi$
$547$	−24.3132	+	7.79572i	−1.03956	+	0.333321i	−0.263951	+	0.964536i	$0.585026\pi$
$548$	−1.68937	−	0.197459i	−0.0721664	−	0.00843504i
$549$		0			0
$550$	−33.7046	−	45.2731i	−1.43717	−	1.93045i
$551$	1.67930	−	17.2647i	0.0715407	−	0.735503i
$552$		0			0
$553$	−26.7197	−	16.1254i	−1.13624	−	0.685723i
$554$	2.28721	−	2.62085i	0.0971741	−	0.111349i
$555$		0			0
$556$	0.290678	−	0.607902i	0.0123275	−	0.0257808i
$557$	1.61420	−	27.7147i	0.0683957	−	1.17431i	−0.773186	−	0.634179i	$-0.781338\pi$
$557$	1.61420	−	27.7147i	0.0683957	−	1.17431i	0.841582	−	0.540129i	$-0.181625\pi$
$558$		0			0
$559$	−0.0353385	+	0.0232425i	−0.00149466	+	0.000983054i
$560$	45.6095	−	35.3500i	1.92735	−	1.49381i
$561$		0			0
$562$	−2.59355	+	1.85376i	−0.109402	+	0.0781959i
$563$	−7.95964	−	36.7458i	−0.335459	−	1.54865i	−0.764053	−	0.645154i	$-0.776793\pi$
$563$	−7.95964	−	36.7458i	−0.335459	−	1.54865i	0.428594	−	0.903497i	$-0.359009\pi$
$564$		0			0
$565$	19.3690	−	24.0138i	0.814860	−	1.01027i
$566$	−19.6687	−	34.0673i	−0.826739	−	1.43195i
$567$		0			0
$568$	−1.36815	+	2.36970i	−0.0574061	+	0.0994303i
$569$	−7.46532	−	19.3357i	−0.312963	−	0.810593i	−0.996723	−	0.0808870i	$-0.974225\pi$
$569$	−7.46532	−	19.3357i	−0.312963	−	0.810593i	0.683761	−	0.729706i	$-0.260343\pi$
$570$		0			0
$571$	5.76184	−	5.22859i	0.241126	−	0.218810i	−0.542480	−	0.840069i	$-0.682514\pi$
$571$	5.76184	−	5.22859i	0.241126	−	0.218810i	0.783605	+	0.621259i	$0.213379\pi$
$572$	0.0121841	+	0.125263i	0.000509441	+	0.00523751i
$573$		0			0
$574$	−36.7143	−	14.9994i	−1.53242	−	0.626064i
$575$	−2.19341	−	37.6593i	−0.0914713	−	1.57050i
$576$		0			0
$577$	−23.5926	+	11.8486i	−0.982171	+	0.493265i	−0.866043	−	0.499970i	$-0.833345\pi$
$577$	−23.5926	+	11.8486i	−0.982171	+	0.493265i	−0.116128	+	0.993234i	$0.537048\pi$
$578$	−8.45088	−	12.3217i	−0.351510	−	0.512514i
$579$		0			0
$580$	1.94397	+	0.381783i	0.0807190	+	0.0158527i
$581$	−22.1579	+	12.2262i	−0.919267	+	0.507230i
$582$		0			0
$583$	46.5932	−	21.1792i	1.92969	−	0.877153i
$584$	−9.80243	+	1.14574i	−0.405627	+	0.0474110i
$585$		0			0
$586$	−10.8406	−	25.1313i	−0.447820	−	1.03816i
$587$	4.09908	−	18.9234i	0.169187	−	0.781054i	−0.811325	−	0.584595i	$-0.801253\pi$
$587$	4.09908	−	18.9234i	0.169187	−	0.781054i	0.980512	−	0.196459i	$-0.0629442\pi$
$588$		0			0
$589$	12.5575	−	18.3093i	0.517422	−	0.754420i
$590$	0.212887	−	1.55861i	0.00876442	−	0.0641669i
$591$		0			0
$592$	−26.4862	+	5.20171i	−1.08857	+	0.213789i
$593$	−14.5215	+	12.1850i	−0.596326	+	0.500377i	−0.890262	−	0.455448i	$-0.849479\pi$
$593$	−14.5215	+	12.1850i	−0.596326	+	0.500377i	0.293936	+	0.955825i	$0.405035\pi$
$594$		0			0
$595$	−29.0158	−	24.3471i	−1.18953	−	0.998136i
$596$	0.818266	+	0.451500i	0.0335175	+	0.0184942i
$597$		0			0
$598$	0.696523	−	1.32232i	0.0284830	−	0.0540736i
$599$	3.37182	−	13.0902i	0.137769	−	0.534852i	−0.861848	−	0.507167i	$-0.830693\pi$
$599$	3.37182	−	13.0902i	0.137769	−	0.534852i	0.999617	−	0.0276849i	$-0.00881352\pi$
$600$		0			0
$601$	0.874715	+	1.66061i	0.0356804	+	0.0677375i	0.901953	−	0.431833i	$-0.142133\pi$
$601$	0.874715	+	1.66061i	0.0356804	+	0.0677375i	−0.866273	+	0.499571i	$0.833491\pi$
$602$	−1.12881	+	0.267532i	−0.0460068	+	0.0109038i
$603$		0			0
$604$	−0.298549	−	0.997224i	−0.0121478	−	0.0405765i
$605$	63.7945	+	17.7584i	2.59361	+	0.721982i
$606$		0			0
$607$	0.835002	−	0.130592i	0.0338917	−	0.00530057i	−0.137550	−	0.990495i	$-0.543923\pi$
$607$	0.835002	−	0.130592i	0.0338917	−	0.00530057i	0.171442	+	0.985194i	$0.445157\pi$
$608$	1.96463	−	0.307262i	0.0796762	−	0.0124611i
$609$		0			0
$610$	14.5273	+	4.04395i	0.588193	+	0.163735i
$611$	−0.592530	−	1.97919i	−0.0239712	−	0.0800694i
$612$		0			0
$613$	−34.6224	+	8.20566i	−1.39839	+	0.331423i	−0.859578	−	0.511005i	$-0.829273\pi$
$613$	−34.6224	+	8.20566i	−1.39839	+	0.331423i	−0.538808	+	0.842429i	$0.681125\pi$
$614$	1.74118	+	3.30555i	0.0702683	+	0.133401i
$615$		0			0
$616$	−17.0205	+	66.0776i	−0.685775	+	2.66234i
$617$	0.111271	−	0.211242i	0.00447959	−	0.00850430i	−0.882512	−	0.470290i	$-0.844149\pi$
$617$	0.111271	−	0.211242i	0.00447959	−	0.00850430i	0.886991	+	0.461786i	$0.152791\pi$
$618$		0			0
$619$	25.5316	+	14.0877i	1.02620	+	0.566234i	0.904563	−	0.426340i	$-0.140197\pi$
$619$	25.5316	+	14.0877i	1.02620	+	0.566234i	0.121639	+	0.992574i	$0.461185\pi$
$620$	1.94243	+	1.62989i	0.0780098	+	0.0654580i
$621$		0			0
$622$	−16.0348	+	13.4548i	−0.642936	+	0.539488i
$623$	5.01637	−	0.985184i	0.200977	−	0.0394706i
$624$		0			0
$625$	0.811701	−	5.94271i	0.0324681	−	0.237708i
$626$	−21.0634	+	30.7112i	−0.841864	+	1.22747i
$627$		0			0
$628$	−0.143703	+	0.663406i	−0.00573436	+	0.0264728i
$629$	7.01759	+	16.2686i	0.279810	+	0.648672i
$630$		0			0
$631$	−15.8347	+	1.85081i	−0.630369	+	0.0736795i	−0.425277	−	0.905063i	$-0.639823\pi$
$631$	−15.8347	+	1.85081i	−0.630369	+	0.0736795i	−0.205092	+	0.978743i	$0.565749\pi$
$632$	−19.0697	+	8.66822i	−0.758550	+	0.344803i
$633$		0			0
$634$	−17.8701	+	9.86029i	−0.709711	+	0.391602i
$635$	8.08834	+	1.58850i	0.320976	+	0.0630376i
$636$		0			0
$637$	1.42774	+	2.08170i	0.0565692	+	0.0824800i
$638$	35.2080	−	17.6821i	1.39390	−	0.700042i
$639$		0			0
$640$	−2.12492	−	36.4835i	−0.0839949	−	1.44214i
$641$	−9.38706	−	3.83503i	−0.370766	−	0.151475i	0.185156	−	0.982709i	$-0.440721\pi$
$641$	−9.38706	−	3.83503i	−0.370766	−	0.151475i	−0.555922	+	0.831234i	$0.687635\pi$
$642$		0			0
$643$	−2.90381	−	29.8538i	−0.114515	−	1.17732i	−0.859821	−	0.510595i	$-0.829425\pi$
$643$	−2.90381	−	29.8538i	−0.114515	−	1.17732i	0.745306	−	0.666722i	$-0.232303\pi$
$644$	−1.70847	+	1.55035i	−0.0673230	+	0.0610923i
$645$		0			0
$646$	4.05595	+	10.5052i	0.159579	+	0.413320i
$647$	−13.2999	+	23.0361i	−0.522872	+	0.905642i	0.476773	+	0.879026i	$0.341806\pi$
$647$	−13.2999	+	23.0361i	−0.522872	+	0.905642i	−0.999646	+	0.0266153i	$0.991527\pi$
$648$		0			0
$649$	0.880366	+	1.52484i	0.0345574	+	0.0598552i
$650$	−1.40851	+	1.74628i	−0.0552465	+	0.0684949i
$651$		0			0
$652$	−0.459140	−	2.11963i	−0.0179813	−	0.0830109i
$653$	−9.33689	+	6.67360i	−0.365381	+	0.261158i	−0.749331	−	0.662195i	$-0.769625\pi$
$653$	−9.33689	+	6.67360i	−0.365381	+	0.261158i	0.383951	+	0.923354i	$0.374563\pi$
$654$		0			0
$655$	45.1794	−	35.0166i	1.76530	−	1.36821i
$656$	−21.0523	+	13.8463i	−0.821954	+	0.540608i
$657$		0			0
$658$	3.29471	−	56.5679i	0.128441	−	2.20525i
$659$	16.4622	−	34.4278i	0.641277	−	1.34112i	−0.282899	−	0.959150i	$-0.591296\pi$
$659$	16.4622	−	34.4278i	0.641277	−	1.34112i	0.924176	−	0.381967i	$-0.124753\pi$
$660$		0			0
$661$	3.01092	−	3.45013i	0.117111	−	0.134194i	−0.691887	−	0.722006i	$-0.743220\pi$
$661$	3.01092	−	3.45013i	0.117111	−	0.134194i	0.808998	+	0.587812i	$0.200010\pi$
$662$	41.6979	+	25.1648i	1.62064	+	0.978059i
$663$		0			0
$664$	−1.64446	+	16.9065i	−0.0638175	+	0.656101i
$665$	−30.1392	−	40.4840i	−1.16875	−	1.56990i
$666$		0			0
$667$	26.1544	+	3.05701i	1.01270	+	0.118368i
$668$	0.402413	−	0.129029i	0.0155698	−	0.00499227i
$669$		0			0
$670$	12.2346	+	25.5865i	0.472664	+	0.988492i
$671$	−15.6248	+	6.38344i	−0.603189	+	0.246430i
$672$		0			0
$673$	−0.119391	+	0.348934i	−0.00460219	+	0.0134504i	−0.948425	−	0.317001i	$-0.897324\pi$
$673$	−0.119391	+	0.348934i	−0.00460219	+	0.0134504i	0.943823	+	0.330451i	$0.107201\pi$
$674$	−2.91007	−	1.05918i	−0.112092	−	0.0407980i
$675$		0			0
$676$	−1.29711	+	0.472108i	−0.0498887	+	0.0181580i
$677$	0.449361	+	23.1690i	0.0172704	+	0.890455i	0.903843	+	0.427865i	$0.140734\pi$
$677$	0.449361	+	23.1690i	0.0172704	+	0.890455i	−0.886572	+	0.462590i	$0.846920\pi$
$678$		0			0
$679$	2.96710	+	4.70763i	0.113867	+	0.180662i
$680$	−24.4923	+	6.81789i	−0.939236	+	0.261454i
$681$		0			0
$682$	50.3894	+	1.95534i	1.92951	+	0.0748738i
$683$	6.19803	+	6.56953i	0.237161	+	0.251376i	0.835013	−	0.550231i	$-0.185460\pi$
$683$	6.19803	+	6.56953i	0.237161	+	0.251376i	−0.597852	+	0.801607i	$0.703979\pi$
$684$		0			0
$685$	54.9640	+	13.0267i	2.10007	+	0.497725i
$686$	6.89345	+	26.7620i	0.263193	+	1.02178i
$687$		0			0
$688$	−0.265467	+	0.687576i	−0.0101208	+	0.0262136i
$689$	−1.27723	−	1.58352i	−0.0486587	−	0.0603273i
$690$		0			0
$691$	−24.7420	+	24.2668i	−0.941232	+	0.923153i	−0.997162	−	0.0752812i	$-0.976015\pi$
$691$	−24.7420	+	24.2668i	−0.941232	+	0.923153i	0.0559308	+	0.998435i	$0.482187\pi$
$692$	−1.35953	+	1.44102i	−0.0516816	+	0.0547793i
$693$		0			0
$694$	3.37520	−	11.2740i	0.128121	−	0.427953i
$695$	−11.9320	+	18.9314i	−0.452608	+	0.718111i
$696$		0			0
$697$	11.8082	+	11.5814i	0.447267	+	0.438676i
$698$	25.6136	−	0.993924i	0.969489	−	0.0376206i
$699$		0			0
$700$	2.96508	−	1.78943i	0.112069	−	0.0676342i
$701$	−7.47008	+	42.3649i	−0.282141	+	1.60010i	0.433182	+	0.901307i	$0.357391\pi$
$701$	−7.47008	+	42.3649i	−0.282141	+	1.60010i	−0.715323	+	0.698794i	$0.753720\pi$
$702$		0			0
$703$	4.09956	+	23.2498i	0.154618	+	0.876882i
$704$	30.0326	+	34.4136i	1.13190	+	1.29701i
$705$		0			0
$706$	−24.1298	−	18.7020i	−0.908136	−	0.703859i
$707$	7.68726	+	0.597501i	0.289109	+	0.0224713i
$708$		0			0
$709$	−37.0676	−	33.6371i	−1.39210	−	1.26327i	−0.925473	−	0.378813i	$-0.876332\pi$
$709$	−37.0676	−	33.6371i	−1.39210	−	1.26327i	−0.466630	−	0.884453i	$-0.654532\pi$
$710$	2.74516	−	3.68740i	0.103024	−	0.138385i
$711$		0			0
$712$	1.35908	−	3.15071i	0.0509338	−	0.118078i
$713$	27.4195	+	19.5983i	1.02687	+	0.733962i
$714$		0			0
$715$	0.0810493	−	4.17888i	0.00303107	−	0.156281i
$716$	−0.289042	−	0.844756i	−0.0108020	−	0.0315700i
$717$		0			0
$718$	−12.5681	+	0.976871i	−0.469038	+	0.0364565i
$719$	−16.0882	−	10.5814i	−0.599990	−	0.394620i	0.212868	−	0.977081i	$-0.431719\pi$
$719$	−16.0882	−	10.5814i	−0.599990	−	0.394620i	−0.812859	+	0.582461i	$0.802090\pi$
$720$		0			0
$721$	40.9451	+	20.5634i	1.52488	+	0.765822i
$722$	−1.50750	−	11.0369i	−0.0561034	−	0.410750i
$723$		0			0
$724$	1.68263	+	0.764851i	0.0625346	+	0.0284255i
$725$	−37.6412	−	12.0692i	−1.39796	−	0.448238i
$726$		0			0
$727$	14.0511	+	2.19755i	0.521126	+	0.0815027i	0.409611	−	0.912260i	$-0.365664\pi$
$727$	14.0511	+	2.19755i	0.521126	+	0.0815027i	0.111515	+	0.993763i	$0.464430\pi$
$728$	2.71229			0.100524
$729$		0			0
$730$	16.5805			0.613670
$731$	0.477984	+	0.0747554i	0.0176789	+	0.00276493i
$732$		0			0
$733$	6.44463	+	2.06639i	0.238038	+	0.0763237i	0.421951	−	0.906619i	$-0.361346\pi$
$733$	6.44463	+	2.06639i	0.238038	+	0.0763237i	−0.183913	+	0.982943i	$0.558876\pi$
$734$	8.57430	+	3.89750i	0.316483	+	0.143859i
$735$		0			0
$736$	0.408519	+	2.99089i	0.0150582	+	0.110246i
$737$	−28.3677	−	14.2468i	−1.04494	−	0.524788i
$738$		0			0
$739$	37.0901	+	24.3946i	1.36438	+	0.897369i	0.999433	−	0.0336587i	$-0.0107159\pi$
$739$	37.0901	+	24.3946i	1.36438	+	0.897369i	0.364949	+	0.931027i	$0.381086\pi$
$740$	−2.68820	+	0.208944i	−0.0988204	+	0.00768093i
$741$		0			0
$742$	−18.0637	−	52.7932i	−0.663140	−	1.93810i
$743$	−0.709956	+	36.6051i	−0.0260457	+	1.34291i	0.727768	+	0.685824i	$0.240558\pi$
$743$	−0.709956	+	36.6051i	−0.0260457	+	1.34291i	−0.753814	+	0.657088i	$0.771788\pi$
$744$		0			0
$745$	−25.2504	−	18.0479i	−0.925104	−	0.661225i
$746$	−6.90036	+	15.9968i	−0.252640	+	0.585686i
$747$		0			0
$748$	0.859628	−	1.15468i	0.0314311	−	0.0422193i
$749$	−50.0856	−	45.4502i	−1.83009	−	1.66071i
$750$		0			0
$751$	−31.5453	−	2.45190i	−1.15110	−	0.0894710i	−0.512277	−	0.858820i	$-0.671198\pi$
$751$	−31.5453	−	2.45190i	−1.15110	−	0.0894710i	−0.638828	+	0.769349i	$0.720581\pi$
$752$	−28.4547	−	22.0541i	−1.03764	−	0.804229i
$753$		0			0
$754$	−1.02973	−	1.17994i	−0.0375007	−	0.0429710i
$755$	6.00310	+	34.0453i	0.218475	+	1.23904i
$756$		0			0
$757$	−4.99302	+	28.3168i	−0.181475	+	1.02919i	0.748927	+	0.662652i	$0.230569\pi$
$757$	−4.99302	+	28.3168i	−0.181475	+	1.02919i	−0.930402	+	0.366541i	$0.880542\pi$
$758$	28.7871	−	17.3731i	1.04559	−	0.631019i
$759$		0			0
$760$	−33.8510	+	1.31357i	−1.22790	+	0.0476482i
$761$	−20.1558	−	19.7687i	−0.730648	−	0.716614i	0.236274	−	0.971686i	$-0.424074\pi$
$761$	−20.1558	−	19.7687i	−0.730648	−	0.716614i	−0.966922	+	0.255072i	$0.917901\pi$
$762$		0			0
$763$	−4.83730	+	7.67490i	−0.175122	+	0.277850i
$764$	0.668818	−	2.23401i	0.0241970	−	0.0808235i
$765$		0			0
$766$	−6.75938	+	7.16453i	−0.244226	+	0.258865i
$767$	0.0499668	−	0.0490071i	0.00180420	−	0.00176954i
$768$		0			0
$769$	6.52315	+	8.08744i	0.235231	+	0.291640i	0.882199	−	0.470876i	$-0.156062\pi$
$769$	6.52315	+	8.08744i	0.235231	+	0.291640i	−0.646968	+	0.762517i	$0.723963\pi$
$770$	41.2893	−	106.942i	1.48796	−	3.85392i
$771$		0			0
$772$	0.185195	+	0.718973i	0.00666533	+	0.0258764i
$773$	50.4806	+	11.9641i	1.81566	+	0.430320i	0.990836	−	0.135069i	$-0.0431255\pi$
$773$	50.4806	+	11.9641i	1.81566	+	0.430320i	0.824825	+	0.565388i	$0.191274\pi$
$774$		0			0
$775$	−34.7195	−	36.8006i	−1.24716	−	1.32192i
$776$	3.73222	+	0.144827i	0.133979	+	0.00519899i
$777$		0			0
$778$	−15.5751	+	4.33563i	−0.558395	+	0.155440i
$779$	11.7512	+	18.6446i	0.421031	+	0.668012i
$780$		0			0
$781$	0.0997766	+	5.14446i	0.00357029	+	0.184083i
$782$	−16.0638	+	5.84674i	−0.574440	+	0.209079i
$783$		0			0
$784$	41.3338	+	15.0443i	1.47621	+	0.537296i
$785$	7.29791	−	21.3289i	0.260473	−	0.761262i
$786$		0			0
$787$	46.1465	−	18.8529i	1.64494	−	0.672033i	0.648898	−	0.760876i	$-0.275230\pi$
$787$	46.1465	−	18.8529i	1.64494	−	0.672033i	0.996046	+	0.0888423i	$0.0283167\pi$
$788$	0.223273	+	0.466936i	0.00795378	+	0.0166339i
$789$		0			0
$790$	33.5116	−	10.7450i	1.19229	−	0.382292i
$791$	37.3925	+	4.37056i	1.32953	+	0.155399i
$792$		0			0
$793$	0.400641	+	0.538154i	0.0142272	+	0.0191104i
$794$	−2.57070	+	26.4291i	−0.0912307	+	0.937933i
$795$		0			0
$796$	−0.551661	−	0.332929i	−0.0195531	−	0.0118004i
$797$	−10.8072	+	12.3836i	−0.382809	+	0.438651i	−0.912211	−	0.409720i	$-0.865626\pi$
$797$	−10.8072	+	12.3836i	−0.382809	+	0.438651i	0.529402	+	0.848371i	$0.322416\pi$
$798$		0			0
$799$	−10.1940	+	21.3190i	−0.360639	+	0.754211i
$800$	0.263480	−	4.52378i	0.00931543	−	0.159940i
$801$		0			0
$802$	13.0584	−	8.58867i	0.461109	−	0.303276i
$803$	−14.6684	+	11.3688i	−0.517636	+	0.401198i
$804$		0			0
$805$	62.3325	−	44.5526i	2.19693	−	1.57027i
$806$	−0.424353	−	1.95903i	−0.0149472	−	0.0690039i
$807$		0			0
$808$	3.24911	−	4.02826i	0.114303	−	0.141714i
$809$	−3.89179	−	6.74078i	−0.136828	−	0.236993i	0.789466	−	0.613794i	$-0.210357\pi$
$809$	−3.89179	−	6.74078i	−0.136828	−	0.236993i	−0.926294	+	0.376801i	$0.877024\pi$
$810$		0			0
$811$	23.0848	−	39.9840i	0.810616	−	1.40403i	−0.101818	−	0.994803i	$-0.532466\pi$
$811$	23.0848	−	39.9840i	0.810616	−	1.40403i	0.912434	−	0.409225i	$-0.134201\pi$
$812$	0.870719	+	2.25522i	0.0305563	+	0.0791427i
$813$		0			0
$814$	−39.7097	+	36.0346i	−1.39182	+	1.26301i
$815$	6.97291	+	71.6878i	0.244250	+	2.51111i
$816$		0			0
$817$	0.596767	+	0.243806i	0.0208782	+	0.00852970i
$818$	−2.17047	−	37.2655i	−0.0758887	−	1.30296i
$819$		0			0
$820$	−2.24932	+	1.12965i	−0.0785497	+	0.0394491i
$821$	10.6891	+	15.5851i	0.373053	+	0.543925i	0.965067	−	0.262003i	$-0.0843830\pi$
$821$	10.6891	+	15.5851i	0.373053	+	0.543925i	−0.592014	+	0.805928i	$0.701667\pi$
$822$		0			0
$823$	−28.7023	−	5.63695i	−1.00050	−	0.196492i	−0.334462	−	0.942409i	$-0.608554\pi$
$823$	−28.7023	−	5.63695i	−1.00050	−	0.196492i	−0.666038	+	0.745918i	$0.732011\pi$
$824$	26.9267	−	14.8575i	0.938036	−	0.517587i
$825$		0			0
$826$	1.74751	−	0.794340i	0.0608036	−	0.0276386i
$827$	0.429636	−	0.0502173i	0.0149399	−	0.00174622i	−0.108620	−	0.994083i	$-0.534643\pi$
$827$	0.429636	−	0.0502173i	0.0149399	−	0.00174622i	0.123560	+	0.992337i	$0.460569\pi$
$828$		0			0
$829$	13.6270	+	31.5910i	0.473286	+	1.09720i	0.972957	+	0.230985i	$0.0741948\pi$
$829$	13.6270	+	31.5910i	0.473286	+	1.09720i	−0.499671	+	0.866215i	$0.666546\pi$
$830$	6.04150	−	27.8907i	0.209704	−	0.968099i
$831$		0			0
$832$	1.02691	−	1.49727i	0.0356016	−	0.0519084i
$833$	3.90739	−	28.6071i	0.135383	−	0.991178i
$834$		0			0
$835$	−13.7714	+	2.70462i	−0.476579	+	0.0935971i
$836$	1.46939	−	1.23296i	0.0508199	−	0.0426429i
$837$		0			0
$838$	−39.8552	−	33.4425i	−1.37678	−	1.15525i
$839$	−26.9453	−	14.8678i	−0.930256	−	0.513293i	−0.0558234	−	0.998441i	$-0.517778\pi$
$839$	−26.9453	−	14.8678i	−0.930256	−	0.513293i	−0.874433	+	0.485147i	$0.838766\pi$
$840$		0			0
$841$	−0.655776	+	1.24496i	−0.0226130	+	0.0429297i
$842$	5.10781	−	19.8297i	0.176027	−	0.683377i
$843$		0			0
$844$	−0.0883341	−	0.167698i	−0.00304059	−	0.00577241i
$845$	44.6063	−	10.5719i	1.53450	−	0.363684i
$846$		0			0
$847$	23.1754	+	77.4112i	0.796316	+	2.65988i
$848$	−34.1522	−	9.50690i	−1.17279	−	0.326468i
$849$		0			0
$850$	25.3534	−	3.96520i	0.869616	−	0.136005i
$851$	−35.4084	+	5.53777i	−1.21378	+	0.189832i
$852$		0			0
$853$	7.48270	+	2.08295i	0.256203	+	0.0713190i	0.393893	−	0.919156i	$-0.371128\pi$
$853$	7.48270	+	2.08295i	0.256203	+	0.0713190i	−0.137690	+	0.990475i	$0.543968\pi$
$854$	5.27750	+	17.6281i	0.180592	+	0.603221i
$855$		0			0
$856$	−44.1723	+	10.4690i	−1.50978	+	0.357824i
$857$	5.67881	+	10.7810i	0.193985	+	0.368271i	0.962381	−	0.271704i	$-0.0875870\pi$
$857$	5.67881	+	10.7810i	0.193985	+	0.368271i	−0.768396	+	0.639974i	$0.778945\pi$
$858$		0			0
$859$	1.15119	−	4.46918i	0.0392780	−	0.152487i	−0.945745	−	0.324910i	$-0.894666\pi$
$859$	1.15119	−	4.46918i	0.0392780	−	0.152487i	0.985023	+	0.172424i	$0.0551598\pi$
$860$	−0.0343125	+	0.0651407i	−0.00117005	+	0.00222128i
$861$		0			0
$862$	−7.52471	−	4.15196i	−0.256293	−	0.141416i
$863$	−12.0077	−	10.0756i	−0.408745	−	0.342978i	0.415117	−	0.909768i	$-0.363741\pi$
$863$	−12.0077	−	10.0756i	−0.408745	−	0.342978i	−0.823862	+	0.566790i	$0.808185\pi$
$864$		0			0
$865$	50.4011	−	42.2915i	1.71369	−	1.43795i
$866$	−47.0122	+	9.23290i	−1.59754	+	0.313747i
$867$		0			0
$868$	−0.418738	+	3.06571i	−0.0142129	+	0.104057i
$869$	−22.2793	+	32.4840i	−0.755774	+	1.10195i
$870$		0			0
$871$	−0.267133	+	1.23322i	−0.00905144	+	0.0417861i
$872$	2.41183	+	5.59126i	0.0816750	+	0.189344i
$873$		0			0
$874$	−22.6244	+	2.64442i	−0.765282	+	0.0894487i
$875$	−35.1348	+	15.9707i	−1.18777	+	0.539910i
$876$		0			0
$877$	−12.3249	+	6.80060i	−0.416183	+	0.229640i	−0.677361	−	0.735651i	$-0.736877\pi$
$877$	−12.3249	+	6.80060i	−0.416183	+	0.229640i	0.261178	+	0.965291i	$0.415889\pi$
$878$	10.0603	+	1.97578i	0.339520	+	0.0666795i
$879$		0			0
$880$	−41.1947	−	60.0633i	−1.38867	−	2.02473i
$881$	−5.01744	+	2.51985i	−0.169042	+	0.0848960i	−0.531308	−	0.847179i	$-0.678299\pi$
$881$	−5.01744	+	2.51985i	−0.169042	+	0.0848960i	0.362266	+	0.932075i	$0.382003\pi$
$882$		0			0
$883$	−1.40608	−	24.1415i	−0.0473185	−	0.812427i	−0.935586	−	0.353100i	$-0.885128\pi$
$883$	−1.40608	−	24.1415i	−0.0473185	−	0.812427i	0.888267	−	0.459327i	$-0.151909\pi$
$884$	−0.0529706	−	0.0216409i	−0.00178159	−	0.000727861i
$885$		0			0
$886$	2.43197	+	25.0028i	0.0817035	+	0.839985i
$887$	−14.0805	+	12.7774i	−0.472776	+	0.429022i	−0.873240	−	0.487291i	$-0.837985\pi$
$887$	−14.0805	+	12.7774i	−0.472776	+	0.429022i	0.400463	+	0.916313i	$0.368849\pi$
$888$		0			0
$889$	3.62283	+	9.38336i	0.121506	+	0.314708i
$890$	−2.88237	+	4.99241i	−0.0966172	+	0.167346i
$891$		0			0
$892$	1.15754	+	2.00491i	0.0387572	+	0.0671294i
$893$	−19.7684	+	24.5090i	−0.661524	+	0.820161i
$894$		0			0
$895$	6.27733	+	28.9794i	0.209828	+	0.968674i
$896$	36.2803	−	25.9316i	1.21204	−	0.866314i
$897$		0			0
$898$	−21.6409	+	16.7730i	−0.722168	+	0.559722i
$899$	29.5067	−	19.4069i	0.984103	−	0.647255i
$900$		0			0
$901$	−1.35302	+	23.2304i	−0.0450756	+	0.773918i
$902$	−21.5940	+	45.1601i	−0.719002	+	1.50367i
$903$		0			0
$904$	16.6148	−	19.0385i	0.552601	−	0.633211i
$905$	−52.5542	−	31.7166i	−1.74696	−	1.05430i
$906$		0			0
$907$	−2.72828	+	28.0492i	−0.0905912	+	0.931359i	0.834347	+	0.551240i	$0.185845\pi$
$907$	−2.72828	+	28.0492i	−0.0905912	+	0.931359i	−0.924938	+	0.380118i	$0.875883\pi$
$908$	−0.381011	−	0.511787i	−0.0126443	−	0.0169842i
$909$		0			0
$910$	−4.52592	−	0.529004i	−0.150033	−	0.0175363i
$911$	4.21407	−	1.35119i	0.139618	−	0.0447668i	−0.234695	−	0.972069i	$-0.575409\pi$
$911$	4.21407	−	1.35119i	0.139618	−	0.0447668i	0.374314	+	0.927302i	$0.377878\pi$
$912$		0			0
$913$	13.7792	+	28.8168i	0.456026	+	0.953697i
$914$	−12.1870	+	4.97894i	−0.403110	+	0.164689i
$915$		0			0
$916$	0.338975	−	0.990691i	0.0112000	−	0.0327333i
$917$	65.5445	+	23.8563i	2.16447	+	0.787803i
$918$		0			0
$919$	−55.5150	+	20.2058i	−1.83127	+	0.666528i	−0.838739	+	0.544534i	$0.816707\pi$
$919$	−55.5150	+	20.2058i	−1.83127	+	0.666528i	−0.992531	+	0.121994i	$0.961071\pi$
$920$	−0.997222	−	51.4165i	−0.0328774	−	1.69515i
$921$		0			0
$922$	22.5356	+	35.7551i	0.742169	+	1.17753i
$923$	0.197037	−	0.0548489i	0.00648554	−	0.00180537i
$924$		0			0
$925$	53.7588	+	2.08609i	1.76758	+	0.0685901i
$926$	19.0589	+	20.2013i	0.626315	+	0.663855i
$927$		0			0
$928$	3.07789	+	0.729473i	0.101037	+	0.0239461i
$929$	−2.11083	−	8.19475i	−0.0692541	−	0.268861i	0.924387	−	0.381456i	$-0.124577\pi$
$929$	−2.11083	−	8.19475i	−0.0692541	−	0.268861i	−0.993641	+	0.112596i	$0.964084\pi$
$930$		0			0
$931$	13.8569	−	35.8903i	0.454143	−	1.17626i
$932$	1.41585	+	1.75538i	0.0463778	+	0.0574994i
$933$		0			0
$934$	21.6323	−	21.2168i	0.707830	−	0.694235i
$935$	−32.8074	+	34.7738i	−1.07292	+	1.13722i
$936$		0			0
$937$	−3.69030	+	12.3265i	−0.120557	+	0.402688i	−0.996870	−	0.0790534i	$-0.974810\pi$
$937$	−3.69030	+	12.3265i	−0.120557	+	0.402688i	0.876314	+	0.481741i	$0.159995\pi$
$938$	−18.4532	+	29.2779i	−0.602517	+	0.955958i
$939$		0			0
$940$	−2.56744	−	2.51812i	−0.0837406	−	0.0821322i
$941$	36.8878	−	1.43141i	1.20251	−	0.0466628i	0.570283	−	0.821448i	$-0.306833\pi$
$941$	36.8878	−	1.43141i	1.20251	−	0.0466628i	0.632224	+	0.774785i	$0.282142\pi$
$942$		0			0
$943$	−28.6441	+	17.2868i	−0.932779	+	0.562935i
$944$	0.211778	−	1.20105i	0.00689278	−	0.0390909i
$945$		0			0
$946$	0.254256	+	1.44196i	0.00826658	+	0.0468821i
$947$	−36.9265	−	42.3131i	−1.19995	−	1.37499i	−0.908222	−	0.418488i	$-0.862560\pi$
$947$	−36.9265	−	42.3131i	−1.19995	−	1.37499i	−0.291728	−	0.956501i	$-0.594230\pi$
$948$		0			0
$949$	0.583061	+	0.451907i	0.0189270	+	0.0146695i
$950$	34.0909	+	2.64975i	1.10605	+	0.0859694i
$951$		0			0
$952$	−22.9742	−	20.8480i	−0.744598	−	0.675686i
$953$	21.1818	−	28.4520i	0.686145	−	0.921652i	−0.313465	−	0.949600i	$-0.601490\pi$
$953$	21.1818	−	28.4520i	0.686145	−	0.921652i	0.999609	+	0.0279476i	$0.00889715\pi$
$954$		0			0
$955$	−30.6747	+	71.1119i	−0.992610	+	2.30113i
$956$	0.596861	+	0.426610i	0.0193039	+	0.0137976i
$957$		0			0
$958$	0.293583	−	15.1371i	0.00948523	−	0.489056i
$959$	22.3145	+	65.2166i	0.720573	+	2.10596i
$960$		0			0
$961$	14.1599	−	1.10060i	0.456772	−	0.0355031i
$962$	1.78081	+	1.17126i	0.0574156	+	0.0377629i
$963$		0			0
$964$	−0.530938	−	0.266647i	−0.0171004	−	0.00858812i
$965$	−3.33683	−	24.4299i	−0.107416	−	0.786427i
$966$		0			0
$967$	2.09055	+	0.950274i	0.0672277	+	0.0305587i	0.447142	−	0.894463i	$-0.352442\pi$
$967$	2.09055	+	0.950274i	0.0672277	+	0.0305587i	−0.379915	+	0.925022i	$0.624047\pi$
$968$	51.6474	+	16.5601i	1.66001	+	0.532261i
$969$		0			0
$970$	−6.19959	−	0.969597i	−0.199057	−	0.0311319i
$971$	19.2689			0.618369			0.309184	−	0.951002i	$-0.399944\pi$
$971$	19.2689			0.618369			0.309184	+	0.951002i	$0.399944\pi$
$972$		0			0
$973$	−27.3070			−0.875422
$974$	39.7170	+	6.21163i	1.27262	+	0.199033i
$975$		0			0
$976$	11.1327	+	3.56955i	0.356349	+	0.114259i
$977$	−31.0615	−	14.1192i	−0.993746	−	0.451713i	−0.150134	−	0.988666i	$-0.547970\pi$
$977$	−31.0615	−	14.1192i	−0.993746	−	0.451713i	−0.843612	+	0.536952i	$0.819575\pi$
$978$		0			0
$979$	−0.873213	−	6.39305i	−0.0279080	−	0.204323i
$980$	3.92656	+	1.97199i	0.125429	+	0.0629930i
$981$		0			0
$982$	0.319013	+	0.209818i	0.0101801	+	0.00669557i
$983$	−56.4387	+	4.38677i	−1.80012	+	0.139916i	−0.933389	−	0.358867i	$-0.883163\pi$
$983$	−56.4387	+	4.38677i	−1.80012	+	0.139916i	−0.866727	+	0.498783i	$0.833781\pi$
$984$		0			0
$985$	−5.56458	−	16.2631i	−0.177302	−	0.518186i
$986$	−0.347356	+	17.9096i	−0.0110621	+	0.570358i
$987$		0			0
$988$	−0.0620298	−	0.0443362i	−0.00197343	−	0.00141052i
$989$	−0.387608	+	0.898576i	−0.0123252	+	0.0285730i
$990$		0			0
$991$	−22.5673	+	30.3131i	−0.716873	+	0.962928i	0.283119	+	0.959085i	$0.408631\pi$
$991$	−22.5673	+	30.3131i	−0.716873	+	0.962928i	−0.999993	+	0.00384316i	$0.998777\pi$
$992$	2.99816	+	2.72068i	0.0951916	+	0.0863817i
$993$		0			0
$994$	5.59274	+	0.434702i	0.177391	+	0.0137879i
$995$	16.9134	+	13.1089i	0.536190	+	0.415579i
$996$		0			0
$997$	−33.5041	−	38.3914i	−1.06109	−	1.21587i	−0.975606	−	0.219529i	$-0.929548\pi$
$997$	−33.5041	−	38.3914i	−1.06109	−	1.21587i	−0.0854792	−	0.996340i	$-0.527242\pi$
$998$	−6.63635	−	37.6366i	−0.210070	−	1.19137i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.i.a.10.8		1404
3.2	odd	2		243.2.i.a.13.19	✓	1404
243.56	odd	162		243.2.i.a.187.19	yes	1404
243.187	even	81	inner	729.2.i.a.73.8		1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.13.19	✓	1404	3.2	odd	2
243.2.i.a.187.19	yes	1404	243.56	odd	162
729.2.i.a.10.8		1404	1.1	even	1	trivial
729.2.i.a.73.8		1404	243.187	even	81	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.i (of order \(81\), degree \(54\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.35949 - 0.212621i) q^{2} +(-0.101477 - 0.0325373i) q^{4} +(3.22186 + 1.46451i) q^{5} +(0.584445 + 4.27889i) q^{7} +(2.59035 + 1.30092i) q^{8} +O(q^{10})\)	\(q+(-1.35949 - 0.212621i) q^{2} +(-0.101477 - 0.0325373i) q^{4} +(3.22186 + 1.46451i) q^{5} +(0.584445 + 4.27889i) q^{7} +(2.59035 + 1.30092i) q^{8} +(-4.06871 - 2.67603i) q^{10} +(5.43439 - 0.422394i) q^{11} +(-0.0701422 - 0.204998i) q^{13} +(0.115233 - 5.94140i) q^{14} +(-3.07158 - 2.19543i) q^{16} +(-0.981582 + 2.27556i) q^{17} +(-1.97195 + 2.64879i) q^{19} +(-0.279293 - 0.253445i) q^{20} +(-7.47784 - 0.581224i) q^{22} +(-3.96219 - 3.07093i) q^{23} +(4.94795 + 5.66972i) q^{25} +(0.0517710 + 0.293608i) q^{26} +(0.0799158 - 0.453225i) q^{28} +(-4.49735 + 2.71417i) q^{29} +(-6.71823 + 0.260698i) q^{31} +(-0.429909 - 0.421652i) q^{32} +(1.81829 - 2.88491i) q^{34} +(-4.38350 + 14.6419i) q^{35} +(4.90612 - 5.20018i) q^{37} +(3.24404 - 3.18174i) q^{38} +(6.44053 + 7.98500i) q^{40} +(2.40381 - 6.22602i) q^{41} +(-0.0486951 - 0.189046i) q^{43} +(-0.565210 - 0.133957i) q^{44} +(4.73364 + 5.01736i) q^{46} +(9.52815 + 0.369736i) q^{47} +(-11.2237 + 3.12434i) q^{49} +(-5.52121 - 8.75999i) q^{50} +(0.000447730 + 0.0230849i) q^{52} +(8.82337 - 3.21144i) q^{53} +(18.1274 + 6.59785i) q^{55} +(-4.05260 + 11.8442i) q^{56} +(6.69122 - 2.73366i) q^{58} +(0.139348 + 0.291422i) q^{59} +(-2.94866 + 0.945449i) q^{61} +(9.18884 + 1.07402i) q^{62} +(5.00397 + 6.72149i) q^{64} +(0.0742347 - 0.763199i) q^{65} +(-4.98615 - 3.00916i) q^{67} +(0.173649 - 0.198979i) q^{68} +(9.07252 - 18.9736i) q^{70} +(-0.0548875 + 0.942381i) q^{71} +(-2.84459 + 1.87092i) q^{73} +(-7.77552 + 6.02648i) q^{74} +(0.286292 - 0.204629i) q^{76} +(4.98348 + 23.0063i) q^{77} +(-4.53689 + 5.62486i) q^{79} +(-6.68094 - 11.5717i) q^{80} +(-4.59175 + 7.95315i) q^{82} +(2.11065 + 5.46672i) q^{83} +(-6.49511 + 5.89400i) q^{85} +(0.0260056 + 0.267361i) q^{86} +(14.6265 + 5.97559i) q^{88} +(-0.0688294 - 1.18176i) q^{89} +(0.836172 - 0.419941i) q^{91} +(0.302152 + 0.440548i) q^{92} +(-12.8749 - 2.52854i) q^{94} +(-10.2325 + 5.64607i) q^{95} +(1.17303 - 0.533206i) q^{97} +(15.9229 - 1.86112i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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