LMFDB - Embedded newform 756.2.bo.b.85.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(85,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("756.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bo (of order $9$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			85.3
Character	$\chi$	$=$	756.85
Dual form			756.2.bo.b.169.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24763 - 1.20143i) q^{3} +(0.123908 - 0.702715i) q^{5} +(-0.766044 + 0.642788i) q^{7} +(0.113154 + 2.99787i) q^{9} +O(q^{10})$	\(q+(-1.24763 - 1.20143i) q^{3} +(0.123908 - 0.702715i) q^{5} +(-0.766044 + 0.642788i) q^{7} +(0.113154 + 2.99787i) q^{9} +(-0.102714 - 0.582522i) q^{11} +(-2.94406 + 1.07155i) q^{13} +(-0.998850 + 0.727861i) q^{15} +(-3.64230 + 6.30865i) q^{17} +(-1.83063 - 3.17074i) q^{19} +(1.72800 + 0.118385i) q^{21} +(-0.711913 - 0.597366i) q^{23} +(4.22001 + 1.53596i) q^{25} +(3.46054 - 3.87617i) q^{27} +(-1.89735 - 0.690578i) q^{29} +(6.47147 + 5.43021i) q^{31} +(-0.571708 + 0.850175i) q^{33} +(0.356778 + 0.617957i) q^{35} +(-2.25256 + 3.90154i) q^{37} +(4.96048 + 2.20017i) q^{39} +(-8.98515 + 3.27033i) q^{41} +(2.11952 + 12.0204i) q^{43} +(2.12066 + 0.291943i) q^{45} +(-7.18285 + 6.02712i) q^{47} +(0.173648 - 0.984808i) q^{49} +(12.1236 - 3.49490i) q^{51} +9.58166 q^{53} -0.422074 q^{55} +(-1.52547 + 6.15528i) q^{57} +(2.20393 - 12.4991i) q^{59} +(-7.59058 + 6.36925i) q^{61} +(-2.01367 - 2.22376i) q^{63} +(0.388203 + 2.20161i) q^{65} +(1.72584 - 0.628155i) q^{67} +(0.170512 + 1.60060i) q^{69} +(2.62482 - 4.54633i) q^{71} +(7.69219 + 13.3233i) q^{73} +(-3.41967 - 6.98633i) q^{75} +(0.453122 + 0.380214i) q^{77} +(-4.14126 - 1.50730i) q^{79} +(-8.97439 + 0.678444i) q^{81} +(-2.95557 - 1.07574i) q^{83} +(3.98187 + 3.34119i) q^{85} +(1.53751 + 3.14110i) q^{87} +(-3.72812 - 6.45730i) q^{89} +(1.56650 - 2.71326i) q^{91} +(-1.55000 - 14.5499i) q^{93} +(-2.45496 + 0.893531i) q^{95} +(-0.315639 - 1.79008i) q^{97} +(1.73470 - 0.373839i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9}+O(q^{10}) $ 54 * q + 3 * q^3 - 3 * q^5 - 9 * q^9	$ 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9} + 9 q^{13} + 3 q^{15} + 3 q^{21} + 12 q^{23} + 27 q^{25} + 39 q^{27} + 30 q^{29} - 9 q^{31} - 6 q^{33} + 6 q^{35} - 18 q^{39} - 27 q^{41} + 9 q^{43} - 81 q^{45} + 9 q^{47} + 12 q^{53} - 21 q^{57} - 24 q^{59} - 3 q^{63} - 78 q^{65} - 9 q^{67} + 6 q^{69} - 30 q^{71} + 57 q^{75} + 9 q^{77} + 99 q^{81} + 78 q^{83} + 18 q^{85} + 21 q^{87} + 12 q^{89} - 51 q^{93} - 36 q^{95} + 36 q^{97} + 15 q^{99}+O(q^{100}) $ 54 * q + 3 * q^3 - 3 * q^5 - 9 * q^9 + 9 * q^13 + 3 * q^15 + 3 * q^21 + 12 * q^23 + 27 * q^25 + 39 * q^27 + 30 * q^29 - 9 * q^31 - 6 * q^33 + 6 * q^35 - 18 * q^39 - 27 * q^41 + 9 * q^43 - 81 * q^45 + 9 * q^47 + 12 * q^53 - 21 * q^57 - 24 * q^59 - 3 * q^63 - 78 * q^65 - 9 * q^67 + 6 * q^69 - 30 * q^71 + 57 * q^75 + 9 * q^77 + 99 * q^81 + 78 * q^83 + 18 * q^85 + 21 * q^87 + 12 * q^89 - 51 * q^93 - 36 * q^95 + 36 * q^97 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$	$1$

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
$3$	−1.24763	−	1.20143i	−0.720319	−	0.693643i
$3$	−1.24763	−	1.20143i	−0.720319	−	0.693643i
$4$		0			0
$5$	0.123908	−	0.702715i	0.0554131	−	0.314264i	−0.944485	−	0.328555i	$-0.893438\pi$
$5$	0.123908	−	0.702715i	0.0554131	−	0.314264i	0.999898	+	0.0142918i	$0.00454937\pi$
$6$		0			0
$7$	−0.766044	+	0.642788i	−0.289538	+	0.242951i
$7$	−0.766044	+	0.642788i	−0.289538	+	0.242951i
$8$		0			0
$9$	0.113154	+	2.99787i	0.0377181	+	0.999288i
$10$		0			0
$11$	−0.102714	−	0.582522i	−0.0309696	−	0.175637i	0.965400	−	0.260775i	$-0.0839780\pi$
$11$	−0.102714	−	0.582522i	−0.0309696	−	0.175637i	−0.996369	+	0.0851378i	$0.972867\pi$
$12$		0			0
$13$	−2.94406	+	1.07155i	−0.816535	+	0.297195i	−0.716321	−	0.697771i	$-0.754175\pi$
$13$	−2.94406	+	1.07155i	−0.816535	+	0.297195i	−0.100215	+	0.994966i	$0.531953\pi$
$14$		0			0
$15$	−0.998850	+	0.727861i	−0.257902	+	0.187933i
$16$		0			0
$17$	−3.64230	+	6.30865i	−0.883387	+	1.53007i	−0.0358360	+	0.999358i	$0.511409\pi$
$17$	−3.64230	+	6.30865i	−0.883387	+	1.53007i	−0.847551	+	0.530714i	$0.821924\pi$
$18$		0			0
$19$	−1.83063	−	3.17074i	−0.419975	−	0.727419i	0.575961	−	0.817477i	$-0.304628\pi$
$19$	−1.83063	−	3.17074i	−0.419975	−	0.727419i	−0.995936	+	0.0900584i	$0.971295\pi$
$20$		0			0
$21$	1.72800	+	0.118385i	0.377081	+	0.0258337i
$22$		0			0
$23$	−0.711913	−	0.597366i	−0.148444	−	0.124559i	0.565541	−	0.824720i	$-0.308667\pi$
$23$	−0.711913	−	0.597366i	−0.148444	−	0.124559i	−0.713985	+	0.700161i	$0.753112\pi$
$24$		0			0
$25$	4.22001	+	1.53596i	0.844002	+	0.307191i
$26$		0			0
$27$	3.46054	−	3.87617i	0.665981	−	0.745969i
$28$		0			0
$29$	−1.89735	−	0.690578i	−0.352328	−	0.128237i	0.159792	−	0.987151i	$-0.448918\pi$
$29$	−1.89735	−	0.690578i	−0.352328	−	0.128237i	−0.512120	+	0.858914i	$0.671140\pi$
$30$		0			0
$31$	6.47147	+	5.43021i	1.16231	+	0.975294i	0.999935	−	0.0114345i	$-0.00363979\pi$
$31$	6.47147	+	5.43021i	1.16231	+	0.975294i	0.162376	+	0.986729i	$0.448084\pi$
$32$		0			0
$33$	−0.571708	+	0.850175i	−0.0995215	+	0.147997i
$34$		0			0
$35$	0.356778	+	0.617957i	0.0603064	+	0.104454i
$36$		0			0
$37$	−2.25256	+	3.90154i	−0.370318	+	0.641409i	−0.989614	−	0.143748i	$-0.954085\pi$
$37$	−2.25256	+	3.90154i	−0.370318	+	0.641409i	0.619297	+	0.785157i	$0.287418\pi$
$38$		0			0
$39$	4.96048	+	2.20017i	0.794313	+	0.352309i
$40$		0			0
$41$	−8.98515	+	3.27033i	−1.40325	+	0.510740i	−0.929140	−	0.369729i	$-0.879451\pi$
$41$	−8.98515	+	3.27033i	−1.40325	+	0.510740i	−0.474105	+	0.880468i	$0.657228\pi$
$42$		0			0
$43$	2.11952	+	12.0204i	0.323223	+	1.83309i	0.521877	+	0.853021i	$0.325232\pi$
$43$	2.11952	+	12.0204i	0.323223	+	1.83309i	−0.198653	+	0.980070i	$0.563657\pi$
$44$		0			0
$45$	2.12066	+	0.291943i	0.316130	+	0.0435203i
$46$		0			0
$47$	−7.18285	+	6.02712i	−1.04773	+	0.879147i	−0.992853	−	0.119347i	$-0.961920\pi$
$47$	−7.18285	+	6.02712i	−1.04773	+	0.879147i	−0.0548734	+	0.998493i	$0.517476\pi$
$48$		0			0
$49$	0.173648	−	0.984808i	0.0248069	−	0.140687i
$50$		0			0
$51$	12.1236	−	3.49490i	1.69764	−	0.489384i
$52$		0			0
$53$	9.58166			1.31614			0.658071	−	0.752956i	$-0.271373\pi$
$53$	9.58166			1.31614			0.658071	+	0.752956i	$0.271373\pi$
$54$		0			0
$55$	−0.422074			−0.0569125
$56$		0			0
$57$	−1.52547	+	6.15528i	−0.202053	+	0.815286i
$58$		0			0
$59$	2.20393	−	12.4991i	0.286927	−	1.62724i	−0.411393	−	0.911458i	$-0.634958\pi$
$59$	2.20393	−	12.4991i	0.286927	−	1.62724i	0.698320	−	0.715786i	$-0.253931\pi$
$60$		0			0
$61$	−7.59058	+	6.36925i	−0.971874	+	0.815499i	−0.982844	−	0.184441i	$-0.940953\pi$
$61$	−7.59058	+	6.36925i	−0.971874	+	0.815499i	0.0109699	+	0.999940i	$0.496508\pi$
$62$		0			0
$63$	−2.01367	−	2.22376i	−0.253699	−	0.280168i
$64$		0			0
$65$	0.388203	+	2.20161i	0.0481506	+	0.273076i
$66$		0			0
$67$	1.72584	−	0.628155i	0.210845	−	0.0767414i	−0.234438	−	0.972131i	$-0.575325\pi$
$67$	1.72584	−	0.628155i	0.210845	−	0.0767414i	0.445284	+	0.895390i	$0.353103\pi$
$68$		0			0
$69$	0.170512	+	1.60060i	0.0205273	+	0.192690i
$70$		0			0
$71$	2.62482	−	4.54633i	0.311509	−	0.539550i	−0.667180	−	0.744896i	$-0.732499\pi$
$71$	2.62482	−	4.54633i	0.311509	−	0.539550i	0.978689	+	0.205347i	$0.0658322\pi$
$72$		0			0
$73$	7.69219	+	13.3233i	0.900302	+	1.55937i	0.827102	+	0.562052i	$0.189988\pi$
$73$	7.69219	+	13.3233i	0.900302	+	1.55937i	0.0732007	+	0.997317i	$0.476679\pi$
$74$		0			0
$75$	−3.41967	−	6.98633i	−0.394869	−	0.806712i
$76$		0			0
$77$	0.453122	+	0.380214i	0.0516380	+	0.0433295i
$78$		0			0
$79$	−4.14126	−	1.50730i	−0.465929	−	0.169584i	0.0983785	−	0.995149i	$-0.468634\pi$
$79$	−4.14126	−	1.50730i	−0.465929	−	0.169584i	−0.564307	+	0.825565i	$0.690857\pi$
$80$		0			0
$81$	−8.97439	+	0.678444i	−0.997155	+	0.0753826i
$82$		0			0
$83$	−2.95557	−	1.07574i	−0.324416	−	0.118078i	0.174678	−	0.984626i	$-0.444112\pi$
$83$	−2.95557	−	1.07574i	−0.324416	−	0.118078i	−0.499094	+	0.866548i	$0.666334\pi$
$84$		0			0
$85$	3.98187	+	3.34119i	0.431894	+	0.362402i
$86$		0			0
$87$	1.53751	+	3.14110i	0.164838	+	0.336762i
$88$		0			0
$89$	−3.72812	−	6.45730i	−0.395180	−	0.684472i	0.597944	−	0.801538i	$-0.295985\pi$
$89$	−3.72812	−	6.45730i	−0.395180	−	0.684472i	−0.993124	+	0.117066i	$0.962651\pi$
$90$		0			0
$91$	1.56650	−	2.71326i	0.164214	−	0.284427i
$92$		0			0
$93$	−1.55000	−	14.5499i	−0.160728	−	1.50875i
$94$		0			0
$95$	−2.45496	+	0.893531i	−0.251873	+	0.0916744i
$96$		0			0
$97$	−0.315639	−	1.79008i	−0.0320483	−	0.181755i	0.964582	−	0.263785i	$-0.0849709\pi$
$97$	−0.315639	−	1.79008i	−0.0320483	−	0.181755i	−0.996630	+	0.0820297i	$0.973860\pi$
$98$		0			0
$99$	1.73470	−	0.373839i	0.174344	−	0.0375722i
$100$		0			0
$101$	−10.0045	+	8.39478i	−0.995486	+	0.835312i	−0.986353	−	0.164646i	$-0.947352\pi$
$101$	−10.0045	+	8.39478i	−0.995486	+	0.835312i	−0.00913363	+	0.999958i	$0.502907\pi$
$102$		0			0
$103$	0.203535	−	1.15430i	0.0200549	−	0.113737i	−0.973137	−	0.230227i	$-0.926053\pi$
$103$	0.203535	−	1.15430i	0.0200549	−	0.113737i	0.993192	+	0.116490i	$0.0371643\pi$
$104$		0			0
$105$	0.297303	−	1.19962i	0.0290138	−	0.117071i
$106$		0			0
$107$	−7.58262			−0.733039			−0.366520	−	0.930410i	$-0.619451\pi$
$107$	−7.58262			−0.733039			−0.366520	+	0.930410i	$0.619451\pi$
$108$		0			0
$109$	−8.11248			−0.777034			−0.388517	−	0.921441i	$-0.627013\pi$
$109$	−8.11248			−0.777034			−0.388517	+	0.921441i	$0.627013\pi$
$110$		0			0
$111$	7.49776	−	2.16140i	0.711656	−	0.205151i
$112$		0			0
$113$	−1.35018	+	7.65727i	−0.127015	+	0.720336i	0.853076	+	0.521786i	$0.174734\pi$
$113$	−1.35018	+	7.65727i	−0.127015	+	0.720336i	−0.980091	+	0.198549i	$0.936377\pi$
$114$		0			0
$115$	−0.507989	+	0.426253i	−0.0473702	+	0.0397483i
$116$		0			0
$117$	−3.54550	−	8.70464i	−0.327781	−	0.804745i
$118$		0			0
$119$	−1.26496	−	7.17393i	−0.115958	−	0.657633i
$120$		0			0
$121$	10.0078	−	3.64255i	0.909803	−	0.331141i
$122$		0			0
$123$	15.1392	+	6.71484i	1.36505	+	0.605456i
$124$		0			0
$125$	3.38612	−	5.86493i	0.302864	−	0.524575i
$126$		0			0
$127$	−6.89315	−	11.9393i	−0.611668	−	1.05944i	−0.990959	−	0.134163i	$-0.957165\pi$
$127$	−6.89315	−	11.9393i	−0.611668	−	1.05944i	0.379291	−	0.925277i	$-0.376168\pi$
$128$		0			0
$129$	11.7972	−	17.5434i	1.03869	−	1.54461i
$130$		0			0
$131$	−15.6383	−	13.1221i	−1.36633	−	1.14648i	−0.973972	−	0.226668i	$-0.927217\pi$
$131$	−15.6383	−	13.1221i	−1.36633	−	1.14648i	−0.392353	−	0.919815i	$-0.628339\pi$
$132$		0			0
$133$	3.44046	+	1.25222i	0.298326	+	0.108582i
$134$		0			0
$135$	−2.29505	−	2.91206i	−0.197527	−	0.250630i
$136$		0			0
$137$	−1.25635	−	0.457273i	−0.107337	−	0.0390675i	0.287793	−	0.957693i	$-0.407078\pi$
$137$	−1.25635	−	0.457273i	−0.107337	−	0.0390675i	−0.395130	+	0.918625i	$0.629301\pi$
$138$		0			0
$139$	2.85584	+	2.39633i	0.242229	+	0.203254i	0.755817	−	0.654782i	$-0.227240\pi$
$139$	2.85584	+	2.39633i	0.242229	+	0.203254i	−0.513589	+	0.858037i	$0.671684\pi$
$140$		0			0
$141$	16.2027	+	1.11004i	1.36451	+	0.0934824i
$142$		0			0
$143$	0.926599	+	1.60492i	0.0774861	+	0.134210i
$144$		0			0
$145$	−0.720375	+	1.24773i	−0.0598239	+	0.103618i
$146$		0			0
$147$	−1.39982	+	1.02005i	−0.115455	+	0.0841322i
$148$		0			0
$149$	−2.13597	+	0.777430i	−0.174986	+	0.0636895i	−0.428027	−	0.903766i	$-0.640791\pi$
$149$	−2.13597	+	0.777430i	−0.174986	+	0.0636895i	0.253042	+	0.967455i	$0.418569\pi$
$150$		0			0
$151$	1.78445	+	10.1201i	0.145216	+	0.823563i	0.967193	+	0.254042i	$0.0817601\pi$
$151$	1.78445	+	10.1201i	0.145216	+	0.823563i	−0.821977	+	0.569521i	$0.807129\pi$
$152$		0			0
$153$	−19.3246	−	10.2053i	−1.56230	−	0.825047i
$154$		0			0
$155$	4.61775	−	3.87475i	0.370907	−	0.311228i
$156$		0			0
$157$	0.659025	−	3.73752i	0.0525959	−	0.298286i	−0.947151	−	0.320788i	$-0.896052\pi$
$157$	0.659025	−	3.73752i	0.0525959	−	0.298286i	0.999747	+	0.0225021i	$0.00716325\pi$
$158$		0			0
$159$	−11.9543	−	11.5116i	−0.948041	−	0.912933i
$160$		0			0
$161$	0.929336			0.0732419
$162$		0			0
$163$	12.5282			0.981281			0.490640	−	0.871362i	$-0.336763\pi$
$163$	12.5282			0.981281			0.490640	+	0.871362i	$0.336763\pi$
$164$		0			0
$165$	0.526592	+	0.507090i	0.0409951	+	0.0394769i
$166$		0			0
$167$	3.72816	−	21.1435i	0.288494	−	1.63613i	−0.404038	−	0.914742i	$-0.632393\pi$
$167$	3.72816	−	21.1435i	0.288494	−	1.63613i	0.692531	−	0.721388i	$-0.256495\pi$
$168$		0			0
$169$	−2.43931	+	2.04682i	−0.187639	+	0.157448i
$170$		0			0
$171$	9.29832	−	5.84677i	0.711060	−	0.447113i
$172$		0			0
$173$	−1.32609	−	7.52062i	−0.100821	−	0.571782i	−0.992808	−	0.119721i	$-0.961800\pi$
$173$	−1.32609	−	7.52062i	−0.100821	−	0.571782i	0.891987	−	0.452061i	$-0.149311\pi$
$174$		0			0
$175$	−4.22001	+	1.53596i	−0.319003	+	0.116107i
$176$		0			0
$177$	−17.7664	+	12.9464i	−1.33541	+	0.973109i
$178$		0			0
$179$	−0.731896	+	1.26768i	−0.0547045	+	0.0947509i	−0.892081	−	0.451876i	$-0.850755\pi$
$179$	−0.731896	+	1.26768i	−0.0547045	+	0.0947509i	0.837376	+	0.546627i	$0.184088\pi$
$180$		0			0
$181$	−11.6215	−	20.1290i	−0.863819	−	1.49618i	−0.868215	−	0.496188i	$-0.834733\pi$
$181$	−11.6215	−	20.1290i	−0.863819	−	1.49618i	0.00439580	−	0.999990i	$-0.498601\pi$
$182$		0			0
$183$	17.1224	+	1.17305i	1.26572	+	0.0867145i
$184$		0			0
$185$	2.46256	+	2.06633i	0.181051	+	0.151920i
$186$		0			0
$187$	4.04904	+	1.47373i	0.296095	+	0.107770i
$188$		0			0
$189$	−0.159371	+	5.19371i	−0.0115926	+	0.377787i
$190$		0			0
$191$	−15.7896	−	5.74694i	−1.14249	−	0.415834i	−0.299681	−	0.954039i	$-0.596880\pi$
$191$	−15.7896	−	5.74694i	−1.14249	−	0.415834i	−0.842814	+	0.538205i	$0.819102\pi$
$192$		0			0
$193$	−8.24612	−	6.91932i	−0.593569	−	0.498064i	0.295802	−	0.955249i	$-0.404413\pi$
$193$	−8.24612	−	6.91932i	−0.593569	−	0.498064i	−0.889371	+	0.457186i	$0.848857\pi$
$194$		0			0
$195$	2.16073	−	3.21318i	0.154733	−	0.230101i
$196$		0			0
$197$	10.5409	+	18.2573i	0.751006	+	1.30078i	0.947335	+	0.320243i	$0.103765\pi$
$197$	10.5409	+	18.2573i	0.751006	+	1.30078i	−0.196329	+	0.980538i	$0.562902\pi$
$198$		0			0
$199$	−3.22556	+	5.58683i	−0.228654	+	0.396040i	−0.957409	−	0.288734i	$-0.906766\pi$
$199$	−3.22556	+	5.58683i	−0.228654	+	0.396040i	0.728756	+	0.684774i	$0.240099\pi$
$200$		0			0
$201$	−2.90789	−	1.28977i	−0.205107	−	0.0909731i
$202$		0			0
$203$	1.89735	−	0.690578i	0.133168	−	0.0484691i
$204$		0			0
$205$	1.18478	+	6.71922i	0.0827486	+	0.469291i
$206$		0			0
$207$	1.71027	−	2.20181i	0.118872	−	0.153037i
$208$		0			0
$209$	−1.65900	+	1.39206i	−0.114755	+	0.0962911i
$210$		0			0
$211$	−1.25524	+	7.11880i	−0.0864140	+	0.490078i	0.910629	+	0.413226i	$0.135598\pi$
$211$	−1.25524	+	7.11880i	−0.0864140	+	0.490078i	−0.997043	+	0.0768521i	$0.975513\pi$
$212$		0			0
$213$	−8.73688	+	2.51860i	−0.598641	+	0.172572i
$214$		0			0
$215$	8.70952			0.593984
$216$		0			0
$217$	−8.44791			−0.573481
$218$		0			0
$219$	6.40991	−	25.8641i	0.433141	−	1.74773i
$220$		0			0
$221$	3.96311	−	22.4759i	0.266588	−	1.51190i
$222$		0			0
$223$	−6.86287	+	5.75863i	−0.459572	+	0.385626i	−0.842973	−	0.537955i	$-0.819197\pi$
$223$	−6.86287	+	5.75863i	−0.459572	+	0.385626i	0.383402	+	0.923582i	$0.374752\pi$
$224$		0			0
$225$	−4.12708	+	12.8248i	−0.275139	+	0.854988i
$226$		0			0
$227$	2.54684	+	14.4438i	0.169040	+	0.958671i	0.944801	+	0.327645i	$0.106255\pi$
$227$	2.54684	+	14.4438i	0.169040	+	0.958671i	−0.775762	+	0.631026i	$0.782634\pi$
$228$		0			0
$229$	23.7227	−	8.63436i	1.56764	−	0.570574i	0.595170	−	0.803600i	$-0.297085\pi$
$229$	23.7227	−	8.63436i	1.56764	−	0.570574i	0.972471	+	0.233026i	$0.0748626\pi$
$230$		0			0
$231$	−0.108529	−	1.01876i	−0.00714066	−	0.0670294i
$232$		0			0
$233$	−3.94174	+	6.82730i	−0.258232	+	0.447271i	−0.965768	−	0.259406i	$-0.916473\pi$
$233$	−3.94174	+	6.82730i	−0.258232	+	0.447271i	0.707536	+	0.706677i	$0.249807\pi$
$234$		0			0
$235$	3.34534	+	5.79430i	0.218226	+	0.377978i
$236$		0			0
$237$	3.35586	+	6.85597i	0.217986	+	0.445343i
$238$		0			0
$239$	4.48867	+	3.76644i	0.290348	+	0.243631i	0.776313	−	0.630347i	$-0.217087\pi$
$239$	4.48867	+	3.76644i	0.290348	+	0.243631i	−0.485965	+	0.873978i	$0.661532\pi$
$240$		0			0
$241$	21.1140	+	7.68486i	1.36007	+	0.495025i	0.916076	−	0.401004i	$-0.131339\pi$
$241$	21.1140	+	7.68486i	1.36007	+	0.495025i	0.443995	+	0.896029i	$0.353561\pi$
$242$		0			0
$243$	12.0118	+	9.93562i	0.770558	+	0.637370i
$244$		0			0
$245$	−0.670522	−	0.244050i	−0.0428381	−	0.0155918i
$246$		0			0
$247$	8.78710	+	7.37325i	0.559110	+	0.469149i
$248$		0			0
$249$	2.39503	+	4.89302i	0.151779	+	0.310083i
$250$		0			0
$251$	2.11313	+	3.66005i	0.133380	+	0.231020i	0.924977	−	0.380022i	$-0.124084\pi$
$251$	2.11313	+	3.66005i	0.133380	+	0.231020i	−0.791598	+	0.611043i	$0.790750\pi$
$252$		0			0
$253$	−0.274855	+	0.476063i	−0.0172800	+	0.0299298i
$254$		0			0
$255$	−0.953710	−	8.95248i	−0.0597236	−	0.560626i
$256$		0			0
$257$	−0.697741	+	0.253957i	−0.0435239	+	0.0158414i	−0.363690	−	0.931520i	$-0.618483\pi$
$257$	−0.697741	+	0.253957i	−0.0435239	+	0.0158414i	0.320166	+	0.947361i	$0.396261\pi$
$258$		0			0
$259$	−0.782304	−	4.43667i	−0.0486100	−	0.275681i
$260$		0			0
$261$	1.85557	−	5.76613i	0.114857	−	0.356915i
$262$		0			0
$263$	−10.1210	+	8.49251i	−0.624086	+	0.523671i	−0.899085	−	0.437774i	$-0.855767\pi$
$263$	−10.1210	+	8.49251i	−0.624086	+	0.523671i	0.274999	+	0.961445i	$0.411323\pi$
$264$		0			0
$265$	1.18724	−	6.73317i	0.0729315	−	0.413615i
$266$		0			0
$267$	−3.10665	+	12.5354i	−0.190124	+	0.767153i
$268$		0			0
$269$	−7.70858			−0.470000			−0.235000	−	0.971995i	$-0.575509\pi$
$269$	−7.70858			−0.470000			−0.235000	+	0.971995i	$0.575509\pi$
$270$		0			0
$271$	−18.4759			−1.12233			−0.561165	−	0.827704i	$-0.689647\pi$
$271$	−18.4759			−1.12233			−0.561165	+	0.827704i	$0.689647\pi$
$272$		0			0
$273$	−5.21419	+	1.50311i	−0.315577	+	0.0909721i
$274$		0			0
$275$	0.461274	−	2.61601i	0.0278159	−	0.157752i
$276$		0			0
$277$	6.88823	−	5.77991i	0.413874	−	0.347281i	−0.411953	−	0.911205i	$-0.635153\pi$
$277$	6.88823	−	5.77991i	0.413874	−	0.347281i	0.825827	+	0.563924i	$0.190709\pi$
$278$		0			0
$279$	−15.5468	+	20.0151i	−0.930760	+	1.19827i
$280$		0			0
$281$	4.17842	+	23.6970i	0.249264	+	1.41365i	0.810378	+	0.585907i	$0.199262\pi$
$281$	4.17842	+	23.6970i	0.249264	+	1.41365i	−0.561114	+	0.827738i	$0.689627\pi$
$282$		0			0
$283$	20.6908	−	7.53082i	1.22994	−	0.447661i	0.356361	−	0.934348i	$-0.384017\pi$
$283$	20.6908	−	7.53082i	1.22994	−	0.447661i	0.873576	+	0.486688i	$0.161795\pi$
$284$		0			0
$285$	4.13639	+	1.83465i	0.245018	+	0.108675i
$286$		0			0
$287$	4.78090	−	8.28076i	0.282208	−	0.488798i
$288$		0			0
$289$	−18.0327	−	31.2335i	−1.06075	−	1.83727i
$290$		0			0
$291$	−1.75685	+	2.61257i	−0.102988	+	0.153152i
$292$		0			0
$293$	0.919478	+	0.771534i	0.0537165	+	0.0450735i	0.669251	−	0.743037i	$-0.266615\pi$
$293$	0.919478	+	0.771534i	0.0537165	+	0.0450735i	−0.615534	+	0.788110i	$0.711060\pi$
$294$		0			0
$295$	−8.51021	−	3.09746i	−0.495484	−	0.180341i
$296$		0			0
$297$	−2.61340	−	1.61770i	−0.151645	−	0.0938686i
$298$		0			0
$299$	2.73602	+	0.995830i	0.158228	+	0.0575903i
$300$		0			0
$301$	−9.35020	−	7.84575i	−0.538936	−	0.452221i
$302$		0			0
$303$	22.5676	+	1.54610i	1.29648	+	0.0888213i
$304$		0			0
$305$	3.53524	+	6.12321i	0.202427	+	0.350614i
$306$		0			0
$307$	−1.55457	+	2.69260i	−0.0887241	+	0.153675i	−0.906972	−	0.421191i	$-0.861612\pi$
$307$	−1.55457	+	2.69260i	−0.0887241	+	0.153675i	0.818248	+	0.574865i	$0.194946\pi$
$308$		0			0
$309$	−1.64074	+	1.19561i	−0.0933387	+	0.0680158i
$310$		0			0
$311$	−20.7918	+	7.56759i	−1.17899	+	0.429119i	−0.855846	−	0.517230i	$-0.826963\pi$
$311$	−20.7918	+	7.56759i	−1.17899	+	0.429119i	−0.323147	+	0.946349i	$0.604741\pi$
$312$		0			0
$313$	1.17881	+	6.68538i	0.0666304	+	0.377880i	0.999829	+	0.0185177i	$0.00589469\pi$
$313$	1.17881	+	6.68538i	0.0666304	+	0.377880i	−0.933198	+	0.359362i	$0.882994\pi$
$314$		0			0
$315$	−1.81218	+	1.13950i	−0.102105	+	0.0642033i
$316$		0			0
$317$	−0.133791	+	0.112264i	−0.00751445	+	0.00630537i	−0.646537	−	0.762883i	$-0.723783\pi$
$317$	−0.133791	+	0.112264i	−0.00751445	+	0.00630537i	0.639023	+	0.769188i	$0.279339\pi$
$318$		0			0
$319$	−0.207392	+	1.17618i	−0.0116117	+	0.0658534i
$320$		0			0
$321$	9.46029	+	9.10995i	0.528022	+	0.508468i
$322$		0			0
$323$	26.6708			1.48400
$324$		0			0
$325$	−14.0698			−0.780453
$326$		0			0
$327$	10.1214	+	9.74654i	0.559712	+	0.538985i
$328$		0			0
$329$	1.62822	−	9.23409i	0.0897666	−	0.509092i
$330$		0			0
$331$	−18.7165	+	15.7050i	−1.02875	+	0.863224i	−0.990702	−	0.136052i	$-0.956558\pi$
$331$	−18.7165	+	15.7050i	−1.02875	+	0.863224i	−0.0380481	+	0.999276i	$0.512114\pi$
$332$		0			0
$333$	−11.9512	−	6.31138i	−0.654921	−	0.345862i
$334$		0			0
$335$	−0.227569	−	1.29061i	−0.0124334	−	0.0705134i
$336$		0			0
$337$	9.45341	−	3.44076i	0.514960	−	0.187430i	−0.0714505	−	0.997444i	$-0.522763\pi$
$337$	9.45341	−	3.44076i	0.514960	−	0.187430i	0.586410	+	0.810014i	$0.300541\pi$
$338$		0			0
$339$	10.8842	−	7.93129i	0.591147	−	0.430768i
$340$		0			0
$341$	2.49851	−	4.32754i	0.135302	−	0.234349i
$342$		0			0
$343$	0.500000	+	0.866025i	0.0269975	+	0.0467610i
$344$		0			0
$345$	1.14589	+	0.0785049i	0.0616928	+	0.00422656i
$346$		0			0
$347$	18.4583	+	15.4883i	0.990893	+	0.831458i	0.985697	−	0.168528i	$-0.0539015\pi$
$347$	18.4583	+	15.4883i	0.990893	+	0.831458i	0.00519629	+	0.999986i	$0.498346\pi$
$348$		0			0
$349$	−8.87427	−	3.22997i	−0.475029	−	0.172896i	0.0934004	−	0.995629i	$-0.470226\pi$
$349$	−8.87427	−	3.22997i	−0.475029	−	0.172896i	−0.568429	+	0.822732i	$0.692449\pi$
$350$		0			0
$351$	−6.03452	+	15.1198i	−0.322099	+	0.807036i
$352$		0			0
$353$	−7.68486	−	2.79706i	−0.409024	−	0.148873i	0.129310	−	0.991604i	$-0.458724\pi$
$353$	−7.68486	−	2.79706i	−0.409024	−	0.148873i	−0.538334	+	0.842732i	$0.680946\pi$
$354$		0			0
$355$	−2.86954	−	2.40783i	−0.152299	−	0.127794i
$356$		0			0
$357$	−7.04074	+	10.4701i	−0.372636	+	0.554139i
$358$		0			0
$359$	−8.17667	−	14.1624i	−0.431548	−	0.747463i	0.565459	−	0.824777i	$-0.308699\pi$
$359$	−8.17667	−	14.1624i	−0.431548	−	0.747463i	−0.997007	+	0.0773133i	$0.975366\pi$
$360$		0			0
$361$	2.79759	−	4.84556i	0.147241	−	0.255030i
$362$		0			0
$363$	−16.8623	−	7.47911i	−0.885042	−	0.392552i
$364$		0			0
$365$	10.3156	−	3.75456i	0.539942	−	0.196523i
$366$		0			0
$367$	5.62068	+	31.8765i	0.293397	+	1.66394i	0.673646	+	0.739054i	$0.264727\pi$
$367$	5.62068	+	31.8765i	0.293397	+	1.66394i	−0.380249	+	0.924884i	$0.624162\pi$
$368$		0			0
$369$	−10.8207	−	26.5662i	−0.563304	−	1.38298i
$370$		0			0
$371$	−7.33997	+	6.15897i	−0.381072	+	0.319758i
$372$		0			0
$373$	−0.189821	+	1.07653i	−0.00982858	+	0.0557406i	−0.989328	−	0.145708i	$-0.953454\pi$
$373$	−0.189821	+	1.07653i	−0.00982858	+	0.0557406i	0.979499	+	0.201449i	$0.0645650\pi$
$374$		0			0
$375$	−11.2709	+	3.24909i	−0.582026	+	0.167782i
$376$		0			0
$377$	6.32589			0.325800
$378$		0			0
$379$	6.72984			0.345688			0.172844	−	0.984949i	$-0.444704\pi$
$379$	6.72984			0.345688			0.172844	+	0.984949i	$0.444704\pi$
$380$		0			0
$381$	−5.74407	+	23.1774i	−0.294278	+	1.18741i
$382$		0			0
$383$	2.56880	−	14.5684i	0.131260	−	0.744411i	−0.846132	−	0.532974i	$-0.821074\pi$
$383$	2.56880	−	14.5684i	0.131260	−	0.744411i	0.977392	−	0.211437i	$-0.0678144\pi$
$384$		0			0
$385$	0.323327	−	0.271304i	0.0164783	−	0.0138269i
$386$		0			0
$387$	−35.7956	+	7.71419i	−1.81960	+	0.392134i
$388$		0			0
$389$	−0.334705	−	1.89821i	−0.0169702	−	0.0962430i	0.975146	−	0.221562i	$-0.0711156\pi$
$389$	−0.334705	−	1.89821i	−0.0169702	−	0.0962430i	−0.992116	+	0.125319i	$0.960004\pi$
$390$		0			0
$391$	6.36157	−	2.31542i	0.321718	−	0.117096i
$392$		0			0
$393$	3.74558	+	35.1598i	0.188939	+	1.77358i
$394$		0			0
$395$	−1.57233	+	2.72336i	−0.0791127	+	0.137027i
$396$		0			0
$397$	5.66570	+	9.81329i	0.284354	+	0.492515i	0.972452	−	0.233102i	$-0.0748877\pi$
$397$	5.66570	+	9.81329i	0.284354	+	0.492515i	−0.688099	+	0.725617i	$0.741554\pi$
$398$		0			0
$399$	−2.78796	−	5.69577i	−0.139573	−	0.285145i
$400$		0			0
$401$	11.1251	+	9.33507i	0.555561	+	0.466171i	0.876819	−	0.480821i	$-0.159661\pi$
$401$	11.1251	+	9.33507i	0.555561	+	0.466171i	−0.321258	+	0.946992i	$0.604106\pi$
$402$		0			0
$403$	−24.8711	−	9.05235i	−1.23892	−	0.450930i
$404$		0			0
$405$	−0.635243	+	6.39050i	−0.0315655	+	0.317547i
$406$		0			0
$407$	2.50410	+	0.911419i	0.124124	+	0.0451774i
$408$		0			0
$409$	9.67326	+	8.11683i	0.478312	+	0.401351i	0.849816	−	0.527080i	$-0.176713\pi$
$409$	9.67326	+	8.11683i	0.478312	+	0.401351i	−0.371504	+	0.928432i	$0.621158\pi$
$410$		0			0
$411$	1.01808	+	2.07992i	0.0502180	+	0.102595i
$412$		0			0
$413$	6.34596	+	10.9915i	0.312264	+	0.540857i
$414$		0			0
$415$	−1.12216	+	1.94363i	−0.0550845	+	0.0954091i
$416$		0			0
$417$	−0.684010	−	6.42080i	−0.0334961	−	0.314428i
$418$		0			0
$419$	9.24015	−	3.36314i	0.451411	−	0.164300i	−0.106302	−	0.994334i	$-0.533901\pi$
$419$	9.24015	−	3.36314i	0.451411	−	0.164300i	0.557713	+	0.830034i	$0.311679\pi$
$420$		0			0
$421$	−0.382439	−	2.16892i	−0.0186390	−	0.105707i	0.974069	−	0.226251i	$-0.0726471\pi$
$421$	−0.382439	−	2.16892i	−0.0186390	−	0.105707i	−0.992708	+	0.120545i	$0.961536\pi$
$422$		0			0
$423$	−18.8813	−	20.8512i	−0.918039	−	1.01382i
$424$		0			0
$425$	−25.0603	+	21.0281i	−1.21561	+	1.02001i
$426$		0			0
$427$	1.72064	−	9.75826i	0.0832678	−	0.472235i
$428$		0			0
$429$	0.772136	−	3.11558i	0.0372791	−	0.150422i
$430$		0			0
$431$	24.0416			1.15804			0.579022	−	0.815312i	$-0.303434\pi$
$431$	24.0416			1.15804			0.579022	+	0.815312i	$0.303434\pi$
$432$		0			0
$433$	−8.08045			−0.388322			−0.194161	−	0.980970i	$-0.562198\pi$
$433$	−8.08045			−0.388322			−0.194161	+	0.980970i	$0.562198\pi$
$434$		0			0
$435$	2.39781	−	0.691222i	0.114966	−	0.0331415i
$436$		0			0
$437$	−0.590845	+	3.35085i	−0.0282640	+	0.160293i
$438$		0			0
$439$	12.5560	−	10.5357i	0.599266	−	0.502844i	−0.291944	−	0.956436i	$-0.594302\pi$
$439$	12.5560	−	10.5357i	0.599266	−	0.502844i	0.891210	+	0.453592i	$0.149858\pi$
$440$		0			0
$441$	2.97197	+	0.409138i	0.141522	+	0.0194828i
$442$		0			0
$443$	1.17776	+	6.67943i	0.0559572	+	0.317349i	0.999919	−	0.0127047i	$-0.00404414\pi$
$443$	1.17776	+	6.67943i	0.0559572	+	0.317349i	−0.943962	+	0.330054i	$0.892933\pi$
$444$		0			0
$445$	−4.99958	+	1.81970i	−0.237003	+	0.0862620i
$446$		0			0
$447$	3.59892	+	1.59627i	0.170223	+	0.0755008i
$448$		0			0
$449$	13.6143	−	23.5806i	0.642498	−	1.11284i	−0.342376	−	0.939563i	$-0.611232\pi$
$449$	13.6143	−	23.5806i	0.642498	−	1.11284i	0.984873	−	0.173276i	$-0.0554352\pi$
$450$		0			0
$451$	2.82794	+	4.89814i	0.133163	+	0.230645i
$452$		0			0
$453$	9.93222	−	14.7700i	0.466657	−	0.693956i
$454$		0			0
$455$	−1.71255	−	1.43700i	−0.0802854	−	0.0673675i
$456$		0			0
$457$	1.42574	+	0.518928i	0.0666935	+	0.0242745i	0.375151	−	0.926964i	$-0.377591\pi$
$457$	1.42574	+	0.518928i	0.0666935	+	0.0242745i	−0.308458	+	0.951238i	$0.599813\pi$
$458$		0			0
$459$	11.8491	+	35.9495i	0.553067	+	1.67798i
$460$		0			0
$461$	30.2175	+	10.9983i	1.40737	+	0.512241i	0.930357	−	0.366655i	$-0.119497\pi$
$461$	30.2175	+	10.9983i	1.40737	+	0.512241i	0.477013	+	0.878896i	$0.341719\pi$
$462$		0			0
$463$	−7.72536	−	6.48235i	−0.359028	−	0.301260i	0.445375	−	0.895344i	$-0.353070\pi$
$463$	−7.72536	−	6.48235i	−0.359028	−	0.301260i	−0.804403	+	0.594084i	$0.797515\pi$
$464$		0			0
$465$	−10.4165	−	0.713630i	−0.483052	−	0.0330938i
$466$		0			0
$467$	16.9701	+	29.3931i	0.785282	+	1.36015i	0.928830	+	0.370505i	$0.120815\pi$
$467$	16.9701	+	29.3931i	0.785282	+	1.36015i	−0.143548	+	0.989643i	$0.545851\pi$
$468$		0			0
$469$	−0.918302	+	1.59054i	−0.0424032	+	0.0734445i
$470$		0			0
$471$	−5.31257	+	3.87126i	−0.244790	+	0.178378i
$472$		0			0
$473$	6.78444	−	2.46933i	0.311949	−	0.113540i
$474$		0			0
$475$	−2.85515	−	16.1923i	−0.131003	−	0.742955i
$476$		0			0
$477$	1.08421	+	28.7245i	0.0496424	+	1.31521i
$478$		0			0
$479$	−20.0787	+	16.8480i	−0.917419	+	0.769806i	−0.973516	−	0.228620i	$-0.926579\pi$
$479$	−20.0787	+	16.8480i	−0.917419	+	0.769806i	0.0560971	+	0.998425i	$0.482134\pi$
$480$		0			0
$481$	2.45096	−	13.9001i	0.111754	−	0.633790i
$482$		0			0
$483$	−1.15947	−	1.11653i	−0.0527575	−	0.0508038i
$484$		0			0
$485$	−1.29703			−0.0588949
$486$		0			0
$487$	−27.4391			−1.24338			−0.621692	−	0.783262i	$-0.713554\pi$
$487$	−27.4391			−1.24338			−0.621692	+	0.783262i	$0.713554\pi$
$488$		0			0
$489$	−15.6305	−	15.0516i	−0.706835	−	0.680659i
$490$		0			0
$491$	7.32996	−	41.5703i	0.330796	−	1.87604i	−0.134543	−	0.990908i	$-0.542957\pi$
$491$	7.32996	−	41.5703i	0.330796	−	1.87604i	0.465339	−	0.885132i	$-0.345932\pi$
$492$		0			0
$493$	11.2673	−	9.45440i	0.507454	−	0.425805i
$494$		0			0
$495$	−0.0477596	−	1.26532i	−0.00214663	−	0.0568720i
$496$		0			0
$497$	0.911591	+	5.16989i	0.0408905	+	0.231901i
$498$		0			0
$499$	−6.61727	+	2.40849i	−0.296230	+	0.107819i	−0.485860	−	0.874037i	$-0.661493\pi$
$499$	−6.61727	+	2.40849i	−0.296230	+	0.107819i	0.189630	+	0.981856i	$0.439271\pi$
$500$		0			0
$501$	−30.0537	+	21.9001i	−1.34270	+	0.978423i
$502$		0			0
$503$	−6.02210	+	10.4306i	−0.268512	+	0.465077i	−0.968478	−	0.249100i	$-0.919865\pi$
$503$	−6.02210	+	10.4306i	−0.268512	+	0.465077i	0.699966	+	0.714177i	$0.253199\pi$
$504$		0			0
$505$	4.65950	+	8.07050i	0.207345	+	0.359132i
$506$		0			0
$507$	5.50246	+	0.376972i	0.244373	+	0.0167419i
$508$		0			0
$509$	24.9134	+	20.9048i	1.10427	+	0.926590i	0.997705	−	0.0677164i	$-0.0215713\pi$
$509$	24.9134	+	20.9048i	1.10427	+	0.926590i	0.106562	+	0.994306i	$0.466016\pi$
$510$		0			0
$511$	−14.4566	−	5.26177i	−0.639522	−	0.232767i
$512$		0			0
$513$	−18.6253	−	3.87664i	−0.822327	−	0.171158i
$514$		0			0
$515$	−0.785926	−	0.286054i	−0.0346320	−	0.0126050i
$516$		0			0
$517$	4.24872	+	3.56510i	0.186858	+	0.156793i
$518$		0			0
$519$	−7.38100	+	10.9761i	−0.323990	+	0.481799i
$520$		0			0
$521$	21.7819	+	37.7273i	0.954282	+	1.65286i	0.736003	+	0.676978i	$0.236711\pi$
$521$	21.7819	+	37.7273i	0.954282	+	1.65286i	0.218278	+	0.975887i	$0.429956\pi$
$522$		0			0
$523$	18.8626	−	32.6710i	0.824804	−	1.42860i	−0.0772641	−	0.997011i	$-0.524618\pi$
$523$	18.8626	−	32.6710i	0.824804	−	1.42860i	0.902069	−	0.431593i	$-0.142048\pi$
$524$		0			0
$525$	7.11034	+	3.15372i	0.310321	+	0.137640i
$526$		0			0
$527$	−57.8283	+	21.0478i	−2.51904	+	0.916856i
$528$		0			0
$529$	−3.84393	−	21.8000i	−0.167128	−	0.947828i
$530$		0			0
$531$	37.7200	+	5.19275i	1.63691	+	0.225346i
$532$		0			0
$533$	22.9485	−	19.2561i	0.994010	−	0.834074i
$534$		0			0
$535$	−0.939544	+	5.32842i	−0.0406200	+	0.230368i
$536$		0			0
$537$	2.43616	−	0.702277i	0.105128	−	0.0303055i
$538$		0			0
$539$	−0.591509			−0.0254781
$540$		0			0
$541$	38.4829			1.65451			0.827254	−	0.561828i	$-0.189902\pi$
$541$	38.4829			1.65451			0.827254	+	0.561828i	$0.189902\pi$
$542$		0			0
$543$	−9.68421	+	39.0759i	−0.415589	+	1.67691i
$544$		0			0
$545$	−1.00520	+	5.70076i	−0.0430579	+	0.244194i
$546$		0			0
$547$	−16.1579	+	13.5581i	−0.690861	+	0.579701i	−0.919157	−	0.393890i	$-0.871129\pi$
$547$	−16.1579	+	13.5581i	−0.690861	+	0.579701i	0.228296	+	0.973592i	$0.426684\pi$
$548$		0			0
$549$	−19.9531	−	22.0348i	−0.851576	−	0.940423i
$550$		0			0
$551$	1.28369	+	7.28019i	0.0546872	+	0.310147i
$552$		0			0
$553$	4.14126	−	1.50730i	0.176104	−	0.0640968i
$554$		0			0
$555$	−0.589816	−	5.53660i	−0.0250363	−	0.235016i
$556$		0			0
$557$	−8.47416	+	14.6777i	−0.359062	+	0.621913i	−0.987804	−	0.155700i	$-0.950237\pi$
$557$	−8.47416	+	14.6777i	−0.359062	+	0.621913i	0.628743	+	0.777614i	$0.283570\pi$
$558$		0			0
$559$	−19.1204	−	33.1175i	−0.808708	−	1.40072i
$560$		0			0
$561$	−3.28112	−	6.70329i	−0.138529	−	0.283013i
$562$		0			0
$563$	−17.5789	−	14.7504i	−0.740861	−	0.621656i	0.192208	−	0.981354i	$-0.438435\pi$
$563$	−17.5789	−	14.7504i	−0.740861	−	0.621656i	−0.933069	+	0.359698i	$0.882880\pi$
$564$		0			0
$565$	5.21358	+	1.89759i	0.219337	+	0.0798321i
$566$		0			0
$567$	6.43869	−	6.28835i	0.270399	−	0.264086i
$568$		0			0
$569$	30.5895	+	11.1337i	1.28238	+	0.466747i	0.891218	−	0.453576i	$-0.149852\pi$
$569$	30.5895	+	11.1337i	1.28238	+	0.466747i	0.391159	+	0.920323i	$0.372074\pi$
$570$		0			0
$571$	18.7888	+	15.7656i	0.786285	+	0.659772i	0.944823	−	0.327581i	$-0.106234\pi$
$571$	18.7888	+	15.7656i	0.786285	+	0.659772i	−0.158538	+	0.987353i	$0.550678\pi$
$572$		0			0
$573$	12.7950	+	26.1401i	0.534520	+	1.09202i
$574$		0			0
$575$	−2.08675	−	3.61436i	−0.0870235	−	0.150729i
$576$		0			0
$577$	10.8184	−	18.7379i	0.450374	−	0.780070i	−0.548035	−	0.836455i	$-0.684624\pi$
$577$	10.8184	−	18.7379i	0.450374	−	0.780070i	0.998409	+	0.0563848i	$0.0179574\pi$
$578$		0			0
$579$	1.97505	+	18.5398i	0.0820805	+	0.770490i
$580$		0			0
$581$	2.95557	−	1.07574i	0.122618	−	0.0446292i
$582$		0			0
$583$	−0.984174	−	5.58153i	−0.0407603	−	0.231163i
$584$		0			0
$585$	−6.55619	+	1.41290i	−0.271065	+	0.0584163i
$586$		0			0
$587$	19.4058	−	16.2834i	0.800962	−	0.672087i	−0.147470	−	0.989067i	$-0.547113\pi$
$587$	19.4058	−	16.2834i	0.800962	−	0.672087i	0.948432	+	0.316979i	$0.102669\pi$
$588$		0			0
$589$	5.37094	−	30.4601i	0.221306	−	1.25509i
$590$		0			0
$591$	8.78372	−	35.4424i	0.361314	−	1.45791i
$592$		0			0
$593$	7.98896			0.328067			0.164034	−	0.986455i	$-0.447549\pi$
$593$	7.98896			0.328067			0.164034	+	0.986455i	$0.447549\pi$
$594$		0			0
$595$	−5.19796			−0.213096
$596$		0			0
$597$	10.7365	−	3.09502i	0.439414	−	0.126671i
$598$		0			0
$599$	7.75248	−	43.9665i	0.316758	−	1.79642i	−0.245431	−	0.969414i	$-0.578929\pi$
$599$	7.75248	−	43.9665i	0.316758	−	1.79642i	0.562189	−	0.827009i	$-0.309959\pi$
$600$		0			0
$601$	−7.69247	+	6.45475i	−0.313782	+	0.263295i	−0.786053	−	0.618159i	$-0.787879\pi$
$601$	−7.69247	+	6.45475i	−0.313782	+	0.263295i	0.472271	+	0.881454i	$0.343434\pi$
$602$		0			0
$603$	2.07841	+	5.10276i	0.0846395	+	0.207801i
$604$		0			0
$605$	−1.31963	−	7.48399i	−0.0536506	−	0.304268i
$606$		0			0
$607$	−41.8182	+	15.2206i	−1.69735	+	0.617785i	−0.995519	−	0.0945586i	$-0.969856\pi$
$607$	−41.8182	+	15.2206i	−1.69735	+	0.617785i	−0.701831	+	0.712344i	$0.747634\pi$
$608$		0			0
$609$	−3.19686	−	1.41794i	−0.129543	−	0.0574577i
$610$		0			0
$611$	14.6884	−	25.4410i	0.594228	−	1.02923i
$612$		0			0
$613$	−21.2794	−	36.8570i	−0.859466	−	1.48864i	−0.872439	−	0.488723i	$-0.837463\pi$
$613$	−21.2794	−	36.8570i	−0.859466	−	1.48864i	0.0129727	−	0.999916i	$-0.495871\pi$
$614$		0			0
$615$	6.59447	−	9.80651i	0.265915	−	0.395437i
$616$		0			0
$617$	27.3252	+	22.9286i	1.10007	+	0.923069i	0.997430	−	0.0716493i	$-0.0228262\pi$
$617$	27.3252	+	22.9286i	1.10007	+	0.923069i	0.102641	+	0.994718i	$0.467271\pi$
$618$		0			0
$619$	37.3902	+	13.6089i	1.50284	+	0.546989i	0.956794	−	0.290767i	$-0.0939104\pi$
$619$	37.3902	+	13.6089i	1.50284	+	0.546989i	0.546045	+	0.837756i	$0.316133\pi$
$620$		0			0
$621$	−4.77909	+	0.692288i	−0.191778	+	0.0277806i
$622$		0			0
$623$	7.00658	+	2.55019i	0.280713	+	0.102171i
$624$		0			0
$625$	13.4991	+	11.3271i	0.539964	+	0.453084i
$626$		0			0
$627$	3.74227	+	0.256382i	0.149452	+	0.0102389i
$628$		0			0
$629$	−16.4090	−	28.4212i	−0.654268	−	1.13323i
$630$		0			0
$631$	1.57834	−	2.73377i	0.0628328	−	0.108830i	−0.832898	−	0.553427i	$-0.813320\pi$
$631$	1.57834	−	2.73377i	0.0628328	−	0.108830i	0.895731	+	0.444597i	$0.146653\pi$
$632$		0			0
$633$	10.1188	−	7.37354i	0.402185	−	0.293072i
$634$		0			0
$635$	−9.24402	+	3.36455i	−0.366838	+	0.133518i
$636$		0			0
$637$	0.544040	+	3.08541i	0.0215557	+	0.122248i
$638$		0			0
$639$	13.9263	+	7.35443i	0.550915	+	0.290937i
$640$		0			0
$641$	31.5213	−	26.4495i	1.24502	−	1.04469i	0.247904	−	0.968785i	$-0.420258\pi$
$641$	31.5213	−	26.4495i	1.24502	−	1.04469i	0.997115	−	0.0759096i	$-0.0241860\pi$
$642$		0			0
$643$	−1.12466	+	6.37826i	−0.0443522	+	0.251534i	−0.998920	−	0.0464594i	$-0.985206\pi$
$643$	−1.12466	+	6.37826i	−0.0443522	+	0.251534i	0.954568	+	0.297993i	$0.0963173\pi$
$644$		0			0
$645$	−10.8662	−	10.4638i	−0.427858	−	0.412013i
$646$		0			0
$647$	24.4838			0.962558			0.481279	−	0.876567i	$-0.340172\pi$
$647$	24.4838			0.962558			0.481279	+	0.876567i	$0.340172\pi$
$648$		0			0
$649$	−7.50738			−0.294690
$650$		0			0
$651$	10.5399	+	10.1495i	0.413089	+	0.397791i
$652$		0			0
$653$	−2.17212	+	12.3187i	−0.0850018	+	0.482069i	0.912354	+	0.409401i	$0.134262\pi$
$653$	−2.17212	+	12.3187i	−0.0850018	+	0.482069i	−0.997356	+	0.0726677i	$0.976849\pi$
$654$		0			0
$655$	−11.1588	+	9.36334i	−0.436010	+	0.365856i
$656$		0			0
$657$	−39.0709	+	24.5677i	−1.52430	+	0.958478i
$658$		0			0
$659$	2.23719	+	12.6878i	0.0871487	+	0.494245i	0.996872	+	0.0790303i	$0.0251824\pi$
$659$	2.23719	+	12.6878i	0.0871487	+	0.494245i	−0.909723	+	0.415215i	$0.863706\pi$
$660$		0			0
$661$	−12.7738	+	4.64928i	−0.496843	+	0.180836i	−0.578274	−	0.815843i	$-0.696273\pi$
$661$	−12.7738	+	4.64928i	−0.496843	+	0.180836i	0.0814303	+	0.996679i	$0.474051\pi$
$662$		0			0
$663$	−31.9477	+	23.2802i	−1.24074	+	0.904129i
$664$		0			0
$665$	1.30626	−	2.26250i	0.0506544	−	0.0877360i
$666$		0			0
$667$	0.938218	+	1.62504i	0.0363279	+	0.0629218i
$668$		0			0
$669$	15.4809	+	1.06059i	0.598525	+	0.0410048i
$670$		0			0
$671$	4.48989	+	3.76747i	0.173330	+	0.145441i
$672$		0			0
$673$	0.784975	+	0.285708i	0.0302586	+	0.0110132i	0.357105	−	0.934064i	$-0.383764\pi$
$673$	0.784975	+	0.285708i	0.0302586	+	0.0110132i	−0.326847	+	0.945077i	$0.605986\pi$
$674$		0			0
$675$	20.5571	−	11.0422i	0.791244	−	0.425016i
$676$		0			0
$677$	−34.7649	−	12.6534i	−1.33612	−	0.486310i	−0.427535	−	0.903999i	$-0.640618\pi$
$677$	−34.7649	−	12.6534i	−1.33612	−	0.486310i	−0.908590	+	0.417689i	$0.862840\pi$
$678$		0			0
$679$	1.39243	+	1.16839i	0.0534367	+	0.0448387i
$680$		0			0
$681$	14.1757	−	21.0804i	0.543213	−	0.807802i
$682$		0			0
$683$	−3.48326	−	6.03318i	−0.133283	−	0.230853i	0.791657	−	0.610966i	$-0.209219\pi$
$683$	−3.48326	−	6.03318i	−0.133283	−	0.230853i	−0.924940	+	0.380112i	$0.875885\pi$
$684$		0			0
$685$	−0.477004	+	0.826195i	−0.0182254	+	0.0315673i
$686$		0			0
$687$	−39.9707	−	17.7286i	−1.52498	−	0.676388i
$688$		0			0
$689$	−28.2090	+	10.2672i	−1.07468	+	0.391150i
$690$		0			0
$691$	3.87395	+	21.9703i	0.147372	+	0.835788i	0.965432	+	0.260655i	$0.0839386\pi$
$691$	3.87395	+	21.9703i	0.147372	+	0.835788i	−0.818060	+	0.575133i	$0.804950\pi$
$692$		0			0
$693$	−1.08856	+	1.40142i	−0.0413509	+	0.0532356i
$694$		0			0
$695$	2.03780	−	1.70991i	0.0772980	−	0.0648607i
$696$		0			0
$697$	12.0953	−	68.5957i	0.458141	−	2.59825i
$698$		0			0
$699$	13.1203	−	3.78222i	0.496256	−	0.143057i
$700$		0			0
$701$	−38.4920			−1.45382			−0.726912	−	0.686730i	$-0.759045\pi$
$701$	−38.4920			−1.45382			−0.726912	+	0.686730i	$0.759045\pi$
$702$		0			0
$703$	16.4944			0.622097
$704$		0			0
$705$	2.78768	−	11.2483i	0.104990	−	0.423636i
$706$		0			0
$707$	2.26784	−	12.8616i	0.0852909	−	0.483709i
$708$		0			0
$709$	1.77719	−	1.49124i	0.0667439	−	0.0560048i	−0.608805	−	0.793320i	$-0.708351\pi$
$709$	1.77719	−	1.49124i	0.0667439	−	0.0560048i	0.675549	+	0.737315i	$0.263907\pi$
$710$		0			0
$711$	4.05007	−	12.5855i	0.151890	−	0.471993i
$712$		0			0
$713$	−1.36330	−	7.73167i	−0.0510561	−	0.289553i
$714$		0			0
$715$	1.24261	−	0.452273i	0.0464710	−	0.0169141i
$716$		0			0
$717$	−1.07509	−	10.0919i	−0.0401502	−	0.376890i
$718$		0			0
$719$	−1.71478	+	2.97008i	−0.0639503	+	0.110765i	−0.896228	−	0.443594i	$-0.853703\pi$
$719$	−1.71478	+	2.97008i	−0.0639503	+	0.110765i	0.832278	+	0.554359i	$0.187037\pi$
$720$		0			0
$721$	0.586055	+	1.01508i	0.0218258	+	0.0378034i
$722$		0			0
$723$	−17.1096	−	34.9547i	−0.636314	−	1.29998i
$724$		0			0
$725$	−6.94612	−	5.82849i	−0.257972	−	0.216465i
$726$		0			0
$727$	−15.3167	−	5.57481i	−0.568063	−	0.206758i	0.0419906	−	0.999118i	$-0.486630\pi$
$727$	−15.3167	−	5.57481i	−0.568063	−	0.206758i	−0.610054	+	0.792360i	$0.708852\pi$
$728$		0			0
$729$	−3.04937	−	26.8272i	−0.112940	−	0.993602i
$730$		0			0
$731$	−83.5522	−	30.4105i	−3.09029	−	1.12477i
$732$		0			0
$733$	−20.8164	−	17.4670i	−0.768872	−	0.645160i	0.171548	−	0.985176i	$-0.445123\pi$
$733$	−20.8164	−	17.4670i	−0.768872	−	0.645160i	−0.940420	+	0.340016i	$0.889568\pi$
$734$		0			0
$735$	0.543355	+	1.11007i	0.0200419	+	0.0409454i
$736$		0			0
$737$	−0.543183	−	0.940821i	−0.0200084	−	0.0346556i
$738$		0			0
$739$	−9.42377	+	16.3224i	−0.346659	+	0.600431i	−0.985654	−	0.168780i	$-0.946017\pi$
$739$	−9.42377	+	16.3224i	−0.346659	+	0.600431i	0.638995	+	0.769211i	$0.279351\pi$
$740$		0			0
$741$	−2.10462	−	19.7561i	−0.0773153	−	0.725759i
$742$		0			0
$743$	−9.24039	+	3.36323i	−0.338997	+	0.123385i	−0.505909	−	0.862587i	$-0.668843\pi$
$743$	−9.24039	+	3.36323i	−0.338997	+	0.123385i	0.166912	+	0.985972i	$0.446621\pi$
$744$		0			0
$745$	0.281648	+	1.59731i	0.0103188	+	0.0585208i
$746$		0			0
$747$	2.89049	−	8.98213i	0.105757	−	0.328639i
$748$		0			0
$749$	5.80862	−	4.87401i	0.212242	−	0.178093i
$750$		0			0
$751$	−5.64866	+	32.0351i	−0.206123	+	1.16898i	0.689541	+	0.724247i	$0.257812\pi$
$751$	−5.64866	+	32.0351i	−0.206123	+	1.16898i	−0.895663	+	0.444732i	$0.853299\pi$
$752$		0			0
$753$	1.76087	−	7.10515i	0.0641698	−	0.258926i
$754$		0			0
$755$	7.33265			0.266863
$756$		0			0
$757$	−38.0661			−1.38353			−0.691767	−	0.722121i	$-0.743168\pi$
$757$	−38.0661			−1.38353			−0.691767	+	0.722121i	$0.743168\pi$
$758$		0			0
$759$	0.914871	−	0.263732i	0.0332077	−	0.00957287i
$760$		0			0
$761$	7.88183	−	44.7001i	0.285716	−	1.62038i	−0.417000	−	0.908906i	$-0.636919\pi$
$761$	7.88183	−	44.7001i	0.285716	−	1.62038i	0.702716	−	0.711470i	$-0.251970\pi$
$762$		0			0
$763$	6.21452	−	5.21460i	0.224981	−	0.188781i
$764$		0			0
$765$	−9.56586	+	12.3152i	−0.345854	+	0.445256i
$766$		0			0
$767$	6.90491	+	39.1597i	0.249322	+	1.41397i
$768$		0			0
$769$	28.2106	−	10.2678i	1.01730	−	0.370268i	0.221069	−	0.975258i	$-0.429045\pi$
$769$	28.2106	−	10.2678i	1.01730	−	0.370268i	0.796233	+	0.604990i	$0.206823\pi$
$770$		0			0
$771$	1.17563	+	0.521440i	0.0423394	+	0.0187792i
$772$		0			0
$773$	−8.68106	+	15.0360i	−0.312236	+	0.540809i	−0.978846	−	0.204598i	$-0.934411\pi$
$773$	−8.68106	+	15.0360i	−0.312236	+	0.540809i	0.666610	+	0.745407i	$0.267745\pi$
$774$		0			0
$775$	18.9691	+	32.8554i	0.681390	+	1.18020i
$776$		0			0
$777$	−4.35430	+	6.47519i	−0.156210	+	0.232296i
$778$		0			0
$779$	26.8179	+	22.5029i	0.960850	+	0.806249i
$780$		0			0
$781$	−2.91794	−	1.06204i	−0.104412	−	0.0380030i
$782$		0			0
$783$	−9.24263	+	4.96467i	−0.330305	+	0.177423i
$784$		0			0
$785$	−2.54475	−	0.926213i	−0.0908260	−	0.0330580i
$786$		0			0
$787$	−15.1230	−	12.6897i	−0.539076	−	0.452338i	0.332146	−	0.943228i	$-0.392227\pi$
$787$	−15.1230	−	12.6897i	−0.539076	−	0.452338i	−0.871222	+	0.490890i	$0.836672\pi$
$788$		0			0
$789$	22.8303	+	1.56410i	0.812782	+	0.0556835i
$790$		0			0
$791$	−3.88770	−	6.73369i	−0.138231	−	0.239423i
$792$		0			0
$793$	15.5221	−	26.8851i	0.551207	−	0.954719i
$794$		0			0
$795$	−9.57063	+	6.97412i	−0.339435	+	0.247346i
$796$		0			0
$797$	13.4625	−	4.89993i	0.476864	−	0.173564i	−0.0923949	−	0.995722i	$-0.529452\pi$
$797$	13.4625	−	4.89993i	0.476864	−	0.173564i	0.569259	+	0.822158i	$0.307230\pi$
$798$		0			0
$799$	−11.8609	−	67.2666i	−0.419609	−	2.37972i
$800$		0			0
$801$	18.9363	−	11.9071i	0.669080	−	0.420716i
$802$		0			0
$803$	6.97100	−	5.84936i	0.246001	−	0.206419i
$804$		0			0
$805$	0.115152	−	0.653058i	0.00405857	−	0.0230173i
$806$		0			0
$807$	9.61744	+	9.26128i	0.338550	+	0.326012i
$808$		0			0
$809$	27.5116			0.967257			0.483629	−	0.875273i	$-0.339318\pi$
$809$	27.5116			0.967257			0.483629	+	0.875273i	$0.339318\pi$
$810$		0			0
$811$	1.39567			0.0490087			0.0245043	−	0.999700i	$-0.492199\pi$
$811$	1.39567			0.0490087			0.0245043	+	0.999700i	$0.492199\pi$
$812$		0			0
$813$	23.0511	+	22.1974i	0.808436	+	0.778497i
$814$		0			0
$815$	1.55233	−	8.80372i	0.0543758	−	0.308381i
$816$		0			0
$817$	34.2335	−	28.7253i	1.19768	−	1.00497i
$818$		0			0
$819$	8.31124	+	4.38914i	0.290418	+	0.153369i
$820$		0			0
$821$	−7.88218	−	44.7021i	−0.275090	−	1.56011i	−0.738676	−	0.674061i	$-0.764548\pi$
$821$	−7.88218	−	44.7021i	−0.275090	−	1.56011i	0.463586	−	0.886052i	$-0.346563\pi$
$822$		0			0
$823$	−1.00219	+	0.364768i	−0.0349342	+	0.0127150i	−0.359428	−	0.933173i	$-0.617028\pi$
$823$	−1.00219	+	0.364768i	−0.0349342	+	0.0127150i	0.324494	+	0.945888i	$0.394806\pi$
$824$		0			0
$825$	−3.71844	+	2.70963i	−0.129460	+	0.0943371i
$826$		0			0
$827$	−4.12221	+	7.13988i	−0.143343	+	0.248278i	−0.928754	−	0.370697i	$-0.879119\pi$
$827$	−4.12221	+	7.13988i	−0.143343	+	0.248278i	0.785410	+	0.618976i	$0.212452\pi$
$828$		0			0
$829$	14.7256	+	25.5055i	0.511441	+	0.885842i	0.999912	+	0.0132617i	$0.00422147\pi$
$829$	14.7256	+	25.5055i	0.511441	+	0.885842i	−0.488471	+	0.872580i	$0.662445\pi$
$830$		0			0
$831$	−15.5381	−	1.06451i	−0.539010	−	0.0369275i
$832$		0			0
$833$	5.58033	+	4.68245i	0.193347	+	0.162237i
$834$		0			0
$835$	−14.3959	−	5.23967i	−0.498190	−	0.181326i
$836$		0			0
$837$	43.4432	−	6.29308i	1.50162	−	0.217521i
$838$		0			0
$839$	8.95273	+	3.25853i	0.309083	+	0.112497i	0.491904	−	0.870649i	$-0.336301\pi$
$839$	8.95273	+	3.25853i	0.309083	+	0.112497i	−0.182822	+	0.983146i	$0.558523\pi$
$840$		0			0
$841$	−19.0923	−	16.0203i	−0.658354	−	0.552424i
$842$		0			0
$843$	23.2571	−	34.5851i	0.801016	−	1.19118i
$844$		0			0
$845$	1.13608	+	1.96776i	0.0390825	+	0.0676929i
$846$		0			0
$847$	−5.32506	+	9.22327i	−0.182971	+	0.316915i
$848$		0			0
$849$	−34.8621	−	15.4627i	−1.19646	−	0.530680i
$850$		0			0
$851$	3.93427	−	1.43196i	0.134865	−	0.0490869i
$852$		0			0
$853$	2.05690	+	11.6653i	0.0704269	+	0.399411i	0.999560	+	0.0296650i	$0.00944404\pi$
$853$	2.05690	+	11.6653i	0.0704269	+	0.399411i	−0.929133	+	0.369746i	$0.879445\pi$
$854$		0			0
$855$	−2.95648	−	7.25852i	−0.101109	−	0.248236i
$856$		0			0
$857$	−12.9946	+	10.9038i	−0.443887	+	0.372465i	−0.837161	−	0.546956i	$-0.815787\pi$
$857$	−12.9946	+	10.9038i	−0.443887	+	0.372465i	0.393275	+	0.919421i	$0.371342\pi$
$858$		0			0
$859$	1.48323	−	8.41183i	0.0506072	−	0.287008i	−0.948992	−	0.315299i	$-0.897895\pi$
$859$	1.48323	−	8.41183i	0.0506072	−	0.287008i	0.999600	+	0.0282907i	$0.00900641\pi$
$860$		0			0
$861$	−15.9135	+	4.58742i	−0.542331	+	0.156339i
$862$		0			0
$863$	−32.5947			−1.10954			−0.554768	−	0.832005i	$-0.687193\pi$
$863$	−32.5947			−1.10954			−0.554768	+	0.832005i	$0.687193\pi$
$864$		0			0
$865$	−5.44916			−0.185277
$866$		0			0
$867$	−15.0266	+	60.6327i	−0.510332	+	2.05920i
$868$		0			0
$869$	−0.452667	+	2.56720i	−0.0153557	+	0.0870863i
$870$		0			0
$871$	−4.40788	+	3.69865i	−0.149355	+	0.125324i
$872$		0			0
$873$	5.33070	−	1.14880i	0.180417	−	0.0388810i
$874$		0			0
$875$	1.17599	+	6.66935i	0.0397556	+	0.225465i
$876$		0			0
$877$	18.9480	−	6.89649i	0.639827	−	0.232878i	−0.00167578	−	0.999999i	$-0.500533\pi$
$877$	18.9480	−	6.89649i	0.639827	−	0.232878i	0.641503	+	0.767121i	$0.278311\pi$
$878$		0			0
$879$	−0.220227	−	2.06727i	−0.00742807	−	0.0697273i
$880$		0			0
$881$	−12.3841	+	21.4499i	−0.417230	+	0.722664i	−0.995660	−	0.0930682i	$-0.970333\pi$
$881$	−12.3841	+	21.4499i	−0.417230	+	0.722664i	0.578429	+	0.815733i	$0.303666\pi$
$882$		0			0
$883$	−20.8502	−	36.1137i	−0.701666	−	1.21532i	−0.967881	−	0.251408i	$-0.919107\pi$
$883$	−20.8502	−	36.1137i	−0.701666	−	1.21532i	0.266215	−	0.963914i	$-0.414227\pi$
$884$		0			0
$885$	6.89621	+	14.0889i	0.231814	+	0.473592i
$886$		0			0
$887$	5.49312	+	4.60928i	0.184441	+	0.154764i	0.730333	−	0.683091i	$-0.239365\pi$
$887$	5.49312	+	4.60928i	0.184441	+	0.154764i	−0.545892	+	0.837855i	$0.683809\pi$
$888$		0			0
$889$	12.9549	+	4.71519i	0.434493	+	0.158142i
$890$		0			0
$891$	1.31701	+	5.15810i	0.0441214	+	0.172803i
$892$		0			0
$893$	32.2596	+	11.7415i	1.07953	+	0.392916i
$894$		0			0
$895$	0.800131	+	0.671389i	0.0267454	+	0.0224421i
$896$		0			0
$897$	−2.21712	−	4.52955i	−0.0740276	−	0.151237i
$898$		0			0
$899$	−8.52864	−	14.7720i	−0.284446	−	0.492675i
$900$		0			0
$901$	−34.8992	+	60.4473i	−1.16266	+	2.01379i
$902$		0			0
$903$	2.23949	+	21.0221i	0.0745257	+	0.699573i
$904$		0			0
$905$	−15.5850	+	5.67246i	−0.518061	+	0.188559i
$906$		0			0
$907$	4.58341	+	25.9938i	0.152190	+	0.863111i	0.961310	+	0.275468i	$0.0888328\pi$
$907$	4.58341	+	25.9938i	0.152190	+	0.863111i	−0.809121	+	0.587643i	$0.800056\pi$
$908$		0			0
$909$	−26.2985	−	29.0423i	−0.872266	−	0.963272i
$910$		0			0
$911$	8.17990	−	6.86375i	0.271012	−	0.227406i	−0.497145	−	0.867667i	$-0.665618\pi$
$911$	8.17990	−	6.86375i	0.271012	−	0.227406i	0.768157	+	0.640261i	$0.221174\pi$
$912$		0			0
$913$	−0.323063	+	1.83218i	−0.0106918	+	0.0606363i
$914$		0			0
$915$	2.94592	−	11.8868i	0.0973889	−	0.392966i
$916$		0			0
$917$	20.4144			0.674142
$918$		0			0
$919$	38.8143			1.28037			0.640183	−	0.768223i	$-0.278859\pi$
$919$	38.8143			1.28037			0.640183	+	0.768223i	$0.278859\pi$
$920$		0			0
$921$	5.17448	−	1.49166i	0.170505	−	0.0491518i
$922$		0			0
$923$	−2.85602	+	16.1973i	−0.0940070	+	0.533140i
$924$		0			0
$925$	−15.4984	+	13.0047i	−0.509584	+	0.427592i
$926$		0			0
$927$	3.48347	+	0.479555i	0.114412	+	0.0157507i
$928$		0			0
$929$	−3.12628	−	17.7300i	−0.102570	−	0.581704i	−0.992163	−	0.124950i	$-0.960123\pi$
$929$	−3.12628	−	17.7300i	−0.102570	−	0.581704i	0.889593	−	0.456754i	$-0.150988\pi$
$930$		0			0
$931$	−3.44046	+	1.25222i	−0.112756	+	0.0410400i
$932$		0			0
$933$	35.0323	+	15.5382i	1.14691	+	0.508699i
$934$		0			0
$935$	1.53732	−	2.66272i	0.0502757	−	0.0870801i
$936$		0			0
$937$	30.4046	+	52.6624i	0.993276	+	1.72041i	0.596896	+	0.802319i	$0.296401\pi$
$937$	30.4046	+	52.6624i	0.993276	+	1.72041i	0.396381	+	0.918086i	$0.370266\pi$
$938$		0			0
$939$	6.56126	−	9.75713i	0.214119	−	0.318412i
$940$		0			0
$941$	23.0888	+	19.3738i	0.752672	+	0.631567i	0.936208	−	0.351446i	$-0.114310\pi$
$941$	23.0888	+	19.3738i	0.752672	+	0.631567i	−0.183536	+	0.983013i	$0.558754\pi$
$942$		0			0
$943$	8.35023	+	3.03923i	0.271921	+	0.0989711i
$944$		0			0
$945$	3.62995	+	0.755532i	0.118082	+	0.0245775i
$946$		0			0
$947$	24.2246	+	8.81703i	0.787194	+	0.286515i	0.704169	−	0.710032i	$-0.251320\pi$
$947$	24.2246	+	8.81703i	0.787194	+	0.286515i	0.0830248	+	0.996547i	$0.473542\pi$
$948$		0			0
$949$	−36.9228	−	30.9819i	−1.19856	−	1.00572i
$950$		0			0
$951$	0.301798	+	0.0206761i	0.00978648	+	0.000670470i
$952$		0			0
$953$	−15.5009	−	26.8483i	−0.502122	−	0.869702i	−0.999997	−	0.00245252i	$-0.999219\pi$
$953$	−15.5009	−	26.8483i	−0.502122	−	0.869702i	0.497875	−	0.867249i	$-0.334114\pi$
$954$		0			0
$955$	−5.99491	+	10.3835i	−0.193991	+	0.336002i
$956$		0			0
$957$	1.67184	−	1.21827i	0.0540429	−	0.0393810i
$958$		0			0
$959$	1.25635	−	0.457273i	0.0405696	−	0.0147661i
$960$		0			0
$961$	7.00968	+	39.7539i	0.226119	+	1.28238i
$962$		0			0
$963$	−0.858007	−	22.7317i	−0.0276489	−	0.732518i
$964$		0			0
$965$	−5.88406	+	4.93732i	−0.189415	+	0.158938i
$966$		0			0
$967$	−4.83119	+	27.3990i	−0.155361	+	0.881093i	0.803095	+	0.595851i	$0.203185\pi$
$967$	−4.83119	+	27.3990i	−0.155361	+	0.881093i	−0.958455	+	0.285242i	$0.907926\pi$
$968$		0			0
$969$	−33.2753	−	32.0430i	−1.06896	−	1.02937i
$970$		0			0
$971$	−16.0783			−0.515976			−0.257988	−	0.966148i	$-0.583060\pi$
$971$	−16.0783			−0.515976			−0.257988	+	0.966148i	$0.583060\pi$
$972$		0			0
$973$	−3.72803			−0.119515
$974$		0			0
$975$	17.5539	+	16.9038i	0.562175	+	0.541356i
$976$		0			0
$977$	−3.70694	+	21.0231i	−0.118595	+	0.672588i	0.866312	+	0.499504i	$0.166484\pi$
$977$	−3.70694	+	21.0231i	−0.118595	+	0.672588i	−0.984907	+	0.173084i	$0.944627\pi$
$978$		0			0
$979$	−3.37859	+	2.83497i	−0.107980	+	0.0906061i
$980$		0			0
$981$	−0.917963	−	24.3201i	−0.0293083	−	0.776481i
$982$		0			0
$983$	6.61795	+	37.5323i	0.211080	+	1.19709i	0.887581	+	0.460652i	$0.152384\pi$
$983$	6.61795	+	37.5323i	0.211080	+	1.19709i	−0.676501	+	0.736442i	$0.736505\pi$
$984$		0			0
$985$	14.1358	−	5.14501i	0.450404	−	0.163934i
$986$		0			0
$987$	−13.1255	+	9.56453i	−0.417789	+	0.304442i
$988$		0			0
$989$	5.67165	−	9.82359i	0.180348	−	0.312372i
$990$		0			0
$991$	18.8360	+	32.6248i	0.598344	+	1.03636i	0.993066	+	0.117561i	$0.0375077\pi$
$991$	18.8360	+	32.6248i	0.598344	+	1.03636i	−0.394722	+	0.918801i	$0.629159\pi$
$992$		0			0
$993$	42.2195	+	2.89245i	1.33980	+	0.0917892i
$994$		0			0
$995$	3.52628	+	2.95890i	0.111790	+	0.0938033i
$996$		0			0
$997$	33.5541	+	12.2127i	1.06267	+	0.386780i	0.813430	−	0.581662i	$-0.197598\pi$
$997$	33.5541	+	12.2127i	1.06267	+	0.386780i	0.249238	+	0.968442i	$0.419820\pi$
$998$		0			0
$999$	7.32798	+	22.2327i	0.231847	+	0.703412i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bo.b.85.3	✓	54
27.7	even	9	inner	756.2.bo.b.169.3	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bo.b.85.3	✓	54	1.1	even	1	trivial
756.2.bo.b.169.3	yes	54	27.7	even	9	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24763 - 1.20143i) q^{3} +(0.123908 - 0.702715i) q^{5} +(-0.766044 + 0.642788i) q^{7} +(0.113154 + 2.99787i) q^{9} +O(q^{10})\)	\(q+(-1.24763 - 1.20143i) q^{3} +(0.123908 - 0.702715i) q^{5} +(-0.766044 + 0.642788i) q^{7} +(0.113154 + 2.99787i) q^{9} +(-0.102714 - 0.582522i) q^{11} +(-2.94406 + 1.07155i) q^{13} +(-0.998850 + 0.727861i) q^{15} +(-3.64230 + 6.30865i) q^{17} +(-1.83063 - 3.17074i) q^{19} +(1.72800 + 0.118385i) q^{21} +(-0.711913 - 0.597366i) q^{23} +(4.22001 + 1.53596i) q^{25} +(3.46054 - 3.87617i) q^{27} +(-1.89735 - 0.690578i) q^{29} +(6.47147 + 5.43021i) q^{31} +(-0.571708 + 0.850175i) q^{33} +(0.356778 + 0.617957i) q^{35} +(-2.25256 + 3.90154i) q^{37} +(4.96048 + 2.20017i) q^{39} +(-8.98515 + 3.27033i) q^{41} +(2.11952 + 12.0204i) q^{43} +(2.12066 + 0.291943i) q^{45} +(-7.18285 + 6.02712i) q^{47} +(0.173648 - 0.984808i) q^{49} +(12.1236 - 3.49490i) q^{51} +9.58166 q^{53} -0.422074 q^{55} +(-1.52547 + 6.15528i) q^{57} +(2.20393 - 12.4991i) q^{59} +(-7.59058 + 6.36925i) q^{61} +(-2.01367 - 2.22376i) q^{63} +(0.388203 + 2.20161i) q^{65} +(1.72584 - 0.628155i) q^{67} +(0.170512 + 1.60060i) q^{69} +(2.62482 - 4.54633i) q^{71} +(7.69219 + 13.3233i) q^{73} +(-3.41967 - 6.98633i) q^{75} +(0.453122 + 0.380214i) q^{77} +(-4.14126 - 1.50730i) q^{79} +(-8.97439 + 0.678444i) q^{81} +(-2.95557 - 1.07574i) q^{83} +(3.98187 + 3.34119i) q^{85} +(1.53751 + 3.14110i) q^{87} +(-3.72812 - 6.45730i) q^{89} +(1.56650 - 2.71326i) q^{91} +(-1.55000 - 14.5499i) q^{93} +(-2.45496 + 0.893531i) q^{95} +(-0.315639 - 1.79008i) q^{97} +(1.73470 - 0.373839i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9}+O(q^{10}) \) 54 * q + 3 * q^3 - 3 * q^5 - 9 * q^9	\( 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9} + 9 q^{13} + 3 q^{15} + 3 q^{21} + 12 q^{23} + 27 q^{25} + 39 q^{27} + 30 q^{29} - 9 q^{31} - 6 q^{33} + 6 q^{35} - 18 q^{39} - 27 q^{41} + 9 q^{43} - 81 q^{45} + 9 q^{47} + 12 q^{53} - 21 q^{57} - 24 q^{59} - 3 q^{63} - 78 q^{65} - 9 q^{67} + 6 q^{69} - 30 q^{71} + 57 q^{75} + 9 q^{77} + 99 q^{81} + 78 q^{83} + 18 q^{85} + 21 q^{87} + 12 q^{89} - 51 q^{93} - 36 q^{95} + 36 q^{97} + 15 q^{99}+O(q^{100}) \) 54 * q + 3 * q^3 - 3 * q^5 - 9 * q^9 + 9 * q^13 + 3 * q^15 + 3 * q^21 + 12 * q^23 + 27 * q^25 + 39 * q^27 + 30 * q^29 - 9 * q^31 - 6 * q^33 + 6 * q^35 - 18 * q^39 - 27 * q^41 + 9 * q^43 - 81 * q^45 + 9 * q^47 + 12 * q^53 - 21 * q^57 - 24 * q^59 - 3 * q^63 - 78 * q^65 - 9 * q^67 + 6 * q^69 - 30 * q^71 + 57 * q^75 + 9 * q^77 + 99 * q^81 + 78 * q^83 + 18 * q^85 + 21 * q^87 + 12 * q^89 - 51 * q^93 - 36 * q^95 + 36 * q^97 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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